Basics of the density functional theory
Abstract
The density functional theory (DFT) established itself as a well reputed way to compute the
electronic structure in most branches of chemistry and materials science. In the formulation given by
Kohn, Hohenberg and Sham in the 1960’s, the many-electron wave function is replaced by the electron
density, so that the energy is just a functional of the latter. The DFT is applied, with low computational
cost and reasonable accuracy, to predict diverse properties as binding or atomization energies, shapes
and sizes of molecules, crystal structures of solids, energy barriers to various processes, etc. In the
mid 1980s, it became an attractive alternative to the well developed wave function techniques such as
Hartree-Fock, when crucial developments in exchange-correlation energy has been taken into account,
since the Hartree-Fock method treats exchange exactly but neglects correlation.
This article is an introduction to the conceptual basis of the DFT in a language accessible for readers
entering the field of quantum chemistry and condensed-matter physics. It begins with a presentation of
the Thomas-Fermi atomic model and follows by the essentials of the density functional theory based
on the works of Hohenberg, Kohn and Sham. With a discussion of the exchange and correlation eects,
possible improvements are then presented. Lastly, mention is made of the main hybrid functionals and
of the software packages successfully applied to diverse materials of chemical, physical and biological
interest.