C..9 B97R: Density functional part of B97 Re-parameterized by Hamprecht et al

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C..9 `B97R`: 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. See reference [13] for more details.

$\begin{dmath} K= \left( \epsilon \left( \rho_{\alpha},\rho_{\beta} \right) -\ep... ...\chi_{s} \right) ^{2},\lambda_{{3}} \right) \right) ^{2} \right) ,\end{dmath}$ where $\begin{dmath} d=1/2\, \left( \chi_{\alpha} \right) ^{2}+1/2\, \left( \chi_{\beta} \right) ^{2} ,\end{dmath}$ $\begin{dmath} \eta \left( \theta,\mu \right) ={\frac {\mu\,\theta}{1+\mu\,\theta}} ,\end{dmath}$ $\begin{dmath} \epsilon \left( \alpha,\beta \right) = \left( \alpha+\beta \right)... ...ht) \left( \zeta \left( \alpha,\beta \right) \right) ^{ 4} \right) ,\end{dmath}$ $\begin{dmath} r \left( \alpha,\beta \right) =1/4\,\sqrt [3]{3}{4}^{2/3}\sqrt [3]{{ \frac {1}{\pi \, \left( \alpha+\beta \right) }}} ,\end{dmath}$ $\begin{dmath} \zeta \left( \alpha,\beta \right) ={\frac {\alpha-\beta}{\alpha+\beta}} ,\end{dmath}$ $\begin{dmath} \omega \left( z \right) ={\frac { \left( 1+z \right) ^{4/3}+ \left( 1-z \right) ^{4/3}-2}{2\,\sqrt [3]{2}-2}} ,\end{dmath}$ $\begin{dmath} e \left( r,t,u,v,w,x,y,p \right) =-2\,t \left( 1+ur \right) \ln ... ...}{t \left( v\sqrt {r}+wr+x{r}^{3/2}+y{r}^{p+1} \right) }} \right) ,\end{dmath}$ $\begin{dmath} c= 1.709921 ,\end{dmath}$ $\begin{dmath} T = [ 0.031091, 0.015545, 0.016887] ,\end{dmath}$ $\begin{dmath} U = [ 0.21370, 0.20548, 0.11125] ,\end{dmath}$ $\begin{dmath} V = [ 7.5957, 14.1189, 10.357] ,\end{dmath}$ $\begin{dmath} W = [ 3.5876, 6.1977, 3.6231] ,\end{dmath}$ $\begin{dmath} X = [ 1.6382, 3.3662, 0.88026] ,\end{dmath}$ $\begin{dmath} Y = [ 0.49294, 0.62517, 0.49671] ,\end{dmath}$ $\begin{dmath} P = [1,1,1] ,\end{dmath}$ $\begin{dmath} A = [ 0.955689, 0.788552,- 5.47869] ,\end{dmath}$ $\begin{dmath} B = [ 0.0820011, 2.71681,- 2.87103] ,\end{dmath}$ $\begin{dmath} C = [ 0.789518, 0.573805, 0.660975] \end{dmath}$ and $\begin{dmath} \lambda = [ 0.006, 0.2, 0.004] .\end{dmath}$ To avoid singularities in the limit $\rho_{\bar{s}}\rightarrow 0$ $\begin{dmath} G= \epsilon \left( \rho_{s},0 \right) \left( B_{{0}}+B_{{1}}\eta \... ...\chi_{s} \right) ^{2},\lambda_{{3}} \right) \right) ^{2} \right) .\end{dmath}$

molpro@molpro.net
Oct 10, 2007