# Removing t1-noise in DNP-enhanced NMR at natural isotopic abundance using two-spin order filter

Quentin Reynard-Feytis, Subhradip Paul, Sabine Hediger, Gaël de Paëpe

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Quentin Reynard-Feytis, Subhradip Paul, Sabine Hediger, Gaël de Paëpe. Removing t1-noise in DNP-enhanced NMR at natural isotopic abundance using two-spin order filter. 2025. hal-05344475

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# Removing $t_1$-noise in DNP-enhanced NMR at natural isotopic abundance using two-spin order filter

Quentin Reynard-Feytis,¹ Subhradip Paul,¹ Sabine Hediger,¹ and Gaël De Paëpe¹, *

¹Univ. Grenoble. Alpes, CEA, CNRS, IRIG, MEM, 38000 Grenoble, France

MAS-DNP has markedly improved the inherently low sensitivity of NMR, enabling advanced applications such as multidimensional correlation experiments (e.g., ¹³C-¹³C, ¹³C-¹⁵N) at natural isotopic abundance (NA). However, these experiments are frequently hindered by $t_1$-noise, an artifact resulting from experimental instabilities during the indirect evolution period. Due to its multiplicative nature, $t_1$-noise presents a particular challenge for NA samples, as cross-peaks from correlated spins may be obscured by noise contributions from uncorrelated nuclei, leading to spectral ambiguities and compromised data interpretation. Here, we introduce a novel strategy to suppress $t_1$-noise in ¹³C-¹³C DQ-SQ correlation spectroscopy acquired on samples at NA. The method relies on converting DQ coherences into longitudinal two-spin order (zz-terms), allowing the selective elimination of transverse magnetization from uncoupled ¹³C nuclei via a zz-filter. We demonstrate the effectiveness of this approach in both J- and dipolar-based correlation experiments, achieving dramatic improvements in spectral clarity on both a commercial MAS-DNP system at 100 K and also at 30 K using a custom-built He-spinning MAS-DNP instrument. Notably, we show that the suppression of $t_1$-noise reveals previously hidden cross-peaks corresponding to long-range correlations, with improvement in signal-to-noise ratio in the indirect dimension of up to a factor ~6, enabling the first ¹³C-¹³C DQ-SQ spectrum at 30 K at NA.

## Introduction

Solid-State Nuclear Magnetic Resonance under Magic Angle Spinning (MAS ssNMR) [1, 2] has emerged as a versatile and powerful spectroscopy to study structure and dynamics at the atomic scale of a large variety of systems ranging from biomolecules to materials [3–6]. This was enabled by many methodological and instrumental developments that include access to higher magnetic fields, faster MAS probes, and also by the advent of high-power microwave sources (gyrotrons) [7, 8] and the development of high-frequency Dynamic Nuclear Polarization under MAS (MAS-DNP) [3, 4, 7–18]. These advancements have markedly broadened the scope of NMR, enabling increasingly challenging applications. Notably, it facilitated 2D homonuclear and heteronuclear correlation experiments between low-γ/low natural isotopic abundance nuclei [19, 20]. As demonstrated in 2012, MAS-DNP applied to systems at natural abundance (NA) enables the detection of one bond ¹³C-¹³C correlations [21, 22], as well as long-range ¹³C-¹³C polarization transfers within hours [21, 23]. This strategy has proven key in various contexts, including the study of organic microcrystals [21, 22, 24], self-assembled peptides and proteins [20, 23, 25], and for the identification of pharmaceutical polymorphs [26]. In addition, this approach significantly advances the feasibility of biomolecular NMR at natural abundance. Remarkable applications include investigations of amyloid fibrils relevant to Huntington’s disease [27], bone-tissue materials, including GAG-collagen interactions in cartilage [28, 29], and ligno-cellulosic materials [30–35]. These developments are particularly significant as they overcome long-standing limitations that had severely constrained previous ssNMR studies [19]. Beyond the primary advantage of eliminating the need of isotopic labeling, which is often costly and not applicable to all systems, working at natural isotopic abundance offers additional inherent benefits. These include simplified spin dynamics, and the ability to probe long-range magnetization transfer [19–21, 23, 26]. In 2017, Märker et al. demonstrated the feasibility of achieving strong agreement

between experimental and simulated dipolar build-up curves, arising from the superposition of various distances up to 7 Å in NA organic solids [36]. The steady increase in MAS-DNP sensitivity over the past decade, driven by advances in polarizing agents [24, 37–42] and innovations in hardware that enable experiments at ultra-low temperatures with cryogenic helium sample spinning [12, 43–46], has significantly enhanced our ability to explore natural-abundance systems with up to two orders of magnitude of sensitivity improvement. However, this increased sensitivity also places greater demands on hardware stability. When experimental reproducibility is insufficient, multidimensional NMR experiments can be affected by a phenomenon known as $t_1$-noise, which results from fluctuations in the detected signal due to experimental instabilities. In multidimensional NMR experiments, these fluctuations introduce an additional incoherent modulation of the signal along the indirect evolution time ($t_1$). Due to its multiplicative nature, $t_1$-noise is proportional to the detected signal intensity [47]. If $t_1$-noise exceeds thermal noise, it leads to signal-proportional ridges along the $f_1$ dimension in the Fourier-transform spectrum, which can significantly degrade data quality. This issue becomes particularly problematic when cross-peaks of interest are of similar or lower intensity than the $t_1$-noise, as often encountered in DNP-enhanced correlation experiments involving low abundance nuclei (e.g. ¹³C NA 1.1 %). In such cases, $t_1$-noise can obscure meaningful spectral features, posing a significant obstacle to the broader application and further development of multidimensional NA spectroscopy. Herein we present a novel approach to suppress $t_1$-noise in the context of ¹³C-¹³C DQ-SQ correlation spectroscopy at NA. It consists in converting double-quantum (DQ) coherences into longitudinal two-spin order (zz-terms) to selectively eliminate, through a “zz-filter”, unwanted magnetization of abundant, uncoupled ¹³C nuclei, which constitute the main $t_1$-noise contribution. This methodology is explained theoretically and demonstrated for both isotropic J- (through-bond) and anisotropic dipolar- (through-space) based polarization transfers. We demonstrate that, despite a twofold reduction in signal intensity, the zz-filter effectively suppresses $t_1$-noise to the level of thermal noise. Using a commercial MAS-DNP setup at 100 K, we first show that spectral clarity is significantly enhanced, enabling straightforward assignment

<footnote>* gael.depaepe@cea.fr</footnote>
of numerous previously obscured cross-peaks corresponding to long-range correlations. We then apply the *zz*-filter at 30 K using a custom-built He-spinning MAS-DNP system [44], where ultra-high sensitivity, about one order of magnitude larger than at 100 K due to both larger signal enhancement and reduced thermal noise, leads in more pronounced $t_1$-noise artefacts. With the approach introduced here, we achieve a remarkable 6× improvement in signal-to-noise along the $f_1$-dimension, enabling the acquisition of 30 K $^{13}$C-$^{13}$C DQ-SQ spectrum of small molecules at NA. These results pave the way for more challenging applications at NA with MAS-DNP, including precise measurements of build-up curves for the extraction of long-range interatomic distances in organic and biomolecular solids. Finally, we extend the *zz*-filter application to the heteronuclear context using the TEDOR experiment [48]. Notably, we show that the *zz*-filter, originally implemented by Jaroniec and coworkers to dephase multiple quantum coherences (MQCs) in $^{13}$C,$^{15}$N labelled system, is equally essential in NA experiments for the suppression of $t_1$-noise artefacts.

## Results and Discussion

### $t_1$-noise and multidimensional $^{13}$C-$^{13}$C correlation experiments at natural isotopic abundance

$t_1$-noise artefacts are typically encountered in multidimensional correlation experiments involving nuclei with weak natural isotopic abundance. In such cases, cross-peaks coexist with unwanted signals from uncoupled spins that can be orders of magnitude more intense. Although these stronger signals are typically canceled out using phase cycling, it is well known that minor experimental fluctuations can induce $t_1$-noise of comparable intensity to the cross-peaks, thereby contaminating the 2D spectrum [49]. In $^{13}$C-$^{13}$C correlation experiments at NA, DQ filtration via phase cycling is typically used to remove the large contribution from uncoupled nuclei, in order to detect weaker contributions from coupled pairs [50, 51] (Fig. 1A and Fig. 1C). Even if the latter can largely be removed, its fluctuation from one scan to another can lead to significant $t_1$-noise artefacts under DNP conditions. This is especially true when using the latest generation of polarizing agents [24, 39, 42, 52] and when experiments are conducted at ultra-low temperatures (< 100 K) since it increases the signal while decreasing the thermal noise [44]. Despite excellent experimental stability, the sensitivity can be so high with MAS-DNP that $t_1$-noise can be present, degrading the spectral quality and preventing unambiguous assignment of weak cross-peaks (see Fig. 2A and Fig. 5A for experiments recorded at 100 K and 30 K respectively). While improving instrumental stability is the most direct way to mitigate $t_1$-noise, identifying the relative contribution of the various potential sources of instabilities (probe detuning, MAS fluctuations, gyrotron instabilities, etc.) and refining the instrumentation accordingly is a complex and long-term undertaking, which cannot always be fully achieved. For this reason, additional strategies have been proposed, which generally fall into two main categories: post-processing methods and improved data-acquisition strategies. Post-processing methods typically aim to separate the signal from $t_1$-noise by using the specific characteristics of either the signal or the noise

