Garcia-Padilla Eduardo, Qiu Guanqi
Max-Planck-Institut für Kohlenforschung Kaiser-Wilhelm-Platz 1 45470 Mülheim an der Ruhr Germany
Chem Sci. 2025 Aug 21. doi: 10.1039/d5sc04829j.
What governs the relationship between the reaction rate and thermodynamic driving force? Despite decades of rate theory, no general physically grounded equation exists to relate rate and driving force across all regimes. Classical models, such as the Marcus equation and Leffler equations, either rely on under-realistic assumptions or only capture the local behaviour, failing outside narrow regimes. We derive a general, non-linear equation from microscopic reversibility, arriving at three physically meaningful parameters: a minimum preorganisational barrier ( ), a reaction symmetry offset ( ), and a kinetic curvature factor (). This model captures global behaviour, recovers known limits, and explains why classical models like Leffler equation exhibit the rate-driving force responsiveness (the Brønsted slope) as they do, by revealing their physical origin, not by fitting them. The model enables a causal reinterpretation of experimentally observed curved rate-driving force plots, such as in hydrogen atom transfer to Fe(iv)[double bond, length as m-dash]O. Importantly, this model does not require replacing existing models, it explains their physical foundations, enabling chemists to continue using them while understanding when and why they apply, and where they break down. Beyond case studies including hydride shifts, rearrangements, and cyclisations, the framework's strength lies in its deductive foundation enabling the physically grounded design of reactions with desired kinetics across diverse chemical systems. By revealing the global structure of the rate-driving force relationship, this framework enables chemists to recognise, predict, and design reactivity that would otherwise appear anomalous or inaccessible, better clarifying the unknowns. Examples include highly exergonic regimes near , where further increases in exergonicity offer little rate improvement, and control shifts to structural factors; even when the rate-driving force plot appears linear, the model uncovers hidden curvature and deeper physical meaning.
是什么决定了反应速率与热力学驱动力之间的关系?尽管速率理论已经发展了数十年,但尚无一个基于物理原理的通用方程能够描述所有情况下的速率与驱动力之间的关系。经典模型,如马库斯方程和莱夫勒方程,要么依赖于不切实际的假设,要么只能捕捉局部行为,在狭窄范围之外就不再适用。我们从微观可逆性出发推导出一个通用的非线性方程,得到三个具有物理意义的参数:最小预组织能垒( )、反应对称偏移( )和动力学曲率因子( )。该模型能够捕捉全局行为,恢复已知的极限情况,并通过揭示其物理根源而非通过拟合来解释为什么像莱夫勒方程这样的经典模型会呈现出它们所具有的速率 - 驱动力响应性(布朗斯特斜率)。该模型能够对实验观察到的弯曲的速率 - 驱动力曲线进行因果重新解释,例如在氢原子转移到Fe(iv)[双键,长度为m破折号]O的过程中。重要的是,该模型并不要求取代现有模型,而是解释它们的物理基础,使化学家能够继续使用它们,同时理解它们何时以及为何适用,以及在何处失效。除了包括氢化物迁移、重排和环化反应的案例研究之外,该框架的优势在于其演绎基础,能够基于物理原理设计具有所需动力学的各种化学系统中的反应。通过揭示速率 - 驱动力关系的全局结构,该框架使化学家能够识别、预测和设计那些否则可能显得异常或难以实现的反应活性,从而更好地阐明未知情况。例如,在接近 的高度放能区域,放能性的进一步增加对速率的提升很小,控制作用转向结构因素;即使速率 - 驱动力曲线看似线性,该模型也能揭示隐藏的曲率和更深层次的物理意义。