Optimisation of ¹H PMLG homonuclear decoupling at 60 kHz MAS to enable ¹⁵N–¹H through-bond heteronuclear correlation solid-state NMR spectroscopy

Abstract

The Lee–Goldburg condition for homonuclear decoupling in ¹H magic-angle spinning (MAS) solid-state NMR sets the angle θ, corresponding to arctan of the ratio of the rf nutation frequency, ν₁, to the rf offset, to be the magic angle, θ_m, equal to tan⁻¹(√2) = 54.7°. At 60 kHz MAS, we report enhanced decoupling compared to MAS alone in a ¹H spectrum of ¹⁵N-glycine with at θ = 30° for a ν₁ of ∼100 kHz at a ¹H Larmor frequency, ν₀, of 500 MHz and 1 GHz, corresponding to a high chemical shift scaling factor (λ_CS) of 0.82. At 1 GHz, we also demonstrate enhanced decoupling compared to 60 kHz MAS alone for a lower ν₁ of 51 kHz, i.e., a case where the nutation frequency is less than the MAS frequency, with θ = 18°, λ_CS = 0.92. The ratio of the rotor period to the decoupling cycle time, Ψ = τ_r/τ_c, is in the range 0.53 to 0.61. Windowed decoupling using the optimised parameters for a ν₁ of ∼100 kHz also gives good performance in a ¹H spin-echo experiment, enabling implementation in a ¹H-detected ¹⁵N–¹H cross polarisation (CP)-refocused INEPT heteronuclear correlation NMR experiment. Specifically, initial ¹⁵N transverse magnetisation as generated by ¹H–¹⁵N CP is transferred back to ¹H using a refocused INEPT pulse sequence employing windowed ¹H decoupling. Such an approach ensures the observation of through-bond N–H connectivities. For ¹⁵N-glycine, while the CP-refocused INEPT experiment has a lower sensitivity (∼50%) as compared to a double CP experiment (with a 200 μs ¹⁵N to ¹H CP contact time), there is selectivity for the directly bonded NH₃⁺ moiety, while intensity is observed for the CH₂¹H resonances in the double CP experiment. Two-dimensional ¹⁵N–¹H correlation MAS NMR spectra are presented for the dipeptide β-AspAla and the pharmaceutical cimetidine at 60 kHz MAS, both at natural isotopic abundance. For the dipeptide β-AspAla, different build-up dependence on the first spin-echo duration is observed for the NH and NH₃⁺ moieties demonstrating that the experiment could be used to distinguish resonances for different NH_x groups.

---

1. Introduction

Direct ¹H detection is increasingly important for solid-state NMR study of pharmaceuticals^1–4 and biological molecules.^5–8 The availability of ever faster Magic Angle Spinning (MAS) frequencies reduces line broadening due to ¹H homonuclear dipolar couplings.^9–14 In particular, ¹H detection is advantageous for the identification of specific correlations to nuclei with low gyromagnetic ratio, γ, such as the two natural-abundant isotopes of nitrogen, ¹⁴N and ¹⁵N. Our focus here is on the spin I = 1/2 ¹⁵N, though it is to be noted that there is increasing application of ¹⁴N–¹H experiments for the much higher natural abundance (99.6%) spin I = 1 nucleus.^15–22 The low sensitivity of ¹⁵N, associated with its low natural abundance and gyromagnetic ratio, can be overcome by the use of ¹⁵N–¹H correlation experiments with proton acquisition, thanks to the high natural abundance and γ that characterise protons, provided that fast MAS can achieve sufficient ¹H line narrowing.^23–26 We note that an ¹⁵N-detected MAS-J-HMQC ¹H–¹⁵N two-dimensional spectrum has also been recorded at natural abundance and 12.5 kHz MAS using Frequency Switched Lee–Goldburg (FSLG) ¹H homonuclear decoupling.²⁷¹H-detected heteronuclear ¹⁵N–¹H correlation experiments can be achieved by inverse polarization, CP, as applied to small molecules^{23,25,26,28–30} and ¹⁵N-labelled proteins as a hNH experiment.^31–33 An alternative to CP-based dipolar-mediated through-space transfer is a J coupling mediated through-bond refocused INEPT solid-state NMR experiment.^34–37 Specifically, we consider the CP-refocused INEPT correlation experiment,^38,39 whereby J coupling mediated ¹⁵N–¹H back-transfer, following CP to give maximum initial ¹⁵N magnetisation, ensures only the observation of peaks due to through-bond transfer in a ¹⁵N–¹H spectrum.²⁶ However, fast dephasing due to strong ¹H homonuclear dipolar couplings shortens ¹H coherence lifetimes, reducing sensitivity, making J coupling based experiments challenging. Even 60 kHz MAS is not sufficient to completely average out ¹H homonuclear dipolar couplings.⁴⁰ The application of ¹H homonuclear decoupling^41–44 under fast MAS during the ¹⁵N–¹H coherence transfer improves sensitivity sufficiently for refocused INEPT transfer.^26,39

While a large number of ¹H homonuclear decoupling schemes have been optimised under static conditions for operation at low (5–10 kHz) and moderate (∼15 kHz) MAS frequencies;^41–54 there have only been a few papers presenting ¹H homonuclear decoupling at faster MAS frequencies of (35+ kHz)^55,56 and (60+ kHz).^57–621H homonuclear decoupling is clearly not being applied under quasi-static conditions under such fast MAS and the performance is dependent upon the ratio between the rotor period, τ_r, and the cycle time of the ¹H homonuclear decoupling, τ_c. Lee–Goldburg^45,46,49,59 and DUMBO^50,62 based decoupling are characterized by short cycle times which makes them compatible with faster MAS implementations. Nevertheless, a short cycle time means high ¹H nutation frequencies, ν₁, for the scheme which can be demanding on the instrumentation. In this work, we consider the application of phase-modulated Lee–Goldburg (PMLG)⁴⁹ in a 1D ¹H Combined Rotation and Multiple-Pulse Sequence (CRAMPS)⁶³ experiment at 60 kHz MAS using relatively low nutation frequencies. The performance of PMLG depends on multiple factors such as the type of PMLG-block, frequency offset, and ¹H nutation frequency;^41,42,53,541H homonuclear decoupling sequences are usually evaluated through three principal parameters: the chemical shift scaling factor (λ_CS),^57,58,64 and linewidth improvement reflected in sensitivity and resolution determined through observation of the chemical shift evolution,⁶² and extended coherence lifetimes as observed through spin-echo experiments.⁵⁷ A bimodal Floquet theory analysis shows that ¹H homonuclear decoupling requires a fine optimization at MAS above 40 kHz owing to the considerable number of zero- and first-order degeneracies.⁶⁵ The two types of degeneracy arise when nν_r + kν_c = 0, where ν_r is the MAS spinning frequency and ν_c is the cycle frequency of the decoupling block, and n and k are integers. When these conditions are met, degeneracies occur within the diagonal block of the Floquet Hamiltonian and the effective Hamiltonian⁶⁶ leading to dipolar line-broadening.

In this paper, we first demonstrate, at 60 kHz MAS, enhanced decoupling compared to MAS alone in a ¹H solid-state NMR spectrum of ¹⁵N-glycine for an angle θ, corresponding to arctan of the ratio of the rf nutation frequency, ν₁, to the rf offset, that is far from the ideal magic angle, θ_m, equal to tan⁻¹(√2) = 54.7°. Moreover, the application of windowed decoupling with parameters based on those optimised for the one-pulse spectrum gives enhanced dephasing times in a ¹H spin-echo experiment. In this way, we systematically investigate the ¹H homonuclear decoupling parameters that affect sensitivity in the ¹⁵N–¹H CP-refocused INEPT experiment under ¹H homonuclear decoupling and fast MAS. It is shown that optimized decoupling enables the recording of two-dimensional through-bond ¹⁵N–¹H MAS NMR correlation spectra for moderately sized organic molecules such as the dipeptide β-AspAla and the pharmaceutical cimetidine.

2. Experimental

¹⁵N-Labelled glycine, and natural abundance (NA) glycine, β-AspAla and cimetidine were purchased from Sigma Aldrich or Bachem (β-AspAla) and packed as received into 1.3 mm zirconia rotors. ¹⁵N-Glycine was packed into a restricted volume in the centre of the rotor using silicone spacers. ¹⁵N-Labelled glycine was used to optimise ¹H homonuclear decoupling in 1D and 2D correlation experiments and the 2D ¹⁵N–¹H CP-refocused INEPT experiment. Glycine, β-AspAla and cimetidine, all at natural abundance, were used to test the ¹⁵N–¹H natural abundance CP-refocused INEPT correlation experiment.

The experiments were performed on a Bruker Avance III (500 MHz) or Avance NEO (600 MHz, 1 GHz) spectrometer operating at a ¹H Larmor frequency of ν_0H = 500.13 MHz (11.7 T), 599.45 MHz (14.1 T), 1000.40 MHz (23.5 T) and sample spinning using a Bruker 1.3 mm HXY probe at 60 kHz. The 90° pulse duration of 2.5 μs (ν₁ = 100 kHz) for ¹H and 4 μs (ν₁ = 62.5 kHz) or 3.5 μs (ν₁ = 71.4 kHz, cimetidine) for ¹⁵N was calibrated using a one-pulse experiment and a CP followed by a 90° pulse experiment, respectively. A recycle delay of 3 s or 5 s (cimetidine) was used.

¹H chemical shifts are externally referenced with respect to tetramethylsilane (TMS) viaL-alanine at natural abundance as a secondary reference (1.1 ppm for the CH₃¹H resonance) corresponding to adamantane at 1.85 ppm.^67,6815N chemical shifts are referenced relative to liquid CH₃NO₂ at 0 ppm,⁶⁹ using the NH₃⁺ peak of glycine (at natural abundance) at −347.4 ppm as a secondary reference. To convert to the chemical shift scale frequently used in protein NMR, where the alternative IUPAC reference (see Appendix 1 of ref. 70) is liquid ammonia at −50 °C, it is necessary to add 379.5 to the given values.⁷¹¹H and ¹⁵N chemical shifts can be experimentally determined to an accuracy of ±0.2 and ±0.1 ppm, respectively. The ¹⁵N RF transmitter frequency was centred at −304.5 ppm (or −291.5 ppm cimetidine). Where the ¹H resonance offset is referred to, 0 kHz refers to on-resonance with the NH₃⁺ peak of glycine at 8.4 ppm, with a positive resonance offset referring to a move of the RF transmitter frequency to higher ppm.

