Splitting zero-field

In the triplet molecule, the three triplet states (To,T ) are not degenerate, but are decoupled because of the dipolar interaction (i.e. the 25+1 degeneracy is removed). This is known as zero field splitting. The expression for the dipolar Hamiltonian between two electrons can be written as 

D y I and 5 being the electron spin operator along each of the molecular axes i = X, y, z. The Hamiltonian in Eq. (3.46) can now be rewritten in terms of the ladder operators as 

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The zero Field splitting (ZFS) parameters D and of the triplet exciton are ... 

These mixed-valence compounds have magnetic moments around 4/tB, indicating an S = 3/2 (quartet) ground state, in keeping with their ESR spectra, which resemble those of Cr3+ compounds with a big zero-field splitting (gj = 4, g = 2) [99]. 

Magnetic exchange, 1,257, 267 polymetallic complexes, 1,138 Magnetic moment, 1, 259 Magnetic properties atomic systems, 1,260 cubic field systems, 1,263 free-atom states and terms, I, 260 lower symmetry, 1, 264 zero-field splitting, 1,262 Magnetic susceptibility, 1,256, 259 Magnetism... 

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.

Ground State Properties and Zero-Field Splitting... 

Neese, F. Zero-field splitting. In Kaupp, M., Biihl, M., Malkin, V. (eds.) The Quantum Chemical Calculation of NMR and EPR Properties, p. 541. Wiley, Heidelberg (2004)... 

The maximum zero-field splitting in the ligand-centered luminescence of [Ir(5,6-Me2-phen)2-Cl2]+ in glycerol is 3 0.5cm-1, compared to clcnO1 for [Ir(phen)3]3+.151... 

Figure 6.1. Jablonski-type diagram for pyrazine. The zero-field splittings (between tx, tV) t2) are not drawn to scale. Spin polarization ( x x x) resulting from the most probable intersystem crossing routes and part of the emission spectrum where different vibronic bands (v = /,/, k) have different zf origins are schematically indicated. (After El-Sayed.(17))...

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. 

Figure 6.2 Zero-field splitting of a triplet state.

This corresponds to an EPR-silent sample that gives no detectable ESR spectrum at X-band frequencies because it possesses a zero-field splitting larger than the Zeeman interaction (see Chapter 6), and the energy spacing between the two lowest levels is too large to be spanned by a microwave quantum at X-band. Nevertheless, higher frequencies are able to induce transitions. Since... 

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