J . Phys. Chem. 1994, 98, 2056-2061
2056
Ab Initio and Molecular Mechanics Calculations on the Inversion of C,to C2 Conformations of 1,3-CycIoheptadiene Neysa Nevins, Eugene L. Stewart, Norman L. AUinger, and J. Phillip Bowen' Computational Center for Molecular Structure and Design, Department of Chemistry, The University of Georgia, Athens, Georgia 30602 Received: September 13, 1993"
Ab initio calculations at the Hartree-Fock (HF) and second-order Maller-Plesset (MP2) levels have been carried out on 1,3-~ycloheptadienein an attempt to resolve previously determined conflicting experimental and computational results. Inversion barriers from the C, to the C2 structures were calculated at these levels of theory utilizing the 6-31G** basis set. Transition states and minima were located at all levels of theory and, at the HF level, verified through vibrational frequency calculations. Additionally, point calculations at the MP3 level were performed on the MP2/6-31G** stationary points using the same basis set. The HF result shows the C2 structure to be 2.5 kcal/mol above the C,, while the MP2 calculation finds both conformers to be nearly energetically equal, with the C2 lower in energy by 0.3 kcal/mol. The MP3/6-31G**//MP2/6-31G** results predict the C, structure to be 0.8 kcal/mol lower in energy than the C2 structure. The C, structure at the MP2 level is in excellent agreement with the available microwave and electron diffraction data. The HF energetic results agree with the molecular mechanics calculations and seem to confirm the electron diffraction and microwave determination of a C, structure, while the MP2 and MP3 energetic results allow for the possibility of the presence of a C2 structure, as evidenced by NMR data.
Introduction With the rapid advance of computer technology, the field of computational chemistry has grown enormously. As a tool, computational chemistry allows us to expand our knowledge of chemical structure and dynamics for compounds where there is currently no experimental data. These calculations have been among the most useful applications of theoretical chemistry since its introduction. Other significantuses of computational methods are to verify existing experimental data and to aid the experimentalist in the investigationof a particular system. As evidence of this significance,the case of 1,3-cycloheptadieneis presented. In this instance, ab initio and molecular mechanics calculations have been undertaken in an attempt to resolve conflicting experimental results. Additionally, other conclusions have been drawn that may lead to further experimental investigations. Current experimentaldata and computationalinformation seem to confirm the existence of a usemiplanar" C, conformation for 1,3-~ycloheptadiene,with the methylene at the c6 position out of the plane (see Figure 1). Supporting evidence for the C, conformer includeselectron diffraction,' microwavespectroscopy,2 ab initio MO theory utilizing small basis sets,3 and molecular mechanics calculations. However, in contrast to other experimental methods, nuclear magnetic resonance (NMR) spectroscopy results have been interpreted as indicating that the molecule is twisted about the diene region of the molecule, a C2 conformatione4 Although experiment seems to clearly indicate the presence of the C, conformation, it does not rule out the possible existence of a C2 structure also. The most recent electron diffracton structure was determined at room temperature in 1972 by Hagen and Traetteberg.1 They ruled out the possibility of the C2 conformer, citing that the experimental radial distribution function was incompatible with this model. The results are reported in Table 1. A microwave study by Avirah, Malloy,andCookZin 1979alsoseemedtoconfirm the presence of a C, structure. Using the C, model of Hagen and Traetteberg, they obtained good agreement between their measured and calculated moments of inertia (rotational constants) (see Table 2). Furthermore, they located a small second e Abstract
published in Adoance ACS Abstracts, January 1, 1994.
