Migration of hydrogen radicals through clathrate hydrate cages

Chemical Physics Letters 479 (2009) 234–237

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Migration of hydrogen radicals through clathrate hydrate cages Saman Alavi a,b,*, John A. Ripmeester b a b

Department of Chemistry, University of Ottawa, Ottawa, Ontario, Canada K1N 6N5 Steacie Institute for Molecular Sciences, National Research Council of Canada, Ottawa, Ontario, Canada K1A 0R6

a r t i c l e

i n f o

Article history: Received 26 June 2009 In final form 19 August 2009 Available online 21 August 2009

a b s t r a c t Electronic structure calculations are used to determine energy barriers to hydrogen radical migration in structure II clathrate small and large cages. Migration of H-radicals through pentagonal and hexagonal faces of small and large cages are considered and energies barriers calculated at the MP2 level with the 6-311++G(d,p) basis set are 61 and 17 kJ mol1, respectively. Energy barriers (with tunneling corrections) are used to estimate escape rates from the cages and to explain results of recent experiments on the transformation of n-propyl radical in the propane hydrate and the behavior of hydrogen radicals in tetrahydrofuran/H2 hydrates. Ó 2009 Elsevier B.V. All rights reserved.

1. Introduction Many scientific and practical applications have been developed for clathrate hydrates [1,2]. An interesting low temperature application of the open and relatively inert clathrate hydrate environment is as a medium for trapping and studying hydrogen and hydrocarbon free radicals species. Free radical species can be formed by the irradiation of hydrocarbon, hydrogen, or binary clathrate hydrates with c-radiation and these species are often sufficiently long-lived in the clathrate hydrate structure that they can be studied with electron spin resonance (ESR) and solid-state NMR spectroscopy. The hydrogen radical is observed to diffuse relatively freely through the clathrate hydrate water network and can recombine with other H-radicals or other radical species in the medium. Larger hydrocarbon or organic radicals, on the other hand, cannot diffuse between the clathrate hydrate cavities. These larger radicals can undergo secondary reactions with their neighboring encapsulated guests or with H-radicals diffusing in the clathrate medium. In this work, we characterize the energy barriers and migration rates of the H-radical in the clathrate hydrate medium and use this information to interpret some recent experiments with free radical species on clathrate hydrates. Ohgaki et al. [3] recently subjected the propane structure II (sII) clathrate hydrate to c-radiation which lead to the formation of the normal-propyl (n-propyl) and isopropyl (i-propyl) radicals as seen through the ESR spectrum of the system. Their experiments show that in the 240–260 K temperature range, initially formed n-propyl radicals in the large sII clathrate cages abstract H-radicals from undissociated propane molecules in adjacent large cages to form the more stable i-propyl radicals. Their experiments with the pure * Corresponding author. Address: Department of Chemistry, University of Ottawa, Ottawa, Ontario, Canada K1N 6N5. Fax: +1 613 947 2838. E-mail address: [email protected] (S. Alavi). 0009-2614/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2009.08.044

propane clathrate hydrate, equimolar binary propane/SF6 sII clathrate hydrate, and propane D2O-clathrate hydrate illustrate that the n-propyl radical directly abstracts an H-radical from the propane molecule in an adjacent cage and not from intramolecular H-transfer or H-radical transfer from the clathrate lattice water. This intermolecular proton transfer occurs through migration between the hexagonal faces of the large sII cages. They extracted an activation energy of 34 ± 3 kJ mol1 for proton migration which leads to the conversion of the enclathrated n-propyl radical in one cage to an i-propyl radical in the neighboring cage. To understand the properties of H-radicals in condensed media, Lee and coworkers [4] recently subjected tetrahydrofuran (THF) – H2 binary structure II clathrate hydrate to c-rays. They studied the production and migration of H-radicals formed by the decomposition of H2 guests and the homolytic bond cleavage of C–H bonds in THF guests. The formation of THF and H-radicals were monitored through ESR spectra of the clathrate and the migration of H-radicals was followed by studying the temperature dependence of the 1H NMR signal for the clathrate. Migration of the Hradical in the clathrate was observed to start at 183 K. In previous work, we studied the energy barriers to migration of H2 molecules through sII hexagonal and pentagonal faces [5]. We showed that the barrier to H2 migrations through the pentagonal faces of the small sII cages is 105 kJ mol1 while the barrier to migration of H2 through the larger hexagonal faces of the large sII cages is 21 kJ mol1. In this work, we study the energetics of one-dimensional H-radical migration through hexagonal faces of the large sII cages and pentagonal faces of the small sII cages from MP2 and B3LYP level calculations with the 6-311++G(d,p) basis set. The energy barriers determined in these two cases should be the upper and lower limits to the barriers of H-radical migration in the sII clathrate phase. We have not calculated the barrier for Hradical migration through pentagonal faces of large sII cages, but this barrier should be between the two limiting values determined

