Skip to main content
Log in

On molecular similarity in communication theory of the chemical bond

  • Original Paper
  • Published:
Journal of Mathematical Chemistry Aims and scope Submit manuscript

Abstract

The molecular similarity problem is addressed within the recently proposed information-theoretic (IT) approach to molecular electronic structure. In this Communication Theory of the chemical bond the direct criteria of the overall similarity are formulated in terms of the conditional-entropy (average noise, IT-covalency) and mutual-information (information flow, IT-ionicity) descriptors of the compared molecular communication systems, and the associated variational principles for their maximum entropy/information resemblance are formulated and discussed. Implications for molecular similarity from the parallel and sequential arrangements of the compared information channels of molecules or their fragments are investigated and tested on illustrative π-electron systems.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • R.A. Fisher, Proc. Cambridge Phil. Soc. 22, 700 (1925); see also: B.R. Frieden, Physics from the Fisher Information—A Unification (Cambridge University Press, Cambridge, 2000)

  • C.E. Shannon, Bell System Tech. J. 27, 379, 623 (1948); see also: C.E. Shannon, W. Weaver, The Mathematical Theory of Communication (University of Illinois, Urbana, 1949)

  • S. Kullback, R.A. Leibler, Ann. Math. Stat. 22, 79 (1951); see also: S. Kullback, Information Theory and Statistics (Wiley, New York, 1959)

  • Abramson N. (1963). Information Theory and Coding. McGraw-Hill, New York

    Google Scholar 

  • R.F. Nalewajski, Information Theory of Molecular Systems (Elsevier, Amsterdam, 2006) and refs. therein

  • Hirshfeld F.L. (1977). Theoret. Chim. Acta (Berl.) 44: 129

    Article  CAS  Google Scholar 

  • R.F. Nalewajski, Int. J. Mol. Sci. 3, 237 (2002); Adv. Quant. Chem. 43, 119 (2003); Chem. Phys. Lett. 372, 28 (2003); 375, 196 (2003)

    Google Scholar 

  • R.F. Nalewajski, R.G. Parr, Proc. Natl. Acad. Sci. USA 97, 8879 (2000); J. Phys. Chem. A 105, 7391 (2001)

    Google Scholar 

  • Nalewajski R.F. and Loska R. (2001). Theoret. Chem. Acc. 105: 374

    CAS  Google Scholar 

  • R.F. Nalewajski, Phys. Chem. Chem. Phys. 4, 1710 (2002); Chem. Phys. Lett. 372, 28 (2003); J. Phys. Chem. A 107, 3792 (2003)

  • Parr R.G., Ayers P.W. and Nalewajski R.F. (2005). J. Phys. Chem. A 109: 3957

    Article  CAS  Google Scholar 

  • Nalewajski R.F. and Broniatowska E. (2006). Theor. Chem. Acc. 117: 7

    Article  Google Scholar 

  • R.F. Nalewajski, E. Świtka, A. Michalak, Int. J. Quantum Chem. 87, 198 (2002); R.F. Nalewajski, E. Świtka, Phys. Chem. Chem. Phys. 4, 4952 (2002); R.F. Nalewajski, Use of fisher information in quantum chemistry, Int. J. Quantum Chem. (K. Jankowski issue). (in press)

  • R.F. Nalewajski, E. Broniatowska, J. Phys. Chem. A 107, 6270 (2003); Int. J. Quantum Chem. 101, 349 (2005)

  • Nalewajski R.F., Köster A.M. and Escalante S. (2005). J. Phys. Chem. A 109: 10038

    Article  CAS  Google Scholar 

  • Nalewajski R.F. and Broniatowska E. (2003). Chem. Phys. Lett. 376: 33

    Article  CAS  Google Scholar 

  • R.F. Nalewajski, J. Phys. Chem. A 107, 3792 (2003); Ann. Phys. (Leipzig) 13, 201 (2004); Mol. Phys. 104, 255 (2006)

  • Nalewajski R.F. (2000). J. Phys. Chem. A 104: 11940

    Article  CAS  Google Scholar 

  • Nalewajski R.F. (2004). Mol. Phys. 102: 531, 547

    Google Scholar 

  • Nalewajski R.F. (2005). Mol. Phys. 103: 451

    Article  CAS  Google Scholar 

  • R.F. Nalewajski, Mol. Phys. 104, 365, 493, 1977, 2533 (2006)

