Next: C..9 B97R: Density functional Up: C. Density functional descriptions Previous: C..7 B88: Becke88 Exchange


C..8 B95: Becke95 Correlation Functional

$\tau$ dependent Dynamical correlation functional. See reference [12] for more details.

\begin{dmath} K= {\frac {E}{1+l \left( \left( \chi_{\alpha} \right) ^{2}+ \left(... ...ht) }{H \left( 1+\nu\, \left( \chi_{s} \right) ^{2} \right) ^{2}}} ,\end{dmath} where \begin{dmath} E=\epsilon \left( \rho_{\alpha},\rho_{\beta} \right) -\epsilon \left( \rho_{\alpha},0 \right) -\epsilon \left( \rho_{\beta},0 \right) ,\end{dmath} \begin{dmath} l= 0.0031 ,\end{dmath} \begin{dmath} F=\tau_{s}-1/4\,{\frac {\sigma_{ss}}{\rho_{s}}} ,\end{dmath} \begin{dmath} H=3/5\,{6}^{2/3} \left( {\pi }^{2} \right) ^{2/3} \left( \rho_{s} \right) ^{5/3} ,\end{dmath} \begin{dmath} \nu= 0.038 ,\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} and \begin{dmath} P = [1,1,1] .\end{dmath} To avoid singularities in the limit $\rho_{\bar{s}}\rightarrow 0$ \begin{dmath} G= {\frac {F\epsilon \left( \rho_{s},0 \right) }{H \left( 1+\nu\, \left( \chi_{s} \right) ^{2} \right) ^{2}}} .\end{dmath}

molpro@molpro.net
Oct 10, 2007