Accurate fixed-node quantum Monte Carlo method

Abstract

A new method for fixed-node quantum Monte Carlo calculations is proposed in this paper. In contrast to the conventional fixed-node method, the present approach is able to calculate the total electronic energy of atoms and molecules up an arbitrary accuracy. We derived an eigenvalue expansion for the total energy of a system and proved that the energy calculated from the conventional fixed-node method is only the zeroth order approximation of the eigenvalue expansion. Using the present approach, with only a little addition of computer time (<1% of total CPU time), we can readily calculate the first, second, and higher order approximations. As illustrations, we have calculated energies of the zeroth, first, and second order approximations for the 1 1A 1 state of CH 2, 1A g ( C 4 h , acet) state of C 8, and ground state energies of H 2, LiH, Li 2, and H 2O molecules. The results show that it only requires the second order approximation to obtain up to 97% of the total electronic correlation energy for these systems, demonstrating that the present method is excellent in performance in regard to both accuracy and efficiency.