Separation of the electric polarization into fast and slow components: A comparison of two partition schemes

The study of nonequilibrium solvation with a dielectric continuum model requires splitting the electric polarization into two terms characterized by different relaxation times. There exist various schemes to perform this partition. We show that contrary to what had previously been indicated, the two most commonly used partition schemes, Pekar and Brady and Carr, yield the same value for the total reaction field and for the nonequilibrium free energy whenever one assumes a linear response regime. The confusion appears because in the older Pekar partition the part of the fast polarization in equilibrium with the nuclear polarization is included in the slow component.