C..35 M06HFX: M06-HF Meta-GGA Exchange Functional

\begin{dmath}
g=-3/4\,{\frac {\sqrt [3]{6}\sqrt [3]{{\pi }^{2}} \left( \rho \lef...
... }}+{\it eslsda}\,h \left( \chi \left( s \right) ,{\it zs
} \right)
,\end{dmath}

\begin{dmath}
G=-3/4\,{\frac {\sqrt [3]{6}\sqrt [3]{{\pi }^{2}} \left( \rho \lef...
... }}+{\it eslsda}\,h \left( \chi \left( s \right) ,{\it zs
} \right)
,\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=[ 0.1179732,- 1.066708,- 0.1462405, 7.481848, 3.776679,- 44.36118,-
18.30962, 100.3903, 38.64360,- 98.06018,- 25.57716, 35.90404]
,\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 eslsda}=-3/8\,\sqrt [3]{3}{4}^{2/3}\sqrt [3]{{\pi }^{-1}} \left(
\rho \left( s \right) \right) ^{4/3}
,\end{dmath}

\begin{dmath}
d=[- 0.1179732,- 0.002500000,- 0.01180065, 0.0, 0.0, 0.0]
,\end{dmath}

\begin{dmath}
\alpha= 0.001867
,\end{dmath}

\begin{dmath}
{\it zs}=2\,{\frac {{\it tausMFM}}{ \left( \rho \left( s \right)
\right) ^{5/3}}}-{\it cf}
,\end{dmath}

\begin{dmath}
h \left( x,z \right) ={\frac {d_{{0}}}{\lambda \left( x,z,\alpha
...
...}{z}^{2}}{ \left( \lambda \left( x,z,\alpha \right) \right) ^{3}
}}
,\end{dmath}

\begin{dmath}
\lambda \left( x,z,\alpha \right) =1+\alpha\, \left( {x}^{2}+z \right)
,\end{dmath}

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

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



molpro@molpro.net 2018-10-21