J. Cioslowski et al., CATASTROPHES, BIFURCATIONS AND HYSTERETIC LOOPS IN TORSIONAL POTENTIALS OF INTERNAL ROTATIONS IN MOLECULES, Molecular physics, 91(3), 1997, pp. 413-420
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.