where r i j is the distance between the i-th and j-th MM atoms, and σ is the width of Gaussian functions used to damp the electrostatic interaction between neighboring atoms. The diagonal block of T is formed by the atomic capacitance (c i ) and polarizability (α i ) for charge and dipole self-interactions at i-th MM atom, respectively. F tot is the total external generalized field exerted on the MM sites, including both potentials and fields (-V, E). Using the variational condition, the stationary solution is given by solving a linear equation,