Symmetry operation measures.
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.
Pinsky
Mark
M
Institute of Chemistry, The Lise Meitner Minerva Center for Computational Quantum Chemistry, Hebrew University of Jerusalem, Jerusalem 91904, Israel.
Casanova
David
D
Alemany
Pere
P
Alvarez
Santiago
S
Avnir
David
D
Dryzun
Chaim
C
Kizner
Ziv
Z
Sterkin
Alexander
A
D000042:Absorption; D000465:Algorithms; D019295:Computational Biology / Q000379:methods*; D003198:Computer Simulation; D015394:Molecular Structure; D012399:Rotation; D014894:Weights and Measures