Equivalent C-C bonding element for representing the force-energy relation of carbon-carbon covalent bond

Based on the quadratic potential function of C-C bond from the Born-Oppenheimer approximation, the stretching along the bond axis and the rotating in the σ or π plane of C-C bond are analyzed. With the linearly elastic theory near the origin equilibrium position, the balance equations are expressed through the displacements of atomic nuclei. Based on the defined six degree of freedoms of two atoms on a C-C covalent bond, an equivalent C-C bonding element is constructed. The C-C bonding element can characterize the three properties of covalent bond: length, angle and energy, when it is used to model the hexagonal structure of crystal carbon. The force constants of C-C bonding element have been obtained through calculation and comparison with the experimental results of the graphite and C₆₀ molecular vibration (Raman spectrum). The tensile modulus of carbon nanotube is investigated by the C-C bonding element, and reasonable results have been obtained, which implies that the C-C bonding element can provide an effective method for large-scale calculations of molecular mechanics.