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The properties and reactivities of transition metal complexes are often discussed in terms of Ligand Field Theory (LFT), and with ab initio LFT a direct connection to quantum chemical wavefunctions was recently established. The Angular Overlap Model (AOM) is a widely used, ligand‐specific parameterization scheme of the ligand field splitting that has, however, been restricted by the availability and resolution of experimental data. Using ab initio LFT, we present here a generalised, symmetry‐independent and automated fitting procedure for AOM parameters that is even applicable to formally underdetermined or experimentally inaccessible systems. This method allows quantitative evaluations of assumptions commonly made in AOM applications, for example, transferability or the relative magnitudes of AOM parameters, and the response of the ligand field to structural or electronic changes. A two‐dimensional spectrochemical series of tetrahedral halido metalates ([MIIX4]2−, M=Mn−Cu) served as a case study. A previously unknown linear relationship between the halide ligands' chemical hardness and their AOM parameters was found. The impartial and automated procedure for identifying AOM parameters introduced here can be used to systematically improve our understanding of ligand–metal interactions in coordination complexes. [ABSTRACT FROM AUTHOR]

Qualitative MO theory predicts degenerate dπ orbitals for planar coordination complexes with formally σ-only ligands and the splitting energy, ΔEπ = E(dxy) − E(dxz,dyz), should be zero. For π-donor ligands, ΔEπ should be positive (dxy > dxz,yz) while for π-acceptors, ΔEπ should be negative (dxy < dxz,yz). However, experimental d–d spectra, ab initio ligand field theory (AI LFT) and crystal field theory for σ-only [M(NH3)4]2+ complexes give pronounced dπ splittings with ΔEπ around +2500 cm−1 for first-row, divalent metal ions. AI LFT further suggests ΔEπ values around +4500 cm−1 for [MF4]2− and +1000 cm−1 for [M(CN)4]2− species. The origins of these dπ orbital splittings can be traced to the effects of the ligand field potential surrounding the metal centre which includes not only the intrinsic metal–ligand π bonding but also substantial contributions from the 'void' regions above and below the molecular plane. The π component of the 'void cell' potentials increases ΔEπ which, if not explicitly taken into account, artificially enhances the apparent π-donor strength of the ligands. With the inclusion of void cell π interactions, even though the AI LFT d orbital sequence always places dxz,yz below dxy, the ligand field analysis provides a chemically-reasonable description of the M–L π interactions with cyanide being a weak π acceptor, ammonia being π-neutral and fluoride being a strong π donor. In the case of [Ni(CN)4]2−, ligand field calculations further show that, contrary to the recent claims of Oppenheim et al. (Inorg. Chem., 2019, 58, 15202) the sequence of the many-electron excited states is not a definitive guide to the underlying order of one-electron d orbital energies and that the observed sequence of nA2g > nEg > nB1g, n = 1 or 3, does not guarantee a d-orbital sequence of dxy < dxz,yz < dz2. [ABSTRACT FROM AUTHOR]

Multi reference CASSCF/NEVPT2 wavefunction calculations on planar cis‐[MA2B2] complexes show that large dxz/dyz splittings are a feature of the symmetry of the ligand field and are not due to the Orgel effect or phase coupled ligation as previously proposed based on the MO version of the angular overlap model. Instead, the splitting can be attributed to the π components of the local ligand fields in the "void" regions above and below the molecular plane. The potential in these regions is lower than the d orbital barycentre leading to negative parameter values which is fully consistent with the cellular ligand field interpretation of ligand field theory. The wider implications of ligand field effects from coordination voids are considered. [ABSTRACT FROM AUTHOR]

Abstract: A ligand field molecular mechanics (LFMM) force field has been constructed for the spin states of [Fe(bpp)2]2+ (bpp=2,6‐di(pyrazol‐1‐yl)pyridine) and related complexes. A new charge scheme is employed which interpolates between partial charges for neutral bpp and protonated [H3bpp]3+ to achieve a target metal charge. The LFMM angular overlap model (AOM) parameters are fitted to fully ab initio d orbital energies. However, several AOM parameter sets are possible. The ambiguity is resolved by calculating the Jahn–Teller distortion mode for high spin, which indicates that in [Fe(bpp)2]2+pyridine is a π‐acceptor and pyrazole a weak π‐donor. The alternative fit, assumed previously, where both ligands act as π‐donors leads to an inconsistent distortion. LFMM optimisations in the presence of [BF4]− or [PF6]− anions are in good agreement with experiment and the model also correctly predicts the spin state energetics for 3‐pyrazolyl substituents where the interactions are mainly steric. However, for 4‐pyridyl or 4‐pyrazolyl substituents, LFMM only treats the electrostatic contribution which, for the pyridyl substituents, generates a fair correlation with the spin crossover transition temperatures, T1/2, but in the reverse sense to the dominant electronic effect. Thus, LFMM generates its smallest spin state energy difference for the substituent with the highest T1/2. One parameter set for all substituted bpp ligands is insufficient and further LFMM development will be required. [ABSTRACT FROM AUTHOR]