1D CRAMPS

The acquisition window was optimized to acquire 40 complex data points, each corresponding to 0.1 μs, with a ringdown delay of 1.0 μs and a deadtime optimized to be 2.2 μs, corresponding to a total acquisition window, τ_w, of 7.2 μs. The total acquisition time was 15 ms. Both and ¹H homonuclear decoupling schemes were optimized over a ¹H nutation frequency, ν₁(¹H), range from ∼10 to ∼120 kHz.

2D ¹⁵N–¹H CP-refocused INEPT

Cross polarization (CP) from ¹H to ¹⁵N was used for the initial excitation of ¹⁵N transverse magnetisation, where the ¹H nutation frequency was ∼80 kHz (or ∼95 kHz for cimetidine) using a zero-quantum (ZQ) match condition;^72,73 and a ¹⁵N nutation frequency of ∼20 kHz (or ∼25 kHz for cimetidine) with a linear ramp⁷⁴ (70–100%) on the ¹⁵N channel (glycine and β-AspAla) or ¹H (cimetidine). A CP contact time of 2 ms (or 4 ms for cimetidine) was used. The MISSISSIPPI suppression scheme⁷⁵ was applied with a spinlock nutation frequency of ∼30 kHz for four intervals of 2 ms (or 5 ms for cimetidine) to remove residual ¹H transverse magnetisation. Low-power⁷⁶ heteronuclear ¹H and ¹⁵N decoupling was applied during t₁ evolution and ¹H acquisition, respectively, using WALTZ64^77,78 at a nutation frequency of ∼10 kHz. The pulse sequence used corresponds to a modified version of that presented by Althaus et al. (Fig. 1b).²⁶

Fig. 1 (a) Pulse sequence for the ¹⁵N–¹H CP-refocused INEPT experiment utilised in this paper. Narrow lines and filled black rectangles represent π/2 and π pulses, respectively. Where not stated, the phase of a pulse is x. The following phase cycle is applied: ϕ₂ = {x*2, −x*2}, ϕ₄ = {−y*4, y*4}, ϕ₅ = {y*8, −y*8}, ϕ₇ = {x, −x} and acquisition ϕ_rec = {x, −x, −x, x, −x, x, x, −x, −x, x, x, −x, x, −x, −x, x}. States-TPPI is implemented on ϕ₄. (b) A ¹⁵N–¹H (ν₀ = 500 MHz) 2D CP (contact time = 2 ms)-refocused INEPT MAS (ν_r = 60 kHz) NMR correlation spectrum with skyline projections of natural abundance glycine and its molecular structure. was applied at a ¹H nutation frequency of 106 kHz (τ_LG = 2.92 μs) during both τ₁ = 2.091 ms (179τ_c) and τ₂ = 0.993 ms (85τ_c) at a ¹H transmitter offset of −2.6 kHz, with a zero offset corresponding to being on resonance with the NH₃⁺ peak. 192 transients were coadded for each of 96 t₁ FIDs, corresponding to a total experimental time of 16 hours. The base contour is at 40% of the maximum intensity.

Each ¹H-detected FID was acquired for 30 ms with a spectral width of 80 ppm (or 40 ppm for cimetidine). The ¹⁵N dimension was acquired with 96 (glycine NA and β-AspAla) or 64 (cimetidine) t₁ FIDs with a dwell time of 300 μs (glycine NA) or 142 μs (β-AspAla) or 160 μs (cimetidine), corresponding to a ¹⁵N spectral width of 66 ppm (glycine NA) or 138 ppm (β-AspAla) or 102 ppm (cimetidine) and a maximum t₁ of 15 ms (glycine NA), 6.9 ms (β-AspAla), or 5.1 ms (cimetidine). The States-TPPI method was employed to achieve sign discrimination in the indirect dimension.

3. Results and discussion

3.1 ¹⁵N–¹H CP-refocused INEPT – pulse sequence and product operator analysis

Our implementation of the ¹⁵N–¹H CP-refocused INEPT experiment at 60 kHz MAS is shown in Fig. 1a. Note that the pulse sequence in Fig. 1a corresponds to a modified version of that used by Althaus et al. at ν_r = 40 kHz.²⁶ The pulse sequence begins with an initial ¹H to ¹⁵N CP transfer to provide the largest pool of polarization possible for the low-γ and natural abundance ¹⁵N nucleus. The ¹⁵N transverse magnetisation is allowed to evolve during t₁. The desired magnetisation is stored during a z-filter period, in which ¹H magnetisation suppression using the MISSISSIPPI sequence⁷⁵ is implemented to remove the background proton signals. A ¹⁵N–¹H refocused INEPT element is used to transfer the magnetization back to proton for acquisition. INEPT utilizes the ¹H–¹⁵N J couplings to restrict the signals observed to those with direct one-bond H–N connections. Each spin-echo duration should be an integer number of rotor periods to ensure that the chemical shift anisotropy is completely averaged by MAS. Homonuclear ¹H decoupling, here PMLG,⁴⁹ is applied during the two spin-echoes of the refocused INEPT element. Under fast MAS, at a spinning frequency of 60 kHz in this work, low power heteronuclear decoupling,⁷⁶ specifically WALTZ-64⁷⁸ decoupling, is applied on ¹H and ¹⁵N during t₁ and t₂, respectively. The resulting spectrum is a 2D ¹⁵N–¹H through-bond correlation spectrum, as illustrated in Fig. 1b for natural abundance glycine.

For a ¹⁵N–¹H spin pair, a product-operator analysis (see Section S1,ESI‡) shows a product of sine terms dependence on the heteronuclear ¹⁵N–¹H J_IS coupling active during the two spin-echo (τ–π–τ) durations, τ₁ and τ₂:

(NH)  sin(2πJ_ISτ₂)sin(2πJ_ISτ₁) (1)

i.e., this predicts maximum transfer, for sin(π/2), i.e., τ = 1/(4J_IS), i.e., 2.7 ms, for a one-bond ¹⁵N–¹H scalar coupling (~90 Hz) for fast MAS alone. When the proton magnetization is along the transverse plane, for example as Î_yŜ_z during τ₂, the ¹H–¹H dipolar couplings shorten the coherence lifetime compared to when the ¹H magnetization is longitudinal, as during τ₁.³⁹ As expanded upon below, the different influence of the interactions is evident in the optimum length of the τ₁ and τ₂ periods: the spectrum in Fig. 1b was recorded with τ₂ (1.0 ms) shorter than τ₁ (2.1 ms); as discussed further below, note that ¹H homonuclear decoupling scales the J coupling.^79–81

Analogously to the case of ²⁹Si–¹H J-couplings in SiH_n moieties,^82–84 there is a different dependence on the first spin-echo duration, τ₁, for a NH₃ moiety:

(NH₃) sin(2πJ_ISτ₂)[sin(2πJ_ISτ₁) + sin(6πJ_ISτ₁)] (2)

As discussed below, a consequence of this is that different signal build-up with respect to τ₁ for a NH and a NH₃ moiety (and also for a NH₂ which has a sin(2πJ_ISτ₂)sin(4πJ_ISτ₁) dependence.

3.2 ¹H PMLG homonuclear decoupling under fast MAS

As noted in the above discussion of Fig. 1a, PMLG ¹H homonuclear decoupling is employed during the two spin-echo durations of the refocused INEPT pulse sequence element that transfers magnetisation from ¹⁵N to ¹H. Lee–Goldburg decoupling⁴⁵ can be considered to be analogous to MAS where the sample is rotated around an axis inclined at the magic angle, θ_m, equal to tan⁻¹(√2), to the external magnetic field in that the ratio of the nutation frequency, ν₁, to the resonance offset, Δν_LG, is also set equal to tan⁻¹(√2). This leads to an effective field, ν_{eff_LG}, that is given by Pythagoras’ theorem, as:For fixed ν₁, the Lee–Goldburg condition is satisfied as:i.e., and . In the PMLG implementation⁴⁹ of the LG condition, rf irradiation is applied on resonance for a duration, τ_LG, that is the inverse of ν_{eff_LG}but with an equivalent sweep (in discrete jumps) of the rf phase from 0° to over the duration, τ_LG, whereby ϕ_last depends on Δν_LG according to:An overall rotation, ξ_LG, of 360° around the effective field is achieved:

ξ_LG = 360°·ν_{eff_LG}·τ_LG = 360°. (7)

In the experimental implementation of PMLG under MAS, the duration over which the phase is swept (as discrete steps) from 0° to the ideal ϕ_last value of 207.8°, τ_{LG_expt}, can vary from the ideal value, τ_LG. In this way, the equivalent resonance offset, Δν_expt, changes from the ideal value, Δν_LG, to satisfy: so that .

Nishiyama et al.⁵⁷ have shown that this deviation from the ideal condition can be expressed in terms of how the angle, θ, deviates from the magic angle, θ_m:

The actual effective field, ν_{eff_LG_expt}, that is calculated by Pythagoras’ theorem as √(ν₁² + Δν_{LG_expt}²) is not equal to 1/τ_{LG_expt} and also deviates from the ideal value, ν_{eff_LG}. As a consequence, the overall rotation about the actual effective field, ξ_{LG_expt}, also deviates from ξ_LG = 360° according to:Note that Nishiyama et al. refer to this rotation angle as Ψ, but this symbol is used in this paper to denote the ratio of the rotor period to the cycle time (see later discussion), according to Leskes et al.⁶⁵

Following the notation of Leskes et al.⁸⁵ a PMLG block is specified as where: first, n is the number of finite pulses for each LG cycle, with n equal to 5 or 9 investigated here; second, R is the sense of the initial rotation for the phase steps, m for clockwise and p for counter-clockwise; and third, the initial phase, ϕ, is usually x or −x (denoted x̄). As stated above (see eqn (7)) and as shown in Fig. 2a and b, τ_{LG_expt} is the time to sweep the phase over n discrete steps, i.e., as n finite pulses, from 0° to 207.8°. A single PMLG block, is of duration 2τ_LG with a 180° jump after n finite pulses in the first τ_LG followed by n finite pulses in the second τ_LG, whereby the phase steps are in the opposite direction. This corresponds to changing the sign of the equivalent resonance offset, as in the frequency-switched (FS) LG experiment, where rf irradiation is alternated between +Δν_LG and −Δν_LG.^46,86,87 As further shown by Leskes et al.⁸⁵ supercycling can be achieved as . Specifically, in this work, we use the and implementations.

