Rapid and Stable Determination of Rotation Matrices between Spherical Harmonics by Direct Recursion

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1999-11-01
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Choi, Cheol
Ivanic, Joseph
Ruedenberg, Klaus
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Ames National Laboratory

Ames National Laboratory is a government-owned, contractor-operated national laboratory of the U.S. Department of Energy (DOE), operated by and located on the campus of Iowa State University in Ames, Iowa.

For more than 70 years, the Ames National Laboratory has successfully partnered with Iowa State University, and is unique among the 17 DOE laboratories in that it is physically located on the campus of a major research university. Many of the scientists and administrators at the Laboratory also hold faculty positions at the University and the Laboratory has access to both undergraduate and graduate student talent.

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Chemistry

The Department of Chemistry seeks to provide students with a foundation in the fundamentals and application of chemical theories and processes of the lab. Thus prepared they me pursue careers as teachers, industry supervisors, or research chemists in a variety of domains (governmental, academic, etc).

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The Department of Chemistry was founded in 1880.

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1880-present

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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.

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The following article appeared in Journal of Chemical Physics 111 (1999), 8825, and may be found at doi:10.1063/1.480229.

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Fri Jan 01 00:00:00 UTC 1999
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