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 H, "I,+ , and the three-electron system of linear symmetric HHH, the intermediate for the reaction H + H,-+H2 + H.

A study of H+H2 and several H-bonded molecules by phaseless auxiliary-field quantum Monte Carlo with plane wave and Gaussian basis sets

“…The AE and pseudopotential DFT/GGA results are in excellent agreement with each other, a further indication of the good quality of the H pseudopotential. The DMC calculations [29] are exact in this case, through the use of a cancellation scheme [9,33], which is very effective at eliminating the sign problem for small systems. The AF QMC values are in good agreement with the exact calculated results.…”

Importance sampling in rigid body diffusion Monte Carlo

“…More efficient sampling of excited states within fixed node is often possible by using explicit trial functional forms. Exploration of nodal release, nodal optimization, spectral evolution and other approaches to go beyond the fixed node approximation is an active area of research [10,[24][25][26][27][28][29][30][31][32][33][34].…”

HPFBench

“…The basic algorithm consists of moving random walkers in configuration space (two-dimensional in this model problem) by sampling their steps from the Green's function for the Helmholtz equation, and multiplying their weights by a factor that is a function of configuration space position. For a thorough description of the algorithmic methodology see Anderson et al [1991].…”

“…To mitigate this problem, a walker-cancellation scheme is used, as described in Anderson et al [1991]. This amounts to an N-body problem on the walkers, and it is implemented using the sequential spread algorithm every n c (cancellation number) iteration steps.…”