The electrostatic operator (v es ) describes Coulomb interactions between the core region and the permanent charge densities of the environment. It is constructed from the fragmentbased density matrices (D) as well as nuclear charges (Z) and positions (R), together with the corresponding two-electron repulsion integrals (v µν,γδ ) and one-electron nuclear attraction integrals (v µν (R)). The contribution of this operator to the Fock matrix in an atomic orbital (AO) basis is defined as