C..33 M06C: M06 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 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}=[ 3.741593, 218.7098,- 453.1252, 293.6479,- 62.87470]
,\end{dmath}

\begin{dmath}
{\it cCss}=[ 0.5094055,- 1.491085, 17.23922,- 38.59018, 28.45044]
,\end{dmath}

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

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

\begin{dmath}
x=\sqrt { \left( \chi \left( a \right) \right) ^{2}+ \left( \chi
\left( b \right) \right) ^{2}}
,\end{dmath}

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

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

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

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

\begin{dmath}
z=2\,{\frac {{\it tauaMFM}}{ \left( \rho \left( a \right) \right) ...
...ubMFM}}{ \left( \rho \left( b \right) \right) ^
{5/3}}}-2\,{\it cf}
,\end{dmath}

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

\begin{dmath}
{\it ds}=1-{\frac { \left( \chi \left( s \right) \right) ^{2}}{4\,{
\it zs}+4\,{\it cf}}}
,\end{dmath}

\begin{dmath}
h \left( x,z,{\it d0},{\it d1},{\it d2},{\it d3},{\it d4},{\it d5}...
...,{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 dCab}=[- 2.741539,- 0.6720113,- 0.07932688, 0.001918681,-
0.002032902, 0.0]
,\end{dmath}

\begin{dmath}
{\it dCss}=[ 0.4905945,- 0.1437348, 0.2357824, 0.001871015,-
0.003788963, 0.0]
,\end{dmath}

\begin{dmath}
{\it aCab}= 0.003050
,\end{dmath}

\begin{dmath}
{\it aCss}= 0.005151
,\end{dmath}

\begin{dmath}
f= \left( \epsilon \left( \rho \left( a \right) ,\rho \left( b \ri...
...{{3}},{\it dCab}_{{4}},{\it dCab}_{{5}},{\it aCab} \right)
\right)
,\end{dmath}

\begin{dmath}
g=\epsilon \left( \rho \left( s \right) ,0 \right) \left( {\it Gss...
...t dCss}_{{4}},{\it dCss}_{{5}},{\it aCss} \right) \right) {
\it ds}
,\end{dmath}

\begin{dmath}
G=\epsilon \left( \rho \left( s \right) ,0 \right) \left( {\it Gss...
...t dCss}_{{4}},{\it dCss}_{{5}},{\it aCss} \right) \right) {
\it ds}
.\end{dmath}



molpro@molpro.net 2018-10-23