Structure, Dynamics and Ordering in Structure I Ether Clathrate

Sep 12, 2007 - Steacie Institute for Molecular Sciences, National Research Council Canada, Ottawa, ON ... lies close to the 4 bar axis of the cage on ...
3 downloads 0 Views 168KB Size
Download PDF
11366

J. Phys. Chem. B 2007, 111, 11366-11372

ARTICLES Structure, Dynamics and Ordering in Structure I Ether Clathrate Hydrates from Single-Crystal X-ray Diffraction and 2H NMR Spectroscopy Konstantin A. Udachin, Christopher I. Ratcliffe, and John A. Ripmeester* Steacie Institute for Molecular Sciences, National Research Council Canada, Ottawa, ON. K1A 0R6, Canada ReceiVed: February 16, 2007; In Final Form: May 10, 2007

The structure and dynamics of trimethylene oxide (TMO) and ethylene oxide (EO) structure I (sI) hydrates are reported from single-crystal X-ray diffraction and 2H NMR spectroscopic measurements. The guest molecule positions in the large cage were determined with considerable improvement over previous diffraction work so that a dynamic model that was consistent with these orientations could be developed to explain the 2H NMR data. Reorientations are shown to take place among both symmetry-related and symmetry-independent sites, 16 positions in all. Because of the prochiral nature of the molecules, both guests show 2H NMR line shapes with large asymmetry parameters, rather unusual for guest molecules in the sI hydrate large cage. The results also show that the dipolar axis of the TMO molecule lies close to the 4 bar axis of the cage on average, whereas for EO, this is not the case. For TMO, progressive alignment of the polar axis with decrease of temperature then allows the dipoles to interact more strongly until dipole reversal is quenched at the ordering transition. The lack of ordering of EO is consistent with the much weaker alignment of the molecular dipoles along the 4 bar axis. With the new complementary information on the structure and dynamics from crystallography and NMR, it is possible to understand why the large cage guests order in the large cage of sI hydrate for TMO hydrate but not for EO hydrate.

Introduction Clathrate hydrates are crystalline host-guest materials in which small molecules are trapped in polyhedral cages formed from hydrogen-bonded water molecules.1 The various polyhedral cages stack together to form three-dimensional lattices by sharing vertices or faces, thus giving rise to a number of structural families. A variety of methods have been used to show that guest molecules in the clathrate hydrates are highly disordered and that the disorder is dynamic, with reorientational rates at temperatures near 273 K considerably faster than those in the corresponding pure guest liquid.1-3 The study of the guest location and dynamics are complicated by the fact that individual cages do not have their full crystallographic symmetry because of the disordered water hydrogen positions, leading to dynamics that can formally be described by including a distribution in motional correlation times. The exception is at relatively high temperatures where water molecule reorientation is fast enough to give a high average symmetry,4 and detailed motional models for the guest can be derived. These have been found to correlate closely with the average cage symmetry: cages with pseudospherical symmetry show isotropic motions and sharp NMR resonance lines, and lower symmetry cages show NMR line shapes characteristic of anisotropic motions.4,5 Trimethylene oxide (TMO) is unusual regarding its hydrate formation properties: its size is in an intermediate range (largest van der Waals’ molecular diameter ∼ 0.60 nm) so that it can * To whom correspondence should be addressed. John.Ripmeester@ nrc-cnrc.gc.ca.

stabilize either sI or sII hydrates,1,6,7 with the guest occupying only the large cavity in each structure. The phase diagram for the H2O/TMO system indicates two hydrates with compositions of about 7:1 and 17:1, which show incongruent melting at -20.8 and -9.2 °C8 and which were originally assumed to correspond to sI and sII types, respectively. It is the only hydrate in which an ordering transition of the guest, based on dielectric measurements, has been postulated.9 Dynamic properties for both sI and sII TMO hydrates were obtained from dielectric and broad line NMR measurements.9 For sII hydrate, the usual high mobility of the guests in the large 64512 cage was observed with pseudoisotropic motions and very low activation energies.2 However, for sI hydrate, the dielectric results were interpreted in terms of ordering of the molecular dipoles, assumed to be aligned along the 4 bar axis of the cage, pointing at the six rings of the 62512 cages with the formation of dipolar chains. The 1H relaxation measurements on the sI hydrate were in agreement with such a model in that two relaxation processes were detected,2,10 the lower-temperature motion assigned to reorientation about the dipolar axis, and the higher-temperature one with reorientation of the dipolar axis. Thermodynamic measurements, indeed, show an ordering transition in the region of ∼105 K.11 Various spectroscopic measurements have been made, as well;12,13 however, these have not added to information on guest dynamics and the ordering transition. A recent neutron powder diffraction study14 found that the dipolar axis of the TMO molecule lies close to the 4 bar axis of the cage at low temperatures, with increasingly large deviations from that axis setting in above 160 K. As well,

