Next: C..41 VWN3: Vosko-Wilk-Nusair (1980) Up: C. Density functional descriptions Previous: C..39 THGFL:


C..40 VSXC:

See reference [26] for more details.

\begin{dmath}
p=[- 0.98, 0.3271, 0.7035]
,\end{dmath}

\begin{dmath}
q=[- 0.003557,- 0.03229, 0.007695]
,\end{dmath}

\begin{dmath}
r=[ 0.00625,- 0.02942, 0.05153]
,\end{dmath}

\begin{dmath}
t=[- 0.00002354, 0.002134, 0.00003394]
,\end{dmath}

\begin{dmath}
u=[- 0.0001283,- 0.005452,- 0.001269]
,\end{dmath}

\begin{dmath}
v=[ 0.0003575, 0.01578, 0.001296]
,\end{dmath}

\begin{dmath}
\alpha=[ 0.001867, 0.005151, 0.00305]
,\end{dmath}

\begin{dmath}
g= \left( \rho \left( s \right) \right) ^{4/3}F \left( \chi \left(...
...{2}},q_{{2}},r_{{2
}},t_{{2}},u_{{2}},v_{{2}},\alpha_{{2}} \right)
,\end{dmath}

\begin{dmath}
G= \left( \rho \left( s \right) \right) ^{4/3}F \left( \chi \left(...
...{2}},q_{{2}},r_{{2
}},t_{{2}},u_{{2}},v_{{2}},\alpha_{{2}} \right)
,\end{dmath}

\begin{dmath}
f=F \left( x,z,p_{{3}},q_{{3}},r_{{3}},t_{{3}},u_{{3}},v_{{3}},\al...
... \right) -\epsilon \left( \rho \left( b \right) ,0 \right) \right)
,\end{dmath}

\begin{dmath}
x= \left( \chi \left( a \right) \right) ^{2}+ \left( \chi \left( b
\right) \right) ^{2}
,\end{dmath}

\begin{dmath}
{\it zs}={\frac {\tau \left( s \right) }{ \left( \rho \left( s \right)
\right) ^{5/3}}}-{\it cf}
,\end{dmath}

\begin{dmath}
z={\frac {\tau \left( a \right) }{ \left( \rho \left( a \right)
...
...ight) }{ \left( \rho \left( b
\right) \right) ^{5/3}}}-2\,{\it cf}
,\end{dmath}

\begin{dmath}
{\it ds}=1-{\frac { \left( \chi \left( s \right) \right) ^{2}}{4\,{
\it zs}+4\,{\it cf}}}
,\end{dmath}

\begin{dmath}
F \left( x,z,p,q,c,d,e,f,\alpha \right) ={\frac {p}{\lambda \left(...
...f{z}^{2}}{
\left( \lambda \left( x,z,\alpha \right) \right) ^{3}}}
,\end{dmath}

\begin{dmath}
\lambda \left( x,z,\alpha \right) =1+\alpha\, \left( {x}^{2}+z \right)
,\end{dmath}

\begin{dmath}
{\it cf}=3/5\,{3}^{2/3} \left( {\pi }^{2} \right) ^{2/3}
,\end{dmath}

\begin{dmath}
T=[ 0.031091, 0.015545, 0.016887]
,\end{dmath}

\begin{dmath}
U=[ 0.21370, 0.20548, 0.11125]
,\end{dmath}

\begin{dmath}
V=[ 7.5957, 14.1189, 10.357]
,\end{dmath}

\begin{dmath}
W=[ 3.5876, 6.1977, 3.6231]
,\end{dmath}

\begin{dmath}
X=[ 1.6382, 3.3662, 0.88026]
,\end{dmath}

\begin{dmath}
Y=[ 0.49294, 0.62517, 0.49671]
,\end{dmath}

\begin{dmath}
P=[1,1,1]
,\end{dmath}

\begin{dmath}
\epsilon \left( \alpha,\beta \right) = \left( \alpha+\beta \right)...
...ht) \left( \zeta \left( \alpha,\beta \right) \right) ^{
4} \right)
,\end{dmath}

\begin{dmath}
l \left( \alpha,\beta \right) =1/4\,\sqrt [3]{3}{4}^{2/3}\sqrt [3]{{
\frac {1}{\pi \, \left( \alpha+\beta \right) }}}
,\end{dmath}

\begin{dmath}
\zeta \left( \alpha,\beta \right) ={\frac {\alpha-\beta}{\alpha+\beta}}
,\end{dmath}

\begin{dmath}
\omega \left( z \right) ={\frac { \left( 1+z \right) ^{4/3}+ \left( 1-z
\right) ^{4/3}-2}{2\,\sqrt [3]{2}-2}}
,\end{dmath}

\begin{dmath}
e \left( r,t,u,v,w,x,y,p \right) =-2\,t \left( 1+ur \right) \ln
...
...}{t \left( v\sqrt {r}+wr+x{r}^{3/2}+y{r}^{p+1}
\right) }} \right)
,\end{dmath}

\begin{dmath}
c= 1.709921
.\end{dmath}



molpro@molpro.net
Sep 24, 2008