Comparative first-principles study of elastic constants of covalent and ionic materials with LDA, GGA, and meta-GGA functionals and the prediction of mechanical hardness

Accurate prediction of single-crystal elastic constants is critical for materials design and for understanding phase transition and elastic interactions in materials. In this work, the accuracy of elastic constants calculated with three density functional approximations has been compared, including the local density approximation (LDA), the generalized gradient approximation (GGA), and the recently developed strongly constrained and appropriately normed (SCAN) meta-GGA. The results show that SCAN and PBE describe elastic constants better than LDA. The strong correlation between the mechanical hardness and the stiffness of the softest eigenmode (SSE) has been given for above three density functionals. The correlation is capable of predicting accurately the hardness of covalent, ionic, and mixed covalent-ionic crystals, and providing us a convenient indicator for the discovery of hard or superhard materials.