Born-Oppenheimer approximation intermolecular forces

Keywords intermolecular forces, Born-Oppenheimer approximation, supermolecular method, polar-... 

Various derivations of the Born-Oppenheimer approximation can be found in the literature. See Refs. (23-24) for typical reviews. The applicability of this approximation has been proven on several examples, cf. the seminal works of Kolos and Wolniewicz25-29 for various states of the hydrogen molecule. The results of Kolos and collaborators on H2 and of other authors for other systems were reviewed in several papers, cf., e.g. Refs. (24-32). Since intermolecular forces can only be discussed for fixed geometries of the interacting monomers, the Born-Oppenheimer approximation is a natural framework for the discussion of intermolecular interactions. Therefore, in this section we will briefly review all approximations leading to to the separation of the electronic and nuclear motions, and discuss situations in which this fundamental approximation fails. 

The chemist is concerned with the relative positions of the nuclei in the molecule and with the internal energy, but not with the motions of the molecule as a whole. This motion can be excluded from our consideration, for example, by elimination of the center-of-mass translation. Moreover, the intermolecular (electrostatic) forces acting on electrons and nuclei would be similar. This would cause much slower internal motion of the heavy nuclei in comparison to light electrons. For this reason, the approximate description of electron motion with parametric dependence on the static positions of nudei is justifled. Such reasoning leads to adiabatic approximation and Anally to Born-Oppenheimer approximation. 

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