An alternative Monte Carlo estimator for the one-body density $\rho \left(\mathbf{r}\right)$ is presented. This estimator has a simple form and can be readily used in any type of Monte Carlo simulation. Comparisons with the usual regularization of the delta-function on a grid show that the statistical errors are greatly reduced. Furthermore, our expression allows accurate calculations of the density at any point in space, even in the regions never visited during the Monte Carlo simulation. The method is illustrated with the computation of accurate variational Monte Carlo electronic densities for the Helium atom (one-dimensional curve) and for the water dimer (three-dimensional grid containing up to $51\times 51\times 51=132651$ points).

• Received 14 August 2006

DOI:https://doi.org/10.1103/PhysRevE.75.035701