itself, such as the general assumption of $t_1$-noise homogeneity across the $f_2$ dimension [53] (i.e., all peaks experience similar fluctuations). Consequently, a range of post-processing methods has been developed since the initial observation of $t_1$-noise artifacts [49, 54–62]. While these approaches can be highly beneficial, their applicability can be limited in some contexts by significant drawbacks, such as the unintended generation of artificial cross-peaks or the suppression of true ones. On the other hand, experimental approaches tend to provide clearer and more reliable data by minimizing $t_1$-noise at its source. When $t_1$-noise results from slow-fluctuating instabilities (such as temperature variations), randomizing the acquisition order of the indirect dimension [63] or simply reducing the number of scans for each $t_1$ increment [64] result in its reduction. However, such techniques are ineffective on $t_1$-noise originating from scan-to-scan instabilities which disrupt the reproducibility required for effective signal cancellation via phase-cycling. This situation is typically encountered in solid-state NMR, where MAS fluctuations are commonly presumed to be the primary source of $t_1$-noise. Several methods have recently been proposed. Some of these aim at increasing the sequence robustness against MAS fluctuations, e.g. by the design of “γ-free” sequences [65] or by refocusing the $^{1}$H CSA in HETCOR experiments [66, 67]. Other approaches focus on minimizing the coherences that generate $t_1$-noise, by using selective saturation pulses to suppress specific intense signals [68] or removing isolated nuclear spin magnetization in HETCOR experiments involving low-isotopic abundance nuclei [66, 69]. More recently, Perras and coworkers [70] proposed a simple approach to limit $t_1$-noise by shortening the experimental recovery delay. This easy to implement solution can in principle be applied to any experiment affected by $t_1$-noise. However, it comes with a significant loss of sensitivity, particularly when the $t_1$-noise is much larger than the thermal noise. Additionally, the described approach does not account for the recycle-delay limitations of solid-state NMR probes in the presence of high-power decoupling. In liquid-state NMR, pulsed field gradients (PFGs) have shown tremendous performances for $t_1$-noise suppression [71, 72], although their use often results in lower sensitivity [72]. While the implementation of gradient coils has been widely adopted in the context of high-resolution magic angle spinning (HRMAS) experiments [73, 74], it remains underdeveloped in the context of solid-state NMR experiments.

## Principles and Theory of the *zz*-filter

Herein we consider the introduction of the *zz*-filter pulse sequence element $(\pi/2)_{\theta}-\Delta_{zz}-(\pi/2)_{\theta}$ at the end of the DQ excitation block (Fig. 1A), with $\theta$ the phase of the two $(\pi/2)$-pulses and $\Delta_{zz}$ the delay between them. Isolated $^{13}$C nuclear spins, which account for most of the detected signal in 1D cross polarization (CPMAS) experiments, cannot build any DQ coherences (DQCs) during this time. Considering the ideal case of RF field strength perfectly matching the recoupling condition, and the absence of other interactions and RF inhomogeneity, the $^{13}$C $I_z$ magnetization of isolated spins stays along the z-axis during the DQ excitation block. The first $(\pi/2)_{\theta}$ pulse of the *zz*-filter brings it in the transverse plane as follows:

$$I_z \xrightarrow{(\pi/2)_{\theta}} I_{\theta-\pi/2} \qquad (1)$$
<figure><img src="image_3.png" /><figcaption>Fig. 1. (A) Schematic of a generic DQ/SQ pulse sequence with the zz-filter applied after the DQ-excitation block. The sequence starts with ¹³C Iz magnetization, which can be prepared by a CP transfer followed by a flip-back 90 pulse (not shown on the sequence). The first (π/2)θ pulse of the zz-filter converts half of the DQC into a zz-term and uncoupled spin magnetization, Iz, into SQC. During Δzz, the SQC is dephased while the zz-term is preserved. The second (π/2)θ pulse then converts the zz-term into a mix of DQC and ZQC. The coherence transfer pathway (CTP) of the sequence is given below it. The thick blue lines indicate the CTP of uncoupled spins, while the thin blue-red shaded lines are for coupled spin pairs. (B) Polar plot of the DQ-filtered normalized signal intensity as a function of the pulse phase θ relative to the phase φ of the excited DQC. Blue dots are experimental points acquired with the J-INADEQUATE pulse sequences (see Fig. S3A and Fig. S4) on ampicillin microcrystal powder (see SI), with a zz-filter of 25τr ≈ 3 ms. Experimental error intervals are represented by the shaded regions. The theoretical efficiency (Eq. (11)) is indicated by the dotted blue line. (C) Detected 1D signal in a J-based DQ/SQ experiment as a function of Δzz, with t₁ = 0: (i) single-scan signal showing the strong reduction of SQCs with Δzz as a result of signal dephasing, and (ii) DQ phase-cycled signal over 64 scans showing conserved DQ-filtered signal intensity during Δzz.</figcaption></figure>

The subsequent delay period Δzz leads to a strong reduction of this isolated spin coherence through its dephasing by chemical shift interactions and heteronuclear couplings to protons (if present). Let us now consider the impact of the zz-filter on DQC generated for coupled two-spin system. In the most general case, the DQC created during the DQ excitation block can be defined in the DQ subspace as:

$$DQ_{\phi} = R_z(\phi/2)DQ_x R_z(-\phi/2) \quad (2)$$

where $R_z(\alpha) = e^{-i2\alpha DQ_z}$ is the rotation operator about the z-axis in the DQ subspace, $\phi$ is the phase of DQC, and the DQ subspace is defined by the following operators:

$$DQ_x = \frac{1}{2}(2I_{jx}I_{kx}-2I_{jy}I_{ky}) = \frac{1}{2}(2I_j^+I_k^++2I_j^-I_k^-) \quad (3)$$

$$DQ_y = \frac{1}{2}(2I_{jx}I_{ky}+2I_{jy}I_{kx}) = \frac{1}{2}(2I_j^+I_k^+-2I_j^-I_k^-) \quad (4)$$

$$DQ_z = \frac{1}{2}(I_{jz}+I_{kz}) \quad (5)$$

If we first consider the case $\phi = 0$ for simplicity, the $DQ_x$ coherence evolves under the first $(\pi/2)\theta$ pulse of the zz-filter as follows (full calculation detailed in the SI Sec. S7):

$$DQ_x \xrightarrow{(\pi/2)\theta} \frac{1}{2}c(2\theta)[ZQ_x+DQ_{2\theta}-2I_{jz}I_{kz}] -s(2\theta)(I_{j\theta}I_{kz}+I_{jz}I_{k\theta}) \quad (6)$$

with the notation $s\alpha^n \equiv \sin(\alpha)^n$ and $c\alpha^n \equiv \cos(\alpha)^n$, and the operators $I_{j\theta} = c\theta I_{jx} + s\theta I_{jy}$ and $ZQ_x = \frac{1}{2}(2I_{jx}I_{kx}+2I_{jy}I_{ky})$. The subsequent delay Δzz will lead to the dephasing of terms that do not commute with the chemical shift and heteronuclear dipolar interactions. After dephasing, we expect only the zz-term to be preserved:

$$\Delta_{zz} \xrightarrow{\Delta_{zz}} -\frac{1}{2} \cos(2\theta) 2I_{jz} I_{kz} \quad (7)$$

It is now relevant to generalize the result to any DQC with an arbitrary phase $\phi$. This can be done using Eq. (2) which, after a
<figure><img src="image_4.png" /><figcaption>Fig. 2. (A) Carbonyl region of refocused INADEQUATE DNP-enhanced spectra on natural abundance Ampicillin microcrystals impregnated with cAsymPol-POK, without (on the left) and with (one the right) a zz-filter of 6.25 ms (standard z-filter set to 3 ms). Contour levels are normalized to the maximum intensity in each spectrum. (B) f₁-traces from (A) at 175.2 and 170.1 ppm (red and orange doted lines in (A), left and right panels in (B), respectively) without (upper panels) and with (lower panels) zz-filter. Intensities are normalized according to the maximum intensity in the corresponding trace without zz-filter. The grey region corresponds to noise within three times the standard deviation of the thermal noise 3σth. The t₁-noise standard deviation σt₁ was calculated from regions without any peaks of the f₁-traces (from 0 to 120 ppm and 320 to 400 ppm, see SI Sec. S4 for more details). Sidebands are indicated by orange and red stars. The orange triangle indicates a real signal corresponding to the foot of a more intense peak.</figcaption></figure>

variable change $θ = θ - φ/2$, gives the following result:

$$DQ_{\phi} \xrightarrow{(\pi/2)\theta} \Delta_{zz} \xrightarrow{-\frac{1}{2}} -\frac{1}{2} \cos(2\theta - \phi) 2I_{jz}I_{kz} \quad (8)$$

