Faraday Discuss. Chem. SOC., 1991,91, 191-205 Observation of the Reactive Potential-energy Surface of the Ca-HX* System through van der Waals Excitation B. Soep and C. J. Whitham Laboratoire de Photophysique Molkulaire, Universite' Paris-Sud, Orsay 91 405, France A. Keller and J. P. Visticot Service de Physique des Atomes et des Molkcules, CENSaclay, Gif-sur Yvette 91 191, France The potential-energy surface of the excited-state reactions of calcium with halogen halides has been explored by the optical excitation of a Ca-HX van der Waals complex prepared in a supersonic expansion. Resonances and intense vibrational progressions of van der Waals modes have been observed, and the spectra have been analysed on a local-mode basis. It is seen that the excitation promotes modes involving the Ca-HCI bending coordinate, which appears to be different from the reaction coordinate.There is a renewed interest in the experimental investigation of the transition region in photodissociations and chemical reactions. Energy-resolved and time-resolved experi- ments have been devised which allow the direct exploration of regions of the potential- energy surface that are only indirectly accessible t3 scattering experiments. 1-4 All these experiments make use of the transformation of a bimolecular reaction in a photodissoci- ation-like experiment:'-' the reagents are condensed within a weakly bound species (van der Waals or ion) and the reaction is initiated by optical means. Through the optical selection rules a specific surface will be excited, and through Franck-Condon excitation there will be access to a localized region of a reactive potential-energy surface (PES).In this case, unlike the case of a direct photodissociation experiment, the excited coordinate can be different from the dissociation (reactive) coordinate. From a spectro- scopic point of view this will result in resonances in the spectrum, and from a time- resolved point of view there will be time recurrences due to oscillations on the excited potential-energy surface. These osci!lations, which may exist even in the case of an entirely repulsive surface, are a consequence of the selectivity induced by the optical e ~ c i t a t i o n . ~ ' ~ Two factors will determine the region accessed: first the initial geometry of the ground state complex, resulting from the intermolecular forces; secondly the Franck- Condon factors, which depend upon the relative changes between the ground- and excited-state PES.Among the possible reaction schemes, we have chosen a metal- molecule reaction which is initiated by excitation of the metal part of a van der Waals complex. In this kind of reaction, which is of the harpoon type, occurring at large internuclear distances (3-4 A), Franck-Condon excitation of the complex may allow one to probe the transition state region. We report here the reactions with a van der Waals complex of calcium with hydrogen halides (HCl and HBr) leading to electronically excited calcium halides. These reactions have been quite extensively studied in full collisions of excited calcium beams.''-I4 The electronic excitation of the calcium atom results in a strong chemiluminescence under collisional conditions. The efficiency of this chemiluminescence depends upon the electronic state and the fine-structure component, and the final product state is influenced by the preparation conditions of the collision. In the reaction Ca(4s4p 'PI) + HCl, the direction of the polarization of the P orbital with respect to the collision relative velocity (p, or p,) has an effect on the branching ratio to the products CaC1, A *I3 or B 2Z+.13,14 191192 PES of the Ca-HX* System In the complex, transitions to electronic states correlating at infinite distance to the 4s4p 'P, and 4s3d ID2 states of calcium have been observed in the spectra of the laser-induced reactions.We have analysed the spectra in terms of a local excitation of the calcium and internal van der Waals coordinates (stretching and bending). Indeed, strong resonances are observed in these spectra which can be assigned to van der Waals modes. The excitation of these vibrations allows the exploration of an important region in the excited PES. It should be mentioned that this exploration is more extensive when the laser-excited coordinate is different from the reaction coordinate. In such a case, the longer-lived is the reaction intermediate, the more of the PES will be explored. The excitation of different resonances is reflected in the different widths of the transitions, which are an indication of their reactivities. Experimental Set-up The reaction of