Toward understanding the nature of internal rotation barriers with a new energy partition scheme:: Ethane and n-butane

On the basis of an alternative energy partition scheme where density-based quantification of the steric effect was proposed [Liu, S. B. J. Chem. Phys. 2007, 126, 2441031, the origin of the internal rotation barrier between the eclipsed and staggered conformers of ethane and n-butane is systematically investigated in this work. Within the new scheme, the total electronic energy is decomposed into three independent components, steric, electrostatic, and fermionic quantum. The steric energy defined in this way is repulsive, exclusive, and extensive and intrinsically linked to Bader's atoms in molecules approach. Two kinds of differences, adiabatic (with optimal structure) and vertical (with fixed geometry), are considered for the molecules in this work. We find that in the adiabatic case the eclipsed conformer possesses a larger steric repulsion than the staggered conformer for both molecules, but in the vertical cases the staggered conformer retains a larger steric repulsion. For ethane, a linear relationship between the total energy difference and the fermionic quantum energy difference is discovered. This linear relationship, however, does not hold for n-butane, whose behaviors in energy component differences are found to be more complicated. The impact of basis set and density functional choices on energy components from the new energy partition scheme has been investigated, as has its comparison with another definition of the steric effect in the literature in terms of the natural bond orbital analysis through the Pauli Exclusion Principle. In addition, profiles of conceptual density functional theory reactivity indices as a function of dihedral angle changes have been examined. Put together, these results suggest that the new energy partition scheme provides insights from a different perspective of internal rotation barriers.