Register
ISSN 1000-6818CN 11-1892/O6CODEN WHXUEU
Acta Phys Chim Sin >> 2017,Vol.33>> Issue(12)>> 2491-2509     doi: 10.3866/PKU.WHXB201706132         中文摘要
Chemical Reactivity Description in Density-Functional and Information Theories
NALEWAJSKI Roman F
Department of Theoretical Chemistry, Jagiellonian University, R. Ingardena 3, 30-060 Cracow, Poland
Full text: PDF (1033KB) HTML Export: BibTeX | EndNote (RIS)

In Quantum Information Theory (QIT) the classical measures of information content in probability distributions are replaced by the corresponding resultant entropic descriptors containing the nonclassical terms generated by the state phase or its gradient (electronic current). The classical Shannon (S[p]) and Fisher (I[p]) information terms probe the entropic content of incoherent local events of the particle localization, embodied in the probability distribution p, while their nonclassical phase-companions, S[φ] and I[φ], provide relevant coherence information supplements. Thermodynamic-like couplings between the entropic and energetic descriptors of molecular states are shown to be precluded by the principles of quantum mechanics. The maximum of resultant entropy determines the phase-equilibrium state, defined by “thermodynamic” phase related to electronic density, which can be used to describe reactants in hypothetical stages of a bimolecular chemical reaction. Information channels of molecular systems and their entropic bond indices are summarized, the complete-bridge propagations are examined, and sequential cascades involving the complete sets of the atomic-orbital intermediates are interpreted as Markov chains. The QIT description is applied to reactive systems R=A-B, composed of the Acidic (A) and Basic (B) reactants. The electronegativity equalization processes are investigated and implications of the concerted patterns of electronic flows in equilibrium states of the complementarily arranged substrates are investigated. Quantum communications between reactants are explored and the QIT descriptors of the A-B bond multiplicity/composition are extracted.



Keywords: Density-functional theory   Donor-acceptor system   Electronegativity equalization and electron flows   Information theory   Markov chains   Phase-equilibria  
Received: 2017-04-19 Accepted: 2017-05-31 Publication Date (Web): 2017-06-13
Corresponding Authors: NALEWAJSKI Roman F Email: nalewajs@chemia.uj.edu.pl


Cite this article: NALEWAJSKI Roman F. Chemical Reactivity Description in Density-Functional and Information Theories[J]. Acta Phys. -Chim. Sin., 2017,33 (12): 2491-2509.    doi: 10.3866/PKU.WHXB201706132

