Abstract:

Through computational chemistry the geometry of a molecule can be found by applying classical an quantum mechanics to the molecule and adjusting the geometry of the molecule until the lowest possible energy of the molecule is found.  This optimized molecule can then be subjected to various symbolic experiments to give results which come close to or even match those seen experimentally in the laboratory and in nature.

Introduction¹:

The geometry of a given molecule effects that molecule's physical and chemical properties.  Through computational chemistry, the geometry of a molecule can be optimized, and from this optimization, the physical and chemical properties seen experimentally can be seen computationally.  This geometry optimization is achieved through determining the wavefunctions of electrons and thereby determining the probability of an electron being in a given location within the molecule.  The issue with this determination is that in a many electron molecule (most molecules) the wavefunction can only be known for a single electron.  Only a guess can be made as to the wavefunctions of all the other electrons in the molecule.  What is known is that the lower energy state is always the preferred one in a molecule.  With this in mind, approximations of the wavefunctions of all the other electrons while fixing the wavefunction for one electron in the molecule can be made.  Using geometry generating software, such as MacMolPlt or Jmol, and computational software, such as GamessQ, the geometry of a given molecule can be determined by adjusting the wavefunctions of the electrons and the geometry of the molecule to find the lowest possible energy of the molecule.  This "tweaking" of the molecule is achieved by fixing the wavefunction of one electron and guessing the wavefunctions of the other electrons.  The molecule's geometry is then "tweaked" until the lowest energy is found with a specific molecule geometry.  Then a different electron's wavefunction is fixed and the process begins again.  This process is repeated until the energy of the molecule is brought down to the lowest possible energy which goes with it a specific molecular geometry.  From this geometry a countless number of physical and chemical properties can be found.

Using Jmol software, the geometry optimized molecule can be put through a series of symbolic tests to see how the molecule reacts under certain conditions.  Since the physics is already understood about such physical properties as infrared spectroscopy, bond length, bond angle, etc. the mathematical calculations which give the physical properties desired can be applied to the geometry optimized molecule.  In many cases, these results have matched results seen experimentally using physical samples of the molecules in question.

Geometry optimization calculations can be time consuming and expensive.  To speed up this process, the physics which governs the geometry optimization is applied in "chunks" so to speak.  Classical physics is first applied to the molecule and the geometry optimized using these parameters of physics.  This is then followed by slowly working in all the quantum mechanics needed over a series of a few additional optimizations.  In each optimization, a better model using higher theory is applied to the previous level of theory.  By gradually changing the models used, the compute time for finding the geometry optimization of a given molecule is reduced.

In this experiment CHF3, HBr, and C6H5Cl molecules were optimized and the physical properties tested and compared with experimental results.  Theory levels of 3-21G (or 6-21G), 6-31G, and DZV were applied one after the other until a geometry was found for each molecule which gave the lowest possible energy.  The results of the geometry optimization and the physical and chemical property tests performed can be seen for each molecule by following the links below.

HBr Molecular Orbital Link	CHF3 Molecular Orbital Link	C6H5Cl Molecular Orbital Link

Conclusion:

Given the level of theory used it is not surprising that many of the physical properties found came incredibly close to those found in literature.  A further optimization taking into account geometries which include unpaired electrons could give a geometry with a lower energy level but given the results found the geometries found is pretty good approximations.  Additionally, the Huckel approximation was used in these computations which takes into account only interactions between neighboring atoms.  By removing this approximation, the computing time would increase but the results would be closer to those found in literature.

References:

1. Mihalick, J.; Gutow, J. "Molecular Orbital (MO) Calculations" handout in Chem 371 Class at UW Oshkosh, Spring 2013.