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

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