Entropic bond indices from molecular information channels in orbital resolution: excited configurations

Abstract

The communication approach of Information Theory (IT) to chemical bonds is extended to cover the excited electron configurations within the standard orbital description of the molecular electronic structure. The non-projected AO-promotion channels for excited electronic states, involving probability scattering via the configuration occupied molecular orbitals, do not reflect the bond-order reduction upon electron excitation from the ground-state. The superposition principle of quantum mechanics is coupled with the occupation-weighed orbital projections in the molecular Hilbert space, to generate the system projected information channels reflecting for the given excited electron configuration the effective promotion of bonded atoms relative to the ground and/or other electronic states. The orbital subspaces of the configuration of interest may include the common part or the orthogonal complement of the orbital spaces of other configurations. The orbital projectors are defined for several subspaces of interest in the theory of the IT bond indices in excited electron configurations. The conditional probabilities determining the AO promotion in the projected orbital subspaces are discussed and their information/entropy descriptors of the covalent/ionic components of the system chemical bonds are examined. It is shown that by an appropriate conditioning of orbital probabilities in one configuration, with respect to the specified reference configurations, which may include the ground-state, one accounts for the effects of their mutual orthogonality and extracts useful IT bond-multiplicity descriptors reflecting fractions of the ground-state bond-order, which survive or are being lost as a result of electron excitations. This orbital probability conditioning is directly related to the associated projection in the orbital Hilbert space of the molecule. For such projected information channels the bond indices of the conditional-entropy (IT-covalency) and mutual-information (IT-ionicity) are generated to examine the effect of the diminished IT bond-order in several excited configurations of the two-orbital model of a single chemical bond and in selected π-electron systems (allyl, butadiene and benzene) in the Hückel approximation. These model systems have been used in the past to validate the IT bond descriptors of the ground-state systems.