Fig. 2 (a) Representation of the phase rotation for (dashed line, squares) and (solid line, circles). The phase increments are calculated according to ϕ_last = 207.8° (see eqn (6)), divided by the number of steps. The starting point for both is −x. Pulse sequence for (b) a ¹H 1D CRAMPS experiment with supercycled , where the asterisk represents an acquisition window, τ_w, (c) a ¹H spin-echo and (d) a 2D ¹H–¹H correlation experiment. Thin lines and filled rectangles represent 90° and 180° pulses, respectively, while open rectangles denote tilt pulses. In (c) and (d), the block named PMLG can accommodate either (a and e) windowed, where τ_w is an equivalent period of free evolution, or a windowless sequence, whereby there is continuous rf irradiation during blocks, i.e., there are no tilt pulses and τ_w = 0. The following phase cycle is applied for (b) 1D CRAMPS: ϕ₁ = {x, −x, −x, x}, ϕ_PMLG = {x, −x, −x, x} and acquisition ϕ_rec = {x, −x, −x, x}; (c) ¹H spin-echo: ϕ₁ = {x, −x}, ϕ₂ = {y*2, x*2}, ϕ_PMLG = {x, −x} and acquisition ϕ_rec = {x, −x, −x, x}; (d) ¹H–¹H homonuclear correlation: ϕ₁ = {x, −x}, ϕ₃ = {−x*2, x*2}, ϕ₄ = {x*4, y*4}, ϕ_PMLG = {x, −x} and acquisition ϕ_rec = {x, −x, −x, x, y, −y, −y, y}.

In the windowed implementation of PMLG⁸⁸ acquisition windows of duration τ_W are placed between the blocks (see Fig. 2b and e). In addition, tilt pulses of duration τ_tilt can be used.^{53,54,89–91} The cycle time for a complete or supercycle, τ_c, is:

τ_c = 2τ_w + 4τ_{LG_expt} + 4τ_tilt. (10)

3.3 Optimisation of CH₂ and NH₃ signal intensity in a 1D CRAMPS experiment of ¹⁵N-glycine

The optimization of the ¹H nutation frequency and τ_{LG_expt} is performed differently for windowless and windowed sequences. In this paper, our focus is on windowed sequences that were optimized with a 1D CRAMPS experiment which gives both the chemical shift scaling factor λ_CS and the ¹H linewidths in a few seconds for a particular combination of parameters. Specifically for windowed and , a two variable optimization was performed over a range of ¹H nutation frequencies between 0 and 110–120 kHz and τ_{LG_expt} between 3.5 and 7.5 μs for ¹⁵N labelled glycine – see Fig. 3a for and Fig. S1 (ESI‡) with slices extracted at different peak intensities, hence with different resolution. (Note that the optimisation of the tilt pulses is discussed in Section S3 of the ESI‡.) For windowless sequences, a coarse optimization was performed, starting from optimised parameters from the 1D CRAMPS experiments, using a ¹H spin-echo experiment (Fig. 2c) to find good candidate parameters which yield a long ¹H coherence lifetime. As noted below, the ¹H–¹H correlation experiment (Fig. 2d) was used to determine the λ_CS of the candidate windowless sequences, but can only be used sparingly as the experimental time is relatively long (∼20 minutes for 4 co-added transients and 96 t₁ FIDs for each combination of τ_{LG_expt} and ν₁).

Fig. 3 ¹H MAS (ν_r = 60 kHz) NMR of ¹⁵N-labelled glycine. (a) 1D CRAMPS (see Fig. 2b, τ_tilt = 0.54 μs, Ω = −0.6 kHz) two-variable optimization (ν₀ = 500 MHz) of both τ_{LG_expt} (in steps of 0.25 μs) and the ¹H nutation frequency, ν₁ (0–110 kHz) for the NH₃⁺ peak intensity. (b) Comparison between ¹H (ν₀ = 500 MHz) 1D CRAMPS MAS NMR spectra acquired with windowed (ν₁ = 113 kHz, τ_{LG_expt} = 2.92 μs, τ_tilt = 0.82 μs, Ω = −0.6 kHz), windowed (ν₁ = 106 kHz, τ_{LG_expt} = 3.1 μs, τ_tilt = 0.54 μs, Ω = −0.6 kHz), and a one-pulse MAS-alone experiment. (c) Comparison between ¹H (ν₀ = 1 GHz) 1D CRAMPS MAS NMR spectra acquired with windowed (ν₁ = 108 kHz, τ_{LG_expt} = 3.10 μs, τ_tilt = 0.18 μs, Ω = −7.0 kHz), windowed (ν₁ = 52 kHz, τ_{LG_expt} = 3.63 μs, τ_tilt = 0.70 μs, Ω = −8.6 kHz), and a one-pulse MAS-alone experiment. 8 (a) or 32 (b and c) co-added transients were added for a recycle delay of 3 s. For all experiments, τ_w = 7.20 μs.

Fig. 3a reports on the NH₃^{+ 1}H resonance, noting its relevance in this paper for the ¹H–¹⁵N refocused INEPT experiment. Fig. S2 (ESI‡) shows that optimum performance for the NH₃^{+ 1}H resonance (Fig. S2b, ESI‡) is closely matched by that for the CH₂¹H resonances (Fig. S2a, ESI‡). 1D CRAMPS ¹H NMR spectra of ¹⁵N-glycine for our best implementations of supercycled windowed and at ν₀ = 500 MHz are shown in Fig. 3b, where enhanced resolution compared to MAS alone is evident. Moreover, both and implemented at ν₀ = 500 MHz (Fig. 3b) show better resolution than 60 kHz MAS alone at ν₀ = 1 GHz (Fig. 3c). At ν₀ = 1 GHz, optimised 1D CRAMPS ¹H NMR spectra of ¹⁵N-glycine for windowed at a ¹H nutation frequency of 108 and 51 kHz are presented in Fig. 3c that show enhanced resolution compared to MAS alone. Note that the latter case corresponds to the nutation frequency being less than the MAS frequency.

Table 1 compares the experimentally optimised τ_{LG_expt} values to the ideal τ_LG values: at ν₀ = 500 MHz, the experimental values are less than half the ideal values, i.e., τ_{LG_expt} = 3.10 μs and 2.92 μs compared to 7.70 μs and 7.23 μs, respectively. As Table 1 further shows, with the corresponding changes in Δν_{LG_expt} and ν_{eff_expt}, the angle θ is 29.7°. While a very high nutation frequency of over 200 kHz has been used in the first experimental implementations of PMLG at 65 kHz MAS frequency^59,65 resulting in a θ value of 61° for the spectrum presented by Leskes et al.,⁵⁹ a similar value (of 31.2°) far from the magic angle has been reported by Nishiyama et al. for the implementation of windowed at an MAS frequency of 80 kHz and a ¹H nutation frequency of 125 kHz.⁵⁷ Moreover, the actual rotation, ξ_{LG_expt}, reported by Nishiyama et al. of 243° is similar to that of 239° for our implementation of both windowed and at a MAS frequency of 60 kHz (see Table 1). Table 1 also lists the implementations of by Leskes et al. at 10 kHz MAS⁸⁵ and Mao & Pruski at 12.5, 19.5, 25.0 and 41.7 kHz MAS:⁹² the angle θ is seen to vary between 45° and 64°. It is observed that an angle θ below and above the magic angle corresponds to an actual rotation, ξ_{LG_expt}, less than and more than the ideal 360°, respectively. For the good decoupling performance observed at ν₀ = 1 GHz with windowed for a ¹H nutation frequency of only 51 kHz (see Fig. 3c), the angle θ is only 17.6°.

Table 1 Implementation of and ¹H homonuclear decoupling: variation from the ideal Lee–Goldburg condition for this work and previous publications

Decoupling	ν r (kHz)	ν 1 (kHz)	τ LG (μs)	τ LG_expt (μs)	θ m (deg)	θ (deg)	ΔνLG (kHz)	ΔνLG_expt (kHz)	ν eff_LG (kHz)	ν eff_LG_expt (kHz)	ξ LG (deg)	ξ LG_expt (deg)
a Parameters from this work for Fig. 3b and Table 3. b Parameters from this work for Fig. S3 (ESI). c Parameters from this work for Fig. 3c and Table 3. d Values extracted from Nishiyama et al. Fig. 2 and 3.^57 e Values extracted from Leskes et al. Table 1.^59 f Values extracted from Mao and Pruski,^92 Fig. 3 and 2. g Values extracted from Leskes et al. Fig. 2.^85 h Simulated values extracted from Leskes et al. Fig. 2.^65
Windowed ^a (500 MHz)	60.0	106	7.70	3.10	54.7	29.7	75.0	186.2	129.8	214.3	360.0	239.2
Windowless ^b (500 MHz)	60.0	106	7.70	3.10		29.7	75.0	186.2	129.8	214.3		239.2
Windowed ^a (500 MHz)	60.0	113	7.23	2.92		29.7	79.9	197.7	138.4	227.7		239.4
Windowless ^b (500 MHz)	60.0	113	7.23	2.92		29.7	79.9	197.7	138.4	227.7		239.4
Windowed ^c (1 GHz, ν1 = 108 kHz)	60.0	108	7.56	3.10		30.1	76.4	186.2	132.3	215.3		240.3
Windowed ^c (1 GHz, ν1 = 51 kHz)	60.0	51	16.01	3.63		17.6	36.1	159.3	62.4	167.2		218.2
Literature parameters
^d	80.0	125	6.53	2.80	54.7	31.2	88.4	206.2	153.1	241.1	360.0	243.1
	65.0	216	3.78	4.80		60.9	152.7	120.3	264.5	247.2		427.2
	41.7	155	5.27	3.75		45.2	109.6	154.0	189.8	218.5		294.9
	41.7	155	5.27	7.75		64.3	109.6	74.5	189.8	172.0		479.8
	12.5	78	10.47	12.50		59.4	55.2	46.2	95.5	90.6		407.9
	19.5	126	6.48	8.00		60.2	89.1	72.2	154.3	145.2		418.2
	25.0	162	5.04	6.25		60.3	114.6	92.4	198.4	186.5		419.6
	10.0	95	8.59	7.25		50.0	67.2	79.6	116.4	124.0		323.5
	65.0	250	3.27	5.00		65.2	176.8	115.5	306.2	275.4		495.7

---

Table 2 states the τ_c values, as calculated from τ_{LG_expt}, τ_w and τ_tilt using eqn (10), for the implementations of and in this work, as well as that reported in the literature. An important parameter for predicting decoupling performance is the ratio, Ψ, of the MAS rotor period, τ_r, to the decoupling cycle time, τ_c, and vice versa, the ratio of the corresponding frequency, ν_c = 1/τ_c, to the MAS frequency, ν_r:⁶⁵

