  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.
