Cross-polarization (CP) experiments employing frequency-swept radiofrequency (rf) pulses have been successfully used in static spin systems for obtaining broadband signal enhancements. These experiments have been recently extended to heteronuclear I, S = spin-1/2 nuclides under magic-angle spinning (MAS), by applying adiabatic inversion pulses along the S (low-γ) channel while simultaneously applying a conventional spin-locking pulse on the I-channel (1H). This study explores an extension of this adiabatic frequency sweep concept to quadrupolar nuclei, focusing on CP from 1H (I = 1/2) to 2H spins (S = 1) undergoing fast MAS (νr = 60 kHz). A number of new features emerge, including zero- and double-quantum polarization transfer phenomena that depend on the frequency offsets of the swept pulses, the rf pulse powers, and the MAS spinning rate. An additional mechanism found operational in the 1H–2H CP case that was absent in the spin-1/2 counterpart, concerns the onset of a pseudo-static zero-quantum CP mode, driven by a quadrupole-modulated rf/dipolar recoupling term arising under the action of MAS. The best CP conditions found at these fast spinning rates correspond to double-quantum transfers, involving weak 2H rf field strengths. At these easily attainable (ca. 10 kHz) rf field conditions, adiabatic level-crossings among the {|1,|0,|1} mS energy levels, which are known to complicate the CP MAS of quadrupolar nuclei, are avoided. Moreover, the CP line shapes generated in this manner are very close to the ideal 2H MAS spectral line shapes, facilitating the extraction of quadrupolar coupling parameters. All these features were corroborated with experiments on model compounds and justified using numerical simulations and average Hamiltonian theory models. Potential applications of these new phenomena, as well as extensions to higher spins S, are briefly discussed.

Solid-state nuclear magnetic resonance is a powerful analytical tool for the study of biomolecules and materials.1–6 Enabling many of these studies is cross-polarization7 magic-angle spinning (CPMAS),8 which based on achieving the Hartmann-Hahn (HH) matching condition,7,9 has been widely used for increasing the sensitivity of both spin-1/28,10–15 and quadrupolar16–19 nuclear magnetic resonance (NMR). While very effective under moderate MAS spinning rates and magnetic field strengths, the spin-lock pulses that have to be applied as part of CP’s matching condition are often unsuitable for covering wide spectral bandwidths, particularly as magnet technologies yield platforms operating at fields ≥20 T,20,21 and chemical shift dispersions become concomitantly larger. Further challenges arise for ultra-wideline NMR spectra of quadrupolar nuclei, which usually have patterns that are significantly broader than those of spin-1/2 nuclides, and are influenced by MAS-driven level crossings among the spin-locked states.22–26 

Frequency-swept radio-frequency (rf) pulses have often been utilized to extend the bandwidths of NMR experiments in power-limited excitation,27 inversion,28–30 or decoupling pulse sequences.31,32 For the solid-state NMR of both spin-1/2 and quadrupolar nuclei, swept rf pulses play important roles in the excitation of broad powder patterns,33,34 and in increasing the bandwidth of Carr-Purcell Meiboom-Gill acquisitions.33,35,36 Adiabatically swept radio-frequency (rf) pulses have been combined into the standard cross-polarization scheme for I(1/2)-S(1/2)37–41 and I(1H)-S(2H)42 spin systems under MAS, for the sake of improving HH matching conditions. In these methods, the amplitude and/or frequency of an adiabatic rf pulse were swept through the HH conditions for better polarization transfers. Recently, an improved technique that combines frequency-swept pulses together with CP is the broadband adiabatic inversion cross-polarization (BRAIN-CP) method.33 The BRAIN-CP method is capable of delivering HH matching over a wide range of isotropic and anisotropic frequency dispersions. While initially utilized under static conditions in combination with spin-echoes for obtaining wideline NMR spectra of both spin-1/2 and quadrupolar nuclei,43–48 BRAIN-CP has been recently extended to MAS NMR of spin-1/2 nuclides.34 In this MAS variant, BRAIN-CP proved suitable for uniform excitation and refocusing over wide frequency regions—particularly at the very fast (≥50 kHz) MAS spinning rates that are envisioned for routine use in ultrahigh field NMR experiments.

This manuscript explores the applicability of BRAIN-CPMAS to quadrupolar nuclei. Specifically, the aim of this work was to obtain CP-enhanced 1H–2H wideband MAS spectra.19,49–52 To this end, Wideband Uniform-Rate Smooth-Truncation (WURST)-shaped28 rf adiabatic inversion pulses were applied on the 2H channel, while spin-locking rf pulses were applied on the 1H channel under sample spinning conditions. Due to the frequency sweep on 2H channel multiple HH matching conditions occur, including zero-quantum (ZQ) and double-quantum (DQ) CP modes akin to those observed in BRAIN-CPMAS; also observed were novel static-like matching conditions, arising from a MAS-driven, quadrupolar-enabled rf-dipolar recoupling. Rotary resonance (RR) interferences arising from the modulation of the S-spin shift anisotropy and/or the first-order quadrupolar interaction were also observed. Average Hamiltonian analyses were conducted to understand these phenomena, which were predicted by numerical simulations and corroborated experimentally by spectra of model amino acid compounds. Overall, it is found that BRAIN-CPMAS implemented under suitable conditions can deliver sensitivity-enhanced, distortion-free spectra that closely mimic the ideal 2H line shapes expected under ultrafast spinning rates.

The frequency-modulated (FM) doubly rotating frame Hamiltonian that describes the I = 1/2 → S = 1 CP dynamics of an isolated I-S spin pair under MAS and subject to a frequency-swept adiabatic passage on the S spin is

H(t)=ω1IIxΩSSzω1SA(t)Sx+2b(t)IzSz+HQ(1)(t).
(1)

Here ω1I=γIB1I represents an on-resonance irradiation of the I-spin, ω1S=γSB1S, and ΩS=ΩSωp(t) is an effective offset frequency of the S spin as seen in the FM frame. In this frame, ΩS=ω0ωrf describes the center offset of the sweep and ωp(t)=(Δω/tp)tΔω/2 is the rf’s instantaneous offset frequency, where Δω=2πΔν and tp are the bandwidth of the adiabatic sweep and the duration of a WURST pulse whose rf amplitude envelope is given as A(t) = (1cosn[πt/tp]) (n = even number), respectively.28,30,34 Any potential homonuclear I-I and S-S dipolar coupling interactions and I-and S-spin chemical shift anisotropies (CSAs) are ignored for simplicity, and 2b(t)IzSz is a MAS-modulated heteronuclear dipolar coupling interaction that under MAS is modulated as15 

b(t)=k=2,k02bkeikωrt.
(2)

In Eq. (2), the orientation-dependent {bk} coefficients correlate an I-S dipolar vector defined in its principal axis frame to the rotor frame,15 as related by βd and γd Euler angles. The first-order quadrupolar interaction, HQ(1)(t), is given under MAS by53 

