J. Phys. Chem. 1993,97, 2147-2152
A Crossed Beam Study of D Atom Transfer in Collisions of CJH+ 0.33-1.45 eV
2147
+ D2 at Collision Energies
Martin Sadflek and Zdenek Herman' J . Heyrovskj, Institute of Physical Chemistry and Electrochemistry, Czechoslovak Academy of Sciences, Dolejjkova 3, 182 23 Prague 8, Czechoslovakia
Received: November 30, 1992 Dynamics of the reaction of C3H+ with D2 leading to C3HD0+(C3D2'+) and D' (H') was studied in crossed beam scattering experiments over the collision energy range 0.3-1.5 eV. From the scattering diagrams of the ion products, center-of-mass angular distributions and distributions of the relative translational energies of the products were obtained. Analysis of the data suggests that at these collision energies the reaction proceeded prevailingly through a cyclic intermediate complex c-C3HD2+which dissociated to form the cyclic ion products c-C3HD*+and c-C3D2'+.
1. Introduction
The discovery of a variety of molecular species in interstellar gas clouds by radioastronomers in the early 1970s and the realization that fast reactions of ions with neutrals could be responsible for their formation] greatly stimulated activity in gas phase ion chemistry and in studies of the kinetics of numerous new ion-molecule reactions. These studies led to quantitative ion chemical models which suggest that ion chemistry could indeed be involved in the formation of many molecules. Particular attention has been given to the interaction of C3H+ + H2 the radiative association of which producing C3H3+ was suggested as a precursor to the formation of thecyclopropenylidene molecule, c - C ~ H the ~ , first cyclic hydrocarbon molecule to be detected in interstellar clouds.2J Ternary association of the reactants was first observed using the SIFT technique2s4
+
C3H+ H 2 + H e
-
C3H3++ H e
(1) This is the predominant reaction channel at and below 300 K while at higher temperatures the hydrogen abstraction reaction
+
C3H+ H 2
-
C3H;
+ I1
(2) was observed. Recently, the radiative association rate constant of C3H+with D2has been determined using the 80 K ring electrode ion t r a ~ . 5 . ~ In connection with understanding details of this interesting reaction, the structure of the intermediates C3H3+ and of the product ions, cyclic or linear, is of importance, i.e. which of the following processes actually occurs
C3H+
+ H2
-
-
c-C~H,"
+ H'
(2a)
+
1-C3H;+ H' (2b) In an attempt to provide evidence for the prevailing structures of the intermediate and product ions in the hyperthermal collision energy region, we carried out a crossed-beam scattering study of the reaction
+
C3H+ D2
-
-
C3HD'+ + D'
(3a)
C3D2'+ + H' (3b) in the collision energy region of 0.3-1.45 eV (center of mass, c.m.).' Scattering diagrams for collision energies between 0.33 and 1.45 eV were obtained for both ion products of reaction 3 and cam.angulardistributions and relative product translational energy distributions were derived from them. From the shape of the c.m. angular distributions, we are able to suggest a prevailing
structure of the intermediate in the critical configuration from which the products are formed by an extension of the critical bond. 2. Energetics
The reactant C3H+ is known to be linear in its ground state with the H attached to the terminal C atom;8its heat of formation was given as 1602f 2 1kJ mol-' as a result of both experimenta19J0 and theoretical studies. The most stable structures of a possible intermediateC3H3+are thecyclicform (c-C3H3+,cyclopropenium, AHf= 1075kJ mol-])and the linear form (I-C3H3+,propargylium, AHf = 1175 kJ mol-l).I1 Wong and RadomI2 calculated the isomerization energy of the two forms (408 kJ mol-') and listed other, higher-lying structures of C3H3+. The ion product C3H2'+ exhibits two low-lying structures;l3-l5 the c-C3H2*+(cyclopropenylidene ion) is more stable that the l-C3H2*+(propargylidene ion) by 53 kJ mol-'. Quite recently, high-quality theoretical calculationsI6 have narrowed the gap between the two forms to 31 kJ mol-]. The exact heat of reaction 2 is still a matter of discussion. The ion product of reaction 2a is more stable than that of reaction 2b and it has been suggested that the former reaction is slightly (by 4 kJ mol-') endothermic.2 Other studies suggest that (2a) is slightly exothermic and that there is a barrier on the reaction path.15 The main problem seems to be the determination of the heat of formation of C3H2'+ which has been subjected to many studies.2,4-6-'5J7 Thus the question of the heat of reaction 2a, whether slightly endothermic (4 kJ mol-') or exothermic (130 kJ mol-') to form the cyclic product remains undecided. Determination of such a small reaction heat, however important, appears to be beyond the present accuracy of heat of formation determination (f15-20 kJ mol-]), both experimental and theoretical. The problem has to be decided by a thorough kinetic study, including estimation of entropy changes in the system, and evidently needs further work. Figure 1 summarizes the energetics of reaction 2 as discussed above. We assume in this study that reaction 2 is slightly exothermic (by less than 20 kJ mol-') to form c - C ~ H ~ and *+ endothermic by about 10 kJ mol-' to form l-C3H2'+. 3. Experimental Section
