**9. Application**

In spite of the significance of diamond and silicon, there's still a need for solid hypothetical and exploratory information on the elastic constants of these materials, in specific on the versatile constants of the third-order. This lack of experimental data limits the capacity of researchers to create modern materials with a focus on mechanical reactions. Besides, this lack triggered interest in other theoretical calculations. M. Barhoumi et al. [18] have proposed to calculate the elastic properties with different approximations of DFT and beyond with ACFDT in RPA, since the RPA has significant advantages, especially for those interested in functional density theory. It correctly describes the dispersion and van der Waals interactions. In this direction, they have found that the results obtained with RPA are in good agreement with the previous published [19–33]. Also, it should be noted that from the calculated elastic constants, other structural properties such as elastic modulus, shear modulus, Young's modulus and Poisson's ratio can be derived.
