Ligand field theory method

One way that molecular mechanics methods have been adapted to transition metal applications is by including one orbital-based term in the force field to describe the metal center. These terms are typically based on semiempirical methods or even some variation of ligand field theory. 

H. Watanabe, Operator Methods in Ligand Field Theory, Prentice-Hall, Englewood Cliff s, 1966, p. 147. 

An X-ray atomic orbital (XAO) [77] method has also been adopted to refine electronic states directly. The method is applicable mainly to analyse the electron-density distribution in ionic solids of transition or rare earth metals, given that it is based on an atomic orbital assumption, neglecting molecular orbitals. The expansion coefficients of each atomic orbital are calculated with a perturbation theory and the coefficients of each orbital are refined to fit the observed structure factors keeping the orthonormal relationships among them. This model is somewhat similar to the valence orbital model (VOM), earlier introduced by Figgis et al. [78] to study transition metal complexes, within the Ligand field theory approach. The VOM could be applied in such complexes, within the assumption that the metal and the... 

Any computational treatment of TM systems must account for the LFSE. QM methods achieve this implicitly but d-electron effects must be explicitly added to MM (4). Some effects can be modeled within conventional MM. For example, low-spin d8 complexes are planar by virtue of the LFSE (21,22), but a planar structure can also be enforced using a normal out-of-plane term (22). However, the simplest general model for describing d-orbital energies is ligand field theory (LFT) (23) which was itself derived from the earlier electrostatic crystal field theory (CFT) (24) approach. 

One way to calculate the ZFS parameters is through ligand field theory (52,53) but for quantitative calculations it is nowadays possible to use accurate correlated ab initio methods. It is known that the direct spin—spin contribution (SSC) is dominant for organic molecules, and for a long time it was assumed that for inorganic complexes exclusively the SOC dominates. Nevertheless, exceptions to this rule have been identified (54,55). 

An interesting and useful method of theoretical treatment of certain properties of complexes and crystals, called the ligand field theory, has been applied with considerable success to octahedral complexes, especially in the discussion of their absorption spectra involving electronic transitions.66 The theory consists in the approximate solution of the Schrddinger wave equation for one electron in the electric field of an atom plus a perturbing electric field, due to the ligands, with the symmetry of the complex or of the position in the crystal of the atom under consideration. 

The numerical evaluation of the energies of orbitals and states is fundamentally a matter of making quantum mechanical computations. As indicated in Chapter 1, quantum mechanics per se is not the subject of this book, and indeed we have tried in general to avoid any detailed treatment of methods for solving the wave equation, emphasis being placed on the properties that the wave functions must have purely for reasons of symmetry and irrespective of their explicit analytical form. However, this discussion of the symmetry aspects of ligand field theory would be artificial and unsatisfying without some... 

Ligand field theory may be taken to be the subject which attempts to rationalize and account for the physical properties of transition metal complexes in fairly simple-minded ways. It ranges from the simplest approach, crystal field theory, where ligands are represented by point charges, through to elementary forms of molecular orbital theory, where at least some attempt at a quantum mechanical treatment is involved. The aims of ligand field theory can be treated as essentially empirical in nature ab initio and even approximate proper quantum mechanical treatments are not considered to be part of the subject, although the simpler empirical methods may be. 

In this chapter, we have developed the information content of different excited state spectroscopic methods in terms of ligand field theory and the covalency of L—M bonds. Combined with the ground-state methods presented in the following chapters, spectroscopy and magnetism experimentally define the electronic structure of transition metal sites. Calculations supported by these data can provide fundamental insight into the physical properties of inorganic materials and their reactivities in catalysis and electron transfer. The contribution of electronic structure to function has been developed in Ref. 61. 

The solid state properties of the linear chain compounds are substantially determined by the electronic structure of the molecular [Pt(CN)4]2 units. An ab initio calculation of the electronic structure of the [Pt(CN)4]2 complex including all 132 electrons or at least the 48 valence electrons does not exist as yet. Concerning the optical spectroscopy, however, mainly the highest occupied (HOMO) and the lowest unoccupied (LUMO) molecular orbitals are of interest. Thus, the number of electrons and states, which have to be considered, is restricted drastically compared to the full problem. The method usually applied to the approximative determination of the relevant states and their electronic structures is the molecular-orbital ligand field theory mostly using empirical fitting data50,31). 

In the following pages, the valence bond theory and the crystal field theory are described very briefly to set more recent developments in their historical context. The rest of the chapter describes the ligand field theory and the method of angular overlap, which can be used to estimate the orbital energy levels. These two supply the basic approach to bonding in coordination compounds for the remainder of the book. 

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