Born-Oppenheimer electronic theory scattering

The classical idea of molecular structure gained its entry into quantum theory on the basis of the Born Oppenheimer approximation, albeit not as a non-classical concept. The B-0 assumption makes a clear distinction between the mechanical behaviour of atomic nuclei and electrons, which obeys quantum laws only for the latter. Any attempt to retrieve chemical structure quantum-mechanically must therefore be based on the analysis of electron charge density. This procedure is supported by crystallographic theory and the assumption that X-rays are scattered on electrons. Extended to the scattering of neutrons it can finally be shown that the atomic distribution in crystalline solids is identical with molecular structures defined by X-ray diffraction. 

In Chap. 2, we formulate our basic framework of the chemical theory based on the Born-Oppenheimer approximation. We briefly discuss how valid or how accurate the Born-Oppenheimer approximation for bound states is. Also a theory of electron scattering by polyatomic molecules within the Born-Oppenheimer framework (or the so-called fixed nuclei approximation) is presented. This is one of the typical theories of electron dynamics, along with the theory of molecular photoionization. 

A development of detailed theory, again based on the time-ordered diagrams of Figure 2, establishes the dependence of Raman scattering on a transition tensor which takes on the same role as the polarizability in Rayleigh scattering. Once the usual Born-Oppenheimer separation of electronic and vibrational wavefunctions has been effected, then for the vibrational Raman transition v v involving a normal mode of vibration 2, this tensor takes the form... 

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