Carbon monoxide clathrate hydrate is a potentially important constituent in the solar system. In contrast to the well-established relation between the size of gaseous molecule and hydrate structure, previous work showed that carbon monoxide molecules preferentially form structure-I rather than structure-II gas hydrate. Resolving this discrepancy is fundamentally important to understanding clathrate formation, structure stabilization and the role the dipole moment/molecular polarizability plays in these processes. Here we report the synthesis of structure-II carbon monoxide hydrate under moderate high-pressure/low-temperature conditions. We demonstrate that the relative stability between structure-I and structure-II hydrates is primarily determined by kinetically controlled cage filling and associated binding energies. Within hexakaidecahedral cage, molecular dynamic simulations of density distributions reveal eight low-energy wells forming a cubic geometry in favour of the occupancy of carbon monoxide molecules, suggesting that the carbon monoxide–water and carbon monoxide–carbon monoxide interactions with adjacent cages provide a significant source of stability for the structure-II clathrate framework.
Clathrate hydrates are non-stoichiometric compounds consisting of various types of hydrogen-bonded water polyhedral cages containing guest molecules1. Depending on the cage geometry and connectivity, hydrates usually crystallize in one of the two most common structures, structure-I (sI, space group ) and structure-II (sII, ), both of which are cubic. The sI unit cell contains two pentagonal dodecahedra (512) cages and six tetradecahedron (51262) cages. In a sII unit cell, there are 16 512 cages and 8 large hexakaidecahedral 51264 cages. The structure formed largely depends on the size of guest molecules enclosed in the cages. sI is often formed with small guest molecules such as methane and carbon dioxide, while sII can enclose larger guests such as propane and isobutene. Interestingly, very small molecules, such as H2, N2 and O2, also form sII hydrates. These molecules can stabilize the ice-like framework because sII has a larger number of small cages and because the large 51264 cages can accommodate multiple small molecules. There is yet a third hydrate structure, known as structure H (sH)1,2, which crystallizes in a P6/mmm structure consisting of layers of 512 cages alternating with those of 435663 and 51268 cages. The 512 and 435663 cages are occupied by small molecules such as methane while the molecules in the large interstitial icosahedral (51268) cages are typically larger than 7 Å, such as neohexane and adamantane1,3. Therefore, the stabilization of the sH structure requires the enclosure of both small and large guest molecules. Generally speaking, multiple hydrate structures of small single gases such as CO2, N2, Xe, Kr and CH4 (refs 4, 5, 6, 7, 8, 9, 10) can be formed at various pressure and temperature conditions.
As a cosmochemically important gas molecule and a predominant form of carbon in solar nebulae11, carbon monoxide (CO) occurs in mixed gas hydrates (CO2, H2, N2 and so on), and the formation of these clathrate phases may play important roles in the formation of nebulae, comets and the outer planets of the solar system12,13. For instance, the high CO/N2 ratios in primordial Titan may indicate that CO had a higher possibility to form clathrate relative to N2 if both gases were accreted as clathrates12. In addition, these enclosure compounds are environmentally relevant, as they have potential applications in the sequestration of greenhouse gases and separation of industrial flue gases.
For a given method of measurement, a molecule of CO has a similar size to those of N2 and O2; consideration of only the size effect therefore favours a sII clathrate, based on the guest–hydrate cavity size relation14. In addition, based on the theoretical calculation, Miller13 predicted that sII CO clathrate is energetically more favourable than its sI counterpart. However, contrary to this prediction, all experimental studies show that CO forms sI clathrate hydrate under moderate pressure and temperature conditions15,16,17,18,19,20. Thermodynamic calculations using the classical Lennard–Jones–Devonshire cell model also concluded that CO sI hydrate would be more stable, giving a dissociation pressure that is 20% lower than that for sII clathrate12. Recently, Dartois20 modelled the equilibrium phase diagram of CO clathrate in P–T space using the Ballard and Sloan’s formalism21 and the Kihara potential for CO17. The calculated stability curve for sII lies slightly below that for sI, indicating that the sII clathrate is thermodynamically favoured.
