J. Phys. Chem. 1989, 93, 7315-7319
7315
ARTICLES Structure and Dynamics of Dimethylammonium Ions in Solids Using *H Quadrupole Echo Spectra Ryuichi Ikeda,* Institute for Molecular Science, Myodaiji, Okazaki 444, Japan
Atsushi Kubo,? and Charles A. McDowell* Department of Chemistry, University of British Columbia, 2036 Main Mall, Vancouver, British Columbia, Canada V6T 1Y6 (Received: December 21, 1988; In Final Form: July 3, 1989)
2H NMR powder spectra, obtained by Fourier transforming the quadrupole echo signals, were recorded for [(CD3)2NH2]2MCb (M = Sn, Te) to elucidate motional effects on the line shapes. The observed spectra were analyzed by comparison with line shapes calculated for various jump angles of the CD, group, differences in the cation jump rates, and interpulse spacing times. For both complexes there was a narrowing of the spectral width near room temperature which we associated with a new motional process of the cations. Spectra with a large asymmetry of the electric field gradient tensors, associated with the narrowing process, are explained well by assuming a 180" flip of the cation about its C2axis. From the line-shape analysis, the C-N-C bond angles in the tin and tellurium complexes are evaluated as 116.8' and 119.0', respectively. The ND2 bond angle was also determined to be 103.6' for [(CH3)2ND2]2SnC16.Activation energies and correlation times of the 180" flips of the cations were derived and compared with those of the fully protonated cations, and those for 90' rotational jumps of the complex anions.
Introduction Dynamic processes occurring in solids have been widely studied by the application of N M R spectroscopy. Especially, 'H N M R has been extensively applied to the investigation of molecular motions taking place over a wide range of time scales by measuring spectrum line widths as well as relaxation times.'.2 Recently, high magnetic field 2H Fourier transform (FT) N M R spectroscopy has developed rapidly,'-8 and this provides a new methodology applicable to the study of dynamical phenomena which have not been fully elucidated by 'HN M R methods. Quadrupolar parameters determined from observed 2H FT N M R spectra, such as the quadrupole constant (qcc), and the asymmetry parameter q of the principal components of electric field gradient (efg) tensor, can afford information about motional modes of molecules, because, when the efg is averaged by onset of a new motion, both qcc and q change their values according to the symmetry of the motion. Information obtainable from these parameters is quite local because the efg at an 2H nucleus depends solely on the charge distribution at the resonant nucleus and at the nearest-neighbor atoms chemically bonded to it. In this respect, knowledge derived from efg tensors is complementary to that obtained from line widths, or second moments of 'H NMR spectra, which are mostly determined by magnetic dipolar interactions of interatomic and intermolecular origins. Besides these static quadrupolar parameters for molecular motions, 2H quadrupolar spectra can provide information about dynamical properties such as rotational jumping rates, or correlation times, and also activation energies of the motions in a variety of molecular systems, because the spectral line shapes are quite sensitive to the jump rates when these are of the order of magnitude of the line widths. Moreover, not only may we identify the type of motion occurring, but it is usually also possible to determine the symmetry and the magnitude of the site orienting potential and tilt of the Present address: Department of Chemistry, Faculty of Science, Tokyo Metropolitan University, Fukazawa, Setagaya, Tokyo 158, Japan.
