A Investigation of Exact Quantum Monte Carlo Methods for Small Molecules.

The nonrelativistic ground-state energy of the hydrogen molecule is calculated using an improved Green's function quantum Monte Carlo method without the use of the Born-Oppenheimer or any other adiabatic approximation. A more accurate trial function for importance sampling and the use of exact cancellation combine to yield an energy which is a factor of ten more accurate than that of previous quantum Monte Carlo calculations. The calculated energy is -1.164 0239 +/- 0.000 0009 hartrees. Expressed as the dissociation energy and corrected for relativistic and radiative effects, the result is 36 117.84 +/- 0.2 cm ^{-1}, a value in good agreement with the most recent experimental value of 36 118.11 +/- 0.08 cm^{-1}. The ground-state energy of the clamped-nucleus LiH molecule is calculated using a simplified released -node Green's function quantum Monte Carlo method. The energy determined for an internuclear separation of 3.015 bohrs is -8.07022 +/- 0.00005 hartrees, a value lower than that of the lowest -energy variational calculation, more accurate than prior quantum Monte Carlo calculations, and in excellent agreement with the non-relativistic energy of -8.07021 +/- 0.00010 hartrees determined from experimental measurements. The fixed-node diffusion quantum Monte Carlo method is investigated in calculations of the ground state energies of the LiH and Li_2 molecules. The errors associated with fixed nodes and finite the time steps as well as the small amount of computation time limit the accuracy. But, within their uncertainties, the energies calculated are in agreement with experimental values.