12540
J. Phys. Chem. 1996, 100, 12540-12545
Nature of Barrier Forces in Acetaldehyde Ding Guo and Lionel Goodman* Wright and Rieman Chemistry Laboratories, Rutgers UniVersity, New Brunswick, New Jersey 08903 ReceiVed: January 18, 1996; In Final Form: April 30, 1996X
Natural bond orbital analysis of the internal rotation barrier in ground-state acetaldehyde carried out using HF 6-31G(d,p) wave functions shows that the largest barrier-forming energy terms are weakening of the C-C (σ) and methyl C-H out-of-plane bonds. The analysis rationalizes the weakening of the former (the largest single barrier-forming energy term) to arise from antibonding character introduced into the C-C bond by charge transfer involving bonding and antibonding Cme-Hip and adjacent C-Hald orbitals. Weakening of the Cme-Hop bond is more complicated: e.g., involving antibonding character obtained by charge transfer from both σ- and π-hyperconjugative orbitals. Pauli exchange repulsions are calculated to be unimportant sources of the barrier.
I. Introduction Despite a 60-year history of investigation, the origin of torsional barriers remains controversial. The seven-atom molecule, acetaldehyde, because of its simplicity (one less atom than ethane) and because it exhibits highly resolved microwave, infrared, and Rydberg spectra, has been studied nearly as intensely as the benchmark molecule, ethane. Its equilibrium conformation is the “eclipsed” geometry shown in Figure 1. Internal rotation of the methyl group leaves the molecule in the metastable staggered conformation. The definiteness of the near 400-cm-1 barrier height is largely due to analysis of well-resolved microwave and infrared spectra carried out by Hougen and colleagues,1 and this barrier has been well-simulated by ab initio calculation.2 Ab initio calculations have also revealed the importance of coupling between methyl torsional and out-of-plane aldehyde hydrogen wagging motions as a determinant for the barrier shape.3 Notwithstanding the certainty of the barrier form and height, the nature of the forces that produce the barrier remains unproven. In the widely accepted Hehre-Pople-Devaquet π-fragment model,4 the barrier arises from π interactions, i.e., from increased repulsion between filled methyl group π-like fragment orbitals and filled π orbitals in the CdO double bond, and from decreased attraction between methyl fragment orbitals and HOMO and LUMO π orbitals in the staggered conformation.4,5 Other suggestions for the barrier origin include Pauli repulsion forces between electron clouds in C-H bonds6 involving the CHme-CHald interaction at acetaldehyde’s metastable geometry (Figure 1), breaking of a weak covalent bond between the carbonyl oxygen nonbonding lone pair7 and the eclipsed methyl hydrogen, and dipole polarization effects on the methyl C-H bonds driven by the large CdO bond dipole.8 Recently, Goodman, Kundu, and Leszczynski (GKL)9 decomposed the barrier energy into σ and π components carried out at several ab initio calculation levels. They concluded that contrary to the π-fragment model, the π component ∆Vne(π) and the electron-repulsion interactions are antibarrier. For any attempted calculation level, the principal barrier-forming term is a decrease in magnitude of the σ component of the nuclearelectron attraction energy change, ∆Vne(σ) (Table 1). They further concluded that in order to understand barrier energetics, the multidimensional nature of the torsion (involving flexing X
Abstract published in AdVance ACS Abstracts, July 1, 1996.
