Perturbation Theories for the Thermodynamic Properties of Fluids and Solids

286 Perturbation Theories for Fluids and Solids

where β

−1



[

ρ(r)

]

is the excess free energy density of the nonuniform system. Among

the different approximations proposed to obtain the excess free energy functional,

the simplest one is known as the local density approximation (LDA), based on the

assumption that the excess free energy density of the nonuniform system equals that

of a uniform system with the density ρ replaced with the local density ρ(r), that

is 

[

ρ(r)

]

= 

0

(

ρ(r)

)

, a reasonable approximation only when the latter is slowly

varying enough. For more quickly varying densities, the free energy density may

be expressed as an expansion in series ...