Abstract
In the framework of the Born-Oppenheimer separation (Sect. 7.1), once that the electronic state has been described and the eigenvalue \(E_e(\mathbf {R})\) and wavefunction \(\phi _e (\mathbf {r}, \mathbf {R})\) have been found, then the motions of the nuclei are described by a function \(\phi _{\nu }^{(g)}(\mathbf {R})\), where g represents the quantum label for the electrons and \(\nu \) are the quantum numbers (to be found) for the nuclei.
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Notes
- 1.
This statement regarding the alternative role of symmetric and antisymmetric modes in Raman and infrared activity is a general one, holding in any molecule with inversion symmetry. It is related to the fact that the polarizability upon inversion transforms as a second order tensor while the dipole moment is a vector.
Specific References and Further Reading
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H. Haken and H.C. Wolf, Molecular Physics and Elements of Quantum Chemistry, (Springer Verlag, Berlin, 2004).
G. Herzberg, Molecular Spectra and Molecular Structure, Vol. I, II and III, (D. Van Nostrand, New York, 1964–1966, reprint 1988–1991).
H. Eyring, J. Walter and G.E. Kimball, Quantum Chemistry, (J. Wiley, New York, 1950).
B.H. Bransden and C.J. Joachain, Physics of atoms and molecules, (Prentice Hall, 2002).
J.A. Cronin, D.F. Greenberg, V.L. Telegdi, University of Chicago Graduate Problems in Physics, (Addison-Wesley, 1967).
W. Demtröder, Molecular Physics, (Wiley-VCH, 2005).
R.N. Dixon, Spectroscopy and Structure, (Methuen and Co LTD, London, 1965).
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Rigamonti, A., Carretta, P. (2015). Nuclear Motions in Molecules and Related Properties. In: Structure of Matter. UNITEXT for Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-17897-4_10
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