Spin-orbit coupling vector

Cf. Example 1.8.) This result shows that in the 3x3 model, the spin-orbit coupling vector depends on three factors the coefficient Q + of the in-phase (/d + /d) character of the singlet state, the spin-orbit coupling parameter (heavy atom effect), and the spatial disposition of the orbitals Xa and Xb-actual intersystem crossing rate will also depend on the Franck-Condon-weighted density of states. (Cf. the Fermi golden rule. Section S.2.3.)... 

Figure 4.25. Sum-over-atoms factor in the spin-orbit coupling vector // a) in orthogonally twisted ethylene and b) in (0, 90°) twisted trimethylene biradical, using Equation (4.12) and (4.13) most localized orbitals x - Xh and nonvanishing atomic vectorial contributions from Xh (white through-space, black through-bond).

The analogy between transition moment vectors and spin-orbit coupling vectors extends to the effects of symmetry. In molecules that belong to point groups with symmetry oper-... 

In our approximation, this is equal to the product of the absolute magnitude of Cjy and the length of the spin-orbit coupling vector... 

The vector nature of the addition of the contributions from the individual nuclei ac in the construction of the total spin-orbit coupling vector is important. It is often assumed that introduction of a heavy atom into a molecule cannot but increase the spin-orbit coupling strength (the "heavy-atom effect"). This is clearly wrong. If the additional contribution is a vector that is opposed to the resultant of those already present, the value of SOCi may actually decrease upon the introduction of a heavy atom. We believe to have identified an experimental case of such behavior recently [18]. 

As illustrated above, any p2 configuration gives rise to iD , and levels which contain nine, five, and one state respectively. The use of L and S angular momentum algebra tools allows one to identify the wavefunctions corresponding to these states. As shown in detail in Appendix G, in the event that spin-orbit coupling causes the Hamiltonian, H, not to commute with L or with S but only with their vector sum J= L +... 

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... 

Spin-orbit coupling in conjunction with the trigonal field leads to a zero-field splitting of the 2E levels. In the strong field limit the spin-orbit levels can be obtained by vector addition of cylindrical orbital and spin momenta. Hence the 2IT state will give rise to 2f7 3/2 and 2/7 1/2 components, comprising resp. the 2D 1/2 1) and 2D 1/2 +1) functions. The trigonal symmetries of these functions are as follows ... 

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