# Tarazona's weighted density approximation

Inspired by the exact solution known for the system of 1-dimensional hard rods,
Pedro Tarazona proposed a series of models in the 1980's
^{[1]}
^{[2]}
^{[3]}
^{[4]}
in which the dependence of the Helmholtz energy function is weighted:

- ,

where is an average of the
density distribution and where *A* is the Helmholtz energy function.
The function should vanish at low values of
its argument (so that the excess vanishes and one is left with
the ideal case), and diverge at some saturation density corresponding
to complete packing.

## References

- ↑ P. Tarazona "A density functional theory of melting", Molecular Physics
**52**pp. 81-96 (1984) - ↑ P. Tarazona "Free-energy density functional for hard spheres", Physical Review A
**31**pp. 2672-2679 (1985) - ↑ P. Tarazona "Erratum: Free-energy density functional for hard spheres", Physical Review A
**32**p. 3148 (1985) - ↑ P. Tarazona, U. Marini Bettolo Marconi and R. Evans "Phase equilibria of fluid interfaces and confined fluids: Non-local versus local density functionals" Molecular Physics
**60**pp. 573-595 (1987)