HQ(1)(t)=CQωQ(t){3Sz22},
(3)

where CQ=e2qQ and

ωQ(t)=18sin2βcos(2ωrt+2γ)142sin2βcos(ωrt+γ).
(4)

A detailed description of an S-spin behavior under the action of an adiabatic WURST pulse and MAS is provided in the supplementary material A. Using this single-spin description, physical insight into the nature of the CP process under similar conditions can be gathered by removing the dominant first-order quadrupolar term HQ(1)(t) from Eq. (1). This requires transforming the overall Hamiltonian into a quadrupolar interaction frame defined as54–56 

H=UQHUQ1+i(dUQ1/dt)UQ,
(5)

where

UQ=Texp{i0tCQωQ(t)dt(3Sz22)}.
(6)

When Eq. (5) is considered over a powder, the γ-angle averaged Coriolis term, i(dUQ1/dt)UQγ, vanishes.54 Since all terms in Eq. (1), with the exception the rf Hamiltonian, commute with HQ(1)(t) at all times, only the rf Hamiltonian will be transformed by going into the quadrupolar interaction frame. This will result in

Hrf(t)=ω1SA(t){Sxcos(0t3CQωQ(t)dt)+[SySz+SzSy]sin(0t3CQωQ(t)dt)}.
(7)

The spin-locking behavior of S over the sweep can be evaluated by inspecting the parameter α=ω1S2CQωr, which specifies the extent of adiabaticity in the level-crossings.22 When α=ω1S2CQωr1, the system is said to be in the sudden passage regime; under these conditions, the rf does not promote population redistributions among the |1,|0, and |1 eigenstates during these levels’ crossings. As discussed within the context of Fig. S1 of the supplementary material, ν1S in the 5–16 kHz range fulfills this sudden-passage regime for prototypical 2H sites (e.g., CQ = 168 kHz) at high (νr ≥ 40 kHz) spinning rates. Under such conditions, one can solely consider the term

Hrf(t)ω1SA(t)Sxcos(0t3CQωQ(t)dt)
(8)

in Eq. (7). Accounting in this accelerated frame for HQ(1)(t) simplifies the description of the CP Hamiltonians for both |1|0 and |0|1 subspaces, leading to identical spin-1/2-like expressions for both subspaces (refer to Eqs. (S9) and (S10) in the supplementary material):

H(t)=ω1IIx2ΩS(t)Sz122ω1SA(t)Sx12cos(0t3CQωQ(t)dt)+ 4b(t)IzSz12.
(9)

Assuming further that the rf’s amplitude envelope A(t)=(1cos40[πt/tp]) ≈ 1 and defining Sz=2Sz12, Sx=2Sx12 as pseudo-fictitious spin-1/2 operators possessing the same coefficients as the original spin-1 angular momentum operators, Eq. (9) becomes

H(t)=ω1IIxΩS(t)Szω1SSxcos(0t3CQωQ(t)dt)+ 2b(t)IzSz.
(10)

Applying a final transformation into a doubly tilted frame where all rf fields lie parallel to the z′ axes,15,57 the individual subspace’s CP Hamiltonians become

HT(t)=ωeIIzωeS(t)Sz+ 2sinθIsinθS(t)b(t)IxSx+ 2cosθIcosθS(t)b(t)IzSz2cosθIsinθS(t)b(t)IzSx 2sinθIcosθS(t)b(t)IxSz.
(11)

The effective resonance frequencies along these tilted z′-axes are

ωeI=ω1I,
(12)
ωeS(t)[{ΩS(t)}2+ω1S2cos2(0t3CQωQ(t)dt)];
(13)

while the tilt angles θI and θS(t) that relate the z′-axes to the z-axes in the FM frame are given by

cos(θI)=ΩI/ωeI=0;sin(θI)=ω1I/ωeI=1,
(14)
cos(θS[t])=(ΩS+Δω2Δωtpt)/ωeS(t),
(15)
sin(θS[t])=ω1Scos(0t3CQωQ(t)dt)/ωeS(t)=ω1Sk=AkQexp(ikωrt)ωeS(t),
(16)

where the last relation uses the fact that sin(θS[t]) involves a Bessel integral that can be expanded as an infinite Fourier series. With these definitions and assumptions, and if using only the three initial CP-relevant terms in HT(t), Eq. (11) is reduced to14,15,17

HT(t)=ω1IIzωeS(t)Sz+2sinθS(t)b(t)IxSx=ω1IIzωeS(t)Sz+2ω1Sk=AkQexp(ikωrt)l=22blexp(ilωrt)ωeS(t)IxSx.
(17)

The product of the ωrt-dependent Fourier expansions arising from the modulation of the quadrupolar and dipolar terms in Eq. (17) can be separated into time-independent and time-dependent terms:

HT(t)=ω1IIzωeS(t)Sz+2ω1S[Λ0+Λ±1e±iωrt+Λ±2e±2iωrt+higher-order terms]ωeS(t)IxSx,
(18)

where

Λ0=A1Qb1+A1Qb1+A2Qb2+A2Qb2,
(19)
Λ±1=A0Qb±1+A1Qb±2+A±2Qb1+A±3Qb2,
(20)
Λ±2=A0Qb±2+A±1Qb±1+A±3Qb1+A±4Qb2.
(21)

An explicit derivation of these Λk(k=0,±1,and±2) terms is summarized in the supplementary material. This supplementary material can be used to gauge the magnitude/relevance of these terms. For instance, for a general crystallite orientation (β=45°,γ=0°) of a dipolar coupled 1H–2H pair collinear with the quadrupolar tensor possessing a 1H–2H dipolar coupling of 4 kHz and a CQ = 168 kHz, the magnitude of the quadrupole-driven rf-dipolar recoupled term Λ0 is about 680 Hz. This is a significant coupling strength, which will generate a static-like, k = 0, ZQ0 CP mode even under very fast MAS conditions (vide infra).

