Symmetry forbidden transition

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. 

Symmetry-forbidden transitions. A transition can be forbidden for symmetry reasons. Detailed considerations of symmetry using group theory, and its consequences on transition probabilities, are beyond the scope of this book. It is important to note that a symmetry-forbidden transition can nevertheless be observed because the molecular vibrations cause some departure from perfect symmetry (vibronic coupling). The molar absorption coefficients of these transitions are very small and the corresponding absorption bands exhibit well-defined vibronic bands. This is the case with most n —> n transitions in solvents that cannot form hydrogen bonds (e 100-1000 L mol-1 cm-1). 

The band at 19 kK of relatively low intensity is assigned to the symmetry-forbidden transition - 3A2. Also the two transitions to the A2 and B2 levels are s5nnmetry-forbidden and accordingly appear as shoulders of low intensity. 

Symmetry forbidden transition can be made partially Mowed by vibronic interactions. 

The Laporte rule states that transitions between states of the same parity, u or g, are forbidden i.e. u - g and g - u but g +-> g and u +-> u. This rule follows from the symmetry of the environment and the invoking of the Bom-Oppenheimer approximation, But since, due to vibrations, the environment will not always be strictly symmetrical, these forbidden transitions will in fact occur, though rather weakly (oscillator strengths of the order of 10 4). All the states of a transition-metal ion in an octahedral environment are g states, so that it will be these weak symmetry forbidden transitions (called d-d transitions) that will be of most interest to us when we study the spectra of octahedral complexes. 

Symmetry-Forbidden.—Transitions for which the transition moment vanishes because of the symmetry properties of the integrand. To be nonzero the function totally symmetric since totally symmetric, the transition will only be allowed if the product Mthree components of the dipole operator ordinarily transform differently under the covering operations of the various point groups, a transition may be allowed with polariza-... 

Example 10.2-1 Find if any of the symmetry-forbidden transitions in benzene can become vibronically allowed, given that in the benzene molecule there are normal modes ofB2g and E2g symmetry. 

In the case of 27-29, with the exception of the borderline 28, the radiative rate constant is one order of magnitude lower than the value found for 24-26. This observation, together with the longer values obtained for the natural radiative lifetime (see t°f = tf/< )f)/ is clearly compatible with the forbidden nature of the lowest lying transition/state. The nature of this transition seems to be a 71,71 symmetry forbidden transition/state. 

The d-d spectrum of [P1.CI4I2- in solution is shown in Fig. 8.9.5. Note that the bands are relatively weak, signifying that they are due to symmetry-forbidden transitions. As mentioned previously, three d-d bands are expected indeed, three are observed. Hence the assignment is relatively straightforward ... 

Overall, the band shifts experimentally observed for all kinds of absorptions are the net results of three, partly counteracting contributions electrostatic (dipole/dipole dipole/induced dipole blue shift), dispersion ( red shift), and specific hydrogen-bonding blue shift). Which of these solute/solvent interactions are dominant for the solute under study depends on the solvents used. For example, the results obtained for pyridazine, as shown in Fig. 6-5, clearly implicate hydrogen-bonding as the principle cause of the observed hypsochromic band shift that occurs when the HBD solvent ethanol is added to solutions of pyridazine in nonpolar -hexane [98]. The intensity of n n absorption bands is usually very low because they correspond to symmetry-forbidden transitions, which are made weakly allowed by vibronic interactions cf. Fig. 6-5). 

The azido group affects the spectrum of the hydrocarbon itself in two ways it causes a red shift of the L -band and a smaller red shift of the other bands (the size of the aromatic system is increased) it also reduces the symmetry of the molecule, thus enhancing the extinction of the symmetry forbidden transition at the expense of the associated B-transition (intensity borrowing ). From the size of the effect it can be inferred that the inductive interaction of the azido group with the ring is comparable with, if somewhat weaker than, that of the amino group For the spectra of aromatic diazides see reference 40. 

In applications of these symmetry selection rules it has to be remembered that the symmetry of a molecule can be lowered by vibrational motions so that symmetry-forbidden transitions may nevertheless be observed—for instance, the two longest-wavelength singlet-singlet transitions in benzene. Vibronic coupling and the shape of the absorption bands will be discussed in the following sections. 

In Example 1.9 it was pointed out that symmetry-forbidden transitions may become observable due to symmetry-lowering vibrational motions. This cannot be explained by means of the Franck-Condon principle, which governs only the distribution of intensity due to a nonvanishing transition moment over the various vibrational components of the band. The phenomenon... 

The first term in Equation (1.47) is identical with the expression derived in the last section for electronically allowed transitions. It is presently assumed to be very small or zero. (A/o f - 0 for symmetry-forbidden transitions.) The second term results from vibronic mixing and represents a first-order vibronic contribution to the transition moment. It is seen that in this description the forbidden transition 0->f steals or borrows intensity from the allowed transition 0- b. If A/o f is exactly zero all observed components of the electronic transition will be polarized along the direction of the transition dipole moment A o b. The 0- 0 transition (v = v = 0) will have zero intensity and only vibrational levels of overall symmetry given by the direct product of symmetries of the states % and % will appear. 

The low (<750 M" cm" ) extinction coefficients for the absorption sfwctrum of Cm between 492 and 620 nm indicate that this band, probably Sq S,, is connected with a strongly symmetry-forbidden transition. Similarly, low extinction coefficients are associated with the longest wavelength Tj Tj absorption. 

Vibrational Contributions Contribution of vibrational modes has been described for TPA [5-9, 11-17, 19, 22, 23, 31, 37, 61, 235, 309, 343-345] and for other nonlinear optical processes [346]. One classical example is the 1A j -1 B2u TP transition of benzene, the so-called green band. This electronic transition is allowed due to a vibronic coupling mechanism [346]. Semiempirical [60, 61] as well as ab initio response theory calculations using the Herzberg-Teller expansion [344] demonstrate the role of vibronic coupling. Such contributions can either enhance an allowed transition or intensify a symmetry-forbidden transition. 

In the alkali metal pseudohalides the contribution of cationic wave functions to the valence band structure can be neglected. The optical absorption spectra can therefore be correlated to transitions involving excited states of the anions. However, one can see solid state effects like the superposition of vibronic structure on the molecular symmetry forbidden transition at 5.39 eV in the crystal spectra of the alkali metal azides (76). In the more complex heavy metal and divalent azides, a whole range of optical transitions can occur both due to crystal field effects and the enhanced contributions from cationic states to the valence band. Detailed spectral measurements on a-PbNe (80), TIN3 (57), AgNs (52), Hg(CNO)2 (72) and AgCNO (72) have been made but the level assignments can at best be described as tentative since band structure calculations on these materials are not available at present. 

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