摘要:

337 41 5 425 43 7 45 1 465 479 495 General Discussion Dynamics of Hydrogen Adsorption on Clean and Alkali-metal Covered Cu(ll0) B. E. Hayden and C. L. A. Lamont Probing the Transition State in Dissociative Adsorption S. Holloway and X. Y. Chang A New Mechanism for Absorption: Collision-induced Absorption K. J. Maynard, A. D. Johnson, S. P. Daley and S. T. Ceyer Photochemistry of Adsorbed Molecules. Part 10-Harpooning a Fixed Target: Charge Transfer from Ag or K Substrates to Halide Adsorbates St. J. Dixon- Warren, E. T. Jensen, J. C. Polanyi, G.-Q. Xu, S. H. Yang and H. C. Zeng General Discussion Summarizing Remarks R. A. Marcus Index of Names337 41 5 425 43 7 45 1 465 479 495 General Discussion Dynamics of Hydrogen Adsorption on Clean and Alkali-metal Covered Cu(ll0) B. E. Hayden and C. L. A. Lamont Probing the Transition State in Dissociative Adsorption S. Holloway and X. Y. Chang A New Mechanism for Absorption: Collision-induced Absorption K. J. Maynard, A. D. Johnson, S. P. Daley and S. T. Ceyer Photochemistry of Adsorbed Molecules. Part 10-Harpooning a Fixed Target: Charge Transfer from Ag or K Substrates to Halide Adsorbates St. J. Dixon- Warren, E. T. Jensen, J. C. Polanyi, G.-Q. Xu, S. H. Yang and H. C. Zeng General Discussion Summarizing Remarks R. A. Marcus Index of Names

ISSN:0301-7249    

DOI:10.1039/DC99191FX001

出版商:RSC    

年代:1991

数据来源: RSC

摘要:

GENERAL DISCUSSIONS O F THE FARADAY SOCIETY/FARADAY DISCUSSIONS OF THE CHEMICAL SOCIETY Dare Subject 1907 Osmotic Pressure 1907 Hydrates in Solution 1910 The Constitution of Water 191 I High Temperature Work 1912 Magnetic Properties of Alloys 1913 Colloids and their Viscosity 1913 1913 The Passivity of Metals 1914 Optical Rotatory Power 1914 The Hardening of Metals 1915 The Transformation of Pure Iron 1916 Methods and .4ppliances for the Attainment of High Temperatures in a 1916 Refractory Materials 1917 Training and Work of the Chemical Engineer 19 17 Osmotic Pressure 1917 Pyrometers and Pyrometry 1918 The Setting of Cements and Plasters 1918 Electrical Furnaces 191 8 Co-ordination of Scientific Publication I9 I8 The Occlusion of Gases by Metals 1919 The Present Position of the Theory of Ionization 1919 The Examination of Materials by X-Rays 1920 The Microscope: Its Design, Construction and Applications 1920 Basic Slags: Their Production and Utilization in Agriculture 1920 Physics and Chemistry of Colloids 1920 Electrodeposition and Electroplating 1921 Capillari!y 1921 The Failure of Metals under Internal and Prolonged Stress 1921 Physico-Chemical Problems Relating to the Soil 1921 Catalysis with special reference to Newer Theories of Chemical Action I922 Some Properties of Powders with special reference to Grading by Elutriation 1922 The Generation and Utilization of Cold 1923 Alloys Resistant to Corrosion 1923 The Physical Chemistry of the Photographic Process 1923 The Electronic Theory of Valency 1923 Electrode Reactions and Equilibria 1923 Atmospheric Corrosion.First Report 1924 Investigation on Oppau Ammonium Sulphate-Nitrate 1924 Fluxes and Slags in Metal Melting and Working 1924 Physical and Physico-Chemical Problems relating to Textile Fibres 1924 The Physical Chemistry of Igneous Rock Formation 1924 Base Exchange in Soils 1925 The Physical Chemistry of Steel-Making Processes 1925 Photochemical Reactions in Liquids and Gases I926 Explosive Reactions in Gaseous Media I926 Physical Phenomena at Interfaces, with special reference to Molecular 1927 Atmospheric Corrosion. Second Report 1927 The Theory of Strong Electrolytes 1927 Cohesion and Related Problems 1928 Homogeneous Catalysis 1929 Crystal Structure and Chemical Constitution 1929 Atmospheric Corrosion of Metals. Third Report 1929 Molecular Spectra and Molecular Structure I930 Colloid Science Applied to Biology The Corrosion of Iron and Steel Laboratory Orientation Volume Trans.3* 3* 6* 7* 8* 9* 9* 9* 1 o* I I 12* 12* 13* 13* 13* 14* 14* 14* 14* 15* 15* 16* 16* 16* 16* 17* 17* 17* 17* 18* 18* 19* 19* 19* 19* 19* 20* 20* 20* 20* 21 21* 22* 22* 23* 23* 24* 24’ 25* 25* 26* 26 10: 20;Faraday Discussions of the Chemical Society Da ie I93 I 1932 1932 I933 1933 934 934 935 93 5 936 936 937 937 93 8 938 I939 I939 I940 1941 1941 1942 I943 I 944 I945 1945 1946 1946 I947 I947 1947 1947 I948 I948 I949 I949 1949 I950 I950 I950 I950 1951 I95 I I952 I952 1952 1953 I953 I954 1954 1955 1955 1956 1956 I957 I958 1957 1958 1959 I959 1960 1960 1961 1961 1962 I961 Subject Photochemical Processes The Adsorption of Gases by Solids The Colloid Aspect of Textile Materials Liquid Crystals and Anisotropic Melts Free Radicals Dipole Moments Colloidal Electrolytes The Structure of Metallic Coatings, Films and Surfaces The Phenomena of Polymerization and Condensation Disperse Systems i n Gases: Dust, Smoke and Fog Structure and Molecular Forces in ( a ) Pure Liquids, and ( 6 ) Solutions The Properties and Functions of Membranes, Natural and Artificial React ion Kinetics Chemical Reactions Involving Solids Luminescence Hydrocarbon Chemistry The Electrical Double Layer (owing to the outbreak of war the meeting was The Hydrogen Bond The Oil-Water Interface The Mechanism and Chemical Kinetics of Organic Reactions in Liquid The Structure and Reactions of Rubber Modes of Drug Action Molecular Weight and Molecular Weight Distribution in High Polymers (Joint Meeting with the Plastics Group, Society of Chemical Industry) The Application of Infra-red Spectra to Chemical Problems Oxidation Dielectrics Swelling and Shrinking Electrode Processes The Labile Molecule Surface Chemistry (Jointly with the Societe de Chimie Physique at Bordeaux) Colloidal Electrolytes and Solutions The Interaction of Water and Porous Materials The Physical Chemistry of Process Metallurgy Crystal Growth Lipo-proteins Chromatographic Analysis Heterogeneous Catalysis Physico-chemical Properties and Behaviour of Nuclear Acids Spectroscopy and Molecular Structure and Optical Methods of Investigating Electrical Double Layer Hydrocarbons The Size and Shape Factor in Colloidal Systems Radiation Chemistry The Physical Chemistry of Proteins The Reactivity of Free Radicals The Equilibrium Properties of Solutions on Non-electrolytes The Physical Chemistry of Dyeing and Tanning The Study of Fast Reactions Coagulation and Flocculation Microwave and Radio-frequency Spectroscopy Physical Chemistry of Enzymes Membrane Phenomena Physical Chemistry of Processes at High Pressures Molecular Mechanism of Rate Processes in Solids Interactions in Ionic Solutions Configurations and Interactions of Macromolecules and Liquid Crystals Ions of the Transition Elements Energy Transfer with special reference to Biological Systems Crystal Imperfections and the Chemical Reactivity of Solids Oxidation-Reduction Reactions in Ionizing Solvents The Physical Chemistry of Aerosols Radiation Effects in Inorganic Solids The Structure and Properties of Ionic Melts Inelastic Collisions of Atoms and Simple Molecules abandoned, but the papers were printed in the Transactions) Systems Published by Butterworths Scientific Publications, Ltd Cell Structure High Resolution Nulcear Magnetic Resonance The Structure of Electronically Excited Species in the Gas Phase 1962 Volume 27* 28* 29 29* 30* 30: 31 31* 32* 32* 33* 33* 34* 34* 35* 35* 35* 36* 37* 37* 38 39* 40: 41 42* 42 A* 42 B*, Disc.1 2 Trans. 43* Disc. 3 4* 5" 6 7* 8* Trans. 46* Disc. 9* Trans. 47* Disc. 10* 1 I * 12* 13 14 15* 16* 17* IS* 19 20 21* 22 23 24 25 26 27 28 29 30 31 32* 33* 34 35Faraday Discussions of the Chemical Society Date 1963 1964 1964 1965 1965 1966 1966 1967 1967 1968 1968 1969 1969 1970 1970 1971 1971 1972 1972 1973 1973 1974 1974 1975 1975 1976 1977 1977 1977 1978 1978 1979 1979 1980 1980 1981 1981 1982 1982 1983 1983 1984 1984 1985 1985 1986 1986 1987 1987 1988 1988 1989 1989 1990 1990 Subject Fundamental Processes in Radiation Chemistry Chemical Reactions in the Atmosphere Dislocations in Solids The Kinetics of Proton Transfer Processes Intermolecular Forces The Role of the Adsorbed State in Heterogeneous Catalysis Colloid Stability in Aqueous and Non-aqueous Media The Structure and Properties of Liquids Molecular Dynamics of the Chemical Reactions of Gases Electrode Reactions of Organic Compounds Homogeneous Catalysis with Special Reference to Hydrogenation and Bonding in Metallo-organic Compounds Motions in Molecular Crystals Polymer Solutions The Vitreous State Electrical Conduction in Organic Solids Surface Chemistry of Oxides Reactions of Small Molecules in Excited States The Photoelectron Spectroscopy of Molecules Molecular Beam Scattering Intermediates in Electrochemical Reactions Gels and Gelling Processes Photo-effects in Adsorbed Species Physical Adsorption in Condensed Phases Electron Spectroscopy of Solids and Surfaces Precipitation Potential Energy Surfaces Radiation Effects in Liquids and Solids Ion-Ion and Ion-Solvent Interactions Colloid Stability Structure and Motion in Molecular Liquids Kinetics of State Selected Species Organization of Macromolecules in the Condensed Phase Phase Transitions in Molecular Solids Photoelectrochemistry High Resolution Spectroscopy Selectivity in Heterogeneous Catalysis Van der Waals Molecules Electron and Proton Transfer Intramolecular Kinetics Concentrated Colloidal Dispersions Interfacial Kinetics in Solution Radicals in Condensed Phases Polymer Liquid Crystals Physical Interactions and Energy Exchange at the Gas-Solid Interface Lipid Vesicles and Membranes Dynamics of Molecular Photofragmentation Brownian Motion Dynamics of Elementary Gas-phase Reactions Solvation Spectroscopy at Low Temperatures Catalysis by Well Characterised Materials Charge Transfer in Polymeric Systems Oxidation Volume 36 37 38 39 40 41 * 42* 43 44 45 46 47 48 49 * 50 * 51 52 53 54 55 56 57 58 59 60 61* 62 63 64 65* 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 Structure of Surfaces and Interfaces as studied using Synchrotron Radiation 89 Colloidal Dispersions 90 * Not available; for current information on prices etc., of available volumes, please contact the Marketing Oficer, Royal Society of Chemistry, Thomas Graham House, Science Park, Milton Road, Cambridge CB4 4 WF, stating whether or not you are a member of the Society.

ISSN:0301-7249    

DOI:10.1039/DC991910X003

出版商:RSC    

年代:1991

数据来源: RSC

摘要:

Faraday Discuss. Chem. SOC., 1991, 91, 5-16 Negative-ion Photodetachment as a Probe of Bimolecular Transition States: The F + H, Reaction Alexandra Weaver and Daniel M. Neumark"? Department of Chemistry, University of California, Berkeley, CA 94720, USA The transition-state region of the F+ H,, F+ D2 and F+ HD reactions has been studied by photoelectron spectroscopy of the negative ions FH, , FD, and FDH-. Photodetachment of these anions can access three electronic states of the neutral, but transitions to the ground-state potential-energy surface for the reaction can be observed selectively by adjusting the polariz- ation of the photodetachment laser. Under these conditions, the FH, spec- trum is similar to the recent simulation by Zhang and Miller which used the T5a potential-energy surface for the F+ H, reaction.The spectra of all three isotopic anions are interpreted by comparison to previous reactive scattering calculations. This comparison strongly suggests that several of the peaks in the photoelectron spectra are due to transitions to scattering resonances. The F+H2 reaction has played a central role in the development of reaction dynamics. Next to the H + H2 reaction, it is perhaps the simplest chemical reaction and, until quite recently, the F+ H2 reaction has been far more accessible to complementary experimental and theoretical investigation. This was one of the earliest reactions for which product internal state distributions were obtained, both by chemical laser'72 and infrared chemilumine~cence~~~ measurements.Using crossed molecular beams,5 the F + D2 reac- tion was the first for which product state-resolved angular distributions were determined. These experimental results motivated detailed theoretical investigations of the F + H2 reaction. It was one of the first reactions for which an a6 initio potential-energy surface was calculated6 and has been a favourite target for classical and quantum reactive scattering calculations as the methodology for these calculations developed. The predic- tion of scattering resonances by quantum collinear7 and three-dimensional8 calculations stimulated more recent crossed-beam experiments' which provided the first experimental evidence for reactive resonances. These crossed-beam studies in combination with newer rate-constant measurements showed that the M5 potential-energy surface" used in most scattering calculations prior to 1985 needed to be modified near the saddle point and in the product valley. This has spurred the development of new potential-energy surfaces based on high-level a6 initio calculations."-'s In parallel to this, new scattering methodologies have been developed, resulting in the first accurate calculations of the totalI6 and differential17 reactive cross-sections for the H + H2 reaction. These methods have been applied to the F+H2 reaction using one of the new surfaces, the T5a surface of Truhlar and co- workers." Several investigators have calculated reaction probabilities restricted to total angular momentum J = O for the F+H2,18-21 F+D2,22 and F+HD23 reactions.Total reaction cross-sections for the F + H2 reaction have been ~ a l c u l a t e d , ~ ~ ~ * ~ and Launay'" has recently obtained differential cross-sections for this reaction.A comparison of these scattering calculations with the experimental results shows significant discrepancies. Both the J = 0 and total cross-section calculations predict that HF(v = 3 ) is the dominant vibrational product from the F+ H2 reaction over a wide t NSF Presidential Young Investigator and Alfred P. Sloan Fellow. 56 Negative-ion Photodetachment energy range. The experimental results, however, show that HF( v = 2) dominates. The J = O calculations by Wyatt and c o - w ~ r k e r s ~ ~ , ~ ~ on the F+D2 and F + H D reactions predict DF( v = 4) to be the dominant D F channel, in contrast to the experimental finding that DF( u = 3) dominates.The differential cross-section calculations26 at a collision energy of 0.12 eV predict the HF( v = 3) product to peak at O,, = 0" (forward scattering), which agrees with the crossed-beam experiments.' While both the calculated and experimental angular distribution for HF( = 2) peak at O,, = 180" (backward scatter- ing), the calculated distribution shows a significantly more forward scattering than the experimental distribution. Overall, the comparison between theory and experiment indicates that some modification of the T5a potential-energy surface is required. It is clearly of interest to perform experiments which could indicate which regions of the T5a surface require further refinement. This is the purpose of the results reported here. We present the photoelectron spectra of the negative ions FH,, FD, and FDH-. Previously, we have shown that the photoelectron spectrum of the anion AHB- can be a sensitive probe of the transition-state region of the A+HB reaction, depending on the geometric overlap between the anion and neutral transition state.27 In several of these spectra, we have observed resolved vibrational structure characteristic of the unstable AHB complex formed by photodetachment.The FH,/F+H, system is, in principle, amenable to this technique. Ab initio calculations by Simons and co-workers2' on the anion geometry indicate that it is similar to the saddle-point geometry on the T5a surface, so photodetachment should access this very important region of the F + H2 surface.Zhang and Miller2' have simulated the FH, photoelectron spectrum using Simons' results for the anion and the T5a surface for the neutral reaction. A comparison of the experimental spectrum with their simulation should therefore provide a sensitive test of the T5a surface near the saddle point. As we shall see, comparing the experimental photoelectron spectra to the scattering calculations is quite informative as well. Our first experiment^^^ on FH, yielded a photoelectron spectrum which was consider- ably broader and less structured than the simulated spectrum. At the time, we speculated that some of that discrepancy may have resulted from overlapping transitions to multiple F+H2 electronic states. In this paper, we present spectra in which the contribution from low-lying excited electronic states appears to have been largely eliminated.The resulting spectra of FH, and its isotopic variants show resolved structure which allows a detailed comparison between experiment and theory. Experimental The experiments were performed on the negative-ion time-of-flight photoelectron spec- trometer shown in Fig. 1. Negative ions are generated by expanding a gas mixture through a pulsed molecular beam valve (1) and crossing the resulting free jet with a 1 keV electron beam (2) downstream from the valve orifice. A 15% NF3-85% H2 mixture was used to make FH,; the backing pressure was 5atm.t The presumed mechanism for negative-ion formation is dissociative attachment of electrons to NF, to form NF2 + F- followed by clustering of F- to HZ.Since the ions are formed in the continuum flow region of the free jet expansion, they are expected to cool as the expansion progre~ses.~' We observe rotational temperatures in the 25-50 K range for N3 produced in this type of ion source.31 A 600V negative pulse applied at (3) extracts anions from the free-jet expansion and injects them into a Wiley-McLaren time-of-flight mass ~pectrometer."~ The ions are accelerated to 1 keV, and they separate into bunches according to mass while travelling down a 150 cm flight tube. A series of ion deflectors and lenses (4) is used to optimize the ion signal at the detector ( 5 ) . The ion beam is crossed at (6) by a pulsed t 1 atm = 101 325 Pa.A. Weaver and D. M. Neumark 7 7 1 4 4 4 1- '6" Dd ' TMP' ITM+ Fig.1 Schematic diagram of time-of-flight photoelectron spectrometer. E indicates the laser polarization vector photodetachment laser. The ion of interest is selectively photodetached by varying the delay between the extraction pulse and the firing of the photodetachment laser. The spectra here were taken using the fourth harmonic ( A = 266 nm, hv = 4.66 eV) of a Nd:YAG laser (20 Hz repetition rate). The photoelectrons generated by photodetachment are energy-analysed by a second time-of-flight system. A small fraction (0.01 %) of the ejected photoelectrons traverses a 1CO cm long, magnetically shielded flight tube and is detected with a 40 mm diameter dual-microchannel plate detector (7). The electron flight tube is perpendicular to both the ion and laser beams.The flight time distribution is recorded using a transient digitizer and converted to a kinetic energy distribution. The energy resolution of the analyser is best for low-energy photoelectrons. It is ca. 0.008 eV at an electron kinetic energy (eKE) of 0.65 eV and degrades as eKE3I2 at higher energy. An important feature of the experiment is that the angle 8 between the electric field vector of the laser light and the direction of electron detection (see Fig. 1) can be varied by means of a half-wave plate. This allows one to investigate the photoelectron angular distribution. Results and Analysis The photoelectron spectra of FH,, FD, and FDH- taken at a photodetachment wavelength of 266 nm are shown in Fig. 2-4. For each anion, spectra were obtained at two laser polarization angles, 8 = 0 and 90".Average data acquisition times were ca. 7 h per spectrum (500 000 laser shots). Each spectrum shows fairly broad features at electron kinetic energies below 1.2 eV, as well as two sharp peaks at electron kinetic energies of 1.26 and 1.21 eV. The overall appearance of the spectra below 0.9 eV changes substantially when the laser polarization is rotated. At 8 = 90", the intensity of the electron signal drops slowly from 0.9 to 0.3 eV and the spectra are structureless in this range. In contrast, at 8 = 0", the intensity drops off very rapidly below 0.9 eV, and the spectra for each anion show one or more small peaks between 0.9 and 0.3 eV. In addition, the intensity of the two sharp peaks above 1.2 eV relative to the broad features is considerably higher at 0 = 90".The two sharp peaks are at identical energies to the two peaks seen in the F- photoelectron spectrum at 266 nm. We believe they arise from a two-photon process in8 Negative- ion Photodetach m en t electron kinetic energy/eV Fig. 2 Photoelectron spectra of FH, at 266 nm, at laser polarization angles 6 = 0 and 90". Positions of the labelled peaks (A-D) are given in Table 1. Arrows indicate asymptotic energies of product channels, as follows: ( a ) F+ H2( u = 0 ) , ( 6 ) H + HF( u = 3), (c) H + HF( u = 4), ( d ) F+ H2( u = 1). The peaks at 1.26 and 1.21 eV result from two-photon transitions to F(2P3/2), (2P1,2), as discussed in the text which the first photon dissociates the FH, anion to H2+F-, and the second photon detaches the F-.The two peaks are due to transitions to the F('P3/*) ground state and the spin-orbit-excited F('P,/') state which lies 0.050 eV above the ground state. The broad features below 1.2 eV are of more interest, as they represent transitions to the neutral FH2 complex. At 8 = 0", one can discern four resolved peaks of varying widths in the FH, spectrum and two in the FD, and FDH- spectra; the electron kinetic energy of each peak is given in Table 1. Peaks A and B at 0.997 and 0.942 eV in the FH, spectrum at 8 = 0" are also discernible in the 8 = 90" spectrum. The peaks in the 8 = 0" spectra are noticeably affected by isotopic substitution, Peak A in the FH, spectrum seems to have disappeared in the FD, and FDH- spectra. Peak D at 0.48 eV in the FH, spectrum shifts to progressively higher electron kinetic energies in the FDH- and FD, spectra.Peak C at 0.82 eV in the FH, also appears to shift to higher electron energy in the other two spectra and becomes an unresolved shoulder on the side of peak B. The electron kinetic energy of each peak is related to the internal energy E'O' of the FH2 complex by Here hv is the photodetachment photon energy (4.66 eV), Do is the dissociation energy of the anion ground state to F-+H,(v =0) and E,,(F) is the electron affinity of the fluorine atom (3.401 eV33). E'*' is the internal energy of the FH2 complex relative to F+ H2( u = 0) (this is the same as the collision energy in a scattering experiment involving ground-state reactants), and E ( - ) is the internal energy of the anion.As the anions are eKE = hv - Do- E,,(F) - E"'+ E ( - ) ( 1 )A. Weaver and D. M. Neumark 9 0.3 0.5 0.7 0.9 1.1 1.3 electron kinetic energy/eV Fig. 3 Photoelectron spectra of FD; at 266 nm, at laser polarization angles 8 = 0 and 90". Positions of the labelled peaks (B-D) are given in Table I. Arrows indicate asymptotic energies of product channels, as follows: ( a ) D+DF(u=4), ( b ) F+D2(u=0), (c) D+DF(u=5), ( d ) F+D2(u=1) expected to be cold, we assume E ( - ) = 0. This leaves Do as the remaining unknown in eqn. ( 1 ) The a6 initio calculation on FH, by Simons28 yields De=0.30eV and Do= 0.20 eV. We assume Do to be 0.260 eV based on a comparison of our FH, spectrum at 8 = 0" with the simulation of Zhang and Miller2' (see below). The relation between eKE and E'O' for FH, is then eKE = 0.999 - E'O' We also require Do for the other isotopes.From our value of Do for FH,, we obtain D, = 0.369 eV by applying a zero-point correction which uses the MCSCF harmonic vibrational frequencies for FH, and H2 calculated by Simons. Simons predicts FH, ty have a linear equilibrium geometry with harmonic vibrational frequencies w l = 292 cm- ( H2..-F- stretch), w2 = 773 cm-' (degenerate bend) and w3 = 4143 cm-' (H-H stretch). Using the expected isotope shifts for a linear XYZ m ~ l e c u l e , ' ~ we obtain Do = 0.291 eV for FD,. If we treat linear FHD- and FDH- as distinct species, a reasonable assumption since w2 is relatively high, we obtain Do = 0.270 eV for FHD- and Do = 0.280 eV for FDH-. Thus, (2) eKE = 0.968 - E'O' eKE = 0.979 - E(O) (FDT) (FDH-) eKE = 0.989 - E"' (FHD-) (3) The differences in Do between FDH- and FHD- result from the lower (by 0.10eV) bend frequency in FDH-.The higher value of Do for FDH- means that it should be the form of the anion preferentially populated in our cold-ion beam. By combining eqn. (2) and (3) with the reaction exoergicities for F + H2 (AE = 1.391 eV), F + D2 (1.382 eV), F + H D ---* HF+ D (1.355 eV) and F+ HD -+ DF+ H10 Negative-ion Photodetachment 0.3 0.5 0.7 0.9 1.1 1.3 electron kinetic energy/eV Fig. 4 Photoelectron spectra of FDH- at 266 nm, at laser polarization angles 8 = 0 and 90". Positions of the labelled peaks (B-D) are given in Table 1 . Arrows indicate asymptotic energies of product channels, as follows: (a) F+ DH( u = 0), ( b ) D+ HF ( u = 3), (c) FD( u = 5) + H, ( d ) F+DH(u=l), ( e ) FD(u=5)+H Table 1 Peak positions, 8 = 0" spectra peak position/eV" ion A B C D FH, 0.997 0.942 0.82 0.48 FD, 0.960 - 0.617 FHD- 0.965 - 0.559 " Uncertainties in peak positions are 0.010 eV in peaks A and B, 0.015 eV in peaks C and D.(1.424 eV),3s we can determine the electron kinetic energies which correspond to photo- detaching the anion ground state and forming the various asymptotic states F+ H2( v ) , H + HF( v ) etc. These are indicated in Fig. 2-4. Recall that a feature in the photoelectron spectrum at higher electron kinetic energy than a given asymptotic state corresponds to a state of the neutral complex that lies below the asymptotic state and vice versa. Discussion The discussion of the results presented here covers three general areas.First, the variation of the shape of the photoelectron spectra with laser polarization is discussed. We then compare the FH, spectrum with the simulated spectrum of Zhang and Miller.*' Finally, all three spectra are discussed in the context of scattering calculations and experiments.A. Weaver and D. M. Neumark 11 Laser Polarization Dependence The interpretation of photoelectron spectra can be complicated when there are multiple anion -+ neutral electronic transitions, as we have seen in earlier studies of neutral reaction complexes via photodetachment. The photoelectron of BrHBr-, IHI-, FHI-, ClHI- and FHBr- show well separated bands due to transitions to various electronic states of the neutral complex. A more serious problem arises when the electronic bands overlap; on the basis of a6 initio calculations Yamashita and M o r o k ~ m a ~ ~ proposed that this occurs in the ClHCl- spectrum.The FH, spectra are likely to exhibit multiple and possibly overlapping electronic transitions. The interaction of F with H2 yields three potential-energy surfaces:38 1 2A, 2A" and 2 2A', assuming C, symmetry, or 2Zt/2 and 2111/2 3/2 assuming a collinear ( Cmv) geometry. In the F+ H2 asymptotic region, the 1 2A' and 'An surfaces become degenerate and correlate to F(2P3,2) + H2, while the 2 2A' surface correlates to F(2P,/2) + H2. The 1 2A' surface is the lowest-lying of the three and correlates to ground-state HF('Z+)+ H(2S) products. The other two surfaces are expected to be non-reactive as they correlate to electronically excited products.All three potential-energy surfaces are accessible via photodetachment of FH,. For a linear anion, removal of a 2pa electron accesses the ground-state 1 2A' surface, while the excited states are accessed by removing a 2p7r electron. Simons2* has calculated that the vertical detachment energies to the resulting 2Z+ and *lI states differ by only 0.25 eV. In order to gauge the contribution of multiple electronic states to a photoelectron spectrum, it is useful to characterize the photoelectron angular distribution. This is given by39 d a a dfl 47r - [I +~P,(COS e)] (4) In eqn. (4), 8 is the angle defined in Fig. 1 between the electric field vector of the laser and the direction of electron detection; it is also used to label the photoelectron spectra.The anisotropy parameter p varies from 2 to -1 and determines the form of the angular distribution (cos' 8 for p = 2, sin2 8 for p = -1). For a given anion + neutral electronic transition, p generally shows at most a slow variation with electron kinetic energy, If a band in a photoelectron spectrum is due to a single electronic transition, one might then expect the overall intensity of the band to vary with laser polarization, but the shape of the band should not change significantly. Since the band shapes in FH,, FD, and FDH- spectra vary considerably with laser polarization, we conclude that multiple electronic transitions with different values of p contribute to these spectra. The value of p depends strongly on the symmetry of the anion molecular orbital from which the electron is removed.39340 The transition to the ground-state F+H2 surface involves removal of a cr electron while transitions to the excited states occur by removal of a 7r electron, so one might expect to be able to characterize the complete photoelectron spectrum using only two values of p.We can explain the laser polarization effects by assigning peaks A-D in the 8 = 0" spectra to transitions to the ground-state F+ H2 surface, while the 8 = 90" spectra have contributions from ground-state and excited-state transitions. In the 8 = 90" spectra, the excited-state transitions are responsible for the slowly decreasing electron signal between 0.9 and 0.3 eV which obscures peaks C and D observed in the 8 = 0" spectra. No contribution from excited-state transitions at 8 =O" will occur if p = -1 for these transitions.On the other hand, the intensity of peak B (and peak A in the FH, spectrum) is greater in the 8 = 0" spectra than in the 8 = 90" spectra. This implies p > 0 for the ground-state transition. The assignment of all the structure in the 8 = 0" spectra to ground-state transitions is supported by variations in the peak positions with isotopic substitution, as expected12 Negative-ion Photodetachment I 1 I I I 1 I I I I 1, I . t, Y .- 2 Y C .- I I I . I...... 0.3 0.5 0.7 0.9 1.1 1.3 electron kinetic energy/eV Fig. 5 Photoelectron spectrum of FH, at 266nm, f?=O". The dotted line is the simulated photoelectron spectrum of Zhang and Miller.*' This plot of the simulation assumes Do = 0.260 eV for vibrational transitions within a single electronic band. This assignment is reinforced by comparison of the experimental and simulated spectra in the following section.The ability to eliminate excited-state transitions by varying the laser polarization is an important result. It means that we can use the 8 = 0" spectra to study the ground-state surface for the F+ H2 reaction. Comparison with Simulation The T5a F+ H2 surface can be evaluated by comparing our FHY photoelectron spectrum to the recent simulation by Zhang and Miller." They simulated this spectrum assuming Simons's a6 initio geometry and harmonic frequencies for the anion2' and the T5a surface' for the neutral reaction. The simulated spectrum is obtained by calculating the Franck-Condon overlap between the anion ground vibrational wavefunction and the three-dimensional scattering wavefunctions supported by the T5a surface.The simulation considers only total angular momentum J = 0 for both the anion and neutral. Since we expect the anions to be rotationally cold, it is reasonable to compare a J = 0 simulation (or a scattering calculation, see below) with our data. In Fig. 5 , the simulated spectrum is superimposed on the experimental FH, spectrum at 6 = 0". In drawing Fig. 5, we have assumed Do = 0.260 eV for the FH, dissociation energy. This value was chosen because it aligns the most intense peak in the simulation with the experimental peak B at 0.942 eV; it lies within the uncertainty of Simons's ab initio value of 0.20*0.10 eV.The positions of the remaining two peaks in the simulation are similar to the experimental peaks A and C . Peak D at 0.49 eV lies outside the energy range used in the simulation. The overall agreement between the experimental and simulated spectra is remarkable considering that D,, was the only parameter that was adjusted in drawing Fig. 5. It suggests that the T5a surface is reasonably accurate in the Franck-Condon region, that is, the region of the surface that has good overlap with the anion ground-state wave- function. A comparison of the calculated anion geometry with the T5a surface shows that the Franck-Condon region includes the saddle point and is centred on the reactant side of the saddle point. Thus, even though the anion is weakly bound, it does have good overlap with the neutral transition-state region.There are some differences between the experimental and simulated spectra. The splitting between peaks A and B is 0.055 eV in the experimental spectrum and onlyA. Weaver and D. M. Neumark 13 0.042 eV in the simulation. Also, the experimental spectrum falls off more slowly above 1 .O eV. However, the simulation only considers energies accessible from F + H2 reactants, which means it cuts off at eKE > 0.999 eV (where E‘’) = 0). Photodetachment of FH, can access HF+H neutral scattering states which lie below F+H,(u=O). Thus, the comparison above 1 eV is not valid. Nonetheless, Fig. 5 indicates that calculations on the T5a surface appear to provide a good basis for understanding the experimental spectrum.Interpretation of the Photoelectron Spectrum We now consider the origin of the peaks in our photoelectron spectra. Each peak is due to particularly good overlap of the anion wavefunction with a set of neutral scattering wavefunctions. This can happen under two circumstances. In the case of a scattering resonance, one often finds a set of scattering wavefunctions over a relatively narrow energy range localized in the transition-state region. If the resonance wavefunctions have good spatial overlap with the anion, then a peak in the photoelectron spectrum is observed with a width inversely proportional to the resonance lifetime. Reactive scatter- ing calculations show that resonances often occur right at or just below the energetic threshold for an asymptotic channel.Peaks in the photoelectron spectrum can also occur at energies where there are scattering wavefunctions with nearly zero momentum in the Franck-Condon region along the dissociation coordinate. This can occur at energies well above the nearest asymptotic channel. These ‘direct’ transitions are usually considerably broader than resonance transitions. Schatz41 has discussed these two types of transitions in more detail. In order to determine if the various peaks in our spectra are direct or resonance transitions, the spectra can be compared to reactive scattering calculations. In calcula- tions on the F+H2 reaction using the T5a s ~ r f a c e , ~ ~ - ~ ’ ’ ~ ~ the J = 0 reaction probability for production of HF(v=2) shows a small peak at a collision energy E‘’)=O.O18eV.This peak is assigned to a ‘closed-channel’ resonance because (i) it occurs just below the H + HF ( v = 3) threshold at E“’ = 0.020 eV and (ii) the behaviour of the S matrix in the vicinity of the peak is characteristic of a re~onance.’~”~ The value of E“) = 0.018 eV for the scattering resonance corresponds to eKE = 0.981 eV in the FH, photoelectron spectrum [see eqn. (2)]. This is exactly the energy of the narrow peak in the simulated spectrum and is very close to peak A at 0.997 eV in the experimental spectrum, strongly suggesting that peak A is due to a resonance transition. On the other hand, peak B at eKE = 0.942 eV corresponds to a collision energy of 0.057 eV. This is well above the H + HF( t, = 3) threshold. In the scattering calculations, the reaction probability for HF( v = 3) production at this collision energy is substantial and is varying slowly as a function of energy. Peak B in the FH, spectrum is therefore most likely a direct transition.In contrast to the FH, spectrum, the FD, and FDH- spectra exhibit a single broad peak near 0.96eV. In the calculation of the J = O reaction probability for the F+D2 reaction,22 no resonance is observed near the reaction threshold. This is the case because production of DF(v = 4) is slightly exoergic, so, in contrast to the F+ H2 reaction, a closed DF channel does not exist just above the reaction threshold. On the basis of the scattering calculation, we would expect only a single peak near 1 eV due to a direct transition in the photoelectron spectrum, and this is consistent with what we actually observe.We therefore assign peak B in the FD, spectrum to a direct transition. For the F+ HD reaction, DF( v = 4) production is slightly exoergic while HF( tr = 3) production is endoergic by 0.056 eV. Consistent with this, the F+ HD reactive scattering c a l ~ u l a t i o n ~ ~ shows no resonance in the DF channel but shows a strong resonance at E‘”’ = 0.024 eV in the HF channel. The similarity between the FD, and FDH- photo- electron spectra implies that the resonance is not contributing to the FDH- spectrum. FDH- should dominate over FHD- in our cold ion beam, as discussed in the Results14 Negative-ion Photodetachment and Analysis section, and photodetachment of FDH- should lead primarily to DF+ H and F+HD production.(The anion equilibrium geometry is predicted to be linear.28) The apparent absence of a resonance transition in the photoelectron spectrum may therefore be due to the absence of significant HF+ D production via photodetachment. Note, however, that if there were some FHD- present, the HF+ D scattering resonance would appear at eKE = 0.965 eV, and its contribution to the spectrum might be obscured by peak B. In the summary, the appearance of the peaks near 1 eV in the FH,, FD2 and FDH- photoelectron spectra can be explained with reference to scattering calculations on the F+ H2, F+ D2 and F+ HD reactions. The overall comparison supports our assignment of peak A in the FH, spectrum to a resonance and the other peaks in this region to direct transitions. We next consider peak D in the three spectra.Fig. 2-4 show that in each case, this peak corresponds to a transition to levels of the neutral complex that lie at or slightly below the asymptotic channel for F+ H2( v = l), F+ D2( v = 1) or F+ HD( v = 1). [This channel is labelled d in all three figures.] This suggests that these peaks correspond to resonance transitions in which the scattering wavefunctions are localized on the reactant side of the potential-energy surface. This is consistent with Pack's scattering calculation" which predicts a resonance at the F+ H2( v = 1) threshold. It appears that the important features in our 6 = 0" photoelectron spectra can be explained with reference to the T5a surface. However, as discussed in the Introduction, scattering calculations on the T5a surface predict incorrect product vibrational branching ratios.While scattering calculations sample the entire potential-energy surface, the photoelectron spectra are sensitive only to the region which has good overlap with the anion which, as discussed above, includes the saddle point. The results presented here suggest that the T5a surface is reasonably accurate in the reactant valley up to and including the saddle point. However, the region on the product side of the saddle point may require further modification. This is where energy release occurs, and the details of the surface in this region determine the product state distribution. A related and more complex issue is the nature of the predicted F+H2 resonance at E(O) = 0.018 eV. The FH, photoelectron spectrum supports the existence of this resonance, and we want to consider its effect in the crossed-beam experiments' performed on the F+H2 reaction.Both the scattering calculations and the simulation of Zhang and Miller indicate that the resonance decays to H + HF( v = 2); indeed, for a J = 0 reactive collision, the HF( v = 3) channel is closed. However, the forward-scattered HF( v = 3) product observed in the crossed-beam experiment was interpreted as evidence for resonance decay to HF(v=3) only. The calculations and experiments can be reconciled by noting that E(O) for the J = O resonance lies below the collision energies used in the crossed-beam experiments (0.03-0.15 eV), so these experiments could only access rotationally excited resonance states in collisions with J > 0.These rotationally excited resonances should have enough energy to decay to H + HF( v = 3); only 0.002 eV more energy is required. The recent calculation26 of the F + H2 differential cross-section indeed shows the HF( v = 3) to peak at O,, = O", in agreement with experiment. However, the calculated HF( u = 2) product angular distribution also exhibits significant forward scattering (at O,,=Oo) whereas none was seen in the crossed-beam experiment. Assuming that forward-scattered product is correlated with resonances in this reaction, it appears that the resonance decay products are not quite correctly predicted on the T5a surface. Just as with the product branching ratios, this may also be due to deficiencies in the product region of this surface.Support from the Air Force Office of Scientific Research under Grant No. AFOSR-91- 0084 is gratefully acknowledged. Further support came from a grant-in-aid from theA. Weaver and D. M. Neumark 15 National Academy of Sciences through Sigma Xi, the Scientific Research Society. We thank Jack Simons for sending us the results of his FH, calculation prior to publication. We also thank Bill Miller and John Zhang for several interesting discussions. References 1 J. H. Parker and G. C. Pimentel, J. Chem. Phys., 1969, 51, 91; R. D. Coombe and G. C. Pimentel, J. 2 M. J. Berry, J. Chem. Phys., 1973, 59, 6229. 3 J. C. Polanyi and D. C. Tardy, J. Chem. Phys., 1969, 51, 5717; J. C. Polanyi and K. B. Woodall, J. 4 N. Jonathan, C. M. Melliar-Smith and D.H. Slater, Mol. Phys., 1971, 20, 93. 5 T. P. Schafer, P. E. Siska, J. M. Parson, F. P. Tully, Y. C. Wong and Y. T. Lee, J. Chem. Phys., 1970, 53, 3385. 6 C. F. Bender, P. K. Pearson, S. V. O’Neill and H. F. Schaefer 111, J. Chem. Phys., 56, 4626; Science, 1972, 176, 1412. 7 G. C. Schatz, J. M. Bowman and A. Kuppermann, J. Chem. Phys., 1975, 63, 674; S. L. Latham, J. F. McNutt, R. E. Wyatt and M. J. Redmon, J. Chem. Phys., 1978,69, 3746; J. N. L. Connor, W. Jakubetz and J. Manz, Mol. Phys., 1978,35, 1301; J. M. Launay and M. Le Dourneuf, J. Phys. B., 1982,15, L455. 8 M. J. Redmon and R. E. Wyatt, Chem. Phys. Lett., 1979,63, 209. 9 D. M. Neumark, A. M. Wodtke, G. N. Robinson, C. C. Hayden and Y. T. Lee, J. Chem. Phys., 1985, 82,3045; D. M. Neumark, A. M. Wodtke, G.N. Robinson, C. C. Hayden, K. Shobatake, R. K. Sparks, T. P. Schafer and Y. T. Lee, J. Chem. Phys., 1985,82, 3067. 10 J. T. Muckerman, in Theoretical Chemistry-Advances and Perspectives, ed. H. Eyring and D. Henderson, Academic, New York, 1981, vol. 6A, pp. 1-77. 1 1 R. Steckler, D. G. Truhlar and B. C. Garrett, J. Chem. Phys., 1985, 82, 5499. 12 F. B. Brown, R. Steckler, D. W. Schwenke, D. G. Truhlar and B. C. Garrett, J. Chem. Phys., 1985,82, 188; D. W. Schwenke, R. Steckler, F. B. Brown and D. G. Truhlar, J. Chem. Phys., 1986, 84, 5706; 1987, 86, 2443. 13 H. F. Schaefer, J. Phys. Chem., 1985, 89, 5336; M. J. Frisch, B. Liu, J. S. Binkley, H. F. Schaefer and W. H. Miller, Chem. Phys. Lett., 1985, 114, 1; G. E. Scuseria and H. F. Schaefer, J. Chem. Phys., 1988, 88, 7024.14 C. W. Bauschlicher, S. P. Walch, S. R. Langhoff, P. R. Taylor and R. L. Jaffe, J. Chem. Phys., 1988, 88, 1743. 15 R. J. Bartlett, J. Phys. Chem., 1989, 93, 1697. 16 J. Z. H. Zhang and W. H. Miller, Chem. Phys. Lett., 1988, 153, 465; M. Mladenovic, M. Zhao, D. G. Truhlar, Y. Sun and D. J. Kouri, J. Phys. Chem., 1988,92,7035; D. E. Manolopoulos and R. E. Wyatt, Chem. Phys. Lett., 1989, 159, 123. 17 J. 2. H. Zhang and W. H. Miller, J. Chem. Phys., 1989, 91, 1528; M. Zhao, D. G. Truhiar, D. W. Schwenke and D. J. Kouri, J. Phys. Chem., 1990, 94, 7074. 18 J. D. Kress, Z. Bacic, G. A. Parker and R. T. Pack, Chem. Phys. Lett., 1989, 157, 484; Z. Bacic, J. D. Kress, G. A. Parker and R. T. Pack, J. Chem. Phys., 1990, 92, 2344. 19 C.-H. Yu, D. J. Kouri, M.Zhao and D. G. Truhlar, Chem. Phys. Lett., 1989, 157, 491; C-H. Yu, D. J. Kouri, M. Zhao, D. G. Truhlar and D. W. Schwenke, Int. J. Quantum. Chem. Symp., 1989, 23, 45. 20 J. Z. H. Zhang and W. H. Miller, J. Chem. Phys., 1990,92, 1811. 21 D. E. Manolopouols, M. D’Mello and R. E. Wyatt, J. Chem. Phys., 1990, 93, 403. 22 M. D’Mello, D. E. Manolopoulos and R. E. Wyatt, Chem. Phys. Lett., 1990, 168, 113. 23 D. E. Manolopoulos, M. D’Mello, R. E. Wyatt and R. B. Walker, Chem. Phys. Lett., 1990, 169, 482. 24 J. M. Launay and M. LeDourneuf, Chem. Phys. Lett., 1990, 169, 473. 25 D. Neuhauser, R. S. Judson, R. L. Jaffe, M. Baer and D. J. Kouri, to be published. 26 J. M. Launay, Theor. Chim. Acta, in the press. 27 R. B. Metz, A. Weaver, S. E. Bradforth, T. N. Kitsopoulos and D. M. Neumark, J. Phys. Chem., 1990, 94, 1377; S. E. Bradforth, A. Weaver, D. W. Arnold, R. B. Metz and D. M. Neumark, J. Chem. Phys., 1990, 92, 7205. Chem. Phys., 1972, 59, 251. Chem. Phys., 1972, 57, 1574. 28 J. A. Nichols, R. A. Kendall, S. J. Cole and J. Simons, J. Phys. Chem., in the press. 29 A. Weaver, R. B. Metz, S. E. Bradforth and D. M. Neumark, J. Chem. Phys., 1990, 83, 5352. 30 M. J. DeLuca and M. A. Johnson, Chem. Phys. Lett., 1989, 162, 255. 31 R. E. Continetti, D. R. Cyr, R. B. Metz and D. M. Neumark, to be published. 32 W. C. Wiley and I. H. McLaren, Rev. Sci. Instr., 1955, 26, 1150. 33 C. Blondel, P. Cacciani, C. Delsart and R. Trainham, Phys. Rev. A, 1989, 40, 3698. 34 G. Herzberg, Molecular Spectra and Molecular Structure II. Infrared and Raman Spectra of Polyatomic Molecules, Van Nostrand, New York, 1945, p. 173.16 Negative-ion Photodetachment 35 K. P. Huber and G. Herzberg, Molecular Spectra and Molecular Structure IV. Constants of Diatomic 36 R. B. Metz, S. E. Bradforth and D. M. Neumark, Adv. Chem. Phys., in the press. 37 K. Yamashita and K. Morokuma, J. Chem. Phys., 1990,93, 3716. 38 D. G. Truhlar, J. Chem. Phys., 1972, 56, 3189; J. T. Muckerman and M. D. Newton, J. Chem. Phys., 1972, 56, 3191; N. C. Blais and D. G. Truhlar, J. Chem. Phys., 1973, 58, 1090; J. C. Tully, J. Chem. Phys., 1974,60,3042; F. Rebentrost and W. A. Lester Jr., J. C.kern. Phys., 1975,63,3737; A. Komornicki, K. Morokuma and T. F. George, J. Chem. Phys., 1977,67,5012; V. Aquilanti, R. Candori, D. Cappelletti, E. Luzzati and F. Pirani, Chem. Phys. Lett., 1990, 145, 293. Molecules, Van Nostrand, New York, 1979. 39 J. Cooper and R. N. Zare, J. Chem. Phys., 1968, 48,942. 40 K. J. Reed, A. H. Zimmerman, H. C. Andersen and J. I. Brauman, J. Chem. Phys., 1976, 64, 1368. 41 G. C. Schatz, J. Chem. Phys., 1989, 90, 1237; J. Phys. Chem., 1990, 94, 6157. Paper 1/00233C; Received 16th January, 1991