The crossed beam scattering apparatus EVA I1 was described earlier.'8 In the experiments described here, the reactant ions C3H+ were produced by impact of 90-eV electrons on 1-propyne in a low-pressure ion source (gas pressure of about lo-* Pa). The ions were accelerated to about 150 eV, mass analyzed by a magnetic mass spectrometer, and decelerated to a desired
0022-3654/93/2097-2147$04.00/0Q 1993 American Chemical Society
2148
Sadflek and Herman
The Journal of Physical Chemistry, Vol. 97, No. 10, 1993
E t
'
L c,H'+H,
C,H,
+
c,H+,"H'
Figure 1. Energetics of reaction 2.
laboratory energy (3.5-1 5 eV). The neutral reactant (deuterium) of thermal energy was introduced through a multichannel jetcollimating slit arrangement at right angles to the reactant ion beam. The reactant beams could be rotated about the scattering center between -15' and +60° to provide laboratory angular distributionsof reactant and product ions. The ions were detected by a detection slit, energy-analyzed by a stopping-potentialenergy analyzer, accelerated to 1 keV, mass analyzed by a magnetic mass spectrometer, and registered by an electron multiplier. Phasesensitive detection of the ion products was used to remove background scattering effects. The angular and energy widths of the reactant ion beam were typically 1.5' and 0.2 eV, full width at half maximum (fwhm), respectively. The angular resolution in the center-of-mass frame for the experiments described here was about 15', due to strong forward scattering of the products in the laboratory frame. Angular distributions and energy profiles of the ion products, measured 3-1 0 times at 7-10 scattering angles, were combined to construct the contour scattering diagrams.19 The experiments were carried out at four c.m. collision energies, T: 0.33; 0.62; 0.85; 1.45 eV. Internal Energy of C*+. The C3H+reactant ion produced by electron impact on propyne in the low pressure ion source is a fragment ion which is formed with some internal excitation energy. Weestimated the amount of the internal energy from the threshold photoelectron spectrum and from the C3H+ion relative threshold photoelectronspectrum and from the C3H+ion relative abundance in the breakdown patterns of propyneIOin the photon energy region of 15.8-19 eV (above the appearance energy of CjH+). The procedure will be described separately.20 The estimated internal excitation energy distribution2O extends to about 1 eV, with the mean value &(C3H+) = 0.45 eV. 4. Results
The kinematic conditionsof the experiment are determined by the masses of the reactants: the c.m. velocity vector represents 0.902 of the relative velocity and thus the ion productsare scattered in a narrow cone forward in the laboratory coordinate system. Figures 2 and 3 show the scattering diagrams of C3HD*+and C3D2*+ at the c.m. collision energies 0.33 eV and 1.45 eV, respectively (the lower and upper ends of the collision energy range investigated). The horizontal line indicates the direction of the reactant relativevelocityvector and c.m. marks the position of the tip of the c.m. velocity vector. A full point on the relative velocity shows the position of the tip of the reactant ion laboratory velocity vector and the contour about it is the 50% contour indicating the angular and velocity spread of the reactant ion beam. The designation 0'-180' refers to the c.m. scattering angle, 0 ' being the direction of the reactant ion beam. The scattering diagrams show Cartesian probability contours of the ion product (Le. the probability density of the Cartesian components of the C3HD*+and C3D2*+product c.m. velocity).
&\\\ 0
W'
0.3
Figure 2. Scattering diagram of the ion product C3HD*+(a) and C3D2*+ (b) at thecoilisionenergy P 0 . 3 3 eV. Thehorizontalsolidlinerepresents the direction of the relative velocity; the dot-dash contour shows the 50% contour of the reactant ion laboratory velocity angular and energy distribution (maximum at the solid dot).
