A solid-state deuterium NMR study of internal rotation in p-nitroaniline

JOURNAL

OF MAGNETIC

RESONANCE

91, 30 l-3 15 ( 199 1)

A Solid-State Deuterium NMR Study of Internal Rotation in p-Nitroaniline MICHAELA.

KENNEDY,

REGITZER.VOLD,ANDROBERTL.VOLD

Department of Chemistry, university of California, San Diego, La Jolla, California 92093 Received June 14, 1990 Deuterium quadrupole echo spectra have been obtained at 55.3 MHz and several temperatures between 26 and 133°C for samples of solid p-nitroaniline, deuterated either in the amino group or in the 2,6 positions of the aromatic ring. At all temperatures, the aromatic deuterons exhibit a simple rigid lattice powder pattern which is accurately simulated using a quadrupole coupling constant of 174 + 1 kHz and asymmetry parameter 0.06 + 0.02. Quadrupole echo spectra for the amino deuterons show features characteristic of 180” flips about the D-N-D bisector, and the activation energy for this motion is found to be 49 + 6 kJ/mol, with a rate k = (5.2 f 0.3) X 10’ SK’ at 133°C. For the amino deuterons, the dependence of echo amplitude and spectral lineshape on pulse spacing includes contributions from heteronuclear dipolar coupling as well as from internal rotation. This makes the extraction of accurate rates difficult, unless the lineshape data are supplemented by independent information. The spin-lattice relaxation rate, which is dominated by the flipping motion at high temperature, is very useful in this regard. o 1991 Academic Press. Inc.

Deuterium NMR has been used extensively to study molecular motion in simple crystalline solids (Z-6), polymers ( 7-l l), and inclusion compounds (12-19). The majority of these studies involve deuterium bonded to carbon or oxygen, and typical quadrupole coupling parameters for such systems are by now well characterized. Surprisingly, much less information is available about the quadrupole coupling parameters of deuterium bound to nitrogen, and only a few NMR studies of the dynamics of hydrogen-bonded amino groups have appeared (20, 21). The important role of hydrogen bonding in dictating crystal packing in solids (22) and in determining the structure and function of biological molecules provides impetus for further investigation in this area. In this paper, we report measurements of deuterium quadrupole echoes and spin-lattice relaxation in polycrystalline samples of p-nitroaniline, selectively deuterated in the amino group and in the aromatic ring. Deuterium quadrupole echo spectra of ND2 groups are less readily interpreted than those of CD2 groups. In both cases homonuclear deuteron-deuteron dipolar coupling provides a dephasing mechanism, but the effects of these as well as heteronuclear proton-deuteron dipolar interactions are usually not serious enough to substantially affect the determination of accurate rates of molecular motion. For NDz groups, however, the close proximity of 14N generally leads to dephasing of the 2H quadrupolar echoes at rates which can be competitive with those of interesting dynamic processes. The echo dephasing may simply be the result of static dipolar coupling (23, 24)) or 301

0022-2364191 $3.00 Copyright 0 1991 by Academic Press, Inc. All rights of reproduction in any form reserved.

