1380
J . Phys. Chem. 1985,89, 1380-1383
Rotational Freedom of meet Molecules in Tetrahydrofuran Clathrate Hydrate As Determined by Heat Capaclty Measurements Mary Anne White* and Mark T. Machant Chemistry Department, Dalhousie University, Halifax, Nova Scotia, Canada B3H 4J3 (Received: November 9, 1984)
The measurement of the heat capacity of tetrahydrofuran (THF) clathrate hydrate (THF.16.83H20) from T = 17 to 261 K is reported. The results are consistent with free or nearly free rotation of the THF guest molecules in the host lattice at temperatures above 120 K. At lower temperatures this rotation becomes hindered, but the reduction of rotational freedom is gradual and does not result in a phase transition. The calculation of the heat capacity of the THF guest, from the total heat capacity and that of hexagonal ice, shows that hexagonal ice is a good model for the empty lattice above 120 K, but not below this temperature. The difference is thought to reflect the role of the long-range order in the determination of the low-temperature lattice heat capacity. From the heat capacity of the THF molecule, the barrier to rotation for the THF guest molecule is calculated to be 3.5 kJ mol-l, in good agreement with that determined by other methods.
I. Introduction In the solid state, water molecules are known to enclathrate molecular species such that the guest molecules inhabit well-defined cavities formed by the host lattice. These clathrate hydrates can exhibit two types of structures that differ from one another in the numbers and sizes of the cages in the “ice” lattice, and the observed structure depends therefore on the size of the guest molecule. The changeover from one structure to the other occurs at guest diameters of about 5.5 A, such that larger molecules take up structure I1 (sixteen 5.0 A and eight 6.6 A cages, composition M.16.86H20 if only the larger cages are filled) and smaller molecules take up structure I (two cages of 5.0 A and six of 5.8 A diameter, composition M.5.75H20 if all cages are Although it was thought for many years that very small guests take up structure I, recent structural studies have shown that Ar and Kr fill the sixteen smaller cages of structure IL3 Although clathrate hydrates have been known for more than a century: interest in their physical properties is currently very strong. In part, this is likely due to large deposits of clathrate hydrates of natural gas in arctic regionsS and the importance of understanding their thermal properties in order to recover the natural gas. In addition, there have been studies for some years of the influence of intermolecular potentials on enclathrated species,68 and this interest in combination with the current state of computers has given rise to several recent studies of the molecular dynamics of clathrate hydrates.”’l Tetrahydrofuran (THF) is known12 to form a structure I1 clathrate hydrate of composition THF.16.86H20 and melting point 278.15 f 0.1 K. From measurements of its dielectric relaxationL3 and its NMR,14 infrared,l53l6 and neutron” spectroscopic properties, it is known that the THF molecules can reorient rapidly in the THF clathrate hydrate. One of the main questions to be answered by the present study is whether or not the thermal activation of this reorientation gives rise to a phase transition in THF clathrate hydrate as it does, for example, in H C N quinol clathrate.’* This question is answered here through the measurement of the low-temperature heat capacity of THF clathrate hydrate. Although the high-temperature ( T > 85 K) heat capacity of THF clathrate hydrate has been measured these studies have raised several other questions that also can be answered through heat capacity measurements at lower temperatures: Is ice sufficiently similar to the host lattice of the structure I1 clathrate hydrate to allow it to be used to calculate the lattice (and hence the guest) contributions to the heat capacity? Are the heat capacity contributions of the guest and host exactly separable? Do the barriers to guest reorientation as measured by other techniques coincide with the thermodynamic barrier?
