Raman spectroscopic studies of hydrogen clathrate hydratesTimothy A. Strobel, E. Dendy Sloan, and Carolyn A. Koh Citation: J. Chem. Phys. 130, 014506 (2009); doi: 10.1063/1.3046678 View online: http://dx.doi.org/10.1063/1.3046678 View Table of Contents: http://jcp.aip.org/resource/1/JCPSA6/v130/i1 Published by the AIP Publishing LLC. Additional information on J. Chem. Phys.Journal Homepage: http://jcp.aip.org/ Journal Information: http://jcp.aip.org/about/about_the_journal Top downloads: http://jcp.aip.org/features/most_downloaded Information for Authors: http://jcp.aip.org/authors

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Raman spectroscopic studies of hydrogen clathrate hydratesTimothy A. Strobel, E. Dendy Sloan, and Carolyn A. Koha�

Center for Hydrate Research, Department of Chemical Engineering, Colorado School of Mines, Golden,Colorado 80401, USA

�Received 3 October 2008; accepted 21 November 2008; published online 6 January 2009�

Raman spectroscopic measurements of simple hydrogen and tetrahydrofuran+hydrogen sII clathratehydrates have been performed. Both the roton and vibron bands illuminate interesting quantumdynamics of enclathrated H2 molecules. The complex vibron region of the Raman spectrum hasbeen interpreted by observing the change in population of these bands with temperature, measuringthe absolute H2 content as a function of pressure, and with D2 isotopic substitution. Quadrupleoccupancy of the large sII clathrate cavity shows the highest H2 vibrational frequency, followed bytriple and double occupancies. Singly occupied small cavities display the lowest vibrationalfrequency. The vibrational frequencies of H2 within all cavity environments are redshifted from thefree gas phase value. At 76 K, the progression from ortho- to para-H2 occurs over a relatively slowtime period �days�. The rotational degeneracy of H2 molecules within the clathrate cavities is lifted,observed directly in splitting of the para-H2 roton band. Raman spectra from H2 and D2 hydratessuggest that the occupancy patterns between the two hydrates are analogous, increasing confidencethat D2 is a suitable substitute for H2. The measurements suggest that Raman is an effective andconvenient method to determine the relative occupancy of hydrogen molecules in different clathratecavities. © 2009 American Institute of Physics. �DOI: 10.1063/1.3046678�

I. INTRODUCTION

Clathrate hydrates are molecular inclusion compoundsthat trap small molecules within polyhedral hydrogen-bonded water cavities.1 These compounds crystallize as threecommon structures: structure one �sI�, structure two �sII�,and structure H �sH�. The formation of these structures isgenerally dictated by the size of the guest molecule.2 The sIconfiguration has a cubic unit cell comprised of two 512 �12pentagonal faces� and six 51262 �12 pentagonal faces and 2hexagonal faces� cavities with 46 water molecules. The unitcell of cubic sII clathrate contains sixteen 512 cavities andeight 51264 cavities with 136 waters. Three cavity types,made of 34 water molecules, comprise hexagonal sH clath-rate: 512 �three per unit cell�, 435663 �two per unit cell�, and51268 �one per unit cell�.

Historically, hydrogen was thought to be too small tocontribute to the stability of these compounds and was con-sidered to act as a diluent to the fugacity of other compo-nents in a gas mixture.3 However, over the past decade it hasbeen established that hydrogen can act as a suitable hydrateguest molecule in both single and mixed clathrates.4–6

Simple �one guest� hydrogen clathrate forms sII and maycontain up to four hydrogen molecules in the large cavitiesand one hydrogen molecule in the small cavities.7 In binaryhydrates with hydrogen and other large sII forming mol-ecules such as tetrahydrofuran �THF�, hydrogen may par-tially or completely occupy the small dodecahedralcavities.8,9 Additionally, H2 may be contained within binarystructure I �sI� hydrates10,11 and in binary structure H �sH�hydrates with appropriately sized sH forming molecules such

as methylcyclohexane.12 H2 may also be contained withinthe small cavities of semiclathrate structures,13 as well asisomorphous clathrate analogs.14,15

In the free gas phase, H2 behaves as a near perfect quan-tum rotor with rotational energy levels,

E�J� = BJ�J + 1� , �1�

where B is the rotational constant �59 cm−1 in the groundvibrational state16� and J is the rotational quantum number.

The nuclei of the H2 molecule are composed of twoindistinguishable fermions constraining the overall wavefunction to be antisymmetric under nuclear exchange. Thus,H2 molecules with antiparallel nuclear spins �I=0� can onlyexist with even rotational states, J=0,2 , . . ., and H2 mol-ecules with parallel spins �I=1� can only exist with odd ro-tational states, J=1,3 , . . .. 17 The nuclei of D2 are composedof two indistinguishable bosons constraining the overallwave function to be symmetric. D2 molecules with I=0 or 2can only exist with even rotational states and D2 moleculeswith I=1 only exist with odd rotational states.

These symmetry constraints yield two types of hydro-gen: ortho and para. Ortho is designated as the species withthe greatest statistical weight gs. Ortho-H2 refers to mol-ecules with I=1, odd J, and gs=3, and para-H2 refers tomolecules with I=0, even J, and gs=1. Ortho-D2 refers tomolecules with I=0 or 2, even J, and gs=6, and para-D2

refers to molecules with I=1, odd J, and gs=3. At high tem-peratures �T�Bhc /kB� the ortho to para ratio reduces to theratio of statistical weights—3:1 for H2 and 2:1 for D2. Thesemixtures are termed normal.17

The inclusion of H2 molecules within clathrate hydratecavities presents a unique system to study the quantum dy-namics of confined hydrogen and interactions with the watera�Electronic mail: ckoh@mines.edu.

