Abstract
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.
Highlights
The Lee, Yang and Parr (LYP) correlation functional [1] is one of the most popular correlation functionals used in approximate density functional theory (DFT)
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 critical nuclear charge ZC is the minimum charge required for an atomic system to have at least one bound state
Summary
The Lee, Yang and Parr (LYP) correlation functional [1] is one of the most popular correlation functionals used in approximate density functional theory (DFT). CS assumed the ‘exact’ wavefunction to be the product of a Hartree– Fock (HF) wavefunction and a correlation factor, which takes into account the correlation hole and was chosen to have the correct electron–electron cusp behaviour. Using this wavefunction, CS derived a correlation energy expression. There have been a number of critical analyses of the CS method (see in particular [5] or [6]) there is no doubt that the LYP correlation functional, combined with an appropriate exchange functional, has played a lead role in the success of Kohn–Sham DFT
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