’ 1984 Summer Career Access Internship Award Holder. 0022-3654/85/2089-1380$01 SO10
In addition, recent measurement^^^*^^-^^ of the thermal conductivity (A) of THF clathrate hydrate (and some other structure I1 clathrate hydrates) show an exceptionally low thermal conductivity and an unusual temperature dependence of A. At least to a first approximation, the thermal conductivity and heat capacity, C,are related by the Debye equation
where v is the average velocity of the energy carrier and 1 is the mean free path that the energy carrier travels between collisions. The measurement of the low-temperature heat capacity of T H F ~~~~
~~~~
~
~
~
(1) D. W. Davidson in ‘Water-A Comprehensive Treatise”, Vol. 2,F. Franks, Ed., Plenum Press, New York, 1973,pp 115-234. (2) G. A. Jeffrey in “Inclusion Compounds”, Vol. 1, J. L. Atwood, J. E. D. Davies, and D. D. MacNichol, Eds., Academic Press, London, 1984,pp 135-190. (3) D. W. Davidson, S.K. Garg, S.R. Gough, Y. P. Handa, C. I.Ratcliffe, J. S . Tse, and J. A. Ripmeester, J . Inclusion Phenom., in press. (4) H.Davy, Philos. Trans. R. Soc. London, 101, 1 (1811). (5) G.D. Holder, V. A. Kamath, and S. P. Godbole, Annu. Reu. Energy, 9,427 (1984). (6) J. H. van der Waals, Trans. Faraday SOC.,252, 184 (1956). (7) J. H. van der Waals and J. C. Platteeuw, Adu. Chem. Phys., 2, 1 (1959). (8) J. S.Tse and D. W. Davidson in “Proceedings of the 4th Canadian Permafrost Conference”, March 1981, Calgary, Alberta, National Research Council of Canada, Ottawa, 1982,pp 329-334. (9) J. S.Tse, M. L. Klein, and I. R. McDonald, J . Chem. Phys., 78,2096 (1983). (10)P. L. M. Plummer and T. S . Chen. J. Phys. Chem., 87,4190(1983). (11) J. S.Tse, M. L. Klein, and I. R. McDonald, J. Phys. Chem., 87,4198 (1983). (12) Yu.A. Dyadin, P. N. Kumetsov, I. I.Yakovlev, and A. V. Pyrinova, Dokl. Chem. (Engl. Transl.), 208, 9 (1973). (13) D. W. Davidson, Can. J . Chem., 49, 1224 (1971). (14)S.K.Garg, D. W. Davidson, and J. A. Ripmeester, J. Magn. Reson., 15,295 (1974). (15) D.D.Klug and E. Whalley, Can. J. Chem., 51, 4062 (1973). (16)J. E. Bertie and S. M. Jacobs, J. Chem. Phys., 69,4105 (1978). (17)W. Wegener, J. Vanderhaeghen, S . Hautecler, E. Legrand, and L. Van Gerven, Neutron Inelastic Scattering, Proc. Symp., 1977,1,415(1978). (18) T.Matsuo, H. Suga, andS. Seki, J. Phys. SOC.Jpn., 30,785 (1971). (19)R. G. Ross and P. Andersson, Can. J . Chem., 60,881 (1982). (20)D. G. Leaist, J. J. Murray, M. L. Post, and D. W. Davidson, J. Phys. Chem., 86,4175 (1982). (21)J. E.Callanan and E. D. Sloan, Report GRI-81/0102,U S . National Bureau of Standards, 1982. (22)Y. P. Handa, R. E. Hawkins, and J. J. Murray, J. Chem. Thermodyn., 16,623 (1984). (23)R. G. Ross, P. Andersson, and G. BackstrBm, Nature (London), 290, 322 (1981). (24)J. G. Cook and M. J. Laubitz in ‘Thermal Conductivity”, Vol. 17, J. G.Hurst, Ed., Plenum Press, New York, 1984,pp 745-751. (25)P. Andersson and R. G. Ross, J. Phys. C, 16,1423 (1983). (26)J. G.Cook and D. J. Leaist, Geophys. Res. Luff.,10,397 (1983).
