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On the accuracy of commonly used density functional approximations in determining the elastic constants of insulators and semiconductors

We have performed density functional calculations using a range of local and semi-local as well as hybrid density functional approximations of the structure and elastic constants of 18 semiconductors and insulators. We find that most of the approximations have a very small error in the lattice constants, of the order of 1\%, while the error in the elastic constants and bulk modulus are much larger, at about 10\%. In addition, we find that the error in the elastic constants, $c_{ij}$, are larger compared to the error in the bulk modulus. Depending on the functional and which error estimate that is being used, the difference in the error between the elastic constants and the bulk modulus can be rather large, about a factor of two. According to our study, the overall best performing density functional approximation for determining the structure and elastic properties is the PBEsol, closely followed by the two hybrid functionals PBE0 and HSE, and the AM05 functional.