The barrier to the methyl rotation in Cis-2-butene and its isomerization energy to Trans-2-butene, revisited

We respond to the two questions posed by Weinhold, Schleyer, and McKee (WSM) in their study of cis-2-butene (Weinhold et al., J Comput Chem 2014, 35, 1499), in which they solicit explanations for the relative conformational energies of this molecule in terms of the Quantum Theory of Atoms in Molecules (QTAIM). WSM requested answers to the questions: (1) why is cis-2-butene less stable than trans-2-butene despite the presence of a hydrogen-hydrogen (H...H) bond path in the former but not in the latter if the H...H bond path is stabilizing? (2) Why is the potential well of the conformational global minimum of cis-2-butene only 0.8 kcal/mol deep when the H...H bonding is stabilizing by 5 kcal/mol? Both questions raised by WSM are answered by considering the changes in the energies of all atoms as a function of the rotation of one of the two methyl groups from the minimum-energy structure, which exhibits the H...H bond path, to the transition state, which is devoid of this bond path. It is found that the stability gained by the H...H bonding interaction is cancelled by the destabilization of one of the ethylenic carbon atoms which, alone, destabilizes the system by as much as 5 kcal/mol in the global minimum conformation. Further, it is found that the 1.1 kcal/mol stability of trans-2-butene with respect to the cis-isomer is driven by the considerable destabilization of the ethylenic carbons by 11 kcal/mol, while the changes in the atomic energies of the other corresponding atoms in the two isomers account for the observed different stabilities. The error introduced into QTAIM atomic energies by neglecting the virials of the forces on the nuclei for partially optimized structures is discussed.