S0022-3654(96)00182-7 CCC: $12.00
Figure 1. HF 6-31G(d,p) optimized geometries (in parentheses) for acetaldehyde equilibrium eclipsed and top-of-barrier staggered conformers. Higher order MP2 6-311G(3df,2p) optimized geometries (without parentheses) are also given for comparison.
of the molecular skeleton29) needs to be taken into account. In particular, if the principal flexing coordinate, C-C expansion (Figure 1) is ignored, then ∆Vne becomes antibarrier and electron repulsion (∆Vee, Table 1) changes to barrier forming. From this, they inferred that weakening of the C-C bond plays an important role in forming the barrier. Although GKL conjectured that the σ-energy change has its primary origin in the partial unmaking of this bond, between the methyl carbon and adjacent carbon atoms, they were unable to provide proof. Decomposition of the barrier energy components into symmetry classes does not preclude the possibility of a particular term in an antibarrier symmetry class from being the single dominant barrier-forming term, since the symmetry class energy © 1996 American Chemical Society
Barrier Forces in Acetaldehyde TABLE 1: Acetaldehyde Internal Rotation Barrier Partitioned into Symmetry Terms (cm-1) energy diffa
fully rigid C-C CH3 relaxed rotationb expansionc relaxedd
barrier 373 415 410 400 kinetic energy (∆T) A′(σ) -6321 -4213 -671 -4894 A′′(π) 5955 5495 5324 6444 ∆T(σ+π) -366 1282 -1389 1550 nuclear repulsion (∆Vnn) -4431 1658 -20 468 2160 electron repulsion (∆Vee) -692 3737 -18 010 6674 nuclear-electron attraction (∆Vne) A′(σ) 61 924 45 123 84 656 50 228 A′′(π) -56 062 -51 385 -44 380 -57 112 ∆Vne(σ+π) 5862 -6262 40 276 -6884 a Difference [HF 6-31G(d,p)] between staggered (180°) and equilibrium eclipsed (0°) conformers (Figure 1). b Methyl group rotated by 180° with all bond lengths and angles frozen at eclipsed conformer geometry. c Rigid rotation followed by C-C bond expansion to its length in the fully relaxed staggered conformer. d Methyl group C-H bond angles and lengths are allowed to relax to fully relaxed staggered conformer values, all other bonds frozen at eclipsed conformer geometry.
is a consequence of the totality of its terms. Thus, a total category energy can be far less significant than individual antagonistic terms. Although the electron-repulsion category is in toto antibarrier, an individual Pauli repulsion term could represent the single important barrier source. In addition, although the barrier itself is relatively insensitive to geometric relaxation, the energy decomposition reacts extremely sensitively. A reasonable explanation is that the fully relaxed geometries distribute strain effects among the most easily distorted degrees of freedom. Because relaxations do not cause barriers, barrier models based on rigid rotation frequently predict reasonable barriers (there are exceptions, however, e.g., dimethyl ether28), but they may not get the physics right. Weinhold and colleagues, in a series of papers, have shown how natural bond orbital (NBO) analysis localizes process energetics (including internal rotation) into chemical bonds.10-14 Further, the NBO interactions are themselves more energetically realistic than the large symmetry-decomposed potential energy terms. By utilizing this tool, we try to increase our understanding of the torsional barrier in ground-state acetaldehyde. II. Natural Bond Orbital Analysis NBO analysis employs wave functions which have been transformed into one-center (lone-pair) and two-center (bond) representations.10 The advantage of NBO analyses is that they provide insight into interactions between various parts of the molecule.12,14 The diagonal elements of the Fock matrix in an NBO representation represent the energies of localized bonds, antibonds, and lone pairs. Off-diaagonal elements represent bond-antibond, lone-pair-antibond, and smaller antibondantibond interactions. We dissect the barrier energy (the difference between staggered and eclipsed conformer energies)15 into several nonunique categories: bond and lone-pair energies, bondantibond and lone-pair-antibond interactions. Interactions involving Rydberg orbitals are not considered since these interactions have only a weak orientational dependence.12 Weinhold has shown how this kind of categorization represents a chemically appealing point of view, since the individual energy terms can be understood in terms of Lewis structures and orbital overlaps.14,16 Weinhold’s general conclusion is that changes in non-Lewis bond-antibond interactions represent the most
J. Phys. Chem., Vol. 100, No. 30, 1996 12541 TABLE 2: Principal Barrier-Forming Bond Energy Terms (cm-1) bonda
fully relaxed
rigidb rotation
C-Cc expansion
CH3d relaxed
C-Cme(σ) Cme-Hope C-O(σ)
2223 1100 340
50 1163 110
2127 1029 (-94)
(-127) 1095 108
a ∆ω (calculated from eq 1), the population-weighted natural bond orbital difference for the staggered and eclipsed conformers. Hop: outof-plane methyl hydrogen atom. Threshold: 100 cm-1. b-d See footnotes b-d, Table 1. e Total of Cme-Hop contributions is twice these values.
