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Ab initio study of formation of the clathrate cage in the tetrahydrofuran hydrate
Accepted Manuscript Ab initio study of formation of the clathrate cage in the tetrahydrofuran hydrate Jinxiang Liu, Shaofeng Shi, Zhenwei Zhang, Haiying Liu, Jiafang Xu, Gang Chen, Jian Hou, Jun Zhang PII: DOI: Reference:
S0021-9614(18)30008-9 https://doi.org/10.1016/j.jct.2018.01.007 YJCHT 5300
To appear in:
J. Chem. Thermodynamics
Received Date: Revised Date: Accepted Date:
2 December 2017 11 January 2018 12 January 2018
Please cite this article as: J. Liu, S. Shi, Z. Zhang, H. Liu, J. Xu, G. Chen, J. Hou, J. Zhang, Ab initio study of formation of the clathrate cage in the tetrahydrofuran hydrate, J. Chem. Thermodynamics (2018), doi: https://doi.org/ 10.1016/j.jct.2018.01.007
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Ab initio study of formation of the clathrate cage in the tetrahydrofuran hydrate Jinxiang Liua,b, Shaofeng Shic, Zhenwei Zhangc, Haiying Liub, Jiafang Xua, Gang Chenb, Jian Houa, Jun Zhangd** a
State Key Laboratory of Heavy Oil Processing, College of Petroleum Engineering, China University of Petroleum, Qingdao, Shandong 266580, China b c
School of Physics and Technology, University of Jinan, Jinan, 250022, China
Linyi Academy of Technology Cooperation and Application, Linyi, 276037, P.R. China d
College of Science, China University of Petroleum, Qingdao, 266580, China
Abstract: Despite the potential applications and ubiquity of clathrate hydrates, the molecular mechanism of formation of these compounds remains poorly understood. In the present work, we performed ab initio calculations to investigate the formation of the clathrate cage of the tetrahydrofuran (THF) hydrate and its significance to the adsorption of gas molecules such as the methane, carbon dioxide, and hydrogen. We found that THF and six water molecules cooperatively organize into an initial stable structure that will allow the growth of more water faces. The formation of the clathrate cage is thermodynamically feasible, and the water-THF interactions become more significant with the increasing water molecules. However, the water-water interactions mostly dominate the formation process due to the strong hydrogen bond interactions. Further, for the adsorption of the second guests, there is little change in the structure and stability of the clathrate cage, but these second guests favor to adsorb onto the pentagonal faces rather than the hexagonal faces. Keywords: tetrahydrofuran hydrate; formation; adsorption; ab initio calculation
Corresponding authors. Email: [email protected] Corresponding authors. Email: [email protected]
**
1
1. Introduction Clathrate hydrates are non-stoichiometric solid
compounds consisting of a
hydrogen-bonded water network of polyhedral water cages which encapsulate small gas molecules such as noble gases, methane, nitrogen, carbon dioxide, and oxygen [1-3]. Based on the differences in the cage shape and size, there are three most common clathrate hydrate structures [4-5]: structure I (sI), structure II (sII), and structure H (sH). Clathrate hydrates have attracted great attention from scientific and industrial areas, including carbon cycling and climate change [6], carbon dioxide sequestration and methane recovery [7], gas storage and transportation [8-10], and cooling application [11]. However, they are usually formed by applying pressures, which are primary drawback in the development and application of the hydrate-based technology [12-14]. In contrast, the tetrahydrofuran (THF) hydrate can be produced under atmospheric pressure below 277.4 K [15], providing a proxy of clathrate hydrates of potential use. More importantly, THF molecules have been recognized as one of the most popular hydrate promoters [16-18], which can allow the mixed hydrates of THF and gas molecules to form at dramatically lower pressure and higher temperature. Of particular interest is the THF hydrate that can serve as a promising candidate for hydrogen storage [19-20]. Pure THF hydrate favours to form the sII structure, which is consisted of 16 pentagonal dodecahedron cages (512 cages) and 8 hexakaidecahdron cages (51264 cages) in the unit cell. Due to the large molecular size, the THF molecules occupy the 51264 cages only, leaving the 512 cages vacant. While in the binary and ternary hydrates (THF+ CH 4/CO2/H2) [20-22], the gas molecules are able to occupy the 512 cages. To promote the applications of the THF hydrates, it is essential to gain a detailed knowledge of the molecular mechanism of the hydrate formation. However, because of very small time (nanoseconds) and length (nanometers) scales involved, it is still incredibly challenging to describe the initial hydrate formation process on molecular length scales in real time even with state-of-the-art experimental techniques [23-24]. To date, several different hypotheses have been proposed to explain the hydrate formation such as the labile cluster hypothesis [25-26], the local structuring hypothesis [27],
2
the blob mechanism [28], and the cage adsorption hypothesis [29], and most of the evidence to support or oppose these hypotheses arises from computer simulations [30-34], which shed some important light on this area. In addition, molecular dynamics simulations of Nada [35] have indicated that dissolved THF molecules were arranged at both large and small cage sites on the interface between the hydrate and the solution phase. As the formation of cages progressed, THF molecules that had once been arranged at small cages sites gradually moved from the sites, and finally were arranged at large cages sites only to form the hydrate structure. By investigating the hydrogen bond interactions between THF and water, Shultz and Vu [36] showed that the THF molecules can modify the hydrogen bonding in the water host to promote the hydrate formation and that this modification is mitigated upon guest incorporation. Wu and co-workers [37] suggest that the growth of THF hydrates is a result of two competing effects: the adsorption of THF molecules to the growing interface and the desorption/rearrangement of THF molecules at the interface. They demonstrated that the desorpiton of THF molecules trapped at the wrong sites on the hydrate surface is the rate-limiting step of the hydrate growth. Yagasaki et al. [38] suggested that the slow growth of THF hydrate is attributed to the trapping of THF molecules in open small cages the hydrate surface, and these trapped THF molecules need to cross one or two Gibbs energy barriers to escape from the surface region. Although THF molecules have been used in many experimental studies of the hydrate formation, there are only a limited number of computer simulation studies that examine the microscopic mechanism of formation of the THF hydrate, and our knowledge is still far from being complete. In the present study, we used ab initio calculations to study the formation of clathrate cage in THF hydrate and its significance to the adsorption of gas molecules such as the methane, carbon dioxide, and hydrogen. First, by comparing the small sized pure water clusters with the binary clusters of THF and water, we obtained the structural and energetic properties of the cage precursor. Second, we examined the growth of the cage precursor to form a clathrate cage by adsorbing more water molecules. Finally, we revealed the effects of the THF molecule on the adsorption of gas molecules. We believe that our work is useful for illustrating the general features of the cage formation process, which is responsible to the hydrate nucleation and growth. 3
2. Computational details The geometry optimizations of the THF(H2O)n=1–28 clusters were carried out in vacuum at 0 K by the DMol3 program [39]. The Perdew-Burke-Ernzerhof (PBE) functionals [40] were used in the generalized gradient approximation for the exchange-correlation energy. The triple numerical plus polarization (TNP) basis functions [41] were used to describe the atomic orbitals. The dispersion correction was introduced by the semi-empirical Tkatchenko-Scheffler scheme [42]. The convergence criteria for the total energy, forces, displacement, and SCF interactions were set as 2.6255×10-2 kJ∙mol-1, 5.251×1010 kJ∙(mol·m) -1, 5.0×10-13 m, and 2.6255×10-3 kJ∙mol-1, respectively. The frequency analysis showed that there is no imaginary frequency in all of the cases, confirming that the obtained structures are minima on the potential energy surface. The thermodynamic stability of the THF(H2O)n=1–28 clusters was evaluated by their stabilization energy (Estab, with zero-point energy correction),
Estab
(n EH 2O ETHF ) Ecluster n 1
(1)
where EH 2 O , ETHF , and Ecluster represent the energies of the water molecule, the methane molecule, and the cluster, respectively. The binding strength of the guest molecule to the clathrate cage was characterized by the interaction energy (Eint), defined as Eint ( Eresidue Eguest ) Etotal
(2)
where Eresidue represents the energy of the cluster without the guest molecule, and E guest represents the energy of the guest molecule.
