Hartree-Fock: Roothan Equations

This lecture covers the Hartree-Fock Roothaan Equations, a set of coupled integro-differential equations and basis set expansion matrix equations. It explains the matrix formulation, transformation yielding eigenvalue problems, and the solution of the equations. Different types of Hartree-Fock methods are discussed, including Restricted Hartree-Fock (RHF), Restricted Open-Shell Hartree-Fock (ROHF), and Unrestricted Hartree-Fock (UHF). The lecture also touches on the performance of the Hartree-Fock method, highlighting its relative good and bad performances in various scenarios.