Incorporating the geometric phase effect in triatomic and tetraatomic hyperspherical harmonics.
Hyperspherical harmonics in the democratic row-orthonormal hyperspherical coordinates are very appropriate basis sets for performing reactive scattering calculations for triatomic and tetraatomic systems. The mathematical conditions for incorporating the geometric phase effect in these harmonics are given. These conditions are implemented for triatomic systems, and their explicit analytical expressions in terms of Jacobi polynomials, in both the absence and presence of the geometric phase effect, are given.
Kuppermann
Aron
A
Arthur Amos Noyes Laboratory of Chemical Physics, Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA. aron@caltech.edu