1 Answers
A molecular vibration is a periodic motion of the atoms of a molecule relative to each other, such that the center of mass of the molecule remains unchanged. The typical vibrational frequencies range from less than 10 Hz to approximately 10 Hz, corresponding to wavenumbers of approximately 300 to 3000 cm and wavelengths of approximately 30 to 3 µm.
For a diatomic molecule A−B, the vibrational frequency in sec is given by ν = 1 2 π k μ {\displaystyle \nu ={1 \over {2\pi }}{\sqrt {k \over \mu }}} , where k is the force constant in dyne/cm or erg/cm and μ is the reduced mass given by 1 μ = 1 m A + 1 m B {\displaystyle {\frac {1}{\mu }}={\frac {1}{m_{A}}}+{\frac {1}{m_{B}}}} . The vibrational wavenumber in cm is ν ~ = 1 2 π c k μ , {\displaystyle {\tilde {\nu }}\;={1 \over {2\pi c}}{\sqrt {k \over \mu }},} where c is the speed of light in cm/sec.
Vibrations of polyatomic molecules are described in terms of normal modes, which are independent of each other, but each normal mode involves simultaneous vibrations of different parts of the molecule. In general, a non-linear molecule with N atoms has 3N – 6 normal modes of vibration, but a linear molecule has 3N – 5 modes, because rotation about the molecular axis cannot be observed. A diatomic molecule has one normal mode of vibration, since it can only stretch or compress the single bond.
A molecular vibration is excited when the molecule absorbs energy, ΔE, corresponding to the vibration's frequency, ν, according to the relation ΔE = hν, where h is Planck's constant. A fundamental vibration is evoked when one such quantum of energy is absorbed by the molecule in its ground state. When multiple quanta are absorbed, the first and possibly higher overtones are excited.