Electronic transitions, forbidden molecules

If one of the components of this electronic transition moment is non-zero, the electronic transition is said to be allowed if all components are zero it is said to be forbidden. In the case of diatomic molecules, if the transition is forbidden it is usually not observed unless as a very weak band occurring by magnetic dipole or electric quadnipole interactions. In polyatomic molecules forbidden electronic transitions are still often observed, but they are usually weak in comparison with allowed transitions. 

One of the consequences of this selection rule concerns forbidden electronic transitions. They caimot occur unless accompanied by a change in vibrational quantum number for some antisynnnetric vibration. Forbidden electronic transitions are not observed in diatomic molecules (unless by magnetic dipole or other interactions) because their only vibration is totally synnnetric they have no antisymmetric vibrations to make the transitions allowed. 

Indicate which of the following electronic transitions are forbidden in a diatomic molecule, stating which selection mles result in the forbidden character ... 

A 3 — Ag electronic transition in a molecule belonging to the D2h point group is forbidden. at are the possible symmetry species of a vibration X which would result in the Xq and X transitions being allowed ... 

The blue colour of oxygen in the liquid and solid phases is due to electronic transitions by which molecules in the triplet ground state are excited to the singlet states. These transitions are normally forbidden in pure gaseous oxygen and, in any case, they occur in the infrared region of the spectrum at 7918 cm" ( Ag) and 13 195 cm" ( ]+). However, in the condensed phases a... 

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. 

A further technique exists for the determination of triplet energy levels. This technique, called electron impact spectroscopy, involves the use of inelastic scattering of low-energy electrons by collision with molecules. The inelastic collisions of the electrons with the molecules result in transfer of the electron energy to the molecule and the consequent excitation of the latter. Unlike electronic excitation by photons, excitation by electron impact is subject to no spin selection rule. Thus transitions that are spin and/or orbitally forbidden for photon excitation are totally allowed for electron impact excitation. 

The ro-vibronic spectrum of molecules and the electronic transitions in atoms are only part of the whole story of transitions used in astronomy. Whenever there is a separation between energy levels within a particular target atom or molecule there is always a photon energy that corresponds to this energy separation and hence a probability of a transition. Astronomy has an additional advantage in that selection rules never completely forbid a transition, they just make it very unlikely. In the laboratory the transition has to occur during the timescale of the experiment, whereas in space the transition has to have occurred within the last 15 Gyr and as such can be almost forbidden. Astronomers have identified exotic transitions deep within molecules or atoms to assist in their identification and we are going to look at some of the important ones, the first of which is the maser. 

The selection rules appropriate for a shake-up transition are of the monopole type2, 76. The intensity of a shake-up peak depends on the overlap integral between the lower state molecular orbital from which the electron is excited (in the neutral molecule) and the upper state molecular orbital to which the electron is excited (in the core-ionized molecule). Consequently one expects transitions of the type au au, ag " ag> 7T nu, and irg - ng with g u and u - g transitions forbidden. 

In addition, group theory can be used to assess when transition dipole moments must be zero. The product of the irreducible representations of the two wave functions and the dipole moment operator within the molecular point group symmetry must contain the totally symmetric representation for the matrix element to be non-zero (note that, if the molecule does not contain an inversion center, the operator r does not belong to any single irrep, except for the trivial case of Ci symmetry see Appendix B for more details). A consequence of this consideration is that, for instance, electronic transitions between states of the same symmetry are forbidden in molecules possessing inversion centers. 

The fact that there are many electronic transitions possible, however, does not mean that they can or will occur. There are complex selection rules based on the symmetry of the ground and excited states of the molecule under examination. Basically, electronic transitions are allowed if the orientation of the electron spin does not change during the transition and if the symmetry of the initial and final functions is different these are called the spin and symmetry selection rules, respectively. However, the so-called forbidden transitions can still occur, but give rise to weak absorptions. 

When the symmetry of a given molecule has been determined, electronic transitions fall into the following three categories i a. electric allowed — magnetic forbidden b. magnetic allowed — electric forbidden [Groups C, Cnh, Dnh (n 2), S2n (n, odd), Oh, Td]... 

From these examples it can be seen that CT characters of electronic states vary from 0 to 1, depending on the interaction of the localized orbitals. A CT character of 1 (100%) would correspond to the transfer of a whole electronic charge, and this could exist only if the donor and acceptor orbitals were totally separated in space. Such an electronic transition would be forbidden because the spatial overlap of the orbitals is zero. We shall see however that total charge separation can take place in some rather special cases, though not through a direct transition. Before discussing these twisted intramolecular CT ( TICT ) states, a few words about donor-aromatic-acceptor (DArA) molecules are appropriate. 

Rate Constants of Radiative Transitions. The natural radiative rate constant kr of an electronic transition from a state to a state Sf is related to the transition moment M and thereby to the oscillator strength f. It is convenient to factorize f to highlight the various factors which determine to what extent a transition is allowed if near 1) or forbidden (f near 0). The transition moment includes the displacement of all particles of the molecule during the transition, nuclei as well as electrons. The heavy nuclei move much more slowly than the light electrons so that their motions can be considered to be independent. Within this approximation the transition moment is given as... 

First approximation theory leads to certain wave mechanical selection rules on the basis of which a radiative electronic transition may be classified as allowed (high probability) or forbidden (vanishingly low probability). Some forbidden transitions are indeed too weak to observe easily but in actual practice with polyatomic molecules the selection rules often break down sufficiently to permit reasonably strong absorption processes to occur. The following kinds of transition are forbidden... 

Again, since the d orbitals have even parity, even if the molecule does not have an inversion center there is an approximate selection rule in which transitions that would be g -> g (or u -> u) in a parent group with inversion symmetry are allowed. The odd parity vibrations that dominate the single photon spectrum are forbidden, while the even parity vibrations are allowed, but have no advantage over the pure electronic transitions. Experimental two-photon spectra of the sharp-line transitions of Mn4+ in a Cs2Ge F6 host confirm both the simplicity of the spectrum and the relative prominence of the 0-0 lines [55],... 

As mentioned earlier, in a centrosymmetric complex, d-d transitions are Laporte forbidden. The fact that they are observed at all is due to a mechanism called vibronic interaction, which is a mixing of the vibrational and electronic wave-functions. Qualitatively, we may imagine that an electronic transition occurs at the very moment some vibrational modes of the complex distort the molecule in such a way that the center of symmetry is destroyed. When such a vibration takes place, the g character of the state is lost and the transition becomes (very slightly) allowed. Figure 8.10.1 shows two vibrations, with u symmetry, of an octahedral complex which remove the inversion center. 

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