Improved NMR transfer of magnetization from protons to half- integer spin quadrupolar nuclei at moderate and high MAS frequencies

Half-integer spin quadrupolar nuclei are the only magnetic isotopes for the majority of the chemical elements. 20 Therefore, the transfer of polarization from protons to these isotopes under magic-angle spinning (MAS) can provide precious insights into the interatomic proximities in hydrogen-containing solids, including organic, hybrid, nanostructured and biological solids. Furthermore, this transfer has recently been combined with dynamic nuclear polarization (DNP) in order to enhance the NMR signal of half-integer quadrupolar isotope. Nevertheless, the cross-polarization transfer lacks of robustness in the case of quadrupolar nuclei and we have recently introduced as an alternative technique a through-space refocused 25 insensitive nuclei enhancement by polarization transfer (D-RINEPT) scheme combining hetero-nuclear dipolar recoupling built from adiabatic pulses and continuous wave decoupling. This technique has been demonstrated at 9.4 T with moderate MAS frequencies, νR  10-15 kHz, in order to transfer the DNP-enhanced H polarization to quadrupolar nuclei. Nevertheless, polarization transfers from protons to quadrupolar nuclei are also required at higher MAS frequencies in order to improve the resolution of H spectra. We investigate how this transfer can be achieved at νR  20 and 60 kHz. We demonstrate that the D30 RINEPT sequence using adiabatic pulses still produces efficient and robust transfer but requires large rf-fields, which may not be compatible with the specifications of commonly employed MAS NMR probes. As an alternative, we introduce robust and efficient variants of D-RINEPT and PRESTO (phase-shifted recoupling effects a smooth transfer of order) sequences using symmetry-based recoupling schemes built from single and composite π-pulses. Their performances are compared using the https://doi.org/10.5194/mr-2021-29 Discussions O en A cc es s Preprint. Discussion started: 29 March 2021 c © Author(s) 2021. CC BY 4.0 License.

hereafter). (Nagashima et al., 2020, n.d.;Giovine et al., 2019) These schemes benefit from higher robustness than CPMAS since they do not employ a spin-lock on the quadrupolar channel, but instead a limited number (two or three) of pulses selective to the CT. In these sequences, the dipolar interactions between protons and quadrupolar nucleus are reintroduced by applying on the 1 H channel symmetry-based recoupling sequences, such as R18 2 5 for PRESTO or SR4 1 2 for RINEPT. 70 Brinkmann and Kentgens, 2006a) In the case of recoupling sequences built from single square π-pulses, the RINEPT sequence using SR4 1 2 (denoted RINEPT-SR4 1 2 ) is more efficient than PRESTO at νR ≥ 60 kHz because of its higher robustness to rffield inhomogeneity and 1 H offset and CSA. At νR ≤ 20 kHz, the PRESTO technique is more efficient since the efficiency of RINEPT-SR4 1 2 is reduced by the increased losses due to 1 H-1 H interactions at lower MAS frequencies during the SR4 1 2 recoupling and the windows used to rotor-synchronize the SR4 1 2 blocks, whereas the PRESTO sequence is devoid of these 75 windows. (Giovine et al., 2019a) Recently, we have introduced a novel variant of the RINEPT sequence employing SR4 1 2 recoupling built (i) from tanh/tan (tt) adiabatic inversion pulses, (ii) continuous-wave (CW) irradiations during the windows, and (iii) composite π/2 and π pulses on the 1 H channel, in order to limit the losses due to 1 H-1 H interactions and improve the transfer efficiency at moderate MAS frequencies. (Nagashima et al., 2020, n.d.) This novel RINEPT variant, denoted RINEPT-CWc-SR4 1 2 (tt), is more efficient 80 than PRESTO and CPMAS at νR  12.5 kHz and has been combined with DNP to detect the NMR signal of quadrupolar nuclei with small dipolar coupling with protons, including quadrupolar low-γ isotopes, such as 47,49 Ti, 67 Zn or 95 Mo, and unprotonated 17 O nuclei.