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above. The rate of H-radical migration through clathrate faces is determined using simple transition state theory expressions discussed below. Tunneling and zero-point energy contributions to the migration rate are expected to be much larger for H-migration than the case of H2 migration through the faces and will be discussed. The results will be used to analyze the experiments of Ohgaki et al. and Lee et al. 2. Computational methods Energetic calculations were performed at the unrestricted MP2 and B3LYP level of theory with the 6-311++G(d,p) basis set using the GAUSSIAN 98 suite of programs [6]. The H-radicals were placed in the center of the isolated small dodecahedral 512 cages and the large hexakaidecahedral 51264 sII clathrate cages. The initial positions of the water oxygen atoms in the large and small cages of the sII clathrate taken from the periodic experimental X-ray crystallography data [7]. The disordered hydrogen atoms of the water molecules in the sII clathrate are placed among the oxygen sites in a manner consistent with the ice rules. Each 51264 cage also has four hexagonal faces that are shared between other 51264 cages. We calculated the one-dimensional energy profile for moving the H-radical from the cage center through the center of a pentagonal or hexagonal faces in the small and large cages, respectively. The absence of spin contamination in all configurations was ascertained during the calculations. The cage atoms were frozen while the hydrogen radical was moved from the center outwards towards the center of the faces. This set-up is shown in Fig. 1. The energies of the isolated propane, n-propyl radical, i-propyl radical, THF, a-THF radical, and b-THF radical were determined at the same levels of theory. Transition state energies for the intramolecular proton transfer in the radical species were also studied. The classical transition state theory (TST) expression, kclass(T), for the rate constant of migration of hydrogen radicals through hexagonal and pentagonal faces of the sII clathrate cages is,

kclass ðTÞ ¼ AðTÞ expðE0 =RTÞ;

ð1Þ

where A(T) is the Arrhenius pre-exponential factor at temperature T and E0 is the activation barrier to the migration. In the present calculations, the pre-exponential factor is related to the H-radical rattling frequency in the small and large cages. A quantum mechanical tunneling correction, j(T) [8], must be applied to accurately determine the total migration rate of H-radicals, ktot(T) = j(T)kclass(T). If the barriers to H-radical migration through the cage faces can be fit to a one-dimensional Eckart sech2 model [9,10],

VðxÞ ¼

4E0 expð2px=‘Þ

ð2Þ

½1 þ expð2px=‘Þ2

where E0 is the tunneling barrier and ‘ is a characteristic length, the tunneling correction at different temperatures will be given by,

