Integer-spin ions

In their subsequent analysis Baker and Bleaney (ibidem) decided to ignore the last term on the assumption that gdl 3b hv. Although this is a reasonable approximation for lanthanide and actinide integer-spin ions doped in single crystals, it is not usually an acceptable assumption for the broad-line spectra from metalloproteins. Furthermore, the assumption of a A-distribution around zero (i.e., D 0 but all other zero-field interaction parameters are zero) is equally untenable for biomolecules. Therefore, we go for a later extension of the theory, based on a full Equation 12.9 and on (A) 0, for application to metalloproteins (Hagen 1982b). 

This will have a very different effect on the VTVH MCD data depending on whether the complex is a Kramers (odd number of electrons, half-integer spin) or non-Kramers (even number of electrons, integer spin) ion.33... 

The particles with half-integer spin values must obey the so-called Fermi-Dirac statistics. The requirement that the wave function of the system consisting of particles of this sort must be antisymmetric with respect to the permutation of the coordinates of any two particles is the mathematical expression of this fact. An electron has half-integer spin, therefore, the total wave function of any atom or ion must be antisymmetric with respect to the permutation of the coordinates (or quantum numbers) of each pair of electrons. 

Kramers theorem requires that all half-integer spin systems be at least doubly degenerate in the absence of a magnetic held. Next, note that the splitting of these levels by a magnetic held depends on its orientation relative to the axes of the ZFS tensor of the metal ion. The VTVH MCD saturation magnetization curve behavior reflects the difference in the population of these levels and their spin expectation values in a specific molecular direchon. This direction must be perpendicular to the polarizations of the transition (Mih where i / j are the two perpendicular polarizations... 

For many years, it was believed that the qualitative behaviour of one-dimensional chains with ions of differing spin would be the same. However, in 1983 Haldane made the prediction that one-dimensional antiferromagnetic chains with integer spin would behave differently from those with half-integer spin. 21 xhe former were predicted to show a... 

For this reason, ESR is much more easily done in Kramers ions which have an odd number of electrons and at least a two fold degeneracy in the absence of an applied magnetic field (Kramers theorem). This restricts one to those paramagnetic iron materials which have half integer spin (1/2, 3/2, 5/2) and eliminates those iron materials with spins of 0, 1, 2 unless special efforts are made which we won t discuss here. 

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