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.