The second $(\pi/2)\theta$ pulse then converts this zz-term into a sum of DQ and zero-quantum (ZQ) coherences:

$$2I_{jz}I_{kz} \xrightarrow{(\pi/2)\theta} 2I_{j}(\theta-\pi/2)I_{k}(\theta-\pi/2) = ZQ_{x}-DQ_{2\theta} \quad (9)$$

Therefore, the effect of the zz-filter can be summarized as follows:

$$DQ_{\phi} \xrightarrow{\text{zz-filter}} \frac{1}{2} \cos(2\theta - \phi)(DQ_{2\theta} - ZQ_{x}) \quad (10)$$

Projection of $DQ_{2\theta}$ on the initial state before the zz-filter (i.e. $DQ_{\phi}$) gives the global efficiency of the zz-filter, $\eta_{zz}$:

$$\eta_{zz} = \frac{1}{2} \cos(2\theta - \phi)^2 \quad (11)$$

The zz-filter has, therefore, a maximum efficiency of 1/2, obtained when the phase of the zz-filter pulses satisfies the condition:

$$\theta \equiv \phi/2 \mod \pi/2 \quad (12)$$

with $\phi$ the phase of the generated DQC. The corresponding coherence transfer pathway (CTP) is represented on Fig. 1A below the pulse sequence. Overall, in the ideal case where all generated DQ coherences share the same phase $\phi$, the zz-filter is

expected to significantly suppress signals from uncoupled spins, while scaling the intensity of DQ-filtered signal by a factor of 2. This condition is met with J-based polarization transfer (e.g., with refocused-INADEQUATE), which will serve as a proof-of-concept to assess the efficiency of the zz-filter. Later, we will address the case of dipolar-based transfer, where the anisotropic nature of the dipolar coupling introduces additional complexity. It is to note that we chose to use the terminology “zz-filter” to stress that that the method relies on a two-spin order filtration, even though it is clear that the z-filter terminology introduced by Sørensen and coworkers in 1984 [75] also preserves longitudinal multiple spin order terms ($2I_{jz}I_{kz}$, $4I_{jz}I_{kz}I_{iz}$ ...). The terminology ’zz-filter’ has also been used by Pelton and Wemmer for a case specifically aiming at filtering zz-terms [76]. In modern NMR applications, zz-filters, which refer to double-isotope filters, have been used in liquid-state NMR on natural abundance molecules, in order to specifically select ¹H signal from ¹H-¹³C spin pairs [77–79].

### zz-filter in the case of isotropic J-based correlation experiments

INADEQUATE is a major NMR experiment that enables probing through-bond homonuclear correlations [51, 80–82]. It is based on the use of the isotropic J-coupling to transfer magnetization between nuclei connected through one or more chemical bonds. Due to the isotropic nature of the J-coupling, the phase of the DQC is the same regardless of the crystal-lite orientation. Following the phases of the pulse sequence
used by Cadars and coworkers [82] (see Fig. S3A), DQC s are generated along DQy (φ = π/2). According to Eq. (11), the maximum efficiency of the zz-filter is then expected for pulse phases θ = π/4. This prediction was experimentally verified by measuring the DQ-filtered signal intensity obtained using the zz-filtered refocused-INADEQUATE sequence, as a func- tion of the zz-filter pulse phase θ . The data are plotted as a function of 2θ − φ on the polar plot in Fig. 1B (blue dots), to- gether with the analytical expression from Eq. (11) (blue dashed lines), showing excellent agreement within the experimental er- ror bounds (shaded region). Further experimental details and the complete pseudo-2D spectrum are provided in the Support- ing Information (Sec. S3). The behavior of uncoupled spins magnetization and of the generated DQC s during the zz-filter can be studied by following the signal evolution as a function of the zz-filter length, and is illustrated on Fig. 1C. Signal from uncoupled spins is strongly dominating when the experiment is acquired with a single-scan (Fig. 1C.i), as CTP selection via phase-cycling is then avoided. This strong initial signal, 300- fold more intense than the DQ-filtered signal (with zz-filter) usually detected with phase-cycling, is dephased during the zz-filter and its intensity drastically decreases after a few ms (Fig. 1C.i). On the contrary, the DQ-filtered signal intensity obtained with the complete phase-cycling, which aims at re- moving the strong signal from isolated spins, remains stable throughout the zz-filter (Fig. 1C.ii) on the same time scale. It is worth noting that the isolated spin signal of the carbonyls has not fully vanished after 6 ms of zz-filter duration, unlike that of the other carbons, as a result of a weaker dipolar coupling to $^{1}$H for these quaternary carbons. Therefore, we investigate the possibility of actively reintroducing $^{1}$H-$^{13}$C dipolar interactions during the zz-filter using a DARR recoupling field [83] on the $^{1}$H channel (spin-lock at ω$_{1}$$_{H}$ = nω$_{r}$ with n = 1 or 2). As can be seen in the Supporting Information (Sec. S2), it enables a significantly faster decay of the unwanted SQCs, but does not improve t$_{1}$ -noise suppression in this specific case. However, it might be very useful, or even necessary, when using the zz- filter under different conditions (sample with a lower $^{1}$H content, higher MAS frequencies, etc). The efficiency of the zz-filter to reduce t$_{1}$ -noise in DQ/SQ refocused INADEQUATE experi- ments is illustrated in Fig. 2, using a 6.25 ms zz-filter duration. Fig. 2A compares spectra acquired without and with zz-filter, with contour levels normalized to the maximum intensity in each dataset. The displayed spectra focus on the carbonyl region (see Fig. S3B for full spectra). Very clearly, the zz-filter leads to a strong reduction of the t$_{1}$ -noise, resulting in an increased signal-to-noise ratio (SNR) along signal-containing f$_{1}$ -traces. To evaluate the improvement in SNR, f$_{1}$ -traces taken at 175.2 ppm (C7) and 170.1 ppm (C15) are compared in Fig. 2B. The grey-colored parts of the spectra correspond to intensities which are below 3 times the thermal noise standard deviation σ$_{th}$ (i.e. corresponding to the 99.7% confidence interval of the thermal noise). Further details are provided in the Supporting Informa- tion (Sec. S4). As shown in the upper panels of Fig. 2B, for the INADEQUATE experiment without the zz-filter, the noise in the extracted f$_{1}$ -traces significantly exceeds the 3 σ$_{th}$ threshold due to the presence of t$_{1}$ -noise. This elevated noise level can obscure genuine peaks and potentially introduce artifacts. In contrast, for the INADEQUATE with zz-filter (lower panels in Fig. 2B), most of the noise falls below the 3 σ$_{th}$ threshold, indi- cating that the noise level is now close to the thermal noise limit.

This drastic reduction in t$_{1}$ -noise enables the clear identification of several real signals in both the 2D spectra (Fig. 2A) and f$_{1}$ - traces (Fig. 2B). These signals, marked by stars, were previously hidden in the t$_{1}$ -noise . The standard deviation of the t$_{1}$ -noise, σ$_{t1}$ , was estimated by measuring the standard deviation in a signal-free region of the most contaminated f$_{1}$ -trace (C7), as shown in the Fig. S6A, and comparing it to the thermal noise standard deviation, σ$_{th}$ . The resulting σ$_{t1}$/σ$_{th}$ ratio decreased from 7.1 to 1.4 upon application of the zz-filter, effectively re- ducing the t$_{1}$ -noise level to near the thermal noise limit. This confirms the drastic reduction in t$_{1}$ -noise, while the cross-peak intensities decreased to ≈ 42% of the original signal intensity, which is relatively close to the theoretical value of 50 %.

