Fundamentals of DFT

The foundations of density functional theory (DFT), a computational approach to quantum mechanical modeling, are examined in this chapter. The historical evolution of DFT is covered first, emphasizing how well it approximates the Schrödinger equation and how widely it can be used to determine the electrical and molecular characteristics of different materials. Hohenberg and Kohn's theorems from 1964 address the constraints of the Hartree and Thomas–Fermi models, which are cited as early forerunners. These theorems made electron density a fundamental variable in ground state property calculations. The Kohn–Sham (KS) method, which introduces non-interacting electrons in an effective potential to simplify the many-electron problem, is then discussed. The foundation for self-consistent computations is this framework, which incorporates exchange–correlation functionals to take quantum mechanical interactions into account. The chapter discusses the accuracy and computational cost trade-offs of several exchange–correlation functional types, including hybrid functionals, Generalized Gradient Approximation (GGA), and Local Density Approximation (LDA). The chapter firmly establishes DFT's place in contemporary computational science by highlighting the iterative nature of DFT calculations and the ongoing improvements in functional development to improve accuracy across a variety of chemical and physical systems.