  The extraction of inhomogeneous 3-dimensional densities around tagged solutes
from molecular simulations is known to have a very high computational cost
because this is traditionally performed by collecting histograms, with each
discrete voxel in three-dimensional space needing to be visited significantly.
This paper presents an extension of a previous methodology for the extraction
of 3D solvent number densities with a reduced variance principle [Borgis et
al., Mol. Phys. 111, 3486-3492 (2013)] to other 3D densities such as charge and
polarization densities. The approach is also generalized to cover molecular
solvents with structures described using rigid geometrical constraints, which
include in particular popular water models such as SPC/E and TIPnP class of
models. The noise reduction is illustrated for the microscopic hydration
structure of a small molecule, in various simulation conditions, and for a
protein. The method has large applicability to simulations of solvation in many
fields, for example around biomolecules, nanoparticles, or within porous
materials.
