Abstract.
As a continuation of our previous work for the construction of expansion basis sets for the quantum mechanical treatment of N-body problems of interest for intermolecular and intramolecular and reactive dynamics of polyatomic molecules and clusters, we develop here a group-theoretical procedure which allows us to obtain explicitly the hyperspherical harmonics for the description of the collective motions. The coordinates involved are related to the invariants of the N-body system, which are referred to the moments of inertia. Although this work is limited to the case where both external and internal (kinematic) rotations are zero, and the example of N=4 is explicitly worked out, this method, which gives hyperspherical harmonics as linear combinations of ordinary spherical harmonics, can be extended to cover the general N-body case.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Acknowledgments.
This paper is dedicated to Prof. Jacopo Tomasi on the occasion of his 70th birthday. We thank Simonetta Cavalli and Andrea Beddoni for useful discussions. We acknowledge the support from the EU through the COST D9 Action and the Uman Potential Research Network “Theoretical studies of electronic and molecular processes in molecules and clusters” (contract HPRN-CT99-00005). This work was also supported by the Ministero dell’Istruzione dell’Universitá e della Ricerca, Ente per le Nuove Tecnologie, l’Energia e l’Ambiente and Agenzia Spaziale Italiana.
Author information
Authors and Affiliations
Corresponding author
Additional information
Contribution to the Jacopo Tomasi Honorary Issue
Rights and permissions
About this article
Cite this article
Aquilanti, V., Lombardi, A. & Littlejohn, R. Hyperspherical harmonics for polyatomic systems: basis set for collective motions. Theor Chem Acc 111, 400–406 (2004). https://doi.org/10.1007/s00214-003-0526-3
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00214-003-0526-3