Vibrational spectroscopy overview - selection rules

The spectra corresponding to transitions between vibrational energy levels of the functional groups present in polymers occur in the mid-infrared (MIR) region of the spectrum. 

The formal requirement for these transitions to occur is that the molecular vibration should produce a change in dipole moment. Thus, in a molecule such as carbon dioxide, the symmetrical stretching vibration (vj) will be infrared inactive and the bending (V2) and asymmetric stretch (V3) modes will be active. The fundamental frequency at which a particular vibration will occur is given by the classical formula for a diatomic harmonic oscillator  

For a bending vibration, k will be lower than for stretching a bond, such that in CO2 this frequency is lower (667 cm ) than that for a stretching vibration (2349 cm ). 

The observed spectral bands correspond to allowed transitions between quantized energy levels of energy  

The selection rule for allowed transitions is Av = l, so the energy separation between the levels is hv, which is the observed spectral frequency. The fundamental band observed in the spectrum then corresponds to the transition from v = 0 to v = 1, since at normal temperatures most molecules will occupy the ground vibrational state. 

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Not only do the experimental vibrational predissociation lifetimes require interpretation, so do the increasingly sophisticated theoretical calculations whose results often fall out of a web of coupled differential equations or the convoluted algebra of quantum mechanics. In order to offer a qualitative overview of dynamical processes in van der Waals molecules, we shall introduce a selection rule which can provide insight into possible relaxation channels of vibrationally excited molecules. This selection rule concerns the change in a quantum number, Anj., which is to remain small for efficient vibrational predissociation processes. It bears a close analogy to the selection rules of optical spectroscopy which require small changes in quantum numbers Au, AJ, AS, etc. for efficient transitions between molecular states. Let us review the origin of the vibrational predissociation selection rule which has been developed in more detail elsewhere. ... 

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