An approach to establish the connection between configuration and su(n + 1) algebraic spaces in molecular physics: application to ammonia

• Published in: Molecular physics Vol. 115; no. 24; pp. 3206 - 3223
• Main Authors: Santiago, R. D., Arias, J. M., Gómez-Camacho, J., Lemus, R.
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis 17.12.2017; Taylor & Francis Ltd
• Subjects: Algebra; algebraic realisation; Ammonia; Anharmonicity; configuration space; Configurations; double minimum potential; double morse potential; Molecular physics; Morse potential; Operators (mathematics); Potential barriers; Representations; Second quantisation; Symmetry
• ISSN: 0026-8976; 1362-3028
• DOI: 10.1080/00268976.2017.1358829

An approach aimed to connect configuration and algebraic spaces is discussed. This approach emerges as the need to translate a vibrational description in configuration space to an algebraic representation based on unitary dynamical algebras, where a straightforward connection does not exist e.g. the vibron model case. Our method is based on the mapping of the algebraic to configuration states, a premise that allows arbitrary operators in configuration to be expanded in terms of generators of the dynamical algebra. The coefficients are determined through a minimisation procedure and given in terms of matrix elements defined in configuration space. We apply the general formalism to the Morse potential, representing anharmonic vibrations in a molecule, as a benchmark case where a dynamical symmetry exits, and to the symmetric double-Morse potential, representing vibrations that can tunnel through a potential barrier, as an example in which a dynamical symmetry is not present. We discuss how the tunnelling effect in the double Morse can be described very simply in the su(2) algebraic representation, taking the ammonia inversion vibrational spectrum as an example.