The Kinetics and Quantum Dynamics of Intramolecular Rearrangements in Highly Symmetrical Complexes: The Berry Pseudorotation

Abstract

Abstract It is known that the intramolecular rearrangement of the ligands in trigonal-bipyramidal (TBP) molecules (e.g. PF5) follows a scheme first proposed by Berry and termed the Berry pseudorotation (BPR). There are 20 isomers, which are interconnected by 30 BPR reaction paths. In this paper, the time evolution of a given initial state is treated based on a set of first-order kinetic equations as well as on the basis of state-to-state tunneling processes. The dynamic equations are solved analytically using the eigenvalues and eigenvectors of the reaction-path connectivity matrix. It is shown that in the kinetic case the populations of all isomers approach an equilibrium value pi (∞) = 1/20 while in the quantum case the individual isomers are never equivalent neither in time nor as time average. This fact is related to the strong regularity of the eigenvalue spectrum of the connectivity matrix for the reaction graph network. Consequently, pure quantum effects cannot be the basis for the occurrence of five equivalent ligands in PF5 (as was found experimentally).