J. Phys. Chem. 1994,98, 5234-5239
5234
On the Question of Y-Aromaticity for Trimethylenemethane Dianion and Its Counterionic Stabilized Form, Triaminoammonia Dication, and Mixed Boron/Nitrogen Analogues Anne Skancke Department of Chemistry (IMR), University of Tromse, N-9037 Tromse, Norway Received: November 4, 1993; In Final Form: February 22, 19948
Conformational preferences for trimethylenemethane (TMM) dianion, LizTMM, and triaminoammonia (TAA) dication have been studied. Their energies relative their nonbranched analogues have been studied. The sixa-electron B-(NH2)3 and the two-r-electron N-(BH2)3 have been studied, and energy comparisons done by isodesmic reaction schemes involving BH(NH&, NH(BH2)2, and BH2NH2. For the hydrocarbon species, the G 2 level has been applied; other calculations are based upon HF(6-31G*) and MP2(6-31G*) data.
Introduction An intriguing, much discussed, but still controversial question is the thermodynamic stability of cross-conjugated systems compared to their linear analogues. Several decades ago, the facile formation of the isobutene dianion (in the form of its lithium salt) was pointed out by Klein and Brenner.’ Alternative synthetic routes have recently been d e ~ e l o p e d .The ~ ~ ~special stability of the guanidinium ion (which is inert to boiling water) has been noted by Gund, who attributed this and related observations for branched ionic systems to a special type of aromaticity, coined “Y-ar~maticity”.~N M R studies on substituted methylenemethane dianions supported the view of special stabilization.5 However, Klein has cast doubts on the importance of the role of Y-aromaticity claiming internal Coulombic stabilization to be the dominating factor. The concept of Y-aromaticity has been discussed by Agranat and Skancke: who on the basis of HartreeFock calculations considered the trimethylenemethane dianion (TMM2-) with six r-electrons and the corresponding dication with two r-electrons. They noted small but consistent values for stabilization energies of such systems compared to their linear analogues. This finding was in accord with experience from stabilities in solution7 and electrochemical studies.8 Computational studies applying larger basis sets, diffuse functions known to be important in the description of dianionsg and including correlation corrections did however make the stabilization marginal and on the limit of being significant.1° The whole concept of Y-aromaticity was later criticized by Frenking and co-workers,lI who found that the true minima of TMM2- (and also of butadien anion, BD2-) had pyramidalized methylene groups, and this slight modification of the geometry led to slightly less thermodynamic stability for TMM2- than for BD2-. Moreover, in a recent paper,l2 the application of standard diffuse functions for determining relative energies of isomeric dianions has been evaluated and found to depend critically upon the value of the orbital exponent. Resonance interactions for acyclic systems have been studied by Wiberg, who, on the basis of MP3/6-31 l++G**//6-31G* calculations of a number of branched systems and corresponding ions, rejects the notion of Y-aromaticity, claiming electronegativity effects to be the dominating factor. H e suggests the basisity of the guanidine to stem from hydrogen bonding of the conjugate acid to the s01vent.l~ This idea of hydrogen bonding had also been suggested by Sapse and Massa.14 Inagaki and co-workers have discussed the relative stabilities of conformers in a general way by considering the orbital phase criteria.I5 For the particular case of TMM2-vs BDZ-, the orbitalphase continuity principle should favor the former, which fulfills Abstract published in Advance ACS Absrrucfs, April 1, 1994.
