Dynamics of the Hydrogen-Bonding Arrangement in Solid

Simon J. Kitchin , Mingcan Xu , Heliodoro Serrano-González , Laura J. Coates , S. Zaka Ahmed , Christopher Glidewell , Kenneth D.M. Harris. Journal o...
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J. Phys. Chem. B 1998, 102, 2165-2175

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Dynamics of the Hydrogen-Bonding Arrangement in Solid Triphenylmethanol: An Investigation by Solid-State 2H NMR Spectroscopy Abil E. Aliev and Elizabeth J. MacLean Department of Chemistry, UniVersity College London, 20 Gordon Street, London WC1H 0AJ, United Kingdom

Kenneth D. M. Harris* and Benson M. Kariuki School of Chemistry, UniVersity of Birmingham, Edgbaston, Birmingham B15 2TT, United Kingdom

Christopher Glidewell School of Chemistry, UniVersity of St. Andrews, St. Andrews, Fife KY16 9ST, United Kingdom ReceiVed: September 3, 1997; In Final Form: December 1, 1997

Dynamic properties of the hydrogen-bonding arrangement in a selectively deuterated sample of solid triphenylmethanol (Ph3COD) have been studied by wide-line 2H NMR spectroscopy. In the crystal structure of Ph3COD, the molecules form hydrogen-bonded tetramers, with the oxygen atoms positioned approximately at the corners of a tetrahedron. The tetramer has point symmetry C3 (rather than Td); three of the Ph3COD molecules (denoted as “basal”) are related to each other by a 3-fold rotation axis, and the fourth molecule (denoted as “apical”) lies on this axis. Thus, the oxygen atoms from the four molecules in the tetramer form a pyramidal arrangement with an equilateral triangular base, and the O‚‚‚O distances are consistent with the tetramer being held together by O-H‚‚‚O hydrogen bonds. The 2H NMR line shape for Ph3COD varies with temperature (in the range 97- 373 K), demonstrating clearly that the hydrogen-bonding arrangement is dynamic. Several plausible dynamic models are proposed, and it is found that only one model gives a good fit to the experimental 2H NMR spectra across the full temperature range studied. In this model, the deuteron of the apical molecule undergoes a three-site 120° jump motion by rotation about the C-O bond (with equal populations of the three sites), whereas the deuterons of the basal molecules undergo a two-site 120° jump motion, by rotation about their C-O bonds. In addition, each deuteron undergoes rapid libration (reorientation about the relevant C-O bond) with the libration amplitude increasing as a function of temperature. The behavior of the basal molecules is interpreted in terms of the existence of two possible hydrogen-bonding arrangementssdescribed as “clockwise” and “anticlockwise”son the basal plane of the pyramid. The twosite 120° jump motion for the basal molecules “switches” between these two hydrogen-bonding arrangements and clearly requires correlated jumps of the hydroxyl groups of all three basal molecules. On the assumption of Arrhenius behavior for the temperature dependence of the jump frequencies, the activation energies for the jump motions of the apical and basal deuterons are estimated to be 10 and 21 kJ mol-1 respectively. This dynamic model is further supported by (i) analysis of the dependence of the quadrupole echo 2H NMR line shape on the echo delay and (ii) consideration of 2H NMR spin-lattice relaxation time (T1) data. A full physical interpretation and justification of this dynamic model is presented.

1. Introduction The crystal structure of triphenylmethanol (Ph3COH), determined at ambient temperature from single-crystal X-ray diffraction data,1 comprises hydrogen-bonded tetramers of triphenylmethanol molecules (Figure 1). The geometry of these tetramers is approximately tetrahedral, with the oxygen atoms positioned at the corners of the approximate tetrahedron and the C-O bonds lying along the approximate 3-fold symmetry axes. The space group symmetry is R3h, and the tetramer has point symmetry C3 rather than Td. Thus, the tetramer lies on a crystallographic 3-fold symmetry axis. One molecule lies on this axis, with the other three molecules related to each other by rotation around this axis. The oxygen atoms of the four molecules in the tetramer can be regarded to be positioned at * To whom correspondence should be addressed.

the corners of a pyramid with an equilateral triangular base; the O‚‚‚O distances on the base of the pyramid differ slightly from the O‚‚‚O distances between the apex and the base of the pyramid. Subsequently, we refer to the unique molecule as “apical” and the three molecules that form the base of the pyramid as “basal”. The hydrogen atoms of the hydroxyl groups were not located in structure-determination calculations from X-ray diffraction data at ambient temperature.1 However, the O‚‚‚O distances (ca. 2.9 Å) suggest that the tetramer is held together by O-H‚‚‚O hydrogen bonds. If the hydrogen atoms involved in the hydrogen-bonding are located along (or close to) the O‚‚‚O edges (rather than the faces) of the O4 pyramid (thereby forming the shortest O-H‚‚‚O distances and hence, presumably, the strongest hydrogen bond interactions), the fact that there are four hydrogen atoms distributed between the six edges of the pyramid suggests that, at least at a sufficiently local

S1089-5647(97)02862-9 CCC: $15.00 © 1998 American Chemical Society Published on Web 02/28/1998

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Figure 1. Schematic representation of the tetramer in the crystal structure of triphenylmethanol (Ph3COH). The hydrogen-bonding arrangement shown is only one of several plausible hydrogen-bonding arrangements for the tetramer.