Utilizing the single-transition operator formalism usually employed to analyze CP transfers,15,58 Eq. (18) can be rewritten as follows:

HT(t)=ωΔ(t)IzZQωΣ(t)IzDQ+ω1S[Λ0+Λ±1e±iωrt+Λ±2e±2iωrt+]ωeS(t)(IxZQ+IxDQ),
(22)

where, ωΔ(t)=ω1IωeS(t),ωΣ(t)=ω1I+ωeS(t), and the single-transition operators for the zero-quantum (ZQ) and double-quantum (DQ) coherences are defined by

IzZQ=IzSz2,IzDQ=Iz+Sz2,
IxZQ=I+S+IS+2,IxDQ=I+S++IS2,
IyZQ=I+SIS+2i,IyDQ=I+S+IS2i.
(23)

Since the single transition operators defined in the ZQ and DQ subspaces commute with each other, their time evolutions can be solved separately

HTZQ(t)=ωΔ(t)IzZQ+ω1S[Λ0+Λ±1e±iωrt+Λ±2e±2iωrt+]ωeS(t)IxZQ
(24)

and

HTDQ(t)=ωΣ(t)IzDQ+ω1S[Λ0+Λ±1e±iωrt+Λ±2e±2iωrt+]ωeS(t)IxDQ.
(25)

The oscillating terms associated with Λ±1 and Λ±2 in Eqs. (24) and (25) are analogous to forms that we derived for swept CPMAS NMR for an I = S = 1/2 case,34 meaning that we can use our previous average Hamiltonian analysis to determine their averages over a single rotor period. Notice that Eqs. (24) and (25) possess dual time dependencies, associated to the adiabatic frequency sweeps (Iz terms) and to the MAS-driven modulations (Ix terms), respectively. Under the fast spinning rates and slow adiabatic sweeps of interest in this study, an average Hamiltonian over the time scale of a rotor period may be approximated by assuming quasi-constant offsets ωΔ,Σ(t0) over any given rotor period. This assumption is valid as the rotor periods to be considered (15-30 μs range) will typically be orders-of-magnitude shorter than the adiabatic pulse duration (tp= 5-10 ms). Approximating the ωeS(t) as quasi-constant for time intervals t0tt0+2πωr, the effective resonance frequency along the S channel can be averaged for each rotor period as

ωeS(t0){ΩS+Δω2Δωtpt0}2+ω1S2.
(26)

At a similar level of approximation, an evaluation of the cos2(02πωr3CQωQ(t)dt) term contributing to ωeS(t0) over a rotor period leads to a null average integral, and therefore to cos2(0)=1. With these assumptions, average Hamiltonians over a rotor period HTζav=1τr0τrHTζ(t)dt,ζ= ZQ or DQ can be obtained from Eqs. (24) and (25) via the transformation UpHTζUp1iUpddtUp1, where Up=exp(ikωrtIzζ) and ζ= DQ or ZQ refers to the zero- or double-quantum sub-spaces. This evaluation produces

HTζav=[(ω1Ikωr)+mωeS(t)]Izζ+ω1SΛk2ωeS(t)I+ζ,
(27)

where k=±1 and ±2,I+ζ=Ixζ+iIyζ, m is +1 for the ZQ-CP process, and −1 for the DQ-CP process. In the above equations, t0 has been generalized for simplicity to a suitable time t.

While the k=±1,±2 terms are as usual in CPMAS experiments involving polarization transfer to spin-1/2 nuclides, the static-like CPMAS transfer process involving the Λ0 term is peculiar to CPMAS of quadrupoles and arises due to the interference between the periodic quadrupole-driven modulation of the rf, and the identically periodic MAS-driven modulation of the dipolar coupling. This recoupling effect can be separated from Eq. (24), and for a dipole-coupled I = 1/2 − S = 1 spin pair will be given by

HTZQav=[ω1I+ωeS(t)]IzZQ+ω1SΛ0ωeS(t)IxZQ.
(28)

When ω1I=ωeS(t), this CP mode will transfer I-magnetization to the S-spin. Notice that, as is the case for static solids, only a ZQ HH match is possible; a DQ-HH process is not allowed because there does not exist a condition nulling the coefficient of IzDQ in Eq. (25), ωΣ(t), for any combination of ω1I and ωeS(t).

As in the I = S = 1/2 case, time-progressive ZQ- and DQ-Hartmann-Hahn matching conditions, as well as rotary resonance (RR) inversions, may affect an I = 1/2−S = 1 system over the course of the frequency sweep. To visualize how these happen during BRAIN-CPMAS experiments on quadrupoles, we inspect the time-progressive conditions that make the IzDQ and IzZQ coefficients in Eqs. (27) and (28) zero—which will be the conditions enabling the departure of the system from pure I-spin polarization. A ZQ±k (k = 0, 1, or 2) HH matching condition will therefore be met when the instantaneous frequency offset, ωp(t), introduced by the adiabatic sweep, satisfies νeIνeS(t)=±kνr. In a similar manner, a DQk (k = 1 or 2) HH matching condition will be met when ωp(t) instantaneously satisfies ν1H+νeS(t)=kνr. A third potential phenomenon, a RR inversion, has been shown to arise driven by oscillations of either CSA or quadrupolar interactions, whenever a spin-locked magnetization passes through effective field conditions satisfying νeS(t)=kνr.26,55,59,60 These effects will revert the spin-locked state of the magnetization vis-à-vis the effective field. Given the low-γ nature of 2H nuclei and their relatively small CSA spans (≤1 kHz), RR inversion phenomena of this kind will take place driven mainly by the first order quadrupole interaction HQ(1)(t). To the best of our knowledge, this RR-driven inversion of spin-locked quadrupolar states has so far not been noted, even if a similar effect has been utilized to improve the excitation of multiple-quantum coherences in half-integer quadrupolar nuclei.26 

Figure 1 presents numerical simulations of 1H–2H BRAIN-CPMAS deriving from these considerations. These calculations incorporate different offset frequencies ΩS/2π (0, ±30, and ±60 kHz), null and non-null quadrupole couplings, and varying swept offsets Δν (60 kHz and 110 kHz), assuming a MAS rate of νr = 60 kHz. Also illustrated in the figures are the fulfillment of DQ±k (k = 1, 2), ZQ±k (k = 0, 1, or 2), and RR conditions, as well as the behavior of the spin-locked (Sz) and transverse (Sx) S magnetizations arising from a situation where these are null at the beginning of the swept pulse HH matching, and all polarization exists as Iz. Apart from the scaling effects coming from the 2 and 2 coefficients that are present for the Sz12 and Sx12 operators, respectively, these predictions are similar to those made for the S = 1/2 case. The zero-crossings timings associated with the ZQ and DQ conditions are clearly connected with I → S transfers of spin-locked polarization, and these time points measured at any arbitrary ±ΩS/2π are clear mirror images to each other along t = tp/2. Moreover, when the offset ΩS/2π = 0, the two time points that satisfy the same DQ1 condition become mirror imaged to each other along t = tp/2. These two mirror-imaged processes are associated with similar enhancements but acting on S-polarizations of opposite sign, due to the sign change that the Sz magnetization component experiences when it crosses the equatorial line during the adiabatic sweep. These events move to earlier times during the 0–tp window as the ΩS/2π offset becomes negative, and to later times during the adiabatic sweep as ΩS/2π increases. Still, it is noteworthy how the introduction of CQ ≠ 0 breaks the symmetry of the aforementioned transfer efficiencies of the two DQ1 coherences. This helps to create a non-zero Sz polarization at the conclusion of the sweep. Two differences are also worth noting between the present S = 1 case and earlier spin-1/2 analyses. One concerns the RR inversions, which will now be driven by modulation of the first-order quadrupolar interaction rather than of the CSA—and hence they may arise even in the presence of 2H nuclei with small CSAs. While this RR phenomenon does not play an important role if choosing sweeps Δννr and/or dealing with small ΩS/2π offsets, it becomes visible when this is not the case. The second phenomenon concerns the appearance of new, ZQ0-derived HH transfers.

