J. Phys. Chem. 1996, 100, 633-637
633
Theoretical Study on the Mechanism of the Superacid-Catalyzed Unimolecular Isomerization of n-Butane and 1-Butene M. Boronat,† P. Viruela,‡ and A. Corma*,† Instituto de Tecnologı´a Quı´mica UPV-CSIC, UniVersidad Polite´ cnica de Valencia, c/ Camino de Vera s/n, 46071 Valencia, Spain, and Departament de Quı´mica Fı´sica, UniVersitat de Vale` ncia, c/ Dr. Moliner 50, 46100 Burjassot (Valencia), Spain ReceiVed: May 22, 1995; In Final Form: October 6, 1995X
Owing to the practical interest of the acid-catalyzed isomerization of n-butane and 1-butene, the mechanism of the isomerization and scrambling reactions of the n-butyl cation has been studied theoretically using ab initio methods which include electron correlation and extended basis sets. It has been found that the protonated cyclopropane ring does not appear as a common intermediate for carbon scrambling and branching isomerization of the n-butyl cation, since it is a transition state and not a minimum on the potential energy surface. The transition states for both reactions have been determined and the activation energies calculated. These values are in very good agreement with those obtained experimentally.
Introduction The acid-catalyzed isomerization reactions of hydrocarbons play an important role in the industrial processes of petroleum chemistry.1 This is especially true after the introduction of reformulated gasoline, which has converted the acid-catalyzed isomerization of n-butane and 1-butene to isobutane and isobutene, respectively, in processes of paramount importance. Reaction mechanisms based on carbenium ion rearrangements are generally assumed for homogeneous reactions in superacid media. The question of possible participation of primary carbenium ions and of protonated cyclopropanes as intermediates in these rearrangements is a subject of considerable interest. Carbenium ions allow two types of rearrangements, which differ considerably not only in rate but also in mechanism: nonbranching rearrangements, in which the degree of chain branching remains the same, and branching rearrangements, in which it increases or decreases. The classical mechanism for the nonbranching rearrangements supposes them to proceed by a succession of 1,2-hydrogen and alkyl shifts via secondary ions as intermediates. For branching rearrangements, a mechanism with only 1,2-hydrogen and alkyl shifts would necessarily include primary carbenium ions as intermediates, and consequently the mechanism that is currently accepted involves the intermediacy of a protonated cyclopropane ring (Scheme 1). According to this mechanism, the C+ carbon attacks the β carbon atom and a protonated cyclopropane ring is formed. The opening of the cyclic intermediate at side a leads to a secondary monobranched ion if R is an alkyl group and to an n-butyl in which a terminal and a nonterminal carbon atoms have changed positions (scrambling reaction) if R is a hydrogen atom. The opening of the cyclic intermediate at side b also leads to a secondary monobranched ion if R is an alkyl group. However, if R is a hydrogen atom, the ring opening at this side becomes more difficult since it would lead to a primary carbenium ion.2 This mechanism is apparently supported by the experimental fact that n-butane does not isomerize at an observable rate to isobutane under conditions where n-pentane and n-hexane are rapidly converted into their branched isomers and by the finding * Author to whom correspondence should be addressed. † Instituto de Tecnologı´a Quı´mica UPV-CSIC. ‡ Departament de Quı´mica Fı´sica. X Abstract published in AdVance ACS Abstracts, December 15, 1995.
