From 236b3dc9497ebb50bb50d147f09e15d036a2eb4f Mon Sep 17 00:00:00 2001 From: pierre-24 Date: Wed, 12 Jun 2024 00:37:38 +0200 Subject: [PATCH] even more fixes --- nitroxides.tex | 25 ++++++++++++------------- 1 file changed, 12 insertions(+), 13 deletions(-) diff --git a/nitroxides.tex b/nitroxides.tex index 10cb07c..f85e230 100644 --- a/nitroxides.tex +++ b/nitroxides.tex @@ -459,7 +459,7 @@ \subsection{Impact of the solvent} \label{sec:solv} \clearpage \subsection{Impact of the electrolytes} \label{sec:elect} -So far, the concentration of electrolyte, $[X]$, has been maintained at zero. To evaluate its impact on the redox potentials, the DH correction itself is initially examined in Fig.~\ref{fig:DH}. As anticipated, it remains small within the concentration range considered here (a few tenths of millivolts for $[X] \leq \SI{1}{\mole\per\liter}$ and larger in acetonitrile), increasing with $[X]$. Its sign differs between oxidation and reduction potentials. Additionally, it is diminished for compounds belonging to the IIO and APO families (as they are larger molecules with larger $a$), but amplified for species with a net positive charge (\textbf{11}, \textbf{21}, \textbf{35}), for which the correction for oxidation and reduction potentials is negative. +So far, the concentration of electrolyte, $[X]$, has been maintained at zero. To evaluate its impact on the redox potentials, the DH correction itself, Eq.~\eqref{eq:dh}, is initially examined in Fig.~\ref{fig:DH}. As anticipated due to the amplitude of the charges involved ($z=\pm 1$), it remains small within the concentration range considered here (a few tenths of millivolts for $[X] \leq \SI{1}{\mole\per\liter}$ and larger in acetonitrile), increasing with $[X]$. Its sign differs between oxidation and reduction potentials, since it only affects the charged species, and while \ce{N+} is a reactant, \ce{N-} a product. Additionally, it decrease for compounds belonging to the IIO and APO families (as they are larger molecules with larger $a$), while it is amplified for species with a net positive charge (\textbf{11}, \textbf{21}, \textbf{35}), for which the correction for oxidation and reduction potentials is negative. \begin{figure}[!b] @@ -471,29 +471,30 @@ \subsection{Impact of the electrolytes} \label{sec:elect} \clearpage -Next, the formation of ion pairs is addressed. As noted by other researchers \cite{zhangInteractionsImidazoliumBasedIonic2016,wylieImprovedPerformanceAllOrganic2019a}, the position of the ions significantly impacts the complexation energies. In practice, it is observed that there are two possible positions for the counterion (see Tables S5-S6 and an example in Fig.~\ref{fig:pos-anion}): +Then, the formation of the ion pairs is addressed. As noted by other researchers \cite{zhangInteractionsImidazoliumBasedIonic2016,wylieImprovedPerformanceAllOrganic2019a}, the position of the ions significantly impacts the complexation energies. In practice, it is observed that there are two possible positions for the counterion (see Tables S5-S6 and an example in Fig.~\ref{fig:pos-anion}): \begin{inparaenum}[(i)] - \item near the redox center ($>$\ce{N-O^.}), "in front" of the methyl groups, and + \item near the redox center ($>$\ce{N-O}), "in front" of the methyl groups, and \item near the substituent, "behind" the methyl groups. \end{inparaenum} \begin{figure}[!h] \centering \includegraphics[width=.8\linewidth]{Figure12} -\caption{Impact of the counterion position (a) or (b) on the distance between the counterion and the redox center (the nitrogen in the oxidized form, $>$\ce{N+=O}, or the oxygen in the reduced form, $>$\ce{N-O-}), and on $\Delta G^\star_{cplx}$, using compound \textbf{4} as an example. Calculations were performed at the $\omega$B97X-D/6-311+G(d) level in water (black) and acetonitrile (blue) using SMD, with $[X]=\SI{0}{\mole\per\liter}$.