Wikipedia - Approssimazione di Born-Oppenheimer (it) Born–Oppenheimer (BO) approximation

https://doi.org/10.1351/goldbook.BT07008
Representation of the complete @[email protected] as a product of an electronic and a nuclear part, $\Psi \left(\text{r,R}\right)=\Psi _{\text{e}}\left(\text{r,R}\right)\ \Psi _{\text{N}}\left(\text{R}\right)$ where the two wave-functions may be determined separately by solving two different Schroedinger equations. The validity of the Born–Oppenheimer approximation is founded on the fact that the ratio of electronic to nuclear mass ($$\frac{m}{M}\cong 5\times 10^{-4}$$) is sufficiently small and the nuclei, as compared to the rapidly moving electrons, appear to be fixed. The approximation breaks down near a point where two electronic states acquire the same energy (see @[email protected]). The BO approximation is often considered as being synonymous with the @[email protected] approximation. More precisely, the latter term denotes the case when $$\Psi _{\text{e}}$$ diagonalize the electronic Hamiltonian. Thus, the @[email protected] approximation is an application of the BO approximation.
Source:
PAC, 1999, 71, 1919. (Glossary of terms used in theoretical organic chemistry) on page 1929 [Terms] [Paper]