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Many-orbital probabilities and their entropy/information descriptors in orbital communication theory of the chemical bond

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Abstract

The joint/conditional “probability” measures of simultaneous many-orbital events in chemical bonds, which involve several basis functions, are derived within standard SCF LCAO MO description of molecular systems. These generalized projection/overlap quantities satisfy the symmetry properties and sum rules of the ordinary probabilities, but can exhibit negative values. The associated information-theoretic descriptors of chemical bonds for a general case of several (dependent) orbital probability schemes are examined. The many-orbital theory extends the range of applications of the orbital communication theory to many classical issues in the theory of molecular electronic structure and chemical reactivity. Such probabilities are required in several molecular scenarios, e.g., bimolecular and catalytic reactivity, directing influence of ligands/substituents, the three-centre bonds, etc., which are also identified. Such an approach implies the effect of the IT-ionic activation of the chemisorbed reactants in catalytic systems.

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References

  1. Fisher R.A.: Philos. Trans. R. Soc. Lond. 222, 309 (1922)

    Article  Google Scholar 

  2. Fisher R.A.: Proc. Camb. Phil. Soc. 22, 700 (1925)

    Article  Google Scholar 

  3. Fisher R.A.: Statistical Methods and Scientific Inference. Oliver and Boyd, 2nd edn. London (1959)

    Google Scholar 

  4. C.E. Shannon, Bell Syst. Tech. J. 27, 379, 623 (1948)

  5. Shannon C.E., Weaver W.: The Mathematical Theory of Communication. University of Illinois, Urbana (1949)

    Google Scholar 

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

    Google Scholar 

  7. Kullback S., Leibler R.A.: Ann. Math. Stat. 22, 79 (1951)

    Article  Google Scholar 

  8. Kullback S.: Information Theory and Statistics. Wiley, New York (1959)

    Google Scholar 

  9. Nalewajski R.F.: Information Theory of Molecular Systems. Elsevier, Amsterdam (2006)

    Google Scholar 

  10. Nalewajski R.F., Parr R.G.: Proc. Natl. Acad. Sci. U. S. A. 97, 8879 (2000)

    Article  CAS  Google Scholar 

  11. Nalewajski R.F., Parr R.G.: J. Phys. Chem. A 105, 7391 (2001)

    Article  CAS  Google Scholar 

  12. Nalewajski R.F.: Phys. Chem. Chem. Phys. 4, 1710 (2002)

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  14. Nalewajski R.F., Broniatowska E.: J. Phys. Chem. A 107, 6270 (2003)

    Article  CAS  Google Scholar 

  15. Nalewajski R.F., Broniatowska E.: Chem. Phys. Lett. 376, 33 (2003)

    Article  CAS  Google Scholar 

  16. Nalewajski R.F., Broniatowska E.: Theor. Chem. Acc. 117, 7 (2007)

    Article  CAS  Google Scholar 

  17. Nalewajski R.F., Broniatowska E.: Int. J. Quantum Chem. 101, 349 (2005)

    Article  CAS  Google Scholar 

  18. Nalewajski R.F., Broniatowska E., Michalak A.: Int. J. Quantum Chem. 87, 198 (2002)

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  20. R.F. Nalewajski, Mol. Phys. (a) 102, 531, 547 (2004)

    Google Scholar 

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

    Article  CAS  Google Scholar 

  22. Nalewajski R.F.: Mol. Phys. 104, 365 (2006)

    Article  CAS  Google Scholar 

  23. Nalewajski R.F.: Mol. Phys. 104, 493 (2006)

    Article  CAS  Google Scholar 

  24. Nalewajski R.F.: Theor. Chem. Acc. 114, 4 (2005)

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  27. Nalewajski R.F.: J. Math. Chem. 45, 607 (2009)

    Article  CAS  Google Scholar 

  28. Nalewajski R.F.: J. Math. Chem. 45, 709 (2009)

    Article  CAS  Google Scholar 

  29. Nalewajski R.F.: J. Math. Chem. 45, 776 (2009)

    Article  CAS  Google Scholar 

  30. Nalewajski R.F.: J. Math. Chem. 45, 1041 (2009)

    Article  CAS  Google Scholar 

  31. R.F. Nalewajski, Mol. Phys. 104, 1977, 2533, 3339 (2006)

    Google Scholar 

  32. Nalewajski R.F.: J. Math. Chem. 43, 265, 780 (2008)

    Google Scholar 

  33. R.F. Nalewajski, Int. J. Quantum Chem. 109, 2495 (2009)

    Google Scholar 

  34. Nalewajski R.F.: Int. J. Quantum Chem. 109, 425 (2009)

    Article  CAS  Google Scholar 

  35. Nalewajski R.F.: Adv. Quant. Chem. 56, 217 (2009)

    Article  CAS  Google Scholar 

  36. R.F. Nalewajski, Adv. Quant. Chem., in press

  37. Nalewajski R.F.: J. Phys. Chem. A 107, 3792 (2003)

    Article  CAS  Google Scholar 

  38. Nalewajski R.F.: Ann. Phys. (Leipzig) 13, 201 (2004)

    Article  CAS  Google Scholar 

  39. Nalewajski R.F.: Mol. Phys. 104, 255 (2006)

    Article  CAS  Google Scholar 

  40. Becke A.D., Edgecombe K.E.J.: Chem. Phys. 92, 5397 (1990)

    CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  42. Nalewajski R.F.: Int. J. Quantum. Chem. 108, 2230 (2008)

