MOLPRO

17 THE DENSITY FUNCTIONAL PROGRAM 115
where
Q(x) = 2ln(2) − 2 ( 1 + ax + bx 2 + cx 3 )
π 2 ln
1 + ax + d x 2 , (11)
with a = 5.84605, c = 3.91744, d = 3.44851, and b = d −
3πα/(4ln(2) − 4). The parameters a i (r s ,ζ ) are given by
with
and
a 1 = 4b 6 0C 3 + b 8 0C 5 ,
a 2 = 4b 6 0C 2 + b 8 0C 4 + 6b 4 0εc PW92 ,
a 3 = b 8 0C 3 ,
a 4 = b 8 0C 2 + 4b 6 0 εc PW92 ,
a 5 = b 8 0 εc PW92 ,
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
g ′′ (0,r s ,ζ = 1) = 25/3
5α 2 r 2 s
D 2 (r s ) = e−0.547r s
r 2 s
D 3 (r s ) = e−0.31r s
r 3 s
( 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 ), (12)
b 0 (r s ) = 0.784949r s (13)
1 − 0.02267r s
(1 + 0.4319r s + 0.04r 2 s ) (14)
(
−0.388rs + 0.676rs
2 )
(15)
(
−4.95rs + rs
2 )
. (16)
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
,(17)