Multiple Quantum MAS (MQMAS) 267-271

MQMAS is a 2D experiment that affords resolution of the central transition by using both spin and spatial averaging techniques. The experiment can be conducted on most MAS probe heads and is relatively straightforward to implement.

Figure 2.29 (a). Energy level diagram for spin-3/2 nucleus. (b). Pulse sequence (c). coherence transfer pathways diagram for a basic 3QMAS experiment. Blue and red boxes,indicate the selective and hard

pulses to excite triple quantum (3Q) and transfer this into single quantum (1Q) coherences respectively. Recall that the selection rule for NMR is m ±1, therefore we can only directly observe the 1Q coherence Phase cycling ensures that we detect the p = 0 to -3 to -1 pathway.267

Firstly, the ǀ-3/2↔3/2ǀ energy level, 3Q coherence, is excited using a selective pulse, 1. The frequency of this transition can be written, under

MAS, from the equation in Figure 2.27 as:

Under MAS, the second rank term in Eq. 2.34 vanishes and during the first evolution period, t1, the coherences evolves under the zero and

fourth-rank terms. At the end of t1, 3Q coherence is transferred into

the ǀ-1/2↔1/2ǀ energy level i.e. 1Q coherence. We can write the frequency of the central transition as:

Again, the second-rank term is averaged under MAS leaving the evolution of 1Q coherence under the zero and fourth rank-terms. 1Q coherence is allowed to evolve for a time, kt1, where k is equal to the ratio of the fourth-

rank terms in both the 3Q and 1Q frequencies, given by (C4 term is expanded

to make it clearer)

Therefore, for a spin-3/2 nuclei = 7/9 and is known as the MQMAS ratio. When k = 7/9, (the ratio can be positive or negative and depends on which coherence pathway we want to select267) the evolution of the 3Q coherence under fourth rank-terms is undone or refocused by the evolution of the 1Q coherence under its fourth rank-term and occurs at the end of kt1. At the end

of time t1 + kt1 the net evolution of the remaining 1Q coherence is governed

only by the zero term i.e. the isotropic quadrupolar terms (The isotropic term is identical for every crystalline orientation in the powder hence we do not have to mechanically spin at two angles!) and is then recorded as an FID in the t2 period. A double Fourier transformation of the time domains signals; t1

and t2 into their respective frequency domains, f1 and f2 produces an NMR

Figure 2.30 (a). 23Na MQMAS unsheared spectrum (b). 23Na MQMAS spectrum with shearing (c). to (e). extracted line shapes from dimension with simulated spectra giving the quadrupolar parameters for each sodium site

For example, Figure 2.30 (a). shows the 23Na MQMAS NMR spectrum of Rongalite (HOCH2SO2-+Na) which has three distinct sodium environments.272

The resulting NMR projection lies at a ridge governed by the MQMAS ratio. It is still not clear as to how many sites are present as the spectrum requires a shearing transformation (a phase correction) to ensure isotropic line shapes, Figure 2.30 (b). Once sheared, the f1 side corresponds to the

isotropic dimension whilst f2 is the MAS (anisotropic) dimension. Extraction

of sites from the MAS dimension can be simulated using dmfit273 or TopSpin to give the , and η quadrupolar parameters; Figure 2.30 (c) to (e).

These parameters give insight into the local atomic environment and symmetry of the nucleus in question. The main limitation of the MQMAS experiment is that site populations are not quantitative as the intensities (area) depends on the ability to excite and convert 3Q coherence into 1Q coherence, which, in turn, is dependent upon the strength of the quadrupolar interaction:

Figure 2.31 The dependence of the 3Q to 1Q conversion (selecting the p = –3 to p = –1 pathway), of the spin I = 3/2 central transition amplitude on the quadrupolar coupling constant, , is the same as , where the pulse,

, power is equal to 300 kHz (solid line), 100 kHz (dashed line), and 75 kHz (dotted line). In each case, the flip angles of the on-resonance excitation and reconversion pulses were 240° and 60°, respectively. Reproduced from S. Brown’s PhD thesis.274

Clearly, we can see from Figure 2.31 that as the quadrupolar interaction increases there is a decrease in signal amplitude. In our work, excitation powers comparable to that of the dashed line are used to excite and convert 3Q-1Q coherence states and indeed, our results reported chapter 4, are in agreement with those in Figure 2.31. In light of this, Gan275 introduced a similar experiment known as satellite transition (ST) MAS NMR. In this experiment satellite transitions ǀ±3/2 ↔±1/2ǀ are correlated with the central transition ǀ-1/2↔+1/2ǀ in a 2D experiment under MAS. The form of the refocusing of the fourth-rank terms in the ST and CT takes on different ratios to that in the MQMAS experiment to yield the isotropic CT276. However, because the STs are 1Q coherence states, excitation can be achieved much more efficiently resulting in an improvement in resolution:

Figure 2.32 Comparing the isotropic projections obtained from STMAS and MQMAS on 87Rb (spin-3/2) in RbNO3. In each experiment in 192 scans were

used with a recycle interval of 250 ms. The MAS rate was 20 kHz. Experiments were performed using a conventional 2.5 mm Bruker MAS probe with a maximum radiofrequency field strength of = 180 kHz. Adapted from Askbrook et al.277

Application of heteronuclear decoupling schemes during MQ or STMAS acquisition can also significantly improve resolution.208, 278 To date, the newest method of obtaining high resolution NMR spectra for spin-3/2 nuclei was reported in 2008 by Thrippleton et al.279 with the experiment called satellite transitions acquired in real time by magic angle spinning (STARTMAS). It involves modifying the STMAS pulse sequence by transferring the STs into double-quantum (DQ) coherence states and then finally back to 1Q coherence. Essentially, it allows for ultrafast acquisition of isotropic NMR spectra similar to that obtained from DOR.