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.

$$K = - a {\left(\rho^2-\hat \rho^2\right) \over \left(1+d\rho^{-1/3}\right)\rho}$$

$$- a b \omega(\rho) \left\{ {\textstyle\frac{1}{4}}\left(\rho^2-\h... ...{2/3} \left((\rho+\hat \rho)^{8/3}+(\rho-\hat \rho)^{8/3}\right) \right.\right.$$

$$\left.\left. +\left({\textstyle\frac{47}{18}}-{\textstyle\frac{7}... ...style\frac{1}{36}}\delta(\rho)\right)(\sigma+\hat {\hat \sigma}) \right.\right.$$

$$\left.\left. +\left({\textstyle\frac{11}{36}} - {\textstyle\frac{... ...t(\sigma+\hat {\hat \sigma} + 2\hat \rho\hat \sigma/\rho\right) \right] \right.$$

$$\left. -{\textstyle\frac{1}{3}}\rho^2\left(\sigma-\hat {\hat \sig... ...left(\sigma+\hat {\hat \sigma}\right) +\frac12\rho\hat \rho\hat \sigma \right\}$$ (17)

where

$$\delta(\rho) = c \rho^{-1/3} + {d \rho^{-1/3} \over 1 + d\rho^{-1/3} }$$ (18)

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

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