J. Phys. Chem. 1995,99, 9363-9367
9363
Intrinsic Activation Barriers for a Prototype Hydrogenolysis Reaction D CH3 in C3" Symmetry
+
+ C2H6 - DCHJ
Wei Ti Lee and Richard I. Masel* University of Illinois, 600 S.Mathews, Urbana, Illinois 61801 Received: January 6, 1995; In Final Form: March 7, 1995@
The presence of intrinsic barriers to reaction are very important to the theory of reactions, but at present accurate values of the intrinsic barriers to reaction for hydrogenolysis reactions do not appear in the open literature. In this paper we use ab initio methods to estimate the intrinsic barrier for a prototype hydrogenolysis CH3CH3 DCH3 CH3. A potential reaction for the abstraction of a methyl group from ethane: D energy surface for this reaction was calculated at the UMP2/6-31G* level of theory. Then a variety of methods up to QCISD(T)/6-3 1 lG(d,p) were used to estimate the activation barrier and intrinsic activation energy for this reaction. It was found that this reaction has an intrinsic barrier of 48 f 2 kcal/mol. By comparison experimental results suggest that the intrinsic barrier to hydrogen abstraction from ethane, D CH3CH3 DH CH2CH3, is only 13 kcal/mol. These results show that the intrinsic barriers to hydrogen abstraction are much lower than the intrinsic barriers to methyl abstraction, in agreement with previous experiments.
+
-
+
+
+
Introduction In 1936, Evans and Polayni' proposed that one can relate Ea, the activation barrier for a given reaction is related to AHH,, the heat of reaction via
where E," is called the intrinsic barrier to reaction and y p is called the transfer coefficient. Equation 1 is now called the Polayni relationship. Many investigators have used the Polayni relationship to make important predictions about reactions on catalysts. Brgnsted and Pederson2 used an earlier version of the Polayni relationship to derive what is now called the Brgnsted catalysis law, Tempkin and Pyskev3 used the Polayni relationship to derive the Tempkin rate equation, Balandin4 and Boudart et al.5 used the Polayni relationship to show why volcano plots arise and to derive the principle of Sabatier. On a more fundamental level, the Polayni relationship has provided a framework to think about activation barriers for reactions. According to eq 1, the activation energy for a given reaction is the difference between two terms, E:, the intrinsic barrier to reaction and -y p A H the energy gain as one partially converts reactants to products. Physically, the intrinsic activation barrier is essentially the energy that it takes to distort the reactants to the transition-state geometry (including quantum resonance effects). If one knows the intrinsic barriers to reactions and the heat of reaction, one can predict the activation barrier for the reaction. As a result, one can tell if a reaction is feasible or not and in favorable cases even predict the relative likelihood of two different mechanistic pathways. To do that, however, one would need to have fairly accurate values for the intrinsic barriers to reaction. In the previous literature there have been many studies of the intrinsic barriers for neucleophilic exchange reactions, and a few studies of hydrogen transfer reactions. Recent examples include refs 2023. However, so far nothing appears to have been done on prototype hydrogenolysis reactions.
* Send correspondence to this author. @
Abstract published in Advance ACS Abstracts, May 15, 1995.
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In this paper we will use ab initio methods to estimate the intrinsic barriers to the reaction
Reaction 2 is a simple model of a hydrogenolysis reaction. To our knowledge, reaction 2 has never been observed in the gas phase. Instead Oldershaw et al.,' Nicholas et al.,* and Adrian et aL9 found that when a deuterium collides with an ethane, one either gets a hydrogen abstraction reaction
or a simple WD exchange: D
+ C2H6 - DCH2CH3+ H
(4)
However, reaction 2 is thought to be a key step a widely studied catalytic reaction, ethane hydrogenolysis. Therefore, it is quite an interesting reaction. One important question is why is reaction 2 not observed experimentally in the experiments of Oldershaw et al.? Nicholas et aL8 or Adrian et aL9 After all, the carbon-carbon bonds in ethane are generally weaker than the carbon-hydrogen bonds. According to data in the JANAF tables, reaction 2 is about 15.5 kcaVmo1 exothermic, while reaction 3 is only 6 kcaVmol exothermic and reaction 4 is almost thermodynamically neutral. Therefore, based on thermodynamics, one would expect reaction 2 to be favored over reactions 3 and 4. However, experimentally, the rates of reaction 3 and 4 are much larger than the rate of reaction 2. Mase16 speculated that reaction 2 must have a much higher intrinsic barrier than reactions 3 and 4. After all, if the intrinsic barrier to reaction 2 was comparable to that for reactions 3 and 4,then according to equation 1, reaction 2 would have a low activation barrier. In such a case, reaction 2 would be observed in Nicholas's experimenk8 Consequently, the fact that reaction 2 is not seen must imply that reaction 2 has a high intrinsic barrier. However, it is unclear how high the intrinsic barrier is, since no data for reaction 2 is available in the literature. In this paper we will use ab initio methods to estimate the intrinsic barriers to reaction 2 for the first time. Previous
0022-3654/95/2099-9363$09.00/0 0 1995 American Chemical Society
Lee and Masel
9364 J. Phys. Chem., Vol. 99, No. 23, 1995
Y C H l
RCH2
Y 2.875 c.
