\[U_L \approx -\frac{1.2025\times10^{-4}\,\nu\,|z_+z_-|}{r_+ + r_-}\left(1 - \frac{3.45\times10^{-11}}{r_+ + r_-}\right)\ \mathrm{J\,mol^{-1}\,m}\]
常用形式：d = r₊ + r₋，以 pm 为单位practical form with d = r₊ + r₋ in pm
\[U_L \approx -\frac{1.2025\times10^{5}\,\nu|z_+z_-|}{d}\left(1 - \frac{34.5}{d}\right)\ \mathrm{kJ/mol}\]含义Meaning
不需要知道晶体结构即可估算晶格能：卡普斯京斯基注意到 M/ν 在各结构间近乎常数，用离子半径之和代替 r₀。
Estimates lattice energy without knowing the structure: M/ν is nearly constant across structures, and the sum of ionic radii replaces r₀.
符号说明Symbols
| 符号Symbol | 含义 Meaning | 单位 Unit |
|---|---|---|
| \(\nu\) | 化学式中离子数number of ions per formula unit | 1 |
| \(r_+, r_-\) | 离子半径ionic radii | m |
推导Derivation
以玻恩–迈耶方程为起点，把 M 换成 \(0.874\nu\)（各结构 M/ν 的近似平均）。
Start from Born–Mayer and replace M by \(0.874\nu\).
r₀ 用 \(r_+ + r_-\)，ρ 取 34.5 pm，代入常数整理。
Use \(r_+ + r_-\) for r₀ and ρ = 34.5 pm.
反过来，已知晶格能可求复杂离子（SO₄²⁻、NO₃⁻）的“热化学半径”。
Conversely, known lattice energies give thermochemical radii of complex ions.
适用条件与局限Assumptions & limitations
估算精度约 ±5%；对共价性强的盐偏差大。
About ±5 %; worse for covalent salts.
例题Worked example
NaCl：ν = 2，d = 102 + 181 = 283 pm：U ≈ −1.2025×10⁵×2/283×(1 − 34.5/283) ≈ −746 kJ/mol（玻恩–哈伯值 −787）。
NaCl: ν = 2, d = 283 pm → U ≈ −746 kJ/mol (Born–Haber −787).