Role of electronic kinetic energy and resultant gradient information in chemical reactivity

Abstract

The role of resultant gradient-information concept, reflecting the kinetic energy of electrons, in shaping the molecular electronic structure and reactivity preferences of open reactants is examined. This quantum-information descriptor combines contributions due to both the modulus (probability) and phase (current) components of electronic wavefunctions. The importance of resultant entropy/information concepts for distinguishing the bonded (entangled) and nonbonded (disentangled) states of molecular fragments is emphasized and variational principle for the minimum of ensemble-average electronic energy is interpreted as a physically equivalent rule for the minimum of resultant gradient-information, and the information descriptors of charge-transfer (CT) phenomena are introduced. The in situ reactivity criteria, represented by the populational CT derivatives of the ensembleaverage values of electronic energy or resultant information, are mutually related, giving rise to identical predictions of electron flows in the acid(A)base(B), reactive systems. The virial theorem decomposition of electronic energy is used to reveal changes in the resultant information content due to the chemical bond formation, and to rationalize the Hammond postulate of reactivity theory. The complementarity principle of structural chemistry is confronted with the regional hard (soft) acid and bases (HSAB) rule by examining the polarizational and relaxational flows in such acceptor-donor reactive systems, responses to the external potential and CT displacements, respectively. The frontier-electron basis of the HSAB principle is reexamined and the intra-and inter-reactant communications in A-B systems are explored.

Resultant gradient information, kinetic energy and molecular virial theorem

“…besides the remaining constraints, now multiplied by the "scaled" conjugate intensities [5][6][7][8] : information "potential"…”

“…The Quantum Information Theory (QIT) [1][2][3][4] has been shown to provide a solid, unifying basis for understanding -in chemical terms -the electronic structure of molecules, and explaining general trends in their chemical behavior, [5][6][7][8] . Thermodynamic energy principle has been interpreted as physically equivalent rule for the resultant content of the overall gradientinformation in electronic wavefunction, the dimensionless descriptor related to the state average kinetic energy.…”

“…The latter combines the classical (probability) and nonclassical (current) contributions,due to the modulus and (local) phase components of the molecular wavefunction, respectively. The proportionality between the resultant gradient-information and the system kinetic energy also suggests the use of molecular virial theorem [10] in general reactivity considerations [5][6][7][8] .…”

“…The classical Information Theory (IT) of Fisher and Shannon [28][29][30][31][32][33][34][35] has been successfully applied to generate the chemical interpretation of molecular probability distributions, [36][37][38][39] . Information principles have been explored [5][6][7][8][40][41][42][43][44][45] and density pieces attributed toAtoms-in-Molecules(AIM) have been approached, [36][37][38][39][43][44][45][46][47] providing the information basis for the intuitive (stockholder) division of Hirshfeld [48] . Patterns of chemical bonds in molecules have been extracted from electronic orbital communications, [1,[36][37][38][49][50][51][52][53][54][55][56][57][58][59] and entropy/information densities have been explored.…”

“…The resultant QIT descriptor will be introduced and its classical and nonclassical components identified. Populational derivatives of its thermodynamic, ensemble-average value generate alternative indices of chemical reactivity, adequate in predicting both the direction and magnitude of electron flows in donor-acceptor systems [5][6][7][8] . The molecular virial theorem will be used to generate the information perspective on the bond-formation and the Hammond [81] postulate of reactivity theory.…”