J . Phys. Chem. 1989, 93,1495-7502
7495
*H and "gS NMR Line-Shape Studies of the Molecular Motion in the Liquid and Solid Phases of Hydrogen Sulfide and the Solid I 1 Phase of Hydrogen Selenidet M. J. Collins, C. I. Ratcliffe,* and J. A. Ripmeester Division of Chemistry, National Research Council of Canada, Ottawa, Ontario, Canada K l A OR6 (Received: January 23, 1989; In Final Form: May 22, 1989)
ZHNMR line shapes of the solid phases of D2S and solid I1 of D2Se have been studied as a function of temperature. In phase 111 D2S at 77 K the molecules are virtually static, but by 105 K a motion, which is more consistent with 2-fold flips of crystallographically inequivalent D2S molecules than with earlier 4-site flip models, is almost in the fast motion limit. In phase I1 D2S and D2Se the line shapes at all temperatures indicate a rapid axially symmetric motion and a dramatic, nonlinear decrease in the 2H quadrupole coupling constant with increasing temperature. A unique interpretation of these results is not possible, but two plausible models are discussed. One involves a temperature dependence of the angles describing the orientation of the molecule with respect to the reorientation axis. The second involves flips among four reorientation axes, which correspond to the diagonals of a cube, one of which has a higher population than the others. The energy difference between these orientations has a critical temperature dependence, leading to equivalent populations and pseudoisotropic reorientation at the I1 I phase transition. Apparent activation energies for the isotropic reorientational motions of the solid I and liquid phases of H2S and D2S were determined from 33SNMR line widths and 2H NMR T,'s as a function of temperature. The 33Squadrupole coupling constant was estimated to be 45.5-52.5 MHz.
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Introduction Recently we reported a 2H and 77SeN M R study of the solid phases of hydrogen selenide from which we were able to obtain detailed information about the rmrientational processes occurring.' The phase behavior of hydrogen sulfide is very similar to that of hydrogen selenide: and although hydrogen sulfide has been studied more extensively, there remain a number of questions and ambiguities concerning the motions in the different phases. In order to put the current work into perspective, it is necessary first to describe critically some of the previous work on solid HIS. Much of the work on solid H2Shas been reviewed by Parsonage and Staveley.' The phase transition temperature (K) and entropy changes (ASIR)are summarized as follows:2
107.82
132.85
187.14
From the available X-ray and neutron powder diffraction results phase 111 is tetragonal P42 and ordered, phase I1 is cubic Pa3 with the molecules possibly disordered among six orientations, and phase I is face-centered cubic! Phase I, like phase I of H2Se, is a plastic crystal. It has been suggested from electron diffraction studies on phase I11 that there are two tetragonal phases, one of which is t r a n ~ i e n t ,although ~.~ no other evidence has so far been produced to confirm this. Recent studies of the Raman spectra of H2S at 25 K have indicated that a new solid phase is stable in the high-pressure range of 30-80 kbare7 Earlier Raman studies on phase 111 gave results consistent with the proposed structure.8 Dielectric studies9-I1 showed considerable reorientational freedom in phases I1 and I and no dipole reorientation in phase 111. Several IH N M R second moment ( M z )and spin relaxation studies have been concerned with motions in solid H2S.12-19 There was some variance in the earlier determinations of the value of the IH second moment at temperatures below 77 K: -8 G2,13 9.9 G2,I4 14 f 5 G2.I6 The low value of 8 G 2 led to some speculation about the possible involvement of 180° tunneling motions, and a tunneling model was therefore developedI8 that also tried to explain the two TI, minima observed by Look, Lowe, and Northby14 discussed below. However, a very careful second moment study carried out later to resolve this problem gave 1 1.2 f 0.3 G2 at 58 K,I7 which is in satisfactory agreement with values 'Published as NRCC No. 30219.