For low to moderate MAS frequencies, small integer values of Ψ are to be avoided since these values correspond to recoupling rather than decoupling conditions.^{53,91,93–95} For fast MAS (of at least 40 kHz), there are more values of Ψ that need to be avoided.^62,65,92 Specifically, by employing bimodal Floquet theory, Leskes et al. have identified values of n and k that result in deteriorated decoupling due to zero-order and first-order recoupling conditions, according to:

nν_r + kν_r = 0, (12)

where n takes values 1, 2, 3, 4 while −15 ≤ k ≤ −1.⁶⁵ While there is a dense set of degeneracies for values of Ψ below 1.50, there are windows of good decoupling performance that can be found. The Ψ value of both the windowless sequences, (Ψ = 1.34) and (Ψ = 1.43), are in line with the value of 1.40–1.60 reported by Mao et al. (in Tables 1 and 2 of their paper) for spectra acquired among a range of different spinning frequencies (12.5 kHz to 41.7 kHz) and ¹H nutation frequencies (78–162 kHz).⁹² For windowed sequences, the Ψ value is usually lower. For the 1D CRAMPS spectra presented in Fig. 3b, Table 2 shows that Ψ equals 0.58 and 0.57 for windowed and windowed , respectively, at ν₀ = 500 MHz, and 0.61 and 0.53 at ν₀ = 1 GHz for a ¹H nutation frequency of 108 and 51 kHz, respectively. These Ψ values are similar to the values of 0.60 and 0.63 for the experimental implementation of windowed by Nishiyama et al. at an MAS frequency of 80 kHz and a ¹H nutation frequency of 125 kHz⁵⁷ and by Leskes et al. at an MAS frequency of 65 kHz and a ¹H nutation frequency of 216 kHz,⁵⁹ respectively.

Table 2 Implementation of and ¹H homonuclear decoupling: scaling factors and comparison of rotor period to cycle time for this work and previous publications

	τ LG_expt (μs)	τ w (μs)	τ tilt (μs)	τ c (μs)	τ r (μs)	Ψ	λ CS_calc	λ CS_expt
a Parameters from this work for Fig. 3b and Table 3. b Parameters from this work for Fig. S5 (ESI). c Parameters from this work for Fig. 3c and Table 3. d Values extracted from Nishiyama et al. Fig. 2 and 3.^57 e Values extracted from Leskes et al. Table 1.^59 f Values extracted from Mao and Pruski,^92 Fig. 3 and 2. g Values extracted from Leskes et al. Fig. 2.^85 h Simulated values extracted from Leskes et al. Fig. 2.^65 i λ CS is calculated with eqn (15) as stated in this paper, following from Nishiyama et al.^57 j λ CS is calculated with eqn (16) as stated in this paper, following from Nishiyama et al.^57 k Ψ is calculated with eqn (12), following from Leskes et al.^65
Windowed ^a (500 MHz)	3.10	7.20	0.54	28.96	16.67	0.58	0.76^j	0.82
Windowless ^b (500 MHz)	3.10	—	—	12.40	16.67	1.34	0.76^i	0.66
Windowed ^a (500 MHz)	2.92	7.20	0.82	29.36	16.67	0.57	0.77^j	0.76
Windowless ^b (500 MHz)	2.92	—	—	11.68	16.67	1.43	0.78^i	0.60
Windowed ^c (1 GHz, 108 kHz)	3.10	7.20	0.18	27.52	16.67	0.61	0.74^j	0.82
Windowed ^c (1 GHz, 51 kHz)	3.63	7.20	0.70	31.70	16.67	0.53	0.90^j	0.92
Literature parameters
^d	2.80	4.84	—	20.88	12.50	0.60	0.86^i	0.82
	4.80	2.70	—	24.60	15.38	0.63	0.40^i	0.48
	3.75	—	—	15.00	24.00	1.60	0.50^i	0.36
	7.75	—	—	31.00	24.00	0.77	0.19^i	0.21
	12.50	—	—	50.00	80.00	1.60	0.26^i	—
	8.00	—	—	32.00	51.20	1.60	0.25^i	—
	6.25	—	—	25.00	40.00	1.60	0.25^i	—
	7.25	4.35	—	37.70	100.00	2.65	0.55^i	0.47
	5.00	—	—	20.00	15.38	0.77	0.18^i	—

---

3.4 Windowed and windowless PMLG ¹H decoupling, ¹H spin-echo dephasing and scaling factors

It is well established that the application of rf ¹H homonuclear decoupling leads to a chemical shift scaling: for a static sample, the chemical shift scaling factor, λ_CS, for perfect decoupling cannot exceed cos⁻¹(θ_m) = 1/√3 = 0.577.^64,95,96 The 1D ¹H CRAMPS spectra presented in Fig. 3b and c have chemical shift axes that have been corrected for this scaling, i.e., a scaling is applied so as to ensure that the chemical shift separation between the NH₃⁺ peak and the lower ppm CH₂ peak corresponds to the MAS-only ¹H chemical shifts, i.e., 8.4–3.0 = 5.4 ppm. The full width at half maximum, (FWHM), of the three ¹H resonances before and after scaling for the spectra presented in Fig. 3b and c are presented in Table 3. Table 3 also states that λ_CS equals 0.82 and 0.76 for windowed and windowed , respectively, at ν₀ = 500 MHz, and 0.82 and 0.92 at ν₀ = 1 GHz for a ¹H nutation frequency of 108 and 51 kHz, respectively. Table 3 also reports, as a measure of decoupling efficiency, K, given bywhere a K closer to 1 corresponds to better decoupling performance. FWHM_MAS is obtained under MAS alone, FWHM_PMLG is the linewidth recorded using PMLG, and FWHM after scaling, FWHM_scaled, is equal to FWHM_PMLG/λ_CS. High scaling factors that are significantly above 0.577, like those stated in Table 3, have been reported for 60 kHz MAS by Salager et al. for an experimental optimisation protocol based on a quality factor considering the intensity of the two most intense resonances, CH₃ and NH₃, in β-AspAla as well as their peak separation in Hz.⁵⁸ Specifically, λ_CS equals 0.73 and 0.84 for the eDUMBO-PLUS-1 and eDUMBO-PLUS-large sequences, respectively, for 60 kHz MAS and a ¹H nutation frequency of 170 kHz, with optimum resolution observed for eDUMBO-PLUS-1. Salager et al. have further presented a scaling factor theorem for homonuclear decoupling, derived for a static system of homonuclear I = 1/2 spins coupled by a dipolar interaction that are subject to cyclic rf irradiation:where λ_D is the dipolar scaling factor, i.e., zero corresponds to perfect decoupling, showing that λ_CS cannot exceed 1/√3, when λ_D = 0.⁶⁴

Table 3 Analysis of windowed and ¹H homonuclear decoupling efficiency for ¹H (ν₀ = 500 MHz and 1 GHz) CRAMPS NMR at ν_r = 60 kHz of ¹⁵N-glycine^a

	δ (ppm)	FWHMMAS (Hz)	FWHMMAS (ppm)	FWHMPMLG (Hz)	FWHMPMLG (ppm)	FWHMscaled (Hz)	FWHMscaled (ppm)	Scaling factor, λCS	K	FWHMPMLG (Hz)	FWHMPMLG (ppm)	FWHMscaled (Hz)	FWHMscaled (ppm)	Scaling factor, λCS	K
a See spectra in Fig. 3b (ν0 = 500 MHz) and Fig. 3c (ν0 = 1 GHz), for the pulse sequence in Fig. 2b and experimental parameters in Table 2. b Calculated with eqn (13). c FWHM extracted from the indirect dimension of a 2D ^1H–^1H correlation experiment with MAS alone, see Fig. S4 in the ESI.
ν 0 = 500 MHz				(ν1 = 106 kHz)						(ν1 = 113 kHz)
NH3^+	8.4	664	1.33	230	0.46	280	0.56	0.82	0.58	273	0.55	359	0.72	0.76	0.46
CH2	4.2	800^c	1.60	217	0.43	264	0.53		0.67	213	0.43	280	0.56		0.65
CH2	3.0	800^c	1.60	224	0.45	273	0.55		0.66	232	0.46	305	0.61		0.62
ν 0 = 1 GHz				(ν1 = 108 kHz)						(ν1 = 51 kHz)
NH3^+	8.4	700	0.70	583	0.58	711	0.71	0.82	−0.02	475	0.48	516	0.52	0.92	0.26
CH2	4.2	740	0.74	346	0.35	422	0.42		0.43	448	0.45	487	0.49		0.34
CH2	3.0	740	0.74	311	0.31	379	0.38		0.49	440	0.44	478	0.48		0.35

---

For , Nishiyama et al. report a λ_CS of 0.82 at 80 kHz MAS and a ¹H nutation frequency of 125 kHz. Nishiyama et al. further state equations for calculating λ_CS for decoupling without and with tilt pulses:

These calculated λ_CS values are presented in Table 2 for the experimental implementations of in the literature, as well as and in this work. Deviation of the experimental scaling factor compared to theoretical behaviour can arise from phase transients that cause phase propagation delays.^91,97

As well as scaling the chemical shifts, ¹H homonuclear decoupling also scales evolution under a heteronuclear J coupling by the same factor.^37,57,79 For magnetisation transfer from ¹⁵N to ¹H during the spin echoes of the refocused INEPT pulse sequence element, the efficiency depends upon this scaling of the ¹⁵N–¹H J couplings, but also the spin-echo dephasing time, .^92,98,99

Fig. 4 compares spin-echo dephasing curves (see pulse sequence in Fig. 2c) for MAS alone to those for windowed and windowless and , with the values for experimental parameters and extracted presented in Table 4. (Note that homonuclear decoupling was implemented with a slightly changed nutation frequency of ν₁ = 109 kHz, as compared to ν₁ = 113 kHz for the 1D CRAMPS spectrum in Fig. 3b). In windowless PMLG decoupling, there is continuous rf irradiation, i.e., there are no tilt pulses and τ_w = 0, while, in the windowed version, τ_w is replaced by a delay (Fig. 2e.) Note that the first implementation of PMLG was in the indirect dimension of a two-dimensional ¹H–¹H experiment where there is evolution under MAS alone in the direct dimension.⁴⁹ Such a 2D experiment (see Fig. 2d) is used to measure λ_CS for our implementation of windowless and , as reported in Tables 2 and 4 (spectra are presented in Fig. S4, ESI‡).

