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+ 9 8 (1 − ζ ) 4/3<br />

C DENSITY FUNCTIONAL DESCRIPTIONS 453<br />

ω (z)<br />

= (1 + z) 4/3 + (1 − z) 4/3 − 2<br />

2 3 √<br />

2 − 2<br />

,<br />

e(r,t,u,v,w,x,y, p)<br />

=<br />

−2t (1<br />

c = 1.709921.<br />

+ 1/2<br />

(532)<br />

(533)<br />

(<br />

+ ur)ln 1<br />

)<br />

1<br />

t (v √ r + wr + xr 3/2 + yr p+1 ,<br />

)<br />

(534)<br />

C.43 VWN3: Vosko-Wilk-Nusair (1980) III local correlation energy<br />

VWN 1980(III) functional<br />

√<br />

√<br />

x = 1/4 6 34<br />

5/6 1<br />

6<br />

(535)<br />

π ρ , (536)<br />

ζ =<br />

ρ (a) − ρ (b)<br />

,<br />

ρ<br />

f = ρ e,<br />

k = [0.0310907,0.01554535,<br />

l = [<br />

m = [13.0720,20.1231,1.06835],<br />

n = [42.7198,101.578,11.4813],<br />

e = Λ + z(λ<br />

(537)<br />

(538)<br />

−1/6π −2 ],<br />

(539)<br />

−0.409286,<br />

−0.743294,<br />

−0.228344],<br />

(540)<br />

(541)<br />

(542)<br />

− Λ),<br />

(543)<br />

y = 9 8 (1 + ζ ) 4/3<br />

− 9/4,

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