F i p e 1. Numbering scheme and
T
and w torsion definitions for 1,3-
cycloheptadiene. component of the molecular dipole moment, which they could confirm due to the presence of Stark lobes on both sides of the Q-branches in the spectrum. This second moment is consistent with the C, conformation. However, Avirah, Malloy, and Cook stated that the presence of a C2 form would be difficult to detect, requiring larger modulation fields for observation. Thus, both the electron diffraction and microwave experiments seem to confirm the presence of a C, conformer, but they do not definitively eliminate a C2 structure as a minor component. An NMR study by Crews in 1971 presented evidence for a twisted (C2) form of 1,3-cycloheptadiene.4 He determined J23 (see Figure 1) to be 6.89 Hz. Using the empirical evidence for seven-membered-ring structures in Table 3, he concluded that 1,3-cycloheptadienemust be twisted on the basis of the observed trends for cycloheptatriene4.5 (2a), thiepin-1,l-dioxide6.' (2b), and tropone*v9(2c). As the structures become more planar, the coupling constant for the HCCH torsion displayed in Figure 2 increases. These data, however, may not directly translate to cycloheptadiene-type systems. The energetics of the two conformers is a balance between the large angle strain due to the planar diene portion in the C, conformation and the increased torsional energy resulting from
0022-3654/94/2098-2056%04.5~/0 0 1994 American Chemical Society
Inversion of 1,3-Cycloheptadiene Conformations
The Journal of Physical Chemistry, Vol. 98, No. 8, 1994 2057
TABLE 1: Electron Diffraction, Molecular Mechanics, and ab Initio Comparison of Bond Distances and Angles for C, 1,3-Cycloheptadiene electron diffPe MM3(92)* diff RHF/6-3 1G** diff MP2/6-3 1G** diff 1.106 +0.014 CI-H 1.092 i 0.003 1.079 -0.013 1.085 -0.007 cz--c3 CI=G
c4-cs cS46
Cs-H
CICZC3 C7CIC2 HZWI 64
1.450 f 0.006 1.347 i 0.002 1.509 A 0.008 1.522 A 0.008 1.102
1.466 1.344 1.506 1.529 1.115
+0.016 -0.003 4.003 +0.007 +0.013
1.475 1.326 1SO6 1.529 1.088
+0.025 -0.021 -0.003 +0.007 -0.014
1.463 1.350 1.500 1.527 1.093
+0.013 +0.003 -0.009 +0.005 -0,009
129.1 129.1 117.5 63.9
128.7 129.9 115.8 59.6
-0.4
129.9 128.7 116.4 58.9
+0.8 -0.4 -1.1 -5.0
129.9 128.1 115.9 60.6
-1 .o -1.6 -3.3
+0.8 -1.7 -4.3
+0.8
All bond lengths are in angstroms (A), and all bond angles are in degrees. Both electron diffraction and MM3 bond lengths represent rs values and, therefore, should be longer than re values from ab initio results. The electron diffraction data are taken from: Hagen, K.; Traetteberg, M. Acta Chem. Scad. 1972, 26, 3643. The angle S is defined as the plane angle between the c&C7c6 and CSCSC~ planes. Q
TABLE 2 Microwave, Molecular Mechanics, and ab Initio Comparison of Moments of Inertia for the C, 1,3-Cycloheptadiene Conformer moments micro% RHF/ % MP2/ % of inertia“ waveb MM3(92) diff 6-31G** diff 6-31G** diff I, I,
147.797 150.664 1.9 147.310 -0.33 147.148 -0.44 153.271 151.332 -1.3 152.439 -0.54 153.106 -0.11 280.772 281.836 0.38 280.990 0.08 280.777 0.00
Zz
All moments of inertia are expressed in p A z . The microwave data are taken from: Avirah, T. K.; Malloy, T. B., Jr.; Cook, R. L. J. Chem. Phys. 1979, 71,2194.
