Dynamics of Methyl Iodide Clathrate Hydrate, Investigated by MD Simulations and QENS Experiments

Published: June 15, 2011

r 2011 American Chemical Society 12689 dx.doi.org/10.1021/jp110971h | J. Phys. Chem. C 2011, 115, 12689–12701

ARTICLE

pubs.acs.org/JPCC

Dynamics of Methyl Iodide Clathrate Hydrate, Investigated by MDSimulations and QENS ExperimentsA. Desmedt,‡,* J.C. Soetens,‡ M. Prager,§,† M. Russina,^ and J. Ollivier||

‡Institut des Sciences Mol�eculaires, UMR5255 CNRS - Universit�e de Bordeaux, 351 cours de la Lib�eration, F-33405 Talence, France.§Institut f€ur Festk€orperforschung, Forschungszentrum J€ulich, D-52425 J€ulich, Germany^Helmhotz Zentrum Berlin, BENSC, Glienickerstr. 100, D-14109 Berlin, Germany

)Institut Laue-Langevin, 6 rue Jules Horowitz, BP 156, F-38042, Grenoble Cedex 9, France

bS Supporting Information

1. INTRODUCTION

Clathrates hydrates are a class of organic nanoporous crystalsmade of guest molecules embedded within polyhedral cagelikestructure (host lattice) formed by means of water molecules.1

The cages are formed from polygonal rings of water moleculesconnected at their edges by means of a hydrogen bond, the moststable being a pentagon (example of 51264 and 512 cages areshowed in Figure 1; the 512 cage refers to a dodecahedron be-cause this cavity is constituted of 12 pentagonal faces). Numer-ous arrangements of these cages exist to form a 3D crystallinestructure, depending on the encapsulated molecules. Under ap-propriated thermodynamic conditions, clathrates hydrates crys-tallize into three major types of structure: two cubic structurestermed type I and type II,2,3 and one hexagonal structure termedtype H.4

The natural occurrence of gas hydrate in permafrost area orocean shelves in large quantities, the hazardous risk due to their

formation in oil and gas pipeline, and their potential utilizationfor gas transportation in soft conditions (i.e., close to atmosphericpressure and room temperature) makes clathrate hydrates parti-cularly interesting and fascinating for energy and environmentalapplications.5 At a fundamental level, host�guest interactionsand coupling, as well as anharmonicity, play an important role inthe specific properties met in clathrate hydrates.6,7 This isprobably typified by the anomalous behavior of heat transportin clathrate hydrates.8 Several hypotheses have been made aboutthe origin of the glasslike thermal conductivity observed in thesecrystalline systems. Neglecting the host�guest interactions, thelow thermal conductivity involve structural disorder originat-ing from the guest dynamics9 with water lattice contributions,

Received: November 17, 2010Revised: May 6, 2011

ABSTRACT: This article presents a comprehensive study of the dynamic proper-ties of the methyl iodide molecule encapsulated in the large cage of thecorresponding type II clathrate hydrates between 150 K and room temperature.An approach combining quasi-elastic neutron scattering (QENS) and moleculardynamics (MD) simulations provide insights into dynamics across a time scaleranging from tenths to hundreds of picoseconds. MD-derived QENS spectra havebeen computed with the help of the atomic MD trajectories and directly comparedwith the experimental ones. The successful agreement between experimental andtheoretical spectra allows the validation of the MD simulations, so that a detailedmodel of dynamic properties is elaborated. The results of both the QENS and MDstudies demonstrate that no water molecule relaxation occurs on the probed time scale, whereas relaxation together with a low-energy excitation (observed on experimental andMD-derived QENS spectra) of the guest molecule is observed. Modeling this low-energy excitation shows that the strongly anharmonic rattling of guest molecules within the cage originates from a translationalmode (at 1.31( 0.03 meV with a damping of 1.49( 0.03 meV) coupled to a librational mode (at 0.85( 0.05 meV with a dampingof 1.19 ( 0.01 meV) of the whole molecule. The localized translational relaxation of the guest molecules within the cage ischaracterized by a diffusion constant of 1.22( 0.06 ps�1 at 270K with low activation energy of 1.5( 0.1 kJ/mol. Moreover, wholereorientations of guest molecules are characterized with a diffusion constant of 2.47( 0.55 ps�1 at 270 K and a low activation energyof 0.8( 0.1 kJ/mol (in addition to fast rotations of the methyl group). By modeling the structure factor and analyzing orientationaldistribution functions, it is found that the guest molecules are off-centered and undergo strongly anisotropic reorientations withinthe cages. Guest molecules preferentially adopt orientations that are different from cage to cage due to a static (with respect to theprobed time scale) disorder of the H-bond network. The various local environment leads to a distribution of energy landscapesexplored by the guest molecules in terms of geometrical characteristic but not in terms of characteristic times of guest moleculesdynamics in the present combined MD-QENS investigation.

12690 dx.doi.org/10.1021/jp110971h |J. Phys. Chem. C 2011, 115, 12689–12701

The Journal of Physical Chemistry C ARTICLE

resulting in phonon scattering characterized by a thermal in-dependent and short mean free path.10 However, it has beenproposed that strong coupling between localized guest vibrationsand the lattice modes,11 leading to symmetry avoided crossings ofthe localized guest motions with the acoustic branches of thelattice, would be responsible for the almost temperature inde-pendent thermal conductivity. The investigation of such host�guest coupling has required multitechnique approach by meansof inelastic neutron scattering,12,13 inelastic X-ray scattering,14 andmolecular or lattice dynamics simulations.15�18 In addition, theanharmonicity of the host�guest coupling has been identified asbeing dominant in the mechanism involved in the glasslikebehavior.15,19

The investigation of clathrate hydrates dynamics is a prere-quisite for better understanding the specific properties of thesesystems. According to structural analysis, each oxygen atom ofthe host substructure is surrounded by four equiprobable (halfoccupied) hydrogen sites,20�22 so that the hydrogen atoms of theaqueous submatrix are dynamically disordered. Moreover,H-bond defects (Bjerrum defects, ionic defects, etc.) might existand thus increase the degree of disorder in the system. For instance,the time scale of water molecules reorientation will be affected bythe concentration of defects. Indeed, the water molecules undergoereorientations on a microsecond time scale in a standard clathratehydrates.20 In ionic clathrate hydrates (made with strong acid guestmolecules), the concentration of H-bond defects is increased(the acid molecules is deprotonated, so that the host latticebecomes cationic23) and the water molecules reorientations occuron a nanosecond time scale.24 Another consequence of thedisordered host lattice concerns the dynamics properties of theguest molecules. Indeed, the various possibilities of the H-bondsdistribution lead to different local environment explored by theguest molecules with respect to the time scale of the dynamics.This leads to distribution of the properties that could be inter-preted in terms of dynamical or structural heterogeneities (forinstance, see the studies performed on tetrahydrofuran clathratehydrates by means of deuterium NMR25�27).

