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Crystallographic structure refinement with quadrupolar nuclei: a combined solid-state NMR and GIPAW DFT example using MgBr2w Cory M. Widdifield and David L. Bryce*

Downloaded by University of Ottawa on 23 June 2011 Published on 22 June 2009 on http://pubs.rsc.org | doi:10.1039/B911448N

Received 10th June 2009, Accepted 12th June 2009 First published as an Advance Article on the web 22nd June 2009 DOI: 10.1039/b911448n Solid-state NMR spectroscopy and GIPAW DFT calculations reveal the pronounced sensitivity of 79/81Br and 25Mg quadrupolar coupling constants to subtle aspects of solid state structure which were not previously detected by pXRD methods. Single crystal X-ray diffraction (XRD) experiments are routinely used to determine crystal structures, but when suitable crystals are not available or other complicating effects are present, ‘‘NMR crystallography’’ methods are potentially useful for crystal structure determination. By measuring the chemical shifts (CS) of I = 1/2 nuclei under magic-angle spinning (MAS) conditions, information regarding the asymmetric unit, molecular symmetry, and space group can be obtained.1 Recent approaches have combined CS tensor measurements in ultrahigh magnetic fields (B0 4 18.8 T) with quantum chemical calculations and powder XRD (pXRD) data to improve zeolite structures.2 Similar approaches have been used to propose structures for host–guest complexes,3 organic molecules,4 biomolecules,5 and 14N-containing (I = 1) compounds.6 Here, we describe an example of a combined solid-state NMR (SSNMR) and gauge-including projector-augmentedwave (GIPAW) density-functional theory (DFT) crystallographic structure refinement, which relies primarily on quadrupolar coupling data that are unavailable for spin-1/2 nuclei. Compared to I = 1/2 nuclei, quadrupolar nuclei have the potential to provide additional long-range crystallographic information, due to the sensitivity of their NMR spectra to the electric field gradient (EFG) at the nucleus. MgBr2 is an excellent text case, due to the small number of degrees of structural freedom and the resulting lack of ambiguity in the interpretation of the NMR data. From a technical standpoint, there are particular challenges associated with 25Mg and 79/81 Br SSNMR experiments and computations; hence, MgBr2 represents a rigorous test case in these respects. For over 100 years, MgBr2 has been of great importance in synthetic chemistry as part of various Grignard reagents,7 and has been used to treat nervous system disorders,8 as a catalyst in esterification reactions,9 and luminesces when doped with Ti(II).10 Using pXRD data, its crystal structure under ambient conditions was proposed in 1929;11 however, it is anticipated

Department of Chemistry and Centre for Catalysis Research and Innovation, University of Ottawa, 10 Marie Curie Pvt, Ottawa, Ontario, Canada. E-mail: [email protected]; Fax: +1 (1)613 562 5170; Tel: +1 (1)613 562 5800 ext. 2018 w Electronic supplementary information (ESI) available: Detailed experimental and computational information, pXRD data and SSNMR spectra acquired at 11.75 T. See DOI: 10.1039/b911448n

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that the atomic positions in the crystalline lattice can be further refined using NMR crystallography methods. Both bromine isotopes (79/81Br) are present in high natural abundance and possess magnetogyric ratios (g) similar to 13C. On this basis, one might expect 79/81Br SSNMR experiments to be routine. This is not the case, as noted in a recent review.12 Few (B5) 79/81Br SSNMR reports exist where the Br does not possess nearly cubic or tetrahedral site symmetry. This scarcity is due to the rather large quadrupole moment (Q) associated with both isotopes (Q(79Br) = 313(3) mb; Q(81Br) = 262(3) mb),13 as well as considerable Sternheimer antishielding factors.14 Thus, a small external EFG produces a sizable quadrupolar coupling constant (CQ) and a very broad (order of hundreds of kHz to MHz) line width for the central transition (m = +1/2 2 1/2) NMR signal for powdered samples. The 79/81Br SSNMR spectra of a stationary powdered sample of MgBr2z exhibit characteristic second-order quadrupolar broadened powder patterns whose line widths exceed the available excitation bandwidth of the probe (Fig. 1). The total spectra were thus acquired in a piecewise fashion using variable-offset data acquisition methods (see ESIw). Without recourse to simulations or calculations, the spectra indicate that the EFG tensor at the bromine nuclei is nonzero. Br-81 SSNMR spectra acquired at B0 = 21.1 T (Fig. 1b) and B0 = 11.75 T (ESIw, Fig. S1) are complimentary, and analytical lineshape simulations15 produce the following quadrupolar

Fig. 1 Experimental 81Br (b) and 79Br (d) static SSNMR spectra of MgBr2 at B0 = 21.1 T. Analytical line shape simulations are given in (a) and (c). Bromine chemical shifts are w.r.t. dBr(KBr(s)) at 0.0 ppm.

