Modified Poisson equations for calculating solvation free energy

The dielectric polarization (P) is the key factor in calculating the solvation free energy. P can be decomposed into the product of the electric dipole per solvent (p) and the relative solvent molecular density (g). p can be calculated from the electric field (E), and g can be calculated from the mean force (F), where the electric component of F is calculated from ∇_xE. The Poisson equations were modified for E and ∇_xE. Strategies to estimate the boundary conditions of E and ∇_xE were proposed. The dependences of P and g on the parameters used for the numerical analysis were explored. For two charged atoms in a water cluster, the values of P and g obtained by these equations were similar to those obtained from molecular dynamics simulations. The electric potential at the solute atoms and the solvation free energy determined using these equations were similar to those obtained from molecular dynamics simulations.