摘要:

Crossed Beam Studies of Endoergic Bimolecular Reactions : Production of Stable Trihalogen Radicals BY JAMES J. VALENTINI, MICHAEL J. C~GGIOLA AND YUAN T. LEE* Lawrence Berkeley Laboratory and Department of Chemistry, The University of California, Berkeley, California 94720 Received 3rd May, 1976 The trihalogens IIF and CIIF and the pseudo-trihalogen HIF have been directly observed as the products of the endoergic bimolecular reactions of F2 with I*, ICl and HI in a crossed molecular beam experiment. At high collision energies a second reactive channel producing IF becomes important. Product angular and velocity distributions show that this IF does not result from a four- centre exchange reaction. Observed threshold energies for the formation of IIF, ClIF and HIF yield lower bounds on the stability of these molecules (with respect to the separated atoms of 69, 81 and 96 kcal mol-', respectively.Analysis of the product centre-of-mass angular distributions indicate that a slightly non-linear approach is most effective in bringing about reaction to form the stable triatomic radical. These studies reveal a potentially important mechanism for the F2 + I2 --t 21F bulk gas phase reaction. The understanding of reaction dynamics from the features of a potential energy surface has improved significantly in recent years. For a simple system, such as F + H2, accurate ab initio calculations have become possible,l and the experimentally observed product angular2 and energy distributions can be explained satisfactorily. For many complicated systems, one does not expect to be able to calculate the potential energy hypersurface as accurately, but if there are certain dominant features, then the reaction dynamics can still be understood without detailed information about the hypersurface. One example is the formation of long-lived " collision complexes ", such as F + C2H2C12 -+ C2H2C12FS.4 The dynamics of product formation will be dominated by statistical features of the decomposition of the collision complex. There are many simple reactions involving heavy atoms, such as F + I2 + IF + I, for which reliable potential energy surface calculation is quite difficult, and for which there is no reason to believe the statistical theory will be applicable. Important features of the potential energy surface for these cases are often inferred at present from experimental observation rather than the other way round.Actually, all three systems mentioned above have similar exoergicities, -30 kcal, and the differ- ences in the potential energy surface along the reaction coordinate which are respon- sible for such drastic differences in reaction dynamics are shown schematically in fig. 1. The surface for F + Iz + IF + I drawn here is derived from qualitative observation in previous crossed molecular beam experiments.' The observed near forward-backward symmetry in the angular distribution and the extremely high vibrational excitation of the IF molecule indicate that the potential energy surface must be an early downhill attractive surface with a " sticky " 12F intermediate.The stability of the 12F reaction intermediate is of great interest and importance. Whether the potential energy of 12F lies slightly above or below the product IF + I, may not be very important in the general understanding of the reaction dynamics ofJAMES J . VALENTINI, MICHAEL J . COGGIOLA AND YUAN T. LEE 233 the very exoergic F + I2 4 IF + I reaction. However, whether 12F is a chemically stable species or just an unstable transient in the F + I2 reaction is extremely import- ant in the understanding of the macroscopic reaction mechanism and energy pathways of the reaction involving Fz and Iz.6 There have been several discussions on the stability of these trihalogen systems in the past, based on molecular orbital theory,' the dynamics of atom-molecule exchange reactions,s and thermolecular recombination s t ~ d i e s .~ The observation of trihalogen radical molecules in matrix isolation experi- ments has been reported in the past,1° but the direct gas phase, mass spectrometric identification has only very recently been made in our laboratory? 10 F-H-H F+ H, F+ I, F + C,H,C I, " -10 E L g -20r- z-30 I F + I HF+ H C2H2CIF+ CL -40L - 50 FIG. 1.-Idealized representation of the potential energy curves for the reactions F + H2, I2 and CZHzC12. There are two different approaches one can take using the crossed molecular beam method for deriving information about the stability of collision complexes. One approach attempts to infer information about complex stability by investigating the lifetime of the complex. In a crossed molecular beam experiment the rotational period of the complex can be conveniently used as a clock, since the product angular distribution displays forward-backward symmetry only if the lifetime of the complex is longer than one rotational period? By adjusting collision energies in the reaction of F + CH31, it has been shown13 that the lifetime of the complex can be adjusted to match the rotational period.Once the lifetime of the complex is estimated from the evaluation of the rotational period, one can use statistical theory and information on the exoergicities of the chemical reactions to calculate the stability of the com- plexes. The stability of CH31F estimated by this method is quite close to a value obtained by the synthetic method l4 outlined below.However, the applicability of this method depends on the successful matching of the rotational period and the life- time of the complex, and the validity of statistical theory in describing the decomposi- tion of the collision complex. The former is not easily accomplished experimentally for most of the systems, and the latter may not obtain, especially at high collision energies. The second method, which we used in this work, involves the direct synthesis of the radical molecules in question through endoergic molecule-molecule ~eactions,'~ such as F2 + I2 + 12F + F. By adjusting collision energies, the threshold energy of formation of the radical molecules can be obtained, and this in turn provides a lower bound on the binding energy of the radical molecules. In this paper, we will discuss the energetics of a series of radical molecules, 12F, ClIF and HIF, obtained by the molecular beam synthetic method; the dynamics of the molecule-molecule234 CROSSED BEAM STUDIES OF ENDOERGIC BIMOLECULAR REACTIONS reactions of F2 with 12, ICI and HI; and the important role 12F might play in the mechanism and energy pathways in macroscopic reactions involving Fz and 12.EXPERIMENTAL The crossed molecular beam apparatus employed in these experiments has been described in detail el~ewhere.'~ Both reactant beams were generated by supersonic expansion using differentially pumped beam sources. Mixtures of molecular fluorine (1-273 in He or He/Ne carrier gases were used to vary the collision energy. Additional control of the fluorine beam energy was provided by a resistance heated nickel oven operated between 300 and 900 K, without appreciable F atom production.The I2 and ICl beams were produced using 10- 15% mixtures of the halogens in Ar, while the HI beam was generated without use of a carrier gas. A glass nozzle maintained at a constant temperature (300-400 K) was used to fix the energy of these beams. This arrangement resulted in a range of collision energies from 3 to 20 kcal mol-l, with a spread in energy of &225%. Product molecules were detected in the plane of the reactant beams using a rotatable quadrupole mass spectrometer equipped with an electron bombardment ionizer utilizing ion counting techniques. In addition to the measurement of the angular distribution of the products, the product velocity distributions were also determined by means of cross correlation time-of-flight l6 using on-line computer control and data reduction.This technique provided a velocity resolution of better than Angular distribution data were obtained using counting times between 40 and 100 s for each point, and periodically returning to a reference angle to provide long-term normaliza- tion. Plotted angular distributions represent the average of several separate scans. Time- of-flight data were recorded for 15 to 45 min depending on the signal level. All velocity distributions were converted from the measured number density to laboratory flux with corrections for the shutter function and finite ionizer length. Product angular and velocity distributions were measured in this way for several collision energies.In addition, separate experiments were carried out to determine accurately the energy threshold for product formation. 10%. RESULTS AND ANALYSIS Any attempt to observe the trihalogen species XIF as a product of the endoergic reaction of F2 and XI, F2 + XI+ XIF + F, (1) will only be successful if reaction (1) is less endoergic than the reaction F2 + XI+X + IF + F, (2) that is, if XIF decomposition into IF and X is endoergic; and provided that the four- centre exchange mechanism does not dominate. The present investigation shows that above threshold energies of 4,6, and 11 kcal mol-I respectively collisions between F2 and XI(X = I, C1, H) do produce principally XIF and F as in (1). As the collision energy is increased, reaction (2) becomes important, first for F2 + 12, and later for F2 + ICI also, but not for F2 + HI at the collision energies used here.Angular distributions of both 12F (m/e 273) and IF (m/e 146) products of the F2 + I2 reaction at two collision energies are shown in fig. 2. In each case, part of the measured IF+ signal resulted from break-up of 12F in the detector ionizer, hence a fraction of the 12F signal has been subtracted from the IF signal, and the corrected IF angular distributions are also shown. The correction factor was determined from the fractionation ratio, 12F+ :IF*, of 12F produced at collision energies at which IFJAMES J . VALENTINI, MICHAEL J . COGGIOLA AND YUAN T. LEE 235 is not expected to form directly. Here 12F+ :IF+ was -2.0 for 200 eV ionizing electrons.Fig. 3 shows the corresponding angular distributions of ClIF (m/e 181, C135 IF) and IF from the F2 + ICI reaction. Corrections to the IF signal for ClIF fractiona- tion have been made as for 12F/IF. The ClIF fractionation ratio, ClIF+ :IF+, was -1.0 under these conditions. Although the reactive channel F2 + ICl -+ C1 + IF + F is energetically inaccessible (19 kcal mol-l endoergic) at the nominal collision lab scattering ang!e B/deg FIG. 2.--I2 + F2 -W I2F + F --t I + IF + F.0-Experimental laboratory angular distribution of IF produced in the reaction F2 + I2 at collision energies of (a) 12.9 and (b) 9.7 kcal mol-l; 0-experi- mental laboratory angular distribution of 12F produced in the same reaction; 0-IF angular distribu- tion connected for 12F+/IF+ fractionation [IF - 0.5(12F)], see text.energies indicated, there are F2/ICI collisions involving F2 molecules from the high velocity tail of the supersonic velocity distribution (&20% spread in energy) which are sufficiently energetic to produce IF. That this channel is open can be seen from the corrected (for ClIF fractionation) IF distributions of fig. 3. No IF distributions are shown in fig. 4 for the F2 + HI system, as the reactive channel (2) producing IF is prohibitively endoergic (41 kcal mol-l). Some IF+ was produced by ionizer fractionation, as determined from an investigation at high mass resolution, but the angular distributions shown were taken with less than unit mass resolution and represent the sum of the HIF+ (m/e 147) and IF+ (m/e 146) signals. It is important to note that for the F2 + ICl system there were no peaks in the mass spectrum at m/e 56 (C137F) or m/e 54 (C135F).In addition, for F2 + HI no peak at m/e 20 (HF) was observed. This strongly suggests that the observed products236 CROSSED BEAM STUDIES OF ENDOERGIC BIMOLECULAR REACTIONS are indeed ClIF and HIF, with the F atom attached to I, not to C1 or H as IClF or HIF. This is in agreement with the unfailingly regular pattern of nuclear arrange- ments in triatomic ABC systems, which always have the least electronegative atom of the three at the middle position of the molecule. For all molecules with more than twelve valence electrons this general conclusion follows from the fact that the charge distribution of the 7t orbitals is generally more concentrated at the terminal atoms than at the centre of the molecule.10 30 50 70 u 91 lab scattering angle @ /deg. FIG. 3.-ICl + Ft --t ClIF + F + C1 + IF + F. .-Experimental laboratory angular distri- bution of IF produced in the reaction F2 + ICl at collision energies of (a) 17.4 and (b) 16.1 kcal mol-'; +experimental laboratory angular distribution of ClIF produced in the same reaction; 0-IF angular distribution connected for ClIF+/IF+ fractionation [IF - l.O(ClIF)], see text. These results indicate the F2 + XI reaction does not proceed via a highly exoergic four-centre exchange mechanism to produce XF and IF. For F2 + ICl and Fz + HI no ClF or HF products were detected. For F2 + I2 the four-centre exchange pro- duces only IF, but this mechanism is exoergic by more than 60 kcal mol-l.If even a relatively small fraction of this energy appeared as product translation, the IF angular distributions would be much broader. Also, since the four-centre exchange mechan- ism does produce two identical molecules, the product distributions would have forward-backward symmetry in the centre-of-mass coordinate system, and be roughly symmetric about the centre-of-mass angle in the laboratory under our experimental conditions. From the angular distributions shown and from time-of-flight velocity analysis of the products, centre-of-mass contour maps of product flux have been constructed. These are shown in fig. 5, 6 and 7.JAMES J . VALENTINI, MICHAEL J . COGGIOLA AND YUAN T. LEE 237 lab scattering angle @ / deg.FIG. 4.-F2 + HI -b HIF + F. 0-Experimental laboratory angular distribution of HIF pro- duced in the reaction F2 + HI at collision energies of (a) 16.1 and (b) 14.9 kcal mol-'. L i _L FIG. 5.-Contour map of 12F flux density in the centre-of-mass coordinate system produced in the reaction F2 + I2 -f 12F + F at a collision energy of 12.9 kcal mol-'. These contours were obtained by fitting the experimental laboratory angular and velocity distributions.238 CROSSED BEAM STUDIES OF ENDOERGIC BIMOLECULAR REACTIONS 90 t FIG. 6.-Contour map of ClIF flux density in the centre-of-mass coordinate system produced in the reaction F2 + ICl +- ClIF + F at a collision energy of 17.4 kcal mo1-'. These contours were obtained by fitting the experimental laboratory angular and velocity distributions.t goo ,,--. 50m s-1 " IC1 c- 180' "F: UF? 0" -+ i 270' FIG. 7.-Contour map of HIF flux density in the centre-of-mass coordinate system produced in the reaction F2 + HI+ HIF + F at a collision energy of 16.1 kcal mol-'. These contours were obtained by fitting the experimental laboratory angular and velocity distributions. These contour maps of Ic.,,(O,u), the centre-of-mass doubly differential reactive scattering cross section, were constructed by iterative deconvolution of the measured ILAB(@,v) cross section data, using a modified version of a computer method due to Siska.17 This technique solves the equation: iteratively for Icqrn.(O,u). The summation is taken over the range of transformation Newton diagrams generated by the finite widths of the beam velocity distributions and angular spreads, andfi is the weighting factor for the i'th Newton diagram.Quantities with a bar indicate beam velocity and intersection angle averaged quanti- ties.JAMES J . VALENTINI, MICHAEL J . COGGIOLA AND YUAN T. LEE 239 By assuming that the monochromatic Zc,,,(O,u) is related to a monochromatic I L A B ( ~ , V ) by a single " canonical " Newton diagram: (4) V2 LAB(@, V) = 2 1,. ~ . ( Q P ) , The initial guess for ZLAB is just the experimental distribution, ZLABEXPT. Corrections to ILAB are then generated by a ratio method, i.e. : The iteration is repeated until JZABEXPT/Q& 21 1. This technique allows the " ideal " monochromatic centre-of-mass distribution to be obtained without any assumption about the functional form of the distribution.For substantially endoergic reactions at collision energies not far in excess of the threshold, the reactive cross section is expected to be quite strongly dependent on the collision energy. This is certainly the case for the reactions studied here. In the case of F2 + I2 and F2 + ICl, the energy dependence of the cross section for produc- tion of 12F or ClIF is complicated by the presence of a second reactive channel, that which results in IF production. In order to obtain a centre-of-mass distribution which would accurately reproduce the experimental data it was necessary to weight the Newton diagrams according to the energy dependence of the reactive cross sections. Hence, eqn ( 5 ) becomes: The cross section energy dependence used in fitting all three systems was similar, namely a veiy rapid rise from threshold with increasing collision energy, gradually tapering off to a near plateau.The energy dependence was partly determined from experimental relative cross section measurements. However, in energy regions for which the experimental measurement was not made or was insufficiently detailed, adjustments or extrapolations of the experimental energy dependence data were made. The adjustments and extrapolations were chosen so as to give an accurate fit to the experimental angular and velocity data, i.e., ILAB(@,v), and so as to be physically consistent, that is to give a smoothly varying cross section energy depend- ence in good agreement with the experimental relative cross section data.This energy weighting makes the most probable Newton diagram larger (-5%) than that which maximizes the quantity: (V12 3- v,2)1'2nl(vl)n2(v2), (9) the product of the relative velocity and the number densities of the two beams. This larger N.D. is used as the " canonical " one [eqn (4)] for the deconvolution. This energy weighting also makes the most probable collision energy larger (-10%) than the nominal collision energies, also derived from the maximum in eqn (9), given in the figures. The experimental data and laboratory data calculated from the deconvoluted centre-of-mass flux distributions are compared in fig. 8 and 9. The fit to the lab.240 CROSSED BEAM STUDIES OF ENDOERGIC BIMOLECULAR REACTIONS -2 1.0 0.8, Y a \ ii; Y 0.61 + 0.4r 0.2: - I laboratory velocity / loom 5-1 FIG.9.-n-Experimental laboratory velocity distribution of 12F produced in the reaction Fz + Iz at a collision energy of 12.9 kcal mol-' at four laboratory angles (a) 0 = 70.0, (6) 0 = 72.5, (c) 0 = 75.0, ( d ) 0 = 80.0; laboratory velocity distribution derived from the centre-of-mass product distribution shown in fig. 5.JAMES J . VALENTINI, MICHAEL J . COGGIOLA AND YUAN T. LEE 241 8. *. 0.8 0 . 0 . 0. ( 0 ) 0.6 - *. 0.4 0. 0.2 . ..* ..*... ... - ! I .*.. f - .* . . l*O:' ,:*:i ' * e l . ' ' I ' .- 2 0. I . 1 1 1 ; 1 1 1 I 1 I - 2 = 1.0- 0.8 I- x - a - ( b ) $ Oms- 0 0.4 ~- \ - 0.2- 4r *:..p...:....* 0 - 0 . . - .I- 0.. . - 0 ~ ~ ~ ~ ~ ; ] l l l l " K 1.0 - f-.. - 0 . - . . 0.8 - 0 -I . 0.6- oo ( C ) angular distributions and 12F lab velocity distributions are quite good.Fits to the ClIF and HIF velocity distributions, not shown, are equally satisfactory. The centre-of-mass contour maps show the sharply forward peaked nature of the XIF products. It is significant that the 12F distribution is considerably narrower in recoil velocity than either the ClIF or HIF products. In part this is a consequence of the more restrictive kinematics of the 12F + F system, for which the detected product is more than 14 times the mass of the other. However, it is also indicative of a " thermodynamic " constraint of the products to large recoil velocity (energy) due to the low stability of 12F with respect to I + IF. This thermodynamic con- straint allows formation of the trihalogen only when the excess energy channelled into translation of products is such that internal excitation of 12F is not sufficient to dissociate it into IF and I.This behaviour is evident in the 12F lab angular distribu- tions of fig. 2, which show only slight variation in going from 9.6 kcal mo1-I collision energy (-5.6 kcal mo1-I excess energy) to 12.9 kcal mol-l collision energy (-8.9 kcal rno1-I excess energy). No such constraint exists, at the collision energies studied, for either ClIF or HIF and this is reflected in both the centre-of-mass contour maps and lab angular distributions. The thermodynamic constraint of the 12F/F recoil energy distribution is even more clearly evident in fig. 10, which gives the intensity, P(E',), against recoil energy, ElT, i.e., 2 ICan,.(O,EfT) where IC..,Jt3, E'T) oCI,.,,(O,u)/u, for the systems studied.The e -I242 CROSSED BEAM STUDIES OF ENDOERGIC BIMOLECULAR REACTIONS 12F/F distribution is much more sharply peaked than that for ClIF/F or HIF/F and peaks at an energy which represents a much larger fraction of the available energy than the ClIF/F distribution. The average product translational energy, P(E'T)'E'T -- x EIT - P(E'T) is -30% of the total available energy for ClIF production, while for the 12F + F products more than 50% (5.1 kcal mol-') of the available energy appears in translation. For HIF production the average energy in translation is again high, 2.8 kcal mol-', -47%. Any such comparison of product translational energies must, of course, recognize the rather substantial change in the reaction kinematics in changing the F atom abstracting species from I2 to ICl to HI.However, the F2 + I2 and F2 + ICl systems would seem to be similar enough kinematically to allow one to attribute the recoil distribution differences to the operation of this thermodynamic constraint. It is clear that the increased sharpness of the 12F lab angular distributions relative to those for ClIF and HIF is due to the sharpness in recoil velocity (energy) and not in recoil angle. This can be seen in fig. 11, which shows the centre-of-mass angular ((I 1 ( b 1 (C) centre of mass scattering angle 0/deg. FIG. 11 .-0-Centre-of-mass angular distributions of (a) 12F, (6) ClIF and (c) HIF produced in the reactions F2 + Iz, F2 + ICl and Fz + HI at collision energies of 12.9, 17.4 and 16.1 kcal mol-', respectively, obtained by averaging Ic.,,,.(8,E'=) over recoil energy, for centre-of-mass angles 13 < 180; 0-corresponding centre-of-mass angular distributions for centre-of-mass angles 0 B 180, plotted for 2n - 8; - smoothed centre-of-mass angular distribution representing the smoothed average of each set of points. distributions, where Z(0) = &, Ic.m,(O,E'T). The 12F distribution is actually broader (-30" HWHM) than either the HIF or ClIF distributions (-15" HWHM). It is not clear whether the relative broadness of the 12F distribution is dynamically signifi- cant or merely a consequence of the more unfavourable kinematics of the 12F/F system which makes ratio method deconvolution of the centre-of-mass distribution more difficult.DISCUSSION The stabilities of the XIF species (X = I, Cl, CH3, H) have been derived from the experimentally measured thresholds for the reactions: F2 + XI XIF + F, and the known1* F2 and XI dissociation energies. Fig. 12 is a schematic energy diagram for the trihalogens and pseduo-trihalogens discussed. It is interesting to note that 12F is only 3 kcal mol-' more stable than I + IF. The stability of this radical is dueJAMES J . VALENTINI, MICHAEL J . COGGIOLA AND YUAN T. LEE 243 primarily to the strength of the 11-F bond. As the terminal atom (group) in XIF is changed through the sequence I, C1, CH3, H the trihalogen stability increases due to an increase in the X-IF bond strength, a reflection of the increased X-I diatomic (polyatomic) bond strength. Indeed, when X=H the stability of the pseudo-trihalogen is due more to the H-IF bond than to the HI-F bond.C I + I + F CH3+I+F H+I+F -. I + I + F - _ _ _ _ CH3I t F 33 I 26 FIG. 12.-Schematic energy diagram showing the stabilities of the XIF, X = I, C1, CH3 and H tri- halogens and pseudo-trihalogens. All energies are in kcal mol-I with respect to the separated atoms shown at the top. The very sharply forward-peaked distributions for all three systems would seem to indicate a preference for a bent geometry for F atom abstraction by XI, that is a preference for an F-F-I angle or F-I-X angle of less than 180" in F-F-I-X. When X=H the mass of X is negligible in comparison with I, and the F-I-X angle will not be an important determinant of the product angular distribution.The forward peaking of HIF is thus a consequence of the bent F-F-I angle. Of course high energy collisions tend to favour forward peaking, and it is important to note that the IF produced in the I + F2 reaction, kinematically identical to the HI + F2 system, is backward peaked at thermal energies,lg indicating that the bending angle of F-F-I must not be very large. The forward scattering of HIF observed in this work, in contrast to the backward peaking of IF from I + Fa, can be attributed to the dif- ference in collision energy rather than to a larger bending angle for F-F-IH compared to F-F-I. For X = I or C1 the mass of X is no longer negligible in comparison with I and both the F-F-I and F-I-X angles will be important. For the F2 + I2 and F2 + ICl systems backward scattering of FIX is only possible if all four atoms are aligned collinearly in the critical configuration.The observed forward peaking of FIX clearly argues against such a geometry, favouring bending of one or both of F-F-I and F-I-X. Simple molecular orbital considerations20 lead one to expect the F-F-I and F-I-X angles to be quite similar, SO it is likely that both F-F-I and F-I-X are slightly bent.244 CROSSED BEAM STUDIES OF ENDOERGIC BIMOLECULAR REACTIONS There are no ABC molecules with 21 valence electrons whose molecular geometry is exactly known, so it is difficult to predict precisely a preference for a particular F-F-I or F-I-X angle, nor can an unambiguous answer be determined from a simple MO picture. However, C1F2 is thought to have a bond angle -145".'*'O All known triatomic molecules with 20 valence electrons are bent (-100" bond angle), and those with 22 electrons are linear.It is thus not inconsistent to expect a bent F-F-I and F-I-X geometry in F2 + XI reactions. The potentially important role played by stable radicals in promoting bimolecular chemical reactions such as F2 + XI had not been suspected previously. The fact that a fluorine atom, which can initiate a chain reaction in F2 + XI mixtures, can be generated in a collision between F2 and XI through reaction (1) at a relative kinetic energy as low as 4 kcal mol-' (for F2 + 12) is intriguing. This is especially so consider- ing that 37 kcal mol-I is necessary to dissociate F2 and at least 37 kcal rno1-l to dissociate XI. The threshold energy of reaction (2), which also produces an F atom, as well as an X atom, can be calculated from bond dissociation energies18 and is 7 kcal mol-l, 19 kcal rnol-', and 41 kcal mol-' for X = I, C1, and H respectively.For the F2 + I2 and F2 + ICl systems these energies are also smaller than the F2 or XI bond dis- sociation energies. Even if XIF production by reaction (1) is not important, reaction (2) could be a significant source of F and X atoms in F2 + XI mixtures. The results presented here have an important bearing on the interpretation of the results of a recent study6 of the gas phase kinetics of the F2 + I2 system. If 12F were not stable, and consequently of no significance in the F2 + I2 reaction mechanism, the only exoergic source of IF in F2 + I2 mixtures would be the F + I2 and I + F2 reactions, since IF2 is not expected to be stable and was not observed in this work.Each of these reactions is -30 kcal mo1-l exoergic, insufficiently exoergic to be responsible for the IF chemiluminescence observed6 in F2 + I2 mixtures. However, since 12F is stable, another exoergic IF producing channel is open, namely the reaction F + I2F 3 2IF. This reaction is exoergic by 64 kcalmol-I, and the IF chemiluminescence observed may be due exclusively to the operation of reaction (10). (10) This work is supported by the U.S. Office of Naval Research and U.S. Energy Research and Development Administration. C. F. Bender, P. K. Pearson, S. V. O'Neil and H. F. Schaefer, J . Chem. Phys., 1972,56,4626. T. P. Schafer, Ph.D. Thesis (University of Chicago, Chicago, Illinois, 1973).3((r) M. J. Berry, J. Chem. Phys., 1973, 59, 6229; ( b ) J. C. Polanyi and K. B. Woodall, J. Chem. Phys., 1972,57, 1574; ( c ) J. H. Parker and G. C. Pimentel, J. Chem. Phys., 1969,51, 91. K. Shobatake, S. A. Rice and Y . T. Lee, J. Chem. Phys., 1973,59, 12. Y . C. Wong and Y . T. Lee, Disc. Faraday SOC., 1973, 55, 383. J. W. Birks, S. D. Gabelnick and H. S . Johnston, J. Mol. Spectr., 1975, 57, 23. '(=) S. D. Peyerimhoff and R. J. Buenker, J. Chem. Phys., 1968,49,2473; (b) R. J. Buenker and S. D. Peyerimhoff, Chem. Rev., 1974, 74, 125; S. R. Ungemach and H. F. Schaefer, J. Amer. Chem. SOC., 1976,98, 1658. wa) Y . T. Lee, J. D. McDonald, P. R. LeBreton and D. R. Herschbach, J. Chern. Phys., 1968,49, 2447; ( b ) Y . T. Lee, P. R. LeBreton, J. D. McDonald and D. R. Herschbach, J. Chem. Phys., 1969, 51, 455. D. L. Bunker and N. Davidson, J . Amer. Chem. SOC., 1958, 80, 5090. L. Y . Nelson and G. C. Pimentel, J. Chem. Phys., 1967, 47, 3671; ( b ) G. Mamantov, E. J. Vasini, M. C. Moulton, D. G. Vickroy and T. Maekawa, J. Chem. Phys., 1971,54, 3419. l1 J. J. Valentini, M. J. Coggiola and Y . T. Lee, J. Amer. Chem. SOC., 1976, 98, 853. l2 W. B. Miller, S. A. Safron and D. R. Herschbach, Disc. Faraday SOC., 1967, 44, 108.JAMES J . VALENTINI, MICHAEL J . COGGZOLA AND YUAN T. LEE 245 l3 J. M. Farrar and Y. T. Lee, J. Chem. Phys., 1975, 63, 3639. l4 J. M. Farrar and Y . T. Lee, J. Amer. Chem. SOC., 1975, 96, 7570. l5 Y . T. Lee, J. D. McDonald, P. R. LeBreton and D. R. Herschbach, Rev. Sci. Znstr., 1969, 40, l6 V. L. Hirschy and J. P. Aldridge, Rev. Sci. Instr., 1971, 42, 381. l7 P. E. Siska, J. Chem. Phys., 1973, 59, 6052. 1 8 ( a J. Berkowitz and A. C. Wahl, Adv. Fluorine Chem., 1973, 7 , 147; ( b ) B. Darwent, Bond Dis- sociation Energies in SimpZe Molecules (National Bureau of Standards, Washington, 1970), 1402. NSRD-NBS-31. l9 Y. C. Wong, unpublished. 2o A. D. Walsh, J. Chem. SOC., 1953, 2266.

ISSN:0301-7249    

DOI:10.1039/DC9776200232

出版商:RSC    

年代:1977

数据来源: RSC

摘要:

Radiative Transitions for Molecular Collisions in an Intense Laser Field” BY THOMAS F. GEORGE,? JIAN-MIN YUAN, I. HAROLD ZIMMERMAN AND JOHN R. LAING Department of Chemistry, The University of Rochester, Rochester, New York 14627, U.S.A. Received 2 1 st April, 1976 Quantum mechanical and semiclassical approaches are discussed for the study of molecular collisions in an intense laser field. Both a coherent state and Fock state representation of the photon field are investigated. The collision dynamics is described in terms of transitions between two electronic-field potential energy surfaces, where each surface depends on the field-free adiabatic surfaces and electric dipole transition matrix elements as functions of nuclear coordinates. The electronic-field surfaces exhibit avoided crossings (on the real axis) due to the radiative coupling at the resonance nuclear configurations, and other parts of these surfaces are similar to the field-free adiabatic surfaces with one of them shifted by tiW for single photon processes.Metastable states, formed at some collision energies, are conjectured to occur in the field, although absent from the field- free case. From a spectroscopic point of view, changes in energy spectra are expected from those of the individual collision-free species. Numerical results are presented for the collinear collision process Br(’P3,J + Hz(u = 0) + Am -+ Br(’PIl2) + H2(u = 0). 1. INTRODUCTION There are recent experimental studies on the enhancement of electronically in- elastic collision cross sections due to intense optical radiationlg2 and on photon absorption spectra due to the intermediate resonant molecular states of collision proce~ses.~ There has also been recent theoretical effort”15 to describe the combined effects of collisional and optical excitations.Some main reasons for the continuation of such effort and the development of new theories to describe the interaction of molecular systems with radiation are the following: (a) a molecular system in the gaseous phase interacting with a radiation field is often better characterized as dynamic rather than static. For example, in ordinary molecular beams a typical collision takes place in about s, i.e., about the cycle of an infrared laser, in which case a collision and a photon absorption should not be viewed as separate processes, particularly when absorption takes place in an intense laser field; (b) for intense field strengths and/or multiphoton processes, time-dependent perturbation theory is not valid; (c) the effect of the interaction with a quantized field as well as a classical field should be investigated for molecular systems.In this paper we are interested in atom-atom and atom-diatom collision processes in the presence of an intense laser field. In order to maintain a clear and simple physical picture, we shall focus on single photon processes for a two-(electronic) state molecular system in a single mode laser, although our formal presentation can be extended readily to more general case^.'^^'^ A related, interesting work is that of * Research supported by the Air Force Office of Scientific Research and the National Science Foundation.7 Camille and Henry Dreyfus Teacher-Scholar, Alfred P. Sloan Research Fellow.THOMAS F. GEORGE, ET AL. 247 Kroll and Watson' which deals with single- and multi-photon processes for a two- level collision system in a single field mode, using a number representation for photon states. This theory has been extended by Lad2 to a multi-level system interacting with single and multi-field modes. While these treatments are indeed interesting, they are perhaps a bit too complicated to give a simple physical picture. On the other hand, their assumption about near-adiabatic scattering is somewhat restrictive for a realistic treatment of atom-diatom collisions. Within a two-(electronic) state approximation, a semiclassical model 1 4 9 1 5 of mole- cular scattering in a strong external field has been developed recently in our labora- tory, and from this model atom-atom and atom-diatom collision cross sections can be calculated.An analogous quantum mechanical theory16 has also been derived, and in the next section of this paper we shall outline some of the key results of this theory, where we shall first use a coherent state and then the Fock state as representa- tions of the photon field. We shall also discuss the main feature of the semiclassical model. In the third section we shall present some numerical results from both the semiclassical and quantum mechanical theories for the process BI-(~P,,,) + H2(v = 0) + fiw -+ Br(,P,,,) + H2(u = 0).The description of a process such as (1.1) involves the construction of electron-field potential energy surfaces,17 which depend on the original field-free adiabatic surfaces and electric dipole (or sometimes magnetic dipole and electric quadrupole) transition matrix elements between electronic states as a function of nuclear configurations. It will become evident from our presentation in the next two sections that there is a need for ab initio and/or semiempirical studies of radiative transition matrix elements as a function of nuclear configurations as well as studies of field-free surfaces and non- adiabatic coupling. 2. THEORY OF MOLECULAR SCATTERING I N A QUANTIZED FIELD The time-dependent Schrodinger equation for a molecular collision process in an electromagnetic field is where the total Hamiltonian is x(~,q,t) = Tq + Hel(~,q) + Hrad + Hint(x,q,t), (2.2) and x and q stand for electronic and nuclear coordinates, respectively.The field- free electronic Hamiltonian is given as Tq and T, are the nuclear and electronic kinetic energy operators, respectively, and V is the electrostatic interaction among electrons and nuclei. Hrad is the Hamiltonian for the free radiation field of a single cavity mode with frequency co, where ci and 8 are the photon annihilation and creation operators. Hi,, is the Hamiltonian for the interaction between the radiation field and the molecular system, Hedx,q) = TX + V ( X , d . (2.3) Hrad = f i ~ ~ d ' d , (2.4) Hint(x,q,t) = 2 ejQj Ej, (2.5) J I, (2.6) i E. = iEIO[&i(k'Q,-wt-b) - ate-(fk*Qj-wt-b)248 RADIATIVE TRANSITIONS FOR MOLECULAR COLLISIONS where Q, represents the collective electronic and nuclear coordinates, e, is the particle charge, El0 is related to the strength and polarization of the field, k is the wave vector of magnitude m/c and the summation is over all particles.The phase p is arbitrary and may be chosen at our convenience. If the wavelength of the field is much longer than the molecular dimension, we can invoke the dipole approximation, namely, to keep only the first term of the power series expansion of exp (ik*Q,), so that Hint becomes Hillt(x,q,t) = P(x,q)-E(t) (2.7) where and the transition dipole operator p is defined as E(t) = iEA[de-i(Wf+s' - htei(~t+B)], The interaction given by eqn (2.7) is of a simpler form than eqn (2.5); however, for molecular systems where the electric dipole transition is very small, higher order transitions such as the orbital part of the magnetic dipole [to get the spin part extra terms related to spin should be added to eqn (2.5)] or electric quadrupole can be considered by including higher terms in the expansion of exp (%a&).The coherent state is often a good representation for a laser field, and since it results in simple expressions for our problem, we shall first consider it for the photon state. The expectation values of Hraa and Hint in the coherent state o! are < W r a d l a > = a2fiu, (2.10) (2.1 1) (aIHintla) = E,.C ejQjcos(k.Qj - wt), i where Eo = 2aE0 and we have chosen real a and p = 4 2 . With the dipole approxi- mation eqn (2.1 1) becomes <.IHin,la) = p*Eocos(cot).(2.12) We can also set (aIHra&) equal to zero since it is a constant and simply provides an overall energy shift. To solve eqn (2.1) we expand Y in terms of the complete set of real field-free adiabatic electronic wave functions pz(x,q) as (2.13)249 THOMAS F. GEORGE, ET AL. (2.18) (2.19) Pjl = (P,jlPlPl>- (2.20) For atom-atom systems mk is the reduced mass and the sum over k is restricted to a single term; for atom-diatom systems the sum is over two terms, one corresponding to the diatom internuclear vector and the other to the vector pointing from the centre of mass of the diatom to the atom. Invoking a two-(e1ectron)state approximation we can reduce eqn (2.15) to where pjj has been set to zero for simplicity (this rigorously vanishes in homonuclear atom-atom systems and contributes weakly to electronic transitions in other systems).Making the rotating wave (or resonance) approximation, we drop highly oscillatory terms to obtain in matrix form (H + Y)a = Ea (2.22) where a = (::). (2.23) (2.24) (2.25) Since we are concerned with very large field strengths, the " Rabi precession fre- quency" Ipltl IEol/h at fixed nuclear configurations can be very large. Therefore the adiabatic surfaces W, and W2 are so strongly coupled through the radiative inter- action that the scattering process is most appropriately solved in terms of electronic- field surfaces, which are found through a unitary transformation on Y: I6 (F'HF +Elf = Ef (2.26) where E = F'Y F = (? ;J (2.27) f = F t a (2.28) (2.29) (2.30) (2.3 1) R = [S(S + A)/2I1/*.(2.32)250 RADIATIVE TRANSITIONS FOR MOLECULAR COLLISIONS The electronic-field surfaces El and E2 are given as (- Ej = i(W1 + Wz + ha) + ~ [ ( w 2 - w1 - hm)2 + (~12.E0)(~21.E0)11/2. (2.33) Eqn (2.26) is then integrated numerically, where the scattering amplitude (S-matrix) is obtained through appropriate boundary conditions on$ [In practice it may be more efficient to integrate an equivalent equation such as eqn (2.22), in analogy to field-free cases where a diabatic representation is more efficient than the adiabatic repre~entation.1~~9~' Through a path integral appr~ach'~*l~ or simply by inspection we can derive a semi-classical approximation to the S-matrix which is the direct semiclassical analogue to eqn (2.26).The semiclassical 5'-matrix element for the transition from initial state i of reactants to final state f of products is Sfi = zlvfi ei-+i/* (2.34) where Afi is calculated in terms of a classical action as Afi = E(t2 - tl) + f*dt[T - El] + I" dt[T - E2], (2.35) tl t* t1+ -a, t2 + co. Nfi is a normalization factor like that used for field-free collisions,20-23 Tis the classical nuclear kinetic energy and t, is a time at which the electronic-field surfaces intersect in the complex plane. The summation in eqn (2.34) is over all classical paths which propagate from i to f, switching surfaces at t, (there can, of course, be more than one t,). A close look at eqn (2.22) or (2.26) reveals that field-free nonadiabatic coupling terms, i.e., (TJjl + 22(PJjl*Pk, are absent, so that our results are most appropriate for processes which are electronically adiabatic in the absence of the field.Further- more, our results are restricted to single photon processes due to the use of the rotating wave approximation. Within the context of our discussion so far, a portion of the field-free nonadiabatic coupling can be readily included by means of a vibronic representation which is discussed in the next section. As a more rigorous alternative, we may wish to begin at an earlier stage of the theory to retain the field-free non- adiabatic coupling and to further allow for multiphoton transitions. For this purpose we shall consider the Fock representation of the photon states. Expanding the total wave function in terms of products of Fock states and field-free adiabatic electronic states as Y(x,q,t) = 2 2 c * " ( q ) e - i ~ t / ~ l ~ ~ ) l n ) , (2.36) substituting into eqn (2.1), representing the field as in eqn (2.6) with /? again chosen to be n/2, and multiplying by (ml and {qjI we obtain k I n (2.37) Defining B1, through the equationTHOMAS F.GEORGE, ET AL. we can rewrite eqn (2.37) as 25 1 (2.38) While in principle we can solve eqn (2.38) directly, in practice we can make it more tractable by introducing a two-state approximation whereby the coupling between the levels (l,mo + 1) and (2,mo) is significantly larger than either of the two with a third level [in the level notation (2,m,), 2 represents the upper electronic state and m, is the photon number, etc.] With this approximation we again restrict ourselves to single photon processes.Setting E = E’ - m&co and p l l = 0, we then have the following two coupled differential equations which contain field-free nonadiabatic coupling : where Hi, is a matrix element of H from eqn (2.23). Eqn (2.38) and (2.39) are infinite matrix equations and can be solved by iterative methods. However, since we are first interested in single-photon processes, we may simplify these equations by limiting the photon indices to just two values, say m, and mo + 1, so that B2(mo+2) - Blcmo-l) = 0. For an intense field where m, is much greater than one, we may assume Blmo = Bl(m,+l) and B2(rno+1> = B2mo, in which case (H’ + U’) B = EB (2.40) where (2.41) (2.42) Ei = 2 6 E A (2.44) (2.45) Eqn (2.22) and (2.40) are similar except that eqn (2.40) has retained the field-free nonadiabatic coupling terms H12 and HZ1.[Eqn (2.40) is still restricted to single- photon processes, and if we are interested in multi-photon (and multi-surface) pro- cesses, we must resort to eqn (2.38).] Having thus coupled the surfaces W, and W2 by combined nonadiabatic and radiative interaction terms, we have introduced a resonance approximation in which either kind of coupling can generate transitions between the electronic-field configurations. This point must be kept in mind when interpreting numerical results from eqn (2.40).252 RADIATIVE TRANSITIONS FOR MOLECULAR COLLISIONS 3. CALCULATIONS Sample calculations have been carried out for reaction (1.1) restricted to collinear collisions.The (field-free) electronic degrees of freedom were represented in terms of a 2 x 2 diatomics-in-molecules matrix as used previ~usly.~~ For this model the interaction of the field with the molecular system was determined from the asymptotic collision species alone, wherein the magnetic dipole term for bromine dominates. Hence, the magnetic component of the laser field appears for Eo in the previous section. A calculated value of 1.153 atomic units has been reported for the magnetic dipole transition (2P3,2 -+ 2Pl,z) matrix element for a halogen atom,25*16 and this value was used for p12 (and p2,) appearing in the previous section. A field strength of 5.1 x lo6 V cm-I was chosen which corresponds to atomic units. Since the Br + H2 system displays a resonance behaviour between electronic and vibra- tional degrees of freedom (in the absence of a field), it was necessary to retain (field-free) vibrational nonadiabatic coupling terms, i.e., (Tp)jl + 2(P),,*P where P = -itivp/2/zmp with p as the vibrational coordinate.This was done in the quantum calculations using eqn (2.22) - (2.25), where vibronic curves as a function of just the translational coordinate were inserted for W, and W2. These curves were obtained by diagonalizing the electronic Hamiltonian plus the vibrational part of the nuclear kinetic energy operator within a two-(vibronic)state basis as described in ref. (26). The lower curve correlates to Br(2P3/2) + H2(u = 0) while the upper cor- relates to Br(2P112) + H2(u = 0). The two curves are shown schematically as W, and W’ in fig.l(a). f I I I ‘0 ‘0 la) (6) FIG. l.-(a) Schematic drawing of the two field-free vibronic curves Wl and W2 as a function of the translational coordinate r. Wl correlates to Br(2P312) + H2(u = 0) and W, correlates to Br(2P3,2) + H2(0 = 0). ro = 2.5 8, is the point at which the field is in resonance with the two curves. Each is a function of W,, W2 and the magnetic dipole-field interaction, where this interaction equals the splitting between (b) Schematic drawing of the two electronic-field curves El and E2. them at the avoided crossing (ro). Solving eqn (2.22) numerically, we obtained the transition probability for reaction (1.1) as a function of the total energy measured relative to the reaction threshold. Results are shown by the solid curve in fig.2 for the case where Aw is 1.001 times the asymptotic spin-orbit splitting in bromine. This value of Am matches the energy difference between the vibronic curves when bromine is 2.5 A from the centre of H2. The dotted curve is taken from the field-free-coupled-channel calculations of ref. (24).THOMAS F. GEORGE, ET AL. 253 Clearly there is an enhanced probability for the process Br(2P3,2) + H,(v = 0) + Semiclassical calculations were carried out using eqn (2.34) and (2.35), where the two vibronic curves were used for Wl and W2 appearing in the expression given by eqn (2.33) resulting in vibronic-field curves El and E2, which are displayed schematic- ally in fig. l(6). Analytically continuing these vibronic-field curves to the intersection point in the complex translational coordinate plane, we integrated classical trajec- tories which switched curves smoothly at this point.The results are shown by the dashed line in fig. 2. In computing these results we used a form for the normalization Br(2P,,2) + HZ(0 = 0). E / eV FIG. 2.-Probabilities for the collinear reaction Br(2P3,2) + Hz(u = 0) + Itw -+ Br(ZP1,2) + H2 (u = 0) as a function of total energy, measured relative to the reaction threshold. The value of ko is 1.001 times the asymptotic spin-orbit splitting. Shown are the results from the quantum calculations using the two-(vibronic)state model (solid line), quantum coupled-channel results with the field turned off (dotted line) and results from semiclassical calculations using the two-(vibronic)- state model (dashed line).The probabilities for the field-free transition (dotted line) have been multiplied by 100. factor N,, which is analogous to that discussed by Nikitin2628 for a purely exponential potential splitting of two diabatic curves (in the field-free case), which is similar to our problem. There are several obvious shortcomings of the above calculations presented for reaction (1. l), two of which are the restriction to collinear collisions and the neglect of electric dipole transition matrix elements (which can be important when bromine is close to H2). Inclusion of these elements would generate effects similar to those illustrated in fig. 2 for a field strength considerably smaller than 5.1 x lo6 V cm-l. Such shortcomings will be dealt with in future calculations.4. DISCUSSION Without carrying out extensive calculations, we can gain insight into how the field can affect a collision process by looking closely at the electronic-field surfaces El and E2 defined by eqn (2.33). Away from the resonance radiative coupling region of nuclear configurations, El approaches W2 and E2 approaches W, + hcc, (assuming p12 to be small asymptotically). However, around resonance where A = W2 - W, - tzco z 0, there is an avoided crossing due to radiative coupling and El and E2 become = [(W, + W2 + hu) -& I,ul2-E01]/2. Therefore, by shining a radiation field in resonance with W2 - W, at some nuclear configuration of the system, we can induce electronic transitions, whether the system is electronically adiabatic or non-254 RADIATIVE TRANSITIONS FOR MOLECULAR COLLISIONS adiabatic in the absence of the field.Furthermore, the upper electronic-field surface may have a well which can support metastable states (long-lived complexes) at certain collision energies which are absent in the field-free case. At the same time, there may be a potential barrier arising from the radiative coupling, and this can give rise to special effects such as orbiting resonances. In the case where p12 is still very large in the asymptotic regions, even more special phenomena may occur which are absent in the field-free case. From a spectroscopic point of view, it is clear that the radiation coupling effect can result in new absorption or emission spectra which are not expected for the individual (noninteracting) collision species.Extensive calculations can give us accurate information concerning the above effects as well as collision cross sections and radiative transition probabilities. How- ever, an important ingredient in these calculations is the electronic transition moments as a function of nuclear coordinates (the electric dipole contribution is usually the only one required, but sometimes the magnetic dipole and/or electric quadrupole contributions will be important) in addition to field-free potential energy surfaces and nonadiabatic coupling. These moments can be found by ab initio and/or semi- empirical technique^.^^-^^ We have assumed the field to be linearly polarized, and in calculations one can find the averaged value of the radiative coupling pl2.E0 over all orientations. Polar- ization effects can also be studied by considering the directional dependence of the radiative coupling, and this will be carried out in future investigations.D. B. Lidow, R. W. Falcone, J. F. Young and S. E. Harris, Phys. Rev. Letters, 1976,36,462. S . E. Harris and D. B. Lidow, Phys. Rev. Letters, 1974, 33, 674. C. B. Collins, B. W. Johnson, M. Y. Mirza, D. Popescu and I. Popescu, Phys. Rev. A, 1974,10, 813. L. I. Gudzenko and S. I. Yakovlenko, Sov. Phys. JETP, 1972,35, 877. N. F. Perel’man and V. A. Kovarskii, Sov. Phys. JETP, 1973,36,436. A. A. Mikhailov, Opt. Spectr., 1973, 34, 581. N. M. Kroll and K. M. Watson, Phys. Rev. A, 1976, 13, 1018. A. A. Varfolomeev, Sov. Phys. JETP, 1975, 39, 985. * V. S. Lisitsa and S. I.Yakovlenko, Sov. Phys. JETP, 1974, 39, 759. lo R. 2. Vitlina, A. V. Chaplik and M. V. Entin, Sov. Phys. JETP, 1975,40, 829. l1 L. I. Gudzenko and S. I. Yakovlenko, Sov. Phys. Tech. Phys., 1975, 20, 150. l2 A. M. F. Lau, Phys. Rev. A, 1976, 13, 139. l3 J. I. Gersten and M. H. Mittleman, J. Phys. B, 1976, 9, 383. l4 J.-M. Yuan, T. F. George and F. J. McLafTerty, Chem. Phys. Letters, 1976, 40, 163. l5 J.-M. Yuan, J. R. Laing and T. F. George, J. Chem. Phys. l6 I. H. Zimmerman, J.-M. Yuan and T. F. George, J. Chem. Phys. l7 M. V. Fedorov, 0. V. Kudrevatova, V. P. Makarov and A: A. Samokhin, Opt. Cornm., 1975, 13, 299. I. H. Zimmerman and T. F. George, J. Chem. Phys., 1975,63,2109. l9 M. Baer, Chem. Phys. Letters, 1975, 35, 112. 2o W. H. Miller and T. F. George, J. Chem. Phys., 1972, 56, 5637. 21 T. F. George and Y.-W. Lin, J. Chem. Phys., 1974,60, 2340. z2 F. J. McLafferty and T. F. George, J. Chem. Phys., 1975,63,2609. 23 W. H. Miller, Adv. Chem. Phys., 1974, 25, 69. 24 I. H. Zimmerman and T. F. George, Chem. Phys., 1975,7, 323. 25 A. M. Naqvi, Ph.D. Thesis (Harvard University, 1951); see also A. M. Maqvi and S. P. Talwar, Monthly Not. Roy. Astron. Soc., 1957, 117, 463. 26 J. R. Laing, T. F. George, I. H. Zimmerman and Y.-W. Lin, J. Chem. Phys., 1975, 63, 842. 27 E. E. Nikitin, Adv. Quantum Chem., 1970, 5, 135. 28 R. K. Preston, C. Sloane and W. H. Miller, J. Chem. Phys., 1974, 60, 4961. 29 P. S. Julienne, D. Neumann and M. Krauss, J. Chem. Phys., 1976, 64, 2990. 30 K. K. Docken and J. Hinze, J. Chem. Phys., 1972,57,4936. 31 C. F. Render and E. R. Davidson, J. Chem. Phys., 1968,49,4222. 32 R. S. Mullikan and C. A. Rieke, Rept. Prog. Phys. (London), 1941,8, 231.

ISSN:0301-7249    

DOI:10.1039/DC9776200246

出版商:RSC    

年代:1977

数据来源: RSC

摘要:

Alkali Atom-Dimer Exchange Reactions: Na + Rb, BY DAVID J. MASCORD, PETER A. GORRY AND ROGER GRICE* Department of Theoretical Chemistry, Cambridge University, Cambridge CB2 1EW Received 5th May, 1976 Velocity analysis measurements of reactive scattering from the reaction Na + Rbt 3 NaRb + Rb are reported. The product translational energy distribution is close to that predicted by a long- lived collision complex model with an average product translational energy ITav - 30% of the total available energy. A limited range of angular forms for the differential reaction cross section is compatible with the experimental data. The total reaction cross section is large Q = 120 &- 20 A', indicating that a major fraction of collisions captured by the long-range van der Waals attraction, leads to reaction.These features of the reactive scattering are discussed in terms of the form of the reaction potential energy surface, with particular regard to the orientation dependence of reaction. The exchange reactions of alkali atoms with alkali dimers M' + Mz 3 M'M + M (1) have previously been observed in a molecular beam angular distribution study1 of reactive scattering for M' = Na, K and M2 = Cs2, Rb2, K2. These measurements indicated that the reactions have large total reaction cross sections Q - 100 A2 and dispose only a small fraction -20% of the total available energy into product trans- lation. However, the measurements did not permit the form of the differential reaction cross section to be determined. In this paper, we give a brief account of a velocity analysis study of the reaction Na + Rbz + NaRb + Rb (2) which has been undertaken to improve the resolution of the differential reaction cross section.A detailed account of these velocity analysis experiments and their analysis has been given elsewhere., Large total reaction cross sections Q - 100 Hi2 are also indicated3 for the symmetrical exchange reactions with M = M' = Rb, Cs, in order to explain the nuclear spin relaxation times of alkali dimers observed in the n.m.r. of optically pumped alkali vapours. The potential energy surfaces for alkali atom-dimer exchange reactions offer an interesting example of interaction between three highly polarisable atoms, involving little change in the nature of the chemical bonding. Semi-empirical potential energy surfaces have been calculated both for the Li3 trimer4 and for all the triatomic com- bination~~ of Li and Na, and indicate the existence of bound triatomic molecules.Having only three valence electrons, the triatomic alkali systems also invite quantum mechanical calculation. Ab initio calculations on the Li, trimer have been performed using both the molecular orbital6 and the valence bond' methods. These calcula- tions confirm the stability of the Li3 molecule but raise a question as to its most stable geometry and electronic state, The pseudopotential method has been employed 8-10 for calculations involving heavier alkali atoms. The Na,, K3 and Cs, trimers have been observed" in molecular beams from supersonic nozzle expansions of the alkali256 ALKALI ATOM-DIMER EXCHANGE REACTIONS : Na+Rb, vapour.The e.s.r. spectra of matrix isolated Na, and K3 indicate l2 that these trimers are chemically bound rather than being simply van der Waals complexes. Finally, extensive Monte Carlo trajectory c a l c ~ l a t i o n s ~ ~ ~ ~ ~ have been carried out on the semi- empirical potential energy surfaces' for the reactions Li + Li2, Li + Na2 and Na + Liz. EXPERIMENTAL The apparatus employed in these experiments, shown in fig. 1, is the same as that used in the angular distribution study,l augmented by a small slotted disc velocity selector. A supersonic nozzle beam source gives a mixed beam of Rb atoms and Rb, dimers with -25 mole per cent15 of Rb, dimers. An inhomogeneous magnetic field deflects the Rb atoms, FIG.1.-Schematic diagram of the apparatus: A, alkali dimer oven; B, alkali atom oven; D, detector and velocity selector; F, beam flag; M, magnet; S, collimating slits; T, tantalum radiation shield; LN2, liquid nitrogen cooled cold shield; H20, water cooled cold shield. while the undefiected Rb, dimer beam passes into the scattering chamber with a residual impurity Q 10% of Rb atorns.l6 The Na atom beam effuses from the multichannel source of the cross beam oven. The head temperature of the oven is maintained -100 K hotter than the body in order to suppress the density of the Na2 dimer impurity to 70.2% of the Na atom density. The detector, consisting of a quadrupole mass spectrometer equipped with a surface ionization ion-source, is mounted on the rotatable lid of the apparatus.The small velocity sele~tor,'~ mounted in front of the detector, has a very compact disc assembly. This permits the detector to be maintained in the same position as that used in the angular distribution study1 and does not significantly restrict the angular range accessible to scattering measurements. The velocity distributions of the incident beams were measured with the velocity selector in the same configuration as that used for the scattering measurements. The Rb, dimer beam has a narrow velocity distribution, -20% full width at half maximum intensity, and a peak velocity, vpk = 655 m s-'. The Na has a Maxwell-Boltzmann velocity distribution with a most probable number density velocity, a, = 753 m s-l. RESULTS Since the Pt/W alloy ribbon of the surface ionisation ion-source ionises both reactively scattered NaRb, Rb and elastically scattered Rb2 with near unit efficiency to yield Rb + ions, the quadrupole mass spectrometer cannot directly distinguish between reactive and elastic scattering.This distinction may be achieved l v 2 by kinematic discrimination, since a heavy Rb2 dimer undergoes only a small deflection in laboratory coordinates due to an elastic collision with a light Na atom. ThusDAVID J. MASCORD, PETER A . GORRY AND ROGER GRICE 257 Rb2 elastic scattering is constrained close to the Rb, beam at laboratory scattering angle 0 = 90"; the Na beam is at 0 = 0". The reactive scattering by eqn (2), separates the heavy Rb atoms. Thus the NaRb, Rb reaction products can be disposed over a much wider range of laboratory scattering angles. Detailed analysis shows that Rb+ intensity at laboratory scattering angles 0 3 100" can be identified as reactive scattering.Velocity distributions of Rb+ intensity measured at 0 = loo", 105", 107.5", 110" are shown in fig. 2 and 3. The velocity distribution measurements and the previous angular distribution measurements' have been analysed, by the stochastic method of Entemann l8 which determines the differential reaction cross section in the factorised form Zcn,(9,u) = T(9)U(u) = T(B)uP(E') (3) lo-' -. U t I tr- L- \ 9 100 300 500 700 900 1100 0 1300 1500 laboratory velocity / m s-' FIG. 2.-Laboratory flux density velocity distributions of Rb+ for Na + Rb2 showing fits calculated for loose complex models. Loose complex, - a = 0.834, b = 0.083, * a = 0.5, b = 0.25; loose isotropic, --- a = 1.0, b = 0.0.(a) 0 = 110," (b) 0 = 107.5", (c) 0 = 105", (d) 0 = 100".258 ALKALI ATOM-DIMER EXCHANGE REACTIONS : Na+Rb, FIG. 3.-Laboratory flux density velocity distributions showing fits calculated for a tight stripping model (-, a = 0.5, b = 0.25) and a loose sideways peaked complex (---, H* = 70"). (a) 0 = 110", (b) 0 = 107.5", (c) 0 = 105", (d) 0 = 100". where 8 and u are the centre-of-mass scattering angle and velocity of the detected product and E' is the product translational energy. The RRKM-AM of scattering via a long-lived collision complex requires that the angular function T(8) be symmetric about 0 = 90" and gives the product translational energy distribution in the form P(E') = (E'/B',)2'3(Etot - E')' E' < B', = (E,,, - E')4 E'> B', (4) where B', = (,U/,U')~/~(C/C')~EDAVID J .MASCORD, PETER A . GORRY AND ROGER GRICE 259 and p,p' denote the reactant and product reduced masses; C,C' the van der Waals coefficients. The table lists the values, appropriate to the most probable Newton diagram, for the reactant translational energy E, the total available energy Etot and the maximum centrifugal barrier to complex dissociation Btm. The total available TABLE EN ENERGIES (kJ mol-l) FOR MOST PROBABLE NEWTON DIAGRAM energy is given by Etot = E + AD, where AD, denotes the reaction exoergicity. As shown in fig. 2, the RRKM-AM model for a loose complex (parameter q = 1) gives a good fit to the velocity distribution data, when the angular functions T(8) shown in fig.4 are employed, which range from sharply forward-backward peaked to iso- tropic. The best fit is found for a mildly forward-backward peaked angular function. t + I 1 1 1 1 1 1 1 1 1 1 1 1 0 30 60 90 120 150 30 60 90 120 150 centre of mass scatterkg cingle 8 FIG. 4.-Angular functions T(0) employed in the stochastic kinematic analysis : (a) isotropic a = 1 .O, b = 0.0; (b) mildly peaked complex n = 0.834, b = 0.083; (c) sharply peaked complex n = 0.5, b -- 0.25; (d) sideways, 0" = 70". For the functional forms see ref. (2). Since the surface ionization detector yields Rb" from both NaRb and Rb reaction products, which have nominally equal mass, conservation of linear momentum in centre-of-mass coordinates demands that the observed Rb + intensity distribution be nearly symmetric about 6 = go", independent of the lifetime of the collision complex.Consequently, the observed reactive scattering data will be insensitive to the symmetry of the differential reaction cross section about 6 = 90". Fig. 3 shows that a sharply peaked stripping differential cross section with NaRb recoiling in the forward hemi-260 ALKALI ATOM-DIMER EXCHANGE REACTIONS : Na+Rb, sphere I9 < 90" and Rb in the backward hemisphere 19 > 90°, also gives a reasonable fit to the data, when the parameter q = 2 appropriate to a tight complex is employed. However, a rebound distribution with Rb recoiling forward and RbNa backward does not give an acceptable fit.2 Fig. 3 also shows that a sideways peaked differential cross section, as illustrated in fig.4, does not give an acceptable fit to the velocity t ( a ' 0 ? I - .- s o-*C a c Y c' 1 0 0 t o I 1 110 108 106 104 102 100 98 laboratory scattering angle @ FIG. 5.-Fits to laboratory angular distribution of Rb+ for Na + Rbz, for three loose complex models (a) loose isotropic, a = 1.0, b = 0.0; (b) loose complex, a = 0.834, b = 0.083; (c) loose complex, a = 0.5, b = 0.25 (see fig. 2) and (d) tight stripping model a = 0.5, b = 0.25 (see fig. 3). distribution measurements, being shifted to lower velocity. The three long-lived collision complex models and the stripping model, which give the best fits to the velocity distribution measurements, are compared in fig. 5 with the angular distribu- tion measurements,l and give good fits in all cases.Consequently, the angular distribution measurements do not distinguish further between these differential reac- tion cross sections. Thus the velocity and angular distribution measurements doDAVID J . MASCORD, PETER A . GORRY AND ROGER GRICE 26 1 not permit the lifetime of the collision complex to be determined, and admit a range of possible angular functions between sharply peaked and isotropic. The best fit to the data is obtained for a long-lived collision complex with an angular function exhibiting mild forward and backward peaks and a loose transition state for complex dissociation. The data determine the admissible form of product velocity distribution U(u) much more closely than the angular function T(8) in the differential reaction cross section.A product translational energy distribution P(E') close to that predicted by the RRKM-AM model of eqn (4), ( 5 ) is required in fitting the data. The energies listed in the table for a loose complex, corresponding to the most probable Newton diagram, indicate that the peak of the P(E') distribution given by B', occurs at f'pk = 0.16 and the average product translational energy Elav at ffav = 0.33, where f ' = E'/Etot denotes the fraction of the total available energy disposed into translation. These values show that the product NaRb molecules have substantial internal energy. If the average internal excitation Ei,, given in the table, were mainly vibration, it would correspond to -25% of the NaRb bond energy. The limit, in which the total available energy is disposed into NaRb vibration, corresponds to -40% of the NaRb bond energy.The total reaction cross section Q can also be determined's2 by normalizing the observed reactive scattering to the small angle Rbz elastic scatter- ing. This procedure l8 involves integration over the differential reaction cross section and is relatively insensitive2 to the assumed angular function T(9) in these experiments. An average value is estimated2 as Q = 120 & 20 A2. DISCUSSION The large magnitude of the total reaction cross section Q - 120 A2 for Na + Rb,, indicates that reaction must occur in collisions at large impact parameters b - 6 A, where the intermolecular potential is due to van der Waals interaction. The capture cross section Qcap for collisions, which are attracted by the van der Waals potential and spiral into small internuclear distance, is given20 by Qcap = zb&b = (3~/2)(2C/E)"~ where borb is the orbiting impact parameter.This yields Qcap - 160 A2. Thus collision trajectories drawn into small internuclear distance by the van der Waals interaction lead to reaction for a majority of initial Rb2 orientations. This gives an estimate of the steric factor2' for reaction, p - 0.75. The form of product translational energy distribution for Na + Rb2, which is close to that predicted by the RRKM-AM modellg for a long-lived collision complex, indicates that the potential energy surface remains attractive at smaller internuclear distance inside the range of van der Waals interaction. However, our inability using present data to determine the relative magnitude of the reactive intensity in the forward direction compared with the backward direction, precludes a determination of the depth (or even the existence) of a well in the potential energy surface for the exoergic Na + Rb, reaction. The potential energy surface for the Li + Na, reaction, for which semi-empirical calculations5 have been performed, should be similar to that for Na + Rb2, since both reactions have the similar exoergicities.Comparison of the semi-empirical calculations5 for Li3 with ab initio valence bond calculations' in the collinear con- figuration shows good qualitative agreement; potential well depth = 37 kJ mol-' (semi-empirical), 28 kJ mol-' (adjusted ab initio). Comparison with more limited molecular orbital calculations6 in the bent configuration indicates a similar level of262 ALKALI ATOM-DIMER EXCHANGE REACTIONS : Na+Rb2 qualitative agreement.Consequently, we may expect the semi-empirical potential energy surfaces for Li + Na2 to exhibit the correct qualitative behaviour. As fig. 9 of the angular distribution study1 illustrates, the collinear LiNaNa potential energy surface exhibits a shallow well (depth - 17.5 kJ mol-' with respect to products) at small internuclear distance, which blends smoothly into the van der Waals attraction without an energy barrier in either the entrance or exit valleys. A second well in the potential energy surface for the NaLiNa collinear configuration, is -8 kJ mol-' more stable than the well for the LiNaNa configuration.Moreover, the dynamics of the Li + Na, reaction should be similar to the Na + Rbz reaction, since the atomic masses are in similar proportion. Monte Carlo calculations have been performed by Whiteheadi4 using the semi-empirical Li + Naz potential energy surface. At the initial translational energy of the present experi- ments, they show a product angular distribution peaking equally in the forward and backward directions and a product translational energy distribution in close accord with the RRKM-AM model for a loose complex. These results are thus compatible with the best fit found in the kinematic analysis of the Na + Rb, experimental data. In addition, the Monte Carlo calculations find a probability of reaction P(b) -0.5 out to an impact parameter b - 8 A.This indicates a high steric factor p > 0.5 in accord with our experimental conclusions. It is of interest to examine the form of the potential energy surface for these alkali-atom dimer exchange reactions, in order to establish the reason for the high steric factors. Fig. 6 shows a contour map of the semi-empirical potential energy R / A FIG. 6.-Potential energy contour map for approach of a Li atom to a Naa molecule held at its equilibrium bond length. surface for approach of Li to Na, as a function of the orientation angle cc and distance of approach R, when the Na, bond length is held rigid at the equilibrium value. This potential energy map is attractive for all directions of approach, particularly for the collinear orientation a = 0". The potential energy surface for the collinear LiNaNa configuration mentioned above, develops from this map with cc = 0" when the Na, bond is allowed to extend, and is shown in fig.9 of our previous angular distribution study.' The map of fig. 6 suggests that approach in bent orientations a 40" would lead to reaction in the nearly collinear LiNaNa configuration. Fig. 7(a) shows the minimum energy profile on the contour map of fig. 6 for the Li atom to moveDAVID J . MASCORD, PETER A . GORRY AND ROGER GRICE 263 -1 4 - 18 -20 -22 -24 - 2 6 -28 -30 f- - -2E* _- 10 20 30 A0 50 SO 70 80 90 ct E+ Li -20 - -4 01 reaction path O\ ? P - FIG. 7.-Potential energy profiles for the Li + Naz surface. Energy zero refers to the Li+ Naz asymptotic energy, 0 Li, Na; (a) Li + Nap (fixed Na-Na bond length), (6) Li + Naz, (c) Li+Naz.-32 -34 -36 -38 ’264 ALKALI ATOM-DIMER EXCHANGE REACTIONS : Na+Rb2 round from the perpendicular (a = 90") to collinear (a = 0') orientation. This profile shows a monotonic decline, which would reorient a Li atom from a bent toward a collinear orientation on approach to a rigid Na, molecule. However, the effect on these conclusions of allowing the Na, bond to respond to the approaching Li atom must also be considered. This is likely to be most important in the more strongly bent configurations. Fig. 7(b) shows the minimum potential energy profile for perpendicular (a = 90") approach of a Li atom to an unconstrained Na, molecule. The attraction is much stronger than in the perpendicular approach to a rigid Na, molecule. The descent of this profile for the lower E- potential energy surface is interrupted by an upward cusp before descending sharply into the potential energy well corresponding to the collinear NaLiNa configuration.This cusp is a section through the lower cone of a conical intersection22 of the lower E - and upper E+ potential energy surfaces.' For perpendicular approach with C,, symmetry, the electronic wavefunction of the lower E- surface belongs to the representation ,Al for R > R, and to ,B2 for R < R,, where R, denotes the internuclear distance at the intersection. The continuation of the electronic wavefunctions onto the cone of the upper E , potential energy surface is shown by dashed curves in fig. 7(b). Clearly, a trajectory for Li approaching Na, which passes through or very close to such a point of intersection,? must propagate diabatically onto the upper E+ potential energy surface and experience strong repulsion. However, for directions of approach other than cc = 90" the system no longer has CZ0 symmetry.The electronic states of both the upper and lower potential energy surfaces belong to the representation ,A'. The surfaces have an avoided intersection corresponding to the flanks of the double cone. Consequently, most collisions approaching with a broadside orientation (say a 3 50') will adiabatically follow the lower E- potential energy surface, " side-stepping " the conical inter~ection,~~ and reach the potential well corresponding to the NaLiNa configuration, i.e., insertion into the Na, bond. The propensity of trajectories to reach this most stable NaLiNa configuration is illustrated by the potential energy profile of fig.7(c). This shows the minimum potential energy as the Li atom is brought round from the collinear LiNaNa con- figuration with increasing a, just as in the profile of fig. 7(a) but allowing the Na, bond to extend. The profile now shows only a hump before descending rapidly into the potential energy well of the NaLiNa configuration. Thus even trajectories which approach initially in the near collinear orientation, may insert the Li into the Na, bond if substantially bent configurations are attained during the motion. Indeed, trajectories which are fairly long-lived may involve multiple transitions between the potential energy wells corresponding to the LiNaNa, NaLiNa and NaNaLi configura- tions.Such mobility seems likely to be most pronounced for the symmetrical alkali atom-dimer exchange reactions, where M = M' and all the potential energy wells are equivalent. In this case, the collision complex would have a very " floppy" structure and this should be apparent in the Monte Carlo calculation^.^^*^^ Thus, it is apparent that the form of the potential energy surfaces for alkali atom- dimer exchange reactions favours reaction for all orientations of approach, except a narrow region near a = 90". This is in accord with the high steric factor estimated from our experiments. The steric factor for reaction may be less than unity partly because of dynamical motion which reflects some trajectories back into the entrance valley of the potential energy surface.This will be of increasing importance at higher initial translational energies when trajectories increasingly sample the repulsive wall 7 The locus of all such points of intersection describes a line in the four dimensional space of the full potential energy surface. The line is generated for ci = 90" by the variation of R, with the Na2 bond length.DAVID J . MASCORD, PETER A. GORRY AND ROGER GRICE 265 of the potential energy surface at small internuclear distances. The Monte Carlo calculation^^^ for Li + Na, exhibit just this effect. At low initial translational energies the reaction probability P(b) > 0.5 is high but decreases with increasing initial translational energy at all but the smallest impact parameters.The topographical structure of the Li + Na2 potential energy surface is shown by the contour map of fig. 8, which is drawn in the coordinate system commonly FIG. 8.-Normal coordinate representation of the Li + Naz potential energy surface. Dashed line shows qualitatively the locus of profile (6) of fig. 7; dotted line profile (c). to display Jahn-Teller distortion of molecules of D,,, symmetry. The coordin- ates Ql,Q2, are the degenerate components of the E’ normal mode of vibration of a D,,, molecule, which treat all the bonds of the Li + Na, system equivalently. This contour map for Li + Na, may be compared with the same representati~n~~ of the H + H2 potential energy surface. This demonstrates that the H + H2 reaction is confined to the collinear configuration at low energies because the conical intersection for H, occurs at energies well above that of the H + H2 asymptotic energy.Conse- quently the lower cone provides a substantial barrier to reaction in the broadside orientation for H + H2 in contrast to the Li + Na, reaction where the tip of the cone lies below the Li + Na, asymptotic energy. of such conical intersections confirms that this is the dominant effect in determining the orientation dependence of atom-diatomic molecule reactions at low energy. Examination of other Support of this work by the Science Research Council is gratefully acknowledged.266 ALKALI ATOM-DIMER EXCHANGE REACTIONS : Na+Rb, J. C. Whitehead and R. Grice, Furuduy Disc. Chem. SOC., 1973, 55, 320, 374. D. J. Mascord, H.W. Cruse and R. Grice, MoZ. Phys., 1976,32, in press. R. Gupta, W. Happer, G. Moe and W. Park, Phys. Rev. Letters, 1974,32, 574. A. L. Companion, D. J. Steible and A. J. Starshak, J. Chem. Phys., 1968, 49, 3637. J. C. Whitehead and R. Grice, MoZ. Phys., 1973, 26,267; 1975,29, 324. D. W. Davies and G. del Conde, Furuduy Disc. Chem. SOC., 1973,55, 369; Chem. Phys., 1976 R. N. Yardley and G . G. Balint-Kurti, Chem. Phys., 1976, 16, 287. B. T. Pickup and W. Byres Brown, MoZ. Phys., 1972,23, 1189. G. A. Hart and P. L. Goodfriend, MoZ. Phys., 1975, 29, 1109. 12,45. lo D. J. Mascord, Ph.D. Thesis (Cambridge University, 1976). l1 P. J. Foster, R. E. Leckenby and E. J. Robbins, J. Phys. B, 1969,2, 478. l2 D. M. Lindsay, D. R. Herschbach and A. L. Kwiram, Mol. Phys., 1976. l3 J. C. Whitehead, Mol. Phys., 1975, 29, 177. l4 J. C. Whitehead, Mol. Phys., 1976, 31, 549. l5 R. J. Gordon, Y. T. Lee and D. R. Herschbach, J. Chem. Phys., 1971,54,2393. l6 P. B. Foreman, G. M. Kendall and R. Grice, Mol. Phys., 1972, 23, 117. l7 R. Grice, Ph.D. Thesis (Harvard University, 1967). l9 S. A. Safron, N. D. Weinstein, D. R. Herschbach and J. C. Tully, Chem. Phys. Letters, 1972, 2o L. D. Landau and E. M. Lifshitz, Mechanics (Pergamon Press, Oxford, 2nd edn., 1969), p. 51. 21 S. Glasstone, K. J. Laidler and H. Eyring, Theory of Rate Processes (McGraw-Hill, N.Y., 22 G. Herzberg and H. C. Longuet-Higgins, Disc. Furuduy SOC., 1963,35, 77. 23 C . A. Coulson, Disc. Furaduy SOC., 1963,35, 221. 24 G. Herzberg, Spectra of Polyutomic Molecules (Van Nostrand, 1966), p. 48. 25 R. N. Porter, R. M. Stevens and M. Karplus, J. Chem. Phys., 1968, 49, 5163. 26 Y. T. Lee, R. J. Gordon and D. R. Herschbach, J. Chenz. Phys., 1971, 54, 2410. 27 R. Grice and D. R. Herschbach, Mol. Phys., 1974,27, 159. 28 D. St. A. G. Radlein, J. C. Whitehead and R. Grice, Mol. Phys., 1975, 29, 1813. E. A. Entemann, Ph.D. Thesis (Harvard University, 1967). 12, 564. 1941), p. 7.