level, there may be disorder in the hydrogen-bonding arrangement. From the reported structural information,1 it is not possible to establish whether such disorder is dynamic disorder or static positional disorder. It is important to note that the triphenylmethanol tetramer can strictly have a 3-fold symmetry axis only if the hydroxyl hydrogen atom of the apical molecule is distributed equally between different sites related by this symmetry axis. Thus, for example, a triphenylmethanol tetramer with a static hydrogenbonding arrangement could not have point symmetry C3, and the C3 point symmetry observed in the space-averaged and timeaveraged crystal structure determined from diffraction data must arise either from dynamic disorder and/or static disorder of the structure of the tetramer (in the case of static disorder, different unit cells in the crystal would have a different time-averaged structure of the tetramer, and the C3 symmetry of the tetramer would arise only on taking an average, over all unit cells in the crystal, of these time-averaged structures). Thus, at a sufficiently local level (spatially and/or temporally), the point symmetry of the triphenylmethanol tetramer must be lower than C3. To investigate whether the disorder is dynamic, solid-state 2H NMR investigations of triphenylmethanol deuterated selectively in the hydroxyl group (Ph3COD) are reported in this paper. 2H NMR spectroscopy is a powerful approach for studying molecular motion in solids2-4 and has been applied to probe dynamics of hydrogen-bonding arrangements.5 The solid-state 2H NMR line shape is particularly sensitive to molecular motions with characteristic time scales in the range 10-3-10-8 s (the intermediate-motion regime). For motions with time scales in this range, 2H NMR line shape analysis can generally allow the mechanism and rate of motion to be established, with the temperature dependence of the rate of motion leading to information on activation parameters. If the time scale of the motion is shorter than 10-8 s (the rapidmotion regime), the actual rate of motion cannot be established, although 2H NMR line shape analysis can, in general, still be used to determine the geometry and mechanism of the motion. As discussed below, the possibility of distinguishing different dynamic models proposed on the basis of the known geometry of the triphenylmethanol tetramer represents a challenging problem in the application of 2H NMR line shape analysis. In addition to the disorder in the hydrogen-bonding arrangement discussed above, another type of disorder is present in the crystal structure of triphenylmethanol. Specifically, the tetramers are disordered between two different orientations (see ref 1 for full details), with the two tetramer orientations

Aliev et al. populated in the ratio 71:29. The structures of the tetramers in the two orientations are essentially identical [the O‚‚‚O distances are 2.884(10) Å for Oapical‚‚‚Obasal and 2.896(12) Å for Obasal‚‚‚Obasal in the major tetramer and 2.80(3) Å for Oapical‚‚‚Obasal and 2.90(3) Å for Obasal‚‚‚Obasal in the minor tetramer], and it is realistic to assume that the dynamic properties (and other aspects of disorder) of the hydrogen-bonding arrangements in the major and minor tetramers should be very similar or identical. Finally, it is relevant to note that hydrogen-bond dynamics in a system that is structurally analogous to the tetramer in triphenylmethanol have been investigated recently6 by computer simulation techniques. The system studied was a hydrogenbonded tetramer of methanol molecules, based on an idealized tetrahedron with the O‚‚‚O distance along the edge of the tetrahedron taken as the average of the O‚‚‚O distances in the crystal structure of triphenylmethanol.1 The intermolecular electrostatic potential energy of this system was determined using a distributed multipole description of the molecular charge distribution. Full details, together with an assessment of the extent to which the results obtained for the methanol tetramer can be extrapolated to provide insights on the dynamic properties of solid triphenylmethanol, are discussed in ref 6. 2. Experimental Section 2.1. Sample Preparation and Characterization. Triphenylmethanol deuterated selectively at the hydroxyl hydrogen position (denoted Ph3COD) was prepared by dissolving Ph3COH (with natural isotopic abundances) in dry diethyl ether and washing with D2O. The solution was dried, and Ph3COD crystallized from the solution. The degree of deuteration was estimated to be ca. 80% from infrared spectroscopy and solutionstate 1H NMR spectroscopy. 2.2. X-ray Diffraction Experiments. Powder X-ray diffraction data were recorded for Ph3COD at ambient temperature and low temperature using a Stoe STADI/P high-resolution powder X-ray diffractometer operating in transmission mode. Single-crystal X-ray diffraction experiments were carried out for Ph3COD at ambient temperature (ca. 295 K) and 113(2) K on a Rigaku R-Axis II rotating anode/area detector diffractometer, using graphite monochromated Mo KR radiation. The same crystal of Ph3COD was used for the experiments at each temperature. At each temperature, 36 image plate frames were recorded, each covering a crystal oscillation range of 5° with an exposure time of 20 min per frame. The crystal-to-detector distance was 80 mm. Data were processed using the TEXSAN program package,7 and structure refinement was carried out using the SHELXL program.8 2.3. 2H NMR Measurements. 2H NMR spectra were recorded at 46.1 MHz on a Bruker MSL300 spectrometer, using a standard Bruker 5-mm wide-line NMR probe. The stability and accuracy of the temperature controller (Bruker B-VT1000) were ca. (2 K. 2H NMR spectra were recorded using the conventional quadrupole echo [(90°)φ- τ-(90°)φ(π/2-τ-acquire-recycle] pulse sequence.9 Phase cycling was employed to eliminate quadrature phase errors. The recycle delay was taken as ca. 10T1 and ranged from 5 to 60 s depending on the temperature. The 90° pulse duration was in the range 2-3 µs, and the echo delay was τ ) 13 µs. No spectral distortions occur for this value of τ (for the probe used, such distortions are observed only for τ < 10 µs). We note that, in partially deuterated solids, the anisotropic 1H-2H dipole-dipole interactions can affect the

Hydrogen Bonding in Triphenylmethanol quadrupole echo 2H NMR line shape at higher values of the echo delay and may obscure the effects of dynamic processes on the line shape.10 2H spin-lattice relaxation times T were measured by 1 monitoring the maximum echo amplitude following a 180°t-90°-τ-90° inversion recovery sequence (see ref 11 for details of the 32-step phase cycle used), with recovery time t . τ (τ ) 13 µs). 2.4. 2H NMR Line Shape Analysis. Simulations of quadrupole echo 2H NMR spectra were obtained using the TURBOPOWDER12 and MXQET13 programs. The line shape simulations take into account distortions in the intensities of shoulders in the 2H NMR spectrum arising from the finite pulse power. In the line shape simulations, the line-broadening factor was 5 kHz, and typically 60-120 crystal orientations were considered in calculating the powder pattern. In modeling dynamic processes, each 2H site involved in the motion can be defined by the Euler angles {R, β, γ} which specify the orientation (relative to a space-fixed reference frame) of the principal axis system of the electric-field-gradient (EFG) tensor at the 2H nucleus (we use VPAS to denote the EFG tensor, in its principal axis system, at the 2H nucleus). Note: (a) The components of VPAS are taken such that |Vzz| g |Vyy| g |Vxx|. (b) The static quadrupole coupling constant χ is defined as eQVzz/h, where Q is the electric quadrupole moment of the nucleus, Vzz ) ∂2V/∂z2 is the largest principal component of the EFG tensor at the nucleus, and e is the electronic charge. (c) The static asymmetry parameter η is defined as η ) (|Vyy| - |Vxx|)/|Vzz| and is in the range 0 e η e 1 [note that the VPAS tensor is traceless, with Vzz ) -(Vxx + Vyy)]. (d) The z-axis of VPAS is assumed to lie along the direction of the O-D bond, and the y-axis of VPAS (corresponding to the component Vyy of intermediate magnitude) is assumed to be perpendicular to the C-O-D plane (see ref 14). In general, 2H NMR line shapes in the rapid-motion regime (i.e., frequency of motion greater than ca. 108 Hz) can be simulated as though they are “static” spectra but using a motionally averaged (“effective”) quadrupole coupling constant (denoted χ*) and a motionally averaged (“effective”) asymmetry parameter (denoted η*), which generally differ from the static quadrupole coupling constant (χ) and the static asymmetry parameter (η). Furthermore, in considering such spectra to be represented by an “effective” static deuteron with quadrupole interaction parameters χ* and η*, the orientation of the principal axis system of the EFG tensor for this effective deuteron is generally different from the orientation of the principal axis system of the EFG tensor in the sites occupied by the true deuteron during the motion. As discussed below, to obtain satisfactory agreement between experimental and simulated 2H NMR line shapes for Ph3COD, it is necessary to optimize several parameters that define the dynamic process. 2H NMR line shape analysis in the case of dynamic models with a large number of variables are potentially problematic, as the uniqueness of the fitting procedure is not necessarily straightforward to establish. To overcome this difficulty, the work reported here has combined the SIMPLEX optimization technique with the programs for 2H NMR line shape simulations. In this approach, selected variables defining the dynamic model are varied in order to minimize the following function, which quantifies the level of agreement between experimental and simulated 2H NMR line shapes:

( )

J. Phys. Chem. B, Vol. 102, No. 12, 1998 2167 M

R ) 100 ×

(Iexptl - Icalcd )2 ∑ i i i)1

1/2

M

(Iexptl )2 ∑ i i)1

In this expression, Iiexptl is the intensity of the ith digitized data point in the experimental spectrum (i ) 1, 2, ..., M) and Iicalcd is the intensity of the ith digitized data point in the calculated spectrum. Typical values of R for the best fits between the simulated and experimental line shapes were between 2% and 9%. We emphasize that this approach provides an objective assessment of the level of agreement between experimental and simulated 2H NMR line shapes and removes much of the subjectivity that is characteristic of the traditional approach of comparing experimental and simulated 2H NMR line shapes “by eye”. 3. Results and Discussion 3.1. Structural Properties Determined from X-ray Diffraction. The powder X-ray diffraction patterns recorded for Ph3COD and Ph3COH provide qualitative evidence that the crystal structure of triphenylmethanol at ambient temperature is unaffected by deuteration of the hydroxyl groups. Furthermore, there is no evidence from the powder X-ray diffraction data for any structural phase change in Ph3COD between 293 and 128 K. These conclusions are confirmed from our singlecrystal X-ray diffraction results. In particular, there are no significant differences (with respect to experimental errors) between the crystal structure determined in this work for Ph3COD at ambient temperature and the crystal structure for Ph3COH reported previously.1 Furthermore, there are no significant differences between the crystal structures determined for Ph3COD at ambient temperature and 113 K (apart from lattice contraction upon cooling), with no evidence for any structural phase transition in this temperature range. As for Ph3COH, the crystal structure of Ph3COD exhibits disorder between two orientations of the triphenylmethanol tetramer, with the relative proportions of the major and minor tetramers at ambient temperature in close agreement with those found for Ph3COD;1 furthermore, there is no significant change in these relative proportions between ambient temperature and 113 K. No attempt has been made to identify or to refine positions (with fractional occupancies) of the deuterons of the hydroxyl groups in Ph3COD from our single-crystal X-ray diffraction data, as we recognize the inherent uncertainties in refining parameters for partially occupied hydrogen atom sites from X-ray diffraction data (as well as the additional complications that arise in the present case from the coexistence of the major and minor orientations of the tetramers). The question of locating the sites occupied by the hydroxyl hydrogen atoms within the (disordered) hydrogen-bonding arrangement in Ph3COH (or Ph3COD) is much more appropriate for investigation by neutron diffraction than X-ray diffraction, and for this reason a comprehensive single-crystal neutron diffraction investigation of triphenylmethanol is planned. In summary, from our X-ray diffraction results, it is valid to rationalize the dynamic properties of Ph3COD throughout the temperature range investigated on the basis of the structural properties (summarized in Section 1) reported previously.1 3.2. Preliminary Assessment of 2H NMR Results. Experimental quadrupole echo 2H NMR spectra for Ph3COD, recorded as a function of temperature, are shown in Figure 2. The observed changes in the 2H NMR line shape with

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Figure 2. Experimental 2H NMR spectra for Ph3COD recorded using the quadrupole echo pulse sequence with τ ) 13 µs. The temperature at which each spectrum was recorded is shown.

Figure 3. (Bottom) Experimental 2H NMR spectrum for Ph3COD recorded at 97 K. (Top) Simulated “static” 2H NMR spectrum for Ph3COD (assuming no motion of the 2H nucleus) using χ ) 229 kHz and η ) 0.115.

temperature demonstrate incontrovertibly that the 2H nuclei are dynamic with respect to the 2H NMR time scale in the temperature range studied. The 2H NMR spectrum recorded at 97 K is characteristic of a “static” 2H NMR powder pattern and can be fitted (Figure 3) with static quadrupole coupling constant χ ) (229 ( 2) kHz and static asymmetry parameter η ) 0.115 ( 0.005. It is interesting to compare these values of χ and η with those for

