含义Meaning
把反应物和产物的自由能面视为两条相同曲率的抛物线，活化能由重组能 λ 和反应自由能 ΔG° 决定。预言了“反转区”：驱动力超过 λ 后速率反而下降，1984 年被实验证实。马库斯获 1992 年诺贝尔化学奖。
Treats reactant and product free-energy surfaces as parabolas of equal curvature; the barrier depends on reorganisation energy λ and ΔG°. It predicted the inverted region — rates falling once the driving force exceeds λ — confirmed in 1984. Marcus won the 1992 Nobel Prize.
符号说明Symbols
| 符号Symbol | 含义 Meaning | 单位 Unit |
|---|---|---|
| \(\lambda\) | 重组能（内层 + 溶剂）reorganisation energy (inner + solvent) | kJ·mol⁻¹, eV |
| \(\Delta G^\circ\) | 电子转移标准自由能变standard free energy of electron transfer | kJ·mol⁻¹ |
推导Derivation
反应物曲线 \(G_R = \tfrac{\lambda}{4}\cdot 4x^2 = \lambda x^2\)，产物曲线 \(G_P = \lambda(x - 1)^2 + \Delta G^\circ\)（x 为归一化反应坐标）。
Reactant parabola \(\lambda x^2\), product parabola \(\lambda(x-1)^2 + \Delta G^\circ\).
交点（过渡态）：\(\lambda x^2 = \lambda(x-1)^2 + \Delta G^\circ\) ⇒ \(x^\ddagger = (\lambda + \Delta G^\circ)/2\lambda\)。
Crossing at \(x^\ddagger = (\lambda + \Delta G^\circ)/2\lambda\).
代回 \(\Delta G^\ddagger = \lambda x^{\ddagger2} = (\lambda + \Delta G^\circ)^2/4\lambda\)。
Hence the Marcus barrier.
\(-\Delta G^\circ = \lambda\) 时势垒为零（最快）；\(-\Delta G^\circ > \lambda\) 进入反转区。
Barrierless at −ΔG° = λ; inverted beyond.
适用条件与局限Assumptions & limitations
适用于弱耦合（非绝热）外层电子转移；强耦合、量子振动模式需用马库斯–列维奇–约特纳理论修正反转区。
For weakly coupled outer-sphere transfer; quantum modes (Marcus–Levich–Jortner) soften the inverted region.