Analyzing dynamics of the guest molecules encapsulated withinwater cages leads to the exploration of the potential energy surfaceas seen from the guest molecule inside the cage. In this issue,methane clathrate hydrate has been the subject of numerousworks, including molecular dynamics simulations,28�30 inelasticneutron scattering,31 inelastic X-ray scattering,14 and NMR.32,33

In this clathrate hydrate, almost free rotation and very anhar-monic low-frequency translation (so-called rattling mode) are

observed. The quantitative analysis of the molecular dynamics atthe lowest temperature leads to describe the molecular motion assingle-particle quantum rotation in weak rotational potentialsdiffering slightly from cage to cage. This static distribution of thelocal environment owes to different arrangements of the hydro-gen bonds in the cage surface.28 Methane clathrate hydrateprobably represents the prototypical system of non polar clath-rate hydrate. Simple model systems of polar guest molecules areprobably represented by methyl halides clathrate hydrates.34,35

According to literature molecules,36 the three light methyl halidehydrates (CH3X 3 5.75H2O and X= F, Cl, or Br) assume the sametype I cubic crystal structure as methane clathrate. Larger guestmolecules such as methyl iodide require larger cages and crystal-lize within the cubic II structure (Figure 1) with only the largestcages 51264 filled with guest molecules.36 High-energy resolutionneutron scattering experiments have been performed to analyzethe rotational tunneling of guest methyl group in the series ofmethyl halide clathrate hydrates at low temperatures.37�41 Themethyl iodide clathrate hydrate has led to new information on thecomplex potential surface of the water cages: a model, involvingadsorption sites of the guest molecules at the cage surface, hasbeen developed.37 These sites have been associated to theexistence of various types of hydrogen bonds between the watermolecules. Moreover, positional disorder of the protons withinthe host network is at the origin of large broadening of thetunneling transitions. These results outline the host�guest cou-pling in clathrate hydrates and illustrate the structural anddynamical heterogeneity existing in clathrate hydrates at lowtemperatures.

In this article, we focus on a detailed modeling of the dynamicsof methyl iodide molecules encapsulated within the cages of thecorresponding type II clathrate hydrate. Whereas the previousstudies37,38 have permitted us to characterize the quantumdynamics of the methyl iodide clathrate hydrates at low tem-perature, the dynamics properties at high temperature (i.e., above150 K) have not been investigated. To reach this goal, anapproach combining incoherent quasi-elastic neutron scattering(noted QENS) experiments and molecular dynamics (notedMD) simulations is particularly appropriated. Indeed, bothtechniques yield commonobservable (atomic position correlations)in similar time and space domains. The powerfulness of such acombined approach resides in the direct confrontation of experi-mental and theoretical results done through the comparison ofscattering laws. This allows us, on the one hand, to validate thepotential used in the MD simulations and, on the other hand, touse the MD trajectories as a guide for interpreting the experi-mental data and model the complex dynamical processes of theguest molecules. To our knowledge, very few studies are devotedto such a direct comparison of experimental and theoretical datato investigate the guest dynamics in clathrate hydrates.

2. QENS EXPERIMENTS

2.1. Experimental Details. The methyl iodide clathrate hy-drate, CH3I 3 17D2O, has been prepared by following the proce-dure described in ref 37. The host substructure was 97 wt %deuterated. The sample has been grounded to form a fine powderplaced into a flat aluminum container (sealed with indium wire).The angle between the incoming beam and the plane of the sampleholder was 135�. The multiple scattering effects have beenminimized by using a sample thickness less than 0.6 mm so that

Figure 1. Two types of cages forming the type IImethyl iodide clathratehydrate CH3I 3 17H2O. The large cages 5

1264 (on the right) contain theCH3I guest molecule (represented by a black sphere) and the smallcages 512 are empty. The oxygen atoms of the water molecules arelocated at each corner and the H-bonds are contained at the edge.



the effective transmitted beam corresponds to about 90% of theincident beam.QENS experiments with the CH3I 3 17D2O sample have been

performed using the time-of-flight (denoted ToF) spectrometerIN542 at the Institut Laue Langevin (Grenoble, France). Thescattering angles covered by this instrument are in the range 14�to 132� and the energy resolution was ΔE = ∼100 μeV foran incident wavelength λo = 5 Å. By slowly cooling the samplefrom 267 to 13 K at a rate of 0.3 K/min, QENS spectra havebeen continuously recorded with an acquisition time of 10 min.Examples of spectra are shown in Figure 2. For subsequentanalysis and comparison with the MD results, QENS spectrahave been recorded using the ToF spectrometer NEAT43 at theBerlin Neutron Scattering Centre of the Helmholtz ZentrumBerlin (Germany). The scattering angles on this instrument arein the range 13� to 136�, and the energy resolution was ΔE =∼100 μeV for an incident wavelength λo = 5.1 Å. The dataacquisition time was ca. 8 h, and the spectra were recorded (inorder of decreasing temperatures) at 270 and 150 K. Energyresolution functions of both ToF spectrometers have beendetermined by recording QENS spectra of flat vanadium sample.The raw data were corrected for detector efficiency and sample-geometry dependent attenuation. Additionally, the backgroundwas subtracted using the measurement of the empty samplecontainer. The data were normalized to the elastic scattering ofvanadium and transformed to energy scale. Two sets of data havebeen extracted from the neutron scattering experiments. For thestructural analysis, only elastic scattering has been extracted fromthe experimental data at each scattering angle. For QENS anal-ysis, several detectors were grouped together to improve thestatistical accuracy, and Bragg peaks were carefully removed fromexperimental data. These procedures were carried out with theINX software44 and data analysis has been done by using theprogram NEMO.45

2.2. Phenomenological Analysis. With the help of the IN5data, no structural phase transition has been observed between13 and 267 K (the diffraction pattern of the methyl iodideclathrate hydrate is provided as Supporting Information). InFigure 2, QENS spectra averaged over all scattering angles(IN5 spectrometer) are shown as a function of temperature.From this figure, two temperature regimes are clearly identi-fied. In the first regime, below ca. 70 K, at least one inelasticpeak is observed on each energy transfer side. These peaks aredue to the rotational tunneling of the methyl group, aspreviously studied.37 Because of the energy resolution andthe intrinsic properties of the rotational tunneling process(softening of the rotational tunneling frequency with increasingtemperature), these inelastic peaks merge with the elastic peak togive a typical QENS broadening at temperature above ca. 70 K. Inthis second temperature range (of interest in the present article), ashoulder at about ∼1 meV is clearly observed in addition to theQENS broadening. This inelastic peak has been attributed to therattlingmode of themethyl iodidemolecule within the cage on thebasis of qualitative comparison with results obtained in otherclathrate hydrates.37 The overlapping of the broad inelastic peakwith the QENS broadening makes the analysis difficult only onthe basis of the experimental data. A phenomenological analysis ofthe QENS component remains possible by limiting the energywindows to (1 meV. The QENS spectra have been fitted withthe help of the following expression (refs 46 and 47 for detailsabout the relationship between the measured spectra and the

Figure 2. QENS spectra recorded on a powder CH3I 3 17D2O sample atselected temperatures (Tof spectrometer IN5 at ILL with λ0 = 5.0 Å).

