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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 3*N*-6, where *N* is the number of nuclei (3*N*-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.

** Next:** Levels of Theory
** Up:** Electronic Structure Theory
** Previous:** Electronic Structure Theory
*C. David Sherrill*

*2001-03-18*