Adiabatic, born-oppenheimer, and non-adiabatic approaches

Abstract

A detailed derivation of the adiabatic approximation and the Born-Oppenheimer approximation is presented, the difference between these two approximations is discussed and the circumstances under which the adiabatic approximation collapses are discussed. It is shown that the solution of the Schrödinger equation in the adiabatic approximation can be divided into one representing the motion of electrons in the field of fixed nuclei and another one representing the motion of nuclei in the potential generated by the presence of the electrons. The shapes of the potential energy curves generated by the electrons and the motion of the nuclei in these potentials are also analyzed. Finally, the state-of-the-art highly accurate calculations for diatomic molecules performed without the use of the Born-Oppenheimer approximation is presented.