0022-3654/96/20100-0633$12.00/0
that the rate of scrambling or isomerization of n-butane-1-13C to n-butane-2-13C is comparable to that of isomerization of n-pentane to isopentane.3 The accepted values for the activation energies for the carbon scrambling process in the sec-butyl cation and for the conversion of the sec-butyl to the tert-butyl cation are 7.5 and 18.0 kcal/mol, respectively.2,4,9,11 The similarity of the last value to the activation energy for the carbon scrambling in the isopropyl cation (∆G‡ ) 15.7 kcal/mol2a,5) is consistent with the supposition that the isomerization reaction passes through the high-energy primary isobutyl cation. The low barrier obtained for the scrambling process, however, suggests that this reaction passes through a protonated methylcyclopropane species (either corner-6 or edge-protonated7), which is more stable than the primary isobutyl cation. The butyl cation has been the subject of some theoretical work.8 Wiberg and Kass9 studied the structure of the protonated methylcyclopropane using a 6-31G* basis set including geometry optimization at the HF level and subsequent MP2 calculations of the correlation energy. More recently, Schleyer et al.10 have studied the nature of the secondary n-butyl cation at many different theoretical levels including electron correlation, and they have concluded that, when nonclassical structures are included, geometry optimizations at correlated levels are essential. However, the only detailed study of all the structures (intermediates and transition states) involved in the isomerization and carbon scrambling of the n-butyl cation found in the literature was carried out using the semiempirical MINDO/3 method.11 To establish the mechanism of the isomerization and scrambling reactions of the n-butyl cation, we present here a theoretical study of the potential energy surface of the C4H9+ cation using ab initio methods which include electron correlation and extended basis sets. Calculations All ab initio molecular orbital calculations were performed on an IBM 9021/500-2VF computer and on IBM RS/6000 workstations of the University of Vale`ncia using the Gaussian 8812 and Gaussian 9213 computer programs. The geometry of the stationary points of the C4H9+ potential energy surface was first optimized by using the Hartree-Fock procedure and the 6-31G* basis set14 (HF/6-31G*) which has polarization functions (d-type) on nonhydrogen atoms. The Berny analytical gradient15 method was used for the optimizations. © 1996 American Chemical Society
634 J. Phys. Chem., Vol. 100, No. 2, 1996
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SCHEME 1
Since it’s known that electron correlation is needed to treat ionic systems especially when nonclassical bridged forms or three-center bonds are involved,16 these geometries were reoptimized using the second-order Moller-Plesset perturbation theory17 that takes into account the core electrons and the 6-31G* basis set (MP2(fu)/6-31G*). The relative energies were improved by performing single-point calculations on the MP2(fu)/6-31G* optimized geometries, using the 6-31G**18 basis set, which includes polarization functions (p-type) on hydrogens, and the fourth-order MP4(sdtq) treatment19 (MP4(sdtq)/631G**//MP2(fu)/6-31G*). The HF/6-31G* and MP2/6-31G* stationary points were characterized by calculating the Hessian matrix and analyzing the vibrational normal modes.
C3 bond length remains nearly the same (2.582 and 2.549 Å). The most important difference between the correlated and uncorrelated optimized geometries of B is the fact that at the HF/6-31G* level the three-center C-H-C bond is unsymmetric, with C-H bond length values of 1.338 and 1.281 Å, while at the MP2/6-31G* level the two C-H bonds become equivalent, with a value of 1.306 Å. Since, apart from being slightly more stable than B, structure A shows a strong positive charge on a secondary carbon atom, it seems more suitable to induce the cycle formation process, and consequently we have taken it as the starting point for the scrambling and isomerization reactions. Two different structures have been proposed for the protonated methylcyclopropane ring. A corner-protonated species C, formed by adding a proton to the methine carbon atom,6