The distribution is arbitrarily normalized to 10.0 at the peak of the distribution. It can be seen that in all cases the Cartesian probability in Figures 2 and 3 peaks-within the experimental error-at the position of the center-of-mass and the contours show an almost circular symmetry about this peak at 0.33 eV, and at 1.45 eV an elongated shape along the 90'-270' direction (Le. perpendicular to the relative velocity). From the scattering diagrams further dynamic quantities were obtained by an appropriate integration. The relative differential cross section P(I9) (the c.m. angular distribution) was obtained using the integral19 (4)
where PCis the Cartesian probability and ui are the Cartesian components of the product ion velocity. The c.m. angular distributions, P(I9) vs 9,derived from the scattering diagrams in Figures 2 and 3, are shown in Figures 4 and 5, respectively. The graphs at 0.33 eV show an almost isotropic distribution for C3HD*+,with a slightly higher intensity about 90' for C3D2'+. At 1.45 eV the distributions clearly peak at 90' for both ion products and show a symmetry with respect to this angle. Evaluations of the scattering results at 0.62 and 0.85 eV are consistent with a gradual change of P(I9) between 0.33 and 1.45 eV. The distributionsof relative product translational energiesP(T? vs T' were obtained by integration of the scattering diagrams using the expression19
P(T? = u
Pc (u,,u2,uJ)sin 9 dt9
(5)
The P(T3 vs T'distributions for both products at 0.33 and 1.45
D Atom Transfer in CjH+ + D2 Collisions
The Journal of Physical Chemistry, Vol. 97, No. 10, 1993 2149
\
11.0- 1
T=0.33 eV
0
0"
0
0.3
\
\ \
--
I
C3Dl'
0'
90"
/ / 0 - 4
T = 1.45eV.'
0.3
3
Figure 4. Center of mass angular distributions P ( 6 ) of CjHD'+ and CjD2*+ from reaction 3 at T = 0.33 eV. Vertical lines through points indicatetheextent of error when integratingover theangular range0-90180' and (whenever possible) 0-270-180O.
1.0
0
90"
',
1
T=1.45 eV
I
C, HD +*
'.-/
/
/
0"
Figure 3. Scattering diagram of the ion probuct C3HD*+(a) and C3D2'+ (b) at the collision energy T = 1.45 eV. Details same as in Figure 2.
eV are shown in Figures 6 and 7,respectively. The distributions for both products at the same collision energy are-within the experimental error-the same: they peak at a low energy (0.25 and 0.35 eV for the two collision energies, respectively) and decrease toward zero at the total energy available in the reaction ETOT.The arrow marks the total average energy available, i.e. ETOT T + (-A&) + fi;(C,H+), the vertical solid line is then 3 :( T,,, (-A&) the limit of maximum energy availableETOT"'~' + E(C3H+),,,). The P( T') tail which extends even beyond this value results from experimental inaccuracy: the contribution from the weakest outer ridges of the scattering diagram, between contours 0.5 and 0, are strongly weighted by the u factor in eq 6 and may cause an excessive exagerated tailing. The ratio of the integral cross sections of reactions 3a and 3b could also be estimated from the results. This ratio did not change over the collision energy region studied; the two isotopomers were formed in the statistical ratio C3HD*+: C3D2'+ = 2:l.
1.o
90"
1
0.5
+
5. Discussion
Mechnism. Scattering diagrams obtained for both ion products, C3HD*+and C3D2'+, show peaking of the ion products at the center-of-mass, and a distribution which is-within the experimental errorsymmetric with respect to a plane passing through the center-of-massperpendicularly to the relative velocity.
0"
90"
8
Figure 5. Center of mass angular distributions P ( 0 ) of CjHD'+ and CjD2'+ from reaction 3 at T = 1.45 eV. Details same as in Figure 4.
In addition, the relative intensities of these ion products show that all hydrogen atoms are equivalent. This indicates the formation in reaction 3 of an intermediate complex of a mean lifetime much longer than its average rotational period. The formation of such an intermediate may be expected in view of the existence of the deep minima on the potential energy surface (Figure l), corresponding to the cyclic and linear form of the intermediate C3HD2+. A simple RRK calculation shows that the mean lifetime of such an intermediate should be of the order of le8s even at the upper end of the collision energy range
Sadflek and Herman
2 1 9 The Journal of Physical Chemistry, Vol. 97, No. 10, 1993
T=0.33eV I
P(T')If
C,HD*'
If
0
1
0
1
T'L~VI
Figure 6. Relative translational energy distributions P( T') of products of reaction 3a (C3HD'+ + D') and 3b (C3D2'+ + H') at T = 0.33 eV.