ISSN:0301-7249    

DOI:10.1039/DC9776200255

出版商:RSC    

年代:1977

数据来源: RSC

摘要:

The Reaction of F + H, +- HF + H A Case Study in Reaction Dynamics B Y JOHN c. POLANYI AND JERRY L. SCHREIBER Department of Chemistry, University of Toronto, Toronto M5S 1 A1 , Canada Received 9th June, 1976 Concepts developed in recent years as a result of experimental and theoretical studies of the dynamics of reactions A + BC 3 AB + C are examined here in trajectory studies of the reaction F + Hz + HF + H-currently the prototype of exothermic reaction. (i) An " early " barrier, characteristic of substantially exothermic reaction, has the consequence that reagent translation is much more efficient than vibration in promoting reaction, even for energies well in excess of the barrier. (ii) High vibrational excitation in the molecular product stems from the release of H-H repulsion while the new bond, F--H, is still extended (termed " mixed energy-release "); the large zero point vibration in Hz introduces variability in the F--H extension and H-H repulsion, and consequently in the breadth of the observed product vibrational distribution.(iii) Since the product vibrational excitation is governed by the attractive plus mixed energy-release, the slope of the outrun of the energy surface is not, per se, a dominant factor governing product vibrational excitation. (iv) Enhanced reagent vibration, ( A V ) , tends to be channelled into enhanced product vibration, {AV'); the efficiency ((AV'> = 0.81 AV) is dependent on the form of energy surface in the region of " corner-cutting ", corresponding to reaction through extended intermediates F--H--H.(v) Enhanced reagent translation is channelled into product translation plus rotation ((AT') + (AR') = 1.12 ( A T ) ) ; the efficiency provides an indication of the energy required to bend and compress the intermediate FH-H. (vi) The rotational dependence of the reactive cross section, a(J), provides a sensitive probe of the region of the potential-energy hyper-surface along the entry valley up to the barrier. (vii) Enhanced reagent rotational excitation at first decreases product vibrational excitation and then increases it according to experiment; this effect has not been reproduced theoretically. (viii) Product rotational excitation derives in large part from the release of repulsion in bent con- figurations : this gives rise predominantly to coplanarity and opposed directions for the product rotational and orbital motions.(ix) Enhanced reagent excitation of all sorts results in significant enhancement in product rotation, due to reaction through more-compressed and bent configurations; the most efficient conversion is from reagent rotation into product rotation ({AR') = 1.2 {AR)). (x) For thermal (300 K) reaction the computed centre-of-mass angular distribution is sharply back- ward-peaked, and similar for all product vibrational levels. (xi) Enhanced reagent vibration or translation shifts the computed mean scattering angle forward, with AT being markedly more effective than A C the " stripping threshold energy " is high, as anticipated for these masses reacting on a strongly repulsive potential-energy surface favouring collinear approach.1. INTRODUCTION The best understood chemical reaction is ortho-para hydrogen conversion, H + H2(0) + H2(p) + H. However, since it neither liberates nor consumes energy, and since it forms a product that is chemically indistinguishable from the reagent, it takes place across a potential-energy surface that is totally symmetric. The vast majority of chemical reactions, by contrast, take place across an asymmetric land- scape. The best understood process of this type at the present time is the exothermic reaction, F + H2 3 HF + H -AH," = 31.9 kcal mol-l. (1)268 THE REACTION OF F+H2+HF+H Product energy and angular distributions have been investigated for this reaction and its isotopic analogues by chemical laser,l infrared chemiluminescence and molecular beam3 techniques.Total rate constants and activation energies have been determined by mass spectrometry4 and by hot-atom experiment^.^ The potential-energy hypersurface of the ground electronic state of FH2 has been the subject of extensive ab initio computations.6 The best ab initio points6b have been fitted to continuous functions, and have served as a basis for both classical8 and quantumg calculations of reaction probability and product energy distribution. A variety of semi-empirical potential functions 798~10-14 h ave been proposed for this reaction, all of them bearing a strong qualitative resemblance to one another and to the ab initio results.s Some of these semi-empirical potential functions have been used for exact collinear quantum calculation^,^^ as well as for comparison of quantum, semi-classical, and classical results, by calculation of collinear reaction probabilities.16 Many of these surfaces have been used for full 3D calculations7*8s11-14 of product distributions by the classical trajectory approach.Recently a preliminary 3D quantum calculation has been rep01-ted.l~ The influence of higher electronic states" is to produce interaction in the region of the barrier and hence, perhaps, a small potential well on the adiabatic surface ahead of the barrier.19 Crossing between nearby FH2 electronic states has been investigated, and found to occur infrequently at thermal collision energies.2o In the present study we attempt to bring together what has been learned to date about the dynamics of F + H2, using the experimental and theoretical studies men- tioned above, as well as computations described in the following sections.Three- dimensional trajectory studies of the F + H2 system began in this laboratory con- temporaneously with the appearance of the first experimental data regarding k( Y', R', T'), the product energy distribution over vibrational, rotational and translational states.2a The computations 7*8s21 have been extended in the present work. We are concerned here with the effect of the various forms of reagent energy on reactivity and on product energy distributions, as well as with the connection between these properties and the form of the potential energy-surface. 2. POTENTIAL-ENERGY SURFACES AND COMPUTATIONAL METHOD A convenient potential form which has been employed for a variety of systems is the extended London-Eyring-Polanyi-Sat0 (LEPS) equation.The information required to specify the full three-atom potential consists of the spectroscopic para- meters of the ground singlet and first excited triplet state of the fragment diatomic molecules. The singlet can be represented by a Morse potential, lE(r) = 'DX(X - 2) X(r) = exp [-l/3(r - re)] and the triplet by an anti-Morse form due to Sato, 3E(r) = 3DX'(X' + 2) X'(r) = exp [-3/3(r - re)] where S is the " Sat0 parameter ". For surface SE1, I/? = "B; for the other surfacesJOHN C. POLANYI AND JERRY L. SCHREIBER 269 '/? # 3j3. The functions Q(r) and J(P) are obtained from the singlet and triplet curves ~ ( r ) = i[w + 3 ~ w i ~ ( r ) = p ~ ( r ) - 3 ~ ( r ) l .The three-body potential function is made up of the Q's and J's associated with each fragment diatomic pair 3 3 ~ ( Y I , r2, rJ = 2 Q i - (f 2 (Ji - J.d2r i = l i > j - 1 where i = 1, 2, 3 corresponds to diatomic pairs AB, BC and AC respectively. A number of surfaces have been used in the present work. The parameters of these surfaces are given in table 1.21 The principal surface, SE1, is shown in fig. 1. TABLE 1 .-POTENTIAL SURFACE PARAMETERS parameters common to all surfaces (SE1-5) : lkcal mol - 140.519 109.483 HF H2 IgjA-1 2.2247 r,lA 0.9171 parameters specific to individual (SE1-5): surface 3BHF 3 h 2 SE1 2.224 7 1.942 SE2 2.224 7 1.6 SE3 2.224 7 2.5 1.942 0.7416 surfaces SHF sH2 0.15 0.08 0.15 0.08 0.15 0.08 SE4 3 .O SE5 2.75 1.875 -0.087 5 0.08 1.675 -0.06 0.17 The potential energy along the minimum-energy path across the collinear cuts through the four hypersurfaces, is recorded in fig.2. Surface SE1 was selected by varying FIG. 1 .-Contours of equal potential energy for surface SE1. The axes rl and r2 correspond to the F-H distance and H-H distance, for the three atoms constrained to lie along a line; reagents are at lower right, products at upper left. The zero of energy corresponds to F + HS. The symbol (x) indicates the positions of the saddlepoint, which has a height E, = 2.16 kcal mol-I. The coordinates have been skewed by an angle of 43.6", and scaled by a factor t~ = 0.7255 (ie., y = ar2, where y is the distance along the ordinate) so that the motion of the representative point across the surface is that of a " sliding mass ".270 THE REACTION OF F+Hz+HF+H SH2 and S,, in preliminary computations until the experimental mean product vibrational excitation and activation energy were obtained in calculations on F + H2 (v = 0, J = 1).This surface is qualitatively similar to the ab initio collinear surface.8 The other surfaces introduce certain systematic variations on SEl , whose effects will be discussed in subsequent sections of this paper. - CI .- - E g 2 0 - L -24 - - 2 8 L -32 - \ \ \ I I I I , u 1.6 1.2 0.8 0.4 u 0.4 0.8 1.2 -Pi- P" P2-P"-+ bond extension / A FIG. 2.-Minimum-energy-path profiles obtained for the collinear arrangement of FHH on surfaces SE1 -, SE2 -----, SE3 - - - - a , SE4 xxxx and SE5 0000. The abscissa is measured in terms of the displacement of the bond from its equilibrium length (pi = Ri - ri') and the mid-line is the point of equal stretching, p* (the point at which p1 = pz = p*).Thus along the left half of the figure, r1 is decreasing to the value vlo + p". At each value of rl, rz is varied in order to obtain the minimum energy. When r1 has decreased to r1 + p* (i.~., p1 -p * has become zero), pz - p* is also equal to zero. Along the right half of the figure rz is increased, and at each value of rz, rl is varied to obtain the minimum energy. Note that along the entrance coordinate at the left SE1, SE2 and SE3 are all coincident, while along the separation coordinate, SEl, SE4 and SE5 are quite similar and overlap over a considerable range. The computational approach used for these calculations was similar to those previously d e s ~ r i b e d .~ ~ . ~ ~ Importance sampling of relative translational energy22 was used to improve the yield of reactive trajectories over the energy range contribut- ing to the room-temperature thermal average cross section 5 (proportional to the rate constant). In the notation of ref. (22), an order n = 4 was employed to fix the shape of the importance sampling function, with the maximum of the sampling function at 2.0 kcal. This gave good agreement between the distribution of sampling points and the reaction function T.a(T) exp (-T/kT"), where T is the reagent translational energy, a is the reactive cross-section, and To is the temperature in kelvin. For the v = 1 batch on surface SE1 and for the batch on SE4, direct sampling from a Boltz- mann flux distribution p(T) cc T exp (-T/kT") proved sufficiently efficient that importance sampling was unnecessary.In all cases, stratified sampling 22 of impact parameter b was employed. This permitted the impact parameter range to beJOHN C. POLANYI AND JERRY L. SCHREIBER 27 1 gradually increased until further contributions to the total cross section (as judged from histograms of b.P(b) against impact parameter) were judged to be negligible. The trajectory computations described in this work comprise over 25 000 trajec- tories computed over a wide variety of initial conditions. Batches for which only reactive cross sections were required were typically 100 to 200 trajectories each. Batches from which product attribute averages or differential cross sections were obtained were generally 1000 to 2000, resulting in a minimum of 27 reactive (for SE1, v = 0, J = 4) to a maximum of 731 reactive (for SE1, v = 0, J = 1, for which over 4500 trajectories were run).3. VIBRATIONAL AND TRANSLATIONAL EXCITATION I N REAGENTS AND PRODUCTS 3.1 REACTIVE CROSS SECTION AS A FUNCTION OF V AND T The reactive cross section a(T) for F + H2 (u = 0, J = 1) is shown in fig. 3(a). The threshold for reaction lies in the range T = 1.0 - 1.5 kcal mol-1 (Tis the relative translational energy). The total energy in the reagents is well above the classical barrier height, E, = 2.16 kcal mol-l, since the H2 molecule in v = 0 has a zero point energy V , = 6.2 kcal mol-l. (We denote vibrational energy relative to the minimum of the potential-well as Ye, and vibrational energy measured relative to 10 2 0 1 l-+o 3.0 0.0 J / kcalmol -' FIG.3(a).-Translational and vibrational energy dependence of the reactive cross section, 0, for F + H2. The solid line shows the histogram obtained by sorting trajectories from the 300 K batch of F + H2 (v = 0, J = 1) according to initial T (translational energy). The abscissa covers the range of T which contributes significantly to reaction at 300 K. The broken line depicts the histogram of u = 0 as V.) This indicates that the zero point energy of vibration is relatively in- effective in carrying the system across the energy barrier. The relative ineffectiveness of zero point vibrational energy, as well as vibrational energy in excess of the zero point, in promoting reaction is illustrated more explicitly in fig.3(b). The effect of increasing Tfrom 0 to 20 kcal mo1-1 (with V, held constant at 1 kcal mol-') is shown in the upper curve of fig. 3(b) and can be contrasted with the effect, shown in the lower curve, of increasing Ye over the same range (while holding T constant at 1 kcal mol-l). It is noteworthy that the contrasting efficiency holds at least up to energies -10 times the energy of the barrier. reactive cross section obtained for u = 1 ( J selected from a 300 K Boltzmann distribution).272 THE REACTION OF F+Hz+HF+H FIG 3(b).-Cross section functions for the reaction F + HI(J = 1). The upper curve shows the cross section cr against T, with the HZ vibrational energy reduced to V, = 1.0 kcal mol-1 (the normal vibration energy of H2(0 = 0) is V.= 6.22 kcal mol-’). The lower curve shows a( Ve), the cross section versus vibrational energy, with Tfixed at 1.0 kcal mo1-’. The positions of the quantum level energies are indicated along the abscissa. If instead of varying the reagent energies independently we keep the total reagent energy constant and alter the apportionment of energy between T and V, we obtain the result shown in fig. 3(c). (The same ‘‘canstant reagent energy ” condition applies to the experimental data recorded in endothermic triangle plots,24 and in certain theoretical studies of other systems made by the trajectory method25 or by the information-theoretic approach.)26 In fig. 3(c) the total reagent energy is held constant at -4 times the barrier energy, while being re-apportioned between T and V,.The preferred degree of freedom is translation, T. I I I I 4.0 5.0 6. .O Ye / t C O l ml -I7 b0 FIG. 3(c).-Cross section for F 4- Hz(J = 1) at a constant total energy T + V= = 9.22 kcal mol-I, iso-energetic with F + H2(u = 0, T = 3.0 kcal mol-I). As T was varied, V, was altered corres- pondingly, to maintain the total energy at a constant value.JOHN C. POLANYI A N D JERRY L. SCHREIBER 273 The strong preference for T over V, should not be construed as meaning that reagent vibration is without effect on the reactive cross section. In fig. 3(a) the cross section function a(T) is given for both v = 0 and v = 1; the v = 1 curve lies well above the v = 0 curve. However, an -12 kcal mol-1 increase in reagent vibra- tion [V(u = 1) - V(u = O)] has given rise to an enhancement of -10 times in the cross section, for T z 2 kcal mol-l; the same enhancement in 0 would result from an approximately 2 kcal mol-1 increase in collision energy.It follows that in this range of energies, reagent translation is roughly 6 times more effective in promoting reaction than is reagent vibration. This specificity of reagent energy was anticipated some years ago on the grounds (i) that substantially exothermic reactions (A + BC -+ AB + C) would tend to have their barrier crests located in the coordinate of approach,27 and (ii) that reagent translation (as evidenced in a model 3D trajectory study) constitutes a more effective source of momentum directed along the coordinate of approach than does reagent vibration.28 The reaction F + H2 + HF + H meets the criterion of being “ substantially exothermic ”.(The designation of a reaction as being substantially exothermic has been interpreted as meaning exothermic by 2 lOkcal m ~ l - ~ . ) ’ ~ This greater effectiveness of T than V in giving rise to exothermic reaction has been demon- strated qualitatively in experiments on two substantially exothermic reactions ; H + Clz -+ HCl + C17 and H + F2 -+ HF + F.29 Surface SE4 was distinguished from the other four energy surfaces in that a(T) showed no discernible threshold even for u = 0; the zero point energy of vibration (which amounts to -3 times the barrier height) is able in this case to give rise to substantial reaction.For surface SE4 the barrier crest-though still situated slightly ahead of the position of equal bond-extension (fig. 2)-is in a region corresponding to significant extension of both the new and the old bonds. As a consequence vibration (which gives rise to stretching of the old bond) is becoming effective in carrying the system across the barrier. The fact that the barrier crest for surface SE4 is located in a region close to the symmetrically-stretched position, i.e., the region where the minimum energy path curves and consequently the potential exhibits curvature which is no longer separable into components along rl and r2, is also evident from the anomalous value for the “ mixed ” force constant at the barrier crest CfiJ in table 2. TABLE 2.-PROPERTIES OF THE POTENTIAL SURFACES SEl SE2 SE3 SE4 SE5 Ec 2.163 2.266 2 .ox 2.249 2.632 r A a 1.434 1.408 1.472 1.275 1.346 r HtH 0.776 6 0.777 0.776 0.842 0.805 f lib -0.120 6 -0.1 18 2 -0.119 1 -0.344 0 - 0.41 6 8 fi’2 0.826 3 0.820 7 0.831 2 2.060 5 1.454 3 $22 4.327 3 4.335 2 4.316 4 2.415 7 3.441 5 % d m 15.6 15.1 26.2 5.3 19.2 %% 56.5 72.0 43.6 61.6 58.6 % d m 27.8 12.9 30.2 33.1 22.1 - - -2.314 -0.959 PC - rHwH a Internuclear separations, at the crest of the energy barrier (A).- - 1 A98 2.153 - - 0.743 0.742 - - Force constants at the crest of The superscript w refers to the potential well in the entry valley (if any). the barrier (mdyn A-1). E is in kcal moP, i’ in A.274 THE REACTION OF F+HZ+HFf-H 3.2 PRODUCTION ENERGY DISTRIBUTION OVER v' AND T' 3.2.1 THERMAL REAGENTS Since the parameters of SEl were adjusted to give agreement in the mean with the product vibrational distribution, the comparison of the product vibrational distribu- tion from the computations with that from experiment is reasonably good (see table 3 and cf.table 4). The " triangle plots " for calculated and experimentally TABLE 3.rOMPARISON BETWEEN COMPUTED RESULTS ON SEl AND EXPERIMENTAL RESULTS computed experimental EJkcaI mol - 1.937 1.6" log A/cm3 s-l mol-l 13.27 <A, 0.665 0.66' <fT) 0.239 0.26 14.2 <fi> 0.095 0.08 k(v?lkmax v ' = 1 0.22 0.31 v' = 2 [ 1 .OO] [ 1.OOJ v'= 3 0.26 0.47 v'= 1 9.98 9.35 v' = 2 6.51 7.06 v'= 3 3.39 2.40 < J'>,* K. H. Homann, W. C. Solomon, J. Warnatz, H. Gg. Wagner and C. Zetzsch, Ber. Bunsenges.Phys. Chem., 1970,74,585; see also R. Foon and M. Kaufman, Prog. React. Kinetics, 1975, 8, 81. * Polanyi and Woodall; ref. 2(c). K. B. Woodall, Ph.D. Thesis (Universityof Toronto, 1970). 7 Neglecting any correction for the spin orbit states of F(2P1,2, 3/2); see ref. (17). TABLE 4.--SUMhURY OF RESULTS FROM MODEL SURFACES (300 K) SE1 SE2 SE3 SE4 SE5(J= 1) o(300 IS)" 0.178 0.126 0.186 1.75 0.237 ETb 2.08 2.18 2.15 0.25 1.78 f2 0.665 0.507 0.859 0.668 0.706 <fR> 0.095 0.135 0.032 0.071 0.094 <emol> 133.3 12.81 109.5 130.0 132.0 computed from is the average T of reactive collisions at 300 K. determined product vibrational and rotational energy distributions are shown in fig. 4(a) and (b). Though the vibrational distributions agree well overall, the calcu- lated distribution is too narrow, in that both k3/k2 and kl/kz are smaller than those determined experimentally.This failing may be associated with the neglect of tunnelling in the classical trajectory calculations. Another defect of the calculated product energy distribution is that the rotational distribution, despite having close to the correct mean value in each vibrational level, appears to be too broad, extending (with relatively low probability) out to too high a rotational energy. This behaviour has been observed on other surfaces.ll (It should be noted that the low probability contours of the calculated distribution are the least certain, since relatively few trajectories fall into this range of vibration plus rotation.) The potential-energy surfaces explored here and elsewhere6-14 for F + H2 are T and J selected from a 300 K Boltzmann distribution. Translational activation energy, EZ = <T>, - 9 kT, where <T>JOHN C .POLANYI A N D JERRY L . SCHREIBER 275 predominantly “ repulsive ”, that is to say the energy-release occurs for the most part as the products separate. The designation of surfaces as “ repulsive ”, in contrast to “ attractive ”, is based on a simple apportionment of the total energy release as between two perpendicular sections of reaction path on the collinear energy s ~ r f a c e . ~ ~ * ~ ~ For SEl this leads to attractive energy release of dL = 1 %, and a repulsive energy- release of 9L = 99%. 30 - I 0 - E - 2 0 0 0 Y \ i 10 F+H*(v=O, I = I )+HF(v’/’)+I exot herrnic I \ \ 0 10 20 30 R ’/ k c a l mol - I FIG.4.-Contours of equal detailed rate constant k( V‘, R’, T’) from theory and experiment. (a) Contours at 0.015, 0.046, 0.077, 0.11 and 0.15 obtained from trajectories calculated on SE1 for F + H2 (u = 0, J = 1). (This J state constitutes -75% of the reactant at 300 K; triangle plots of the distribution from other J states did not differ significantly.) The plot is normalized so that the maximum value is equal to the maximum on the corresponding experimental plot [(b), below]. The relative rates into different v’ levels [normalized to k(v =’ 2) = 1 .OO] are indicated next to the lines which give the positions of the quantum vibrational energies of HF. Note that the zero of vibrational energy is taken to be the energy of HF(u = 0), in accord with the procedure used in constructing such plots from experimental data.The dashed lines indicate approximate values of the translational energy, calculated assuming that the total energy of any trajectory is equal to the average total energy of all reactive trajectories. As the trajectories actually have a distribution of total energies, it is possible for a few trajectories to lie beyond the line nominally indicating T‘ = 0. Since the release of repulsion resembles, superficially, the second half of a strong collision, the question arises as to how this energy comes to be channelled efficiently and preferentially into high states of product vibration. Broadly stated, the explana- tion is that a force applied while a new bond is still under tension gives rise to strong internal e ~ ~ i t a t i o n .~ ~ ~ * ~ ~ ~ ~ ~ ~ ~ ~ ~ A simple collinear model has been used to demonstrate the efficient forcing of oscillation into a tightening oscillator (FOTO).32 On the col- linear potential-energy surface (fig. 1) the release of repulsion while the new bond is still forming corresponds to a trajectory that cuts the corner of the energy surface. Since this is neither solely attractive nor repulsive energy-release, we term it “ mixed ’’ (symbolized do. For a given mass combination the minimum energy path across the collinear surface can be usefully separated into successive sections designated attractive, mixed276 THE REACTION OF F+Hz+HF+H l b ) 40 30 - I - 0 E - 20 Y \ i 10 0 J F+ H2-->H F ( Y j ‘ ) + H exot herrnic 0 10 20 30 1’1 kcal mol -I FIG.4.-(6) Experimental contours of equal detailed rate constant, k( V’, R‘, T’), into product energy levels, adapted from ref. (2c). This plot is normalized so that the sum of values at the (discrete) v‘J’ levels equals unity for 0’ = 2 (the most populous u’ level). Contours are the same as those given in fig. 4(a). The average total energy is estimated from EtOt = -AH: + E, + 3 kTo where -AH: is the enthalpy of the reaction, E, is the experimentally determined activation energy, k is Boltzmann’s constant, and To is 300 K. FIG. 5.-Average fraction of the available energy going into product vibrational excitation, (f:>, from 3D trajectory computations, against % ( d m + A m ) . The values of d m + dm were determined from the collinear minimum-energy paths of surfaces SEl through SE5 by the method of Kuntz er a!.[ref. (30)]. The extreme points at low <f;> and high (f;> are for surfaces SE2 and SE3. The cluster of points at intermediate <A> correspond to surfaces SE4, SE5 and SE1, reading from left to right [i.e., in order of increasing The solid line corresponds to <f;> = %(dm + A,,,) + 26.6. %(&In + Jfm)l.JOHN C . POLANYI AND JERRY L . SCHREIBER 277 and repulsive; d,, A’m and s m - Both the attractive and mixed energy release result in efficient internal excitation. Fig. 5 shows the correlation between %(dm + Am) and the percentage of the total energy that is channelled (on the average) into product vibration, %( V’), for the five energy surfaces used in the present study of the system F + H,.So long as the reactive masses are held invariant, the correlation is This is particularly instructive for the series SE2, SEl, SE3 in which the repulsive shape of the exit valley (i.e., the force along the coordinate of separation) is made progressively greater. On the present evidence this force would appear to be a secondary factor, since the outcome can be understood in terms of the progressive increase in %d, and (particularly) %dm, which characterize the earlier parts of the interaction along the approach coordinate and the curved region of the minimum- energy path. An index of d, 4 and 9 which is of more general applicability is that based on the path of a single collinear trajectory. The trajectory chosen for this purpose corresponds to reaction with a vibrationless molecular reagent, at close to the threshold collision-energy.The course of the trajectory is apportioned in an analogous fashion to that used for characterizing the minimum energy path to yield the corresponding quantities which in this case are designated dT, dT and BT. For F + H2 on SEl, dT = S%,A, = 35% and gT = 57%. As with the minimum path characterization %(dT + JT) underestimates the mean percentage vibrational excitation in the products (( Y’) = 66.5%) despite correlating quite well with the latter quantity from one surface to another, and, in the case of the sum (dT +AT), from one mass- combination to another. In the light of the fact that AT is large for the mass-combination F + H2 on SEl, it becomes interesting to consider whether the variation in magnitude of mixed energy release within a representative batch of trajectories could account for the breadth in the product vibrational distribution.Previous discussion has been con- cerned only with the mean of the product vibrational excitation, and has attempted to relate this to a representative t r a j e ~ t o r y ~ ~ or mean of several trajectories.’lb The wings of the product energy distribution should, on this view, stem from limiting types of trajectory. In general, the route across the collinear surface will depend on the spread of reagent translational energies, vibrational energies and vibrational phases. In the present example inspection of the trajectories shows, as might be expected in view of the large zero point vibrational energy in H,, that the dominant variable is the vibrational phase in H2 at the moment that F approaches closely.The extent of mixed energy release, AT, could be computed for a representative sample of trajectories (rather than for a single trajectory). It is defined by the energy released between the point at which the trajectory deviates from the entry valley by the classical amplitude of vibration, ra, up to the point that the trajectory first reaches the minimum of the exit valley, i.e., rl = r;. The value of r2 at the termination of mixed energy release is designated r . Rather than measure the energy release from r; to r ; we have chosen to ignore the variation in the point of departure from the entry valley, and simply to characterise individual trajectories by their point of arrival in the exit valley, r ; .This is an incomplete measure of the extent of mixed energy release but may be adequate for the present purpose which is to characterize, in a simple fashion, the range of types of trajectories and the consequent breadth in the outcome. Fig. 6 shows nine trajectories at nine equally-probable phase angles, qu.21 (A definition has been used for qv that makes this quantity linear with time for a non- good.llb,14U278 THE REACTION OF F+HpHF+H J' NR ,\ 1.2 1.4 1.6 ' 1- 'I - I / / / / / 12 14 16 1- b, 7 = 1.24 kcol Y =O.OO kcal FIG. 6.-Plots of collinear trajectories for F + HS ( 0 = 0, T = 1.24 kcal mol-') near the threshold for collinear reaction, depicted in the skewed and scaled coordinates described for fig.1. The nine frames represent nine values of the initial vibrational phase angle, qv, which lies in the range [0,360"] ; qv = 0" corresponds to the H2 bond length being completely extended, qv = 180" to H2 completely compressed. Since qv is a uniformly distributed random variable, equally spaced values of qv have equal probability, and the nine values shown span the entire range of possible initial vibrational phase. qv equals (a) 280", (b) 320", (c) 0", ( d ) 40", (e) 80°, (f) 120°, (g) 160", (h) 200", (i) 240". The path of the trajectory is strongly influenced by the vibration phase as the barrier (indicated by the x) is approached. The resulting product vibrational excitations of the reactive trajectories are (a) V' = 21.3,(6) V'= 24.0, (c) V'= 25.8, ( d ) V'= 27.2, (e) V'= 28.3,(h) V'= 26.5, (i) Y'= 17.0.Trajec- tories which were non-reactive are indicated by NR. rotating Morse ~scillator.)~~ The reagent conditions are approximately representa- tive of thermal reaction. Inspection of the figure shows that r ; , and hence (crudely) the extent of " corner-cutting ", increases as the phase angle is increased from ql, = 240" [frame (i)] to qv = 280", 320", O", and 40" [frames (a)-(d)]. The product vibrational excitation, Y', increases continuously along this sequence. This is in accord with the results shown in fig. 7: for most of the trajectories there is a positive correlation between Y' and r . (The points shown in fig. 7 are once again at equal intervals of q0 and, therefore, have equal a priori probability.They include the phase angles used in drawing the previous figure.)279 JOHN C. POLANYI AND JERRY L. SCHREIBER Fig. 7 includes the correlation between V’ and r for a substantially more attractive surface, designated BOPS. This surface was fitted8 to ab initio points computed by Bender et aL6’ Once again the majority of trajectories exhibit increasing V’ with increase in r ; . Due to the substantial contribution to V’ from attractive energy release, the curve of Y’ against r ; is shifted to markedly higher values of V’. For the same reason the correlation between V’ and r ; is no longer as simple as for SEl. (The rise in V’ for the small proportion of trajectories at very low r $ may be due to enhanced attractive energy-release for trajectories that are directed along the entry valley of BOPS.) I I 35k- I 1 -I FIG.7.-Product vibrational excitation V’ from collinear collisions of F + H2 (u = 0) against r 1, the value of r2 when the trajectory first crosses the line rl = r?. The lower curve is the result of trajectories at T = 1.24 kcal mol-’ on SE1; the x’s represent consecutive values of vibrational phase angle (spaced at intervals 20”). The upper curve, BOPS, is the result of collinear trajectories on the surface fitted to ab initio energies [see ref. (S)]. Again, the points (a) represent equally spaced values of the vibrational phase, at intervals of 20”. The mean value of r2” is shown for thermal reaction on SE1 and BOPS, and also for reaction with enhanced reagent vibration and translation on SE1 (downward-pointing arrows).3.2.2. VIBRATIONALLY, TRANSLATIONALLY OR ROTATIONALLY EXCITED The general question of interaction between reagent and product excitation has been discussed in earlier work both from an experimental and a theoretical standpoint (references are given below). The present discussion follows the lines of that given previously’ but provides a somewhat more explicit documentation, for the case of F + HZ, in terms of an illustrative sampling of collinear trajectories of the type introduced in the previous section. The essential points that need to be made in connection with the effect of enhanced reagent energy A V and AT on product V’ and T’ can be anticipated from an inspection of fig. 6. Trajectories that cut the corner of the energy surface and approach the exit valley from the side oscillate across that valley, i.e., they give rise to large V’.By contrast, trajectories that encounter the repulsive wall near the head of the exit valley tend to be accelerated aZong that valley, i.e., they give rise to large T’. The consequences of enhanced reagent energy can be understood if one considers the extent to which the proportions of these characteristic types of behaviour are modified. Fig. 8 shows for SE1 the effect of enhanced reagent vibrational energy (u = 1, REAGENTS, AV, AT OR AR280 THE REACTION OF F+H,-+HF+H T = 1.24 kcal mol-I). The sample given is a small one. It is evident, nonetheless, that there is a shift toward larger r ; than in the previous figure of this type, fig. 6, and a concurrent increase in V'.In one case, frame (b), the values of r ; and V' were so large that the small product translation, T', almost failed to separate the particles before the reagents reformed. In frame (e) T' - 0, and the reagents were reformed. A special set of circumstances is exemplified in frame (d) ; the H2 bond was entering its phase of compression just as the system reached the far side of the energy barrier. /dl FIG. 8.-Plots of selected collinear trajectories for F + H2, u = 1, with the same value of T (= 1.24 kcal mol-') as in fig. 6. Again, the product vibrational energy of the reactive trajectories V' are (a) 40.3, (b) 42.1, ( d ) 25.6, (e) 35.4. A non-reactive trajectory (c) is indicated by NR. qv values are (a) O", (6) 60°, (c) 80", (d) 260", (e) 300".As a consequence the particles were brought to rl = r-10 with r ; N" r20; this is a strongly compressed configuration ABC, located at the head of the exit valley. Acceleration along the length of the exit valley starting from this point gave the products high T', but low V'. (In certain cases these alternative reaction paths, through the extended or compressed intermediate, can give rise to a bimodality in the product-vibrational d i s t r i b ~ t i o n . ) ~ * ~ ~ s ~ ~ The mean value of r z was computed for a larger batch of 1D trajectories having the initial conditions v = 1, T = 1.24 kcal mol-I, and is indicated by an arrow in fig. 7; it exceeds by 4 . 1 A the mean value of rz for the thermal batch of trajectories on the same surface. The value of ( V'>v=l for the full 3D batch exceeded the 3D thermal value of {V') by 9.7 kcal mol-I.It follows that the increase in reagent vibrational excitation, A V, gave rise to an increase in product vibrational excitation (AV') which could be expressed as (AV') = 0.81 AV. (It should be stressed that the symbol A is reserved for an enhancement in reagent energy-in excess of the barrier energy-and the consequent enhancement in product energy ; this conforms to previous pra~tice.)~ Theory has tended to give (AV') z (AV),7 with the exception of H + F2 for which (AV') w 2AV was obtained.23 Experiment in the only well- studied cases gave for F + HCl+ HF + Cl {AV') w AV,7 and for Ba + HF+ BaF + H (AV') N" 0.6 AV.35 It would appear from the behaviour recorded in fig. 8 that the relation between {AV') and A V provides an indication of the geography of the potential surface in the region of corner-cutting, i.e., information concerning the energy required to form a stretched intermediate A - - B - - C.7*23*35*36JOHN C.POLANYI AND JERRY L . SCHREIBER 28 1 Specimen collinear trajectories with enhanced translation in the reagents are recorded in fig. 9 (T = 13.14 kcal mol-l, V = 0.0 kcal mol-'). Once again the large zero point vibrational energy makes possible a variety of trajectories. They are marked by diminished r ; compared with the thermal case (the trajectories of fig. 6). The diminution in ( I - ; ) , taken from a larger collinear batch, is indicated in fig. 7; it amounts to -0.25 A. This is a greater shift than the shift of (Y;) to larger values when a comparable energy was added to the reagent vibration. This is understand- able since there is a barrier to reaction through extended intermediates A - - B - - C , whereas the " sliding mass " can more readily be robbed of its propensity for corner- cutting.There is a corresponding diminution in the fraction of the available energy being channelled into product vibration. A 3D analysis of the effect of enhanced FIG. 9.-Plots of selected collinear trajectories of F + H2, v = 0, with enhanced collision energy T = 13.14 kcal mol-', chosen so that the trajectories are isoenergetic with those in fig. 8. Product vibrational excitation V' are (a) 32.3, (b) 35.5. Non-reactive trajectories are indicated by NR. qv values equal (a) 120", (6) 140", (c) 220", ( d ) 320", (e) 20".collision energy for the mass combination heavy + light-heavy showed the same effect .22 It should be noted, however, that collinear trajectories provide a poor representa- tion of the actual event for the case of enhanced translation. The representative hot- atom reactive encounter is a stripping reaction in which F carries one of the H atoms along in the forward direction, to give more-forward scattered HF.IIC The collinear arrangement precludes this, hence the preponderance of non-reactive events in fig. 9. In 3D, as fig. 3 indicates, the reactive cross-section increases steeply with enhancement in T. A batch of trajectories were performed for F + H2 (u = 0, J = 1) in 3D at an enhanced collision energy T = 13.88 kcal mol-', for comparison with F + H2 (v = 0, J = 1) with T selected from a 300 K distribution.Since this v = 0, 300 K, batch had a mean collision energy { T ) = 2.91 kcal mol-', the enhancement in reagent translation was {AT) = 10.97. The resultant increase in product translational and rotational excitations were (AT') = 5.97 and (AR') = 6.32 kcal mol-l (hence (AV') - - 1.32 kcal mol-'). The efficiency of conversion of enhanced reagent translation into product translation plus rotation was therefore {AT') + <AR') = 1.12 (AT). The large role of (AR') is further evidence of the limited value of the collinear representation. The diminished fractional conversion of the available energy into282 THE REACTION OF F+Hz+HF+H product vibration is, nonetheless, in qualitative accord with the expectation from the collinear trajectories : diminished ( r ;) is indicative of less efficient vibrational excitation.Decreased {f;) with enhanced T has been obtained theoretically and also experi- mentally for F + D2 + DF + D.' Qualitatively similar results regarding the effect of AT have been obtained experimentally for a number of other s y ~ t e m s . ~ , ~ ~ ~ ~ ~ There is experimental and theoretical evidence concerning the effect of modest changes in reagent rotational energy, AR, on the product vibrational excitation in F + H2. Coombe and Pimentellb*c obtained experimental evidence for a decrease in (f'") (the mean fraction of the available energy being channelled into product vibration) when H2(J = 0) was replaced by H,(J = 1).Experimental work in this laboratoryzf confirmed the decrease in (fV) for reagent J = 0 -+ J = 1 and showed that (f'") increased thereafter as J = 1 -+ J = 2. The individual k(u'IJ = 0), k(u'lJ = 1) and k(u'lJ = 2) were also obtained, but in view of the failure of most classical trajectory studies to account properly for the breadth of vibrational distributions, it is advantageous to compare (yV) = fn(J) from theory and experiment. The small (2-3 %) decrease observed experimentally in (yV> for J = 1 as compared with J = 0 and J = 2 is not obtained from the classical trajectory cross sections of Muckerman"" or the detailed rate constants given by Jaffe and Andenonlob or surface SE1;'l all these results are tabulated in ref. (2f). The most striking consequence of enhanced reagent rotation ( J = 0 + 4) on SEl was enhanced product rotational excitation-see section 4.2.2.The increase in reagent rotation for J = 0 -+ 4 was AR = 3.39 kcal mold'; the corresponding enhancement in mean product translational excitation was ( A T ) = 1.82 kcal mol-', and in vibrational excitation (AV') < 0. 4. ROTATIONAL EXCITATION IN REAGENTS AND PRODUCTS 4.1 REACTIVE CROSS SECTION AS A FUNCTION OF REAGENT ROTATIONAL ENERGY The thermal average of the reactive cross section for the reaction F + H,(J), as a function of reagent rotational quantum number J, has been obtained experimentally for J = 0 - 2;39 the function C(J) was found to be approximately invariant with J. The computed ii(J), with a thermal distribution over T(300 K) and with H2 in v = 0, is shown for three potential-energy surfaces in fig.10. Surfaces SEl and SE4 show markedly contrasting 8(J); SE5 is intermediate. None of the surfaces yield B # fn(J). Surface SE5 was selected as an approximation to the observed minimal dependence on J for low J's. Inspection of the energy profiles in fig. 2 shows that surfaces SE1 and SE4 differ in that the former has no well in the entrance channel, whereas the latter has a 2.3 kcal mol-l well, and consequently has its barrier displaced to a somewhat later posi- tion along the entry valley. These alternative surfaces were chosen for examinationz1 since three sets of workers"'-12 using an energy surface without a potential-well in the entry valley computed b(J) with a maximum at J w 1 , whereas Blais and Truhlar,I4 whose surface had a well, obtained an inverted a(J), i.e., one which passed through a minimum at J w 1.Since then Dosser and Sims have obtained an inverted a(J) for F + H2 using a surface with a well in the entry valley, and also one having neither well nor barrier.40 The ab initio results for F + H26 give no evidence of a potential- well. However, Jaffe, Morokuma and GeorgelgC have pointed out that inclusion of the spin-orbit interaction of F gives a lowest electronic state E , for FH2 with a shallowJOHN C . POLANYI AND JERRY L . SCHREIBER 283 well in the entry valley. SE5 of the present study, which gives the smallest dependence of a on J for intermediate J's, is of this general type. Surfaces SEl, SE4 and SE5 are all in satisfactory accord with the experimental product energy distribution.The shift in barrier location is too small to produce a major change in % ( d m +A,,,) (for the extreme cases SEl and SE4 the values of %(dm +Arn) are 43.4 and 38.4 respectively; cf. fig. 5). All three surfaces are, from this standpoint, eligible for consideration. As already remarked, none are fully acceptable on the basis of the present information concerning a(J). It appears that o(J) may provide a valuable probe for a region of the potential-energy hyper- surface to which the product energy-distribution is insensitive, namely the approach to the barrier crest in hyperspace (icy the entry valleys of the energy surfaces with F-H-H collinear-as in fig. 1-and bent). In a previous computation on model surfaces which exhibited a marked variation in the form of a(J), we attributed the observed changes to an alteration in the ratio of the time spent in the approach coordinate to the time required for appreciable rotation of the molecule under attack.41 If this ratio was small then enhanced reagent rotation gave rise to a (modest) increase in reactive cross section.If this ratio was large, enhanced rotation markedly decreased the reactive cross section. The rationale underlying this explanation was that reaction was more probable for collinear A-B-C. For a rapid approach of A to BC the angular momentum of BC could contribute (to a modest extent) to the momentum of approach of A to B, while approximate col- linearity was maintained. For slow approach, the angular momentum of BC would tend to swing A-B-C out of collinearity before B could be transferred to the attacking atom A.This line of reasoning implies that o(J) will invariably decrease in the limit of high J, since the time required for A to approach BC must be finite. FIG. 10.-Thermal average cross section d against reagent rotational quantum number J. The classical angular momentum of the H2 was taken to be 1/J(J + 1)h. SE1-, SE4 ( x 0.1)--, SE5.. .. . . We can apply this type of reasoning to the changes in a(J) recorded in fig. 10. Since SE4 is a more extreme example of the behaviour exempIified by SE5, we contrast SE5 with SEl. The most conspicuous feature of a(J) for SEl is the fall-off in cross section with increasing J. It would appear that with increased J , H, is rotating out of the preferred F-H-H alignment before reaction can occur.In accord with this line of reasoning we found that a modest increase in mean collision energy (obtained by selecting translation from a 500 M distribution instead of 300 K) diminished the284 THE REACTION OF F+H2+HF+H rate of fall-off in a(J) with J. At higher T there is less time for H2 in a given level J to rotate out of alignment. The most striking difference between SEl and SE5 is the earlier fall-off in a(J) with increasing J on SE1, in contrast to the fall-off in a(J) for SE5 which is evident only at the highest J. Inspection of pairs of trajectories having J = 3 on surface SE1 and SE5, with all initial conditions identical but a non-reactive outcome on SE1 and reactive on SE5, showed that on SE5 the long-range attraction associated with the 0.96 kcal mol-l well accelerated F and H2 toward one another, thereby significantly decreasing the time spent in the approach.This more favourable ratio of approach time to rotation time may possibly account for the successful outcome of the collisions on SE5. At sufficiently high J the curve of a(J) diminishes on SE5; the ratio of the time spent in the approach to the rotational time has increased and has become un- favourable to reaction even on SE5. It is anticipated that a(J) will also diminish at high J for surface SE4; however, our computations were not pursued out to suffi- ciently high J for this to be evident. These arguments pre-suppose that there is a preferred direction of approach for reaction.We have referred to the time required for a “ significant ” rotation of the molecule under attack. What is “ significant ” will depend on the sensitivity of the barrier-height to the bending of A-B-C away from the preferred angle. For the surfaces used here and el~ewhere”’~ for FH2 the preferred direction of approach is collinear; the onset of F.H2 repulsion occurs at a smaller F-H separation if F ap- proaches collinearly. Moreover, for this system since the zero point energy exceeds the barrier height it is possible in principle for the F atom to approach while H is greatly extended, and to experience no F*H2 repulsion. (In practice only a very high energy collision would allow F + H2 to approach while H2 remained effectively at full amplitude; this approach would not be along the minimum of the entry valley at r: in fig.1, but along a line parallel to it displaced to ri = r; + 0.14 A.) The potential energy around H2 is shown in fig. 1 1 as a function of rl and of the F-H-H bending angle, for r2 = r: and for r2 = r;. It is evident that a stretch in the H2 bond which occurs while F-H-H is approximately collinear can readily result in close approach along rl, and hence in reaction. Inspection of bond and force plots for 3D trajectories on SE1 suggested a possible explanation for the small enhancement in a from J = 0 to J = 1. For H2(J = 1) there was a greater incidence of trajectories which remained in a close-to-collinear 5 FIG. 11 .-Contours of equal potential energy for F approaching H2 on SE1. The bond length of H2 is fixed, (a) at the equilibrium length rZ0 = 0.75 A, (6) at the vibrational amplitude of H2 (u = 0), r; = 0.88 A.Contour energies are indicated (in kcal mol-I) relative to that of the diatomic with F removed to infinity.JOHN C. POLANYI AND JERRY L . SCHREIBER 285 FIG. 12.-Plots of bondlengths and forces against time for two F + H2 3D trajectories. Bond lengths ri (-), r2 (----), and v3 (. . .. . .. . .) are shown in the top halves of the two figures, as well as the sum of the two shortest bond lengths (-x-x-). Below the bond lengths are shown the components of force along each of the bonds (the force for a given bond has the same line symbol as the bond length). (a) F + H2, J = 0, unreactive. Note the short period during which r3 = rl + r2, indicative of passage through a collinear geometry, during the course of an unconstrained 3D trajectory.FIG. 12.--(b) F + Hz, J = 1, reactive. The collinear arrangement persists for a longer time. configuration over more than one vibrational period. This could be due to the fact that F " follows " the (slowly) rotating H2 for longer than would be the case if F passed by a non-rotating H2. This is illustrated in fig. 12. An analysis of the reactive trajectories for J = 1 on SEl showed a substantial fraction in which the orbital motion of F was approximately co-planar with, and in the same direction as, the rotational motion of H2-in accord with the suggestion made above. Nonetheless this explanation of a(J = 1) > a(J = 0) on SE1 should be regarded as speculative. The initial decrease in a(J) from J = 0 to J = 1 on SE4 and SE5 remains un- explained.* Further studies of the factors governing a(J) are in progress. * The " correspondence principle " used in this work to relate the rotational quantum number, J, to the magnitude of the classical rotational angular momentum, J, is the standard quasi-classical rule J2 = J ( J + 1)P; this is the customary procedure in classical trajectory studies. An alternative correspondence, frequently used in semi-classical studies of rotational energy transfer, is J2 = ( J + :)z tiz. Use of this procedure would increase the angular momentum associated with J = 0 to :h, which would probably cause a(J = 0) and o(J = 1) to be much closer together in value than was found to be the case in our calculation.We are grateful to Prof. Paul Brumer for helpful discussions on this point.286 THE REACTION OF F+H2-,HF+H 4.2 PRODUCTION ROTATIONAL ENERGY AND PLANE OF ROTATION 4.2.1 THERMAL REAGENTS For reactions exhibiting a large repulsive energy release, and having a mass- combination which permits the product repulsion to exert a substantial torque on the newly-formed molecule, there is evidence that the product repulsion is responsible for much of the product rotation.42 It has been proposed that the reaction F + H2 is of this type; 2d the strong repulsion between the products when released in a slightly bent configuration - HL'L - - (H is a heavy atom, and L a light one) is applied at a point well away from the centre-of-mass of HL and therzore exerts a torque on HL.This simple picture provides a ready explanxon of the change in product rotatiozl excita- tion in going from the reaction F + HD -+ HF, to F + H2, to F + D2, to F + HD 3 DF.2d If the supposition that 9 -+ R' (92 is the product repulsion, and R' the product rotational excitation) is correct, then there should be only a minimal dependence of R' on the initial orbital angular momentum, I,'-which in other systms governs R'. That this is so, is shown in fig. 13. Furthermore there should be a tendency for the 14 ' ' ' 1 - 7 j I--- 0' A a 6 b io I;' l ' ~ 1'6 i e ' I L (81 FIG. 13.-Average values of product rotational quantum number J', against reagent orbital angular momentum L, both measured in units of ti, for F + HD, J = 3, T = 3.72 kcal mol-'. The solid line (-) is for the HF product; the broken line (----) for DF product.rotational motion in the HF to be co-planar with the applied repulsive force, and for the H in HF to recoil in the opposite direction to the ejected H. This implies that the angle between the product rotational angular momentum vector, J', and the product orbital angular momentum vector, L', should be OJJLf E 180". An analysis of the product distribution over OJfL/ bears this out, as shown in fig. 14. Correlations between L and R', and distributions over OrL' have been presented previously for other systems,42 but not for F + H2. The plane of product rotation in F + H2 has not been studied experimentally but has become increasingly accessible through new experimental techniques developed by Herschbach and co-wo~kers.~~ 4 .2 . 2 VIBRATIONALLY , TRANSLATIONALLY OR ROTATIONALLY EXCITED REAGENTS; A v , A T OR AR As noted above, product rotation in F + H2 stems in large part from the release Enhanced reagent energy, AV, AT or AR, of repulsion in bent configurations.JOHN C. POLANYI AND JERRY L. SCHREIBER 237 I 1 I I---- appears to contribute to product rotation either by increasing the repulsive energy release, or by increasing the bending in the intermediate, or both. Increase in reagent vibration from v = 0 to u = 1, i.e., by AV x 12 kcal mol-I, increased (R’) on surface SE1 by (AR’) NN 2.4 kcal mol-l. (The major consequence of AV was enhanced (AV’)-see section 3.2.2 above.) By far the greatest part of this enhancement in product rotational excitation occurred in the lower vibrational states of the reaction product.For example, in v’ = 1 (AR’),! = 12.1 kcal mol-I. The tendency for OJtL) = 180” should be especially marked for the low- V‘ product. I I I I 1 I I 40 80 I20 I60 e,,,, / degrees FIG. 14.-Distribution of BJtLt, the angle between the product orbital and rotational angular moment (L’ and J’), for the products of F + HD, J = 3. The translational energy was selected from a 300 K Boltzmann distribution. At the extreme left QJtLP = 0 corresponds to J’ parallel to L’, while at the extreme right O,*,# = 180” corresponds to J’ anti-parallel to L’, as depicted in the insert. HF product -, DF product -----. Since the low v’ product originates from trajectories that pass through a com- pressed configuration (section 3.2.2), we conclude that the substantially enhanced rotation in v’ = 1 is connected with the enhanced repulsive energy release, and/or increased bending, in the FH*H intermediate that leads to low u’.In fact (AR’),. is significant for all 0’; v’ == 1-3. This is indicative of reaction through a more-bent intermediate, since high v’ involves reaction through stretched configurations (with some residual repulsion-the trajectory does not cross the exit valley at r2 = GO). Enhanced reagent translation, AT, markedly increases product rotation on SE1 (3.2.2). The characteristic of trajectories at enhanced translation is that they pass through more-compressed intermediate configurations, and also that they have the requisite energy to cross the higher energy-barriers corresponding to reaction through bent configurations.Both factors will tend to increase R’. An example is given in section 3.2.2. Enhanced reagent rotation AR = 3.39 kcal mol-’, corresponding to J = 0 -+288 THE REACTION OF F+H2+HF+H J = 4, increased the mean product rotational excitation by (AR') = 4.18 kcal mol-1 on SE1. Previous work has shown that there is insignificant correlation between J and J' on a repulsive surface ; the enhanced product rotational excitation cannot there- fore be explained as being an outcome of the conservation of angular When trajectories were separated into those originating from individual J levels 0-4, the following sequence of product rotational excitations were obtained for a reagent translational temperature of 300K: (R'),=, = 1.63 (R'),=, = 2.68, <R')J=2 = 4.44, {R')J=3 = 4.55 (R'),=, = 5.81, all in kcal mol-'.Inspection of the groups of trajectories coming from J = 0, 1, . . ., etc. shows that the mean collision energy for those that react is almost constant for J = 0 -+ 1 and thereafter increases (approximately linearly) by 1.7 kcal mol-' as J = 1 +- 4. This finding can most easily be summarized by saying that in this region of diminishing a(J) (fig. 10) the threshold collision energy for reaction is increasing with J. The 1.7 kcal mo1-' increase in mean collision energy (noted above) must be partially responsible for the increased product rotational excitation due to reaction through more compressed and bent configurations. Increased rotational energy in the reagents could increase the amount of bending in the intermediate, thus further enhancing R'.5. PRODUCT ANGULAR DISTRIBUTION All of the trajectory studies of this system employ repulsive potential energy surfaces that favour collinear approach, and hence all predict predominantly back- ward scattering of the molecular product for the F + H, mass ~ombination.~~ This is in qualitative accord with the DF scattering from F + D2 observed by Lee and co- w o r k e r ~ . ~ ~ However, whereas the molecular beam workers obtained some evidence of changing centre-of-mass angular-distributions for molecular product in the various o' levels, peaking at 180" for all u' but becoming more forward scattered for the higher levels, the trajectory results on SEl failed to give appreciably different angular distri- butions for different 0'.(These are the only computational data.) The results regarding angular distribution of the molecular product on SEl can be summarized as follows. (a) The differential cross section for the molecular product has a mean value (Omol> = 133" for u = 0, J = 1, with T selected from a 300 K distribution. The angular distribution is shown in fig. 15. (6) The mean angle shifts to a slightly more-forward value when the reagent is in o = 1 (T from a 300 K distribution); viz to (Omol) = 120". The breadth of the distribution increases, as shown in fig. 15. (c) We have examined the effect on Omol of repartitioning the reagent energy from vibration into translation. In (b), above, the mean collision energy for reactive en- counters was (T) x 2.0 kcal mol'l; the balance of the energy was in reagent vibration [E(v = 1) - E(u = 0) = 11.89 kcal mol-'1. In (c) we increased T t o 13.88 kcal rnol-' and decreased E(o = 1) to E(v = 0). The differential cross section broadened markedly (fig.15), and the mean became (Omol) = 102". This represents substan- tially more-forward scattering, though the mean angle is still in the backward hemi- sphere. The " stripping threshold energy "36b (the T which gives predominantly forward scattering) is high, as anticipated for this mass-combination reacting across a strongly repulsive potential-energy surface.44 Judging from Muckerman's study1lC of " hot " F + HD, the stripping threshold for F + H2 (ca. 90% of the molecular product scattered into the forward hemisphere) comes at -5 eV.( d ) The value of (Omol) for individual vibrational states Y' of the product is constant within the statistical uncertainty, i.e., to within approximately &5".JOHN - 0.06- JL eJ "2 0.04- N! 0.02- - 3 mm \ - 0 C . POLANYI AND JERRY L . SCHREIBER o.otq,, 1 I , ' I I * I 1 7 --..-- - 7 - - t ......... I - . . . . . . . . . . . . . . . . . . . . . . * . . . - - L----, * : . . ........... .......... i - ......... ---__ S.....".i I I I 1 : .........: 0 , 1 ' 1 ' do 80 I20 do 289 (e) The value of (OmoJ is invariant with reagent rotational excitation in the range J = 0 - 4, to within a similar uncertainty, approximately &6". This work was made possible by a grant from the National Research Council of Canada. J. C. P. thanks the Canada Council for the award of a Killam Memorial Scholarship. J.H. Parker and G. C. Pimentel, J. C/ieru. Phys., 1969, 51, 91 ; ( b ) R. D. Coombe and G. C . Pimentel, J. Cheni. Pliys., 1973, 59, 251 ; (') R. D. Coombe and G. C. Pimentel, J. Chern. Phys., 1973, 59, 1535; (d) M. J. Berry, J. Chen?. Phys., 1973, 59, 6229. '((I) J. C. Polanyi and D. C. Tardy, J. Chem. Phys., 1969,51,5717; ( b ) N. Jonathan, C. M. Melliar- Smith and D. H. Slater, MoZ. Phys., 1971, 20, 93; (') J. C. Polanyi and K. B. Woodall, J. Chem. Phys., 1972, 57, 1574; ( d ) D. S. Perry and J. C . Polanyi, Chem. Phys., 1976, 12, 37; (e) D. S. Perry and J. C . Polanyi, Chem. Phys., 1976, 12, 419; (f) D. J. Douglas and J. C. Pol- anyi, Chern. Phys., 1976, 16, l . -(') T. D. Schafer, P. E. Siska, J.M. Parson, F. P. Tully, Y . C. Wong and Y . T. Lee, J. Chem. Phys., 1970, 53, 3385; ( b ) Y . T. Lee (VII ICPEAC), The Physics of Electronic and Atomic ColZisions, ed. T. R. Govers and F. J. deHeer (North-Holland, Amsterdam, 1971), p. 357. A. Persky, J. Chern. Phys., 1973, 59, 3612; (b)A. Persky, J. Chern. PJiys., 1973, 59, 5578. xu) E. R. Grant and J. W. Root, J . Cheni. Phys., 1975,63,2970; ( b ) D. F. Feng, E. R. Grant and J. W. Root, J. Chem. Phys., 1976, 64, 3450. 6 ( a ) C . F. Bender, P. K. Pearson, S . V. O'Neil and H. F. Schaefer 111, J. Chem. Phys., 1972, 56, 4626; (') C. F. Bender, S. V. O'Neil, P. K. Pearson and H. F. Schaefer 111, Science, 1972, 176, 1412. A. M. G. Ding, L. J. Kirsch, D. S. Perry, J. C. Polanyi and J. L. Schreiber, Faraduy Disc. CheinSoc., 1973, 55, 252.J. C. Polanyi and J. L. Schreiber, Chem. Phys. Letters, 1974, 29, 319. J. N. L. Connor, W. Jakubetz, and J. Manz, MoZ. Phys., 1975,29, 347. Phys., 1971, 54, 2224; 59, 1128. 1972, 56,2997; (') J. T. Muckerman, J . Chem. Phys., 1972. 57, 3388. loco) J. B. Anderson, J. Chem. Phys., 1970, 52, 3849; ( b ) R. L. Jaffe and J. B. Anderson, J. Chenz. R. L. Jaffe, J. M. Henry and J. B. Anderson, J. Chem. Phy.s., 1973, 11(0) J. T. Muckerman, J. Chem. Phys., 1971, 54, 1155; ( b ) J. T. Muckerman, J. C'heni. Phys.,290 THE REACTION OF F+H,-+HF+H 12(0) R. L. Wilkins, J. Chem. Phys., 1972, 57, 912; cb) R. L. Wilkins, J. Chem. Phys., 1973, 58, 3038; ( c ) R. L. Wilkins, J. Phys. Chem., 1973,77,3081. l3 J. C. Tully, J. Chem. Phys., 1973, 58, 1396. 14(0) N.C. Blais and D. G. Truhlar, J. Chem. Phys., 1973, 58, 1090; ( b ) D. L. Miller and R. E. 15(0) S. F. Wu, B. R. Johnson and R. D. Levine, Mol. Phys., 1973, 25, 839; ( b ) J. M. Bowman, 16(a G. C. Schatz, J. M. Bowman and A. Kuppermann, J. Chem. Phys., 1975, 63, 674, 685; Wyatt, Chem. Phys. Letters, 1976. G. C. Schatz and A. Kuppermann, Chem. Phys. Letters, 1974, 24, 378. ( b ) P. A. Whitlock and J. T. Muckerman, J. Chem. Phys., 1974,61, 4618. D. G. Truhlar, J. Chem. Phys., 1972, 56, 3189; ( b ) J. T. Muckerman and M. D. Newton, J. Chem. Phys., 1972,56, 3191. 19(0) F. Rebentrost and W. A. Lester, Jr., J. Chem. Phys., 1975, 63, 3737; ( b ) F. Rebentrost and W. A. Lester, Jr., J. Chem. Phys., 1976,64, 3879; ( c ) R. L. Jaffe, K. Morokuma, and T. F. George, J. Chem.Phys., 1975,63, 3417. 20(u) J. C. Tully, J. Chem. Phys., 1974, 60, 3042; (*) I. H. Zimmerman and T. F. George, Cherrr. Phys., 1975,7,323; (') J. R. Laing, T. F. George, I. H. Zimmerman and Y. W. Lin, J. Chern. Phys., 1975, 63, 842. l7 M. J. Redmon and R. E. Wyatt, Int. J. Quunt. Chem. Symposium No. 9, 1975,403. 21 J. L. Schreiber, Ph.D. Thesis (University of Toronto, 1973). 22 C. A. Parr, J. C. Polanyi and W. H. Wong, J. Chem. Phys., 1973,58,5. 23 J. C. Polanyi, J. L. Schreiber and J. J. Sloan, Chem. Phys., 1975, 9, 403. 5716; ( b ) J. C. Polanyi and D. C. Tardy, J. Chem. Phys., 1969,51,5717; Polanyi and C. Woodrow Wilson, Jr., Chem. Phys. Letters, 1974, 24,484. C. Rebick, R. D. Levine and R. B. Bernstein, J. Chem. Phys., 1974,60,4977; ( b ) R. B. Bern- stein and R. D. Levine, Adv. Atomic Mol. Phys. (Academic Press, New York), 1975, 11, 21 5. 24(a) K. G. Anlauf, D. H. Maylotte, J. C. Polanyi and R. B. Bernstein, J. Chem. Phys., 1969, 51, D. S. Perry, J. C. 2s D.S. Perry, J. C. Polanyi and C. Woodrow Wilson, Jr., Chem. Phys., 1974, 3, 317. 27 M. H. Mok and J. C. Polanyi, J, Chem. Phys., 1969,51,1451. 28 J. C. Polanyi and W. H. Wong, J. Chem. Phys., 1969, 51, 1439. 29 J. C. Polanyi, J. J. Sloan and J. Wanner, Chem. Phys., 1976, 13, 1. 30 P. J. Kuntz, E. M. Nemeth, J. C. Polanyi, S. D. Rosner and C. E. Young, J. Chem. Phys., 31 J. C. Polanyi, J. Appl. Optics, 1975, Supplement 2, 109. 32 M. D. Pattengill and J. C. Polanyi, Chem. Phys., 1974, 3, 1. 33 W. H. Miller, J. Chem. Phys., 1970, 53, 3578. 34 C. A. Parr, J. C. Polanyi, W. H. Wong and D. C. Tardy, Furuduy Disc. Chem. Soc., 1973, 35 J. G. Pruett and R. N. Zare, J. Chem. Phys., 1976,64, 1774. 1966,44, 1168. 55, 308. 36(0) J. C. Polanyi, Furuduy Disc. Chem. Soc., 1973, 55, 389; (b) J. C. Polanyi, Furuday Disc. Chem. SOC., 1967,44,293. 37 L. T. Cowley, D. S. Horne, and J. C. Polanyi, Chem. Phys. Letters, 1971, 12, 144. 38(0) R. B. Bernstein and A. M. Rulis, Furuduy Disc. Chem. SOC., 1973, 55, 293; ( b ) A. M. Rulis, A. Gonzalez Ureiia B. E. Wilcomb and R. B. Bernstein, J. Chem. Phys., 1974,60,2822; and R. B. Bernstein, J. Chem. Phys., 1974,61,4101. 39 F. S. Klein and A. Persky, J. Chem. Phys., 1974, 61, 2472. 40 L. R. Dosser, Ph.D. Thesis (University of Arkansas, 1975). 41 B. A. Hodgson and J. C. Polanyi, J. Chem. Phys., 1971,55,4745. 42(0) N. H. Hijazi and J. C. Polanyi, J. Chem. Phys., 1975, 63, 2249; ( b ) N. H. Hijazi and J. C. Polanyi, Chem. Phys., 1975 11, 1. 43(a) C. Maltz, N. D. Weinstein and D. R. Herschbach, Mol. Phys., 1972,24, 133; cb) D. S. Y. Hsu and D. R. Herschbach, Furaduy Disc. Chem. SOC., 1973, 55, 116; D. S. Y. Hsu, G. M. McClelland and D. R. Herschbach, J. Chem. Phys., 1974,61,4927; cd) D. S. Y. Hsu, N. D. Weinstein and D. R. Herschbach, Mol. Phys., 1975, 29, 257. 44 J. C. Polanyi and J. L. Schreiber, Physical Chemistry-An Advanced Treatise, Vol. VIA. Kinetics of Gus Reactions, ed. H. Eyring, W. Jost and D. Henderson (Academic Press, New York, 1974), chap. 6, p. 383. See fig. 10. 45(0) T. P. Schafer, P. E. Siska, J. N. Parson, F. P. Tully, Y. C. Wong and Y. T. Lee, J. Chem. Phys., 1970, 53, 3325; ( b ) Y. T. Lee, Physics of Electronic and Atomic Collisions, 1972, 7, 359.