Extension of the zz-filter to the case of dipolar-based correlation experiments

Dipolar-based Double-Quantum spectroscopy is particularly interesting to probe spatial proximities and estimate inter- nuclear distances thanks to the distance dependence of the dipo- lar interaction [84]. Such experiments are typically based on dipolar recoupling sequences that reintroduce the anisotropic dipolar coupling, which is else averaged out by magic angle spinning. In the case of the widely used symmetry-based se- quences introduced by Levitt and coworkers [85–87], the first- order average Hamiltonian [88] can be expressed as:

$$
\begin{equation}
\begin{split}
\tilde{H}^{(1)}(\Omega_{\mathrm{MR}}, t^0) ={}& |\omega_{\mathrm{MR}}(\beta_{\mathrm{MR}})| \\
& \exp\left(-i\phi_{\mathrm{DQ}}(\gamma_{\mathrm{MR}}, t^0)DQ_z\right)DQ_x \exp\left(-i\phi_{\mathrm{DQ}}(\gamma_{\mathrm{MR}}, t^0)DQ_z\right)
\end{split}
\tag{13}
\end{equation}
$$

with Ω$_{MR}$ = ( α$_{MR}$ , β$_{MR}$ , γ$_{MR}$ ) the set of Euler angles defining the rotation of the molecular frame into the rotor frame and t 0 a common time origin for the entire pulse sequence. For these so- called γ -encoded sequences, the phase of the DQ Hamiltonian φ$_{DQ}$ is directly proportional to the Euler angle γ$_{MR}$ associated with each crystallite’s orientation [88]. As a result, the phases of the generated DQC s are uniformly distributed over the DQ subspace. The overall efficiency of the zz-filter, denoted 〈 η$_{zz}$ 〉 , is thus obtained by integrating the filter efficiency η$_{zz}$ (Eq. (11)) over all DQC s’ phases φ :

$$
\langle \eta_{zz} \rangle = \frac{1}{2\pi} \int_{0}^{2\pi} \frac{\cos(2\theta - \phi)^2}{2} d\phi = 0.25 \quad (14)
$$

Consequently, the zz-filter efficiency is reduced to 〈 η$_{zz}$ 〉 = 0.25 for γ -encoded sequences, independently of the zz-filter pulses phase θ . On the other hand, the phase of the first-order av- erage Hamiltonian is independent on the γ -angle in non- γ - encoded sequences, such as Baba-xy16 [89], S$_{0}$S ′ 0 supercy- cled symmetry-based sequences [90], or PR5 [91]. In this case, the zz-filter’s efficiency follows the theoretical framework previously introduced and illustrated with the INADEQUATE example. Notably, this applies to the supercycled dipolar re- coupling sequences such as SR26, for which the γ -encoding property has been lost in favor of increased robustness towards chemical shift anisotropies (CSA) and other higher-order AHT contributions [90, 92]. The zz-filter efficiency difference for γ - and non- γ -encoded sequences is verified experimentally and
<figure><img src="image_5.png" /><figcaption>Fig. 3. Impact of the z- and zz-filters on dipolar-based 2D DQ/SQ correlation experiments. 2D DNP-enhanced DQ/SQ SR26 spectra of NA ampicillin (A) without any zz-filter and only a short z-filter of 100 µs, (B) with a zz-filter of 5 ms in addition to the short z-filter (100 µs), (C) with a longer z-filter of 3 ms and without zz-filter, and (D) with both the long z-filter (3 ms) and the zz-filter of 5 ms. Contour levels are displayed using absolute intensity values and are not normalized to the maximum intensity in each spectrum, in order to accurately reflect the absolute t₁-noise levels. Red lines connect straightforward correlation peaks. Red stars indicate correlations between overlapping or auto-correlation peaks.</figcaption></figure>

computationally (using SIMPSON [93, 94] simulation) in the Supplementary Information (Sec. S5). In Fig. 3, we compare the respective impact of the z- (just before direct acquisition) and zz-filter (after the SR26 DQ excitation block) in mitigating t₁-noise in DNP-enhanced DQ/SQ SR26 experiments on organic microcrystals at NA. Comparing panels A and B, as well as C with D, it is very clear that the zz-filter leads to a strong attenuation of the t₁-noise. Interestingly, however, the t₁-noise is not completely removed with the zz-filter alone (see Fig. 3B). It needs to be combined with a z-filter of sufficient length (3 ms) before detection. This is a noteworthy observation, as it clearly demonstrates that t₁-noise in this experiment arises not only from fluctuations of the longitudinal $I_z$ components of uncoupled nuclei, but also from transverse terms. These transverse coherences are generated due to the non-ideal behavior of the SR26 excitation block, influenced by the ¹³C chemical shift anisotropy (CSA), residual proton couplings, and RF inhomogeneities. As a result, transverse coherences can be generated from the $I_z$ magnetization of isolated ¹³C spins after the excitation block. Even if this signal can be removed by phase cycling and adequate selection of CTP (e.g. DQ filter), its fluctuations can still lead to t₁-noise. While these are not suppressed by the zz-filter, they can be attenuated by a sufficiently long z-filter that

allows for their dephasing. The combination of the z- and zz-filters, dubbed z³-filter, efficiently suppress the t₁-noise present in this experiment. This is illustrated in Fig. 4B, which compares the f₁-traces extracted from the 2D DQ/SQ SR26 experiments of Fig. 3, taken at 175.5 ppm (C7), 170.3 ppm (C15), and 56.2 ppm (C6), with the corresponding ¹³C assignment shown in Fig. 4A. Noise in f₁-traces from the experiment using only a very short z-filter of 100 µs (upper black frames of Fig. 4B) is much larger than the thermal noise, whose 3σ<sub>th</sub> interval is highlighted in grey. Only obvious cross-peaks (black dashed lines on Fig. 4B and black arrows in Fig. 4C), corresponding to one- and two-bonds correlations (Fig. 4C) can be clearly identified. Any further, less intense cross-peaks originating from longer distance correlation are completely hidden in the t₁-noise, preventing the extraction of any quantitative intensity. Extending the z-filter length from 100 µs to 3 ms (middle dark-grey frames) undeniably reduces the t₁-noise, which, however, remains significantly above the thermal noise. Even if additional peaks can be guessed, they are of the same intensity level as the noise, making their interpretation very inaccurate. It is only with the introduction of the zz-filter (5 ms) in addition to the 3 ms z-filter (bottom light-grey frames in Fig. 4B), that the noise of the traces is reduced to the level of the thermal noise, enabling the clear
<figure><img src="image_6.png" /><figcaption>Fig. 4. (A) 1D ¹³C DNP-enhanced CPMAS spectrum of ampicillin at NA. Assignment is given in the Figure. ¹³C chemical shift positions used in (B) and (C) are highlighted with red (175.2 ppm), orange (170.3 ppm), and yellow (56.2 ppm) dashed lines. (B) f₁-traces through the dipolar-based DQ/SQ SR26 2D spectra of Fig. 3 at f₂ chemical shift positions of 175.2 ppm (C7, left panels), 170.3 ppm (C15, middle panels), and 56.2 ppm (C6, right panels), without any zz-filter and only a short z-filter of 100 µs (top panels with black frames), the same with a longer z-filter of 3 ms (middle panels with dark grey frames), and with both the 3 ms z-filter and an additional 5 ms zz-filter (bottom panels with light grey frames). Each set of f₁-traces is normalized relative to the maximum intensity in the z-filtered traces (middle panels with dark grey frames), such that peak intensity can be compared through the different experiments. The grey region in each f₁-trace indicates the thermal noise threshold at 3σ<sub>th</sub>. To help cross-peak identification, 1D CP spectra (in black) shifted according to the corresponding f₂ position are plotted on the top of each f₁-trace obtained with both the z- and zz-filters (bottom panels with light grey frames). Clearly matching cross-peak positions are highlighted with dashed lines, in dark grey for the ones already clearly visible in the experiments with the z-filter alone, and in colors (red, orange and yellow according to the color code given in (A)) for the cross peaks revealed by the use of the zz-filter. Sidebands are indicated by black stars. (C) Ampicillin chemical structure with arrows illustrating the different correlations revealed by the detected cross peaks in the respective traces given in (B), keeping the same color code as in (B).</figcaption></figure>
distinction of the small genuine cross-peaks (highlighted with
colored dashed lines) from longer distance correlations (col-
ored arrows in Fig. 4C). Most the unraveled small cross-peaks
are assigned to 3-bonds correlations. As described previously,
we quantified the σ<sub>t1</sub>/σ<sub>th</sub> ratio on the f<sub>1</sub>-trace of C7, which
shows the highest level of t<sub>1</sub>-noise (see Fig. S6B for further
details on σ<sub>t1</sub>/σ<sub>th</sub> quantification). The ratio (see Fig. 4B) de-
creases progressively from 6.2 using a short z-filter, to 4.4 with
long z-filter, and further down 1.4 when combining the zz-
filter with a long z-filter. Our experiments clearly demonstrate
that the zz-filter significantly reduces t<sub>1</sub>-noise in dipolar-based
DQ/SQ 2D experiments, despite the crystallite-orientation de-
pendence of the Hamiltonian. For a close to complete removal,
the combination with a long-enough z-filter prior to detection
is highly recommended. It is worth noting that the use of a
z-filter prior to detection in the J-refocused INADEQUATE ex-
periment has been nearly systematic since its introduction by
Cadars and coworkers [82] to suppress multiple-quantum co-
herences (MQCs), which can lead to lineshape distortions in
<sup>13</sup>C -labeled solids. In the Supporting Information (Sec. S6),
we show that, under our experimental conditions, inserting a
z-filter can also help reduce the t<sub>1</sub>-noise level in J-refocused
INADEQUATE experiments, but to a lesser extent than in the
SR26 case. This can be rationalized by the fact that sequences
with long pulse trains, such as symmetry-based sequences, are
more likely to build unwanted transverse magnetization for iso-
lated spins. As explained above, such contributions are not
diphased by the zz-filter but can be attenuated by the use of a
z-filter before detection.

