Abstract
One of the most important calculations performed by computational chemists is the
ab initio. This
work used calculation models such as 6-21G, 6-31G, DZV, and TZV which
are the basis sets that are much smaller than the true
ab initio, which would calculate all integrals.
Using these basis sets the physical properties such as bond length,
bond
angle, electrostatic potential, IR absorption, UV absorption, and
partial atomic charge were calculated for the molecules disodium,
dichloromethane, and fluorobenzene. As the DZV and TZV calculations
contained the largest basis sets these methods often produced values
that most closely matched the literature. However, these calculations
never exactly matched the true physical values showing that the basis
sets used were not expansive enough to accurately model reality.
Introduction
Many physical
properties of molecules can be modeled by computer systems. These
computer calculations form the basis of the field known as computational
chemistry which is closely related to physical chemistry
1. The basis
sets used in this calculation were 6-21G, 6-31G, and the double and
triple zeta valence (DZV and TZV). The 6-21G and 6-31G sets rely upon using
Gaussians, 21 and 31 respectively, to model the movement of
electrons. Gaussian functions rather than calculate the position at a
given time, calculate the average probability of position over a given
range. DZV and TZV rely upon creating two and three basis sets for each
atomic orbital to more accurately model electronic motion. Attempting to
perform these calculations by hand would have been an arduous task, but
computers now perform the bulk of these calculations. Many of these
calculations followed the Hartree Fock self consistent field
(HF-SCF) approximation in which the energy is calculated at one molecular
geometry, then molecules are shifted and the calculation is performed
again and again until the lowest possible energy is calculated
2.
Additionally, the Huckel approximation was used in which a linear
combination of atomic orbitals is used to calculate molecular geometry
using only pi molecular orbitals
2.
These calculations began with using Avogadro
3 to build the molecules. The .xyz files produced by Avogadro were then used in wxMacMolPlt
4
to generate molecular optimization files for use in basis set
computations. All basis set computations were performed in the GAMESSQ
5 package. The .log files output by GAMESSQ were opened in the open source program JMol
6
and used to generate the three dimensional graphics shown on these
webpages. These calculations progressed from smallest basis set to
largest basis set in which the .log file from a smaller set was used to
generate the next largest set. The progression of basis sets were from
AM1to 6-21G, 6-31G, and then finally either DZV or TZV. The AM1 basis
set was initially used to set up a framework for future basis sets.
Calculated
values for physical properties such as bond length, bond angle,
electrostatic potential, IR absorption, UV absorption, and partial
atomic charge were calculated using each of these basis sets. In order
to determine the most accurate basis set, calculated values were
compared
against literature values.
You can see graphical representations of these molecules, as well as calculated physical values at the following hyperlinks:
Disodium Dichloromethane Fluorobenzene
Conclusion
Comparing all levels
of theory the DZV and TZV calculations were often the best, however,
6-31G produced the same values for bond length and bond angle as the
zeta valence calculations. Since zeta valence calculations take more
time to compile than Gaussian basis sets it would be recommended to use
6-31G calculations if the objective was only to calculate bond length and
angle. Overall these computational calculations were able to accurately
model diatomics and polyatomics such as disodium and dichloromethane,
but aromatics such as fluorobenzene were difficult to calculate.
Many calculated values deviated
from literature
values. One example being the dipole moment, in which the calculated
value differed from the literature value by 25.73% for fluorobenzene,
16.75% for dichloromethane. This may imply that the number of basis sets
used to perform these calculations may have been too low.
Calculated vibrational
frequencies, reminiscent of those seen on an IR spectrum, more closely
matched literature values
7,8,9 than other calculations. The
best level of theory to perform these calculations was the DZV. In this
work we were unable to calculate an accurate IR frequency for disodium
as it is symmetric and does not absorb in the IR spectrum. More often
than not the DZV model tended to produce the most accurate values for
physical properties of molecules. This work could be improved upon by
switching to larger and larger basis sets.
References
1. Gutow, J.
Molecular Orbital (MO) Calculations. 2015.
2.
Cooksy, A.;
Physical Chemistry, Quantum Chemistry and Molecular Interactions;
Pearson Higher Education: Upper Saddle River, New Jersey,
2014
3. Hanwell, M., Curtis, D., Lonie, D., Vandermeersch, T., Zurek, E., Hutchison, G.;
Avogadro: an advanced semantic chemical editor, visualization, and analysis platform. J. Chem. Info.
4,
2012, 17
4.
Bode, B. M. and Gordon, M. S. J. Mol. Graphics Mod., 16, 1998, 133-138.
5. Mark Gordon's Quantum Theory Group. Ames Laboratory, Iowa State
University. http://www.msg.chem.iastate.edu/GAMESS/GamessQ/; (Accessed
March 7th, 2015).
6.
Jmol: an open-source Java viewer for chemical structures in 3D. http://www.jmol.org/
7.
Listing of experimental data for disodium 2015, http://webbook.nist.gov/chemistry/ (Accessed March 7th 2015).
8.
Listing of experimental data for dichloromethane 2015, http://webbook.nist.gov/chemistry/ (Accessed March 7th 2015).
9.
Listing of experimental data for fluorobenzene 2015, http://webbook.nist.gov/chemistry/ (Accessed March 7th 2015).