Bond-order and entropic probes of the chemical bonds

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 p-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.

On phases and interference of local communications in molecules

“…The information theory (IT) [1][2][3][4][5][6][7][8] has been successfully applied to explore the electron probabilities and patterns of chemical bonds in molecules, e.g., [9][10][11][12][13][14][15][16][17][18][19][20]. Both the electron probability distribution, determined by the wave-function modulus, and the system current density, related to the gradient of the wave-function phase, ultimately contribute to the resultant (quantum) information content of molecular states.…”

“…It has been argued elsewhere that many classical problems of theoretical chemistry can be approached afresh using this novel IT perspective, e.g., [9][10][11][12][13][14][15][16][17][18][19][20]. The displacements of the classical information distribution in a molecule, relative to the promolecular reference consisting of its constituent non-bonded atoms, have been investigated [11][12][13][14][15][17][18][19][20][23][24][25] and the least biased partition of the molecular electron distribution into subsystem contributions, e.g., densities of bonded atoms, has been examined [11][12][13][26][27][28][29][30][31][32][33].…”

“…The displacements of the classical information distribution in a molecule, relative to the promolecular reference consisting of its constituent non-bonded atoms, have been investigated [11][12][13][14][15][17][18][19][20][23][24][25] and the least biased partition of the molecular electron distribution into subsystem contributions, e.g., densities of bonded atoms, has been examined [11][12][13][26][27][28][29][30][31][32][33]. This IT approach has been shown to lead to the "stockholder" atomsin-molecules (AIM) of Hirshfeld [34].…”

“…The non-additive Fisher information in the atomic orbital (AO) resolution has been used as the contra-gradience (CG) criterion for localizing the bonding regions in molecules [11][12][13][14][15][16][17][18][19][20][35][36][37] , while the related information density in the molecular orbital (MO) resolution has been shown [11,38] to determine the vital ingredient of the electron-localization function (ELF) [39][40][41].…”

“…The IT approach introduces into the theory of electronic structure of molecular systems the novel entropy-representation [10][11][12][13][14][15][16][17][18][19][20][21][22], which complements the familiar energy-representation of the molecular quantum mechanics. Such a dual perspective parallels that known from the ordinary thermodynamics.…”