The images that are displayed below show the optimized geometries
for the basis sets AM1, PM3, 6-21G, 6-31G, and DZV. The PM3 basis
set gives the best result for bond length when comparing it to
literature values, however the optimized basis set DZV was used
for the other properties such as HOMO/LUMO and vibration
frequencies.
Literature values for Cl2:
Bond length (nm)
Vibrational frequencies (cm^-1)
0.1988
554
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Optimized Geometry for Cl2_AM1
This diagram
displays the optimized geometry for the basis set AM1. It
displays the bond length of the Cl2 diatomic molecule, which is
0.192 nm.
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Optimized Geometry for Cl2_PM3
This image here
shows the optimized geometry under the basis set of PM3. The
bond length is 0.204 nm, which is the closest calculated value
when compared to the experimental value of 0.1988 nm2.
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Optimized Geometry for Cl2_6-21G
The image here
displays the optimized geometry for the 6-21G basis set. The
bond length for Cl2 is 0.218 nm.
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Optimized Geometry for Cl2_6-31G
This image in the
optimized geometry of Cl2 for 6-31G which actually has a shorter
bond length than the 6-21G basis set.
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Optimized Geometry for Cl2_DZV
The basis set DZV
had the furthest calculated value from the experimental value at
0.219 nm. However, because DZV is the largest basis set, this
optimized geometry was used for the calculations of properties
of the Cl2 diatomic molecule.
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HOMO for DZV of Cl2
As stated above, this HOMO is using the basis set DZV. Because the
HOMO is determined by the total electrons in a molecule divided by
two, molecular orbital 17 was used to display the HOMO of Cl2.
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HOMO degenerate for DZV of Cl2
This image displays
the HOMO degenerate, which is another molecular orbital that
shares the same energy as a different molecular orbital.
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LUMO for DZV of Cl2
LUMO is the lowest unoccupied
molecular orbital, which is simply one molecular orbital higher
than the HOMO. Because the HOMO is molecular orbital 17, the
LUMO must be molecular orbital 18.
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This figure was generated in IGOR and displays the potential energy
(hartrees) of Cl2 vs. the bond length (angstroms). It shows that the
energy is the lowest for the 6-31G basis set, while the energy for
the DZV is actually the second lowest.
Molecular Orbitals:
The image above shows the molecular orbital diagram for Cl2 with the
corresponding molecular orbital images.
The one calculated vibrational frequency for Cl2 came out to be
roughly 516.81 cm^-1. The CCCBDB website has one vibrational
frequency of 554 cm^-12.