ISSN:0301-7249    

DOI:10.1039/DC9776200267

出版商:RSC    

年代:1977

数据来源: RSC

摘要:

The Scattering of Hg(6"P,) by CO, N2 and CO, BY JOHN COSTELLO, MALCOLM A. D. FLUENDY AND KENNETH P. LAWLEY* Department of Chemistry, University of Edinburgh, West Mains Road, Edinburgh EH9 3JJ Received 3rd May, 1976 The differential scattering pattern of a thermal beam of Hg(63Pz) from CO, Nz and CO, has been nxasured from 10" to 160" (CM). Pronounced and regular oscillations are observed over the \thole angular range in each system. However, the envelope is not that of purely elastic scattering, the x4I3 sin xZ(x) plot showing an almost monotonic decrease over the whole angular range. The spacing of the oscillations indicates a deflection function with an unusually broad bowl, interfering branches being 3 A apart. Two models are put forward; both include partial adsorption of the wave front and the operation of two potentials.Detailed fitting of one model shows that a highly attractive long range potential (well depth z 10 kT) is needed, but although the interference structure is well reproduced, the necessary range of the optical potential is not consistent wit.h known quenching cross sections. A second model is given in outline and involves an avoided crossing around 8 8, producing a rapid steepening of the potential gradient at that point. Quenching begins at impact parameters -7 thus indicating a very large quenching cross section unless a rather sharply peaked adscrption function is postulated with a width of only -1 8, to give the known values of oqU. The scattering of many ground electronic state species has now been thoroughly explored over a wide energy range by crossed beam techniques.The scattering of low lying excited electronic species remains largely unexplored and is, in a sense, complementary to ground state scattering in the 10-100 eV range in that there elec- tronic excitation is frequently observed in the products. By starting with an excited state (of necessity a metastable one for beam work), curve crossings and diabatic state mixing become accessible at thermal kinetic energies, and may be expected to lead to marked inelastic scattering. So far, excited state phenomena have largely besn studied through kinetic spectroscopic observation of quenching or collision induced fluorescence l s 2 though the more energetic metastable species (those of the ir:ert gases) have been used in elastic3 and Penning ionization studie~.~ Only relative quenching cross sections for Hg(3P2+1) have been measured in a beam e~periment.~ Hs(~~P,) is an attractive candidate for beam studies in that the nearest electronic state (the 3P1) is only 0.57 eV away and provides a route for quenching.The J = 2 state is not sufficiently energetic (5.4 eV above the ground state) to ionize most small molecules. The following studies of the thermal elastic scattering (or, rather, scattering without change of electronic state) of Hg* by CO, N2 and C02 were undertaken to see if more light could be cast on the known quenching processes in these systems by examining the perturbation of the elastic scattering differential cross section. EXPERIMENTAL The crossed beam apparatus has been described before.6 Hg+(3P2 with less than 15% of the 3P0 state') is generated by electron bombardment (at 10 eV) of an effusive beam of Hg and crosses a thermal effusive beam of the target gas.The angular resolution is 0.5" LAB.292 THE SCATTERING OF H S ( ~ ~ P ~ ) BY CO, N2 AND C 0 2 The detector, a fresh K surface, responds to the 3Pz state, to the 3P0 state with probably lower efficiency but not to the ground state. The 3P1 state decays in flight between scattering centre and detector (transit time 5 x s) and so is not detected. Typical main bemi signals were lo5 C.P.S. and counting techniques were used. The CM scattering patterns, averaged over the stated number of scans, are reproduced as the lowest curve in fig. 1,2 and 3. The factor x4l3 sin x multiplying the scattered intensity conveniently places all the observations within the compass of a linear scale and renders the envelope of scattering from an R6 potential horizontal.The location of the major maxima and minima is reproduced in independent sets of four or five scans, though the peak-to-valley amplitude ratio varies. The envelope is unchanged by selecting different scans for averag- ing. The sudden fall-off in intensity at less than 16" is due to imperfect unfolding of the main beam coupled with the attenuating effect of the x4/3 sin x term at small angles. In the case of CO, closer examination of the data shows a barely visible high frequency structure in the 16-20' CM region with a period N" 1.25'. INTERPRETATION AND FITTING The three scattering patterns are broadly similar (CO and N2 being very similar) in the following respects: (i) the envelope is basically monotonically decreasing across the whole angular range, though in each case there is a maximum around 90-100" (arrowed as xz) and there is a pronounced perturbation of the envelope at 20' in the case of CO and N2 and at 380" for C 0 2 , labelled as xl, (ii) oscillatory structure with an only slowly increasing period extends across the whole angular range, but the amplitude is not regular and is clearly perturbed by another frequency.The envelope must be compared with that expected from purely elastic scattering. For a potential with an R" attractive branch a horizontal (s = 6) or slowly rising (s < 6) envelope with increasing x is found.The absence of a well defined rainbow (the features at x2 do not fall away quickly enough on the dark side to be typical rain- bows) may either mean orbiting, the superposition of scattering from several rather different potentials with an overlapping rainbow structure or extensive adsorption of the incident wave front beginning at impact parameters somewhat greater than the rainbow value. The fact that interference structure is visible at all makes it unlikely that several rather different potentials are operating, for then the supernumerary spacing would be confused by the multiplicity of interfering branches. Although orbiting cannot be ruled out, it would upset the regularity of the supernumerary spacing by introducing further interfering branches (albeit of small amplitude).The same considerations apply to rainbow angles greater than 180'. The near regularity of the interference structure across such a wide angular range (especially noticeable in the case of N2) is unusual because supernumerary rainbow spacing (or inter-branch interference in general when both branches correspond to deflections in the same sense) usually decrease markedly with falling angle of observa- tion as the two branches diverge in impact parameter. The present structure seem to indicate a dominant deflection function with nearly parallel sides, i.e., that the rainbow angle is very large. The fact that the period of oscillation of o(x) nevertheless slowly increases with angle indicates that we are not observing interference structure arising between the positive and negative branches of a deflection function.Putting the remaining experimental observations and the above deductions together, we arrive at the simplest model (I) for a trial fitting: (i) The scattering is predominantly from a single deep potential that gives rise to a rainbow ZlSO",JOHN COSTELLO, ET A L . 293 (ii) The doniinant potential must lead to a deflection function in which the separa- tion of the two attractive branches is ~3 8, at small angles (from Ax = 2z/kAb). (iii) Scattering from a second, shallower potential is needed to account for the maxima in the envelopes of the CO and N2 date around x2 and the change of gradient of the COz scattering in this region. These rainbow positions serve to fix the well depths of the shallow potentials.(iv) Adsorption sets in early on both surfaces and is responsible for the falling envelope of 001). (v) The very high frequency structure with poorly resolved periodicity of -1.25' is interpreted as glory oscillations (interference between the positive and negative branches of the deflection function around x = 0') and serves to assign the impact parameter bo for the inner zero of the deflection function at 5.3 in all cases. In fact, there is not too much latitude in this value if a sensible length parameter (position of the inner zero, a) is to be obtained for the potential especially when very highly attractive potentials are operating. With two potentials the possibility of mutual interference arises. Two different fits were obtained, with and without inter-state interference.Such structure, being predominantly between the outer attractive branches of two deflection functions, is inevitably of much lower angular frequency than that originating across a single deflection function unless the two deflection functions are considerably displaced from each other-in this case by -3 A. In the present model the dominant source of interference structure is between the two negative branches of the deep deflection function ; inter-state interference produces only a small change in the scattering pattern, but agreement with experiment is marginally improved. In order to fit the scattering pattern, a flexible deflection function divided into 7 sections was employed. In each section a simple functional form was adopted subject only to the constraint of a smooth join to the neighbouring sections.In order to complete the partial wave summation, the deflection function was smoothly joined to a tail resulting from the following C(6) values; Hg*/CO, 0.83 x J m6; Hg*/N2 0.77 x J m6. It was found in all three systems that an R" potential could not be used for impact parameters less than -10 A since it gave too slowly varying a deflection function for x > 15", but C6) is not well determined by the present experiments. The best fits are shown as the upper curves in fig. 1,2 and 3, the associated deflec- tion functions in fig. 4, 5 and 6. The potentials derived by Firsov inversion of these deflection functions are plotted in fig. 7, 8 and 9. J m6 and Hg*/C02, 1.12 x DISCUSSION The overall fits are good.Both the dominant angular structure and the envelope are well reproduced, with only isolated features such as the dips in Zk) at x1 un- accounted for. However, this agreement is achieved only with the aid of a pair of unusually long range potentials and an equally long range adsorption function. In fig. 7 the Hg*/CO potential is contrasted with a Lennard-Jones potential with the same well depth and R, value. The much greater width of the potential bowl is apparent. The range of the outer branch of V(R) comes directly from the range of the outer branch of x(1) and this, in turn, comes inescapably from adding the glory lo value to the width AZ across the bowl dictated by the dominant interference structure. Thus, at x = 40" a A1 value of 90-100 is required, giving an impact parameter for this deflection of -7 A. The adsorption function P(b) has to be similarly long range, rising to 0.9 at 9-10 A,294 THE SCATTERING OF Hg(63P2) BY CO, N2 AND C02 10 FIG.1.-Observed angular scattering plot for Hg*/CO (lowest trace), velocity = 680 m s-l, number of scans = 9. Calculated curves (a) and (6) differ only in the upper state deflection function while (c) incorporates interference between upper and lower states (see fig. 4). A displacement of the upper state clearly has little effect on the calculated scattering pattern. centre of mass angle 0 0 FIG. 2.-Scattering in the Hg*/N2 system. Experimental, lowest trace velocity = 614 m s-l, number of scans = 4. (a) is calculated from the sum of scattering from a deep and shallow potential (see fig.3, (b) includes interference between them. so that the scattering down to -20" is affected. The behaviour of P(b) for b < bo is not really probed by the present experiments. The maximum adsorption cross section implied by the above adsorption function is ~3350 Hi2 and the minimum 270 Hi2 in the case of N2, where the two possible shapes of P(b) are sketched in fig. 5. Implied quenching cross sections are slightly larger in the other two systems. Other quenching and depolarization cross section measurements on Hg(3P2) are few and may be summarized by saying that with N2 as partner the total quenching cross section (ie., to all possible final states) is8~9*5 11-19 A2; with C 0 2 as partner the cross section for 3Pz + 3Pr is ~ 0 .4 A2 and with CO as partner the cross section for the J = 2 -+ 1 transition is similar to that with N2. The depolarization cross sections are all much larger8 (up to -600 A2) but they seem to be due to a long range angle dependent term in the potential, probably a quadrupole-quadrupole term not con- nected with electronic state quenching.JOHN COSTELLO, ET A L . r 295 0 FIG. 3.-Scattering in the Hg*/C02 system. Experimental, lowest trace velocity = 466 m s-', number of scans = 6. (a) Is calculated from the sum of scattering from a deep and shallow potential (see fig. 6), (b) includes interference between them. FIG. 4.-Deflection and adsorption functions for fig. 1 (Hg*/CO). The two functions * give rise to the plots (a) and (b) in fig.1, --- to plot (c), both taken in connection with the lower state -; b-scale in A. An observed quenching cross section of -20 A2 implies a maximum impact parameter for quenching rather less than 3 A. This range of attentuation function would, however, produce no detectable effect on the elastic scattering in the angular range of the present experiments unless the intermolecular potential were of rather short range. However, the interference structure points to an unusually long range potential. In interpreting an elastic scattering envelope, there is a direct relationship between V(R) and the adsorption function necessary for a fit. Classically, the differential cross section is proportional to IdX/dbl-lP(b) and without an independent knowledge of P(b) one cannot unambiguously separate the two terms. In the present case, if a296 THE SCATTERING OF Hg(63P2) B Y co, N, AND coz \ i r _ _ - - _ - u i -n L --- - .FIG. 5.-Deflection and adsorption functions for fig. 2 (Hg*/N,). The function - - gives rise to the best fit including interference, --- to the best fit without interference with the lower state -. Two possible continuations of P(b) are shown leading, respectively, to the maximum and minimum quenching cross sections compatible with the postulated deflection function. FIG. 6.-Deflection and adsorption functions for fig. 3 (Hg*/C02). The * * * function gives the best fit without interference with the lower state -, --- optimises the fit with interference. less steeply rising P(b) is required, a more steeply falling deflection function must be employed.In order to preserve the periodicity of the observed interference structure the inner negative branch of the deflection function must be softened as the outer branch is hardened. A rapidly varying potential at 8 A (close to the smallest angle of observation) suggests an avoided crossing in which the diabatic Hg(3P,) - AB(%) pair state is depressed by interaction with another close lying state. A rather sudden change in, gradient of the potential would produce a dip in ak) and tentatively we assign the perturbations at x1 in each of the systems to this cause.JOHN COSTELLO, ET AL. 297 FIG. 7.-Potentials for Hg*/CO. The two upper state potentials - - and --- are derived from the corresponding deflection functions in fig.4. Inset is the Lennard Jones function having the same E and R, values; R scale in A. FIG. 8.-Potentials for Hg*/N,. The upper state potentials . - - and --- are derived from the cor- responding deflection functions in fig. 6. t L- FIG. 9.-Potentials for Hg*/C02. The upper state potentials a a * and --- are derived from the corresponding deflection functions in fig. 7.298 THE SCATTERING OF Hg(63P2) BY CO, N, AND CO, Trying to accommodate the quenching data within the limits set by the scattering results, we construct model 11: (i) The small angle scattering < xl) is from a single potential identified with the shallow state of model I. (ii) This state is perturbed by a second state at a separation A, z 8-8.5 A. The crossing is sufficiently avoided for the motion to be almost adiabatic and most of the trajectories follow the lower surface.Nevertheless, sufficient amplitude ( -10%) is found in the upper state for the shallow rainbow at x2 to be observed, though with low amplitude. At some impact parameter less than b,, adsorption ensues on the lower surface and reaches 90% by the time the forward glory on the lower surface is reached. FIG. 10.-The type of deflection functions needed to minimise the opacity function. The upper state ~ ( 6 ) is taken unchanged from fig. 4. The lower state function is sufficiently steep to produce the observed envelope of a(x). Two possible extrapolations of P(b) are shown, the lower one leading to oSu - 30 A2. (iii) The steepness of the attractive branch of the lower surface is at least three times greater than in model I in order to permit a much reduced P(b) function at large b.The broad features of the deflection function and P(b) function indicated by this model are given in fig. 10. The softening of the inner attractive branch is apparent, though it must be remembered that phase shifts in the presence of an optical potential do contain a contribution from the imaginary part of the potential and it is by no means clear that the ordinary semi-classical analysis holds. The inner branch to the potential must thus be regarded as conjectural. Even with an almost vertical outer branch to x(b) adsorption must set in rapidly at b E b, (the rainbow value) and unless the P(b) function is restricted to a band of b values between 5 and 6 A the implied value of the quenching cross section is still E 150 A in each system. The configuration interaction responsible for the perturbation of the outer branch of the potential energy function is still a matter of conjecture.A steeply plunging ionic state (Hg+AB' seems the more likely charge distributionlO*ll in view of the high I.P. of the molecular partners) has been postulated in the quenching of Hg(",) by Na, but none of the present molecular partners has a positive electron afhnity13JOHN COSTELLO, ET AL. 299 and a crossing of the 3P2 state at "8 A hardly seems feasible. More likely as the source of the perturbation is the interaction of the Hg(3P) - AB(2) pair state with the state dissociating to Hg('S,) - AB(1*311,). All three molecular partners have excited states close to 6 eV in which the In, orbital is occupied and this level is nearly resonant with the Hg 3P2 level at 5.4 eV.Although the overlap of the relevant orbitals would be small at 8 A (neither the 6p nor In orbitals are grossly different from highest occupied orbitals in the ground electronic states) l3 the interaction energy need only be lowered by 4 x erg from the normal dispersion energy at this separation to give the observed potential. CONCLUSIONS The thermal scattering of HgFPJ from CO, N2 and C 0 2 exhibits a fairly simple interference structure that persists out to the largest angle of observation, nearly 180" (CM). Each system also shows evidence of quenching or an attenuation of the elastic scattering compared with that expected from a normal Rd potential which begins at quite small angles of scattering.The very fact that structure is observed at all points to the conclusion that either the three molecular states evolving from the separated species (0 = 0-, 1 and 2 in the linear configuration) have very similar potentials or that selective quenching on some branches simplifies the scattering pattern. The spacing of the interference oscillations leads almost inescapably to a deflection function and hence to a potential that is very broad compared with the Lennard-Jones form. The simplest detailed model that fits most of the scattering data is a two state one correlating with degenerate levels at infinite separation. Adsorption is needed on both surfaces from -10 A inwards. Suitably broad potentials give a good fit to the observed angular structure which is interpreted as supernumerary bows in a deep well.The model, however, leads to unacceptably large values of the quenching cross section (-300 A') and a second model is therefore proposed in which the outer branch of the deflection function is considerably steepened at separations "8-8.5 A to account for some of the fall-off of the elastic scattering with increasing angle. A second, shallow potential is still needed to account for some of the features of the scattering. Even with an outer branch of almost infinite gradient [vanishing contribu- tion to ak)], an adsorption function has to be applied to the inner attractive branch which now becomes the dominant one. Quenching cross sections "150 A2 would thus follow unless the adorption function was rather sharply peaked around 6 A. The Excitedstate in Chemical Physics, ed. J. W. McGowan, Adv. Chem. Phys. (Wiley, New York, 1975), vol. 28. M. Bourene, 0. Dutuit and J. Le Calve, J. Chem. Phys., 1975, 63, 1668. H. Haberland, C. H. Chen and Y. T. Lee, Atom Physics, ed. S. J. Smith and G. K. Walters (Plenum, New York, 1973), vol. 3. D. A. Micha, S. Y. Tang and E. E. Muschlitz, Chem. Phys. Letters, 1971, 8, 587. F. J. Van Itallie, L. J. Doemeny and R. M. Martin, J. Chem. Phys., 1972, 56, 3689. ti T. A. Davidson, M. A. D. Fluendy and K. P. Lawley, Faruduy Disc. Chem. SOC., 1973, 55, 158. H. F. Krause, S. Datz and S. G. Johnson, J. Chem. Phys., 1973, 58, 367. ti M. Baumann, E. Jacobson and W. Koch, 2. Nuturforsch., 1974, 29a, 661. H. F. Krause, S. G. Johnson, S. Datz and F. K. Schmidt-Bleek, Chern. Phys. Letters, 1975,31, 577. lo E. R. Fisher and G. K. Smith, Appl. Optics, 1971, 10, 1803. l1 L. C.-H. Loh, C. M. Sholeen, R. R. Herm and D. D. Parrish, J. Chem. Phys., 1975,63, 1980. lZ M. Krauss and D. Neumann, Chem. Phys. Letters, 1972, 14, 26. j3 M. Krauss and F. H. Mies, Phys. Rev., 1970, A , 1592.

ISSN:0301-7249    

DOI:10.1039/DC9776200291

出版商:RSC    

年代:1977

数据来源: RSC

摘要:

GENERAL DISCUSSION Dr. H. J. Loesch (Bielefeld) said: It is a well known fact that during the collision of two particles-say an atom and a linear molecule-energy transfer from transla- tional to rotational degrees of freedom takes place only if the interaction potential between the colliding particles deviates from spherical symmetry. It is, therefore, likely that rotationally inelastic scattering data depend sensitively on the anisotropy of the potential energy surface. In a molecular beam experiment-which is described in detail elsewhere l-differ- ential and integral angular momentum transfer cross sections have been determined for Ar + C 0 2 at thermal collision energies. Some of the results are shown in fig. 2 and 3. To recover the potential anisotropy from the scattering data the cross sections were simulated as a function of the anisotropy parameter of a model potential by means of a trajectory calculation.The parameter was then adjusted to fit the integral cross sections. Fig. 1 shows a member of the empirical potential surface family used for the cal- culations. Each member is generated by adding two LJ (12,6)-potentials each of them centred around a specific point on the internuclear axis of C02. The surface has 9 0' + 4 0' I - 0 C 0 3 6 distance 1 A FIG. 1.-Contour map of a member of the potential surface family used for the trajectory calculation. The parameters are 8 = 0.009 63 eV, rm = 3.8 8, and A = 0.42 ( I = 2.3242 8,). The energies of the contours are given in units of E. H. J. Loesch, Chem. Phys., to be published.GENERAL DISCUSSION 30 1 in general three parameters, the well depth e of the LJ-potentials, the distance of the potential minimum from the origin r,, as well as the distance I between the two centre points.The distance I which characterizes the anisotropy of the surface is the only parameter to be varied freely. The E and r,-parameters were determined in a way that for each I the spherical mean values of the corresponding angle dependent quan- tities of the surface are equal to the effective values derived from measured transport properties of Ar and CO,. The contour map of the potential surface shown in fig. 1 is calculated for I = 2.3242 A the equilibrium separation of the O-atoms in COz. The surface exhibits qualita- tively realistic features; it allows for a stable, exactly T-shaped van der Waals molecule with an Ar-C bond length of 3.6 8, and a bond strength of 19.3 meV.These findings are reasonably close to data experimentally known for Ar COS as one would expect. The asymmetry of the differential cross sections (fig. 3) with respect to 8 = 90" indicates clearly that direct inelastic collisions prevail, even for amounts of energy transferred which are close to the total available energy. Direct encounters are, of 10 L 01 u Y t U W a u -0 .- d .- c 6 10 20 50 LO final angl;lar momentum j ' FIG. 2.-Absolute angular momentum transfer cross sections for Ar + C 0 2 at a coIlision energy of E = 0.069 eV. The solid circles are experimental data points derived by integration of the corres- ponding differential cross sections of fig. 3.The lines are the smoothed results of the trajectory calculation for various anisotropy parameters A . ( A = 0.80 -- --, 0.42 -, 0.15 ---, 0.052 - - - -.) The initial rotational quantum number is fixed at the most probable experimental value 6. course, a prerequisite to deduce potential parameters from scattering data. The region of the surface responsible for the high angular momentum transfer can be found by application of the Massey criterion. The criterion states that in order to obtain substantial cross sections for collisions transferring the amount of energy AE the inter- action period z N a/fi (a = length of the interaction path, 6 = mean relative velocity S. J . Harris, K. C. Janda, S. E. Novick and W. Klemperer, J. Chem. Phys., 1975, 63, 881 and W.Klemperer, this Discussion.302 GENERAL DISCUSSION during the collision) must be smaller than the transition period T = h/AE. For the system under consideration this leads to an interaction path length a of the order of 1/10 A, indicating that the high angular momentum transfers occur through nearly impulsive interactions with the hard repulsive core of the potential. Therefore, the inelasticity of the collisions will be mainly determined by the anisotropy of this potential region and it appears reasonable to characterize a specific surface by the anisotropy of its repulsion which is described by the expression A = q/rL - l(r,l, r, are the lengths of the main axis of the zero-potential energy surface parallel and per- pendicular to the internuclear axis of C02, respectively). Fig.2 shows the comparison between the experimental and simulated integral cross sections. The strong correlation between the potential anisotropy and the magnitude and shape of the cross sections as a function of the final angular momentum j ’ of C02 permits a sensitive determination of A . The optimal A was found to be A = 0.42 for which the potential of fig. 1 was calculated. The best fit curve simulates the data quantitatively and accounts for the remarkably large cross sections for high angular momentum transfers. Fig. 3 shows the experimental and calculated differential cross sections. The main c u) X .- 6- 30 j - j ’ O g 8 L 0.2 I- n 6-36 40 80 120 160 40 60 120 160 centre of mass scattering ang[e,Q FIG. 3,Differential angular momentum transfer cross sections for Ar + COz at a collision energy of E = 0.069 eV.The smooth lines are the experimental results. The mean final angular momentum quantum number 7 gives a representative value for all j ’ contributing to a specific plot within the experimental energy resolving power. The histograms are calculated employing the potential of fig. 1. experimental features are qualitatively simulated by the calculated results ; the peaks are present, and close to the observed positions. The shift of the peaks towards large angles with increasing angular momentum transfer is also well simulated by the cal- culation. The next step towards a more sophisticated interpretation of these detailed dataGENERAL DISCUSSION 303 would require surfaces with many parameters, particularly, to describe the shape of the attractive branch and the well region.However, this would lead to very extensive and time-consuming numerical calculations, and it has not been attempted yet. On the other hand, there is a more straightforward way to use these data, namely, to check potential surfaces emerging from theoretical approximations. Recently, Preston and Pack1 carried out a trajectory calculation based on an electron gas model potential surface, and good agreement between experiment and calculation was found. Mr. J. S . Carley (Waterloo) said: We would like to report preliminary results for H2-, D2- Xe and H2-, D2- Kr, analogous to the potentials for H2-, Dz- Ar discussed in our contributiom2 These functions have been used by Zandee to predict state-selected integral collision cross-sections (see comment below).Parameters for the Bucking- TABLE 1 .-BUCKINGHAM-~ORNER PARAMETERS FOR H2-, D2-Xe AND H2-, D2-Kr system D O O W Eoo/cm-l R,"O/A eol/cm-l H2-, D2-Xe 3.668 (0.096) H2-, DZ-Kr 3.462 (0.0 70) system Reol/A (0.025) (0.024) H2-, D2-Xe 4.043 H2-, D2-Kr 3.91 5 65.48 (0.45) 58.77 (0.36) e20/cm-' 10.01 (0.23) 8.85 (0.43) 3.9344 (0.0044) 3.7192 (0.003 8) Re20/A 3.980 (0.078) 3.860 (0.052) 53.02 (0.69) 36.95 (0.96) e2'/crn-' 19.1 (5.2) 19.3 (8.4) ham-Corner functional form (cf. eqn (5) and (6) of ref. (2)) are given in the table above. These values were determined by fits to the spectroscopic data of McKellar and Welsh3 subject to the following constraints: 1. and -7 I. pnk = Boo for all n,k the C\!' dispersion constants are fixed as in ref.(2); i.e., Cii = Ci0 x aln = C"," x 1.300 52 c;o = rz x C ~ O C;' = C;: x alng/af = Ci0 x 3.472 26. Langhoff et aL4 give r, = 0.108 for hydrogen with both xenon and krypton, and C"," as 330 600 cm-l (A)6 for H,-Xe and 194 200 cm-l (A)6 for H,-Kr. As previously found by Le Roy and Van Kranendonk,' an additional parameter (i.e., e21) can be fit, with R2,1 being set to the ratio R:O (R,O1/R,OO) for both systems. Finally we find that the isotropic parameters given here are in excellent accord with those which Rulis et aL6 determined from their differential collision cross-sections. R. K. Preston, R. T. Pack, J. Chem. Phys., to be published. A. R. W. McKellar and H. L. Welsh, J. Chem. Phys., 1971,66,595.P. W. Langhoff, R. G. Gordon and M. Karplus, J. Chem. Phys., 1971,66,2126. R. J. Le Roy and J. Van Kranendonk, J. Chem. Phys., 1974, 61, 4750. A. M. Rulis, G. Scoles and K. M. Smith, 1976, personal communication; K. M. Smith, Ph.D. Thesis (University of Waterloo, 1976). * R. J. Le Roy, J. S. Carley and J. E. Grabenstetter, this Discussion.304 GENERAL DISCUSSION Dr. L. Zandee and Dr. J. Reuss (Nijmegen) said: In Nijmegen we have measured the influence of the angle-dependent part of the intermolecular potential ( V2,0) on the total collision cross section for state selected beams. For the analysis we employed LJ(rn,6) potentials, i.e., the type of potential Le Roy et al. [ref. (l)] used for the same systems; H2 + Ar, Kr and Xe. The results were analysed [ref.(2)], however, using a different parametrization of the V2,0 than Le Roy now proposes [ref. (5)]. Instead of R2,0 and e20 we used Aipl = (R:o/Ro,0)m-6 = a,/a, and Aip2 = (R',"/R0,0)6[in/ 6 - (R23R0~)"-6](~20/~00) = 2 a6 - a,,,; Aipl and Aip2, respectively, determine the relative position R:O/R0: of the minimum in the V2,0 and the relative value of V2,0 at R = RY, within our LJ-model. The results are summarized in table 1. We were able to fit the Aipl (Aip2) para- TABLE 1 .-THE RESULTS OF FITS FOR THE Aipl AND Aip2 PARAMETERS AND THEIR DSD VALL'ES WITH RESPECT TO THE ANISOTROPY MEASUREMENTS. I N THE VALUE OF DSD' OUR EXPERIMEh'TAL UNCERTAINTY IN THE BEAM VELOCITY IS TAKEN INTO ACCOUNT ~ system vo.0 V2.0 Aipl Aip2 rn DSD DSD' H2 + Ar ref. 1 ref. 1 1.52 0.095 12 3.44 3.03 1 2 1.35 0.10 12 1.63 1.17 - 3.62 3.17 5 5 4 optimum fit 1.15 0.10 12 1.35 0.97 - - H2 .t Kr 1 1 1.38 0.125 12 9.57 8.68 1 2 1.10 0.11 12 3.03 2.00 - 7.58 6.33 5 5 4 optimum fit 0.9 0.10 12 1.86 0.96 - - H2 $- Xe 1 1 1.14 0.165 13 7.30 5.76 1 2 0.9 0.15 13 6.13 3.2 1 5 5 - - 4.63 2.99 4 optimum fit 0.9 0.13 12 4.69 3.96 (&"R"," + 5%) optimum fit 0.8 0.13 12 2.01 0.70 - meters independently to the low (high) velocity measurements of the total cross section. The choice of the parameters has been dictated by the successful independent fit for the different velocity ranges.Their suitability can be explained considering the R values at which the V2,0 is probed. At high velocities, hu/~OOR0,0 E 1 (the so called transition region), the total cross section is determined by the balance between attractive and repulsive forces at R z Rto.For different state selected beams this balance is influenced by an orientation dependent factor times the relative potential Parameter Aipl is determined by the behaviour of the total cross section in the glory range, ( ~ u / E R , 5 0.4). Here, the change of the phase shift due to V2,3 for gIorj. trajectory, has a dominant of influence on " the relative difference of the total cross section for different state selected beams ", the so called anisotropy " A ". This extra phase shift is composed of two very large contributions which nearly cancel each strength, Aip2 = ( v ~ , O / V O , O ) R = R o ~ = rn 6 a6 - a,. R. J. Le Roy and J. van Kranendonk, J. Chem. Phys., 1974,61,4750. L.Zandee, J. Verberne and J. Reuss, Chem. Phys. Letters, 1976, 37, 1 . J. P. Toennies, W. Welz and G. Wolf, J. Chein. Phys., 1976, 64, 5305. R. Helbing, W. Gaide and H. Pauly, 2. Phys., 1968, 208, 215. R. J. Le Roy, J. S. Carley and J. E. Grabenstetter, this Discussion.GENERAL DISCUSSION 305 other; one stems from the a,-term and the other from the a,,,-term. Consequently, only the ratio a,,,/a, sensitively enters the fit procedure in the glory region. Le Roy has now revised his analysis using a BC-potential which includes an R-8 term in order to bring the a,-value (formerly ca. 0.2) down to the theoretical long range value 0.1. We are somewhat troubled by this assumption. If one does not probe the intermolecular potential really at long range, the constant a, = 0.1 looks artificial. We would have been content if Le Roy had shown explicitly that his fit is nearly in- dependent of the assumed a,-value (and the other long range constants). We took the new Le Roy potentials (H, + Ar from the paper given above, H2 +- Kr, Xe from personal communication) and calculated the anisotropy A .The 10 0 I a J -10 rc) 0 - X .:I G- 10 3 '6: - 1 c: - 2 c L new L o l d Helbing L new L old Helbing + 5 % -- ____ 1000 2coo 3309 V , / m s - ' FIG. 1 .-Measured values of the anisotropy in the total collision cross section A = Aa/al, defined as the relative difference of the cross sections for molecules in the inj = 1 (al) and mi = 0 state. The fit curves L new (L old) correspond to the B.C. (L.J.)-potential as proposed by Le Roy. For other curves the isotropic L.J.potential from Helbing is used and the anisotropy parameters Aipl and Aip2 are opthized. (a) Hz-Kr, (6) Hz-Xe.306 GENERAL DISCUSSION results show large shifts for Kr and Xe compared with those obtained from Le Roy's old potential parameters, e.g., see fig. 1. For krypton the fit has been improved somewhat as can be seen also from the DSD-value [definition in ref. (5)] in table 1. In addition to the transition region, for the system H2 + Xe a complete glory minimum in A is also measured and calculated. There the truth seems to lie in between the old and new Le Roy potentials. In agreement with the results of Toennies et al. ref. (3), p. 304, we obtain better agreement for H2 + Ar and H2 + Kr using the Helbing isotropic potential ref.(4) for our cross section measurements in the glory range (see DSD-values in table 1). If Helbing's co0RO,O value for H2 + Xe is increased by 5% (the uncertainty quoted by Helbing) a minimum DSD-value of 0.7 is obtained. In fig. 2 of Le Roy's contribution our and both his V2,0 (R) curve cross at R z Ato. We found the same behaviour for H2 + Kr and H2 + Xe. The fact that Le Roy's LJ- and BC-curves coincide there, suggests that the IR-measurements are sensitive to the V2,0 at this particular intermolecular distance. The fact that our curves also cross Le Roy's at this particular intermolecular distance, demonstrates (again) that our measurements probe the V2,0 at R = Rt0. The discrepancy between Le Roy's and our results come mainly from the relative position of the minimum of V2,0 (R~o/Ro~)"-6, which our experiments in the glory region implies should have smaller value than what Le Roy obtains.Prof. R. J. Le Roy (Waterloo) said: One of the main weaknesses in our analysis of the hydrogen + inert gas systems' is the fact that we were unable to exploit the in- formation about the potential anisotropies contained in the cross-section anisotropy measurements of Zandee and c o - ~ o r k e r s . ~ ~ ~ I am, therefore, very pleased that Zandee has been able to test the ability of our new potentials to predict his data. The discrepancies he found imply that the two types of experiment are complementary, in that they depend on somewhat different features of the potential anisotropy. Clearly some type of combined analysis will be required for truly optimizing the anisotropy strength function V2,(R).Zandee observed that the intersection of our V2,,(R) curves with his lies very near Rt0; the fact that this occurs for all three species H2 + Ar, H2 + Kr and H2 + Xe suggests that this coincidence is no accident. However, it would be wrong to infer that the spectroscopic data are especially sensitive to V20(R) at this particular inter- molecular distance. As described previously, the potential anisotropy enters the eigenvalue calculation as a radial expectation value, ( N = 0, LI V2,(R)IN = 0, L').4 Since the turning points of the levels in question are separated by 1-2 A, and the wave function maxima lie at distances greater than R0:, it would be unreasonable to attribute to the spectroscopic data any special sensitivity to V20(R) in the immediate neighbourhood of R:.Moreover, the presence of significant errors in the high velocity cross-section anisotropy predicted from the spectroscopic potential, in spite of the near coincidence of the various V20(R) curves at RY, suggests that there may be considerable model dependence in Zandee's association of his high velocity results with his parameter Aip 2. The dependence of the spectroscopic data on averages of V20(R) over 1-2 A in- tervals in the region 3.2-5.2 A also illustrates why these data are not particularly sensi- tive to the asymptotic relative anisotropy-strength, as. The fact that use of the simple R. J. Le Roy, J. S. Carley and J. E. Grabenstetter, Furaduy Disc. Chem. SOC., 62 (this Discussion).H. Moerkerken, L. Zandee and J. Reuss, Chenz. Phys., 1975,11, 87. L. Zandee, J. Verberne and J. Reuss, Chem. Phys. Letters, 1976,37, 1. R. J. Le Roy and J. Van Kranendonk, J. Chem. Phys., 1974,61,4750.GENERAL DISCUSSION 307 LJ(12,6) model for V2,(R) yielded a value of as which was a factor of 1.6 too large, while the present analysis achieved an equally good fit to the same data with a, held fixed at its known theoretical value, further emphasizes this insensitivity. It there- fore seems highly appropriate “ artificially ” to fix a, at this theoretical value in order that the resulting V’,(R) function may be as realistic as possible. Zandee determined V’,(R) parameters from fits to his cross-section anisotropy data which held Voo(R) fixed as either the LJ(12,6) function Helbing et aZ.l obtained from elastic total cross section data, or the LJ(12,6) function determined in our original analysis of the spectroscopic data.For H2 + Kr and H2 + Xe, he found that the Helbing et aZ. potentials allowed a much closer fit to his experimental cross-section anisotropies. On the other hand, Helbing’s potentials support fewer bound and quasibound levels than have been observed, and hence are unacceptable to the spectroscopic data. This type of disagreement between potential curves obtained from different sources, each being unable to give reliable predictions of the property from which the other was determined, is a familiar problem in chemical physics. However, the accuracy of their predictions of the elastic differential cross section data suggests that this type of complaint may not be so severe for the isotropic parts of our new (spectroscopic) BC and/or HFD potentials for Hz + Ar and Hz + Xe.The fact that these functions are constrained to have the correct C,, constant should also facilitate their giving reasonable predictions for total cross-sections in the low velocity “glory” range. Thus, we suspect that a fit of V2,(R) to Zandee’s cross-section anisotropy data, which holds V,,(R) fixed as the spectroscopically derived BC or HFD function, should be quite good. In conclusion, while we believe that the isotropic parts of our new hydrogen + inert gas potential energy surfaces are reasonably close to the truth, their diatom stretching dependent and anisotropic parts are more model dependent and uncertain.The cross-section anisotropy data described by Zandee therefore appear essential to a reliable determination of the anisotropy strength functions for these species. Dr. M. S. Child (Oxford) said: The beautiful experiments performed by Klem- perer’s group and the calculations of Le Roy, Carley and Grabenstetter concern the anisotropy of the Van der Waals potential. I should like to comment on experiments relating to translational-vibrational interactions in such systems, traditionally studied by vibrational relaxation measurements. The extraordinary resolution of the molecular beam electric resonance technique opens the way to the extraction of much more detailed information on this part of the potential, either by observation of com- bination bands in the vibrational spectrum of the Van der Waals complex, or by a study of the vibrational predissociation lifetimes of individual vibration-rotation levels. Mr.C. J. Ashton in my research group has made calculations of such lifetimes for the ArHCl complex, based on a crude dumb bell model for the interaction similar to that employed by S0rensen2 in interpreting the vibrational relaxation data.3 The total Van der Waals potential used was V(R, r, 0) = A1 exP(- a1RArH) + A 2 exP(- a2RArCL) + ViSdR) Al = 560 eV, A2 = 9150 eV, al = 3.53 A-l, 012 = 4.0 A-1 where r is the H-Cl distance, R and 8 are as used by Klemperer, and the isotropic ’ R. Helbing, W. Gaide and H. Pauly, 2. P h y ~ . , 1968, 208,215. G. D. B. Ssrensen, J. Chem. Phys., 1972,57, 5241.R. V. Stele Jr. and C. B. Moore, J. Chem. Phys., 1974,60,2794.308 GENERAL DISCUSSION potential V,,, was based on that of Farrar and Lee.l Two types of estimate of pre- dissociation lifetimes following 1-quantum vibrational excitation of complexed HC1 were obtained by Fano's Golden Rule summed over final states. The first (I) was based on isotropic wavefunctions, while the second (11) used bound wavefunctions appropriate to the full model potential. Typical results are shown below, where n denotes excitation of the low-frequency ( v - 30 cm-l) Ar - HCl vibration, and I, j and J label the orbital, HCl rotational and total angular momenta respectively (all with reference to the isotropic limit). Primes denote final states. bound state lifetime /s predominant j' r r I j J I I I1 0 0 0 0 0 1 1 0 0 1 0 1 0 0 1 1 0 1 1 1 4 1 1 1 0 2 0 2 0 1 1 2 5.0 1.6 5.0 3.4 6.7 0.0021 5 .O 3.2 0.90 4.2 120.0 0.54 1.5 0.24 3 .O 0.72 15 15 15 15 15 15 15 15 15 15 16 16 15 15 15 15 * Radial integrals estimated semiclassically: error estimate & 10-1 5%.It can be seen that the dominant mode of predissociation yields highly rotationally excited HCl and a minimum of product translational energy. The surprisingly long lifetimes (typically --I s) are well outside the range of possible direct experimental measurement, but may be of considerable relevance to the feasibility of experiments on vibrationally excited complexes. We are extending this work and hope to publish a fuller account. Prof. R. J. Le Roy (Waterloo) said: The linewidths of - 10-l' cm-l which Ashton and Child3 have calculated for the " vibrational-relaxation predissociation " of Ar + HCl are too small to be readily observed.In cases like this, where the pre- dissociation line width is very small, information about translation-vibration inter- action (i.e., about the c-dependence of the interaction potential) may be readily obtained from the line positions, using the techniques of ref. (4)-(5). However, the latter approach depends on a precise determination of the level shifts arising when a component (diatom) of the van der Waals molecule becomes vibrationally or rotation- ally excited. It, therefore, cannot be used for situations in which the predissociation line width is as large as or larger than these shifts. It is in this rapid-predissociation case that an analysis of linewidth should prove most useful.However, the fact that vibrational relaxation is generally relatively slow suggests that this type of approach may prove more useful for learning about translation-rotation interaction (i.e., about potential anisotropies) than about translation-vibration interaction. In this regard, Muckerman and Bernstein6 have J. M. Farrar and Y . T. Lee, Chem. Phys. Letters, 1974,26,428. M. S . Child, Furuduy Disc. Chem. Soc., 1976,62 (preceding comment). R. J. Le Roy and J. Van Kranendonk, J. Chem. Phys., 1974,61,4750. R. J. Le Roy, J. S . Carley and J. F. Grabenstetter, Faraday Disc. Chem. Soc., 1976, 62. J . T . Muckerman and R. B. Bernstein, Chem. Phys. Letters, 1969,4, 183. * M. S . Child, Mol.Phys., 1975,29, 1421.GENERAL DISCUSSION 309 reported calculations for H, + Xe and D, + Xe which predicted " rotational-relaxation predissociation " linewidths of 0.02-0.5 cm-'. While I believe that these widths are somewhat too large, it seems clear that the corresponding widths for more strongly anisotropic systems such as HC1 + Ar should be significantly larger than this, and should provide useful information about the potential anisotropies. Dr. D. A. Dixon and Prof. D. R. Herschbach (Haruard University) said: We are delighted to learn of the theoretical study by Ashton and Child, which finds a remark- ably long lifetime (-1 s!) for predissociation of a vibrationally excited Ar . . . HCl van der Waals complex, even though the vibrational quantum of HCl (8.5 kcal/mol) is far larger than the van der Waals bond strength (0.4 kcal/mol).We have experi- mental results for an analogous system which likewise imply an extremely long lifetime for vibrational predissociation. These results1 pertain to inelastic scattering of the C1, . . . C1, van der Waals dimer in collisions with Br,, HI or Xe. Supersonic molecular beam techniques were used to produce the van der Waals molecules and to generate collision energies from E - 3 to 21 kcal/mol. The energy transfer was determined by comparing the velocity of scat- tered molecules with that expected for elastic scattering. At the low end of the col- lision energy range, the observed energy loss from translation at the peak of the product distribution is about AET = - 1.6 kcal mol-'.As the collision energy in- creases, the inelastic energy transfer becomes larger and for E > 8 kcal mol-' it attains a maximum of roughly AET = -3.5 kcal mol-'; larger values produce collision- induced dissociation of the chlorine dimers. Since the form of the angular distribu- tion implies that the rotational excitation is low, we infer that the observed energy loss corresponds primarily to vibrational excitation. Since A& proves to be practically the same for Br,, HI or Xe as the collision partner, we infer that the energy transfer represents vibrational excitation of the chlorine dimer molecule. The dissociation energy of the C1, . . . C1, van der Waals bond is only roughly known, but is estimated from gas viscosity data as -1 kcal mol-I. It seems very unlikely that this could be in error by more than a factor of two.Hence, although the inelastic energy transfer observed at low collision energies might possibly be accommodated by the van der Waals bond, the high energy results must be attributed to excitation of vibration in the CI2 monomer units. Indeed, the vibrational quantum for the Cl, molecule is 1.6 kcal mol-'. Thus it appears that even at low collision energies the process may involve primarily excitation of the first vibrational quantum of Cl,, whereas the limit attained at high energies may be accounted for by excitation of two C1, quanta, either with both the CI, monomer units excited to the first vibrational state or one of them excited to the second state. In any case, these results imply that the chlorine dimer molecule can survive long enough to travel to the detector even though the vibrational excitation exceeds the dissociation energy of the van der Waals bond.This gives a lower limit of about loe4 s for the lifetime of the vibrationally excited diiner, which corresponds to at least lo8 vibrational periods. Prof. W. Klemperer (Haruard) said: The question of rotation for van der Waals molecule lends itself to considerable amusement. Just what is seen as a molecule depends upon the eyes of the beholder. The rotational constant, Boy and hyperfine structure constants of the species designated Ar + HCl are known to a much higher precision than the rotational constant, Bo, and hyperfine structure constants of the well D. A. Dixon and D. R. Herschbach, J.Ainer. Chem. SOC., 1975,97,6268; Ber. Bimsenges. phys. Chem., 1977, to be published.310 GENERAL DISCUSSION known molecule N,. In that sense, ArHCl may thus be said to be a better char- acterized molecule than N2 although their binding energies obviously differ. Somewhat more seriously, at this stage, it is not at all obvious that the bonding and structure of van der Waals molecules is not determined by the same interactions that exist in chemically bonded molecules. The classification of bond type entirely on energy appears to be somewhat lacking in generality. For example, the bonding in H2 and Cs, are certainly similar conceptually although there is a considerable differ- ence in binding energy. It is far from clear that the bonding in BH3C0 and BF3C0 are drastically different although the B-C bond lengths are 1.54 and 2.90 A, re- spectively, and their binding energy probably differ by a factor of 20.Dr. R. J. Whitehead, Mr. S. Swaminathan, Mr. E. Guth and Prof. D. L. Beveridge (New York) said: We have calculated an intermolecular potential function based on quantum mechanical calculations for the prototype solute-solvent interaction of form- aldehyde in water. Using ab initio methods, it is only feasible to use a pairwise- additive approximation to the intermolecular potential function. Thus a data base is generated corresponding to various positions of the system in configuration space and the calculated energies of these configurations are fitted to an analytical form for the potential function. In this procedure a number of variables have to be considered such as the size and quality of the data base, a strategy for determining the points in the data base, some functional form for the potential, any weighting of the data points and some evalua- tion of the quality of the potential function.Our aim has been to establish a system- atic and well-characterised approach to the problem, based on a heuristic method in which certain of the variables are allowed to evolve in the course of determining the function. The set of coordinates Ri for each configuration of the system was obtained by randomly deploying the water molecule about the formaldehyde within a shell radius of 5.5 A. The corresponding energy El was calculated by the SCF method using an STO 6-31 G basis.The following form for the potential was used VAB = 2 + Vk; j E A, k E B jk rji r j k in which a and b are the parameters to be determined and i a n d j represent atomic and pseudo-atomic centres on water and formaldehyde respectively. In order to give more importance to the low energy regions of the system, the points in the data base were weighted by a function of the form 1 + 100 e-AEilkET. Initially 100 points were used in the data base and after curve-fitting, the energies had a standard deviation of 0.47 kcal mol-l. To test the quality of the potential func- tion, coordinates of a further 25 data points were generated and the quantum mechan- ical energies compared with those predicted from the potential function. The stan- dard deviation of the test set was 0.51 kcal mol-l.This procedure can be repeated until the desired tolerance of the function is obtained. The results for a total of 225 data points are summarised in the table. The standard deviation of the initial sample is TABLE.-STANDARD DEVIATIONS IN THE DIFFERENCES BETWEEN QUANTUM MECHANICAL AND HEURISTIC POTENTIAL FUNCTION ENERGIES IN kcal mol-' FOR DIFFERENT DATA BASE SIZES points in initial test total data base sample sample sample 100 0.47 0.5 1 0.48 125 0.47 0.43 0.47 150 0.37 0.41 0.38 175 0.37 1.34 0.59 200 0.44 0.45 0.44GENERAL DISCUSSION 31 1 fairly constant although there are larger fluctuatioiis in the test set. Fig. 1 gives a comparison between the quantum-mechanical energies of the 225 points and those predicted from the potential function.Generally the fit is well within 0.5 kcal mol-I and higher deviations occur only for points well above the minimum. 23 1 cn L E 7 a LL [L I 3 - 1 - 5 -5 - 1 3 7 11 15 19 23 Q M e n er g y / kcal mot-' FIG. 1 .-Comparison of quantum mechanical and heuristic potential function energies for 225 data points. The potential surface was searched for most probable configurations of the system by minimising the energy with respect to orientation of the water molecule for con- figurations in which the centre of mass of the water was constrained to be in the plane of the formaldehyde. The resulting isoenergetic contour plot together with the corresponding position of the water is shown in fig. 2, p. 312. Two minima are apparent; one in which a hydrogen on water is directed almost linearly towards the oxygen of formaldehyde and the other in which the oxygen on water is directed between the hydrogens of formaldehyde.Prof. W. Kutzelnigg (Bochum) said : The remarks on exchange perturbation theory were formulated in a rather provocative way since I expected some experts in this field to be present and I wanted to challenge them. To give a fair impression of the present state of exchange perturbation theories one should give some additional more recent references1-7 and also refer to a quite up to date bibliography.s As far as variationa D. M. Chipman, J. D. Bowman, and J. 0. Hirschfelder, J. Chem. Phys., 1973,59, 2830. D. M. Chipman and J. 0. Hirschfelder, J. Chem. Phys., 1973, 59, 2838. E. Beretta and F. Vetrano, Itzt. J. Quant.Chern., 1973, 7, 333. N. Suzuki and Y. J. I'Haya, Chein. Phys. Letters, 1975,36,666. D. M. Chipman, Chem. Phys. Letters, 1976, 40, 147. W. N. Whitton and W. Byers Brown, Int. J. Quaizt. Chem., 1976, 10, 71. P. R. Certain and L. W. Bruch, in MTP International Review ofScience, Theoretical Chemistry (Physical Chemistry Series One), Volume 1, W. Byers-Brown ed. (Butterworths, London, 1972), p. 113. ' J. P. Daudey, P. Claverie and J. P. Malrieu, Int. J. Quant. Chem., 1974, 8, 1.312 GENERAL DISCUSSION 4.1 3.2 2.3 OQ 1 . 4 $ 0.5 \ c -0 - 1 . 3 - 2 . 2 - 3 . 1 -4.0 -4.60 -2.82 -1.04 0.74 2.52 4.40 d i s t a n c e 1 A action. The lowest energy contour is -5.735 kcal mol-' and the interval is 0.6 kcal mol-'. FIG. 2.-Minimum energy contour map and water orientation for the formaldehyde-water inter- calculations are concerned the contributions of Murrell and coworkers' as well as of the van der Avoird group2g3 deserve credit.Perturbation theory surely has, and will continue to have, an important place in the field of the calculation of intermolecular potential curves and also as a guide when one applies variational methods. However, the problems pointed out here in the frame- work of a variational approach cannot be circumvented by the use of perturbation theory, unless one relies on fortuitous cancellation of errors. The obvious advantage of perturbation theory, namely that one does not have to calculate small differences between large numbers is less relevant than one might think because numerical stability is not the crucial problem in the variational calculations.The crucial problems are the coupling of inter- and intra-correlation effects as well as the variation of the intra- correlation energy with distance. On the other hand, it is obvious that calculations at the level of the sophistication outlined here can only be limited to small systems. It is, therefore, important to learn from these calculations as much as possible that can simplify the calculation for large systems. We have learnt, e.g., that the intra-inter-coupling can be simulated by a simple scaling of the inter-contributions such that they are asymptotically correct. Some very simple approaches to describe the interaction between systems in closed shell states have proved to be successful, like the combination of the Hartree-Fock repulsion and the sum c62?-6 + C8R-' + CloR-", possibly multiplied by a damping factor4s5 or the electron gas model of Kim and Gordon.6 A theoretical foundation of these methods that also indicates in which respect they ought to be improved should * J.N. Murrell and J. J. C. Teixeira-Dias, MoZ. Phys., 1971, 22, 535. P. E. S . Wormer and A. van der Avoird, J. Chem. Phys., 1975,62, 3326. P. J. M. Geurts, P. E. S. Wormer and A. van der Avoird, Chenz. Phys. Letters, 1975,35,W. J. P. Toennies, Chem. Phys. Letters, 1973, 20, 238. J. Hepburn, G. Scoles and R. Penco, Chem. Phys. Letters, 1975,36,451. Y. S . Kim and R. G. Gordon, J. Chem. Phys., 1974,61, 1.GENERAL DISCUSSION 313 be possible starting froin the general analysis given here. One aspect that one cannot yet handle in a simple way is that of the anisotropy of the interaction, though even here rather simple approaches have had some success.' Prof.J. N. Murrell (Sussex) said: The example given by Dewar of the Cope re- arrangement illustrates that feature of the MINDO method which probably gives most ammunition to its opponents. By parameterizing the method to give agreement be- tween calculated and observed heats of atomization the MINDO method goes beyond the SCF approximation and allows for changes in correlation energy on bond break- ing. The question then arises whether more correlation should be introduced in transition states which entail partial bond breaking, by limited configuration inter- action. The example given shows not only that the predicted activation energies can depend on whether CI is included or not, but also that the nature of the transition state, or predicted reaction path can also change.Are there any firm rules in the MINDO method for telling us whether or not to introduce CI? Prof. K. F. Freed (Uniuersity of Clzicago) said: We have heard a number of familiar comments questioning the validity of the whole semiempirical procedure for treating molecular electronic structure. It is much more productive, however, to examine the precise relationship between the full molecular electronic Schrodinger equation and the semiempirical theories, as such an analysis can provide considerable insight into the nature of the semiempirical theories, generate systematic means for their improve- ment, and also suggests useful new approaches to purely ab initio calculation^.^^ The full molecular Schrodinger equation presents us with the Hamiltonian, X, for the electrons (usually taken in the Born-Oppenheimer approximation).Then some convenient subdivision is made into the core and valence shells by introducing sets of core, (c), and valence, (u), orbitals. The choice of the size and nature of each of the sets is at the disposal of the researcher as is the choice of the orbitals (c, v). Suppose that some good initial choice has been provided, and for convenience, we assume that the core represents a closed shell with the number of c-orbitals equal to one-half the number, n,, of core electrons. Exact ab iizitio calculations would require, in addition to (c, v), a complete set of excited orbitals (el which are complementary to (c, u) in order to generate an exact representation of the wavefunction as a super-position of all possible N-electron determinantal functions constructed with this complete basis.Given some choice of (c, v], we have shown that it is possible to exactly define an effective valence shell Hamiltonian, SV, with the following properties : 1. only operates on functions represented solely in terms of the ( u } set-it acts as if only the valence shell orbitals were present. 2. Zv produces the exact potential energy surfaces for the valence electronic states. It, therefore incorporates all correlation effects normally associated with the ( e ) set (and c -+ v excitations) in ab initio calculations.3. These exact energies are obtained from the effective Schrodinger equation *p= E(D (1) with q~ constructed as a superposition of all possible n, = N - n, electron functions generated only by the (0) set. P. J. M. Geurts, P E. S. Wormer and A. van der Avoird, Chem. Phys. Letters, 1975 35,444. K. F. Freed, J. Cheni. Phys., 1974, 60, 1765; Chern. Pliys., 1974, 3, 463; Cheiiz. Phys. Letters, 1974,24,275. K . F. Freed, in Modern Theoreticd Chenzistry, ed. G. A. Segal (Plenum, New York, 1976). S. Iwata and K. F. Freed, Chern. Phys. Letters, 1976, 38, 425; J. Cheni. Phys., 1976, 65, 1071.GENERAL DISCUSSION 314 4. The eigenfunctions, q, of are the projections of the exact molecular wave- functions on the subspace of frozen-core wavefunctions with the remaining N - n, = n, electrons distributed amongst valence orbitals (u}.Hence, XV is the effective Hamiltonian which all semi-empirical theories attempt to describe by choosing a model form, 2 6 , on the basis of chemical intuition, and then by fitting the parameters in 2 6 to experiment. MINDO chooses to parameterize X'&rNDo with self-consistent field theory calcula- tions. When these calculations differ negligibly from the complete configuration interaction calculations in (l), then is an approximate representation of the true 2"'. Otherwise, an SCF parameterized MINDO involves a further simplification than the complete valence shell configuration interaction theory (1). The former has not yet been formally derived from the full Schrodinger equation, while the latter is just our ZV.An interesting feature of the true fl is that it contains terms that are not present in the customary semiempirical 2"; with their usual one- and two-electron integrals. This is to be contrasted with Zv which has 1,2, . . ., 2Mv-electron operators. (Mv is the number of orbitals in the (u} set.) The many electron terms arise because 2' is an effective Hamiltonian that must reproduce the exact energies; this cannot be done with just one- and two-electron interactions. These new many-electron terms correspond to a dynamical variable electronegativity correction with rather interesting physical implications. For example, consider the pi electron Hamiltonian, 2f'G for ethylene. The n -+ n* transition energies for the cation and anion are identical for 3;.The cation has two basis functions which, respectively, have an electron on carbon atom a or one on 6. The n -+ n* transition energy is then equal to twice the resonance integral. The anion has two functions with a hole on atoms a or b, so again the splitting is twice the resonance integral. However, in the former case the electron jumps between + centres while in the latter it jumps between formally neutral ones. Hence, the true P leads to different transition energies in the anion and cation.' Recent experiments on butadiene and hexatrienes have observed 0.4 eV shifts between cation and anion spectra.2 While these dynamical variable electronegativity effects are expected to be small for pi systems, their presence may be of considerable impor- tance in bonding in transition metal systems where considerable intershell charge transfer effects can arise.The structure of Zv also provides the opportunity for highly accurate ab initio cal- culations on small molecules to directly test some of the assumptions of semiempirical theories.' For instance, consider a series of molecules with a single valence orbital where the only parameters in Zv are then the one-centre Coulomb integral, a, and the one-centre repulsion integral, y. Accurate calculations of energies for planar CH3*, CH3CH2* with a planar radical end, CFH2CH2*, etc., can yield the molecule dependence of a and y to determine the limits of accuracy of a pi electron theory be- cause of errors in transferability assumptions. Similar tests can be generated for all valence electron theories.There are many equivalent ways to derive'*3 Z", and an even larger number of ones for its approximate In recent work' we have obtained a 2, with individual one-, two-, . . . electron integrals which are independent of the number of valence electrons in a fashion customarily assumed for fl&. The matrix elements of Xv can be evaluated approximately by sum-of-the-pair type methods analogous to l S. Iwata and K. F. Freed, Chem. Phys. Letters, 1976,38,425; J. Chem. Phys., 1976, 65, 1071. T. Shiba, to be published. K. F. Freed in Modern Theoretical Chemistry, ed. G. A. Segal (Plenum, N.Y. 1976).GENERAL DISCUSSION 315 those in the theories of Kelly, Nesbet, Sinanofjlu and 0thers.l Some of our calcula- tions on ethylene have been reported;2 others on butadiene are still in progress.Pseudopotential theories do not contain the excited orbital set {e)-only {c) and ( v } are present. Hence, the effective 3” in model pseudopotential theories exactly in- clude all effects of core reorganization, core correlation, and valence-core correlation. Because of the absence of (el, the 2” for pseudopotentials is but a simple special limit of the general case of effective valence shell Hamiltonians where the valence shell has just become somewhat l a ~ g e r ~ * ~ (to include everything absent in (c), that is, what was formerly {u) and {e)). We hope to apply our theory to explicitly include correlation and reorganization effects into ab initio pseudopotential theories. Prof. W. L. Hase (Wayne State Uniuersity) said: We do not view either the STO-3G or STO-4-31G ab initio techniques sufficiently accurate to look for a possible 3 kcal mol-’ potential energy barrier in the H + C2H4 --f CzH5 reaction.However, our potential energy calculations for C2H5 decomposition do suggest from which molecular forces such a barrier may originate. In very simple terms, the molecular forces which vary as an H atom adds to ethylene are: (1) the formation of a C-H bond; (2) the rupture of a C-C double bond and formation of a C-C single bond; (3) the repulsions between the attacking H atom and remaining two H atoms in the H-CH2 moiety; and (4) the repulsions between the H-CH2 and CH2 groups. Our calculations show at a C-H distance of 2.1 A for the leaving H atom the equilibrium angles for the remaining C2H4 framework are nearly those for ethylene, while the equilibrium C-C distance is 0.06 longer than that in ethylene.The equilibrium C-C distance does not become that of ethylene until the leaving H atom is -3 A away from the carbon atom. These results suggest that a barrier for the H + C2H4 reaction arises from coupling between the CH and CC stretches. Prof. H. C. Longuet-Higgins (Sussex) said: It might be considered a little dangerous to attempt to do orbital correlation a la Woodward-Hoffman on the reaction between I2 + F2. The strong spin-orbit coupling in the iodine atom will spoil the classification of orbitals into g, n, etc. The effect will be to permit certain electronic transitions which would otherwise be symmetry-forbidden. Dr. J. J. C.Mulder (Leiden) said: My remarks have been prompted by a striking coincidence in two papers. Thus in the paper by Engelke et al., the following observation is made: “The observation that the reaction of ground state I2 with ground state F2 does not produce ground- or excited state IF, indicates that factors other than energetics are important in selecting the reaction channel. It has been suggested that orbital symmetry restrictions based on an application of the Woodward- Hoffman rules prevent the formation of IF in the ground state by a four centre mechanism.” Whereas in the paper by Dixon et al., one can read: “ However they also illustrate that qualitative criteria such as those provided by orbital correlations need to be supplemented by an energetic criterion in order to predict whether a re- action is concerted.” These two quotations show-at least in my view-that there is a misunderstanding regarding the application of orbital symmetry arguments and/or the Woodward- Hoffmann rules.K. F. Freed, Ann. Rev. Phys. Chem., 1971,22, 313. K. F. Freed, Chem. Phys. Letters, 1974,29, 143. ’ S. Iwata and K. F. Freed, J. Chem. Phys., 1974,61, 1500; Chern. Phys. Letters, 1974, 28, 176.316 GENERAL DISCUSSION The monograph written on the subject by Woodward and Hoffmann, is called “ The conservation of orbital symmetry ”. This is due to the fact that the rules were derived using orbital symmetry arguments. However, as has been recognized by the founding fathers, the rule is independent of its derivation. The final formulation, which makes no reference to orbitals, shows this clearly.In it is put forward the combined influence of the number of electron pairs (n) and the number of out of phase overlaps (v) in the cyclic array of atomic orbitals that is relevant for the description of the transition state. An “ allowed ” reaction requires n + v = odd. The purpose of the rule was and still is to understand the relation between the stereochemistry of reactants and products and the stereospecificity of the reaction. In no way does the rule predict high or low activation energies. An allowed reaction may have a high activation energy; a formally forbidden reaction can proceed with only little activation energy. Still, the rule is an energetic one. It predicts, as was shown by Oosterhoff, van der Lugt, van der Hart and Mulder l-4 the following situa- tion: - - - -.