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

J. Chem. Phys. 126, 244112 (2007); doi:10.1063/1.2746029

Published 29 June 2007

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Julien Toulouse
Cornell Theory Center, Cornell University, Ithaca, New York 14853

Roland Assaraf
Laboratoire de Chimie Théorique, Université Pierre et Marie Curie and Centre National de la Recherche Scientifique, 75005 Paris, France

C. J. Umrigar
Cornell Theory Center, Cornell University, Ithaca, New York 14853 and Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, New York 14853
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. ©2007 American Institute of Physics
History: Received 30 March 2007; accepted 9 May 2007; published 29 June 2007
Permalink: http://link.aip.org/link/?JCPSA6/126/244112/1
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KEYWORDS and PACS

Keywords
PACS
  • 31.10.+z
    Theory of electronic structure, electronic transitions, and chemical binding in atoms and molecules
  • YEAR: 2007

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