Article pubs.acs.org/JPCA
Stability and Vibrations of Guest Molecules in the Type II Clathrate Hydrate: A First-Principles Study of Solid Phase Xiaoxiao Cao,†,‡ Yan Su,*,†,‡ and Jijun Zhao†,‡ †
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 ABSTRACT: Natural gas mixtures are inclusion compounds composed of major light hydrocarbon gaseous molecules (CH4, C2H6, C3H6, and C3H8). Previous ab initio calculations were mainly limited by the cluster models. For the first time, we report first-principles calculations on the stability and vibrational properties of the gas molecules inside the crystalline lattice of type II clathrate. In accordance with our calculations, the larger the size of guest molecule, the more stable the clathrate hydrate for small-sized alkane guest molecules (CnHm, n ≤ 3, m ≤ 8). The interaction energy per guest molecule gradually increases as the number of guest molecules increase for both sII pure and sII mixed hydrates. In addition, the vibrational frequencies of guest molecules trapped in sII hydrate are also simulated. The C−C stretching frequency shows a blue shift as the amount of guest molecules increase. Our theoretical results prove to be valuable insight for identifying the types of guest molecules from experimental spectroscopic data.
1. INTRODUCTION Clathrate hydrates (or gas hydrates) are a class of nonstoichiometric crystalline inclusion compounds. In the clathrate hydrates, water molecules form hydrogen-bonded loose framework built by interlinked cages, in which the gas molecules as “guest” are encapsulated in the water cages as “host”.1 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 Gas hydrates have been recognized as a potentially abundant natural gas resource because huge amounts of natural gases are stored in the crystalline hydrates in deep sea sediments and in permafrost.3 Meanwhile, one has to be aware of the negative influences of gas hydrates, for instance, dissociation of large amount of hydrate deposits would induce geological disasters, and release of methane gas from hydrate deposits into the atmosphere would aggravate the greenhouse effect.4 Therefore, understanding the fundamental properties of gas hydrates is crucial for their future exploitation and applications. Small hydrocarbon molecules, such as methane (CH4), ethane (C2H6), cyclopropane (C3H6) and propane (C3H8) are the major components of natural gas.5 Most of these molecules can be encapsulated in the clathrate framework as guest molecules. As a consequence, there are three kinds of crystalline structures for the gas hydrates of hydrocarbon molecules: structure I (sI), structure II (sII), and structure H (sH).6 The specific hydrate structure depends on not only the size of guest molecule but also the external temperature−pressure condition.7 For example, small guest molecules such as CH4, C2H6, © 2015 American Chemical Society
and C3H6 form sI hydrate, whereas large guest molecules like C3H8 form sII hydrate.8 However, as temperature changes, structural transformation from structure I to II or structure II to I as well as the possible coexistence of structure I and II may occur in gas clathrates.9−12 Moreover, the phase transformation can be triggered by addition of other guest molecules. For example, adding a small amount of propane gas in methane hydrate will convert structure I into II.1,13 Due to the importance of gas hydrates, tremendous experimental and theoretical efforts have been devoted to exploring the structure, phase stability, formation and dissociation mechanisms, and physical properties of gas hydrates. Experimentally, a variety of spectroscopic approaches were employed to monitor the formation of clathrate hydrate. For example, X-ray diffraction and Raman spectroscopic data showed that mixed hydrate of structure II formed from the gas mixture of methane and propane; however, sI clathrate of methane come into being during the next step of hydrate formation when the partial pressure of methane was above the equilibrium pressure of methane hydrate.14 A time-resolved neutron diffraction and Raman spectroscopy study on the formation of hydrate from methane and ethane gas mixture suggested that fast formation of structure II mixed hydrate occurred initially, followed by the transition from structure II (noted as a kinetic product) to the thermodynamically stable structure I.15 For the ternary gas mixture of methane, ethane, Received: May 10, 2015 Revised: June 4, 2015 Published: June 14, 2015 7063
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Figure 1. Structures of single molecule occupied in the smaller 512 cage and larger 51264 cage of sII hydrate. These clathrate cages are shown in stick models with oxygen atoms only (in red). For the guest hydrocarbon molecules, the gray sticks represent the carbon atoms and the white sticks represent the hydrogen atoms.
between host cage and guest molecules as well as the thermodynamic stability of guest molecules in water cavities of clathrate hydrates. For instance, Liu et al. systematically evaluated the performance of 20 density functionals for the description of the intermolecular interaction in methane hydrates.28 Ramya et al. employed the M05-2X functional to demonstrate basis set dependence on guest−host interaction energies in methane hydrates.29 In 2011, Kumar et al. calculated the interaction of a variety of guest molecular species (He, CO, CH4 and NH3, H2) captured in (H2O)20 dodecahedral water cage at the MP2/CBS level of theory.30 Due to high computational costs of MP2 calculations, they also used the B3LYP,31 M06-HF,32 M06-L33 M06-2X,34 and BLYP-D335 functionals to investigate the interaction between the dodecahedral water cage and several guest species later. Srivastava et al. studied the viability of five standard water cavities for CO2 capture using the B3LYP method.36 Using density functional theory (DFT) calculations at the B97-D/6311++G(2d, 2p) level, we investigated the capacity of water cavities (512, 435663, 51262, 51264, and 51268) for storing CH4 and CO2 gaseous molecules25 and also explored the stability of 18 alkane guest molecules (CnHm, n ≤ 6, m ≤ 14) in two standard water cavities (51262 and 51264).26 Despite the above-mentioned efforts of the natural gas hydrates, previous ab initio studies were only limited by the cluster models. To date, a systematic study for guest molecules encapsulated in crystalline hydrate is absent in literature to the best of our knowledge. Moreover, the natural gas in deposit is usually a mixture of small alkane molecules with one to three carbon atoms [i.e., from methane (CH4) to propane (C3H8)], deeper understanding of the sII hydrates encapsulated with these alkane molecules is crucial for exploitation and applications of the natural gas hydrates. In this regard, here we conduct ab initio calculations on the sII clathrate hydrates with CH4, C2H6, C3H6, and C3H8 guest molecules and explore the energetic stability as well as the vibrational frequencies of the C−C stretching mode of guest molecules. Our theoretical results provide valuable insights into the stability and vibrational properties of hydrocarbon hydrates. Especially, the trends of C−C stretching vibrations of hydrocarbon molecules in solid hydrate can be used to identify the species/amount of guest molecules in natural gas hydrate.
