The only small parameter in the electronic structure problem is the inverse nuclear mass 1/M, i.e. the nuclear kinetic energy terms. The adiabatic or Born-Oppenheimer approximation is a systematic expansion in the small parameter that is fundamental to all electronic structure theory. It comes to the fore in the theory of phonons, electron-phonon interactions, and superconductivity (Ch. 19).
C.1 General formulation
The fundamental hamiltonian for a system of nuclei and electrons, Eq. (3.1), can be written
where U contains all the potential interaction terms involving the set of all-electron ...