3. Results and discussion 3.1 Formation of the cage precursor Researchers [24, 29, 34, 43-44] have suggested that before the formation of the hydrate, the rings emerge and gradually grow in number, acting as nucleation seeds, and then lead to the formation of a face-saturated incomplete cage that is regarded as an intermediate structure between independent rings and fully developed cages. To illustrate these initial structures of the hydrate nucleation and to evaluate the THF-water and water-water interactions, we firstly 4
investigated the most stable structures of the pure (H 2O)n=2–6 clusters and the binary THF·(H2O)n=1–6 clusters on the potential energy surface and calculated their stabilization energies. Figure 1 shows that the pure water clusters (n=2–6) have a unique planar cyclic structures, in accordance with theoretical results of Shields et al. [45]. This implies that our calculations are reliable enough. Specially, the growth of the pure water clusters is thermodynamically feasible, because the stabilization energy gradually increases with increasing cluster size, and the growth pattern is the ring expansion that one water molecule inserts into a small ring to form a large ring. With increasing cluster size, the planar cyclic structure becomes thermodynamically unfavourable for pure water clusters [45], and the number of larger rings significantly lowers than that of pentagonal and hexagonal rings from the kinetic point of view [34, 44]. Therefore, we do not further discuss the formation of the larger water rings with the size of n>6. Figure 2 indicates that a typical hydrogen bond forms between the hydrogen atom of the water molecule and the ether oxygen atom of THF, with the hydrogen bond length of 2.75×10-10 m (the O−H···O distance), but the hydrogen bond does not occur between the oxygen atom of water and a hydrogen atom of the α-methylene carbon of THF. The stabilization energy increases with the number of water molecules in the cluster, suggesting that the formation of the binary THF·(H2O)n=1–6 clusters is thermodynamically favorable, while the THF-water interactions become more complex. In detail, the structure a shows that one water molecule donates a hydrogen bond to THF and that the hydroxyl group is almost coplanar with the THF ring. While in the structure b, two water molecules locate themselves above or below the plane of the THF ring to form two hydrogen bonds, and one additional hydrogen bond forms between two water molecules, leading to the formation of a trigonal cyclic structure. For THF·(H2O)3, there are three configurations that can be classified into two conformer groups based on their hydrogen bonding topology. One conformer group is that two water molecules donate two hydrogen bonds to THF and simultaneously bind to a third water molecule via the hydrogen bonding interactions, forming a tetragonal cyclic structure (c1). The other conformer group is that three water molecules form a trigonal cyclic structure that interacts with THF by forming a hydrogen bond (c2 and c3). Despite of the same number of the hydrogen bonds, c2 and c3 have large stabilization energies than c1, because the 5
hydrogen bonding interactions between THF and water are relatively weak. Further, c3 has a larger stabilization energy than c2, suggesting that the THF ring favours to be parallel to the trigonal ring of water molecules. In the case of THF·(H2O)4 and THF·(H2O)5, THF can also participate in forming the cyclic structure with water molecules, but the hexagonal ring (e1) is less stable than the pentagonal ring (d1), implying that such cyclic structure becomes unstable with increasing water molecules. Further, d1 has smaller stabilization energy than c3, which suggest that THF is unlikely to form two hydrogen bond with the water molecules for a cluster of size n>3. Instead, THF prefers to adsorb on one side of the tetragonal (d2 and d3) or pentagonal (e2 and e3) ring of water molecules, and the parallel adsorption of THF (d3 or e3) is more thermodynamically favourable by ~2.026 kJ∙mol-1 than the vertical adsorption (d2 or e2). For THF·(H2O)6, whether the THF ring is parallel or vertical to the hexagonal ring of water molecules in the initial structure, the optimized structure is always the parallel adsorption of THF on one side of the water ring, and the distance between the water ring and the THF ring is roughly 3.09×10-10 m. For the nucleation of the methane hydrate, Walsh et al. [24] have suggested that the cage precursor is the methane adsorbed onto a pentagonal ring of water molecules. Since THF has a large molecular size, we can infer that the cage precursor of the THF hydrate should be THF adsorbed horizontally onto a hexagonal ring of water molecules. In addition, we note that all binary THF·(H2O)n=1–6 clusters have smaller stabilization energies than the pure water clusters of the same size, implying that the latter has greater stability. Although the kinetic mechanisms of the cluster formation are beyond the scope of this paper, it is possible to comment on the structural relationship between these cluster, and then to conclude that the formation of the cage precursor should be that a thermal fluctuation causes water molecules to be arranged into a planar hexagonal ring, which further attracts one THF on its side. This result also suggests that the water-water interactions play a predominant role in the formation of the cage precursor. 3.2 Growth of the cage precursor Figure 3 shows the growth of the cage precursor to form a clathrate cage by adsorbing
6
more water molecules. The structural and energetic properties of the binary THF·(H 2O)n=7–28 clusters involved in the formation process are given in Table 1. For the cluster size of n = 7, one adding water molecule can mediate interactions between THF and the hexagonal water ring via forming hydrogen bonds both with THF and the water ring, resulting in the sandwich-like structure (7a). Due to the steric hindrance effect, THF becomes a little far away from the bottom water face (3.09×10-10 m →3.51×10-10 m). On the other hand, this water molecule can bind to THF only through donating one hydrogen bond (7b). This results in the strong interaction between THF and water molecules. However, 7a is more likely to form, because it has a larger stabilization energy than 7b (25.376 kJ∙mol-1 versus 23.735 kJ∙mol-1), which can be attributed to that the water-water interaction is more significant than the THF-water interaction. For the adsorption of two water molecules (n = 8), they form a tetragonal ring on the side of the bottom face with the help of two water molecules of the cage precursor. THF forms one hydrogen bond with one adsorbed water molecule rather than the water molecules at the bottom face. For THF·(H2O)9, three adsorbed water molecules favor to form a pentagonal ring by hydrogen bonding with two adjacent water molecules of the bottom