Windowed Symmetry Pulses for Enhanced Heteronuclear Dipolar Recoupling in Solid-State MAS NMR

Abstract

Dipolar recoupling techniques play a fundamental role in solid-state NMR spectroscopy, enabling precise structural characterization of solid materials under magic-angle spinning (MAS). Among these, the supercycled R4₁ (SR4) stands out for its efficiency and stability in recoupling heteronuclear dipolar interactions under fast MAS conditions (≥40 kHz). However, its performance significantly degrades at slow-to-moderate MAS rates (<35 kHz), which restricts its wide applications. To overcome this limitation, herein we introduce a practical modification of SR4 through the strategic incorporation of adjustable window delays between the recoupling π pulses, dubbed windowed SR4 (wSR4). This design introduces the variability of pulse duration and rf amplitude, which simplifies the recoupling optimization procedure, while enabling enhanced recoupling performance and improved tolerance to experimental imperfections. Theoretical analysis and NMR experiments collectively confirm that wSR4 substantially boosts heteronuclear dipolar recoupling efficiency while effectively suppressing undesired spin interactions, particularly under slow MAS conditions. The practical utility of wSR4 is further validated in in situ NMR experiments on SAPO zeolite, where the markedly improved 2D correlation spectroscopy provides deeper insights into local structures. This approach enables precise dipolar measurement, efficient polarization transfer, and the establishment of high-fidelity heteronuclear correlations, all of which are critical for structural elucidation in complex solid systems. Moreover, the windowed SR4 design strategy introduced here is expected to provide a generalizable framework for optimizing symmetry-based recoupling sequences across a wide range of MAS conditions.

Introduction

Atomic spatial proximity is a fundamental structural descriptor in materials science. Solid-state nuclear magnetic resonance (NMR), as a powerful tool for probing local chemical structures, can unveil such local atomic environments by directly detecting through-space interactions between nuclear spin pairs. This interaction, known as the dipole–dipole coupling or dipolar coupling, is anisotropic and encodes rich structural and dynamic information, including interatomic distance, spatial orientation, and atomic mobility. − In a static powder sample, the anisotropy of dipolar coupling leads to a characteristic line shape in the NMR spectrum, which, in principle, allows for the direct extraction of interatomic distances. However, in practical applications, spectral resolution is severely compromised by the overlap of lineshapes from multiple sites and line broadening induced by other anisotropic spin interactions, rendering the direct dipolar measurement extremely challenging.

To overcome these limitations, the combination of magic-angle spinning (MAS) with radiofrequency (rf) pulse sequences has been established as a cornerstone methodology. − The fast mechanical rotation of MAS drastically reduces or even averages out anisotropic spin interactions, yielding liquid-like high-resolution NMR spectra in solids. Complementarily, a well-designed rf pulse sequence can interfere with the evolution of spin Hamiltonians under mechanical rotation, selectively preventing the MAS average of certain anisotropic spin interactions, dubbed as recoupling. This selective reintroduction of dipolar interaction is usually referred to as dipolar recoupling. Over the years, tremendous efforts have been devoted to the development of high-performance dipolar recoupling sequences under MAS conditions, aiming to achieve precise distance measurement and spatial correlations between atoms with high accuracy, efficiency, and robustness. ,

The development of heteronuclear dipolar recoupling has progressed significantly over the past few decades. Early representative sequences include R³ (Rotary Resonance Recoupling) , and REDOR (Rotational-Echo Double-Resonance). , Among them, REDOR has been widely adopted for dipolar measurement due to its less sensitivity to resonance offset and rf inhomogeneity. , Nevertheless, a major limitation of REDOR is its susceptibility to interference from homonuclear dipolar couplings, which can introduce significant experimental errors and lead to inaccurate structural parameters. Consequently, the applications of REDOR are generally restricted to spin systems with an isolated spin pair, imposing stringent requirements on sample preparation, such as the need for selective isotopic labeling or extensive deuteration. Subsequent developments, including the T-MREV (transverse MREV-8) sequence, demonstrated a certain capability in suppressing homonuclear dipolar coupling, but their practical application was often limited by the demand for high rf field strengths (e.g., v ₁ = 16v _r). ,

A significant advancement came with the establishment of symmetry pulse sequence theory, which enabled the design of a family of R-symmetry sequences (e.g., R18₂ ) that recouple single-quantum (SQ) heteronuclear dipolar coupling while effectively suppressing homonuclear dipolar couplings. , While this breakthrough facilitated accurate determination of ¹H–¹³C/¹⁵N dipolar coupling in protonated protein without the need for deuteration, , these SQ recoupling sequences are inherently constrained by dipolar truncation, where only the strongest coupling in a multispin system is measured. Furthermore, the application of these R-symmetry sequences is hampered by sensitivity to rf inhomogeneity and low scaling factors (typically ≤ 0.3), even though the latter methods like PARS, wPARS, and iSR-sequences offered partial compensation for the interferences from resonance offset and chemical shift anisotropy (CSA). −

