# Density-functional theory

This is a set of theories in statistical mechanics that profit from the fact that the free energy of a system can be cast as a functional of the density. That is, the density (in its usual sense of particles per volume), which is a funtion of the position in inhomogeneous systems, uniquely defines the free energy. By minimizing this free energy one arrives at the true free energy of the system and the equilibrium densify function. This is a mathematical theorem by ... The situation parallels the better known electronic density functional theory, in which the energy of a quantum system is shown to be a functional of the electronic density (a theorem by Kohn and Sham.)

Starting from this fact, approximations are usually made in order to approach the true functional of a given system.

- Ebner-Saam-Stroud
- Fundamental-measure theory
- Hohenberg-Kohn-Mermin theorems
- Quantum density-functional theory
- Ramakrishnan-Youssouff
- Weighted density approximation
- Tarazona
- Dynamical density-functional theory

## Interesting reading

- Robert Evans "Density Functionals in the Theory of Nonuniform Fluids", in "Fundamentals of Inhomogeneous Fluids" (ed. D. Henderson). Marcel Dekker.
- Robert G. Parr "Density Functional Theory", Annual Review of Physical Chemistry
**34**pp. 631-656 (1983) - C. Ebner, H. R. Krishnamurthy and Rahul Pandit "Density-functional theory for classical fluids and solids", Physical Review A
**43**pp. 4355 - 4364 (1991)