(1) Fisher, R. A. Proc. Cambridge Phil. Soc. 1925, 22, 700. doi: 10.1017/S0305004100009580
(2) (a) Shannon, C. E. Bell System Tech. J. 1948, 27, 379, 623. doi: 10.1002/j.1538-7305.1948.tb01338.x (b) Abramson, N. Information Theory and Coding; McGraw-Hill: New York, 1963.
(3) Nalewajski, R. F. Quantum Information Theory of Molecular States; Nova Science Publishers: New York, 2016.
(4) (a) Nalewajski, R. F. Ann. Phys. (Leipzig) 2013, 525, 256. doi: 10.1002/andp.201200230 (b) Nalewajski, R. F. J. Math. Chem. 2013, 51, 369. doi: 10.1007/s10910-012-0088-5
(5) Nalewajski, R. F. J. Math. Chem. 2014, 52, 588, 1292, 1921. doi: 10.1007/s10910-013-0280-2; 10.1007/s10910-014-0311-7; 10.1007/s10910-014-0357-6
(6) Nalewajski, R. F. Mol. Phys. 2014, 112, 2587. doi: 10.1080/00268976.2014.897394
(7) Nalewajski, R. F. Int. J. Quantum Chem. 2015, 115, 1274. doi: 10.1002/qua.24750
(8) Nalewajski, R. F. J. Math. Chem. 2015, 53, 1126. doi: 10.1007/s10910-014-0468-0
(9) Nalewajski, R. F. J. Math. Chem. 2016, 54, 1777. doi: 10.1007/s10910-016-0651-6
(10) Hohenberg, P.; Kohn, W. Phys. Rev. 1964, 136B, 864. doi: 10.1103/PhysRev.136.B864
(11) Kohn, W.; Sham, L. J. Phys. Rev. 1965, 140A, 1133. doi: 10.1103/PhysRev.140.A1133
(12) Levy, M. Proc. Natl. Acad. Sci. U. S. A. 1979, 76, 6062. doi: 10.1073/pnas.76.12.6062
(13) Parr, R. G.; Yang, W. Density Functional Theory of Atoms and Molecules; Oxford University Press: New York, 1989.
(14) Nalewajski, R. F.; Korchowiec, J. Charge Sensitivity Approach to Electronic Structure and Chemical Reactivity; World Scientific: Singapore, 1997.
(15) Nalewajski, R. F.; Korchowiec, J.; Michalak, A. Topics in Current Chemistry 1996, 183, 25. doi: 10.1007/3-540-61131-2
(16) Nalewajski, R. F. Structure and Bonding 1993, 80, 115. doi: 10.1007/BFb0036803
(17) Geerlings, P.; de Proft, F.; Langenaeker, W. Chem. Rev. A 2003, 103, 1793. doi: 10.1021/cr990029p
(18) Chattaraj, P. K. Chemical Reactivity Theory: A Density Functional View; CRC Press: Taylor & Francis, Boca Raton, 2009.
(19) (a) Mulliken, R. S. J. Chem. Phys. 1934, 2, 782. doi: 10.1063/1.1749496 (b) Iczkowski, R. P.; Margrave, J. L. J. Am. Chem. Soc. 1961, 83, 3547. doi: 10.1021/ja01478a001
(20) Sanderson, R. T. J. Am. Chem. Soc. 1952, 74, 272. doi: 10.1021/ja01121a522
(21) Gyftopoulos, E. P.; Hatsopoulos, G. N. Proc. Natl. Acad. Sci. U. S. A. 1965, 60, 786.
(22) Parr, R. G.; Donnelly, R. A.; Levy, M.; Palke, W. E. J. Chem. Phys. 1978, 69, 4431. doi: 10.1063/1.436433
(23) Perdew, J. P.; Parr, R. G.; Levy, M.; Balduz, J. L. Phys. Rev. Lett. 1982, 49, 1691. doi: 10.1103/PhysRevLett.49.1691
(24) Pearson, R. G, Hard and Soft Acids and Bases; Dowden, Hatchinson, Ross: Stroudsburg, 1973.
(25) Parr, R. G.; Pearson, R. G. J. Am. Chem. Soc. 1983, 105, 7512. doi: 10.1021/ja00364a005
(26) Parr, R. G.; Yang, W. J. Am. Chem. Soc. 1984, 106, 4049. doi: 10.1021/ja00326a036
(27) Liu, S. Chemical Reactivity Theory: A Density Functional View; Chattaraj, P. K. Ed. CRC/Taylor & Francis: Boca Raton, 2009; p. 179.
(28) Baekelandt, B. G.; Janssens, G. O. A.; Toufar, H.; Mortier, W. J.; Schoonheydt, R. A.; Nalewajski, R. F. J. Phys. Chem. 1995, 99, 9784. doi: 10.1021/j100024a020
(29) Nalewajski, R. F. Preceedings of the NATO ASI on Density Functional Theory; Dreizler, R. M.; Gross, E. K. U. Eds.; Plenum: New York, 1995; p 339.
(30) Cohen, M. H. Topics in Current Chemistry 1996, 183, 143.
(31) Nalewajski, R. F. Computers Chem. 2000, 24, 243. doi: 10.1016/S0097-8485(99)00070-4
(32) Nalewajski, R. F. Adv. Quant. Chem. 2006, 51, 235. doi: 10.1016/S0065-3276(06)51006-8
(33) Nalewajski, R. F.; B?a?ewicz, D.; Mrozek, J. J. Math. Chem. 2008, 44, 325. doi: 10.1007/s10910-007-9312-0
