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A mathematical model of the logical structure of chemistry. A bridge between theoretical and experimental chemistry and a general tool for computer-assisted molecular design

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Summary

A mathematical model of the logical structure of chemistry is suggested. The model is based on the phenomenon of convertibility between chemical species which is expressed by the so-called convertibility function Γ. In the center of the model there is the potential energy (hyper)surface, PES. A heuristic modification of the general convertibility function is presented. Several algorithms have been developed for an analysis of PES which is described by paths, and for heuristic obtaining of PES paths. The notion ofK-barrier of conformational PES is introduced as well as an algorithm for its computation.

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References

  1. CHEMLAB. Molecular Design Ltd. 1986. CHEM-X. Chemical Design Ltd. 1986. MacroModel. Columbia University 1986

  2. Dugundji J, Ugi I (1973) Top Cur Chem 39:19

    Google Scholar 

  3. Dugundji J, Gillespie P, Marquarding D, Ugi I, Ramirez F (1976) Metric spaces and graphs representing the logical structure of chemistry. In: Balaban AT (ed) Chemical applications of graph theory. Academic Press, New York, p 107

    Google Scholar 

  4. Kratochvíl M (1981) Chem Listy 75:675

    Google Scholar 

  5. Kratochvíl M (1983) Chem Listy 77:225

    Google Scholar 

  6. Plath PJ, Hass EC (1983) Logic of chemical ideas. In: Chemical applications of topology and graph theory. Elsevier, Amsterdam, p 392

    Google Scholar 

  7. Born M, Oppenheimer R (1927) Ann Phys 84:457

    Google Scholar 

  8. Tomasi J (1988) J Mol Struct (Theochem) 179:273

    Google Scholar 

  9. Kvasnička V (1983) Coll Czech Chem Commun 48:2097, 48:2118 Kvasnička V (1984) Coll Czech Chem Commun 49:1090

    Google Scholar 

  10. Kvasnička V, Kratochvíl M, Koča J (1983) Coll Czech Chem Commun 48:2284

    Google Scholar 

  11. Koča J (1989) J Math Chem 3:73, 3:91

    Google Scholar 

  12. Koča J, Kratochvíl M, Kvasnička V, Matyska L, Pospíchal J (1989) A synthon model of organic chemistry and synthesis design. Lecture notes in chemistry, vol 51. Springer-Verlag, Berlin Heidelberg

    Google Scholar 

  13. Kvasnička V, Pospíchal J (1990) Int J Quant Chem 38:253

    Google Scholar 

  14. Slanina Z (1986) Contemporary theory of chemical isomerism. Academia and Reidel, Prague and Dordrecht

    Google Scholar 

  15. Mezey PG (1987) Potential energy hypersurfaces. Elsevier, Amsterdam

    Google Scholar 

  16. Mezey PG (1982) Theor Chim Acta (Berl.) 60:409

    Google Scholar 

  17. Mezey PG (1984) Int J Quant Chem, Quant Chem Symp 18:675

    Google Scholar 

  18. Zhuravlev VI, Krivoshey IV, Sleta LA (1975) Zh Strukt Khimii 16:951; Krivoshey IV, Sleta LA (1976) Theor Chim Acta (Berl.) 43:165

    Google Scholar 

  19. Sevcenko SM (1983) Theoretical and Experimental Chemistry, No 6:672 (in Russian)

  20. Fukui KJ (1970) J Phys Chem 74:4161

    Google Scholar 

  21. Koča J, Carlsen PHJ (in preparation)

  22. Mezey PG (1981) Theor Chim Acta 58:309; Mezey PG (1981) Int J Quant Chem, Quant Biol Symp 8:185; Mezey PG (1982) Theor Chim Acta 62:133

    Google Scholar 

  23. Chang G, Guida WC, Still WC (1989) J Am Chem Soc 111:4379

    Google Scholar 

  24. Fusco R, Caccianotti L, Tosi C (1986) Il Nuovo Cimento 8:211

    Google Scholar 

  25. Dolata DP, Carter RE (1987) J Chem Inf Comp Sci 27:36

    Google Scholar 

  26. Ugi I, Dugundji J, Kopp R, Marquarding D (1984) Perspectives in theoretical stereochemistry. Lecture notes in chemistry, vol 36. Springer-Verlag, Berlin Heidelberg

    Google Scholar 

  27. Mezey PG (1980) Theor Chim Acta 54:95

    Google Scholar 

  28. Van de Graaf B, Baas JMA, van Veen A (1980) Recueil, J Royl Neth Chem Soc 99:175; Lugovskoy AA, Dashevsky VG, Kitaigorodsky AI (1973) Tetrahedron 29:287; Jørgensen P, Jensen HJA, Helgaker T (1988) Theor Chim Acta 73:55; Berry RS, Davis HL, Beck TL (1988) Chem Phys Let 147:13; Ischtwan J, Collins MA (1988) J Chem Phys 89:2881; Beyer A, Wolschann P (1989) J Mol Struct 196:371

    Google Scholar 

  29. Gilbert KE, Gajewski JJ (1987) The Program MMPMI, Indiana University

  30. Johnson MA (1989) J Math Chem 3:117

    Google Scholar 

  31. Arteca GA, Jammal VB, Mezey PG (1988) J Comput Chem 9:608; Mezey PG (1988) J Math Chem 2:299; Arteca GA, Mezey PG (1989) J Phys Chem 93:4746; Arteca GA, Heal GA, Mezey PG (1990) Theor Chim Acta 76:377

    Google Scholar 

  32. Frühbeis H, Klein R, Wallmeier H (1987) Angew Chem Int Ed Engl 26:403

    Google Scholar 

  33. Slanina Z (1989) J Mol Struct (Theochem) 185:217

    Google Scholar 

  34. Ugi I, Gillespie P (1971) Angew Chem Int Ed Engl 10:914

    Google Scholar 

  35. Matyska L, Koča J, J Chem Inf Comp Sci (in press)

  36. Koča J (1988) Coll Czech Chem Commun 53:1007

    Google Scholar 

  37. Hendrickson JB, Grier DL, Toczko AG (1985) J Amer Chem Soc 107:5228

    Google Scholar 

  38. Barone R, Chanon M (1989) MATCH 24:39

    Google Scholar 

  39. Mezey PG (1987) J Mol Struct (Theochem) 149:57; Mezey PG (1986) Reaction topology. In: Smith VH, Schaefer HF, Morokuma K (eds) Applied quantum chemistry, Proceedings of the Nobel Laureate Symposium on Applied Quantum Chemistry in Honour of Herzberg G, Mulliken RS, Fukui K, Lipscomb W and Hoffman R, Honolulu, Hawaii, Reidel New York

    Google Scholar 

  40. Gordon JE, Brockwell JC (1983) J Chem Inf Comp Sci 23:117; Gordon JE (1984) J Chem Inf Comp Sci 24:81; Gordon JE (1988) J Chem Inf Comp Sci 28:100

    Google Scholar 

  41. Koča J (1991) Theor Chim Acta 80

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Koča, J. A mathematical model of the logical structure of chemistry. A bridge between theoretical and experimental chemistry and a general tool for computer-assisted molecular design. Theoret. Chim. Acta 80, 29–50 (1991). https://doi.org/10.1007/BF01114750

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  • DOI: https://doi.org/10.1007/BF01114750

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