0 1985 American Chemical Society
Guest Molecules in T H F Clathrate Hydrate
The Journal of Physical Chemistry, Vol. 89, No. 8, 1985 1381 TABLE I Smoothed Heat Capacity Values for THF-16.83H20 T/K CJJ K-'g-' T/K C,/J K-' g-' 20 25 30
35 40 45 50
55
T/K Figure 1. The heat capacity per gram of tetrahydrofuran clathrate hydrate (THF.16.83H20)as a function of temperature: (0),present re-
sults; (-), from Handa et aLZ2 clathrate hydrate therefore may also be useful to future studies of the unusual thermal conductivity of clathrate hydrates. In this paper, we report the first measurement of a thermal property of a clathrate hydrate at temperatures below the nitrogen boiling point, viz. the heat capacity of THF clathrate hydrate from 17 to 216 K. 11. Experimental Procedure THF clathrate hydrate of composition THF.16.83H20 was prepared directly in the calorimeter vessel by mass from doubly distilled deionized water and analytical grade (99.5%, BDH) tetrahydrofuran. This particular composition was chosen to be close to the correct stoichiometry for structure I1 clathrate hydrates (M.16.86HzO) but slightly richer in the guest in order to prevent ice formation. Postcalorimetric analysis by refractive index, camed out to check for possible loss of the more volatile component during sample loading and soldering of the calorimetric vessel, indicated the composition to be THFa(16.8 f 0.1)H20. A small amount (mol) of helium exchange gas was added to facilitate thermal contact between the sample and the calorimeter. The following thermal treatment was carried out to give stable structure I1 THF clathrate hydrate. The liquid sample was cooled from room temperature to 263 K at a rate of 8 X K s-l and maintained a t 263.0 f 0.2 K for 24 h. The sample was subsequently cycled from 263 to 243 to 263 K three times by using heating and cooling rates of 1 X K s-' and holding the sample at 263.0 f 0.2 and 243.0 f 0.2 K for a period of 8-12 h before the next temperature change. The final cooling before taking measurements was from 263 to 80 K at a rate of 1 X K s-I, and further temperature changes did not exceed this rate. The calorimetric measurements of 9.962 g of THF.1 6.83H20 were made in an adiabatic calorimeter using the heat pulse method and a platinum resistance thermometer. The temperature range of the experiment was 17-261 K, limited at the low end by the relative insensitivity of the Pt thermometer below 20 K. The overall precision and accuracy of the heat capacity measurements, as discussedz7in a more complete description of the calorimeter, were respectively *OS% and f l % .
111. Experimental Results The experimentally determined heat capacity of THF.16.83H20 is illustrated and compared with the results of Handa et a1.2zin Figure 1. (Comparison with the results from ref 19-21 is not given since the results from ref 19 are only given graphically; those from ref 20 are corrected in ref 22; those for ref 2 1 are only for T > 245 K.) The present values are about 2% lower than the earlierzz measurements for 90 < T < 240 K the difference is just at the limit of the sum of the quoted uncertainties. The sudden drop in the heat capacity that was observed by Handa et aLu below 90 K was not seen in this study, and it is likely therefore that it was due to experimental limitations in the earlier investigation at the lower end of their temperature range. (27)M.A. White, Thermochim. Acta, 74,55 (1984).
60 65 70 75 80 85 90 95 100
0.141 0.204 0.266 0.330 0.394 0.458 0.516 0.575 0.626 0.670 0.712 0.749 0.787 0.824 0.860 0.896 0.928
110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260
0.982 1.033 1.081 1.130 1.185 1.239 1.292 1.347 1.408 1.474 1.539 1.608 1.681 1.157 1.854 1.966
Although ice is known2" to undergo a glassy phase transition a t about 100 K, there was no evidence for such a transition in THF clathrate hydrate. In fact, throughout the experimental temperature range the relaxation times following heat pulses were similar to those for many inorganic solids that had been measured previously in this same calorimeter (10-20 min), in contrast with very long relaxation times (up to several hours) that have been observed in a poor thermal conductor in similar experiment^.^^ Smoothed heat capacity values from 20 to 260 K based on the present measurements are given in Table I.
IV. Discussion Figure 1 shows the heat capacity of THF.16.83Hz0 to be a smooth function of temperature, without any singularity characteristic of a phase transformation. We show below that although there is no phase transition in THF clathrate hydrate, the heat capacity does show thermal activation of disorder in the THF molecules. It therefore appears that, in contrast with the HCN quinol clathrate'* for example, the reorientational motion of the THF molecules in the ice lattice is a gradual process and one that takes place without a discontinuity in the derivatives of the free energy of the host lattice. The contrast with the H C N quinol clathrate is probably the result of the following properties of the THF clathrate hydrate: a smaller guest molecule dipole moment, weaker guest-guest interactions, a more isotropic cavity in the host lattice, and a host lattice with sufficient disorder of its own to accommodate disorder in the guest molecules. Primarily in order to understand the dynamics of the guest molecule, it is usual to separate the guest and host contributions to the total heat capacity. Although the basis for this practice has been questioned,'" and it seems unreasonable to expect this separation to be exact since certainly there are guest-host interactions, it does seem reasonable to use this as a starting point to understand the heat capacity of THF clathrate hydrate. We will see later that although there are more serious limitations to this procedure than the assumption of guest-host separability, we can still learn from it. In order to calculate the heat capacity of the guest species from the measured heat capacity of a clathrate, it is necessary to know the heat capacity of the host lattice as a function of temperature. In clathrates for which the empty host lattice is not stable, its heat capacity has been deduced from the heat capacities of clathrates of different guest concentrations, extrapolated to zero guest c o n c e n t r a t i ~ n . Due ~ ~ ~to the small range of concentrations over (28)0.Haida, T.Matsuo, H. Suga, and S . Seki, J . Chem. Thermodyn. 6,815 (1974). (29)M.A. White, C. Chieh, A. Anderson, and L.A. K. Staveley, J. Chem. Phys., 80, 1254 (1984). (30) N. G. Parsonage and L. A. K. Staveley, Mol. Phys., 2,212 (1959). (31) N.G.Parsonage and L. A. K.Staveley, Mol. Phys., 3, 59 (1960). (32)N.R.Grey and L. A. K. Staveky, Mol. Phys., 1, 83 (1963). (33) G.L.Stepakoff and L. V. Coulter, J . Phys. Chem. Solids, 24, 1435 ( 1963).