important term in forming internal rotation barriers, even though bond-antibond interactions are orders of magnitude less important than bond-bond interactions or the diagonal orbital energies.12,13 We will show, however, that in the case of acetaldehyde, the most important single barrier energy term involves a bond energy change. A. Calculations. The analysis employs a complete set of all-electron 6-31G(d,p) Hartree-Fock NBO interactions carried out at optimized geometries obtained at the same level. Since this calculation level satisfies the virial theorem, ∆E ) -∆T (Table 1), predicts a reasonable barrier, and reproduces the signs and orderings of higher level energy-symmetry decomposition calculations,9 it is expected to correctly describe the physics of the barrier. The number of Rydberg interactions are also relatively small for this basis set. The analysis was carried out at four geometries for the metastable staggered conformer: (1) the fully relaxed one shown in Figure 1; (2) rigid rotation in which the skeleton, skeletal hydrogens, and methyl group bond lengths and internal angles are all frozen at their values in the eclipsed conformer (except that the methyl hydrogens are rotated by 180°); (3) partially relaxed rotation where only the C-C bond distance in (2) is lengthened to its ultimate length appropriate to (1); and (4) partially relaxed rotation where only the methyl group in (2) is allowed to relax to the staggered geometry in the fully relaxed conformer. Much of the analysis was carried out by selective interaction deletions. The deletion procedure allows individual interactions as well as the skeletal geometry changes that accompany internal rotation to be probed, as discussed in considerable detail by Weinhold.11,13 The goal of this study is to define the major barrier sources, and in this context, we do not focus on accurate reproduction of the 1.1 kcal/mol barrier energy, which requires large basis sets and extensive correlation.2 Most computations were performed on the Hewlett-Packard 9000/735 processor in the High Performance Computation Project of the Rutgers Chemistry Department using the NBO 3.0 module in GAUSSIAN 94 software.17 Orbital plots utilized ORBPLOT18 linked to the GAUSSIAN NBO19 output and were adapted to our Silicon Graphics 1HX 4D/75 GTX work station. Geometry optimizations were carried out on the Cray C-90 processor at the Pittsburgh Supercomputer Center. B. Energetics. 1. Bond Energies. Table 2 shows the principal barrier-forming bond energy changes, ∆ω, accompanying the internal rotation. These have been obtained from the relation
∆ω ) SFS - EFE
(1)
where S and E represent NBO energies for the staggered and eclipsed conformers, respectively, and FS and FE are the corresponding NBO occupations. The largest barrier-forming term, by far, is the bond energy change involving σ electrons in the Cme-CCdO bond. Further, this bond energy change
12542 J. Phys. Chem., Vol. 100, No. 30, 1996
Guo and Goodman
TABLE 3: C-C and Cme-Hop Natural Bond Orbital Compositionsa composition (%) NBO
eclipsed
staggered
(2s) (2p) (total) (2s) (2p) (total)
36.74 63.09 47.73 26.48 73.37 52.27
36.49 63.34 47.70 26.39 73.47 52.30
(2s) (2p) (total) (1s) (total)
24.05 75.80 61.76 99.93 38.24
24.37 75.50 62.40 99.93 37.60
C-C CC)O Cme Cme-Hopb Cme Hop
a In terms of natural atomic orbital (NAO) contributions. b Hop: outof-plane methyl hydrogen atom.
