correlation with hammet comes from somewhere!

nitroxides.tex

@@ -428,7 +428,8 @@ \subsection{Structure-activity relationships} \label{sec:sar}
 \end{inparaenum}
 As a consequence, \textbf{55} exhibits the highest oxidation and reduction potentials among all the compounds studied in this paper.
 
-To elucidate these effects, attempts are made to correlate both potentials with Hammett constants for P5O ($\sigma_m$) and P6O ($\sigma_p$), but the correlations are found to be very weak, especially for reduction.  A better correlation, especially for reduction, is obtained using the inductive constants ($\sigma_I$) derived by Taft \cite{hanschSurveyHammettSubstituent1991}, thought on a limited subset of compounds  (Fig.~S5).
+To elucidate these effects, attempts are made to correlate both oxidation and reduction potentials with Hammett constants for P5O ($\sigma_m$) and P6O ($\sigma_p$). Contrary to previous studies \cite{hodgsonOneElectronOxidationReduction2007,zhangEffectHeteroatomFunctionality2018}, these correlations are found to be very weak, particularly for reduction. A better correlation, especially for reduction, is achieved using the inductive constants ($\sigma_I$) derived by Taft \cite{hanschSurveyHammettSubstituent1991}, though this is based on a limited subset of compounds (Fig.~S5).
+
 
 The electrostatic interaction model [Eq.~\eqref{eq:Er}] provides more insights. Results are presented in Fig.~\ref{fig:corr} (see also Table S4). It should be noted that this model fails to account for the effect of substituting methyl groups with ethyl groups. Moreover, including the disubstituted compounds (e.g., \textbf{9}, \textbf{10}, \textbf{20}, ...) worsens the correlation ($R^2 \sim 0.5$ and 0.3 for oxidation and reduction, respectively). Compounds \textbf{56} and \textbf{58} remain outliers for reduction. Therefore, all these sets of compounds are treated as outliers in the following discussion.
 Though the correlation is poorer for reduction than for oxidation (probably because the electron delocalization means that the nitrogen atom is not the atom that should be used to define the origin in that case), this model helps explaining the general trends. For instance, the increase in oxidation (and reduction) potential for aromatic compounds correlates with an increase in quadrupole moment ($Q_{xx} > \SI{5}{\elementarycharge\bohr\squared}$ for most members of IIO or APO). Additionally, modifications due to donor/acceptor substituents are linked to changes in the dipole moment. For example, aromatic compounds with \ce{NH2} as a substituent (\textit{e.g.}, \textbf{51}) are characterized by $\mu_{x} < 0$, which increases for compounds with \ce{COOH} (\textit{e.g.}, \textbf{39}) or \ce{NO2} (\textit{e.g.}, \textbf{54}). Furthermore, members of P5O generally present a smaller value of $U_q$ than P6O (\textit{e.g.}, \textbf{17} versus \textbf{5}), which correlates with the increase in oxidation potential observed between these two families. The same trend is observed between APO and IIO.