Extensions and foundations of the continuous symmetry measure

Match

Volumn 62, Issue 1, 2009, Pages 105-114

  Estrada, Ernesto ^a,b   Carbó Dorca, Ramón ^c  

^a Department of Mathematics ^*

^b UNIVERSITY OF STRATHCLYDE   (United Kingdom)

^c UNIVERSITY OF GIRONA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 72149125334     PISSN: 03406253     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (35)

1. H. Zabrodsky, S. Peleg, D. Avnir, J. Am. Chem. Soc. 114 (1992) 7843.
2. H. Zabrodsky, S. Peleg, D. Avnir, J. Am. Chem. Soc. 115 (1993) 8278.
3. D. Avnir, H. Zabrodsky Hel-Or, P. G. Mezey, in Encyclopedia of Computational Chemistry, P. von-Rague Schleyer, Ed. Wiley, Chichester, 1998, Vol. 4, p. 2890
4. D. Avnir, O. Katzenelson, S. Keinan, M. Pinsky, Y. Pinto, Y. Salomon, H. Zabrodsky Hel-Or, in Concepts in Chemistry: A Contemporary Challenge, D. H. Rouvray, Ed., Research Studies Press Ltd., Taunton, 1997, Chap. 9, p. 283.
5. P. Holme, F. Liljeros, C. R. Edling, B. J. Kim, Phys. Rev. E 68 (2003) 056107.
6. E. Estrada, J. A. Rodríguez-Velázquez, Phys. Rev. E 72 (2005) 046105.
7. T. Doslic, Chem. Phys. Lett. 412 (2005) 336.
8. D. R. Kanis, J. S Wong, T. J. Marks, M. A. Ratner, H. Zabrodsky, S. Keinan, D. Avnir, J. Phys. Chem. 99 (1995) 11061.
9. H. Zabrodsky, D. Avnir, J. Am. Chem. Soc. 117 (1995) 462.
10. S. Grimme, Chem. Phys. Lett. 297 (1998) 15.
11. S. Keinan, M. Pinsky, M. Plato, J. Edelstein, D. Avnir, Chem. Phys. Lett. 298 (1998) 43.
12. J. Cirera, P. Alemany, S. Alvarez, Chem.-Eur. J. 10 (2004) 190.
13. K. B. Lipkowitz, M. C. Kozlowski, Synlett 10 (2003) 1547.
14. S. Alvarez, J. Am. Chem. Soc. 125 (2003) 6795.
15. D. Casanova, J. Cirera, M. Llunell, P. Alemany, D. Avnir, S. Alvarez, J. Am. Chem. Soc. 126 (2004) 1755.
16. D. Yogev-Einot, D. Avnir, Acta Cryslallogr., Sect. B: Struct. Sci. 60 (2004) 163.
17. The hexagon in figures 1A and 1B due that the distance of two vertices which are not opposite to each other is changed, the center of gravity of the hexagon also changes. However, the present mathematical treatment requires that the center of gravity shall be retained. Thus, one should first move the distorted hexagon, so its center of gravity coincides with the center of gravity of the perfect hexagon, then one can calculate the distances. Equation (1) in the present study is correct only if both compared objects have the same center of gravity. Otherwise the obtained CSM will depend on the location of the investigated object.
18. ij = 1 if atoms i and j are directly connected to each other and zero in any other case.
19. L. Paoloni, M. Giambiagi and M. S. de Giambiagi, Estratto da Atti delta Societa di Naturalisti e Matamatici di Modena, Volume speciale per il 1° Convegno Internazionali dei Chimici Teorici di Lingua Latina. Vol C (1969) 90.
20. L. Amat, R. Carbó-Dorca, J. Comput. Chem. 18 (1997) 2023.
21. L. Amat, R. Carbó-Dorca, J. Comput. Chem. 20 (1999) 911.
22. L. Amat, R. Carbó-Dorca, J. Chem. Inf. Comput. Chem. Sci. 40 (2000) 1188.
23. X. Gironés, R. Carbó-Dorca, P. G. Mezey, J. Mol. Graph. Model. 19 (2001) 343.
24. L. Amat, R. Carbó-Dorca, Int. J. Quant. Chem. 87 (2002)
25. E. Besalii, A. Gallegos, R. Carbó-Dorca, MATCH Commun. Math. Comput. Chem. 44 (2001) 41.
26. E. Besalú, X. Gironés, L. Amat, R. Carbó-Dorca, Acc. Chem. Res. 35 (2002) 289
27. P. Bultinck, M. Mandado, R. Mosquera, J. Math. Chem. 43 (2008) 111.
28. T. K. Lim, M. A. Whitehead, J. Chem. Phys. 45 (1966) 4400.
29. G. Simmons, A. K. Schwartz, J. Chem. Phys. 60 (1974) 2272.
30. L. Vescelius, A. A. Frost, J. Chem. Phys. 61 (1974) 2983.
31. E. Estrada, N. Hatano, Chem. Phys. Lett. 439 (2007) 247.
32. E. Estrada J. A. Rodríguez-Velázquez, Phys. Rev. E 71 (2005) 056103.
33. J. A. de la Peña, I. Gutman, J. Rada, Lin. Algebra Appl. 427 (2007) 70.
34. I. Gutman, A. Graovac, Chem. Phys. Lett. 436 (2007) 294.
35. R. Carbó-Dorca, J. Math. Chem. 44 (2008) 373.