face (9b), instead of forming two tetragonal rings by hydrogen bonding with three adjacent water molecules of the bottom face (9a). This further indicates that the water-water interactions are more significant than the THF-water interactions and that the water molecules prefer to be arranged in a planar pentagonal cyclic structure. In contrast, for THF·(H2O)10, the formation of a new hexagonal ring of water molecules (10b) is unfavorable than the formation of a pentagonal ring and a tetragonal ring (10a), and THF has a larger interaction energy with the water molecules in the configuration 10a. This can be understood by the aforementioned structures of Figure 2. When the THF ring is vertical to the cyclic structures of water molecules, the trigonal, tetragonal, and pentagonal rings can occur, while the hexagonal ring is thermodynamically unfavourable. In the binary THF·(H2O)11 cluster, both the stabilization energy and the interaction energy demonstrate that five adsorbed water molecules prefer to form the double pentagonal ring than to form a pentagonal ring plus two tetragonal rings, implying that the pentagonal rings are most likely to occur during the formation of the clathrate cage. This reasonably agrees well with the molecular dynamics simulations of Bai et al. [34, 44], which suggested that the number of pentagonal rings 7
considerably exceeds that of hexagonal or tetragonal rings during the hydrate formation. As the clusters extend to n = 12–18, each adsorbed water molecule leads to the formation of a new water face, being alternated with the tetragonal and pentagonal rings. The water-water interactions and the THF-water interactions become more significant, because the stabilization energy increases from 30.200 kJmol-1 to 33.191 kJ∙mol-1 and the interaction energy increase from 147.429 kJ∙mol-1 to 191.233 kJ∙mol-1, which leads to the formation of the semi-cage structure (n = 18) that has a hexagonal and six pentagonal water faces. Interestingly, THF always form one hydrogen bond with the dangling hydrogen atom of one adsorbed water molecule for these clusters. However, due to the steric effects, the distance between the THF ring and the bottom water face keeps to increase (3.66×10-10 m → 3.83×10-10 m) as the cluster size increases. This implies that the water-water interactions are so remarkable that some water molecules can keep closer to the bottom face than THF. By sequentially adsorbing more water molecules, new water faces continually form, and the stabilization energy and the interaction energy maintain to increase. For example, a new tetragonal water face occurs for n = 19, and the tetragonal + pentagonal water faces occur for n = 20. However, for the THF·(H2O)21 cluster, we found that the hexagonal ring of water molecules (21b) is more favourable to form than the pentagonal ring (21a), which results from the reorientation of the THF ring that has the growing trend in parallel with the second hexagonal face. Further, there are two additional tetragonal rings to form in 21b, although this conformer has two fewer pentagonal faces than 21a. In the case of THF·(H2O)22, it has the similar scenario that the formation of the hexagonal face (22b) is thermodynamically more feasible, featuring with the stabilization energy of 35.699 kJ∙mol-1 and the interaction energy of 228.380 kJ∙mol-1. For n = 23, the adsorbed water molecule will insert into a tetragonal ring and lead to the formation of a new pentagonal water face. While in THF·(H 2O)24, the adsorbed water molecule results in the transformation of a pentagonal face to the hexagonal face, accompanied with two tetragonal faces and seven pentagonal faces. By adsorbing one more water molecule, a new pentagonal face appears for n = 25, but this is still an opened cage-like structure. When the number of water molecules reaches to 26, a closed irregular cage occurs, denoted as 4151064, and the hydrogen bond between THF and water molecules disappears. This irregular cage transforms into the irregular 4 251064 cage for n = 27, and then 8
into the intact 51264 cage for n = 28. Note that the distance between the THF ring and the bottom hexagonal water face gradually decreases from 3.62×10-10 m to 3.20×10-10 m as the cluster size increases from n = 19 to n = 26, and maintains 3.20×10-10 m for n = 27 and 28. This is because THF is not large enough to support the continual growth of water faces in vertical orientation. Alternatively, the newly-formed water faces tends to converge on a center line of the bottom face, leading to the decreased distance. Further, THF tends to move to the centre of a closed cage structure, and thus this distance is same for n = 26–28. As for the hydrogen bond length, it changes little during the formation of the clathrate cage. 3.3 Effect of THF on the adsorption of gas molecules As a hydrate promoter, THF can form the binary hydrate with gas molecules, thus we chose CH4, CO2 and H2 molecules as representatives to investigate the effects of THF on the attraction of water faces on the second guest. Figure 4 shows the optimized geometries for adsorption of CH4, CO2 and H2 molecules on the water faces of the clathrate cage. Obviously, three gas molecules preferentially locate themselves along the central axis of the adsorption face. When the gas molecules are adsorbed onto the hexagonal water face (a, b, and c), the THF ring is roughly parallel to the adsorption face. While when the gas molecules are adsorbed onto the pentagonal water face (d, e, and f), the THF ring inclines upward because of the steric effect. This phenomenon suggests that THF will adjust itself to suit the adsorption of the gas molecules. Table 2 gives the stabilization energies, the interaction energies of THF and the gas molecules, and the distance (d) between the gas molecules and the adsorption face. We found that the stabilization energies are quite similar for adsorption of CH 4, CO2 or H2 molecule, regardless of the adsorption face is pentagonal or hexagonal. The interaction energies between THF and water molecules are almost independent on the shape of the adsorption faces and the types of the gas molecules. This phenomenon implies that the formation of a cage should be the first stage in the hydrate nucleation, because it is stable enough to attract the gas molecules to catalyse the formation of the new cages by sharing a face [29, 46]. However, the interaction energies between the gas molecules and the clathrate cage shows that CH4, CO2 and H2 molecules are more likely to adsorb on the pentagonal face than the 9
hexagonal face, although they stay farther away from the pentagonal face than the hexagonal face. This is similar to the scenario of the formation of their pure hydrates [24, 43-44]. As compared with the THF hydrate, this difference suggests that the occurrence of the initial clathrate cage mainly depends on the size of the guest molecules.
