In vibrational spectroscopy, an overtone band is the spectral band that occurs in a vibrational spectrum of a molecule when the molecule makes a transition from the ground state (v=0) to the second excited state (v=2), where v is the vibrational quantum number (a non-negative integer) obtained from solving the Schrödinger equation for the molecule.
Generally, in order to study the vibrational spectra of molecules, chemical bond vibrations are assumed to be approximable as simple harmonic oscillators. Thus a quadratic potential is used in the Schrödinger equation to solve for the vibrational energy eigenstates and their eigenvalues.These energy states are quantized, meaning they can assume only some "discrete" values of energy. When electromagnetic radiation is shined on a sample, the molecules can absorb energy from the radiation and change their vibrational energy state. However, the molecules can absorb energy from radiation only under certain condition, namely- there should be a change in the electric dipole moment of the molecule when it is vibrating. This change in the electric dipole moment of the molecule leads to the transition dipole moment of the molecule, for transition from the lower to higher energy state, being non-zero which is an essential condition for any transition to take place in the vibrational state of the molecule (due to selection rules).