To date, the controversy between experiments and theoretical predictions has not been resolved. One school of thought attributes the discrepancy to the electrostatic properties (that is, dipole moment and molecular polarizability) of the CO molecule during clathration. This hypothesis is worth exploring because the dipole moment is an important factor that influences the hydrate stability; other factors include the size of guest molecules, short range guest–host interactions and hydrogen bonding22. Unlike other molecules such as H2, CO2, CH4 and especially N2, which is isoelectronic with CO, the CO molecule has a non-zero dipole moment of 0.122 D. The exact nature of the dipole interaction between CO and clathrate cages is not currently known. It has also been argued that the crystallization of CO clathrate requires high concentration of gaseous molecules to overcome a significant energy barrier to nucleation. As a result, nucleation would be more efficient in a pressure region where the sI CO clathrate is favoured20. In the absence of thermodynamic equilibrium data for the sII CO clathrate, such as framework stability and cage occupancy, one is left with an inconclusive hypothesis that warrants further experimental validation.
In this work, we conduct time-dependent neutron diffraction experiments on the D2O(s)–CO(g) system at simultaneously low temperature and high hydrostatic pressure conditions. We successfully synthesize sII CO hydrate and determine its cage gas filling as a function of time. We also perform density functional theory (DFT) calculations to evaluate the thermodynamic properties of this system. On the basis of the obtained results, the stability of CO hydrates appears to be primarily controlled by the cage occupancy and the binding energy between CO and D2O molecules. Using combined analyses of Rietveld refinement, maximum entropy method (MEM) and molecular dynamics (MD) simulations, we investigate the distribution of CO molecules in sII cages and their interaction with, and stabilization in, the host water framework.
Figure 1 shows neutron diffraction patterns of CO hydrates obtained in two different synthesis experiments. Consistent with the earlier finding15,16, CO hydrate crystallized in sI at 173 bar and 243 K. Over the initial period of two and a half weeks, the CO gas continued to react with D2O ice to form sI hydrate. Interestingly, in both experiments, sII hydrate started to form and coexisted with sI hydrate after staying at the same conditions for additional amounts of time. These observations indicate that the formation of sII CO hydrate at these P–T conditions is thermodynamically favoured but not kinetically favoured. They also indicate that between the two competing pathways leading to CO hydrates, the activation energy for sI is lower than that for sII. Hence, the earlier nucleation of sI hydrate is kinetically controlled. Further inspection of Fig. 1 reveals that after the appearance of sII hydrate the relative diffraction intensities between sI and sII hydrates do not show notable changes with time, indicating that the two hydrates may have formed via two separate nucleation paths. When the pressure was decreased from 173 to 100 bar while the temperature was kept at 252 K for 12 weeks, a pure phase sII hydrate was finally obtained. To gain further insight into the kinetics of sII hydrate formation, we performed a third experiment at a lower pressure, 100 bar, and 252 K. However, neither sI nor sII hydrate was observed over a period of three and a half weeks. This is not totally unexpected because the formation of both sI and sII CO hydrates requires a threshold pressure to trigger the nucleation of the clathrate phase. Clearly, in the system CO(g)–D2O(s), the applied pressure of 100 bars was too low to fulfil this requirement.
In a given system, pressure and temperature are the most important thermodynamic parameters. From this point of view, it is quite unexpected that D2O ice first reacts with CO molecules to form sI hydrate at 173 bar and 243 K and then to form sII hydrate at the same P–T conditions, either through the same reaction or a phase transformation. However, composition is yet another important thermodynamic variable, especially for clathrate hydrates. Because hydrates are intrinsically non-stoichiometric, their compositions are closely tied to the filling of the cages, which would in turn influence their thermodynamic stability. To gain insight into this effect, we refined the cage occupancies using the data shown in Fig. 1. Our results indicate that the small cages in sI and sII clathrates are fully or close to fully occupied (100±5% uncertainty); therefore, to a first approximation, they were fixed at a full occupancy during the subsequent refinements. For 51262 cages in sI, the occupancies are 1.13, 1.18, 1.34 and 1.39, in hydrates synthesized for 1, 2.5, 5 and 17 weeks, respectively. For 51264 cages in sII, they are 1.59 and 2, in hydrates synthesized for 5 and 17 weeks, respectively. As expected, the cage occupancies increase gradually on increasing the synthesis time. Note that, over a given period of time, the number of CO molecules in each 51262 cage is substantially smaller than that in 51264 cage.
