1 8 A pr 2 00 6 Path integral evaluation of the kinetic isotope effects based on the quantum instanton approximation

A general method for computing kinetic isotope effects is described. The method uses the quantum-instanton approximation and is based on the thermodynamic integration with respect to the mass of the isotopes and on the path-integral Monte-Carlo evaluation of relevant thermodynamic quantities. The central ingredients of the method are the Monte-Carlo estimators for the logarithmic derivatives of the partition function and the delta–delta correlation function. Several alternative estimators for these quantities are described here and their merits are compared on the benchmark hydrogen-exchange reaction, H+H2 →H2+H on the Truhlar–Kuppermann potential energy surface. Finally, a qualitative discussion of issues arising in many-dimensional systems is provided.