Quadrupolar nutation NMR to discriminate central and satellite transitions: Spectral assignments for a Ziegler-Natta catalyst.

In this contribution we used solid state 35Cl (I=3/2) quadrupolar NMR to study a MgCl2/2,2-dimethyl-1,3-dimethoxypropane (DMDOMe) adduct that serves as a model system for Ziegler-Natta catalysis. Employing large Radio-Frequency (RF) field strengths we observe three spectral features with strongly varying line widths. The assignment of the spectra is complicated because of the large difference in quadrupolar interactions experienced by the different sites in the system. The satellite transitions (ST) of relatively well-defined bulk Cl sites are partially excited and may overlap with the central transition (CT) resonances of more distorted surface sites. We show that nutation NMR of the ST of I=3/2 spins yields a unique pattern that makes a clear distinction between an extensively broadened central transition and the satellite transitions of a component with a smaller quadrupolar interaction. This allows us to unambiguously unravel the spectra of the MgCl2 adduct showing that we observe CT and ST of the bulk phase of MgCl2-nanoparticles with a CQ of 4.6MHz together with the CT of surface sites displaying an average CQ of ∼10MHz.


Introduction
Solid state nuclear magnetic resonance (NMR) spectroscopy is extensively used in materials science owing to the sensitivity of the nuclear spin to the local environment. In this paper we focus on the MgCl 2 -support in a binary adduct between MgCl 2 nanoparticles and an organic electron donor (2,2-dimethyl-1,3-dimethoxy propane/DMDOMe), see Figs. SI 1 and SI 2. This adduct serves as a model system for Ziegler-Natta catalysis [1,2] and is studied using 35 Cl solid state NMR.
The structure of a-MgCl 2 consists of Cl-Mg-Cl triple layers in which each Mg is octahedrally coordinated by the chlorine [3]. This results in a moderate quadrupolar parameter for the 35 Cl nucleus: C Q = 4.6 MHz [4]. The MgCl 2 nanoparticles in our adduct still have a relatively well-defined bulk phase, with some distribution in the quadrupolar parameters resulting from the heterogeneity of the sample. Besides this, they also have large surface areas that expose unsaturated sites which are important for catalysis. The focus in the literature is in particular on the (1 0 4)-and (1 1 0)-surface sites [5][6][7] as well as surface defects [1,8] which, due to their asymmet-ric environment, are both expected to exhibit large quadrupolar couplings. In a previous publication, we calculated that the quadrupolar parameters for the (1 0 4)-and (1 1 0)-surface sites are 10-16 MHz [9], yielding line widths ($250-700 kHz) that cannot be averaged by current MAS technology thus implying that they should be detected and characterized by static 35 Cl experiments. In our current binary system at least part of these surface sites will be coordinated by the organic donor. The NMR parameters of such donor-bound surface sites are not reported, although preliminary calculations suggest that they are comparable to the naked surfaces. It is of great interest to learn more about the exact coordination of the donor on the support, and the detection of relevant surface sites is key to this.
In the case of nuclei with I > 1/2 (such as 35 Cl, so-called quadrupolar nuclei) the resulting NMR spectrum can be complex due to the overlap of multiple, broad powder patterns. When spectra lack clear features, as is the case for disordered or heterogeneous samples like our catalyst, the interpretation of the spectrum becomes even more troublesome. Magic angle spinning (MAS) already significantly narrows the quadrupolar broadened lines by a factor of $3 [10,11]. Yet, the second-order broadened line shapes may still overlap and analysing the 1D spectrum can be complicated. The MQMAS pulse sequence [12,13] has been successfully introduced as a method to resolve overlapping sites in a 2D fashion. Alternatively, nutation NMR under static conditions [14,15] can be used to differentiate between overlapping sites and extract the relevant NMR (quadrupolar) parameters.
The heydays of nutation NMR were the 80's and 90's, before the introduction of the MQMAS sequence. However, recently our group [16] showed that nutation NMR, owing to the high RF field strengths available when using milli-and microcoils, can be a valuable tool for systems where the quadrupolar interaction becomes too large to be averaged by means of MAS. At an RF field strength of 100 kHz spin systems with quadrupolar frequencies, x Q ¼ 3C Q =ð2Ið2I À 1ÞÞ, of up to 1 MHz can be studied. This is extended to 10 MHz when the RF is increased to 1 MHz, which means that, for I = 3/2, spin systems with quadrupolar coupling constants, C Q ¼ e 2 qQ =h, of up to 20 MHz become accessible [15]. For larger spin quantum numbers even much larger C Q 's can be handled. Such systems would require spinning speeds of many hundreds of kilohertz, that cannot be achieved by current MAS technology.
Very broad resonances can still be observed using static approaches and over the years multiple techniques have been developed for the characterization of wideline spectra [17]. Frequency-swept pulses of the WURST-class [18,19] are used for broadband excitation. They are combined with QCPMG detection [20][21][22] for enhanced sensitivity and are sometimes combined with frequency stepped acquisition [23] for ultra-wideline spectra. These approaches work well and even the presence of multiple non-equivalent sites has been shown [24][25][26]. However, despite the large quadrupolar parameters and hence asymmetric environments, they are still well-defined crystallographic sites.
A problem arises in the characterization of systems containing sites with a certain degree of disorder combined with large differences in their respective quadrupolar parameters. In such cases line shapes lack distinct spectral features and satellite transitions (ST) of relatively symmetric sites and central transitions (CT's) of distorted sites will overlap. Hence the identification of ST line shapes versus CT line shapes becomes obscured. An example includes the 75 As spectra of Al x Ga 1Àx As semiconductors, which give rise to two narrow lines from locally symmetric As½Al 4 and As½Ga 4 sites that can be straightforwardly observed [27]. CT signals from the other As½Al n Ga 4 À n (n = 1, 2, 3) sites span >1 MHz and could only be characterized using high RF fields [28], but there is strong overlap between the satellite transitions (ST) and central transitions (CT's). In this example distinct quadrupolar features and DFT modelling aids in the final assignment of the spectra. Another example of ST/CT overlap is the 91 Zr study of a zirconocene where dominant signals from chlorine ST almost obscure the 91 Zr CT signal [25]. In general, it can become very difficult to infer to what extent broad resonances are the results of ST from sites with low C Q or CT's from sites with much higher C Q , or even a combination of both. This is especially the case for disordered or heterogeneous samples which lack clear quadrupolar features in their line shapes. In this contribution we show how nutation NMR can be exploited to differentiate between a satellite transition and an extensively broadened central transition and in this way we can unambiguously interpret the 35 Cl spectrum of our MgCl 2 -nanoparticles.

