Journal of Mathematical Chemistry

, Volume 51, Issue 10, pp 2718–2730 | Cite as

Information content of molecular graph and prediction of gas phase thermal entropy of organic compounds

Original Paper

Abstract

Entropy is a fundamental thermodynamic property that has attracted a wide attention across domains, including chemistry. Inference of entropy of chemical compounds using various approaches has been a widely studied topic. However, many aspects of entropy in chemical compounds remain unexplained. In the present work, we propose two new information-theoretical molecular descriptors for the prediction of gas phase thermal entropy of organic compounds. The descriptors reflect the bulk and size of the compounds as well as the gross topological symmetry in their structures, all of which are believed to determine entropy. A high correlation (\(\hbox {r}^{2} = 0.92\)) between the entropy values and our information-theoretical indices have been found and the predicted entropy values, obtained from the corresponding statistically significant regression model, have been found to be within acceptable approximation. We provide additional mathematical result in the form of a theorem and proof that might further help in assessing changes in gas phase thermal entropy values with the changes in molecular structures. The proposed information-theoretical molecular descriptors, regression model and the mathematical result are expected to augment predictions of gas phase thermal entropy for a large number of chemical compounds.

Keywords

Thermal entropy Molecular descriptor Information content Regression model 

References

  1. 1.
    N. Rashevsky, Bull. Math. Biophys. 17, 229 (1955)CrossRefGoogle Scholar
  2. 2.
    C.E. Shannon, W. Weaver, Mathematical Theory of Communication (University of Illinois Press, Urbana, 1949)Google Scholar
  3. 3.
    L. Brillouin, Science and Information Theory (Academic Press, New York, 1956)Google Scholar
  4. 4.
    M. Valentinuzzi, M.E. Valentinuzi, Bull. Math. Biophys. 24, 11 (1962)Google Scholar
  5. 5.
    H. Morowitz, Bull. Math. Biophys. 17, 81 (1955)CrossRefGoogle Scholar
  6. 6.
    M. Gordon, J.W. Kennedy, J. Chem. Soc. Faraday Trans. II 69, 484 (1973)Google Scholar
  7. 7.
    N. Trinajstic, Chemical Graph Theory (CRC Press, Boca Raton, 1983)Google Scholar
  8. 8.
    A.T. Balaban (ed.), Chemical Application of Graph Theory (Academics Press, London, 1967)Google Scholar
  9. 9.
    A.J. Stuper, W.E. Brugger, P.C. Jurs, Computer Assisted Studies of Chemical Structure and Biological Function (Wiley-Interscience, New York, 1979)Google Scholar
  10. 10.
    G. Klopman, C. Raychaudhury, J. Comput. Chem. 9, 232 (1988)CrossRefGoogle Scholar
  11. 11.
    C. Raychaudhury, A. Banerjee, P. Bag, S. Roy, J. Chem. Inf. Comput. Sci. 39, 248 (1999)CrossRefGoogle Scholar
  12. 12.
    C. Raychaudhury, I. Ghosh, Internet Electron. J. Mol. Des. 3, 350 (2004)Google Scholar
  13. 13.
    C. Raychaudhury, D. Pal, Curr. Comput.-Aided Drug Des. 8, 128 (2012)CrossRefGoogle Scholar
  14. 14.
    L.B. Kier, L.H. Hall, Molecular Connectivity in Chemistry and Drug Research (Academic Press, New York, 1976)Google Scholar
  15. 15.
    C. Raychaudhury, S.C. Basak, A.B. Roy, J.J. Ghosh, Indian Drugs 18, 97 (1980)Google Scholar
  16. 16.
    D. Bonchev, Information Theoretic Indices for Characterization of Chemical Structures (Wiley-Research Studies Press, Chichester, 1983)Google Scholar
  17. 17.
    L.B. Kier, L.H. Hall, Molecular Connectivity in Structure-Activity Analysis (Wiley-Research Studies Press, Letchworth, 1986)Google Scholar
  18. 18.
    H. Hosoya, Bull. Chem. Soc. Jpn. 44, 2332 (1971)CrossRefGoogle Scholar
  19. 19.
    E. Trucco, Bull. Math. Biophys. 18, 129 (1956)CrossRefGoogle Scholar
  20. 20.
    D. Bonchev, N. Trinajstic, J. Chem. Phys. 67, 4517 (1977)CrossRefGoogle Scholar
  21. 21.
    C. Raychaudhury, S.K. Ray, J.J. Ghosh, A.B. Roy, S.C. Basak, J. Comput. Chem. 5, 581 (1984)CrossRefGoogle Scholar
  22. 22.
    G. Klopman, C. Raychaudhury, J. Chem. Inf. Comput. Sci. 30, 12 (1990)CrossRefGoogle Scholar
  23. 23.
    P. Sarkar, A.B. Roy, P.K. Sarkar, Math. Biosci. 39, 299 (1978)Google Scholar
  24. 24.
    S.C. Basak, A.B. Roy, J.J. Ghosh, in Second International Conference on Mathematical Modeling, vol. 2, University of Missouri, Rolla (1979), p. 851Google Scholar
  25. 25.
    C. Raychaudhury, J.J. Ghosh, in Third Annual Conference of the Indian Society for Theory of Probability and its Applications, (Wiley Eastern Limited, New Delhi, 1981)Google Scholar
  26. 26.
    S.C. Basak, V.R. Magnuson, Arzneim.-Forsch./ Drug Res. 33, 501 (1983)Google Scholar
  27. 27.
    A.B. Roy, C. Raychaudhury, J.J. Ghosh, S.K. Ray, S.C. Basak, in Quantitative Approaches to Drug Design, (Elsevier, Amsterdam, 1983), p. 75Google Scholar
  28. 28.
    C. Hansch, A. Leo, Substituent Constant for Correlation Analysis in Chemistry and Biology (Wiley, New York, 1979)Google Scholar
  29. 29.
    D. Bonchev, D. Kamenski, V. Kamenska, Bull. Math. Biol. 38, 119 (1976)Google Scholar
  30. 30.
    L.A. Curtiss, M. Blander, Chem. Rev. 88, 827 (1988)CrossRefGoogle Scholar
  31. 31.
    J.E. Dean (ed.), Langes’ Hand Book of Chemistry. Table 9–2, 13 Edition (McGraw-Hill, New York, 1985)Google Scholar
  32. 32.
    G.H. Wannier, Statistical Physics (Wiley, New York, 1966)Google Scholar
  33. 33.
    C.A. Shelley, M.E. Munk, J. Chem. Inf. Comput. Sci. 17, 110 (1977)CrossRefGoogle Scholar
  34. 34.
    C. Jochum, J. Gasteiger, J. Chem. Inf. Comput. Sci. 17, 113 (1977)CrossRefGoogle Scholar
  35. 35.
    R.E. Carhart, J. Chem. Inf. Comput. Sci. 18, 108 (1978)CrossRefGoogle Scholar
  36. 36.
    F. Harary, Graph Theory (Addison-Wesley, Reading, 1972)Google Scholar
  37. 37.
    Minitab-16: Minitab Statistical Software: PA, USA (2013)Google Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Bioinformatics Centre and Supercomputer Education and Research CentreIndian Institute of ScienceBangaloreIndia

Personalised recommendations