Fundamentals of First-Principles Studies

With increasing computational resources available, materials simulation is central to understanding the electronic, optical, mechanical, and thermodynamic properties of materials. In addition to computing the known properties of materials, material simulations are now widely used at predicting and discovering novel materials with engineered properties. First-principles calculations based on density functional theory (DFT) have been widely used in materials science and condensed matter physics research community, while its applications extend well beyond the conventional systems, ranging from biology to geology. The underlying equations governing the material properties were formulated in the 1920s with the development of Quantum Mechanics. However, the underlying theorems that led to the DFT formulation were only proposed in 1965. DFT is an exact theory for solving quantum mechanical equations of a many-body interacting system. However, several simplifications and approximations are used in modern DFT, enabling its use in real systems with a judicious balance between the accuracy and computational cost involved. Starting from the many-body time-independent Schrödinger equation, we discuss the difficulties involved in solving the equation for a many-body interacting system and the approximations and simplifications that have been employed over the years that led to the application of modern DFT in realistic systems.