Abstract
The measurement of the degree of symmetry proved to be a useful tool in the prediction of quantitative structural–physical correlations. These measurements have been based, in the most general form, on the folding/unfolding algorithm, for which we provide here a new and simpler proof. We generalize this proof to the case of objects composed of more than one (full) orbit. An important practical issue we consider is the division of the graph into symmetry orbits and the mapping of the symmetry group elements onto the points of the graph. The logical constraints imposed by the edges of the graph are reviewed and used for the successful resolution of the coupling between different orbits.
Similar content being viewed by others
References
D. Avnir, O. Katzenelson, S. Keinan, M. Pinsky, Y. Pinto, Y. Salomon and H. Zabrodsky Hel-Or, in: Concepts in Chemistry: A Contemporary Challenge, eds. D.H. Rouvray and E. Kirby (Research Studies Press, Somerset, 1996) pp. 283–324.
D. Avnir, H. Zabrodsky Hel-Or and P.G. Mezey, Continuous symmetry and chirality measures, in: Encyclopedia of Computational Chemistry, Vol. 4, ed. P. von Rague Schleyer (Wiley, Chichester, 1998) pp. 2890–2901.
V. Buch, E. Gershgoren, H. Zabrodsky and D. Avnir, Chem. Phys. Lett. 247 (1995) 149–153.
R. Cammi and E. Cavalli, Acta Cryst. B 48 (1992) 245–252.
C. Grimme, Chem. Phys. Lett. 297 (1998) 15–21.
O. Katzenelson, H. Zabrodsky Hel-Or and D. Avnir, Chem. Eur. J. 2 (1996) 174–181.
S. Keinan and D. Avnir, J. Am. Chem. Soc. 120 (1998) 6152–6159; http://chem.ch.huji.ac.il/_david/shahar/QSAR/qsar.html.
S. Keinan, J. Edelstein, M. Plato, M. Pinsky and D. Avnir, Chem. Phys. Lett. 298 (1998) 43–50.
V.E. Kuzmin, I.B. Stelmakh, M.B. Bekker and D.V. Pozigun, J. Phys. Org. Chem. 5 (1992) 295–298.
A.Y. Meyer and W.G. Richards, J. Comput. Aided Mol. Design 5 (1991) 427–439.
P.G. Mezey, J. Am. Chem. Soc. 112 (1990) 3791–3802.
G. Moreau, J. Chem. Inf. Comput. Sci. 37 (1997) 929–938.
M. Pinsky and D. Avnir, Inorg. Chem. 37 (1998) 5575–5582.
Y. Pinto, P.W. Fowler, D. Mitchell and D. Avnir, J. Phys. Chem. 102 (1998) 5776–5784.
Y. Pinto, H. Zabrodsky Hel-Or and D. Avnir, J. Chem. Soc. Faraday Trans. 92 (1996) 2523.
G. Rucker and C.J. Rucker, Chem. Inf. Comput. Sci. 30 (1990) 187–191.
Y. Salomon and D. Avnir, J. Comput. Chem. 20 (1999) 772–780.
I. Saragusti, I. Sharon, O. Katzenelson and D. Avnir, J. Archeol. Sci. 25 (1998) 817.
A. Seri-Levy and W.G. Richards, Tetrahedron: Asymmetry 4 (1993) 1917–1923.
N. Weinberg and K. Mislow, J. Math. Chem. 17 (1995) 35–53.
H. Zabrodsky and D. Avnir, Adv. Mol. Struct. Res. 1 (1995) 1; http://www.cs.biu.ac.il:8080/_hagit/papers/chemistry3.ps.Z.
H. Zabrodsky, S. Peleg and D. Avnir, J. Am. Chem. Soc. 114 (1992) 7843.
H. Zabrodsky, S. Peleg and D. Avnir, J. Am. Chem. Soc. 115 (1993) 8278–8289.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Salomon, Y., Avnir, D. Continuous symmetry measures: A note in proof of the folding/unfolding method. Journal of Mathematical Chemistry 25, 295–308 (1999). https://doi.org/10.1023/A:1019144702913
Issue Date:
DOI: https://doi.org/10.1023/A:1019144702913