10.1021/jp071342v CCC: $37.00 Published 2007 by the American Chemical Society Published on Web 09/12/2007

Structure I Ether Clathrate Hydrates

J. Phys. Chem. B, Vol. 111, No. 39, 2007 11367

anomalous expansion of the small cage was noted in that temperature region, although the thermal expansion of the unit cell is not unusual. The unique ordering of TMO in the sI hydrate large cage still is not well understood. In this study, we report single-crystal diffraction on sI TMO hydrate and 2H NMR studies on the deuteriated TMO guest in order to elaborate on the structure and dynamics of the TMO molecule in its sI hydrate. Ethylene oxide (EO) is the only other ether molecule that forms sI hydrate, and for comparison, we also reexamine the structure of ethylene oxide hydrate15,16 and its dynamic properties.17-20 The structural and dynamic data available up to now do not allow a detailed model to be constructed for the guest dynamics. A comparison of the structures and dynamic processes in the ether hydrates leads to additional insights into the guest dynamics and the ordering process. Experimental SI TMO hydrate single crystals suitable for X-ray analysis were prepared from TMO and water at a stoichiometry of 1:6. After degassing and sealing the sample, it was quenched in liquid nitrogen and left to crystallize at -40 °C for 4 months. Transparent octahedral crystals were found to grow on the walls of the sealed tube. A single crystal of EO hydrate was prepared from EO and degassed water at a stoichiometry of 1:6. After degassing and sealing the sample, it was quenched in liquid nitrogen and partially melted several times and left to crystallize at -40 °C for 1 month. The X-ray diffraction data were collected with Mo KR radiation (λ ) 0.71073 Å, 2θmax ) 57.5°, ω scan mode) on a Bruker Smart 1000 CCD diffractometer, at 173 K. The structure was solved by direct methods using the SHELXTL suite of programs.21 Disordered positions of the hydrogen atoms in the water framework were found from Fourier electron density maps and refined with isotropic thermal parameters. The two positions of TMO and EO inside the cages were initially found from electron density maps. All bond lengths and angles in the guest molecules were fixed, but the TMO molecules were allowed to flex. Hydrogen atoms on guest molecules were placed in calculated positions and allowed to ride on the parent atoms. Several different orientations of the guest molecule were examined, on the basis of the distribution of electron density, and the best orientations (based on R1 value and thermal parameters) were chosen for the final refinement in each case. Within error, the electron density indicated complete filling of the large cages for both TMO and EO. SI TMO and EO hydrate samples suitable for NMR spectroscopy were prepared from deuteriated ethers (MSD Isotopes) and water at a stoichiometry of 1:7.6. After degassing and sealing the samples, they were quenched in liquid nitrogen. The TMO hydrate sample was then conditioned at -40 °C, just below the incongruent decomposition point, for two weeks. EO hydrate was conditioned for several days at ∼4 °C. 2H spectra were recorded at a frequency of 27.63 MHz on a Bruker CXP 180 NMR spectrometer. A quadrupolar echo sequence was used with a delay time of 20 µs and 90° pulse lengths of 3 µs. Results and Discussion TMO sI Hydrate. The sI hydrate has all of the TMO O atoms pointing toward the six-ring faces of the large cage. There are two symmetry-independent sites with populations of 0.3064 (A) and 0.6936 (B) (Figure 1a), and each has eight symmetry-related positions, leading to a total of 16 disordered orientations of the TMO (Figure 1b). From the X-ray results obtained at 173 K