2.25
Figure 1. The geometries for reaction 2 considered in this paper.
workers have found that ab initio techniques can be used to predict accurate values of activation barriers for reactions in a wide variety of hydrocarbon reaction^.'^-^^) There have been a few previous attempts to use ab initio methods to estimate intrinsic barriers such as those in refs 21-24. However, these workers used the Marcus equation27which in effect assumes that y is approximately 0.5. Years ago BokrisIo noted that one can calculate y directly from a potential energy surface. In this paper, we will use ab initio methods to directly calculate the parameters in Bokris' analysis for the first time. In this we will extend the ab initio methods to also calculate intrinsic barriers to reactions. In that way we will produce the first accurate values of the intrinsic barriers for simple hydrogenolysis reactions.
Calculational Methods All of the calculations done in this paper were done using the GAUSSIAN92 package.14 It was assumed that the deuterium approached the ethane along the ethane's carbon-carbon bond axis as shown in Figure 1. Most of the calculations were done at second-order Moller-Plesset perturbation theory (uMp2) level with spin projection.IS The (S2) values were all such that spin projection did not affect the energies of the stable molecules. However, spin projection was important to the transition states. We also did calculations at the UMP4, QCISD(T), and G-2 calculation procedures.I6 The potential energy surface was calculated using a 6-3 1G* basis set. However, the energies of the reactants, products, and transition states were recalculated using a variety of higher basis sets as outlined below. There is one other detail of note. One does not usually put polarization functions on the hydrogen for a standard G-2 calculation. However, our transition-state structure contained a hydrogen with an unusually long bond. Therefore, we included polarization functions on the hydrogen in the G-2 structural optimizations and the zero-point energy calculation.
Results Figure 2 shows a potential energy surface calculated by fixing the C-D and C-C bond length in the D-C2H6 complex and allowing all of the other bond energies and bond angles in the molecule to relax. Most of the calculations assumed that the C3"axis through the carbon-carbon bond was preserved during the reaction. However, a few calculations were done where each hydrogen was allowed to move independently. The latter change had no effect on the potential energy surface. The potential energy surface was calculated at the UMP2 level of theory with a 6-31G* basis set. It was also found that use of a basis set, STO-3G* does not change the general picture of the potential energy surface. The potential energy surface in Figure 2 is similar to those reported previously for SN2 reactions. The energy goes up as
i
. o ~ , , , 0.5 1.25
,
,
, , 2.0
,
, , , 2.75
D-C Distance (Angstroms)
,
, , 3.5
Figure 2. A potential energy surface calculated for the reaction D + C2Hs CH3D + CH3 calculated for a deuterium atom approaching an ethane along the ethane's carbon-carbon bond. The calculation used a 6-31G*basis set and an UMP2 (moderately accurate) calculational procedure. Contour lines are 5 kcal/mol apart. Energies are relative to the total energy of reactants.
-.