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tensor parameters: |CQ(81Br)| = 21.93 MHz; ZQ = 0.02. As 79 Br and 81Br nuclei possess similar g, but different Q values, the 79Br SSNMR spectrum must be similar to the 81Br SSNMR spectrum, except for a scaling factor in the measured line width.12 The experimentally measured value for CQ(79Br) matches, within experimental error, the a priori estimated value (Fig. 1c,d). While 79/81Br CS anisotropy (CSA) is expected in MgBr2, it is beneath our detection limits (O o 50 ppm), even at 21.1 T. As the extracted 79/81Br SSNMR parameters are consistent amongst all four bromine NMR spectra (Fig. 1 and ESIw, Fig. S1), the EFG at the Br nucleus is conclusively nonzero. This result is in marked disagreement with prior calculations based on the currently accepted crystal structure,11 which indicate that the EFG at the bromine nuclei should be very close to zero.16 25 Mg NMR experiments were performed to provide further structural information. Magnesium-25 possesses a smaller Q (199.4(20) mb),13 but has a low g, and is 10.03% abundant, and hence conducting meaningful 25Mg SSNMR experiments at natural abundance is often challenging. Recent accounts (many involving expensive isotopic enrichment) have used 25 Mg SSNMR to study inorganic alloys,17a organometallic materials,17b magnesium-containing organic systems,17c and bio-inorganic systems.17d The observed 25Mg MAS SSNMR spectra of MgBr2 (Fig. 2b and ESIw, Fig. S2) possess several key features which allow for discussion of the local electronic environment about the 25Mg nuclei. First, lineshape simulations which assume an axially symmetric 25Mg EFG tensor are in excellent agreement with the observed spectra. This finding is consistent with the accepted site symmetry. The derived quadrupolar tensor magnitude, CQ(25Mg) = 850 kHz, highlights a rather small EFG at the magnesium. The magnesium CS, 16.25(0.15) ppm is highly shielded, which hints that contributions to the paramagnetic shielding mechanism are minor. This is consistent with the highly ionic bonding character of MgBr2. GIPAW DFT calculations18 of the magnetic shielding and EFG tensors, carried out using the accepted crystal structure, are in clear disagreement with the experimental SSNMR data (Table 1). Most striking are the calculated CQ(79/81Br) values, which are almost an order of magnitude smaller than observed, while the calculated CQ(25Mg) overestimates experiment by a factor of four. To the best of our knowledge, GIPAW DFT calculations of NMR parameters have not been

Fig. 2 Experimental 25Mg (b) MAS SSNMR spectrum of MgBr2 (nrot = 5 kHz) at B0 = 21.1 T. Analytical line shape simulation is given in (a). Magnesium chemical shifts are w.r.t. dMg(1 M MgCl2(aq)) at 0.0 ppm.

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Table 1 MgBr2a Nuclide

Experimental and computed NMR parameters for solid |CQ|/MHz

ZQ

siso/ppm

Experimental from SSNMR spectra 81 Br 21.93(0.20) 0.02(0.02) — 79 Br 26.25(0.20) 0.02(0.02) — 25 Mg 0.85(0.20) 0 — Computed using fully optimized structure 81 Br 21.81b 0.00 2306.8 25 Mg 2.74 0.00 553.9 Computed using previously accepted pXRD structure 81 Br 3.90 0.00 2274.7 25 Mg 3.47 0.00 552.9

diso/ppm 285(10) 285(15) 16.25(0.15) 320.9 — 353.1 —

a

GIPAW DFT computations used the PBE method, a 1200 eV energy cutoff and a 10  10  6 k-point grid. CQ = eQV33/h; ZQ = (V11  V22)/V33; siso = (s11 + s22 + s33)/3; O = s33  s11; k = 3(siso  s22)/O. For further details, see the ESI.w b Calculated |CQ(79Br)| = 26.06 MHz.