Figure 1. The TMO molecule in the large cage of sI hydrate as determined from single-crystal X-ray diffraction at 173K: (a) the two symmetry-independent sites and (b) all allowed positions.

the angle between the TMO O-C2 axis and the 4 bar axis of the cage is 3.7° for molecules in position A and 30.5° for those in position B. The angle obtained from the neutron powder diffraction results,14 estimated by interpolating the angle versus temperature plot to 173 K, is 35 ( 3° (note that the neutron data were modeled with only one crystallographic site type). This corresponds reasonably well to the majority B site in the single crystal study. Figure 2 shows 2H NMR spectra obtained for TMO-d6 hydrate over a range of temperatures. These 2H NMR line shape studies were initiated long before structural details regarding the guest were available, ostensibly to determine a dynamic model for the TMO. However, without prior knowledge that there are two site types, a model which would fit the results could not be found, so the structural model obtained from neutron diffraction cannot be used to explain the NMR data. Now, with complementary information from the X-ray structural study, a consistent dynamic model can, indeed, be developed. 2H NMR lineshapes are dominated by the coupling between the nuclear electric quadrupole moment and the electric field gradient.22 The two allowed 2H NMR transitions normally give rise to a symmetric powder line shape that has either two or three pairs of characteristic features (edges, shoulders, and peaks) separated by frequencies

∆νzz )3CQ/2 ∆νyy ) 3CQ(1 + η)/4 ∆νxx ) 3CQ(1 - η)/4 (1) where CQ is the quadrupole coupling constant and η ) (∆νyy - ∆νxx)/∆νzz is the asymmetry parameter. If ∆νyy ) ∆νxx then η ) 0, and the line shape is described as axially symmetric. The ∆νii are proportional to the magnitude of the principal axis components of the second-rank tensor that describes the effective quadrupole coupling. For a static C-D, the largest component of this tensor is aligned to a good approximation along the bond

11368 J. Phys. Chem. B, Vol. 111, No. 39, 2007

Udachin et al.

Figure 2. 2H NMR spectra of TMO-d6 in the large cage of sI hydrate as a function of temperature. Left: experimental; right: simulated.

direction. Motions that change the orientation of the tensor affect the 2H NMR line shape, and once reorientational rates are ∼107 jumps s-1 or faster (the fast-motion limit), the line shape can be described by an averaged effective tensor. Analytical expressions for the parameters governing the fast-motion limit line shapes are relatively easy to obtain.23 The tensor must first be described in a reference frame in terms of the Euler angles, R, β, and γ

V(R, β, γ) ) RVpasR-1

(2)

where R is the Euler angle rotation matrix describing the coordinate transformation, and Vpas is the static tensor in its principal axis system. The fast-motion limit line shape then represents the effective tensor Veff, which is the populationweighted average of the tensor components in the reference frame for all the sites (orientations) visited during the motion,

(3)

Figure 3. Temperature dependence of the widths of the 2H NMR quadrupolar line shape features of TMO-d6 in the large cage of sI hydrate.

with pi the population factor of site i. Note that to calculate the dynamic line shapes, it is necessary to know the quadrupolar parameters for the static tensor. The spectra in Figure 2 show a sharp central line, which we assign to residual TMO in solution or sII TMO hydrate. The main components of each spectrum are two overlapping powder line shapes, one showing axial and one nonaxial symmetry in a ratio of 1:2 (obtained from shape simulations of the resonances at two different temperatures; Figure 2b), which would correspond to the two Ds on C2, and the four Ds on C1 and C3. These are fast-motion limit line shapes, and both are much narrower than expected for rigid TMO molecules. Below 193 K, the lines broaden to the extent that simple powder patterns are no longer discernible. We interpret this as being due to the slowing down of water molecular motion and the individual cages losing their high average symmetries because of the

frozen-in proton disorder. The widths of the powder line shape features ∆νii are plotted as a function of temperature in Figure 3, from which it is seen that the axially symmetric tensor is hardly temperature-dependent, whereas the nonaxially symmetric tensor has a strong temperature dependence. The latter suggests that guest molecule orientations are changing quite markedly with temperature, in accord with the powder diffraction results.14 The superposition of axially and nonaxially symmetric averaged line shapes arising from the same molecule is an unusual and interesting feature and was initially puzzling, because this mixture of different symmetries seemed contrary to expectations. This can be rationalized, however, as follows: the cage has two mirror planes and a 4 bar symmetry axis, which give the eight symmetry-related positions for each crystallographically distinct site. The molecule itself has a 2-fold axis if it is assumed to be planar. (Although, in fact, TMO is

