DFT: Kohn-Sham Formulation

This lecture covers the precursors of Kohn-Sham Density Functional Theory (DFT), starting with the Thomas-Fermi Model and its limitations in approximating the kinetic energy. It then introduces the Kohn-Sham formulation of DFT, which maps the many-electron problem onto an auxiliary noninteracting reference system. The lecture explains the Kohn-Sham equations, the KS energy functional, and the types of Exc[p] approximations, such as Local Density Approximation (LDA) and Generalized Gradient Approximations (GGAs). It also delves into the performance of LDA, the exchange-correlation functionals, and meta-GGAs, hybrids, and double hybrids in DFT calculations.