} +\caption{$\Delta G^\star_{cplx}$ of compound \textbf{4} as a function of counterion poisition. The distance between the redox center (the nitrogen in the oxidized form, $>$\ce{N+=O}, or the oxygen in the reduced form, $>$\ce{N-O-}) and the counterion are also given. Calculations were performed at the $\omega$B97X-D/6-311+G(d) level in water (black) and acetonitrile (blue) using SMD, with $[X]=\SI{0}{\mole\per\liter}$.} \label{fig:pos-anion} \end{figure} -In both solvents, the radical (\ce{N^.}) interacts with \ce{C+} in the first position \cite{zhangEffectHeteroatomFunctionality2018}. Then, in water, the complexation energies for the \ce{N+A-} and \ce{N^-C+} pairs are positive and significant. The difference in complexation energies between the two positions is generally small (a few \si{\kilo\joule\per\mole}), but the second position is favored in most of the case. Interestingly, this results in a larger nitroxide-to-counterion distance, indicating a less significant electrostatic interaction between the redox center and the counterion and suggesting that the substituent also plays a role in lowering the complexation energy. Another contributing factor is the quadrupole-ion interaction due to the aromatic systems present in compounds from the IIO and APO families, which is particularly important in the \ce{N^-C+} pair. Here, the difference in energy between the two positions is more pronounced. +In both solvents, the radical (\ce{N^.}) interacts with \ce{C+} in the first position, near $>$\ce{N-O^.} \cite{zhangEffectHeteroatomFunctionality2018}. Then, in water, the complexation energies for the \ce{N+A-} and \ce{N^-C+} pairs are positive and significant. The difference in complexation energies between the two positions is generally small (a few \si{\kilo\joule\per\mole}), but the second position is favored in most of the case. Interestingly, this type of interaction corresponds to a larger nitroxide-to-counterion distance, indicating a smaller electrostatic interaction between the redox center and the counterion and suggesting that the substituent also plays a role in lowering the complexation energy. Another contributing factor is the quadrupole-ion interaction due to the aromatic moieties present in compounds from the IIO and APO families, which is particularly important in the \ce{N^-C+} pair. Here, the difference in energy between the two positions is more pronounced. -In acetonitrile, however, the lower dielectric constant leads to reduced charge screening. A significant decrease (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 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}. +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 most stabilizing. 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. +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. \begin{figure}[!h] \centering \includegraphics[width=\linewidth]{Figure13} - \caption{Value of the complexation equilibrium constants $K_{01}$ (round markers, $\bullet$), $K_{11}$ (round markers, $\blacktriangle$), and $K_{21}$ (square markers, $\blacksquare$), as computed at the $\omega$B97X-D/6-311+G(d) level in water (top) and acetonitrile (bottom) using SMD and $[X]=\SI{1}{\mole\per\liter}$. The dashed line is for visualization purposes.} + \caption{Value of the complexation equilibrium constants $K_{01}$ (triangular markers, $\bullet$), $K_{11}$ (round markers, $\blacktriangle$), and $K_{21}$ (square markers, $\blacksquare$), as computed at the $\omega$B97X-D/6-311+G(d) level in water (top) and acetonitrile (bottom) using SMD and $[X]=\SI{1}{\mole\per\liter}$. The dashed line is for visualization purposes.} \label{fig:Kx1} \end{figure} @@ -514,17 +515,15 @@ \subsection{Impact of the electrolytes} \label{sec:elect} \label{tab:Kx1} \end{table} -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. - -A notable exception to thse trends is the P6O family, which shows larger complexation equilibrium constants for the \ce{N^-C+} pair (with $\Delta G^\star_{cplx} > \SI{40}{\kilo\joule\per\mole}$) than others. This is a geometric effect: in such compounds, the \ce{N+=O} group (in oxoammonium) occupies an equatorial position, while the \ce{N-O-} bond (in the hydroxylamine anion) adopts an axial position. Nearby methyl groups hinder electrostatic interaction in the first case, especially for bulky counterions such as \ce{NMe4+}, as seen in Fig.