Tarazona's weighted density approximation

$A_{\mathrm {hard~sphere} }^{\mathrm {excess} }[\rho ({\mathbf {r} })]=\int \rho ({\mathbf {r} })a_{\mathrm {excess} }[{\overline {\rho }}({\mathbf {r} })]{\mathrm {d} }{\mathbf {r} }$

References

1. P. Tarazona "A density functional theory of melting", Molecular Physics 52 pp. 81-96 (1984)
2. P. Tarazona "Free-energy density functional for hard spheres", Physical Review A 31 pp. 2672 - 2679 (1985)
3. P. Tarazona "Erratum: Free-energy density functional for hard spheres", Physical Review A 32 p. 3148 (1985)
4. 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)