Results and Discussion According to Scheme 1, four structures have to be localized and characterized: the secondary n-butyl cation, the protonated methylcyclopropane ring, the primary isobutyl cation, and the tertiary isobutyl cation. The structure of the secondary n-butyl cation has already been studied at many standard theoretical levels. Both the partially methyl-bridged form A and the trans hydrogen-bridged form B (see Figure 1) have been found to be minima on the potential energy surface when electron correlation is included, structure A being slightly more stable than structure B at every considered theoretical level.10 In the present work the geometries of A and B have been completely optimized without symmetry restrictions at the HF/ 6-31G* and MP2/6-31G* levels. The total and relative energies, together with the nature of the stationary points, are summarized in Table 1. At the HF/6-31G* level structure A is 4.14 kcal/ mol more stable than B. When electron correlation is included, the H-bridged structure is stabilized. At the MP2/6-31G* level the A-B energy difference is only 2.47 kcal/mol, and at the MP4(sdtq)/6-31G**//MP2/6-31G* level it is reduced to 0.74 kcal/mol. Analysis of the force constants reveals that B is not a local minimum at the HF/6-31G* level, because it shows an imaginary vibration frequency corresponding to conversion to minimum A. At the MP2/6-31G* level, however, both structures A and B are local minima on the potential energy surface. The optimized bond lengths depicted in Figure 1 show the changes in geometry due to the inclusion of electron correlation. The degree of methyl bridging in A becomes more important when electron correlation is included, as can be observed from the fact that the C2+C3C4 angle is closed from 102.4° at the HF/6-31G* level to 77.5° at the MP2/6-31G* level. This implies an important shortening of the C2+-C4 bond length from 2.364 Å (HF/6-31G*) to 1.923 Å (MP2/6-31G*), while the C1-
Figure 1. Structures of the C4H9+ cation. The HF/6-31G* bond lengths are given first, followed by the MP2/6-31G* in parentheses.
Unimolecular Isomerization of n-Butane and 1-Butene
J. Phys. Chem., Vol. 100, No. 2, 1996 635
TABLE 1: Absolute (hartrees) and Relative (kcal/mol) Energies and Characterization of the Stationary Points Found on the C4H9+ Potential Energy Surface HF/6-31G* structure
Eabs
Erel
A B C D E F
-156.420 807 -156.414 208 -156.398 531 -156.392 382 -156.390 130 -156.442 549
13.64 17.78 27.62 31.48 32.89 0.00
MP2/6-31G* MIN TS TS TS TS MIN
Eabs
Erel
-156.942 144 -156.938 211 -156.929 166 -156.927 999 -156.906 081 -156.959 671
11.00 13.47 19.14 19.87 33.63 0.00
MP4(sdtq)/6-31G**//MP2/6-31G* MIN MIN TS TS TS MIN
Eabs
Erel
-157.061 915 -157.060 743 -157.048 624 -157.048 491 -157.029 109 -157.081 078
12.02 12.76 20.36 20.45 32.61 0.00
SCHEME 2
and an edge-protonated species D (see Figure 1), in which the proton is shared by two neighboring methylene carbon atoms.7 The structure of the protonated methylcyclopropane ring has already been studied by Wiberg and Kass,9 who have also considered a third structure formed by adding a proton to a methylene carbon atom. They have carried out geometry optimizations of the three structures at the HF/3-21G and HF/ 6-31G* levels, and they have found that this third structure corresponds to the open form of the secondary n-butyl cation A. Consequently, neither the addition of a proton to a methylene carbon atom nor the sharing of the proton by a methine and a methylene carbon atom has been considered, because as the resulting species are markedly unsymmetrical, they will directly lead to the secondary n-butyl cation A. It has also been suggested by Wiberg and Kass that the corner- and edgeprotonated methylcyclopropane species