Hamiltonian zero-field splitting term

The third term in the spin Hamiltonian is the so-called zero-field splitting term which arises in systems containing more than one... 

The EPR spectra have always been interpreted2994 using an effective S = 2 spin Hamiltonian including the Zeeman term, /iBB g-S, and the hyperfine term, ICa-A-S, which describes the interaction of the unpaired electrons with the copper nucleus (7Cu = I). The spectra are very sensitive to the ratio between the isotropic coupling constant J and the local zero field splitting of nickel(II), Z)Ni.2982 In the limit J DNi it can easily be shown that the following relations hold ... 

To derive Eq. (52), it was assumed, as usual, that J was the leading term in the Hamiltonian (2). The 0) level arising from the triplet state has been taken as the origin of the energies. D = 3 Dizz/2 is the axial zero field splitting parameter for the triplet state. As for gj, g2 and Dt, they are expressed as ... 

Except in the highest symmetry cases, ab initio calculation of zero-field splitting in organic molecules requires the use of H , an operator that has only a two-electron part. Then the heavy computation involving two-electron terms cannot be avoided regardless of what spin-orbit Hamiltonian is used. These calculations are difficult because the correlation of the electrons has to be described very well before the zero-field splitting parameters are calculated accurately. Of the... 

The advantage of this high-temperature expansion is that we need not determine the individual energy levels but can use the theorem of the invariance of the trace of a matrix. For example, to find the value of e2 we square the Hamiltonian and pick out only the diagonal terms. On summing these terms over all possible values, many of the sums cancel. For example, the zero-field splitting Hamiltonian of the form... 

Ground states with 5 > i have an additional term in the spin Hamiltonian which allows for the 25 -I- 1 spin degeneracy in Ms to split in energy even in the absence of a magnetic field. This is called zero field splitting (ZFS), which is given by Eq. (23) ... 

If the crystal field is rigorously cubic both D and E arc zero and there is no zero field splitting however, there may be small contributions from a spin Hamiltonian containing quartic terms. For a tetragonal field E = 0. In the present case < < 1 (37). 

The triplet esr spectra are determined primarily by the dipole-dipole interaction of the two unpaired electrons. This interaction causes a splitting (the so called zero-field-splitting (ZFS)) of the threefold degenerate triplet state even in the absence of an external magnetic field H. The Hamiltonian for the triplet states is obtained by adding to Equ. (11) a term, H ps, which takes care for the dipole-dipole interaction ... 

For purposes of discussing the EPR of iron-semiquinone interactions in reaction centers, simplified simulations of the spectra are given in Figure 14. The parameters chosen for the simulation are similar to those of Calvo et al. [36], The spin Hamiltonian relevant to a one-electron reduced Qa-Fc-Qb system has terms involving the iron zero-field splitting and the semiquinone-iron electron spin-spin interactions ... 

The zero-field splitting in the excited triplet states of polyatomic molecules is described by the tensor Dij, which is widely used to analyze EPR and ODMR spectra. It defines the effective spin Hamiltonian given by the scalar products of the following terms [20] ... 

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 ... 

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