Coordination Chemistry Reviews 253 (2009) 575–593 Contents lists available at ScienceDirect Coordination Chemistry Reviews journal homepage: www.elsevier.com/locate/ccr Review Kohn-Sham DFT results projected on ligand-field models: Using DFT to supplement ligand-field descriptions and to supply ligand-field parameters Claus E. Schäffer, Christian Anthon, Jesper Bendix ∗ Department of Chemistry, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen, Denmark Contents 1. Introduction ......................................................................................................................................... 576 2. Methodologies for bridging between DFT and LFT ................................................................................................. 578 3. Results for axially compressed systems with one strong-donor ligand ............................................................................ 579 3.1. Strong-donor systems with observable d–d transitions .................................................................................... 579 3.2. The ligand-field description of electronically, strongly compressed systems .............................................................. 580 3.3. On the reference geometry for [Cr(N)X 4 ] 2- – a distorted linear or a distorted octahedral system? ....................................... 582 3.4. Additive ligand-field parameterizations: avoiding over-parameterization by extension of the DFT-LFT mapping with vibronic coupling expressions (DFT-LFT-VC) ....................................................................... 583 4. Quantitative ligand-field theory: results for tetrahedral complexes ............................................................................... 584 4.1. Density functional theory partnering ligand-field theory: the ligand field and the interelectronic repulsion ............................. 584 4.2. Electron–electron interaction exemplified by LFR analysis of AOC-KS-DFT computational results for CrX 4 of T d symmetry ............. 585 4.3. Exemplification of one-to-one connections between AOC-KS-DFT and LFR: bisphenoidally distorted tetrahedral complexes of D 2d symmetry ................................................................................................................. 589 4.4. Quantitative ligand-field theory: history and outlook ...................................................................................... 590 5. LFT and DFT symbiosis in the future – conclusions ................................................................................................ 590 References .......................................................................................................................................... 592 article info Article history: Received 23 June 2008 Accepted 15 September 2008 Available online 25 September 2008 Keywords: Ligand field DFT AOM Nitrido Tetrahedral Vibronic abstract The use of density functional theory (DFT) as a means of providing otherwise inaccessible parameters of ligand-field theory (LFT) is discussed. This application of DFT strengthens both models: it revitalizes ligand-field theory by helping it relieving its permanent burden of over-parameterization, especially when applied to low-symmetry chemical systems, while LFT simultaneously provides a conceptual framework on which the plentiful numerical data from DFT computations can be reduced to familiar values of famil- iar parameters. The revived LFT contains information that cannot be extracted from DFT, but which, in principle, can be projected back on to DFT, thus providing the complete energy matrix of the partially filled d q configuration. Application to two kinds of chemical systems will be described: electronically strongly anisotropic nitride complexes and tetrahedral d 2 systems. In the former applications, focus is on the ligand field, its symmetry partition, and its additivity. In the d 2 systems, the focus is on extracting repulsion parameters, but also parameters of the angular overlap model will be discussed. Structural and spectroscopic studies corroborated by DFT computations demonstrate that complexes containing the {Cr(N)} 2+ moiety coordinated to weak auxiliary ligands are better considered as per- turbed linear systems than axially compressed octahedral systems. Average-of-configuration (AOC) computations on the tetrahedral systems, analysed by using two electronic interaction models, the Slater–Condon–Shortley model and the Parametrical Multiplet Term model, both formulated in terms of mutually orthogonal, barycentered coefficient operators, illuminate two-electron interactions. Thereby the quantitative influence of the individual parameters associated with these operators becomes the nov- elty of the analysis. The SCS model has D terms and E terms, where D is Jørgensen’s spin-pairing energy parameter and E is proportional to the Racah parameter B. The PMT model has four terms, two D terms ∗ Corresponding author. Tel.: +45 35320101. E-mail address: bendix@kiku.dk (J. Bendix). 0010-8545/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.ccr.2008.09.010