THE JOURNAL OF CHEMICAL PHYSICS 130, 014506 �2009�

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host lattice. Features such as multiple cavity occupation andH2–H2 separation distances smaller than those observed insolid hydrogen17 demonstrate unique characteristics warrant-ing additional studies. Furthermore, a fundamental under-standing of these compounds is required if they are to berealized as functional hydrogen storage materials. In thiswork we have investigated the molecular behavior of hydro-gen molecules contained with various clathrate hydrate cavi-ties via Raman spectroscopy. The experimental approach tothis work is outlined in Sec. II, and experimental results forvibrational and rotational spectroscopy are given in Sec. III.Section IV provides discussion of this work and Sec. V givesconclusions.

II. EXPERIMENTAL

Simple sII hydrogen clathrate hydrate samples wereformed in a high pressure stainless steel vessel by pressuriz-ing finely ground de-ionized water ice ��180 �m� with hy-drogen or deuterium �H2: 99.999% air gas; D2: 99.999%; D:99.8%; Matheson� at 250 K. Formation pressures rangedfrom 125 to 200 MPa and were held constant by using alarge gas reservoir relative to the sample volume. Severalexperiments were conducted to determine the absoluteamount of hydrogen contained within the clathrate samplesas a function of the formation time. In agreement with pre-vious neutron diffraction studies,7 the absolute amount of gascontained within the clathrate was equivalent for samplesformed for 1 and 48 h, suggesting rapid hydrate formation.Additionally, the formation of pure sII clathrate was con-firmed via x-ray diffraction measurements. Although the con-version from ice Ih to sII clathrate was determined to occurrapidly, all hydrate samples were formed for at least 24 h toallow for the H2 occupancy distribution within the clathratecavities to equilibrate. Similarly, binary sII THF+H2 clath-rate hydrate samples were formed by pressurizing groundpreformed stoichiometric �5.6 mol %� THF hydrate.

After the hydrate formation period, the pressure vesselwas quenched in liquid nitrogen to cool the sample into theregion of atmospheric pressure stability. Once the sampletemperature reached 76 K, the gas pressure was released, andthe pressure vessel was detached from the pressure assemblywhile the sample was maintained in liquid nitrogen. Whenremoving the hydrate sample from the pressure vessel, ex-treme care was taken to maximize the time the sample waskept in physical contact with liquid nitrogen. During thesample extraction from the cell and transfer to the cryostat,the sample was not in physical contact with liquid nitrogenfor less than 5 s. A series of preliminary Raman measure-ments were performed, and it was determined that heating asa result of a 10 s exposure to ambient conditions duringsample transfer is sufficient to change the H2 cavity popula-tion distribution. Once the hydrate samples were safely trans-ferred to the liquid nitrogen cryostat, ex situ Raman measure-ments were performed.

To ensure that the ex situ measurements were represen-tative of the formation conditions, we also performed somein situ measurements on H2 hydrates formed within fusedsilica square walled capillary tubes. In this scenario, Raman

measurements were made while the hydrate sample was un-der pressure. Details of this procedure are given by Strobelet al.18 Trends in the Raman bands for the in situ experimentsagreed well with the ex situ experiments, and the remainingexperiments were conducted ex situ to alleviate experimentalchallenges associated with the small capillary tubes.

Raman measurements were performed using a HoribaJobin Yvon LabRamHR spectrometer utilizing a 532 nm di-ode laser as an excitation source. The excitation laser lightwas filtered to about 2 mW power to avoid any local heatingand was focused onto the sample through a long workingdistance 20� objective. Scattered light was collected inbackscatter geometry through the entrance slit �typically50 �m� and dispersed off a 1800 or 2400 gratings/mm grat-ing over an 800 mm focal length to a charge coupled devicedetector. Typical spectral resolution ranged from 0.5 to0.9 cm−1.

III. RESULTS

A. Vibrational spectroscopy

The general features of the Raman spectrum for simpleH2 clathrate in the region of H2 vibration have been previ-ously assigned by comparison with the spectrum of stoichi-ometric THF+H2 hydrate.18 In contrast with the original as-signment by Mao et al.5 the lowest frequency bands of thespectrum were assigned to H2 occupied within the smaller512 cavities, and the highest frequency contributions havebeen assigned to H2 located within the large cavities. For thecase of THF+H2 hydrate, only the small 512 cavities of theclathrate may be occupied by H2 as the larger 51264 cavitiesare essentially completely occupied by THF. Thus, contribu-tions from H2 to the Raman spectrum of stoichiometricTHF+H2 hydrate reflect only singly occupied 512 cavities.

Figure 1 shows Raman spectra for THF+H2 hydrateformed at 150 MPa and 250 K, measured immediately afterthe formation period at atmospheric pressure and 76 K andafter 6 days in liquid nitrogen. These spectra are comparedwith the Q1�1� ��=0, J=1→�=1, J=1, ortho� and Q1�0���=0, J=0→�=1, J=0, para� Raman bands of free gaseousH2 at 296 K and 0.01 MPa. At 76 K, only these two bandsare observed in the Raman spectrum as only the J=0 and J=1 rotational states are populated. Like the gaseous phase,the spectrum for THF+H2 hydrate measured immediatelyafter the formation period contains two bands separated byabout 6 cm−1 which are assigned to the Q1�1� and Q1�0�transitions. These bands are perturbed to lower frequencyfrom the free gas values by �34 cm−1.

