Amrit
Venkatesh
ab,
Xuechen
Luan
a,
Frédéric A.
Perras
b,
Ivan
Hung
c,
Wenyu
Huang
ab and
Aaron J.
Rossini
*ab
aDepartment of Chemistry, Iowa State University, Ames, IA 50011, USA. E-mail: arossini@iastate.edu
bUS DOE Ames Laboratory, Ames, Iowa 50011, USA
cNational High Magnetic Field Laboratory (NHMFL), Tallahassee, FL 32310, USA
First published on 28th August 2020
Heteronuclear correlation (HETCOR) spectroscopy is one of the key tools in the arsenal of the solid-state NMR spectroscopist to probe chemical and spatial proximities between two different nuclei and enhance spectral resolution. Dipolar heteronuclear multiple-quantum coherence (D-HMQC) is a powerful technique that can be potentially utilized to obtain 1H detected 2D HETCOR solid-state NMR spectra of any NMR active nucleus. A long-standing problem in 1H detected D-HMQC solid-state NMR experiments is the presence of t1-noise which reduces sensitivity and impedes spectral interpretation. In this contribution, we describe novel pulse sequences, termed t1-noise eliminated (TONE) D-HMQC, that minimize t1-noise and can provide higher sensitivity and resolution than conventional D-HMQC. Monte-Carlo and numerical simulations confirm that t1-noise in conventional D-HMQC primarily occurs because random MAS frequency fluctuations cause variations in the NMR signal amplitude from scan to scan, leading to imperfect cancellation of uncorrelated signals by phase cycling. The TONE D-HMQC sequence uses 1H π-pulses to refocus the evolution of 1H CSA across each SR421 recoupling block, improving the stability of the pulse sequence to random MAS frequency fluctuations. The 1H refocusing pulses also restore the orthogonality of in-phase and anti-phase magnetization for all crystallite orientations at the end of each recoupling block, enabling the use of 90° flip-back or LG spin-lock trim pulses to reduce the intensity of uncorrelated signals. We demonstrate the application of these methods to acquire 1H detected 2D 1H{35Cl} and 1H{13C} HETCOR spectra of histidine·HCl·H2O with reduced t1-noise. To show generality, we also apply these methods to obtain 2D 1H{17O} spectra of 20%-17O fmoc-alanine and for the first time at natural abundance, 2D 1H{25Mg} HETCOR spectra of magnesium hydroxide. The TONE D-HMQC sequences are also used to probe 1H–25Mg and 1H–27Al proximities in Mg–Al layered double hydroxides and confirm the even mixing of Mg and Al in these materials.
Heteronuclear multiple-quantum coherence (HMQC) is a fundamental pulse sequence that is widely used in solution NMR spectroscopy.20 HMQC is a valuable experiment for SSNMR spectroscopy because in principle it can be applied to indirectly observe any NMR active nucleus that is coupled to a “spy” nucleus, usually 1H, 13C or 31P. Many HMQC SSNMR experiments using heteronuclear scalar (J-) or dipolar (D-) interactions for coherence transfer have been described.21–28 Delevoye and co-workers recently demonstrated that 27Al{1H} D-HMQC is more robust and efficient in comparison to CP for the surface characterization of γ-alumina related catalysts.29 We recently used D-HMQC to indirectly observe half-integer quadrupolar nuclei and spin-1/2 nuclei with large chemical shift anisotropy (CSA).30,31 More recently, we have implemented frequency-selective HMQC schemes that offer enhanced sensitivity by reducing recycle delays.32 Fast MAS, proton-detected D-HMQC experiments are most commonly performed with the SR421 recoupling pulse sequence33 as it offers a heteronuclear dipolar coupling scaling factor of ca. 0.25, effective 1H homonuclear decoupling, tolerance to rf inhomogeneity and is not dipolar truncated. However, t1-noise34 often plagues 1H-detected 2D D-HMQC SSNMR spectra partly due to the high sensitivity of the recoupling sequence to rotor synchronization.27,28,30,31 Recently, random signal fluctuations observed in 1H{14N} RESPDOR experiments have also been attributed to MAS instability.35 Generally, the strategies such as spin-lock trim pulses,36 BIRD filters37,38 or pulsed field gradients39 often used to suppress t1-noise in HMQC solution NMR experiments are either incompatible with existing pulse sequences, or simply cannot be implemented with current SSNMR probes. A number of t1 sampling and processing techniques have been proposed to reduce t1-noise in solution NMR experiments.40–44 However, some of these rely on the fact that t1-noise in solution NMR experiments often arises from slow signal intensity modulations; as such these methods are ineffective in solids where the t1-noise is largely time-independent. Perras and Pruski pointed out that since t1-noise scales linearly with the signal amplitude, relaxation delays in D-HMQC SSNMR experiments should be set to values far shorter than the 1.3 × T1 value that is optimal in one-dimensional spectroscopy.45 Robertson et al. demonstrated the use of selective saturation pulses to reduce t1-noise in fast MAS 1H SSNMR experiments.46
One way to reduce t1-noise is to change the recoupling sequence. For example, γ-encoded recoupling sequences such as rotary resonance recoupling (R3) and symmetry based R-sequences are robust with respect to MAS fluctuations.47 However, the γ-encoded sequences are sensitive to rf inhomogeneity and suffer from dipolar truncation. As such, they typically offer lower efficiency than SR421 and adiabatic zero-quantum recoupling methods.48,49 Alternatively, in the TRAPDOR-HMQC (T-HMQC) experiment presented by Carravetta and co-workers,50 long duration, high power pulses are used for both heteronuclear dipolar recoupling and excitation of the indirectly detected nucleus. T-HMQC has recently been shown to provide more sensitivity than D-HMQC with SR421 applied on the 1H channel for 1H{14N} experiments.51 Part of the sensitivity gains with T-HMQC arise from a lessened t1-noise, likely because the signal intensity is insensitive to MAS frequency variations.51 However, T-HMQC requires large B1 fields for long recoupling durations. T-HMQC also results in simultaneous recoupling of the central (CT) and satellite transitions (ST) for half-integer quadrupolar nuclei.52 Further, only the irradiated peak will be excited, preventing detection of anisotropic sideband manifolds with T-HMQC.51
In this contribution, we present a family of novel pulse sequences called t1-noise eliminated D-HMQC (TONE D-HMQC). As shown below, MAS instability is the leading cause of t1-noise for fast MAS 1H{X} D-HMQC experiments that use SR421 recoupling. TONE D-HMQC sequences minimize t1-noise by refocusing 1H CSA after each recoupling block to reduce the variation of the NMR signal intensity with MAS frequency fluctuations and by reducing (saturating) signals from uncorrelated magnetization. The TONE D-HMQC sequences are shown to provide enhanced sensitivity for proton detected D-HMQC experiments with a wide range of spin-1/2 and half-integer quadrupolar nuclei such as 13C, 17O, 25Mg, 27Al and 35Cl.
