Transition forbidden

Figure Bl.6.8 Energy-loss spectra of 200 eV electrons scattered from chlorine at scattering angles of 3° and 9° [10]. Optically forbidden transitions are responsible for the intensity in the 9° spectrum that does not appear in the 3 ° spectrum.

C3.4.6 EXCHANGE MECHANISM OF ENERGY TRANSFER IN FORBIDDEN TRANSITIONS... 

The transition probability R is related to selection mles in spectroscopy it is zero for a forbidden transition and non-zero for an allowed transition. By forbidden or allowed we shall mostly be referring to electric dipole selection mles (i.e. to transitions occurring through interaction with the electric vector of the radiation). 

The symbols and indicate allowed and forbidden transitions, respectively, whichever is the upper state. 

Fig. 4.19. Allowed electronic transitions to the K shell and corresponding X-ray lines after ionization of an atom (two forbidden transitions are also shown as dashed lines).

A < 640 nm (or 1.9 < E < 2.5 eV), weak absorption takes plaee, and is associated with electric dipole-forbidden transitions between the one-electron HOMO level w ith /i symmetry and the one-electron Uu LUMO level. 

Theoretical predictions must be compared to appropriate high quality experimental results. Allowed transitions (having oscillator strength greater than 0) may be compared to standard one-photon spectroscopic data. However, forbidden transitions must be compared to multi-photon experiments, and both types must be considered before a complete characterization of a system s excited states can be made. 

Finally, it is to be remarked that the molecular symmetry in itself may be sufficient to modify radiation resistance. This is suggested by the well-known fact that a change in symmetry may transform a forbidden transition into an allowed one.31 This case is realized for n-n transitions in benzene and its less symmetrical halogen derivatives. The phenomenon might occur on condition that the transitions considered play a sufficient relative part in radiation resistance. 

For forbidden transitions in atoms and molecules this phenomenon may be experimentally observed in spectra induced by collisions. As is known, the selection rules on some transitions may be cancelled during collision. The perturbers are able to induce a dipole moment of transition having the opposite direction in successive collisions due to intercollisional correlation. Owing to this, the induced spectra do involve the gap (Fig. 1.7), the width of the latter being proportional to the gas density [46, 47], Theorists consider intercollisional correlation to be responsible for the above phenomenon [48, 49, 50]. 

The first two terms in the expansion are strictly zero because of the spin selection rule, while the last two are non-zero, at least so far as the spin-selection rule is concerned. So a spin-forbidden transition like this, X VT , can be observed because the descriptions X and are only approximate that is why we enclose them in quotation marks. To emphasize the spin-orbit coupling coefficients for the first row transition elements are small, the mixing coefficients a and b are small, and hence the intensities of these spin-forbidden transitions are very weak. 

Here we comment on the shape of certain spin-forbidden bands. Though not strictly part of the intensity story being discussed in this chapter, an understanding of so-called spin-flip transitions depends upon a perusal of correlation diagrams as did our discussion of two-electron jumps. A typical example of a spin-flip transition is shown inFig. 4-7. Unless totally obscured by a spin-allowed band, the spectra of octahedral nickel (ii) complexes display a relatively sharp spike around 13,000 cmThe spike corresponds to a spin-forbidden transition and, on comparing band areas, is not of unusual intensity for such a transition. It is so noticeable because it is so narrow - say 100 cm wide. It is broad compared with the 1-2 cm of free-ion line spectra but very narrow compared with the 2000-3000 cm of spin-allowed crystal-field bands. 

Blue [CrlRxantla] (R = Me, Et, or L-menthyl) complexes have been prepared and characterized (103, 106, 107), and these complexes, together with some of the dialkyldithiocarbamate complexes, show spin-forbidden transitions, E, Ti A2, and T2 2, the last two... 

It would thus seem that promotion of a given electron in a molecule could result either in a singlet or a triplet excited state depending on the amount of energy added. However, this is often not the case because transitions between energy levels are governed by selection rales, which state that certain transitions are forbidden . There are several types of forbidden transitions, two of which are more important than the others. 

Symmetry-Forbidden Transitions. Among the transitions in this class are those in which a molecule has a center of symmetry. In such cases, a g g or M —> M transition (see p. 5) is forbidden, while ag—or u— g transition is allowed. 

In 1944, Lewis and Kasha (52) identified phosphorescence as a forbidden" transition from an excited triplet state to the ground singlet state and suggested the use of phosphorescence spectra to identify molecules. Since then, phosphorimetry has developed into a popular method of analysis that, when compared with fluorometry, is more sensitive for some organic molecules and often provides complimentary information about structure, reactivity, and environmental conditions (53). 

Figure 10. Electron excitations in radicals (a) Collective representation of one-electron transitions of the A, B, and C types if denotes MO (b) LCI energy-level scheme (Jablonski diagram) for doublet and quartet states indicating why with radicals fluorescence (- - -) but not phosphorescence is observed. Spin-forbidden transitions are represented by dashed lines.

Figure 14. Absorption curves of the tetracene radical ions (157) and results of the semiempirical open-shell PPP-like calculations (59). The latter are indicated by vertical lines (allowed transitions) and by wavy lines with arrows (forbidden transitions) f stands for theoretical oscillator strength.

---