Abstract:
Molecular orbital theory is used to determine certain values for molecules. Using calculations based on the basis sets AM1, PM3, 3-21G, 6-21G, 6-31G, and DZV, properties of molecules can be found and compared to experimental values. This was done on hydrogen bromide (HBr), methanol (CH3OH) and o-dichlorobenzene (C6H4Cl2). DZV gave the best results for some properties, and different values compared to experimental for other properties. None of the basis sets were exactly correct at all properties calculated.

Introduction/Experimental:
Quantum mechanics can be used to model molecules and calculate many of their properties.  The calculation methods include semi-empirical ones such as AM1 and PM3, which base part of their calculations on experimentally-determined values.  Another method is ab initio, which calculates everything from scratch with no experimentally-determined values included.  These basis sets include 3-21G, 6-21G, 6-31G, and DZV (double zeta valence).
With increased processing capacity, it has become faster and easier to do quantum mechanics calculations using a computer program.

The geometry and properties of the molecules hydrogen bromide/ hydrobromic acid (HBr), methanol (CH3OH), and o-dichlorobenzene (C6H4Cl2) were calculated using different basis sets.  First, all three molecules were drawn in Avogadro.⁷ Using wxMacMolPlt⁸, AM1 and PM3 input files were created. The input files were used to run geometry optimization calculations in GAMESS⁹, using GamessQ¹⁰ to submit them. The results were used as the starting points for geometry optimizations using the higher-level basis sets.  HBr was optimized using 3-21G, 6-31G, and DZV.  Methanol and o-dichlorobenzene were optimized using 6-21G, which was used as the starting point for 6-31G, which was used as the starting point for DZV.  After the geometry optimizations were done, the following was calculated for each molecule: bond lengths and angles, HOMO and LUMO orbitals, electrostatic potential maps, partial atomic charges, the best dipole moment, and vibrations. Additionally, for o-dichlorobenzene, predicted UV-Vis peaks were calculated. All of these calculations were done using GAMESS and visualized using Jmol¹¹.

Access to the results of the calculations for each molecule:
hydrogen bromide, methanol, o-dichlorobenzene

Conclusion:
These calculations were useful in some areas and not helpful in others. For the best optimized geometry, DZV, the bond lengths and angles were helpful. All values were very close to the experimental. It also was very useful in being able to visualize the HOMO and LUMO orbitals along with the electrostatic potential maps.
Some parts of the calculations were not as useful as they deviated from the experimental values. UV-Vis predictions on o-dichlorobenzene were way lower than the experimental value. Also, the vibrational wavenumbers were not close in most instances. There were more calculated vibrations than peaks on the IR spectrum.
In most cases, some theories worked better than others. For the dipole moment, the semi-empirical levels of theory gave the closest in all three molecules. The only way to get DZV close to the dipole was by putting in different values for diffuse orbitals. This process was long and tedious and not an efficient use of time.
The size of the basis set did not always matter. The values from the largest basis set, DZV, were not always closest to the experimental values. Also. without the experimental values, it would be difficult to determine if the calculated vales were correct.

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