Non-Born–Oppenheimer nuclear and electronic densities for a three-particle Hooke–Coulomb model

• Published in: Computational and theoretical chemistry 2013-08, Vol.1018, p.26-34
• Main Authors: Rodríguez, C.G., Urbina, A.S., Torres, F.J., Cazar, D., Ludeña, E.V.
• Format: Article
• Language: English
• Subjects: Hooke–Coulomb model; Non-Born–Oppenheimer; One-particle densities
• ISSN: 2210-271X
• DOI: 10.1016/j.comptc.2013.05.033

[Display omitted] •A three-particle quantum system is investigated within the non-Born–Oppenheimer regime.•The method for the calculation of NBO one-particle densities is described.•The described method is applied to the H−, H2+, and Ps− systems.•It is not possible to derive a unique molecular structure form NBP electronic densities. Non-Born–Oppenheimer, nBO, one-particle nuclear and electron densities for a Hooke–Coulomb model of a three-body system are presented. These densities are obtained using exact closed-form analytic solutions to this problem as well as variational solutions. Moreover, the densities are calculated using different reference points, such as the global center of mass [cm], the geometric centers between both identical [gc12] and non-identical particles [cm13], and the location of the non-identical particle [p3]. It is shown that the topology of these nBO densities depends upon the choice of the reference points. This result is in turn used to argue that in a nBO regime the topological properties of the one-particle density cannot be univocally correlated with molecular structure, in the way it is done for the Born–Oppenheimer approximation.