address morning thoughts

analyses/plot_pot_exp.py

@@ -48,7 +48,7 @@ def plot_corr(ax, data: pandas.DataFrame, solvent: str):
     ax.plot(x, result.slope*x + result.intercept, 'k--')
 
     x = .95 * x.min()+ .05 * x.max()
-    ax.text(x + .05, result.slope*x + result.intercept, '{:.2f} $\\times E^0_{{rel}}$ + {:.2f}\n($R^2$={:.2f}, MAE={:.2f} V)'.format(result.slope, result.intercept,result.rvalue **2, mae))
+    ax.text(x + .05, result.slope*x + result.intercept, '{:.2f} $\\times E^f_{{rel}}$ + {:.2f}\n($R^2$={:.2f}, MAE={:.2f} V)'.format(result.slope, result.intercept,result.rvalue **2, mae))
 
 parser = argparse.ArgumentParser()
 parser.add_argument('-i', '--input', default='../data/Data_pot.csv')

analyses/plot_pot_matsui.py

@@ -63,7 +63,7 @@ def plot_corr(ax, data: pandas.DataFrame, solvent: str):
     ax.plot(x, result.slope*x + result.intercept, 'k--')
 
     x = .95 * x.min()+ .05 * x.max()
-    ax.text(x + .05, result.slope*x + result.intercept, '{:.2f} $\\times E^0_{{rel}}$ + {:.2f}\n($R^2$={:.2f}, MAE={:.2f} V)'.format(result.slope, result.intercept, result.rvalue **2, mae))
+    ax.text(x + .05, result.slope*x + result.intercept, '{:.2f} $\\times E^P_{{rel}}$ + {:.2f}\n($R^2$={:.2f}, MAE={:.2f} V)'.format(result.slope, result.intercept, result.rvalue **2, mae))
 
 parser = argparse.ArgumentParser()
 parser.add_argument('-i', '--input', default='../data/Data_pot.csv')

nitroxides.tex

@@ -383,7 +383,7 @@ \section{Methodology} \label{sec:methodo}
 \label{fig:nitroxides}
 \end{figure}
 
-Geometry optimizations and subsequent vibrational frequency calculations were performed at the $\omega$B97X-D/6-311+G(d) level in water and acetonitrile (described using the SMD \cite{marenichUniversalSolvationModel2009} approach) with Gaussian 16 C02 \cite{g16}. With other possible candidates, this functional have been demonstrated to provide reliable results  \cite{flores-leonarFurtherInsightsDFT2017,maierG4AccuracyDFT2020} (see also Fig.~S4).  For compound \textbf{1}-\textbf{54}, the geometries obtained by Hodgson et al. \cite{hodgsonOneElectronOxidationReduction2007} have been used as a starting point, taking advantage of their extensive conformational search. All radical forms are considered to have a doublet ground state  [$\braket{S^2}=\frac{3}{4}$]. Then, the same calculations were preformed in acetonitrile for the subset of compounds for which experimental redox potentials are available (listed in Fig.~\ref{fig:nitroxides}).\todo{and the complexes were also optimized} Finally, to study the influence of the substituent on the redox potential with the model presented in Section \ref{sec:eleczhang}, single point calculation are performed at the $\omega$B97X-D/6-311+G(d) level in gas phase, using the optimized geometries of  the radical states of each nitroxides (in water) in which $>$\ce{N-O^.} moiety is substituted by \ce{CH_2} (the rest of the geometry is kept fixed).
+Geometry optimizations and subsequent vibrational frequency calculations were performed at the $\omega$B97X-D/6-311+G(d) level in water and acetonitrile (described using the SMD \cite{marenichUniversalSolvationModel2009} approach) with Gaussian 16 C02 \cite{g16}. With other possible candidates, this functional have been demonstrated to  provide reliable geometries (see Ref.~\citenum{wylieImprovedPerformanceAllOrganic2019a}) and results  \cite{flores-leonarFurtherInsightsDFT2017,maierG4AccuracyDFT2020} (see also Fig.~S4).  For compound \textbf{1}-\textbf{54}, the geometries obtained by Hodgson et al.~\cite{hodgsonOneElectronOxidationReduction2007} have been used as a starting point, taking advantage of their extensive conformational search. All radical forms are considered to have a doublet ground state  [$\braket{S^2}=\frac{3}{4}$]. Then, the same calculations were preformed in acetonitrile for the subset of compounds for which experimental redox potentials are available (listed in Fig.~\ref{fig:nitroxides}). The geometries of the complexes (Fig.~\ref{fig:cip}) were then optimized at the same level of approximation, for which different positions of the counterions have been assessed (\textit{vide supra}). Finally, to study the influence of the substituent on the redox potential with the model presented in Section \ref{sec:eleczhang}, single point calculation are performed at the $\omega$B97X-D/6-311+G(d) level in gas phase, using the optimized geometries of  the radical states of each nitroxides (in water) in which $>$\ce{N-O^.} moiety is substituted by \ce{CH_2} (the rest of the geometry is kept fixed).
 