n

Veff )

n

Vi(r, β, γ)pi / ∑pi ∑ i)1 i)1

Structure I Ether Clathrate Hydrates

J. Phys. Chem. B, Vol. 111, No. 39, 2007 11369

a12 ) [-cos2 βVxx + Vyy - sin2 βVzz ] sin γ cos γ

Figure 4. Prochirality of the TMO molecule. Distinct D atoms cannot physically occupy their mirror image positions.

very slightly nonplanar, it can be treated as essentially planar on time average, since the very low ring puckering barrier of 15.5 cm-1 means that very rapid ring inversion must occur.24) This gives the four equivalent C1, C3 Ds and the two equivalent C2 D’s, butsand this is crucial for understanding the 2H NMR resultssif one of the Ds on C1 or C3 can be labeled, the molecule becomes chiral, that is, the mirror images are nonsuperimposable (Figure 4), and hence, the molecule can be classified as prochiral. This is not the case if one of the two Ds on C2 is labeled, because the 2-fold molecular axis allows interchange. Although the four Ds on C1, C3 behave identically, the NMR experiment is really only looking at the effects on each individual D, that is, which sites does one particular D visit during the motion. Put another way, although reflection is an allowed crystal symmetry operation, any specific D atom on C1 or C3 cannot physically occupy its mirror image site. To calculate the dynamically averaged NMR line shape, the orientations of each of the sites visited by one particular D must be known and defined in one reference frame. Here, the natural choice of reference frame is to place the z-axis parallel to the 4 bar axis of the cavity with the x and y axes parallel to the two mirror planes of the cage. One needs to average the tensor, as described above, over the orientations of all the 8 crystal symmetry-related sites visited, and this actually gives rise to 16 sites when exchange about the molecular 2-fold axis is included. The other Ds behave identically but visit their own particular sets of sites. Initially, this looks complicated, but making use of the reflection and 4 bar symmetries and taking account of where one atom is allowed to be, much simplification can be achieved. It is readily found that the 16 sites visited by one D on C1 or C3 fall into four sets of four with orientations related to the orientations of the four C-Ds in one molecule. Assuming that the static tensor is axially symmetric (see below), simplification is possible, since in this case, the Euler angle, R, can be set to zero. Working through the math, one can then determine the averaged tensors.

a11 a12 a13 Veff ) a21 a22 a23 a31 a32 a33 where a12 ) a21 and a23 ) a32

(4)

(a) The dynamically averaged tensor components for D atoms on C1 and C3 are given by the following expressions, once these are averaged over the (β, γ) angles for each of the four C-D bond orientations on one molecule of TMO.

a11 ) a22 ) 1/2[cos2 βVxx + Vyy + sin2 βVzz] a33 ) sin2 βVxx + cos2 βVzz a13 ) 0 and a23 ) 0

(5)

These expressions allow the calculation of the components for each of the two crystallographically distinct TMO orientation sets, which must then be population-weighted to give the final averaged tensors. Note that in the chosen frame, the off-diagonal terms a12 ) a21 are nonzero, and diagonalization will give a nonaxially symmetric tensor. (b) The dynamically averaged tensor components for D atoms on C2 are given by the following expressions, once these are averaged over the β angles for each of the two C2-D bond orientations on one molecule of TMO.

a11 ) a22 ) 1/2[cos2 βVxx + Vyy + sin2 βVzz]

