双语化学辞典Chem Lexicon
研究生Graduate 结构、立体化学与物理有机 Structure, stereochemistry & physical organic chemistry

贝尔–埃文斯–波拉尼原理Bell–Evans–Polanyi principle

\[E_a = E_0 + \alpha\,\Delta_r H\]

含义Meaning

同一类反应中活化能与反应焓线性相关:放热越多,能垒越低。\(\alpha\) 介于 0 与 1 之间,反映过渡态位置(哈蒙德假说的定量形式)。

Within a reaction family, activation energy is linear in reaction enthalpy: more exothermic means a lower barrier; α (0–1) locates the TS — a quantitative Hammond postulate.

符号说明Symbols

符号Symbol含义 Meaning单位 Unit
\(E_a\)活化能activation energykJ·mol⁻¹
\(E_0\)该类反应的固有能垒intrinsic barrier of the familykJ·mol⁻¹
\(\alpha\)过渡态位置参数transition-state position parameter1

推导Derivation

  1. 用两条交叉的势能曲线(反应物、产物)近似:产物曲线下移 \(\Delta H\) 时,交点(过渡态)下移约 \(\alpha\Delta H\)。

    Model reactant and product curves as intersecting lines; lowering the product curve by ΔH lowers the crossing point by about αΔH.

  2. 直线近似给出线性关系;用抛物线则得马库斯方程,α 随 ΔH 变化。

    Linear curves give a linear law; parabolas give Marcus theory with ΔH-dependent α.

适用条件与局限Assumptions & limitations

  • 只在同一反应家族、ΔH 变化不大时成立。

    Only within one family over a modest ΔH range.

例题Worked example

自由基夺氢:Cl· 夺取 C–H 放热、能垒低、选择性差;Br· 吸热、能垒高、选择性好(叔 > 仲 > 伯)。

H abstraction: Cl· is exothermic and unselective; Br· endothermic and selective (3° > 2° > 1°).