Theory
A nutation experiment follows the modulation of the observed NMR signal as a function of the duration of the excitation pulse (t 1 dimension). The presence of a strong quadrupolar interaction cannot be neglected during the pulse duration and the effective Hamiltonian during the pulse has therefore contributions from both RF and quadrupolar parts. This leads to mixing of the Zeeman states during the evolution period t 1 such that the CT coherences is mod-ulated by 2I frequencies during the pulse, in the case of onresonance irradiation. The resulting nutation profile can be used to deduce the quadrupolar parameters of the systems under study and resolve the presence of overlapping sites in the 1D spectrum [29][30][31].
At various relative strengths of m Q and m RF the observed nutation behaviour of the CT of a quadrupolar nucleus can deviate strongly from the expected RF field strength, see During rf-irradiation the spin states, labelled 1-4 for a spin I = 3/2, are mixtures of the jI; mi functions. Their energy levels are shown in Fig. 1A as a function of X Q =m RF , with the angular dependent quadrupolar frequency X Q = x Q =2ðð3 cos 2 h À 1Þ þ g Q cos 2/ sin 2 hÞ.
In the absence of a quadrupolar interaction (X Q =m RF % 0) four equally spaced energy levels are found with an energy difference of m RF . The associated transition frequencies for the most prominent transitions are shown in Fig. 1B and they show a strong dependence on X Q =m RF . The evolution of these transitions contribute differently to the transitions between the jI; mi spin levels observed directly after the nutation pulse. Evolution of the density matrix allows the computation of the amplitude factors ðR i;j Þ m;n describing the contribution of a transition i () j during rf-irradiation to an observed transition m () n during detection [32].   2B shows a simulated 23 Na (I = 3/2) full 2D nutation spectra with contributions from both CT and ST. This spectrum is simulated for a model system: Na 2 SO 4 , which is characterized by C Q = 2.60 MHz and g = 0.58 [33] using m RF = 133 kHz at a magnetic field of 9.4 T. The projected trace in F2 shows the regular 1D spectrum where some features of the satellites can just be identified. The projected trace in F1 is generally referred to as the nutation spectrum that can also be obtained by an alternative pseudo 2D processing: direct Fourier transformation of the FID maximum. The advantage of a full 2D spectrum is that the nutation frequencies of every point in the regular 1D spectrum can be retrieved, although it requires a high S/N-ratio to see the satellites. Fig. 2 shows that the satellite transition nutation frequencies display a characteristic pattern. The on-resonance ST powder pattern is always symmetric, because both satellite transitions are observed simultaneously. The nutation spectrum is therefore, in principle, symmetric around the isotropic shift of the ST. The pattern that is observed corresponds to the calculated transitions frequencies in 1B. Any particular position in the satellite manifold, at a frequency AEm relative to the isotropic shift, has a certain angular dependent quadrupolar frequency, X Q and it will thus give the three nutation frequencies corresponding to the ratio X Q =m RF . This creates a unique butterfly-like pattern which can be clearly set apart from the much broader and distributed nutation profile of any CT that may resonate at the same position. The position-dependency of the nutation frequencies means that, independent of C Q , the satellite nutation pattern will in principle always have the same shape and just stretches out further along the F2 dimension for systems with higher C Q . This is shown in Fig. 2D, which is simulated using the same m RF as matter if the system under study has well-defined or distributed quadrupolar parameters.

