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 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.

13 pages, 9 figures, published version

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Cited by in corpus (15)

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• Use the force! Reduced variance estimators for densities, radial distribution functions and local mobilities in molecular simulations
• Heavy-tailed random error in quantum Monte Carlo
• Intracule densities in the strong-interaction limit of density functional theory
• Sampling mobility profiles of confined fluids with equilibrium molecular dynamics simulations
• Reduced variance analysis of molecular dynamics simulations by linear combination of estimators
• Radial distribution function in a diffusion Monte Carlo simulation of a Fermion fluid between the ideal gas and the Jellium model
• The scaling properties of exchange and correlation holes of the valence shell of second row atoms
• Measuring correlated electron motion in atoms with the momentum-balance density
• Semiclassical approximations of photoabsorption cross sections beyond the continuum threshold
• Hellmann and Feynman theorem versus diffusion Monte Carlo experiment
• Quadriexciton binding energy in electron-hole bilayers