Storage Capacity and Vibration Frequencies of Guest Molecules in CH

Article pubs.acs.org/JPCA

Storage Capacity and Vibration Frequencies of Guest Molecules in CH4 and CO2 Hydrates by First-Principles Calculations Xiaoxiao Cao,†,‡ Yan Su,*,†,‡ Yuan Liu,†,‡ Jijun Zhao,†,‡ and Changling Liu§,∥ †

Laboratory of Materials Modification by Laser, Ion and Electron Beams, Dalian University of Technology, Ministry of Education, Dalian 116024, China ‡ College of Advanced Science and Technology, Dalian University of Technology, Dalian 116024, China § Key Laboratory of Marine Hydrocarbon Resources and Environmental Geology, Ministry of Land and Resources, Qingdao 266071, China ∥ Qingdao Institute of Marine Geology, Qingdao 266071, China ABSTRACT: Using first-principle calculations at B97-D/6-311++G(2d,2p) level, we systematically explore the gas capacity of five standard water cavities (512, 435663, 51262, 51264, and 51268) in clathrate hydrate and study the inclusion complexes to infer general trends in vibrational frequencies of guest molecules as a function of cage size and number of guest molecules. In addition, the Raman spectra of hydrates from CO2/CH4 gases are simulated. From our calculations, the maximum cage occupancy of the five considered cages (512, 435663, 51262, 51264, and 51268) is one, one, two, three, and seven for both CH4 and CO2 guest molecules, respectively. Meanwhile, the optimum cage occupancy are one, one, one, two, and four for CO2 molecules and one, one, two, three, and five for CH4 molecules, respectively. Both the C−H stretching frequency of CH4 and the C−O stretching frequency of CO2 gradually decrease as size of the water cages increases. Meanwhile, the C−H stretching frequency gradually increases as the amount of CH4 molecules in the water cavity (e.g., 51268) increases.

1. INTRODUCTION Clathrate hydrates are a class of nonstoichiometric crystalline inclusion compounds formed by water molecules and suitably sized gas molecules (CH4, C2H6, C3H8, H2, CO2, Ar, Kr, etc.).1 Water molecules constitute a cage network interlinked by hydrogen bonding, in which the gas molecules as “guest” are encapsulated in the water cages as “host”. The van der Waals (vdW) interactions between the host cages and the guest molecules maintain the stability of clathrate crystals at appropriate temperatures and pressure conditions.2 As an important backup energy resource, methane hydrates are globally widespread in permafrost regions and beneath the sea in sediment of outer continental margins.3 In the past two decades, the amount of methane discovered in the form of gas hydrates is enormous, and the estimated amount of organic carbon in the methane hydrate reservoir greatly exceeds that in many other reservoirs of the global carbon cycle.4 Meanwhile, the possible consequences of addition of methane to the atmosphere from destabilized methane hydrates is a critical concern related to the global warming. Carbon dioxide hydrates have also recently attracted great attentions because the CO2 molecules are potential threatening to the global environment if they are released. In general, carbon dioxide molecules can be captured via smart materials such as activated carbon,5 zeolites,6,7 silica adsorbents,8 carbon nanotubes,9 nanoporous silica-based molecular baskets,10 and so on. However, in industrial applications these materials suffer © 2013 American Chemical Society

from lower weight percentage and regeneration of the captured gas. Alternatively, it is possible to take advantage of clathrate hydrates to reduce the greenhouse effect by storing carbon dioxide. It was also proposed to exploit the methane hydrate deposits in the deep ocean via replacing methane with carbon dioxide, which is considered to be a promising solution to simultaneously access an unconventional fossil fuel reserve and counteract atmospheric CO2 increase.11−13 Ideally, one may extract methane gas from the methane hydrates and seal carbon dioxide into the ocean in the form of hydrate. To date, the fundamental physical/chemical properties of clathrate hydrates have been explored by various spectroscopic means, in particular the Raman spectroscopy. Experimentally, Sum et al. reported a variety of measurements on clathrate hydrates via Raman spectroscopy, including spectra of hydrated and gaseous CH4, CO2, and C3H8.14 Prasad et al. synthesized THF + CH4 mixed hydrates at ambient pressure and various temperatures to obtain Raman signatures for methane molecules using THF as a coguest in mixed hydrates and to elucidate how dissociation temperature varies in the mixed hydrates system as a function of THF concentration.15 Uchida et al. performed Raman spectroscopic analyses on various mixtures of CH4 and C2H6 to obtain the guest molecule Received: September 2, 2013 Revised: November 25, 2013 Published: December 9, 2013 215

