MOLPRO

C DENSITY FUNCTIONAL DESCRIPTIONS 425
with
and
C 2 = − 3(1−ζ 2 )g c (0,r s ,ζ = 0)
8rs
3
C 3 = −(1−ζ 2 ) g(0,r s,ζ = 0)
√
2π r 3 s
C 4 = − 9c 4(r s ,ζ )
64rs
3
C 5 = − 9c 5(r s ,ζ )
40 √ 2πrs
3
( ) (
1+ζ
2
c 4 (r s ,ζ ) =
g ′′
2
( ( 2
g ′′ 0,r s
1−ζ
( ) (
1+ζ
2
c 5 (r s ,ζ ) =
g ′′
2
g ′′ (
0,r s
( 2
1−ζ
( 2
0,r s
1+ζ
) )
1/3
, ζ = 1
) )
1/3 ( 1−ζ
, ζ = 1 +
2
) 2
×
+ (1−ζ 2 )D 2 (r s ) − φ 8(ζ )
5α 2 rs
2
( ) )
2
1/3 ( ) 1−ζ 2
0,r s , ζ = 1 + ×
1+ζ
2
) )
1/3
, ζ = 1
+ (1−ζ 2 )D 3 (r s ), (190)
b 0 (r s ) = 0.784949r s (191)
g ′′ (0,r s ,ζ = 1) = 25/3
5α 2 r 2 s
D 2 (r s ) = e−0.547r s
r 2 s
1 − 0.02267r s
(1 + 0.4319r s + 0.04r 2 s )
(
−0.388rs + 0.676r 2 s
)
(192)
(193)
D 3 (r s ) = e−0.31r s
r 3 s
(
−4.95rs + rs
2 )
. (194)
Finally, εc
PW92 (r s ,ζ ) is the Perdew-Wang parametrization of the correlation energy of the standard
uniform electron gas [J.P. Perdew and Y. Wang, Phys. Rev. B 45, 13244 (1992)], and
g(0,r s ,ζ =0) = 1 2 (1 − Br s +Cr 2 s + Dr 3 s + Er 4 s )e −dr s
, (195)
is the on-top pair-distribution function of the standard jellium model [P. Gori-Giorgi and J.P.
Perdew, Phys. Rev. B 64, 155102 (2001)], where B = −0.0207, C = 0.08193, D = −0.01277,
E = 0.001859, d = 0.7524. The correlation part of the on-top pair-distribution function is
g c (0,r s ,ζ =0) = g(0,r s ,ζ =0) − 1 2 .
C.16 EXERF: Short-range LDA correlation functional
Local-density approximation of exchange energy
for short-range interelectronic interaction erf(µr 12 )/r 12 ,