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

Significance

Among 18 known ice structures, ice XVI and XVII were produced by emptying the guest atoms/molecules encapsulated in cavities of porous ices. We demonstrate simulation evidence that the ultralow-density porous EMT ice (named according to zeolite nomenclature) is thermodynamically stable under negative pressures. Such a low-density solid (∼60% of the mass density of ice XVI) can be exploited for hydrogen storage with H₂ mass density of 12.9 wt %, which is more than twice that (5.3 wt %) achieved by sII clathrate hydrate. With EMT ice, the temperature–pressure phase diagram of water under negative pressures is reconstructed. Like ice XVII, EMT ice could be produced by pumping off guest molecules in EMT hydrates preformed at high pressure.

Abstract

The recent back-to-back findings of low-density porous ice XVI and XVII have rekindled the century-old field of the solid-state physics and chemistry of water. Experimentally, both ice XVI and XVII crystals can be produced by extracting guest atoms or molecules enclosed in the cavities of preformed ice clathrate hydrates. Herein, we examine more than 200 hypothetical low-density porous ices whose structures were generated according to a database of zeolite structures. Hitherto unreported porous EMT ice, named according to zeolite nomenclature, is identified to have an extremely low density of 0.5 g/cm³ and the largest internal cavity (7.88 Å in average radius). The EMT ice can be viewed as dumbbell-shaped motifs in a hexagonal close-packed structure. Our first-principles computations and molecular dynamics simulations confirm that the EMT ice is stable under negative pressures and exhibits higher thermal stability than other ultralow-density ices. If all cavities are fully occupied by hydrogen molecules, the EMT ice hydrate can easily outperform the record hydrogen storage capacity of 5.3 wt % achieved with sII hydrogen hydrate. Most importantly, in the reconstructed temperature–pressure (T-P) phase diagram of water, the EMT ice is located at deeply negative pressure regions below ice XVI and at higher temperature regions next to FAU. Last, the phonon spectra of empty-sII, FAU, EMT, and other zeolite-like ice structures are computed by using the dispersion corrected vdW-DF2 functional. Compared with those of ice XI (0.93 g/cm³), both the bending and stretching vibrational modes of the EMT ice are blue-shifted due to their weaker hydrogen bonds.

Water is a unique form of matter with many intriguing properties. One such physical property is its wide variety of stable and metastable crystal structures. To date, 18 different crystalline ice phases have been established experimentally (1–3). Many more ice phases ranging from 1D to 3D have been predicted from computer simulations (4–10). Another known ice form is ice clathrate hydrates with large internal cavities that can host guest molecules. Clathrate natural gas hydrates have received considerable attention because they are an enormous energy source on Earth. Indeed, the amount of carbon in natural gas hydrates is estimated to be at least twice that in all other fossil energies combined (11). Clathrate hydrogen hydrates have also received growing attention as they are a renewable and carbon-free energy source (12).

In previous computer simulation studies, guest-free clathrate hydrates of type sII were independently predicted to be a stable phase at negative pressures by Jacobson et al. (13), Conde et al. (14), and Huang et al. (8). Remarkably, the guest-free clathrate hydrate of type sII was recently produced in the laboratory by Falenty et al. (2) by pumping off guest Ne atoms from the cavities of sII clathrate hydrate, confirming earlier theoretical predictions. This porous ice phase is named ice XVI. Later, ice XVII, a metastable porous ice phase, was also produced by emptying the clathrate hydrogen hydrate (3). The mass density of both ice XVI and XVII is in the range of 0.81–0.85 g/cm³, lower than that (0.93 g/cm³) of normal ice Ih. Note that among the known clathrate hydrogen hydrates, the highest capacity for hydrogen storage is 5.3 wt %, achieved by the sII type (15, 16). This record hydrogen storage among ice clathrate hydrates can be broken if a stable porous ice with a lower mass density than the sII type can be produced in the laboratory. Several guest-free porous ices with ultralow density were predicted recently via computer simulations (9, 17, 18). One ice phase, named guest-free sIV, was predicted to be a stable phase in the temperature–pressure (T-P) phase diagram of water ice at deeply negative pressures (9).

