Entropic measures of bond multiplicity from the information theory

The entropic character of the bond multiplicity concept of chemistry is explored within the information theory. The probability schemes of finding a single and two electrons on specified atoms are used to formally interpret a molecule as the ''communication system. with the molecular or the separated atom input probabilities and the network of conditional two-electron probabilities in atomic resolution, which determine the molecular one-electron atomic probabilities, defining the system output probabilities. Several measures of uncertainties in such a molecular communication system are then introduced, including the average eutropies of the two-electron joint and conditional probabilities, as well as the average mutual information between the input and output probability schemes. The average entropy of the conditional probabilities between molecular input and output probability schemes is then identified as the information theoretic measure of the global covalent bond multiplicity in a molecule. Similarly, the global ionic bond order is found to be well reflected by the mutual information between molecular output and the atomic equiprobability input schemes. These identifications are tested by comparing the entropy predictions for the two- and three-orbital models and the pi bonds in butadiene and benzene (Huckel approximation) with the corresponding results from the earlier Wiberg-type and two-electron difference approaches. Finally, the bond entropy concept is introduced to provide a direct measure of the covalent bond component for each pair of atoms. It is demonstrated that this entropic bond order is in good agreement with both the chemical intuition and earlier predictions for all illustrative systems examined, thus providing a novel atrractive tool for chemical interpretation of calculated molecular electronic structures.