Currently, one of the most prevalent methods is the supercycled R4₁ sequence, denoted herein as SR4. , As a method originally designed for heteronuclear dipolar recoupling under fast MAS conditions, SR4 employs a low rf amplitude, i.e., twice the spinning frequency (2ν_r), and, notably, features a large scaling factor of 0.5. Its popularity stems from its robustness against rf inhomogeneity, homonuclear dipolar coupling, and CSA. Moreover, SR4 recouples zero-quantum (ZQ) heteronuclear dipolar terms ( I _z S _z ) that commute between different spin pairs, thereby eliminating the influence of dipolar truncations and enabling the detection of weak dipolar coupling even in the presence of strong ones. , However, the reliability of SR4 is limited to fast and ultrafast MAS conditions, which constitutes its primary limitation. Crucially, under slow-to-moderate MAS conditions (particularly below 20 kHz), the low rf amplitude required for SR4 leads to a pronounced decrease in stability and recoupling efficiency. Additionally, fast MAS probes are expensive and typically designed for small-volume, proton-detected experiments, while probes with large sample volumes (e.g., with an outer diameter of 3.2–7.5 mm) are more frequently employed in practical applications.

In this work, we propose a windowed SR4 (wSR4) sequence with an adjustable rf amplitude to address this critical limitation. Through comprehensive theoretical analysis and numerical simulations, the superior performance of wSR4 for dipolar recoupling at all MAS rates has been rigorously demonstrated. It is revealed that wSR4 not only achieves a larger scaling factor but also exhibits superior robustness against experimental imperfections and undesired interactions, particularly under slow MAS conditions. The enhanced performance of wSR4 has also been validated through distance measurements and heteronuclear correlation experiments in both organic and inorganic materials. Most notably, under a slow MAS regime, the high robustness of wSR4 significantly improves the efficiency of dipolar-based heteronuclear multiple-quantum correlation (D-HMQC), paving the way to rapid acquisition of operando two-dimensional (2D) solid-state NMR spectra for complex systems previously inaccessible to conventional recoupling techniques.

Pulse Sequences and Theory

The pulse sequences of SR4 and wSR4 are shown in Figure a. For consistency, both sequences employ the same (0, 180°) two-step supercycling. To systematically evaluate the performance enhancements, the effects of window modification and supercycling are analyzed separately. We first examine the window modification within the R4₁ unit using the framework of symmetry pulse sequence developed by Levitt and co-workers.

1.

Pulse sequence and window modification of SR4. (a) SR4­(upper) and wSR4­(lower) sequences; (b) illustration of the window delays in wSR4; (c) scaling factors of the recoupled heteronuclear and homonuclear terms in wR4₁ , as a function of the window fraction.

R4₁ Sequence and Recoupled Terms

The R4₁ sequence belongs to the R-symmetry class, RN _n , with symmetry number (N, n, ν) = (4, 1, 2), denoting four (N) π-pulses occupying one (n) rotor period with alternating phases of ±90° (±πν/N). Based on average Hamiltonian theory, RN _n recouples first-order Hamiltonian terms ${\mathcal{H}}_{\mathit{lm}\lambda \mu }$ if the symmetry numbers match the following rules

$$mn-\mu \nu =\frac{N}{2}{Z}_{\lambda }$$ 1

where the integer numbers (l, m) and (λ, μ) represent the spatial and spin symmetries of the interaction under physical rotation (MAS) and rf manipulation, respectively. The Z _λ takes even (0, ± 2, ± 4,···) or odd (±1, ± 3, ± 5,···) integer values depending on the parity of λ. According to eq , the R4₁ recouples two types of dipolar terms: zero-quantum (ZQ) heteronuclear dipolar terms with (l, m, λ, μ) = (2, ± 2, 1, 0) and single-quantum (SQ) homonuclear dipolar terms with (l, m, λ, μ) = (2, ± 2, 2, ± 1) & (2, ± 2, 2, ∓ 1). Terms within each category have identical scaling factors.