z³-filter DNP-enhanced ¹³C-¹³C NA spectroscopy at Ultra-Low Temperature

In the sections above, we have shown that t₁-noise can be
present in ¹³C-¹³C NA DNP-enhanced correlation spectra
recorded at 100 K using a commercial setup. We expect this
issue to get even worse at lower temperature since the thermal
noise becomes smaller while the signal can be further enhanced.
This hypothesis was tested on an experimental setup developed
in house, composed of a closed-loop cryogen-free Helium cryo-
stat and an ultra-low temperature probe that enables conducting
MAS-DNP experiments down to 20-30 K. The overall stability
of this DNP system with respect to sample spinning and RF /
microwave power was discussed previously and is expected to
be similar than for the 100 K experiments reported above [44].
Up to one order of magnitude improvement in sensitivity have
been reported previously conducting DNP experiments at 20-
30 K compared to 100 K [12, 43–45, 95–97]. As shown in the
30 K DNP spectrum reported on the left-hand side of Fig. 5A,
we observe a significant t₁-noise contribution when using only
a z-filter of 3 ms. Interestingly, the t₁-noise in the spectrum
of Fig. 5A on the left has a clear antiphase character along the
f₂ direct detection dimension, significantly different from the
shape of the t₁-noise previously observed at 100 K. This obser-
vation underlines the variability of t₁-noise depending on the
various potential contributions. Impressively, the introduction
of a zz-filter of 3 ms drastically reduces the t₁-noise, leading
to a spectrum of unprecedented quality obtained under ULT-
MAS-DNP conditions (Fig. 5A right). Comparison of the three
f₁-traces in Fig. 5B, taken through both 2D spectra at 64.4 ppm

(C5), 74.8 ppm (C3), and 170.1 ppm (C15), clearly show that
the introduction of the zz-filter drastically reduces the t₁-noise
to the thermal noise level (grey region of the trace). On the
f₁-trace of C5, the σt₁/σth ratio decreases from 11.8 (z-filter
only) to 1.0 when combining the z- and zz-filters (Fig. S6C).
Considering the 2-fold DQ-filtered signal attenuation induced
by the zz-filter, this corresponds to an SNR improvement by
a factor 6. Further details about the spectrum representation
and the σt₁/σth measurements are provided in the Supporting
Information (Sec. S4). Similar to the 100 K case, the elimina-
tion of t₁-noise enables the clear and unambiguous assignment
of many correlations that were not distinguishable before (red
dashed lines). The application of a z³-filter leads to the first
artefact-free DQ/SQ 2D ¹³C-¹³C DNP spectrum recorded at 30
K on a sample at NA.

Application of the zz-filter to the heteronuclear case

Although we focus in this study essentially on homonuclear
DQ/SQ correlation experiments, it is interesting to note that the
zz-filter present in the heteronuclear z-filtered TEDOR experi-
ment [48] can also be used to mitigate t₁-noise problems. The
zz-filter was originally introduce to dephase undesired MQCs
encountered in spin labeled spin systems. The authors used a
delay between the two 90° pulses that convert I<sub>y</sub>S<sub>z</sub>- into I<sub>z</sub>S<sub>y</sub>-
terms, in order to preserve zz-terms only (see Fig. S1). For
samples at natural abundance, the formation of such undesired
MQCs is very unfavored and this extra delay is theoretically
unnecessary. However, we demonstrate in the supplementary
information (Sec. S1) that it is still useful to effectively suppress
t₁-noise, similarly to the homonuclear case presented above.

Conclusion

In this work, we introduced a new approach for *t*₁-noise sup-
pression in MAS-DNP ssNMR experiments in the context of
samples at natural abundance. This method, called here *zz*-filter
consists in the conversion of DQCs into longitudinal two-spin
order (*zz*-terms), while the strong magnetization of uncoupled
spins is rotated to the transverse plane. The subsequent *zz*-filter
delay leads to the dephasing of the unwanted signal from un-
coupled spins by chemical shift and heteronuclear proton inter-
action terms. The preserved longitudinal 2-spin order *zz*-terms
are then converted into a mixture of ZQCs and DQCs. The lat-
ter follow then the DQ to SQ CTP before being detected. This
*zz*-filter is simple to implement and is, in principle, effective
regardless of the source of instability leading to *t*₁-noise. We
show that this approach is compatible with both J- and dipolar
based DQ/SQ homonuclear experiments and, despite the sole
trade-off of a two- to three-fold loss in signal intensity, it enables
a tremendous reduction of the *t*₁-noise level, leading to spectra
of improved sensitivity in the regions of *t*₁-noise. Demon-
strated on a commercial Bruker MAS-DNP system, the *zz*-filter
brings the *t*₁-noise to the thermal noise level, which enables
the unambiguous distinction of small signals from longer-range
correlations, which were previously masked by the *t*₁-noise.
The performances of the *zz*-filter are even more impressive for
DNP experiments at ultra-low temperature (~30K), performed
<figure><img src="image_7.png" /></figure>

Fig. 5. Impact of the *zz*-filter on dipolar-based 2D DQ/SQ correlation experiments at 30 K using cryogenic He spinning. (A) 2D DNP-enhanced DQ/SQ SR26 spectra of NA ampicillin with only a *z*-filter of 3 ms (left spectrum with dark-grey frame), and with an additional *zz*-filter of 3 ms as well (right spectrum with light-grey frame). Contour levels are normalized to the maximum intensity in each spectrum. (B) *f*₁-traces through the dipolar-based DQ/SQ SR26 2D of (A) at *f*₂ chemical shift positions of 64.4 ppm (C5), 74.8 ppm (C3), and 170.1 ppm (C15), with the *z*-filter only (top panels with dark grey frames), and with both the *z*- and *zz*-filter (bottom panels with light grey frames). To account for the antiphase character of the *t*₁-noise along the *f*₂ (direct) dimension under these conditions (see zooms in panels (i) and (ii) of (A)), we chose to display the modulus (absolute value) of the complex spectrum along *f*₂, while retaining the real part along the indirect dimension (*f*₁). Each pair of *f*₁-traces is normalized relative to the maximum intensity in the corresponding *z*-filtered trace (top panels with dark grey frames), such that peak intensities can be compared between both experiments. The grey area in each trace indicates the thermal noise threshold, set at 3*σ*<sub>th</sub>, with *σ*<sub>th</sub> estimated assuming a Rayleigh distribution. Further details regarding the representation of the *f*₁-traces and the determination of *σ*<sub>th</sub> are provided in the Supplementary Information (Sec. S4). To help cross-peak identification, 1D CP spectra (in black) shifted according to the corresponding *f*₂ position are plotted on top of each *f*₁-trace obtained with both the *z*- and *zz*-filters. Cross-peaks revealed by the application of the *zz*-filter are highlighted using red dashed lines.

on a home-built He-spinning MAS-DNP system, where the in-
creased sensitivity leads to an even more pronounced *t*₁-noise.
The latter is almost completely suppressed when the *zz*-filter, in
combination with a *z*-filter prior to detection, is applied, leading
to a 6-fold SNR improvement along the *t*₁-noise polluted *f*₁-

traces. This leads to spectra of unprecedented quality in such
conditions, at ultra-low temperatures on NA samples, and to
the first-ever reported 2D DQ/SQ spectrum at NA recorded at
30K. The development described paves the way for many appli-
cations, for which *t*₁-noise was the most limiting factor. This
includes the study of more complex biomolecular / organic sys-
tems using ultra-low temperature MAS-DNP, including the fast
and accurate measurement of dipolar build-ups extracted from
2D datasets.

Supporting Informations

The authors have cited additional references within the Sup-
porting Information. [98–103].

Data Availibility

Data will be made available on request.

Acknowledgements

This work was supported by the French National Research
Agency in the framework of the “France 2030” program (ANR-

17-EURE-0003 through the labEx Arcane, ANR-15-IDEX-02 through the CDP Glyco@Alps2, ANR-22-CE07-0046-03). Part of this work, carried out on the Platform for Nanocharacterisation (PFNC), was supported by the “Recherches Technologiques de Base” program of the French National Research Agency (ANR) and the FEDER Program of the Region Auvergne-Rhône-Alpes.

Conflict of interest

The authors declare no conflicts of interest.

