Libxc - a library of exchange and correlation functionals - TDDFT.org

An example: Perdew & Wang 91 (an LDA)
Perdew and Wang parametrized the correlation energy per unit
particle:
e c (r s , ζ) = e c (r s , 0) + α c (r s ) f (ζ)
f ′′ (0) (1 − ζ4 ) + [e c (r s , 1) − e c (r s , 0)]f (ζ)ζ 4
The function f (ζ) is
f (ζ) = [1 + ζ]4/3 + [1 − ζ] 4/3 − 2
,
2 4/3 − 2
while its second derivative f ′′ (0) = 1.709921. The functions e c (r s , 0),
e c (r s , 1), and −α c (r s ) are all parametrized by the function
g = −2A(1 + α 1 r s ) log
{
1 +
1
2A(β 1 r 1/2
s + β 2 r s + β 3 r 3/2
s + β 4 r 2 s )
}
M. A. L. Marques Libxc