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17.1.4 LYP: Lee-Yang-Parr (1988) gradient-corrected correlation energy

C. Lee, W. Yang and R. G. Parr, Phys. Rev. B 37 (1988) 785; B. Miehlich, A. Savin, H. Stoll and H. Preuss, Chem. Phys. Letters 157 (1989) 200.
$\displaystyle K$ $\textstyle =$ $\displaystyle - a {\left(\rho^2-\hat \rho^2\right) \over \left(1+d\rho^{-1/3}\right)\rho}$  
    $\displaystyle - a b \omega(\rho) \left\{ {\textstyle\frac{1}{4}}\left(\rho^2-\h...
...{2/3} \left((\rho+\hat \rho)^{8/3}+(\rho-\hat \rho)^{8/3}\right)
\right.\right.$  
    $\displaystyle \left.\left.
+\left({\textstyle\frac{47}{18}}-{\textstyle\frac{7}...
...style\frac{1}{36}}\delta(\rho)\right)(\sigma+\hat {\hat \sigma})
\right.\right.$  
    $\displaystyle \left.\left.
+\left({\textstyle\frac{11}{36}} -
{\textstyle\frac{...
...t(\sigma+\hat {\hat \sigma} +
2\hat \rho\hat \sigma/\rho\right)
\right]
\right.$  
    $\displaystyle \left.
-{\textstyle\frac{1}{3}}\rho^2\left(\sigma-\hat {\hat \sig...
...left(\sigma+\hat {\hat \sigma}\right)
+\frac12\rho\hat \rho\hat \sigma
\right\}$ (17)

where
$\displaystyle \delta(\rho)$ $\textstyle =$ $\displaystyle c \rho^{-1/3} + {d \rho^{-1/3} \over 1 + d\rho^{-1/3} }$ (18)
$\displaystyle \omega(\rho)$ $\textstyle =$ $\displaystyle {\exp \left(-c\rho^{-1/3}\right) \over 1 + d\rho^{-1/3} }
\rho^{-11/3}$ (19)

and the constants are $a=0.04918, b=0.132, c=0.2533, d=0.349$.

P.J. Knowles and H.-J. Werner
molpro-support@tc.bham.ac.uk
Mar 8, 2000