dx.doi.org/10.1021/jp408763z | J. Phys. Chem. A 2014, 118, 215−222

The Journal of Physical Chemistry A

Article

cavities, a small pentagonal dodecahedral cavity, namely 512 (12 pentagonal faces), and a large tetrakaidecahedral cavity denoted as 51262 (12 pentagonal faces and 2 hexagonal faces). Structure II (or sII) also has two types of cavities, a small 512 cavity and a large hexakaidecahedral cavity denoted as 51264 (12 pentagonal faces and 4 hexagonal faces). Structure H (or sH) has three types of cavities: a small 512 cavity, a midsized 435663 cavity, and a large icosahedral 51268 cavity (12 pentagonal faces and 8 hexagonal faces).27 The structural type of gas hydrates mainly depends on the size of guest molecules and the external temperature−pressure conditions.28 Here the initial positions of oxygen atoms in the sI, sII, and sH clathrate lattices were taken from experimental data by Gutt et al.,29 Rawn et al.30 and Udachin et al.,31 respectively. The hydrogen atoms were then randomly added and carefully reoriented to satisfy the Bernal−Fowler rule.32 Finally, the structures of five cages (512, 435663, 51262, 51264, and 51268) as basic building units of clathrate hydrate lattices were directly cut from the crystalline structures of sI, sII, or sH hydrates. In clathrate hydrates, the hydrogen bond between water molecules and the vdW interaction between guest molecules and water cages are fundamental. Hence, accurate description of these intermolecular noncovalent interactions is the key to guarantee accurate results of first-principles calculations. With the aid of high-level ab initio methods, our group assessed the capability of twenty DFT methods to describe the intermolecular interactions in methane hydrate.33 Among the evaluated DFT methods, B97-D34 combined with the 6-311++G(2d,2p) basis set was recommended due to their reasonable performance as well as affordable computational expense. In this study, our focus is to computationally examine the stability of clathrate cages and their CO2 and CH4 inclusion complexes. All calculations were performed using the Gaussian 09 program.35 We sequentially added CO2 and CH4 molecules in 512, 435663, 51262, 51264, and 51268 cages and determined the maximum cage occupancy in terms of energetics. The interaction energy (ΔEcage−guest) defined as

spectra, which was used to determine the host structure and guest composition in the hydrate phase.16 Beeskow-Strauch et al. performed a microscopic and laser Raman in situ study to investigate the effects of SO2-polluted CO2 and mixed CH4− C2H6 hydrate on the exchange process.17 Subramanian et al. studied the Raman spectra of guest molecules trapped in clathrate hydrate cages to infer the general trends in vibrational frequencies of guest molecules as a function of cage size, molecular size, molecular vibrational mode, and pressure.18 On the theoretical side, Tse et al. studied the stretching vibrations of methane in the small and large cavities of type-I clathrate hydrate with ab initio molecular dynamics using a linear scaling pseudopotential density functional method.19 Ramya et al. adopted density functional theory (DFT) with the dispersion corrected B97-D functional to characterize the Raman frequency vibrational modes of CH4 and surrounding water molecules in the 512, 51262, and 51264 cages.20 Similarly, Ramya et al. also simulated the vibrational Raman modes of pure and THF doped hydrogen clathrate hydrates.21 In addition to the vibrational properties, many first-principles studies have been devoted to gas hydrates, mainly focusing on the host−guest interaction. For instance, both Lebsir22 and Khan23 performed ab initio calculations on the regular and irregular dodecahedron water clusters of (H2O)20 with and without the presence of guest molecules. They found that incorporating a guest molecule in the (H2O)20 cage could provide a better stabilization for the irregular dodecahedron (435663) cage. Khan carried out ab initio studies of the (H2O)28 hexakaidecahedral cluster with Ne, N2, CH4, and C2H6 guest molecules in the cavity and revealed that the cluster with single occupancy is more stable than that with the double occupancy.24 To reach a better understanding of storage capacities and stability of water cavities, Chattaraj et al. studied the clathrate hydrates of hydrogen using standard DFT calculations and they found that the 512 and 51262 cages may accommodate up to two hydrogen molecules and 51268 cage may store at most six hydrogen molecules.25 Srivastava investigated the viability of five standard water cavities for CO2 capture using B3LYP, M052X and MP2 methods and concluded that the maximum numbers of occupied CO2 molecules are one, two, two, two, and seven for the 512, 435663, 51262, 51264, and 51268 cages, respectively.26 Although many studies on five standard water cavities of hydrates (512, 435663, 51262, 51264, and 51268) are closely related to their storage capacity, previous theoretical simulations have only considered the storage of H2 and CO2 molecules and described the noncovalent interactions using conventional functional (like B3LYP).25,26 Moreover, the storage for CH4 molecules has not been explored yet. These unsolved issues motivate us to conduct systematical calculations on CH4 and CO2 hydrates with high-level ab initio methods to further understand the storage capacities. In addition, the vibrational frequencies and Raman spectra of all considered cages and their CO2 and CH4 inclusion complexes are simulated. These theoretical results provide valuable insights into the stability and spectroscopic properties of CO2 and CH4 hydrates, which would be useful for their future exploitation and applications.

