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Numerically exact lineshape simulations of double-quantum-filtered MAS NMR spectra (S. Dusold and A. Sebald)

We have recently demonstrated for a number of small isolated dipolar coupled spin systems that numerically exact spectral lineshape simulations are feasible for the determination of all parameters describing the spin system, provided that efficient numerical methods are employed. Applying these lineshape-simulation approaches to MAS NMR (magic-angle spinning nuclear magnetic resonance) spectra of spin systems containing more than two coupled spins-1/2 in principle permits the determination of the complete structure of an entire molecule or a molecular fragment from straightforward one-dimensional MAS NMR spectra. However, in many practical applications, the presence of numerous additional resonances in the MAS NMR spectra will severely hamper any lineshape-simulation procedures. For such cases it is necessary to suppress unwanted (background) resonances and to selectively filter out only those resonances of interest. Spectral filtering can be achieved by various so-called double-quantum-filtration (DQF) pulse sequences. DQF is demonstrated in Figure 3.7-10a for ¹³C MAS NMR spectra of a mixture of Na-pyruvate with ¹³C in natural abundance (90%) and 2,3-¹³C₂-labelled Na-pyruvate (10%): the conventional ¹³C MAS NMR spectrum (top) displays all ¹³C resonances, after DQF the ¹³C MAS NMR spectrum (bottom) only shows the resonances of the 2,3-¹³C₂-labelled spin pair. In order to extract unknown parameters from the lineshapes in these DQF MAS NMR spectra, it is necessary to include the effects of the entire pulse sequence in the simulations. That it is possible to simulate DQF MAS NMR spectra very accurately is shown in Figure 3.7-10b, where an experimental (top) DQF MAS NMR spectrum is compared to the corresponding simulated spectrum (bottom). We expect these and similar methods to become useful MAS NMR approaches for the accurate determination of internuclear distances in a wide variety of spin systems, including ²⁹Si and ³¹P in inorganic silicates and phosphates.

Fig. 3.7-10: a) conventional (top) and double-quantum-filtered (bottom) 13C MAS NMR spectra of a mixture of Na-pyruvate with 13C in natural abundance (90%) and 2,3-13C2-labelled Na-pyruvate (10%); b) comparison of an experimental (top) and a simulated (bottom) DQF 13C MAS NMR spectrum of 2,3-13C2-labelled Na-pyruvate.

Disorder in solid C(SnMe₃)₄ (X. Helluy, J. Kümmerlen and A. Sebald, in collaboration with P. Bernatowicz and R. Dinnebier/Bayreuth)

Previous single-crystal X-ray diffraction experiments on C(SnMe₃)₄ have indicated the presence of a pseudo-fivefold disorder in this material. Diffraction techniques alone can not distinguish between static and dynamic orientational disorder. We have employed one- and two-dimensional ¹¹⁹Sn NMR techniques to investigate further the disorder in solid C(SnMe₃)₄. Variable-temperature ¹¹⁹Sn NMR experiments in the temperature range T = 150-290 K positively identify the dynamic nature of the pseudo-fivefold disorder by exploiting information encoded in the ¹¹⁹Sn chemical shielding tensor. Amongst numerous different possible dynamic-disorder models, a model where each tin atom in the C(SnMe₃)₄ molecule occupies the twenty corners of a dodecahedron with equal probability agrees best with the combined experimental one- and two-dimensional ¹¹⁹Sn NMR evidence. This is illustrated in Figure 3.7-11, where the twenty-fold exchange over the corners of the dodecahedron is illustrated schematically (Fig. 3.7-11a). Note that this mode of molecular reorientation requires the simultaneous occurrence of small- and large-angle reorientational jumps of the C(SnMe₃)₄ molecule. In Figure 3.7-11b the contour plot of a low-temperature two-dimensional ¹¹⁹Sn exchange experiment is shown in comparison with the best-fit calculated spectrum according to the twenty-fold exchange model. The combined exchange-rate constants from all variable-temperature one- and two-dimensional ¹¹⁹Sn NMR experiments yield an activation energy E_a 32 kJmol^-1 for the twenty-fold exchange process in solid C(SnMe₃)₄.

Fig. 3.7-11: a) pictorial representation of the dynamic disorder model in solid C(SnMe3)4; b) contour plots of 119Sn two-dimensional exchange NMR spectra under non-spinning conditions at T = 150 K with short mixing time ( m = 5 ms); left: experimental spectrum, right: best-fit simulated spectrum.

