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Spiers Memorial Lecture Stereochemistry and control in molecular reaction dynamics John P. Simons Physical and T heoretical Chemistry L aboratory South Parks Road Oxford UK OX1 3QZ Received 15th July 1999 The evolving understanding of the stereodynamics of atomic and molecular reactions has led quite naturally to the evolution of strategies for their control. The excitement of designing reaction control machinery has captured the imagination of many theoreticians who aspire to becoming molecular quantum ìmechanicsœ and at the same time the challenge of implementing their ideas is also exciting many reaction dynamical ìengineersì. A key tool is provided by the laser and the Discussion which this lecture introduces could equally well have been titled ìLaser control of chemical reactionsœ.The Lecture provides a survey of the current status of stereodynamics and control principally of bimolecular reactions. It includes a review of strategies for the passive control of chemical reactions evolving ììunder their own steamœœ and of their stereodynamics and of strategies for their active control under the in—uence of continuous wave or pulsed optical –elds where reactions are ììmade to dance according to the theoreticiansœ and increasingly the experimentersœ tuneœœ. 1 Faraday Discuss. 1999 113 1»25 1. Origins and intimations In the words of its Organisers ìì this Discussion is (designed) to bring together (those) working on applications of Dynamical Stereochemistry and Control with a view to de–ning the state-of-theart .. . and outlining its future prospectsœœ. The latter will I am sure be ful–lled admirably by Professor Raphy Levine with his customary vision at the end of the Discussion and the remainder will I am equally sure be wonderfully ful–lled by you the practitioners. So what is left for the poor Spiers Lecturer to do? Well he can read the literature look back over a long career in molecular stereodynamics try to make sense of it all and report back. That was the original intention but what a literature ! Stereochemistry and Control and Molecular Reaction Dynamics or so it seemed at the start. Fortunately however reaction (stereo)dynamics and reaction control are two sides of the same coin. The evolving understanding of the dynamics of atomic and molecular reactions has led quite naturally to the evolution of strategies for their control while the control of elementary chemical reactions either requires or may lead to a (better) understanding of their (quantum) dynamics.Moving from the obverse to the reverse of the coin is essentially an inversion problem. The excitement of designing reaction control machinery is now motivating many theoreticians who aspire to becoming molecular quantum ìmechanicsœ while the challenge of implementing their ideas is also exciting many reaction dynamical ìengineersœ who work in the machine-shop. They too are part of the same coin. A key tool in the machine-shop is provided by the laser This journal is( The Royal Society of Chemistry 1999 (astonishingly a device once looking for applications).Perhaps the same astonishment will be felt one day in respect of the key tool in the quantum mechanicsœ and dynamical engineersœ workshops »the reaction control machine which undoubtedly will incorporate one or more lasers ! Indeed this Discussion could equally well have been titled ìLaser Control of Chemical Reactionsœ. How did ìStereodynamics and Controlœ all start ? As so often in the past the Faraday Discussions provide a unique lens through which the evolution of our current ideas and achievements can be viewed see Fig. 1. Discussion comments particularly have often provided –rst intimations of new directions. In the 1962 Faraday Discussion ì Inelastic Collisions of Atoms and Simple Moleculeœ we read1 ìì . . . the scattering of K]HBr beams indicates that .. . the angular momentum of KBr is predicted to be strongly polarized with j@ nearly perpendicular to the direction of the initial relative velocity vector . . . KBr An experiment is being attempted at Berkeley (D. R. Herschbach)œœ»the birth of stereodynamics and vector correlations in the products of bimolecular reactions. In the 1967 Discussion ìMolecular Dynamics of the Chemical Reactions of Gasesœ John Polanyi2 dreamt of using ìì . . . energy-selected and molecularly-oriented beams (coupled) with the spectroscopic examination of the products as a function of their scattering angleœœ. The –rst successful experiments with pol- Fig. 1 The road to enlightment Faraday milestones. Faraday Discuss. 1999 113 1»25 2 3 and H (v1\1) CH4(v3\1) (to which we shall return in Section 3).arised (oriented) reagent beams which marked the birth of Dynamical Stereochemistry and passive control were reported by Brooks and Jones,3 and Bernstein and co-workers4 a few years later and were debated5 at the 1973 Discussion ìMolecular Beam Scatteringœ. The new science came of age in 1986 when it was famously celebrated at a meeting organised by Raphy Levine Richard Bernstein and Dudley Herschbach held in the Fritz Haber Institute in Jerusalem6 but it took a further decade before John Polanyiœs dream was fully and –nally achieved in Richard Zareœs laboratory7 in a brilliant stereodynamical study of the reaction of Cl atoms with optically aligned CD Intimations of active quantum control can be traced through remarks made by Stuart Rice in summing up the 1979 Faraday Discussion ìKinetics of State Selected Speciesœ when he listed the topics which had not been discussed.8 He noted ìì Insufficient attention was devoted to the nature of the prepared state how it evolves and how this evolution in—uences what we observe.. . . We must learn how to interpret and manipulate the dressed states representing the interaction between a molecule and some exciting –eld since an understanding of these will enable us to direct chemical processes if and when that is possible. . . . Insufficient attention (was) focused on how to generate wave packet initial states which must be used if we hope to excite bonds or localised regions of large moleculesœ. All this in April 1979! It was these strictures which in part prompted the follow-up Discussion in 1983 on ìIntramolecular Kineticsœ where Rice continued to develop the same theme.9 ìì If the excitation process is coherent it ought to be possible to alter the time evolution of the system by tailoring the properties of that excitation process.. . . The principle that continuous control of the phase of the excitation source and molecule will permit control of the time evolution of an excited state (will) I expect be used (to promote) measurable changes in the . . . ratio of yields of products of a reaction. . . . T he immediate challenge is to devise a scheme for the interaction between the molecule and external –elds which permits intervention in the evolution of a ìpumped state œ.œœ We shall re-encounter these concepts repeatedly in the present Discussion.They re-surfaced –rst at the 1986 Discussion ìDynamics of Photofragmentationœ when Brumer and Shapiro10 presented their multiple path quantum interference strategy for phase coherent control and Rice11 discussed the alternative ì interventionist œ pump»dump schemes (to which we shall also return in Section 4) of Tannor KosloÜ and Rice12,13» at which point history ends and modern times begin. What follows is a ì retiring œ personœs idiosyncratic snapshot of the current status of stereodynamics and control primarily of bimolecular reactions. In Sections 2 and 3 the emphasis will be on strategies for passive control of chemical reactions evolving ììunder their own steamœœ and on their stereodynamics.Section 4 will review some of the strategies for active control in which reactive systems evolve under the in—uence of continuous wave (cw) or pulsed optical –elds and are ììmade to dance according to the theoreticiansœ and increasingly the experimentersœ tuneœœ. 2. State-to-state dynamics energy utilisation speci–city and mode selective control The discovery of speci–city in the disposal of energy released in exothermic bimolecular reactions led through the principle of microscopic reversibility to thinking about speci–city in the modes of energy utilisation in the reverse endothermic process. The result was Polanyiœs Rules»the recognition that the most eÜective mode(s) would be associated with motion of the collision system along the reaction coordinate.14 Experiments that probed the speci–city of energy utilisation or disposal provided clues about the topography of the potential energy hypersurface or at least those regions of the hypersurface through which the reaction coordinate passed.If the barrier to reaction lay in the entrance channel better to increase the reagent translational energy; if it lay in the exit channel better to excite vibrational motion along the chemical bond to be broken. Fine for a diatomic reagent but what about a polyatomic molecular target ? How localised could its molecular vibration(s) be and for how long might the localisation be sustained ? How many vibrational modes might couple to the reaction coordinate? Was mode selectivity likely to be a vain quest forever dissipated by intermode coupling and rapid intramolecular vibrational redistribution (IVR) or could it be demonstrated and applied given the right intelligent choice of reagents and reagent state preparation ? Faraday Discuss.1999 113 1»25 3 As is now well-known the pessimistic answer looked the more likely until Crim and co-workers experiments with HOD.15 The barrier to its endothermic reaction (1a) ]H2]OD H]HOD ]HD]OH (1b) is ca. 90 kJ mol~1 equivalent to two quanta in the l(O»H) mode or nearly three in l(O»D). Crim and co-workers discovered that the prior deposition of respectively four or –ve quanta in the l(O»H) or l(O»D) modes through laser excitation of the two vibrational overtones preferentially enhanced channel (1b) over (1a) or vice versa by a factor in excess of 200.16 The laser induced —uorescence (LIF) spectra made the point dramatically.Similar but less dramatic results were still obtained when (translationally excited) H atoms collided with HOD17 or D2O18 endowed with only a single quantum of vibration in the l(O»H) or l(O»D) stretching mode excitation of the bending mode was ineÜective however.18 The choice of target molecules and their excitation modes were of course intelligent ones. The likely success or otherwise of promoting mode selectivity in reactive collisions was best informed by (any) prior intelligence regarding (a) the ì isolation/localisation œ of the vibrational modes excited in the target molecule; (b) the (distorted) molecular geometry of the target molecule in the region of the transition state and the degree to which the reagentœs vibrational motion matched the movement towards the transition state structure.NH3 `]ND3. ( Selective excitation of the ion into its umbrella mode l2) through reso- Type (a) intelligence had been provided experimentally by the remarkable selectivity in O»H vs. O»D bond rupture following the vibrationally mediated photodissociation of HOD.19 The local mode character of the l(O»H) and l(O»D) overtones could be retained despite the nanosecond time interval between the initial state preparation and its subsequent projection onto the repulsive electronically excited potential energy surface. Type (b) intelligence had been provided theoretically through Schatz et al.œs ab initio calculation20 of the stretched HH»OH transition state structure in the reaction H]H2O]H2]OH (1c) The combination of (a) and (b) led naturally to a favourable view in respect of (c) and also demonstrated the synergism between theory and experiment now so vital in the –eld of molecular reaction dynamics.Finally the chosen reaction followed a ì direct œ pathway minimising the risk of vibrational redistribution from the initially prepared state. Its dynamics are revisited in the present Discussion theoretically on a new potential energy surface by Schatz et al.21 and experimentally by Smith and co-workers.22 A contrasting demonstration23 of mode selectivity was provided by the ion»molecule collision system nantly enhanced multiphoton ionization actively promoted electron transfer from the neutral molecule (associated with a planar-to-pyramidal geometry change in the acceptor ion) ; selective excitation of the symmetric stretching mode (l was ineÜective again in agreement with theory.24 1) In both examples there was a direct correspondence between the character of the ìpromotingœ mode and the intuitive or theoretically informed view of its projection onto the reaction coordinate.Despite the spectacular success of these and one or two other examples25,26 however without prior intelligence the search for mode selectivity in more complex systems must be a ì hit and missœ aÜair ; its pursuit is as much a study of intramolecular dynamics in vibrationally excited polyatomic molecules and of their state-resolved reactive collision dynamics as of mode selectivity.27 Again we can see two sides of the same coin. ììBond-selected bimolecular reactions require the proper interplay of excitation scheme and reaction dynamics to succeed (Crim27).œœ If the dominant elements in the reactive state-to-state scattering matrix can be identi–ed experimentally or theoretically then attention can be paid to optimising the excitation scheme. The ìpassiveœ way to do this is to let the reactive system ì report backœ to the experimentalist or to the scattering theorist on what suits it best. Recent experiments in Zareœs laboratory on the slightly endothermic reaction (2) Cl(2P3@2)]CH4(v\0)]HCl]CH3 Faraday Discuss. 1999 113 1»25 4 3\3019 cm~1 (36 kJ mol~1). Which is the more eÜective ? Not illustrate beautifully this alternative approach.7,28,29 The barrier to reaction which is ca.15 kJ mol~1 only can easily be surmounted in principle either by translational energy (in the attacking Cl atom) or by a single quantum in vibration (in the target molecule). Translational energy can be provided by the energy released in the photodissociation of a suitable precursor Cl2. Vibrational excitation can be provided by the prior laser excitation of a suitable mode in the target e.g. the asymmetric stretching mode l surprisingly at a collision energy of 16 kJ mol~1 excitation of l increased the reaction cross- 3 section by a factor D120.28,29 What was surprising however was the discovery that the lower energy thermally populated vibrational levels l (torsion) D18 kJ mol~1 and/or l (bend) D16 2 4 kJ mol~1 were even more eÜective increasing the reactivity by a factor D200 at a collision energy of 24 kJ mol~1 and providing clear evidence of mode speci–city.29 (3) These experiments exploited a new approach to the exploration of state resolved molecular reaction dynamics (reviewed recently in ref.30»32). Velocity aligned atomic reagents produced by polarised laser photodissociation of a suitable precursor are allowed to collide with the target molecule either in the bulk gas or co-expanded in a molecular beam. The scattered products are detected state-selectively either through polarised Doppler-resolved LIF spectroscopy or resonantly enhanced ionisation coupled with time of —ight (tof) analysis. Their velocities and angular distributions are re—ected in the experimental Doppler pro–les projected onto the probe laser axis (in an LIF experiment) or the time of —ight pro–les measured along the mass spectrometer axis (in a tof experiment) ; simpli–ed Newton diagrams for the reaction A]BC(v J)]AB(v@ J@)]C are shown in Fig.2. The key equation which links the product velocity (in the laboratory frame) øAB h \øCM]wAB with the scattering angle t (in the centre of mass frame) is provided by the Law of Cosines (hence the acronym PHOTOLOC coined by Zare and co-workers30) (4) vAB2\vCM2]wAB2]2vCMwAB cos ht Since AB is state-selected the remaining terms are determined through energy conservation (provided C carries no internal excitation) and measurements of the Doppler pro–les recorded under parallel and perpendicular detection geometries lead to the product state-resolved diÜerential cross section P(cos ht)4(2p/p) dp/dut .When the partner product does carry internal excitation for example in the reaction (5) A]BCD]AB(v@ J@)]CD(vA JA) a series of measurements using alternative detection geometries can provide both the diÜerential cross-section (DCS) of the observed product and the correlated translational energy distribution P( fT) of the two scattered products which re—ects the internal energy distribution P(vA JA) in the unobserved products that accompany AB (v@ J@). The new strategy has been applied recently to Fig. 2 The PHOTOLOC strategy ìcollapsedœ Newton diagrams (for a target molecular velocity øBCD0). 5 Faraday Discuss. 1999 113 1»25 two reaction systems both of which involve ìcomplexœ as opposed to ì direct œ reaction mechanisms; they each address the question of IVR within the lifetime of a short-lived collision complex.The –rst endothermic reaction (6) H]CO2 ]MHOCONE J ]OH(v@ J@)]CO(vA JA) presents an energy barrier ca. 100 kJ mol~1. Fig. 3 shows the DCSœs translational energy distributions and angle-velocity contour maps for the ground X\3/2 and excited X\1 spin»orbit 2 states of OH(v@\0 N@\1) determined33,34 at a translational collision energy of 248 kJ mol~1. While the products in the excited spin»orbit state are scattered predominantly backwards the angular distribution of those in the ground state is relatively isotropic. The CO molecules accompanying OH(X\1/2) carry somewhat less internal excitation than those accompanying OH(X\3/2) and in both cases their internal energy distributions are ìcolderœ than predicted by phase space theory calculation.Similar results are found for OH(v@\1 N@\1) at the same collision energy and also for OH (v@\0 N@\1) at a lower energy 180 kJ mol~1 though the OH(X\1/2) fragments are now scattered preferentially forwards. They imply the operation of two distinct microscopic mechanisms. The channel leading to the excited (X\1/2) spin»orbit state proceeds through a short-lived intermediate with an average lifetime td less than its mean rotational period tr . It is accessed through small impact parameter collisions associated with a narrow cone of acceptance. The channel that leads to the ground spin»orbit state OH (X\3/2) proceeds through the intermediacy of a transient rotating complex with tdDtrD2.5 ps.In neither case is the interaction time long enough to allow full IVR but more signi–cantly in the present context it is also not short enough to prevent some limited IVR. An interesting by-product of these results is the possible resolution of a long-standing anomaly35 associated with two ultrafast studies of reaction (6) initiated within a van der Waals (vdW) complex of HI (or HBr) and CO The rate of appearance of OH (v@\0 N@\1 or 6) in the 2. lower spin»orbit state (X\3/2) measured by Zewail Bernstein and co-workers36 on a picosecond time scale was around an order of magnitude slower than the average apparently non state-resolved rate of appearance of OH (v@\0 N@\2»20 X\1/2 3/2) measured by Wittigœs group37,38 on a femtosecond time scale see Fig.4. A subsequent analysis39 of the OH (A»X) spectral features sampled by the broad band femtosecond laser pulse reveals however that despite the poor energy resolution the great majority of the OH fragments sampled actually occupied low rotational levels N@ of the upper spin»orbit state X\1/2 ! These are just the products that X H scattered from the reaction ]CO2 ]OH]CO reagent collision energy Fig. 3 DiÜerential cross-sections correlated translational energy distributions and angle»velocity contour maps for OH (v@\0 N@\1) 248 kJ mol~1. Faraday Discuss. 1999 113 1»25 6 N@\1 6) Fig. 4 Ultrafast kinetics of the photo-initiated vdW complex reaction (HI]hl]) H ]CO2 ]MHOCONE J ]OH]CO.Energy dependent rate constants k(E) for the appearance of OH (v@\0 (Zewail and co-workers36) and OH (v@\0 N@) (Wittig and co-workers37,38). 3@2 X Fig. 5 DiÜerential cross-section correlated translational energy distribution and angle»velocity contour map for OH (v@\0 N@\5) scattered from the reaction O(1D)]CH kJ mol~1 (ref. 40). 4 ]OH]CH3 mean collision energy 39 7 Faraday Discuss. 1999 113 1»25 appear from the state-resolved DCS measurements to be generated via a faster more ì direct œ pathway. The second example40 involves the strongly exothermic insertion reaction (7) O(1D2)]CH4 ]MCH3OHNE J ]OH(v@ J@)]CH3(vA JA KA) which generates OH fragments with high rotational excitation in all accessible vibrational levels v@O4.DCSœs translational energy distributions and scattering angle»velocity contour maps determined for vibrationally cold OH (v@\0 N@\5) at a mean collision energy of 39 kJ mol~1 are shown in Fig. 5. The strong backward scattering of OH (v@\0) suggests a preference for low impact parameter collisions a narrow ìcone of acceptanceœ and a complex lifetime (estimated to be ca. 3 ps41) that is shorter than its mean rotational period. The low fraction of energy released into translation also indicates the disposal of high internal energy into the accompanying CH3 fragment. A phase space theory calculation reproduced the correlated internal energy distributions in the CH fragments which appeared to be dynamically unconstrained but the uncorrelated 3 product state distributions were colder than those calculated on the basis of a statistical prior.The results could be understood if a dynamical constraint restricts the coupling of the OH vibrational MOCH motion to the other degrees of freedom within the 4N complex at least during its short transient existence.40 Despite this evidence for incomplete IVR on very short time scales (e.g. the picosecond lifetimes of transiently bound collision complexes) and the evidence of mode selectivity/passive control in the bimolecular reactions of a few vibrationally excited hydrides such behaviour is the exception rather than the rule. Passive control of chemical reaction by prior optical excitation of a selected vibrational mode in one of the reagents is generally defeated by the rapidity of IVR in the interval between preparation and collision.Even when the vibrational excitation does remain localised only rarely is there a sufficiently close correspondence between the selected vibrational mode and the reaction coordinate that links the reagents to the (selected) products for IVR to be kept at bay. The molecular dynamics are controlled by a global molecular Hamiltonian. (1c) (2a) (2b) 3. State to state dynamics dynamical stereochemistry and steric control Since its ìcoming of ageœ6 and its subsequent welcome at a Faraday Discussion ìOrientation and Polarisation EÜects in Reactive Collisions,œ held in Bad Honnef in 1988,40 the –eld of Dynamical Stereochemistry has been very thoroughly reviewed»in articles,30h32 43h45 in conference proceedings41 46h48 and in the Memorial Volume in honour of one of its chief architects Richard Bernstein.49 The idea of a ìcone of acceptanceœ through which reactive collision trajectories must pass in order to access the transition state was a key early concept.Reactive collisions are possible only when the angles of approach and the impact parameters lie within the spread and range of the ìcone of acceptanceœ. Those that fall outside in the ìcone of non-reactionœ are inelastic. The ìchemical shapeœ of the reagent molecules is conferred in part by the anisotropy of the reagent interaction potential but the cone of acceptance is also a dynamical concept its dimension is sensitive to the collision energy and to the internal vibrational motion of the interacting reagent(s).An increase in either may lead initially to a widening of the cone angle and subsequently to the creation of an increasingly broad funnel. This is manifested by an increase in the integral reactive cross-section and when the reaction is direct by a broadening of the productsœ diÜerential crosssection. Ultimately the reactive cross-section may increase to the point where the short-range ìchemical shapeœ is lost and like the smile on the face of the Cheshire cat,50 all that remains then of the cone of acceptance is the concept. These eÜects are well illustrated by recent PHOTOLOC studies of the two collision systems introduced in Section 2 H]H2O (v\0)]OH (v@\0 N@)]H2 and Cl(2P or v4\1)]HCl (v@\0 1 J@)]CH3 Cl(2P3@2)]CH4 (v\0)]HCl (v@\0 J@)]CH3 3@2)]CH4(v2 v3 Faraday Discuss.1999 113 1»25 8 (We shall see that ìLOCœ is an acronym for ìLine of Centresœ as well as ìLaw of Cosinesœ !). Consider –rst reaction (1c) investigated by Brouard and co-workers51 at a high collision energy 135 kJ mol~1 which is ca. 45 kJ mol~1 above threshold. The state-resolved DCS for the scattered OH shown in Fig. 6(a) displays a broad angular spread which peaks in the sideways direction (and is well reproduced by Bradley and Schatzœ QCT calculations on a high level ab initio potential energy surface52). In contrast a crossed beam measurement of the DCS for the reverse reaction (of OH with D conducted very close to threshold (collision energy 26 kJ mol~1) by 2) Casavecchiaœs group53 [see Fig. 6(c)] reveals strong backward scattering»explicable if reaction at low energy requires a near collinear H»H»O(H) transition state con–guration and a narrow cone of acceptance.The spreading of the DCS at high collision energy (but not the sideways peaking) and also the enhanced reactivity of vibrationally excited HOD(lOH lOD) discussed earlier in Section 2 have both been explained in terms of an increase in the cone angle and qualitatively modelled in terms of an angle-dependent potential energy barrier using Smithœs modi–ed hard sphere line-of-centres model.53v57 A widening ìfunnel of acceptanceœ might provide a better description. Subsequent comparisons by Brouardœs group,58 of the product angular distribution from the isotopic reaction (1d) H]D2O]OD (v@\0 N@)]HD found a marked increase in the proportion of backward scattered products see Fig.6(b). A narrowing in the cone angle resulting from the considerable reduction in the zero point energy in the deuterated reaction would account for this.56 3) Similar qualitative arguments have been employed by Zare et al.7,28,29 to account for the produced through reactions (2a) and (2b). The DCS for 4(v\0) broadens with increasing collision energy from backwards angular distributions of HCl (and CH HCl(v@\0) scattered from CH near threshold towards sideways scattering,29 again consistent with a model in which wider angle impacts can impart a sufficient velocity component along the line of centres to overcome the barrier to reaction. Collisions with CH4(v3\1) optically excited into the asymmetric stretching mode generate a more complex scattering pattern which is summarised pictorially in the ìdartboardœ representation shown in Fig.7. The reactive collisions now generate both HCl(v@\0 J@) and (v@\1 J@). The molecules in (v@\0) are rotationally excited and scattered broadly but predominantly sideways and backwards (small impact parameters preferred but associated with a wide angle of acceptance). Those in (v@\1) are mostly rotationally cold and are scattered predominantly forwards implying a preference for large impact parameter (or equivalently large cone angle) ìperipheral collisions œ.59 A small proportion of the HCl in (v@\1 J@\3) is scattered both forwards and backwards clearly at the detailed level of state-to-state resolution the picture becomes more complex.60 None the less as might be expected for direct endothermic reactions such as (1) and (2) which present a ì late barrier œ the ìchemical shapeœ of the unexcited molecular target (as seen by the attacking atom) and the stereodynamics of the reaction are dictated by H]H Fig.6 Collision energy dependence of diÜerential cross-sections for the reaction 2OHOH]H2 (and its isotopic variants). (a) OH (v@\0 N@\1) scattered from H/H2O:5 collision energy 135 kJ mol~1 (b) OD (v@\0 N@\1) scattered from H/D2O:58 collision energy 135 kJ mol~1 (c) HOD scattered from OH/D2:53 collision energy 26 kJ mol~1. 9 Faraday Discuss. 1999 113 1»25 Fig. 7 Schematic representation of the state-to-state collision dynamics of the reaction7,28,29 Cl(2P3@2) ]CH4(v3\1)]HCl(v@ J@)]CH3 .The –gure is adapted from ref. 28. short-range interactions. These are manifested (amongst other observables) in the product state distributions and diÜerential cross-sections. The observables are also sensitive to the consequences of internal state-selected excitation (control) of the molecular target ; they re—ect the changes in its dynamical ìchemical shapeœ as viewed through the lens of state-speci–c opacity functions. What are ìthe other controls and observablesœ ? The most important by far are the reagent and product polarisations the relative orientation (heads vs. tails) or alignment (broadside vs. end-on) of the interacting reagents and the correlated linear and rotational angular momentum spatial distributions in the scattered products.The initial conditions prior to collision can be brought under the experimenterœs (partial) control but the –nal results»the observables»although sensitive to the initial conditions are dictated by the dynamics the forces and torques operating during the course of the reactive collision and by the conservation laws. It is for this reason that controls exerted prior to reaction are termed passive. The response to the control aids dynamical understanding but does not actively direct the course of the reaction. Controlling the orientation or alignment of the collision partners for example simply selects a sub-set of the pre-collision conditions from the complete set that would have been sampled had the collisions been unconstrained.Once again the broadside attack7 on the dynamics of the state-resolved reaction (2c) Cl(2P3@2)]CH4 (v3\1)]HCl (v@\1 J@\1)]CH3 and its isotopic variant (2d) Cl(2P3@2)]CD3H (v1\1)]HCl (v@\1 J@\1)]CD3 provides an instructive illustration of ì sterically controlled understandingœ. 3.1 Reagent polarisation In CD the C»H vibrational axis and the target molecular rotational angular momentum can 3H be aligned preferentially parallel or perpendicular to the reagent velocity vector by exciting the C»H stretching mode l1 with linearly polarised infra-red radiation and by selection of an appropriate rotational branch P,R vs. Q. Measurements of the DCS for the scattered HCl under alternative parallel and perpendicular polarisation geometries,7 explore the anisotropy of the reactive scattering.§ In agreement with the ìperipheral collision œ model proposed earlier on the basis of § The mixture of axial/vibrational alignment and rotational alignment complicates the quantitative picture since estimates of the eÜective level of axial alignment must include the consequences of rotational/precessional averaging (and also nuclear hyper–ne coupling).7 Faraday Discuss.1999 113 1»25 10 the ìuncontrolledœ DCS measurements more forward scattered HCl(v@\1 J@\1) can be detected for an initial ìperpendicularœ axial alignment than for a ì parallel œ alignment»which favours broadside over end-on collision geometries and implies a T-shaped transition state.7 Surprisingly similar results were obtained with vibrationally aligned CH4(v3\1) indicating the retention of a localised asymmetric C»H vibration and of mode speci–city despite the presence of four equivalent C»H bonds and the possibility of collisional scrambling.The in—uence of reagent translational energy on ìchemical shapeœ has been explored by Loeschœs group in a study of the simpler triatomic reaction of Sr atoms with optically aligned HF (v\1 J\1).61 As the collision energy increased the steric preference changed from broadside to end-on; in a similar study of K]HF (v\1) the preference changed from end-on to isotropic. In each of these examples the linear polarisation of the optical –eld restricts the polarisation control to the alignment of vibrationally excited reagents. Historically of course the –rst stereo-control experiments3h5 31 45 focused (literally) on the complementary situation orientation of the reagent molecules in their ground vibrational state.o J K MT state selection and consequent molecular orientation (for J K and M all non-zero) were –rst achieved (for polar symmetric top molecules) by hexapole focusing of the molecular reagent beam followed by adiabatic passage through a uniform electric –eld at the collision zone which oriented the molecular axes along the relative velocity to allow either ìheadsœ or ì tails œ bimolecular collision geometries. o J K MT state selection alone is also being used by Baugh and coworkers62 to probe the state-resolved stereodynamics of molecular predissociation. The alternative ìbrute-forceœ strategy initially developed and exploited by Loesch and coworkers63 to study the stereodynamics of bimolecular reactions has also been exploited (by Miller and co-workers64) to study unimolecular vibrational predissociation dynamics (of polar van der Waals dimers).The ìbrute forceœ method simply uses a strong uniform electric –eld to orient dipolar molecules which brings in the picture of ìpendular states œ generated through the coherent superposition or ìhybridisationœ of the –eld-free molecular rotational eigenfunctions.65 When the applied –eld is sufficiently intense and the temperature is very low e.g. in a molecular beam environment the interaction energy can become much larger than the mean thermal energy kT and the molecular rotational constant B. In this situation the ensemble of oriented molecular dipoles which can now include diatomic and linear species as well as symmetric and asymmetric tops librates about the applied electric –eld vector65 (see the contribution by Nauta Moore and Miller66).Paramagnetic (non-polar) molecules and molecular ions can also be aligned (but not oriented) in a similar way in a strong magnetic –eld. In either case zero-–eld quantum state selectivity is lost of course as a result of the rotational state mixing. A similar result can be achieved for non-polar molecules through the interaction of their anisotropic polarisability with the optical –eld of an intense polarised laser pulse,67 both on- and oÜ-resonance.68 In this situation the alternating nature of the radiation –eld promotes molecular alignment (via the induced dipole) rather than orientation.The interaction with a high intensity laser –eld creates a large non-resonant Stark shift and if the laser is focused the local –eld gradient can generate a lateral force. This provides an additional control that can be used to de—ect or to focus a reagent molecular beam,69 and which opens up the exciting new –eld of molecular optics (see Corkum et al. to be presented at this Discussion70). The pulsed character of the intense laser –eld introduces additional factors that must be addressed before its use in any stereo-dynamical application.71 When the duration of the laser pulse q is long compared with h/2pB the individual molecular axial alignment follows the molecule»–eld interaction adiabatically to produce a single pendular eigenstate as in the static situation.At the other short-pulse extreme qOh/2pB the interaction is non-adiabatic and a coherent superposition of pendular eigenstates is generated producing an intensity-dependent coherent rotational wave-packet at the end of the laser pulse and subsequent periodic recurrences of the molecular alignment.67,68,71,72 Quantum control strategies for generating transient molecular orientation have been proposed by Vrakking and Stolte73 and Bandrauk and co-workers;74 phase-locked laser pulses are used to excite transitions involving an odd and even number of photons typically with u1\2u2 to create a coherent superposition of opposite parity rotational quantum states. The time-dependent orientation results from the symmetry-breaking associated with the mixed parity excitation schemes.In general the polarisation generated in any particular situation will depend upon the duration intensity and shape of the ìpolarisingœ laser pulse.71 11 Faraday Discuss. 1999 113 1»25 Before its use as a control device we have to learn how to ìcontrol the controller œ. In doing that something may be learnt about the mechanism of the control as well as the mechanism of the process over which control is sought. A third strategy for molecular orientation or alignment exploits the anisotropy of the reagentsœ intermolecular –eld which itself may be a principal focus of a stereochemical investigation. For example the anisotropy may lead to molecular re-orientation as the reagents begin to collide particularly when the interaction occurs at long range or at low relative velocities and/or when one or other of the reagents has a small moment of inertia.75 Very recently the anisotropy in the intermolecular potential between Cl(2P3@2) H2 which leads to a ììT-shapedœœ van der Waals and minimum at long range has been found76 to have a dramatic in—uence on the isotopic branching ratio HCl/DCl in the reaction (8) Cl(2P3@2)]HD]HCl/DCl]D/H At collision energies not too far above threshold DCl is very much the preferred product.Reorientation of the HD towards the linear transition state geometry favours the heavier isotope since the centre of mass of HD is closer to the D atom»a classical interpretation which has been quantitatively reproduced through ab initio quantum scattering as well as QCT calculations76 (see Fig.8). If the collisions are non-reactive molecular polarisation (referenced to the laboratory frame) can be introduced dynamically via the interactions in an expanding molecular beam77h79 (see also ref. 80). Alternatively it can be introduced in a reagent pair or their precursors (in a ìmolecularœ frame) within a stabilised van der Waals (vdW) complex. This approach was –rst introduced by Soep and co-workers,81,82 to explore the consequences of electronic orbital alignment (referenced Fig. 8 (a) Experimental and calculated collision energy dependent branching ratios76 in the reaction Cl(2P3@2) ]HD]HCl(DCl)]D(H). (b) Ab initio potential energy surface and classical trajectories exposing the control exerted through the angular anisotropy.Faraday Discuss. 1999 113 1»25 12 Fig. 9 Vectorial diagram for the (k k@ j@) correlation. The reagent momentum k de–nes the z-axis ; the product momentum k@ lies in the xz plane and the spatial distribution of the product rotational angular momentum j@ is de–ned by the polar angles hj rj . to the intermolecular framework via the electronic transition dipole) and subsequently by Wittig and co-workers,37,83,84 initially to explore the consequences of restricting the range of reagent impact parameters. As so often there was good news and bad news. The bad news was that the wide amplitude vibrational motion characteristic of weakly bound vdW complexes could seriously compromise the constraint on the range of impact parameters.The good news was that comparisons of product state37,83 and angular distributions84 scattered from precursor geometry limited (PGL) reagents with those from ì free collisions œ generated many (interesting) new questions. Most importantly in the present context the preparation of ìpre-reactionœ complexes provided a means of initiating bimolecular reactive collisions under ultra-fast conditions at a known time origin.37v40,85 The –nal approach introduced by Polanyi in his 1987 Spiers Lecture ìThe Dynamics of Elementary Reactions,86 exploits the anisotropy of surface»adsorbate interactions to address the photodissociation dynamics of surface oriented adsorbates and the stereochemical control of bimolecular reactions at surfaces.87 Fast surface aligned photofragments are ì–redœ at –xed surface-adsorbed molecular targets to achieve a limited distribution of impact parameters a strategy which combines elements both of the PGL and photon-initiated ìPHOTOLOCœ strategies.3.2 Product polarisation30,31,88h91 Dynamical stereochemistry addresses the vectorial aspects of reactive collisions or half-collisions it focuses on the directional momentum correlations between the linear momenta and the rotational and orbital angular momenta k j l and kº jº lº of the reagents and products or between the product momenta and the polarisation of an incident photon in a photodissociation experiment. 88 As the author wrote in an early review,89 ììthe measurement (of vector correlations) provides an entry into the anisotropy of molecular interactions an approach to understanding the stereospeci–city of chemical reactivity and a means of charting the collision dynamics in three dimensionsœœ.Precise control of the impact parameter remains to be achieved so correlations involving the orbital angular momenta cannot be measured experimentally (though they are accessible to computationally minded theoreticians). If the rotational angular momentum of the reagent(s) has not been pre-aligned/oriented the remaining observable correlations will re—ect the relative spatial distribution of k kº and jº. For a triatomic A]BC collision system this is characterised semiclassically by the probability density function,88 (9) and P(ut uj w)\P(ut uj)d(w[wf)\(1/p)(d2p/dut duj)d(w[wf) where w w is the product speed in the CM frame and is its speed in the selected –nal state o fT (at a f (ht rt\0)4ut (hj rj)4uj given total energy) ; are the polar coordinates of k@ and jº as 13 Faraday Discuss.1999 113 1»25 j). P(h de–ned in Fig. 9. The probability density function t hj rj) represents the rotational polarisation of a state-selected product scattered at angle ht and referenced to the scattering plane de–ned by k kº.î If the distribution is integrated over the scattering angle it can be represented as a polar map of P(u A highly instructive example is shown in Fig. 10(a) which presents a quasiclassical (QCT) trajectory calculation92 of the average spatial angular momentum distribution P(uj) in HF(v@\3 J@) generated through the reaction (10) F(2P3@2)]H2 (v\0 J\0)]HF (v@\3 J@)]H (see the contribution by Nesbitt93).The distribution favours jº//kxkº i.e. it is strongly oriented along the axis perpendicular to the collision plane. How could this arise ? Firstly we must note that the state-selected channel (10) is near thermo-neutral and unlike the remaining channels leading to HF(v@O2 J@) it leads to forward rather than backward scattering.94 The reactive collisions leading to HF(v@\3 J@) are ìperipheralœ/forward scattered since there is very little energy available for release into relative product translation.95 In consequence the –nal orbital angular momentum lº will be directed nearly parallel to the reagent angular momentum l. Furk@ B1 thermore the reduced mass in the product channel 2k and if l@D12 l the conservation constraint will force the remaining angular momentum jº to be oriented parallel to l (and l@) as shown in the sketch Fig.10(b). The full rotational angular momentum spatial distribution P(ht hj rj) can be expressed semiclassically as an expansion in bipolar or spherical harmonics.96v98 The advent of the PHOTOLOC strategy which uses polarised Doppler-resolved laser radiation to monitor the scattered products has provided a powerful new means of determining moments of the quantum state Fig. 10 (a) A QCT calculation92 of the angular momentum orientation in HF (v@\3 J@) scattered from the reaction F(2P3@2)]H2 (v\0 J\0)]HF(v@ J@)]H. (b) Angular momentum conservation. density function can be expressed as î In more complex systems e.g.A]BCD]AB o fT]CDo f @T where the internal energy distribution P(f @) in the unobserved product CD is re—ected in the correlated product speed distribution P(w) the probability P(ut uj w)\P(ut uj) P(w) assuming separability. Faraday Discuss. 1999 113 1»25 14 resolved spatial distribution experimentally. When the distribution is polarised both the intensity and the contour of the Doppler spectrum vary with the alignment of the probe laser beam and with the character of the selected rotational feature QC vs. P RC. This information can be used96,97 to extract the low order bipolar or spherical multipole moments of the classical probability density distribution P(ht hj rj) the multipole moments (1/p)d2pkq/duj dut are generalised polarisation dependent diÜerential cross-sections PDDCSs).97 Even moments of the distribution re—ecting the alignment are (and have been) obtained using linearly-polarised probe laser detection ; odd moments re—ecting the orientation can be obtained (in principle) using circularly polarised detection.QCT92 or full quantum scattering99 calculations of course provide the complete set see for example Fig. 10(a). In a quantum description the classical probability P(h density t hj rj) is replaced by a density matrix o (omm{(cos ht) o re—ecting the distribution over m states ; a full quantum mechanical treatment of product rotational polarisation in bimolecular J reactions has recently been presented99,100 and applied to the benchmark reactions of H with D299 and OH with H2 (see the paper by de Miranda et al.to be presented at this meeting101). A —avour of what measurements (or calculations) of state-resolved product rotational polarisation can tell us about the stereodynamics of reactive collisions is provided by re-visiting some of the key systems discussed earlier. Consider –rst reaction (2c). (2c) Cl(2P3@2)]CH4 (v3\1)]HCl (v@\1 J@\1)]CH3 The rotational alignment of the HCl(v@\1 J@\1) which is predominantly forward scattered was found to lie preferentially parallel to the reagent momentum k but the rotation axis was increasingly tilted away from k as the scattering angle decreased. This at –rst surprising result could be reproduced qualitatively by an impulsive hard sphere collisional model in which the force generating the rotational torque was directed along the line of centres,102 which tilts away from k as the impact parameter increases.P(uj) of OH(v@\0 N@\11) scattered Fig. 11 shows polar plots of the rotational alignment into the p(AA) lambda doublet state via reaction (6). (6) H]CO2 ]MHOCONE J ]OH(v@ J@)]CO The rotational angular momentum j@ is now aligned preferentially parallel to the product momentum k@ i.e. with a ìpropellerœœ type of motion and it lies preferentially in the scattering plane k k@. This is seen even more clearly in Fig. 12 where the OH fragments monitored via the p(AA) component of the (v@\0 N@\5) quantum state,103 have been scattered from the analogous (but H]CO Fig. 11 Rotational angular momentum alignment of OH [v@\0 N@\11; p(AA)] scattered from the reaction 2 ]OH(v@ N@)]CO.15 Faraday Discuss. 1999 113 1»25 N@\5; p(AA)] scattered from the reaction H]N Fig. 12 Scattering angle dependence of product rotational angular momentum alignment OH [v@\0 2O]OH]N2 . (11) exothermic) iso-electronic reaction,° H]N2O]MHNNONE J ]OH(v@ J@)]N2 Here the rotational angular momentum distributions scattering angles»which is almost as state-resolved as one can reach. The state-resolved diÜerential cross section displays both forward and backward peaks and the preferred alignment j@//k@ is shown equally in both consistent with reaction via an intermediate short-lived rotating collision complex. In the reaction with CO2 P(uj cos ht) are shown over a range of the preferred ìpropellerœ motion could be explained by a ì frontierthere is a very strong preference for the H atom to attack the ìwrong endœ orbital œ model in which the electron associated with the attacking H atom is initially accepted into the lowest unoccupied anti-bonding p*-orbital in the target molecule.Its nodal structure would promote torsional motion within the collision complex (as well as bending of the heavy atom frame) ; the torsional motion would lead to OH rotation aligned preferentially with j@// k@. In the reaction with N2O of the target to form initially an MHNNON complex before H atom migration allows the exit con–guration MHONNN to be accessed.104 In this system the ìpropellerœ alignment of the scattered OH is probably associated with the non-adiabatic transfer onto the –nal exit potential energy surface.There is also a striking analogy with the ìpropellerœ alignment found by Comes ° The alignment of the corresponding p(A@) lambda doublet is much weaker both for the reaction with CO2 and with N2O. Faraday Discuss. 1999 113 1»25 16 3 N2O. Gericke et al.,105 in the NH(a 1*) fragments generated through the p]p* photodissociation of HN which is iso-electronic with As a –nal example both the measured and computed106 rotational alignments P(uj) of OH (2%) generated in the rotationally excited (v@\0 N@\14) quantum state through the insertion reaction (12) O(1D2)]H2(v\0 J@)]OH(v@ J@)]H are shown in Fig. 13. This time the spatial distribution of j@(OH) has been integrated over the spread of scattering angles. In contrast to the previous examples and as expected for an insertion pathway governed by an attractive long-range potential the average rotational alignment of the preferentially populated p(A@) lambda-doublet,“ is now directed perpendicular to the scattering plane i.e.with M @ k kº. The QCT calculations based upon the modi–ed Schinke»Lester potential energy function for the ground electronic state (now somewhat dated) or on the more recent ìKœ surface of Schatz et al. qualitatively reproduce the experimental result. Further analysis,107 based upon the ìKœ surface leads to the predicted spatial distributions for the (unobservable) reagent and product orbital angular momenta l,l@ as well as the rotational angular momentum j@; those for the set of rotationally excited products OH(v@\0 J@\21»32) are shown in Fig.14(a). They indicate an isotropic distribution for l but strongly polarised angular distributions of l@ and j@. However the product angular momenta are strongly correlated see Fig. 14(b) with j@ directed anti-parallel to l@ which supports the picture of an insertion pathway proceeding through a bent transition state and generating high product angular momenta j@ l@A1. j Fig. 13 (a) Experimental and (b) computed rotational alignment of OH (v@\0 N@\14) scattered from the reaction O(1D)]H2 ]OH(v@ N@)]H. “ Interestingly the more weakly populated p(AA) lambda-doublet is rotationally aligned in the scattering plane presumably because the unpaired electron density is in each case preferentially localised in the H»O»H plane.The QCT calculations cannot of course distinguish between the two components. 17 Faraday Discuss. 1999 113 1»25 (ø@\0 J@\20»32) populated through the reaction Fig. 14 QCT calculations of (a) the spatial distributions of the reagent/product orbital angular momentum l l@ and the rotational angular momentum j@ for the product channels OH O(1D)]H2 ]OH(v@ J@)]H; (b) the angular correlation between l@ and j@. Alternative pathways proceeding through a linear transition state over the initially repulsive electronically excited surface(s) associated with the orbital degeneracy of the O(1D2) atom should also be accessible at slightly elevated collision energies.108 Their contribution if separately detectable would generate rather diÜerent quantum state dependent angular momentum correlations among the scattered OH fragments.A possible passive control mechanism which would also serve as a ìdiagnosticœ for an ìabstractionœ pathway could be provided if the long range interaction of O(1D) and H /HD also favours a ìT-shapedœ con–guration and perhaps a van der Waals 2 Cl(2P minimum cf. the interaction of /HD,76 discussed earlier in Section 3.1. ìPre- 3@2) H2 and orientedœ collisions with HD proceeding over the excited surface(s) at collision energies just above the threshold for abstraction should strongly favour the production of OD over OH. These examples provide a snapshot of the sensitivity of state-resolved product rotational polarisation as a dynamical indicator. The broad spectrum of polarisation behaviour that has already been revealed re—ects the broad spectrum of possible reaction pathways and illustrates the value of measuring the vectorial as well as the scalar attributes of reactive collisions as an aid to understanding their dynamics.Given that (limited) understanding let us turn now to considering some of the strategies and/or opportunities for actively controlling the course of chemical reaction. 4. Quantum control The idea of exploiting the phase coherence and/or the high intensities of cw or pulsed laser radiation to control the course of a chemical reaction has caught the imagination of many theoreticians a rapidly growing number of experimentalists»and the organisers of this Discussion. The range of strategies and the status of their present experimental implementation have been very thoroughly reviewed109 and since a major new monograph is also in prospect,110 this is not the place for an extended discourse but rather an opportunity to set the scene and take stock.The Faraday Discuss. 1999 113 1»25 18 emphasis is now focused on strategies that utilise optical control –elds to direct the course of a chemical reaction during its evolution from reagent(s) to product(s) i.e. active rather than passive control. 4.1. Multiple path interference strategies (nhl The scheme –rst presented by Brumer and Shapiro,10,111 was a simple one. If two (or more) independent pathways leading to a pair (or a set) of degenerate –nal states o fjT could be accessed coherently through optical excitation the –nal outcome would be modulated by their quantum mechanical interference.Their relative contributions to the summed amplitude could be controlled in the laboratory by tuning the relative intensities and/or the phases of the two (or more) optical control –elds. A simple experimental realisation could involve parallel single (hln) and multitransitions from a single starting state o iT such that photon ln\nlm or in general,112 m) (13) *Ei?f\mhln\nhlm l If the harmonic frequency l n were derived from the fundamental (cw) laser frequency m the relative phases of the two optical –elds could be simply controlled e.g. by passage through a dispersive gas. Variation of the gas pressure would lead to a modulation in the –nal outcome for example unimolecular photodissociation into alternative product channels following excitation into a continuum state.In contrast to mode selective dynamics its success would not depend upon any detailed prior knowledge of the photodissociation dynamics. For (m]n) even (preserving parity) the (successful) experimenter would gain control over the relative integral cross-sections for each channel.111 Alternatively for (m]n) odd the mixed parity of the degenerate continuum states would allow coherent phase control over the orientation of the product angular distributions i.e. control over their diÜerential cross-sections.113 Experimental realisations of each type of control have been achieved.109,110 Some major early successes included control of predissociation (vs. auto-ionisation) in diatomic molecules e.g.HI DI114 (see the paper of Gordon Seidemann et al.115) and of ionisation in H2S;115,116 control of predissociation (vs. multiphoton ionisation) or bound state to bound state transitions in larger polyatomic molecules e.g. NH tri-ethylamine . . .117 and control of the angular photo- 3 CH3I electron distribution in the photo-ionisation of NO.118 An alternative high –eld variant of the multiple path interference scheme introduced and implemented by Brumer and Shapiro,119,120 employed a pulsed single frequency pump laser o iT]o f tuned to the transition jT together with a second laser which provided a pulse that coupled the degenerate target states of the system to a third previously unoccupied state omT at o iT]o f lfm . The additional pathway the Stokes frequency jT]omT]o fjT introduces the possibility of quantum interference and the potential for product selectivity.Ampli–cation of the Stokes laser intensity allows a repeated sequence of cyclic transitions o fjT]omT]o fjT]omT]o fjT . . . which leads to an exact cancellation of the phase and the need for phase coherence in the two optical –elds is eliminated. The strategy is closely related to the ìstimulated Raman rapid adiabatic passageœ (STIRAP) scheme121 for promoting population transfer (from o iT to o fT). Like STIRAP it is most eÜective if the intense laser –eld that couples the intermediate and –nal states omT and o fT is established before the (overlapping) pulse which excites the transition o iT]omT. The original three-level STIRAP scheme does not provide a reaction path control mechanism but a higher order extension has been developed by Kobrak and Rice,122 which can allow reaction control by introducing a third laser –eld to couple the reactive channels ofjT to a further best choice intermediate state.Tannor KosloÜ and Bartana123 present a generalised multilevel version of this strategy in the Discussion. 4.2. Pumpñdump strategies and optimal control In the pump»dump strategy –rst introduced by Tannor Rice and KosloÜ,12,13 control was exercised primarily through the timing of two ultra-fast laser pulses. The –rst was used to launch a vibrational wave-packet which evolved through translation (and dephasing) on an electronically excited state potential energy surface (or the ground state surface following infra-red excitation) hopefully towards a nuclear con–guration leading to the desired outcome.After an appropriate 19 Faraday Discuss. 1999 113 1»25 Fig. 15 Feedback control of product channels in the photodissociation of a transition metal complex dicarbonylchloro(g5-cyclopentadienyl)iron Gerber et al.136 An evolutionary genetic algorithm is used to maximise/minimise the intensities of alternative fragment ion channels by controlling the spectral phase of a femtosecond laser pulse. (a) The experiment (b) the result. delay some of its amplitude was transferred back to another region of the ground state surface (or an excited state surface) by a second ìdumpœ laser pulse. Typically the optimum con–guration would be on the far side of a barrier to reaction on the ground state surface or at a point where the momentum of the wave-packet was directed towards the transition state for reaction or to a surface intersection.There have been many variations on this basic theme all of which are directed towards its optimisation. Control can be exercised most simply by varying the delay time,124 to achieve (or approach) an optimised ìdumpœ con–guration; or by introducing an optimised sequence of pulses ; or by engineering the spectral amplitudes phases and temporal pro–les of the sequence of pump and/or dump pulses to tailor the wave-packet amplitudes and momenta and combat dispersion of the local amplitude through dephasing/IVR.125 Leone126 presents an elegant demonstration of wave-packet control in this Discussion; Stolow127 has used wave-packet control to eÜect isotopic 79Br separation of 2/81Br2 .Control over the interfering amplitudes to allow ìwave-packet interferometryœ can be exercised by using a phase-locked pump»dump sequence.128 The degree of wave-packet dephasing can be controlled by ìchirpingœ the frequency spectrum of the laser pulses either linearly with the highest frequencies arriving either early or late (negative or positive chirp) or by more complex optimal pulse shaping schemes129»see the contributions from Vivie-Riedle et al.130 and Dantus and co-workers.131 The optimal control schemes132,133 are designed to engineer the pump (and/or dump) control –elds that will be most eÜective in achieving the desired end result. Some are designed through a series of iterative forward»backward quantum calculations others by optimally ìtrackingœ the evolving amplitude during its progress towards the desired end result»ìlocal optimisationœ (see Tannor KosloÜ and Bartana123).Calculation of the optimally tailored –elds will be computationally feasible however only for the simplest systems (see Shah Faraday Discuss. 1999 113 1»25 20 and Rice this Discussion134) and alternative learning algorithm ìfeedbackœ strategies have been devised and in one or two cases implemented.129,135,136 Very encouragingly Baumert Gerber and co-workers have succeeded in demonstrating the eÜectiveness of the ì feedbackœ approach experimentally,137 by using it to control the branching ratio between alternative channels in the multiphoton ionisation of a polyatomic metal-centred complex (see Fig.15). Although the vast majority of systems so far studied whether by theoretical modelling or experimentally have explored the control of unimolecular processes photo-dissociation isomerisation ionisation and so on there is no reason why the evolving system need not be a supermolecule »i.e. involving two potential reagents. What are the prospects for controlling bimolecular reactions ? The two theoretical papers by Vivie-Riedle and co-workers130 and by Brumer and Shapiro and co-workers138 provide examples of two generalised strategies designed to meet this challenge. Vivie-Riedle and her co-workers explore the optimal control of a ìreactionœ (energy transfer) by focusing a wave-packet evolving over the bound ìexciplexœ surface of a supermolecule towards an intersection with its unbound ground state.Brumer and Shapiro and coworkers138,139 formulate bimolecular coherent control showing that it requires the design of energy correlated scattering states to achieve control via quantum interference. In its most general form this approach proposes using matter interferometry techniques to create the initial states but the authors also provide a simpli–ed example in the control over the diÜerential cross-section of atom»diatom collisions via a superposition of diatomic m states. Shapiro has also proposed a j pump»dump ì laser catalysis œ scheme in which a reactive collision system is coupled to a bound excited surface an intermediate state which ìbridgesœ across the ground transition state region.140 This scheme is closely related to the STIRAP route for population transfer in this case between the reagent and product continuum states (see Fig.16). Unfortunately experimental demonstrations of bimolecular reaction control remain very rare. A crucial factor has been the need to limit the range of collision energies to allow the preparation of a sufficiently localised wave-packet. This can be achieved if the collision pair can be trapped within a weak vdW complex or ìcapturedœ as an instantaneous collision pair through oÜresonance excitation (wing absorption cf. ì transition-state spectroscopyœ) (or perhaps by laser cooling). Marvet and Dantus and co-workers141,142 have used this approach to demonstrate the possibility of wave-packet control in the photo-association of Hg… … …Hg collision pairs (see Fig.17) while Zewail and co-workers143 were able to demonstrate control of the harpoon reaction (14) Xe](I`I~)*]XeI(B C)]I where (I`I~)* represents an excited ion-pair state of I2 populated through sequential two-photon excitation mediated via I (B). Earlier experiments by Qin and Setser144 would appear to con–rm 2 the ìcaptureœ of Xe… … …I collision pairs in Zewailœs experiment but since the control was exerted by 2 wave-packet motion in the intermediate state I (B) and the need to access the ion-pair state(s) at 2 an energy above the threshold for reaction it was not possible to exclude the possibility of reaction also proceeding via secondary collisions of (I`I~)* with Xe.None the less the potential of this approach for the control of bimolecular reaction systems e.g. the pursuit of wave-packet control in reactions photo-initiated within parent geometry limited vdW complexes remains to be Fig. 16 ìBridgingœ the transition state laser catalysis ? (a) The idea :139 on the red side of the collisionly broadened radiative transition transmission through the barrier is suppressed by interference between the non-radiative (nr) and optically assisted pathways. On the blue side however transmission becomes facile. (b) The STIRAP scheme120 for population transfer via rapid adiabatic passage; when the intensity of the Stokes ìcouplingœ pulse is sufficiently high the transient population in the intermediate state omT approaches zero.21 Faraday Discuss. 1999 113 1»25 Fig. 17 Photo-association a pump»dump (or ìbind-probe@) control scheme.140,141 (a) The idea (b) the results obtained140 for the photo-association 2Hg]Hg2*. The decaying anisotropy of the LIF signal from Hg2* re—ects its rotational dephasing; vibrational recurrences could not be detected however. fully exploited. It is a great challenge but ììan optimist is someone who thinks the future is uncertainœœ.145 5. Acknowledgements I am very grateful to the Organising Committee and the Faraday Divisional Council for inviting this lecture and to Professor Stuart Rice who thoughtfully provided me with a draft version of his monograph with Dr. Meishan Zhao Optical Control of Molecular Dynamics. 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ISSN:1359-6640    

