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C..23 P86:

Gradient correction to VWN. See reference [19] for more details.

\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
Sep 24, 2008