ISSN:0301-7249    

DOI:10.1039/DC9919100005

出版商:RSC    

年代:1991

数据来源: RSC

摘要:

Furuduy Discuss. Chem. Soc., 1991, 91, 17-30 Resonances in Heavy + Light-Heavy Atom Reactions: Influence on Differential and Integral Cross-sections and on Transition-state Photodetachment Spectra George C. Schatz" Department of Chemistry, Northwestern University, Evanston, IL 60208-31 13, USA D. Sokolovski and J. N. L. Connor Department of Chemistry, University of Manchester, Ilfanchester M13 9PL, UK The effect of resonances on the observable properties of chemical reactions is studied theoretically, in particular for I + H I - + I H + I and CI+HCI-+CIH+Cl. All of our calculations use hyperspherical coordinates and accurate coupled- channel solutions to the Schrodinger equation for reactive scattering in three dimensions. For I + HI, we investigate the effect of potential surface variation on transition-state IHI- photodetachment spectra for total angular momen- tum quantum number equal to zero.Four different I + HI London-Eyring- Polanyi-Sat0 (LEPS) surfaces are used, with classical barrier heights varying from 0.048 to 0.243eV. The low-energy portion of the photodetachment spectra are examined in detail; it is found that peaks in the spectra arising from resonances and from direct scattering move up and broaden in energy as the barrier height is increased. An approximate match of the theoretical peak widths and spacings with the experimental ones is obtained for one of the surfaces. However, the peak intensities differ, suggesting that LEPS surfaces may not be adequate to characterize fully the observed spectra. For C1+ HCI, we perform a centrifugal-sudden hyperspherical calculation in order to examine the scattering properties of the single isolated resonance with transition-state quantum numbers ( v l , v2, v3) = (0, 0,2) (where v l = symmetric stretching, v2 = bending, v3 = asymmetric stretching quantum numbers).This relatively narrow (width 4 meV) resonance produces sub- stantial peaks in certair. state resolved reaction probabilities, which leads to a smooth step-like behaviour in the integral cross-sections, and Breit- Wigner (or Lorentzian) peaks in the differential cross-sections. Simple dynamical models are developed which explain these results 1. Introduction During the past two years, the study of resonances associated with the transition-state region of bimolecular reactions has made exciting progress.These resonances were originally seen in reduced dimensionality calculations',* for reactions like H + H2 -+ H2 + H, and then subsequently in accurate three-dimensional (3 D) quantum scattering compu- tatiow3 The experimental observation of resonances has proven difficult, however, as illustrated by the continuing uncertainty over the interpretation of the Lee group experiments on F+ H2 -+ HF+ H.4 In addition, experimental5 and theoretical6 results for H + H2 have now refuted earlier experimental data' which reported observable resonance effects in the state-to-state integral cross-sections. 1718 Resonances in H + LH Atom Reactions EIeV Fig. 1 Comparison of experimental2' ( a ) and theoretical16 ( b ) IHI- photodetachment spectra us.E. The J = 0 theoretical spectrum, which has only been calculated for E < 0.5 eV, has been shifted up in energy by 0.1 eV More fruitful progress has taken place in studies of heavy + light-heavy (H + LH) atom reactions, such as C1+ HCl + ClH + C1 and I + HI - IH + I. Resonances in col- linear (1D) models of these reactions have been known for some and simple adiabatic models8710911 are able to determine resonance energies with great precision. Often the 1D resonances are narrow (width <10-4eV), reflecting the weak coupling between the fast H-atom motion, where energy is trapped in the resonant state, and the slow halogen atom motions that are responsible for the decay of the resonance. The 3D analogue of these resonances has recently been found in accurate quantum reactive scattering calculations for both C1+ HCl,12-14 and I + HI.15716 Many properties of these resonances, such as the resonance energies and spacings, are what one would expect from the 1D results, with the simple addition of transition-state bending motions in going from 1D to 3D.A number of simple models which accurately predict the 3D resonance energies have also been given.I7-l9 The resonance widths obtained in the accurate 3D calculations12-16 are, however, significantly broader (by factors of ca. lo2) than in either the 1D calculation^^^^ or in 3D models that include bending motions adiabatically. l 9 The accurate 3D calculations show that the resonances decay primarily into excited rotations of the product diatomic molecule,16320 suggesting that the larger widths in 3D are the result of the decay of the resonance via bending rather than stretching motions.Probably the most exciting feature of resonances in H+LH reactions is that they have been observed experimentally via photodetachment spectroscopy by Neumark and his g r ~ u p . ~ ' - ~ ' (This type of experiment was suggested in Ref. 17.) The most conclusive results to date are for I+HI,21 where the stable molecule IHI- has been photodetached to produce IHI close to its transition state. Fig. l ( a ) shows the measured spectrum, plotted as a function of the total energy E of IHI, measured relative to the minimum of the HI potential well. The spectrum shows three groups of peaks separated by ca. 0.19 eV. This separation is in good agreement with theoretical predictions16720 for twice the asymmetric stretch spacing of the IHI transition state (only even states are Franck- Condon allowed).The three groups of peaks correspond to an asymmetric stretchingG. C. Schatz, D. Sokolovski and J. N. L. Connor 19 quantum number v3 of 0 (at E = 0.25 eV), 2 (0.44 eV) and 4 (0.63 eV). Fig. l ( 6 ) shows the predicted spectrum from Ref. 16. It is clear there is a reasonable correspondence between theory and experiment for both the coarse and fine structure in the spectrum. Note particularly that the v3 = 2 group of peaks in both the theoretical and experimental spectra consists of three main peaks separated by ca. 0.01 eV. From the theoretical work, it is known that these correspond to individual resonances having a symmetric stretching quantum number vl equal to 0, 1 and 2, and a bending quantum number v2=0.Since rotational broadening is negligible, the peak widths directly give the resonance lifetimes, ca. 0 . 0 5 ~ s in the experimental results and 0.3ps in the theory. Although the agreement is far from perfect, it is good enough to provide confidence in the assignment of these peaks as resonances. The v3=0 group of peaks is more complex, with theory predicting two narrow resonances at low E and then broader ‘rotational threshold’ peaks16 at higher E. The measured spectrum agrees better with the rotational threshold peaks, and indeed the observed peak locations are consistent with HI rotor levels ranging from j = 11 to j = 16. Thus it appears that the v3=0 peaks are not due to resonances.From the point of view of theory, although the results in Fig. 1 are encouraging, there are still several significant issues that need to be resolved (and which are therefore the subjects of this paper). One is that the comparison between theory and experiment for IHI- photodetachment is still far from perfect. The v3 = 0 peaks in Fig. 1 are not in a one-to-one correspondence, probably as a result of inaccuracies in the I+HI potential surface used in the calculations. In addition, there is a 0.1 eV shift in energy between the theoretical and experimental spectra that was subtracted when plotting Fig. 1. Although this shift may be due to experimental energy uncertainties, it is more likely to arise from errors in the potential surface.To study these problems, we have calculated IHI- photodetachment spectra for four different potential surfaces. The comparison with experiment will comprise section 2 of this paper. Another significant issue concerns the influence of resonances on differential and integral cross-sections. All experiments that have attempted to observe resonances so far (except for the photodetachment studies) have involved scattering of some t ~ p e , ~ , ~ . ’ but none of them has studied H+LH reactions. Since the observation of resonances for other types of reaction has proved to be difficult, it is important to find out whether resonances cause measurable changes in scattering properties for H + LH reactions. We have chosen to consider for this part of our paper the ( v l , u2, v3) = (0, 0,2) resonance in the C1+ HCI reaction.This resonance has similar properties to those for the v3 = 2 group of I+HI shown in Fig. 1. However, unlike I+HI, it is an isolated resonance (with no nearby v,>O counterparts), and therefore it seems a better candidate for observation in scattering experiments. In addition, the potential surface for C1+ HC1 is known better than for I + HI,24 and the non-resonant scattering properties of C1+ HC1 have been studied more t h o r o ~ g h l y . ~ ~ - ~ ~ Our calculations on C1+ HCl will be described in section 3. The two studies presented in this paper have in common that they use the same method to solve the time independent Schrodinger equation for a reactive collision. In this method,33 hyperspherical coordinates are employed to set up coupled-channel equations, and the equations propagated by standard numerical techniques to obtain the scattering wavefunction. Details concerning the application of this method to I + HI and C1+ HCI have been described p r e v i ~ u s l y ’ ~ ~ ’ ~ ~ ’ ~ and have not changed in the present work.In the I+HI calculations, only the partial wave with total angular momentum quantum number J = O has been considered, as this is sufficient to determine the photodetachment spectrum. For C1+ HCl, we have calculated all the partial waves (J,,, = 160) necessary to converge the reactive differential and integral cross-sections. For this purpose a centrifugal sudden (CS) approximation has been used. The accuracy of this approximation (denoted CSH) has been discussed previously.14333 In Ref.14 we20 Resonances in H+LH Atom Reactions Table 1 Properties of the four LEPS IHI potential surfaces quantity A B C D S 0.1900 0.1608 0.1490 0.1200 VS/eV 0.048 0.128 0.161 0.243 r'l Qo 3.376 3.395 3.403 3.424 o / cm- ' 146 144 143 141 w,/cm-' 362 3 64 365 366 o,/cm-' 447i 761i 855i 1051i V' + zero-point energy/eV 0.102 0.182 0.215 0.297 have presented CSH integral cross-sections that complement the new results reported in this paper. 2. Photodetachment Spectra for IHI- --+ I + HI + e- The potential surface used to generate the results presented in Fig. l was surface A of Manz and Romeltg (here denoted simply as surface A). This surface is based on the extended LEPS function,34 using a single Sat0 parameter, S = 0.190.The barrier height for this surface is 0.048 eV. Prior to the appearance of the photodetachment spectrum, there were no experimental data available to help calibrate the accuracy of the surface. Since the photodetachment spectrum indicates that the surface is inaccurate, with a barrier that is probably lower than it should be, we have used three new LEPS surfaces, which we denote B, C and D, to study the variation of the photodetachment spectrum with surface. Because the calculation of the photodetachment spectrum for each surface requires substantial computational effort, we will only consider the u3 = 0 region of each spectrum. In order to keep our study simple, the new surfaces we use still only have a single Sat0 parameter. By analogy with C1HC1,24727,35 it is likely that the correct IHI surface has a non-collinear saddle point (whilst all our LEPS saddle points are collinear).However, there is no simple way to sample systematically surfaces with non-collinear saddle points without introducing many unknown parameters, so we have chosen to ignore this problem in the present study. Table 1 presents the saddle-point properties (barrier height V*, H-I distance r*, harmonic frequencies w I , w 2 , w 3 , and V*+ zero-point energy) for the four surfaces A-D. Surface B was constructed to have a barrier height 0.08 eV higher than that of surface A, an energy difference suggested by an early comparison between theoretical and experimental photodetachment ~pectra.'~ Surfaces C and D were constructed to have still higher barriers, after it was discovered that the shift in the spectrum on going from A to B was substantially smaller than the difference in barrier heights.Surface D's barrier height of 0.243 eV is probably an upper bound to the correct result, since the IHI barrier height should be lower than ClHCl, which has a barrier height of ca. 0.32 eV in a6 initio calculation^.^^ Note that most of the saddle-point properties, other than barrier height and w 3 , are approximately the same for the four surfaces. We have used the four surfaces just described to calculate J = 0 reaction probabilities and photodetachment Franck-Condon factors. The IHI- wavefunction was identical to that used p r e v i o ~ s l y . ' ~ ~ ' ~ ~ ~ ~ The results are presented as a function of E in Fig. 2 and 3.Fig. 2 shows the J = 0 cumulative reaction probability PJ"(E), which is the sum over all open initial and final rovibrational states-of the state-to-state reaction probability ~l;2 v 3 j ( ~ ) , i.e.G. C. Schatz, D. Sokolovski and J. N. L. Connor 1.0 0.0 1.0 0.0 21 - A - - - ' Fig. 2 h 4 4 v 0 Y I1 2*o Cumulative reaction probability PJeO( E) for I + HI us. E for the four LEPS surfaces A- D EIeV Fig. 3 Calculated IHI- photodetachment Franck-Condon factors S"'(E) us. E for the LEPS surfaces A-D. Also shown is the v3 = 0 part of the experimental spectrum from Fig. 1, which has been shifted down in energy by 0.04eV Fig. 3 presents the total Franck-Condon factor SJ'"(E), which is a sum over all asymptotic HI states of the square of the overlap between the IHI- ground-state vibrational wavefunction and the IHI scattering wavefunction.The SJYo( E ) values were all normalized to a peak value of unity over the energy range considered. Fig. 2 and 3 show that as the height of the barrier increases, the two resonances seen at low E move up in energy and broaden considerably, disappearing completely on surface D. The features associated with direct scattering in Fig. 2 and 3 also move up in energy with increasing barrier height. It is interesting to note that this shift is greater22 Resonances in H+LH Atom Reactions for PJ”(E) than for SJ’O(E). To understand this effect, we first note that the reaction probability threshold occurs at an energy that corresporids approximately to the height of the adiabatic barrier to reaction.On surface A, this barrier is well removed from the saddle p ~ i n t ~ . ~ ~ because the barrier is low and the change in zero-point energy between I +HI and IHI is large. Thus in Fig. 2 the surface A threshold occurs at 0.165 eV, which is much higher than 0.102 eV, the V*+zero point energy value (see Table 1 ) . As the barrier height increases, the adiabatic barrier also becomes higher and moves closer to the saddle point. As a result, the threshold for surface D, ca. 0.270 eV, is now below V* + zero-point energy. Consider next the spectra in Fig. 3 . For surface A, the intensity is large over a wide range of E near the reaction threshold. This means that the adiabatic barrier must be in the Franck-Condon region. The latter occurs at an 1-1 distance of 7.332a0.I5 As the barrier height increases, the spectral features broaden considerably (reflecting a steeper potential), and the peak intensities occur at energies that are below the height of the adiabatic barrier.This means that the Franck-Condon region (still at 7.332a0) is now located out towards the reagents or products region, away from the barrier top. This is consistent with the fact that the adiabatic barrier has moved in towards the saddle point. The saddle point 1-1 distance is 6.8ao for all four surfaces. In Fig. 3 we have also superimposed the v3 = 0 portion of the experimental data on the surface C spectrum to show that the width and spacing of the measured peaks approximately matches the calculated spectrum. However, the match is still far from satisfactory, as the intensity drops off more quickly in the calculated spectrum.Also, to improve the agreement between theory and experiment, the measured spectrum has been shifted down in energy by 0.04 eV. A shift of this size is well within the experimental uncertainty, but the discrepancy in the intensity is still serious. Finally, we note that the rotational quantum numbers associated with the surface C peaks ( j = 6 - 1 1 ) are lower than those reported by Waller et aL2’ ( j = 11-16) based on a match to the asymptotic HI states. 3. Resonant Differential and Integral Cross-sections for C1+ HCI + CIH + C1 Our calculations use the LEPS surface of Bondi et aL8 (which is denoted BCMR). The non-resonant dynamics of Cl+HCl on this surface have been extensively studied in In particular, thermal rate coefficients computed by the cen- trifugal-sudden distorted-wave (CSDW) method match experiment a c ~ u r a t e l y .~ ~ Although the position of the saddle point on the BCMR surface (which is collinear) does not match the best ab i n i t i ~ ~ ~ predictions (non-collinear), this difference has a relatively small effect on the reaction dynamics.24727 In an earlier study of the (0, 0 , 2 ) resonance for C1+ HCl,14 we examined the state-to-state J = 0 reaction probabilities in detail, and found that only certain of them are strongly perturbed by the resonance. Specifically, we found that HCl rovibrational states (v,j) having v = 0 and j = 14-16 in either reagents or products are perturbed, as well as transitions having v = 1 and j = 0-8.We have selected three transitions from this set of quantum numbers for study. They are: past work. 8-1 2- 14,19,24-33 ( a ) v = O , j = 1 5 -+ v’=O,j’=15 ( b ) v = l , j = 5 ---* u’=O,j’=15 ( c ) v = l , J = 5 + v ’ = l , j ‘ = 5 These transitions were chosen because each has the largest J = 0 reaction probability for the indicated v and u‘ combination at a total energy of E = 0.642 eV, which is the (0, 0 , 2 ) resonance energy.G. C. Schatz, D. Sokolovski and J. N. L. Connor h 4 v a - 0.62 0.64 0.66 0.68 0.70 23 E/eV Fig. 4 J = 0 reaction probability us. E for C1+ HCl for transitions ( a ) v = 0, j = 15 + u’ = 0, j ’ = 15 (solid curve), (b) u = l , j = 5 + v‘=O,j’=15 (dashed curve) and ( c ) v = l , j = 5 + u ’ = l , j = 5 (dotted curve) In the following we will use the results from our CSH computations to study reaction probabilities, S-matrix phases, and integral and differential cross-sections for transitions ( a ) - ( c) for energies close to the (0, 0,2) resonance ( E = 0.620-0.700 eV).For J = 0, we calculated scattering matrices at 0.001 eV intervals over the indicated range (81 energies). For 0 < J S 160, calculations were done for every partial wave at 0.620, 0.642, 0.660, 0.680 and 0.700 eV. In addition, at 0.640,0.646 and 0.650 eV calculations were performed for every J with 0 J S 30, and then for every fifth J thereafter up to J,,, = 160. Reaction Probabilities Fig. 4 shows the energy dependence of the J = 0 reaction probabilities Pi;. v 3 g ( E ) for the three transitions (a)-( c). Near E = 0.642 eV, each probability possesses a typical resonance shape, with transitions (6) and (c) having nearly Breit-Wigner (or Lorentzian) behaviour, i.e. where Ere, = 0.642 eV, r = 0.004 eV, A is P;;: ,j.,( Ere,) and P”,zc,( E ) is a small, slowly varying, direct scattering contribution. [Subscript, uj -+ v y ’ , and superscript, J = 0, have been omitted from most of the terms in eqn. ( 1 ) for notational convenience.] Transition ( a ) has a larger background contribution, and shows significant interference between the direct and resonant scattering. S-matrix Phases Fig. 5 shows the phases 8;;: .,,(E) = arg S;;?, ”),( E ) of the S-matrix elements for the three transitions as a function of E. All three phases decrease with E, as would be expected for direct reactive scattering on a repulsive potential.” For E =r E,,,, the phases show small wiggles, although their slopes are negative in all cases (implying negative24 Resonances in H + LH Atom Reactions E/eV Fig.5 J = 0 phase of the S-matrix element us. E for the same transitions as in Fig. 4 for C1+ HCl time delays).” In earlier it was found that the phase of the resonant part of an S-matrix element often increases rapidly on passing through a resonance. However, this behaviour can be masked by a rapid energy dependence in the phase of the direct scattering. Fig. 5 shows that the S-matrix phases do not increase by 27r on passing through the resonance. Evidently, the E dependence of the phases is not simple because of interference between the resonant and direct scattering.There is a slight second wiggle in the phase of transition (6) near 0.678 eV, which coincides with a dip in the corresponding reaction probability in Fig. 4. This could be due to a weakly excited symmetric stretching resonance labelled by the quantum numbers ( 1 , 0, Z), as the energy spacing between the (1, 0,2) and (0, 0,2) resonances (0.036 eV) is consistent with that deduced from the harmonic symmetric stretching frequency at the saddle point (namely 0.043 eV). This resonance is extremely weak, however, so we will ignore it in our discussion. Probably the most important conclusion to be drawn from Fig. 4 is that the phase of the direct scattering contribution has a dependence on E that is almost as rapid as the resonant contribution. This makes it difficult to separate out the resonant part of the S matrix (for the purpose of determining resonant time delays), and it also makes an analysis based on Argand diagram^'^ not very useful.This problem with the direct contribution is probably more important for H + LH reactions than most others, because the phase is proportional to the asymptotic wavenumber which is large when the translational reduced mass is large. Integral Cross-sections The crosses in Fig. 6 show the E dependence of the degeneracy-averaged integral cross-sections Q , - j , ( E ) obtained from our CSH calculations. For transitions (6) and ( c ) , there is a sudden rise near Ere, = 0.642 eV with a width equal to the width of the peaks in Fig. 4. Transition ( a ) , by contrast, shows only a small wiggle at 0.642 eV, presumably reflecting the larger contribution from direct scattering.It is possible to explain the results in Fig. 6 using the following simple m0de1.I~ The cross-section Q , - L , , , j ( E ) is related to the reaction probability P i , + o,,p( E ) via the usualG. C. Schatz, D. Sokolovski and J. N. L. Connor 25 N O U \ h 4 v a t 0 Y 3- O - r 0.1 0.0 I I I 0.62 0.64 0.66 0.68 0.70 EIeV Fig. 6 Degeneracy-averaged CSH integral cross-sections us E for C1+ HCl for the same transitions as in Fig. 4. The smooth curves are results from the J = 0 approximate model [eqn. (4)] while the crosses are the full partial wave summed CSH results formula (2) I T w Q v j 4 .?,(E) = (2j+ 1)-' 7 C ( 2 J + l ) P i j , v 3 p ( E ) kuj J = O where k, is the translational wavenumber for the initial state.Since a large number of J s contribute to the cross-section (ca. 160) and P i j - .?,(E) varies smoothly with J, the sum in eqn. (2) can be approximately replaced by an integral. We also invoke a J-shifting a p p r o x i m a t i ~ n ' ~ ' ~ ~ ' ~ ~ ~ ~ ~ in order to relate the J and E dependence of Pi,- ".,(E) via Pij - L,,,,( E ) Pi:: .?,[ E - B*J( J + l ) ] (3) where B* is the rigid rotator constant for ClHCl at the transition state. The validity of eqn. (3) has been established in Ref. 14 and 30. Combining eqn. (2) and (3), we find This formula allows the cross-sections to be calculated from the J = 0 reaction prob- abilities in Fig. 4. The continuous curves in Fig. 6 were obtained by numerical evaluation of eqn.(4) using these J=O probabilities. The agreement between the (partial wave summed) CSH and J = 0 model cross-sections is generally good. A simple analytical expression for the resonant contribution to the cross-section can be obtained by substituting eqn. (1) into eqn. (4). This results in where Q$YtU3,(E) is the cross-section arising from the direct probability in eqn. ( 1 ) . The resonant part of eqn. (5) has a smooth step-like dependence on E that is consistent with the accurate CSH results. The step arises from the sum over resonances for many26 Resonances in H + LH Atom Reactions =l,j=5--v‘=l,j’=5 (x5.0) 0.700 eV f o.680 ev 0.660 eV (b)v=l,j=5-v‘=O,j’=15 (x4.0) 0.5 Fig. 7 Differential cross-section aOj- u‘,r( 8,) us. OR for C l f HCl for transition (a) u = 0, j = 15- u ’ = O , j ’ = 1 5 , ( b ) u = l , j = S - * u ’ = O , j ’ = 1 5 and ( c ) u = l , j = 5 + u ’ = l , j ’ = 5 .The cross- sections plotted are from CSH partial wave sum calculations at E = 0.620 eV (solid curve), 0.642 eV (dots), 0.660 eV (short dash), 0.680 eV (long dash), 0.700 eV (dash-dot) Js, each being shifted by its rotational energy B*J(J+ 1) from the J = 0 resonance, but otherwise having approximately the same widths and amplitudes. This energy depen- dence should be typical for resonances in H+LH systems, as it only requires that the resonance widths be larger than the transition-state rotational constant (B* = 1.25 x eV for CIHCI) and that J-shifting be accurate, both of which are accurately satisfied in calculations done so far.’2-16930 Differential Cross-sections Fig.7 presents the differential cross-sections uuj+ u3,( 6,) as a function of the scattering angle t?R (Ref. 24) for the three transitions ( a ) - ( c) at the five energies where all partial waves have been calculated. For transitions (6) and (c), the cross-section at 0.620 eV is very small; it therefore appears as a horizontal line on the scale of the plot. Fig. 7 shows that, for all three transitions, there is a shift from backwards to sideways peaking as E increases from 0.620 to 0.700 eV. Since transition ( a ) is dominated by direct scattering while (6) and (c) have stronger resonance contributions, this shift in the angular distributions does not appear to be a unique property of either mechanism. Evidently the identification of resonance effects in angular distributions needs to be investigated more carefully.In the present case, this can be achieved by generalizing a semiclassical optical model that we have previously shown to work well in describing CSDW angular distributions at lower E for C1+ HCl,24*26 and C1+ DCl,24 (see also Ref. 29). In this model, we use the classical expression for the reactive differential cross-section where P , --. b( OR)] is the reaction probability as a function of the impact parameterG. C. Schatz, D. Sokolovski and J. N. L. Connor 27 Fig. 8 Differential cross-section uu, + n r j , ( 6,) us. 6, for C1+ HCl for the same transitions as in Fig. 7 but using the J-shifted semiclassical optical model expression eqn. (8). For transitions ( b ) and ( c ) , the value of Ork calculated from eqn.( 1 1 ) for each energy (>Oh42 eV) is indicated by an arrow on the abscissa 6( OR). If 6( 6,) and db( 6,)/deR are evaluated using the hard-sphere expression 6( 6,) = 2r cos( 6R/2), we find (7) u u j + u,jt(6R) = r2P"j -. u T j p [ b( OR)] where r is the hard-sphere radius. Next we equate P, -. ,>,( 6) with the quantum reaction probability Pij + ">.( E), making the approximation 6 = A J / p , where p is the initial (state-dependent) relative momentum. If J-shifting [ i.e. eqn. (3)] is also assumed, then eqn. (7) becomes 'Tuj - t,'j'( 6,) = rZPi,=2 o'j'{ E - B*J( 6 R ) [ J ( 6,) + 11) = r 2 P i , 2 .,JE - (4~'r'p'/ A') cos2 ( 6 , / 2 ) ] (8) where in eqn. (8) we have assumed J(J + 1) = J 2 , and have approximated J ( 6,) by the hard-sphere formula.Eqn. (8) provides a simple relation between the J = 0 reaction probability and the differential cross-section, which is similar in form to previously derived expression^.^^-^' Fig. 8 shows the angular distributions corresponding to Fig. 7, that have been calculated using eqn. (8). The radial parameter r was adjusted to optimize agreement of the peak positions with Fig. 7; this resulted in r = 2 . 4 4 ~ ~ for transition (a), r = 2 . 4 0 ~ ~ for (b), and r = 2 . 3 0 ~ ~ for (c). All these values are close to those derived in a CSDW ~ t ~ d y ~ ~ , at lower energies for non-resonant scattering. The agreement between Fig. 7 and 8 is generally good, with the peaks in Fig. 7 being somewhat broader at most energies. Note also that at 0.642 eV, the absolute magnitudes of the differential cross-sections given by the J-shifted optical model for 6 , = 180" are in good agreement (ca.20%) with the CSH results. For transitions (6) and (c), the model shows that the resonance produces the dominant backward peak, which rapidly moves to smaller 6R as E increases. The direct scattering also contributes to aVj+ ">/( 6,) at large OR for E 3 0.660 eV, but its contribution can be clearly distinguished at most energies. For transition (a), the dominant peak at OR = 130" for E = 0.660 eV is due to direct scattering. In the J-shifted optical model28 Resonances in H+LH Atom Reactions calculations, the resonance produces a wiggle near the top of this peak, but even this is largely washed out in the CSH results of Fig.7. We can obtain a more detailed description of the resonant contribution to the differential cross-section by substituting eqn. ( 1 ) into eqn. (8). This yields which shows that the resonant part has a Breit-Wigner (or Lorentzian) dependence on cos2 (&/2). If E s E,,,, the peak in uuj- u'i7( 8,) occurs at e y k = 180". If we denote by (&)1/2, the value of OR where the cross-section equals half its value at epReak = 180°, then for E = Ere, we find (&)1/2 is determined by The factor (r/2B')1'2 in this formula is approximately the maximum partial wave that contributes to the resonant part of the cross-section when E = Ere, (which will be denoted JE:x),14 while 2 r p / h is approximately Jk:x, the maximum value of J that contributes to the hard-sphere cross-section. The angle (&)1/2 is thus determined by the ratio of these two quantities, i.e.cos [ (8,),,,/2] = J',"ix/ J k z x . One way eqn. (10) might help in analysing experimental data is to use the measured value of (&)1/2 together with estimates of the geometrical parameters BS and r, to determine the width r. It is also possible to use the resonant part of eqn. (9) to study the shift of the peak in uuj - u'jn( 6,) with energy for the case E > E,,,. For example, the peak in uuj - uj-.( 0,) moves to OpReak=Oo when E - Ere, 3 4B*r2p2/ A2 = B*(Jk:x)2 Forward scattering thus occurs when E - E r e , matches the rotational energy for an angular momentum that corresponds to scattering at an impact parameter equal to the hard-sphere diameter (i.e.6k:x = 2 r ) . B ' ( J ~ : ~ ) ~ is given by The value of for which uvj - .>,( 0,) is a maximum for 0 s E - E,,. To see how well this expression works, note from the arrows in Fig. 8 that OKak for transition ( c ) matches that in Fig. 7 accurately at all the energies plotted, with r fixed at r = 2 . 3 0 ~ ~ . For transition (6) the correspondence between Orak and Fig. 8 is less good, as the direct and resonant contributions to the cross-section in Fig. 7 are badly overlapped for E > 0.660 eV. A practical application of eqn. ( 1 1 ) to the interpretation of data would be to extract the transition-state rotational constant B* from plots of cos ( 6rak/2) vs. ( E - 4. Conclusions We have examined the influence of transition-state resonances on a number of measurable quantities for chemical reactions.Photodetachment intensities show great sensitivity to resonances, although rotational thresholds can also contribute. Even these thresholds are sensitive to the form of the potential surface, as is evident from our results in Fig. 3 for IHI-. Our attempt at improving agreement between theory and experiment by varying the Sat0 parameter in the LEPS function has only been moderately successful, which suggests that further improvement will require a non-LEPS surface. For CI + HCI, we have studied the energy dependence of both integral and differential cross-sections. The integral cross-sections show a smooth step-like increase at the resonance energy which can be used to find the J = 0 resonance energy and width. ThisG.C. Schatz, D. Sokolovski and J. N. L. Connor 29 means that the partial wave averaging does not necessarily destroy information about resonance properties. The resonance appears more clearly in the differential cross- sections, which show a Breit-Wigner (or Lorentzian) peak, which moves rapidly from the backward direction to sidewards as the energy increases. We have developed a simple J-shifted model for the energy dependence of the cross-sections, which was successful in explaining the behaviour of both the integral and differential CSH cross- sections. More importantly, these models show how one can use angular distributions to derive information about the resonance widths and transition state rotational constants. This research was supported by NSF Grant CHE-9016490 and by the UK SERC.The computations were carried out at the Manchester Computing Centre and at the National Center for Supercomputing Applications at the University of Illinois. References 1 M. S. Child, Mol. Phys., 1967, 12, 401; J. N. L. Connor, Mol. Phys., 1968, 15, 37; 1970, 19, 65; 1973, 25, 1469; W. N. Whitton and J. N. L. Connor, Mol. Phys., 1973, 26, 1511. 2 R. D. Levine and S-f. Wu, Chem. Phys. Lett., 1971, 11, 557; S-f. Wu and R. D. Levine, Mol. Phys., 1971, 22, 881; D. G. Truhlar and A. Kuppermann, J. Chem. Phys., 1970, 52, 3841; 1972, 56, 2232. 3 G. C. Schatz and A. Kuppermann, Phys. Rev. Lett., 1975, 35, 1266. 4 D. M. Neumark, A. M. Wodtke, G. N. Robinson, C. C. Hayden and Y. T. Lee, J. Chem. Phys., 1985, 82, 3045; C-h. Yu, Y. Sun, D.J. Kouri, P. Halvick, D. G. Truhlar and D. W. Schwenke, J. Chem. Phys., 1989,90,7608; J. Z . H. Zhang and W. H. Miller, J. Chem. Phys., 1989,90,7610; J. M. Launay and M. Le Dourneuf, Chem. Phys. Lett., 1990, 169, 473. 5 D. A. V. Kliner, D. E. Adelman and R. N. Zare, J. Chem. Phys., 1991,94, 1069. 6 J. Z. H. Zhang and W. H. Miller, Chem. Phys. Lett., 1988,153,465; 1989,159, 130; D. E. Manolopoulos and R. E. Wyatt, Chem. Phys. Lett., 1989, 159, 123; J. Chem. Phys., 1990, 92, 810; J. M. Launay and M. Le Dourneuf, Chem. Phys. Lett., 1989,163, 178. See also: M. Mladenovic, M. Zhao, D. J. Truhlar, D. W. Schwenke, Y. Sun and D. J. Kouri, Chem. Phys. Lett., 1988, 146, 358. 7 J-c. Nieh and J. J. Valentini, Phys. Rev. Lett., 1988, 60, 519. 8 D. K. Bondi, J. N. L. Connor, J.Manz and J. Romelt, Mol. Phys., 1983, 50, 467; D. K. Bondi, 9 J. Manz and J. Romelt, Chem. Phys. Lett., 1981, 81, 179. J. N. L. Connor, B. C. Garrett and D. G. Truhlar, J. Chem. Phys., 1983, 78, 5981. 10 J. Romelt, Chem. Phys., 1983, 79, 197. 11 J. Manz, R. Meyer, E. Pollak and J. Romelt, Chem. Phys. Lett., 1982, 93, 184. 12 G. C, Schatz, Chem. Phys. Lett., 1988, 151, 409. 13 G. C. Schatz, J. Chem. Phys., 1989,90, 3582. 14 G. C. Schatz, D. Sokolovski and J. N. L. Connor, J. Chem. Phys., 1991, 94, 4311. 15 G. C. Schatz, J. Chem. Phys., 1989, 90, 4847. 16 G. C. Schatz, J. Phys. Chem., 1990, 94, 6157. 17 D. C. Clary and J. N. L. Connor, Chem. Phys. Lett., 1983, 94, 81; J. Phys. Chem., 1984, 88, 2758. 18 E. Pollak, Chem. Phys. Lett., 1983, 94, 85. 19 B. Gazdy and J.M. Bowman, J. Chem. Phys., 1989, 91, 4615; J. M. Bowman and B. Gazdy, J. Phys. Chem., 1989, 93, 5129; J. M. Bowman, B. Gazdy and Q. Sun, J. Chem. Soc., Faraday Trans., 1990,86, 1737. 20 G. C. Schatz, Israel J. Chem., 1989, 29, 361; J. Chem. SOC., Faraday Trans., 1990, 86, 1729. 21 A. Weaver, R. B. Metz, S. E. Bradforth and D. M. Neumark, J. Phys. Chem., 1988,92,5558; I. M. Waller, T. N. Kitsopoulos and D. M. Neumark, J. Phys. Chem., 1990, 94, 2240. 22 R. B. Metz, T. Kitsopoulos, A. Weaver and D. M. Neumark, J. Chem. Phys., 1988, 88, 1463; R. B. Metz, A. Weaver, S. E. Bradforth, T. N. Kitsopoulos and D. M. Neumark, J. Phys. Chem., 1990,94,1377. 23 D. M. Neumark, Adv. Chem. Phys., in the press. 24 G. C. Schatz, B. Amaee and J. N. L. Connor, J. Chem. Phys., 1990,93, 5544. 25 G. C. Schatz, B. Amaee and J. N. L. Connor, Chem. Phys. Lett., 1986, 132, 1. 26 G. C. Schatz, B. Amaee and J. N. L. Connor, Comput. Phys. Commun., 1987,47,45. 27 G. C. Schatz, B. Amaee and J. N. L. Connor, J. Phys. Chem., 1988, 92, 3190. 28 B. Amaee, J. N. L. Connor, J. C. Whitehead, W. Jakubetz and G. C. Schatz, Faraday Discuss. Chem. SOC., 1987, 84, 387. 29 For a review, see J. N. L. Connor and W. Jakubetz, in Supercomputer Algorithms for Reactivity, Dynamics and Kinetics of Small Molecules, Proceedings of the NATO Advanced Research Workshop, Colombella de Perugia, Italy, ed. A. Lagana, Kluwer, Dordrecht, 1989, pp. 395-411.30 Resonances in H+LH Atom Reactions 30 Q. Sun, J. M. Bowman, G. C. Schatz, J. R. Sharp and J. N. L. Connor, J. Chem. Phys., 1990,92, 1677. 31 G. C. Schatz, B. Amaee and J. N. L. Connor, J. Chem. Phys., 1990, 92, 4893. 32 A. Persky and H. Kornweitz, J. Phys. Chem., 1987,91, 5496; H. Kornweitz, M. Broida and A. Persky, J. Phys. Chem., 1989, 93, 251; A. Persky and H. Kornweitz, Chem. Phys., 1989, 130, 129; Chem. Phys. Lett., 1989, 159, 134; H. Kornweitz and A. Persky, Chem. Phys., 1989, 132, 153. 33 G. C. Schatz, Chem. Phys. Lett., 1988, 150, 92. 34 S. Sato, J. Chem. Phys., 1955, 23, 2465; P. J. Kuntz, E. M. Nemeth, J. C. Polanyi, S. D. Rosner and C. E. Young, J. Chem. Phys., 1966, 44, 1168. 35 B. C. Garrett, D. G. Truhlar, A. F. Wagner and T. H. Dunning Jr., J. Chem. Phys., 1983, 78, 4400. 36 D. G. Truhlar, B. C. Garrett, P. G. Hipes and A. Kuppermann, J. Chem. Phys., 1984, 81, 3542. 37 G. C. Schatz and A. Kuppermann, J. Chem. Phys., 1973,59,964. 38 E. P. Wigner, Phys. Rev., 1955, 98, 145. 39 J. M. Bowman, Adu. Chem. Phys., 1985, 61, 115. 40 J. M. Bowman and A. F. Wagner, in The Theory of Chemical Reaction Dynamics, ed. D. C . Clary, 41 W. H. Miller and J. Z. H. Zhang, J. Phys. Chem., 1991, 95, 12. Proceedings of the NATO Advanced Workshop, Orsay, Reidel, Dordrecht, 1986, pp. 47-76. Paper 1/00035G; Received 2nd January, 1991

ISSN:0301-7249    

DOI:10.1039/DC9919100017

出版商:RSC    

年代:1991

数据来源: RSC

摘要:

