A theoretical overview of adiabatic proton transfer to HCCH in the 1Σg+ ground and 1,3Au excited states

Journal of Molecular Structure (Theochem), 165 (1988) 353-363 Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands

353

A THEORETICAL OVERVIEW OF ADIABATIC PROTON TRANSFER TO HCCH IN THE %!&+GROUND AND ‘13Au EXCITED STATES

PETER S. MARTIN, KEITH YATES and IMRE G. CSIZMADIA Department of Chemistry, University of Toronto, Toronto, Ontario, M5S 1Al (Canada) (Received 19 August 1987)

ABSTRACT RHF-SCF 3-21G calculations are reported for the ‘Cc, 1-3B2,1-3Bu,lP3A and ‘*3AUstates of HCCH and the IA, and 1,3A” states of the classical C2H3 + : the equilibrium2electronic structure is qualitatively described in terms of Lewis/Resonance illustrations. The calculated proton affinities suggest that ‘A, and 3A, are of greatly enhanced basicity relative to ‘z:. Critical comparison is made with available theoretical and experimental results. INTRODUCTION

The dramatic changes in the acidity or basicity of an organic molecule that accompany photoexcitation are most conveniently rationalized in terms of the Fiirster equation [ 11, dpK=pI&+ -pKnn+ =Nh( VB-vBH+)/2.303RT, from which it follows that if the transition BH ++BH+* is red-shifted relative to B+B* (i.e., VB> VBH+ ) then B*/BH+* must be a stronger base/weaker acid than B/BH+ (i.e., pK*su+ > p&n+) and vice versa for a blue-shifted transition. However, for gaseous molecules the proton affinity (PA), defined to be -dI-&s for the reaction B + H+ +BH+ and for which LCAO-MO-SCF calculations provide the estimate PA (B ) SI EsCF ( B) - Escr (BH+ ) , rather than pK is usually employed in the measurement of acid/base processes. Although two independent investigations [ 2,3] concerning state dependent protonation of acetylene (HCCH) previously appeared in the literature, they were both lacking, in that non-correlating states were considered and no comparison with available experimental data was made: in view of the renewed interest [ 41 in this subject, a more comprehensive study has been undertaken. COMPUTATIONAL

DETAILS

Ab initio LCAO-MO-SCF calculations were performed utilizing the program MONSTERGAUSS [ 51, in conjunction with a GOULD 32/9705 minicomputer. The split valence 3-21G basis set [ 61, was employed in this study.

0166-1280/88/$03.50

0 1988 Elsevier Science Publishers B.V.

354

Proper spin eigenfunctions were obtained for all closed (ground) and open (excited) shell systems via Restricted Hartree-Fock (RHF) [ 71 theory. The geometry of the ground and low-lying excited states was energy optimized by the Optimally Conditioned (OC) [ 81 gradient-variable metric technique. All optimizations were terminated length, when the gradient where qi are the internal coordinates and the sum ].&?I = [zi(6E/~qi)2/N11’2, is over the N optimized qi, was reduced to below 5 x 10m4 mdynes and subject to the condition that all internal coordinate derivatives (6E/6qi) were less than 1 x 10m3 mdyne. This criterion generally yields structures within 1 x 10m4 A, or 0.01” of the true theoretical optimum values and energies stable below the p hartree level. Ground state geometries were taken as those predicted by the Valence Shell Electron Pair Repulsion Theory (VSEPR) [ 91. Starting covalent bond lengths were selected from a standard geometrical model [lo] based on Lewis/Resonance structures of the molecule in question. Low-lying excited states of both singlet and triplet multiplicity were assumed to be of valence type, arising from z -+ n* excitation and possessing planar bent structures. RESULTS AND DISCUSSION

The optimized geometries and total energies for ground and excited state HCCH are given in Table 1. The 3-21G predicted bond lengths for the ground state, r( CC) = 1.19 A and r( CH ) = 1.05 A, are in good agreement with the corresponding experimental [ 111 lengths of 1.20 A and 1.06 A. In Dab geometries the ground state ( ’ Cz ) molecular orbital (MO) configuration of HCCH is (la,) 2 (la,) 2 ( 20,) ’ ( 20,) 2 ( 30,) 2 (lx,) 4 and, as is well known, can be simply described in terms TABLE I RHF-SCF 3-21G energies (hartree) and optimized bond lengths (Bngstrijm) and angles (degree) for ground and excited HCCH State

r(CC)

r(CH)

