Density functional theory (DFT) is a quantum-mechanical method used in chemistry and physics to calculate the electronic structure of atoms, molecules, and solids. The low-cost method saves time and has been used to compute the physical characteristics of systems with high precision.
Traditional electronic structure methods attempt to find approximate solutions to the Schrödinger equation of N interacting electrons moving in an external, electrostatic potential (typically the Coulomb potential generated by the atomic nuclei). However, this approach is nontrivial to solve, even for small numbers of electrons generating complicated wave functions while requiring significant computational resources. Instead, researchers use approximates to make the problem solvable. DFT is a leading method of obtaining an approximate solution to the Schrödinger equation for a many-body system. DFT replaces the many-body wave function with a one-body density. As the density is a function of only three spatial coordinates, DFT is computationally feasible even for large systems. Accurately applying DFT requires a precise exchange-correlation function, utilizing density to represent advanced many-body phenomena.
DFT first became popular in the 1970s, being applied to computational solid-state physics problems. However, improvements in the 1990s led to the method becoming more widely used, in particular for quantum-chemical applications. DFT can be applied to a wide range of problems across physics and chemistry when a system needs to be modeled at an atomic level.