Quantum chemistry by random walk: Higher accuracy

Abstract

The random walk method of solving the Schrödinger equation is extended to allow the calculation of eigenvalues of atomic and molecular systems with higher accuracy. The combination of direct calculation of the difference δ between a true wave function ψ and a trial wave function ψo with importance sampling greatly reduces systematic and statistical error. The method is illustrated with calculations for ground-state hydrogen and helium atoms using trial wave functions from variational calculations. The energies obtained are 20 to 100 times more accurate than those of the corresponding variational calculations.