The Hamiltonians of certain interactions recoupled by symmetry sequences can be expressed as

$${\mathcal{H}}_{\mathit{lm}\lambda \mu }^{\mathrm{\Lambda }}(t)=d_{\mu 0}^{\lambda }[-{\beta }_{\mathrm{rf}}(t)]{\omega }_{\mathit{lm}}^{\mathrm{\Lambda }}\exp \{i\mu {\gamma }_{\mathrm{rf}}(t)+\mathit{im}{\omega }_{r}t\}{\mathit{T}}_{\lambda \mu }^{\mathrm{\Lambda }}$$ 2

where Λ represents a specific interaction, (l, m, λ, μ) indicates a component with specific symmetries, and t is the evolution time. The β_rf (t) and γ_rf (t) correspond to Euler angles of rf pulses at time t, and the ω_r means MAS frequency in the unit of rad·s^–1 (ω_r = 2πν_r). d _μ0 [θ] is the reduced Wigner element. T _λμ is the μth component of the spin tensor of rank λ for interaction Λ. ω _lm is the amplitude of the (l, m, λ, μ) term determined by spatial orientation,

$${\omega }_{\mathit{lm}}^{\mathrm{\Lambda }}={[{\mathit{A}}_{\mathit{lm}}^{\mathrm{\Lambda }}]}^R{d}_{m0}^l[{\beta }_{\mathrm{RL}}]\exp \{-\mathit{im}{\alpha }_{\mathrm{RL}}^0\}$$ 3

where [ A _lm ] ^R defines the rotational properties of the spin interaction under mechanical rotation. {α_RL , β_RL} are Euler angles of the rotor frame relative to the principal frame at t = 0.

In the RN _n sequence, the γ_rf(t) in eq evolves after each π-pulse according to the phase-time symmetry: γ_rf (t + nτ_r/N) = γ_rf (t) – 2πν/N. Accordingly, the rf-modulated component can be written as follows

$${\mathrm{\Omega }}_{m\lambda \mu }(t)=d_{\mu 0}^{\lambda }[-{\beta }_{\mathrm{rf}}(t)]\exp \{i\mu [{\gamma }_{\mathrm{rf}}(t)-\frac{\pi \nu }{N}]+\mathit{im}{\omega }_{\mathrm{r}}t\}$$ 4

In the dipolar recoupling scheme, the first-order time-averaging of the Ω _mλμ(t) can be expressed as follows

$$\begin{array}{l}{\omega }_{m\lambda \mu }\left(\tau \right)={\tau }^{-1}{\int }_{t_0}^{t_0+\tau }{\mathrm{\Omega }}_{m\lambda \mu }(t)\mathrm{d}t\\ ={\tau }^{-1}{\int }_{t_0}^{t_0+\tau }{d}_{\mu 0}^{\lambda }[-{\beta }_{\mathrm{rf}}(t)]\exp \{i\mu [{\gamma }_{\mathrm{rf}}(t)-\frac{\pi \nu }{N}]+\mathit{im}{\omega }_{\mathrm{r}}t\}\mathrm{d}t\end{array}$$ 5

where τ is an arbitrary period and t ₀ means the starting time of the first basic element. For simplicity, let t ₀ start from 0, then ω _mλμ (τ;t ₀) = ω _mλμ (τ). For τ = k·(nτ_r/N), k = 1,2,3···, the scaling factor κ _lmλμ of the pulse sequence can be given as follows

$${\kappa }_{\mathit{lm}\lambda \mu }=d_{m0}^l({\beta }_{\mathrm{RL}}){\omega }_{m\lambda \mu }(n{\tau }_{\mathrm{r}}/N)$$ 6

where β_RL is often set to magic angle (θ _m = arccos $(1/\sqrt{3})$ ) in most NMR experiments. d _m0 [θ] is the reduced Wigner element, which is a constant when θ is fixed. Given that the spatial indices (l, m) = (2, ± 2) are identical for heteronuclear and homonuclear dipolar terms under consideration, we express κ _lmλμ in the unit of $d_{m0}^l\left({\theta }_m\right)(=\sqrt{3/8}{\sin }^2({\theta }_m))$ for simplicity.

Window Modification

The windowed SR4 (wSR4) sequence is constructed by inserting adjustable, evenly spaced delays between π-pulses within the traditional SR4 framework, as shown in Figure b. A parameter of window fraction (f _w) is defined to describe the proportion ratio of the window durations, with f _w = 0 corresponding to the windowless SR4.

