Adiabatic Passage through Level Anticrossings in Systems of Chemically Inequivalent Protons Incorporating Parahydrogen: Theory, Experiment, and Prospective Applications

Abstract

Level anticrossings (LACs) are ubiquitous in quantum systems and have been exploited for spin-order transfer in hyperpolarized nuclear magnetic resonance spectroscopy. This paper examines the manifestations of adiabatic passage through a specific type of LAC found in homonuclear systems of chemically inequivalent coupled protons incorporating parahydrogen (pH₂). Adiabatic passage through such a LAC is shown to elicit translation of the pH₂ spin order. As an example, with prospective applications in biomedicine, proton spin polarizations of at least 19.8 ± 2.6% on the methylene protons and 68.7 ± 0.5% on the vinylic protons of selectively deuterated allyl pyruvate ester are demonstrated experimentally. After ultrasonic spray injection of a precursor solution containing propargyl pyruvate and a dissolved Rh catalyst into a chamber pressurized with 99% para-enriched H₂, the products are collected and transported to a high magnetic field for NMR detection. The LAC-mediated hyperpolarization of the methylene protons is significant because of the stronger spin coupling to the pyruvate carbonyl ¹³C, setting up an ideal initial condition for subsequent coherence transfer by selective INEPT. Furthermore, the selective deuteration of the propargyl side arm increases the efficiency and polarization level. LAC-mediated translation of parahydrogen spin order completes the first step toward a new and highly efficient route for the ¹³C NMR signal enhancement of pyruvate via side-arm hydrogenation with parahydrogen.

Figure 1.

Rotating frame eigenvalue correlation diagrams for model Hamiltonians of types C1 and C3 as a function of the static magnetic field with ${\overline{J}}_{12}=25\text{ Hz}$ and ${\bar{J}}_{23}=5Hz$ (upper diagrams) or ${\bar{J}}_{23}=0Hz$ (lower diagrams). (a) C1, $\left\{{\delta }_1,{\delta }_2,{\delta }_3\right\}=\{0,+10,-10\}$ ppm. (b) C3, $\left\{{\delta }_1,{\delta }_2,{\delta }_3\right\}=\{+10,-\mathrm{10,0}\}$ ppm. The LAC is seen in the dashed red box. Orange, blue, and burgundy arrows indicate polarized single spin transitions of H¹, H², and H³, respectively. In the absence of a LAC, transitions of H³ remain unpolarized. The correlation diagram for C2 is analogous to C1. Curves were calculated using the SpinDynamica package in Wolfram’s Mathematica.

Figure 2.

(a) Block diagram of the ultrasonic spray injection reactor system interfaced to the flow NMR spectrometer. The tubing connecting the withdrawal syringe to the reaction chamber outlet, including the $60\mu \text{L}$ flow cell, is initially prefilled with solvent, and the reaction chamber is pressurized to 6 bars with 99% pH₂. The precursor solution is infused through an ultrasonic nozzle (3.5 W, 120 kHz) into the chamber at a flow rate of 5 mL/min. Products accumulate at the bottom of the funnel-shaped chamber and are drawn into the NMR probe at precisely controlled syringe pump flow rates. BPR = back-pressure regulator (5.17 bars). Further details are provided in the Supporting Information. (b) Numerical density matrix calculations of the spin polarization (neglecting spin relaxation) of individual protons in APd₂ as a function of the syringe pump withdrawal rate, estimated from the transport time ${\tau }_{\text{tr}}$ used in the simulation, the volume (0.33 mL), and the measured field profile of the Bruker 9.4 T Ultrashield magnet along the flow trajectory. Spin polarizations were computed using Spinach.

Figure 3.

(a, b) 400 MHz ¹H ALTADENA experimental spectra (in red) and numerically simulated ¹H ALTADENA spectra (in blue) of AP and APd, respectively, obtained by hydrogenation of 8 mM propargyl pyruvate precursors with pH₂ using 2 mM Rh catalyst in the 2.4 mT fringe field followed by transport into the flow probe at a flow rate of 3 mL/min for detection at 9.4 T using a 90°RF pulse. The spectra have been normalized to the H² peak. (c) 400 MHz ¹H ALTADENA spectra of AP (in blue) and APd (in red) obtained by hydrogenation as in panels (a) and (b) but with 40 mM propargyl pyruvate and 10 mM Rh catalyst. The H² peak in the spectrum of AP has been scaled to match the H² peak of the APd spectrum. (d) Thermally polarized spectra of the reaction product solutions of panel (c), acquired by accumulation of four transients and plotted on the same vertical axis as panel (c).

Scheme 1.

Hydrogenation of Selectively Deuterated Propargyl Esters with Parahydrogen

Scheme 2.

Molecular Embodiments under Study^{a a}AP = allyl 2-oxopropanoate-1-¹³C; APd = (Z)-allyl-3-d 2-oxopropanoate-1-¹³C; APd₂ = (Z)-allyl-1,3-d 2-oxopropanoate-1-¹³C; BPd₄ = 3-d₃−1-d-buten-2-yl; DMM = dimethyl maleate.