Šrut Adam, Lear Benjamin J, Krewald Vera
Department of Chemistry, Theoretical Chemistry, TU Darmstadt Peter-Grünberg-Straße 4 64287 Darmstadt Germany
Department of Chemistry, The Pennsylvania State University University Park PA 16802 USA
Chem Sci. 2023 Aug 8;14(34):9213-9225. doi: 10.1039/d3sc01402a. eCollection 2023 Aug 30.
The Marcus model forms the foundation for all modern discussion of electron transfer (ET). In this model, ET results in a change in diabatic potential energy surfaces, separated along an ET nuclear coordinate. This coordinate accounts for all nuclear motion that promotes electron transfer. It is usually assumed to be dominated by a collective asymmetric vibrational motion of the redox sites involved in the ET. However, this coordinate is rarely quantitatively specified. Instead, it remains a nebulous concept, rather than a tool for gaining true insight into the ET pathway. Herein, we describe an approach for quantifying the ET coordinate and demonstrate it for a series of dinitroradical anions. Using sampling methods at finite temperature combined with density functional theory calculations, we find that the electron transfer can be followed using the energy separation between potential energy surfaces and the extent of electron localization. The precise nuclear motion that leads to electron transfer is then obtained as a linear combination of normal modes. Once the coordinate is identified, we find that evolution along it results in a change in diabatic state and optical excitation energy, as predicted by the Marcus model. Thus, we conclude that a single dimension of the electron transfer described in Marcus-Hush theory can be described as a well-defined nuclear motion. Importantly, our approach allows the separation of the intrinsic electron transfer coordinate from other structural relaxations and environmental influences. Furthermore, the barrier separating the adiabatic minima was found to be sufficiently thin to enable heavy-atom tunneling in the ET process.
马库斯模型构成了所有现代电子转移（ET）讨论的基础。在这个模型中，电子转移导致非绝热势能面发生变化，这些势能面沿着电子转移核坐标分开。这个坐标考虑了促进电子转移的所有核运动。通常认为它主要由参与电子转移的氧化还原位点的集体不对称振动运动主导。然而，这个坐标很少被定量确定。相反，它仍然是一个模糊的概念，而不是一个深入了解电子转移途径的工具。在此，我们描述了一种量化电子转移坐标的方法，并对一系列二硝基自由基阴离子进行了演示。通过在有限温度下的采样方法结合密度泛函理论计算，我们发现可以利用势能面之间的能量分离和电子定域程度来跟踪电子转移。导致电子转移的精确核运动随后作为简正模式的线性组合获得。一旦确定了坐标，我们发现沿着它的演化会导致非绝热态和光激发能发生变化，正如马库斯模型所预测的那样。因此，我们得出结论，马库斯 - 赫什理论中描述的电子转移的单一维度可以被描述为一种明确的核运动。重要的是，我们的方法允许将内在电子转移坐标与其他结构弛豫和环境影响分开。此外，发现分隔绝热极小值的势垒足够薄，能够在电子转移过程中实现重原子隧穿。
