Born-Oppenheimer Approximation

The Born-Oppenheimer Approximation

Since nuclear motion is much slower than electron motion the electronic wavefunction, or energies, can be calculated assuming a fixed position of the nuclei and nuclear motion can be considered assuming and average distribution of electron density.

This approximation allows us to:

1. Construct energy level diagrams like:

2. Total energy of a molecular state is the sum of:

E_total = E_electronic + E_vibrational + E_rotational

3. Total wavefunction is the product of wavefunctions for the electrons and nuclei with vibrational and rotational parts.

y_Total = y_electronicy_vibrational y_rotational

4. Nuclei remain fixed during much faster electronic transition - transitions are vertical.

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