The pseudo-cubic phases of SiP₂O₇ and TiP₂O₇ as seen by various ³¹P MAS NMR experiments (X. Helluy and A. Sebald, in collaboration with C. Marichal/Mulhouse)

Spin-diffusion based ³¹P MAS NMR investigations (see Annual Report 1997) on the pseudo-cubic phase of SiP₂O₇ have now been completed and include full characterization of the isostructural phase TiP₂O₇ as well. The combined results may be summarized as follows:

• various ³¹P MAS NMR techniques fully and independently confirm for both phases the cubic space group with a 3 x 3 x 3 superstructure as the correct choice, as had been previously proposed from refinement of X-ray diffraction data of both phases;
• a simple comparison of one-dimensional ³¹P MAS NMR spectra of the two isostructural phases (see Fig. 3.7-12) demonstrates that common qualitative, isotropic ³¹P chemical-shielding-based assignment schemes to identify ³¹P resonances with individual P sites in the structure are not generally applicable to condensed phosphate systems;

Fig. 3.7-12: Comparison of 31P MAS NMR spectra of SiP2O7 (top) and TiP2O7 (bottom). Also indicated are the pairwise P-O-P connectivities as determined by J-coupling connectivities; resonances D (SiP2O7) and E (TiP2O7) correspond to special P-O-P sites with magnetically equivalent intra-P2O7 31P spin pairs and hence do not display the corresponding intra-P2O7 31P J-coupling connectivity.

• constraints from J-coupling-based ('through-bond') ³¹P NMR experiments successfully identify P-O-P subunits in the structures and thus are extremely useful for the reduction of the originally very large number of possible assignment permutations;
• full and unambiguous assignment requires additional dipolar-coupling-based ('through-space') ³¹P NMR experiments. So-called single-quantum - double-quantum ³¹P correlation MAS NMR experiments yield unique assignment for both phases. So-called zero-quantum ('spin diffusion') ³¹P MAS NMR experiments, however, are successful for spectral assignment only for SiP₂O₇ but fail for TiP₂O₇, owing to the lesser ³¹P NMR spectral resolution as compared to SiP₂O₇.

The final complete assignment of the ³¹P resonances to the crystallographic P sites P1 to P11 in the structures of SiP₂O₇ and TiP₂O₇ is given below (compare Fig. 3.7-12):

MAS NMR techniques for the determination of molecular conformations (M. Bechmann, S. Dusold and A. Sebald, in collaboration with M. Stumber, U. Haeberlen/Heidelberg, H. Förster/Karlsruhe, T. Lis/Wroclaw and J.N.S. Evans/Washington)

The recently started, extended joint project (see Annual Report 1998), aiming to develop and apply MAS NMR techniques for the direct determination of molecular conformations and focussing on the biochemically important phosphoenol-pyruvate (PEP) moiety has accomplished some of its initial tasks. First, the orientations of all ³¹P and ¹³C chemical shielding tensors in a suitable PEP-model compound of known structure had to be determined. (NH₄)₃(PEP) was chosen for this purpose. From ³¹P single-crystal NMR studies and ¹³C-³¹P heteronuclear dipolar recoupling MAS NMR experiments on (NH₄)₃(PEP) with ¹³C in natural abundance, the absolute orientation of the ³¹P and the ¹³C2 chemical shielding tensors in the molecular frame of the PEP moiety are now known (see Fig. 3.7-13). In order to determine the ¹³C1 and ¹³C3 chemical shielding tensor orientations, it is necessary to carry out ¹³C MAS NMR experiments on fully ¹³C-enriched U-¹³C-(NH₄)₃(PEP): the remaining unknown orientational parameters of the ¹³C spin systems are encoded in the lineshapes of various different rotational-resonance ¹³C MAS NMR spectra (see Fig. 3.7-14). Once this data analysis is complete, the first stage of the project is complete. The following phase will be concerned with the selection and testing of suitable MAS NMR experiments to correlate the ¹³C1-¹³C2 chemical shielding tensors.

Fig. 3.7-13: The orientation of the 31P and 13C2 chemical shielding tensors in the molecular frame of (NH4)3(PEP).

Fig. 3.7-14: Comparison of an experimental (bottom) and a best-fit calculated (top) 13C MAS NMR spectrum of U-13C-(NH4)3(PEP).