# Molecular Spectra

There are always electronic configuration change in atomic spectroscopy transitions. In addition to electronic transitions it is also possible to have vibrational and rotational transitions in molecules, that gives rise to more complicated spectra than for atomic spectra, but we have to know the binding forces and molecular structure in order to study these spectra.
If we make an assumption about special couplings the total energy E will be just the sum of electronic Eel, vibrational Evib and rotational energies Erot of molecule:

E = Erot + Evib + Eel

The state energies have different meanings:

hνrot <<hνvib<<hνel

νrot→ Transitions between nearby rotational levels in far IR and microwave regions
νvib→ pure vibrational transitions in IR (about 1000cm-1)
νel→ electronic transitions in visual/UV

Electronic transitions usually give rise to vibration and rotation changes. The allowed transitions are given by the selection rules. For this electronic transition a molecule shouldn't have any constant dipole moment since electrical field of absorbed (or emitted) light may directly "move" the electronic distribution. Nevertheless, for rovibronic transitions in the electronic state limits the electric needs to have "origin of force" in order to begin transition, i.e. it's necessary to have constant electric dipole moment (or it must be induced by special conditions).

Formulas must be written down for rotational energy levels firstly and according to selection rules the pure rotational spectrum can be then analysed. If an energy is so high that it's possible to have vibrational transition then rotational and vibrational transitions are excited simultaneously; and if an energy is more higher then we will have electronic transition together with rotational transition.

Generally, the transition probability from state n into state m is as follows:

<m|µ|n>º-∞∫+∞ym* µ yn dτ

where dτ is the volume element and it can readily be calculated whether we know µ and both wavefunctions.