Spectroscopic constants of diatomic molecules computed correcting Hartree-Fock or general-valence-bond potential-energy curves with correlation-energy functionals

The Kohn-Sham energy with exact exchange [using the exact Hartree-Fock (HF) exchange but an approximate correlation-energy functional] may be computed very accurately by adding the correlation obtained from the HF density to the total HF energy. Three density functionals are used: local spin density (LSD), LSD with self-interaction correction, and LSD with generalized gradient correction. This scheme has been extended (Lie-Clementi, Colle-Salvetti, and Moscardo–San-Fabian) to be used with general-valence-bond (GVB) energies and wave functions, so that the extra correlation included in the GVB energy is not counted again. The effect of all these approximate correlations on HF or GVB spectroscopic constants (${\mathit{R}}_{\mathit{e}}$,${\mathrm{\omega }}_{\mathit{e}}$, and ${\mathit{D}}_{\mathit{e}}$) is studied. Approximate relations showing how correlation affects them are derived, and may be summarized as follows: (1) the effect on ${\mathit{R}}_{\mathit{e}}$ and ${\mathrm{\omega }}_{\mathit{e}}$ depends only on the correlation derivative at ${\mathit{R}}_{\mathit{e}}$, and (2) the effect on ${\mathit{D}}_{\mathit{e}}$ depends mainly on the correlation difference between quasidissociated and equilibrium geometries. A consequence is that all the correlation corrections tested here give larger ${\mathrm{\omega }}_{\mathit{e}}$ and ${\mathit{D}}_{\mathit{e}}$ and shorter ${\mathit{R}}_{\mathit{e}}$ than the uncorrected HF or GVB values. This trend is correct for ${\mathit{D}}_{\mathit{e}}$ for both HF and GVB. For ${\mathit{R}}_{\mathit{e}}$ and ${\mathrm{\omega }}_{\mathit{e}}$, it is correct in most cases for GVB, but it often fails for the HF cases. A comparison is made with Kohn-Sham calculations with both exchange and correlation approximated. As a final conclusion, it is found that, within the present scheme, a qualitatively correct HF or GVB potential-energy curve, together with a correlation-energy approximation with correct dissociation behavior, is crucial for obtaining good estimates of spectroscopic constants.