Zeolite-like ices belong to the hypothetical low-density porous ices because of their large cavities that can potentially be exploited for gas storage. In fact, the three most common types of ice clathrate hydrates, sI, sII, and sH, are isostructural with various silica clathrate minerals, i.e., MEP with sI, MTN with sII, and DOH with sH, based on the nomenclature of zeolites (19). In particular, the tetrahedrally coordinated frameworks of oxygen in 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 hydrates (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 networks. 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 ice could be a highly effective medium for gas storage.

Results and Discussion

Construction and Screening of Zeolite-Like Porous Ices.

Based on the tetrahedral structural frameworks of zeolites in the IZA-SC database (http://www.iza-structure.org/databases/), more than 200 hypothetical zeolite-like porous ice structures were generated with the oxygen atoms occupying the tetrahedral positions of the zeolite frameworks. For each hypothetical ice structure, the Bernal–Fowler ice rules were met through an annealing simulation from 800 to 100 K with a step size of 100 K after two hydrogen atoms were randomly added to each oxygen atom (see Methods for more simulation details). At each given temperature, 1 ns molecular dynamics (MD) simulations in the NVT ensemble were carried out with oxygen atoms fixed to achieve proper hydrogen-atom arrangement for meeting the ice rules. To this end, the CVFF (26) force field was used to describe intermolecular interactions. All of the zeolite-like porous ice structures generated in this work are listed in SI Appendix, Table S2; the structures with two-/three-coordinated H₂O were prescreened without further consideration. The tetrahedral networks with three-member rings were also not considered for further MD simulation and first-principles computation due to excessive local strain induced by the three-member rings.

Fig. 1 presents the mass densities of 207 hypothetical zeolite-like ice structures. To seek new ultralow density ice phases in deeply negative pressure region of the T-P phase diagram of water, the ice structures except AFY with mass density lower than 0.6 g/cm³ were selected for further simulation studies. This is because AFY has too many four-member rings. To construct the T-P phase diagram, the ice structures except AFY with mass density lower than 0.6 g/cm³; four benchmark porous ice phases, i.e., MEP (guest-free sI), MTN (guest-free sII), DOH (guest-free sH), and SOD (guest-free sVII) (17, 22), whose clathrate hydrates have been experimentally established; and two structures (CHA and SAS) with similar water cavities to the previously reported structure sIII, as well as the ultralow-density structure ITT (17), were considered. Since hypABCB, SBE, SBS, SBT, and TSC are not in the water phase diagram, based on free energy computation, they are not subjected to the first-principles calculations.

Fig. 1.

Mass densities of hypothetical zeolite-like porous ices generated from the tetrahedral frameworks of zeolite structures in the IZA-SC database and relaxed by using the TIP4P/2005 potential in the NPT ensemble for 5 ns at 10 K and 1 bar.

Structure Properties and Equations of States.

When a dumbbell-shaped water cage (H₂O)₄₈ (consisting of two H-bonded 4⁶6⁸ water cages) is taken as the structure motif or a supermolecule (Fig. 2A and SI Appendix, Fig. S1A), the two ultralow-density EMT and FAU ices (Fig. 2C and SI Appendix, Fig. S1C and Tables S3 and S4) can be viewed as supramolecular crystals with hexagonal close-packed (hcp) and face-centered cubic (fcc) structures, respectively. Here the larger water cavity, (H₂O)₆₀ (4²¹6⁶12⁵ cage), surrounded by the dumbbell-shaped water motifs is shown in Fig. 2B, and it has an average radius of 7.88 Å for the EMT ice. For the FAU ice, the large cavity, (H₂O)₄₈ (4¹⁸6⁴12⁴ cage) (SI Appendix, Fig. S1B), has an average radius of 7.16 Å. Table 1 also lists the average radii of the small-sized (3.90 Å) and midsized (4.66 Å) cavities of the MTN ice based on density functional theory (DFT) computations using the nonlocal dispersion corrected vdW-DF2 functional, which are consistent with the measured values of 3.91 Å for the small-sized cavity and 4.73 Å for the midsized cavity (11, 27). Note that the radius of the larger water cavity of the EMT ice is the largest among all of the selected zeolite-like porous ices considered and is ∼1.7 times larger than that of the larger cavity of the MTN ice (or ice XVI) (2). Hence, the EMT ice can be a more effective gas storage material than other zeolite-like ices.

