Polyatomic molecules electronic spectra

Figure 3.25 Outline of the absorption spectrum of a rigid polyatomic molecule. The bands corresponding to electronic transitions are broad as they include vibrational and rotational transitions and they coalesce to form an absorption continuum...

First, we describe briefly the calculation of the absorption spectrum for bound-bound transitions. In order to keep the presentation as clear as possible we consider the simplest polyatomic molecule, a linear triatom ABC as illustrated in Figure 2.1. The motion of the three atoms is confined to a straight line overall rotation and bending vibration are not taken into account. This simple model serves to define the Jacobi coordinates, which we will later use to describe dissociation processes, and to elucidate the differences between bound-bound and bound-free transitions. We consider an electronic transition from the electronic ground state (k = 0) to an excited electronic state (k = 1) whose potential is also binding (see the lower part of Figure 2.2 the case of a repulsive upper state follows in Section 2.5). The superscripts nu and el will be omitted in what follows. Furthermore, the labels k used to distinguish the electronic states are retained only if necessary. 

If we require similar information regarding the ground state potential energy surface in a polyatomic molecule the electronic emission spectrum may again provide valuable information SYLF spectroscopy is a particularly powerful technique for providing it. 

Condition 4. For most polyatomic molecules monochromatic light is impossible to obtain. Monochromatic light for experiments of this type would be defined as one for which the absorption coefficient is constant. To say the least, the incident radiation will cover much unresolved rotational structure within a single band. The more common case found with high-pressure arcs and color filters will be that two or more vibration transitions within a given electronic transition will be involved. Since the absorption coefficient will never be a true constant, the strongly absorbing parts of the spectrum will be important at low pressures and will decrease in relative importance as the pressure increases. 

The same approach can be used to understand the chemical bonding in polyatomic molecules and polymers. The electronic spectrum of a polymer can be described as the sum of the spectra of individual diatomic components (Fig. 3). Since the orbital... 

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. 

According to the selection rule for the harmonic oscillator, any transitions corresponding to An = 1 are allowed (Sec. I-2). Under ordinary conditions, however, only the fundamentah that originate in the transition from u = 0 to u = 1 in the electronic ground state can be observed because of the Maxwell-Boltzmann distribution law. In addition to the selection rule for the harmonic oscillator, another restriction results from the symmetry of the molecule (Sec. 1-9). Thus the number of allowed transitions in polyatomic molecules is greatly reduced. The overtones and combination bands of these fundamentals are forbidden by the selection rule of the harmonic oscillator. However, they are weakly observed in the spectrum because of the anharmonicity of the vibration... 

The importance of the Raman spectrum lies especially in the fact that it also occurs for homonuclear molecules, which, according to sections 22 and 23, have no rotation and vibration-rotation spectra. Hence, it may be used to supplement the evidence derived from electronic bands, regarding the energy of vibrational and rotational levels in the ground state, and for a confirmation of the values of and thus obtained. Researches of this sort have actually been carried out on HCl by Wood and on Hg, Ng, Og, CO by Rasetti (for literature see G) and (lO)) and, more recently, on CO by Amaldi(is). Really essential, however, is the Raman effect in analysing the possible vibrations of polyatomic molecules, as we shall see in the next chapter. For such molecules very rarely have sharply defined electronic bands, while the rotation and vibration-rotation data usually are insufficient to arrive at a unique description of the molecular behaviour. 

The LIF of polyatomic molecules opens possibilities to recognize perturbations both in excited and in ground electronic states. If the upper state is perturbed its wave function is a linear combination of the BO wave functions of the mutually perturbing levels. The admixture of the perturber wave function opens new channels for fluorescence into lower levels with different symmetries, which are forbidden for unperturbed transitions. The LIF spectrum of NO2 depicted in Fig. 1.56 is an example where the forbidden vibrational bands terminating on the vibrational levels (ui, U2, U3) with an odd number U3 of vibrational quanta in the asymmetric stretching vibrational mode in the electronic ground state are marked by an asterisk [182]. 

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