 Since all thermochemical quantities are $\kappa$-dependent, analyses were performed using custom Python scripts. When required (e.g., in Eq.~\eqref{eq:dh}), the value of $a$ (the radius of the solute cavity) is taken as half the largest distance between two atoms in the molecule. Although this is an approximation, it provides a consistent method to treat all molecules proportionally to their size and is consistent with other publications \cite{matsuiDensityFunctionalTheory2013}.  Furthermore, a value of $\varepsilon_{r,wa}=80$ for water and $\varepsilon_{r,ac}=35$ for acetonitrile is used. These relative permittivities correspond to those of the pure solvents and are known to be lower in the respective electrolyte solutions \cite{silvaTrueHuckelEquation2022}. These variations can be substantial; for example, $\varepsilon_r \approx 70$ for a solution containing \SI{1}{\mol\per\kilo\gram} of \ce{NaCl} in water \cite{kontogeorgisDebyeHuckelTheoryIts2018, silvaTrueHuckelEquation2022}, but they depend on the nature of the electrolyte, so it was not considered here.
 
@@ -418,8 +418,8 @@ \subsection{Structure-activity relationships} \label{sec:sar}
 
 
 To elucidate these effects, attempts were made to correlate both potentials with Hammett constants for P5O and P6O, but the correlations were found to be very weak, especially for reduction (see Fig.~S5). The electrostatic interaction model [Eq.~\eqref{eq:Er}] provides more insights. Results are presented in Fig.~\ref{fig:corr} (see also Table S3). However, this model fails to account for the effect of substituting methyl groups with ethyl groups. Moreover, including the disubstituted compounds (e.g., \textbf{9}) 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 three sets of compounds were treated as outliers.
-On the positive side, this model helps explain some of the effects mentioned above: 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 member of IIO or APO), while the modification due to donor/acceptor substituents is linked to changes in the dipole moment. For example, aromatic compounds that have \ce{NH2} has substituent (\textit{e.g.}, \textbf{51}) are characterized by  $\mu_{x} < 0$, which gets larger for coumpounds have \ce{COOH} (\textit{e.g.}, \textbf{39}) or \ce{NO2} (\textit{e.g.}, \textbf{54}). It also accounts for some effects due to the position of the substituent (see, e.g., \textbf{49}-\textbf{51}), which was not the case with the original model by Zhang and co-workers (resulting in weak correlations, $R^2 \leq 0.3$).\todo{Why is the correlation lower for reduction?}
-Finally, although it is not directly applicable to charged substituents (\textbf{11}, \textbf{21}, and \textbf{35}), for which the multipole moments are ill-defined, the leading term $q/r$ would result in a positive contribution to $E_r$, which correlates well with the increase in oxidation and reduction potential for these compounds.
+On the positive side, though the correlation is lower for reduction than for oxidation, this model helps explain some of the effects mentioned above: 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 member of IIO or APO), while the modification due to donor/acceptor substituents is linked to changes in the dipole moment. For example, aromatic compounds that have \ce{NH2} has substituent (\textit{e.g.}, \textbf{51}) are characterized by  $\mu_{x} < 0$, which gets larger for coumpounds have \ce{COOH} (\textit{e.g.}, \textbf{39}) or \ce{NO2} (\textit{e.g.}, \textbf{54}). It also accounts for some effects due to the position of the substituent (see, e.g., \textbf{49}-\textbf{51}), which was not the case with the original model by Zhang and co-workers (resulting in weak correlations, $R^2 \leq 0.3$).
+Finally, although it is not directly applicable to charged substituents (\textbf{11}, \textbf{21}, and \textbf{35}), for which the multipole moments are ill-defined, the leading term $q/r$ would result in a positive contribution to $E_r$ (and to a destabilizing interaction with \ce{N+} and \ce{N^.}, while stablizing \ce{N-}, see Fig.~\ref{fig:dipole}), which correlates well with the increase in oxidation and reduction potential for these compounds.
 
