Analysis of nondynamical correlation in the metal–ligand bond. Pauli repulsion and orbital localization in MnO−4

The nondynamical correlation error in first row transition metal complexes is studied through calculations on the permanganate ion. The source of the error is the well-known Hartree–Fock failure in the weak-interaction limit, which is shown to exist for both the metal–ligand and the ligand–ligand bonds: the metal–ligand and the ligand–ligand distances are large compared to the size of the metal 3d and ligand 2p atomic orbitals (AO’s). Pauli repulsion between ligand orbitals and 3s/3p orbitals prevent the metal–ligand and ligand–ligand distances to become small enough for efficient overlap and bonding. In multiply bonded systems the Hartree–Fock error does not show up in excessive electron repulsion, but leads to localization of the bonding orbitals (which sometimes requires symmetry breaking), resulting in a loss of covalent character. It is shown how, in the MnO−4 ion, the bonding electrons of E symmetry are localized on the oxygens while the T2 electrons are localized on the metal. The mechanism behind this (unphysical) localization is studied in detail, making use of a simple model system. The covalent character is reintroduced in configuration interaction or multiconfiguration self-consistent-field calculations: density is transferred from the ligand to the metal in the E bonds and vice versa in the T2 bonds. The total metal 3d occupation, however, remains unchanged. Several configuration selection schemes in the space of bonding, nonbonding, and antibonding orbitals are tested with the purpose to recover a large fraction of the nondynamical correlation error but still retain a manageable wave function. It is shown that the ‘‘nonbonding’’ O2p orbitals play an important role in the correlation process and cannot be excluded (kept closed) in a correlated calculation if quantatively correct results are required.