To understand the effects of cage occupancy on the stability of CO hydrates, we performed DFT calculations to determine the binding energies, ΔE, of COm-(H2O)n clusters, which are calculated as
where m and n are the numbers of enclosed CO and water molecules in the cage, respectively. The values of n corresponding to 512, 51262 and 51264 cages are, respectively, 20, 24 and 28. Our optimized geometries for H2O cages are in good agreement with previous predictions by Patchkovskii et al.23 For the CO-(H2O)20 cluster, the calculated binding energies are 3.47 and 2.59 kcal mol−1 without and with zero point energy (ZPE) corrections, respectively. These values are comparable to the binding energy of the CO-H2O complex24. The optimized structure shows that a CO molecule occupies the centre of each 512 cage, with the C atom being 0.5 Å from the cage centre. This is consistent with the MD simulation results using a classical force field, which will be discussed later. Instead of forming a single CO-H2O complex, each CO molecule interacts with all surrounding H2O molecules. The binding energies without and with ZPE correction for CO-(H2O)24 (51262 cage) are 3.08 and 2.37 kcal mol−1, respectively, and those for CO-(H2O)28 (51264 cage) are 2.76 and 2.14 kcal mol−1, respectively. Thus, water molecules in larger cages tend to have weaker binding (specifically van der Waals interaction) with CO molecules due to their larger separation. For the two CO molecules encapsulated in either a 51262 (sI) or 51264 (sII) cage, several trial positions, such as cage centre and cage edges facing the hexagonal and pentagonal rings, were also explored for possible CO occupancies. In both cases, no breakdown in cage symmetries was found, and the CO molecules eventually became equilibrated at the stabilized positions. However, the calculated binding energies for the optimized (CO)2-(H2O)28 cluster without and with ZPE are 2.68 and 1.12 kcal mol−1, respectively, both of which are substantially lower than the sums of the corresponding binding energies for the two CO-(H2O)28 clusters. The binding energies of (CO)2-(H2O)24 cluster with the ZPE correction are found to be very low or even negative, which is obviously due to the size effect of the sI large cage (51262). The occupation of two CO molecules in each 51262 cage can therefore significantly destabilize the sI CO clathrate structure.
Figure 2 shows a schematic plot of the calculated binding energies for single and double occupancies of CO molecules in the large cages of sI and sII clathrates. Strikingly, there is a crossover in binding energy, indicating that beyond a critical point of cage occupancy the 51264 cages are energetically favoured over the 51262 cages in the clathrate structure. Also plotted in Fig. 2 are the cage occupancies determined from the neutron data shown in Fig. 1. The sI clathrate was initially observed after the synthesis time of 1 and 2.5 weeks because the 51262 cages are energetically favoured at small cage occupancies. However, when CO molecules are concentrated over a long period of time, the energetics is in favour of the 51264 cages enclosing two CO molecules and hence the sII hydrate. Our experiments show that relative to the sI phase, sII hydrate is thermodynamically favoured (lower Gibbs free energy) but not kinetically favoured (higher activation energy for the formation of stable, critical-sized hydrate nuclei). Therefore, at the final equilibrium state, sII hydrate must have higher binding energy than sI hydrate as illustrated in the inset of Fig. 2. This thermodynamic view is qualitatively consistent with our binding energy calculations. As also shown in Fig. 2, there is a region where sI and sII hydrates can coexist (marked by horizontal dot lines that intersect the two bold lines), which corresponds to the hydrates synthesized at 173 bar for 5 and 17 weeks. It should be pointed out that such coexistence can only be possible when P–T conditions are in the vicinity of the sI–sII hydrate phase boundary. As shown in the top pattern of Fig. 1, a phase-pure sII CO clathrate was obtained when the synthesis pressure was significantly lowered. On the other hand, an increase in pressure at a given temperature would favour the formation of sI hydrate20.