However, several NMR experiments require the transfer of 1 H magnetization to quadrupolar nuclei at νR > 12.5 kHz. In particular, MAS frequencies of νR ≥ 20 kHz are needed to avoid the overlap between the center-bands and the spinning 85 sidebands of satellite transitions (ST) in 27 Al spectra at 18.8 T. In addition, magnetization transfers at νR ≥ 60 kHz are advantageous to acquire 2D hetero-nuclear correlation spectra between protons and quadrupolar nuclei endowed with high resolution along the 1 H dimension since fast MAS averages out the 1 H-1 H dipolar couplings.
Concurrently, we have demonstrated that the efficiency of PRESTO transfers using the R16 7 6 recoupling can be improved at νR = 62.5 kHz using 270090180 composite π-pulses as a basic inversion element, where the standard notation for composite 90 pulses is used: ξϕ denotes a rectangular, resonant rf-pulse with flip angle ξ and phase ϕ in degrees. (Giovine et al., 2019a) More recently, SR4 1 2 and R12 3 5 recoupling schemes built from 90−45904590−45 composite π-pulses have been proposed, but they have not yet been incorporated into RINEPT transfers. (Perras et al., 2019) Globally, no systematic study of R  recouplings built from composite π-pulses has been carried out.
In the present article, we investigate the use of RINEPT-CWc using an adiabatic recoupling scheme at the higher MAS 95 frequencies of νR = 20 and 62.5 kHz. We demonstrate using numerical simulations of spin dynamics and experiments on γalumina and isopropylamine templated microporous aluminophosphate  that the rf requirement of this technique increases with the 1 H-1 H dipolar interactions and is not compatible with the specifications of most MAS probes at νR ≥ 20 kHz. As an alternative, we introduce variants of the PRESTO and RINEPT sequences by selecting with AH https://doi. org/10.5194/mr-2021-29 Discussions Open Access Preprint. Discussion started: 29 March 2021 c Author(s) 2021. CC BY 4.0 License.
(average Hamiltonian) the recoupling schemes built from single rectangular or composite π-pulses. Finally, using experiments 100 on γ-alumina and AlPO4-14, which feature different 1 H-1 H dipolar interactions, we identify the most robust and efficient PRESTO and RINEPT transfers at B0 = 18.8 T with νR = 20 and 62.5 kHz.

II-1-1. Single-quantum hetero-nuclear dipolar recoupling
A R  sequence, where N is an even positive integer and n and ν are integers, consists of N/2 pairs of elements RϕR'−ϕ with R an inversion pulse with a duration of nTR/N, where TR = 1/νR = 2/R is the rotor period, R' an inversion pulse derived from R by changing the sign of all phases and ϕ = πν/N radians an overall phase shift. The rf-field requirement of R  is equal to: 115 where = ∑ =1 is the sum of the flip angles of the P individual pulses of the R element.
In the PRESTO sequence (Fig.1a), symmetry-based γ-encoded R  schemes applied to the 1 H channel reintroduce the | | = 2 space components and the single-quantum (SQ) terms of the hetero-nuclear dipolar couplings between the protons and the quadrupolar nuclei, as well as the 1 H CSA, while they suppress the contributions of 1 H isotropic chemical shifts, the hetero-120 nuclear J-couplings with protons, and the 1 H-1 H dipolar couplings to the first-order average Hamiltonian. (Zhao et al., 2004) The hetero-nuclear dipolar interaction is characterized by a space rank l and a spin rank . A γ-encoded | | = 2 SQ hetero- nuclear dipolar recoupling must selectively reintroduce the two components {l, m, , μ} = {2, 2, 1, μ} and {2, −2, 1, − μ} of the hetero-nuclear dipolar coupling and 1 H CSA with μ = 1, while other components must be suppressed.