For the basic R4₁ sequence, the γ_rf(t) in eq is constant according to the phase-time symmetry

$${\gamma }_{\mathrm{rf}}(t)\equiv \frac{\pi }{2}$$ 7

Consequently, only β_rf (t) accounts for the analysis

$${\beta }_{\mathrm{rf}}(t)={\int }_0^t{\omega }_{\mathrm{nut}}(t^{\prime })\mathrm{d}{t}^{\prime }$$ 8

where

$${\omega }_{\mathrm{nut}}(t)=\pm {\omega }_{\mathrm{rf}}(t)=\{\begin{array}{l}\pm \frac{2{\omega }_{\mathrm{r}}}{1-f_{\mathrm{w}}},\mathrm{d}\mathrm{uring}\mathrm{pulse}\mathrm{period}\\ 0,\mathrm{d}\mathrm{uring}\mathrm{window}\mathrm{period}\end{array}$$ 9

As seen, increasing f _w decreases the duration of π-pulses and elevates the rf amplitude. Crucially, the window modification does not alter the symmetry selection rules in eq , but it changes the scaling factors of the recoupled terms, constituting the key determinant of the recoupling performance. Combining eqs , , and , the rf-related part of the heteronuclear dipolar term ${\mathcal{H̃}}_{2210}^{\mathrm{dipole}}$ can be obtained as follows

$$\begin{array}{l}{\mathrm{\Omega }}_{210}\left(t\right)=d_{00}^1[-{\beta }_{\mathrm{rf}}(t)]\exp \{2i{\omega }_{\mathrm{r}}t\}\\ =\cos [-{\beta }_{\mathrm{rf}}(t)]\exp \{2i{\omega }_{\mathrm{r}}t\}\end{array}$$ 10

According to eqs and , the scaling factor of the heteronuclear dipolar term ${\mathcal{H̃}}_{2210}^{\mathrm{dipole}}$ can be obtained from the first-order average of Ω₂₁₀(t) over τ = τ_r/4

$${\kappa }_{2210}=\frac{2}{\pi }\frac{\sin (\pi f_{\mathrm{w}}/2)}{f_{\mathrm{w}}(2-f_{\mathrm{w}})}\left(\mathrm{in}\mathrm{unit}\mathrm{of}\sqrt{\frac{3}{8}}{\sin }^2({\theta }_m)\right)$$ 11

Similarly, the evolution of the homonuclear dipolar term ${\mathcal{H̃}}_{2221}^{\mathrm{dipole}}$ is governed by

$$\begin{array}{l}{\mathrm{\Omega }}_{221}\left(t\right)=d_{10}^2[{-\beta }_{\mathrm{rf}}(t)]\exp \{2i{\omega }_{\mathrm{r}}t\}\\ =-\sqrt{\frac{3}{8}}\sin [{-2\beta }_{\mathrm{rf}}(t)]\exp \{2i{\omega }_{\mathrm{r}}t\}\end{array}$$ 12

$${\kappa }_{2221}=\frac{\sqrt{6}}{\pi }\frac{(1-f_{\mathrm{w}})\cos (\pi f_{\mathrm{w}}/2)}{(3-f_{\mathrm{w}})(1+f_{\mathrm{w}})}\left(\mathrm{in}\mathrm{unit}\mathrm{of}\sqrt{\frac{3}{8}}{\sin }^2({\theta }_m)\right)$$ 13

Equations and elucidate the fundamental distinction in the behaviors of heteronuclear and homonuclear dipolar terms corresponding to window modification. During the window delays, the cosine part of the heteronuclear terms in eq is ±1, whereas the sine part in eq becomes zero. Clearly, the heteronuclear terms remain fully active and are not scaled down during window delays, while the homonuclear terms are averaged to zero in the first-order average Hamiltonians. This selective recoupling mechanism is the core principle of the window modification in the SR4 sequence. As illustrated in Figure c, the scaling factors of heteronuclear term (κ₂₂₁₀) and homonuclear term (κ₂₂₂₁) exhibit a strictly monotonic variation trend over the entire range of f _w. Specifically, κ₂₂₁₀ increases monotonically with f _w, thereby enhancing the recoupling efficiency for the desired heteronuclear couplings; conversely, κ₂₂₂₁ decreases monotonically, leading to more effective suppression of the undesired homonuclear couplings. More details of these trends will be discussed in the following section.

