Related Experiment Video
Updated: Jun 17, 2026

Multimodal Nonlinear Hyperspectral Chemical Imaging Using Line-Scanning Vibrational Sum-Frequency Generation Microscopy
Published on: December 1, 2023
Analytical derivation of row-orthonormal hyperspherical harmonics for triatomic systems
Desheng Wang1, Aron Kuppermann
1Arthur Amos Noyes Laboratory of Chemical Physics, Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA.
Abstract:
Hyperspherical harmonics for triatomic systems as functions of row-orthonormal hyperspherical coordinates, (also called democratic hyperspherical harmonics) are obtained explicitly in terms of Jacobi polynomials and trigonometeric functions. These harmonics are regular at the poles of the triatomic kinetic energy operator, are complete, and are not highly oscillatory. They constitute an excellent basis set for calculating the local hyperspherical surface functions in the strong interaction region of nuclear configuration space. This basis set is, in addition, numerically very efficient and should permit benchmark-quality calculations of state-to-state differential and integral cross sections for those systems. The approach used for their derivation is new and should be applicable to systems of more than three atoms.
More Related Videos
Related Concept Videos
Atomic Orbitals
Hybridization of Atomic Orbitals I
Orthogonal Trajectories
Hybridization of Atomic Orbitals II
The Quantum-Mechanical Model of an Atom
Molecular Orbital Theory II