(6)

a33 ) sin2 βVxx + cos2 βVzz All off-diagonal terms are zero, and this tensor is already diagonal and axially symmetric. In the first round of calculations, the averaged tensors were calculated using the geometries of the two TMO molecules, A and B, determined in the X-ray refinement, and assuming that the starting tensor is the same as for the static tensor of tetrahydrofuran (THF), that is, Vzz ) 267.8, Vxx,yy ) -133.9 kHz.25 To make a more direct comparison of these calculated results with experimental NMR values (Table 2), it is necessary to extrapolate the linear plots of the NMR line shape features of Figure 3 back to 173 K, the temperature at which the X-ray results were obtained. (The actual line shapes that were obtained at 173 K are very indistinct because of the static water proton disorder (see above)). It was initially disappointing to find very poor agreement between the calculated and observed NMR line shape parameters. (Likewise, averaging of either of the two crystallographically distinct sites individually gives calculated line shapes that are not in accord with the experimental results.) Consequently, the whole range of possible combinations of spatial orientations for the two molecules was investigated: an average molecular geometry was first determined from the X-ray results. The orientations of both molecules were then defined by iterating through three Euler angle rotations for each. For each configuration,the C-D bond orientations were calculated, and the population-weighted averaging was carried out as defined by the models described above. Not too surprisingly, it was found that there is no unique solution, but there are very many combinations that give close agreement with the NMR results. Thus, by adjusting the orientation angles for the molecules starting from the X-ray values, it was possible to find solutions that bring the X-ray and NMR results into reasonable congruence; for example, one such result is given in Table 2. (Note that for this case, only the orientation angles were changed for the majority B molecule.) When these orientations are fed back into the X-ray model keeping the position of the center of the C1-C3 vector fixed, the R factor is 0.0684. Although this is worse than for the best X-ray refinement obtained, R ) 0.0138 (Table 1), it may still be regarded as quite reasonable. Since the X-ray refinements fit electron density dispersed over a large volume and with 8-fold disorder for each molecule, there is clearly a lot of positional overlap, and it is likely that many possible orientations give refinements within a reasonable range of R factors 0.02-0.06. For example, with just one distinct type of TMO instead of two, the best R factor is 0.0282. Numerous factors could contribute to the differences between calculation and experiment, the most significant of which are likely to be (a) the assumed magnitude

11370 J. Phys. Chem. B, Vol. 111, No. 39, 2007

Udachin et al.

TABLE 1: X-ray Crystallographic Information empirical formula formula weight temperature, C° wavelength crystal system, space group unit cell dimensions, Å volume, Å3 Z, calculated density, g cm-3 crystal size, mm θ range for data collection reflections collected/unique data/restrains/parameters final R indices [I > 2σ(I)] R indices (all data) largest diff. peak and hole, eÅ-3

TMO

EO

C3H21.33O8.67 196.20 173.0(1) 0.71073 cubic, Pm-3n 12.069 (3) 1757.8 (7) 6, 1.112 0.45 × 0.4 × 0.4 2.39-28.70 18936/441 441/65/105 0.0138 0.0182 0.061, -0.058

C2.28H19.90O8.81 141.31 173.0(1) 0.71073 cubic, Pm-3n 11.945 (2) 1704.5 (5) 6, 1.101 0.3 × 0.2 × 0.2 2.41-28.73 17717/428 428/52/117 0.0125 0.0237 0.065, -0.046

of the static tensor, (b) additional dynamic averaging due to small amplitude librational motions, (c) error in the population weightings, and (d) error in the TMO geometry used. Another consideration is that the different orientations of the NMR model might give better R factors if the molecule could be allowed to translate but not rotate in the refinement. (2H NMR is sensitive only to the orientations and dynamics of the molecules, whereas X-ray measurements are sensitive to orientation and position.) In conclusion, we can say with confidence that the X-ray and NMR results are consistent with each other and that, consequently, we have a good model of the structure and the dynamic disorder. EO sI Hydrate. Like the TMO structure, the new singlecrystal structure of EO hydrate shows two crystallographically independent sites, A and B, in the large cage with populations 0.49 and 0.51, respectively, each with 8-fold disorder (Figure 5). Unlike the TMO case, however, one set (B) locates its O atoms pointing toward the six-ring faces, wheras for the other set (A), the O atoms point more toward the equator of the cage. The tilt angles between the EO 2-fold/dipolar axes and the 4 bar axis were 29° and 82°, respectively. This contrasts with the single-crystal X-ray diffraction models of McMullan and Jeffrey,15 for which in one model (which we will call J1), the EO molecule was located in two disordered positions, with the molecular 2-fold axis oriented along the 4 bar axis of the cage (0° tilt angle), with the O atoms pointing only at the six-rings. In their second model (J2), evidence for a further reorientational disorder was modeled by additional positions displaced on either side of the planes of mirror symmetry. In model J1, the guest molecule was constrained to occupy special positions, and this resulted in short C-O distances in the EO molecule (1.32 Å instead of 1.44 Å in the current work). During the refinement, we fixed the bond distances in the EO molecule and allowed it to occupy general positions. The final result gave us one set of EO molecules oriented with the O toward the hexagonal face, as found in J1, but tilted off the 4 bar axis. The distance between atomic positions of the EO molecules found here and for J1 varies from 0.2 to 0.6 Å. In a later single-crystal neutron diffraction study, Hollander and Jeffrey16 developed a third model (J3) with 24-fold disorder to account for observed C atom density in the vicinity of the O atom of the EO (close to the hexagonal face). In addition to an 8-fold disorder arising from placing the EO in general positions, they introduced a 3-fold reorientational disorder about an axis perpendicular to the OCC plane (in effect, an in-plane rotation). We note that our new X-ray structure also has O and C density in proximity (in this case, from the two molecular site types, A and B). We also found electron density in the small cages, corresponding to