DOI:10.1039/a905761g

出版商:RSC    

年代:1999

数据来源: RSC

摘要:

Orientation as a probe of photodissociation dynamics Zee Hwan Kim Andrew J. Alexander S. Alex Kandel,§ T. Peter Rakitzisî and Richard N. Zare* Department of Chemistry Stanford University Stanford CA 94305 USA 1. Introduction Atomic and molecular photofragment vector properties have fascinated physical chemists since the early days of gas-phase reaction dynamics. The vector properties associated with molecular photodissociation provide insight not usually available from their scalar counterparts. For example the correlation of the fragment recoil velocity with the polarization of the photolysis light provides information about the symmetry of the initially excited dissociating state.1 This correlation is usually expressed by the translational anisotropy parameter b which ranges from ]2 for a pure parallel transition to [1 for a pure perpendicular transition.Intermediate values of b indicate a transition of mixed parallel and perpendicular character within the axial recoil approximation. Unfortunately measurement of the photofragment translational anisotropy is not a sensitive diagnostic of the dynamics that occur after the initial excitation. Instead as we show measurement of the correlation of the angular momentum vector of an atomic or molecular photofragment with respect to its recoil velocity vector can provide important information for understanding the dynamics of photodissociation far from the Franck»Condon region. There have been extensive theoretical and experimental studies of photofragment angular momentum polarization.2,3 Dixon formulated a semiclassical description of photofragment angular momentum polarization using bipolar moments measured in the laboratory frame and showed how to extract these parameters from the analysis of Doppler-broadened line shapes.2 The quantum mechanical nature of angular momentum polarization manifests itself in eÜects such as coherence and interference between the photofragment quantum states these eÜects are more § Present address Department of Chemistry The Pennsylvania State University 152 Davey Laboratory University Park PA 16802 USA.î Present address Department of Chemistry University of Crete and Institute of Electronic Structure and Laser Foundation for Research and Technology-Hellas 71110 Heraklion-Crete Greece.27 Faraday Discuss. 1999 113 27»36 Received 9th March 1999 Molecular chlorine (Cl was photodissociated in the wavelength range 270»400 nm with 2) linearly polarized light and the orientation of the excited-state chlorine atom Cl*(2P1@2) was measured by 2]1 resonance enhanced multiphoton ionization (REMPI) using circularly polarized light. The degree of orientation of the Cl* photofragment is found to oscillate as a function of photolysis wavelength. The oscillation is a result of quantum mechanical coherence arising from electronic states of diÜerent symmetry that correlate to the same separated-atom asymptote. A simple curve-crossing model using ab initio potential energy curves reproduces the general shape of the oscillation but fails to give a quantitative –t.This journal is( The Royal Society of Chemistry 1999 2 . a [a pronounced in the case of atomic photofragments owing to the low angular momentum quantum numbers. In 1968 van Brunt and Zare4 predicted that atomic photofragments could be polarized. Full quantum mechanical treatments of photofragment polarization allowing for mixed transitions and photofragment coherence have been given by Vasyutinskii,5 Siebbeles et al.,6 and by Chen and Pei.7 Several experiments have since demonstrated the polarization of atomic fragments and quantum mechanical eÜects.8v11 For example Vigueç et al.10 observed the anomalous polarized emission from Ca atoms in Ca photodissociation which can be explained by a coherent 2 excitation of K\1 and K\[1 states. More recently Eppink et al.11 reported the production of maximally aligned O (1D) atoms in the photodissociation of O Rakitzis and Zare12 showed how to measure the complete photofragment angular momentum distribution in the molecular frame using the specialized polarization parameters aq ( k)(p) aq ( k)(o) and q ( k)(p,o).The aq ( k) parameters are decoupled from the translational anisotropy of the fragments to provide a clear physical picture of the dissociation process. Furthermore the aq ( k) formalism explicitly accounts for contributions from the coherence between photofragments associated with repulsive states of diÜerent symmetry q ( k)(p,o)] as well as individual contributions from [aq ( k)(p)] q ( k)(o)] parallel q ( k) and perpendicular transitions.The power of using the formalism was demonstrated in measurements of the mass-dependent polarization of the Cl-atom in the photolysis of ICl.13h15 The large diÜerences in the observed alignment and orientation of (ground-state) 35Cl and 37Cl atoms arise solely from the quantum mechanical interference between two or more dissociating states with diÜerent symmetries. In addition it was demonstrated that it is possible to prepare an atomic photofragment with well-de–ned helicity (orientation) with respect to the photofragment velocity vector. The measurement of the orientation parameter Im[a(1)(p,o)] as a 1 function of excitation energy was shown to be highly sensitive to the shapes of potential energy curves involved. Consequently measurement of Im[a(1)(p,o)] opens the possibility for this param- 1 eter to serve as a powerful probe of molecular photodissociation dynamics.Rakitzis et al.14 discussed the analogy with the famous Youngœs double slit experiment in which there is a de–nite phase relationship between rays of light that have travelled diÜerent paths. The phase relationship can provide information on the nature of the paths travelled and indeed on the radiation source itself. (2P a C1%u(1)[X1&g `(0`) (o*Xo\1) perpendicular transition which adiabatically correlates to 2 3@2)]Cl (2P3@2) atoms. At longer excitation wavelengths around 430 nm B3%u `(0`)[X1&g `(0`) (o*Xo\0) parallel transition which see Fig. 1. Matsumi et al.16 used Doppler spec- For many photodissociation processes nonadiabatic interactions»resulting from a breakdown of the Born»Oppenheimer approximation»may have a signi–cant in—uence on the photofragmentation dynamics.Unfortunately it is not straightforward to obtain detailed information on the nature of nonadiabatic interactions from more traditional experiments such as measurements of –ne structure branching ratios or angular distributions of the products. The measurement of the orientation parameter however can reveal important information on the nature of nonadiabatic interactions. The nonadiabatic interactions in—uence the phases as well as the amplitudes of the dissociating wave functions and so the Im[a(1)(p,o)] which is sensitive to the asymptotic phase 1 diÜerence between these dissociating wave functions can carry a ìì–ngerprintœœ of the nonadiabatic interaction.Nonadiabatic interactions have been shown to occur in the molecular photodissociation of Cl2 around 330 nm.16,17 The major channel for the photodissociation of Cl at this wavelength is via the ground-state Cl absorption is dominated by the Cl*(2P adiabatically correlates to 1@2)]Cl (2P3@2) troscopy to measure the translational anisotropy of chlorine atomic fragments and noted a gradual change of the b parameter of Cl* as a function of excitation wavelength. At a photolysis wavelength of 400 nm b(Cl*) was measured to be close to 2 which allowed them to assign the B3% photodissociation process to the u `(0`)[X1&g `(0`) parallel transition whereas at 308 nm b(Cl*) was found to be [0.7 which indicated the existence of a perpendicular transition resulting in production of Cl*.They attributed the perpendicular transition component as initial excitation to the C state followed by radial derivative coupling to other states of the same symmetry with two of the states correlating to the Cl]Cl* channel. Recently Samartzis et al.17 have re–ned previous measurements of the Cl* translational anisotropy using the velocity-mapped photofragment imaging technique. They attributed the perpendicular portion of the Cl* fragments to initial excitation of the C state followed by curve crossing to the B state which correlates with Cl]Cl*. [a Faraday Discuss. 1999 113 27»36 28 Fig. 1 Ab initio potential energy curves18 of Cl relevant to the present discussion.Excitation to the C state is 2 a perpendicular transition and correlates adiabatically to ground-state Cl]Cl. Excitation to the B state is a parallel transition and correlates adiabatically to Cl]Cl*. The ab initio B and C state potential energy curves cross each other at 3.16 Aé . The curve crossing probability which they estimated using a combined analysis of measurements of the ground-state Cl fragment velocity distribution and measurements of b(Cl*) was found to decrease with an increase in available energy. This –nding supports their assumption of a curve crossing mechanism of the Landau»Zener type from the C to the B state. In summary two recent experimental works have indicated the importance of nonadiabatic interactions in the photodissociation of Cl around 330 nm.However the mechanism for the nonadiabatic transition has 2 yet to be fully characterized. Im[a(1)(p,o)] of the 1 1@2 Cl2 using linearly polarized Cl*) in the photodissociation of In this discussion we report measurements of the orientation moment excited-state chlorine atom (2P photolysis light (270»400 nm) and circularly polarized probe light for detection of the product atoms. In the intermediate region of excitation wavelengths employed (around 330 nm) the parallel and perpendicular transition components leading to Cl]Cl* products contribute in comparable amounts. The orientation of Cl* photofragments arises from quantum mechanical interference between products originating from the mixed parallel/perpendicular transition. (1) 2.Detection of photofragment angular momentum polarization Using the formalism of Rakitzis and Zare,12 the polarization of an ensemble of Cl* (J\1/2) fragments can be fully described by only two moments with k\0 (isotropic moment proportional to the population) and k\1 (orientation moment). Orientation of photofragments via photolysis with linearly polarized light can arise only from quantum interference between parallel and perpendicular transitions. In addition the use of linearly polarized photolysis light allows only the existence of the imaginary part of the photofragment orientation parameter Im[a(1)(p,o)]. The 1 angular momentum distribution of photofragments with J\1/2 from photodissociation with linearly polarized light is given by DA,M(h r he b)\1]J2 Im[a1(1)(p,o)]sin he cos he sin h sin r/[1]bP2(cos he)] In the molecular frame the z-axis is de–ned to lie along the photofragment velocity vector ø; phot) with respect to the z-axis is given he .The xz plane contains both the velocity and the photolysis polarization vectors. h and r see Fig. 2. The polar angle of the photolysis polarization (e by represent the polar and azimuthal angles of the product angular momentum vector (J) with Faraday Discuss. 1999 113 27»36 29 vector and h and r are the polar Fig. 2 The molecular frame and coordinates used in this paper. The z-axis is de–ned by the product photofragment velocity ø ø and the y-axis is normal to the plane containing and the photolysis polarization vector ephot . he is the angle between ø and phot H and U are polar angles of eprobe e and azimuthal angles of the photofragment angular momentum (J) in the molecular frame.respect to the molecular frame P is the second-order Legendre polynomial. As can be seen asym- 2 metry of the distribution with respect to the xz molecular plane occurs for a non-zero Im[a(1)(p,o) 1 moment. Im[a(1)(p,o)] moment is proportional to the sine of the asymptotic 1 M[/A) between the radial parts of the outgoing wavefunctions from It can be shown that the phase diÜerence (*/\/ parallel and perpendicular transitions modulated by the product of transition amplitudes for these transitions5,6,12 (2) Im[a(1)(p,o)]PoAAooAMosin */ 1 oA where A Ao o Mo are the moduli of transition amplitudes for parallel and perpendicular tran- and sitions leading to the same product quantum state.For a pure (parallel or perpendicular) tranoA Im[a(1)(p,o)] sition the product of the two amplitudes AooAMo in eqn. (2) will be zero and the 1 will vanish. The asymptotic phase diÜerence */ and hence the Im[a(1)(p,o)] is sensitive to the 1 kinetic energy available to the photofragments the shapes of the potential energy pathways encountered for fragments of parallel or perpendicular origin and therefore the occurrence (if any) of nonadiabatic interactions for these fragments during the dissociation process. The REMPI detection of photofragments with polarized light is sensitive to the photofragment angular momentum polarization and provides a convenient tool for detection of the Cl* atom photofragments.The relative detection probability of Cl* (J\1/2) photofragments using 2]1 REMPI with circularly polarized probe light can be expressed in terms of the Im[a(1)(p,o)] 1 moment I[H U he Im[a1(1)(p,o)]\1]J2G1s1 Im[a1(1)(p,o)]sin he cos he (3) [J3 ( for the particular transition 2P used. ]sin H sin U/[1]bP (cos h )] 2 e where G1 is the long-time limit of nuclear hyper–ne depolarization ratio.19,20 For the excited-state chlorine atom (J\1/2 nuclear spin I\3/2) G1 is calculated to be 0.375 ; s is the detection 1 sensitivity21 for the k\1 moment which depends on the details of transition of the resonant absorption step and is calculated to be 3@2[2P1@2) Faraday Discuss. 1999 113 27»36 30 refers to the direction either parallel (left-circular The angles H and U specify the direction of the probe radiation polarization vector ; see Fig.2. For the circularly polarized probe light eprobe polarization) or antiparallel (right-circular polarization) to the propagation direction of the light. 3. Experiment Detailed descriptions of the experimental apparatus and techniques have been given elsewhere,22 and only a brief overview is given here. Molecular chlorine (Matheson 99.999%) was premixed with high-purity helium (Liquid Carbonic 99.995%) in a dilute mixture (less than 5% by volume) before supersonic expansion through a pulsed nozzle (General Valve 9-Series 0.6 mm ori–ce) into high vacuum. The stagnation pressure of the sample used was varied from 100 to 400 Torr. The 270»400 nm photolysis light was generated by frequency-doubling the output of a dye laser pumped by a Nd3` YAG laser (Continuum ND6000 and PL9020).The probe light (236.53 nm) for 2]1 REMPI detection of Cl* via the 3s23p34p1 2P3@2[3s23p4 2P1@2 transition was generated by frequency-doubling the output of a dye laser pumped by a second Nd3` YAG laser (Spectra-Physics PDL-3 and DCR-2A; Exciton Coumarin 480 dye). Photolysis and probe beams were loosely focussed onto the unskimmed expansion within the extraction region of a Wiley- McLaren time-of-—ight (TOF) mass spectrometer operated under velocity-sensitive conditions. The relatively high natural abundance of the chlorine-37 isotope (24%) allowed the simultaneous measurement of 35Cl* and 37Cl* ion arrival TOF pro–les. The intensities of the photolysis and probe beams were attenuated to avoid unwanted distortion of TOF pro–les caused by space charge eÜects.Circular polarization of the probe radiation was achieved by placing a quarter-wave plate with its optical axis at 45° with respect to the linear polarization vector of the probe UV light. A photo-elastic modulator (PEM Hinds International PEM-80) was placed before the quarter-wave plate to —ip the polarization to be either left-circularly polarized (LCP) or right-circularly polarized (RCP) with respect to the propagation axis of the beam on an every-other-shot basis. To achieve maximum sensitivity to the detection of the orientation moment the polarization of the pump laser was tilted by 45° with respect to the TOF detection axis using a double Fresnel rhomb (Optics for Research RFU-1/2-U).The time delay between photolysis and probe pulses was kept within 20 ns to avoid unwanted —y-out of photofragments from the detection region. Purity of polarization was found to be critical for these experiments and therefore care was taken to avoid unwanted distortions of the polarizations of both photolysis and probe beams. TOF pro–les taken using left-circularly polarized probe light IRCP LCP and right-circularly polarized probe light were recorded separately on a shot-to-shot basis. Isotropic (I B (B I iso\ILCP]IRCP) and anisotropic (Ianiso\ILCP[IRCP) TOF pro–les were evaluated and orientation moments extracted by –tting these composite experimental pro–les. Isotropic and anisotropic basis functions were generated by Monte-Carlo simulation12 using and iso aniso) eqns.(1) and (3). Experimental composite TOF pro–les and are least-squares –tted using aniso iso the following equations (4) (5) I iso\c Biso Ianiso\c Im[a1(1)(p,o)]Baniso I where c is determined by –tting eqn. (4) –rst. The translational anisotropy parameters b needed for generating the basis functions were taken from the work of Samartzis et al.17 The same b parameter was used for each of the two isotopes of the Cl* atom although slight diÜerences might occur that result from a mass-dependent efficiency in the nonadiabatic transition of the perpendicular transition. Moreover the –tting procedures were found to be insensitive to small variations (ca. 5%) in the values of the b parameters.4. Results Fig. 3 shows representative anisotropic TOF pro–les for 35Cl* and 37Cl* atoms obtained from the photodissociation of Cl at 320 nm and 340 nm together with the –t obtained using the basis 2 I Faraday Discuss. 1999 113 27»36 31 I 2 Fig. 3 Anisotropic composite time-of-—ight pro–les (solid squares) for 35Cl* and 37Cl* photofragments from the photodissociation of Cl at (A) 320 nm and (B) 340 nm. Solid lines in (A) and (B) represent –ts to the aniso data using basis functions Baniso generated by Monte-Carlo simulation see text for details. functions generated by Monte-Carlo simulations. The anisotropic TOF pro–le Ianiso at a photolysis wavelength of 320 nm shows the characteristic shape of a positive Im[a(1)(p,o)] parameter Ianiso re—ects negative values for both 35Cl* and 37Cl* photofragments.Posi- whereas at 340 nm 1 tive and negative signs of the orientation moment correspond to a preference for J pointing along ]y (ììtopspinœœ) and [y (ììbackspinœœ) directions respectively. It is worthwhile to note that the ground-state Cl atom generated simultaneously with Cl* would be expected to have an orientation equal and opposite to its partner Cl* fragments so that angular momentum is conserved. However for the present experiment measurement of ground-state Cl atom orientation is rendered impracticable because of a limited instrumental resolution and the much larger Cl signal generated from photolysis on the C state alone. Indeed the ratio of photodissociation crosssections for C and B states p(C)/p(B) is estimated to be about 170 at 350 nm excitation and increases drastically at shorter wavelengths.17 Im[a(1)(p,o)] over the photolysis wavelength range of 270»400 nm are plotted in 1Im[a(1)(p,o)] as a function of photolysis wavelength has the form of a Analysis of TOF pro–les at a photolysis wavelength of 320 nm gives Im[a(1)(p,o)]\0.14^0.1 1 for 35Cl* and 0.07^0.1 for 37Cl* the mass dependence of the orientation is caused by the diÜerence in de Broglie wavelengths associated with the two isotopes.The results of repeated measurements of Fig. 4(B). The plot of 1 sinusoidal curve modulated by an envelope. The envelope has maximum amplitude at around 330 nm and decays at longer and shorter wavelengths. Photolysis below 270 nm and above 400 nm does not produce any observable orientation of the photofragments.Also note the ììphase lagœœ between the 35Cl* and the 37Cl* photofragments in the oscillation of Im[a(1)(p,o)]. This behavior 1 again is caused by the diÜerence in de Broglie wavelengths associated with the two chlorine isotopes. Im[a1 The (1)(p,o)] parameter can be roughly modeled23 as sinMaJm[JE[JE[*V ]N where E is the total energy available to the photofragment of mass m and *V is the average diÜerence of potential energy for parallel and perpendicular transitions within a characteristic interaction range a. The diÜerence in the de Broglie wavelengths for the two isotopes at a given total energy Faraday Discuss. 1999 113 27»36 32 Fig. 4 (A) The envelope of oscillation as a function of the change in b parameter (b) over the photolysis wavelength range modeled by Ab\J(1]b)(1[b/2).(B) Experimentally determined Im[a(1) 1 (p,o)] parameters for 35Cl* (open circle) and 37Cl* (solid square) as a function of photolysis wavelength. Error bars represents one standard deviation derived from replicate measurements. Also shown are the results of the model calculation for 35Cl* (dash»dot lines) and 37Cl* (solid lines) see text for details. causes a diÜerence in the period of oscillation of the orientation parameter which appears as a Jm dependence in the above expression. Compared with the previous measurements of (ground-state) Cl-atom orientation in the photodissociation of ICl,14,15 the period of oscillation of Im[a(1)(p,o)] for the Cl photolysis is slow the 1 2 Im[a(1)(p,o)] parameter changes sign only once over a photolysis wavelength range 270»400 nm.1 The change of [JE[JE[*V ] as a function of E slows down and approaches zero as the excitation energy is increased ; hence the period of the oscillation of the orientation moment increases as the available energy is increased. In the photodissociation of ICl the photolysis wavelengths used were just above the dissociation threshold leading to rapid oscillations whereas in Cl photodissociation the available energy for the Cl* fragment is much greater (3000»5000 2 cm~1) leading to a much slower oscillation of Im[a(1)(p,o)]. The envelope of the oscillation 1 reaches its maximum amplitude at around 330 nm and decays on either side. The behavior of the envelope agrees with our picture of interference between dissociative motion on the parallel and perpendicular surfaces the amplitude is maximum when the two contributing components are equal in magnitude and it dies out as one of the components dominates the other.The envelope of the oscillation can be modeled as the geometric mean of contributions from parallel and perpen- A dicular transitions b\J(1]b)(1[b/2). Fig. 4(A) show a plot of Ab as a function of wavelength in which the wavelength-dependent b parameter has been interpolated from the experimental measurements of Samartzis et al.17 The calculated envelope correctly predicts the position of the maximum amplitude of oscillation. To model the observed behavior of Cl* photofragment orientation we assume that the perpendicular transition component of Cl* originates from initial excitation to the C state followed by a nonadiabatic transition to the B state to give Cl]Cl*.At present the matrix elements that would be required to accurately model the nonadiabatic radial derivative coupling are not available although recent calculations24 suggest that this type of nonadiabatic coupling may be of great importance. Furthermore the recent experimental work of Samartzis et al.17 indicates a curve crossing probability that decreases with increasing photofragment kinetic energy which is at variance with a radial derivative coupling model. For these reasons we have employed a simple curve crossing model of the chlorine photodissociation using the available (adiabatic) ab initio potential energy curves of Yabushita18 to provide a yardstick with which we can compare the experimental data.We have modeled the nonadiabatic transition with a single eÜective potential energy curve VNA(R) which switches smoothly from the C state to the B state by employing a phenomenological coupling element that has the form of a Gaussian function with half-width at half-maximum of 0.42 Aé centered on the curve crossing point Rx\3.16 Aé . The amplitude of this coupling term was 33 Faraday Discuss. 1999 113 27»36 and / varied to produce an acceptable –t to the experimental data. The radial Schroé dinger equation was solved numerically25 on the VB(R) and on the V functions /B Im[a(1)(p,o)] is compared with A sin(/ NA(R) potentials and the phases of the radial wave NA were evaluated at the asymptote.In Fig. 4(B) the experimental b B[/NA) obtained from the calculations. As can be seen in 1 Fig. 4(B) the model calculation correctly predicts the phase shift between the two isotopes and the general energy dependence of the orientation moment although it gives a somewhat broader envelope than experimentally observed. From an experimental viewpoint the discrepancy between the experimental and theoretical envelopes might arise from the occurrence of another dissociating state with either parallel or perpendicular character although the discrepancy may re—ect systematic errors in the measurement of the translational anisotropy. Our model of envelope of oscillation is based on the interference between two dissociating states and even a minute contribution of another state can aÜect the envelope of oscillation.The eÜect of including a centrifugal potential in the calculations which can be modeled by N(N]1)Å2/2kR2(where N is the nuclear rotational quantum number k is a reduced mass of diatomic molecule and R is a internuclear distance) was found to be negligible. Overall the simple crossing model calculations appear able to reproduce the qualitative general features of the observed oscillation of the orientation moment but fail to give a full quantitative agreement. Each component experi- 5. Discussion For a mixed transition in which two dissociating states are accessed via parallel and perpendicular transitions respectively the overall transition dipole moment vector l lies between the parallel and perpendicular axes.Classically the transition dipole moment vector can be viewed as an oscillating electric dipole the initial direction of which is determined by the polarization of the photolysis light ephot . The transition dipole moment vector depends parametrically on the internuclear separation R and on the phase of the radial part of the dissociating wave function. As is shown schematically in Fig. 5(A) the initially prepared transition dipole moment can be decomk posed into a parallel component k z and a perpendicular component x . Fig. 5 Schematic view of a classical interpretation of orientation resulting from excitation to a mixed transition (A) excitation with linearly polarized light induces oscillating electric dipole of electrons.(B) as the dissociation proceeds parallel and perpendicular components of the transition dipole acquire a phase diÜerence */ which induces a circular component in the oscillating transition moment. (C) at in–nite separation of photofragments the net phase diÜerence */ can be non-zero i.e. the separated fragments each retain some circularity. Positive and negative signs of the orientation parameter correspond to ììtopspinœœ and ììbackspinœœ of the photofragments respectively. Faraday Discuss. 1999 113 27»36 34 ences a diÜerent potential energy surface during the subsequent dissociation and hence a phase diÜerence (*/) between the oscillations of the parallel and perpendicular components is acquired as the internuclear distance increases.The phase diÜerence */ between the two oscillating electric dipoles leads to a circular component (helicity) in the motion of the electronic charge distribution i ø .e. a net electronic angular momentum above or below the plane containing ephot and see Fig. 5(B). At in–nite separation of the photofragments where the two potential energy surfaces converge to the same product asymptote the phase diÜerence */ also converges to its –nal value. The asymptotic phase diÜerence and the out-of-plane component of the angular momentum are determined by the exact shapes of the potential energy curves encountered by each of the parallel and perpendicular components during motion along the dissociation pathway see eqn. (2) and Fig. 5(C). The above model gives an intuitive physical picture of the development of helicity as a phase diÜerence between two orthogonal oscillations.This picture does not represent the actual experimental situation however because the dissociation process cannot simply be viewed as the motion of fragments with well-de–ned positions that develop as a function of time. Such a picture would be more applicable to wavepackets that can be excited using femtosecond laser pulses.26 For a physical understanding of the present experiment we must turn to a picture of a quasi steady-state excitation to the dissociation continuum as that which would be obtained for example using a nanosecond excitation pulse. Indeed the present experiments rely on our ability to excite and probe a set of energetically well-de–ned continuum wavefunctions with an outgoing boundary condition enabling us to measure their asymptotic radial phase diÜerence.The simple model calculations of the nonadiabatic transition presented in Section 4 do not fully reproduce the experimentally observed energy dependence of the Cl* atom photofragment orientation. The coupling matrix element for the nonadiabatic transition was arbitrarily chosen to be independent of the kinetic energy of the photofragment and localized at the crossing point. In general nonadiabatic coupling matrix elements are kinetic energy dependent and the range of nonadiabatic interactions are nonlocal. Although our use of a phenomenological (gaussian shaped) nonadiabatic coupling based on a curve crossing mechanism can reproduce qualitatively the experimental data this fact does not validate the curve crossing mechanism for Cl* generation in Cl photodissociation.A more complete knowledge of the nonadiabatic (both curve crossing 2 and radial derivative type) coupling matrix elements along with the corresponding potential energy curves is required to produce a more complete model of this system. We hope that revised theoretical calculations along with the experimental measurements of the Cl* atom photofragment orientation and translational anisotropy will allow a more detailed understanding of the mechanism behind nonadiabatic interaction in the photodissociation of molecular chlorine. In conclusion the outlook for applying measurements of (coherent) angular momentum orientation to photodissociation in other systems seems very bright.The technique is relatively simple and straightforward to carry out the photofragment orientation is highly sensitive to mixing between states of diÜerent symmetries and the interpretation of the results seems to oÜer insight into the photodissociation dynamics not readily discernible from the measurement of other parameters that do not contain quantum phase information. We are most grateful to S. Yabushita for providing us with his ab initio potential energy curves and to T. N. Kitsopoulos and D. H. Parker for providing us with a preprint of their work prior to publication. SAK thanks the US National Science Foundation for a predoctoral fellowship and gratefully acknowledges receipt of a Dr. Franklin Veatch memorial fellowship.The funding for this work was provided by the US National Science Foundation under grant No. CHE-93-22690. References 1 R. N. Zare and D. R. Herschbach Proc. IEEE 1963 51 173. 2 R. N. Dixon J. Chem. Phys. 1986 85 1866. 3 G. E. Hall and P. L. Houston Annu. Rev. Phys. Chem. 1989 40 375. 4 R. J. van Brunt and R. N. Zare J. Chem. Phys. 1968 48 4304. 5 O. S. Vasyutinskii Opt. Spectrosk. 1983 54 524. 6 L. D. A. Siebbeles M. Glass-Maujean O. S. Vasyutinskii J. A. Beswick and O. Roncero J. Chem. Phys. 1994 100 3610. 35 Faraday Discuss. 1999 113 27»36 7 K.-M. Chen and C.-C. Pei J. Chem. Phys. 1998 109 6647. 8 O. S. Vasyutinskii Sov. Phys. JET P (Engl. T ransl.) 1980 31 428. 9 E. W. Rothe U. Krause and R. Duren Chem. Phys. L ett.1980 72 100. 10 J. Vigueç P. Grangier G. Roger and A. Aspect J. Phys. L ett. 1981 42 L531. 11 A. T. J. B. Eppink D. H. Parker M. H. M. Janssen B. Buijsse and W. J. van der Zande J. Chem. Phys. 1998 108 1305. 12 T. P. Rakitzis and R. N. Zare J. Chem. Phys. 1999 110 3341. 13 T. P. Rakitzis S. A. Kandel and R. N. Zare J. Chem. Phys. 1998 108 8291. 14 T. P. Rakitzis S. A. Kandel A. J. Alexander Z. H. Kim and R. N. Zare Science 1998 281 1346. 15 T. P. Rakitzis S. A. Kandel A. J. Alexander Z. H. Kim and R. N. Zare J. Chem. Phys. 1999 110 3351. 16 Y. Matsumi K. Tonokura and M. Kawasaki J. Chem. Phys. 1992 97 1065. 17 P. C. Samartzis B. Bakker T. P. Rakitzis D. H. Parker and T. N. Kitsopoulos J. Chem. Phys. 1999 110 5201. 18 S. Yabushita 1998 unpublished results.The ab initio points are rescaled by a constant factor of 0.926 to match the bound part of B-state curve to the experimentally obtained B-state RKR potential energy curve see J. A. Coxon J. Mol. Spec. 1980 82 264. 19 A. J. Orr-Ewing and R. N. Zare Annu. Rev. Phys. Chem. 1994 45 315. 20 R. N. Zare Angular Momentum Understanding Spatial Aspects in Chemistry and Physics Wiley- Interscience New York 1988. 21 A. C. Kummel G. O. Sitz and R. N. Zare J. Chem. Phys. 1986 85 6874. 22 W. R. Simpson A. J. Orr-Ewing S. A. Kandel T. P. Rakitzis and R. N. Zare J. Chem. Phys. 1995 103 7299. 23 For this model we have assumed that the potential energy curves are of a square well type with in–nite wall at R\0 see also ref. 14. 24 S. Yabushita 1999 personal communication. 25 B. R. Johnson J. Chem. Phys. 1977 67 4086. 26 It might be wondered what information would be yielded by a femtosecond pump»probe experiment. Such an experiment could in principle distinguish between and follow the two diÜerent dissociation pathways because the wavepackets on the two diÜerent surfaces take a diÜerent time to separate into asymptotic fragments. In this case however the interference eÜect is removed because the diÜerent pathways can be distinguished. An intermediate regime occurs in which the interference would appear but its description would depend sensitively on the temporal forms of the pump and probe pulses. For a cogent discussion of what is prepared in a bound-to-continuum transition see J. L. Kinsey and B. R. Johnson J. Phys. Chem. A 1998 102 9660. Paper 9/01828J Faraday Discuss. 1999 113 27»36 36

ISSN:1359-6640    

DOI:10.1039/a901828j

出版商:RSC    

年代:1999

数据来源: RSC

摘要:

Femtosecond time-resolved photoelectron imaging Li Wang,§ Hiroshi Kohguchi and Toshinori Suzuki* Institute for Molecular Science Myodaiji Okazaki 444-8585 Japan. E-mail suzuki=ims.ac.jp Introduction Owing to the advent of ultrafast laser technology real-time studies of molecular dynamics have made rapid progress in recent years.1 Time-resolved photoelectron spectroscopy (PES) has several advantages in probing the photo-induced dynamics of molecules and clusters in the gas phase.2h6 First both the singlet and triplet states can be detected thereby enabling the direct observation of intersystem crossing and internal conversion processes. Second wavepacket motion on the neutral potential surface is probed through projection to the cationic state which is accurately determined from spectroscopic and quantum chemical studies.Third the method exhibits a high sensitivity since photoionization is an induced process and the electrons can be collected efficiently by an electromagnetic –eld. Finally as with Raman spectroscopy the ionization laser can be frequency- –xed while the photoelectron energy is dispersed which is favorable when applying an ultrafast laser with limited tunability. As for the analysis of electron kinetic energy in photoelectron spectroscopy (Table 1) the timeof-—ight (TOF) method has been widely used with pulsed light sources. However a standard TOF method has a rather poor collection efficiency 10~3»10~4. The magnetic bottle spectrometer developed by Kruit and Read signi–cantly improved the efficiency but angular resolution was sacri–ced.7 Photoelectron imaging (PEI) on the other hand allows routine measurement of the speed and angular distributions of photoelectrons with unit collection efficiency of the electrons.8 Although the energy resolution of PEI may be lower than the conventional methods the uncertainty principle limits the energy resolution obtainable in ultrafast spectroscopy so PEI is ideally suited for femtosecond pump»probe experiments.Another feature of PEI to note is that it is applicable to (pseudo)continuous light sources such as discharge lamps high repetition-rate lasers and synchrotron radiation. Photoion imaging developed by Chandler and Houston,9 is well established as a method of probing asymptotic properties such as scattering distributions and state distributions of photofragments.Time-resolved PEI probes short-range and short-time dynamics involving electronic § Permanent address Dalian Institute of Chemical Physics Dalian China. 37 Faraday Discuss. 1999 113 37»46 Received 12th April 1999 Femtosecond time-resolved photoelectron imaging (FS-PEI) is presented for the –rst time. This novel method is tested with two-color photoionization of NO via the A 3sr state and applied to ultrafast dephasing in the intermediate case molecule pyrazine. The results illustrate the high-performance of FS-PEI in probing short-time dynamics in isolated molecules and clusters. This journal is( The Royal Society of Chemistry 1999 Table 1 Comparison of the methods for photoelectron spectroscopy Equipment required Angular distribution Acceptance angle/sr CW modeb Method Resolution/ meVa Fine electrodes Yes [5 10~2»10~3 Inef–cient Electrostatic analyzer TOF Magnetic bottle [3 10~3»10~4 Inef–cient Impossible Routine Fast digitizer Fast digitizer CCD camera No No Yes Imaging [10 [20c 2p\ 4p a The best energy resolution for 1 eV electrons.b Applicability to continuous light sources. c The value at the energy of 1 eV using an ordinary imaging set-up. relaxation. The combination of time-resolved photoelectron and time-resolved photoion imaging10 will allow us to observe the photo-induced dynamics of molecules and clusters from time t\0 to O with a single apparatus. With this goal in mind this paper reports the –rst femtosecond time-resolved photoelectron imaging (FS-PEI) on two-color photoionization of NO via the A 3sr state and ultrafast dephasing in pyrazine.Experimental The molecular beam apparatus consists of a beam source and a main chamber both of which are pumped by magnetically suspended turbo-molecular pumps. A sample gas expanded from a piezoelectric valve in the source is skimmed and introduced into the main chamber as a molecular beam 2 mm in diameter. The pulse width of the beam was 150»200 ls. The molecular beam is crossed with pump and probe laser beams in the stacked acceleration electrodes in the main chamber where the pump pulse excites the molecules and the probe pulse ionizes them. The electrons thus produced are accelerated parallel to the molecular beam and are then projected onto a position-sensitive imaging detector.9h11 The acceleration –eld provides two-dimensional space focussing so that only the velocities (or linear momentum) of the electrons parallel to the detector face were observed in the image.11 The –eld-free region (44 cm) of the TOF spectrometer was shielded with a l-metal tube to avoid external magnetic –elds that might otherwise de—ect the electron trajectories.The imaging detector consists of a microchannel plate (MCP) a phosphor screen and an intensi–ed charge-coupled device (CCD) camera (768]572 pixels). The image on the phosphor screen is captured by the camera and integrated for 1800»36 000 shots. In order to observe the total photoelectron intensity the emission from the phosphor screen was monitored with a photomultiplier tube (PMT).The ratio between the acceleration energy and the kinetic energy of photoelectron was larger than 1500/1. The solid-state laser system consists of an oscillator an ampli–er and non-linear wavelength tuning devices. The oscillator is a 5 W diode pumped Ti:sapphire laser (80 fs 82 MHz). The output from this oscillator is introduced into a Ti :sapphire regenerative ampli–er pumped by a 10 Hz Nd:YAG laser (250 mJ pulse~1 at 532 nm). The output from the ampli–er (120»150 fs \10 mJ pulse~1 at 786 nm) is split into two beams. One beam is introduced into a traveling wave optical parametric ampli–er (OPA) system (Topas Light conversion). The fourth harmonic of the signal wave provided wavelengths down to 300 nm.Shorter wavelength UV light (210»250 nm) was generated by mixing the output from the OPA with the other half of the fundamental beam in a b-BaB (BBO) crystal. The tunable UV light and the remaining fundamental light (\5 mJ 2O4 pulse~1) emitted coaxially from the crystal were separated by a dichroic mirror to introduce the fundamental light into the BBO crystals to produce its harmonics (the second and third harmonics centered at 393 and 262 nm in the present experiment). The tunable UV light was optically delayed and realigned with the harmonics of the fundamental and the two beams irradiated onto the molecular beam (through the focussing lenses depending on the experiment). The observed images of the electrons were inverted to generate the speed»angular distributions by inverse Abel transform.12,13 Faraday Discuss.1999 113 37»46 38 Results and discussion [1+ 1º ] REMPI of NO characterization of the method Femtosecond time-resolved photoelectron imaging was tested by observing the [1]1@] REMPI of NO via the A 2&` state. A molecular beam of 5% NO seeded in He was crossed with the pump (225 nm) and probe (262 nm) light and the resulting electrons and NO` ions were measured by 1D TOF and 2D imaging. Fig. 1(a) shows the time pro–le of the photoelectron signal. Since the A state of NO has a lifetime of 200 ns,14 the signal exhibits a —at plateau after a sharp rise determined by crosscorrelation (450 fs) of the pump and probe pulses. The photoelectron image observed at a pump» probe time delay of 1 ps is shown in Fig.1(b). It is seen that the photoelectron angular distribution qualitatively follows a cos2 h distribution with respect to the polarization of the probe laser. This is because the A 2&` state of NO is almost a pure 3sr Rydberg state (94% of s and 5% of d Rydberg characters)15 and the outgoing photoelectron becomes predominantly a p-wave according to the selection rule of *l\^1 in an atom (l) is the orbital angular momentum). For the limiting case of a pure p-wave the angular distribution I(h) is characterized h) with b I(h)P1]b Fig. 1 (a) Time dependence of the total photoelectron signal in femtosecond [1]1@] REMPI of NO via the A 2&` v@\0 level. The pump and probe wavelengths are 225 and 262 nm respectively.From the rising edge the cross-correlation of the pump and probe pulses is estimated to be 450 fs. (b) Photoelectron image observed at a pump»probe delay of 1 ps. The image was integrated for 18 000 laser shots. The pump and probe laser polarizations are aligned vertically in the –gure. One-color background signals due to [1]1] REMPI are barely seen. (c) Inverse Abel transform of the image shown in (b). The angular distribution was expressed by 20P2(cos 20\1.7^0.1. The –t was sufficiently good without including the P4 term. 39 Faraday Discuss. 1999 113 37»46 Fig. 2 (a) Time dependence of the total photoelectron signal in femtosecond [1]2@] REMPI of pyrazine via the S1 B3u(n,p*) 00 level. The pump and probe wavelengths are 323 and 396 nm respectively.(b) Photoelectron signal for a kinetic energy E[630 meV. (c) Photoelectron signal for a kinetic energy E\630 meV. by I(h)P1]bP (cos h) 2 with the anisotropy parameter b\2.16,17 P2(x) is the second-order Legendre polynomial. The angle h is a polar angle from the polarization of ionization light. However quantitative analysis of our data yielded b\1.7^0.1. This deviation from the atomic model is due to a noncentrosymmetric electron»NO` potential in which the outgoing electron is partially scattered into an f-wave.18h22 Previous theoretical and experimental studies on the [1]1@] photoionization of NO via the A state by McKoy and coworkers,18,19 and Leahy and coworkers20h22 have shown that the angular distribution of photoelectrons in the parallel pump»probe polarization con–guration is expressed by 20P2(cos h)]b40P4(cos h) b20\1.6»1.7.18h22 Our result is consistent with these previous I(h)P1]b with the dominant contribution of works.Faraday Discuss. 1999 113 37»46 40 Intramolecular dephasing in pyrazine The S1 B3u state of pyrazine is a well known example of an intermediate case in radiationless transition.23h31 It is predicted that broad-band coherent excitation of an intermediate case molecule provides biexponential —uorescence decay where the –rst component is the dephasing of an optically prepared singlet state into the mixed singlet»triplet character and the second component is the population decay of this mixed state.24 In the 1980s biexponential —uorescence decay of S1 pyrazine was extensively studied and lengthy debate ensued as to whether the fast decay was due to dephasing or Rayleigh»Raman scattering.With the development of picosecond spectroscopy Lorincz et al.,28 and Zewail and coworkers29,30 presented convincing evidence for ultrafast dephasing (qD100 ps) and the result was also found to be consistent30,31 with ultrahigh-resolution molecular eigenstate spectroscopy pioneered by Kommandeur and coworkers.32 We have reexamined this classic problem using time-resolved photoelectron imaging. Pyrazine in a molecular beam 0.3»3% seeded in He (a stagnation pressure of 1 atm to the vacuum) was excited to the S vibronic levels by a single-photon transition at 320»350 nm and subsequently 1 ionized by two-photon absorption at 393 nm. This probe wavelength energetically allows twophoton ionization from both the singlet and triplet states (ionization potential IP\74 908 cm~1) ;33 the excess energy in ionization from the S 00 level is 6947 cm~1 while the S 1 1»T1 gap is 4055 cm~1.The power density of our pump laser at the interaction region was less than 1010 W cm~2 whereas that of the probe laser was about 5]1010 W cm~2. For these power densities a shift of the photoelectron kinetic energies by a ponderomotive potential and the alignment of a ground-state molecule in the laser –eld can be neglected. Furthermore the results obtained were not aÜected by diÜerent partial pressures of pyrazine over the range 0.3»3 % indicating that the eÜect of cluster formation is negligible. The bandwidth of our femtosecond laser does not allow selective excitation of rotational lines and excites the whole rotational contour although only a few rotational levels are expected to be populated in a molecular beam.Fig. 2 shows the observed photoelectron intensity as a function of time delay. As seen in Fig. 2(a) the total electron current (\the integral photoionization cross-section) shows no timedependence which apparently contradicts the fast —uorescence decay data reported previously. 25h30 Note however that photoionization can occur both from the singlet and triplet manifolds. Therefore Fig. 2(a) simply implies that the population decay from the mixed singlet» triplet state does not occur in this time range. Clearly a partial photoionization cross-section measurement is necessary to examine the dephasing.Inspection of the photoelectron image shown in Fig. 3 immediately reveals the ionization from the singlet and triplet characters as the outer and inner rings respectively. According to the He I photoelectron spectrum,34 the –rst excited state (p~1) of the cation is located 1 eV higher than the Fig. 3 Photoelectron image of the [1]2@] REMPI of pyrazine via the S1 B3u(n,p*) 00 level observed at a time delays of 2 ps. The image is 300]300 pixels. 41 Faraday Discuss. 1999 113 37»46 IP (n~1) and cannot be reached in our experiment. Therefore the low energy electrons cannot be 0 attributed to ionization from the singlet to the second cationic state (p~1) but rather must be due to ionization from the triplet states to the lowest cationic state (n~1).Ionization from the triplet results in low photoelectron energy because the triplet states that are isoenergetic to the singlet state have large vibrational energies and the Franck»Condon overlap favors ionization to the highly vibrationally excited states of the cation. (The bright spot in the middle of the image is due to the low energy tail of the inner ring. The photoelectrons with near zero kinetic energy are concentrated in the centre of the image with a weighting factor that scales with the kinetic energy of the electron or the image radius squared.) The time evolution of the singlet and triplet characters were easily measured by masking the phosphor screen and selectively observing the outer and inner part of the image with the PMT.In Fig. 3 the approximate boundary of the masking is indicated. When the particular energy region of the electrons is monitored in this way the high energy electrons showed a decay with q\108^2 ps (Fig. 2(b)) while the low energy electrons exhibited a corresponding increase with q\98^4 ps (Fig. 2(c)). As far as we know this is the –rst observation of a growth of triplet character due to dephasing from optically prepared S pyrazine. 1 More detailed dynamics can be learned from the snapshots of electron scattering distributions 1 taken at diÜerent time delays shown in Fig. 4. The decay of the singlet character and the buildup of the triplet character can be easily seen in these snapshots. Careful inspection also reveals that the radius of the triplet signal shrinks over time suggesting a relaxation in the triplet manifold.To examine this more quantitatively the photoelectron kinetic energy distributions extracted from the data are presented in Fig. 5. The feature at 160 meV appears instantaneously with the light pulse and decays rapidly. It has been speculated that T2(p,p*) exists below S (n,p*) and couples 1 strongly with S through a direct spin-orbit interaction. The peak at 160 meV is tentatively assign- 1 ed to ionization from T2(p,p*). The peak observed at 100 meV is assigned to ionization from T (n,p*). Fig. 2(a) must be compared with the [1]2@] picosecond ionization experiment via the S 00 1 level of Knee et al.29 They observed a double exponential decay (qs\118 ps) in the parent mass 00 level at time delays of (a) 0.3 (b) 30 (c) 200 and (d) 500 ps.The original images were 1 B3u(n,p*) Fig. 4 Inverse Abel transforms (300]300 pixels) of the photoelectron images of [1]2@] REMPI of pyrazine via the S integrated for 36 000 laser shots. The photoelectron kinetic energy resolution is 70 meV at 700 meV. Faraday Discuss. 1999 113 37»46 42 Fig. 5 Photoelectron kinetic energy distributions in femtosecond [1]2@] REMPI of pyrazine via the S1 B (n,p*) 00 level at time delays of (a) 0.3 (b) 30 (c) 200 and (d) 500 ps. 3u signal although the slow component was signi–cantly stronger than in —uorescence decay measurements. Why could the dephasing be observed in the total ion current in their experiment? A plausible explanation is as follows. The probe wavelength of 402.6 nm used by Knee et al.29 E of 5700 cm~1 above the IP provides an E 0 which is 150 meV smaller than in our excess excess experiment.This means that the electrons with E\150 meV in Fig. 5 from ionization of T (n,p*) 1 state were missing in their experiment. In other words the detection efficiency of the triplet states at a probe wavelength of 402.6 nm is lower than at that used in our experiment or 396 nm which allowed them to observe the decay of the singlet character in the total ion current. As seen in Fig. 5 two-photon ionization at 396 nm covers the Franck»Condon region in ionization from T1 so that the total ionization signal does not show time dependence in our experiment. The angular anisotropy of the photoelectron distribution exhibited weak time-dependence and the b values at 60 ps were 1.1 and 1.7 for the singlet and triplet channels respectively.We are unfortunately unable to interpret the anisotropy parameter data fully because of the two-photon nature of the ionization step. It is possible that two-photon ionization involves Rydberg states as the virtual states and if so this might in—uence the angular anisotropy of the photoelectron distribution. It is necessary to use a [1]1@] ionization scheme and to compare the results with a [1]2@] scheme in order to examine this possibility. In our experiment a static electric –eld (\700 V cm~1) was used to extract the photoelectrons and to project them onto the detector. This –eld might induce a Stark eÜect on the molecule. However previous work has shown that a noticeable change in the level structure is only induced by a –eld strength an order of magnitude larger ([10 kV cm~1).35,36 Thus the eÜect of the extraction –eld on the short-time dynamics of pyrazine can be excluded.We also note that the dephasing time we obtained is in good agreement with the previous –eld-free data.25h30 2 B2u(p,p*) is located 7000 cm~1 above the S1 B3u(n,p*) 2(p,p*)^S0 absorption band is broad due to ultrafast S2 ]S1 electronic dephasing. The second singlet state of pyrazine S state. The S Seel and Domcke have produced a seminal work on the theory of femtosecond time-resolved photoelectron spectroscopy for this dephasing process.37 Although our time resolution (450 fs) is much lower than the estimated electronic dephasing time of 30 fs,37 we nonetheless applied FS-PEI to this problem.We excited pyrazine in a molecular beam of 264 nm light to within the vicinity of the zero vibrational level in S2(p,p*) and subsequently ionized the excited molecules with 220 nm light. As shown in Fig. 6(a) the total photoelectron (and parent mass) signal decayed with the lifetime of 43 Faraday Discuss. 1999 113 37»46 Fig. 6 Time dependence of the photoelectron signal in femtosecond [1]1@] REMPI via S state of (a) 2 pyrazine-h4 and (b) pyrazine-d4. 1 although it is undetectable with our apparatus. The intersystem crossing yield from S pyra- 22^1 ps. A similar measurement on pyrazine-d4 determined the lifetime of this system to be 39^1 ps (Fig. 6(b)). The observed lifetime for pyrazine-h4 is in agreement with the lifetime 25 ps of the higher vibronic level of S measured by Yamazaki et al.27 from which we assign the 1 observed decay to the electronic relaxation from the S manifold after ultrafast dephasing from S2 1 zine is known to fall oÜ sharply near 280 nm,27 so the observed decay is ascribed to S1 ]S0 state at a time delay of 1 ps.The image was integrated for 36 000 laser shots. The b value was 2 B2u(p,p*) Fig. 7 Inverse Abel transform of the photoelectron image (250]250 pixels) observed for [1]1@] REMPI via S found to be 0.5^0.1. Faraday Discuss. 1999 113 37»46 44 internal conversion. The longer lifetime observed for pyrazine-d4 is ascribed to the reduction of the Franck»Condon overlap for the accepting modes between S and S0 . 1 Conclusions The –rst femtosecond time-resolved photoelectron imaging (FS-PEI) study has been presented.The method was characterized by photoionization of NO and further applied to ultrafast dephasing in pyrazine. Intermediate case behavior in a radiationless transition was clearly observed in the time-resolved photoelectron kinetic energy distribution. The results demonstrate that FS-PEI allows observation of short-time dynamics with a much improved efficiency compared with conventional photoelectron spectroscopies. It is anticipated that the uni–ed approach of time-resolved photoelectron and photoion imaging10 will allow the possibility of observing photon-induced dynamics from time t\0 to O with a single apparatus. Acknowledgement This work was supported in part by Grant-in-Aid from the Ministry of Education Science Sports and Culture (Nos.09440208 and 09044110) and the New Energy and Industrial Technology Development Organization. References 1 Chemical reactions and their control on the femtosecond time scale Advances in Chemical Physics V ol. 101 ed. P. Gaspard and I. Burghardt John Wiley & Sons New York 1997. 2 High Resolution L aser Photoionization and Photoelectron Studies W iley Series in Ion Chemistry and Physics ed. I. Powis T. Baer and C.-Y. Ng John Wiley & Sons Chichester 1995. 3 D. R. Cyr and C. C. Hayden J. Chem. Phys. 1996 104 771. 4 V. Blanchet and A. Stolow J. Chem. Phys. 1998 108 4371. 5 T. Schultz and I. Fischer J. Chem. Phys. 1998 109 5812. 6 B. J. Greenblatt M. T. Zanni and D. M.Neumark Science 1997 276 1675. 7 P. Kruit and F. H. Read J. Phys. E Sci. Instrum. 1983 16 313. 8 H. Helm N. Bijerre M. J. Dyer D. L. Huestis and M. Saeed Phys. Rev. L ett. 1993 70 3221. 9 D. W. Chandler and P. L. Houston J. Chem. Phys. 1987 87 1445. 10 (a) T. Shibata H. Li H. Katayanagi and T. Suzuki J. Phys. Chem. A 1998 102 3643; (b) T. Shibata and T. Suzuki Chem. Phys. L ett. 1996 262 115. 11 A. T. J. B. Eppink and D. H. Parker Rev. Sci. Instrum. 1997 68 3477. 12 B. J. Whitaker in Research in Chemical Kinetics V olume I ed. R. G. Compton and G. Hancock Elsevier Amsterdam 1993. 13 C. Bordas F. Pauling H. Helm and D. L. Huestis Rev. Sci. Instrum. 1996 67 2257. 14 L. G. Piper and L. M. Cowles J. Chem. Phys. 1986 85 2419. 15 K. Kaufmann C. Nager and M.Jungen Chem. Phys. 1985 95 385. 16 H. A. Bethe in Handbuch der Physik V ol. 24 Springer Berlin 1933. 17 J. Cooper and R. N. Zare J. Chem. Phys. 1968 48 942. 18 S. N. Dixit D. L. Lunch V. McKoy and W. M. Huo Phys. Rev. A 1985 32 1267. 19 H. Rudolph and V. McKoy J. Chem. Phys. 1989 91 2235. 20 S. W. Allendorf D. L. Leahy D. C. Jacobs and R. N. Zare J. Chem. Phys. 1989 91 2216. 21 K. L. Reid D. L. Leahy and R. N. Zare J. Chem. Phys. 1991 95 1746. 22 K. L. Reid and D. L. Leahy in High-resolusion laser photoionization and photoelectron studies ed. I. Powis T. Baer and C.-Y. Ng John Wiley & Sons Chichester 1995. 23 A. Frad F. Lahmani A. Tramer and C. Tric J. Chem. Phys. 1974 60 4419. 24 F. Lahmani A. Tramer and C. Tric J. Chem. Phys. 1974 60 4431. 25 D.E. McDonald G. R. Fleming and S. A. Rice Chem. Phys. 1981 60 335. 26 S. Okajima H. Saigusa and E. Lim J. Chem. Phys. 1982 76 2096. 27 I. Yamazaki T. Murao T. Yamanaka and K. Yoshihara Faraday Discuss. Chem. Soc. 1983 75 395. 28 A. Lorincz D. D. Smith F. Novak R. KosloÜ D. J. Tannor and S. A. Rice J. Chem. Phys. 1985 82 1067. 29 J. L. Knee F. E. Doany and A. H. Zewail J. Chem. Phys. 1985 82 1042. 45 Faraday Discuss. 1999 113 37»46 30 P. M. Felker and A. H. Zewail Chem. Phys. L ett. 1986 128 221. 31 B. J. van der Meer H. Th. Jonkman J. Kommandeur W. L. Meerts and W. A. Majewski Chem. Phys. ” B. brink Oè . Jonsson and E. Lindholm Int. J. Mass. Spectrom. Ion Phys. 1972 8 101. L ett. 1982 92 565. 32 P. J. de Lange K. E. Drabe and J. Kommandeur J. Chem. Phys. 1986 84 538. 33 L. Zhu and P. Johnson J. Chem. Phys. 1993 99 2322. 34 C. Fridh L. 35 M. Okruss F. Penn and A. Hase J. Mol. Struct. 1995 348 119. 36 N. Ohta and T. Takemura Chem. Phys. L ett. 1990 169 611. 37 M. Seel and W. Domcke J. Chem. Phys. 1991 95 7806. Paper 9/02866H Faraday Discuss. 1999 113 37»46 46

