# Computing three-dimensional densities from force densities improves statistical efficiency

## TL;DR

This paper introduces an improved method for calculating 3D densities from molecular simulations, significantly reducing computational noise and variance, especially for complex solvent models and biological systems.

## Contribution

It extends a previous variance reduction technique to various 3D densities and rigid solvent models, enhancing efficiency in solvation density calculations.

## Key findings

- Reduced variance in density estimates demonstrated
- Applicable to diverse solvent models including water
- Effective in complex biological and material systems

## Abstract

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.