Ab initio thermodynamics of liquid and solid water

TL;DR

It is shown that nuclear-quantum effects contribute a crucial 0.2 meV/H2O to the stability of ice Ih, making it more stable than ice Ic, and the ab initio description leads to structural properties in excellent agreement with experiments and reliable estimates of the melting points of light and heavy water.

Abstract

Thermodynamic properties of liquid water as well as hexagonal (Ih) and cubic (Ic) ice are predicted based on density functional theory at the hybrid-functional level, rigorously taking into account quantum nuclear motion, anharmonic fluctuations and proton disorder. This is made possible by combining advanced free energy methods and state-of-the-art machine learning techniques. The ab initio description leads to structural properties in excellent agreement with experiments, and reliable estimates of the melting points of light and heavy water. We observe that nuclear quantum effects contribute a crucial 0.2 meV/H$_2$O to the stability of ice Ih, making it more stable than ice Ic. Our computational approach is general and transferable, providing a comprehensive framework for quantitative predictions of ab initio thermodynamic properties using machine learning potentials as an intermediate step.

Figures (7)

• Figure 1: Classical (CL) and quantum (Q) density isobars for ice Ic, ice Ih, and liquid water (L) at $P=1$ bar computed via (PI)MD simulations using the NN potential. The predicted densities of ice Ic and Ih almost overlap both at the quantum and the classical level. The experimental results for undercooled water are taken from Ref. hare1987density.
• Figure 2: Oxygen-oxygen, oxygen-hydrogen, and hydrogen-hydrogen radial distribution functions (RDF) at 300 K and experimental density computed via (PI)MD simulations in the NVT ensemble using the NN potential. The experimental O-O RDF was obtained from Ref skinner2014structure, and the experimental O-H and H-H RDFs were taken from Ref. soper2000radialchen2016ab.
• Figure 3: The difference in the chemical potential $\Delta\mu_{\textrm{NN}} \equiv \mu - \mu_{\textrm{NN}}$ between revPBE0-D3 and NN-based MD simulations at $P=1~\textrm{bar}$. Standard errors of the mean are indicated by the error bars. The violet (green) crosses indicate the results from 16 different 64-molecule proton-orderings of Ic (Ih). The violet (green) line shows the average $\Delta\mu_{\textrm{NN}}$ across proton-orderings.
• Figure 4: Temperature dependence of the chemical potential difference between ice Ih and Ic at 1 bar. The errors associated with the classical and quantum-mechanical revPBE0-D3 values arise predominantly from the differences in $\Delta\mu_{\textrm{NN}}$ between different proton-orderings.
• Figure 5: Temperature dependence of the chemical potential difference between liquid water and ice Ih at 1 bar. Blue crosses indicate $\Delta \mu^{\text{L}\rightarrow\text{Ih}}_{\text{cl,NN}}$ from independent interface pinning simulations, and the blue dashed line indicates the best fit of these results to the TI expression in Eqn \ref{['eq:ti-T']}. The experimental values were calculated from the heat capacities reported in Ref. haji2015direct.