Results and Discussion

Effects of Window Modification in wSR4

As mentioned above, the heteronuclear interaction recoupled by R4₁ is the ZQ terms, ${\mathcal{H̃}}_{2210}^{\mathrm{dipole}}$ and ${\mathcal{H̃}}_{2\mathrm{2̅}10}^{\mathrm{dipole}}$ , which remain invariant in the SR4 supercycling, as shown in Figure a. Given their identical scaling factors, the following analysis will focus on ${\mathcal{H̃}}_{2210}^{\mathrm{dipole}}$ alone. As f _w increases from 0 to 0.5, the scaling factor |κ₂₂₁₀| of the recoupled heteronuclear dipolar coupling increases from 0.50 to 0.60. This enhancement stems from the inserted delays where the Hamiltonian ${\mathcal{H̃}}_{2210}^{\mathrm{dipole}}$ has the highest amplitude, as illustrated in Figure c. At f _w = 0.5, the required rf amplitude of wSR4 is four times the MAS frequency, i.e., ω₁ = 4ω_r, which is moderate and readily achievable on the ¹H channel for most commercial NMR probes. Further increasing f _w from 0.5 to 1 (infinitely short π-pulse) yields only a marginal gain in scaling factor, from 0.60 to 0.64. This dependency of the scaling factor on f _w follows a functional form identical to the REDOR and PMRR recoupling methods, as described in prior studies. ,

2.

Simulated evolution and time-averaging of the R4₁ recoupled terms in SR4 and wSR4 sequences. Evolution of the real part (left) and time-averaging (right) of the heteronuclear dipolar term ${\mathcal{H̃}}_{2210}^{\mathrm{dipole}}$ of SR4 (a) and wSR4 (c); evolution of the real part (left) and time-averaging (right) of the homonuclear dipolar term ${\mathcal{H̃}}_{2221}^{\mathrm{dipole}}$ of SR4 (b) and wSR4 (d). In the wSR4 sequence, f _w = 0.5.

In contrast, research on the impact of window modification and supercycling on homonuclear dipolar terms in heteronuclear dipolar recoupling sequences is rather limited. ,− This is a critical consideration, as the heteronuclear dipolar recoupling sequence is applied on ¹H nuclei, and the strong ¹H–¹H dipolar coupling can severely interfere with the recoupling efficiency, particularly under slow MAS. In SR4 and wSR4, the recoupled homonuclear dipolar terms, ${\mathcal{H̃}}_{2221}^{\mathrm{dipole}}$ , ${\mathcal{H̃}}_{2\mathrm{2̅}2\mathrm{1̅}}^{\mathrm{dipole}}$ , ${\mathcal{H̃}}_{222\mathrm{1̅}}^{\mathrm{dipole}}$ , and ${\mathcal{H̃}}_{2\mathrm{2̅}21}^{\mathrm{dipole}}$ are SQ terms that can be canceled to the first order via inversion (phase supercycles). However, such cancellation is effective only upon the completion of supercycle, as illustrated in Figure b. Crucially, within the basic R4₁ element, unlike the recoupled heteronuclear dipolar terms, the homonuclear terms are reintroduced exclusively during the π-pulses. As a result, employing narrower π-pulses (i.e., a larger f _w) directly reduces the duration available for the evolution of homonuclear couplings, thus weakening their net recoupling effect, as shown in Figure d. This is reflected in the scaling factor of the homonuclear term ${\mathcal{H̃}}_{2221}^{\mathrm{dipole}}$ , which decreases substantially from 0.26 to 0.074 as the f _w increases from 0 to 0.5. Theoretically, this term can be fully suppressed as f _w approaches 100% (e.g., infinitely short pulse) (Figure c).

It should be noted that in both SR4 and wSR4 recoupling sequences, except for the completion time points of each supercycle at t = 2nτ_r, the homonuclear dipolar terms are nonzero, as clearly shown in Figure b,d. Since ${\mathcal{H̃}}_{2221}^{\mathrm{dipole}}$ and ${\mathcal{H̃}}_{2210}^{\mathrm{dipole}}$ terms do not commute, the recoupled homonuclear dipolar terms interfere with the heteronuclear dipolar terms, and this interference accumulates over time. Unfortunately, this accumulating interference cannot be fully compensated by the phase supercycles, and it will ultimately reduce the efficiency of heteronuclear dipolar recoupling. Although the window modifications in wSR4 cannot completely suppress the homonuclear dipolar interaction, they significantly alleviate its interference on heteronuclear dipolar couplings, e.g., 0.26 (f _w = 0) vs 0.074 (f _w = 0.5) vs 0.003 (f _w = 0.9). Notably, such a suppression continuously occurs throughout the entire recoupling period, as shown in Figure .

