Molecular communication channels of model excited electron configurations†

Abstract

In the Communication Theory of the chemical bond, molecular systems are interpreted in atomic resolution as the information channels, in which ‘signals' of the electron allocations to constituent atoms are propagated from the molecular/promolecular input (‘source'), to the molecular output (‘receiver'). The electron delocalization throughout the system is responsible for the effective ‘noise' affecting the transmission of such atom-assignment signals. The conditional entropy and mutual-information descriptors of such molecular communication channels, measuring the average noise and the amount of information flowing through the molecular channel, respectively, provide measures of the covalent and ionic bond components, respectively. This work examines the influence of the relative phases of the atomic orbitals (AO) in the occupied molecular orbitals (MO) on these entropy/information indices of the chemical bond in the 2-AO, two-electron model. First, the singly- and doubly-excited-state configurations of the model are examined to investigate the influence of the occupied bonding and anti-bonding molecular orbitals on the previously proposed (phase-insensitive) entropy/information descriptors of the ground-state configuration. They in principle correctly identify the non-bonding character of the singly-excited configuration, but fail to recognize the anti-bonding character of the doubly-excited state. This is because the relative phases of AO in MO and those of the elementary valence-bond structures in the configuration wave-function are lost in the corresponding electron probabilities, which determine the molecular channel. A resolution of this difficulty is proposed through partition of the overall input probabilities of the molecular channel into the partial (phase-dependent) ‘forward' and ‘backward' inputs, which determine the entropy/information flows associated with the ‘positive' and ‘negative' phases of the wave-function components in the AO representation. †Dedicated to Professor A. Sadlej on the occasion of his 65th birthday.