title: Symmetry operation measures.
abstract: We introduce a new mathematical tool for quantifying the symmetry contents of molecular structures: the Symmetry Operation Measures. In this approach, we measure the minimal distance between a given structure and the structure which is obtained after applying a selected symmetry operation on it. If the given operation is a true symmetry operation for the structure, this distance is zero; otherwise it gives an indication of how different the transformed structure is from the original one. Specifically, we provide analytical solutions for measures of all the improper rotations, S n p, including mirror symmetry and inversion, as well as for all pure rotations, C n p. These measures provide information complementary to the Continuous Symmetry Measures (CSM) that evaluate the distance between a given structure and the nearest structure which belongs to a selected symmetry point-group.
authors.affiliation: Institute of Chemistry, The Lise Meitner Minerva Center for Computational Quantum Chemistry, Hebrew University of Jerusalem, Jerusalem 91904, Israel.
authors.forename: Mark
authors.initials: M
authors.lastname: Pinsky
authors.forename: David
authors.initials: D
authors.lastname: Casanova
authors.forename: Pere
authors.initials: P
authors.lastname: Alemany
authors.forename: Santiago
authors.initials: S
authors.lastname: Alvarez
authors.forename: David
authors.initials: D
authors.lastname: Avnir
authors.forename: Chaim
authors.initials: C
authors.lastname: Dryzun
authors.forename: Ziv
authors.initials: Z
authors.lastname: Kizner
authors.forename: Alexander
authors.initials: A
authors.lastname: Sterkin
mesh_terms: D000042:Absorption; D000465:Algorithms; D019295:Computational Biology / Q000379:methods*; D003198:Computer Simulation; D015394:Molecular Structure; D012399:Rotation; D014894:Weights and Measures