Aliev et al. D2O (χ ) 213-236 kHz; η ) 0.1-0.2),15 CH3OD (χ ) 203 kHz; η ) 0.17),15 ferrocene-1,1′-diylbis(diphenylmethanol)-d2 (χ ) 227 kHz; η ) 0.13),5 and (PhCH2)3COD (χ ) (241 ( 2) kHz; η ) 0.04 ( 0.01 (determined at 128 K)).16 In contrast to Ph3COD and ferrocene-1,1′-diylbis(diphenylmethanol)-d2, the hydroxyl groups of (PhCH2)3COD are not involved in hydrogenbonding,17 resulting in a higher value of χ and a lower value of η for (PhCH2)3COD. 3.3. Description of Dynamic Models. We now consider plausible models for the dynamics of the hydroxyl deuterons in Ph3COD, proposed on the basis of the known geometry of the tetramer in the crystal structure. The dynamic models can be subdivided into two types: in models A-D, all deuterons in the tetramer have identical dynamic behavior, whereas in model E, the dynamic behavior of the deuteron in the apical molecule is different from the dynamic behavior of the deuterons in the basal molecules (which have identical behavior). In effect, models A-D imply that the geometry of the tetramer should be strictly tetrahedral. As discussed above, however, the space-averaged and time-averaged geometry (as determined from X-ray diffraction) is only approximately tetrahedral. Thus, while models A-D have the advantage of simplicity, only model E strictly conveys the true space-averaged and time-averaged symmetry of the tetramer in the crystal structure. In general, all proposed dynamic models imply a high degree of correlation between the motions of all the deuterons (or a subset of the deuterons) within a given tetramer. However, the ability of each model to fit the 2H NMR data does not rest upon the question of whether the motions of the different deuterons are correlated, but rather correlation between the motions of the different deuterons is required for the dynamic models to be structurally and chemically sensible. In simulating 2H NMR line shapes based on these dynamic models, the geometry of the O4 unit of the tetramer was taken from the major tetramer in the reported crystal structure.1 As the C-O-H bond angle in triphenylmethanol was not determined in this structure, the C-O-D bond angle 108.53° determined for gaseous methanol (by microwave spectroscopy18) was assumed in our simulations. In describing our dynamic models, we often refer to sites in which the deuteron lies “on” or “close to” an O‚‚‚O edge of the O4 pyramid. This means that the rotation angle about the C-O bond is such that the deuteron lies as close as possible to the O‚‚‚O edge of the pyramid, and the corresponding rotation angles (φ) are designated as 120° × n (where n ) 0, 1, 2 represent the three O‚‚‚O edges “available” to a given deuteron). We emphasize that the deuteron cannot actually lie exactly on the O‚‚‚O edges of the pyramid, as the C-O-D angle (ca. 109°) and the C-O‚‚‚O angle (ca. 145°) are not equal. Model A. This model comprises 3-fold jumps of each deuteron by 120° rotation around the relevant C-O bond (recall that the C-O bond of each Ph3COD molecule lies along an approximate 3-fold symmetry axis of the O4 pyramid). Clearly, this model assumes that all deuterons are equivalent with respect to the dynamic process. Nominally, the three sites occupied by each deuteron could be considered to lie close to different O‚‚‚O edges of the O4 pyramid, although the “absolute” location of the three sites with respect to rotation around the C-O bond is arbitrary (in the case of 2H NMR for a polycrystalline sample). Clearly model A is structurally and chemically sensible only if the motions of the four deuterons in the tetramer are correlated, in the sense that it is not plausible for two deuterons to lie simultaneously along the same O‚‚‚O edge of the O4 pyramid.

Hydrogen Bonding in Triphenylmethanol In the general case, the populations (denoted p1, p2, and p3) of the three sites occupied by the deuteron may be unequal, giving rise to two independent population variables p1 and p2 (with p3 ) 1 - p1 - p2). In the present work, several different sets of populations were considered, of which only the following representative cases are discussed here: model A1 {p1 ) 1/3, p2 ) 1/3, p3 ) 1/3}; model A2 {p1 ) 0.4, p2 ) 0.4, p3 ) 0.2}; model A3 {p1 ) 0.45, p2 ) 0.45, p3 ) 0.1}; model A4 {p1 ) 0.6, p2 ) 0.3, p3 ) 0.1}. As a further modification to the case of 3-fold jumps with equal populations of the sites (model A1), we have considered rotational diffusion in a 3-fold cosine potential, described as follows

V(φ) ) 1/2V0[1 - cos(3φ)] V0 ) 2kBTγ where kB is the Boltzmann constant, γ is the effective potential barrier for the rotation, and φ denotes the rotation angle around the C-O bond. The finite difference approximation to the Smoluchowski equation was used in order to simulate 2H NMR line shapes for this model (see ref 12 for details). The dimension of the rate matrix was taken as N ) 36, corresponding to a grid spacing of 10° on a circle. This is described as model A5. Model B. Model B represents the reversible transfer of each deuteron between two oxygen atoms [i.e., O‚‚‚H-O f O-H‚‚‚O]. This model assumes that all deuterons in the tetramer are equivalent with respect to the dynamic process, allowing the 2H NMR spectrum of the tetramer to be simulated on the basis of a single deuteron jumping between two sites. If each deuteron jumps between a pair of oxygen atoms in the real system, it is highly probable that the jumps of all four deuterons in the tetramer are correlated, as this ensures that, at any instant, each oxygen atom is directly bonded to only one deuteron. This model has been considered for several different sets of populations for the two sites occupied by the deuteron, of which only the following representative cases are discussed here: model B1 {p1 ) 0.5, p2 ) 0.5}; model B2 {p1 ) 0.6, p2 ) 0.4}; model B3 {p1 ) 0.7, p2 ) 0.3}; model B4 {p1 ) 0.9, p2 ) 0.1}. In these models it is important to specify the jump angle, defined as the angle between the O-D vectors in the two deuteron sites involved in the motionsthe value of this angle is ca. 106.8° (estimated on the basis of the C-O‚‚‚O angles determined from the crystal structure and the assumption that the C-O-D angle is ca. 108.5°, as discussed above). Model C. Model C is a 12-site jump model that can be regarded as a combination of models A and B. This model combines three-site jumps by 120° rotation about each C-O bond and transfer of the deuteron between pairs of oxygen atoms along the O‚‚‚O edges of the O4 pyramid. In this model, the three deuteron sites associated with each oxygen atom correspond to rotation angles φ ) 120° × n (n ) 0, 1, 2)si.e., the deuteron sites lie as close as possible to the O‚‚‚O edges of the O4 pyramid. Model D. Model D considers jumps of each deuteron between three sites located above a given face of the O4 pyramid. In each site, the deuteron is directly bonded to one oxygen atom and hydrogen bonded to the other two oxygen atoms on the face. This gives rise to three equivalent sites on each face, with only one of these sites occupied at any given instant. Inherent in this model is the assumption that the jumps of the four deuterons in the tetramer (each confined to a different face of the O4 pyramid) are correlated with each other, thus ensuring that, at any instant, each oxygen atom is directly

