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

  • ️Sun Jan 01 2023

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

Ali Eltareb et al. J Phys Chem B. 2023.

Abstract

We study the nuclear quantum effects (NQE) on the thermodynamic properties of low-density amorphous ice (LDA) and hexagonal ice (Ih) at P = 0.1 MPa and T ≥ 25 K. Our results are based on path-integral molecular dynamics (PIMD) and classical MD simulations of H2O and D2O 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 Ih. While MD simulations (no NQE) predict that the density ρ(T) of LDA and ice Ih increases monotonically upon cooling, PIMD simulations indicate the presence of a density maximum in LDA and ice Ih. MD and PIMD simulations also predict a qualitatively different T-dependence for the thermal expansion coefficient αP(T) and bulk modulus B(T) of both LDA and ice Ih. Remarkably, the ρ(T), αP(T), and B(T) of LDA are practically identical to those of ice Ih. The origin of the observed NQE is due to the delocalization of the H atoms, which is identical in LDA and ice Ih. 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.

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Conflict of interest statement

The authors declare no competing financial interest.

Figures

Figure 1.
Figure 1.

Density ρ(T) of H2O at P=0.1MPa from (a) PIMD and (b) classical MD simulations using the q-TIP4P/F water model. Green circles are the densities of water in the equilibrium liquid state; red circles are the densities upon cooling liquid water from T=240K into the glass (LDA) state using a cooling rate of qT=10K/ns. The magenta and orange squares are the experimental densities of LDA from refs and . The blue circles are the densities of q-TIP4P/F water in the ice Ih state; the brown circles are the experimental densities of ice Ih reported in ref . While the densities of LDA and ice Ih are remarkably well reproduced by the PIMD simulations in (a), classical MD simulations overestimate considerably the corresponding densities. PIMD simulations (which include NQE) are consistent with the presence of a very weak density maximum in LDA and ice Ih. A very weak density maximum is also present in the experimental data of ice Ih (brown circles).

Figure 2.
Figure 2.

(a) Thermal expansion coefficient αP(T) and (b) bulk modulus B(T) of ice Ih and during the liquid-to-LDA transformation at P=0.1MPa. Results are from PIMD (red lines) and classical MD simulations (blue lines). Dashed-lines are the results for H2O during the isobaric cooling process from T=240K (liquid) into the LDA state (qT=10K/ns). The solid lines correspond to H2O in the equilibrium ice Ih state. For comparison, also included are the experimental values of αP(T) and B(T) for H2O ice Ih (brown circles) from refs and . Only the PIMD simulations (which include NQE) are able to reproduce approximately the behavior of αP(T) and B(T) for ice Ih. B(T) is calculated using eq 3; the orange square in (b) corresponds to the value of B(T) at T=125K obtained using eq 2.

Figure 3.
Figure 3.

(a), (c), and (e) are the oxygen−oxygen, oxygen−hydrogen, and hydrogen−hydrogen RDF of H2O for LDA. (b), (d), and (f) are the OO, OH, and HH RDF of H2O for ice Ih at T=80K and P=0.1MPa. Red and blue lines are the RDF obtained from PIMD and MD simulations, respectively, using the q-TIP4P/F model for water; black lines in (a) and (b) are the experimental OO RDF from ref (ice Ih) and ref (LDA). The inclusion of NQE reduces the maxima in the OO, OH, and HH RDF, leading to a less structured LDA and ice Ih.

Figure 4.
Figure 4.

(a) Tetrahedral order parameter 〈q(T)〉, and (b) 〈dfs(T)〉 order parameter, for H2O at P=0.1MPa. Circles are the order parameters for ice Ih; lines are the order parameters upon cooling the equilibrium liquid from T=240K into the glass state (LDA) using a cooling rate of qT=10K/ns. Red and blue colors are results from PIMD and MD simulations using the q-TIP4P/F model for water. The similar values of 〈q(T)〉 and 〈dfs〉 in the MD and PIMD simulations suggest that the inclusion of NQE on the local order of water are rather weak.

Figure 5.
Figure 5.

