Entropy descriptors of the chemical bond in information theory. I. Basic concepts and relations

Abstract

The elements of the ‘communication theory’ of the chemical bond are outlined. The average uncertainties of the information theory characterizing the communication channels are summarized. The molecular system in atomic resolution is interpreted as the ‘communication’ channel, in which signals of the electron allocations to constituent atoms are propagated from the molecular input (‘source’), determined by the atomic ‘promolecule’, to the molecular output (‘receiver’), via the system chemicals bonds. This transmission network, connecting the free atoms of the promolecule reference and the bonded atoms-in-a-molecule, is determined by the molecular conditional two-electron probabilities in atomic resolution. Owing to the electron delocalization, the molecular information channels exhibit a chemical ‘noise’, which affects the transmission of the atom-assignment signals and the associated flow of information through the communication system. Several entropy/information concepts, including the conditional entropy, mutual information and information distance (cross-entropy, entropy deficiency), between the input and output probability distributions, are used to characterize the chemical bond and its covalent and ionic components. The conditional entropy and mutual information are identified as overall measures of the covalent and ionic bond components, respectively. Several reference input probabilities for probing different aspects of the chemical bond are examined. A distinction between the electron-sharing and the pair-sharing (coordination) bonds is explored and the entropic indices of the localized bonds are proposed. The average entropies of the local ‘stockholder’ communication channel, generated by the Hirshfeld partition of molecular electron densities, are proposed as complementary information descriptors of the chemical bond.