White and MacLean
1382 The Journal of Physical Chemistry, Vol. 89, No. 8, 1985
the measured heat capacity and C,,(2) anharmonicity, (3) the failure of the guest-host separability assumption, and (4) inar . dequacy of hexagonal ice as a model for the empty host lattice. The 8R maximum for the pseudorotational, rattling, and rotational degrees of freedom is the maximum heat capacity at constant volume, C,, whereas the heat capacities that are measured in this experiment are C,values, the heat capacities of the solid in equilibrium with its saturated vapor. C,is related to C,,the @,, .. .... ... . . , ..... , . ,.. ..... .-.. l.' -, -. -, -. -. -. --. ............ 4 heat capacity at constant pressure, by3* OL/.. -.-~-L-._0 100 200 T/ K Figure 2. The molar heat capacity of the THF molecule in THF. 16.83H20and calculated contributions to the heat capacity: (0),cHFwhich is related to C,by3* derived from experimental results for THF.16.83H20, as described in the text; (- -), the calculated pseudorotational contribution; the cal(3) culated Poschl-Teller vibrational rattling contribution; (---), the calwhere V is the molar volume, p is the coefficient of cubic exculated hindered rotational contribution (from Pitzer functions); (-), the sum of the calculated pseudorotational, vibrational rattling, and pansion, and x T is the isothermal compressibility. Well below hindered rotational contributions. The error bar at T = 120 K represents the melting point, where the vapor pressure is quite low, the f l % in the total heat capacity. difference between C,and C, is negligible. However, the difference between C, and C,may be important in this same temperature which the THF clathrate hydrate is stable,I2 this method cannot range, and it could account for part of the THF heat capacity be used here. The most reasonable alternative in this case is to in excess of 8R. Using the values of p and x r from Bathe et al.39 assume that the heat capacities of hexagonal ice and the host and Roberts et al.$O respectively, C, - C, for THF clathrate lattice are equal. Although this is not an entirely satisfactory way hydrate at 200 K is 3% of C,, and it seems therefore that the major to proceed since the structures of ice and the host lattice differ reasons for the difference between the heat capacity of the guest in the presence of cages and in the orientations of their hydrogen and 8R must be sought elsewhere. bonds, detailed calculations have revealed similar local structures The 8R value represents the upper limit of the heat capacity for the clathrate hydrate lattice and hexagonal ice.34 The simif pseudorotation, rotation, and vibrational rattling can be repilarity of the rigid-lattice 'H N M R second moments for THF-d, resented by harmonic oscillators. While the motions are likely clathrate hydrate' and hexagonal ice35 (33.4 f 1.5 G2 at 100 K slightly anharmonic, and the total heat capacity would therefore and 32.4 f 1.1 G 2 at 75 K, respectively) gives further support be expected to exceed 8R, the increase is likely of the order of for the use of this approximation. We have calculated the molar a few percent, not the 10% excess observed. heat capacity of the THF guest, pF, using these approximations, One of the underlying assumptions in this treatment of the heat and the results are illustrated in Figure 2. capacity of the guest molecules is that of exact separability of the Above 200 K, the calculated guest heat capacity rises rather guest and host contributions to the heat capacity. This has some rapidly, until it maximizes at the melting point. This steep increase tacit support from the fact that the THF guest molecules behave is almost certaintly due to premelting and the inability of hexindependently' and the successful separation of guest and host agonal ice to adequately reflect the empty host lattice heat capacity heat capacities in other clathrate ~ysterns.