Figure 2. Midbond C-C(σ) NBO contours for (a) eclipsed and (b) staggered (fully relaxed) conformers. The left contours are taken in the skeletal plane with the carbonyl carbon on the right; the right contours are perpendicular to the middle of the bond. Outermost contour is at 0.3, with each inner contour increasing by 0.005.
Virtually Vanishes for rigid rotation. It is only slightly affected by details of methyl group relaxation (compare columns 3 and 5 in Table 2), however. If FS is set equal to FE ) 2, then ∆ω ) 2222 cm-1, nearly unchanged from that calculated by eq 1, but if S is set equal to E, ∆ω is reduced to 2 cm-1. These results indicate that the barrier-forming C-C bond energy change does not arise from alteration of the C-C NBO population. That the polarization (slightly toward the methyl carbon) and natural atomic orbital (NAO) makeup are virtually unchanged between the eclipsed and staggered conformations is shown in Table 3. The C-C bond orbital contours are shown in Figure 2 for the midbond region. These contours illustrate the alteration of the σ-charge distribution in the fully relaxed staggered conformation, with consequent bond weakening. Another measure of the weakening is the 0.006-Å increased length (Figure 1) in the staggered conformation. Final confirmation for the lengthening effect is obtained by the partially relaxed rotation where the C-C bond alone is expanded to its length in the fully relaxed staggered conformer, with other geometric parameters remaining frozen. The bond energy then drops to close to the value found for fully relaxed internal rotation (Table 2). There is another important bond energy change involving the Cme-Hop bond; its magnitude is less than half of the dominant C-C bond term. Unlike the C-C bond, this bond energy change is insensitive to relaxation of the skeletal framework. It
TABLE 4: Oxygen Lone-Pair Energy Terms (cm-1)a lone pair
fully relaxed
rigidb rotation
C-Cc expansion
CH3d relaxed
O(n) O(σ)
709 176
917 329
879 250
898 176
a Calculated from eq 1; see footnote a, Table 2. b-d, Table 1.
b-d
See footnotes
is also insensitive to methyl relaxation (Table 2). In contrast to the composition invariance exhibited by the C-C NBO (Table 3), the highly polarized toward the methyl carbon CmeHop NBO undergoes nearly 1% increase in carbon atom population on going to the staggered conformer, suggesting that this bond is weakened in the staggered conformer primarily through increased polarization of the Cme-Hop orbital. For internal rotation models lacking C-C bond flexing, such as rigid rotation,20 the Cme-Hop bond energy change becomes the largest barrier-forming bond energy term (note that there are two terms, one for each out-of-plane hydrogen). The extreme sensitivity of the C-C bond energy to skeletal relaxation explains the sensitivity of the global energysymmetry decomposition found by GKL, to geometric relaxation. The origins of the C-C bond lengthening and Cme-Hop NBO alteration accompanying internal rotation are discussed in sections III and 3, respectively. 