A variational definition of electrostatic potential derived charges

In a recent work [Laio, A., VandeVondele, J., Rothlisberger, U. J. Phys. Chem. B2002106, 7300] a novel method has been proposed to define dynamical electrostatic potential derived (D-RESP) charges for systems described within a quantum mechanics/molecular mechanics (QM/MM) scheme. Here, we derive the analytic dependence of these charges on the quantum charge density and on the atomic positions. This variational property can be exploited for defining interaction potentials between the quantum and the classical subsystems that depend explicitly on the value of the D-RESP charges. Such potentials can be used for a multitude of different purposes, such as improving the computational efficiency of the electrostatic coupling between the QM and the MM subsystems and for defining a QM/MM analogue of the exclusion schemes commonly used in classical biomolecular force fields.