ISSN:1359-6640    

DOI:10.1039/a902866h

出版商:RSC    

年代:1999

数据来源: RSC

摘要:

Molecular science with strong laser �elds P. B. Corkum,* Christoph Ellert,§ Manjusha Mehendale Peter Dietrich,î Steven Hankin,° Sergey Aseyev David Rayner and David Villeneuve Steacie Institute for Molecular Science National Research Council of Canada Ottawa Ontario Canada K1A 0R6 Introduction When a two level system is placed in a strong static –eld the Stark shift that results is given by Us\^kE where E is the electric –eld and k is the sum of the induced and permanent dipole moment. The lower level is always shifted down in energy and the upper level is shifted up. § Current address CEA Saclay 91191 Gif-sur-Yvette CEDEX France. î Current address Institute fur Experimentalphysik Freie Universitat Berlin Arnimallee 14 14195 Berlin Germany. ° Current address ESAT Department of Chemistry Heriot-Watt University Riccarton Edinburgh UK EH14 4AS.47 Faraday Discuss. 1999 113 47»59 Received 29th April 1999 The electric –eld of a laser pulse exerts a force on charged particles which can be on the order of (or exceed) the forces that bind electrons to atoms molecules solids or that bind atoms together in molecules or solids. With modern laser technology this force can be applied with almost 1 fs 1 lm precision. Even if the –eld is lower than the –eld required to ionize atoms or molecules large nonresonant Stark shifts can be achieved. The Stark shift gives us a means to control molecules. The dependence of the Stark shift with respect to the intensity pro–le of the laser focus determines the spatial force exerted on the molecule.The dependence of the Stark shift on the orientation of the molecule with respect to the laser polarization determines the torque exerted on the molecule. Through these forces we can control position orientation and linear and/or angular velocity. The Stark shift also depends on the internuclear co-ordinates giving us some degree of control over the structure of the potential energy surface in molecules. The ability to control these basic forces with precision depends on our ability to control optical pulses. Progress towards producing high power pulses with almost arbitrary time-dependent infrared –elds will be discussed. In even stronger –elds where ionization occurs the shifting and mixing of states becomes extreme. Measurement in this complex spectroscopic environment is difficult.Intuition based on perturbation theory is of limited value. Yet strong –eld probing allows us to supply a lot of electronic energy to a molecule very rapidly and to localize measurements in space and time. We illustrate molecular alignment and strong –eld probing together in one experiment where we study femtosecond dissociative ionization. This journal is( The Royal Society of Chemistry 1999 Table 1 Stark shift predicted for representative atoms and moleculesa Stark shift/meV Atom/molecule Maximum –eld/ W cm~2 70 32 90 I H2 CS CS 2 2 2 30 30 He 5]1012 3]1013 8]1012 3.5]1011 2.5]1014 a Ionization rate was approximately 106 s~1 for these calculations.However truly static –elds place a severe limit on the maximum Stark shift that can be achieved. The presence of electrodes always limits the magnitude of the static –eld that can be applied. Much stronger –elds can be achieved in focused laser beams. If the –eld has a slow (harmonic) time dependence compared to electronic times but is fast compared to other time scales in the molecule then it is useful to consider (1) the time averaged Stark shift a Us\^0.25kab Eb Ea where E represents the ath component of the peak external –eld [E= E cos ut)] and k represents the polarizability of a non-polar molecule (2) the instantaneous second order Stark shift given by ab Us\^0.5kab Eb cos(ut)Ea cos(ut) For many symmetric atoms or small molecules with the –rst electronic absorption line in the ultraviolet U gives an adequate description of the ground state stark shift when infrared light is s used.Fig. 1 A characteristic intensity that is approximately the saturation intensity for a number of volatile organic molecules plotted as a function of the ionization potential of the molecule. The molecules plotted as solid points include ethane ethene propane propene propyne cyclopropane hexane cyclohexane hex-1-ene cyclohexene hexa-1,3-diene cyclohexa-1,3-diene cyclohexa-1,4-diene hexa-1,3,5-triene benzene toluene ethylbenzene n-propylbenzene i-propylbenzene 2-methoxyethanol methanol dimethylether. For reference helium neon and xenon are plotted as open points. The solid curve shows the characteristic intensity calculated using ADK tunneling theory.Note saturated ionization in molecules appears to occur at somewhat higher intensity for molecules than atoms of the same ionization potential. Faraday Discuss. 1999 113 47»59 48 The ground state static polarizability of many molecules or atoms is tabulated1 allowing us to estimate the upper bound of available nonresonant Stark shifts as long as the molecule remains in the ground state. For atoms in infrared –elds we know that ionization occurs when the laser –eld is strong enough that the tunneling rate leads to depletion of the neutral population for high ionization potential. So-called ADK (Ammosov Delone Krainov) ionization rates describe this process well.2 In fact surprisingly ADK ionization rates also approximately describe ionization of many small neutral molecules,3 at least with femtosecond infrared (800 nm and longer) pulses.Substituting electric –elds that correspond to ADK ionization rates of 106 s~1 leads to the peak intensities shown in Table 1 for some common small molecules and the associated angle averaged non-resonant Stark shift. Table 1 shows that nanosecond to microsecond pulses can produce Stark shifts in small ground state molecules in their equilibrium geometry of about 50»100 meV and instantaneous Stark shifts about twice that value. With shorter pulses the Stark shifts that can be achieved without ionization should be somewhat greater. Although there has been much less work done on large molecules Fig. 1 shows that volatile organic molecules experience saturated ionization at approximately (in fact slightly above) the intensity predicted by ADK theory for the ionization potential.The underlying physics is likely to be much more complex however. The detailed method by which we make these measurements will be described in a forthcoming paper.4 th) approximately describes the It is interesting to note that the classical ionization threshold (I laser intensity (–eld) required for infrared nonresonant ionization rates3 of about 1014 s~1 (femtosecond ionization). Ith\ e0 2 c p4 16Z2 C4pe0 e3 D I where I represents the ionization potential of the molecule and all other symbols have their usual p meaning. F\ LU(r h) ; q\ LU(r h) Lh Lr Molecular optics The stark shifts that we show in Table 1 occur only where the intensity is high.In a laser focus the highest intensity occurs at the center of the focus and there is little or no shift in the periphery. The force con–ning the molecule is given by the gradient of the potential. The molecule is not only con–ned in space but if the molecule is anisotropic the laser beam can also apply a torque to the molecule resulting in angular acceleration (or angular trapping). The force F and the torque q that the molecule experiences is given by where r is the position within the laser focus (assumed cylindrical) and h is the angle between the laser polarization direction and the molecular axis. To the extent that we can precisely control laser beams we can also precisely control molecules through these basic forces.The aim is to use laser beams to control gas phase molecules with a- ngstrom precision. Experimental The experiments that we will describe used a variety of lasers but most used an 80 fs pulse produced by a colliding pulse mode-locked oscillator followed by a 10 Hz ampli&ndh;er. The dye ampli–er was pumped with 0.53 lm light from a frequency doubled Nd YAG laser. The femtosecond pulse contained a maximum of 300 lJ and could be focused to a spot size u0D2.5 lm. That corresponds to a peak intensity of more than 1016 W cm~2 although experiments often require only \1 lJ of energy. We are currently converting to a Ti sapphire laser producing 35 fs pulses with pulse energy in the 1»10 mJ range. As we show below we compress the pulse to below approximately 12 fs and hope to reach approximately 5 fs soon.49 Faraday Discuss. 1999 113 47»59 Fig. 2 Schematic of the experimental arrangement. The molecular beam expands through a 250 lm nozzle and crosses at right angles to the laser beam(s) and the axis of the time-of-—ight mass spectrometer. We used a time-of-—ight (TOF) mass spectrometer illustrated in Fig. 2 to determine the charge mass and velocity of the ions. The time-of-—ight mass spectrometer consisted of an accelerating region de–ned by two plates separated by 3 cm and an equal length –eld-free drift region. A small (usually 1 mm diameter) aperture in both plates allowed us to de–ne the direction of the ions that we choose to monitor. After passage through the –eld-free region the ions were accelerated to their –nal energy of about 2 keV.Molecular ions with an initial velocity component towards the detector arrived at the microchannel plate detector earlier than a zero velocity ion. Similarly ions with velocity away from the detector arrived later. A 10 Hz pulsed molecular beam was formed by expanding a gas of interest directly into the vacuum chamber with the average background pressure of about 10~6 Torr. The gas could be seeded in argon neon or helium and expanded from the initial pressure of 1 atm. The nozzle diameter of the jet was 250 lm. The molecular beam axis was perpendicular to the TOF axis. The molecules travel freely for D8 cm after which they are crossed at 90° by the focused beams. The system is described more fully elsewhere.5 2 Molecular acceleration (de—ection) With the basic concept of the nonresonant dipole forces now clear and the common elements of our experimental apparatus described we describe an experiment demonstrating the strong nonresonant dipole force.A molecule that enters the focus of a laser beam is accelerated by the gradient6 of the Stark shift. If the force is applied for a long enough period of time then the molecular beam is redirected by the acceleration and the de—ection of the molecular beam can be observed. Although we have performed experiments with either a focused beam from a 100 ns duration 10.6 lm (CO2) laser or a 15 ns 1.06 lm (Nd Yag) laser,6 here we will outline the CO results. The pulsed 10 Hz CO laser consisting of a hybrid CO oscillator and a double-passed CO 2 2 2 ampli–er produced a 10.6 lm pulse with approximately 50% of the pulse energy of 600 mJ in a 70 ns (FWHM) gain switched peak.The remaining energy was in a long tail and was not used in this experiment. The temporal structure of the pulse was monitored to ensure single longitudinal mode operation using a photon-drag detector. The laser beam is focused inside the target chamber with an on-axis parabolic mirror. We measured the diameter of the focal spot at (j\10.6 lm with the CO ampli–er switched oÜ. For 2 that measurement the parabolic mirror was placed outside the vacuum chamber. The measured focal spot diameter is about 35 lm (FWHM). Thus we estimate the intensity in the beam waist as 4.5]1011 W cm~2 limited by the Fd of our mirror and the energy that our laser could provide.We measure the velocity change along the TOF axis (i.e. perpendicular to the molecular velocity before the interaction). To do this we multiphoton ionize the neutral molecules using the tightly focused femtosecond laser beam described above and observe the distribution of —ight times of the CS2 ` ions from the interaction region to the micro-channel plate detector. Molecules de—ected towards the detector arrive early those de—ected away are delayed. We measure a shift of Faraday Discuss. 1999 113 47»59 50 Fig. 3 A segment of the time-of-—ight-record that shows the arrival-time of the molecular ions as the detection (ionization) region is moved across the de—ection beam. the time-of-arrival that is proportional to the velocity that the molecules have acquired from the de—ecting –eld.The nonlinearity of multiphoton ionization allows us to restrict the probe volume to a region much smaller than the CO focal volume by adjusting the focal spot size as well as the intensity of 2 the femtosecond beam. Therefore we can use the femtosecond pulse to probe the spatial dependence of the induced dipole force simply by moving its focus with respect to the larger CO focus. 2 We use the molecular beams velocity to allow us to make measurements below the CO laser 2 focus ensuring that the strong 10 lm –eld does not perturb the measurement. Examples of the relevant portion of three TOF spectra are shown in Fig. 3. Each time-of-—ight spectrum was the average of 250»500 shots.There was no ionization by the CO laser pulse. To 2 eliminate the in—uence of the timing jitter between the CO and dye pulses time-of-—ight spectra were only recorded if the two pulses arrived at the proper delay. Fig. 3 shows the successive CS2 ` 2 spectra recorded at diÜerent horizontal positions of the de—ecting beam relative to the measurement beam. We emphasize that our measurement is restricted to those molecules that pass through the very small focal spot of the femtosecond laser. This illustrates one of the major advantages in using strong –eld probe pulses the ability to probe only very localized regions in space and time. Fig. 4 Variation of the arrival-time compared to an unde—ected molecule plotted against the position where the molecular beam crosses the laser focus.This is a direct measurement of the velocity acquired by the molecules from the de—ection beam. The solid curve shows the spatial derivative of a 30 lm FWHM beam. 51 Faraday Discuss. 1999 113 47»59 Fig. 4 shows the shift in the arrival-time and the associated transverse velocity given to the U\[1 U0\4 meV. This value can be compared 4aE2 at our estimated experimental molecule by the de—ecting –eld plotted as a function of the position across the laser focus. The u solid line corresponds to the normalized derivative of a Gaussian pro–le with 0\30 lm. This magnitude is in satisfactory agreement with our estimated beam waist of the infrared beam described above. We can use these results to determine to a well depth of about 4.5 meV obtained using intensity of 4]1011 W cm~2.2 Other applications of the nonresonant dipole force Focusing molecules The experiment described above shows as a corollary a method of focusing molecules.6 Molecules that pass near the center of the de—ection beam gain a velocity that is proportional to their distance from the center. These molecules must meet at a common point below the laser focus. For example the molecules in Fig. 4 gain a transverse velocity of 5 m s~1 at an oÜset from the beam center of 5 lm. They reach the axis in 1 ls. During that time the CS molecules moving 2 with a longitudinal velocity of 500 m s~1 travel 500 lm. Consequently the focal length of the molecular lens is f+500 lm. Two dimensional trapping molecular quantum wires Molecular quantum wires are also implied by the results that we have just described.That is con–ning molecules (or atoms) in two dimensions with con–nement so strong that their transverse translational energy is quantized. Molecules propagating in a molecular quantum wire would be the analogue of light propagating in an optical –ber. What makes molecular quantum wires especially exciting is that it appears that molecules can be con–ned to within about 10 A »40 é not much larger than a molecular dimension. Producing a molecular quantum wire does not require a large extrapolation over the experiment that we just described. Consider the output of a long pulse Nd YAG (1.06 lm) laser focused to produce a line of high intensity radiation. Such a line can be achieved using an axicon or a hollow core wave-guide.Alternatively a standing wave pattern produced by counter propagating beams in two perpendicular directions produces an array of molecular quantum wires. The diameter of a line focus can be less than one wavelength of light (the FWHM diameter of a standing wave is approximately j/4). The length of the line focus is not con–ned by physics but is of course con–ned by the size and complexity of the laser required. Assuming the con–nement potential characteristic of a standing wave in one dimension U0 cos2(2pr/j) the potential well structure near the well minimum is given by U\[U0[1 [(4p2/j2)r2] so the zero point energy of the ground state is Eg\[p+(2U0)1@2]/(jm1@2). For realistic parameters (j\1 lm U0\50 meV and taking the H2 mass for m we obtain EgD10~4 eV.The approximate dimensions of the square of the ground state wavefunction would be about 35 ”. For heavier molecules the zero point energy is reduced as is the diameter of the ground state wavefunction. Having determined the level spacing in the quantum wire we now discuss the issues involved in coupling molecules into the fundamental mode of the wire. kin In our molecular de—ection experiment the molecular beam had an estimated lateral kinetic E energy of about 10~7 eV in the region of the laser focus. This is orders-of-magnitude less than the zero point energy in the molecular wire. The major problem to be overcome is coupling this beam of molecules into the wire without simultaneously converting some of its longitudinal energy into transverse motion.In analogy with optical –bres where laser light is coupled into the fundamental mode of the –bre using lenses we believe that molecular lenses such as we have just described will be very helpful. Three dimensional trapping molecular quantum dots The approximately j/4 dimensions of a two dimensional trap can also be achieved in three dimensions. With well depths of 50 meV the zero point energy of H will again be approximately 10~4 Faraday Discuss. 1999 113 47»59 52 Fig. 5 A chirped femtosecond pulse showing the kind of control over the time history of the pulse that can be easily achieved using femtosecond technology. The pulse contains about 3 mJ of energy. The modulation that is visible is due to weak satellite pulses before or after the main pulse.eV. It is clear that trapping is possible even for molecules at or near room temperature. For a molecular temperature of approximately 1 K the ground state will be preferentially populated. An accelerator for neutral molecules dl\2Va/j. In an optimally accelerated standing wave with a gradient of the Stark shift of If the Stark shift can be on the order of 100 meV approximately one order-of-magnitude greater than those measured here the gradient of the Stark shift can be much larger still. The largest intensity gradient that can be produced without a surface present occurs in standing waves where the regions of highest and lowest intensity are separated by 0.25j. If j\1.06 lm this is more than two orders of magnitude smaller than the scale length of the intensity gradient that we used and it should lead to much higher acceleration.Molecules trapped in a standing wave can be accelerated if the pattern is accelerated. Acceleration of a standing wave pattern occurs if one of the pulses is appropriately chirped. The velocity V of a pattern is determined by the frequency diÜerence dl between the counter propagating a beams 4]105 V m~1 (i.e. 100 meV per 0.25 lm) a hydrogen molecule will achieve a velocity Va\ 20 km s~1 in 1 ns corresponding to a kinetic energy of 4 eV. For such a short acceleration length the maximum frequency diÜerence dl between the counter propagating beams is only about 40 GHz. Since the kinetic energy increases quadratically with time a kinetic energy of 400 eV is possible after 10 ns and the required frequency chirp is within the bandwidth of a picosecond pulse.The required pulses are available in many laboratories today. Accelerating neutral rotationally and vibrationally cold molecules to hundreds of keV energies appears feasible. Alignment A molecule in a laser –eld also experiences a torque that tends to align the direction of the induced dipole moment with the laser –eld. (This torque is well known to those with a background in laser technology since it leads to the optical Kerr eÜect. The optical Kerr eÜect was exploited for its technical signi–cance in the early days of lasers.7) Alignment is the angular analogue of trapping. Measurement of the degree of alignment however can be complex if it is performed while the –eld is present.Any diagnostic of alignment must be spatially localized since alignment only occurs where the intensity of the alignment laser is large. In order for the diagnostic region to be localized in space measurement must involve at least two photons. However measurements with only two photons inside a strong –eld that can supply many other photons must be treated with great care. 53 Faraday Discuss. 1999 113 47»59 Fig. 6 A 13 fs pulse (a) as measured using frequency resolved optical gating. The pulse energy was approximately 100 lJ. We illustrate the quality of the reconstruction by showing the original frequency resolved spectrogram in (b) and the reconstructed spectrogram in (c). In (b) and (c) the shading steps represent 0 20 40 60 80 and 100%.Many authors have studied alignment.8 Sakai et al.8 have compared diÜerent methods of measurement and clearly observe very strong alignment of I molecules. In this paper we will concen- 2 trate on alignment during dissociative ionization. We will present these measurements below where they are used to emphasize the problems and opportunities of measurement in and with strong –elds. However we are also using shaped 800 nm pulses (shown in Fig. 5) for controlled alignment experiments. These measurements were brie—y described in response to questions by Prof. Suzuki (p. 95) and Dr Zare (p. 99). Spinning Just as a molecule can be accelerated in space by a moving intensity structure so also a molecule can be spun,9 even to very high energy by varying the laser polarization –rst rotating it slowly and then with increasing speed.In ref. 9 it is shown theoretically that molecular chlorine can be spun until the centrifugal force on the atomic constituents of the molecule exceeds the binding force. When this happens the chemical bond breaks. An experiment is underway in our laboratories. Faraday Discuss. 1999 113 47»59 54 ììMode-lockingœœ a trapped molecule If it is possible to trap a molecule by populating the ground vibrational (or pendular) state of a trap as we suggest above it should be possible to further localize the molecule by locking many modes of the trap together. Just as the radiation in a femtosecond laser is concentrated into a short pulse with dimensions much smaller than the cavity length so also a molecule can be localized to a dimension smaller than the ground state wavefunction.This opens the opportunity of localizing molecules to nearly molecular dimensions although as with a femtosecond pulse in a cavity they will move in their con–ning potential. The essential issue for this and all other aspects of molecular optics is control of the laser radiation. Controlling laser –elds Laser physics is rapidly approaching the ability to produce arbitrarily time dependent –elds both in the visible and in the infrared. The key development has been near single period pulses. These have the bandwidth of phased radiation to produce almost any signal consistent with Maxwellœs equations. In the mid-infrared single period pulses are produced by direct optical recti–cation of very short visible pulses.10 In this way the full time-dependent –eld of the pulse is known.In the visible high-power compression has allowed mJ pulses to be compressed producing 10 fs or shorter pulses11 containing in excess of 100 lJ. Fig. 6 shows a FROG (frequency resolved optical gate) trace of a 13 fs pulse produced by hollow-core-–ber self-phase modulation followed by prism dispersion compensation. Although it is not yet possible to control or even measure how the –eld oscillations –t within this pulse envelope in Fig. 6 (the absolute carrier phase of the radiation) a robust method of measurement has been proposed.12 It seems likely that we will soon know the full time dependent electric –eld structure of 800 nm pulses and from there it is a short step to synthesizing any structure.We illustrate the kind of control that we already have over laser pulses through the following example. Our aim is to apply a strong –eld slowly (adiabatically) to an anisotropic molecule allowing it to align adiabatically8,13 with rotational states evolving into pendular states of the molecule orientationally trapped by the –eld. If the laser –eld is terminated abruptly then the molecule is released from the trap non-adiabatically and the resulting wave packet dephases. If the cut-oÜ of the laser beam is fast enough the molecule is left –eld-free but aligned for the time it takes to rotationally dephase. Using femtosecond laser technology we produce laser pulses with the appropriate time structure.Fig. 5 shows an optical pulse that is produced by linearly chirping a 1 mJ 35 fs optical pulse in a grating stretcher. The abrupt truncation results from abruptly truncating the spectrum of the pulse. However the pulse in Fig. 5 is modulated and it rotationally heats our molecules. This modulation is a sensitive measure of pre- or post-pulses. It is in fact a very sensitive method for diagnosing the quality of a femtosecond beam.14 Towards controlling the internal variables of molecules The Stark shifts also oÜer a route toward controlling the internal variables of a molecule. For light fragments such as hydrogen atoms or ions or for longer wavelengths it is often inappropriate to average over the cos(ut) oscillation of the –eld. Rather dynamics occurs on the full time-dependent Born»Oppenheimer surfaces.15 The extent of the time dependent changes in these surfaces is illustrated in Fig.7 where the curves plot the two lowest lying potential energy surfaces of H2 ` for a static –eld of 0 (solid curves) and 2 V ”~1 (dashed curves). By the time the molecule is exposed to a laser intensity of about 3 V ”~1 (equivalent to the maximum –eld when the laser intensity is 1014 W cm~2) the Stark shifts are so great that the ground state loses its bonding character. Through control of the laser –eld we exercise signi–cant control over the potential energy surface. It has been shown experimentally that hydrogen-bearing ions such as H2 ` and HCl` can be readily dissociated with strong infrared –elds.3 Faraday Discuss.1999 113 47»59 55 Measurements in strong –elds and with strong –elds Thus far when discussing Stark shifts we have concentrated on the in—uence of the strong –eld on the ground electronic state since we know that the strong laser –eld lowers the ground state energy. We have also avoided both resonances and ionization. This allows a simplicity that can lead to control. However neither resonances nor ionization can be ignored if we wish to measure during a strong –eld or to use strong –elds for measurement. Excited states are much more complex. The Stark shift can move excited states up in energy or down depending on the laser frequency transition moments and the location of other states. There is every reason (see for example Fig. 7) to believe that the average level shift is as great or even greater than the shift of the ground state level at the equilibrium position (see for example Fig.7). Measurement in this complex spectroscopic environment bathed in a very high density of photons can be difficult. Although strong –eld probing must be treated with caution it oÜers (1) localized probing; (2) an ionization method that does not require complex short wavelength sources ; (3) access to unusual spectroscopies such as Coulomb explosion imaging.16 However it comes at a cost. We can not rely on our intuition based on perturbation theory although at very high intensities classical physics intuition can be useful. At the meeting discussion was encouraged on two issues (1) measurement in strong –elds and (2) measurement with strong –elds so we conclude the paper with a simple example of the measurement of molecular alignment during dissociative ionization.It is an example where strong –eld measurements were originally misinterpreted. It has been widely assumed that small molecules in the gas phase strongly align during femtosecond multielectron dissociative ionization just as we described alignment above.17 However it is not necessarily true. Although the laser –eld is large especially for molecules that reach highcharged states and so the torque can also be very large the time available for the molecule to align to the –eld is small limited by the dissociation time of the molecule or by the laser pulse duration. However early experiments have seemed to support the rapid alignment interpretation.18 The observation has been that almost all highly charged fragments are found primarily along the laser polarization direction implying the molecules might have been aligned before they exploded. Pump»probe experiments also appear to support the alignment interpretation.19 There is an alternative interpretation of the alignment of the fragments observed in femtosecond dissociative ionization experiments. Studies of strong-–eld ionization of diatomic molecules have revealed that the molecular ionization rate can be highly dependent on both the molecular orientation and on the internuclear separation. ììEnhanced ionizationœœ even occurs in classical physics. Quantum mechanical (classical) calculations of the ionization rate (threshold) peaks for aligned R molecules separated by a critical internuclear separation R where is about 1.5 times the cr cr equilibrium internuclear separation.5 The anisotropic fragment distribution observed in dissociative ionization experiments could therefore be the result of the high ionization rate for molecules that are aligned to the –eld.Fig. 7 The potential curves of H2 ` approximated by the rg ru levels without –eld (solid line) and in an external dc –eld of 2 V ”~1. Note the –eld shifts the ground state to lower energy and the upper state is raised. Faraday Discuss. 1999 113 47»59 56 Since this is inherently a strong –eld phenomenon there is no choice but to develop a strong –eld method for distinguishing between these two interpretations.We introduce the following approach. (1) We select a direction (approximately ^10°) for observation of fragment ions from dissociative ionization. An aperture in our time of —ight mass spectrometer provides this selection. (2) We gain a measure of control of any possible alignment of the molecule during dissociative ionization by using linearly or circularly polarized light. Alignment to a given direction is only possible in linearly polarized light. In circularly polarized light molecules can only align to a plane. Circularly polarized light allows us to calibrate ionization in the absence of alignment. we con–rm that ionization is mainly dependent on (3) Using the iodine fragments from CH2I2 the component of the electric –eld parallel to the internuclear axis.That is in the absence of alignment the same dissociative ionization signal should be observed for parallel and circularly polarized light provided they have the same maximum –elds. (4) Given (3) any diÜerence in the fragmentation pattern between linearly polarized (electric vector parallel to the time-of-—ight axis) and circular polarized light provided they have equal maximum –eld must then be due to alignment of the molecule in the laser –eld. The experiment is performed in a vacuum chamber and with the dye laser described above. We begin by studying diiodomethane a molecule chosen because the I»I fragments can not align to the laser –eld (because of the high moment of inertia of the molecule and the low anisotropic polarizability).We show that only the component of the laser –eld along the I»I axis is important for the ionization rate. That is we show that a laser –eld polarized parallel to the axis with amplitude E and a circularly polarized –eld with an additional –eld component of equal amplitude but phase shifted by p/2 and perpendicular to the molecular axis should have the same I circ\2IA. This ionization probability. While the former has an intensity of I the latter has A behaviour is characteristic of quantum mechanical and classical calculations of enhanced ionization. Fig. 8 is a time-of-—ight record for three polarization states with respect to the I»I axis of diiodomethane. By parallel we mean laser polarization parallel to the direction of the TOF axis and also parallel to the axis de–ned by the apertures in the TOF electrodes (direction of observation).As expected for any case where ionization is due to enhanced ionization and where the molecule cannot align to the –eld the parallel and circular polarization show approximately equal intensity for the three channels 2»1 2»2 and 2»3. This observation provides the basis of our method for measuring molecular alignment. We will now apply the method to the series of diatomic molecules for which the alignment can not be excluded a priori as it was for diiodomethane. The method is as follows since alignment can be excluded for circular polarization we compare the fragment ion intensities for parallel polarization with respect to circular polarization. In Fig. 9 the time-of-—ight spectra in the region of the doubly charged iodine atomic ions is shown for three Fig.8 Kinetic energy distribution of I2` resulting from the explosion of CH2I2 for circularly polarized light as well as for light polarized parallel or perpendicular to the axis of the TOF and therefore to the molecular axis. The ion signals for parallel and circular polarization are approximately equal. 57 Faraday Discuss. 1999 113 47»59 Fig. 9 Flight time distribution of the ionic fragments for chlorine (above) and iodine (below). The I2` intensities for parallel and circular polarization are nearly equal whereas they diÜer signi–cantly for Cl2` showing the absence of alignment for iodine and partial alignment for chlorine. diÜerent polarizations parallel perpendicular with respect to the detector axis and circular.The diÜerent fragmentation channels are named with the two charge states of the two ionic fragments. It can be seen that the intensity of the 2»1 channel is identical for parallel and circular polarization while for 2»2 only a slight diÜerence can be detected. For comparison in Fig. 9 the Cl2 portion of the TOF spectra shows a large diÜerence between parallel and circular polarization. We attribute this diÜerent behavior of iodine and chlorine to the diÜerent alignment response for the two molecules. The ratio of the circular to the parallel intensities for various channels was measured for the molecules iodine bromine chlorine and oxygen. For the lighter molecular ions the increase in the intensity for parallel polarization compared to circular is stronger.That is the molecule aligns signi–cantly before it can dissociate. Furthermore for higher charge states the ratio S(Icirc)/S(IA) (where S is the observed ion signal) decreases indicating a stronger alignment as well. Conclusion Although strong –elds have been available since the very –rst days of lasers until now they have had little in—uence on molecular science. It is only when they are combined with the precise control that we are gaining over laser radiation that intense laser pulses become tools»both for measurement and for control. As we look ahead it is inevitable that this major direction of laser science will continue to in—uence molecular science. Controlling the electric force the basic force of molecular science with precision is important especially when it is strong enough to compete with intermolecular forces.It is easy to foresee for example that such unusual measurement techniques as Coulomb explosion imaging16 will become widely available bringing particle physics-like technology to molecular science. In addition there is a chance of gaining control over gas phase molecules using a strong –eld that approaches the relative precision with which we control a pencil with our –ngers. References 1 K. J. Miller J. Am. Chem. Soc. 1990 112 8543. 2 M. V. Ammosov N. B. Delone and V. P. Krainov Sov. Phys. JEPT . 1986 64 1191. Faraday Discuss. 1999 113 47»59 58 3 P. Dietrich and P. B. Corkum J. Chem. Phys. 1992 97 3187; P. Dietrich and P. B. Corkum Comments At.Mol. Phys. 1993 28 357; M. Y. Ivanov et al. Phys. Rev. A 1996 54 1541; F. Ilkov et al. Phys. Rev. A 1995 51 R2695. 4 S. Hankin and D. M. Rayner unpublished results. 5 E. Constant H. Stapelfeldt and P. B. Corkum Phys. Rev. L ett. 1996 76 191. 6 H. Stapelfeldt H. Sakai E. Constant and P. B. Corkum Phys. Rev. L ett. 1997 62 2787; T. Seideman J. Chem. Phys. 1997 106 2881; H. Sakai A. Tarasevitch J. Danilov H. Stapelfeldt R. W. Yip C. Ellert E. Constant and P. B. Corkum Phys Rev. 1998 A57 2794. 7 M. A. Dugay and J. W. Hansen Appl. Phys. L ett. 1969 15 192. 8 H. Sakai C. P. Safvan J. J. Larsen K. M. Hilligsoe K. Hald and H. Stapelfeldt J. Chem. Phys. 1999 110 10235; W. Kim and P. M. Felker J. Chem. Phys. 1996 104 1147. 9 J. Karczmarek J. Wright P.Corkum and M. Ivanov Phys Rev L ett 1999 82 3420. 10 A. Bonvalet J. Nagle V. Berger A. Migus J. L. Martin and A. JoÜre Phys. Rev. L ett. 1996 76 4392. 11 M. Nisoli S. De Silvestri O. Svelto R. Szipocs K. Ferencz Ch. Spielmann S. Sartania and F. Krausz Opt. L ett. 1997 22 522. 12 P. Dietrich F. Krausz and P. B Corkum Opt. L ett. submitted. 13 B. A. Zon and B. G. Katsnelœson Sov. Phys. JEPT 1976 42 595; B. Fredrich and D. Herschbach Phys. Rev. L ett. 1995 74 4623 14 S. Aseyev and D. Villeneuve unpublished results 15 P. B. Corkum M. Yu. Ivanov and J. S. Wright Ann. Rev. Phys. Chem. 1997 48 387. 16 H. Stapelfeldt E. Constant and P. B. Corkum Phys. Rev. L ett. 1995 74 3780; C. Ellert H. Stapelfeldt E. Constant H. Sakai J. Wright D. M. Rayner and P. B. Corkum Philos. T rans. R. Soc. L ondon A 1998 356 329; Z. Vager R. Naaman and E.P. Kanter Science 1989 244 426. 17 M. Brewczyk K. Rzazewski and C. W. Clark Phys. Rev. L ett. 1997 78 191; A. Giusti-Suzor and F. H. Mies Phys. Rev. L ett. 1992 68 3869; B. Friedrich and D. Herschbach Phys. Rev. L ett. 1995 74 4623. 18 J. L. Frasinski K. Codling P. Hatherly J. Barr I. N. Ross and W. T. Toner Phys. Rev. L ett. 1987 58 2424; K. Boyer T. S. Luk J. C. Solem and C. K. Rhodes Phys. Rev. 1989 A39 1186; D. T. Strickland Y. Beaudoin P. Dietrich and P. B. Corkum Phys. Rev. L ett. 1992 68 2755. 19 D. Normand. L. A. Lompre and C. Cornaggia J. Phys. 1992 B25 L497; P. Dietrich D. T. Strickland M. Laberge and P. B. Corkum Phys. Rev. A 1993 47 2305. Paper 9/03428E 59 Faraday Discuss. 1999 113 47»59

ISSN:1359-6640    

DOI:10.1039/a903428e

出版商:RSC    

年代:1999

数据来源: RSC

摘要:

The role of molecular and resonance phases in the coherent control of chemical reactions Jeanette A. Fiss,a Ani Khachatrian,a Langchi Zhu,a Robert J. Gordona and Tamar Seidemanb a Department of Chemistry (m/c 111) University of Illinois at Chicago 845 W est T aylor Street Chicago IL 60607-7061 USA b Steacie Institute National Research Council 100 Sussex Drive Ottawa Canada K1A0R6 (1) 1 Introduction Recent work1h3 has suggested that the tools developed for phase control of chemical reactions4,5 can serve as a route to valuable dynamical information that is not available from more conventional experiments. The basis of coherent control is the principle of quantum mechanics that the probability of producing a given –nal state is equal to the squared modulus of the sum of the transition amplitudes for all independent pathways connecting that state with a given initial state.6 The application of this principle to the control of chemical reactions was formulated by Brumer and Shapiro at an earlier Faraday Discussion.4 An example of a two-pathway excitation is absorption of m photons of frequency u simultaneously with n photons of frequency u n m such mu that n\num .An essential condition for this control scheme is that the diÜerent frequency photons are phase-locked i.e. the electromagnetic –elds must have a de–nite phase relation so that by altering their relative phase it is possible to control the interference between the two transition amplitudes. If a superposition of continua that correlate asymptotically with two or more product channels is reached by the two paths altering the relative phase of the paths allows control over the relative yields of the various channels.7 For the oft-cited example of one- and three-photon excitation,8 the diÜerential transition probability (i.e.the probability of observing a reaction product S with energy E and scattering angle k � ) is given by where f respectively and 3 S eid3 S and f 1 S eid1 S are the transition amplitudes for the absorption of 1 and 3 photons /\3/1[/3 is the relative phase of the electromagnetic –elds. After integration 61 Faraday Discuss. 1999 113 61»76 Received 25th March 1999 Coherent control of the photoionization and photodissociation of HI and the photoionization of H were obtained in the region of the 5d(n d) resonance of HI.2S Interference between one- and three-photon excitation paths caused modulation of the HI` I` and H2S` signals. Phase lags between the diÜerent modulated signals measured as a function of excitation energy revealed the roles played by molecular and resonance phases. A theory of the phase lag arising from a set of overlapping rotational resonances was developed and used to interpret the observations. pS(E k � )\o f 3 S (E k � )]f 1 S (E k � )ei(’`d1 S ~d3 S ) o2 This journal is( The Royal Society of Chemistry 1999 over k � (and summation over any product indices not resolved in the experiment) the total probability of observing product S is given by (2) pS(E)\p1 S (E)]p3 S (E)]2 o p13 S (E) o cos(/]d13 S (E)) and the ììphase shift,œœ where d13 S is a property of the material target de–ned by4 pj S\( f j S)2 (3) o p13 S o eid1 S 3\Pdk � Sg oD1 (3) o ESk� ~TSESk� ~oD1 (1) o gT.In eqn. (3) o gT denotes the initial state o ESk� ~T is a continuum eigenfunction of the complete (–eld-free) Hamiltonian and D1 (j)\e~i’(j)D(j) is a ììphase-adjustedœœ dipole operator D(j) being a j-photon dipole operator and /(j) its phase.9 Eqn. (2) predicts that the yield of product S is a sinusoidal function of the laser phase /. Experimentally one observes a ììphase lagœœ *d(A B) between the phase-shifts of channels S\A and S\B (4) *d(A B)\d13 A [d13 B . The goal of this paper is to explore the physical origin and information content of the phase lag using the photoionization and photodissociation of hydrogen iodide as a case study.Early experiments designed to demonstrate the experimental feasibility of implementing the Brumer»Shapiro scheme involved discrete bound-to-bound transitions.10h13 Modulation depths of the –nal state population as high as 75% were eventually achieved,14 in agreement with the prediction that full modulation is possible for such processes.12 The next key step was to apply the method to bound-to-continuum transitions without product state resolution.15h18 The modulation depths of the products were typically half of those observed for discrete transitions under similar experimental conditions showing that the existence of incoherent channels (products that are dipole allowed via only one of the excitation schemes) and the average over the ensemble distribution of initial states need not signi–cantly degrade the level of control.In experiments that demonstrated the full power of coherent control the phase lag between diÜerent channels19 was measured as a function of excitation energy.2,20,21 Phase lags close to 180° have been observed in these experiments. Other control schemes which we shall not discuss involve ììdiamondœœ con–gurations (in which diÜerent intermediate levels are accessed in the two competing paths22) and ììlambdaœœ con–gurations (in which excitation from an unoccupied level is used to dress the upper state23). In recent work1h3,19h21,24 we investigated the structure of d13 S 1~T in the common case shown schematically in Fig.1 where the continuum is accessed both directly and via resonances embedded in the continuum. The properties of the phase-shift for that case are best illustrated within a Feshbach partitioning formalism o ESk� ~T\(P]Q) o ESk� ~T where P projects onto the scattering manifold and Q onto the bound manifold.1 Focusing on the competing photoionization and photodissociation reactions of HI and DI as a test case we demonstrated both experimentally and theoretically that there are two generic types of phases that determine the value of the phase lag. These are the so-called ììmolecular phases,œœ which are derived from the phase of the complex continuum projection1 of the wave function denoted o ESk� 1~T below,20 and ììresonance phasesœœ which are associated with the properties of quasi-bound states coupled to one or more continua.2 As we shall show further in this paper these phases have qualitatively diÜerent energy dependences.The molecular phases on the one hand make the largest contribution to *d far from resonance. In the special case of a single resonance the phase lag falls to a deep minimum near resonance where the excitation and decay processes become uncoupled.1,20 The resonance phases (which include what is sometimes referred to as the Breit»Wigner phase25) on the other hand have their maximum eÜect on resonance. In previous studies1h3,20,24 we explored the necessary conditions for the molecular and resonance phases to be observed. Partial-wave decomposition of the scattering component o ESk� showed that the molecular phase vanishes if the phases of the partial waves are coordinateindependent.1 This condition requires that the scattering Hamiltonian be purely elastic. Observation of a non-zero phase lag far from resonance is therefore direct experimental evidence of exit channel interactions. Faraday Discuss. 1999 113 61»76 62 Fig. 1 Four-slit model of the control mechanism showing the one-photon resonant and three-photon resonant (1r and 3r) paths on the left and the one-photon direct and three-photon direct (1d and 3d paths) on the right. One may similarly ask what are the conditions for a non-zero phase lag near resonance. For an isolated resonance in the absence of a direct path the interference term of eqn.(3) reduces to1 (5) o p13 S o eid1 S 3\Pdk � Sg oD(1) o iTSi o ( H E M [ o ESk E � 1~TSESk� 1~oHM o 2 where o iT is an eigenstate of the bound projection of the Hamiltonian QHMQ Ei is the corresponding eigenenergy C D H is the matter Hamiltonian and and are respectively the shift and M i i width of the eigenenergy induced by the coupling to the continuum. Eqn. (5) demonstrates the uncoupling of the excitation and decay processes referred to previously. Assuming for now that D(3) is real we see that d13 S vanishes. The only way for the phases not to cancel (for real transition operators26) is if there exist two or more coupled1 overlapping resonances. 2S H2S`) o we observed that o *d(HI` is Our earlier measurements of the phase lag for photodissociation versus photoionization of HI were made in the vicinity of the 5sr resonance which is centered at 118.036 nm27 and lies above the X2%3@2 ionization threshold.These results are collected in Fig. 2. In one study,20 working with either pure HI or pure DI we demonstrated that *d(HI` I) and *d(DI` I) fall to sharp minima near this resonance. In a second experiment,20 we measured the phase lag for the ionization channels of a mixture of molecules. For a mixture of HI and DI we observed that *d(HI` DI`) is approximately zero across the resonance. This result proved that the isotope eÜect for the pure gases [i.e. the energy-dependent value of *d(HI` I)[*d(DI` I)] is caused exclusively by the dissociation channel.It is also consistent with the theoretical result that the molecular phase for ionization of HI is zero.28 For a mixture of HI and H close to zero far from resonance and reaches a maximum near resonance in accord with our expectation for a resonance phase in the absence of a molecular phase. A preliminary theoretical treatment of the resonance phase for a single rotational level was presented in ref. 2. The present study tests and extends our earlier work by examining the energy dependence of HI`(2% core and autoionize30 to produce 1@2) H3@2).I` (2% *d(HI` I) and *d(HI` H2S`) in the vicinity of the overlapping 5dp and 5dd resonances of HI,29 which are centered at 118.726 nm.27 The sharp ns and the broad nd resonances are members of Rydberg series that converge to the Control of the branching between ionization and dissociation of the 5d states provides a much needed test of the theoretical ideas developed in our earlier study of the 5s resonance.At the same time the diÜerent electronic structure of the 5d resonances provides an opportunity for new interference eÜects to be observed. This paper is organized as follows in the following section is a formal derivation of the phase shift produced by a set of overlapping rotational resonances. Following presentation of the 63 Faraday Discuss. 1999 113 61»76 Fig. 2 Summary of all phase lag measurements to date for HI DI and H2S. The circles denote intramolecular phase lags *d(HI` I) and *d(DI` I). The squares denote *d(HI` DI`) measured for a mixture of HI and DI and the triangles are *d(HI` H2S`) H measured for a mixture of HI and Error bars indicate a single standard deviation for typically 10 measurements.2S. general problem we focus on the case of a single electronic resonance and an elastic continuum. The case of coupled electronic resonances interacting with continua that are themselves nonadiabatically coupled is discussed elsewhere.31 Section 3 outlines the experimental methods and Section 4 presents the experimental results. The –fth section contains a discussion of the data and Section 6 concludes. (6) SQRo EnSk� JMX 2 Theory Fig. 1 motivates partitioning of the scattering wavefunction o EnSk� ~T in eqn. (3) into a bound and a scattering component as32 (Q]P) o EnSk� ~T\[I]F(E)QGQHM]Po EnSk� 1~T where we indicated explicitly the electronic index n Q and P project onto the excited bound states and the continua respectively and a derivation.Consider next a partial wave decomposition of o EnSk� F(E)\I](E~[PHMP)~1PHM I is the unit operator QGQ is an eÜective Greenœs operator,1 H is the matter Hamiltonian and (7) Po EnSk � 1~T are solutions of its scattering projection PHMP. We refer the reader to ref. 1 for details M 1~T 1~T\ ; SQRo EnSJMXTSk � oJMXT* (8) where Q denotes the electronic coordinates R\Rå R is the internuclear vector J and M are the total angular momentum and its space-–xed z projection and X is the projection of the angular momentum onto the molecular axis. We denoted by SQRo EnSJMXT a vibronic wavefunction to allow for the possibility of a nonadiabatically coupled scattering manifold and Sk � oJMXT\[(2) Faraday Discuss.1999 113 61»76 64 ]1)/4p]1@2DXM J (k � ). With eqns. (6) and (7) the j-photon matrix elements in eqn. (3) take the form33 Sn exp[idJg J d (j) ]]f (J j g)JM r exp[id(J j g)J r]NSk � oJMXT* (9) g JgMg oD1 (J) o EnSk� ~T\ ; M f jgJM d (j) JMX g\(ng Jg Mg) d stands for direct r stands for and where we speci–ed the initial state indices n is a vibronic index. In eqn. (9) f dJg J (j) are real arithmetic JgJM (j) g resonance-mediated and functions de–ned through (10) exp[idJg J d (j) ]\Sng JgMg oD1 (j) o EnSJMXT f JgJM d (j) and (11) (j) exp[id f JgJM r Jg J r (j) ]\Sng JgMg oD1 (j)FQGQHM o EnSJMXT. In order to avoid cluttering the notation we omitted all but essential indices from f (j).The interference term of eqn. (3) is thus f (3) JgJM d exp[[i(dJg J d (1) [dJg J d (3) )] p13 S (Jg M)\; (1) J f JgJM d exp[[i(d(1) [d(3) )] Jg Ji r Jg Ji d (1) ]; M f Jg JiM d f Jg JiM r (3) (12) ji (1) ]f Jg JiM r f Jg JiM d (3) (3) Jg Ji r ]f (1) Jg JiM r f Jg JiM r exp[[i(d(1) [d(3) )] Jg Ji r Jg Ji d exp[[i(d(1) [d(3) )]N Jg Ji r where J enumerates the rotational resonances spanned by the laser pulse. In eqn. (12) we noted M\Mg\Mi is conserved throughout because linearly polarized –elds are considered and i M couple diÜerent total that that neither the Green operator G nor the molecular Hamiltonian H angular momentum states.1 In the experiments considered here the initial state is a thermal distribution of rotational levels and hence eqn.(12) needs to be Boltzmann averaged (13) p13 S \o p13 S o eid1 S 3s\ ; nJg p13 S (JgM) Jg M where ) JgJM d (1) sin(d [df (3) JgJM d f J(3) g JM d (1) JgJM d C n are thermal weight factors. Finally the phase shift in channel S is given as Jg 13 S \[G; tan d ; f J [d(3) ) Jg JiM d nJg Jg M (1) (3) ]; ( f JgJMi r f JgJMi d sin(d(1) Jg JiM r ) Jg JiM r sin(d(1) [d(3) Jg JiM d Ji (1) ]f Jg JiM d f Jg JiM r (3) Jg JiM r sin(d(1) [d(3) Jg JiM r (1) ]f Jg JiM r f Jg JiM r (3) ) JgJM d cos(d(1) [d(3) JgJM d ))DH C (1) ; f Jg JiM d f Jg JiM d (3) J ]G; nJg Jg M ) Jg JiM d cos(d(1) ]d(3) Jg JiM r (1) ]; ( f Jg JiM r f Jg JiM d (3) [d(3) cos(d(1) Jg JiM d Ji (1) ]f Jg JiM d f Jg JiM r (3) (14) (1) [f Jg JiM r f Jg JiM r (3) cos(d(1) [d(3) Jg JiM r Jg JiM r Jg JiM r )) )DH~1.Eqn. (14) is general but not straightforward to visualize as a function of the photon energy. In order to obtain a more physically transparent expression for part of relevance for interpretation of the experimental results below. First we assume that the potential PHM P Faraday Discuss. 1999 113 61»76 d13 S we consider a speci–c case of gives rise to elastic scattering only. In that case SQRo EnSJMXT in eqn. (8) can be 65 written as a product of a single electronic state SQo nT and a nuclear function,1 (15) SRå RoESJMT\eidJ S SRo ESJTSRå oJMT where SRo ESJT is real and SRå oJMT is a spherical harmonic noting that in the case of elastic scattering the partial wave phases are coordinate independent.To simplify the discussion that follows we set X\0 in eqn. (15) for a & scattering state and because a single scattering potential energy curve is considered we omitted the index n. Because of the coordinate independence of the partial wave phases the direct phases cancel out upon integration over scattering angles in eqn. (3).1 Similarly we write the nuclear part of the initial state as (16) sol;SRo ng JgTSRå o JgMT. Next we assume that the pulse spans a single vibronic resonance ni having multiple rotational components. Hence (17) QGQ\; o ni JiMT(E[Eni Ji[Dni Ji[iCni Ji /2)~1Sni JiMo Ji where we expand Q as QH o ni JiMT Q\;Ji Mo ni JiMTSni JiMo and assume Xi\0.Eni Ji is the eigenvalue of MQ corrresponding to the eigenstate (18) SRå Ro ni JiMT\SRo ni JiTSRå o JiMT are respectively the resonance width and Dni Ji and Cni Ji (19) Cni Ji\2nSni JiMoHM d(E[PHM P)HM o ni JiMT i Ji oHM o ESJiT o2 \2n ; o Sn S and resonance shift Dni Ji\Sni JiMoHMPv(E[PHMP)~1HM o ni JiMT (20) P dE@ E[E@ o Sni Ji oHM oE@SJiT o2 \; Pv S P being the principle value. vIn order to perform the M-summation in eqn. (14) we proceed by expressing the partial wave matrix elements in eqns. (10) and (11) as products of a geometric part an integral over the Euler angles and a dynamical part an integral over the internal variables that is independent of M (21) Sng JgMoD1 (1) oESJMT\T (1)(ng Jg o ESJ)W (1)(JgMo J) and (22) T (3)(ng Jg o J1 J2 o ESJ)W (3)(JgMo J1 J2 o J) Sng JgMoD1 (3) oESJMT\ ; J1 J2 where (23) T (1)(ng Jg o ESJ)\Sng Jg o k o ESJT (24) T (3)(ng Jg o J1 J2o ESJ)\ ; (E n1n2 Sng Jg o k o n1 J1TSn1J1o k o n2 J2TSn2 J2o k o ESJT ng Jg]2u1[En2 J2 )(Eng Jg]u1[En1J1 ) u is the frequency of the 3-photon –eld [g] i W (1)\SJgMo cos h oJMT (25) \([1)MJå g Jå AJ 0 g 1 0 J 0BA[M Jg 1 0 M J B Faraday Discuss.1999 113 61»76 66 and W (3)\SJgMo cos h o J1MTSJ1Mo cos h o J2MTSJ2Mo cos h oJMT \([1)MJå g Jå 1 2 Jå 2 2 Jå AJ 0 g 1 0 J 0 1BA[ J M g 1 0 M J1B (26) 1 0 M J2BAJ2 1 J 0BA J2 1 M J B. 0 [M 0 0 ]AJ1 J BA J 1 2 0 0 0 [M 1 In eqns.(23)»(26) k(R) is the (parallel) transition dipole function h is the polar Euler angle Lå \J2L ]1 J and J are rotational quantum numbers of the one- and two-photon intermediate levels and and n are the corresponding vibronic indices. n1 2 2 1 Similarly Sng JgMg oD1 (1)FQGQHM oESJMT\GT b(1)(ng Jg o ni Ji)W (1)(JgMo Ji) C P dE@ E[E@ T (1)(ng Jg oE@S@Ji)W (1)(JgMo Ji)SE@S@Ji oHM o ni JiT ]; Pv S{ ]ipT (1)(ng Jg o ES@Ji)W (1)(JgMo Ji)SES@Ji oHM o ni JiTDHSn * i E Ji oHM o ESJiT (27) ni Ji[iCni Ji where T b(1) is an integral over the body-–xed variables a bound»bound analogue of T (1) and (28) *Eni Ji\E[Eni Ji[Dni Ji 1 is the detuning of the photon energy from the (shifted) resonance position. An analogous expression to eqn.(27) holds for the three-photon resonant element with T (1) and W (1) replaced by T (3) and W (3) and the complete expression summed over J and J2 . With eqns. (25)»(27) the M-dependent terms in eqn. (14) can be analytically summed over.31 J dependence of T (3) allows the J1 J2 sum in eqn. (22) to be carried out Neglect of the J and 1 2 analytically as well. This assumption amounts to neglecting the minor dependence of the body- –xed intermediate wavefunctions and their energies on rotations and is a standard approximation in studies of multiphoton process.34 Finally substituting eqns. (10) (11) and (21)»(27) into eqn. (14) and con–ning our attention to a single arrangement channel we obtain (29) tan d 2 ; (qJg Ji (1) [qJg Ji (3) )(eJg Ji 2 ]1)~1pJg Ji Jg Ji (qJg Ji (1) ]qJg Ji (3) )]qJg Ji (1) qJg Ji (3) ](eJg Ji 2 ]1)~1pJg Ji 13\ 1] ; [3[e Jg Ji Jg Ji where eJg Ji is Fanoœs reduced energy variable,35 (30) eJg Ji\2(E[EJi[DJi )/CJi E\EJg]3u1\EJg]u3 resolved).We de–ne by and in order to simplify the notation we omit the vibrational indices (which are experimentally qJg Ji (j) generalized j-photon asymmetry parameters analogous to the asymmetry parameter of ref. 35 qJ ( j g) \ Ji pSESJ Sng Jg oD1 (j) oUni Ji T i oHM o ni JiTSng Jg oD1 (j) o ESJiT T (31) b ( j)(ng Jg o ni Ji)]Pv E[E@ T (j)(ng Jg) oE@SJi)SE@SJi oHM o ni JiT P dE@ \ pSESJi oHM o ni JiTT (j)(ng Jg o ESJi) 67 Faraday Discuss. 1999 113 61»76 being the analogue of Fanoœs ììmodi–edœœ (through interaction with the continuum) wave- Uni Ji function (32) Uni Ji\o ni JiT]Pv PE d [ E@ E@ SE@SJi oHM o ni JiT oE@SJiT.In eqn. (29) we denoted by pJg Ji the ratio (33) pJg Ji\ n ; J g n tJg Ji (1) tJg Ji (3) Jg{ tJg{ J (1) tJg{ J (3) (34) tJg J (j) \T (j)(Jg o ESJ)J(2J Jg{ g J ]1)(2J]1) AJ 0 g 1 0 J 0B2 . 2 Neglecting the dependence of T (j) on J and J an approximation equivalent to neglect of the J1 g J dependence of T (3) and using the orthogonality properties of the 3-j symbols in eqn. (33) we –nd B2 (35) Jg (2Jg]1)(2Ji]1)AJ 0 g 1 0 J 0 i . n pJg Ji\ ; Jå g @2nJg{ Jg{ We note that the numerator of eqn. (35) is the line-strength factor of the spectroscopic transition.36 The above results extend to the case of nonzero X in either (or all) electronic state(s).31 Although the derivation is considerably more complicated in the general case the end result diÜers essentially only by replacement of the 3-j symbols in the de–nition of p by Jg Ji 1 X J X iB. Because o n g [X g[X g are at most weakly energy-dependent eqn. (29) describes a shifted Lorentzian g JgT it is readily seen to reduce to (36) i A J qJ ( j g) Ji function of energy; in the limit of a single initial state tan d13 S \ [e[12(q(1)]q(3))]2][4[14(q(1)[q(3))2] . 2(q(1)[q(3)) We –nd therefore that within a single and fairly standard approximation d13 S takes a very simple form which can be readily modeled and compared with measurements without knowledge of the Hamiltonian.The generalized channel-dependent Fano parameters q(j) serve as physically meaningful parameters in this approach containing all the system-dependent information. To help visualize these results we evaluate eqn. (29) as a function of excitation energy for a Boltzmann distribution of HI molecules at various temperatures. Representative plots of d13 are (l[l0)/B shown in Fig. 3 as a function of where l is the one photon excitation energy l is the 0 origin of the transition and B is the rotational constant of the molecule (assumed equal for the ground and excited electronic states). The width of the resonance C is assumed to be independent of J and is written in units of 2B. Fig. 3 displays representative calculations of &^& (upper panels) and %^& (lower panels) transitions.At T \0 K the phase shift is a simple (shifted) Lorentzian whereas for higher temperatures it mimics the rotational spectrum. Direct comparison with the measured values of *d (vide infra) is not possible because the angular momentum scheme for the resonance states that we studied correspond to Hundœs case (e) (or a hybrid of cases (c) and (e).37 Nevertheless the qualitative similarity within a single rotational branch is apparent for CB2B. 1 3 Experimental methods Details of the experiment have been presented before,12 and only an outline will be given here. A commercial excimer-pumped dye laser was used to generate a UV beam of frequency u with a Faraday Discuss.1999 113 61»76 68 Fig. 3 Model calculations of the phase shift eqn. (29) calculated using the rotational constant of HI assuming a Hundœs case (a) coupling scheme and treating the asymmetry ratios [eqn. (31)] as parameters. See the text for details. Panels (a) and (b) are for X\0^Xg\0 transitions and panels (c) and (d) are for X\ 1^X tribution of rotational population is assumed with temperatures of 0 50 and 100 K. In all panels the asym- g\0 transitions. The columns correspond to C/2B\0.1 (left) and C/2B\1 (right). A Boltzmann dismetry parameters q(1)]q(3)\5 and q(1)[q(3)\1 were used. (u typical pulse energy of 5.5 mJ. The third harmonic VUV beam 3\3u1) was generated by focusing the UV beam with an S1-UV lens ( f\7.6 cm) into a cell containing 1»8 Torr of Xe.The relative phase of the two beams was controlled by passing them through a cell containing a variable pressure of H gas.38 The H pressure was monitored with a capacitance manometer. A 2 2 pair of dielectrically coated concave mirrors ( f\20.3 cm) was used to focus the beams to a common spot in a vacuum chamber having a pressure of approximately 4]10~6 Torr during an experimental run. A mixture of HI and H2S was injected into the chamber by a 10 Hz pulsed nozzle. The molecular beam and laser beams crossed at right angles between the repeller and extractor electrodes of a Wiley»McLaren time-of-—ight mass spectrometer spaced 1.9 cm apart. Typical electrode voltages were 3.6 and 2.0 kV respectively. The ions traveled through a 1 m long –eld-free —ight tube at the end of which was mounted a dual microchannel plate biased at 2 kV.Signals corresponding to the mass peaks of HI` I` and H2S` were captured and averaged by a gated multichannel boxcar and stored in a laboratory computer. In a typical experimental run the three ion signals and the H pressure were continuously 2 monitored as the H gas pressure was slowly varied from 1 to 10 Torr over a period of about 10 2 min. The Xe pressure was adjusted so that the signal from the combined UV and VUV beams was approximately double that of the UV beam alone. In all cases a minimum of –ve oscillations of 69 Faraday Discuss. 1999 113 61»76 Fig. 4 Resonance-enhanced multiphoton ionization spectrum of HI showing rotational structure of the b 3%2 ^X1&` transition.The lower panel shows the parent ion and the upper panel shows the atomic iodine fragment produced by predissociation. The arrow indicates the –eld-free three-photon ionization threshold of HI. the modulated ion signals were recorded. The modulated signals were later –tted by least squares to the functional form a]b cos((x[c)/d) where x is the H pressure. The phase lag between any 2 pair of channels is given by *d\(c[c@)/d. In a separate experiment we recorded the one- and three-photon photoionization and photoall in the vicinity of the dissociation spectra of HI and the photoionization spectrum of H2S 5d(p d) resonance of HI. The three-photon spectra were all recorded under the same experimental conditions that were employed in the control experiments but with no Xe in the tripling cell.A 1]3 photon photodissociation spectrum of HI was recorded using the same optical con–guration but with an excess of Xe in the tripling cell to enhance the VUV intensity. In this measurement the fundamental UV radiation was used to ionize the neutral iodine fragment. The one-photon photoionization spectra of HI and H were recorded using an S1-UV ( f\10.2 cm) 2S lens to focus the UV beam into a tripling cell mounted onto a side port of the vacuum chamber. VUV\7.6 ( f UV\8.9 An MgF lens f cm cm) mounted at the exit of the third harmonic generation 2 cell focused the VUV beam to the center of the reaction chamber. The diÜerent focal points of the UV and VUV beams guaranteed that ions produced by the UV beam were not detected.None of the reported spectra were corrected for variations in laser intensity. 2 ^X1&` transition. The lower 4 Experimental results HI. The rotational structure is produced by the two-photon Fig. 4 shows a scan of the UV resonance-enhanced multiphoton ionization (REMPI) spectrum of b 3% Faraday Discuss. 1999 113 61»76 70 dissociation. The plots are averages of typically –ve scans. The arrow indicates the –eld-free three-photon Fig. 5 Three-photon UV spectra of (a) H2S photoionization (b) HI photoionization and (c) HI photoionization threshold of H2S. panel shows the parent ion while the upper panel displays the I` signal produced from the neutral iodine atoms generated by predissociation of the intermediate b 3% state. The strong 2 dependence of the ratio of photoionization to predissociation on rotational angular momentum of HI is an interesting subject in its own right which will be explored in a future publication.and HI [panels (a) and (b)] is clearly Fig. 5 shows a more detailed scan of the photoionization of H2S and the photodissociation of HI [panel (c)]. The photoionization threshold of H2S visible in Fig. 5(a). The shape of the threshold region is determined by –eld ionization of high Rydberg states of the molecule between the repeller and extractor electrodes and by rotational broadening. The 2u rotational structure of Fig. 4 is also evident in Figs. 5(b) and 5(c). There is no 1 evidence of three-photon resonances in any of the spectra of Fig. 5. Fig. 6 shows the one-photon photoionization spectra of H2S` and HI` [panels (a) and (b)] and the 1]3 photodissociation spectrum of HI [panel (c)].The rotational structure visible in Fig. 6(c) is part of the 2]1 REMPI spectrum of the b 3% state of HI generated by the UV beam which 2 photoionizes both the iodine fragment and the parent molecule. The one-photon 5d(p d) resonance is clearly visible. Typical phase modulation curves for H2S` HI` and I` taken at a UV wavelength of 356.08 nm are shown in Fig. 7. The phase lags at this wavelength are *d(HI` I)\185.7^2.8° and *d(HI` H2S`)\83.1^3.0°. The wavelength dependence of the phase lags is plotted in Fig. 8 where it is compared with the one-photon ionization spectrum of HI. The points are averages of typically 10 scans. The fall-oÜ of the third harmonic generation efficiency of Xe prevented us from performing experiments at longer wavelengths.As expected both *d(HI` I) and *d(HI` H2S`) Faraday Discuss. 1999 113 61»76 71 Fig. 6 (a) One-photon VUV spectrum of H2S photoionization (b) one-photon VUV spectrum HI photoionization and (c) 1]3 photon spectrum of HI photodissociation. The plots are averages of typically –ve scans. display extrema in the vicinity of the 5d resonance. What is surprising and in contrast to our earlier observations for the 5sp resonance (see Fig. 2) is that the phase lags reach maxima near the 5d(p d) resonance. The signi–cance of this –nding is discussed in the following section. 5 Discussion In order to obtain a global understanding of the similarities and diÜerences between the 5s and 5d phase lags it is useful to think of the control mechanism in terms of a four-slit Youngœs experiment.The four slits shown schematically in Fig. 1 correspond to one-photon direct one-photon resonance-mediated three-photon direct and three-photon resonance-mediated (1d 1r 3d 3r) pathways. The overall transition probability for channel S (ionization or dissociation) is given by33 p (3) (3) (3) (3) (1) (1) (1) (1) S\Pdk � o f S d exp[idS d]]f S r exp[idS r]]exp(i/)M f S d exp[idS d]]f S r exp[idS r]N o2 (37) S d (j) f S r (j) are the amplitudes for the j-photon direct and resonance-mediated transitions and f dS d d( (j) and S, j)d are the respective phases. After integration over scattering angles four cross (PHMP) in both the 5s and 5d regions is not purely elastic.Similarly our obserwhere and terms (1d3d 1r3r 1d3r and 1r3d) contribute to the interference term p13 S as shown in eqn. (12). DiÜerent types of interference eÜects may be observed depending on the relative magnitudes of the four terms. For example far from resonance only the 1d3d term contributes. Our observations of nonzero essentially —at values of *d(HI` I) oÜ-resonance provides evidence that the scattering Hamiltonian vation that *d(HI` H2S`) vanishes oÜ-resonance in both regions suggests that the ionization continuum for both molecules is purely elastic in the regime probed. Together the two sets of Faraday Discuss. 1999 113 61»76 72 Fig. 7 Modulation curves for the (a) H2S` (b) HI` and (c) I` signals recorded at 356.08 nm.The heavy curves are least-squares –ts of a sinusoidal function. observations imply that the Hamiltonian for predissociation of HI is inelastic. In other words it is the inelastic predissociation channel that is responsible for the nonzero values of *d(HI` I) oÜresonance. Near resonance the four terms arising from eqn. (37) oduce diverse interference eÜects. In the case of an isolated resonance if both direct and resonance-mediated paths are available (i.e. all four slits are active) and the direct route carries a phase then the absolute value of the phase lag falls to a minimum at the resonance position. This phenomenon occurs because on resonance the 1r3r term dominates and neglecting the direct routes the interference term reduces to eqn. (5).1 In the limit where the direct routes may be neglected the Breit»Wigner phases cancel out.This is the scenario for dissociation of HI near the 5sp resonance. In contrast for the ionization of HI and H2S (M P) is elastic and the molecular phase accordingly vanishes. PH the scattering Hamiltonian Proper description of the phase in that case requires that the (real) direct term be retained at the resonance position producing as shown in Section 2 a phase shift that is due solely to the resonance. Accordingly o *d(HI` H2S`) o reaches a maximum at the resonance energy. For a single rotational transition d13 S is a Lorentzian function of the reduced energy [eqn. (36)]. Experimentally we –nd that the phase lag is broadened by rotational congestion as given by eqn. (29) and illustrated by Fig.3. For the 5d resonance a somewhat diÜerent situation prevails. In this case the three-photon resonance is not observable under our experimental conditions implying that only three slits contribute to the inferference. The absence of the 1r3r term implies that on resonance the directresonant interferences dominate. Consequently both o *d(HI` I)o and o *d(HI` H2S`) o have maxima near resonance. The sign of the phase shift depends on the signs and relative magnitudes of q(1) and q(3) as seen in eqn. (36). Because ionization of H2S has neither a molecular nor a resonance phase in the regions studied the measured values of *d(HI` H are derived entirely 2S) Faraday Discuss. 1999 113 61»76 73 Fig. 8 Phase lags (upper panel) and VUV photoionization spectrum of HI (lower panel) in the vicinity of the 5d(p d) resonance.from the resonances of HI. For HI *d(HI` I) has a maximum value on resonance because the q(j) asymmetry parameters diÜer for the autoionization and predissociation channels. Future double resonance experiments designed to resolve the rotational structure should provide values of q(3) thereby testing this interpretation of the phase lag. 2S`) suggests ionization process carries no phase in the studied energy regime. They do not In the region of the 5d(p d) resonance the similarity of *d(HI` I) and *d(HI` H that the H2S however conclusively rule out the possibility that either or both rotational autoionizaton39 and rotational predissociation contribute to the observed phase lag.This question may be addressed by reducing the energy spacing between data points to resolve the rotational structure. More generally it is important to develop a physically transparent expression for the energydependence of d13 S in the case of coupled resonances interacting with continua which themselves are nonadiabatically coupled. By analogy to the application of the formalism of Section 2 and ref. 1 to the cases of an isolated resonance and an elastic continuum discussed above such an expression combined with measurements may elucidate the coupling mechanism in the general case. This work will be reported elsewhere.31 6 Conclusions Measurements of the phase lag between the ionization and dissociation channels of HI and between the ionization of HI and H in the vicinity of the 5d(p d) resonance of HI provide a 2S much needed test of our understanding of the roles played by diÜerent types of phases in the coherent control of a chemical reaction.As we previously found for the 5sp resonance of HI a Faraday Discuss. 1999 113 61»76 74 PHM P which is likely to arise from nonadiabatic coupling in the scatslowly varying phase lag *d(HI` I) far from resonance is produced by the molecular phase for a direct transition to the dissociation continuum. Together with the theoretical analyses of ref. 1 and Section 2 above the observed phase lag provides direct experimental evidence of an inelastic scattering Hamiltonian tering manifold. The vanishing of *d(HI` H2S`) for ionization of the gas mixture far from resonance suggests that the ionization continua are purely elastic in the regime probed.Near resonance we found that both types of phase lags mimic the rotational envelope of the 5d(p d) resonance. The surprising observation of a maximum in the absolute value of *d(HI` I) is attributed to resonance phase. The observation of a maximum in *d(HI` H2S`) re—ects the signs of the Fano asymmetry parameters for this particular resonance. The present results illustrate two compelling reasons for performing coherent control experiments. The phase lag near the 5d resonance is the largest ever observed in a coherent control experiment and underscores the potential usefulness of this method for controlling molecular processes. The energy dependence of the phase lag provides evidence of interactions in the scattering manifold and of the interference between direct and resonant-mediated pathways to the continuum.7 Acknowledgements We wish to thank Mr. Kunihiro Suto for measuring the REMPI spectrum of the b 3% state of 2 HI. The generous support of the National Science Foundation is gratefully acknowledged. 1 References 1 T. Seideman J. Chem. Phys. 1998 108 1915. 2 J. A. Fiss L. Zhu R. J. Gordon and T. Seideman Phys. Rev. L ett. 1998 81 65. 3 R. J. Gordon and T. Seideman Acc. Chem. Res. in press. 4 P. Brumer and M. Shapiro M. Faraday Discuss. Chem. Sec. 1986 82 177. 5 R. J. Gordon and S. A. Rice Annu. Rev. Phys. Chem. 1997 48 601. 6 P. P. Feynman and A. R. Hibbs Quantum Mechanics and Path Integrals McGraw Hill New York 1965.7 P. Brumer and M. Shapiro Acc. Chem. Res. 1989 22 407. 8 M. Shapiro J. W. Hepburn and P. Brumer Chem. Phys. L ett. 1988 149 451. 9 Two types of notation are commonly used to label the diÜerent paths. A superscript ( j) denotes operators and quantities associated with the absorption of j photons such as D(j) and /(j). Alternatively subscripts m and n denote respectively the absorption of n and m photons as in eqn. (1) and in the relation m/(n)\n/(m). 10 C. Chen Y. Y. Yin and D. S. Elliott Phys. Rev. L ett. 1990 64 507. 11 S. M. Park S. Lu and R. J. Gordon J. Chem. Phys. 1991 94 8622. 12 S. Lu S. M. Park Y. Xie and R. J. Gordon J. Chem. Phys. 1992 96 6613. 13 X. Wang R. Bersohn K. Takahashi M. Kawasaki and H. L. Kim J. Chem. Phys. 1996 105 2992.14 G. Xing X. Wang X. Huang R. Bersohn and B. Futz J. Chem. Phys. 1996 104 826. 15 Y. Y. Yin C. Chen and D. S. Elliott Phys. Rev. L ett. 1992 69 2353. 16 Y. Y. Yin D. S. Elliott R. Shehadeh and E. R. Grant Chem. Phys. L ett. 1995 241 591. 17 V. D. Kleiman L. Zhu X. Li and R. J. Gordon J. Chem. Phys. 1995 102 5863. 18 V. D. Kleiman L. Zhu J. Allen and R. J. Gordon J. Chem. Phys. 1995 103 10800. 19 L. Zhu V. D. Kleiman X. Li L. Lu K. Trentelman and R. J. Gordon Science 1995 270 77. 20 L. Zhu K. Suto J. A. Fiss R. Wada T. Seideman and R. J. Gordon Phys. Rev. L ett. 1997 79 4108. 21 J. A. Fiss L. Zhu K. Suto G. He and R. J. Gordon Chem. Phys. 1998 233 335. 22 F. Wang C. Chen and D. S. Elliott Phys. Rev. L ett. 1996 77 2416. 23 A. Shnitman I. Sofer I.Golub A. Yogev M. Shapiro Z. Chen and P. Brumer Phys. Rev. L ett. 1996 76 2886. 24 R. J. Gordon J. A. Fiss L. Zhu and T. Seideman in Coherent Control in Atoms Molecules and Semiconductors ed. W. A. Poé tz and W. A. Schroeder Kluwer Dordrecht 1999. 25 J. J. Sakurai Modern Quantum Mechanics Addison-Wesley Reading 1994. 26 D(3) will be complex if for example there exists a quasibound level near the energy of one or two u photons. 27 D. J. Hart and J. W. Hepburn Chem. Phys. 1989 129 51. 28 H. Lefebvre-Brion J. Chem. Phys. 1997 106 2544. 29 J. H. D. Eland and J. Berkowitz J. Chem. Phys. 1971 67 5034. 30 H. Lefebvre-Brion A. Giusti-Suzor and G. Raseev J. Chem. Phys. 1985 83 1557. 31 T. Seideman J. Chem. Phys. submitted. 75 Faraday Discuss. 1999 113 61»76 32 For a general introduction to partitioning techniques see e.g. R. D. Levine Quantum Mechanics of Molecular Rate Processes Clarendon Press Oxford 1969. and (j) (j) dJgJ d (j) f f dJgJ r (j) 33 The partial wave amplitudes and phases and in eqn. (9) should not be JgJM d confused with the amplitudes and phases in eqn. (37). Also the phases and amplitudes in eqns. (1) and (37) JgJM r should not be confused. 34 W. M. McClain and R. A. Harris in Excited States ed. E. C. Lim. Academic New York 1977 vol. 3 pp. 1»56. 35 U. Fano Phys. Rev. 1961 124 1866. 36 R. N. Zare Angular Momentum Wiley New York 1988. 37 A. Mank M. Drescher T. Huth-Fehre N. Boé wering U. Heinzmann and H. Lefebvre-Brion J. Chem. Phys. 1991 95 1676. 38 R. J. Gordon S. Lu S. S. M. Park K. Trentelman Y. Xie L. Zhu A. Kumar and W. J. Meath J. Chem. Phys. 1993 98 9481. 39 K. Wang M.-T. Lee V. McKoy R. T. Wiedemann and M. G. White Chem. Phys. L ett. 1994 219 397. Paper 9/02403D Faraday Discuss. 1999 113 61»76 76