    Article  CAS  Google Scholar 

  43. R.F. Nalewajski, J. Math. Chem., in press. doi:10.1007/s10910-009-9594-5

  44. R.F. Nalewajski, P. de Silva, J. Mrozek, in Kinetic Energy Functional, ed. by A. Wang, T.A. Wesołowski, (World Scientific, Singapore, 2009, in press)

  45. S.B. Sears, Applications of Information Theory in Chemical Physics. Ph.D. Thesis (University of North Carolina, Chapel Hill, 1980)

  46. Sears S.B., Parr R.G., Dinur U.: Isr. J. Chem. 19, 165 (1980)

    CAS  Google Scholar 

  47. Frieden B.R.: Am. J. Phys. 57, 1004 (1989)

    Article  Google Scholar 

  48. Frieden B.R.: Physics from the Fisher Information—a Unification. Cambridge University Press, Cambridge (2000)

    Google Scholar 

  49. Reginatto M.: Phys. Rev. A 58, 1775 (1998)

    Article  CAS  Google Scholar 

  50. Reginatto M.: Erratum: Phys. Rev. A 60, 1730 (1999)

    Article  CAS  Google Scholar 

  51. Dirac P.A.M.: The Principles of Quantum Mechanics, 4th edn. Clarendon, Oxford (1958)

    Google Scholar 

  52. Wiberg K.A.: Tetrahedron 24, 1083 (1968)

    Article  CAS  Google Scholar 

  53. M.S. Gopinathan, K. Jug, Theor. Chim. Acta (Berl.) 63, 497, 511 (1983)

    Google Scholar 

  54. K. Jug, M.S. Gopinathan, in Theoretical Models of Chemical Bonding, vol. 2, ed. by Z.B. Maksić, (Springer, Heidelberg, 1990), p. 77

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

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  57. Nalewajski R.F., Mrozek J.: Int. J. Quantum Chem. 51, 187 (1994)

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

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

    Article  Google Scholar 

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

    Article  CAS  Google Scholar 

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

    CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  63. Pearson R.G.: J. Am. Chem. Soc. 85, 3533 (1963)

    Article  CAS  Google Scholar 

  64. Pearson R.G.: Science 151, 172 (1966)

    Article  Google Scholar 

  65. Pearson R.G.: Hard and Soft Acids and Bases. Dowden, Hatchinson and Ross, Stroudsburg (1973)

    Google Scholar 

  66. Jørgensen C.K.: Inor. Chem. 3, 1201 (1964)

    Article  Google Scholar 

  67. Parr R.G., Pearson R.G.: J. Am. Chem. Soc. 105, 7512 (1983)

    Article  CAS  Google Scholar 

  68. Nalewajski R.F.: J. Am. Chem. Soc. 106, 944 (1984)

    Article  CAS  Google Scholar 

  69. Nalewajski R.F., Korchowiec J., Michalak A.: Top. Curr. Chem. 183, 25 (1996)

    CAS  Google Scholar 

  70. Nalewajski R.F., Korchowiec J.: Charge Sensitivity Approach to Electronic Structure and Chemical Reactivity. World-Scientific, Singapore (1997)

    Google Scholar 

  71. Nalewajski R.F.: Adv. Quant. Chem. 51, 235 (2006)

    Article  CAS  Google Scholar 

  72. Chandra A.K., Michalak A., Nguyen M.T., Nalewajski R.F.: J. Phys. Chem. A 102, 10182 (1998)

    Article  CAS  Google Scholar 

  73. Nalewajski R.F.: Top. Catal. 11(12), 469 (2000)

    Article  Google Scholar 

  74. Gutmann V.: The Donor Acceptor Approach to Molecular Interactions. Plenum, New York (1978)

    Google Scholar 

  75. R.F. Nalewajski, Entropy/information coupling between orbital-communications in molecular systems”, J. Math. Chem., in press

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Authors and Affiliations

  1. Department of Theoretical Chemistry, Jagiellonian University, R. Ingardena 3, 30-060, Cracow, Poland

    Roman F. Nalewajski

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  1. Roman F. Nalewajski
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Correspondence to Roman F. Nalewajski.

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Throughout the paper P denotes a scalar quantity, P stands for a row-vector, and P represents a square/rectangular matrix.

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Nalewajski, R.F. Many-orbital probabilities and their entropy/information descriptors in orbital communication theory of the chemical bond. J Math Chem 47, 692–708 (2010). https://doi.org/10.1007/s10910-009-9595-4

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