-.. c - - - ----- I- reactants n +Y=odd pro I g r o u n d state However, the figure is valid only for two possible modes of the same reaction, with opposite stereochemical consequences. What is the relation of this rule with the 412 + 2 rule or the concept of aromaticity? The left side corresponds to the 4n + 2 or “ aromatic ” monocyclic polyene, the right side to the 412 or “ anti-aromatic ” case. Care should be taken to recognise that it is not so much thermodynamic stability but reactivity that is involved here. As was already clear to Hiickel, the question is, whether the ground- and excited- state are close or not. The fact that our analysis was performed using Valence Bond theory has had two important consequences : 1. The rule for thermal reactions is complemented in a logical way for photo- chemical processes through the use of the deeper well above the higher barrier. 2.In the VB-approach there is always correlation between ground state of re- actants and excited state of products and vice versa. The “ allowed ” process has stronger interaction and thus the two energy levels are pushed further apart. Prof. W. Klemperer (Haruard) said: Could the reaction I; + F2 be regarded not W. Th. A. M. van der Lugt and L. J. Oosterhoff, J.C.S. Chein. Comm., 1968, 1235. W. Th. A. M. van der Lugt and L. J. Oosterhoff, J. Amer. Chem. Soc., 1969,91,6042. J. J. C. Mulder and L. J. Oosterhoff, J.C.S. Chem. Comm., 1970, 305. J. J. C. Mulder and L. J. Oosterhoff, J.C.S.Chem. Comm., 1970, 308. W. J. van der Hart, J. J. C. Mulder and L. J. Oosterhoff, J. Amer. Chein. Soc., 1972, 94, 5724.GENERAL DISCUSSION 317 as a four-centre reaction, but an atomic reaction? l;(B37ro) is known to be pre- dissociated; thus, can the reaction be either that of atomic iodine or should a pre- dissociating molecular state be regarded as unique ? Dr. F. Engelke, Dr. J. C. Whitehead and Prof. R. N. Zare (Columbia University) said: Klemperer has suggested that our results on 11 + F2 may not indicate a four- centre reaction, but instead a more complicated mechanism involving reaction with an iodine atom. It(& u' = 43) is about 50% predissociated into two ground state iodine atoms (2P3/2). However, the reaction I(2P3/2) + F2 -+ IF + F has insufficient energy to populate either the A or B states of I F even including the energy released into trans- lation of the iodine atoms.Using crossed molecular beams, in which iodine atoms from the thermal dissociation (90%) of molecular iodine are crossed with a thermal beam of F2, we observe no IF emission. Excited iodine atoms I(2Pl,2) could only be produced from collisional dissociation of 1; and this would be inconsistent with our observation of a linear dependence on F2 pressure. In addition, the reaction I(2P1/2) + F2 -+ IF + F has only sufficient energy to populate the A state of IF and could not explain our B state emission. Thus we conclude that the IF* emission that we observe comes from the four-centre reaction 1; + Fi. Prof. J. N. Murrell (Sussex) said: The information provided by Valentini and co- workers on the energies of trihalogen complexes would, if combined with some force field data on these species, provide approximate triatomic and tetra-atomic potentid surfaces according to the procedure described iii my paper with Varandas.These would allow trajectory studies of the bimolecular halogen reactions which would illuminate the possible reaction mechanisms. Dr. R. C. Estler, Mr. D. Lubman and Prof. R. N. Zare (Columbia University) (coin- nzunicated): The high pressure (non-beam) cherniluminescent studies of I F in the gas- phase reaction of I2 + F2 by Birks, Gabelnick, and Johnston' have been extended to include the reactions of F, + CH31, CF31, CH212, and HI. All the resulting chemiluniinescent spectra are very similar to F2 + I2 with the exception of that obtained from the reaction of F2 + CH31.Whereas the former are characterized by sharply defined bandheads of the B-X transition, the I F emission from the CH3T reaction gives rise to rotationally broadened bands above a high un- resolvable background. On the basis of the proposed trihalogen and pseudo- trihalogen models of Valentini, Coggiola, and Lee2 and of Dixon and Her~chbach,~ one would expect the pseudo-trihalogen stability of CH,I-F, CF31-F, and CH211-F to be approximately the same since the X-I (X = CH3, CF3, CH21) bond energies are comparable. Therefore, under similar experimental conditions, one might expect similar spectra, which is not observed by us to be the case. Although extracting mechanistic details out of high-pressure studies is dangerous, if not foolhardy, our studies would seem to indicate that the overall formation of IF* in the above reactions is still not well understood.Indeed, an attempt has been made (October 1976) to measure variation of the the 1; + F2 cross-section with laser polarization, but so far we have not been able to repeat the observation of IF* emission. Prof. J. N. Murrell (Sussex) said: The paper by George and co-workers should be welcomed at this meeting for its presentation of a new idea. I would like to ask J. W. Birks, S. D. Gabelnick and H. S. Johnston, J. Mol. Spectr., 1975,57, 23. J . J. Valentini, M. J. Coggiola and Y . T. Lee, Faraduy Disc. Chem. SOC., 1976,62, this Discussion. D. Dixon and D. R. Herschbach, For*oJoy Disc.Cheni. Soc., 1976, comment at this Discussion.318 GENERAL DISCUSSION whether it has any relevance to the inverse problem which is the probability of a bi- molecular reaction over an excited-state potential surface, which is possibly repulsive, being accompanied by emission of a photon and the formation of a stable ground state complex. A* + B -+ AB + hv Prof. T. F. George (Rochester) said: This problem is not directly related to the paper which we presented, because the interaction term is so small that we may simply use intermediate quasimolecular states and perturbation theory, instead of electronic- field surfaces. One problem we are studying which is more closely related is A + B + h ~ i --+ C + D + h ~ 2 , where we assume the stimulated radiation field (ho,) to be intense and the emitted radiation (hco2) is much weaker.In this case the electronic-field states provide the spectrum for emission, whose rate as a function of frequency can be determined through perturbation theory. The inverse problem of that posed by Murrell, A + h ~ l + B + C --+ €3 + c + hUz, is a photodissociation process which is under investigation in our group. Once again we assume the stimulated field ( h q ) to be intense so that the electronic-field repre- sentation is appropriate. Mr. Peter A. Gorry and Dr. Roger Grice (Cambridge Uniuersity) said: We should point out that the locus of the minimum energy profile c of fig. 7 of our paper can be represented only qualitatively on the normal coordinate representation of fig.8. A family of such representations exists corresponding to variation of the Qo symmetric stretch normal coordinate. Fig. 8 shows the choice of Qo which minimises the height of the tip of the conical intersection; denoted qo = 0 in the displacements of Karplus.' However, the accurate locus of profile c requires only modest variation of the Qo normal mode, Ro + qo - 3.1-3.6 A. Hence the locus of fig. 8 gives a good qualitative guide to the minimum energy path. This leads us to suggest a specific criterion for the onset of orientation dependence in reactions at low energy proceeding over potential energy surfaces of this form. Reaction will start to become inhibited in the broadside orientation (a - 90') when the tip of the conical intersection of lowest height rises above the asymptotic energy of the reaction entrance valley.This hypothesis could be tested by Monte Carlo trajectory calculations on trial surfaces of the London type, which permit ready variation of the cone height. The family of alkali atom-dimer exchange reactions might also provide an experimental testing ground where variation of the constituent alkali atoms would change the height and location of the conical intersection. The alkali atom plus halogen molecule reactions provide an example where the tip of the conical intersection lies at the reactant asymptotic energy. These reactions are indeed thought to exhibit an orientation dependence favouring the near collinear orientation (a - 30"). The precise collinear configuration (a = 0') is of course inhibited by the solid angle factor sin a.The effect of conical intersections on the orientation dependence of reaction exemplifies a topological3 feature which is not removed by modest variation in the R. N. Porter, R. M. Stevens and M. Karplus, J. Chem. Phys., 1968,49, 5163. R. Grice and D. R. Herschbach, Mol. Phys., 1974, 27, 159. H. C. Longuet-Higgins, Proc. Roy. Soc. A, 1975, 344, 147.GENERAL DISCUSSION 319 nature of the participating atoms but whose effect depends on its quantitative magni- tude and position. Similar considerations apply to the topological features which determine the Woodward-Hoffman rules as discussed by Herschbach.l Prof. J. C. Polanyi, Dr. J. L. Schreiber and Dr. W. J. Skrlac (University of Toronto) said: In their discussion of the exchange reactions of alkali atoms with alkali dimers, exemplified by Li + Na2 --+ LiNa + Nay Mascord, Gorry and Grice2 suggested, on energetic grounds, that the attacking atom may approach more-or-less collinearly and subsequently insert between the atoms of the molecule under attack.They point out that this path has the energetic advantage that it brings Li into the favoured NaLiNa configuration, while avoiding a (localised) barrier to lateral approach which stems from interaction between an upper and lower electronic state in the C2, configuration. Comparable dynamics have in fact been found to be of importance in 3D trajectory studies3 on a variety of potential-energy hypersurfaces which show points of similarity to Li + Na,. The four potential-energy surfaces were LEPS surfaces that made use of the spectroscopic parameters for the system HIC1.All favoured collinear ap- proach, and all had an energy barrier of E, - 0 for approach from the I end of ICl, as well as a potential-well at this end of the molecule (well-depth approximately 20 kcal mol-I, for IC1 held rigid). The approach from the C1 end of the molecule involved the crossing of a low energy-barrier (typically 1.6 kcal mol-I), and exhibited no potential-well. It was, therefore, the approach from the I end that resembled in its broad features the approach of Li to Na,. It was found that an important reaction path involved the approach of H from the J end of ICl to form a vibrating-rotating incipient HI (see fig. 1, at right). The re- microscopic branching direct reaction migration and insertion FIG. 1 .-Schematic representation of two distinctive (concurrent) types1of molecular dynamics for the reaction-H 4- IC1- HC1 + I.action is exothermic to form either HI or HCl. The attractive interaction for ap- proach from the I end of the ICl leaves relatively little repulsive energy to separate the heavy I and Cl atoms. There is time for the H to rotate around the:I, and then to insert into the somewhat extended IC1 bond. D. R. Herschbach, this Discussion. D. J. Mascord, P. A. Gorry and R. Grice, this Discussion. J. C. Polanyi, J. L. Schreiber and W. J. Skrlac, Chern. Phys., in preparation.320 GENERAL DISCUSSION In the course of insertion the oscillating H-atom can approach the C1 sufficiently closely that the Cl-H attraction exceeds the H-I attraction.In this case insertion is accompanied by migration, and, despite the fact that the initial interaction was with I, HCl product is formed. (This is an over-simplification. The outcome is not assured until I and C1 have separated to such an extent that H can no longer hop between the two heavy atoms. Several to-and-fro migrations can occur before this rICl separation is reached. The system is passing through the same configuration-space as is explored by the reaction C1 + HI -+ ClH + I; the hopping of H to-and-fro in the course of this reaction is pictured in a film made some years ago.)”, The same product, HCl, can also be formed by direct reaction (shown, schematic- ally, at the left in fig. 1). The small barrier to approach from the C1 end ensures that at room temperature the bulk of the reaction is formed by the indirect mechanism, reminiscent of the dynamics proposed for Li + Na, by Mascord, Gorry and Grice.The existence of two distinctive types of molecular dynamics both resulting in the formation of the same chemical species, constitutes “ microscopic branching ”. We have proposed that microscopic branching is responsible for the observation of two distinctive product energy-distributions for the single product HCl in the reaction H + ICI --+ HCl + I,3 From the present discussion it is evident that microscopic branching should bc more conspicuous (both in terms of the relative yield of the product migratory re- action, and the difference in energy-distribution between the two reaction paths) as one goes along the series H + C12 -+ HCl + C1, H + BrCl-+ HC1 + Br, H + ICl -+ HCI + I.Briefly stated, in H + X Y -j HY + X there will be a diminished barrier for approach from the “ far end ” of the molecule (migratory reaction from X to Y) only if, and to the extent that, HXY constitutes a stable arrangement. This, in turn, requires that the electronegativity of X be less than that of Y ; 3*4 a condition which is not met for X = Y = C1, but is met increasingly for XY = BrCl and XY = ICI. Experimental data are now available for the detailed rate constants into specified product vibrational and rotational states, k(u‘, J’), for all three reaction^.^,^ The findings are in accord with this simple rationale; the yield and the “ distinctiveness ” of the product HY formed by migration of H increases as XY changes from CI, -+ BrCl+ ICl.Mr. Peter A. Gorry and Dr. Roger Grice (Cambridge University) said: The dis- cussion of our paper merely traces out minimum energy paths on the potential energy surface. The actual dynamical motion over the potential energy surface does not necessarily follow such paths efficiently. The comments concerning orientation de- pendence refer to the entrance valley and are likely to be quite secure. However, the path relating to migration may be much more sensitive to the details of dynamical motion. The potential energy surface for the reaction of hydrogen atoms with halogen molecules involves p orbitals and, therefore, differs in detail from the simplest case of three s valence electrons. However, the molecular orbital correlation diagrams of Maltz6 for H + C12 suggest that a conical intersection exists for the perpendicular C.A. Parr, J. C. Polanyi and W. H. Wong, J. Clzem. Phys., 1973, 58, 5. M. A. Nazar, J. C. Polanyi and W. J. Skrlac, Chem. Phys. Letters, 1974, 29, 473. J. D. MacDonald, P. R. LeBreton, Y. T. Lee and D. R. Herschbach, J. Chem. Phys., 1972,56, 769. J. C. Polanyi and W. J. Skrlac, Chem. Phys., to be published. C. Maltz, Chem. Phys. Letters, 1971, 9, 251. * The film, Some Concepts in Reucriorz Dyiumics, is available on loan.GENERAL DISCUSSION 32 1 approach (a = 90') which is above the asymptotic entrance valley and constrains reaction to near collinear orientations. In the unsymetrical H + ICl reaction the conical intersection no longer occurs for perpendicular approach (a = 90') but rather moves round toward the CI atom.Consequently the flanks of the conical inter- section now inhibit approach of the H atom to the Cl end of the ICl (E, - 10 kJ mol-1 similar to H + C12) much more than approach to the I end (E, - 0). The flanks of the conical intersection leave a much wider and lower potential energy valley for approach to the I end, thus favouring reaction at that end. This displacement of the conical intersection and consequent distortion of the shape of the cone flanks are apparently responsible for the existence of a potential energy path permitting migra- tion. Certainly the experimental observations and Monte Carlo trajectory calcula- tions to which Polanyi refers do offer reassurance that when such a pathway exists, dynamical motion does permit it to be followed efficiently, at least for the light and mobile H atom.Dr. P. S. Bagus, Dr. @. del Conde (IBM, San Jose) and Dr. D. W. Davies (Uni- uersity of Birmingham) said: We have continued the ab initio calculations for the potential surface of Li3 reported at the 1973 Discussion1 and extended later to include a limited number of configurations.2 With the same Is, ls', 2s, 2s', 2p, 2p' Gaussian basis set, we have calculated the energies for various approaches of an Li atom to an Li2 molecule, using full valency CI. The preliminary results for linear, perpendicular and bent (135") approaches of the Li atom are as follows: (Energies are in kcal mol-1 and relative to Li + Li, distances are in a.u.) linear: equal bond lengths Li .. . Li 5.4 5.5167 5.5667 5.6 5.6167 5.8 energy 5.18 5.26 5.32 5.29 5.29 4.98 Li, . . . Lib 5.5556 Lib. . . Li, 5.5667 I1 linear: unequal bond lengths energy 5.34 angle 53.8" 71.05' base 5.265 6.22 height 5.185 4.3561 111 perpendicular (isosceles triangles) energy 9.16 (2A1) 9.32 ('BJ IV bent (135") Li, . . . Lib 7.2092 Lib. . . Li, 5.05 energy 5.59 This work confirms the previous results that the perpendicular approach leads to the lowest energy. Relative to Li + Li,, the " acute " angled 2A1 and the " obtuse " angled 2B2 isosceles triangles (i.e., < 60" and >60') are about 9 kcal mo1-l more stable, and the optimum linear and bent geometries are about 5% kcal mol-1 more stable. Dr. I. H. Hillier (Manchester) said: We have carried out3 large scale configuration interaction calculations of the potential energy surface of the simplest alkali-metal trimer, Li,.The major prediction which emerges is that the triangular configurations are more stable than linear ones, with the ,B2 and *A1 states having different equilib- rium geometries, but essentially the same energies. Both are bound by 9.2 kcal mol" D. W. Davies and G. del Conde, Faraday Disc. Chem. Soc., 1973,554 369. D. W. Davies and G. del Conde, Chem. Phys., 1976,12,45. J. Kendrick and I. H. Hillier, Mol. Phys., in press.322 GENERAL DISCUSSION with respect to Li2 and Li. The most stable linear configuration is symmetric, unlike the prediction of restricted Hartree Fock calculations, with a Li-Li bond length of 5.5 au and a binding energy of 5.3 kcal mol-l.Dr, R. E. Wyatt, Mr. J. A. McNutt, Mr. S. L. Latham and Dr. M. J. Redmon (Univ. of Texas) said: Polanyi and Schreiberl have presented an amazingly detailed analysis of both experimental and classical trajectory results for the F + H2 reaction. We wish to present several comments relating to quantum mechanical studies of this reaction. An interesting feature of the collinear reaction is the presence of sharp resonance peaks in the quantum2 (but not in the quasi-classical) state-to-state reaction probabilities Po-,", (E). For example, on the Muckerman V potential s~rface,~ the first peak occurs in the 0 3 2 transmission curve near 0.284 eV (total energy measured FIG. 1.-Quantum mechanical probability density p = Y* Y from the scattering (12 channels) wavefunction at Etotal = 0.284 eV.Mass weighted skewed coordinates (2, z) have been used. The top right corner of the viewing region is at (3.4ao, 5.75ao), the lower left corner is at ( 1 0 . 7 5 ~ ~ ~ 0.50ao). The peak value of p in the figure is 9 . l ~ ~ - ~ . from the floor of the entrance valley), just prior to the v' = 3 reaction threshold (at 0.288 eV). Fig. 1 shows the quantum scattering density p = Y* Y at 0.284 eV plotted over a coordinate grid which links the reactant and product valleys4 (the skew angle between the asymptotic valleys is 46.4'). Clearly evident5 are interference extrema in the entrance valley due to elastic reflected waves in the v = 0 channel inter- J. C. Polanyi and J. L. Schreiber, Disc.Favaduy SOC., 1976, 62, 267. G. C. Schatz, J. M. Bowman, and A. Kuppermann, J, Chem. Phys., 1975,63,674. The parameters for this LEPS surface are listed in ref. (2). For other recent studies on flux and density in scattering processes, see J. 0. Hirschfelder and K. T. Tang, J. Chem. Phys., 1976,65,470, and references therein. See for example E. A. McCullough, Jr., and R. E. Wyatt, J. Chem. Phys., 1971, 54, 3578.GENERAL DISCUSSION 323 fering with the incoming reactant wave. Also, the triple peaked v' = 2 density in the product valley is shown evolving from the " lumpy " density in the curved portion of the interaction region. Of particular interest is the structure of p in the interaction region; the peak density in this region is about a factor of two larger than for energies just off resonance.In addition, the peak density occurs for FHH intermediates which are expanded relative to those following the usual steepest-descent reaction path. This may be a quantum analogue of an observation by Polanyi and Schreiber,' namely, that the potential " ledge '' (corresponding to expanded FH2 intermediates) alongside the curved portion of the reaction path is very important in the inversion mechanism. In attempting to interpret the resonance structure,l it is useful to examine the vibrational energy correlation diagram in fig. 2. The reaction path potential V, and s la,) FIG. 2.-Vibrational correlation diagram for the FH2 reaction. The reaction path potential Vl and the Morse vibrational energies W,(u = 0, 1, . . .5) relative to the reaction path potential are plotted against the translational coordinate s.(The translational coordinate is the arc length along a circular arc reference curve with turning centre in skewed coordinates at 2 = 6.5ao, z = 2.37ao.) The vibrational energies were obtained by fitting Morse curves to the potential along vibrational axes perpendicular to the reference curve. The energy of the first 0 4 2 resonance is Ere,. the local Morse oscillator energies W, = V, + EuMorse relative to the reaction path potential are plotted against the translational coordinate s (which measures pro- gression from reactants to products). The potentials W, directly enter the quantum close-coupling equations as " distortion potentials ". A very important feature of the upper distortion potentials is the presence of wells for 0.0 5 s 5 l.Oa,.These are caused by the broadening and subsequent contraction of the vibrational valley on the approach to products, rather than by an actual depression in the surface. In order to assess the importance of the wells in relation to the resonance structure, we have con- sidered a model in which all wells below the v = 4 distortion potential were artificially eliminated (by adjustment of the Morse parameters). Quantum close-coupling results on a 10 channel basis were then obtained with the modified set of distortion potentials. A state path sum analysis of some features of the FH2 reaction has been presented, J. Manz, Mol. Phys., 1975, 30, 899. Wells in the vibrational energy correlation diagram and their im- portance for resonances were first discussed by R.D. Levine and S . F. Wu, Chenz. Pkys. Letters, 1971,11,557; S . F. Wu, B. R. Johnson, and R. D. Levine, MoZ. Phys., 1973,25, 839.324 GENERAL DISCUSSION Additional calculations were then performed in which either one or a pair of (original) wells were reintroduced back into the modified set of distortion potentials. We found that a single well reintroduced into v = 2 led to a wide (-0.2 eV) Pw2 reaction prob- ability curve and that a single well reintroduced into v = 3 did not lead to low energy 0 --+ 2 inversion (PWr dominated). A better model for the low energy behaviour was obtained by adding wells back into the modified v = 2 and u = 3 distortion potentials. As a result, 0 -+ 2 inversion dominated at low energy, but the resonance width was about a factor of five too large.However, as additional wells were added, the reson- ance width decreased toward the exact value. The location of the resonance is at least partially due to the shape of the downhill portion of the distortion potentials from about s = -0.50 to s = +0.20a0. Models were examined which varied the descent of the vibrational levels in this region (except for the levels v = 2 and v = 3), with a resulting range for the 0 -+ 2 resonance maximum of 0.30 eV to 0.36 eV. The model which produced a resonance farthest from the “ exact ” peak at 0.284 eV corresponded to a late drop in the vibrational levels and a surface with a smoothly widening potential valley. The best facsimile resonance, on the other hand, came from a model which closely mimicked the fall of the “ true ” level structure up to s = -0.1, and which exhibited, like the Muckerman V surface, a sudden expansion and contraction of the potential valley around s = 0.The resonance width and position are clearly sensitive functions of the vibrational broadening of the potential on the steep and curved exothermic portion of the exit valley. Further details on the scattering density and flux near resonance, and on resonance models will be presented e1sewhere.l Dr. W. Jakubetz and Dr. J. N. L. Connor (Uniuersity of Marzchester) said: For the F + H2 reaction on the Muckerman V surface,2 Schatz et aZ.,3 have shown there are considerable differences between collinear quantum and classical trajectory calcula- tions.In particular at energies below the classical threshold for reaction, there is considerable population of the u’ = 2 state in the quantum calculation. It appears there are also similar differences in three dimension^.^.^ Now the Muckerman V surface has been selected by optimizing agreement between classical trajectory results and experiment for a series of surfaces; and for the Muckerman V surface the agree- ment with experiment is good. However, the quantum results differ from the classical trajectory ones; hence they cannot be in agreement with experiment, and the Mucker- man V surface cannot be the “ correct ’’ one for the F + H2 reaction. In order to bring the quantum results into closer agreement with experiment, a surface with a different low energy (threshold) behaviour is required.Threshold be- haviour is very much influenced by the barrier region, and consequently the barrier region of the “ correct ” surface should differ from that of the Muckerman V surface. It is, therefore, very interesting to learn that Schaefer’s new extended ab initio calcula- tion6 shows the barrier height to be significantly greater than in all previously used surfaces including Muckerman V. A higher barrier may be expected to reduce the amount of tunnelling, which in the case of the Muckerman V surface leads to a relative over-population of the v’ = 2 state. Differences between quantum and classical calculations of the type discussed above J. McNutt, S. Latham, M. Redmon and R. Wyatt, to be published. J. T. Muckerman, personal communication, 1974.G. C. Schatz, J. M. Bowman and A. Kuppermann, J. Chem. Phys., 1975,63, 674. M. J. Redmon and R. E. Wyatt, Int. J. Quant. Chem. Symp., 1975,9,403. R. E. Wyatt, personal communication, 1976. ti S. R. Ungernach, M. F. Schaefer and B. Liu, this Discussion.GENERAL DISCUSSION 325 make it difficult to derive the correct potential energy surface by adjusting trajectory data to experimental results, because this may produce the wrong saddle point pro- perties. On the other hand, selection of potential surfaces by exact quantum calcula- tions is entirely impracticable at the present time. A better approach may be to fix the general topology of the surface by trajectory calculations (which will not reproduce experimental results quantitatively) and determine the saddle point properties by accurate ab initio calculations.Prof. J. N. Murrell and Dr. S . J. Fraser (Sussex) said: As Jakubetz has pointed out in his comments on the paper by Polanyi and Schreiber’ discrepancies may occur between the results of classical trajectory calculations and quantum mechanical cal- culations on the same potential energy surface. We would like to suggest one im- portant reason for this discrepancy, Even for a smooth surface like that for collinear H3 one can find classical trajec- tories which cover configurations close to the saddle point but which have no con- nection with the reactant or product channels.2 This may, for example, be due to a softening of the symmetric mode force constant at the saddle point or it may arise from the curvature of the reaction coordinate. The figure shows the Poincari surface of section for two typical bound orbits of this type for a harmonic saddle point plus cubic term axs2 (s being the reaction co- ordinate and x being orthogonal to this), both coordinates measured from the saddle - ” ... . . . * . . . .. * . . . . . . . . . . . . .. . . . . . . . . . . . . . .. . . .. .. S + . . . . . .. . .. . . . . . . P S . . . . . . . . . . .. . I . . . . . . . . . .” The Hamiltonian for the system is H = &(p2 + p$ + x2 - 0 . 1 2 5 ~ ~ + 0.4~~’); E = 1 .O, E is the total energy. The surface of section for two trajectories is taken at the plane x = 0 and the signs refer to the sense of p x at this plane. The outer & branches belong to one trajectory and the inner L- branches to the other.Paper by Polanyi and Schreiber, this Discussion. Mol. Phys., 1976, 31,469.326 GENERAL DISCUSSION point as origin. Such trajectories are dynamically isolated from the classical scatter- ing states and cannot be incorporated into an unmodified classical scattering theory. However, in a quantum mechanical description of scattering processes we may rather loosely say that no points of phase space are inaccessible. We suggest that classical bound states, as illustrated in the figure, corresponding to good action variables1 are associated with quantum mechanical resonances for such surfaces. As Wyatt has shown in this discussion resonances are associated with the accumulation of prob- ability density at the saddle point for particular energies.Dr. W. Jakubetz and Dr. J. N. L. Connor (University of Manchester) said : Polanyi and S~hreiber~.~ have pointed out how the shape of the corner region of potential energy surfaces, and in particular the location of the inner wall (the “ shoulder ”), affects product vibrational distributions of chemical reactions. For the F + H2 reaction, the shoulder occurs at a larger H - F distance on the ab initio SCFCI “ BOPS ” surface4 than on the LEPS surfaces SE-1 2*3 or Muckerman V5 and gives rise to too large an amount of product vibrational energy. The shift in the location of the shoulder may be caused by too great a drop in energy in the corner region since the exothermicity is too large by 0.1 1 eV in the ab initio calculation. Thus a wrong exothermicity might indirectly give rise to an incorrect product vibrational distribu- tion.We would also like to indicate how a wrong exothermicity may, in a more direct way, influence the detailed relative rate constants for a reaction. Consider the Muckerman V surface for the F + H2 reaction. This surface has the correct exothermicity and spectroscopic constants for reactant and product molecules and hence the correct thresholds for all individual u -+ v’ reactive transitions. In particular, the 0 --f 3 transition opens at a translational energy of 0.017 35 eV, which corresponds to about (2/3)kT at room temperature. Collinear quantum calculations by Schatz et aZ.,6 for the Muckerman V surface show that the 0 -+ 2 transition is the dominant one in this energy range.They find the collinear rate constants kZc0 and k3- are in the ratio 18: 1 at 300 K. Only at higher values of the translational energy (Etrans 20.16 eV) is strong population inversion obtained, the degree of which is influenced by the location of the shoulder. For example, at Etrans = 0.165 eV, the reaction probabilities P2- and Psc0 are in the ratio 1:lO. The situation is quite different for the BOPS surface. Due to the wrong exo- thermicity, the 0’ = 3 threshold lies 0.094 10 eV below the absolute threshold for reaction. Thus in contrast to the Muckerman V surface, the u’ = 3 state is open at all translational energies. In collaboration with J. Manz of Munich, we have used a rotated Morse cubic spline adaptation of the BOPS surface to obtain collinear reaction pr~babilities.~ We find the ratio Pzc0 :P3t0 to be about 1 : 20 for energies close to threshold as well as over the whole thermal energy range (the rate constants k2-:k3+,, are in the ratio 1 : 19 at 300 K).Thus the population inversion is twice that for the Muckerman V surface (at energies away from the 0’ = 3 threshold); this is a consequence of the different Paper by Handy, Colwell and Miller, this Discussion. J. C. Polanyi and J. L. Schreiber, Chem. Phys. Letters, 1974, 29, 319. C. F. Bender, S . V. O’Neil, P. K. Pearson and H. F. Schaefer, Science, 1972, 176, 1412. J. T. Muckerman, personal communication 1974, see ref. (3) and (6). G. C. Schatz, J. M. Bowman and A. Kuppermann, J. Chem. Phys., 1975,63,674. * J. C. Polanyi and J. L. Schreiber, this Discussion.’ J. N. L. Connor, W. Jakubetz and J. Manz, in preparation.GENERAL DISCUSSION 327 shoulder locations on the two surfaces. On the other hand, the rate constant ratio kZt0 to k3t0 at 300 K differs by a factor of about 150 for the two surfaces. These numbers will be modified for three dimensional reactions. Nevertheless, we believe the qualitative features will be not altered significantly. Preliminary three dimensional quantum calculations by Redmon and Wyatt suggest the relative energy dependence of the reaction probabilities for the collinear and three dimensional reactions is similar for the Muckerman V surface. For reactive scattering calculations, it appears to be important that the exo- thermicity and individual thresholds be correct to better than kT.This suggests that experimental information on these quantities shouId be used, for instance, by ap- propriately rescaling the ab initio calculated energies. Dr. A. Komornicki, Prof. T. F. George and Prof. K. Morokuma (Rochester, N. Y.) said : The results we have just heard concerning F + H2 are based on the assumption that the interaction potential can be adequately represented by the lowest adiabatic poten- tial energy surface. Since it is known that there are three low lying electronic surfaces for this reaction, we have recently undertaken an investigation to determine the role and the influence of multiple electronic surfaces for this reaction. We would like to present here our classical three-dimensional Monte-Carlo results, where for the first time all three surfaces have been explicitly incl~ded.~ The switching probability, for each trajectory, was calculated using a recently published decoupling appr~ximation.~ Within this approximation the local switching probability is given by p = exp(-26), where 6 is a local one-dimensional action integraL4 The results are presented in fig. 1 6 - L - N “Q, b 2 - 0.2 0.4 0.6 0.8 1.0 EIeV FIG.1 M. J. Redmon and R. E. Wyatt, Int. J. Quant. Chem. Symp., 1975, 9,403. R. E. Wyatt, personal communication, 1976. A. Komornicki, Thomas F. George and Keiji Morokuma, J. Chem. Phys., 1976, 65, 4312. A. Komornicki, T. F. George and K. Morokuma, J. Cltem. Phys., 1976,65,48.328 GENERAL DISCUSSION where total reactive cross sections are plotted versus relative translational energy.The present results are limited to the following set of initial conditions. The hydrogen molecule was chosen in a quasiclassical fashion with u = 0, while the rotational states (with integer quantum numbers) were chosen to correspond to a rotational tempera- ture of 400 K. The results for the primary process F(2P1,2) + H2 are depicted in curve a. For comparison we also ran trajectories on just the lowest surface for F(2P3,2) + H2, and the results are shown by curve by and c. For curve b we assumed a local switching probability of zero to the excited state surface, and for curve c we included the actual value of the switching probability so that each trajectory accumulated a probability of not switching to the excited state surface. Our results show that electronic quenching followed by reaction is a significant process within the energy range considered.Further, our results suggest the need for more refined experimental and theoretical investigations. Experimentally, results based on a state selected spin-orbit state are needed to substantiate our predictions. Theoretically, our results suggest that a single surface treatment of this reaction may be incomplete even at low energies. We thank the donors of the Petroleum Research Fund, administered by the American Chemical Society, the Air Force Office of Scientific Research and the National Science Foundation for support. Miss B. A. Blackwell, Prof. J. C. Polanyi and Dr. J. J. Sloan (University of Toronto) said: There has been discussion of the fact that in a number of systems enhanced reagent vibration, <A V ) , tends to be channelled efficiently into enhanced product vibration, (AV’).’” This raises the intriguing possibility that a thermoneutral re- action (-AH,” = 0) could, with appropriate reagent vibrational excitation, give rise to highly vibrationally excited reaction products.If such an effect is demonstrated, then it will be clearly evident that it is the reagent energy that is being transposed more-or- less “ adiabatically into product energy, rather than that the presence of reagent vibrational excitation has caused the exothermicity to be more efficiently channelled into product vibrational excitation. We have been able to observe (AV) -+ (AV’) for the nearly-thermoneutral re- action with (AV} as high as 75 kcal mol-l and (AY’) as high as 75 kcal mol-l.The experimental method combined two techniques in use in this laboratory: chemi- luminescence depletion was used to study the consumption of the OHT(u’), and infra- red chemiluminescence (under conditions approaching arrested relaxation) was used to study the formation of HClT(u”). The source of OH?(u’) was a “ pre-reaction ”.4 Two different pre-reactions were used; pre-reaction I gave OH? in high vibrational states, and pre-reaction I1 gave OH? in low vibrational states. The two pre-reactions were, C1 + OHt(u’) -+ HCl?((u”) + 0 -AH: = 0.9 kcal rno1-l (1) H + O3 --f OHt(u’ = 6-9) + O2 H + NO2 4 OH~(U’ = 1-3) + NO. I I1 Directly below the pre-reactor, pulses of atomic C1 were introduced. The OH? A. M. G. Ding, L. J.Kirsch, D. S. Perry, J. C. Polanyi and J. L. Schreiber, Faraduy Disc. Chem. Soc., 1973,55,252. J. G . Pruett and R. N. Zare, J. Chem. Phys., 1976,64, 1774, give evidence of less efficient con- version. D. J. Douglas, J. C. Polanyi and J. J. Sloan, J. Chem. Phys., 1973,59,6679; Chem. Phys., 1976, 13, 15. * J. C. Polanyi and J. L. Schreiber, this Discussion.GENERAL DISCUSSION 329 100 90 80 - 70 al 0 L 60 d b V Y x Cn . 50 L 40 30 20 10 0 CI OH'lvj -----+ HCI'(v3 10 r---- V " 1 I 8-m - I 7 -: . I I - i -- -- 5 . ~ --- I - i I 3 7 --- 2 1 - expt.2 I - 4 - 3 > aJ ZI ul \ . 2 t t 0, 1 0 0 0.5 1.0 0 0.5 1.0 1.5 d e p l e t i o n formation FIG. 1.