Understanding Electronic Structure and Chemical Reactivity: Quantum-Information Perspective

Abstract

Several applications of quantum mechanics and information theory to chemical reactivity problems are presented with emphasis on equivalence of variational principles for the constrained minima of the system electronic energy and its kinetic energy component, which also determines the overall gradient information. Continuities of molecular probability and current distributions, reflecting the modulus and phase components of molecular wavefunctions, respectively, are summarized. Resultant measures of the entropy/information descriptors of electronic states, combining the classical (probability) and nonclassical (phase/current) contributions, are introduced, and information production in quantum states is shown to be of a nonclassical origin. Importance of resultant information descriptors for distinguishing the bonded (entangled) and nonbonded (disentangled) states of reactants in acid(A)–base(B) systems is stressed and generalized entropy concepts are used to determine the phase equilibria in molecular systems. The grand-canonical principles for the minima of electronic energy and overall gradient information allow one to explore relations between energetic and information criteria of chemical reactivity in open molecules. The populational derivatives of electronic energy and resultant gradient information give identical predictions of electronic flows between reactants. The role of electronic kinetic energy (resultant gradient information) in chemical-bond formation is examined, the virial theorem implications for the Hammond postulate of reactivity theory are explored, and changes of the overall structure information in chemical processes are addressed. The frontier-electron basis of the hard (soft) acids and bases (HSAB) principle is reexamined and covalent/ionic characters of the intra- and inter-reactant communications in donor-acceptor systems are explored. The complementary A–B coordination is compared with its regional HSAB analog, and polarizational/relaxational flows in such reactive 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.…”