In atomic spectroscopy, all transitions reflect changes in the configuration of electrons. Molecules are, in addition, subject to rotational and vibrational states. In consequence, their spectra are more complex but yield as well information on the structure of a molecule and the strength of bonds. Assuming indepent modes of motion, we can split the total energy of a molecule into the components Eel, vibrational Evib and rotational Erot energy.
E = Erot + Evib + Eel
The energies related to changes between these modes differ to a great degree:
hνrot << hνvib << hνel
νrot | Transistions between neighbouring rotational levels | far infrared or microwaves |
νvib | Transitions purely related to vibrational modes | within infrared (around 1000 cm-1) |
νel | electronic transitions | visible and ultraviolet light |
In general, electronic transitions introduce subsequent changes in the rotational and vibrational mode as well. Selection rules determine whether transitions are allowed or not. As the electric field of absorbed or emitted light is able to affect the distribution of electrons within a molecule, there is no need for the molecule to display a permanent dipol moment. In contrast, for rotational-vibrations transitions within a defined electronic state, such a dipole moment is a precondition or has to be introduced for a transition to take place.
First in this chapter, a mathematical description of the energy levels related to rotation is delivered. Taking as well selection rules into account, an analysis of pure rotational spectra is feasible. For quantities of energy which are able to lift the molecule into a vibrational mode, simultaneous excitation of rotation is to be expected. For even larger energies that change as well the state of electrons, the vibrational and rotational state of a molecule will be affected as well.
The probability for a transition from state n to state m is
Expression dτ represents volume elements. It is possible to determine this probability for known pairs of wave functions.