The desired HMQC signal arises from the fraction of 1H magnetization that is converted to anti-phase coherence, multiple quantum coherence, back to anti-phase and then ultimately reconverted to in-phase magnetization for detection. The intensity of the desired HMQC signal is denoted as correlated signal intensity (Scorr). The remaining 1H magnetization that stays as in-phase/single spin operators throughout the HMQC sequence is responsible for the uncorrelated magnetization/NMR signal, denoted Suncorr. Experimentally, the desired HMQC signal is retained, and signals from uncorrelated magnetization are eliminated, by synchronous 180° phase alternation of the receiver and one of the X-channel π/2 pulses on subsequent scans. As shown below, random fluctuations of the MAS frequency can cause Suncorr to vary from scan to scan, leading to the imperfect cancellation of the uncorrelated signal by phase cycling and substantial t1-noise when the ratio Scorr/Suncorr is small. Scorr/Suncorr will be small in cases where the X spin natural abundance is low and when the 1H and X spins are weakly coupled. Here, weakly coupled means that the inverse of the scalar coupling or scaled dipolar coupling that evolves in the HMQC pulse sequence is larger than the 1H refocused transverse relaxation time T2′.
Fig. 1B–E show redesigned D-HMQC sequences that reduce t1-noise by improving the robustness of the pulse sequence to MAS frequency variations and by reducing the magnitude of uncorrelated 1H magnetization with flip-back or saturation pulses. TONE D-HMQC-1 features simultaneous, rotor-synchronized π pulses on the 1H and X channel that break each recoupling block into two symmetric parts (Fig. 1B). The simultaneous 1H and X π pulses sandwiched within each dipolar recoupling block permit evolution of the heteronuclear dipolar coupling while refocusing the 1H CSA across each recoupling block. Refocusing the 1H CSA restores the orthogonality of the correlated, anti-phase (2IySz) and uncorrelated, in-phase 1H magnetization (Ix) for all crystallite orientations. As discussed below, refocusing the 1H CSA across each recoupling block also improves the robustness of the pulse sequence towards MAS frequency fluctuations. Analogous ideas but in different contexts have been reported previously; for instance, π pulses have been used to refocus the residual effects of dipolar coupling in continuous wave decoupling sequences55 and the CSA contributions in T1ρ measurements,56 whereas the perfect echo sequences in solution NMR use π/2 pulses to refocus anti-phase components.57 Brinkmann et al. have proposed the use of dual channel symmetry-based recoupling sequences to selectively recouple heteronuclear dipolar interactions while suppressing CSA terms.58
TONE D-HMQC-2 is similar to TONE D-HMQC-1, except a π/2±y pulse is appended at the end of the first refocused dipolar recoupling block (Fig. 1C). The π/2±y pulse acts as a flip-back pulse for uncorrelated, in-phase Ix magnetization, transforming it to longitudinal magnetization (∓Iz). This flip-back pulse will reduce the magnitude of Suncorr, helping to suppress the t1-noise by increasing the ratio Scorr/Suncorr,. The TONE D-HMQC-3 sequence replaces the flip-back pulse with a long duration (∼1 ms) Lee-Goldburg (LG) trim pulse.36 The LG trim pulse spin-locks the correlated 1H magnetization, while the uncorrelated magnetization rotates around the tilted effective B1 field of the LG spin-lock pulse, resulting in dephasing due to rf inhomogeneity (Fig. 1D).36 The LG condition suppresses 1H spin-diffusion of the spin-locked, correlated magnetization. Suppression of 1H spin diffusion is critical to ensure the anti-phase magnetization can be reconverted to in-phase magnetization in the second part of the sequence. We have previously identified low- and high-rf field LG conditions compatible with fast MAS frequencies.59
