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We analyze the Colle–Salvetti correlation functional and propose a new simplified correlation functional called the one-parameter progressive (OP) functional. It contains only one semiempirical parameter with no adjusted fundamental constant. The functional can be adapted to any kind of exchange functional. Different from generalized gradient approximation type functionals, OP is not derived to obey necessary conditions of the exact correlation functional. However, it is proved that OP satisfies all these conditions if the exchange part is chosen to obey the conditions of the exact exchange functional. Compared to conventional correlation functionals, OP is found to give more accurate correlation energies for atoms, helium through argon, and equivalent chemical properties for the G2 set of molecules.
Tsuneda et al. (Tue,) studied this question.