Born-Oppenheimer approximation

1. Nov 19, 2009

jaejoon89

I'm trying to figure out what the Hamiltonian for a simple molecule is using the Born-Oppenheimer approximation.

1) My textbook gives the Hamiltonian for a simple system like H2 when you hold the internuclear distance constant. The only terms that drop out are the ones where you take the Laplacian for the atoms. Since the B-O approximation separates the wavefunction into nuclear and electronic components, I'm guessing this must be the electronic component.

2) But what does the nuclear Hamiltonian look like?

2. Nov 20, 2009

transience

Are you trying to find the full Hamiltonian? If so you need to add up all contributions to the energy from the different sources and then apply the Born-Oppenheimer approximation.

The Born-Oppenheimer treats the nuclei as fixed, so they have zero kinetic energy and the interaction between them is constant, this will simplify the full Hamiltonian and give you a chance of separating electronic and nuclear potential energy.