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Numerical generation of hyperspherical harmonics for tetra-atomic systems

Lepetit, Bruno and Wang, Desheng and Kuppermann, Aron (2006) Numerical generation of hyperspherical harmonics for tetra-atomic systems. Journal of Chemical Physics, 125 (13). Art. No. 133505. ISSN 0021-9606. https://resolver.caltech.edu/CaltechAUTHORS:LEPjcp06

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Abstract

A numerical generation method of hyperspherical harmonics for tetra-atomic systems, in terms of row-orthonormal hyperspherical coordinates—a hyper-radius and eight angles—is presented. The nine-dimensional coordinate space is split into three three-dimensional spaces, the physical rotation, kinematic rotation, and kinematic invariant spaces. The eight-angle principal-axes-of-inertia hyperspherical harmonics are expanded in Wigner rotation matrices for the physical and kinematic rotation angles. The remaining two-angle harmonics defined in kinematic invariant space are expanded in a basis of trigonometric functions, and the diagonalization of the kinetic energy operator in this basis provides highly accurate harmonics. This trigonometric basis is chosen to provide a mathematically exact and finite expansion for the harmonics. Individually, each basis function does not satisfy appropriate boundary conditions at the poles of the kinetic energy operator; however, the numerically generated linear combination of these functions which constitutes the harmonic does. The size of this basis is minimized using the symmetries of the system, in particular, internal symmetries, involving different sets of coordinates in nine-dimensional space corresponding to the same physical configuration.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1063/1.2218515DOIArticle
Additional Information:© 2006 American Institute of Physics (Received 6 April 2006; accepted 6 June 2006; published online 5 October 2006) This work has been supported in part by CNRS to one of the authors (B.L.) and NSF (Grant No. CHE981). The authors are also grateful to CNRS and NSF for allocations of computing time at IDRIS and SDSC, respectively.
Funders:
Funding AgencyGrant Number
Centre National de la Recherche Scientifique (CNRS)UNSPECIFIED
NSFUNSPECIFIED
Subject Keywords:numerical analysis; matrix algebra; functional analysis
Issue or Number:13
Record Number:CaltechAUTHORS:LEPjcp06
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:LEPjcp06
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:5657
Collection:CaltechAUTHORS
Deposited By: Archive Administrator
Deposited On:27 Oct 2006
Last Modified:20 Nov 2020 22:52

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