Hahn echo
All 35 Cl experiments were performed using a home-built probe with an inner-coil diameter of 1.2 mm which reached an RF field strength (m RF ) of 480 kHz at a power of 1120 W and a frequency m L of 78.3 MHz. Fig. 3 shows the 35 Cl Hahn echo spectrum of the MgCl 2 /DMDOMe adduct (bottom trace) at this high RF field strength. Crystalline MgCl 2 is characterized by a 35 Cl C Q of 4.6 MHz, with g = 0 [4]. In the case of nanoparticles, as studied here, the resulting 35 Cl spectrum will be a somewhat less welldefined, because of the heterogeneity in the sample giving a distribution of quadrupolar parameters [4,9]. Still, this gives a 'narrow' CT line, which is AE50 kHz broad at a static magnetic field of 18.8 T. This corresponds to spectral component A (CT A ) in Fig. 3. Since 35 Cl has a spin quantum number of I = 3/2, the corresponding satellite transitions of the bulk (ST A ) will span a frequency range of approximately À2.3 to +2.3 MHz. Due to its width and the limited bandwidth of the probe the full satellite pattern is not readily observed in a single experiment. Consequently, the spectrum obtained near the resonance frequency of CT A , will only show part of the signal from ST A which will overlap with potential signal from the surface sites. showing the full spectrum. The spectrum is divided into three different components, which are for illustrative purposes approached by Gaussian functions. They are labelled A, B and C and are coloured red, blue and green respectively. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) Besides the 'narrow' CT A , the bottom trace in Fig. 3 shows a second broader component spanning $350 kHz. This spectral component B also lacks well-defined features. Owing to our high RF field strength we can be sure of a proper excitation of this component. It is also observed with somewhat lower RF field strengths and field dependent measurements show an inverse scaling with the magnetic field. The signal can therefore be assigned to a CT of a site with a moderate quadrupolar coupling (C Q $ 10 MHz). This assignment is further corroborated by the nutation experiments (vide infra). Spectral component B can be identified as a surface site of the MgCl 2 nanoparticles. A further detailed description of this surface site is beyond the scope of this article and will be addressed in a forthcoming publication studying different adducts.
A vertical expansion (the top trace) shows yet another, much broader component spanning almost 2 MHz, spectral component C. Owing to the high RF field, we are able to excite such a broad resonance. The interpretation of this spectral feature is bound to be troublesome. Spectral component C is rather symmetric without specific features. Its width might be limited by the probe's bandwidth. Due to its rather featureless appearance and the uncertainty in its exact span, it is unsure how this signal should be interpreted: is it a second surface site, or is it part of ST A or an overlap of both? It should be noted that the broad component has a significant intensity (AE1/3 estimated from the FID), although experimental conditions do not permit an exact quantitative interpretation.

