"truly" use E^f in Fig. 15

analyses/Makefile

@@ -13,6 +13,7 @@ all:
 	python plot_pot_vs_Hodgson.py -o ../FigureS4.pdf
 	python plot_pot_hammet.py -o ../FigureS5.pdf
 	python plot_cplx_Gx1.py -o ../FigureS6.pdf
+	python  plot_pot_exp.py -R -o ../FigureS7.pdf
 
 tab:
 	python plot_pot.py --table pot.tab

analyses/plot_pot_exp.py

@@ -5,7 +5,7 @@
 import argparse
 import scipy
 
-from nitroxides.commons import dG_DH, AU_TO_ANG, LabelPositioner, AU_TO_EV, EPSILON_R, E_SHE
+from nitroxides.commons import dG_DH, AU_TO_ANG, LabelPositioner, AU_TO_EV, AU_TO_KJMOL, EPSILON_R, E_SHE, G_NME4, G_BF4, RADII_BF4, RADII_NME4, dG_DH_cplx_Kx1, EPSILON_R
 
 LABELS = {'water': [], 'acetonitrile': []}
 POINTS_POSITION ={'water': [], 'acetonitrile': []}
@@ -14,17 +14,46 @@
 
 EXCLUDE = [57, 51, 59]
 
-def prepare_data(data: pandas.DataFrame, data_exp: pandas.DataFrame, solvent):
+T = 298.15
+R = 8.3145e-3 # kJ mol⁻¹
+F =  9.64853321233100184e4  # C mol⁻¹
+
+
+def Ef_ox(E0: float,X: float, k01: float, k02: float, k11: float, k12: float):
+    return E0 + R * T / F * numpy.log((1+k11*X+k12*X**2) / (1+k01*X+k02*X**2))
+
+
+def prepare_data(data: pandas.DataFrame, data_exp: pandas.DataFrame, data_Kx1: pandas.DataFrame, solvent, correct: bool = True):
     subdata = data[data['solvent'] == solvent]
     subdata.insert(1, 'compound', [int(n.replace('mol_', '')) for n in subdata['name']])
     subdata = subdata.join(data_exp[data_exp['E_ox_exp_{}'.format(solvent)].notnull()].set_index('compound'), on='compound', how='inner')
 
+    subdata_Kx1 = data_Kx1[data_Kx1['solvent'] == solvent]
+    subdata = subdata.join(subdata_Kx1[['name', 'r_AX_ox', 'r_AX_rad', 'G_cplx_ox', 'G_cplx_rad']].set_index('name'), on='name', how='inner')
+
+    dG_DH_k01 = dG_DH_cplx_Kx1(subdata['z'] + 1, subdata['z'] + 1, 1, subdata['r_ox'] / AU_TO_ANG, subdata['r_AX_ox'] / AU_TO_ANG, RADII_BF4[solvent] / AU_TO_ANG, EPSILON_R[solvent], c_elt=0.1)
+    dG_DH_k11 = dG_DH_cplx_Kx1(subdata['z'], subdata['z'], 1, subdata['r_rad'] / AU_TO_ANG, subdata['r_AX_rad'] / AU_TO_ANG, RADII_NME4[solvent] / AU_TO_ANG, EPSILON_R[solvent], c_elt=0.1)
+
+    dG_k01 = (subdata['G_cplx_ox'] - G_BF4[solvent] + dG_DH_k01) * AU_TO_KJMOL
+    dG_k11 = (subdata['G_cplx_rad'] - G_NME4[solvent] + dG_DH_k11) * AU_TO_KJMOL
+
+    subdata.insert(1, 'dG_cplx_ox', dG_k01)
+    subdata.insert(1, 'dG_cplx_rad', dG_k11)
+
+    subdata.insert(1, 'k01', numpy.exp(-dG_k01 / (R * T)))
+    subdata.insert(1, 'k11', numpy.exp(-dG_k11 / (R * T)))
+
     subdata['E_ox_exp_{}'.format(solvent)] /= 1000
 