Arrow at ETOTshows the total average energy available, solid vertical line the maximum total energy available, ETOT"'~'(upper limit of the distribution of the constituent quantities-see text).
T= 1.45eV
0
2
4
6
basically the collision energy and the internal excitation energy of the reactant ion) appears as internal energy of the ion product. The peak value is about 70% and 80% of ETOT at collision energies of 0.33 and 1.45 eV, respectively (see Figures 6 and 7). Center of Mass Angular Distributions; Structure of the Intermediate. The c.m. angular distributions of both ion products (Figures 4 and 5 ) show almost isotropic distributions with a progressive tendency for sideways peaking with increasingcollision energy. In the followingwe analyze the c.m. angular distributions in an attempt to relate it to a prevailing structure of the intermediate C3HDz+ion. Theshapeof the c.m. angular distribution of reaction products, formed by a decomposition of a complex with a lifetime long in comparisonwith its rotational period, is determined by thedisposal of the angular momentum of the system. The treatment of statistical complex decomposition, the relationship among the angular momenta of the colliding systems, and the shape of the product angular distribution are given in the classical paper by Miller, Safron, and Herschbach.22 Recently, Grice and cow o r k e r ~ ~have ~ - * addressed ~ the problem in a series of papers, treating the decomposition of a transition stateof an intermediate in terms of the RRKM model, for both symmetric- and asymmetric-top configurations. In this paper, we will use the Miller-Safron-Herschbach statistical complex model treatmentz2 to analyze the angular distributions of products of reactions 3a and 3b. The model assumes that the total angular momentum of the system, Jlot,and its projection onto the product relativevelocityvector are constants of motion. The rotational states of the complex are populated statistically and during the passage through the critical region a statistical equilibrium allows a rotational temperature TR*to be ascribed to the system. The rotation of the complex is approximated by the rotation of a symmetric top whose rotational energy is related to the moments of inertia with respect to the symmetry axis, I I , and with respect to the principal axis perpendicular to it, I,. For many chemical reactions Lmax >> Jmax (L,,, is the maximum orbital angular momentum of reactants, J,,, is the sum of the maximum rotational momenta of individual reactants) and thus JtOt= L (where L = C ( D R ~is the reactant orbital angular momentum). The angular distribution is then specified by a single parameter X = L,,,/K,, where
and
0
2
Trevl
Figure 7. Relative translational energy distributions P( T') of products
of reaction 3a (C3HD'+ + D') and 3b (C3D2'+ Details same as in Figure 6.
+ H')
at T = 1.45 eV.
investigated. The experimental data make it possible to estimate only the lower limit of the complex average lifetime: the symmetry of the scattering diagram is fully developed after 6-10 average rotations of the intermediate.2' Estimation of the mean rotational period of C3HD2+gave values of 0.7-1.1 ps, and 1-1.4 ps for the cyclicand linear int&mediates, respective&, in the collision energy range investigated. The conclusion from the experiment is thus only that the mean lifetime of the complex is longer than 6-10 PS. The shape of the product translational energy distribution, P( T?,shows that most of the energy available in the process (i.e.
The shape of the angular distribution depends on whether the complex can be characterized as a prolate ( I , I*) symmetric top. Miller et ai.zz calculated a variety of angular distributions for prolate and oblate statistical complexes with X as a parameter (see Figure 10 in ref 22). It seemed worthwhile to apply this model to the angular distributions of the products of reactions 3a and 3b, as the two expected forms of the intermediate, cyclic or linear, represent typical examples of an oblate and prolate nearly-symmetric top, respectively. To apply the model, we had to estimate three basic quantities to calculatex the maxima orbital angular momentum, L,,,; the rotational temperature of the complex, TR*; and the moments of inertia of the complex of an assumed structure, I I ,12, and hence
.
