An ultralow-density porous with the largest internal cavity identified in the phase diagram

Yuan Liua,b,1, Yingying Huangc,d,1, Chongqin Zhub,e,f, Hui Lia, Jijun Zhaod, Lu Wangg,2, Lars Ojamäeh, Joseph S. Franciscob,e,f,2, and Xiao Cheng Zenga,b,2

aBeijing Advanced Innovation Center for Soft Matter Science and Engineering, Beijing University of Chemical Technology, 100029 Beijing, China; bDepartment of Chemistry, University of Nebraska–Lincoln, Lincoln, NE 68588; cShanghai Advanced Research Institute, Chinese Academy of Sciences, 201210 Shanghai, China; dKey Laboratory of Materials Modification by Laser, Ion and Electron Beams, Dalian University of Technology, Ministry of Education, 116024 Dalian, China; eDepartment of Earth and Environmental Science, University of Pennsylvania, Philadelphia, PA 19104-6316; fDepartment of Chemistry, University of Pennsylvania, Philadelphia, PA 19104-6316; gCollaborative Innovation Center of Chemistry for Energy Materials, Department of Materials Science and Engineering, University of Science and Technology of China, 230026 Hefei, China; and hDepartment of Physics, Chemistry, and Biology, Linköping University, SE-58 183 Linköping, Sweden

Contributed by Joseph S. Francisco, April 25, 2019 (sent for review January 15, 2019; reviewed by Ben Slater and Amadeu K. Sum) The recent back-to-back findings of low-density porous ice XVI and dictions. This porous ice phase is named ice XVI. Later, ice XVII, XVII have rekindled the century-old field of the solid-state physics a metastable porous ice phase, was also produced by emptying the and chemistry of water. Experimentally, both ice XVI and XVII crystals clathrate hydrogen hydrate (3). The mass density of both ice XVI can be produced by extracting guest atoms or molecules enclosed in and XVII is in the range of 0.81–0.85 g/cm3, lower than that the cavities of preformed ice clathrate hydrates. Herein, we examine (0.93 g/cm3) of normal . Note that among the known more than 200 hypothetical low-density porous whose struc- clathrate hydrogen hydrates, the highest capacity for hydrogen tures were generated according to a database of zeolite structures. storage is 5.3 wt %, achieved by the sII type (15, 16). This record Hitherto unreported porous EMT ice, named according to zeolite hydrogen storage among ice clathrate hydrates can be broken if a nomenclature, is identified to have an extremely low density of 3 stable porous ice with a lower mass density than the sII type can be 0.5 g/cm and the largest internal cavity (7.88 Å in average radius). produced in the laboratory. Several guest-free porous ices with The EMT ice can be viewed as dumbbell-shaped motifs in a hexago- ultralow density were predicted recently via computer simulations nal close-packed structure. Our first-principles computations and mo- (9, 17, 18). One ice phase, named guest-free sIV, was predicted to lecular dynamics simulations confirm that the EMT ice is stable under be a stable phase in the temperature–pressure (T-P) phase dia- negative pressures and exhibits higher thermal stability than other ultralow-density ices. If all cavities are fully occupied by hydrogen gram of water ice at deeply negative pressures (9). molecules, the EMT ice hydrate can easily outperform the record Zeolite-like ices belong to the hypothetical low-density porous hydrogen storage capacity of 5.3 wt % achieved with sII hydro- ices because of their large cavities that can potentially be exploited gen hydrate. Most importantly, in the reconstructed temperature– for gas storage. In fact, the three most common types of ice pressure (T-P) phase diagram of water, the EMT ice is located at clathrate hydrates, sI, sII, and sH, are isostructural with various deeply negative pressure regions below ice XVI and at higher tem- silica clathrate minerals, i.e., MEP with sI, MTN with sII, and perature regions next to FAU. Last, the phonon spectra of empty-sII, DOH with sH, based on the nomenclature of zeolites (19). In FAU, EMT, and other zeolite-like ice structures are computed by particular, the tetrahedrally coordinated frameworks of oxygen in using the dispersion corrected vdW-DF2 functional. Compared with those of ice XI (0.93 g/cm3), both the bending and stretching vibra- Significance tional modes of the EMT ice are blue-shifted due to their weaker hydrogen bonds. Among 18 known ice structures, ice XVI and XVII were produced by emptying the guest atoms/molecules encapsulated in cavities porous ice | ultralow density | EMT ice | reconstructed temperature– of porous ices. We demonstrate simulation evidence that the pressure phase diagram | record hydrogen storage capacity ultralow-density porous EMT ice (named according to zeolite nomenclature) is thermodynamically stable under negative ater is a unique form of matter with many intriguing pressures. Such a low-density solid (∼60% of the mass density of Wproperties. One such physical property is its wide variety ice XVI) can be exploited for hydrogen storage with H2 mass of stable and metastable crystal structures. To date, 18 different density of 12.9 wt %, which is more than twice that (5.3 wt %) crystalline ice phases have been established experimentally (1– achieved by sII . With EMT ice, the temperature– 3). Many more ice phases ranging from 1D to 3D have been pressure phase diagram of water under negative pressures is predicted from computer simulations (4–10). Another known ice reconstructed. Like ice XVII, EMT ice could be produced by form is ice clathrate hydrates with large internal cavities that can pumping off guest molecules in EMT hydrates preformed at high host guest molecules. Clathrate natural gas hydrates have re- pressure. ceived considerable attention because they are an enormous energy source on Earth. Indeed, the amount of carbon in natural Author contributions: Y.L., L.O., J.S.F., and X.C.Z. designed research; Y.L., Y.H., L.W., and X.C.Z. performed research; C.Z., H.L., J.Z., L.O., J.S.F., and X.C.Z. contributed new reagents/ gas hydrates is estimated to be at least twice that in all other analytic tools; Y.L., Y.H., C.Z., H.L., J.Z., L.W., L.O., J.S.F., and X.C.Z. analyzed data; and Y.L., fossil energies combined (11). Clathrate hydrogen hydrates have Y.H., L.W., J.S.F., and X.C.Z. wrote the paper. also received growing attention as they are a renewable and Reviewers: B.S., University College London; and A.K.S., Colorado School of Mines. carbon-free energy source (12). The authors declare no conflict of interest. In previous computer simulation studies, guest-free clathrate Published under the PNAS license. hydrates of type sII were independently predicted to be a stable 1Y.L. and Y.H. contributed equally to this work. phase at negative pressures by Jacobson et al. (13), Conde et al. 2To whom correspondence may be addressed. Email: [email protected], frjoseph@sas. (14), and Huang et al. (8). Remarkably, the guest-free clathrate upenn.edu, or [email protected]. hydrate of type sII was recently produced in the laboratory by This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10. Falenty et al. (2) by pumping off guest Ne atoms from the cav- 1073/pnas.1900739116/-/DCSupplemental. ities of sII clathrate hydrate, confirming earlier theoretical pre- Published online June 10, 2019.