Variable offset cumulative spectra
To obtain the full spectrum the best approach would be to take spectra at variable offsets, using broadband excitation techniques to minimize the number of frequency steps that needs to be taken. We performed variable offset cumulative spectra (VOCS) over a frequency range from 74.1 to 81.1 MHz using high power excitation (m RF $ of 480 kHz), see Fig. 4 and Fig. SI 5. Due to the low vertical intensity of the satellite signal, many scans were needed to get a decent quality for each individual echo. All echoes were acquired with recycle delays of 200 ms with up to 400,000 scans each, giving an experimental time per echo of almost 22 h. The complete VOCS therefore took more than a full week to record. Fig. 4 shows signal spanning from À5 to +3 MHz. At $74.4 MHz we reach the Larmor frequency of 91 Zr and observe the signal from the ZrO 2 rotor [35]. The satellite transitions of this Zr site also explain the features at 74.8 and 75.5 MHz. The resulting 35 Cl signal seems to extend a bit beyond the theoretical value of AE2.3 MHz, but this may well be related to the distribution in quadrupolar parameters of MgCl 2 . The observed signal lacks well-defined features. It is most intense near the central transition and decreases in intensity at larger offsets, again in agreement with the distribution in quadrupolar parameters. Fig. 4 includes a simulation of the full spectrum (CT + ST) of a system with C Q = 4.6 MHz and g = 0.6.
A decent agreement between the simulation and experiment is achieved, suggesting that spectral component A and C could be assigned as CT A and ST A .
However, agreement between simulation and experiment is not perfect and it cannot be excluded that there is still overlap between ST A and potential surface sites. To this end we would need field dependant VOCS measurements, but this is a time consuming process and therefore not the most optimal experiment. We resort to nutation NMR to study spectral component C in more detail. The experimental on-resonance 35 Cl nutation spectrum for the MgCl 2 adduct is shown in Fig. 5 along with some simulated nutation spectra. These nutation spectra are obtained by Fourier transformation of the FID maxima. This processing procedure is chosen because the intensity of spectral component ST A contributes significantly to the intensity in the FID while it hardly stands out of the noise in the spectra due to its width. The resulting experimental nutation profile will thus include the contribution from all the potential CT's and ST present in the spectrum. An exception to this procedure is the bottom spectrum in Fig. 5B, which shows a slice from the full 2D experimental nutation spectrum at the position of the transmitter offset. Consequently this will almost exclusively give signal from CT A .

On-resonance nutation
Simulated nutation spectra are performed for a 35 (Fig. 5B). CT A gives a weak peak at 490 kHz and a stronger signal around 900 kHz. This frequency of 900 kHz is somewhat below 2 Â m RF . Spectral component B has a much larger C Q than bulk MgCl 2 and m Q =m RF reaches the limit of the intermediate nutation regime, therefore CT B will nutate at % 2 Â m RF . This is indeed what is simulated in the top trace of Fig. 5A. Its corresponding ST span 10 MHz which, in combination with its lower intensity, mean that it will not be detected The experimental nutation spectrum (Fig. 5A) shows two frequencies: a dominant broad band at 950 kHz and a weaker peak at 490 kHz. The slice taken at the position of the transmitter offset shows a slightly different nutation spectrum (Fig. 5B). It is dominated by an intense peak at 900 kHz and the peak at 490 kHz is even weaker. This matches quite well with the simulated nutation