TABLE 3 NMR Coupling Constants and o Torsions for Compounds 2a-c JQ a(expt1b) a(MM3)
Za
2b
ZC
5.5 40.5 i 2 21.8
7.0 22.8 28.8
8.2 0 0
The coupling constant J is expressed in hertz. a is expressed in degreesand is defined as in Figure 2d. Structures20 and 2c are measured by electron diffraction (ED). Structure 2b was measured by X-ray diffraction. Q
H
H
2a
2b
0
H
zc
Methodology For the ab initio results in this study, the Gaussian 9210 suite of programs was used mainly on a cluster of IBM RS/6000 machines. Optimizations were carried out a t the HartreeFock (HF) level of theory with the standard STO-3G and 6-31G** basis sets and the second-order Merller-Plesset (MP2) level with the 6-31G** basis set only. Additionally, point calculations a t the MP3 level were performed on the resulting MP2/6-31G** extrema utilizing the same basis set. All HF calculations were restricted Hartree-Fock calculations, and all M P calculations utilized the frozen core approximation. Stationary points were identified as minima or maxima on the basis of the frequency calculations. This verification was only possible a t the HartreeFock level due to inadequate available resources for frequency calculations a t the MP2 level. First, the inversion barrier of 1,3-cycloheptadiene was calculated at the HF and MP2 levels of theory through a reaction coordinate method. The reaction coordinate was that suggested by Burkert and Allinger in their MM2 study of this inversion surface.” This reaction coordinate is T as defined in Figure 1. The inversion barriers were calculated by rotation of this internal coordinatefrom-28.9 t 0 6 7 . 8 ~in incrementsof loo. Thisrotation essentially reproduced the inversion of the C, structure to the Cz structure. Once these inversion barriers were determined, minima were located on the surfaces by releasing constraints on a nearby conformation and allowing the structure to fully optimize. Transition states were determined in a similar manner by utilizing the H F force constants in the search. Transition states at the MP2 level also utilized the HF force constant matrix. Point calculations at the MP3 level were then performed on the MP2/ 6-31G** maximaandminima with thesamebasisset. All relative energies were not corrected by the zero-point energies since only the HF vibrational frequencies could be calculated. Lastly, the molecular mechanics inversion barriers were calculated on a Silicon Graphics IRIS 4D/3 lOGTX utilizing the MM2(92)I2and MM3(93)13 programs. The standard torsional driving algorithm of these packages was used, and the reaction coordinate was driven in the same manner as described above. The MM3 transition state was determined by performing a vibrational frequency calculation and examining the normal modes. The MM2 “transition state” was determined to be the structure along the potential energy surface with the highest energy, utilizing the dihedral angle driver option.
2d
Figure 2. Structures for cycloheptatriene(ZP), thiepin 1,l-dioxide(Zb),
and tropone (Zc). partially eclipsed hydrogens (of Cg and C7 in Figure 1) in the Cz conformation. If these forces are nearly equal, then both forms could exist. In this case, N M R would detect an average of the twist and semiplanar forms.
Results and Discussion Energetics. The results of the reaction coordinate method a t the different levels of theory are shown in Figure 3. Also included are the MM2(92) and MM3(93) results. As shown in this figure, the inversion barriers are continuous at all levels of theory which did not make the search for minima and transition states difficult. Minima and transition states were found on these surfaces, and
2058
4.75
P8
-
The Journal of Physical Chemistry, Vol. 98, No. 8, 1994
-
3.75
-
2.75
-
1.75
-
w
HFISTO-3G HF16-31G** M W 6 - 3 1G** MMZ(92) MM3(93)
#'
.....*.... .....*...* --*--
I
P\*',
i
\
8,
0.75
-0.25: -35
.
I
-15
.
I
5
.
I
25
-
I
45
.
I
1
65
Angle (Degrees)
Figure 3. Ab initio inversion barriers for 1,3-~ycloheptadiene.
