选择定则Selection rule

电偶极跃迁强度正比于 |⟨ψ_f|μ̂|ψ_i⟩|²。根据对称性，只有当初态、偶极算符和末态的直积包含全对称表示时，积分才不为零。主要选择定则包括：原子光谱 Δl = ±1；自旋选律 ΔS = 0（单重态↔三重态禁阻）；拉波特规则——中心对称分子中 g↔g、u↔u 跃迁禁阻（所以八面体配合物的 d-d 跃迁很弱、颜色较淡）；谐振子振动 Δv = ±1，且分子偶极矩须随振动变化才有红外活性；拉曼活性要求极化率随振动变化；转动光谱要求分子有永久偶极矩，ΔJ = ±1。

Electric-dipole intensity is proportional to |⟨ψ_f|μ̂|ψ_i⟩|². By symmetry, the integral is non-zero only if the direct product of initial state, dipole operator and final state contains the totally symmetric representation. Key rules: Δl = ±1 in atomic spectra; ΔS = 0 for spin (singlet↔triplet is forbidden); the Laporte rule, forbidding g↔g and u↔u transitions in centrosymmetric molecules (so d–d bands of octahedral complexes are weak and colours pale); Δv = ±1 for a harmonic oscillator, with infrared activity requiring the dipole moment to change during the vibration; Raman activity requiring the polarisability to change; and rotational spectra requiring a permanent dipole, with ΔJ = ±1.

选择定则最初是从原子光谱数据中总结出的经验规律。1918 年玻尔的对应原理给出了初步解释，1920 年代量子力学建立后，狄拉克等用跃迁矩阵元严格推导出这些规则。1925 年拉波特提出了宇称选律。

Selection rules began as empirical regularities in atomic spectra. Bohr's correspondence principle of 1918 gave a first explanation, and after quantum mechanics arrived in the 1920s Dirac and others derived them rigorously from transition matrix elements. Laporte stated the parity rule in 1925.

禁阻跃迁并非完全不能发生：自旋-轨道耦合使重原子化合物中单重态-三重态跃迁变得较强（磷光、系间窜越）；振动耦合使拉波特禁阻的 d-d 跃迁获得一定强度（振电耦合）；四面体配合物无对称中心，d-d 跃迁较强，颜色更深（如 [CoCl₄]²⁻ 呈深蓝色）。磁偶极和电四极跃迁比电偶极跃迁弱几个数量级。

Forbidden transitions are not impossible: spin–orbit coupling makes singlet–triplet transitions stronger in heavy-atom compounds (phosphorescence, intersystem crossing); vibronic coupling lends Laporte-forbidden d–d transitions some intensity; and tetrahedral complexes, lacking an inversion centre, have stronger d–d bands and deeper colours (such as deep-blue [CoCl₄]²⁻). Magnetic-dipole and electric-quadrupole transitions are orders of magnitude weaker than electric-dipole ones.