  Integral equation theory of molecular liquids based on statistical mechanics
is quite promising as an essential part of multiscale methodology for chemical
and biomolecular nanosystems in solution. Beginning with a molecular
interaction potential force field, it uses diagrammatic analysis of the
solvation free energy to derive integral equations for correlation functions
between molecules in solution in the statistical-mechanical ensemble. The
infinite chain of coupled integral equations for many-body correlation
functions is reduced to a tractable form for 2- or 3-body correlations by
applying the so-called closure relations. Solving these equations produces the
solvation structure with accuracy comparable to molecular simulations that have
converged but has a critical advantage of readily treating the effects and
processes spanning over a large space and slow time scales, by far not feasible
for explicit solvent molecular simulations. One of the versions of this
formalism, the three-dimensional reference interaction site model (3D-RISM)
integral equation complemented with the Kovalenko-Hirata (KH) closure
approximation, yields the solvation structure in terms of 3D maps of
correlation functions, including density distributions, of solvent interaction
sites around a solute (supra)molecule with full consistent account for the
effects of chemical functionalities of all species in the solution. The
solvation free energy and the subsequent thermodynamics are then obtained at
once as a simple integral of the 3D correlation functions by performing
thermodynamic integration analytically.
