Efficient Monte Carlo Calculations of the One-Body Density

Roland Assaraf (1) , Michel Caffarel (2) , Anthony Scemama (3)

1 LCT - Laboratoire de chimie théorique
2 LPQ - Laboratoire de Physique Quantique
3 CERMICS - Centre d'Enseignement et de Recherche en Mathématiques, Informatique et Calcul Scientifique

An alternative Monte Carlo estimator for the one-body density rho(r) 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 (1D curve) and for the water dimer (3D grid containing up to 51x51x51=132651 points).

Mots clés: Monte Carlo; one-body density

Domaines: Physique Numérique [physics.comp-ph]; Mécanique statistique [cond-mat.stat-mech]

Roland Assaraf, Michel Caffarel, Anthony Scemama. Efficient Monte Carlo Calculations of the One-Body Density. 2006. ⟨hal-00107403⟩