Our calculated binding energies for the optimized (CO)2-(H2O)28 clusters are substantially lower than the sum of the binding energies for two individual CO-(H2O)28 clusters. Therefore, the (CO)2-(H2O)28 clusters in an isolated state are energetically unfavourable and may readily dissociate into CO-(H2O)28+CO. However, the interaction between (CO)2-(H2O)28 clusters and their adjacent cages may play an important role in stabilizing the doubly occupied 51264 cages. The 51264 cages in sII clathrate, for example, are tightly connected to other 512 cages and 51264 cages by sharing pentagonal faces and hexagonal faces. To gain insight into the distribution of CO molecules in hydrate cages and their intra- and inter-cage interactions, we performed a combined analysis of Rietveld refinement, MEM and MD simulations.
In sII CO hydrate, the 512 cages share pentagons to form linear chains along the  direction, and each 51264 cage shares four hexagons with four neighbouring 51264 cages to form a diamond-shaped cage centre (Supplementary Fig. 1). The volume thermal expansion data were fitted to yield the parameters β=8.2(17) × 10−6 K−1 and γ=8.7(2) × 10−7 K−2 (Supplementary Fig. 2). Because CO molecule is smaller than the cage size of 512 or 51264 and because the interaction between CO and the cages is via weak van der Waals force and even weaker dipole interactions, CO molecules in both cages have a disordered distribution. Figure 3 shows the distribution of CO molecules in 51264 and 512 cages at 25 K. CO molecules partially occupy small and large cages with the occupancy of 1/6 (Table 1). Difference Fourier nuclear maps reveal that CO molecules are off-centred, as also demonstrated by the CO distribution from MD simulations in Fig. 3b and nuclear density distribution from MEM in Fig. 3c. The off-centred character agrees well with the computed positions of the CO molecules in sI clathrate18,25. Note that, as a result of the disordered nature of guest molecules in the cages22,26, the described CO distribution is only one of the most probable structural configurations from our Rietveld analyses, which, however, does not provide insight into the dynamics of guest molecules in the cages. On the other hand, a previous nuclear magnetic resonance (NMR) study on sI clathrate shows15,16 that the CO molecules in the large cages undergo anisotropic reorientation with substantial mobility even at 77 K. The proposed model involves rapid motion of CO molecules among sites over each of the 14 faces, with the CO axis orientated towards the cage centre. Clearly, other techniques, such as NMR, Raman, infrared and inelastic scattering spectroscopies, are needed to provide more comprehensive understanding of the disordered state and dynamics of CO molecules in sII clathrate cages.
In the 51264 cages of sII clathrate, there are eight low-energy wells in two different groups favouring the occupancy of CO molecules: four in one group facing the four hexagonal rings of the 51264 cage, along the body diagonal of the unit cell, and the remaining four in the second group facing the co-vertex of three pentagonal rings of the 51264 cage, also along the body diagonal. Together, these eight positions form a cubic geometry with an edge length of ~3 Å, which has the same orientation as the unit cell. In the 51264 cages, CO molecules are distributed at the eight vertices of the cube, which is different from the oblate shape of the CO distribution at the 14 sites towards each face of 51262 cage in sI clathrate15,16. Such distributions suggest that the intra-cage CO-H2O interaction and inter-cage CO-CO interaction can provide a significant source of stability for the sII framework. To corroborate this assumption, we have estimated the relative contribution of long-range interaction to the total stabilization of CO molecules in the large cage by calculating the trajectory average interaction energy of CO molecules within the 51264 cage. The stabilization energy of a CO molecule provided by the 51264 cage is determined to be ~65% of the total interaction energy of the CO molecule, indicating that the molecules in the adjacent cages contribute 35% of the interaction energy for CO molecules in the doubly occupied cages. We have also found that the interaction between CO molecules inside a single cage has negative contribution to the stabilization of the system by energy decomposition analysis. Both of these findings are in good agreement with the results of our DFT calculations. It is worth pointing out that the structure and thermodynamic stability of clathrate hydrates are generally determined by two main factors: intermolecular interaction between guest and host molecules and the configurational entropy. The present work has focused on the former, but the latter contribution to the Gibbs free energy can also be important for guest molecules that strongly interact with the host framework water molecules. In addition, the stabilization mechanism by the adjacent cage interaction is yet to be fully understood, which represents another important area for future investigations. In 512 cage, our MEM analysis demonstrates that CO molecules exhibit a doughnut-shaped density distribution, which is normal to the <111> cubic diagonals (Fig. 3c). Compared with the single occupancy in a 512 cage, the enclosure of two CO molecules in a 51264 cage will increase the positional disorder and the scattering distributions (lower-symmetric position), which would in turn result in larger isotropic thermal motion (Uiso) and displacement of CO from the cage centre.