ΔEcage − guest = −(Ecomplex − Ecage − Eguest)

(1)

and stabilization energy (ΔEtotal) defined as ΔEtotal = −(Ecomplex − nE H2O − Eguest)

(2)

were individually calculated at the B97-D/6-311++G(2d,2p) level of theory, where n is the number of water molecules, E complex , E cage , E H 2 O , and E guest are energies of the (CH4)n@(H2O)n and (CO2)n@(H2O)n complex, (H2O)n cluster, water monomer, methane, and carbon dioxide monomer, respectively. The vibrational frequencies were computed within the second-order harmonic approximation, which is a standard procedure of our computational code (Gaussian 0935) and often adopted in previous theoretical studies of clathrate cages.36 Raman intensity was calculated using the harmonic approximation and is written as37 ⎛ ∂ 3E ⎞2 Raman intensity ∝ ⎜ ⎟ ⎝ ∂R ∂F 2 ⎠

(3)

where E is the potential energy, R is the nuclear geometry, and F is the external electric field. Among all these major building blocks of three clathrate crystals (sI, sII, and sH), we considered five different cages as host, namely 512, 435663, 51262, 51264, and 51268 to investigate

2. STRUCTURAL MODELS AND COMPUTATIONAL METHODS Structures I, II, and H are the most common crystal structures of clathrate hydrates. Structure I (or sI) has two types of 216



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the storage capacity of hydrates of methane and carbon dioxide. We calculated the interaction energies using eq 1 and stabilization energies using eq 2. Addition of CH4 and CO2 molecules (guest) to clathrate hydrate (host) are treated as a series of chemical reactions shown below: (CO2 /CH4)n + host → (CO2 /CH4)n @host (n = 1−7)

Table 1. Interaction Energy of CH4 Molecule Encapsulation into Five Different Clathrate Cages Calculated at the B97-D/ 6-311++G(2d,2p) Levela

(4)

(host = 512 , 4356 63, 512 62 , 512 6 4 , and 512 68)

To find the lowest energy configuration of multiply occupied cages, Fleischer et al.38 examined the guest position and orientation in clathrate cages using molecular mechanics. In this study, starting from the five empty host cages, guest molecules (CH4 or CO2) are gradually placed into the cage one by one. For each stoichiometry of multiply occupied cage, several different initial configurations were considered to guarantee the true minimum geometry. Typically, the final geometry does not sensitively rely on the initial position and orientation of inserted guest molecules.

water cage

no. of CH4

ΔEcage‑guest (kJ/mol)

ΔEtotal (kJ/mol)

512 435663 51262

1 1 1 2 1 2 3 1 2 3 4 5 6 7

22.1 22.5 23.6 23.9 30.7 49.8 51.6 23.2 69.7 63.2 70.9 84.4 53.9 50.2

865.7 837.2 965.2 965.7 277.2 1161.0 1145.0 1481.0 1528.0 1521.0 1529.0 1452.0 1512.0 1508.0

51264

51268

dC−C (Å)

3.165 3.336 3.526 3.983 3.740 3.954 3.910 3.964 4.074

dO−O (Å) 2.759 2.770 2.785 2.810 2.849 2.790 2.387 2.773 2.822 2.774 2.783 2.774 2.754 2.668

a

The average C−C distance (dC−C) and O−O distance (dO−O) from B97-D calculations are also listed.

