An efficient routine for computing symmetric real spherical harmonics for high orders of expansion

Andrzej Kudlicki, Malgorzata Rowicka-Kudlicka, Mirosław Gilski, Zbyszek Otwinowski

Research output: Contribution to journalArticle

4 Scopus citations


A numerically efficient method of constructing symmetric real spherical harmonics is presented. Symmetric spherical harmonics are real spherical harmonics with built-in invariance with respect to rotations or inversions. Such symmetry-invariant spherical harmonics are linear combinations of non-symmetric ones. They are obtained as eigenvectors of an appropriate operator, depending on symmetry. This approach allows for fast and stable computation up to very high order symmetric harmonic bases, which can be used in e.g. averaging of non-crystallographic symmetry in protein crystallography or refinement of large viruses in electron microscopy.

Original languageEnglish (US)
Pages (from-to)501-504
Number of pages4
JournalJournal of Applied Crystallography
Issue number3
StatePublished - Jun 2005
Externally publishedYes


ASJC Scopus subject areas

  • Condensed Matter Physics
  • Structural Biology

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