Metody matematyczne w chemii : wybrane zastosowania teorii grafów

• Autorzy: Nowakowski J.

Warianty tytułu

EN

Mathematical methods in chemistry : some applications of graph theory

• Języki publikacji: PL

Abstrakty

EN

The mathematization of chemistry has a long history. In 1874 Brown, one of the great pioneers of chemical structure theory, prophesied that " ... chemistry will become a branch of applied mathematics ... and enable to justify results obtained by experiment and predict entirely novel discoveries". This prophesy was soon to be fulfilled. In 1875 the British mathematician Cayley enumerated both the isomers of alkanes and alkyl radicals based on the graph theory. He realized that chemical graphs could be used to present molecules because of the isomorphism that exists between such graphs and molecular structures. This relation plays an important role in application of the graph theory in modern chemistry. In the article a brief description of the results in the field of enumeration and generation of isomers is given. The connections between chemical terms and quantities of mathematical graph theory are shown. Illustrative examples, are chosen and mathematical principles of the methods are presented. Recent papers on enumeration of isomers are compiled. The topological matrix in Hückel molecular orbital method is isomorphic with the adjacency matrix of molecular graph. Isospectral graphs within the Hückel molecular orbital method correspond to conjugated molecules having the same set of orbital energies and related physical and chemical properties. Therefore the generation of isospectral graphs may be used to find similar chemical compounds. The methods of such generation based on some quantumchemical and informative characteristics are described. Computers enable today the practical use of the mathematical methods mentioned in the article. Even the personal computers are useful in the topic. Some calculations can be done on-line by Internet or with the use of commercial computer programs.

Słowa kluczowe

PL

teoria grafów; teoria informacji; zliczanie izomerów; generowanie izomerów; chemia matematyczna

• Wydawca: Polskie Towarzystwo Chemiczne
• Czasopismo: Wiadomości Chemiczne
• Rocznik: 2000
• Tom: [Z] 54, 5-6
• Strony: 371--388
• Opis fizyczny: schem., bibliogr. 64 poz.

Twórcy

autor

Nowakowski J.

• Zakład Chemii Teoretycznej, Instytut Chemii Uniwersytetu Śląskiego ul. Szkolna 9, 40-006 Katowice

• Zakład Chemii Teoretycznej, Instytut Chemii Uniwersytetu Ślaskiego, ul. Szkolna 9, 40-006 Katowice