FIG. 1.

CP transfer and RR inversion conditions simulated for a swept BRAIN-CPMAS experiments (νr= 60 kHz), for (a) Δν=νr and (b) Δν>νr. Simulations were carried out for CQ = 0 and CQ = 168 kHz, with the common parameters: δCSA= 921 Hz; ν1S= 5 kHz; ν1S= 47 kHz). DQ1 (blue line), DQ2 (green line), ZQ0 (red line), ZQ-1 (pink line), and RR (black line) matching conditions can be identified at the specified ΩS offsets by the time points at which CP signal transfer or RR inversion conditions cross zero. Time propagations of an initial Ix state (black) and of the CP-enhanced Sx (green) and Sz (red) magnetizations are demonstrated for both zero and non-zero values of CQ. Notice that within small Ωs/2π offsets, the RR inversion points are avoided when Δν=νr: RR1 inversion points are visible only at Ωs/2π=±60 kHz in case (a) although these points are visible in both Ωs/2π=±32 and ±60 kHz conditions in case (b). Moreover, ZQ0 conditions are missing at the on-resonance condition in case (a), although these points are present for every offset frequency for case (b).

FIG. 1.

CP transfer and RR inversion conditions simulated for a swept BRAIN-CPMAS experiments (νr= 60 kHz), for (a) Δν=νr and (b) Δν>νr. Simulations were carried out for CQ = 0 and CQ = 168 kHz, with the common parameters: δCSA= 921 Hz; ν1S= 5 kHz; ν1S= 47 kHz). DQ1 (blue line), DQ2 (green line), ZQ0 (red line), ZQ-1 (pink line), and RR (black line) matching conditions can be identified at the specified ΩS offsets by the time points at which CP signal transfer or RR inversion conditions cross zero. Time propagations of an initial Ix state (black) and of the CP-enhanced Sx (green) and Sz (red) magnetizations are demonstrated for both zero and non-zero values of CQ. Notice that within small Ωs/2π offsets, the RR inversion points are avoided when Δν=νr: RR1 inversion points are visible only at Ωs/2π=±60 kHz in case (a) although these points are visible in both Ωs/2π=±32 and ±60 kHz conditions in case (b). Moreover, ZQ0 conditions are missing at the on-resonance condition in case (a), although these points are present for every offset frequency for case (b).

Close modal

DQ1 effects dominate the HH transfers under conditions of small ΩS/2π offsets. For Δν=νr (Fig. 1(a)), only the DQ1 time points satisfy a condition for CP polarization transfer at a small ΩS/2π(±νr/4). For instance, at ΩS/2π = 0, the DQ1 time points are visible in Fig. 1(a) at t1 = 2.27 ms and t2 = 5.73 ms (tp= 8 ms). As ΩS/2π increases, the ZQ0, DQ2, RR1, and ZQ−1 conditions also play roles during the 0–tp time window. Among these events, a ZQ0, νr-independent event originating from the quadrupole-driven rf/dipolar recoupling effect arises for CQ ≠ 0, as predicted by Eq. (28). Thus, when ΩS/2π = 32 kHz, a time point is found at t = 2.04 ms for a ZQ0 HH transfer, in addition to the time point found at 6.67 ms for the DQ1—notice that only a single DQ1 time point appears in the 0–tp time window at |ΩS/2π| > 15 kHz. When ΩS/2π = 32 kHz, the ZQ0 condition found at t = 5.96 ms and the DQ1 time found at 1.33 ms are the mirror images of those arising when ΩS/2π = 32 kHz. At a further increased offset frequency, ΩS/2π = 60 kHz, both time points of the DQ1 condition disappear from the 0–tp time window, but ZQ0 and DQ2 conditions arise. Additionally, a RR1 condition is found at 4.03 ms, at which a signal inversion occurs due to the presence of the first-order quadrupolar interaction. The phenomena observed at ΩS/2π = 60 kHz and visible at 2.23 ms, 5.71 ms, and 3.97 ms for ZQ0, DQ2, and RR1 conditions, respectively, are then mirror imaged when ΩS/2π = 60 kHz.

For bigger Δν sweeps exceeding the νr value, for instance Δν= 110 kHz (Fig. 1(b)), additional ZQ0, DQ2, RR1, etc. conditions come into play within the 0–tp time window, in addition to the main DQ1 events that dominated the CP events at a smaller ΩS/2π. For instance, two ZQ0 time points that are mirror images of each other along tp/2 are visible at 0.60 ms and 7.40 ms with ΩS/2π = 0. Time points of various other CP conditions arise when ΩS/2π=±32 kHz and ±60 kHz for this Δν= 110 kHz case, as compared to the previous Δν= 60 kHz instance (Fig. 1(b)). Overall, the interaction between the various ZQ and DQ polarization transfer processes for these wide-sweep conditions—building magnetization with opposite spin temperatures and acting on a polarization that is being adiabatically swept over the course of the chirped pulse—is quite involved.

While the polarization transfers at time points that satisfy the DQ1 zero crossing at near on-resonance conditions are visible in the simulations, it is interesting to notice the differences arising if considering or disregarding the presence of sizable quadrupolar couplings. For the former case and ΩS = 0, DQ1-driven transfers are clearly visible at the two symmetric zero-crossing points. For a Cq = 168 kHz, however, the latter DQ1-driven transfer is attenuated. Notice that the sweep window width Δν incorporated in Fig. 1(a) is matched to the MAS spinning rate νr (= 60 kHz). Under this sweeping condition, a relatively small ν1S (<12 kHz) provides a single, optimal DQ1-driven transfer mode. Extending Δν beyond νr (Fig. 1(b)) provides multiple Sz inversions, creating the chance for undesirable RR inversion conditions due to the first-order quadrupolar interaction when ΩS 0. These cases are further analyzed in the Results section (vide infra).

