玻恩-奥本海默近似Born–Oppenheimer approximation

质子质量约为电子的 1836 倍，电子几乎能瞬时跟随核的运动调整分布。在此近似下，总波函数写成电子波函数与核波函数的乘积 Ψ ≈ ψ_e(r; R)·χ(R)。电子能量 E_e(R) 随核构型变化形成势能面，分子的平衡几何、键长、振动频率、过渡态和反应路径都由势能面描述。没有这一近似，就没有“分子结构”和“势能面”的概念。

A proton is about 1836 times heavier than an electron, so electrons adjust almost instantly as nuclei move. In this approximation the total wavefunction is a product, Ψ ≈ ψ_e(r; R)·χ(R), and the electronic energy E_e(R), varying with nuclear configuration, forms a potential energy surface that defines equilibrium geometry, bond lengths, vibrational frequencies, transition states and reaction paths. Without it there would be no concepts of molecular structure or potential energy surfaces.

1927 年德国物理学家马克斯·玻恩和他当时的研究生、美国物理学家罗伯特·奥本海默在《物理年鉴》上发表论文，用电子与核质量比的微扰展开证明了这种分离的合理性。奥本海默后来领导了曼哈顿计划。

In 1927 the German physicist Max Born and his then doctoral student, the American physicist Robert Oppenheimer, published a paper in Annalen der Physik justifying the separation by a perturbation expansion in the electron-to-nuclear mass ratio. Oppenheimer later led the Manhattan Project.

当两个电子态的势能面接近或相交时（锥形交叉点），电子运动与核运动强烈耦合，近似失效。这对光化学非常重要：视紫红质中视黄醛的光异构化、DNA 碱基的超快光稳定性都依赖锥形交叉点上的非绝热跃迁。姜-泰勒效应和重氢同位素效应的精确处理也需要超越这一近似。

When two electronic surfaces approach or cross, at conical intersections, electronic and nuclear motions couple strongly and the approximation fails. This is vital in photochemistry: the photoisomerisation of retinal in rhodopsin and the ultrafast photostability of DNA bases both rely on non-adiabatic transitions at conical intersections. Accurate treatments of the Jahn–Teller effect and of isotope effects also require going beyond it.