A parameter-free statistical model for two-dimensional carbon nanostructures

TL;DR

This paper introduces a parameter-free statistical model that predicts the properties of two-dimensional carbon nanostructures by lifting energy degeneracy, providing accurate electron density and bonding energy predictions without external parameters.

Contribution

The model uniquely combines the octet rule with a statistical approach to determine properties of carbon nanostructures, diverging from traditional quantum mechanics methods.

Findings

Accurately predicts bonding energies and electron densities in carbon nanostructures.

Enhances electronic structure predictions through bond occupancy numbers.

Provides insights into quantum behavior of electrons in 2D carbon materials.

Abstract

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 parameter-free 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 minimizing bonding free energy 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.