Importance of zero-point energy for crystalline ice phases: A comparison of force fields and density functional theory.

Density functional theory (DFT) including van der Waals (vdW) interactions and accounting for zero-point energy (ZPE) is believed to provide a good description of crystalline ice phases [B. Pamuk et al., Phys. Rev. Lett. 108, 193003 (2012)]. Given the computational cost of DFT, it is not surprising that extensive phonon calculations, which yield the ZPE, have only been done for a limited amount of ice structures. Computationally convenient force fields on the other hand are the method of choice for large systems and/or dynamical simulations, e.g., of supercooled water. Here, we present a systematic comparison for seven hydrogen-ordered crystalline ice phases (Ih, IX, II, XIII, XIV, XV, and VIII) between many commonly used nonpolarizable force fields and density functionals, including some recently developed meta-GGA functionals and accounting for vdW interactions. Starting from the experimentally determined crystal structures, we perform space-group-constrained structural relaxations. These provide the starting point for highly accurate phonon calculations that yield effectively volume-dependent ZPEs within the quasiharmonic approximation. In particular, when including ZPE, the force fields show a remarkably good performance for equilibrium volumes and cohesive energies superior to many density functionals. A decomposition of the cohesive energies into intramolecular deformation, electrostatic, and vdW contributions quantifies the differences between force fields and DFT. Results for the equilibrium volumes and phase transition pressures for all studied force fields are much more strongly affected by ZPE than all studied density functionals. We track this down to significantly smaller shifts of the O-H-stretch modes and compare with experimental data from Raman spectroscopy.