Selection rules, spectral

Transitions between states are subject to certain restrictions called selection rules. The conservation of angular momentum and the parity of the spherical harmonics limit transitions for hydrogen-like atoms to those for which A/ = 1 and for which Am = 0, 1. Thus, an observed spectral line vq in the absence of the magnetic field, given by equation (6.83), is split into three lines with wave numbers vq + (/ bB/he), vq, and vq — (HbB/he). 

Atomic spectra are much simpler than the corresponding molecular spectra, because there are no vibrational and rotational states. Moreover, spectral transitions in absorption or emission are not possible between all the numerous energy levels of an atom, but only according to selection rules. As a result, emission spectra are rather simple, with up to a few hundred lines. For example, absorption and emission spectra for sodium consist of some 40 peaks for elements with several outer electrons, absorption spectra may be much more complex and consist of hundreds of peaks. 

With its substitution in Eq. (99) it becomes evident from the orthogonality of the Hermite polynomials, that all matrix elements are equal to zero, with the exception of v = v — 1 and vf = u +1. Thus, the selection rule for vibrational transitions (in the harmonic approximation) is An — 1. It is not necessary to evaluate the matrix elements unless there is an interest in calculating the intensities of spectral features resulting from vibrational transitions (see problem 18). It should be evident that transitions such as Av - 3 are forbidden under this more restrictive selection rule, although they are permitted under the symmetry selection rule developed in the previous paragraphs. 

Unfortunately, the different selection rules that apply to resonant and normal Raman scattering were not taken into account in this spectral interpretation. In the following, it is shown that the conclusions and assignments mentioned above have to be modified on the basis of symmetry considerations as discussed by Ricchiardi et al. (41). 

In the investigations of molecular adsorption reported here our philosophy has been to first determine the orientation of the adsorbed molecule or molecular fragment using NEXAFS and/or photoelectron diffraction. Using photoemission selection rules we then assign the observed spectral features in the photoelectron spectrum. On the basis of Koopmans theorem a comparison with a quantum chemical cluster calculation is then possible, should this be available. All three types of measurement can be performed with the same angle-resolving photoelectron spectrometer, but on different monochromators. In the next Section we briefly discuss the techniques. The third Section is devoted to three examples of the combined application of NEXAFS and photoemission, whereby the first - C0/Ni(100) - is chosen mainly for didactic reasons. The results for the systems CN/Pd(111) and HCOO/Cu(110) show, however, the power of this approach in situations where no a priori predictions of structure are possible. 

Figure 9 shows the effect of deprotonation of adsorbed formic acid which occurs on warming the surface to above 270 K. Spectrum (a) can be assigned by comparison with the photoelectron spectrum of the free molecule. The formate species also gives rise to four spectral bands and, since the number of expected orbitals is the same, it is tempting to assume a one-to-one correspondence, allowing of course for the change in symmetry from Cs to C2v- The application of selection rules proves, however, that such an... 

For more complicated spin systems than the one presented in Fig. 1, the number of EPR lines becomes much greater than the number of ENDOR lines. This is due to the different selection rules for EPR and ENDOR transitions. In an EPR spectrum (Ams = 1, Ami = 0) the number of lines increases multiplicatively with the number of nonequivalent nuclei, whereas in ENDOR (Ams = 0, Amt = 1) the corresponding increase is only additive7. Since on the other hand the total spectral widths in EPR and ENDOR are of the same order of magnitude (expressed in units of energy), the average spectral... 

Before we deal with the spectral shape of a ci>), let ns examine the selection rule imposed by the conservation of momenrnm. For a given transition. 

For some direct-gap materials, the quantum electronic selection rules lead to = 0. However, this is only strictly true at / = 0. For 0, it can be assumed, in a first order approximation, that the matrix element involving the top valence and the bottom conduction states is proportional to k that is, Pif k. Within the simplified model of parabolic bands (see Appendix Al), it is obtained that Tuo = Tuog + flp., and therefore Pif k co — cog). Thns, according to Equations (4.31) and (4.32), the absorption coefficient for these transitions (called forbidden direct transitions) has the following spectral dependence ... 

Expansion of the data bases in Module 1 to include spectroscopic and electrochemical data to be used by the detector selection rules of Module 3. (This would include UV absorbance spectral properties of organic molecules, fluorescence quenching and activating properties of solvent environments, and electro-... 

Attractive spectral properties and advantageous selection rules... 

Due to limitations in signal-to-noise ratio available for the then common dispersive IR instruments, peptide and protein vibrational spectroscopic studies shifted to emphasize Raman measurements in the 1970s 29-32 Qualitatively the same sorts of empirical correlations as discussed above have been found between frequencies of amide bands in the Raman and secondary structure. However, due to the complementary selection rules for Raman as compared to IR and to the multi-component nature of these polymeric spectral bands, the... 

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