are involved in the carbon scrambling of the 2-butyl cation, but no characterization of these structures has been performed. The geometry of structures C and D has been initially optimized assuming Cs symmetry. The corner-protonated structure C has been found to be 6.79 and 3.54 kcal/mol more stable than the edge-protonated structure D at the HF/6-31G* and MP2/6-31G* levels, respectively. Characterization of the stationary points indicates that at both levels of theory C is a transition state showing only one imaginary frequency, but D has to be classified as a hilltop because it exhibits two imaginary frequencies. The geometry of both structures has been then completely reoptimized without symmetry constraints, and while structure C has conserved the Cs symmetry, structure D has evolved to a new and more stable stationary point which exhibits a partially distorted Cs symmetry. Analysis of the vibrational normal modes indicates that this new stationary point is a transition state on the potential energy surface, the negative frequency being clearly associated to the movement of the bridged hydrogen atom toward one of the methylene carbon
atoms. The imaginary frequency in C, however, has significant contributions from all the hydrogen atoms. With respect to the relative stability of both structures, at the HF/6-31G* level the corner-protonated species C is 3.86 kcal/ mol more stable than the edge-protonated one D (Table 1). However, as the electron correlation stabilizes the nonclassical H-bridged structures, at the MP2/6-31G* level C is only 0.73 kcal/mol more stable than D, and at the MP4(sdtq)/6-31G**// MP2/6-31G* level this difference is reduced to 0.09 kcal/mol. The bond length values depicted in Figure 1 suggest that the corner-protonated methylcyclopropane ring C could be best described as a complex between the CH3CH2+ cation and the CH2dCH2 molecule. At the HF/6-31G* level the C3-C4 bond length is 1.365 Å, which is closer to the calculated length of the CdC double bond of ethylene (1.317 Å) than to the single C-C bond of ethane (1.528 Å). Electron correlation strengthens the three-center bond complex; the C2-C3 (or C2-C4) bond lengths which are 1.866 Å at the HF/6-31G* level reduce to 1.786 Å at the MP2/6-31G* level, and the C3-C4 bond length increases to 1.386 Å. The only significant change that electron correlation introduces in the geometry of the edge-protonated form D is a shortening of the C3-C4 bond length, from 1.763 Å at the HF level to 1.717 Å at the MP2 level. According to these results, it’s not possible to definitively settle whether the structure of the methylcyclopropane ring is corner- or edge-protonated. What can be assured is that, since both structures are not minima but transition states, not only at the HF/6-31G* but also at the MP2/6-31G* level, the methylcyclopropane ring cannot be a true intermediate of the isomerization and scrambling reactions, but only a species through which the reaction passes. The geometry of the tertiary isopropyl cation F has been completely optimized without any symmetry constraint. As can be seen in Figure 1, the conformation adopted minimizes the repulsions between the hydrogen atoms and also between the
636 J. Phys. Chem., Vol. 100, No. 2, 1996
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Figure 2. Energy profile corresponding to the scrambling and isomerization reactions of the secondary n-butyl cation: (s) MP2/631G*, (‚‚‚) MP4(sdtq)/6-31G**//MP2/6-31G*. At both theoretical levels the tertiary ion has been taken as the origin of energies.
TABLE 2: Calculated and Experimental Energies of Activation (kcal/mol) for the Scrambling and Isomerization Reactions of C4H9+ Cation process scrambling direct isomerization reverse isomerization
HF/ MP2/ MP4(sdtq)/6-31G**// 6-31G* 6-31G* MP2/6-31G* exptl 17.84 19.25 32.89
8.87 22.63 33.63
8.43 20.59 32.61
7.5 18.0 32.0
