Efficient and robust quantum Monte Carlo estimate of the total and spin electron densities at nuclei

The computational performance of two different variational quantum Monte Carlo estimators for both the electron and spin densities on top of nuclei are tested on a set of atomic systems containing also third-row species. Complications due to an unbounded variance present for both estimators are circumvented using appropriate sampling strategies. Our extension of a recently proposed estimator [Phys. Rev. A 69, 022701 (2004)] to deal with heavy fermionic systems appears to provide improved computational efficiency, at least an order of magnitude, with respect to alternative literature approaches for our test set. Given the importance of an adequate sampling of the core region in computing the electron density at a nucleus, a further reduction in the overall simulation cost is obtained by employing accelerated sampling algorithms.