12684–12691 | PNAS | June 25, 2019 | vol. 116 | no. 26 www.pnas.org/cgi/doi/10.1073/pnas.1900739116 Downloaded by guest on September 23, 2021 ice can be identified to be isomorphic with the corresponding silicon frameworks in silica (17, 20–23). Hence, a large number of hypothetical zeolite-like porous ices can be generated based on the structural frameworks of zeolites in the IZA-SC database (http://www.iza-structure.org/databases/). For example, Tribello and Slater proposed hypothetical SGT and DDR clathrate hy- drates (23). Matsui et al. (17) identified ultralow-density ITT ice after examining many hypothetical zeolite-like ices. Based on first- principles computations, Liu and Ojamäe predicted a metastable crystalline ice phase, named clathrate ice sL, in the negative- pressure region (18). Engel et al. (24) predicted many crystalline ice structures from data mining of the tetrahedral zeolite net- works. Kumar et al. (25) theoretically studied how to nucleate and grow water zeolites. In this work, we examined more than 200 hypothetical low-density porous ices whose structures are generated according to a database of zeolite structures. Most importantly, we identified ultralow-density porous EMT ice that is not only energetically favorable but also thermodynamically stable in the reconstructed phase diagram of water ice. In view of its larger cavities and lower mass density than the sII type, the EMT Fig. 1. Mass densities of hypothetical zeolite-like porous ices generated from the tetrahedral frameworks of zeolite structures in the IZA-SC database ice could be a highly effective medium for gas storage. and relaxed by using the TIP4P/2005 potential in the NPT ensemble for 5 ns at 10 K and 1 bar. Results and Discussion Construction and Screening of Zeolite-Like Porous Ices. Based on the tetrahedral structural frameworks of zeolites in the IZA-SC structures, respectively. Here the larger water cavity, (H2O)60 database (http://www.iza-structure.org/databases/), more than (42166125 cage), surrounded by the dumbbell-shaped water mo- 200 hypothetical zeolite-like porous ice structures were gener- B

