18.1.29 PW92C: Local Spin Density Approximation Correlation Energy

J. P. Perdew and Y. Wang, Phys. Rev. B 45, 13244 (1992)

Electron-gas correlation energy.

$$K= \rho \epsilon(\rho_{\alpha},\rho_{\beta}) ,$$ (152)

where

$$\epsilon(\alpha,\beta) = e(r(\alpha,\beta),T_{{1}},U_{{1}},V_{{1}},W_{{1} },X_{{1}},Y_{{1}},P_{{1}})$$

$$- {{e(r(\alpha,\beta),T_{{3}},U_{{3}},V_ {{3}},W_{{3}},X_{{3}},Y_{{... ...P_{{3}})\omega(\zeta(\alpha,\beta))\left (1-\zeta^4(\alpha,\beta)\right )}/{c}}$$

$$+ \left (e(r( \alpha,\beta),T_{{2}},U_{{2}},V_{{2}},W_{{2}},X_{{2}},Y_{{2}},P_{{2}})\right.$$

$$- \left.e(r(\alpha,\beta),T_{{1}},U_{{1}},V_{{1}},W_{{1}},X_{{1}},Y_{{1}},P_{{1 }})\right )\omega(\zeta(\alpha,\beta))\zeta^{4}(\alpha,\beta) ,$$ (153)

$$r(\alpha,\beta)=\left (\frac {3}{4\pi \left (\alpha+\beta\right )} \right )^{1/3} ,$$ (154)

$$\zeta(\alpha,\beta)={\frac {\alpha-\beta}{\alpha+\beta}} ,$$ (155)

$$\omega(z)={\frac {\left (1+z\right )^{4/3}+\left (1-z\right )^{4/3}-2}{ 2^{4/3}-2}} ,$$ (156)

$$e(r,t,u,v,w,x,y,p)=-2 t\left (1+ur\right )\ln \left(1+{\fra... ...t \left (v\sqrt {r}+wr+x{r}^{3/2}+y{r}^{p+1}\right )}}\right) ,$$ (157)

$$c= 1.709921 ,$$ (158)

$$T = [ 0.031091, 0.015545, 0.016887] ,$$ (159)

$$U = [ 0.21370, 0.20548, 0.11125] ,$$ (160)

$$V = [ 7.5957, 14.1189, 10.357] ,$$ (161)

$$W = [ 3.5876, 6.1977, 3.6231] ,$$ (162)

$$X = [ 1.6382, 3.3662, 0.88026] ,$$ (163)

$$Y = [ 0.49294, 0.62517, 0.49671]$$ (164)

and

$$P = [1,1,1] .$$ (165)

LSDAC and LSDC are aliased to PW92C