During these recoupling schemes, the contribution of the dipolar coupling between I = 1 H and S nuclei to the first-order 125 Hamiltonian is equal to: (Zhao et al., 2004) where I ± = Ix  iIy are the shift operators, and the magnitude and phase of the recoupled I-S dipolar coupling are given by and 130 respectively, where bIS is the dipolar coupling constant in rad/s, and κ is the scaling factor of the recoupled hetero-nuclear dipolar interaction, which depends on the R  symmetry and the R element. The Euler angles {0, , , , } relate the I-S vector to the MAS rotor frame, and t 0 refers to the starting time of the recoupling. The norm of ̅ , (1) does not depend on the , angle, since these recoupling schemes are -encoded. (Pileio et al., 2007;Martineau et al., 2012) The Hamiltonian of Eq.2 135 does not commute among different spin-pairs, and therefore the PRESTO sequence is affected by dipolar truncation, i.e., the transfer to distant nuclei is attenuated by the stronger couplings with nearby spins.
As mentioned above, the SQ hetero-nuclear dipolar recoupling schemes also reintroduce the 1 H CSA with the same scaling factor κ, but without commuting with the recoupled 1 H-S dipolar interactions. Therefore, in the case of large 1 H CSA, for instance at high magnetic fields, this interaction can interfere with the 1 H-S dipolar couplings, especially with small ones. 140 These interferences can be limited by the use of the PRESTO-III variant, depicted in Fig.1a,c,(Zhao et al., 2004) in which three CT-selective pulses are applied to the S nucleus. Indeed, the CT-selective π-pulses partly refocus the 1 H CSA, which limits these interferences.
For νR = 20 kHz, according to the AH, the R  sequence with the highest robustness to 1 H-1 H dipolar interactions is R22 2 7 (180 0 ). However, this recoupling is slightly less robust to 1 H CSA and offset than R18 2 5 (180 0 ), which has already been reported. For this MAS frequency, the R  schemes using the chosen composite pulses either required rf-fields greater than 120 kHz, e.g. ν1 = 130 and 173 kHz for the R26 3 7 schemes built from 90−45904590−45 and 270090180 pulses, or did not suppress 190 efficiently the second-order cross-terms between 1 H-1 H interactions because of small rf-field (ν1 ≤ 62.5 kHz).

195
For νR = 62.5 kHz, the R  sequences using composite π-pulses recouple the 1 H-S dipolar interaction with a higher scaling factor than those built from single π-pulses. According to AH, the 90024090900 basic element leads to the highest robustness to 1 H-1 H interferences. Even if the amplitude of the cross-terms is inversely proportional to the MAS frequency (Eq.5), the amplitude of these terms is lower at νR = 20 than 62.5 kHz. The 270090180 element is less robust to 1 H-1 H interferences, but benefits from a high robustness to offset. The selected R  symmetries for this element include R14 6 5 and R16 7 6 , which have 200 already been employed for the measurement of 1 H CSA and the transfer of 1 H polarization to half-integer quadrupolar nuclei at νR ≥ 60 kHz. (Giovine et al., 2019a;Pandey et al., 2015) As the scaling factors κ of the 1 H-S dipolar interaction of the R  schemes built from single π-pulses with 45° ≤ ϕ ≤ 135° are small, we also selected in Table 3 R  schemes built from single π-pulses with κ ≥ 0.15, but with extended ϕ ranges. These recoupling schemes are less robust to offset than the R  schemes built from 270090180 element. 205 Table 2. Selected  | | = 2 SQ hetero-nuclear dipolar recoupling with 45° ≤ ϕ ≤ 135° for νR = 62.5 kHz.

