Kramer’s doublets

FIGURE 5.9 Effective g-values for half-integer spin systems in axial symmetry. The scheme gives the values for all transitions within the Kramer s doublets of S = nl2 systems assuming gmal = 2.00 and S S S B. 

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... 

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 ... 

Tucker, E.B. 1966. Spin-lattice coupling of a Kramer s doublet Co2+ in MgO. Physical Review 143 264-274. 

Abragam and Pryce (224) have discussed the theory of d1 in an octahedral field with small tetragonal and trigonal distortions. They found that the value of g for the transition between the two states of the Kramer s doublet was very sensitive to distortions in the crystal field and were able to account for the observed values readily in terms of the theory. 

In the discussion of the Kramer s doublets we have dealt entirely with the properties of the atomic orbitals of the heme iron. In a different approach the electronic states are expressed in terms of molecular orbitals. This is particularly interesting for aromatic radicals because the unpaired electron spreads out over the entire conjugated system of -orbitals. 

The free-ion levels of an odd fN configuration (which are half-integral 7 s) in any noncubic symmetry are split by crystal field into levels that are doubly degenerate, the so-called Kramer s doublets. Thus each J level (j for one-electron) splits into (J + 1/2) Stark levels in D3h symmetry. 

The ESE-detected EPR spectrum of the Fe(II)NO form of TauD treated with aKG and taurine shows axial symmetry with g = 4.00 and gy = 2.00 (insets, Figure 8a and 8c). This observation is typical for Fe(II)NO complexes and arises from the nts = 1/2 Kramer s doublet of the... 

The VFe protein of A. vinelandii shows a weak, poorly resolved EPR signal with apparent g values of 5.8 and 5.4, which have been assigned to the low-field inflexion of the transition from the ground to the first excited state of the Kramer s doublets of an S = 3/2 spin system (39). The intensity of this signal integrates to 0.89 spin per V atom and it provided the first spectroscopic evidence for the presence of a V-con-... 

---