For the spectrum taken initially after the formation pe-riod, the hydrate sample was rich in ortho hydrogen, ob-served in the intensity of the Q1�1� band. This compositionreflects the fact that the clathrate was formed from a normalmixture of ortho- and para-H2, and the ortho to para conver-sion rate is slow compared to the time scale of quenchingand measuring the sample.17,19 After storage in liquid nitro-gen for 6 days, H2 contained within the clathrate followedthe expected ortho-para conversion trend, resulting in aslightly para-rich composition.20 Therefore, at 76 K, the con-

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tributions to the Raman spectrum are due to vibrational tran-sitions of H2 molecules in the two lowest energy rotationalquantum states.

Based on these results and the Raman spectra in Fig. 1, itis expected that two bands �Q1�0� and Q1�1�� comprise thetotal vibron contribution for any singly occupied hydratecavity at 76 K. At higher temperatures additional rotationalstates become populated and additional peaks are observedin the spectra. We have clearly observed this feature forTHF+H2 hydrate above 150 K with the population of theQ1�2� band. As temperature increases the natural peak widthof each vibrational band increases, resulting in a single broadfeature for hydrogen in the clathrate at higher temperatures��280 K�.6,21

Simple hydrogen hydrate was synthesized at 150 MPaand 250 K. After the formation period, the hydrate was mea-sured at 76 K and atmospheric pressure �Fig. 2�. The spec-trum measured immediately after the formation period �day1� showed six distinct contributions. As in the THF+H2 hy-drate at 76 K, each hydrogen environment is actually repre-sented by two bands �ortho-and para-H2�. These ortho andpara contributions are separated by �6 cm−1 and are ini-tially rich in ortho-H2. Therefore, the six bands shown in Fig.2 �day 1� actually represent three separate hydrogen environ-ments �a fourth environment near 4130 cm−1 is also present,see discussion below�. The ortho-para pairs in Fig. 2, sepa-rated by about 6 cm−1, have been connected with arrows. Aswith the THF+H2 hydrate, after 6 days in liquid nitrogen, thesimple H2 clathrate ortho-para distribution changed to reflecta slightly para-rich composition �Fig. 2, day 6�.

Neutron diffraction measurements performed at ambientpressure by Lokshin et al.7 suggest that the occupancy ofhydrogen in the large sII cavity can vary between two andfour hydrogen molecules. In this neutron diffraction study, as

the temperature was increased from about 80 to 160 K, theoccupancy in the large cavity began to diminish from four totwo hydrogen molecules. Because each individual cavitymust contain integer values of hydrogen molecules, powderaveraged noninteger occupancy values must be caused bysome distribution of multiply occupied cavities, each con-taining two, three, or four H2 molecules. The small cavityoccupancy remains unity until the thermodynamic meltingtemperature ��160 K� is achieved.7 Therefore, if simple H2

clathrate is heated from 76 K, the change in the large cavityoccupancy distribution should be evident in the Raman spec-tra, and the individual occupancy contributions can be as-signed.

Figure 3�a� shows H2 hydrate formed at 200 MPa and250 K, measured at 76 K and atmospheric pressure. Thishydrate sample was then heated to 150 K and requenched inliquid nitrogen �Fig. 3�b�� and heating/quenching was re-peated two additional times �Figs. 3�c� and 3�d��. The hy-drate was heated in order to stimulate a decrease in the H2

occupancy and quenched to stop this process as well as in-crease resolution by narrowing the band widths. By examin-ing the evolution and regression of bands over these heatingand quenching cycles, the individual contributions from qua-druple, triple, and double occupancies were assigned.

The unperturbed sample �Fig. 3�a�� shows the ortho andpara small cage contributions also observed for THF+H2

clathrate, as well as two additional ortho-para pairs with theortho components located at �4144 and �4137 cm−1. Thepara partner of the ortho band at 4137 cm−1 is presumablyconvoluted with the ortho band at 4144 cm−1. After the firstheat quench cycle �Fig. 3�b��, the intensities of the highestfrequency environment bands decreased considerably rela-tive to the intensity of the small cage environment bands�small cage occupancy remains constant�. Also, the intensity

4110 4120 4130 4140 4150 4160 4170

Raman Shift (cm-1)

NormalizedIntensity(A.U.)

Q1(1)ortho

Q1(0)para

Q1(0)para

Q1(1)ortho

FIG. 1. �Color online� Raman spectra of gaseous H2 at 0.1 MPa and 296 K�dashed�, THF+H2 hydrate at 0.1 MPa and 76 K directly after formation�solid�, and THF+H2 hydrate at 0.1 MPa after 6 days at 76 K �dotted�.

4100 4110 4120 4130 4140 4150 4160 4170

Raman Shift (cm-1)

Intensity(A.U.)

Day 1

Day 6

512 51264

FIG. 2. �Color online� Vibron spectra for simple H2 clathrate measured at 76K and 0.1 MPa at day 1 �bottom� and the same sample after 6 days in liquidnitrogen �top�. Arrows connect ortho Q1�1� and para Q1�0� pairs separatedby �6 cm−1.

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of the ortho band at 4137 cm−1 grew to nearly equal inten-sity as the small cage ortho band and its para partner ap-peared at �4143 cm−1. Additionally, a new environment ap-peared with the ortho component located at �4129 cm−1.

After the second heat/quench cycle �Fig. 3�c��, the high-est frequency large cavity ortho-para bands were nearlygone, while the other two large cavity environment bandsgrew in intensity. Finally, after the third heat/quench cycle�Fig. 3�d��, the highest frequency bands were completelygone, the middle frequency large cavity bands were dimin-ished in intensity relative to the previous spectrum �Fig.3�c��, and the lowest frequency large cavity bands were themost intense large cavity contribution. A fourth heat/quenchcycle resulted in complete decomposition of the clathratesample.