II-2-1. Zero-quantum hetero-nuclear dipolar recoupling
In the D-RINEPT sequence, the 1 H-S dipolar interactions are reintroduced under MAS by applying non-γ-encoded two-spin 215 order dipolar recoupling to the 1 H channel. These recoupling schemes reintroduce the m= 2 space components and the zeroquantum (0Q) terms of the 1 H-S dipolar interaction and 1 H CSA, i.e., the rotational components {l, m, , μ} = {2, 2, 1, 0}, while they suppress the contributions of 1 H isotropic chemical shifts, the hetero-nuclear J-couplings with protons, and the 1 H-1 H dipolar couplings to the first-order average Hamiltonian. (Brinkmann and Kentgens, 2006a, b) The contribution of the 1 H-S dipolar coupling to this Hamiltonian is equal to: (Giovine et al., 2019a;Brinkmann and Kentgens, 2006a;Lu et al., 2012) where , = sin 2 ( , )cos (2 ), The norm of ̅ , (1) depends on the  phase, given by Eq.4, and hence on the , angle. Therefore, these two-spin order dipolar recoupling schemes are non--encoded. The Hamiltonian of Eq.7 commutes among different spin pairs and hence, these 225 recoupling schemes are not affected by dipolar truncation. Similarly, the recoupled 1 H CSA contribution to the first-order Hamiltonian is proportional to Iz and hence, commutes with the recoupled 1 H-S dipolar interactions and does not interfere with the hetero-nuclear dipolar recoupling.

II-2-2. Selection of the recoupling sequence
Different R  sequences have been proposed to achieve non-γ-encoded | | = 2 two-spin order dipolar recoupling, including 230 (i) symmetries R(4 ) 2 −1 = R12 3 5 , R16 4 7 , R20 5 9 , R24 6 11 , R28 7 13 and R32 8 15 for n = 3, 4, 5, 6, 7 and 8 using single π-pulses as basic element, which have been employed to measured 1 H-17 O dipolar couplings at νR = 50 kHz, (Brinkmann and Kentgens, 2006b) (ii) SR4 1 2 recoupling built from a single π-pulse, which corresponds to the [R4 schemes using a 90−45904590−45 composite π-pulse as a basic element, which have been incorporated into D-HMQC sequences 235 at νR = 36 kHz, (Perras et al., 2019) and (iv) SR4 1 2 schemes built from a tanh/tan adiabatic pulse, which have been used in RINEPT sequence at νR  36 kHz. (Nagashima et al., 2020, n.d.) During the tanh/tan pulse, the instantaneous rf-amplitude is equal to: where ω1,max is the peak amplitude of the rf-field, t refers to the time since the start of the pulse, which lasts TR/4 when 240 incorporated into the SR4 1 2 recoupling scheme. The parameter ξ determines the rise and fall times of the pulse. Hence, in the frequency-modulated (FM) frame, (Garwood and DelaBarre, 2001) the frequency offset i where Δ0,max is the peak amplitude of the carrier frequency modulation and  determines the frequency sweep rate in the center of the pulse. Here, we employed ξ = 10 and θ = 87° = atan(20). (Nagashima et al., 2020;Kervern et al., 2007;Nagashima 245 et al., 2018) We screened here the R  schemes built from 1800, 270090180, 90024090900 and 90−45904590−45 elements. A total of 58 R  symmetries with 2 ≤ N ≤ 30, 2 ≤ n ≤ 7 and 1 ≤ ν ≤ 11 were found which recouple the {2, 2, 1, 0} rotational components of the 1 H-S dipolar coupling and 1 H CSA. We only considered the R  symmetries with 60° ≤ ϕ ≤ 120° since the currently employed non-γ-encoded | | = 2 two-spin order hetero-nuclear dipolar recoupling schemes have 75° ≤ ϕ ≤ 90°. 250 We calculated the scaling factor of the recoupled 1 H-S dipolar interaction and the Euclidean norm and ‖ { , } 1 × 2 ‖ 2 of the cross-terms between 1 H-1 H interactions using the 'C and R symmetries' Mathematica package. (Carravetta et al., 2000;Brinkmann and Levitt, 2001;Brinkmann et al., 2000;Brinkmann and Edén, 2004) For each basic element R, we selected the The selected R  sequences are listed in Table 4. The parameters of the SR4 1 2 schemes built from the different basic element R are also listed in Table 4  According to the AH, the 90024090900 composite -pulse yields the highest robustness to 1 H-1 H dipolar interactions. However, the rf-field requirement of the R  sequences built from this composite pulse, 1 = 4.66R, i.e., 1 = 291 kHz at R = 62.5 kHz, is not compatible with most 1.3 mm MAS probes. Furthermore, the highest robustness to 1 H CSA and offset is achieved using 260 the 270090180 composite -pulse. The SR4 1 2 schemes benefit from the highest robustness to 1 H CSA, because of the three-step multiple-quantum super-cycle. (Brinkmann and Edén, 2004;Brinkmann and Kentgens, 2006a) Contrary to the R  | | = 2 SQ hetero-nuclear dipolar recouplings, the rf-field of the R  | | = 2 two-spin orders is always higher than 2R since these R  symmetries with 2n > N, such as R12 9 5 , lead to vanishing κ scaling factor.
