Spin-orbit coupling transitions

Spin-orbit coupling decreases as the orbital angular momentum quantum number f increases. This is illustrated by the fact that the Pj and P3 transitions, split by only about 70 eV, are not resolved. 

Let us return to the nonadiabatic chemical processes. When a PES has been built, a part of the total Hamiltonian may remain unaccounted for, and this part, acting as a perturbation, induces transitions from the initial to the final state. There are several types of such a perturbation, namely (i) an unaccounted part of the electronic interaction (ii) non-adiabaticity (iii) spin-orbit coupling. 

The mixing coefficients a and b in (4.10) depend upon the efficiency of the spin-orbit coupling process, parameterized by the so-called spin-orbit coupling coefficient A (or for a single electron). As A O, so also do a or b. Spin-orbit coupling effects, especially for the first period transition elements, are rather small compared with either Coulomb or crystal-field effects, so the mixing coefficients a ox b are small. However, insofar that they are non-zero, we might write a transition moment as in Eq. (4.11). 

The first two terms in the expansion are strictly zero because of the spin selection rule, while the last two are non-zero, at least so far as the spin-selection rule is concerned. So a spin-forbidden transition like this, X VT , can be observed because the descriptions X and are only approximate that is why we enclose them in quotation marks. To emphasize the spin-orbit coupling coefficients for the first row transition elements are small, the mixing coefficients a and b are small, and hence the intensities of these spin-forbidden transitions are very weak. 

In fact, for 5d transition-metals relativistic contributions, and in particular spin-orbit coupling, can be of the same order of magnitude as chemical bonding. 

In this section the effect of spin-orbit coupling on radiative and radiationless intercombinational transitions (transitions occurring between states of different multiplicity) will be investigated. We will be particularly concerned with the use of internal and external heavy atoms to induce spin-orbit coupling. The effect of heavy atoms on intercombinational processes occurring in aromatic hydrocarbons, carbonyl compounds, and heterocyclic compounds will be discussed. 

---