Journal of Mathematical Chemistry

, Volume 50, Issue 6, pp 1437–1457 | Cite as

Basis set dependence of molecular information channels and their entropic bond descriptors

  • Roman F. Nalewajski
  • Dariusz Szczepanik
  • Janusz Mrozek
Open Access
Original Paper


Information channels from SCF MO calculations using different basis sets and their entropic bond descriptors are compared within the orbital communication theory. In this information-theoretic (IT) treatment of communications between basis functions the overall covalency and ionicity bond components reflect the average communication noise and information flow, respectively, in the resolution level specified by the adopted set of basis functions. The basis-set dependence of the orbital conditional probabilities and their entropic descriptors of the information covalency/ionicity content is explored. Compared to the minimum set \({{\bf \chi}}\) of the occupied atomic orbitals of the separated constituent atoms, the extended basis sets of Gaussian orbitals and/or their formal contractions generally give rise to a higher IT-covalency and lower IT-ionicity descriptors of the system chemical bonds. In the augmented set case, \({{\bf \chi}^{aug.} = ({\bf \chi},{\bf \psi})}\) , containing the polarization function complement \({{\bf \psi}}\) of \({{\bf \chi}}\) , the use of only \({{\bf \chi} \rightarrow {\bf \chi}}\) communications is advocated in a semi-quantitative chemical interpretation of the IT bond indices. The maximum-overlap criterion is used to transform the general (orthonormal) extended basis \({{\bf \xi}}\) to its semi-augmented form \({\widetilde{\bf \chi}^{aug.} = \widetilde{\bf \xi}=(\widetilde{\bf \chi}, \widetilde{\bf \psi}),}\) in which \({\widetilde {\bf \chi} \approx {\bf \chi}}\) and \({\widetilde {\bf \psi} \approx{\bf \psi}}\), which facilitates the near minimum basis set interpretation of bond descriptors and extraction of communications involving the polarization functions \({{\widetilde {\mathbf \psi}}}\) . A similar transformation using the minimum information distance criterion can be also envisaged. The effect of the atomic reduction of the molecular channels, which misses the effect of the “internal” communications (bonds) on constituent atoms, is also examined. As intuitively expected, the IT descriptors of such reduced channels are found to be less sensitive to the basis set enlargement.


Basis set dependence Bond covalency/ionicity Chemical bond multiplicities Entropic bond descriptors Information theory Maximum overlap criterion Minimum information distance rule Molecular information channels Orbital communication theory 


Open Access

This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited.


