Density Functional Theory

An Introduction Page


Basics:

The first Hohenberg-Kohn theorem asserts that the density of any system determines all ground-state properties of the system, that is, E=E[n0], where n0 is the ground-state density of the system. Moreover, the second H-K theorem shows that there exists a variational principle for the above energy density functional E[n]. Namely, if n' is not the ground state density of the above system, then E[n'] > E[n0].

Significance:

(1). The wavefunction psi of an N-electron system includes 3N variables, while the density, no matter how large the system is, has only three variables x, y, and z. Moving from E[psi] to E[n] in computational chemistry significantly reduces the computational effort needed to understand electronic properties of atoms, molecules, and solids.

(2). Formulation along this line provides the possibility of the linear scaling algorithm currently in fashion, whose computational complexity goes like O(NlogN), essentially linear in N when N is very large.

(3). The other advantage of DFT is that it provides some chemically important concepts, such as elctronegativity (chemical potential), hardness (softness), Fukui function, response function, etc.. These concepts can be conveniently used to explain chemical properties and changings of molecules.


Problems:

(1). The exact form of the universal energy density functional is unknown. What we only know is that there exists such a functional in principle. No one knows what its form should be. The strategy presently employed by our fellow DFTers is to APPROXIMATE it by various models including LDA, WDA, and GEA/GGA. Widely used formulas such as SVWN, BLYP, B3PW91, etc., are famous examples of these models. However, it is well known that there is no such a systematical way in DFT to improve its results as in the conventional ab initio theory.

(2). Extension to excited states is no obvious. DFT is a ground-state theory. Although in many cases it is enough, it is not at all satisfactory as a well-established theory. Possible ways to overcome the problem are available in the literature, but no final solution exists yet.


Useful Links of DFT:

  • More Detailed Introductions of DFT:

    DFT Introduction from MSI
    Overview by Jan K. Labanowski
    By Matthew D. Segall
    By Stephen Jenkins
    By Jesper Dahlberg
    By Peter D. Haynes
    By Philip Clark
    By E. Wimmer
    By David B. Cook
    DFT Keywords by GAUSSIAN
    Application Examples of DFT by Thomas V. Russo
    Something related: Bader's AIM Theory

  • DFT Software:
    DMol
    SPARTAN (PC) and Spartan Unix
    Gaussian 94
    DeFT
    CADPAC
    UniChem
    MOLPRO 96
  • DFT Books:
    Parr & Yang Book -- the first book in DFT
    Edited by J.M. Seminario & P. Politzer
    DFT in BamesandNoble.com Books

  • Active DFT Researchers (in random order):

    Walter Kohn
    Delano P. Chong
    Robert G. Parr
    John A. Pople
    Lee Bartolotti
    Peter Gill
    Gustavo E. Scuseria
    Frank De Proft
    Nicholas Handy
    Giovanni Vignale
    Melvyn P. Levy
    Alain St-Amant
    Weitao Yang
    Kieron Burke
    John Perdew
    Eberhard K.U. Gross
    Evert J. Baerends
    Axel D. Becke
    Rodney J. Bartlett
    Pratim K. Chattaraj
    Morrel Cohen
    John Dobson
    Eduardo Ludena
    Robert C. Morrison
    Norman March
    Agnes Nagy
    Roman Nalewajski
    Peter Politzer
    Dennis Salahub
    Andreas Savin
    Tom Ziegler

    Last modified: Feb. 21, 1998