弗兰克-康登原理Franck–Condon principle

由于玻恩-奥本海默近似，跃迁矩可分离为电子部分与振动重叠积分 ⟨χ_v′|χ_v″⟩ 的乘积。若激发态平衡键长与基态相同，主要发生 0→0 跃迁，谱带尖锐；若激发态键长明显变长，最大重叠出现在较高振动能级，吸收谱表现为一系列振动精细结构（振动级数），最强峰不在 0–0 处。这解释了分子电子吸收带的宽度和形状。

Within the Born–Oppenheimer approximation the transition moment separates into an electronic part times a vibrational overlap ⟨χ_v′|χ_v″⟩. If the excited state has the same equilibrium bond length as the ground state, the 0→0 transition dominates and the band is sharp; if the bond lengthens on excitation, maximum overlap lies at higher vibrational levels, giving a progression of vibrational structure whose strongest peak is not at 0–0. This explains the width and shape of molecular absorption bands.

1926 年德国物理学家詹姆斯·弗兰克根据经典图像提出：电子跃迁时核间距和核速度都不变。同年美国物理学家爱德华·康登把这一想法用量子力学严格表述为振动波函数的重叠积分。弗兰克此前与赫兹因弗兰克-赫兹实验（证明原子能级量子化）获 1925 年诺贝尔物理学奖。

In 1926 the German physicist James Franck, using a classical picture, proposed that internuclear distance and nuclear velocities do not change during an electronic transition. That year the American physicist Edward Condon gave the idea its rigorous quantum form as an overlap of vibrational wavefunctions. Franck had shared the 1925 Nobel Prize in Physics with Hertz for the Franck–Hertz experiment, which proved atomic energy levels are quantised.

该原理解释了吸收光谱与荧光光谱的近似镜像关系和斯托克斯位移；用于分析光电子能谱中的振动结构以判断电离后键长变化（成键电子电离使键变长）；解释了电子转移反应中马库斯理论的重组能；也是理解染料、发光材料光谱形状的基础。

The principle explains the approximate mirror symmetry of absorption and fluorescence spectra and the Stokes shift; is used to analyse vibrational structure in photoelectron spectra to see how bond lengths change on ionisation (removing a bonding electron lengthens the bond); accounts for the reorganisation energy of Marcus theory in electron transfer; and underlies the spectral shapes of dyes and emitters.