The Raman spectra presented in Fig. 3 reveal criticalinformation regarding the occupancy distribution of H2 con-tained within the large sII clathrate cavities. During the heat/quench cycles H2 cannot re-enter the clathrate structure asthe measurements were conducted at ambient pressure in theabsence of a surrounding hydrogen atmosphere. Thus, theprogression of the spectra represents a decrease in the totalamount of H2 contained within the large cavities. The clath-rate must start with the highest H2 content. Therefore, weassign the highest frequency large cage contribution to qua-druply occupied cavities, the middle frequency large cagecontribution to triply occupied large cavities, and the lowestfrequency large cage contribution to doubly occupied largecavities. This assignment is entirely consistent with the neu-tron scattering results of Lokshin et al.7 Additionally, thisassignment is consistent with the observed frequency shifttrend: as more H2 molecules are packed into a large cavity,the vibrational frequency increases, reflecting a more repul-sive potential energy surface.

The spectra presented in Fig. 3 also clearly demonstrate

that the vibrational frequencies for H2 within different largecavity environments are distinct. Each environment is repre-sented by two clearly resolvable ortho and para bands. Thissuggests that H2 molecules contained within the same mul-tiply occupied large cavity vibrate at similar frequencies,within the peak width.

The trends presented in Fig. 3 were highly reproducible,and we conducted a similar experiment for a para-rich clath-rate sample which displayed all of the same trends but withthe para bands being the most intense peaks for every envi-ronment. It is worth noting that a H2 clathrate with onlydouble occupancy in the large cavity and single occupancy inthe small cavity was never observed in this study; a smallamount of large cavity triple occupancy was always requiredfor stability at these conditions.

In order for the large cavity hydrogen occupancy tochange from four to three to two molecules without decom-position of the crystal structure, a diffusive process must takeplace, in which H2 can progress through the clathrate. Thehexagonal faces of the 51264 cavities of sII hydrate are ar-ranged with tetrahedral symmetry and each hexagonal face isshared with another 51264 cavity as the 512 cavities possessno such faces.22 This hexagonal face sharing creates an ex-tended network of large cavities throughout the crystal struc-ture. Figure 4 shows one such hexagonal face sharing path-way through a single unit cell.

We propose that this hexagonal face sharing connectivityprovides a migration pathway for hydrogen molecules to dif-fuse through the crystal structure, without affecting the smallcavity occupancy. Recently, the energy barrier for a H2 mol-ecule to migrate through a pentagonal face was calculated tobe between 25 and 29 kcal/mol whereas the barrier for mi-gration through a hexagonal face was calculated to be only5–6 kcal/mol.23 Additionally, the experimental hexagonalface barrier, estimated from NMR line widths, was calcu-lated to be 3.8 kcal/mol.24 Clearly, the energy barrier forhydrogen migration through a hexagonal face is much lowerthan that of a pentagonal face; thus, the hexagonal face dif-fusive pathway appears to be that of the least resistance.

The assignment of the large cavity contribution to theRaman spectra presented in Fig. 3 is consistent with the neu-tron scattering results of Lokshin et al.7 However, it may be

4100 4120 4140 4160Raman Shift (cm-1)

Intensity(A.U.)

4L3L2L1s

(a)

(b)

(c)

(d)

FIG. 3. �Color online� �a� Vibron Raman spectra of unperturbed hydrogenhydrate formed at 200 MPa and 250 K, measured at 76 K and 0.1 MPa.��b�–�d�� Heat �150 K�/quench �76 K� cycles �see text�. Vertical lines indi-cate ortho and para cavity contributions: 1H2/small cage �1s�, 2H2/largecage �2L�, 3H2/large cage �3L�, and 4H2 /large cage �4L�.

FIG. 4. �Color online� Portion of sII unit cell showing hexagonal face shar-ing large cavities.

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feasible that alternative assignments are possible for the largecavity environments represented by ortho-para couples pre-sented in Fig. 3. For example, these couples could potentiallyrepresent singly, doubly, and triply occupied cavities, as inthe assignment of Giannasi et al.,25 rather than doubly, triply,and quadruply occupied cavities as in the present assign-ment. However, this alternative assignment is inconsistentwith the observed trends in peak intensity presented inFig. 3.

In order to verify the assignment presented in Fig. 3, theabsolute hydrogen content of simple H2 clathrate was mea-sured as a function of the formation pressure. Simple H2

clathrate was formed at 125, 160, and 200 MPa at 250 K.The samples were quenched in liquid nitrogen, and the vol-ume of gas released as the hydrate dissociated was measured.Measurements for each formation pressure were repeated atleast once.

Figure 5 shows the volume of H2 gas collected from thedissociated hydrate �per mass of water used to form the hy-drate� as a function of the formation pressure. The horizontallines in Fig. 5 represent the theoretical amount of gas �atexperimental conditions� that would be obtained if the smallcavities contained one hydrogen molecule, and the largecavities contained four, three, two, or one hydrogenmolecule.

The volume of hydrogen gas collected increased in pro-portion to the formation pressure. With a formation pressureof 200 MPa, the volume of gas collected was consistent withthe large cavities containing a mixture of three and four mol-ecules. At 160 MPa, the volume of gas collected suggestedthat the average large cavity occupancy was approximatelythree molecules, and at 125 MPa the average large cage oc-cupancy was less than three molecules. The evidence fromthe absolute hydrogen content of the simple H2 clathrate, aswell as the neutron data from Lokshin et al.,7 supports theassignment of the Raman bands.

