The Born-Oppenheimer Approximation

The Born-Oppenheimer Approximation is the assumption that the electronic motion and the nuclear motion in molecules can be separated. It leads to a molecular wave function in terms of electron positions r_i and nuclear positions R_j.

This involves the following assumptions

• The electronic wavefunction depends upon the nuclear positions R_j but not upon their velocities, i.e., the nuclear motion is so much slower than electron motion that they can be considered to be fixed.
• The nuclear motion (e.g., rotation, vibration) sees a smeared out potential from the speedy electrons.