0022-3654/94/2098-5234$04.50/0
the requirement of the donating orbitals being out of phase, the donating and ampting orbitals in phase and the accepting orbitals in phase. Since free dianions do not exist in solutions but are stabilized by counterions, the present work considers dilithium-stabilized dianions. LizTMM (dilithio-2-methylpropene or dilithium isobutene) has been considered by comparing it to the open-chain dilithium-stabilized butadiene analogue. The present work will focus on the stability, conformational preference, and degree of covalency of these salts. The concept of aromaticity is not limited to carbon chemistry. Among the second-row atoms one may also consider other systems with the general formula X(XH2)3z and X(YH& (where2 is the charge), some of which would have a suitable number of electrons for aromatic stability and could be expected to display a aromatic character provided the mutual orientations and the active orbitals aresuitable. This may be illustrated by the “neoclassical” B(BH2)3 and its dianion which recently have been studied.16 This dianion is isoelectronic with TMM2+and has been found to be most stable in the planar form, while for the neutral, the stability increases sequentially as the BHz groups are rotated out of the plane of the boron atoms due to hyperconjugation. The thermodynamic and kinetic stabilities of the system N(NH2)s (triaminoammonia, TAA) have been the topic of a recent article17 which considers also the other species within the series NH3, H z N - N H ~ HN-(NH&, , and N(NH2)3. Structural aspects of the related and possible aromatic dication N(NH2)3*+ were briefly discussed. This species was found to have a global minimum for a near-planar 0 3 form. The present paper will discuss this more fully, comparing the Y-shaped isomer to its corresponding linear form. Moreover, the present article discusses in some detail the thermodynamic stabilities of mixed boron-nitrogen compounds of the form X ( Y H Z )with ~ ~ X # Y.
Method of Calculation The GAUSSIAN 92 computer programL8 has been used throughout this work. The nature of the stationary points have been confirmed from analytic frequencies a t the HF/6-31G* level. Charges were analyzed by fitting to the electrostatic potential by the Merz-Singh-Kollman s ~ h e m e las~ implemented -~~ in the GAUSSIAN 92 program. Since the unsubstituted hydrocarbon systems trimethylenemethanelbutadiene dianions may be considered as the specimen test system for Y-aromaticity, particular care has been taken in the calculation of these dianions. The G2 method has been employed in the calculation of the free dianions. The G121 and G2 methods have been shown to be capable of predicting energy 0 1994 American Chemical Society
The Journal of Physical Chemistry, Vol. 98, No. 20,1994 5235
Y-Aromaticity for TMM2-
TABLE 1: Total Energies, n Denotes the Number of Imaginary Frequencies molecule SYm E(HF)/6-3 1G* n E(MP2)/6-31G* c2 -154.5497 0 -1 55.0940 e-BD2TMM2-
cs
BH3 H2B-NH2 HB-(NH2)2 B-(NH2)3 NH3 H2N-BH2 HN-(BHh N-(BH2)3 NH2NHNHNHz2+
D3h
TAA2+
Do
cz, cz, c,
9”
-154.5598 -26.3900 -8 1.489 1 -136.5683 -191.6380 -56.1844
Cz,
cz, &h
c2 c2
-106.78 14 -1 32.0602 -220.4133 -220.4237 -220.4437
0 0 0 0 0 0 0 0 0 1 1 0
n
G2
-154.5595 -26.4642 -81.73 12 -136.9718 -192.2014 -56.3542
0 0 0 0 0 0 0 0
-155.521 05 -155.458 45
-107.091 7 -132.4388 -221.0907 -221.1003 -22 1.1069
0 0 0 0 0
comment
see above transoid form cisoid form
Total Energies (atomic units) for Conformers I and I1 of Dilithium Isobutene and Dilithium Butadiene methcd/basis set system HF/6-31G* HF/6-3 1+G* MP2/6-31GS MP4/6-31GS QCISD/6-31G* -169.800 59 -170.343 84 -170.403 16 -170.381 96 dilithioisobutene,Li2TMM (I) (a) -169.795 47 -170.407 38 -170.38 54 -169.803 68 -170.351 16 DilithioisobuteneLi2TMM (11) (b) -169.798 06 -170.315 64 -170.373 75 -170.352 26 -169.763 38 -169.768 36 Dili-BD, Li2BD (c) E1 (kcal/mol) (c-a) 20.14 20.22 17.70 18.45 18.64 ,511 (kcal/mol) (c-b) 21.76 22.16 22.29 21.10 20.80 a The two bottom lines give the relative energies in kcal/mol. See text for complete description of basis sets.