Finally, in TONE D-HMQC-4 the LG spin-lock/trim pulse is applied symmetrically about the central 1H π pulse for the entire duration of the indirect evolution period (t1) (Fig. 1E). The LG pulses dephase the uncorrelated magnetization while spin-locking the correlated magnetization throughout the duration of the t1 period. We have previously applied constant-time D-HMQC to enable arbitrary spectral widths,30 however, the constant echo duration in the central part of the sequence causes reduced sensitivity because of 1H transverse relaxation.31 The TONE D-HMQC-4 sequence offers the improved spectral resolution associated with a constant-time experiment and allows arbitrary indirect spectral widths, but reduces relaxation losses since the relaxation is determined by the 1H spin-diffusion rate under the LG pulse, rather than 1H T2′ as occurs in the other HMQC sequences. Note that TONE D-HMQC-4 can also be performed in an incremented fashion by eliminating uncorrelated signals with LG spin-lock or flip-back pulses added prior to the t1-period (discussed below; Fig. S7, ESI†). Various 1H homonuclear decoupling schemes have previously been implemented into D-HMQC and D-HSQC (dipolar heteronuclear single quantum coherence) pulse sequences to improve resolution.60,61
Numerical SIMPSON62–64 and Monte Carlo simulations were used to demonstrate how random MAS frequency fluctuations cause t1-noise and understand how the TONE family of pulse sequences can reduce t1-noise (Fig. 2, see the ESI† for additional details and the input files). First, SIMPSON simulations of a 1H–13C spin system were used to determine the MAS frequency dependence of 1D D-HMQC and TONE D-HMQC-2 signal intensities at a magnetic field of 9.4 T. Profiles showing the signal intensity as a function of the deviation from the set MAS frequency (ΔMAS) were calculated for both the correlated magnetization (HMQC signal, Fig. 2A and B) and uncorrelated magnetization (background signals, Fig. 2C and D). For simplicity we compare standard D-HMQC and TONE D-HMQC-2 in this section as the analysis will be similar for comparison of D-HMQC and any of the TONE sequences. The SIMPSON simulations were performed with 1H reduced anisotropy (δaniso) values of 1, 10, 17 and 34 ppm to illustrate the contribution of improper refocusing of the 1H CSA to t1-noise. For reference, a plane-wave DFT GIPAW calculation predicts that the ammonium 1H NMR signal at 17.2 ppm in histidine has a reduced anisotropy of 17 ppm. Doubling the static Zeeman field from 9.4 T to 18.8 T would double the size of the CSA in units of Hz, hence, calculations were also performed with a 1H δaniso of 34 ppm to mimic the effects of higher static magnetic fields. The simulations were performed with a model 1H–13C spin system and a heteronuclear dipolar coupling of 2 kHz. The total recoupling time was separately optimized in SIMPSON and set to a total duration of 72 rotor cycles (1.44 ms) in all simulations. In these simulations the recoupling pulse widths, timings and echo durations were calculated and fixed based upon an MAS frequency of 50 kHz, then the signal intensities were calculated in SIMPSON for different input MAS frequencies.
Fig. 2A–D show the variation of the correlated and uncorrelated D-HMQC and TONE D-HMQC-2 signal intensities for ΔMAS = ± 200 Hz. A flip-back pulse with a tip angle of 75° was used in the TONE D-HMQC-2 simulations to account for rf inhomogeneity (Fig. 2B and D). With δaniso = 1 ppm (blue dashed curves) the dependence of the correlated and uncorrelated D-HMQC and TONE D-HMQC-2 signals on ΔMAS is relatively flat in the range of ΔMAS = ±50 Hz, which is the range of most interest as experimental MAS fluctuations will likely be less than 50 Hz. However, the D-HMQC and TONE D-HMQC-2 signal intensity-MAS frequency profiles considerably sharpen as δaniso increases. Notably, the profiles for both correlated and uncorrelated TONE D-HMQC-2 signals are broader than the corresponding profiles for D-HMQC (when comparing profiles with the same δaniso), illustrating the improved tolerance of TONE D-HMQC-2 to MAS frequency variations. Additionally, for each value of δaniso, the profiles for the uncorrelated signal are slightly sharper than the corresponding profile for the correlated signal. This observation suggests that experimental random fluctuations of MAS frequency could cause substantial t1-noise because uncorrelated signals will be imperfectly cancelled by phase cycling. Therefore, in the absence of extremely stable MAS frequencies (variations of 1–2 Hz), reducing the magnitude of the uncorrelated signal is critical to reducing t1-noise.
