Entropic bond indices from molecular information channels in orbital resolution: ground-state systems

The molecular communication channels of Information Theory (IT) are constructed within the orbital description of molecular electronic structure using the superposition principle of quantum mechanics. Two types of such information systems are introduced, called the “geometric” and “physical” channels. The communication network of the former is determined by all molecular orbitals (MO), occupied and virtual, which result from the specified set of atomic orbitals (AO). The geometric channel thus reflects the relative “rotation” of MO relative to AO in the molecular Hilbert space, and the associated “promotion” of AO in the molecule due to the probability scattering via the communication network generated by the complete set of MO. They are devoid of the physical content embodied in the MO-occupations, which distinguish one electron configuration of the molecule from another. The latter information is included in the physical AO-promotion channels, which involve the probability scattering via the occupied MO alone. The probability conditioning is shown to be related to the appropriate projection in the orbital Hilbert space. The geometric and the physical (ground-state) bond indices of the conditional-entropy (IT-covalency) and mutual-information (IT-ionicity) are generated for the 2-AO model and selected π-electron systems (ethylene, allyl, butadiene, and benzene) in the Hückel approximation. They are shown to compare favorably with the previously reported IT bond-orders obtained from the two-electron molecular information channels in atomic resolution.