C..66 VWN3: Vosko-Wilk-Nusair (1980) III local correlation energy

VWN 1980(III) functional \begin{dmath}
x=1/4\,\sqrt [6]{3}{4}^{5/6}\sqrt [6]{{\frac {1}{\pi \,\rho}}}
,\end{dmath}

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

\begin{dmath}
f=\rho\,e
,\end{dmath}

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

\begin{dmath}
l=[- 0.409286,- 0.743294,- 0.228344]
,\end{dmath}

\begin{dmath}
m=[ 13.0720, 20.1231, 1.06835]
,\end{dmath}

\begin{dmath}
n=[ 42.7198, 101.578, 11.4813]
,\end{dmath}

\begin{dmath}
e=\Lambda+z \left( \lambda-\Lambda \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}
\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}
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}
z=4\,{\frac {y}{9\,\sqrt [3]{2}-9}}
.\end{dmath}



molpro@molpro.net 2018-12-10