A Monte-Carlo style code built in MATLAB was used to simulate the variation of t1-noise in 2D HMQC experiments with the different pulse sequences (Fig. 2E–H). The code performs the following steps: First, a Gaussian probability function is used to randomize the MAS frequency for each scan. Then, the scaling factors for the correlated and uncorrelated signals are calculated using the randomly generated MAS frequency and the intensity-MAS frequency profiles obtained from SIMPSON (Fig. 2A–D). The scaling factors are then used to calculate the correlated and uncorrelated time domain signal intensities for each scan followed by the calculation of the final time domain intensity for each t1-point by summing across 16 scans. This procedure was repeated for 500 t1-points with Δt1 = 10 μs and the resulting noised-FID was subject to Fourier transformation and signal-to-noise ratio (SNR) measurements. A more detailed description of the MATLAB code with examples is provided with the ESI.†
Fig. 2E shows a plot of the calculated SNR of the indirect dimension as a function of σMAS for standard D-HMQC with different δaniso values. There are two clear and expected trends: the SNR worsens as σMAS increases and as δaniso increases. An increase in σMAS corresponds to less stable MAS, and as illustrated in Fig. 2A and C, the amplitude of correlated and uncorrelated signals show greater variation with MAS frequency as δaniso increases. On the other hand, in all cases TONE D-HMQC-2 is more robust to changes in σMAS (Fig. 2F). For instance, with δaniso of 17 ppm and σMAS of 4 Hz, the SNR with D-HMQC is calculated to be 46 whereas the SNR with TONE D-HMQC-2 is calculated to be 94, which corresponds to a factor 2 gain in SNR. Furthermore, taking into consideration the reference SNR was 95, the calculations suggest that TONE D-HMQC-2 has effectively eliminated the t1-noise arising from MAS instability. The predicted gain in SNR with TONE D-HMQC-2 is plotted in Fig. 2G. There is no appreciable gain in SNR with TONE when δaniso is 1 ppm or when σMAS is close to zero. However, the SNR with the TONE sequence is predicted to increase by a factor 2–8 when δaniso is 17 or 34 ppm and when σMAS > 4 Hz. Finally, Fig. 2H shows the effects of varying the tip angle of the flip-back pulse in TONE D-HMQC-2 for a fixed δaniso of 17 ppm. Tip angles of less than 90° were considered to illustrate the effects of rf inhomogeneity. As the pulse tip-angle is reduced from 90° to 60° the SNR reduces slightly due to an imperfect flip-back of the uncorrelated magnetization. In summary, the simulations demonstrate that TONE D-HMQC reduces t1-noise by improving the robustness of the sequences to MAS fluctuations and suppressing undesired uncorrelated 1H NMR signals. The similarity of the predicted and experimentally observed sensitivity gains for 1H{35Cl} D-HMQC experiments validates the model of D-HMQC t1-noise arising from the random variation of signal intensities because of MAS frequency fluctuations (vide infra).
The TONE D-HMQC pulse sequences were experimentally tested for 1H detection of a variety of NMR active nuclei including 35Cl, 25Mg, 13C and 17O. Fig. 3 shows experimental data acquired with the different D-HMQC pulse sequences on histidine hydrochloride monohydrate, denoted as histidine, at 9.4 T and 50 kHz MAS frequency. For these experiments σMAS was estimated to be 2 Hz based upon analysis of the MAS frequency log output by the spectrometer (Fig. S1, ESI†), but the true experimental σMAS values are likely larger considering that spectrometer outputs time-averaged MAS frequencies.65 1D 1H{35Cl} D-HMQC spectra (from the first t1-increment of the 2D experiment) obtained with the different pulse sequences are shown in Fig. 3A–E. The relative intensity of the 1H signals at 9.0 ppm and 12.7 ppm are indicated. The 35Cl spectra shown in Fig. 3F–J were extracted from the most intense column (the ammonium signal at δiso = 9.0 ppm) of the corresponding 2D D-HMQC spectra (Fig. S2, ESI†). TONE D-HMQC-1 has 1H signal intensities that are reduced by ca. 35–45% as compared to D-HMQC (Fig. 3B). 1D 1H NMR spectra acquired with recoupled echo pulse sequences show minimal losses due to the incorporation of CSA refocusing π pulses on the 1H channel (Fig. S3, ESI†). Therefore, the significant reduction in 1H intensity observed with TONE D-HMQC-1 must be due to the efficiency of the CT-selective π inversion pulses (Fig. 3B). Indeed, a reduction in intensity due to imperfect CT-selective inversion pulses is also predicted by SIMPSON simulations (Fig. S4, ESI†). However, despite the reduction in the direct dimension signal intensity, the sensitivity (S = SNR/√time) of the 35Cl trace increases from 1.7 to 3.1 min−1/2, corresponding to a gain of 1.8 (3.1/1.7 min−1/2), due to reduction of t1-noise (Fig. 3G). This gain demonstrates the efficacy of refocusing the 1H CSA across each recoupling block.
Surprisingly the 1H signal intensity given with TONE D-HMQC-2 was higher by ca. 16–19% in comparison to the conventional D-HMQC sequence (Fig. 3C). This result is unexpected because additional pulses typically reduce the efficiency of SSNMR experiments. With the addition of the π/2 flip-back pulse, the symmetry of the TONE D-HMQC-2 pulse sequence is reminiscent of the perfect echo pulse sequences,57 which are known to refocus homonuclear 1H couplings. 2-Spin 1H–1H SIMPSON numerical simulations and experiments with dipolar recoupled perfect echo pulse sequences show increased 1H signal intensity, suggesting that the introduction of purge pulses (π/2 or LG spin-lock) may refocus 1H homonuclear dipolar couplings (Fig. S3, ESI†). In summary, the intensity lost in TONE D-HMQC-1 due to the inefficiency of the inversion π pulses on the 35Cl channel is compensated by the intensity gained from the partial refocusing of the 1H homonuclear dipolar couplings by the purge pulse, resulting in an overall net gain in signal with TONE D-HMQC-2. The TONE D-HMQC-2 35Cl trace shows a similar intensity (I = 0.94) in comparison to the conventional D-HMQC spectrum, but the 35Cl sensitivity is 2.1 times better with TONE D-HQMC-2. On comparing TONE D-HMQC-2 with TONE D-HMQC-1, we note that the intensity of the 35Cl trace improves by a factor 1.74 (0.94/0.54), while there is only a modest gain in 35Cl sensitivity by a factor 1.2 (3.6 min−1/2/3.1 min−1/2) (Fig. 3H). As t1-noise is multiplicative, meaning it is proportional to the signal intensity, the t1-noise is likely also higher in the case of TONE D-HMQC-2 and this leads to a smaller gain in sensitivity with respect to TONE D-HMQC-1.45 A slight improvement in sensitivity could possibly be obtained with TONE D-HMQC-2 by removing pre-saturation pulses and adjusting the phase of the flip-back pulse to always return uncorrelated magnetization to +Iz. Preserving the uncorrelated magnetization could result in reduced optimal recycle delays as is observed with flip-back CP66 or FS-HMQC sequences.32Fig. 3D and I show the 1H and 35Cl traces, respectively, acquired using TONE D-HMQC-3 with a LG spin-lock trim pulse duration of 497.85 μs (25 rotor cycles). The 1D 1H intensity is comparable to D-HMQC (0.98 and 1.15 for the 1H signals at 9.0 and 12.7 ppm). The 35Cl sensitivity improves to 5.4 min−1/2, corresponding to an overall gain in sensitivity by a factor 3.2 (5.4 min−1/2/1.7 min−1/2) with respect to conventional D-HMQC. The duration of LG spin-lock trim pulse in TONE D-HMQC-3 should be experimentally optimized to find the best compromise between minimizing HMQC signal losses and eliminating t1-noise (Fig. S5, ESI†).
