The quantum Monte Carlo method : application to problems in statistical physics

Abstract

The diffusion Monte Carlo method for performing quantum calculations on many body systems is extended and applied to a number of areas of chemical physics. An ab initio quantum Monte Carlo procedure for simulating wave functions with nodal surfaces is presented. Some few Fermion problems are treated using this technique. A method for using the ground state wave function obtained from a diffusion Monte Carlo calculation to determine the vibrational spectrum of a molecular cluster is presented. Very accurate vibrational spectra can be obtained with this approach. Results of quantum Monte Carlo calculations on the water dimer and trimer using an improved intramolecular potential and the intermolecular potential of Reimers, Watts and Klein (1981) have been used to assign cluster spectra obtained from molecular beam experiments. It is demonstrated that the vibrational predissociation spectrum of a molecular cluster is sensitive to the details of the intermolecular potential and different surfaces may be tested by comparing calculated spectra with experimental results. The diffusion Monte Carlo method is applied to calculate the thermodynamic and structural properties of liquid ^He and solid molecular hydrogen. Importance sampling must be used if efficient bulk phase calculations are to be performed. When the spherical part of the interaction potential due to Buck et al. (1983) is used in diffusion Monte Carlo calculations on solid H₂ good agreement with experiment is found. Anisotropy may be important for this system at higher densities. Methods for using the diffusion Monte Carlo method to study the behaviour of systems at non-zero temperatures are developed. Improved high temperature approximations must be employed as initial conditions when systems with mixed "classical" and "quantum" degrees of freedom' are considered . The properties of neon gas and the water dimer are studied with this method.