tifs is shown in Fig. 2 , and it has an average radius of 7.88 Å for CHEMISTRY 18 4 4 ated with the oxygen atoms occupying the tetrahedral positions the EMT ice. For the FAU ice, the large cavity, (H2O)48 (4 6 12 of the zeolite frameworks. For each hypothetical ice structure, cage) (SI Appendix,Fig.S1B), has an average radius of 7.16 Å. the Bernal–Fowler ice rules were met through an annealing Table 1 also lists the average radii of the small-sized (3.90 Å) and simulation from 800 to 100 K with a step size of 100 K after two midsized (4.66 Å) cavities of the MTN ice based on density hydrogen atoms were randomly added to each oxygen atom (see functional theory (DFT) computations using the nonlocal dis- Methods for more simulation details). At each given tempera- persion corrected vdW-DF2 functional, which are consistent with NVT ture, 1 ns molecular dynamics (MD) simulations in the the measured values of 3.91 Å for the small-sized cavity and 4.73 Å ensemble were carried out with oxygen atoms fixed to achieve for the midsized cavity (11, 27). Note that the radius of the larger proper hydrogen-atom arrangement for meeting the ice rules. To water cavity of the EMT ice is the largest among all of the selected this end, the CVFF (26) force field was used to describe in- zeolite-like porous ices considered and is ∼1.7 times larger than that termolecular interactions. All of the zeolite-like porous ice of the larger cavity of the MTN ice (or ice XVI) (2). Hence, the SI Appendix structures generated in this work are listed in , Table EMT ice can be a more effective gas storage material than other S2; the structures with two-/three-coordinated H2O were pre- zeolite-like ices. screened without further consideration. The tetrahedral net- The unit cell of each ice polymorph is fully relaxed using the works with three-member rings were also not considered for nonlocal dispersion corrected vdW-DF2 (28) functional [vdW- further MD simulation and first-principles computation due to DF2 is also denoted as rPW86-vdW2 (29) and rPW86-DF2 (30)], excessive local strain induced by the three-member rings. one of the most accurate DFT functional for computing the Fig. 1 presents the mass densities of 207 hypothetical zeolite- lattice energies of ices (29–31). In SI Appendix, Table S5, the like ice structures. To seek new ultralow density ice phases in computed relative energies between FAU and EMT are also deeply negative pressure region of the T-P phase diagram of shown with the SCAN [another accurate functional for water water, the ice structures except AFY with mass density lower study (31)] and PBE functional (32), and the results are consis- than 0.6 g/cm3 were selected for further simulation studies. This tent with the vdW-DF2 computation. By fitting the lattice energy is because AFY has too many four-member rings. To construct T P versus volume curve with the Birch–Murnaghan equation (33), the - phase diagram, the ice structures except AFY with mass – density lower than 0.6 g/cm3; four benchmark porous ice phases, the equilibrium volume, average distance of the nearest O O i.e., MEP (guest-free sI), MTN (guest-free sII), DOH (guest-free atoms, mass density, lattice energy, and bulk modulus of each ice polymorph are computed (Table 2). Compared with the experi- sH), and SOD (guest-free sVII) (17, 22), whose clathrate hy- – drates have been experimentally established; and two structures mental data for ice XI and MTN ice (34 36), the computed mass (CHA and SAS) with similar water cavities to the previously densities are underestimated by 2.7 and 3.1%, respectively. The – reported structure sIII, as well as the ultralow-density structure ITT average O O distance of the nearest water molecules is over- (17), were considered. Since hypABCB, SBE, SBS, SBT, and TSC estimated by 1.2% for ice XI and 1.0% for MTN. Compared with are not in the water phase diagram, based on free energy com- the experimental value, the lattice energy of ice XI is over- putation, they are not subjected to the first-principles calculations. estimated by 6.7% (35). The optimized lattice parameters of the FAU ice are a = b = c = 15.79 Å and α = β = γ = 60°, while those Structure Properties and Equations of States. When a dumbbell- of the EMT ice are a = b = 15.84 Å, c = 25.63 Å, and α = β = 90°, 6 8 γ = shaped water cage (H2O)48 (consisting of two H-bonded 4 6 120°. water cages) is taken as the structure motif or a supermolecule The computed lattice energy of each ice structure (Table 2) is (Fig. 2A and SI Appendix, Fig. S1A), the two ultralow-density generally proportional to the density. For example, ice XI has EMT and FAU ices (Fig. 2C and SI Appendix, Fig. S1C and the greatest lattice energy (63.05 kJ/mol) and the highest density Tables S3 and S4) can be viewed as supramolecular crystals with (0.91 g/cm3) among the ice polymorphs considered. The density hexagonal close-packed (hcp) and face-centered cubic (fcc) of the MTN ice is 0.8 g/cm3, and its lattice energy is 61.51 kJ/mol,

