Evidence for stable square ice from quantum Monte Carlo

Abstract

Recent experiments on ice formed by water under nanoconfinement provide evidence for a two-dimensional (2D) "square ice" phase. However, the interpretation of the experiments has been questioned and the stability of square ice has become a matter of debate. Partially this is because the simulation approaches employed so far (force fields and density functional theory) struggle to accurately describe the very small energy differences between the relevant phases. Here we report a study of 2D ice using an accurate wave-function based electronic structure approach, namely diffusion Monte Carlo (DMC). We find that at relatively high pressure, square ice is indeed the lowest enthalpy phase examined, supporting the initial experimental claim. Moreover, at lower pressures, a "pentagonal ice" phase (not yet observed experimentally) has the lowest enthalpy, and at ambient pressure, the "pentagonal ice" phase is degenerate with a "hexagonal ice" phase. Our DMC results also allow us to evaluate the accuracy of various density functional theory exchange-correlation functionals and force field models, and in doing so we extend the understanding of how such methodologies perform to challenging 2D structures presenting dangling hydrogen bonds. DOI: 10.1103/PhysRevB.94.220102 Recent transmission electron microscopy (TEM) measurements and classical molecular dynamics simulations report that a new two-dimensional (2D) square phase of ice forms [1]. This phase is not part of the bulk ice phase diagram, but it was suggested that it is stabilized under confinement because of lateral pressure, estimated to be in the gigapascal (GPa), arising from the van der Waals (vdW) attraction between the graphene sheets. However, these experiments have been questioned [2], with it even being suggested that it is sodium chloride contamination and not ice that is responsible for the square symmetry observed. So far, it is not clear under what conditions (if any) square ice is stable.Theoretical investigations of the stability of confined 2D ice at high lateral pressures can, in principle, help in disentangling this issue and in complementing experimental findings [3][4][5][6][7][8][9][10]. From a theoretical perspective, the prediction of square 2D ice can be traced back to Nagle's 1970's "unit model" of ice [3]. However, later atomistic force field (FF) simulations found that 2D ice prefers a buckled rhombic structure [4,5]. More recently, density functional theory (DFT) based investigations [6-9] have been performed. However, these have produced qualitatively different results depending on the precise details of the calculations and, in particular, on the choice of exchange-correlation (XC) functional. For instance, Chen et al. [7] found hexagonal and pentagonal structures to be stable phases at low pressures (Fig. 1). They also found that square ice is only stable in the GPa pressure * angelos.michaelides@ucl.ac.uk Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further...

Variational and diffusion quantum Monte Carlo calculations with the CASINO code

“…DMC methods have also been used to predict the phase diagram of water ice trapped between two graphene sheets, finding that the hexagonal and pentagonal phases that are most stable at ambient pressure transition to a square structure at higher pressure. 208 These results are of relevance to transmission electron microscopy studies of water confined between graphene sheets. Again, the DMC results reveal inconsistencies and the need for improvement of van der Waals-inclusive DFT functionals.…”

Complete steric exclusion of ions and proton transport through confined monolayer water

“…horizontal bar is the statistical error in determining V 0 using measurements for several monolayer devices. Inset: Square-like ice is one of the possible ices expected inside the 2D channels at room temperature, as found from molecular dynamics analyses 18,28,29 Proton transport can be probed more directly using Nafion instead of HCl (ref. 24).…”

Interaction between water and carbon nanostructures: How good are current density functional approximations?

“…The two-dimensional ice polymorphs have been constructed in Ref. 59 by confining a single water layer resulting in four stable polymorphs of hexagonal, pentagonal, square, and rhombic ice structures. The three bulk ice phases cover the subtle balance of the competing polymorphs Ih, II and the high-pressure form VIII.…”

“…The reference values for the 2-dimensional ice crystals are taken from Ref. 59, while for the three bulkice crystals are given in Ref. 54.…”