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A general method for the direct evaluation of the temperature dependence ofthe quantum-mechanical reaction rate constant in many-dimensional systems isdescribed. The method is based on the quantum instanton approximation for therate constant, thermodynamic integration with respect to the inversetemperature, and the path integral Monte Carlo evaluation. It can describedeviations from the Arrhenius law due to the coupling of rotations andvibrations, zero-point energy, tunneling, corner-cutting, and other nuclearquantum effects. The method is tested on the Eckart barrier and thefull-dimensional H + H_2 -> H_2 + H reaction. In the temperature range from300K to 1500K, the error of the present method remains within 13% despite thevery large deviations from the Arrhenius law. The direct approach makes thecalculations much more efficient, and the efficiency is increased even further(by up to two orders of magnitude in the studied reactions) by using optimalestimators for reactant and transition state thermal energies. Which of theestimators is optimal, however, depends on the system and the strength ofconstraint in a constrained simulation.

Direct evaluation of the temperature dependence of the rate constant based on the quantum instanton approximation