Fig. 4 Dephasing of the ¹⁵N-glycine (a) CH₂ (the higher ppm ¹H resonance is considered) and (b) NH₃⁺ proton resonances as a function of the spin-echo (see Fig. 2c) duration, τ, with no ¹H homonuclear decoupling (empty circles), windowed (empty diamonds), windowed (full diamonds), windowless (empty triangles), and windowless (full triangles) for nutation frequencies and resonance offsets as stated in Table 4. Fits to an exponential decay function are shown, with the spin-echo dephasing times, , as listed in Table 4. 16 transients were co-added for a recycle delay of 3 s. For all experiments with windowed ¹H homonuclear decoupling, τ_w = 7.20 μs.

Considering Fig. 4 and Table 4, the ¹H dephasing times, , for the CH₂ (the higher ppm resonance is considered) and NH₃⁺ peaks are 0.22 ms and 0.25 ms for 60 kHz MAS alone. With ¹H homonuclear decoupling the ¹H dephasing time for both groups increases. The longest CH₂ dephasing time is observed for windowed , , slightly longer than for windowed , where is equal to 1.10 ms. However, the scaling by λ_CS needs to be considered and Table 4 reports the product of λ_CS and in each case. After this scaling (Table 4), windowed achieves an over 4 fold improvement with respect of MAS alone, compared to the slightly under 4 fold improvement of windowed . A similar comparison can be made for the NH₃⁺ peak, where windowless shows the longest equal to 1.15 ms and the longest value of the product, λ_CS of 0.69 ms, thanks again to the large λ_CS; this corresponds to a just under 3 fold improvement with respect to MAS alone.

3.5 Optimisation of the ¹⁵N-glycine NH₃⁺ signal intensity in a 1D-filtered CP-refocused INEPT NMR spectrum for PMLG ¹H decoupling at 60 kHz MAS

Under a ¹H homonuclear decoupling sequence such as PMLG, the proton offset frequency influences the performance;^53,54 this is linked to the overall z-rotation that the spins need under decoupling to avoid artifacts and RF imperfections.⁸⁵ As shown by Leskes et al.,⁸⁹ the non-supercycled m-block is particularly beneficial in narrowing lines of strong coupled spins, as for the CH₂ groups of ¹⁵N-glycine, close to the on-resonance position. With the implementation of supercycled PMLG schemes,⁹⁰ the sign of the offset is no longer a determining factor as the supercycle brings the effective rotation of the spins closer to the z-axis.¹⁰⁰ However, the choice of the optimum offset still plays a significant role for achieving good decoupling performance, therefore it is necessary to investigate both positive and negative offsets. Here the optimization was performed directly on the ¹⁵N–¹H CP-refocused INEPT experiment, where windowed was applied over a wide range of offset values from ∼+10 kHz to −12 kHz, whereby on-resonance corresponds to the NH₃⁺ peak. Fig. 5 shows that the best offsets in term of sensitivity are at +1 kHz and −3.5 kHz, highlighted by dashed vertical lines. Between the two best performing offsets, the sensitivity experiences a fluctuation (Fig. 5) corresponding to the on-resonance position (solid line), dropping to zero for a small negative offset of −0.5 kHz. It is then important to optimize the offset avoiding the on-resonance position. The need for a fine optimization of this parameter is emphasized by the considerable change in sensitivity that is observed for a small variation of the offset.^53,54,95 For example, the relative sensitivity of the NH₃⁺ peak falls from over 0.8 to 0.5 when switching the offset from ∼−3.5 to −2.5 kHz. In general, in Fig. 5 the offsets close to the on-resonance position yield better sensitivity symmetrically in a range between ±4 kHz, in agreement with the rotation improvement brought by the supercycled ¹H homonuclear decoupling.⁸⁹

Fig. 5 ¹H RF carrier optimization for a 1D-filtered (t₁ = 0) ¹⁵N–¹H (ν₀ = 500 MHz) CP (contact time = 2 ms)-refocused INEPT MAS (ν_r = 60 kHz) NMR experiment for ¹⁵N-labelled glycine, whereby windowed ¹H homonuclear decoupling was applied with τ_{LG_expt} = 3.1 μs, τ_tilt = 0.54 μs and a ¹H nutation frequency, ν₁, of 106 kHz during τ₁ (1.999 ms, 69τ_c) and 104 kHz during τ₂ (1.391 ms, 48τ_c). 16 transients were coadded. For all experiments with windowed ¹H homonuclear decoupling, τ_w = 7.20 μs. The zero-offset is set with the carrier being on resonance with the NH₃⁺ peak, corresponding to the solid vertical line. Dashed vertical lines indicate the two highest signal intensities at +1 kHz and −3.5 kHz.

The same offset optimization was carried out on the different PMLG-block types, and similar trends were shown with a better sensitivity in the proximity of the on-resonance position. As stated in Table 4, the offsets which gave the maximum sensitivity were 0.75 kHz for windowed , −0.25 kHz for and +1 kHz for (the same as windowed ) (see Fig. S5, ESI‡).

Table 4 ¹H dephasing time, , and scaled by the experimental λ_CS, λ_CS, as determined by a ¹H spin-echo MAS NMR experiment^a for ¹⁵N-glycine with optimised rf carrier offset and ν₁

	Offset (kHz)	ν 1 (kHz)	λ CS	NH3^+ (ms)	NH3^+λCS (ms)	CH2  ^b (ms)	CH2λCS (ms)
a As implemented at ν0 = 500 MHz and νr = 60 kHz, see Fig. 4a for the CH2 resonance and Fig. 4b for the NH3^+ peak. τtilt is equal to 0.54 μs for windowed and 0.82 μs for windowed . b For the CH2 group, the of the higher-ppm ^1H resonance is stated.
No decoupling	2	—	1	0.25	0.25	0.22	0.22
Windowed	1	106	0.82	1.04	0.85	1.14	0.93
Windowed	0.75	109	0.76	0.91	0.69	1.10	0.84
Windowless	1	106	0.66	0.86	0.57	0.80	0.53
Windowless	−0.25	109	0.60	1.15	0.69	0.78	0.47

---

The implementation of the ¹H decoupling scheme into the heteronuclear correlation experiment required the further optimisation of the spin-echo durations during the refocused INEPT transfer. This was carried out separately for τ₁ and τ₂ (see pulse sequence in Fig. 1a) because, as stated in Section 3.1, for the two spin echoes, different spins are along the transverse plane, ¹⁵N for the first and ¹H for the second spin echo. To ensure the best conditions, a double-optimisation of ¹H homonuclear decoupling nutation frequency vs. τ₁ and τ₂ was carried out. Specifically, the two-variable optimisation was performed for ¹⁵N-labelled glycine for windowed or windowless and for the best offset (see Table 5) and the results are reported in Table 5. The dependence with respect to the second spin-echo duration, τ₂, is presented in Fig. 6. Note from eqn (2), a sine dependence is expected from which the scaled J coupling could be extracted.

Table 5 Optimised rf carrier offset, spin-echo duration and nutation frequencies for four implementations of PMLG ¹H homonuclear decoupling and MAS-alone for a ¹⁵N–¹H CP-refocused INEPT MAS NMR experiment for ¹⁵N-glycine^a

^1H homonuclear decoupling	Offset^b (kHz)	λ CS	τ 1 (ms)	λ CS τ 1 (ms)	ν 1 (kHz) for τ1	τ 2 (ms)	λ CS τ 2 (ms)	ν 1 (kHz) for τ2	Relative intensity^d
a As implemented at ν0 = 500 MHz and νr = 60 kHz. τtilt is equal to 0.54 μs for windowed and 0.82 μs for windowed . See Fig. 6. b Relative to the NH3^+ 1H resonance. c τ 1 = nτc, τ2 = mτc, where n and m are positive integers. d See Fig. 7.
No decoupling	2.00	1.00	1.600	1.600	—	0.300	0.300	—	0.08
Windowed	1.00	0.82	1.999 (69τc)	1.639	106	1.391 (48τc)	1.140	106	1.00
Windowed	0.75	0.76	2.085 (71τc)	1.585	104	1.498 (51τc)	1.138	106	0.80
Windowless	1.00	0.66	2.096 (169τc)	1.383	102	0.496 (40τc)	0.327	102	0.52
Windowless	−0.25	0.60	2.091 (179τc)	1.254	104	1.192 (102τc)	0.715	102	0.48

---

Fig. 6 Dependence upon the second spin-echo duration, τ₂, for ¹⁵N-labelled glycine of the NH₃⁺ peak in a 1D-filtered (t₁ = 0) ¹⁵N–¹H (ν₀ = 500 MHz) CP (contact time = 2 ms)-refocused INEPT MAS (ν_r = 60 kHz) NMR spectrum for: windowed (τ_{LG_expt} = 3.1 μs, τ_tilt = 0.54 μs, ν₁ = 106 kHz for τ₁ and 106 kHz for τ₂ full diamonds), windowless (same conditions but with no tilt pulses, full triangles, with ν₁ = 102 kHz for τ₁ and 102 kHz for τ₂), windowed (τ_{LG_expt} = 2.92 μs, τ_tilt = 0.82 μs, ν₁ = 104 kHz for τ₁ and 106 kHz for τ₂ empty diamonds), windowless (same conditions but with no tilt pulses, empty triangles, with ν₁ = 104 kHz for τ₁ and 102 kHz for τ₂), MAS alone (empty circles). 8 transients were coadded. For all experiments with windowed PMLG, τ_w = 7.20 μs.

Considering Table 5, the ¹H nutation frequencies are in the range of 102–106 kHz for all the PMLG-block types, with a maximum of 2 kHz difference between that applied in τ₁ and τ₂ for the same PMLG block. For τ₁, the optimum values for PMLG decoupling are 2.0 or 2.1 ms, as compared to 1.6 ms from MAS alone. However, as discussed in Section 3.4, it is the product λ_CS·τ, that needs to be considered, in which case similar values are obtained as compared to MAS alone. By comparison, a clear difference is observed for τ₂, where the evolution of ¹H coherence is markedly affected by the ¹H–¹H dipolar couplings. Indeed, the coherence transfer increases from 0.3 ms for MAS alone to 1.5 ms for windowed and 1.4 ms for windowed . After scaling, the product λ_CSτ₂, 1.14 ms for both windowed and , are still ∼4 times longer than the optimum τ₂ for MAS alone. We note a discrepancy for τ₂ under windowless , which is considerably shorter (0.3 ms after scaling) with respect to the other ¹H homonuclear implementations.

