Line-widths in NMR spectra are often broad due to inhomogeneous broadening arising from susceptibility effects, sample heterogeneity, or imperfect static field homogeneity. The SHARPER (Sensitive, Homogeneous, And Resolved PEaks in Real time) method enables exceptionally narrow NMR resonances by suppressing dephasing arising from chemical shift evolution and magnetic field inhomogeneities during acquisition (Jones et al., 2017; Davy et al., 2022; Dickson et al., 2022). In its conventional form, however, SHARPER can refocus only one or two resonance frequencies, precluding simultaneous linewidth reduction across multiple chemically distinct spins. To achieve line-narrowing on multiple peaks, we have developed a method that we shall refer to as Selective Spin-Locking (SSL), which is based on our earlier work on “polychromatic decoupling” (Carnevale et al., 2012), where a number of short pulses with small flip angles are inserted in the intervals between the sampling points of the free induction decay (FID). Such short pulses are reminiscent of selective irradiation by Delays Alternating with Nutations for Tailored Excitation (DANTE) (Bodenhausen et al., 1976; Morris and Freeman, 1978), and Irradiation of Narrow Frequency Envelopes by Repeated Nutation and Orbiting (INFERNO) (Morris and Freeman, 1978), which are selective excitation methods that are widely used in NMR spectroscopy which use a comb of equidistant low-power RF pulses to achieve selective excitation of specific nuclear resonances. A suitable choice of the phases of these short pulses allows one to generate an irradiation spectrum where multiple peaks of interest are hit simultaneously. The combs of short pulses have the effect of spin-locking the magnetisation vectors belonging to the irradiated singlets or multiplets in their local rotating frames, thus preventing the phase dispersion due to the static field inhomogeneity and to J-couplings. In this case, the decay of the spin-locked transverse magnetisation will be determined by exp⁡{-t/T1ρ} rather than by exp⁡{-t/T2*} so that the narrowest possible line-width, ΔνminSSL, is determined by the dissipation of the selectively spin-locked magnetisation in the rotating frame (Redfield, 1955), i.e., ΔνminSSL=1/πT1ρ.

Many common one-dimensional (1D) experiments designed to probe molecular motions can benefit from Selective Spin-Locking (SSL). Inversion Recovery (IR) experiments provide longitudinal relaxation times (T1), enabling one to estimate rotational correlation times (τc), among other parameters. Carr-Purcell-Meiboom-Gill (CPMG) spin-echo experiments yield transverse relaxation times (T2), allowing for the assessment of chemical exchange effects and other line-broadening mechanisms, such as scalar relaxation of the second kind. Other measurements that use pulsed field gradients (PFG) in order to determine diffusion coefficients can also benefit from SSL. Beyond 1D experiments, SSL can be combined with the many two-dimensional (2D) experiments used in NMR. For many studies, multiplet structures are essentially a nuisance, making the use of SSL valuable.

The pulse sequence in Fig. 1 shows how mono- or polychromatic SSL during the acquisition of a Free Induction Decay (FID) is applied after a preparation period that can represent any arbitrary NMR experiment.

In SSL experiments, the preparation period usually includes a “hard” non-selective π/2 pulse, typically of 10 µs for a peak RF amplitude ω1/(2π)=25 kHz, followed by the SSL sequence comprising M short equidistant pulses applied during the acquisition block. The “soft” SSL pulses, separated by intervals τ=1.1 µs have a duration τp, which ranges typically from 1.5 to 7 µs, with a peak RF amplitude on the order of 2 kHz. As a result, the individual pulses have small nutation angles in the range 1°<β<10°. Each sequence of M short pulses τpm,n with m=1,2…M and n=1,2…N constitutes a “comb” in the manner of DANTE (Carnevale et al., 2012; Bodenhausen et al., 1976; Morris and Freeman, 1978). The phase of the π/2 pulse must be alternated between x and -x, to remove artefacts arising from RF breakthrough. The phases of SSL pulses are initially applied along y, so that they are shifted by 90° with respect to the π/2 pulse. The phase of the receiver must be alternated. These considerations entail that SSL experiments require a minimum of two scans.