302

KENNEDY,

VOLD,

AND

VOLD

a consequence of rapid 14N spin-lattice relaxation. Static dipolar dephasing was found to be a major contributor to deuteron T2 in urea-d, (25)) while 14N spin-lattice relaxation was observed to influence the quadrupole echo decays in urea clathrates ( 29). Extracting reliable rate information from quadrupole echo lineshapes in these situations is not a trivial task, and one purpose of the present investigation of p-nitroaniline is to determine in practice the feasibility of separately identifying contributions from motion-the exchange of the two amino deuterons via 180” flips-and dipolar dephasing. p-Nitroaniline has a high intrinsic hyperpolarizability (26)) which makes it a candidate for use in nonlinear optical materials. By itself p-nitroaniline crystallizes in a centrosymmetric form ( space group P2 I / n) , but when included in several host materials it shows high second-order harmonic generation (27, 28). Crystalline p-nitroaniline (mp 148°C) forms inter-molecularly hydrogen-bonded chains (29, 30)) such that one of the amino hydrogens interacts with both oxygens of the nitro group in a neighboring molecule (hydrogen bonding scheme R:( 4)) according to Etter et al. (31)) while the other amino hydrogen interacts with one oxygen in the neighboring chain. On the basis of anisotropic thermal parameters determined (29) for the C, N, and 0 atoms, the phenyl ring appears to be stationary, whereas there is significant torsional motion of the nitro group. A two-dimensional neutron diffraction study (32) of selectively deuterated p-nitroaniline is generally consistent with the X-ray structure (29,30), but the fractional coordinates of the oxygen atoms in the nitro group and neighboring Hbonded deuterons differ somewhat in the two studies. Unfortunately, full three-dimensional neutron diffraction data are not available. The hydrogen-bonded chains of p-nitroaniline lie in planes defined by the crystallographic a and c axes. These planes are separated (b direction) by 6.07 A. Pairs of chains, polarized in opposite directions, contain phenyl rings parallel to one another and separated by no more than 3.7-3.8 A. Since a phenyl ring is approximately 3.6 A thick (33) and its van der Waals radius of revolution about the 1,4 axis is about 3.2 A, steric considerations suggest that the phenyl rings should be stationary. On the other hand, the van der Waals radius of revolution of the amino group about the CN bond is only about 1.9 A, suggesting that it might be capable of rotating in the crystal. The diffraction data (29, 30) show that the amino group is nearly coplanar with the phenyl ring, and they rule out free rotation of either the amino or the nitro groups about their CN bonds. However, sudden jumps between equilibrium orientations are invisible to diffraction methods and this type of motion produces large, easily recognizable changes in deuterium NMR spectra. EXPERIMENTAL

METHODS

Two different deuterated derivatives of p-nitroaniline (Aldrich) were used in this study. Deuteration of the amino group was performed by recrystallization ( 3X ) of pnitroaniline from boiling D20. Selective deuteration in the aromatic ring was accomplished following a procedure described by Tichy and Prelsenik (32), whereby pnitroaniline (3.0 g) was dissolved in 50 ml of 5.5 N DC1 in D20 and heated to 100°C for 3 days. The product, 4-nitroaniline-N,N,2,6-d4, was recrystallized (3X) from boiling H20. This causes back-exchange of the amino protons, leaving only the C2 and Cs

INTERNAL

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IN SOLID p-NITROANILINE

303

ring carbons deuterated. Proton NMR spectra of the product, 4-nitroaniline-2,6-d, in CDC& solution showed that deuteration of the 2,6 positions was in excess of 95%. Deuterium quadrupole echo spectra were obtained at 55.4 MHz using a homebuilt spectrometer equipped with a wide-bore 360 MHz Oxford magnet. The temperature was maintained by blowing heated air over the sample and controlled with a Lakeshore Cryotronics DR9 1C controller. Data were accumulated using a Nicolet 2090 transient recorder and 1280 computer and transferred to a Celerity C 1200 minicomputer for processing and analysis. Quadrupole echo spectra were obtained using the usual 90,” -T--90; pulse sequence, with a 90” pulse width of 1.8 ps. The spin-lattice relaxation time T, was measured by prepending a 180” pulse and a variable delay to the quadrupole echo sequence. In both experiments the phases were cycled to suppress double-quantum artifacts as well as amplitude imbalance between the two quadrature channels. Typically, 4K data points were accumulated with a dwell time of 0.5 ps. Recycle delays varied from several seconds for high-temperature spectra to 1200 s for low-temperature spectra with large T, values. LINESHAPE

SIMULATIONS

Quadrupole echo spectra, partially narrowed by molecular motion in the guise of site-to-site jumps, were simulated by standard methods using the program MXQET, which is described elsewhere in detail ( 34). In essence, the calculations involve solving the equation MT,,

