Michael Patt and Nate Rocha
Abstract:
Varying levels of molecular orbital theory analysis
were performed computationally for Carbon Monosulfide, Trifluoromethane, and
Styrene. For each species the geometries, bond lengths, highest occupied
molecular orbital, lowest unoccupied molecular orbital, dipole moments, electrostatic
potential, partial atomic charge, and vibrational energies were computed
experimentally using computer software programs Avogadro, Jmol, GamessQ, and MacMolpit.
Using these programs for digitized modeling and analysis the ab initio calculations for the
three
species were performed at the 6-21G, 6-31G, and DZV levels of theory.
Doing so
allowed for comparison with literature values to see how varying the
basis set
size impacted the accuracy of the experimental results. Generally, the
larger the basis set used, the greater the correlation with
literature values and, the results were never exactly the literature
value. Additionally, this trend was not always true. This
means that the basis sets used in these levels of theory were not large
enough
to provide a perfectly accurate estimate, and future work could be done
using
more expansive basis sets at greater levels of theory and determining
which basis sets work best with certain types of molecules.
Much
can be understood about the physical properties of molecules through the use of
computerized modeling programs. These computer programs can produce 3-D models, from which experimental values can be calculated1.
When these models
are studied more in depth using more sophisticated software, the
electronic
structures and behavior not immediately visible or obvious, can be
analyzed. Electronic structure is particularly useful because it
determines numerous
properties of the molecule. For example, partial
atomic charges, dipole moments, electrostatic potentials, vibrational
frequencies, IR absorption and UV absorption, can all be explored in
great detail. These properties further help to
understand the physical appearance of molecular orbitals, optimized
geometries,
and probable electron location and behavior. As technology has evolved,
so too
has computational capabilities. In the past, calculations
of electronic structure were done by hand making it impossible to
perform calculations
for larger molecules with more complex interactions.
The
basis sets used in these calculations were AM1, PM3, 6-21G, 6-31G, and DZV.
These levels of theory are arranged respectively from smallest to largest basis
set. In theory, the largest basis set will give the most accurate result. These methods follow the Hartree Fock
self-consistent field method (HF-SCF) where optimized geometries are found by
individually calculating the energy of different molecular arrangements until
the least energy geometry is determined2. According to the
variational principle, the model with the lowest energy is the closest
representation of the actual molecule or atom. The Huckel
approximation method was also used, which is a linear combination of atomic orbitals molecular orbitals (LCAO MO) method for the determination of energies of molecular orbitals of pi electrons in conjugated systems2. With this method, sigma electrons are ignored, only pi electron molecular orbitals are included because they determine the species
general properties.
The calculations for the experiment began using
Avagadro. This computer
software program builds 3-D models of molecules. After building the
three
molecules with Avagadro the .xyz files produced were saved and then
opened in
MacMolPit. These .xyz files were uploaded to MacMolPit and optimized.
The new optimized molecule files were produced for analysis at the
varying levels
of theory. The optimized structures and information were then saved as
input
files to be used in GamessQ. The GamessQ computational software received
the
input files for all the different levels of theory, which were then
converted
by the software into .dat and corresponding .log files. The
approximations
performed started with the smallest basis sets AM1 and PM3, and
progressed
stepwise through the larger basis sets 6-21G, 6-31G, and DZV. Upon exiting gracefully and outputting our log
files, they were then used in determining characteristics such as dipole
moments and partial atomic charges. The .log files were finally opened using
the open source program JMol. JMol was then used to produce the 3-D graphics
and animations of the three molecules: CS, CHF3, and Styrene. It was also used to analyze and compare the accuracy of properties
such as bond length, bond angle, partial atomic charge, vibrational
frequencies, and electrostatic potential at varying levels of theory. These
visual representations of the different molecules and their molecular orbitals were
then uploaded to the website as three pages, one for each molecule.
Use the following hyperlinks to see the calculated values and animations
of:
CS (Carbon Monosulfide), CHF3 (Trifluoromethane), C8H8 (Styrene)
Conclusion:
Upon completion of the analysis at the different levels of theory,
results were compared to literature values to determine the accuracy of each
method. As expected, the DZV level of theory, which had the largest basis
set, usually produced the most accurate results. For example, when determining the best dipole moment of CHF3
, DZV produced the value closest to the literature value. In all three
molecules 6-31G also gave
accurate estimates of bond length. This means that using the Gaussian
6-31G method may be the
most efficient computationally; if the same results, or satisfactorily
accurate results can be obtained while performing less calculations,
this is preferred. Usually the DZV level of theory provided the best estimates
for everything from dipole moments to bond length and vibrational frequencies.
This shows that as the size of the basis sets increase so too does the
accuracy of the estimate. For example, the DZV level of theory gave a dipole moment of 0.131452 debye
for Styrene. This is an error of 1.12%. Compared to the 18.10% error
acheived by 6-21G we see that in this specific case DZV is significantly
more accurate. Further work could continue using larger and larger
basis sets until a desired level of estimate accuracy has been achieved. Similarly the DZV level of theory gave the best estimate of bond length in Carbon Monosulfide.
The experimentally determined length at the DZV level of theory was 1.57
Angstroms, compared to the literature value of 1.535 Angstroms. This is once
again a very accurate estimate differing only by 1.82% from the literature
value. Future work could be
done using
more expansive basis sets at greater levels of theory and determining
which basis sets work best with certain types of molecules.
References
1.
Gutow,
J. Molecular Orbital Calculations. 2015.
2.
Cooksy, A.; Physical
Chemistry, Quantum Chemistry and Molecular Interactions; Pearson Higher
Education: Upper Saddle River, New Jersey, 2014.
3. National Institute of Standards and Technology. http://webbook.nist.gov/chemistry. (Accessed March 3, 2015)
4. Computational Chemistry Comparison and Benchmark Database. All data in CCCBDB for C6H5CHCH2. http://cccbdb.nist.gov/alldata2.asp?casno=100425. (accessed Mar 10, 2015)