A density-matrix adaptation of the Hückel method to weak covalent networks

The coupled-monomers model is built as an adaptation of the Hückel MO theory based on a self-consistent density-matrix formalism. The distinguishing feature of the model is its reliance on variable bond and Coulomb integrals that depend on the elements of the density matrix: the bond orders and partial charges, respectively. Here the model is used to describe electron reactivity in weak covalent networks X_n^±, where X is a closed-shell monomer. Viewing the electron as the simplest chemical reagent, the model provides insight into charge sharing and localisation in chains of such identical monomers. Data-driven modelling improves the results by training the model to experimental or ab initio data. Among key outcomes is the prediction that the charge in X_n^± clusters tends to localise on a few (2-3) monomers. This is confirmed by the properties of several known cluster families, including He_n⁺, Ar_n⁺, (glyoxal)_n^?, and (biacetyl)_n^?. Since this prediction is obtained in a purely coherent covalent regime without any thermal excitation, it implies that charge localisation does not require non-covalent perturbations (such as solvation), decoherence, or free-energy effects. Instead, charge localisation is an intrinsic feature of weak covalent networks arising from their geometry relaxation and is ultimately attributed to the correlation between covalent bond orders and equilibrium bond integrals.