Bibliografia

• [1] I. Kant, Metaphysische Anfangsgründe der Naturwissenschaft, Hartknoch Verlag, Riga 1786.
• [2] A. C. Brown, Rept. Brit. Assoc. Sei., 1874, 45.
• [3] D. Bonchev, D. H. Rouvray, Chemical Graph Theory, Abacus Press, New York 1991.
• [4] A. Pyka, Wiad. Chem., 1997, 51, 783.
• [5] J. Tomczak, Wiad. Chem., 1997, 51, 803.
• [6] A. Pyka, Wiad. Chem., 1998, 52, 9.
• [7] L. Euler, Comment. Acad. Scient. Imper. Petropolitanae, 1736. 8, 128.
• [8] G. R. Kirchhoff, Ann. Phys. Chem., 1847, 72, 497.
• [9] A. Cayley, Ber. Dtsch. Chem. Ges. 1875, 8, 1056.
• [10] W. Higgins, A Comparative View of the Phlogistic and Antiphlogistic Theories, Murray, London 1789.
• [11] F. A. Kekulé, Zeitschr. Chem., 1867, 2, 217.
• [12] D. H. Rouvray, J. Mol. Struct. (Theochem), 1989, 185, 1.
• [13] N. L. Biggs, E. K. Lloyd R. J. W ilson, Graph Theory 1736-1936, Clarendon Press. Oxford 1977.
• [14] J. L. Kulikowski, Zarys teorii grafów, PWN, Warszawa 1968.
• [15] R. J. Wilson, Wprowadzenie do teorii grafów, PWN, Warszawa 1985.
• [16] N. Trinajstić, S. Nikolić, J. V. Knop, W. R. Muller, K. Szymański, Computational Chemical Graph Theory, Ellis Horwood, New York 1991.
• [17] I. Gutman, D. Vidovié, L. Popovié, J. Chem. Soc., Faraday Trans., 1998, 94, 857.
• [18] A. Cayley, Ber. Dtsch. Chem. Ges., 1875, 8, 1056.
• [19] R. T. Morrison, R. N. Boyd, Chemia organiczna (tłum. z jęz. angielskiego), tom 1, PWN, Warszawa 1996, s. 111.
• [20] H. R. Henze, C. M. Blair, J. Amer. Chem. Soc., 1931, 53, 3042.
• [21] H. R. Henze, C. M. Blair, ibid., 1932, 54, 1098.
• [22] H. R. Henze, C. M. Blair, ibid., 1932, 54, 157.
• [23] D. H. Rouvray, Chem. Soc. Rev., 1974, 3, 355.
• [24] G. Pólya, Acta Math. 1937, 68, 145.
• [25] I. V. Krivoshei, Zh. Strukt. Khim., 1963, 4, 757; 1965, 6, 322; 1966, 7, 430; 1966, 7, 638; 1957, 8, 321.
• [26] S. Basil, Combinatorial Organic Chemistry: an Educational Approach, New Science Publ, 1999.
• [27] J. V. Knop, W. R. Muller, K. Szymański, N. Trinajstić, Computer Generation of Certain Classes of Molecules, SKTH, Zagreb 1985.
• [28] H. Dolhaine, H. Hoenig, M. v. Almsick, MATCH, 1999, 39, 21.
• [29] C. Benecke, R. Grund, R. H ohberger, A. Kerber, R. Laue, T. Wieland. Anal. Chim. Acta, 1995, 314, 141.
• [30] http://www-orgc.tu-graz.ac.at
• [31] S. Fujita, Bull. Chem. Soc. Japan, 1999, 72, 13.
• [32] S. J. Cyvin, B. N. Cyvin, J. Brunvoll, J. J. Wang, J. Mol. Struct., 1998, 445, 127.
• [33] B. N. Cyvin, J. Brunvoll, S. J. Cyvin, Rev. Roum. Chim, 1997, 42, 1113.
• [34] B. N. Cyvin, E. Brendsdal, S. J. Cyvin, J. Brunvoll, ibid., 1997, 42, 1071.
• [35] I. Gutman, S. J. Cyvin, V. Ivanovpetrovic, Z. Naturforsch. Sec A-A J. Phys. Sei., 1998, 53, 699.
• [36] S. J. Cyvin, B. N. Cyvin, J. Brunvoll, I. Gutman, C. R ongsi, S. El basil, Z. Fuji, ibid., 1997, 52, 867.
• [37] B. N. Cyvin, E. Brendsdal, S. J. Cyvin, J. Brunvoll, Rev. Roum. Chim., 1997, 42, 1071.
• [38] B. N. Cyvin, J. Brunvoll, I. Gutman, G Rongsi, S. E lbasil, Z. Fuji, Z. Naturforsch. Sec. A-A J. Phys. Sei., 1997, 52, 867.
• [39] M. S. Molchanova, N. S. Zefirov, J. Chem., Inf. Comput. Sei., 1998, 38, 8.
• [40] S. J. Cyvin, J. J. Wang, J. Brunvoll, S. M Li-Y Cao, B. N. Cyvin, Y. G. Wang, J. Mol. Struct., 1997, 413, 227.
• [41] G. Brinkmann, A. W. M. Dress, S. W. Perrey, J. Stoye, Math. Programm., 1997, 79, 71.
• [42] S. Shojania, Chemosfere, 1999, 38, 2125.
• [43] W. Y. C. Chen, J. D. Louck, J. Comb. Theor. Ser. A, 1999, 86, 151.
• [44] A. A. Woolf, J. Fluor. Chem., 1995, 75, 187.
• [45] Y. H. Shao, Y. S. Jiang, J. Phys. Chem., 1996, 100, 1554.
• [46] S. J. Cyvin, E. K. Lloyd, B. N. Cyvin, J. Brunvoll, Struct. Chem., 1996, 7, 183.
• [47] J. Brunvoll, S. J. Cyvin, B. N. Cyvin, Z. Fuji, X. F. Guo, ibid., 1996, 7, 119.
• [48] P. A. Agaskar, W. G. Klemperer, Inorg. Chim. Acta, 1995, 229, 355.
• [49] J. R. Dias, J. Chem. Inf. Comput. Sei, 1995, 35, 148.
• [50] N. Trinajstić, Chemical Graph Theory, vol. II, CRC Press, Boca Raton, 1983.
• [51] N. J. A. Sloane, S. Plouffe, The Encyclopedia of Integer Sequences, Academic Press, San Diego 1995.
• [52] Sloanés On-Line Encyclopedia in Integer Sequences, AT& T Labs. Research, USA; Internet; http://www.research.att.com/access.cgi/asnjas/sequences/
• [53] R. Grund, A. Kerber, R. Laue, T. W ieland, MATCH, 1992, 27, 87.
• [54] T. Wieland A. Kerber, R. Laue, J. Chem. Inf. Comput. Sei., 1995, 36, 413.
• [55] Internet, http://btm2d2.mat.uni-bayreuth.de/molgenseite/molstart.htm
• [56] M. Mastalerz, Podręcznik chemii organicznej, Wydawnictwo Chemiczne, Wrocław 1996.
• [57] C. Benecke, R. Grund, A. Kerber, R. Laue, T. W ieland, J. Chem. Edu., 1995, 72, 403.
• [58] C. F. Shannon, Beli Systems Tech. J„ 1948, 27, 379.
• [59] T. Wieland, Arzneim.Forsch./Drug res., 1996, 46(1), 223.
• [60] N. Trinajstić, Chemical Graph Theory, vol. I, CRC Press, Boca Raton, 1983.
• [61] M. Randić, M. Barysz, J. Nowakowski, S. Nikolić, N. Trinajstić, J. Mol. Struct. (Theochem), 1989, 185, 95.
• [62] A. Gołębiewski, Elementy mechaniki i chemii kwantowej, PWN, Warszawa 1982.
• [63] S. Wolfram , Mathematica, second edition, Addison-Wesley, Champaign 1993.
• [64] J. Nowakowski, wyniki niepublikowane.

Uwagi

PL

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).