In this letter, we investigated the higher-order effect on third-order elastic constants (TOECs) of diamond using longitudinal stress-uniaxial strain (LSUS) approach based density functional theory. The result shows that TOECs is not negligible in shock wave experiments and similar calculations, errors are about 28% (C111), 43% (C112), 121% (C123), 486% (C144), 56% (C155) 75% (C456). By taking ...