angles between diffusion and the magnetic axes from detailed analysis of the N M R line shapes.'-20 It has been pointed out by Spiess and Sillescu8 that the quadrupole echo technique for recording 2H FT spectra yields distorted line shapes originating from the T2anisotropy associated with motional processes. This effect makes the spectra more complicated, but detailed analysis can afford additional information about processes occurring in the slow motion region. In the present work, we studied the ZHFT quadrupole echo spectra (1) Abragam, A. Principles of Nuclear Magnetism; Clarendon Press: Oxford, U.K., 1961. (2) Mehring, M. Principles of High Resolution NMR in Solids, 2nd ed.; Springer: New York, 1983. (3) (a) Solomon, I. Phys. Reu. 1958, 110, 61. (b) Davis, J. H.; Jeffrey, K. R.; Bloom, M.; Valic, M. I.; Higgs, T. P. Chem. Phys. Lett. 1976, 42, 90. (4) Seelig, J. Q.Rev. Biophys. 1977, 10, 353. (5) Boden, M.; Clark, L. D.; Hanlon, S. M.; Mortimer, M. Furuduy Symp. Chem. SOC.1978, 13, 109. (6) Spiess, H. W. NMR Busic Principles and Progress; Diehl, P., Fluck, E., Kosfeld, R., Eds.; Springer: Berlin, 1978; Vol. 15, p 55. (7) Spiess, H. W. Chem. Phys. 1974, 6, 217. (8) Spiess, H. W.; Sillescu, H. J . Mug. Reson. 1981, 42, 381. (9) Rice, D. M.; Wittebort, R. J.; Griffith, R. G.; Meirovitch, E.; Stimson, E. L . Meinwald, Y. G.; Freed, J. H.; Scheraga, H. A. J . Am. Chem. SOC. 1981:103, 7707. (10) Spiess, H. W. Developments in Oriented Polymers; Ward, I. M., Ed.; Applied Science: Barking, U.K., 1983; p 47. (1 1) Spiess, H. W. Colloid Polym. Sci. 1983, 261, 193. (12) Schwartz, L. J.; Meirovitch, E.; Ripmeester, J. A.; Freed, J. H. J . Phys. Chem. 1983,87, 4453. (13) Meirovitch, E.; Belsky, I.; Vega, S. J . Phys. Chem. 1984, 88, 1522. (14) Spiess, H. W. Adv. Polym. Sci. 1985, 66, 23. (15) Jelinksi, L. W. Annu. Reu. Muter. Sci. 1985, 15, 359. (16) Meirovitch, E.; Belsky, I.; Vega, S. Mol. Phys. 1985, 56, 1129. (17) Siminovich, D. J.; Raleigh, D. P.; Olejniczak, E. T.; Griffin, R. G. J . Chem. Phys. 1986,84, 2556. (18) Greenfield, M. S.; Ronemus, A,; Vold, R. L.; Vold, R. R.; Ellis, P. D.; Raidy, T. E. J . Mugn. Reson. 1987, 72, 89. (19) Wittebort, R. J.; Olejniczak, E. T.; Griffin, R. G. J. Chem. Phys. 1987, 86, 541 1. (20) Vega, A. J.; Luz, Z. J . Chem. Phys. 1987, 86, 1803.
0022-3654/89/2093-73 15$01.50/0 0 1989 American Chemical Society
7316
The Journal of Physical Chemistry, Vol. 93, No. 21, 1989
of partially deuterated dimethylammonium ions, (CD3)2NH2+and (CH3)2ND2+ions abbreviated to DMA-d6+, DMA-d2+, respectively, in (DMA-d6)2SnC&(DMA-d)$SnC&, and (DMA-d6)2TeC16 which have isomorphous crystal structures, in an attempt to explain the cationic motions taking place near room temperature. The presence of a new unknown cationic motion at room temperature in these complexes has been reported2' from studies of 'H N M R spin-lattice relaxation times, T I ,and second moment measurements. As a possible mode for this new motion, 180' flips of the cation about its pseudo-C2 axis was suggested, although the observed TI data could not be explained well by this process. At the same time, relaxation studies of 35ClNQR on these complexes revealed the onset of 90' rotational jumps of the bulky octahedral anions22-23 [SnC16]2- and [TeC1612-,about the Cl-M-Cl axes at unusually low temperatures (around 200 K), compared with similar complexes such as24(NH4)2SnC16and25(CH3NH3)2SnCb. The onset of this anionic motion at low temperatures is expected to have some relationship with the foregoing unknown cationic motion. To understand the relation between these motional processes of the cations and anions, it seemed to be important to determine the motional mode of the cation and its jump rate in the low-temperature range. Experimental Section The 2H N M R measurements were performed using a Bruker CXP-200 spectrometer at a Larmor frequency of 30.7 MHz, equipped with a temperature variable probe for experiments between 200 and 360 K. Absorption spectra were obtained by Fourier transformation of the echo signal observed by the phase alternating quadrupole echo m e t h ~ dconsisting , ~ ~ ~ ~of~four sets of a pair of n/2 pulses separated by variable intervals from 25 to 200 ps; a n/2 pulse width of 6 ps was employed. The samples were sealed in a glass ampule of 6 mm outer diameter and 20 mm length. The sample temperature was controlled by use of a Bruker VT- 1000 temperature controller. Partially deuterated polycrystalline samples of [(CD3)2NH212SnC16,[ ( C H ~ ) ~ N D Z I ~and S ~[(CD3)2NH&TeC16, C~~, prepared for the 'H N M R study already reported,2' were used in the present measurements. Line-Shape Simulation As mentioned earlier, detailed analysis of the 2H N M R line shapes can provide extensive information about the nature of various types of molecular motions in solids and the rates of those processes. The basic mathematical methods used for the line-shape analysis are given by Abragam' and Mehring.2 More recently, however, more elegant and sophisticated procedures have been described.8-20 Our simulations of the 2H spectra for the case of two-site jumps of the direction of the principal axes of the efg tensor were carried out in a manner similar to that discussed by Abragam' and Mehring.z Distorted spectra due to a finite interpulse spacing time were also simulated according to the method reported by Spiess and Sillescu.s In the two-site jump model employed, an equal population at each site was assumed. The peak intensities of all spectra were normalized and, hence, the intensity changes with different values of T were not considered. The effect of the pulse width on the spectra was neglected unless otherwise noted. The spectra were analyzed by comparison of the experimental spectra and those calculated theoretically by using a comprehensive . ~ ~adequacy computer program RJUMPF written by P r a t ~ m The of the results of the present calculations was confirmed by com(21) Ishida, H.; Ikeda, R.; Nakamura, D. Ber. Bunsen-Ges. Phys. Chem. 1984, 88, 546.
