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C..27 M052XC: M05-2X Meta-GGA Correlation Functional

\begin{dmath}
T=[ 0.031091, 0.015545, 0.016887]
,\end{dmath}

\begin{dmath}
U=[ 0.21370, 0.20548, 0.11125]
,\end{dmath}

\begin{dmath}
V=[ 7.5957, 14.1189, 10.357]
,\end{dmath}

\begin{dmath}
W=[ 3.5876, 6.1977, 3.6231]
,\end{dmath}

\begin{dmath}
X=[ 1.6382, 3.3662, 0.88026]
,\end{dmath}

\begin{dmath}
Y=[ 0.49294, 0.62517, 0.49671]
,\end{dmath}

\begin{dmath}
P=[1,1,1]
,\end{dmath}

\begin{dmath}
\epsilon \left( \alpha,\beta \right) = \left( \alpha+\beta \right)...
...ght) \left( \zeta \left( \alpha,\beta \right) \right) ^{
4} \right)
,\end{dmath}

\begin{dmath}
r \left( \alpha,\beta \right) =1/4\,\sqrt [3]{3}{4}^{2/3}\sqrt [3]{{
\frac {1}{\pi \, \left( \alpha+\beta \right) }}}
,\end{dmath}

\begin{dmath}
\zeta \left( \alpha,\beta \right) ={\frac {\alpha-\beta}{\alpha+\beta}}
,\end{dmath}

\begin{dmath}
\omega \left( z \right) ={\frac { \left( 1+z \right) ^{4/3}+ \left( 1-z
\right) ^{4/3}-2}{2\,\sqrt [3]{2}-2}}
,\end{dmath}

\begin{dmath}
e \left( r,t,u,v,w,x,y,p \right) =-2\,t \left( 1+ur \right) \ln
\...
...1}{t \left( v\sqrt {r}+wr+x{r}^{3/2}+y{r}^{p+1}
\right) }} \right)
,\end{dmath}

\begin{dmath}
c= 1.709921
,\end{dmath}

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

\begin{dmath}
{\it ds}=2\,{\it tausMFM}-1/4\,{\frac {\sigma \left( {\it ss} \right) }
{\rho \left( s \right) }}
,\end{dmath}

\begin{dmath}
{\it Gab} \left( {\it chia},{\it chib} \right) =\sum _{i=0}^{n}{\i...
..., \left( {{\it chia}}^{2}+{{\it chib}
}^{2} \right) }} \right) ^{i}
,\end{dmath}

\begin{dmath}
{\it Gss} \left( {\it chis} \right) =\sum _{i=0}^{n}{\it cCss}_{{i...
...}\,{{\it chis}}^{2}}{1+{\it yCss}\,{{\it chis}
}^{2}}} \right) ^{i}
,\end{dmath}

\begin{dmath}
n=4
,\end{dmath}

\begin{dmath}
{\it cCab}=[ 1.0, 1.09297,- 3.79171, 2.82810,- 10.58909]
,\end{dmath}

\begin{dmath}
{\it cCss}=[ 1.0,- 3.05430, 7.61854, 1.47665,- 11.92365]
,\end{dmath}

\begin{dmath}
{\it yCab}= 0.0031
,\end{dmath}

\begin{dmath}
{\it yCss}= 0.06
,\end{dmath}

\begin{dmath}
f= \left( \epsilon \left( \rho \left( a \right) ,\rho \left( b \ri...
...t Gab} \left( \chi
\left( a \right) ,\chi \left( b \right) \right)
,\end{dmath}

\begin{dmath}
g=1/2\,{\frac {\epsilon \left( \rho \left( s \right) ,0 \right) {\it
Gss} \left( \chi \left( s \right) \right) {\it ds}}{{\it tausMFM}}}
,\end{dmath}

\begin{dmath}
G=1/2\,{\frac {\epsilon \left( \rho \left( s \right) ,0 \right) {\it
Gss} \left( \chi \left( s \right) \right) {\it ds}}{{\it tausMFM}}}
.\end{dmath}



molpro@molpro.net 2018-04-19