4. Conclusions The formation process of the clathrate cage of the THF hydrate and its significance to the adsorption of CH4, CO2 and H2 gas molecules were studied by ab initio calculations. The results show that the initial structure of the cage is THF adsorbed onto one side of a hexagonal ring of water molecules. This structure will attract more water molecules to form pentagonal or hexagonal rings in turn. During the formation process, a closed irregular 4151064 cage occurs when the number of water molecules reaches up to 26, and then transforms into the common 51264 cage consisting of 28 water molecules. For the adsorption of the second guests such as CH4, CO2 and H2, they have little effect on the stability of the clathrate cage. Due to the small molecular size, the second guests are more likely to adsorb on the pentagonal face than the hexagonal face. These results will enable us to study in the future the kinetic formation processes of the THF-containing hydrates, as well as the regulating the formation rate and cage occupancy of the second guest for the gas storage and transportation. Work in these directions is in progress and will be reported elsewhere.
Acknowledgements This work was supported by the National Natural Science Foundation of China [Grant numbers 11504133, 11374128]; China Posdoctoral Science Foundation [Grant number 2017M612376]; National Science Foundation for Distinguished Young Scholars [Grant number 51625403]; Postdoctoral Application Research Project of Qingdao [Grant number 2016216]; and Key Laboratory of Gas Hydrate, Guangzhou Institute of Energy Conversion, Chinese Academy of Sciences [Grant number Y707kg1001].
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Figure Captions: FIGURE 1. Minimum energy structures for the (H2O)n=2–6 clusters and their stabilization energies (Estab, kJ∙mol-1) calculated using the PBE-D/TNP level. FIGURE 2. Minimum energy structures for the binary THF·(H2O)n=1–6 clusters and their stabilization energies (Estab, kJ∙mol-1) calculated using the PBE-D/TNP level. FIGURE 3. Minimum energy structures for the binary THF·(H2O)n=7–28 clusters in the formation pathway of the clathrate cage calculated using the PBE-D/TNP level. FIGURE 4. Minimum energy structures for adsorption of CH4, CO2 and H2 molecules on the hexagonal (a, b, and c) and pentagonal (d, e, and f) water faces of the clathrate cage of the THF hydrate.
13
FIGURE 1.
14
FIGURE 2.
15
FIGURE 3.
16
FIGURE 4.
17
TABLE 1 The stabilization energies (Esta), the interaction energies (Eint) between THF and water molecules, the number of tetragonal (fT), pentagonal (fP), and hexagonal (fH) faces of water molecules, the average hydrogen bond length (L), and the distance (D) between the plane of the THF ring and the bottom hexagonal ring for the binary THF·(H 2O)n=7–28 clusters. n
Estab
Eint -1
-1
L/ D/ -10 (×10 m) (×10-10 m)
fT
fP
fH
0
0
1
2.75
3.51
0 1
0 0
1 1
2.76 2.75
3.26 3.51
/(kJ∙mol )
/(kJ∙mol )
25.376 23.735
99.187 99.669
27.305
104.590
27.402 28.463
109.125 114.624
2
0
1
2.75
3.53
0
1
1
2.75
3.57
29.235 28.656
127.167 118.580
1
1
1
2.76
3.62
30.007
137.877
0 0
0 2
2 1
2.77 2.76
3.65 3.67
11, (b)
29.138
133.825
2
1
1
2.75
3.61
12 13
30.200
147.429
30.489
156.981
1 0
2 3
1 1
2.75 2.75
3.66 3.69
14
30.779 31.165
163.542 168.752
1
3
1
2.75
3.73
32.226
174.252
0 2
4 4
1 1
2.75 2.77
3.79 3.81
17 18
32.515
185.155
33.191
191.233
1 0
5 6
1 1
2.75 2.75
3.83 3.83
19
34.252 34.831
197.891 203.680
1
6
1
2.75
3.62
34.638
203.294
1 1
7 8
1 1
2.76 2.77
3.45 3.20
35.410 34.831
214.100 227.705
2
6
2
2.77
3.32
228.380 238.511
9 7
1 2
2.77 2.77
3.14 3.27
23
35.699 36.085
1 2 1
8
2
2.76
3.27
24
36.375
242.660
2
7
3
2.76
3.25
25
36.761 37.243
252.501 264.465
2
8
3
2.76
3.23
37.629
264.851
1 2
10 10
4 4
2.75 2.75
3.20 3.20
39.462
265.527
0
12
4
2.75
3.20
7, (a) 7, (b) 8 9, (a) 9, (b) 10, (a) 10, (b) 11, (a)
15 16
20 21, (a) 21, (b) 22, (a) 22, (b)
26 27 28
TABLE 2 The stabilization energies (Esta), the interaction energies (Eint) of THF and the gas molecules (CH4, CO2 and H2), and the distance (d) between the gas molecules and the nearest water faces. -1
Eint /(kJ∙mol-1) of
Eint /(kJ∙mol-1) of
THF
Gas
Estab /(kJ∙mol ) Gas
d /(×10-10 m)
Hexa-
Penta-
Hexa-
Penta-
Hexa-
Penta-
Hexa-
Penta-
CH4
39.559
39.559
266.106
266.106
15.245
16.306
2.41
2.91
CO2
39.655
39.655
266.009
266.009
11.578
13.025
2.83
2.87
H2
39.655
39.655
266.202
266.106
12.350
13.894
2.11
2.31
19
1. The cage precursor is THF adsorption onto the hexagonal water face. 2. THF has a weak hydrogen bond with the water molecule. 3. The water-water interactions mostly dominate the formation of cages. 4. Gas molecules are likely to adsorb on the pentagonal faces of cages.
