with the integrals F βα and S βα defining the elements of the so called Fock matrix F and overlap matrix S, respectively. The Fock matrix comprises terms from the oneelectron contributions to ĤMF (kinetic energy and external potential) also referred to as core Hamiltonian h core , from the classical Hartree contribution J, explicit exchange K in hybrid DFT or HF, and from the exchange-correlation potential V xc in DFT. Note that in general, the basis functions are normalized but not orthogonal to each other, and S ̸ = 1.