TABLE 2
cs c2
ClC2Wc4.18O.W
CS (Isomer I)
C2 (Isomer 11)
c2
Figure 1. Calculated geometries for TMM*-, BD2-, LizTMM, and Li2BD. Numbers in parentheses from HF(6-3 1G*) optimizations,other numbers from MP2(6-31G*) optimizations. differences with an average absolute error of 2 kcal/mol or better. The G1 method assumes that corrections for diffuse functions, polarization functions, and higher order correlation corrections are mutually independent and involves the following steps: (1) Zero-point energy is calculated from analytical vibrational frequencies computed at the HF/6-31G1 and scaled by 0.893. (2) Equilibrium geometries are calculated at the MP2/6-31G* level (including core electron correlation). (3) The total energy is calculated a t the MP4/6-31G** level. This value is modified by corrections for diffuse functions (from an MP4/6-3 1l+G** computation), higher polarizations on nonhydrogens (MP4/63 1lG(Zdf,p)), correlation beyond fourth-order perturbation theory (QCISD(T)/6-31 lG**), and higher level contributions. The G2 procedure requires an additional MP2/6-311+G(3df,2p) calculation to take into account the nonadditivity of some of the basis set effects. The reader is referred to the original
articles for a complete description of the G1 and G2 procedures. Energy values are given in Tables 1 and 2.
Results and Discussion
TMM~/BDL.SystemsandRelatedLithium Salts. The stability of trimethylenemethane (“TMM2-”), has been analyzed by comparing it to the linear isomer trans-butadiene dianion (BDZ-). The transoid rather than the cisoid form was selected to avoid consideration of 1,4 interactionsof this system. For both systems, the lowest energy form has been selected for comparison, and energy minima have been verified by computation of analytical frequencies. The corresponding geometries and symmetries are given in Figure 1, and the energies are given in Table 1. As noted by Frenking and co-workers, the methylene groups are pyramidalized for both systems. The optimum geometry for TMMZhas C, symmetry, and the optimum geometry for the transoid
Skancke
5236 The Journal of Physical Chemistry, Vol. 98, No. 20, 1994
+0.37
-0.14 rO.40
r0.43
+0.40
Figure 2. Atomic charges calculated from the Merz-Kollman scheme at MP2(6-31G*) level.
BD2- species has C2 symmetry. As is seen from Table 1, the TMM2- system has the lower energy by about 6 kcal/mol at the H F level, while at the MP2 level of BD2- system is the more stable. To invoke diffuse functions and a t the same time correlation effects, calcualtions have been performed on the two dianions using the G2 method (see paragraph on computational procedures for details). At this very high level, the BDZ- system is the more stable by 39.3 kcal/mol. The finding that BD2- is more stable than TMM2- a t the MP2 level and more so at the G2 level is at variace with previous results, although increasing basis sets, invoking diffuse functions and applying correlation methods all favor the open-chain isomer more than the Y species. See ref 10. In solutions, these dianionic species do however not exist as isolated entities but as salts stabilized by counterions. Calculations have therefore been performed on dilithium salts of the dianions. Such salts have found wide use in synthetic chemistry,22 and their energetics and structures are therefore of general interest. The covalency vs ionic character of these salts is the point of interest in discussing the nature of these lithium compounds. In this connection the review by Setzer and Schleyer23 should be recommended as a comprehensive account of structural aspects of lithium compounds. The calculationson the dilithiated species have been performed at five different levels of sophistication: HF/6-31G*//6-3 1G*, HF/6-31+G*//6-31+G*, MP2/6-3 lG*/MP2/6-3 1G*, MP4/ 6-31G*/MP2/6-31G*, and QCISD/6-31G*/HF/6-31G*. Moreover, for the dilithioisobutene system, two different stable conformers have been found with structures given in Figure 1. At the HartreeFock level, no imaginary frequencies were found for the structures given in Figure 1. Absolute and relative energies are given in Table 2. As is seen in the table, the two conformers derived from TMM2- are quite similar in energy with form I1 (with the two lithiums on opposite sides of the carbon framework) being the slightly more stable one. This form corresponds to the
form reported by Wiberg24 and is the form favored by Coulombic attraction arguments. A similar structure has been computed for dilithiopr~pene.~~ The increased stability of such bridged structures has been interpreted by Streitwieser as being due to ionic (rather than multicenter) bonding.26 As shown in Table 2, the energy difference between the two isomers I and I1 is only a few kilocalories and is practically unaffected by the quantum chemical procedure and basis set. The degree of covalency may be judged from the changes as calculated from the Merz-Kollman scheme. These are given in Figure 2, which gives charges on the basis of MP2 calculations. The figure shows for these three species positive charged lithium atoms, a positive central carbon area, negatively charged peripheral carbon atoms, and positive hydrogen atoms. As is seen from the figure the “ion triplet” form (isomer 11), which is favored of the basis of electrostatic arguments, may be described as having mainly ionic bonding between the carbons and the metal. This is precisely what has been suggested in the above mentioned work by Streitwieser. Somewhat more unexpected is the rather high ionic character of isomer I. This species could be described as an Liz+ TMM- system, although covalent bonding is also present. It is instructive to compare the computed Li-Li distance (2.88 8, a t the HF level) and the corresponding frequency of this form (285 cm-1) with corresponding data of Liz and Liz+. At the same level the distances are 2.81 and 3.17 8, and the stretching frequencies 340 and 224 cm-l, respectively. Thus, on the basis of the frequency data, isomer I has 50% ionic character. The more stable of the dilithio-2-methylpropene salts is slightly more than 20 kcal/mol more stable than the butadiene salt at all levels of sophistication. The less stable dilithio-2-methylpropene salt is more stable than the butadiene salt by slightly less than 20 kcal/mol for all the applied levels. From the above data, the Y shaped dianion is not the more stable naked dianion form, but in the more realistic, counterionic
The Journal of Physical Chemistry, Vol. 98, No. 20, 1994 5231
Y-Aromaticity for TMM2-
M D W l l a O ) 120.M E W 110.0) ll0.W HlNlHh( llS.41) 111.11 n a ~ y i i r . r i 112.10 )
HSI(1BNl.( 0.0)14.18 IUNSSN14 100.0) 104.0 HlNlBNh(0.0)10.30
CI
m
C2V
8:”
1.481
&) c2v
D3h
Figure 3. Calculated geometries for aminoborane, HB-(NH&, B-(NH2)3, HN-(BH2)2, and N-(BH2)3. Notation as in Figure 1.
stabilized form, the dilithio-2-methylpropene salt is the more stable salt. It is worth noticing that the C2 form of the dilithio2-methylpropene compound may be regarded as being akin to the C2 form of o,o’-dilithiobiphenyl:
op Li system, and the C, form may be redrawn as a doubly bridged system:
For the biphenyl series, a doubly bridged system has been found (by MNDO calculations) to be more stable than the C2 form. The thermodynamic stability of both isomers of the dilithio salt is greater than the open-chain form. Concerning this latter species, it should be mentioned that no other stable form was found. E N Systems. Table 1 gives the energy of the boron-nitrogen species considered, and Figure 3 shows the computed structures for the most stable forms (all having zero imaginary frequencies). The charges are given in Figure 2. Aminoborane and related systems are in focus in the form of internal complexes in biological ~ystems.2~The parent aminoborane structure has been extensively analyzed previously, and its planarity has been established by various experimental methods,28 in accord with some degree of B-N A-bonding. For all the boron-nitrogen systems in this study, the length of this dative bond of about 1.40 A clearly shows a normal covalent bond with a bond order of about 1.O. The bonding scheme of this molecule has recently been analyzed from an electron propagator study29 where the planar minimum energy form has been compared to a 90° twisted form and a transition state with pyramidal nitrogen. Twisting the B-N bond results in a marked destabilization reflected in a lowering of the ionization potential
