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