Catastrophes, bifurcations and hysteretic loops in torsional potentials of internal rotations in molecules

Abstract

Three approaches to the calculation of torsional potentials V ϕ of internal rotations in molecules, namely rigid rotation, relaxed rotation and reaction path, are discussed. The rigid-rotation approach produces V ϕ Values that are anomaly free but insufficiently accurate in general. In systems in which the hindrances that impede the internal rotation can be relieved or entirely avoided at relatively low cost in energy by relaxation of the other degrees of freedom, catastrophe points and hysteretic loops may be present in the relaxed-rotation V ϕ. Although V ϕ obtained within the reaction-path approach are guaranteed to be continuous and to encompass all the relevant minima and transition states, they may possess bifurcation points. These anomalies all stem from the projection of the multivariate total energy U(R) onto the univariate V ϕ. Their presence in V ϕ of such simple systems as 2,6,2',6'-tetrabromobiphenyl and oxamide raises questions about the general validity and usefulness of the concept of torsional potentials.