(22) Horiuchi, K.; Ikeda, R.; Nakamura, D. Ber. Bunsen-Ges. Phys. Chem. 1987, 91, 1351.
(23) Ishikawa, D.; Horiuchi, K.;Ikeda, R.;Nakamura, D. J. Mol. Srrucr., in press. (24) Dimitropoulos, C.; Pelzl, J. J . Mol. Srrucr. 1980, 58, 107. (25) Furukawa, Y.; Kiriyama, H.; Ikeda, R. Bull. Chem. SOL.Jpn. 1977, 50, 1927. (26) Demco, D. E.; VanHecke, P.; Waugh, J. S . J . Magn. Reson. 1974, 16, 461.
Ikeda et al.
d--
e-?
&
E
i----^--'
i-_I-
Fred (kHz) 40 Figure 1. 2H NMR spectra of [(CD3)2NH2]2TeC1, (left) and [(CD,),NH2I2SnCl6(right) observed by employing a pulse delay time of 25 ps; (a) 200 K, (b) 240 K, (c) 260 K, (d) 270 K, (e) 320 K; (A) 200 K, (B) 310 K, (C) 320 K, (D) 340 K, (E) 360 K. Each spectrum was accumulated 400 times with recycle delays of 0.5-5 s. -40
paring our spectra with those reported by earlier authors.*J9 The computer simulations of the spectra were performed with a HITAC S-820/80 supercomputer in the Computer Centre of the Institute for Molecular Science at Okazaki, Japan. Results and Discussion 1. 2H Quadrupole Coupling Constants (qcc) and Motional Modes ofthe Cations. The FT spectra of (DMA-d6)2SnC16and (DMA-d6)2TeC16observed at various temperatures are shown in Figure 1 . These spectra were recorded with a time interval T = 25 ps between the two n/2 pulses in the quadrupole echo measurements. Narrowing of the spectrum width observed around rmm temperature for both complexes clearly indicates the presence of a dynamic process averaging the efg at the 2H nuclei, which takes place with about the same frequency as the spectrum width. One of expected molecular motions in this cation is random reorientation of the CD3 group by 120' about its C3 axis. This motion was already studied in detail for fully protonated [(CH3),NH2]2SnC16, abbreviated hereafter to (DMA-h8)2SnC16and (DMA-h&Tecl6, by the 'H N M R technique.21 According to this study, the C3 reorientations of the CH3 groups in the cation are already excited at far below room temperature, and, hence, the efg at the 2H nuclei in a CD3 group is completely averaged by this C3 reorientation. The observed spectra at 200 K for both complexes shown in Figure 1 are considered to result from this averaging. Since these spectra at 200 K show a line shapeI5 typical for 7) = 0, we determined the qcc values from the observed spectra to be 52.0 f 0.2 and 49.5 f 0.2 kHz for the tin and tellurium complexes, respectively. When a C-D bond axis performs random reorientational jumps rapid enough among more than three directions with a symmetry higher than C3,the value of qcc decreases by a factor of (1/2)(3 cos2 8 - l ) , where 8 is the angle between the rotation axis and the C-D direction, and 7) = 0 if a static C-D group is a s s ~ m e d . ~ Then, the qcc value in a CD3 group is reduced to 1/3 of its original value under rapid reorientations about its C3 axis provided tetrahedral bond angles in the CD3 group are assumed. The evaluated qcc values (52.0 and 49.5 kHz for the tin and tellurium complexes, respectively) are quite reasonable if one compares these values with those for rigid CD3 groups which have been reported4 as 165-175 kHz. The narrowing of the spectra observed near room temperature indicates the onset of another motional process of the cation. The spectra observed at 360 K the (DMA-d&%Cl6, and at 320 K for (DMA-d6)2TeC16shown in Figure 1, can be considered to be narrowed mainly by this motion because there was no further decrease on increasing the temperature. Each of these spectra is a typical example of a system with a finite 7) value. The qcc
Structure and Dynamics of Dimethylammonium Ions
The Journal of Physical Chemistry, Vol. 93, No. 21, 1989 7317
Z
V (80)
I
(701 2e,delree
I601
Figure 3. Jump angle dependences of the asymmetry parameter 7 of the electric field gradient tensor (solid line) and reduction factor of the quadrupole coupling constant I$Qq,Yl/le2Qqoi (broken line) on the motional process (see ref 27). Angles given with, and without, parentheses provide the same values.
