Gross selection rule

It is tempting to take the carbon insertion mechanisms to the extreme and look for the completely unsaturated carbon allotropes of graphite and diamond. Graphite has been postulated for many years but there is at present no IR evidence for it in the ISM. This is partly due to the problems of detection. The gross selection rule for an IR spectrum requires a change in dipole moment during a vibration and the... 

D13.3 (I) Rotational Raman spectroscopy. The gross selection rule is that the molecule mustbe anisotropically polarizable, which is to say that its polarizability, or, depends upon the direction of the electric field relative to the molecule. Non-spherical rotors satisfy this condition. Therefore, linear and symmetric rotors are rotationally Raman active. 

There also exists the gross selection rule that, in order for electromagnetic radiation to be absorbed, the dipole moment of the molecule must change during the vibration, which means that a diatomic molecule must possess a permanent dipole moment in order to absorb IR radiation. (These selections rules will be discussed in detail in the section on the intensity of IR transitions.)... 

Equation [71] shows the origin of the gross selection rule that the dipole moment of a molecule must change in the course of a normal coordinate excursion for the vibration to absorb IR radiation. The transition moment in eqn [57] is only nonzero for the case where only one vibration is excited and for the situation in which the quantum number of the vibration involved changes by +1. Hence the selection rule given earlier in eqn [17]. 

The vibrational transitions of a molecule can be probed directly using infrared spectroscopy and are subject to the gross selection rule that for a change in a vibrational state brought about by the absorption or emission of a photon, there must be an accompanying change in the dipole moment of the molecule. Homo-nuclear diatomics are an important group of molecules which do not absorb IR radiation because of this selection rule. 

Molecules that don t have a permanent dipole moment are rotating, of course, but they do not follow the gross selection rule for pure rotational spectra. Their rotations cannot be observed directly using microwave spectroscopy. 

As with rotational spectroscopy, there are several ways of stating selection rules for spectral transitions involving vibrational states of molecules. There is a gross selection rule, which generalizes the appearance of absorptions or emissions involving vibrational energy levels. There is also a more specific, quantum-number-based selection rule for allowed transitions. Finally, there is a selection rule that can be based on group-theoretical concerns, which were not considered for rotations. 

Raman spectroscopy also has selection rules. The gross selection rule for a Raman-active vibration is related to the polarizability of the molecule. Polarizability is a measure of how easily an electric field can induce a dipole moment on an atom or molecule. Vibrations that are Raman-active have a changing polarizability during the course of the vibration. Thus, a changing polarizability is what makes a vibration Raman-active. The quantum-mechanical selection rule, in terms of the change in the vibrational quantum number, is based on a transition moment that is similar to the form of M in equation 14.2. For allowed Raman transitions, the transition moment [a] is written in terms of the polarizability a of the molecule ... 

Unfortunately, for electronic transitions, gross selection rules are not as straightforward to define. Therefore, we will consider the selection rules for electronic transitions as they arise in the discussion of the material. The electronic spectrum of the hydrogen atom, for example, has a relatively simple selection rule. The electronic spectrum of the benzene molecule, as a counter-example, follows more complex rules. 

Now we turn to vibrational Raman spectroscopy, in which the incident photon leaves some of its energy in the vibrational modes of the molecule it strikes or collects additional energy from a vibration that has already been excited. The gross selection rule for vibrational Raman transitions is that the molecular polarizability must change as the molecule vibrates. The polarizability plays a role in vibrational Raman spectroscopy because the molecule must be squeezed and stretched by the incident radiation in order that a vibrational excitation may occur during the photon-molecule collision. Both homonuclear and heteronuclear diatomic molecules swell and contract during a vibration, and the control of the nuclei over the electrons, and hence the molecular polarizability, changes too. Both types of diatomic molecule are therefore vibrationally Raman active. It follows that the information available from vibrational Raman spectra adds to that from infrared spectroscopy. 

The gross selection rule for the vibrational Raman spectrum of a polyatomic molecule is that the normal mode of vibration is accompanied by a changing polarizability. However, it is often quite difficult to judge by inspection when this is so. The symmetric stretch of COj, for example, alternately swells and contracts the molecule this motion changes its polarizability, so the mode is Raman active. The other modes of CO2 leave the polarizability unchanged (although that is hard to justify pictorially), so they are Raman inactive. 

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