Zero field splitting tensor

Neese, F. 2007. Calculation of the zero-field splitting tensor on the basis of hybrid density functional and Hartree-Fock theory. The Journal of Chemical Physics 127 164112/1-9. 

Second rank (bilinear after pseudospin) zero-field splitting tensor Dap (i.e. the conventional D tensor), its main values and the main anisotropy axes (Xa,Ya,Za). 

D is the zero-field splitting tensor, a traceless, rank-two tensorial quantity. The ZFS tensor is a property of a molecule or a paramagnetic complex, with its origin in the mixing of the electrostatic and spin-orbit interactions (80). In addition, the dipole dipole interaction between individual electron spins can contribute to the ZFS (81), but this contribution is believed to be unimportant... 

Figure 12 Zero field splitting of an orbitally non-degenerate triplet ground state. D and E are related to the zero field splitting tensor by D = 3/2Dzx and E - DXX — Dyy). The states are labelled according to the z components of the spin...

The Schonland procedure is also applicable for the determination of hyperfine coupling tensors by ESR and ENDOR, for the zero-field splitting tensor (S > V2) by ESR, and the nuclear quadrupole couplings for / > Vi by ENDOR and ESEEM, discussed in the following sections. 

X32, Schonland type analysis for S > V2. The software is based on the 2nd order perturbation theory by Iwasaki [19] to obtain the principal values and directions of tensors for S > V2 species including zero-field splittings. The program is in obsolete code (Quickbasic), and is not maintained. It has been applied by the authors for the analysis of zero-field splitting tensors which requires a modification of the Schonland method in accordance with Eq. (3.5) that apparently is not implemented in the other programs in Table 3.4. 

ESR is applied for the analysis of anisotropies of g- hyperfine and (for S > Vi) the zero-field splitting tensors of powder samples under the same conditions as for single crystals. 

J is the electron exchange parameter and D the zero-field splitting tensor. D is symmetric and traceless, i.e. 

S. Sinnecker, F. Neese. Spin-Spin Contributions to the Zero-Field Splitting Tensor in Organic Triplets, Carbenes and Biradicals — A Density Fimctional and Ab Initio Study. /. Phys. Chem. A, 110 (2006) 12267-12275. 

The third column (g Faktor/a Value/D, E Values) lists the elements of the g tensor (when reported in the literature). If for one compound four values are given, the first three are the principal values of g, the fourth is the isotropic part. If only one value is given, this is always the isotropic one. The a value contains the absolute values of the elements of the hyperfine tensors a. The D and E values are the elements of the zero-field-splitting tensor D in the usual form. The units for the D and E values have been given as reported, usually they are in cm ... 

The third column (g Faktor/D, E Values) lists the elements of the g tensor (when reported in the literature). The D and E values are the elements of the zero-field-splitting tensor D in the usual form. The units for the D and E values have been given in cm ... 

X, Y and Z are the components of the so-called zero-field-splitting tensor, which is defined in the molecular fixed (principal) coordinate system x, y, z. For photochemically excited triplet states 0.1 cm ... 

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