Related Experiment Video
Updated: Jul 13, 2026

A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments
Published on: March 1, 2022
Zero-variance zero-bias quantum Monte Carlo estimators of the spherically and system-averaged pair density
Julien Toulouse1, Roland Assaraf, C J Umrigar
1Cornell Theory Center, Cornell University, Ithaca, New York 14853, USA. toulouse@tc.cornell.edu
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.
Related Concept Videos
Estimation of the Physical Quantities
Maxwell-Boltzmann Distribution: Problem Solving
This distribution function f(v) is defined by saying that the expected number N (v1,v2) of particles with speeds between v1 and v2 is given by
Root Mean Square
For example, consider the velocity of gas molecules in a container. The gas molecules are moving in different directions, which might impart positive and negative...
The Uncertainty Principle
Gravitation Between Spherically Symmetric Masses
Reduced Mass Coordinates: Isolated Two-body Problem