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

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