9, t) = exp(At)exp(A72)exp(A*71)M(O),

111 where M stands for the vector of site magnetizations, M( 0) is a vector composed of equilibrium site populations, A is a complex non-Hermitian matrix whose imaginary part contains site frequencies on the diagonal and whose real part is the kinetic matrix which defines the site-to-site jumps, 71 is the time between the two pulses of the quadrupole echo sequence, 72 is the time from the second pulse to the echo, and Fourier transformation of the sum of the components of M with respect to t yields the quadrupole echo spectrum. A similar procedure was used to simulate quadrupole echoes obtained in the inversion-recovery experiments, except that M( 0) in Eq. [ l] was replaced with a vector of site populations calculated according to the prescription of Wittebort and Szabo (35), using the same kinetic matrix as that defined above. In these calculations. a correction was made for finite pulse width of the inversion pulse. Specifically, the components Mj( 0) in Eq. [l] were replaced with J,fj(7) = 1 - dje-rlwJ), 121 where p and y are Eulerian angles which specify crystallite orientation, and the partially relaxed lineshape is obtained by summing over P and y. In Eq. [2], dj is given by (36)

d, =

COS OjCOS(

fCOjtw)

+

bj(

1 + bT)-“‘sin

Oj= Cdlt,( 1 + bf)“’

OjSiIl(

$Wjlw)

Dl

[3bl

304

KENNEDY,

VOLD,

AND VOLD

bj = fwj/‘wf.

[3cl

Here t, is the width of the inversion pulse, wI is the RF field strength, and wj is the imaginary part of the jth eigenvalue of the matrix A in Eq. [ 1] . Equation [ 31 was first derived by Vega and Pines (36) for the case of a single, nonexchanging deuteron (in which case our wj becomes their wq) . Here, we assume that the same formulation can be applied to each site in the case of multisite exchange. Normally, one adjusts the width of the inversion pulse so that w,t, = ?r, but we retain both w1 and t, in Eq. [ 31 to allow for the possibility of minor m&adjustments. The formulation presented here is the time-domain equivalent of that described by Wittebort et al. (37). Griffin and co-workers (38, 39) have further developed this formalism in studies of T, anisotropy in lipid alkyl chains, where they note that T, in Eq. [ 21 is orientation dependent and may include contributions not only from the same motion which affects the lineshape directly, but also from other processes with shorter correlation times. RESULTS AND DISCUSSION

Figure 1 shows deuterium quadrupole echo spectra of p-nitroaniline-2,6-d, obtained at three temperatures between 28 and 120°C. Faithful simulations of the spectra at all three temperatures were achieved using values of 174 kHz and 0.06 for the quadrupole coupling constant and asymmetry parameter, respectively. No change in the quadrupole coupling parameters was observed upon heating the sample from 28 to 120°C. T, for the aromatic deuterons was too long for convenient measurement-it was necessary to wait 1200 s between scans to obtain the spectrum at 28°C and even at 120°C the waiting time was 240 s. This combination of long T, and an essentially temperature-independent quadrupole coupling constant demonstrates the absence of any significant motion of the aromatic C-D bonds. The value found for e2qQ/ h , 174 + 1 kHz, is low compared with that in benzene, 183 * 1 kHz, probably due to the electron donating property of the neighboring amino group (40). Figure 2 shows that the quadrupole echo spectra of amino deuterons are strongly influenced by motion at elevated temperatures. The spectra obtained at 68°C and above are quite well reproduced by a simple two-site 180” jump model about an axis bisecting the amino D-N-D angle. The calculated spectra (dashed lines) shown in Fig. 2 were obtained by Fourier transformation of calculated echo decays, and we found it necessary to include both Gaussian and Lorentzian apodization in an effort to account for effects of unresolved dipolar coupling. Unfortunately, the effects of jump rate and apodization on the lineshape are not entirely independent. The intensity of the sharp features near the center of the spectra is both a good measure of the rate of motion and particularly sensitive to line broadening by apodization. For example, at 133°C an increase in intensity of one of the sharp features introduced by a 10% increase in the jump rate could be totally masked by the application of an additional 1 kHz line broadening. In order to resolve this ambiguity, it is necessary to appeal to additional experimental measurements. For reasons discussed below, the pulse spacing dependence of the quadrupole echo lineshapes is not suitable for this purpose, but T, inversion-recovery experiments are useful in this regard. Figure 3 shows experimental lineshapes obtained in an inversion-recovery experi-

