Electron correlation energy with a combined complete active space and corrected density-functional approach in a small basis versus the reference complete basis set limit: A close agreement

Highlights: • A CASΠDFT scheme for calculation of the total correlation energy is considered, in which the non-dynamic component is calculated with the complete active space (CAS) approach in a small basis, while the dynamic one is calculated in the same basis with a functional of density functional theory (DFT) corrected for the suppression of dynamic correlation with an original damping function. • CASΠDFT reproduces closely the reference complete basis set limit for the multiple-bonded H₂, HCN, C₂, and N₂ molecules. -- Abstract: Approximate CASΠDFT scheme of the $E_c$ calculation is considered, in which its non-dynamic $E_c^{\mathrm{nd}}$ and dynamic $E_c^d$ components are calculated with the complete active space (CAS) configuration interaction (CI) for valence bonds in a small basis and density functional theory (DFT) in the same basis, respectively. The DFT contribution is corrected for the suppression of dynamic correlation (SDC) with non-dynamic correlation. The present CASΠDFT closely reproduces both complete basis set (CBS) $E_c$ limits and their trends in the series of the prototype multiple-bonded molecules C₂, HCN, N₂, and CO.