Comment on the rate of isomerization in molecules with a symmetric triple well potential

Abstract

The classical theory of the rate of unimolecular isomerization developed by Gray and Rice, and extended by Zhao and Rice, is applied to the calculation of the rate of isomerization in model systems which have linear symmetric triple well potentials. Two of these wells define equally stable isomers A and A′; the third well, which defines a less stable intermediate B, is positioned along the reaction coordinate between A and A′. The model system also has a state C which corresponds to conformations with energies greater than the barrier energy between A and B. Both ‘‘direct’’ conversion A→C→A′ and ‘‘indirect’’ conversion A→C→B→C→A′ are allowed by the dynamics of the system. Then the rate of isomerization A→A′ depends on the extent to which the intermediate state B modifies the flow of points in the system phase space, and it is the dynamics associated with that modification which is the major point of interest in our study. We find a straightforward relationship between the areas in the Poincaré surface of section for the model system associated with states A, A′, B, and C and the rate of isomerization, namely, the larger the ratio of areas of C to B the faster the transformation A→A′. We also find that the Zhao–Rice version of the classical theory of isomerization rate yields values in good agreement with those derived from trajectory calculations and from the reactive island theory of DeLeon and co-workers.