3. RESULTS AND DISCUSSION 3.1. Cage Deformation Due to Encapsulation of Guest Molecules. During the geometry optimization, the cages with multiple guest molecules (CH4 and CO2) are allowed to deform. The optimized structures of five standard cages (512, 435663, 51262, 51264, and 51268) are illustrated in Figure 1, with

Table 2. Interaction Energy of CO2 Molecule Encapsulation into Five Different Clathrate Cages Calculated at the B97-D/ 6-311++G(2d,2p) Levela water cage

no. of CO2

ΔEcage‑guest (kJ/mol)

ΔEtotal (kJ/mol)

512 435663 51262

1 1 1 2 1 2 3 1 2 3 4 5 6 7

17.8 21.4 26.1 17.1 32.7 50.5 33.4 26.1 56.4 90.1 92.8 82.6 46.8 66.7

861.1 836.0 967.8 959.0 1163.0 1132.0 1173.0 1484.0 1514.0 1548.0 1551.0 1541.0 1505.0 1508.0

51264

51268

dC−C (Å)

3.107 3.020 3.925 3.503 3.545 3.745 3.887 4.121 4.685

dO−O (Å) 2.771 2.778 2.789 2.788 2.930 2.741 2.632 2.774 2.772 2.813 2.739 2.593 2.514 2.603

a

The average C−C distance (dC−C) and O−O distance (dO−O) from B97-D calculations are also listed.

Figure 1. B97-D/6-311++G(2d,2p) optimized clathrate cages in stick model with oxygen atoms that are considered in this study along with their stabilization energies given in the parentheses.

3.2. Interaction Energy of CH4 and CO2 Molecule in Clathrate Hydrates. In this section, we first consider the regular (512) and irregular (435663) cages of (H2O)20 clusters, with or without the presence of CH4 and CO2 guest molecules. B97-D/6-311++G(2d,2p) optimized structures of five considered cages with the relative energies are depicted in Figure 1. According to the computed energies, a 512 cage is more stable than a 435663 cage by about 28.9 kJ/mol. The interaction energies for the regular (5 12 ) and irregular (4 3 5 6 6 3 ) dodecahedron with a CH4 molecule and a CO2 molecule are listed in Tables 1 and 2, which show that encapsulating a CH4 or CO2 guest molecule in the cage structure leads to different situations. Compared to the regular 512 cage, the guest molecule provides better stabilization for the irregular dodecahedron (435663) cage. This result is in line with the previous finding by Kumar39 and Khan.23 Second, we consider four different sized cavities (512, 51262, 12 4 5 6 , and 51268) with inclusion of one guest molecule (CH4 or

average O−O distances around 2.760, 2.771, 2.790, 2.792, and 2.934 Å, respectively. Tables 1 and 2 list the average O−O distance of optimized complexes in which the CH4 and CO2 guest molecules are encapsulated. It can be inferred that there is only minor change in the size of the host cages (512, 435663, and 51262), whereas encapsulation of the guest molecules in 51264 and 51268 cages results in some degree of deformation. For (CH4)n@(51264) and (CO2)n@(51264), the average O−O distances variy from 2.849 to 2.387 Å and 2.930 to 2.632 Å. Thus, adding a single guest molecule to the 51264 cage leads to slight expansion, but a further increase in the number of guest molecules results in cage contraction. For (CH4)n@(51268) and (CO2)n@(51268), the average O−O distances reduce from 2.773 to 2.668 Å and 2.774 to 2.603 Å; both are less than that of the 51268 cage (2.934 Å). In other words, adding multiple guest molecules to the 51268 cage makes them substantially smaller upon relaxation. 217



