Modeling
the Molecular Orbitals of Quantum Mechanics |
Robert
Hoppe and Kimberly R. Hopfensperger
University of Wisconsin -- Oshkosh Physical Chemistry |
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Optimized geometry for nitrogen at the 6-31G level of theory. A bond length of 1.083 Angstroms was compared against the experimental data on the NIST website. The accuracy of this value to the experimental was what determined 6-31G to be the best level of theory. |
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This is the HOMO, or the highest occupied molecular orbital, for the molecule of nitrogen. This is level where electrons will react with another molecule. Note, however, nitrogen HOMO is doubly occupied, which explains why this molecule is not exceptionally reactive. |
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This is a graph of the of the
potential energy vs. bond length distance (Angstroms) for the three ab
initio. As shown, the lowest energy of configuration was
calculated by the 6-311g(2d,p), which makes this the most
accurate. Note, this level of theory used the highest
number of basis sets. |
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Note, when when placed on top of each other, all levels of calculation give the same shaped curvature for geometry. |
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Optimized geometry for hydrofluoric acid, where the bond length of 0.9004928 Angstroms was compared against the experimental data on the NIST website. The accuracy of this value to the experimental was what determined 6-31G to be the best level of theory. |
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This is the HOMO, or the highest occupied molecular orbital, for the molecule of hydrofluoric acid. This is level where electrons will react with another molecule. Note, however, hydrofluoric acid HOMO is singly occupied, which explains this molecule's acidity. |
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This is a graph of the of the potential energies vs. bond length distance (Angstroms) for the three ab initio for hydrofluoric acid. Again, as found in the nitrogen above, the lowest energy of configuration was calculated by the 6-311g(2d,p), which makes this the most accurate. Note, this level of theory used the highest number of basis sets. |
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Again the energies are placed on
top of each other, all levels of calculation give the same generally
shaped curvature for geometry. |
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Optimized geometry for nitrobenzene. When compared to the the experimental data on the NIST website, the most accurate level was the 6-311G(2d,p) level of theory. |
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This is the HOMO, or the highest occupied molecular orbital, for the molecule of nitrobenzene. This is level where electrons will react with another molecule. These areas of reactivity are on the ring. |
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Above is the experimentally derived IR spectrum of nitrobenzene. When compared with the NIST website's IR spectrum for this compound, it can be seen that the peaks are shifted to a higher wavenumber and, in general, are not as intense. |
Excited State |
Wavelength (nm) |
Oscillator Strength |
|
Excited State |
Wavelength
(nm) |
Oscillator
Strength |
1 |
230.1 |
0.000000 |
1 |
241.3 | 0.000000 | |
2 |
218.0 |
0.000369 |
2 |
172.8 | 0.000604 | |
3 |
211.6 |
0.034349 |
3 |
160.6 | 0.000117 | |
4 |
207.7 |
0.105517 |
4 |
155.5 | 0.394369 | |
5 |
169.9 |
0.000000 |
5 |
148.5 | 0.256104 | |
6 |
169.3 |
0.0006224 |
6 |
139.2 | 0.000000 | |
7 |
164.8 |
0.030938 |
7 |
125.3 | 0.12147 | |
8 |
163.7 |
0.982578 |
8 |
117.7 | 1.015837 | |
9 |
159.6 |
0.028036 |
9 |
115.7 | 0.016794 | |
10 |
154.9 |
0.962891 |
10 |
113.8 | 0.000000 | |
The UV-Vis data from 6-21G level of theory. | The UV-Vis data from 6-31G(d,p) level of theory. |
These
values for both theory levels share the same trend as the spectrum on
the NIST website but
results have been deemed inconclusive as the range of values for the
generated data do not fit the one of the standard experimental
spectrum. A larger value in oscillator strength correlates to a greater dipole transition from the excited state to the ground state, making it a greater contributer to the overall dipole moment of the molecule. |
![]() The potential energy graph of
nitrogen
|
![]() The potential energy graph of
hydrofluoric acid.
|
Comparing
the two graphs above for a homonuclear molecule (nitrogen) to a
heteronuclear (hydrofluoric acid), the energy change between the
different levels of theory has a greater shift in the latter's
case. Also, there is a steeper incline out of the well in the
heteronuclear case. |