INTERNAL

ROTATION

-200

-100

IN SOLID p-NITROANILINE

100

305

200

iiequenc; (kHz) FIG. 1. Solid-state deuterium quadrupole echo spectra of 4-nitroaniline-2,6-d. The experimental spectra were. obtained in 256 shots using a pulse spacing 7 = 40 PS, and a 1.0 kHz Gaussian and a 500.0 Hz Lorentzian apodization were applied prior to Fourier transformation. The simulated spectra, displayed superimposed on the experimental spectra, were calculated using e*qQ/h = 174 kHz and n = 0.06. Also, 2 kHz Gaussian and 1 kHz Lorentzian broadening was used in the simulations, the extra broadening being used to account for unresolved dipolar broadening to nearby spins. The match between simulated and experimental spectra is noticeably degraded if e’qQ/h is changed by more than about + 1 kHz or n is changed by more than +0.02.

ment at 133°C together with simulations based on Eqs. [ l]-[ 31 using an exchange rate chosen to yield the best overall match to the experimental spectra and a T, of 0.62 + 0.04 s. The best-fit value, k = (5.2 f 0.3) X lo5 SK’, was used to constrain the choice of jump rate used to simulate the quadrupole echo lineshape measured at 133°C. It was then possible to select a unique set of apodization parameters-2 kHz Gaussian and 1 kHz Lorentzian-to achieve good agreement with the experimental spectrum at 133°C. The slight mismatch in the center of the spectrum reflects the shortcoming of the simple model used in which dipolar effects are ignored. These same apodization parameters were then used for spectra obtained at temperatures between 80 and 133°C while slightly larger values were needed at lower temperatures: 3 kHz Gaussian and 1.5 kHz Lorentzian apodization were used for the 68°C spectrum and 4 kHz Gaussian and 2 kHz Lorentzian apodization yielded better agreement with

KENNEDY,

306

-is0

-1 50

VOLD,

AND VOLD

-50

150

250

Freauencv ikFl!i FIG. 2. Solid-state deuterium quadrupole echo spectra ofp-nitroaniline-l\r, N-d*. All experimental spectra were obtained with pulse spacing of 40 ps, and 2 kHz Gaussian and 1 kHz Lorentzian apodization were applied prior to Fourier transformation. The number of shots required for acceptable signal-to-noise ratio varied between 200 and 2000. Simulated spectra, displayed superimposed directly on the experimental spectra, were calculated using the program MXQET (34) as described in the text. The best-fit quadrupole coupling constants were found to decrease from 221 kHz at 26°C to 217 kHz at 68°C 215 kHz at 82°C 2 13 kHz at 112°C and 2 11 kHz at 133°C. All spectra are plotted with the same height. Best-fit rates for two-site 180” flips are noted to the right of each spectrum.

the 26°C spectrum. The best fit values of k are indicated in Fig. 2, and an Arrhenius plot of the rates (see Fig. 4) yields an activation energy E, = 49 + 6 kJ/mol for the 180” jump process. The poorer simulation of the spectrum at 26°C is reflected in the much higher error bar assigned to this data point. Since the two amino protons in p-nitroaniline are crystallographically distinct (2931), they may have different quadrupole coupling constants. Any such difference would be averaged out in high-temperature spectra, but should in principle be detectable at room temperature, where the flipping rate is no larger than about 4000 SK’. Unfortunately, 14N-2H dipolar interactions limit the resolution of the 26°C spectrum shown in Fig. 2, but we can nevertheless conclude that quadrupole coupling constants for the two amino deuterons do not differ by more than 1 or 2 kHz. We therefore