In the case of the adiabatic R  (tt) sequences, the determination of the scaling factors of first-and second-order terms of the 265 effective Hamiltonian is more cumbersome since they depend on the 1,max, Δ0,max, ξ and θ parameters. (Nagashima et al., 2018) For example, the scaling factor of the R12 3 5 and SR4 1 2 schemes is κ = 0.31 for 1,max/Δ0,max = 0.685, ξ = 10 and θ = 87°, and this value monotonously decreases for increasing 1,max/Δ0,max ratios. 270

II-2-3. D-RINEPT-CWc sequence
The D-RINEPT-CWc sequence is displayed in Fig.1b,c. The 1 H-S dipolar couplings are reintroduced by applying the R  schemes listed in Table 4 during the defocusing and refocusing delays , which are identical in this article, even if distinct defocusing and refocusing delays can improve the transfer efficiency. (Nagashima et al., 2020) As the two-spin order 275 recoupling schemes are non-γ-encoded, they must be rotor-synchronized. We used here a delay of TR between two successive R  blocks. In the D-RINEPT-CWc sequence, a CW irradiation is applied during these delays in order to limit the losses due to 1 H-1 H dipolar interactions. (Nagashima et al., n.d π and second π/2 pulses by composite 90018090900 and 9090900 pulses, respectively, the CW irradiation being applied between 280 the individual pulses. (Freeman et al., 1980;Levitt and Freeman, 1979) III. Numerical simulations

III-1. Simulation parameters
All simulations were performed using the version 4.1.1 of SIMPSON package (Bak et al., 2000, p.200 (Bak and Nielsen, 1997b), while the MR angles were regularly stepped from 0 to 360°.
To accelerate the simulations, the 1 H 15 N RINEPT transfer was used, instead of the 1 H 27 Al one, because the computing time is proportional to the cube of the size of the density matrix. Furthermore, in RINEPT experiments, only CT-selective pulses are applied to the quadrupolar nuclei and hence, the contribution of STs to the signal can be disregarded. The 1 H 15 N 290 RINEPT transfer was simulated for a 15 N 1 H4 spin system. A similar approach has already been applied for the simulation of the RINEPT transfer from protons to quadrupolar nuclei (Nagashima et al., n.d.;Giovine et al., 2019b). This 15 N 1 H4 spin system comprises a tetrahedron of four protons with a 15 N nucleus on one of its symmetry axis. The dipolar coupling constants between protons are all equal to bHH/(2π) = 1, 7 or 15 kHz. The dipolar coupling between 15 N nucleus and its closest 1 H neighbor is bHN/(2π) = 2575 Hz, corresponding to a 1 H-27 Al distance of 2.3 Å, typical of the distance between the protons 295 of hydroxyl groups and the Al atoms of the first surface layer of hydrated γ-alumina (Lee et al., 2014). All protons were subject to a CSA of 6 kHz, i.e., 7.5 ppm at 18.8 T, their asymmetry parameters were null, and their principal axis coincide with the 3fold rotational axes of the 1 H4 tetrahedron.