and propane, the mixed hydrate of structure II formed; whereas a mixture of sII and sI hydrates was detected below the transition line.16 Vibrational spectroscopic techniques were also used for characterizing the guest molecules of gas hydrates. For pure hydrate, Sum et al. reported the Raman spectra of hydrated and gaseous CH4, CO2, and C3H8.17 Subramanian et al. revealed that the frequency of symmetric C−C stretching mode of isobutene in the large 51264 cavity of sII hydrate was 12.8 cm−1 higher than that in gas phase.18 Such increase in frequency upon encapsulation is similar to the shift of C−C stretching mode of propane in the 51264 cage of sII and that for C−C stretching mode of ethane in sI hydrate.19 For the mixed hydrate, Sum et al.17 measured the Raman spectra of various double hydrates (CH4+CO2/THF/C7D14) and observed the peak shift, which can be explained by the so-called “loose cagetight cage” model originally developed by Pimentel and Charles in 196320 and further elaborated by Subramanian and Sloan in 2002.19 On the other hand, there exist only a few theoretical studies on the molecular vibrations of the guest molecules encapsulated in clathrate hydrates. These studies provided valuable insights into the fundamental properties of gas hydrates from atomistic point of view and may complement the available experimental data on thermodynamic and kinetic aspects. In 2000, Tse et al. first carried out ab initio molecular dynamics simulation to evaluate the vibrational spectra of CH4 in the sI clathrate hydrate. They found that the C−H vibrational frequency in the large 51262 cage shifted to lower frequency with respect to the small 512 cage.21 Later, Hiratsuka22,23 gave details of vibrational characteristics of guest molecule in sI and sH clathrates by changing C−H bond length, H−C−H bond angles, C−H vector direction, and center of mass velocity of CH4, and obtained consistent finding with Tse. Ramya and co-workers adopted the vibrational and librational modes of CH4 and surrounding water molecules in the 512, 512, 51262, and 51264 cages by ab initio computations using a dispersion-corrected B97D functional.24 Recently, we performed ab initio calculations to study the vibrational frequencies of five water cavities and their CH4 and CO2 inclusion complexes.25 In addition, we also simulated the Raman spectra of 18 hydrocarbon molecules from methane to hexane with different carbon skeletons encapsulated in standard 51262 and 51264 cages.26 Liu et al. simulated the Raman spectra of the C−C stretching vibrational modes of seven hydrocarbon gas molecules (CH4, C2H6, C3H6, C3H8, C4H8, i-C4H10, and n-C4H10) in various water cages utilizing a dispersion-corrected ωB97X-D functional together with the 6-311++G(2d, 2p) basis set and found red-shift of the frequency as radius of water cages increases.27 In addition to the vibrational properties, previous ab initio calculations on gas hydrates mainly focused on the interaction
2. STRUCTURAL MODELS AND COMPUTATIONAL METHODS There are three types of known hydrate structures: sI, sII, and sH. Structure I is a cubic structure with stoichiometry of 2(512) · 6(51262) · 46H2O per unit cell. Structure II hydrate is also cubic with stoichiometry of 16(512) · 8(51264) · 136H2O per unit cell. Hydrate of sH has a hexagonal structure with stoichiometry of 2(435663) · 3(512) · 1(51268) · 34H2O per unit 7064
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All the DFT calculations reported in this work are performed using the DMol3 package.39,40 Due to the lack of long-range dispersion interactions, conventional DFT methods are usually insufficient to describe the vdW interactions between the guest molecules (like methane) and the host water molecules.41−43 To overcome this deficiency, some DFT methods with dispersion correction (DFT-D) were developed by adding a dispersion energy term to the Kohn−Sham energy. Among them, Perdew-Burke-Enzerhof (PBE) functional44 with dispersion correction scheme developed by Grimme45 combined with double numerical basis set including the d-polarization function (DNP) were chosen here.46 Table 1 lists the interaction energy of one CH4 molecule inside the smaller 512 cage of sII hydrate, we can see that the PBE functional gives a strength of vdW (25.778 kJ/mol) that is reasonably close to the benchmark value (25.690 kJ/mol) at the MP2/CBS level.28,30 Thus, the PBE functional can serve as an acceptable approach for describing the intermolecular interactions in methane hydrate. In this work, our focus is to computationally examine the stability of light hydrocarbon gas molecules (CH4, C2H6, C3H6, and C3H8) in the host lattice of sII clathrate. The guest molecules are initially placed in the center of appropriate cages, and their positions are allowed to relax during optimization. The host−guest interaction energies (ΔEcage‑guest) per guest molecule were calculated using the following expression:
cell. Occupation of both large and small cages by appropriately sized molecules is necessary to stabilize the hydrate of structures I, II, and H.6 The initial positions of oxygen atoms in clathrate lattice of sII type were taken from experimental data by X-ray diffraction,37 and the orientations of hydrogen atoms in the water molecules were referenced by Takeuchi.38 Since natural gases of C2H6, C3H6, and C3H8 are known to form the structure II clathrate hydrate with CH4 as a helping gas, here we consider only the type II hydrate. All calculations are performed with the (1 × 1 × 1) unit cell of structure II hydrate of 17.32 × 17.32 × 17.32 Å3 dimensions, and the lattice constants were fixed during geometry optimization. Meanwhile, only single molecule occupancy was considered for each water cavity (see Figure 1). Tables 1 and 2 list details of the Table 1. Interaction Energy Per Guest Molecule of Guest Molecule Encapsulation of Different Cages of sII Hydrate Is Listed cage type sII small (512)
sII large (51264)
guest
ΔEcage‑guest (kJ/mol)
ΔEcage‑guest (kJ/mol)
CH4 C2H6 C3H6 C3H8
25.778 − − −
17.372 32.448 40.484 44.067
Table 2. Host−Guest Interaction Energies (ΔEcage‑guest) per Guest Molecule for Pure Hydrates and Mix Hydrates are Listed no. of guest
n
unit cell formula 136H2O·mCH4·nCH4
136H2O·mCH4·nC2H6
136H2O·mCH4·nC3H6
136H2O·mCH4·nC3H8
0 2 4 6 8 2 4 6 8 2 4 6 8 2 4 6 8
m=0
m = 16
ΔEcage‑guest (kJ/mol)
ΔEcage‑guest (kJ/mol)
− 17.532 17.535 17.537 17.539 32.871 32.988 33.316 33.442 40.949 41.205 41.588 42.025 44.645 44.784 44.944 46.002
26.410 25.507 25.508 25.510 25.511 27.316 28.015 28.678 29.217 28.236 29.760 31.101 32.195 29.345 31.260 32.952 34.232
ΔEcage − guest =
−(Ecomplex − E(H 2O)136 − x·Eguest) x
(1)
where x = m + n is the total number of guest molecules, Ecomplex, E(H2O)136, E(H2O), and Eguest are energies of the clathrate structure with guest molecule, empty clathrate lattice, water monomer, and gas-phase guest molecules, respectively. The vibrational frequencies of guest molecules trapped in the sII clathrate were also computed with the same PBE-Grimme scheme.44,45 DMol3 program computes the Hessian of a system by finite differences of analytic gradients to obtain the vibrational frequencies.39,40
3. RESULTS AND DISCUSSION 3.1. Interaction Energy of Guest Molecule in sII Hydrate. We first compute the host−guest interaction energy of an individual CH4 guest molecule encapsulated in sII hydrate and discuss the effect of cage sizes of sII hydrate on the interaction energies. As summarized in Table 1, one can see that the interaction energy of one CH4 molecule inside the smaller 512 cage of sII hydrate is 25.778 kJ/mol, which is 8.406 kJ/mol larger than that in the 51264 cage of sII hydrate (17.372 kJ/mol). This is probably because the vdW radius of small guest molecule like methane fits the size of the smaller 512 cage better. We then consider the sII hydrate with the presence of one guest molecule to infer general trends of stabilization as a function of the size of guest molecule. The previous experiment47 shows that the small size alkane guest molecules (CnHm, n ≤ 3, m ≤ 8) are the major components in natural gas hydrate deposits, while the content of larger size alkane guest molecules (CnHm, n ≥ 4) are rather scarce. In addition, previous theoretical and experimental results7 show that methane can occupy both small and large cages of sII clathrate, while ethane, cyclopropane, and propane are expected to occupy only the large 51264 cages in sII hydrate.18 Hence, we will discuss the stabilization as a function of the size of guest
considered systems of 136H2O·mCH4·nCH4/C2H6/C3H6/ C3H8, where m and n are the numbers of guest molecules encapsulated in larger 51264 cavities and smaller 512 cavities, respectively. For the pure hydrates, the 16 smaller 512 cavities are left vacant (m = 0), and the eight larger 51264 cavies are encapsulated with different types and numbers of guest molecules (n = 1 to 8), forming 20 compositions of sII hydrates. For the mix hydrates, the 16 smaller cavities (512) are fully occupied by methane molecules (m = 16), while the eight larger cavities (51264) are stuffed with other guest molecules (n = 1 to 8), forming 16 compositions of sII hydrates. 7065
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The Journal of Physical Chemistry A molecule when the guest molecules are occupied in the large 51264 cage of structure II clathrate. For sII clathrate hydrates, the guest−host interaction energies of 136H2 O·1CH4 , 136H2O·1C2H6, 136H2O·1C3H6, and 136H2O·1C3H8 are 17.372, 32.448, 40.484, and 44.067 kJ/mol, respectively. The relationship between the interaction energy and the size of guest molecules is depicted in Figure 2, which clearly shows
Figure 3. Clathrate hydrate with the sII structure, which contains 136 molecules of water that form 16 512 and eight 51264 cages per unit cell: (a) pure hydrate, in which guest molecule occupies all the 51264 cages; (b) mix hydrate, in which CH4 occupies all the smaller 512 cages and guest molecule occupies all the larger 51264 cages. The larger blue spheres represent the CH4, C2H6, C3H6, or C3H8 molecules, while the smaller green spheres represent the CH4 molecules.
