Symmetric versus asymmetric discretization of the integral equations in polarizable continuum solvation models

Discretization of the integral equations that define widely-used ‘polarizable continuum’ solvation models fails to preserve certain properties of the integral operators. Consequently, the appropriate form of the finite-dimensional matrix equations is ambiguous, with two different asymmetric versions and also a symmetrized version as obvious possibilities. We demonstrate cases where solvation energies differ by as much as 24 kcal/mol amongst these variants. These differences are sometimes exacerbated by new discretization procedures that guarantee smooth potential energy surfaces. Formal and numerical arguments favor one particular formulation of the matrix equations.