Liu et al. PNAS | June 25, 2019 | vol. 116 | no. 26 | 12685 Downloaded by guest on September 23, 2021 Fig. 2. (A) A structural motif of EMT ice with two H-bonded 4668 cages, (B)thelargerwatercageinEMT,(C) the unit cell structure of EMT ice, (D)topviewofa3× 3 × 1 supercell, and (E) side view of a 3 × 1 × 2 supercell. If the dumbbell-shaped structure motif is takenasasupermolecule,EMTicecanbeviewedasasupra- molecular crystal with an hcp structure. Red and white balls represent oxygen and hydrogen atoms, respectively. Black dashed lines represent hydrogen bonds.

while the SAS ice has a density of 0.64 g/cm3 and lattice energy Based on the Birch–Murnaghan equation of state (33), the of 57.41 kJ/mol. For the LTA, RHO, and CHA ices, their density lattice energy versus volume per molecule (E versus V)curvesofice is ∼0.6 g/cm3, while their lattice energy is lower than that of SAS. XIandotherzeolite-likeicesareshowninFig.3A. The equation of Among all of the porous ice polymorphs considered, ITT, FAU, state of each structure is consistent with the relation between lattice and EMT have the lowest density of ∼0.5 g/cm3 (Table 2), as well energy and mass density since the mass density and volume are as the lowest lattice energy of ∼56 kJ/mol. In addition, the bulk inversely proportional to one another. LTA and RHO have almost modulus of the ice structures appears to be proportional to the the same equilibrium volume. LTA seems slightly more stable than density. For example, the bulk modulus of ice XI is the highest RHO, as reflected by the lower position of the E versus V curve among all of the ice structures (Table 2). The volume per mol- than that for RHO. Likewise, FAU seems slightly more stable than ecule of the FAU and EMT ices is 58.10 and 58.64 Å3, re- EMT at 0 K. spectively, ∼1.5 times that of guest-free sII (38.09 Å3), while for In Fig. 3B, the relative enthalpies of zeolite-like ices with re- both the LTA and RHO ices, the volume per molecule is spect to ice XI are plotted versus pressure at 0 K. The pressure of 1.36 times that of sII. The ultralow densities of FAU and EMT the solid–solid phase transition at 0 K can be inferred from Fig. are due to the much larger cavities of their tetrahedral networks 3B. Ice XI can transform into MTN at −4,114 bar, consistent than those of other porous ices. with the result of −4,009 bar reported previously (8). Between

Table 1. Structural properties (cage type, coordination number n, and average radius r) of the water cages in various zeolite-like porous ices MTN (sII) FAU EMT LTA RHO CHA SAS

Water cages Small Large Small Large Small Large Small Medium Large Large Large Large

Cage 512 51264 4668 41864124 4668 42166125 46 4668 4126886 4126886 4126286 4861082 n 20 28 24 48 24 60 8 24 48 48 36 40 r (Å) 3.90 (3.91*) 4.66 (4.73*) 4.42 7.16 4.42 7.88 2.44 4.42 6.47 6.47 5.68 5.75

Note that 4x5y6z8v12w means the cage is made up of x four-, y five-, z six-, v eight-, and w twelve-member rings. *Refs. 11 and 27.

12686 | www.pnas.org/cgi/doi/10.1073/pnas.1900739116 Liu et al. Downloaded by guest on September 23, 2021 Table 2. Structural, energetic, and mechanical properties of ice XI (as a reference ice) and various zeolite-like porous ices 3 3 Phase NVcell (Å ) do-o (Å) Average angle∠OOO ρ (g/cm ) Elatt (kJ/mol) B0 (GPa)

† ‡ Ice XI 8 264 (257*) 2.77 (2.74*) 109.48 (109.5 ) 0.91 (0.93*) −63.05 (−59.07 ) 12.46 † † † † MTN (sII) 136 5,022 2.75 109.4 0.81 ── MTN (sII§) 34 1,295 2.78 110.75 0.79 −61.51 10.91 LTA 24 1,241 2.79 117.11 0.58 −56.39 7.02 RHO 48 2,492 2.80 114.87 0.58 −55.96 7.14 FAU 48 2,789 2.81 113.13 0.52 −56.54 5.74 EMT 96 5,629 2.80 110.15 0.51 −55.67 5.56 ITT 46 2,834 2.81 104.85 0.49 −55.70 4.68 CHA 36 1,770 2.81 105.46 0.61 −56.24 7.18 SAS 32 1,503 2.79 109.41 0.64 −57.41 7.53

Elatt = (Etotal − N × Emonomer)/N, where Etotal is the total energy of the unit cell, N is the number of water molecules in the unit cell, and Emonomer is the total energy of a water molecule. Number of water molecules per unit cell (N), equilibrium volume of the unit cell (Vcell), average O-O distance between the nearest water molecules (do-o), mass density (ρ), lattice energy per molecule (Elatt), and bulk modulus (B0). *Ref. 34. † Ref. 2. ‡ Refs. 35 and 36. §Primitive cell of sII.

