Computation of pair distribution functions and three-dimensional densities with a reduced variance principle

No fancy statistical objects here, we go back to the computation of one of the most basic and fundamental quantities in the statistical mechanics of fluids, namely the pair distribution functions. Those functions are usually computed in molecular simulations by using histogram techniques. We show here that they can be estimated using a global information on the instantaneous forces acting on the particles, and that this leads to a reduced variance compared to the standard histogram estimators. The technique is extended successfully to the computation of three-dimensional solvent densities around tagged molecular solutes, quantities that are noisy and very long to converge, using histograms.