0022-3654/89/2093-7495$01.50/0
calculated for a rigid lattice, based on the most reliable crystal structure. Spin-lattice relaxation times in the static frame (TI) have been obtained at several f r e q ~ e n c i e s ~and ~ * also ~ ~ Jin ~ the rotating frame (Tl,,).l4 Both the M 2 and TI results for phase 111 show a motion which, to be compatible with the dielectric data, must be reQrientation about the dipole axis, coincident with the molecular 2-fold axis. Activation energies (E,) of 4.0 kcal/mol,13 3.6 kcal/mol,14 and 3.8 kcal/mol16 were obtained from the T1studies. The simplest motion assignable is a 180' flip. However, Look, Lowe, and Northby'sI4 T I ,data for this phase show two minima with corresponding E ~ ofs 5.5 kcal/mol (fof the high-temperature minimum) and 3.6 kcal/mol (lower temperature minimum). They proposed a four-site flip motion with the intermediate 90' positions of higher energy AE = 0.45 kcal/mol to account for the T I result and the low-temperature T1, minimum but were unable to assign a definite motion to the second TI, minimum. Later, however, Tsai19 developed a similar four-site model that could account for both the T1, minima. He suggested from this model that at lower temperatures the relaxation was largely due to intramolecular (1) Facey, G.; Wasylishen, R. E.; Collins, M. J.; Ratcliffe, C. I.; Ripmeester, J. A. J. Phys. Chem. 1986, 90, 2047. (2) Kruis, A.; Clusius, K. Z. Phys. Chem. 1937, B38, 156. (3) Parsonage, N. G.; Staveley, L. A. K. Disorder in Crystals; Clarendon: Oxford, UK, 1978; p 562. (4) Sandor, E.; Ogunade, S. 0. Naiure 1969,224,905, and references cited therein. (5) Kitamura, N.; Harada, J. J. Phys. SOC.Jpn. 1%2, I7 Suppl. B-11, 245. (6) Harada, J.; Kitamura, N. J . Phys. SOC.Jpn. 1964, 19, 328. (7) Anderson, A.; Demoor, S.; Hanson, R. C. Chem. Phys. Lett. 1987,140, 471. (8) Anderson, A.; Binbrek, 0.S.; Tang, H. C. J . Raman Specirosc. 1977, 6, 213. (9) Kemp, J. D.; Denison, G. H. J. Am. Chem. SOC.1933,55, 251. (10) Smyth, C. P.; Hitchcock, C. S. J. Am. Chem. Sdc. 1934, 56, 1084. (1 1) Havriliak, S.; Swenson, R. W.; Cole, R. H. J. Chem. Phys. 1955, 23, 134. (12) Alpert, N. L. Phys. Reu. 1949, 75, 398. (13) Budke, B. de K.; Gordon, M. I.; Hoch, M. J. R. In Magnetic Resonance and Relaxation; Proceedings of the 14th Amp?xe Colloquium, Ljubljana, 1966; Blinc, R.,Ed.; North-Holland: Amsterdam, 1967, p 396. (14) Look, D. C.; Lowe, I. J.; Northby, J. A. J. Chem. Phys. 1966, 44, 3441. (15) Look, D. C.; Lowe, I. J.; J . Chem. Phys. 1966, 44, 3437. (16) Loehlin, J. H.; Mennitt, P. G.;Waugh, J. S . J . Chem. Phys. 1966, 44, 3912. (17) El Saffar, Z. M.; Schultz, P. J . Chem. tlhys. 1972, 56, 2524. (18) Hoch, M. J. R.; Budke, B. de K. J. Magn. Reson. 1972, 7, 359. (19) Tsai, C.-C. Ph.D. Thesis, University of Pittsburgh, 1974.
Published 1989 by the American Chemical Society
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The Journal of Physical Chemistry, Vol. 93, No. 21, 1989
diple-dipole interactions in 90" jumps between inequivalent sites and at higher temperatures the main contribution to relaxation was from intermolecular interactions as the molecule jumped between 180" sites. In phase I1 the low M 2 values indicated considerable motional averaging and the TI curves indicated a correlation time 7c < 5 X IO-'s, but it was not possible to determine the nature of the motion. A slower motion observed by TI, was assigned to translational diffusion. The results from phase I indicated translational diffusion at the higher temperature end, with E, 7.4 kcal/mol, and an indication of an undetermined motion at the lower temperature end. Look, Lowe, and Northby14 obtained their M 2 results by fitting to the free induction decays obtained from an N M R pulse experiment. At the same time this method supposedly allowed a separation of the intra- and intermolecular contributions to M2. They relied heavily on the fact that the intramolecular M 2 thus obtained falls with increasing temperature, whereas the intermolecular M2 stays constant, to substantiate their 90" jump model for phase 111, since 180' flips alone should not change the intramolecular contribution. It is, however, very odd that the intermolecular M z contribution does not appear to change at all, since either 180' or 90' flip motions should also cause some decrease in this component. Furthermore, since their claimed intermolecular M2observed in phase I11 only amounts to -2.2 G2even at 4 K compared with the total calculated intermolecular M2 for the rigid structure (based on the neutron diffraction structure4) of 3.47 G2," one must seriously question whether the separation of intra- and intermolecular contributions by this method has worked. The report of a IH NMR chemical shift anisotropy of 11.1 ppm in phase I of H2SZomust be erroneous, if, as the ,HN M R results appear to indicate, the molecule is undergoing isotropic reorientation (Le., it should be possible to determine only the isotropic chemical shift in the plastic phase). The early continuous wave (CW) method for obtaining 2H N M R lineshapes produced rather poor results for phases I11 and 11, though the results for phase I clearly showed isotropic (or pseudoisotropic) reorientational motion2* There was thus clearly ,H a lot of scope for the use of modern Fourier transform (IT) N M R to produce much better line shapes for phases I11 and 11, which could then be used to determine the nature of the motions involved. The rapid pseudoisotropic nature of the reorientations in phase I also suggested that it might be feasible to obtain 33S N M R line shapes for this phase as well as the liquid.