−4,335 and −4,114 bar, the MTN ice is the most stable with the free sII phase always arises as the most stable ice polymorph in lowest enthalpy. At −4,335 bar, the MTN ice can in principle the T-P phase diagram below ice Ih. At deeply negative pres- transform into the FAU ice. sures, however, the sII phase is replaced by the FAU ice below ∼110 K and by the EMT ice above ∼110 K. As a result, a triple- CHEMISTRY A Reconstructed T-P Phase Diagram of Water via Free-Energy point of sII-FAU-EMT appears at −3,430 bar and 104 K. By Computations. Despite the existence of hundreds of hypotheti- extrapolating to 0 K, ice Ih undergoes a solid–solid transition to cal zeolite-like porous ice structures in the literature, it is im- sII at −2,510 bar and then to FAU ice at −3,826 bar (the cor- portant to examine their thermodynamic stabilities and, if stable, responding transition pressures are at −4,114 and −4,335 bar, their location in the T-P phase diagram of water ice in the respectively, based on DFT calculations). The EMT ice is the negative pressure region. Fig. 4 displays a reconstructed T-P most stable phase in the T-P phase diagram from the triple-point phase diagram of water, with a main focus on the deeply nega- to 240 K and −2,777 bar. Since the computed melting point of tive pressure region, based on the Einstein molecule approach TIP4P/2005 ice Ih is 252 K at 1 bar (38), the EMT ice can be a (37) with the TIP4P/2005 (38) water potential (see Methods for stable phase not too far from room temperature at −3,000 bar. details). The latter model can very well describe the melting At negative pressure, it is hard for pure water to directly crys- point, mass density, and phase transition between liquid water tallize into ice (also called self-crystal ice). In the laboratory, the and ice phases (39). Moreover, both lattice energies and mass pure water ice can only be formed spontaneously under appro- densities determined from the TIP4P/2005 model are very close priate external P-T condition, e.g., ice Ih, Ic, and II-XV. How- to those based on the vdW-DF2 computation (SI Appendix, ever, the porous ice phases, e.g., EMT and FAU, can be Table S6). experimentally obtained only in the form of cocrystal ice. Spe- Interestingly, the free-energy calculation indicates that only cifically, clathrate hydrates can be first formed from water with the FAU and EMT ice phases arise in the deeply negative guest atoms/molecules mixture under a certain P-T condition. pressure region below the experimentally confirmed ice phase sII Next, the guest atoms/molecules can be pumped off the solid (MTN). ITT (17) is not on the T-P phase diagram, as it is a water frameworks to produce the cocrystal ice, e.g., ice XVI and metastable ice phase. As shown by Conde et al. (14), the guest- XVII. Likewise, gas hydrate EMT and FAU phases could be

Fig. 3. (A) Lattice energies (Elatt) of ice XI (as the reference ice) and various porous ices versus the volume per water molecule computed based on the vdW- DF2 functional. (B) Relative enthalpy per molecule at 0 K versus the pressure for various porous ices with respect to that of ice XI computed based on vdW-DF2. The pressures at the crossing points between ice XI and MTN ice, between MTN and FAU ices, and between MTN and EMT ices are −4,114, −4,335, and −4,410 bar, respectively.