~'However, there is in this temperature range.m,22This can perhaps be illustrated best no satisfactory way to test the error introduced by this assumption by stating that the increase in pHF at 250 K over that at 200 here. K disappears if the estimate of the empty host lattice heat capacity The model for the empty lattice heat capacity is likely the major at 250 K is increased by 6%. source of the discrepancy between 8R and the observed guest heat From about 120 to 200 K, there is little temperature dependence capacity (-9R) in the THF clathrate hydrate in this temperature to the calculated heat capacity of the THF guest, and this indicates range (120-200 K). Because the derived guest heat capacity is that the number of degrees of freedom available to the guest is extremely sensitive to the host contribution in the T H F clathrate constant over this temperature range. In principle, the degrees hydrate due to the high host-to-guest mole ratio, a 2% increase of freedom could include intramolecular vibrations, the motions in the host heat capacity in this temperature range would reduce of the center of mass within the cages (vibrational rattling), and the guest heat capacity to 8R. The earlier studies20*22 of the heat the rotations of the guest molecules. Although heat capacity capacity of THF clathrate hydrate in this temperature range contributions from intramolecular vibrations are usually very small ignored the contribution of the pseudorotation of the THF guest, at these temperatures, five-membered rings are well-known to be and on their basis one might have concluded that hexagonal ice dynamically planar, with small barriers between the puckered ring is an inadequate model for the empty host lattice. We have now configuration^.^^ The THF molecule has two low-frequency shown that, in the temperature range from 120 to 200 K, hexvibrational modes associated with these motions (so-called pseuagonal ice is surprisingly accurate as a model for the heat capacity do rotation^),^' each of which could contribute R to the heat of the empty host lattice, and the pseudorotational, vibrational capacity. In the harmonic equipartition limit, the vibrational rattling, and rotational modes of the THF guest molecules are rattling and full-molecule rotations could each contribute 3R, for fully excited throughout this temperature range. a total of 8R. The observed heat capacity of the THF guest in At lower temperatures ( T < 120 K), the heat capacity of the this temperature range is about 9R, which indicates that these guest molecules increases with temperature to a maximum at about degrees of freedom (pseudorotations, vibrational rattling, and full 85 K and then decreases slightly. This behavior is characteristic rotations) are all fully excited. of the thermal activation of rotational states, and we will show The difference between the observed heat capacity (9R) and that although current models give only semiquantitative agreement the high-temperature harmonic oscillator limit of the heat capacity with the observed guest heat capacity, the maximum in the heat (8R)may reflect some of the following: (1) the difference between n. ,-i
151
1 /,.;-------
J8
,I,
-,
-
~
r=._
(e-),
(34) Y.A. Majid, S . K. Garg, and D. W. Davidson, Can. J . Chem., 46, 1683 (1968). (35) S . W. Rabideau, E. D. Finch, and A. B. Denison, J . Chem. Phys., 49, 4660 (1968). (36) J. E. Kilpatrick, K.S . Pitzer, and R. Spitzer, J . Am. Chem. SOC.,69, 2483 (1947). (37) J. A. Greenhouse and H. L. Straws, J . Chern. Phys., 50, 124 (1969).
(38) J. G. Aston and J. J. Fritze in 'Thermodynamics and Statistical Thermodynamics", Wiley, New York, 1959. (39) M. Bathe, S . Vagle, G. A. Saunders, and E. F. Lambson, J . Mater. Sci. Lett., 3, 904 (1984). (40) R. B. Roberts, C. Andrikidis, R. J. Tainsh, and G. K. White, ICEC10, Helsinki, 1984. (41) J. C. Burgiel, H. Meyer, and P. L. Richards, J. Chem. Phys., 43,4291 (1965).
The Journal of Physical Chemistry, Vol. 89, No. 8,1985 1383
Guest Molecules in THF Clathrate Hydrate capacity can be used to determine the barrier to rotation. The heat capacity of the guest molecules can be described as having pseudorotational, vibrational rattling, and rotational contributions. As discussed earlier, the barrier to peudorotations (i.e. out-of-plane vibrations) of the THF molecule is very and therefore this motion contributes significantly to the heat capacity, even a t low temperatures. Based on the infrared measurements of Greenhouse and Strauss,3' the heat capacity due to pseudorotations has been calculated and is represented in Figure 2 by the dot-dash line. The vibrational rattling contribution also can be calculated,4' based on the Poschl-Teller potential V(x) =
h2a(a - 1)
8mdo2 sin2 ( [ ( x / d o ) - 0.51)
(4)
where m is the guest molecule mass, dois the diameter of the box, h is Planck's constant, and a is a parameter governing the stiffness of the walls. The energy levels for this potential are E, = (h2/8mdo2)(a+ n)2 = B(a
+ n)2
n = 0, 1, 2, ...
