18.1.39 VSXC:

T. Van Voorhis and G. E. Scuseria, J. Chem. Phys. 109, 400 (1998)

$$K = F(x,z,p_{{3}},q_{{3}},r_{{3}},t_{{3}},u_{{3}},v_{{3}},\alpha_{{3}... ...lpha},\rho_{\beta})-\epsilon(\rho_{\alpha},0)- \epsilon(\rho_{\beta},0)\right )$$

$$+ \sum_s \left (\rho_{s}\right )^{4/3}F(\chi_{s},{\it z_s},p_{1},q_{{1}},r_{{1} },t_{{1}},u_{{1}},v_{{1}},\alpha_{{1}})$$

$$+{\it d_s} \epsilon(\rho_{s},0)F (\chi_{s},{\it z_s},p_{{2}},q_{{2}},r_{{2}},t_{{2}},u_{{2}},v_{{2}}, \alpha_{{2}}) ,$$ (219)

where

$$x=\chi_{\alpha}^{2}+\chi_{\beta}^{2} ,$$ (220)

$${\it z_s}={\frac {\tau_{s}}{\rho_{s}^{5/3}}}-{\it c_f} ,$$ (221)

$$z={\frac {\tau_{\alpha}}{\rho_{\alpha}^{5/3}}}+{\frac { \tau_{\beta}}{\rho_{\beta}^{5/3}}}-2 {\it c_f} ,$$ (222)

$${\it d_s}=1-{\frac {\chi_{s}^{2}}{4 {\it z_s}+4 {\it c_f} }} ,$$ (223)

$$F(x,z,p,q,c,d,e,f,\alpha)={\frac {p}{\lambda(x,z,\alpha)}}+{... ...{\frac {d{x}^{4}+e{x} ^{2}z+f{z}^{2}}{\lambda^3(x,z,\alpha)}} ,$$ (224)

$$\lambda(x,z,\alpha)=1+\alpha \left ({x}^{2}+z\right ) ,$$ (225)

$${\it c_f}=3\left (3{\pi }^{2}\right )^{2/3}/5 ,$$ (226)

$$p = [- 0.98, 0.3271, 0.7035] ,$$ (227)

$$q = [- 0.003557,- 0.03229, 0.007695] ,$$ (228)

$$r = [ 0.00625,- 0.02942, 0.05153] ,$$ (229)

$$t = [- 0.00002354, 0.002134, 0.00003394] ,$$ (230)

$$u = [- 0.0001283,- 0.005452,- 0.001269] ,$$ (231)

$$v = [ 0.0003575, 0.01578, 0.001296] ,$$ (232)

$$\alpha = [ 0.001867, 0.005151, 0.00305]$$ (233)

and ${\epsilon(\alpha,\beta)}$ is the correlation energy per particle of the Local Spin Density Approximation(PW92C).

VS99 is aliased to VSXC.