Quantum chemistry by random walk: Importance sampling for H+3

Abstract

The use of importance sampling with the random-walk method of solving the Schrödinger equation in a way devised by Ceperley is examined in its application to determining the electronic energy of ground state H+3. The improved method yields energies of higher accuracy than prior random-walk or variational calculations. The required computation effort remains large for high accuracy but might be reduced by improved trial wave functions used in importance sampling. For the equilateral triangle configuration with side length of 1.6500 a.u., the calculated total energy is −1.3439±0.0002 a.u. This value lies below the upper bound of −1.34335 a.u. established in the lowest-energy variational calculations by Salmon and Poshusta and above their estimate of −1.3447 a.u. as the true value. Energies calculated for four other nuclear configurations of interest in determining the vibrational frequencies of H+3 are found to be, typically, 0.001 to 0.003 a.u. lower than those of the most accurate variational calculations, but relative values of the energies are probably less accurate than those of the variational calculations.