Y
Figure 2. Two site jumps of a CD, group in coordinate systems ( x , y ,
(X,V,Z)representing the principal axes of the electric field gradient tensors in the slow- and rapid-motion limits, respectively. CD, group jumps by an angle 28 about the Z axis and in the XZ plane. z ) and
and 7 values determined from the observed spectrum widths are 25.4 f 0.2 kHz and 0.70 f 0.01 for (DMA-d6)zSnC16 and 24.3 f 0.2 kHz and 0.63 f 0.01 for (DMA-d6)zTeC16, respectively. The most probable motion which averages the efg and provides such large 7 values is expected to be a two-site jump of the whole CD3group. This is because 7 usually vanishes when any rotational jump takes place among more than three equivalent sites, namely, if the rotational potential has a higher symmetry than C3. Since the observed spectra indicate that the two CD3 groups in a cation perform the same movement in this new motional process, we consider, hereafter, a single CD, group jumping between two sites separated by 20 in the coordinate system shown in Figure 2. Here the Z axis is along the bisector of the directions of the two N - C bonds before, and after, a jump, and the Y and X axes are perpendicular and parallel, respectively; to the plane made by these two N-C bonds. These axes become the principal axes of the 2H efg tensor in the limit of rapid two-site jumps. When this motion is slow enough, the principal axes ( x , y, z ) of the 2H quadrupole tensor, where the relationship lqLzl> lqxxl = Iqyylis assumed for the three principal components of the efg tensor, can be taken as shown in Figure 2. The N-C bond direction is along z axis because of the rapid CD3 group rotation about that bond. Since the observed value of 7 is almost zero before the onset of this jump, both the x and y axes can be taken to be any directions perpendicular to z axis so long as they are perpendicular to each other. The relationships among the three principal components of the efg tensor before, and after, the averaging of this jump are given by qxu = qxxcos2 0 + qrr sinZO 4w =
qyy
qZz = qxx sin2 0
+ qZ2cosz 0
(1)
In the present case, we can assume qxx = qyy;then q,y,y=
(1/2)q2,(3
COS'
0 - 1)
4w = -(1/2)qzz qzz = (1 /2)q2,(3 cos2 0
where we used Laplace equation, qxx show f r o m eq 2 t h a t 1q221 2
- 1)
+ qyy+ qrr = 0.
(2)
We can
I q d 2 Iqxd: 7
= 3 sin2 0/(3 cosz 0 - 1)
Iqd L 1qzz1 1 Iq,yd:
7
=3
lqd 1 Iq,yd 1 1qzz(: 7 = -3
COS
20
COS
Iqxd 2 I q d 2 Iqzzl: 7 = 3 cosz 0/(3 sin2 0 - 1)
26
0 5 0 I35.26' 35.26' I0 5 45' 45' I 0 I 54.74' 54.74' I0 I90'
(3)
9 ,, -30 ! L1 , ,) & I
-30
ii1iol~w
i i i ~li.i
Figure 4. Jump angle dependence of the 2Hspectra simulated for rapid two-site jumps. 28 = 124' (a), 120' (b), 116' (c), 112' (d), 108' (e), 104' (f), 100' (g), 96' (h). The value of $Qq was set equal to 43 kHz.
