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C DENSITY FUNCTIONAL DESCRIPTIONS 454<br />

Λ = q(k 1 ,l 1 ,m 1 ,n 1 ),<br />

λ = q(k 2 ,l 2 ,m 2 ,n 2 ),<br />

(544)<br />

(545)<br />

q(A, p,c,d)<br />

( (<br />

x 2 )<br />

= A ln<br />

X (x,c,d)<br />

( ) Q(c,d)<br />

+ 2carctan (Q(c,d)) −1<br />

2x + c<br />

( ( ) (x − p)<br />

2<br />

− cp ln<br />

X (x,c,d)<br />

+ 2 (c<br />

+ 2 p)arctan<br />

(546)<br />

( )<br />

Q(c,d)<br />

)(Q(c,d))<br />

)(X −1 (p,c,d)) −1 ,<br />

2x + c<br />

Q(c,d)<br />

√<br />

= 4d − c 2 ,<br />

X (i,c,d)<br />

= i 2 + ci<br />

+ d,<br />

y<br />

z = 4 √ .<br />

9 3 2 − 9<br />

(547)<br />

(548)<br />

(549)<br />

C.44 VWN5: Vosko-Wilk-Nusair (1980) V local correlation energy<br />

VWN 1980(V) functional. The fitting parameters for ∆ε c (r s ,ζ ) V appear in the caption of table<br />

7 in the reference.<br />

√<br />

√<br />

x = 1/4 6 34<br />

5/6 1<br />

6<br />

(550)<br />

π ρ , (551)<br />

ζ =<br />

ρ (a) − ρ (b)<br />

,<br />

ρ<br />

f = ρ e,<br />

k = [0.0310907,0.01554535,<br />

l = [<br />

m = [3.72744,7.06042,1.13107],<br />

(552)<br />

(553)<br />

−1/6π −2 ],<br />

(554)<br />

−0.10498,<br />

−0.325,<br />

−0.0047584],<br />

(555)

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