INTERNAL

ROTATION

IN SOLID p-NITROANILINE

307

Calculated

Experimental

e

360ms

h

180 ms

-250

-125 0 125 Frequency (kHz)

250

-250

-125 0 125 Frequency (kHz)

250

FIG. 3. Inversion-recovery spectra of p-nitroaniline-N,N-dr at 133°C obtained in 512 scans using an inversion pulse width of 3&s and quadrupole echo detection. T, = 0.62 + 0.03 s was determined at several points on the lineshape as well as at the echo maximum. Simulated lineshapes were obtained using Eqs. [l]-[ 31 as described in the text, with a rate k = 5.2 X 10’ SK’. Additional simulations carried out for different values of k indicate that noticeably poorer fits are obtained if k is changed by more than -to. 1 X 10’ s-’ . This uncertainty is approximately three times smaller than that obtained from quadrupole echo lineshape analysis at the same temperature.

assumed for purposes of lineshape simulation that both deuterons in the ND2 group have the same quadrupole coupling constant. Initially, efforts to match simulated lineshapes to the experimental ones in Fig. 2 were carried out using a temperature-independent value of the quadrupole coupling constant, chosen to best match the 26°C spectrum. It was then found that for any combination of rate and apodization parameters which fitted the central sharp features at high temperatures, the separation between broad outer features in the simulated spectra was too large. To achieve the good agreement between simulation and experiment shown in Fig. 2, it was necessary to use progressively smaller quadrupole coupling constants at higher temperatures. As indicated in the caption of Fig. 2, best-fit values of the quadrupole coupling constant decrease from 221 ? 1 kHz at 26°C to 211 + 1 kHz at 133°C. This decrease is most easily rationalized in terms of an increasing

308

KENNEDY,

-I

2.4

l

I

2.6

VOLD,

I

1

AND VOLD

I

2.8

I

3.0

I

I

1

3.2

I.

3.4

(1 O3 K-' ) FIG. 4. Arrhenius plot of exchange rates for the 180” flipping ofthe deuterated amino group in p-nitroanilineN, N-d*. The error bars represent the range of rates at each temperature which yielded visually acceptable fits between simulated and experimental lineshapes as illustrated in Fig. 2. The open points were obtained from analysis of quadrupole echo lineshapes and the solid point at 133°C from a T, inversion-recovery measurement.

amplitude of restricted, fast libration of the N-D bonds about their equilibrium orientations. Assuming that the in-plane and out-of-plane torsional modes of this libration can be represented as uniform, diffusive wobbling in a cone of half-angle &, the quadrupole coupling constant (e’qQ/ h) is reduced according to ( e2qQ/h)

= 4 ( e2qQ/h&os

OO(1 + cos &),

[41

where ( e2qQ/ h )o is an unaveraged quadrupole coupling constant. The value of this latter parameter is not known. However, if one adopts a value of 5” for &, at 26°C (this small value is supported by the very long *H 7’, ), then the measured splitting at 26°C implies that ( e2qQ/h)o = 223 kHz, and the drop to 2 11 kHz at 133°C corresponds to increasing the cone angle to 15.5”. Alternatively, if it is simply assumed that no libration occurs at room temperature, then the 10 kHz decrease in quadrupole splitting corresponds to a librational amplitude of 14” at 133°C. While these numbers should