-    dG_DH_ = dG_DH(subdata['z'] + 1, subdata['z'], subdata['r_ox'] / AU_TO_ANG, subdata['r_rad'] / AU_TO_ANG, EPSILON_R[solvent], 0.1) * AU_TO_EV
-    subdata.insert(1, 'E_ox_theo_{}'.format(solvent), subdata['E_ox'] - dG_DH_ - E_SHE[solvent])
+    dG_DH_ = dG_DH(subdata['z'] + 1, subdata['z'], subdata['r_ox'] / AU_TO_ANG, subdata['r_rad'] / AU_TO_ANG, EPSILON_R[solvent], c_elt=0.1) * AU_TO_EV
+
+    if correct:
+        subdata.insert(1, 'E_ox_theo_{}'.format(solvent), subdata['E_ox'] - dG_DH_ - E_SHE[solvent])
+        # subdata.insert(1, 'E_ox_theo_{}'.format(solvent), Ef_ox(subdata['E_ox'] - dG_DH_, 0.1, subdata['k01'], 0, subdata['k11'], 0) - E_SHE[solvent]) → some data are missing for the moment
+    else:
+        subdata.insert(1, 'E_ox_theo_{}'.format(solvent), subdata['E_ox'] - E_SHE[solvent])
 
-    return subdata[['compound', 'family', 'E_ox_theo_{}'.format(solvent), 'E_ox_exp_{}'.format(solvent)]]
+    return subdata[['compound', 'family', 'E_ox_theo_{}'.format(solvent), 'E_ox_exp_{}'.format(solvent), 'k01', 'k11']]
 
 
 def plot_exp_vs_theo(ax, data: pandas.DataFrame, solvent: str, family: str, color: str):
@@ -63,18 +92,21 @@ def plot_corr(ax, data: pandas.DataFrame, solvent: str):
 parser = argparse.ArgumentParser()
 parser.add_argument('-i', '--input', default='../data/Data_pot.csv')
 parser.add_argument('-i2', '--input2', default='../data/Data_pot_ox_exp.csv')
+parser.add_argument('-i3', '--input3', default='../data/Data_cplx_Kx1.csv')
 parser.add_argument('-r', '--reposition-labels', action='store_true')
 parser.add_argument('-o', '--output', default='Data_pot_ox_exp.pdf')
+parser.add_argument('-R', '--raw', action='store_true')
 
 args = parser.parse_args()
 
 data = pandas.read_csv(args.input)
 data_exp = pandas.read_csv(args.input2)
+data_Kx1 = pandas.read_csv(args.input3)
 
 figure = plt.figure(figsize=(5, 9))
 ax1, ax2 = figure.subplots(2, 1)
 
-subdata_wa = prepare_data(data, data_exp, 'water')
+subdata_wa = prepare_data(data, data_exp, data_Kx1, 'water', correct=not args.raw)
 
 plot_exp_vs_theo(ax1, subdata_wa, 'water', 'Family.P6O', 'tab:blue')
 plot_exp_vs_theo(ax1, subdata_wa, 'water', 'Family.P5O', 'black')
@@ -94,7 +126,7 @@ def plot_corr(ax, data: pandas.DataFrame, solvent: str):
 
 positioner.add_labels(ax1)
 
-subdata_ac = prepare_data(data, data_exp, 'acetonitrile')
+subdata_ac = prepare_data(data, data_exp, data_Kx1, 'acetonitrile', correct=not args.raw)
 
 plot_exp_vs_theo(ax2, subdata_ac, 'acetonitrile', 'Family.P6O', 'tab:blue')
 plot_exp_vs_theo(ax2, subdata_ac, 'acetonitrile', 'Family.P5O', 'black')