To irradiate M chemical shifts fm simultaneously, one must apply a superposition of pulses m=1,2,…,M, incrementing their phases from one interval Δt to the next (n=1,2,…N) by phase-shifts ΔΦm,n=nΔφm, where the “phase roll” Δφm can be calculated by the following equation: 1Δφm=2πΔtΔfm where, as shown in Fig. 2, Δfm corresponds to the difference in frequency (in Hz) between the RF carrier frequency and the mth peak of interest. Using Δfm, the phase shift required to apply the mth short pulse, Δφm, to the mth peak of interest can be calculated using Eq. (1). For monochromatic SSL (Fig. 1a), the carrier frequency can be set to be on-resonance with the peak of interest so that Δφm=0°.

Signal acquisition occurs during a short time interval, designated by the delay “tRX” in the sequences, during which the receiver is activated in so-called oversampling mode. As illustrated in Fig. 1, the delay Δt remains the same for mono- or polychromatic sequences; the variable delay is “tRX” which becomes shorter for experiments with a larger number M of SSL pulses. The total number of points is observed after N repetitions of the SSL sequence (Fig. 1, bracketed section). Typically, N can be as large as 32 k or more. One can replace the intervals marked “tRX” in Fig. 1 by empty delays, in which case the line-narrowing method can be inserted in one or several evolution intervals of n-dimensional experiments.

The peak RF field amplitude of the short pulses is typically ω1/(2π)=2 kHz. The average RF field strength is proportional to the duty cycle: 2〈ω1/(2π)〉=ω1/(2π)τp/Δt

In our work, the duty cycle is typically τp/Δt=0.0125 so that 〈ω1/(2π)〉 =25 Hz in our examples, corresponding to ca. 2 mW for each of the M interleaved DANTE sequences, well below the maximum power that can safely be applied to commercial solution-state NMR probes. The average RF field amplitude should be comparable to 1/(πT2*) if one wishes to narrow a single inhomogeneously broadened line, and comparable to J if one wishes to collapse a multiplet at the same time.

The long-range J-couplings of the nine magnetically equivalent methyl protons in sodium trimethylsilylpropanesulfonate (DSS) to neighbouring protons are negligible, so that one can focus on the ability of SSL to overcome the effects of B0 inhomogeneity. A conventional proton spectrum was measured after a π/2 pulse, using a 5 mm Bruker NEO iProbe at 11.7 T (500 MHz for ¹H), where a full width at half-height (FWHH) of approximately 1 Hz was achieved by rough shimming (Fig. 3, blue line). By deliberately mis-setting the z1-gradient of Bruker's room temperature shim system, the line was broadened to ca. 40 Hz (Fig. 3, light blue line).

As mentioned before, the smallest line-width that can be achieved is determined by the transverse relaxation time in the rotating frame, T1ρ (Redfield, 1955). For the methyl protons of DSS, T1ρ=3.04 s at 298 K and 11.7 T, as measured by applying the INFERNO method (Morris and Freeman, 1978) with increasing durations between 1 ms and 40 s after an initial π/2 excitation pulse. Therefore, the theoretical minimum line-width that can be achieved in the case of these methyl protons is Δνmin=1/πT1ρ=0.105 Hz. The T1 of these protons is equal to 3.13 s; the fact that T1ρ and T1 are nearly equal shows that the extreme narrowing regime (ω0τc<1) is fulfilled to a good approximation.

The monochromatic SSL sequence (Fig. 1a) was applied to the middle of the inhomogeneously broadened resonance of the methyl groups of DSS, setting the duration of the short pulses τp=2.85 µs (nutation frequency =2.0 kHz for ¹H), applied within Δt=152 µs (spectral width 6579 Hz), to achieve an average RF amplitude 〈ω1/(2π)〉=37.5 Hz. The monochromatic SSL leads to a narrow peak (dark blue line in Fig. 3) with a Δν=0.23 Hz, about 2.2 times broader than the theoretical limit Δνmin = 0.105 Hz. This demonstrates that SSL with very weak RF fields can overcome severe inhomogeneous broadening. Monochromatic SSL was also applied to the well-shimmed proton signal (Fig. 3, blue line) with Δν=1.0 Hz. The resulting line-narrowed spectrum, not shown in Fig. 3, also led to Δν=0.23 Hz. The line-narrowed peaks resulting from both the inhomogeneously broadened peak and from the well-shimmed peak show the same line-widths illustrating the ability of SSL to surmount different degrees of broadening.