20
21
S0021-9614(18)30008-9 https://doi.org/10.1016/j.jct.2018.01.007 YJCHT 5300
To appear in:
J. Chem. Thermodynamics
Received Date: Revised Date: Accepted Date:
2 December 2017 11 January 2018 12 January 2018
Please cite this article as: J. Liu, S. Shi, Z. Zhang, H. Liu, J. Xu, G. Chen, J. Hou, J. Zhang, Ab initio study of formation of the clathrate cage in the tetrahydrofuran hydrate, J. Chem. Thermodynamics (2018), doi: https://doi.org/ 10.1016/j.jct.2018.01.007
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Ab initio study of formation of the clathrate cage in the tetrahydrofuran hydrate Jinxiang Liua,b, Shaofeng Shic, Zhenwei Zhangc, Haiying Liub, Jiafang Xua, Gang Chenb, Jian Houa, Jun Zhangd** a
State Key Laboratory of Heavy Oil Processing, College of Petroleum Engineering, China University of Petroleum, Qingdao, Shandong 266580, China b c
School of Physics and Technology, University of Jinan, Jinan, 250022, China
Linyi Academy of Technology Cooperation and Application, Linyi, 276037, P.R. China d
College of Science, China University of Petroleum, Qingdao, 266580, China
Abstract: Despite the potential applications and ubiquity of clathrate hydrates, the molecular mechanism of formation of these compounds remains poorly understood. In the present work, we performed ab initio calculations to investigate the formation of the clathrate cage of the tetrahydrofuran (THF) hydrate and its significance to the adsorption of gas molecules such as the methane, carbon dioxide, and hydrogen. We found that THF and six water molecules cooperatively organize into an initial stable structure that will allow the growth of more water faces. The formation of the clathrate cage is thermodynamically feasible, and the water-THF interactions become more significant with the increasing water molecules. However, the water-water interactions mostly dominate the formation process due to the strong hydrogen bond interactions. Further, for the adsorption of the second guests, there is little change in the structure and stability of the clathrate cage, but these second guests favor to adsorb onto the pentagonal faces rather than the hexagonal faces. Keywords: tetrahydrofuran hydrate; formation; adsorption; ab initio calculation
Corresponding authors. Email: [email protected] Corresponding authors. Email: [email protected]
**
1
1. Introduction Clathrate hydrates are non-stoichiometric solid
compounds consisting of a
hydrogen-bonded water network of polyhedral water cages which encapsulate small gas molecules such as noble gases, methane, nitrogen, carbon dioxide, and oxygen [1-3]. Based on the differences in the cage shape and size, there are three most common clathrate hydrate structures [4-5]: structure I (sI), structure II (sII), and structure H (sH). Clathrate hydrates have attracted great attention from scientific and industrial areas, including carbon cycling and climate change [6], carbon dioxide sequestration and methane recovery [7], gas storage and transportation [8-10], and cooling application [11]. However, they are usually formed by applying pressures, which are primary drawback in the development and application of the hydrate-based technology [12-14]. In contrast, the tetrahydrofuran (THF) hydrate can be produced under atmospheric pressure below 277.4 K [15], providing a proxy of clathrate hydrates of potential use. More importantly, THF molecules have been recognized as one of the most popular hydrate promoters [16-18], which can allow the mixed hydrates of THF and gas molecules to form at dramatically lower pressure and higher temperature. Of particular interest is the THF hydrate that can serve as a promising candidate for hydrogen storage [19-20]. Pure THF hydrate favours to form the sII structure, which is consisted of 16 pentagonal dodecahedron cages (512 cages) and 8 hexakaidecahdron cages (51264 cages) in the unit cell. Due to the large molecular size, the THF molecules occupy the 51264 cages only, leaving the 512 cages vacant. While in the binary and ternary hydrates (THF+ CH 4/CO2/H2) [20-22], the gas molecules are able to occupy the 512 cages. To promote the applications of the THF hydrates, it is essential to gain a detailed knowledge of the molecular mechanism of the hydrate formation. However, because of very small time (nanoseconds) and length (nanometers) scales involved, it is still incredibly challenging to describe the initial hydrate formation process on molecular length scales in real time even with state-of-the-art experimental techniques [23-24]. To date, several different hypotheses have been proposed to explain the hydrate formation such as the labile cluster hypothesis [25-26], the local structuring hypothesis [27],
2
the blob mechanism [28], and the cage adsorption hypothesis [29], and most of the evidence to support or oppose these hypotheses arises from computer simulations [30-34], which shed some important light on this area. In addition, molecular dynamics simulations of Nada [35] have indicated that dissolved THF molecules were arranged at both large and small cage sites on the interface between the hydrate and the solution phase. As the formation of cages progressed, THF molecules that had once been arranged at small cages sites gradually moved from the sites, and finally were arranged at large cages sites only to form the hydrate structure. By investigating the hydrogen bond interactions between THF and water, Shultz and Vu [36] showed that the THF molecules can modify the hydrogen bonding in the water host to promote the hydrate formation and that this modification is mitigated upon guest incorporation. Wu and co-workers [37] suggest that the growth of THF hydrates is a result of two competing effects: the adsorption of THF molecules to the growing interface and the desorption/rearrangement of THF molecules at the interface. They demonstrated that the desorpiton of THF molecules trapped at the wrong sites on the hydrate surface is the rate-limiting step of the hydrate growth. Yagasaki et al. [38] suggested that the slow growth of THF hydrate is attributed to the trapping of THF molecules in open small cages the hydrate surface, and these trapped THF molecules need to cross one or two Gibbs energy barriers to escape from the surface region. Although THF molecules have been used in many experimental studies of the hydrate formation, there are only a limited number of computer simulation studies that examine the microscopic mechanism of formation of the THF hydrate, and our knowledge is still far from being complete. In the present study, we used ab initio calculations to study the formation of clathrate cage in THF hydrate and its significance to the adsorption of gas molecules such as the methane, carbon dioxide, and hydrogen. First, by comparing the small sized pure water clusters with the binary clusters of THF and water, we obtained the structural and energetic properties of the cage precursor. Second, we examined the growth of the cage precursor to form a clathrate cage by adsorbing more water molecules. Finally, we revealed the effects of the THF molecule on the adsorption of gas molecules. We believe that our work is useful for illustrating the general features of the cage formation process, which is responsible to the hydrate nucleation and growth. 3
2. Computational details The geometry optimizations of the THF(H2O)n=1–28 clusters were carried out in vacuum at 0 K by the DMol3 program [39]. The Perdew-Burke-Ernzerhof (PBE) functionals [40] were used in the generalized gradient approximation for the exchange-correlation energy. The triple numerical plus polarization (TNP) basis functions [41] were used to describe the atomic orbitals. The dispersion correction was introduced by the semi-empirical Tkatchenko-Scheffler scheme [42]. The convergence criteria for the total energy, forces, displacement, and SCF interactions were set as 2.6255×10-2 kJ∙mol-1, 5.251×1010 kJ∙(mol·m) -1, 5.0×10-13 m, and 2.6255×10-3 kJ∙mol-1, respectively. The frequency analysis showed that there is no imaginary frequency in all of the cases, confirming that the obtained structures are minima on the potential energy surface. The thermodynamic stability of the THF(H2O)n=1–28 clusters was evaluated by their stabilization energy (Estab, with zero-point energy correction),
Estab
(n EH 2O ETHF ) Ecluster n 1
(1)
where EH 2 O , ETHF , and Ecluster represent the energies of the water molecule, the methane molecule, and the cluster, respectively. The binding strength of the guest molecule to the clathrate cage was characterized by the interaction energy (Eint), defined as Eint ( Eresidue Eguest ) Etotal
(2)
where Eresidue represents the energy of the cluster without the guest molecule, and E guest represents the energy of the guest molecule.