number of guest molecules, the corresponding interaction energy per guest molecule reaches a maximum of 44 kJ/mol for the C3H8 molecule, suggesting that the hydrates with encapsulation of C3H8 are the most stable. Finally, we discuss the interaction energy per guest molecule of sII mixed hydrates. For simplicity, we assumed that the larger cages of structure II clathrate are occupied by large guest molecules only; although previous theoretical and experimental results7 show that methane molecules stay in either small or large cages. The optimized structure of sII clathrate with 16 smaller 512 cavities fully stuffed with CH4 guest molecules and the eight larger 51264 cavities fully stuffed with other guest molecules is displayed in Figure 3b. The calculated interaction energies are also given in Table 2. One can see that the interaction energy per guest molecule for 16 smaller 512 cavities fully occupied by CH4 molecules is 26.410 kJ/mol, which is about 8 kJ/mol larger than in larger 51264 cavities (17.536 kJ/ mol by average). When further incorporation CH4 guest molecules to the larger 51264 cavities, the interaction energy per guest molecule gradually increase as the number of guest molecule increases, but it is 1 kJ/mol smaller than that in 16 smaller cavities. Similarly, with further incorporation of other guest molecules (C2H6, C3H6, and C3H8) into the larger 51264 cavities, all the interaction energies per guest molecule increase as the number of guest molecules increase, but they are 5−12 kJ/mol smaller than corresponding pure hydrates. Hence, from thermodynamic point of view, the mix hydrates are less stable than the corresponding pure hydrates. 3.2. C−C Stretch Vibration of Guest Molecule in sII Hydrate. The vibrational C−C stretching frequencies of guest molecules can be used to identify the types of guest molecules.27 Here we simulate the light hydrocarbon hydrates (C2H6, C3H6, and C3H8) to infer general trends in C−C stretching vibrational frequencies of guest molecules as a function of guest size, number of guest molecules, and make detailed comparison with previous experimental data. The relevant theoretical results may provide vital information to establish the relationship between the vibrational frequencies and the species/amount of guest molecules. Table 3 lists frequencies of the symmetric and asymmetric C−C stretching modes for an individual C2H6, C3H6, and C3H8 molecule trapped into the sII clathrate lattice. The simulated frequency of C−C stretching vibration for C2H6 in sII hydrate
Figure 2. Interaction energy of a single guest molecule (CH4, C2H6, C3H6, and C3H8) is encapsulated into the sII hydrate unit cell.
that the larger the size of guest molecule, the more stable the clathrate hydrate. However, this trend is only valid for small size alkane guest molecules (CnHm, n ≤ 3, m ≤ 8). For instance, we considered a larger butane (C4H10) molecule occupied in the 51264 cage of sII clathrate, and the computed host−guest interaction energy decreases to 37.153 kJ/mol. Thus, we can conclude that the stabilization effect due to guest molecule gradually increases with molecule size for a sufficiently large host cage; however, an excessive enlargement in guest size will diminish such stabilization. We further discuss the interaction energy per guest molecule of pure sII hydrates (CH4, C2H6, C3H6, or C3H8) to gain general insight into the dependence of stabilization effect on occupation number of guest molecules. CH4, C2H6, C3H6, and C3H8 molecules are expected to occupy the large hexakaidecahedral cavity (51264) of sII clathrate. Hence, the allowed number of guest molecules per unit cell is up to eight. The optimized structure of sII clathrate with eight larger 51264 cavities fully stuffed with guest molecules are shown in Figure 3a, and the calculated interaction energies per guest molecule are shown in Table 2. With insertion of only two CH4, C2H6, C3H6, and C3H8 molecules inside the larger 51264 cages of sII hydrate, the interaction energies per guest molecule are 17.532, 32.871, 40.949, and 44.645 kJ/mol, respectively. After more guest molecules (n = 4−8) are encapsulated, the host−guest interaction energies per guest molecule increase by about 0.002, 0.190, 0.359, and 0.452 kJ/mol, respectively. Moreover, we also considered larger C4H8 molecules occupied in the 51264 cage of sII clathrate hydrate. The computed host−guest interaction energy per guest molecule of 136H2O·2C4H8 and 136H2O· 8C4H8 are 58.817 and 59.819 kJ/mol, respectively. Thus, we can conclude that with the increase of the number of guest molecules, the hydrates become slightly more stable. In addition, when the larger cages of sII hydrate store the same 7066
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is 977 cm−1, and those for the symmetric and symmetric C−C stretching vibration of C3H8 are 874 and 1045 cm−1, respectively. In a previous experiment by Meng et al.48 and Liu et al.,49 the C−C stretching vibration for C2H6 appeared at 991 cm−1, and that for C3H8 appeared at 875 and 1058 cm−1, respectively. Clearly, our theoretical frequencies of guest molecules in the hydrates show a ∼10 cm−1 red shift compared to the experimental values. In Liu theoretical results,27 the C−C stretching vibration for C2H6 in the 51264 cluster appeared at 993 cm−1 and that for C3H8 appeared at 881 cm−1. Our theoretical frequencies of guest molecules in the sII hydrates show a 7−16 cm−1 red shift compared to the guest molecules in
Table 3. Vibration Frequencies (cm−1) and Frequency Shifts of C−C Stretching Bands of an Individual C2H6, C3H6, and C3H8 Molecule in the sII Clathrate Hydrate Compared with Experimental Data guest
vibrational mode
vgas
vguest
Δv
C2H6 C3H8
symmetric stretching symmetric stretching antisymmetric stretching antisymmetric stretching symmetric stretching
996a 869a 1056a 870a 1196a
977 874 1045 882 1202
−19 +5 −11 +12 +6
C3H6 a
Ref 50.
