19.1.18 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)

$$K = 4\,{\frac {A\rho_{\alpha}\rho_{\beta}Z}{\rho}}+AB\omega\sigma\left ( \rho_{\alpha}\rho_{\beta}\left (47-7\,\delta\right )/18-2{\rho}^ {2}/3\right )$$

$$+ \sum_s AB\omega\,\biggl (\rho_{s}\rho_{\bar s}\left (8\,{2}^{2/3}... ...}- {\frac {\left (\delta-11\right )\rho_{s}\sigma_{ss}}{9\rho}}\right )\biggr..$$

$$\biggl.+ \left (2{\rho}^{2}/3-\rho_{s}^{2}\right ) \sigma_{\bar s \bar s}\biggr ) ,$$ (83)

where

$$\omega={e^{-{\frac {c}{{\rho}^{1/3}}}}}Z{\rho}^{-11/3} ,$$ (84)

$$\delta={\frac {c+dZ}{{\rho}^{1/3}}} ,$$ (85)

$$B= 0.04918 ,$$ (86)

$$A= 0.132 ,$$ (87)

$$c= 0.2533 ,$$ (88)

$$d= 0.349 ,$$ (89)

$$e=\frac{3}{10}\left (3\pi^2\right )^{2/3}$$ (90)

and

$$Z=\left (1+{\frac {d}{{\rho}^{1/3}}}\right )^{-1} .$$ (91)