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

柯廷–哈米特原理Curtin–Hammett principle

\[\frac{[\mathrm{P_B}]}{[\mathrm{P_A}]} = \frac{k_\mathrm{B}}{k_\mathrm{A}}K = \exp\!\left(-\frac{G^\ddagger_\mathrm{B} - G^\ddagger_\mathrm{A}}{RT}\right)\]

含义Meaning

两个快速互变的构象(或异构体)分别生成不同产物时,产物比只取决于两个过渡态的绝对自由能差,而与基态布居无关。

When two rapidly interconverting conformers give different products, the product ratio depends only on the free-energy difference of the two transition states, not on ground-state populations.

符号说明Symbols

符号Symbol含义 Meaning单位 Unit
\(K\)构象平衡常数 [B]/[A]conformer equilibrium constant [B]/[A]1
\(k_\mathrm{A}, k_\mathrm{B}\)各构象生成产物的速率常数rate constants from each conformers⁻¹
\(G^\ddagger\)过渡态自由能(同一参照)transition-state free energy (common reference)kJ·mol⁻¹

推导Derivation

  1. 设 A ⇌ B 快速平衡(\(k_{AB}, k_{BA} \gg k_\mathrm{A}, k_\mathrm{B}\)),则任何时刻 \([\mathrm{B}] = K[\mathrm{A}]\)。

    With fast A ⇌ B equilibrium, \([\mathrm{B}] = K[\mathrm{A}]\) at all times.

  2. \(d[\mathrm{P_B}]/d[\mathrm{P_A}] = k_\mathrm{B}[\mathrm{B}]/(k_\mathrm{A}[\mathrm{A}]) = Kk_\mathrm{B}/k_\mathrm{A}\)。

    The ratio of formation rates is \(Kk_\mathrm{B}/k_\mathrm{A}\).

  3. \(K = e^{-(G_\mathrm{B} - G_\mathrm{A})/RT}\),\(k_i = (k_\mathrm{B}T/h)e^{-(G^\ddagger_i - G_i)/RT}\);相乘时基态能量 \(G_\mathrm{A}, G_\mathrm{B}\) 抵消。

    Multiplying the Boltzmann and Eyring factors, ground-state energies cancel.

适用条件与局限Assumptions & limitations

  • 前提是构象互变远快于生成产物;若互变慢(非 Curtin–Hammett 条件),产物比反映初始布居。

    Requires interconversion much faster than product formation; otherwise the ratio reflects initial populations.

例题Worked example

N-甲基哌啶类的 N-烷基化:主要构象未必生成主要产物。

N-alkylation of substituted piperidines: the major conformer need not give the major product.