Anisotropy of the chemical shift tensor for solid nitrogen

JOURNAL

OF MAGNETIC

RESONANCE

27,23-28

(1977)

Anisotropy of the Chemical Shift Tensor for Solid Nitrogen* L. M . ISHOLt AND T. A. SCOTT Department of Physics, University of Florida, Gainesville, Florida 32611 Received December 10, 1976 The chemical shift anisotropy of the nitrogen molecule in solid nitrogen at 4.2 K has been measured by lJN NMR of a sample enriched to 99.5% r5N. The NMR powder pattern spectrum consists of a Pake doublet, due to the intramolecular dipolar interaction, superposed on the chemical shift. The spectrum was studied as a function of magnetic field and it is pointed out that the reversal of one-half of the Pake doublet, which occurs with increasing field, provides a simple and sensitive way to measure the chemical shift anisotropy. Computer simulation of the lineshapeyields (a,, - 0,) = 520 & 20 ppm, as averaged by zero-point motion in the crystal. The chemical shift anisotropy of a static molecule is given by (q - o,)/% where r, the orientational order parameter, has the value 0.866 k 0.009 at 0 K for lSN,. The static result is o,, - OIL= 603 + 28 ppm, which is in good agreement with an estimated value based on a molecular beam measurement of the spin-rotational interaction and ab initio calculations. INTRODUCTION

The study of magnetic shieldingin m o leculeshas long been one of the most important applications of magnetic resonance.A recent review of the theoretical and experimental status of the field has been given by Appleman and Dailey (1). Until the advent of various coherent averaging techniquesand high-magnetic-fieldsolenoidspractically all experimental research was restricted to the liquid and gaseousstates where only the isotropic shielding parameter may be measured.Even now, comparatively few solidstate chemical shift tensors have been determined and some of the most conspicuous absencesare systems containing small m o lecules,which, of course, are precisely those that are most tractable for ab initio theoretical calculations. In this paper we report a measurementof the chemical shift anisotropy for 15N,obtained from the NMR powderpattern lineshape at low temperature. Although there have been several extensive theoretical calculations of the shielding tensor for nitrogen (2, .?), the only published experimentaldata are from a m o lecular b e a m measurement(4,5) of the spin rotational constant, from which the isotropic chemical shift may be deducedby making use of a theoretical relationship connectingthe rotational constant and the paramagneticpart of the chemical shift. EXPERIMENTAL

The sample, which was the same one used in a previously reported (6) relaxation study of solid and liquid nitrogen, contained 99.5% 15Nand 0.5% i4N. Practically all * Research performed with support from the National Science Foundation under Grants DMR7302565AOl and DMR75-20161 t Presently at Naval Coastal Systems Laboratory, Panama City, Fla. 32401. Copyright @ 1971 by Academic Press, Inc. 23

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ISSN 0022.2364

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SCOT-I

the i4N combined with 15N to form isotopically mixed molecules, leaving 99% of the molecules as i5N,. For the relaxation study 0, impurity concentration had been reduced to about 1 ppm by passing the gas through an Oxisorb molecular sieve (7); however, the spin-lattice relaxation time at 4.2 K was then longer than 7 hours, making a lineshape study by cw techniques inconvenient. Hence about 0.1% 0, was deliberately added to the sample to shorten the relaxation time. Comparison between cw spectra of the sample with and without the 0, indicated slight additional inhomogenous broadening of the former, but this had practically no effect on the accuracy of the chemical shift determination. All spectra were recorded at 4.2 K using a conventional cw spectrometer with a Robinson oscillator (8). Magnetic field sweep and modulation were employed. First derivatives of the lineshape were accumulated in a Nicolet model 1072 digital signal averager, and the integration capability of this instrument was employed to obtain absorption spectra. Simulation of the spectra was performed on a PDP-8/e computer interfaced to the Nicolet. Experimental and theoretical curves were plotted on an X-Y recorder for careful comparison. DISCUSSION

Nitrogen at its equilibrium vapor pressure crystallizes in two structures depending upon temperature. For T < 35.6 K the structure is simple cubic (a-N,), while for 35.6 < T < 63.14 K (triple point) the structure is hexagonal close packed (8-N,). A comprehensive review of experimental and theoretical research on solid and liquid nitrogen has been given by Scott (9). The effective chemical shift at the 15Nnucleus in an N, molecule oriented at an angle 19with respect to an applied magnetic field H, is given by the well-known equation Ueff= jf(U,,- a,)(3

COS’

0 - l) + UisoT

where (T,,and uI are the principal components of the chemical shift tensor parallel and orthogonal to the molecular axis, respectively, and uisO= +(a,,+ 2u,) is the isotropic shift. The effective chemical shift expressedby Eq. 111must be averaged appropriately over molecular motion in the solid. The molecular motion is markedly different in the two crystalline phases of nitrogen. In the /I phase it is well established (9) from NMR and Raman spectroscopy that the molecules execute rapid reorientational jumps while maintaining an angle of approximately 54.7O with respect to the crystal c axis in accordance with the form of the crystal potential, which has sixfold minima in azimuthal angle at this polar orientation. Rapid reorientation of the molecule at an angle y about a crystal axis which is fixed at an angle 0, with respect to H, produces a motionally averagedeffective chemical shift given by (%T> = 3h - a,) (3 co9 8, - l)i(3 cos*y - 1) + uisO.