∼42% occupancy by EO (since air was excluded in the preparation, this cannot be a significant component). The 2H NMR line shapes of ethylene oxide-d4 hydrate (Figure 6) are already considerably narrower than those of TMO hydrate, with the consequence that the smearing out of the line shape features due to freezing-in of the water molecule dynamics as the temperature decreases has a greater effect at higher temperatures. The line shape features are in effect lost below 225 K. Nevertheless, the spectrum at 235 K shows a very clear line shape characterized by a single set of parameters and a large asymmetry parameter (Table 2). The four deuterons of EO have the same prochiral properties as the C1 and C3 deuterons of TMO; thus, a nonaxially symmetric averaged line shape was to be expected. Again, when an averaging calculation was performed using the new X-ray structural parameters, agreement was poor. Thus calculations were done by varying the orientation angles away from the X-ray values to search for solutions that bring the two sets of results into reasonable agreement; one such result is given in Table 2. Unfortunately it is not possible to extrapolate the NMR results graphically in this case for comparison with the structure at 173 K, but a reasonable estimate was made by assuming the EO results scale by the same factor as the TMO results over the same temperature range. When these orientations are fed back into the X-ray model, the R factor is 0.0333, which compares reasonably favorably with the lowest R factor obtained, R ) 0.0125 (Table 1). Furthermore, although the new structural model and NMR results are found to be in harmony, it can be shown that the disordering in models J1-J315,16 is incompatible with the observed dynamically averaged 2H NMR line shape: For J1 and J2, the averaged line shapes would be very much broader (e.g., for J1, CQ ) 140.4 kHz, η ≈ 0), and for J3, the averaging would result in an axially symmetric tensor. Likewise, the simple 180° rotation about the dipole axis postulated in a quasielastic neutron scattering study20 would also give a much broader averaged line shape than that observed. The ordering of the TMO dipoles can be understood as follows. Both EO and TMO have two independent guest positions in the sI large cage. However, for TMO, each position constrains the molecules to have their polar axes close to the 4 bar axes, the population-weighted average angle being ∼22° at 173K, and this alignment becomes stronger with decreasing temperature. On the other hand, for EO, the average angle between the polar axis and the 4 bar axis is ∼55° at 173 K, so the dipole lies closer to the equatorial plane than the 4 bar axis of the cage, and there is no tendency for “locking in” of the dipoles. The fact that the TMO guest has expanded the unit cell to 12.069 Å, as compared to 11.945 Å, for EO also suggests that the TMO molecule has a much tighter fit in the sI hydrate large cage. The “locking in” of the molecular dipoles can therefore be attributed to the steric constraints imposed by the large cage on the orientations of the TMO molecules. Summary Again, the methods used in this study do not give direct evidence of the ordering transition observed in sI TMO hydrate. However, the results do elucidate further why this molecule in sI hydrate shows such a transition. The X-ray structure, in agreement with the original conjecture and the neutron diffraction results, shows that the molecular dipoles align more or less with the 4 bar axis. From diffraction and 2H NMR, the alignment becomes greater as the temperature decreases. Evidence for dipole reversal above the ordering transition comes from dielectric and 1H NMR measurements, with the only motion

