Accurate electron densities from quantum Monte Carlo calculations using real-space grids

We provide accurate energies and electronic densities for Li2, C, and N2 from the diffusion Monte Carlo (DMC) method in the fixed node approximation based on orbitals from a real-space grid approach. With relatively simple single-determinant trial wave functions, we demonstrate the benefits of an all-electron approach in conjunction with a highly accurate grid method for calculating the orbitals that build the determinant. Our DMC ground state energies match with those of more elaborate single-reference quantum Monte Carlo (QMC) methods based on orbital basis sets. The binning technique is revisited to calculate the electronic density on a spatial grid. We examine the dependence of the resulting mixed estimator and extrapolated density on the trial wave function, specifically on the density functional generating the orbitals, by employing two distinctly different functionals, namely, the local density approximation and the exact-exchange functional. Residual statistical artifacts in the QMC densities are readily corrected by using a regularization method, resulting in smooth densities. As an example for the insight that can be gained from an accurate density, we verify that in the carbon atom, the density along one specific direction can have an asymptotic decay that differs from the decay found in all other directions. We relate this observation to previously published work, which discussed the implications that such a nodal feature may have for the exact Kohn-Sham potential.