Finally, we observe that TONE D-HMQC-4 with total LG spin-lock pulse duration of 1315.7 μs (33 rotor cycles) shows a reduction in 1H signal by only ca. 6% as compared to D-HMQC (Fig. 3E). On comparing 1D 1H{35Cl} TONE D-HMQC-3 and TONE D-HMQC-4 spectra acquired with a two rotor cycle LG spin-lock duration, we observed that the TONE D-HMQC-4 1H signal is higher by ca. 20%, likely due to partial refocusing of 1H homonuclear dipolar couplings (Fig. S6, ESI†). However, the rate of decay of the 1H signal under the LG spin-lock is slightly faster with TONE D-HMQC-4 than TONE D-HMQC-3 (Fig. S5, ESI†) causing the HMQC intensities to become similar, despite the longer LG spin-lock duration used in TONE D-HMQC-4 (Fig. 3D and E). The signal loss in TONE D-HMQC-4 occurs due to residual 1H–1H spin-diffusion during the central LG pulses, likely between 1H sites with the same chemical shift within the lattice.59 When a correlated 1H spin undergoes spin exchange (diffusion) with an uncorrelated 1H spin, the 1H HMQC signal is not refocused or recoupled properly, resulting in an increased rate of signal loss. Fig. 3J shows that the 35Cl trace obtained with TONE D-HMQC-4 has a sensitivity of 4.4 min−1/2. The overall gain in sensitivity with TONE D-HMQC-4 is 2.6 compared to conventional D-HMQC (Fig. 3E and J). The efficacy of t1-noise elimination is evident from the comparison of 2D D-HMQC and 2D TONE D-HMQC-4 spectra shown in Fig. 3K and L. Additionally, the resolution of the 35Cl trace offered by TONE D-HMQC-4 is dramatically higher than any other method because it is a constant-time sequence.30 The LG pulses used in TONE D-HMQC-4 increase sensitivity as compared to a constant time D-HMQC experiment because the correlated 1H magnetization will decay more slowly under the LG spin-lock than it does under transverse free-evolution (Fig. S5, ESI†).
Fig. S7 (ESI†) shows an additional pulse sequence, denoted as TONE D-HMQC-5, which combines TONE D-HMQC-3 and -4 to enable t1-noise elimination and incremented t1 periods. The resolution decreases slightly with the TONE D-HMQC-5 as compared to TONE D-HMQC-4 because relaxation during the variable LG spin-lock used in TONE D-HMQC-5 results in slight additional broadening of the indirect dimension signals (Fig. S5, ESI†). When the decay of the 1H magnetization is slower under the LG spin-lock than for 1H transverse relaxation, both TONE D-HMQC-4 and TONE D-HMQC-5 sequences are expected to perform similarly, whereas when the LG spin-lock decay rate is comparable to the transverse decay rate, TONE D-HMQC-5 will provide more signal, but with lower resolution.
35Cl traces extracted from the 2D NMR spectra at a 1H shift of 12.7 ppm demonstrates the feasibility of using the TONE D-HMQC sequences to observe correlations between weakly dipolar coupled spin pairs (Fig. 3M). A plane-wave density-functional theory (DFT) optimized structure of histidine shows that the shortest H–Cl distance (2.26 Å or dipolar coupling (b/2π) of 1021 Hz) corresponds to the ammonium 1H signal at 9 ppm, in agreement with the observation that this 1H signal shows the most intense correlations in the 2D D-HMQC spectra (Fig. 3K and Fig. S2, ESI†). Weaker 1H–35Cl heteronuclear correlations were observed in the 2D D-HQMC spectra for the amine 1H NMR signal at 12.7 ppm and ammonium 1H NMR signal at 17.2 ppm because of longer H–Cl internuclear distances and lower heteronuclear dipolar couplings (2.84 Å, b/2π = 514 Hz and 3.84 Å, b/2π = 208 Hz, respectively). Weak heteronuclear dipolar interactions will lead to smaller ratios of correlated magnetization to uncorrelated magnetization, which was predicted above to lead to increased t1-noise. Consequently, with conventional D-HMQC it is very challenging, if not impossible, to observe the correlations between 35Cl and the 1H NMR signals at 12.7 ppm and 17.2 ppm with reasonable SNR (Fig. 3K and top slice in Fig. 3M). These correlations are even more challenging to observe at higher static magnetic fields due to the increase in 1H CSA (Fig. S8, ESI†). Notably, as shown in Fig. 3L and Fig. S2 (ESI†), the 1H–35Cl correlations at a 1H shift of 12.7 ppm and 17.2 ppm can be clearly observed with TONE D-HMQC-2–4, with TONE D-HMQC-4 providing the best resolution of the 35Cl site. These results demonstrate the value of proton detected TONE D-HMQC sequences for indirectly detecting high resolution quadrupolar powder patterns of half-integer quadrupolar nuclei and extracting meaningful spatial proximity information from 2D HETCOR spectra.