the complex Ca*-HX -+ CaX*(A 'IT, B 2Z+), with X = C1, Br, was observed in the silent zone of a pulsed supersonic expansion after excitation of the Ca-HX complex with a pulsed, tunable dye laser. The complex was formed by laser evaporation of a rotating calcium rod in a classical arran ernent.I5-l9 The resulting on a phototube.The tunable laser was generated in the range 4000-43OOA by mixing the fundamental frequency of a YAG laser with the output of a red dye laser (DCM, LDS698) pumped by the same YAG laser. In the range 4300-5OOOA direct pumping of coumarin dyes by the third harmonic of the YAG laser was used. Great care was taken to eliminate super-radiance light in the case of direct pumping, while frequency mixing acted almost completely as a filter of this super-radiance.A delay of a few microseconds between the laser vaporization pulse (created by the second harmonic of another synchronized YAG laser) and the laser excitation pulse was needed to allow the calcium atoms or complexes to reach the excitation zone. This delay depended upon the carrier gas (10 ps for He and 35 ps for Ar), and its accurate adjustment was crucial for the observation. A temperature of 5 K was achieved in argon expansion, allowing the formation of complexes. We found, as in our study of calcium free radicals, that helium was less efficient a coolant in our beam configuration.18 The expansion was characterized by the weak appearance of the Ca, bands at 4840A; the rotational contour of the B-X(13-0) band in the expansion of calcium in pure argon corresponded to a temperature of 5 K.The calcium evaporation power was kept low, typically at 0.7 mJ, in order to optimize the formation of calcium metal with respect to metal clusters and to obtain the lowest beam temperatures. A 1% mixture of HX in argon was further diluted in argon in a continuous fashion, allowing the concentration range of HX to be varied between and emission was dispersed through a small monochromator (50 1 resolution) and collected Characterization of the Ca-HCl Complex We made three observations. First, the chemiluminescence signal of CaX resulting from the complex excitation was linear with HX concentration. Secondly, it was only observed intensely in the expansion of argon (with HX). Thirdly, when HCl, HBr or HF was added in minute quantities to the pure argon expansion, the Ca, dimer signal disappeared.We concluded (from the linear dependence on HX and cold expansion) that the observed chemiluminescence originated from a Ca- HX complex whose the binding energy was greater than that of Ca2 (1075 cm-').20321B. Soep, C. J. Whitham, A. Keller and J. P. Visticot C a + H + X C a ( ' P ) + H X Ca('D)+ HX,\T ~ CaXIB2X*l + H C a X ( A * f l ) + H D$HX) I I hu I I I I I To(A->X 1 I I I I I 193 Ca-HX Fig. 1 Schematic diagram of the energetics of the Ca+ HX reaction. The optical excitation takes the Ca-HX van der Waals complex from the ground state to an excited state correlated with the Ca 'P or 'D states, which then reacts and forms the excited CaX* product Resu 1 t s Several types of experiment have been conducted: ( 1 ) dispersed fluorescence of the product CaX*; (2) action spectra, where the reaction product fluorescence is monitored as a function of the excitation laser; (3) pump-and-probe experiments, where the excitation laser is tuned to a particular resonance of the action spectrum and the state distribution of CaX is probed with a second laser. These last experiments will be reported in a forthcoming paper.Ca-HCI Action Spectra Action spectra have been recorded in long scans between 4000 and 5000 A, monitoring the CaCl A-X (or B-X) emission. This region covers the Ca('S,-ID,) and ('So-'P1) transitions and does not overlap with CaCl transitions. No chemiluminescence signal is observed at wavelengths >5000 A as a result of the energetic threshold for CaX* formation (see Fig.1 and the Discussion section). The action spectrum presented in Fig. 2 reveals two sets of bands localized near each of the two calcium transitions. Both sets extend over about 1000 cm-', with broad structures in their red part and narrow structures in their blue part. A close-up of the band corresponding to the Ca('So-'P1) transition is presented in Fig. 3 ( a ) , and the pattern of a vibrational progression merges from the figure. This pattern is slightly complicated by satellites within the bands which either appear as non-symmetrical in shape or display shoulders. The ultimate width of the transitions may be given by one band, located at 24 360 cm-', which appears sharp and therefore has been recorded under a higher laser resolution (0.1 cm-') in Fig.4. It exhibits a quasi-lorenztian lineshape with no fine structure indicative of rotational transitions; therefore the band- width depends only on the diffuseness of the transition.194 PES of the Ca-HX* System Cr..HCl-> CICI(A) + H 2oooo 2 lo00 22OOo 23000 24000 25000 26000 Elcm-' Fig. 2 Action spectrum of the Ca-HC1 van der Waals complex. The laser exciting the complex has been swept between 21 000 and 25 000 cm-' while recording the intensity of the CaCl(A-, X) transition The large spacing between the bands in Fig. 3(a) (the 'PI region) must correspond to vibrational transitions in the excited Ca-HCl complex. In order to assign these bands, we have substituted DC1 for HCl. The corresponding spectrum is displayed in Fig.3( 6). A strong isotopic effect is observed resulting in a considerable decrease of the band spacings. The spectrum of the deuterated complex also has narrow structures in the blue part and broader structures in the red part, and the separation between these two sets of bands is even more conspicuous here. It is obvious that the motion of the H/D atom is involved in these progressions. In the discussion sectim, we shall demonstrate that the main features of the transitions within the blue envelope of the spectrum pertain to the Ca-HCl bending. A similar effect of the deuteration on the band spacing has been observed in the 'D2 region, but because of the smaller number of identified transitions, we could not make a conclusive assignment. Ca-HCl Fluorescence Spectrum The spectrum obtained by dispersing the fluorescence when fixing the excitation laser frequency on a transition of the Ca-HCl complex is displayed in Fig.5. This spectrum is characteristic of the CaCl A *n-X *E+ and B *E+-X 'E+ emission. It consists of two series of short vibrational progressions that are well separated. The spectral resolution is, however, insufficient to resolve either the band sequences (a few cm-') or the spin-orbit separation in the A 211 state (60 cm-'). The spectrum in Fig. 5 permits the estimation of the branching ratio of the reaction to the A or B states of CaC1. This ratio is approximately statistical and is the same as for the gas-phase reaction Ca(4s4p 'PI) + HCl.14 We observed in two ways that this ratio remained constant throughout the excitation spectrum: first by recording this fluores- cence spectrum for various excitation frequencies and secondly by observing identical action spectra with the A-X or B-X transition.Ca-HBr Action Spectra The spectra have been recorded in the eame conditions as for HCl and are very similar in appearance. In Fig. 6 ( a ) , an overview of the action spectrum is presented. As for23000 23400 23800 24200 24600 25000 E l m - ' I v = 3 1 - 23000 23400 23800 Elcm-' = 4 j = 5 1 I v $ 1 Y .- [ I Y .- I 23000 23400 23800 24200 24600 25000 E l m - ' j = ! v = 3 ::i2, j v = o 23000 23400 23800 24200 24600 25000 24200 24600 25000 Elcm-' Fig. 3 ( a ) Expansion of Fig. 2 in the region of the Ca('P) state. The sharp line at 23 652 cm-' is the Ca('S ---* 'P) resonance line: the excited Ca atoms are reacting with the background HCl gas.( b ) The same as part (a), but replacing HCl by DCl. (c) Simulation of the Ca-HCl action spectrum with a bending model. The bending potential has been adjusted to reproduce the positions of the lines in the short-wavelength part of Fig. 3(a). The intensities have been obtained with the assumption of a harmonic ground-state potential with a 70 cm-' bending frequency (ref. 19). They should be compared to the integrals of the bands in Fig. 3(a). (d) Isotopic substitution of H by D in the simulation. This should be compared with the action spectrum in Fig. 3 ( b ) Q 3196 PES of the Ca-HX* System L -10 -5 0 5 10 Elcm-' Fig. 4 Band of the Ca-HCl van der Waals complex at 24 360 cm-' recorded with a higher resolution of the exciting laser (0.1 cm-').The band appears to be continuous and has a quasilorentzian shape Ca-HC1, the spectrum consists of two regions close to the calcium atomic transitions; these regions can also be further divided into two sets of bands. The main differences from the Ca-HCl spectra appear in the ID2 region, where the red part is now structured with a regular separation of about 60 cm-', decreasing slightly towards the blue. In the 'PI region, although the bands exhibit the same spacing as in the Ca-HCl spectrum, their width is somewhat broader. A spectrum has also been recorded with DBr and is presented in Fig. 6 ( 6 ) ; unfortunately, the spectral structures have vanished throughout the spectrum of the deuterated compound, except for the band at 23 400 cm-', which splits into three sub-bands.CaCl B2C + I 0 550 600 650 A/nm Fig. 5 Fluorescence spectrum of the Ca-HCI van der Waals complex. The excitation laser has been fixed on an absorption band of the complex (see Fig. 2) and the fluorescence has been dispersed. The saturated line at 532 nm originates from the scattered light of the evaporation laserB. Soep, C. J. Whitham, A. Keller and J. P. Visticot 1.2 1 197 1 0.8 5 0.6 2 .E 0.4 0.2 .