Numerical simulations have been further conducted to validate this improvement, as demonstrated by the comparative ¹H–¹³C dipolar dephasing dynamics during the first supercycle period by SR4 and wSR4 at a MAS rate of 10 kHz (Figure ), in which the evolution details are analyzed at the end of each π-pulse. Considering a three-spin system (¹H–¹H–¹³C), the evolution of the coupled ¹H–¹³C spin pair is inevitably influenced by the additional ¹H–¹H dipolar coupling, with rf irradiation of either SR4 or wSR4 sequences, leading to noticeable deviations from the ideal isolated ¹H–¹³C spin pair. As shown in Figure a, such deviation accumulates within both the first block (R4₁ )₀ and the second block (R4₁ )₁₈₀ of the supercycled SR4, although it is partially compensated in the second block due to the phase inversion. In comparison, the wSR4 sequence with f _w = 0.9 notably suppresses the ¹H–¹H dipolar interaction, reducing the scaling factor |κ₂₂₂₁| to just 0.003. Since this suppression is active through the entire recoupling time, the resulting deviation is significantly minimized, as presented in Figure b. This enhancement is further confirmed by the accuracy evaluation of the ¹H–¹³C dipolar measurement (Figure c), where larger f _w leads to better stability against homonuclear dipolar coupling. Additionally, wSR4 also shows enhanced robustness against other interferences, such as resonance offset and rf inhomogeneity, as confirmed by numerical simulations (Figure S1) and in agreement with prior studies.

3.

Simulated interferences from the ¹H–¹H dipolar coupling. The interfered ¹H–¹³C dipolar dephasing of (a) SR4 and (b) wSR4 (f _w = 0.9) during a single SR4/wSR4 recoupling block. (c) The accuracy of ¹H–¹³C distance measurements, as functions of different ¹H–¹H dipolar coupling and f _w. The simulations were performed for a 14.1 T magnetic field and a 10 kHz MAS speed.

Taken together, these theoretical and numerical results demonstrate the advantage of applying window modification in SR4. In short, a larger f _w is generally preferred under slow-to-moderate MAS conditions. Although increasing f _w beyond 0.5 yields only a marginal improvement of the scaling factor of heteronuclear dipolar terms, it significantly enhances the tolerance against homonuclear dipolar coupling and other experimental imperfections. This effect becomes especially important in systems with a strong ¹H–¹H coupling network, where the performance gains of wSR4 will be further demonstrated by NMR experiments below.

Applications of wSR4 in Distance Measurement

The window modification in wSR4 is specially designed for slow-to-moderate MAS frequencies, hence the following NMR experiments will be focused on typical MAS rates below 20 kHz. The first sets of experiments are performed to showcase the performance of wSR4 in measuring the internuclear distance. For this purpose, the bonded ¹³Cα–¹⁵N in a ¹³C, ¹⁵N uniformly labeled tripeptide, U-¹³C, ¹⁵N-fMLF, was chosen as the model system with the presence of the ¹³C–¹³C homonuclear dipolar network. These measurements were carried out using symmetry-based REDOR (S-REDOR), where the windowless SR4 or wSR4 sequences can be applied, as shown in Figure a. In the experiments, the sample is center-packed in a 3.2 mm rotor, and the carrier frequency of wSR4 is set on resonance with the ¹³Cα nuclei. This setup minimizes the effects of rf inhomogeneity and resonance offset, leaving ¹³C–¹³C dipolar coupling as the major interference to the ¹³C–¹⁵N distance measurements. The ¹³C–¹⁵N internuclear distance was derived by fitting the ¹³Cα dephasing curves (S₀ – S)/S₀, where S and S₀ represent the signal with and without ¹⁵N refocusing π pulse, respectively. In comparison to the fitting results using the isolated ¹³C–¹⁵N spin pair, the experimental dephasing curves in Figure b clearly show the accumulating deviation caused by ¹³C–¹³C dipolar coupling at longer recoupling times. On the contrary, the dephasing curve from wSR4 (f _w = 0.5) aligns closely with that of an isolated ¹³C–¹⁵N spin, exhibiting faster dephasing due to its 20% larger scaling factor for heteronuclear dipolar recoupling. The series of experiments conducted with varying f _w consistently demonstrates that increasing the window fraction in wSR4 can enhance the effective suppression of ¹³C–¹³C dipolar coupling, leading to a more accurate ¹³C–¹⁵N internuclear distance measurement. For wSR4 with f _w of 0.5 and above, the obtained ¹³Cα–¹⁵N DCCs are in good agreement with previously reported values, corresponding to a typical ¹³C–¹⁵N bond length of 1.50 ± 0.02 Å (Figure c).

4.

¹³C–¹⁵N distance measurements were performed using wSR4-REDOR. (a) Pulse sequence of wSR4-REDOR; (b) ¹³C­{¹⁵N} dipolar dephasing curves by SR4 (open circles) and wSR4 (f _w = 0.5, solid circles); and (c) ¹³C–¹⁵N DCCs measured by wSR4 with different f _w. The experiments were recorded at a magnetic field of 18.8 T and a MAS rate of 10 kHz.

