物理化学学报  2017, Vol. 33 Issue (12): 2491-2509    DOI: 10.3866/PKU.WHXB201706132 所属专题： 密度泛函理论中的化学概念特刊
 论文
Chemical Reactivity Description in Density-Functional and Information Theories
NALEWAJSKI Roman F*()
Chemical Reactivity Description in Density-Functional and Information Theories
Roman F NALEWAJSKI*()
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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.

Abstract:

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.

Key words: Density-functional theory    Donor-acceptor system    Electronegativity equalization and electron flows    Information theory    Markov chains    Phase-equilibria

 中图分类号: O646

 Fig 1  Orbital networks of classical communications in polarized reactive system Rn+ = (A+|B+): AO-resolved (Panel Ⅰ) and MO-resolved (Panel Ⅱ) Fig 2  Concerted flows (Panel Ⅰ) in the complementary (c) arrangement of subsystems in the bimolecular reactive system ${{\bf{R}}_{\bf{c}}} \equiv \left( {\begin{array}{*{20}{c}} {{\mathit{\boldsymbol{a}}_{\bf{A}}}\mathit{\boldsymbol{ - - - }}{\mathit{\boldsymbol{b}}_{\bf{B}}}} \\ {{\mathit{\boldsymbol{b}}_{\bf{A}}}\mathit{\boldsymbol{ - - - }}{\mathit{\boldsymbol{a}}_{\bf{B}}}} \end{array}} \right);$here aα and bα denote the acidic (a) and basic (b) parts of reactant α = A, B, and most important cascade communications via single orbital intermediates (Panel Ⅱ). The latter combine either two external (inter-reactant) CT propagations (solid arrows), two internal (intra-reactant) P scatterings (broken arrows), or single external and internal communications Fig 3  A qualitative diagram of the chemical-potential equalization and the Polarizational (P) or Charge-Transfer (CT) electron flows in the complementary reactive complex Rc of Fig.2I. First, the equalized levels of the chemical potential within isolated reactants Rα0 = (A0, B0) are split on their (mutually-closed) acidic (aα) and basic (bα) fragments, due to the perturbation created by the presence of the nearby bβ and aβ parts of the reaction partner Rβ0. These shifts within the initially polarized reactants {Rα+ = (aα+|bα+)} then trigger the P-flows {δNα}, which regain electronegativity equalization in {Rα+ = (aα+|bα+)} at their internal chemical-potential levels {μX+}. The resulting chemical-potential difference △μ+ = μA+ -μB+ < 0 ultimately determines the direction B+ → A+ and amount NCT of the subsequent inter-reactant CT, which establishes the global equilibrium in Rc as a whole, with equal levels of the chemical potential of the whole bonded (mutually-open) reactants {Rα* = (aα*|bα*)} and their constituent acidic {aα*} and basic {bα*} parts. One observes that a presence of B destabilizes A, △μA(B) > 0, while A stabilizes B, △μB(A) < 0 Fig 4  Qualitative diagram of the chemical potential displacements in the complementary complex Rc+ = (A+|B+), due to the primary CT perturbations nCT(1) and nCT(2) in RCT, and subsequent induced responses IA and IB of Fig.2.I. The CT perturbations split the initially equalized levels of the chemical potential within each reactant, {a0 = (aa*|ba*)}, with the inflow (outflow) of electron increasing (decreasing) the site chemical potential in {α+ = (aα+|bα+)}. These primary shifts subsequently trigger the polarizational flows {Ia}, which eventually generate the global electronegativity equalization in Rc as a whole: Rc = (A*|B*) = (aA*|bA*|aB*|bB*) ≡ RCT*