ISSN:1359-6640    

DOI:10.1039/a902403d

出版商:RSC    

年代:1999

数据来源: RSC

摘要:

General Discussion Prof. Levine communicated with regard to the Spiers Memorial Lecture You mentioned the Cl]HD reaction and suggested that the preferred formation of DCl is possibly due to the rotation of the DH towards the incoming Cl atom. The center of mass is nearer to the D atom so it has a shorter way to go. We1 have previously compared experimental results for the F]HD reaction with an alternative and possibly simpler point of view. The potential seen by a halogen atom approaching HD has symmetry about the geometric center of HD. This is because in the Born»Oppenheimer approximation this potential is the same for H2 D2 . HD and On the other hand the dynamics of the collision must be referenced to the center of mass of HD. This immediately implies that the cone of acceptance for reaction must be higher at the D end Fig.1. Rotation of HD can almost be counter productive precisely because as you say the H atom extends a longer arm about the center of mass. It means that when the rotation is fast (and as rotations go it is inherently fast in HD) the H atom can screen the D atom. 1 G. W. Johnston H. Kornweitz I. Schechter A. Persky B. Katz R. Bersohn and R. D. Levine J. Chem. Phys. 1991 94 2749. Prof. Stolte opened the discussion of Prof. Zareœs paper I have enjoyed very much the beautiful experiments and the elucidative insights oÜered by your paper. Is or will it be possible to extract from the interference observations between perpendicular and parallel transition dipole moments some information about their sign ? Prof.Vasyutinskii said I would like to comment on Prof. Stolteœs question concerning the possibility of measurement of the sign of the transition moment from vector correlation experiments. To my knowledge the sign of the transition moment cannot be isolated and measured separately as the transition moment phase appears in theory as part of a more general expression for the photodissociation phase amplitude. Prof. Zare responded The transition dipole moment refers to the separation of positive and negative charge during the transition which oscillates at the transition frequency. As such the transition dipole moment does not have an absolute sign in the sense that a permanent dipole moment does. Fig. 1 The potential around the geometrical center of HD is symmetric for either direction of attack.But the center of mass (c.m.) is displaced from the center of charge. Hence for a given value of the barrier the angle of attack c is larger with respect to the D atom. Also shown is the (repulsive due to the barrier) force F on the approaching F atom. In reference to the center of charge the force is symmetric at both ends. But the motion is dictated by the components of the force in reference to the center of mass. The angular anisotropy is such that the force on the D atom rotates it in the direction of the attacking atom. The –gure is adapted from Johnston et al.1 77 Faraday Discuss. 1999 113 77»106 This journal is( The Royal Society of Chemistry 1999 In a parallel transition the transition dipole moment oscillates back and forth along the bond axis (internuclear axis) of a diatomic molecule.In a perpendicular transition the transition dipole moment oscillates to and fro perpendicular to the bond axis. In a mixed transition both motions occur but with a –xed phase relation so that the oscillating charge distribution circulates in general either clockwise or counterclockwise. The experiments we have carried out in which the orientations of the photofragment angular momenta are measured provide direct information on the phase diÜerence between these two motions of the oscillation charge distribution. Dr Wrede Dr Brown Dr Orr-Ewing and Prof. Ashfold said Zare and co-authors demonstrate the value of polarisation measurements for unravelling new and detailed aspects of the photodissociation dynamics of Cl2 .We would like to point out that the more traditional methods of high resolution spectroscopy and measurements of angular distributions and branching fractions can also constitute a powerful route to determining potential energy curves their non-adiabatic couplings and thus much detailed insight into photofragmentation dynamics. This is exempli–ed by our recent ion imaging work involving the IBr molecule.1 Fig. 2 shows optimised potential energy curves of the A3%(1) B3%(0`) (diabatic) and 1%(1) states of IBr. These were obtained from RKR points calculated using the best available spectroscopic data2h4 for the bound regions of the A3%(1) and B3%(0`) states and from deconvolution of the absorption spectrum in the Franck»Condon region.This deconvolution is guided by the results of ion imaging experiments which detect ground state I atom fragments and both the (2P ground and spin»orbit excited 2P 3@2) (1@2 henceforth Br*) bromine atom products formed at 18 diÜerent photolysis wavelengths in the range 600[j[420 nm. Analysis of these images can yield total photofragment angular distributions (summed over all velocities) which we then decompose into fractional parallel (b\2) and perpendicular (b\[1) contributions to the total absorption. The former we associate with the B3%(0`)[X1&`(0`) transition (see Fig. 3). This procedure is legitimate provided that (i) the axial recoil approximation is valid and (ii) neither the I nor Br/Br* fragments are signi–cantly aligned.Evidence that such is the case is provided by the observation of identical b-parameters for both fragments from the I]Br and I]Br* product channels. Having so determined the B»X absorption the pro–les of the A»X and 1%(1)»X can be optimised by comparison of the results of wavepacket propagation on the relevant excited state curves with the residual perpendicular absorption as shown in Fig. 3. Current and future work will involve further wavepacket propagation on the fully-coupled potential energy curves to allow comparison of the wavelength-dependent calculated and measured branching fractions and product channel anisotropy parameters. Fig. 2 IBr potential curves. X1&`(0`) modi–ed Morse potential adapted from ref. 5. A3%(1) extended Rydberg potential –tted to RKR points calculated from spectroscopic constants.4 B3%(0`) (diabatic) extended Rydberg potential –tted to RKR points2,3 and to match the excitation function of the parallel component of the total absorption.1%(1) Biexponential –tted to corresponding absorption. Y3%(0`) (diabatic) Biexponential (preliminary). The Franck»Condon region for excitation from the ground state (vO3) is indicated. Faraday Discuss. 1999 113 77»106 78 Fig. 3 Deconvolution of the absorption spectrum as described in the text. In order to reproduce the absorption spectrum a weighted sum over the wavepacket results for v\0 . . . 3 is necessary to re—ect the vibrational distribution of the IBr molecules at room temperature. 1 E. Wrede A. Brown A. J. Orr-Ewing and M.N. R. Ashfold in preparation. 2 M. S. Child Mol. Phys. 1976 32 1495; personal communications. 3 M. A. A. Clyne and M. C. Heaven J. Chem. Soc. Faraday T rans. 2 1980 76 49. 4 D. R. T. Appadoo P. F. Bernath and R. J. LeRoy Can. J. Phys. 1994 72 1265. 5 B. Nelander V. Sablinskas M. Dulick V. Braun and P. F. Bernath Mol. Phys. 1998 93 137. Prof. Zare responded I agree that much useful information on nonadiabatic transitions can be obtained by combined measurements of the photofragment anisotropy and the branching ratio into diÜerent spin»orbit states of the separated photofragments. I would like to stress however that the measurement of the orientation of the photofragments is particularly sensitive to the possible existence of nonadiabatic transitions. This sensitivity arises from the nature of the process which involves the interference of two or more states of diÜerent symmetry that converge asymptotically to the same –nal quantum states of the separated photofragments.As such the degree of orientation involves a cross term between the transition amplitudes to the states of diÜerent symmetry. Then just as in heterodyne spectroscopy the presence of a transition having a small amplitude is made apparent by its product with a transition having a large amplitude. Let me illustrate this situation by a simple calculation. Suppose that 99.75% of the transition intensity is for a parallel transition with b\2 and 0.25% of the transition intensity is for a perpendicular transition with b\[1. Thus the anisotropy factor is b\1.99.Then the expected time-of-—ight pro–le for this mixed transition shown in Fig. 4A can hardly be distinguished from that expected for a pure parallel transition (b\2.00). Hence the small degree of mixing cannot be discerned through measurement of the spatial anisotropy of the photofragments. The factor 2[(1]b)(1[b/2)]1@2\0.24 makes the photofragment orientation much more sensitive to this mixing as can be seen by examining Fig. 4B which shows the time-of-—ight pro–les detected using left- and right-circularly polarized radiation with the linearly polarized photolysis beam having its electric –eld pointing 45° to the time-of-—ight axis. B@(3% B(3% Prof. Stolte§ commented Interesting curve crossing and curve following interferences are also 0 `) occurring between the and the B@(0`) electronically excited potential curves.1 Schematically Fig.5 shows these curves (in cm~1) with respect to the ground state. Transition to the 0 `) is optically allowed from the X(1&) ground state and the possibility of a subsequent § Also A. E. Wiskerke R. Mooyman and E. A. Volkers Vrije Universiteit Amsterdam and M. J. J. Vrakking FOM Institute The Netherlands. 79 Faraday Discuss. 1999 113 77»106 Fig. 4 Calculated time-of-—ight pro–les (A) a pure transition with the spatial anisotropy b\2 and a mixed transition with the spatial anisotropy b\1.99 in which the photofragments are detected with linearly polarized radiation having its electric –eld parallel to the time-of-—ight axis ; (B) a mixed transition with the spatial anisotropy b\1.99 using left- and right-circularly polarized probe radiation with the photolysis polarization being linearly polarized at 45° to the time-of-—ight axis.transfer to the outgoing part of the B@(0`) curve leads to the formation of the I and Br atomic B(3% ground state fragments. The predissociative behaviour of the 0 `) state of IBr has been studied by measuring its absorption spectrum in a cold molecular beam by REMPI detection of isotopically selected atomic photofragments. Excitation to discrete vibrational states that are embedded in a predissociation continuum give rise to asymmetric Fano shapes. As can be seen in Fig. 5 the linewidth C of the vibrational levels of the adiabatic well residing between the B(3%0 `) and the B(0`) potential curves and of the diabatic well of the B(3%0 `) potential itself nearly coincide which leads to the slowest decay rate is shown to posses at least about a factor 10 slower decay rate than that of maximum C occurring near v@\25.Our –ndings in the frequency domain corroborate the observations of the femtosecond pump»probe experiments and provide the input data that can be used to simulate the outcome in the time domain of these ultrafast observations.2 1 M. S. Child Mol. Phys. 1976 32 1495. 2 M. Shapiro M. J. J. Vrakking and A. Stolow J. Chem. Phys. 1999 110 2465. Dr Wrede Dr Brown Dr Orr-Ewing and Prof. Ashfold communicated The curve crossing of the B 3%(0`) and Y3%(0`) diabatic potentials (leading to the B3%(0`) and B@(0`) adiabatic potential curves) is indeed a very interesting feature of the IBr molecule.The existence of vibrational levels in the predissociative continuum of the B 3%(0`) and B@(0`) potential wells reported by Prof. Stolte should lead to a signi–cant change in the anisotropy of the photolysis process Fig. 5 Measured spectra of IBr showing oscillating line widths together with the diabatic potential curve B(3%0 `) and B(0`) showing the crossing at about 17 000 cm~1 responsible for the detected photofragment Br. Faraday Discuss. 1999 113 77»106 80 depending on whether such a resonant level or the unstructured continuum is excited. A corresponding experimental and theoretical study is under way in our laboratory. The combination of the spectral data presented by Prof. Stolte and the ion imaging results should permit a very detailed description of the B and Y state potentials and their curve crossing as well as a re–ned determination of the corresponding coupling.Prof. Dantus said to Prof. Zare (1) The method presented could be one of the most sensitive V and VC . The curve- spectroscopic tools for mapping repulsive potential energy surfaces here B crossing probability is usually determined using Landau»Zenerœs formula having a coupling matrix element between the two surfaces VBC . Have you considered the possibility of studying the energy dependence of VBC ? This parameter is usually assumed independent of kinetic energy based on a Born»Oppenheimer approximation. It may be interesting to explore changes on VBC as the potential energy curves of a molecular system are modi–ed by a static electric –eld.(2) Have you considered applications and implications of phase measurements as presented here using femtosecond laser pulses ? For this consideration it may be easier to think of two bound states. Consider the following experiment on halogen molecules which have families of ion pair states that are easy to reach by one or two photon excitation. The experiment would consist of exciting a coherent superposition of states that contains vibrations from two types of electronic states one having X\0 and the other X\1. The resulting wavepacket would show alternating anisotropy because of the parallel and perpendicular transitions that formed it provided that probing does not discriminate between the two states for example Coulomb explosion.It would be important to balance the total excitation energy the diÜerence between T e of the electronic states and the energy and temporal width of the laser pulses. The ideal combination would have a few phase cycles in the time it takes for one half of a vibrational period. Prof. Zare responded I welcome the suggestion that nonadiabatic transitions in Cl or other 2 molecules could be studied with advantage by varying the energy released into the recoiling photofragments or by application of some external –eld. In the present experiment we do vary the recoil energy by changing the photolysis wavelength but this eÜect also changes the asymptotic phase diÜerence between the wavefunctions belonging to the two diÜerent symmetry states.Zee Hwan Kim has looked into the question of what can be learned from femtosecond pump» probe studies that are the time-dependent analogue of our experiment. Here is what he –nds the femtosecond pump beam prepares localized wavepackets located on the two or more repulsive potential energy curves in a way that is sensitive to the duration of the pulse and phases of each Fourier component. In analogy with our measurement with a nanosecond laser beam in which the measured orientation is proportional to the product of two transition amplitudes multiplied by the asymptotic phase diÜerence we may de–ne the corresponding observable as the normalized cross-correlation of the two wavepackets (1) X(t)\ImC[SW SWA(t) oWM(t)T A(t) oWA(t)TSWM(t) oWM(t)T]1@2D where WA(t) and WM(t) are wavepackets on the repulsive excited states associated with parallel and perpendicular transitions respectively.In Fig. 6A we show the propagation of wavepackets on two model potentials. Excitation with a 5 fs pulse prepares wavepackets sharply localized in coordinate space at t\0. As the wavepackets evolve in time the cross correlation function X(t) oscillates in time and this oscillation is a sensitive function of the time evolution of the wavepackets. Each wavepacket experiences a diÜerent potential energy curve and hence the wavepackets begin to separate from each other leading to the fast decay of the amplitude of oscillation even with the spontaneous dispersion of the wavepackets. Excitation with a longer pulse (100 fs) prepares broader wavepackets that overlap more strongly in coordinate space hence in time space shows a larger amplitude of oscillation of X(t) as time evolves.(See Fig. 6B). Experimentally to probe the coherence between the wavepackets that are prepared the probe process should be able to preserve/detect the coherence of the wavepackets. Hence the probe 81 Faraday Discuss. 1999 113 77»106 Fig. 6 (A) Propagation of wavepackets with mass 10 u on two model potentials. Excitation with a q\5 fs pulse prepares sharply localized wavepackets that separate from each other in coordinate space as time evolves. However excitation with a q\100 fs pulse prepares broader wavepackets and there is appreciable overlap of the wavepackets. (B) Normalized cross correlation X(t) of the two wavepackets excited with q\5 fs and q\100 fs excitation pulses respectively.process should not distinguish between the wavepackets on the two states. This condition may be realized by exciting the wavepackets to a common resonant state using either REMPI or LIF as a probe provided that the Franck»Condon overlap is sufficiently favorable. Comparison of the diÜerent behaviors for a 5 fs and a 100 fs photolysis pulse shows the sensitivity of the real-time orientation measurement to the temporal characteristics of the laser source as well as the dissociation dynamics. Prof. Baugh said It is now clear that frequency domain polarization experiments can determine the phase-shift of the scattered wavefunction on excited state potentials.Since the derivative of the phase-shift with respect to energy gives directly the scattering delay-time (or reaction-time) on a single excited potential as a function of energy it should also be possible to determine ultra-fast time-domain information from these experiments. In your experiments scattering appears to occur on at least two excited potential curves and the phase-shift diÜerence between the two potentials was measured as a function of photolysis laser energy. Can this information be used to determine the diÜerence in reaction-times on these two surfaces ? Also while frequency and time domain experiments are equivalent it appears that these frequency domain studies might be more practical in some cases for these very fast processes than time domain experiments in the same way as rotationally coherent spectroscopy was for large molecules.Indeed would not the reaction times derived from your experiments be less sensitive to laser characteristics i.e. bandwidth and pulsewidth when performed with state-of-the-art laser systems? Prof. Zare responded Prof. Baugh is correct in suggesting that these time-independent measurements as a function of photolysis energy can allow us to infer information about the time evolution of the system. We are looking into this question in more detail. We believe that with some assumptions it should be possible to invert the phase shift diÜerences as a function of photolysis energy that we measure into diÜerences in the potential energy curves. Once the potential energy curves are known then the time evolution can also be calculated.Whether this method proves to be more convenient or more robust than real-time measurements remains to be demonstrated. We can state however that our procedure is quite straightforward. (please see my previous reply to Prof. Dantus.) Dr Orr-Ewing commented The model proposed by Kim et al.1 for the orientation of the atoms from C1% (1) u(0`) state. Such non-adiabatic transitions from an X\1 to an X\0 state u Cl(2P1@2) Cl2 photodissociation involves non-adiabatic transitions from the state to the require rotational coupling (which is proposed to occur at long range) and would suggest a rotational temperature dependence to the measured eÜects. Is such a temperature dependence anticipated or is it possible that the non-adiabatic transitions are instead to an X\1 state correlating to Cl(2P B3% 3@2)]Cl(2P1@2) ? Faraday Discuss.1999 113 77»106 82 We previously proposed this latter mechanism to account for the variation of anisotropy parameters (b) for the process Br2]hl]Br(2P3@2)]Br(2P1@2) as measured by photofragment ion imaging.2 1 Z. H. Kim A. J. Alexander S. A. Kandel T. P. Rakitzis and R. N. Zare Faraday Discuss. 1999 113 27. 2 M. J. Cooper E. Wrede A. J. Orr-Ewing and M. N. R. Ashfold J. Chem. Soc. Faraday T rans. 1998 94 2901. Dr A. Alexander and Prof. Zareî communicated in response Yes rotational coupling is needed to cause the X\1 state to mix with the X\0 state and it follows that some sensitivity should exist to the rotational state distribution of the parent molecules.We readily admit that the treatment we presented was a very crude one in which this fact was ignored and the coupling was treated as centered on a crossing point with an arbitrary adjustable Gaussian functional form. Since our paper was written Prof. S. Yabushita Keio University has improved his calculations of the Cl potential energy curves including the eÜects of nonadiabatic interactions. Here are the 2 –ndings. He recently carried out detailed ab initio calculations of Cl2 including the radial coupling matrix elements ij\TWi Kd d R WjU g 3& C1% between C1% (1) and other X\1 states that produce Cl]Cl*. He found that the coupling u between u `(1) is dominant and has a maximum value at 6.16 a0 .His calculation (1) and u based on a radial coupling mechanism for Cl* reproduces quite well the experimental spin»orbit state branching ratio. Using the Rosen»Zener»Demkov semiclassical expression for the radial C1% (1) and the 3& derivative coupling between the u `(1) states he could reproduce our orienta- u tion moment data of Cl* with reasonable agreement; see Fig. 7. The approximations used in this semiclassical calculation are that the nonadiabatic transition occurs only at the position of maximum amplitude of the radial derivative matrix element and that the only nonadiabatic tran- C1% (1) and 3& sition is between the u `(1) states. Also he pointed out that the simulated orienta- u tion of Cl* is extremely sensitive to the location of the maximum of the radial matrix element.This calculation uses no adjustable parameters. Therefore it is likely that the radial derivative coupling between the X\1 states is principally responsible for the nonadiabatic interaction that yields Cl* photofragments. derivative coupling between the u Fig. 7 Observed and calculated orientation moment of the Cl* photofragment as a function of photolysis wavelength. The calculation by S. Yabushita (personal communication) is based on the nonadiabatic radial C1% (1) and 3&u `(1) states. î Also S. Yabushita Keio University Yokohama Japan and Z. H. Kim Stanford University USA. 83 Faraday Discuss. 1999 113 77»106 Prof. Gordon asked How do the phase shifts that you measure depend on coupling between the continuum states ? Prof.Zare responded What we obtain from measuring the degree of orientation of the photofragments is a measure of the phase diÜerence between interacting continua of diÜerent symmetries that converge to the same –nal asymptotic states. It is from this measurement that we hope to infer the nature of the coupling. Conversely the predicted nature of the coupling can be tested against our measurements. Prof. Seideman said The phase shift measured in the experiments of Prof. Zare and co-workers depends on coupling between continuum states in the same way as d13 of ref. 1. If attention is focussed on the case of a structureless dissociation continuum of diatomics as in ref. 2 the observation of a nonzero phase in either experiment implies that the continuum consists of a superposition of electronic states.This requires that either the electronic curves cross (at some level of approximation) or that they become energetically degenerate in the atomic limit. In the latter case kinetic (radial derivative) coupling is generally nonnegligible since it is likely to become comparable to the energy separation before the potential curves become a constant function of the internuclear distance (see e.g. ref. 3). 1 J. A. Fiss A. Khachatrian L. Zhu R. J. Gordon and T. Seideman Faraday Discuss. 1999 113 61. 2 Z. H. Kim A. J. Alexander S. A. Kandel T. P. Rakitzis and R. N. Zare Faraday Discuss. 1999 113 27. 3 S. J. Singer K. F. Freed and Y. B. Band J. Chem. Phys. 1983 79 6060. Prof. Hancock asked Molecular chlorine is often used as a source of velocity aligned Cl atoms with polarised products being observed as a result of their bimolecular reactions.Do you expect eÜects of the orientation of the Cl atom in such bimolecular reactions and how would you predict these eÜects to be manifested ? Prof. Zare responded Yes I do expect that the orientation of the Cl atom might alter the consequences of any chemical reaction that subsequently takes place. We can expect such behavior from various reactive scattering studies involving aligned excited atoms such as Ca(1P)]HCl; see for example ref. 1. In the case of atomic chlorine hyper–ne depolarization causes the eÜect of any initial orientation to be small. Moreover the production of ground-state chlorine atoms by photodissociation of Cl at 355 nm is dominated by photolysis from the C state that does not produce oriented photo- 2 fragments.1 C. T. Rettner and R. N. Zare J. Chem. Phys. 1982 77 2416. Prof. M. Alexander asked One intriguing result of our ongoing investigation of the F(2P)]H2 reaction as discussed at this meeting and mentioned elsewhere,1,2 is the strong dependence of the reactivity on the alignment of the F atom in the 2P state. Atoms with a projection of the 3@2 m electronic angular momentum of ja\^1/2 with respect to the initial relative velocity vector account for virtually all of the total reaction cross section particularly at low energy. In the Cl]HD experiments described by Dr A. Alexander and Prof. Zare laser photolysis is used to prepare the Cl atom reactant. Would it be feasible (or even possible) to vary the alignment of the atoms with respect to the direction of the HD beam in order to investigate the dependence of the reactivity on this alignment? 1 M.H. Alexander H.-J. Werner and D. E. Manolopoulos J. Chem. Phys. 1998 109 5710. 2 D. Manolopoulos Faraday Discuss. 1999 110 223. Prof. Zare responded In principle Prof. M. Alexanderœs suggestion is a good one; in practice it is hard to achieve any substantial polarization of the chlorine atoms because of hyper–ne depolarization (see my response to Prof. Hancockœs earlier question). Dr Auerbach asked The comparison of experimental results and model for Im[a(1)] you pre- 1 sented is interesting and provocative. I note that in Fig. 4B of your paper the experimentally Faraday Discuss.1999 113 77»106 84 determined Im[a(1)] decays to zero more rapidly than the model results. In other words the 1 experiment is narrower than the model. Most eÜects that I can think of if added to the model would produce a yet broader curve. Are there changes to the model that would go in the direction of predicting a narrower curve? If not it seems likely that other states are involved. Prof. Zare responded Dr Auerbachœs observation is most pertinent to whether we have or have not achieved a full understanding of those factors aÜecting the interpretation of our experiment. Dr A. Alexander has pointed out to me that the sensitivity of the envelope function [(1]b)(1[b/ 2)]1@2 to the value of the spatial anisotropy of the photofragments (the b parameter) varies more markedly near the extrema of the b parameter that is for b\2 and b\[1.Thus small measurement errors in b might account for the large discrepancy in the wings. Of course this explanation may not be the only one. Because the sensitivity to the exact value of b near the extrema is essentially in–nite it might be that the measurement of the degree of orientation of the photofragment may be ultimately a more sensitive measure of its spatial anisotropy for nearly pure transitions. Prof. Shapiro commented The analysis presented by Prof. Zare regarding the emergence of orientation due to interference between perpendicular and parallel transitions also applies to alignment. In addition we have shown1h4 that such interference eÜects manifest themselves whenever more than one helicity (the projection of the internal angular momentum on the recoil direction) contributes to a given process.The interfence between parallel and perpendicular transitions is but one way of making diÜerent helicities (in diatomic molecules the helicity is the projection of the electronic angular momentum on the internuclear axis) interfere. 3 .3 Interferences have also been shown to potentially give rise to backward» Such interference eÜects have been analyzed theoretically in the context of the photodissociation of HI2 and CH forward asymmetric angular distributions of m-selected photofragments.4 1 G. G. Balint-Kurti and M. Shapiro Chem. Phys. 1981 61 137. 2 I. Levy and M. Shapiro J. Chem. Phys. 1988 89 2900. 3 M. Shapiro J.Phys. Chem. 1986 90 3644. 4 A. Peœer M. Shapiro and G. G. Balint-Kurti J. Chem. Phys. 1999 110 11928. Prof. Zare responded The fact that our work applies to alignment has already been noted by us experimentally1,2 and theoretically.3,4 We –rst observed this behavior in analyzing the align- Cl(2P ment of photofragments in the photolysis of iodine monochloride (ICl).1,2 We found that 3@2) the alignment of the photofragment depends on a number of moments. In contrast the orientation of the photofragment depends exclusively on the interaction of two continua of diÜerent symmetries terminating on the same –nal state of the separated atoms. Thus we believe that real advantage exists for measuring the orientation rather than the alignment of the photofragments.1 T. P. Rakitzis S. A. Kandel and R. N. Zare J. Chem. Phys. 1998 108 8291. 2 T. P. Rakitzis S. A. Kandel A. J. Alexander Z. H. Kim and R. N. Zare J. Chem. Phys. 1999 110 3351. 3 T. P. Rakitzis S. A. Kandel A. J. Alexander Z. H. Kim and R. N. Zare Science 1998 281 1346. 4 T. P. Rakitzis and R. N. Zare J. Chem. Phys. 1999 110 3341. Prof. Anderson commented Your experiments measure interesting details about the coherent excitation of two (or more) molecular states because the amplitudes on the diÜerent states experience re-coupling at larger internuclear distances to produce the diÜerent –ne structure states of chlorine atoms. This re-coupling depends sensitively on the relative phases of the wavefunction for the diÜerent states at the re-coupling point and the importance of such re-coupling has been long appreciated for atomic collisions.In particular in your experiments photoexcitation initially produces chlorine atoms on Hundœs case ììaœœ repulsive states and re-coupling occurs at larger internuclear distances to Hundœs case ììcœœ states. The re-coupling occurs when the V&[V% splitting is greater than the spin»orbit interaction and it is well understood for –ne structure changing or intramultiplet mixing collisions. It would be interesting to model your experiments with the radial coupling theories that are used to describe –ne structure changing collisions. In this case diabatic S and P states (Hundœs 85 Faraday Discuss. 1999 113 77»106 ììaœœ) with given V and V potentials are coupled with a constant spin»orbit interaction.Presum- & % ably this interpretation of your experiments would be as successful as the model in your paper. Your photodissociation experiments are reaching the sophistication of atomic collisional excitation experiments. For the latter the excited states are commonly speci–ed as Stokes vectors and it might be useful to start reporting the results of detailed state resolved photodissociation experiments in the same way. Prof. Vasyutinskii said In my comment I would like to present our results which are similar to those presented here by Prof. Zare. The work was done in the IoÜe Institute St. Petersburg and in TU Berlin by K. O. Korovin B. V. Picheyev O. S. Vasyutinskii H. Valipour and D. Zimmermann. We investigated the photofragment orientation arising from photolysis with circularly polarized light.The experiment was carried out on Rbl photodissociation at 266 nm and resulted in spin-oriented ground state Rb atoms (see Fig. 8). The detection procedure was of the Doppler spectroscopy type where we used the paramagnetic Faraday eÜect to measure the fragment orientation. An additional external magnetic –eld was applied to the reaction volume to separate population and Faraday detection signals and to increase the experimental signal-to-noise ratio. The experimental results are presented in Fig. 9. The upper curve is the Doppler resolved absorption line of the Rb fragments while the lower curve is the Faraday signal resulting from the fragment orientation. The Faraday signal can be presented as a superposition of two theoretical curves shown in Fig.10 each related to a certain dissociation mechanism. These are (1) incoherent excitation into the X\1 molecular state and (2) excitation into the coherent superposition of the X\1 0 molecular states. The ratio of the corresponding orientation anisotropy parameters was found to be a1/c1B [0.3. These two mechanisms complement very nicely the mechanism of photofragment orientation by linearly polarized light studied by Prof. Zare and co-workers that can be illustrated by the vector model shown in Fig. 11 (ref. 1). Here the fragment orientation coming through photolysis by linearly polarized light results in a component of the total fragment angular momentum that is normal to the plane containing the recoil vector k and the photolysis polarization vector e.The two mechanisms coming through photolysis by circularly polarized light result in components of the total fragment angular momentum which are (a) parallel to the recoil axis and (b) perpendicular to the recoil axis and lying in the plane containing the recoil vector k and the photolysis direction Z. Fig. 8 Potential curves of RbI molecule. Faraday Discuss. 1999 113 77»106 86 Fig. 9 Determination of the anisotropy parameters. 1 L. D. A. Siebbeles M. Glass-Maujean O. S. Vasyutinskii J. A. Beswick and O. Roncero J. Chem. Phys. 1994 100 3610. Prof. Gordon opened the discussion of Prof. Suzukiœs paper We wish to comment on two aspects of Prof. Suzukiœs paper. The beautiful femtosecond photoelectron images in this paper clearly resolve the photodissociation dynamics of singlet and triplet states.A further point made in this paper is that for two-photon excitation the properties of the intermediate state can have a signi–cant eÜect on the dissociation dynamics. We report similar eÜects observed in nanosecond photoionization images of iodobenzene (IBz). The false color image in Fig. 12 is a twodimensional projection of the velocity distribution of I(2P3@2) produced by the photodissociation Fig. 10 Dispersion cross-section D10(u). 87 Faraday Discuss. 1999 113 77»106 Fig. 11 Molecular frame vector model. of IBz by a single 266 nm photon. The fourth harmonic of a Nd Yag laser was used to photodissociate the parent molecule and to photoionize the fragment atom in a pulsed molecular beam.The velocity distribution was obtained using the method of velocity»map imaging.1 Further experimental details will be published elsewhere.2 The image consists of a set of three concentric rings indicating diÜerent partionings of energy between translation and internal excitation of the phenyl ring. The anisotropy of the rings indicates that the transitions are largely parallel in character. The channel producing the outer ring has been assigned to direct dissociation of a n,p* state.3 The channel corresponding to the inner ring has been assigned to predissociation of a singlet3 or triplet4 p,p* state. The channel corresponding to the middle ring has not been previously reported. The photofragment image obtained at 532 nm (produced by the second harmonic of the Nd Yag laser) shown in Fig.13 is strikingly diÜerent from that obtained at 266 nm. Although the outer two rings are still present the inner one is replaced by a continuous ììhourglassœœ distribution peaked at zero velocity which is indicative of high internal excitation of the phenyl fragment. We have ruled out experimentally a number of possible mechanisms including cluster formation5 and intense –eld dressed state eÜects,6 and additional experiments designed to identify the nature of the intermediate level are in progress. 1 A. T. J. B. Eppink and D. H. Parker Rev. Sci. Instrum. 1997 68 3477. 2 L. Zhu S. Unny Y. Du K. Truhins R. J. Gordon A. Sugita M. Mashino M. Kawasaki Y. Matsumi and T. Seideman to be submitted.Fig. 12 Two-dimensional photofragment image of I(2P3@2) produced by photodissociating iodobenzene with 266 nm radiation. Faraday Discuss. 1999 113 77»106 88 Fig. 13 Two-dimensional photofragment image of I(2P3@2) produced by photodissociating iodobenzene with 532 nm radiation. 3 J. E. Freitas H. J. Hwang and M. A. El-Sayed J. Phys. Chem. 1993 97 12481. 4 H. J. Hwang and M. A. El-Sayed J. Chem. Phys. 1992 96 856. 5 J. A. Syage Chem. Phys. 1996 207 411. 6 D. W. Chandler and D. H. Parker Adv. Photochem. 1999 25 39. Prof. Suzuki replied They are interesting experimental data suggesting the possibility of controlling non-adiabatic dissociation dynamics via diÜerent photoexcitation schemes. As an example of a non-adiabatic dissociation mechanism revealed by ion imaging I would like to brie—y mention photodissociation of OCS.We have studied photodissociation of OCS in the UV region by observing the scattering distribution of S atoms.1,2 Fig. 14 shows the ion images of S atoms observed for 235 nm photodissociation. There are two sets of image data obtained by using (2]1) REMPI of S atoms via 1F and 3P states. These two REMPI schemes have diÜerent 3 1 sensitivity to the multipole moments of S atoms (orbital alignment),3,4 so they exhibit diÜerent image patterns. Fig. 14(e) shows most clearly the three velocity components fast (parallel transition) fast (perpendicular) and slow (parallel). I would like to call your attention to the fact that the slow component occurs only from the parallel transition.By comparing the experimental results with ab initio wave packet calculations we con–rmed that this slow component is due to using (2]1) REMPI via (a)»(d) 1F and (e)»(h) 3P1. Fig. 14 Ion images of S(1D2) produced by 235 nm photodissociation of OCS. The images were taken by 3 89 Faraday Discuss. 1999 113 77»106 Fig. 15 (a) Walsh diagram for 16 valence electron ABC triatomic molecule. (b) Potential energy curves of 2A@(1*) and 1A@(1&`) for the bending coordinate of OCS calculated by an ab initio method and non-adiabatic transition in the bending coordinate (bond distances are –xed to ” ” r\1.13 and R\2.2 ). non-adiabatic transition from the 2A@(1*) to the 1A@(1&`) state. As a Walsh diagram,5 Fig. 15(a) predicts the energies of HOMO and LUMO in a 16 valence electron system are reversed by bending deformation which means that the 2A@(1*) and 1A@(1&`) states undergo avoided crossing at a certain bending angle [Fig.15(b)]. Since the 2A@ state has bent geometry photoexcitation induces rapid bending deformation that induces non-adiabatic transition to the ground state with the yield as high as 35%. 1 T. Suzuki H. Katayanagi S. Nanbu and M. Aoyagi J. Chem. Phys. 1998 109 5778. 2 H. Katayanagi and T. Suzuki unpublished. 3 Y. Mo H. Katayanagi M. C. Heaven and T. Suzuki Phys. Rev. L ett. 1996 77 830. 4 Y. Mo and T. Suzuki J. Chem. Phys. 1998 109 4691. 5 A. D. Walsh J. Chem. Soc. 1953 2266. Prof. Seideman° said During the past few years we have been looking into the information content of photoelectron energy and angular distributions in femtosecond pump»probe experiments.1,2 The main goal of this work has been to explore the ability of future experiments of the type that Prof. Suzuki describes to unravel molecular coupling mechanisms. In an application to NO,2 which we did as a test of the theoretical scheme,1 we found very weak time-dependence of the photoelectron angular distribution (PAD) and essentially no dependence on the probe intensity which agrees with the observations reported in the paper of Prof. Suzuki and co-workers and indeed was expected. This is not the general case however. In the presence of coupling mechanisms that involve rotations one expects the PAD to vary with time re—ecting the evolving rotational composition of the wavepacket and I think that the technique described by Suzuki et al.is a beautiful way of ° Also S. C. Althorpe. Faraday Discuss. 1999 113 77»106 90 looking at such problems. In more recent work3 we have found for instance that the presence of rotation»vibration coupling shows up in the PAD as vibrational –ne structure in the ionization asymmetry parameter b arising from dephasing of the rotational components as time progresses. Fig. 16 shows the asymmetry parameter for ionization of a diatomic wavepacket as a function of the pump»probe time delay. In this case the structure arises from the relatively weak centrifugal coupling and therefore appears on a relatively long time-scale. In polyatomic molecules similar –ne structure (typically of shorter time-scale) is expected to be observed in response to (typically stronger) Coriolis coupling.Meaningful time-dependence of the photoelectron angular distribution is expected similarly in the presence of electronically nonadiabatic transitions where the electronic character changes with time as the wavepacket moves in coordinate space. In fact one might expect a more dramatic eÜect in the latter case. I think however that pyrazine may not be the best choice of system to illustrate the potential of the technique of Prof. Suzukiœs paper. It seems that because of the favourable energetics and Frank»Condon propensities the photoelectron energy distribution alone provides a rather complete picture of the nonadiabatic dynamics for this particular system. It may well be that more conventional techniques that do not give simultaneously the angular distribution but allow a better energy resolution would resolve also the vibrational energy redistribution that is induced by the electronic coupling.We see this eÜect in calculations of timeresolved photoelectron energy distributions in decatetraene which has a similarly large energy gap between the coupled states and hence allows a similar discrimination of the electrons originating from the two.4 This is observed also in time-resolved experiments in decatetraene by Blanchet et al.4 Photoelectron angular distributions however promise to be more generally applicable. 1 T. Seideman J. Chem. Phys. 1997 107 7859. 2 S. C. Althorpe and T. Seideman J. Chem. Phys. 1999 110 147. 3 S. C.Althorpe and T. Seideman J. Chem. Phys. submitted. 4 V. Blanchet M. Zgierski T. Seideman and A. Stolow Nature (L ondon) 1999 401 52. Prof. Suzuki responded We were aware of the –ne work by Althorpe and Seideman.1 Unfortunately the time-dependence of photoelectron angular anisotropy from NO is rather small and we have not examined this subtle feature closely. But it is certainly an interesting problem to investigate in the future. As Prof. Seideman mentioned pyrazine may not be the best system for demonstrating the potential of time-resolved photoelectron imaging. We presented the result on pyrazine as a clear example of electronic dephasing. The dynamic change of electron orbital during a chemical reaction is the most interesting problem to examine with this technique.For instance the A state of NO is a pure 3s Rydberg state but the NO»Ar van der Waals complex has p-character mixing Fig. 16 Time-evolution of the asymmetry parameter b calculated for a diatomic system. The wavepacket is prepared with a 20 fs pump pulse and probed with a time-delayed 20 fs pulse. 91 Faraday Discuss. 1999 113 77»106 into it due to the presence of Ar. So during the course of predissociation of NO»Ar in the A state photoelectron angular anisotropy was expected to change as a function of time. Our attempt to observe NO»Ar was unfortunately hampered by the strong background signal of NO dimer but similar experiments on solvated electrons in microclusters will be very exciting. If the angular distribution is not of interest are conventional methods more useful than photoelectron imaging? We pointed out that if the photoelectron kinetic energy resolution desired is ca.20 meV at 1 eV an imaging method provides the simplest and the most efficient way of measuring the photoelectron spectrum. Fig. 17 compares the [1]1@] photoelectron imaging data with the ZEKE spectrum reported by Zhu and Johnson.2 Our photoelectron imaging spectrometer has not been fully optimized and the energy resolution is only 40»50 meV for 400 meV electrons. However the data agree well with the ZEKE spectrum. The energy resolution of photoelectron imaging can be improved by at least another factor of 5. PEI resolving vibrational structure will allow the investigation of intramolecular vibrational redistribution (IVR).1 S. C. Althorpe and T. Seideman J. Chem. Phys. 1999 110 147. 2 L. Zhu and P. M. Johnson J. Chem. Phys. 1999 99 2322. Prof. Stolte asked Your real time observation of a growth of the triplet character (q\97^8 ps) due to dephasing from optically prepared S pyrazine is very striking. Is there a possibility of 1 comparing your results in more detail with those obtained in the high resolution frequency domain as carried out by Uit de Haag and Meerts,1 Kommandeur et al.,2 and Parmenter et al.,3 in terms of a strength of vibronic singlet»triplet coupling? 1 P. Uit de Haag and W. L. Meerts Chem. Phys. 1991 156 197. 2 J. Kommandeur W. A. Majewski W. L. Meerts and D. W. Pratt Annu. Rev. Phys. Chem. 1987 38 433. 3 A. E. W. Knight C. M. Lawburgh and C. S. Parmenter J.Chem. Phys. 1975 63 4336. Prof. Suzuki responded The measurements of pyrazine in the time and frequency domains have been compared by Kommandeur and co-workers1 and Felker and Zewail.2 Both of these groups have found reasonable agreement between the time and frequency domain data although I do not think the agreement was quite perfect. The time evolution of the fast electron signal we observed is quite similar to the —uorescence decay data reported previously so our data is also consistent with the frequency domain measurements. I do not think our photoelectron data provide further information regarding the comparison of the time and frequency domain data. A photoabsorption spectrum is a Fourier transform of the autocorrelation function of an optically prepared state so it is the view of excited state dynamics seen through a narrow window.The advantage of photo- Fig. 17 Comparison of the [1]1@] photoelectron energy spectrum obtained from imaging data (pump 324.7 nm and probe 212.1 nm; both are nanosecond lasers) with the [1]1@] ZEKE spectrum reported by Zhu and Johnson. The ZEKE spectrum with sharp spikes was convoluted with our experimental resolution for comparison. Faraday Discuss. 1999 113 77»106 92 electron spectroscopy is that it explores dynamics away from the Franck»Condon region on the upper state potential energy surface. 1 P. J. de Lange K. E. Drabe and J. Kommandeur J. Chem. Phys. 1986 84 538. 2 P. M. Felker and A. H. Zewail Chem. Phys. L ett. 1986 128 221. Dr Orr-Ewing commented Prof. Suzuki and co-workers have reported very interesting results on the fast time evolution of photoelectron spectra using electron imaging techniques.These authors comment however on the complications of interpreting the photoelectron angular distributions (PADs) in their experiments. The value of measuring the evolution of PADs on the picosecond timescale is illustrated by very recent results from Dr K. L. Reid and Dr T. A. Field (University of Nottingham UK) and Dr M. Towrie and Dr P. Matousek (Rutherford Appleton Laboratory UK).1 Their experiments are similar to those alluded to in Prof. Seidemanœs earlier comment. In the experiments by Reid et al. two separate 257 nm laser pulses of duration 1 ps were used –rst to promote para-di—uorobenzene (pDFB) to the 3151 vibrational level of its –rst excited singlet (S1) state and then to ionize the electronically excited pDFB.PADs were recorded at various time delays between the excitation and ionization pulses by simultaneous rotation of the linear polarizations of the two pulses. The excited electron in the S state occupies an orbital 1 localized along the C»F bond direction and thus the PAD re—ects the alignment of the C»F bond direction in space. The photoelectron spectrum for pDFB is shown in Fig. 18 for ionization to a variety of vibrational levels of the ground electronic state of the ion. PADs corresponding to the formation of pDFB` in the 31 vibrational level of its electronic ground state are shown in Fig. 19 for diÜerent time delays between the excitation and ionization laser pulses.The evolution of the PADs re—ects the motion of the rotational or rovibrational wavepacket and a recurrence is clearly seen. Modelling of the expected times for pure rotational recurrences using the known spectroscopic constants for the S state predicts time intervals of 208 ps (for rotation about the a-axis) 1 and 44 ps (for rotation about the b and c axes). Since neither of these intervals matches the measured recurrence time the PADs thus demonstrate that the S wavepacket dynamics is in—u- 1 enced not only by molecular rotation but also by an additional mechanism that is most likely to be vibration»rotation coupling. 1 K. L. Reid T. A. Field M. Towrie and P. Matousek J. Chem. Phys. 1999 111 1438. Prof. Suzuki responded We have observed an interesting variation of anisotropy parameter as a function of time in the [1]2@] photoionization of pyrazine via the S state.This variation is 1 also re—ected in the time-dependence of photoelectron current reported in our paper if you examine Fig. 2 of our paper closely the earliest part of the signal in (b) and (c) shows spikes. This behavior is ascribed to rotational coherence. Fig. 18 Photoelectron counts vs. ion internal energy following excitation via the 3151 level in S paradi —uorobenzene. This spectrum corresponds to a summation of data sets gathered at each of the ten polariza- 1 tion geometries. 93 Faraday Discuss. 1999 113 77»106 Fig. 19 Photoelectron angular distributions for the 31 ion peak with parallel excitation and ionization polarizations for six time delays as labelled.The radius of the polar plot to each data point is proportional to the number of photoelectron counts at that angle and the error bars are statistical. The solid line represents a –t to the function I(h,/)\;L/0,2,4 bL0 YL0(h /). The angle h is de–ned to be the angle between the probe polarization direction and the photoelectron ejection direction and the direction corresponding to h\0° points vertically in the plot. It is interesting that photoelectron angular distribution of para-di—uorobenzene suggests rotation»vibration coupling. It would also be helpful to measure photoelectron spectra as a function of time-delay for examining a signature of IVR. If a transform-limited picosecond laser pulse with longer pulse duration 3»10 ps is employed selective excitation of low J and high J levels will be possible for the samples in an eÜusive beam that has relatively high rotational temperature.Prof. Suzuki summarised Time-resolved photoelectron imaging provides a powerful means to probe electron and nuclear dynamics in unimolecular reaction. I would like to point out some interesting possibilities for the future. When a femtosecond VUV probe laser is employed it will allow us to project the electronic wavefunction to various electronic states in the cation and to map out the variation of electron con–guration during the course of reaction ; the non-adiabatic transition will be clearly observed by this method. Introduction of the coincidence measurements between photoelectron and daughter ions will provide the photoelectron angular distribution in the ìmolecularœ frame,1 providing further insight into the electronic dynamics in chemical reactions.The energy resolution in photoelectron imaging can be improved to be comparable with TOF methods (*E/E\0.5%) and the time»energy resolution will approach the limit of the uncertainty principle. Although ZEKE spectroscopy2 has achieved the best energy resolution in photoelectron spectroscopy ZEKE has the potential problem of state-dependent autoionization processes that aÜect the signal intensities. Direct ionization is free from this problem and photoelectron imaging will become one of the most convenient tools for obtaining vibrationallyresolved photoelectron spectra. 1 E. Shigemasa J. Adachi M.Oura and A. Yagishita Phys. Rev. L ett. 1995 74 359. 2 K.Mué ller-Dethlefs High Resolution L aser Photoionization and Photoelectron Studies W iley Series in Ion Chemistry and Physics ed. I. Powis T. Baer and C.-Y. Ng John Wiley & Sons Chichester 1995. Prof. Stolte opened the discussion of Dr Corkumœs paper You presented very exciting and splendid novel methods to control molecules with strong laser –elds. How far are these potential developments from state of the art practical possibilities and how close is one towards realis- Faraday Discuss. 1999 113 77»106 94 ation ? Which of your schemes for stirring up molecular rotation for creating an accelerator for neutral molecules for achieving molecular quantum wires and for resulting quantum dots do you prospect to be either easy or difficult ? Dr Corkum responded We believe that all of the ideas that we suggest in the accompanying paper are feasible at least for small molecules.We do not know for large molecules. Let us choose two examples to keep the answer short. Spinning and acceleration We start with the assumption that the torque that strong laser –elds can apply to molecules is well understood and demonstrated during the early days of lasers (the optical Kerr eÜect). Controlling the torque is simply a matter of controlling the laser beam. To exercise this control high power femtosecond pulses are a tremendous resource. We know the phase of all frequencies that make up the pulse. If it were not so the pulse would not be short. Starting with perfectly phased radiation we can synthesize any pulse for which we know the Fourier transform by moving to the Fourier plane and controlling the amplitude and phase of the individual frequency components of the pulse.This technology is well developed. Of course practical difficulties may emerge if we wish to synthesize pulses more than 1 ns in duration but since the relevant times are rotational periods that is no problem for small molecules. Concerning experiments we believe that we are very close to spinning Cl molecules in our laboratory. 2 Quantum wires and quantum dots First let me clarify that we are in—uenced by solid state physics in naming these quantum wires and dots. We might equally have called a molecular quantum wire a molecular –ber in analogy with optical –bers.Since strong –eld molecular optics requires substantial intensity there is an experimental motivation for keeping the laser focus small. The feature size in a standing wave clearly illustrates the j/4 physical limit on the size of a focal spot. Practically a good lens or mirror would be the easiest way to get three-dimensional con–nement an axicon the easiest way to get two-dimensional con- –nement. With a good lens or mirror a typical focal spot dimension need not be too much larger than the j/4 minimum. Con–ning molecules for 10œs or 100œs of microseconds with a Nd Yag laser should not be too difficult. If the experiment demands it cooling molecules so they occupy the lowest state in the con–ning potential is the greatest problem. Prof. Zare asked How far can we go in cooling atoms and molecules with lasers ? Dr Corkum responded We think that cold helium would be a very eÜective way to cool warmer molecules.In fact the Doyle group at Harvard has been very successful using collisions with helium to cool molecules. Helium would be a very good working gas for strong –eld molecular optics. The low polarizability of helium means that it will be almost unaÜected by –elds that are strong enough to produce very deep traps for most molecules. Molecular cooling was the subject of Prof. Tannorœs talk at the meeting and stimulated by that talk in the discussion following it Dr Corkum proposed a method for using strong laser –elds combined with collisions (or spontaneous emission) to cool quantum systems (cooling molecular translation and rotation appear feasible).Prof. Tannor responded to Prof. Zare We have learned the hard way that the cooling requires spontaneous emission essentially to carry away the entropy from the system. I will discuss this more fully in my talk. Therefore the strong –elds used by Prof. Corkumœs group can do wonderful things to molecules but cannot cool them. Prof. Suzuki commented I agree with Dr Corkum that laser science will continue to have large impacts on molecular science. In this regard I would like to mention ion imaging with intense laser –elds to illustrate its potential for non-spectroscopic analysis of molecular structure. We irradiated an intense femtosecond laser pulse (\10 mJ pulse~1 at 10 Hz 760 nm 120»150 fs) to a supersonic molecular beam and observed scattering distributions of multiply-charged atomic fragments.1 Fig. 20 shows the distribution of nitrogen atomic ions created from molecular nitrogen. The ions are primarily ejected along the laser polarization indicating strong alignment of molecular axis along the laser polarization as discussed by Dr Corkum. Considering the conservation of 95 Faraday Discuss. 1999 113 77»106 Fig. 20 Ion images of nitrogen atomic ions generated by multielectron dissociative ionization of molecular nitrogen. The polarization of the laser is vertical in the –gure. The laser power is estimated to be in the order of 1014 W cm~2. 2O in the laser –eld. On the other hand in an intense laser –eld. The two ion linear momentum straightforward assignment can be made on the product pairs Nn`]Nm` without coincidence measurements.The product angular distribution in (n,m) processes extracted from the data are shown in Fig. 21. High powers in the cosk h function indicate strong molecular alignment. In principle the dissociation in an intense laser –eld can be used for molecular structural analysis. However accurate determination of molecular structure requires (1) the laser pulse to be sufficiently short to avoid molecular deformation during the pulse (2) the laser pulse to be sufficiently strong to strip a large number of electrons from a molecule to minimize exchange interaction of electrons and make the interaction potential to be nearly Coulombic and (3) the coincidence measurement of all the ionic fragments.All of these are highly technically demanding. Nevertheless I would like to point out that even a simple ion imaging measurement without coincidence technique could be useful for chemical analysis. Fig. 22 shows the ion images of oxygen and nitrogen atoms in dissociative ionization of N clouds of oxygen atoms are due to two orientations of N2O the three clouds of nitrogen atoms are due to two orientations]two nitrogen sites in the mol- Fig. 21 Angular distribution of (n,m) channels in dissociative ionization of molecular nitrogen. The –ts of cosk h function are also shown. Faraday Discuss. 1999 113 77»106 96 Fig. 22 Ion images of O2` and N2` in dissociative ionization of N2O. ecule namely the central and end positions. The data clearly indicates that this type of measurement tells us at least the sequence of atoms or atomic groups in the molecule even if it does not provide an accurate bond distance and angle.We think that the structural analysis with ion imaging will be an interesting application of intense lasers. 1 T. Suzuki and H. Li in preparation. Dr Corkum responded Thank you for your contribution. Indeed it is possible to observe the direction of the fragments that emerge from strong –eld ionization. A highly ionized molecule is on a very repulsive potential curve and therefore will dissociate much faster than the time required for it to align to the –eld. Assuming very rapid ionization the direction of the fragments is a measure of the moleculeœs alignment at the time of rapid ionization.As you point out this has very exciting implications for measurement of molecular structure and it is very technically demanding. Concerning alignment we should warn readers of one potential error. So-called enhanced ionization1,2 makes ionization much easier for molecular ions that are aligned with the –eld. Assuming a random distribution of orientations enhanced ionization ensures that we observe more molecular fragments that are aligned to the –eld. As we note in the text of our paper without great care the greater number of fragments that are measured along the laser polarization than perpendicular can be incorrectly interpreted as alignment. 1 T. Seideman M. Yu. Ivanov and P. B. Corkum Phys. Rev. L ett. 1995 75 2819. 2 E. Constant H.Stapelfeldt and P. B. Corkum Phys. Rev. L ett. 1996 76 4140. Dr Auerbach commented Your paper has many exciting suggestions for future directions and applications of strong laser –elds to manipulating molecules. Some such as the focusing of molecules seem to be a simple extension of the experimental work you have presented. Others are more speculative. I would like to draw your attention to two of these namely the suggestion of trapping in three dimensions and the related suggestion of an accelerator for neutral molecules. Speci–cally could you comment on (1) How do you envisage j/4 trapping in three dimensions? Would you use a very tight focus or two orthogonal laser beams to de–ne the region. How would the trap be loaded? (2) For the accelerator again do you imagine using (a) crossed laser –elds or (b) a tight focus to de–ne the ììbucketsœœ of the accelerator ? If (a) would the crossing point of the lasers have to be moved to achieve acceleration and if so how? If (b) you could move the buckets by chirping the laser but would the focus have to be moved and if so how? How would the buckets be –lled ? (3) To be useful an accelerator has to have a narrow energy spread and a high brightness (small emittance).Can you estimate the energy spread and the emittance (angular spread) ? Dr Corkum responded In response to the earlier question by Prof. Stolte we discussed how we would attempt an experiment on molecular quantum dots. However trapping experiments need not be so ambitious at –rst and we will attempt a less ambitious experiment.Since we can produce well depths that are very large it should be possible to trap molecules from a beam where the translational motion is slowed by mixing the molecule of interest (H2) with a heavier gas (such as neon). In this case the laser pulse (trap) would be activated non-adiabatically so that some molecules –nd themselves at the bottom of the well when the laser beam is turned on and can not get out. If the well (beam) is then turned oÜ non-adiabatically molecules will be moving in directions that are determined by their trajectories in the trap. The trajectories of these molecules can 97 Faraday Discuss. 1999 113 77»106 be measured in much the same way that we have measured de—ection. That is we can tag the molecules by –eld ionization and their velocity can be imaged on a detector.We have not performed an acceleration experiment. However acceleration is similar to spinning an experiment that we are currently working on. We have thought quite a bit about acceleration and ultimately we may design an experiment to accelerate molecules. For acceleration our preferred approach would be to form a standing wave by counter propagating two beams. That would lead to an intensity modulation with high intensity regions separated by j/2. The molecules will be trapped in these j/4 ììbucketsœœ. If one beam is linearly chirped the pattern will accelerate with a velocity that is determined by the rate change of the frequency diÜerence (chirp). If the potential well depth is 50 meV then H molecules could be 2 accelerated to 4 eV in 1 ns by beams that must reach a frequency diÜerence of about 40 GHz.Of course the velocity increases linearly in time so an energy of about 400 eV could be achieved in 10 ns. [Pulses with an appropriate bandwidth (as high as 1 THz or even greater) can be produced at 1 lm.] One approach to producing chirped pulses would be to send a transform limited short pulse down long dispersive optical –bers. Ampli–cation in a Nd Yag or Nd glass ampli–er would easily allow sufficient pulse energy. Any molecular beam that could be produced in this way would have a very low beam divergence very small energy spread (it must be con–ned to a relatively shallow well) and be rotationally cold. This is a very exciting future direction.Prof. Miller asked Room temperature trapping of molecules in the way you describe requires very deep traps which I assume means short pulses. In the limit of femtoseconds there is really no diÜerence between trapped and free molecules since they do not move on this timescale. What is the timescale that you are likely to be able to trap molecules at room temperature with the available laser intensities ? Dr Corkum responded Substantial trap depths do not require femtosecond lasers. For example a 10 meV well for I CS or molecules requires an intensity of about 1012 W cm~2. Assuming a 1 2 2 lm focal spot diameter that means a power of only 10 kW. This is easily achieved with pulsed Nd Yag laser technology and so there is no problem sustaining a deep trap for 10»100œs of microseconds.You may be concerned whether the molecule can withstand such high intensities for such a long time. The numbers that we have presented for the depth of potential wells assume that ionization provides the upper limit on the light intensity that the molecule can withstand. For comparison purposes we have assumed that the maximum ionization rate that could be tolerated is about 106 s~1. That means that the average molecule would survive for about 1 ls. To calculate ionization rates we have assumed the tunneling model (called the ADK model) that has proven very accurate for atomic ionization in the long wavelength limit. It is not justi–ed for molecules but at least in femtosecond experiments it appears to overestimate the ionization rate.Therefore the numbers that we quote should be taken as approximate. We have performed experiments on CS and I with multi-longitudinal-mode 14 ns Nd Yag 2 2 laser pulses and measured well depths of 6 meV. This is a severe underestimate of what the molecule can withstand due to the large intensity —uctuations that occur in such lasers. We believe that well depths that are near or exceed room temperature are achievable and can be maintained for microseconds or even longer. It is interesting to ask what would happen if we were to change the condition for the ionization rate allowing it to approach 1012. Then the typical ground Stark shifts would greatly exceed 100 meV. In fact we know experimentally that such large Stark shifts occur. Even such strongly bound molecules as H2 ` and HCl` (ref.1 and 2) lose their ground state bounding due to their large (exceeding 1 eV) Stark shifts. 1 P. Dietrich and P. B. Corkum J. Chem. Phys. 1992 97 3187. 2 P. Dietrich M. Yu. Ivanov F. A. Ilkov and P. B. Corkum Phys. Rev. L ett. 1996 77 4153. Prof. Anderson asked (1) What is the pressure that would be exerted on matter for quantum wire and 3D con–nement in high laser –elds ? What matter densities might be achieved by these techniques ? Faraday Discuss. 1999 113 77»106 98 (2) In your paper you have only considered the leading term in the polarizability expansion of the interaction of an atom or molecule with an electric –eld and this term results in an interaction energy that is proportional to the square of the electric –eld.At what laser intensities must higher order terms be added to the interaction energy and what would be the eÜect of such interactions in the applications that you describe in your paper? Dr Corkum responded (1) We do not know what density could be achieved in deep potential well. The pressure could be estimated knowing the force that a molecule experiences in the gradient of the laser –eld. However there will be a dipole»dipole force between molecules and so their interaction will not be like an ideal gas.1 In fact we expect laser-induced polymerization. (2) In all of the estimates that we have made we have ignored the hyperpolarizability. There are a number of ways to judge whether this is a limitation. For example at 1013 W cm~2 the peak –eld is about 1 V ”~1.To achieve a Stark shift of 50 meV would require one charge unit separated by less than 0.1 ”. That means that the charge re-arrangement responsible for the Stark shift is not very great and so we suspect that ignoring the hyperpolarizability will not lead to large errors. In fact we estimate that it becomes important at about 1016 W cm~2. 1 M. Yu. Ivanov D. R. Matusek and J. S. Wright Chem. Phys. L ett. 1996 225 232. Prof. Shapiro asked Have you considered applying the Coulomb explosion imaging technique to the analysis of the angular distribution of photo-fragments following dissociation by short pulses ? One of the advantages of Coulomb imaging would seem to be that one would be able to measure in ììreal-timeœœ the shape of the cloud of fragments as they emerge from the dissociation region.In this way one would be able to monitor some fascinating phenomena including the veri–cation of the prediction1 that with short pulse excitation the angular distribution would continuously undulate between the parallel and axial forms until the pulse of emerging photofragments comes to an end. The reason for this undulation is that the ratio between the continuum P and R branches (whose mutual interference determines the nature of the anisotropy parameter) changes in time in the pulsed dissociation case. 1 J. R. Waldeck M. Shapiro and R. Bersohn J. Chem. Phys. 1993 99 5924. Dr Corkum responded We are working hard to develop timed Coulomb explosion imaging for observing the nuclear motion during (small) polyatomic molecular dynamics.Our approach to Coulomb explosion imaging is to excite the molecular dynamics of interest with a pump pulse and then to use very intense very short probe pulses to explode the molecule.1 The explosion is powered by the removal of many electrons from a molecule in a time short compared to the time required for nuclear motion of the neutral molecule or on the molecular ion. The explosion occurs on the potential surfaces of the highly charged ion (assumed Coulombic). The current state-of-theart for short high power pulses is about 5 fs. There are many applications for timed Coulomb explosion imaging. One of the most interesting is to ììcatch a molecule in the middle of photodissociationœœ distinguishing it from those molecules that have already dissociated and those that are yet to dissociate.2 We have not considered the speci–c case that you refer to but we will.1 H. Stapelfeldt E. Constant and P. B. Corkum Phys. Rev. L ett. 1995 74 3780. 2 C. Ellert H. Stapelfeldt E. Constant H. Sakai J. Wright D. M. Rayner and P. B. Corkum Philos. T rans. R. Soc. L ondon Ser. A. 1998 356 329. Prof. Zare asked What are the conditions necessary to measure the photofragment angular anisotropy as represented by the b parameter using a Coulomb explosion technique? When should I worry about the electric –eld of the laser probe distorting and mixing electronic states ? Dr Corkum responded For a highly charged molecule the potential curve are so strongly repulsive that no other motion can compete and so the direction of the fragments is an accurate map of the orientation of a diatomic molecule at the time that it reached such a strongly dissociative state.The argument is analogous for small polyatomic molecules»only more complex 99 Faraday Discuss. 1999 113 77»106 because it is necessary to follow the trajectories of all of the fragments as they evolve on the approximately Coulombic potential surfaces. Errors arise if the exploding pulse turns on slowly. Then the molecule can accumulate momentum (or even re-orient or dissociate) before ionization. A good experimentalist will avoid such problems by using very short exploding pulses. Optically triggered Coulomb explosion has a great advantage over classical Coulomb explosion imaging in that the process can be accurately modeled at least for simple systems allowing us to assess possible errors.1 These studies show that aside from details the ionization process is largely irrelevant for Coulomb explosion imaging as long as ionization is fast and so level mixing and distortion will not be too important.What could be more ììbrute forceœœ than the ion/foil collision technique that is used for classical Coulomb explosions ? Although providing the pulse is short and the states are Coulombic the image will be accurate in many experiments the sensitivity of the ionization rate to molecular parameters can lead to mistakes. For example many experiments on molecular alignment during dissociative ionization fail to distinguish between real alignment and alignment sensitive ionization rates.We have commented on this in our paper. These errors can be avoided. 1 S. Chelkowski P. B. Corkum and A. D. Bandrauk Phys. Rev. L ett. 1999 82 3416. Prof. Kawasaki commented A molecule placed in an electric –eld can be aligned because of the anisotropy of its polarizability tensor. As an alternative to high static electric –elds the electric –eld of a pulsed laser can be used for alignment.1 The alignment can be demonstrated by the measurement of the control of the anisotropy of photodissociated fragments generated by polarized light.2 3@2) We report results obtained on alignment of methyl iodide. The angular distribution of I(2P atoms from the photodissociation of CH3I at 304 nm was measured with a photofragment imaging machine.3 The following processes occur.CH3I]hl(1.06 m 10 mJ pulse~1 5 ns)]CH3I (aligned) CH3I (aligned)]hl(304.67 nm 0.1 mJ pulse~1 3 ns)]CH3]I(2P3@2) 1 B. Friedrich and D. Hershbach Phys. Rev. L ett. 1995 74 4623. 2 H. Sakai C. P. Safvan J. Larsen K. M. Hilligsoe K. Hald and H. Stepelfeldt J. Chem. Phys. 1999 110 10235. 3 A. Sugita M. Mashino M. Kawasaki Y. Matsumi. R. J. Gordon and R. Bersohn submitted. Prof. Vasyutinskii said I have a question to Prof. Kawasaki. I wonder if the presented experimental results of a change in the b parameter can be explained simply by saturation of the dissociation transition of the molecule by a strong UV dissociating –eld ? Prof. Kawasaki responded The anisotropy parameter b for the photofragments increased with IR laser intensity only when the IR and UV lasers had parallel polarizations and were simultaneously –red.For the c.m. translational energy distributions with and without the IR laser –eld the two distributions are essentially the same indicating that the IR laser –eld is not absorbed by the molecules but aligns them. Prof. Miller said I would like to ask Dr Corkum to expand somewhat on his discussion of the spinning of molecules. Are there any limitations in how fast you can spin the molecules that is other than the dissociation limit ? It takes time for molecules to respond to a change in the direction of the quantization axis de–ned by the electric –eld. It seems to me that at some point the –eld required to keep the molecule in phase with the rotating –eld will become unrealistically high.Dr Corkum responded Molecular alignment is well established. It has been known since the early days of lasers and is the basis of the optical Kerr eÜect. Thinking classically strong –eld Faraday Discuss. 1999 113 77»106 100 alignment can be understood as follows a molecule that begins to rotate out of alignment experiences a torque returning it towards alignment. In the harmonic oscillator-like well it exercises pendular motion. In the rotating frame a spinning molecule also undergoes pendular motion. Perhaps a reader may be concerned by the increase in the level separation between rotational levels. Because the E\1 energy is given by 2Iu2 the small pendular motion contributes more to the total energy in a rapidly moving frame than in a slowly rotating frame.As long as everything remains adiabatic there is no limit to the speed of rotation. Of course dissociation is non-adiabatic. Prof. Seideman communicated An interesting question in connection with the possibility of manipulating the center-of-mass motion of molecules which Dr Corkum demonstrated,1 is whether one could repel molecules with light. In recent work we generalized the concepts of molecular focussing2 and molecular optics3 to include also repulsive molecular optics elements.4 We –rst note that laser manipulation of the center-of-mass motion is based on the interaction of the molecular polarizability tensor a(ul) with a nonresonant inhomogeneous laser –eld V \[aI(x,y,z)/4 where I(x,y,z) is the space-dependent intensity u is the laser frequency and l Mx,y,zN are the space-–xed coordinates.In the low frequency limit to which the method of ref. 1»3 pertains the polarizability has converged to its DC value which is positive and hence the interaction is purely attractive ; the molecules are attracted to the high intensity regime. The DC-like interaction can serve to focus molecular beams,2 as Dr Corkum showed and it extends also to other molecular optics elements3 but it does not provide a mechanism for repelling molecules. 01 * Repulsive molecular optics elements are expected to open a variety of new opportunities. These may include molecular waveguiding along the low-intensity axis of a TEM (doughnut) mode laser where long time con–nement would be possible while ionization is minimized trapping in a low-intensity region where again ionization could be minimized combining optical elements to optical devices and studying problems of interest in scattering theory such as hard-wall collisions.In the parallel –eld of atom optics most of the work during the past few years has been based on repulsive interactions.5 In order to reverse the sign of the polarizability tensor one requires large laser frequencies as e uv) such that the –eld would destabilize rather than stabilize u a(u converges to the DC limit a(ul)]a[0. This limit corresponds to the scheme of ref. (u compared to system frequencies the electron. For ground electronic states the l@ue requirement is not practical. It is readily attained however with high Rydberg states where the electronic level spacing scales as n~3.Fig. 23 shows the dynamic polarizability a(u vs. the ratio of the laser frequency and the electronic l) level spacing ueDn~3. We stress that Fig. 23 is based on a semiclassical approximation of the electronic wavefunctions and hence should be regarded as qualitative only.4 In the low frequency limit l) 1»3. As the frequency is scanned through the discrete spectrum a(u undergoes a series of reso- l) nances and in the high frequency limit it scales as l~2. In this regime the laser induced potential converges to the ponderomotive energy of a free electron I/4ul2. u Fig. 23 Schematic illustration of the electronic polarizability for l\5 (solid) 10 (dashed) 20 (dot»dashed) vs. the –eld frequency measured in units of the level spacing.The polarizability is estimated within a semiclassical approximation. Reprinted with permission from ref. 4. Copyright 1999 American Institute of Physics. Faraday Discuss. 1999 113 77»106 101 Fig. 24 illustrates for instance a negative lens based on the repulsive interaction. The dashed contours show the intensity pro–le and the solid curves are the molecular trajectories. The molecules are repelled from the high intensity centers and are funneled through the low intensity ììgateœœ focussing downstream. A potential advantage of the negative lens over the positive lenses described in ref. 2 is that the demagni–cation ratio (the ratio of the image size to the initial beam dimension) may be smaller since parts of the molecular beam are selectively repelled.An experimental realization of the scheme4 has been initiated by Prof. Gordonœs group at UIC. 1 P. B. Corkum C. Ellert M. Menendale P. Dietrich S. Hankin S. Aseyev D. Rayner and D. Villeneuve Faraday Discuss. 1999 113 47. 2 T. Seideman J. Chem. Phys. 1997 106 2881; T. Seideman Phys. Rev. A 1997 56 R17; H. Stapelfeldt H. Sakai E. Constant and P. B. Corkum Phys. Rev. L ett. 1998 79 2787. 3 T. Seideman J. Chem. Phys. 1997 107 10420. 4 T. Seideman J. Chem. Phys. 1999 111 4397. 5 G. M. Gallatin and P. L. Gould J. Opt. Soc. Am. B 1991 8 502; J. J. McClelland and M. R. Scheinfein J. Opt. Soc. Am. B 1991 8 1974; A. Landragin J.-Y. Courtois G. Labeyrie N. Vansteenkiste C. I. Westbrook and A. Aspect Phys. Rev. L ett. 1996 77 1464; P.Szriftgiser D. Gueç ry-Odelin M. Arndt and J. Dalibard Phys. Rev. L ett. 1996 77 4. Dr Corkum summarised Strong –eld molecular optics promises control over (small) molecules that is analogous to the control that we have with our –ngers over a pencil. This control is exercised through the modi–cation of the ground state which we understand well. Strong –elds arise not only in laser science where we can apply the –elds with femtosecond precision they also occur in biological science where the geometric structure of a molecule allows the –eld to be placed with Angstroé m precision. Strong –elds severely modify and mix the excited potential energy surface. Although it will be complex it may be possible for strong –elds to guide molecular processes in time just as biology uses strong –elds to guide molecular processes in space.Prof. Ashfold Dr Orr-Ewing Mr Regan and Dr Wrede“ opened the discussion of Prof. Seidemanœs paper We have investigated the resonance enhanced multiphoton ionisation (REMPI) of jet-cooled HI molecules at wavelengths D365 nm. As Fig. 25 shows the one colour excitation spectra for forming the parent and both fragment ions are richly structured and show many features in common though the relative peak intensities show large variations. The H` fragment ion channel has been investigated further by one colour ion imaging methods. Fig. 26 displays two representative examples of 2D slices through the reconstructed 3D velocity distributions each recorded with the laser polarisation aligned vertically.The entire image in both cases is obtained in a single laser shot without the need to scan across the H atom Doppler pro–le. Such an Fig. 24 Focussing in a ììnegative lens œœ. The dashed contours show the intensity distribution and the solid curves show the molecular trajectories. Reprinted with permission from ref. 4. Copyright 1999 American Institute of Physics. “ Also S. R. Langford University of Bristol UK. Faraday Discuss. 1999 113 77»106 102 Fig. 25 Excitation spectra for forming parent (HI`) and fragment (I` and H`) ions following pulsed laser excitation of a jet-cooled HI sample in the wavenumber range 27 315»27 520 cm~1. (a) and (b) indicate the wavenumbers at which the H` ion images displayed in Fig. 26 were recorded. Also shown is the wavenumber appropriate for 3]1 REMPI of H(n\1) atoms.observation is most readily accommodated by assuming that the H` ions arise via one or more continuum^bound transitions. This tends to rule out one photon parent dissociation and subsequent MPI of ground state H atoms as a signi–cant contributor to the measured image. Such a view is con–rmed by (i) the exceedingly weak parent absorption at such long wavelengths; (ii) the observed angular anisotropy (which indicates a parallel excitation process in contradiction to all assignments of the longest wavelength absorption in HI1) ; (iii) the number and size of the various rings evident in the images none of which match with the recoil velocity expected for formation of ground state H and I atoms; and (iv) the fact that the H` ion yield shows no obvious enhancement at D364.6 nm [the wavelength required for 3]1 REMPI of H(n\1) atoms].Rather by systematic investigation of the way the radii of the various rings within the images evolve with change in excitation wavelength we can show that the outermost ring»the radius of which scales with the square root of four times the photon energy»arises as a result of the following four Fig. 26 Images of the H` ions formed following one colour excitation of jet-cooled HI at 27 406 cm~1 (364.88 nm) and 27 439 cm~1 (364.44 nm) using linearly polarised laser radiation with the E vector aligned vertical. 103 Faraday Discuss. 1999 113 77»106 photon excitation process HI »»»’ 4hl H(n\2)]I(2P3@2) followed by one photon excitation of the H(n\2) atom leading to H` ion formation.The diameters of the inner rings scale with the square root of the one photon energy and are most readily understood in terms of four (or more) photon ionisation of HI resulting in formation of HI`(X) in high vibrational levels which then undergo a further one photon absorption and dissociate directly to the products H`]I. We have not attempted to image the corresponding I` product channel(s) but given the energies involved and the higher I atom electronic state density (as compared with H) it would not be surprising to –nd that several diÜerent fragmentation/ ionisation combinations contribute to the measured I` yield. In the context of the work of Profs. Seideman and Gordon HI fragmentations occurring at the 3u energy should show a phase shift 1 relative to the parent ion signal but if these lead to more than one state of the I atom there is no a priori reason why these should all show the same phase shift.Conversely contributions to the I` ion yield arising from dissociations at the two or four photon energy (with subsequent multiphoton ionisation of the I atom product if necessary) should not exhibit such coherent control and merely reduce the amplitude of the modulation of the overall dissociation signal. This begs the questions How generally should we expect to discern clear modulations in a dissociation yield signal and what are the prospects for interpreting any measured phase lag between the ionisation and dissociation channels in cases where more than one ìcontrolledœ fragmentation channel may be contributing to the dissociation yield ? 1 S.R. Langford P. M. Regan A. J. Orr-Ewing and M. N. R. Ashfold Chem. Phys. 1998 231 245. Prof. Seideman and Prof. Gordon replied Prof. Ashfold and colleagues raise two diÜerent issues which we would like to address separately. (1) In the event that several internal product states are produced at the same total energy and the detection scheme does not discriminate between them (as for instance in the case discussed by Prof. Ashford and colleagues where photodissociation of HI produces several I atom states) the measured signal is an incoherent sum over the open channels. It is then a simple matter to show that the phase shift of channel S is the argument of a sum over internal states of the right hand side of eqn.(3) in ref. 1 Pdk � \g oD1 (3) o EnSk� ~TSEnSk� ~oD1 (1) o gT d13 S \arg ;n where n denotes the internal state and all other symbols are de–ned in the paper. If n is not resolved the phase shift is a property of the S product channel (the dissociation channel in the case discussed). (2) Competing processes which produce the same product as the process under study are often to be expected and as Prof. Ashfold and colleagues pointed out HI is a sufficiently complex system to allow several such processes. To examine their eÜect it is important to separate the issue of the measurement and interpretation of a phase shift from the problem of coherent control. In general competing processes would occur via a single excitation route and hence merely decrease the modulation depth.In that event d13 S can still be accurately measured and the information it conveys regarding the continuum is not altered. (Ongoing experiments measure the phase shift of HI ionization at d13 is 1D353 nm where the modulation depth is as small as 10% but yet completely reproducible with a relative error of ^3%.) From the view-point of coherent control on the other hand the reduced modulation depth implies a decreased range of control. u One might also envisage competing processes that do take place via both excitation routes and hence exhibit modulations. The results of ref. 1 for instance could conceivably have been interpreted as coherent one- and three-photon ionization of I atoms generated by dissociation of HI.Our current understanding of the possible origins of a phase shift and the relation between its energy dependence and system properties can be applied to rule out such processes in all cases that come to mind see e.g. Fig. 27 later. 1 J. A. Fiss A. Khachatrian L. Zhu R. J. Gordon and T. Seideman Faraday Discuss. 1999 113 61. Faraday Discuss. 1999 113 77»106 104 Prof. Brumer also replied To answer the question directly you are implying that if there are many pathways to the products then this will lead to something more complicated than a simple phase lag this is in fact not the case. A phase lag will be generated if there are two diÜerent products formed and there is the minimal kind of coupling described by Seideman et al.1 The additional number of routes to product does not alter the picture of a simple diÜerence between two phases.2 1 J.A. Fiss A. Khachatrian L. Zhu R. J. Gordon and T. Seideman Faraday Discuss. 1999 113 61. 2 P. Brumer and M. Shapiro Chem. Phys. L ett. 1986 126 541. Prof. Seideman summarised The phase shift d13 should not be regarded as merely a tool for coherent control. It is a de–nitive signature of control and hence a theoretical understanding of its origin eliminates a blind search for controllable systems. More importantly however it is a tool for understanding molecular excited states. Furthermore phase shifts are not limited to coherent control type experiments. We will point out later that they are a more general phenomenon which can be observed also in other types of experiments.The physical origin of the phase shift is summarized schematically in Fig. 27 which relates d13 to properties of the system. In essence d13 diÜers from zero provided break-up (dissociation or ionization) occurs via at least two routes (irrespective of the excitation mode). It may thus be regarded a simple manifestation of Youngœs two slits principle in matter waves. As shown in Fig. 27 panel (a) the phase shift vanishes in the case that the continuum potential induces only elastic scattering. If the continuum is nonadiabatically coupled but structureless (b) d13 is a smooth nonzero function of energy. In this case the phase shift arises from the interference of continuum states ; in the speci–c limit of two coupled electronic states it probes the diÜerence between the partial wave phase shifts of the corresponding scattering eigenstates.Structure in the continuum is revealed by corresponding structure in the phase shift. An isolated resonance that interacts with a purely elastic continuum (c) gives rise to a maximum at the resonance energy. Here d13 arises from the interference of the direct and resonance-mediated routes and is maximized where interference is constructive (i.e. at e\(q(1)]q(3))/2 in eqn. (36) of ref. 1 see ref. 2). In the case that an isolated resonance interacts with a coupled continuum the phase shift is nonzero oÜ-resonance and falls to a minimum on-resonance [panel (d)]. Whereas an isolated resonance with no direct route to the continuum does not produce a phase (d) coupled resonances give rise to a nonzero modulated phase shift regardless of the availability of a direct route (e).In this case d13 arises from the interference between resonances. Finally panel (f) predicts a structured maximum superimposed on a nonzero slowly varying background produced by coupled resonances interacting with a coupled (i.e. inelastic) continuum. Fig. 27 Schematic illustration of the phase shift that arises from diÜerent coupling mechanisms in the continuum. 105 Faraday Discuss. 1999 113 77»106 Fig. 28 Phase lags (upper panel) and VUV photoionization spectrum of HI (lower panel) in the vicinity of the 5d(n,d) resonance. The secondary peak at 355.2 nm is likely to be due to the rapidly predissociating 9d level converging to v\1 of the 2%3@2 ion state,5 illustrating one example where a feature absent from the spectrum appears in the phase lag. Fig. 27 also suggests the type of information that could be derived from phase shift measurements. Near resonance d13 is a spectroscopic observable that complements the information contained in the absorption spectrum inasmuch as it depends on the phase rather than on the modulus of the dipole matrix elements. If a given resonance carries too small an oscillator strength to be distinguished from noise in the absorption spectrum it may nevertheless be present in the phase shift spectrum. An example is given in Fig. 28 where a peak is found in the phase lag spectrum to the blue of the 5d(n,d) resonance of HI that is absent in the photoionization spectrum. At large detuning d13 carries dynamical long range information. Ref. 1 focuses on a phase shift that arises from and re—ects properties of the –nal continuum. Elsewhere we show that a qualitatively diÜerent phase shift arises from complex intermediates in the multiphoton process.2,3 The latter re—ects properties of the intermediate manifold. Signi–- cantly it can be inverted directly to yield the cross correlation function governing the dynamics in the intermediate manifold.4 1 J. A. Fiss A. Khachatrian L. Zhu R. J. Gordon and T. Seideman Faraday Discuss. 1999 113 61. 2 T. Seideman J. Chem. Phys. 1999 in the press. 3 J. A. Fiss A. Khachatrian L. Zhu R. J. Gordon and T. Seideman Phys. Rev. L ett. in preparation. 4 T. Seideman in preparation. 5 H. Lefebvre-Brion personal communication. Faraday Discuss. 1999 113 77»1

ISSN:1359-6640    

DOI:10.1039/a906730b

出版商:RSC    

年代:1999

数据来源: RSC

摘要:

State-to-state reaction dynamics in crossed supersonic jets threshold evidence for non-adiabatic channels in F+ H2 Sergey A. Nizkorodov Warren W. Harper and David J. Nesbitt* JIL A University of Colorado and National Institute of Standards and T echnology and Department of Chemistry and Biochemistry University of Colorado Boulder CO 80309-0440 USA 3@2) com Received 9th March 1999 2 The reaction of F]n-H to form HF(v,J)]H is studied in a crossed jet apparatus under single collision conditions using high-resolution direct absorption spectroscopy to probe the nascent rotational HF distributions. The J-dependent reactive cross-sections into HF(v\3,J) are investigated over a range of center-of-mass collision energies well below the 1.9 kcal mol~1 barrier for adiabatic chemical reactions with ground state F(2P atoms.The energy dependent reaction cross-sections decrease much more slowly with E F(2P than predicted by exact quantum calculations on the adiabatic 3@2)]H2 surface (K. Stark and H. Werner J. Chem. Phys. 1996 104 6515). In addition product states in the HF(v\3) manifold are observed that are energetically accessible only to the excited spin»orbit state F*(P1@2)]H2( j\0,1) channel. These observations strongly suggest that non-adiabatic reactions with spin»orbit excited F*(P1@2) contribute signi–cantly in the near threshold region in good agreement with recent calculations by M. Alexander H. Werner and D. Manolopoulos (J. Chem. Phys. 1998 109 5710). Finally the feasibility of high-resolution IR laser Dopplerimetry on the nascent products is illustrated on collision free HF(v,J) distributions formed from reactions of F]CH4 .2 I Introduction It has been long recognized that chemistry in typical gas-phase environments ranging from the Earthœs atmosphere to the interstellar medium is driven primarily by reactions involving transient species such as free radicals and molecular ions as these reactions are frequently characterized by high rates and low activation energies. Though the scienti–c community has made substantial progress towards the dynamics of such reactions in recent years our understanding of elementary chemical processes is far from complete. Even the prototypic F]H reaction system which has been under intense scienti–c scrutiny for several decades,1h4 still has several key issues to be resolved.As one example of central relevance to the present work the importance of F/F* electronic spin»orbit excitation or alternatively stated the role of adiabatic vs. non-adiabatic reaction pathways in chemical reactions remains an outstanding and yet crucial question in reaction rate theory.5 The very fundamental level of these questions underscores the need for further experimental and theoretical eÜorts to elucidate ììsimpleœœ atom abstraction dynamics at the state-to-state level. Recently the dynamics of the F]H reaction has been investigated in our laboratory with crossed supersonic jets.6 The full nascent state distribution of the HF products has been obtained 107 2 Faraday Discuss. 1999 113 107»117 This journal is( The Royal Society of Chemistry 1999 4 at Ecom\2.4(6) kcal mol~1 under single collision conditions using direct infrared absorption highresolution spectroscopy.These direct absorption studies have become experimentally feasible due to a combination of near shot-noise limited absorption sensitivity and an efficient source of atomic free radicals developed in our group.6 The source utilizes an electrical discharge struck in the jet stagnation region to generate high radical densities followed by supersonic expansion. Spectroscopic measurements in this laboratory show that the radical number densities of 1015 cm~3 at the ori–ce can be routinely achieved. In the present work we report results at center-of-mass collision energies substantially below the 1.9 kcal mol~1 reaction barrier theoretically predicted3,7 F(2P for the lowest adiabatic 3@2)]H2 potential energy surface (PES).This choice of center-ofmass collision energy greatly suppresses reactive encounters on the ground spin»orbit adiabatic surface and thereby selectively enhancing the importance of non-adiabatic pathways with spin» orbit excited F*(2P1@2) atoms. Additionally we demonstrate the experimental feasibility of obtaining state-to-state diÜerential cross-section information from high-resolution IR laser Dopplerimetry as brie—y tested by application to the F]CH reaction. The F]H reaction system represents one of the quintessential paradigms of chemical reaction 2) 2 dynamics. As a consequence the body of existing experimental and theoretical knowledge is immense; the interested reader is referred to an excellent review by Manolopoulos3 for a more detailed discussion and further references.The key points most relevant to the present study can be summarized as follows. (i) The high reaction exothermicity (*E\32.001(14) kcal mol~1 for F(2P3@2)]H2( j\0)]HF(v\0,J\0)]H) is primarily released into a vibrationally inverted HF(vO3) product distribution which has been characterized by a number of experimental methods at increasing levels of quantum state resolution.6,8h11 (ii) The unpaired electron in the F results in multiple potential energy surfaces which asymptotically correlate with either the lower F(2P F*(2P or upper 3@2) spin»orbit states. Most importantly reactions initiated on the surfaces 1@2) other than the lowest PES are repulsive in the transition state region and therefore predicted to be forbidden in the Born»Oppenheimer (i.e.purely adiabatic) approximation.12,13 Though theory claims that this restriction can be lifted by means of weak non-adiabatic interactions no experiments to date have been able to unambiguously con–rm the presence of the F*]H reaction 2 channel.3 (iii) The relevant potential energy surfaces have been calculated by ab initio methods by Stark and Werner (SW) with the stated global accuracy of better than ^0.2 kcal mol~1,7 and later extended to include the spin»orbit interaction by Hartke and Werner (SHW).14 (iv) Classical trajectory and full quantum-mechanical calculations performed on the lowest adiabatic SW/SHW PES can qualitatively reproduce much of the prevailing experimental data on the F]H reac- 2 tion including diÜerential cross-sections,15h18 thermal rate constants,19,20 and nascent HF product state distributions.6 The major focus of this work is to examine the possibility of non-adiabatic channels in this most basic and extraordinarily well studied of chemical reactions.The essential idea is schematically summarized in Fig. 1. The radical source generates both ground (F) and spin»orbit excited (F*) atoms in the high pressure discharge region (most likely in a near statistical B4 2 ratio) which are inefficiently cooled in the subsequent supersonic expansion. These F/F* atoms collide with jet cooled H molecules at a center-of-mass collision energy dictated by the jet velocities which are 2 measured by direct time-of-—ight and/or high resolution IR Dopplerimetry on each jet.By operating at center-of-mass collision energies well below the barrier (1.9 kcal mol~1) we can signi–- cantly suppress the adiabatic (F]H2) reaction channel and thereby greatly enhance experimental sensitivity for probing non-adiabatic (F*]H channels. The analysis in this paper proceeds in two ways. First we investigate the total reaction cross- F]H reactions but become energetically accessible with the additional (*EspinhorbitB 2 kcal mol~1 22) spin»orbit excitation along the F*]H path. Most importantly since the section as a function of center-of-mass collision energy and then compare these results with adiabatic quantum dynamical calculations18,21 on the state-of-the-art F]H potential energy 2 surface.Secondly we can also exploit the high spectral resolution of the laser based product state detection to maximal advantage and look for HF(v,J) products that are rigorously inaccessible to adiabatic 1.15 2 relative energies of the reagents/products are known to high precision from previous spectroscopic studies,23,24 this second approach relies solely on conservation of energy and is therefore independent of details of the potential surface such as barrier heights transition states geometries tunneling widths etc. The complete center-of-mass collision energy dependence of this reaction will be Faraday Discuss. 1999 113 107»117 108 3@2) F*(P1@2)]H2 com\0.54(10) E Fig. 1 Simpli–ed energy diagram for the F(P kcal mol~1 (the reaction at curves on the left are the experimental Ecom distributions).At these low collision energies the range of HF(v\3,J) levels that can be populated is radically diÜerent for F and F*. For this particular example the highest energetically allowed state is HF(v\3,J\5) for F* and HF(v\3,J\2) for F. Thus rotationally resolved studies in the HF(v\3) vibrational manifold provides an unusually sensitive probe of non-adiabatic reaction dynamics. reported elsewhere in greater detail ;25 this work focuses explicitly on a few selected collision energies well below the adiabatic F]H reaction barrier. 2 com). The F]H experiment (Ecom\0.3»2.4 kcal 2 2»95% He yielding a ìì fast œœ F 2»20% Ne»75% Ar yielding a ììslowœœ F atom speed of II Experimental The reactive scattering apparatus used in this work comprises two pulsed molecular jets crossed at right angles B5 cm downstream from the respective ori–ces.For the F]H experiment an 2 argon/hydrogen mixture is expanded from the –rst source through a 145^5 lm pinhole at a total backing pressure of 900 Torr. This corresponds to a measured peak density of B2]1013 cm~3 in the middle of the intersection region during the 300 ls long pulse duration. Seeding with Ar (0»40%) is used to slow the jet and thereby control the center-of-mass collision energy (E second jet contains F atoms produced in a pulsed mini-slit (300 lm]5 mm) discharge source.6 To achieve the maximal collision energy coverage in the mol~1) two diÜerent precursor mixtures are employed (i) 5% F atom jet speed of 1.48 km s~1 and (ii) 5% F 0.59 km s~1.For the F]CH reaction described at the end of this paper a 10% F 4 2»40% Ne»50% Ar mixture is used to obtain ììintermediateœœ F atom speeds of 0.64 km s~1. Typical conditions correspond to discharge currents of 100»500 mA at a backing pressure of 30»45 Torr where the pressures have been optimized for discharge stability. The estimated peak densities (i.e. including carrier gases) are O5]1013 cm~3 in the intersection region. These backing pressures and densities are chosen to be sufficiently low to ensure reactive/inelastic collision probabilities of less than a few percent per reactant and/or product molecule which makes the probability of H]F secondary reactions such as 2 ]HF]F or rovibrational relaxation of the product HF(v J) negligible.The HF(v,J) products formed in the intersection region are probed via direct absorption spectroscopy in a Harriot multipass cell with a tunable single-mode F-center laser as the IR radiation source. The extremely narrow instrumental resolution (O0.0001 cm~1) of the single mode source allows full quantum resolution of the HF product states as well as velocity resolution of B10 m s~1. The transient absorption signal due to HF(v,J) is registered as the diÜerence between signal and reference InSb detectors during the temporal overlap of both gas pulses with the electrical discharge pulse. For each probed HF(v@,J@)^HF(vA,JA) transition the full Doppler absorbance 109 Faraday Discuss. 1999 113 107»117 pro–le is recorded (B2500 MHz scans 3 MHz step size).The pro–les can be integrated over the frequency to provide the absolute column integrated density diÜerences between upper (v@,J@) and lower (vA,JA) product states and ultimately analyzed to yield quantum state populations. Averaged over 4»8 pulses the experimental detection limit for the product HF is estimated to be better than 108 molecules cm~3 per quantum state.6 It is worth noting that the HF absorbances are recorded in absolute units and thus the HF product densities are determined absolutely. At present however we do not directly probe F atom densities in the intersection zone and thus all measurements reported are with respect to a reference product state (typically HF(v\3,J\1) measured on v\4^3 R(1)).This approach yields excellent day-to-day reproducibility and thus also facilitates rigorous comparison over the many days of data collection necessary to extract the full nascent quantum state distributions. Due to the high experimental sensitivity extremely weak background absorption can sometimes be observed from residual HF impurities in the F discharge. The magnitude of this background HF 2 is quite small (\10% of typical peak signals) and can be reliably subtracted by background scans in the absence of the H jet. The reference probe and background scans are obtained multiple 2 times (typically interleaving –ve successive scans) under constant F source and H jet conditions 2 to further improve the statistics. 2 2( j\1) nuclear spin state is 2( j\0) is also included.From bond dissociation cm~1)23 the F]H2( j\1) reac- 2) III Results and discussion Fig. 1 shows a schematic portion of the F]H energy diagram for understanding the essential strategy of this experiment. For simplicity only the most populated H considered but the principle is identical if H (D0\47311(5) cm~1)24 and energies of HF 2 (D0\36118.6(5) H tion exothermicity can be determined with an unusually high precision *E\32.348(14) kcal mol~1. When released in the reaction this energy —ows into the relative translation of the H and HF products and into the internal degrees of freedom of HF. The purely rotationless HF(v\3 J\0) state lies very close to the energetic reaction threshold with ground state F atoms and in fact is only accessible to collisions with F* atoms for EcomO0.17 kcal mol~1 (Fig.1). At EcomP 0.17 kcal mol~1 both F and F* reactions can energetically produce HF(v\3,J) but with a signi–cantly diÜerent range of J levels. For example at Ecom\0.54 kcal mol~1 reactions with the ground spin»orbit state F can only produce up to HF(v\3,J\2) whereas spin»orbit excited F* reactions can energetically yield up to HF(v\3,J\5). Thus studies of quantum state resolved reactive cross-sections into HF(v\3,J) under low collision energy conditions can provide an especially sensitive probe for possible non-adiabatic (F*]H channels. With this in mind the absorption signals out of an HF(v\3,J) vibrational manifold have been measured from EcomB0.3»2.4 kcal mol~1. Sample raw data representing Doppler pro–le scans over individual HF rovibrational transitions (v\4^3; R(0)-R(5)) at Ecom\2.35 kcal mol~1 and 1.10 kcal mol~1 are shown in Fig.2. The salient points can be summarized as follows (i) For a given J level the relative HF(v\3,J) transition intensities noticeably decrease re—ecting variation in the corresponding state-to-state reaction cross-sections with Ecom . (ii) On the other hand the shape of the J distribution is much less sensitive to Ecom contrary to what one might anticipate from the F]H reaction energetics (see Fig. 1). It is important to point out that the Doppler 2 pro–les for the HF(v\3,J) product manifold are largely dominated by angular divergence in the E jets and as a result are independent of both and J. This is essentially due to the large mass com diÜerence between H and HF products which deposits most of the excess recoil energy into H atom recoil.Indeed as con–rmed by detailed Monte-Carlo simulations described elsewhere,25 the HF Doppler widths for F]H reactions can be well described by such angular divergence eÜects. 2 F]CH For recoil objects with more comparable masses such as from 4 ]HF]CH3 reactions this will of course no longer be true. The diÜerent kinematics of such reactions with more than one ììheavyœœ (i.e. non-hydrogenic) atom can therefore lead to a quantum state sensitive Doppler structure in the high resolution absorption pro–les which is brie—y addressed at the end of this paper. The above observations for F]H reactions can be put on a more quantitative basis in the 2 following way.The relative integrated absorbances are –rst transformed into column integrated densities i.e. / [HF(v,J)]dl using known Einstein A coefficients for HF26 as described in ref. 6. This relies on the absence of population in the v\4 manifold which is energetically inaccessible Faraday Discuss. 1999 113 107»117 110 Fig. 2 Sample scans over individual lines of HF in the R-branch of v\4^3. (a) Ecom\2.35(46) kcal mol~1 com\1.44(24) kcal mol~1. Note the strong uniform decrease in HF product intensity but rather small (b) E shift in product state rotational distributions. by P8 kcal mol~1 (i.e. to both F and F* reagents) and can be directly tested by v\5^4 absorption. Previous work6 showed that the density to —ux transformation for F]H is essen- 2 tially —at (O5%) due to the favorable ììheavy]light-light œœ reaction kinematics.Thus the column integrated densities are directly proportional to the state resolved integrated product —uxes. The —uxes must scale linearly with the integrated reaction cross-sections densities of both reagents and relative velocity in the collision. (Note that the last two quantities are both varied in order to tune Ecom .) Thus for constant F atom discharge conditions the relative integrated cross-section into a given –nal J state can be calculated from (1) pJ(Ecom)P/ [HF(v\3,J)] dl /Ar 2 2 XJE where X is the mole fraction of H in the respective com H mixture. The proportionality sign re—ects the lack of information on the absolute density of F atoms; all cross-sections are calculated relative to the reference state transition i.e.for a jet expansion of neat hydrogen (X\1) and v\4^3 R(1) transition. The data obtained for the ìì fast œœ and ììslowœœ —uorine jets are treated independently and then scaled by a single parameter to provide best agreement in the overlapping region of collision energies (EcomB1.0»1.7 kcal mol~1). The dependence of the resulting reaction cross-section on E 2 is shown in Fig. 3. In the interest com of space only the total (summed over the J states) HF(v\3) cross-sections are shown; a complete breakdown by –nal HF(v,J) rovibrational quantum state as well as a more detailed comparison with exact quantum calculations will be presented elsewhere.25 The cross-sections are seen to E increase monotonically with Ecom\0.3»2.4 kcal com; no apparent threshold is observed over this mol~1 range.Even at Ecom\0.3 kcal mol~1 i.e. the lowest collision energy sampled in the present experiment the reactive cross-sections for forming HF(v\3,J) are still quite appreciable. In fact the HF(v\3) cross-sections at 0.3»0.9 kcal mol~1 collision energies are down by onlyB6-fold i.e. considerably higher than one might initially expect for reactions at energies more than a kcal mol~1 below the adiabatic (B1.9 kcal mol~1) barrier predicted theoretically. This indicates the dramatic importance of quantum tunneling and/or non-adiabatic eÜects in the F]H reaction dynamics. This last point becomes particularly clear if the experimental cross-sections are compared with theoretical predictions from ììexactœœ (i.e.fully converged) quantum dynamics calculations on adiabatic potential energy surfaces (PES). Arguably the most rigorous F]H reactive scattering cal- 2 culations in the energy range of interest have been performed by Castillo et al.18,21 on the PES of 111 Faraday Discuss. 1999 113 107»117 F]H2( j) j\0 (long dash) ; j\1 (short dash) ; j\2 (dotted) ; n-H cooled down to 2 Fig. 3 Total HF(v\3) reaction cross-sections as a function of Ecom . Open and closed circles represent data km s~1) and 2 (vfB0.59 km s~1) discharge mixtures respectively. The taken with Ne/F 2 (vfB1.48 He/F theoretical curve is the result of fully converged quantum mechanical scattering calculations on the lowest adiabatic SW PES for E 200 K (thick solid line).The axis is shifted by 0.38 kcal mol~1 for the theoretical data to re—ect spin»orbit com eÜects (see text for details). The vertical axis is dimensionless for the experimental data and is in ”2 for the theory. The experimental cross-sections drop oÜ much more slowly with energy than predicted theoretically consistent with additional contributions from non-adiabatic F*]H reactions. 2 F]H2( j)]HF(v\3 all J)]H integral reactive cross-sections of Castillo 2 n-H (200 K) data above E Stark and Werner (SW PES).7 A more accurate SHW PES which includes the eÜects of spin»orbit interaction is now available14 but adiabatic calculations on this surface have been performed only for a limited number of energy points.17 The reaction barrier on the lowest SHW PES is 0.38 kcal mol~1 higher than on the SW PES re—ecting lowering the adiabatic F]H asympote curve by 2 approximately 1/3*Espinhorbit .The shape of the barrier however remains essentially unchanged by the inclusion of the spin»orbit eÜects. The energy dependences of the cross-sections calculated on SW and SHW surfaces are therefore predicted to be quantitatively very similar apart from a 0.38 kcal mol~1 relative shift in the energy scale.17,21,27 Consequently the extensive calculations on the SW PES are taken as the most reliable theoretical prediction of the adiabatic reaction E dynamics simply shifting the axis upward by this 0.38 kcal mol~1 spin»orbit induced com increase in the barrier height. Fig. 3 compares the and Manolopoulos21 with the experimental results.The theoretical data are presented for H in 2 j\0 1 and 2 rotational states as well as for n-H at 200 K (i.e. nuclear spin equilibrated at room 2 temperature but cooled rapidly in the jet expansion). The 200 K curve is the most appropriate for comparison with our experiments since this represents our best rotational temperature estimate for neat H expansions (based on data of refs. 28»31 and on extensive simulations of the experi- 2 mental Ar/H jet velocities). The relative experimental cross-sections are scaled overall to match the theoretical com\1.9 kcal mol~1 where the calculations are expected 2 to depend least on transition state geometry barrier widths tunneling contributions etc. Note that the theoretical cross-sections decrease signi–cantly more steeply with E than experimen- EcomB0.7 kcal mol~1 the theoretical reactivity for 200 K becomes tally observed.Indeed by com vanishingly small whereas the experimental cross-sections remain signi–cant down to the lowest measurements at Ecom\0.31(7) kcal mol~1. We next consider reasons for this observed discrepancy. The –rst question is whether theory is performing accurately enough at low Ecom which since the quantum dynamics calculations are numerically exact for a given adiabatic surface relies on the quality of the potential surface. Indeed until the present work the F]H calculations have only been tested against extensive EcomP1.84 kcal mol~1.3,16h18,32 A closely related issue is that the molecular beam studies at 2 SHW PES is known to underestimate the global reaction exothermicity by B0.2 kcal mol~1 which would be expected to in—uence these calculations most at low Ecom .The eÜect of such Faraday Discuss. 1999 113 107»117 112 The possibility that the enhanced reactivity at low asymptotic potential surface errors on the reaction cross-sections is difficult to estimate and depends on where this 0.2 kcal mol~1 diÜerence accrues. For example a 0.2 kcal mol~1 error is localized in the exit channel would have a negligible eÜect on the energy dependent cross-sections whereas if it were localized in the entrance channel the cross-sections for forming HF(v\3) would have the same shape as in Fig. 3 only shifted down by 0.2 kcal mol~1 along the E axis. com However even such a shift would fail to bring the experiment and theory in agreement the latter still severely underestimating the reaction cross-sections at low Ecom .Thus though potential surface errors in the asymptotic exothermicity may have some eÜect it is not likely to be the main contributor to the underpredicted cross-sections observed experimentally. (i.e. j[1) is due to rotationally hot H2 Trot\200 K for the jets is a realistic upper limit (lower for H jets seeded with Ar) with completely negligible Ecom also does not agree with the observations. First rotational excitation of H is predicted to have 2 only a small in—uence on the reaction cross-sections,33,34 as explicitly con–rmed by the calculations of Castillo and Manolopoulos. Secondly a rotational temperature of H2 2 rotational heating of H due to collisions on the way to the intersection region.Though the 2 F]H for higher j the calculated E reaction threshold shifts to lower 2( j\2) cross-sections com below 1 kcal mol~1 are still far too small to account for the experimental observation. In fact even theoretical predictions for a jet of ììneatœœ H2( j\2) would still qualitatively fail to reproduce the experimental cross-sections. E The most credible explanation of the enhanced reactivity at low is via non-adiabatic reac- com tion of F* with H The spin»orbit excited F* atoms produced in the discharge carry 2 . *Espinhorbit\1.15 kcal mol~1 internal energy compared to F and can energetically produce com\0 (Fig. 1). The most compelling evidence in favor of this hypothe- F*]H2( j\0,1) channel. The essential idea in this analysis is based on HF(v,J)Nmax\Ecom]*E for a given initial state of F/H2 reagents and a known center-of-mass HF(v\3,J\0) even at E sis comes from observation of HF(v\3,J) product states which can only be accessed energetically via the non-adiabatic simple energy conservation arguments.The exothermicity of the F]H reaction is known very 2 accurately from spectroscopic measurements;23,24 *E\32.001(14) and 32.348(14) kcal mol~1 for F]H reactions 2( j\0) and F]H2( j\1) respectively. Furthermore the H atom product can only be in the (1S) ground state which means that this excess energy must be converted into either (i) internal rotation and vibration of the HF(v,J) or (ii) relative recoil kinetic energy (Erecoil) of the H]HF products in the center of mass frame.Thus EHF(v,J)]Erecoil\Ecom]*E which because EME must be non-negative leads to a rigorous upper limit on the HF internal state energy of recoil collision energy. By way of testing this idea Fig. 4 displays the –nal quantum state resolved HF(v\3,J) reaction F]H Ecom\0.54(10) kcal mol~1. The distributions are plotted as a function of the (Ethr\EHF(v,J)[ *Ej/1) which is the minimal collision energy required to make 2( j\1)]HF(v\3,J)]H energetically accessible. States with Ethr[Ecom are cross-sections for threshold energy the process rigorously closed for the ground state F reaction and can only be produced from the nonadiabatic channel. The distributions of E in the jet intersection region (obtained from extensive com high resolution Dopplerimetry and Monte-Carlo simulations described elsewhere25) are also shown in the –gure.The data at Ecom\0.54(10) kcal mol~1 clearly indicate three HF(v\3,J) states (i.e. J\3 4 and 5) experimentally observed in these distributions that are energetically F]H inconsistent with the adiabatic 2( j\1) reactions and only become energetically accessible by non-adiabatic channels built on F*]H Such non-adiabatic eÜects in the F]H reaction have proven elusive to detect in previous 2( j\1). 2 crossed beam experiments. Indeed the only previous report of a non-adiabatic reaction channel prior to this work was in studies of the F]D reaction by Faubel and coworkers,35 where a peak 2 in the DF product TOF spectra was observed at arrival times consistent with F*]D ener- 2 getics.35 Somewhat surprisingly recent crossed beam studies in F]H collisions by these same 2 workers did not reveal inelastic E»T or near-resonant E»R energy exchange in F*/F]H colli- 2 sions,36 which might be expected to be have comparable cross-sections to H atom abstraction.3 In this regard it is important to note that the current studies are based on threshold phenomena and are performed at collision energies signi–cantly below the adiabatic reaction barrier as well as at much lower energies than previously investigated.In conjunction with complete quantum state resolution of the –nal product states oÜered by IR laser detection this near threshold mode of 113 Faraday Discuss. 1999 113 107»117 F]H2( j\1) reaction. The smooth Gaussian-like curves 2( j\1) (dashed line) F]H2( j\1) (solid line) and F*]H F]H2( j\1) and can only be produced from the Fig.4 Rotational populations of HF(v\3,J) observed at Ecom\0.54(10) kcal mol~1 vs. threshold collision energy required to produce a given J state from the are the distributions of energy available from reactions. All shaded J states are energetically closed for F*]H non-adiabatic channel. 2 operation allows one to selectively suppress the adiabatic reaction pathways (i.e. by looking below the barrier or at states energetically inaccessible to F]H2). This leads to a corresponding enhancement in experimental sensitivity for non-adiabatic pathways that makes them much easier to isolate and detect than in the competing presence of conventional adiabatic channels. EcomB0.75 kcal mol~1 By way of contrast many theoretical studies have predicted sizable non-adiabatic eÜects in the F]H reaction (see ref.3 and references therein). However it has been extremely challenging to 2 incorporate these non-adiabatic eÜects rigorously in a full multisurface calculation. It is therefore noteworthy that Alexander et al.27 have recently succeeded in performing full quantum reactive scattering calculations for F]H including all three SHW PES Born»Oppenheimer derivative 2 coupling spin»orbit and Coriolis coupling eÜects. These results predict signi–cant reaction probability for the non-adiabatic F*]H channel into HF(v\3,J)]H speci–cally on the order of F]H channel at near and above threshold energies (EcomB2 kcal mol~1). 10% of the adiabatic 2 2 Even more importantly the calculated non-adiabatic cross-sections for reactive scattering to form HF(v\3,J) decrease much more slowly with E than the adiabatic ones and therefore dominate com the reaction at low collision energies i.e.in qualitative agreement with the present experimental observations. Indeed these full surface calculations indicate that below essentially all HF(v,J) products in the v\3 manifold arise from the non-adiabatic F*]H2( j\1) channel. Even with a maximum possible shift in these predictions due to B0.2 kcal mol~1 asymptotic errors in the potential this would still imply that the product state distributions in Fig. 4 at Ecom\0.54 kcal mol~1 re—ect very substantial contributions from non-adiabatic F*]H2 reaction pathways. One important caveat in these predictions is that multisurface calculations have only been successfully performed for the lowest partial wave (i.e.Jtot\1/2) and are not yet converged with respect to total angular momentum. It will be therefore be quite interesting to see the results of fully converged calculations as well as the threshold dynamical behaviors predicted for reaction of F F* and H2( j\0,1,2) into each –nal HF(v,J) state for the most rigorous comparison with the current experimental data. 2 IV Velocity distributions from high resolution IR laser dopplerimetry As a –nal comment we turn to a discussion of further potential applications of high resolution direct absorption methods in the crossed jet apparatus. Speci–cally the *l\0.0001 cm~1 resolution of Doppler absorbance pro–les probes quantum state resolved velocity distributions along the laser detection axis which can also be used to extract information on state-to-state diÜerential cross-sections.This is currently difficult for us to detect in the F]H reaction for Faraday Discuss. 1999 113 107»117 114 4 . unskimmed jets since the vast majority of the excess recoil energy appears in the light H atom and not the heavy HF product. However for other H atom abstraction reactions such as F ]CH4 ]HF]CH3 the product masses are more equally balanced thus providing a much stronger ììkickœœ on the recoiling HF product. We thus conclude this paper with preliminary Dopplerimetry data on quantum state resolved velocity distributions from reactions of F]CH An example of a typical Doppler pro–le is given in Fig.5 which displays the v\3^2 P(2) transition of HF produced in the jet intersection region at Ecom\1.7(5) kcal mol~1. Both the upper HF(v@\3 J@\1) and lower HF(vA\2 JA\2) states connected by the transition are populated by the reaction each characterized by its own angular and product speed distribution. Due to the high spectral resolution of the laser each frequency detuning corresponds uniquely to a certain projection of HF velocity onto the laser axis. In this particular case the population is inverted ([HF]@[[HF]A) for the molecules moving in the low velocity subgroup leading to net stimulated emission rather than absorption in the center of the pro–le. The situation changes dramatically at larger frequency detuning (corresponding to recoil velocities of B1.3]105 cm s~1).With a maximum recoil energy (Erecoil) do not have enough available energy to acquire such a velocity. On the other hand up to B10 kcal mol~1 of energy is in principle available for relative HF/CH translation in the v\2 mani- 3 fold (depending on the internal state of the methyl radical) permitting the HF(v\2) product to be considerably speedier. As a result for this velocity subgroup only the lower state is populated and the signal becomes purely absorptive. We note that similar absorption/stimulated emission Doppler spectral signatures were also observed and reported for our previous studies of F]H2 reactive scattering,6 but due to smaller HF recoil speeds and lower signal to noise the eÜects were much more subtle.com of B1 kcal mol~1 available the HF(v@\3,J@\1) products In order to isolate the velocity distribution for individual rovibrational states the data are analyzed as follows. Since the upper v\4 state is far above the energetic reaction limit the HF(v\3,J) velocity distributions can be directly determined from the set of v\4^3 Doppler pro–les. The HF(v\2,J) distributions are then obtained from the compound Doppler pro–les connecting the v\2 and v\3 states like the one shown in Fig. 5. The velocity distributions for each lower HF state of interest can be obtained by successively working down the vibrational manifold. The resulting distributions can then be modeled to infer the product angular distribution in the center-of-mass frame using a singular value decomposition strategy similar to that previously demonstrated for HF]Ar inelastic scattering.37 Brie—y the center-of-mass scattering angle H is divided into bins of equal cos(Hcom) increments.For scattering into each angular bin a model Doppler pro–le (ììbasis functionœœ) is predicted from a detailed Monte-Carlo integration of Fig. 5 A sample high resolution scan over the v\3^2 P(2) transition from nascent HF(vA\2,JA\2) formed by reactive scattering of F]CH4 . The Doppler pro–le is determined by the relative densities and velocity distributions of the HF(vA\2,JA\2) and HF(v@\3,J@\1) states in the jet intersection zone and carries information about the center-of-mass angular distribution of the nascent HF. 115 Faraday Discuss. 1999 113 107»117 the appropriate experimental conditions.The experimental Doppler pro–le is then least-squares –tted to a linear combination of the model ììbasis functionsœœ with coefficients corresponding to relative weights in the product angular distribution. A complete data analysis is currently underway38 but a few trends are already clear from –ts for the most populated HF(v\2) manifold. (i) A major fraction of the exothermicity goes into internal rovibrational energy of the HF(v,J) product. (ii) For all but the highest vibrational manifold of product HF(v\3) the recoil kinetic energy between the HF and CH fragments represents the 3 next largest energy sink. (iii) The HF(v\2) products appear to be predominantly scattered in the backward/forward vs. sideward direction.(iv) A relatively minor fraction of the excess energy goes into internal energy of the CH fragments. This is consistent with the results of Sugawara et al.39 CH3 (T who demonstrated that the rotB300 K) product is relatively unexcited both rotationally (TvibB1000 K in the umbrella mode). To the best of our knowledge no reaction and vibrationally 3 diÜerential cross-section studies have been reported for F]CH4 which makes the present Dopplerimetry results particularly valuable. Unfortunately theoretical data for the reaction are still rather scarce,40h42 which precludes a more rigorous direct comparison between experiment and theory. It is our hope that such results on product state and velocity distributions in F]CH4 F]H (and other systems such as will provide the necessary stimulus to both the ab initio and 2O) quantum dynamics community for further studies of atom]polyatomic reaction dynamics at the fully quantum state-to-state level.2 ]HF(v\3,J) for several energies below the 1.9 kcal com 2 . The cross-sections are below the barrier essen- EcomB0.7 kcal mol~1. Experimental cross-sections drop oÜ more slowly with com V Summary and are still measurable at the lowest center-of-mass energies sampled (E 3@2)]n-H2. F Preliminary results on the crossed jet reactions between ]CH4 are also High resolution IR direct absorption spectroscopy is applied to study the dynamics of hydrogenabstraction reactions by F atoms from H and CH under single collision conditions in a crossed 2 4 supersonic jet apparatus.Rovibrationally resolved cross-sections for the F]H ]H reaction have been observed as a function of E mol~1 adiabatic barrier for reactions of ground spin»orbit F with n-H compared with exact quantum dynamics calculations21,27 on the recent fully ab initio potential energy surface.7,14 Theoretical cross-sections decrease rapidly with E tially vanishing by E comB0.3 kcal com mol~1). Furthermore several additional product rotational states in HF(v\3,J) are observed E that are energetically inaccessible at a given from adiabatic reactions with ground spin»orbit n-H2( j\0,1). This latter observation is especially informative since it depends only F atoms with com on the asymptotic properties of the potential surface well characterized by previous spectroscopic studies.These observations are most convincingly explained by contributions from non-adiabatic F*(2P1@2)]n-H2 channels which have been selectively enhanced in these studies by operation at collision energies signi–cantly below the adiabatic reaction barrier theoretically predicted for F(2P reported which successfully demonstrate that HF(v,J) velocity distributions can be obtained in state-to-state reactive scattering via high-resolution direct absorption measurements. Acknowledgements This work has been supported by grants from the Air Force Office of Scienti–c Research and the National Science Foundation. We are indebted to J. Castillo and D. Manolopoulos for sharing their calculations with us prior to publication as well as many stimulating discussions.References 1 H. Shaefer III J. Phys. Chem. 1985 89 5336. 2 J. C. Polanyi and J. L. Schreiber Faraday Discuss. Chem. Soc. 1977 62 267. 3 D. Manolopoulos J. Chem. Soc. Faraday T rans. 1997 93 673. 4 J. Anderson Adv. Chem. Phys. 1980 41 229. 5 L. J. Butler Annu. Rev. Phys. Chem. 1998 49 125. 6 W. B. Chapman Jr. B. W. Blackmon S. Nizkorodov and D. J. Nesbitt J. Chem. Phys. 1998 109 9306. 7 K. Stark and H. Werner J. Chem. Phys. 1996 104 6515. Faraday Discuss. 1999 113 107»117 116 8 R. D. Coombe and G. C. Pimentel J. Chem. Phys. 1973 59 251. 9 S. Lu C. Liu X. Yang K. Li Y. Gu and Y. Tao J. Chem. Phys. 1988 88 2379. 10 D. M. Neumark A. M. Wodtke G. N. Robinson C. C. Hayden and Y. T. Lee J. Chem. Phys. 1985 82 3045. 11 N. Jonathan C.M. Mellier-Smith and D. H. Slater Mol. Phys. 1971 20 93. 12 D. Truhlar J. Chem. Phys. 1972 56 3189. 13 J. T. Muckerman and M. D. Newton J. Chem. Phys. 1972 56 3191. 14 B. Hartke and H. Werner Chem. Phys. L ett. 1997 280 430. 15 G. Dharmasena K. Copeland J. Young R. Lasell T. Phillips G. Parker and M. Keil J. Phys. Chem. A 1997 101 6429. 16 F. Aoiz L. Banares B. MartinezHaya J. Castillo D. Manolopoulos K. Stark and H. Werner J. Phys. Chem. A 1997 101 6403. 17 J. F. Castillo B. Hartke H. J. Werner F. J. Aoiz L. Banares and B. Martinez-Haya J. Chem. Phys. 1998 109 7224. 18 J. Castillo D. Manolopoulos K. Stark and H. Werner J. Chem. Phys. 1996 104 6531. 19 E. Rosenman and A. Persky Chem. Phys. 1995 195 291. 20 F. Aoiz L. Banares V. Herrero K. Stark and H.Werner Chem. Phys. L ett. 1996 254 341. 21 J. Castillo and D. Manolopoulos personal communications. 22 JANAF T hermochemical T ables NSRDS-NBS 37 2nd edn. 1971. 23 W. C. Stwalley Chem. Phys. L ett. 1970 6 241. 24 W. T. Zemke W. C. Stwalley J. A. Coxon and P. G. Hajigeorgiou Chem. Phys. L ett. 1991 177 412. 25 S. A. Nizkorodov W. W. Harper W. B. Chapman Jr. B. W. Blackmon and D. J. Nesbitt J. Chem. Phys. submitted. 26 E. Arunan D. W. Setset and J. F. Ogilvie J. Chem. Phys. 1992 97 1734. 27 M. Alexander H. Werner and D. Manolopoulos J. Chem. Phys. 1998 109 5710. 28 J. E. Pollard D. J. Trevor T. T. Lee and D. A. Shirley J. Chem. Phys. 1982 77 4818. 29 P. Huber-Walchli and J. W. Nibler J. Chem. Phys. 1982 76 273. 30 R. J. Gallagher and J. B. Fenn J. Chem. Phys. 1974 60 3492. 31 K. Dharmasena J. JeÜeries G. Mu J. Young B. Bergeron R. Littell and N. Shafer-Ray Rev. Sci. Instrum. 1998 69 2888. 32 M. Baer M. Faubel B. Martinez-Haya L. Rusin U. Tappe and J. Toennies J. Chem. Phys. 1998 108 9694. 33 J. Harrison L. Isakson and H. Mayne J. Chem. Phys. 1989 91 6906. 34 J. B. Song and E. A. Gislason J. Chem. Phys. 1995 103 8884. 35 M. Faubel B. Martinezhaya L. Rusin U. Tappe and J. Toennies Z. Phys. Chem. 1995 188 197. 36 M. Faubel L. Rusin S. Schlemmer F. Sondermann U. Tappe and J. Toennies J. Chem. Soc. Faraday T rans. 1993 89 1475. 37 W. Chapman M. Weida and D. Nesbitt J. Chem. Phys. 1997 106 2248. 38 W. W. Harper S. A. Nizkorodov and D. J. Nesbitt J. Chem. Phys. in preparation. 39 K. Sugawara F. Ito T. Nakanaga H. Takeo and C. Matsumura J. Chem. Phys. 1990 92 5328. 40 A. Gauss Jr. J. Chem. Phys. 1976 65 4365. 41 J. C. Corchado and J. S. Espinosa-Garcia J. Chem. Phys. 1996 105 3160. 42 H. Kornweitz A. Persky and R. D. Levine Chem. Phys. L ett. 1998 289 125. Paper 9/01824G 117 Faraday Discuss. 1999 113 107»117

ISSN:1359-6640    

DOI:10.1039/a901824g

出版商:RSC    

年代:1999

数据来源: RSC

摘要:

