A graph-based statistical model for carbon nanostructures

Energy degeneracy in physical systems may be induced by symmetries of the Hamiltonian, and the resonance of degeneracy states in carbon nanostructures can effectively enhance the stability of the system. Combining the octet rule, we introduce a statistical model to determine the physical properties by lifting the energy degeneracy in carbon nanostructures. This model offers a direct path to accurately ascertain electron density distributions in quantum systems, akin to how charge density is used in density functional theory to deduce system properties. Our methodology diverges from traditional quantum mechanics, focusing instead on this unique statistical model by maximizing bonding entropy to determine the fundamental properties of materials. Applied to carbon nanoclusters and graphynes, our model not only precisely predicts bonding energies and electron density without relying on external parameters but also enhances the prediction of electronic structures through bond occupancy numbers, which act as effective hopping integrals. This innovation offers insights into the structural properties and quantum behavior of electrons across various dimensions.