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## Supplementary Information

# Removing t₁-noise in DNP-enhanced NMR at natural isotopic abundance using two-spin order filter

Quentin Reynard-Feytis,¹ Subhradip Paul,¹ Sabine Hediger,¹ and Gaël De Paëpe,¹,*

¹ Univ. Grenoble. Alpes, CEA, CNRS, IRIG, MEM, 38000 Grenoble, France

## S1. Application of the zz-filter to the heteronuclear TEDOR experiment

The combination of z- and zz-filter has already been implemented in the zfr-TEDOR by Jaroniec and coworkers [48] in the context of ¹³C, ¹⁵N-labelled molecules. However, their purpose was not to address t₁-noise, but to suppress MQCs and antiphase terms generated by the J-coupling, which lead to spurious cross-peaks and line shape distortions. The zz-filter occurs after the first REDOR block, which creates antiphase coherences such as

$$ I_x \xrightarrow{\mathcal{H}_{\text{REDOR}} \propto 2I_z S_z} \cos\left(\frac{\omega t_{\text{mix}}}{2}\right) I_x + \sin\left(\frac{\omega t_{\text{mix}}}{2}\right) 2I_y S_z \quad (\text{S1}) $$

where the $I_i$ and $S_i$ operators, with $i \in \{x, y, z\}$, correspond respectively to ¹³C and ¹⁵N nuclei. In this case, the design and implementation of the zz-filter is straightforward, as it just required to set accordingly the delay $\Delta_{zz}$ between the $(\pi/2)_{x,i}$ and the $(\pi/2)_{x,s}$ pulses (see Fig. S1A). The first pulse converts the antiphase $2I_y S_z$ into zz-terms, which pass the zz-filter, while uncoupled spins components remain along x and are dephased. At natural abundance, unwanted MQCs that cause problems are negligible. As shown in Fig. S1B, the zz-filter originally implemented to remove MQCs artefacts also efficiently reduce t₁-noise in experiments at NA.

<figure><img src="image_8.png" /><figcaption>Fig. S1. (A) 2D ¹³C, ¹⁵N zfr-TEDOR sequence. $\pi$ and $\pi/2$ pulses are represented by narrow and wide black rectangles, respectively, $t_{\text{mix}}$ corresponds to the TEDOR mixing time and the z- and zz-filter delays are $\Delta_z$ and $\Delta_{zz}$, respectively. The detailed sequence with pulse phases is described in ref [48] (B) 2D ¹⁵N-¹³C TEDOR spectra recorded on natural abundance Ampicillin with 3 ms z-filter only (i) and with both z- and zz-filter of 3 ms (ii). The contour levels are normalized to the maximum intensity in each spectrum.</figcaption></figure>
S2. Accelerating dephasing of SQCs from isolated spins by adding a DARR-field during the zz-filter

In the scope of this study, we showed the implementation of the zz-filter to suppress t₁-noise in relatively low MAS spinning speeds (<10kHz), on a model system with abundant ¹H. Under such conditions, ¹H-¹³C and ¹H-¹H dipolar as well as ¹³C largest CSA (for aromatics and carbonyls) interactions are not completely averaged out by MAS, which enables efficient dephasing of transverse coherences during the zz-filter. Depending on the ¹³C chemical site, SQCs are more or less efficiently dephased, and we observed that the dephasing of carbonyl ¹³C takes more time than of aliphatics and therefore requires a longer zz-filter delay (Fig. S2A). For experiments at higher spinning frequencies or samples with less ¹H, the introduction of a DARR field [83] on the ¹H channel during the zz-filter delay, which satisfies the conditions ω₁H = nωr with n = 1 or 2, can then help for a faster dephasing, as shown in Fig. S2B. Both conditions reintroduce both the CSA and ¹H-¹³C heteronuclear dipolar interactions, while the first condition (n = 1) also reintroduces ¹H-¹H homonuclear dipolar coupling. While the signals from COs are not completely dephased after ≈ 3 ms of zz-filter without irradiation (Fig. S2A.i), they are completely dephased after only ≈ 1 ms of zz-filter with the application of a DARR-field on the ¹H channel (Fig. S2B.i). The use of the DARR field during the zz-filter has no impact on the DQ signal, which successfully pass through the zz-filter (Fig. S2A.ii vs Fig. S2B.ii). In terms of t₁-noise suppression, the DARR-field was not mandatory in the regime we tested it, but might become crucial in other experimental conditions, especially at high-spinning frequencies.

<figure><img src="image_9.png" /><figcaption>Fig. S2. (A) 1D signal detected in a J-refocused INADEQUATE experiment as a function of the zz-filter duration Δ<sub>zz</sub>, with t<sub>1</sub> = 0: (i) single-scan signal showing the dephasing of SQCs, and (ii) phase-cycled signal of 64 scans data showing conserved DQ-filtered signal intensity during Δ<sub>zz</sub>. (B) Same as (A) but with a DARR field (ω<sub>1H</sub> = 2ω<sub>r</sub>) of 16 kHz applied on the ¹H channel during the zz-filter Δ<sub>zz</sub>.</figcaption></figure>
<figure><img src="image_10.png" /><figcaption>Fig. S3. (A) z- and zz-filtered J-refocused-INADEQUATE pulse sequence. (B) DQ/SQ refocused-INADEQUATE DNP-enhanced spectra on natural abundance Ampicillin microcrystals impregnated with cAsymPol-POK, without (on the left) and with (on the right) a zz-filter of 6.25 ms (standard z-filter set to 3 ms). Contour levels are normalized to the maximum intensity in each spectrum.</figcaption></figure>

## S3. Materials and Methods

### Sample preparation

Ampicillin (D-()--aminobenzylpenicillin) was purchased from Sigma Aldrich. Before impregnation, the powder was grinded by hand using a mortar to reduce the grain size. 45 mg of powder was impregnated with 12 µL of 40 mM cAsymPol-POK [24] in $d_8$-glycerol/$D_2O/H_2O$ (60:30:10; v:v:v). The sample was then packed in two 3.2 mm rotors: a sapphire one for experiments at 100 K and a zirconia one for experiments at 30 K.

### DNP experiments at 100 K

DNP experiments at 100 K were carried out on a Bruker Advance III spectrometer operating at 9.4 T, equipped with a Bruker low temperature 3.2 widebore MAS probe and a 263 GHz (9.4 T) gyrotron. With microwave irradiation, the sample temperature was estimated at 106 K. The spinning speed was set to 8 kHz for all experiments.

#### ◇ Z3F-Refocused INADEQUATE experiments:

The 2D $^{13}$C-$^{13}$C DQ/SQ z-filtered refocused INADEQUATE [51, 80–82] (Fig. S3A) spectra presented in Fig. 2 (Fig. S3.B for the entire spectra) were acquired with 240 increments of 64 scans each using States-TPPI [98] for quadrature detection, a recycle delay of 3 s and 100 kHz SWf-TPPM [99–101] $^{1}$H decoupling. Acquisition times were 20 ms for the direct ($f_1$) and 3 ms for the indirect ($f_2$) dimension, respectively, leading to an overall experimental time of 13.5 h. The delay $τ$ was set to 29 rotor periods, corresponding to 3.6 ms (note that the $T'_2$ on the ampicillin samples was measured at 54.5 ms). As recommended in the zfr-refocused-INADEQUATE [82], a 3 ms z-filter prior to the detection has been used. The CP contact time was set to 1 ms
with a ramped (80 – 100%) CP spin-lock on the ¹H channel. For the *zz*-filtered experiment, dubbed DQ/SQ *z³*-filtered refocused INADEQUATE, the *zz*-filter length was set to 50 rotor periods, corresponding to 6.25 ms, without the application of DARR-field on the ¹H channel. Data were zero-filled prior to Fourier transform, and a line broadening of 50 Hz was used on the direct dimension. For the results presented in Fig. 1, we used the same sequence with 64 scans (except for Fig. 1C.ii with 1 scan only), a recycling delay of 4.2 s and 15 ms of acquisition time. The delay $τ$ was set to 31 rotor periods, which corresponds to 3.9 ms. We also used a *z*-filter of 3 ms and the *zz*-filter length was set to 25 rotor periods, corresponding to 3.1 ms. Data were zero-filled prior to Fourier Transform, and a line broadening of 150 Hz was used on the 1D spectra of Fig. 1C.i for better visualization. For Fig. 1B, the phase $φ$ of the generated DQCs was fixed to $π/4$ according to the phases used in ref [82], and we varied the phase of the *zz*-filter pulses, $θ$. The resulting pseudo-2D spectrum is represented in Fig. S4, the normalized signal intensity represented in Fig. 1B (blue dots) was obtained by taking the integral of the DQ-filtered signal for each angle increment on the region represented by red-shaded regions. The signal intensities were then normalized by the intensity obtained for $2θ−φ = 0$.

