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.

The indirect (through-bridge) components of chemical interactions between atomic orbitals (AO) are shown to originate from the indirect dependencies between AO due to the orbital intermediaries in the bond system of the molecule. They are expressed in terms of the bridge-coupling elements of the density matrix via the chain rule transformation of the implicit derivatives between the indirectly bonded AO in the molecular bond system. The elements of the charge-and-bond-order (CBO) matrix are interpreted as the canonical derivatives between the AO-projections onto the bond subspace combining the occupied Molecular Orbitals (MO). The chain-rule manipulations are then used to express the scattering amplitudes via AO intermediaries in terms of the relevant elements of the CBO matrix. The squares of such amplitudes are related to the Wiberg-type indirect bond components, which complement the familiar direct Wiberg bond-order contributions. The interference implications of the probability scatterings via the multiple cascades involving all basis functions are examined. These probability propagations are shown to preserve the stationary conditional probabilities of the underlying molecular communication channel in AO resolution.Keywords Bond orders · Chemical interactions · Direct/indirect bonds · Information-theoretic bond multiplicities · Interference of molecular communications · Orbital Communication Theory · Wiberg bond order Throughout the paper A denotes a scalar quantity, A stands for a row-vector, and A represents a square or rectangular matrix.