J. Phys. Chem. B, Vol. 102, No. 12, 1998 2169 bonded only to one deuteron. In this model, all faces of the O4 pyramid are regarded as identical, and the 2H NMR spectrum of the tetramer can be simulated on the basis of a single deuteron located above one (arbitrary) face of the O4 pyramid. This model has been considered for several different sets of populations for the three sites occupied by the deuteron, of which only the following representative cases are discussed here: model D1 {p1 ) 1/3, p2 ) 1/3, p3 ) 1/3}; model D2 {p1 ) 0.4, p2 ) 0.4, p3 ) 0.2}; model D3 {p1 ) 0.45, p2 ) 0.45, p3 ) 0.1}; model D4 {p1 ) 0.6, p2 ) 0.3, p3 ) 0.1}. Model E. Model E allows the dynamics of the hydroxyl groups of the apical and basal molecules to be different and conveys the true space-averaged and time-averaged structure of the tetramer determined from X-ray diffraction data. In this model, the deuteron of the apical molecule undergoes a threesite jump motion (by 120° rotation about the C-O bond, as in model A1) with equal populations of the three sites. The deuterons of the three basal molecules are also allowed to undergo three-site jumps (by 120° rotation about the relevant C-O bond), with no symmetry-imposed restrictions on the relative populations (denoted pb1, pb2, and pb3) of the three sites occupied by each basal deuteron. We recall that the symmetry of the tetramer does not impose any relationships between the populations of the three deuteron sites for a given basal molecule, although the symmetry does imply that the values of pb1 for all three basal molecules are equal, the values of pb2 for all three basal molecules are equal, and the values of pb3 for all three basal molecules are equal. It is probable that each basal deuteron will have a unique site (with population denoted pb3) corresponding to the deuteron lying on the Obasal‚‚‚Oapical edge of the pyramid between the relevant basal molecule and the apical molecule. The populations (pb1 and pb2) of the deuteron sites on the two Obasal‚‚‚Obasal edges involving a given basal molecule are expected to be more similar (or even equal). Model E is considered in two forms, first with the same jump frequency for the apical and basal deuterons (model E1) and second with different jump frequencies for the apical and basal deuterons (model E2). Finally, we note that as the apical and basal deuterons contribute to the 2H NMR spectrum in the ratio 1:3, the fitting of simulated line shapes to experimental line shapes probably provides a more sensitive assessment of the parameters describing the motion of the basal deuterons. 3.4. 2H NMR Results. Representative simulations of 2H NMR spectra for the dynamic models defined above are shown in Figures 4-11, and we now compare these simulated line shapes with the experimental line shapes recorded in the temperature range 108-173 K. 2H NMR line shape simulations for models A1-A4 are shown in Figure 4. For Model A1 in the rapid-motion regime, the simulated line shape is a Pake powder pattern with axial symmetry (η* ) 0) and with the width of this powder pattern scaled by a factor of ca. 1/3 compared with that in the slowmotion regime [note that the geometric characteristics are similar to those for methyl group rotation]. For models A2-A4 in the rapid-motion regime, the simulated 2H NMR line shapes correspond to motionally averaged asymmetry parameters η* in the range 0.5-1.0. None of these models gives a satisfactory description of the experimental 2H NMR line shape in the rapidmotion regime. Furthermore, for the intermediate-motion regime, there is no resemblance between the line shapes simulated for these models and the experimental line shapes. For Model A5 (rotational diffusion in a 3-fold cosine potential), the simulated line shapes for four different values of γ (0.5, 1, 2.5, and 5) are shown in Figure 5. Again, none of these sets of

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Figure 4. Simulated 2H NMR spectra for Ph3COD using the following dynamic models: (a) model A1; (b) model A2; (c) model A3; (d) model A4. Τhe jump frequency (κ) used to simulate each spectrum is indicated.

Figure 5. Simulated 2H NMR spectra for Ph3COD using model A5 (rotational diffusion model in a 3-fold cosine potential) for the following values of γ: (a) 0.5; (b) 1; (c) 2.5; (d) 5. Τhe inverse correlation time (τc-1) used to simulate each spectrum is indicated.

simulated line shapes give a satisfactory fit to the experimental line shape throughout the temperature range investigated. 2H NMR line shape simulations for models B1-B4 are shown in Figure 6. For model B1, the simulated line shapes resemble the experimental line shape only in the slow-motion regime. For models B2-B4 (with unequal populations of the sites), it is found that only model B2 (with p1 ) 0.6) approaches some resemblance to the experimental line shape, and this is only for certain spectra in the upper intermediate-motion

regime. The quality of fit in this regime is improved by considering a distribution of jump angles; as an illustration, line shapes simulated for model B2 assuming a static distribution of five jump angles equally spaced (and equally populated) in the range 105.5°-113.5° are shown in Figure 7. However, this model fails to describe adequately the experimental line shape in the lower intermediate-motion regime and in the rapidmotion regime, and on this basis the model can be clearly rejected.

Hydrogen Bonding in Triphenylmethanol

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Figure 6. Simulated 2H NMR spectra for Ph3COD using the following dynamic models: (a) model B1; (b) model B2; (c) model B3; (d) model B4. Τhe jump frequency (κ) used to simulate each spectrum is indicated.

Figure 7. Simulated 2H NMR spectra for Ph3COD using model B2 and a static distribution for the jump angle φ. Five different values (105.5°, 107.5°, 109.5°, 111.5°, 113.5°) of φ were considered in the distribution, with equal proportions of each of these values of φ. 2H

NMR line shape simulations for Model C are shown in Figure 8. This motion generates an “isotropic” 2H NMR line shape in the rapid-motion regime, as the rapid three-site jumps produce “effective” deuterons oriented along each 3-fold axis

