Inverted ligand field theory

Inverted ligand field theory (ILFT) describes a phenomenon in the bonding of coordination complexes where the lowest unoccupied molecular orbital is primarily of ligand character. This is contrary to the traditional ligand field theory or crystal field theory picture and arises from the breaking down of the assumption that in organometallic complexes, ligands are more electronegative and have frontier orbitals below those of the d orbitals of electropositive metals. Towards the right of the d-block, when approaching the transition-metal–main group boundary, the d orbitals become more core-like, making their cations more electronegative. This decreases their energies and eventually arrives at a point where they are lower in energy than the ligand frontier orbitals. Here the ligand field inverts so that the bonding orbitals are more metal-based, and antibonding orbitals more ligand-based. The relative arrangement of the d orbitals are also inverted in complexes displaying this inverted ligand field.

History

The first example of an inverted ligand field was demonstrated in paper form 1995 by James Snyder. In this theoretical paper, Snyder proposed that the [Cu(CF3)4]− complexes reported by Naumann et al. and assigned a formal oxidation state of +3 at the copper would be better thought of as Cu(I). By comparing the d-orbital occupation, calculated charges and orbital population of [Cu(CF3)4]− "Cu(III)" complex and the formally Cu(I) [Cu(CH3)2]− complex, they illustrated how the former could be better described as a d10 copper complex experiencing two electron donation from the CF−3 ligands. The phenomenon, termed an inverted ligand field by Roald Hoffman, began to be described by Aullón and Alvarez as they identified this phenomenon as being a result of relative electronegativities. Lancaster and co-workers later provided experimental evidence to support the assignment of this oxidation state. Using UV/visible/near IR spectroscopy, Cu K-edge X-ray absorption spectroscopy, and 1s2p resonant inelastic X-ray scattering in concert with density functional theory, multiplet theory, and multireference calculations, they were able to map the ground state electronic configuration. This showed that the lowest unoccupied orbital was of primarily trifluoromethyl character. This confirmed the presence of an inverted ligand field and started building experimental tools to probe this phenomenon. Since the Snyder case, many other complexes of later transition metals have been shown to display inverted ligand field through both theoretical and experimental methods.

Probing inverted ligand fields Computational and experimental techniques have been imperative for the study of inverted ligand fields, especially when used in cooperatively.

Computational Computational methods have played a large role in understanding the nature of bonding in both molecular and solid-state systems displaying inverted ligand fields. The Hoffman group has completed many calculations to probe occurrence of inverted ligand fields in varying systems. In a study of the absorption of CO on PtBi and PtBi2 surfaces, on an octahedral [Pt(BiH3)6]4+ model with a Pt thought of having a formal +4 oxidation state, the team found that the t2g metal orbitals were higher energy that the eg orbitals. This inversion of the d orbital ordering was attributed to the bismuth based ligands being higher in energy than the metal d orbitals. In another study involving calculations on Ag(III) salt KAgF4, other Ag(II), and Ag(III) compounds, the Ag d orbitals were found to be below those of the fluoride ligand orbitals, and was confirmed by Grochala and cowrokers by core and valence spectroscopies. The Mealli group developed the program Computer Aided Composition of Atomic Orbitals (CACAO) to provide visualised molecular orbitals analyses based on perturbation theory principles. This program successfully displayed orbital energy inversion with organometallic complexes containing electronegative metals such as Ni or Cu bound to electropositive ligand atoms such as B, Si, or Sn. In these cases the bonding was described as a ligand to metal dative bond or sigma backdonation.

Alvarez and coworkers used computational methods to illustrate ligand field inversion in the band structures of solid state materials. The group found that, contrary to the classical bonding scheme, in calculated MoNiP8 band structures the eg-type orbitals of the octahedral nickel atom were found to be the major component of an occupied band below the t2g set. Additionally, the band around the fermi level which included the Ni+ antibonding orbitals were found to be mostly of phosphorus character, a clear example if an inverted ligand field. Similar observations were made in other solid state materials like the skutterudite CoP3 structure. A consequence of the inverted ligand field in this case is that the conductivity in skutterudites is associated with the phosphorus rings rather than the metal atoms.

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