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

Amorphous ices are usually classified as belonging to low-density or high-density amorphous ice (LDA and HDA) with densities ρLDA ≈ 0.94 g/cm3 and ρHDA ≈ 1.15−1.17 g/cm3. However, a recent experiment crushing hexagonal ice (ball-milling) produced a medium-density amorphous ice (MDA, ρMDA ≈ 1.06 g/cm3) adding complexity to our understanding of amorphous ice and the phase diagram of supercooled water. Motivated by the discovery of MDA, we perform computer simulations where amorphous ices are produced by isobaric cooling and isothermal compression/decompression. Our results show that, depending on the pressure employed, isobaric cooling can generate a continuum of amorphous ices with densities that expand in between those of LDA and HDA (briefly, intermediate amorphous ices, IA). In particular, the IA generated at P ≈ 125 MPa has a remarkably similar density and average structure as MDA, implying that MDA is not unique. Using the potential energy landscape formalism, we provide an intuitive qualitative understanding of the nature of LDA, HDA, and the IA generated at different pressures. In this view, LDA and HDA occupy specific and well-separated regions of the PEL; the IA prepared at P = 125 MPa is located in the intermediate region of the PEL that separates LDA and HDA.

In the main manuscript, we compare the structure factor S(k) of the intermediate amorphous (IA) ices obtained by cooling at different pressures.Here, we focus on the location of the first-peak of S(k).Fig. S2 shows the location of the structure factor first-peak, k 1 (P ), of the equilibrium liquid at T = 240 K (magenta and green symbols) and the corresponding IA at T = 80 K (brown and blue symbols), as a function of pressure P and density ρ. k 1 (P ) shown in Fig. S2(a) increases with increasing pressure, with a pronounced but rather continuous increase as the IA evolve from LDA-like, at low cooling pressure, to HDA-like at higher pressures.Similarly, k 1 (ρ) [Fig.S2(b)] is a continuous function of the density, which indicates that k 1 (P ) exhibits no discontinuity for the IA states (since ρ(P ) is also a continuous function of P).

III. SUPPLEMENTARY NOTE 3
A. IR Spectra Figs.S3(a) and S3(b) show magnifications of the IR spectra for the IA included in Fig. 1(h), for the frequency ranges (i) ω < 1800 cm −1 and (ii) ω > 3000 cm −1 .The changes in the IR spectra with increasing cooling pressures are rather mild and are not inconsistent with experiments.For comparison, we show in Fig. S3(c) the IR spectra of the IA in the OH stretching region [ω > 3000 cm −1 ] together with the corresponding experimental data for LDA and HDA reported in Refs.[2,3].The experimental IR spectra are shifted by δω = +200 cm −1 .Nonetheless, in both cases, we see that the IR maximum in Fig. S3(c) shifts towards large frequencies as the system evolves from LDA to HDA.

IV. SUPPLEMENTARY NOTE 4 A. Structural Changes in the IA During Decompression
Here, we compare the structure of the IA produced at T = 80 K (i) after isobaric cooling at pressure P > 0, and (ii) after further isothermal decompression from the corresponding cooling P down to P = 0.1 MPa (at T = 80 K).Fig. S4 shows the OO radial distribution function, structure factor S(k), and infrared spectra of the IA at T = 80 K and prepared at P = 100, 400, 1000 MPa.The studied structural properties of the IA before (solid lines) and after the isothermal decompression (dashed-lines) are barely affected.

V. SUPPLEMENTARY NOTE 5
A. Compression rate dependence: q P = 10, 100 MPa/ns In this section, we study the effects of varying the compression/decompression rate, q P , on the PEL properties sampled by the system during the pressure-induced LDA-HDA transformations at T = 80 K. Specifically, we compare the evolution of the IS energy, IS pressure, and shape function (E IS , P IS , and S) during the LDA-HDA transformation with compression/decompression rates q P = 10, 100 MPa/ns.As shown in Fig. S5, the values of E IS (ρ), P IS (ρ), and S(ρ) during the pressure-induced LDA-HDA transformation with compression FIG. S1.Comparison of MD simulations results obtained for systems composed of N = 512 [solid lines, taken from Figs. 1 and 3(a) of the main manuscript] and N = 5118 [dashed lines] water molecules (cooling rate q T = 10 K/ns; compression/decompression rate q P = 100 MPa/ns).(a) Density of q-TIP4P/F water during isobaric cooling at P = 0.1, 100, 125, 200, 400, 600, 800 and 1000 MPa (dots, bottom-to-top) from T = 240 down to 0 K; three independent runs are included for each pressure.Size effects are negligible within the fluctuations among the three runs performed at a given pressure and N .Fluctuations at a given cooling pressure, among the corresponding three independent runs, are reduced with increasing N -except for P = 125 MPa and in the proximity of the LLCP in q-TIP4P/F water.(b) Density of the IA at T = 80 K produced during the isobaric cooling runs included in (a).Inset: fraction of LDA molecules in the IA states included in the main panel.(c)(d) OO RDF of water in the equilibrium liquid (c) and amorphous ice states (d) included in (b).(e)(f) Structure factor S(k) of the liquid and amorphous ices included in (c) and (d), respectively.(g) Isothermal compression-induced LDA-to-HDA transformation at T = 80 K followed by the isothermal decompression of HDA from P = 2000 MPa to negative pressures (T = 80 K).Red lines are from Fig. 3(a) in the main manuscript for the case N = 512; dashed lines are from MD simulations with N = 5118.In all panels, system size effects are negligible.
FIG. S4.(a) OO radial distribution function, (b) structure factor S(k), and (c) infrared spectra of the IA at T = 80 K.The solid lines are the results for the IA at their preparation pressure P = 100 (blue), 400 (magenta), and 1000 MPa (maroon); the dashed-lines are for the IA after their further isothermal decompression (T = 80 K) to P = 0.1 MPa.The structural changes in the IA induced by the decompression process are minor, if any.