Quantum Calculations of Molecular Properties for Chlorine, Dichlorine Dioxide, and Ethylbenzene

Kara Gillette and Tanner Stille

Abstract: Quantum mechanical methods at different levels of theory and basis sets was used to calculate the electronic properties of chlorine, dichlorine dioxide, and ethyl benzene. Initial calculations were done using classical mechanical models using Avogadro molecular modeling software. The initial values were then used to calculate the lowest energy molecular geometries using the semi-empirical PM3 model and AM1 model. The lowest energy geometry from the semi-empirical model was then used to perform geometry optimization calculations using ab initio theory with increasing basis sets from 6-21G, 6-31G, to DZV. The results of the calculations were compared to experimental values and discussed.

Introduction1

        Recent advances in computing power have made complex calculations for molecular geometries more accessible. The software programs that perform these calculations make assumptions about the way the electrons and nuclei interact to form molecules; from relatively simple classical mechanic models to highly complex and computationally taxing quantum mechanical models. However, it is through these quantum mechanical models that one can attempt to predict electronic characteristics of a molecule including stability, polarizibility, dipole moment, vibrational frequencies, and electronic transitions. These predictions are accomplished through the use of the variational principle, in which the parameters of a linear combination of wavefunctions that describe the molecular orbitals are adjusted to produce trial wavefunctions. The energy of the linear combination of the trial wavefunctions is determined for a given set of parameters, the parameters are adjusted and the calculation run again. This process is repeated until the lowest energy version of the trial wavefunctions are found. Basis sets are used to form the trial wavefunctions with larger basis sets forcing additional restrictions on the adjustable parameters. The additional restrictions increase the computation time, but generally produce more accurate predictions. This experiment performed calculations for chlorine (Cl2), dichlorine dioxide (Cl2O2), and ethyl benzene (C8H10) at two different levels of theory: semi-empirical quantum mechanics using the Hamiltonian operators PM3 and AM1; and ab initio for the highest level of theory. Ab initio theory uses a Hartree-Frock self-consistent field (SCF) model with a finite basis set. Three basis sets were used for the ab initio calculations, 6-21G, 6-31G, and double zeta valence (DZV). Using the results of the ab initio DZV calculations, the bond lengths, bond angles, energy levels of molecular orbitals, and vibrational frequencies were calculated for all three molecules and compared with experimental values. Additionally, the electronic transitions of ethyl benzene were calculated as well as the polarizability of dichlorine dioxide.

Experimental1

        Initial geometries of the three molecules were calculated using a classical harmonic oscillator model in the Avogadro (version 1.2.0) molecular editing software. In each step, the  results from previous optimized calculations were fed into wxMacMolPlt (version 7.7) software to generate a calculation file. GamessQ (version 1.2.1) was then used to interface with GAMESS which performed the calculations prepared in wxMacMolPlt and generated a log containing the results of the new calculation.

        Unless otherwise noted, the calculations described were performed on all three molecules examined. The "best", i.e. lowest energy geometry from a given basis set was used as the starting point for the subsequent basis set. The optimized geometry generated by Avogadro was used to calculate the optimal geometry using the MOPAC PM3 method with RHF SCF. This was then used to calculate the optimum geometry using the MOPAC AM1 method with RHF SCF. The data log from the AM1 calculations were then used to perform ab initio calculations using the 6-21G basis set. Results from the ab initio 6-21G calculations were fed into optimization calculations using the ab initio 6-31G basis set. This was in turn used to calculate the optimum geometry using the ab initio DZV basis set. The dichlorine dioxide was also optimized using the UHF SCF for the MOPAC PM3, then MOPAC AM1, and ab initio 6-21G basis sets. Although the energy calculated at each level of the UHF series were similar to the equivalent RHF calculation, the geometries were inconsistent with experimental results. As a result, the ab initio 6-31G basis set with UHF SCF was not calculated. However, the ab initio 6-31G with RHF SCF was used to calculate the optimal geometry from the ab initio DZV basis set with UHF SCF.

        Additional calculations were performed using the basis set that had produced the lowest energy with a geometry that displayed bond lengths and bond angles closest to experimental values. These calculations included determining the vibrational frequencies of all three molecules, rerunning geometry optimizations of the dichlorine dioxide molecule using polarization functions, calculating the potential energy vs. bond length for chlorine at each level of theory, and determining the electronic transitions of the ethyl benzene molecule.

Results and Discussions

The results and discussion of these calculations can be found by following the links below to the appropriate molecule.

Chlorine                       Dichlorine dioxide                        Ethyl benzene

Conclusions

        The ab initio with DZV basis set was the highest level of theory and the largest basis set used in the calculations, which should have generated the best results of all the calculations performed. However, this was not always the case. The chlorine calculations had the best optimized geometry at the PM3 level. The potential energy versus bond length had the lowest energy at the 6-31G basis set. For the dichlorine dioxide, the PM3 and AM1, the simplest levels of theory used, provided better bond lengths and angles than the ab initio with larger basis sets. The vibrational frequency calculations for dichlorine dioxide included some vibrations that are not observed experimentally and for the frequencies that are observed, the calculated frequency was significantly different from the experimental values. The ethyl benzene was the only one of the three that produced the best results from the ab initio DZV calculations. The vibration frequency calculations however, seemed to have the same issues as was seen with the dichlorine dioxide though definitive conclusions are difficult to draw since the vibrations of aromatic molecules are generally fairly vague (C-H stretch, C=C aromatic stretch, etc) without consulting a character table.

References

  1. Gutow, J. In Quantum Calculations of Molecular Properties; Chemistry 371 Lab Manual; UW Oshkosh: 2019; Vol. Fall, pp 17-28.
  2. Computation Chemistry Comparison and Benchmark Database. https://cccbdb.nist.gov/introx.asp (accessed 09/18, 2019).
  3. NIST Dichlorine dioxide. https://webbook.nist.gov/cgi/cbook.cgi?ID=C12292238&Mask=800#Electronic-Spec (accessed 09/18, 2019).