 
 \begin{figure}[!h]
@@ -433,7 +433,9 @@ \subsection{Structure-activity relationships} \label{sec:sar}
 
 \subsection{Impact of the solvent} \label{sec:solv}
 
-The difference between redox potentials computed in water and acetonitrile is illustrated in Fig.~\ref{fig:watvsac} (see also Table S2): except for compound \textbf{12}, the oxidation potential is only minimally affected, while there is a disparity of greater than \SI{0.5}{\volt} for the reduction potentials. In first approximation, the Born model [Eq.~\eqref{eq:born}] can account for these findings: for oxidation, the change in potentials in the two solvents, $E^0_{ac} - E^0_{wa}$, is proportional to $\varepsilon_{r,ac}^{-1}-\varepsilon_{r,wa}^{-1}$, which is positive (assuming that \ce{N^.} is neutral, which holds true for the subset of compounds considered here), whereas for reduction, it is proportional to $\varepsilon_{r,wa}^{-1}-\varepsilon_{r,ac}^{-1}$, which is negative. Since this impact is systematic, similar trends (in terms of the impact of substituents) between redox potentials in water and acetonitrile are observed.
+The solvent exerts a significant stabilizing effect on the charge. In the gas phase, $E^0_{abs}(\ce{N+}|\ce{N^.})$ values are around \SI{7}{\volt} (and up to \SI{10}{\volt} for \textbf{11}, \textbf{21}, and \textbf{35}), while $E^0_{abs}(\ce{N^.}|\ce{N-})$ values are approximately \SI{0.3}{\volt} (around \SI{3}{\volt} for \textbf{11}, \textbf{21}, and \textbf{35}). The modifications due to the solvent, primarily resulting from the stabilization of the charges (as indicated by the Born model), but also including moderate geometry changes, amount to about \SI{2}{\volt} (\SI{200}{\kilo\joule\per\mole}).
+
+The difference between redox potentials computed in water and acetonitrile is reported in Fig.~\ref{fig:watvsac} (see also Table S2):  the oxidation potential is only minimally affected, while there is a disparity of greater than \SI{0.5}{\volt} for the reduction potentials. In first approximation, the Born model [Eq.~\eqref{eq:born}] can, again, account for these findings: for oxidation, the change in potentials in the two solvents, $E^0_{ac} - E^0_{wa}$, is proportional to $\varepsilon_{r,ac}^{-1}-\varepsilon_{r,wa}^{-1}$, which is positive (assuming that \ce{N^.} is neutral, which holds true for the subset of compounds considered here), whereas for reduction, it is proportional to $\varepsilon_{r,wa}^{-1}-\varepsilon_{r,ac}^{-1}$, which is negative. Since this impact is systematic, similar trends (in terms of the impact of substituents) between redox potentials in water and acetonitrile are observed.
 
 
 \begin{figure}[!h]