jðTÞ ¼ 1 þ

2   1 hms kT 1 þ 24 kT E0

ð3Þ

The magnitude of the imaginary frequency corresponding to the tunneling barrier, ms is given by jms j2 ¼ E0 =2‘2 l. 3. Results and discussion The energy profiles for the H-radical at different distances from the center of the small and large sII clathrate cages moving towards the center of the pentagonal and hexagonal faces are shown in Fig. 1. At the MP2 level, the one-dimensional barriers to the passing of the H-radical through a hexagonal face of a large cage and the pentagonal face of small cage are 17 kJ mol1 and 62 kJ mol1, respectively. The corresponding values from B3LYP calculations and the same basis set are considerably lower at 11 and 46 kJ mol1, respectively. The differences between the migration barriers at the two levels of theory are consistent with the observation that barriers to proton transfer reactions determined at the MP2 level often are predicted to be higher than barriers determined with DFT calculations with the same basis set [11,12]. For these one-dimensional pathways, the H-migration barriers are symmetric with respect to the maximum of the plots since the H-radical enters a new cage of the same type after passing through a face. The barrier shapes can be fit well to the Eckart sech2 potential and the fit parameters are given in Table 1. In the empty clathrate cages, the H-radical will have a significant zeropoint energy which can affect the tunneling barrier with respect to the values calculated in Table 1. The quantum mechanical translation/rotation eigenvalues and eigenstates of H2 in the small and large sII clathrate cages give a zero-point energies of 8 kJ mol1 and 2.5 kJ mol1, respectively [13–19]. For the H-radical, the corresponding zero-point energies in the small and large sII cages will be larger than these values and this will change the effective energy and rate of passing over the diffusion barrier compared to the values calculated below. Furthermore, the H-radicals are highly delocalized in the three-dimensional sII cages. As the radical approaches center of the pentagonal or hexagonal face to migrate from one cage to the next, it becomes increasingly constricted (‘squeezed’) in the directions orthogonal to the reaction coordinate shown in Fig. 1. This will undoubtedly lead to a significant zero-

Table 1 Parameters for the fit of the calculated migration energies to the Eckart sech2 potential for H-radical through the small and large sII clathrate hydrate cages. Fig. 1. The energy profile for H-radical in the sII small (black) and large (red) cages starting from the cage center and moving towards the center of pentagonal or hexagonal faces. Calculations are performed at the UMP2 (full lines) and B3LYP (dashed lines) levels with the 6-311++G(d,p) basis set. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Atom (assignment)

H in small cage H in large cage

E0 (kJ mol1)

ms

‘ (Å)

(1012 s1)

MP2

B3LYP

MP2

B3LYP

MP2

B3LYP

61.93 16.77

50.33 11.27

3.22 3.33

4.61 3.33

17.23 8.66

10.84 7.10

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point energy for modes perpendicular to the reaction coordinate which will change the effective migration barrier. The over all energy profile would need to account for zero-point energies in the reaction coordinate and the two directions orthogonal to the reaction pathway. The complete determination of the threedimensional energy profile for the H-radical migration and the determination of zero-point energy effects for this profile will remain for future work. The energy barriers and profiles shown in Fig. 1 are used to estimate migration rates of the H-radical from the cages between 150 to 260 K using a simple Arrhenius expression with tunneling corrections (without zero-point energy contributions), Eqs. (1)–(4). To determine the Arrhenius pre-exponential factor of Eq. (1), we performed a normal mode analysis of the H-radical in the small dodecahedral cages at the B3LYP/6-311++G(d,p) level, and found rattling vibrations involving the H-radical to be in the range of 50–100 cm1. This gives H rattling frequencies and pre-exponential factor A(T) values in the range of 1.5  1012 to 3.0  1012 s1. The rattling frequency for H in the large sII cages is expected to be in this range and taken as A(T) = 1012 s1. The resulting estimates for the rate of hydrogen radical migration are shown in Fig. 2. These should be considered lower limits to the one-dimensional migration rates since we have ignored the effects of zeropoint energy. We can see that of rates of migration of the H-radicals from the hexagonal faces are many orders of magnitude larger than migration rates through the smaller pentagonal faces. To study the role of the H-radical migration in the hydrogen abstraction by the n-propyl radicals from propane molecules of neighboring cages, we determine the homolytic C–H bond dissociation energies in propane. The results are given in Table 2. The ipropyl radical is 11 kJ mol1 lower in energy than the n-propyl radical. However, since there are three times more methyl protons than methylene protons in propane, more n-propyl radicals will be initially produced as a result of exposure to the energetic cor UV-radiation. The activation barrier to intramolecular conversion of the n-propyl radical to the more stable i-propyl radical is seen to be very large at 187 kJ mol1. This high activation barrier is the reason why intramolecular rearrangement of the n-propyl