C-H and C-C bonds. Both at the HF/6-31G* and at the MP2/ 6-31G* levels structure F is the most stable minimum on the potential energy surface. The calculated energy differences between the secondary A and the tertiary F butyl cations, 13.64 kcal/mol at the HF/6-31G* level, 11.00 at the MP2/6-31G* level, and 12.02 at the MP4(sdtq)/6-31G**//MP2/6-31G* level, are in good agreement with the experimental values of the enthalpy of rearrangement of the sec-butyl to the tert-butyl cation, which are 15-1720 and 14-1521 kcal/mol in the gas phase and in solution, respectively. The structure of the primary isobutyl cation E (see Figure 1) has been more difficult to obtain. Taking as a starting point the optimized geometry of the tertiary isobutyl cation F, the distance between H and C2 has been slowly varied from 2.037 Å (the optimized value in F) to 1.075 Å (already corresponding to a primary cation). In each calculation the C2-H distance has been fixed and all other parameters have been allowed to fully optimize. Then, the geometry of the primary cation has been completely reoptimized using the eigenvector following transition state search technique. The stationary point obtained has also been characterized by force constant calculations, and it’s been found to be a transition state with only one imaginary vibration frequency, both at the HF/6-31G* and at the MP2/631G* levels. Taking into account all these data and the idea that a transition state must be connecting two minima on a potential energy surface, a new mechanism (Scheme 2) is proposed for the scrambling and isomerization reactions of the n-butyl cation. In this mechanism, minimum A is the starting point for both reactions, the minimum A′, the product of the scrambling reaction, and the minimum F, the product of the isomerization reaction, being equivalent. The localized stationary points C, D, and E are not true intermediates but only species through
which the reactions pass, because they are transition states and not minima on the potential energy surface. The positive charge on C2 carbon atom in A attacks the C4 carbon atom and then two different processes can take place: (a) A simultaneous strengthening of the C2-C4 bond and breaking of the C3-C4 bond in A directly leads to transition state E, and from this, a shift of H5 from C2 to C3 leads to minimum F. The primary cation is the transition state for the isomerization reaction of n-butyl to tert-butyl. (b) Strengthening of the C2-C4 bond in A together with a migration of a hydrogen atom either to C2 or to a shared position between C3 and C4 leads to transition states C or D, respectively. If the C2-C3 bond is then broken and the hydrogen atom migrates to C3, the minimum A′ is reached and the scrambling reaction has occurred. Consequently, the protonated methylcyclopropane ring is only the transition state for the scrambling reaction, at least in the case of C4H9+ cation. As we have seen before, it’s impossible to settle whether the methylcyclopropane ring implied in the scrambling reaction is corner- or edge-protonated taking into account only energetic criteria, because the calculated stabilities of structures C and D are quite similar. But from the mechanism depicted in Scheme 2 and the geometries shown in Figure 1, several reasons arise that make us think that the edge-protonated methylcyclopropane ring is the most probable transition state for the scrambling reaction. The geometric changes necessary to convert A into D affect mainly the C2-C4 bond length, which has to be shortened by 0.427 Å. The C2-C3 and C3-C4 bond lengths only need an increase of 0.090 and 0.064 Å, respectively, and the hydrogen atom which forms the bridge needs to elongate the C-H bond length less than 0.20 Å. In the conversion of A into C, however, the C2-C3 bond length is increased 0.383 Å and the C3-C4 and C2-C4 bond lengths are decreased 0.267 and 0.137 Å, respectively. In addition, a hydrogen atom must migrate from C4 to C2. That’s to say, conversion of A into D implies formation of a C-C bond and elongation of a C-H bond, while conversion of A into C implies migration of a hydrogen