Abstract
In this experiment, quantum calculations were performed to determine several molecular properties of diatomic fluorine, dioxygen difluoride, and styrene. Properties determined included: molecular geometries, molecular orbitals, dipole moments, partial atomic charges, vibrational frequencies, electrostatic potential, as well as electronic transitions and energy vs. bond length for select molecules. Basis sets used to evaluate these properties included AM1, PM3, 6-21G, 6-31G, and DZV. In comparison to literature values, DZV theory usually gave the best results. However, even the best basis set had significant amount of error (>10%) in most cases, suggesting that even higher levels of theory are not always reliable.

Introduction
Quantum calculations play an important role in the field of physical chemistry, allowing chemists to learn many properties of a molecule that cannot normally be observed. These properties are determined by the electronic structure of a molecule and play an important role in many physical processes. Wavefunctions are mathematical models that give scientists needed information about the a given molecule. Unfortunately, only atoms with a single atom can be solved exactly for the corresponding eigenvalues and eigenfunctions. Therefore, to make estimates about multi-electron molecules, computer software is used to make predictions using "trial" wavefunctions in attempt to estimate the exact values. While mathematically, this could be solved on paper, it would be extremely cumbersome so calculations are normally performed using computers.

The variational principle expresses the approximate wavefunction as a linear combination of trial wavefunctions. The constants (c_i) in front of each psi represent the contribution to each psi listed in the sum. Using this information, the software then tries to find the set of coefficients that will give the overall wavefunction the lowest energy. The expectation value of the energy is computed beacause the trial wavefunction is not a "true" solution to the Schrodinger equation. As the level of theory increases, the more calculations the computer will make in an attempt to minimize the energy of the wavefunction. In theory, higher basis sets should give more accurate results as they perform more calculations, and therefore a lower overall energy of the trial wavefunction. The objective of this experiment was to use various levels of theory to perform quantum calculations on diatomic fluorine, dioxygen difluoride, and styrene, and compare these results with literature values to asses the validity of each basis set

Experimental
To carry out the quantum calculations for each of the following molecules, the following software packages were used.
-Avogadro
-wxMacMolPlt
-GamessQ
-Jmol (also used in development of website along with SeaMonkey)

Instructions for using these software packages were found in Chem371 Lab Manual Fall 2019¹.

Discussion
Results and discussion of results for each of the following molecules can be found by clicking the hyperlinks below.
Diatomic Fluorine
Diatomic Fluorine Vibration
Dioxygen Difluoride
Dioxygen Difluoride Vibrations
Dioxygen Difluoride Partial Atomic Charges
Styrene

Conclusion
Using various computational software, we were able to calculate several molecular properties of diatomic fluorine, dioxygen difluoride, and styrene. Given the relative error for each of the basis sets, in general, the higher level of theory produced more accurate predictions. However, these results prove that it is important to obtain data from multiple basis sets. Additionally, the practicing scientist should be skeptical of the predictions made and should use his/her best judgement when interpreting results.

References
 1.    Gutow, J. Chemistry 371 Lab Manual Fall 2019, 2019 pg. 17-28
 2.    Lide, D.R.; Handbook of Chemistry and Physics 73rd Edition; CRC, 1993
 3.    National Institute of Standards and Technology, NIST Chemistry Webbook, https://webbook.nist.gov/chemistry/, accessed 2019
 4.    Oberhammer, H. Gas Phase Structures of Peroxides: Experiments and Computational Problems, ChemPhysChem 2015, 16, 282-290
 5.  Loos, K.R., et. al.; Dioxygen Difluoride: Infrared Spectrum, Vibrational Potential Function and Bonding, J. Chem. Phys. 1970, 52, 4418