The simulations were performed for a static magnetic field of 18.8 T, for which the 1 H and 15 N Larmor frequencies were equal to 800 and 81 MHz, respectively using MAS frequencies of R = 20 or 62.5 kHz (Liang et al., 2018). 1 H  15 N RINEPT-CWc 300 sequences incorporating either SR4 1 2 (tt) or R12 3 5 (tt) recoupling schemes were simulated. The defocusing and refocusing periods were both equal to their optimal values  = 650 or 640 μs at R = 20 or 62.5 kHz, respectively. The rf-field nutation frequency on the 1 H channel was equal to 200 kHz during the /2 and -pulses, which do not belong to the recoupling sequence, as well as the CW irradiation, whereas the pulses applied to S = 15 N nuclei were considered as ideal Dirac pulses. Simulations were performed for recoupling schemes made of tanh/tan adiabatic pulses with ν1,max and Δν0,max parameters ranging from 305 0.5R to 10R and from 10R to 200R, respectively. The other pulses were applied on resonance. The density matrix before the first pulse was equal to I1z + I2z + I3z + I4z. We normalized the transfer efficiency of 1 H 15 N RINEPT sequences to the maximal signal for a 1 H  15 N through-bond RINEPT sequence made of ideal Dirac pulses in the case of a 15 N-1 H spin system with a J-coupling constant of 150 Hz.

III-2. Optimal adiabatic recoupling
The transfer efficiency of RINEPT using R  schemes built from adiabatic pulses, depends on ν1,max and Δν0,max parameters. For a similar 15 N 1 H4 spin system with bHN/(2π) = 2.575 and bHH/(2π) = 7 kHz, spinning at R = 12.5 kHz, we showed 320 using numerical simulations of spin dynamics that a maximal transfer efficiency was achieved provided that ν1,max = 0.07Δν0,max and ν1,max/R ≥ 8. (Nagashima et al., n.d.) In practice, we used ν1,max = 11R = 137 kHz and Δν0,max = 160R = 2 MHz. Similar simulations were performed here for R = 20 or 62.5 kHz. As seen in Fig.2a-c, at a given MAS frequency, higher 1 H-1 H dipolar couplings require higher rf-field and broader carrier frequency sweep so that the tanh/tan pulses remain adiabatic in spite of the modulation of the 1 H-1 H dipolar couplings by MAS. (Nagashima et al., n.d.;Kervern et al., 2007) For bHH/(2π) 325 = 7 kHz, the minimal ν1,max/R ratio decreases for higher MAS frequencies (compare Figs.2b and d)  the modulation of 1 H-1 H dipolar couplings by MAS to the first adiabaticity factor is proportional to (ν1,max) 2 /R and hence, ν1,max values proportional to √ , i.e. ν1,max/R ratio inversely proportional to √ , are sufficient to maintain the adiabaticity of the pulses. (Kervern et al., 2007) Nevertheless, Fig.2d indicates that SR4 1 2 (tt) recoupling requires ν1,max ≥ 313 kHz for R = 62.5 kHz. This rf field is not compatible with the specifications of most 1.3 mm MAS probes. Similar transfer efficiencies were 330 simulated for the RINEPT sequence with R12 3 5 (tt) recoupling scheme (not shown).