Quantum stereodynamics of four-atom reactions theory and 1 @ v2 @ v3 @ (1) application to H2+ OHºH2O+ H Marcelo P. de Miranda,a Sergei K. Pogrebnyab and David C. Claryb a Universidade Estadual de Campinas Instituto de Quïç mica Departamento de Fïç sico- Quïç mica Caixa Postal 6154 13083-970 Campinas SP Brazil b Department of Chemistry University College L ondon 20 Gordon Street L ondon UK W C1H 0AJ Received 11th March 1999 2 This article presents a theoretical quantum method for the description of the stereodynamics of four-atom reactions of the type AB(vAB jAB)]CD(vCD jCD)%ABC(v j@)]D. The method is based on density matrix techniques and angular momentum algebra and requires knowledge of the scattering matrix. Reagents and products are treated on an equal footing and the reaction stereodynamics can be analysed either in the rotational polarisation or in the molecular polarisation representation.The formalism is applied to the H (0 jH2)]OH(0 jOH)%H O(0 0 0 0)]H reaction at zero total angular momentum and reveals state-speci–c correlations between the polarisations of the diatomic molecules their approach or recoil directions and the reaction probability. 2 AB(vAB jAB) ]CD(vCD jCD)%ABC(v 1. Introduction 2 It is sometimes said that when quantum scattering theory is applied to chemical reaction dynamics it yields ììtoo much information.œœ This can be true if one is interested only in properties summed or averaged over quantum states of reagents and products (e.g. thermal reaction rates).When one is interested in the stereodynamics of reactive collisions on the other hand the detailed information generated in quantum scattering calculations becomes absolutely necessary. A quantum analysis of the reaction stereodynamics requires not only the speci–cation of vibrational rotational and magnetic quantum numbers of reagents and products but also the speci–cation of the relative phases among the corresponding eigenstates.1,2 In other words the stereodynamical analysis requires not only knowledge of the transition probabilities between the quantum states of the reagents and products but also the corresponding probability amplitudes. Such probability amplitudes are precisely the primary output of the quantum scattering calculations. They are the elements of the scattering matrix S.3,4 The quantum formalism describing the stereodynamics of three-atom reactions of the type A]BC(v j)%AB(v@ j@)]C has already been published,5,6 and applied to the bench-mark H ]D reaction.6,7 The main goal of the present paper is to extend this method to four-atom reactions of the type 119 1 @ v2 @ v3 @ j@)]D.As an illustrative example we apply this general formalism to the H2]OH%H2O]H reaction. The recent progress in quantum scattering calculations has made it possible to obtain the full Faraday Discuss. 1999 113 119»132 This journal is( The Royal Society of Chemistry 1999 scattering S matrix for such a reaction at total angular momentum J\0 (see ref. 8 and references therein). The method of stereodynamical analysis of four-atom reactions presented here is not restricted to J\0.As in the atom»diatom case,5h7 the method is based on density matrix techniques1,2 and angular momentum algebra.9,10 Reagents and products are treated on an equal footing and the reaction stereodynamics can be analysed either in the rotational polarisation or in the molecular polarisation representation. While the rotational polarisation representation describes the stereodynamics in terms of preferences for particular planes and directions of molecular rotation,6 the molecular polarisation representation describes it in terms of relative orientations between the molcular interatomic axes.11,12 The paper is organized as follows. Section 2 presents the methods of the stereodynamical analysis of the scattering matrix and Section 3 describes the application and results for the H2]OH%H2O]H reaction.Concluding remarks close the paper in Section 4. (2a) (2b) g2{ g2 J2* (3) (h)S AB QAB KCD QCD g1 g2 X1 @ X2 @ J1 K oqj{ (Kj{)( j1 @ j2 @ ) oQAB (KAB) and J2 . Here oQCD (KCD)( j1CD j2CD) are the multipolar rotational polarisation moments1,5,6 (also called state multipoles,2 statistical tensors2 or multipole moments9) of ABC AB and CD respectively ; the corresponding polarisation operators1,2,5 (also called irreducible tensor operators1,2 or state 2. Stereodynamical analysis of the scattering matrix The stereodynamics of the AB]CD%ABC]D reaction is described by a set of –ve vectors. DiÜerent sets can be used with the –ve vectors chosen among the reagent-approach and productrecoil directions the internuclear axes of the molecules and the rotational and orbital angular momentum vectors.We will focus on the Mk jAB jCD k@ j@N set although on occasion we will replace jAB and jCD by rAB and rCD. Here k is the relative velocity between AB and CD and k@ is the relative velocity between ABC and D; jAB jCD and j@ are the rotational angular momenta of AB CD and ABC; rAB and rCD are the interatomic axes of the diatomic molecules. Note that since the orbital angular momenta l and l@ are perpendicular to k and k@ and the internuclear axes of the diatomics are perpendicular to the corresponding rotational angular momenta the other possible descriptions of the reaction stereodynamics are closely related to that obtained with the Mk jAB jCD k@ j@N set.2.A. k‘jAB‘jCD‘kº‘jº correlation in the uncoupled helicity representation i In the uncoupled helicity representation the elements of the S matrix at total angular momentum J are labeled by g and gi @ i gi4vABjiABXiABvCDjiCDXiCD gi @ 4v1 @ v2 @ v3 @ ji @ Xi @ . Here XAB XCD and X@ are helicity quantum numbers (projections of rotational angular momenta on the relative directions of motion k and k@; X@ is also the projection of J on k@; the projection of J on k is XAB]XCD). Note that while the rotational angular momentum and helicity quantum numbers have subscripts vibrational quantum numbers do not. This is so because we will have to consider coherence among rotational and helicity states but not among vibrational states (polarisation operators are diagonal with respect to vibrational quantum numbers10).The derivation of the k[jAB[jCD[k@[j@ correlation formulae is very similar to that for the k[j[k@[j@ correlation in the atom»diatom case which was presented in ref. 5. For this reason we will not present a detailed derivation here. A summary of the derivation is given in Appendix A. The –nal expression in the uncoupled helicity representation reads oqj{ (Kj{)( j1 @ j2 @ )\ 4 1 p ; Sj1ABX1AB o T (Q K AB AB) o j2ABX2ABTS j1CDX1CD o T (Q K CD CD) o j2CDX2CDTS j1 @ X1 @ o T (q Kj { j{) o j2 @ X2@ T ](2J g1{ g1 J1 (2J2]1)dX J2 2{ (X2AB`X2CD) 1]1)dX1{ (X1AB`X1CD)(h)S J1 ]oQAB (KAB)( j1AB j2AB)oQCD (KCD)( j1CD j2CD) where the sum is over ( j1AB j2AB) and Faraday Discuss.1999 113 119»132 120 multipoles9) are T (Kj{) T (KAB) and T (KCD). The polarisation operators and polarisation moments are spherical tensors9,10 with ranks indicated by their superscripts and components indicated by their subscripts. The symbol SJ stands for the scattering matrix at total angular momentum J while dJ(h) stands for the reduced rotation matrix; h is the scattering angle (i.e. the angle between k and k@). The matrix elements of polarisation operators are given by2 (4) S j1X1 o T Q ( K) o j2X2T\A2 2 K j ]1B1@2 S j2X2 KQo j1X1T 1]1 S j is a Clebsch»Gordan coefficient in Zareœs notation.9 where 2X2 KQo j1X1T Eqn. (3) is referred to two body-–xed frames.The –rst frame xyz (z parallel to k y parallel to k]k@) is used for the AB]CD arrangement; Q indicates that the components of the polarisation operators are referred to the xyz frame. The second frame x@y@z@ (z@ parallel to k@ y@ parallel to k]k@) is used for the ABC]D arrangement; q indicates that the components of the polarisation operators are referred to the x@y@z@ frame. Note also that the polarisation moments appearing in eqn. (3) relate to speci–c vibrational levels of AB CD and ABC and that the relationship between the polarisation moments depends on the scattering angle h; our notation is not explicit in this sense. As written above eqn. (3) refers to the AB]CD]ABC]D reaction. If we know the polarisation moments of the reagents AB and CD we can calculate the ABC polarisation produced by the reaction.The formula for the reverse reaction is entirely analogous to eqn. (3) ; all we have to do is to interchange the polarisation moments of reagents and products putting o(Q K AB AB)( j1AB j2AB)o(Q K CD CD) ( j1CD j2CD) on the left-hand side of the equation and oq ( Kj { j{)( j1 @ j2 @ ) in the summation on the right-hand side which will then be over Kj @ qj @ g1 @ g2 @ X1 X2 J1 and J2 . 2.B. Polarisation-dependent diÜerential cross-sections and polarisation parameters DiÜerent authors have used diÜerent notations and conventions in their work on chemical reaction stereodynamics. In order to avoid the confusion created by the diÜerent notations de Miranda et al.have recently proposed a unifying set of conventions.7 For ease of comparison with our previous work on atom»diatom reactions in Section 2.A. and Appendix A we did not follow the conventions proposed by those authors. In the remainder of this paper however we shall use them. The new set of conventions determines that instead of the polarisation moments we used in the previous section one should use the ììpolarisation-dependent diÜerential cross-sections œœ (PDDCSs for short) and ììpolarisation parametersœœ introduced by Shafer-Ray and co-workers.13 PDDCSs depend on the scattering angle. In the case of well de–ned rotational levels (to which we shall restrict ourselves hereafter) they are related to the polarisation moments by7 2p (5) p dp du kq\ (2k]1)1@2/ ([1)qo~ ( k)q( j) ~1 1 o0(0)( j) d cos h .In particular the PDDCS with k\q\0 is directly related to the integral (p) and diÜerential (dp/du) cross-sections as usually de–ned:14h16 2p (6) p P2p dp du d/\ 2 p p d(cos h) dp dp du 00\ p 1 0 Because of their physical meaning it is also useful to de–ne renormalized PDDCSs:7 (7) B d d p p 00 kq/d /d u u \A2 p p d d p u kqBNA2 p p d d p u 00 \ (2k ([ ] 1) 1) qo 1@2 ~ ( k) o q ( (0) 0 j) ( j) . Polarisation parameters do not depend on the scattering angle. They are de–ned by7 (8) q (k)\P1 2 p p d d p u kq d cos h. a ~1 In general the PDDCSs and polarisation parameters in eqns.(5)»(8) are complex numbers whose physical meanings are not directly related to well de–ned directions in real threedimensional space.6,7 In order to analyse the stereochemical aspects of reaction mechanisms in 121 Faraday Discuss. 1999 113 119»132 restriction (the notation is a Table 1 Physical meanings and classical (CM) ranges of real polarisation parameters whose numerical values are reported in this article ; classical ranges correspond to large-j limits of quantum ranges without J\0 QABB KKAL aQCDB KKCDL) Meaning when negative Meaning when positive Parameter CM range [[12 1] a0 K0La0 K2L jCD aligned perpendicular to z jAB isotropically distributed. jAB oriented antiparallel to z jCD aligned parallel to z jAB isotropically distributed.jAB oriented parallel to z and [[1 1] [[1 1] jCD also oriented parallel to z and jCD oriented parallel to z or jAB oriented antiparallel to or jAB oriented parallel to z z and jCD also oriented and jCD oriented antiparallel antiparallel to z. toz. jAB oriented antiparallel to x [[1 1] jAB oriented parallel to x and jCD also oriented parallel to x and jCD oriented parallel to x or jAB oriented antiparallel to or jAB oriented parallel to x x and jCD also oriented and jCD oriented antiparallel antiparallel to x. tox. jAB oriented antiparallel to y jAB oriented parallel to y and jCD also oriented parallel to y and jCD oriented parallel to y or jAB oriented antiparallel to or jAB oriented parallel to y y and jCD also oriented and jCD oriented antiparallel antiparallel to y.toy. jAB oriented antiparallel to x [[S3h 2 S 23h ] jAB oriented parallel to x and jCD aligned parallel to y]z and jCD aligned parallel to or jAB oriented antiparallel to y]z or jAB oriented parallel x and jCD aligned parallel to to x and jCD aligned parallel y[z. toy[z. jAB oriented antiparallel to y [[S3h 2 S 23h ] jAB oriented parallel to y and jCD aligned parallel to x]z or jAB oriented antiparallel to y and jCD aligned parallel to x[z. [[12 1] and jCD aligned parallel to x]z or jAB oriented parallel to y and jCD aligned parallel to x[z. jAB aligned parallel to z and jCD aligned perpendicular z or jAB aligned perpendicular to z and jCD aligned parallel to z.jAB aligned parallel to z and jCD also aligned parallel to z or jAB aligned perpendicular to z and jCD also aligned perpendicular to z. [[34 34 ] jAB aligned parallel to x]z and jCD also aligned parallel to x]z or jAB aligned parallel to x[z and jCD also aligned parallel to x[z. [[34 34 ] jAB aligned parallel to x]z and jCD aligned parallel to x[z or jAB aligned parallel to x[z and jCD aligned parallel to x]z. jAB aligned parallel to y]z and jCD aligned parallel to y[z or jAB aligned parallel to y[z and jCD aligned parallel a0 K1La0 K1L a1` K1L a1` K1L a1~ K1L a1~ K1L a1` K1L a1~ K2L a1~ K1L a1` K2L a0 K2La0 K2L a1` K2L a1` K2L a1~ K2L a1~ K2L a [[34 34 ] 2` K2L a2` K2L jAB aligned parallel to y]z and jCD also aligned parallel to y]z or jAB aligned parallel to y[z and jCD also aligned parallel to y[z.toy]z. jAB aligned parallel to x and jCD aligned parallel to y or jAB aligned parallel to y and jAB aligned parallel to x and jCD also aligned parallel to x or jAB aligned parallel to y and jCD also aligned parallel to y. a [[34 34 ] 2~ K2L a2~ K2L jCD aligned parallel to x. jAB aligned parallel to x]y and jCD aligned parallel to x[y or jAB aligned parallel to x[y and jCD aligned parallel to x]y. jAB aligned parallel to x]y and jCD also aligned parallel to x]y or jAB aligned parallel to x[y and jCD also aligned parallel to x[y.Faraday Discuss. 1999 113 119»132 122 terms of well de–ned directions it is convenient to introduce real quantities. We follow ref. 7 and use the Hertel»Stoll scheme17 in the de–nition of real PDDCSs and polarisation parameters. The de–nition is the same in both cases. For the latter it reads (9a) q` KkL \([1)q21@2 Re[aq ( k)]\ 1 [([1)q aq ( k)]a~ ( k)q] 1OqOk a J2 (9b) [([1)qaq ( k)[a~ ( k)q] 1OqOk q~ KkL \([1)q21@2 Im[aq ( k)]\ iJ2 a 1 (9c) a0 K kL\a0 ( k) Real PDDCSs and polarisation parameters allow us to analyze reaction mechanisms in terms of preferences for particular planes and directions of molecular rotations. For instance the polarisaa tion parameter 1~ K1L describes vector orientation along the k]k@ direction and its value is within a well de–ned range that depends on the rotational level considered ; a minimum value indicates maximum preference for left-handed rotation in the scattering plane (the plane containing k and k@) while a maximum value indicates maximum preference for right-handed rotation.6,7 The physical meanings and allowed ranges of real polarisation parameters and PDDCSs have been discussed in detail before,6,7 and for that reason we will not repeat the discussion here.Note however that in the AB]CD%ABC]D case it is not possible to separate the AB and CD polarisations. We can calculate ììcorrelatedœœì PDDCSs and polarisation parameters (e.g. aQAB` KKAL aQCD` KKCDL ) but not ììindividualœœ ones such as for example aK Q K AB AB` L .The physical meanings of the real polarisation parameters whose numerical values will be reported in Section 3 are described in Table 1. 2.C. Axial distribution of diatomic molecules is2 Spatial distributions of interatomic axes of diatomic molecules are directly related to their PDDCSs and polarisation parameters.2 In the case of an AB molecule in a jAB state the probability density of –nding the interatomic axis rAB along the direction speci–ed by the polar angles hAB and /AB (10) o(hAB /AB)\ 4 1 p ; (2KAB]1)S jAB0 KAB 0 o jAB0TAKAB (hAB /AB) KAB where (11) AKAB (hAB /AB)\a0 K KABLC0 K KABL(hAB ,/AB) QAB` KKABL CQAB` KKABL (hAB /AB)]aQAB~ KKABL CQAB~ KKABL (hAB /AB). ] ; a QAB;0 CQABB KKABL (hAB /AB) are real modi–ed spherical harmonics de–ned as in eqn.(9). The probability density function in eqn. (10) is integrated over the scattering angle. In order to obtain an expression for the h-dependent probability one has to replace the polarisation parameters by renormalized PDDCSs. Note also that in the AB]CD%ABC]D case it is not possible to separate the AB and CD polarisations. We can calculate the ììcorrelatedœœ probability density function (12) o(hAB /AB hCD /CD)\o(hAB /AB)o(hCD ,/CD) but not ììindividualœœ probabilities such as the one in eqn. (10). 3. Application to H2 + OHºH2O+ H A novel feature to be considered in the stereodynamical analyses of four-atom reactions is the possibility of mutual orientation of the diatomic molecules. For this reason this section focuses on the stereodynamical eÜects in the H2]OH arrangement of the H2]OH%H2O]H reactions.After a brief description of the quantum scattering calculations used to determine the scattering matrix for these reactions (Section 3.A.) we examine the rotational and molecular polarisations of Faraday Discuss. 1999 113 119»132 123 0)]H]H (0 jH2)]OH(0 jOH) reactions 2 H O(0 Fig. 1 Reaction probabilities calculated for H O(0 0 0 2 without reagent polarisation. The results are also valid for maximal probability H2(0 jH2)]OH(0 jOH)] 0 0 0) reactions. 2 2 2 and OH when these molecules are produced by H H 2O]H collisions without stereodynamical constraints (Section 3.B.) and the rotational and molecular polarisations of H and OH that maximize or minimize the reaction probability when H and OH collide (Section 3.C.).2 The results presented in this section are restricted to J\0 simply due to the lack of scattering matrices at higher total angular momenta. Nevertheless the results for J\0 do show how the stereodynamical analysis can reveal details of reaction mechanisms. Note that the J\0 restriction implies an absence of scattering angle dependence. We would also like to mention the existence of the symmetries and selection rules for the polarisation parameters. They are due on one hand to the J\0 condition and on the other hand to the non-chirality of the reactions considered here. The J\0 condition implies that complex polarisation parameters with QH2D[QOH vanish and that (13a) (13b) aQ` KKH2LaQ` KKOHL\aQ K K ~ H 2LaQ K K ~OHL aQ` KKH2LaQ K K ~OHL\[aQ K K ~ H 2LaQ` KKOHL.The non-chirality appears because we are not considering the polarisation eÜects in the H2O]H arrangement and means that the results must be invariant under re—ection about the scattering plane. It implies the following selection rules KH2]KOH is evenFaQ ( KH2)a~Q (KOH) is real (14a) (14b) (14c) (14d) aQ` KKH2LaQ K K ~OHL vanishes ; KH2]KOH is oddFaQ ( KH2)a~Q (KOH) is pure imaginary aQ` KKH2LaQ` KKOHL and a0 K KH2La0 K KOHL vanish. In eqns. (13) and (14) we are assuming Q to be positive. We shall follow this convention throughout this section. 3.A. Quantum scattering calculations The arrangement channel hyperspherical coordinates method used in our quantum scattering calculations on the H2]OHHH2O]H reaction was described in detail in ref.8. In this method apart from the common hyper-radius diÜerent coordinates are introduced for the diÜerent arrangement channels of the reaction. Using such coordinates we obtain a non-orthogonal set of channel rovibrational basis functions which is then used to –nd the total surface wavefunction. Faraday Discuss. 1999 113 119»132 124 Having found this function on a grid of –xed values of the hyper-radius we can derive and solve a set of coupled channel diÜerential equations to determine the scattering matrix. The present calculations have been performed for J\0 in full (6D) dimensions and a newly developed potential energy surface18 has been used.We carried out calculations for four symmetry blocks as explained in ref. 8. Typically the basis set consists of about 700 rovibrational functions in the H2]OH arrangement and 2200 in the H2O]H arrangement. This is a sufficient basis set to ensure the convergence of the relative trends in state-to-state reaction probabilities although the absolute values of these small probabilities are very hard to converge. The total energy con- (E sidered here T\0.769 eV) corresponds to a collision energy of 0.842 eV measured from the ground rovibrational state of H2O and to a collision energy of 0.3 eV with respect to H (0 0)]OH(0 0). 2 3.B. Product stereodynamics of H2O+ H«H2 + OH Fig. 1 shows state-to-state H O(0 0 0 0)]H]H (0 jH2)]OH(0 jOH) reaction probabilities as a 2 2 function of the rotational quantum numbers of the products.While comparing jH2\2 to jH2\3 reaction probabilities an interesting correlation is observed between the relative populations in product rotational states of H and OH. In the jH2\2 case the reaction probability is relatively 2 high at jOH\1 and at jOH\3 but relatively low at jOH\2. In the jH2\3 case this behaviour is reversed the reaction probability is relatively low at jOH\1 and at jOH\3 but relatively high at jOH\2. We will now consider the polarisations of H and OH to examine if there is a stereoche- 2 mical eÜect associated with these correlations of the reaction probability. Table 2 shows the values and allowed ranges of H and OH polarisation parameters calculated 2 jH2\2 jOH\1»3.The polarisation parameters shown in this table do not vanish by symmetry H2 O2 KOHO2. Note that the other non-vanishing polarisation parameters for and have ranks K with such ranks can be obtained by use of the symmetries of eqn. (13). Inspection of Table 2 shows no obvious pattern as one goes from jOH\1 to jOH\3. The same can be said about the polarisation parameters of higher ranks and about those associated with reactions leading to jH2\3 jOH\1»3 (these polarisation parameters are not presented here). The rotational polarisation representation does not give an easily rationalizable description of the stereodynamics of the reactions we are considering. Let us now consider the molecular polarisation representation which furnished the data in Figs.2 and 3. We will see that in contrast to the rotational polarisation representation the molecular polarisation representation reveals a clear stereodynamical pattern associated with the oscillations of the reaction probability found for jH2\2»3 jOH\1»3. Fig. 2 shows the spatial distributions of the OH interatomic axis generated in H2O]H reactions leading to jH2\2»3 jOH\1»3. These distributions were obtained from the ììcorrelatedœœ o(hH2 /H2 hOH /OH) probability density functions (see Section 2.C.) by –xing the position of the h H rH2 is parallel to the y axis and therefore interatomic axis at This means that 2 H2\/H2\90°. 0)]H]H2 Table 2 Allowed quantum ranges and calculated values of some non-vanishing polarisation parameters for (0 2)]OH(0 2)]OH(0 jOH) reactions without reagent polarisation and also for the O(0 the H O(0 0 0 maximal probability H (0 2 0 0 0)]H reactions (the notation is a jOH)]H QB KKH2LaQB KKOHL) 2 2 jOH\3 jOH\2 jOH\1 Value Range Value Range Value Range Parameter [0.30 [0.20 [0.08 [0.13 [0.09 0.19 [[0.52 0.00] [[0.47 0.00] [[0.40 0.40] [[0.17 0.17] [[0.53 0.53] [[0.25 0.25] [0.31 [0.14 [0.09 [0.11 [0.31 0.11 [[0.53 0.53] [[0.67 0.00] [[0.39 0.39] [[0.23 0.23] [[0.53 0.53] [[0.23 0.23] 0.25 [0.27 [0.16 [0.06 [0.29 0.03 [[0.63 0.32] [[0.29 0.00] [[0.35 0.35] [[0.27 0.27] [[0.53 [0.27] [[0.13 0.13] a a a a a a 0.21 0.09 0.09 [0.06 0.05 0.24 0.12 [0.05 [0.05 [0.00 0.28] [[0.17 0.17] [[0.22 0.22] [0.07 0.29] [[0.22 0.22] [[0.21 0.21] [[0.08 0.34] [[0.10 0.10] [[0.25 0.25] 0 K0La0 K2L 0 K1La0 K1L 1` K1L a1` K1L 1` K1L a1~ K2L 0 K2La0 K0L 1` K2L a1~ K1L a0 K2La0 K2L a1` K2L a1` K2L a2` K2L a2` K2L 125 Faraday Discuss.1999 113 119»132 Fig. 2 Spatial distributions of the OH interatomic axis calculated for H O(0 0 0 0)]H]H (0 jH2) 2 2 ]OH(0 jOH) reactions without reagent polarisation. These distributions are also valid for maximal probability H2(0 jH2)]OH(0 jOH)]H O(0 0 0 0)]H reactions. The H interatomic axis is –xed at hH2 \/H2 \ 2 90°. The z axis is parallel to the relative direction of motion between H and OH and xz is the scattering 2 2 OH\0 h sin hOH dhOH contributions from h plane.Note that due to the volume element OH\180° vanish and when integrating over hOH . perpendicular to the scattering plane xz. Fig. 3 shows how the rOH distribution obtained for jH2\ jOH\2 changes with the position of rH2. jH2\2 jOH\2 to jH2\3 jH2\2 jOH\1 to jH2\2 jOH\3 or to jH2\3 jOH\2) are those that do The reactions with relatively low probability (i.e. the ones leading to jOH\1 or to jH2\3 jOH\3) are those that favour product-recoil conformations in which rH2 and rOH are approximately parallel or antiparallel. The reactions with relatively high probability (the ones leading to not favour product-recoil conformations in which rH2 and rOH are parallel or antiparallel.In fact h Fig. 2 shows that when these reactions lead to H2\90° the probability of –nding rH2 and rOH lying along the same direction is zero. The jH2\2 jOH\3 reaction favours product-recoil conformations in which the plane containing rOH and the recoil direction k is preferentially perpendicular to the plane containing rH2 and k and rOH is at oblique angles with regard to k. This preference for oblique angles between rOH and k is also found in the jH2\3 jOH\2 and jH2\2 jOH\1 reactions but the situation with regard to the planes containing rOH and k or rH2 and k changes. In the jH2\3 jOH\2 case rOH rH2 and k are preferentially coplanar while for the jH2\2 jOH\1 reaction there is no preference in this sense. 3.C. Reagent stereodynamics of H2+ OH«H2O+ H If the H and OH reagents are prepared in the coherent state 2 (15) o tT\o vH2T o vOHT ; cX o jH2XT o jOH[XT X Faraday Discuss.1999 113 119»132 126 Fig. 3 Same as Fig. 2 but with jH2\jOH\2 H and diÜerent positions for the interatomic axis. Clockwise 2 from top left the –gure starts with rH2 parallel to z ; next rH2 is rotated around y until it becomes parallel to x; then it is rotated around z until it becomes parallel to y; –nally it is rotated around x so that it returns to its original position (parallel to z). (remember that the J\0 condition implies XH2]XOH\0) where c are complex coefficients such that (16) P\; o c ;X o cX o2\1 then the H2]OH reaction probability is X Sg{g J/0 o2 X where g@ is the set of quantum numbers that identi–es the ground rovibrational state of H2O and g\vH2jH2XvOHjOH[X (we have vH2\vOH\0).Using standard numerical methods it is possible to choose sets of coefficients that maximize or c are related to the polarisation parameters via the density matrix. minimize this reaction probability and thus to identify the reagent polarisations that maximize or minimize it. The coefficients Explicitly the relationship between the c values and the polarisation parameters of H and OH is (17) a X 2 Q ( KH2)a~Q (KOH)\([1)KOH ; cX1 c*X 2 S jH2X1 KH2 Qo jH2X2TS jOHX1 KOHQo jOHX2T. 2 X X1 X2 Because of microscopical reversibility the H H2]OH reaction probability are necessarily the ones naturally generated by the reverse H2 ]OH reaction with unpolarized reagents.Note however that the H and OH polarizations that 2 minimize the reaction probabilities cannot be obtained from the reverse reaction. As we shall see below a comparison between the minimal and maximal probability reactions can be useful for stereodynamical analyses. Fig. 1 shows the maximum H2]OH reaction probabilities one can obtain by polarisation of jH2 ( jH2\2 jOH\1) ( jH2\2 the reagents plotted as a function of and jOH. In particular the jOH\3) and ( jH2\3 jOH\2) reaction probabilities can be taken up to relatively high values while the ( jH2\2 jOH\2) ( jH2\3 jOH\1) and ( jH2\3 jOH\3) probabilities can only be increased up to a relatively low value. Partial illustration of the reagents polarisations leading to X and OH polarisations that maximize the Faraday Discuss.1999 113 119»132 127 2 Table 3 Values of some non-vanishing polarisation parameters of H and OH calculated for minimal probabiljOH)] H 2)]OH(0 ity H (0 0 0 0)]H reactionsa O(0 2 2 In-phasea Out-of-phasea Parameter jOH\3 jOH\2 jOH\3 jOH\2 a a a [0.22 [0.27 0.07 0.03 0.07 [0.04 0.24 [0.48 0.19 [0.04 0.24 0.04 [0.39 [0.12 0.00 0.00 [0.27 0.00 [0.27 [0.17 0.00 0.00 [0.27 0.00 0 K0La0 K2L 0 K1La0 K1L 1` K1L a1` K1L a1` K1L a1~ K2L a a0 K2La0 K0L 1` K2L a1~ K1L 0.11 [0.02 0.20 0.21 [0.20 0.11 0.10 0.00 [0.21 0.07 0.00 [0.21 a0 K2La0 K2L a1` K2L a1` K2L a2` K2L a2` K2L a Ranges and notation as in Table 2.b The terms ìì inphaseœœ and ììout-of-phaseœœ refer to the relative phase between reagent states with opposite helicities (see text). H2 ). The stereodynamical description given by 2]OH reaction are given by Table 2 (polarisation parameters of KH2 O2 KOHO2) and Figs. 2 and 3 (spatial distributions of the OH jH2 jOH hH2 and / maximal probability for the H H and OH with ranks 2 interatomic axis at –xed values of the rotational polarisation representation is more difficult to rationalize than the one given by the molecular polarisation representation. The reaction whose probability cannot go beyond relatively low values is favoured by reagent-approach conformations in which the interatomic axes of the two diatomics lie approximately along the same direction.The reaction whose probability can be increased up to relatively high values is favoured by other reagent-approach conformations not the ones in which rH2 and rOH are preferentially parallel or antiparallel. Let us consider the minimal probability reaction. There are two solutions of the minimization X\[c~X). problem leading to zero reaction probability. They diÜer by the relative phase between eigenstates (c with opposite helicities. For the in-phase solution the phase diÜerence equals zero X\c~X) and for the out-of-phase one the phase diÜerence is 180° (c Table 3 shows the values of the H and OH polarisation parameters calculated for the minimal H2]OH reactions discussed above. The polarisation parameters shown in this table probability 2 K are those that do not vanish by symmetry and have ranks H2 O2 KOHO2.Their allowed ranges can be found in Table 2. Note also that the other non-vanishing polarisation parameters with such ranks can be obtained by use of the symmetries of eqn. (13). Inspection of Table 3 shows that out-of-phase minimal probability reactions rationalize the stereodynamics if we consider the polarisation parameters only. In this case several polarisation parameters vanish and one can describe the stereodynamics as follows. Out-of-phase minimal probabilities are dominated by reagent-approach con–gurations in which (i) both jH2 and jOH have negative alignment with regard to the approach direction k; (ii) jH2 and jOH have opposite orientations with regard to k; (iii) jH2 and jOH are aligned along mutually perpendicular directions in the xy plane (which is the plane perpendicular to k).In terms of the planes and directions of rotational motion this means that minimal probability out-of-phase reactions are dominated by reagentapproach conformations in which (i) the planes of rotation of the reagents are at oblique angles with regard to their approach direction being more nearly parallel than perpendicular to k; (ii) H2 and OH rotate in opposite directions with regard to their approach direction ; (iii) the planes of rotation of the diatomics are perpendicular to each other. 4. Conclusions In this paper we have presented new quantum-mechanical equations describing the k[jAB[jCD[k@[j@ correlation in AB]CD%ABC]D reactions.These equations when used in conjunction with full-dimensional quantum scattering calculations furnish a complete Faraday Discuss. 1999 113 119»132 128 description of the reaction stereodynamics in the rotational polarisation representation. Furthermore the –ve-vectors correlation formulae can be easily reduced to expressions describing the correlations among fewer vectors. All one has to do is set the ranks of the operators associated with the unobserved vectors to zero. This leads to partial descriptions of the stereodynamics such as those used in our application to H2(0 jH2)]OH(0 jOH)HH O(0 0 0 0)]H. 2 DiÜerent versions of the –ve-vectors correlation formula corresponding to diÜerent representations of the scattering problem were presented.We found that the simplest of them all is the one in the uncoupled helicity representation. If the scattering calculations are done in another representation in general it will be easier to –rst transform the S matrix to the uncoupled helicity representation and then to do the stereodynamical analysis rather than to do the analysis in the original representation. In any case the computational cost of the stereodynamical analysis will be small if compared to that of the quantum scattering calculations. In this paper the vector correlation formulae were written in the rotational polarisation representation of the stereodynamics which describes the reaction mechanisms in terms of the preferences for particular planes and directions of molecular rotation.The transformation to the molecular polarisation representation (in which the reaction mechanisms are analyzed in terms of the relative orientations among the molecules of reagents and products not in terms of their relative directions of motion) however is rather simple. The equations presented here allow for a direct comparison between theory and experiment. They are stated in terms of the quantities that are accessible to experimentalists the polarisations of angular momenta and the angular distributions of reagents and products. Furthermore we formulated the problem with density matrices. This formulation accounts on the one hand for situations where the experimental ensemble cannot be represented by a pure quantum state and on the other hand for the fact that not all the quantum numbers are measured in scattering experiments.A comparison with experiments involving polarized molecules is also possible if the theoretical results are expressed in the molecular polarisation representation. The methods we employed to obtain the correlation formulae can be applied to other more complex chemical reactions. For instance it would not be difficult to write six-vector correlation formulae for the AB]CD]AD]CB reaction. The application of the general theoretical formalism introduced in this paper to the H2]OH%H2O]H reaction although restricted to zero total angular momentum showed how the stereodynamical analysis reveals details of the reaction mechanism. Considering either direct or reverse reactions we have observed state-speci–c correlations between the polarisations of the diatomics their approach or recoil directions and the reaction probability.We have also found that the rotational polarisation representation is better suited for the quantitative description of the reaction stereodynamics while the molecular polarisation representation is useful in rationalizing the stereodynamical aspects of the reaction mechanisms. Acknowledgements M.P.M. would like to thank Rogerio Custodio and his research group at Unicamp for their kind assistance and for valuable computational support. Finantial support from Fapesp is also gratefully acknowledged. The work in London was supported by EPSRC NERC and the TMR Programme of the European Union. (A1a) (A1b) Appendix A Derivation of k‘jAB‘jCD‘kº‘jº correlation formulae In contrast to the atom»diatom case,5 when treating the AB]CD%ABC]D reaction we have to deal with an arrangement (AB]CD) where we have to couple not two but three angular momenta ( jAB jCD and l) to form the total angular momentum J.If we want to follow the derivation procedure used in the atom»diatom case it is convenient to adopt the following coupling scheme jAB]jCD\jch l]jch\J. We shall refer to jch as the ììchannel rotational angular momentum.œœ Faraday Discuss. 1999 113 119»132 129 The other important diÜerence arises in the de–nitions of the spherical tensor operators to be used in the expansions of the density matrices of reagents and products (see below). As in the atom»diatom case,5 ììcorrelationœœ operators come into play whenever angular momenta are coupled.Therefore in the four-atom case we have to use the following coupling scheme for correlation operators in the AB]CD arrangement (A2a) (A2b) [Y (Kl)?W KABKCD(Kch)] [T (KAB)?T (KCD)]Q ( K ch ch)\W K Qch ABKCD(Kch) Q ( K)\W Q KlKABKCDKch(K) where the T œs are polarisation operators the Y œs the angular distribution operators (spherical harmonics regarded as tensor operators see ref. 5) and the W œs the correlation operators.5 The symbol ? stands for tensor product.9,10 We now turn to the actual derivation of the –ve-vectors correlation formulae. Taking into account the diÜerences mentioned above it is possible to derive the vector correlation formulae for four-atom reactions by following the procedure used for atom»diatom reactions in ref.5. The derivation procedure is described below. I. Start with the orbital angular momentum representation in which the quantum numbers are J (total angular momentum) M (projection of J on a space-–xed axis) (A3a) ci4vABjiABvCDjiCDjichli (A3b) ci @ 4v1 @ v2 @ v3 @ ji @ li @ . II. Establish the relationship between the density matrices for the AB]CD and ABC]D arrangements (A4) Sc1 @ J1M1 o o o c2 @ J2M2T\ ; Sc J 1{ 1c1 Sc J 2{ 2c* 2 Sc1J1M1 o o o c2 J2M2T c1 c2 S where c{c J is an element of the l-representation scattering matrix. III. Expand the density matrices for the ABC]D and AB]CD arrangements in a series of W Kl{ Kj{(K{) and W KlKABKCDKch(K) respectively.matrix elements of the correlation operators IV. Rewrite the expanding coefficients then obtained as tensor products of the coefficients (polarisation moments) related to the polarisation and angular distribution operators and to the corresponding angular momentum subspaces. V. Substitute the expressions5 (A5a) (A5b) oQl (Kl)(l1l2)\J4p Y KlQl * (hk /k) oQl{ (Kl{)(l1 @ l2 @ )\J4p Y Kl{Ql{ * (hk{ /k{) VII. Substitute (which follow from the fact that l is perpendicular to k and randomly distributed around it and similarly for l@ and k@) for the expansion coefficients related to the l and l@ subspaces. VI. Simplify the resulting expression using well known formulae9,10 for sums involving Clebsch»Gordan and 9-j coefficients or spherical harmonics (e.g.orthogonality of Clebsch» Gordan or 9-j coefficients completeness of spherical harmonics). This leads to an expression for the k[jAB[jCD[k@[j@ correlation in the orbital angular momentum representation when referred to a space-–xed frame. k\0 hk{\h and /k{\0 into the space-–xed correlation formula (h is the dQ K j{ j{ ,qj { (h) and sum h scattering angle). Multiply both sides by the reduced rotation matrix element over Qj @ . Use the rotation formula for spherical tensor moments,1,2 (A6) ; dQj{,qj{ Kj{ (h)oQj{ (Kj{)( j1 @ j2 @ )\oqj{ (Kj{)( j1 @ j2 @ ) Qj{ and the Clebsch»Gordan series to simplify the resulting expression. This leads to an expression for the k[jAB[jCD[k@[j@ correlation in the orbital angular momentum representation when referred to the body-–xed frames xyz and x@y@z@ (see Section 2.A.).This expression reads oqj{ Kj{( j1 @ j2 @ )\; Sc1 J1pW KlKABKCDKchKpc2 J2TSc1 @ J1pW Kl{Kj{Kpc2 @ J2TRK QAB lKAB QCD KCD Qch K qchj{ Kl{Kj{K(h) (A7) ]Sc J 1{ 1c1 Sc J 2{ 2c*2 oK QAB AB( j1AB j2AB)oQ K CD CD( j1CD j2CD) Faraday Discuss. 1999 113 119»132 130 where the sum is over K c1 c2 Kl @ l1 @ l2 @ J1 and J2 and the Kl KAB QAB KCD QCD Kch Qch term containing the directional dependence is given by RQABQCDQchqj{ KlKABKCDKchKl{Kj{K(h)\SKABQAB KCDQCD oKchQchTSKl 0 KchQch oKQchTSKl @ 0 Kj @ qj @ o Kqj@T (A8) [(2Kl]1)(2Kl @ ]1)]1@2 dK (h). ] Qchqj{ 2K]1 The symbols S… … …pW Kp… … …T in eqn.(A7) stand for the reduced matrix elements of the correlation operators. In the case of W Kl{Kj{(K) (remember that W Kl{Kj{(K)\[Y (Kl{)?T (Kj{)](K)) for instance the l @ reduced matrix Sc elements 1 are given by9,10 ]Sl 2 @ J1pW Kl{Kj{Kpc2 @ J2T\[(2J1 1 @ ] pY 1)(2 Kl{pl J 2@ TS ] j1 @ 1)(2 pT K K j{p ] j2@ T 1)] 7K l l 1@2 1 @ 2 @ K j j 1 @ 2 @ J J K 1 28 (A9) j @ where M… … …N is a 9-j symbol.9,10 The expressions for the reduced matrix elements of the spherical harmonic and polarisation operators are9,10 (A10a) Sl1 @ pY Kl{pl2@ T\C(2l2 @ ]1)(2 4p Kl @ ]1)D1@2 Sl2 @ 0 Kl @ 0 o l1 @ 0T (A10b) S j1 @ pT Kj{p j2@ T\(2Kj @ ]1)1@2.Note that the operator W KlKABKCDKch(K) de–ned by eqn. (A2) is formed by coupling a spherical harmonic to another correlation operator. Its reduced matrix elements are more complex than those of W Kl{Kj{(K). For instance they involve two 9-j symbols not only one. VIII. Transform from the orbital angular momentum to the coupled helicity representation using the formula5 (A11) Sci{ ci Ji \;Sji @ Xi @ Ji[Xi @ o li @ 0TSai{ai Ji S jichXich Ji[Xich o li 0T (A12a) ai4vABjiABvCDjiCDjichXich (A12b) J1 (h)Sa J 1{ 1a1 (2J2]1)dX J 2{ 2X2ch(h)Sa J 2{ 2a*2 (A13) (A14) XiAB,XiCD Xi Xi{ for the scattering matrix elements. Here we have ai @ 4v1 @ v2 @ v3 @ ji @ Xi @ where Xch is the total helicity in the AB]CD arrangement (projection of jch and J onto k) and X@ is the helicity in the ABC]D arrangement (projection of j@ and J onto k@).Simplify using well known formulae9,10 for sums involving Clebsch»Gordan coefficients 9-j coefficients and rotation matrices. This leads to an expression for the k[jAB[jCD[k@[j@ correlation in the coupled helicity representation referred to the body-–xed frames xyz and x@y@z@. This expression is oqj{ Kj{( j1 @ j2 @ )\ 4 1 p ; Sj1ABj1CDj1chpW KABKCDKchp j2ABj2CDj2chT ]S j1chX1ch o T Qch Kch) o j2chX2chTS j1 @ X1 @ o T qj{ (Kj{) o j2 @ X2@ T ](2J1]1)dX1{ X1ch ]SKABQAB KCDQCD oKchQchToQAB KAB( j1A j2AB)oQCD KCD( j1CD j2CD) KAB QAB KCD QCD Kch Qch a1 a2 X1 @ X2 @ J1 and J2 .where the sum is over IX. Transform from the coupled to the uncoupled helicity representation using the formula Sai{ ai Ji \;SjiABXiAB jiCDXiCD o jichXichTSgi{gi J for the scattering matrix elements. Here g g and are the sets of quantum numbers speci–ed in eqn. i i @ (2). Use a few more angular momentum algebra formulae9,10 to simplify the resulting expression. The –nal expression»the k[jAB[jCD[k@[j@ correlation formula in the uncoupled helicity representation»is eqn. (3). 131 Faraday Discuss. 1999 113 119»132 By comparing eqn. (3) to eqns. (A7) and (A13) we see that the simplest vector-correlation formula is the one in the uncoupled helicity representation. There is no 9-j coefficient in it and this is the formula involving less summation indexes and less Clebsch»Gordan coefficients.It is this simplicity that makes the uncoupled helicity representation the most convenient for stereodynamical analyses of reaction mechanisms. It is simpler to –rst transform the scattering matrices calculated in other representations to the uncoupled helicity form and then to do the stereodynamical analysis than to do the analysis in the original representation. This was indeed the procedure we adopted in our work our scattering calculations were done in the coupled helicity representation but our stereodynamical analysis was done in the uncoupled representation. Paper 9/01948K References 1 M. Auzinsh and R. Ferber Optical Polarisation of Molecules Cambridge University Press Cambridge 1995. 2 K. Blum Density Matrix T echniques and Applications Plenum New York 2nd edn. 1996. 3 R. G. Newton Scattering T heory of W aves and Particles McGraw-Hill New York 1966. 4 J. Z. H. Zhang T heory and Application of Quantum Molecular Dynamics World Scienti–c Singapore 1999. 5 M. P. de Miranda and D. C. Clary J. Chem. Phys. 1997 106 4509. 6 M. P. de Miranda D. C. Clary J. F. Castillo and D. E. Manolopoulos J. Chem. Phys. 1998 108 3142. 7 M. P. de Miranda F. J. Aoiz L. Ban8 ares and V. Saç ez-Raç banos J. Chem. Phys. 1999 111 in the press. 8 S. K. Pogrebnya J. Echave and D. C. Clary J. Chem. Phys. 1997 107 8975. 9 R. N. Zare Angular Momentum Understanding Spatial Aspects in Chemistry and Physics Wiley New York 1988. 10 D. A. Varshalovich A. N. Moskalev and V. K. Khersonskii Quantum T heory of Angular Momentum World Scienti–c Singapore 1988. 11 H. J. Loesch Annu. Rev. Phys. Chem. 1995 46 555. 12 A. J. Orr-Ewing J. Chem. Soc. Faraday T rans. 1996 92 881. 13 N. E. Shafer-Ray A. J. Orr-Ewing and R. N. Zare J. Phys. Chem. 1995 99 7591. 14 A. M. Arthurs and A. Dalgarno Proc. R. Soc. L ondon Ser. A 1996 256 540. 15 R. T. Pack J. Chem. Phys. 1974 60 633. 16 G. C. Schatz and A. Kuppermann J. Chem. Phys. 1976 65 4642. 17 I. V. Hertel and W. Stoll Adv. At. Mol. Phys. 1978 13 113. 18 G. Ochoa de Aspuru and D. C. Clary J. Phys. Chem. 1998 102 9631. Faraday Discuss. 1999 113 119»132 132