Fig. 2.

(A) A structural motif of EMT ice with two H-bonded 4⁶6⁸ cages, (B) the larger water cage in EMT, (C) the unit cell structure of EMT ice, (D) top view of a 3 × 3 × 1 supercell, and (E) side view of a 3 × 1 × 2 supercell. If the dumbbell-shaped structure motif is taken as a supermolecule, EMT ice can be viewed as a supramolecular crystal with an hcp structure. Red and white balls represent oxygen and hydrogen atoms, respectively. Black dashed lines represent hydrogen bonds.

Table 1.

Structural properties (cage type, coordination number n, and average radius r) of the water cages in various zeolite-like porous ices

Water cages	MTN (sII)		FAU		EMT		LTA			RHO	CHA	SAS
	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 4^x5^y6^z8^v12^w means the cage is made up of x four-, y five-, z six-, v eight-, and w twelve-member rings.

^*Refs. 11 and 27.

The unit cell of each ice polymorph is fully relaxed using the nonlocal dispersion corrected vdW-DF2 (28) functional [vdW-DF2 is also denoted as rPW86-vdW2 (29) and rPW86-DF2 (30)], one of the most accurate DFT functional for computing the lattice energies of ices (29–31). In SI Appendix, Table S5, the computed relative energies between FAU and EMT are also shown with the SCAN [another accurate functional for water study (31)] and PBE functional (32), and the results are consistent with the vdW-DF2 computation. By fitting the lattice energy versus volume curve with the Birch–Murnaghan equation (33), the equilibrium volume, average distance of the nearest O–O atoms, mass density, lattice energy, and bulk modulus of each ice polymorph are computed (Table 2). Compared with the experimental data for ice XI and MTN ice (34–36), the computed mass densities are underestimated by 2.7 and 3.1%, respectively. The average O–O distance of the nearest water molecules is overestimated by 1.2% for ice XI and 1.0% for MTN. Compared with the experimental value, the lattice energy of ice XI is overestimated 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 of the EMT ice are a = b = 15.84 Å, c = 25.63 Å, and α = β = 90°, γ = 120°.

Table 2.

Structural, energetic, and mechanical properties of ice XI (as a reference ice) and various zeolite-like porous ices

Phase	N	Vcell (Å3)	do-o (Å)	Average angle∠OOO	ρ (g/cm3)	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

E_latt = (E_total − N × E_monomer)/N, where E_total is the total energy of the unit cell, N is the number of water molecules in the unit cell, and E_monomer is the total energy of a water molecule. Number of water molecules per unit cell (N), equilibrium volume of the unit cell (V_cell), average O-O distance between the nearest water molecules (d_o-o), mass density (ρ), lattice energy per molecule (E_latt), and bulk modulus (B₀).

^*Ref. 34.

^†Ref. 2.

^‡Refs. 35 and 36.

^§Primitive cell of sII.

The computed lattice energy of each ice structure (Table 2) is generally proportional to the density. For example, ice XI has the greatest lattice energy (63.05 kJ/mol) and the highest density (0.91 g/cm³) among the ice polymorphs considered. The density of the MTN ice is 0.8 g/cm³, and its lattice energy is 61.51 kJ/mol, while the SAS ice has a density of 0.64 g/cm³ and lattice energy of 57.41 kJ/mol. For the LTA, RHO, and CHA ices, their density is ∼0.6 g/cm³, while their lattice energy is lower than that of SAS. Among all of the porous ice polymorphs considered, ITT, FAU, and EMT have the lowest density of ∼0.5 g/cm³ (Table 2), as well as the lowest lattice energy of ∼56 kJ/mol. In addition, the bulk modulus of the ice structures appears to be proportional to the density. For example, the bulk modulus of ice XI is the highest among all of the ice structures (Table 2). The volume per molecule of the FAU and EMT ices is 58.10 and 58.64 ų, respectively, ∼1.5 times that of guest-free sII (38.09 ų), while for both the LTA and RHO ices, the volume per molecule is 1.36 times that of sII. The ultralow densities of FAU and EMT are due to the much larger cavities of their tetrahedral networks than those of other porous ices.

