Premium
Time step error in diffusion Monte Carlo simulations: An empirical study
Author(s) -
Rothstein Stuart M.,
Patil Narayan,
Vrbik Jan
Publication year - 1987
Publication title -
journal of computational chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.907
H-Index - 188
eISSN - 1096-987X
pISSN - 0192-8651
DOI - 10.1002/jcc.540080418
Subject(s) - monte carlo method , diffusion monte carlo , random walk , sampling (signal processing) , statistical physics , diffusion , computer science , algorithm , quantum monte carlo , energy (signal processing) , space (punctuation) , hybrid monte carlo , mathematics , physics , statistics , markov chain monte carlo , quantum mechanics , filter (signal processing) , computer vision , operating system
Diffusion Monte Carlo ( DMC ) is a random walk computational method for solving the ground‐state Schrödinger equation for atoms or molecules. One obtains a biased simulated energy which is used to estimate the exact energy, where the bias increases with the time step used in the simulation. We present six new DMC algorithms, all of which have the same theoretical justification. Yet, when applied to the LiH and H 2 molecules, the algorithms give results with markedly different error. Furthermore, algorithms which exhibit a small error when applied to one molecule show significantly greater error for the other. The explanation for these results relates to sampling of configuration space in the neighborhood of the nuclei. We investigate this issue hoping that our results will aid in the design of more efficient DMC algorithms.