## 1 Introduction
However, for nuclei with smaller \(\gamma\) and those with larger chemical shift ranges such as fluorine, chemical shifts are observable at LF (_vide infra_). Therefore, by leveraging LF NMR in the strong heteronuclear \(J\)-coupling regime, NMR Larmor frequencies, heteronuclear \(J\)-couplings, homonuclear \(J\)-couplings, and, potentially, chemical shift information may all be obtained, which constitutes the primary information metrics used in high field NMR for chemical analysis. Despite the wealth of information available in the strong heteronuclear \(J\)-coupling regime, the JCS of only 22 compounds have been published to the best of our knowledge, and a majority of these studies have focused on six different heteronuclear spin systems, such as \({}^{11}\)B- [19], \({}^{13}\)C- [15; 16; 24; 25; 43], \({}^{14}\)N- [19; 26; 36], \({}^{19}\)F- [17; 18; 21; 23; 25; 27; 28; 29; 30; 31; 32; 33; 34; 35; 36], \({}^{29}\)Si- [17; 16; 17], and \({}^{31}\)P-1H [15; 22; 25; 27; 29; 37; 38; 39; 40; 41], and the majority of these compounds do not contain homonuclear \(J\)-couplings. The lack of systematic study and subsequent application may be a result of the decreased sensitivity of low-magnetic fields, even with modest prepolarization techniques, which require large spin densities and sample volumes (mL samples, neat concentrations). The JCS of \({}^{19}\)F-\({}^{1}\)H compounds are the most widely studied, and nine unique \({}^{19}\)F-containing compounds have been investigated in the LF strong heteronuclear \(J\)-coupling regime. Most of these studies have only investigated heteronuclear \(J\)-couplings in either the \({}^{1}\)H or \({}^{19}\)F portions of the spectrum, but not both. Therefore, structural changes on the JCS have not been thoroughly and completely examined in the \({}^{19}\)F-\({}^{1}\)H system, and this provides an opportunity to develop the basis for chemical analysis of small molecules in the strong heteronuclear \(J\)-coupling regime. We have recently developed an LF NMR instrument that is capable of detecting small sample volumes (200 uL) in a laboratory environment with minimal \(B_{0}\) inhomogeneity (\(\approx\)35 ppm, 0.07 Hz) over the sample [43]. As such, we can now begin to probe how structure impacts the JCS and investigate what information can be obtained in the strong heteronuclear \(J\)-coupling regime. In this study, we chose to investigate the JCS of a suite of nine C\({}_{6}\)H\({}_{6-x}\)F\({}_{x}\) (\(x=0\), 1, 2,..., 6) fluorobenzene compounds in the strong heteronuclear \(J\)-coupling regime with \(B_{0}\)\(\approx\) 51.5 uT. Using multinuclear excitation and detection of \({}^{19}\)F and \({}^{1}\)H, the JCS signatures of both nuclei were simultaneously measured. The fluorobenzene system is ideal for systematically studying LF NMR phenomena since each of the fluorobenzene compounds has at least one strong heteronuclear \(J\)-coupling at this \(B_{0}\) in addition to containing H-H and F-F homonuclear \(J\)-couplings. The impact of F or H substitution can be investigated by systematically increasing the number of F atoms from zero to six. Furthermore, different fluorinated isomers (i.e., 1,2- 1,3- and 1,4-difluorobenzenes) can also be investigated, directly probing the effect of atomic position and its influence on the JCS. Finally, the relative sign of hetero- and homonuclear \(J\)-couplings in these compounds has been shown to be variable, and the impact of the relative signs of the observed \(J\)-couplings on the JCS has yet to be explored at these low magnetic fields [44; 45]. All experimental JCS have been corroborated with _ab initio_ calculations and simulated JCS, and the results demonstrate that JCS provides a sensitive probe of the stoichiometry and atomic arrangement in a molecule. Both the magnitude and the relative signs of heteronuclear and homonuclear \(J\)-couplings impact measurable differences in the JCS and inform the structure of the compound.