Liu et al. PNAS | June 25, 2019 | vol. 116 | no. 26 | 12687 Downloaded by guest on September 23, 2021 molecule for the FAU (56.54 kJ/mol) and the EMT (55.67 kJ/mol) ices than for ice XI (63.05 kJ/mol). The thermal stabilities of the EMT, FAU, ITT, MEP, MTN, and DOH ice phases are examined via a superheating limit test based on MD simulation in the NPT ensemble, with the pressure controlled at 1 bar while raising the temperature in steps of 10 K from a low temperature to a temperature at which the normal tetrahedral ice structure is completely disrupted (40). The system size ranges from 700 to 1,500 water molecules, depending on the specific ice structure. The average mass density of the system at each temperature step is also recorded. Starting from 200 K, the mass density of the FAU and EMT ices is ∼0.52 g/cm3 at 1 bar, consistent with the value obtained from the DFT computation (Table 2). However, the mass density increases to 0.96 g/cm3 for both FAU and EMT ices at 220 K within 100 ns simulations (Fig. 6 A and B), indicating that the crystalline structures of the FAU and EMT ices are easily disrupted at 220 K. We also performed an independent MD simulation to examine the thermal stability Fig. 4. T-P phase diagram of water under negative pressure by free energy of the hypothetical ultralow-density ITT ice (17). The initial computations employing TIP4P/2005 water potential. Zeolite-like ultralow- temperature was set at 150 K while controlling the pressure at density porous ices, FAU and EMT, arise below ice XVI (or the guest-free sII). 1 bar. The ITT structure was completely disrupted within 100 ns at 160 K (Fig. 6C), much lower than the temperature of 220 K observed for the FAU and EMT ices. This result suggests that formed with water and guest molecules with suitable size at ITT exhibits a lower superheating limit than the FAU and EMT appropriated pressure and temperature. The EMT and FAU ices, largely due to the existence of three-membered rings in the porous ices can be obtained by emptying the guest molecules ITT structure, which can induce excessive local strain in the from their cavities. This approach has been used to reveal ice tetrahedral networks. For the well-established guest-free sI, sII, XVI and XVII, which had been obtained by pumping off the and sH structures, the superheating limit appears at 300, 310, guest molecules of earlier formed gas hydrates in the corre- and 300 K, respectively (Fig. 6 D–F), slightly lower than that (320 sponding phases (2, 3). K) of ice Ih, consistent with the known fact that ice Ih is the most Both FAU and EMT are made up of small regular water cages thermodynamically stable phase at 1 bar. Notably, the de- and large water cavities encompassed by the connected small composition of EMT, FAU, sI, sII, and sH is very quick, as water cages. The size difference between the small cage and the shown by the increase of density in Fig. 6, due to the collapse of large cavity of both FAU and EMT is relatively large. It would be the H-bond network in these structures. For EMT, FAU, sI, sII, challenging to synthesize the FAU and EMT hydrates with a and sH, the water cages are homogeneously distributed in space, single type of guest molecules. Based on the adsorption energy of and only one layer of H-bonded water molecules is shared by two aC fullerene encapsulated in the large cavity of EMT (SI 20 connected cages as shown in Fig. 2 and in SI Appendix, Figs. Appendix, Fig. S3), C guest molecules can lead to good stability 20 S1 and S2 A–C. If one defect arises, the corresponding water (SI Appendix, Table S7). As such, EMT and FAU hydrates could cage will be quickly crushed, while the whole structure will be be synthesized from binary mixtures of small (e.g., He, Ne, Ar, collapsed. However, for ITT, it contains tunnels in certain di- and H ) and large (e.g., C ) guest molecules and water in the 2 20 rection, and the two H-bonded water layers are shared by the laboratory. Next, the EMT and FAU cocrystal ice could be nearest tunnels as shown in SI Appendix, Fig. S2D. The de- achieved by emptying all enclosed guest molecules. composition rate of the tunnel’s wall, which is made up of two Dynamic Stabilities and Thermal Stabilities of Zeolite-Like Porous Ices. To confirm the dynamic stabilities of the zeolite-like po- rous ices considered, both the phonon spectra and vibrational density of states (DOS) of MEP (guest-free sI), experimentally obtained MTN (guest-free sII), DOH (guest-free sH), ITT, FAU, and EMT are computed by using the density perturbation functional theory (Methods). In SI Appendix, Figs. S4–S10 (Fig. 5), the phonon spectra (vibrational DOS) are presented. Small negative frequencies for the acoustic phonon modes are ob- served for some phases, most likely due to the inaccurate han- dling of the translational invariance originating from the discreteness of the fast-Fourier transform grids. Compared with the reference ice XI or guest-free sI, sII, and sH ices with rela- tively high density, the ultralow-density porous FAU and EMT ices exhibit a blueshift in both their bending modes and stretching modes (Fig. 5). For example, for ice XI, the bending modes and stretching modes are located in the range of 1,600– − 1,700 and 3,100–3,400 cm 1, whereas for FAU and EMT ice, the two modes are located in the range of 1,620–1,750 and 3,200– − 3,500 cm 1, respectively. Since the OH stretching is correlated with the strength of the hydrogen bond (18, 36), the strength of Fig. 5. Computed vibrational DOS of ice XI (reference ice); the guest-free the hydrogen bond for the FAU and EMT ices is weaker than clathrate ices sI, sII (or ice XVI), and sH; and the ultralow-density porous ices that for ice XI, consistent with the lower lattice energy per water FAU and EMT.

12688 | www.pnas.org/cgi/doi/10.1073/pnas.1900739116 Liu et al. Downloaded by guest on September 23, 2021 CHEMISTRY

Fig. 6. Computed average density versus NPT MD simulation time for the ultralow-density porous ices (A) EMT, (B) FAU, and (C) ITT and the guest-free clathrate hydrates of types (D) sI, (E) sII, and (F) sH at 1 bar and various temperatures. The TIP4P/2005 water model is used in the MD simulations.

