The Wigner Functional

An extremely simple form for the correlation energy was suggested by Wigner in 1938 [114], which has subsequently been shown to perform better than E_c^VWN [115]. The functional form contains two parameters, and there have been a number of reparametrizations [116,117,118], each with its own strengths. The functional occurs as a term in E_c^LYP, and simply sticking with these parametisations (and pairing with E_x^B88) yields an accuracy surprisingly close to BLYP [118]. The spin-polarized functional form is
$$\begin{align}E_{c}^{W38}[\rho_{\alpha},\rho_{\beta}] = - 4a\int \frac{1}{1+d(\rh... ...c{\rho_{\alpha}\rho_{\beta}}{\rho_{\alpha}+\rho_{\beta}} \, d{\bf r} \end{align}$$
with the parameters a=0.04918 and d=0.349. The Wigner form does satisfy limiting conditions [115], but it is perhaps of most importance due to its simplicity, showing that current correlation functionals (such as E_c^LYP) may be unnecessarily complicated.