Next, the same experiments were repeated with forma-tion pressures of 125, 160, and 200 MPa. However, this time

the hydrate was not dissociated but was measured via Ramanspectroscopy. Figure 6 shows the Raman spectra obtainedfrom these hydrates. The gas evolution results �Fig. 5� for thesample formed at 200 MPa contained an amount of hydrogenconsistent with a significant population of quadruply and tri-ply occupied cavities. The 200 MPa Raman spectrum in Fig.6 is consistent with the gas evolution results. The Ramanspectrum shows a large contribution from quadruply occu-pied cavities, as well as a contribution from triply occupiedcavities �following the assignment in Fig. 3�. The Ramanspectra of the samples formed at 160 and 125 MPa are alsoconsistent with the macroscopic amount of gas released andthe assignment in Fig. 3.

We note that a small degree of intensity variation wasalways observed within the same sample for a given forma-tion pressure depending on the laser focal point. This varia-tion can be observed between Figs. 3�a� and Fig. 6 for twoseparate samples formed at 200 MPa. This reflects smallchanges in the large cavity H2 population between differentcrystallites in the polycrystalline powder samples, potentiallycaused by sample handling. However, all spectra shown arerepresentative of the average spectrum obtained over manyindependent measurements of the same sample.

Given the agreement between the large cavity Ramanband assignment, the macroscopic gas evolution results, andthe neutron scattering results of Lokshin et al.,7 the largecavity occupancy of H2 consists of a distribution of two,three, and four hydrogen molecules. Additionally, the inten-sity of the Raman bands in Fig. 6 qualitatively follows theabsolute hydrogen content presented in Fig. 5. The degree towhich the ratio of Raman band intensities follows the abso-lute occupancy will be discussed in Sec. IV; however, thequalitative trends presented here suggest that Raman is apowerful and convenient tool for determining absolute thehydrogen content.

250

300

350

400

450

500

550

600

650

100 125 150 175 200 225

Pressure (MPa)

VolumeperM

ass(mLH2/gH2O)

4L 1s

3L 1s

2L 1s

1L 1s

FIG. 5. �Color online� Volume of H2 gas collected per mass of water as afunction of formation pressure. Horizontal lines represent the theoreticalvolume of gas contained within a hydrate with 1H2 /512 and 4H2 /51264 �1s-4L�, 1H2 /512 and 3H2 /51264 �1s-3L�, 1H2 /512 and 2H2 /51264 �1s-2L�, and1H2 /512 and 1H2 /51264 �1s-1L�.

FIG. 6. �Color online� Raman spectra for simple H2 clathrate formed at 200,160, and 125 MPa. Samples were measured at atmospheric pressure and76 K.

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In order to reinforce the Raman peak assignments pre-sented for H2, experiments were performed on D2 bearinghydrates. In the case of D2, the differences in spin statisticsand relative frequency shifts allow for the unambiguous as-signment of observed Raman bands. Figure 7 shows Ramanspectra for THF+D2 hydrate at 76 K and atmospheric pres-sure, formed at 150 MPa and 265 K, measured directly afterformation and after a 10 day period in liquid nitrogen. At 76K, the three lowest rotational states of D2 are populated asseen in the three bands �Q1�0�, Q1�1�, and Q1�2�� in Fig. 7.This is in contrast with H2 which only has two rotationalstates populated at 76 K. In normal D2, the ortho �J=0 and 2�to para �J=1� ratio is 2:1 �66.67% ortho�. However, the ro-tational constant for D2 �B=30 cm−1� is about half that of H2

�B=59 cm−1�.16 As a result, the equilibrium gas phaseortho-D2 concentration at 76 K �70%� is only �5% differentfrom the normal value. In the case of para-H2, the equilib-rium concentration at 76 K �51%� is over two times the nor-mal value. Thus, no significant change was observed for theTHF+D2 hydrate after storage at 76 K, whereas the intensityof the ortho- and para-H2 bands of THF+H2 hydrate re-versed after storage at 77 K. After 4 months of storage inliquid nitrogen, a small decrease in the para band of THF+D2 hydrate was observed.

For the free D2 molecule, the Q branch transitions Q1�0�,Q1�1�, and Q1�2� occur at 2993.5, 2991.4, and 2987.2 cm−1

respectively.16 For the THF+D2 hydrate, these bands wereredshifted by �25 cm−1. In the case of H2 hydrates, theseparation between the free gas Q1�0� and Q1�1� bands�6 cm−1� was in agreement with that of H2 contained withinany of the various cavity environments. For the THF+D2

hydrate spectra �Fig. 7�, the frequencies Q1�0�-Q1�1�=2 cm−1 and Q1�1�-Q1�2�=4 cm−1 also agree with the gasphase separations.

Pure D2 hydrate was formed at 192 MPa and 260 K.

Figure 8 represents the same procedure for D2 hydrate as wasperformed for H2 hydrate in Fig. 3. Figure 8�a� shows theunperturbed D2 hydrate sample with predominantly qua-druple occupancy of the large cavity and single occupancy ofthe small cavity, although as with the H2 hydrate at similarformation conditions, triple large cavity occupancy was alsopresent. After the first heat/quench cycle �Fig. 8�b��, qua-druple occupancy of the large cage was reduced, and doubleand triple occupancies increased relative to the small cagebands. The second heat quench cycle �Fig. 8�c�� showed pri-marily triple large cage occupancy with some double andquadruple occupancies. After the third cycle �Fig. 8�d��, thelarge cavities were mainly doubly occupied by D2 with asmall amount of triple large cavity occupancy. These resultsare directly applicable to the H2 data and unambiguouslyconfirm the Raman peak assignments.

Additionally, the spectra presented for D2 suggest thatH2 follows the same occupancy patterns under similar for-mation conditions and increases confidence that D2 is a rep-resentative substitute for H2. As with the THF+D2 hydrate,after 10 days in liquid nitrogen, the simple D2 hydrateshowed nearly identical Raman band intensities when com-pared with the measurement directly after formation.