of the “approximate tetrahedron”, and rapid exchange between these “effective” deuteron sites is a tetrahedral jump motion that gives rise to an isotropic line shape. It is clear that there is no agreement between the simulated line shapes for this model and the experimental line shapes over the range of temperatures investigated. 2H NMR line shape simulations for models D1-D4 are shown in Figure 9. In all cases, well-resolved inner peaks are observed in the range ca. 30-70 kHz throughout the intermediate- and rapid-motion regimes, in complete disagreement with the experimental line shapes. It is clear that model D fails to account for the experimental line shape throughout the temperature range investigated. In summary, none of the models A-D (which assume identical dynamic behavior for all deuterons in the tetramer) describe adequately the evolution of the experimental 2H NMR line shape with temperature. We now consider model E, which has different dynamic behavior for the apical and basal deuterons such that the symmetry of the hydrogen-bonding arrangement averaged over the time scale of the motion is the same as the average symmetry of the tetramer determined from X-ray diffraction. However, more parameters are required to describe model E than the models discussed above, and caution must be observed in handling these parameters when fitting simulated line shapes to the experimental line shapes. First, we consider model E1 in which the apical and basal deuterons undergo three-site jumps by 120° rotation about their C-O bonds, with the populations of the sites equal for the apical deuteron, but not necessarily equal for the basal deuterons and with the motions of the apical and basal deuterons occurring at the same frequency. Initially, the population of one site (pb3) for the basal deuterons was varied and the populations of the other two sites were kept equal [i.e., pb1 ) pb2 ) (1 - pb3)/2]. On this basis, the simulated line shapes (Figure 10) are in satisfactory agreement with the experimental line shapes in the upper intermediate-motion regime only if pb3 ≈ 0. Thus, in this case, each basal deuteron effectively undergoes two-site

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Figure 8. Simulated 2H NMR spectra for Ph3COD using model C. Τhe jump frequency (κ) used to simulate each spectrum is indicated.

jumps rather than three-site jumps. Given the discussion in Section 3.3, the unique site that is not accessible to each basal deuteron (i.e., the site with population pb3 ≈ 0) is likely to be along the Obasal‚‚‚Oapical edge of the pyramid, implying that the deuterons of the basal molecules are confined only to the Obasal‚‚‚Obasal edges of the pyramid (with the three Oapical‚‚‚Obasal edges “occupied” only by the apical deuteron). With the three basal deuterons confined to the three Obasal‚‚‚Obasal edges of the pyramid, there are two plausible hydrogen-bonding arrangementssdescribed as “clockwise” and “anticlockwise”son the basal plane of the pyramid, as shown below. Note that these arrangements exclude the highly unlikely possibility that two deuterons “occupy” the same Obasal‚‚‚Obasal edge. The two-site jump process can be interpreted as “switching” between the clockwise and anticlockwise hydrogen-bonding arrangements via a highly correlated process in which all basal deuterons simultaneously undergo 120° jumps around their C-O bonds:

However, it is clear from Figure 10 that the agreement between experimental and simulated line shapes in the lower intermediate-motion regime is unsatisfactory for model E1, in which the motions of the apical and basal deuterons are constrained to occur at the same frequency. 2H NMR line shapes were then simulated for the case (model E2) in which the jump frequencies for the apical and basal

Aliev et al. deuterons are different (with populations pb1 ) 0.5, pb2 ) 0.5, pb3 ) 0 for the basal deuterons, as discussed above). These simulated line shapes reproduce well the overall line shape changes observed as a function of temperature. However, the simulated line shapes are slightly broader than the experimental line shapes, suggesting that an additional rapid motion occurs with increasing amplitude as temperature increases. In line shape simulations, such rapid motion can be considered to give rise to motionally averaged quadrupole interaction parameters χ* and η*, which can be used as “static” quadrupole interaction parameters in line shape simulations for model E2. This rapid motion can be completely accounted for by rapid libration of each deuteron about the relevant C-O bond between azimuthal extrema (Φ, with the center of the range (Φ corresponding to the deuteron lying as close as possible to the O‚‚‚O edge of the pyramid. In this librational motion, all positions of the deuteron inside this range are assumed to be equally populated. Values of χ* and η* for this model can be determined as a function of Φ using the formalism developed in ref 19. Line shape simulations using model E2 together with values of χ* and η* calculated for this librational motion require optimization of four parameters: the jump frequencies κa and κb for the apical and basal deuterons, and the libration amplitudes Φa and Φb for the apical and basal deuterons. Using the SIMPLEX algorithm for optimization of the four parameters by fitting the simulated line shape to the experimental line shape recorded at 173 K leads to Φa ) 0. On this basis, the value of Φa was fixed subsequently at Φa ) 0 for 173 K and all lower temperatures, thus simplifying the optimization to only three parameters (Φb, κa, and κb) for these temperatures. In fixing the value of Φa in this way, we recognize that the actual value of Φa may be small but nonzero; however, as there is only one apical deuteron compared to three basal deuterons, the overall 2H NMR line shape is less sensitive to the parameters defining the motion of the apical deuteron than the parameters defining the motion of the basal deuterons. For spectra recorded at higher temperatures (293 and 373 K) the jump motions are in the rapid regime, and the simulated line shapes are therefore insensitive to the actual value of jump frequency provided it is greater than ca. 108 Hz. In our simulations at these temperatures, κa and κb were fixed at 1011 Hz and both Φa and Φb were optimized. We note that the proposed librational motion is consistent, in qualitative terms, with conclusions from our theoretical study of the methanol tetramer.6 Thus, the hydrogen-bonding arrangement with minimum energy for the methanol tetramer corresponds to the deuterons occupying sites in which the rotation angles about each C-O bond are φ ≈ (120° × n) ( 12° [for n ) 0, 1, 2], and a range of low-energy configurations, corresponding to values of φ in the region of 120° × n, are accessible to the system (see ref 6 for full details). As shown in Figure 11, simulated line shapes for model E2 (including the rapid librational motion) give a satisfactory fit to the experimental line shapes throughout the complete temperature range 108-373 K studied. The optimum values of the parameters at each temperature are shown in Table 1. The proposed model E2 was further tested by considering the dependence of the 2H NMR line shape on the echo delay τ at 163 K and the intensity losses of the powder pattern at 163 K. Figure 12 shows the experimental and simulated 2H NMR line shapes for echo delay τ ) 50 µs. The optimum values of the parameters defining the dynamic model (κa ) 4.95 × 106 Hz, κb ) 9.84 × 105 Hz, Φb ) 27°) required to fit the 2H NMR line shape for this value of τ are in close agreement with those

Hydrogen Bonding in Triphenylmethanol

J. Phys. Chem. B, Vol. 102, No. 12, 1998 2173

Figure 9. Simulated 2H NMR spectra for Ph3COD using the following dynamic models: (a) model D1; (b) model D2; (c) model D3; (d) model D4. Τhe jump frequency (κ) used to simulate each spectrum is indicated.