of from 11.29 to 9.02 eV of the top a (bl) orbital and a concurrent shift of the electron density from the bond to the nitrogen atom. In agreement with theVSEPR model, somestabilization is gained from pyramidalizing the nitrogen atom, but not sufficient to compensate for the lack of delocalization. Many-body perturbation28 theory gives a value of 32.9 kcal/mol for the nitrogen pyrimidalization. Thus, planar aminoborane is more stable than a nitrogen-pyramidalized form by this value, while planar ammonia is less stable than pyramidalized by 5.8 kcal/mol (experimental value).30 The HB-(NH& molecule is seen to have a structure very similar to HN-(BH2)2 with planar (2%symmetry. The lengthening of the B-N bond in these systems relative aminoborane may easily be understood in terms of less welectron density in these systems. In diaminoborane, two electrons are in a N - E N threecenter bond and two in a nonbonding orbital, while in HN-(BH2), there are only two A electrons available. The two triply substituted molecules are seen to display different structural properties. N-(BH2)3 has its two-a-electron system in a D3h form while the six-a-electron system B-(BH& shows a C, form with a planar heavy-atom framework. At the HF level, the molecule appeared planar, but MP2 optimization resulted in slight (about 15O) pyramidalization of all amino groups, the unique NH2 group being pyramidalized opposite from the two others. This structure is similar to the form of TMMZ- optimized by Frenking and co-workers for ref 11, but it should be pointed out that the pyramidalization is very much smaller in the case of triaminoborane. While for TMM2- the average value for the pyramidalization of the two different CH2 groups was 4 5 O , the amino groups in triaminoborane were found to be only about 1 7 O using the same computational level. Since there are no obvious linear isomers to these “mixed” species, relative stabilities may be studied from isodesmic reaction schemes. This procedure has been followed for the “mixed” and possibly Y-aromatic species B-(NH2)3 (with six-*-electrons) and N-(BHZ)~(with two a-electrons). Reaction schemes involving their less substituted analogues have been constructed. The series BH3, HzB-NHz, HB-(NH&, and B-(NH& may be considered as results of successive amination of BH3. From the energy data of Table 1 the reaction
5238
Skancke
The Journal of Physical Chemistry, Vol. 98, No. 20, 1994 D3h
D3
0
(1.009)
HNNN- (16.5) 18.0
(1234) 1.317
\
-
HN2N3H ( 9 . 3 1 ) X S
(1.021 )
158.82 1.029 117.67
i,027 NNN-(126.15) 123.97 NNNN I(169.13) 155.00
NNNN 4 4 . 8 2 ) -5.86 NNN 4123.7) 122.14
Figure 4. Calculated geometries for TAA2+ in the D3 minimum and D3h transition state, and cisoid and transoid N4H6*+. Notation as in Figure 1.
is exothermic by 5.99 kcal/mol at the H F level of theory and 6.89 kcal/mol at the MP2 level. Furthermore, the isodesmic reaction B(NH,),
H2BNH2
-+
+ HB(NH,),-BH,
isexothermic by 18.47 kcal/mol (HF) and 23.45 kcal/mol (MP2). From these data, it is clear that the triply substituted, Y-shaped and six 7-electron species is not stabilized relative to the other members of the homologue series. As a way to analyze the extent of the donation from the nitrogen to the boron lone pair
oa,
->B-
for the various members of the series, the charges have been calculated and are given in Figure 2, which shows the largest electron density at the aminoborane boron. Successive amination of aminoborane reduces the electron density on the boron atom corresponding to less donnation from each nitrogen. Within the seriesNH3, H2NBH2, HN(BH2)2, and N(BH2)3, the boron charge remains nearly constant, while the nitrogen charge is dramatically reduced to the vale of -0.12 electrons for N(BH2)3. This parallels the very long distance for this species. See Figure 3. The relative stabilities within the series NH3, H2NBH2, HN(BH2)2, and N(BH2)3 may be considered through the isodesmic reactions N(BH,), N(BHJ3
-+
-
2NH(BH2)2 - NHzBH2
H2BNH2 + HN(BH2)2 - NH3
The first reaction is found to be exothermic by 8.4 kcallmol by both applied methods and the last is isothermic by 16.70 kcal/ mol (HF) and 18.75 kcal/mol (MP2). Thus, from these isodesmic reactions, neither N(BH2)s nor B(NH2), is stabilized relative to their homologues. The absence of appreciable stabilization of N(BH2)3 and B(NH2)3 relative to their linear homologues is in line with the rationale formulated by Inagaki and Hirabayashi that in the case of B-N systems,