the deuterium approaches the ethane, reaches a saddle point and then goes down. There is a small van der Waals well on the product side, but not on the reactant side. Table 1 shows the effect of variations in the basis set on the total energy of the reactants, products, and the heat of reaction. UMP4/6-3 1 1G(d,p), QCSID(T)/6-31 1G(d,p), are included for comparison. The table also includes literature heats of reaction and heats of reaction calculated with the G-2 method which includes zero-point corrections and higher level approximations. The heat of reaction calculated via the G-2 method are reasonably accurate, as suggested previously for these types of molecules.I6 None of the UMP2 calculations give accurate total energy values, and the UMP2/STO-3G* results are particularly inaccurate. However, the heats of reaction are surprisingly accurate given the simplicity of the UMP2 method. Generally, the activation barrier is more accurately predicted when the polarization functions (d,p) are added to the wave function. However, the addition of the diffuse functions (+) had only a small effect on the total energy. We do not have a way to evaluate the accuracy of the activation barriers in Table 1 since there are no experimental values. However, previous investigators have found that high level ab initio calculations can give accurate activation barriers for hydrocarbon r e a c t i o n ~ . ' ~ If - ~we ~ assume that the QCISD(T) values are accurate, we find that the UMP2 results are also surprisingly good. All of the calculations except the UMP2/ ST03G* calculation give activation barriers 40 f 2 kcal/mol. The calculations show that a good basis set with the inclusion of polarization functions (d,p) is quite important to the results. However, the diffuse functions have a much smaller effect. To use the results in Table 1 to estimate the intrinsic activation barrier for reaction, we also need a value of the transfer coefficient, yp. B ~ k r i sand ' ~ Marcus" have suggested different ways to estimate transmission coefficients for reactions. Both methods come from similar formalisms; one assumes that the potential energy surface for the transfer of an atom H from a ligand L to a second ligand R is given as a function of the potential for the L-H and H-R bonds. Marcus' formalism assumes perfectly parabolic potentials, while Bokris' formalisms
,
J
J. Phys. Chem., Vol. 99, No. 23, I995 9365
A Prototype Hydrogenolysis Reaction
TABLE 1: Comparison of the Reaction Barriers, Heats of Reactions and Transfer Coefficient Calculated from Different Methods methodhasis UMPIZ/STO-3G(d) UMP2/6-3 lG(d)
reactants (atomic units)
products (atomic units)
-78.879 91 -79.992 97 -80.041 63 -80.044 02 -80.044 4 1 -80.025 72 -80.070 70 -80.071 29 -80.071 48 -79.995 6 1 -80.046 40 -80.049 92 -80.050 98 -80.1 14 33 -80.1 I5 60 -80.130 88 -80.130 88 -80.130 90
-78.900 66 -80.003 30 -80.059 25 -80.064 09 -80.064 44 -80.036 12 -80.088 4 1 -80.089 93 -80.090 18 -80.009 36 -80.067 5 I -80.070 73 -80.071 38 -80.135 80 -80.138 13 -80.155 97 -80. I59 06 -80.155 97
UMP2/6-31G(d.p) UMP2/6-3 1+G(d,p) UMP2/6-3 I ++G(d,p) UMP2/6-31 lG(d) UMP2/6-31 lG(d,p) UMP2/6-3 1 1+G(d,p) UMP2/6-3 I 1++G(d,p) UM P2/D95(d) UMP2/D95(d,p) UM P2/D95+(d,p) UM P2/D95++(d,p) UMP4/6-3 1 1G(d,p) QCISD(T)/6-3I IG(d,p) G-2 (all H) G-2 (deuterium) literature
transition state (atomic units)
-78.793 -79.919 -79.973 -79.978 -79.979 -79.954 -80.007 -80.008 -80.008 -79.924 -79.980 -79.986 -79.987 -80.047 -80.052 -80.071 -80.072
n
a, -
E
$40.0 Y
13 04 49 24 06 76 25 45 85 28 61 54 81 94 58 32 39
reaction bamer (kcal/mol)
54.5 46.4 42.8 41.3 41.0
44.5 39.8 39.4 39.3 44.8 41.3 39.8 39.6 41.7 39.5 37.4 36.7 >41
heats of reaction (kcal/mol )
intrinsic reaction bamer (kcal/mol)
-13.0 -6.5
63.7 55.6 52.0 50.5 50.2 53.7 49.0 48.6 48.5 54.0 50.5 49.0 48.9 50.9 48.8 46.6 45.9
-11.1
-12.6 -12.6 -6.5 -1 1.1 - 1 1.7 - 1 1.7
-8.6 -13.2 -13.1
- 12.8 - 13.5 -14.1 -15.7 - 17.7 -15.5
Q-
83
c+
a
a) Start of Reaction
W
v)
.e
C
3 30.0 V
0
cr
0
x m
d+
20.0
b
b) Transition State
a, t W
$ 10.0
.0 CI
a,
LT
0.0
-3.0
-2.0
-1.0 0.0 1.0 Reaction Path
2.0
3.0
Figure 3. A trace of the energy of the system as the follow the minimum energy reaction pathway. The calculation was done using a
c) Products
-
Figure 4. The changes in geometry during the reaction D + C2H6 CHJD + CH3 calculated for a deuterium atom approaching an ethane along the ethane’s carbon-carbon bond.
