Born-Oppenheimer Approximation

Born-Oppenheimer Approximation

The Born- Oppenheimer approximation (also called the Adiabatic Model) explains that the wave functions of atomic nuclei and electrons in a molecule can be treated separately depending on the fact that the nuclei are heavier than the electrons. This approach is named after Max Born and J. Robert Oppenheimer.
An isolated molecule in space has various form of energy due to its different kinds of motion and intramolecular interactions. The molecule possesses translation energy due to the motion of the molecule as a whole. It may possess rotational energy due to the rotation of body about an axis perpendicular to the internuclear axis and passing through it's centre of gravity. The molecule exhibit vibrational energy due to periodic displacement of its atoms from their equilibrium position.

It also possesses electronic energy since the electrons associated with each atom and bonds are in constant motion. Electronic energy is associated with the transition of an electron from the ground state energy level to an excited state energy level of the molecule due to the absorption of a photon of suitable frequency. The molecule exhibits energy due to nuclear and electron spin. As a first approximation, the total energy of a molecule can be expressed as the sum of translational, rotational, vibrational, electron, spin and nuclear energies.
E_total = E_trans + E_rot + E_vib + E_el + E_spin + E_nuclear
It is assumed that the various types of energy associated with different motions of the molecule are independent of one another. A molecule has several levels of these energies. The translational energy is not quantized whereas all the energies are quantized. It means molecule can exist only in certain discrete rotational, vibrational, electronic, spin and nuclear states. The separation between energy level is given as-
E_el >> E_vib >> E_rot >> E_trans
Since the translation energy is negligibly small, the Born- Oppenheimer approximation can be written as-
E = E_rot + E_vib + E_el
Although the Born Oppenheimer approximation is valid in most materials and molecular systems, there are a few situations in which it does not hold, including some low atomic weight compounds, intercalated graphite and graphene.