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four CH4 molecules into the 51264 cage cavity leads to structural deformation of the host cage. Thus we conclude that the 51264 cage can accommodate at most three CH4 molecules. For the (CH4)n@(51268) clusters, encapsulation of the first CH4 molecule into the cage cavity results in an interaction energy of 23.2 kJ/mol. In the case of five CH4 molecules inside the 51268 cavity, the interaction energy reaches a maximum; in other words, the optimum cage occupancy for the 51268 cage is five CH4 molecules. Further incorporation of six or seven CH4 molecules in the 51268 cavity shows a decreasing trend in the interaction energies. Finally, encapsulation of the eighth CH4 molecule inside the 51268 cavity leads to severe structural deformation, i.e., collapse of cage and escape of CH4 molecule from the cavity. Because of its larger size, the 51268 can accommodate up to seven CH4 molecules. For (CO2)n@host (host = 512, 435663, 51262, 51264, and 51268) clusters, similar behaviors are observed, which are summarized in Table 2. The numbers of maximum guest molecules and the optimum cage occupancies for CH4 and CO2 hydrates are depicted in Figure 2. For both CH4 and CO2 guest molecules, the

CO2) to infer general trends of stabilization as a function of cage size. After one guest molecule is encapsulated in the 512, 51262, and 51264 cages, the corresponding interaction energy increases and reaches maximum of 30.7 kJ/mol for CH4 molecule and 32.7 kJ/mol for CO2 molecule (Tables 1 and 2), respectively. However, with insertion of one CH4 or CO2 molecule into the largest 51268 cage, the interaction energy decreases to 23.2 kJ/mol for the CH4 molecule and 26.1 kJ/ mol for the CO2 molecule, respectively. Thus, we conclude that the stabilization effect due to the guest molecule gradually increases with the size of water cages; however, an excessive enlargement in cage size will diminish stabilization. Obviously, more guest molecules are needed to further stabilize the oversized cavities. Finally, we compared the interaction energies of CH4 (Table 1) and CO2 (Table 2) occupying small (512) and larger (51262, 51264, and 51268) cavities to gain general insight into the stabilization effect as a function of guest size. As shown in Tables 1 and 2, the interaction energy of (CH4)1@(512) is somewhat larger than (CO2)1@(512), whereas the interaction energy of one CO2 molecule occupying larger (51262, 51264, and 51268) cavities is fairly larger in comparison with the case of one CH4 guest molecule. This suggests that the CO2 molecule is less suitable for the small cavity because of its larger size compared with CH4, but it is more suitable for the larger cavity. Indeed, the match between the size of guest molecule and host cage are essential for stabilization of a clathrate hydrate.1 3.3. Storage Capacity and Stability of CH4 and CO2 Clathrate Hydrates. Previous ab initio calculations by Kumar et al. revealed the viability of clathrate cages (512, 435663, 51262, 51264, and 51268) as CO2 storage agents and showed the maximum cage occupancies for all five considered cages are one, two, two, two, and seven CO2 molecules, respectively.26 Similarly, Fleischer et al. employed molecular mechanics to calculate the stability of multiple occupancy in the various cages (512, 51262, 51264, and 51268) by placing a number of guest molecules (CH4 and CO2) in the cage.38 They found that the maximum cage occupancies for all four considered cages are one, one, three, and five for CH4, and one, one, two, and four for CO2, respectively. In view of the above argument regarding the encapsulation of CO2 and CH4 in the five cavities, we performed geometry optimization on the building cages (512, 435663, 51262, 51264, and 51268) of clathrate, and CO2/CH4 encapsulated cages at the B97-D/6-311++G(2d,2p) level of theory. The calculated interaction energies for all (CH4)n@host systems (host = 512, 435663, 51262, 51264, and 51268 cages) are listed in Table 1. For the (CH4)n@(512) and (CH4)n@(435663) clusters, both cages can form stable complexes upon inclusion of an individual CH4 molecule. However, encapsulation of a second CH4 molecule was not favorable for the 512 and 435663 cages. For the (CH4)n@(51262) clusters, the interaction energy of (CH4)1@(51262) hydrate is 23.6 kJ/mol. In the case of two CH4 molecules inside a 51262 cavity, the interaction energy slightly increases to 23.9 kJ/mol. However, encapsulation of the third CH4 molecule leads to structural deformation, indicating that the 5 1262 cage can only accommodate up to two CH4 molecules. For the (CH4)n@(51264) clusters, because of its larger size, similar behavior can be also observed in Table 1; that is, the interaction energy gradually increases from 30.7 kJ/ mol and reaches a maximum at 51.6 kJ/mol as the number of CH4 molecules increases. However, further encapsulation of