6-3 1 G** basis set and a UMP2 calculational procedure. instead linearizes the potentials near the transition state. We have chosen Bokris’ formalism here, because it seems to give more realistic values of yp (i.e., values greater than 0.5 for a late transition state). In actual practice, Bokris’ method starts with a plot of the energy vs the reaction coordinate. One then calculates the slopes (eV/A) at the inflection points in the curves. The transfer coefficient is then given by 1
yp
=1
+ (ratio of slopes)
(5)
where the ratio of slopes is the ratio of the slopes at the left and right inflection points in the plot. Figure 3 shows a plot of the energy vs reaction coordinate calculated at the UMpW6-31 G(d,p) level of theory. Notice that the slope of the energy is larger on the reactant side of the potential energy surface than on the product side, which implies a somewhat late transition state. Following, Bokris,Iowe have calculated the transfer coefficient using the slopes of the tangents to the curves in Figure 3. The transfer coefficient worked out to be 0.585, which again implies a slightly late transition state.
By comparison if we use Marcus’ equation, we calculate y = 0.453, i.e., a transfer coefficient indicative of an early transition state. Calculations of the geometry of the transition state in Tables 2 and 3 also indicate a late transition state (i.e., a bond angle greater than 90’). Therefore we have used Bokris’ method rather than Marcus’ to estimate yp. Finally, one can plug the 0.585 into eq 1 to calculate an intrinsic barrier to the reaction. Table 1 shows the results. In the calculations it was assumed that the heat of reaction was 15.5 kcavmol. According to the calculations, the intrinsic barrier to reaction was 48 f 2 kcaVmol basically independent of how the calculations were done, provided the polarization functions were included in the basis set.
To put these results in perspective, to our knowledge this is the first time that ab initio methods have been used to estimate the transfer coefficients for hydrogenolysis reactions. We choose a case where the intrinsic barrier was not known. However, the calculations were easy, and the results were fairly independent of how the calculations were done. Previous
Lee and Masel
9366 J. Phys. Chem., Vol. 99,No. 23, 1995 TABLE 2: Comparison of the Transition-State Structure Calculated at UMP2 Level Using Various Basis Sets structure basis set
6-31G(d) 6-31G(d,p) 6-31+G(d,p) 6-31++G(d,p) 6-311G(d) 6-311G(d,p) 6-31l+G(d,p) 6-31l++G(d,p) D95(d) D95(d,p) D95+(d,p) D95++(d,p)
E(PMP2) (hartrees) -79.919 04 -79.973 49 -79.978 24 -79.979 06 -79.954 76 -80.007 25 -80.008 45 -80.008 85 -79.924 28 -79.980 61 -79.986 54 -79.987 81
RCD 1.383 1.370 1.367 1.366 1.375 1.364 1.364 1.363 1.396 1.379 1.364 1.363
RCC 1.875 1.853 1.850 1.851 1.871 1.855 1.852 1.852 1.876 1.852 1.851 1.850
RCH 1 1.085 1.082 1.082 1.082 1.084 1.086 1.086 1.087 1.090 1.086 1.086 1.086
RCH2 1.089 1.085 1.086 1.086 1.088 1.090 1.090 1.090 1.094 1.090 1.090 1.090
AHCC1 91.7 92.5 92.6 92.6 91.9 92.5 92.6 92.6 92.0 92.9 92.6 92.6
AHCC2 107.0 107.2 107.0 106.9 107.0 107.0 106.9 106.9 107.1 107.3 107.1 107.0
Frozen-core optimization was used.
