Splitting zero-field, axial

Fig. 9. Zero-field splitting of the S = 2 ground state of [Fe3S4] clusters. Constructed for D = -2.5 and E/D = 0.23, where D and E are the axial and rhombic zero-field splitting parameters, respectively.

Sweeney, W. V., D. Coucouvanis et al. (1973). ESR of spin 5/2 systems with axial symmetry and moderately large zero-field splittings. Application of line-shape calculations to the interpretation of randomly oriented microcrystallite spectra. J. Chem. Phys. 59 369-379. 

Molecular g value, axial and rhombic zero field splitting, exchange interaction... 

Notice that if the molecule has axial symmetry, Dxx = Dyy so that E=0. If the molecule has octahedral symmetry, Dxx = Dyy = Dzz so that D = E=0. Thus the appearance of a zero-field splitting into two or three levels tells the spectroscopist something about the symmetry of the molecule. It is possible, of course, to do spectroscopy on these energy levels at zero magnetic field. Our concern here is the effect of zero-field splitting on the ESR spectrum where a magnetic field is applied. 

Fig. 18. Zero Field Splitting for d8, 3S, Systems in Pseudo-Axial Symmetry...

For axial symmetry (i.e., / = 0) this is a diagonal matrix with only two eigenvalues D and -D and a zero-field splitting AE = D —D = 2D as we have previously noted in... 

So the zero-field splitting can be seen to be a function of the rhombicity, and ranges from 2-D in axial symmetry to (4/3)DV3 for maximal rhombicity (EID = 1/3). 

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 ... 

The first term is characterized by a scalar, 7, and it is the dominant term. Be aware of a convention disagreement in the definition of this term instead of -27, some authors write -7, or 7, or 27, and a mistake in sign definition will turn the whole scheme of spin levels upside down (see below). The second and third term are induced by anisotropic spin-orbit coupling, and their weight is predicted to be of order Ag/ge and (Ag/ge)2, respectively (Moriya 1960), when Ag is the (anisotropic) deviation from the free electron -value. The D in the second term has nothing to do with the familiar axial zero-field splitting parameter D, but it is a vector parameter, and the x means take the cross product (or vector product) an alternative way of writing is the determinant form... 

Fig. 4. Effect of (A) axial zero field splitting for the spin systems S = 1,3/2,2, and 5/2 (with Bo applied along the z direction of the ZFS tensor), and (B) isotropic hyperfine coupling with the metal nucleus for systems with I = 1/2, S = 1/2 and I = 3/2, S = 1/2.

The diaqua and aqua (hydroxo) hemin complexes encapsulated in the micelles [20] are found to be high-spin (peff = 5.7 — S.Sps). Their high-spin nature is further confirmed from the ESR spectra at 4.2 K (Fig. 4). The spectra are characteristic of high-spin ferric porphyrins with a large zero-field-split Ai ground state with Mg = 1/2 lying lowest. The spectra are axially symmetric (gf = 2.05, = 6.0) for the diaqua complex, while for the aqua (hydroxo)... 

High-spin hemes have a strong axial zero field splitting which splits these states into three doublets, and because the value of the zero field splitting parameter D is positive (typically 5-10 cm ) for hemes the doublet consisting of the Sj = -1-, — states is lowest lying. There is usually also a smaller rhombic term E which cannot split the Kramers doublets but mixes states differing in by 2. The main net effect of E is to remove the equivalence of the x and y (in heme plane) directions so that g, and gy are unequal. 

Abbreviations CF - crystal field SH - spin Hamiltonian ZFS - zero-field splitting MA - magnetic anisotropy TIP - temperature-independent paramagnetism MP - magnetic parameter averaged (gav, /tip), axial (gz> g > D /up) CSC - complete space calculation. 

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