Molecular Orbital Calculations of Hydrogen Fluoride, Cyclopropane, and Anisole
By: Danielle Kraak and Kevin
Koerber
Abstract
In this experiment, different levels of optimization were used to determine properties of hydrogen fluoride, cyclopropane, and anisole. There were two levels used at the MOPAC: AM1 and PM3. There were three levels used at the ab initio: 6-21G, 6-31G, and DZV. DZV is known as the lowest energy therefore the highest level of optimization. The difference between these is the number of trial wave functions, or Gaussians, used. The energy decreases as the number of Gaussians increases. Though DZV is the lowest energy, is not always the best calculation, it depends on the molecule as well as the property being measured.
Introduction
When talking about molecules, it is
very important to understand the electronic structure. With the knowledge of the electronic
structure, it makes predicting properties like dipole moments, polarizability,
vibrational frequencies, probability of visible light, and tendency to donate
electrons very useful. Calculating
electronic structures were initially done using pen and paper, but computers
have proven to be more reasonable considering the length of some of these
calculations as well as the number of interactions that had to be taken into
account with larger molecules. The
calculations involve calculating the expectation value of the energy with trial
wave functions to calculate the lowest energy.
The variation principle states that the lowest energy version of the wave
function is the best approximation to the actual wave function. The wave function is dependent upon the
location of all the electrons and the nuclei.
There are different basis sets that use different variations of the
electrons and nuclei relative to each other to obtain trial wave functions. The number of probable arrangements of
electrons and nuclei are known as Gaussians.
Basis sets are what are used to determine the lowest possible energy;
basis sets improve by the number of Gaussians (trial wave functions) used in
the calculation. Computers allow uses of
different basis sets, which improves the prediction of the geometries and
energies. There is a wide variety of
basis sets, but the ones used in this experiment are AM1, PM3, 6-21G, 6-31G. The difference among these different
optimization levels is the amount of Gaussians used in the calculations. The goal is to obtain the lowest possible
energy using the maximum number of Gaussians.
The MOPAC is a semi-empirical method, which uses empirical data to
provide estimates of the values for two electrons overlap integrals needed for
calculating the expectation value. The
choices of optimization in this method were AM1 and PM3. This doesn’t give the lowest energy usually
because of the moderate neglect of differential overlap. The best level of basis sets is the ab initio,
which contains the 6-21G, 6-31G, and DZV respectively decreasing in energy.
In this experiment, several
calculations were made to determine different properties of hydrogen fluoride,
cyclopropane, and anisole. Majority of
the calculations done were done using GAMESSQ because this software contains
many methods for doing the calculations done in this experiment. The first guesses of the structure of the
molecules were done using a software program called Avagadro. Using these initial structures, the software
MacMol Plt was used to generate AM1 and MM3 geometry optimization input files. GamessQ was used to submit these to the
GAMESS package. Doing this further
optimized the structures to give more accurate structure. The AM1 optimization was then further
optimized to the 6-21G, and then the 6-21G was further optimized to the 6-31G,
which was finally optimized to the DZV.
After all these calculations, the lowest energy optimization was
determined and placed into Jmol to determine different properties like bond
lengths and angles, electric potential, dipole moments, vibrational
frequencies, and UV-Vis data.
These calculated values can be seen using these links to
each molecule: Hydrogen Fluoride Cyclopropane Anisole
Conclusion
Overall, it is clear that the expected level of optimization
isn’t always the correct level. For
example, in a couple cases the 6-31G proved to be more accurate than the DZV
even though the DZV is the minimum energy for optimization. The values obtained in hydrogen fluorine had
small error values. For the dipole
compared to literature it was 1.1% and for the vibrational frequency, it was
2.32%. The errors calculated in
cyclopropane’s vibrational frequencies ranged from 2% to 10%. Looking at these two it becomes clear that
these calculations done are better for smaller molecules compared to larger
molecules. This is because the number of
interactions of electrons and nuclei are being increasing making more possible
wave functions. Even though the DZV optimization
takes into account many trial wave functions, it is still an estimate that
isn’t always correct. Even though this
doesn’t always give ideal solutions, it is a faster and more efficient way of predicting
the electronic structure to go on and predict properties of the molecules.
References
1. Anisole, 2011,
National Institute of Standards and Technology. http://webbook.nist.gov/cgi/cbook.cgi?Name=Anisole&Units=SI
2. Cyclopropane, 2011,
National Institute of Standards and Technology. http://webbook.nist.gov/cgi/cbook.cgi?Name=cyclopropane&Units=SI
3. General Chemistry. http://www.vias.org/genchem/dipole_moment_table.html
(accessed Mar 9, 2015)
4. Gutow, J. Molecular Orbital
(MO) Calculations; Lab Manual: University of Wisconsin-Oshkosh, revised Feb.
2015
5. Hydrogen fluoride, 2011,
National Institute of Standards and Technology. http://webbook.nist.gov/cgi/cbook.cgi?ID=C7664393&Units=SI