Editing Born–Oppenheimer approximation (section)

{{Short description|The notion that the motion of atomic nuclei and electrons can be separated}}
{{Distinguish|text=the [[Born approximation]]}}In [[quantum chemistry]] and [[molecular physics]], the '''Born&ndash;Oppenheimer''' ('''BO''') '''approximation''' is the assumption that the [[wave function]]s of [[Atomic nucleus|atomic nuclei]] and [[electron]]s in a molecule can be treated separately, based on the fact that the nuclei are much heavier than the electrons. Due to the larger relative mass of a nucleus compared to an electron, the coordinates of the nuclei in a system are approximated as fixed, while the coordinates of the electrons are dynamic.<ref>{{cite web |last1=Hanson |first1=David |title=The Born-Oppenheimer Approximation |url=https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Book%3A_Quantum_States_of_Atoms_and_Molecules_(Zielinksi_et_al)/10%3A_Theories_of_Electronic_Molecular_Structure/10.01%3A_The_Born-Oppenheimer_Approximation |website=Chemistry Libretexts |publisher=Chemical Education Digital Library |access-date=August 2, 2022}}</ref> The approach is named after [[Max Born]] and his 23-year-old graduate student [[J. Robert Oppenheimer]], the latter of whom proposed it in 1927 during a period of intense ferment in the development of quantum mechanics.<ref name="BornOppie">{{cite journal |author1=Max Born |author2=J. Robert Oppenheimer |year=1927 |title=Zur Quantentheorie der Molekeln |trans-title=On the Quantum Theory of Molecules |journal=Annalen der Physik |language=de |volume=389 |issue=20 |pages=457–484 |bibcode=1927AnP...389..457B |doi=10.1002/andp.19273892002 |doi-access=free}}</ref><ref>{{Cite book |last1=Bird |first1=Kai |title=American Prometheus: The Triumph and Tragedy of J. Robert Oppenheimer |last2=Sherwin |first2=Martin K. |publisher=Vintage Books |year=2006 |isbn=978-0375726262 |edition=1st |pages=65–66 |language=English}}</ref>

The approximation is widely used in quantum chemistry to speed up the computation of molecular wavefunctions and other properties for large molecules. There are cases where the assumption of separable motion no longer holds, which make the approximation lose validity (it is said to "break down"), but even then the approximation is usually used as a starting point for more refined methods.

In molecular [[spectroscopy]], using the BO approximation means considering molecular energy as a sum of independent terms, e.g.: <math display="block">E_\text{total} = E_\text{electronic} + E_\text{vibrational} + E_\text{rotational} + E_\text{nuclear spin}.</math> These terms are of different orders of magnitude and the nuclear spin energy is so small that it is often omitted. The electronic energies <math>E_\text{electronic}</math> consist of kinetic energies, interelectronic repulsions, internuclear repulsions, and electron&ndash;nuclear attractions, which are the terms typically included when computing the electronic structure of molecules.