INTERNAL

ROTATION

IN

SOLID

p-NITROANILINE

309

not be taken too literally, they do provide a reasonable estimate of the amplitude of fast libration at the bottom of the potential wells which define the site orientations. The peak separation of the sharp inner features of spectra simulated with rates above 5 X lo5 SK’ was found to be exquisitely sensitive to the time-independent angle PObetween the principal deuteron field gradient and the flipping axis. Thus by matching simulated to experimental spectra we obtain PO= 59.5 + 0.1’. If it is assumed that the field gradient lies along the N-D bond direction, this corresponds to a D-N-D bond angle 2& = 119”, which is somewhat larger than the value 112 + 5” deduced from X-ray diffraction patterns (29). The discrepancy could be due to the fact that the principal component of the deuterium electric field gradient tensor does not lie exactly along the N-D bond, or could simply be due to the large uncertainties typically associated with X-ray determination of proton positions. The activation energy, E, = 49 ? 6 kJ/mol, determined for the internal rotation of the p-nitroaniline amino group falls in the range observed for amides and other compounds with a C-N bond with partial double-bond character (41) and is slightly higher than that expected for aromatic amines with electronegative substituents (4244). The barrier in p-nitroaniline, or in N,N-dimethylaniline, cannot be obtained in solution by traditional NMR lineshape methods since the molecules are symmetric and the exchange leaves the spectrum unchanged. The barrier in 4-nitro-N-methylaniline, AGS = 46 kJ/mol in acetone solution at -48°C (42), is, however, expected to be similar and falls within experimental error of the value reported here for pnitroaniline. One might expect in going from the bulky -NHCH, group to the less sterically hindered -NH2 group that the activation energy might be smaller. However, for solid p-nitroaniline, the similar activation energy most likely reflects a compensating effect of the intermolecular hydrogen bonding, perhaps in conjunction with an increase in the double-bond character of the amino C-N bond. X-ray diffraction data (29, 30) show that the nitro group undergoes torsional oscillations of amplitude 14” about its CN bond. Our analysis of the temperature dependence of the amino deuteron quadrupole coupling constant yields a similar number for oscillation of the ND2 group. This does not, of course, imply that the two motions are in any sense concerted. It is not known whether the nitro group is undergoing 180’ flips, but on the basis of steric considerations one would argue that any such motion should be slow. “0 NMR spectra would reveal the extent of internal rotation of the nitro group, but concerted rotations of the amino and the nitro groups cannot be demonstrated by such measurements. EFFECTS

OF

DEUTERIUM-NITROGEN

DIPOLAR

INTERACTIONS

Figure 5a shows experimental quadrupole echo spectra for the amino deuterons obtained at several pulse spacings at 133°C plotted on the same, absolute intensity scale. It is apparent that all parts of the spectrum decay at the same rate-there is no significant anisotropy of T2. An anisotropy in T2 is more readily observed in the simulated spectra shown in Fig. 5b. These spectra were calculated using an exchange rate k = 5.2 X lo5 s-’ , which reproduced the lineshape obtained with a pulse spacing r = 40 ps. The perpendicular edges of the simulated spectra are seen to decay more

310

KENNEDY,

VOLD,

AND VOLD

b

a 320 us &;I':

260 us A1111

-200

ktizO

200 -200

ktizO

200

FIG. 5. Quadrupole echo spectra ofp-nitroaniline-NJ’-& (a) obtained at 133°C as a function of spacing 27 between the first pulse and the top of the echo. The theoretical spectra (b) were calculated using a model with 180” flips only, at a rate k = 5.2 X IO5 s-l. All spectra were obtained using 512 scans.

slowly than other parts of the spectrum, and the overall decay is considerably slower than that observed experimentally. The discrepancy between experimental and calculated quadrupole echo decay rates is further illustrated in Fig. 6, where we plot total echo intensity versus pulse spacing. A least-squares fit (solid line) of measured echo amplitudes to a single exponential yields R2 = 1 / T2 = 4500 + 400 SK’. Also shown in Fig. 6 (dashed line) is the echo decay calculated for two-site 180” flips, with a jump rate k = 5.2 X lo5 s-‘. Clearly, this motional process cannot account for the dependence of echo amplitude and lineshape on pulse spacing, even though it does suffice to explain the temperature dependence of lineshapes obtained with short pulse spacing. Specifically, for pulse spacings longer than about 50 PS,an additional dephasing mechanism shortens the echo decay and affects the quadrupole echo lineshape.