- Y n 23000 21200 22400 23600 24800 26000 Elcm-' 2.5 2 1.5 5 .9 1 Y .- v) Y 0.5 0 20000 21000 22000 23000 24000 25000 26000 Elcrn-' Fig. 6 (a) Action spectrum of the Ca-HBr van der Waals complex. The laser exciting the complex has been swept between 20 000 and 25 000 cm-' while recording the intensity of the CaBr(A + X) transition. ( b ) The same as part (a), but replacing HBr by DBr Ca-HBr Emission Spectra A typical spectrum is shown in Fig.7. The main features are the same as for Ca-HCI, i.e. the observation of the A and B states of CaBr with short progressions. However, in contrast, the ratio of the A to B emission strikingly depends on the excitation region ('PI or 'D2), or on which set of bands is excited in each region. In summary, the decay pattern is characteristic of each set of bands previously mentioned, to the blue or red of each atomic line 'PI or 'D2, thus contributing further to the individuality of each set. This will be analysed in detail in a forthcoming paper. Discussion We now describe the nature of the observed transitions in the action spectra in terms of local excitation and local modes.Before this discussion, it seems necessary to summarize what can be stated about the structure of the Ca-HCI van der Waals complex and what can be inferred with regard to the energetics of the reaction.198 PES of the Ca-HX* System 57 0 59 4 618 64 2 666 6 90 A/nm Fig. 7 Fluorescence spectrum of the Ca-HBr van der Waals complex. The excitation laser has been fixed on the absorption band at 4175 A of the complex [see Fig. 6(a)J and the fluorescence has been dispersed Structure of the Ca-HCl Complex The geometries of the known complexes of an atom with HCl are linear, with the hydrogen atom lying between the two heavy partners.22 This also applies to the Hg-HCl van der Waals complex23 and should also be true for Ca-HCl in the ground state, as the calcium atom is even more polarisable (25 A)24 than Hg (5.1 A3)25 and interacts strongly with the HCl quadrupole.Following Buckingham’s developments, Hutson calculated the anisotropy of rare-gas-HX complexes and found that the major contribu- tion arose from the induction forces.26 In this model the HCl dipole imposes a linear geometry, and the HCl quadrupole leads to H having the central position. Therefore, in Ca-HCl, with a 3.5 A centre-of-mass separation, the barrier to linearity is high (ca. 700 cm-’) and the second well is shallow. This value is not inconsistent with the existence of a deep well, as stated in the Experimental section. We cannot make such definitive statements in the case of HBr because of the possible failure of a point-charge electrostatic model for a bulkier atom such as Br: nevertheless, we can safely assume a linear geometry for Ca-HBr, once this complex is also strongly bound.In conclusion, for HCl, the structure of the complex is a linear Ca-HCl geometry which is further confirmed by the initial results of a6 initio calculation^^^ in accordance with the intuitive partial charge transfer between the calcium and the HX. This charge transfer will involve the S orbital of Ca and the antibonding orbital of HX located mainly on the H atom. Experiments would be welcome to confirm this structure. Energetics of the Ca + HX Reactions The schematic diagram in Fig. 1 represents the various levels of the reagents and of the products. At first, a lower limit to the CaX dissociation energy may be found in the frequency extension of the observed action spectra.In order to produce chemilumines- cence, the energy given to the Ca-HX complex by optical excitation should exceed the energy of the first excited state of the CaX product. This sets the limit: DG(CaX)l T,(A -+ X)+DG(HX)+DG(Ca-HX)-hv where v is the frequency of the reddest band in the action spectra. Assuming a 0.2 eVt binding energy for the Ca-HX complex, we obtained DG(CaC1) L 4.03 eV and Tl eV= 1.60218 x J.B. Soep, C. J. Whitham, A. Keller and J. P. Visticot 199 DG(CaBr) I 3.44 eV. The first value compares with the previous experimentally deter- mined D: of CaCl (4.28 eV)," while the value determined by Hildenbrand for CaBr (3.18 eV)28 must be an underestimate.Note that these limits are compatible