Achieving Accurate Reduction Potential Predictions for Anthraquinones in Water and Aprotic Solvents: Effects of Inter- and Intramolecular H‑Bonding and Ion Pairing

In this combined computational and experimental study, specific chemical interactions affecting the prediction of one-electron and two-electron reduction potentials for anthraquinone derivatives are investigated. For 19 redox reactions in acidic aqueous solution, where AQ is reduced to hydroanthraquinone, density functional theory (DFT) with the polarizable continuum model (PCM) gives a mean absolute deviation (MAD) of 0.037 V for 16 species. DFT­(PCM), however, highly overestimates three redox couples with a MAD of 0.194 V, which is almost 5 times that of the remaining 16. These three molecules have ether groups positioned for intramolecular hydrogen bonding that are not balanced with the intermolecular H-bonding of the solvent. This imbalanced description is corrected by quantum mechanics/molecular mechanics (QM/MM) simulations, which include explicit water molecules. The best theoretical estimations result in a good correlation with experiments, V(Theory) = 0.903V(Expt) + 0.007 with an R2 value of 0.835 and an MAD of 0.033 V. In addition to the aqueous test set, 221 anthraquinone redox couples in aprotic solvent were studied. Five anthraquinone derivatives spanning a range of redox potentials were selected from this library, and their reduction potentials were measured by cyclic voltammetry. DFT­(PCM) calculations predict the first reduction potential with high accuracy giving the linear relation, V(Theory) = 0.960V(Expt) – 0.049 with an R2 value of 0.937 and an MAD of 0.051 V. This approach, however, significantly underestimates the second reduction potential, with an MAD of 0.329 V. It is shown herein that treatment of explicit ion-pair interactions between the anthraquinone derivatives and the cation of the supporting electrolyte is required for the accurate prediction of the second reduction potential. After the correction, V(Theory) = 1.045V(Expt) – 0.088 with an R2 value 0.910 and an MAD value reduced by more than half to 0.145 V. Finally, molecular design principles are discussed that go beyond simple electron-donating and electron-withdrawing effects to lead to predictable and controllable reduction potentials.本研究结合计算与实验手段，探究了影响蒽醌（anthraquinone, AQ）衍生物单电子与双电子还原电势预测结果的特定化学相互作用。针对酸性水溶液中19条AQ还原为氢蒽醌（hydroanthraquinone）的氧化还原反应，采用结合极化连续介质模型（Polarizable Continuum Model, PCM）的密度泛函理论（Density Functional Theory, DFT）对16个物种进行计算，得到的平均绝对偏差（Mean Absolute Deviation, MAD）为0.037 V。然而，DFT-PCM方法对其中3个氧化还原对的预测结果存在显著高估，平均绝对偏差达0.194 V，约为其余16个物种偏差值的5倍。这三类分子的醚基团可形成分子内氢键，但其与溶剂的分子间氢键作用并不匹配。这种描述失衡的问题可通过包含显式水分子的量子力学/分子力学（Quantum Mechanics/Molecular Mechanics, QM/MM）模拟得到修正。最优的理论预测结果与实验数据相关性良好，拟合公式为V(理论) = 0.903V(实验) + 0.007，决定系数（R²）为0.835，平均绝对偏差为0.033 V。除上述水相测试集外，本研究还探究了非质子溶剂中的221个蒽醌氧化还原对。从该库中选取了5个覆盖不同还原电势范围的蒽醌衍生物，并通过循环伏安法（Cyclic Voltammetry, CV）测定了它们的还原电势。DFT-PCM计算可高精度预测首次还原电势，拟合公式为V(理论) = 0.960V(实验) – 0.049，决定系数R²为0.937，平均绝对偏差为0.051 V。但该方法对二次还原电势的预测存在显著低估，平均绝对偏差达0.329 V。本研究表明，若要精准预测二次还原电势，需考虑蒽醌衍生物与支持电解质阳离子之间的显式离子对相互作用。修正后，拟合公式变为V(理论) = 1.045V(实验) – 0.088，决定系数R²为0.910，平均绝对偏差较修正前降低超一半，降至0.145 V。最后，本研究还讨论了超越简单给电子、吸电子效应的分子设计原则，可实现还原电势的可预测与可控调节。