The sensitivity of the TONE D-HMQC sequences can be further improved using the population transfer (PT) scheme.67 In PT D-HMQC experiments, saturation pulses are applied to the satellite transitions of the quadrupolar spin concurrent with the 1H recoupling scheme. The RAPT pulses68 are easily incorporated into the TONE D-HMQC pulse sequences as shown in Fig. S9 and S10 (ESI†) providing further improvements in sensitivity by a factor 1.5–2. The ‘TONE’ concept can also be extended to D-HSQC experiments.6,27 Fig. S11 (ESI†) shows that 1D 1H{35Cl} TONE D-HSQC has 10% higher signal in comparison to conventional D-HMQC. Notably, the 35Cl NMR spectra obtained using TONE D-HSQC show similar resolution to those obtained with D-HMQC, suggesting the time constant for 1H spin diffusion is similar to the 1H T2′ (Fig. S11 and S12, ESI†). Notably, the 35Cl slice extracted from the 2D TONE D-HSQC spectrum has a sensitivity of 4.4 min−1/2, which is comparable to the sensitivities obtained with the various TONE D-HMQC sequences (Fig. S11, ESI† and Fig. 3G–J). Therefore, the ideas presented in this article will also aid the further development of D-HSQC pulse sequences in the future.
25Mg solid-state NMR spectroscopy has been used for the characterization of metal–organic frameworks (MOFs),69 layered double hydroxides,70 and a number of other organic/inorganic compounds.71 Unfortunately, 25Mg is a spin-5/2 quadrupolar nucleus with a low natural abundance of 10% and a low Larmor frequency (ca. 2.6 MHz T−1), which makes observation of its NMR spectra at natural abundance very challenging. The development of natural abundance 2D 1H{25Mg} proton detected HETCOR methods to improve sensitivity and probe 1H–25Mg spatial proximities would be helpful for the characterization of magnesium containing materials. Fig. 4A shows the application of 2D 1H{25Mg} HETCOR solid-state NMR to Mg–Al layered double hydroxides.72–74 The 1D 1H spectrum (Fig. 4A, red trace) of the MgAl-27.8-NO3− sample (the molar percentage of Al3+ was determined using ICP) shows three signals corresponding to the Mg3OH (1.2 ppm), Mg2AlOH (3.3 ppm) and water sites (4.8 ppm), in good agreement with previous reports (Fig. S13, ESI†).72–74 The 1H signals at 1.2 and 3.3 ppm are both correlated to broad MAS 25Mg second-order quadrupolar powder patterns. Simulations of these patterns give CQ values of 4.5–4.8 MHz in agreement with previous studies (Fig. S14, ESI†).73 Upon reducing the total dipolar recoupling from 1.732 to 0.8 ms, the correlation between the 1H at 1.2 ppm and the expected brucite-like 25Mg site becomes clearer (Fig. S14, ESI†). The observed correlations suggests an even mixing of Mg and Al rather than the formation of domains, in agreement with 2D 1H SQ-DQ correlations experiments.73 The result is further corroborated with 1H{27Al} TONE D-HMQC-4 experiments that show an intense correlation between the 1H site at 3.3 ppm and the single 27Al site (Fig. 4B). Notably, TONE D-HMQC-4 provides the highest resolution in the 27Al spectrum amongst the D-HMQC and D-HSQC pulse sequences, while the best absolute 27Al resolution is provided by 27Al → 1H D-RINEPT because 1H heteronuclear decoupling can be applied during t1 evolution (Fig. S15 and S16, ESI†). These results demonstrate the utility of fast MAS, proton detected TONE D-HMQC methods for the precise characterization of local structure in heterogeneous materials.
