含义Meaning
描述中性分子（尤其稀有气体）之间相互作用的经验势能（1924）：r⁻⁶ 吸引项来自色散力（范德华力），r⁻¹² 排斥项近似电子云重叠的泡利排斥。分子模拟中最常用的非键势。
An empirical pair potential for neutral molecules, especially noble gases (1924): the r⁻⁶ attraction is London dispersion, the r⁻¹² repulsion approximates Pauli overlap. The most common non-bonded potential in molecular simulation.
符号说明Symbols
| 符号Symbol | 含义 Meaning | 单位 Unit |
|---|---|---|
| \(\varepsilon\) | 势阱深度well depth | J |
| \(\sigma\) | 势能为零处的距离（碰撞直径）distance where V = 0 (collision diameter) | m |
| \(\alpha'\) | 极化率体积polarisability volume | m³ |
| \(I\) | 电离能ionisation energy | J |
推导Derivation
二阶微扰：两分子的瞬时偶极–诱导偶极相互作用给出 \(-C_6/r^6\)（伦敦，1930）。
Second-order perturbation theory gives the −C₆/r⁶ dispersion (London, 1930).
排斥实际近似指数形式，取 r⁻¹² 是因为计算方便（恰为 r⁻⁶ 的平方）。
Repulsion is really exponential; r⁻¹² is used for convenience.
令 \(dV/dr = 0\) 得 \(r_\text{min} = 2^{1/6}\sigma\)，代回得 −ε。
dV/dr = 0 gives r_min and −ε.
适用条件与局限Assumptions & limitations
排斥项过陡；极性分子还需静电（偶极、氢键）项；参数（如 Ar：ε/k_B = 120 K，σ = 3.4 Å）由第二维里系数或黏度拟合。
The repulsion is too steep; polar molecules need electrostatics; parameters come from virial or viscosity data (Ar: ε/k_B = 120 K, σ = 3.4 Å).