Error compensation without a time penalty: robust spin-lock-induced crossing in solution NMR

TL;DR

The paper tackles rf-amplitude sensitivity in spin-lock-induced crossing (SLIC) for generating long-lived singlet order in solution NMR of strongly coupled spin pairs. It introduces compensated-SLIC (cSLIC), a repetition-based scheme using two amplitude levels to counter rf errors without increasing total sequence duration. Through simulations and experiments on [1-13C]-fumarate, cSLIC outperforms SLIC and adSLIC in robustness and transfer efficiency, including contexts relevant to parahydrogen-enhanced NMR. The results indicate cSLIC is practical for a wide range of singlet-state manipulations and can be enhanced via supercycling, with implications for PHIP and long-lived spin-state experiments.

Abstract

A modification of the widely-used spin-lock-induced crossing (SLIC) procedure is proposed for the solution nuclear magnetic resonance (NMR) of strongly coupled nuclear spin systems, including singlet NMR and parahydrogen-enhanced hyperpolarised NMR experiments. The compensated-SLIC (cSLIC) scheme uses a repetitive sequence where the repeated element employs two different radiofrequency field amplitudes. Effective compensation for deviations in the radiofrequency field amplitude is achieved without increasing the overall duration of the SLIC sequence. The advantageous properties of cSLIC are demonstrated by numerical simulations and by representative experiments.

Figures (5)

• Figure 1: Contour plots for the transformation amplitude of transverse magnetisation into singlet order, defined by $\langle I_{x}\rightarrow Q_{\rm SO}\rangle={\rm Tr}\{Q_{\rm SO}U I_{x}U^{\dagger}\}/{\rm Tr}\{Q_{\rm SO}Q_{\rm SO}\}$, where $U$ represents the propagator for a specific SLIC element. Results are shown for (a) SLIC, (b) adSLIC, (c) cSLIC against resonance offset (horizontal axis) and deviations in the rf amplitude (vertical axis). All simulations are performed for a two-spin system with $J = 15$ Hz and $\Delta = 1.9$ Hz. The total durations of the elements $T$ are: 375 ms (SLIC and cSLIC) and 1560 ms (adSLIC) respectively. For cSLIC, the repetition number is $n=6$ and $\alpha=0.99$. For adSLIC, the rf-amplitude modulation is given by Equation \ref{['eq:AdPulseShape']} with $\Delta_{\rm{max}} = 0.5$ and $\xi = 0.9$.
• Figure 2: Pulse sequence schematic for cSLIC. (a) The basic element consists of a concatenation of two weak pulses separated by a strong pulse. The weak pulses are of amplitude $\omega^{\rm weak}_{\rm nut}=\omega_{J}$, duration $\tau_{w}$ and produce a net rotation of $(\alpha \pi)$ along the $x$-axis. The strong central pulse is of amplitude $\omega^{\rm strong}_{\rm nut}>\omega_{J}$, duration $\tau_{s}$ and produces a net rotation of $(\alpha 2\pi)$ along the $-x$-axis. The parameter $\tfrac{1}{2}\leq\alpha\lesssim1$ is defined by equation \ref{['eq:alpha factor']}. The pulse durations are constrained by $2\tau_{w}+\tau_{s}=\tau_{J}$. (b) cSLIC-based singlet excitation consists of $n=\lfloor J/(\sqrt2\Delta)\rceil$ repetitions of the basic element shown in (a).
• Figure 3: (a) Pulse sequence for heteronuclear polarization transfer from $\mathrm{^1H}$ to $\mathrm{^{13}C}$, through an intermediate $\mathrm{^1H}$ singlet state, in systems of two $\mathrm{^1H}$ nuclei and one $\mathrm{^{13}C}$ nucleus, as in figure \ref{['fig:FumarateSpectra']}. An initial $90^{\circ}_{y}$ pulse generates transverse proton magnetisation, followed by a singlet preparation element using one of the SLIC variants shown in (b). After singlet-order preparation, a filter element removes any spurious density-operator terms. A second SLIC variant transforms singlet order into heteronuclear magnetisation. (b) SLIC elements used in this work. (i) The basic SLIC element consists of a single $x$ pulse with amplitude $\omega_{J}$. (ii) Adiabatic SLIC consists of an amplitude-modulated $x$ pulse following the functional form given in Equation \ref{['eq:AdPulseShape']}. (iii) The cSLIC element follows the procedure outlined in fig. \ref{['fig:cSLIC']}.
• Figure 4: $\mathrm{^{13}C}$ spectra of [1-$^{13}$C]-fumarate dissolved in $\mathrm{D_2 O}$. Inset shows the chemical structure and the J-coupling parameters. Fourier transform (green) of the free-induction decay generated by a single 90$^\circ$$\mathrm{^{13}C}$ pulse applied to a sample in thermal equilibrium. $\mathrm{^{13}C}$ spectra for SLIC (pink), adSLIC (blue), and cSLIC (black) were obtained using the pulse sequence strategy shown in Figure \ref{['fig:FumaratePulseSequences']}. 0.5 Hz of line broadening was applied to all spectra. The pulse sequence parameters are summarised in the experimental details.
• Figure 5: Experimental $\mathrm{^{13}C}$ signal amplitude for singlet-mediated heteronuclear polarisation transfer in [1-$^{13}$C]-fumarate, as a function of the fractional $\mathrm{^{13}C}$ nutation amplitude mismatch, defined in Equation \ref{['eq:FractionalrfDeviation']}. Signal amplitudes have been normalised against the amplitude of the central peak in the $90$$^\circ$ spectrum.