Figure 2. Number of optimum and maximum cage occupancy for CH4 and CO2 molecules encapsulation into five building cages of clathrate.

maximum cage occupancies of the five considered cages (512, 435663, 51262, 51264, and 51268) are one, one, two, three, and seven, respectively; in contrast, the optimum cage occupancies are one, one, two, three, and five for CH4, and one, one, one, two, and four for CO2, respectively. For completeness, the equilibrium structures of the inclusion complexes for all five cages with optimum number of CH4 and CO2 molecules are shown in Figure 3. 3.4. Simulated Raman Spectra of CH 4 and CO 2 Hydrates. Here we simulated the Raman spectra of CH4 and CO2 inclusion complexes to infer general trends in vibrational frequencies of guest molecules as a function of cage size, number and species of guest molecules. Our results are also compared with the qualitative loose-cage/tight-cage model by Pimentel and Charles.40 218



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Figure 3. Optimized structures of optimum possible CO2 and CH4 inclusion complexes in five cages. The clathrate cages stick model with oxygen atoms only are gray. The larger black spheres represent the carbon atoms, and the smaller green spheres represent the hydrogen atoms and red spheres represent the oxygen atoms.

Table 3. Raman Frequencies (cm−1) Peak Assignments for CO2 and CH4 Molecule in Five Cages Compared with Experimental Data Raman peak position (cm−1)

a

molecule

symmetric stretch

CH4

C−H

CO2

C−O

12

5 this work expt this work expt

2957 2915a 1325

435663

51262

51264

51268

2949 2905a 1325

2942 2905a 1321 1275b

2929 2904a 1317 1275b

2933 1317

Reference 14. bReference 17.

Dependence of Frequency Shifts on Cage Size for Guests Occupying Cages. Table 3 lists frequencies of the symmetric C−H stretching mode of CH4 and the C−O stretching mode of CO2 trapped in five different cages. Clearly, the theoretical frequencies of CH4 and CO2 molecules in the water cage show about 50 cm−1 blue shift compared to the experimental values by Sum and Beeskow-Strauch.14,17 However, our theoretical trends qualitatively agree with the experimental finding; that is, the C−H stretching frequency of CH4 gradually decreases by about 10 cm−1 as the size of water cages increases. However, the C−O stretching frequency of CO2 remains unchanged. A distinct trend in frequency shift for the C−H stretching vibration of CH4 and C−O stretching vibration of CO2 between the different cages are shown in Figure 4. We can also see that both the C−H and C−O stretching frequencies gradually decrease as the size of water cages increases. Intuitively, an increase in cage size implies a looser cage environment for the trapped molecule; therefore, the larger the cavity, the lower the frequency of the stretching vibration. This is in line with the previous finding by Subramanian.18 In a previous study, Raman spectra of symmetric C−H stretching mode for methane molecules in the low-energy isomers of (CH4)n@(H2O)n (n = 16, 18, 20, 22, 24) clusters were simulated by Tang et al.36 They found a distinct red-shift trend for the C−H stretching mode as cage size increases from n = 16 to 24. For completeness, here we also simulated the Raman spectra of the investigated molecules in the hydrate state. As displayed in Figure 5, the C−H stretching frequency of CH4 and C−O stretching frequency of CO2 in a large cage shows a red shift with regard to those in a small cage, consistent with the finding by Tang et al.36 Dependence of Frequency Shift on Number of Guest Molecules. CH4 molecules are expected to occupy the large

Figure 4. Symmetric and asymmetric stretch vibrations for CH4 and CO2 molecules encapsulated in the 512, 435663, 51262, 51264, and 51268 cages.

51268 cage. The allowed number of molecules ranges from one to seven. Hence, it is worthwhile to consider the trend in the symmetric C−H stretching frequencies as a function of number of guest molecules when the CH4 molecules occupy the 51268 cage. The theoretical frequencies are shown in Figure 6. Evidently, as the number of guest molecules trapped in the 51268 cage increases, the values for the symmetric C−H stretching frequency become progressively more positive. This can be attributed to the enhanced repulsive interactions 219



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Figure 5. Raman spectra showing the symmetric C−H stretching mode for CH4 molecules and symmetric C−O stretching mode for CO2 molecules in the five standard water cavities.

