Ab initio theory and modeling of water

Abstract

Water is of the utmost importance for life and technology. However, a genuinely predictive ab initio model of water has eluded scientists. We demonstrate that a fully ab initio approach, relying on the strongly constrained and appropriately normed (SCAN) density functional, provides such a description of water. SCAN accurately describes the balance among covalent bonds, hydrogen bonds, and van der Waals interactions that dictates the structure and dynamics of liquid water. Notably, SCAN captures the density difference between water and ice Ih at ambient conditions, as well as many important structural, electronic, and dynamic properties of liquid water. These successful predictions of the versatile SCAN functional open the gates to study complex processes in aqueous phase chemistry and the interactions of water with other materials in an efficient, accurate, and predictive, ab initio manner.

Keywords: ab initio theory; density functional theory; hydrogen bonding; molecular dynamics; water.

Fig. 1.

RDFs (A) goo(r) and (B) goh(r) of liquid water predicted by PBE and SCAN at 330 K, as well as that from X-ray diffraction experiments (5) for goo(r) and joint X-ray/neutron diffraction experiments (4) for goh(r). An elevated temperature of 30 K was used in AIMD simulations to mimic NQEs (35).

Fig. 2.

(A) DOS of liquid water, averaged over SCAN and PBE trajectories, as well as from photoemission spectroscopy (43). The peaks are labeled according to the symmetric orbitals of a water molecule with $C_{2v}$ symmetry. Data are aligned (44) to the $1b_1$ peak of the experimental (EXP) data. (B) Distributions of the centers of maximally localized Wannier functions (MLWFs) with respect to the oxygen position for lone and bonding electron pairs. Inset shows a representative snapshot of the MLWFs of a water molecule; lone and bonding pair MLWFs are colored green and blue, respectively.

Fig. S1.

Density fluctuations of liquid water and ice Ih as obtained from both SCAN and PBE trajectories using the isobaric-isothermal ensemble (NpT). A relatively shorter trajectory was generated for ice Ih because its density of solid phase converges quickly. The PBE functional incorrectly predicts that ice Ih (green line) is denser than water (orange line), while the SCAN functional successfully captures the larger density of water (blue line) than that of ice Ih (pink line). The black dashed and dotted lines represent the approximate experimental values of water density at ambient conditions (300 K) and ice density at 273 K under ambient pressure. An additional 30 K was applied to water to mimic the NQE (35). The averaged densities are listed Table 1.

Fig. 3.

(A) Distributions of the number of hydrogen bonds in liquid water from SCAN and PBE. Inset illustrates an ideal tetrahedral H-bonding structure. Oxygen and hydrogen atoms are respectively depicted in red and white; H bonds are shown with dashed lines. (B and C) Bond angle distributions $P_{\mathrm{OOO}}(\theta )$ from (B) PBE and (C) SCAN. $P_{\mathrm{OOO}}(\theta )$ is decomposed into contributions arising from waters with a fixed number of HBs (2, 1, and 0) between a central oxygen and its two nearest neighbors. The experimental $P_{\mathrm{OOO}}$ of ${\text{D}}_2$O is inferred from experiments (4), and the area of $P_{\mathrm{OOO}}$ is normalized to unity. (D and E) Free energies ($F$) as a function of $\theta$ and the oxygen–oxygen distance $r$ from (D) PBE and (E) SCAN. The free energy minimum is identified by the red circle and referenced to zero. The direction of change of the free energy minimum with increasing $r$ is shown with a red arrow. The cutoff distance used for computing the free energies is the same as that for $P_{\mathrm{OOO}}$ and is shown with a dashed red line.

Fig. S2.

MSDs for the SCAN and PBE systems consisting of 64 water molecules. Shaded regions indicate one SE.

Fig. S3.

Second-order rotational time correlation functions, $C_2(t)$, for the O–H bond vector of water as described by SCAN and PBE. B is the same as A, but zoomed in on the region from 0 to 0.5 ps.

Fig. S4.

Oxygen–oxygen RDFs $g_{\mathrm{OO}}(r)$ for 32 water molecules in condensed phase as obtained from the SCAN functional implemented in Vienna Ab initio Simulation Package (VASP) and Quantum ESPRESSO electronic structure packages.

Fig. S5.

Zoomed-in RDF $g_{OH}$ (as shown in Fig. 1B) as obtained from SCAN- and PBE-based AIMD simulations.