Keywords: ab initio calculations; angular overlap model; ligand effects; ligand field theory; transition metal complexes EN ab initio calculations angular overlap model ligand effects ligand field theory transition metal complexes 1 1 1 02/21/22 20220216 NES 220216 B Our work on ligand field theory b - an automated fitting procedure for Angular Overlap Model (AOM) parameters - is reflected by Van Gogh's I Field with Irises near Arles i . Ab initio calculations, angular overlap model, ligand effects, ligand field theory, transition metal complexes The perspective in van Gogh's field resembles a correlation we found between the halide ligands' AOM parameters and their chemical hardness. [Extracted from the article]

Transition metal complexes with triply-degenerate T ground states are formally Jahn–Teller active but do not usually display the significant bond length distortions familiar from their E ground state counterparts like d9Cu(ii). The electronic ‘asymmetry’ for T-state systems lies in the dπorbitals, which interact with the ligands relatively weakly compared to the stronger σ-type interactions for E-state systems. However, in combination with asymmetric M-L π bonding, T-type systems have an additional mechanism for relieving the electronic strain. Density functional theory, ligand field theory and ligand field molecular mechanics calculations are used to show how rotations around the M–L bonds can affect their π–π (dπ–Lπ) interactions and lead to significant energy lowering. For example, d6[Fe(OH2)6]2+, which has a 5Tgstate in cubic Thsymmetry, ‘distorts’ to an S6structure 4.4 kcal mol−1lower in energy (by DFT) but with six equal Fe–O distances viaFe–O rotations of ∼ 20° and thus masquerades as an apparently regular geometry. Using model systems, we show that this effect is not restricted to formally Jahn–Teller active complexes. The combination of asymmetric π bonding and asymmetric dπorbital occupations can generate an M–L ‘torque’ worth up to 6 kcal mol−1per bond which can ‘lock’ the ligand in a particular orientation relative to the partially-occupied d orbital(s). The effect is particularly marked for imidazole, the donor group of histidine, which, in a model low-spin d5Fe(iii) system, shows almost no orientational preference in its neutral form but a very strong (∼6 kcal mol−1) orientational preference in its deprotonated form. [ABSTRACT FROM AUTHOR]

Abstract: The development and application of molecular mechanics methods which include an explicit treatment of d-electron effects are reviewed. The origins of the authors’ ligand field molecular mechanics (LFMM) method are traced from Hitchman''s simple expression for predicting the M–L bond length change accompanying a d–d transition through to the general implementation of LFMM within the molecular operating environment, including analytical energy gradients, explicit M–L π-bonding and d–s mixing effects, plus a term for handling different spin states. The LFMM applications cover simple coordination complexes of Cu(II) where a single parameter set treats multiple coordination numbers; the treatment of the complete Jahn–Teller effect in six-coordinate d9 Cu(II) complexes including elongated and compressed structures and the intervening barrier height; the parameterisation of Co(III) and Ni(II) species to enable both high- and low-spin complexes to be treated with a single parameter set; the unusual and highly distorted Type 1 centre in ‘blue copper’ enzymes; and dinuclear species containing the [Cu2O2]2+ moiety found in Type 3 copper enzymes and the important Cu–O π-bonding effects. The LFMM has also spawned two approaches, the ligand field extension of the sum of interactions between fragments ab initio (SIBFA) model and an extension to the general utility lattice program (GULP). The former has been applied to some simple Cu(II) species while the latter has been applied to d4 Mn(III)-oxides. Both are limited to σ effects only. In addition, the related effective crystal field model of Tschougreeff is discussed and compared with the LFMM approach. Providing one is prepared to develop the necessary parameters, the LFMM and related approaches are capable of delivering DFT-quality results but up to four orders of magnitude faster. [Copyright &y& Elsevier]

Constructs an electronic energy term for transition metals for extending molecular mechanics to open-shell, Werner-type coordination compounds. Use of d-orbital energies from a generalized ligand field calculation to compute the cellular ligand field stabilization energy; Geometrical effects of the stereochemical activity of d electrons.

The article presents a study that demonstrates how ligand-field molecular mechanics (LFMM) can be utilized to design new spin crossover (SCO) and light-induced excited spin state trapping (LIESST) complexes. The study is conducted through the reevaluation of the new designs with density functional theory (DFT). Results of the study conclude that the search for new SCO and LIESST systems require better theoretical tools.

Copper(II) complexes of bispidines (bispidine = tetra-, penta-, or hexadentate ligand, based on the 3,7- diazabicyclo[3.3.1]nonane backbone) display several isomeric forms. Depending on the substitution pattern of the bispidine and the type of coligands used, the structure elongates along one of the three potential Jahn-Teller axes. In an effort to develop a computational tool which can predict which isomer is observed, 23 bispidine-copper(II) complexes with 19 different ligands are analyzed theoretically by ligand field molecular mechanics (LFMM). With two exceptions, the lowest-energy LFMM structure and the experimental solid-state structure agree concerning the Jahn-TeIler axis. However, in most cases and especially for six-coordinate complexes, LFMM predicts a second local minimum within a few kilojoules per mole. Although detailed analysis reveals that the current force field is too "stiff", reasonable quantitative reproduction of the structural data is achieved with Cu-L bond length root mean square (rms) deviations for nine complexes of 0.05 Å or less and with 20 reproduced to a rms deviation of 0.1 A or less. Across all of the complexes, the Cu-amine and Cu-pyridyl bond length rms deviations are 0.07 and 0.12 Å, respectively. [ABSTRACT FROM AUTHOR]