(CH4)5@(51268) clusters, the Raman spectra have two resonance peaks at 2943 and 2951 cm−1 and at 2966 and 2971 cm−1, respectively. For the (CH4)7@(51268) cluster, the Raman symmetric stretching mode of CH4 in pure CH4 hydrates can be decomposed into four peaks from 2971 to 2990 cm−1. From Figure 7b, a similar situation was also observed for CO2 hydrates; that is, the single Raman peak of one CO2 molecule splits into two and three peaks as the number of CO2 molecules increases due to guest−host interactions. Dependence of Frequency Shifts for Mixed Guest Molecules. Because CH4 and CO2 molecules are the common components of natural gas hydrates, it is important to distinguish the CH4 and CO2 molecules in hydrates via their vibrational frequencies. Typical Raman spectra of mixed hydrates with guest molecules of CH4 and CO2 in a large 51268 cage are given in Figure 8. In the C−H stretching region, the band at 2937 cm−1 was assigned to the C−H stretching in mixed hydrates and the band at 2933 cm−1 was attributed to CH4 hydrates, which show a blue shift with regard to pure CH4 hydrates. In the C−O stretching region, it is difficult to distinguish CO2 from pure CO2 hydrates and CH4−CO2 mixed hydrates, as the spectrum displays the same value (at 1317 cm−1). The present results suggest that in the C−O stretching region, spectroscopic investigation of CO2-containing clathrate hydrates would be complicated, and one cannot simply distinguish hydrate species with Raman spectroscopy. This is consistent with the finding by Seitz et al. that the peak position of the upper Fermi diad member for CO2 is relatively insensitive in the CO2−CH4 system.41

Figure 6. Vibration frequency for (CH4)n (n = 1−7) molecules in 51268 cage.

between the guest molecules and the outer cage, which result in a tighter cage environment for the molecular vibration. Figure 7 presents a stacked plot of four Raman spectra over the frequency ranges 2850−3050 and 1240−1380 cm−1, marked as (a) and (b), respectively. Figure 7a corresponds to the odd number of CH4 molecules, which shows splitting of the Raman spectrum and a blue shift of the stretching frequency of CH4 as the amount of guest molecules increases. For the (CH4)1@(51268) cluster, one clear signal at 2933 cm−1 can be resolved in the spectrum. For each of the (CH4)3@(51268) and

4. CONCLUSIONS From our B97-D/6-311++G(2d,2p) calculations, the maximum occupancies of 512, 435663, 51262, 51264, and 51268 water cages 220



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Figure 7. Raman spectra of CO2 and CH4 molecule in 51268 cage showing unique and splitting peaks under different numbers.

experiments to establish the relationship between the Raman spectrum and the species/amount of guest molecules as well as the type of hydrate cages.

■

AUTHOR INFORMATION

Corresponding Author

*Y. Su: e-mail, [email protected]. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS This work was supported by the National Natural Science Foundation of China (No. 11174045 and No. 11304030) and the Fundamental Research Funds for the Central Universities of China (No. DUT12YQ05).

■

Figure 8. Raman spectrum of mixed hydrates compared to pure CO2 and CH4 hydrates.

REFERENCES

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are one, one, two, three, and seven for both CH4 and CO2 molecules, respectively. The optimum cage occupancies are one, one, one, two, and four for CO2 molecules and one, one, two, three, and five for CH 4 molecules, respectively. Furthermore, Raman spectra of the five standard water cavities with CH4 or CO2 guest molecules were simulated. The stretching frequencies of both C−H bonds in CH4 and C−O bonds in CO2 gradually decrease as the size of water cage increases. In addition, the C−H and C−O stretching frequencies blue shift as the amount of CH4 or CO2 molecules stored in a water cavity (e.g., 51268) increases. In the case of a gas mixture containing one CO2 and one CH4 molecule, the existence of a CO2 molecule in mixed hydrates retains the same Raman signature as the pure CO2 hydrates, whereas the existence of CH4 shows a blue shift by 4 cm−1 compared to the case with pure CH4 hydrates. The storage capacity, thermodynamic stability, and Raman spectra provide vital information on clathrate hydrates. We expect that the present study may provide some useful guidance for effective replacement of CO2/CH4 and trigger new 221



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Storage Capacity and Vibration Frequencies of Guest Molecules in CH

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