Spin-forbidden transitions interactions

We then turn to the question of how to eliminate the spin-orbit interaction in four-component relativistic calculations. This allows the assessment of spin-orbit effects on molecular properties within the framework of a single theory. In a previous publication [13], we have shown how the spin-orbit interaction can be eliminated in four-component relativistic calculations of spectroscopic properties by deleting the quaternion imaginary parts of matrix representations of the quaternion modified Dirac equation. We show in this chapter how the application of the same procedure to second-order electric properties takes out spin-forbidden transitions in the spectrum of the mercury atom. Second-order magnetic properties require more care since the straightforward application of the above procedure will extinguish all spin interactions. After careful analysis on how to proceed we... 

CsNiCl3-type). Table 6 summarizes results on electronic spectra. The three spin-allowed transitions are usually observed and extensive vibrational contribution has been observed in single crystal spectra.120,121 Intense spin-forbidden transitions may also be observed122 due to exchange interactions in the solid phase. The diiodide123,124 and the complex halides121 show trigonal distortion. 

However, the Ne(2s2) state has some triplet character due to mixing with Ne(2s4). It is of considerable interest to investigate the restrictive effect of an overall spin-change in any electronic process. It has been noted that, of the inert gases, only Xe induces collisional deactivation of 0(2 lD) to 0(2 3P), which may be due either to chemical interaction, or to the spin-orbit coupling in the heavy atom. Most gases will induce the spin forbidden transition... 

In addition to causing fine-structure splitting, magnetic interactions may couple states of different spin multiplicities. As a consequence, so-called spin-forbidden transitions yield some intensity. Well-known examples for this phenomenon are phosphorescence and nonradiative transitions at intersystem crossings. 

Besides fine-structure splitting, the occurrence of spin-forbidden transitions is the most striking feature in which spin-orbit interaction manifests itself. Radiative spin-forbidden transitions in light molecules usually take place at the millisecond time scale, if the transition is dipole allowed. A dipole- and spin-forbidden transition is even weaker, with lifetimes of the order of seconds. Proceeding down the periodic table, spin-forbidden transitions become more and more allowed due to the increase of spin-orbit coupling. For molecules containing elements with principal quantum number 5 or higher (and the late first-row transition metals Ni and Cu), there is hardly any difference between transition probabilities of spin-allowed and spin-forbidden processes. 

Rates for nonradiative spin-forbidden transitions depend on the electronic spin-orbit interaction matrix element as well as on the overlap between the vibrational wave functions of the molecule. Close to intersections between potential energy surfaces of different space or spin symmetries, the overlap requirement is mostly fulfilled, and the intersystem crossing is effective. Interaction with vibrationally unbound states may lead to predissociation. 

Unless (v iG)spin = ( i E)spin. then the spin component is zero and the transition is spin-forbidden. Nevertheless, spin-forbidden transitions are observed as weak features (as in Fig. 2.18) typically with 10 -10 the intensity of fully allowed transitions. This is because of the interaction between the electron spin magnetic moment and the magnetic moment due to the orbital motion of the electron (spin-orbit coupling). The La-porte selection rule, furthermore, states that only transitions between wave functions with one having gerade and the other ungerade character are allowed (hence all d-d transitions are Laporte forbidden). This arises since the spatial component can be further broken down ... 

In the spin-forbidden transition > A2 there is no change in the geometry of the electronic orbitals and the equihbrium position of the ground and excited configuration is almost unchanged (see Fig. 2) the transition is sharp, the vibronic interaction weak and the situation of the R lines in ruby or alexandrite resembles that of rare earths. In contrast, the spin-allowed transition T2 -> A2 arises from the e set to the t2 set. Since... 

The absolute phosphorescence quantum yield (Op) of 02( Ag) sensitized by phenalenone and its lifetime have been determined in a range of different solvents, and from measurements of the radiative rate constant and lifetime of OiC Ag) in various solvents, it has emerged that charge transfer interaction is the main factor responsible for removing the prohibition on the radiative spin-forbidden transition Ag Low temperature photolysis... 

In order to use this energy level diagram to predict or interpret the spectra of octahedral complexes of d2 ions, for example, the spectrum of the [V(H20)6]3 + ion, we first note that there is a quantum-mechanical selection rule that forbids transitions between states of different spin multiplicity. This means that in the present case only three transitions, those from the 3Tj ground state to the three triplet excited states, 3T2, 3A2 and 3T1 P), will occur. Actually, spin-forbidden transitions, that is, those between levels of different spin multiplicity, do occur very weakly because of weak spin-orbit interactions, but they are several orders of magnitude weaker than the spin-allowed ones and are ordinarily not observed. 

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