Ligand electronic effect, theory

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. 

The obvious deficiency of crystal-field theory is that it does not properly take into account the effect of the ligand electrons. To do this a molecular-orbital (MO) model is used in which the individual electron orbitals become a linear combination of the atomic orbitals (LCAO) belonging to the various atoms. Before going into the general problem, it is instructive to consider the simple three-electron example in which a metal atom with one ligand atom whose orbital contains two electrons. Two MO s are formed from the two atomic orbitals... 

L. Bernasconi and M. Sprik (2005) Time-dependent density functional theory description of on-site electron repulsion and ligand field effects in the optical spectrum of hexa-aquoruthenium(H) in solution. J. Phys. Chem. B 109,... 

In this section, we provide a mathematical formulation of the connection between LFT and AI electronic structure theory. Let us start from an elementary and slightly abstract ligand field construction scheme. The exposition will be based on the strong-field coupling scheme which is the one that maps most readily onto AI theory. We give a construction scheme that cleanly connects the two areas. It is certainly not the only possible one but one that we find particularly transparent and illuminating. We stay at the nonrelativistic level in this section as the inclusion of relativistic effects brings in no new aspects. 

In the previous chapter, we saw that molecular geometry was a consequence of the tradeoff between electronic effects (the electron-electron repulsions that result from the Pauli principle) and steric effects (the nuclear-nuclear repulsions between the ligands on the central atom). In this chapter, we are concerned with the determination of molecular symmetry. While molecular geometry is concerned with the shapes of molecules, molecular symmetry has to do with the spatial relationships between atoms in molecules. As we shall see, it is the three-dimensional shape of a molecule that dictates its molecular symmetry and we can use a mathematical description of symmetry properties, known as group theory, to describe the structure, bonding, and spectroscopy of molecules. 

Why then bother about much more expensive QM-based models One reason is that MM may only lead to accurate results for molecules of the same type used for the optimization and validation of the force field, i.e. extrapolation is seen to be dangerous if not impossible [9], This also extends to transition states and shortlived, unstable intermediates and therefore to chemical reactivity. Since electrons are not considered explicitly in MM, electronic effects related to structural distortions, specific stabilities and spectroscopy cannot be modeled by MM. However, in all other areas, there is no good reason for not using a well-optimized and validated MM model. Also, there are MM-based approaches to deal with most of the deficiencies listed above [9,20-28]. In the last decade, there have been a number of approaches, which have, based on simple rules [29], valence bond theory [30-33] and ligand-field theory [20-23], allowed the simplification of the force-field optimization and validation procedures and/or inclusion of electronic effects in MM models. 

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