By P.A. Gorry (Auth.)
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Extra info for Basic Molecular Spectroscopy
1 A diatomic molecule An important quantity for describing the energy of rotation is the moment of inertia, /, defined by /=Σ"ν? 3) m1rl=m2r2 and the fact that the bond length is given by r = rl+r2. 7) is true for any linear molecule, not just diatomics. 1. The potential energy may be set to zero since there is no change in bond length during the rotation. The detailed solution will not be given here but it can be found in any standard text on quantum mechanics. The energy levels obtained are given by the formula J = 0,l,2...
We have already stated that a molecule must first possess a permanent dipole moment. 32). 15) AJ= 1 corresponds to absorption and AJ= — 1 to emission. This rule is very powerful since it simplifies the spectrum considerably— indeed we need only consider adjacent levels when constructing the spectrum. 4 illustrates how application of this rule leads to the spectral lines arising from molecular rotational transitions. 16) Ej = 2B(J + l) The lines in the rotational spectrum are thus expected to occur at 23, 4B, 6B....
In order for a symmetric top molecule to exhibit a rotational spectrum it must possess a permanent dipole moment. Most symmetric top molecules have this dipole moment directed along the unique axis—if this is the case then we find the following selection rules AJ = 0, ±1 ΔΚ = 0 (Κ#0) AJ=±1 AK = 0 (K = 0) The fact that transitions between different K levels do not arise from photon absorption is not a surprise since the K quantum number signifies rotation about the unique axis—and hence the dipole.