## 4 Discussion
### Homonuclear J-Coupling Effects in JCS  
Each subspectrum is governed by the heteronuclear and homonuclear \(J\)-couplings, the impact of which is shown in Figure 9 for 1,4-difluoroobenzene. In this figure, the \(J\)-couplings were successively added into the simulation from largest to smallest, beginning with heteronuclear couplings and ending with homonuclear couplings. The \(R\)-factors for the \({}^{19}\)F and \({}^{1}\)H portions of the spectra are provided on the side of each spectrum, and each additional \(J\)-coupling parameter is denoted between each spectrum.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Compound**} & \multicolumn{2}{c}{\({}^{1}\)**H-\({}^{19}\)F**} & \multicolumn{2}{c}{\({}^{1}\)**H-\({}^{19}\)F**} & \multicolumn{2}{c}{\({}^{1}\)**H-\({}^{19}\)F**} & \multicolumn{2}{c}{**Experimental**} & \multicolumn{1}{c}{**Simulated**} \\  & **Stoichiometric** & **Experimental** & **Simulated** & **Error (\%)** & **Error (\%)** \\ \hline Benzene + Hexafluorobenzene & 1.00 & 1.16 [0.963] & 1.12 [0.930] & 15.6 [3.69] & 11.7 [6.92] \\ Monofluorobenzene & 5.00 & 7.04 [5.86] & 5.62 [4.68] & 40.8 [17.3] & 12.4 [6.37] \\
1,2-Difluorobenzene & 2.00 & 2.26 [1.88] & 2.25 [1.87] & 12.9 [5.99] & 12.2 [6.49] \\
1,3-Difluorobenzene & 2.00 & 2.20 [1.84] & 2.26 [1.88] & 10.1 [8.27] & 12.7 [6.09] \\
1,4-Difluorobenzene & 2.00 & 2.37 [1.98] & 2.24 [1.87] & 18.7 [1.14] & 12.2 [6.53] \\
1,2,4-Trifluorobenzene & 1.00 & 0.979 [0.815] & 1.11 [0.928] & 2.14 [18.5] & 11.4 [7.20] \\
1,2,4,5-Tetrafluorobenzene & 0.500 & 0.687 [0.572] & 0.568 [0.473] & 37.4 [14.5] & 13.7 [5.30] \\ Pentafluorobenzene & 0.200 & 0.292 [0.243] & 0.229 [0.191] & 46.0 [21.7] & 14.7 [4.41] \\ \hline \hline \end{tabular}
\end{table}
Table 4: Quantitation results for fluorobenzene compounds. Values within brackets ([:]) indicate values obtained after scaling the area by the receptivity factor \(\Xi\) (Equation (5).  
As is evident from Figure 9, if only the heteronuclear couplings \({}^{3}\)J\({}_{\rm HF}\) and \({}^{4}\)J\({}_{\rm HF}\) were considered, a poor simulation of the experimental spectrum is obtained. However, once \({}^{5}\)J\({}_{\rm FF}\) is added, the spectra are split into the correct subspectra. Here, \({}^{19}\)F has five subspectra regions, while \({}^{1}\)H has three subspectra regions. Addition of the \(J_{\rm HH}\) then refined the positions and intensities within each subspectra. It is interesting to note that \({}^{5}\)J\({}_{\rm FF}>\)\({}^{3}\)J\({}_{\rm HF}-\)\({}^{4}\)J\({}_{\rm HF}\)] (17.65 Hz \(>\) 3.93 Hz) and this observation disagrees with that proposed by [PERSON] et al. (Equation (2)), and indicates that homonuclear \(J\)-couplings are measurable as long as the magnetic equivalence between the homonuclear spins is broken by a heteronuclear \(J\)-coupling to either of the nuclei [16].  
Figure 8: The Pople notation for the fluorobenzene compounds studied here. For each compound, there are two different Pople notations—the top is the traditional Pople notation for a high field spectrum in the strong homonuclear \(J\)-coupling limit, while the bottom notation is the Pople notation for the same system at LF, in the strong heteronuclear \(J\)-coupling limit. Note that at LF, the Larmor frequency difference was such that none of the nuclei were well separated and must all be considered as a single system.  
Figure 9: The simulated (red) and experimental spectra (black) of the \({}^{19}\)F (top) and \({}^{1}\)H (bottom) regions of 1,4-difluorobenzene. From bottom to top, the simulated spectra each contained an additional \(J\)-coupling, which appears to the right of each spectrum. Clearly, the subspectra in the experimental spectrum are well simulated only when all heteronuclear and homonuclear \(J\)-couplings were included, as denoted by the \(R\)-factor, which is included to the left of each simulated spectrum.