2. Lone-Pair Energies. The electronic structure of acetaldehyde is essentially described in terms of NBOs by four C-H, one C-C, and two C-O (one σ and one π) bonds and two localized lone pairs on the oxygen atom. These bonding and lone-pair NBOs account for 99.269% aand 99.292% of the electron charge in the eclipsed and staggered conformations, respectively. The two lone-pair orbitals are (1) a virtually pure py-nonbonding orbital (corresponding to the nonbonding orbital in formaldehyde) and (2) an s0.545px0.455 hybrid (x-axis nearly along the CdO bond). Both lone-pair orbitals are nonnodal in the skeletal plane and thus are classifiable in the acetaldehyde Cs point group as a′ symmetry σ orbitals. To avoid confusion, we will in accord with custom refer to the former as n, the latter as lone pair. The oxygen n and lone-pair energy changes, calculated by eq 1, are given in Table 4. The more important n lone-pair energy change is much smaller than the fully relaxed rotation C-C(σ) bond energy term in Table 2. Since it is relatively insensitive to relaxation, it becomes, after the Cme-Hop bond energy change, a significant barrier-forming term for rigid rotation. 3. Bond-Antibond Interactions. Bond-antibond interaction energies were estimated by an indirect procedure initiated by Weinhold.12 First, the difference between staggered and eclipsed conformer energies was calculated with the Fock matrix element, Fij* between the bonding (or lone-pair) NBO φi (occupancy near 2) and a virtually unoccupied antibonding orbital, φj* deleted,
∆E[Fij*del] ) ES[Fij*del] - EE[Fij*del]
(2)
(In eq 2, Fij*del denotes Fij* deleted). The barrier contribution energy (∆2E[Fij*del]) is defined as the difference between the barrier energy without deletion, ∆E(B) ) ES - EE, and the barrier energy calculated from eq 2, ∆E[Fij*del]
∆2E[Fij*del] ) ∆E(B) - ∆E[Fij*del]
(3)
Since φj* always lies above φi, these interactions are all stabilizing. There are three important barrier-forming interactions: the pair of σ-electron interactions, Cme-Hip/C-Hald* and C-Hald/Cme-Hip*, and Cme-Hop/C-O(σ)*, given in Table
Barrier Forces in Acetaldehyde
J. Phys. Chem., Vol. 100, No. 30, 1996 12543
TABLE 5: Principal Barrier-Forming Bond-Antibond Interaction Terms (cm-1) donor/acceptora
calcd barrierb
barrier contributionc
Cme-Hip/CC)O-Hald* CC)O-Hald/Cme-Hip* Cme-Hop/C-O(σ)* C-O(π)/Cme-Hop* Cme-Hop/C-O(π)*
-796 -564 -248 -53 208
1169 937 621d 426d 165d
a H and H ip op refer to in-plane and out-of-plane methyl hydrogen atoms, respectively; Hald, aldehyde hydrogen. b Barrier energy calculated by deletion of designated interaction. c Difference between fully relaxed barrier energy (without deletion) and barrier energy calculated in column 2. d See footnote e, Table 2.
Figure 4. Orbital contour diagrams showing overlap of acetaldehyde C-Hald bonding and Cme-Hip antibonding pre-NBOs as in Figure 3.
Figure 3. Orbital contour diagrams for acetaldehyde Cme-Hip bonding and C-Hald antibonding pre-NBOs (not orthogonal) in eclipsed (a) and staggered (b) conformations illustrating the more favorable bondantibond overlap for the eclipsed conformation. The contours are taken in the skeletal plane. Outermost contour is at 0.03, with each inner contour increasing by 0.01.