Figure 4. Vibrational frequencies of guest molecules in sII clathrate crystal lattice showing unique frequency shifts under different numbers. (a) C2H6 hydrate; (b) C3H6 hydrate; and (c) C3H8 hydrate. The colorful lines are the average values. 7067
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The Journal of Physical Chemistry A the 5 12 6 4 clusters. This comparison provides valuable information on clathrate hydrates, which would be useful for further understanding the frequency difference between the theoretical calculation and experimental measurements. Table 3 also lists the frequency shifts, Δv = vguest − vgas, that is, frequency change for the C2H6, C3H6, and C3H8 molecules due to encapsulation inside the sII hydrate as a guest. The band assignments for C2H6, C3H6, and C3H8 in the free gas phase were adopted from Schrader et al.50 One can see that the Δv value is negative (−19 cm−1) when a C2H6 guest molecule is trapped in the sII hydrate. However, Δv becomes positive when C3H6 and C3H8 guest molecules are incorporated in sII hydrate except for the antisymmetric stretching vibration of the C3H8 molecule. Dependence of Frequency Shifts on the Size of Guest Molecule. At low pressures (∼1−2 MPa), ethane and propane are expected to occupy only the large 51264 cages in the sII hydrate.18 The molecule size increases from ethane to propane. These two molecules have only one symmetric C−C stretching vibrational mode due to the existence of only one type of C−C bond in each molecule. These frequencies along with the frequency shifts (Δvb) are listed in Table 3. Evidently, as the size of the guest molecule increases, the Δv value for the symmetric C−C stretching frequency becomes progressively more positive, and it is consistent with the theoretical finding by Subramanian.18 This is because increasing repulsive interactions between the guest and the cage with guest size cause the vibration to occur in a progressively tight cage environment. Dependence of Frequency Shift on the Number of Guest Molecules. Recently, we have simulated the Raman spectra of symmetric C−H stretching mode for multiple CH4 molecules trapped in 51268 water cluster.25 We found that the symmetric C−H stretching frequency becomes progressively more positive as the number of guest molecules increases. Here we explore the influence of multiple C2H6, C3H6, and C3H8 guest molecules (occupy adjacent water cage) encapsulation in the sII hydrate crystal on the vibration frequency. The number of guest molecules range from one to four, and the theoretical frequencies are presented in Figure 4. For the C2H6 hydrate, C−C stretching frequency is 977 cm−1 when one C2H6 molecule per unit cell is stored in the clathrate lattice. After encapsulating four C2H6 guest molecules inside the sII hydrate, the C−C stretching frequency increases and reaches a maximum on 983 cm−1 (average value). For the C3H6 hydrate, the asymmetric C−C stretching mode is located at the lower frequency region, and the symmetric mode is in the higher frequency region. Both symmetric and asymmetric C−C stretching frequencies increase as the number of C3H6 molecules increase. Similarly, as the occupation of C3H8 guest molecules increases, the frequencies for the symmetric and asymmetric C−C stretching modes all become progressively more positive and show a blue shift. These may be attributed to the enhanced repulsive interactions between the guest molecules and the outer cage, which result in a tighter cage environment for the molecular vibration.18
interaction energy of one CH4 molecule inside the smaller 512 cage is larger than that in the larger 51264 cage. We also investigate the effect of size of guest molecule on the interaction energy per guest molecule. For small size alkane guest molecules (CnHm, n ≤ 3, m ≤ 8), the larger the size of guest molecule, the more stable the clathrate hydrate. We discuss the influence of the number of guest molecules on the interaction energy per guest molecule and reveal that the interaction energy per guest molecule gradually increases as the number of guest molecules increases. In addition, the vibrational frequencies of guest molecules trapped in the sII hydrate are simulated. The C−C stretching frequency becomes progressively more positive and shows a blue shift as the amount of guest molecules increases. The present theoretical results on the thermodynamic stability and vibrational frequencies provide vital information on the clathrate hydrates and would serve as useful guidance to establish the relationship between the vibrational frequencies and the species/amount of guest molecules.
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AUTHOR INFORMATION
Corresponding Author
*E-mail: [email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This work was supported by the National Natural Science Foundation of China (Grants 11174045 and 11304030) and the Fundamental Research Funds for the Central Universities of China (Grants DUT12YQ05 and DUT14LK19).
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REFERENCES
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4. CONCLUSIONS Using first-principle calculations, we explore the thermodynamic stability of sII clathrate crystal with insertion of a series of hydrocarbon gas molecules (CH4, C2H6, C3H8, and C3H6). We compare the difference of interaction energy between two different cages of sII hydrate and find that the guest−host 7068
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The Journal of Physical Chemistry A (12) Prasad, P. S. R.; Shiva Prasad, K.; Thakur, N. K. FTIR Signatures of Type-II Clathrate of Carbon Dioxide in Natural Quartz Veins. Curr. Sci. 2006, 90, 1544−1547. (13) Erfan-Niya, H.; Modarress, H.; Zaminpayma, E. Computational Study on the Structure II Clathrate Hydrate of Methane and Large Guest Molecules. J. Inclusion Phenom. Macrocyclic Chem. 2011, 70, 227−239. (14) Uchida, T.; Moriwaki, M.; Takeya, S.; Ikeda, I. Y.; Ohmura, R.; Nagao, J.; Minagawa, H.; Ebinuma, T.; Narita, H.; Gohara, K.; Mae, S. Two-Step Formation of Methane-Propane Mixed Gas Hydrates in a Batch-Type Reactor. AlChE J. 2004, 50, 518−523. (15) Murshed, M. M.; Kuhs, W. F. Kinetic Studies of MethaneEthane Mixed Gas Hydrates by Neutron Diffraction and Raman Spectroscopy. J. Phys. Chem. B 2009, 113, 5172−5180. (16) Schicks, J. M.; Naumann, R.; Erzinger, J.; Hester, K. C.; Koh, C. A.; Sloan, E. D. Phase Transitions in Mixed Gas Hydrates: Experimental Observations Versus Calculated Data. J. Phys. Chem. B 2006, 110, 11468−11474. (17) Sum, A. K.; Burruss, R. C.; Sloan, E. D. Measurement of Clathrate Hydrates via Raman Spectroscopy. J. Phys. Chem. B 1997, 101, 7371−7377. (18) Subramanian, S.; Sloan, E. D. Trends in Vibrational Frequencies of Guests Trapped in Clathrate Hydrate Cages. J. Phys. Chem. B 2002, 106, 4348−4355. (19) Subramanian, S.; Kini, R. A.; Dec, S. F.; Sloan, E. D. Evidence of Structure II Hydrate Formation from Methane+Ethane Mixtures. Chem. Eng. Sci. 2000, 55, 1981−1999. (20) Pimentel, G. C.; Charles, S. W. Infrared Spectral Perturbations in Matrix Experiments. Pure Appl. Chem. 1963, 7, 111−124. (21) Tse, J. S. Vibrations of Methane in Structure I Clathrate Hydrate-an ab initio Density Functional Molecular Dynamics Study. Supramol. Chem. 2002, 2, 429−433. (22) Hiratsuka, M.; Ohmura, R.; Sum, A. K.; Yasuoka, K. Vibrational Modes of Methane in the Structure H Clathrate Hydrate from ab initio Molecular Dynamics Simulation. J. Chem. Phys. 2012, 137, 144306. (23) Hiratsuka, M.; Ohmura, R.; Sum, A. K.; Yasuoka, K. Molecular Vibrations of Methane Molecules in the Structure I Clathrate Hydrate from ab initio Molecular Dynamics Simulation. J. Chem. Phys. 2012, 136, 044508. (24) Ramya, K. R.; PavanKumar, G. V.; Venkatnathan, A. Raman Spectra of Vibrational and Librational Modes in Methane Clathrate Hydrates Using Density Functional Theory. J. Chem. Phys. 2012, 136, 174305. (25) Cao, X. X.; Su, Y.; Liu, Y.; Zhao, J. J.; Liu, C. L. Storage Capacity and Vibration Frequencies of Guest Molecules in CH4 and CO2 Hydrates by First-Principles Calculations. J. Chem. Phys. A 2014, 118, 215−222. (26) Cao, X. X.; Su, Y.; Zhao, J. J.; Liu, C. L.; Zhou, P. W. Stability and Raman Spectroscopy of Alkane Guest Molecules (CnHm, n ≤ 6, m ≤ 14) in 51262 and 51264 Water Cavities by Density Functional Theory Calculations. Acta Phys.−Chim. Sin. 2014, 30, 1437−1446. (27) Liu, Y.; Ojamäe, L. C-C Stretching Raman Spectra and Stabilities of Hydrocarbon Molecules in Natural Gas Hydrates: A Quantum Chemical Study. J. Phys. Chem. A 2014, 118, 11641−11651. (28) Liu, Y.; Zhao, J. J.; Li, F. Y.; Chen, Z. F. Appropriate Description of Intermolecular Interactions in the Methane Hydrates: An Assessment of DFT Methods. J. Comput. Chem. 2013, 34, 121−131. (29) Ramya, K. R.; Venkatnathan, A. Stability and Reactivity of Methane Clathrate Hydrates: Insights from Density Functional Theory. J. Phys. Chem. A 2012, 116, 7742−7745. (30) Kumar, P.; Sathyamurthy, N. Theoretical Studies of Host-Guest Interaction in Gas Hydrates. J. Phys. Chem. A 2011, 115, 14276− 14281. (31) Stephens, P. J.; Devlin, F. J.; Chabalowski, C. F.; Frisch, M. J. Ab Initio Calculation of Vibrational Absorption and Circular Dichroism Spectra Using Density Functional Force Fields. J. Phys. Chem. 1994, 98, 11623−11627. (32) Zhao, Y.; Truhlar, D. G. Density Functional for Spectroscopy: No Long-Range Self-Interaction Error, Good Performance for