Figure 4 shows the detailed CO distributions in sII cages obtained from MD simulation. As is shown, both C and O atoms in CO molecules are distributed off the centre of the 51264 cage. The a–b plane projection of the density distributions displays four overlapped intensity maxima for the CO positions in the 51264 cage, indicating that the C atoms are localized with the O atoms rotating around them, even though the CO molecules are allowed to move freely in the 51264 cage. Since such a configuration results from the combined effect of inter-cage CO-CO and CO-H2O interactions, the hollow shape of the CO distribution is expected to constitute a core that stabilizes both the 51264 cage of sII clathrate and the CO dimer contained within. Increasing the temperature would further delocalize the distribution of CO molecules in the cages, but they would still be confined within the potential energy surface well (Supplementary Fig. 4).
The radial distribution functions (RDFs) of CO molecules in sII clathrate from MD calculations are shown in Fig. 5. For the 512 cage, the RDF is in excellent agreement with that reported for sI clathrate18,24. This is not unexpected given the similar cage geometries in sI and sII clathrates, even though the cages in the two structures have different symmetries. However, the RDF for CO molecules in the 51264 cage is significantly different from that in sI18. The peak values of both C and O atoms are lower for sII than for sI. There is no zero point at any distance as in the case of sI. This suggests that in the large cage of sII hydrate, CO molecules are more delocalized than those in sI and hence have a smoother potential energy surface. Thus, the larger cage size in sII not only increases the binding energy but also significantly lowers the potential barriers for CO molecules to move. The delocalization behaviour of CO is similar to that of D2 observed in hydrogen clathrate hydrate27, which also has a sII structure containing large 51264 cages. Thus, like all other hydrates of small guest molecules, the guest–framework interactions in CO clathrate hydrates may be dominated by the delocalization of encapsulated molecules inside their cages.
In contrast to other clathrate hydrates, especially N2 and O2 hydrates, the structural behaviour of sI/sII CO hydrates has not been well established. For both sII N2 and O2 clathrates, the gas molecules in 51264 cages are doubly occupied, shifted off the cage centre and oriented along the diagonals of their cubic unit cells28,29, while in 512 cages they are singly occupied at the cage centres and oriented along the <100> axes. MD simulations of the dynamic behaviour of N2 and O2 in sII clathrates indicate that the molecular positions and orientations are essentially the same for N2 and O2 and are independent of the cage size and distortion30. For comparison, the CO molecules in both 512 and 51264 cages are off-centred. Notably, the CO molecules in 51264 cages rotate around the centre by forming a cubic symmetry, and in 512 cages they are slightly off-centred with a pseudosphere configuration. In addition, an increased molecular freedom for CO molecules in large cages results in a distinct distribution of CO molecules with a hollow cubic geometry, whereas in small cages CO molecules are more confined/localized around the cage centre. With regard to the roles that dipole moment may play in the clathrate formation and stabilization, the present work does not provide a conclusive evidence. However, because CO has a small dipole moment, while N2 is non-dipole (note they are isoelectronic), the different formation sequences observed for CO hydrates may presumably arise from the CO dipole effect during the nucleation stage, although the difference in the guest chemistry can also be a determining factor. More specifically, the dipole moment could act as a turbulence factor through the interaction with the dipolar water molecule during the nucleation stage. This is a process that is difficult to address experimentally and warrants future kinetic MD simulations using high-performance computing. For instance, the kinetic MD simulations may be performed by starting with a mixture of CO gas+water and determining the role of the dipole moment in the polyhedral cage formation at early stages of hydrate nucleation. Together with NMR or Raman/IR spectroscopic experiments, the formation sequence of sI and sII CO clathrates and associated crystallization and growth kinetics can be established. It should be stressed that the present work is relevant only to the growth of CO hydrates after their nucleation. The early nucleation of clathrate hydrates, as demonstrated by molecular simulations, typically involves densification and high local concentration of guest molecules to form individual cages31,32,33. These simulations also show that the clathrate nuclei are an amorphous mixture of polyhedral cages with structural motifs of a clathrate structure; hence, they do not have the same symmetry as the stable crystalline grains. In addition, the amorphous structure formed contains other types of cages that are not expected in an equilibrium hydrate structure. These characteristics of nucleation cannot be resolved using diffraction experiments.
