Thermal energies and the structures of molecules

Translational energy, which may be directly calculated from the classical 

Rotational energy, which, as its name implies, is the energy a molecule contains by virtue of rotations around the centre of mass. These energy levels are quite narrowly spaced from the energetic point of view, but they 

Vibrational energy, which is associated with the alternate extension and compression of the chemical bonds. For small displacements from the low-temperature equilibrium distance, the vibrational properties are those of simple harmonic motion, but at higher levels of vibrational energy, an anharmonic effect appears which plays an important role in the way in which atoms separate from the molecule. The vibrational energy of a molecule is described in the quantum theory by the equation 

D is the chemical energy of dissociation which can be obtained from thermodynamic data, and ji is the reduced mass of the diatomic molecule 

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