Off-resonance nutation
The on-resonance experiments are dominated by spectral component A, the CT of the bulk Cl signal in MgCl 2 , which partially obscures the signals from the satellites. The on-resonance nutation spectrum indicates that spectral component C is due to the ST of bulk MgCl 2 . To verify that no contributions of other broadened components are present nutation spectra are taken at a large resonance offset so that contributions of the bulk CT is strongly diminished. Fig. 4 shows the 35 Cl Hahn echo spectra of the MgCl 2 adduct taken at a range of offsets. Fig. 7A shows the spectrum obtained at 77.6 MHz (À700 kHz off-resonance from the CT) in more detail. Comparable to Fig. 3, the spectrum contains the CT around 0 kHz and a $2 MHz featureless broad signal centred around the transmitter; we will refer to this as spectral component D. Although CT A still dominates the spectrum on the vertical scale, component D is now relatively much more intense compared to component C in Fig. 3 as also becomes clear from the off-resonance nutation spectra. The contribution from spectral component B is also strongly diminished in the off-resonance spectra.
The top spectra in Fig. 7B show the nutation profile obtained from Fourier transformation of the echo maxima of the FID. The introduction of a resonance offset alters the mixture of the jI; mi states during the pulse which can again be described by evolution of the density matrix under the appropriate Hamiltonian [32]. The experimental trace shows two peaks at 740 and 840 kHz which are also observed in the simulation, that includes contributions from CT A and ST A . However, the other features in the simulation (400, 1150 and 1400 kHz) are barely observed in the experiment. As can be seen from the traces of the 2D nutation spectra at the position of the CT of bulk MgCl 2 (Fig. 7B, bottom spectra) those features all belong to components resulting from the off-resonance nutation [32] of CT A , the CT of bulk MgCl 2 . The signals at 400, 1150 and 1400 kHz are more prominent in both the simulated as well as the experimental trace. Also the changed relative intensities of the peaks around 800 kHz match well.
The simulated 2D nutation spectrum (see Fig. 8A) shows a banana-shaped feature in F1 at 700-800 kHz for the part of the satellite pattern that is close to the transmitter offset. This feature can be recognized in the experimental 2D spectrum as well. Similar to the on-resonance nutation spectrum, the central transition When the transmitter is put at even larger offset from CT A , the contribution from this CT will diminish even more. This can be seen in Fig. 7A which also shows the Hahn echo spectrum obtained at a transmitter frequency of 79.7 MHz (+1.4 MHz off-resonance). In the echo spectrum hardly any signal is left for the CT of bulk MgCl 2 while again there is a broad band of almost 2 MHz (spectral component E). The experimental nutation spectrum, see Figs. 9 and SI 6, will thus almost exclusively be composed of contributions from this component. Similar to the À700 kHz off-resonance nutation experiment, the ST display a banana-shaped pattern centred around the transmitter offset. As the CT lays outside the bandwidth of the probe, we do not observe the broad range of nutation frequencies at À1400 kHz in the experimental spectrum. We only observe a banana-shaped pattern which clearly originates from the ST. Even the asymmetry matches perfectly with the simulation, which shows that more intensity is observed on the right-hand side. This off-resonance nutation spectrum was acquired in only 19 h. There is excellent agreement between experimental and simulated nutation spectra. Again we find no evidence for the contribution of additional components. We therefore conclude that all the broad spectral components observed at different resonance offsets C, D and E are solely composed of one signal which is part of the satellite pattern of the MgCl 2 bulk phase (ST A ).

