## 1 Introduction  
One of the most utilitarian applications of nuclear magnetic resonance (NMR) spectroscopy is to elucidate molecular structure, which can be leveraged to study the structure of small molecules, peptides, proteins, inorganic solids, and glasses [1; 2; 3]. Arguably, NMR is most routinely used to determine the structure of low molecular weight organic molecules. Chemical analysis of small molecules uses three important NMR parameters to deduce structure: the Larmor frequency, the chemical shift, and the \(J\)-couplings. These parameters manifest as the observable peak frequencies and intensities providing information about the NMR active nuclei contained in the molecule, the local electronic environment, and the connectivity (structure) of the molecule [4; 5; 6]. Traditionally, NMR employs large, homogeneous, external magnetic fields (\(B_{0}\)), generated by superconducting magnets, which necessitates the need for cryogens. Presently, liquid He is required for most high field NMR applications, but He is a finite resource with rapidly declining stockpiles [7; 8]. Significant technological advances must be made to develop superconducting magnets composed of a high temperature superconductor that use liquid N\({}_{2}\). Alternatively, magnetic fields must be generated by other means such as using permanent magnets or electromagnets. Commercially available benchtop spectrometers, operating between 1-2 T using permanent magnets, have risen to meet the challenges imposed by the liquid He crisis [9]. Additionally, the absence of a need for liquid cryogens reduces size and increases the portability and affordability of NMR instrumentation. Unlike most superconducting systems, which can achieve \(<\)0.2 Hz linewidths, benchtop systems typically report linewidths of 0.5-1.8 Hz, indicating slightly higher \(B_{0}\) inhomogeneity than their superconducting counterparts [9; 10]. While the effects of magnetic field inhomogeneities can be refocused through echo train acquisitions, the observed resolution of benchtop systems is hindered because of a reduced chemical shift scale and T\({}_{2}\) relaxation phenomena. This is exemplified in Figure 1a for 1,4-difluorobenzene, showing the \({}^{1}\)H spectrum collected using a superconducting magnet at 9.4 T and a permanent magnet benchtop system operating at 1.43 T. The spectrum at 1.43 T is substantially broader than the 9.4 T spectrum. Since the primary \({}^{1}\)H relaxation mechanism is caused by field independent dipolar relaxation, the linewidth scales in parts per million (ppm) by the ratio of \(B_{0}\)[11]. Figure 1: Comparison of the \({}^{1}\)H spectra for 1,4-difluorobenzene (**a**) and 1,2,4-trifluorobenzene (**b**) using a superconducting high magnetic field (9.4 T, black), a permanent high magnetic field (1.43 T, red), and permanent low field magnetic field (51.5 \(\upmu\)T, blue). The high field spectra are plotted on a chemical shift axis (bottom scale) and the low field spectrum is plotted on a frequency axis (top scale). As the field is decreased, in the high field regime, there is significant overlap of the peaks, which becomes problematic when multiple chemical shifts are present (b). The low field NMR spectrum has additional peaks in the spectrum that are not captured by either high field spectrum, and also provides fewer overlapping resonances in the case of the 1,2,4-trifluorobenzene (b). \(J\)-couplings, like dipolar relaxation, are also independent of \(B_{0}\)[4]; consequently, the same \(J\)-coupling is separated by a larger ppm difference on the chemical shift scale at lower magnetic fields. The 1,4-difluorobenzene spectrum (Figure 1a) consists of an apparent triplet with splitting from the \(J\)-coupling of \(\approx\)6.2 Hz (vide infra). The splitting between peaks is equivalent to a 0.0155 ppm separation at 9.4 T (Figure 1a, black) and a 0.103 ppm separation at 1.4 T (Figure 1a, red).