In summary, based on the time-dependent study of the clathrate hydrate formation in the CO-H2O system, we have demonstrated that sII hydrate can be formed in a time-evolving sequence after sI hydrate has initially crystallized. This finding validates previous hypotheses that sII CO hydrate would become more stable than sI CO hydrate when the concentration of CO molecules is saturated. This behaviour is associated with the difference in CO binding energy between 51262 and 51264 cages, where the 51264 cage in the sII structure is energetically favoured over the 51262 cage in the sI structure for double occupancy of CO molecules. More importantly, this is attributed to the crossover in the binding energy-cage occupancy space between the two cage types. As a result, a sII hydrate enclosing two CO molecules in 51264 cages can be stabilized at certain P–T conditions through kinetically controlled cage filling. However, the (CO)2-(H2O)28 clusters in an isolated state are energetically unfavourable and can readily dissociate into CO-(H2O)28 and CO. Our MD simulations suggest that the interactions between adjacent cages including CO-H2O and CO-CO interactions provide a significant source of stability for the double-CO occupancy of hexakaidecahedral cage. Previous studies of CO hydrates indicate that both sI and sII CO hydrates may exist in the icy bodies of outer planets of the solar system, making them potentially important candidates for interpreting observed molecular anomalies12,13. Our comprehensive studies on their formation process, thermodynamic stability and encapsulation dynamics have provided valuable information for spectroscopic simulation and hence for detecting their occurrence in the solar system.
Neutron diffraction data collection
Time-of-flight neutron experiments were conducted at the HIPPO beamline, Los Alamos Neutron Science Center. The pressure cell was made of vanadium, which has a small coherent scattering for neutrons and can hold pressures up to 200 bar. To minimize the background of neutron patterns, deuterated water (D2O) instead of H2O was used for hydrate synthesis. Polycrystalline samples were prepared in a pressure vessel from ground D2O ice and gaseous CO at the initial pressure and temperature conditions (173 bar and 243 K) used in ref. 15, 16 As confirmed by our neutron diffraction measurements, the sI CO clathrate was initially formed during the first 1–4 weeks at 173 bar and 243 K. A mixture of sI and sII CO clathrates was observed after 5 weeks, and, finally, a single-phase sII CO clathrate was obtained at ~100 bar and 252 K after 17 weeks (Fig. 1).
Rietveld refinement and MEM analysis
All neutron diffraction data were analysed using the GSAS package34, and the CO positions in the clathrate cages were determined from the difference Fourier nuclear maps and refined by subsequent Rietveld analyses. The initial atomic coordinates for the D2O framework were taken from a previous neutron diffraction study of N2 clathrate29. The D2O framework of sII CO clathrate and of the residual ice were both refined using Pauling’s half-hydrogen model with an average occupancy of 0.5 for each deuterium atom35. D2O in the framework can adopt six possible configurations as a result of the disordered orientation. However, diffraction experiments can only provide space- and time-averaged intra- and inter-molecular distances29, which may not reflect the instantaneous interactions between the framework cages and the guest molecules inside. The isotopic exchange between D in D2O ice and H atoms in atmospheric moisture was negligible and was ignored for all the refinements. To obtain the CO distributions in both small and large cages, difference nuclear Fourier maps were constructed after the best fit for the D2O framework was achieved. Our final Rietveld analysis revealed that in sII framework, each small cage is occupied by one CO molecule, whereas each large cage can be occupied by up to two CO molecules, resulting in a CO/D2O ratio of ~4/17 when all the cages are fully occupied. The refined occupancies for CO molecules indicated one molecule in the 512 cage and two in the 51264 cage; they were fixed in the subsequent analysis to better constrain the CO distributions in cages. In this study, the distribution of CO molecules in sII hydrate over a range of temperatures was analysed by the MEM/Rietveld analyses using data from four detector banks at 2θ=144.45°, 119.89°, 90.00° and 39.30°. The corresponding d-spacings are in the range of 0.5–10.5 Å (Supplementary Fig. 5). The observed structure factors, Fo, and standard uncertainties, (|Fo|), were estimated with Alchemy36 from relevant data in files output by GSAS and analysed by MEM with Dysnomia37. The unit cell was divided into 128 × 128 × 128 voxels. The detailed method for MEM analysis has been described in ref. 36.