The line-narrowing by a factor of ca. 5 leads to a gain in signal-to-noise ratio (SNR) by a factor of ca. 5. Note the slight displacement of the line-narrowed peak (Fig. 3, dark blue line), with respect to the conventional 1D spectrum. This arises from problems in accurately determining the centre of gravity of the inhomogeneously broadened light blue line. To verify that the quantitative aspect of proton NMR is conserved when applying monochromatic SSL, we compared the integrals of the conventional 1D and line-narrowed spectra and found them to be equal.

Although phosphorus-31 resonances at high fields are broadened due to rapid relaxation driven by the chemical shift anisotropy, which cannot be eliminated by SSL, various other line-broadening mechanisms are amenable to line-narrowing. To assess this, we looked at the three ³¹P nuclei in Adenosine Triphosphate (ATP). In addition to the decoupling of homonuclear J(³¹P, ³¹P) interactions, a significant line-narrowing effect was observed (Fig. 11). In the conventional spectrum, the individual lines of the left-hand doublet have widths of about Δν=1.3 Hz, and lines of the right-hand triplet have Δν=2.3 Hz. The two doublets span widths of about 20 Hz while the triplet spans a width of ca. 40 Hz. By applying trichromatic SSL to all three chemical shifts, the multiplets are decoupled and their lines are narrowed to 0.7 Hz. One can notice a significant enhancement of the SNR for P_α compared to the other signals which arises from the decoupling of hetero-nuclear coupling with neighbouring protons which broaden this doublet. Note that the noise level is increased in the SSL experiments of Fig. 11 by a factor of ca. 2. The optimised parameters for this experiment were τp=3.8 µs, Δt=152 µs and 〈ω1/(2π)〉=35 Hz. The carrier frequency was set half-way between the outer multiplets at -16.9 ppm (black wavy arrow in Fig. 11). The irradiation frequencies were Δf1=-1239.9 Hz, Δf2=-1132.3 Hz and Δf3=+1239.9 Hz. The fact that the three peaks have nearly the same heights suggests that SSL yields quantitative intensities, i.e., that the peak heights are proportional to the numbers of spins and hence to the concentrations.

The transverse relaxation time in the rotating frame of the central ³¹P nucleus was measured by the INFERNO method (Morris and Freeman, 1978) to be T1ρ=0.357 s, so that the narrowest theoretically possible line-width achievable by SSL for these nuclei is Δνmin=1/πT1ρ=0.89 Hz. The experimental line-widths were even narrower since a linewidth Δν=0.7 Hz is measured at all three sites.

By applying mono- or polychromatic SSL to selected singlets or multiplets in high-resolution NMR spectra of ¹H, ¹⁹F, ³¹P and other nuclei, one can collapse both homo- and heteronuclear scalar couplings, eliminate inhomogeneous broadening, and thus obtain very narrow signals. The decay of the spin-locked transverse magnetisation is in principle limited by exp⁡{-t/T1ρ} rather than by exp⁡{-t/T2*}, so that the line-widths upon Fourier transformation can approach the theoretical limit Δνmin=1/πT1ρ rather than the inhomogeneous width 1/πT2*.

The reduction of line-widths and decoupling of multiplets leads to an increase in peak heights, ranging from factors 4 to 40 in the examples discussed in this work. This should make it possible to reduce the detection level, i.e., the minimum concentration that is required to detect the NMR signals, provided the identity of the molecules under investigation and their chemical shifts are known. This may be of interest for metabolomic studies.

