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Thermodynamic Stability of Hydrogen Clathrates

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Thermodynamic Stability of Hydrogen Clathrates Thermodynamic stability of hydrogen clathrates Serguei Patchkovskii and John S. Tse* Steacie Institute for Molecular Sciences, National Research Council of Canada, Ottawa, ON, Canada K1A 0R6 Edited by Russell J. Hemley, Carnegie Institution of Washington, Washington, DC, and approved October 13, 2003 (received for review February 14, 2003) The stability of the recently characterized type II hydrogen clath- and raised the prospect of using clathrate hydrate as an efficient rate [Mao, W. L., Mao, H.-K., Goncharov, A. F., Struzhkin, V. V., Guo, H2 storage medium. Q., et al. (2002) Science 297, 2247–2249] with respect to hydrogen Under normal conditions, clathrate hydrates are known to occupancy is examined with a statistical mechanical model in have three distinct crystalline structures (10). Both structure I conjunction with first-principles quantum chemistry calculations. It and II clathrate hydrates have a cubic structure and a guest:host is found that the stability of the clathrate is mainly caused by water ratio of Ϸ1:6 (10). Usually, very small guest (rare gas) dispersive interactions between H2 molecules and the water form- favors the formation of the type II structure (10). For a very large ing the cage walls. Theoretical analysis shows that both individual guest molecule, the hexagonal structure H with larger cavities is hydrogen molecules and nH2 guest clusters undergo essentially often formed (11). It was a general perception that hydrogen free rotations inside the clathrate cages. Calculations at the ex- molecules are too small to fit into the hydrate cages, and no kPa) and 250 K stable clathrate hydrate structure can be formed (10). Not until 100 ؍ perimental conditions ؊ 2,000 bar (1 bar confirm multiple occupancy of the clathrate cages with average recently, under high-pressure conditions, hydrogen clathrate 12 occupations of 2.00 and 3.96 H2 molecules per D-5 (small) and with the type II structure was synthesized and characterized (9). 12 4 H-5 6 (large) cage, respectively. The H2–H2O interactions also are More surprisingly, the hydrogen clathrate was found to have an O ͞ responsible for the experimentally observed softening of the H H unusually high H2 H2O ratio (1:2) by high-pressure x-ray dif- stretching modes. The clathrate is found to be thermodynamically fraction, Raman, and infrared spectroscopy (9). The chemical stable at 25 bar and 150 K. composition of these clathrates can only be accounted for if multiple (up to quadruple) occupancies of the clathrate cages are lathrate hydrates are a class of inclusion compounds in which assumed. Moreover, the new clathrate remains apparently stable Cguests (noble gases or small organic molecules) occupy, fully even at the normal atmospheric pressure as long as the temper- or partially, cages in the host framework made up of H-bonded ature is below 150 K. The experimental observations clearly water molecules (1). Clathrate hydrate research is of fundamen- indicate that hydrogen incorporation in these structures is tal and practical importance and involves a broad variety of associated with a low free-energy process, much lower than scientific disciplines. The behavior of clathrate hydrates under would be expected for the mechanical encapsulation of the pressure can provide valuable information on water–water in- hydrogen gas. Additionally, the experimentally observed HOH teractions and interactions of water with a wide range of guests. stretching modes in the new clathrate are softened as compared Methane hydrate is the most abundant natural form of clathrate. to the free molecule (9). This observation is in contrast to the CHEMISTRY An estimate of the global reserve of natural gas in the hydrate behavior of hydrogen gas under similar pressures (Ͻ1 GPa) (12). form buried in the permafrost and sediments underneath the Multiple occupancy of the clathrate cavities is a rare phenom- continental shelf is significantly larger than that from traditional enon. The only existing example is nitrogen clathrate synthesized fossil fuels and will be a valuable future energy resource (2). On under pressurized nitrogen atmosphere (13). The purpose of this the negative side, the blockage of natural gas pipeline by solid article is to investigate the stability of hydrogen clathrate, in hydrocarbon hydrates is a potentially hazardous and expensive particular, the effects of occupancy in the empty cavities, by problem that has not been fully resolved (3). Methane hydrates using statistical mechanical theory with first-principles quantum also represent a potential source of climate instability. As chemistry calculations. warming proceeds downward toward the seafloor and reaches the limits of hydrate