Collins et al.
D2S Phase
I
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Experimental Section H2S (Matheson) or D2S (M.S.D. Isotopes) was condensed into a IO-mm-0.d. glass sample tube at 77 K on a vacuum line. Several freeze-pumpthaw cycles were used to degas the sample before sealing the tube. 2H N M R spectra were obtained mainly at 27.63 MHz (Bruker 4.24Tcryomagnet) by use of a Bruker CXP 180 pulse spectrometer and a variable-temperature N,-gas-flow probe with a Bruker B-VT-1000 temperature controller. A few spectra were also obtained at 9.2 MHz by use of the same spectrometer with a Bruker 1.41T electromagnet and an Andonian crystat. A phase alternated quadrupole echo pulse sequence22was employed with a delay time of 35 p s between X and Y pulses of 2.6-3.0-ps duration. 2HT, measurements for solid I D2S were made by use of a 180°-r-900 pulse sequence at 27.63 MHz. 33SN M R line shapes were obtained as a function of temperature at 23 MHz by use of a Bruker MSL 300 spectrometer and the same probe as for the 2H measurements. A RIDE23 pulse sequence was used (with 10-ps 90' pulse lengths) to remove the effects of receiver deadtime on the signal. Generally 1000 scans (20) Ryan, L. M.; Wilson, R. C.; Gerstein, B. C. Chem. Phys. Lett. 1977, 52, 341.
(21) O'Reilly, D. E.; Eraker, J. H. J. Chem. Phys. 1970, 52, 2407. (22) Davis, J. H.; Jeffrey, K. R.; Bloom, M.; Valic, M. I.; Higgs, T. P. Chem. Phys. Lett. 1976, 42, 390. (23) Belton, P. S.;Cox, I. J.; Harris, R. K. J. Chem. Soc., Faraday Trans. 2 1985. 81, 63.
II 126
f
0
100 kHz
Figure 1. Characteristic *HN M R line shape of DzS in its three solid phases.
D2S
R n K 105
100 kHz Figure 2. Temperature variation of the 2H N M R line shape of D,S in phase 111.
were acquired, except for the three lowest temperatures where the number was increased to 4000 scans. The D2Se sample was the same one used in an earlier study.'
Results and Discussion D2S: 2H N M R . 2H N M R line shapes of solid D2S are shown in Figures 1-3. Comparison of the new line shapes with those
The Journal of Physical Chemistry, Vol. 93, No. 21, 1989 1491
Molecular Motion in H2S and H2Se
K
kHz, q = 0.1 12,29and HDO (vapor), QCC = 3 0 7 . 9 , ~= 0.13530). There is also a significant increase in D2S bond angle in the solid, 94.5 f 1.504 relative to the gas, 92.1°,25 which presumably is related. Although 2H T,'s were not measured, the recycle delay times required to collect the spectrum at 77 K indicated a long T Iof the order of several seconds. This rules out the possibility that the large QCC reduction from gas to solid could be due mainly to a large-amplitude librational motion. Line narrowing occurs as the temperature is increased above 77 K. Just below the transition to phase I1 the residual cusps on the dYydiscontinuities of the spectra suggest that this narrowing is almost, but not quite, in the fast motion limit. (The cusps also appear in the simulated line shapes, discussed later, for T~ > s). The line shape is quite well defined and yields QCC = 70.5 kHz and v = 0.231. Initial impressions of the motionally averaged line shape close I1 transition suggest that the molecules are all to the 111 undergoing simple 2-fold flips, since the Auyy component of the static line shape remains unchanged in the averaged line shape. ( Vyyis known, from the microwave to be perpendicular to the molecular plane and 2-fold flips would not affect this). One must consider, however, whether the 4-site models of Look, Lowe, and NorthbyI4 and Tsai19 could be compatible. It is relatively easy to calculate averaged line shapes for the fast motion limit, Le., motions faster than lo7 Hz.2493'-32 The orientation of the second rank static electric field gradient tensor must first be described in a reference coordinate system in terms of the Euler angles. The complete Euler angle description has been given in ref 32. A population weighted average of the tensor components over the different orientations visited during the motion then gives an effective tensor which governs the line shape observed in the fast motion limit. The model assumes that the D2S molecule reorientates among four sites around its C2 axis, with sites a,b at 0,180' having populations (1 + x) and sites c,d at 90,270' having populations (1 - x). The ratio of populations at any particular temperature ( T ) is governed by a Boltzmann distribution
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I
50 kHz
I
Figure 3. Axial 2H NMR powder line shapes of D2Ssolid I1 close to its low- and high-temperaturephase transitions. The line shapes show trace amounts of phase I11 in the 108 K spectrum and of phase I (isotropic line) in the 132 K spectrum.