Based on the Birch–Murnaghan equation of state (33), the lattice energy versus volume per molecule (E versus V) curves of ice XI and other zeolite-like ices are shown in Fig. 3A. The equation of state of each structure is consistent with the relation between lattice energy and mass density since the mass density and volume are inversely proportional to one another. LTA and RHO have almost the same equilibrium volume. LTA seems slightly more stable than RHO, as reflected by the lower position of the E versus V curve than that for RHO. Likewise, FAU seems slightly more stable than EMT at 0 K.

Fig. 3.

(A) Lattice energies (E_latt) 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.

In Fig. 3B, the relative enthalpies of zeolite-like ices with respect to ice XI are plotted versus pressure at 0 K. The pressure of the solid–solid phase transition at 0 K can be inferred from Fig. 3B. Ice XI can transform into MTN at −4,114 bar, consistent with the result of −4,009 bar reported previously (8). Between −4,335 and −4,114 bar, the MTN ice is the most stable with the lowest enthalpy. At −4,335 bar, the MTN ice can in principle transform into the FAU ice.

A Reconstructed T-P Phase Diagram of Water via Free-Energy Computations.

Despite the existence of hundreds of hypothetical zeolite-like porous ice structures in the literature, it is important to examine their thermodynamic stabilities and, if stable, their location in the T-P phase diagram of water ice in the negative pressure region. Fig. 4 displays a reconstructed T-P phase diagram of water, with a main focus on the deeply negative pressure region, based on the Einstein molecule approach (37) with the TIP4P/2005 (38) water potential (see Methods for details). The latter model can very well describe the melting point, mass density, and phase transition between liquid water and ice phases (39). Moreover, both lattice energies and mass densities determined from the TIP4P/2005 model are very close to those based on the vdW-DF2 computation (SI Appendix, Table S6).

Fig. 4.

T-P phase diagram of water under negative pressure by free energy computations employing TIP4P/2005 water potential. Zeolite-like ultralow-density porous ices, FAU and EMT, arise below ice XVI (or the guest-free sII).

Interestingly, the free-energy calculation indicates that only the FAU and EMT ice phases arise in the deeply negative pressure region below the experimentally confirmed ice phase sII (MTN). ITT (17) is not on the T-P phase diagram, as it is a metastable ice phase. As shown by Conde et al. (14), the guest-free sII phase always arises as the most stable ice polymorph in the T-P phase diagram below ice Ih. At deeply negative pressures, 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-point of sII-FAU-EMT appears at −3,430 bar and 104 K. By extrapolating to 0 K, ice Ih undergoes a solid–solid transition to sII at −2,510 bar and then to FAU ice at −3,826 bar (the corresponding transition pressures are at −4,114 and −4,335 bar, respectively, based on DFT calculations). The EMT ice is the most stable phase in the T-P phase diagram from the triple-point to 240 K and −2,777 bar. Since the computed melting point of TIP4P/2005 ice Ih is 252 K at 1 bar (38), the EMT ice can be a stable phase not too far from room temperature at −3,000 bar. At negative pressure, it is hard for pure water to directly crystallize into ice (also called self-crystal ice). In the laboratory, the pure water ice can only be formed spontaneously under appropriate external P-T condition, e.g., ice Ih, Ic, and II-XV. However, the porous ice phases, e.g., EMT and FAU, can be experimentally obtained only in the form of cocrystal ice. Specifically, clathrate hydrates can be first formed from water with guest atoms/molecules mixture under a certain P-T condition. Next, the guest atoms/molecules can be pumped off the solid water frameworks to produce the cocrystal ice, e.g., ice XVI and XVII. Likewise, gas hydrate EMT and FAU phases could be formed with water and guest molecules with suitable size at appropriated pressure and temperature. The EMT and FAU porous ices can be obtained by emptying the guest molecules from their cavities. This approach has been used to reveal ice XVI and XVII, which had been obtained by pumping off the guest molecules of earlier formed gas hydrates in the corresponding phases (2, 3).

