An internal coordinate quantum Monte Carlo method for calculating vibrational ground state energies and wave functions of large molecules: A quantum geometric statement function approach

Abstract

An internal coordinate quantum Monte Carlo (ICQMC) method using importance sampling is illustrated for a 100 atom model polyethylene chain. Importance sampling with an internal coordinate guiding wave function yields smoother, more physically reasonable wave functions and lower ground state energies than Cartesian importance sampling, in good agreement with normal coordinate analysis results. A novel geometric statement function (GSF) method for economizing expressions involving first and second derivatives of stretch, bend, and torsion internal coordinates by up to 2 orders of magnitude allows QMC calculations to be performed even for large molecules in reasonable times on standard workstations. The ICQMC method with quantum GSF is eminently suitable for large molecules with complicated, strongly coupled potential energy surfaces such as polymer chains.