L17.4 Molecules and energy scales
PROFESSOR: The molecules and Born-Oppenheimer approximation. OK, we all know that molecules are a lot harder to solve than atoms, and even atoms are not that easy once you have more than one electron because of the electrostatic repulsion, but molecules are significantly different in that one of the greatest simplicities that we had with atoms is that the atom is such that the potential created by the nucleus is spherically symmetric. When you have a molecule you have separate nuclei and therefore your spherical symmetry is gone, and whether you have one electron or more than one electron, there is no spherical symmetry. All our tools of angular momentum don't help us much. We have to start the problem anew. So the difficulty with molecules is basically that the potential for the electrons, where they move is not spherically symmetric. There is another thing that helps us, however, is that there's a nice separation of mass scales. You have the mass, little m, of t...