Introduction
In quantum chemistry the ultimate goal is to find a way to
accurately describe the structure of atoms and molecules. A large part of this is to identify the wave
functions and orbitals that can be used to represent the placement of the
electrons in the atom. Unfortunately, for anything with more than one nucleus
and one electron the exact solution cannot be found. As such, it is necessary
to make a variety of assumptions about the atom. The first assumption that is
usually made is the Born-Oppenheimer approximation, which states that the
motion of the electrons can effectively be separated from the motions of the
nucleus due to the much larger size of the latter. This difference in size
makes the impact due to the electrons on the kinetic energy of the system small
enough as to make the assumption valid.
Once this assumption has been made a Hartree Fock calculation can be
begun. The purpose of this calculation is to find the electron specific wavefunction for an initial geometry, then
vary
the coefficients in the function to minimize the total energy. This
calculation then has to be done for each electron in each atom for the
entire molecule. Then if the energy of the system has been minimized,
the calculation can be stopped, but if it has not the calculation is
repeated until it has been. The Hartree Fock calculation uses a linear
combination of gaussian functions to model the orbital functions, which
makes the necessary integrations much easier. Many levels of calculation
can be done that vary on the number of gaussian functions they use to
model the orbitals. The information shown on this website was gathered
using four levels of calculation, an initial AM1 calculation, a 6-21
calculation( using 21 gaussian functions), a 6-31 calculation, and a DZV
(double-zeta valence) calculation.
This experiment used the program Avogadro to
generate the molecules. The program wxMacMolPlt and GamessQ was then
used to optimize and collect data on the molecules. Jmol was then used
to generate the pictures.
Figure 0.1 is an example of a geometry optimization done on the molecule ethylene.
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