Rapid and stable determination of rotation matrices between spherical harmonics by direct recursion | Zendy

Cheol Ho Choi | Zendy; Joseph Ivanic | Zendy; Mark S. Gordon | Zendy; Klaus Ruedenberg | Zendy

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Rapid and stable determination of rotation matrices between spherical harmonics by direct recursion

Author(s) -

Cheol Ho Choi,

Joseph Ivanic,

Mark S. Gordon,

Klaus Ruedenberg

Publication year - 1999

Publication title -

the journal of chemical physics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.071

H-Index - 357

eISSN - 1089-7690

pISSN - 0021-9606

DOI - 10.1063/1.480229

Subject(s) - spherical harmonics , rotation (mathematics) , spin weighted spherical harmonics , harmonics , rotation matrix , recursion (computer science) , rotation group so , zonal spherical harmonics , euler angles , matrix (chemical analysis) , simple (philosophy) , atomic orbital , euler's formula , vector spherical harmonics , mathematics , solid harmonics , classical mechanics , mathematical analysis , pure mathematics , physics , geometry , quantum mechanics , chemistry , algorithm , voltage , philosophy , epistemology , chromatography , electron

Recurrence relations are derived for constructing rotation matrices between complex spherical harmonics directly as polynomials of the elements of the generating 3×3 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.

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