Modified Poisson equations for calculating solvation free energy

•Poisson equations were modified for the electric field and electric field gradient.•The solvent density and dielectric polarization were solved.•The electric potentials at the solute atoms were solved.•The solvation free energies of solutes were solved.•These results were similar to those obtained from MD simulations.

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.

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