IV-1. Samples and experimental conditions
L-[U-15 N]-histidine·HCl (hereafter referred to as "histidine") and isotopically unmodified -alumina were purchased from Merck, and AlPO4-14 was prepared as described previously. (Antonijevic et al., 2006) 335 All 1 H  S RINEPT-CWc and PRESTO-III experiments were performed at B0 = 18.8 T on Bruker BioSpin Avance NEO spectrometers equipped with double-resonance 1 H/X probes. 1 H 15 N RINEPT-CWc experiments using SR4 1 2 (tt) recoupling (denoted RINEPT-CWc-SR4 1 2 (tt) hereafter) on histidine were performed with 1.3 and 0.7 mm MAS probes spinning at R = 40 or 62.5 kHz, with defocusing and refocusing delays equal to  = 375 or 384 s, respectively. The rf-field of the 1 H /2 and  pulses, which do not belong to the recoupling scheme, was 340 equal to 200 kHz, that of the continuous wave irradiation to ν1,CW = 100 kHz, and that of the 15 N pulses to 62 kHz. 1 H decoupling with a rf-field of 16 kHz was applied during the acquisition. The pulses on the 1 H channel were applied on resonance, whereas those on 15 N channel were applied at the isotropic chemical shift of the 15 NH  signal (172 ppm). These 1D spectra resulted from averaging 8 transients with a relaxation delay of 3 s. The 15 N isotropic chemical shifts were referenced to an aqueous saturated solution of NH4NO3 using [ 15 N]-glycine as a secondary reference. 345 1 H 27 Al RINEPT-CWc and PRESTO-III experiments on -alumina and AlPO4-14 were performed with a 1.3 mm MAS probe spinning at R = 20 (to test the R  schemes with large rf-fields) or 62.5 kHz. The tested recoupling schemes are listed in Tables 5 and 6 for R = 20 kHz and Tables 7 and 8 for R = 62.5 kHz. The rf-field of the 1 H /2 and  pulses, which do not belong to the recoupling scheme, was equal to 208 kHz, that of the continuous wave irradiation to ν1,CW = 147 kHz, and the 27 Al CT-selective one for π/2 and π pulses to 10 kHz. The defocusing and refocusing delays  are given in Table 5

IV-2. Optimal adiabatic recoupling
Figs.2e and f show the efficiency of 1 H  15 N RINEPT-SR4 1 2 (tt) transfer for histidine as function of ν1,max/R and Δν0,max/R for R = 40 or 62.5 kHz, respectively. These experimental data indicate that at higher MAS frequency, an efficient adiabatic recoupling can be achieved for lower ν1,max/R and Δν0,max/R ratios. This result agrees with the numerical simulations of Figs.2b 360 and d.

365
 delay and 1/1,max rf-field were fixed to their optimum values given in Tables 5 and 7. IV-3. PRESTO and RINEPT performances for R = 20 kHz
The highest transfer efficiency is obtained with the RINEPT-CWc sequence incorporating an adiabatic recoupling. This recoupling also leads to the highest robustness to offset and rf inhomogeneity, and SR4 1 2 (tt) and R12 3 5 (tt) yield identical transfer efficiency and robustness. Hence, the three-step multiple-quantum super-cycle of the SR4 1 2 symmetry does not improve the 390 robustness in the case of a tanh/tan basic element. However, these recoupling schemes require maximum rf fields of 1,max  8νR = 160 kHz, which may exceed the rf power specifications of most 3.2 mm MAS probes.
The efficiency of the RINEPT-CWc-SR4 1 2 (270090180) sequence, with rf-field ν1 = 4νR, is comparable to that of PRESTO-R18 2 5 (1800), but with a higher robustness to offset and rf inhomogeneity. We can notice that amplitude modulated recoupling schemes, for which the phase shifts are equal to 180°, such as SR4 1 2 (270090180) and SR4 1 2 (1800), exhibit a high robustness to offset (Fig.5). (Carravetta et al., 2000) The use of 270090180 composite pulses in SR4 1 2 symmetries instead of single π pulses 400 improves their transfer efficiency as well as their robustness to offset and rf field inhomogeneity.