TABLE 3: Full-Electron Optimization of the Transition-State Structure at UMP2 Level and Using the Double Valence (6-31G) Basis Sets structure basis set E(PMP2) (hartrees) RCD RCC RCH 1 RCH2 AHCC1 AHCC2 1.088 91.7 107.0 1.874 1.085 -79.928 02 1.382 6-31G(d) 1.080 1.084 92.5 107.2 1.368 1.852 6-31G(d,p) -79.983 57 92.6 107.0 1.081 1.085 1.366 1.849 6-31+G(d,p) -79.988 41 1.081 1.085 92.6 106.9 1.365 1.850 6-31++G(d,p) -79.989 30 workers have found that similar calculations give accurate activation barriers for other reactions of hydrocarbon^.'^-^^ That gives us confidence that the results are correct. In this paper we only considered a linear geometry. However, we have also done calculations for nonlinear geometries and always found even higher intrinsic barriers. In particular, when the deuterium approaches perpendicularly to the C-C bond, the barrier is 61 kcdmol. Therefore, there is reason to believe that the intrinsic barrier for reaction 2 will be at least 48 f 2 kcal/mol. Just to keep that number in perspective, note that reaction 3 (Le,, hydrogen abstraction from the ethane) has been examined experimentally. No one has measured a transfer coefficient for the reaction. However, if one assumes a transfer coefficient of 0.585, one calculates that the intrinsic barrier to reaction 3 is only 13 kcal/mol, Le., much less than the 47 kcdmol calculated here. This results quantifies a speculation of Mase16 that the intrinsic barriers to the scission of C-C bonds are much higher than the intrinsic barriers to the scission of C-H bonds. In our view, the result that the intrinsic barrier to carboncarbon bond scission is much higher than the intrinsic barrier to C-H bond scission is quite important. It implies that if everything else is equal, C-C bonds are much harder to break that C-H bonds. That is why reaction 2 is not observed under conditions where reactions 3 and 4 are seen. The calculations in this paper allow one to understand why the intrinsic barriers for reaction 2 are so high. Tables 2 and 3 show the geometry of the transition state calculated using a variety of procedures. There are some small variations according to how we do the calculations. However, the big result is that the ethane molecule needs to be highly distorted in order for reaction 2 to occur. Notice, for example that in the transition state, the C-H bond angle on the carbon atom closest to the deuterium has been distorted from the 111' in ethane to about 92" in the transition state. In effect, during the reaction, the C-H bonds in the ethane must flip over to face the wrong way. According to the calculations the flipping motion has an intrinsic barrier of about 48 kcal/mol, Le., a relatively large barrier. By comparison, in unpublished work, we have also examined the intrinsic barrier for the hydrogen abstraction reaction, reaction 3. The transition state for reaction 3 is basically an ethane with
one extended C-H bond. There is very little distortion of the other C-H bonds in the ethane. The lesser orbital distortion in reaction 3 explains why reaction 3 has a smaller intrinsic barrier than reaction 2. Now it is interesting to speculate whether the intrinsic barriers to hydrogen abstraction are always lower than the intrinsic barriers to methyl abstraction. Consider the reaction of a deuterium atom with a methyl group: D
+ CH,R - products
(6)
Three reaction pathways are possible. A hydrogen abstraction D
+ CH,R - DH + CH,R
(7)
D
+ CH,R - H + DCH,R
(8)
HD exchange
and a methyl abstraction D
+ CH,R - DCH, + R
(9)
Notice that reaction 8 is a generalization of reaction 2. The CH bonds need to distort during reaction which implies that reaction 8 should have a high intrinsic barrier. By comparison reaction 6 should not. It is possible to lower the barrier to reaction 8 due to quantum resonance effects. As one changes the R group in reaction 8, the resonance effects change. Previous workers have found that in other reactions of hydrocarbons, such effects can induce 1- 10 kcal/mol changes in the intrinsic barriers to reaction. Notice, however, that a 10 k c d mol change in the intrinsic barriers will not matter to the main effects found here. The intrinsic barrier to C-C bond scission will still be much larger than the intrinsic barrier to C-H bond scission. If the intrinsic barrier to the abstraction of a methyl ligand were much higher than the intrinsic barrier to the abstraction of a hydrogen, one would expect reaction 6 to dominate over reaction 8 except in cases where the C-R bond was exceptionally weak. Wesley" and Kerr and MossI2 report kinetic data for over 100 reactions of the form in eq 5. In all cases but one, reaction 6 proceeds with a modest barrier while reaction 8 is
A Prototype Hydrogenolysis Reaction
J. Phys. Chem., Vol. 99,No. 23, 1995 9367
not observed. The one exception is the reaction
D
+ CH,CN - DCH, + CN
(10)
which is reported to proceed with an expectedly low barrier, 2 kcal/mol. Note however, that according to data in the CRC handbook, reaction 9 is 23 kcal/mole endothermic, so the true activation barrier must be more than 23 kcal/mol. In unpublished QCISDT/6-3 1lG**//UMP2/6-3 1G** calculations we calculate a barrier of 46 kcdmol. Therefore, it is likely that the data for reaction 9 in Kerr and Moss is wrong. In all the other cases, either only abstraction of a hydrogen atom is seen, or the hydrogen abstraction reaction proceeds with a barrier of at least 20 kcdmol less than the activation barrier for the methyl abstraction reaction. Therefore, it seems that the experimental results are in general accord with the suggestion that the intrinsic barriers for the abstraction of a methyl group are considerably larger than the intrinsic barriers for the abstraction of a hydrogen although additional results are needed to clarify the findings.
