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 thesolute sites of model Na(+q)-Cs(-q) molecules were computed bysumming over either solvent charges (q-summation) or solventmolecular centers (M-summation) from molecular dynamics simulations.These were compared with values obtained by solving Poisson equation withthe dielectric boundary defined by R(eff) = (R(atom)+R(gmax) )/2.q-summation using cut-offs that are ≤ 10 Å generallyunderestimates or overestimates the magnitude of (a) the potentials and field components atNa(+q) and Cs(-q) relative to the theoretical values and (b)electrostatic solvation free energies of the dipolar solutes assuminglinear solvent response relative to the respective values from free energysimulations. Furthermore, the q-summed electric potentials showedsignificant oscillations even beyond the second hydration shell. Incontrast, the corresponding M-summed potentials plateaued after thefirst hydration shell. Although the different water molecular centersyielded different converged potential values, the dipole center producedvalues in remarkable agreement with the theoretical values for solutecharges ranging from 1 to 0.1e, indicating the existence of an a convenient molecular center for computing these quantities. In contrast to theM-summed potentials, the electrostatic field components andelectrostatic solvation free energies from linear response relationshipswere found not to be sensitive to the choice of the molecular centerfor typical cut-off distances (8 to 12 Å) used in most simulations.