<figure><img src="image_11.png" /><figcaption>Fig. S4. DQ-filtered normalized signal of refocused-INADEQUATE with *zz*-filter with respect to $2θ−φ$, $θ$ being the *zz*-filter 90° pulses phase and $φ$ the phase of the generated DQCs (i.e., 90° in this case). The black line shows the projection among the horizontal axis, red squares indicate the region selected to integration and calculate the normalized signal intensity for each $2θ−φ$ value. The intensity is represented with the blue dots on the left and normalized to the initial points $2θ−φ=0°$. The blue dashed line corresponds to the theoretical value obtained analytically $cos (2θ−φ)^2$</figcaption></figure>

### ◇ Z3F-SR26 experiments:

2D ¹³C-¹³C DQ/SQ dipolar correlation experiments of Fig. 3 and Fig. 4 were performed with the SR26 recoupling sequence [90, 92] combined with StiC phase shifts [103]. They were acquired with 240 increments of 16 scans each using the States-TPPI for the quadrature detection, and a recycle delay of 4.5 s, leading to an overall experimental time of 4.5 h. For both the DQ excitation and reconversion blocks, one cycle of SR26 was used, corresponding to an overall mixing time of 4 ms, with 100 kHz continuous wave Lee-Goldburg (CW-LG) [102] ¹H decoupling. 100 kHz SWf-TPPM ¹H decoupling was applied during both the direct and indirect evolution time of 15 and 3 ms, respectively. The CP contact time was set to 2 ms with a ramped (80 – 100%) CP spin-lock on the ¹H channel. For the *zz*-filtered experiment, the *zz*-filter length was set 40 rotor periods, corresponding to 5 ms, under a DARR-field of ~8 kHz on the ¹H channel ($ω_{1H} = ω_r$). The phases of the *zz*-filter were incremented for the States-TPPI quadrature detection along with the SR26 reconversion block to filter the DQCs. The data were zero-filled prior to Fourier transform, without any apodization.

### ◇ Z3F-TEDOR experiments:

The 2D zfr-TEDOR [48] spectra presented in Fig. S1 were acquired with 64 increments of 128 scans each using Stats-TPPI for quadrature detection, a recycle delay of 4 s and 100 kHz SWf-TPPM ¹H decoupling. Acquisition times were 8 ms for the direct
$(f_2)$ and 4 ms for the indirect ($f_1$) dimension, respectively, leading to an overall experimental time of 9.5 h. The mixing time was set to 4 ms, which corresponds to 4 TEDOR block, during which a 100 kHz CW-LG decoupling was applied on the $^1$H channel. For both experiments, we used a z-filter of 3 ms prior to detection and we added for the zz-filtered TEDOR a zz-filter of 24 rotor period, corresponding to ~3 ms. We didn't use any DARR field on the $^1$H channel during the zz-filter. The CP contact time was set to 2 ms with a ramped (80-100%) CP spin-lock on the $^1$H channel. The data were zero-filled prior to Fourier transform, without any apodization.

## Experiments at 30 K

DNP experiments at 30 K were carried out on a Bruker Advance III spectrometer operating at 9.4 T, equipped with a 263 GHz (9.4 T) gyrotron and a self-developed closed-loop cryogenic He-spinning system, made of a cryogenic ultra-low temperature 3.2 widebore MAS probe and its associated cryostat [44]. With microwave irradiation, the sample temperature was estimated at 30 K. The spinning speed was set to 6850 Hz. 2D $^{13}$C-$^{13}$C DQ/SQ dipolar correlation experiments of Fig. 5 were performed with the SR26 recoupling sequence combined with StiC phase shifts. They were acquired with 256 increments of 16 scans each using the States-TPPI for the quadrature detection, and a recycle delay of 4.5 s, leading to an overall experimental time of 5 h. For both the DQ excitation and reconversion blocks, one cycle of SR26 was used, corresponding to an overall mixing time of 4.7 ms, with 100 kHz CW-LG $^1$H decoupling. 100 kHz SWf-TPPM $^1$H decoupling was applied during both the direct and indirect evolution time of 20 and 3.2 ms, respectively. The CP contact time was set to 2 ms with a ramped (80-100%) CP spin-lock on the $^1$H channel. For the zz-filtered experiment, the zz-filter length was set 30 rotor periods, corresponding to 4.3 ms, without any DARR field on the $^1$H channel. The phases of the zz-filter were incremented for the States-TPPI quadrature detection along with the SR26 reconversion block to filter the DQCs. The data were zero-filled prior to Fourier transform, without any apodization.

<figure><img src="image_12.png" /><figcaption>A</figcaption></figure>

Fig. S5. Schema of the color gradient used to represent $f_1$-traces based on the thermal noise standard deviation $\sigma_{th}$ in the case of a normal distribution $N(0, \sigma_{th})$ (A) and a Rayleigh distribution $R(\sigma_{th})$ (B).

<figure><img src="image_13.png" /><figcaption>B</figcaption></figure>

## S4. Noise analysis

Noise is generally modeled as following a normal distribution $N(0, \sigma)$, centered at zero with its standard deviation $\sigma$ used to quantify its intensity. Accordingly, when displaying the $t_1$-noise polluted or corrected $f_1$-traces from various spectra (Fig. 2, Fig. 4), we employed a grey-to-dark blue color gradient to represent the 99.7% confidence interval of thermal noise, corresponding to the $\pm 3\sigma_{th}$ limit. The thermal noise standard deviation, $\sigma_{th}$, was directly measured from signal-free $f_1$-traces at different positions across the spectra. For all experiments, we selected $f_1$-traces at $f_2$ values of 100, 50, 0, 225, 250, 275, and 300 ppm. The color gradient used in Figs. 2 and 4 is illustrated in Supplementary Fig. S5A. For the 30 K MAS-DNP measurements, a zoom on Fig. 5 (main text) shows that the $t_1$-noise in the 2D spectrum is predominantly antiphase along the $f_2$ dimension. As the $f_1$-trace representation does not effectively convey the clarity of the spectrum, we instead represented the data by taking the absolute value along $f_2$ and the real part along $f_1$. Assuming the real and imaginary components of the signal are independent and both follow a normal distribution $N(0, \sigma_{th})$, the resulting magnitude spectrum follows a Rayleigh distribution $R(\sigma_{th})$. In this case, the noise standard deviation $\sigma_{th}$
can be estimated from the measured noise mean $\mu$, using the relation:

$$ \sigma_{th} = \mu\sqrt{2/\pi} \qquad (S2) $$

To quantitatively assess the $t_1$-noise reduction using the zz-filter, we estimated the $t_1$-noise standard deviation $\sigma_{t1}$ from the most noise-polluted $f_1$-trace, both with and without the zz-filter. This was done similarly to the thermal noise measurement, but using signal-free regions within the $f_1$-trace (highlighted in red in Fig. S6). We then calculated the ratio $\sigma_{t1}/\sigma_{th}$, which reflects the relative amplitude of $t_1$-noise with respect to thermal noise. These ratios are shown in Supplementary Fig. S6, corresponding to: (A) the refocused INADEQUATE spectrum (Fig. 2), (B) the SR26 dipolar-recoupling at 100 K (Fig. 4), and (C) the SR26 dipolar-recoupling at 30 K (Fig. 5).

<figure><img src="image_14.png" /><figcaption>Fig. S6. Representation of the $f_1$-traces with the detail of the $\sigma_{t1}$ measurements for the calculation of the $\sigma_{t1}/\sigma_{th}$ ratio in the case of the refocused INADEQUATE corresponding to the Fig2 (A), the dipolar-recoupling SR26 sequence at 100 K corresponding to the Fig4 (B) and at 30K corresponding to the Fig5 (C). Each $f_1$-trace is represented and normalized to the trace of the spectrum without zz-filter and with a long z-filter (3 ms). The red shaded regions represent the part of the $f_1$-traces which is used to calculate the noise standard deviation.</figcaption></figure>
S5. zz-filter efficiency for γ-encoded/non-γ-encoded sequences

As explained in the main text, we chose to apply the zz-filter on SR26 [90, 92], which is a non-γ-encoded dipolar recoupling sequence, because the zz-filter theoretical efficiency is higher than for γ-encoded sequences (0.5 instead of 0.25). In addition, supercycled sequences such as SR26 showcase an increased robustness regarding CSA and are therefore more robust for long-distance correlation measurements. To attest our theoretical calculations, we present in Fig. S7A the DQ-filtered signal for SR26 vs R26, with and without the application of a zz-filter. To attest a good match with the theoretical efficiencies, we normalized the spectra obtained with zz-filter by the theoretical efficiency for each sequence. Both sequences have been recorded in similar conditions, on the 100K Bruker MAS-DNP system described above with a spinning speed of 6.5 kHz, a mixing time of 4.9 ms and a zz-filter of 7.6 ms. On the other hand, we also performed build-up simulation using SIMPSON [93, 94] on SR26 and R26, with and without zz-filter, represented on Fig. S7B. We used for the simulations a coupling constant of 1.5 kHz, no chemical shift, the rep144 crystal file with 40 γ-angles, and a spinning speed of 8 kHz. As represented on Fig. S7B, we verified the 0.5/0.25 zz-filter theoretical efficiencies for γ- and non-γ-encoded sequences, respectively.

