CATASTROPHES, BIFURCATIONS AND HYSTERETIC LOOPS IN TORSIONAL POTENTIALS OF INTERNAL ROTATIONS IN MOLECULES

Three approaches to the calculation of torsional potentials V(phi) of internal rotations in molecules, namely rigid rotation, relaxed rotati on and reaction path, are discussed. The rigid-rotation approach produ ces V(phi) 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 poi nts and hysteretic loops may be present in the relaxed-rotation V(phi) . Although V(phi) obtained within the reaction-path approach are guara nteed to be continuous and to encompass all the relevant minima and tr ansition states, they may possess bifurcation points. These anomalies all stem from the projection of the multivariate total energy U(R) ont o the univariate V(phi). Their presence in V(phi) of such simple syste ms as 2,6,2',6'-tetrabromobiphenyl and oxamide raises questions about the general validity and usefulness of the concept of torsional potent ials.