含义Meaning
跃迁只有在跃迁偶极矩不为零时才是允许的。用群论可判断：直积必须含全对称表示。红外活性模式按 x, y, z 变换，拉曼活性模式按二次函数变换。
A transition is allowed only if its transition dipole is non-zero. Group theory decides: the direct product must contain the totally symmetric representation. IR-active modes transform like x, y, z; Raman-active modes like quadratic functions.
符号说明Symbols
| 符号Symbol | 含义 Meaning | 单位 Unit |
|---|---|---|
| \(\hat{\boldsymbol\mu}\) | 电偶极算符electric dipole operator | C·m |
| \(\Gamma\) | 不可约表示irreducible representation |
推导Derivation
费米黄金定则：跃迁速率 \(\propto |\langle f|\hat H'|i\rangle|^2\)，光场微扰 \(\hat H' = -\hat{\boldsymbol\mu}\cdot\mathbf E\)。
Fermi’s golden rule with \(\hat H' = -\hat\mu\cdot\mathbf E\).
积分在对称操作下必须不变才可能非零，所以被积函数须含全对称分量。
The integral can be non-zero only if the integrand contains the totally symmetric representation.
中心对称分子：IR 只允许 g↔u，拉曼只允许 g↔g（互斥规则）；拉波特规则禁止 d–d 跃迁（使其很弱）。
Centrosymmetric molecules: IR needs g↔u, Raman g↔g (mutual exclusion); Laporte forbids d–d.
适用条件与局限Assumptions & limitations
“禁阻”跃迁可通过振动耦合、自旋–轨道耦合、磁偶极或电四极机制弱弱地出现。
Forbidden transitions appear weakly via vibronic or spin–orbit coupling, or magnetic-dipole/quadrupole mechanisms.