Abstract
By expanding Feynman path integrals in a Fourier series a practical Monte Carlo method is developed to calculate the thermodynamic properties of interacting systems obeying quantum Boltzmann statistical mechanics. Working expressions are developed to calculate internal energies, heat capacities, and quantum corrections to free energies. The method is applied to the harmonic oscillator, a double-well potential, and clusters of Lennard-Jones atoms parametrized to mimic the behavior of argon. The expansion of the path integrals in a Fourier series is found to be rapidly convergent and the computational effort for quantum calculations is found to be within an order of magnitude of the corresponding classical calculations. Unlike other related methods no special techniques are required to handle systems with strong short-range repulsive forces.
Highlights
Monte Carlo simulations[1] provide an extremely valuable method of determining the thermodynamic properties of complex interacting many-body systems
At best, when realistic intermolecular forces are used, Monte Carlo calculations provide information which can be compared with experimental results or used to supplant results for which experiments are unavailable
We are unaware ofany method which has been used to treat systems simultaneously having a large number of quantum degrees of freedom and potentials with strong repulsive cores. For such general systems the convergence difficulties associated with short interval approximations to path integrals imply a need to find alternative approaches to quantum statistical mechanics
Summary
Monte Carlo simulations[1] provide an extremely valuable method of determining the thermodynamic properties of complex interacting many-body systems. Using the short interval approximation, path integral methods have been successfully applied to a number ofsystems It has been noted[2] that systems with strongly repulsive short range interactions (such as Lennard-Jones forces) are poorly treated in the short interval approximation. We are unaware ofany method which has been used to treat systems simultaneously having a large number of quantum degrees of freedom and potentials with strong repulsive cores For such general systems the convergence difficulties associated with short interval approximations to path integrals imply a need to find alternative approaches to quantum statistical mechanics. In a recent noteS we reported a Monte Carlo approach to quantum Boltzmann statistical mechanics which utilized an alternative method of evaluating the required Feynman path integrals.
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