<title>Regular and anomalous torsional splitting patterns: a trend in ethane-like molecules and general perspectives</title>

Abstract

It is shown that torsional Coriolis coupling can alter the torsional splittings in molecules with hindered internal rotation. Splitting patterns that would occur in the absence of any vibrational contribution to the torsional angular momentum, with reference to a molecular axis system (IAM), are called regular. It is shown that different sets of vibrational coordinates, corresponding to vibrational states with different splitting patterns, can be defined for modes normal to the internal rotation axis. The forms of normal coordinates appropriate to basis vibrational states with regular and inverted splitting patterns are identified. It is found that in normal coordinates appropriate to vibrational states with regular torsional splitting patterns, the relative orientation of the displacements of pairs of atoms belonging to different molecular moieties is independent of the internal rotation angle, and relative displacements normal to the internal rotation axis can be cis or trans at any conformation. On the contrary, in normal coordinates appropriate to vibrational states with inverted torsional splitting patterns the relative orientation of such displacements changes by π(cis-trans interchange) upon half the internal rotation converting two neighbor equivalent conformations (as in a staggered-eclipsed conformational conversion). The formation of the actual torsional splitting patterns in degenerate vibrational states of CH₃CH₃-type molecules depends on the joint effect of torsional Coriolis and head-tail coupling. The torsional Coriolis operator can tune pairs of levels to resonance for the action of typical head-tail coupling operators (torsion-dependent vibrational operators), depending on the values of the torsional Coriolis coefficients, generating vibrational states with either regular or inverted torsional splitting patterns and affecting the splitting magnitude. It is shown that operators with a sin3τ-type torsional dependence favor the formation of inverted splitting patterns. In less symmetric molecules torsional Coriolis coupling affects the torsional splitting patterns by the same mechanism as in CH₃CH₃-type molecules, but the torsion-dependent operators are different and their action is expected to be less effective. Typical anomalous perpendicular splitting patterns can be predicted for non-degenerate modes localized in a single molecular moiety, normal or with a component normal to the internal rotation axis, having fixed orientation in that moiety (as the C=O or C-H stretchings of acetaldehyde). Adopting a barrier-hindered torsional basis, where the lower torsional levels can be seen as vibrational states with quantum numbers v_τexhibiting tunneling splitting, one finds that all operators generating matrix elements with Δv_τ=±1, or in general odd, work toward the formation of inverted splitting patterns, generating anomalous patterns.