Applications of wSR4 in Polarization Transfer

In addition to the internuclear distance measurement, the recoupled dipolar interactions can also mediate the spin polarization transfer. The dipolar-based polarization transfer between unlike spins is of central importance in solid-state NMR, providing through-space heteronuclear correlations for revealing the atomic spatial proximity. When the polarization is transferred from abundant spin I with a high gyromagnetic ratio (γ) (e.g., ¹H) to dilute low-γ spin S (e.g., ¹³C, ¹⁷O, ²⁷Al), the sensitivity of spin S can be enhanced (∝ γ _I /γ _S ). This mechanism also enables spectral editing by selectively enhancing correlated signals with the spatial proximity. These dipolar-based polarization transfer methods are of fundamental importance in investigating detailed local structures and active sites in materials. Two well-established approaches include dipolar-based refocused insensitive nuclei enhanced by polarization transfer (D-RINEPT) , and dipolar-based heteronuclear multiple-quantum coherence (D-HMQC). , Compared to the cross-polarization (CP) method routinely used in spin-1/2 systems, D-RINEPT and D-HMQC can offer effective polarization transfer not only between spin-1/2 nuclei but also between spin-1/2 and quadrupolar nuclei, , making them especially valuable in material research. ,− However, the transfer efficiency in D-RINEPT and D-HMQC experiments largely depends on the performance of the applied heteronuclear dipolar recoupling sequences, e.g., scaling factor, tolerance against other interactions, and experimental imperfections. Achieving high-efficiency ¹H–X dipolar recoupling is particularly challenging for samples with rich protons due to the strong ¹H–¹H dipolar couplings, especially under slow-to-moderate MAS conditions, which can significantly reduce the efficiency of heteronuclear polarization transfer. Therefore, employing a robust dipolar recoupling sequence like wSR4 is essential.

To evaluate the performance of wSR4 in heteronuclear polarization transfer, D-RINEPT experiments with the SR4 (f _w = 0) and wSR4 (f _w = 0.6) sequences were performed on protonated U-¹³C, ¹⁵N-fMLF. The pulse sequence is shown in Figure a. The ¹H → ¹³C transfer efficiencies were assessed by comparing the signal-to-noise (S/N) ratios of spectral projections along both the direct and the indirect dimensions of the resulting 2D ¹H–¹³C D-RINEPT spectra. At a MAS rate of 15 kHz, the ¹H → ¹³C transfer efficiency obtained using wSR4-D-RINEPT with f _w = 0.6 is 3.27 and 3.29 times higher than that achieved with SR4 in direct and indirect dimensions, respectively, as indicated in Figure b,c. This sensitivity gain is mainly attributed to the more effective suppression of the interference from strong ¹H–¹H dipolar coupling by wSR4.

5.

Polarization transfer and sensitivity enhancement using wSR4-D-RINEPT. (a) Pulse sequence of wSR4-D-RINEPT. 2D ¹H–¹³C HETCOR spectra using (b) SR4-D-RINEPT (f _w = 0) and (c) wSR4-D-RINEPT (f _w = 0.6) at 15 kHz MAS. The signal-to-noise ratios are presented next to each projection spectrum. Experiments are operated in an 18.8 T magnetic field.

The advantage of wSR4 becomes particularly crucial under slow MAS conditions (ν _r ≤ 10 kHz), commonly encountered in the current dynamic nuclear polarization (DNP) NMR and in situ NMR, where large-size rotors (e.g., 4.0 or 7.0 mm) are usually used. Highly efficient recoupling techniques are pivotal for real-time structural monitoring and sensitivity enhancement. Our group has developed 4 mm zirconium rotors capable of operating under high temperature (up to 573 K) and high pressure (up to 6 MPa) for in situ MAS NMR, albeit with a maximum MAS speed of 10 kHz. In proton-rich samples, such slow MAS conditions often render most existing recoupling methods ineffective for achieving efficient ¹H–X dipolar recoupling with the presence of a strong ¹H–¹H dipolar network.

