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Quantum similarity and discrete representation of molecular sets

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Abstract

This study describes how quantum similarity theoretical framework can provide arbitrary molecular sets with discrete, general, unbiased, systematic and homogeneous numerical descriptions of their elements. Necessarily associated to quantum objects, such discrete descriptions can be related to a sequence of tensor collections of increasing rank. When choosing a specific tensor rank description of any molecular set, such a molecular descriptor set can be also considered a set of linearly independent arrays, which can act in turn as a basis set of some vector space of the appropriate dimension, equal to the cardinality of the supporting molecular set. Straightforward manipulation of the metric matrix of such tensor basis sets permits the ordering of the molecules in the set, among other interesting possibilities. Assorted Kruskal tree examples on Cramer steroid set are given.

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References

  1. Todeschini R., Consonni V.: Methods and Principles in Medicinal Chemistry. In: Mannhold, R., Kubinyi, H., Timmerman, H. (eds) Molecular descriptors for chemoinformatics, vol. 41, Wiley, London (2009)

    Chapter  Google Scholar 

  2. Hohenberg P., Kohn W.: Phys. Rev. 136, B864 (1964)

    Article  Google Scholar 

  3. Carbó R., Leyda L., Arnau M.: Intl. J. Quant. Chem. 17, 1185–1189 (1980)

    Article  Google Scholar 

  4. Carbó R., Domingo L.: Intl. J. Quant. Chem. 32, 517–545 (1987)

    Article  Google Scholar 

  5. Carbó R., Calabuig B.: Intl. J. Quant. Chem. 42, 1681–1693 (1992)

    Article  Google Scholar 

  6. Carbó R., Calabuig B.: Intl. J. Quant. Chem. 42, 1695–1709 (1992)

    Article  Google Scholar 

  7. Carbó R., Besalú E., Calabuig B., Vera L.: Adv. Quant. Chem. 25, 253 (1994)

    Article  Google Scholar 

  8. Carbó R., Besalú E.: Theoretical Foundation of Quantum Similarity. In: Carbó, R. (eds) Molecular similarity and reactivity: from quantum chemical to phenomenological approaches, understanding chemical reactivity, vol. 14, pp. 3–30. Kluwer Academic Publishers, Amsterdam (1995)

    Google Scholar 

  9. Carbó R., Besalú E., Amat L., Fradera X.: J. Math. Chem. 19, 47 (1996)

    Article  Google Scholar 

  10. Carbó-Dorca R., Besalú E.: J. Molec. Struct. (Theochem) 451, 11 (1998)

    Article  Google Scholar 

  11. R. Carbó-Dorca, L. Amat, E. Besalú, M. Lobato, in Quantum Similarity. Advances in molecular similarity, vol. 2, (JAI Press Inc, Greenwich (Conn.), 1998), pp. 1–42

  12. Carbó-Dorca R., Besalú E.: Intl. J. Quan. Chem. 88, 167 (2002)

    Article  Google Scholar 

  13. Carbó-Dorca R.: J. Math. Chem. 36, 241 (2004)

    Article  Google Scholar 

  14. R. Carbó-Dorca, E. Besalú, Shells, point cloud huts, generalized scalar products, cosines and similarity tensor representations in vector semispaces IQC Technical Report TC 2001-1

  15. R. Carbó-Dorca, Quantum Similarity Volume Functions and Generalized Carbó Indices, IQC Technical Report TC 2001-2

  16. Carbó-Dorca R.: J. Math. Chem. 22, 143 (1997)

    Article  Google Scholar 

  17. Carbó-Dorca R.: J. Math. Chem. 23, 353 (1998)

    Article  Google Scholar 

  18. R. Carbó-Dorca, Advances in molecular similarity vol. 2, (JAI Press Inc, Greenwich (Conn.), 1998) p. 43

  19. Messiah, A. : Quantum Mechanics. Dover Publications, New York (1999)

    Google Scholar 

  20. Carbó-Dorca R., Besalú E.: Intl. J. Quan. Chem. 88, 167 (2002)

    Article  Google Scholar 

  21. Carbó-Dorca R., Gallegos A.: Quantum Similarity and Quantum QSPR (QQSPR). In: Meyers, R. (eds) Encyclopedia of complexity and systems science, pp. 7422–7480. Springer, New York (2009)

