Displaced-points path integral method for including quantum effects in the Monte Carlo evaluation of free energies

A semiclassical approximation was used for Monte Carlo quantum mechanical path integral calculation of free energies of molecules and generalized transition states. The approximation replaced sum over paths with the sum over points displaced from classically sampled points. Harmonic potentials were calculated by adjusting the displacements and using perturbation theory. Classical mechanical calculations were performed using double sampling.