(34) Nalewajski, R. F. J. Math. Chem. 2010, 48, 752. doi: 10.1007/s10910-010-9708-0
(35) Nalewajski, R. F. J. Math. Chem. 2015, 53, 1. doi: 10.1007/s10910-014-0405-2
(36) Nalewajski, R. F. Information Theory of Molecular Systems; Elsevier: Amsterdam, 2006.
(37) Nalewajski, R. F. Information Origins of the Chemical Bond; Nova Science Publishers: New York, 2010.
(38) Nalewajski, R. F. Perspectives in Electronic Structure Theory; Springer: Heidelberg, 2012.
(39) Nalewajski, R. F. Indian J. Chem. A 2014, 53, 1010.
(40) Nalewajski, R. F. Phase Description of Reactive Systems. in Conceptual Density Functional Theory; Islam, N. Ed., Apple Academic Press: Waretown, 2017, in press.
(41) Nalewajski, R. F. Entropy Continuity, Electron Diffusion and Fragment Entanglement in Equilibrium States. In Advances in Mathematics Research; Nova Science Publishers: New York, 2017, in press.
(42) Toro-Labbé, A.; Gutiérez-Oliva, S.; Politzer, P.; Murray, J. S. Chemical Reactivity Theory: A Density Functional View; Chattaraj, P. K. Ed.; CRC/Taylor & Francis: Boca Raton, 2009; p. 293.
(43) López-Rosa, S.; Esquivel, R. O.; Angulo, J. C.; Antolín, J.; Dehesa, J. S.; Flores-Gallegos, N. J. Chem. Theory Comput. 2010, 6, 145. doi: 10.1021/ct900544m
(44) López-Rosa, S. Information-Theoretic Measures of Atomic and Molecular Systems; Ph. D. Dissertation, University of Granada: Granada, 2010.
(45) Nalewajski, R. F. J. Math. Chem. 2011, 49, 371. doi: 10.1007/s10910-010-9747-6
(46) Nalewajski, R. F. J. Math. Chem. 2011, 49, 546. doi: 10.1007/s10910-010-9761-8
(47) Nalewajski, R. F. J. Math. Chem. 2011, 49, 806. doi: 10.1007/s10910-010-9777-0
(48) Nalewajski, R. F.; Gurdek, P. J. Math. Chem. 2011, 49, 1226. doi: 10.1007/s10910-011-9815-6
(49) Nalewajski, R. F. Int. J. Quantum Chem. 2012, 112, 2355. doi: 10.1002/qua.2321
(50) Nalewajski, R. F.; Gurdek, P. Struct. Chem. 2012, 23, 1383. doi: 10.1007/s11224-012-0060-9
(51) Nalewajski, R. F. J. Math. Chem. 2011, 49, 2308. doi: 10.1007/s10910-011-9888-2
(52) Dirac, P. A. M. The Principles of Quantum Mechanics, 4th ed; Clarendon: Oxford, 1958.
(53) Harriman, J. E. Phys. Rev. A 1981, 24, 680. doi: 10.1103/PhysRevA.24.680
(54) Zumbach, G.; Maschke, K. Phys. Rev. A 1983, 28, 544. doi: 10.1103/PhysRevA.28.544; Erratum: Phys. Rev. A 1984, 29, 1585.
(55) von Weizsäcker, C. F. Z. Phys. 1935, 96, 431.
(56) Callen, H. B. Thermodynamics: an Introduction to the Physical Theories of Equilibrium Thermostatics and Irreversible Thermodynamics; Wiley: New York, 1960.
(57) Kullback, S.; Leibler, R. A. Ann. Math. Stat. 1951, 22, 79. doi: 10.1214/aoms/1177729694
(58) Kullback, S. Information Theory and Statistics; Wiley: New York, 1959.
(59) Nalewajski, R. F. Topics in Catalysis 2000, 11, 469. doi: 10.1023/A:1027273730694
(60) Shaik, S.; Danovich, D.; Wu, W.; Hiberty, P. C. Nat. Chem. 2009, 1, 443. doi: 10.1038/NCHEM.327
(61) Heitler, W.; London, F. Z. Physik 1927, 44, 455.
(62) Sveshnikov, A. A. Problems in Probability Theory, Mathematical Statistics and Theory of Random Functions; Dover: New York, 1968.
(63) Rozanov, Y. A. Probability Theory: A Concise Course; Dover: New York, 1969.
(64) Pfeifer, P. E. Concepts of Probability Theory; Dover: New York, 1978.
(65) Hirshfeld, F. L. Theoret. Chim. Acta (Berl.) 1977, 44, 129. doi: 10.1007/BF00549096
(66) Chandra, A. K.; Michalak, A.; Nguyen, M. T.; Nalewajski, R. F. J. Phys. Chem. A 1998, 102, 100182. doi: 10.1021/jp983122a

Copyright © 2006-2016 Editorial office of Acta Physico-Chimica Sinica
Address: College of Chemistry and Molecular Engineering, Peking University, Beijing 100871, P.R.China
Service Tel: +8610-62751724 Fax: +8610-62756388 Email:whxb@pku.edu.cn
^ Top