MOLPRO

C DENSITY FUNCTIONAL DESCRIPTIONS 415
C.2 B86MGC: Xαβγ with Modified Gradient Correction
B86 with modified gradient correction for large density gradients.
g = −c(ρ (s)) 4/3
(75)
− β (χ (s)) 2 (ρ (s)) 4/3
(1 + λ (χ (s)) 2 ) 4/5 ,
G = −c(ρ (s)) 4/3
(76)
− β (χ (s)) 2 (ρ (s)) 4/3
(1 + λ (χ (s)) 2 ) 4/5 , (77)
c = 3/8 3 √
34
2/3 3 √
π −1 ,
β = 0.00375,
λ = 0.007.
(78)
(79)
C.3 B86R: Xαβγ Re-optimised
Re-optimised β of B86 used in part 3 of Becke’s 1997 paper.
g = − c(ρ (s)) 4/3 ( 1 + β (χ (s)) 2)
1 + λ (χ (s)) 2 ,
G = − c(ρ (s)) 4/3 ( 1 + β (χ (s)) 2)
1 + λ (χ (s)) 2 ,
c = 3/8 3 √
34
2/3 3 √
π −1 ,
β = 0.00787,
λ = 0.004.
(80)
(81)
(82)
(83)
(84)
C.4 B88: Becke 1988 Exchange Functional
G = −(ρ (s)) 4/3 (c
+
(85)
β (χ (s)) 2 )
,
1 + 6β χ (s)arcsinh(χ (s))
g = −(ρ (s)) 4/3 (c
c = 3/8 3 √
34
2/3 3 √
π −1 ,
β = 0.0042.
+
(86)
β (χ (s)) 2 )
,
1 + 6β χ (s)arcsinh(χ (s))
(87)
(88)