Quantum chemistry by random walk: Methane

The total energy of tetrahedral CH4 at the equilibrium bond length of 2.05 bohr is calculated by the fixed-node random walk method with importance sampling. The best result is obtained with a single-determinant trial function of double-zeta STO-basis-set quality. This yields an upper bound to the total energy of −40.506 hartree which is 0.048 hartree below the expectation value of the energy from the best variational calculations and only 0.008 hartree above the experimental nonrelativistic energy. Extended calculations with array processors and extrapolation to zero time step were used to obtain a statistical precision of 0.002 hartree (1.4 kcal/mol) for the random walk result.