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    "title": "Born and Oppenheimer: separate the energy scales of electrons, vibration and rotation",
    "summary": "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.\n\nA molecule contains light electrons and much heavier nuclei. Their motions have different energy scales, so treating everything at once obscures useful structure. Born and Oppenheimer used quantum mechanics to organize the calculation: first solve the electronic problem with the nuclei fixed, then use that electronic energy as a potential for small nuclear vibrations near a stable equilibrium and for rotation. In their expansion, vibration enters at second order and rotation at fourth order in the fourth root of the mass ratio. They illustrated the method for two-atom molecules and connected transition intensities to earlier Franck-Condon work. This is an approximation scheme with explicit exclusions, rather than an exact universal separation. The paper set aside electronic degeneracies and detailed higher-order coupling. The body read here is an identified, later English translation with named emendations; a literal comparison against the original German formulas remains outstanding.",
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      "statement": "# Born and Oppenheimer: separate the energy scales of electrons, vibration and rotation\n\nBorn 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.\n\nA molecule contains light electrons and much heavier nuclei. Their motions have different energy scales, so treating everything at once obscures useful structure. Born and Oppenheimer used quantum mechanics to organize the calculation: first solve the electronic problem with the nuclei fixed, then use that electronic energy as a potential for small nuclear vibrations near a stable equilibrium and for rotation. In their expansion, vibration enters at second order and rotation at fourth order in the fourth root of the mass ratio. They illustrated the method for two-atom molecules and connected transition intensities to earlier Franck-Condon work. This is an approximation scheme with explicit exclusions, rather than an exact universal separation. The paper set aside electronic degeneracies and detailed higher-order coupling. The body read here is an identified, later English translation with named emendations; a literal comparison against the original German formulas remains outstanding.\n\n## Scientific scope\n\nThis 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.\n\n## People and systems\n\nM. Born; R. Oppenheimer\n\n\n\n## Original sources\n\n- [Born andOppenheimer, On the Quantum Theory of Molecules,identifiedBlindertranslation withemendations,Radboudcopy](https://www.theochem.ru.nl/files/dbase/born-oppenheimer-translated-s-m-blinder.pdf)\n- [Wiley Crossrefdeposit for1927Born/Oppenheimeroriginal](https://api.crossref.org/works/10.1002%2Fandp.19273892002)\n",
      "summary": "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.\n\nA molecule contains light electrons and much heavier nuclei. Their motions have different energy scales, so treating everything at once obscures useful structure. Born and Oppenheimer used quantum mechanics to organize the calculation: first solve the electronic problem with the nuclei fixed, then use that electronic energy as a potential for small nuclear vibrations near a stable equilibrium and for rotation. In their expansion, vibration enters at second order and rotation at fourth order in the fourth root of the mass ratio. They illustrated the method for two-atom molecules and connected transition intensities to earlier Franck-Condon work. This is an approximation scheme with explicit exclusions, rather than an exact universal separation. The paper set aside electronic degeneracies and detailed higher-order coupling. The body read here is an identified, later English translation with named emendations; a literal comparison against the original German formulas remains outstanding.",
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