  • Nalewajski R.F. (2004). Struct. Chem. 15: 391

    Article  CAS  Google Scholar 

  • Nalewajski R.F. (2005). J. Math. Chem. 38: 43

    Article  CAS  Google Scholar 

  • Nalewajski R.F. (2005). Theoret. Chem. Acc. 114: 4

    Article  CAS  Google Scholar 

  • R.F. Nalewajski, K. Jug, in Reviews of Modern Quantum Chemistry: A Celebration of the Contributions of Robert G. Parr, vol. I, ed. by K.D. Sen (World Scientific, Singapore, 2002), p. 148

  • Nalewajski R.F. (2004). Chem. Phys. Lett. 386: 265

    Article  CAS  Google Scholar 

  • Nalewajski R.F. (2006). Mol. Phys. 104: 2533, 3339

    Google Scholar 

  • Nalewajski R.F. (2007). J. Phys. Chem. A 111: 4855

    Article  CAS  Google Scholar 

  • R.F. Nalewajski, Entropic bond indices from molecular information channels in orbital resolution: ground-state systems. J. Math. Chem. (in press)

  • R.F. Nalewajski, Chemical bonds through probability scattering: information channels for intermediate-orbital stages. J. Math. Chem. (in press)

  • R.F. Nalewajski, Entropic bond-descriptors of molecular information systems in local resolution. J. Math. Chem. (in press)

  • Wiberg K.A. (1968). Tetrahedron 24: 1083

    Article  CAS  Google Scholar 

  • M.S. Gopinathan, K. Jug, Theor. Chim. Acta (Berl.) 63, 497, 511 (1983); see also: K. Jug, M.S. Gopinathan, in Theoretical Models of Chemical Bonding, vol. II, ed. by Z.B. Maksić (Springer, Heidelberg, 1990), p. 77

  • Mayer I. (1983). Chem. Phys. Lett. 97: 270

    Article  CAS  Google Scholar 

  • F. Nalewajski, Köster A.M. and Jug K. (1993). Theoret. Chim. Acta (Berl.) 85: 463

    Article  Google Scholar 

  • Nalewajski R.F. and Mrozek J. (1994). Int. J. Quantum Chem. 51: 187

    Article  CAS  Google Scholar 

  • Nalewajski R.F., Formosinho S.J., Varandas A.J.C. and Mrozek J. (1994). Int. J. Quantum Chem. 52: 1153

    Article  CAS  Google Scholar 

  • Nalewajski R.F., Mrozek J. and Mazur G. (1996). Can. J. Chem. 100: 1121

    Article  Google Scholar 

  • Nalewajski R.F., Mrozek J. and Michalak A. (1997). Int. J. Quantum Chem. 61: 589

    Article  CAS  Google Scholar 

  • Mrozek J., Nalewajski R.F. and Michalak A. (1998). Polish J. Chem. 72: 1779

    CAS  Google Scholar 

  • W. Heitler, F. London, Z. Physik 44, 455 (1927); for an English translation see: H. Hettema, Quantum Chemistry Classic Scientific Paper (World Scientific, Singapore, 2000); F. London, Z. Phys. 455, 46 (1928)

  • S. Shaik, in New Theoretical Concepts for Understanding Organic Reactions, NATO ASI Series, Vol. C267, ed. by J. Bertran, I.G. Czismadia (Kluwer Academic Publ., Dordrecht, 1989), p. 165; S. Shaik, P.C. Hiberty, Adv. Quant. Chem. 26, 100 (1995); K. Jug, A.M. Köster, J. Am. Chem. Soc. 112, 6772 (1990); S. Shaik, A. Shurki, D. Danovich, P.C. Hiberty, Chem, Rev, 101, 1501 (2001)

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Roman F. Nalewajski.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Nalewajski, R.F. On molecular similarity in communication theory of the chemical bond. J Math Chem 45, 607–626 (2009). https://doi.org/10.1007/s10910-007-9345-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10910-007-9345-4

Keywords

Navigation