Faraday Discuss. Chem. SOC., 1991, 91, 31-46 Diffuse Structures and Periodic Orbits in the Photodissociation of Small Polyatomic Molecules Reinhard Schinke,* Klaus Weide and Bernd Heumann Max-Planck-Institut f u r Stromungsforschung, 0-3400 Gottingen, Germany Volker Engel Fa kulta t f u r Ph ysik, Herman n - Herder3 tr, 3, Albert - Lud w igs- Un iversi ta t Freibu rg, D- 7800 Freiburg, Germany The relation of diffuse vibrational structures in UV-absorption spectra of (small) polyatomic molecules and internal vibrational motion in excited electronic states are investigated. The method of choice is the propagation of time-dependent wavepackets with the autocorrelation function serving as the link between the energy dependence of the spectrum and the time dependence of the molecular motion in the excited electronic state.For the purpose of this paper we characterize diffuse structures as very short-lived resonances with 'lifetimes' of the order of at most one internal vibrational period. In particular, we study a model system for the photodissociation of symmetric triatomic molecules ABA such as H20, C 0 2 and 03, the photodis- sociation of H 2 0 in the second continuum, and the fragmentation of H2S. The existence of unstable periodic orbits and their influence on the dissoci- ation dynamics is especially elucidated. In the case of H2S we demonstrate that the diffuse absorption structures are caused by symmetric stretch motion in a binding state which is strongly coupled to a dissociative state. Diffuse structures can be regarded as very broad resonances in excited electronic states.They manifest transition-state spectroscopy in the original sense of the word. 1. Introduction Many UV-absorption spectra of polyatomic molecules exhibit so-called diffuse vibra- tional structures, i.e. structures which are relatively broad and not well resolved. Fig. 1 shows two typical examples, namely the absorption-spectrum-of water in the two lowest bands. The corresponding excited electronic states, A 'B1 and B 'Al, are both dissociative and correlate with H('S) + OH(211) and H( 'S) + OH(*Z), respectively. Both spectra are composed of a broad background with superimposed weak undulations. The background indicates fast and direct dissociation on a timescale much shorter than an internal vibrational period, whereas the undulations manifest temporary excitation of an internal mode in the excited complex.The books of Robin' and Okabe2 contain many similar examples of diffuse structures in absorption spectra of polyatomic molecules. The central spectroscopical questions are: 1, what type of internal molecular motion is concealed by diffuse structures? 2, What is the timescale for internal trapping? 3, What is the appropriate 'zeroth-order' picture? Despite their simplicity, absorption spectra like those shown in Fig. 1 are very difficult to reveal and the likelihood to incorrectly assign the diffuse structures by using an oversimplistic model is actually high. The very weak undulations superimposed to the first abs9rption band of water were originally ascribed to excitation of the bending mode in the A state.3 Detailed theoretical studies employing an accurate potential-energy surface (PES), however, have undoubtedly proved this assignment to be wrong.4 The 3132 Difuse Structures and Periodic Orbits 1 I I I I I I ( a ) base \in( I I I I 1 I I I I 150 160 17 0 180 190 120 130 140 h /nm Fig.1 ( a ) Comparison of the measured3 (- - -) and the calculated4 (-) absorption spectrum of H20 in the first continuum. Theory and experiment are normalized at the maximum. ( b ) Comparison of the measured (- - -) and the calculated’ (-) absorption spectrum of H 2 0 in the second continuum. The arrow indicates the threshold energy for the production of H + OH(’X) structures superimposed to the second continuum of water were attributed to bending excitation as well.3 Although this interpretation is in principle correct, the picture which evolves from a recent dynamical analysis5 substantially differs from the conventional spectroscopic conception.Usually one interprets distinct structures in absorption or emission spectra in terms of normal modes and assumes that the coupling between the various degrees of freedom is weak. Any assignment presumes, in one way or another, that the full multidimensional Schrodinger equation describing the nuclear motion can be approximatel? cast into separate one-dimensional equations (adiabatic separation); this allows one to label each peak in the spectrum by a set of quantum numbers ( u , , v2, u3, . . . ) which specify the degree of excitation in each mode, e.g.stretching, bending etc. This procedure is undoubtedly correct and extremely prolific in extracting information on the structure of the excited electronic state from the absorption spectrum, provided the underlying assumptions, namely small displacements from equilibrium and/ or adiabatic separabil- ity, are indeed valid? The spectra for bound-bound transitions with total energies well below the dissociation threshold of the upper-state PES can be analysed in this way. However, as the excitation energy increases, the molecule performs oscillations of larger and larger amplitudes and the assumption of separability breaks down, i.e. theR. Schinke et al. 33 coupling between the various modes becomes significant and cannot be neglected. The conventional spectroscopic picture gradually loses its applicability and at last, when the classical motion is chaotic, it becomes useless.As the photon excites the molecule to still higher energies, above the dissociation threshold, at least one of the coordinates becomes unbound and the complex ultimately dissociates. Nevertheless, the excited molecule may live long enough to allow the development of broad structures in the spectrum, even for energies high above the dissociation threshold. Since the motion is unbound, normal coordinates are completely impractical and an exact solution of the multidimensional Schrodinger equation using scattering, i. e. Jacobi coordinates, is compulsory. The aim of this article is to demonstrate that diffuse absorption structures, which from the ordinary spectroscopic point of view look rather uninteresting, may hide very rich molecular motion in the excited electronic state.However, in order to reveal the beauty and the complexity of this internal motion it is absolutely necessary to have a good deal of information about the PES on which the dissociation proceeds and to perform exact dynamical calculations. Simple models with a few adjustable parameters may satisfactorily reproduce the spectrum, but that does not guarantee that these models are realistic and that we have learnt anything about the actual motion in the excited state. 2. Theory Absorption spectra can be calculated in the time-inde~endent”~ as well as the time- dependent’,’’ approach of photodissociation. In the time-independent picture we solve the stationary Schrodinger equation ( H - E)*ex(E,f) = O (1) in the excited electronic state (index ex) for fixed energy E = Ei+ ho, where Ei is the energy in the ground electronic state and Aw is the energy of the photon.The index f distinguishes via the appropriate boundary conditions the possible product channels. Assuming a weak light-matter interaction the various partial absorption cross-sections for absorbing a photon with energy ho and generating the products in channel f are calculated by the Golden rule expression’ ‘,12 where qgr(Ei) is the nuclear wavefunction in the ground electronic state (index gr); the transition dipole function p is usually assumed to be independent of the coordinates and therefore it is in most cases omitted. Summing over all final product channels, yields the total absorption cross-section, i.e.the spectrum. alternatively the time-dependent Schrodinger equation In the time-dependent approach of spectroscopy and photodissociation’~l’ we solve where a,,,( t ) represents the wavepacket evolving in the excited electronic state. Eqn. (4) is solved subject to the initial condition a,,,( t = 0) = pqgr( Ei). The total absorption cross section follows then from the Fourier-transformation34 Difuse Structures and Periodic Orbits Fig. 2 Schematic illustration of the two-dimensional PES for a symmetric triatomic molecule ABA for fixed bending angle. R , and Rz denote the two A-B bond distances. The shaded area at short distances indicates the Franck-Condon region and the two arrows illustrate the main dissociation path of classical trajectories starting in the FC region with S( t ) being the autocorrelation function The autocorrelation function contains the entire history of the wavepacket, for example, how fast it escapes from and how often it recurs to its place of birth. Eqn.( 5 ) relates the time-dependent dynamics in the upper state to the energy dependence of the absorption spectrum and is therefore ideally suited to analysing vibrational structures in the spectrum. The time-independent and time-dependent approaches are completely equivalent and comprise the same basic postulates (weak light-matter interaction); they merely provide different views and methods to calculate absorption cross-sections. 3. Photodissociation of Symmetric Triatomic Molecules As a first example of diffuse structures we consider the photofragmentation of a symmetric triatomic molecule ABA such as C02, O3 and H20.Owing to the symmetry, the excited molecule can dissociate in two identical ways: A+ BA and AB+ A. Fig. 2 depicts a typical PES of the LEPS type, for fixed ABA bending angle. It has a sadd!e at short A-B bond distances and two identical product channels. The PES of H,O(A 'Bl), for example, has for each bending angle an overall behaviour of this type.4 The standard coordinates used to describe the bound motion in the ground electronic state are the symmetric and asymmetric stretch coordinates as illustrated in Fig. 2. In the course of the fragmentation the asymmetric stretch mode turns into the dissociation mode and the symmetric stretch coordinate becomes the vibrational coordinate of the AB fragment.Upon excitation in the Franck-Condon region (indicated by the shaded area) the wavepacket o r alternatively a swarm of trajectories, if we treat the photodissociation classically, will immediately slide down the potential slope at the inner wall of theR. Schinke et al. 35 2.0 3.0 4.0 5.0 EIeV Fig. 3 Calculated absorption spectra for the model C 0 2 system as a function of the energy in the excited state. The vertical lines in (a) indicate the eigenenergies ( nss = 0, 1,2, . . .) of the symmetric stretch (ss) motion in the excited electronic state. The spectra in (b) and (c) are calculated with the same excited-state PES but using different equilibrium bond distances for the ground electronic state in order to ‘magnify’ the low- and high-energy branches of the spectrum.Adapted from Ref. 4 saddle and disappear in the two product channels as indicated by the heavy arrows in Fig. 2. The dissociation is fast and direct and leads to a broad absorption spectrum. The time-independent calculations of Kulander and Light,13 considered as a model for the photodissociation of C 0 2 , confirmed this view. Fig. 3( a ) depicts the absorption spectrum obtained from a time-dependent wavepacket cal~ulation;’~ it agrees essentially with the original spectrum reported by Kulander and Light. The spectrum is rather broad, but superimposed with diffuse structures which, especially on the blue side of the spectrum, look quite irregular. ‘Magnification’ of the high-energy side by shifting the ground-state equilibrium inward to smaller bond distances [Fig.3( c)] actually reveals a quite erratic looking spectrum. We emphasize that these structures are real and not caused by a numerical artifact! Several attempts have been made in the past to analyse this spectrum, however, only with modest S U C C ~ S S . ‘ ~ ~ ’ ~ - ” Following the models of Pack’’ and Heller,”36 Difuse Structures and Periodic Orbits 0 40 80 120 t/fs Fig. 4 Autocorrelation function S ( t ) corresponding to the spectrum shown in Fig. 3(a). T , , T2 and T3 denote the periods of the unstable periodic orbits shown in Fig. 5 ( a ) , ( c ) and ( d ) , respectively which were actually established before the calculations of Kulander and Light, the main progression, indicated by the vertical lines in Fig.3 ( a ) , have been ascribed to excitation of symmetric stretch motion on top of the barrier of the excited-state PES. This assignment is correct, as the following discussion will elucidate, but it explains only part of the diffuse structures. What type of internal motion causes the additional structures, especially in the spectrum shown in Fig. 3(c)? The picture becomes substantially simpler in the time-dependent approach. Fig. 4 depicts the autocorrelation function corresponding to the spectrum of Fig. 3( a ) . The rapid drop from the original value S ( 0 ) = 1 to zero within a few femtoseconds reflects the immediate ‘dephasing’ of the wavepacket due to the strong acceleration towards the saddle point.The main part of the wavepacket actually follows the route indicated by the arrows in Fig. 2. After ca. 35 fs, however, the autocorrelation function shows three well resolved recurrences with small amplitudes; they show that a small portion of the evolving wavepacket does not dissociate directly but recurs to its place of birth. A certain fraction of the quantum-mechanical wavepacket or of the swarm of classical trajectories is trapped in the inner region for at least one internal period. Fourier- transformation of each recurrence separately yields Gaussian-type ‘spectra’ modulated by cos ( 2 n / T.). Since the three recurrence times TI, T2, and T3 are incommensurable the addition of these partial ‘spectra’ explains the complicated structures superimposed on the broad background, which stems from the major peak of the autocorrelation function at t = 0.In this way we can rationalize the diffuse structures in terms of a series of well resolved but unrelated recurrences with periods T,. However, we really understand this generic fragmentation process only if we know what kind of molecular motion causes the recurrences. The time-dependent wavepacket itself is not prolific in this case because the portion that dissociates directly obscures the fraction that is temporarily trapped. Moreover, the wavepacket contains simultaneously all energies as well as all different types of internal motion and this superposition additionally complicates the analysis. The incommensurability of TI, T2 and T3 suggests that three different forms of short-time trapping are actually involved in the dissociation process.Classical trajectories provide the real understanding of the molecular motion. Launching trajectories randomly in the transition region and following their evolution reveals that, as expected, the majority dissociate directly with a high degree of vibrational excitation of the CO fragments. However, a small fraction do not immediately escape but return once to the FC region. A more careful analysis brings to light three genericR. Schinke et al. 37 2 3 2 3 R,l% R,l% Fig. 5 Unstable periodic orbits for the model C02 system. The energy is 2.5 eV for each trajectory. The heavy dot at short bond distances indicates the Franck-Condon point. For a more detailed discussion see the text unstable periodic orbits which, loosely speaking, guide some of the randomly started trajectories.Periodic orbits are unique features of the upper-state Hamiltonian; they live for ever, despite the fact that their total energy is high above the dissociation threshold. On the other hand, the relevant periodic orbits are very unstable and fragile; the slightest distortion rapidly destroys the perfect periodicity and initiates rapid dissoci- ation. Fig. 3( a), ( c ) and (d) display the three special trajectories relevant for the present model system; the energy corresponds to the maximum of the absorption spectrum in Fig. 3(a). The first periodic orbit is actually very simple and known for a long time from the work of Heller;" it represents symmetric stretch motion on top of the saddle between the two product channels. Its period T, agrees exactly with the time of the first recurrence.The analysis of scattering resonances in exchange reactions like H + H2 -P H,+ H has laid bare the corresponding 'asymmetric stretch' or 'hyperspherical' periodic orbit shown in Fig. 5(6);*' it has motion 'perpendicular' to the symmetric stretch periodic orbit. Since it is well separated from the FC region, where the motion in the upper state begins, this orbit by itself, however, cannot explain the two remaining recurrences. For a recurrence to occur the wavepacket must return to its place of birth at the inner wall of the saddle region, and this is possible only if symmetric stretch motion is involved as well. Thus, the asymmetric stretch periodic orbit can support a recurrence only in combination with symmetric stretch motion.Fig. 5 ( c ) and (d) depict the two simplest types of periodic motion that combine symmetric and asymmetric stretch motion. The corresponding times elapsed between the start at the inner slope of the PES and the first return to the FC region, T2 and T,, agree exactly with the two later recurrences observed in Fig. 4. The periodic orbits influence the dissociation in the excited electronic state in the following way. If we launch randomly a large number of trajectories in the FC region some of them might begin their journey very close to one of the periodic orbits. If the38 Difuse Structures and Periodic Orbits 'displacement' (in four-dimensional phase-space) is sufficiently small these trajectories stay for at least one period in the proximity of the periodic orbit and manage to return to their place of birth. There they start again with new initial conditions and most likely they succeed to dissociate.The periodic orbits act like guidelines for the trajectories rushing down the hill towards the product channels. Since they are highly unstable only trajectories that start extremely close to them have a chance to become temporarily trapped. According to the semiclassical theories of Gutzwiller,21 Balian and Bloch,22 and Berry and Tabor,23 based on the path-integral formulation of quantum mechanics due to Feynman and H i b b ~ , ~ ~ the classical periodic orbits guide the quantum-mechanical wavepacket in the same way. The extremely good agreement between the recurrence times of the quantum-mechanical wavepacket on one hand and the periods of the classical periodic orbits on the other hand provides sufficient evidence that the periodic orbits are indeed the real cause for the diffuse structures superimposed to the broad absorption spectrum.The amplitudes of the recurrences of S( t ) and consequently the amplitudes of the diffuse structures reflect the stability and the robustness of the underlying classical periodic orbit. Excitation of symmetric stretch motion on top of the barrier between the two identical product channels as predicted by Pack" and Heller," rather than bending motion as assumed by Wang et aZ.,3 causes the very weak diffuse structures in the first continuum of water [Fig. 1 ( a ) ] .The calculated autocorrelation function25 has a small recurrence after ca. 20 fs, which clearly stems from symmetric stretch motion of the quantum- mechanical wavepacket. The bending angle was fixed in this calculation. Actually, including the bending motion additionally blurs the diffuse structures because the barrier height and therefore the energies of the symmetric stretch mode depend slightly but noticeably on the HOH bending angle.4 The absorption spectrum of ozone in the Hartley band resembles qualitatively the model spectrum shown in Fig. 3( c ) . * ~ Using the a6 initio PES of Sheppard and Walker,27 Johnson and Kinsey2' related some of the recurrences of the autocorrelation function, obtained by Fourier-transformation of the measured spectrum, to various types of unstable periodic trajectories.Neither is the experimental spectrum fully resolved (thermal broadening), nor is the calculated PES one hundred per cent correct, which makes the direct relation between the recurrences on one hand and the periodic orbits on the other hand disputable. In this regard see also the exact wavepacket calculations of Le Qu6r6 and L e f o r e ~ t i e r ~ ~ using the PES of Sheppard and Walker. To make the analysis most rigorous one needs a full three-dimensional PES of high quality3' and exact dynamical calculations. 4. Large-amplitude Bending Motion in the Photodissociation of H,O(fi) The photodissociation of water in the second continuum, % 'A, --+ fi 'A, provides a second example for the usefulness of unstable periodic orbits. The experimental spec- trum shown in Fig.1 (6) exhibits a regular undulating structure superimposed on a broad background, wkich has been ascribed to excitation of high overtones of the bending motion in the B state.3 The explanation goes as follows: the ground state is bent with an equilibrium angle of a,= 104". Since the excited state is linear, a,= 180°, the one-fiimensional Franck-Condon overlap with the zero-point bending wavefunction in the X siate is appreciable only if the bending motion is higbly excited_. Strong quenching of the B state, caused by non-adiabatic coupling with the A and/or X state, significantly broadens each bending band and the result is a broad overall absorption spectrum with a regular progression of spikes sticking out of the background. The diffuse structures represent the remnants of the individual bending lines. This conventional spectroscopic picture rests on the adiabatic separation of the bending motion from the stretching degrees of freedom.In accordance with this picture, Wang et aZ.3 uniquelyR. Schinke et al. 39 60L I I I I \ \ I I \ I I I 1 2 3 4 5 6 Fig. 6 Two-dimensional PES for the fi ‘A, state of water. a is the HOH bending angle and RH--OH is the distance from one H atom to the OH fragment. The other 0-H bond distance is fixed at the equilibrium separation in the ground electronic state. Energy normalization is such that E = O corresponds to H+OH(’Z). The potential is based on the ab initio calculations of Theodorakopoulos, Petsalakis and Buenker, Chem.Phys., 1985, 96, 217. The cross marks the equilibrium in the ground state and the ellipse indicates the corresponding zero-point wavefunction. The heavy arrow illustrates the main dissociation path for the quantum-mechanical wavepacket or a swarm of classical trajectories. The dashed curve represents the unstable periodic orbit discussed in the text for an energy of 0.5 eV above the dissociation threshold labelled each peak of the spectrum by a bending quantum with the maximum correspond- ing to v 2 = 11-12. This picture is essentially wrong! The equilibrium configurations in the k and in the fi state are significantly displaced not only in the angular coordinate but also-in the H-OH stretch coordinate. Fig. 6 shows a two-dimensional representation of the B-state PES as a function of the H-OH bond and the HOH bending angle a ; the other 0-H bond is fixed at its value in the ground electronic state.The deep well in the linear configuration arises from a conical intersection with the ground electronic st_ate; it dominates the entire dissociaticn dynamics. The equilibrium separation in the X state is 1.8a0 compared to 3a, in the B state. As a consequence of this immense displacement in both directions the absorption of the photon is confined to en_ergie_s slightly below and mainly above the H+OH(*C) dissociation threshold. The X -+ B transition is a bound-continuum rather than a bound-bound transition! In this high-energy region, however, the bending motion does not adiabatically separate from the stretching motion and any decoupling scheme is meaningless.Below the threshold the (bound) motion is chaotic (in terms of classical mechanics) and above the threshold H20 dissociates40 Difluse Structures and Periodic Orbits rapidly into products H + OH( ’Z). The two-dimensional bound-state wavefunctions for energies in the re ion of the dissociation energy clearly prove the adiabatic separation Fig. 1 (6) compares the experimental spectrum with an exact quantum-mechanical, time-dependent wavepacket calculation using the two-dimensional PES of Fig. 6.5 The calculation includes two degrees of freedom: one of the H-0 bonds, which becomes the dissociation coordinate, and the HOH bending angle. It reproduces the overall shape of the measured spectrum remarkably well, especially the broad background and the superimposed diffuse structures. The amplitude of the undulatips at the onset of the spectrum is artificially large because strong quenching of the B state, caused by non-adiabatic coupling to the lower electronic states, is not taken into account in the model. The corresponding autocorrelation function (Fig.4 in Ref. 5 ) reveals a weak recurrence after ca. 40 fs whose amplitude is of the order of only 5% of the initial value for t = 0. This single recurrence causes the diffuse structures on top of the broad background. As in the foregoing case discussed in section 3, the exact quantum-mechanical wavepacket does not bring to light in a clear way what kind of internal motion is actually responsible for the recurrence. Running a few classical trajectories again yields real insiKht.The majority of trajectories, ca. 95%, starting randomly at the steep slope of the B-state PES above the ground-state equilibrium immediately slide down into the deep potential well, cross the linear H -0- H configuration, and dissociate directly, as indicated schematically by the heavy arrow in Fig. 6.32 These trajectories lead to extremely high rotational excitation of the OH(2Z) products, as known from the earliest experiments on the photodissociation of water in the second continuum.33 The remaining trajectories do not dissociate directly but perform, on average, one large-amplitude bending and stretching oscillation in the potential well. They swing to the other side of the well and return, like a boomerang, to their starting position.After the first recurrence they make a second try with different initial conditions and dissociate. This type of motion evinces strong coupling between the bending and the stretching degree of freedom. Taking into consideration only the bending mode is inadequate! In view of the foregoing section it is no surprise that an unstable periodic orbit ‘guides’ those trajectories which are ‘trapped’ for one period in the well before they manage to e ~ c a p e . ~ One example is depicted in Fig. 6. Although this periodic orbit has a total energy of 0.5 eV above the dissociation threshold it does not break apart but lives for ever. Its curvature clearly manifests the coupling between bending and stretching motion. As the ejected trajectories are drawn into the deep potential well the periodic orbit, pictorially speaking, captures a minor fraction of them in its proximity.Since the periodic orbit is very fragile, however, the captured trajectories do not survive for more than one period before they escape and dissociate. Deep inside the well at low energies the periodic orbit describes pure bending motion with a small amplitude. Owing to the coupling with the stretching coordinate the curvature of the orbit increases with energy and at the same time the amplitude grows as well. This type of periodic orbit persists from low energies, where the motion is regular, to very high energies in the region of the dissociation threshold, where the classical motion is chaotic, and even up into the continuum. Its stability or robustness gradually decreases as the energy rises.There are several other types of periodic orbits, which, however, do not take part in the overall dissociation dynamics. The simplest one is certainly pure H-OH stretching motion for a fixed bending angle of a = 180”. However, the overall dissociation path runs roughly perpendicular to this orbit such that the probability for capturing a trajectory that rushes down the potential slope is negligibly small. It must be emphasized that the extremely short ‘lifetime’ of the excited complex prohibits labelling of the individual absorption peaks by quantum numbers ! The stationary wavefunctions do not exhibit any clear nodal structure which would allow such an a~signrnent.~’ to be inadequate. 5R. Schinke et al. 41 Segev and S h a p i r ~ ~ ~ were the first to attempt ajynamical interpretation of the diffuse structures in the absorption spectrum of H20( B).They performed two-dimensional calculations in the time-independent approach using the PES of Flouquet and H ~ r s l e y . ~ ~ The spectrum of Segev and Shapiro exhibits a mixture of broad and very narrow resonances which were attributed to pure bending motion supported by a shallow rim at short H-OH distances. This interpretation is essentially different from ours; Segev and Shapiro did not consider the possibility of trapping inside the deep potential well. 5. Non-adiabatic Effects in the Photodissociation of H2S The absorption spectrum of H2S in the first continuum provides another interesting example of the relation between molecular motion in excited electronic states and diffuse structures.Like the spectrum of H20(A), the spectrum of hydrogen sulphide shows a progression of weak undulations on top of a broad backgr~und'~~'' which, as in the case of water, had been ascribed to excitation of internal bending motion in the upper electronic state.36 This assignment, which essentially rests on the approximate agreement of the energy spacing (1118 cm-') with the bending frequency in the ground electronic state (1290 cm-I), was still used in the late eighties to explain some unexpected findings for the rotational state distributions of the e S fragment.38 After the detailed theoretical analysis of the dissociation of water in the A state4'*' it also appears believable to relate the diffuse structures to excitation of the symmetric stretch motion on top of the saddle between the two identical product channels.This conjecture has been put forward by Xie et aZ.39 Both the interpretation in terms of bending excitation and in terms of symmetric stretch motion on the barrier of a dissociative PES are wrong in the light of recent a6 initio calculations. The actual dynamics of the photodissociation of H2S are much more involved. Recent a6 initio calculation^^^ unambiguously show that, unlike the photodissociation of water, the dissociation of H2S involves two excited electronic states. In C, symmetry they both have 'A" symmetry and therefore crossing of the corresponding PES is forbidden in the adiabatic representation. In CZv symmetry, however, they have different electronic symmetries, B1 and 'A2 , and the resulting potential curves actually can cross.The lower adiabatic PES is dissociative if one H-S bond is cleaved and the upper adiabatic PES is bound. For a fixed bending angle of 92" the two surfaces cross twice on the CZv symmetry h e , at ca. 2.5 a, and at 3.4 a,. The crossing in the inner region occurs right at the transition point and therefore it makes a rigorous dynamical treatment extremely difficult (and challenging, of course). In water the binding excited state is much higher in energy and therefore it does not at all take part in the excitation in the first continuum. Our earlier dynamical calculations40 were performed in the adiabatic representation with the HSH angle fixed at 92".The coupling strength between the two Born-Oppen- heimer states was adjusted to reproduce roughly the diffuseness of the spectral features. The coordinate dependence of the coupling was completely unknown at that time. In the meantime we extended the previous study with respect to both the a6 initio and the dynamical calculation^.^^ Although these new calculations are still regarded as pre- liminary, we present at this stage our present result for the absorption spectrum in order to illustrate the complexity of molecular motion that can be concealed by diffuse vibrational structures. The new ab initio calculations are performed at the MRDCI level" at ca. 2000 nuclear geometries, varying both H-S bonds as well as the bending angle In this way we construct two adiabatic PES and the corresponding transition dipole surfaces with the ground electronic state.The lower PES, shown in Fig. 7(6) foz a =92", is dissociative with an overall shape similar to the analogous surface for H20(A). Inciden- tally we note that the saddle between the two H + HS channels is significantly narrower42 Difuse Structures and Periodic Orbits a" 2 Q 2 3 4 5 'HS/ 2 3 4 5 R H S I Fig. 7 The binding ( a ) and the dissociative ( b ) adiabatic PES surfaces for H2S for a bending angle of 92". The energy spacing between the contours is 0.5 eV. The closed circles indicate the equilibrium in the ground electronic state. The arrow in (a) illustrates the initial motion of abound( t ) and the arrow in ( b ) indicates the dissociative motion of t ) than for H,O with the consequence that trapping in the symmetric stretch coordinate as described in section 3 is negligibly weak. Taking into account only this PES and neglecting the other electronic state does not yield diffuse structures! The other PES depicted in Fig.7 ( a ) is binding in all directions. In addition we extract from the MRDCI calculations the so-called mixing angle 0 which describes the mixing of the two leading electronic configurations; it changes from 0 to n / 2 across an avoided cro~sing.~' The mixing angle allows us to transform fromR. Schinke et al. 43 -2.0 -1.5 -1.0 -0.5 0 EIeV Fig. 8 Calculated absorption spectrum for H2S in the first continuum. us, denotes the quantum numbers of the symmetric stretch mode in the binding electronic state.E = 0 corresponds to three ground-state atoms, i.e. H + H + S the adiabatic to the non-adiabatic repre~entation~~ which, in contrast to Ref. 40, is employed in our new dynamical calculations. The coupling strength between the two non-adiabatic states is thus completely determined by the ab initio calculations. The relatively small energy separation between the two adiabatic potentials in the FC region indicates strong non-adiabatic coupling. The nuclear motion is treated in the time-dependent approach with two two- dimensional wavepackets, @bound(f) and @diss,(t), one evolving in each of the non- adiabatic states. The coupling between them is controlled by the off-diagonal element of the Hamiltonian matrix. It is completely determined by the ab initio calculations.The angular motion is described in the rotational sudden approximation, i e . we perform separate calculations for fixed bending angles a! and finally we average over CY with the square of the bending wavefunction in the ground electronic state serving as weighting function. Incidentally we note that the depcndence on the bending angle is crucial and, in contrast to the photodissociation of H20( A), it cannot be neglected. These calculations yield the absorption spectrum as well as the final vibrational state distribution of the HS fragment. They include two three-dimensional PES two three-dimensional dipole moment functions and the mixing angle, which is also a function of all three coordinates. They are parameter free! All aspects of the calculations will be published in full detail later.Fig. 8 depicts the calculated total absorption cross-section utOt( E ) with energy- normalization such that H + H + S corresponds to E = 0. The calculated spectrum con- sists, like the experimental one, of a broad background with superimposed, very diffuse structures. The spacing of ca. 1050 cm-I agrees reasonably well with the average spacing of 1118 cm-' of the measured spectrum. In contrast to the experiment, the theoretical spectrum is slightly asymmetric. In full accord with the results of van Vecn et al.,45 Xu et aZ.46 and Xie et ~ 1 . ~ ~ [but in contrast to the photodissociation of H,O(A)] HS( n = 0 ) is by far the dominant channel over the entire spectrum. In this paper we consider only the origin of the diffuse structures and defer the discussion of the final vibrational distributions to a forthcoming publication.According to our ab initio calculations the dissociation process proceeds in the following way: first, the photon excites almost exclusively the binding non-adiabatic state whereas the probability for exciting the dissociative state is negligibly small, i.e. I@bound(0))2 = 1 and I@diss.(0)l' = 0. The motion in the non-adiabatic states begins at t = 0 with the wavefunction in the bound state starting to perform an oscillation along the44 Difluse Structures and Periodic Orbits symmetric stretch coordinate as indicated by the arrow in Fig. 7 ( a ) . However, the very strong coupling to the dissociative non-adiabatic state rapidly reduces the probability in the bound state and simultaneously increases the probability for finding the system in the dissociative non-adiabatic state.At each instant an appreciable portion of @bound passes over to the dissociative PES where it immediately escapes as indicated by the arrows in Fig. 7 ( b ) . The quenching is so efficient that the wavepacket in the bound state has time for only one return to its birthplace before the entire wavepacket propagates on the dissociative PES. This leads to a single recurrence of the autocorrelation function with comparably small amplitude. This recurrence in turn induces the weak diffuse structures observed in the spectrum. According to this picture, the diffuse structures in the spectrum of H2S ar the consequence of symmetric stretching motion in a bound rather than a dissociative PES.The quenching rate, i.e. the non-adiabatic coupling strength controls the lifetime in the bound state and therefore the width as well as the amplitudes of the structures. A weaker coupling leads to sharper resonances while an even stronger coupling has the effect to additionally blur the structures. The diffuse structures reflect the eigenenergies of the symmetric stretch motion in the bond non- adiabatic state. In conclusion, the photodissociation of H2S in the first continuum can be classified as Herzberg’s‘ type I predissociation with strong coupling between the binding state, which carries almost 100% of the oscillator strength, and a dissociative state, as van Veen et u Z . ~ ~ originally surmised. Incidentally, note that a modification of the two dipole moment functions (in the non-adiabatic picture) in such a way that (a)bound(0)12/(~diss(o)12 = 0.8 : 0.2 instead of 1 : o tends to increase the spectrum at the low-energy side with the consequence that the agreement with the measured spectrum improves.It is important to note that the overall degree of vibrational excitation of HS as well as the amplitude of the diffuse structures depend sensitively on the coupling strength, the \@bound( O)l’/l@diSS(o)l* ratio, and the bending angle. The dissociation of H2S reveals a wealth of interesting internal motion in two electronic states. The picture evolving from our ab initio calculations is, in our opinion, essentially different from the model suggested recently by Dixon et d4’ These authors assume that the photon excites preferentially a dissociative state which is weakly coupled to a bound state.The vibrational eigenstates of the latter give rise to narrow resonances superimposed on the broad spectrum that originates from the dissociative state. In order to mimic the diffuseness revealed by the measured spectrum Dixon et al. introduce a phenomenological damping term. Our calculations yield automatically the right degree of diffuseness without any artificial fit parameter! Furthermore, Dixon et al. neglect the dependence on the bending angle which is not justified according to our experience. The present calculations are preliminary in so far as the rotational degree of freedom is treated in the rotational sudden ap roximation. In order to compare with the measured rotational state distributions of HS3 and with Raman spectra, which in contrast to H20 show substantial excitation of the bending the rotational degree of freedom should be treated exactly.Such calculations are in progress. The transformation from the adiabatic to the non-adiabatic representation is very crucial. The method we employed in the present calculations is one possibility. In the future we will examine other possibilities and their influence on the various observables. P 6. Discussion Diffuse structures can be viewed as very broad or short-lived resonances; they manifest short-time trapping in the intermediate region between the excited complex and the dissociation products. Diffuse structures in absorption spectra illustrate transition-state spectroscopy in the most general ~ e n s e .~ ” ~ ’R. Schinke et al. 45 Because of the extremely short ‘lifetime’ the time-independent approach is not useful for analysing and interpreting diffuse structures, except when an adiabatic separation is obvious.52 The time is too short to allow the development of a clear nodal structure which would facilitate one to classify the underlying molecular motion. The time- dependent picture, with the autocorrelation function as the link between the molecular dynamics and the absorption spectrum, is more generative. A single recurrence immedi- ately shows that some fraction of the quantum-mechanical wavepacket or the swarm of classical trajectories is temporarly trapped and returns to its starting position.Running classical trajectories provides the deepest insight into the molecular motion. They elucidate unambiguously the kind of molecular motion that the recurrences and therefore the diffuse structures conceal. Once the general behaviour of the trapped trajectories is uncovered, it is relatively easy to find the corresponding unstable periodic orbits which actually influence and guide the dissociation dynamics. Usually, symmetry considerations are very helpful to find the appropriate periodic orbits. For a given system there are often many periodic orbits, but only one or at most several of them actively take part in the dissociation dynamics. Other periodic orbits may be relevant for full collisions, for example. The instability of the orbits controls the ‘lifetime’ of the complex and therefore the diffuseness of the spectral features.Unstable periodic orbits are exceedingly important for the analysis of spectra in energy regimes where conventional spectroscopic means are not applicable anymore (large-amplitude motion of strongly coupled oscillators). A beautiful example is the hydrogen atom in a strong magnetic field (see Ref. 53 for a recent review and an extensive list of references). Molecular examples include Na354 and H f.55 Periodic orbits provide the real understanding of diffuse vibrational structures and their dynamical message. Can we attribute a specific lifetime to the diffuse structures? Our answer is negative! Let us consider, for example, the photodissociation of water in the second continuum.The vast majority of trajectories dissociate immediately on a timescale of cu. 10 fs. Very few trajectories are trapped for at most one vibrational period before they dissociate as well. Under such circumstances we find it meaningless to extract a lifetime. Diffuse structures superimposed on a broad background, like the examples in Fig. 1, look very simple and probably can be reproduced by several more or less sophisticated models, but only one explanation can be correct ! The spectrum of H2S clearly illustrates this ambiguity. It is very dangerous to try to interpret such a spectrum, regardless of how simple it appears, without some reasonable information about the overall topology of the corresponding multidimensional potential energy surface or surfaces.The chance of missing the true explanation is very high. Diffuse structures hide a lot of fascinating molecular dynamics and they are a real challenge for accurate a6 initio calculations. References 1 M. B. Robin, Higher Excited States, Academic Press, New York, 1974. 2 H. Okabe, Photochemistry of Small Molecules, Wiley, New York, 1978. 3 H-t. Wang, W. S. Felps and S. P. McGlynn, J. Chem. Phys., 1977, 67, 2614. 4 V. Engel, R. Schinke and V. Staemmler, J. Chem. Phys., 1988, 88, 129. 5 K. Weide, K. Kuhl and R. Schinke, J. Chem. Phys., 1989,91, 3999. 6 G. Herzberg, Electronic Spectra and Electronic Structure of Poly-atomic Molecules, van Nostrand Rein- 7 M. Shapiro and R. Bersohn, Annu. Rev. Phys. Chem., 1982, 33, 409. 8 R. Schinke, in Collision Theory for Atoms and Molecules, ed.F. Gianturco, Plenum, New York, 1989. 9 R. G. Gordon, Adv. Magn. Reson., 1968, 3, 1 . 10 E. J. Heller, Ace. Chem. Res., 1981, 14, 368; Potential Energy Surfaces and Dynamics Calculations, ed. D. G. Truhlar, Plenum, New York, 1981. 11 R. Loudon, The Quantum Theory of Light, Oxford University Press, Oxford, 1983. 12 C. Cohen-Tannoudji, B. Diu and F. Laloe, Quantum Mechanics, Wiley, New York, 1977, vol. 11. 13 K. C. Kulander and J. C. Light, J. Chem. Phys., 1980, 73, 4337. 14 R. Schinke and V. Engel, J. Chem. Phys., 1990, 93, 3252. hold, New York, 1966.46 Difluse Structures and Periodic Orbits 15 R. Schinke and V. Engel, Chem. Phys. Lett., 1986, 124, 504. 16 K. C. Kulander, Chem. Phys. Lett., 1986, 129, 353. 17 J. P. Henshaw and D. C. Clary, J.Phys. Chem., 1987,91, 1580. 18 R. T. Pack, J. Chem. Phys., 1976, 65,4765. 19 E. J. Heller, J. Chem. Phys., 1978, 68, 3891. 20 E. Pollak and M. S. Child, Chem. Phys., 1982, 60, 23; J. Manz, E. Pollak and J. Romelt, Chem. Phys. 21 M. C. Gutzwiller, J. Math. Phys., 1967, 10, 1004; 1970, 11, 1791; 1971, 12, 343; Phys. Rev. Lett., 1980, 22 R. Balian and C. Bloch, Ann. Phys. ( N . Y.), 1972,69, 76. 23 M. V. Berry and M. Tabor, J. Phys. A , 1977, 10, 371. 24 R. P. Feynman and A. R. Hibbs, Quantum Mechanics and Path Integrals, McGraw-Hill, New York, 1965. 25 N. E. Henriksen, J. Zhang and D. G. Imre, J. Chem. Phys., 1988,89, 5607. 26 D. E. Freeman, K. Yoshino, J. R. Esmond and W. H. Parkinson, Planet. Space Sci., 1984, 32, 239. 27 M. G. Sheppard and R. B. Walker, J. Chem. Phys., 1983, 78, 7191. 28 B. R. Johnson and J. L. Kinsey, Phys. Rev. Left., 1989, 62, 1607. 29 F. Le QuCri and C. Leforestier, J. Chem. Phys., 1990, 92, 247. 30 A. Banichevich, S. D. Peyerimhoff and F. Grein, Chem. Phys. Lett., 1990, 173, 1. 31 M. von Dirke and R. Schinke, to be published. 32 K. Weide and R. Schinke, J. Chem. Phys., 1989, 90, 7150. 33 T. Carrington, J. Chem. Phys., 1964, 41, 2012. 34 E. Segev and M. Shapiro, J. Chem. Phys., 1980, 73, 2001; 1982, 77, 5604. 35 F. Flouquet and J. A. Horsley, J. Chem. Phys., 1974, 60, 3767. 36 S. D. Thompson, D. G. Caroll, F. Watson, M. O’Donnell and S. P. McGlynn, J. Chern. Phys., 1966, 37 L. C. Lee, X. Wang and M. Suto, J. Chem. Phys., 1987, 86, 4353. 38 B. R. Weiner, H. B. Levene, J. J. Valentini and A. P. Baronawski, J. Chern. Phys., 1989, 90, 1403. 39 X. Xie, L. Schnieder, H. Wallmeier, R. Bottner, K. H. Welge and M. N. R. Ashfold, J. Chern. Phys., 1990,92, 1608. 40 K. Weide, V. Staemmler, R. Duren and R. Schinke, J. Chern. Phys., 1990, 93, 861. 41 B. Heumann, K. Weide and R. Schinke, to be published. 42 R. J. Buenker and S. D. Peyerimhoff, Chim. Acta (Berlin), 1974, 35, 33; 1975, 39, 217. 43 H. J. Werner, B. Follmeg, M. H. Alexander and D. Lemoine, J. Chem. Phys., 1989, 91, 5425. 44 H. Koppel, W. Domcke and L. S. Cederbaum, Adv. Chem. Phys., 1984, 57, 59. 45 G. N. A. van Veen, K. A. Mohamed, T. Baller and A. E. de Vries, Chern. Phys., 1983, 74, 261. 46 Z. Xu, B. Koplitz and C. Wittig, J. Chem. Phys., 1987, 87, 1062. 47 R. N. Dixon, C. C. Marston and G. G. Balint-Kurti, J. Chem. Phys., 1990, 93, 6520. 48 R. J. Brudzynski, R. J. Sension and B. Hudson, Chem. Phys. Lett., 1989, 165, 487. 49 M. D. Person, K. Q. Lao, B. J. Eckholm and L. J. Butler, J. Chem. Phys., 1989,91, 812. 50 H.-J. Foth, J. C. Polanyi and H. H. Telle, J. Phys. Chem., 1982, 86, 5027. 51 P. R. Brooks, Chem. Rev., 1988, 88, 407. 52 R. Schinke, S. Hennig, A. Untch, M. Nonella and J. R. Huber, J. Chem. Phys., 1989, 91, 2016. 53 H. Friedrich and D. Wintgen, Phys. Rep., to be published. 54 J. M. Gomez-Llorente and H. S. Taylor, J. Chem. Phys., 1989, 91, 953. 55 J. M. Gomez-Llorente, J. Zakrzewski, H. S. Taylor and K. C. Kulander, J. Chern. Phys., 1988,89, 5959; J. M. Gomez-Llorente and E. Pollak, J. Chern. Phys., 1988, 89, 1195. Lett., 1982, 86, 26; K. Stefanski and E. Pollak, Chem. Phys., 1989, 134, 37. 45, 150. 45, 1367. Paper 01055726; Received 11 th December, 1990

