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Born-Oppenheimer Approximation

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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_{electronic}y_{vibrational}
y_{rotational}

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

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