Being able to understand the electronic structure of a molecule allows one to determine the reactivity of the molecule.  It also allows one to predict the locations of the electrons, vibrational frequencies, potential energy, and the UV-Visible transitions.  These properties are useful to determine whether a molecule will react in a reaction or not.  To find these properties, wavefunctions for the electrons are formulated.  The expectation value of energy is calculated by taking the integral of the wavefunction multiplied by the Hamiltonian operator and the conjugated wavefunction.  The calculations are complicated and require computer technology.  For the purposes of this experiment, the computer program GAMESS was used to calculate the integrals.  Two methods of calculations were used, MOPAC and ab initio.  Ab initio is the best level of theory.  It calculates all the integrals, but the calculations can be lengthy depending upon the molecule.  From these calculations, diagrams of the highest occupied molecular orbital (HOMO) and potential energy curves were created and information about the vibrational frequencies and UV-Visible transitions were collected for the molecules fluorine (F₂), carbon monoxide (CO), and para-dibromobenzene (C₆H₄Br₂).

    The optimized geometry for each molecule was essential to determine before completing any additional calculations.  The ideal geometry was chosen by comparing the calculated values for bond lengths with the literature values.  The basis set with the closest bond length was chosen.  For fluorine, the 631Gd calculated value for the bond length of 1.412529 Aº was closest to the literature value of 1.4119 Aº.  For carbon monoxide, the 321G calculated value for the bond length of 1.128936 Aº was closest to the literature value of 1.1283 Aº. The literature values were obtained from the NIST Computational Chemistry Comparison and Benchmark Database.

                          Fluorine Optimized Geometry                                                 Carbon Monoxide Optimized Geometry

The calculated bonds for each of the levels of theory were compared to the literature values for para-dibromobenzene.  The double zeta calculation proved to be the closest to the literature values (Table 1). 

                                                                           Para-dibromobenzene Optimized Geometry
The calculated transition energy values were compared to literature values obtained from the Journal of American Chemical Society.  In Hellmann and Bilbo's study published in 1953, they determined the value for the primary band to be 43898 cm^-1 and the secondary bands to be at 36590 and 35448 cm^-1.  As can be seen, the calculated values were much greater than the literature values.  Hellmann and Bilbo's results can be found at: http://pubs.acs.org/cgi-bin/archive.cgi/jacsat/1953/75/i18/pdf/ja01114a512.pdf

From the vibrational frequency and transition energy calculations, it can be seen that their ab initio calculations were not good predictors of literature values.  The bond length calculations used to determine the optimized geometry were very close to literature values.  Therefore, ab initio could be used to optimize molecules but would not be accurate in predicting vibrational frequencies and transition energies.