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 conformer | s⁻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
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.
\(d[\mathrm{P_B}]/d[\mathrm{P_A}] = k_\mathrm{B}[\mathrm{B}]/(k_\mathrm{A}[\mathrm{A}]) = Kk_\mathrm{B}/k_\mathrm{A}\)。
The ratio of formation rates is \(Kk_\mathrm{B}/k_\mathrm{A}\).
\(K = e^{-(G_\mathrm{B} - G_\mathrm{A})/RT}\),\(k_i = (k_\mathrm{B}T/h)e^{-(G^\ddagger_i - G_i)/RT}\);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.