Figure 10. Simulated 2H NMR spectra for Ph3COD using model E1 (κa ) κb) with pb1 ) pb2 ) 0.5 and pb3 ) 0. Τhe jump frequency (κ) used to simulate each spectrum is indicated.

found for τ ) 13 µs at 163 K (Table 1). Furthermore, the observed integrated intensity for τ ) 50 µs is less by a factor of about 60% than that for τ ) 13 µs, in agreement with the factor of 57.7% predicted theoretically on the basis of model E2.

Figure 11. (Right column) Simulated 2H NMR spectra for Ph3COD using model E2 (κa * κb) with pb1 ) pb2 ) 0.5 and pb3 ) 0, and including the rapid librational motion discussed in the text. The simulated spectra shown are for the values of jump frequencies (κa and κb) and libration amplitudes (Φa and Φb) that give rise to the best fit to the experimental spectra recorded at each temperature shown. These optimum values of the jump frequencies (κa and κb) and libration amplitudes (Φa and Φb) at each temperature are given in Table 1. (Left column) Experimental 2H NMR spectra recorded for Ph3COD with τ ) 13 µs. The temperature at which each spectrum was recorded is shown.

On the assumption of Arrhenius behavior [κ ) A exp(-E/ RT)] for the temperature dependences of κa and κb in the intermediate-motion regime (temperature range 108-173 K),

2174 J. Phys. Chem. B, Vol. 102, No. 12, 1998

Aliev et al.

TABLE 1: Parameters Used To Calculate the Simulated 2H NMR Spectra for Model E2 Shown in Figure 11a T/K

κa/Hz

κb/Hz

Φa/(deg)

Φb/(deg)

108 133 143 158 163 173 293 373

1.23 × 105 7.22 × 105 1.51 × 106 2.71 × 106 4.00 × 106 8.22 × 106 1011 [F] 1011 [F]

5.74 × 102 1.38 × 104 2.87 × 104 7.17 × 105 9.25 × 105 3.1 × 106 1011 [F] 1011 [F]

0 [F] 0 [F] 0 [F] 0 [F] 0 [F] 0 [F] 46 47

7 17 23 25 26 35 48 54

a

Fixed parameters are denoted [F].

Figure 13. Relative intensity of the quadrupole echo maximum in the series of inversion recovery experiments as a function of recovery time t (with τ ) 13 µs) for Ph3COD at 160 K. The dotted line shows the fit using one exponential component [T1 ) 4.6 ms]; the solid line shows the fit using two exponential components [T1(1) ) 25.5 ms, T1(2) ) 3.8 ms, with the ratio of the normalized echo maximum intensities I(1)/ I(2) ) 2.92].

fit than the use of one exponential component, as indicated by a 23-fold decrease in the “root sum of squares”. The significantly better fit obtained with two exponential components suggests that there are (at least) two different types of deuterons with different dynamic properties in solid Ph3COD. Furthermore, the relative intensity contributions (approximately 3:1; see Figure 13) for the two exponential components are in close agreement with the relative numbers of the two different types of deuterons (basal and apical) involved in model E2. 4. Concluding Remarks

Figure 12. (Top) Experimental 2H NMR spectrum for Ph3COD at 163 K recorded using the quadrupole echo pulse sequence with τ ) 50 µs. (Bottom) Simulated quadrupole echo 2H NMR spectrum for τ ) 50 µs, assuming dynamic model E2 with κa ) 4.95 × 106 Hz, κb ) 9.84 × 105 Hz, Φb ) 27°.

the activation parameters [determined from a graph of ln(κa/ Hz) versus T-1/K-1] for the three-site 120° jump motion of the apical deuteron are estimated to be E ) 10 kJ mol-1 and A ) 5 × 109 Hz, and the activation parameters [determined from a graph of ln(κb/Hz) versus T-1/K-1] for the two-site 120° jump motion of the basal deuterons are estimated to be E ) 21 kJ mol-1 and A ) 3 × 1012 Hz. The values of the activation energies are discussed, within the context of the physical description of this dynamic model, in Section 4. The existence of two types of deuterons with different dynamic behavior in solid Ph3COD, as implied by model E2, is further supported by 2H NMR T1 measurements (inversion recovery experiments). Figure 13 shows a plot of relative intensity of the quadrupole echo maximum versus recovery time (t) at 160 K, together with the results of fitting these data using one exponential component and two exponential components. The use of two exponential components gives rise to a better

The 2H NMR results reported here demonstrate clearly that there is substantial dynamic disorder within the hydrogenbonding arrangement in solid triphenylmethanol. On the basis of the known crystal structure for triphenylmethanol, five basic dynamic models, and variants of these models, were proposed. In four of these models (A-D), all four deuterons in the tetramer have identical dynamic behavior, and the symmetry of the structure averaged over the time scale of these motions should therefore be higher than the C3 symmetry observed in the crystal structure. In this case, it would be difficult to reconcile the space-averaged and time-averaged structure determined by X-ray diffraction with the structure averaged over the time scale of the dynamic process, unless of course the differences between the dynamic properties of the apical and basal deuterons were too small to be detected by 2H NMR. For model E, on the other hand, the structure averaged over the time scale of the motion has C3 symmetry, and this dynamic process is therefore completely consistent with the observed crystal symmetry. It is implicit within all dynamic models considered here that there must be a high degree of correlation between the motions of all the deuterons (or a subset of the deuterons) within a given tetramer, in the sense that it is neither structurally nor chemically plausible for two deuterons to lie simultaneously on (or close to) the same O‚‚‚O edge of the O4 pyramid or to lie simultaneously on (or close to) the same face of the O4 pyramid. Of the dynamic models considered, only model E2 gives an acceptable fit to the experimental 2H NMR spectra recorded over the complete temperature range (108-373 K) investigated. Although there are more variable parameters for model E2 than for the other models considered (and it could therefore be argued that the better fit obtained for model E2 is a consequence of

