Surprising absence of strong homonuclear coupling at low magnetic field explored by two-field nuclear magnetic resonance spectroscopy

Abstract

Strong coupling of nuclear spins, which is achieved when their scalar coupling $2\pi J$ is greater than or comparable to the difference $\Delta \omega$ in their Larmor precession frequencies in an external magnetic field, gives rise to efficient coherent longitudinal polarization transfer. The strong coupling regime can be achieved when the external magnetic field is sufficiently low, as $\Delta \omega$ is reduced proportional to the field strength. In the present work, however, we demonstrate that in heteronuclear spin systems these simple arguments may not hold, since heteronuclear spin-spin interactions alter the $\Delta \omega$ value. The experimental method that we use is two-field nuclear magnetic resonance (NMR), exploiting sample shuttling between the high field, at which NMR spectra are acquired, and the low field, where strong couplings are expected and at which NMR pulses can be applied to affect the spin dynamics. By using this technique, we generate zero-quantum spin coherences by means of a nonadiabatic passage through a level anticrossing and study their evolution at the low field. Such zero-quantum coherences mediate the polarization transfer under strong coupling conditions. Experiments performed with a ${}^{13}C$-labeled amino acid clearly show that the coherent polarization transfer at the low field is pronounced in the ${}^{13}C$ spin subsystem under proton decoupling. However, in the absence of proton decoupling, polarization transfer by coherent processes is dramatically reduced, demonstrating that heteronuclear spin-spin interactions suppress the strong coupling regime, even when the external field is low. A theoretical model is presented, which can model the reported experimental results.

Figure 1

The structure of ${}^{\mathrm{13}}\mathrm{C}$ , ${}^{\mathrm{15}}\mathrm{N}$ L-leucine (a) and 150.9 MHz ${}^{\mathrm{13}}\mathrm{C}$ –NMR spectrum (b) under broadband ${}^{\mathrm{1}}\mathrm{H}$ decoupling. The signal of each carbon nucleus is also shown separately (c–f). The multiplet structure in the spectrum is due to ${}^{\mathrm{13}}\mathrm{C}{-}^{\mathrm{13}}\mathrm{C}$ and ${}^{\mathrm{13}}\mathrm{C}{-}^{\mathrm{15}}\mathrm{N}$ scalar interactions.

Figure 2

Experimental protocols of field-cycling NMR experiments without ${}^{\mathrm{1}}\mathrm{H}$ decoupling at the low field (a) and with 24 kHz WALTZ-64 ${}^{\mathrm{1}}\mathrm{H}$ decoupling at the low field (b). Details of the experiments are as follows. A 6.2 kHz WALTZ-64 composite pulse decoupling on the proton channel was applied at $B_{\mathrm{HF}}$ during 100 ms prior to a selective 180 ${}^{\circ }$ pulse in order to enhance ${}^{\mathrm{13}}\mathrm{C}$ polarization by the nuclear Overhauser effect. The sample shuttle transfer times, $t_{\mathrm{1}}$ and $t_{\mathrm{2}}$ , were 107 and 94 ms, respectively. Selective inversion was performed with a RE-BURP pulse (Geen and Freeman, 1991), with a duration of 46.4 ms, at the ${\mathrm{C}}^{\mathit{\delta }\mathrm{2}}$ resonant frequency covering ca. 100 Hz bandwidth. The delay $\mathit{\tau }$ at the low field was incremented with a 1 ms step. After a sample transfer to the high field, a hard 90 ${}^{\circ }$ pulse-generated ${}^{\mathrm{13}}\mathrm{C}$ transverse magnetization free induction decay (FID) acquisition was done during 1.56 s under 6.2 kHz WALTZ-64 proton decoupling.

Figure 3

Polarization transfer between two strongly coupled nuclei (a) in the absence and (b) in the presence of a heteronucleus. Here, we present the time dependence of $\langle I_{\mathrm{1}z}\rangle$ (black solid lines) and $\langle I_{\mathrm{2}z}\rangle$ (red dashed lines) normalized to the initial value of $\langle I_{\mathrm{1}z}\rangle$ . The density operator at time $t=\mathrm{0}$ is ${\mathit{\sigma }}_{\mathrm{0}}={\widehat{I}}_{\mathrm{1}z}$ . The parameters of the simulation were $\mathrm{\Delta }\mathit{\omega }/\mathrm{2}\mathit{\pi }=\mathrm{10}$  Hz and $J_{\mathrm{12}}=\mathrm{30}$  Hz and (a)  $\mathrm{\Delta }J=\mathrm{0}$  Hz and (b)  $\mathrm{\Delta }J=\mathrm{100}$  Hz.

Figure 4

(a) Energy levels of the $\left\{{\mathrm{C}}^{\mathit{\gamma }},{\mathrm{C}}^{\mathit{\delta }\mathrm{1}},{\mathrm{C}}^{\mathit{\delta }\mathrm{2}}\right\}$ spin system at variable magnetic field strength in the absence of scalar coupling with protons. Levels are assigned at the high field, where the spin system is weakly coupled. (b) Energy levels, corresponding to the $\mathit{\alpha }\mathit{\alpha }\mathit{\beta }$ and $\mathit{\alpha }\mathit{\beta }\mathit{\alpha }$ states at the high field, have a level anticrossing (LAC) at 1.1 T, which is responsible for generation of the zero-quantum coherences. To visualize the energy levels better, in (b) we subtracted the large Zeeman energy from the actual energy to show the energy difference. The calculation is done using the parameters listed in Table 1 and neglecting carbon–proton couplings.

Figure 5

Observed $\mathit{\tau }$ dependence of the polarizations of carbon-13 nuclei, ${\mathrm{C}}^{\mathit{\gamma }}$ , ${\mathrm{C}}^{\mathit{\delta }\mathrm{1}}$ and ${\mathrm{C}}^{\mathit{\delta }\mathrm{2}}$ , measured (a) without ${}^{\mathrm{1}}\mathrm{H}$ decoupling and (b) with ${}^{\mathrm{1}}\mathrm{H}$ decoupling. The NMR intensities are plotted in the percent of the intensities of the NMR signals in the 150.9 MHz ${}^{\mathrm{13}}\mathrm{C}$ spectra (i.e., at 14.1 T) at thermal equilibrium.

Figure 6

Calculated $\mathit{\tau }$ dependence of polarization (lines) overlaid with the observed time traces (points) obtained (a) without ${}^{\mathrm{1}}\mathrm{H}$ decoupling and (b) with ${}^{\mathrm{1}}\mathrm{H}$ decoupling. The slowly relaxing background (compare with the data shown in Fig. 5) has been subtracted from the time traces to enable comparison between theory and simulations. Observed NMR intensities are normalized to intensities in 150.9 MHz (14.1 T) ${}^{\mathrm{13}}\mathrm{C}$ spectra at thermal equilibrium. We use the subtraction procedure because relaxation effects were not taken into account in the calculation; consequently, we are unable to consider polarization decay due to relaxation at $B_{\mathrm{LF}}$ and during the field variation. To enable a comparison of the experiment and calculation results, the amplitude of oscillations in polarization transfer traces were scaled with the same factor; then, the starting polarization values were adjusted individually to give best agreement with the experimental data.