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

Abstract

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.

Calorimetric Signature of Deuterated Ice II: Turning an Endotherm to an Exotherm

“…The computational setup is almost identical to the one used in ref ( 27 ). Briefly, the q-TIP4P/F water model 23 has been evaluated using the Atomic Simulation Environment (ASE) 43 with the Lammps code 44 via the available calculator, whereas a new calculator has been implemented in order to interface with the MB-pol model as developed and implemented by the Paesani group.…”

“…We found in previous work that including zero-point energy (ZPE) with q-TIP4P/F provides a very good description of experimental data for a plethora of different crystalline ice phases—outperforming several density functionals despite its simplicity. 27 Here, we also included the state-of-the-art polarizable many-body force field MB-pol given its excellent description of vibrational properties of ice. 28 , 29 …”

Transferable Potential Function for Flexible H$_2$O Molecules Based on the Single Center Multipole Expansion

“…102 Additionally, the ZPE energies are obtained with the Parlinski-Li-Kawazoe finite-displacement method, 103 as used in the previous work. 104 For further validation of the new flexible model and parameterization based on the scheme below the relative energy differences of all higher lying isomers of the pentamers and hexamers are calculated, which are not included in the fitting data set, and compared to the relative energies from the quantum chemistry references. 99,100 The rigid SCME is shown for comparison.…”

Accurate Water Properties from an Efficient ab Initio Method

“…Calculated and experimental equilibrium volumes ( Å3 /H2O) of different phases of ice. The zero-point-energy106 corrected experimental and DMC values are taken from Ref 105. .…”