## 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:
DFT 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
*