Efficient molecular density functional theory using generalized spherical harmonics expansions*

We show that generalized spherical harmonics are well suited a basis set for representing the space and orientation molecular density for the resolution of the (classical) molecular density functional theory. We consider the common system made of a rigid molecule of arbitrary complexity immersed in a molecular solvent, both represented by molecules with interacting atomic sites and classical force fields. The molecular solvent density ρ(r,Ω) around the solute is a function of the position r and of the three Euler angles Ω 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 ρ(r,Ω). 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 show how this theory must be completed to fulfil thermodynamic consistency, at least in terms of pressure and surface tension. We finaly illustrate the formalism by tackling the solvation of molecules of various complexity in water.