Figure 3 shows the relationshipz7 between 28 and 7 as well as the reduction factor of qcc, namely lsQqaYl/l$QqO1,where e2Qq, is the coupling constant in the fast exchange limit of the jump and sQqo is the 2Qq2, value partly averaged by lattice vibrations. Since these parameters shown in Figure 3 have a angular dependence symmetric with respect to 20 = 90°, jumps for angles of 20 and 180' - 20 result in the same spectra. In Figure 3, we can see that four different 20 values are acceptable for the observed value for 7 of 0.70 in (DMA-d6),SnC16 at 360 K, namely, 20 = 103.6 f 0.2' (or 76.4 f 0.2') and 116.8 f 0.2' (or 63.2 f 0.2'). The same holds for 7 = 0.63 f 0.1 in (DMA-d6)zTeC16satisfying 20 = 104.4' f 0.2' (or 75.6 f 0.2') and 119.0 f 0.2' or 61.0 f 0.2'. These jump angles can be determined accurately from the observed spectra, because we can see from the line-shape simulations that the spectra with different jump angles show quite different line shapes near the angles given above. Figure 4 shows an angle dependence of the simulated line shapes for various angles between 96' and 124' (and 84'-56' at the same time) to help clarify these differences. We cannot determine which jump angle among these four is the most acceptable for the present cases only from the line shapes in the slow, or fast exchange limit. More information can be derived from the analysis of the line shapes observed in the intermediate exchange region between these two limiting cases, which will be discussed in the following section. 2. Dynamic Effects Appearing in the FT Spectra. In the present study, the FT spectra observed were obtained from the quadrupole echo signals resulting from applying two r / 2 pulses.3b The line shapes of the powder spectra detected by this method are known to be strongly distorted by the large anisotropy of T2 caused by distribution of the orientations of crystallites with respect to the direction of the external magnetic field. Spiess and Sillescd have given a detailed theoretical treatment of this distortion and calculated the resulting dynamic spectra as a function of the jump rate, and the time interval ( T ) , between the pulses. Following these authors, we calculated line shapes shown in Figure 5 for T = 25 and 100 p s , and by changing the jump rate up to lo7 Hz. With the jump angle 28 is taken as 118' and qcc as 43 kHz, respectively, and the calculated spectra compared well with the observed ones, and we see that the spectra change shape remarkably with values (27) Sjoblom, R.;Tegenfeldt, J. Acta Chem. Scand. 1972, 26, 3068.
Ikeda et al.
7318 The Journal of Physical Chemistry, Vol. 93, No. 21, 1989 0
104
io5
107~z
106
__
---->
l--+==o
-40 Freq(kHz)
Figure 5. ZH spectra simulated for two-site jumps at jump frequencies of 0-10' Hz, and echo delay times 25 p s (upper) and 100 p s (lower). e2Q9 was set equal to 43 kHz.
20=116.8'
d 2 - 40
103.6'
_-d
L
, L
40
_
I
*
Figure 6. 2H spectra simulated for 28 = 116.8' and 103.6' in the intermediate exchange region. Jump rates: (a) 10 kHz, (b) 5 0 kHz, (c) 100 kHz, (d) 500 kHz. The values of e2Qq and the echo delay time were set equal to 43 kHz and 25 ps, respectively.
