Reparametrization of the Colle–Salvetti formula

We investigate the Colle–Salvetti (CS) formula, the basis of the Lee, Yang and Parr (LYP) correlation functional used in approximate density functional theory. The CS formula is reparametrized using high-accuracy Hartree–Fock (HF) wavefunctions to determine the accuracy of the formula to calculate anions. Fitting to the hydride ion or the two-electron system just prior to electron detachment at the HF level of theory does not, in general, improve the calculated correlation energies using the parameters derived from the CS/LYP method. An analysis of the CS parameters used in the popular LYP functional demonstrates the ingenuity and perhaps fortuitousness of the original formulation by CS.