ISSN:0301-7249    

DOI:10.1039/DC9919100031

出版商:RSC    

年代:1991

数据来源: RSC

摘要:

Faraday Discuss. Chem. SOC., 1991,91,47-61 Ab Initio Molecular Orbital and Dynamics Study of Transition-state Spectroscopy Koichi Yamashita and Keiji Morokuma Institute for Molecular Science, Myodaiji, Okazaki 444, Japan Recent results on the a b initio potential-energy surface (PES) and dynamics calculations closely related to the experiments of ‘transition-state spectros- copy’ (TSS) are discussed. The topics included are the photodissociations of NaI and ozone, and the unimolecular dissociation of FHF-. The non- adiabatic coupling in the ion-covalent crossing region of the NaI dissociation is calculated based on the CASSCF-MRCI method and compared with experimental and empirical estimates. The PESs of the ozone photodissoci- ation are calculated using the CASSCF-SECI method.Characteristics of the ground and the excited B-state PESs are compared with the existing PESs. The weak structure seen in the Hartley band is explained in terms of transition-state dynamics based on three-dimensional quantum calcula- tions using new PESs. The CEPA PES of the unimolecular dissociation of FHF- to the F-+HF channel is calculated. Based on the quantum- mechanical variational calculation, the vibrationally highly excited FHF- anion above its dissociation threshold is suggested as a candidate of TSS of unimolecular dissociation reactions without a barrier. 1. Introduction Polanyi’ and Brooks2 are the pioneers in the new field generally called ‘transition-state spectroscopy (TSS)’, which has attracted increasing experimental as well as theoretical interest. The final target here is to probe the reacting system spectroscopically in the course of chemical reaction and in the transition-state region where chemical-bonds are formed and broken.Recently Zewai13 and Neumark4 have reached a new stage where the dynamics in transition-state regions are observed with sufficient resolution by a breakthrough in new experimental techniques. Since very little experimental information is available about PES characteristics and dynamics in the region of the transition state, theoretical information is indispensable for interpretation of the observed spectra and the design of new experiments. Two examples are given to illustrate this situation. Neumark and co-worker~~*~ have shown that negative-ion photodetachment can be used as a powerful experimental technique for TSS of a neutral bimolecular reaction, provided that the Franck-Condon region of the stable anion complex corresponds to the transition-state regions of the neutral reaction.They have applied the method to a series of hydrogen-bonded anions, such as symmetric bihalide anions XHX- the corresponding deuterated species. Several peaks observed in the kinetic energy distribution of the detached electron have been assigned to the vibrational progression of the antisymmetric stretching mode in the transition-state region of the neutral complex. Theoretical simulations of photodetachment spectrum of ClHCl- as well as IHI- have been performed by Schatz6 based on a quantum-mechanical scattering method and by Bowman and Gazdy’ using an L2 basis set.Although the simulations for ClHC1- reproduced qualitatively the principal features of the experimental spectrum, the calcu- lated peaks are much narrower and more widely spaced than the experimental peaks. 9 9 ), asymmetric bihalide anions XHI- (X = F, C1, Br5(d)) and (X = ClS(a),(C) Br5(c) I % b ) , ( e ) 4748 Ab Initio MO and Dynamics Study channel a \, absorption Na(3P)+HCI laser quenchir- - NaCI+H Na(3S)+HCi Fig. 1 Scheme for the laser-catalysed Na + HC1 reaction. The dotted line denotes the laser-dressed gound 1 2A' state PES which is lifted by oL and makes a crossing with the excited 2 *A' state. A trajectory starting at the ground-state reactant will be completed as an excited-state non-reactive product (channel a) and a ground-state reactive product (channel b) Reaction Coordinate Neumark and co-workers impliedS'"'~'" that these discrepancies are due to deficiencies in the Cl+ HCl LEPS PES and probably to transitions to low-lying electronic states of [ClHCl].We have performed an a6 initio PES calculation' for ClHCl- and ClHCl and, based on a 1D vibrational calculation on them, have suggested an important contribution of a low-lying electronically excited state in the photodetachment spectra of ClHCl- and ClDCl-. Some peaks in the experimental spectra were assigned to transitions to the vibrational states of the first electronically excited 211 state in addition to those of the ground 'Z+ state in the transition-state region of the neutral complex. The overlap of transitions to these two electronic states should make the spectra broader than the one where only a single state is taken into account.Application of a newly developed high-resolution threshold photodetachment spectrometer by Waller et aZ.5(e) to ClHCl- may provide direct evidence of the contribution of the 211 state, since the intensity of the transition to the 211 state will be significantly reduced and may disappear in threshold photodetachment spectra. Theoretical information of the excited-state PESs, which is otherwise unavailable, provides an opportunity for designing new experiments for TSS. Based on a theoretical study, we have proposed a laser-catalysed Na+ HCl reaction as a possible new system for TSS.9 We note here that for the laser-induced K+ NaCl reaction, we have previously reproduced and explained theoretically" the excitation spectrum observed by Brooks and co-workers." The scheme of the new laser-catalysed reaction for a TSS system is shown in Fig.1. The first step is to start the reaction in the ground 1 2A' state; however, conditions that prohibit formation of the product must be used, i.e. total energy must not be sufficient to overcome the transition-state barrier. Then a laser of wavelength longer than the NaD line is irradiated. onto the reacting system. The laser-dressed ground state, which is lifted energetically by the amount of the photon energy, w L , crosses the electronically excited 22A' state. If the transition occurs at the crossing point, the excited-state reactant Na(3P) + HCl (channel a) will be obtained through an excited-state complex (NaHCl)", and quenching from the complex will also produce the ground-state product NaCl + H (channel b).Since no product is obtained without a laser, we may call channel b a laser-catalysed reaction. Our theoretical study based on the a6 inifio PESs and classical trajectory calculations has shown that the wL dependence of the channel b cross-section which is determined by the non-adiabatic quenching process would contain information concerning the PES and dynamics at the 'transition' complex region.K . Yamashita and K . Morokuma 49 Table 1 Adiabatic dipole moments (pI1, pq2, p12) dissociation energy (0,) and the difference between the sodium ionization potential ( Ei) and the iodine electron affinity E,, R,' = 5.1239 a.R = 18.0 a, method p11/Da p22/D p121D &/ev (E2-E1)/eV (Ei-E,b,) eV CASSCF( 3 1) -9.759 4.763 3.742 2.872 0.659 2.177 CASSCF( 3 1 )-MRCI -9.565 4.455 3.566 3.061 0.555 2.073 expt.' -9.24 3.02 2.075 ~~~~ ~ a 1 D = 3.335 64 x lop3' C m. 15(e). Extrapolated values based on the Rittner model (ref. 14). Ref. In this Discussion, we present our recent studies on the a6 initio PES and dynamics calculations closely relevant to the experiments of TSS. The topics we studied are: (1) the photodissociation processes of NaI and ozone and (2) the FHF- unimolecular reaction. We discuss how a6 initio PES and dynamics calculations are utilized in an interpretation of the observed spectra and design of new experiments. 2. P hotodissociat ion Processes 2.1 NaI Ion-Covalent Curve Crossing For alkali-metal halide molecules, the non-adiabatic potential-energy curves of the ionic ground state and covalent dissociative excited state cross at a long nuclear distance.In the NaI dissociation reaction, Rose and co-workers have observed12 wavepacket oscilla- tions trapped on the excited bound state created by a large off-diagonal coupling element V , , between the non-adiabatic states using 'femtosecond TSS'. No oscillatory behaviour has been observed for NaBr12 in which V,, is not large enough to support an adiabatic bound state. Therefore this type of experiment can provide information about the non-adiabatic interaction in the ion-covalent crossing region. Several theoretical studies have been performed to simulate the wavepacket oscilla- tions.However, the coupling element V12 used in these theoretical studies is an empirical estimate by Grice and Her~chbach'~ based on the Rittner mode114 or that derived spectroscopically15 and has never been qualified by a6 initio calculations. In this section, we present our a6 initio calculations in the ion-covalent crossing region of NaI. The adiabatic potential-energy curves of the ground and first excited states were calculated? by using the state-averaged complete-active-space self-consistent field (av- CASSCF) and the internally contracted multi-reference configuration interaction (MRCI)." The av-CASSCF calculations were performed with equal weight for the ionic and covalent 'X+ states. Two types of active space, (31) and (22), were used, where a set of two numbers in parentheses gives the numbers of active CT and T orbitals. Recently, Bauschlicher and Langhoff demonstrated" on LiF that the state-averaging method avoids discontinuities in the molecular orbital in the crossing region and CASSCF-MRCI converges to the full CI as the CASSCF active space is expanded. Table 1 summarizes the CASSCF(31) and CASSCF(31)-MRCI results.The ground- state dipole moment, p I ], at the experimental equilibrium geometry is in good agreement + For the Na basis set, McLean and Chandler's'' triple-zeta contraction [6s5p] of the (12s9p) basis was used. To this, two d functions (1.5, 0.5) and one f function (1.0) were added. The I basis set was taken from Huzinaga" [ 18s14p8d/12s9p5d] augmented with one p function (0.03), one d function (0.2) and one f function (1.0).The total number of contracted Gaussian functions was 117. The uncontracted CSFs were 454148 and 3318631 for CASSCF(31)-MRCI and CASSCF(22bMRC1, respectively, in C,, symmetry and those were contracted to 145040 and 255585 variational parameters.50 Ab Initio MO and Dynamics Study 1 Q \ OI t- i? + Y 4 . 5 1 -0.51 t- t, -0.52 I I I I I I 11 13 15 17 -0.53 -0.54 96 40 38 CI 3. \ a3 10 El __..> __a' .... /..- ( b ) ...+' ,,.S .......... ...... '. P22 +." Pl 1 Q /.-+. ............... ... + I I I T I 11 ' 13 17 Rlao Fig. 2 Calculated NaI ( a ) adiabatic potential-energy curves El and E2 (in hartree), ( b ) adiabatic dipole moments (in D), (c) non-adiabatic potential-energy curves V , , and V,, (in hartree, R, is the crossing point) and ( d ) non-adiabatic coupling V , , (dotted line by Grice and Herschbach) with the experiment, although the excited state dipole moment, p22, and the transition dipole moment, p I 2 , are not known experimentally.The dissociation energy, D,, and the difference between the Na ionization energy and I electron affinity, Ei-Eea, also agree well with the experiment. The calculated difference E i - E e , was obtained by extrapolating the energy difference, E2 - El , at R = 18.0 a,, where the covalent state is already flat, based on the Rittner model:l4 E~ - E,, = ( E2 - E , ) + 1/ R + a / m 4 where a is the sum of experimental polarizability of Na+ and I-. This estimation avoids a complicated size consistency problem and takes into account the long-range interaction.Fig. 2 shows ( a ) adiabatic potential-energy curves E , and E2, and (b) adiabatic dipole moments p , , , p I 2 and p22. The transformed non-adiabatic potential-energy curves V , , and V,, are shown in Fig. 2 ( c ) and non-adiabatic coupling V , , in Fig. 2 ( d ) . Adiabatic-to-non-adiabatic transformation was performed by the scheme of Werner andK. Yamashita and K. Morokuma n m 51 , .- ' ..*' :::I a. BM I I I I I I I I 11 13 15 1: R l a0 Fig. 2 (continued) Mayer2' using the following equations: v , , ( R ) = E , ( R ) c o s ' [ e ( ~ ) ] + ~ , ( ~ ) s i n ' [ e ( ~ ) ] v,,(R)= E , ( R ) sin2 [~(R)]+E,(R) COS'[~(R)] VI2( R ) = ( E2 - E l ) sin [ 8( R)] cos [ t?( R ) ] where 8 ( R ) is the angle which diagonalizes the adiabatic dipole moment matrix.The El and E2 potential-energy curves show an avoided crossing at around R = 13.5 a,. Correspondingly, the adiabatic dipole moments pll and p2, cross and the transition dipole pI2 has a maximum. The calculated diabatic crossing point, R,= 13.4 a,, agrees nicely with that, R, = 13.3 a,, estimated by the Rittner m0de1.I~ In Fig. 2 ( d ) we show for a comparison an empirical estimate of VI2 by Grice and Her~chbach'~ using the function: VzH(R) =exp [(Ro-R)/AR] where Ro and AR are the fitting parameters. In Table 2 several estimates of the coupling V,, at the crossing are summarized. The a6 initio CASSCF(31)-MRCI V,, is larger than the experimentallempirical values by Grice and Her~chbach,'~ Rose and co-workers12 and Schaefer et aZ.15(a) and a larger calculation CASSCF( 22)-MRCI gives a slightly worse agreement, although the calculated V , , fits nicely with an exponential form in the crossing region.The experimental estimate by Rose and co-workersl* might be too52 Ab Initio MO and Dynamics Study Table 2 Off-diagonal coupling matrix elements VI2 method v12 / cm-I CASSCF(31)-MRCI" 51 1 CASSCF(22)-MRCI" 525 Grice-Herschbachb 442 ref. 12 370 ref. 15(u) 434 chemi-ionization processC 403-524 a Calculated at the crossing R, = 13.4 uo. 13. Ref. 15(d). Ref. small in comparison with the others. However, we should be cautious in drawing conclusions at this stage since V,, is very sensitive to the electronic wavefunctions used," adiabatic-to-non-adiabatic transformation and the crossing point R,. The spin-orbit interaction, not taken into account in the above calculation, could be an origin of this disagreement and is presently under investigation. 2.2 Ozone Hartley Absorption Band Photodissociation experiments offer good opportunities for probing directly the transi- tion state of electronically excited states;21 the idea behind this is as follows.If the Franck-Condon region of a stable molecule corresponds to the transition state of an electronically excited state, it may be possible to probe directly the PES and dynamics of the transition-state region. In particular, many symmetric triatomic and polyatomic molecules show oscillatory structures in their UV photodissociation spectra. Pack2, proposed a simple model to explain this structure, and Heller23 proposed a time- dependent version of Pack's time-independent model.Kulander and Light24 performed the first exact calculation for the collinear photodissociation of a symmetric triatomic molecule. Clary" proposed that reactive scattering resonances might be the origin of oscillating structures and suggested the possibility of transition-state spectroscopy. The idea was explored in realistic calculations on the collinear CO, molecule by Henshaw and C1a1-y~~ and Schinke and Enge1.26 Relating to this interesting aspect of photodissociation, the ozone Hartley band has recently attracted several theoretical s t ~ d i e s . ~ ' - ~ ~ Imre et aL3' observed experimentally the emission during the dissociation of ozone to O2('Ag)+O('D). The intensity of the emission spectrum is governed by the dynamics on the repulsive PES, and can be considered to be a sort of TSS.In this section we intend to explain the origin of the weak structure in the centre of the broad Hartley absorption band in terms of transition state dynamics. The ozone photodissociation process is characterized by the four electronic states shown in Fig. 3. The Hartley band originates from the excitation from the X state to the B state. For the PESs of the ozone photodissociation reaction, Hay et ~ 2 . ~ ~ (HPWH) performed a6 initio calculations and Sheppard and Walker29 (SW) made an empirical fit to the HPWH surface. However, the HPWH PES gives a very poor agreement with experiment. For example, the barrier height in the B state, AE,,, was found to be 1.72 eV while the experimental value is 0.97 eV.The dissociation energy of the ground state, D, = 0.38 eV, was only one third of the experimental value of 1.1 eV. In this situation, we have recently performed new a6 initio PES calculation^^^ of the ground state and the three low-lying excited states of ozone required to describe itsK . Yarnashita and K. Morokuma A 53 0.08 0.04 0.00 B state $ -0.04 I I 1 1 I I I 2.0 3.0 4.0 5.0 Rlao Fig. 4 The potential-energy curves of the X and B state along the 0-0 bond (in hartree, with the other 0-0 bond fixed at 2.5 a, and the angle at 110'). The potential-energy curves of HPWH (ref. 28) and SW (ref. 29) are shown for comparison (broken lines, this work) three-dimensional photodissociation processes. The method? we used was CASSCF- SECI'' with the DZP basis set.Our new AE,, was 1.22 eV, in better agreement with experiment, and D, was 0.89 eV, improved significantly to reproduce ca. 80% of the experimental value. Reproduction of the 0, value has offered a good target for theoretical challenges with new a6 initio techniques33 and has been shown to be quite difficult. t The orbitals for CI calculations were optimized in the state-averaged CASSCF calculation, where 12 electrons were distributed among nine active orbitals, with equal weights for the four A' states. The CI calculation was performed including all the single excitations from the resulting 1292 reference configurations. Quadruple correlation effects were included based on the formula by Feller and Davidson?254 Ab Initio MO and Dynamics Study 0.006 0.005 0.004 0.003 0.002 0.001 0.009 0.0 0.1 0.2 0.3 0.4 tips 0.02 0.01 0.00 0.0 0.1 0.2 0.3 0.4 tips Fig.5 Autocorrelation functions: ( a ) the experimental result by Johnson and Kinsey (ref. 34) and ( 6 ) the theoretical result converged up to time t = 0.2 ps (ref. 31) Several characteristic differences in the X and B PESs are seen among HPWH, SW and ours. Fig. 4 shows the potential-energy curves along an 0-0 bond while the other 0-0 bond is fixed at 2.5 a, and the angle at 110". Since SW forced their X state to reproduce the experimental D, and to have a well on the B state, SW PESs show quite different features in comparison with the original HPWH; for instance, the SW X state has an unrealistic well up to a large 0-0 distance. Our new B state clearly shows a well which is missed by HPWH and enforced by SW.The most important difference that could affect the photoabsorption dynamics is the slope of the B PES at the ground-state Franck-Condon region. Our B state has a steeper slope than HPWH and SW. As shown later, this difference in the slope emerges as an effect on intensities of the recurrence peaks. The only quantum-dynamical study carried out for this system was in two i.e. with fixed bending motion, and reproduced well the general shape of the absorption spectrum, only without oscillation. Only brief discussions have beenK. Yamashita and K. Morokuma 55 given on possible sources for the weak structure. Recently, a dipole-dipole autocorrela- tion function has been obtained by Johnson and Kin~ey’~ as a Fourier transform of the experimentally observed total cross-~ection.~~ The autocorrelation function in the time domain shows the time development of the overlap between the initially excited wavefunction and the wavefunction which travels on the B state. The autocorrelation function by Johnson and K i n ~ e y , ~ ~ Fig.5 ( a ) , first decreases drastically and shows a characteristic recurrence. Le Quere and Lef~restier~~ have succeeded for the first time in performing exact three-dimensional quantum-mechanical calculations of autocorrela- tion function using the grid method. They reproduced the main feature of the experi- mental recurrence, but claimed that the SW B PES used in their calculations is insufficiently repulsive, resulting in intensities that are too strong in recurrence in comparison with that obtained by Johnson and K i n ~ e y .~ ~ In order to see how the ozone photodissociation dynamics are sensitive to the B PES, we collaborated with Leforestier to calculate the autocorrelation function using our new B PES,’l fitted to Murrell-Sorbie analytical functions.37 As shown in Fig. 5( b ) , our preliminary result has also successfully reproduced the main recurrence feature and showed a reduction in intensities by factor of three compared with those with the SW PES.36 Based on a classical trajectory analysis, Johnson and Kin~ey’~ assigned four charac- teristic time-domain peaks to particular types of trapped trajectories in the transition-state region. In quantum mechanics these correspond to the scattering resonance states trapped by vibrationally adiabatic bound states.Schinke and Engle26 have given a similar discussion on the origin of the structure in C 0 2 UV absorption spectrum based on the collinear quantum-mechanical calculation. Photodissociation spectra, involving hardly any averaging over angular momentum and orientation angles that can wash out resonance structure, will yield valuable information on excited-state PESs and dynamics in the transition-state region, which is a challenging target for testing the accuracy of a6 initio PES. 3. Unimolecular Dissociation of FHF- For many years statistical theories have provided useful models for unimolecular reactions. The RRKM theory38 is widely known to give a quantitative interpretation of nearly all unimolecular experiments.Recently, the study of mode-specific non-RRKM behaviour in the unimolecular dissociation of vibrationally/ rotationally highly excited molecules has been made theoretically as well as e~perimentally.~~ State-resolved experiments are beginning to reveal the dynamics of dissociating m01ecules.~~ For the final topic, the unimolecular dissociation reaction of the FHF- anion41 will be discussed in this section. We show that quasi-bound vibrational states can exist over the dissoci- ation threshold of FHF- to the F-+ HF channel and propose this reaction as a good system for spectroscopic studies of the vibrational levels of dissociating molecules, i. e. TSS of unimolecular dissociation reactions. FHF- is a prototype of symmetric bihalide anions which attracted spectroscopic interest4* owing to their peculiar vibrational anhar- monicity and were chosen as targets of photodetachment experiments by Neumark and ~o-workers~?~ (see Introduction).Ab initio PES calculations of the ground-state unimolecular dissociation of FHF- to the F-+ HF channel have been preformedl- using the CEPA (coupled electron pair approach) method.44 The global PES was fitted to the sixth-order Simons-Parr-Finlan analytical form45 and an ion-dipole attraction term was added to describe the long-range interaction. In +The basis sets used were F[9s6p3dlfl and H[5s3pld] by van D ~ i j n e v e l d t ~ ~ augmented with diffuse s (0.07) and p (0.05) functions, three d (4.32, 1.775, 0.745) functions and an f function (2.355) for the F atom and a diffuse s (0.025) function, three p (1.8, 0.6, 0.2) functions and a d function (0.7) for the H atom.1.88 I 1.64 - W \ * 2 1.51 - (a) 1.73 - FH+F- 1.41 4 F-+HF 1.26 I I I I I 1 1 1 1 1 1 l l l l l l l l 6.00 8.00 10.0 12.0 14.0 16.0 P/a, 1.76 1 1*39 1.26 * 2.51 2.64 2.76 2.89 3.01 3-14 B/rad Fig.6 PES of the FHF- unimolecular dissociation in terms of the hyperspherical coordinates p, x, and 8: (a) 6 = 7r and ( b ) p = 8.0 bohr. FHF- has a linear symmetric equilibrium geometry with a well of 1.95 eV. There is no barrier for the F-+ HF dissociation. Contours are drawn for each 0.2 eV order to treat large-amplitude vibrational motion which can break the anion, we used the hyperspherical coordinate system developed by Pack and Parker46 in our three- dimensional (J = 0) quantum dynamics calculations.The eigenstates over the dissoci- ation threshold as well as of the bound states were calculated variationally using the grid method.41 Fig. 6 shows the PES contours in terms of the hyperspherical coordinates, p, x and 8. The coordinate p determines the size of the system and x and 8 the shape of the system. As easily seen from the figure, p corresponds to a dissociation coordinate of F- + FH, and x and 8 approximately correspond to the antisymmetrical motion and the bending motion, respectively. The FHF- anion has a linear symmetric equilibriumK. Yamashita and K . Morokuma - 1.70 - 1.64 - -? 1.57 - * 1.51 - 1.44 57 (a) 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 , , , 1 5.97 8.79 11,61 14.42 17.24 20.06 P l a0 ''70 - ( b ) 1.64 - 'cl * -? 1.57 - 1.51 - 1.44 , I 1 1 1 I I , I , , , , , , , , I I 5.97 8.79 11.61 14,42 17.24 20,06 P l a0 Fig.7 Contours of nuclear wavefunctions with gerude symmetry in terms of the hyperspherical coordinates p and x; ( a ) ug = 52, E = 10 009 cm-', ( p ) = 8.18, (p')= 0.38, ( b ) ug= 50, E = 9966 cm-', ( p ) = 8-83, (P*)~ = 2.65, (c) ug = 173, E = 15 029 cm-', ( p ) = 8.57, ( P ' ) ~ = 1.26, ( d ) ug = 171, E = 14 961 cm-', ( p ) = 10.2, ( P ' ) ~ = 10.3, ( e ) u = 324, E = 17 848 cm-', ( p ) = 8.77, ( P ' ) ~ = 1.63 (resonance state) and (f) og = 321, E = 17 794 ~ r n - ~ ' ( p ) = 12.21, ( P ) ~ = 32.0 (direct scattering state). u, is the eigenstate number and E is the total energy in cm- . ( p ) and ( P ~ ) ~ are the average and dispersion of p, respectively58 1.70 1.64 1.57 1.51 1.44 Ab Initio MO and Dynamics Study I / 5.97 8.79 11.61 14.42 17.24 20.06 P l Qo 1.70 1.64 3 t 1.57 * 1.51 5.97 8.79 11.61 14.42 17.24 20.06 P l % Fig.7 (continued) geometry (p, = 7.63, X, = ~ / 2 , 8, = T) with a deep well of 1.95 eV (15 700 cm-'). There is no barrier for the F-+ HF dissociation. Fig. 7 show a set of wavefunctions of the two energetically close eigenstates for the three cases, the bound states [ca. 10 000 cm--', Fig. 7 ( a ) and ( b ) ] , the states near the threshold [ca. 15 000cm-', Fig. 7 ( c ) and ( d ) ] and the states above the dissociation threshold [ca. 17 800 cm-I, Fig. 7 ( e ) and 0). All the wavefunctions have gerade symmetry or even-,y quantum numbers. Each set shows a localized wavefunction on the left as well as a delocalized one on the right.It is quite interesting that even over theK . Yamashita and K. Morokuma 59 1.70 1.64 1.57 1.51 1.44 5.97 8.79 11.61 14.42 17.24 20.06 P l a o 1.70 1.64 1.57 1.51 1.44 5.97 8.79 11.61 14.42 17.24 20.06 P l a o Fig. 7 (continued) dissociation limit there exist states with localized wavefunctions. These states are very stable with respect to changes in the number of grid points. We may assign the state (f) as a direct scattering state and the state (e) as a resonance state, i.e. a quasi-bound vibrational state over the dissociation threshold. Comparing the two states in each case, the dispersion of p, ( P ’ ) ~ = ( p ’ ) - (p)’ is a good indicator as to whether a wavefunction is localized or delocalized. The analysis of other states over the threshold suggests that there are many resonance states, i.e. states with localized wavefunctions.The mechanism of forming resonance states is clear. The vibrationally adiabatic potential-energy curve along the p dissociation coordinate supports many adiabatic bound states over the60 Ab Initio MO and Dynamics Study dissociation limit, though the present bound states should have a finite lifetime through non-adiabatic couplings with the continuum and therefore quasi-bound states. These resonance states are known as compound (Feshbach) resonance states, and the existence of these has been supposed for many years47 in constructing models of unimolecular reactions. Hase and c o - w ~ r k e r s ~ ~ have studied bound and resonance states extensively for the model H-C-C + H + C=C Hamiltonian semiclassically as well as quantum mechanically. Hyperspherical modes for bound and resonance states of linear ABA molecules have been predicted by Manz and c o - ~ o r k e r s ~ ~ using a Morse- oscillator model.However, the quantum calculations so far have been limited to Our study has shown with a three-dimensional quantum calcula- tion for the first time, as far as we are aware, that resonance states can exist above the unimolecular threshold for a realistic system. FHF- is an ideal system, because it is free from quantum tunnelling caused by a dissociation barrier and, in particular, because there are no electronically excited states in the threshold energy range which could perturb compound resonance states. We believe that the compound resonance states of FHF- are a suitable experimental target for spectroscopy to investigate the uni- molecular transition state without a barrier. 4.Conclusions We have discussed how our theoretical studies based on the ab initio PES and dynamics calculations provide information in the interpretation of the ‘transition-state’ spectra observed in the photodissociations of NaI and ozone. The compound resonance states above the FHF- dissociation threshold are suggested theoretically as a candidate for probing spectroscopically the transition state of unimolecular dissociation reactions. We believe some experimental studies along this line will be realized in the near future. Although much remains to be studied even in gas-phase reactions, TSS in new fields such as reactions on surfaces, in clusters and in condensed phases will materialize in future through extended joint studies between experiment and theory.We gratefully acknowledge Prof. Claude Leforestier for his fruitful collaboration, Dr. Peter Knowles and Prof. Joachim Werner for their generous permission to use the MOLPRO program code, Prof. Pave1 Rosmus for valuable discussions, and Prof. Dan Neumark for providing his results prior to publication and helpful comments. The calculations were carried out at the IMS Computer Center. References 1 J. C. Polanyi, Faraday Discuss. Chem. SOC., 1979, 67, 129; H-J. Foth, J. C. Polanyi and H. H. Telle, J. Phys. Chem., 1982, 26, 5027; B. A. Collings, J. C. Polanyi, M. A. Smith, A. Stolow and A. W. Tarr, Phys.Rev. Lett., 1987, 59, 2551. 2 P. R. Brooks, R. F. Curl and T. C. Maguire, Ber. Bunsenges. Phys. Chem., 1982, 86, 401; P. R. Brooks, Chem. Rev., 1988, 88, 407. 3 A. H. Zewail, Furaday Discuss. Chem. SOC., 1991, 91, 207. 4 A. Weaver and D. M. Neumark, Faraday Discuss. Chem. SOC., 1991, 91, 5. 5 ( a ) R. B. Metz, T. Kitsopoulos, A. Weaver and D. M. Neumark, J. Chem. Phys., 1988, 88, 1463; ( b ) A. Weaver, R. B. Metz, S. E. Bradforth and D. M. Neumark, J. Phys. Chem., 1988,92, 5558; ( c ) R. B. Metz, A. Weaver, S. E. Bradforth, T. N. Kitsopoulos and D. M. Neumark, J. Phys. Chem., 1990, 94, 1377; ( d ) S. E. Bradforth, A. Weaver, D. W. Arnold, R. B. Metz and D. M. Neumark, J. Chem. Phys., 1990,92,7205; ( e ) I. M. Waller, T. N. Kitsopoulos and D. M. Neumark, J.Phys. Chem., 1990,94,2240. 6 G. C. Schatz, J. Chem. Phys., 1989, 90, 3582; J. Chem. Phys., 1989,90, 4847; J. Phys. Chem., 1990,94, 6157. 7 J. M. Bowman and B. Gazdy, J. Phys. Chem., 1989, 93, 5129; B. Gazdy and J. M. Bowman, J. Phys. Chem., 1989,91, 4615. 8 K. Yamashita and K. Morokuma, J. Chem. Phys., 1990, 93, 3716.K . Yamashita and K. Morokuma 61 9 K. Yamashita and K. Morokuma, Chem. Phys. Lett., 1990, 169, 263. 10 K. Yamashita and K. Morokuma, J. Chem. Phys., 1989,91, 7477. 11 T. C. Maguire, P. R. Brooks and R. F. Curl, Phys. Rev. Lett., 1983, 50, 1918; T. C. Maguire, P. R. Brooks, R. F. Curl, J. H. Spence and S. J. Ulvick, J. Chem. Phys., 1986, 85, 844; S. Kaesdorf, P. R. Brooks, R. F. Curl, J. H. Spence and S. J. Ulvick, Phys. Reu. A, 1986, 34,4418.12 T. S. Rose, M. J. Rosker and A. H. Zewail, J. Chem: Phys., 1988, 88, 6672; M. J. Rosker, T. S. Rose and A. H. Zewail, Chem. Phys. Lett., 1988, 146, 175; T. S. Rose, M. J. Rosker and A. H. Zewail, J. Chem. Phys., 1989, 91, 7415. 13 R. Grice and D. R. Herschbach, Mol. Phys., 1974, 27, 159. 14 E. S. Rittner, J. Chem. Phys., 1951, 19, 1030. 15 ( a ) S. H. Schaefer, D. Bender and E. Tiemann, Chem. Phys., 1984,89,65; ( b ) N. J. A. Van Veen, M. S. De Vries, J. D. Sokol, T. Baller and A. E. De Vries, Chem. Phys., 1981, 56, 81; (c) M. B. Faist and R. D. Levine, J. Chem. 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B. Walker and E. J. Heller, J. Phys. Chem., 1982, 86, 862. 29 M. G. Sheppard and R. B. Walker, J. Chem. Phys., 1983, 78, 7191. 30 D. Imre, J. L. Kinsey, A. Sinha and J. Krenos, J. Phys. Chem., 1984, 88, 3956. 31 K. Yamashita, K. Morokuma, F. Le Quere and C. Leforestier, to be published. 32 D. Feller and E. R. Davidson, J. Chem. Phys., 1984, 80, 1006. 33 M. V. Ramakrishna and K. D. Jordan, Chem. Phys., 1987, 115, 423; K. Raghavachari, G. W. Trucks, J. A. Pople and E. Replogle, Chem. Phys. Lett., 1989, 158, 207; J. F. Stanton, R. J. Bartlett, D. H. Magers and W. N. Lipscomb, Chem. Phys. Lett., 1989, 163, 333. 34 B. R. Johnson and J. L. Kinsey, J. Chern. Phys., 1989, 91, 7638. 35 D. E. Freeman, K. Yoshino, J. R. Esmond, and W. H. Parkinson, Planet. Space Sci., 1984, 32, 239. 36 F. Le Quere and C. Leforestier, J. Chem. Phys., 1990, 92, 247. 37 J. N. Murrell, S. Carter, S. C. Farantos, P. Huxley and A. J. C. Varandas, in Molecular Potential Energy Functions, John Wiley, New York, 1984. 38 P. J. Robinson and K. A. Holbrook, in Unimolecular Reactions, John Wiley, New York, 1972. 39 T. Uzer, Adu. At. Mol. Phys., 1988, 25, 417. 40 H. L. Dai, R. W. Field and J. L. Kinsey, J. Chem. Phys., 1985, 82, 1606; Y. S. Choi and C. B. Moore, J. Chem. Phys., 1989, 90, 3875. 41 K. Yamashita, K. Morokuma and C. Leforestier, to be published. 42 K. Kawaguchi and E. Hirota, J. Chem. Phys., 1987,87,6838; K. Kawaguchi, J. Chem. Phys., 1988,88, 4186. 43 F. B. van Duijneveldt, IBM Research Report RJ945, 1971. 44 W. Meyer, J. Chem. Phys., 1976,64,2901; H-J. Werner and E. A. Reinsch, J. Chem. Phys., 1982,76,3144. 45 G . D. Carney, L. A. Curtiss and S. R. Langhoff, J. Mol. Specrrosc., 1976, 61, 371. 46 R. T. Pack and G. A. Parker, J. Chem. Phys., 1987, 87, 3888. 47 R. D. Levine, in Quantum Mechanics of Molecular Rate Processes, Oxford Univ. Press, Oxford, 1969; R. A. Marcus, Faraday Discuss. Chem. SOC., 1973, 55, 34. 48 W. L. Hase, J. Phys. Chem., 1986, 90, 365; K. N. Swamy, W. L. Hase, B. C. Garrett, C. W. McCurdy and J. F. McNutt, J. Phys. Chem., 1986, 90, 3517. 49 J. Manz and H. H. R. Schor, Chem. Phys. Letr., 1984, 107, 542; R. H. Bisseling, R. Kosloff, J. Manz, F. Mrugala, J. Romelt and G. Weichselbaumer, J. Chem. Phys., 1987, 86, 2626. Paper 1/00003I; Received 21st December, 1990