Hydrogen Bonding in Triphenylmethanol this fact), we emphasize (see Section 3.4) that due cognizance was taken of the potential dangers in optimization of an excessive number of parameters in fitting simulated line shapes to experimental line shapes. The fact that appropriate caution was observed, together with the fact that model E2 is highly plausible physically (and completely consistent with the known structural properties), lends considerable support to the assignment of this dynamic model. In model E2, the deuteron of the apical molecule undergoes a three-site 120° jump motion by rotation about the C-O bond, with equal populations of the three sites occupied in this motion, whereas the deuterons of the basal molecules are allowed to undergo three-site 120° jumps (also by rotation about their C-O bonds) with no relationships imposed between the populations of the three sites. In practice, the population of one of these sites tends to zero, and the motion of the basal deuterons is therefore effectively described as a two-site 120° jump motion involving rotation about the C-O bonds. In addition, each deuteron undergoes rapid libration involving reorientation about the relevant C-O bond, with the libration amplitude increasing as temperature is increased. The overall interpretation is that the hydrogen-bonding arrangement for the basal molecules involves all three hydroxyl groups confined to the basal plane of the pyramid in one of two arrangementssdescribed as “clockwise” and “anticlockwise”swith the two-site 120° jump motion interpreted as switching between these two hydrogenbonding arrangements. Clearly this switching process involves correlated jumps of the hydroxyl groups of all three basal molecules. The deuteron of the apical molecule, on the other hand, undergoes three-site 120° jumps, with the interpretation that each site corresponds to the formation of a hydrogen bond between the apical deuteron and the oxygen atom of one of the basal molecules. For this model, there is no requirement that the jump frequencies for the apical and basal deuterons should be equal, and indeed it is found that, at certain temperatures, a satisfactory description of the experimental 2H NMR line shape is obtained only if the jump frequencies for the apical and basal deuterons are different. As discussed in Section 3.4 (see also Table 1), the jump frequency at any given temperature (in the intermediate-motion regime) is higher for the apical deuteron than for the basal deuterons, and the activation energy for the jump motion of the apical deuteron (10 kJ mol-1) over the temperature range studied is significantly lower than the activation energy for the jump motion of the basal deuterons (21 kJ mol-1). Qualitatively, the difference between the activation energies for the apical and basal deuterons may be understood by recognizing that the motion of the apical deuteron involves the breakage and re-formation of only one hydrogen bond, whereas the motion of the basal deuterons is a correlated process requiring the combined breakage and re-formation of three hydrogen bonds. For the apical deuteron, the activation energy will clearly depend on the degree to which the new hydrogen bond begins to form before the old hydrogen bond is completely broken; on this basis, the activation energy should be similar in magnitude to, but probably less than, the energy of a typical O‚‚‚H-O hydrogen bond, as indeed observed from our 2H NMR data.

J. Phys. Chem. B, Vol. 102, No. 12, 1998 2175 For the basal deuterons, although the present information does not allow us to deduce whether the correlated jump process involves all three hydrogen bonds breaking and re-forming in unison, or whether the initial breakage and re-formation of one hydrogen bond triggers the breakage of the other two, it is nevertheless clear that the activation energy for this process should be significantly higher than that for the motion of the apical deuteron. In summary, the present 2H NMR study has revealed detailed insights into the dynamic properties of an intriguing hydrogenbonding arrangement. Further insights into other aspects of the structural and dynamic properties of this system are likely to emerge from the future application of a wide range of other experimental and computational techniques. Acknowledgment. Financial support from EPSRC (general support to K.D.M.H.), Ciba Specialty Chemicals (studentship to E.J.M. and postdoctoral research fellowship to B.M.K.), and University College London (studentship to E.J.M.) is gratefully acknowledged. The University of London Intercollegiate Research Service is thanked for the provision of facilities for solidstate NMR spectroscopy. We are grateful to Professor R. G. Griffin for providing the TURBOPOWDER program and to Professor Z. Luz for valuable discussions. References and Notes (1) Ferguson, G.; Gallagher, J. F.; Glidewell, C.; Low, J. N.; Scrimgeour, S. N. Acta Crystallogr. 1992, C48, 1272. (2) Seelig, J. Q. ReV. Biophys. 1977, 10, 353. (3) Hoatson, G. L.; Vold, R. L. NMR Basic Principles and Progress; Springer-Verlag: Berlin, 1994; Vol. 32, pp 3-67. (4) Vold, R. R. Nuclear Magnetic Resonance Probes of Molecular Dynamics; Tycko, R., Ed. Kluwer Academic Publishers: Dordrecht, 1994, pp 27-106. (5) Aliev, A. E.; Harris, K. D. M.; Shannon, I. J.; Glidewell, C.; Zakaria, C. M.; Schofield, P. A. J. Phys. Chem. 1995, 99, 12008. (6) MacLean, E. J.; Harris, K. D. M.; Price, S. L. Chem. Phys. Lett. 1994, 225, 273. (7) TEXSAN. Single Crystal Structure Analysis Software, Version 1.6, Molecular Structure Corporation, 3200 Research Forest Drive, The Woodlands, TX 77381, 1993. (8) Sheldrick, G. M. SHELXL92, Program for the Refinement of Crystal Structures, University of Go¨ttingen, Germany, 1993. (9) Davis, J. H.; Jeffrey, K. R.; Bloom, M.; Valic, M. I.; Higgs, T. P. Chem. Phys. Lett. 1976, 42, 390. (10) Lin, T.-H.; Vold, R. R. J. Magn. Reson. 1995, 113, 271. (11) Hoatson, G. L.; Tse, T. Y.; Vold, R. L. J. Magn. Reson. 1992, 98, 342. (12) Wittebort, R. J.; Olejniczak, E. T.; Griffin, R. G. J. Chem. Phys. 1987, 86, 5411. (13) Greenfield, M. S.; Ronemus, A. D.; Vold, R. L.; Vold, R. R.; Ellis, P. D.; Raidy, T. R. J. Magn. Reson. 1987, 72, 89. (14) Blinc, R. In The Hydrogen Bond; Schuster, P., Zundel, G., Sandorfy, C., Eds.; North-Holland: Amsterdam, 1976. (15) Chihara, H.; Nakamura, N. Landolt-Bo¨ rnstein, Numerical data and functional relationships in science and technology, New Series, Group III, Vol. 20a, Nuclear quadrupole resonance spectroscopy data; Springer: Berlin, 1988. (16) Aliev, A. E.; MacLean, E. J.; Harris, K. D. M.; Glidewell, C. Unpublished results. (17) Ferguson, G.; Gallagher, J. F.; Glidewell, C.; Liles, D. C.; Zakaria, C. M. Acta Crystallogr. 1993,C49, 820. (18) Lees, R. M.; Baker, J. G. J. Chem. Phys. 1968, 48, 5299. (19) Armstrong, P. A.; Bell, A. T.; Reimer, J. A. Solid State Nucl. Magn. Reson. 1993, 2, 1.