We propose the development of a special- purpose computer for the Hartree-Fock method, which generally suffers quartic time scaling. We conduct a qualitative assessment of the various computational components, with a focus on electron repulsion integrals (ERI), and consequently map various architectural traits to the various computational components. A quantitative analysis of one component is also presented. We go on to mull over the idea of mixed precision arithmetic. These analyses will aid the practical development of a specialized high performance multi-architecture computer.