Orbital Communication Theory of the Chemical Bond

Abstract

The rudiments of the Orbital Communication Theory (OCT) of the chemical bond are presented. Molecules are interpreted as communication systems in which the electron probability (information) is scattered between AO of the basis set of molecular calculations. They are defined by the conditional probabilities derived from the bond-projected superposition principle. The IT multiplicity of all chemical bonds in a molecule is introduced, originating from the orbital interactions between AO of all constituent atoms, and its covalent and ionic components are linked to the channel average communication noise and information flow descriptors, respectively. In the illustrative two-AO model of the single chemical bond this approach conserves the overall bond descriptor for all admissible MO polarizations, from the purely covalent structure to the ion pair configuration. This bond order preservation signifies the competition between the covalent and ionic bond components. The orbital communications are partitioned into the internal (intra-atomic) and external (interatomic) subchannels.

The multiconditional probabilities of orbital events in the chemical bond system of the molecule, required for determining the information theoretic indices of the bond couplings between molecular fragments, are established within the theoretical framework of the one-determinantal orbital representation of molecular electronic structure. They are again derived from an appropriate generalization of the bond-projected superposition principle. The triply conditional probabilities, relating one conditional event to another, are shown to satisfy the relevant nonnegativity and symmetry requirements. The probability/information scattering perspective on the localized diatomic interactions between AO originating from a given pair of AIM is presented. It uses the ensemble averaging, known as the flexible input approach, with the weights provided by the joint (bond) two-orbital probabilities of the interacting AO. This procedure is first applied to the two-orbital model, where it is shown to reproduce (in bits) the corresponding Wiberg measure of the bond order. Its generalization to atoms contributing several AO to the chemical bond system is shown to exactly reproduce the corresponding Wiberg index in diatomic molecules, while closely approximating the latter in larger systems. The coupling effects between chemical bonds, which require conditional probabilities of several AO on molecular subsystems, are examined and the effect of the IT-ionic activation of adsorbates is predicted.

The direct (through-space) and indirect (through-bridge) components of chemical interactions between atomic orbitals are identified in both the Wiberg bond order formalism and in OCT. The illustrative examples using the Hückel description of the conjugated π-bonds in benzene and butadiene are given and the existence of the through-bridge bond between bridgehead carbons in small propellanes is conjectured. The amplitude channels of probability scattering in molecules are introduced and the operator representation of the direct and multiple probability propagations is developed. The independent (principal) AO communications are defined and the stationary probability distribution is shown to be conserved in the multiple bridge propagations of the scattering amplitudes. The bridge amplitudes are expressed in terms of the bond overlap (density) matrix elements using the chain rule expressions for the implicit derivatives between AO in the molecular bond system.