  In this letter, we study the higher-order effect on the third-order elastic
constants (TOECs) of diamond using longitudinal stress-uniaxial strain (LSUS)
approach based on density functional theory. The result shows that the
higher-order effect on TOECs is not negligible in the shock wave experiments
and similar calculations. By taking the higher-order elastic response (up to
fifth order) into consideration, the convergence of TOECs against maximum stain
gets improved significantly and resolves the discrepancy of several different
theoretical methods and experiments.