In Fig. 7, we compare the different peak intensities for the NH₃⁺ peak of ¹⁵N-labelled glycine for the windowless and windowed implementation of and in a ¹⁵N–¹H CP-refocused INEPT 1D filtered (t₁ = 0) spectrum. The best performance is for our optimum implementation of windowed with a 12.5 times better relative sensitivity compared to MAS alone.

Fig. 7 Comparison of the sensitivity of 1D-filtered (t₁ = 0) ¹⁵N–¹H (ν₀ = 500 MHz) CP (contact time = 2 ms)-refocused INEPT MAS (ν_r = 60 kHz) NMR spectra of ¹⁵N-glycine recorded with the application of different optimised PMLG ¹H decoupling conditions, (i)–(iv) compared to MAS alone, (v): (i) windowed (τ_{LG_expt} = 3.1 μs, τ_tilt = 0.54 μs, τ₁ = 1.999 ms (69τ_c) with ν₁ = 106 kHz; τ₂ = 1.391 ms (48τ_c) with ν₁ = 106 kHz), (ii) windowed (τ_{LG_expt} = 2.92 μs, τ_tilt = 0.82 μs, τ₁ = 2.085 ms (71τ_c) with ν₁ = 104 kHz; τ₂ = 1.498 ms (51τ_c) with ν₁ = 106 kHz), (iii) windowless (τ_{LG_expt} = 3.1 μs, τ₁ = 2.096 ms (169τ_c) with ν₁ = 102 kHz; τ₂ = 0.496 ms (40τ_c) with ν₁ = 102 kHz), (iv) windowless (τ_{LG_expt} = 2.92 μs, τ₁ = 2.090 ms (179τ_c) with ν₁ = 104 kHz; τ₂ = 1.192 ms (102τ_c) with ν₁ = 102 kHz), (v) no decoupling τ₁ = 1.6 ms (96τ_r) and τ₂ = 0.3 ms (18τ_r). For all experiments with windowed ¹H homonuclear decoupling, τ_w = 7.20 μs. All the spectra were acquired with 16 coadded transients and the corresponding ¹H transmitter offset reported in Table 5.

Finally, in this section, we compare the sensitivity and selectivity of the CP refocused INEPT experiment to that of a hNH double CP experiment. Specifically, the right-hand side of Fig. 8 compares 1D-filtered MAS NMR spectra of ¹⁵N-glycine recorded using the CP refocused INEPT experiment (red) or a hNH double CP experiment with a back (¹⁵N to ¹H) CP contact time of 200 μs (blue). In both cases, the ¹H to ¹⁵N CP contact time is 3.7 ms, i.e., CP is used initially to efficiently generate ¹⁵N transverse magnetisation. While the sensitivity of the CP refocused INEPT spectrum is half that of the double CP experiment, there is no intensity for the CH₂¹H resonances. Fig. 8 also shows, for the double CP experiment, the dependence on the back (¹⁵N to ¹H) CP contact time, with a plateau in intensity reached after 200 μs, though note that CH₂¹H resonance signal is already evident from 100 μs.

Fig. 8 Comparison of the sensitivity of 1D-filtered (t₁ = 0) ¹⁵N–¹H (ν₀ = 600 MHz) MAS (ν_r = 60 kHz) NMR spectra of ¹⁵N-glycine recorded with a double CP experiment (blue) or a CP-refocused INEPT experiment (red). The build-up for the double CP experiment as a function of the ¹⁵N to ¹H CP contact time is also shown. In both cases, the ¹H to ¹⁵N CP contact time is 3.7 ms. For refocused INEPT ¹⁵N to ¹H transfer, windowed (τ_{LG_expt} = 3.19 μs, τ_tilt = 0.5 μs and τ_w = 7.20 μs) is applied at a nutation frequency of 106 kHz for τ₁ = 2.334 ms (140τ_r) and τ₂ = 1.401 ms (84τ_r). All the spectra were acquired with 16 co-added transients and a ¹H transmitter offset of −4 kHz.

3.6 2D ¹⁵N–¹H CP-refocused INEPT NMR spectra with PMLG ¹H decoupling at 60 kHz MAS of a dipeptide and a pharmaceutical at natural abundance

Due to the better sensitivity of windowed observed for glycine, it was selected as the ¹H homonuclear decoupling sequence for a ¹⁵N–¹H correlation experiment recorded for the β-AspAla dipeptide at natural isotopic abundance, with the improvement of resolution achieved in the 1D ¹H CRAMPS compared here with a ¹H one-pulse recorded at Larmor frequency of 500 MHz and 1 GHz (Fig. 9a). Note that a ¹⁵N CP MAS spectrum for the β-AspAla dipeptide has been presented in Tatton et al.²² The ¹⁵N–¹H CP-refocused INEPT experiment was implemented with the offset and coherence transfer delays optimised for ¹⁵N-labelled glycine, as stated in Table 5, i.e., τ_{LG_expt} = 3.1 μs, τ_tilt = 0.54 μs, τ₁ = 2.0 ms with ν₁ = 106 kHz, v₂ = 1.4 ms with ν₁ = 106 kHz, and an offset of +1 kHz. High-performance ¹H homonuclear decoupling achieved with a finely optimised implementation of windowed enables the recording at natural abundance of a 2D ¹⁵N–¹H correlation spectrum at 60 kHz MAS with a through-bond back transfer (Fig. 9b). The sensitivity of the windowed implementation is compared to a ¹⁵N–¹H CP-refocused INEPT spectrum recorded with no decoupling at the optimum τ₁ = 1.6 ms and τ₂ = 0.3 ms values in Table 5 for ¹⁵N-labelled glycine; only noise is observed in Fig. 9c.

Fig. 9 MAS (ν_r = 60 kHz) NMR spectra of (a–c) the dipeptide β-AspAla and (d) the pharmaceutical cimetidine, in both cases at natural isotopic abundance, employing windowed (τ_{LG_expt} = 3.1 μs, τ_tilt = 0.54 μs and τ_w = 7.20 μs). (a) Comparison of a ¹H 1D CRAMPS spectrum acquired with windowed (at ν₀ = 500 MHz, with ¹H one-pulse spectra recorded at ν₀ = 500 MHz and 1 GHz. (b and c) 2D ¹⁵N–¹H (ν₀ = 500 MHz) CP (contact time = 2 ms)-refocused INEPT MAS NMR spectra with (b) windowed ¹H homonuclear decoupling during the spin-echo durations used for ¹⁵N–¹H refocused INEPT coherence transfer or (c) MAS alone. In (b), windowed was implemented with ν₁(¹H) = 106 kHz during τ₁ (1.999 ms, 69τ_c) and ν₁(¹H) = 106 kHz during τ₂ (1.391 ms, 48τ_c), with the transmitter frequency centred at 10.3 ppm. For both (b) and (c), 224 transients were co-added for each of 96 t₁ FIDs, corresponding to a total experimental time of 23 h with a recycle delay of 3 s. The base contour is at 50% of the respective maximum intensity in (b) and (c). (d) A 2D ¹⁵N–¹H (ν₀ = 600 MHz) CP (contact time = 4 ms)-refocused INEPT MAS NMR spectrum with windowed ¹H homonuclear decoupling (ν₁(¹H) = 106 kHz during τ₁ (2.491 ms, 86τ_c) and ν₁(¹H) = 106 kHz during τ₂ (1.999 ms, 69τ_c)), with the transmitter frequency centred at 11.0 ppm. 1024 transients were co-added for each of 64t₁ FIDs, corresponding to a total experimental time of 92 h with a recycle of 5 s. The base contour is at 30% of the maximum intensity.

As noted in Section 3.1, there is a different dependence on the duration of the first spin echo, τ₁, for a NH and NH₃⁺ moiety, compare eqn (1) and (2). This is evident from Fig. 10 that shows the build-up of intensity in a 1D-filtered ¹⁵N–¹H CP-refocused INEPT spectrum of the dipeptide β-AspAla. Two peaks are resolved for the higher-ppm NH and the lower-ppm NH₃⁺ resonances (see deconvolution in Fig. 10b), and it is evident maximum intensity is reached at a shorter spin-echo duration for the lower-ppm NH₃⁺ peak at ∼2.1 ms as compared to ∼3.5 ms for the higher-ppm NH peak. As shown in Fig. S7 of the ESI,‡ this is expected as based from a consideration of eqn (1) and (2). Such an experiment could hence be used to distinguish different NH_x moieties, as for example has been demonstrated analogously for SiH_x groups.^82–84

Fig. 10 (a) Dependence upon the first spin-echo duration, τ₁, for a 1D-filtered (t₁ = 0) ¹⁵N–¹H (ν₀ = 600 MHz) CP (contact time = 3.7 ms)-refocused INEPT MAS (ν_r = 60 kHz) NMR spectrum for the dipeptide β-AspAla at natural isotopic abundance, recorded using ¹H homonuclear decoupling (τ_{LG_expt} = 3.19 μs, τ_tilt = 0.50 μs, with ν₁ = 106 kHz) for τ₂ = 2.101 ms (126τ_r). All the spectra were acquired with 1024 co-added transients and a ¹H transmitter offset of −2 kHz. A deconvolution of the NH (red) and NH₃ (blue) peaks is shown in (b).

Furthermore, windowed was employed to record a 2D ¹⁵N–¹H CP-refocused INEPT spectrum of the pharmaceutical cimetidine at natural abundance (Fig. 9d), for which ¹H, ¹⁵N CPMAS and ¹⁴N–¹H spectra have been presented in ref. 101 and 102. (For comparison, note that in ref. 101, Tatton et al. use a simple ¹⁵N–¹H heteronuclear spin echo with ¹H homonuclear decoupling to demonstrate spectral editing.) In this case, spin-echo curves were recorded, because, as discussed above, the optimum τ₁ and τ₂ durations in the refocused INEPT pulse sequence element depends both on the J coupling between the involved nuclei and the ¹H dephasing . The ¹H coherence lifetime (see Fig. S6 and Table S1 (ESI‡) in comparison to Table 4) for two of the protons directly bonded to the nitrogens, N3 and N10, is longer than the NH₃⁺ of ¹⁵N-glycine acquired with the same windowed ¹H decoupling. In addition, considering the above discussion of Fig. 10 and eqn (1) and (2), note that for a NH group, a maximum signal is observed at a longer τ₁ as compared to a NH₃⁺ group. For this reason, τ₁ and τ₂ were increased to 2.5 ms and 2.0 ms, respectively. Note that weaker intensity is observed for the proton directly bonded to N15, where the respective ¹H is ∼0.5 ms after scaling (Table S1, ESI‡). Further investigation is required to understand the shorter for this proton and the very weak signal for the N15–H15 cross peak in the 2D CP-refocused INEPT spectrum in Fig. 9d.

