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C DENSITY FUNCTIONAL DESCRIPTIONS 433<br />

B = 0.04918, (272)<br />

A = 0.132, (273)<br />

c = 0.2533, (274)<br />

d = 0.349, (275)<br />

e = 3 (<br />

3π<br />

2 ) 2/3<br />

10<br />

(276)<br />

and<br />

(<br />

Z = 1 + d ) −1<br />

ρ 1/3 . (277)<br />

C.23 MK00: Exchange Functional for Accurate Virtual Orbital Energies<br />

π (ρ (s)) 3<br />

g = −3<br />

τ (s) − 1/4υ (s) .<br />

(278)<br />

C.24 MK00B: Exchange Functional for Accurate Virtual Orbital Energies<br />

MK00 with gradient correction of the form of B88X but with different empirical parameter.<br />

π (ρ (s)) 3<br />

g = −3<br />

τ (s) − 1/4υ (s) − β (ρ (s)) 4/3 (χ (s)) 2<br />

(279)<br />

1 + 6β χ (s)arcsinh(χ (s)) , (280)<br />

β = 0.0016,<br />

π (ρ (s)) 3<br />

G = −3<br />

τ (s) − 1/4υ (s) − β (ρ (s)) 4/3 (χ (s)) 2<br />

1 + 6β χ (s)arcsinh(χ (s)) .<br />

(281)<br />

C.25 P86: .<br />

Gradient correction to VWN.<br />

f = ρ e + e−Φ C (r)σ<br />

dρ 4/3 ,<br />

(282)<br />

√<br />

r = 1/4 3 √<br />

34<br />

2/3 3<br />

1<br />

(283)<br />

π ρ , (284)<br />

x = √ r,<br />

ζ =<br />

ρ (a) − ρ (b)<br />

,<br />

ρ<br />

(285)

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