Density Functional Theory


characteristic density gradient of silicon
Characteristic density gradient for Silicon (dia)

Brief introduction

Density Functional Theory (DFT) is a general approach to the ab initio description of quantum many-particle systems, in which the original many-body problem is rigorously recast in the form of an auxiliary single-particle problem (for an overview see [1]). For the most simple case of (nondegenerate) stationary problems, DFT is based on the fact that any ground state observable is uniquely determined by the corresponding ground state density n, i.e. can be understood as a functional of n. This statement in particular applies to the ground state energy, which allows a representation of the particle-particle interaction effects in an indirect form via a density-dependent single-particle potential. In addition to the Hartree (direct) contribution, this potential contains an exchange-correlation (xc) component, which is obtained from the so-called xc-energy functional. The exact density functional representation of this crucial quantity of DFT is not known, the derivation of suitable approximations being the major task in DFT.

Extensions of this scheme to relativistic [2] and time-dependent [3] systems, utilizing the four current and the time-dependent density as basic variables, are also available. Furthermore, a DFT approach to quantum hadrodynamics (as a model for the relativistic description of nuclei) has been developed [4]. The main areas for applications of DFT are condensed matter and cluster physics as well as quantum chemistry.

Our research focuses on the development of more accurate density functional methods and a deeper understanding of the foundations of relativistic DFT. Applications to critical classes of systems (like van-der-Waals bond molecules or Mott insulators) serve as a test of new functionals. In addition, density functional methods are used to study the structure and dynamics of molecules, clusters and solids.


  1. E. Engel and R. M. Dreizler, Density Functional Theory: An Advanced Course, (Springer, Berlin, 2011);
  2. E. Engel, in: Relativistic Electronic Structure Theory, Part 1. Fundamentals, edited by P. Schwerdtfeger (Elsevier, Amsterdam, 2002), p.524-624.
  3. E. K. U. Gross, J. F. Dobson, and M. Petersilka, Top. Curr. Chem. 181, 81 (1996).
  4. C. Speicher, R. M. Dreizler, and E. Engel, Ann. Phys. (N.Y.) 213, 312 (1992).

Research topics

Instructive topics

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Last revision: Nov 15, 2009