B. Rotational spectroscopy

The rotational Raman spectra for gaseous hydrogen at0.1 MPa and 296 K and for binary THF+H2 clathrate formedat 150 MPa and 250 K and simple H2 clathrate formed at 200MPa and 250 K measured at 0.1 MPa and 76 K are shown inFig. 9. For the simple H2 clathrate spectrum in Fig. 9, thelarge cage H2 occupancy was intentionally reduced to anaverage of less than three molecules for comparison. The twobands in the gaseous phase spectrum arise from purely rota-tional transitions: S0�0� 354 cm−1 �J=0→J=2, para� andS0�1� 587 cm−1 �J=1→J=3, ortho�. In the clathrate phase,these bands are significantly broadened; however, the near

2955 2960 2965 2970 2975 2980Raman Shift (cm-1)

Intensity(A.U.)

Q1(0)

Q1(1)

Q1(2)

t=0

t=10 days

FIG. 7. �Color online� Raman spectra for THF+D2 hydrate formed at 100MPa and 265 K. Solid line: Raman measurements directly after formation;dashed line: Raman measurement after 10 days in liquid nitrogen. The in-creasing contribution at higher frequency ��2980 cm−1� is from THF.

2950 2960 2970 2980 2990 3000

Raman Shift (cm-1)

Intensity(A.U.)

4L3L2L1s

(a)

(b)

(c)

(d)

FIG. 8. �Color online� �a� Vibron Raman spectra of unperturbed D2 hydrateformed 192 MPa and 260 K measured at 76 K and 0.1 MPa. ��b�–�d�� Heat�150 K�/quench �76 K� cycles �see text�. Vertical lines indicate ortho Q1�0�and para Q1�1� cavity contributions: 1D2/small cage �1s�, 2D2/large cage�2L�, 3D2/large cage �3L�, and 4D2/large cage �4L�. Q1�2� positions are notlabeled for clarity.

014506-6 Strobel, Sloan, and Koh J. Chem. Phys. 130, 014506 �2009�

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coincidence in frequency with the gaseous peaks indicatesthat the enclathrated hydrogen molecules undergo relativelyfree rotations. It is of interest that the S0�0� band in theclathrate phase is split into three distinguishable peaks sepa-rated by about 4 cm−1.

For the free hydrogen molecule, the rotational energylevels are degenerate by a value of 2J+1.17 These degeneratelevels of J, m, may take on values of J, �J−1�, �J−2�, −J.When J is equal to zero, m can only have a value of zero andthe spherical harmonic probability density is given by asphere with no orientational dependence. When J is equal to1, m may take on values of 0 or �1 and the spherical har-monic probability densities are given by elongated or flat-tened spheroids.26 For the free molecule, these equal energylevels affect the rotational population factor reflected in theRaman peak intensity.

It is well known that anisotropic crystal fields may liftthe degeneracy of the H2 rotational levels.26 If the degen-eracy was completely lifted, the J=0→J=2 transition couldoccur between the J=0, m=0 level to any one of the fivedifferent m levels for J=2. However, this would mean thatfive transitions should be observed for the para-H2 band inFig. 9 and in these data only three peaks are resolvable.

Recently, five dimensional quantum calculations havebeen performed for a single hydrogen molecule in a small sIIcavity.27 These results demonstrate the splitting effect withfive separate energy levels for the J=2 state at 348.6, 349.6,356.0, 363.4, and 364.3 cm−1. The differences between thefirst two and last two values are very small �1.0 and0.9 cm−1�, while the differences between the middle valueand first and last values are about 8 cm−1.

This result suggests that although the five m are split intoseparate energies, only three of these transitions may be re-solvable as differences in energy between the first and lasttwo are very small. Based on the available calculations,27–29

we suspect that the three split bands in Fig. 9 actually con-tain all five of these transitions with two of them convolutedin the lowest and highest frequency peaks. Figure 10 com-pares the S0�0� bands for THF+H2 and THF+D2 clathrateswith the small cavity frequencies calculated by Xu et al.27

For the ortho-H2 band in the clathrate phase, no direct

splitting was detected. Considering that the J=1 level will besplit into three sublevels and that the J=3 level will be splitinto seven sublevels, the possibility of numerous rotationaltransitions separated by small energies provides that it islikely that this may appear as one broad band in the spec-trum.

As demonstrated in Fig. 9, the rotational bands forTHF+H2 and simple H2 clathrate are very similar when thelarge cavity H2 loading is low �less than three molecules�.This similarity and frequency separation of the S0�0� bandfine structure between the two samples suggest that theanisotropies between the orientational potentials of the smalland large cavities are comparable. However, this picturechanges substantially when the H2 loading in the large cavityis high.

Figure 11�a� shows the evolution of the rotational bandstructure at different H2 loadings in the large cavity. Thetrends in the large cavity H2 loadings were confirmed withthe vibrational spectra �Fig. 11�b��, as well as the absolute H2

content as in Fig. 5. The structure near the tops of the rota-tional bands remained essentially independent of the largecavity H2 content, while the bases of the bands broadenedsubstantially with increasing H2 content. At the lowest largecavity H2 loadings, the band structures approximate those ofTHF+H2 clathrate where only the small cavities are occu-pied. This result suggests a noticeable increase in the aniso-tropy of the large cavity orientational potential, as well as anincreased barrier to free rotation for large cavities with highhydrogen content �approximately four molecules�.

For the rotational spectrum of D2 hydrate, the same gen-eral trends with H2 hydrate were observed. However, in thecase of D2, three rotational bands were present rather thantwo. The S0�0� ortho-D2 band was split into three resolvablepeaks separated by about 4 cm−1. The S0�1� and S0�2� bandswere not resolvable into separate components. These resultssuggest that the anisotropy of the environments for both H2

and D2 are similar.

