Analysis of discrete and continuum dielectric models:Application to the calculation of protonation energies in solution

We present a simple model to deal with long range electrostatic interactions in computer simulations of solvated molecules and ions. The model combines a discrete molecular description of the first two or three solvation layers with a continuum description of the bulk solvent. The solute is described quantum mechanically. For a series of amines good agreement with experimental protonation energies in water is obtained, when the position of the continuum boundary takes properly into account the volume of the enclosed particles. A comparison is made with periodic boundary simulations and with existing continuum models. The accuracy depends not only on the dielectric model itself, but at least as much on details of the electrostatic potential and on inductive interaction