Selection rules and transition moments
المؤلف:
Peter Atkins، Julio de Paula
المصدر:
ATKINS PHYSICAL CHEMISTRY
الجزء والصفحة:
ص435-436
2025-12-03
31
Selection rules and transition moments
We met the concept of a ‘selection rule’ in Sections 10.3 and 12.6 as a statement about whether a transition is forbidden or allowed. Selection rules also apply to molecular spectra, and the form they take depends on the type of transition. The underlying classical idea is that, for the molecule to be able to interact with the electromagnetic field and absorb or create a photon of frequency ν, it must possess, at least transiently, a dipole oscillating at that frequency. We saw in Section 9.10 that this transient dipole is expressed quantum mechanically in terms of the transition dipole moment, µfi, between states ψi and ψf:
where ¢ is the electric dipole moment operator. The size of the transition dipole can be regarded as a measure of the charge redistribution that accompanies a transition: a transition will be active (and generate or absorb photons) only if the accompanying charge redistribution is dipolar (Fig. 13.6). We know from time-dependent perturbation theory (Section 9.10) that the transition rate is proportional to |µfi|2. It follows that the coefficient of stimulated absorption (and emission), and therefore the intensity of the transition, is also proportional to | µfi|2. A detailed analysis gives
Only if the transition moment is nonzero does the transition contribute to the spectrum. It follows that, to identify the selection rules, we must establish the conditions for which µfi ≠ 0.
A gross selection rule specifies the general features a molecule must have if it is to have a spectrum of a given kind. For instance, we shall see that a molecule gives a rotational spectrum only if it has a permanent electric dipole moment. This rule, and others like it for other types of transition, will be explained in the relevant sections of the chapter. A detailed study of the transition moment leads to the specific selection rules that express the allowed transitions in terms of the changes in quantum numbers. We have already encountered examples of specific selection rules when discussing atomic spectra (Section 10.3), such as the rule ∆l =±1 for the angular momentum quantum number.
Fig. 13.6 (a) When a 1s electron becomes a 2s electron, there is a spherical migration of charge; there is no dipole moment associated with this migration of charge; this transition is electric-dipole forbidden. (b) In contrast, when a 1s electron becomes a 2p electron, there is a dipole associated with the charge migration; this transition is allowed. (There are subtle effects arising from the sign of the wavefunction that give the charge migration a dipolar character, which this diagram does not attempt to convey.)
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