Communications in molecules: local and multi-configuration channels and their entropic descriptors of bond multiplicity and composition

Abstract

The Orbital Communication Theory of the chemical bond, in which molecules are treated as information systems transmitting "signals" of electron allocations to Atomic Orbitals, is extended to cover the local resolution level of electron distributions and the Configuration-Interaction (CI, multi-determinantal) description of molecular states. These communication systems generate the information-theoretic measures of both the absolute and relative multiplicities of chemical bonds, as well as the bond covalent (communication-noise) and ionic (information-flow) components. The orbital/local communications via the CI ensembles of the occupied molecular orbitals in such generalized molecular states are investigated. Illustrative two-orbital model and its prototype Valence-Bond structures are examined in a more detail.

On phases and interference of local communications in molecules

“…This development can be straightforwardly generalized into the multi-determinantal (CI) description using eithr the CI ensembles of the occupied SMO [80,81] or the natural orbital (NO) framework [44].…”

“…As also indicated above, these communications are generated by the magnitude (modulus) of the associated quantum (complex) amplitudes A(χ |χ) = {A( j|i) = A i→ j }, of the emitting (input) states a = |χ = {|χ i } among the monitoring/receiving (output) states b = |χ = {|χ j }. A deeper understanding of the molecular electronic structure ultimately calls for the continuous, local ("fine-grained") description [81,83], to complement the discrete, orbital ("coarse-grained") resolution adopted in OCT. The original orbitalcommunication development can be indeed naturally generalized into this extreme level of resolving electron distributions in molecules, when one examines the information propagations between infinitesimal volume elements around r ∈ in the channel input and r ∈ in its output, respectively, with or containing the whole physical space of all admissible electron localizations.…”

“…This local description [81,83], which we shall further develop in the present analysis, uses the basis functions {|r } of the familiar position representation of quantum mechanics, identified by the continuous labels of the spatial coordinates of an electron. They determine both the input a = {|r } and output b = {|r } of the local molecular channel determined by the relevant conditional probabilities,…”

“…(30)], disappears in P(r → r ; r ). This is not the case in the parallel cascades generated by the multi-determinantal wave functions of the configurationinteraction (CI) theory [44,80,81]. These single-cascade results can be straightforwardly generalized into any bridgeorder.…”