Density-functional theory prediction of the elastic constants of ice I_h

We assess the elastic stiffness constants of hexagonal proton-disordered ice I_h as described by density-functional theory calculations. Specifically, we compare the results for a set of nine exchange-correlation functionals, including standard generalized-gradient approximations (GGAs), the strongly constrained and appropriately normed (SCAN) metaGGA functional, and a number of dispersion-corrected versions based on the van der Waals (vdW) and VV10 schemes. Compared to the experimental data, all functionals predict an excessively stiff response to tensile and compressive distortions, as well as shear deformations along the basal plane, with the SCAN metaGGA functional displaying the largest deviations as compared to the experimental values. These discrepancies are found to correlate with underestimates of inter-molecular distances, on the one hand, and overestimates of intra-molecular separations, on the other. The inclusion of non-local vdW corrections according to the vdW approach generally improves these structural parameters and softens the elastic response functions compared to their parent GGA functionals. The dispersion-corrected SCAN-rVV10 functional, however, acts in the opposite direction, further worsening the comparison to experiment. In this view, it appears useful that the database employed to gauge the quality of exchange-correlation functionals for water includes an assessment of their elastic response of ice I_h and possibly other crystalline phases.