In summary, for R = 20 kHz in γ-alumina, the RINEPT-CWc-SR4 1 2 (270090180) sequence achieves efficient and robust transfers of magnetization from protons to 27 Al nuclei using a moderate rf field of ν1 = 4νR. For 1 H spectra with a width smaller than 20 and -(270090180). For each curve  was fixed to its optimum value given in Table 5.  a AlO6 signal normalized to that with 1 H 27 Al RINEPT-CWc-SR4 1 2 (tt). b FWHM of the robustness to offset. c FWHM of the robustness to rf-field. d Only a lower bound of rf-field could be determined due to probe rf specifications (Fig.4). 2 ppm assigned to AlO4, AlO5 and AlO6 sites, respectively. (Ashbrook et al., 2008) The AlO5 and AlO6 sites are directly bonded to OH groups. The 1 H MAS spectrum is shown in Fig.S1. According to the literature, the 27 AlO4 signal subsumes the resonances of two AlO4 sites with quadrupolar coupling constants CQ = 1.7 and 4.1 MHz, whereas the CQ constants of 27 AlO5 and 27 AlO6 sites are equal to 5.6 and 2.6 MHz, respectively. (Fernandez et al., 1996;Antonijevic et al., 2006) The 1 H-1 H dipolar couplings within the isopropylamine template molecule are larger than in γ-alumina. We used the most intense peak, AlO4, to 425 compare the 1 H  27 Al transfer efficiencies of RINEPT-CWc and PRESTO sequences with different recoupling schemes, and the results are given in Table 6. The six sequences yielding the highest transfer efficiencies are the same for AlPO4-14 and γalumina and their relative efficiencies are comparable for the AlO4 peak of AlPO4-14 and the AlO6 signal of γ-alumina.    Al RINEPT-CWc-SR4 1 2 (tt). b FWHM of the robustness to rf-field was not measured for RINEPT-SR4 1 2 (tt) and -R12 3 5 (tt) (Fig.S1). 450

IV-4. PRESTO and RINEPT performances for R = 62.5 kHz
Similar comparisons of the performances of the various RINEPT-CWc and PRESTO sequences were performed for γ-alumina and AlPO4-14 at R = 62.5 kHz.
Nevertheless, the nominal rf requirements of the RINEPT sequences using adiabatic pulses or 270090180 composite π-pulses correspond to ν1max = 5νR (313 kHz: Fig.2d) or 4νR (250 kHz), which exceeds the specifications of our 1.3 MAS probe, and the sequences were tested only up to ν1max = 208 kHz (Fig.7). This suboptimal rf field could potentially limit the transfer 460 efficiencies of these sequences.

V. Conclusions
In this work, we have introduced novel symmetry-based hetero-nuclear dipolar recoupling schemes, which can be incorporated 525 into the RINEPT and PRESTO sequences to transfer the magnetization from protons to half-integer quadrupolar nuclei at R = 20 or 62.5 kHz. These novel recouplings have been compared to existing schemes. We have shown that the RINEPT-CWc-SR4 1 2 (tt) sequence, which produces efficient and robust transfers at R  10-15 kHz, (Nagashima et al., 2020) requires rf-fields incompatible with the specifications of most MAS probes for R ≥ 20 kHz. Conversely, the introduced RINEPT-CWc- at R = 20 kHz to transfer the magnetization from protons to quadrupolar nuclei. At R = 62.5 kHz, the RINEPT-CWc-SR4 1 2 (270090180) and PRESTO-R16 7 6 (270090180) sequences with rf-requirements of 4νR and 2.3νR, respectively, result in the most robust and efficient transfers. At both MAS frequencies, the RINEPT and PRESTO techniques complement each other since the latter is dipolar truncated, whereas the former is not. As result, the RINEPT sequences must be chosen to observe simultaneously protonated and unprotonated sites, whereas the PRESTO schemes can be employed for the selective 535 observation of quadrupolar nuclei in proximity to protons. These techniques are expected to be useful for transferring the DNPenhanced magnetization of protons to quadrupolar nuclei in indirect MAS DNP experiments at R ≥ 20 kHz, notably used at high magnetic fields. (Nagashima et al., 2020, n.d.;Rankin et al., 2019;Berruyer et al., 2020) Author contributions: JSG, AGMR and JT carried out the NMR experiments on γ-alumina and AlPO4-14. YT performed the 540 spin dynamics simulations and carried out the NMR experiments on l-histidine·HCl. OL derived average Hamiltonian theory for the investigated recoupling sequences. OL and JPA wrote the manuscript. All the authors contributed to the editing of the manuscript.