C..67 VWN5: Vosko-Wilk-Nusair (1980) V local correlation energy

VWN 1980(V) functional. The fitting parameters for $\Delta\varepsilon_{c}(r_{s},\zeta)_{V}$ appear in the caption of table 7 in the reference. \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=[- 0.10498,- 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+\alpha\,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) \alpha}}
-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}
\alpha=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}



molpro@molpro.net 2018-09-21