Both FAU and EMT are made up of small regular water cages and large water cavities encompassed by the connected small water cages. The size difference between the small cage and the large cavity of both FAU and EMT is relatively large. It would be challenging to synthesize the FAU and EMT hydrates with a single type of guest molecules. Based on the adsorption energy of a C₂₀ fullerene encapsulated in the large cavity of EMT (SI Appendix, Fig. S3), C₂₀ guest molecules can lead to good stability (SI Appendix, Table S7). As such, EMT and FAU hydrates could be synthesized from binary mixtures of small (e.g., He, Ne, Ar, and H₂) and large (e.g., C₂₀) guest molecules and water in the laboratory. Next, the EMT and FAU cocrystal ice could be achieved by emptying all enclosed guest molecules.

Dynamic Stabilities and Thermal Stabilities of Zeolite-Like Porous Ices.

To confirm the dynamic stabilities of the zeolite-like porous 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 observed for some phases, most likely due to the inaccurate handling 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 relatively 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 the hydrogen bond for the FAU and EMT ices is weaker than that for ice XI, consistent with the lower lattice energy per water molecule for the FAU (56.54 kJ/mol) and the EMT (55.67 kJ/mol) ices than for ice XI (63.05 kJ/mol).

Fig. 5.

Computed vibrational DOS of ice XI (reference ice); the guest-free clathrate ices sI, sII (or ice XVI), and sH; and the ultralow-density porous ices FAU and EMT.

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 of the hypothetical ultralow-density ITT ice (17). The initial temperature was set at 150 K while controlling the pressure at 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 ITT exhibits a lower superheating limit than the FAU and EMT ices, largely due to the existence of three-membered rings in the ITT structure, which can induce excessive local strain in the tetrahedral networks. For the well-established guest-free sI, sII, and sH structures, the superheating limit appears at 300, 310, and 300 K, respectively (Fig. 6 D–F), slightly lower than that (320 K) of ice Ih, consistent with the known fact that ice Ih is the most thermodynamically stable phase at 1 bar. Notably, the decomposition of EMT, FAU, sI, sII, and sH is very quick, as shown by the increase of density in Fig. 6, due to the collapse of the H-bond network in these structures. For EMT, FAU, sI, sII, and sH, the water cages are homogeneously distributed in space, and only one layer of H-bonded water molecules is shared by two connected cages as shown in Fig. 2 and in SI Appendix, Figs. S1 and S2 A–C. If one defect arises, the corresponding water cage will be quickly crushed, while the whole structure will be collapsed. However, for ITT, it contains tunnels in certain direction, and the two H-bonded water layers are shared by the nearest tunnels as shown in SI Appendix, Fig. S2D. The decomposition rate of the tunnel’s wall, which is made up of two H-bonded water layers, is slower than that of the structures with homogeneously distributed cages.

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.

H₂ Storage in Porous Ice EMT.