(a) Average distance between two oxygen atoms forming a hydrogen-bond, 〈dOOHB(T)〉, as a function of temperature and at P=0.1MPa. Circles are the 〈dOOHB(T)〉 for ice Ih; lines are the 〈dOOHB(T)〉 for water upon cooling the equilibrium liquid from T=240K into the glass state (LDA) using a cooling rate qT=10K/ns. Red and blue colors are results from PIMD and classical MD simulations using the q-TIP4P/F model for water. Experimental values of dOOOHB(T) in LDA from IR spectroscopy experiments are indicated by black squares (from ref 62).(b) Average HOO angle formed between two hydrogen-bonded watermolecules, 〈θHOOHB(T)〉, as a function of temperature at P=0.1MPa. Same symbols and colors as in (a) are used. The inclusion of NQE leads to slightly longer hydrogen-bond lengths (larger 〈dOOHB(T)〉) and less linear hydrogen-bonds (larger 〈θHOOHB(T)〉) than predicted by classical MD simulations.

Figure 6.
Figure 6.

Delocalization of the O and H atoms in ice Ih and during the isobaric cooling of liquid water into LDA (P=0.1MPa). Results are from classical MD and PIMD simulations using the q-TIP4P/F water model. (a) Schematic diagram showing a water molecule and the corresponding reference frame used in (b)−(d). For a given water molecule, the reference frame origin is located on the O centroid. R→OHj is the vector pointing from the O centroid to the centroid of Hj(j=1,2). The x-, y-, and z-axis are defined as indicated in the figure. (b) Radius of gyration Rg(T) of the ring-polymers associated with the O and H atoms as a function of temperature. Red and blue lines are the Rg(T) for the H and O during the cooling process from T=240K (liquid state) to T=25K (LDA) using a cooling rate qT=10K/ns; the red and blue triangles are the Rg(T) of the O and H in ice Ih. The delocalization of the O and H atom is identical for water in the liquid/LDA and ice Ih states, probably due to the similar local structure. O and H atoms are more delocalized in the low-density vapor state (magenta triangles), particularly at low temperatures. (c, d) Delocalization of the ring-polymers associated with the O and H1 atoms along the x- and z-axis, respectively (similar results are obtained along the y- and z-axis). Rg,x2 and Rg,z2 are the x- and z-radius of gyration (see text). Same symbols as in (b) are used. For the O atoms, Rg,x2≈Rg,z2, meaning that the O delocalization is isotropic. Instead, for the H1 atoms, Rg,z2>Rg,x2, i.e., the H atoms are more delocalized along the directions perpendicular to the corresponding OH covalent bonds than along the OH bond direction; see Figure 7.

Figure 7.
Figure 7.

Snapshots of an H2O molecule obtained from PIMD simulations of ice Ih at P=0.1MPa and T = 25, 80, 150, and 250 K (similar results hold for H2O in the LDA state, see Figure S3 of the SI). In (a)−(d), the water molecule is laying on the x-y plane defined in Figure 6a. The O and H ring-polymer beads are shown by small red and white spheres, respectively; all ring-polymers are composed of nb=128. (e−h) Snapshot of the water molecule shown in (a)−(d), showing the O atom and only one of the H atoms; the view is along the corresponding OH covalent bond. The delocalization of the O atom is rather isotropic, i.e., the red cloud of ring-polymer beads is rather spherical. The delocalization of the H atoms is anisotropic; the white cloud of ring-polymer beads are spread preferentially along the directions perpendicular to the OH covalent bond direction (than along the OH covalent bond direction). Similar results are also obtained for D2O in ice Ih and LDA, see Figures S10 and S12 of the SI.

Figure 8.
Figure 8.

Contour maps for the probability distribution to find a ring-polymer bead. P=0.1MPa and T = 25, 80, 150, and 250 K. (a)−(d) Ring-polymer bead probability distribution associated with the O (top) and H (bottom) atoms in ice Ih (similar results hold for the case of LDA, see Figure S4 of the SI); see also Figure 6a–d. Contour maps are projected on the x-y plane shown in Figure 6a; see also Figure 7a–d. (e)−(h) are the contour maps for the probability distribution associated with the H atoms projected on the plane perpendicular to the corresponding OH covalent bond (i.e., viewed along the OH covalent bond; see also Figure 7e–h). All probability distributions are averaged over time and over all atoms in the system. Similar results are obtained for D2O in the ice Ih and LDA states; see Figures S11 and S13 in the SI.

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