4. Conclusions and outlook

This paper has identified ¹H homonuclear decoupling conditions for the supercycle at 60 kHz MAS that give enhanced resolution in a 1D NMR spectrum as compared to MAS alone. At 1 GHz, we report what we believe to be the first example of effective homonuclear decoupling achieved by using a rf nutation frequency lower than the MAS frequency. The establishing of 2D ¹⁵N–¹H heteronuclear correlation for natural abundance solids using a ¹H detected CP-J coupling based refocused INEPT MAS NMR experiment^26,38,39 has been demonstrated at 60 kHz MAS. The application of ¹H homonuclear decoupling, specifically the supercycle^26,39,57,85 results in a factor of 12.5 sensitivity enhancement as compared to MAS alone. Notably, in our implementation at 500 MHz, a comparatively low ¹H nutation frequency, for a 1.3 mm rotor, of 100 kHz was used, with this being associated with a high chemical shift scaling factor of 0.82 and a large deviation from the ideal Lee–Goldburg condition. Future work could further probe the suitability and optimisation of such windowed and windowless decoupling sequences for applications involving spin-echo evolution. In addition, nutation-frequency-selective pulses that reduce rf inhomogeneity could also be explored.¹⁰³ The CP-refocused INEPT pulse sequence is complementary to dipolar coupling-based double CP or the use of symmetry-based decoupling to establish ¹⁵N–¹H heteronuclear correlation under fast MAS.^26,29,30,104 Note that the use of symmetry-based recoupling is more prone to t₁ noise.^105–107 In future work, the extension of our approach to 100+ kHz MAS could be considered, noting an increasing number of applications to pharmaceuticals and other small and moderately sized organic molecules.^9,108–114

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

J. T. thanks Bruker and EPSRC for a PhD studentship through the EPSRC Centre for Doctoral Training in Molecular Analytical Science, grant number EP/L015307/1. The UK High-Field Solid-State NMR Facility used in this research was funded by EPSRC and BBSRC (EP/T015063/1), as well as, for the 1 GHz instrument, EP/R029946/1. The renewal of the 600 MHz solid-state NMR console (Avance NEO) was funded by BBSRC (BB/T018119/1), EPSRC and University of Warwick. We thank Dr Andrew P. Howes and Patrick Ruddy for supporting the operation of the Millburn House Magnetic Resonance Laboratory. Data for this study are provided as a supporting data set from the University of Warwick Research Datasets portal at https://wrap.warwick.ac.uk/166703/.

