Electronic spectra of polyatomic molecules

The electronic spectrum of a nonlinear polyatomic molecule is very complicated. In addition to three modes of rotation with distinct moments of inertia, there are 3N — 6 modes of vibration. While some of these may be forbidden in the infrared or Raman spectrum on the basis of symmetry, there is no rule to forbid their appearance in the electronic spectrum, which is extraordinarily complex as a consequence. For our purposes here, we mention only a few fundamental points and present one example. 

The wave functions and levels in polyatomic molecules are described in terms of their symmetry. (See Sections 23.14 and 23.16.2). For example, if we consider the water molecule, its symmetry requires that any molecular wave function either be invariant or change only in algebraic sign under any symmetry operation. This requirement severely restricts the form of the wave functions. These wave functions can be of only four types—denoted by the letters 2 5 and Z 2 ach of which belongs to a particular symmetry species. The symmetry properties of each type are summarized in the character table of the group C2y, Table 23.5. 

As we pointed out in Section 23.16.2, the ground state electronic configuration for the water molecule is 

Because most chemical species are polyatomic molecules, a discussion of the electronic spectra of molecules covers most matter. However, the subject is so large (the saying books are written about it is especially true here) that we can cover only a few specific topics. 

The electronic states of polyatomic molecules can be labeled using the irreducible representations of the symmetry point group of the molecule. (This is another example of how symmetry is important in the understanding of spectra.) As such, the same rule involving the direct product of the irreducible representations applies  

For polyatomic molecules, the point group has enough symmetry elements (or rather, classes, and so therefore irreducible representations) that the following statement is usually applicable The ground electronic state and the allowed excited states are usually of different irreducible representation labels. 

Unless otheiwise noted, all art on this page is Cengage teaming 2014. 

Predict whether the following molecules would have color. That is, will electronic 

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Duschinsky F 1937 On the interpretation of electronic spectra of polyatomic molecules. I. Concerning the Franck-Condon Principle Acta Physicochimica URSS 7 551... 

G. Herzberg, Moleculer Spectra and Molecular Structure III. Electronic Spectra of Polyatomic Molecules, Van Nostrand, New York, 1967. 

As is the case for diatomic molecules, rotational fine structure of electronic spectra of polyatomic molecules is very similar, in principle, to that of their infrared vibrational spectra. For linear, symmetric rotor, spherical rotor and asymmetric rotor molecules the selection mles are the same as those discussed in Sections 6.2.4.1 to 6.2.4.4. The major difference, in practice, is that, as for diatomics, there is likely to be a much larger change of geometry, and therefore of rotational constants, from one electronic state to another than from one vibrational state to another. 

Herzberg, G. (1966). The Electronic Spectra of Polyatomic Molecules , p. 442. Van Nostrand, Princeton, New Jersey... 

For a tabulation of vibration frequencies of polyatomic molecules, see Herzberg, Electronic Spectra of Polyatomic Molecules, pp. 580-668. 

The Jahn-Teller theorem says nothing about the magnitude of the departure of the equilibrium geometry from a symmetric geometry, and in many cases, the actual departures are less than the magnitudes of zero-point vibrations. For more on the Jahn-Teller theorem, see Herzberg, Electronic Spectra of Polyatomic Molecules, pp. 40-51 F. S. Ham, Int. J. Quantum Chem., 5S, 191 (1971). 

The major changes in the new edition are as follows There are three new chapters. Chapter 1 is a review and summary of aspects of quantum mechanics and electronic structure relevant to molecular spectroscopy. This chapter replaces the chapter on electronic structure of polyatomic molecules that was repeated from Volume I of Quantum Chemistry. Chapter 2 is a substantially expanded presentation of matrices. Previously, matrices were covered in the last chapter. The placement of matrices early in the book allows their use throughout the book in particular, the very tedious and involved treatment of normal vibrations has been replaced by a simpler and clearer treatment using matrices. Chapter 7 covers molecular electronic spectroscopy, and contains two new sections, one on electronic spectra of polyatomic molecules, and one on photoelectron spectroscopy, together with the section on electronic spectra of diatomic molecules from the previous edition. In addition to the new material on matrices, electronic spectra of polyatomic molecules, and photoelectron... 

A more detailed presentation of the general field of electronic spectra of polyatomic molecules may be found in Herzberg.2a... 

The degeneracies of the vibrational states are given in parentheses after the frequencies. The imaginary frequency of the activated complex is not included. The vibrational frequencies of CH3CI correspond to the data in G. Herzberg, Electronic spectra of polyatomic molecules. 

One very useful convention that was proposed by J. C. D. Brand, J. H. Callomon and J. K. G. Watson in 1963 is applicable to electronic spectra of polyatomic molecules, and I have... 

The multiplicity of the modes of vibration and rotation considerably complicates the interpretation of experimental data, and little progress has so far been made with the analysis of the electronic spectra of polyatomic molecules. The study of vibrational-rotational (infra-red) spectra is less difficult and has led to the determination of interatomic distances, valency angles and vibrational frequencies of some of the simpler polyatomic molecules. 

G. Herzberg, "Electronic Spectra of Polyatomic Molecules", D. Van Nostrand Co., Inc., New York, 1966... 

Electronic Spectra of Polyatomic Molecules Srb, Czech. J. Phys. 17, IHO (1967)... 

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