5. The first, at 1169 cm-1, only half of the C-C bond energy change found in section 1, represents the largest single bondantibond interaction contribution to the barrier. Figure 3a depicts the orbitals involved in this interaction for the eclipsed conformation, showing the significant favorable overlap (evidenced by the Fock matrix element ) 0.065 a.u). In contrast, the same C-Hald* antibond is plotted in Figure 3b with the Cme-Hip bond in the staggered geometry. The markedly decreased overlap exhibited for the staggered conformation (reducing Fij to 0.011 au) explains why this interaction, involving charge transfer from the methyl group into the C-Hald region, is an important barrier-forming interaction. Orbital contour diagrams shown for the conjugate C-Hald/ Cme-Hip* σ-electron interaction in Figure 4 illustrate similar decreased overlap on going to the staggered conformation. Figure 5 shows similar contour diagrams for the less important
Cme-Hop/C-O(σ)* interaction. These again illustrate more favorable bond-antibond interactions occurring in the eclipsed conformation. The two smallest interactions, C-O(π)/Cme-Hop* and CmeHop/C-O(π)*, are important in examining the preferred conformer stabilization predictions of the π-fragment model. In effect, the π-fragment model serves as an alias for these bondantibond interactions. The former interaction, involving charge transfer from the C-O(π) bonding orbital to the π-hyperconjugative Cme-H antibond, is more important. This barrierforming interaction, however, is less important than either of the σ interactions shown in Figures 3 and 4, and the sum of barrier-forming π bond-antibond interactions is far less than the σ sum (Table 5). The importance of the π-hyperconjugative bond-antibond interactions is not in their direct contributions to the barrier energy, since, as we have already pointed out, the sum of barrierforming π bond-antibond interactions is far less than the σ sum. This conclusion holds for both fully relaxed and rigid rotation descriptions of internal rotation. However, there is one crucial difference between the bond energy barrier contributions in the two descriptions. For fully relaxed rotation, the bond energy contribution is approximately equally split between C-C(σ) and Cme-Hop terms. For rigid rotation, it is virtually entirely in the latter term. The outcome is that the importance of π barrier-forming terms appears to strongly increase if skeletal relaxation is neglected. In effect, the π-fragment model has as a subrosa assumption, rigid rotation. We are left with lone-pair-antibond interactions. However, all of these energies are small, only the O(n)/C-Hald* term approaching 100 cm-1.
12544 J. Phys. Chem., Vol. 100, No. 30, 1996
Guo and Goodman TABLE 6: Effect of Bond-Antibond Interaction Deletion on C-C Bond Length (Å) r(C-C) deleted interaction
a
no deletion barrier-forming terms Cme-Hip/C-Hald* C-Hald/Cme-Hip* Cme-Hop/C-O(σ)* C-O(π)/Cme-Hop* Cme-Hop/C-O(π)* antibarrier terms Cme-Hip /C-O(σ)* Cme-Hop/C-Hald* C-Hald/Cme-Hop*
∆r(C-C)b
eclipsed
staggered
1.5032
1.5093
0.0061
1.5223 1.5208 1.5124 1.5131 1.5291
1.5108 1.5106 1.5098 1.5156 1.5335
-0.0115 -0.0102 -0.0026 0.0025 0.0044
1.5079 1.5032 1.5032
1.5291 1.518 1.5157
0.0212 0.0148 0.0125
a See footnote a, Table 5. b Change in C-C bond length upon internal rotation. See footnote a, Table 1.
methyl orbital to a C-O(σ) antibond (Figure 5), shows the least decrease in bonding overlap and has the smallest bond-stretching effect (Table 6). In summary, three interactions, all involving σ electrons, Cme-Hip/C-Hald*, C-Hald/Cme-Hip*, and Cme-Hop/C-O(σ)*, weaken the C-C bond upon internal rotation. IV. Conclusions
Figure 5. Orbital contour diagrams showing overlap of acetaldehyde Cme-Hop bonding and C-O(σ) antibonding pre-NBOs as in Figure 3.
