Cellular ligand field theory: Hans Bethe's crystal field legacy revitalised

This perspective traces the development and current status of ligand field theory (LFT). From Bethe's point-charge model, LFT addressed the perceived lack of covalency effects using orbital overlap. By the mid-1960s, LFT was synonymous with molecular orbital (MO) theory despite the severe shortcomings for d-electron systems of the underpinning Hartree-Fock and Wolfsberg-Helmholtz (WH) approximations. MO calculations could not reproduce experiment. In contrast, crystal-field-like calculations which utilised the WH-based angular overlap model were very successful. In the early 1980s, Gerloch and Woolley sought the theoretical justification for this empirical success which resulted in cellular ligand field theory (C-LFT). In C-LFT, the dⁿ configuration is derived from the formal metal oxidation state and is both well-defined and physically significant as are the local σ and π bonding parameters. The d-electron count is fixed and independent of the ligand field, d-orbital covalency is formally zero, and d orbital overlap is not involved in M-L bond formation. During the later 1980s, C-LFT was advocated as an alternative to MO-LFT but was not widely adopted. However, the case for rejecting MO-LFT in favour of C-LFT has gained a significant boost. Ab initio ligand field theory frees C-LFT from its dependence on experiment and provides 'first principles' data which augment and validate the original parametric C-LFT analyses and illustrate the consequences of the inadequate treatment of electron correlation in MO-LFT. Significantly, C-LFT correctly captures the highly localised nature of the d electrons demanded by the physics of crystalline paramagnetic insulators. It applies equally to both coordination and organometallic systems. Therefore, in the C-LFT regime, d-block elements use their outer valence orbitals in bonding, just like main group elements, while deviations from ideal geometries are due to stereochemically-active lone pairs, just like in main group chemistry. For transition-metal systems, these 'lone pairs' are the d electrons. C-LFT thus provides a uniform model spanning coordination, organometallic, d-block and main-group chemistries. However, actual calculations require a partially-occupied d shell and therefore C-LFT is not universally applicable although its conceptual picture often remains valid. A generalised extension of C-LFT is suggested which addresses this issue.