INTERNAL

ROTATION

o.oit, I 0

I

200

311

IN SOLID p-NITROANILINE

I

I

400

I

/

600

I

I

800

I

21: (us) FIG. 6. Quadrupole echo amplitudes of p-nitroaniline-N,N-& obtained at 133°C as a function of pulse spacing 27. The circles are experimental data, and the solid line represents the least-squares best fit to the data. The solid line represents T, = 220 + 25 PS.The dashed curve is an echo decay calculated for 180” flips with k = 5.2 X lo5 s-‘.

At first glance, this situation is reminiscent of the spectra reported by Heaton et al. ( 19) for urea deuterons in urea-& at 30°C. In that system, however, the rate of motion is low at room temperature (45) and the echo decay was lightly modulated as a consequence of static *H- 14N dipolar interactions. In p-nitroaniline at 133” this interaction is certainly reduced by virtue of the 180” flips and then further averaged by 14N scalar relaxation. This “dipolar relaxation of the second kind” (to paraphrase Abragam (46)) has been observed previously in powder (25) and single-crystal (47) samples of alkane/ deuterated urea inclusion compounds and in proton single-crystal spectra of transdiiodoethylene (48). By analogy with calculations (46, 49, 50) for the analogous “scalar relaxation of the second kind,” it can be shown that the deuterium transverse relaxation rate R2( *H) can be expressed as a sum of the direct motional contribution R2( exch ) and a dipolar dephasing term: R2(2H) = R2(exch) + y

(D)*,(w’

+ 2W*).

151

312

KENNEDY,

VOLD,

AND

VOLD

Here IV, and IV’, are single- and double-quantum transition probabilities for i4N quadrupolar spin-lattice relaxation (R IN = IV, + 2W2), and D = -yDyNh/r& is the *H- 14N dipolar coup lm ’ g constant. For a 1 A N-D bond length, D = 1332 Hz. In the present case, the dipolar coupling should be averaged over the fast (k = 5.2 X lo5 SK’) flipping motion, hence the angular brackets on D in Eq. [ 5 1. Since the N-D bond makesanangle~0=59.5”withtheflippingaxis,(D)= f(3cos2(59.5)l)D= 151 Hz. Equation [ 51 is valid only when R iN & 27r( 0); otherwise a more complicated treatment is needed (47). If RIN is on the order of 1500 s-l the second term in Eq. [ 5 ] amounts to 1600 s-’ , which is comparable in magnitude to the first term. Equation [ 51 is valid for a single crystallite in a powder sample, and the powder lineshape is obtained by summing spectra over all crystallite orientations specified by Eulerian angles p and y. The first term in Eq. [ 5 1, R2( exch), depends on both p and y even in simple caseswhere the transition frequency associated with a given isochromat depends on p alone (51) . In the present case, with a nonnegligible deuterium asymmetry parameter, analytic expressions for this dependence are too complicated to be of much use. However, as noted above, spectra calculated with different pulse spacings show that in general for two-site 180” flips, the perpendicular edges of the powder pattern relax more slowly than the center and outer parts. Apparently, this T2 anisotropy is compensated by anisotropy of the opposite sign arising from the second term in Eq. 151. To see how this might happen, we first note that if the electric field gradient tensor at the 14N nucleus has all its principal axes coincident with the flipping frame, then 180” flips will leave this tensor unchanged and produce no 14N relaxation. In the crystal, of course, the field gradient tensor is not constrained to the flipping frame by symmetry. Furthermore, the X-ray data for p-nitroaniline (30) indicate that the planes defined by the amino group and the phenyl ring are not coplanar, the deviation being about 7’. Detailed calculations (47)) too lengthy to reproduce here, show that with a distortion angle of 7” one expects an orientation-independent RIN of a few hundred SK’. Of course, relaxation of 14N can also occur by virtue of rapid, but restricted, librational motion in the bottom of the potential well whose barrier determines the flip rate. At any rate, we can conclude that the major orientation dependence of the second term in Eq. [ 51 arises from that of(D)‘, which varies as [ 4 (3 cos*p - 1 )] *, where p is the angle between the flipping axis and the static field. Thus we expect to observe the smallest contributions near the middle of the *H lineshape and larger contributions at the perpendicular edges-just the opposite of the first term in Eq. E51. While there is little doubt that dipolar dephasing contributes to the echo decay at long pulse spacings, one is left with the uncomfortable feeling that neglect of this phenomenon during analysis of the data in Fig. 2 may have introduced systematic error into the determination of the jump rates. Because of dipolar dephasing, these rates could not be checked against experimental spectra obtained as a function of pulse spacing. However, dipolar dephasing is not expected to be a major contributor to quadrupole echo lineshapes obtained at short pulse spacings. Furthermore, the fact that T, inversion-recovery experiments at 133°C yield a jump rate which is close to that obtained by analyzing the lineshape for a 40 pts pulse spacing indicates that the lineshape analysis is not grossly in error.

