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High-Field NMR Characterization and Indirect $J$-Spectroscopy of a Nuclear Spin Chain [U-$^{13}$C,$^{15}$N]-butyronitrile

Alexey Kiryutin, Ivan Zhukov, Danil Markelov, Erik Van Dyke, Alexandra Yurkovskaya, Danila Barskiy

Abstract

One-dimensional chains of coupled spins are minimal models of strongly correlated quantum matter, and have been proposed as wires for transporting quantum information. In liquids, rapid molecular tumbling averages anisotropic dipolar couplings and leaves effective isotropic scalar $J$-coupling Hamiltonians. At zero- to ultralow-field (ZULF) conditions, differences in frequency between nuclear spins of different types are quenched and the internal Hamiltonians can be closely approximated by an isotropic Heisenberg model. In this work, we present [U-$^{13}$C,$^{15}$N]-butyronitrile as a chemically engineered nuclear spin chain whose full spin-spin coupling network can be determined and validated by combining high-field NMR detection with evolution at ultralow fields. Starting from high-field (16.4 T) NMR spectra of $^1$H, $^{13}$C, and $^{15}$N nuclei, we extract all relevant $J$-couplings within a 12-spin network (four $^{13}$C, one $^{15}$N, and seven $^1$H). We then employ a mechanical field-cycling apparatus to prepolarize the spins at high field, shuttle them into a magnetically shielded region for evolution at <50 nT, and detect signals after returning to high field. Fourier analysis of the ultralow-field evolution yields indirect $J$-spectra that are conceptually analogous to ZULF NMR spectra but measured by a high-field NMR spectrometer. We observe clear spectral features at $J$, 1.5$J$, and 2$J$, in good agreement with simulations using the extracted coupling matrix. Finally, we demonstrate 2D experiments that correlate high-field chemical shifts and, thus, fully map interactions within the molecular spin chain. Our results establish [U-$^{13}$C,$^{15}$N]-butyronitrile as an extremely well-characterized spin chain model system and provide a quantitative Hamiltonian benchmark for future hyperpolarization and quantum-control studies.

High-Field NMR Characterization and Indirect $J$-Spectroscopy of a Nuclear Spin Chain [U-$^{13}$C,$^{15}$N]-butyronitrile

Abstract

One-dimensional chains of coupled spins are minimal models of strongly correlated quantum matter, and have been proposed as wires for transporting quantum information. In liquids, rapid molecular tumbling averages anisotropic dipolar couplings and leaves effective isotropic scalar -coupling Hamiltonians. At zero- to ultralow-field (ZULF) conditions, differences in frequency between nuclear spins of different types are quenched and the internal Hamiltonians can be closely approximated by an isotropic Heisenberg model. In this work, we present [U-C,N]-butyronitrile as a chemically engineered nuclear spin chain whose full spin-spin coupling network can be determined and validated by combining high-field NMR detection with evolution at ultralow fields. Starting from high-field (16.4 T) NMR spectra of H, C, and N nuclei, we extract all relevant -couplings within a 12-spin network (four C, one N, and seven H). We then employ a mechanical field-cycling apparatus to prepolarize the spins at high field, shuttle them into a magnetically shielded region for evolution at <50 nT, and detect signals after returning to high field. Fourier analysis of the ultralow-field evolution yields indirect -spectra that are conceptually analogous to ZULF NMR spectra but measured by a high-field NMR spectrometer. We observe clear spectral features at , 1.5, and 2, in good agreement with simulations using the extracted coupling matrix. Finally, we demonstrate 2D experiments that correlate high-field chemical shifts and, thus, fully map interactions within the molecular spin chain. Our results establish [U-C,N]-butyronitrile as an extremely well-characterized spin chain model system and provide a quantitative Hamiltonian benchmark for future hyperpolarization and quantum-control studies.
Paper Structure (13 sections, 1 equation, 4 figures, 1 table)

This paper contains 13 sections, 1 equation, 4 figures, 1 table.

Table of Contents

  1. Introduction
  2. Methods
  3. Results and Discussion
  4. Conclusions

Figures (4)

  • Figure 1: (A) Molecular structure of [U-$^{13}$C,$^{15}$N]-butyronitrile and a magnetic field cycling protocol used in this work. The protocol consists of the following stages: prepolarization at 9.4 T, adiabatic shuttling to 50 $\mu$T, sudden (100 $\mu$s) switch to ultralow field ($<$50 nT) for a variable time $\tau$, and subsequent adiabatic return to the high field for the free induction decay (FID) detection. At each stage, different nuclear spins are entangled, as shown by the gray-shaded areas: e.g., only equivalent $^{1}$H nuclei are entangled at 9.4 T, whereas all nuclei are entangled at 50 nT. (B) Selected regions of high-field (9.4 T) $^1$H, $^{13}$C, and $^{15}$N NMR spectra with and without decoupling.
  • Figure 2: Experimental (colored) and simulated (black) $^1$H, $^{13}$C, and $^{15}$N NMR spectra of [U-$^{13}$C,$^{15}$N]-butyronitrile at 16.4 T fitted with ANATOLIA ANATOLIA. Insets show residuals (experiment minus simulation).
  • Figure 3: (Left) Evolution of NMR signal intensities from different nuclei as a function of evolution time at 50 nT. (Right) Indirectly measured $J$-spectra obtained by Fourier transformation of the signals on the left. Vertical gray boxes indicate approximate positions of $J$-, $1.5J$-, and 2$J$-peaks, where $J$ is the most relevant heteronuclear single-bond $J$-coupling. As in conventional ZULF NMR spectra, features at $J$ and $2J$ are observed for $^{13}$CH$_3$ group (subplots 8 and 5), and $3J/2$ peak is observed for $^{13}$CH$_2$ groups (subplots 3+4, 6 and 7).
  • Figure 4: (Left) $^{15}$N-$^{1}$H-ZULF-TOCSY NMR spectra, taken with (red) and without (green) 180-degree refocusing pulse at $^{13}$C radio-frequency channel in the middle of evolution period $t_1$. Experimental parameters: relaxation delay - 6 s, transfer time (one direction) - 479 ms, mixing time at ZULF conditions $t_{\rm mix} =$ 50 ms, ZULF evolution field $\lesssim$-50 nT, TD($^{1}$H) = 128, TD($^{15}$N) = 2048, States-TPPI acquisition mode. Processing parameters: pure cosine-squared window function in both dimensions, SI($^{1}$H) = 512, SI($^{15}$N) = 4096. (Right) $^{13}$C-$^{1}$H-ZULF-TOCSY NMR spectrum. Experimental parameters: relaxation delay - 6 s, transfer time (one direction) - 479 ms, mixing time at ZULF conditions $t_{\rm mix} =$ 10 ms, ZULF evolution field - $\lesssim$50 nT, TD($^{1}$H) = 256, TD($^{13}$C) = 32768, States-TPPI acquisition mode. Processing parameters: pure cosine-squared window function in both dimensions, SI($^{1}$H) = 512, SI($^{13}$C) = 4096.