3. Results and discussion 3.1 Formation of the cage precursor Researchers [24, 29, 34, 43-44] have suggested that before the formation of the hydrate, the rings emerge and gradually grow in number, acting as nucleation seeds, and then lead to the formation of a face-saturated incomplete cage that is regarded as an intermediate structure between independent rings and fully developed cages. To illustrate these initial structures of the hydrate nucleation and to evaluate the THF-water and water-water interactions, we firstly 4
investigated the most stable structures of the pure (H 2O)n=2–6 clusters and the binary THF·(H2O)n=1–6 clusters on the potential energy surface and calculated their stabilization energies. Figure 1 shows that the pure water clusters (n=2–6) have a unique planar cyclic structures, in accordance with theoretical results of Shields et al. [45]. This implies that our calculations are reliable enough. Specially, the growth of the pure water clusters is thermodynamically feasible, because the stabilization energy gradually increases with increasing cluster size, and the growth pattern is the ring expansion that one water molecule inserts into a small ring to form a large ring. With increasing cluster size, the planar cyclic structure becomes thermodynamically unfavourable for pure water clusters [45], and the number of larger rings significantly lowers than that of pentagonal and hexagonal rings from the kinetic point of view [34, 44]. Therefore, we do not further discuss the formation of the larger water rings with the size of n>6. Figure 2 indicates that a typical hydrogen bond forms between the hydrogen atom of the water molecule and the ether oxygen atom of THF, with the hydrogen bond length of 2.75×10-10 m (the O−H···O distance), but the hydrogen bond does not occur between the oxygen atom of water and a hydrogen atom of the α-methylene carbon of THF. The stabilization energy increases with the number of water molecules in the cluster, suggesting that the formation of the binary THF·(H2O)n=1–6 clusters is thermodynamically favorable, while the THF-water interactions become more complex. In detail, the structure a shows that one water molecule donates a hydrogen bond to THF and that the hydroxyl group is almost coplanar with the THF ring. While in the structure b, two water molecules locate themselves above or below the plane of the THF ring to form two hydrogen bonds, and one additional hydrogen bond forms between two water molecules, leading to the formation of a trigonal cyclic structure. For THF·(H2O)3, there are three configurations that can be classified into two conformer groups based on their hydrogen bonding topology. One conformer group is that two water molecules donate two hydrogen bonds to THF and simultaneously bind to a third water molecule via the hydrogen bonding interactions, forming a tetragonal cyclic structure (c1). The other conformer group is that three water molecules form a trigonal cyclic structure that interacts with THF by forming a hydrogen bond (c2 and c3). Despite of the same number of the hydrogen bonds, c2 and c3 have large stabilization energies than c1, because the 5
hydrogen bonding interactions between THF and water are relatively weak. Further, c3 has a larger stabilization energy than c2, suggesting that the THF ring favours to be parallel to the trigonal ring of water molecules. In the case of THF·(H2O)4 and THF·(H2O)5, THF can also participate in forming the cyclic structure with water molecules, but the hexagonal ring (e1) is less stable than the pentagonal ring (d1), implying that such cyclic structure becomes unstable with increasing water molecules. Further, d1 has smaller stabilization energy than c3, which suggest that THF is unlikely to form two hydrogen bond with the water molecules for a cluster of size n>3. Instead, THF prefers to adsorb on one side of the tetragonal (d2 and d3) or pentagonal (e2 and e3) ring of water molecules, and the parallel adsorption of THF (d3 or e3) is more thermodynamically favourable by ~2.026 kJ∙mol-1 than the vertical adsorption (d2 or e2). For THF·(H2O)6, whether the THF ring is parallel or vertical to the hexagonal ring of water molecules in the initial structure, the optimized structure is always the parallel adsorption of THF on one side of the water ring, and the distance between the water ring and the THF ring is roughly 3.09×10-10 m. For the nucleation of the methane hydrate, Walsh et al. [24] have suggested that the cage precursor is the methane adsorbed onto a pentagonal ring of water molecules. Since THF has a large molecular size, we can infer that the cage precursor of the THF hydrate should be THF adsorbed horizontally onto a hexagonal ring of water molecules. In addition, we note that all binary THF·(H2O)n=1–6 clusters have smaller stabilization energies than the pure water clusters of the same size, implying that the latter has greater stability. Although the kinetic mechanisms of the cluster formation are beyond the scope of this paper, it is possible to comment on the structural relationship between these cluster, and then to conclude that the formation of the cage precursor should be that a thermal fluctuation causes water molecules to be arranged into a planar hexagonal ring, which further attracts one THF on its side. This result also suggests that the water-water interactions play a predominant role in the formation of the cage precursor. 3.2 Growth of the cage precursor Figure 3 shows the growth of the cage precursor to form a clathrate cage by adsorbing
6
more water molecules. The structural and energetic properties of the binary THF·(H 2O)n=7–28 clusters involved in the formation process are given in Table 1. For the cluster size of n = 7, one adding water molecule can mediate interactions between THF and the hexagonal water ring via forming hydrogen bonds both with THF and the water ring, resulting in the sandwich-like structure (7a). Due to the steric hindrance effect, THF becomes a little far away from the bottom water face (3.09×10-10 m →3.51×10-10 m). On the other hand, this water molecule can bind to THF only through donating one hydrogen bond (7b). This results in the strong interaction between THF and water molecules. However, 7a is more likely to form, because it has a larger stabilization energy than 7b (25.376 kJ∙mol-1 versus 23.735 kJ∙mol-1), which can be attributed to that the water-water interaction is more significant than the THF-water interaction. For the adsorption of two water molecules (n = 8), they form a tetragonal ring on the side of the bottom face with the help of two water molecules of the cage precursor. THF forms one hydrogen bond with one adsorbed water molecule rather than the water molecules at the bottom face. For THF·(H2O)9, three adsorbed water molecules favor to form a pentagonal ring by hydrogen bonding with two adjacent water molecules of the bottom