Analytical and Parameter-Free Hückel Theory Made Possible for Symmetric H x Clusters.

It is widely accepted that energetics of chemical bond breaking and formation can be described with simple mathematical forms only at the expense of extensive parameterization. In this work, the discovery of a simple tight-binding-type mathematical framework that can accurately predict the relative energetics of regular H x polygons (2 ≤ x ≤ 15) in the ground states with their respective spin multiplicities using no parameters has been reported. The framework recasts Hückel theory in a density functional theory form by making use of Anderson and Adams-Gilbert theories of localized orbitals. For the systems examined, the method exhibits mean absolute errors of ∼0.02 Å (edge lengths) and ∼0.15 eV/atom (energy minima) relative to correlated-electron quantum chemistry calculations. Its accuracy is found to be comparable to the generalized gradient approximation and superior to standard parameterized tight binding and reactive potentials applied to H x structures. Generalization of the theoretical framework to systems of many-electron atoms is presented, along with the comparison of the method to existing semiempirical tight binding and bond order potential approaches.