analyses/pot_exp_acetonitrile.pos

@@ -1,21 +1,20 @@
 ,label,x,y
-0,2,0.4438765569262125,0.863574837692712
-1,3,0.6380742125349317,0.9158479300242165
-2,4,0.4990128117934539,1.0719899405624358
-3,6,0.6023732713819644,0.8685674877080033
-4,12,1.0239349110638034,1.0486768407787257
-5,61,0.589239734873345,1.0041899563697234
-6,15,0.6870675331884576,0.9639531638510436
-7,58,0.6758656895238815,1.0723399504851525
-8,59,0.6268593775023655,1.1219396529446857
-9,23,0.7260609862688812,1.0545933041732607
-10,24,0.6965460171829495,1.098701120295577
-11,25,0.6308788347422332,0.9787325871562836
-12,26,0.659682000261976,1.0422272120167466
-13,27,0.7262888839864805,1.0210822039614267
-14,33,0.7417052682040323,1.1397951321460615
-15,60,0.7518951563656074,1.1125329355624394
-16,36,0.6802621245781908,0.9986929933273532
-17,51,0.5606225155388862,1.0991846864321788
-18,54,0.8278892082092979,1.0913083929576781
-19,55,0.8473861464286029,1.1864842797688635
+0,2,0.47107081656256083,0.8626264562847373
+1,3,0.6230082353797602,0.9097436873361786
+2,4,0.5150577324929498,1.0777505761329897
+3,6,0.57622874744584,0.8621035654793175
+4,12,1.0268763344908078,1.0491506684024725
+5,15,0.6886598816640135,0.965439278848284
+6,58,0.6751958417970293,1.0764762306693323
+7,59,0.6280358102900123,1.1212636224600396
+8,23,0.7336737985377431,1.0461970279475303
+9,24,0.7316620174253338,1.0750174779414738
+10,25,0.6292338759738931,0.9800426591338034
+11,26,0.661703136896908,1.043490004299524
+12,27,0.7227473476140649,1.0152558467884893
+13,33,0.7572007640617795,1.1371366491138988
+14,60,0.7240714710440453,1.1078034374927888
+15,36,0.6312510424732102,1.013406601014792
+16,51,0.5937250173093498,1.0869825136490716
+17,54,0.8203968994456231,1.0858583165511493
+18,55,0.8439753693864817,1.165234303933909

analyses/pot_exp_water.pos

@@ -1,13 +1,13 @@
 ,label,x,y
-0,2,0.8016241939476328,0.7494547108349441
-1,3,0.8921938703337926,0.7959887712792744
-2,4,0.8364497746535255,0.8221175463499808
-3,6,0.9097162361834388,0.828025178946801
-4,11,0.9872895934870578,0.8970893702286521
-5,12,1.0166476326054266,0.9080869664872327
-6,13,0.8549317829674,0.7850659804605586
-7,15,0.9643818057629958,0.8772758630808144
-8,18,0.8727712323384526,0.8220489695851109
-9,56,0.9103404528884366,0.8665625659413435
-10,57,0.7833279815320551,0.8623753149610659
-11,58,1.0305238936280707,0.9483210702134718
+0,2,0.8124121697934003,0.7465247830424631
+1,3,0.891946961740928,0.7959117676668113
+2,4,0.8357142595897417,0.8199954910719995
+3,6,0.910057900275304,0.8231421924373752
+4,11,0.9889085505132582,0.8992988790020404
+5,12,1.0206408835824246,0.9096848828819359
+6,13,0.8517600630200663,0.7862212525596723
+7,15,0.9616440515077036,0.8728792246412183
+8,18,0.8681894571043665,0.8239660968167094
+9,56,0.9096805893995387,0.8710278641417291
+10,57,0.7795159782062109,0.8458979417174098
+11,58,1.0325533195111207,0.9526216912921555

