Spin-orbit coupling atomic vector contributions

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 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]. 

Anisotropic Hyperfine Interaction. The anisotropic component of the hyperfine coupling has two contributions a local anisotropy owing to spin density in p- or type orbitals on the atom of observation, and nonlocal dipolar coupling with spin on other atoms. The first type of interaction is proportioned to the orbital coefficient (squared) of the pid orbiteds. To a first approximation the second term can be considered as a classic point dipolar interaction between the nucleus and the electron spin on a nearby atom. This depends on the total electron spin density at the neighbor (p ), the distance between the spins (r,2), and the orientation of the vector between them with respect to the external magnetic field (denoted by angle 0). In the point dipole approximation,... 

---