Intercombination

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. 

Robinson and Frosch<84,133> have developed a theory in which the molecular environment is considered to provide many energy levels which can be in near resonance with the excited molecules. The environment can also serve as a perturbation, coupling with the electronic system of the excited molecule and providing a means of energy dissipation. This perturbation can mix the excited states through spin-orbit interaction. Their expression for the intercombinational radiationless transition probability is... 

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 effect of the substitution of a heavy-atom directly onto the nucleus of aromatic compounds (internal heavy-atom effect) on intercombinational radiative and nonradiative processes can be seen by examination of experimental data obtained for naphthalene and its derivatives. The data obtained by Ermolaev and Svitashev<104) and analyzed by Birks(24) to obtain individual rate constants for the various processes are collected in Table 5.9. 

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... 

It has been possible to employ the heavy-atom solvent effect in determining the rate constants for the various intercombinational nonradiative transitions in acenaphthylene and 5,6-dichIoroacenaphthylene.<436,c,rate constants, which are not accessible in light-atom solvents due to the complexity of the mechanism and the low efficiency of intersystem crossing from the first excited singlet to the first excited triplet, can be readily evaluated under the influence of heavy-atom perturbation. 

Some of the corresponding combinations of singlet terms and of intercombinations between singlet and triplet terms of Pb III have been found by the writer. A more comprehensive account of the spectra of mercurylike atoms will be given at a later date. 

A linear correlation with the atomic number Z, for 1S- -sP1 transition in Gr IIatoms is illustrated in Figure 3.7. The heavy atom Hg has considerable intensity for intercombination transitions. The S->-T transition is said to borrow intensity from S -> S transition. 

Let us consider the intercombination transitions. Then, we shall retain only the corrections containing the spin operator in the expansion. To find the form of the operator describing the electric multipole intercombination transitions and absorbing the main relativistic corrections, one has to retain in the corresponding expansion the terms containing spin operator S = a and to take into account, for the quantities of order v/c, the first retardation corrections, whereas, for the quantities of order v2/c2 one must neglect the retardation effects. Then the velocity form of the electric dipole transition probability may be written as follows ... 

Thus, the kind and quantity of relativistic corrections to the length and velocity forms of 1-radiation are different. From this point of view the concept of the equivalency of these forms must be improved both forms will lead to coinciding transition values for the accurate (exact) wave functions only if we account for the relativistic corrections of order v2/c2 to the transition operators (in practice, only for the velocity form). The other conclusion accounting for the relativistic effects leads to qualitatively new results, namely, to new operators, which allow not only improved values of permitted transitions, but also describe a number of lines, which earlier were forbidden. These relativistic corrections usually are very small, but they are very important for weak intercombination lines of light neutral atoms (see Chapter 30). 

Approximate selection rules. Intermediate coupling. Intercombination lines... 

However, the quantum numbers L and S are not rigorous, due to the existence of the spin-orbit interaction between the respective momenta. Therefore, the above-mentioned selection rules hold only approximately. In intermediate coupling the selection rules with respect to L and S change and allow many more transitions. For example, the isolation of the condition AS = 0 leads to the occurrence of the so-called intercombination E 2- and M 1-lines. For the configuration 3d3 in intermediate coupling, instead of (27.10) and (27.11) we obtain... 

As was shown in Chapter 4 (formula (4.22)), relativistic corrections of the order a2 to the intercombination 1-transitions in length form for accurate wave functions compensate each other. It follows from formulas (4.18)-(4.20) that for the velocity form of the 1-transition operator the relativistic corrections are of the order a2 and may be presented in length, velocity and acceleration forms. Calculations of the 1-radiation for the Be isoelectronic sequence (Z = 4 92) indicate that these relativistic cor-... 

The purpose of the present paper is twofold first, to place the existing spectroscopic and magnetic data in the perspective of the theoretical shell description, second, to draw attention to some unresolved problems which require further experimental studies. Attention will be limited to the interactions which affect the electronic origins of the intercombination bands in hexacoor-dinated chromium (III) complexes. The wealth of information contained in the vibrational fine structure will not be discussed. A full covering of the spectroscopic material is not intended. Further data can indeed be found in existing reviews [5,6]. It should be noted that new interesting information is also discussed in other contributions to the present volume [7]. 

Figure 16 Intensity ratio of the resonance (r) to the intercombination (i) line as function of the plasma screening parameter X. Results are shown for the two ions Fe XXIII and Mo XXXIX. Reprinted with permission from [241] 2006, American physical Society...

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