the energy differences and absolute energies are displayed in Table 4 along with the MP3/6-31G**//MP2/6-3lG** results. Also listed in Table 4 are the 7 and w values as defined in Figure 1. At the H F level of theory and in the MM3 calculations, vibrational frequencies were calculated to verify minima or maxima. In the H F and molecular mechanics calculations, the C, structure is the global minimum, with the CZstructure being a local minimum 2.2-3.2 kcal/mol higher in energy. The transition states at the H F level are in agreement with that found in MM2-approximately 4.1 kcal/mol above the C, minimum. The MM3 result differs slightly and is about 5.3 kcal/mol above theglobal minimum. Thus, the HFand the molecular mechanics energetics seem to be in good agreement with each other. The energy difference between the C, and C;, conformations is in good agreement with the Saeb~rand Boggs result of 2.5 kcal/mol. Figure 3 and Table 4 also show the results of the MP2 inversion barrier. The results obtained using this method are inconsistent with those obtained by molecular mechanics and lower levels of MO theory. In this case, two minima and two transition states werediscovered. The first minimum (w = -15.6O) isa C1 structure similar in geometry to the C, structure but calculated to be 0.09 kcal/mol lower in energy. The second minimum (w = -40.2O) is the Cz structure which at the MP2 level is calculated to be the global minimum and a structure lying 0.24 kcal/mol lower in energy than the CIstructure. The first transition state (w = Oo) was found to be the C, structure which at the H F level was determined to be a minimum. The second transition state (w = 35.2') is the inversion transition between the Cl and the C2 conformations but lies significantly lower in energy than those at the H F level of theory (only 3.21 kcal/mol above the Cl structure). The results of point calculations at the MP3/6-31G** level on the MP2 geometries are illustrated in Table 4. These results show that further electron correlation has lowered the energy of the C, structure, resulting in an energy difference that favors the C, over the C2 conformation by 0.81 kcal/mol. Again, a switch in the minima has occurred, but the energy difference is still significantly lower than that obtained at the H F level (approximately 2.5 kcal/mol). A point calculationon the transition state at this level has also increased the barrier slightly to 3.27 kcal/ mol relative to the energy of the C, structure. The C1 conformer, found to be the lowest energy structure at the MP2 level, is slightly higher in energy (0.04 kcallmol) than the C, structure in the MP3/6-31G**//MP2/6-3 1G** calculations. With the inclusion of electron correlation, the 1,3-cycloheptadiene energetics is influenced more by the conjugated diene portion of the molecule. Specifically, the electronic energy contribution seems to play a role in reducing the energy of
Nevins et al. molecules containing gauche diene regions. For instance, in contrast to experiment,14 at most levels of theoryI5 cis dienes have been found to be energy maxima with the gauche conformers being energetically favored. This phenomenon also appears to be present in the MP2 and MP3 results of 1,3-cycloheptadiene, which contains a diene portion, particularly at the 0, -15.6, and -40.2O conformers. At thew = 0' conformation, which contains a cis diene moiety, the energy is at a maximum. At w = -15.6O, possessing a gauche diene portion, a minimum structure exists. The diene portion of this molecule is most gauche at the w = -40.2O conformation and, therefore, by the above reasoning, is the global minimum. In other words, as the diene region of 1,3cycloheptadienebecomes more twisted, the molecule is stabilized by the lowering of the electronic energy. The stabilization of the transition state at the MP2 and MP3 levels may also be due to this gauche diene portion, although the energy is primarily due to steric interactions of the methylene groups about carbons 6 and 7 (see Figure 1). Thus, unlike most dienes, conjugation in this molecule does not play a major role in its energetics until electron correlation is included. At lower levels of theory, steric effects seem to play the prominent role, giving results similar to those obtained by molecular mechanics. Compared with HF, MP2 and MP3 clearly stabilize the Cz conformer and thus lower the energy difference between the CZ and