LHCC

E SCF

‘CC % “B, 3A”

1.187 1.318 1.318 1.364 1.337 1.363 1.331 1.332 1.272

1.051 1.076 1.071 1.080 1.078 1.080 1.078 1.117 1.141

180.0 128.5 130.4 124.0 134.3 125.5 136.1 129.4 141.4

- 76.39596

"A* ‘A, l-42 ‘B, ‘B,

-

76.28867 76.27655 76.24765 76.23757 76.21565 76.20160 76.07262 76.02736

355

of a “sp-sp” hybridized framework with two mutually perpendicular II bonds. All the low-lying valence excited states are derived from the configuration ... (lZn,)” (ln,*)l, arising from rc,+np* excitation. More specifically these Frank-Condon states are obtained from the direct-product decomposition as ‘I7 x “l7, = 1*3ZU++ 1,3C; + ‘s3Au, some of which are predicted, on the basis of Wish’s rules [ 121, to be stabilized by cis and truns bending. Referring to the Walsh diagram for ground state HCC bending, given in Fig. 1, the doubly occupied 1~” MO is found to split into an in-plane 0 and an out-of-plane n component of symmetry species a, (a), b, ( n), b, ( a) and a, ( n) , the numerical and alphabetical subscripts differentiating between the CzVand Cab symmetry associated with cis and trans planar deformations respectively and the orbital energies being such that a, (0) > b, (n) and b,(a) c a,, ( 7~). Similarly, the virtual In,* MO separates into an in plane cr*and an out of plane rc*component of symmetry species b2( CT*), a2 ( n*) , up ( a*) and b, ( n*) . However, the orbital energies in this case indicate that while the former is greatly stabilized by both cis and tram bending, the latter exhibits negligible angular dependence, i.e., b,(o*)
r

1

TRANSK2h)

I

I

Hi

I

I

1

CIS K,,)

Fig. 1. Walsh diagram for In, and Is,* MO energies as a function of ‘Z: qualitative comparisons only).

HCC bending (for

356

An extensive ab initio study [ 131 employing the frozen core method in which all MO’s occupied in the ground state are taken unchanged from an SCF calculation predicted the energy ordering of the Frank-Condon states to be ‘Cl c”Zc,’ < 34, < 1,3C; < ‘d, < ‘C,’ , of which the o* states are strongly stabilized by ci.s and trans bending such that 31Bz(3Z,+ ) < 31B,(3C~) < 31A,(3~,) < 31A2(34,) and ‘lA,(‘C;) < ‘lAg(lZy) c ‘lBz(‘d,) c ’ lB, ( ‘A,), for which the reader is referred to Fig. 2, while the higher-lying and weakly bent x* states stabilize in a gauche (C,) conformation, achieved via where 32B(3~,) c~~A(~C;) and dihedral twisting to L HCCH = 90’) ‘2A (ld ) < ‘Zt (linear Rydberg state), i.e., for these states “32B,, ‘~~2&, ‘p32A,, and ‘,32A2 represent false cis and tram minima. Having gone unnoticed to the best of the authors’ knowledge, it is perhaps worth mentioning that HCCH (‘~~4,) is a Renner-Teller molecule [ 141, i.e., the degeneracy of the electronic state is split by nuclear deviations from linearity. More specifically, the state d, possesses a type (C ) Renner-Teller potential energy surface in which both components decrease in energy as the molecule is distorted and become two separate, non-linear equilibrium electronic states of the molecule. In this case 31Az and ‘l& are the lower components for cis bending, 31A, and ‘1B, being their counterparts for trans bending and 32B and ‘2A forming the upper components resulting from additional HCCH twisting. While both the Renner-Teller and the more familiar Jahn-Teller effect [ 151, applying to non-linear molecules in degenerate E or T electronic states, are due to vibronic interactions when a nonBorn-Oppenheimer molecule in a degenerate electronic state experiences an

1000 TRANSK2,)

1400

1800 H%

Cl s QJ)

Fig. 2. Angular potential curves for (r* states of HCCH (drawn to approximate scale for illustrative purposes only).