with the preparation of a Ca-HX complex in the ground state, even in the absence of a barrier. In such a case, for a complex to be formed in the calcium ground state, the reaction should be endoergic, implying a larger binding energy for HX than for CaX, i.e. D:(CaCl) 5 4.34 eV and D",CaBr) I 3.76 eV. Nature of the Action Spectra Localization of the Excitation Energy The Ca-HX complex is a weakly bound species in the ground state, as we have seen in the preceding sections. How can we then describe the optically accessed states when we know that these excited states are reactive and probably react through the harpoon mechanism? This mechanism has been po~tulated'~"~ by analogy with reactions of an excited alkaline earth with an alkali metal (in the ground state) and HX.The open shell Ca(4s4p) of the ionisable calcium can easily yield an electron jump to HX,t the crossing radius being 3.5 f 0.1 A for Ca'P+ HCl between the covalent and Ca+, HC1- surfaces. Therefore the vertical excitation of the complex should lead directly to the reaction domain. The ionic curve is directly attained by optical excitation neither for Ca-HCl nor for Ca-HBr, as can be seen by inspection of the action spectra in Fig. 2 and 6. If it were, the spectrum should be continuous and unstructured, as are the charge-transfer spectra; this results from the rapidly varying nature of the ionic potential (ca. 1 eV k'). Rather, the spectra display sets of bands close to the calcium singlet transitions at strikingly similar positions for both the Ca-HCl and Ca-HBr complexes.We therefore think that the observed transitions derive their oscillator strength from the calcium transitions. In such conditions, the reaction surfaces correlating at an infinite distance with Ca('P, 'D) + HX should split into several A components under the molecular field.677 We thus expect two classes of transitions (2' and 'TI') as allowed by electric dipole transitions for each excited atomic configuration. Indeed, in the spectra displayed in Fig. 2 and 6, the structures correlating with Ca('P, 'D) are split into two groups of bands which appear in all cases, i.e. HCl, DCl, HBr and DBr. Vibrational Excitation A closer examination of the previous spectra reveals vibrational structures that we shall analyse as follows in terms of Iocal modes of the excited complex Ca-HX.We therefore assume that the optical excitation process allows us to make one-dimensional cuts through the excited potential-energy surface along the van der Waals stretch and bend and the HCl coordinates. We shall combine the information contained in the spectra of both Ca-HC1 and Ca-HBr, provided that they bear a close resemblance. The ID2 Ca-HBr Stretching Progression At the long-wavelength end of the CaHBr spectrum (the 'D region), we notice a long progression of closely spaced peaks (ca. 60 cm-I). These peaks, which have a width of ca. 40 cm-', can be described by a one-dimensional Morse oscillator with o, = 70 cm-' w,x, = 0.24 cm-' (assuming that the first band observed corresponds to the origin).This long low-frequency progression suggests a van der Waals mode. The first observed band P The isolated HCI- ion is unstable but is easily stabilised in the Ca+ field in the range of distances of the complex (3-4 A).PES of the Ca-HX* System is located at 1580 crn-' to the red of the 'D line; thus the potential-energy surface in the excited state of the complex is deeper by at least 1580 cm-'. In such case the Ca-HCl distance should be appreciably reduced in the excited state, and the progression must pertain to the van der Waals stretching mode. The resulting dissociation energy is Do = w:/4w,xe = 5000 cm-' in the excited state. The order of magnitude of the stretching frequency in excited states of Ca-HX will be kept in the following as <70cm-' (depending on the well depth of the relevant potential).The same portion of the CaDBr spectrum is reproduced in Fig. 6(6): to our dis- appointment, it does not display the same stretching progression that would be expected in a local-mode analysis. Rather, the observation of a quasicontinuum is surprising. The onset of a continuum could be due to a greater number of bands, possibly of increased breadth as a result of an increase in reactivity. The increase of the bending level density on going from Ca-HBr to Ca-DBr may cause the appearance of a great number of bend-stretch combination bands. Such an increase of the complexity of the spectra as a result of deuteration has already been observed at a certain level of excess energy in the Hg-NH3 and Hg-H20 van der Waals complexes.29730 This complexity could be