atom, breaking of a C-C bond, and conversion of a single C-C bond into a double CdC bond. The species thus formed is best represented as a complex between the CH3CH2+ cation and the CH2dCH2 molecule, without any chemical meaning in the scrambling reaction studied. According to this new mechanism, the activation energy for the scrambling process can be calculated as the energy difference between the protonated methylcyclopropane ring D and structure A, and the activation energies for the direct (n-butyl f tertbutyl) and reverse (tert-butyl f n-butyl) isomerization reactions as the energy differences between the primary cation E and structures A and F, respectively (see Figure 2). The calculated activation energies, together with experimental data, are summarized in Table 2. At the HF/6-31G* level the energy barrier for the scrambling process is 17.84 kcal/mol, a value too high as compared with the experimental value of 7.5 kcal/mol. When electron correlation is included, the protonated methylcyclopropane ring is stabilized and the calculated activation energy is 8.87 kcal/mol at the MP2/6-31G* level and 8.43 kcal/mol at the MP4(sdtq)/6-31G**//MP2/6-31G* level, much closer to the experimental value. These results indicate that the HF/6-31G* level is not adequate to study reaction mechanisms in which nonclassical species are involved; to treat these species correctly, inclusion of electron correlation is essential. The calculated activation energies for the direct and reverse isomerization reactions at the HF, MP2, and MP4 levels are quite similar (19.25, 22.63, and 20.59 kcal/mol, respectively, for the direct reaction and 32.89, 33.63, and 32.61 kcal/mol, respectively, for
Unimolecular Isomerization of n-Butane and 1-Butene the reverse reaction) and in good agreement with the experimental values of 18.0 kcal/mol for the direct and 32.0 kcal/mol for the reverse reaction. Conclusions A complete study of the potential energy surface of C4H9+ cation including geometry optimization and characterization of the stationary points at correlated levels has been carried out to establish the mechanism of the scrambling and isomerization reactions of the n-butyl cation. The results obtained suggest an alternative mechanism for these reactions to that empirically proposed by Brouwer,2,3 the main difference being the nature of the protonated methylcyclopropane ring. According to Brouwer’s mechanism, the protonated methylcyclopropane ring is an intermediate, from which two different routes lead to the tertiary isobutyl cation (isomerization) or to a secondary n-butyl cation in which a terminal and a nonterminal carbon atom have changed positions (scrambling). Our results for the n-butyl cation, however, indicate that the protonated methylcyclopropane ring cannot be an intermediate because it’s a transition state and not a minimum on the potential energy surface. The new mechanism (Scheme 2) supposes that, from the first moment, the two reactions follow different reaction paths. In the isomerization reaction minimum A (secondary n-butyl cation) is converted into minimum F (tertiary isobutyl cation) through transition state E (primary isobutyl cation) with an activation energy of 20.59 kcal/mol, and in the scrambling reaction minimum A is converted into the equivalent minimum A′ through transition state D (the edge-protonated methylcyclopropane ring, which, as has been explained before, seems to be more probable than the corner-protonated species C) with an activation energy of 8.4 kcal/mol. The activation energies calculated assuming this new mechanism agree well with the experimental data. Since the effect of alkyl substituents on the relative energies and nature of the protonated cyclopropane ring and the classical and nonclassical carbenium ions is not known, it’s not possible to extrapolate the conclusions obtained for the C4H9+ cation to higher aliphatic carbenium ions. The mechanism of branching rearrangement for other systems may be different and consequently should be calculated. From the results obtained at the different levels of calculation, it can also be concluded that to study reaction mechanisms in which nonclassical bridged structures or three-center bonds are involved, it’s necessary to introduce the electron correlation in the geometry optimization calculations and in the characterization of the stationary points. Thus, the MP2/6-31G* basis set would be the lowest acceptable level of calculation.
