The Born-Oppenheimer Approximation

Since the forces on both the electrons and ions are of the same order of magnitude, their momenta are also comparable. However since the ions are so massive in comparison to the electrons, the kinetic energy of the ions is much smaller than that of the electrons. This idea forms the basis of the Born-Oppenheimer approximation. The electrons are assumed to respond instantaneously to the motion of the ions. For any ionic configuration, we assume that the electrons are in the instantaneous ground-state and calculate the total energy of the system. Varying the ionic positions defines a multi-dimensional ground-state potential energy surface, and the motion of the ions can then be treated as classical particles moving in this potential.

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