ISSN:0301-7249    

DOI:10.1039/DC9919100047

出版商:RSC    

年代:1991

数据来源: RSC

摘要:

Faraday Discuss. Chem. SOC., 1991,91, 63-72 State-to-state Photodissociation Dynamics in Formic Acid M. Brouard, J. P. Simons and J.-X. Wang Department of Chemistry, The University, Nottingham NG7 2RD, UK Photofragment mapping and l 8 0 isotopic labelling have been used to probe the character of the transition state for the predissociation channels HC02H(A 'A) -+ HCO(k 'A)+OH(X 'll) in jet-cooled, vibronically state selected formic acid, and the nature of the vibronic states initially accessed in the Franck-Condon region. The dynamics on the excited potential-encrgy surface are compared with those in the isoelectronic molecule HONO(A ' A ) . Almost all the available energy above the dissociation limit is concentrated into fragment recoil, regardless of the initial vibronic state selection: the experimental data indicate a substantial, late exit barrier and trajectories funnelled through a near col- linear HO-C-0 structure at the transition state.Students of molecular photodissociation dynamics have at their disposal (in principle) a powerful range of methods for probing the structural changes that accompany passage through the transition state. The most direct methods 'look at the transition-state region' on femtosecond timescales via time-resolved kinetic spectroscopy,' resonance Raman or fluorescence emission spectros~opy~-~ or resonantly enhanced multiple photon absorp- tion.' These strategies can be likened to an 'aerial photography of the passage through the transition-state region'. Alternative, indirect methods probe the distributions of energy and momentum among the molecular and atomic fragments descending from the transition-state-photofragment mapping.6 Scalar (energy) quantum-state distribu- tions and vectorial (linear and angular momentum) correlations reflect the forces and torques promoting structural changes in the transition-state In some systems it may also be possible to probe mode selectivity in gaining access to this region - a kind of 'base camp photography'.Structural rearrangements can be probed by the use of isotopic labelling to flag the atomic composition of molecular fragments which may conceivably have 'changed partners' en route through the transition state. In the present study, photofragment mapping and isotopic labelling have been used to probe the character of the transition state for the predissociation channel, HCO*H(A lA) - HCO(% *A') + OH(X *n) (1) in formic acid.''*'' The choice of formic acid has proved serendipitous. Its first (n -+ n&) electronic transition, although predissociated, excites long progressions of vibronic bands, associated with v3(C=O) stretch, v,(O-C-0) bend, vs(C-H) out-of- plane and vg( 0- H) torsional motions.'* Their rotational contours become increasingly complex and diffuse as their energy increases and the most highly excited overtones (e.g.36, and associated combination bands) appear to display homogeneously broadened features with lifetimes of ca. 400fs. In this spectral region there are close analogies with the predissociated (n -+ T;=~) transition in the isoelectronic molecule HON0.'3*'4 Since the nascent OH and HCO fragments can be detected via LIF and REMPI spectroscopy, formic acid provides an ideal system for state-to-state dynamical studies, 6364 Photodissociation Dynamics in Formic Acid with additional selectivity based upon the spectrally shifted isotopomers HC1800H and HC0180H.Quantum-state distributions, kinetic energy disposals and vector correlations in the recoiling OH and HCO fragments have been probed using Doppler-resolved polarised laser techniques; vibronically resolved photo fragment yield spectra have also been recorded, principally under jet-cooled conditions but also at 300 K. Experiments conducted with mixed samples of HC1800H and HC0180H have probed the character of the vibronic states initially accessed by photon absorption, as well as the (possible) incidence of (0)H-atom tunnelling during passage through the transition-state region.Central questions addressed in the discussion include (i) the character of the highly excited 0-C-0 skeletal vibrations in the photoexcited molecule, (ii) the preferred geometry of the molecule at the transition state and (iii) the qualitative topography of the ‘predissociative’ potential-energy surface, particularly in relation to that of HONO. Experimental The experimental techniques used are similar to those described in an earlier preliminary report.” A single excimer laser pumped two dye lasers which provided the tuneable photolysis (267-225 nm) and probe (ca. 281 nm or ca. 400 nm; optical delay ca. 10 ns) pulses. The dye lasers could be operated broad-band or etalon narrowed (bandwidth ~0.08 cm-’) and the beams were counter-propagated into the reaction chamber with their polarisation vectors either mutually parallel or perpendicular.The OH photofrag- ments were probed via the ( 1 , O ) band of the A(2E)-X(211) transition” and were detected in emission on the (1,l) band (centred at ca. 310 nm) using an interference filter and photomultiplier. The HCO fragments were probed via the 2 + 1 resonance-enhanced multiphoton ionisation (REMPI) signal (resonant with the 3p ’II Rydberg and detected using a simple parallel-plate probe with home-built amplifier. l8 Both signals were recorded on boxcar integrators and transferred on a shot-by-shot basis to a microcomputer for data averaging and storage.All the experiments reported here employed jet-cooled formic acid, except those in which HCO fragments were detected. Jet-cooling was achieved using a commercial pulsed molecular beam source (Newport Corporation) with typical backing pressures of helium ~6 atm. The helium was see_de_d with <0.1% HC02H vapour. As discussed in the next section, both the HC02H (A-X) laser induced fluorescence (LIF) spectrum and the OH photofragment yield spectrum are readily assignable to the monomer (consistent with the small OH quantum yield, c $ ~ ~ < 0.15 at 222 nm, recently determined for photodissociation of the dimer, at 300 K).19 0-enriched samples of formic acid were synthesised by reaction of methyl formate ( l 6 0 ) with Na180H,20 followed by hydrolysis of the sodium formate with CC12HC02H.The isotopic composition of the resulting formic acid was determined by mass spec- trometry to be HC160160H : HC’60180H: HC180160H: HC180180H 4: 1 : 1 : 0. The sample was stored under vacuum; its isotopic composition was regularly checked and found not to change over the duration of the experiments. Several strategies have been ad_opt_ed to probe the reaction dynamics in HC02H(&. Close to the origin band of the A-X transition (ca. 267 nm), where the molecule is fluorescent, it has been possible to record its LIF spectrum under jet-cooled conditions. At higher excitation energies, where the fluorescence quantum yield becomes too small to allow parent molecular fluorescence detection, OH photofragment yield spectra have been recorded, again under jet-cooled conditions, with the wavelength of the probe laser tuned to t,he OH(A-X) Q1( 1) transition.Scanning the photolysis laser reveals the rovibronic ( A-X) predissociation spectrum of HC02H. Finally, fully dispersed LIF( OH) and REMPI (HCO) spectra recorded at room temperature have been used to upravel the energy and momentum disposals in the nascent vibronic states in HC02H (A). 18M. Brouard, J. P. Simons and J.-X. Wang . -. 22918 h/nm 234I1 23315 A/nm 240:05 65 239'2 A/nm mi2 Fig. 1 Low-resolution OH yield spectrum of jet-cooled HCO,H(A) obtained by fixing the probe laser on the Q,(1) transition of the OH photofragments Results Predissociation Spectra of HC0J-I The low-resolution OH yield spectrum of jet-cooled HC02H between 250 and 225 nm (see Fig.1 ) reveals dominant vibronic features readily assignable to the 3," progressions in monomeric HC0,H; these have been previously observed at room temperature via absorption" and, more recently, LIF" spectroscopy. No detectable OH LIF signal could be found following excitation into vibronic bands lying below the 3i9; feature ( Evib = 2440 cm-') either in thermal or jet-cooled samples. In the region spanned by the 3; and 34, transitions, the yield spectrum remains relatively uncongested and the vibronic structure closely mirrors that observed (via the parent-molecule LIF spectrum) between the 0; and 3; bands.I2 At higher excitation energies, however, the OH yield spectrum becomes increasingly congested and perturbed, exemplified by the high- resolution spectra of the 9;, 3:, 3: and 3; bands shown in Fig. 2.The rotational structure of the 9:) band, which has been assigned on the basis of the asymmetric rigid rotor analysis of the 3; band of thermal HCO,H," indicates a rotation+ temperature of ca. 3.5 K. The structure is consistent with the non-planar HCO,H(A) state equilibrium geometry proposed by Moule and coworkers" in which both H atoms lie out of the plane of the 0-C-0 moiety. The 3; and 3 ; bands display more complex rotational structures but still exhibit sharp spectral features (at 0.08 cm-' resolution), but such features cannot be resolved in the 3: transition (Evib ==: 6400 cm-') owing to spectral66 Photodissociation Dynamics in Formic Acid 9: I 3: -- 4'1433.2 fi/ cm- ' 41713.32 Fig.2 High-resolution (0.08 cm-') jet-cooled HC02H (A-k) LIF spectra, ( a ) 9; and (b) 3; bands and OH yield spectra, ( c ) 34, and (d) 36, bands showing the degradation of rotational structure at the higher excitation energies (see text) congestion and line broadening.? Assuming the narrowest features recorded in the 3:, 3; 9; and 3; 7; 9; bands to be homogeneously broadened allows an estimate of the parent molecular lifetime of ca. 400fs. This can be compared with lifetimes of ca. 30-5011s in vibronic levels close to the band origin. Photofragment Energy and Momentum Disposals Energy and momentum disposals in the OH fragments arising from photodissociation of HC02H at 300 K have been reported previously." The results obtained in the earlier study may be summarised as follows: (i) the OH photofragments are born rovibrationally cold ((fg") = 0.06, (f?") = 0); (ii) Doppler analysis of the photofragmentt spectra indi- cates that ca.80% of the available energy is concentrated into fragment translation, leaving only 12% for the average internal excitation of the sister fragment, HCO; (iii) the correlations between the vectors p, troH and joH are all small (Pgv =r 0, Puj = +0.2, Ah2) = 0), indicative of a long dissociation lifetime and/or (more probably) a parent molecular transition moment, p, having components along all three HC02H inertial axes.' 1,2' t The harmonic oscillator vibrational denscy of states at Evib = 6400 cm-' (= v3 = 6) is < 10 per cm-' based on the experimental and calculated HC02H( A) vibrational frequencies given by Moule and coworkers.I2M.Brouard, J. P. Simons and J.-X. Wang 67 r- 390.0 hlnm 392.88 Fig. 3 HCO (2 + 1) REMPI spectra obtained via photodissociation at room temperature of HC0,H at A =: 225 nm. The assignments (upper spectrum) are those of Grant and c~workers'~~" and refer to ( v ; , u ; , v ; ) ( K ' , K") Point (ii) above was particularly surprising, since photon absorption at 225 nm correspondslto the deposition of six quanta into the (nominal)? C=O stretching mode in HC02H(A). That very little of this initial excitation appears as HCO vibrational excitation is confirmed in the present study by directly probing the HCO fragment using 2 + 1 REMPI spectroscopy (see Fig. 3). Comparison with the REMPI spectrum obtained by Grant and establishes the absence of any contribution from vibrational hot bands: it is also apparent that the HCO fragment is born with a rotational temperature close to 300K (though a detailed analysis of the rotational intensity distribution has not yet been attempted). It might also be noted that impulsive recoil from a bent 0-C-0- parent molecular geometry [cJ: the equilibrium OCO angle =111", in HC02H( A)I2' would necessarily have generated HCO fragments with high rotational excitation, (f:"") =: 0.3.These new data suggest that the estimated kinetic energy release (fT) = 0.8 based upon the preliminary Doppler analysis, actually represents an underesti- mate. Direct, Fourier-transform of the Doppler-resolved R2( 1) feature (Fig. 4) in the LIF spectrum of OH generated through predissociation at 225 nm (exciting the 3:7:9: vibronic band) gives (fT) = 0.84 f 0.05.Isotopic Labelling Experiments Insight into the character of the vibrational motions excited in the HCO,H(A) prior to and during its dissociation has been obtained from experiments employing 180-enriched samples of formic acid. Attention has been focussed on the 3; transition, which in the unlabelled molecule, is centred at 233.871 nm; a portion of the OH yield spectrum from unlabelled, jet-cooled formic acid is shown in Fig. 5(a). The corresponding 160H yield spectrum from jet-cooled, '80-enriched formic acid is shown in Fig. 5(6). In addition t See later discussion.68 Photodissociation Dynamics in Formic Acid frequency shift/cm-' Fig. 4 The R,(1) rotational feature in the OH(A-X) LIF spectrum arising from the A = 225 nm photodissociation of jet-cooled HC02H (see text) to the original 3: band associated with the unlabelled HC02H, it displays a new feature displaced 85.5 cm-' to the red and centred at 234.340 nm.LIF spectra of the OH fragments generated via photodissociation from both the shifted and unshifted bands and shown in Fig. 5(i) and 5(ii), respectively, establish the absence of any 180H fragments. OH fragments were detected, however, when the photolysis laser was tuned to a new, weaker absorption band in the isotopically enriched formic acid, that was centred at 234.075 nm, 37 cm-' to the red of the 3; band in the unlabelled HC02H. The 180H yield spectrum from the jet-cooled 180-enriched sample, shown in Fig. 5( c ) , displays only this new feature; the two vibronic bands associated with production of 160H are both absent.Fig. S(iii), which shows the LIF spectrum of the OH fra ments generated by photodissociation from the new feature, confirms the presence of OH, (the 160H, which is also produced, arises from underlying absorption associated with the unlabelled HC0,H - still the dominant component in the partially "0-enriched sample). If the 3: transition in formic acid were associated with a pure C=O stretching local mode, then substitution of C="O for C=l60 would have displaced the transition by 122cm-' to the red (see Discussion); however, no such feature could be detected in either the 160H or the "OH photofragment yield spectra. 18 f 8 Discussion The near-UV absorption spectrum of HC02H is superficially similar to that of its isoelectronic analogue HONO.Both are associated with n + T* electronic transitions localised on the C=O (N=O) moiety and both absorption spectra are dominated by vibronic progressions (nominally) involving the C=O (N=O) stretching motion. The vibronic bands in HONO are all diffuse. In HC02H, the progressions are more extensive, and in contrast to HONO, all bands lying below the fourth overtone (33 display rich rotational structures. These characteristics, and the observation of a very high kinetic energy release in the recoiling OH and HCO fragments ((fT) a 0.8) indicate a markedlyM. Brouard, J. I? Simons and J.-X. Wang 69 t 1 235 h/nm 233.5 I 1 - 282.308 - 281.85 232.29 235 h/nm 233.6 281.85 r 1 - 235 233.6 281.85 282.38 Fig.5 (a) 160H Ql(l) yield spectrum from unlabelled, jet-cooled HC02H. (b) and ( c ) 160H and 180H Q1( 1) yield spectra from 180-enriched, jet-cooled samples of HC02H. (i)-(iii) Photofragment OH LIF spectra associated with the vibronic features shifted by 85.5, 0 and 37 cm-', respectively, from the 3; band in unlabelled formic acid. The asterisks indicate Q,(N) lines associated with "OH; all other lines are due to 160H h/nm higher barrier for the photodissociation HCO,H(A) + HCO(%)+OH(X) than for its analogue Ab initio calculations of the potential-energy surface (PES) of HONO(A) indicate a predissociation barrier < 1500 cm-', for the vikrationless in contrast, t@e threshold for generation of OH from HCO,H(A) lies some 2400 cm-' above the (A-X) band origin, which by chance is nearly isoenergetic with the OH f HCO dissociation limit.'2921 _Given the possibility of barrier tunnelling, the barrier height in the vibrationless HCO,H(A) molecule must be 22400 cm-'.HONO(& -+ NO(X) + OH(X) (3)70 Photodissociation Dynamics in Formic Acid Dissociation on the A state of HONO (and other RON0 species) is thought to follow two distinct mechanisms, one vibrationally adiabatic and the other non- adiabatic.24 The former proceeds via tunnelling through the barriers in the v ~ = ~ = n adiabatic vibronic surfaces, and leads to the generation of NO fragments with n quanta. The second mechanism can be viewed as one involving vibration-translation coupling between the N=O and N-OH stretching coordinates, leading to NO fragments with n - 1, n - 2, .. . quanta of vibrational excitation. In the dynamical calculation^^^ this last mechanism was dominant, but its importance may have been overestimated owing to the neglect of the dependence of the barrier heights on the 0 - N - 0 bending coordinate. The experimental work of Dixon and riel^,^ (see also ref. 3) indicates that the adiabatic pathway is more important than was found in the calculations, and they inferred that the barrier heights were indeed sensitive to the 0-N-0 bending angle; the importance of the bending degree of freedom has also been established in the predissociation of CH30N0.26 The behaviour in HCO,H(A) is in striking contrast with that in HONO(&. The increased barrier height on the vibrationless potential has a profound affect on the reaction dynamics.As many as six quanta can be excited in the C=O stretching mode of the parent molecule, but regardless of the number of quanta excited this energy is channelled almost exclusively into the reaction coordinate: none of the excess energy appears in HCO vibration and both partner fragments are born rovibrational!y unexcited. Several qualitative features of the transition state region of the HCO,H(A) PES may be inferred from the measured photofragment properties. (i) The barrier to dissociation along the reaction coordinate must be later than in HONO, thus ensuring that in the transition-state region the C=O stretching force constant and internuclear separation lie close to those found in free HCO. (ii) This, in turn, implies that the barrier heights in the (C=O) vibrationally adiabatic curves must increase significantly with C=O stretching quanta ( v 3 ) , cf: HONO (ref.25). The implication is supported by the fact that the pattern of photofragment energy disposals is insensitive to the excess energy, EAVL, and to the initial vibronic state selected.23 This would not be the case if the barrier height were constant (i.e. >2400 cm-', irrespective of the vibrational mode excited) and the remainder of the excess energy were distributed? for example, statistically over the a_vailable product quantum states. In this respect the dynamical behaviour-in HCO,H(A) appears similar to that in the molecular predissociation channel in H,CO(A); H,CO(A) + H2C0(k)vi,, + H,+CO (4) where the exit barrier height is nearly equal to EAVL.As with HC02H all the dynamics are determined in the exit channel and the initial state selection is not reflected in the final stat: distrib~tions.~~ (iii) A further conclusion concerning the nature of the HCO,H(A) PES in the transition-state region is that the 0-C-OH angle must be nearly linear. If it were not, substantial HCO rotational excitation would have been generated by the impulsive energy release in the exit channel. The highly selective nature of the energy redistribution in HCO,H(A) is intriguing: how is the energy initially deposited in the C=O stretch so effectively channelled into the reaction coordinate? To address this question it is helpful to understand the character of the initial vibronic motion on the A-state PES, as determined from the "0 isotopic experiments.Based on the values of me and oex, ( 1 107.5 and -7.3 cm-', respectively) derived from the frequencies of the 3," progression reported here and in ref. 12 and 21, and assuming pure local-mode behaviour, the calculated isotopic shift between C= l 6 0 and C="O for the 3: transition would be -122cm-'. In the absence of (0)H-atom migration in HC'80160H this excitation would lead exclusively to 160H fragments. The observed peak shifted by -85 cm-' in the 160H yield spectrum is consistent with C=O mode character, but it cannot be purely local in character. The peak in the "OH yieldM. Brouard, J. P. Simons and J.-X. Wang 1.4- ? 1.3- 2 1.2- 71 0.5 1 .o 1.5 rc-018, Fig. 6 Schematic diagram of the HCO,H(A) potential along the T ~ = ~ and rc-o stretching coordinat_es: 0, the Franck-Condon accessed region;*’ @, minimum-energy configuration jn HCO,H(A) as reported in ref.21; 0, the theoretically derived geometry of HC02H(A) reported by Moule and coworkers12 spectrum shifted by -37 cm-’ may then be assigned to the 3: transition in the isotopomer HC160180H. Clearly the two (nominal) C-0 stretching coordinates in formic acid cannot be equivalent because the species HC180160H and HC’60180H have different vibrational frequencies. If the two C-0 bonds were equivalent the two new features in the OH yield spectra would have to be assigned to symmetric and antisymmetric 0-C-0 stretching modes, but this assignment can be discarded as it implausibly requires both HC180160H and HC160180H to yield exclusively 160H or 180H products depending on which vibrational mode is excited.In conclusion, the initial vibrational motion following excitation to the A state PES of HC02H is neither purely local C=O stretching in character, nor are the-two C-0 bonds in HC02H( A) equivalent. The schematic potential-energy diagram shown in Fig. 6 helps clarify the character of this initial vibrational motion away from the Franck-Condon accessed region: it may be thought of as a ‘symmetric’ type motion primarily involving the ‘C=O’ group (i.e. $C=O motion; fC-OH motion). The ‘anti- symmetric’ mode v5 loosely characterised as the ‘C-OH’ stretching vibration, is not active in the absorption spectrum. The experiments with 180-enriched formic acid also eliminate an intramolecular H-atom mechanism, where passage across the barrier is promoted by H-atom transfer from the (vibrationally cold) C-OH moiety to the (vibrationally excited) C=O group.This is al%o sonsistent with the absence of activity of the 0-H stretching mode in the HCO,H(A-X) absorption spectrum, and with the quantum calculations of Iwata and Morokuma28 which indicate a barrier of CQ. 15 000 cm-’ to H-atom migration in each of the low-lying singlet and triplet (n + T* and T- T*) states of HC0,H. We are most grateful to Dr. J. O’Mahony, Mr. P. A. Enriquez and Mr. R. Mabbs for computational and experimental assistance, and to Profs. R. N. Zare and C. B. Moore and Drs. P. J. Sarre and 1. Powis for helpful discussions. J-X. Wang was supported by grants from the British Council and the People’s Republic of China.72 References Photodissociation Dynamics in Formic Acid 1 A.H. Zewail, Annu. Rev. Phys. Chem., 1990, 41, 15. 2 D. Imre, J. L. Kinsey, A. Sinha and J. Krenos, J. Phys. Chem., 1984, 88, 3956. 3 P. G. Wang, Y. P. Zhang, C. J. Ruggles and L. D. Ziegler, J. Chem. Phys., 1990, 92, 2806. 4 K. Q. Lao, M. D. Person, P. Xayariboun and L. J. Butler, J. Chem. Phys., 1990,92, 823. 5 C. P. Li, R. J. Lipert, J. Lobue, W. A. Chupka and S. D. Colson, Chem. Phys. Lett., 1988, 151, 325. 6 M. Brouard, M. T. Martinez, J. O’Mahony and J. P. Simons, Philos. Trans. R. SOC. London Ser. A, 7 R. N. Dixon, J. Chem. Phys., 1986, 85, 1866. 8 P. L. Houston, J. Phys. Chem., 1987, 91, 5388. 9 J. P. Simons, J. Phys. Chem., 1987, 91, 5378. 1990,332, 245. 10 T. Ebata, T. Amano and M. Ito, J. Chem. Phys., 1989,90, 112. 11 M. Brouard and J:O’Mahony, Chem. Phys. Lett., 1988, 149, 45. 12 F. Ioannoni, D. C. Moule and D. J. Clouthier, J. Phys. Chem., 1990, 94, 2290. 13 R. Vasudev, R. N. Zare and R. N. Dixon, J. Chem. Phys., 1984, 80, 4863. 14 G. W. King and D. Moule, Can. J. Chem., 1962,40,2057. 15 I. L. Chidsey and D. R. Crossley, J. Quantum Spectrosc. Radiat. Transfer, 1990, 23, 187. 16 P. J. H. Tjossen, P. M. Goodwin and T. A. Cool, J. Chem. Phys., 1986,84, 5334. 17 P. J. H. Tjossen, T. A. Cool, D. A. Webb and E. R. Grant, J. Chem. Phys., 1988, 88, 617. 18 e.g. M. N. R. Ashfold, J. M. Bayley and R. N. Dixon, Chem. Phys., 1984,84, 35. 19 D. L. Singleton, G. Paraskevopoulos and R. S. Irwin, J. Phys. Chem., 1990, 94, 695. 20 G. Hsing Kwei and R. F. Curl Jr., J. Chem. Phys., 1960, 32, 1592. 21 T. L. Ng and S. Bell, J. Mol. Spectrosc., 1974, 50, 166. 22 A. Ticktin and J. R. Huber, Chem. Phys. Lett., 1989, 156, 372. 23 M. Brouard, P. A. Enriquez, J. O’Mahony and J-X. Wang, unpublished work. 24 S. Hennig,X. Untch, R. Schinke, M. Nonella and J. R. Huber, Chem. Phys. Lett., 1989, 129, 93. 25 R. N. Dixon and H. Rieley, J. Chem. Phys., 1989, 91, 2308. 26 M. Nonella, J. R. Huber, A. Untch and R. Schinke, J. Chem. Phys., 1989,91, 194. 27 D. J. Bamford, S. V. Filseth, M. F. Foltz, J. W. Hepburn and C. B. Moore, J. Chem. Phys., 1985,82,3032. 28 S. Iwata and K. Morokuma, Theor. Chim. Acta, 1977, 44, 324. Paper 1/001011; Received 9th January, 1991

ISSN:0301-7249    

DOI:10.1039/DC9919100063

出版商:RSC    

年代:1991

数据来源: RSC

摘要:

Faraday Discuss. Chem. SOC., 1991,91, 73-78 Exchange Reactions of Hydrogen Atoms with SiD,: An Inversion Mechanism? Benjamin Katz Department of Chemistry, Ben Gurion University, Beersheba, Israel Jeunghee Park, Sunita Satyapa1,t Shintaro Tasaki, Arun Chattopadhyay, Whikun Yi and Richard Bersohn Department of Chemistry, Columbia University, New York, NY 10027, USA The reaction H + SiD4 -+ D + SiH3D is found to have a much lower threshold than the corresponding exchange reaction of H with CD4. The D atom carries away most of the initial translational energy of the H atom. When the H-atom velocity distribution is anisotropic, the D-atom velocity distribu- tion is anisotropic in the same sense. The exchange cross-sections for the reaction H + SiH3D are about one half of those for SiD,.All this evidence leads to the conclusion that the mechanism of the exchange is an inversion. Isotope-exchange reactions are interesting because of the near symmetry between reactants and products. The potential surface is symmetric, which reduces somewhat the labour of its construction. Reactions in which hydrogen-atom isotopes are substituted are of particular interest, again because the construction of a potential surface is made less formidable. The H+D, (or HD) reaction is of course the centrepiece of all hydrogen-atom exchange reactions. In addition to all of its other simplifications it has the advantage that abstraction and exchange are the same reactions. For all other hydrides there are always two possibilities, exchange and abstraction RD+H -+ RH+D ( 1 ) RD+H ---* R+HD (2) The exchange reactions H + MD4 -+ MHD3 + D are interesting from several points of view.First of all, at least part of an a6 initio potential surface has been constructed for the CH5 system'.' and this could, in principle, be done also for the SiH, system. Secondly, there already exist experimental data on isotopic variants of the CH5 system, namely T+ CH4 and T+ CD, .3 At thermal energies only abstraction could be observed. At a relative kinetic energy of 65 kcal mol-', the ratio of the cross-section for abstraction to that for exchange was 16 for T+CD, and 3 for T+CH,. At Euclear recoil energies (keV) the ratio was 0.8. The threshold energy for abstraction was 10 * 2 kcal mol-' and that for exchange was 35* 10 kcal mol-'. In the H+CD, reaction we have found by laser-induced fluorescence (LIF) weak D-atom signals at relative kinetic energies of 57 and 73 kcal mol-I.These experiments will be discussed in a later report. Bunker and c o ~ o r k e r s ~ , ~ devised a potential for the CH5 system which fitted the known bond energies and force constants. Using this potential they calculated and averaged over numerous classical trajectories for a number of values of relative kinetic energy. They found that the experimental cross-section ratios at the relative energy of 65 kcal mol-' could not be fitted unless more than three atoms were involved in the t Present address: Vassar College, Poughkeepsie, NY. 7374 Exchange Reactions of Silanes- Inversion ? exchange reaction. Inversion is therefore suggested.In contrast all exchange reactions of hydrogen isotopes so far observed in optically active molecules CHXYZ, where X, Y and Z are not hydrogen atoms, take place with retention of configuration. Because preliminary experiments produced only weak D-atom signals in the exchange reaction with CD,, we decided to try SiD, instead. It has longer bond lengths ( 1 . 4 8 ~ ~ . 1.08 A) and weaker bonds (92 vs. 99 kcal mol-*).6 The frequencies of SiH4 and CH, can be fitted using a central force model with a stretching force constant and two bending force constants.' In units of lo5 dyn cm-' the stretching force constant diminishes from 2.66 to 1.96 in going from CH, to SiH,. The bending force constants diminish from 0.60 to 0.22 and from -0.79 to -0.35 in the same units.In short, silane is a much looser and floppier molecule than the rigid methane. Because the hydrogen atoms are so much farther apart, during a collision with a fast atom, it should be much easier to change the shape of silane than methane. Experimental Our basic experiment is to generate H atoms by dissociating a suitable precursor with a pulsed laser and probing the H-atom reactant and the D-atom product by laser-induced fluorescence. The target molecule, in this case H2S, was dissociated by an excimer laser to produce H atoms of fairly well known energy. At a short time later, typically 70- 100 ns the probe laser was fired, producing 121.6 nm light which excited the hydrogen atoms. This technique has been described in previous papers from this lab~ratory.'~~ The 121.6 nm Lyman (Y light was generated by four-wave mixing in two different ways.In the early experiments this was done by frequency tripling, that is, by mixing three 364.8 nm photons in Kr to give a fourth wave at 121.6 nm. One exploits in this way the near resonance with the Kr absorption at 123.6 nm. Later a still more efficient method was used involving the mixing of two 212.56 nm photons and an 845 nm photon, both dye lasers having been pumped by the same XeCl excimer laser. The 212.56nm light is obtained by frequency-doubling 424.1 1 nm light in a barium metaborate crystal which was cut at such an angle that 212nm light entering normal to one face would have the maximum probability of being doubled. The energy of two 212.56 nm photons is exactly resonant with a g + g transition to the 5p[O1/2] state of Kr; by use of both resonances much more intense VUV is generated at the expense of added experimental complexity.Silane is transparent at both 248 and 193 nm and furthermore it was explicitly shown that no D-atom signals appeared when SiD, was irradiated in the absence of H2S. SiH3D was synthesized by reacting LiAlH, with SiC13D (obtained from Merck Isotopes) in ether." Just before an experiment the deuterated silane was frozen in liquid nitrogen and pumped on to remove any hydrogen which might have formed by reaction with traces of water. The results are all obtained from the LIF excitation curves of H and D atoms. Their peaks conveniently are 21 cm-' apart, far enough so the curves do not overlap and near enough so that the laser parameters remain constant during the sweep from one resonance to the other.The results are categorized as follows: (1) cross-section of H with SiD,, (2) cross-section s f H with SiH3D, (3) average kinetic energy of the D product and (4) alignment of the D-atom velocity when the H-atom velocity is aligned. Cross-sections for H + SiD, ---* SiDJH + D The rate constant k for the above reaction can be extracted from the rate equation: d(D)/dt = k(SiD,)(H) (3)B. Katz et al. 75 - 5 0 5 detuning wavenumber/ cm- ' - 4 - 2 0 2 4 detuning wavenumber/cm-' 2 4 Fig. 1 H-atom and D-atom fluorescence excitation spectra taken 100 ns after dissociation of H2S with polarized 193 nm light in the presence of SiD4. The heavy (light) lines are spectra taken with the E vector perpendicular (parallel) to the probe laser beam.The curves have been normalized to equal maximum amplitude whose solution at short times is (D)/(H) = k(SiD,)t (4) Fig. 1 shows typical LIF excitation curves for an H reactant and a D product. The H curve is nearly unchanged in times of the order of 500 ns whereas the much weaker D signal increases linearly with time. In eqn. (4) c is the time between the pump (dissociat- ing) and the probe pulses. In general a second-order rate constant is an average ( U(T( u ) ) , that is the product of the relative speed of the reactants times the cross-section averaged over the distribution of relative speeds. When one of the reactants is produced by a photodissociation and is much faster than the other, the distribution in relative transla- tional energies is much sharper than with thermal reactions.One can show' that the average relative translational energy is given by: and the mean-square fluctuation in Erel is76 Exchange Reactions of Silanes- Inversion ? Table 1 Relative translational energies and cross-sections for reactions of H atoms with deuterated silanes parent wavelength of average relative cross-section molecule dissociation/nm energyleV /A2 silane H2S 193.3 2.08 f 0.05 0.36 f 0.03 SiD4 H2S 193.3 2.07 f 0.05 0.17 f 0.03 SiH3D pi,j is the reduced mass of particles i andj, HX is the H-atom precursor and M is the species with which the H atom reacts. P is the momentum gained by the photodissoci- ation and is equal and opposite for the two fragments.The H atoms used in these experiments were generated by photodissociation of H2S" at 193.3 nm. At this wavelength only 63% of the SH radicals are in the v = 0 state, with a corresponding H-atom relative speed of 2.09 x lo6 cm s-l. The other SH radicals are in higher u states with lower speeds for their H-atom partners, but the average speed is 1.94 x lo6 cm s-l. The average relative energy under these conditions is listed in Table 1. The average relative energy was calculated from eqn. (5) and the uncertainties quoted are the square roots of the values calculated from eqn. (6). The rate constatnt for these H atoms was (0.70f0.07) x lo-'' molecule-' s-l. Dividing by the average speed we obtain a cross- section of 0.36 f 0.03 A'. We also found D signals when H2S was dissociated at 248 nm.Thus the potential barrier is less than 1 eV, the energy of these H atoms. Cross-sections for H + SiH3D -+ SiH4 + D The rate constant for the exchange of H with SiH3D under the same conditions as with SiD, is (0.33 f 0.03) x lo-'' molecule-' s-l. The corresponding cross-section is 0.17 f 0.03 A'. The main point is that the cross-section is more than one quarter of the corresponding cross-section for SiD,. Kinetic Energy of the Product D Atoms As described in the introduction, the kinetic energy is simply calculated from the second moment of the fluorescence excitation curve. How elastic is the exchange reaction? In other words, what fraction of the original kinetic energy of the reactant H atom is retained in the product D atom? At 193 nm we find that the average initial kinetic energy is 2.08 eV and the leaving D atom has a kinetic energy of 1.78 f 0.22 eV.Relatively little energy is left behind in the SiHD3 molecule. Alignment of D-Atom Velocities An H,D exchange reaction is very favourable for an angular distribution study because the laboratory and centre-of-mass velocities are negligibly different. Photodissociation with polarized light can generate an anisotropic velocity distribution of the reactant H atoms which has the form f(K,.> = 1 / 4 4 1 +PRP'(COS R , d (7) where Ou,E is the angle between the electric vector of the light wave and the velocity o of the H atom. PR is the anisotropy parameter for the alignment of the velocity of the reactant H. To obtain the distribution of velocity directions u' of the product D atoms, we must integrate over all initial directions of the reactant H atom using the addition theorem for Legendre polynomials with the result W'(C0S %,d = (P'(C0S @))P,(COS 0 u d (8)B.Katz et al. 77 The distribution function for the direction of the D-atom velocity is where pp = PR(P2(c0s 0)) is the product D anisotropy parameter and 0 is the angle between the velocity vectors t, and u'. The necessary conditions for anisotropy of the product D atom are that both the reactant velocity and the differential cross-section be anisotropic. By averaging over the distribution function of eqn. (7) or (9) one can show that the anisotropy parameters PR or pp can be extracted from the experimental fluorescence excitation curves (as shown in Fig.1): where 11 (I) means that the probing laser beam is parallel (perpendicular) to the E vector of the dissociating laser. For H2S at 193 nm the value -0.82 f 0.08 was obtained. When corrected for the 95% polarization of the light, this value agrees with the previously reported value of -0.96." For the SiD, exchange reaction the D atoms had an uncorrec- ted anisotropy parameter, pp = -0.72 f 0.35. Discussion What can we conclude about the mechanism of the reaction from the evidence? Does it take place by a direct substitution analogous to an s N 1 reaction in which the main players are the entering H atom and the Si and D atom of a Si-D bond? Or does it take place by an inversion analogous to an sN2 reaction in which the D atom departs from the side of the molecule opposite to the side which the H atom attacks? In the inversion every atom of the molecule plays a role.The angular dependence of the reaction cross-section implicit in the fact that ( P2( cos 0)) = 0.88 (+0.12 - 0.41) leads to a typical reactive scattering angle 0 = 16". The positive sign for the average means that the H and D velocity vectors are generally either parallel or antiparallel to each other. We believe that a direct localized attack of the H atom on an Si-D bond would cause the D atom to recoil at a fairly large angle, making ( P 2 ( 0 ) ) small or even negative. In an inversion both velocities are generally in the same direction. The fact that the typical angle is 16" rather than zero may be explained qualitatively by the fact that the silane molecule is rotating prior to the collision and that the reacting H atom does not have to be incident exactly along the threefold axis.The inversion mechanism is nicely consistent with but not completely proven by the alignment of the D-atom velocity. Evidence against a direct attack of an H on a C-D bond is given by the ratios of the cross-sections of H with CD4 and CD3H. These would be in the ratio of four to one for a direct attack. However, the actual ratios show that the H atoms make the C-D bond more susceptible to attack. This is easily understood in the inversion model because the three non-reacting hydrogen atoms have to move quickly during the collision to reach the presumed trigonal-bipyramidal transition state. If these three atoms are heavier with more inertia, it will take longer for the atoms to reach the transition state.In the meantime the attacking H atom may just bounce away. The fact that half of the incident H-atom energy is retained in the exiting D atom is also an argument for inversion. During an inversion bond angles have to change but only two bond distances are changed, the new one and the one which is broken. When these two bonds are opposite each other as in an inversion, the most efficient transfer of momentum and energy will take place. Indeed because the D atom has twice the mass of the H atom and half of its velocity, the momentum of the leaving D atom is about the same as that of the entering H atom.78 Exchange Reactions of Silanes-Inversion ? On the basis of the above evidence the inversion mechanism seems to be the most natural explanation.Trajectory calculations which fit the many data given here should be helpful in obtaining a potential which will discriminate between inversion and direct attack mechanisms. The following simple model gives an overall picture of the reactive collisions between a hydrogen atom and silane. The forces between a hydrogen atom, all of whose electrostatic moments are zero, and silane, whose lowest non-zero moment is an octupole moment, are very short range. Therefore the fast incident H atom can be thought of as attacking a nearly stationary silane which is not reoriented before the collision. The collisions can be divided into three types, those for which the H, D and Si atoms are nearly collinear, those for which the H atom is directed to or near to the Si atom, i.e.opposite to an Si-D bond, and those collisions with a substantial impact parameter relative to the Si atom. The first type are well suited to transfer energy from the incident H atom to the weaker Si-D bond, forming HD molecules with low rotational energy. The second type result in the exchange reaction and the third type cause non-reactive inelastic processes in which rotations and bending vibrations of the silane are excited. This model can certainly be tested by probing the HD molecules formed by abstraction. Finally, we give some more chemical explanations of the mechanism. The force constants previously quoted show that silane offers considerable resistance to bond- length changes but very little to bond-angle changes.The inversion mechanism involves bond angle changes but no bond length changes of the non-reacting silicon-hydrogen bonds. It therefore should have a lower barrier to reaction than other mechanisms. Also because the high-frequency stretches (except for those of the newly made and newly broken bonds) are unaffected by the reaction, less vibrational energy should be released in the molecular product. The briefest explanation for the large difference in barriers to exchange between CH4 and SiD, is that the Si atom, being a second-row element requires much less energy to expand its valence shell, becoming pentavalent or even hexavalent. But even this explanation implies an inversion mechanism. The counter argument is that the Si-D bond being much weaker than the C-D bond is much more readily exchangeable.We conclude that at the energies used here exchange takes place by inversion. This research was supported by the U.S. National Science Foundation and the Petroleum Research Fund. Note added in proof: Maitre and Pellissier (Chem. Phys. Lett., 1990, 166, 49) used an ab initio study to show that SiH5 is not a stable radical but rather dissociates spon- taneously into H + SiH,. The calculation of a potential-energy surface at CASSCF level showed also that the transition state is of D3h geometry. References 1 K. Morokuma and R. E. Davis, J. Am. Chem. SOC., 1972, 94, 1060. 2 G. C. Schatz, S. P. Walch and A. F. Wagner, J. Chem. Phys., 1980, 73, 4536. 3 C. C. Chou and F. S. Rowland, J. Chem. Phys., 1969, 50, 2763; 5133. 4 D. L. Bunker and M. D. Pettengill, J. Chem. Phys., 1970, 53, 3041 5 T. Valencich and D. L. Bunker, J. Chem. Phys., 1974, 61, 21. 6 P. Ho, M. F. Coltrin, J. S. Buckley and C. F. Melius, J. Phys. Chem., 1986, 90, 3379. 7 G. Herzberg, infrared and Raman Spectra of Polyatomic Molecules, D. Van Nostrand, New York, 1945, 8 G. W. Johnston, S. Satyapal, R. Bersohn and B. Katz, J. Chem. Phys., 1990, 62, 2065. 9 G. W. Johnston, J. Park, S. Satyapal, N. Shafer, K. Tsukiyama, R. Bersohn and B. Katz, Acc. Chem. Res., 1990, 23, 232. 10 A. E. Finholt, A. C. Bond, K. E. Wilzbach and H. I. Schlesinger, J. Am. Chern. SOC., 1947, 69, 2692. 1 1 X. Xie, L. Schnieder, H. Wallmeier, R. Boettner, K. H. Welge and M. N. R. Ashfold, J. Chem. Phys., 1990, 92, 1608. Paper 0/05727D; Received 19th December, 1990 p. 167.

ISSN:0301-7249    

DOI:10.1039/DC9919100073

出版商:RSC    

年代:1991

数据来源: RSC

摘要:

Faraday Discuss. Chem. SOC., 1991, 91, 79-90 Product Rotational Alignment for the Reaction o(3~) + cs(x lz+) + co(x I,+) + s(3~) Finn Green, Graham Hancock” and Andrew J. Orr-Ewing Physical Chemistry Laboratory, Oxford University, South Parks Road, Oxford OXI3QZ, UK Rotational alignment of the CO(X ‘C+, u ’ = 14) product of the O(3P)+ CS(X ‘E+) reaction has been measured relative to the velocity vector k of the reagents. O(3P) atoms were produced with k aligned in the laboratory frame by pulsed laser photolysis of NOz, and the CO product was detected by polarised laser-induced fluorescence. Transformation of the measured laboratory-frame rotational alignments to the required values of the align- ment parameter (P,(J‘ * k)) were carried out using previously determined values of the translational anisotropy for the photodissociation of NO2, making allowances for both the thermal distribution of CS radicals and the spread of recoil energies of the 0-atom fragment.Values of (P2(J’ - k)) were measured for J ’ between 12 and 35, and found to be close to zero to within the range 0 f 0.25, with the mean value being slightly positive. Measurements of the Doppler profiles of the transitions are in qualitative agreement with those predicted for an isotropic distribution of product velocities about the k direction. These preliminary results illustrate the scope of laser based methods of extracting quantum-state-resolved data on scattering dynamics under experimental conditions which do not involve the use of molecular beam methods. Since the first crossed molecular beam experiments were carried out in the mid-l95Os,’ reaction dynamicists have been interested in the vector properties of the outcome of a chemical reaction, as well as the scalar attributes of the distribution of energy in the degrees of freedom of the products.The first vector correlations to be measured were between k and k’, the relative velocity vectors of reagents and products, and gave rise, for example, to the now commonplace terms of forward and backward scattering. As more vector correlations have become amenable to experimental study, the field has matured, been the subject of two recent symposia,233 and has been comprehensively r e ~ i e w e d . ~ - ~ This report describes laser-based measurements of the correlation between the relative velocity vector k of reagents in an atom-exchange reaction, and the rotational angular momentum J’ of the diatomic product.Correlations of this kind are normally observed in systems which possess cylindrical symmetry about a laboratory axis (which might be, for example, the axis of the velocity vector k ) , and are described in terms of expectation values of Legendre polynomials (P,,(J’ k ) ) , with odd and even values of n relating to ‘oriented’ and ‘aligned’ populations, re~pectively.~” Experimental condi- tions normally result in the production of aligned products only, and yield measurements of (P,(J’ k ) ) , reflecting the quadrupole moment of the J‘ vectors about k. Alignments of this kind in reaction products have been measured by molecular beam deflection methods,8-10 by observation of the polarisation of fluorescence from electronically excited products,831 ‘-19 and by laser-induced fluorescence (LIF) probing of the ground-state species.20 The last method has found wide use in photodissociation processes, where correlations between J’ and k’, the fragment velocity vector, have been measured, and 7980 Product Rotational Alignment for O(3P) + CS(X 'E+) the mutual correlations of these vectors to p, the transition dipole in the parent molecule, have been exp10red.~-~ For collisional processes the LIF technique also has the potential, via Doppler profile measurements of the products' recoil velocity distribution, of providing insight into the ways in which k, k' and J' are mutually related.Such 'multiple vector correlations' are still in their infancy, but examples are emerging from both collisional reactions' ' and energy-transfer2' processes.Laboratory-frame measurement of product rotational alignment by LIF is now a straightforward task under the condition of axially symmetric reagent preparation, thanks to the 'experimentally friendly' description of the procedures in the literat~re.~ In previous studies of J',k correlations in reactive processes, the alignment has been referenced to the laboratory-frame velocity vector of the reactants when the latter is defined by crossed molecular beam9-" or by beam-gas12-20 collisions. An alternative method of reagent velocity selection has been used in the present study, namely laser photolysis of a suitable precursor molecule whose product velocity distribution relative to the polarisation vector of the photolysis laser is known.Time-resolved LIF detection of the reaction products is then used to measure the J', k correlation and, via Doppler profile measurements, to explore if k' is related to k. The technique is simply the vector extension of the method used in many previous studies of the scalar properties of reaction dynamics,22 has been used previously, in studies of the 0 + HC123" and H + 0,236 reactions, and is under investigation in the O( ID) + N20 The technique is not without its difficulties, as the photodissociation process will inherently yield a velocity distribution which, although well defined, will be less anisotropic, and possibly less monochromatic, than those produced by molecular beam methods.The effect of the velocity distribution is to place a reduction on the limits expected for the alignment, but these limits, as will be shown below, are still within experimental observation. The reaction studied is the atom-exchange process, o ( ~ P ) + CS(X IZ+) -, CO(X lz+) + q3p) ( 1 ) Previous work has shown that a high degree of the reaction exothermicity is channelled into product vibration through attractive energy release before the nascent CO bond reaches its equilibrium ~ a l u e . ~ ~ - ~ ' These highly energetic products (the vibrational population peaks at v' = 13) can be detected by LIF of the CO A 'n-X 'Z+ transition, using excitation wavelengths [for example the (6, 14) band at 220 nm], which can be straightforwardly generated by standard dye laser systems.The fluorescence is anti- Stokes shifted [e.g. the ( 6 , l ) band lies at 140.9 nm] into the vacuum UV region, and can thus be observed by a solar-blind photomultiplier in a highly sensitive and noise-free fashion.32 An added advantage for alignment measurements in CO is that the 'X+ state possesses only rotational angular momentum, and degradation of the alignment by coupling to electronic and nuclear momenta (as occurs for example in ground-state OH and NO) is avoided.33 Velocity alignment of the O(3P) reagent is achieved by laser photolysis of NO2 at 355 nm. The alignment in the laboratory frame is described by the translational anisotropy parameter p, defined by the expression for the intensity distribution o( 8) of fragments scattered at angle 8 between the electric vector &ph of the photolysis beam, and k, the fragment's relative velocity vector where cos 8 is the scalar product k 'Eph, and N is a normalisation factor.For NO2, p has been measured as between 0.9 and 0.46 for this wavelength r e g i o r ~ , ~ ~ - ~ ~ some way from its limiting values of 2 and -1 (the limits which would occur for prompt dissociation of a linear molecule). The 0-atom distribution of kinetic energies is also not ideal (i.e. not 'monochromatic'), the photolysis at 347 nm showing two peaks corresponding toF. Green, G. Hancock and A. J. Orr-Ewing Nd:YAG laser 81 I 1 I L r Fig. 1 Schematic diagram of the experimental arrangement. NOz was photolysed at 355 nm using horizontally polarised radiation (E,,, in the plane of the diagram). CO was probed using both horizontally and vertically probed radiation, and LIF was detected by a solar-blind photomultiplier viewing fluorescence emitted in the direction perpendicular to the plane of the diagram the formation of NO( v = 0) and ( v = 1 ) with mean 0-atom kinetic energies of 25 and 12.5 kJ mol-’, respectively.These values still largely define k, as the velocities of the CS reagent (formed thermalised by a microwave discharge in CS2) are an order of magnitude smaller. All these smearing effects, however, can be accounted for and used to predict the range of alignment parameters expected from the reaction dynamics. Many previous studies of J‘, k, correlations have observed the effects of kinematic constraints in reactions in which a light atom is formed in an A+BC In such cases, angular momenta in reagents and products are dominated by orbital ( L ) and rotational ( J ’ ) values respectively, and thus in this limit k (which is perpendicular to L ) is perpendicular to J’.Reaction ( 1 ) is not such a limiting case, and although under such conditions alignment affects are expected to be less pronounced, they should be far more sensitive to the details of the potential-energy surface.6 No ab initio calculations for such a surface exist for reaction ( l ) , but classical trajectories on a surface derived from MNDO/CI calculations have reproduced the vibrational energy distribu- tion, and predicted the rotational energy partitioning and some degree of angular scattering for thermalized (300 K) reagents.” We present below our first measurements of the alignment of CO formed by reaction (1) in one vibrational level, u’= 14, together with preliminary data on the Doppler linewidths. These results suggest that the distributions both of J’ and k’ relative to k are close to isotropic.Nascent rotational distributions in CO have also been determined for u’ = 12 and 14. The results show that for thermal reagents the fraction of the available energy appearing in rotation, f r , is considerably lower than that for translation, f t . However, the ratio fr/ft increases markedly for the translationally hot 0 atoms produced by photodissociation of NO2, indicating an efficient conversion of this energy into rotation of the CO product.Details of these results, and of their comparisons with trajectory calculations on a LEPS surface, will be published e l ~ e w h e r e . ~ ~ Experimental Fig. 1 shows the experimental arrangement. CS radicals were formed by a low-power microwave discharge in a flow of CS, at a pressure of ca. 1 Torr, and admitted to the reaction vessel through a pinhole. The distribution of the internal states of CS was82 Product Rotational Alignment for O(3P) + CS( X ‘Z+) measured as Boltzmann at 300 K by LIF observations of the A ‘II-X ‘X+ transition. An approximately equal flow of NO2 was added to make the total pressure (as measured at the centre of the reaction vessel by a Penning gauge) between 5 x Torr, maintained by a partially throttled 700 dm3 s-’ diffusion pump. NO2 was photolysed at 355 nm by the frequency-tripled output from an Nd3+ YAG laser (JK System 2000).The output was horizontally polarized and apertured to give a beam of 2 mm diameter at a fluence of CQ. 0.1 J cm-2 at the centre of the cell. CO was detected by LIF of the (6,14) band near 220 nm, the radiation being generated by a frequency-doubled excimer pumped dye laser (Lambda Physik DL 3000). The dye laser output was reduced to ca. 100 p J per pulse, and expanded to a diameter of 6 mm before passing into the reaction vessel collinearly with the 355 nm beam at a time delay of 1 ps from the firing of the latter. The dye laser polarisation was controlled by a KD*P Pockels cell, and was switched between horizontal and vertical polarizations for a preset number of laser shots before the dye laser was stepped to a new wavelength position.The dye laser bandwidth was 0.4cm-’ for the alignment scans, and reduced to 0.04cm-’ by means of an etalon for the Doppler profile measurements. Fluorescence was detected by a solar-blind photomultiplier (EM1 Gemcon G-26E3 14LF) perpendicular to the laser beams’ axis, and the collection of the data, firing of the lasers, and the stepping of the dye laser wavelength were controlled by a microcomputer (IBM PC XT). Laser energies were stored for each shot and used for data normalisation. and At the combination of total pressures and delay times between the two lasers, a nascent CO molecule formed immediately following firing of the photolysis laser has a probability of between 10 and 20% of undergoing a gas-kinetic collision, with these probabilities reduced for molecules formed at later times.Population ratios, alignments and Doppler profiles were invariant with pressure in this narrow range: lower pressures and delay times produced inadequate signal-to-noise ratios. The most compelling evidence that the data collected under the collisions are not substantially affected by collisional processes, comes from the observation of Doppler lineshapes, in which (as discussed below) velocity distributions were observed corresponding to the full release of kinetic energy from the reaction. The combination of pressure and delay time is similar to that used in previous studies of pump and probe dynamics.22 Care was taken to ensure that both the photolysis and probe lasers did not saturate the NO, and CO transitions, respectively, and LIF signals were measured to be linear with laser power in both cases over the range of energies used.The probe laser beam was deliberately expanded to be larger in diameter than the photolysis beam to ensure that nascent reactants were not able to fly out of the detection volume during the 1 ps delay betwen photolysis and probe lasers. Fig. 2 shows part of the LIF excitation spectrum of the nascent CO near 220nm, with the wavelength positions marked for P, Q and R branches in the (6, 14) band of the A ‘ll-X ‘Z+ transition. Rotational populations peak around J’ = 25, in marked contrast to the far lower rotational excitation found in the reaction of thermal (300 K) reagents.” The raw data for the determination of CO alignment were obtained by scanning the dye laser (0.4 cm-’ bandwidth) over a non-overlapped line and measuring at each dye laser wavelength the LIF signal for both horizontal and vertical polarisations of the probe laser (corresponding to the electric vector of the probe laser E~~ parallel and perpendicular to that of the photolysis laser, &ph, respectively).In principle the ratio of these intensities, integrated over the complete lineshape, can be related to (P,(J’ Eph)), where the reference direction is taken as the (horizontal) electric vector &,h of the photolysis laser.’ In practice it was found that the ratios of the signals for the probe laser horizontal ( E ~ ~ 1) &ph) and vertical (&pr I Eph) were greater than unity forE Green, G.Hancock and A. J. Orr-Ewing Pc 30 3 32 33 36 35 36 27 28 (2,. 22 23 24 25 26 . 16 I 220.2 17 ii 1.3 19 1 2 20 n 2 .4 22 ?11 220.6 83 A/nm Fig. 2 Part of the LIF excitation spectrum of CO(X ‘X+, u’ = 14) formed in the 0 + CS reaction. The positions of P- Q- and R-branch lines in the A ‘n-X ‘X+(6,14) band are marked. 0 atoms formed from NOz photolysis at 355 nm, CS radicals produced by microwave discharge of CS2 both Q branch and P or R branch measurements, although the values of the ratios were different in the two cases. It appears that our excitation and detection system was more sensitive for horizontal than vertically polarised probe light. Careful checks were made to ensure that the laser beam energy measurements were not polarisation sensitive, that the shape of the probe beam did not change position markedly with polarisation, that the Pockels cell switching resulted in full polarisation rotation of the beam, and that the response to the solar-blind photomultiplier was not polarisation sensitive. Small changes in the intensity distribution over the beam profile may have been responsible for these effects, and they were allowed for in the following way.A ratio of signals for horizontally and vertically polarized probe light was measured for Q-branch excitation, QH/ Qv. The dye laser wavelength was then moved to the corresponding P- or R-branch line, and the ratio, P, RH/P, R,, measured. The ratios of these two measurements S = ( QH/ Qv)/( P, RH/ P, R,) were then taken as the raw data.The same procedure was carried out for an isotropic distribution of thermal NO excited in the A 211-X 2C+ (0,O) band near 226nm, and the ratios S measured agreed within experimental error to the (non-unity) values predicted theoretically’ for the present excitation geometry. Table 1 lists the raw data for CO as a function of J’, with the values indicating the extent of the reproducibility of measurements carried out over a period of several weeks. With the dye laser narrowed to a bandwidth of 0.04 cm-’, line profiles were measured for J’=4,17 and 28 in the (6, 14) band. The experimental geometry has so far only allowed these profiles to be measured in one configuration, namely with the probe laser propagation axis perpendicular to Eph (see Fig.1). Fig. 3 shows the profiles of the Q(4) and Q( 17) lines taken with E~~ parallel to Eph (the data for epr perpendicular to &ph were almost identical, but showed ca. 10% narrower linewidths), and the expected trend of increasing linewidth with decreasing J’ was observed. Measurements of the profiles for the reaction between thermal 0 atoms and CS at low pressures showed considerably84 Product Rotational Alignment for O(3P) + CS(X '2+) I 1 I -0.4 -0.2 0 0.2 0.4 displacement from line centre/cm-' Fig. 3 Measured Doppler profiles of the Q(4) and Q( 17) lines in the CO A'II-X 'V (6,14) band. The experimental arrangement was such that the propagation vector of the probe laser was perpendicular to the electric vector of the NOz photolysis laser &ph, and thus perpendicular to the most probable value of k, the 0-atom velocity vector. The solid lines show calculated Doppler profiles for an isotropic distribution of the CO product velocities k' about k as explained in the text lower translational excitation, and for measurements taken at high pressure (200 mTorr Ar added to the system) and long delays (100 ps), the expected room-temperature Doppler profiles were recorded.Discussion We first note the magnitudes of the ratios of polarisations S ( J ' ) listed in Table 1. An isotropic distribution of CO molecules will produces values of S ( J ' ) which are not unity, and these are shown in Table 1 to be close to those experimentally observed. ToF. Green, G. Hancock and A. J. Orr-Ewing 85 Table 1. Values of the parameter S for different values of J ‘ for excitation of CO(u’= 14) pro- duced in reaction (1) 12 1.44 17 1.29, 1.24, 1.27, 1.45 18 1.18 23 1.40, 1.50 24 1.22, 1.36 26 1.40, 1.01, 1.42, 1.13 29 1.24, 1.24 32 1.57 35 1.34, 1.51 1.24 1.25 1.25 1.25 1.25 1.26 1.25 1.26 1.26 S is defined as the ratio (QH/QV)/ (P, RH/ P, Rv), where the QH and Qv are signals for Q-line excitation with the probe beam horizontally and vertically polarised respec- tively, and P, RH and P, Rv are the correspond- ing signals for the P- or R-branch line.Also listed are the values of Siso expected for an isotropic distribution of CO. v c - 0 V 8 0 0 0 B 0 0 - 0.54 0 I I I 0 10 20 30 c J ’ Fig. 4 Values of the alignment parameter (P2(J‘ k)) as a function of J’ for CO(X ‘X+, u’ = 14) formed in the 0 + CS reaction.k was defined by polarised laser dissociation of NO2 at 355 nm, and the values of (P2(J‘ . k)) were calculated from the measured alignments in the laboratory frame by the formulae given in the text and in the Appendix. The limits of alignment + 1 (J’ 1) k and -0.5 (J’ I k) are shown. The data points at each J’ have not been averaged and their scatter gives an indication of the limits of precision of the measurements. To within these limits (ca. *0.25) the alignment is seen to be zero86 Product Rotational Alignment for O(3P) + CS(X ‘X+) see if this implies that k and J’ are not correlated we first need to make estimates of the range of alignment parameters that might be expected experimentally. In the following analysis we assume that the measured polarisation is sensitive only to the even multipole moments of the alignments of J’ along the chosen symmetry axis (the horizontal axis in the laboratory which coincides with &ph),7 we neglect the contribu- tion of the hexadecapole moment in comparison with the quadrupole moment of J’ relative to &ph,7’20’40 and we assume that the angular distributions of products are sampled with equal probability’ (in these measurements the laser bandwidth exceeded the experimental linewidth).With these restrictions we first convert the measured polarisa- tions to the quadrupole alignment (P,(J’ &ph)) using the formalism given by Greene and Z a ~ e . ~ To relate these values to the alignment of J’ with k we use the azimuthally averaged addition t h e ~ r e m ~ ” ~ (P2(J’ .Eph)) = (P2(J’ k))(P2(k &ph)) (2) We thus need to calculate the value of( P,(k Eph)), which applies to the photodissociation of NO, in our experiment. For a single-photon process, the probability w ( k , E p h ) of finding vectors k and &ph related by their scalar product is o ( k , &ph) = “1 + PP2(k &ph)l (3 1 where p is the translational anisotropy factor. A comparison of the expansion of o(k, &ph) in terms of Legendre polynomials with eqn. (3) yields the identity i.e. (P,(J‘ & p h ) ) = $ ( P , ( J ’ k ) ) . (4) The term & represents the smearing of the alignment of J’ with k when reagents are produced by photodissociation with an angular distribution described by the parameter p (-1 d /3 2) and with a single value of the recoil speed.A further smearing occurs due to ( a ) the 0 atoms interacting with a set of thermally distributed CS radicals and (b) the 0 atoms produced from the 355 nm photolysis of NO, not being mononergetic. Appendix 1 outlines the way in which this changes p in eqn. (4) to an effective value PeFf. The smearing due to ( a ) is calculated to be 3-4% when 0 atoms are given the mean velocity of those produced by photolysis at 348 nm,34 confirming the intuitive view that thermal motion in the heavier CS reagent has little effect on the dynamics of reaction with ‘hot’ 0 atoms. The effect of the distribution of energies for 0 atoms was treated similarly: the combined effects yielded a value of Peff that was ca. 0.9p. Three sets of measurements appear in the literature of the translational anisotropy of fragments in the photolysis of NO, at wavelengths between 347 and 349 nm.34-37 The values of p range from 0.7 to 0.9 for the NO co-product formed in v = 0, and from 0.46 to 0.6 for NO ( v = 1).Photolysis at 355 nm has been studied only for the v = 1 fragment, where the p value was unchanged from that at 34811m.~~ At 347nm approximately equal amounts of NO in the two vibrational levels are formed,34 and if we assume this will be true also at 355 nm then an average value of p over v = 0 and 1 from all these studies can be taken to be 0.65. If we now take the value of Peff = 0.9 p, this results in the values of (P2(J’ k ) ) from eqn. (4) being ca. nine times larger than the (P,(J‘ &ph)) values derived from the experimental measurements.