含义Meaning
原子核比电子重约 2000 倍，运动慢得多；因此可先固定核构型求电子能量 \(E_\text{el}(\mathbf R)\)，它构成核运动的势能面。“分子结构”“势能面”“过渡态”等概念都建立在这一近似上。
Nuclei are ~2000 times heavier than electrons and move far more slowly, so electrons are solved for fixed nuclei; \(E_\text{el}(\mathbf R)\) becomes the potential-energy surface — the basis of ‘structure’, ‘PES’ and ‘transition state’.
符号说明Symbols
| 符号Symbol | 含义 Meaning | 单位 Unit |
|---|---|---|
| \(\mathbf r, \mathbf R\) | 电子、原子核坐标electron and nuclear coordinates | m |
| \(E_\text{el}(\mathbf R)\) | 势能面potential-energy surface | J |
推导Derivation
分子哈密顿量 \(\hat H = \hat T_n + \hat T_e + \hat V_{ee} + \hat V_{en} + \hat V_{nn}\)。
Molecular Hamiltonian with nuclear and electronic kinetic and potential terms.
固定 R，略去 \(\hat T_n\)，解电子方程得 \(E_\text{el}(\mathbf R)\)（含 \(V_{nn}\)）。
Fix R, drop \(\hat T_n\), solve for \(E_\text{el}(\mathbf R)\).
代入乘积形式，忽略 \(\hat T_n\) 作用在 \(\psi_\text{el}\) 上的项（非绝热耦合，量级 \(\sqrt{m_e/M}\)），得核方程 \([\hat T_n + E_\text{el}(\mathbf R)]\chi = E\chi\)。
Neglecting \(\hat T_n\) acting on \(\psi_\text{el}\) (non-adiabatic terms ~\(\sqrt{m_e/M}\)) gives the nuclear equation on that surface.
适用条件与局限Assumptions & limitations
两个电子态能量接近（锥形交叉、避免交叉）时失效，导致无辐射跃迁、光化学反应等非绝热过程。
Fails near conical intersections and avoided crossings — the origin of non-adiabatic photochemistry.
同位素效应（如 H/D 零点能差）在该近似下来自核运动而非势能面。
Isotope effects arise from nuclear motion on the same surface.