C, conformers. However, the MP2 calculation indicates the Cz form is lowered by 2.9 kcal/molcompared to HF, which favors the Czform over the C,by 0.3 kcal/mol. The MP3 calculations result in a Cz form lowered by only 1.7 kcal/mol compared to the H F result, favoring the C, conformation by 0.8 kcal/mol. This phenomenon is an example of oscillating energy differences between conformers and is often observed when calculations at the H F and higher levels of M~rller-Plessettheory are compared. Thus, if H F tends to overestimate these energy differences, MP2 will underestimate them, and vice versa. Higher levels of MallerPlesset theory (MP3, MP4, etc.) usually oscillateabout the actual energy difference and, in the limit, converge to this energy difference. Therefore, the true energy should occur between the H F and MP2 limits, usually closer to the latter. If this is the case for 1,3-~ycloheptadiene,the energy difference between the two minima may be overestimated by H F and underestimated by MP2, in which case the C, structure would be favored. The MP3 point calculations seem to validate this trend, with the C, conformer being preferred by 0.8 1 kcal/mol. These results suggest that inclusion of higher order correlation will result in an energy difference of about 0.2-0.5 kcal/mol, favoring the C, conformer. Utilization of higher levels of theory, though, may not be able to elucidate a true global minimum. Lastly, a Boltzmann distribution of conformers as described by Bowen et a1.16 is listed in Table 5. As shown, the H F and molecular mechanics calculations predict that the C, structure should be found almost exclusivelyin a mixture of all conformers. Incontrast, theMP2resultsshowthattheC1 andC2conformations should be found in a ratio of 40% to 60%. As illustrated in Table 4 and Figure 3, the MP2 barrier between the C, and C1 conformationsis almost negligible, and on the basis of the predicted zero point energy (approximately 0.2 kcalfmol), the C1 structure is probably well below the first vibrational level; therefore, the C, conformer will be considered the minimum and its abundance assessed to be 40% of the mixture. In the MP3/6-31G**// MP2/6-3 1G**results, the C,structurewould be theconformation in 80% of the mixture. It would seem that low-temperature NMR studies might be able to verify the inversion barrier if both the C, and C2 structures could be detected. However, if the two forms are interconverting over an approximately 3 kcal/mol barrier, it would be difficult to achieve a temperature sufficiently low to resolve the two conformers. If the H F and molecular mechanics calculations
Inversion of 1,3-Cycloheptadiene Conformations
The Journal of Physical Chemistry, Vol. 98, No. 8, 1994 2059
TABLE 4 T , w, Absolute, and Relative Energies from the ab Initio and Molecular Mechanics Calculations of Various Conformers of 1,3-Cycloheptadiene RHF/STO-3G
-30.6 0.0 -267.6186 0.000 -28.9 0.1 -270.8792 0.000 -29.2 0.1 -271.8360 0.334
9 wa
abs energy re1 energy RHF/6-31GS*
T
w
abs energy re1 energy MP2/6-31Gt*
T 0
MP3/6-3 1G**//MP2/6-31G**b MM2(92)
abs energy re1 energy abs energy re1 energy 7c
re1 energy MM3(93)
-10.2 -15.6 -27 1.836 1 0.244 -271.8933 0.037
-271.8934 0.000 -29.6 -0.8 0.000 -28.9 0.0 0.000
we T
u
TS
cz
42.8 -36.6 -267.6119 4.212 41.7 -35.6 -270.8724 4.23 1 42.8 -35.2 -27 1.83 14 3.207 -271.8882 3.267 41.2 -39.5 4.096 41.5 -37.5 5.330
68.4 -42.2 -267.6144 2.649 67.9 -40.7 -270.8751 2.560 73.4 -40.2 -271.8365 0.000 -271.8921 0.805 69.9 -44.2 2.190 71.1 -41.2 3.200
c1
C*
re1 energy and w are expressed in degrees. The absolute and relative energies are expressed in hartrees and kcal/mol, respectively. b ‘Iand w are the same as in the MP2/6-31GS* results. The structures calculated from both MM2(92) and MM3(93) were actually mirror images of those calculated ab initio. For this reason, T and w had the opposite sign as the Gaussian T and w. Thus, for comparison, the sign of the MM2 and MM3 values were changed. aT
TABLE 5 Conformational Boltzmann Distributions of 1,3-Cycloheptadiene Structures at 298 K RHF/STO-3G RHF/6-3 1G** MP2/6-3 1G** MP3/6-3 1G**//MP2/6-3 1G** MM2(92) MM3(93)
B
C*
c 2
98.9O 98.7 39.9 79.6 97.6 99.6
1.1 1.3 60.1 20.4 2.4 0.4
The distribution is expressedas a percentageof the total mixture and was calculated through a Boltzmann distribution as with: Bowen, J. P.; Reddy, V. V.; Patterson, D. G., Jr.; Allinger, N. L. J . Org. Chem. 19%8,
I
a
53, 5471.