357

asymmetric normal coordinate distortion, there is no predictability in the case of the former. Although a positive Renner-Teller effect may result in a nontotally symmetric, normal coordinate deformation, a non-zero Jahn-Teller effect must result in there being at least one such coordinate which removes the electronic degeneracy and results in a non-linear equilibrium configuration. Subsequent to the aforesaid study, an in-depth analysis employing a double zeta plus polarization basis set (DZ + P) of contracted gaussians in conjunction with large scale self-consistent-field configuration interaction wave functions, comprised of spin and symmetry adapted configurations arising from all Hartree-Fock interacting single and double excitations (CISD) , was completed on the structures and energies of the singlet [ 161 and triplet [ 171 states of the planar bent o* manifold. It is important at this point to evaluate the performance of the less refined, fully variational single-configuration wavefunctions, obtained via RHF-SCF theory and which, out of both practical and economic considerations, form the basis of the present study. While the present results systematically underestimate the bond lengths on average by 0.02 A for ‘p3Au, ‘T~A~,and ‘,3B2 and 0.04 A in the case of 1*3BU, overestimate the bond angles by an average of 4” for 1*3A2,uand show a mean absolute deviation of only lo for 1’3B2,uwith respect to those reported in refs. 15 and 16, it is apparent that reasonable agreement is achieved. Further confidence in the RHF-SCF results is established when energy differences between corresponding geometrical isomers, i.e., states of the same multiplicity and configuration, differing only in the relationship (ck or tram) of the two H atoms, systematically underestimate the extensive CISD results on average by only 3 kcal mol-’ in three of the four cases; the exception being an unsatisfactory overestimation of 9 kcal mol-i in the case of lB isomers. However, due to the fact that ‘& ( C,,) and ‘B, (C&) states HCCH do not correlate with ‘A”( C,) states of C, H: and because this study concerns itself solely with adiabatic proton transfer, the discrepancy is of no consequence. Unfortunately, there is not enough known experimentally about excited valence states of HCCH to invite much comparison with theory. The most detailed investigation to date was performed twenty-five years ago by Ingold and King [ 181 who analyzed both the vibrational and rotational fine structure of the 2400-2100 A absorption and assigned the upper state as ‘lA,. On the basis of a large isotope shift they ascribed the observed progression to the bending vibrational mode and concluded that the excited state was tram bent, in addition to which they reported rotational constants, vibrational frequencies for both tram bending and CC stretching, the O-O transition energy of 120.6 kcal mol-1 as well as the geometrical parameters r( CC) = 1.38 A, r (CH) = 1.08 A and L HCC = 120”. Comparison with the predicted RHF-SCF geometry of r (CC ) = 1.36 A, r( CH) = 1.08 A and L HCC = 125’, while indicating excellent bond length agreement, is not as successful with regard to the L HCC, but is

