Crystal field theory generality

Crystal field splitting parameter, 2, 309 Crystal field theory, 1, 215-221 angular overlap model, 1, 228 calculations, 1, 220 generality, 1,219 low symmetry, 1,220 /-orbital, 1, 231 Crystal hydrates, 2, 305,306 bond distances, 2, 307 Crystals... 

The spectrochemical series was established from experimental measurements. The ranking of ligands cannot be fully rationalized using crystal field theory, and more advanced bonding theories are beyond the scope of general chemistry. 

For ionic compounds, crystal field theory is generally regarded a sufficiently good model for qualitative estimates. Covalency is neglected in this approach, only metal d-orbitals are considered which can be populated with zero, one or two electrons. To evaluate (Vzz)vai 4t the Mdssbauer nucleus, one may simply take the expectation value of the expression — e(3cos 0 — for every electron in a valence orbital i/, of the Mdssbauer atom and sum up,... 

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... 

As a number of excellent books and review articles have been written on the topic of crystal-field theory (10-14) and the general aspects of luminescence (75-79), these subjects are not considered per se. 

Although crystal field theory quite successfully rationalizes observed structures of the spinels of the first transition series, it must be applied with care to other examples. In comparing structures in which other factors (ionic radii, covalency, etc.) are more dissimilar, d orbital splittings alone generally do not explain the observations. In these cases, a broader analysis is required. 

Effects of crystal field (if an ion is embedded into a crystal or a glass) give rise to the last term in eq. (1). In the framework of the crystal field theory, the potential created by the crystal lattice at the position of an impurity ion can be expressed in general case as follows ... 

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