It is the effective 1-body Hamiltonian, consisting of a "core" part and contracted 2-body part. The elements of this matrix are the kinetic, nuclei-interaction, AO electron density matrix, and the 2-body Hamiltonian (commonly consisting of just the Electron Repulsion Integral (ERI) term). These terms other than the electron density, are obtained by Gaussian-Basis-Function integrators, which compute the integral between these two basis functions. This is a tedious task which may be outsourced to or . While the AO density-matrix may be constructed knowing the MO orbital occupation, given by the MO density-matrix, and the MO coefficient shielding. We begin by discussing the MO Density Matrix for the HF-state, this matrix is diagonal with the MO occupations on the diagonal, i.e. D σ pq = B HFσp δ pq . Then the AO-Density Matrix is given as: