Non-Kramer’s doublets

However, the effect of introducing a hnite rhombicity is very different from that for half-integer spins in Figure 5.12 the non-Kramer s doublets are actually split by the rhombic zero-held interaction, and this results in a change in gNeff in the direction of higher values, that is, in the direction of lower helds. For pronounced rhombicities all h1- " disappear in inhnity (zero held) in other words, the rhombicity-induced... 

FIGURE 5.13 Effective -values for integer spin systems in axial symmetry. The scheme gives the g-values for all transitions within the non-Kramer s doublets of S = n systems assuming greal = 2.00 and 5 5 5 B cubic zero-field terms are ignored. 

The rhombic zero-field splitting in non-Kramer s doublets is more pronounced the lower the ms value of the doublet. For example, for S = 2 the zero-field splitting of the 1 doublet is 6E, while that of the 2 doublet is 3E2ID (ibidem 212), and obviously 3E2/D 6E because EID < 1/3. Consequently, the effective of lower... 

An example is the S = 2 spectrum from a mononuclear high-spin Fe site in the protein desulfoferrodoxin given in Figure 5.14. A relatively sharp effective feature is observed from within the ms = 2 non-Kramer s doublet, but the z-value is shifted from the axial g = 8 value (cf. Equation 5.39) to a higher g-value (i.e., lower field). Also, an extremely broad feature from the ms = 1 doublet, expected at gz > gN = 4, extends over the whole field range of the figure. 

FIGURE 7.2 Zero-field manifold for 5 = 2. The energy levels on the left hand are for axial symmetry (E = 0 and a = 0), that is, two non-Kramer s doublets and a singulet. The degeneracy of the doublets is lifted by addition of an E-term and subsequent addition of an a-term. 

For higher integer spins the number of allowed zero-field interaction terms further increases, and so does the convolution of comparable effects, except once more for a unique term that directly splits the highest non-Kramer s doublet. For S > 3 we have the addition, valid in cubic (and, therefore, in tetragonal, rhombic, and triclinic) symmetry ... 

As an illustration consider then a zero-field Hamiltonian for S = 4 in which we have retained only the familiar axial D- and rhombic E-term plus the cubic terms that split the non-Kramer s doublets in first order ... 

From the first two /22i s we obtain the resonance condition for the non-Kramer s doublet ... 

Fig. 13. Energy level diagram for a S = 2 state. Left to right Effects of positive and negative axial zero field splitting, rhombic splitting of the non-Kramers 2 doublet, and Zeeman effect on this doublet.

Hagen, W.R. 1982b. EPR of non-Kramers doublets in biological systems characterization of an S = 2 system in oxidized cytochrome c oxidase. Biochimica et Biophysica Acta 707 82-98. 

Figure 13 When there is a non-Kramers doublet ground state, complex nested magnetizations are observed at different temperatures (a). The ZFS of the ground state of a D4h symmetry metal porphyrinoid complex with S = 2 based on positive (b) and negative (c) values for the axial parameter, D. (Reprinted from Mack, Stillman and Kobayashi, Elsevier 2007)...

S and gj) for the ground state non-Kramers doublet described in Section... 

For a doublet ground state of an ion (it may be the Kramers doublet, the non-Kramers doublet or two states divided by a small interval do), an effective Hamiltonian may be written as a linear combination of S, Sy, Sz operators S = ). In general, the Kramers doublet is split at an arbitrary orientation of an applied magnetic field, and the corresponding effective spin Hamiltonian is... 

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