INTERNAL

ROTATION

IN

SOLID

313

p-NITROANILINE

The inversion-recovery lineshapes in Fig. 3 suggest that the spin-lattice relaxation rates are anisotropic in p-nitroaniline. However, it is worth noting that spectral lineshapes in the vicinity of the “null” can be deceptive-even with a composite inversion pulse outer parts of the line are less perfectly inverted than those in the middle. In order to see whether in fact a T, anisotropy is present, it is absolutely essential to measure full recovery curves for different points on the lineshape and to not just restrict attention to the lineshapes near the null. Remarkably, we observe 110 T, anisotropy either in the experimental lineshapes or in the simulations. This is unexpected because analytic expressions for relaxation via two-site jumps with (47) or without (52) quadrupolar asymmetry include a strong dependence of T1 on both the Euler angles 0 and y needed to define crystallite orientation. Hiyama et al. (21) first noted this anomaly in their study of p-fluorophenylalanine and ascribed it to spin diffusion. This cannot be correct, because spin diffusion is not incorporated in simulations like those shown in Fig. 6, and yet the orientation dependence of T1 is lost when Eq. [ 2] is summed over p and y. In principle, this leads to a multiexponential decay at each point on the lineshape, but in practice the superposition of many exponentials masks the anisotropy. We have “measured’ T1 for several points on partially relaxed lineshapes calculated using Eqs. [ l]-[ 31, and the value appears to be orientation independent. Hiyama al. (22) and Rice et al. (6) have averaged an exact expression (52) for T, due to two-site flips over crystallite orientations, obtaining the result et

1/T, = R, = ~k(wQ/00)2sin22&,

[cl

where k is the flipping rate, = i( e2qQ/ h), w. is the deuterium Lannor frequency, and POis the angle between the C-D bond and the flipping axis. This relation is valid only when k 4 as well as k < wo, but in this region it provides a convenient and accurate way to extract exchange rates for two-site flips from experimental T, measurements. However, in the intermediate exchange regime < k < wo), Eq. [6] breaks down and would lead to, in the present case, a 20% error in the estimate of the k. wQ

up

(wQ

CONCLUSIONS

At temperatures below 133°C the phenyl ring in solid p-nitroaniline undergoes no motion detectable by deuterium NMR spectroscopy. In the same temperature range the amino group of p-nitroaniline-N&V-& undergoes 180” flips about the CN bond, with an activation energy E, = 49 f 6 kJ/mol and k = (5.2 +- 0.3) X lo5 s-’ at 133°C. Motion on this time scale can be accurately determined by analysis of deuterium quadrupole echo lineshapes, supplemented by TI inversion-recovery experiments to resolve ambiguities in the choice of jump rate and apodization parameters. The barrier to 180” flips is higher than that expected from solution studies of related aromatic amines, suggesting that intermolecular hydrogen bonding in solids is a factor determining internal rotation rates. Studies of such processes in the different environments encountered in solid inclusion compounds might consequently be expected to yield valuable information about the nature of intermolecular potentials. The quadrupole echo decay rate for most ND2 groups in solids is strongly affected by “dipolar relaxation of the second kind,” a process in which *H-14N dipolar coupling

314

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VOLD,

AND

VOLD

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