stability, the hydrate will decompose, and Theoretical Background some of the methane gas will escape to the atmosphere and Hydrogen clathrate forms a type II structure (14) with 136 water increase the greenhouse effect. There are recent reports sug- molecules and 24 cages per unit cell. Sixteen of the cages are gesting that a cause of ancient global warming and mass extinc- pentagonal dodecahedra (D-512). The remaining eight cages are tion of many forms of life 183 million years ago may be traced 16-hedra (H-51264; see refs. 1 and 10 for nomenclature and to sudden eruption of oceanic methane hydrate (4, 5). Clathrate further information). To avoid possible confusion with the hydrates also may be the most abundant form of volatile hydrogen guest, we will refer to the D-512 and H-51264 as S (for materials in the solar system. The possible existence of gas small) and L (for large) cages, respectively. The structures of the hydrate is crucial to the modeling of bodies in the solar system. cages are shown in Fig. 1. Experimentally, it was found that the The identification of several high-pressure forms of methane new clathrate contains 61 Ϯ 7 (9) hydrogen molecules, distrib- hydrates has helped to reconcile the origin of the presence of uted among the cages, per unit cell. Placing two guest molecules large amount of methane in the atmosphere of Saturn’s moon in each S cage and four in each L cage would give an approximate ͞ Titan (6). Solid clathrate hydrate also has been suggested to exist 1:2 H2 H2O clathrate composition. in comets in order to explain the large difference between the The structure and stability of several multiple-occupancy ice latent heats of vaporization of the various ices in the Whipple’s clathrates have been examined with molecular dynamics meth- model (7). Recently, the discovery of new species of centipede- ods (15, 16). Here, we adopt a statistical thermodynamics ͞ like worms living on and within mounds of methane hydrate on approach to investigate the thermodynamics of H2 H2O clath- the floor of Gulf of Mexico challenges the conventional view that rate formation. Encapsulation of successive hydrogen molecules deep sea bottom is a monotonous habitat and indicates that methane hydrate may play a role in marine ecosystem (8). More This paper was submitted directly (Track II) to the PNAS office. recently, the synthesis of H2 hydrate, a hydrate with the smallest guest with multiple occupancy, questioned the conventional Abbreviations: DFT, density functional theory; MP2, second-order Mo¨ller-Plesset. theory for the prediction of the stability of clathrate hydrate (9) *To whom correspondence should be addressed. E-mail: [email protected]. www.pnas.org͞cgi͞doi͞10.1073͞pnas.2430913100 PNAS ͉ December 9, 2003 ͉ vol. 100 ͉ no. 25 ͉ 14645–14650 Downloaded by guest on September 25, 2021 Table 1. DFT and MP2 reaction energies* (kcal͞mol) for hydrogen encapsulation reactions at optimized DFT geometries † naked ‡ Reaction ⌬rE0 (DFT) ⌬rE0 (MP2͞͞DFT) ⌬rE0 (MP2͞͞DFT) § 1H2ϩS ϭ 1H2@S Ϫ0.49 Ϫ1.84 ϩ0.04 2H2ϩS ϭ 2H2@S ϩ3.56 Ϫ9.00 ϩ0.99 3H2ϩS ϭ 3H2@S ϩ15.44 Ϫ6.09 ϩ3.63 ¶ 1H2ϩL ϭ 1H2@L Ϫ0.87 Ϫ0.54 ϩ0.01 2H2ϩL ϭ 2H2@L ϩ0.73 Ϫ3.90 ϩ0.36 3H2ϩL ϭ 3H2@L ϩ3.41 Ϫ5.77 ϩ0.93 4H2ϩL ϭ 4H2@L ϩ5.42 Ϫ11.00 ϩ0.92 5H2ϩL ϭ 5H2@L ϩ14.37 Ϫ7.79 ϩ5.67 MP2 formation enthalpies for the naked hydrogen clusters with the water cage walls removed are given for comparison. *Not including zero-point vibration corrections. †S, small (D-512) cage; L, large (H-51264) cage. 12 12 4 ‡ Fig. 1. Structure of the S (D-5 )andL(H-5 6 ) cages of the type II ice Free cluster of nH2 molecules by using geometry optimized inside the cage. § clathrate. Positions of the hydrogen atoms are omitted for clarity. The coor- H2 molecule at cage center. For the true, off-center MP2 minimum, ⌬rE0 dinate axes correspond to the orientation of the model cages used in the (MP2) ϭϪ2.85 kcal͞mol (see text). ¶ calculations. H2 molecule at cage center. For the true, off-center MP2 minimum, ⌬rE0 (MP2) ϭϪ2.54 kcal͞mol (see text). is treated as a series of chemical reactions between gaseous hydrogen with an (initially empty) ice cage C: The small cage was modeled with a 20-molecule water cluster (Fig. 1). In this structure, 8 oxygen atoms are arranged in a ϩ ϭ 1H2(g) C 1H2@C [1] perfect cube (Oh) 3.83 Å from the cage center. The remaining ϩ ϭ 12 oxygen atoms are placed 3.96 Å from the center of the cage 2H2(g) C 2H2@C [2] and transform according to the Th subgroup of Oh. For the large ϩ ϭ cage, a 28-molecule model cluster was constructed in a distorted 3H2(g) C 3H2@C [3] Td symmetry. Oxygen atoms in this cluster are located between ϩ ϭ 4H2(g) C 4H2@C [4] 4.32 and 4.84 Å from the cage center. For both model cages, hydrogen atoms, with a fixed OOH bond distance of 1.0 Å, were ϩ ϭ 5H2(g) C 5H2@C [5] placed so as to maximize the hydrogen-bonded network.
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