One compelling example is the in situ investigation of SAPO zeolite crystallization, modulated by Et₄NOH as a structure-directing agent at elevated temperatures (394–473 K). In this system, the template molecules interact with the developing zeolite framework, and such interactions can be effectively probed by using 2D ²⁷Al–¹H D-HMQC NMR experiments. While proton-detected D-HMQC is generally preferred due to the high sensitivity of ¹H detection, the coexistence of strong ¹H–¹H dipolar coupling and slow relaxation due to molecular motion introduces severe interference with heteronuclear dipolar recoupling, resulting in unavoidable t ₁-noise and reduced spectral quality in proton-detected experiments. The solution is to employ a ²⁷Al-detected D-HMQC sequence, as shown in Figure a, in which wSR4 with a large f _w is applied on ¹H to achieve optimal dipolar recoupling efficiency, while WURST irradiation is applied on ²⁷Al to further enhance sensitivity by saturating the satellite transitions.

6.

2D ²⁷Al–¹H wSR4-D-HMQC experiments in SAPO zeolite with an Et₄NOH template. (a) The wSR4-D-HMQC pulse sequence and 2D ²⁷Al–¹H wSR4-D-HMQC spectra with (b) f _w = 0.8 and (c) f _w = 0, using 5120 scan number. (d) 1D ²⁷Al­{¹H} wSR4-D-HMQC spectra with and without window modification. (e) 2D ²⁷Al–¹H wSR4-D-HMQC spectrum using f _w = 0.8 and 512 scans. These spectra are recorded at 9.4 T and a MAS rate of 6 kHz.

The experimental results show that window modification in wSR4-D-HMQC plays an indispensable role in the observation of 2D ²⁷Al–¹H correlation signals. At a MAS rate of 6 kHz, the wSR4-D-HMQC with f _w = 0.8 yields a well-resolved 2D ²⁷Al–¹H correlation spectrum, where the cross peaks between four- and six-coordinated ²⁷Al sites (denoted as ²⁷Al­(IV) and ²⁷Al­(VI), respectively) and ¹H from −CH₃, −CH₂, and –AlOH groups can be clearly identified (Figure b). In contrast, the 2D ²⁷Al–¹H spectrum recorded by windowless SR4-D-HMQC shows mainly cross peaks involving only ²⁷Al­(IV), as presented in Figure c. Notably, upon increasing f _w from 0 to 0.8, the S/N of the spectrum projected at the ²⁷Al­(IV) dimension is improved by 7.1 times, rising from 4.3 to 30.4. This substantial enhancement highlights the effectiveness of wSR4 in facilitating the rapid, highly efficient acquisition of in situ 2D ²⁷Al–¹H HMQC spectra, which are otherwise challenging under slow MAS conditions.

To achieve fast 2D acquisition, the scan number must be reduced. For SR4-D-HMQC, decreasing the scan number from 5120 to 512 nearly eliminates the ²⁷Al signals, as presented in Figure d, making the 2D ²⁷Al–¹H observation impractical. In contrast, wSR4-D-HMQC with f _w = 0.8 retains clear signals of ²⁷Al­(IV)/²⁷Al­(VI) (Figure d), even with reduced scans. In an experiment with 512 scans, the acquisition of a 2D ²⁷Al–¹H correlation spectrum requires only 15 min, yielding decent spectral quality with S/N of 12.2, as shown in Figure e. These results underscore the potential of wSR4-D-HMQC for in situ 2D NMR studies of SAPO zeolite crystallization. While a detailed discussion of the crystallization mechanism is beyond the scope of this work, these findings clearly demonstrate that employing the wSR4 dipolar recoupling sequence is crucial for enabling efficient polarization transfer and achieving rapid, time-effective 2D heteronuclear correlation spectroscopy.

Conclusions

In this work, we have demonstrated that the introduction of window durations into the SR4 sequence markedly enhances the performance of heteronuclear dipolar recoupling, particularly under slow-to-moderate MAS conditions. The resulting windowed SR4 (wSR4) sequence has been systematically evaluated both theoretically and numerically. As the window fraction (f _w) increases, the efficiency of heteronuclear dipolar recoupling is enhanced, with the scaling factor being improved from 0.5 up to over 0.6, while the interferences from homonuclear dipolar coupling is drastically suppressed. The wSR4 sequence also exhibits enhanced robustness against rf inhomogeneity and resonance offset, making it a versatile and reliable recoupling method. Furthermore, the performance of wSR4 has been experimentally validated in heteronuclear distance measurements and polarization transfers, underscoring the critical role of window modification in enhancing heteronuclear dipolar recoupling efficiency and improving tolerance against experimental imperfections and undesired interactions. This work also offers a general and powerful strategy for designing highly efficient symmetry-based recoupling sequences, promising to facilitate accurate structural determination and through-space correlation spectroscopy in a wide range of materials.

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/prechem.5c00364.

• Details on materials, methods, simulations, and experiments (PDF)

• SIMPSON and TOPSPIN codes (ZIP)

The authors declare no competing financial interest.