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C..8 B97RDF: Density functional part of B97 Re-parameterized by Hamprecht et al

Re-parameterization of the B97 functional in a self-consistent procedure by Hamprecht et al. This functional needs to be mixed with 0.21*exact exchange. \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}
A=[ 0.955689, 0.788552,- 5.47869]
,\end{dmath}

\begin{dmath}
B=[ 0.0820011, 2.71681,- 2.87103]
,\end{dmath}

\begin{dmath}
C=[ 0.789518, 0.573805, 0.660975]
,\end{dmath}

\begin{dmath}
\lambda=[ 0.006, 0.2, 0.004]
,\end{dmath}

\begin{dmath}
d=1/2\, \left( \chi \left( a \right) \right) ^{2}+1/2\, \left( \chi
\left( b \right) \right) ^{2}
,\end{dmath}

\begin{dmath}
f= \left( \epsilon \left( \rho \left( a \right) ,\rho \left( b \ri...
...}} \left( \eta \left( d,
\lambda_{{1}} \right) \right) ^{2} \right)
,\end{dmath}

\begin{dmath}
\eta \left( \theta,\mu \right) ={\frac {\mu\,\theta}{1+\mu\,\theta}}
,\end{dmath}

\begin{dmath}
g=\epsilon \left( \rho \left( s \right) ,0 \right) \left( B_{{0}}+...
... s \right) \right) ^{2},\lambda_{{3}}
\right) \right) ^{2} \right)
,\end{dmath}

\begin{dmath}
G=\epsilon \left( \rho \left( s \right) ,0 \right) \left( B_{{0}}+...
... s \right) \right) ^{2},\lambda_{{3}}
\right) \right) ^{2} \right)
,\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}



molpro@molpro.net 2018-07-18