Due to efficient suppression of t1-noise, the application of PT TONE DHMQC-3 results in a gain in sensitivity in the 25Mg dimension by a factor 2.5 compared to 1H{25Mg} PT D-HMQC, while TONE D-HMQC-1 and 2 provide less sensitivity gain (Fig. S17, ESI†). TONE D-HMQC-4 produced a low quality spectrum due to a short 1H T1ρ under the LG spin-lock pulse (Fig. S18, ESI†). While it was not tested, TONE D-HMQC-5 would probably work well for this sample. TONE D-HMQC-4 provided a well-resolved 25Mg quadrupolar pattern for magnesium hydroxide (Fig. S19, ESI†). These results suggest that judicious choice of TONE D-HMQC-2, -3 or -4 should be made based on the lifetime of the TONE D-HMQC signal under the LG spin-lock pulse. The lifetime can be easily determined by varying the LG spin-lock pulse and monitoring the 1D TONE D-HMQC signal intensities. While TONE D-HMQC-4 is a valuable experiment that can provide increased resolution in the indirect dimension, TONE D-HMQC-3 appears to provide the highest sensitivity (Fig. 4 and Fig. S17, ESI†). As explained in the previous section, TONE D-HMQC-4 is susceptible to signal losses due to residual spin-diffusion during the LG spin-lock pulse. This problem is exacerbated when the fraction of uncorrelated spins is higher and/or when the heteronuclear dipolar coupling constant is weaker.59 Therefore, differences in the residual 1H spin diffusion rate under the LG spin-lock pulse may explain the more negative impact on the TONE D-HMQC-4 experiments with 25Mg than 27Al (Fig. S18, ESI†). TONE D-HMQC-4 requires a LG spin-lock lifetime that is long enough to capture the decay of the indirect dimension signals and will only be effective in samples where the loss of signal due to this residual 1H spin-diffusion is minimal. In cases, where TONE D-HMQC-4 is ineffective, TONE D-HMQC-3 or TONE D-HMQC-2 may work more efficiently as observed here. Based on the high efficiency of TONE D-HSQC observed with 1H{35Cl} experiments described earlier, we expect TONE D-HSQC to also be a suitable alternative.
13C has a natural abundance of 1.1% which means that approximately 1% of protons in the sample may participate in the D-HMQC experiment and approximately 99% of the 1H NMR signal must be canceled out through phase cycling.27,75 Furthermore, the ca. 50% maximum efficiency of the dipolar recoupling induces further losses. Therefore, there is a high probability for the observation of t1-noise in a natural abundance 1H{13C} D-HMQC experiment, even with slight MAS instabilities of a few Hz. We note that 1H{13C} idHETCOR pulse sequences that use efficient CP blocks for 1H–13C magnetization transfer and saturation pulses to eliminate uncorrelated 1H magnetization are preferred for proton-detected natural abundance 13C SSNMR.11,13 However, as a proof-of-concept, 1H{13C} D-HMQC experiments were performed with natural isotopic abundance histidine. As expected, there is considerable t1-noise in the conventional 2D 1H{13C} D-HMQC spectrum (Fig. 5A). The amine and ammonium 1H NMR signals at 12.7 and 17.2 ppm display the most t1 noise because both these sites also have the largest 1H CSA. This result is consistent with the simulations presented above. Fig. 5B shows a TONE D-HMQC-3 spectrum that is essentially devoid of t1-noise, similar to the 1H–35Cl data shown in Fig. 2. As shown in Fig. S20 (ESI†) while setting the relaxation delay according to Perras45 also improves the signal to noise ratio, a far more successful approach is to simply eliminate t1-noise at the source, demonstrating the value of TONE D-HMQC.
Fig. 5C shows a 1H{17O} population transfer (PT) D-HMQC spectrum of 20% 17O labeled fmoc-alanine.76 The t1-noise arising from the large fraction of uncorrelated low-frequency 1H signals in the D-HMQC spectrum is easily eliminated with the use of the TONE D-HMQC-3 method (Fig. 5D). Owing to the large 1H–17O dipolar coupling (ca. 13.5 kHz) for the carboxylic acid proton at 14 ppm, each block is only 40 μs in duration in the D-HMQC experiments. Despite the fact that only a short recoupling time was required, TONE D-HMQC-3 still increases the sensitivity of 17O column at a 1H chemical shift of 14 ppm by a factor of 1.5 as compared to PT D-HMQC. TONE D-HMQC-4 did not improve the 17O sensitivity further, likely because the correlated HMQC signal has a short lifetime under the LG spin-lock pulse, as was discussed earlier.
Based upon the observations made here there are some general considerations to guide the selection of pulse sequence for 1H detected fast MAS HMQC/HSQC experiments. The only disadvantage of the TONE D-HMQC-2 or TONE D-HSQC sequences as compared to conventional D-HMQC is that a π inversion pulse is required on the X channel. Hence, TONE D-HMQC-2 or TONE D-HSQC experiments are recommended in place of D-HMQC for indirect detection of spin-1/2 and half-integer quadrupolar nuclei. TONE D-HMQC-3, -4 and -5 pulse sequences utilize LG spin-lock pulses to eliminate t1-noise and enhance indirect dimension resolution and were found to give better performance than TONE D-HMQC-2. The downside of the TONE D-HMQC-3, -4 and -5 pulse sequences is that LG pulse durations need to be optimized and the rf-field should be correctly selected. The LG spin-lock pulse ν1 should be more than 2.5 × νr or between 0.1 × νr and 0.25 × νr to avoid rotary resonance conditions in fast MAS experiments.59 LG trim pulses with durations between 250 μs and 1 ms were found to be sufficient to reduce the uncorrelated signal in the TONE D-HMQC-3–5 pulse sequences. Unfortunately the decay rate of spin-locked anti-phase magnetization (IySz) during the LG spin-lock pulse is sample dependent, therefore the LG pulse duration should be experimentally optimized with both high- and low-rf field LG pulses