Spectroscopic selection rules

Another related issue is the computation of the intensities of the peaks in the spectrum. Peak intensities depend on the probability that a particular wavelength photon will be absorbed or Raman-scattered. These probabilities can be computed from the wave function by computing the transition dipole moments. This gives relative peak intensities since the calculation does not include the density of the substance. Some types of transitions turn out to have a zero probability due to the molecules symmetry or the spin of the electrons. This is where spectroscopic selection rules come from. Ah initio methods are the preferred way of computing intensities. Although intensities can be computed using semiempirical methods, they tend to give rather poor accuracy results for many chemical systems. 

The theory of molecular symmetry provides a satisfying and unifying thread which extends throughout spectroscopy and valence theory. Although it is possible to understand atoms and diatomic molecules without this theory, when it comes to understanding, say, spectroscopic selection rules in polyatomic molecules, molecular symmetry presents a small barrier which must be surmounted. However, for those not needing to progress so far this chapter may be bypassed without too much hindrance. 

The recombination should be governed by the same selection rules as spectroscopic transitions. Let us consider the recombination of an oxygen ion 2s2 2p3 4S°. When one p electron is added to the 4S ion we expect to obtain one of the states 5P and 3P. However, if the 2s2 2p4 state of the atom is obtained, it can only exist in the states 3P, lD, or lS. Thus the recombination can only give 2s2 2p4 3P. Sometimes the selection rules are not strictly valid. In this case, however, no transitions 2s2 2p3 4S° nx - 2s2 2p4 XD or lS have been observed by the spectros-copists (57) which shows that in this case the selection rules are strictly valid. 

If no transfer of translational energy occurs, then the charge exchange process probably takes place when the distance between the ion and the molecule is large. This means, however, that the ion and the molecule can be considered as isolated from each other, and therefore, the recombination process of the ion and the ionization process of the molecule must obey the spectroscopic transition laws. On the other hand, if a large transfer of translational energy takes place, then the process probably takes place when the distance is small, and possibly then all selection rules break down. 

If a charge exchange process, A + + B- A -f- B +, occurs when the distance between the two particles is large, we expect that no transfer of translational energy takes place in the reaction and that the same selection rules govern the ionization as in spectroscopic transitions. This means that if the molecule B is in a singlet state before the ionization, the ion B + will be formed in a doublet state after ionization of one electron without rearrangements of any other electrons, at least for small molecules. 

Although the resulting direct product may not be reduced, it can be made so by application of the magic formula, or often by inspection. The nonvanishing of the integral is then determined by the existence of the totally symmetric representation in the resulting direct sum. This procedure will be illustrated by the development of spectroscopic selection rules in Section 12.3.3. 

The quantity bm 2 represents the probability of the transition m - n. Clearly, the number of transitions per unit time depends on the intensity of the incident radiation, which is proportional to < J 2, and the square of the matrix element (m px n). The latter determines the selection rules for spectroscopic transitions (see the following section). 

General selection rules that govern spectroscopic transitions are derived from., > t moment and the wavefunctions involved. 

A second, independent spectroscopic proof of the identity of 4 as rans-[Mo(N2)2(weso-prP4) was provided by vibrational spectroscopy. The comparison of the infrared and Raman spectrum (Fig. 7) shows the existence of two N-N vibrations, a symmetric combination at 2044 cm-1 and an antisymmetric combination at 1964 cm-1, indicating the coordination of two dinitrogen ligands. In the presence of a center of inversion the symmetric combination is Raman-allowed and the antisymmetric combination IR allowed. The intensities of vs and vaK as shown in Fig. 2 clearly reflect these selection rules. Moreover, these findings fully agree with results obtained in studies of other Mo(0) bis(dinitrogen)... 

When deriving selection rules from character tables it is noted that vibrations are usually excited from the ground state which is totally symmetric. The excited state has the symmetry of the vibration being excited. Hence A vibration will be spectroscopically active if the vibration has the same symmetry species as the relevant operator. 

Spectroscopic techniques look at the way photons of light are absorbed quantum mechanically. X-ray photons excite inner-shell electrons, ultra-violet and visible-light photons excite outer-shell (valence) electrons. Infrared photons are less energetic, and induce bond vibrations. Microwaves are less energetic still, and induce molecular rotation. Spectroscopic selection rules are analysed from within the context of optical transitions, including charge-transfer interactions The absorbed photon may be subsequently emitted through one of several different pathways, such as fluorescence or phosphorescence. Other photon emission processes, such as incandescence, are also discussed. 

Recent theoretical and spectroscopic studies indicate that in aliphatic dienes and trienes, excitation to the spectroscopic l1 state usually results in facile twisting about the termini in the stereochemical sense dictated by orbital symmetry selection rules for the appropriate electrocyclic ring closure, motions which are often accompanied by some degree of planarization of the carbon framework. In general, relatively minor distortions... 

---