The static-like Hamiltonian in Eq. (28) and the rotationally averaged Hamiltonians in Eq. (27) not only allow one to rationalize the behavior observed in numerical simulations but also to analytically propagate the spin density matrix throughout the whole course of the adiabatic frequency sweep. Starting from a ρ(t=0)=Iz=IzDQIzZQ state, the CP signals accrued along the spin locked S-channel at a time tp, given by Sz in the FM frame, is given as58 

Sz(tp)=trace{IzDQUDQ(tp)IzDQUDQ(tp)}trace{IzZQUZQ(tp)IzZQUZQ(tp)}
(29)

with

Uζ(tp)=exp(i0tpdt[HTζav(t)]),
(30)

where ζ stands for a DQ- or ZQ-coherence. As the Izζ and I+ζ terms in HTζav do not commute, Eq. (30) must, in principle, be evaluated numerically for an exact calculation. However, if the adiabaticity of the WURST pulse employed is sufficiently high and the dθs(t)/dt1 condition is satisfied, one can assume that perturbations in θS(t) are negligible, and hence, the angle between the S-spin magnetization and the effective field remains constant. In such a case, an approximate average Hamiltonian over the whole mixing time, HTζav(t)¯=1tp0tpHTζav(t)dt may be obtained, by integrating Izζ and I+ζ terms separately.30 In that case, the spins’ evolution operator, Eq. (30), can be approximated as

Uζ(tp)exp(itpHTζav(t)¯)=exp(iϕζIzζ)exp(iθζIyζ)exp(iψζIzζ)exp(iθζIyζ)exp(iϕζIzζ).
(31)

Eq. (31) represents a rotation in {ζ} subspace through an angle ψζ about an axis whose orientation is given with a polar angle set (θζ,ϕζ). Given these separate fictitious-spin-12 rotations, evaluation of Eq. (29) leads to

Sz(tp)=sin2(θZQ)sin2(12ωeffZQtp)sin2(θDQ)sin2(12ωeffDQtp),
(32)

where

ωeffζ=ψζ/tp=Γζ,
(33)
sin2(θζ)=Ck2Π12ω1S2Γζ,
(34)
Γζ=(Π0+Π1mω1I)2+2mkωr(Π0+Π1mω1I)+k2ωr2+Λk2Π12/ω1S2,
(35)
Π0=12Δω{(ΩS+Δω2)ω1S2+(ΩS+Δω2)2(ΩSΔω2)ω1S2+(ΩSΔω2)2},
(36)

and

Π1=ω1S22Δωln{(ΩS+Δω2)+ω1S2+(ΩS+Δω2)2(ΩSΔω2)+ω1S2+(ΩSΔω2)2}.
(37)

Under these simplifications, the behavior for a quadrupolar nucleus will be identical to that derived earlier for S = 1/2,34 except that the additional quadrupole-driven k = 0 ZQ-CP condition and the spin-dependent factors serve to scale the effects of the rf nutation rate.

All the frequency-swept CPMAS simulations that are described consider Hamiltonians in their appropriate rotating frames. Their propagation was carried out utilizing in-house written Matlab® (The Mathworks, Inc.) programs, where time evolutions were evaluated numerically by calculating the time propagation of density matrices using piecewise (2 μs) time increments. This temporal propagation accounted for variations in the rf waveforms’ amplitudes and phases (including the frequency sweeps), and for the MAS-driven rotational modulations of the quadrupolar, dipolar, and CS interactions. An isolated S = 1 (based on glycine’s 2H parameters treated so far) site was considered for examining the inversion, adiabatic level-crossing, and RR effects that could result from the application of the frequency swept pulses. The actual CP process was examined by considering an isolated I = 1/2/S = 1 spin pair and a suitable MAS-modulated dipolar Hamiltonian (dipolar coupling constant = 8 kHz). Powder averaging calculations for all interactions were accounted for by considering 538 different crystal orientations subtending the ZCW Euler angle set,61 assuming for simplicity that all of the dipolar, quadrupolar, and CS tensors are axially symmetric and coincident along the directions of their components of largest absolute magnitude.

Conventional CPMAS and BRAIN-CPMAS experiments were carried out on powdered samples of glycine-2,2-d2 and L-tyrosine-(phenyl-3,5-d2)⋅HCl. Samples were purchased from Sigma-Aldrich (St. Louis, MO) and used without further treatment except for the L-tyrosine-(phenyl-3,5-d2), which was dissolved in 1M hydrochloric acid and recrystallized by slow evaporation. About 3 mg of each sample was packed into a 1.3 mm Bruker rotor for obtaining MAS rates in the 40-65 kHz range. All experiments were carried out at room temperature in a 14.1 T magnet equipped with a Bruker Avance® console operating at 1H and 2H frequencies of 600.92 and 92.1 MHz, respectively. The swept rf pulse shapes were constructed by utilizing the shaped pulse tool of the Bruker Topspin® software. The WURST pulse employed in the BRAIN-CPMAS experiments utilized an amplitude-modulated profile ν1s(1cos40[πt/τp]) and a chirped frequency profile undergoing a linear sweep between 0 andtp. 2000 data points were employed to digitize these WURST pulse shapes. Suitable frequency sweep windows (Δν) and CP mixing times (tp) were sought over 40–400 kHz and 2–14 ms ranges, respectively. For νr= 60 kHz, optimal BRAIN-CPMAS matching parameters were found for Δν = νr = 60 kHz and tp = 8 ms. Optimal 2H and 1H rf power conditions were found experimentally by sweeping both rf channels independently. In accordance with Fig. 1, these parameters were usually found to satisfy the DQ1 condition νeS=νrν1H (where νeS includes the instantaneous offset frequency coming from the adiabatic sweep); for instance, when νr= 60 kHz, the optimal rf pulse powers were found at ν1S= 5 ± 15 kHz with ν1I= 42 − 47 kHz. The performance of the BRAIN-CPMAS experiment was evaluated within a Ωs/2π = ±120 kHz2H offset-frequency range. For comparison, conventional CPMAS NMR experiments were also carried out with independent rf pulse power optimizations, employing a ramped (90%-110%) spin-lock pulse62,63 along the 1H channel while simultaneously applying a rectangular spin-lock pulse on the 2H. The mixing time used in these CPMAS experiments ranged from 0.5 to 2 ms, also based on optimizations. All NMR spectra were acquired by co-adding 128 transients with recycle delays of ca. 4 s. The hard 90° 1H and 2H pulses were 2 μs for all experiments. SPINAL-6464 proton decoupling was used during the acquisition period, with a 100 kHz decoupling rf field.

The objective of our experiments was to verify some of the basic derivations of Sec. II, as well as to explore BRAIN-CPMAS features arising upon enhancing 2H NMR signals over a range of offsets at fast spinning conditions. Figure 2 shows the optimal 1H and 2H rf field strengthsdetermined experimentally for the BRAIN-CPMAS (a and b) and for ramped HH-CPMAS (c and d), using partially deuterated glycine as model. For the BRAIN-CPMAS case, an optimal 2H rf field ν1S was found at 8 ± 4 kHz (Fig. 2(b)), when ν1H was set at 47 ± 5 kHz and Δν = νr= 60 kHz. This corresponds to the DQ1 condition; other modes visible in the rf pulse sweep profiles, such as DQ2 (ν1H=116 ± 5 kHz; ν1S= 8 ± 4 kHz) and ZQ1 (ν1H= 78 ± 5 kHz; ν1S= 8 ± 4 kHz), are not as efficient as the DQ1 mode (Figs. 2(a) and 2(b)). For a ramped HH-CPMAS case incorporating a 90%-110% ramp on the 1H channel, optimized 2H and 1H rf fields were found at the DQ1 (ν1S = 11±4 kHz; ν1H = 49 ± 5 kHz) and ZQ1 (ν1S = 73 ± 4 kHz; ν1H = 130 ± 5 kHz) conditions. The y-axes of the various plots are scaled relative to the largest absolute magnitude, which is normalized to one.

