text: 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(BiH)] model with a Pt thought of having a formal 4+ oxidation state, the team found that the t metal orbitals were higher energy that the e 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 KAgF, 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 MoNiP band structures the e-type orbitals of the octahedral nickel atom were found to be the major component of an occupied band below the t 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 CoP 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.