ABSTRACT
Initially, this chapter deals with the function and functionals, and it has been tried to differentiate between the two terms by citing examples. It also gives proofs of Hohenberg–Kohn theorem 1 and 2 mathematically. The proofs of these theorems have also been cited alternatively. It also comprises the mathematical derivation of Kohn–Sham energy, Kohn–Sham equations, local density approximation (LDA) comments, and applications of LDA. Further, electron gas, the local spin density approximation (LSDA), generalised gradient approximation (GGA) and its mathematical formulation, meta-generalised gradient and its mathematical formulation, and hybrid orbitals (mathematical formulation). It also provides the mathematical form of time-dependent density functional theory (DFT). Lastly, it comprises applications of the DFT and shortcomings of the DFT. Questions on concepts have also been given at the end for providing better understanding to the readers.
