Progressions and sequences

In electronic spectra there is no restriction on the values that Au can take but, as we shall see in Section 1.2.53, the Franck-Condon principle imposes limitations on the intensities of the transitions. 

Vibrational transitions accompanying an electronic transition are referred to as vibronic transitions. These vibronic transitions, with their accompanying rotational or, strictly, rovibronic transitions, give rise to bands in the spectrum, and the set of bands associated with a single electronic transition is called an electronic band system. This terminology is usually adhered to in high-resolution electronic spectroscopy but, in low-resolution work, particularly in the liquid phase, vibrational structure may not be resolved and the whole band system is often referred to as an electronic band. 

Quite apart from the necessity for Franck-Condon intensities of vibronic transitions to be appreciable, it is essential for the initial state of a transition to be sufficiently highly populated for a transition to be observed. Under equilibrium conditions the population 1, of any v level is related to that of the u = 0 level by 

Answer. Equation (7.83), derived from the Boltzmann equation, gives the ratio of the population Vj of the v = I level to the population, Aq, of the v = 0 level as 

Note that the values given for Wq limit the number of significant figures to four for H2 and to three for F2 and I2. 

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Vibronic transitions may be divided conveniently into progressions and sequences. A progression, as Figure 7.18 shows, involves a series of vibronic transitions with a common... 

Figure 7.1 8 Vibrational progressions and sequences in the electronic spectrum of a diatomic molecule...

It is clear from Figure 7.18 that progressions and sequences are not mutually exclusive. Each member of a sequence is also a member of two progressions. However, the distinction is usefiil because of the nature of typical patterns of bands found in a band system. Progression members are generally widely spaced with approximate separations of cOg in absorption and co" in emission. In contrast, sequence members are more closely spaced with approximate separations of cOg — co". 

As for diatomic molecules (Section 7.2.5.2) fhe vibrational (vibronic) transitions accompanying an electronic transition fall into the general categories of progressions and sequences, as illustrated in Figure 7.18. The main differences in a polyatomic molecule are that there are 3A — 6 (or 3A — 5 for a linear molecule) vibrations - not just one - and that some of these lower the symmetry of the molecule as they are non-totally symmetric. 

Figure 8.6 Progress and sequence of advance in the design of Siemens fuel cell electrodes leading up to the 2007 Delta 8 reformation (displayed at the bottom of the stack).

Caution The death rate from untreated pneumonic plague can reach almost 100 percent. Once a human is infected with plague, a progressive and potentially deadly illness usually results unless antibody therapy is administered. In a progressional sequence, the patient develops blood infection which leads to lung infection. 

Aside from the direct techniques of X-ray or electron diffraction, the major possible routes to knowledge of three-dimensional protein structure are prediction from the amino acid sequence and analysis of spectroscopic measurements such as circular dichroism, laser Raman spectroscopy, and nuclear magnetic resonance. With the large data base now available of known three-dimensional protein structures, all of these approaches are making considerable progress, and it seems possible that within a few years some combination of noncrystallo-graphic techniques may be capable of correctly determining new protein structures. Because the problem is inherently quite difficult, it will undoubtedly be essential to make the best possible use of all hints available from the known structures. 

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