Fundamental Aspects of Parahydrogen Enhanced Low-Field Nuclear Magnetic Resonance

We report new phenomena in low-field ${}^1\mathrm{H}$ nuclear magnetic resonance (NMR) spectroscopy using parahydrogen induced polarization (PHIP), enabling determination of chemical shift differences, $\delta \nu$, and the scalar coupling constant $J$. NMR experiments performed with thermal polarization in millitesla magnetic fields do not allow the determination of scalar coupling constants for homonuclear coupled spins in the inverse weak coupling regime ($\delta \nu <J$). We show here that low-field PHIP experiments in the inverse weak coupling regime enable the precise determination of $\delta \nu$ and $J$. Furthermore we experimentally prove that observed splittings are related to $\delta \nu$ in a nonlinear way. Naturally abundant ${}^{13}\mathrm{C}$ and ${}^{29}\mathrm{Si}$ isotopes lead to heteronuclear $J$-coupled ${}^1\mathrm{H}$-multiplet lines with amplitudes significantly enhanced compared to the amplitudes for thermally prepolarized spins. PHIP-enhanced NMR in the millitesla regime allows us to measure characteristic NMR parameters in a single scan using samples containing rare spins in natural abundance.

Figure 1

Fundamental differences between thermally and PHIP prepolarized NMR. (a) Simulated NMR spectra ($\pi /2$ excitation) of a thermally prepolarized $J$-coupled two-spin $I_1\mathrm{\text{−}}{I}_2$ system at different fields ($x=6$, 1, 0.15) and a three-spin system $S\mathrm{\text{−}}{I}_1\mathrm{\text{−}}{I}_2$ (fourth panel) using one heteronuclear coupling constant $J_{S\mathrm{\text{−}}I1}=J_{\mathrm{het}}=60\mathrm{Hz}$. (b) Same as (a) but with PHIP. (c) Ratio $R=|A_4|/|A_3|$ as a function of $x=\delta v/J$ for thermally prepolarized spins (dashed line), PHIP after $\pi /4$ excitation (dotted line), and $\pi /2$ excitation (solid line). The discontinuity for $\pi /4$ excitation is caused by a change in sign of the amplitude of the inner transition lines [25]. (d) Theoretical SNR of the $I_1\mathrm{\text{−}}{I}_2$ spin system as a function of $x$ for thermal prepolarization at 2 T (dashed line) and PHIP after $\pi /4$ excitation (dotted line), and $\pi /2$ excitation (solid line).

Figure 2

Experimental setup and procedure. (a) The nuclear spins of a liquid sample are either prepolarized by a 2 T Halbach magnet or by PHIP. After $\pi /2$ or $\pi /4$ excitation the free induction decay of the nuclear spins is acquired and processed. (b) Reaction of 1-(tert-butyldiphenylsilyl)-2-(ethoxy)ethyne ($\mathbf{1}$) to ($\mathbf{2}$) in the presence of a Rhodium (Rh) catalyst and 5 bar p-${\mathrm{H}}_2$. (c) Single scan ${}^1\mathrm{H}$ FID of $40\mu \mathrm{l}$ of ($\mathbf{2}$) after prepolarization at 2 T and $\pi /2$ excitation. (d) Fourier transformed spectrum of (c) measured at 500 kHz shows two broad lines.

Figure 3

${}^1\mathrm{H}$-low-field NMR of a parahydrogen polarized two-spin system. (a) PHIP ${}^1\mathrm{H}$ FID at 500 kHz of 1-(tert-butyldiphenylsilyl)-2-(ethoxy)ethen measured at 12 mT with $\pi /2$ excitation. (b) Spectrum of (a) ($\mathrm{\text{linewidth}}\sim 0.7\mathrm{Hz}$). (c) Simulated spectrum referring to (b). Red arrows indicate line positions of the $I_1\mathrm{\text{−}}{I}_2$ system, other lines correspond to the hetero- and homonuclear $J$-coupled systems $S\mathrm{\text{−}}{I}_1\mathrm{\text{−}}{I}_2$. (d) Same as (b) but at measured 166 kHz ${}^1\mathrm{H}$ frequency.

Figure 4

Chemical shift of $p\mathrm{\text{−}}{\mathrm{H}}_2$ polarized two- and three-spin systems. (a) Frequency difference $v_1-v_4$ measured at 166, 335, 500, and 666 kHz ${}^1\mathrm{H}$ frequency (squares). Axis on top denotes the corresponding values of $x$. Solid line represents $v_4-v_1=2{}^{3}J_{\mathrm{HaHb}}(1+0.25x^2)$ with ${}^{3}J_{\mathrm{HaHb}}=8.48\mathrm{Hz}$. (b) Single-scan ${}^1\mathrm{H}$-spectrum of $40\mu \mathrm{L}$ PHIP hyperpolarized 1-(tert-butyldiphenylsilyl)-2-ethoxyethen measured at 500 kHz with $\pi /4$ excitation.