## 1 Introduction
For 1,4-difluorobenzene, which only has a single proton environment due to the chemical equivalence of the hydrogen environments, the increased spectral breadth and line broadening does not interfere with a structural interpretation. However, unsymmetrical 1,2,4-trifluorobenzene contains three distinct proton environments (Figure 1b, black). For this compound, all three chemical shifts are separated by less than 0.3 ppm and contain complex multiplets from the significant overlap of several \(J\)-couplings [12] observed between two of the three environments at 9.4 T (Figure 1b, black). The resolution degrades considerably (spectral lines broaden) as the magnetic field is lowered to 1.43 T, and identification of any specific proton environment is, at best, challenging due to the overlap of the chemical shifts, \(J\)-couplings, and additional broadening of the resonances. The overlap issue may be partially alleviated by various NMR tools such as heteronuclear decoupling, pure shift NMR, and multidimensional pulse sequences [1,13]. However, employing decoupling reduces or eliminates \(J\)-coupling information. Thus, there are still outstanding issues using permanent magnet benchtop systems for chemical analysis, particularly if the chemical shifts and \(J\)-couplings cause significant overlap between environments. Fortunately, other viable options for chemical analysis exist for compounds containing heteronuclear \(J\)-couplings since the NMR experiment can be performed at magnetic fields that satisfy the strong heteronuclear \(J\)-coupling conditions [14; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26; 27; 28; 29; 30; 31; 32; 33; 34; 35; 36; 37; 38; 39; 40; 41]. The strong heteronuclear \(J\)-coupling condition is met when the Larmor frequency difference between heteronuclei, here hydrogen and fluorine, is on the order of the \(J\)-coupling values (Figure 1a,b blue). The range of magnetic fields that satisfy this condition is known as the strong heteronuclear \(J\)-coupling regime and is relatively large:  
\[\sqrt{\frac{2\Delta\
u}{(\gamma_{1}-\gamma_{s})^{2}}}\leq B_{2}^{ULF}\leq \frac{4I}{(\gamma_{1}+\gamma_{S})}\leq B_{exact}^{LF}\leq\frac{\left(1+\frac{ 1}{\sqrt{2}}\right)}{(\gamma_{1}-\gamma_{S})}\leq B_{3}^{LF}\leq\sqrt{\frac{3 ^{2}}{4\Delta\
u(\gamma_{1}-\gamma_{s})^{2}}}\leq B_{2}^{LF}\leq\frac{\left. \right.\right]^{2}}{2\Delta\
u(\gamma_{1}-\gamma_{s})}\leq B_{1}^{high\ field}. \tag{1}\]  
Here, \(J\) is the heteronuclear \(J\)-coupling interaction; \(\Delta\
u\) is the linewidth; and \(\gamma_{l}/\gamma_{S}\) are the heteronuclear gyromagnetic ratios for spins \(I\) and \(S\), respectively [14]. The magnetic fields are denoted by \(B_{2}\)\({}^{y}\), where \(z\) is the perturbation order (or exact theory) needed to describe the observed spectral transitions, and \(y\) denotes the magnetic field--high field, low field (LF), or ultra-low field (ULF). The high field heteronuclear \(J\)-coupling follows a first order perturbation, where the relative intensities and frequency differences are described by the Pascal triangle for spin 1/2 nuclei. The transition from high field to LF (\(B_{1}\)\({}^{\text{high field}}\to B_{2}\)\({}^{\text{LF}}\)) is marked by the transition into the strong heteronuclear coupling regime. It should be noted that the strong heteronuclear \(J\)-coupling regime in ULF requires angular momentum quantum numbers that are different from \(m_{I}\) and \(m_{S}\) commonly employed in NMR spectroscopy. This is the basis of zero- to ultra-low field (ZULF) NMR [14; 42]; however, for the following discussion, we are restricting the discussion to only the LF strong heteronuclear \(J\)-coupling regime in which the angular momentum quantum numbers \(m_{I}\) and \(m_{S}\) remain valid. Several important differences distinguish the use of LF NMR for chemical analysis compared to high field NMR.