IV. DISCUSSION

The assignments presented for the bands comprising thevibrational spectra of simple H2 clathrate are supported by

330 370 410 450 490 530 570 610

Raman Shift (cm-1)

Intensity(A.U.)

H2 gasTHF+H2 hydrateH2 Hydrate

335 345 355 365

Raman Shift (cm-1)

Intensity(A.U.)

560 570 580 590 600

Raman Shift (cm-1)

Intensity(A.U.)

FIG. 9. �Color online� Rotational Raman spectra for gaseous H2, THF+H2 clathrate, and simple H2 clathrate with low large cavity occupancy.

155 165 175 185 195

Raman Shift (cm-1)

Intensity(A.U.)

330 340 350 360 370

Raman Shift (cm-1)

Intensity(A.U.)

D2 H2

FIG. 10. �Color online� Comparison of the S0�0� bands for THF+D2 hydrate�left� and THF+H2 hydrate right. Vertical lines indicate calculated frequen-cies �Ref. 27�.

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�1� the relative changes in the intensity of these bands uponthermal stimulation, �2� the agreement between the intensi-ties of the assigned bands with the macroscopic amount ofgas contained within the clathrate as a function of pressure,�3� the transferability of the assignment to D2 clathratesformed under the same conditions, and �4� the agreementbetween the trends in intensity of the assigned bands withneutron scattering results for simple D2 clathrate. The evi-dence presented extensively supports the current assignment.

Recently, Giannasi et al.25 reported Raman spectra forsimple H2 and D2 clathrates that were comparable to thosepresented here; however, the assignment presented was strik-ingly different. Giannasi et al.25 assumed only a negligiblenumber of large cages with a population of four moleculesand ascribed the large cage ortho-para peak pairs, from lowto high frequency to triply, doubly, and singly occupied cavi-ties. The current assignment marks these contributions asdoubly, triply, and quadruply occupied cavities.

The assignment of Giannasi et al.25 was based on theintegrated Raman intensities between the small and largecavity contributions. By assuming a small cage occupancy ofone molecule, accounting for the different cross sections ofortho and para molecules, and accounting for the sII stoichi-ometry �2 512:1 51264�, Giannasi et al.25 calculated the aver-age large cage occupancy of D2 to be �1.7 for a spectrumsimilar to Fig. 8�c�. From this result the assumption of neg-ligible quadruple occupancy was justified, and the single,double, and triple occupancy bands were assigned, providing

a distribution that matched an average of �1.9 molecules.However, when we measured the macroscopic amount ofgas contained within the clathrate for a spectrum similar toFig. 8�c� �see 125 MPa for Figs. 5 and 6�, the clathrateclearly contained an average value closer to three moleculesper large cavity.

The above apparent discrepancy cannot be explained bya decrease in small cavity occupancy as the calculated largecavity occupancy from Raman band intensity is already toolow. Double occupancy of the small cavity could potentiallyexplain the discrepancy; however, this result would createinconsistencies with the gas evolution and neutron scatteringresults, as well as inconsistencies with numerous measure-ments of THF+H2 hydrate.8,9,30,31 Therefore, we suggest thatthe discrepancy between the H2 occupancy values obtainedfrom integrated Raman band intensities arises from inad-equacies of the implicit assumption that the scattering crosssection of H2 remains constant between the various cavityenvironments.

Raman cross sections may change appreciably when theeffects of local fields are introduced.32 The difference in H2

vibrational frequency between a singly occupied small cavityand a quadruply occupied large cavity ��23 cm−1� suggeststhat the polarizability of H2 between these different environ-ments will change. Additionally, increased guest-guest andguest-host interactions at high H2 loadings will likely affectthe degree to which H2 interacts with electromagnetic radia-tion. Increased interactions at high H2 loading is evidenced

320 370 420 470 520 570 620

Raman Shift (cm-1)

Intensity(A.U.)

320 330 340 350 360 370 380

Raman Shift (cm-1)

Intensity(A.U.)

550 560 570 580 590 600 610 620

Raman Shift (cm-1)

Intensity(A.U.)

4100 4120 4140 4160

Raman Shift (cm-1)Intensity(A.U.)

Mostly 4L

Mostly 3L

< 3L

(b)

Mostly 4LMostly 3L< 3L

Mostly 4LMostly 3L< 3L

(a)

FIG. 11. �Color online� �a� Rotational Raman spectra for simple H2 clathrate as a function of large cavity H2 content. Insets show the details of the S0�0� andS0�1� bands. �b� Vibrational spectra corresponding to �a�.

014506-8 Strobel, Sloan, and Koh J. Chem. Phys. 130, 014506 �2009�

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by the breadths of the quadruple occupancy bands �see Fig.3�, as well as a clear change in the sII lattice parameter uponincorporation of a fourth H2 molecule.7

It is beyond the scope of this paper to accurately calcu-late the change in polarizability of H2 between in the variouscavity environments. However, following the procedure out-lined by Giannasi et al.,25 the average large cavity occupan-cies from the integrated Raman band intensities in Fig. 6 are1.9 �125 MPa�, 2.3 �160 MPa�, and 2.7 �200 MPa� mol-ecules, respectively, and by comparing these values with themacroscopic values obtained in Fig. 5, we estimate that theaverage large cavity H2 cross section is �27% less than thesmall cavity cross section. Clearly this approach is approxi-mate; a more quantitative approach could be obtained withNMR cross calibration33,34 �for ortho-H2� if the different H2

environments are resolvable in the magic angle spinning�MAS� spectrum. However, calculations of NMR shieldingconstants suggest that the chemical shift range of enclath-rated H2 is very limited.35

Nevertheless, the intensity trends in the assigned Ramanbands do appear to qualitatively follow the H2 content of theclathrate as well as approximate the occupancy distribution.It is clear that a correction factor is needed to accuratelyquantify the hydrogen content solely through Raman spec-troscopy. Until such a correction factor can be accuratelydetermined, Raman still appears to be a powerful tool toobserve relative trends occupancy patterns.