ISSN:1359-6640    

DOI:10.1039/a901948k

出版商:RSC    

年代:1999

数据来源: RSC

摘要:

Crossed beam studies of the O(3P,1D) + CH3I reactions Direct evidence of intersystem crossing Michele Alagia,§a Nadia Balucani,a Laura Cartechini,a Piergiorgio Casavecchia,*a Michiel van Beek,îa Gian Gualberto Volpi,a Laurent Bonnet,b and Jean Claude Rayezb a Dipartimento di Chimica Universita` di Perugia V ia Elce di Sotto 8 06123 Perugia Italy. E-mail piero=dyn.unipg.it b L aboratoire de Physico-Chimie Moleç culaire Universiteç Bordeaux 1 33405 T alence Cedex France Received 13th April 1999 The angular and velocity distributions of the IO product from the reactions O(3P,1D) ]CH3I have been obtained in crossed beam experiments with a rotating mass spectrometer detector at collision energies of 55.2 and 64.0 kJ mol~1. The center of mass product angular and translational energy distributions for both the O(3P) and O(1D) reactions have been derived and the eÜect of electronic excitation and the role of intersystem crossing (ISC) assessed.The O(3P) reaction proceeds with comparable cross-section both via a direct mechanism on the triplet potential energy surface with rebound dynamics and via a long-lived complex mechanism following ISC from the triplet to the singlet surface. The O(1D) reaction proceeds on the singlet surface via formation of a complex that lives about one rotational period and also with comparable cross-section via direct rebound dynamics following a nearly collinear O»I»CH approach geometry. ISC from the triplet to the singlet surface is attributed to the presence of the heavy halogen atom and occurs for bent geometry.These –ndings are corroborated by recent theoretical calculations on the stationary points of the potential energy surfaces for the system. Calculations based on phase space theory which assumes conservation of energy and angular momentum and takes into account the various degrees of freedom involved have been performed; the product angular and translational energy distributions derived for the O(3P) reaction proceeding via ISC and long-lived collision complex formation are in very good agreement with the experimental quantities. I. Introduction The role of multiple potential energy surfaces (PESs) and electronically nonadiabatic transitions in reaction dynamics is a topic of considerable current interest. So far most dynamical studies have dealt with reactions of the type atom]molecule occurring on the ground state PES.In many cases the eÜect of the internal (vibrational and rotational) and translational energies of the § Present address INFM Sincrotrone Elettra 34012 Trieste Italy. î Present address Department of Molecular and Laser Physics University of Nijmegen 6500 GL Nijmegen The Netherlands. 133 3 Faraday Discuss. 1999 113 133»150 This journal is( The Royal Society of Chemistry 1999 reagent on the integral and diÜerential reactive cross-sections has been examined both at the experimental and theoretical levels.1h3 Among the various forms of energy that can be supplied to reagents electronic energy is quite peculiar. Indeed the extent of electronic excitation is usually such that even reactions which are strongly endoergic for the ground state species are made energetically open.4 More importantly the role of electronic excitation is that of driving the reaction on a PES that is diÜerent from the ground state PES and it is the diÜerent topology of the excited PESs that determines the diÜerent reactivity of the various electronic states.4,5 A species whose ground and excited states and their interactions are of great interest is atomic oxygen.A distinguishing feature of many atomic oxygen reactions is the interplay between the ground state PES (originating from ground state O(3P)) and the –rst electronically excited PES (originating from the –rst electronically excited state O(1D) whose energy content is 190 kJ mol~1 above the ground state) as they correlate with the same products.In fact even though the triplet PES starts lower in energy the singlet PES originating from the O(1D) reactant usually supports a strongly bound intermediate and therefore ììcrossesœœ the triplet surface becoming the lower of the two up to the products.6 Intersystem crossing (ISC) is then possible from the triplet to the singlet PES (and vice versa) making the dynamics that involve motion on the underlying singlet PES diÜerent from those involving motion only over the triplet PES. As a consequence a full understanding of atomic oxygen reactions can not disregard the possibility of triplet to singlet nonadiabatic transitions. Detailed studies on the reaction dynamics of O(3P) and O(1D)have been performed pointing out their diÜerences,6h9 but only rarely was a direct comparison of the two possible.10,11 Here we report on the results of a crossed beam investigation of the reaction of CH with both O(3P) and 3I O(1D) under the same experimental conditions ; the purpose is to assess the eÜect of electronic excitation on the reaction dynamics and the role and extent of ISC for this system where the presence of the heavy iodine atom is thought to facilitate its occurrence.Thermodynamically allowed products for the reaction O(3P)]CH3I are \[2.9 kJ mol~1 ° \[7.5 kJ mol~1 ]IO]CH3 ]OH]CH \[48.1 kJ mol~1 2I O(3P)]CH3I]H]I]CH2O \[140.6 kJ mol~1 *H298 K ° *H298 K ° *H298 K ° *H298 K ° \[346.4 kJ mol~1 ]I]CH3O ]HI]CH2O *H298 K ° being even larger including also the formation of (1a) (1b) (1c) (1d) (1e) HOI]CH and 2 O(1D)]CH3I with the list ICH2O]H.Measurements of the absolute rate constants between 213 and 364 K and product yields at 298 formation and \5% for HI formation. 3I has not been determined. being 1.9]10~10 and 1.8]10~10 cm3 3I. Argon 3IO 2 K have been recently reported for reaction (1).12 Channels (1a) and (1b) were found to account for 44% and 16% of the global rate constant respectively ; product yields for the minor channels are reported to be B7% for H formation \3% for CH3O The observation of numerous products suggested that the O(3P)]CH3I reaction is quite complex and occurs on multiple PESs. The detailed kinetic study by Gilles et al.12 has established that the IO]CH channel in the O(3P) reaction is the dominant one and increases in importance with 3 increasing temperature the IO yield increases from 38% at 254 K to 58% at 370 K while the global temperature coefficient of reaction (1) (k298\(1.8^0.2)]10~11 cm3 molecule~1 s~1) shows a small negative temperature dependence providing support for formation of a long-lived collision complex.The rate constant for the reaction O(1D)]CH However recent kinetic studies13 provided room temperature rate constants for the analogous O(1D)]CH reactions O(1D)]CH Br 3Cl and 3 molecule~1 s~1 respectively ; it is reasonable to expect a similar value for O(1D)]CH matrix experiments14 revealed the existence of an addition intermediate CH (iodosylmethane) after the irradiation of CH3I …O3 complexes; CH3IO was also seen to rearrange to either iodomethanol (ICH OH) or methyl hypoiodite (CH OI) or to eliminate HI.3 ° The enthalpy of formation of IO is somewhat uncertain with values reported in the literature ranging from \120.5 kJ mol~1 * ° fH298 K \108 kJ mol~1 to \172 * ° fH298 K kJ mol~1. Here we have used * ° fH298 K recently estimated by Gilles et al.12 For a list of enthalpies of formation see ref. 12. Faraday Discuss. 1999 113 133»150 134 3I with ISC represented symbolically. As can be inferred 3IO CH3OI The derived surto above the triplet reaction.15 Misra et al.15 used ab initio theory to calculate the energies and geometries of the various reaction intermediates and products involved in reactions (1) they characterized the transition states that connect the various species and have used the results to develop the singlet and triplet PES for the reactions O(3P,1D)]CH3I.Statistical calculations15 for the O(3P) reaction predict IO to be the dominant product below 2000 K but other products are also possible. Fig. 1 depicts the singlet and triplet PESs for O]CH from Fig. 1 O(3P) can either react on the triplet PES giving IO]CH3 or can undergo ISC to the singlet PES forming the bound OICH intermediate which will decompose because of its 3 high energy content. O(1D) will instead react on the singlet PES forming a bound CH IO/CH 3 3OI intermediate that dissociates to products; ISC to the triplet PES can occur as well. The theoretical calculations suggest that ISC does not occur for the strictly collinear collisions between O(3P) and CH3I since the singlet surface is always higher in energy in linear geometry.The crossing between the triplet and singlet PESs permits access to the rich chemistry that has been observed in kinetic studies. The calculations put the barrier for isomerization of CH reactant asymptote thus explaining the lack of a signi–cant yield of CH3O]I. faces satisfactorily explain the complex kinetics and the branching ratios observed for the O(3P) ]CH3I Another reason to pursue a detailed dynamical study of the title reactions is due to their relevance in atmospheric and combustion chemistry. Indeed the reactions of atomic oxygen both O(3P) and O(1D) with halogenated compounds are of interest in determining the impact of the surface release of halogen-containing molecules on the atmosphere and especially on the ozone natural balance.More speci–cally while the active forms of chlorine and bromine contribute to stratospheric ozone depletion it has been suggested that the tropospheric ozone balance may be aÜected signi–cantly by iodine compounds.16 Iodine was proposed to account also for the observed depletion of lower stratospheric ozone (below 20 km altitudes where chlorine and bromine are not very eÜective for ozone destruction) at midlatitudes.17 The main source of atmospheric iodine is natural methyl iodide (principally) chloroiodomethane and diiodomethane are highly signi–cant metabolic byproducts of marine biota. Although industrial sources of iodocarbons appear to be negligible compared to oceanic sources iodocarbons generated by biomass burning could contribute to the iodine reaching the stratosphere ; it is highly likely that CH3I is also released in this way because of the signi–cant elemental abundance of iodine in plant matter.Although CH3I has a short lifetime (about 4 d) in the troposphere due to its rapid photodecomposition and this would preclude signi–cant transport of it into the stratosphere research shows that convective clouds can transport insoluble material (as just iodoalkanes) very rapidly ]CH Fig. 1 Singlet (… … … … … … …) and triplet (» » » ») potential energy surfaces (schematic) for the reactions O(3P,1D) 3I]IO]CH3 with inter system crossing (ISC) indicated (the energies are taken from ref.15). 135 Faraday Discuss. 1999 113 133»150 from low altitudes to the upper troposphere and even lower stratosphere particularly in the tropics.17 The amount of iodine in the stratosphere is still unknown but the work of Solomon et al.17,18 demonstrates that iodine chemistry merits consideration in the studies of ozone destruction mechanisms. The main products of the reactions of CH3I radicals and the possibility of rapid interhalogen reactions involving iodine (such as IO]ClO and IO]BrO)19 could play an important role in understanding the ozone losses in the lower stratosphere at midlatitudes and in the troposphere at polar sunrise. Another important reaction in models of ozone losses in the stratosphere is HO the marine boundary layer very recently.21 Finally the reactions of O(3P,1D) atoms with halogen containing molecules are also of relevance in the combustion chemistry of halogenated compounds for their use as –re extinguishers (for instance iodine containing molecules have been considered as potential substitutes for halon –re suppressants).with O(3P) and O(1D) are IO 2]IO.20 The IO radical has been detected in In previous work from this laboratory we reported the results of direct dynamical investiga- 3I tions using the crossed molecular beam (CMB) method on the reactions of O(1D) with some halogenated molecules (HCl HBr HI CF Br)8,9,11,22h25 and of O(3P,1D) with H2S,8h11 which 3 are also of relevance in atmospheric and combustion chemistry. For none of them however was the occurrence of ISC evidenced.The group of the late Roger Grice carried out an extensive amount of work on the reactive scattering of O(3P) with halogen and interhalogen molecules,26 and with alkyl iodides (C2H5I C3H5I (CH3)2CHI (CH3)3CI)27h29 and haloalkyl iodides (CF CF3CH2I CH2ICl)30h32 giving some evidence of ISC to the singlet PES.27h33 In this contribution we report the –rst dynamical study of the reaction of oxygen atoms with the prototype alkyl iodide CH which makes it possible to compare directly the dynamic behavior of O(3P) and 3I O(1D) and to determine the extent of triplet to singlet ISC. Our –ndings are discussed in the light of recent ab initio calculations15 of the triplet and singlet PESs. Calculations based on phase space theory are performed and compared with experimental results.II. Experimental The scattering experiments were carried out in a universal crossed molecular beam apparatus described in detail elsewhere.8,11,34 Fig. 2 shows a schematic diagram of the set-up. Brie—y two supersonic beams of the reactants doubly diÜerentially pumped and well collimated in angle and velocity are crossed at 90° under single collision conditions in a large scattering chamber kept Fig. 2 Cross-sectional view (from the top) of the crossed molecular beam instrument with rotating mass spectrometer detector and time-of-—ight analysis. Faraday Discuss. 1999 113 133»150 136 (E values 55.2 and 64.0 kJ mol~1 which were obtained by using beams ofH c) C3I a 25% mixture ofHseeded in Ar at 0.6 bar was c C a 7% mixture ofH3 I beam angular divergence was 2.1°.below 5]10~7 mbar. The angular and velocity distributions of the reaction products are recorded by a rotatable triply diÜerentially pumped ultrahigh vacuum (10~11 mbar) electron impact ionization quadrupole mass spectrometer detector using time-of-—ight (TOF) analysis. We have exploited the capability of generating intense and continuous supersonic beams of oxygen atoms containing mostly O(3P) with a small percentage of O(1D) by radio-frequency (rf ) discharge8,11,35,36 in a water-cooled quartz nozzle (0.24 mm diameter) at high pressure (220 mbar) of dilute (4%) O (isotopically enriched in 18O2) in He gas mixture and high rf power (300 W). The 2 oxygen beam has a peak velocity of 2625 m s~1 an angular divergence of 2.3° and a speed ratio of 6.7 as measured from single-shot TOF analysis.Experiments were carried out at two diÜerent collision energy having diÜerent velocities. For the lower Ec C3I expanded through a 0.1 mm stainless-steel nozzle kept at 470 K to minimize cluster formation; the peak velocity and speed ratio were 564 m s~1 and 11. For the high E in He at 2.5 bar was used; the nozzle temperature was 570 K the peak velocity 1314 m s~1 and the speed ratio 13. The CH3I The use of a beam of 18O was mandatory for the success of these experiments in which the main reaction product is IO. In fact the natural abundance of 13C in the CH3I beam would produce a strong interference at the mass of the IO product (m/z\143) making its detection 13CH difficult due to the elastically scattered Use of 18O allowed us to detect the 18OI product 3I.at m/z\145 which can be well separated in mass from the m/z\143 elastic contamination. Under our experimental conditions we have observed only the IO product from the title reac- Nlab(H v)\Ic.m.(h u)v/u2. tions which is indeed the major reaction product.12 HOI formation was not seen to occur. Product detection for the other possible reaction channels is kinematically unfavored or hindered by dissociative ionization of elastically scattered CH3I in the ionizer. Angular distributions of the IO product were obtained by taking at least –ve scans of 30»60 s counts at each angle (every 4°) depending on signal intensity. The oxygen beam was modulated at 160 Hz with a tuning fork chopper for background subtraction.The signal-to-noise ratio was about 70 and 90 for the low and high E experiments respectively. The velocity distributions of the products were obtained at c selected laboratory angles using the cross-correlation TOF technique37 with four 127 bit pseudorandom sequences. High time resolution was achieved by spinning the TOF disk located at the entrance of the detector at 246.1 Hz which corresponds to a dwell time of 8 ls channel~1. The —ight length was 24.6 cm. Counting times varied from 15 to 60 min depending upon the signal intensity. The scattering measurements were carried out in a laboratory (lab) system of coordinates while for the physical interpretation of the scattering process it was necessary to transform the data (angular N(H) and velocity N(H v) distributions) to a coordinate system moving with the center of mass (c.m.) of the colliding system.38 The transformation is fairly straightforward and the relation between lab and c.m.—uxes is given by Ilab(H v)\Ic.m.(h u)v2/u2 (where H and v are the lab angle and velocity respectively and h and u are the corresponding c.m. quantities) i.e. the scattering intensity observed in the laboratory is distorted by the transformation Jacobian v2/u2 from that in the c.m. system.38 Since the electron impact ionization mass spectrometric detector measures the number density of the products N(H) not their —ux the actual relation between the lab density and the c.m. —ux is given by Because of the –nite resolution of the experimental conditions i.e.the –nite angular and velocity spread of the reactant beams and angular resolution of the detector the lab to c.m. transformation is not single valued and therefore analysis of the laboratory data is carried out by forward convolution procedures over the experimental conditions of trial c.m. distributions (i.e. c.m. angular and velocity distributions are assumed averaged and transformed to the lab frame for comparison with the data). The –nal outcome is the generation of velocity —ux contour maps of the reaction products i.e. a plot of intensity as a function of the angle and velocity in the c.m. system Ic.m.(h u). These contour maps can be regarded as images of the reaction. III. Results and analysis Laboratory angle distributions of IO product number density at Ec\55.2 kJ mol~1 and Ec\ 64.0 kJ mol~1 are shown in Figs.3 and 4 together with the corresponding velocity vector 137 Faraday Discuss. 1999 113 133»150 E Fig. 3 Laboratory angular distribution (Ö) of the IO product at c\55.2 kJ mol~1 from the reactions O(3P,1D)]CH3I]IO]CH3 . The circles in the velocity vector (ììNewtonœœ) diagram delimit the maximum velocity that the IO product can attain on the basis of energy conservation if all the available energy for the triplet and the singlet reactions goes into product translational energy. The separate contributions to the total lab angle distribution (»»») from the triplet direct reaction (----) the triplet reaction via ISC (»») the singlet-direct reaction (»…»…»…) and the singlet reaction via osculating complex ( » » ) are shown.E Fig. 4 As for Fig. 3 but at Faraday Discuss. 1999 113 133»150 138 c\64.0 kJ mol~1. Fig. 5 Time-of-—ight distributions of the IO product from the reactions O(3P,1D)]CH3I]IO]CH3 at E the indicated lab angles at c\55.2 kJ mol~1. Best –t global and partial distributions (lines as in Fig. 3) from the various triplet and singlet micromechanisms are shown. and have both a peak and a shoulder at angles close to H (ììNewtonœœ) diagrams. The error bars indicated represent ^1 standard deviation. The corresponding TOF spectra at selected lab angles are shown in the Figs. 5 and 6; they have been normalized to the relative intensities at each angle. Because of the increased CH3I beam velocity the c.m.Hc.m.\60° at the low E to about position moves from about Hc.m.\76° at high Ec (see Figs. 3 c and 4). As the Newton diagrams show the laboratory angle ranges within which the IO product formed from the O(3P) reaction can be scattered are limited (on the basis of linear momentum constraints and energy conservation) to angles from HB33° to 88° at Ec\55.2 kJ mol~1 and from HB62° to 90° at Ec\64.0 kJ mol~1. In contrast owing to the extra 190 kJ mol~1 of energy the IO product formed from the O(1D) reaction can spread over a much broader laboratory angle range. The measured lab angle distributions at both E values show that the product c is distributed on both sides of Hc.m. c.m. . E Fig. 6 As for Fig. 5 but at c\64.0 kJ mol~1. 139 Faraday Discuss. 1999 113 133»150 Fig.7 Best –t center of mass product angular (top) and translational energy (bottom) distributions for the O(3P) reaction [(a) (b)] and for the O(1D) reaction [(c) (d)] at Ec\55.2 kJ mol~1. Two remarkable features are the peak sharpness and the large width of the two angular distributions ; in particular the tails of the angular distributions extend well beyond the range of the O(3P) reaction and they cannot be reproduced during data analysis unless a signi–cant contribution from the O(1D) reaction is invoked. Analogously the TOF data reveal contributions from both the O(3P) and the O(1D) reactions. For instance the fast part of the H\36° TOF spectrum at c\64.0 kJ mol~1 can only originate from the O(1D) reaction. Preliminary Ec\55.2 kJ mol~1 can energetically only come from the O(1D) reaction while the whole spectrum at H\98° for E attempts at –ts which invoked a set of uncoupled angular and translational energy distributions for each electronic state of oxygen proved unsuccessful since the range of velocities that the products reached turned out not to be the same in diÜerent directions for both reactions.To be speci–c the lab distributions measured suggest by themselves that two competing micromechanisms are involved for both the O(3P) and the O(1D) reactions and this led us to use four distinct contributions (two for the O(1D) and two for the O(3P) reaction) in the forward convolution trial and error –tting procedure to express the global c.m. product —ux according to ]b[T (h)P(E Ic.m.(h ET)\[T (h)P(ET)]tripletvdirect]a[T (h)P(ET)]tripletvcomplex T)]singletvcomplex]c[T (h)P(ET)]singletvdirect where T (h) and P(ET) are the c.m.angular and translational energy distributions (assumed to be uncoupled) and complex and direct refer to micromechanisms by long lived (or osculating) complex formation and by direct reaction respectively. The coefficients a b and c weigh the various contributions with respect to the –rst one and were treated as adjustable parameters during the –tting procedure. The best –t values are aB0.5 and bBcB1 at Ec\55.2 kJ mol~1; the values obtained at Ec\64.0 kJ mol~1 are very similar with only a being a little smaller (B0.4). They correspond to the following ratios amongst the integral reaction cross-sections p ptripletvdirect/ptripletvcomplex\0.9 and 1.1 for the low and high energy experiment respectively and singletvdirect/psingletvcomplexB1 at both Ec .The reaction cross-section for each micromechanism is Faraday Discuss. 1999 113 133»150 140 obtained by integrating over the corresponding diÜerential cross-section p\2p / T (h)sin h dh 0p and accounting for the corresponding weight factor. The resulting weight of the O(1D) contribution to the total c.m. function is slightly larger than that from O(3P). This is not surprising since the oxygen beam largely consists of O(3P) but the rate constant for O(1D) should be larger than that for O(3P). Fig. 7 depicts the set of best –t c.m. product angular and translational energy distributions for the two micromechanisms for the O(3P) and O(1D) reactions at Ec\55.2 kJ mol~1.The best –t c.m. functions at Ec\64.0 kJ mol~1 are very similar to those at the lower Ec i.e. the P(ET) values scale with the slight diÜerence in total available energy the only noticeable diÜerence being that the forward O(1D) component is slightly more forward than at lower Ec . Fig. 8 reports the product velocity —ux contour maps at Ec\55.2 kJ mol~1 for the four separate contributions. The I c.m. contour maps c.m.(h u) have been obtained after a straightforward transformation to convert the —ux distribution in the energy space Ic.m.(h ET) into that in the velocity space Ic.m.(h u). The heavy solid line in Figs. 3»6 represents the total angular distributions calculated from the best –t c.m. functions while the light solid long dashed dashed and dashed dotted lines correspond to the four separate contributions.r As depicted by Fig. 7(a) and (b) and in the c.m. —ux contour maps of Fig. 8 (bottom left) one of the two O(3P) micromechanisms is characterized by a symmetric backward/forward peaked angular distribution that is quite polarized (i.e. the intensity in the forward and backward directions is much larger than in the sideways direction) and by a product translational energy distribution peaking at low energy. These –ndings are attributed to the reaction proceeding through the formation of a long-lived CH3IO complex following ISC from the triplet to the singlet PES. The singlet adduct formed after ISC has an internal energy of about 220 kJ mol~1 (the well depth with respect to IO]CH products B160 kJ mol~1 plus the exoergicity and the relative collision 3 energy) and will dissociate to products.The symmetric c.m. angular distribution suggests that the lifetime of the complex is larger than its rotational period. This is con–rmed by estimating the ratio of the lifetime q q to the rotational period for the singlet CH3IO complex from the RRKM Fig. 8 Center of mass polar —ux (velocity and angle) contour maps of the IO product at Ec\55.2 kJ mol~1 showing the IO distribution from the O(1D) reaction via an osculating complex (top left) from the O(3P) reaction via ISC to the singlet PES and long-lived complex formation (bottom left) and from the O(1D) and O(3P) reactions occurring with direct (rebound) mechanism (top and bottom right respectively).141 Faraday Discuss. 1999 113 133»150 formula33,39,40 (2) qBl~1M(Ec[*rH°]E0)/(Ec[*rH°)Ns~1 and from the relation (3) qr\2pI/L max max v \kvr bmax where k is the reduced mass of the reactants r is the initial relative of E is the well depth (B160 kJ mol~1) of the complex * where rH° is the reaction enthalpy at 0 K 0 I is the moment of inertia of the complex and L max is the maximum initial orbital angular momentum (L bmax is the maximum impact parameter). For velocity and Ec\55.2 kJ mol~1 when using L max\2.3 Aé ) a moment of inertia B152h/(2p) (corresponding to a maximum impact parameter b max IB2.13]10~45 kg m2 a geometric mean vibrational frequency l\4.0]1013 s~1 and an eÜective number of modes s\6 corresponding to the heavy atom motion with frequencies estimated from the ab initio calculations15 for CH3IO and the spectroscopic values for CH3I the calculated q q is 19 ps and 0.8 ps.Therefore q/q is B23 which indicates that the complex lives a sufficiently r r long time to lose the memory of the initial approach direction of the reactants. As can be clearly seen in Figs. 7(a) and (b) and 8 (bottom right) the second micromechanism from O(3P) is characterized by a preferentially backward peaked c.m. angular distribution with a high product recoil energy and it is attributed to a direct abstraction reaction over the triplet PES (see Fig. 1 and next section). TT\&P(ET)ET/&P(ET) is 14 kJ mol~1 TOT released as product translational energy is very diÜerent in the two cases. ETOT\Ec[*rH°]Eint where rH° is the enthalpy of reaction and Eint is the internal energy of the reactants namely the Because of the signi–cant relaxation occurring during supersonic expandoes not contribute signi–cantly to the total available energy The average product translational energy de–ned as SE for the –rst mechanism and 26 kJ mol~1 for the second one i.e.the percentage of the total available energy E In this type of experiment the total available energy is given by * internal energy of CH3I. sion the rotational energy of CH3I (the low frequency vibrational modes may be excited at the nozzle temperature and may not be completely relaxed in the beam but their energy weighs little and therefore can be neglected). As we have already seen the enthalpy of reaction is not accurately known since the enthalpy of formation of the IO radical has not been accurately established yet (see ref.41 for a recent review on the enthalpies of formation and other properties of iodine oxides). We have used the values recently derived from a crossed beam study25 of the reaction O(1D)]HI]IO]H namely *rH° (0 K)\121.3 kJ mol~1 which is in agreement with the values derived by Radlein and coworkers,42 and Buss and coworkers,43 with a recent theoretical estimation44 and with the T \298 K value reported by Gilles and coworkers12 and by others.45 With this value of *rH° the resulting average fractions of energy in translation are 24% and 44% of the total available energy for the complex forming mechanism and the direct abstraction mechanism respectively.r\0.44 is derived. This value can be compared with the q/qr value of 0.5 (for CH3IO) and 1.6 value corresponds to b The O(1D) reaction was also found to occur via two micromechanisms the –rst one is witnessed by the forward peaked c.m. angular distribution with a moderate fraction of recoil energy (about 24% at both E values) while the second one exhibits a backward peaked c.m. angular distribu- c tion (re—ecting a rebound reaction) with a large fraction (about 50% at both E values) of product c recoil energy (see Fig. 7(c) and (d) and Fig. 8(top)). The forward peaked angular distribution may well re—ect the formation of an osculating complex following O(1D) addition and/or insertion along the singlet PES. In fact according to the osculating complex model for chemical reaction,46 a forward intensity enhancement is expected when the complex lifetime is a fraction of or comparable to its rotational period.An estimate of the ratio between the lifetime of the decomposing q/q complex and its rotational period can be obtained from the observed T (h) asymmetry by r means of T (180°)/T (0°)\exp([qr/2q) where T (0°) and T (180°) are the values assumed by the T (h) function at the two poles. From the experimental asymmetry T (180°)/T (0°)\0.32 a ratio for q/q (for CH OI) obtained from eqns. (2) and (3) when using an initial orbital angular momentum maxB200h/(2p) ( and the proper moment of inertia Imax\2.77]10~45 kg m2 for CH3OI). The L L 3 max maxB3 Aé obtained assuming the O(1D) reaction without any entrance potential barrier and dominated by dispersion forces.1 Faraday Discuss.1999 113 133»150 142 3I The backward peaked angular distribution from the O(1D) reaction re—ects a direct reaction mechanism in which the O(1D) atom approach to the CH molecule on the iodine side is nearly collinear at relatively small impact parameters thereby not experiencing the deep potential well and giving rise to a rebound dynamics. The large fraction (50%) of available energy released as recoil energy witnesses the strong repulsion among the separating moieties in the exit channel. Similar results were observed for the O(1D)]HX]XO]H (X\Cl Br) reactions where the backward scattered XO was attributed to direct abstraction of the halogen atom with rebound dynamics via H»X»O con–gurations.22,23 Regarding the accuracy of the best –t c.m.distributions the –t of the laboratory data has proved to be quite sensitive to the rise and the peak position of the P(ET) values while slightly less sensitive to the fall-oÜs. The backward/forward ratios of the asymmetric angular distributions are within ^10%. Phase space theory (PST) calculations It is well established that phase space calculations47 oÜer a method of predicting the product angular and translational energy distributions arising from a long-lived collision complex dissociating without an exit barrier and by comparison with experiment of assessing the extent of energy randomization. and in relation to the complex forming mechanism For the reaction between O(1D) and CH3I we have assumed the following.3 (1) The reagent CH3I is in its rovibrational ground state. (2) The probability of the formation of fragments other than IO]CH is negligible. (3) The interaction forces between the fragments (either the reagents or the products) are of the V (R)\[C6/R6 where R is 6 dispersion type. The corresponding potential energy V (R) is given by the distance between fragments and C is the dispersion coefficient (see ref. 48). (4) The lifetime of the intermediate complex is sufficiently long for a complete energy randomization to be achieved. Such an assumption together with assumption (3) makes equally likely all of the –nal states available to the system,48 subject to conservation of the total energy and the total angular momentum.proceeding through ISC the dynamics in (5) The internal vibrations of the fragments are treated quantum mechanically whereas the rotational and translational motions are treated by classical mechanics.49 Because of assumption (4) all internal vibrations of the –nal fragments are taken into account. In the case of the reaction between O(3P) and CH3I the entrance channel are not governed by long range forces. Instead we have assumed the following. (6) Complex formation takes place via intersystem crossing. As shown by Misra et al.,15 ISC is most probable in the entrance channel at an O A »I distance of B2.3 é and a bent O»I»C con–guration of 109° for which the potential energy E is equal to B30 kJ mol~1. Using the angular 0 dependent line of center (ADLOC) model,50 a reasonable estimation of the opacity function can then be made from which a distribution of the orbital angular momentum consistent with complex formation is deduced.The remaining assumptions are the same as previously. The technical details of the calculations will be given elsewhere.51 The product translational energy and angular distributions for the O(3P) reaction calculated E of 51 kJ mol~1 a ratio of about one between the direct dynamics over the triplet PES from PST show very good agreement with the experimental distributions (see Fig. 9 for Ec\55.2 kJ mol~1). The symmetrical angular distribution corresponds to a lifetime of the collision complex of many rotational periods and the statistical product translational energy distribution indicates that there is a complete energy randomization in the complex before it decomposes to products.This con–rms that an IO component characterized by a symmetric angular distribution arises from a long-lived singlet CH3IO complex formed by ISC from the triplet to the singlet PES in small impact parameter collisions with b\2.3 Aé . Similar good agreement between extended PST calculations and experimental product angular and translational energy distributions was also reported in a study of the O(3P)]C2H5I]IO]C2H5 reaction at Ec\16 kJ mol~1 which was found to proceed by ISC at that energy.27 It is interesting to note that for the same reaction at higher c 143 Faraday Discuss. 1999 113 133»150 Fig. 9 Product angular distribution and translational energy distribution for IO scattering at Ec\55.2 kJ mol~1 calculated from phase space theory (dashed curve) compared with the experimental distributions (solid line).3I. and ISC to the singlet PES was determined which is very similar to that found for O(3P)]CH3I O(3P)]CH ICl]IO]CH c\46 E in the present study. For the reaction kJ mol~1 the 2 2Cl at pISC/pdirect ratio is B0.35 and notably the product angular and translational energy distributions32 bear a close resemblance to those derived here for O(3P)]CH The PST calculations for the O(1D) reaction assumed to proceed via a long-lived complex give a product translational energy distribution corresponding to about 17% of recoil energy when all seven vibrations are assumed to participate in the intramolecular energy redistribution.This number is somewhat lower than the experimental value of 24% and suggests that collision complexes that persist for only one rotational period do not achieve complete energy equilibration. IV. Discussion The c.m. product angular and translational energy distributions shown in Fig. 7 allow an evaluation of the dynamical in—uence of the PESs and of the kinematic constraints on the reactions O(3P,1D)]CH3I]IO]CH3 . The ab initio calculations of Misra et al.15 and Fig. 1 form the basis of the following discussion. O(3P) reaction dynamics Regarding the backward/forward symmetry of the IO angular distribution from the O(3P) reaction this is the expected result for reactions proceeding through the formation of a long-lived complex which implies the existence of a deep potential well supporting a bound intermediate.As shown by recent ab initio calculations15 the triplet surface is not characterized by the presence of such a bound intermediate ; however if a considerable amount of the reactive encounters of O(3P) do not proceed adiabatically on the triplet PES but undergo a nonadiabatic transition from the Faraday Discuss. 1999 113 133»150 144 3I. triplet to the singlet PES the deep well of the bound CH3IO singlet intermediate may be accessed. These suggestions are in line with what was proposed by Grice and coworkers in their studies on a series of O(3P)]alkyl iodide27h29 and also haloalkyl iodide30h32 reactions. These authors found that direct dynamics over the triplet PES is responsible for back scattered IO product formed with high translational energy as result of small impact parameter collisions whereas ISC to the singlet PES supporting a long-lived intermediate yields backward/forward scattered IO product with low translational energy.For alkyl iodide reactions crossed molecular beam (CMB)27 and Fourier transform infrared emission studies52 proved the formation of singlet HOI product indicating that HOI is formed via a triplet to singlet ISC followed by passage through a singlet intermediate and a –ve-member ring transition state for the intramolecular abstraction of a b-hydrogen. Recent ab initio calculations on O(3P,1D)]C2H5I support this picture.53 In contrast for the simplest alkyl iodide CH3I investigated here the spin-forbidden channel leading to HOI formation cannot occur because of the lack of a b-hydrogen in CH The ratio of cross-sections between the triplet reaction via ISC and the direct triplet reaction is kJ mol~1.That is the direct Ec\55.2 kJ mol~1 and B0.9 at p Ec\64.0 ISC/pdirB1.1 at abstraction reaction increases with increasing collision energy. An increase of the direct mechanism contribution to the total reaction could be explained with the presence of a small barrier along the triplet PES. Even though such a barrier was not identi–ed by ab initio calculations,15 we recall that a similar trend was also observed in studies of the series O3P]RI (R\C2H5 (CH3 and )2CH (CH3)3C).27h29 For the system most closely related to the present study namely O(3P)]C2H5I reaction the IO angular distribution was found27 to be symmetric at low Ec Ec\36 kJ mol~1 suggesting that 3I as well.the while it started to show some preferred backward scattering at a new channel opens up at this energy since the system has enough energy to surmount the barrier to IO formation on the triplet PES. Theoretically,53 the barrier on the triplet PES is found to be much larger than the experimental value. On the contrary since the triplet/singlet crossing is E located below the energy of the reactants the ISC channel is open at any Stevens et al.53 have c . quanti–ed the spin»orbit coupling between the singlet and the triplet states at the crossing for the O(3P)]C2H5I system. The calculated value is 2.5 kJ mol~1 a substantial value ; a similar result can be expected for O(3P)]CH In our experiment the total available energy for the 3; spin»orbit states (spin»orbit splitting of IO (2% 3@2,1@2)]H.54 IO]CH products is 58.2 kJ mol~1 at the 3 E lowest Since for the micromechanism via ISC 25% of this energy goes as product recoil c.energy the remaining 75% is channeled into internal excitation of the molecular fragments. The internal energy of the products can be rovibrational energy for both IO and CH in addition IO can be formed in both 2%3@2 1@2 3@2,1@2) is 25.1 kJ mol~1 and the vibrational spacing about 8.4 kJ mol~1).41 Rotational excitation of the fragments should be relatively low since the moment of inertia of CH is small. Hence there should be a 3 considerable amount of vibrational excitation ; in particular the l umbrella mode of CH is 2 3 expected to be considerably excited because of the change in geometry from tetrahedral to trigonal planar in proceeding from reactants to products.IO will likely be formed mainly in the ground electronic state 2% and only the lowest vibrational levels will be populated. Correlation 3@2 diagrams for spin multiplet states of O(3P2,1,0) atoms reacting with alkyl iodide molecules in the collinear and in the bent con–guration (with Renner»Teller interaction) (see Fig. 11 of ref. 27 and Fig. 9 of ref. 28) indicate that the most favorable channel should be that leading to IO(2%3@2) ]CH3(2A2 A ). However nonadiabatic coupling may readily take place in the exit channel in this multisurface system containing the heavy iodine atom as already observed in the reaction O(1D) ]HCl]ClO(2% The signi–cant polarization of the symmetric c.m.angular distribution (T (h\90°)/ T (h\0°)\0.5) for the O(3P) reaction proceeding via ISC and long-lived complex formation indicates a signi–cant correlation between the initial and –nal orbital angular momenta L and L@ (i.e. L and L@ are parallel or antiparallel). It is worth mentioning that the disposal of angular momentum is intimately connected with the molecular mechanism of the reaction as was pointed out long ago by Herschbach.55 Because the CH3I reactant is produced in a supersonic expansion the rotational angular momentum j is quite small and the orbital angular momentum L becomes the total angular momentum J. Prior to separation of the complex to products the rotational angular momentum of the complex equals J and the almost prolate nature of the complex require that k the projection of J on the symmetry axis must be small.Under these circumstances the 145 Faraday Discuss. 1999 113 133»150 complex rotates in a plane perpendicular to J and the products are expected to be emitted isotropically in this plane. Since the mass of the departing CH is very similar to that of the O atom 3 which attaches to the heavy I atom one would expect a large fraction of the total angular momentum to be disposed primarily as product orbital angular momentum L@. This fact coupled with the fact that ø L is perpendicular to (the relative velocity vector) creates the 1/sin h form factor consistent with forward/backward peaking of the c.m.angular distribution. The backward peaked angular distribution of the direct O(3P) reaction mechanism indicates O»I»CH that the preferred geometry for reaction on the triplet PES is nearly collinear The ab 3 . initio calculations15 –nd that for collinear geometry the triplet PES always lies below the singlet PES and therefore ISC cannot occur. The same calculations predict a triplet/singlet crossing as the system deviates from collinearity which allows ISC to occur more readily for bent triplet geometry. The large fraction (44%) of available energy appearing as product recoil energy indicates a strong repulsion between the products in the exit valley of the PES. O(1D) reaction dynamics complex from the O(3P) reaction via ISC.The q/q ratio at Ec\ r complex and B1.6 3IO kJ mol~1 obtained using eqns (2) and (3) is B0.5 for the singlet CH The forward peaked IO angular distribution describing one of the two competitive micromechanisms of the O(1D) reaction (see Fig. 7(c) and the c.m. velocity IO contour maps depicted in Fig. 8 (top left)) suggest that part of the O(1D) reaction proceeds through an osculating complex i.e. formation of a singlet complex that lives only a fraction of or a time comparable to its rotational period following O(1D) addition to iodine or insertion into the C»I bond along the singlet PES. In fact because of the large exoergicity of the O(1D) reaction the total energy available to the reactants is much larger than the binding energy of the complex and consequently the complex lifetime reduces strongly (see eqn.(2)) thus giving rise to an osculating complex. From the RRKM formula one obtains lifetime values of 0.3 and 1.3 ps for the CH3IO and CH3OI complexes respectively from the O(1D) reaction which are signi–cantly shorter than the value of 19 ps obtained for the CH 55.2 3IO for CH OI. A comparison with the experimental ratio of 0.44 might suggest that the CH 3 3IO isomer is that mainly involved (following O(1D) addition to CH3I) ; however because of the numerous approximations of the model we cannot rule out that the CH3OI isomer also plays a role (following O(1D) insertion into the I»CH bond and/or interconversion of CH IO). The frac- 3 3 tion (24%) of energy released as product recoil energy is similar to that of the O(3P) reaction via ISC but is somewhat larger than the value of 17% predicted by phase space calculations assuming a long-lived complex and energy randomization.We therefore can envisage that energy randomization is not complete within the time of about one rotational period. For the O(1D) reaction large electronic and vibrational excitation of the products is possible because of the much larger energy available. Extensive nonadiabatic eÜects in the exit channel are also likely which can lead to a non-statistical population of spin»orbit states of IO(2%). It is interesting to compare the c.m. product angular distribution of the reaction O(1D) ]CH3I]IO]CH3 proceeding via an osculating complex with that of the reaction O(1D)]HI]IO]H studied previously,25 which proceeds via an osculating complex as well.The former is considerably forward peaked but it is also suggestive of a signi–cant polarization (as con–rmed by PST calculations) while the latter is almost isotropic although with preferred forward scattering. In these two reactions a notable diÜerence in the disposal of the rotational energy of the complex was observed. E about 46% of product recoil energy is seen for O(1D)]HI]IO]H (a) c For comparable O(1D)]CH and only 24% for 3I]IO]CH3 (b) (the exothermicities are equal to 126 and 188 kJ mol~1 for reactions (a) and (b) respectively). Such a fact can be explained as follows. First of all the distribution of the reagent orbital angular momentum L consistent with the formation of the complex is roughly the same for both processes since the mechanical parameters responsible for this distribution have close values.Second the maximum value L m @ (consistent with the available energy E@) is much lower in case (a) than in case (b) mainly due to the fact that the reduced mass of H with respect to IO is about 15 times less than that of CH with respect to IO. Therefore the SL@/L m@ T is larger in case (a) than in case (b). Since values of L@ close to L m @ lead to average value 3 large recoil energies the recoil energy distribution is expected to be more excited in case (a) than Faraday Discuss. 1999 113 133»150 146 3. in case (b). If in addition to that we take into account the rovibrational degrees of freedom of CH which can consume part of the available energy we understand that all factors favor more 3 translational excitation between IO and H than between IO and CH It is worth noting that PST calculations56 –nd a fraction of the energy in translation form for O(1D)]HI in agreement with experiment.25 Regarding the backward peaked IO angular distribution of the O(1D) reaction (see Fig.7(c) and Fig. 8 (top right)) this may arise from a direct process at small impact parameters for nearly collinear geometry on the singlet PES. About the possibility of singlet to triplet ISC this is not expected to take place for collinear geometry because of the lack of curve crossing ;15 it could occur for bent geometry but there is no direct evidence of it since the angular distribution is sharply peaked at h\180°.The large fraction (50%) of energy released in translation re—ects a strong repulsion among the fragments while they separate on the exit valley of the singlet PES. Direct backward scattering on the singlet PES accompanied by a similarly large fraction of recoil energy was also observed in CMB studies of the reactions O(1D)]HX]XO]H (X\Cl Br).22,23 Notably this backward feature was absent in O(1D)]HI.25 Recent quasiclassical trajectory calculations on an ab initio PES corroborate the experimental backward scattering micromechanism for O(1D)]HCl]ClO]H and attribute it to side attachment of O(1D) to the Cl atom at small impact parameters.57 Comparison with the reactions K+ CH3I F and 3I + CH It may be interesting to compare the dynamics of O(3P)]CH3I with those of the well studied reactions of alkali and alkaline-earth atoms and also of halogen atoms with CH3I.The reactions of alkali atoms with methyl iodide have played a signi–cant role in the developwith an hexapole –eld it was shown that the reaction preferentially occurs when the alkali molecule.59 More recently the 3I K3I ]CH reaction approach geometry 3I which witnesses similarities in the topology of the PESs involved. ment of reaction dynamics.1 In particular the exoergic reaction K]CH3I]KI]CH3 (*HB[88 kJ mol~1) has been studied in CMB since the early days of the technique.58 These systems have been benchmarks for the investigation of chemical stereodynamics by orienting CH3I atom collides with the iodine end of the CH was studied by using the brute force technique to control the CH3I (stereodynamical control).60 Strong backward scattering of KI (with respect to the K atom direction) was found both at low and high collision energies and the results were rationalized in terms of the DIPR (direct impulse product repulsion) model,1 if a 108° wide cone of acceptance centered around the collinear conformation K»I»CH is assumed.60 A tight correlation exists 3 between the orientation of the axis of I»CH and the scattering angle of the products in the c.m.3 system. The product recoil energy is very high (up to 60»70% of the maximum). The direct abstraction of iodine atoms by O(3P) from CH3I on the triplet PES exhibits very similar features to K]CH The abstraction of I atoms from CH by F atoms is an exoergic reaction (*HB[45 kJ 3I c E (B60 kJ mol~1).This is due to c complex by about 105 kJ mol~1 with respect to the reagents. Notably proceeding via a long-lived/osculating complex on the singlet PES exhibits a A common feature of these reactions is mol~1) with a mechanism involving a collision complex with a lifetime that depends on the collision energy.61 A long-lived complex occurs at low E (B11 kJ mol~1) with about 30% of product recoil energy while an osculating complex is occurring at high the stability of the CH3IF the product energy distribution in the reaction F]CH3I was shown to be fairly consistent with phase space statistical models. The formation of IO from the reactions of O(3P) via ISC and also of O(1D) with CH3I reaction dynamics similar to that of F atoms with CH3I.the existence of a bound complex intermediate along the minimum energy path of the PES. V. Conclusion The reaction of atomic oxygen with CH O]CH proceeds with diÜerent mechanisms 3I I 3 to form depending on the electronic state of the atom and of the geometry of the approach of the reactants. For nearly collinear geometry of approach the O(3P) reaction proceeds on the triplet PES with rebound dynamics similar to that exhibited by K atoms with CH3I both reactions exhibit a backward peaked angular distribution and a strong repulsive product energy release. However in 147 Faraday Discuss. 1999 113 133»150 the case of the O atom reaction for bent geometry there is a signi–cant probability of a nonadiabatic transition from the triplet to the singlet PES which leads the reactants to experience the deep singlet well and via formation of a long-lived complex intermediate to IO]CH formation 3 with a backward/forward symmetric angular distribution and a much higher internal excitation of the products.These –ndings are corroborated by recent ab initio calculations on the O(3P,1D) ]CH3I system which highlight the role of intersystem crossing for bent geometry15 and are in line with the interpretation of previous CMB experiments on the similar reactions of O(3P) with larger alkyl and haloalkyl iodides.27h33 Electronic excitation of the oxygen atom to the (1D) state drives the reaction with CH3I directly on the singlet PES. In this case both the addition and insertion complex are possible.Because of the much larger exoergicity with respect to the O(3P) reaction the bound singlet complex lives only a time comparable to its rotational period and the IO angular distribution is forward peaked. DiÜerences in the polarization of the product angular distributions as well as in the product recoil O(1D)]CH energy distribution between 3I]IO]CH3 and the similar reaction of O(1D)]HI]IO]H are due to diÜerences in mass combination and to the fact that CH has 3 internal degrees of freedom and this is corroborated by phase space theory calculations. A second mechanism for O(1D) on the singlet PES exhibits backward scattered product with large repulsive energy release and arises from small impact parameter collisions which do not sample the potential well.This same micromechanism was also observed for O(1D)]HCl and HBr leading to ClO and BrO formation while notably not for O(1D)]HI. The dynamics of the O(3P) reaction via ISC and long-lived complex formation appears to be statistical as shown by the very good agreement between the experimental product angular and translational energy distributions and the results of a phase space theory that imposes conservation of energy and angular momentum. In contrast the dynamics of the O(1D) reaction proceeding through an osculating singlet complex is not fully statistical indicating that complete energy randomization does not occur within one rotational period of the collision complex. Support by the Italian ììConsiglio Nazionale delle Ricercheœœ and ììMinistero Universita` e Ricerca Scienti–caœœ and the AFOSR (grant F617-08-94-C-0013) through EOARD (grant SPC-94-4042) is gratefully acknowledged.References 1 R. D. Levine and R. B. Bernstein Molecular Reaction Dynamics and Chemical Reactivity Oxford University Press New York 1987. 2 M. J. Bronikowski W. R. Simpson and R. N. Zare J. Phys. Chem. 1993 97 2194; ibid. 1993 97 2204; R. B. Metz J. M. PfeiÜer J. D. Thoemke and F. F. Crim Chem. Phys. L ett. 1994 221 347. 3 J. M. Bowman and G. C. Schatz Annu. Rev. Phys. Chem. 1995 46 169. 4 R. J. Donovan and D. Husain Chem. Rev. 1970 70 489; K. Scho–eld J. Phys. Chem. Ref. Data 1979 8 723. 5 G. C. Schatz A. Papaioannou L. A. Pederson L. B. Harding T-S. Ho T. Hollebeek and H. Rabitz J. Chem. Phys. 1997 107 2340. 6 R.Grice Acc. Chem. Res. 1981 14 37. 7 See for instance A. B. McCoy M. W. Lufaso M. Veneziani S. Atrill and R. Naaman J. Chem. Phys. 1998 108 9651; A. J. Alexander D. A. Blunt M. Brouard J. P. Simons F. J. Aoiz L. Banares Y. Fujimura and M. Tsubouchi Faraday Discuss. 1997 108 375; G. M. Sweeney A. Watson and K. G. McKendrick J. Chem. Phys. 1997 106 9172; R. Grice Int. Rev. Phys. Chem. 1995 14 315; R. Zhang W. J. Van den Zande M. J. Bronikowski and R. N. Zare J. Chem. Phys. 1991 94 2704; A. M. Schmoltner P. M. Chu R. J. Brudzynski and Y. T. Lee J. Chem. 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Lee J. Chem. Phys. 1975 63 3639. Paper 9/02949D Faraday Discuss. 1999 113 133»150 150

