Discussion
In the Born-Oppenheimer approximation for molecular Hamiltonian, the following terms are included (choose the correct alternatives from below) :
Answer: A
The included terms are the kinetic energy of the electrons and the electron-nucleus, electron-electron and nucleus-nucleus Coulomb energies.
In the Born-Oppenheimer approximation the nuclei are so much heavier than the electrons that they are treated as fixed while the electronic problem is solved. The nuclear kinetic energy is therefore dropped from the electronic Hamiltonian, which keeps:
- the kinetic energy of the electrons;
- the electron-nucleus attraction;
- the electron-electron repulsion;
- the nucleus-nucleus repulsion, which is a constant for a given nuclear arrangement.
The options with the kinetic energy of the nuclei instead of the electrons have it the wrong way round, and the option with no kinetic energy at all leaves the electrons without the term that gives them their quantum energy levels.
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