\[\lg\frac{k}{k_0} = \rho^*\sigma^* + \delta E_s\]
含义Meaning
把哈米特方程推广到脂肪族体系，把取代基效应分为极性（诱导）项 \(\sigma^*\) 和立体项 \(E_s\)。
Extends Hammett to aliphatic systems by separating polar (inductive) \(\sigma^*\) and steric \(E_s\) contributions.
符号说明Symbols
| 符号Symbol | 含义 Meaning | 单位 Unit |
|---|---|---|
| \(\sigma^*\) | 极性取代基常数polar substituent constant | 1 |
| \(E_s\) | 立体取代基常数（甲基为 0）steric substituent constant (Me = 0) | 1 |
| \(\rho^*, \delta\) | 反应对极性、立体效应的敏感度sensitivities to polar and steric effects | 1 |
推导Derivation
酯的酸催化水解过渡态与基态电荷几乎相同，对极性不敏感，速率差主要反映立体效应：\(E_s = \lg(k/k_0)_{\mathrm{H^+}}\)。
Acid-catalysed ester hydrolysis is insensitive to polar effects, so its rates define steric \(E_s\).
碱催化水解对极性和立体都敏感，两者相减消去立体项，得到极性常数：
Base-catalysed hydrolysis is sensitive to both; subtracting removes sterics:
\[\sigma^* = \frac{1}{2.48}\left[\lg\left(\frac{k}{k_0}\right)_{\mathrm{OH^-}} - \lg\left(\frac{k}{k_0}\right)_{\mathrm{H^+}}\right]\]
适用条件与局限Assumptions & limitations
极性与立体效应的完全分离只是近似；共振效应未单列。
The polar/steric separation is approximate; resonance is not separated.