Next: C..21 MK00: Exchange Functional Up: C. Density functional descriptions Previous: C..19 LTA: Local Approximation


C..20 LYP: Lee, Yang and Parr Correlation Functional

C. Lee, W. Yang and R. G. Parr, Phys. Rev. B 37, 785(1988); B. Miehlich, A. Savin, H. Stoll and H. Preuss, Chem. Phys. Letters 157, 200 (1989)


$\displaystyle K$ $\textstyle =$ $\displaystyle 4\,{\frac {A\rho_{\alpha}\rho_{\beta}Z}{\rho}}+AB\omega\sigma\lef... ...\rho_{\alpha}\rho_{\beta}\left (47-7\,\delta\right )/18-2{\rho}^ {2}/3\right )$  
  $\textstyle +$ $\displaystyle \sum_s AB\omega\,\biggl (\rho_{s}\rho_{\bar s}\left (8\,{2}^{2/3... ...}- {\frac {\left (\delta-11\right )\rho_{s}\sigma_{ss}}{9\rho}}\right)\biggr..$  
    $\displaystyle \biggl.+ \left (2{\rho}^{2}/3-\rho_{s}^{2}\right ) \sigma_{\bar s \bar s}\biggr ) ,$ (32)

where
\begin{displaymath} \omega={e^{-{\frac {c}{{\rho}^{1/3}}}}}Z{\rho}^{-11/3} ,\end{displaymath} (33)


\begin{displaymath} \delta={\frac {c+dZ}{{\rho}^{1/3}}} ,\end{displaymath} (34)


\begin{displaymath} B= 0.04918 ,\end{displaymath} (35)


\begin{displaymath} A= 0.132 ,\end{displaymath} (36)


\begin{displaymath} c= 0.2533 ,\end{displaymath} (37)


\begin{displaymath} d= 0.349 ,\end{displaymath} (38)


\begin{displaymath} e=\frac{3}{10}\left (3\pi^2\right )^{2/3} \end{displaymath} (39)

and
\begin{displaymath} Z=\left (1+{\frac {d}{{\rho}^{1/3}}}\right )^{-1} .\end{displaymath} (40)


Next: C..21 MK00: Exchange Functional Up: C. Density functional descriptions Previous: C..19 LTA: Local Approximation

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Sep 24, 2008