MOLPRO

C DENSITY FUNCTIONAL DESCRIPTIONS 442
C (d,α,β)
= K (Q,α,β)
+ M (Q,α,β),
(395)
M (d,α,β)
= 0.5ν (φ (r (α,β))
− κ
K (d,α,β)
− 3/7Z)d 2 e −335.9789467 32/3 d
3√
2
π 5 ρ
,
= 0.2500000000λ 2 ln
(
1
(396)
(397)
ι ( d 2 + N (α,β)d 4) )
+ 2
λ (1 + N (α,β)d 2 + (N (α,β)) 2 d 4 ι −1 ,
)
N (α,β)
(
(398)
= 2ιλ −1 ι ε(α,β)
−4
e λ 2 )
− 1
−1 ,
Q = 1/12
√
σ (ss)
3√
23
5/6
6√
π −1 ρ 7/6 .
(399)
C.31 PW91X: Perdew-Wang 1991 GGA Exchange Functional
g = 1/2E (2ρ (s)),
G = 1/2E (2ρ (s)),
(400)
(401)
E (n)
=
−3/4
3√ 3√
3 π 2 n 4/3 F (S)
,
π
(402)
S = 1/12 χ (s)62/3
3√ ,
π 2
(403)
F (S)
=
1 + 0.19645Sarcsinh(7.7956S) +
(
0.2743 − 0.1508e −100S2) S 2
1 + 0.19645Sarcsinh(7.7956S) + 0.004S 4 .
(404)