Conclusion
In this contribution we demonstrated the use of nutation NMR to characterize the 35 Cl spectrum of a model system for Ziegler-Natta catalysis: the binary adduct MgCl 2 /DMDOMe. Owing to a millicoil allowing the generation of very high radiofrequency field Nutation NMR was used to study the broad spectral features in detail. Simulations predict characteristic nutation profiles for satellite transitions, both under on-resonance as well as under offresonance conditions, and show how it is possible to set the ST apart from broad CT's. Our experimental results match well with the simulations. We can therefore conclude that we observe broad spectral components that are part of satellite transitions. There are no signs of a distorted surface site other than component B.
Finally, it is worth noting that a full nutation experiment with decent S/N-ratio could be acquired within a day, while the full VOCS took more than a week of measurement time. With VOCS it is difficult to resolve overlapping CT and ST components of sites with different C Q values and measurements at, at least, two different external field strengths are needed to confirm the nature of resonances. Nutation NMR thus proves to be a viable tool to analyze complex multicomponent systems where sites with largely different quadrupolar interaction parameters and a certain degree of disorder coincide.

Sample preparation
Anhydrous MgCl 2 [9] and the organic donor DMDOMe were put together in a Retsch PM-100 planetary ball mill equipped with an airtight chemically inert ceramic jar (Y-stabilized ZrO 2 ). The jar (internal volume of 50 mL) was loaded inside a glovebox along with 87 g of grinding balls (also made of ZrO 2 , diameter 3 mm). The sealed jar was then transferred into the mill. The rotation speed was set to the 650 rpm (maximum value), and the rotation motion was inverted at 20 min. intervals to prevent as far as possible encrustations on the inside walls of the jar. XRD measurements show that the MgCl 2 nanoparticles have average particle dimensions of hL c i = 2.84 and hL a i = 4.37 nm. Magnesium content of the sample has been quantified using ICP-OES. Solution state NMR of the adduct dissolved in deuterated methanol has been used to quantify the donor content using an internal standard and was found to corresponds to 10% per Mg atom. 35 Cl spectra were recorded at room temperature on a Varian 800 MHz spectrometer (18.8 T, 78.3 MHz for 35 Cl) using a static home-built probe with an inner-coil diameter of 1.2 mm. Samples were packed in commercial 1.2 mm ZrO 2 rotors. Solid NaCl was used to calibrate the RF field strengths (m RF = 480 kHz) and as a chemical shift reference. The RF field strength at 77.6 MHz (m RF = 495 kHz) was calibrated after lowering the probe a few cm to the spot where the Cl resonance was found at 77.6 MHz. In the used settings the probe could tune from 74.1 MHz to 81.1 MHz. The RF field strength was assumed to be rather uniform over the whole frequency range also because the power output of the amplifier decreased by a maximum of 10% when going down in frequency to 74.1 MHz. 23 Na experiments were performed at room temperature on a Varian 400 MHz spectrometer (9.4 T, 105.8 MHz for 23 Na) using a commercial 3.2 mm probe.

Solid-state NMR measurements
To overcome problems related to probe ringing, all 35 Cl experiments (including the nutation experiments) are performed using a Hahn echo. Typical solid pulse lengths used are p 2 = 0.4 ls and p = 0.75 ls. To account for build-up of the pulse these pulse lengths are somewhat longer than expected from the RF field strength.

Simulations
The simulations of nutation spectra are performed using either Simpson [36] or an in-house MATLAB implementation of regular density matrix formalisms (available on request). Simulations for 23 Na are performed using a quadrupolar coupling parameter C Q of 2.6 MHz with g = 0.58 for NaSO 4 and C Q = 5.0 MHz with g = 0.2 for a fictive spin system. Simulations were run using 196,417 crystal orientations using the ZCW scheme [37]. For 35 Cl C Q was set to either 4.6 MHz or 10 MHz for component A and B. Because of the distributed line shape of MgCl 2 g is set to 0.6 and 17,710 crystal orientations were run using the ZCW scheme. The simulations do not take into account the probe detection bandwidth and thus produces the full quadrupolar line shape. Hence, they will always include more signal from ST than the experiment. However, using the full 2D nutation experiment, it is possible to deduce the contributions from the different transitions by taking traces at appropriate positions.