IR
Maximum Orbital Angular Momentum. In order to estimate
L,,,, we assumed that the complex is formed for all imact parameters up to thecutoff at b,,,, determined by the ion-induced
D Atom Transfer in C3H+
+ D2 Collisions
1.O
a5
0"
90"
4
Figure 8. Comparison of experimental and calculated c.m. angular distributions P(8)for ion products of reactions 3a and 3b at the collision energies T = 0.33 eV and T = 1.45 eV: experiment, open points C3HD'+, full points C3D2'+; solid line, calculated assuming cyclic intermediate c-C3HD2+; dashed line, calculated assuming linear intermediate l-C3HDi+.
dipole forces between the interacting particles. Thus
where a is the polarizability of 0 2 (0.793 X lO-3O m3), e is the elementary electron charge, p the reduced mass of the reactants, and 60 the permitivity of vacuum. We calculated L,,,(0.33 eV) = 70h and L,,,(1.45 eV) = 1OOh. RotationalTemperature. We estimated the internal rotational temperature of the complex in the critical configuration by assuming that the rotational and vibrational temperature in the critical region is the same, TR* = Tv*, and that the vibrational temperature is determined by the equipartition principle, Tv* = E r o ~ / ( 3 N -6 ) k ~ .We obtained at 0.33 eV Tv* 950 K and 657 K and at 1.45 eV Tv* 2032 K and 1741 K for the cyclic and linear form of the intermediate, respectively. Moments of Inertia. We assume that the rotating complex behaves as an approximately symmetric top (thus neglecting the asymmetry due to partial D-substitution in the cyclic form, and the fact that the linear form has a CZ, symmetry only). The moments of inertia were calculated for structural parameters as published re~ently:2~~~6 cyclic form, R(C-C) = 0.1364 nm, R(CH) = 0.1079 nm;linear form,R(CI-C2) = 0.1231 nm,R(C2-C3) = 0.1357 nm, R(C1-H) = 0.1076 nm, R(C3-H) = 0.1090 nm, and both D atoms were supposed to be on C3. The calculated moments of inertia are: cyclic form, II = 8.3 X 1 V 6 ,1 2 = 3.6 X 10-46,I R = 6.36 X loA6;linear form, I , = 0.49 X I2 = 10.5 X 1V6, ZR = 0.514 X loA6 (all in units of kg m2). Using eqs 7, 8, and 9, we obtained K, 28h and 41h for the cyclic form and K, 7h and 11h for the linear form at the two collisionenergies, 0.33 and 1.45 eV, respectively. The parameter X is then (2.5 and 2.4 for the cyclic (oblate) complex, and 10.0 and 9.1 for the linear (prolate) complex, at the two collision energies, respectively. The shapes of the angular distributions P(8)derived with the use of these parameters from Figure 10 of ref 22 are shown in
The Journal of Physical Chemistry, Vol. 97, No. 10, 1993 2151 Figure 8 together with experimental data points. The full curve refers to the cyclic (oblate) complex and the dashed curve to the linear (prolate) complex. It can be clearly seen that the experimental results for the collision energy of 1.45 eV fit quite well the shape of the angular distribution expected for the decomposition of the cyclic C3HD2+ complex to form cyclic C3HD'+(C,D2'+) and D'(H'). For the collision energy 0.33 eV the agreement is not so good: the prominent peaking at 90°, which is predicted for the decomposition of the cyclic intermediate, is not reproduced by the experiment which gave almost isotropic distribution with only a slight indication of peaking at 90°. This seems to suggest that the angular distribution at 0.33 eV may result from decomposition of a near-equal mixture of the cyclic (sidewaypeaking) and linear (strong forward-backward peaking) intermediate. However, it appears quite improbable that the participation of the endoergic channel (linear intermediate to linear product, reaction 2b) would increase with collision energy decreasing toward the threshold. We would rather see the disagreement between the experiment and the Miller-SafronHerschbach model at 0.33 eV as a consequence of the fact that the model is not quite applicable at this energy. Relating the angular distribution to the parameter X of the assumes that L,,, >> J,,,. In our experiments the reactant ion C3H+was formed by dissociativeionization of 1-propyne and the dissociative process (presumably a consecutive loss of H and H2) results in some, higher than thermal, rotational excitation of the reactant ion. Thus the condition L,,, >> J,,, may not be fulfilled,especially at the lowest collision energy. The analysis should work better at 1.45 eV, where L,,, is larger than at 0.33 eV. It is difficult to estimate the magnitude of J,,, in our case; however, one may expect qualitatively that with increasing (randomly oriented) J,,, with respect to L,,, the sideways peaking in the angular distribution would be smeared and the distribution would have a tendency to become more isotropic. The experimental results in no way indicate peaking at Oo and 180° expected for the decomposition of a linear C3HD2+ intermediate to linear C3HD*+(C3D2*+)and D' (He). Therefore, we may conclude that the analysis of the angular distributions of the ion products of reactions 3a and 3b showed that at 1.45 eV the prevailing path of the reactions was the formation of the cyclic form of the intermediate C3HD2+ which decomposed to form the cyclic product C3HD*+(C3D2'+). Very likely, this was the case at 0.33 eV, too, though the analysis of the angular distributions was not quite in agreement with the applied model. This study applied the classical MillerSafron-Herschbach model of a statistical complex decomposition in describing the shape of angular distributions of products of ion-molecule reactions. It shows that the shape of the c.m. angular distribution of a product of a bimolecular ion-molecule reaction can be used to estimate the structure of the statistical intermediate complex in its critical configuration.