    Google Scholar 

  22. Carbó-Dorca R.: SAR and QSAR Environ. Res. 18, 265 (2007)

    Article  Google Scholar 

  23. Carbó-Dorca R., Van Damme S.: Theor. Chem. Acc. 118, 673 (2007)

    Article  Google Scholar 

  24. Carbó-Dorca R., Van Damme S.: Afinidad 64, 147 (2007)

    Google Scholar 

  25. Carbó-Dorca R., Van Damme S.: Intl. J. Quan. Chem 108, 1721 (2007)

    Article  Google Scholar 

  26. Carbó-Dorca R., Gallegos A., Sánchez A.J.: J. Comput. Chem. 30, 1146 (2008)

    Article  Google Scholar 

  27. Bultinck P., Carbó-Dorca R.: J. Math. Chem. 36, 191 (2004)

    Article  CAS  Google Scholar 

  28. Carbó R., Calabuig B., Besalú E., Martínez A.: Mol. Eng. 2, 43 (1992)

    Article  Google Scholar 

  29. Robert D., Carbó-Dorca R.: J. Chem. Inf. Comp. Sci. 38, 620 (1998)

    CAS  Google Scholar 

  30. Carbó-Dorca R.: J. Math. Chem. 32, 201–223 (2002)

    Article  Google Scholar 

  31. Carbó-Dorca R.: J. Math. Chem. 44, 628 (2008)

    Article  Google Scholar 

  32. Carbó-Dorca R.: J. Math. Chem. 47, 331 (2010)

    Article  Google Scholar 

  33. Cramer R.D. III, Patterson D.E., Bunce J.D.: J. Am. Chem. Soc. 110, 5959 (1988)

    Article  CAS  Google Scholar 

  34. Wagener M., Sadowski J., Gasteiger J.: J. Am. Chem. Soc. 117, 7769 (1995)

    Article  CAS  Google Scholar 

  35. Lobato M., Amat L., Besalú E., Carbó-Dorca R.: Quant. Struct. Act. Relat. 16, 1 (1997)

    Article  Google Scholar 

  36. Robert D., Amat L., Carbó-Dorca R.: J. Chem. Inf. Comp. Sci. 39, 333 (1999)

    CAS  Google Scholar 

  37. Carbó-Dorca R., Amat L., Besalú E., Gironés X., Robert D.: J. Mol. Struct. (Theochem) 504, 181 (2000)

    Article  Google Scholar 

  38. Besalú E., Gironés X., Amat L., Carbó-Dorca R.: Acc. Chem. Res. 35, 289 (2002)

    Article  Google Scholar 

  39. Carbó-Dorca R., Van Damme S.: Intl. J. Quant. Chem. 108, 1721 (2008)

    Article  Google Scholar 

  40. Carbó-Dorca R., Besalú E., Mercado L.D.: J. Comp. Chem. 32, 582 (2011)

    Article  Google Scholar 

  41. Carbó-Dorca R.: J. Math. Chem. 47, 331 (2010)

    Article  Google Scholar 

  42. Constans P., Carbó R.: J. Chem. Inf. Comp. Sci. 35, 1046 (1995)

    CAS  Google Scholar 

  43. P. Constans, X. Fradera, L. Amat, R. Carbó, in Quantum Molecular Similarity Measures (QMSM) and the Atomic Shell Approximation (ASA). Proceedings of the 2nd Girona Seminar on Molecular Similarity. July 1995. Advances in molecular similarity, vol. 1. (JAI Press Inc, Greenwich (Conn.), 1996), p. 187

  44. Amat L., Carbó-Dorca R.: J. Comput. Chem. 18, 2023 (1997)

    Article  CAS  Google Scholar 

  45. Amat L., Carbó-Dorca R.: J. Comput. Chem. 20, 911 (1999)

    Article  CAS  Google Scholar 

  46. Carbó R., Besalú E.: Afinidad 53, 77 (1996)

    Google Scholar 

  47. Gaussian 03, Revision B.05, M.J. Frisch, G.W. Trucks, H.B. Schlegel, G.E. Scuseria, M.A. Robb, J.R. Cheeseman, J.A. Montgomery, Jr., T. Vreven, K.N. Kudin, J.C. Burant, J.M. Millam, S.S. Iyengar, J. Tomasi, V. Barone, B. Mennucci, M. Cossi, G. Scalmani, N. Rega, G.A. Petersson, H. Nakatsuji, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, M. Klene, X. Li, J.E. Knox, H.P. Hratchian, J.B. Cross, V. Bakken, C. Adamo, J. Jaramillo, R. Gomperts, R.E. Stratmann, O. Yazyev, A.J. Austin, R. Cammi, C. Pomelli, J.W. Ochterski, P.Y. Ayala, K. Morokuma, G.A. Voth, P. Salvador, J.J. Dannenberg, V.G. Zakrzewski, S. Dapprich, A.D. Daniels, M.C. Strain, O. Farkas, D.K. Malick, A.D. Rabuck, K. Raghavachari, J.B. Foresman, J.V. Ortiz, Q. Cui, A.G. Baboul, S. Clifford, J. Cioslowski, B.B. Stefanov, G. Liu, A. Liashenko, P. Piskorz, I. Komaromi, R.L. Martin, D.J. Fox, T. Keith, M.A. Al-Laham, C.Y. Peng, A. Nanayakkara, M. Challacombe, P.M.W. Gill, B. Johnson, W. Chen, M.W. Wong, C. Gonzalez, J.A. Pople (Gaussian Inc., Wallingford CT, 2004)

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Authors and Affiliations

  1. Institut de Química Computacional, Universitat de Girona, 17071, Girona, Catalonia, Spain

    Luz Dary Mercado & Ramon Carbó-Dorca

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  1. Luz Dary Mercado
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  2. Ramon Carbó-Dorca
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Correspondence to Ramon Carbó-Dorca.

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Mercado, L.D., Carbó-Dorca, R. Quantum similarity and discrete representation of molecular sets. J Math Chem 49, 1558–1572 (2011). https://doi.org/10.1007/s10910-011-9841-4

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