Fig. 2. The rate of hydrogen radical migration through the pentagonal (lower panel) and hexagonal (upper panel) sII cages at different temperatures. The rates calculated using the MP2 barriers are shown in black and those for the B3LYP barrier are shown in red. The hydrogen migration rates for the pentagonal faces of the small cages calculated from MP2 energy barriers cannot be seen on the scale of the figure. The rates without the tunneling contribution are shown with solid lines and the rates with the tunneling contribution are shown with dashed lines. Zeropoint energy corrections are not considered. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Table 2 The formation energies for radical propane and THF species determined from MP2/6311++G(d,p) level calculations. The activation energy for the conversion of the npropyl radical to the i-propyl radical is also given. Reaction

Energy (kJ mol1)

CH3CH2CH3 ? CH3CH2CH2 + H CH3CH2CH3 ? CH3CHCH3 + H CH3CH2CH2 ? CH3CHCH3 THF ? a-THF + H THF ? b-THF + H

DEreact = 441 DEreact = 430 DEact = 187 DEreact = 407 DEreact = 429

radical is not experimentally observed. As the barrier to migration of the proton through the large sII cage hexagonal face is only 17 kJ mol1 (excluding zero-point energy), the abstraction of a H-radical from the C2 position of a propane from a neighboring large sII clathrate cage by a n-propyl radical as the mechanism of i-propyl production in the clathrate [3] is very plausible. A schematic representation of the pathway for the H-radical transfer between a propane molecule and n-propyl radical to form the i-propyl radical is shown in Fig. 3. As mentioned in Section 1, the activation energy for the H-radical transfer between neighboring propane and n-propyl radicals was determined to be 34 kJ mol1. From Fig. 1, we can estimate that roughly 17 kJ mol1 of the activation energy can be the contribution of passing the H-radical through the hexagonal face of the large sII cages. This is much smaller than the 180 kJ mol1 activation energy required for the intramolecular H-radical. The experiment of Lee and coworkers indicates that the H-radicals were generated by 15 kGy c-ray irradiation at 77 K in liquid nitrogen and were observed to be stably enclathrated in isolated cages through the 1H MAS NMR maintained at 173 K. They observe that at higher temperatures, the 1H NMR peaks in the hydrogen region merge into a broad peak and H-radicals recombine into H2 species. The high energy barrier calculated for the migration of H-radicals from the pentagonal faces of the small sII clathrate cages (61–46 kJ mol1) can provide an explanation for this experimental observation. The H-radical migration rates calculated above are estimates to the actual migration rates. The clathrate cages in our calculations are considered to be rigid and a simulation allowing flexibility in the water molecules may lead to opening of the polyhedral faces as a result of water lattice vibrations and a corresponding decrease

Fig. 3. The hydrogen radical transfer pathway from the C2 atom of a propane molecule to the C1 atom of an adjacent n-propyl radical. The result of the transfer is the formation of the more stable i-propyl radical.

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in the energy barriers to H-radical migration. Furthermore, the barriers to H-radical migration were determined for clathrate cages with isolated H-radicals, without the presence of other radical fragments in the same cage. For example, the presence of the THF radical in the large cage can limit the mobility of the H-radical, while changing the migration pathway for the radical. These effects will all affect the H-radical migration rates. References [1] E.D. Sloan Jr., C. Koh, Clathrate Hydrates of Natural Gases, third edn., CRC Press, Boca Raton, FL, 2008. [2] Proceedings of the 6th International Conference on Gas Hydrates, ICGH, Vancouver, BC, Canada, 2008. [3] K. Ohgaki, K. Nakatsuji, K. Takeya, A. Tani, T. Sugahara, Phys. Chem. Chem. Phys. 10 (2008) 80. [4] S.-H. Yeon, J. Seol, Y. Park, D.-Y. Koh, Y.S. Kang, H. Lee, J. Am. Chem. Soc. 130 (2008) 9208.

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