Ground-state Kramers degenerate

Kramers Ions The High-Spin Fe(III) S = 5/2 Case The effects of the ZFS and Zeeman terms in Equation 1.8 on an S 5/2 ground state are shown in Figure 1.10 for a rhombic Fe(III) site with D> 0. First, note that the sixfold degenerate Ms values of... 

In the case of tetrahedral and trigonal bipyramidal coordinations the orbitally non-degenerate quartet ground state is split by spin orbit coupling into two Kramers doublets. The energy separation is generally of the order of 10 cm-1 so that it is relevant to the interpretation of the magnetic susceptibility at low temperature and to EPR spectra. 

For degenerate ground states, both orbital and spin, B and C terms are possible, and this is the case for high spin cobalt(II) where the minimum degeneracy is two (Kramers doublet). In order to recognize B and C terms, it is necessary to record spectra at different temperatures, since C terms are temperature dependent, while B terms are not. This can be easily done with single crystals, but in this case the requirement is that the crystals possess an optical axis. 

Although most lanthanide ions are paramagnetic, because of rapid relaxation effects, spectra can be obtained only at low temperatures (often 4.2 K) in most cases. From the point of view of the chemist, EPR spectra are readily obtained (at room temperature) only from the f Gd +, with its 87/2 ground state. The sublevels of this state are degenerate in the absence of a crystal field (in a free Gd + ion), but are split into four Kramers doublets, with M/-values of 1/2, 3/2, 5/2 and 7/2. The application of a magnetic field removes the degeneracy of each doublet, and transitions can occur on irradiation with microwave radiation, subject to the usual selection rule of AM/ = 1. 

Axial and rhombic zero-field splitting parameters of Kramers doublet ground states and ligand field splitting parameters of non-Kramers doublet degenerate ground states can be determined from the variable temperature variable field data. 

ForNd3+ion, J = 9/2 and hence the ground state multiplet is tenfold degenerate. Under the influence of a crystal field of hexagonal symmetry, the degeneracy is partially removed. Five Kramer s doublets are formed with the eigenstates, 1/2),... 

State, which must be totally symmetric. The second emerges from the extended Kramers theorem, which imposes half-integer J rotational states to be degenerate. Thus, the lowest rotational state for the electronic ground state of Li3 corresponds to J = j, and must be degenerate. 

The Jahn-Teller theorem states that degenerate ground states are not possible There will always be a normal coordinate in the point group of the complex or molecule which provides a mechanism for lifting this degeneracy. While the theorem is valid in all symmetries with the exception of linear molecules for orbitaUy degenerate states there is a restriction in the case of in degeneracy in so far as Kramers doublets... 

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