of the jump rates of lo4 - los Hz, where a strong dependency of the spectral shape on T is also obvious. Figure 6 presents spectra simulated for the two possible jump angles (26 = 103.6' and 116.8') for the tin complex, in the intermediate region of the jump rate values where the line shape shows a marked jump rate dependency. When the observed spectra shown in Figure l are compared with those simulated for the two different jump angles, it is evident that the observed spectra agree very well with those calculated for 26 = 116.8', but disagree when 6 = 103.6'. As for the remaining two possible angles, 116.8' and 63.2', it is difficult to decide which angle is acceptable from only the spectral simulations, because these two angles give rise to the same line shapes. The bond angle C N C in a DMA-h8 ion in (DMA-h&SnC16 has been shown28p29to be 115.9' and 116.9' from single-crystal X-ray diffraction studies. The fact that these bond angles agree well with one of the foregoing two jump angles indicates that the most probable model for the jump equation is a 180' flip of the cation about the bisector of the C-N-C skeleton. This model is highly acceptable because the X-ray diffraction studies reveal nondisordered positions of the carbon atoms in the crystalsZBwhich are consistent with the 180' flip model, but not with 63.2' jumps. We determined the jump rates of this 180' flip at various temperatures for both complexes by comparing the observed and the simulated spectra for different interpulse separation times T . Examples of the comparison carried out for (DMA-d6)&C16 are shown in Figure 7 . From these simulations, the qcc values corresponding to the rotating CD3 group about the C-N bond in the slow limit of the 180' flip are evaluated to be about 43 f 1 and 42 f 1 kHz, respectively, for the tin and tellurium complexes above 300 K. The fact that these qcc values are 1 5 1 8 % smaller than those determined at 200 K (52.0 and 49.5 kHz in the same order) indicates that averaging of the efg due to librations associated with the cations are enhanced with increasing temperature. In the IH TI studyz1on (DMA-hs)2TeC16,a shallow T I minimum was observed around 380 K a t a Larmor frequency of 20 MHz. The motion corresponding to this minimum can be attributed to 180' flips of the cation. It has been pointed out, however, that the observed T I minimum value (90 ms) is much larger than the theoretical value (38.0 ms) for this flip. This (28) Knop, 0.;Cameron, T. S.; James, M. A,; Falk,M.Can. J . Chem. 1983, 61, 1620. (29) Ben Ghozlen, M. H.; Daoud,A.; Bats, J. W . Acta Crystallogr. 1981, B37, 1415.
C
__
1
-
40 - 40 Figure 7. Comparison of observed (left) and simulated (right) line shapes of 2H spectra for [(CD3),NH2],SnC1,. (A) Spectra at 300 K for echo delay times of 25 p s (a), 100 p s (b), 200 p s (c). (B) Spectra a t 3 5 0 K for echo delay times of 25 p s (a), 50 p s (b), 100 ps (c). The simulations were calculated for jump rates of 15 kHz (A) and 200 Wz (B), and with a value of e2Qq = 43 kHz.
Figure 8. Temperature dependences of the 180' flip correlation times of dimethylammonium hexachlorostannate(1V) (a) and hexachlorotellurate(1V) (b). Correlation times T~ for (CD3)2NH2+ion (closed circle); correlation time for (CH3)2NH,+ ion determined by 'H NMR (broken line); 90' jump correlation time sClof complex anions (fine solid line); best fitted straight line to evaluate activation energies (bold solid line). disagreement can be explained by partial averaging of the magnetic dipolar interactions between the protons due to cationic librations with a large amplitude which are responsible for the marked decrease of the qcc values at high temperatures. The correlation times T D of the 180' flips of the cations can be derived from the jump frequency k , using the a relation34k = (1 / 2 ) 7 D - ' . Temperature dependences of T D determined by comparing the observed and simulated spectra are shown in Figure 8 for (DMA-d6)2SnC16and (DMA-d6)2TeC16. In Figure 8, we also show the temperature dependence of the 'H correlation times T~ for the 180' flip of @MA&)+ ions evaluated from 'H TI data observed a t high temperatures for (DMA-h8)2TeC16. The activation energy E, for the motion, defined by the relation
Structure and Dynamics of Dimethylammonium Ions
The Journal of Physical Chemistry, Vol. 93, No. 21, 1989 7319
TABLE I: Quadrupole Coupling Constants e3Qq/h, and Asymmetry Parameters q, of the Electric Field Gradient for ' H in the Limit of Slow and Rapid 180' Jumps, Jump Angles 28, and Activation Energies for the Cationic Flips in I(CDq),NHzl2MCL(M = Sn, Te) -.,
,
tl
28/deg EJkJ mol-'
0.70 f 0.01 116.8 f 0.2 45 f 1
0.63 f 0.01 119.0 f 0.2 38 f 1 (38Id