combined with a larger width of the individual peaks. The reaction can have a very strong angular dependence, with a maximum close to the equilibrium angle.As the vibrational amplitude will be smaller for Ca-DBr than for Ca-HBr, one could expect a greater reactivity for the deuterated compound. In any case, the long progression ( 1 100 cm-') with a small positive anharmonicity observed in Ca-HBr must be assigned to the Ca-HBr stretch. The 'P Ca-HX Bending Progressions We shall now analyse the spectra displayed in Fig. 3. A progression in the blue part of Ca-HCl spectrum is observed with an irregular spacing of ca. 200 cm-', a value implying a van der Waals mode progression. We already noticed a large H/D isotope effect on the band spacing.Furthermore, the relative positions of the four bands in the shortest- wavelength part of the spectrum closely match the energy separations of free HCl rotor lines for J = 4-7 [EJ = bJ(J+ l ) , where 6 is the HCl ground-state rotational constant]. This is confirmed by the observation in the corresponding Ca-DCl spectrum of four transitions matching the J = 5-8 line positions of a free DCl rotor. This correspondence indicates that these ensembles of transitions lead to upper levels beyond the barrier to free rotation of HCl/DCl within the excited state of the complex. On the contrary, the other members of the progression relate to the bending motion associated with the anisotropy of the excited Ca-HCl potential. The observation of quasi-free rotation has also been reported recently in the transition region of IHI.8 To be more quantitative, we have used a bending model described in the Appendix with its selection rules (Amj=O).The transitions in the Ca-HC1 complex arise from the vibrationless state of the linear geometry, without angular momentum mj along the complex axis. The selection rules allow only the access of excited mi = 0 states, as it is shown in the Appendix that for Z -j I3 transitions the AA = 1 change is cancelled by the change in the total angular momentum projection, AhR = 1. Therefore these Amj = 1 transitions should be minor, as they are only due to Coriolis coupling, which we have neglected. Such transitions have been observed by Nesbitt et al. in the case of strong Coriolis coupling of degenerate levels.31 We have fitted the bending potential V(0) of the excited state to reproduce the positions and intensities of most of the transitions of the Ca-HC1 'P region.The result of the fit is presented in Fig. 3 ( c ) and the best potential in Fig. 8. The calculated levels and intensities reproduce correctly the pattern of the blue bands in Fig. 3 ( a ) , with the origin taken on the calcium line. The details of the fit have been given in a previous article." We mention here the essential points of this fit for Ca-HC1: the barrier to freeB. Soep, C. J. Whitham, A. Keller and J. P. Visticot \ 840 - P) M 9 560 E s 280 I----- j = 8 I - J = 7 j = 5 j = L I' - 201 "0 45 90 135 180 Fig. 8 Bending potential of the excited state of Ca-HCl corresponding to the fits in Fig.3. It has been obtained under the assumption of a linear ground-state complex and a bending model described in the text. The parameters have been adjusted to reproduce the positions of the bands in the short-wavelength part of Fig. 3(a) rotation in the excited state has been deduced from the onset of the free rotation in the spectrum, the geometry changes from a linear ground state to a T-shaped excited state and the well depth is the same in the ground and excited states. With these parameters, we could directly obtain the Ca-DC1 transitions in Fig. 3 ( d ) by only changing the masses. This indicates that the main progressions in the blue part of the spectra in Fig. 3 are bending progressions of the Ca-HCl complex. This agreement between experi- mental and calculated positions of peaks for Ca-HCl and Ca-DCl also implies that the origin of this progression changes by only 30 cm-' upon deuteration.This is compatible with a local-mode description in which the HCl bond is reduced in the excited state by only ca. 200 cm-'. This model was designed to give the framework of the transitions showing that one-dimensional local-mode excitation was promoted by the optical pulse. However, it does not account for all the transitions observed in Fig. 3. If we look more closely at the blue part of the spectrum of Fig. 3, we see some unassigned transitions appearing as satellites or shoulders displaced by 20-50 cm-' from the main peaks of the bending progression. This separation is compatible with a stretching mode spacing in a shallower potential (1500 cm-') than