nevertheless reasonable in terms of the errors associated with the method [ 191. Although subsequent investigations have determined the ‘Cc -+l lB, and 31B2+31A2 transition energies to be 154.7 [ 201 and 21.2 [ 211 kcal mol-’ respectively, no specifics concerning the structural parameters of these states have as yet been revealed. Despite the fact that present results account for approximately 94% of the ‘Cc + ’ lA, excitation energy, this increases to 149% and 151% for the ‘.Zc +’ lB, and 31B2+31A2 transitions, as favourable agreement is not expected for processes that involve electron unpairing or a change of symmetry as in the case of the latter. An important aspect that has been largely ignored until now, is the schematic representation of the electronic structure for the excited states in question. For the purpose of clarity, the electronic configuration for each of the symmetry types A,, AZ, B, and B2 will be subdivided into three components classified as core, framework and valence. For all types, the filled core and framework canonical molecular orbitals ( CMO’s) possess the occupancy (1~) 2 ( lb2,,) 2 and ( 2~,,~) 2 ( 2&J 2 ( 3~~,~)2 respectively, where the dual subscripts distinguish between CaV(cis) and Cgh( tram) symmetry. The valence CMO’s are unique to each individual case and are given in sequence for A,, A2, B,andB,as (3b,)2 (1%)’ (4o,)‘, (4~1)~ (I&)’ (3&)‘, (1~)~ (3&)’ (4~~)’ and (lb, ) 2 ( 4ul ) ’ ( 3b2) ‘. This having been accomplished, it is now possible to formulate a localized molecular orbital (LMO) description that can be represented schematically as a Lewis/Resonance structure. Taking the linear combinations l~~,~+ lb2,uand 3~~,~+ 2b2,”and the 2u, orbital allows for generation of the two C “Is” core, two “sp2-s” C-H bonding and “sp2-sp2” C-C bonding LMO’s respectively, thereby accounting for all the core and framework electrons. The remaining “sp2” LMO’s on each of the two C atoms and the rc bond can be derived from the valence orbital combinations la, ? 4u,, and 3b,, lb, 2 3b2 and 4u,, 3b, t 4u, and la, and 4u, ? 3b2 and lb1 in order for states of symmetry types A,, A2, B, and B2. The differences between 1p3B2,U and 1,3A2,U states, as far as the pictorial representation is concerned, result from their respective LMO occupancies of (n) 2 ( “sp2”) ’ ( “sp2”) ’ and (n) ’ ( “sp2”) 2 ( “sp2”) ’ (or equally (7c)’ (“Sp2”)1 (“sp2’y2). The Lewis/Resonance structures corresponding to the LMO description for the states ‘s3AU,‘s3A2,1*3BUand 1*3B2are given in Fig. 3, where the dashed line indicates a singly occupied x orbital. While it is thus proper to portray the lowest triplet (3B2) as a “cis vinyl biradical”, one must regard the lowest excited singlet ( ‘A,) to be zwitterionic-like (in that resonance contributors conveying charge separation can be drawn) as opposed [ 3,221 to a “tram vinyl biradical” appropriate to ‘B,. That the two valence LMO’s are not exactly nonbonding orbitals ( NBO’s) , but actually interact to form a weak bonding orbital (BO) and a slightly antibonding orbital ( ABO) , is evident from the fact that on average for the 1*3A2,U states r (CC) = 1.35 A, which is 0.03 A less than that calculated for benzene [ 231 thereby suggesting a bond order > 1.5. This is of

359 I + G

H-CEC-H

H

Hy=f

H

@q ..._ lH

/c-c\H H

‘*“A2 H

‘,3A”

Fig. 3. Lewis/Resonance structures for the ‘Z.$ , ‘*3B2,ls3Bu,‘*3A2and ‘*3A, states of HCCH and the ‘A, and ‘TEA fl states of C2H3 + .

no consequence for the 1*3B2,U states in which the 71orbital is doubly occupied, since the individually occupied BO and ABO would contribute nothing to the overall bond order of 2 and as such there is excellent agreement between the average r( CC) = 1.31 A and that predicted for ethylene (r( CC) = 1.31 A [ 231). This is also consistent with the small difference between the average L HCC associated with the four states 1’3B2,U(132 ’ ) however for 1’3A2,u (130” ) , one would predict, by the VSEPR model, an L HCC somewhat closer to 120” (associated with the repulsion of three full “ap2” orbitals) for the spatial rejection of two “sp2” BO’s and one “sp2” NBO containing an average of 1.5 electrons. While on the topic of geometries it is worth noting that the four cis states possess essentially the same average geometry as the trurw, i.e., with r( CC) = 1.33 A and L HCC’s of 132” and 130” respectively and that corresponding singlets and triplets deviate on average by only 0.01 A and lo, with the exception of the B, states with differences of 0.05 A and 11’. The vinyl cation (C,H,+ ) is particularly interesting in that it comprises the simplest carbocation with a possible classical or bridged structure. Both structures were previously subjected to unconstrained, analytic gradient optimization at the DZ + P SCF and CISD level of theory which predicted the classical bridged-energy difference to be - 5.0 and 0.6 kcal mol-’ respectively [ 241. An alternate study [ 251 employing a basis of comparative quality (6-31G*) in conjunction with second order Moller-Plesset perturbation theory for electron correlation, in the space limited to single and double substitutions ( MP2SD ) ,