H-bonded water layers, is slower than that of the structures with as depicted in Fig. 7A. The maximum occupation of the EMT homogeneously distributed cages. small cage is seven H2. For the large water cavity of EMT, the optimal occupation and the maximum occupation are 60 and 80 H2 Storage in Porous Ice EMT. Porous ice is a promising alternative H2 molecules, respectively, as shown in Fig. 7B. A unit cell with medium for H2 storage. The clathrate hydrate of type sII has been 96 H2O of EMT phase is made up of eight small water cages and synthesized at 200–300 MPa pressure and 240–249 K temperature two large cavities encompassed by the small water cages. There- with hydrogen mass density of 5.3 wt % (15). A higher hydrogen fore, as depicted in Fig. 7C, the hydrogen storage capacity of EMT storage capacity was achieved in the laboratory by a filled ice could amount to 12.9 wt % with each small water cage occupied by C2 with hydrogen content of 11.2 wt % at much higher pressure two H2 and each large cavity occupied by 60 H2.ThisH2 storage (2,300 MPa at 300 K to 600 MPa at 190 K) (15). However, the capacity is higher than that of clathrate ice sL, 7.7 wt % as pre- extreme condition to form pure hydrogen hydrates can be ap- dicted by DFT computations (18), or two times higher than that of parently reduced to low pressures with promoter guest molecules sII (5.3 wt %) (15), and almost three times of the 2020 US De- (e.g., with the presence of THF), and sII hydrogen clathrate hy- partment of Energy (DOE) target value (4.5 wt %) (44). drate can be stable at 5 MPa and 280 K (41). Binary sH clathrate hydrates of H2 with promoter molecules of MCH, DMCH, or Conclusion MTBE were reported to be stable under 100 MPa at 270 K or In conclusion, hitherto unreported porous EMT ice is identified under 0.1 MPa at 77 K (42, 43). Thus, it is expected that hydrogen to have an extremely low density of 0.5 g/cm3 due to the exis- hydrate of EMT phase could also be obtained at special P-T range tence of the largest internal cavities. Among several porous ices 3 with large promoter guest molecules, e.g., C20 molecule. A large with ultralow density (density < 0.6 g/cm ) reported in the lit- stability (−121.50 kJ/mol) is obtained by the large cavity of EMT erature, the EMT ice is found to be a thermodynamically stable occupied by a C20 molecule based on the DFT computations with the phase, occupying a sizable region in the reconstructed T-P phase nonlocal dispersion corrected vdW-DF2 functional (SI Appendix, diagram of water ice at deeply negative pressures and over a wide T P Table S7). Moreover, a large amount of H2 molecules can still be temperature range up to near 240 K. Specifically, in the - encapsulated in the large cavity of EMT with a C20 occupation, as phase diagram of water ice, the EMT ice is below ice XVI (or suggested by the adsorption energy of −400.90 kJ/mol in the large guest-free sII) and is on the right side of the FAU ice (a ther- cavity of EMT with a C20 and 50 H2 cooccupation. modynamically stable phase over a temperature range up to The optimal occupation of the small water cage of EMT is two ∼110 K). The special characteristics of ultralow density and good hydrogen molecules with −8.08 kJ/mol adsorption energy per H2, thermal stability (with a stability limit closer to ambient temperature

Liu et al. PNAS | June 25, 2019 | vol. 116 | no. 26 | 12689 Downloaded by guest on September 23, 2021 Methods Structures of zeolite-like porous ices are generated by replacing atoms in zeolite frameworks with oxygen. Next, to enforce the randomly added hy- drogen atoms according to the Bernal–Fowler ice rules, annealing simula- tions with the constant temperature and constant volume (NVT) ensemble are carried out with oxygen atoms fixed while lowing the temperature from 800 to 100 K. In the process of adjusting hydrogen-atom arrange- ment, the CVFF (26) force field is used. The method to generate ice structures with appropriate hydrogen-atom arrangements has been used in our previous work (18, 45). As suggested from previous studies of ice Ih and Ic with various hydrogen-atom arrangements, lattice energy of ice structure is sensitive to the hydrogen-atom arrangements (36, 46). The largest energy differences among the structures of ice Ih and Ic with dif- ferent hydrogen-atom arrangements are separately 0.67 and 0.71 kJ/mol at the level of DFT calculations (36, 46). For hydrogen-atom–disordered ice structures, there will be a large amount of isomers with different hydrogen-atom arrangements, e.g., 685,686,200 isomers of sI, 3.4 × 109 isomers of sII, and 1,245,636 isomers of sH were reported in previous studies of hydrogen-atom arrangements in sI, sII, and sH clathrate hydrate unit cells (47, 48). To examine whether our method of hydrogen-atom arrangements in the hypothetical ice structures are reliable or not, we made a benchmark comparison of the structures of sI (MEP), sII (MTN), and sH (DOH) generated by our method and the recommended structures of sI, sII, and sH, screened from a large amount of isomers in ref. 47. As listed in SI Appendix,TableS1, lattice energies per water molecule of all of the structures are computed by nonlocal dispersion corrected vdW-DF2 functional. For the sI phase, the structure generated by our method is 0.23 kJ/mol higher than the recommended sI structure in ref. 47. However, for sII phase and sH phase, the structures generated by our methods are separately 0.07 and 0.11 kJ/mol lower than the recommended sII and sH structures in ref. 47. Thus, the hydrogen-atom arrangements of the hypothetical ice structures by our method are reliable and efficient. All of the zeolite-like porous ice structures generated in this work are listed in SI Appendix, Table S2, and the structures with two-/three-coordinated

