Abstract
    The geometries of bond length and angles, highest occupied molecular orbital, lowest occupied molecular orbital, electrostatic potential, dipole moments, partial atomic charges, and vibrational energies were calculated for bromoflouride, ethylene, and ethylbenzene using three different levels of molecular orbital theory for each molecule. The three theories were 3-21G, 6-21G, 6-31G, and DZV. The best level of theory was DZV then 6-31G, 6-21G, and lastly 3-21G. The reason one basis set was better than another is that it used more basis sets in the calculations. The best level of theories were different when finding certain characteristics. The best level of theory for vibrational frequencies was DZV, for geometries it was AM1, and for dipole moments it was 6-31G.

Use hyperlinks to view information of the molecules Ethylbenzene Bromoflouride Ethylene

Introduction
    The important properties of a molecules can be predicted from its know electronic structure since it predicts much of its reactivity. Using this knowledge predicting other useful properties like dipole moment, polarizablity, vibrational frequencies, probability of absorption of light, and tendency to donate electrons. Potential energy operators becomes more important when there are more atoms present in the molecule. The lowest energy of a molecule is in its lowest occupied orbital. The optimized geometry is present in the molecule with the lowest energy. The basis sets the theories used was made by linear combinations of wavefunctions. This is all done using the variational principle. The expectation value of the hamiltonians was used since the wavefuntions didn't have eigenvalues, since they were not eigenfunctions. The expectation value was then divided by the normalization constant. The calculations are very long to do by hand so a computer program was used to do the calculations very quickly. It was then possible to find many important qualities of molecules which were stated above.
    Three theories of molecular geometry calculations were used to determine important aspects of the molecules. The reason three different theories were used was to see which ones would give the best values. It wasn't always the largest basis sets that gave the best values, this could be that the calculations were to large and gave large values. The AM1 and PM3 theories were used first to optimize the molecules geometries. The best calculations of these theories is called Ab initio which all the integrals are calculated. The list of largest basis set theory to smallest is as follows, DZV, 6-31G, 6-21G, and 3-21G.
    A computer program known as GAMESSQ was used to calculate the molecular orbitals of all our molecules. First the molecules were all built on Avogadro. Opening the molecule in MacMol and optimizing geometries was the next step. Then the optimized geometries were further calculated in GAMESS to create a 3-21G, 6-21G, 6-31G and a DZV basis set which all gave different geometry optimizations. Using the best theory dipole moments, vibrational transitions, and UV-Vis data could then be found and compared to thortical calculations.

Discussion
    Each level of theory gave different results but the 6-31G theory gave the best geometry optimizations. DZV also gave good values for bond geometries and for some calculations was better than the 6-31G theory. The dipole moments for the molecules found using the theories was close to the theoretical values and were about 10% off the theoretical. For our non-polar molecule the DZV theory gave a dipole measurement which could result from the large amount of basis sets used in the calculations.
    The vibrational frequencies were found very easily using the calculations and give a good depiction of hoow molecules move when they are excited. DZV gave good vibrational frequencies but the values were not very close to the values found on NIST. Overall the calculations done using the theories were helpful for visualizing vibrational frequencies, and molecular orbitals of molecules. They were not very close in values to the theoretical but they were close enough that the calculations gave valid depictions of what should be observed.

References

    1. Gutow, J. Molecular Orbital Calculations 2014, p 1-3
    2. CRC Handbook of Chemistry and Physics; 68th edition; Weast, R; CRC Press, Inc.: Boca Raton 1987
    3. List of experimental data for ethylbenzene, bromofluoride, and ethylene 2015, http://cccbdb.nist.gov/exp2.asp accessed Mar. 5, 2015