The ethane rotational barrier and wave function analysis

1 The ethane rotational barrier and wave function analysis 

Simple yet important mechanistic cases concern the computation of rotational barriers around single bonds. A timely case in point is the rotational barrier of ethane, an old yet much debated subject [27, 28]. While the notion of hindered rotation in ethane is often 

In the ethane case, however, the AIM analysis helps in understanding the overlap of the bonds and the location of the electrons as derived from the density picture, but it does not tell us anything about the origin of the rotational barrier. For that, we need methods that quantitatively give us energies that can be associated with the effects of donor-acceptor bonding (hyperconjugation) and electron-electron repulsion (Pauli repulsion) as noted above. 

A simple and robust quantitative MO-type approach (as opposed to density approaches) is the ubiquitous Mulliken population analysis [40]. The key concept of this easily programmed and fast method is the distribution of electrons based on occupations of atomic orbitals. The atomic populations do not, however, include electrons from the overlap populations, which are divided exactly in the middle of the bonds, regardless of the bonding type and the electronegativity. As a consequence, differences of atom types are not properly accommodated and the populations per orbital can be larger than 2, which is a violation of the Pauli principle a simple remedy for this error is a Lowdin population analysis that 

The results of a valence bond treatment of the rotational barrier in ethane lie between the extremes of the NBO and EDA analyses and seem to reconcile this dispute by suggesting that both Pauli repulsion and hyperconjugation are important. This is probably closest to the truth (remember that Pauli repulsion dominates in the higher alkanes) but the VB approach is still imperfect and also is mostly a very powerful expert method [43]. VB methods construct the total wave function from linear combinations of covalent resonance and an array of ionic structures as the covalent structure is typically much lower in energy, the ionic contributions are included by using highly delocalised (and polarisable) so-called Coulson-Fischer orbitals. Needless to say, this is not error free and the brief description of this rather old but valuable approach indicates the expert nature of this type of analysis. 

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