## 1 Introduction
At LF magnetic fields, the J-coupling is usually much larger than any of the chemical shift differences; therefore, spectra acquired in the strong heteronuclear \(J\)-coupling regime are referred to as \(J\)-coupled spectrum/spectra or JCS. JCS may theoretically be observed for any system containing spin-active heteronuclei with an external magnetic field in the range \(0\leq B_{0}\leq B_{2}\)\({}^{\text{LF}}\) provided \(J>\Delta\
u\). Performing the NMR experiment in the strong heteronuclear \(J\)-coupling regime also leads to additional observable heteronuclear \(J\)-coupling resonances in the spectrum that are not observed in traditional high field NMR. For example, at LF, XH\({}_{2}\) and XH\({}_{3}\) (X is a spin \(\frac{1}{2}\) heteronucleus) will have four and eight resonances observable in the \({}^{1}\)H portion of the NMR spectrum, respectively. This is substantially different from high field NMR in which each \({}^{1}\)H spectrum is a simple doublet separatedby the \(J\)-coupling [14; 15]. When multiple heteronuclear \(J\)-couplings exist in a system, homonuclear \(J\)-couplings also become observable, provided the following condition is satisfied,  
\[|J_{IK}-J_{IL}|\geq J_{KL} \tag{2}\]  
Here, \(J_{IK}\) and \(J_{IL}\) are heteronuclear \(J\)-couplings and \(J_{KL}\) is a homonuclear \(J\)-coupling [16]. [PERSON] and co-workers [16] first demonstrated distinguishable homonuclear \(J\)-couplings in \({}^{13}\)C-1-ethanol and \({}^{13}\)C-2-ethanol in the strong heteronuclear \(J\)-coupling regime. A caveat to observing homonuclear \(J\)-coupling is that one of the heteronuclear \(J\)-couplings must be larger than \(\Delta\
u\) in order to break the magnetic equivalence between the homonuclei. At high field, this condition is not necessary as homonuclei with different chemical shifts are neither chemically nor magnetically equivalent. Correspondingly, complex JCS are observed for small molecules, thus providing a spectral fingerprint of the molecule. This is clearly demonstrated in Figure 1a,b (blue, top) for the fluorobenzene compounds previously discussed. At a field of 51.5 \(\mu\)T, complex, yet characteristic, splitting patterns are observed for both molecules. For example, the LF spectrum of 1,\(A\)-difluorobenzene (Figure 1, blue) shows more peaks in the LF spectrum than either of the high field spectra, indicating more chemical information for structural and quantitative analysis may be observable at LF compared to high field NMR. It should be noted here that the sensitivity of the LF spectrum is substantially less than the high field instruments, even under identical prepolarization and noise parameters, as the detectable NMR signal is proportional to the Larmor frequency. At LF, the Larmor frequency distribution for all NMR active nuclei is reduced from hundreds of MHz to several kHz. Therefore, simultaneous excitation and detection of \({}^{1}\)H and \({}^{19}\)F becomes feasible and has previously been demonstrated for 1,4-difluorobenzene and trifluoroethanol by several groups [21; 23; 25; 27; 28; 29; 30; 31]. Thus, at LF, the number of total experiments needed to acquire all relevant NMR active nuclei can be significantly reduced. This is particularly advantageous for determining the structure of an unknown compound because all nuclei with nonzero spin can be acquired in a single experiment. JCS also demonstrate narrow linewidths, on the order of 53 mHz, which correspond to the natural linewidth of the molecular group, indicating that \(B_{0}\) is exceptionally homogeneous over the course of the measurement [15]. Despite the extremely narrow linewidths, proton chemical shifts are not observed. For example, consider 1,2,\(A\)-trifluorobenzene where the three proton chemical shifts are within a range of \(\approx\)0.3 ppm at 51.5 \(\mu\)T. The chemical shift difference of 659 \(\mu\)Hz is typically smaller than the natural linewidths that can be observed at this frequency.