Vibrational motions and energies

2 The physical basis molecular vibrations 8.2.1 Vibrational motions and energies 

Structural Methods in Molecular Inorganic Chemistry, First Edition. David W. H. Rankin, Norbert W. Mitzel and Carole A. Morrison. 2013 John Wiley Sons, Ltd. Published 2013 by John Wiley Sons, Ltd. 

Vibrating diatomic molecule showing the equilibrium positions of atoms as dashed circles, instantaneous positions as solid circles, and restoring forces F. This is equivalent to the classical model of two masses connected by a spring. 

Because of the Uncertainty Principle (Section 2.5), a molecule cannot have zero vibrational energy if it had, we could specify both the positions and the momenta of the atoms in a molecule precisely. All molecular vibrations therefore have some zero-point energy, and this can be shown to be equal to one half of a quantum, so that the total vibrational energy of a molecule with only one normal vibration, such as a simple diatomic, is 

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Vierheilig A, Chen T, Waltner P, Kiefer W, Materny A, Zewail AH (1999) Femtosecond dynamics of ground-state vibrational motion and energy flow polymers of diacetylene. Chem Phys Lett 312 349... 

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