Structure I Ether Clathrate Hydrates

J. Phys. Chem. B, Vol. 111, No. 39, 2007 11371

TABLE 2: Comparison of Calculated and Experimental 2H NMR Quadrupole Coupling Tensor Parameters tensor components (kHz) obs. at 238 K D atoms on C1 and C3

D atoms on C2

D atoms on C1 and C2

Vzz′ Vyy′ Vxx′ CQ η Vzz′ Vxx,yy′ CQ η Vzz′ Vyy′ Vxx′ CQ η

obs. at 235K

orientations

obs f 173 Ka

calcd X-rayb

calcd

X-ray angles

caldc angles

TMO 92 64 28 61.3 0.391 28.5 14.25 19.0 0

143.2 -85.4 -57.8 95.5 0.193 19.5 9.75 13.0 0

93.5 -66.7 -26.8 62.3 0.426 30.1 15.05 20.1 0

A R ) 8.6 β ) 3.7 γ ) 125 B R ) 20.0 β ) 30.5 γ ) 171.5

A R ) 8.6 β ) 3.7 γ ) 125 B R ) 28.5 β ) 36.5 γ ) 178

EO 14 11 3 9.33 0.571

-81.9 71.0 10.9 54.6 0.733

-14.3 11.1 3.2 9.5 0.552

A R ) 12.3 β ) 82.2 γ ) 39.3 B R ) 77.7 β ) 29.0 γ ) 178.2

A R)1 β ) 82.2 γ ) 43 B R ) 65.0 β ) 29.0 γ ) 165.0

55.0 38.0 17.0 36.7 0.382 29.5 14.75 19.7 0 8.9 7.05 1.85 5.96 0.582

a Extrapolated to 173 K for TMO using Figure 3, and estimated at 173 K for EO by scaling the parameters at 235 K by similar factors as for TMO. b Calculation based on the X-ray structure with the lowest R factor.

Figure 5. The EO molecule in the large cage of sI hydrate as determined from single-crystal X-ray diffraction at 173 K showing the two symmetry-independent sites.

occurring below the transition being reorientation about the molecular dipole. It is pertinent to note that closely related molecules in terms of shape, size, and dipole moments do not show such an ordering transition. For instance, ethylene oxide does not order in the large cage of sI hydrate, and THF forms only a sII hydrate. Interestingly, like TMO, dimethyl ether (DME) does form two hydrate structures (or at least two structures, because there may be yet others), but for DME, these are sII and a hydrate with a unique, dense structure determined only a few years ago.26 The dynamics for both TMO and EO is modeled very well in terms of the new crystal structure information, assuming reorientation (a) about the molecular 2-fold axis, (b) among the eight crystal symmetry related sites, and (c) among the two crystallographically distinct types of site. Consideration of the molecular orientations and the dynamics of TMO and EO allows one to formulate an explanation for the observation of the ordering transition of the guest TMO molecules in the large cage of sI hydrate. Supporting Information Available: X-ray diffraction CIF files for TMO hydrate and EO hydrate. This material is available free of charge via the Internet at http://pubs.acs.org

Figure 6. 2H NMR spectra of EO-d4 in the large cage of sI hydrate as a function of temperature.

References and Notes (1) Davidson, D. W. In Water, A ComprehensiVe Treatise; Franks, F., Ed.; Plenum: New York, 1973. Jeffrey, G. A. In ComprehensiVe Supramolecular Chemistry; Atwood, J. L., Davies, J. E. D., MacNicol, D. D., Vogtle, F., Lehn, J.-M., Eds.; Pergamon, Elsevier Science: New York, 1996; Vol. 6, Chapter 23. (2) Davidson, D. W.; Ripmeester, J. A. In Inclusion Compounds; Atwood, J. L., Davies, J. E. D., MacNicol, D. D., Eds.; Academic Press: London, 1984; Vol. 3, Chapter 3. (3) Ripmeester, J. A.; Ratcliffe, C. I. In ComprehensiVe Supramolecular Chemistry; Atwood, J. L., Davies, J. E. D., MacNicol, D. D., Vogtle, F., Lehn, J.-M., Eds.; Pergamon, Elsevier Science: New York, 1996; Vol. 8, Chapter 8, pp 323-380. (4) Ripmeester, J. A.; Ratcliffe, C. I. In Inclusion Compounds; Atwood, J. L., Davies, J. E. D., MacNicol, D. D., Eds.; Oxford University Press, 1991; Vol. 5, Chapter 2, pp 37-89. (5) Davidson, D. W.; Ratcliffe, C. I.; Ripmeester, J. A. J. Inclusion Phenom. 1985, 2, 239. Collins, M. J.; Ratcliffe, C. I.; Ripmeester, J. A. J. Phys. Chem. 1990, 94, 157 .