(47)d 'Values in the slow-motion limit. b q = 0 is assumed. cValuesin the rapid-motion limit. d E , for fully protonated cations. can be derived from the slope of T~ in Figure 8. The resulting E, values of 40 f 1 and 38 f 1 kJ mol-' for (DMA-d6)2TeC16 and (DMA-h6)2TeC16,respectively, are in good agreement. For the tin complex, the E, value of 45 kJ mol-' determined for the (DMA-d6)+ ions show good agreement with the value of 47 kJ mol-' for the (DMA-h8)+ ions obtained from proton TI measuremenk2' These E, values are summarized in Table I together with the other parameters obtained in the present study. The difference between the correlation times T~ and T~ seems to be explainable by the mass effect for this motion of the cations. it has been reported that 90' From chlorine NQR reorientational jumps of octahedral complex ions about the C1M-C1 axes in crystals of (DMA-h8)2SnC16and (DMA-h8)2TeC16 contribute markedly to chlorine quadrupolar relaxation times in the temperature range above 200 K. It has been pointed out22 that the reorientation of such bulky ions occurring at the low temperatures is quite unusual. From the analysis of the temperature dependence of the quadrupolar spin-lattice relaxation time Tlq, correlation times T~~ of the jump process for the octahedral anions given23by
were determined around 200 K. In Figure 8, we also show the temperature dependence of T~~ in comparison with the cationic parameters. We see that the time scales of the cationic 180' flips, and the anionic reorientations, are very close to each other, although effects originating from mass differences in (DMA-d,)' and (DMA-h8)+ ions cannot be neglected. Since the presence of hydrogen bonds between the cations and anions are reported from an X-ray diffraction study,28the present results suggest that the rotational motions of both ions may be coupled in the crystals. The onset of the reorientation of the complex ions observed at unusually low temperatures as compared with similar types of complexes, as mentioned above, seems to be connected with these coupled motions of the cations. It is reasonable to expect that (30) Horiuchi, K.; Ishida, K.; Nakamura, D. Bull. Chem. Soc. Jpn. 1985, 58,2590. (31) Hunt, M. J.; MacKay, A. L. J . Magn. Reson. 1974,IS,402. (32) Bloom, M.; Davis, J. H.; Valic, M. I. Can. J . Phys. 1980,58,1510. (33) Pratum, T.K.; Klein, M. J . Magn. Reson. 1989,81, 350. (34) Torchia, D. A,; Szabo, A. J . Magn. Reson. 1982, 49, 107.
FA,, , ,
,
100 Figure 9. Observed 2H spectra of [(CH3)2ND2]2SnC16 at 350 K (a). Simulated line shapes for jump frequency of 200 kHz and jump angles of 103.6O (b) and 116.8O (c). Simulated spectra include the effect from the finite pulse width (6 ps) employed in the experiment.32 The echo -100
FREO(KHZ1
delay time for all spectra is 25 ps. the motion of the light cation triggers the reorientation of the larger complex ions. To obtain more information about the motional process of the cation excited near room temperature, we performed measurements of the 2H quadrupolar echo spectra of [(CH3)2ND2]2SnC16 at 350 K. Figure 9a shows a spectrum observed for T = 25 p s , exhibiting a large asymmetry of efg tensor (7 = 0.70 f 0.01); this can be explained by the two-site jump model in conformity with the CD3 spectra discussed earlier. Four possible values for the jump angles 20 are also obtained from Figure 3 as 103.6 f 0.2' (or 76.4 f 0.2') and 116.8 f 0.2' (or 63.2 f 0.2'), where the angles in parentheses provide the same line shape as the previous value. Theoretical spectra shown in Figure 9b,c were simulated for these two jump angles using a jump frequency of 200 kHz determined from the CD3 spectra observed at the same temperature. These simulated spectra clearly show that the jump angle of 103.6' (or 76.4') can explain the observed spectrum. When the 180' flip model was applied for the motion of the cations, the D-N-D bond angle was found to be 103.6', whereas the other possibility of 76.4' can be excluded because the DD distance in an ND2 grou calculated from this angle is unreasonably short (about 1.29 by using 1.04 A for the N-H length) to explain magnetic dipolar interactions in the fully protonated system as observed by 'H NMR.21 Now, we can determine the bond angle in an ND2+ group of (DMA-d6)+ ion as 103.6', a quantity which has been difficult to obtain from other experiments.
8:
Acknowledgment. We thank the Natural Sciences and Engineering Research Council of Canada for grants to C.A.McD. to support this research. We are much indebted to Dr. T. K. Pratum of the Department of Chemistry, University of Washington, for providing us with his RJUMPF computer program for calculating the 2H line shapes. We are also grateful to Dr. A. L. Mackay in the Department of Physics, University of British Columbia, for help in peforming the simulations of the 2H line shapes. R.I. thanks the Yoshida Foundation for Science and Technology for the support of his travelling expenses to the University of British Columbia in 1987. Registry No. [(CH,)2NH2]2SnC16, 60607-43-4; [(CH3)zNH2]2TeC16, 91373-34-1.
