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

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

2007-05-05

arxiv.org/abs/0705.0721v2

Journal of Chemical Physics 126, 244112 (2007)

Physics

Chemical Physics

13 pages, 9 figures, published version

Scientific paper

10.1063/1.2746029

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 non-local 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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