Rydberg and Charge-Transfer States, and Better Performance on Average than B3LYP for Ground States. J. Phys. Chem. A 2006, 110, 13126−13130. (33) Zhao, Y.; Truhlar, D. G. A New Local Density Functional for Main-Group Thermochemistry, Transition Metal Bonding, Thermochemical Kinetics, and Noncovalent Interactions. J. Chem. Phys. 2006, 125, 194101. (34) Zhao, Y.; Truhlar, D. G. The M06 Suite of Density Functionals for Main Group Thermochemistry Thermochemical Kinetics, Noncovalent Interactions, Excited States, and Transition Elements: Two New Functionals and Systematic Testing of Four M06-Class Functionals and 12 other Functionals. Theor. Chem. Acc. 2008, 120, 215−241. (35) Grimme, S.; Antony, J.; Ehrlich, S.; Krieg, H. A Consistent and Accurate ab initio Parametrization of Density Functional Dispersion Correction (DFT-D) for the 94 Elements H-Pu. J. Chem. Phys. 2010, 132, 154104. (36) Srivastava, H. K.; Sastry, G. N. Viability of Clathrate Hydrates as CO2 Capturing Agents: A Theoretical Study. J. Phys. Chem. A 2011, 115, 7633−7637. (37) Rawn, C. J.; Rondinone, A. J.; Chakoumakos, B. C.; Stern, S.; Circone, L. A.; Kirby, S. H.; Ishii, Y. Neutron Powder Diffraction Studies as a function of Temperature of Structure II Hydrate Formed from Propane. Can. J. Phys. 2003, 81, 431−438. (38) Takeuchi, F.; Hiratsuka, M.; Ohmura, R.; Alavi, S.; Sum, A. K.; Yasuoka, K. Water Proton Configurations in Structures I, II, and H Clathrate Hydrate Unit Cells. J. Chem. Phys. 2013, 138, 124504. (39) Delley, B. An Allelectron Numerical Method for Solving the Local Density Functional for Polyatomic Molecules. J. Chem. Phys. 1990, 92, 508−517. (40) Delley, B. From Molecules to Solids with the DMol3 Approach. J. Chem. Phys. 2000, 113, 7756−7764. (41) Kohn, W.; Meir, Y.; Makarov, D. E. Van der Waals Energies in Density Functional Theory. Phys. Rev. Lett. 1998, 80, 4153−4156. (42) Dion, M.; Rydberg, H.; Schröder, E.; Langreth, D. C.; Lundqvist, B. I. Van der Waals Density Functional for General Geometries. Phys. Rev. Lett. 2004, 92, 246401. (43) Grimme, S. Density Functional Theory with London Dispersion Corrections. Comput. Mol. Sci. 2001, 1, 211−228. (44) Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1996, 77, 3865. (45) Grimme, S. Semiempirical GGA-Type Density Functional Constructed with a Long-Range Dispersion Correction. J. Comput. Chem. 2006, 27, 1787−1799. (46) Zheng, Z. Y.; Zhao, J. J.; Sun, Y. Y.; Zhang, S. B. Structures and Lattice Energies of Molecular Crystals Using Density Functional Theory: Assessment of a Local Atomic Potential Approach. Chem. Phys. Lett. 2012, 550, 94−98. (47) Liu, C. L.; Ye, Y. G.; Meng, Q. G.; Lu, Z. Q.; Zhu, Y. H.; Liu, J.; Yang, S. X. Raman Spectroscopic Characteristics of Natural Gas Hydrate Recovered from Shenhu Area in South China Sea and Qilian Mountain Permafrost. Acta Chim. Sin. 2010, 68, 1881−1886. (48) Meng, Q. G.; Liu, C. L.; He, X. L.; Ye, Y. G.; Zhu, Y. H.; Xia, N. Laser-Raman Spectroscopy Characteristics of Natural Gas Hydrates from Qilian Mountain Permafrost. Geol. Bull. Geol. Surv. China 2011, 30, 1863−1867. (49) Liu, C. L.; Ye, Y. G.; Meng, Q. G.; Lu, Z. Q.; Zhu, Y. H.; Liu, J.; Yang, S. X. Raman Spectroscopic Characteristics of Natural Gas Hydrate Recovered from Shenhu Area in South China Sea and Qilian Mountain Permafrost. Acta Chim. Sin. 2010, 68, 1881−1886. (50) Schrader, B. Raman/Infrared Atlas of Organic Compounds; VCH: Germany, 1989.
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Stability and Vibrations of Guest Molecules in the Type II Clathrate Hydrate: A First-Principles Study of Solid Phase Xiaoxiao Cao,†,‡ Yan Su,*,†,‡ and Jijun Zhao†,‡ †
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 ABSTRACT: Natural gas mixtures are inclusion compounds composed of major light hydrocarbon gaseous molecules (CH4, C2H6, C3H6, and C3H8). Previous ab initio calculations were mainly limited by the cluster models. For the first time, we report first-principles calculations on the stability and vibrational properties of the gas molecules inside the crystalline lattice of type II clathrate. In accordance with our calculations, the larger the size of guest molecule, the more stable the clathrate hydrate for small-sized alkane guest molecules (CnHm, n ≤ 3, m ≤ 8). The interaction energy per guest molecule gradually increases as the number of guest molecules increase for both sII pure and sII mixed hydrates. In addition, the vibrational frequencies of guest molecules trapped in sII hydrate are also simulated. The C−C stretching frequency shows a blue shift as the amount of guest molecules increase. Our theoretical results prove to be valuable insight for identifying the types of guest molecules from experimental spectroscopic data.
1. INTRODUCTION Clathrate hydrates (or gas hydrates) are a class of nonstoichiometric crystalline inclusion compounds. In the clathrate hydrates, water molecules form hydrogen-bonded loose framework built by interlinked cages, in which the gas molecules as “guest” are encapsulated in the water cages as “host”.1 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 Gas hydrates have been recognized as a potentially abundant natural gas resource because huge amounts of natural gases are stored in the crystalline hydrates in deep sea sediments and in permafrost.3 Meanwhile, one has to be aware of the negative influences of gas hydrates, for instance, dissociation of large amount of hydrate deposits would induce geological disasters, and release of methane gas from hydrate deposits into the atmosphere would aggravate the greenhouse effect.4 Therefore, understanding the fundamental properties of gas hydrates is crucial for their future exploitation and applications. Small hydrocarbon molecules, such as methane (CH4), ethane (C2H6), cyclopropane (C3H6) and propane (C3H8) are the major components of natural gas.5 Most of these molecules can be encapsulated in the clathrate framework as guest molecules. As a consequence, there are three kinds of crystalline structures for the gas hydrates of hydrocarbon molecules: structure I (sI), structure II (sII), and structure H (sH).6 The specific hydrate structure depends on not only the size of guest molecule but also the external temperature−pressure condition.7 For example, small guest molecules such as CH4, C2H6, © 2015 American Chemical Society
and C3H6 form sI hydrate, whereas large guest molecules like C3H8 form sII hydrate.8 However, as temperature changes, structural transformation from structure I to II or structure II to I as well as the possible coexistence of structure I and II may occur in gas clathrates.9−12 Moreover, the phase transformation can be triggered by addition of other guest molecules. For example, adding a small amount of propane gas in methane hydrate will convert structure I into II.1,13 Due to the importance of gas hydrates, tremendous experimental and theoretical efforts have been devoted to exploring the structure, phase stability, formation and dissociation mechanisms, and physical properties of gas hydrates. Experimentally, a variety of spectroscopic approaches were employed to monitor the formation of clathrate hydrate. For example, X-ray diffraction and Raman spectroscopic data showed that mixed hydrate of structure II formed from the gas mixture of methane and propane; however, sI clathrate of methane come into being during the next step of hydrate formation when the partial pressure of methane was above the equilibrium pressure of methane hydrate.14 A time-resolved neutron diffraction and Raman spectroscopy study on the formation of hydrate from methane and ethane gas mixture suggested that fast formation of structure II mixed hydrate occurred initially, followed by the transition from structure II (noted as a kinetic product) to the thermodynamically stable structure I.15 For the ternary gas mixture of methane, ethane, Received: May 10, 2015 Revised: June 4, 2015 Published: June 14, 2015 7063
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Figure 1. Structures of single molecule occupied in the smaller 512 cage and larger 51264 cage of sII hydrate. These clathrate cages are shown in stick models with oxygen atoms only (in red). For the guest hydrocarbon molecules, the gray sticks represent the carbon atoms and the white sticks represent the hydrogen atoms.