are valid, then low-temperature N M R should observe only one conformation: the C, conformer. As further evidence of a mixture of the C, and C2 conformers, the Crews study4 reports a twist of approximately 20° for the diene portion, while the MP2 results indicate a twist of 40° for the Cz structure and Oo for the C, structure. An approximately equal mixture of C, and C2 structures, as indicated by the 40:60 ratio, respectively, for the conformers, would result in an average twist of about 20°. Whether one believes there is a C,, an average of C, and C2, or only a C2 structure depends on one’s interpretation of the available empirical evidence of ~ J H Hand ’ S experimental angles showing deviation from planarity. Structure. Once the minima and transition states were located, these structures were examined and compared with the available experimental data. The ab initio and molecular mechanics C, structures are shown in Table 1, where they are compared with electron diffraction data. The resulting moments of inertia from the computational study are shown in Table 2 and compared with the moments from the microwave study. Figures 4-6 illustrate the calculated C,, inversion transition state, and Cz bond lengths, respectively, and are compared with experimental data where available. Figures 7-9 report the bond angles of these same conformations, again, compared with experimental values when possible. As seen in Tables 1 and 2, the MP2 C, structure is in excellent agreement with both the electron diffraction and microwave results. Most of the errors in the calculated bond lengths are within the experimental error. In many cases, as expected, the
A Figure 4. Bond lengths (in angstroms) for the C, structure of 1,3-
cycloheptadiene.
WISTO-3G Wlb31G** Wb31G**
1.532 1.531
MMZ(92)
MM3 (93) 1.116 1.114
I
1.524
1.513
Figure 5. Bond lengths (in angstroms) for the inversiontransition state of 1,3-~ycloheptadiene.
bond lengths have been calculated to be slightly shorter than the experimental bond lengths. The exceptions are the C2-C3 and C1=Cz bond lengths, which are still close to or within the experimental error. The HF bond lengths are somewhat more
2060
The Journal of Physical Chemistry, Vol. 98, No. 8, 1994
r r
RHFISTO-3G RHF/6-3 1G** MPU6-31 G" MMZ(92) MM3(93)
Figure 6. Bond lengths (in angstroms) for the Cz structure of 1,3cycloheptadiene. OUl4-Rn
63.9 (12)
58.9
60.6
E.6
Nevins et al.
1
Electron Difhaction (rg) RHF/6-31G** MW6-3 1G**
116.1 115.6
MMZ (92) MM3 (93)
115.2
115.8
Figure 9. Bond angles (in degrees) for the C2 structure of 1,3cycloheptadiene.
with those reported in the diffraction study. Excellent agreement in the 6 plane angle (see Table 1 for definition of 6) was found between the MP2 and the experimental results. As shown in Table 2, the calculated moments of inertia are all in good agreement with the microwave results. The MP2 results are the most noticeable, being in error less than 1% for all of the moments. The HF structure is also in good agreement with errors less than 1%.
Conclusions
Figure 7. Bond angles (in degrees) for the C, structure of 1,3cycloheptadiene.
B
RHFISTO-3G RHFlb31G** MPU6-31G** MMz (92) m3 (93) 112.7
Figure 8. Bond angles (in degrees) for the inversion transition state of 1,3-~ycloheptadiene.
