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C..30 M05X: M05 Meta-GGA Exchange Functional

\begin{dmath}
g=-3/4\,{\frac {\sqrt [3]{6}\sqrt [3]{{\pi }^{2}} \left( \rho \lef...
...^{4/3}F \left( S \right) {\it Fs} \left( {\it ws}
\right) }{\pi }}
,\end{dmath}

\begin{dmath}
G=-3/4\,{\frac {\sqrt [3]{6}\sqrt [3]{{\pi }^{2}} \left( \rho \lef...
...^{4/3}F \left( S \right) {\it Fs} \left( {\it ws}
\right) }{\pi }}
,\end{dmath}

\begin{dmath}
S=1/12\,{\frac {\chi \left( s \right) {6}^{2/3}}{\sqrt [3]{{\pi }^{2}}}
}
,\end{dmath}

\begin{dmath}
F \left( S \right) =1+R-R \left( 1+{\frac {\mu\,{S}^{2}}{R}} \right) ^{
-1}
,\end{dmath}

\begin{dmath}
R= 0.804
,\end{dmath}

\begin{dmath}
\mu=1/3\,\delta\,{\pi }^{2}
,\end{dmath}

\begin{dmath}
\delta= 0.066725
,\end{dmath}

\begin{dmath}
n=11
,\end{dmath}

\begin{dmath}
A=[ 1.0, 0.08151,- 0.43956,- 3.22422, 2.01819, 8.79431,- 0.00295,
9.82029,- 4.82351,- 48.17574, 3.64802, 34.02248]
,\end{dmath}

\begin{dmath}
{\it Fs} \left( {\it ws} \right) =\sum _{i=0}^{n}A_{{i}}{{\it ws}}^{i}
,\end{dmath}

\begin{dmath}
{\it ws}={\frac {{\it ts}-1}{{\it ts}+1}}
,\end{dmath}

\begin{dmath}
{\it ts}={\frac {{\it tslsda}}{{\it tausMFM}}}
,\end{dmath}

\begin{dmath}
{\it tslsda}=3/10\,{6}^{2/3} \left( {\pi }^{2} \right) ^{2/3} \left(
\rho \left( s \right) \right) ^{5/3}
,\end{dmath}

\begin{dmath}
{\it tausMFM}=1/2\,\tau \left( s \right)
.\end{dmath}



molpro@molpro.net 2018-07-18