Triplet states perturbation

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. 

I have elected to include a discussion of the variational principle and perturbational methods, although these are often covered in courses in elementary quantum mechanics. The properties of angular momentum coupling are used at the level of knowing the difference between a singlet and a triplet state. 1 do not believe that it is necessary to understand the details of vector coupling to understand the implications. 

Substituents perturb the relative energies of the singlet and triplet states. In general, alkyl groups resemble hydrogen as a substituent and dialkylcarbenes are ground state... 

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... 

Hence the steady-state population of triplets should increase under heavy-atom perturbation. However, this conclusion is valid only if unimolecular decay is the main route leading to triplet state depopulation. If bimolecular triplet quenching as shown below is more important than unimolecular decay by several orders of magnitude, kd could be increased as much or more than klte without decreasing the steady state triplet population<136) ... 

In contrast to aromatic hydrocarbons, heavy-atom substitution onto carbonyl and heterocyclic molecules appears to have little effect on radiative and nonradiative intercombinational transitions. Wagner(138) has shown that as determined by the type II photoelimination, aliphatic ketones (n -> it excited states) are not sensitive to external heavy-atom perturbation. As seen previously in our discussion of type II photoelimination, aliphatic ketones undergo this cleavage from both the excited singlet and triplet states (in... 

Fig. 29. Group-theoretical predictions of the polarizations of the vibronic transitions, allowed to second order, from the individual zero-field levels of the lowest triplet state of 2,3-dichIoro-quinoxaline to vibrational levels of the ground electronic state. Solid line transitions gain intensity by spin-orbit mixing between states which differ in the electronic type of one electron e.g., S n and T . The dashed line transitions require the mixing to occur between states of the same electronic type (e.g., S and T n ) and is expected to be weaker. The dash-dotted transition could involve the favorable mixing between states that differ in the electronic type of one electron, but a spin-vibronic perturbation is needed. (From Tinti and El-Sayed, Ref. ))...

Substituents perturb the relative energies of the singlet and triplet state. In general, alkyl groups resemble hydrogen as a substituent, and dialkylcarbenes have triplet ground-states. Substituents that act as electron-pair donors stabilize the singlet state more than the triplet state by delocalization of an electron pair into the empty p orbital.55,56... 

These considerations clearly suggest that kinetic stabilization is a far better way to stabilize the triplet states of carbenes than thermodynamic stabilization. It is also important to note that thermodynamic stabilization usually results in the perturbation of electronic integrity of the reactive center, as has been seen in the case of phosphinocarbene and imidazol-2-ylidene (112). " On the other hand,... 

From these arguments it may be concluded that a low-lying triplet state may be induced in a planar complex either by axial perturbation or by weakening of the in-plane field, or by both effects acting simultaneously. Weakening of the in-plane field is likely in iraws-planar complexes where the two types of ligand are very different. 

When the quencher contains heavy atoms nonradialive relaxation of the exciple occurs via the triplet state (heavy atom perturbation). A second mode of exciplex dissociation is through electron transfer between the excited molecule and the quencher. Ionization potential of the donor, electron affinity of the acceptor and solvent dielectric constant are important parameters in such cases. 

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