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

Frank Mentch, James B. Anderson

Published Jun 18, 2007• 1 citation

Abstract

Abstract In this paper the combination of importance sampling° with diffusion QMC was shown to be remarkably effective in improving the accuracy of electonic structure calculations for molecular systems. The key to success was the use of a simple, fairly accurate trial wavefunction ΨT for which the function itself, its derivatives and the local energy Eioc may be easily computed. This, used in combination with the diffusion-with-drift expression for walkers corresponding to the product f = ΨΨT according to allows the energy to be evaluated as an average for all walkers of every step after reaching a fluctuating steady state. Since there is a time-step error associated with the simulation of diffusion, drift, and multiplication, varying the time-step and an extrapolation to zero step size are required. The result for H3+ in its triangular configuration of side length 1.6500 bohr was -1.3439 ± 0.0002 hartrees, a value well below the lowest variational energy levels at the time and having an error bar straddling the best modern value of -1.343 835 hartrees. The use of importance sampling along with higher computer speeds resulted in an uncertainty about a factor of 60 lower than that of the previous calculation.b

DOI: 10.1093/oso/9780195310108.003.0019

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