FIG. 2.

CP-enhanced 2H signal intensities obtained by BRAIN-CPMAS ((a), (b)) and ramped HH-CPMAS (c,d) on a glycine-2,2-d2 powder spinning at νr= 60 kHz, upon varying the 1H ((a), (c)) and 2H ((b), (d)) rf fields, as controlled by the attenuation decibels used for controlling rf pulse power by the Bruker console (x-axes). The 2H rf field was set at ν1S= 8 kHz for panel (a) and ν1S= 17 kHz (c); the 1H rf field was set at ν1I= 47 kHz for panel (b) and ν1I= 130 kHz for panel (d). Swept pulse parameters employed for the BRAIN experiments were Δν=60 kHz, tp=8 ms; the HH experiment used a 2 ms long contact time. Rf fields at the local or global maxima are indicated, as derived from individual 90° pulse calibrations. Notice that the DQ1 and ZQ1 modes yield the maximum signal intensities for BRAIN-CPMAS and HH-CPMAS experiments, respectively; these are observed at ν1S= 8±4 kHz, ν1I=47 ± 5 kHz and ν1S=73 ± 4 kHz, ν1I= 130 ± 5 kHz, respectively.

FIG. 2.

CP-enhanced 2H signal intensities obtained by BRAIN-CPMAS ((a), (b)) and ramped HH-CPMAS (c,d) on a glycine-2,2-d2 powder spinning at νr= 60 kHz, upon varying the 1H ((a), (c)) and 2H ((b), (d)) rf fields, as controlled by the attenuation decibels used for controlling rf pulse power by the Bruker console (x-axes). The 2H rf field was set at ν1S= 8 kHz for panel (a) and ν1S= 17 kHz (c); the 1H rf field was set at ν1I= 47 kHz for panel (b) and ν1I= 130 kHz for panel (d). Swept pulse parameters employed for the BRAIN experiments were Δν=60 kHz, tp=8 ms; the HH experiment used a 2 ms long contact time. Rf fields at the local or global maxima are indicated, as derived from individual 90° pulse calibrations. Notice that the DQ1 and ZQ1 modes yield the maximum signal intensities for BRAIN-CPMAS and HH-CPMAS experiments, respectively; these are observed at ν1S= 8±4 kHz, ν1I=47 ± 5 kHz and ν1S=73 ± 4 kHz, ν1I= 130 ± 5 kHz, respectively.

Close modal

Figure 3 compares BRAIN-CPMAS, ramped HH-CPMAS, and direct-excitation 2H spectra measured for glycine-2,2-d2, which were acquired to evaluate the effectiveness of the various 1H-2H CPMAS methods. Spectra were acquired using MAS spinning rates of 40, 50, and 65 kHz; included for completion on the bottom panels are ideal 2H MAS line shapes of a 2H site simulated with CQ = 168 kHz. Both BRAIN-CPMAS and ramped HH-CPMAS NMR spectra were acquired after optimizations of ν1S and ν1H for each spinning rate according to the strategy introduced in Figure 2. The number shown beside each spectrum represents the relative integrated intensity of all the sideband manifolds as compared to the DQ1 mode spectrum arising from HH-CPMAS whose centerband possesses the strongest intensity for every MAS rate and whose height has been used to normalize the intensities of all the remaining spectra. Notice that although both DQ1 and ZQ1 HH-CPMAS modes are included in this comparison, only the DQ1 BRAIN-CPMAS condition is presented, as this provides the highest intensity and best fidelity line shape, while employing the weakest 2H rf pulse powers. Features to notice from these comparisons are as follows: (i) The centerband obtained from HH-CPMAS’ DQ1 mode is the highest at every νr, and although this does not hold when considering the overall spectral intensity if integrated among all sidebands plus centerband, its results resemble nearly isotropic spectra. (ii) The BRAIN-CPMAS DQ1 condition yields MAS sideband patterns at every spinning rate that are in excellent agreement with ideal simulations; the experimental conditions in each case feature relatively undemanding 1H and 2H rf fields (e.g., ν1S = 8 ± 4 kHz and ν1H = 47 ± 4 kHz for νr= 60 kHz). (iii) Although the ZQ1 mode of HH-CPMAS method also provides an MAS sideband pattern that matches well with simulations, it does so at the expense highrf pulse power requirements for both 1H and 2H channels (e.g., ν1S = 73 ± 4 kHz and ν1H = 130 ± 5 kHz for νr= 60 kHz).

FIG. 3.

BRAIN-CPMAS, ramped HH-CPMAS, and direct excitation MAS 2H spectra of glycine-2,2-d2 at spinning rates νr=40 (a), 50 (b), and 60 (c) kHz. Indicated for each rate are the CP modes involved, and (in red) the relative intensities of the integrated sideband manifolds. Except for the indicated 90° direct excitation panels, all spectra are shown with equally normalized vertical scales, for equal gains, and same number of scans. The bottom spectrum in each column is an ideal MAS line shape simulated for the corresponding spinning rates. Every experimental spectrum was obtained by independently optimizing 1H and 2H rf fields. For instance, the rf fields for the DQ1 BRAIN-CPMAS acquisition and for the ZQ1 of HH-CPMAS spectrum at νr= 60 kHz are as given in Figure 2; see text for additional details. All experimental spectra were obtained by co-adding 128 transients with a 4 s recycling delay.

FIG. 3.

BRAIN-CPMAS, ramped HH-CPMAS, and direct excitation MAS 2H spectra of glycine-2,2-d2 at spinning rates νr=40 (a), 50 (b), and 60 (c) kHz. Indicated for each rate are the CP modes involved, and (in red) the relative intensities of the integrated sideband manifolds. Except for the indicated 90° direct excitation panels, all spectra are shown with equally normalized vertical scales, for equal gains, and same number of scans. The bottom spectrum in each column is an ideal MAS line shape simulated for the corresponding spinning rates. Every experimental spectrum was obtained by independently optimizing 1H and 2H rf fields. For instance, the rf fields for the DQ1 BRAIN-CPMAS acquisition and for the ZQ1 of HH-CPMAS spectrum at νr= 60 kHz are as given in Figure 2; see text for additional details. All experimental spectra were obtained by co-adding 128 transients with a 4 s recycling delay.