  1. 1.
    Fisher R.A.: Proc. Cambridge Philos. Soc. 22, 700 (1925)CrossRefGoogle Scholar
  2. 2.
    C.E. Shannon, Bell Syst. Tech. J. 27, 379, 623 (1948)Google Scholar
  3. 3.
    Shannon C.E., Weaver W.: The Mathematical Theory of Communication. University of Illinois, Urbana (1949)Google Scholar
  4. 4.
    Kullback S., Leibler R.A.: Ann. Math. Stat. 22, 79 (1951)CrossRefGoogle Scholar
  5. 5.
    Kullback S.: Information Theory and Statistics. Wiley, New York (1959)Google Scholar
  6. 6.
    Abramson N.: Information Theory and Coding. McGraw-Hill, New York (1963)Google Scholar
  7. 7.
    Pfeifer P.E.: Concepts of Probability Theory, 2nd edn. Dover, New York (1978)Google Scholar
  8. 8.
    Frieden B.R.: Physics from the Fisher Information—A Unification, 2nd edn. Cambridge University Press, Cambridge (2004)CrossRefGoogle Scholar
  9. 9.
    R.F. Nalewajski, Information Theory of Molecular Systems (Elsevier, Amsterdam, 2006), and refs. thereinGoogle Scholar
  10. 10.
    R.F. Nalewajski, Information Origins of the Chemical Bond (Nova Science Publishers, New York, 2010), and refs. thereinGoogle Scholar
  11. 11.
    R.F. Nalewajski, Perspectives in Electronic Structure Theory (Springer, Heidelberg, 2011), in press, and refs. thereinGoogle Scholar
  12. 12.
    Nalewajski R.F., Parr R.G.: Proc. Natl. Acad. Sci. USA 97, 8879 (2000)CrossRefGoogle Scholar
  13. 13.
    Nalewajski R.F., Parr R.G.: J. Phys. Chem. A 105, 7391 (2001)CrossRefGoogle Scholar
  14. 14.
    Nalewajski R.F., Loska R.: Theor. Chem. Acc. 105, 374 (2001)CrossRefGoogle Scholar
  15. 15.
    Nalewajski R.F.: Phys. Chem. Chem. Phys. 4, 1710 (2002)CrossRefGoogle Scholar
  16. 16.
    R.F. Nalewajski, J. Phys. Chem. A 107, 3792 (2003)CrossRefGoogle Scholar
  17. 17.
    Nalewajski R.F.: Chem. Phys. Lett. 372, 28 (2003)CrossRefGoogle Scholar
  18. 18.
    Parr R.G., Ayers P.W., Nalewajski R.F.: J. Phys. Chem. A 109, 3957 (2005)CrossRefGoogle Scholar
  19. 19.
    Nalewajski R.F.: Adv. Quantum Chem. 43, 119 (2003)CrossRefGoogle Scholar
  20. 20.
    Nalewajski R.F., Broniatowska E.: Theor. Chem. Acc. 117, 7 (2007)CrossRefGoogle Scholar
  21. 21.
    Hirshfeld F.L.: Theor. Chim. Acta (Berl.) 44, 129 (1977)CrossRefGoogle Scholar
  22. 22.
    Nalewajski R.F., Świtka E., Michalak A.: Int. J. Quantum Chem. 87, 198 (2002)CrossRefGoogle Scholar
  23. 23.
    Nalewajski R.F., Świtka E.: Phys. Chem. Chem. Phys. 4, 4952 (2002)CrossRefGoogle Scholar
  24. 24.
    Nalewajski R.F., Broniatowska E.: J. Phys. Chem. A. 107, 6270 (2003)CrossRefGoogle Scholar
  25. 25.
    Nalewajski R.F., Köster A.M., Escalante S.: J. Phys. Chem. A 109, 10038 (2005)CrossRefGoogle Scholar
  26. 26.
    Nalewajski R.F.: Int. J. Quantum Chem. 108, 2230 (2008)CrossRefGoogle Scholar
  27. 27.
    R.F. Nalewajski, P. de Silva, J. Mrozek, in Theoretical and Comutational Developments in Modern Density Functional Theory, ed. by A.K. Roy (Nova Science Publishers, New York, 2011), in pressGoogle Scholar
  28. 28.
    Nalewajski R.F.: J. Math. Chem. 47, 667 (2010)CrossRefGoogle Scholar
  29. 29.
    Nalewajski R.F., de Silva P., Mrozek J.: J. Mol. Struct. THEOCHEM 954, 57 (2010)CrossRefGoogle Scholar
  30. 30.
    Nalewajski R.F.: J. Phys. Chem. A 104, 11940 (2000)CrossRefGoogle Scholar
  31. 31.
    Nalewajski R.F.: Int. J. Quantum Chem. 109, 425 (2009)CrossRefGoogle Scholar
  32. 32.
    Nalewajski R.F.: Int. J. Quantum Chem. 109, 2495 (2009)CrossRefGoogle Scholar
  33. 33.
    Nalewajski R.F.: Adv. Quantum Chem. 56, 217 (2009)CrossRefGoogle Scholar
  34. 34.
    Nalewajski R.F.: J. Math. Chem. 47, 692 (2010)CrossRefGoogle Scholar
  35. 35.
    R.F. Nalewajski, J. Math. Chem. 49, 592, 2308 (2011)Google Scholar
  36. 36.
    Nalewajski R.F., Szczepanik D., Mrozek J.: Adv. Quantum Chem. 61, 1 (2011)CrossRefGoogle Scholar
  37. 37.
    R.F. Nalewajski, in Mathematical Chemistry, ed. by W.I. Hong (Nova Science Publishers, New York, 2011), pp. 247–325Google Scholar
  38. 38.
    R.F. Nalewajski, in Chemical Information and Computation Challenges in 21st Century, ed. by M.V. Putz (Nova Science Publishers, New York, 2011), in pressGoogle Scholar
  39. 39.
    Becke A.D., Edgecombe K.E.: J. Chem. Phys. 92, 5397 (1990)CrossRefGoogle Scholar
  40. 40.
    Silvi B., Savin A.: Nature 371, 683 (1994)CrossRefGoogle Scholar
  41. 41.
    Savin A., Nesper R., Wengert S., Fässler T.F.: Angew. Chem. Int. Ed. Engl. 36, 1808 (1997)CrossRefGoogle Scholar
  42. 42.
    Nalewajski R.F.: Theor. Chem. Acc. 114, 4 (2005)CrossRefGoogle Scholar
  43. 43.
    Nalewajski R.F.: J. Math. Chem. 49, 371 (2011)CrossRefGoogle Scholar
  44. 44.
    Nalewajski R.F.: J. Math. Chem. 49, 546 (2011)CrossRefGoogle Scholar
  45. 45.
    Nalewajski R.F.: J. Math. Chem. 49, 806 (2011)CrossRefGoogle Scholar
  46. 46.
    R.F. Nalewajski, Int. J. Quantum Chem. (in press)Google Scholar
  47. 47.
    Nalewajski R.F., Gurdek P.: J. Math. Chem. 49, 1226 (2011)CrossRefGoogle Scholar
  48. 48.
    Dirac P.A.M.: The Principles of Quantum Mechanics, 4th edn. Clarendon, Oxford (1958)Google Scholar
  49. 49.
    R.F. Nalewajski, P. Gurdek, Struct. Chem. (M. Witko issue), in pressGoogle Scholar
  50. 50.
    A. Gołȩbiewski, Trans. Faraday Soc. 57, 1849 (1961)Google Scholar
  51. 51.
    Gołȩbiewski A.: Acta Phys. Pol. 23, 243 (1963)Google Scholar
  52. 52.
    Nalewajski R.F., Gołȩbiewski A.: Chem. Phys. Lett. 29, 441 (1974)CrossRefGoogle Scholar
  53. 53.
    Wiberg K.A.: Tetrahedron 24, 1083 (1968)CrossRefGoogle Scholar
  54. 54.
    Boys S.F., Bernardi F.: Mol. Phys. 19, 553 (1970)CrossRefGoogle Scholar

Copyright information

© The Author(s) 2012

Authors and Affiliations

  • Roman F. Nalewajski
    • 1
  • Dariusz Szczepanik
    • 2
  • Janusz Mrozek
    • 2
  1. 1.Department of Theoretical ChemistryJagiellonian UniversityCracowPoland
  2. 2.Department of Computational Methods in ChemistryJagiellonian UniversityCracowPoland

Personalised recommendations