Rotational spectra linear polyatomics

As with diatomic molecules, the principal selection rule is that a permanent dipole moment is required for a molecule to produce a microwave spectrum. Linear polyatomic molecules have rotational wave functions exactly like those of diatomic molecules, so their rotational selection rules and spectra are the same as those of diatomic molecules. A symmetric linear molecule such as acetylene (ethyne) has no permanent dipole moment, and does not have a microwave spectrum. The fact that N2O has a microwave spectrum establishes the fact that it is NNO, not NON. Spherical top molecules such as CCI4 and SFe are so symmetrical that they cannot have a nonzero permanent dipole moment, and they have no microwave spectrum. A symmetric top molecule with a permanent dipole moment will have a microwave spectrum. A microwave spectrum is always observed for an asymmetric top molecule, because it has so little symmetry that it must have a nonzero permanent dipole moment. 

In the previous chapter, vibrational/rotational (i.e. infrared) spectroscopy of diatomic molecules was analyzed. The same analysis is now applied to polyatomic molecules. Polyatomic molecules have more than one bond resulting in additional vibrational degrees of freedom. Rotation of linear polyatomic molecules is mechanically equivalent to that of diatomic molecules however, the rotation of non-linear polyatomic molecules results in more than one degree of rotational freedom. The result of the additional vibrational and rotational degrees of freedom for polyatomic molecules is to complicate the vibrational/rotational spectra of polyatomic molecules relative to spectra of diatomic molecules. Though the spectra of polyatomic molecules are more complicated, many of the same features exist as in the spectra of diatomic molecules. As a result, a similar approach wiU be used in this chapter. The mechanics of a model system will be solved, determine the selection rules, and the features of a spectrum will be predicted. 

Figure 5.15 Rotational Raman spectrum of a diatomic or linear polyatomic molecule...

A linear polyatomic molecule such as HCN, 0=C=0 or HC=CH has a rotational spectrum closely analogous to that of a diatomic molecule, if one takes into account the more complicated form of the moment of inertia. Consider the most general case of a linear triatomic molecule ... 

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. 

Transitions between the rotational states of a polyatomic molecules can produce a microwave spectrum. We will not discuss the details of the microwave spectra of polyatomic molecules, but make some elementary comments. As with diatomic molecules, we apply the rigid-rotor approximation, assuming that a rotating polyatomic molecule is locked in its equilibrium conformation. Any molecule in its equilibrium conformation must belong to one of four classes linear molecules, spherical top molecules, symmetric top molecules, and asymmetric top molecules. 

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