<figure><img src="image_15.png" /><figcaption>Fig. S7. (A) DQ-filtered signal for SR26 and R26 without zz-filter (blue curve) and with zz-filter (orange curve) with a mixing time of 4 ms. The spectra recorded with the use of the zz-filter are represented with their intensity divided by the theoretical efficiency of the zz-filter for both sequences (0.5 and 0.25 for SR26 and R26 respectively). (B) Build-up simulation of the zz-filter efficiency for SR26 (left panel) and R26 (right panel) with and without zz-filter (blue and orange dashed lines respectively).</figcaption></figure>

S6. Impact of the z-filter on the t₁-noise level for the refocused-INADEQUATE

In the main text, we discussed the importance of applying a z-filter prior to detection in dipolar-based polarization transfer experiments to suppress residual t₁-noise which remains when using only a zz-filter. We also noted that we didn't face this issue in J-based refocused INADEQUATE experiment, where a z-filter is almost systematically applied prior to detection, as originally proposed by Cadars and co-workers [82], to dephase multiple-quantum coherences (MQCs) that lead to spurious peaks and peak
distortions in labeled spin systems. Here, we investigate the impact of the z-filter on the t₁-noise level in refocused-INADEQUATE experiments. The results shown in Fig. S8 were acquired under conditions similar to those in Fig. 1 and Fig. 2. The short and long z-filter delays correspond to 10 µs and 3 ms, respectively, and the zz-filter delay was set to approximately 3.1 ms when applied. A comparison of panels A and C of Fig. S8 shows that, similar to the SR26 dipolar-based experiments, the application of a z-filter alone appears to reduce t₁-noise. However, repeating the same experiment as panel C later the same day yielded the spectrum in panel D, which displays significantly less t₁-noise, despite identical conditions. This suggests that the observed t₁-noise may be influenced by external factors whose stability varies over time. Consequently, the level of t₁-noise may fluctuate between otherwise equivalent experiments. Importantly, the combination of both zz-filter and z-filter consistently prevents t₁-noise contamination, offering a robust strategy for its suppression.

<figure><img src="image_16.png" /><figcaption>Fig. S8. Figure S8. 2D DNP-enhanced DQ/SQ refocused-INADEQUATE spectra of NA ampicillin (A) with a 3 ms long z-filter and no zz-filter, (B) with a 3 ms zz-filter in addition to the 3 ms long z-filter, (C) with a shorter z-filter of 100 µs and (D), in the same conditions than (C) but repeated later within the same day.</figcaption></figure>

## S7. Derivation of Eq. (6)

Double quantum spectroscopy is based on the use of a sequence that introduces a double-quantum effective Hamiltonian which generates DQC noted as:

$$DQ_{\phi} = \cos(\phi)DQ_{x} + \sin(\phi)DQ_{y} \qquad (S3)$$

with the DQ and ZQ operators in Eq. (S4) forming the DQ and ZQ subspaces respectively:

$$ \begin{aligned} DQ_x &= I_{jx}I_{kx} - I_{jy}I_{ky} = I_j^+I_k^+ + I_j^-I_k^- & DQ_y &= I_{jx}I_{ky} + I_{jy}I_{kx} = -i(I_j^+I_k^+ - I_j^-I_k^-) \\ ZQ_x &= I_{jx}I_{kx} + I_{jy}I_{ky} = I_j^+I_k^- + I_j^-I_k^+ & ZQ_y &= I_{jy}I_{kx} + I_{jx}I_{ky} = -i(I_j^+I_k^- - I_j^-I_k^+) \end{aligned} \qquad (S4) $$

Let's suppose that we generate DQCs among $DQ_x$, we can study the way $\rho$ is transformed by a generic $(\pi/2)_{\theta}$ pulse. For this, we can introduce the operators $I_{j\theta}$ and $I_{j\bar{\theta}}$, whose expression can be given by:

$$ I_{j\theta} = c\theta I_{jx} + s\theta I_{jy} \qquad I_{j\bar{\theta}} = -s\theta I_{jx} + c\theta I_{jy} \qquad (S5) $$
with the notation $s\alpha^n \equiv \sin(\alpha)^n$ and $c\alpha^n \equiv \cos(\alpha)^n$. Reciprocally we can write:

$$I_{jx} = c\theta I_{j\theta} - s\theta I_{j\bar{\theta}} \qquad I_{jy} = s\theta I_{j\theta} + c\theta I_{j\bar{\theta}} \qquad (S6)$$

One can note that the $I_{\theta}$ and $I_{\bar{\theta}}$ operators satisfy the same commutation property than $I_x$ and $I_y$

$$[I_{\theta}, I_{\bar{\theta}}] = iI_z \qquad (S7)$$

This allows us to calculate the effect of an arbitrary $(\pi/2)_\theta$ pulse

$$I_{jx} \xrightarrow{(\pi/2)\theta} c\theta^2 I_{jx} + c\theta s\theta I_{jy} - s\theta I_{jz} \qquad I_{jy} \xrightarrow{(\pi/2)\theta} s\theta c\theta I_{jx} + s\theta^2 I_{jy} + c\theta I_{jz} \qquad (S8)$$

Now that these relations are established, we can calculate the effect of a general $(\pi/2)_\theta$ pulse on DQCs. A convenient way to tackle this problem is to calculate this on $DQ_x$, before generalizing it.

$$DQ_x = I_{jx}I_{kx} - I_{jy}I_{ky} \xrightarrow{(\pi/2)\theta} (c\theta^2 I_{jx} + c\theta s\theta I_{jy} - s\theta I_{jz})(c\theta^2 I_{kx} + c\theta s\theta I_{ky} - s\theta I_{kz}) \\ -(c\theta s\theta I_{jx} + s\theta^2 I_{jy} + c\theta I_{jz})(c\theta s\theta I_{kx} + s\theta^2 I_{ky} + c\theta I_{kz}) \qquad (S9)$$

This can be developed and simplified using the notation $I_{v\mu} = I_{jv}I_{k\mu}$

$$= (c\theta^4 I_{xx} + c\theta^3 s\theta I_{xy} - c\theta^2 s\theta I_{xz} + c\theta^3 s\theta I_{yx} + c\theta^2 s\theta^2 I_{yy} - c\theta s\theta^2 I_{yz} - c\theta^2 s\theta I_{zx} - c\theta s\theta^2 I_{zy} + s\theta^2 I_{zz}) \\ -(c\theta^2 s\theta^2 I_{xx} + c\theta s\theta^3 I_{xy} + c\theta^2 s\theta I_{xz} + c\theta s\theta^3 I_{yx} + s\theta^4 I_{yy} + c\theta s\theta^2 I_{yz} + c\theta^2 s\theta I_{zx} + c\theta s\theta^2 I_{zy} + c\theta^2 I_{zz}) \qquad (S10)$$

and we can rearrange the expression

$$\begin{aligned} & \overbrace{DQ_y}^{DQ_x} = (c\theta^2 - s\theta^2)[c\theta^2 I_{xx} + s\theta^2 I_{yy} + c\theta s\theta(I_{xy} + I_{yy}) - I_{zz}] - 2c\theta s\theta[\overbrace{I_{\theta z}}^{I_{xz}} + \overbrace{s\theta I_{yz}}^{I_{z\theta}} + \overbrace{c\theta I_{zx} + s\theta I_{zy}}^{I_{z\theta}}] \\ &= c(2\theta)[(1 - s\theta^2)I_{xx} + s\theta^2 I_{yy} + c\theta s\theta DQ_y - I_{zz}] - s(2\theta)[I_{\theta z} + I_{z\theta}] \\ & \overbrace{\frac{1}{2}(DQ_x + ZQ_x)}^{DQ_x} = c(2\theta)[\overbrace{I_{xx}}^{I_{xx}} - s\theta^2(\overbrace{I_{xx} - I_{yy}}^{I_{xx} - I_{yy}}) + c\theta s\theta DQ_y - I_{zz}] - s(2\theta)[I_{\theta z} + I_{z\theta}] \\ &= c(2\theta)[\frac{1}{2}ZQ_x + \frac{1}{2}(c\theta^2 - s\theta^2)DQ_x + \frac{1}{2}s(2\theta)DQ_y - I_{zz}] - s(2\theta)[I_{\theta z} + I_{z\theta}] \\ &= \frac{1}{2}c(2\theta)[ZQ_x + \overbrace{DQ_x + s(2\theta)DQ_y - 2I_{zz}}^{DQ_{2\theta}}] - s(2\theta)[I_{\theta z} + I_{z\theta}] \end{aligned} \qquad (S11)$$

Finally, the final expression of the transformation of $DQ_x$ under a pulse $(\pi/2)_\theta$ is given by

$$DQ_x \xrightarrow{(\pi/2)\theta} \frac{1}{2}c(2\theta)[ZQ_x + DQ_{2\theta} - 2I_{zz}] - s(2\theta)[I_{\theta z} + I_{z\theta}] \qquad (S12)$$