Figure 3. Momentum transfer dependence (top) and temperaturedependence (bottom) of the EISFmeasured on a powder CH3I 3 17D2Osample at selected temperatures and momentum transfer indicated inthe figure (Tof spectrometer IN5 at ILL with λ0 = 5.0 Å).



scattering function):

SðQ ,ωÞ ¼ A0ðQ ÞδðωÞ þ ½1� A0ðQ Þ�LðΔÞ ð1ÞThe Lorentzian function represents the QENS broadening forwhich the half-width at half-maxima (denoted hwhm),Δ, provideinformation about the characteristic times of the motions, whereasthe elastic incoherent structure factor (EISF) A0(Q) provides theamplitude of the elastic term represented by a Dirac functionδ(ω). The fitted EISFs are shown in Figure 3. This elastic termincludes the contribution of the host-substructure, which is immo-bile with respect to the probed time scale: it leads to experi-mental EISF greater than 0.5 (Supporting Information for detailsabout this contribution). The temperature dependence of theEISF atQ= 1.40Å�1 shown on bottomof Figure 3 exhibits a slopediscontinuity at ca. 100 K. This observation suggests the existenceof, at least, two dynamical processes. The one activated at thelowest temperature has been attributed to rotational diffusion ofthe methyl group about the C3 molecular axis, whereas the dyna-mical process activated at ca. 100 K has been attributed to reorien-tation of the whole molecules.37

3. MOLECULAR DYNAMICS SIMULATIONS

3.1. Strategy andDetails.The potential function used in thesesimulations is rigid and pairwise additive. A Lennard�Jones typepotential combinedwith an electrostatic point charge potential hasbeen used to reproduce the interaction between all particles inthe systems. The interaction energy between two molecules inthe system is thus expressed as a sum of interactions betweenatomsR ofmolecule A and atomsβ ofmoleculeB separated by thedistance rRβ.

UðrR, rβÞ ¼ ∑R ∈ A

∑β ∈ B

σRβ

rRβ

!12

� σRβ

rRβ

!624

35þ qRqβ

rRβð2Þ

In this equation εRβ and σRβ are the Lennard�Jones parameterscomputed according to the geometric mixing rules and qR is thepartial charge located on atomR. The SPC/Emodel of Berendsenet al. is used to describe water.48 Parameters formethyl iodide havealready been published for the simulation of pure liquid.49 Never-theless, the validity of a direct combination of two differentmodelsis not guaranteed. In this purpose, few ab initio calculations atHF/6-311G** level50 have been performed on methyl iodide moleculeand on the H2O�CH3I pair. The optimized geometry of methyliodide obtained at this level of calculation presents C�I and C�Hbond length of 2.16 Å and 1.08 Å respectively and a I�C�H angleof 107�. The water/methyl iodide configuration corresponding tothe minimum of the dimer potential energy surface (SupportingInformation) corresponds to interaction energy of�14.1 kJ/mol.

Moreover, four different relative orientations have been consid-ered to improve electrostatic potential fitted charges (originallyobtained from isolated CH3I molecules) and Lennard�Jonesparameters for the CH3I molecules. The final set of Lennard�Jones parameters and charges for water and methyl iodide arereported in Table 1.The MD simulations were carried out at 150, 210, and 270 K

on systems containing 64 methyl iodide guest molecules and1088 host water molecules. The simulation box was built on thebasis of fractional coordinates of the type II clathrate hydrate51

within which only the large cages are filled with methyl iodidemolecules.37,38 Thus, the system corresponds to 8 cubic unitcells, which leads to a cubic box of 34 Å length containing 64occupied large cages (51264) and 128 empty small cages (512).The usual periodic boundary conditions have been consideredand a molecular cut off distance corresponding to half of the edgeof the simulation box has been applied. The simulations havebeen carried out using the MDpol package52 in the microcano-nical NEV ensemble and using a time step of 4 fs. The trajectorieswere integrated using the leapfrog quaternion algorithm ofFincham53 and properties were collected during runs of 10 nsfollowing an appropriated equilibration period.3.2. Dynamical and Structural Properties of the Host

Substructure. Specific observables have been computed tocheck the simulated clathrate structure. The radial pair distribu-tion functions, gOO(r), for the oxygen atoms of the watermolecules (Supporting Information) indicates that the averagedistance between host oxygen atoms is 2.75 Å, in agreement withdiffraction results.51 The corresponding coordination number(obtained by integrating the first peak) confirms that each watermolecule is surrounded by 4 water molecules. Moreover, theaverage intermolecular distance between the hydrogen atomsand the oxygen atoms of water molecules is within the range ofnormal hydrogen bonding: the first peak of the radial pairdistribution functions, gOH(r), is at 1.76 Å (Supporting In-formation). Because the associated coordination number is 2,each water molecule accepts and donates two hydrogen bonds.The well pronounced peak observed on the radial distributionfunctions gOH(r) and gOO(r) are typical of a crystalline materialsand the distribution of the H-bonds within the water substru-cture respects the ice rule, as expected for an ideal clathratehydrate. Moreover, no long-range translational motions of waterand methyl iodide molecules are observed because their meansquare displacements tend toward a plateau at the three studied

Table 1. Values of the Parameters Used in the IntermolecularInteraction Potential (eq 2) a

atom ε [kJ/mol] σ [Å] q [e]

O 0.65017 3.16556 �0.8476

H (water) 0 0 0.4238

I 3.59835 3.704 �0.154

C 2.87108 3.498 �0.200

H (methyl iodide) 1.25913 1.612 0.118aOriginal SPC/E parameters for water48 and ab initio derived para-meters for methyl iodide.

