Hartree-Fock Theory developed by , , and is the basis of much of physical chemistry. It succeeds in obtaining most of the binding energy between electrons and nuclei. Being a mean-field-theory it cannot account for the total binding energy, and the energy deficit from the true binding energy (full-CI) is defined as the correlation energy. Post-Hartree-Fock methods attempt to correct for this correlation energy in a variety of methods. Most post-Hartree-Fock methods start with a Hartree-Fock calculation, as a spring-board, and so this brief introduction serves to give an overview of this method. It even inspired Kohn-Sham (KS) theory, using Density Functional Theory (DFT) to compensate for some lost correlation energy. In our implementation, the electrons exist in a predefined finite basis, consisting of linear combinations of Gaussian orbitals (centered on classical nuclei). Because of the creation of the 2-electron integrals, the HF method is naïvely a O(N 4 ) method (N being the number of basis functions). If methods such as density fitting are used this can be reduced to O(N 3 ), and if large enough samples are considered this can be further reduced to O(N 2 ) (although with a large O(N 4 ) prefactor), . The Hartree-Fock (HF) approximation to electronic-distribution is implemented in 3 broadly different forms: Restricted , Unrestricted , and Generalized form. They all map an atomic basis into an orthonormal molecular basis. They have practical implementations using the Basis-Set-Ansatz, i.e. LCAO, and in molecular systems the Gaussian-Basis-Set as promoted by many, i.e. . HF is perhaps the most well developed electronic structure/distribution method, having many modifications to achieve better results. The computationally cheapest method of proceeding, is working with the AO basis form, which we shall describe below.