Computing three-dimensional densities from force densities improves statistical efficiency

Abstract

The costs of simulations is always at the forefront of the mind of the computational chemist. Which simulations they can make within a given CPU allowance or a given time guides the development of the field. Among properties of interest, the extraction of inhomogeneous 3-dimensional densities around tagged solutes is known to have a very high computational cost since this is performed traditionally by collecting histograms, with each discrete voxel in threedimensional 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. 2013 111 3486-3492] 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. arXiv:1905.11696v1 [physics.chem-ph] 28 May 2019where z = {z 1 , . . . , z K } is a specific value of the vectorial collective variable, U(r N ) is the potential energy of the micro-scopic configuration and

Hydration free energies and solvation structures with molecular density functional theory in the hypernetted chain approximation

“…Panel b shows the isosurfaces P y (r) = ±0.035 Debye/A 3 obtained by MDFT with a grid size of 0.25 Å, whereas Panel c shows the same quantity obtained by col-lecting histograms of identical voxel size along a 50-ns-long MD trajectory (25000 independent configurations). These 3D plots look familiar compared to previous simulations 75 with a change of sign when crossing the symmetry plane. The two rather loose, upper caps correspond to the solvent donor molecules presenting their hydrogens to the solute oxygen negative partial charge.…”

“…In the case of molecular simulations, one would have to accumulate such data during a long trajectory, averaging in spatial voxels of typical size 0.25-0.5 Å for a series of orientations. For just positions, this can be tackled nowadays, especially with the recent approach using an estimator based on forces rather than simple binning to decrease the variance of the estimate of g [73][74][75] . Nevertheless, accumulating data in the full sixdimensional orientation and position space is a daunting task, even more difficult than computing SFE's.…”

Local Molecular Field Theory for Nonequilibrium Systems

“…Flexible water models are more computationally intensive as well, so for this reason it is useful to derive a shake correction to the force sampling method. A similar correction was derived recently and independently by Coles et.al [46][47].…”

Use the force! Reduced variance estimators for densities, radial distribution functions and local mobilities in molecular simulations

“…As a final illustration on a more complex system, Figure 5, also from Ref. 32, compares the number and charge densities around a small protein, lysozyme. Following Eq.…”