Entropy/information descriptors of the chemical bond revisited

Abstract

Information-theoretic (IT) indexing of the chemical bond multiplicities and their covalent/ionic contributions in the Orbital Communication Theory is reexamined. The molecules are interpreted as information channels in the Atomic Orbital (AO) resolution, in which the signals (probabilities) of the electron-allocation to AO events are propagated between the channel “inputs” and “outputs”. The molecular conditional-entropy descriptor of such a probability network measures the average communication “noise” due to electron delocalization via the framework of all occupied molecular orbitals (MO) and provides a measure (in bits) of the bond IT-covalent component. The complementary IT-ionic bond multiplicity has been previously characterized by the channel average mutual-information (information-capacity, flow) descriptor, between the promolecular input and molecular output distributions, which reflects a degree of the deterministic character of such AO communications. The consistency of using this promolecule → molecule channel, reflecting the “history” of the bond formation process, as the stationary information network is validated using the classical cascade of the sequential molecular channels, effecting the multiple probability propagations. The “normalization” of the global bond descriptor of this channel to the sum of the molecular Shannon entropy and the information distance between the two compared AO distributions is demonstrated analytically and tested numerically. The promolecule (M0) → molecule (M) transition channel is formulated in the general basis set case and its overall bond multiplicity index is determined. The mixed channels are examined, with different sets of the input and output events. The displacement in the density matrix reflecting the M0→ M transition provides the AO representation of the corresponding difference between the molecular and promolecular density operators. Finally, the closed communication loops are proposed, consisting of the molecular and promolecular cascades, respectively, which generate the difference entropy/information descriptors of the system chemical bonds, between the corresponding molecular indices and their promolecular analogs, with the latter reflecting the internal communications in the isolated atoms.