Conclusions In summary then, in this paper we have used ab initio methods to estimate the intrinsic barrier for a prototype hydrogenolysis reaction D CH3CH3 DCH3 f CH3. We find that the hydrogenolysis reaction has an intrinsic barrier of about 48 kcaY mol. By comparison experimental results suggest that the intrinsic barrier to hydrogen abstraction is only 13 kcavmol. These results show that the intrinsic barriers to hydrogen abstraction are much higher than the intrinsic barriers to methyl abstraction, in agreement with previous experiments.
+
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Acknowledgment. This work was supported by the National Science Foundation under grant CTS 94-03840. References and Notes (1) Evans, M. G. ;Polayni, M. Trans Faraday SOC. 1936, 32, 133. (2) Brmsted, J. N.; Pederson, K. Z. Phys. Chem. 1924, 108, 185.
(3) Tempkin, M. I.; Pyzhev, U. Acta. Phys. Chem. 1940, 12, 327. (4) Balandin, A. A. Adv. Catal. 1969, 19, 1. (5) Boudart, M.; Djtgo-Mariadassou, M. Kinetics Of Heterogeneous Catalytic Reactions, Princeton University Press: Princeton, NJ, 1984. (6) Masel, R. I. Principles Of Adsorption And Reaction On Solid Surfaces; Wiley: New York, in press p 816. (7) Oldershaw, G. A.; Gould, R. L. J. Chem SOC., Faraday Trans 2 1985, 81, 1507. (8) Nicholas, J. E.; Bayrakeeken, F.; Fink, R. D. 1972, 56, 1008. (9) Adrian, F. J.; Bohandy, J.; Kim, B. F. J. Chem Phys. 1994, 100, 8010. (10) Bokris, J. 0. Modem Electrochemistry; Plenum: New York, 1970; VOl. 2, p 1110. (11) Wesley, F. E. Tables Of Recommended Rate Constants For Reactions Occurring In Combustion; National Bureau of Standards: Washington, DC, 1980. (12) Kerr, A. J.; Moss, S. J. CRC Handbook of Bimolecular and Termolecular Reactions, CRC Press: Boca Raton, FL, 1981. (13) Germann, G. J.; Huh, Y . D.; Valenti, J. J. J. Chem. Phys. 1992, 96, 5694; J. Chem. Soc., Faraday Discuss. 1991, 91, 173. (14) Gaussian 92/DFT, Revision G.2; Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Gill, P. M. W.; Johnson, B. G.; Wong, M. W.; Foresman, J. B.; Robb, M. A.; Head-Gordon, M.; Replogle, E. S.; Gomperts, R.; Andres, J. L.; Raghavachari, K.; Binkley, J. S.; Gonzales, C.; Martin, R. L.; Fox, D. J.; Defrees, D. J.; Baker, J.; Stewart, J. J. P.; Pople, J. A. Gaussian, Inc.: Pittsburgh, PA, 1993. (15) Schlegel, H. B. J. Phys. Chem. 1988, 92, 3075. (16) Curtiss, L. A,; Raghavachari, K.; Trucks, G. W.; Pople, J. A. J. Chem. Phys. 1991, 94, 7221. (17) Gonzalez, C.; Sosa, C.; Schlegel, H. B. J. Phys. Chem. 1989, 93, 2435. (18) Bach, R. D.; Su, M.-D.; Aldabbagh, E.; Andrks, J. L.; Schlegel, H. B. J. Am. Chem. SOC.1993, 115, 10237. (19) Jino, H.; von Ragn.6 Schleyer, P. J. Chem. Soc., Faraday Trans. 1994, 90, 1559. (20) Jensen, F. Chem. Phys. Lett. 1992, 196, 368. (21) Wladkowski, B. D.; Allen, W. D.; Brauman, J. I. J. Phys. Chem. 1994, 98, 13532. Wladkowski, B. D.; Lim, K. F.; Allen, W. D.; Brauman, J. I. J. Am. Chem. SOC.1992, 114, 9136. (22) Buhl, M.; Schaefer, H. F. J. Am. Chem. SOC. 1993, 115, 9143. (23) Lluch, J. M.; Bertran, J.; Dannenberg, J. J. Tetrahedron 1988.44, 7621. (24) Marcus, R. A. J. Phys Chem. 1968, 72, 891 JP950101X