face (9b), instead of forming two tetragonal rings by hydrogen bonding with three adjacent water molecules of the bottom face (9a). This further indicates that the water-water interactions are more significant than the THF-water interactions and that the water molecules prefer to be arranged in a planar pentagonal cyclic structure. In contrast, for THF·(H2O)10, the formation of a new hexagonal ring of water molecules (10b) is unfavorable than the formation of a pentagonal ring and a tetragonal ring (10a), and THF has a larger interaction energy with the water molecules in the configuration 10a. This can be understood by the aforementioned structures of Figure 2. When the THF ring is vertical to the cyclic structures of water molecules, the trigonal, tetragonal, and pentagonal rings can occur, while the hexagonal ring is thermodynamically unfavourable. In the binary THF·(H2O)11 cluster, both the stabilization energy and the interaction energy demonstrate that five adsorbed water molecules prefer to form the double pentagonal ring than to form a pentagonal ring plus two tetragonal rings, implying that the pentagonal rings are most likely to occur during the formation of the clathrate cage. This reasonably agrees well with the molecular dynamics simulations of Bai et al. [34, 44], which suggested that the number of pentagonal rings 7
considerably exceeds that of hexagonal or tetragonal rings during the hydrate formation. As the clusters extend to n = 12–18, each adsorbed water molecule leads to the formation of a new water face, being alternated with the tetragonal and pentagonal rings. The water-water interactions and the THF-water interactions become more significant, because the stabilization energy increases from 30.200 kJmol-1 to 33.191 kJ∙mol-1 and the interaction energy increase from 147.429 kJ∙mol-1 to 191.233 kJ∙mol-1, which leads to the formation of the semi-cage structure (n = 18) that has a hexagonal and six pentagonal water faces. Interestingly, THF always form one hydrogen bond with the dangling hydrogen atom of one adsorbed water molecule for these clusters. However, due to the steric effects, the distance between the THF ring and the bottom water face keeps to increase (3.66×10-10 m → 3.83×10-10 m) as the cluster size increases. This implies that the water-water interactions are so remarkable that some water molecules can keep closer to the bottom face than THF. By sequentially adsorbing more water molecules, new water faces continually form, and the stabilization energy and the interaction energy maintain to increase. For example, a new tetragonal water face occurs for n = 19, and the tetragonal + pentagonal water faces occur for n = 20. However, for the THF·(H2O)21 cluster, we found that the hexagonal ring of water molecules (21b) is more favourable to form than the pentagonal ring (21a), which results from the reorientation of the THF ring that has the growing trend in parallel with the second hexagonal face. Further, there are two additional tetragonal rings to form in 21b, although this conformer has two fewer pentagonal faces than 21a. In the case of THF·(H2O)22, it has the similar scenario that the formation of the hexagonal face (22b) is thermodynamically more feasible, featuring with the stabilization energy of 35.699 kJ∙mol-1 and the interaction energy of 228.380 kJ∙mol-1. For n = 23, the adsorbed water molecule will insert into a tetragonal ring and lead to the formation of a new pentagonal water face. While in THF·(H 2O)24, the adsorbed water molecule results in the transformation of a pentagonal face to the hexagonal face, accompanied with two tetragonal faces and seven pentagonal faces. By adsorbing one more water molecule, a new pentagonal face appears for n = 25, but this is still an opened cage-like structure. When the number of water molecules reaches to 26, a closed irregular cage occurs, denoted as 4151064, and the hydrogen bond between THF and water molecules disappears. This irregular cage transforms into the irregular 4 251064 cage for n = 27, and then 8
into the intact 51264 cage for n = 28. Note that the distance between the THF ring and the bottom hexagonal water face gradually decreases from 3.62×10-10 m to 3.20×10-10 m as the cluster size increases from n = 19 to n = 26, and maintains 3.20×10-10 m for n = 27 and 28. This is because THF is not large enough to support the continual growth of water faces in vertical orientation. Alternatively, the newly-formed water faces tends to converge on a center line of the bottom face, leading to the decreased distance. Further, THF tends to move to the centre of a closed cage structure, and thus this distance is same for n = 26–28. As for the hydrogen bond length, it changes little during the formation of the clathrate cage. 3.3 Effect of THF on the adsorption of gas molecules As a hydrate promoter, THF can form the binary hydrate with gas molecules, thus we chose CH4, CO2 and H2 molecules as representatives to investigate the effects of THF on the attraction of water faces on the second guest. Figure 4 shows the optimized geometries for adsorption of CH4, CO2 and H2 molecules on the water faces of the clathrate cage. Obviously, three gas molecules preferentially locate themselves along the central axis of the adsorption face. When the gas molecules are adsorbed onto the hexagonal water face (a, b, and c), the THF ring is roughly parallel to the adsorption face. While when the gas molecules are adsorbed onto the pentagonal water face (d, e, and f), the THF ring inclines upward because of the steric effect. This phenomenon suggests that THF will adjust itself to suit the adsorption of the gas molecules. Table 2 gives the stabilization energies, the interaction energies of THF and the gas molecules, and the distance (d) between the gas molecules and the adsorption face. We found that the stabilization energies are quite similar for adsorption of CH 4, CO2 or H2 molecule, regardless of the adsorption face is pentagonal or hexagonal. The interaction energies between THF and water molecules are almost independent on the shape of the adsorption faces and the types of the gas molecules. This phenomenon implies that the formation of a cage should be the first stage in the hydrate nucleation, because it is stable enough to attract the gas molecules to catalyse the formation of the new cages by sharing a face [29, 46]. However, the interaction energies between the gas molecules and the clathrate cage shows that CH4, CO2 and H2 molecules are more likely to adsorb on the pentagonal face than the 9
hexagonal face, although they stay farther away from the pentagonal face than the hexagonal face. This is similar to the scenario of the formation of their pure hydrates [24, 43-44]. As compared with the THF hydrate, this difference suggests that the occurrence of the initial clathrate cage mainly depends on the size of the guest molecules.