DFT and MD calculations
DFT was utilized in this work to provide further investigation on the stability of CO clathrate hydrates. The calculations utilized the Gaussian09 program package38. We optimized the structures of (H2O)20 (512 cage in both sI and sII), (H2O)28 (51264 cage in sII) and (H2O)24 (51262 cage in sI and their corresponding CO complexes, at the level of Becke 3-Parameter for exchange and Lee, Yang and Parr parameters for correlation). DFT (B3LYP)/6-31+G(d) was used with the Coulomb-attenuating method39,40,41. All the stationary points were confirmed as minima by means of frequency calculations. To compare with our Rietveld refinement results of CO distributions in sII cages, we performed MD simulations with one CO molecule in each 512 cage and two CO molecules in 51264 cage. A total of ~100,000 points from CO trajectories in 5 ns were projected on the a–b plane, and the cage centres of both 512 and 51264 cages were set as the zero points. The MD calculations were carried out at temperatures ranging from 25 to 260 K in canonical NVT (N-moles, V-volume, and T-temperature) ensembles obtained using the Nosé–Hoover thermostat42,43. The dimensions of the simulation cells and their initial configurations were adopted using the experimental lattice parameters and geometries at corresponding temperatures. Three-dimensional periodic boundary conditions were applied. For the selection of proton configuration, the ‘ice rules’ (Bernal–Fowler ice rules) have been obeyed and the proton configuration with the minimum total dipole moment was selected. The TIP4P water model44 was used to calculate the interaction between H2O molecules. The interactions between CO and H2O molecules were modelled by the summation of electrostatic and Lennard–Jones-type interactions. The parameters were taken from Manesh et al.18, who used them to study the distribution of CO molecules in sI clathrate. The bond length of the CO molecule was fixed at the experimental value, 1.128 Å (ref. 45). The Lennard–Jones parameters are 3.55 and 0.3089, kJ mol−1 for C atoms and 2.95 and 0.5120, kJ mol−1 for O atoms. The partial charges on the C and O atoms of the CO molecule were ±0.0223 in atomic units. The long-range electrostatic interactions were calculated with the Particle-Particle Particle-Mesh method46. The dimensions of the periodic simulation boxes were 34 × 34 × 34 3, which were constructed by 2 × 2 × 2 unit cells. Therefore, the simulation domain included a total of 128 512 cages and 64 51264 cages that incorporated a total of 1,088 water molecules. Each calculation was performed for 5.0 ns simulation time with a 1.0 fs time step. The RDF and spatial density distribution of CO molecules respective to the centre of the corresponding cages were obtained from MD trajectories. All MD simulations in this work were performed using the LAMMPS program suite47.
How to cite this article: Zhu, J. et al. Encapsulation kinetics and dynamics of carbon monoxide in clathrate hydrate. Nat. Commun. 5:4128 doi: 10.1038/ncomms5128 (2014).
This work was supported by the laboratory-directed research and development (LDRD) program of Los Alamos National Laboratory, which is operated by Los Alamos National Security LLC under DOE Contract No. DE-AC52-06NA25396. The experimental work has benefited from the use of the Lujan Neutron Scattering Center at Los Alamos Neutron Science Center, which is funded by the US Department of Energy's Office of Basic Energy Sciences. The work at Institute of Physics, Chinese Academy of Sciences (IOPCAS) was funded by CAS project under contract Nos: KJCX2-YW-W26 and XDB07000000. We thank the High Pressure Science and Engineering Center (HiPSEC), UNLV for support. This research was sponsored in part by the National Nuclear Security Administration under the Stewardship Science Academic Alliances program through DOE Cooperative Agreement #DE-NA0001982.
Supplementary Figures 1-5
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Chemical Physics (2019)