Interatomic forces breaking carbon-carbon bonds

We compare computational methods for determining the force between carbon atoms as a function of bond length, in order to establish which ones are capable of accurately simulating carbon-carbon bonds breaking due to applied mechanical strain in nanomaterials. Results from Tight-binding, density-functional theory and molecular mechanics potentials are compared to Møller-Plesset perturbation theory and complete-active-space self-consistent-field method through application to bond breaking in small molecules. Of the two molecular mechanics and three tight-binding parameter sets chosen only DFTB3 gives results which are broadly similar to those from the first-principles methods; the others fail to give physically meaningful variation of the forces with internuclear separation. This method and the molecular mechanics potentials are then applied to a periodic carbon nanoribbon under tensile strain. The molecular mechanics methods fail even qualitatively to reproduce the single catastrophic failure shortly after the peak stress indicated by DFTB3. This shows the importance of the electronic behaviour for the carbon-carbon interatomic forces relevant to the determination of the mechanical strength of materials at atomic-length scales.