between host cage and guest molecules as well as the thermodynamic stability of guest molecules in water cavities of clathrate hydrates. For instance, Liu et al. systematically evaluated the performance of 20 density functionals for the description of the intermolecular interaction in methane hydrates.28 Ramya et al. employed the M05-2X functional to demonstrate basis set dependence on guest−host interaction energies in methane hydrates.29 In 2011, Kumar et al. calculated the interaction of a variety of guest molecular species (He, CO, CH4 and NH3, H2) captured in (H2O)20 dodecahedral water cage at the MP2/CBS level of theory.30 Due to high computational costs of MP2 calculations, they also used the B3LYP,31 M06-HF,32 M06-L33 M06-2X,34 and BLYP-D335 functionals to investigate the interaction between the dodecahedral water cage and several guest species later. Srivastava et al. studied the viability of five standard water cavities for CO2 capture using the B3LYP method.36 Using density functional theory (DFT) calculations at the B97-D/6311++G(2d, 2p) level, we investigated the capacity of water cavities (512, 435663, 51262, 51264, and 51268) for storing CH4 and CO2 gaseous molecules25 and also explored the stability of 18 alkane guest molecules (CnHm, n ≤ 6, m ≤ 14) in two standard water cavities (51262 and 51264).26 Despite the above-mentioned efforts of the natural gas hydrates, previous ab initio studies were only limited by the cluster models. To date, a systematic study for guest molecules encapsulated in crystalline hydrate is absent in literature to the best of our knowledge. Moreover, the natural gas in deposit is usually a mixture of small alkane molecules with one to three carbon atoms [i.e., from methane (CH4) to propane (C3H8)], deeper understanding of the sII hydrates encapsulated with these alkane molecules is crucial for exploitation and applications of the natural gas hydrates. In this regard, here we conduct ab initio calculations on the sII clathrate hydrates with CH4, C2H6, C3H6, and C3H8 guest molecules and explore the energetic stability as well as the vibrational frequencies of the C−C stretching mode of guest molecules. Our theoretical results provide valuable insights into the stability and vibrational properties of hydrocarbon hydrates. Especially, the trends of C−C stretching vibrations of hydrocarbon molecules in solid hydrate can be used to identify the species/amount of guest molecules in natural gas hydrate.
and propane, the mixed hydrate of structure II formed; whereas a mixture of sII and sI hydrates was detected below the transition line.16 Vibrational spectroscopic techniques were also used for characterizing the guest molecules of gas hydrates. For pure hydrate, Sum et al. reported the Raman spectra of hydrated and gaseous CH4, CO2, and C3H8.17 Subramanian et al. revealed that the frequency of symmetric C−C stretching mode of isobutene in the large 51264 cavity of sII hydrate was 12.8 cm−1 higher than that in gas phase.18 Such increase in frequency upon encapsulation is similar to the shift of C−C stretching mode of propane in the 51264 cage of sII and that for C−C stretching mode of ethane in sI hydrate.19 For the mixed hydrate, Sum et al.17 measured the Raman spectra of various double hydrates (CH4+CO2/THF/C7D14) and observed the peak shift, which can be explained by the so-called “loose cagetight cage” model originally developed by Pimentel and Charles in 196320 and further elaborated by Subramanian and Sloan in 2002.19 On the other hand, there exist only a few theoretical studies on the molecular vibrations of the guest molecules encapsulated in clathrate hydrates. These studies provided valuable insights into the fundamental properties of gas hydrates from atomistic point of view and may complement the available experimental data on thermodynamic and kinetic aspects. In 2000, Tse et al. first carried out ab initio molecular dynamics simulation to evaluate the vibrational spectra of CH4 in the sI clathrate hydrate. They found that the C−H vibrational frequency in the large 51262 cage shifted to lower frequency with respect to the small 512 cage.21 Later, Hiratsuka22,23 gave details of vibrational characteristics of guest molecule in sI and sH clathrates by changing C−H bond length, H−C−H bond angles, C−H vector direction, and center of mass velocity of CH4, and obtained consistent finding with Tse. Ramya and co-workers adopted the vibrational and librational modes of CH4 and surrounding water molecules in the 512, 512, 51262, and 51264 cages by ab initio computations using a dispersion-corrected B97D functional.24 Recently, we performed ab initio calculations to study the vibrational frequencies of five water cavities and their CH4 and CO2 inclusion complexes.25 In addition, we also simulated the Raman spectra of 18 hydrocarbon molecules from methane to hexane with different carbon skeletons encapsulated in standard 51262 and 51264 cages.26 Liu et al. simulated the Raman spectra of the C−C stretching vibrational modes of seven hydrocarbon gas molecules (CH4, C2H6, C3H6, C3H8, C4H8, i-C4H10, and n-C4H10) in various water cages utilizing a dispersion-corrected ωB97X-D functional together with the 6-311++G(2d, 2p) basis set and found red-shift of the frequency as radius of water cages increases.27 In addition to the vibrational properties, previous ab initio calculations on gas hydrates mainly focused on the interaction
2. STRUCTURAL MODELS AND COMPUTATIONAL METHODS There are three types of known hydrate structures: sI, sII, and sH. Structure I is a cubic structure with stoichiometry of 2(512) · 6(51262) · 46H2O per unit cell. Structure II hydrate is also cubic with stoichiometry of 16(512) · 8(51264) · 136H2O per unit cell. Hydrate of sH has a hexagonal structure with stoichiometry of 2(435663) · 3(512) · 1(51268) · 34H2O per unit 7064
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All the DFT calculations reported in this work are performed using the DMol3 package.39,40 Due to the lack of long-range dispersion interactions, conventional DFT methods are usually insufficient to describe the vdW interactions between the guest molecules (like methane) and the host water molecules.41−43 To overcome this deficiency, some DFT methods with dispersion correction (DFT-D) were developed by adding a dispersion energy term to the Kohn−Sham energy. Among them, Perdew-Burke-Enzerhof (PBE) functional44 with dispersion correction scheme developed by Grimme45 combined with double numerical basis set including the d-polarization function (DNP) were chosen here.46 Table 1 lists the interaction energy of one CH4 molecule inside the smaller 512 cage of sII hydrate, we can see that the PBE functional gives a strength of vdW (25.778 kJ/mol) that is reasonably close to the benchmark value (25.690 kJ/mol) at the MP2/CBS level.28,30 Thus, the PBE functional can serve as an acceptable approach for describing the intermolecular interactions in methane hydrate. In this work, our focus is to computationally examine the stability of light hydrocarbon gas molecules (CH4, C2H6, C3H6, and C3H8) in the host lattice of sII clathrate. The guest molecules are initially placed in the center of appropriate cages, and their positions are allowed to relax during optimization. The host−guest interaction energies (ΔEcage‑guest) per guest molecule were calculated using the following expression:
cell. Occupation of both large and small cages by appropriately sized molecules is necessary to stabilize the hydrate of structures I, II, and H.6 The initial positions of oxygen atoms in clathrate lattice of sII type were taken from experimental data by X-ray diffraction,37 and the orientations of hydrogen atoms in the water molecules were referenced by Takeuchi.38 Since natural gases of C2H6, C3H6, and C3H8 are known to form the structure II clathrate hydrate with CH4 as a helping gas, here we consider only the type II hydrate. All calculations are performed with the (1 × 1 × 1) unit cell of structure II hydrate of 17.32 × 17.32 × 17.32 Å3 dimensions, and the lattice constants were fixed during geometry optimization. Meanwhile, only single molecule occupancy was considered for each water cavity (see Figure 1). Tables 1 and 2 list details of the Table 1. Interaction Energy Per Guest Molecule of Guest Molecule Encapsulation of Different Cages of sII Hydrate Is Listed cage type sII small (512)
sII large (51264)
guest
ΔEcage‑guest (kJ/mol)
ΔEcage‑guest (kJ/mol)
CH4 C2H6 C3H6 C3H8
25.778 − − −
17.372 32.448 40.484 44.067
Table 2. Host−Guest Interaction Energies (ΔEcage‑guest) per Guest Molecule for Pure Hydrates and Mix Hydrates are Listed no. of guest
n
unit cell formula 136H2O·mCH4·nCH4
136H2O·mCH4·nC2H6
136H2O·mCH4·nC3H6
136H2O·mCH4·nC3H8
0 2 4 6 8 2 4 6 8 2 4 6 8 2 4 6 8
m=0
m = 16
ΔEcage‑guest (kJ/mol)
ΔEcage‑guest (kJ/mol)
− 17.532 17.535 17.537 17.539 32.871 32.988 33.316 33.442 40.949 41.205 41.588 42.025 44.645 44.784 44.944 46.002
26.410 25.507 25.508 25.510 25.511 27.316 28.015 28.678 29.217 28.236 29.760 31.101 32.195 29.345 31.260 32.952 34.232
ΔEcage − guest =
−(Ecomplex − E(H 2O)136 − x·Eguest) x
(1)
where x = m + n is the total number of guest molecules, Ecomplex, E(H2O)136, E(H2O), and Eguest are energies of the clathrate structure with guest molecule, empty clathrate lattice, water monomer, and gas-phase guest molecules, respectively. The vibrational frequencies of guest molecules trapped in the sII clathrate were also computed with the same PBE-Grimme scheme.44,45 DMol3 program computes the Hessian of a system by finite differences of analytic gradients to obtain the vibrational frequencies.39,40
3. RESULTS AND DISCUSSION 3.1. Interaction Energy of Guest Molecule in sII Hydrate. We first compute the host−guest interaction energy of an individual CH4 guest molecule encapsulated in sII hydrate and discuss the effect of cage sizes of sII hydrate on the interaction energies. As summarized in Table 1, one can see that the interaction energy of one CH4 molecule inside the smaller 512 cage of sII hydrate is 25.778 kJ/mol, which is 8.406 kJ/mol larger than that in the 51264 cage of sII hydrate (17.372 kJ/mol). This is probably because the vdW radius of small guest molecule like methane fits the size of the smaller 512 cage better. We then consider the sII hydrate with the presence of one guest molecule to infer general trends of stabilization as a function of the size of guest molecule. The previous experiment47 shows that the small size alkane guest molecules (CnHm, n ≤ 3, m ≤ 8) are the major components in natural gas hydrate deposits, while the content of larger size alkane guest molecules (CnHm, n ≥ 4) are rather scarce. In addition, previous theoretical and experimental results7 show that methane can occupy both small and large cages of sII clathrate, while ethane, cyclopropane, and propane are expected to occupy only the large 51264 cages in sII hydrate.18 Hence, we will discuss the stabilization as a function of the size of guest
considered systems of 136H2O·mCH4·nCH4/C2H6/C3H6/ C3H8, where m and n are the numbers of guest molecules encapsulated in larger 51264 cavities and smaller 512 cavities, respectively. For the pure hydrates, the 16 smaller 512 cavities are left vacant (m = 0), and the eight larger 51264 cavies are encapsulated with different types and numbers of guest molecules (n = 1 to 8), forming 20 compositions of sII hydrates. For the mix hydrates, the 16 smaller cavities (512) are fully occupied by methane molecules (m = 16), while the eight larger cavities (51264) are stuffed with other guest molecules (n = 1 to 8), forming 16 compositions of sII hydrates. 7065
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The Journal of Physical Chemistry A molecule when the guest molecules are occupied in the large 51264 cage of structure II clathrate. For sII clathrate hydrates, the guest−host interaction energies of 136H2 O·1CH4 , 136H2O·1C2H6, 136H2O·1C3H6, and 136H2O·1C3H8 are 17.372, 32.448, 40.484, and 44.067 kJ/mol, respectively. The relationship between the interaction energy and the size of guest molecules is depicted in Figure 2, which clearly shows
Figure 3. Clathrate hydrate with the sII structure, which contains 136 molecules of water that form 16 512 and eight 51264 cages per unit cell: (a) pure hydrate, in which guest molecule occupies all the 51264 cages; (b) mix hydrate, in which CH4 occupies all the smaller 512 cages and guest molecule occupies all the larger 51264 cages. The larger blue spheres represent the CH4, C2H6, C3H6, or C3H8 molecules, while the smaller green spheres represent the CH4 molecules.
number of guest molecules, the corresponding interaction energy per guest molecule reaches a maximum of 44 kJ/mol for the C3H8 molecule, suggesting that the hydrates with encapsulation of C3H8 are the most stable. Finally, we discuss the interaction energy per guest molecule of sII mixed hydrates. For simplicity, we assumed that the larger cages of structure II clathrate are occupied by large guest molecules only; although previous theoretical and experimental results7 show that methane molecules stay in either small or large cages. The optimized structure of sII clathrate with 16 smaller 512 cavities fully stuffed with CH4 guest molecules and the eight larger 51264 cavities fully stuffed with other guest molecules is displayed in Figure 3b. The calculated interaction energies are also given in Table 2. One can see that the interaction energy per guest molecule for 16 smaller 512 cavities fully occupied by CH4 molecules is 26.410 kJ/mol, which is about 8 kJ/mol larger than in larger 51264 cavities (17.536 kJ/ mol by average). When further incorporation CH4 guest molecules to the larger 51264 cavities, the interaction energy per guest molecule gradually increase as the number of guest molecule increases, but it is 1 kJ/mol smaller than that in 16 smaller cavities. Similarly, with further incorporation of other guest molecules (C2H6, C3H6, and C3H8) into the larger 51264 cavities, all the interaction energies per guest molecule increase as the number of guest molecules increase, but they are 5−12 kJ/mol smaller than corresponding pure hydrates. Hence, from thermodynamic point of view, the mix hydrates are less stable than the corresponding pure hydrates. 3.2. C−C Stretch Vibration of Guest Molecule in sII Hydrate. The vibrational C−C stretching frequencies of guest molecules can be used to identify the types of guest molecules.27 Here we simulate the light hydrocarbon hydrates (C2H6, C3H6, and C3H8) to infer general trends in C−C stretching vibrational frequencies of guest molecules as a function of guest size, number of guest molecules, and make detailed comparison with previous experimental data. The relevant theoretical results may provide vital information to establish the relationship between the vibrational frequencies and the species/amount of guest molecules. Table 3 lists frequencies of the symmetric and asymmetric C−C stretching modes for an individual C2H6, C3H6, and C3H8 molecule trapped into the sII clathrate lattice. The simulated frequency of C−C stretching vibration for C2H6 in sII hydrate
Figure 2. Interaction energy of a single guest molecule (CH4, C2H6, C3H6, and C3H8) is encapsulated into the sII hydrate unit cell.
