Energies and wavenumbers of molecular vibrations

The zero point energy of a molecule corresponds to the energy of its lowest vibrational level (vibrational ground state). 

Consider a diatomic molecule, XY. The vibrational frequency of the bond depends on the masses of atoms X and Y, and on the force constant, k, of the bond. The force constant is a property of the bond and is related to its strength. If we return to stretching a spring, then the force constant is a measure of the stiffness of the spring. If atoms X and Y are of similar mass, they contribute almost equally to the molecular vibration. However, if the masses 

For a diatomic molecule, the transition from the vibrational ground state to the first excited state gives rise to a fundamental absorption in the vibrational spectrum. Equation 4.5 gives the frequency of this absorption. 

Absorptions in IR spectra are usually quoted in wavenumbers (wavenumber = 1/wavelength, P = 1/A) rather than frequencies, and eq. 4.5 then becomes eq. 4.6. 

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