MOLPRO

C DENSITY FUNCTIONAL DESCRIPTIONS 423
C.10 BRUEG: Becke-Roussel Exchange Functional — Uniform Electron Gas Limit
A. D. Becke and M. R. Roussel,Phys. Rev. A 39, 3761 (1989)
As for BR but with γ = 0.8.
C.11 BW: Becke-Wigner Exchange-Correlation Functional
Hybrid exchange-correlation functional comprimising Becke’s 1998 exchange and Wigner’s
spin-polarised correlation functionals.
α = −3/8 3 √
34
2/3 3 √
π −1 ,
(175)
g = α (ρ (s)) 4/3
−
β (ρ (s)) 4/3 (χ (s)) 2
(176)
1 + 6β χ (s)arcsinh(χ (s)) , (177)
G = α (ρ (s)) 4/3
−
β (ρ (s)) 4/3 (χ (s)) 2
1 + 6β χ (s)arcsinh(χ (s)) , (178)
f = −4cρ (a)ρ (b)ρ −1 (1
+ d )
√ −1 ,
3 ρ
β = 0.0042,
c = 0.04918,
d = 0.349.
(179)
(180)
(181)
C.12 CS1: Colle-Salvetti correlation functional
R. Colle and O. Salvetti, Theor. Chim. Acta 37, 329 (1974); C. Lee, W. Yang and R. G. Parr,
Phys. Rev. B 37, 785(1988)
CS1 is formally identical to CS2, except for a reformulation in which the terms involving υ are
eliminated by integration by parts. This makes the functional more economical to evaluate. In
the limit of exact quadrature, CS1 and CS2 are identical, but small numerical differences appear
with finite integration grids.