The SSL method should also be useful for special probes where several samples can be studied in parallel, where the static homogeneity and hence the line-widths may suffer from imperfect shimming (Van Dyck et al., 2026).

Applications of SSL are not limited to small molecules. The line-widths in proton spectra of macromolecules at high fields are usually dominated by homogeneous T2 relaxation, and T1ρ is usually close to T2 rather than T1 as in small molecules, so that line-narrowing by SSL is not likely to be very effective. However, decoupling of homo- and heteronuclear scalar interactions (Cavanagh et al., 2007) such as J(¹H, ¹H), J(¹³C, ¹H) and J(¹⁵N, ¹H) may be useful in macromolecules. Furthermore, the lines can be broadened by chemical exchange, in particular by exchange between major and minor conformers, and the effects of SSL should be investigated empirically.

All magnetic resonance imaging (MRI) methods achieve spatial resolution by using pulsed field gradients, including “frequency encoding” during signal observation. Spin-locking should obviously not be applied during signal observation (Mosher and Smith, 1990). However, in a sub-class of MRI experiments that have come to be known as magnetic resonance spectroscopy (MRS), where the signals are observed in the absence of gradients to determine the chemical shifts, spin-locking can be applied during signal observation. This can be used inter alia to determine the concentrations of various constituents or metabolites in the brains of rodents and humans, as well as phosphorylated molecules like ATP (Chung et al., 2024), phosphocreatine, etc., in various organs. At high fields, the line-widths in phosphorus-31 spectra are usually dominated by homogeneous T2 relaxation, particularly if the chemical shift anisotropy (CSA) is the dominant line-broadening mechanism. A priori, such line-widths are not amenable to narrowing by SSL. However, we have shown that significant line-narrowing can be achieved in addition to decoupling of J(³¹P, ³¹P) interactions. Furthermore, the line-widths of ¹H, ³¹P or ¹³C resonances in vivo are broadened by discontinuities in tissues, variations in susceptibility, and motions due to arterial or respiratory effects. Such static or dynamic line-broadening effects should be largely mitigated by mono- or polychromatic SSL during signal acquisition.

In Magic Angle Spinning (MAS) solid-state NMR, the line-widths in proton spectra are usually dominated by residual dipole-dipole interactions (Chávez et al., 2021) that cannot be suppressed by SSL. However, the line-widths in MAS spectra of ¹³C and other dilute nuclei are often broadened by disorder in amorphous or polycrystalline materials. Their line-widths could therefore be narrowed by SSL, in as far as the modulations due to sample spinning do not interfere with the short pulses used in SSL. Synchronisation of these pulses with the rotor period can alleviate such problems (Caravatti et al., 1983).

In solids spinning at the magic angle, half-integer spins like ⁷Li and ²³Na feature central transitions between the m=±1/2 levels that are broadened by inhomogeneous second-order quadrupole interactions. Such line-shapes could be collapsed to their average positions by applying SSL near the frequency of their first moment. A superposition of M overlapping sites (as occurs in battery materials) could be separated by a two-dimensional method where M-chromatic SSL is applied in the detection period but not in the evolution interval.

The SSL method might be applicable to other two-level systems such as occur in optical spectroscopy, although broadening by Doppler effects might not be amenable to line-narrowing.

A wide range of methods collectively known as “pure shift spectroscopy” have been derived from two-dimensional J-spectroscopy (Aguilar et al., 2010; Castañar and Parella, 2015). These ingenious methods allow one to collapse multiplets due to scalar couplings. While the final result bears similarities to mono- or polychromatic SSL, in particular since decoupling is accompanied by line-narrowing (in principle limited only by the homogeneous line-width 1/πT2 for pure shift spectroscopy), the mechanisms are quite distinct, and mono- or poly-chromatic spin-locking is more efficient in terms of signal-to-noise per unit time. Similar considerations can be applied to the SHARPER method (Jones et al., 2017; Davy et al., 2022; Dickson et al., 2022). By contrast, the DREAMTIME method (Jenne et al., 2022) uses doubly selective irradiation tailored for known compounds.