Spin-Orbit Coupling Distortions

Indeed, in. some cases it is probable that V2 is not ob.served at all, but that the fine. structure arises from term splitting due to spin-orbit coupling or to distortions from regular octahedral symmetry. 

However, there also exists a third possibility. By using a famous relation due to Dirac, the relativistic effects can be (in a nonunique way) divided into spin-independent and spin-dependent terms. The former are collectively called scalar relativistic effects and the latter are subsumed under the name spin-orbit coupling (SOC). The scalar relativistic effects can be straightforwardly included in the one-electron Hamiltonian operator h. Unless the investigated elements are very heavy, this recovers the major part of the distortion of the orbitals due to relativity. The SOC terms may be treated in a second step by perturbation theory. This is the preferred way of approaching molecular properties and only breaks down in the presence of very heavy elements or near degeneracy of the investigated electronic state. 

Foyt et al. [137] interpreted the quadrupole-splitting parameters of low-spin ruthenium(II) complexes in terms of a crystal field model in the strong-field approximation with the configuration treated as an equivalent one-electron problem. They have shown that, starting from pure octahedral symmetry with zero quadrupole splitting, A q increases as the ratio of the axial distortion to the spin-orbit coupling increases. 

For these latter systems, the effects of static distortions have been considered for a separation, A, of the erstwhile degenerate components of the n or 5 levels, in the absence of spin-orbit coupling, and expressions for the g values are readily derived (68, 72,101). 

For the temperature range we are interested in, spin-orbit coupling effects can be neglected compared with the level splitting owing to a particular distorted arrangement of point charges around an Fe ion. 

In general, fluctuations in any electron Hamiltonian terms, due to Brownian motions, can induce relaxation. Fluctuations of anisotropic g, ZFS, or anisotropic A tensors may provide relaxation mechanisms. The g tensor is in fact introduced to describe the interaction energy between the magnetic field and the electron spin, in the presence of spin orbit coupling, which also causes static ZFS in S > 1/2 systems. The A tensor describes the hyperfine coupling of the unpaired electron(s) with the metal nuclear-spin. Stochastic fluctuations can arise from molecular reorientation (with correlation time Tji) and/or from molecular distortions, e.g., due to collisions (with correlation time t ) (18), the latter mechanism being usually dominant. The electron relaxation time is obtained (15) as a function of the squared anisotropies of the tensors and of the correlation time, with a field dependence due to the term x /(l + x ). 

It has been shown, however, that the orbital degeneracy of the 3Ti(F) state would be lifted by spin-orbit coupling 142). In this case there is no longer any need for Jahn-Teller distortion, and when the four ligands are identical the tetrahedral complexes may be quite regular. 

Liehr has shown (142) that the orbital degeneracy of the ground state in a tetrahedral nickel(II) complex may be lifted by spin-orbit coupling. This means that these complexes may not be liable to Jahn-Teller distortion as has been thought for some time. Such coupling would also have the effect of splitting all transitions into several components, the exact number... 

The direct dipole-dipole interaction between electron spins given in Eq. (14) can also contribute to D and E in the spin Hamiltonian. Various estimates of its contribution have shown it to be much smaller than the spin-orbit terms for transition-metal ions. For systems in which the crystal field is greatly distorted, this term can become large, however, and it is found to be the major source of D in the spin Hamiltonian of organic triplet-state molecules, where the spin-orbit terms are small as a result of the small size of the spin-orbit coupling parameter. 

Values for the spin Hamiltonian are given in Table XIV. The 5D state of d6 has three orbital states for the ground state in octahedral symmetry. Since these three states are connected by the spin-orbit coupling, the spin-lattice-relaxation time is quite short and the zero-field splitting very large. In a distorted octahedral field the large zero-field distortion makes detection of ESR difficult. In the case of ZnF2 the forbidden AM = 4 transition was measured and fitted to Eq. (164). 

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