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C DENSITY FUNCTIONAL DESCRIPTIONS 446<br />

C.36 TH3: .<br />

Density and gradient dependent first and second row exchange-correlation functional.<br />

t = [7/6,4/3,3/2,5/3, 17 11<br />

,3/2,5/3,<br />

12 6 ,5/3, 11 6<br />

11<br />

13<br />

,2,5/3, ,2,7/6,4/3,3/2,5/3,<br />

6<br />

(444)<br />

12 ], (445)<br />

u = [0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,0],<br />

v = [0,0,0,0,1,1,1,1,2,2,2,0,0,0,0,0,0,0,0],<br />

w = [0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,0,0,0,0],<br />

(446)<br />

(447)<br />

ω = [<br />

n = 19,<br />

R i = (ρ (a)) t i<br />

+ (ρ (b)) t i<br />

,<br />

( )<br />

ρ (a) − ρ (b) 2u<br />

S i =<br />

i<br />

,<br />

ρ<br />

X i = 1/2<br />

Y i =<br />

( √σ ) (<br />

(aa)<br />

v √σ )<br />

i<br />

+ (bb)<br />

v i<br />

ρ 4/3v i<br />

(<br />

σ (aa) + σ (bb) − 2 √ σ (aa) √ )<br />

σ (bb) w i<br />

ρ 8/3 ,<br />

,<br />

(448)<br />

−0.142542,<br />

−0.783603,<br />

−0.188875,0.0426830,<br />

−0.304953,0.430407,<br />

−0.0997699,0.00355789,<br />

−0.0344374,0.0192108,<br />

−0.00230906,0.0235189,<br />

−0.0331157,0.0121316,0.441190,<br />

−2.27167,4.03051,<br />

−2.28074,0.0360204],<br />

(449)<br />

(450)<br />

(451)<br />

(452)<br />

(453)<br />

f =<br />

n<br />

∑<br />

i=1<br />

ω i R i S i X i Y i ,<br />

(454)<br />

G =<br />

n<br />

∑<br />

i=1<br />

(√ ) ( )<br />

1/2ω i (ρ (s)) t i σ (ss) vi σ (ss) ( )<br />

w i (ρ (s))<br />

4/3v i −1<br />

(ρ (s)) 8/3 .<br />

(455)

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