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 The ground state of a quantum-mechanical system is its stationary state of lowest energy; the energy of the ground state is known as the zero-point energy of the system. An excited state is any state with energy greater than the ground state ...

(v=0) to the second

excited state In quantum mechanics Quantum mechanics is the fundamental physical Scientific theory, theory that describes the behavior of matter and of light; its unusual characteristics typically occur at and below the scale of atoms. Reprinted, Add ...

(v=2), where v is the vibrational quantum number (a non-negative integer) obtained from solving the

Schrödinger equation The Schrödinger equation is a partial differential equation that governs the wave function of a non-relativistic quantum-mechanical system. Its discovery was a significant landmark in the development of quantum mechanics. It is named after E ...

for the molecule. Generally, in order to study the vibrational spectra of molecules,

chemical bond A chemical bond is the association of atoms or ions to form molecules, crystals, and other structures. The bond may result from the electrostatic force between oppositely charged ions as in ionic bonds or through the sharing of electrons a ...

vibrations are assumed to be approximable as simple

harmonic oscillator In classical mechanics, a harmonic oscillator is a system that, when displaced from its equilibrium position, experiences a restoring force ''F'' proportional to the displacement ''x'': \vec F = -k \vec x, where ''k'' is a positive const ...

s. 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 Discrete may refer to: *Discrete particle or quantum in physics, for example in quantum theory * Discrete device, an electronic component with just one circuit element, either passive or active, other than an integrated circuit * Discrete group, ...

" 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 The electric dipole moment is a measure of the separation of positive and negative electrical charges within a system: that is, a measure of the system's overall Chemical polarity, polarity. The International System of Units, SI unit for electric ...

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 rule In physics and chemistry, a selection rule, or transition rule, formally constrains the possible transitions of a system from one quantum state to another. Selection rules have been derived for electromagnetic transitions in molecules, in atoms, in ...

s). Importantly, under the simple harmonic approximation, it can be shown that the transition dipole moment is non-zero only for transitions where ∆v=±1. Hence for an ideal, simple-harmonically vibrating bond, the vibrational spectrum contains no overtones. Of course, real molecules do not vibrate perfectly harmonically, because a bond's potential is not precisely quadratic but better approximated as a Morse potential. Solving the Schrödinger equation with the Morse potential for the molecule under consideration yields vibrational energy eigenstates with the interesting property that when one calculates transition dipole moments for various vibrational energy level transitions, the transition dipole moment is not zero for the transitions where ∆v=±2,±3,±4, etc. Thus, for real molecules, the allowed transitions are those for which ∆v=±1,±2,±3,±4, etc. The overtone band observed in the IR spectrum is one such transition with ∆v=2, from v=0 to v=2 energy state. It has been experimentally found that the

intensity Intensity may refer to: In colloquial use * Strength (disambiguation) *Amplitude * Level (disambiguation) * Magnitude (disambiguation) In physical sciences Physics *Intensity (physics), power per unit area (W/m2) *Field strength of electric, m ...

of the overtone band is very low compared to the fundamental band, validating the harmonic approximation.

References

*C.N.Banwell and E.M.McCash:Fundamentals of Molecular Spectroscopy, Tata McGraw-Hill Fourth Edition Raman spectroscopy Infrared spectroscopy {{spectroscopy-stub

See also

References