Figure 4. Distribution P(R) of the averaged cage radius R containingthe methyl iodide molecules obtained from MD simulations at 150 K(dotted line), 210 K (dashed line), and 270 K (solid line).



temperatures. Finally, the radius of the cage containing themethyl iodide molecule has been computed at each time step ofthe MD simulations and their distributions (corresponding tothe time-average) are shown in Figure 4. This radius is defined asthe average distance between the center of mass of each cage(defined as the center of mass of the water molecules forming it)and the oxygen atoms of these molecules. The cage radiuses are4.63, 4.64, and 4.64 Å at 150, 210, and 270 K respectively, and thenarrow Gaussian distributions are characterized by full-widths athalf-maxima of 2.3%, 2.6%, and 3.1% of their mean values at 150,210, and 270 K, respectively. These variations of the cage radiusesare in full agreement with the thermal behavior observed bymeans of structural analysis of clathrate hydrate.54

Finally, the orientational autocorrelation function of watermolecules is shown in Figure 5. Clear host-substructure excita-tions are observed but these functions do not totally relax: theirvalues are greater than 0.9 over the probed time scale whateverthe temperature is. In other words, the water molecules reor-ientations are observed on time scale significantly longer than theone of the MD simulations (10 ns length). Such results are inagreement with the reorientation characteristic time expected tobe on the order of microseconds in clathrate hydrate.20,25�27

Thus, the water submatrix is immobile in terms of water re-orientations on the MD time scale, so that no relaxation of theH-bonds arrangement is expected to be observed in the pre-sent study.

4. METHYL IODIDE DYNAMICS

4.1. Bare Comparison of Experimental and MD-DerivedScattering Laws.To compare the time-of-flight neutron scatter-ing data and the MD-simulations data � that is to switch fromdirect (MD) to reciprocal (QENS) space� the calculation of theintermediate scattering function is required. This procedure hasbeen performed by using the program nMoldyn for which detailsof the calculation can be found in ref 55. TheMD-derived QENSscattering laws of the methyl iodide clathrate hydrate has beencalculated by considering the following expression:

SMDðQ ,ωÞ

¼ FðQ Þ 12π

Z þ¥

�¥fRðQ , tÞðICH3I

MD ðQ , tÞð1� pÞ þ pÞge�iωtdt þ BðQ Þ ð3Þ

In this expression, only the incoherent contribution of the guestmolecules has been taken into account for computing theintermediate scattering function IMD

CH3I(Q,t). The experimentshaving been performed on powder samples, an isotropic ave-rage over the momentum transfer orientations has been con-sidered in these calculations. As previously described, the watermolecules dynamics occur on a time scale significantly longerthan the observation time of the MD simulations (10 ns) andof the QENS experiment (on the order of picoseconds), sothat the incoherent contribution of the deuterated watermolecules to the QENS spectra is purely elastic. This contribu-tion has been taken into account by adding a constant, noted p,to the intermediate scattering functions of the methyl iodidemolecules (with p = 0.5 as described in the SupportingInformation). The obtained MD-derived intermediate scatter-ing functions have been normalized and then folded (in thetime domain) with the experimental resolution function, notedR(Q,t), determined on the basis of the Gaussian function fittedto the experimental vanadium QENS spectrum. Finally, theinelastic contribution of water molecules has been taken intoaccount by adding a phenomenological background, denotedB(Q) in expression 3. By applying a scaling factor F(Q), theresulting MD-derived spectra have been directly compared tothe experimental QENS spectra as shown in Figure 6. It shouldbe noted that the phenomenological background was indep-endent of the energy transfer (i.e., equal to a constant) forall momentum transfer values. Slight discrepancies could beobserved for the highest Q values of the spectra recorded atT = 270 K. In this Q�T range, the inelastic scattering of thewater molecules (represented by dashed lines in Figure 6)slightly contribute to the spectrum for two main reasons: as thetemperature is increased, (i) the population of the excitationlevels increases and (ii) the mean square amplitudes Æu2æ of thevibrational motions increase (from MD trajectories, Æu2æ are0.407, 0.279, and 0.184 Å2 at 270, 210, and 150 K, respectively)leading to the amplification of the inelastic structure factors(given by Q2Æu2æe�Æu2æQ2

if one considers the first order of thephonon expansion in the harmonic approximation) in the con-sidered Q range with a maximum at ca. 1.5 Å�1. The con-sequent agreement between the experimental and theoreticalspectra observed at both temperatures in Figure 6 allows theMD potential to be validated and a model reproducing the guestmolecule dynamics to be developed on the basis of the MDtrajectories, as described in the next section.4.2. Modeling the Guest Molecules Dynamics. Decompos-

ing the Hydrogen Trajectories.To analyze the complex dynamicalprocesses of the methyl iodide within the cages, the definitions ofspecific molecular vectors is required. In this issue, let decomposethe hydrogen atomic positions rB(t) into three terms with respectto the fixed MD box frame (OXYZ):

rBðtÞ ¼ gBðtÞ þ uBðtÞ þ mBðtÞ ð4Þ

where the three vectors are represented in Figure 7. The vectorgB(t) defines the position of the methyl iodide center of mass(noted G) with respect to the MD-box frame. The vector uB(t) isdefined between G and the projection of the hydrogen atoms onthe C�I bond axis (noted P); its norm is 2.28 Å. The vectormB(t)is formed between P and the position of the hydrogen atoms (i.e.,normal to the C�I bond); its norm is 1.03 Å. This decomposi-tion of the hydrogen atomic position yields to disentangle thedifferent dynamical mechanisms through the decomposition of

Figure 5. Orientational autocorrelation function of water moleculesobtained from MD simulations at 150 K (solid line), 210 K (dashedline), and 270 K (dotted line). The Z axis corresponds to the C2

molecular axis, whereas the X axis is perpendicular to the plane of themolecule.



the function IMDCH3I(Q,t) of eq 3 as:

ICH3IMD ðQ , tÞ ¼ IcomMD ðQ , tÞIrotatMD ðQ , tÞImethylMD ðQ , tÞ

with

IcomMD ðQ , tÞ ¼ Æe�i QB gBð0ÞeiQB gBðtÞæ

IrotatMD ðQ , tÞ ¼ Æe�i QB uBð0ÞeiQBuBðtÞæ

ImethylMD ðQ , tÞ ¼ Æe�i QBmBð0ÞeiQBmBðtÞæ

8>>>><>>>>:

ð5Þ

Fictive H atoms were considered to compute (with the help ofthe nMoldyn program) the three intermediate scattering func-tions IMD

com(Q,t), IMDrotat(Q,t), and IMD

methyl(Q,t) up to t = 200 ps. Inthis way, the intermediate scattering function, IMD

com(Q,t), pro-vides information on the localized translational motion of theguest molecules within the cage. The reorientations of thewhole molecules (i.e., the reorientations of the C3 molecular

axis) within the cage is analyzed through the intermediatescattering function, IMD

rotat(Q,t). Finally, the rotation of themethyl group about the C3 molecular axis is probed via theintermediate scattering function, IMD

methyl(Q,t).Methyl Rotation. Examples of the intermediate scattering func-

tion IMDmethyl(Q,t) are given in Figure 8. To analyze the rotational

dynamics of themethyl group, its orientation at any time is definedwith the help of the angleψ(t) between the vectormB(t) andmB(0)within a molecular reference frame (Figure 7). The normalizedorientational distribution functions P(ψ) have been calculatedby following a procedure similar to that described in the refs 56and 57. P(ψ) is constant with respect to the angle ψ. Thisindicates that the rotation of the methyl group about the C3

molecular axis can then be described by a rotational diffusion ona circle in agreement with previous results.37,38 Unfortunately,no analytical expression of the associated intermediate scatter-ing function exist in the case of a powder sample (i.e., for an

