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C..42 P86: .

Gradient correction to VWN. \begin{dmath}
f=\rho\,e+{\frac {{e^{-\Phi}}C \left( r \right) \sigma}{d{\rho}^{4/3}}}
,\end{dmath}

\begin{dmath}
r=1/4\,\sqrt [3]{3}{4}^{2/3}\sqrt [3]{{\frac {1}{\pi \,\rho}}}
,\end{dmath}

\begin{dmath}
x=\sqrt {r}
,\end{dmath}

\begin{dmath}
\zeta={\frac {\rho \left( a \right) -\rho \left( b \right) }{\rho}}
,\end{dmath}

\begin{dmath}
k=[ 0.0310907, 0.01554535,-1/6\,{\pi }^{-2}]
,\end{dmath}

\begin{dmath}
l=[- 0.10498,- 0.325,- 0.0047584]
,\end{dmath}

\begin{dmath}
m=[ 3.72744, 7.06042, 1.13107]
,\end{dmath}

\begin{dmath}
n=[ 12.9352, 18.0578, 13.0045]
,\end{dmath}

\begin{dmath}
e=\Lambda+\omega\,y \left( 1+h{\zeta}^{4} \right)
,\end{dmath}

\begin{dmath}
y={\frac {9}{8}}\, \left( 1+\zeta \right) ^{4/3}+{\frac {9}{8}}\,
\left( 1-\zeta \right) ^{4/3}-9/4
,\end{dmath}

\begin{dmath}
h=4/9\,{\frac {\lambda-\Lambda}{ \left( \sqrt [3]{2}-1 \right) \omega}}
-1
,\end{dmath}

\begin{dmath}
\Lambda=q \left( k_{{1}},l_{{1}},m_{{1}},n_{{1}} \right)
,\end{dmath}

\begin{dmath}
\lambda=q \left( k_{{2}},l_{{2}},m_{{2}},n_{{2}} \right)
,\end{dmath}

\begin{dmath}
\omega=q \left( k_{{3}},l_{{3}},m_{{3}},n_{{3}} \right)
,\end{dmath}

\begin{dmath}
q \left( A,p,c,d \right) =A \left( \ln \left( {\frac {{x}^{2}}{X
...
... ^{-1} \right) \left( X \left( p,c,d \right) \right) ^{-1}
\right)
,\end{dmath}

\begin{dmath}
Q \left( c,d \right) =\sqrt {4\,d-{c}^{2}}
,\end{dmath}

\begin{dmath}
X \left( i,c,d \right) ={i}^{2}+ci+d
,\end{dmath}

\begin{dmath}
\Phi= 0.007390075\,{\frac {z\sqrt {\sigma}}{C \left( r \right) {\rho}^{
7/6}}}
,\end{dmath}

\begin{dmath}
d=\sqrt [3]{2}\sqrt { \left( 1/2+1/2\,\zeta \right) ^{5/3}+ \left( 1/2-
1/2\,\zeta \right) ^{5/3}}
,\end{dmath}

\begin{dmath}
C \left( r \right) = 0.001667+{\frac { 0.002568+\alpha\,r+\beta\,{r}^{2
}}{1+\xi\,r+\delta\,{r}^{2}+10000\,\beta\,{r}^{3}}}
,\end{dmath}

\begin{dmath}
z= 0.11
,\end{dmath}

\begin{dmath}
\alpha= 0.023266
,\end{dmath}

\begin{dmath}
\beta= 0.000007389
,\end{dmath}

\begin{dmath}
\xi= 8.723
,\end{dmath}

\begin{dmath}
\delta= 0.472
.\end{dmath}



molpro@molpro.net 2018-04-21