Abstract
An overview of the recent bond-order and entropy/information measures of the chemical bond multiplicity and of its covalent/ionic composition is given. The former include the Wiberg index of the molecular orbital (MO) theory and its atomic/diatomic components, while the latter explore the communication-noise (covalency) and information-flow (ionic) descriptors of molecular information channels in the atomic-orbital (AO) resolution. The illustrative application to the two-orbital model is presented and the atomic resolution of bond contributions is presented. Alternative information distributions, including densities of the displacement in the system Shannon entropy and its entropy deficiency relative to the “promolecule,” are advocated as effective probes of chemical bonds. They complement the familiar density difference diagrams of electron redistributions accompanying the bond formation process. These quantities are applied to investigate the central bond in small propellanes and the contragradience criterion, based upon the non-additive Fisher information in electron distribution, is shown to efficiently locate the bonding regions in butadiene and benzene. The novel, indirect bonding mechanism through the orbital intermediaries, inferred from the orbital communication theory in the AO resolution, is probed in these two illustrative π-electron systems using the generalized Wiberg bond-orders. It is shown to give rise to a more realistic representation of the second-neighbor interactions, which have previously been diagnosed as the direct (through-space) non-bonding. In MO theory, these through-bridge bond components are due to the implicit dependencies between the (non-orthogonal) AO projections onto the molecular bonding subspace of the occupied MO. They do not require the bond-charge accumulation between the nuclei of bonded atoms and can be realized at longer distances. The effective range of such indirect interactions is probed in representative polymers. Finally, the entropy/information concepts for three dependent probability distributions are used to qualitatively examine the promotion of reactants in catalysis. The chemisorbed species are predicted to undergo an ionic promotion, compared to the gas-phase reference, thus exhibiting more deterministic communications on the catalytic surface.
Highlights
This paper is devoted to Professor Malgorzata Witko.Throughout the paper, A denotes scalar quantity, A stands for the row or column vector, and A represents a rectangular or square matrix.The tion, eflreocmtrotnhereedleiscttrriobnutdioennsaitcycoqm0 p=anPyinXgqtX0hedubeontod formamolecularly placed free atoms {X0} of the system ‘‘promolecule,’’exhibiting the grouPnd-state densities {qX0 }, to the molecular distribution q = XqX generated by electron densities{qX} of the bonded atoms {X}, is marked by the familiar difference function, Dq = q - q0 between these resultant molecular and promolecular electron densities
Struct Chem (2012) 23:1383–1398 entropy/information content of these distributions provides a basis for a novel information-theoretic (IT) perspective on the molecular electronic structure, e.g. [1,2,3] and references therein
Elimination of such lone-pair contributions to the resultant IT bond indices of diatomic fragments in molecules requires an ensemble approach [2, 3, 33, 34], in which the input probabilities are derived from the joint probabilities of two AO centered on different atoms, which reflect the simultaneous participation of the given pair of basis functions in the inter-atomic chemical bonds
Summary
This paper is devoted to Professor Malgorzata Witko. Throughout the paper, A denotes scalar quantity, A stands for the row or column vector, and A represents a rectangular or square matrix. The underlying conditional probabilities determining the communication network in molecules are generated from the (bond-projected) superposition principle of quantum mechanics [26, 36] They have been shown to be proportional to the squares of the corresponding elements of the first-order density matrix in the AO representation, being related to the Wiberg [37] quadratic index of the chemical bond multiplicity and its subsequent generalizations [38,39,40,41,42,43,44,45,46,47]. The recently discovered mechanism of indirect chemical bonding [3, 18, 48,49,50,51,52] will be emphasized
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