published for either 25Mg or 79/81Br. As part of an ongoing comprehensive study of alkaline earth metal bromides, we have carried out 79/81Br SSNMR experiments and GIPAW DFT calculations on these compounds.19 As a result, we have established an excellent correlation between experimental and computed 79/81Br EFG tensors. At the same time, we note that universal agreement between experimental and computed 25 Mg EFG tensors has not been established.20 As the bromine pseudopotential generally offers excellent agreement with observed quadrupolar tensor values, the bromine SSNMR parameters are now used as tools for the refinement of the accepted pXRD structure. According to the pXRD structure, MgBr2 belongs to the trigonal space group, P 3m1, with the Br and Mg2+ ions at 3m and  3m sites, respectively. As all observed SSNMR line shapes were precisely fit using an axially-symmetric EFG tensor, the point symmetry at all NMR-active nuclei must be at least C3. If we work within the space group that was assigned previously (simple CdI2 packing), then mirror site symmetry must be present at all ion sites. Hence, we conclude that the Wyckoff positions, as originally assigned using pXRD data, are correct. Under these assumptions, it is realized that there is one freely adjustable structural parameter: the position (expressed in fractional coordinates) of the Br ions parallel to the c unit cell axis (c(Br)). In the prior pXRD study, it was assumed that c(Br) = 0.25. By computationally optimizing only c(Br) and holding the unit cell constant, greatly improved agreement between the computed and observed bromine CQ values is achieved (|CQ(81Br)| increases from 3.90 to 14.89 MHz), and the computed energy decreases (Fig. 3 and ESIw). When the MgBr2 structure is subjected to a full geometry optimization (i.e., both the unit cell and c(Br) were optimized), an energy minimum is found near c(Br) = 0.21, with an accompanying increase in the c value. For this ‘fully optimized’ structure, the measured and calculated CQ(79/81Br) values agree within experimental error (Table 1) and the calculated diso(Br) and CQ(25Mg) values are also in better agreement with the experimental SSNMR values. By performing GIPAW DFT calculations where the c(Br) value is incremented stepwise, a linear correlation between the calculated CQ(79/81Br) and c(Br) values is established (R2 = 0.9998) Phys. Chem. Chem. Phys., 2009, 11, 7120–7122 | 7121

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could envisage the use of iterative refinement algorithms such as those developed for CS tensors in zeolites.2 The authors thank NSERC for funding, V. Terskikh, G. Facey, and T. Maris for technical support, and Prof. M. Murugesu for use of his glovebox. Access to the 900 MHz NMR spectrometer was provided by the National UltrahighField NMR Facility for Solids (http://www.nmr900.ca).

Downloaded by University of Ottawa on 23 June 2011 Published on 22 June 2009 on http://pubs.rsc.org | doi:10.1039/B911448N

Notes and references z MgBr2 (98%) was purchased from Aldrich and used without modification. Br-79/81 SSNMR signals were primarily acquired using a Solomon echo pulse sequence. GIPAW DFT computations were carried out using v4.1 of CASTEP. Geometry optimizations and NMR calculations were performed using the Perdew–Burke– Ernzerhof (PBE) exchange–correlation functional.21 Fig. 3 CQ(81Br) vs. nc(Br) for MgBr2. For comparison, CQ(81Br) calculated using: (’) accepted pXRD structure, (m) c(Br) optimized geometry. CQ(81Br) calculated from the fully optimized geometry and the experimental value are indistinguishable ( ). (E series, best fit: CQ(MHz) = 223.01(nc)  21.71). Inset: schematic of the fully optimized MgBr2 unit cell, viewed parallel to a. Vectors originating at the Br represent the displacement direction when moving (as shown) along the positive c axis.

(Fig. 3). This extreme sensitivity of the EFG at the Br nuclei to the structure (notably, for a fixed cell, that a change in Br position of ca. 0.04 A˚ can increase |CQ(81Br)| by B11 MHz), and the experimental observation that CQ(79/81Br) is nonzero, clearly shows that c(Br) is not at the previously assumed value of 0.25, but is rather very likely to be near 0.21. It is also clear that the c unit cell length should be larger than previously determined. Both of these findings are consistent with new pXRD data that were collected using modern equipment (see ESIw). In this context, we emphasize that NMR crystallographic methods are complementary to, rather than a replacement for, established X-ray diffraction methods. In summary, we have presented an example of an experimental and computational structural refinement approach for simple inorganic materials composed solely of quadrupolar nuclei. Qualitative information was first obtained by briefly considering the experimental data, and a quantitative change in structure was substantiated using experimental SSNMR data to cross-validate the computational results. The 79/81Br SSNMR spectra are the first to be presented for bromine in a non-cubic environment acquired using modern variable-offset techniques. The sensitivity of the method to crystal lattice EFGs is advantageous, as this represents an additional parameter that is not available for spin-1/2 nuclei, and because the EFG is generally more sensitive to long-range crystallographic features (e.g., intermolecular contacts) than are chemical shifts. Indeed, the CS tensor parameters in the present study are less sensitive to structural changes than are the EFG tensor parameters. The general approach is expected to be important for quadrupolar nuclei in other purely inorganic systems, as the more extensively developed methods of 1H NMR crystallography cannot be used. For more complex structures with multiple crystallographic sites, one

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