nitroxides.tex

@@ -277,8 +277,8 @@ \subsection{Impact of ion-pair formation on redox potentials}
 	\item the redox potentials of the ion-pair complexes are smaller than the one of the free species.
 \end{inparaenum}
 Within these assumption, the following electrolyte concentration-dependent (formal) redox potentials are obtained:\begin{align}
-	E^f_{abs}(\ce{N+|N^.}) &= E^0_ {abs}(\ce{N+|N^.})+\frac{RT}{F}\,\ln\left[\frac{1+K_{11}\,[X]+K_{12}\,[X]^2}{1+K_{01}\,[X]+K_{02}\,[X]^2}\right],\\
-	E^f_{abs}(\ce{N^.|N-}) &= E^0_ {abs}(\ce{N^.|N-})+\frac{RT}{F}\,\ln\left[\frac{1+K_{21}\,[X]+K_{22}\,[X]^2}{1+K_{11}\,[X]+K_{12}\,[X]^2}\right],
+	E^f_{abs}(\ce{N+|N^.}) &= E^0_ {abs}(\ce{N+|N^.})+\frac{RT}{F}\,\ln\left[\frac{1+K_{11}\,[X]+K_{12}\,[X]^2}{1+K_{01}\,[X]+K_{02}\,[X]^2}\right],\label{eq:ef1}\\
+	E^f_{abs}(\ce{N^.|N-}) &= E^0_ {abs}(\ce{N^.|N-})+\frac{RT}{F}\,\ln\left[\frac{1+K_{21}\,[X]+K_{22}\,[X]^2}{1+K_{11}\,[X]+K_{12}\,[X]^2}\right],\label{eq:ef2}
 \end{align}
 in which $K_{ij}= \exp\left[-\frac{\Delta G_{cplx}^\star}{RT}\right]$, where $\Delta G_{cplx}^\star$ is the free Gibbs energy change [computed with Eq.~\eqref{eq:gtot}] for a given complexation reaction.
 
@@ -525,13 +525,14 @@ \subsection{Impact of the electrolytes} \label{sec:elect}
 \clearpage
 \subsection{Comparison to experiment} \label{sec:exp}
 
-A comparison between theoretical (including all corrections discussed above) and experimental oxidation potentials is shown in Fig.~\ref{fig:expvstheo}.\todo{This is not really $E^f$ for the moment ;)} Excluding compounds bearing an \ce{NH2} group (\textbf{51}, \textbf{57}, and \textbf{59}) results in an excellent linear correlation ($R^2>0.9$). The computed potentials for these compounds are higher (by $>\SI{0.1}{\volt}$) than the fit line, suggesting that the amine group might be protonated under the experimental measurement conditions. This is indeed consistent with other cases (\textit{e.g.}, \textbf{25} vs \textbf{35}) discussed in Section \ref{sec:sar}. The remaining results indicate that the method used in this paper tends to overestimate the oxidation potentials in water and systematically underestimate them in acetonitrile, with a large mean average error (MAE), indicating that the value for $E^0_{abs}(\text{SHE)}$ might not be appropriate in this solvent.
+A comparison between theoretical (including all corrections discussed above) and experimental oxidation potentials is shown in Fig.~\ref{fig:expvstheo}. Excluding compounds bearing an \ce{NH2} group (\textbf{51}, \textbf{57}, \textbf{59}, and \textbf{4} in acetontrile) results in an excellent linear correlation ($R^2 > 0.9$). The computed potentials for these compounds are higher (by $>\SI{0.1}{\volt}$) than the fit line, suggesting that the amine group might be protonated under the experimental measurement conditions. This is indeed consistent with other cases (\textit{e.g.}, \textbf{25} vs \textbf{35}) discussed in Section \ref{sec:sar}. 
 
+The remaining results indicate that the method used in this paper tends to overestimate the oxidation potentials in water and systematically underestimate them in acetonitrile, with a large mean average error (MAE). This suggests that the value for $E^0_{abs}(\text{SHE})$ might not be appropriate in this solvent. The impact of the different corrections (see Fig.~S7) is to decrease the potential, mainly due to the DH correction (given the value of the complexation equilibrium constants for the oxidation reaction, see Table \ref{tab:Kx1}), as seen in Fig.~\ref{fig:DH}. While this improves the slope and MAE in water, the opposite effect is observed in acetonitrile.
 