In the work of Subramanian and Sloan,36 a general ob-servation was made that for symmetric stretching modes ofguest molecules within clathrate cavities, the larger the cav-ity in which a guest molecule resides, the lower the fre-quency of vibration. Additionally, the vibrational frequenciesof enclathrated species are lower than those of the free gasphase. This trend was explained conceptually using the“loose cage–tight cage” model of Pimentel and Charles,37

which was based entirely on a solvation model proposed byBuckingham.38,39

In this model the vibrational frequency shift of a sol-vated or encaged molecule, compared with the free vibra-tional frequency ���n.0�, is related to the first and secondderivatives of the solute-solvent interaction potential withrespect to the internal stretching coordinate of the solute�U�, U��,

��n,0 =nBe

hc�e�U� − 3AU��,0, �2�

where � �,0 indicates a statistical average over all configura-tions �� when the solute is in the ground vibrational state,and n, Be, h, c, �e, and A represent the excited vibrationalstate, the equilibrium rotational constant, Planck’s constant,the speed of light, the equilibrium vibrational frequency, andthe anharmonicity constant, respectively. This model hascommonly been used to qualitatively describe the heuristicrelating the cage size to guest vibrational frequency.36,40,41

Variants of this model have also been applied to describe thevibrational frequencies of matrix isolated species42,43 andother molecular systems.44–46

The term in Eq. �2� associated with U� arises from achange in the harmonic force constant due to intermolecular

interaction, and the term associated with U� arises from ashift in the equilibrium displacement and will influence thefrequency if the vibration is anharmonic. Depending on thenature of the intermolecular potential, both negative andpositive frequency shifts, relative to the free gas phase, arepossible. It has been argued that for hydrate cages the inter-action potential provides that the frequency shift is negative,although for some systems, e.g., filled ice phases, the shift ispositive.47

The observed trends in the vibrational frequency of H2

within the various clathrate environments suggest an attrac-tive dominant potential as all frequencies are redshifted fromthe free gas phase. The “loosest” environment observed iswhen H2 singly occupies the 512 cavity, marked by a−34 cm−1 shift. As hydrogen is packed into the large cavitythe potential becomes increasingly repulsive �“tighter”�. Thefrequency shift for a doubly occupied large cavity is−26 cm−1, while shifts for triply and quadruply occupiedcavities are −18 and −11 cm−1, respectively. Although H2

contained within the large cavities vibrates at a higher fre-quency than small cavity H2, this picture is still consistentwith general clathrate frequency trends. Multiple occupantsof the large cavity create an effectively smaller “cage” for anindividual H2, thus creating a tighter environment and a morepositive frequency shift.

In general, the fine structure of the S0�0� band consists ofthree resolvable peaks with the lowest frequency componentbeing the most intense. This feature appears to remain nor-mally consistent throughout a given sample and independentof thermally induced occupancy modifications and ortho-para concentration. However, we note that several spectrawere obtained that exhibited a more equal intensity S0�0�band splitting. The cause of this intensity variation is pres-ently unclear, and currently no theoretical intensity calcula-tions are available.

V. CONCLUSIONS

Raman spectroscopic measurements of simple and bi-nary hydrogen/deuterium clathrate hydrates have been per-formed. Both the roton and vibron bands illuminate interest-ing quantum dynamics of enclathrated H2 molecules. At 76K, the structure of the vibrational bands for each H2 environ-ment consists of an ortho and a para component. At 76 K, theprogression from ortho- to para-H2 occurs over a relativelyslow time period �days�. Hydrogen contained in both singlyand multiply occupied cavities vibrates at a considerablylower frequency than the free gaseous phase. Single occu-pancy is the most perturbed environment with an �34 cm−1

shift, followed by double, triple, and quadruple large cavityoccupancies with increasing frequency.

The assignments presented for the large cavity vibra-tional transitions are supported by the change in populationof these bands with temperature, measuring the absolute H2

content as a function of pressure, D2 isotopic substitution,and agreement with previous neutron scattering results. Inte-gration of the vibrational Raman bands provides too small ofa large cavity H2 content. We suggest that this discrepancyarises from inadequacies in the assumption of a constant

014506-9 Raman studies of H2 clathrates J. Chem. Phys. 130, 014506 �2009�

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scattering cross section between different cavity environ-ments, which would indicate that small cavity H2 is morepolarizable than large cavity H2.

The rotational degeneracy of H2 molecules within theclathrate cavities is lifted, observed directly in splitting of thepara-H2 roton band. The orientational anisotropies of thelarge and small cavity environments appear similar at lowlarge cavity H2 loadings. This feature is observed in the con-stant energy peak splitting and band shape between THF+H2 and simple H2 clathrate. However, when high large cav-ity loadings are achieved, the peak shapes differ substan-tially, indicating increased orientationally dependent rotationas well as a larger barrier to free rotation.

Raman spectra from H2 and D2 hydrates suggest that theoccupancy patterns between the two hydrates are analogous,increasing confidence that D2 is a suitable substitute for H2.The measurements suggest that Raman is an effective andconvenient method to determine the relative occupancy ofhydrogen molecules in different clathrate cavities.

ACKNOWLEDGMENTS

We are grateful to Yongkwan Kim for performing someof the hydrogen gas release and Raman measurements. Thiswork was supported under DOE Contract No. DE-FG02-05ER46242.

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