References

1. P. C. Vioglio, M. R. Chierotti and R. Gobetto, Adv. Drug Delivery Rev., 2017, 117, 86.
2. E. Pindelska, A. Sokal and W. Kolodziejski, Adv. Drug Delivery Rev., 2017, 117, 111.
3. X. Lu, Y. Tsutsumi, C. Huang, W. Xu, S. R. Byrn, A. C. Templeton, A. V. Buevich, J.-P. Amoureux and Y. Su, Phys. Chem. Chem. Phys., 2020, 22, 13160.
4. M. Li, W. Xu and Y. Su, Trac, Trends Anal. Chem., 2021, 135, 116152.
5. J. R. Lewandowski, J.-N. Dumez, Ü. Akbey, S. Lange, L. Emsley and H. Oschkinat, J. Phys. Chem. Lett., 2011, 2, 2205.
6. D. Lacabanne, J. Boudet, A. A. Malär, P. Wu, R. Cadalbert, L. Salmon, F. H.-T. Allain, B. H. Meier and T. Wiegand, J. Phys. Chem. B, 2020, 124, 11089.
7. V. Jirasko, A. Lends, N. A. Lakomek, M. L. Fogeron, M. E. Weber, A. A. Malär, S. Penzel, R. Bartenschlager, B. H. Meier and A. Böckmann, Angew. Chem., 2021, 133, 5399.
8. S. Bahri, R. Silvers, B. Michael, K. Jaudzems, D. Lalli, G. Casano, O. Ouari, A. Lesage, G. Pintacuda, S. Linse and R. G. Griffin, Proc. Natl. Acad. Sci. U. S. A., 2022, 119, e2114413119.
9. U. Sternberg, R. Witter, I. Kuprov, J. M. Lamley, A. Oss, J. R. Lewandowski and A. Samoson, J. Magn. Reson., 2018, 291, 32.
10. Y. Nishiyama, Solid State Nucl. Magn. Reson., 2016, 78, 24.
11. A. A. Malär, S. Smith-Penzel, G.-M. Camenisch, T. Wiegand, A. Samoson, A. Böckmann, M. Ernst and B. H. Meier, Phys. Chem. Chem. Phys., 2019, 21, 18850.
12. M. Schledorn, A. A. Malär, A. Torosyan, S. Penzel, D. Klose, A. Oss, M. L. Org, S. Wang, L. Lecoq, R. Cadalbert, A. Samoson, A. Böckmann and B. H. Meier, ChemBioChem, 2020, 21, 2540.
13. Z. Zhang, A. Oss, M.-L. Org, A. Samoson, M. Li, H. Tan, Y. Su and J. Yang, J. Phys. Chem. Lett., 2020, 11, 8077.
14. E. C.-Y. Yuan, S.-J. Huang, H.-C. Huang, J. Sinkkonen, A. Oss, M.-L. Org, A. Samoson, H.-C. Tai and J. C. C. Chan, Chem. Commun., 2021, 57, 4110.
15. Z. Gan, J. P. Amoureux and J. Trébosc, Chem. Phys. Lett., 2007, 435, 163.
16. S. Cavadini, S. Antonijevic, A. Lupulescu and G. Bodenhausen, J. Magn. Reson., 2006, 182, 168.
17. J. A. Jarvis, M. Concistre, I. M. Haies, R. W. Bounds, I. Kuprov, M. Carravetta and P. T. F. Williamson, Phys. Chem. Chem. Phys., 2019, 21, 5941.
18. M. Grüne, R. Luxenhofer, D. Iuga, S. P. Brown and A.-C. Pöppler, J. Mater. Chem. B, 2020, 8, 6827.
19. K. Bártová, I. Císařová, A. Lyčka and M. Dračínský, Dyes Pigm., 2020, 178, 108342.
20. M. K. Pandey and Y. Nishiyama, Phys. Chem. Chem. Phys., 2018, 20, 25849.
21. A. Pugliese, M. Toresco, D. McNamara, D. Iuga, A. Abraham, M. Tobyn, L. E. Hawarden and F. Blanc, Mol. Pharm., 2021, 18, 3519.
22. A. S. Tatton, J. P. Bradley, D. Iuga and S. P. Brown, Z. Phys. Chem., 2012, 226, 1187.
23. Y. Ishii and R. Tycko, J. Magn. Reson., 2000, 142, 199.
24. Y. Ishii, J. P. Yesinowski and R. Tycko, J. Am. Chem. Soc., 2001, 123, 2921.
25. D. H. Zhou, G. Shah, C. Mullen, D. Sandoz and C. M. Rienstra, Angew. Chem., Int. Ed., 2009, 48, 1253.
26. S. M. Althaus, K. Mao, J. A. Stringer, T. Kobayashi and M. Pruski, Solid State Nucl. Magn. Reson., 2014, 57–58, 17.
27. A. Lesage, P. Charmont, S. Steuernagel and L. Emsley, J. Am. Chem. Soc., 2000, 122, 9739.
28. T. Kobayashi, K. Mao, P. Paluch, A. Nowak-Król, J. Sniechowska, Y. Nishiyama, D. T. Gryko, M. J. Potrzebowski and M. Pruski, Angew. Chem., 2013, 125, 14358.
29. S. L. Veinberg, K. E. Johnston, M. J. Jaroszewicz, B. M. Kispal, C. R. Mireault, T. Kobayashi, M. Pruski and R. W. Schurko, Phys. Chem. Chem. Phys., 2016, 18, 17713.
30. C. Guzmán-Afonso, Y.-l Hong, H. Colaux, H. Iijima, A. Saitow, T. Fukumura, Y. Aoyama, S. Motoki, T. Oikawa, T. Yamazaki, K. Yonekura and Y. Nishiyama, Nat. Commun., 2019, 10, 3537.
31. E. K. Paulson, C. R. Morcombe, V. Gaponenko, B. Dancheck, R. A. Byrd and K. W. Zilm, J. Am. Chem. Soc., 2003, 125, 15831.
32. V. Chevelkov, K. Rehbein, A. Diehl and B. Reif, Angew. Chem., Int. Ed., 2006, 45, 3878.
33. D. H. Zhou, G. Shah, M. Cormos, C. Mullen, D. Sandoz and C. M. Rienstra, J. Am. Chem. Soc., 2007, 129, 11791.
34. C. Fyfe, K. Wong-Moon, Y. Huang and H. Grondey, J. Am. Chem. Soc., 1995, 117, 10397.
35. O. Soubias, V. Réat, O. Saurel and A. Milon, J. Magn. Reson., 2002, 158, 143.
36. B. Alonso and D. Massiot, J. Magn. Reson., 2003, 163, 347.
37. B. Elena, A. Lesage, S. Steuernagel, A. Böckmann and L. Emsley, J. Am. Chem. Soc., 2005, 127, 17296.
38. K. Mao, J. W. Wiench, V. S.-Y. Lin and M. Pruski, J. Magn. Reson., 2009, 196, 92.
39. K. Mao and M. Pruski, J. Magn. Reson., 2009, 201, 165.
40. G. P. Holland, B. R. Cherry, J. E. Jenkins and J. L. Yarger, J. Magn. Reson., 2010, 202, 64.
41. P. K. Madhu, Solid State Nucl. Magn. Reson., 2009, 35, 2.
42. K. R. Mote, V. Agarwal and P. K. Madhu, Prog. Nucl. Magn. Reson. Spectrosc., 2016, 97, 1.
43. P. Hodgkinson, Annu. Rep. NMR Spectrosc., 2011, 72, 185.
44. E. Vinogradov, P. K. Madhu and S. Vega, New Techniques Solid-State NMR, 2005, p. 33.
45. M. Lee and W. I. Goldburg, Phys. Rev., 1965, 140, A1261.
46. M. H. Levitt, A. C. Kolbert, A. Bielecki and D. J. Ruben, Solid State Nucl. Magn. Reson., 1993, 2, 151.
47. M. Hohwy and N. C. Nielsen, J. Chem. Phys., 1997, 106, 7571.
48. M. Hohwy, P. Bower, H. Jakobsen and N. Nielsen, Chem. Phys. Lett., 1997, 273, 297.
49. E. Vinogradov, P. K. Madhu and S. Vega, Chem. Phys. Lett., 1999, 314, 443.
50. D. Sakellariou, A. Lesage, P. Hodgkinson and L. Emsley, Chem. Phys. Lett., 2000, 319, 253.
51. P. K. Madhu, X. Zhao and M. H. Levitt, Chem. Phys. Lett., 2001, 346, 142.
52. M. E. Halse and L. Emsley, Phys. Chem. Chem. Phys., 2012, 14, 9121.
53. F. M. Paruzzo and L. Emsley, J. Magn. Reson., 2019, 309, 106598.
54. C. Coelho, J. Rocha, P. K. Madhu and L. Mafra, J. Magn. Reson., 2008, 194, 264.
55. I. Schnell, S. P. Brown, H. Y. Low, H. Ishida and H. W. Spiess, J. Am. Chem. Soc., 1998, 120, 11784.
56. J.-P. Amoureux, B. Hu, J. Trébosc, Q. Wang, O. Lafon and F. Deng, Solid State Nucl. Magn. Reson., 2009, 35, 19.
57. Y. Nishiyama, X. Lu, J. Trebosc, O. Lafon, Z. Gan, P. K. Madhu and J.-P. Amoureux, J. Magn. Reson., 2012, 214, 151.
58. E. Salager, J.-N. Dumez, R. S. Stein, S. Steuernagel, A. Lesage, B. Elena-Herrmann and L. Emsley, Chem. Phys. Lett., 2010, 498, 214.
59. M. Leskes, S. Steuernagel, D. Schneider, P. K. Madhu and S. Vega, Chem. Phys. Lett., 2008, 466, 95.
60. J.-P. Amoureux, B. Hu and J. Trébosc, J. Magn. Reson., 2008, 193, 305.
61. Z. Gan, P. K. Madhu, J.-P. Amoureux, J. Trébosc and O. Lafon, Chem. Phys. Lett., 2011, 503, 167.
62. E. Salager, R. S. Stein, S. Steuernagel, A. Lesage, B. Elena and L. Emsley, Chem. Phys. Lett., 2009, 469, 336.
63. B. Gerstein, R. Pembleton, R. Wilson and L. Ryan, J. Chem. Phys., 1977, 66, 361.
64. E. Salager, J.-N. Dumez, L. Emsley and M. H. Levitt, J. Magn. Reson., 2011, 212, 11.
65. M. Leskes, P. K. Madhu and S. Vega, J. Magn. Reson., 2009, 199, 208.
66. R. Ramesh and M. S. Krishnan, J. Chem. Phys., 2001, 114, 5967.
67. S. Hayashi and K. Hayamizu, Bull. Chem. Soc. Jpn., 1991, 64, 685.
68. E. K. Corlett, H. Blade, L. P. Hughes, P. J. Sidebottom, D. Walker, R. I. Walton and S. P. Brown, CrystEngComm, 2019, 21, 3502.
69. S. Hayashi and K. Hayamizu, Bull. Chem. Soc. Jpn., 1991, 64, 688.
70. R. K. Harris, E. D. Becker, S. M. C. De Menezes, P. Granger, R. E. Hoffman and K. W. Zilm, Pure Appl. Chem., 2008, 80, 59.
71. G. E. Martin and C. E. Hadden, J. Nat. Prod., 2000, 63, 543.
72. B. H. Meier, Chem. Phys. Lett., 1992, 188, 201.
73. S. Laage, J. R. Sachleben, S. Steuernagel, R. Pierattelli, G. Pintacuda and L. Emsley, J. Magn. Reson., 2009, 196, 133.
74. G. Metz, X. Wu and S. O. Smith, J. Magn. Reson. Ser. A, 1994, 110, 219.
75. D. H. Zhou and C. M. Rienstra, J. Magn. Reson., 2008, 192, 167.
76. M. Ernst, M. A. Meier, T. Tuherm, A. Samoson and B. H. Meier, J. Am. Chem. Soc., 2004, 126, 4764.
77. A. Shaka, J. Keeler and R. Freeman, J. Magn. Reson. (1969), 1983, 53, 313.
78. Z. Zhou, R. Kümmerle, X. Qiu, D. Redwine, R. Cong, A. Taha, D. Baugh and B. Winniford, J. Magn. Reson., 2007, 187, 225.
79. A. Lesage, S. Steuernagel and L. Emsley, J. Am. Chem. Soc., 1998, 120, 7095.
80. A. S. Tatton, I. Frantsuzov, S. P. Brown and P. Hodgkinson, J. Chem. Phys., 2012, 136, 084503.
81. A. Lesage, L. Emsley, M. Chabanas, C. Coperet and J.-M. Basset, Angew. Chem., 2002, 114, 4717.
82. M. P. Hanrahan, E. L. Fought, T. L. Windus, L. M. Wheeler, N. C. Anderson, N. R. Neale and A. J. Rossini, Chem. Mater., 2017, 29, 10339.
83. R. W. Dorn, E. A. Marro, M. P. Hanrahan, R. S. Klausen and A. J. Rossini, Chem. Mat., 2019, 31, 9168.
84. B. J. Ryan, M. P. Hanrahan, Y. Wang, U. Ramesh, C. K. A. Nyamekye, R. D. Nelson, Z. Liu, C. Huang, B. Whitehead, J. Wang, L. T. Roling, E. A. Smith, A. J. Rossini and M. G. Panthani, Chem. Mat., 2020, 32, 795.
85. M. Leskes, P. K. Madhu and S. Vega, Chem. Phys. Lett., 2007, 447, 370.
86. M. Mehring and J. S. Waugh, Phys. Rev. B: Condens. Matter Mater. Phys., 1972, 5, 3459.
87. A. Bielecki, A. C. Kolbert and M. H. Levitt, Chem. Phys. Lett., 1989, 155, 341.
88. E. Vinogradov, P. K. Madhu and S. Vega, Chem. Phys. Lett., 2002, 354, 193.
89. M. Leskes, P. K. Madhu and S. Vega, J. Chem. Phys., 2006, 125, 124506.
90. S. Paul, R. S. Thakur, M. Goswami, A. C. Sauerwein, S. Mamone, M. Concistre, H. Forster, M. H. Levitt and P. K. Madhu, J. Magn. Reson., 2009, 197, 14.
91. V. E. Zorin, M. Ernst, S. P. Brown and P. Hodgkinson, J. Magn. Reson., 2008, 192, 183.
92. K. Mao and M. Pruski, J. Magn. Reson., 2010, 203, 144.
93. S. Hafner and H. W. Spiess, J. Magn. Reson., Ser. A, 1996, 121, 160.
94. E. Vinogradov, P. K. Madhu and S. Vega, Chem. Phys. Lett., 2000, 329, 207.
95. A. Lesage, D. Sakellariou, S. Hediger, B. Eléna, P. Charmont, S. Steuernagel and L. Emsley, J. Magn. Reson., 2003, 163, 105.
96. J. S. Waugh, L. M. Huber and U. Haeberlen, Phys. Rev. Lett., 1968, 20, 180.
97. A. J. Vega, J. Magn. Reson., 2004, 170, 22.
98. A. Lesage, M. Bardet and L. Emsley, J. Am. Chem. Soc., 1999, 121, 10987.
99. V. E. Zorin, S. P. Brown and P. Hodgkinson, J. Chem. Phys., 2006, 125, 144508.
100. L. Bosman, P. K. Madhu, S. Vega and E. Vinogradov, J. Magn. Reson., 2004, 169, 39.
101. A. S. Tatton, T. N. Pham, F. G. Vogt, D. Iuga, A. J. Edwards and S. P. Brown, CrystEngComm, 2012, 14, 2654.
102. K. Maruyoshi, D. Iuga, A. E. Watts, C. E. Hughes, K. D. M. Harris and S. P. Brown, J. Pharm. Sci., 2017, 106, 3372.
103. K. Aebischer, N. Wili, Z. Tošner and M. Ernst, Magn. Reson., 2020, 1, 187.
104. F. A. Perras, T. W. Goh, L.-L. Wang, W. Huang and M. Pruski, Solid State Nucl. Magn. Reson., 2019, 98, 12.
105. A. J. Robertson, M. K. Pandey, A. Marsh, Y. Nishiyama and S. P. Brown, J. Magn. Reson., 2015, 260, 89.
106. M. Shen, S. Wegner, J. Trébosc, B. Hu, O. Lafon and J.-P. Amoureux, Solid State Nucl. Magn. Reson., 2017, 87, 111.
107. A. Venkatesh, X. Luan, F. A. Perras, I. Hung, W. Huang and A. J. Rossini, Phys. Chem. Chem. Phys., 2020, 22, 20815.
108. Y. Nishiyama, M. Malon, Y. Ishii and A. Ramamoorthy, J. Magn. Reson., 2014, 244, 1.
109. Y. Nishiyama, T. Kobayashi, M. Malon, D. Singappuli-Arachchige, I. I. Slowing and M. Pruski, Solid State Nucl. Magn. Reson., 2015, 66, 56.
110. J. Struppe, C. M. Quinn, M. Lu, M. Wang, G. Hou, X. Lu, J. Kraus, L. B. Andreas, J. Stanek, D. Lalli, A. Lesage, G. Pintacuda, W. Maas, A. M. Gronenborn and T. Polenova, Solid State Nucl. Magn. Reson., 2017, 87, 117.
111. J. Struppe, C. M. Quinn, S. Sarkar, A. M. Gronenborn and T. Polenova, Mol. Pharm., 2019, 17, 674.
112. R. Zhang, Y.-l Hong, T. Ravula, Y. Nishiyama and A. Ramamoorthy, J. Magn. Reson., 2020, 313, 106717.
113. P. Moutzouri, F. M. Paruzzo, B. Simões de Almeida, G. Stevanato and L. Emsley, Angew. Chem., Int. Ed., 2020, 59, 6235.
114. P. Moutzouri, B. Simões de Almeida, D. Torodii and L. Emsley, J. Am. Chem. Soc., 2021, 143, 9834.

---

Footnotes

† Dedicated to Shimon Vega (1943–2021).

‡ Electronic supplementary information (ESI) available: Additional experimental solid-state NMR and simulated data. See DOI: https://doi.org/10.1039/d2cp01041k

---