obtained many years ago by the C W technique2, shows the vast improvement brought by Fourier transform NMR. The only agreement occurs in the observation of a single sharp line for phase I and broad anisotropic line shapes in phases I1 and 111. 2H N M R is influenced by the interaction of the nuclear quadrupole with the electric field gradient tensor, whose components are denoted in the following by the terms V,. The resulting quadrupole coupling tensor (components e Q v i / h ) acts as a perturbation on the Zeeman interaction, but in most cases it is still the dominant factor determining the powder line shapeeZ4 Such line shapes are symmetric about the Zeeman frequency and show either two or three pairs of features separated by the frequencies: Avzz = vq Avyy = 1/2Vq(l + V) AUXX = '/uq(l - V)
(1)
where the quadrupole coupling constant (QCC) e2qQ/h = 2 / 3 ~ q and the asymmetry parameter v = (Avyy- Avxx)/Av,,. For the so-called axial case Au,, = Auyy and v = 0. Molecular motion at sufficiently high rates can cause averaging of the coupling tensor and thus the line shape can narrow and modify. ( a ) Solid IZZ ( 1 kcal/mol the four-site and two-site models become indistinguishable within the experimental error. The only other type of reorientational motion, except for the rather unlikely case of a partial rotation between two sites, that leaves the dipole orientation unchanged (as required by the dielectric results) is n-fold reorientation (n 2 3) about the molecular C, axis and this would give the same averaged line shape as the four equivalent sites model; Le., for x = 0, QCC = 27.1 kHz, q = 0. Thus it must be concluded that 180° flips are most likely the motion responsible for the narrowed 2H line shape. One can then investigate whether the old IH NMR results could, after all, be compatible with this:
fi
3E4
,
100hHz
L
1E7
,
Figure 5. Simulated ZHquadrupole echo line shapes for D2S undergoing 2-fold flip reorientation at the different rates indicated. The echo delay time was 35 ps. The inset shows the sum of the line shapes at rates 1E4 and 3E6 weighted by their echo amplitudes.
Look, Lowe, and NorthbyI4 and TsaiI9 developed their models without knowledge of the powder neutron diffraction structure, and they assumed that all the H2S were equivalent. Much of the reasoning behind their models was based upon their supposed separation of the M2 data into intra- and intermolecular contributions. We have already pointed out some reasons for being skeptical about this separation, and indeed, if one were to assume that it is incorrect, the changes in total M2 and the ‘H T I and T I ,results may be accommodated in terms of 180’ flips of different types of H2S. The neutron diffraction study in fact shows that there are four crystallographically inequivalent m o l e c ~ l e s . ~ This observation does not rule out the four-site model, since the reorientational potentials for all four sites could be very similar, but it does permit the possibility of having 2-fold flips with different molecules reorienting at different rates. Note that OReilly and Eraker2’ concluded much earlier, on the basis of their own analysis of the old M2, T I ,and T I ,data, that 180’ flips occurred and that the two T I , minima were due to different molecules. From the theory of spin-lattice relaxation in the rotating frame T1,33,34 it is easy to find that at the TI, minimum, since W ~ T >> , 1, T, = 1/2w, (where w1 is the radial frequency of the spin-locking field HI). Hence, for H I = 4.2 and 19.4 GI4 the correlation times at the T I , minima should be 7, = 4.45 X 10” s and 7c = 9.63 X lO-’s, respectively. It is thus clear that, for the motion giving rise to the lower temperature T l pminimum, T, at 105 K will be
