Quantum chemistry by random walk: Exact treatment of many-electron systems

Abstract

We report an improved Monte Carlo method for quantum chemistry which permits the exact treatment of many-electron systems. The method combines many of the best features of earlier fixed-node, released-node, and positive/negative cancellation methods with new ideas for relocation after node crossing, self-cancellations, multiple cancellations, maximum use of symmetry in promoting cancellations, and rigorous evaluation of energies using importance sampling with trial wave functions. The method is illustrated with applications to the problems of the first excited state of a particle in a two-dimensional box, the two-electron system of excited H2 3Σ+u, and the three-electron system of linear symmetric HHH, the intermediate for the reaction H+H2→H2+H.