Charge flow between ions and a dielectric continuum. 2. Variational methodfor distributing charge into the dielectric

The paper presents a variational method to distribute the charge transferre d (CT) between an ion and a dielectric continuum onto a boundary element (B E) grid used to represent the dielectric continuum media. The CT charge is transferred into the dielectric using a methodology that combines a semiemp irical effective Hamiltonian with a modified Poisson-Boltzmann equation, wh ich includes CT in the form of a surface charge density positioned at the d ielectric interface. The variational method eliminates the bias of our earl ier method used to distribute CT charge into the dielectric, i.e., the need to specify the solute atoms used in constructing the BE grid. The surface "pattern" of the magnitudes of the CT charges placed onto the BE grid is ob tained by minimizing an energy functional defined as the sum of the CT char ge self-interaction energy and the energies due to CT charge interaction wi th the reaction field (RF) and solute partial atomic charges. The total amo unt of charge, distributed on the BE grid, is constrained to the amount of charge transferred from/to the solute HOMO/LUMO molecular orbital, by using the method of Lagrange multipliers.