Born-Oppenheimer Approximation

One of the central approximations in the application of quantum mechanics to chemistry (``quantum chemistry'') is the Born-Oppenheimer approximation, which states that the electronic and nuclear degrees of freedom are nearly separable. This is a good approximation because the electrons are much lighter than the nuclei, so they move much faster and can rearrange themselves to a stable configuration almost as soon as the nuclei move. Hence, to a good approximation, one can fix the nuclei at a given set of coordinates and solve for the probability distribution of the electrons; this is called the ``electronic structure'' problem. If one obtains the electronic energy for a series of nuclear arrangements, one can map out the potential energy surface (PES) of the molecule. Since the electronic energy is independent of the orientation or translation of the molecule (assuming no external electromagnetic fields), the PES of a molecule has dimension 3N-6, where N is the number of nuclei (3N-5 for a linear molecule). To get a really complete model of a molecule, one would have to obtain the PES and then simulate the motion of the nuclei on that PES; this procedure is called dynamics and is necessary for a complete understanding of reaction mechanisms and other properties. However, quite a lot of information can be obtained considering only electronic structure, and that is the focus of this lab.