Building on the previous discussion of Hartree-Fock Theory, I discuss the inclusion of basis functions to produce the Roothaan equations, and the method of solving these using self-consistent field methods. I then provide an introduction into techniques to incorporate electron correlation by adding Slater determinants, focusing on the Configuration Interaction method. I then provide a brief overview of semi-empirical methods, Density Functional Theory, and molecular mechanics. Recommended pre-listening is Episode 119: Computational Chemistry Part 1.
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