the potential of Ca-HBr in the 'D2 region.Therefore a possible explanation for the existence of such bands relies on a combination of bend- stretch modes which are not easily predicted in the model. Inspection of the Ca-HBr spectrum in the same 'P region shows a very similar pattern for the transitions, similar spacings but a more diffuse appearance. We have not attempted a bending analysis because the Ca-DBr spectrum is almost continuous, as in the 'D2 domain, and probably for the same reason, i.e. a greater bend-stretch coupling. The previous analysis clearly confirms the existence of a second group of transitions which appear most distinctly in the red part of the Ca-DCl (Ca-DBr) spectrum (Fig. 3) and bear no relation to the group of bending transitions.We can exclude the contribution of Ca-(HX),, n > 1, in both the HCl and HBr spectra, as these bands are sensitive to H/D substitution. Another interpretation for this group of bands would be the existence of a Ca-XH isomer in the ground state, which, on the basis of electrostatics, seems unlikely. The correlation of atomic and complex states implies, in the case of calcium 'P, the presence of a second electronic state. We have already noticed the separation into two groups of the transitions observed in the spectra of Ca-HBr and Ca-DBr, a result which fits this interpretation.202 Reactivity of the Ca-HX States The purpose of the previous analysis has been to show that one could represent the excited complex by one-dimensional modes on surfaces correlated to excited atomic calcium. This description may appear surprising, for we have been probing a reactive surface, and we could conclude from the observation of structured spectra and resonances that we only had access to the entrance valley of this reaction. On the other hand, the chemiluminescent reaction of excited calcium with HCI is known to occur with high cross-sections, ranging from 25 A2 (ID2)'' to 68 A' ('P).l4 These cross-sections agree with a crossing of the ionic and covalent surfaces without a barrier at 3.5 Hence, we must expect a direct and fast reaction. In addition, in Fig.3(a) the bending bands become increasingly sharp with excitation, so that the bending Ca- HCl vibration displaces the system away from a favourable conformation.We thus interpret the observation of distinct progressions, as opposed to featureless continua, in the action spectra as due to the excitation of local modes perpendicular to the reaction coordinate. PES of the Ca-HX" System Appendix: The Ca-HX Bending Model We describe here a simple to calculate the bending levels of a Ca-HCl van der Waals complex and to yield selection rules for the optical transitions. The levels of Ca-HCI have been calculated within the hindered rotor model in a body-fixed frame ( O X ~ Z ) . ~ ~ To describe the internal degrees of freedom we use the Jacobi coordinates R, r and 8, which are well adapted to this type of problem; here they have the following meanings: R is the distance between the calcium atom and the HCl centre of mass, r is the HCI bond length and 8 is the angle between the vectors R and r.We shall also make the following approximations. We separate the electronic and nuclear motion in the Born-Oppenheimer approximation. Furthermore, we consider, as justified in the text, the electronic excitation to be localized on the calcium atom, and thus the electronic wavefunction to be a perturbed atomic Hence, the perturbation of an excited calcium atom with angular momentum L by the HCl molecule splits up the components of L. In a linear geometry of the complex, the projection A of L on the body-fixed Oz axis is a constant. However, states of the complex correlating with different values of L may be mixed. The 'P and 'D atomic states will be mixed in the complex, as their separation (1803 cm-I) is comparable to the interaction energy between Ca and HC1 (ca.1500 cm-I). This is the origin of the absorption observed in the complex in the 'D region, while it is forbidden within the atom by the optical selection rule AL = 0, *l. Here this absorption becomes allowed owing to the interaction between states of same .A (X and ll states, respectively). We shall make an additional approximation in considering A to be a good quantum number even in the case of a bent geometry, as R >> r in the complex. In other words, we assume the electronic cylindrical symmetry to be little perturbed in twisting the geometry of the Ca-HCl complex. A model for the bending will be made in the approximation of the separation of the internal coordinates ( R , r, 8 ) .While the separation of r and ( R , 