( P2(J’ k)) lie within the limits +1 (J’ 11 k) and -0.5 (J’ I k), and thus the (P2(J’ &ph)) values are constrained by this factor of p/5, so that experimental errors in the determination of the laboratory-frame alignment will be amplified when this is transformed to the alignment about k. Fig. 4 shows the values of ( P2(J k)) calculated from the data of Table 1 and using Peff = 0.58, with the limits of +1 and -0.5 shown. The figure shows that the precision of the derived values of (P2(J’ k)) indicated by the scatter of the data for different experiments at theF. Green, G. Hancock and A. J. Orr-Ewing 87 same J’ is quite low (ca. * 0.25), but that there is no marked trend with J‘, and that the majority (>70%) of the values lie within k0.25 of zero (all the values with two exceptions lie in the range 0.4 to -0.2).The average value of (P2(J’ k ) ) is > O , but care should be taken not to overinterpret this fact in the light of the experimental uncertainties in the data. We conclude that the alignment parameters are far from their limiting values, and our experiment is unable to distinguish their mean value from that expected for an isotropic distribution, i.e. there is no clear J’, k correlation. Before we discuss possible reasons for this, we note the limits of uncertainty in the data imposed by the photolytic method of 0-atom production. The value of 0 = 0.65 is a factor of three lower than that expected for prompt dissociation of a linear molecule in a parallel transition. Had such a convenient source of O(’P) been available to us the precision of the derived values of (P2(J’ k ) ) would have increased by a factor of three.Although this would still not have produced as aligned a source of 0 atoms as in an atomic beam, it illustrates that useful data can be extracted from photolytic preparation of reagents, and that the present 0-atom source is regrettably not the most suitable for high-precision studies. Previous studies of vector correlations in reaction dynamics have shown that for cases in which there is no obvious kinematic constraint ( i e . where a light atom is not a reactant or product) values of (P2(J’ k ) ) lie in the range -(0.1-0.3),9~10~15916~20 less aligned than the kinematically constrained limit of -0.5. In the present reaction both the reagent orbital angular momentum L and the CS rotational angular momentum J are of the same order of magnitude (from the measured rate constant26 ILI can be estimated as 10 h, and the most probable value of (JI for CS at 300 K is 1 1 h ) and thus the initial total angular momentum is less well defined than in the constrained systems.We have carried out trajectory calculations on a LEPS surface which reproduces the product vibrational d i ~ t r i b u t i o n . ~ ~ Values of (P2(J’ k ) ) were found to be markedly negative (ca. -0.35) in contrast to the experimental results, and this may well reflect the colinear lowest-energy path that this surface favours. A bent transition state has been invoked to explain the results of the O+ HCl where a lack of correlation was observed between J’ and both k and the alignment of the reactant molecular axis.Although a linear geometry has been calculated for the transition state for reaction on the lowest OCS38 triplet surface, the influence of bent geometries may be of increasing importance at high reagent kinetic energies where we find a larger proportion of the available energy appearing in product rotation than for thermal 0 + CS reagents. Trajectories on the OCS triplet surface have shown that there is no pronounced purely forward or backward scattering or products at the present values of the reagents’ kinetic energies.38 Information from the Doppler profiles can in principle be used to provide some indication of the correlation between reactant and product velocity vectors, i.e.the differential cro~s-section,~~ and methods of extraction of data from such systems have been described in the l i t e r a t ~ r e . ~ ~ Fig. 3 shows preliminary data on the profiles of two lines in the (6, 14) band, each taken with the single experimental configuration of the probe laser’s propagation vector perpendicular to &ph (and hence perpendicular to the most probable velocity vector k ) . The data need to be improved in S I N ratio before quantitative information can be extracted from the profiles, and here we consider only what the predicted lineshape would be if CO was formed in the limiting case of its velocity k’ being isotropically distributed about k. Along a given direction (for example the probe beam’s propagation axis z ) the CO velocity component takes the simple form P( v , ) = 2 n j up( u ) du where p ( v ) is the (isotropic) speed distribution of the CO molecules.For a monoenergetic distribution at a speed vo this predicts a ‘top-hat’ profile centred at frequency vo with width 2 ~ ~ 2 1 ~ / c . In Fig. 3 the profiles are calculated using a p ( u ) function which reflects m I U I I88 Product Rotational Alignment for O(3P) + CS(X ‘Z+) the energy available for partitioning into translation due to the exothermicity of the process o(~P,) + cs( ‘z+) -+ co(x ‘z+, U’ = 14, J ’ ) + s(~P,) calculated from the AH: value43 together with the kinetic energy distribution in 0 atoms as measured by Busch and Wilson.34 The latter contribution to p ( v ) does not change the Doppler profile markedly from the ‘top-hat’ shape and when this is convoluted with the dye laser profile, this simple prediction is seen to fit the data tolerably well.The observed shapes certainly indicate that there is no strong preference for the velocity vector of CO to lie parallel (forward or backward scattering) or perpendicular (sideways scattering) to k. Conclusions For the O+CS reaction, no alignment of the rotational angular momentum J’ in CO( v’ = 14) relative to the velocity vector k of the reagents could be discerned within the experimental precision offered by the photolysis method of production of 0 atoms. Values of (P2( J’ - k)) lay between -0.2 and 0.4 with the majority in the region *0.25, the limit of the experimental precision. Analysis of the Doppler lineshapes shows that a simple model of isotropic scattering gives at least qualitative agreement with the results.For this particular range of reagent and product energies there appears to be little correlation between k and either J‘ or k‘. The results and analysis presented in this paper are clearly preliminary, but illustrate the potential of the purely laser based methods of studying alignment relative to the initial velocity vector of the reagents in a chemical reaction. Future experiments with improved data collection times, with varying laser polarisations and with different 0-atom sources are planned in order to put the present conclusions on a more quantitative basis. Appendix To calculate the effect of a thermal distribution of CS radical velocities on the transla- tional anisotropy p we first assume a singZe recoil speed uo for the 0 atom produced by NO2 photolysis, ie.the velocity distribution takes the form p ( U ) du = N [ 1 + pP2( u Eph)]6( u - UO) du where 6( u - u,) is a Dirac S function. The distribution of relative velocities u thus takes the form of a modified Maxwell-Boltzmann distribution 1 p ( q u ) do = {exp -( u - ~ ) ~ / 2 u * ] du u3(2 p2 where u2 = k,T/m. To obtain the full distribution of relative velocities, p ( u , u ) must be integrated over all values of the velocity u (remembering that this integration is now only over the angular part of u, as we assume lul= uo is a constant): This integral takes the form1 .o 0.8 0.6 0.4 0.2 0.0 Q. 3 6 NO(v=I) NO(V-0) E Green, G. Hancock and A. J. Orr-Ewing 89 D Fig.5 Values of the ratio of the effective anisotropy factor, Peff, to the measured value, P, for the 0 + CS system as a function of the relative velocity of the reactants. Marked on the x axis are the values of the 0-atom velocities for the photolysis of NOz at 347 nm forming NO( o = 0) and NO( o = 1) fragments. The value of Peff varies by only 3-4% over the range of relative velocities expected from 0 atoms produced with NO( u = 0) and NO( u = 1) cofragments. Peff = 0.9 /3 rep- resents the smearing of the translational anisotropy over all reasonable 0-atom velocities. P was taken as 0.65 (see text) resulting in Peff = 0.58 where 8, is the angle between o and &ph, and the I , / 2 , 5 / 2 are modified spherical Bessel functions. Allowance is made for a spread in the oxygen-atom speeds, caused by the internal excitation of the NO cofragment, by numerical integration over a distribution of speeds estimated from the time-of-flight data of Busch and Wil~on,’~ using Monte Carlo techniques.It was necessary to resort to numerical integration because the analytical form of the integral for a Gaussian distribution of speeds proved intractable. A fit of the resulting data points to a general Legendre expansion yielded an expression contain- ing only zeroth- and second-order terms, from which Peff, corrected for the oxygen atom speed distribution, can be deduced. From the functional form of Peff it is apparent that the separation of the distribution of relative velocities into angular and speed terms is not complete.Calculations of the variation of Peff with v are shown in Fig. 5 and demonstrate that for all but low values of v, Peff is close to its limiting value, and essentially constant. Marked in the figure are the average relative velocities for oxygen atoms formed with NO( v = 0) and NO( v = l ) , showing that for the purposes of our experiment, we can assume a constant value of Peff. The calculation illustrates the limitations of this experimental method as the speed of the photofragment approaches the mean speed of the thermal gas (i.e. as v approaches zero). We are grateful to Dr. N. J. B. Green for help with the calculation of the Peff values and to Prof. J. P. Simons and Dr. M. Brouard for valuable discussions. The research90 Product Rotational Alignment for O(3P) + CS(X 'Z+) reported herein has been sponsored in part by the United States Army through its European Research Office. We are grateful to the SERC for a maintenance grant (A.J.0-E.).References 1 E. H. Taylor and S. Datz, J. Chem. Phys., 1955, 23, 1711. 2 Dynamical Stereochemistry, Jerusalem, 1986, J. Phys. Chem., 1987, 91, 5365-5509. 3 Orientation and Polarisation Effects in Reactive Collisions, Bad Honnef, 1988, J. Chem. SOC., Furuduy 4 J. P. Simons, J. Phys. Chem., 1987, 91, 5378. 5 G. E. Hall and P. L. Houston, Annu. Rev. Phys. Chem., 1989, 40, 375. 6 J. P. Simons, in Selectivity in Chemical Reactions, ed. J. C. Whitehead, Kluwer Academic Publishers, 7 C. H. Greene and R. N. Zare, J. Chem. Phys., 1983, 78, 6741. 8 D. R. Herschbach, Furuduy Discuss.Chem. SOC., 1973, 55, 233. 9 C. Maltz, N. D. Wienstein and D. R. Herschbach, Mol. Phys., 1972, 24, 133; D. S. Y. Hsu, N. D. Wienstein and D. R. Herschbach, Mol. Phys., 1975, 29, 257. 10 D. S. Y. Hsu, G. M. McClelland and D. R. Herschbach, J. Chem. Phys., 1974, 61, 4927. 11 S. Stolte, H. Jalink, D. Parker and G. Nicholason, J. Chem. SOC., Furuduy Trans. 2, 1989, 85, 1115. 12 K. Johnson, J. P. Simons, P. A. Smith, C. Washington and A. Kvaran, Mol. Phys., 1986, 57, 255. 13 M. S. DeVries, G. W. Tyndall, C. L. Cobb and R. M. Martin, J. Chem. Phys., 1986, 84, 3753. 14 M. G. Prisant, C. T. Rettner and R. N. Zare, J. Chem. Phys., 1981, 75, 2222. 15 R. J. Hennessey and J. P. Simons, Mol. Phys., 1981, 44, 1027. 16 R. J. Hennessey, Y. Ono and J. P. Simons, Mol. Phys., 1981, 43, 181.17 K. M. Johnson, R. Pease, J. P. Simons, P. A. Smith and A. Kvaran; J. Chem. Soc., Furuduy Trans. 2, 1986,82, 1281. 18 R. J. Donovan, P. Greenhill, M. A. MacDonald, A. J. Yencha, W. S. Hartree, K. Johnson, C. Jouvet, A. Kvaran and J. P. Simons, Furuduy Discius. Chem. Soc., 1989, 84, 221. 19 W. Hartree and J. P. Simons, J. Chem. SOC., Furuduy Trans., 1990, 86, 11. 20 F. Engelke and K. H. Meiwes-Broer, Chem. Phys. Lett., 1984, 108, 132. 21 A. J. McCaffery and K. L. Reid, personal communication. 22 See, e.g. K. G. McKendrick, D. J. Rakestraw and R. N. Zare, Furuduy Discuss. Chem. Soc., 1987, 84, 39; J. Wolfrum; Furaduy Discuss. Chem. Soc., 1987,84,191; M. J. Bronkowski, R. Zhang, D. J. Rakestraw and R. N. Zare, Cbem. Phys. Lett., 1989, 156, 7. 23 ( a ) K. G. McKendrick, J. Chem. SOC., Furaduy Trans. 2, 1989,85, 1255; ( b ) J. Wolfrum, J. Phys. Chem., 1986,90, 375. 24 J. P. Simons, personal communication. 25 G. Hancock, C. Morley and I. W. M. Smith, Cbem. Phys. Lett., 1971, 12, 193. 26 G. Hancock, B. A. Ridley and I. W. M. Smith, J. Chem. SOC., Furuday Trans. 2, 1972, 68, 2127. 27 S. Tsuchia, N. Nielson and S. H. Bauer, J. Phys. Chem., 1973, 77, 2455. 28 H. T. Powell and J. D. Kelly, J. Chem. Phys., 1974, 60, 2191. 29 N. Djeu, J. Chem. Phys., 1974, 60, 4109. 30 J. W. Hudgens, J. T. Gleaves and J. D. McDonald, J. Chem. Phys., 1976, 64, 2528. 31 D. S. Y. Hsu, W. M. Shaub, T. L. Burks and M. C. Lin, Chem. Phys., 1979,44, 143. 32 G. Hancock and H. Zacharias, Chem. Phys. Lett., 1987, 82, 402. 33 R. Vasudev, R. N. Zare and R. N. Dixon, J. Chem. Phys., 1984, 80, 4863. 34 G. E. Busch and K. R. Wilson, J. Chem. Phys., 1972, 56, 3626; 3638. 35 M. Mons and 1. Dimicoli, Chem. Phys. Lett., 1986, 131, 298. 36 M. Mons and 1. Dimicoli, Chem. Phys., 1989, 130, 307. 37 M. Kawasaki, H. Sato, A. Fukudora, T. Kikeuchi, S. Kobayashi and T. Arikawa, J. Chem. Phys., 1987, 38 R. Sayos, M. Gonzales and A. Aguilar, Chtm. Phys., 1990, 141, 401. 39 A. J. Orr-Ewing and G. Hancock, to be published. 40 R. N. Dixon, J. Chem. Phys., 1986, 85, 1866. 41 B. Girard, N. Billy, G. Gouedard and J. Vigue, J. Chem. SOC., Furuduy Trans. 2, 1989, 85, 1270. 42 J. L. Kinsey, J. Chem. Phys., 1977, 66, 2560; C. A. Taatjes, J. I. Cline and S. R. Leone, J. Chem. Phys., 1990,93, 6554. 43 H. Okabe, Photochemistry of Small Molecules, Wiley, New York, 1978. Trans., 1989, 85, 975-1376. 1988, p. 221. 86, 4431. Paper 1/00002K; Received 28 th December, 1990

ISSN:0301-7249    

DOI:10.1039/DC9919100079

出版商:RSC    

年代:1991

数据来源: RSC

摘要:

Faraday Discuss. Chem. SOC., 1991, 91, 91-96 Two-colour Sub-Doppler Circular Dichroism: A Four-vector Correlation Molecular Dynamics Experiment for Inelastic and Reactive Collisions Timothy L. D. Collins, Anthony J. McCaffery and Michael J. Wynn School of Chemistry and Molecular Sciences, University of Sussex, Brighton BNl 9QJ, UK The technique of two-colour sub-Doppler circular dichroism (SDCD) is described and a four-vector correlation molecular dynamics experiment is demonstrated. Results are given for elastic and inelastic collisional processes between Liz and the rare gases Ar and Xe. The technique is of wide applicability and could be used to study the dynamics of elastic, inelastic and reactive collisions. Experimental probes of the structure of the transition state utilise methods by which collision frame events may be pre- and post-determined from laboratory-frame experi- ments.The means through which this transformation is achieved varies widely in technique and in efficacy, but the concept of vector ~orrelation”~ provides a framework for classifying most experiments that seek to achieve this objective. The differential scattering cross-section (DCS) provides a measure of the ( v , v ) or relative velocity-relative velocity correlation. This is conventionally obtained from molecular-beam scattering, but we have shown recently374 that the state-to-state DCS may be measured in two-colour sub-Doppler spectroscopic experiments. This is feasible owing to the selection of molecular velocities (magnitude and direction relative to the laser or detuning axis) inherent in sub-Doppler laser With appropriate choice of collision partner it is possible to transform reliably from molecular to relative velocity and thus obtain the ( u, u ) correlation from double-resonance lineshape analysis.When this method is allied to high-precision polarisation techniques there is the potential for high-order vector correlation since polarisation provides a measure of the ( j , j ) correlation, generally in the laboratory fame. Sub-Doppler excitation with circularly polarised light provides the opportunity to correlate initial v and j vectors and a measurement of the shift and broadening of the circular dichroism signal in the exit channel of the collision system provides the final-state (u, j ) correlation in addition to In this contribution we describe the first results of this novel experimental technique.The example chosen is a rotationally inelastic process in a diatomic molecule-rare-gas atom collision using optical-optical double resonance. It will be apparent that the cell spectroscopic method we describe has wider potential applicability and is not limited to inelastic processes or to the optical region of the spectrum. At this stage the initial results are described along with the experimental method. Further developments will be reported at the Discussion. We recently demonstrated4 and analysed’ atom-diatom collision dynamical data from a three-vector correlation experiment that yielded direct information on stereochemical dynamics. In that work, Doppler velocity selection was allied to high- precision polarisation techniques in the entrance and exit channels to specify initial relative momentum ui together with the magnitude and dominant multipole distribution of the rotational angular momentum vector, j i .Following inelastic collisions the state multipoles of the final j , distribution were determined as a function of laser detuning. (u, u ) and ( j , j ) . 9192 Two-colour Sub- Doppler CD This ( U i , J i , jf) correlation was observed for rotationally inelastic collisions between Liz (A ' X i ) and Xe. This contribution demonstrates that these basic high-resolution spectroscopic methods can be extended and a four-vector correlation experiment may be constructed based on this principle.I2 This method allies polarisation methods of high precision and sensitivity with sub-Doppler pump and probe which provide velocity and angle discrimination in input and output channels.The pump laser is circularly polarised and thus a Lorentzian velocity distribution of oriented molecules is excited, leaving a similarly oriented hole in the ground-state velocity distribution. The probe laser measures the shift and broadening of this distribution in either labelled state, as a circular dichroism (CD) following collision. It thus becomes a four-vector correlation experiment in which ( vi , vf, ji , j , ) are correlated. Here we describe the results of such a study of elastic and inelastic collisions in Li2-Xe and Ar, but emphasise that the technique is of wide applicability since non- reactive and reactive collisions may be studied using this or closely related methods.Its strength is that laboratory frame observations of gas-phase collisional processes may be interpreted in the molecule or the collision frame with all relative directional processes specified in that frame. The demonstration that data of this dynamical specificity may be obtained from relatively simple collision cell experiments indicates that a wide range of intermolecular processes may soon be studied on a routine basis. Experimental The determination of initial and final relative momentum (velocity) vector magnitudes and directions by Doppler shift has been described by us recently."" Fig. 1 illustrates the general principle. In brief the relation between laser detuning vL and molecular velocity magnitude and direction is given by: -v: sin2 a - ( vmz - v, cos a)2 ~ [ c o s ( a ) , v,, v,,] = vf exp where s, = J( m,/ kT) (x denotes an atom or molecule). The pump laser selects this distribution from the Doppler profile and the probe laser examines the shift and width of the distribution following collision. It has been shown that the shift Avmz may be related to the centre-of-mass scattering angle 8c.13714 The following equation expresses the relation including the extra factors for 'out-of-plane' scattering: AV,, = (5) v,(cos a cos 8, + sin a sin e, cos x - cos a ) ma + mrn where 8, is the centre-of-mass scattering angle and x is the rotation of the final relative velocity vector out of the plane.Fig. 1 ( b ) displays these relationships.Use of a light molecule with heavy collider atom allows molecular velocity and relative velocity to be interrelated with some precision. This lineshift method thus permits the (v, v) correlation to be obtained, yielding the most probable scattering angle. Correlation to the angular momentum vector is achieved using circularly polarised pump and probe. Excitation in this fashion produces excited molecules having a dipolar distribution o f j vectors relative to the propagation direction and thusj and v are parallel in the wings but perpendicular at line centre. The probe laser measures the sub-Doppler circular dichroism (SDCD), i.e. the difference in absorption coefficient for left and right circularly polarised light of the pumped distribution following collision.This is measured in two separate ways. First, as a probe of the near-Lorentzian spike of population excited by the pump into theT. L. D. Collins, A. J. McCafery and M. J. Wynn 93 Fig. 1 (a) Newton diagram showing the relationship between the relative velocity vectors and the molecular velocity vectors, before and after collision. The angle 8, is the centre of mass scattering angle. (b) Centre-of-mass frame diagram showing the out of plane scattering Liz A state or alternatively to probe the hole left behind in the ground state. Thus we are able to study separately Li,-rare-gas collisions for ground and first excited state Liz molecules. The SDCD signal is in one sense a measure of the double resonance lineshape but in addition it yields the loss of correlation of final with initial j-vector directions. Its shift and shape give the (u, u ) correlation information, i e .the differential scattering cross-section, whilst the shape and magnitude of the CD signal relative to the quantity a++ cr-, which is measured simultaneously, yield the ( j , j) and the (j, u ) correlation. A single-frequency tunable ring dye laser (pump) is circularly polarised using a Fresnel rhomb and is directed into a heated cell containing lithium metal and buffer gas where it overlaps the probe laser. The second laser is also a single-frequency tunable source and is passed through a second Fresnel rhomb and then a photoelastic modulator just prior to entering the cell. The CD is detected from the difference in fluorescence intensities for left and right circularly polarised probe light.This yields a direct measure of the K = 1 state multipole (orientation) of the j distribution whilst the sum of these is proportional to the K = O or population moment. The former signal comes from a lock-in detector whilst the latter is obtained using a d.c. amplifier. The pump laser excites a narrow, but variable, distribution of velocity vectors from the Doppler profile of a (u", j") = (1,14) level of X 'X; Li2 to (15,15) of A 'X:. This spike in the A state posseses well defined velocity and angle relative to the laser propagation axis and a well characterised distribution of j-vector directions referenced to the same axis. The hole remaining in the X-state distribution is similarly well defined. The probe laser measures the CD of this spike or of the hole by exciting to (u, j ) levels94 Two-colour Sub-Doppler CD of the G 'n, state in the former case, or from (o", j " ) levels of X state in the latter.In this way collisions of ground-state or of excited-state Li, with the collision partner could be studied. Experiments were performed for Aj=O and A j = 2 processes by careful choice of probe laser frequency. Signals for the inelastic process could not be obtained on studying the hole in the X-state profile. In experiments on the A-state spike, a very wide range of initial velocities (out to ca. 4800 ms-') could be studied by tuning the pump laser because of the excellent signal-to-noise ratio. A phenomenological expression for the Doppler free laser-induced CD may be written: l4 where I is the probe beam intensity, L is the pathlength of the pumped region where A a = a+ - a-, the difference in absorption coefficient for left and right circularly polarised light.This expression assumes AaL<< 1. A a is related to the pump intensity and absorption cross-section through known expressions given full identification of initial and final states. The CD detection method relies on the retention of some memory of initial orientation through elastic and inelastic collisions. There is e~perimental'~.'~ and theoretical' ',I7 evidence of strong rn conservation under these collisional circum- stances both for excited and for ground molecular states. We have recently reviewed this topic," and from this discussion it will be apparent that we may use elastic circular polarisation ratios to calibrate inelastic values and thus evaluate the ( j , j ) correlation from SDCD magnitude. In this Discussion we demonstrate the power of sub-Doppler spectroscopy in achieving the first realisation of the four-vector correlation experiment in molecular collision dynamics.This is illustrated in a study of elastic and inelastic collisions between Li2 molecules and argon or xenon atoms. Some sub-Doppler double resonance CD line- shapes are shown in Fig. 2. This displays two CD signals one with pump laser tuned to line centre and the other well into the wing at a relative velocity of ca. 1800msC'. These both represent an X-A, A-G double resonance and thus collisions of the excited A state with rare gas atoms are probed.In this figure the upper lineshape represents the circular dichroism in the form u+-u- whilst the lower curve in each case is the 'unpolarised' intensity measured as u+ + u-. The former signal in density matrix terms represents the K = 1 or orientation multipole whilst the latter is a close approximation to the K = O or population multipole. Their ratio yields the ( j , j ) correlation. Further we may infer the moments of the projection o f j on the final relative velocity axis. Fig. 3 illustrates a range of SDCD lineshapes for the alternative experiment X-A, X-A where now collisions of the rare gas with ground-state lithium molecules are probed. This signal is considerably more noisy since now there are numerous competing processes which will attempt to repopulate the pumped hole from surrounding quantum states.However, this is an experimental configuration of considerable potential since it may be adapted to the study of reactive collisions. Further developments of this double resonance technique in which pump and probe originate on the ground-state potential- energy surface may be anticipated. Conclusions We have presented data from a four-vector correlation molecular dynamics experiment. The method is a two-colour sub-Doppler optical-optical double resonance in whichT. L. D, Collins, A. J. McCafery and M. J. Wynn 95 I , , I , I I I 1 I 7 -4.00 -3.50 -3.00 -2.50 -2.00 -1.50 - 1 .GO -0.50 0.00 0.50 1 .00 GHz I 1 I I I I I I I , I -4.30 -3.50 -3.00 -2.50 -2.00 - 1 .50 - 1 .OO -0.50 0.00 0.50 1 .GO GHz Fig.2 Sub-Doppler double resonance lineshapes showing the a.c. and d.c. (lower) components of the signal at line centre and with uL =r 1850 m s-' diatomic molecules are selected in relative velocity and j-vector orientation (as well as in quantum state) prior to collision by a narrow line circularly polarised pump laser. The shift, broadening and magnitude of the probe circular dichroism signal may be analysed to give the scattering angle and the j-vector reorientation for preselected relative velocities. This represents the highest level of vector correlation in structureless atom-C state diatomic scattering and is therefore of considerable significance as a molecular dynamics experiment. Our data are preliminary and are for rotationally elastic and inelastic collisions, but the technique has wider capabilities.It is not limited to optical frequencies and pump or probe lasers might just as easily be infrared or ultraviolet sources. Extension of the method to study reactive collisions is readily envisaged.96 Two-colour Sub-Doppler CD I I 1 4 I I I 1 i i 1 -5.00 - 4 . 2 0 -3.40 - 2 . 6 0 -1.80 - 1 .OO -0.20 0.60 1.40 2 . 2 0 3.00 GHz Fig. 3 A Doppler scan for the alternative experiment where pump and probe beams both excite X-A transitions. Here the collision partner is Ar We thank the SERC for financial support and for a studentship to T.L.D.C. Dr Katharine Reid is thanked for numerous helpful discussions and Dr Neil Smith for a helpful suggestion improving the treatment of the lineshapes. References 1 D. A. Case and D. R. Hershbach, Mol. Phys., 1975, 30, 1537. 2 See J. Phys. Chem., 1987, 91, 5365. 3 K. L. Reid, A. J. McCaffery and B. J. Whitaker, Phys. Rev. Lett., 1988, 61, 2085. 4 K. L. Reid and A. J. McCaffery, J. Chem. Phys., submitted. 5 J. L. Kinsey, J. Chem. Phys., 1977, 66, 2560. 6 J. A. Serri, J. L. Kinsey and D. E. Pritchard, J. Chem. Phys., 1981, 75, 633, 7 N. Smith, T. P. Scott and D. E. Pritchard, J. Chem. Phys., 1984,81, 1229. 8 P. Houston, J. Phys. Chem., 1987, 91, 5338. 9 C. P. Fell, A. J. McCaffery, K. L. Reid, A. Ticktin and B. J. Whitaker, Laser Chem., 1988, 9, 219. 10 R. A. Gottscho, R. W. Field, R. Bacis and S. J. Silvers, J. Chem. Phys., 1980, 73, 599. 11 K. L. Reid, A. J. McCaffery, C. P. Fell and A. Ticktin, J. Chem. Phys., submitted. 12 T . L. D. Collins, A. J. McCaffery and M. J. Wynn, Phys. Rev. Lett., to be published. 13 K. L. Reid and A. J. McCaffery, J, Chem. Phys., submitted. 14 W. Demtroder, Laser Spectroscopy, Springer Verlag, Berlin, 1982. 15 M. D. Rowe and A. J. McCaffery, Chem. Phys., 1979,43, 35. 16 A. Mattheus, A. Fischer, G. Ziegler, E. Gottwald and K. Bergmann, Phys. Rev. Lett., 1986, 56, 712. 17 V. Khare, D. J. Kouri, D. K. Hoffman, J. Chem. Phys., 1982, 76, 4493. Paper 0/05729K; Received 18th December, 1990

ISSN:0301-7249    

DOI:10.1039/DC9919100091

出版商:RSC    

年代:1991

数据来源: RSC