Crystal fields

Mulliken symbols The designators, arising from group theory, of the electronic states of an ion in a crystal field. A and B are singly degenerate, E doubly degenerate, T triply degenerate states. Thus a D state of a free ion shows E and Tj states in an octahedral field. 

Orgel diagrams Simple graphs showing the relation between the energies of various electronic slates and the crystal field splitting. 

One of the first cluster embedding schemes was put forth by Ellis and co-workers [172]. They were interested in studying transition metal impurities in NiAl alloys, so they considered a TMAl cluster embedded in a periodic self-consistent crystal field appropriate for bulk p -NiAl. The field was calculated via calculations, as was the cluster itself The idea was to provide a relatively inexpensive alternative to supercell DET calculations. 

For Iran sition metals th c splittin g of th c d orbitals in a ligand field is most readily done using HHT. In all other sem i-ctn pirical meth -ods, the orbital energies depend on the electron occupation. HyperCh em s m oiccii lar orbital calcii latiori s give orbital cri ergy spacings that differ from simple crystal field theory prediction s. The total molecular wavcfunction is an antisymmetrized product of the occupied molecular orbitals. The virtual set of orbitals arc the residue of SCT calculations, in that they are deemed least suitable to describe the molecular wavefunction, ... 

For transition metal complexes, techniques derived from a crystal-field theory or ligand-field theory description of the molecules have been created. These tend to be more often qualitative than quantitative. 

Crystal field and ligand field molecular orbitals... 

Transition metals readily form complexes, such as [Fe(CN)6], the ferrocyanide ion, Ni(CO)4, nickel tetracarbonyl, and [CuC ], the copper tetrachloride ion. MO theory applied to such species has tended to be developed independently. It is for this reason that the terms crystal field theory and ligand field theory have arisen which tend to disguise the fact that they are both aspects of MO theory. 

Figure 7.41 Perturbation of crystal field molecular orbitals (MOs) by ligand MOs...

The and 72 states are broadened as a result of slight variations in the crystal field. The 72 and E states are sharper but the E state is split into two components, 29 cm apart, because of the slight distortion of the octahedral field. Population inversion and... 

Figure 9.7 Energy levels in (a) free and (b) Nd split by crystal field interactions...

The arc and spark spectra of the individual lanthanides are exceedingly complex. Thousands of emission lines are observed. For the trivalent rare-earth ions in soUds, the absorption spectra are much better understood. However, the crystal fields of the neighboring atoms remove the degeneracy of some states and several levels exist where only one did before. Many of these crystal field levels exist very close to a base level. As the soUd is heated, a number of the lower levels become occupied. Some physical properties of rare-earth metals are thus very sensitive to temperature (7). 

Color from Transition-Metal Compounds and Impurities. The energy levels of the excited states of the unpaked electrons of transition-metal ions in crystals are controlled by the field of the surrounding cations or cationic groups. Erom a purely ionic point of view, this is explained by the electrostatic interactions of crystal field theory ligand field theory is a more advanced approach also incorporating molecular orbital concepts. 

The quest for a comprehensible theory of coordination chemistry has given rise to the use of valence-bond, crystal-field, hgand-field, and molecular-otbital... 

E. Basolo and R. G. Pearson, Mechanisms of Inorganic Reactions, 2nd ed., John Wiley Sons, Inc., New York, 1967. An excellent volume that stresses the reactions of complexes ia solution a background and a detailed theory section is iacluded that is largely crystal field theory, but some advantages and disadvantages of molecular orbital theory are iacluded. 

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