[21

By coincidence, the angle y in p nitrogen is very near the magic angle y = arccos (l/3 l’*) and hence (a,& = ulsO.Thus a single narrow line is observed in this phase. However, on transforming to the a phase the molecules take up orientations along the four-body diagonals of the cube and execute rapid librations about these preferred directions. The NMR spectrum consists of a combined Pake doublet and chemical shift anisotropy powder pattern, both of which are averaged by the molecular librations. Owing to the

CHEMICAL

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OF NITROGEN

fortuitous circumstances that the intermolecular dipolar interaction is approximately an order of magnitude smaller than either the intramolecular dipolar interaction or the chemical shift anisotropy, the structure is well defined. In fact, the field inhomogeneity of our electromagnet was the primary source of broadening at high fields. Motional averaging of the chemical shift due to the librational normal modes of the crystal may be treated theoretically in the same way as averaging of the electric field gradient tensor in nuclear quadrupole resonance (10). This averaging factor, appropriately called the orientational order parameter, has been studied in great detail for a nitrogen (9) and at 0 K has the value 0.863 + 0.008 for 14N2and 0.866 f 0.009 for lsN,.

a;, -

a;, I 0

v

20! FIG. 1. Evolution of an unbroadened Pake doublet powder pattern produced by chemical shift anisotropy as the magnetic field increases. Arrows indicate direction and tensor component governing frequency displacement of the edges of the spectrum when u,, > 0, uI < 0. The component between -cr and 2a collapses to zero width and infinite amplitude when oil - a,)yH~2x = 3o, where a = 3y2fi/8nr3 represents the dipolar interaction between the two nuclei. -EIT

-CY

a

The type of spectrum observed for cr nitrogen has been discussedtheoretically for a rigid lattice by VanderHart and Gutowsky (II) and has been observed in solid fluorine by O’Reilly et al. (12), who reported their measurements without estimation of the motional correction. An interesting feature of this spectrum appears not to have been emphasized,however. It is well known that the functional form of the axially symmetric chemical shift powder pattern is identical with one-half of a Pake doublet, the other half of the doublet being reversed.Consequently, as the magnetic field is increased from zero the lineshape evolves as shown in Fig. 1. The half of the Pake doublet which is properly phased with respect to the chemical shift powder pattern simply widens without change of shape while the other half contracts at the same rate and eventually reversesitself. At the crossover field H,, the linewidth is lim ited only by the intermolecular dipolar interaction, which for nitrogen is less than 100 Hz. Hence, observation of either the linewidth of the contracting component or the relative heights of the two peaks of the doublet as a function of magnetic field in the vicinity of H,,, can be a simple and sensitive way of measuring the chemical shift anisotropy provided the available magnetic field strength is adequateto achieve the crossover condition Ho, = 9d2y(o,,

- GI),

[31

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where d = hyf,/2m3 is the intramolecular dipolar interaction parameter and yIs is the magnetogyric ratio. We have used both this method and computer simulation of the lineshapeto deduce c,, - uI for nitrogen.

Ijo=

G

I kHz

FIG. 2. NMR powder patterns from solid 15N, at 4.2 K for three values of magnetic field. Experimental spectra are shown as solid curves; computer simulation is indicated by dashed line where deviation from the experimental data occurs. The frequency scale is different for the three spectra, as indicated.

The lsN, lineshape was observed at 4.2 K as a function of magnetic field HO between 625 and 9000 G. Selectedspectra at three representativevalues of H,, near the ends and m iddle of this range are shown in Fig. 2.