(5)
where a and B can be derived experimentally from the n = 0 to n = 1 and n = 1 to n = 2 transition frequencies. From the infrared study of Bertie and Jacobs,I6 we can derive a = 20 and B = 0.6 cm-' for THF clathrate hydrate. The calculated heat capacity for Poschl-Teller rattling is shown by the dotted line in Figure 2. The contributions to the heat capacity from hindered rotations of the THF guests can be assessed from Pitzer function^^^.^^ in which the partition function, Q, is given by
Q = 2.8 15( 1 0 3 8 Z ~ 0 . 5 / n
(6)
where Z is the moment of inertia in g cmz and n is the number of minima per revolution in the potential energy function. Using an average value of Z of 1.7 X g cm2 (Z, = 1.2 X 1 0-38g cm2, Z, = 2.09 X lo-'* g cm2)I6and the spectroscopic v a l u e ~ ' ~ J ~ of n of 4.1 and of the barrier to rotation (Vo)of 3.89 kJ mol-', we have evaluated the heat capacity of a three-dimensional hindered rotor, and it is illustrated by a dashed line in Figure 2. The sum of the hindered rotations, the Poschl-Teller rattling, and the pseudorotational contributions is also shown in Figure 2, as a solid line. It is clear that the calculated heat capacity is an overestimate at low temperatures ( T < 40 K) and an underestimate at higher temperatures, and calculations of other models of hindered rotation, such as that due to Stepakoff and C ~ u l t e rdo , ~ not ~ significantly change this result. Although the observed maximum
in the heat capacity is also seen in the calculations, it would appear that the difference between the calculated and observed heat capacity at low temperatures reflects the breakdown of the assumption that the host heat capacity is adequately represented by that of hexagonal ice. While hexagonal ice appears to be a reasonable model at higher temperatures (vide supra), the difference in long-range order in ice and the clathrate hydrate would be expected to give rise to differences in their heat capacities at low temperatures. Although the heat capacity of the THF guest is therefore sufficiently uncertain (due to the problem in the evaluation of the empty host lattice) to make quantitative comparisons futile, the maximum in drHF at 85 K can be used with Pitzer's hindered rotational function^^^^^^ to deduce a barrier to rotation of 3.5 kJ mol-', in good agreement with 3.81, 3.89, and 3.85 kJ mol-' from dielectric mea~urements,'~ infrared spectro~copy,'~~'~ and NMR,I4 respectively. V. Conclusions Heat capacity measurements of tetrahydrofuran clathrate hydrate (THF.16.83H20) are consistent with free or nearly free rotation of the THF guest molecules in the host lattice at temperatures above about 120 K. At lower temperatures, this rotation becomes hindered, but the reduction of rotational freedom is gradual and does not result in a phase transition. Although the guest-host interactions may not be exactly separable, partitioning of the measured heat capacity into guest and host components shows that hexagonal ice is a fair model for the empty host lattice heat capacity at high temperatures ( T > 120 K), but not at lower temperatures. However, the calculation of the heat capacity of the THF guest by this method allows an assessment of its barrier to rotation, and this value (3.5 kJ mol-') is in good agreement with that determined by other methods.
Acknowledgment. We express our thanks to Dr. Y. P. Handa, Dr. J. Tse, Dr. J. Ripmeester, and Dr. D. W. Davidson for their interest in this work and for valuable discussions, to Prof. R. J. P. Williams and Prof. R. E. Wasylishen for input with regard to pseudorotations in five-membered rings, and to the referee for drawing our attention to ref 39 and 40. Research support from the Natural Sciences and Engineering Research Council (Canada) through a grant to M.A.W. is gratefully acknowledged. Registry No. THF.16.83H20, 18879-05-5. Supplementary Material Available: Raw heat capacity data for THF.16.83H20 from 17 to 261 K (1 page). Ordering information is given on any current masthead page. (42)K.S.Pitzer, J . Chem. Phys., 5, 469 (1937). (43)K. S. Pitzer and W.D.Gwinn, J . Chem. Phys., 10,428 (1942).