Close modal

Figure 4 shows the offset dependence of the BRAIN-CPMAS method, as explored by collecting a series of spectra under DQ1 matching conditions when ΩS = 0, as a function of the 2H centerband’s offset vs. the width of the adiabatic sweep. Three different spinning rates (νr = 40, 55, and 60 kHz) were utilized, while setting Δν=νr in order to satisfy a “single MAS spinning-band sweep” case. Remarkably, for every νr, “modes” arise where peaks change their signs as the frequency is swept, with the width of each mode spanning ∼0.5νr, and the sign change influenced solely by the effective offset between the centerband and the center of the chirped pulse. All these offset dependencies are nearly symmetric with respect to the ΩS = 0 position. These periodic inversions cannot be entirely ascribed to RR phenomena, as no such effects are expected over the offset range νr2ΩS/2π+νr2 for the small values of ν1S, while the first inversions are observed at |ΩS/2π|νr4. The origin of these sign changes in the experimental offset-swept spectra can be heuristically understood by investigating the offset-swept profile of time-progressive ZQ- and DQ-CP matching conditions. For this purpose, Figure 5 illustrates the time-progressive HH matching conditions that are satisfied by the DQ±1, DQ±2, ZQ0, ZQ±1, and ZQ±2 BRAIN-CPMAS modes, during the course of an 8 ms long WURST-40 pulse. As derived in Eqs. (24)(28), these conditions are given as ν1IνeS(t)=0 and ν1IνeS(t)±kνr=0. Also shown in Fig. 5 are the positions where RR conditions will arise as a function of carrier offset ΩS/2π and of the contact time. Notice that for small offsets and for sweeps spanning a range Δν, two different lines for each CP mode are present due to the quadratic dependence of veS(t) on the sweep’s offset—even if only one of these promoted a significant IS polarization transfer, as discussed for Fig. 1. Figure 5(a) was derived assuming Δν=νr= 60 kHz, ν1S = 5 kHz, and ν1H = 47 kHz; the experimental offset-swept spectrum shown in Fig. 4, collected employing the same experimental parameters, is placed on the top for purposes of comparing the frequency positions of the sign inversions. From this comparison between experiments and the various potential CP transfer modes, it appears that the changes in the S-spin polarization arising at |Ωs/2π|νr/4,3νr/4, and 5νr/4, coincide with a change in the mode that is affecting the transfer—from DQ to ZQ, and vice versa. Indeed, all spectral sign changes coincide with the starting or ending of one of these HH transfer modes. This is reasonable, as these modes will polarize Sz in opposite directions—cf. Eqs. (29)–(32). Furthermore, it appears that when multiple potential HH modes can become active over the course of the contact time for a particular ΩS offset value, one of them usually dominates the sign of the resulting S-magnetization. Moreover, much weaker effects are here observed upon traversing a RR condition than in the spin-1/2 BRAIN CPMAS case, apparently due to the higher efficiency of the shielding anisotropy to enable these processes.28 

FIG. 4.

Influence of the effective isotropic 2H offset on the BRAIN-CPMAS performance for different spinning rates. Experimental CP-enhanced profiles of the 2H polarizations were obtained for glycine-2,2-d2 by varying the central carrier ΩS of the adiabatic sweeps involved, with individually optimized ν1S and ν1I values. The sweep frequency span Δν was always matched to the MAS rate νr. Each ΩS-swept CP-enhanced profile shown consists of an entire BRAIN-CPMAS 2H spectrum measured at a specific ΩS value, as illustrated by the inset figure (corresponding to a spectrum measured at ΩS/2π = −4 kHz with νr=Δν=60 kHz, ν1S = 5 kHz, and ν1H = 47 kHz). Offset increments of 1-2 kHz were used to record the entire sets of experiments. Notice the spectral sign inversions observed around the central on-resonance frequency position, at offsets within the range 0.25νrΩS/2π0.25νr.

FIG. 4.

Influence of the effective isotropic 2H offset on the BRAIN-CPMAS performance for different spinning rates. Experimental CP-enhanced profiles of the 2H polarizations were obtained for glycine-2,2-d2 by varying the central carrier ΩS of the adiabatic sweeps involved, with individually optimized ν1S and ν1I values. The sweep frequency span Δν was always matched to the MAS rate νr. Each ΩS-swept CP-enhanced profile shown consists of an entire BRAIN-CPMAS 2H spectrum measured at a specific ΩS value, as illustrated by the inset figure (corresponding to a spectrum measured at ΩS/2π = −4 kHz with νr=Δν=60 kHz, ν1S = 5 kHz, and ν1H = 47 kHz). Offset increments of 1-2 kHz were used to record the entire sets of experiments. Notice the spectral sign inversions observed around the central on-resonance frequency position, at offsets within the range 0.25νrΩS/2π0.25νr.

Close modal
FIG. 5.

Analysis of the experimentally observed periodic magnetization inversions observed using BRAIN-CPMAS on a glycine-2,2-d2 sample, and the time-progressive fulfillment of DQ1 (blue line), DQ2 (green line), ZQo (purple), ZQ−1 (red), and RR (black) matching conditions, within a HH process involving a linearly chirped pulse lasting for a duration tp. Plots are shown as a function of offset frequency ΩS/2π. Shown in (a) is the νr=Δν= 60 kHz case, and in (b) is the νr= 55 kHz and Δν=100 kHz case, both with ν1S=5 kHz and ν1I=47 kHz. Placed on the top of each 2D map is the experimental ΩS-dependent spectrum measured using identical parameters as in Fig. 4. The width of each CP matching condition line in the 2D map as projected along the ΩS axis corresponds to the sweep width Δν itself. Sign changes occur in the ΩS-swept profile at the beginning or ending position of the line indicating each CP matching condition. When νr=Δν (a), there exist no overlaps between different CP modes, maximizing the width of the central DQ1 mode that maintains the same sign over the sweep range ±0.5νr. When Δν > νr (b), the time-progressive CP matching condition lines on the 2D map overlap one another, and the range over which the DQ1 mode maintains a single, constant sign, becomes narrower.

FIG. 5.

Analysis of the experimentally observed periodic magnetization inversions observed using BRAIN-CPMAS on a glycine-2,2-d2 sample, and the time-progressive fulfillment of DQ1 (blue line), DQ2 (green line), ZQo (purple), ZQ−1 (red), and RR (black) matching conditions, within a HH process involving a linearly chirped pulse lasting for a duration tp. Plots are shown as a function of offset frequency ΩS/2π. Shown in (a) is the νr=Δν= 60 kHz case, and in (b) is the νr= 55 kHz and Δν=100 kHz case, both with ν1S=5 kHz and ν1I=47 kHz. Placed on the top of each 2D map is the experimental ΩS-dependent spectrum measured using identical parameters as in Fig. 4. The width of each CP matching condition line in the 2D map as projected along the ΩS axis corresponds to the sweep width Δν itself. Sign changes occur in the ΩS-swept profile at the beginning or ending position of the line indicating each CP matching condition. When νr=Δν (a), there exist no overlaps between different CP modes, maximizing the width of the central DQ1 mode that maintains the same sign over the sweep range ±0.5νr. When Δν > νr (b), the time-progressive CP matching condition lines on the 2D map overlap one another, and the range over which the DQ1 mode maintains a single, constant sign, becomes narrower.