Porous ice is a promising alternative medium for H₂ storage. The clathrate hydrate of type sII has been synthesized at 200–300 MPa pressure and 240–249 K temperature with hydrogen mass density of 5.3 wt % (15). A higher hydrogen storage capacity was achieved in the laboratory by a filled ice C2 with hydrogen content of 11.2 wt % at much higher pressure (2,300 MPa at 300 K to 600 MPa at 190 K) (15). However, the extreme condition to form pure hydrogen hydrates can be apparently reduced to low pressures with promoter guest molecules (e.g., with the presence of THF), and sII hydrogen clathrate hydrate can be stable at 5 MPa and 280 K (41). Binary sH clathrate hydrates of H₂ with promoter molecules of MCH, DMCH, or MTBE were reported to be stable under 100 MPa at 270 K or under 0.1 MPa at 77 K (42, 43). Thus, it is expected that hydrogen hydrate of EMT phase could also be obtained at special P-T range with large promoter guest molecules, e.g., C₂₀ molecule. A large stability (−121.50 kJ/mol) is obtained by the large cavity of EMT occupied by a C₂₀ molecule based on the DFT computations with the nonlocal dispersion corrected vdW-DF2 functional (SI Appendix, Table S7). Moreover, a large amount of H₂ molecules can still be encapsulated in the large cavity of EMT with a C₂₀ occupation, as suggested by the adsorption energy of −400.90 kJ/mol in the large cavity of EMT with a C₂₀ and 50 H₂ cooccupation.

The optimal occupation of the small water cage of EMT is two hydrogen molecules with −8.08 kJ/mol adsorption energy per H₂, as depicted in Fig. 7A. The maximum occupation of the EMT small cage is seven H₂. For the large water cavity of EMT, the optimal occupation and the maximum occupation are 60 and 80 H₂ molecules, respectively, as shown in Fig. 7B. A unit cell with 96 H₂O of EMT phase is made up of eight small water cages and two large cavities encompassed by the small water cages. Therefore, as depicted in Fig. 7C, the hydrogen storage capacity of EMT could amount to 12.9 wt % with each small water cage occupied by two H₂ and each large cavity occupied by 60 H₂. This H₂ storage capacity is higher than that of clathrate ice sL, 7.7 wt % as predicted by DFT computations (18), or two times higher than that of sII (5.3 wt %) (15), and almost three times of the 2020 US Department of Energy (DOE) target value (4.5 wt %) (44).

Fig. 7.

Adsorption energy per H₂ molecule of (A) the small water and (B) the large water cavity of the EMT unit cell with different number of H₂ molecules occupation by DFT computations with vdW-DF2. (C) Hydrogen storage capacity in the forms of clathrate hydrates sII, sL, and EMT and in filled ice C2.

Conclusion

In conclusion, hitherto unreported porous EMT ice is identified to have an extremely low density of 0.5 g/cm³ due to the existence of the largest internal cavities. Among several porous ices with ultralow density (density < 0.6 g/cm³) reported in the literature, the EMT ice is found to be a thermodynamically stable phase, occupying a sizable region in the reconstructed T-P phase diagram of water ice at deeply negative pressures and over a wide temperature range up to near 240 K. Specifically, in the T-P phase diagram of water ice, the EMT ice is below ice XVI (or guest-free sII) and is on the right side of the FAU ice (a thermodynamically stable phase over a temperature range up to ∼110 K). The special characteristics of ultralow density and good thermal stability (with a stability limit closer to ambient temperature than those of other ultralow-density ices) render the EMT ice a potentially effective medium for gas storage, especially for hydrogen storage. Indeed, based on the adsorption energy computations by vdW-DF2, the hydrogen storage capacity of EMT ice could be 12.9 wt %, which is markedly higher than the 2020 DOE target (4.5 wt %).

Methods

Structures of zeolite-like porous ices are generated by replacing atoms in zeolite frameworks with oxygen. Next, to enforce the randomly added hydrogen atoms according to the Bernal–Fowler ice rules, annealing simulations 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 arrangement, 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 different 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, Table S1, 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 temperatures 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 associated with hydrogen-atom–disorder are added to the free energies as Pauling’s formula [βA_Pauling/N = −ln(3/2)] (53) when the free energies are calculated. The structures with high symmetries are hydrogen-atom–ordered 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 structures with P1 symmetry obtained from the annealing method. Thus, configurational entropies are added when computing the total free energies of structure with P1 symmetry. Once the free energy at a reference point is determined, the thermodynamic integration method is used to compute the free energies under other thermodynamic conditions. By comparing the free energies under different thermodynamic conditions, the phase boundaries can be obtained.