Critical comparison of approximate and accurate quantum-mechanical calculations of rate constants for a model activated reaction in solution

Abstract

Accurate quantum-mechanical calculations of rate constants for a model of reaction in solution are used as benchmarks for two approximate methods: variational transition-state theory with semiclassical corrections for reaction coordinate motion, and the path-integral centroid density method. The reaction model corresponds to a single solute coordinate coupled to a harmonic bath mode. When the harmonic frequency of the bath oscillator is sufficiently high, the results of the approximate methods agree well with the accurate quantum-mechanical ones. For the lowest-frequency bath oscillator considered, the agreement is not as good, but still satisfactory; the worst discrepancies are a factor of 2.0 for the centroid density methods and a factor of 3.3 for variational transition-state theory with semiclassical tunneling corrections. Applications of the approximate methods to models including up to ten bath oscillators indicate that a single bath oscillator provides a reasonable model of a converged harmonic bath.