J. Phys. Chem., Vol. 100, No. 2, 1996 637 Acknowledgment. We thank the Centro de Ca´lculo and Departamento de Quı´mica Fı´sica of the University of Valencia for computing facilities. This work has been supported by the C.I.C.Y.T. project MAT 94-0359. M.B. thanks the Conselleria de Cultura, Educacio´ i Cie`ncia de la Generalitat Valenciana, for a grant. References and Notes (1) (a) Jenkins, J. H.; Stephens, T. W. Hydrocarbon Process. 1980, 60, 163. (b) Condon, F. E. In Catalysis; Emmet, P. H., Ed.; Reinhold Publishing Corp.: New York, 1958; Vol. VI, Chapter 2. (2) (a) Brouwer, D. M.; Hogeveen, H. Prog. Phys. Org. Chem. 1972, 9, 179. (b) Brouwer, D. M. In Chemistry and Chemical Engineering of Catalytic Processes; Prins, R., and Schuit, G. C. A., Eds.; Sijthoff and Noordhoff: Alphen aan Rijn, The Netherlands, 1980; p 137. (3) Brouwer, D. M. Recl. TraV. Chim. Pay-Bas 1968, 87, 1435. (4) Saunders, M.; Hagen, E. L.; Rosenfeld, J. J. Am. Chem. Soc. 1968, 90, 6882. (5) Olah, G. A.; White, M. J. Am. Chem. Soc. 1969, 91, 5801. (6) M. Saunders, P. Vogel, E. L. Hagen and J. Rosenfeld, Acc. Chem. Res. 1973, 6, 53. (7) (a) Baird, L.; Aboderin, J. Tetrahedron Lett. 1963, 235. (b) Idem. J. Am. Chem. Soc. 1964, 86, 262. (8) (a) Radom, L.; Pople, J. A.; Schleyer, P. v. R. J. Am. Chem. Soc. 1972, 94, 5935. (b) Kohler, H. J.; Lischka, H. J. Am. Chem. Soc. 1979, 101, 3479. (c) Clark, D. T.; Harrison, A. Chem. Phys. Lett. 1981, 82, 143. (9) Wiberg, K. B.; Kass, S. R. J. Am. Chem. Soc. 1985, 107, 988. (10) de Carneiro, J. W.; Schleyer, P. v. R.; Koch, W.; Raghavachari, K. J. Am. Chem. Soc. 1990, 112, 4064. (11) Carbo´, S.; Planelles, J.; Ortı´, E.; Viruela, P.; Toma´s, F. J. Mol. Struct. (THEOCHEM) 1987, 150, 33. (12) Frisch, M. J.; Head-Gordon, M.; Schlegel, H. B.; Raghavachari, K.; Binkley, J. S.; Gonzalez, C.; DeFrees, D. J.; Fox, D. J.; Whiteside, R. A.; Seeger, R.; Melius, C. F.; Baker, J.; Martin, R. L.; Kahn, R. L.; Stewart, J. J. P.; Fluder, E. M.; Topiol, S.; Pople, J. A. Gaussian 88; Gaussian: Pittsburgh, PA, 1988. (13) Frisch, M. J.; Trucks, G. W.; Head-Gordon, M.; Gill, P. M. W.; Wong, M. W.; Foresman, J. B.; Johnson, B. G.; Schlegel, H. B.; Robb, M. A.; Replogle, E. S.; Gomperts, R.; Anches, J. L.; Raghavachari, K.; Binkley, J. S.; Gonzalez, C.; Martin, R. L.; Fox, D. J.; DeFrees, D. J.; Baker, J.; Stewart, J. J. P.; Pople, J. A. Gaussian 92; Gaussian: Pittsburgh, PA, 1992. (14) For a discussion of the standard basis sets and procedure, see: (a) Hehre, W. J.; Radom, L.; Schleyer, P. v. R.; Pople, J. A. Ab Initio Molecular Orbital Theory; Wiley-Interscience: New York, 1986. (b) Hariharan, P. C.; Pople, J. A. Chem. Phys. Lett. 1972, 16, 217. (15) Schlegel, H. B. J. Comput. Chem. 1982, 3, 214. (16) Raghavachari, K.; Whiteside, R. A.; Pople, J. A.; Schleyer, P. v. R. J. Am. Chem. Soc. 1981, 103, 5649. (17) (a) Moeller, C.; Plesset, M. S. Phys. ReV. 1934, 46, 618. (b) Binkley, J. S.; Pople, J. A. Int. J. Quantum Chem. 1975, 9, 229. (18) Hariharan, P. C.; Pople, J. A. Theor. Chim. Acta 1973, 28, 213. (19) Krishnan, R.; Pople, J. A. Int. J. Quantum Chem. 1978, 14, 91. (20) (a) Franklin, J. L. In Carbonium Ions; Olah, G. A., Schleyer, P. v. R., Eds.; Interscience: New York, 1968; Vol. 1. (b) Lossing, F. P.; Semeluk, G. P. Can. J. Chem. 1970, 48, 955. (c) Solomon, J. J.; Field, F. H. J. Am. Chem. Soc. 1975, 97, 2625. (21) (a) Bittner, E. W.; Arnett, E. M.; Saunders, M. J. Am. Chem. Soc. 1976, 98, 3734. (b) Arnett, E. M.; Petro, C. J. Am. Chem. Soc. 1978, 100, 5408.
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