use the correct symmetry number for NMe4

TODO.md

@@ -20,6 +20,7 @@
 - [ ] Entropy in cplx
 - [ ] Sign $U_q$
 - [ ] Extra explanation solv. (diff of $\varepsilon$ is not enough)
+- [ ] All tables in the SI should be updated (!)
 
 - [ ] Fig. or Figure?
 - [ ] PACS code, MSC code?

analyses/nitroxides/commons.py

@@ -4,8 +4,16 @@
 from scipy.spatial import distance_matrix
 
 # -- Electrolytes, from wB97X-D/6-311+G(d)
-G_NME4 = {'water': -214.096721, 'acetonitrile': -214.104109} # Eh
-G_BF4 = {'water': -424.654435, 'acetonitrile': -424.656267}  # Eh
+# using T_d (symmetry number = 12)
+S_BF4 = {'water':  1.10930898e-04, 'acetonitrile': 1.10898588e-04}  # Eh K⁻¹
+H_BF4 = {'water': -4.24623707e+02, 'acetonitrile': -4.24625549e+02}  # Eh
+G_BF4 = {'water': -4.24654435e+02, 'acetonitrile': -4.24656267e+02}  # Eh 
+
+# using T_d (symmetry number = 12)
+S_NME4 = {'water':  1.20348114e-04, 'acetonitrile': 1.20369406e-04} # Eh K⁻¹
+H_NME4 = {'water': -2.14060409e+02, 'acetonitrile': -2.14067632e+02} # Eh
+G_NME4 = {'water': -2.14093945e+02, 'acetonitrile': -2.14101174e+02} # Eh
+
 RADII_NME4 = {'water': 2.108130614275878, 'acetonitrile': 2.098320849223868}  # angstrom
 RADII_BF4 = {'water': 1.151806660832909, 'acetonitrile': 1.1520489206428235}  # angstrom
 

nitroxides.tex

@@ -488,8 +488,8 @@ \subsection{Impact of the electrolytes} \label{sec:elect}
 
 In acetonitrile, however, the lower dielectric constant leads to a reduced charge screening. A significant decrease of the complexation energy (10 to \SI{20}{\kilo\joule\per\mole}) is observed for the \ce{N^-C+} pair when \ce{C+} is near the nitroxyl group (first position). This aligns with the model for ion pair formation [Eq.~\eqref{eq:pair}], particularly when considering the impact of the ratio between the radii of the cavities. Since \ce{NMe4+} has a larger radius (\SI{2.1}{\angstrom}) than \ce{BF4-} (\SI{1.5}{\angstrom}), the former is closer in size to nitroxides ($>$\SI{3}{\angstrom}). The second position remains generally favored in the \ce{N+A-} pair, though only by a few \si{\kilo\joule\per\mole}.
 
-Using the most stable positions for each complex, the corresponding equilibrium constants are reported in Fig.~\ref{fig:Kx1} (see also Tables S7-S8 and Fig.~S6). The average value in each family, in water, is also reported in Table \ref{tab:Kx1}. In general, $K_{11} < K_{01} < K_{21} < 1$, indicating that the interaction between the hydroxylamine anion and the cation is the less destabilizing. Furthermore, while these equilibrium constants are of the same order of magnitude ($\sim \num{e-5}$) for \textbf{1}, significant differences appear in the other families. 
-In particular, in water, the equilibrium constants $K_{01}$ and $K_{21}$ for aromatic compounds, IIO and APO, are two orders of magnitude larger due to ion-quadrupole interactions. The latter family contains compounds with some of the lowest complexation energies. However, correlating the nature of the substituent with the complexation energy remains challenging. In the literature, perpendicular $\pi$-cation interactions are stabilized by electron-rich aromatic rings (and thus donor substituents), while $\pi$-anion interactions are stabilized by electron-poor rings (acceptor substituents) \cite{pappFourFacesInteraction2017}. Despite this, compounds with either donor (\textit{e.g.}, \textbf{42}) or acceptor (\textit{e.g.}, \textbf{54}) substituents exhibit small complexation energies, likely due to variations in ion positioning across different systems. Regarding acetonitrile, while $K_{21}$ increases for the reasons discussed, this is not necessarily the case for the other constants. 
+Using the most stable positions for each complex, the corresponding equilibrium constants are reported in Fig.~\ref{fig:Kx1} (see also Tables S7-S8 and Fig.~S6). The average value in each family, in water, is also reported in Table \ref{tab:Kx1}. In general, $K_{11} < K_{01} < K_{21} < 1$, indicating that the interaction between the hydroxylamine anion and the cation is the less destabilizing. Furthermore, while these equilibrium constants are of the same order of magnitude ($\sim \num{e-4}$) for \textbf{1}, significant differences appear in the other families. 
+In particular, in water, the equilibrium constants $K_{01}$ are one order of magnitude larger and $K_{21}$ are two order of magnitude larger for aromatic compounds (IIO and APO), due to ion-quadrupole interactions. The latter family contains compounds with some of the lowest complexation energies. However, correlating the nature of the substituent with the complexation energy remains challenging. In the literature, perpendicular $\pi$-cation interactions are stabilized by electron-rich aromatic rings (and thus donor substituents), while $\pi$-anion interactions are stabilized by electron-poor rings (acceptor substituents) \cite{pappFourFacesInteraction2017}. Despite this, compounds with either donor (\textit{e.g.}, \textbf{42}) or acceptor (\textit{e.g.}, \textbf{54}) substituents exhibit small complexation energies, likely due to variations in ion positioning across different systems. Regarding acetonitrile, while $K_{21}$ increases for the reasons discussed, this is not necessarily the case for the other constants. 
 
 \begin{figure}[!h]
 	\centering
@@ -504,11 +504,11 @@ \subsection{Impact of the electrolytes} \label{sec:elect}
 		\hline
 		& $pK_{01}$ & $pK_{11}$ & $pK_{21}$ \\
 		\hline
-		AMO & 4.13 & 4.65 &  5.15  \\
-		P6O & 3.20 $\pm$ 0.70 & 5.54 $\pm$ 0.73 &  7.52 $\pm$ 1.36 \\
-		P5O & 4.38 $\pm$ 1.83 & 5.44 $\pm$ 1.84 &  3.80 $\pm$ 1.85 \\
-		IIO & 3.24 $\pm$ 0.54 & 4.64 $\pm$ 0.40 &  3.22 $\pm$ 0.81 \\
-		APO & 3.22 $\pm$ 0.39 & 5.26 $\pm$ 1.83 &  2.41 $\pm$ 1.18 \\
+		Family.AMO & 4.13 & 3.37 & 3.88  \\
+		Family.P6O & 3.29 $\pm$ 0.67 & 4.27 $\pm$ 0.73 & 6.24 $\pm$ 1.36 \\
+		Family.P5O & 4.38 $\pm$ 1.83 & 4.17 $\pm$ 1.84 & 2.52 $\pm$ 1.85 \\
+		Family.IIO & 3.24 $\pm$ 0.54 & 3.36 $\pm$ 0.40 & 1.94 $\pm$ 0.81 \\
+		Family.APO & 3.22 $\pm$ 0.39 & 3.98 $\pm$ 1.83 & 1.13 $\pm$ 1.18 \\
 		\hline
 	\end{tblr}
 	\caption{Mean value of the cologarithm ($pK = -\log_{10}K$) of the complexation equilibrium constants for each family (reported as mean $\pm$ standard deviation), as computed at the $\omega$B97X-D/6-311+G(d) level in water using SMD and $[X]=\SI{1}{\mole\per\liter}$.}