neighboring interactions rather than the number of electrons in conjugation is the dominating factor.31 N-( NH2)32+(TAA2+)and HzH-NH-NH-NHz*+. The chemistry of hydro nitrogens, apart from such familiar species as ammonia, hydrazine, and diimide, is little known. Conjugation in hydronitrogen chains and rings has been discussed in a paper by Inagaki and G 0 t 0 . ~In ~ ref 16 we discussed the Y-shaped TAA and suggested this to be kinetically stableand thus a possible target for synthesis. Despite a destabilizing electrostatic repulsions, hydrogen bonding was found to be a stabilizing factor. The dication of triaminoammonia, TAA2+,relieved from some of the repulsive forces, is a candidate for Y-aromaticity with its six a-electrons. Its structural aspects were reported in ref 16. The system was found to have a near-planar 0 3 symmetry with inplane nitrogens. Obviously, removing the lone-pair electrons from the central nitrogen of TAA would mean a substantial decrease in destabilizating forces. Comparison has been made between this dication and the cis and trans form of its linear isomer. As is reported in Table 1, the cisoid form has a lower energy than the transoid form, and the 6 kcal/mol energy difference is easily explained in terms of hydrogen bonding. As is shown in Figure 4, the terminal groups of the cisoid form are pyramidalized and oriented to maximize hydrogen bonding. A nonbonded H-N distance of 2.55 A compares well withdistancesof about 2.5 A found for a hydrogenbonded isomer of neutral triazane. The nitrogen framework is almost planar. There is a considerable lengthening of the central N-N bond resulting from the pertubational treatment, and the near-equal bond lengths indicate an even distribution of charge. The transoid form does not have any possibility for intramolecular hydrogen bonding and has the highest energy of the three isomers. The TAA2+ system has a minimum at a near-planar nonpyramidalized 0 3 form with a planar nitrogen framework. The hydrogens are twisted only 18O from planarity. According to Table 1 this form is the most stable NdH62+ form, but the allplanar (D3h) form is only 0.56 kcal/mol less stable. As was the case for the neutral TAA, a networkof hydrogen bonds stabilizes the structure of the dication. See the dotted lines in Figure 4. At the MP2/6-3 lG* level TAA2+is 4 kcal/mol more stable than the cisoid form and 10 kcal/mol more stable than the transoid form. The exact role of hydrogen bonding in explaining these
Y-Aromaticity for TMM2energy differences is not possible in estimating the reference models for the TAA2+, and the open chains are different. In conclusion, although TMM*- stabilized by counterions is found to be more stable than its nonbranched isomer, this work does not support the idea of Y-aromaticity as a general principle. It should be noted, however, that all energy differences relevant to that question are quite small, and one cannot exclude that another conclusion may be reached from more refined calculations.
Acknowledgment. I wish to thank the Norwegian Research Council for granting CPU time a t the Cray-YMP a t the SINTEF Supercomputer Center in Trondheim. References and Notes (1) Klein, J.; Brenner, S. J . Am. Chem. Soc. 1969, 91, 3094-3096. (2) Ludvig, M. M.; Lagow, R. J. J . Org. Chem. 1990, 55, 4880-4883. (3) Ludvig, M. M.; Kawa, H.; Lagow, R. J. Synth. Commun. 1990,20, 1657-1 664. (4) Gund, P. J . Chem. Educ. 1972, 49, 100-103. (5) Rajca, A.; Tolbert, L. M. J . Am. Chem. SOC.1985, 107,698-699. (6) Agranat, I.; Skancke, A. J . Am. Chem. SOC.1985, 107, 867-871. (7) Klein, J.; Medlik, A. Chem. Commun. 1973, 275-276. (8) Simmons, A.-M. M.; Mills, N. S.; Iyer, S. R. Inorg. Chim. Acta 1986, 116, 43-46. (9) Spitznagel, G. W.; Clark, T.; Chandrasekhar, J.; Schleyer, P. v. R. J. Comput. Chem. 1982,3,363-371. (b) Hehre, W. J.; Random, L.; Schleyer, P. v. R.; Pople, J. A. In Ab initio molecular orbital theory; Wiley: New York, 1986. (10) Agranat, I.; Radhakrishnan, T. P.; Herndon, W. C.; Skancke, A. Chem. Phys. Lett. 1991,181, 117-122. (1 1) Gobbi, A.; MacDougall, P. J.; Frenking, G. Angew. Chem., Int. Ed. Engl. 1991, 30, 1001, 1003. (12) Guerra, M. Chem. Phys. Lett. 1992, 197, 205-212. (13) Wiberg, K. B. J . Am. Chem. SOC.199O,II, 41774182.
