Inverted ligand fields: a conceptual dilemma for molecular orbital theory

Ligand field theory (LFT) is generally formulated either as an application of the linear combination of atomic orbitals (LCAO) molecular orbital (MO) model (LFT-MO) or as freely-parameterised crystal field theory with the global crystal field replaced by the local cellular ligand field (CLF) formalism (LFT-CLF). LFT-MO and LFT-CLF are conceptually and numerically different. These differences are highlighted by the LFT-MO concept of an 'inverted ligand field' (ILF). Using formally low-spin d⁸ and d⁷ ML₄ complexes, it is demonstrated that the LFT-MO ILF concept does not account for how the structures and reactivities of these systems change as a function of L or formal metal oxidation state. The LFT-MO overlap picture is an incomplete representation of how the sub-shell d electrons in transition metal complexes actually interact with their surroundings. The LFT-CLF picture of d electrons localised on the metal, but sensitive to the topology of the ligand field potential, V_LF, is a better model. However, V_LF does not invert. Instead, the 'internal redox' chemistry that the ILF concept attempts to rationalise is described via the LFT-CLF d-level breach. Conceptually, a d-level breach occurs when the bonding levels get too high or the d levels get too low. The empty d levels are filled and the integrity of the original dⁿ configuration is compromised. A d-level breach should be abrupt with a significant impact on the geometric and electronic structure. This behaviour is confirmed computationally. The d-level breach is thus a significant descriptor for predicting enhanced ligand electrophilicity while the absence of a breach unambiguously and definitively confirms the dⁿ configuration and metal oxidation state. In contrast, the %d components of canonical LCAO-type MOs used to invoke an ILF are unreliable descriptors and cannot be used to assign oxidation states. In general, ILFs have little chemical relevance but they are important here since they highlight several conceptual and numerical deficiencies of the theory which has underpinned the LFT-MO picture of TM systems for over 60 years.