ISSN:1359-6640    

DOI:10.1039/a902949d

出版商:RSC    

年代:1999

数据来源: RSC

摘要:

Reaction of H with highly vibrationally excited water activated or not ? G. C. Schatz,*a G. Wu,a G. Lendvay,b De-Cai Fangc and L. B. Hardingc a Department of Chemistry Northwestern University Evanston IL 60208-3113 USA b Institute of Chemistry Chemical Research Center Hungarian Academy of Sciences H-1525 Budapest P.O. Box 17 Hungary c T heoretical Chemistry Group Argonne National L aboratory Argonne IL 60439 USA Introduction The in—uence of vibrational excitation on the rates of activated bimolecular reactions has been of longstanding interest in chemical reaction dynamics. For atom»diatom reactions (i.e. A]BC) this issue was considered in some depth in the classic work of Mok and Polanyi,1 and general rules that correlate the behavior to be expected to the shape of the potential energy surface were developed.Much less is known about reactions involving more complicated molecules although there has been attention given to this issue during the last 10 years for endoergic reactions like H]H2O]H2]OH.2 A focus of much of this work has been on whether such a reaction can exhibit mode-speci–c or state-speci–c reaction dynamics,3 wherein the rate coefficient depends on the speci–c vibrational mode (or state) excited prior to reaction. Such behavior has indeed been observed in some cases but what is not considered in most of these studies is whether the excited molecule exhibits activated kinetics (meaning that the reaction has a –nite threshold energy or not). 151 Faraday Discuss. 1999 113 151»165 Received 11th March 1999 The dynamics of the collisions of H atoms with vibrationally excited H2O were studied using quasiclassical reactive and quantum mechanical non-reactive scattering calculations using the recently developed potential surface from Ochoa and Clary (OC).The trajectory calculations show that this endoergic reaction is activated for water in its vibrational ground state and with one quantum of OH stretch but excitation by two or more OH stretch quanta results in diverging cross-sections at low translational energy. The reactive rate coefficients are very large for these states being a signi–cant fraction of the gas kinetic rate coefficient. This behavior is qualitatively diÜerent from what is obtained using the I5 surface of Isaacson which shows activated behavior even for excitation as high as (04)~.To verify the accuracy of the OC surface we have performed high quality ab initio calculations for H]H2O considering geometries in the reagent region that correspond to high OH stretch excitation and we –nd that the OC surface is qualitatively correct but with too long a range in its attractive tail. Our quantum calculations of the total inelastic rate coefficients for collisions with water initially excited in OH stretch overtone states give values that are comparable in magnitude with the reactive rate coefficients for the same states. This suggests that in the recent measurements by Smith and coworkers of the rate coefficients for total loss of excited water reaction and vibrational energy transfer are of comparable importance.This journal is( The Royal Society of Chemistry 1999 What we expect to –nd is that an endoergic reaction will exhibit activated behavior for low vibrational excitation then switching to activationless behavior as as excitation is increased. However the transition from one limit to the other has not been characterized nor is it known if the energy of transition between these limits depends on the speci–c vibrational modes being excited or how the transition energy relates to the barrier for reaction. In this paper we would like to address these questions in detail for the H]H classical trajectories quantum scattering calculations and electronic structure calculations. 2O reaction by using a combination of quasi- The issues we are addressing have become of interest as a result of some recent experiments by 2O Hawthorne et al.4 in which the absolute rate coefficient for reaction of thermal H atoms with H initially having four quanta of OH local mode vibrational excitation (the (04) state) was measured.Additional results for other initial states of water are reported elsewhere in this issue of the Faraday Discussions.5 These measurements follow up earlier measurements by Sinha et al.6h10 by Crim,11 by Bronikowski et al.12h14 and by Honda et al.15 in which the eÜect of vibrational excitation on the relative magnitudes of the reaction rate coefficients was measured. These relative rate coefficient measurements demonstrated signi–cant mode-speci–c and state-speci–c propensities for excitation of high overtones of water; however it is not known from these measurements if the reaction in the excited state was activated or not.The Hawthorne et al.4 measurement has therefore provided valuable information although the results are not completely unambiguous. What Hawthorne et al. did was to measure the rate of formation of OH resulting from the reaction of excited water with thermal H atoms. The rise of the OH concentration is sensitive to depletion of the excited water molecules but this depletion can come from two sources reaction to produce OH and energy transfer in non-reactive H]H2O collisions. What they observed was that the loss from the initially excited water was very fast 4.3]10~10 cm3 s~1 a substantial fraction of the gas-kinetic rate. If this is entirely due to the H]H2O reaction then it would suggest activationless reaction dynamics.Very large rate coefficients have also been found in more recent measurements by Smith and co-workers5 for lower states of water including states that we will label (13)~ (12)~ (03)~ and (02)~2. (Here the two numbers in parenthesis indicate the quanta of excitation in the OH stretch local modes and the number after the parentheses which is only given if it is non-zero is the bend mode quantum. Also the ìì~œœ sign signi–es that the antisymmetric linear combination of the (nm) and (mn) stretch states has been used to generate a properly symmetrized eigenstate of water.) These new results would again be consistent with activationless behavior if collisional deactivation is not important.2O H2O in a collisions with However a theoretical study done recently by Lendvay et al.16 using potential energy surfaces that are able to successfully explain many features of the reaction dynamics for low levels of vibrational excitation does not support the activationless reaction mechanism. This study used quasiclassical trajectory methods to calculate reactive cross-sections and quantum scattering methods to calculate vibrationally inelastic cross-sections for H]H variety of states that vary from the ground state to the (04)~ state. The potential surface used for the reactive calculations was the I5 surface of Isaacson.17 This surface which is based on ab initio calculations,18 had been used with great success in a paper by Bradley and Schatz19 in studies of reaction from the ground state of water where it was able to accurately describe angular distributions alignment factors integral cross-sections and product state distributions better than the early WDSE surface of Walch»Dunning»Schatz»Elgersma.20 The reactive calculations of Lendvay et al.16 indicated that for the (04)~ state the I5 surface predicts activated reactive dynamics with a reactive threshold of about 2 kcal mol~1.This is similar behavior to what was found earlier (for diÜerent initial states) for the WDSE surface and surfaces derived from WDSE based on quasiclassical trajectory calculations21h23 and reduced dimensionally quantum reactive scattering calculations. 24,25 For the I5 surface and the (04)~ state Lendvay et al.calculated a reactive rate coefficient at 300 K of 1.5]10~12 which is well below the Hawthorne et al. result. However they also obtained a total vibrational energy transfer rate coefficient of 4.5]10~10 in good agreement with Hawthorne et al. and thereby suggesting that almost all of the Hawthorne et al. rate coefficient is due to energy transfer. Note however that the calculated energy transfer rate coefficient was not for the I5 surface as it was found that the I5 surface was not suitable for energy transfer calculations (because it has unphysical long range behavior and is not symmetric upon permutation of the two water hydrogen atoms). Instead the Lendvay et al. calculation developed a new surface based on a very high quality intramolecular force –eld for water,26 and an intermolecular Faraday Discuss.1999 113 151»165 152 Very recently a new potential surface has been developed for the potential that was based on an accurate H]HF potential.27 This potential has realistic long range behavior and it allows for reaction with a barrier that is similar to that for H]H2O but its accuracy is otherwise unknown. One point that was noted in the Lendvay et al. paper is that collisional deactivation of the (04)~ is expected to be efficient because there is another state (of mixed character) that is very close in energy (13.1 cm~1) to (04)~. However the new results from Smith and co-workers5 for states of water that are lower in energy would seem to provide a serious challenge to this idea as the nearest states for energy transfer have much larger energy gaps.reaction,28 that H]H2O allows us to reconsider the interpretation of Smithœs experiments. This surface which we denote OC (for Ochoa de Aspuru and Clary) is based on –ts to high quality ab initio calculations.29 This function is properly symmetrized with respect to permutation of all three hydrogen atoms and it describes the OH]H reaction dynamics accurately.30 In this paper we use the OC surface in 2 trajectory and quantum scattering calculations that are similar to what was presented earlier for the I5 surface and we –nd that the results are dramatically diÜerent compared to what was obtained by Lendvay et al.,16 especially for the reactive cross-sections. This diÜerence is tied to the shape of the potential surface and in particular it is connected to the transition from activated to activationless reaction dynamics as the water is vibrationally excited.To test whether this transition is correctly described by the OC surface we present new ab initio results which study the long range behavior of the surface. In Section II of this paper we brie—y summarize the methods used in the dynamics calculations. The reactive results are presented in Section III and the inelastic results in Section IV. The new ab initio calculations are presented in Section V and our conclusions are summarized in Section VI. II. Theoretical methods II.A. Classical trajectories Standard technology quasiclassical trajectory calculations (QCT) were used31 to determine the reactive cross-sections and rate coefficients using the OC potential function.To de–ne the initial conditions we generated quasiperiodic trajectories with quantized vibrational actions associated with the two O»H stretch local modes and the bend mode and then we sampled coordinates and momenta randomly from this trajectory to de–ne the initial conditions for the collision calculations. By ììquantizedœœ we mean that the action variable for each mode is equal to (N]12)+ where the quantum number N is determined by the corresponding quantum state. The actions corresponding to the modes were calculated by a Sorbie»Handy type FFT method.32 Note that in the primitive semiclassical treatment that we use it is not possible to symmetrize the water states with respect to interchange of the H atoms so the (04)~ and (04)` states cannot be distinguished.However we still use the (04)~ label so as to avoid confusion in making comparisons with experiment. For the states (00) (01)~ (02)~ (03)~ and (04)~ the energies of the OC semiclassical states are 13.4 24.2 34.3 43.5 and 52.8 kcal mol~1 respectively. This means that relative to the ground state energy the energies are 10.8 20.9 30.1 and 39.4 kcal mol~1 for 1 2 3 and 4 quanta of OH stretch excitation respectively. Typically we did 2500 trajectories for each state considered and each translational energy but for states with small cross-sections (like the ground and (01)~ state) we did more trajectories (10 000) at selected energies and 30»50 000 at energies just above the reactive threshold.The bmax was chosen to be 3.2 a0 maximum impact parameter for (00) and (01)~ 7.5 a for (02)~ 8.1 a 0 for (03)~ and 8.7 a for (04)~. These very large values of bmax for the higher states were necessary0 0 to converge the cross-sections at low energies where the reaction dynamics is governed by a capture mechanism. We will see later that bmax is unusually large because the OC surface has a long range attractive region that is somewhat exaggerated compared to what we get from ab initio calculations. Reactive trajectories were analyzed by calculating the vibrational and rotational actions of the resulting diatomic molecules. We found in agreement with earlier work,3 that physically meaningful threshold energies (energies that are not signi–cantly below the zero point corrected barrier height) are obtained only if the trajectories which lead to H molecules that have less than zero 2 153 Faraday Discuss.1999 113 151»165 point energy are discarded. A similar zero point constraint was not applied to the OH stretch excited state for reasons that have been discussed previously.3 In addition to calculating cross-sections for reaction with the excited H atom in the water molecule we also obtained cross-sections for abstraction with the unexcited H atom and for the exchange process (H@]H2O]H@HO]H). Of course for the ground state of water we summed together the two equivalent abstraction cross-sections. However for the excited state calculations the cross-sections for abstraction with the unexcited H atom and for exchange are negligible compared to abstraction of the excited H atom so we have neglected these processes.Since the potential surface was not optimized to describe exchange we do not expect these cross-sections to be meaningful. In fact we –nd that the OC potential has unphysical bumps in the region corresponding to exchange. II.B. Quantum scattering Our studies of H]H2O inelastic scattering have been done using a vibrational coupled-channel in–nite-order-sudden (VCC-IOS) quantum scattering method the details of which are described elsewhere.16,33 We note that Clary and Kroes,34 have performed extensive studies of collisional energy transfer using the VCC-IOS method including studies of the H]H2O system. Also Bissonnette and Clary35 have performed coupled states and coupled channel studies of collisional energy transfer in H]H2O using the WDSE surface including for rotation of the water.These studies were restricted to signi–cantly lower energies than we consider here. We used quantum rather than classical methods for these calculations for several reasons. First for inelastic scattering calculations it is very difficult to calculate the –nal quantum number from the good action variables as this requires a more precise determination of the action variables than is provided by the Sorbie»Handy method described above. Second the probabilities of many inelastic processes are so small that they are forbidden classically. Third the determination of the maximum impact parameter is numerically ill-behaved for near resonant inelastic scattering processes.By using VCC-IOS the determination of absolute cross-sections for elastic and inelastic scattering is computationally well-behaved. H]H2O is a good system for invoking the IOS approximation as the rapidly moving H atom is able to approach the water molecule with minimal rotation of the molecule. One worry is the fact that reaction has been ignored in the VCC-IOS calculation (by using a basis set that does not allow the system to distort much past the saddle-point to reaction). This is a good approximation when reaction is a small perturbation on the collision dynamics,36 but we will see later that the reactive cross-sections are comparable to the total vibrationally inelastic cross-sections for the higher states that we consider.Further re–nement is therefore desirable. However since the potential surface also requires revision (described later) we have not pursued this. In the quantum calculations the three modes of the water molecule are described by the zero angular momentum Watson Hamiltonian. The intramolecular force –eld of water as well as the intermolecular poential was taken from OC. The eigenvalues and eigenfunctions were calculated using a discrete variable representation (DVR) method using a grid of 1500 points for the three vibrational modes. States were assigned based on the nodal pattern of the wavefunction. In the present work we use the local mode labels to describe all the states even the ground state. The coupled-channel equations were solved by a sector based numerical method similar to R-matrix propagation including the lowest 80 states in all calculations.The cross-sections were determined by averaging over H2O orientations using grids in the two Euler angles. The calculations were repeated for each partial wave and over a grid of total energies and the thermal state-to-state energy transfer rate coefficients were determined by integration of the spline-–tted cross-sections over the translational energy grid. Elastic cross-sections were calculated by solving the radial equation with vibrationally adiabatic potentials from the coupled channel calculations including enough partial waves to converge the partial wave sum. II. C. Potential energy surface (PES) Table 1 compares the stationary point properties of the OC28 and I517 potential surfaces including the geometries energies and harmonic vibrational frequencies for the H2O OH and H mol- 2 ecules and the HHOH saddle-point.Experimental results37,38 are also given where available. Faraday Discuss. 1999 113 151»165 154 Table 1 Reagent product and saddle-point properties (energies in kcal mol~1 distances in a0 angles in degrees frequencies in cm~1) OCc I5b Propertya H2O» Rh u 1 1.810 104.3 3855 1658 3915 13.5 1.837 103.1 3811 1655 3929 13.4 1 u2 u ZPE 3 E(H2O]H) 0 0 0 1.832 3738 1.865 3696 OH» Re u H2R u » e 1.401 4401 14.9 1.430 4334 15.5 E(OH]H2) Saddle-point» b»O) a) a»Hc) 1.833 2.561 1.554 95.1 160.8 474 1.863 2.491 1.601 97.2 164.0 555 R(H R(O»H R(H /(Ha»O»Hb) t(O»Ha»Hc) u u 818 1104 2585 3507 1102i 12.1 684 1086 2205 3730 1476i 12.3 1 2 u u3 4 u u5 6 20.7 21.5 ZPE E(sp) 37 (OH H and 38HO).a Notation taken from ref. 28. b Ref. 17. c Ref. 28 although note that here we provide harmonic frequencies for H2O that were not given in ref. 28. d Refs. 2) (2 Note that each of the surfaces provides an accurate –t to the underlying ab initio calculations so diÜerences between the surfaces primarily re—ect diÜerences in the ab initio methods used. However the diÜerences between the two PESs are quite small with the barrier to reaction diÜering by 0.8 kcal mol~1. Note that although some of the saddle-point frequencies diÜer by 300 cm~1 the zero point energies diÜer by only 0.2 kcal mol~1 (i.e.the diÜerences cancel out in taking the sum over frequencies). Since the zero point energies in water and the saddle-point are only about 1 kcal mol~1 diÜerent the zero point corrected barrier is only 1 kcal mol~1 smaller than the uncorrected barrier (20.4 kcal mol~1 for I5 and 19.3 kcal mol~1 for OC). This barrier corresponds to somewhat less than two quanta of excitation of the OH stretch mode of water. II. D. Ab initio calculations The ab initio calculations were done using multi-reference con–guration interaction (MR-CI) methods with Dunningœs augmented polarized valence double zeta39 (aug-cc-pvdz) basis set. In particular the orbitals were optimized using an eight orbital eleven electron complete active space (CAS) wavefunction.The active orbitals were then resolved using a Fock matrix diagonalization (to identify the 1s orbital). In the –nal MR-CI calculations the 1s orbital is kept doubly occupied so the CI reference wavefunctions consists of a seven orbital nine electron CAS (490 con–gurations total 280 of which are of 2A@ symmetry). Single and double excitations from these reference con–gurations generate a total of 888,916 con–gurations of 2A@ symmetry. This calculational Faraday Discuss. 1999 113 151»165 Exptd Ab initio (pvdz) 1.827 103.7 3783 1644 3899 13.3 1.809 104.5 3832 1649 3942 0 13.5 1.832 3738 1.851 3684 1.401 4401 16.1 1.440 4338 15.9 1.849 2.578 1.587 96.8 163.7 555 672 1020 2576 3692 1191I 12.2 21.7 155 method is denoted CAS]1]2/aug-pvdz.To test this choice of method and basis set we calculated the barrier height for the H atom abstraction transition state obtaining an energy of 21.7 kcal mol~1 which is very close to that obtained by Alagia et al.29 (whose calculations were used to –t the OC potential). Other properties of the transition state reactants and products from these calculations are summarized in Table 1. As a further test of the convergence of these results with respect to the basis set a small number of additional calculations were carried out using the larger augmented polarized valence triple zeta basis set (aug-cc-pvtz) of Dunning and coworkers.39 All calculations were carried out using the COLUMBUS program package.40 Since the primary reason for doing the calculations was to study the interaction of H with we studied only a limited range of geometries.In particular we highly vibrationally excited H examined the approach of Hc 2.0 to 3.0 a0 O»Hb –xed at 1.85 a0 H the on a two-dimensional grid of points surrounding the H atom. 2to O, Ha»O»Hb O with the »Ha distance –xed at values ranging from 1»O»H2 angle –xed at 80 95 and 120° and Hc located a III. Reactive cross-sections and rate constants (p for the Fig. 1 presents reactive cross-sections ]H r) H 2O abstraction reaction as a function of (E translational energy with water in the ground state and the stretch excited states (0v)~ with tr) v\1 2 3 4.These results include error bars associated with the statistical uncertainty in the quasiclassical trajectory (QCT) calculation. To provide a point of reference Fig. 2 presents similar reactive cross-sections for the I5 PES as obtained from the calculations of Lendvay et al.16 What we see in the two –gures is that the I5 cross-sections have a non-zero threshold energy for all the states plotted while the OC results have a non-zero threshold only for the ground state and the (01)~ state. The higher states all exhibit a cross-section that appears to diverge at low energies ; in fact we have done calculations for energies as low as 0.07 kcal mol~1 and we –nd no deviation from the divergent behavior.Plots of log(cross-section) vs. log (translational energy) are presented in Fig. 3 for the (02)~ (03)~ and (04)~ states from the OC calculations and we see that the plots are approximately linear especially over the range of translational energies from 0.7 to 20 kcal mol~1 with slope parameters of [0.96 [0.71 and [0.61 respectively. In the standard capture model of reaction where one assumes a power law potential V (R)\AR~p the cross-section Q has the energy dependence Q\E~2@p so the behavior that we –nd would suggest values of p\2.1 2.8 and 3.3 for the three states studied. These powers are unphysically small compared to what the potential actually looks like (see later) probably because an important component of the energy dependence of the cross-section comes from the variation of the cone of acceptance that leads to reaction.However the important conclusion of this Fig. 1 The reactive cross-section of reaction (1) as a function of the initial translational energy obtained in classical trajectory calculations on the OC potential surface for the (0v)~ states of water. Faraday Discuss. 1999 113 151»165 156 Fig. 2 Reactive cross-sections analogous to Fig. 1 but for the I5 potential surface. analysis is that the excited states above (01)~ in the H]H2O reaction have cross-sections that have an inverse power law dependence on energy. To further explore the in—uence of vibrational excitation in Fig. 4 we present cross-section vs. energy for the (13)~ and (02)~2 states (the latter state having two quanta of bend excitation in addition to two of OH stretch).The (02)~ and (03)~ cross-sections are also included in the –gure for reference. The –gure shows that the (02)~2 cross-section is virtually identical to (02)~ (this is also true for the (02)~1 state) and (13)~ is only modestly higher than (03)~ (and by comparison with Fig. 1 smaller than (04)~). The –rst comparison indicates that bend excitation has basically no eÜect on the reactive cross-section (at least for a state that has a diverging cross-section even without the bend excitation). The second comparison indicates that excitation of the ììspectatorœœ OH stretch mode i.e. the OH that is not involved in reaction increases the reactive cross-section by less than would be obtained by putting the same excitation into the reactive OH stretch mode.Table 2 presents the thermal rate coefficients (at 300 K) that have been derived from the crosssections in Fig. 1 2 and 4. To generate these results we have –tted the energy dependence of the cross-sections that have zero activation energy to an inverse power law result Q\AE~q and Fig. 3 Log»log plot of cross-section vs. translational energy using the results in Fig. 1 for the states with v\2 3 and 4. 157 Faraday Discuss. 1999 113 151»165 Fig. 4 Reactive cross-sections for the OC potential as in Fig. 1 but for the states (02)~ (02)~2 (03)~ and (13)~. t E )p@2 (for E[Et) with t being the threshold energy. For the OC PES these –ts to ”2 yield the parameters Et\17.3 t\5.8 kcal mol~1 p\1.673 and A\10~3.889 for (01)~. then integrated the usual Boltzmann average of the velocity times cross-section analytically.For cross-sections with a –nite threshold energy we have –tted the results to a cross-section of the form Q\A(E-E the cross-section expressed in kcal mol~1 p\1.65 and A\10~3.683 for the ground state and E The resulting OC rate coefficients in Table 2 increase by seven orders of magnitudes at 300 K in going from (00) to (01)~ and eight orders of magnitude from (01)~ to (02)~. However the increase is much more gradual for higher states (factor of 2.7 for (02)~ to (03)~ and 1.7 for (03)~ to (04)~). We also see that the (02)~2 rate coefficient is very similar to (02)~ and (13)~ is between (03)~ and (04)~. The corresponding I5 results are signi–cantly higher for the ground state and (01)~ but the higher states have lower rate coefficients re—ecting the fact that the OC cross-sections diverge at zero energy.The ground state thermal rate coefficients may be compared with experiment,41h44 which give k\3.2]10~26,41 4.4]10~26 42 2.0]10~25 43 and 8.5]10~27 44 cm3 s~1 at 300 K. Evidently the OC result is in the range spanned by the experiments and the I5 result is much too Table 2 Reactive thermal rate coefficients (in cm3 v~1 s~1) State OC Potential» (00) (01)~ (02)~ (03)~ (04)~ (02)~2 (13)~ Boltzmann ave I5 Potential» (00) (01)~ (02)~ (03)~ (04)~ Boltzmann ave a Ref. 16. Faraday Discuss. 1999 113 151»165 158 1000 K 300 K 4]10~17 9]10~15 3.7]10~11 1.4]10~10 2.7]10~10 4.5]10~11 2.0]10~10 3]10~26 2]19~19 6.5]10~11 1.8]10~10 3.1]10~10 5.1]10~11 2.2]10~16 5]10~16 3]10~26 2]10~14 8]10~13 9.5]10~12 1.0]10~11 3.7]10~11 6]10~20 6]10~16 3.8]10~13 1.0]10~13 1.5]10~12 2]10~14 6]10~20 high.Note that the experimental rate coefficient measurements generally refer to higher temperature so the 300 K result represents a signi–cant extrapolation and there is signi–cant dispersion in the results. At 1000 K the corresponding measured rate constants k\5.0]10~15,41 7.9]10~15,42 4.9]10~15 43 and 4.4]10~15 44 cm3 s~1 are generally in better agreement. Table 2 shows that the OC result is signi–cantly lower and the I5 result is a bit higher. Note that the result labeled ììBoltzmann averageœœ which involves a simple Boltzmann weighted average of the rate coefficients for speci–c vibrational states is the same as the ground state rate coefficient except for the OC surface at 1000 K.In this case one –nds that the (02)~ rate coefficient is so much larger than (00) that its contribution to the Boltzmann average greatly exceeds the ground state contribution. Other states not listed in the table such as (02)~1 also contribute noticeably to the Boltzmann average but (02)~ is the most important. The calculated (04)~ rate coefficient 3.1]10~10 cm3 s~1 is only slightly less than the Hawthorne estimate for the total rate of loss of the (04)~ state. This is a dramatically diÜerent result than was obtained by Lendvay et al.16 for the I5 PES. We will discuss this point further below after we have presented the vibrationally inelastic rate coefficients.Another comparison with experiment is provided by the ground state cross-section measurements of Jacobs et al.,45 who report cross-sections of 0.03^0.02 and 0.25^0.07 ”2 at translational energies of 23 and 51 kcal mol~1 respectively. The OC results at these energies are 0.004 and 0.07 ”2 and the corresponding I5 results are 0.02 and 0.11 ”2. Evidently the two theoretical results are fairly consistent with each other but they are lower than experiment. If we had not constrained the H to have zero point energy we would have obtained results that were much 2 closer to experiment (though still low). However doing this would have generated thermal rate coefficients that are much too high.Thus we are unable to generate results that are consistent with both sets of experiments. H]H O(0n)]H]H 2 2O(ij)k obtained in quantum IV. Non-reactive cross-sections and rate constants The quantum inelastic scattering rate coefficients obtained using the OC PES for the (02)~ (03)~ and (04)~ stretch excited states of water are shown in Fig. 5. For comparison we show in Fig. 6 the corresponding results calculated using the intramolecular water potential (PJT2) combined with the reactive intermolecular interaction borrowed from the H]HF reaction (denoted as PJT2]6SEC; for details see ref. 16). In the –gures we plot the thermal (300 K) inelastic rate coefficients for all transitions originating from the selected initial state as a function of the energy of the –nal state.In the earlier study we found that the possibility for reaction signi–cantly increases the chance of inelastic collisions. A comparison of Figs. 5 and 6 shows that the inelastic Fig. 5 The thermal inelastic rate coefficients for the scattering calculations on the OC surface for n\2 3 and 4. Faraday Discuss. 1999 113 151»165 159 H]H O(0n)]H]H 2 2O(ij)k obtained in quantum Fig. 6 The thermal inelastic rate coefficients for the scattering calculations on the PJT2]6SEC surface for n\2 3 and 4. rates are also relatively large on the OC PES although qualitative diÜerences can be observed. The absolute magnitude of the largest inelastic rate coefficient are larger on the PJT2]6SEC surface but they decay quickly with increasing energy gap while on the OC PES the inelastic rates are smaller near the elastic peak but decay more slowly.In our earlier calculations16 on a potential surface that did not allow reaction (PJT2]LJ) we found that although the inelastic probability decreased slowly with increasing energy gap even the largest inelastic rates were relatively small (down by a factor of 5 compared to PJT2]6SEC for the (04)~ state). Relative to this the two reactive potential surfaces OC and PJT2]6SEC give more comparable results. The only exception to this arises for the (02)~ and (03)~ states. These will be described further below. The diÜerent behavior that we see between OC and PJT2]6SEC can partly be traced back to diÜerences in the water intramolecular potentials. These diÜerences lead to diÜerences in the calculated energy spectrum with not only the energy gaps but even the ordering of the states being diÜerent.On the PJT2 potential the Watson Hamiltonian yields many pairs or clusters of states that are closely spaced and strongly coupled. Such cases enhance the possibility of transitions between these states as a result of collisional interaction. On the OC PES we observed fewer strongly coupled states and as a consequence the inelastic transition probabilities are smaller even if the intermolecular potential supports the transition. In Table 3 the total inelastic rate coefficients are collected for the three pure asymmetric stretch states and some close-lying states obtained on the diÜerent potential surfaces. For the (04)~ state the OC total inelastic rate is very similar to that for the PJT2]6SEC.Indeed we –nd that for many of the highly excited states (including all the states in the table except (02)~ and (03)~) the inelastic rate coefficient summed over all –nal states is large ([10~10 cm3 s~1). The rate coeffi- Table 3 The total thermal inelastic rate coefficients for diÜerent initial states calculated with diÜerent potential surfaces (in units of 10~10 cm3 s~1) OC State/PES PJT2]LJ PJT2]6SEC 0.18 0.48 0.46 0.25 1.00 0.96 0.84 2.31 2.84 0.82 3.25 3.30 3.90 4.54 0.46 2.09 1.35 0.40 3.85 2.72 6.93 (02)~ (02)~2 (02)~3 (03)~ (31)~ (13)~ (04)~ Faraday Discuss. 1999 113 151»165 160 cients listed in Table 3 for the (02)~ and (03)~ are lower than the average mostly due to the absence of nearby states on the OC PES that are strongly coupled to the initial state.Before comparing the thermal inelastic rate coefficients with the reactive ones we should emphasize that a non-negligible uncertainty is expected in the quantum scattering results as these did not take into account the loss of —ux due to reaction. Keeping this in mind one can see that the calculated quasiclassical reactive rate coefficient is comparable to the total quantum inelastic rate coefficient for the (04)~ state. This is contrary to what the calculations on the I5 potential yielded mostly because the reactive rate coefficient is much smaller. We –nd that the reactive rate coefficients for the (02)~ and (03)~ states are larger than the quantum inelastic rates.This qualitatively diÜerent result on the OC PES compared to I5 leads us to the conclusion that in the experiments of Hawthorne et al.,4 the loss of vibrationally excited water from reaction plays a role that is comparable to that of energy transfer. 0. HaO H2O 0 is B1.85 a (the The equilibrium distance for OH) a to 2.6 a0 as noted on the –gure. a»O»Hb angle is –xed at the saddle-point value of 95°. The 0 V. Ab initio calculations In Fig. 7 we present the results of ab initio calculations that are designed to test the accuracy of the OC potential surface in regions that are important in determining the thresholds for reaction involving vibrationally excited water. Both aug-pvdz and aug-pvtz results are included and for reference we show results for the OC surface.The plot shows the potential energy as a function of the HcHa distance where the HbO HaOHb distance the angle and the HcHaO angle are all frozen at the values determined for the saddle-point. Curves are shown for four diÜerent choices of the H a aO distance ranging from 2.2 to 2.6 same as the HbO H distance). Thus the curves in Fig. 7 all correspond to distances greater than aO that of equilibrium H2O (the distances were chosen to mimic the eÜect of vibrational excitation). The energy zero is taken to be in–nitely separated reagents at equilibrium. The saddle-point a»O distance (denoted R to have values ranging from 2.2 O»H distance is –xed at 1.85 a0 H and the c»Ha»O angle is also –xed at the saddle-point value (160°) and the system is constrained to be planar.The Fig. 7 Ab initio potentials for the Hc]Ha»O»Hb system as a function of the Hc»Ha distance. Here we have chosen the H H The b solid symbols and solid lines show the results of ab initio calculations using the aug-pvdz basis while the open symbols show the corresponding results using the pvtz basis. The dashed lines show the corresponding results of the OC potential for the same coordinates. 161 Faraday Discuss. 1999 113 151»165 Fig. 8 Contours of ab initio and OC potentials plotted as a function of the coordinate of the atom Hc aO»Hb H with the location of taken as the origin and the relative to H a»O bond taken along the negative H y axis and the H is oriented so that its x-coordinate is positive and y-coordinate is negative.In these a a»O distance is given three possible values 2.2 2.4 and 2.55 a0 O while the »Hb distance is b a»O»Hb internal angle is chosen to be 95° (close to the saddle-point value) and the 2O calculations the H –xed at 1.85 a0 H the four-atom system is assumed to be planar. The contour increment is 1 kcal mol~1. Solid contours denote positive energies and dashed lines denote negative. In each plot the energy zero is chosen to be the energy of the in–nitely separated H and H2O H fragments (with the –xed in the same distorted geometry.) geometry corresponds to H (roughly the minimum of the H HaO\2.4 a0 the ab initio result has a positive slope indicating purely attractive interc Ha\1.55 a0 HaO\2.56 a0 and an energy of 21 kcal mol~1 aO\2.6 a0 curve).The lowest value of H a0 which corresponds to an energy aO that is included in the –gure is 2.2 of 15 kcal mol~1 relative to the H]H2O ground state. This energy is somewhat below the 20.9 kcal mol~1 needed to excite the (02)~ state. (We subtract the zero point energy in this discussion but note that since the diÜerence in zero point energy between the reagents and products is nearly zero the analysis with zero point energy included would not be much diÜerent except for an overall shift in energies.) What we see in Fig. 7 is that the HaO\2.2 a0 curve always has a negative slope which means that in order for reaction to occur it will be necessary to supply some translational energy.This means that the reaction will be activated. On the other hand when we consider action between H and the water molecule. Note also that this change in behavior arises in both c the aug-pvdz and aug-pvtz results indicating that the change from purely repulsive behavior at HaO\2.2 a0 to purely attractive behavior at HaO\2.4 a0 is not sensitive to the basis set used in the ab initio calculations. For HaO\2.3 a0 we see a repulsive curve at long range and then attractive closer in which means that there would be a very small (a few tenths of a kcal mol~1) threshold to reaction for this amount excitation. The excitation energy in this case is about 21 kcal mol~1 which is slightly above the (02)~ threshold. This energy is also nearly the same as the barrier height noted above which means that activationless behavior should have its onset as soon as the energy is sufficient to surmount the barrier.This indicates that the (03)~ and (04)~ states should have zero thresholds. It also appears that the (02)~ state will have a zero threshold but here we should note that zero point energy in other modes will play an important role in determining precisely what happens. Faraday Discuss. 1999 113 151»165 162 The results for the OC potential in Fig. 7 are generally very similar to the ab initio curves except that for OC one sees attractive behavior for all values of HaO (repulsive behavior is seen for HaO\2.0 a0). Note also that the OC potential fails to —atten out for large values of the Ha»Hc distance while the ab initio results do.This means that the OC potential has a much longer range. The results in Fig. 7 refer to a direction of approach of the hydrogen atom that is close to the with the other coordinates –xed at the saddlea OHb c minimum energy path for abstraction. To examine the shape of the potential energy surface more globally in Figs. 8 and 9 we present the contours of the ab initio calculations as a function of the location of atom Hc Ha with the atom –xed at the origin and the OH bond taken to be along a the y axis. The right side of these –gures shows the results of the aug-pvdz calculations and the left side shows the OC potential for the same coordinate de–nitions. For all plots the energy has been taken to be zero for H in–nitely separated from a distorted water molecule.In Fig. 8 we c show how the potential surfaces vary with HaO point value while in Fig. 9 we show both the dependence on the Ha»O»Hb angle with HaO –xed at 2.4 a and the potential for moving H out of the H plane around H 0 a . c Fig. 8 shows the repulsive contours around the atom H for H a HaO\2.4 a0 H and this well becomes deeper for aO\2.6 a0 . The correspond- attractive well for aO\2.2 a0 but there is an ing behavior of the OC potential is somewhat diÜerent with an attractive well being apparent even for HaO\2.2 a0 and the region of attractive behavior being much broader and longer ranged than in the ab initio result. There are also some ripples in the OC potential at long range that are probably due to artifacts in the –t. Fig. 9 shows that the diÜerences between the OC potential and the ab initio potential hold both for a wide range of Ha»O»Hb angles and for out of-plane approaches of H to the water molecule.The results in Figs. 7»9 suggest that the OC potential will overestimate the reactivity of the excited states of water due to a combination of an attractive component of the potential that is too long range and a switch from repulsive to attractive behavior that occurs at too low an energy. Of these two eÜects the more important one is the longer range of the attractive potential Fig. 9 Contours of ab initio and OC potentials as in Fig. 8 but –xing theHa»O distance at 2.4 a and setting 0 the Ha»O»Hb internal angle to be 80° 95° and 120°. 163 Faraday Discuss. 1999 113 151»165 as this will produce cross-sections that are too large compared to the correct results.The switch between activated and activationless behavior is less important as even the ab initio potential predicts zero activation energy as soon as the vibrational energy matches the barrier height. However the lower threshold for attractive behavior in the OC potential should have an eÜect on non-reactive H]H2O collisions resulting in complex formation that allows for enhanced energy transfer compared to what would come from the ab initio surface. The behavior noted in Fig. 9 suggests that exciting the bend mode of H2O will have little eÜect on the rate of reaction using either the ab initio surface or the OC surface. Of course we have already seen this result for the OC surface in the results presented in Fig.4. We have made plots similar to Figs. 8 and 9 for the I5 potential and for this we –nd repulsive behavior at long range for HaO\3.0 a0 or more corresponding to an excitation energy of 58 kcal mol~1 or more. This explains why we see activated behavior in the I5 cross-sections for states up to (and above) the (04)~ state. 2O potential surface. The results indicate that the OC surface is VI. Conclusions In this paper we have studied the H]H2O reaction dynamics using the OC potential surface and we –nd qualitatively diÜerent results concerning the eÜect of water vibrational excitation on the reaction rate coefficient compared to what was found in earlier studies. In particular we –nd that the reactive threshold energy is zero for states with two or more quanta of OH stretch excitation and as a result the thermal rate coefficient associated with these states is quite large.In fact the excited state rate coefficients are so much larger than the ground state that at high temperatures we –nd that the Boltzmann averaged rate coefficient can be dominated by excited vibrational states. Our results suggest that reaction makes a signi–cant contribution to the experiments of Smith and coworkers.4,5 The rate of loss of excited water due to reaction is comparable for the OC potential to that due to collisional energy transfer. The inelastic rate coefficients are comparable to those found in the earlier study with a reactive potential and they are much larger than for a potential that does not allow reaction.To test the accuracy of the OC potential we have performed high quality ab initio calculations in the reagent region of the H]H qualitatively correct in predicting activationless behavior for states starting at (02)~ but it is too attractive at long range and thus the rate coefficients that we have calculated for the OC surface are larger than they should be. However even if this is corrected we expect to –nd that reaction will still be a signi–cant contributor to the measurements of Smith and coworkers.4,5 Note that the OC and I5 surfaces give dramatically diÜerent rate coefficients but they have very similar saddle-point properties. This demonstrates how features of the surface well away from the saddle-point can play a crucial role in reactions involving highly excited molecules.In future work we plan to use the ab initio results that we have generated to produce an improved potential surface for determining rate coefficients. We also plan to explore more generally the issue of activated vs. activationless reaction kinetics for vibrationally excited reagent molecules. Acknowledgements GW and GCS were supported by the NSF Grant 98-73892. GL and GCS were supported by the US-Hungarian Joint Fund Grant 411 and GL by the Hungarian Scienti–c Research Fund Grant T-15819. LBH and DCF were supported by the U.S. Department of Energy Division of Chemical Sciences under Contract No. W-31-1109-Eng-38. The authors thank Prof. I. W. M. Smith for his willingness to share preliminary results and for many helpful discussions.We also thank Prof. D. C. 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ISSN:1359-6640    

DOI:10.1039/a901950b

出版商:RSC    

年代:1999

数据来源: RSC