0) is justified by a large difference in the frequencies of the HC1 stretching (ca. 3000 cm-I) and van der Waals (ca. 100 cm-I) modes, the separation of R and 8 is much cruder, and this will be improved in the future. The bending wavefunction is a solution of the Schrodinger equation with the H a m i l t ~ n i a n ~ ~ b B A A H => j 2 + i l ' + V " ( 8 ) where j is the angular momentum of the HCI molecule, 1 is the angular momentum forB. Soep, C. J. Whitham, A. Keller and J. P. Visticot 203 the overall rotation of the complex, V(6) is the bending potential for the A electronic state considered, and 6 and B are the rotational constants of HC1 (10.6 cm-') and of the overall rotation of the complex ( B =: 0.15 cm-' for R =: 3.5 A), respectively.The wavefunction is expanded* over the basis set IJMfl)ljmj) where IJMfl), the Wigner rotation matrix element DLn(Q>, 0, +), describes the rotation of the molecular frame in space, and Ijmj) = Y i , ( 0,O) describes the rotation of HCl in the molecular plane.34 J is the total angular momentum, M its projection on the space-fixed axis and SZ its projection on the body-fixed axis ( R ) . We have the relation J = j + l + L where it follows, projecting j on the body fixed axis 02, that mj = SZ - A because Z, = 0. Finally, the wavefunction is written as m J c C;yblJMfl)ljmj) j = O R=-J where ub labels the bending level and the coefficients Ci;.'"b may be obtained by diagonalizing H. In this basis, the matrix elements o f j 2 and Z2 are easily calculated: 1' = ( J - L - j ) 2 = J 2 + L2 +j2 - ( J + j - + J-j+ + J+ L- + J-L+ - j , L- -j-L+) Z2 can couple the function corresponding to the quantum numbers SZ, M and A to the functions f l f 1, M f 1 and A f 1.This is the Coriolis interaction due to the overall rotation of the complex. These terms can be neglected here because B << 6, and therefore fl is a good quantum number. The wavefunction can be written as J M A n = f CjM '3n"hlJMfl)ljCl -A) j = O Ub j' is diagonal in this representation, and, as V(0) is taken to depend solely on 6, it couples functions corresponding to different j only. In the framework of these approximations, to obtain the main transitions we must solve the Schrodinger equation with the hamiltonian: h A H => j ' + V(6) To solve this eigenvalue problem, we expand the potential V ( 6) in Legendre polynomials: hmdx 0) = c CkPk[COS ( 0 ) l k = O and the bending wavefunction is expanded over spherical harmonic functions: 'ma, J =o xl#, = c 'l#,,J q,o( '7 O) With these requirements, the matrix elements of H are analytic.The diagonalization of this matrix gives the energy levels and the wavefunction describing the bending motion of HCl in the V(6) potential. Transition Selection Rules Because the geometry of the ground-state Ca-HCI complex will be taken as linear, fixing the J, M quantum numbers, the lower bending state corresponds to Z)b=0, f l = O and the first excited state to ?& = 0, fl= 1. The energy gap between these two states is204 PES of the Ca-HX* System approximately the bending frequency cob (of the order of 100-200 cm-').In the super- sonic beam, where the temperature is <10 K, only the ground bending state will be populated, thus J, M, f2 = 0, A = 0 and mj = f2 - A = 0. The intensity of the absorption is proportional to where E is the polarization of the electric field and p the dipole operator for the molecule. E is defined in the space-fixed frame, whereas p is defined in the molecular frame, thus &P = c (-1)p&-pP9D;9(@, @,#I p , q = o=t 1 where pq and E~ are the usual tensorial notations for vector component operators. We can thus write Afe = ( ~ o ~ I x v f > c (-l)p&-p(J~M,szelo;(CP, @,#)IJfMffifXAelpqIAf) p.9 =o+ 1 As usual, two types of transitions can occur: ( a ) if q = 0, then Ae = Af (2 + I; transitions); ( b ) if q = kl, then A, = Afk 1 (I; -+ TI or n -+ I; transitions).When q = 0 the selection rules come from the terms: The integration over the angles 0 and CP gives the usual selection rules: ]Jf - lI(Je(lJf+ 11, and Me = Mf, Mf f 1, depending on the value of p . The integration over the # angle gives sze = Rf This last relationship, combined with the fact that A, = A,, implies: mj, = mj, fie = f2f+ 1 When q = f l the selection rules can be derived in the same way, yielding: but in this case A, = Af* 1 and we again have m. = m . Jc JI We see that only states with mj = 0 may be accessed from the ground state, mi = 0, which is the only state populated in the supersonic expansion. References 1 P.R. Brooks, Chem. Rev., 1988, 88, 407. 2 A. H. Zewail, Science, 1988, 242, 1645. 3 M. 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