On the charge and molecule based summations of solvent electrostatic potentials and the validity of electrostatic linear response in water

Solvent-induced electrostatic potentials and field components at the solute sites of model Na(+)q-Cs(-)q molecules were computed by summing over either solvent charges (q-summation) or solvent molecular centers (M-summation) from molecular dynamics simulations. These were compared with values obtained by solving Poisson equation with the dielectric boundary defined by R-eff = (R-atom +R-gmax)/2. q-summation using cut-offs that are less than or equal to 10 Angstrom generally underestimates or overestimates the magnitude of (a) the potentials and field components at Na+q and Cs-q relative to the theoretical values and (b) electrostatic solvation free energies of the dipolar solutes assuming linear solvent response relative to the respective values from free energy simulations. Furthermore, the q-summed electric potentials showed significant oscillations even beyond the second hydration shell. In contrast, the corresponding M-summed potentials plateaued after the first hydration shell. Although the different water molecular centers yielded different converged potential values, the dipole center produced values in remarkable agreement with the theoretical values for solute charges ranging from 1 to 0.1e, indicating the existence of an a convenient molecular center for computing these quantities. In contrast to the M-summed potentials, the electrostatic field components and electrostatic solvation free energies from linear response relationships were found not to be sensitive to the choice of the molecular center for typical cut-off distances (8 to 12 Angstrom) used in most simulations.