~\ref{fig:pos-anion}. This effect is less pronounced in other families, where the skeleton prevents the oxygen from adopting such a position (particularly in IIO and APO), resulting in larger complexation equilibrium constants when the i ion is in close interaction with the redox center. +A notable exception to these trends is the P6O family, which shows smaller complexation equilibrium constants for the \ce{N^-C+} pair (with $\Delta G^\star_{cplx} > \SI{40}{\kilo\joule\per\mole}$) than others. This is a geometric effect: in such compounds, the \ce{N+=O} group (in oxoammonium) occupies an equatorial position, while the \ce{N-O-} bond (in the hydroxylamine anion) adopts an axial position. Nearby methyl groups hinder electrostatic interactions in the first case, especially for bulky counterions such as \ce{NMe4+}, as seen in Fig.~\ref{fig:pos-anion}. This effect is less pronounced in other families, where the skeleton prevents the oxygen from adopting such a position (particularly in IIO and APO), resulting in larger complexation equilibrium constants when the i ion is in close interaction with the redox center. -Finally, complexation to the \ce{AC} pair is considered (Fig.~\ref{fig:Kx2}, Tables S9-S10). Based on the positioning of the ions in the pairs that were previously discussed, for the \ce{NAC^-} and \ce{NAC^.} complexes, the cation is placed near the nitroxyl moiety, while the anion is placed near the substituent. The opposite is done for \ce{NAC^+}. As expected, the equilibrium constants are smaller (by about four orders of magnitude, $\Delta G^\star_{cplx} \sim \SI{50}{\kilo\joule\per\mole}$) than the ones previously discussed. However, the trends are similar: for example, in acetonitrile, the \ce{NAC^-} complexes are more stable than the others, as also observed previously \cite{wylieImprovedPerformanceAllOrganic2019a}. The stabilization of \ce{NAC^.} is however less important in this work than observed by this team, probably because of the larger dielectric constant used here. +Finally, the complexations of the nitroxides to the \ce{AC} pair is considered (Fig.~\ref{fig:Kx2}, Tables S9-S10). Based on the positioning of the ions in the pairs that were previously discussed, for the \ce{N^-AC} and \ce{N^.AC} complexes, the cation is placed near the nitroxyl moiety, while the anion is placed near the substituent. The opposite is done for \ce{N^+AC}. As expected, the equilibrium constants are smaller (by about four orders of magnitude, $\Delta G^\star_{cplx} \sim \SI{50}{\kilo\joule\per\mole}$) than the ones previously discussed. However, the trends are similar: for example, in acetonitrile, the \ce{NAC^-} complexes are more stable than the others, as also observed previously \cite{wylieImprovedPerformanceAllOrganic2019a}. The stabilization of \ce{NAC^.} is however less important in this work than observed by this team, probably because of the larger dielectric constant used here. \begin{figure}[!h] \centering \includegraphics[width=\linewidth]{Figure14} -\caption{Value of the complexation equilibrium constants $K_{02}$ (round markers, $\bullet$), $K_{12}$ (triangular markers, $\blacktriangle$) and $K_{22}$ (square markers, $\blacksquare$) for the 3 oxidation state of nitroxides, as computed at the $\omega$B97X-D/6-311+G(d) level in water (top) and acetonitrile (bottom) using SMD and $[X]=\SI{1}{\mole\per\liter}$. The dashed line is there to help visualization. } +\caption{Value of the complexation equilibrium constants $K_{02}$ (round markers, $\bullet$), $K_{12}$ (triangular markers, $\blacktriangle$) and $K_{22}$ (square markers, $\blacksquare$) for the 3 oxidation state of nitroxides, as computed at the $\omega$B97X-D/6-311+G(d) level in water (top) and acetonitrile (bottom) using SMD and $[X]=\SI{1}{\mole\per\liter}$. The dashed line is used to help visualization. } \label{fig:Kx2} \end{figure}