The Journal of Physical Chemistry, Vol. 98, No. 20, 1994 5239 (14) Sapse, A. M.; Massa, L. J. J . Org. Chem. 1980, 45, 719-721. (15). (a) Inagaki, S.;Hirabayasi, Y . Chem. Lett. 1982, 709-710. (b) Inagah, S.;Kawata, H.; Hirabayashi, Y. Bull. Chem. SOC.Jpn, 1982, 55, 3724-3732. (c) Inagaki, S.;Iwase, K.; Goto, N. J . Org. Chem. 1986, 51, 362-366. (d) Iwase, K.; Inagaki, S. Chem. Lett. 1993, 1619-1622. (16) Skancke, A.; Liebman, J. F. J. Mol. Struct. 1992, 259, 411429. (17) Schlegel, H. B.; Skancke, A. J. Am. Chem. SOC.1993,115, 7465747 1. (18) GAUSSIAN 92, Revision C: Frisch, M. J.; Trucks, G.; Head-Gordon, W. M.; Gill, P. M. W.; Wong, M. W.; Foreman, J. B.; Johnson, B. G.; Schlegel, H. B.; Robb, M. A.; Replogle, E. S.;Gomperts, R.; Andres, 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, Inc.: Pittsburgh, PA, 1992. (19) Singh, U. C.; Kollman, P. A. J . Compur. Chem. 1984,5, 129-145. (20) Besler, B. H.; Merz, K. M., Jr.; Kollman, P.A. J . Comput. Chem. 1990, 11,431439. (21) Curtiss, L. A,; Jones, C.; Trucks, G. W.; Raghavachari, K.; Pople, J. J. Chem. Phys. 1990, 93, 2537-2545. (22) Stowell, J. C. Carbanions in Organic Synthesis; Wiley-Interscience: New York, 1979. (23) Setzer, W. N.; Schleyer, P. v. R. Adu. Organomet. Chem. 1985,24, 353-451. (24) See ref 13. (25) (a) Kost, D.; Klein, J.; Streitwieser, A,, Jr.; Schriver, G. W . Proc. Nail. Acad. Sci., U.S.A. 1982, 79, 3922-3926. (b) Schleyer, P. v. R.; Kos, A. J. Chem. SOC.,Chem. Commun. 1982,448450. (26) Streitwieser, A., Jr. Acc. Chem. Res. 1984, 17, 353-357. (27) Bodor, N.; Prokai, L. Int. J . Quantum Chem. 1992, 14, 795-805. (28) (a) Sugie, M.; Takeo, H.; Matsumara, C. J . Mol. Spectrosc. 1987, 123,286-292. (b) Gerry, M. C. L.; Lewis-Bevan, W.; Merer, A. J.; Westwood, N. P. C. J . Mol. Spectrosc. 1985,110, 153-163. (c) Thorne, L. R.; Gwinn, W. D. J. Am. Chem. Soc. 1982, 104, 3822-3827. (29) Ortiz, J. V. Chem. Phys. Lett. 1989, 156, 489493. (30) Swalen, J. D.; Ibers, J. A. J . Chem. Phys. 1962, 36, 1914-1918. (31) Inagaki, S.;Hirabayashi, Y.Inorg. Chem. 1982, 21, 1798-1805. (32) Inagaki, S.;Goto, N. J . Am. Chem. SOC.1987, 109, 3234-3240.
