The proof of the metric properties of a fuzzy chirality measure of molecular electron density clouds

Journal of Molecular Structure: THEOCHEM

Volumn 455, Issue 2-3, 1998, Pages 183-190

  Mezey, Paul G ^a  

^a UNIVERSITY OF SASKATCHEWAN   (Canada)

Author keywords

Electron density clouds; Hausdorff type distance; Metric properties

Indexed keywords

EID: 0008302007     PISSN: 01661280     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0166-1280(98)00514-4     Document Type: Article

References (36)

1. Á. Kucsman, Acta Chim. Acad. Sci. Hung 3 (1953) 47.
2. Á. Kucsman, I Kapovits, Stud. Org. Chem. (Org. Sulfur Chem.) 19 (1985) 191.
3. R.S. Cahn, C.K. Ingold, V. Prelog, Angew. Chem Internat. Ed. Engl. 5 (1966) 385.
4. D.M. Walba, Tetrahedron 41 (1985) 3161.
5. P.G. Mezey, Shape in Chemistry: An Introduction to Molecular Shape and Topology, VCH Publishers, New York, 1993.
6. A.B. Buda, T. Auf der Heyde, K. Mislow, Angew. Chem. Int. Ed. Engl. 31 (1992) 989.
7. A. Rassat, Compt. Rend. Acad. Sci. (Paris) II 299 (1984) 53.
8. A.I. Kitaigorodskii, Organic Chemical Crystallography, ch. 4., Consultants Bureau, New York, 1961.
9. G. Gilat, Chem. Phys. Lett. 121 (1985) 9.
10. G. Gilat, L.S. Schulman, Chem. Phys. Lett. 121 (1985) 13.
11. G. Gilat, J. Phys. A 22 (1989) L545.
12. P.G. Mezey, Topology of molecular shape and chirality, in: J. Bertran and I.G. Csizmadia (Eds.), New Theoretical Concepts for Understanding Organic Reactions, Nato ASI Series, Kluwer Academic Publishers, Dordrecht, 1989, pp 77-99.
13. P.G. Mezey, Three-dimensional topological aspects of molecular similarity, in: M.A. Johnson, G.M. Maggiora (Eds.), Concepts and Applications of Molecular Similarity, Wiley, New York, 1990, pp 321-368.
14. P.G. Mezey, A Global approach to molecular chirality, in: P.G. Mezey (Ed.) New Developments in Molecular Chirality, Kluwer Academic Publishers, Dordrecht, 1991.
15. A.B. Buda, T.P.E. Auf der Heyde, K. Mislow, J. Math. Chem. 6 (1991) 243.
16. T.P.E. Auf der Heyde, A.B. Buda, K. Mislow, J. Math. Chem. 6 (1991) 255.
17. A.B. Buda, K. Mislow, Elem. Math. 46 (1991) 65.
18. A.B. Buda, K. Mislow, J. Amer. Chem. Soc. 114 (1992) 6006.
19. H. Zabrodsky, S. Peleg, D. Avnir, J. Amer. Chem. Soc. 114 (1992) 7843.
20. P.G. Mezey, J. Math. Chem. 11 (1992) 27.
21. H. Zabrodsky, S. Peleg, D. Avnir, J. Amer. Chem. Soc. 115 (1993) 8278.
22. H. Zabrodsky, D. Avnir, Adv. Mol. Struct. Res. 1 (1995) 1.
23. H. Zabrodsky, D. Avnir, J. Amer. Chem. Soc. 117 (1995) 462.
24. K. Mislow, R. Bolstad, J. Amer. Chem. Soc. 77 (1955) 6712.
25. K. Mislow, P. Poggi-Corradini, J. Math. Chem. 13 (1993) 209.
26. P.G. Mezey, J. Math. Chem. 17 (1995) 185.
27. P.G. Mezey, J. Math. Chem. 18 (1995) 133.
28. L.A. Zadeh, Inform. Control, Control 8 (1965) 338.
29. G.J. Klir, B. Yuan, Fuzzy Sets and Fuzzy Logic, Theory and Applications, Prentice-Hall, Englewood Cliffs,NJ, 1995.
30. S.T. Ali, H.D. Doebner, J. Math. Phys. 17 (1976) 1705.
31. S.T. Ali, E. Prugovecki, J. Math. Phys. 18 (1977) 219.
32. P.G. Mezey, Potential Energy Hypersurfaces, Elsevier, Amsterdam, 1987.
33. P.G. Mezey, Molecular similarity measures of conformational changes and electron density deformations, Advances in Molecular Similarity, Vol. 1 (1996) 89-120.
34. P.G. Mezey, Functional groups in quantum chemistry, Adv. Quantum Chem 27 (1996) 163-222.
35. P.G. Mezey, Fuzzy Measures of Molecular Shape and Size, in: D.H. Rouvray (Ed.), Fuzzy Logic in Chemistry, Academic Press, New York, 1997, pp 139-223.
36. F. Hausdorff, Set Theory (Transl. By J.R. Auman), Chelsea, New York, 1957, pp 166-168.