In summary, the major bond-antibond interaction contributions to the barrier in acetaldehyde inVolVes σ-electron charge transfer. We show in the next section that these interactions play a fundamental role in the C-C bond weakening. III. C-C Bond-Weakening Causes The key to the C-C bond weakening can be found in the overlaps of not orthogonalized NBOs involved in the important barrier-forming bond-antibond interactions pictured in Figures 3-5. For the important Cme-Hip/C-Hald* interaction (Figure 3), the large bonding overlap in the equilibrium conformation becomes antibonding in the C-C bond region of the staggered conformation, with resultant bond weakening. In order to explicitly examine the effect of specific interactions on the C-C bond length, geometry optimization was carried out with the relevant Fock matrix element set equal to zero. The decrease in C-C bond length found by geometry optimizations for eclipsed and staggered conformations following deletion of the bond-antibond interaction (Table 6) confirms that bond weakening results from these interactions. The C-C length changes for all of the important interactions, both barrier and antibarrier, are also given in Table 6. All important barrier-forming interaction deletions (and some antibarrier ones) are active in determining the C-C bond length. Figure 4 shows that for the conjugate C-Hald/Cme-Hip* interaction, the bonding overlap in the equilibrium conformation is strongly reduced on going to the staggered one. Deletion of this interaction again shortens the bond (Table 6). Thus, a decrease in bonding overlap between Cme-Hip and C-Hald orbitals involving σ-charge transfer back and forth between Cme-Hip and C-Hald regions has the effect of lengthening the C-C bond. The third, relatively less important, interaction involving charge transfer from a bonding σ-hyperconjugative
NBO analysis of acetaldehyde internal rotation provides a connection between various ways of rationalizing the barrier. The confusing mix of previous ideas, e.g., energy partitioning, π-fragment interactions, dipole polarization, and O-H bonding effects, is reduced to a more unified picture. Steric (Pauli exchange) repulsions are calculated to be unimportant barrierforming terms.21 The picture of the barrier forces that emerges emphasizes the role of weakening of the C-C σ bond as well as that of the Cme-H π-hyperconjugative bond. The principal force behind the C-C bond weakening appears to be antibonding character induced by σ-electron transfer back and forth between Cme-Hip and C-Hald bonding and antibonding σ orbitals. The importance of these charge transfers is in accord with Weinhold’s general conclusion that bond-antibond interactions are a major source of internal rotation barriers.12,13 However, in acetaldehyde, the decreases of the C-C and CmeHop bond energies are calculated to be the most important barrier-forming energy terms. The former (the largest single barrier-forming term) involves σ electrons and validates GKL’s inference9 (obtained from non-region-specific global energysymmetry analysis) that σ-electron effects involving the C-C bond play an important barrier role. Thus, although strain effects do not cause the acetaldehyde barrier, they play an important role in defining the barrier forces. An application of these ideas is found in the 700-cm-1 propene barrier,24,25 nearly double that of acetaldehyde. NBO analysis (using the same HF 6-31G(d,p) basis set) shows that weakening of the Cme-C σ bond is again the largest barrierforming term. However, the weakening (i.e., ∆ω > 3300 cm-1)26 is much greater than for acetaldehyde. The nearly 0.01-Å lengthening of this bond accompanying propene internal rotation27 (compared to 0.006 Å for acetaldehyde) supports this conclusion. As in acetaldehyde, σ-charge transfer back and forth between bonding and antibonding Cme-Hip orbitals and C-H orbitals involving the bond adjacent to the methyl group appears to be the principal force behind the C-C bond weakening. In propene, these charge transfers are more pronounced, however.26 The π-fragment model also predicts from charge polarization effects a larger propene barrier than for acetaldehyde.4 How-
