The Importance of Nuclear Quantum Effects on the Thermodynamic and Structural Properties of Low-Density Amorphous Ice: A Comparison with Hexagonal Ice

Abstract

We study the nuclear quantum effects (NQE) on the thermodynamic properties of low-density amorphous ice (LDA) and hexagonal ice (I h ) at P = 0.1 MPa and T ≥ 25 K. Our results are based on path-integral molecular dynamics (PIMD) and classical MD simulations of H 2 O and D 2 O using the q-TIP4P/F water model. We show that the inclusion of NQE is necessary to reproduce the experimental properties of LDA and ice I h . While MD simulations (no NQE) predict that the density ρ(T) of LDA and ice I h increases monotonically upon cooling, PIMD simulations indicate the presence of a density maximum in LDA and ice I h . MD and PIMD simulations also predict a qualitatively different Tdependence for the thermal expansion coefficient α P (T) and bulk modulus B(T) of both LDA and ice I h . Remarkably, the ρ(T), α P (T), and B(T) of LDA are practically identical to those of ice I h . The origin of the observed NQE is due to the delocalization of the H atoms, which is identical in LDA and ice I h . H atoms delocalize considerably (over a distance ≈ 20−25% of the OH covalent-bond length) and anisotropically (preferentially perpendicular to the OH covalent bond), leading to less linear hydrogen bonds HB (larger HOO angles and longer OO separations) than observed in classical MD simulations.

A continuum of amorphous ices between low-density and high-density amorphous ice

“…Indeed, for classical glasses, the density at low temperatures varies linearly with T (see refs. 31 , 41 , 42 ). It follows from Fig.…”

“…The corresponding thermodynamic states at which the system departs from equilibrium are indicated by LDL1 and LDL2. The system vitrifies at lower temperatures below which ρ increases linearly with T upon further cooling (note that nuclear quantum effects can weaken the T -dependence of the density in amorphous ices 41 ). At this low pressure, depending on the cooling rate, the final amorphous ice formed at T = 80 K may ( q 1 ) or may not ( q 2 ) be located within the coexistence region.…”

“…The q-TIP4P/F water model incorporates intramolecular flexibility by modeling the O-H covalent bond potential energy with a fourth-order polynomial expansion of a Morse potential and a simple harmonic potential to model the potential energy of the HOH angle. The q-TIP4P/F water model has been optimized to be used in path-integral molecular dynamics (PIMD) simulations and it reproduces remarkably well the properties of liquid water 71 , 77 , 78 as well as ice I h and LDA at P = 0.1 MPa 41 , 79 . At low pressures and approximately T > 150 K, differences in many of the thermodynamic (e.g., density, isothermal compressibility), structural (e.g., radial distribution functions), and dynamic properties (e.g., diffusion coefficient) of liquid water obtained from PIMD simulations and classical MD simulations are minor, if any 41 , 77 .…”

“…The q-TIP4P/F water model has been optimized to be used in path-integral molecular dynamics (PIMD) simulations and it reproduces remarkably well the properties of liquid water 71 , 77 , 78 as well as ice I h and LDA at P = 0.1 MPa 41 , 79 . At low pressures and approximately T > 150 K, differences in many of the thermodynamic (e.g., density, isothermal compressibility), structural (e.g., radial distribution functions), and dynamic properties (e.g., diffusion coefficient) of liquid water obtained from PIMD simulations and classical MD simulations are minor, if any 41 , 77 . This is due to the approximate cancellation of competing quantum effects in q-TIP4P/F water 71 .…”

The Harmonic and Gaussian Approximations in the Potential Energy Landscape Formalism for Quantum Liquids

“…Understanding the behavior of liquids at low temperatures, close to their glass transition temperature, and understanding the nature of the associated glass state have been fundamental issues in material science for many decades. − Numerous theoretical/computational approaches have been proposed to address these issues. ,− In most of these approaches, the focus is on classical liquids and glasses, where nuclear quantum effects (NQEs) are neglected. While this is justified in the case of high-temperature glass-formers, such as silica, the role of atom delocalizations due to NQEs cannot be ignored in substances composed of light elements, such as H 2 and He, as well as in liquids/glasses composed of small molecules containing H, including water. , The case of water is a clear example since computer simulations show that NQE can alter the thermodynamic properties of crystalline and amorphous ice (glassy water) at cryogenic temperatures …”