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Two different geometry optimizations were used to calculate geometries
using the highest three theories of optimization. PM3 was the
optimization used for all the other three theories.
AM1 was the other geometry optimization calculation but it was not used for any of the other theories used.
Once the PM3 geometry was found the 3-21G theory was used to calculate
the optimized geometry. It was the lowest theory for geometry
optimization.
6-31G was the second level of geometry optimization theory. This theory
gave a geometry optimization closest to the theoretical value for bond
length which was found to be 0.1759nm
DZV was the highest level of theory used to determine geometry
optimization but didn't give a value as close to the theoretical bond
length as the 6-31G.
The highest occupied molecular orbital was at orbital 22. That number
was calculated by summing all the electrons in both molecules dividing
the number of electrons by 2.
The lowest unoccupied molecular orbital was at orbital 23 which was
calculated by adding one more electron to the HOMO. This would be the
next orbital to be occupied when an electron from the HOMO was excited
enough to increase to the next orbital.
The electrostatic potential is shown here, where the blue represents the
highest potential and the red shows the lowest potential. The other
colors represent the intermediate potentials the more blue the higher
the potential.
The partial atomic charges are shown in black, and created by an asymmetric distribution of electrons in the chemical bond.
Table 1: Valence Shell Orbitals on the bromoflouride atom. The
S-orbital is the lowest energy increasing to the P-orbital and shows the
bonding and anti-bonding characteristics.
Types of Bonding
|
Orbital
|
S sigma bonding
|
|
S sigma anti-bonding
|
|
P bonding
|
|
P anti-bonding
|
|
P2 bonding
|
|
P2 anti-bonding
|
|
The potential energies during bond stretching were
different depending on the level of theory that was used. The lower the
potential energy the more accurate the level of theory was in predicting
the lowest potential energy. The "bumps" on the graph shows the
interactions of the electrons that the theory doesn't take into account
in the calculations. If the potential energy was measured experimentally
the "bump" would not appear on the graph.
Figure 1: The potential energies at different bond lengths
calculated using different levels of theory. The "bumps" for the 6-31G
and DZV theory were small so a zoomed in graph was also added to show
the dip in the graphs. The two graphs were manufactured on IGOR Pro.
The vibrational frequency using the 6-31G theory was
found to be 691cm^-1. Using NIST the theoretical vibrational frequency
was found to be 720 cm^-1 which gave an error of 4.20%.
Using all the levels of theory the dipole moments
were found and compared to the theoretical dipole moment that was found
on NIST.
Table 2: Dipole moments found using each of the levels of theory.
Percent error for each of the measurements were calculated comparing
experimental measurements to the theoretical found on NIST.
Theory
|
Dipole Moments (D)
|
Error in Experimental Calculations (%)
|
3-21G
|
1.768
|
10.6
|
6-31G
|
1.730
|
13.0
|
DZV
|
1.809
|
8.07
|
From the data it can be seen that the DZV theory gave
the best dipole moment value. Since DZV is the highest theory that was
used it is not surprising that it gave the dipole closest to the
theoretical. The 6-31G theory should have been closer to the theoretical
than the 3-21G theory since it uses more basis sets in the calculations,
the more basis sets a theory uses the more accurate the values it calculates are.
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