MO LAB, Barbara Bass and Yuqi She
Abstract
Using
several different computer software programs, the molecular geometries, bond
lengths, bond angles, electrostatic potentials, dipole moments, vibrational
frequencies, energy levels, and partial atomic charges of three separate
molecules were found. These three include the small polar molecule Chlorine
Monofluoride (FCl), the nonpolar molecule carbon dioxide (CO2), and the
aromatic compound O-Xylene. The different calculations run on each molecule
include AM1, PM3, 6-21G, 6-31G, and DZV. Interestingly, the best level used to
find geometry and dipole moments of FCl was AM1. O-Xylene and CO2
geometry was best found using ab initio
level 6-21G.
Introduction
In
determining the electronic structure of a molecule, much of the molecule’s
reactivity is also known. Additionally, by observing different energy levels
and where the electrons are most likely to be, different properties of the
molecule may be estimated. These predicted properties include molecular dipole
moments, vibrational frequencies, polarizability, absorption of visible light
probabilities, and a molecule’s tendency to donate electrons.
In
calculating basic wave functions and molecular orbitals, according to the
variational principle, the wavefunction with the lowest energy is the best
approximation of the true wavefunction. Using this principle, the optimized
geometry of a molecule can be predicted, as it is the most stable in its lowest
energy form. In calculating an optimized geometry of a molecule, finding the
arrangement that forms a system of minimal energy is needed. Preferably, a
large basis set wavefunctions is used to find the trial wavefunction and then
it is normalized. A larger basis set will most likely lead to a more accurate
energy estimate. Large basis sets could not be used until the rise and common
use of computers; they are almost impossible to calculate by hand due to their
complexity and the amount of time it would take to do so.
The
computer program used to initially guess the correct molecular structure is Avogadro1.
This program “treats molecules as a collection of harmonic oscillators,” and
“adjusts atom positions to minimize stress on the molecule.”2 The
method for calculation depends on the number of atoms and not number of
electrons, making it easier to use for large systems. AM1 and PM3 are two
Hamiltonian choices that need semi-empirical data used for two electron overlap
integrals. Because only two overlap integrals are being calculated, AM1 and PM3
are the quickest method used. The methods in which all integrals are calculated
is ab initio- the best level of
theory. Steven K Burger and Weitao Yang in their study of Linear-scaling quantum calculations using non-orthogonal localized
molecular orbitals go into more detail about non-orthogonal orbitals in
particular. They state, “conventional semi-empirical and ab initio methods are
constrained by nonlinear-scaling operations associated with constructing the
one-electron Hamiltonian.”3
The basis sets used in order of
increasing size are: 6-21G, 6-31G, and double zeta valence (DZV).
The
three molecules FCl, CO2, and O-Xylene (C6H4(CH3)2)
were made in Avogadro. To refine the geometries, the program wxMacMolPlt was
used. Then, the file created in Avogadro and run through wxMacMolPlt was put
into the software GamessQ to perform the integral calculations at AM1, PM3, and
the three ab initio levels. Jmol was
used to model the calculations and values to add to this website. The following
hyperlinks are where properties of each molecule can be observed: Chloride Monofluoride Carbon Dioxide O-Xylene
Conclusion
The best level of
theory used to find geometries and dipole moments overall was AM1. However,
because the basis set used only 2 overlap integrals, it could not be utilized
as much. Therefore, the ab initio
theory of 6-21G was the main level used. Our percent error for the FCl molecule’s
dipole moment was 28.5% and 3.79% for bond length using the 6-21G level. Using
the 6-21G level of theory our percent error for O-Xylene’s dipole moment was
1.1%. For CO2 6-21G was also used to yield a percent error of 1.81%
for its optimized geometry.
The DZV level of
theory was used to calculate the wavelengths of the vibrational frequencies
that would absorb energy. The calculated wavelengths were compared to an IR
spectrum of each molecule, if there was one available. These can be observed in
their respective webpages. Although DZV was used for vibrational frequencies,
note that for most calculations the DZV level of theory was not the most
accurate. The inconsistency in all the levels of theory when calculating values
for each molecule may present a problem for anyone wanting to obtain these
values using this software.
References
1. Avogadro
software. http://sourceforge.net/projects/avogadro/
(accessed February 17, 2015).
2. Gutow,
J. Molecular Orbital (MO) Calculations 2014, p 1-3.
3. Burger,
Steven K.; Yang, Weitao. Journal of
Physics: Condensed Matter 2008, Volume 20, Issue 29, 294209.
4. NIST
Website: Constants, Units, and Uncertainty. http://physics.nist.gov/cuu/Constants/index.html
(accessed February 17, 2015)
5. NIST
Website: NIST Chemistry WebBook http://webbook.nist.gov/chemistry/
(accessed February 15, 2015).
6. CRC
HANDBOOK of CHEMISTRY and PHYSICS; 68TH ed;
Weast, Robert C., Ed.; CRC Press, Inc.: Boca Raton 1987-1988.
7. Electrostatic Potential Maps. http://chemwiki.ucdavis.edu/Theoretical_Chemistry/Chemical_Bonding/General_Principles/Electrostatic_Potential_maps
(accessed March 7, 2015).