Early model of density functional theory

Density functional theory can be traced back to Thomas-Fermi model developed by Thomas and Fermi in 1920s. They expressed the kinetic energy of atoms as the functional of electron density, and added the classical expressions of nuclear-electron and electron-electron interaction (both of which can be expressed by electron density) to calculate the energy of atoms.

Thomas-Fermi model is an important first step, but the accuracy of Thomas-Fermi equation is limited because the atomic exchange energy pointed out by Hartley-Fokker theory is not considered. 1928 Dirac added the exchange energy functional term to the model.

However, Thomas-Fermi-Dirac theory is not accurate enough in most applications. The biggest error comes from the expression of kinetic energy, followed by the error of exchange energy and the complete neglect of electronic correlation.