Relative orientation of quadrupole tensors from two-dimensional multiple-quantum MAS NMR.

Several methods have been proposed for obtaining highresolution NMR spectra of half-integer spin quadrupolar nuclei (I ) /2, /2, etc.) in powdered solids. The double-rotation (DOR), dynamic-angle spinning (DAS), multiple-quantum magic-angle spinning (MQMAS), and satellite-transition magic-angle spinning (STMAS) techniques1 have attracted great interest owing to the importance of the nuclides 11B, 23Na, 71Ga (I ) /2) and 17O, 27Al (I ) /2) in the NMR of ceramics, glasses, and microporous materials.2 Although the “isotropic” spectra supplied by these techniques yield the quadrupole coupling constant, CQ, and asymmetry, η, of each crystallographic site, they provide no information that can be used to relate two quadrupole tensors. In this communication, we show that using a modified version of the two-dimensional MQMAS technique to cross-correlate secondorder broadened NMR line shapes allows the relative orientation of quadrupole, and hence electric field gradient, tensors to be determined. The nuclear quadrupole moment, eQ, couples with the surrounding electric field gradient to give rise to an anisotropic interaction that broadens NMR spectra of spin I > /2 nuclei in powdered solids.3 The quadrupole tensor Q ) eQV/2I(2I 1)p is usually parametrized by a coupling constant CQ ) eQVzz/h and an asymmetry η ) (Vxx Vyy)/Vzz, where the Vii are the principal axes of the field gradient tensor V and are defined such that |Vzz| g |Vyy| g |Vxx|. The quadrupole coupling constants of nuclei such as 17O, 23Na, and 27Al typically lie in the range 0-15 MHz and usually only the “central” transition, that between the mI ) +/2 and -/2 eigenstates, is observed by conventional NMR techniques as this is not quadrupole broadened in first order. The central transition is broadened by anisotropic second-order quadrupole effects, however, and this inhomogeneous broadening, although typically only several kilohertz, normally prevents the resolution of crystallographically distinct sites. Magic-angle spinning (MAS) is widely used to remove inhomogeneous broadening due to first-order dipolar couplings and chemical shifts from NMR spectra of powdered solids. The method cannot fully remove the second-order quadrupole broadening of a central transition powder line shape, however, as only that part of the anisotropy of the second-order interaction that has rank l ) 2 is fully averaged. The remaining rank l ) 4 part is incompletely averaged and the resulting line shape, although narrower than that of the static solid, is still inhomogeneously broadened.4 The MQMAS technique exploits the property that the rank l ) 4 broadening of a transition between the mI ) +n/2 and -n/2 (n ) 3, 5, ..., 2I) eigenstates is scaled relative to that of the central transition. Thus, by using MAS to remove the l ) 2 broadening and by correlating multiple-quantum against singlequantum coherences, it is possible to refocus the second-order quadrupole broadening and obtain a two-dimensional NMR spectrum from which an isotropic spectrum can be extracted. Figure 1a shows the two-dimensional 23Na triple-quantum MAS NMR spectrum of sodium molybdate dihydrate, Na2MoO4‚2H2O. Two important features of MQMAS are that the anisotropic second-order quadrupole broadenings of the two Na sites are still present in the spectrum in Figure 1a, producing “ridge” line shapes with a gradient of -/9, and that resolution has been achieved through the two-dimensional dispersion of these ridges. This spectrum can be analyzed to find the quadrupole coupling constant, CQ, and asymmetry, η, of each crystallographic site and this yields CQ1 ) 0.88 MHz and η1 ) 0.23 and CQ2 ) 2.68 MHz and η2 ) 0.08, confirming the literature values.5 However, an MQMAS experiment provides no information that can be used to relate one quadrupole tensor to another, such as internuclear distances or relative orientations. The relative orientation of two interaction tensors can be determined using a two-dimensional NMR experiment that crosscorrelates the powder spectra. Although originally discussed for static solids and first-order interactions, the same principles apply to half-integer spin quadrupolar nuclei under MAS conditions.6 * To whom correspondence should be addressed. Fax: +44-1392-263434. E-mail: [email protected]. (1) (a) Samoson, A.; Lippmaa, E.; Pines, A. Mol. Phys. 1988, 65, 1013. (b) Llor, A.; Virlet, J. Chem. Phys. Lett. 1988, 152, 248. (c) Frydman, L.; Harwood, J. S. J. Am. Chem. Soc. 1995, 117, 5367. (d) Gan, Z. J. Am. Chem. Soc. 2000, 122, 3242. (2) (a) Maciel, G. E. Science 1984, 226, 282. (b) Oldfield, E.; Kirkpatrick, R. J. Science 1985, 227, 1537. (3) (a) Abragam, A. The Principles of Nuclear Magnetism; Oxford University Press: Oxford, 1961. (b) Slichter, C. P. Principles of Magnetic Resonance; Springer-Verlag: Berlin, 1989. (4) Ganapathy, S.; Schramm, S.; Oldfield, E. J. Chem. Phys. 1982, 77, 4360. (5) Skibsted, J.; Jakobsen, H. J. Solid State Nucl. Magn. Reson. 1994, 3, 29. Figure 1. (a) 23Na triple-quantum MAS NMR spectrum of Na2MoO4‚ 2H2O. (b) Corresponding correlation spectrum with τm ) 200 ms. (c) Expansions of low-field cross-peak in (b) and corresponding simulation with â′ ) 24° and γ ′ ) 0°. Experimental parameters: ν0 ) 105.8 MHz; MAS rate, 9 kHz. 8135 J. Am. Chem. Soc. 2001, 123, 8135-8136