Spin-orbit coupling singlet-triplet mixing

As seen in the radiationless process, intercombinational radiative transitions can also be affected by spin-orbit interaction. As stated previously, spin-orbit coupling serves to mix singlet and triplet states. Although this mixing is of a highly complex nature, some insight can be gained by first-order perturbation theory. From first-order perturbation theory one can write a total wave function for the triplet state as... 

The perturbations in this case are between a singlet and a triplet state. The perturbation Hamiltonian, H, of the second-order perturbation theory is spin-orbital coupling, which has the effect of mixing singlet and triplet states. 

In ruthenocene it also proved possible at 77 K to resolve the broad band containing the 12+ -> 1n, and 1Z+ -+ x4> transitions, but as for Fe(Cp)2 only one spin-forbidden d-d band, assigned as shown in Table 11, could be found, despite a spin-orbit coupling constant of the order of 1 kK. Note that although the 3I1 (on S4), 34 (o2 tr 5 3), and 3II (o2 n 6 3) levels are predicted (81) to be split by , %, and 31, respectively, abnormally large band widths would not be anticipated since only one component of each triplet level is capable of mixing with the nearby singlet states. 

On the other hand, if the spin-orbit coupling is large and the electronic gap is small, the singlet state and triplet state will strongly mix these states should be diagonalized and the radiationless fraction can be treated in the IC manner. For the displaced surfaces, Eq. (72) becomes... 

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