Figure 6. Comparison of the experimental QENS spectra (opened circles) with the MD-derived scattering laws (continuous line) at two differenttemperatures (left-hand, T = 150 K; right-hand, T = 270 K). The dashed lines represent the phenomenological background due to the inelasticcontribution of the host cages (text for details).



isotropic average over momentum transfer orientations).Nevertheless, such a model can be approximated by consider-ing jumps over N equivalent sites on a circle, for which the

intermediate scattering law writes:46

ImethylðQ , tÞ ¼ ∑N � 1

j¼ 0AjmethylðQ Þe�t=τjmethyl ð6Þ

The characteristic times write:

τjmethyl ¼ D�1methyl

sinðπ=NÞsinðjπ=NÞ ð7Þ

whereDmethyl is the rotational diffusion constant. The structurefactors are given by:

AjmethylðQ Þ ¼ 1

N ∑N

k¼ 1j0ðQrkÞ cos 2jkπ

N

� �with

rk ¼ 2r sinkπN

� �ð8Þ

where r is the radius of rotation. Assuming r = 1.03 Å for themethyl group, the structure factors for N > 15 contributesfor Q > 2.5 Å�1, that is outside the accessible Q range in thepresent case. Thus, the eq 6 with N = 15 has been fitted tothe MD-derived intermediate scattering function with r andDmethyl as free parameters. A good agreement between theMD-derived data and the theoretical dynamic model is ob-served (Figure 8). The value of the rotation radius fitted tothe whole set of data, that is at 150, 210, and 270 K, is r =1.07 ( 0.04 Å, in good agreement with the value of 1.03 Åexpected for a methyl group. The extracted rotational dif-fusion constant has been represented as a function of thetemperature in Figure 8, together with previous resultsobtained at lower temperatures from a phenomenologicalanalysis of the QENS broadening.37 The temperature depen-dence of the rotational diffusion constant deviates from anArrhenius law and exhibits linear behavior as expected in viewof the weak barrier height involved in such a rotationaldiffusion.37

Translations.The intermediate scattering function IMDcom(Q,t) is

shown in Figure 9 at T = 270 K. In addition to a relaxationprocess, this function exhibits features characteristic of a dampedoscillator with a low frequency (observed at the three simulatedtemperatures). Such translational damped excitation can beattributed to the rattling motion of the methyl iodide within

Figure 7. Representation of the angles and vectors referring to themethyl iodide orientations and positions with respect to the MD-boxframe (OXYZ). G is the methyl iodide center of mass and P is theprojection of the hydrogen atoms on the axis definedwith the C�I bond.

Figure 9. MD-derived intermediate scattering function IMDcom (Q,t)

calculated with fictive H atoms located at the center of mass of themethyl iodide at T = 270 K (circles) for various Q values. Thecontinuous line represents the fitted model (text for details).

Figure 8. Top: MD-derived intermediate scattering function IMDmethyl(Q,t)

atT = 270 K (circles) for variousQ values. The continuous line representsthe fitted model (rotational diffusion on a circle). Bottom: Rotationaldiffusion constant of the methyl group determined from the presentstudy (filled circles) and derived from a previous QENS study38 (openedcircles, QENS analysis; open triangles, width of the tunneling bands). Thecontinuous line is a guide to the eyes. It should be noted that the tunnelingregime between 40 and 80 K induces deviations in this temperaturerange.38



the cage. To quantitatively analyze these two translationalprocesses, the following function has been fitted:

IcomMD ðQ , tÞ ¼ ItransðQ , tÞIdhoðQ , tÞ ð9ÞThe relaxation function Itrans(Q,t) is phenomenologically givenby the sum of an elastic term and an exponential decayingfunction:

ItransðQ , tÞ ¼ A0transðQ Þ þ ½1� A0

transðQ Þ�e�t=τtransðQ Þ ð10Þwhere Atrans

0 (Q) is the translational EISF and τtrans(Q) is thecharacteristic time of localized translational diffusive motion.The damped oscillator function Idho(Q,t) is given by the phononexpansion:46

IdhoðQ , tÞ ¼ e�AdhoðQ Þ limN f ¥ ∑

N

k¼ 0AdhoðQ ÞΓðtÞ

k!

� �k( )ð11Þ

where Adho(Q) is the structure factor of the damped oscillator.The correlation function Γ(t) describing the damped oscillatorof frequency ωdho and damping factor Γdho writes:

58

ΓðtÞ ¼ e�Γdhot=2 cosðΦtÞ þ Γdho

2Φsin ðΦtÞ

� �with

Φ ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiωdho

2 þ Γdho

4

2s

ð12Þ

under the assumption that ωdho > Γdho/2.The intermediate scattering functions IMD

com(Q,t) have beenfitted with eq 9 by considering up to the sixth harmonic, that isN = 6 in eq 11. It should be noted that the MD-derived functionscould not be reproduced by considering only the dampedoscillator, that is Itrans(Q,t) = 1 in eq 9. The free parameters inthe fitting procedure where Γdho, ωdho, Adho(Q), τtrans(Q), andAtrans0 (Q). A good agreement has been obtained for all fitted

temperatures and an example of fitted curves at T = 270 K isshown in Figure 9.The damping factor Γdho and the frequency ωdho of the

damped oscillator are given in Table 2. It is interesting to notethat its frequency decreases when cooling. That suggests ananharmonic character of the damped oscillator, as corroboratedby the fitted structure factors shown in Figure 10. Indeed, theMD-derived structure factors Adho(Q) of the damped oscillatorexhibit a clear deviation from the quadratic law forQ greater thanca. 1.7 Å�1. The dashed lines represented in Figure 10 have beenobtained by fitting the data at Q < 2.0 Å with the help of anisotropic harmonic law of the structure factor (i.e., Adho (Q) =1/3Æu2æQ2 and the fitted mean square displacements Æu2æ aregiven in Table 2).As seen in Figure 10, the high value of the EISFs Atrans

0 (Q) inthe available Q range suggests that the methyl iodide mol-ecules undergo translational diffusive motion into a restricted

volume. The volume dynamically explored by the center ofmass of the methyl iodide may be estimated by fitting a modelof diffusion on a sphere. For such a localized diffusive mo-tion,46 the EISF writes:

A0onðQ Þ ¼ j0ðQaÞ2 ð13Þ

where j0(x) is the spherical Bessel function of zero order andthe diffusion occurs on a sphere of radius a. The EISFsAtrans0 (Q) have been fitted by means of eq 13 (Figure 10)

and the fitted sphere radiuses are given in Table 2. The radiusof the sphere (0.34 Å at 270 K) on which the guest center ofmass diffuses is significantly smaller than the cage radius (4.95Å at 270 K, Figure 4). It follows that two main hypotheses maybe done: on a time-averaged, (i) the guest molecules arecentered in the cage or (ii) they are off-centered. To discri-minate these two possibilities, the averaged distance betweenthe guest center of mass and the center of mass of thecorresponding cage has been computed with the help of theMD trajectories. The time-averaged distribution shown on theFigure 11 clearly indicates that the guest molecules are off-centered within the cage by ca. 0.92 Å at 270 K and that theguest molecules diffuses on a shell possessing a thickness of

Table 2. Values of the Parameters Obtained by Fitting theTranslational Intermediate Scattering Function IMD

com(Q,t)(Text for Details)

T (K) Γdho [meV] ωdho [meV] Æu2æ [Å2] Æτtransæ [ps] a [Å]

270 1.31 ( 0.03 1.49 ( 0.01 0.252 ( 0.009 0.41 ( 0.02 0.34 ( 0.01

210 1.17 ( 0.03 1.36 ( 0.01 0.228 ( 0.009 0.47 ( 0.02 0.33 ( 0.01

150 1.14 ( 0.03 1.34 ( 0.01 0.192 ( 0.006 0.50 ( 0.02 0.30 ( 0.01

Figure 10. EISF (opened symbols) and DHO structure factor (filledsymbols) measured from the MD-derived intermediate scattering func-tion IMD

com(Q,t) atT = 270 K (squares),T = 210 K (circles), andT = 150 K(triangles). The continuous and dashed lines represent fitted models(text for details).

Figure 11. Distribution P(L) of the averaged distance L between theguest center of mass and the cage center calculated fromMD simulationsat 150 K (dotted line), 210 K (dashed line), and 270 K (solid line).



0.6 Å at 270 K (corresponding to the fwhm of the distribution)over the 10 ns MD simulations. Whereas the shell thickness ison the order of twice the radius of the sphere dynamicallyexplored by the guest center of mass, the off-centering distanceis significantly smaller than this radius. Thus, on the picose-cond time scale, the guest molecule does not diffuse on thewhole cage surface: the translational diffusion occurs on arestricted volume (of 0.34 Å radius at 270 K) that is off-centered with respect to the cage (at ca. 0.92 Å from the centerof the cage at 270 K).In the probed Q range (i.e., Q e 2.5 Å�1), the product Qa is

smaller than unity, so that only the first QENS structure factorcontribute to the relaxation process. This is confirmed by the factthat the fitted characteristic translational time τtrans(Q) did notsignificantly depend on the momentum transferQ (their averagedvalues Æτtransæ are given in Table 2). It follows that the characteri-stic time is constant, as “MD-experimentally” determined and the

diffusion constant is given by:46

Dtrans ¼ 12Æτtransæ

ð14Þ

Fitting the temperature dependence ofDtrans (by using the valuesof Table 2) follows an Arrhenius law with a prefactor Dtrans

0 =1.5 ( 0.5 ps�1 and an activation energy Ea = 1.5 ( 0.1 kJ/mol.Such low activation energy is expected due to the weak potentialbarrier characterizing such a translational diffusive process.Whole-Molecule Reorientations. To analyze the rotational

dynamics of methyl iodide within the cage, orientational dis-tribution functions (noted ODF in the following) have beencomputed. The orientation of eachmethyl iodidemolecule at anytime is defined with the help of the polar (θ(t) in Figure 7) andazimuth (j(t) in Figure 7) angles of vector uB(t) in the MDreference frame OXYZ. The normalized orientational distribu-tion functions P(θ,j) of the vector uB(t) have been calculated byfollowing a procedure similar to that described in refs 56 and 57.The P(θ,j) function, shown as a colored density distribution inFigure 12 for the three studied temperatures, reflects the complexenergy landscape explored by guest molecules. These distribu-tions exhibit preferred orientations of the guest molecules. Bydecreasing the temperature, the number of preferred orientationsdecreases suggesting an ordering process with respect to the MDtime scale. In addition, these distributions do not respect thesymmetry of the 51264 occupied cages, that is Td. Indeed, in sucha case, one would have expected to observe four equally weightedmaxima at (θ,j) values of (52�,j1), (128�, j1 þ 90�), (52�,j1þ 180�) and (128�, j1þ 270�) with j1 = 45�. Instead, eightmaxima (at j = 45�, 135�, 225�, 315� for θ = 52� and for θ =128�) are observed on the ODF at 270 K with different heights.Such behavior may find its origin in symmetry properties. Indeed,the type II unit cell contains 51264 cages with two possibleorientations related by an inversion center, with respect to thecubic unit cell frame. It follows that the ODF calculated in thepresent study should be the superimposition of two tetrahedralODF related by an inversion center, leading to an averaged ODF(calculated with respect to theMD box frame) possessing a cubicsymmetry, that is Oh. However, in such a case, one would haveexpected the eight maxima to be equally weighted. Thus, it isprobable that these ODFs do not represent the time-averaged

Figure 12. Orientation distribution function P(θ,j) of the C�I bondwithin the cage calculated with the trajectories at 270, 210, and 150 K(from top to bottom).

Figure 13. MD-derived intermediate scattering function IMDrotat(Q,t)

representing whole reorientations of the methyl iodide at T = 270 K(circles) for various Q values. The continuous line represents the fittedmodel (text for details).



dynamical disorder of each individual methyl iodide moleculewith respect to the MD probed time scale: it may be a staticdisorder in addition to the dynamical disorder.To test this hypothesis, let focus on the analysis of the

intermediate scattering functions IMDrotat(Q,t) (shown in Figure 13

at T = 270 K). First, the long time limit of IMDrotat(Q,t) has been

determined and defined as the rotational EISF Arotattmax (Q):

AtmaxrotatðQ Þ ¼ lim

tftmax

IrotatMD ðQ , tÞ ð15Þ

where tmax is 200 ps in the present case. With the help of theorientational distribution functions P(θ,j), the EISF can also becalculated by taking into account for a powder average over allorientations (Θ,Ψ) of the momentum transfer vector QB:

AdistrotatðQ Þ

¼ 14π

Z 2π

0dΨZ π

0dΘ sin Θ

�� 14πZ 2π

0djZ π

0dθ sin θeiQBðΘ,ΨÞ uBðθ,jÞPðθ,jÞ

��2

ð16Þ

where j uBðθ,jÞj = 2.28 Å. The EISF calculated by means ofeqs 15 and 16 are reported in Figure 14. The EISFs calculatedwith the help of the ODFs do not significantly depend on thetemperature. In contrary, the EISF calculated with the help of thelong-time limit of the intermediate scattering function at 150 Ksignificantly differs from those at 270 and 210 K. In addition, theODF-calculated EISFs do not match the long-time limit of theintermediate scattering function, especially at 150 K. The differ-ences are significant for Q values smaller than ca. 2 Å�1. In thelarge Q values region, the EISF calculated by means of the twomethods are in good agreement. These two observations suggestthat the geometrical properties of the reorientations are wellreproduced on a short space-range by means of the ODFs.However, on a longer space-range, this comparison demonstratesthat the ODF is not entirely due to the individual dynamicdisorder: it confirms the plausible existence of a static disorder onthe MD-time scale (10 ns).To model the individual rotational process of the methyl

iodidemolecules, it is required to analyze the time dependence ofthe rotational intermediate scattering function. As in the case ofthe translational motion, the rotational law (Figure 13) exhibits adamped periodic signal together with a relaxation process, so thatIMDrotat(Q,t) has been fitted by means of:

IrotatMD ðQ , tÞ ¼ IrotatðQ , tÞIdhoðQ , tÞ ð17Þwhere the intermediate scattering function Irotat(Q,t) is given by aphenomenological function similar to eq 10 and the dampedoscillator Idho(Q,t) of rotational origin writes as the expression11. In the fitting procedure, the free parameters were Γdho,ωdho,and Adho(Q) for the excitation in addition to the characteristicrotational time τrotat(Q) and the rotational EISF, Arotat

0 (Q) forthe relaxation process. A good agreement has been obtained atthe three studied temperatures (example at 270 K in Figure 13).The obtained damping and frequency of the harmonic oscillatorare given in Table 3. The rotational excitation exhibits ananharmonic character because its frequency slightly decreaseswith temperature and its structure factor (shown in Figure 14)clearly deviate from a quadratic law (the mean square displace-ments Æu2æ fitted by considering the data for Q < 1.5 Å are givenin Table 3).The EISF associated with the rotational diffusion, Arotat

0 (Q),did not significantly depend on the temperature; the tempera-ture-averaged rotational EISF is represented in Figure 14. Toreproduce the relaxation process of the C3 molecular axis, it isinteresting to notify that Arotat

0 (Q) is close to the long time limitof IMD

rotat(Q,t) at 150 K (Figure 14). On the basis of this observa-tion, a model can be developed by considering the maincharacteristic of the ODF at 150 K (Figure 12), that is allorientations (there is no angular range for which the probabilityis equal to zero) are permitted with a single preferred orientation.Such an orientational distribution function could be reproducedby means of the superimposition of a constant p (i.e., spherical

Figure 14. Top: EISF determined by means of the long time limit of theMD-derived intermediate scattering function IMD

rotat(Q,t) (270 K, openedsquares; 210 K, opened circles; 150 K, opened triangles) and EISFcalculated by means of the orientational distribution function P(θ,j)(270 K, dashed line; 150 K, dotted line). EISF (averaged over the threestudied temperatures) determined by fitting the MD-derived intermedi-ate scattering function IMD

rotat(Q,t) (filled circles) and the continuous linecorrespond to the fit of this EISF by means the anisotropic rotationaldiffusion model (text for details). Bottom: Structure factors of thedamped oscillator at T = 270 K (squares), T = 210 K (circles) andT = 150 K (triangles). The dotted lines are guide for the eyes andthe dashed lines represent the harmonic model fitted for Q < 1.5 Å (textfor details).

Table 3. Values of the Parameters Obtained by Fitting theRotational Intermediate Scattering Function IMD

rotat(Q,t) (Textfor Details)

T (K) Γdho [THz] ωdho [THz] Æu2æ [Å2] Drotat [ps�1]

270 0.85 ( 0.05 1.19 ( 0.01 1.17 ( 0.07 2.47 ( 0.55

210 0.66 ( 0.03 1.17 ( 0.01 0.71 ( 0.03 2.15 ( 0.44

150 0.63 ( 0.03 1.12 ( 0.01 0.31 ( 0.01 1.84 ( 0.36



symmetry) and a bidimensionnal Gaussian function reproducingthe preferred orientation:

PDðθ,jÞ ¼ 14π

p

þ ð1� pÞ 12πσD

2 sin θexp �ðθ� θ0Þ2 þ ðj� j0Þ2

2σD2

!

ð18ÞThe EISF can be numerically computed with the help of eqs 16and 18. Because a powder average over Q orientations is per-formed, the values of θ0 and j0 have been arbitrarily chosen as90� and 180�, respectively. This model yields an excellent agree-ment, as shown in Figure 14, with a rotation radius of 2.28 Å andthe free parameters p = 0.19 ( 0.02 and σD = 24.9� ( 0.8�. Itshould be noted that several additional models have beenconsidered and disproved (tetrahedral jump model,59 octahedraljump model60 with equiprobable and nonequiprobable sites;Supporting Information for details).The determination of the rotational diffusion constant for the

anisotropic rotational diffusion model would require the devel-opment of the complete intermediate scattering law. This task isnot straightforward because it would be necessary to solve a 2DFokker�Planck equation.46,57 However, it is possible to estimatea rotational diffusion constant with the help of the rotational timerate, τrotat

�1(Q), averaged over all momentum transfer values,that is Drotat � Æτrotat�1(Q)æ. Their values are given in Table 3.The temperature dependence of Drotat follows an Arrheniusbehavior with a prefactor Drotat

0 = 3.53 ( 0.24 ps�1 and anactivation energy Ea = 0.8 ( 0.1 kJ/mol. Such low activationenergy is in full agreement with the experimental QENS data.Indeed, the whole reorientation of the methyl iodide is thermallyactivated at a temperature of 99.4 K according to the analysis ofthe MD-derived intermediate scattering function and at a tem-perature of 100 K according to the phenomenological analysis ofthe QENS spectra (Figure 3).

5. SUMMARY AND CONCLUDING REMARKS

A detailed model of the dynamics of methyl iodide moleculesencapsulated in the large cages of the type II clathrate hydrate hasbeen investigated and developed for temperatures rangingbetween 150 and 270 K. The methodology used in this work isbased on the combination of incoherent QENS experiments andMD simulations. The MD simulations have been run over 10 nsin the microcanonical ensemble on a supercell consisting of 8elementary unit cells (i.e., 1088 water molecules and 64 guestmolecules) with periodic boundary conditions. The SPC/Epotential has been used to describe the host molecules, whereasab initio calculations on water/methyl iodide systems have beenperformed to accurately parametrize the Lennard�Jones andelectrostatic point charges guest potential. The QENS experi-ments have been performed on a sample in which the hostlattice was deuterated so that only the incoherent signal of theguest molecules was collected. The incoherent neutron scatter-ing law calculated from the MD trajectories have been directlycompared to the experimental ones. This drastic test leads to asuccessful agreement between the experimental and theore-tical results. This validation of the MD simulations has thenpermitted to develop a model of the methyl iodide clathratehydrate dynamics with an observation time ranging from tenthsto hundreds of picoseconds.