 \begin{figure}[!h]
 	\centering
-	\includegraphics[width=.8\linewidth]{Figure15}
-	\caption{Comparison between experimental ($E^0_{rel} $ vs SHE, from Table S11) and computed relative oxidation potential ($E^f_{rel}$ vs SHE), as computed at the $\omega$B97X-D/6-311+G(d) level in water (left) and acetonitrile (right) using SMD and $[X]=\SI{0.1}{\mole\per\liter}$.  The dashed line is a linear regression.}
+	\includegraphics[width=.75\linewidth]{Figure15}
+	\caption{Comparison between experimental ($E^0_{rel} $ vs SHE, from Table S11) and computed relative oxidation potential ($E^f_{rel}$, computed using \eqref{eq:ef1}, vs SHE), as computed at the $\omega$B97X-D/6-311+G(d) level in water (top) and acetonitrile (bottom) using SMD and $[X]=\SI{0.1}{\mole\per\liter}$.  The dashed line is a linear regression.}
 	\label{fig:expvstheo}
 \end{figure}
 
@@ -540,8 +541,8 @@ \subsection{Comparison to experiment} \label{sec:exp}
 
 \begin{figure}[!h]
 	\centering
-	\includegraphics[width=.8\linewidth]{Figure16}
-	\caption{Comparison between experimental ($E^0_{rel} $ vs SHE, from Table S11) and corrected oxidation potential using the scheme of Matsui et al. \cite{matsuiDensityFunctionalTheory2013} [Eq.~\eqref{eq:matsui}, with the parameters $E_{abs}^0(\text{SHE})$, $f$, and $\mu$ obtained by a least-square procedure], as computed at the $\omega$B97X-D/6-311+G(d) level in water (left) and acetonitrile (right). The dashed line is a linear regression, obtained without the DH correction. }
+	\includegraphics[width=.75\linewidth]{Figure16}
+	\caption{Comparison between experimental ($E^0_{rel} $ vs SHE, from Table S11) and corrected oxidation potential using the scheme of Matsui et al. \cite{matsuiDensityFunctionalTheory2013} [Eq.~\eqref{eq:matsui}, with the parameters $E_{abs}^0(\text{SHE})$, $f$, and $\mu$ obtained by a least-square procedure, on calculated data without the DH correction], as computed at the $\omega$B97X-D/6-311+G(d) level in water (top) and acetonitrile (bottom). The dashed line is a linear regression. }
 	\label{fig:matsui}
 \end{figure}
 

nitroxides_SI.tex

@@ -582,7 +582,8 @@
 		note{a} = {From Ref.~\citenum{goldsteinStructureActivityRelationship2006}.},
 		note{b} = {From Ref.~\citenum{morrisChemicalElectrochemicalReduction1991}, converted from SCE to SHE with +\SI{244}{\milli\volt} \cite{pavlishchukConversionConstantsRedox2000}.},
 		note{c}={From Ref.~\citenum{blincoExperimentalTheoreticalStudies2008}.},
-		note{d}={From Ref.~\citenum{zhangEffectHeteroatomFunctionality2018}, converted from Fc to SHE with +\SI{624}{\milli\volt} \cite{pavlishchukConversionConstantsRedox2000}.}
+		note{d}={From Ref.~\citenum{zhangEffectHeteroatomFunctionality2018}, converted from Fc to SHE with +\SI{624}{\milli\volt} \cite{pavlishchukConversionConstantsRedox2000}.},
+		label={tab:exp}
 	]{colspec={>{\bfseries}lX[c]X[c]c>{\bfseries}lX[c]X[c]}, width = 0.85\linewidth,rowhead=1}
 	\hline
 	& Water & Acetonitrile  & & & Water & Acetonitrile\\
@@ -604,9 +605,17 @@
 	\hline
 \end{longtblr}
 
+\begin{figure}[!h]
+	\centering
+	\includegraphics[width=.75\linewidth]{FigureS7}
+	\caption{Comparison between experimental ($E^0_{rel} $ vs SHE, from Table \ref{tab:exp}) and computed relative oxidation potential ($E^f_{rel}$ vs SHE), as computed at the $\omega$B97X-D/6-311+G(d) level in water (top) and acetonitrile (bottom) using SMD and no correction due to DH or pair formation.  The dashed line is a linear regression.}
+	\label{fig:expvstheo}
+\end{figure}
+
 \clearpage
 
 
+
 \bibliographystyle{unsrt} 
 \bibliography{biblio}