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

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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.