Barrier Forces in Acetaldehyde ever, in the case of propene, the NBO analysis indicates that the C-C bond σ effect outweighs the π terms. Steric repulsions, as for acetaldehyde, are calculated to be unimportant barrierforming terms.21 For both molecules, repulsion between the Cme-Hip bond and the adjacent C-H bond is found to be antibarrier. Acknowledgment. We thank Professor Frank Weinhold for lengthy discussions concerning NBO calculation procedures and analysis and for calculating the exchange repulsions. Support by National Science Foundation is gratefully acknowledged, as is a grant of C-90 computer time from the Pittsburgh Supercomputer Center. References and Notes (1) Kleiner, I.; Hougen, J. T.; Suenram, R. D.; Lovas, F. J.; Godefroid, M. J. Mol. Spectrosc. 1991, 148, 38. Kleiner, I.; Hougen, J. T.; Suenram, R. D.; Lovas, F. J. J. Mol. Spectrosc. 1992, 153, 578. Belov, S. P.; Tretyakov, M. Yu.; Kleiner, I.; Hougen, J. T. J. Mol. Spectrosc. 1993, 160, 61. (2) Leszczynski, J.; Goodman, L. J. Chem. Phys. 1993, 99, 4867. (3) (a) Goodman, L.; Leszczynski, J.; Kundu, T. J. Chem. Phys. 1994, 100, 1274. (b) Nino, A.; Munoz-caro, C.; Moule, D. C. J. Phys. Chem. 1994, 98, 1519. (4) Hehre, W. J.; Pople, J. A.; Devaquet, A. J. P. J. Am. Chem. Soc. 1976, 98, 664. (5) Dorigo, A. E.; Pratt, D. W.; Houk, K. N. J. Am. Chem. Soc. 1987, 109, 6591. (6) (a) Sovers, O. J.; Kern, C. W.; Pitzer, R. M.; Karplus, M. J. Chem. Phys. 1968, 49, 2592. (b) Pitzer, R. M. Acc. Chem. Res. 1983, 16, 207. (7) (a) Jorgensen, W. L.; Allen, L. C. J. Am. Chem. Soc. 1971, 93, 567. (b) Munoz-Caro, C.; Nino, A.; Moule, D. C. Theor. Chim. Acta 1994, 88, 299. (8) Hadad, C. M.; Foresman, J. B.; Wiberg, K. B. J. Phys. Chem. 1993, 97, 4293.
J. Phys. Chem., Vol. 100, No. 30, 1996 12545 (9) Goodman, L.; Kundu T.; Leszczynski, J. J. Am. Chem. Soc. 1995, 117, 2082. (10) Foster, J. P.; Weinhold, F. J. Am. Chem. Soc. 1980, 102, 7211. (11) Brunck, T. K.; Weinhold, F. J. Am. Chem. Soc. 1979, 101, 1700. (12) Wesenberg, G.; Weinhold, F. Int. J. Quant. Chem. 1982, 21, 487. (13) Reed, A. E.; Weinhold, F. Isr. J. Chem. 1991, 31, 277. (14) Reed, A. E.; Curtiss, L. A.; Weinhold, F. Chem. ReV. 1988, 88, 899. (15) The zero-point energy change is not believed to have a significant contribution.9 (16) Carpenter, J. E.; Weinhold, F. THEOCHEM 1988, 169, 41. (17) Frisch, M. J.; Head-Gordon, M.; Trucks, G. W.; Foresman, J. B.; Schlegel, H. B.; Raghavachari, K.; Robb, M.; 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, L. R.; Stewart, J. J. P.; Topiol, S.; Pople, J. A. GAUSSIAN 94; Gaussian Inc.: Pittsburgh, PA, 1994. (18) Obtained from Professor Frank Weinhold, Chemistry Department, University of Wisconsin. (19) Version 3.0: Glendening, E. D.; Reed, A. E.; Carpenter, J. E.; Weinhold, F. (20) Goodman, L.; Kundu, T.; Leszczynski, J. J. Phys. Chem. 1996, 100, 3026. (21) Pauli exchange repulsion calculations were carried out by Professor Frank Weinhold utilizing the procedure described by Bakenhoop and Weinhold22,23 on University of Wisconsin computer facilities. (22) Bakenhoop, J. K.; Weinhold, F. J. Chem. Phys. 1996, 104. (23) Bakenhoop, J. K.; Weinhold, F. J. Chem. Phys. 1996, 104. (24) Hollenstein, H.; Winther, F. J. Mol. Spectrosc. 1978, 71, 118. (25) Durig, J. R.; Guirgis, G. A.; Bell, S. J. J. Phys. Chem. 1989, 93, 3487. (26) Gu, H. Doctoral Dissertation, to be submitted to Rutgers University, 1996. (27) Kundu, T.; Goodman, L.; Leszczynski, J. J. Chem. Phys. 1995, 103, 1523. (28) Ozkabak, A. G.; Goodman, L. Chem. Phys. Lett. 1991, 176, 19. (29) Ozkabak, A. G.; Goodman, L. J. Chem. Phys. 1992, 96, 5958.
JP960182C