CHEMICAL

SHIFT ANISOTROPY OF NITROGEN

21

Since the dipolar interaction has been measured for 14N2at 4.2 K to be hyi4/2nr3 = 405 + 5 Hz (13), one may calculate d for 15N, using the magnetic moment ratio (14) and isotopic mass correction to the order parameter. The result is d = 600 k 8 Hz. Alternatively, d may be determined directly in this work from a computer fit to the lowfield spectra where the Pake doublet is the dominant feature. Using this procedure we were gratified to find d = 600 ? 5 Hz. The exact agreementconfirms the accuracy and self-consistency of the earlier data. More importantly, the new data provide the most accurate determination to date of the intramolecular nuclear separation in the solid, which has been difficult to measurewith high accuracy (9). This distance is found to be 1.101 f 0.003 A. The value of magnetic field H, that collapses the low-frequency peak of the Pake doublet was deduced to be 8200 + 200 G. Application of Eq. [31 yields (a,, - a,) = 510 ? 20 ppm, where the brackets indicate that this number is averaged by the zeropoint motion. Since computer simulation takes advantage of information in the entire spectrum, it should in general provide the most accurate determination of the chemical shift anisotropy, provided the experimental line is not affected by unknown factors that may introduce systematic errors. The theoretical unbroadened powder pattern was convoluted with a lineshape function involving an adjustable m ixture of Gaussian and Lorentzian. Good fits were obtained with a pure Gaussian lineshape;however, the fits at higher magnetic fields were improved slightly by adding up to 50% Lorentzian. Furthermore, the linewidth of the broadening function was found to increase with Ho from about 93 Hz at 95 1 G to 160 Hz at 9 kG. This increase was due primarily to field inhomogeneity of the electromagnet, but may also be attributed in part to inhomogenous broadening caused by the 0.1% 0, impurity added to shorten Ti. However, the magnitude of the chemical shift anisotropy deduced from the fit is relatively insensitive to linewidth adjustments. The match of experimental and theoretical curves, as shown in Fig. 2, is excellent, particularly at higher fields. At low fields a disparity exists in the center of the Pake doublet which may be a genuine feature deserving additional attention; but because of poor signal-to-noise ratio and other difficulties associated with operating the spectrometer at this very low frequency (0.4 MHz), it seems imprudent to speculate on the origin without further study. The mean value of the chemical shift anisotropy obtained from the computer fits is (a,, - a,) = 520 + 20 ppm, in good agreementwith the crossover calculation. To obtain the chemical shift anisotropy for a static molecule the above result should be divided by the orientational order parameter. In principle, corrections should be made also for translational modes and the stretching vibration. However, there is no simple procedure for doing this. In the case of nuclear quadrupole resonance of 14N, it has been demonstrated (13) that these vibrations have a practically negligible effect on the electric field gradient at the nucleus, and it is reasonable to suppose that this is also true for the chemical shift. Applying the librational correction gives o,, - cI = 603 ? 28 ppm. This result is in good agreement with the estimated value 657 + 20 reported in Ref. (I), based on molecular beam measurements of the spin-rotational interaction and theoretical calculations. The agreement implies therefore that the theoretical extrapolations used by the authors in relating the two quantities are accurate. Moreover, since the molecular beam measurement was made on free molecules and ours on a solid, it is evident that the chemical shift is affected very little by condensation.

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We should mention for the record that i5N NMR experiments were also performed on the m ixed molecule i4N-15N in a sample containing that species in high concentration. In this case the intramolecular dipolar interaction varies with H,, as the Zeeman Hamiltonian competes with the large quadrupolar interaction experienced by 14N.A theoretical treatment of the resulting triplet spectrum for a dipolar spin-$nucleus coupled to a quadrupolar spin-l nucleus has been given by Parker (15). The 14N-15N molecule provides perhaps the best example of this situation, but with the added presence of chemical shift anisotropy. Apart from being an interesting experimental exercise in quantum mechanics, however, the additional complexity of the 14NJ5N spectra as compared with the 15N, spectra renders them less useful for accurate determination of u,, - a,; therefore, these data will not be presented. ACKNOWLEDGMENTS The useful advice and comments of our colleagues, J. R. Brookeman, P. C. Canepa, E. Fukushima, and A. V. Gibson are gratefully acknowledged. REFERENCES 1. B. R. APPLEMANAND B. P. DAILEY, in “Advances in Magnetic Resonance” (J. S. Waugh, ed.), Vol. 7, p. 23 1, Academic Press, New York, 1974. 2. H. J. KOHLERAND M. KARPLUS,J. Chem. Phys. 41,1259 (1964). 3. E. A. LAWS, R. M. STEVENS,AND W. N. LIPSCOMB,J. Chem. Phys. 54,4269 (1971). 4. M. R. BAKER,C. H. ANDERSON,AND N. F. RAMSEY,Phys. Rev. 133,Al533 (1964). 5. S. I. CHAN, M. R. BAKER, and N. F. RAMSEY, Phys. Rev. 136,Al224 (1964). 6. L. M. ISHOLAND T. A. SCOTT,J. Magn. Resonance 23,313 (1976). 7. Commercial product, available from MG Scientific, 1100 Harrison Ave., Kearny, N.J. 07029. 8. F. N. H. ROBINSON,J. Sci. Znstrum. 36,481 (1959). 9. T. A. Scorr, Phys. Rep. (Phys. Let. C) 27,89 (1976). 10. See, e.g., T. P. DAS AND E. L. HAHN, in “Nuclear Quadrupole Resonance Spectroscopy” (F. Seitz and D. Turnbull, eds.), Academic Press, New York, 1958; also Ref. (9). II. D. L. VANDERHARTAND H. S. GUTOWSKY,J. Chem. Phys. 49,261 (1968). 12. D. E. O’REILLY, E. M. PETERSON,Z. M. EL SAFFAR,AND C. E. SCHEIE,Chem. Phys. Lett. 8,470 (1971). 13. J. R. BROOKEMAN,M. M. MCENNAN,AND T. A. Scan, Phys. Rev. B 4,366l (1971). 14. H. R. BROOKER,P. J. HAIGH, AND T. A. SCOTT,Phys. Rev. 123,2143 (1961). 15. P. M. PARKER,J. Chem. Phys. 24, 1096 (1956).