11372 J. Phys. Chem. B, Vol. 111, No. 39, 2007 (6) Hawkins, R. E.; Davidson, D. W. J. Phys. Chem. 1966, 70, 18891894. (7) Sargent, D. F.; Calvert, L. D. J. Phys. Chem. 1966, 70, 26892691. (8) Rosso, J.-C.; Carbonnel, L. C. R. Acad. Sci. (Paris) 1972, 274C, 1108-11. Carbonnel, L.; Rosso, J.-C. J. Solid State Chem. 1973, 8, 304311. (9) Gough, S. R.; Garg, S. K.; Davidson, D. W. Chem. Phys. 1974, 3, 239-247. (10) Jacobs, D. M.; Zeidler, M. D.; Kanert, O. J. Phys. Chem. A 1997, 101, 5241. (11) Handa, Y. P. Can. J. Chem. 1985, 63, 68-70. Kuratomi, N.; Yamamuro, O.; Matsuo, T.; Suga, H., J. Therm. Anal. 1992, 38, 1921. (12) Bertie, J. E.; Jacobs, S. M. Can. J. Chem. 1977, 55, 1777. (13) Subramanian, S.; Lance, M. J.; Rawn, C. J.; Chakoumakos, B. C.; Rondinone, A. J. Can. J. Phys. 2005, 83, 941. (14) Rondinone, A. J.; Chakoumakos, B. C.; Rawn, C. J.; Ishii, Y. J. Phys. Chem. B 2003, 107, 6046. (15) McMullan, R. K.; Jeffrey, G. A. J. Chem. Phys. 1965, 42, 2725. (16) Hollander, F.; Jeffrey, G. A. J. Chem. Phys. 1977, 66, 4699. (17) Garg, S. K.; Morris, B.; Davidson, D. W. J. Chem. Soc. Faraday Trans. II 1972, 68, 481.

Udachin et al. (18) Ripmeester, J. A. Can. J. Chem. 1976, 54, 3677-3684; 1977, 55, 78-81. (19) Hayward, R. J.; Packer, K. J. Mol. Phys. 1973, 25, 1443. (20) Wegener, W.; Vanderhaeghen, J.; Hautecler, S.; Legrand, E.; Van Gerven, L. Proceedings IAEA Symposium on Inelastic Neutron Scattering, IAEA-SM-219/75, 1978, p 415. (21) Sheldrick, G. M. Acta Crystallogr. 1990, A46, 467; 1993, A49 (Suppl.), C53. (22) Cohen, M. H.; Reif, F. Solid State Phys. 1957, 5, 321. Barnes, R. G. AdV. Nucl. Quad. Reson. 1974, 1, 335. (23) Greenfield, M. S.; Ronemus, A. D.; Vold, R. L.; Vold, R. R.; Ellis, P. D.; Raidy, T. E. J. Magn. Reson. 1987, 72, 89. Wittebort, R. J.; Olejniczak, E. T.; Griffin, R. G. J. Chem. Phys. 1987, 86, 5411. Ratcliffe, C. I. J. Phys. Chem. 1987, 91, 6464. (24) Jokisaari, J.; Kauppinen, J. J. Chem. Phys. 1973, 59, 2260-2263. (25) Rinne, M.; Depireaux, J. AdV. Nucl. Quad. Reson. 1973, 1, 357374. (26) Udachin, K. A.; Ratcliffe, C. I.; Ripmeester, J. A. Angew. Chem. Intl. Ed. 2001, 40, 1303-1305.