random in their errors with the most significant error, as expected, occurring in theconjugated portion of the ring. The MM3 results are in good agreement except for the C-H bond lengths and the central C2-C3 bond. The C-H bonds calculated by molecular mechanics and measured experimentally are rg,and because of anharmonicity, they are longer than the corresponding ab initio lengths (re). In all of the calculated results, the Cz-C3 bond is calculated to be somewhat longer than the experimental one. It would seem that this bond should indeed be longer due to ring strain in the C,conformer. Thus, it appears that the calculations reflect this strain while the experimental results do not. The bond angles are also shown and are in excellent agreement
Both Hartree-Fock and second-order Moller-Plesset calculations have been performed on 1,3-cycloheptadiene, utilizing the standard 6-31G** basis set. Point calculations have also been performed at the MP3 level on the resulting MP2 geometries. Inversion barriers were calculated and both minima and transition states were located at the HF and MP2 levels. On the basis of these energetic results, conformational Boltzmann distributions at 298 K were calculated for all levels of theory. At the HF level of theory, the C, conformer was dominant; a t the MP2 and MP3 levels, the C, and CZwere found to be in a ratio of 40 to 60 and 80 to 20, respectively, implying that both conformers should be present. Electron diffraction and microwave results indicate the presence of a lone C, structure. HF, MM3, and MP3/6-31G**//MP26-31G**resultsindicate thepresenceofbothaC,andC*structure with the C, structure as the lower minimum. As mentioned previously, though, the experimental results do not entirely rule out the presence of a Cz structure. Finally, the calculated structures of the C,, transition state, and CZare reported and compared to experimental data where available. The results for the C, structure showed excellent agreement between the MP2 structure and both microwave and electron diffraction data.
References and Notes (1) Hagen, K.;Traetteberg, M. Acru Chem. Scund. 1972, 26, 3643. (2) Avirah, T. K.; Malloy, T. B.,Jr.; Cook, R. L. J. Chem. Phys. 1979, 71, 2194. (3) Saebo, S.; Boggs, J. E. THEOCHEM 1982, 87,365. (4) Crews, P. 0. Chem. Commun. 1971, 11, 583. (5) Traetteberg, M. J . Am. Chem. Soc. 1964, 86,4265. (6) Williamson, M. P.; Mock, W. L.; Castellano, S.M. J. Mugn. Reson. 1970. 2. -sn. . . -, -, -. (7) Ammon, H. L.; Watts, P. H.,Jr.; Stewart, J. M.; Mock, W. L. J . Am. Chem. SOC.1968, 90,4501. (8) Bertelli, D. J.; Andrews, T. G., Jr.; Crews, P. 0.J. Am. Chem. SOC. 1969, 91, 5286. (9) Ogasawara, M.; Iijima, T.; Kimura, M. Bull. Chem. Soc. Jpn. 1972, 45, 3277. (10) Gaussian 92, Revision B. Frisch, M. J.; Trucks,G. W.; Head-Gordon,
M.; Gill, P. M. W.; Wong, M. W.; Foreman, J. B.;Johnson, B.G.; Schlegel, H. B.;Robb, M. A.;Replogle,E.S.;Gompcrts,R.;Andres, J.L.;Raghavachari,
Inversion of 1,3-Cycloheptadiene Conformations 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. (11) Burkert, U.; Allinger, N. L. J. Comput. Chem. 1983,$40. (12) TheprogramMM2(92), which isanextendedbut otherwiseunchanged version of MM2 (Allinger, N. L.; Yuh, Y. QCPE Newsletter 1980,IZ,399, is available from the Quantum Chemistry Program Exchange, Department of Chemistry, University of Indiana, Bloomington, IN 47401,and from Tripos Associates, Inc., 1699 South Hanley Road, Suite 303,St. Louis, MI 63144. (13) The program MM3(93) is available from the Quantum Chemistry Program Exchange, Department of Chemistry, University of Indiana,
The Journal of Physical Chemistry, Vol. 98, No. 8, 1994 2061 Bloomington, IN 47401,and fromTripos Associates, Inc., 1699South Hanley Road, Suite 303,St. Louis, MI 63144. (14) (a) Carreira, L.A. J. Chem. Phys. 1975,62,3851.(b) Mliller, G.; Gneuss, K. D.; Kriemler, H.-P.; Scott, A. I.; Irwin, A. J. J. Am. Chem. Soc. 1979,101,3657. (c) Fisher, J. J.; Michl, J. J. Am. Chem. Soc. 1987,109, 1056. (15) (a)Bock,C. W.;Panchenko,Y.N. THEOCHEM1989,187,69.(b) Alberts, I. L.; Schaefer, H. F., 111. Chem. Phys. Lett. 1989,161, 375. (16) Bowen, J. P.;Reddy, V. V.; Patterson, D. G., Jr.; Allinger, N. L. J. Org. Chem. 1988,53,5471.
