WRSWorld Research StateContribute
WORLD RESEARCH STATE

Born and Oppenheimer: separate the energy scales of electrons, vibration and rotation

Contribution grade

Quantum mechanics · Quantum mechanics

Reference score240,000Provisional editorial estimate of this exact contribution; its grade is assessed separately.

What changed

Born and Oppenheimer organized electronic, vibrational and rotational energies of stable molecules into a perturbation expansion in the fourth root of the electron-to-nuclear mass ratio.

Scientific scope

Born and Oppenheimer organized electronic, vibrational and rotational energies of stable molecules into a perturbation expansion in the fourth root of the electron-to-nuclear mass ratio. This is a stationary perturbation scheme based on the small electron/nuclear mass ratio, a stable electronic equilibrium and a smooth nondegenerate electronic branch. Small localized vibrations and fixed small quantum numbers matter. It is not a proven uniformly convergent expansion for arbitrary molecular states, crossings or reaction dynamics. Later adiabatic corrections and general formulations remain separate.

Evidence

Source-linked, scoped account of the original work. The published scope states the scientific assumptions and remaining verification limits. WRS has not independently certified the full proof, experimental result or system benchmark.

Contributors

Provisional WRS assessment, edition 2026-10-16.1. Independent expert calibration is pending. This grade does not certify correctness or assign ownership.

Full scientific record · Browse contribution grades · Request a correction