H2O and the structures containing three-member rings are prescreened without further consideration. Note that for those structures taken for next-stage MD simulations and DFT computations, not even one defect is included. For the DFT computations, the nonlocal dispersion corrected vdW-DF2 (28) functional and PAW potentials implemented in the VASP (Vienna Ab Initio Simulation Package) 5.4 program are used (49, 50). The plane-wave cutoff energy is set to 800 eV, and the k point grids are sampled by a uniform spacing of 2π × 0.04 Å−1. For the phonon spectrum calculations, the cutoff energy is 700 eV, and the k point grids are sampled with a uniform spacing − of 2π × 0.05 Å 1 by using the density functional perturbation theory method (with the vdW-DF2 functional) implemented in the Phonopy package associated with the VASP program (51). The T-P phase diagram of ice polymorphs is constructed based on the Einstein molecule method and TIP4P/2005 potential (38). First, to obtain reliable configurations of the ice polymorphs, isothermal–isobaric Monte Carlo (MC) simulations are performed using homemade code with temper- atures set from 10 to 240 K (with 10-K increments) and pressures from −6,000 to 2,000 bar (with 1,000-bar increments). For each specific ice phase, the configurations obtained from MC simulations are used to calculate the free energy on the basis of the Einstein molecule approach using the GROMACS program (52). In the free-energy calculations, the Ewald sum method with a real-space cutoff of 8.5 Å is adopted to treat the electrostatic interactions, while the pair potential is truncated at 8.5 Å. As shown in SI Appendix, Fig. S11, the lattice energy is converged beyond the cutoff of 8.5 Å. As listed in SI Appendix, Table S2, the symmetries of the hydrogen-atom– ordered structures obtained by our method are presented. For the hydrogen-atom–disordered ice structures, the configurational entropies as- Fig. 7. Adsorption energy per H2 molecule of (A) the small water and (B)the sociated with hydrogen-atom–disorder are added to the free energies as large water cavity of the EMT unit cell with different number of H2 molecules Pauling’s formula [βAPauling/N = −ln(3/2)] (53) when the free energies are occupation by DFT computations with vdW-DF2. (C) Hydrogen storage capacity calculated. The structures with high symmetries are hydrogen-atom–ordered in the forms of clathrate hydrates sII, sL, and EMT and in filled ice C2. ice phases, and the structures with P1 symmetry are considered as hydrogen- atom–disordered ice phases, e.g., the experimentally confirmed hydrogen- atom–disordered clathrates sI (MEP), sII (MTN), and sH (DOH) are all struc- than those of other ultralow-density ices) render the EMT ice a tures with P1 symmetry obtained from the annealing method. Thus, con- potentially effective medium for gas storage, especially for hydrogen figurational entropies are added when computing the total free energies of storage. Indeed, based on the adsorption energy computations by structure with P1 symmetry. Once the free energy at a reference point is vdW-DF2, the hydrogen storage capacity of EMT ice could be determined, the thermodynamic integration method is used to compute the free energies under other thermodynamic conditions. By comparing the free 12.9 wt %, which is markedly higher than the 2020 DOE target energies under different thermodynamic conditions, the phase boundaries (4.5 wt %). can be obtained.

12690 | www.pnas.org/cgi/doi/10.1073/pnas.1900739116 Liu et al. Downloaded by guest on September 23, 2021 ACKNOWLEDGMENTS. This work was supported by the National Natural Centre (Swedish National Infrastructure for Computing). X.C.Z. and J.S.F. Science Foundation of China (No. 21703006), by the China Postdoctoral were supported by US NSF Grant CHE-1665324 and by University of Science Foundation (No. 2017M620582), by the Swedish Research Council, Nebraska Holland Computing Center. X.C.Z. was also supported by a grant from and by computer resources from the Swedish National Supercomputer University of Nebraska–Lincoln Nebraska Center for Energy Sciences Research.

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