Zero-variance zero-bias quantum Monte Carlo estimators of the spherically and system-averaged pair density - Sorbonne Université Access content directly
Journal Articles Journal of Chemical Physics Year : 2007

Zero-variance zero-bias quantum Monte Carlo estimators of the spherically and system-averaged pair density

Abstract

We construct improved quantum Monte Carlo estimators for the spherically and system-averaged electron pair density i.e., the probability density of finding two electrons separated by a relative distance u , also known as the spherically averaged electron position intracule density I (u) , using the general zero-variance zero-bias principle for observables, introduced by Assaraf and Caffarel. The calculation of I (u) is made vastly more efficient by replacing the average of the local delta-function operator by the average of a smooth nonlocal operator that has several orders of magnitude smaller variance. These new estimators also reduce the systematic error or bias of the intracule density due to the approximate trial wave function. Used in combination with the optimization of an increasing number of parameters in trial Jastrow-Slater wave functions, they allow one to obtain well converged correlated intracule densities for atoms and molecules. These ideas can be applied to calculating any pair-correlation function in classical or quantum Monte Carlo calculations.
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Dates and versions

hal-00979441 , version 1 (16-04-2014)

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Cite

Julien Toulouse, Roland Assaraf, C. J. Umrigar. Zero-variance zero-bias quantum Monte Carlo estimators of the spherically and system-averaged pair density. Journal of Chemical Physics, 2007, 126, pp.244112. ⟨10.1063/1.2746029⟩. ⟨hal-00979441⟩
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