## 5 Conclusions  
A series of fluorobenzene compounds were investigated in the strong heteronuclear \(J\)-coupling regime at a magnetic field of \(\approx\)51 uT. Using simultaneous excitation and detection of \({}^{19}\)F and \({}^{1}\)H nuclei, the spectra were well simulated on the basis of \(J\)-couplings, chemical shift, and relaxation properties, and the resultant spectra were analyzed qualitatively and quantitatively. The JCS are quantitative, allowing for pseudo-empirical formulas or relative concentrations to be derived. Further, operation in the strong heteronuclear \(J\)-coupling regime allows for more complex spin systems to be developed since all spins are strongly coupled. Pople notation may be applied in the strong heteronuclear \(J\)-coupling regime, providing a basis for describing the symmetries of JCS spectra between different compounds. The result is a JCS containing heteronuclear and homonuclear \(J\)-coupling interactions, whose relative signs can be established with fewer spins than a strongly coupled homonuclear system. Homonuclear \(J\)-couplings are observed if at least one heteronuclear \(J\)-coupling breaks the magnetic equivalence of the nucleus being detected. Additionally, in multiple instances, the LF JCS provides a more detailed spectra than high field NMR and allows the JCS to access magnetically inequivalent spins in the system for structural analysis. Furthermore, for non-H nuclei, the chemical shift becomes an important parameter for accurate simulation of the JCS. As the magnetic field homogeneity of these LF systems improves, it is likely that chemical shift will also serve to break the chemical equivalence of homonuclei.  
The following are available online at [[http://www.mdpi.com/2076-3417/10/11/3836/s1](http://www.mdpi.com/2076-3417/10/11/3836/s1)]([http://www.mdpi.com/2076-3417/10/11/3836/s1](http://www.mdpi.com/2076-3417/10/11/3836/s1)), Figures S1-S8: \({}^{19}\)F NMR spectra of fluorobenzene collected at 9.4 T with \({}^{1}\)H decoupling. Example MATLAB functions and scripts are also provided.  
Figure 12: The experimental high field (9.4 T) NMR spectrum (black) and JCS (blue) of 1,2,4,5-tetrafluorobenzene for both the \({}^{19}\)F (**left**) and \({}^{1}\)H (**right**) portions of the spectra. The high field spectrum was simulated (red) using the same parameters obtained from the experimental JCS. Multiple peaks in the simulated subsetpectra in the \({}^{1}\)H region indicated that the experimental subsetpectra information was likely hidden at this field due to line broadening. The \({}^{19}\)F high field simulated spectrum showed no subspectra structure. Clearly, the JCS provides more detailed subspectra than either high field spectrum.  
**Author Contributions:** Conceptualization, D.C.K., M.T.J., M.A.E., and R.F.W.; methodology, D.C.K. and M.T.J.; software, D.C.K.; validation, D.C.K., R.K.F., and M.T.J.; formal analysis, D.C.K.; investigation, D.C.K., M.T.J., R.K.F., P.E.M., T.N., and G.A.-T.; resources, R.J.B.; data curation, D.C.K., R.K.F., T.N., G.A.-T.; writing--original draft preparation, D.C.K.; writing--review and editing, D.C.K., P.E.M., R.J.B., R.K.F., M.T.J., T.N., G.A.-T., M.A.E., and R.F.W.; visualization, D.C.K., M.T.J., R.K.F., P.E.M., and R.J.B.; supervision, R.F.W. and M.A.E.; project administration, R.F.W. and M.A.E.; funding acquisition, D.C.K., R.F.W., and M.A.E. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This research was funded by Los Alamos National Laboratory (LANL) Laboratory Directed Research and Development Projects #20170048 DR and 20190641 PRD3.  
**Acknowledgments:** This work is released for publication in accordance with Los Alamos National Laboratory LA-UR-19-30126 by Triad National Security, LLC (Los Alamos, NM, USA) operator of the Los Alamos National Laboratory under contract no. 89233218 CNA000001 with the U.S. Department of Energy.  
**Conflicts of Interest:** The authors declare no conflict of interest.