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 Hx 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 Hx 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.