-Reagent and product vibrational distributions for C1 + OH7 4 HClt + 0. Heavy bars at the left record the decrease in population of each OH7 vibrational level, resulting from the intro- duction of C1 atoms.Bars at the right are taken from a concurrent record of the amount of HClt formed. In expt. 1 the OH? was produced in the prior reaction H + 0 3 -, OH7 + 02; in expt. 2 the pre-reaction was H + NO2+ OHt + NO. depletion spectrum and the HClt formation spectrum were recorded concurrently, using an amplifier locked to the C1 pulsing frequency. The results are shown in fig. 1, where the (relative) population changes in each of the indicated vibrational levels of the reagent and product are given, along with the energies of the levels. The top part of the figure shows the result of an experiment in which pre-reaction I was used. In this case OH? was produced in vibrational levels u' = 6-9.The amounts removedfrom each of these levels are indicated by the heavy bars in the upper left-hand side of the figure [the bars are relative to OHf(zl' = 9)]. In this experiment the product, HClt(u"), was observed exclusively in vibrational levels v" = 8-1 1. The amount produced in each vibrated level is indicated by the length of the heavy bar, relative to the population change of the reagent OHt(d = 9) level. The lower part of the figure shows the result obtained using pre-reaction I1 to produce the OH? reagent. In this case the first three OH? vibrational levels were observed. The amount by which the population of each vibrational level decreased in the presence of C1 atoms is shown by the length of the heavy bar [normalised to OHt(u' = l)]. The HClt produced in this experiment is shown on the lower right- hand side of the figure. The population increases in the HClt vibrational levels are330 GENERAL DISCUSSION indicated by the heavy bars, normalised to the (reagent) OH (u’ = 1) population change.These results illustrate that, for the nearly thermoneutral reaction (l), vibrational excitation in the reagent molecule becomes largely vibrational excitation of the product molecule. There is evidence of a slight net loss of vibrational energy to other degrees of freedom, as the mean energy of the reagent OH? is greater than the mean energy of the HClt produced. Some of this energy is channelled into rotation in the HC1 product ; substantial product rotational excitation was observed-much in excess of the reagent rotation. It is also likely that some reagent energy was lost in inelastic collisions with the C1, by way of V --f T energy transfer.In principle one could distinguish the reactive and the inelastic contributions to the depletion of OH?, by measuring the yield of HCl? per OH? removed. In practice, the comparative Einstein transition probabilities for HClt and OH? are not sufficiently well known to make this feasible. However, the in- elastic component of the total OH? removal rate cannot be large compared to reaction [for the case of OH? (u’ = 6-9)] since substantial OH? deactivation would result in the appearance of the deactivated OH? in levels u’ < 6. There was no measurable in- crease in these populations. The picture of the reactive event suggested by these observations is one in which the light H-atom is transferred even in large impact-parameter (grazing) collisions, from the strongly vibrating OH to the Cl atom. Reaction through an extended Cl-H-0 intermediate1P2 gives rise to product with large internal excitation.Since the amount of angular energy which the HClt product can have is limited by its small moment of inertia, most of this internal excitation appears as vibration. The formation of excited product with up to 75 kcal mol-1 of vibrational energy in a thermoneutral reaction suggests the possibility that in cases where there exists a con- venient source of some species ABT but no such source of a desired product AD?, one might use a variety of “ parasitic ” reactions D + AB? to devour AB? and transform it efficiently to AD?.This could be a useful expedient in the construction of lasers, or in state-selected chemistry. From a fundamental standpoint the phenomenon is of interest in view of the fact that it opens the way to the quantitative study of the efficiency of ( A Y ) + (AY‘) and (AR) -+ (AR‘) on contrasting potential-energy hypersurfaces ; ex~thermic,~-~ thermoneutral and endothermic. One could achieve these three situations in a homologous series by changing the attacking atom in the pre- sent study from X = F -+ Cl -+ Br. An experiment of this type is being attempted. A fuller account of the present experiments is in preparati~n.~ Dr. S. R. Ungemach, Prof. H. F. Schaefer and Dr. B. Liu (California) said: Some- what more than four years ago, Bender, O’Neil, Pearson and Schaefer4 (BOPS) reported an ab initio potential energy surface for the F + H2 system. The theoretical methods used appeared to be sufficiently reliable to provide a qualitatively correct surface.Further the predicted barrier height of 1.66 kcal agreed well with the experi- mental activation energy5 (roughly 1.6 kcal), as did the exothermicity (34.4 kcal theoretical as opposed to the experimental value6 31.5 & 0.5 kcal). A. M. G. Ding, L. J. Kirsch, D. S. Perry, J. C. Polanyi, and J. L. Schreiber, Faraday Disc. Chem. SOC., 1973, 55,252. J. C. Polanyi and J. Sloan, this Discussion. B. A. Blackwell, J. C. Polanyi and J. Sloan, Chem. Phys., in preparation. C. F. Bender, S. V. O’Neil, P. K. Pearson, and H. F. Schaefer, Science, 1972,176, 1412.R. Foon and M. Kaufman, Progr. Reaction IEnetiCs, 1975,8, 81. J. W. C. Johns and R. F. Barrow, Proc. Roy. Sac. A , 1959, 251, 504; W. A. Chupka and J. Berkowitz, J. Chem. Phys., 1971,54,5126. This exothermicity is obtained by subtracting 109.5 kcal (D, for H2) from 141.0 rt 0.5 kcal (D, for HF).GENERAL DISCUSSION 33 1 During the past year we have been re-examining the F + H2 surface with much more reliable theoretical methods. Specifically much larger basis sets (of one particle functions) and more complete configuration interaction (CI) treatments have been employed. It is well known‘ that in the (unattainable) limit of a complete basis set and CI expansion, one obtains the exact solution to Schrodinger’s Equation, and hence the exact potential surface.Although our current study is not yet completed, it is appropriate to present our preliminary results at this time, in light of the paper just presented by Polanyi and Schreiber.2 The goal of our current research is to obtain an FH2 surface of sufficiently high reliability to be used directly (or with a very modest amount of scaling) in detailed dynamical studies. Among the most critical features of a repulsive potential surface such as FH2 are the barrier height, saddle point position, and exothermicity. Indirect information (via activation energies) concerning the first and a reasonably accurate value of the third of these features is available from experiment. The saddle point represents a unique point on the surface and is of special interest here since BOPS predicted rsp(F - H) = 1.54 A, rsp(H - H) = 0.767 A, while Polanyi and Schreiber3 have suggested (on the basis of classical trajectory studies) that dynamics more harmonious with experiment are obtained with a smaller value of rs,(F - H).However, the most widely used semiempirical FH, surface, the Muckerman V ~urface,~ is essentially in perfect agreement with BOPS as regards the saddle point position. If one assumes a reasonable saddle point position, a large number of ab initio surfaces can be tested rather quickly, by performing three computations only: for the reactants, saddle point, and products. In the present study this procedure has been adopted for several types of electronic wave functions. In addition, however, in a few cases the saddle point has been located by the more arduous process of direct search, requiring 16-25 points on the potential surface.Table 1 summarizes the results to date of our theoretical endeavours. The first entry was based on the basis set used by Cade and HUO’ in their near Hartree-Fock study of the HF diatomic. This basis does not describe the isolated H atom well and hence yields a much smaller exothermicity than experiment.6 The second through seventh entries describe the results of a reasonably exhaustive set of configuration tests using what is termed the “ small basis ”. The latter is a Slater basis with fluorine 2p functions taken from the F- negative ion basis optimized by Bagus and Gilbert.7 This follows the observation that molecular wave functions often utilize basis functions somewhat more diffuse than are required for the constituent neutral atoms.The use of a single reference configuration (a 1 in column 3) implies that all interactings singly- and doubIy-excited configurations were included relative to the Hartree-Fock configuration la2 2a2 302 40 ln4. (1) H. F. Schaefer, The Electronic Structure of Atoms arid Molecules: A Survey of Rigorous Qiiantuni Mechanical Results (Addison-Wesley, Reading, Massachusetts, 1972). J. C. Polanyi and J. L. Schreiber, this Discussion. J. C. Polanyi and J. L. Schreiber, Chetir. Phys. Letters, 1974, 29, 319. P. A. Whitlock and J. T. Muckerman, J. Chem. Phys., 1975, 61,4618. P. E. Cade and W. M. Huo, J. Chent. Phys., 1967,47, 614. J. W. C. Johns’and R. F. Barrow, Proc. Roy. SOC. A , 1959, 251, 504; W.A. Chupka and J. Berkowitz, J. Chem. Phys., 1971,54,5126. This exothermicity is obtained by subtracting 109.5 kcal (Dc for H2) from 141 .O f 0.5 kcal (Dc for HF). J. Hinze, J . Chem. Phys., 1973,59, 6424. ’ P. S. Bagus, T. L. Gilbert and C. C. J. Roothaan, J . Chem. Phys., 1972,56, 5195.w w h, TABLE 1.-Ab initio POTENTIAL SURFACE FEATURES FOR THE F + H- + FH + H REACTION calculation basis reference frozen number E(FH + H) saddle point barrier height exo t hermici t y number set configurations orbitals configurations /hartrees rsp(F-H) rsp(H-H) /kcal mo1-l /kcal mol-I 1 Cade-Huo F(5s4p2dlf) H(3slgld) small basis F(4s3p 1 d) H(2slp) small basis small basis small basis small basis small basis large basis F( 6s4p3d If) H( 3s2pl d) large basis large basis modified to describe F- 3 2 3954 - 100.7013 2.79 1.47 3.99 26.5 28.2 2 1 2 588 - 100.7040 2.79 1.47 5.22 1081 1598 3279 2142 468 1 5966 - 100.7532 - 100.7075 - 100.7564 - 100.7075 - 100.7564 - 100.8432 2.79 2.79 2.79 2.79 2.79 2.79 1.47 1.47 1.47 1.47 1.47 1.47 5.26 3.55 3.64 2.95 2.97 6.03 27.5 29.6 28.3 29.6 28.3 28.7 2 2 - 100.7645 - 100.7630 2.79 a 2.79 1.47" 1.47 3.93 3.99 32.6 32.6 9 10 3 3 Theoretically determined saddle point for this calculation.Approximate natural orbitals used to select 6874 from a total possible 8790 configurations.GENERAL DISCUSSION 333 Similarly, where three reference configurations are included, these are, in addition 1 0 2 2a2 4c 5 0 2 in4 to (1) and (2) la2 2a2 3a 4a 5a In4. (3) Finally the seven reference configuration studies include all single and double excita- tions relative to the seven configurations in the full CI involving the 30, 40, and 5 0 orbitals and the outer three electrons.In each case the starting 1, 3 or 7 configura- tion wave functions were obtained by the multi-configuration self-consistent-field (MCSCF) meth0d.l Focusing on the results with only one orbital frozen or doubly-occupied in all configurations, one must conclude that a CI including only single and double excita- tions relative to the single SCF configuration leaves out important correlation effects, In particular the barrier height goes from 5.26 to 3.64 to 2.97 kcal as the reference configurations are increased from 1 to 3 to 7. We also see that the effect of holding the 2 0 (roughly fluorine 2s) orbital doubly-occupied has little effect on the barrier height but increases the exothermicity by -1.3 kcal.Thus we conclude that for truly quantitative accuracy, the FH2 potential surface requires a very complete treatment of electron correlation. The last three entries were obtained using a much larger basis, synthesized from the very accurate theoretical studies of Liu2 on HF and Ungemach3 on H2. With one reference state and only the fluorine 1s doubly-occupied, all single and double excita- tions were included, and again the barrier appears much too large. However, as with the smaller basis, going to three reference configurations substantially reduces the predicted barrier. Modifying the fluorine 2p functions to describe F- is seen to have little effect on the theoretical predictions.The most reliable saddle point position predicted here is rsp(F - H) = 1.48 A, rSp(H - H) = 0.778 A. Although this saddle point occurs somewhat " later " than BOPS or Muckerman V it remains earlier than the Polanyi-Schreiber result of 1.434 A, 0.7766 A. By combining the small and large basis set results, we can estimate the results of a " complete " (seven reference configurations, one frozen orbital) treatment using the large basis. The predicted barrier is (3.93 - 0.58) = 3.35 kcal and the exothermicity (32.6 - 1.3) = 31.3 kcal. The exothermicity thus obtained lies within the limits of experimental uncertainty: while the barrier height is considerably greater than either the observed activation energy or the barrier height of 1.06 kcal adopted in the Muckerman V surface.Nevertheless it seems improbable that our predicted barrier is more than 1 kcal larger than the exact value. In a later paper we will attempt to reconcile this result with experiment. Dr. D. E. Klimek and Prof. J. C . Polanyi (University of Toronto) said: The suc- cessful application of laser-induced fluorescence, by Zare and co-workers, as a power- ful new tool for the study of molecular vibration and rotation under beam condition^,^ has rekindled interest in the possibility of the Doppler measurement of velocities under A. D. McLean and B. Liu, J . Chem. Phys., 1973,58,1066. B. Liu, unpublished. S. R. Ungemach, unpublished. R. N. Zare and P. J. Dagdigian, Science, 1974,185, 739.334 GENERAL DISCUSSION the same conditions.' There is experimental evidence2 to show that for a number of chemical reactions the product translational energy-distribution will exhibit resolved structure corresponding to the distinctive translational energies of separate product vibrational as well as, in some cases, rotational energies.This should be reflected in the Doppler line-broadening. The F + H2 = HF + H reaction examined in the foregoing paper provides an example for discussion. There will be important intensity advantages in examining the laser-induced fluorescence from the atomic product rather than the molecular one. Recent advances in vacuum ultraviolet laser technology3 make this a possibility for many atomic species, including atomic H. The case is rendered more advantageous by the large recoil velocity of the light H atom, and also the enhanced Doppler shift at high frequency.A complication is the existence of two adjacent Lyman-a transi- tions for H which, when Doppler-broadened, will be excited simultaneously. These are the l'S, -+ 22P3,, transition centred at 82 259.25 cm-', and the l'S, -+ 22P+ transition at 82 255.65 cm-', with an intensity ratio of 2: 1. Fig. 1 gives a schematic laser . FIG. 1 .-Schematic representation of crossed molecular beams and vacuum ultra-violet laser-beam. The photomultiplier tube, PMT, could be located in either of two positions: position (1) for fig. 2, and position (2) for fig. 3. representation of the atomic and molecular beams, and the tunable laser beam. Fig. 2(a) shows the computed fluorescence intensity as a function of the frequency of the exciting radiation assuming that a 300 K effusive source of F atoms (a Boltzmann dis- tribution with most probable velocity, umP = 5.12 x lo4 cm s-') is crossed at 90" with a supersonic jet of H2 expanding from a 500' K orifice (amp = 3.5 x lo5 cm s-'-the small distribution of speeds about this mean was ignored). The angular spread in the reagent beams was not included in the calculation of fig.2, since the major broadening of the product velocity stems in this instance from the product angular distribution. For early measurements of velocity distributions of atomic and molecular fragments by Doppler- shape measurement see T. R. Hogness and J. Franck, 2. Phys., 1927,44,26, and also A. C . G . Mitchell, 2. Phys., 1928, 49, 228.The emitting species were formed directly in electronically- excited states by molecular photodiesociation. The same process was examined from a theore- tical standpoint by R. N. Zare and D. R. Herschbach, Pruc. I.E.E.E., 1963,51,173; J . Appl. Opt., 1965,2,193. (a) J. C. Polanyi and D. C . Tardy, J. Chent. Phys., 1969, 51, 5717; (6) K. G. Anlauf, P. E. Charters, D. S. Horne, R. G . Macdonald, D. H. Maylotte, J. C. Polanyi, W. J. Skrlac, D. C. Tardy and K. B. Woodall, J. Chem. Phys., 1970,53,4091; (c) T. P. Schaefer, P. E. Siska, J. M. Parson, F. P. Tully, Y . C. Wong and Y . T. Lee, J. Chenz. Phys., 1970, 53, 3385; (d) K. G. Anlauf, D. S. Horne, R. G . Macdonald, J. C . Polanyi and K. B. Woodall, J. Chem. Phys., 1972, 57, 1561 ; ( e ) J. C . Polanyi and K.B. Woodall, J. Chem. Phys., 1972,57, 1574. (a) R. B. Miles and S . E. Harris, l.E.E.E.-JQE, 1973,9,470; (b) R. T. Hodgson, P. R. Sorokin and J. J. Wynne, Phys. Rev. Letters, 1974,32,343 ; (c) S. C. Wallace and G . Zdasiuk, Appl. Phys. Letters, 1976, 28,449.GENERAL DISCUSSION 335w w Q\ I I I I MA 5.73 1215.71 1215.69 1215.67 1215.6 I I I I 82255 82256 82257 8,2258 v /cm" 82259 82260 82261 x / A 5.73 1215.71 1215.69 1215.67 1215.65 I 1 $1,; 22p3,2 transition energy 61 FIG. 3.-Doppler line shapes for atomic H, calculated for the case in which the PMT is located at position (2). The major peaks can be identified with u' = 1-3 in the molecular product (reading from the left); the finer structure is indicative of the rotational population distribution. In this calculation the F atom velocities were selected from a 77 K Boltzmann distribution.Peak intensities in fig. 3(a) and (b) have been normalized to the same value. 0 zGENERAL DISCUSSION 337 The angular distribution of the atomic product was assumed to be the same for all molecular product energy states, namely a Gaussian centred on the forward direction with a breadth of 60" to l/e of the peak intensity ref. (2e). The translational energy dis- tribution of the atomic product was obtained from fig. 10 of ref. (2e); the distribution is resolved into separate contributions corresponding to the individual vibrational- rotational states of the molecular product. The contributions of the individual vibrational states to the product Doppler line-shape are indicated in fig.2(a) and (6). In the absence of any state-selection of the products (which could, however, be pro- duced by perturbing the individual vibrational states of HF with a pulsed infra-red HF-laser) the Doppler profile will be that obtained from the superposition of the vibrational contributions. This envelope exhibits structure in fig. 2(a) which is readily interpreted once the contributions from the 2P3,2 and the weaker 2P+ absorp- tion lines has been de-convoluted as indicated in fig. 2(b). It will be noted that the rotational structure has been lost in the Doppler envelopes of fig. 2(a) and 2(b), despite the fact that full allowance was made for it in the calcula- tion. As indicated, this is due to the breadth of the (full) product angular distribu- tion. If the vacuum ultra-violet laser were used to excite atomic H in a restricted angular interval1 of approximately 30°,2 as shown in fig.3(a) and (b), then the rota- tional structure begins to emerge. It is encouraging that the peak intensity is calcu- lated to decrease by only a factor of 5 when the photomultiplier is moved from position 1 to 2. In an actual experiment the vib-rotational distribution of fig. 3 would, of course, be characteristic of the particular range of centre-of-mass angles under observation. We are much indebted to Dr. J. L. Schreiber for helpful discussions of the com- putations described here. Dr. A. Ding (Berlin) said: Ionic systems are another class where the scattering of electronically excited species can be easily undertaken; for there always exists at least one charge exchanged excited state identical in symmetry with the ground state.Ion experiments can furthermore be performed at a wide range of kinetic energy thus enabling the investigation of velocity dependent curve crossing phenomena. In order to start on the excited potential curve the atom of higher ionization poten- tial has to be used for the primary ions. Xenon is one possible target atom which, because of its low ionization potential, offers itself for such experiments. Earlier the scattering of protons on Xe had been explained using a multistate appr~ach.~ Recently other ions (Of, C + , F+) have been used for elastic scattering experiments on Xe.4 We want to present preliminary results on the ground and excited state potentials of 0+-Xe. There are 3 low lying asymptotic states for this system: O+(4S-) + Xe(lS,), (a) P.J. Dagdigian and R. N. Zare, J. Chem. Phys., 1974,61,2464; (6) G. P. Smith and R. N. Zare, J. Chem. Phys., 1976, 64, 2632. The angular spread in the H2 and F beams (10' and 20" respectively) results in an extended reaction zone. With the photomultiplier tube -10 cm from the centre of this zone, fluorescence will be observed from H atoms whose laboratory recoil angle varies by h15". In view of the large H-atom velocity relative to that of the centre-of-mass, this angular spread will be similar when viewed in the centre-of-mass frame. H. P. Weise, H. U. Mittmann, A. Ding and A. Henglein, 2. Naturforsch., 1971,26a, 1122; C. Kubach, V. Sidis and J. Dump, J. Phys. B, 1975,8, 1129.A. Ding, J. Karlau and J. Weise, unpublished results.338 GENERAL DISCUSSION and O(3p) + Xe+(2f'l12). (4 The splitting of the ground state of O(3P) is negligible, and this state is, therefore, regarded as triply degenerate. The experimental arrangement has been described ear1ier.I Angular distributions of the scattering of O+(4S) on Xe('So) have been obtained between ELAB = 10 eV and 92 eV. Fig. 1 shows a typical result. Generally 3 types of interference structure 0 10 20 30 40 50 L A Bide FIG. 1.-Differential cross section for the elastic scattering of O+(4S-) on Xe('So). The structures around 13 deg. are rainbow oscillations of the bound ground state, the broad undulations between 15 and 50 deg. are Stueckelberg oscillations. EL = 71 eV. 4 t V FIG.2.-Ground and excited state potentials for XeO+. The solid lines are the adiabatic excited and diabatic ground state potential, the dashed line (b) is the diabatic excited state potential. An HI2 of 0.2 eV was assumed in the crossing region. The diabatic excited state potential arising from O(3P) and Xe+(zP112) is shown as a dotted line (c) for comparison, can be observed. At intermediate and high energies rainbow and Stueckelberg oscillations can be distinguished. Towards lower energies the Stueckelberg oscil- 1 H. U. Mittmann, H. P. Weise, A. Ding and A. Henglein, 2. Naturforsch., 1971, %a, 11 12; A. Ding, J. Karlau and J. Weise, Chem. Phys. Letters, in press.GENERAL DISCUSSION 339 lations are slowly damped out and a second rainbow structure appears at small angles.From the energy behaviour of the Stueckelberg oscillations we infer that only the O+(4S-)-Xe(1S0) and the 0(3P)-Xe(2P3,2) curves have to be considered; this is probably due to the greater statistical weight of the Xe'('P,,2) and to the larger inter- action (the interaction HI, will strongly decrease with increasing distance) as the cross- ing of curve a and b is at smaller interatomic distance than the crossing of a and c. Partial wave calcuIations have been performed using WKB phase shifts and the simplified assumption of constant transition probability between the curves a and b. This reproduces the positions, but not the amplitudes of maxima and minima. Fig. 2 shows the resulting best fit potentials. Calculations using realistic Landau Zener transition probabilities are under way and should give the coupling energy H12 be- tween curves a and b.Dr. V. Aquilanti, Dr. G. Liuti, Dr. F. Pirani, Dr. F. Vecchiocattivi and Dr. G. G. Volpi (Perugia, Italy) said: Jn the paper by Costello, Fluendy and Lawley, systems where the interaction is due to more than one potential are studied. We would like to report our recent experimental results1 on other similar systems. We have measured absolute total cross sections for collisions of ground state (") oxygen atoms with He, Ne, Ar, Kr and Xe as a function of collision energy in the range between 0.03 eV and 0.33 eV. The experimental cross sections show glory structures for the 0 + Ar, 0 + Kr and 0 + Xe systems. For Kr and Xe the glory amplitudes appear to be damped compared with those due to the usual potential models such as LJ(12,6) and As an example the glory structure in the total cross section for the 0 + Xe system is shown in fig.1, where the dotted line is the best structure obtained for an LJ(12,6) exp (4). 320 1 t 300 ;- I 280 ! ! . . .... .,.. .. LL 1.0 ' 1 ' ! 0.5 v - ' I s krn-' FIG. 1 .-Centre of mass total cross section, Q(u), for 0 + Xe system multiplied by uZl5 as a function of inverse relativevelocity. The dotted line is calculated for an LJ(12,6) with e = 10.4 meV, rm = 3.73 A. The full line is calculated for two LJ(12, 6), one with e = 9.4 meV, Y, = 3.79 8, and 2/3 as statistical weight and other with E = 13.5 meV, r, = 3.57 %, and 1/3 as statistical weight. potential forced to reproduce the long range Van der Waals constant evaluatedl from the v-2/5 component in the absolute cross section velocity dependence.Under our experimental conditions the 3P2, 3P1, 3P0 oxygen atom states are populated according only to their multiplicities. Therefore the interaction with the 'So state rare gas atoms can be described by a two potential model, one of II symmetry and the other of C V. Aquilanti, G. L i d , F. Pirani, F. Vecchiocattivi and G. G. Volpi, J . Chew. Phys., 1976, 65, 475 1.340 GENERAL DISCUSSION symmetry with 2/3 and 1/3 statistical weights respectively. The full line in fig. 1 shows the calculation performed using a model interaction given by two LJ(12,6) potentials forced to the same long range behaviour and properly weighted. From these results the effect of more than one potential appears to show up in a sensitive way also in total elastic cross section measurements.Although a full under- standing of the true interactions in these systems evidently needs information from further experiments both on total and differential cross section, we think it would be worthwhile to do some theoretical work on the computation of potential energy curves for these interesting systems. Dr. K. P. Lawley (Edinburgh) said: In the elastic scattering experiments just re- ported by Ding, by Shobatake, by Vecchiocattivi and Costello et aZ., a distinction can be made between the results from atoms or ions with the valence electrons in a spheric- ally symmetric distribution and anisotropic atoms. Thus, in O+ (4S3,2) and in Ar* (3Pz,0) the molecular states evolving from the separated atoms with inert gas partners will be very similar.For the O+ + Xe system the two lowest diatomic states will be the nearly degenerate 3& and 3Z0 and in the case of Ar* the S and n potentials will only begin to diverge once the 4s shell is penetrated and the effect of the anisotropic Ar+ core is felt. In contrast, for 0 (3Pz,l,0) and Hg (3P2) the 3C and 3H states would be expected to diverge even at large separations, initially because of the anisotropy of the atomic polarisability. It is perhaps for this reason that in the O+ + Xe and Ar* + Xe systems well defined single rainbows are reported, whereas for 0 + inert gas and Hg* + molecule systems two or more potentials are needed to fit the scattering pat- tern. The correlation diagrams can also give some guidance on the weighting of the potentials used in a trial fitting.Thus, for O(3PJ) with the three J states present in the ratio 5: 3: I, the ratio of Z to ll states in Hund's case (a) is 1 :2. For Hg* (3Pz) this ratio is 3:2, but spin-orbit interaction further splits the 3E1 and 3E0- states. Our scattering results for Hg* with small linear molecules show that distinct rainbows are no longer observed, though at least one deep potential ( ~ 2 4 0 x erg) is un- doubtedly operating, together with shallower ones. Dr. J. Costello, Dr. M. A. D. Fluendy and Dr. K. P. Lawley (Edinburgh) said: Transfer of energy from translation to target molecule rotation would indeed have the effect of diminishing the large angle scattering in the laboratory frame.However, such inelasticity characteristically leads to a " humping " of the scattered intensity around the direction of the centre of mass motion. While such rotationally inelastic collisions are undoubtedly present, they could not account for a monotonic fall in intensity with angle that we observe.GENERAL DISCUSSION 341 ADDITIONAL REMARKS Dr. D. A. Dixon, Prof. D. R. Herschbach and Prof. W. Klemperer (Harvard Uni- uersity) said: We wish to comment further on the intriguing question of long lifetimes for vibrational predissociation of van der Waals complexes. Both the experimental results for the C12 * * CI, dimer and the theoretical calculations for the Ar HCl system indicate lifetimes exceeding lo9 vibrational periods. The long lifetimes would be inexplicable if these systems were viewed as ordinary vibrationally excited molecules undergoing unimolecular dissociation.Only a few degrees of freedom are available to accommodate the internal excitation, which is far higher than the van der Waals bond strength. Thus the lifetimes must be attributed to very weak coupling between the eigenstates of the vibrationally excited van der Waals complex and the trans- lational continuum corresponding to dissociation of the complex without internal excitation of the fragments. This suggests that the lifetimes might be at least qualita- tively related to the transition probabilities for vibrational-to-translational energy transfer from the diatomic molecule contained in the complex. In the literature of vibrational energy transfer, this transition probability is customarily denoted by Zlo, which is the average number of gas-kinetic collisions required to deactivate a molecule from the first excited to the ground vibrational state.If a complex such as Ar - HC1 is regarded as a very weakly occupied system in which the Ar collides with HCI at the inner turning point of each oscillation in the van der Waals well, a rough order-of-magnitude estimate of the vibrational predissociation lifetime can be obtained from where r0 represents the duration of a collision, which is of the order T~ - s for " small " systems like Ar - - HCI. Fig. 1 shows estimates of the vibrational pre- dissociation lifetimes obtained in this way from the vibrational relaxation data avail- able for halogen,1*2 hydrogen halide,3*4 and mixed rare gas-hydrogen halide ~ysterns.~ The abscissa gives the vibration frequency of the diatomic unit.This plot corresponds to the well-known Lambert-Salter correlation of vibrational transition probability with frequency.l It serves to emphasize the extremely wide variation in predissocia- tion lifetime which might be expected. In fact, our estimate should provide a lower limit for the lifetime. For the bound van der Waals complex the inner turning point which produces the " collision " occurs at a lower and less repulsive region of the T. L. Cottrell and J. C. McCoubrey, MolecuZar Energy Transfer in Gases (Butterworth, London, 1961). H. L. Chen and C. B. Moore, J. Chem. Phys., 1971, 54,4072. R. V. Stele, Jr. and C.B. Moore, J. Chem. Phys., 1974,60,2794. ' F. D. Shields, J. Acoust. SOC. Arner., 1960,32,180. ' R. A. Lucht and T. A. Cool, J. Chem. Phys., 1974,60,1026.342 GENERAL DISCUSSION -3 -4 -5 -6 - v) 2 -7 E .- c a, Y- - - -8 CT 0 - -9 -10 -I I I I i 100 I I I I 1 : i 150 I I I I I i 240 / 'He -Y' 1000 2000 m 4000 vibrational frequency /cm-' FIG. 1.-Vibrational predissociation lifetimes derived from z - Zlo x (see text) against vibrational frequency for halogen [ref. (l), (2)], hydrogen halide [ref. (3), (4)] and rare gas-hydrogen halide systems [ref. ( 5 ) ] . Open points pertain to 390 K for halogens and to 300 K for other systems. Full points for chlorine and hydrogen fluoride systems pertain to temperatures indicated. For chlorine the Zlo values at temperatures below 240 K were extrapolated using an Arrhenius function [ref.(l)]. intermolecular potential than is the case for collisions of unbound Ar with HCI. Furthermore, as indicated in the figure, one can anticipate that some systems will show a strong temperature dependence of the vibrational lifetime. This is well documented for the vibrational transition probability, ref. (1-5). In the case of the C12 * CI2 system, since our molecular beam experiments produce the dimer molecules with internal temperatures below about 100 K, we might expect the vibrational lifetime to be a factor of lo3 to lo4 longer than at room temperature. This yields an estimate of > The lower bounds predicted for the vibrational predissociation lifetimes (single quantum excitation at room temperature) vary from the order of s in the case of the HF dimer to as long as s for the Ar * - HCI system.This suggested correla- tion is of course only intended to have heuristic value and is no substitute for a theoretical calculation such as that provided by Ashton and Child. However, it may be useful in designing experiments and choosing systems for study. The short lifetime estimated for the HF dimer is pertinent to experimental results on the pressure dependence of the absorption spectrum of hydrogen fluoride vapour. A vibrational predissociation lifetime of -l0-lo s implies a linewidth of -0.3 cm-'. This is larger than the rotational constant of the dimer molecule, which is about 0.2 cm-'. The dimer contribution to the infrared spectrum thus is likely to appear as a continuum.The observed spectrum at high pressures has a structured absorption s for the vibrational predissociation.GENERAL DISCUSSION 343 near 3970 cm-’ which has previously been attributed to the (HF), dimer.lJ How- ever, the line spacing in this spectrum is -40 % smaller than expected for (HF),. The spacing is close to that expected for the (HF)3 trimer, as pointed out recently by Dyke.3 This result at least suggests that vibrational predissociation may indeed make the (HF), dimer spectrum practically continuous and hence difficult to observe. It also suggests that the (HF)3 trimer can more readily accommodate vibrational excitation and has a substantially longer predissociation lifetime than the dimer. More detailed experimental information about vibrational predissociation of van der Wads complexes should soon be forthcoming.The supersonic expansion tech- nique is easy and can generate such complexes from virtually any combination of volatile monomer molecules. This makes photodissociation by selective laser excita- tion an attractive possibility for isotope separation. For this process, the pre- dissociation lifetime of the complex and the linewidth of excited levels accessible in dipole transitions are important design parameters. Dr. D. A. Dixon and Prof. D. R. Herschbach (Harvard Uniuersity) said: Several papers have referred to “ allowed ” or “ forbidden ” reactions and molecular orbital correlations in the style of Woodward and Hoffmann. Such analysis has proved extremely useful. However, as usual in chemistry, the formulation of ‘‘ rules ” does not provide automatic answers.Supplementary criteria are often required. This was illustrated by two examples mentioned in our paper : the facile four-centre exchange reactions involving ionic bonds and the nonconcerted character of 4m + 2 exchange reactions for hydrogen polygons with m > 1. We wish to note two other examples of four-centre systems for which the correlation diagrams alone give incorrect or in- conclusive predictions. For the Liz + Li, bond exchange proceeding via a square planar Li4 transition state, the correlation diagram is the same as that for the H4 case (fig. 1 of our paper). The reaction is predicted to be “forbidden” since two electrons that reside in a bonding 0 orbital in the reactants enter an antibonding o* orbital in the products.Hoffmann suggested such cases could be expected to have an activation energy higher than the bond dissociation energy of a reactant m~lecule.~ For H4 accurate calcula- tions corroborate this prediction. For Li, such calculations are not yet available, but we expect the activation energy will be very low or negligible. The exchange reaction can proceed readily via electron transfer to form an Li, + + Liz- ion-pair. (A recent calculation finds an electron affinity of 0.5 eV for diatomic lithi~m.~) Furthermore, even without considering ionic states, we find that the diatomics-in-molecules treat- ment predicts square planar Li, to be stable with respect to dissociation to 2Li2 by 13-17 kcal mo1-l. Indeed, the optimum bond length of 2.82 A in Li, is only about 0.15 A larger than that in Li,. The DIM calculation also finds that formation of Li4 from 2Li, occurs with no potential barrier.This covalent valence bond calculation hence predicts that four-centre bond exchange is fully allowed and facile for the Lid s ys tem. This example illustrates three factors which can result in misleading predictions from molecular orbital correlations. (1) Reliable results can only be expected when the crucial orbitals are widely separated in energy.6 This does not hold for the Li, J. L. Himes and T. A. Wiggens, J. Mol. Spectr., 1971, 40, 418. D. C. Smith, J. Mof. Spectr., 1959, 3, 473. T. R. Dyke, personal communication (University of Oregon). R. Hoffmann, J. Chem. Phys., 1968, 49, 3739.D. A. Dixon, J. L. Gole and K. D. Jordan, J. Chem. Phys., 1977. B. H. Mahan, J. Chem. Phys., 1971,55, 1436.344 GENERAL DISCUSSION F - H F H H - F H L - 1 FIG. 1 .-Molecular orbital correlation diagram for the four-centre reaction HF + H’F’ - H’F + HF’ proceeding via a planar rhombic transition-state. The out-of-plane nonbonding (NB) lone pair orbitals are not shown since they correlate properly. The in-plane NB orbitals of the reactants correlate with both the bonding (0) and antibonding (Q*) orbitals of the products. The phase of the hydrogen components is conserved in the Q orbitals for reactants and products, and the electron density on the hydrogen atoms (denoted by x) is assumed to be conserved also. Each of the reactant cr orbitals then contributes density of only (2-x) to a product NB orbital.Likewise, each reactant NB orbital contributes (2-x) to a product Q orbital and hence must contribute the remaining x to a product o* orbital. system. Likewise it does not hold for the excited four-halogen system studied by Engelke, Whitehead, and Zare. (2) Whenever a reaction involves ‘‘ splitting ” elec- tron pairs between atoms which approach from or separate to infinity, the transforma- tion from a molecular orbital basis to a valence bond basis needs to be examined. Detailed analysis of the H4 and HJ, systems shows this does not affect the qualitative results in those cases,l but our DIM calculation demonstrates the contrary for the Li4 system. (3) The orbital correlation rules are likely to be inadequate when attractive forces are dominant.In the DIM treatment of Li, this occurs because the bond lengths are unusually long so that the triplet repulsions become unimportant, whereas there are still significant singlet attractions. Fig. 1 shows an example for which the orbital correlation diagram is at best in- conclusive. This pertains to an exchange reaction such as HF + DCl- DF + HC1, which presumably has a rhombic head-to-tail transition-state. Since there are no symmetry elements which bisect bonds broken or formed in the reaction, the usual R. N. Porter and L. M. Raff, J. Chem. Phys., 1969,50,5216; 1969,51, 1623.GENERAL DISCUSSION 345 procedure for correlating reactant and product orbitals is not applicable. Also, here the lone pair orbitals cannot be neglected (as recommended for the isovalent H2 + I2 system).The nonbonding lone pair orbitals of the reactants correlate with both bonding and antibonding orbitals in the products. The antibonding component cannot be neglected, since it is required to account for the electron density on the hydrogen atoms. For simplicity, in the diagram we denote this density by x and take it to be the same for all orbitals involving hydrogen atoms. The orbital correlations then predict that roughly 2x of the reactant electron density will appear in product antibonding orbitals and thereby introduce some forbidden character. The magni- tude of x is governed primarily by the polarity of the hydrogen halide. The forbidden character will become small for an extremely polar bond, approximating H +X- ; otherwise it may become large. However, again a simple orbital correlation based solely on symmetry or nodal properties is inadequate. Prof. M. J. S. Dewar (Texas) said: The problem which Murrell raises, concerning inclusion of CI in treatments such as MIND0/3, is of major importance in biradical- type systems and we have devoted a great deal of attention to it. While our con- clusions will be reported in detail in a forthcoming paper, I will summarize them briefly here in view of Murrell’s comments. (1) Since CI is simply a device for introducing compensation for electron corre- lation into the orbital approximation, and since electron correlation is taken into account in treatments of the MIND0 type via the parameterization, it is normally incorrect in principle to include CI in such treatments. (2) This distinction is further emphasised by the fact that inclusion of even very extensive CI lowers the MIND0/3 energies of normal closed shell molecules by only -10 kJ mol-I; in contrast to the very large effect in a6 initio SCF treatments. (3) While MIND0/3 apparently allows effectively for electron correlation in closed shell systems of all kinds, and even in radicals and radical ions, it fails to do so in the case of a pair of separated radicals treated as a single system, or a singlet biradical in which the “ radical centres ” are widely separated. Then it is necessary to include CI with the lowest doubly excited configuration, which we term CIo. Inclusion of CI, in such cases leads to a large decrease in the energy, commonly of the order of 200 kJ mol’l. (4) While the distinction between these two extreme cases can be made very easily, intermediate ones occur when inclusion of CI, has an intermediate effect. Studies of several dozen reactions involving biradicaloid species as intermediates have led us to the conclusion that if the lowering in energy (6E) due to inclusion pf CT, is less than -70 kJ mol-l, the value calculated without CI, should be accepted. If 6E > 70 kJ mol-l, the value calculated with CI, is -70 kJ mo1-I less than the actual energy. This difference corresponds to the overestimation of correlation energy in such systems, due to the simultaneous use of CI and of parameters that allow for “ normal ” electron correlation. The correlation effects between the “ unpaired ” electrons in a singlet biradical are of course extreme, but the effect on the energy only becomes greater than in a normal closed shell molecule if the radical centres are widely separated. Here CIo provides a complete correction for the corresponding electron pair correlation. The energy found in this way will then be too negative by the average electron pair correlation energy incorporated in the MIND0/3 parameters. (5) A similar situation arises in the case of singlet excited states which can be regarded as a special class of singlet biradicals. These are treated in MIND0/3 by using excited-state orbitals given by the ‘‘ half-electron ” method or a UHF version346 GENERAL DISCUSSION of MIND0/3, combined with CI. It is interesting to note that the energies of lowest singlet excited states given by this procedure are also systematically too negative by 70 kJ mo1-I and that if this connection is made, the results then agree with experiment as well as do the MIND0/3 energies for the ground states of normal closed shell molecules. (6) Concerning the specific problem raised by Murrell, i.e., the Cope rearrange- ment; inclusion of CI has no significant effect on the energies of the " boat " or " chair " transition states, the decrease in energy being in each case >10 kJ mo1-l. Our general picture of the reactions, involving stable biradicaloid species, and our structures and other properties calculated for the transition states, remain unchanged. These incidentally now include calculated entropies of activation. The additional information given by including CI has led to a clarification of the nature of the stable intermediates, and their relationship to bicyclo[2,2,0] hexane. We now find that the various biradicaloid species delineate a crater in the potential surface, corre- sponding to rapid equilibration of all the various biradicaloid species. The crater wall contains cols leading to the various species (hexadienes and bicyclohexanes) that can be interconverted by passage into and out of the centre. Those leading to hexadienes are the " boat " and " chair " Cope transition states, which we have previously reported. That leading to bicyclohexane is a biradical-like system for which inclusion of CI, is necessary. (7) In conclusion I should point out that the misgivings expressed concerning MIND0/3, both at this symposium and elsewhere, are ones which had already occurred to us and which we have dealt with in papers which are in print, in press, or in preparation. Since the volume of work is so great, and since most of it has been carried out very recently, some time will inevitably have to elapse before it can all be presented. Limitations of space made it impossible for us to make this point in our present paper.

