Response to “Comment on ‘A comparison of the efficiency of Fourier- and discrete time-path integral Monte Carlo’ ” [J. Chem. Phys.111, 7685 (1999)]

Quantitative molecular thermochemistry based on path integrals

The calculation of thermochemical data requires accurate molecular energies and heat capacities. Traditional methods rely upon the standard harmonic normal-mode analysis to calculate the vibrational and rotational contributions. We utilize path-integral Monte Carlo for going beyond the harmonic analysis and to calculate the vibrational and rotational contributions to ab initio energies. This is an application and an extension of a method previously developed in our group [J. Chem. Phys. 118, 1596 (2003)].

Bead-Fourier path integral molecular dynamics

Molecular dynamics formulation of Bead-Fourier path integral method for simulation of quantum systems at finite temperatures is presented. Within this scheme, both the bead coordinates and Fourier coefficients, defining the path representing the quantum particle, are treated as generalized coordinates with corresponding generalized momenta and masses. Introduction of the Fourier harmonics together with the center-of-mass thermostating scheme is shown to remove the ergodicity problem, known to pose serious difficulties in standard path integral molecular dynamics simulations. The method is tested for quantum harmonic oscillator and hydrogen atom (Coulombic potential). The simulation results are compared with the exact analytical solutions available for both these systems. Convergence of the results with respect to the number of beads and Fourier harmonics is analyzed. It was shown that addition of a few Fourier harmonics already improves the simulation results substantially, even for a relatively small number of beads. The proposed Bead-Fourier path integral molecular dynamics is a reliable and efficient alternative to simulations of quantum systems.