Term intersystem crossing

The radiationless transition between two states of same spin is called internal conversion, the one occuring with inversion of spin being termed intersystem crossing. In both processes the excess energy is liberated as heat. All these transitions between different electronic states are customarily preceded by vibrational relaxation, i.e. the deactivation from a higher vibronie level to the v0-level of the same electronic state (Fig. 5). 

The pressure Ap is not expected to affect the probability of intersystem crossing and thus the frequency factor A to any large extent. It is rather the activation energy A that becomes a function of Ap and, since the second term in Eq. (88) is rather small, a function of tid x. 

For the intersystem crossing T Si, the electronic coupling matrix element (T il so S ) often vanishes. In this case, we have to take into account the higher-order terms in Eq. (3.69), that is,... 

Such an enhancement of the fluorescence quantum yield can be explained in terms of the relative locations of the singlet n-n and n-n states. In the absence of cation the lowest excited states has n-n character, which results in an efficient intersystem crossing to the triplet state and consequently a low fluorescence quantum yield. In the presence of cation, which strongly interacts with the lone pair of the carbonyl group, the n-n state is likely to be shifted to higher energy so that the lowest excited state becomes n-n. An outstanding selectivity of Na+ versus K+ was found the ratio of the stability constants is 1300 in a mixture of ethanol and water (60 40 v/v). 

Note the important difference between Eq. 33 and 28. The term has been replaced by since in the case of energy-transfer intersystem crossing in... 

The further assumption that 3M is degenerate with the correlating molecular triplet state 3M provides an estimate of the energy (3M ) of this state in the region (XM ) > (3M ) > E(3M ) which may be spectroscopically inaccessible. Double intersystem crossing to different molecular triplet states of naphthalene87 is also apparently exhibited by the excimer of 1,6-dimethylnaphthalene40 in which the nonradiative process is characterized by a rate constant kf which is the sum of temperature-dependent and temperature-independent terms. The value of the latter is also consistent with a spin-prohibited process (Table XVI). 

If the lower energy state intersects at a point (Figure 5.1) above the zero vibrational level of the transferring state, a temperature dependent factor e w/kT may be involved in the rate constant for intersystem crossing. The energy term W corresponds to the activation energy needed to raise the molecule from the zero point to the point of intersection. 

A time-dependent process, such as radiative absorption, internal conversion, intersystem crossing, unimolecular isomerization, or collision, may be treated in terms of a zero-order Hamiltonian H0 and a perturbation T. An unperturbed eigenstate of H0 evolves in time, since it is not an eigenstate to the perturbed Hamiltonian... 

Such localized states as under discussion here may arise in a system with local permutational symmetries [Aa] and [AB], If [Aa] + [S] and [Ab] = [5], the outer direct product [Aa] 0 [AB] gives rise to a number of different Pauli-allowed [A], If the A and B subsystems interact only weakly, these different spin-free [A] levels will be closely spaced in energy. The extent of mixing of these closely spaced spin-free states under the full Hamiltonian, H = HSF + f2, may then be large. Thus, systems which admit a description in terms of local permutational symmetries may in some cases readily undergo spin-forbidden processes, such as intersystem crossing. 

Radiationless transitions among electronic states of molecules represent a class of relaxation processes that are electronic in nature. The general term electronic relaxation appears to be appropriate for these processes,23 but it is convenient to divide those transitions involving a change in the bound electronic states of a molecule into two categories Transitions between states of the same multiplicity, referred to as internal conversion, and transitions between states of different multiplicity, referred to as intersystem crossing. Although there are several early experimental... 

Now, in aromatic hydrocarbons intramolecular skeletal vibrations, rather than C—H vibrations, dominate the vibronic coupling contribution to the term J m = — . Furthermore, intermolecular vibrations will have negligible effect on the coupling of the electronic states of interest. Thus, in the case of internal conversion, where the (relatively large) matrix elements are solely determined by intramolecular vibronic coupling, no appreciable medium effect on the nonradiative lifetime is to be expected. On the other hand, intersystem crossing processes are enhanced by the external heavy atom effect, which leads to a contribution to the electronic coupling term. 

As an example of the effect of level shifts in the crystalline state, as just described, consider the observed rates of radiationless transitions in anthracene.45 The first excited 1BSu of the isolated anthracene molecule is located about 600 cm-1 above the second triplet state. Hence, 8 < vv and the intersystem crossing process is quite rapid at room temperature. The fluorescence quantum yield is about 0.3 for this molecule in the gas phase and in solution. In the crystal the first excited singlet state is red shifted (from the gas level) by about 1880 cm- while the second triplet state is hardly affected, so that in this case the energy gap between those two states increases in the crystal. Then the coupling term, v, is smaller in the crystalline state than in solution, thereby leading to a decrease in the rate of the intersystem crossing. The result is that the fluorescence yield in the crystal is close to unity.40... 

Simple expressions for these three reaction parameters are given in Eqs. 6-8. Subscripts specify the multiplicity of the excited states. The expression for Du includes the singlet component 0 as well as the triplet one which is given by the product of the intersystem crossing quantum yield 013 and the fraction of triplets which eventually result in products 3. As mentioned previously, the singlet related terms in the three equations are considered negligible when alkyl aryl ketones are the reactants. 

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