Density Functional Theory
An Introduction Page
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].
(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.
(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
Active DFT Researchers (in random order):
Delano P. Chong
Robert G. Parr
John A. Pople
Gustavo E. Scuseria
Frank De Proft
Melvyn P. Levy
Eberhard K.U. Gross
Evert J. Baerends
Axel D. Becke
Rodney J. Bartlett
Pratim K. Chattaraj
Robert C. Morrison
Last modified: Feb. 21, 1998