to identify the best conditions. The LG pulse duration in the TONE D-HMQC-4 pulse sequence must be set to a duration greater than t1,max, hence, this sequence is only applicable to samples which exhibit a slow decay of spin-locked anti-phase magnetization. For the TONE D-HMQC-5 pulse sequence, the duration of the first LG spin-lock pulse is set in the same way as TONE D-HMQC-3, whereas the second LG pulse block is applied throughout t1 in an incremented fashion. Therefore, a slow decay of spin-locked anti-phase magnetization is also required for TONE D-HMQC-5 as well, although it will likely provide higher sensitivity than TONE D-HMQC-4. For experiments with half-integer quadrupolar nuclei, all the pulse sequences reported here can be performed with the population transfer (PT) scheme67,77 (Fig. 1 and Fig. S7, S9 and S11, ESI†). In all cases PT was found to improve sensitivity. The use of PT necessitates optimization of the recoupling duration and the power and offset of satellite transition saturation pulses, although we have found that the same parameters for PT generally work well for a given nucleus. Finally, in cases where the 1H T1 is long or if the t1-noise elimination by TONE is still insufficient, X → 1H D-RINEPT experiments work well.31
The TONE D-HMQC and D-HSQC sequences presented here will allow the acquisition of HETCOR spectra with unreceptive and exotic nuclei, thereby widening the applicability of SSNMR. For instance, the techniques described here for 13C, 17O and 35Cl should be applicable for the characterization of pure and formulated active pharmaceutical ingredients. 25Mg and 27Al experiments should be applicable to characterize a variety of inorganic materials or heterogeneous catalysts. It should also be possible to combine the sequences presented in this paper with other sensitivity enhancement techniques, such as dynamic nuclear polarization (DNP), where fast-MAS was recently introduced.78,79 As pointed out previously, fast MAS DNP probes from Bruker may induce higher t1-noise due to instabilities caused by the VT and Venturi gas flows.45 TONE D-HMQC may enable correlation spectroscopy under DNP conditions with challenging nuclei. Such a combination would be of tremendous use for the characterization of materials and isotopes that were previously inaccessible using conventional solid-state NMR.
All samples were handled under ambient conditions and packed into zirconia rotors that were spun using N2 gas for NMR experiments. 1H rf calibrations were performed using a simple 90°-spin-lock sequence by determining the 0th and 2nd order rotary resonance conditions. The 25Mg rf fields were calibrated using the Bloch–Siegert shift method reported by Hung et al.80 The π/2 pulses used for 1H, 13C, 17O, 25Mg, 27Al and 35Cl were 2.5 μs, 2.5 μs, 4.75 μs, 10 μs, 13.0 μs and 4.75 μs, respectively. For the 18.8 T experiments, a 35Cl π/2 pulse duration of 5.25 μs was used. Pulses on half-integer quadrupolar nuclei 17O, 25Mg, 27Al and 35Cl were central-transition selective. A pulse duration of 1 μs was used for the 35° 1H pulses that sandwich the LG spin-lock pulses. In all cases, the LG spin-lock pulses were applied off-resonance to satisfy the LG condition (Δν0 = ν1/√2, where Δν0 is the calculated transmitter offset and ν1 is the applied rf field).591H–X heteronuclear dipolar recoupling was performed using the SR421 dipolar recoupling sequence33 at the 2nd order rotary resonance condition in all cases. 1H heteronuclear decoupling (in case of D-RINEPT experiments) was performed using pulses applied at the 0th order rotary resonance condition (HORROR condition). 1H pre-saturation was performed using a train of 90° pulses in all 1H excitation experiments to equilibrate the 1H magnetization before each scan. All 2D spectra were acquired using the States-TPPI method. 2D spectra are presented with skyline projects on the F2 and F1 axes unless mentioned otherwise. Further details for all experiments are provided below or in the respective figure captions.
1H chemical shifts were indirectly referenced to neat tetramethylsilane by using adamantane (δiso(1H) = 1.82 ppm). Topspin 3.6.1 was used to process all experimental NMR spectra. The average of four signal-to-noise ratio (SNR) measurements was considered while measuring SNR and calculating sensitivities. Care was taken to acquire and process spectra consistently before making comparisons.
In case of the 18.8 T 2D 1H{35Cl} experiments, optimal total dipolar recoupling durations of 1.52 and 1.76 ms were used in the conventional D-HMQC and TONE D-HMQC experiments, respectively. Total LG spin-lock pulses of durations 100 rotor cycles and 130 rotor cycles were applied at 150 kHz rf for the TONE D-HMQC-3 and 4 experiments, respectively. 38.0 μs WURST pulses were applied at an rf field of ca. 26 kHz on the 35Cl to achieve population transfer. The frequency offset of the WURST pulses was alternated between ±200 kHz.
1H{27Al} (TONE) D-HMQC and TONE D-HSQC 1Ds were obtained with 128 scans and 1.1 s recycle delay whereas the 2Ds were obtained with 8 scans, 1.1 s recycle delay and 40 t1 increments with a 6 kHz F1 spectral width. The 2D D-RINEPT experiment differed only in the recycle delay and the number of scans which were set to 0.2 s and 40 (512 scans for the 1D), respectively. Optimal dipolar recoupling durations of 0.532–0.932 ms were used. LG spin-lock pulses were applied at 150 kHz rf for durations of 15 and 204 rotor cycles in TONE D-HMQC-3 and TONE D-HMQC-4, respectively.
Footnote |
† Electronic supplementary information (ESI) available: Additional tables, figures, pulse programs, SIMPSON input files, 2D NMR datasets and MATLAB scripts. See DOI: 10.1039/d0cp03511d |
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