Close modal

Figure 5(b) illustrates a second example of this offset dependence, this time involving the more complicated case Δν>νr, together with experimental BRAIN CPMAS data collected for νr=55 kHz, Δν=100 kHz, ν1S = 5 kHz, and ν1H = 47 kHz. As previously, the figure also indicates when the various HH matching modes are satisfied, as a function of the pulse’s sweep/contact time and as a function of the S-spin frequency offset ΩS. The fact that the sweep now exceeds the spinning speed means that many more multiple modes can be active over the course of one CP contact period; still, as before, sign polarization inversions occur again at offsets intervals of ˜0.5νr, which coincide with the beginning or ending positions of the lines satisfying the DQ1 or DQ2 conditions.

Fig. 6 shows a practical application of this polarization enhancement approach, with a 1H-2H BRAIN-CPMAS spectrum of L-tyrosine-(phenyl-3,5-d2)⋅HCl collected at a spinning rate νr=50 kHz, compared against a directly acquired trace measured using a 90° pulse. The relative signal intensity gain provided by BRAIN-CPMAS is in this case ca. 11 times, much more than that achieved for glycine-2,2-d2 (ca. 2×). The reason for this improved CP performance is probably the larger number of rigid hydrogen atom positions in L-tyrosine-(phenyl-3,5-d2)⋅HCl than that in glycine-2,2-d2. Glycine-2,2-d2, in its zwitterionic form, only has its three mobile ammonium protons available for transferring their polarization to the deuterons. By contrast, there are 5 rigid hydrogen atoms bonded to carbons which produce much stronger dipolar couplings with deuterons in L-tyrosine-(phenyl-3,5-d2)⋅HCl, in addition to mobile ammonium protons. Therefore, it is expected that this form of CPMAS will be of great value in studies of biomolecules and materials featuring unreceptive nuclides like 2H.

FIG. 6.

1H–2H BRAIN-CPMAS (a) and direct-excitation (b) 2H MAS NMR spectra of L-tyrosine-(phenyl-3,5-d2)⋅HCl at a spinning rate νr= 50 kHz. Both spectra were obtained by co-adding 4096 transient signals with a 3 s recycle delay. The parameters utilized for the BRAIN-CPMAS experiment were tp= 8 ms, Δν=νr= 50 kHz, ν1S= 9.2 kHz, and ν1I= 43 kHz.

FIG. 6.

1H–2H BRAIN-CPMAS (a) and direct-excitation (b) 2H MAS NMR spectra of L-tyrosine-(phenyl-3,5-d2)⋅HCl at a spinning rate νr= 50 kHz. Both spectra were obtained by co-adding 4096 transient signals with a 3 s recycle delay. The parameters utilized for the BRAIN-CPMAS experiment were tp= 8 ms, Δν=νr= 50 kHz, ν1S= 9.2 kHz, and ν1I= 43 kHz.

Close modal

Classical fixed-frequency CPMAS ramped schemes produce good enhancements in solid-state NMR spectra of spin-1 nuclei like 2H, provided that sufficiently strong rf-pulse powers of both 1H and 2H channels are applied. This enables one to bypass MAS-derived level crossing complications, but at the expense of demanding experimental conditions with the potential to damage probe hardware, and creating distortions in the MAS spinning sideband intensities away from their ideal line shapes, which make the accurate determination of quadrupolar and CSA parameters difficult. Herein, we introduce the use of BRAIN-CPMAS to deal with these issues in 1H–2H NMR experiments; the result is a robust method, which is easy to setup, utilizes low rf powers, and delivers undistorted MAS NMR line shapes with high gains in signal intensity compared to conventional methods. This latter feature probably reflects the larger range of coupling values with which a frequency-swept pulse can successfully fulfill the HH conditions for multiple crystallites in a powder, over a square-wave counterpart.

Despite these advantages, limitations and complications also arise in these experiments. One concern is the complex polarization behavior shown in Figs. 4 and 5, which involves multiple sign changes of the peaks as a function of carrier offset frequency, ΩS. From a practical standpoint, however, these are not too relevant, given the relatively narrow chemical shift range and γ-values characterizing 2H. These considerations may become more problematic if considering CP to other integer spin nuclides such as 14N (S = 1) or 10B (S = 3). Based on our repeated experiments, it appears that the optimal sweep width, Δν, for the WURST pulse scheme adopted in the BRAIN-CPMAS sequence is equal to the MAS spinning rate νr. Under such conditions, the BRAIN-CPMAS contact conditions become robust and are satisfied regardless of the values of the quadrupolar coupling constants. However, we have observed few competitive advantages of the 1H–2H BRAIN-CPMAS method over its conventional ramped HH-CPMAS method, when sample spinning happens at lower (e.g., 10-15 kHz) MAS rates.

Besides its practical utility, the occurrence of multiple concurrent time-dependent processes makes the spin physics of BRAIN-CPMAS remarkably interesting. Multiple new processes absent in static counterparts arise, including simultaneous ZQ and DQ HH transfer modes, quadrupolar-based rotary-resonance phenomena, and a static-like ZQ0 driven by a periodic modulation of HQ and a concomitant quadrupole-modulated rf-dipolar recoupling effect. Other potential phenomena, like laboratory frame quadrupolar-dipolar cross terms arising due from perturbation of the Zeeman quantization axes by the quadrupolar interaction, were found to be negligible within the present context (see the supplementary material). It is thus intriguing, both in terms of potential applications and the new underlying physics, what kind of phenomena will arise if such cross-polarization schemes are extended to quadrupolar nuclei with higher nuclear spin numbers. Such investigations are under way.

See supplementary material for (A) the effects of adiabatic pulses on the 2H MAS NMR of rotating powders, (B) the origin of the static-like ZQ0 CP conditions formed by the quadrupole-driven rf-dipolar recoupling interaction, and (C) the effects of laboratory-frame quadrupole-dipole cross-coupling effects on the CP of the spin-1 species.

We are grateful to Dr. Zhehong Gan (National High Magnetic Field Laboratory, NHMFL) for insightful discussions. This work was supported by the NHMFL through the National Science Foundation Cooperative Agreement (No. DMR-0084173) and by the State of Florida. L.F. acknowledges support from the Israel Science Foundation Grant No. 795/13, the Kimmel Institute for Magnetic Resonance (Weizmann Institute), and the generosity of the Perlman Family Foundation. R.W.S. thanks NSERC for funding this research in the form of a Discovery Grant and Discovery Accelerator Supplement, and is also grateful for an Early Researcher Award from the Ontario Ministry of Research and Innovation, and for a 50th Anniversary Golden Jubilee Chair from the University of Windsor.

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