Theoretical Analysis of the Rotational Barrier of Ethane YIRONG MO* ,† AND JIALI GAO* ,‡ Department of Chemistry, Western Michigan University, Kalamazoo, Michigan 49008, and Department of Chemistry and Minnesota Supercomputer Institute, University of Minnesota, Minneapolis, Minnesota 55455 Received March 6, 2006 ABSTRACT The understanding of the ethane rotation barrier is fundamental for structural theory and the conformational analysis of organic molecules and requires a consistent theoretical model to differenti- ate the steric and hyperconjugation effects. Due to recently renewed controversies over the barrier’s origin, we developed a computational approach to probe the rotation barriers of ethane and its congeners in terms of steric repulsion, hyperconjugative interaction, and electronic and geometric relaxations. Our study reinstated that the conventional steric repulsion overwhelmingly dominates the barriers. 1. Perspectives of Current Views on the Origin of the Rotational Barrier in Ethane The existence of hindered rotation about the carbon- carbon single bond is one of the most fundamental concepts in conformational analysis, and an understand- ing of its origin is of great interest. Modern quantum mechanical calculations can yield accurate results on relative conformational energies of organic compounds, and quantum chemical theory has provided fundamental insight into the nature of the torsional barrier. 1,2 However, surprisingly, there is still controversy in a seemingly simple problem that is presented in the very beginning of organic chemistry textbooks. A prototypical example is the hin- dered internal rotation about the C-C bond in ethane, first discovered by K. S. Pitzer in 1936, 3 who showed that only when an internal rotation barrier of about 3 kcal/ mol is taken into account could one obtain thermody- namic quantities in agreement with experiment. 4 The controversy is concerned with the origin of the rotational barrier in ethane, whether it is the result of stronger hyperconjugation stabilization of the staggered conforma- tion than the eclipsed form or the torsional barrier originates from greater steric repulsion in the eclipsed configuration due to electrostatic and Pauli exchange interactions. In this Account, we summarize recent studies that led to a consistent conclusion and present results from our laboratories and others, demonstrating that the internal rotational barrier in ethane is largely due to steric effects with modest contributions from hyperconjugation stabilization. The intuitive, steric repulsion theory was proposed in the early stages of theoretical chemistry, which remains a popular explanation in organic textbooks. 5 This theory suggests that the preference of the staggered structure of ethane over the eclipsed structure comes from reduced Pauli exchange interactions between the two methyl groups. On the other hand, hyperconjugation stabilization of the staggered conformation in ethane, owing to greater orbital overlap, provides another mechanism. 6-9 Here, the hyperconjugation effect refers to the vicinal interactions between occupied σ CH bond orbitals of one methyl group and virtual antibonding σ CH * orbitals of the other methyl group in ethane. Notably, Mulliken laid out a theoretical strategy to analyze hyperconjugative interactions, but he also cautiously predicted that “hyperconjugation in ethane should have little or no direct effect in restricting free rotation” because it is “only of second order”. 6 Brunck and Weinhold first showed that hyperconjugative interactions could be a dominant force responsible for the rotational barrier in ethane. In that work, they expressed molecular orbitals (MOs) as a linear combination of bond orbitals at the semiempirical level. 10 Subsequently, Bader et al. offered an alternative explanation, in terms of the polar- ization of charge density in the central carbon-carbon bond as a result of variations in symmetry. 11 On the basis of the natural bond orbital (NBO) method, 12 Goodman et al. 13-15 recently renewed the hyperconjugation idea 10,16 in a series of publications using a “flexing” analysis in terms of energies associated with structural, steric, ex- change, and hyperconjugative interactions during methyl rotation. Surprisingly, it was found that steric repulsion favors the eclipsed conformation, when σ CH - σ CH * hyper- conjugative interactions were removed in the calculation. 17 The intriguing results of ref 17 triggered additional investigations. 18-20 Bickelhaupt and Baerends evaluated the Pauli and electrostatic interactions explicitly using a zeroth-order wave function constructed from fragment MOs of methyl group. It was concluded that although hyperconjugation favors the staggered ethane conformer, Pauli exchange repulsions are the dominant force respon- sible for the rotational barrier in ethane. 18 This and subsequent calculations 18-20 suggest that hyperconjugative stabilization was overestimated in ref 17 due to the choice of localized orbitals that were not optimal. 17 However, Weinhold 21 analyzed the overlap contamination effect in these calculations, 18 using a four-electron destabilizing- interaction diagram. In this picture, the molecular orbitals * To whom correspondence should be addressed. E-mail: yirong.mo@wmich.edu (Y.M.); gao@chem.umn.edu (J.G.). † Western Michigan University. ‡ University of Minnesota. Yirong Mo received his B.S. in 1986 and Ph.D. in 1992 from Xiamen University (China) on the ab initio valence bond theory with Qianer Zhang. He was a DAAD Visiting Fellow with Paul Schleyer and a Humboldt Research Fellow with Sigrid Peyerimhoff in 1996-1997. In 1998, he joined the group of Jiali Gao as a research associate until 2001. After working as a computational biochemist at Xencor for 1 year, he moved to the Western Michigan University in 2002, where he is presently an Assistant Professor of Chemistry. He is also an Adjunct Professor at Xiamen University. Jiali Gao received a B.S. degree in chemistry from Beijing University in 1982 and a Ph.D. from Purdue University in 1987. After postdoctoral research at Harvard, he joined the faculty of the Chemistry Department at the State University of New York at Buffalo in 1990. He is currently Professor of Chemistry at the University of Minnesota. His research interests include computational enzymology, protein dynamics, and protein interactions. Acc. Chem. Res. 2007, 40, 113-119 10.1021/ar068073w CCC: $37.00  2007 American Chemical Society VOL. 40, NO. 2, 2007 / ACCOUNTS OF CHEMICAL RESEARCH 113 Published on Web 12/01/2006