360

ascertains the energy difference between the two optimized minima to be 4.6 kcal mol-l, calculated an activation barrier to rearrangement of only 0.4 kcal mol-’ and found the connecting transition state to closely resemble the classical structure. However, higher level, single point computations conducted on the previous structures [ 261, that include the effects of triple and quadruple substitution to fourth order and f polarization functions (MP4SDTQ/6311G*), suggests that the rearrangement barrier ultimately disappears and the classical structure becomes the transition state for H scrambling between the end and bridged positions. Although preliminary experimental results “clearly show the non-classical structure to dominate” [ 271 in the gas phase, the final word regarding the precise details is eagerly awaited. Due to the fact that the classical structure is more stable at the SCF level (the method presently employed) and that the Frank-Condon transition ‘A,+lA, is predicted [ 281 to occur at lower energy, i.e., 54.7 kcal mol-l as opposed to 150.6 kcal mol-’ for the bridged structure, only the classical C,H,+ will be considered in this study. The optimized geometries and total energies for the ground and excited C, Hz cation are presented in Table 2. The 3-21G calculated geometrical parameters for the ground state, r(CC) =1.26 A, r(C+-H) =1.07 A, r(C-H) =1.09 A and LHCC+=~~~“, closely mirror the corresponding DZ + P CISD bond lengths and angles of 1.28 A, 1.09 A, 1.10 A and 120”, thereby indicating that electron correlation has little effect on the predicted equilibrium geometry. In CzV geometries C&H,+ TABLE 2 RHF-SCF 3-21G energies (hartree) and optimized bond lengths (kgstrijm) for ground and excited C, H, + a

and angles (degree)

Parameter 1.260 1.086 1.086 1.068 120.9 120.9 180.0

LH,C,C, L H&C, L H&G

- 76.65577

E SCF

1.390 1.078 1.076 1.073 121.1 120.2 133.9 - 76.62167

“Geometrical parameters specified for the following structure:

“‘\,_,/“’ H/’ 2

2

1.396

1.077 1.074 1.075 120.1 120.3 139.4

- 76.59018

361

possess the ground state (‘A,) MO configuration (lai)’ (2~) (3~) 2 (4~1 )2 and can be simply described in terms of a “sp’-sp” hy(5o1)2 W2J2 (W2 bridized “cr” skeleton with a perpendicular “z” (lb,) bond and a vacant p ( 2b2) orbital located on the “sp” carbon bearing the formal positive charge. Although the lowest-lying valence, excited states are obtained from the configuration .. . (lb,) ’ ( 2b2) ‘, resulting from “n “+p excitation, because the virtual 2b, orbital is lowered in energy relative to the doubly occupied lb1 orbital upon HCC bending, the Frank-Condon states are consequently stabilized, in accordance with Walsh’s predictions, by the CzV-+C, symmetry reduction associated with the “sp2-sp”+“sp2-sp2” rehybridization, i.e., ‘v3A2(lbl x2b2) +1,3A”(lu” X 7~‘). A LMO representation of the equilibrium conformation for the relaxed ‘s3A” states (Fig. 3)) consisting of a “sp2-sp2” framework with a singly occupied ‘Y( u”) BO and “sp2” (a’ ) NBO, is compatible with an average r (CC ) z 1.39 Aand ~HCc~l37”. In Fig. 4 the energies of the ground and lowest-lying, valence excited states for HCCH and C,H,+ , i.e., ‘Cc, ‘F~A”,‘y3A2,‘y3BU,1,3J32and ‘AI, ‘p3A” respectively, are plotted relative to that for ‘Cc where, in the interests of clarity and convenience, enumerative symbology is adopted, e.g., HT 1’ denoting the lowest triplet state of C2H3+ etc. From casual inspection it is evident that the excited states of C,H,+ are red-shifted relative to those of HCCH and hence that HCCH* exhibits enhanced basicity. Considering only adiabatic proton transfer between the lowest directly correlating states S,( ‘Cz )+-+ HS, +(‘AI), T3(3A,)*HT1 +(3A”) andS,(‘A,)*HS, +(lA”) andevaluating the expression PA ( HCCH ) E EsCF ( HCCH ) - EsCF ( C, Hz ) , one obtains PA (So) z 163 kcal mol-’ and PA(T,) r PA( S,) ~2235 kcal mol-‘. Although exothermicities of this magnitude are quite common, owing to the instability of the proton (dH,r367 kcal mol-’ [29]), the changes resulting from excitation, dPA ( T3) E LIPA( S1 ) z 72 kcal mol-‘, are extraordinary in that they represent an approximate change in pK of 53 units! There are presently only two experimental results available and both lend support to the theoretical predictions outlined in the preceding paragraph. Recent mass spectroscopic measurements on HCCH have established [ 301 PA (So) = 153 kcal mol-‘, which upon being corrected for the differential zeropoint energy mainly associated with the two additional degrees of vibrational freedom present in C, H3’ and finite temperature, will be well within RHF-SCF uncertainties [ 311. While no evidence yet exists for excited state basicity enhancement in HCCH, it has been clearly demonstrated [ 321 in the case of symmetric, aliphatic alkynes, e.g., cyclodecyne and di-n-butylacetylene, that they undergo sensitized photochemical addition of acetic acid to produce enol acetates under conditions that they are otherwise thermally inert. In short, the present calculations together with the available experimental evidence seem to indicate that excited state basicity enhancement is an inherent characteristic of the acetylenic moiety.

362 - S4 -%_

200-

HCCH

s,

TTq

IOO-

L

L2-

2 z \ 0

_;

:

o-

so

TT

-T PA 163

235

-k

--State

CIE

PlGp

r

so

0

D..h ‘C’

TI T2

67

Cm

3Bpz

75

Cm

T3

93

Cal

36” 3AU

T4

99

C~V

3A2

SI

113

CZh

SZ

122

Czv

‘A” ‘AZ

Ss

203

Cm

‘BP

Se

231

CZh

‘6”

HCCH:

235

State --.--

AE

“IGp

r

HSo+

-163

Cpy

‘Al

H T,+

-142

Cs

‘d’

HS:

-122

Cs

‘A”

Fig. 4. RHF-SCF 3-21G energies for the ‘z:, 1,3Bz, 1s3Bu,‘p3A2and ‘*3Austates of HCCH and ‘Al and ‘*3Ar’ states of CpH, + with PA’s evaluated between the correlating states S,(‘c,‘)*HS, +(‘Al) andT,(3A,)t*HT, ‘(3A”) andS,(‘A,)++HS, +(lA”). ACKNOWLEDGEMENTS

Much gratitude is expressed to Dr. M.R. Peterson for helpful discussions and to the Natural Sciences and Engineering Research Council of Canada for continued financial support.

REFERENCES T. Forster, Z. Elektrochem., 54 (1950) 42. P.S. Martin, K. Yates and I.G. Csizmadia, Theor. Chim. Acta, 64 (1983) 117. G. Winkelhofer, R. Janoschek, F. Fratev and P. v. R. Schleyer, Croat. Chem. Acta, 56 (1983) 509. K. Yates, P. Martin and I.G. Csizmadia, Pure Appl. Chem., (1988), in press. Program MONSTERGAUSS, M.R. Peterson, R.A. Poirier, University of Toronto, 1981. The program incorporates the integral, SCF and analytic energy gradient routines for both UHF and closed shell RHF from GAUSSIAN 80, J.S. Binkley, R.A. Whiteside, R. Krishnan, R. Seeger, D.J. DeFrees, H.B. Schlegel, S. Topiol, L.R. Kahn and J.A. Pople, Carnegie-Mellon

