ℏ 4 quantum corrections to semiclassical transmission probabilities.

The combination of vibrational perturbation theory with the replacement of the harmonic oscillator quantization condition along the reaction coordinate with an imaginary action to be used in the uniform semiclassical approximation for the transmission probability has been shown in recent years to be a practical method for obtaining thermal reaction rates. To date, this theory has been developed systematically only up to second order in perturbation theory. Although it gives the correct leading order term in an ℏ2 expansion, its accuracy at lower temperatures, where tunneling becomes important, is not clear.

Corrections to Semiclassical Transmission Coefficients.

The uniform semiclassical expression for the energy-dependent transmission probability through a barrier has been a staple of reaction rate theory for almost 90 years. Yet, when using the classical Euclidean action, the transmission probability is identical to 1/2 when the energy equals the barrier height since the Euclidean action vanishes at this energy. This result is generally incorrect.

Uniform Semiclassical Instanton Rate Theory.

The instanton expression for the thermal transmission probability through a one-dimensional barrier is derived by using the uniform semiclassical energy-dependent transmission coefficient of Kemble. The resulting theory does not diverge at the "crossover temperature" but changes smoothly. The temperature-dependent energy of the instanton is the same as the barrier height when ℏ = π and not 2π as in the "standard" instanton theory.

Coherent state representation of thermal correlation functions with applications to rate theory.

A coherent state phase space representation of operators, based on the Husimi distribution, is used to derive an exact expression for the symmetrized version of thermal correlation functions. In addition to the time and temperature independent phase space representation of the two operators whose correlation function is of interest, the integrand includes a non-negative distribution function where only one imaginary time and one real time propagation are needed to compute it. The methodology is exemplified for the flux side correlation function used in rate theory.