Acknowledgment. We dedicate this paper to Professor Dudley R. Herschbach on the occasion of his sixtieth birthday. We wish to express our thanks to Dr. J. VanEura, Mg. M. Fdrnlk, and Mg. J. FlIdr who participated in various parts of this study, and to Professor David Smith for many helpful discussions. This work was partially supported by the Research Grant of the Czechoslovak Academy of Sciences, No. 44013. References and Notes (1) Smith, D.; Spaniel, P. Arc. Chem. Res. 1992, 25, 414. Smith, D. Chem. Rev.. in press. (2) Smith, D.; Adams, N . G.Int. J . MassSpecirom. Ion. Processes 1987, 76, 307. (3) Adams, N. G.; Smith, D. Asirophys. J . 1987, 3/7,L25. (4) Smith, D.; Adams, N . G.;Ferguson, E. E. I n t . J . Mass Spectrom. Ion Processes 1984, 67, 15. ( 5 ) Hornig, S.;Sorgenfrei,A,;Gerlich, D. J . Phys. Chem.,in preparation. ( 6 ) Hornig, S.; Gerlich, D. Chem. Reu., in press. (7) Sadllek, M. Thesis, Czech. Acad. Sci., 1992.
2152 The Journal of Physical Chemistry, Vol. 97, No. 10, 1993 (8) Raghavachari, K.; Whiteside, R. A.; Pople, J. A.; Schleyer, P.v.R. J. Am. Chem. Soc. 1981, 103, 5649. (9) Parr, A. C.; Jason, A. J.; Stockbauer, R.; McCulloh, K. In Advunces in Muss Specrromerry; Quayle, A., Ed.; The Institute of Petroleum: London 1979; Vol. 8a, p 62. (IO) Parr, A. C.; Jason, A. J.; Stockbauer. R.; McCulloh, K. Inr. J . Muss Specrrom. Ion Processes 1979, 30, 3 19. ( I I ) Rosenstock, H. M.; Draxl, K.; Steiner, B. W.; Herron, J. T. J. Phys. Chem. Re/. Dum 1977.6, Suppl. I . (12) Wonk M. W.: Radom. L. J. Am. Chem. Soc. 1989. 111. 6976.
( l 3 j DanGcher, 3.1 Heilbronner, E.;Stadelmann, J. P.; Vogt, J. Helv. Chim. Acru 1979,62,2186. (14) Wong. M.W.; Radom. L. Org. Mass Spectrom. 1989, 24, 539. (15) ProdnukS. D.; DePuy,C. H.; Bierbaum, V. M. Inr. J. MassSpecrrom. Ion' Processes 1990, 100, 69j.
Sadflek and Herman (16) Wong, M. W.; Radom, L. J. Chem. Phys., in press. (17) Hansel, A.; Richter, R.; Lindinger, W.; Ferguson, E.E.Inr. J. Muss Specrrom. Ion Processes 1989. 94, 251. ( I 8) VanEura, J.; Herman, Z . Chem. Phys. 1991, 151, 249. (19) Friedrich, B.;Herman, Z . Collecr. Czech. Chem. Commun. 1984.49, 570. (20) Herman, Z. To be submitted for publication. (21) Friedrich, B.; Herman, Z . Chem. Phys. 1982,62,433. (22) Miller, W. B.; Safron, S.A.; Herschbach, D. R. Discuss. Furuduy SOC.1967, 44, 108. (23) Jarvis, R. D.; Grice, R. Mol. Phys. 1988,65, 1205. (24) Jarvis, R. D.; Laming, G. J.; Grice, R. Mol. Phys. 1990, 70, 667. (25) Xie, Y.;Boggs, J. E. J. Chem. Phys. 1989, 90,4320. (26) Lec,T. J.; Willets,A.;Gaw, J. F.;Handy,N. C. J. Chem. Phys. 1989, 90, 4330.
