Efficient molecular density functional theory using generalized spherical harmonics expansions

TL;DR

This paper introduces a computationally efficient method for molecular density functional theory using generalized spherical harmonics, enabling rapid analysis of solvation structures for complex molecules in various solvents.

Contribution

The authors develop a novel approach that replaces expensive angular convolutions with simple products in spherical harmonics, significantly speeding up molecular solvation calculations.

Findings

Achieved a speed-up allowing nanometric solutes to be analyzed in minutes.

Successfully applied the method to solvation of complex molecules in water.

Demonstrated accurate calculation of solvation free energies and solvent structures.

Abstract

We show that generalized spherical harmonics are well suited for representing the space and orientation molecular density in the resolution of the molecular density functional theory. We consider the common system made of a rigid solute of arbitrary complexity immersed in a molecular solvent, both represented by molecules with interacting atomic sites and classical force fields. The molecular solvent density $\rho(\mathbf{r},\mathbf{\Omega})$ around the solute is a function of the position $\mathbf{r}\equiv(x,y,z)$ and of the three Euler angles $\mathbf{\Omega}\equiv(\theta,\phi,\psi)$ describing the solvent orientation. The standard density functional, equivalent to the HNC closure for the solute-solvent correlations in the liquid theory, is minimized with respect to $\rho(\mathbf{r},\mathbf{\Omega})$. The up-to-now very expensive angular convolution products are advantageously replaced by simple products between projections onto generalized spherical harmonics. The dramatic gain in speed of resolution enables to explore in a systematic way molecular solutes of up to nanometric sizes in arbitrary solvents and to calculate their solvation free energy and associated microscopic solvent structure in at most a few minutes. We finally illustrate the formalism by tackling the solvation of molecules of various complexity in water.