Chemistry, Ames Laboratory
Journal or Book Title
Journal of Chemical Physics
Recurrence relations are derived for constructing rotation matrices between complex spherical harmonics directly as polynomials of the elements of the generating3×3 rotation matrix, bypassing the intermediary of any parameters such as Euler angles. The connection to the rotation matrices for real spherical harmonics is made explicit. The recurrence formulas furnish a simple, efficient, and numerically stable evaluation procedure for the real and complex representations of the rotation group. The advantages over the Wigner formulas are documented. The results are relevant for directing atomic orbitals as well as multipoles.
Copyright 1999 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics.
American Institute of Physics
Choi, Cheol Ho; Ivanic, Joseph; Gordon, Mark S.; and Ruedenberg, Klaus, "Rapid and Stable Determination of Rotation Matrices between Spherical Harmonics by Direct Recursion" (1999). Chemistry Publications. 355.