Preferred Label : Born–Oppenheimer (BO) approximation;
IUPAC acronym : BO;
IUPAC definition : Representation of the complete wavefunction as a product of an electronic and a nuclear
part, \[\Psi \left({r,R}\right) \Psi _{{e}}\left({r,R}\right)\ \Psi _{{N}}\left({R}\right)\]
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 (mM 5 x 10E-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 Jahn–Teller effect). The BO approximation is often considered as
being synonymous with the adiabatic approximation. More precisely, the latter term
denotes the case when Ψ e diagonalize the electronic Hamiltonian. Thus, the adiabatic
approximation is an application of the BO approximation.;
Origin ID : BT07008;
Automatic exact mappings (from CISMeF team)
- See also
Representation of the complete wavefunction as a product of an electronic and a nuclear
part, \[\Psi \left({r,R}\right) \Psi _{{e}}\left({r,R}\right)\ \Psi _{{N}}\left({R}\right)\]
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 (mM 5 x 10E-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 Jahn–Teller effect). The BO approximation is often considered as
being synonymous with the adiabatic approximation. More precisely, the latter term
denotes the case when Ψ e diagonalize the electronic Hamiltonian. Thus, the adiabatic
approximation is an application of the BO approximation.