ISSN:0301-7249    

DOI:10.1039/DC9776200300

出版商:RSC    

年代:1977

数据来源: RSC

摘要:

CLOSING REMARKS BY H. CHRISTOPHER LONGUET-HIGGINS In commenting on this discussion I feel rather like a man who has just stepped out of a time machine which he boarded ten years ago. Since that time the Faraday Society has got married to the Chemical Society, but her character has been unspoiled by the change, and Faraday Discussions are as well run and as scientifically exciting as they ever were. It is impossible in five or ten minutes to do justice to all the contributions, so I may be forgiven for merely mentioning one or two points which have crossed my mind in listening to this excellent series of papers and the remarks which have followed them. The variety of topics which have been discussed bears witness to the central role of the potential energy surface as a unifying concept in physical chemistry.Its importance has long been recognised in spectroscopy and chemical kinetics, but ten years ago we knew very little about the potential surfaces of polyatomic molecules except in the immediate neighbourhood of their energy minima. One striking advance in this area has been in the experimental and theoretical investigation of non-rigid, or " floppy ", molecules about which Mills told us in his paper. I was particularly intrigued by the phenomena which he reported on carbon suboxide and related molecules. I hope it will soon be possible to suggest, in descriptive terms, why this molecule is not linear in its ground state and why the effective potential for bending is so markedly affected by excitation of the skeletal stretching vibrations. The reliable determination of potential energy surfaces from vibrational spectra is a mathematically challenging problem, and so is the inverse problem of determining vibrational energy levels from non-separable potentials, where there have been some very significant advances, in the hands of Miller, Handy and others.The use of semi- classical approximations obviously has a rosy future, and one may expect that such methods will also prove valuable in molecular dynamics, where one is anxious to understand scattering cross-sections and product state distributions in terms of pre- sumed potential energy surfaces. This brings one to a consideration of the very considerable experimental advances about which we have heard from Herschbach and many other authors.Herschbach reminded me of an experienced batsman attempting to infer the action of a spin bowler from the way in which the ball bounces from the crease; his lecture revealed the richness of the information which could be obtained from an experimental measurement of all the angular momenta involved in both elastic and inelastic scatter- ing processes. Polanyi set an example of how one should set about interpreting the translational, rotational and vibrational excitation of the products of a simple chemical reaction, at least according to classical molecular dynamics. One presumes that the next stage in such work will be a quantitative improvement in the accuracy with which one can determine the precise form of the energy surface. A particularly intriguing reaction, of which we were given both experimental and theoretical analyses, is that between Nf and HZ.(In passing one may note the con- fidence with which chemists can now handle non-hear as well as linear configurations348 POTENTIAL ENERGY SURFACES of atoms, in discussing reaction mechanisms.) A nice feature of this reaction is the crossing which occurs between the 3B, and 3A2 states when the N+ ion approaches the H2 molecule from the side. As Dewar pointed out, this crossing is directly interpret- able in qualitative terms, and one would like to see more such simple explanations for the rather forbidding results of computations on polyatomic systems. It has always seemed to me that there are three kinds of Chemistry: experimental, theoretical and computational.Most chemists tend to think of molecular computa- tions as belonging to theoretical chemistry, but it could be argued that such computa- tions are really experiments. Conventional experiments are carried out on real atoms and molecules; computational experiments are performed on more or less ‘‘ modest ” and unreliable models of the real thing. So the computational chemist has even more of an obligation than the experimentalist to interpret his results in an intelligible fashion. Unless he can offer a convincing explanation why his numbers come out as they do, there is always room for serious doubt as to whether they may not be artifacts of his basic approximations. This is the substance of most current objections to heavy computations of molecular properties by ab initio methods.If such methods have been well attested for a given class of problems, then it is not unreasonable to attach weight to the computational solution of a further problem in that particular class. Unfortunately, the most interesting problems are usually those with some element of novelty. I cannot close without referring to two matters in particular which have generated much comment during the discussion: the interaction between three alkali metal atoms, and the phenomenon of laser-induced fluorescence. It is delightful to see both theorists and experimentalists hunting down the conical intersections whose existence was predicted by Teller so long ago, and one may hope that before very long it may be possible to obtain concrete evidence for the phase change which is confidently expected to occur in the electronic wave function when one circles round such an intersection. The phenomenon of laser-induced fluorescence is, as George rightly remarked, a new challenge to theory as well as to experiment. Plainly there is no shortage of interest- ing experimental phenomena for the theoretician to get his teeth into, nor of theoretical issues inviting resolution by ingenious experiment,

ISSN:0301-7249    

DOI:10.1039/DC9776200347

出版商:RSC    

年代:1977

数据来源: RSC

摘要:

GENERAL DISCUSSIONS OF THE FARADAY SOCIETY Date 1907 1907 1910 191 1 1912 191 3 1913 1913 1914 1914 1915 1916 1916 1917 1917 1917 1918 1918 1918 1918 1919 1919 1920 1920 1920 1920 1921 1921 1921 1921 1922 1922 1923 1923 1923 1923 1923 1924 1924 1924 1924 1924 1925 1925 1926 1926 1927 1927 1927 1928 1929 1929 1929 1930 1930 Subject Osmotic Pressure Hydrates in Solution The Constitution of Water High Temperature Work Magnetic Properties of Alloys Colloids and their Viscosity The Corrosion of Iron and Steel The Passivity of Metals Optical Rotatory Power The Hardening of Metals The Transformation of Pure Iron Methods and Appliances for the Attainment of High Temperatures in a Laboratory Refractory Materials Training and Work of the Chemical Engineer Osmotic Pressure Pyrometers and Pyrometry The Setting of Cements and Plasters Electrical Furnaces Co-ordination of Scientific Publication The Occlusion of Gases by Metals The Present Position of the Theory of Ionization The Examination of Materials by X-Rays The Microscope : Its Design, Construction and Applications Basic Slags : Their Production and Utilization in Agriculture Physics and Chemistry of Colloids Electrodeposition and Electroplating Capillarity The Failure of Metals under Internal and Prolonged Stress Physico-Chemical Problems Relating to the Soil Catalysis with special reference to Newer Theories of Chemical Action Some Properties of Powders with special reference to Grading by The Generation and Utilization of Cold Alloys Resistant to Corrosion The Physical Chemistry of the Photographic Process The Electronic Theory of Valency Electrode Reactions and Equilibria Atmospheric Corrosion.First Report Investigation on Oppau Ammonium Sulphate-Nitrate Fluxes and Slags in Metal Melting and Working Physical and Physico-Chemical Problems relating to Textile Fibres The Physical Chemistry of Igneous Rock Formation Base Exchange in Soils The Physical Chemistry of Steel-Making Processes Photochemical Reactions in Liquids and Gases Explosive Reactions in Gaseous Media Physical Phenomena at Interfaces, with special reference to Molecular Atmospheric Corrosion. Second Report The Theory of Strong Electrolytes Cohesion and Related Problems Homogeneous Catalysis Crystal Structure and Chemical Constitution Atmospheric Corrosion of Metals. Thud Report Molecular Spectra and Molecular Structure Optical Rotatory Power Colloid Science Applied to Biology Elutriation Orientation Volume Trans.3 3 6 7 8 9 9 9 10 10 11 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 20 21 21 22 22 23 23 24 24 25 25 25 26 26350 GENERAL DISCUSSIONS OF THE FARADAY SOCIETY Date Subject 1931 1932 1932 1933 1933 1934 1934 1935 1935 1936 1936 1937 1937 1938 1938 1939 1939 1940 1941 1941 1942 1943 1944 1945 1945 1946 1946 1947 1947 1947 1947 1948 1948 1949 1949 1949 1950 1950 1950 1950 1951 1951 1952 1952 1952 1953 1953 1954 1954 1955 1955 1956 1956 1957 1958 1957 1958 1959 1959 1960 1960 1961 1961 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 in 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 Reaction Kinetics Chemical Reactions Involving Solids Luminescence Hydrocarbon Chemistry The Electrical Double Layer (owing to the outbreak of war the meeting 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 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 Inves- tigating Cell Structure 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 was abandoned, but the papers were printed in the Transactions) Systems Bordeaux.) Published by Butterworths Scientific Publications, Ltd.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 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32GENERAL DISCUSSIONS OF THE FARADAY SOCIETY 35 1 Date Subject Volume 1962 1962 1963 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 Inelastic Collisions of Atoms and Simple Molecules High Resolution Nuclear Magnetic Resonance The Structure of Electronically-Excited Species in the Gas-Phase 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 Adsorbtion in Condensed Phases Electron Spectroscopy of Solids and Surfaces Precipitation Potential Energy Surfaces Oxidation For current availability of Disciission volumes, see back cover.33 34 35 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

ISSN:0301-7249    

DOI:10.1039/DC9776200349

出版商:RSC    

年代:1977

数据来源: RSC