To disentangle the various dynamical processes met in themethyl iodide clathrate hydrate, the MD trajectories have beendecomposed into the host and guest contributions. Whereas thewater molecules reorients on a time scale significantly longerthan the observation time accessible by means of the combinedMD-QENS approach, relaxation of the guest molecule is ob-served. The quantitative analysis of the guest MD trajectoriesleads to describe the guest molecule dynamics by means of threeprocesses: (i) the methyl group rotation about the C3 molecularaxis, (ii) the reorientation of theC3 molecular axis within the cage(allowing the description of the whole reorientations within thecage), and (iii) the confined translational motion. The methylgroup rotation has been modeled with the help of a diffusivemotion on a circle centered on the C3 molecular axis. Thismotion is not thermally activated: its rotational diffusion con-stant does not follow an Arrhenius behavior. The observed linearthermal dependence of the rotational diffusion constant is notsurprising in view of the weak barrier height involved in such amotion; this result is in full agreement with the analysis of therotational tunneling transitions analyzed at low temperature.38

The whole reorientations of the methyl iodide molecule withinthe cage and the localized translational motions are bothcharacterized by means of a relaxation phenomenon and a low-energy excitation. The low-energy excitation is observed at about1 meV on the experimental and MD-derived QENS spectra. Ithas been previously attributed to the rattling of the methyl iodidewithin the cage.38 Because of overlap with the QENS broadening,the quantitative analysis of this highly damped excitation hasbeen facilitated with the help of the MD trajectories. This broadmode possesses both rotational and translational component: at270 K, the rotational excitation is observed at 0.85 ( 0.05 meV(with a damping of 1.19( 0.01 meV) and the translational one,at 1.31 ( 0.03 meV (with a damping of 1.49 ( 0.03 meV).Moreover, the structure factors of these excitations (that clearlydeviate from the quadratic momentum transfer dependenceexpected for a harmonic oscillator) and the slight decrease oftheir energies with the temperature confirm the strong anhar-monicity of such a rattlingmode.19 The translational relaxation ofmethyl iodide confined within the clathrate cage occurs on apicosecond time scale (the diffusion constant is of 1.22 ( 0.06ps�1 at 270 K) with low activation energy of 1.5 ( 0.1 kJ/mol.The localized translational motion of methyl iodide molecule hasbeen modeled by diffusion over a sphere having a radiusdecreasing from 0.34 ( 0.01 Å at 270 K to 0.30 ( 0.01 Å at150 K. Such model presupposes an off-centering of the guestmolecules within the cage. This off-centered property has beenconfirmed by calculating static properties. The averaged distancebetween cages' and guest molecules' centers of mass is 0.92 Å at270 K. The analysis of selected radial distribution functions(Supporting Information) points toward the same conclusion:the averaged distance between the water molecules and thecarbon atoms of the guest molecules is close to the averageddistance between water molecules and the iodide atoms (about 4Å). Because the guest center of mass is close to the iodide atom,this off-centered location of the guest molecules within thecage is probably due to an attractive interaction between thehalogen atom and the host matrix. This issue has been investi-gated through the analysis of the whole reorientations of methyliodide molecule. This dynamical process is activated at a tem-perature of ca. 100 K (corresponding to activation energy of0.8 ( 0.1 kJ/mol) and occurs on a picoseconds time scale (therotational diffusion constant is 2.47 ( 0.55 ps�1 at 270 K).



A quasi-isotropic model has been developed to reproduce thereorientational dynamics: the guest molecule can adopt allorientations within the cage with a probability distribution thatis not isotropic but characterized by a solid angle region (bi-Gaussian shape) having a higher probability (0.81 ( 0.02) thanall other orientations. In other words, the guest moleculeexplores the whole cage surface but adopts a preferred orienta-tion in its cage with respect to the observation time. The analysisof an orientational distribution function (that does not respectthe symmetry of the cage in which the guest molecules arelocated) clearly confirms that the guest molecules are pointingtoward preferred sites at the cage surface. Moreover, it revealsthat the preferred orientations adopted by the guest moleculesare different from cage to cage. Such a result is in agreement withthe disorder existing in the host H-bond network. Indeed, it iswell-known that the proton in the H-bond host network cannotbe localized: the two possible hydrogen sites between two oxygenatoms have the same probability according to structuralanalysis.20�22 Moreover, no relaxation of the water moleculesis observed on the MD or QENS time scale (the water moleculerelaxes on a microsecond time scale20,25�27), whereas the guestmolecule relaxes on a picoseconds time scale. It follows that, onthe MD or QENS time scale, the H-bond arrangement of watermolecules forming a cage is static and varies from cage to cage.The various local environment leads to a distribution of aniso-tropic energy landscapes (showed by the quasi-isotropic re-orientations) experienced by the guest molecules. Despite thesevarious local environments, the guest molecule relaxation followsan exponential behavior. In other words, no distribution ofcharacteristic time (that would lead to a deviation from theexponential relaxation) is observed in the present combinedMD-QENS investigation.

’ASSOCIATED CONTENT

bS Supporting Information. Neutron scattering experiments:diffraction pattern and details of calculation of the fraction ofimmobile incoherent scatterers; molecular dynamics simula-tions: configuration of the minimum of the water-methyl iodidedimer potential energy surface and radial distribution functionsgOO(r), gOH(r), gOC(r), and gOI(r). Additional models consid-ered for reproducing whole reorientations of methyl iodide. Thismaterial is available free of charge via the Internet at http://pubs.acs.org.

’AUTHOR INFORMATION

Corresponding Author*E-mail: [email protected].

’ACKNOWLEDGMENT

The Berlin Neutron Scattering Centre (Hahn-Meitner Insti-tute, Berlin, Germany) and the Institut Laue-Langevin (Grenoble,France) are thanked for the provision of beam time for QENSexperiments. We thank the European Commission for fundingunder the sixth Framework Programme through the Key Action:Strengthening the European Research Area, Research Infrastruc-tures [Contract No. RII3-CT-2003-505925 (NMI3)].

’DEDICATION†Dedicated to our colleague Dr. Michael Prager, who left ustoo soon.

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Dynamics of Methyl Iodide Clathrate Hydrate, Investigated by MD Simulations and QENS Experiments

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