that the larger the size of guest molecule, the more stable the clathrate hydrate. However, this trend is only valid for small size alkane guest molecules (CnHm, n ≤ 3, m ≤ 8). For instance, we considered a larger butane (C4H10) molecule occupied in the 51264 cage of sII clathrate, and the computed host−guest interaction energy decreases to 37.153 kJ/mol. Thus, we can conclude that the stabilization effect due to guest molecule gradually increases with molecule size for a sufficiently large host cage; however, an excessive enlargement in guest size will diminish such stabilization. We further discuss the interaction energy per guest molecule of pure sII hydrates (CH4, C2H6, C3H6, or C3H8) to gain general insight into the dependence of stabilization effect on occupation number of guest molecules. CH4, C2H6, C3H6, and C3H8 molecules are expected to occupy the large hexakaidecahedral cavity (51264) of sII clathrate. Hence, the allowed number of guest molecules per unit cell is up to eight. The optimized structure of sII clathrate with eight larger 51264 cavities fully stuffed with guest molecules are shown in Figure 3a, and the calculated interaction energies per guest molecule are shown in Table 2. With insertion of only two CH4, C2H6, C3H6, and C3H8 molecules inside the larger 51264 cages of sII hydrate, the interaction energies per guest molecule are 17.532, 32.871, 40.949, and 44.645 kJ/mol, respectively. After more guest molecules (n = 4−8) are encapsulated, the host−guest interaction energies per guest molecule increase by about 0.002, 0.190, 0.359, and 0.452 kJ/mol, respectively. Moreover, we also considered larger C4H8 molecules occupied in the 51264 cage of sII clathrate hydrate. The computed host−guest interaction energy per guest molecule of 136H2O·2C4H8 and 136H2O· 8C4H8 are 58.817 and 59.819 kJ/mol, respectively. Thus, we can conclude that with the increase of the number of guest molecules, the hydrates become slightly more stable. In addition, when the larger cages of sII hydrate store the same 7066
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The Journal of Physical Chemistry A
is 977 cm−1, and those for the symmetric and symmetric C−C stretching vibration of C3H8 are 874 and 1045 cm−1, respectively. In a previous experiment by Meng et al.48 and Liu et al.,49 the C−C stretching vibration for C2H6 appeared at 991 cm−1, and that for C3H8 appeared at 875 and 1058 cm−1, respectively. Clearly, our theoretical frequencies of guest molecules in the hydrates show a ∼10 cm−1 red shift compared to the experimental values. In Liu theoretical results,27 the C−C stretching vibration for C2H6 in the 51264 cluster appeared at 993 cm−1 and that for C3H8 appeared at 881 cm−1. Our theoretical frequencies of guest molecules in the sII hydrates show a 7−16 cm−1 red shift compared to the guest molecules in
Table 3. Vibration Frequencies (cm−1) and Frequency Shifts of C−C Stretching Bands of an Individual C2H6, C3H6, and C3H8 Molecule in the sII Clathrate Hydrate Compared with Experimental Data guest
vibrational mode
vgas
vguest
Δv
C2H6 C3H8
symmetric stretching symmetric stretching antisymmetric stretching antisymmetric stretching symmetric stretching
996a 869a 1056a 870a 1196a
977 874 1045 882 1202
−19 +5 −11 +12 +6
C3H6 a
Ref 50.
Figure 4. Vibrational frequencies of guest molecules in sII clathrate crystal lattice showing unique frequency shifts under different numbers. (a) C2H6 hydrate; (b) C3H6 hydrate; and (c) C3H8 hydrate. The colorful lines are the average values. 7067
DOI: 10.1021/acs.jpca.5b04470 J. Phys. Chem. A 2015, 119, 7063−7069
Article
The Journal of Physical Chemistry A the 5 12 6 4 clusters. This comparison provides valuable information on clathrate hydrates, which would be useful for further understanding the frequency difference between the theoretical calculation and experimental measurements. Table 3 also lists the frequency shifts, Δv = vguest − vgas, that is, frequency change for the C2H6, C3H6, and C3H8 molecules due to encapsulation inside the sII hydrate as a guest. The band assignments for C2H6, C3H6, and C3H8 in the free gas phase were adopted from Schrader et al.50 One can see that the Δv value is negative (−19 cm−1) when a C2H6 guest molecule is trapped in the sII hydrate. However, Δv becomes positive when C3H6 and C3H8 guest molecules are incorporated in sII hydrate except for the antisymmetric stretching vibration of the C3H8 molecule. Dependence of Frequency Shifts on the Size of Guest Molecule. At low pressures (∼1−2 MPa), ethane and propane are expected to occupy only the large 51264 cages in the sII hydrate.18 The molecule size increases from ethane to propane. These two molecules have only one symmetric C−C stretching vibrational mode due to the existence of only one type of C−C bond in each molecule. These frequencies along with the frequency shifts (Δvb) are listed in Table 3. Evidently, as the size of the guest molecule increases, the Δv value for the symmetric C−C stretching frequency becomes progressively more positive, and it is consistent with the theoretical finding by Subramanian.18 This is because increasing repulsive interactions between the guest and the cage with guest size cause the vibration to occur in a progressively tight cage environment. Dependence of Frequency Shift on the Number of Guest Molecules. Recently, we have simulated the Raman spectra of symmetric C−H stretching mode for multiple CH4 molecules trapped in 51268 water cluster.25 We found that the symmetric C−H stretching frequency becomes progressively more positive as the number of guest molecules increases. Here we explore the influence of multiple C2H6, C3H6, and C3H8 guest molecules (occupy adjacent water cage) encapsulation in the sII hydrate crystal on the vibration frequency. The number of guest molecules range from one to four, and the theoretical frequencies are presented in Figure 4. For the C2H6 hydrate, C−C stretching frequency is 977 cm−1 when one C2H6 molecule per unit cell is stored in the clathrate lattice. After encapsulating four C2H6 guest molecules inside the sII hydrate, the C−C stretching frequency increases and reaches a maximum on 983 cm−1 (average value). For the C3H6 hydrate, the asymmetric C−C stretching mode is located at the lower frequency region, and the symmetric mode is in the higher frequency region. Both symmetric and asymmetric C−C stretching frequencies increase as the number of C3H6 molecules increase. Similarly, as the occupation of C3H8 guest molecules increases, the frequencies for the symmetric and asymmetric C−C stretching modes all become progressively more positive and show a blue shift. These may be attributed to the enhanced repulsive interactions between the guest molecules and the outer cage, which result in a tighter cage environment for the molecular vibration.18
interaction energy of one CH4 molecule inside the smaller 512 cage is larger than that in the larger 51264 cage. We also investigate the effect of size of guest molecule on the interaction energy per guest molecule. For small size alkane guest molecules (CnHm, n ≤ 3, m ≤ 8), the larger the size of guest molecule, the more stable the clathrate hydrate. We discuss the influence of the number of guest molecules on the interaction energy per guest molecule and reveal that the interaction energy per guest molecule gradually increases as the number of guest molecules increases. In addition, the vibrational frequencies of guest molecules trapped in the sII hydrate are simulated. The C−C stretching frequency becomes progressively more positive and shows a blue shift as the amount of guest molecules increases. The present theoretical results on the thermodynamic stability and vibrational frequencies provide vital information on the clathrate hydrates and would serve as useful guidance to establish the relationship between the vibrational frequencies and the species/amount of guest molecules.
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AUTHOR INFORMATION
Corresponding Author
*E-mail: [email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This work was supported by the National Natural Science Foundation of China (Grants 11174045 and 11304030) and the Fundamental Research Funds for the Central Universities of China (Grants DUT12YQ05 and DUT14LK19).
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REFERENCES
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