4. Conclusions The formation process of the clathrate cage of the THF hydrate and its significance to the adsorption of CH4, CO2 and H2 gas molecules were studied by ab initio calculations. The results show that the initial structure of the cage is THF adsorbed onto one side of a hexagonal ring of water molecules. This structure will attract more water molecules to form pentagonal or hexagonal rings in turn. During the formation process, a closed irregular 4151064 cage occurs when the number of water molecules reaches up to 26, and then transforms into the common 51264 cage consisting of 28 water molecules. For the adsorption of the second guests such as CH4, CO2 and H2, they have little effect on the stability of the clathrate cage. Due to the small molecular size, the second guests are more likely to adsorb on the pentagonal face than the hexagonal face. These results will enable us to study in the future the kinetic formation processes of the THF-containing hydrates, as well as the regulating the formation rate and cage occupancy of the second guest for the gas storage and transportation. Work in these directions is in progress and will be reported elsewhere.
Acknowledgements This work was supported by the National Natural Science Foundation of China [Grant numbers 11504133, 11374128]; China Posdoctoral Science Foundation [Grant number 2017M612376]; National Science Foundation for Distinguished Young Scholars [Grant number 51625403]; Postdoctoral Application Research Project of Qingdao [Grant number 2016216]; and Key Laboratory of Gas Hydrate, Guangzhou Institute of Energy Conversion, Chinese Academy of Sciences [Grant number Y707kg1001].
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Figure Captions: FIGURE 1. Minimum energy structures for the (H2O)n=2–6 clusters and their stabilization energies (Estab, kJ∙mol-1) calculated using the PBE-D/TNP level. FIGURE 2. Minimum energy structures for the binary THF·(H2O)n=1–6 clusters and their stabilization energies (Estab, kJ∙mol-1) calculated using the PBE-D/TNP level. FIGURE 3. Minimum energy structures for the binary THF·(H2O)n=7–28 clusters in the formation pathway of the clathrate cage calculated using the PBE-D/TNP level. FIGURE 4. Minimum energy structures for adsorption of CH4, CO2 and H2 molecules on the hexagonal (a, b, and c) and pentagonal (d, e, and f) water faces of the clathrate cage of the THF hydrate.
13
FIGURE 1.
14
FIGURE 2.
15
FIGURE 3.
16
FIGURE 4.
17
TABLE 1 The stabilization energies (Esta), the interaction energies (Eint) between THF and water molecules, the number of tetragonal (fT), pentagonal (fP), and hexagonal (fH) faces of water molecules, the average hydrogen bond length (L), and the distance (D) between the plane of the THF ring and the bottom hexagonal ring for the binary THF·(H 2O)n=7–28 clusters. n
Estab
Eint -1
-1
L/ D/ -10 (×10 m) (×10-10 m)
fT
fP
fH
0
0
1
2.75
3.51
0 1
0 0
1 1
2.76 2.75
3.26 3.51
/(kJ∙mol )
/(kJ∙mol )
25.376 23.735
99.187 99.669
27.305
104.590
27.402 28.463
109.125 114.624
2
0
1
2.75
3.53
0
1
1
2.75
3.57
29.235 28.656
127.167 118.580
1
1
1
2.76
3.62
30.007
137.877
0 0
0 2
2 1
2.77 2.76
3.65 3.67
11, (b)
29.138
133.825
2
1
1
2.75
3.61
12 13
30.200
147.429
30.489
156.981
1 0
2 3
1 1
2.75 2.75
3.66 3.69
14
30.779 31.165
163.542 168.752
1
3
1
2.75
3.73
32.226
174.252
0 2
4 4
1 1
2.75 2.77
3.79 3.81
17 18
32.515
185.155
33.191
191.233
1 0
5 6
1 1
2.75 2.75
3.83 3.83
19
34.252 34.831
197.891 203.680
1
6
1
2.75
3.62
34.638
203.294
1 1
7 8
1 1
2.76 2.77
3.45 3.20
35.410 34.831
214.100 227.705
2
6
2
2.77
3.32
228.380 238.511
9 7
1 2
2.77 2.77
3.14 3.27
23
35.699 36.085
1 2 1
8
2
2.76
3.27
24
36.375
242.660
2
7
3
2.76
3.25
25
36.761 37.243
252.501 264.465
2
8
3
2.76
3.23
37.629
264.851
1 2
10 10
4 4
2.75 2.75
3.20 3.20
39.462
265.527
0
12
4
2.75
3.20
7, (a) 7, (b) 8 9, (a) 9, (b) 10, (a) 10, (b) 11, (a)
15 16
20 21, (a) 21, (b) 22, (a) 22, (b)
26 27 28
TABLE 2 The stabilization energies (Esta), the interaction energies (Eint) of THF and the gas molecules (CH4, CO2 and H2), and the distance (d) between the gas molecules and the nearest water faces. -1
Eint /(kJ∙mol-1) of
Eint /(kJ∙mol-1) of
THF
Gas
Estab /(kJ∙mol ) Gas
d /(×10-10 m)
Hexa-
Penta-
Hexa-
Penta-
Hexa-
Penta-
Hexa-
Penta-
CH4
39.559
39.559
266.106
266.106
15.245
16.306
2.41
2.91
CO2
39.655
39.655
266.009
266.009
11.578
13.025
2.83
2.87
H2
39.655
39.655
266.202
266.106
12.350
13.894
2.11
2.31
19
1. The cage precursor is THF adsorption onto the hexagonal water face. 2. THF has a weak hydrogen bond with the water molecule. 3. The water-water interactions mostly dominate the formation of cages. 4. Gas molecules are likely to adsorb on the pentagonal faces of cages.
20
21