363 University, 1980, in addition to automatic geometry optimization by the Optimally Conditioned (OC) method (ref. 8). The RHF open shell SCF is an extensively modified version of the program GSCF, S. Kate and K. Morokuma, Institute for Molecular Science, 1979. The RHF energy gradients were programmed following J.D. Goddard, NC. Handy and H.F. Schaefer III, J. Chem. Phys., 71 (1979) 1525 and S. Kato and K. Morokuma, Chem. Phys. Lett., 65 (1979) 19. 6 J.S. Binkley, J.A. Pople and W.J. Hehre, J. Am. Chem. Sot., 102 (1980) 939. 7 R. Carbo and 0. Gropen, Adv. Quantum Chem., 12 (1980) 159. 8 W.C. Davidon, Mathematical Programming, 9 (1975) 1. The routine used is described in W.C. Davidon and L. Nazareth, Technical Memos 303 and 306, applied Mathematics Division, Argonne National Laboratories, 1977. 9 R.J. Gillespie, Molecular Geometry, Van Nostrand-Reinhold, Princeton, NJ, 1972. 10 M.R. Peterson and I.G. Csizmadia, J. Mol. Struct. (Theochem), 123 (1985) 399. 11 W.J. Lafferty and R.J. Thibault, J. Mol. Spectrosc., 14 (1964) 79. 12 R.J. Buenker and S.D. Peyerimhoff, Chem. Rev., 74 (1974) 127. 13 D. Demoulin, Chem. Phys., 11 (1975) 329. 14 G. Herzberg and E. Teller, Z. Phys. Chem., B21 (1933) 410; R. Renner, Z. Phys., 92 (1934) 172. 15 H.A. Jahn and E. Teller, Proc. R. Sot. London, Ser. A, 161 (1937) 220. 16 S.P. So, R.W. Wetmore and H.F. Schaefer III, J. Chem. Phys., 73 (1980) 5706. 17 R.W. Wetmore and H.F. Schaefer III, J. Chem. Phys., 69 (1978) 1648. 18 C.K. Ingold and G.W. King, J. Chem. Sot., (1953) 2702. 19 L. Farnell, J.A. Pople and L. Radom, J. Phys. Chem., 87 (1983) 79. 20 P.D. Foo and K.K. Innes, Chem. Phys. Lett., 22 (1973) 439. 21 H.E. Hunziker and H.R. Wendt, J. Chem. Phys., 70 (1979) 4044. 22 Y. Inoue, Y. Ueda and T. Hakushi, J. Am. Chem. Sot., 103 (1981) 1806. 23 R.A. Whiteside, J.S. Binkley, R. Krishnan, D.J. DeFrees, H.B. Schlegel and J.A. Pople, Carnegie-Mellon Quantum Chemistry Archive, Carnegie-Mellon University, 1980. 24 T.J. Lee and H.F. Schaefer III, J. Chem. Phys., 85 (1986) 3437. 25 R. Krishnan,R.A. Whiteside, J.A. Pop1eandP.v. R. Schleyer, J. Am. Chem. Sot., 103 (1981) 5649. 26 J.A. Pople, Chem. Phys. Lett., 137 (1987) 10. 27 E.P. Kanter, Z. Vager, G. Both and D. Zajfinan, J. Chem. Phys., 85 (1986) 7487. 28 J. Weber, M. Yoshimine and A.D. McLean, J. Chem. Phys., 64 (1976) 4159. 29 CRC Handbook of Chemistry and Physics, 66th edn., CRC Press, Boca Raton, FL, 1986. 30 D.D. Wagman, W.H. Evans, V.P. Parker, R.H. Schumm, I. Halow, S.M. Bailey, K.L. Churney and R.L. Nuttall, The NBS Tables of Chemical Thermodynamic Properties, J. Chem. Ref. Data 11, Suppl. No. 2,1982. 31 W.J. Hehre, L. Radom, P. v. R. Schleyer and J.A. Pople, Ab Initio Molecular Orbital Theory, Wiley-Interscience, New York, 1986, Chap. 6. 32 K. Fuji@ K. Yamamoto and T. Shono, Tetrahedron Lett., 39 (1973) 3865.