Quantum Mechanical Modeling of
Molecules
Authors: Heidi Galica, Mike Garvey, and Sarah Kieper
Introduction:
This
experiment
analyzed various characteristics of three different molecules:
oxygen (O2), hydrochloric
acid (HCl) and phenol (C6H6O).
The three molecules were built using the Ghemical-GMS computer
program. The geometries of the molecules were then optimized
using Mechanics. The GTK-GAMESS computer program was used to run
calculations on each of the saved files for each geometry, this
resulted in a .log file which was used for analysis in Molden. There
were five different levels of theory studied. Two of them were
called MOPAC, AM-1 and PM-3. The other three levels of theory are
called ab initio, 3-21G, 6-31G and 6-311G. The calculations for
MOPAC were significantly faster than ab initio because ab initio
contain larger basis sets. The characteristics analyzed at each level
of theory for each geometry were: best level of theory, HOMO (highest
occupied molecular orbital), vibrational frequency, potential
energy versus bond stretch, and UV-Vis transitions. The
computer program IGOR was used to plot the potential energy versus bond
stretch for the two diatomic molecules.
Oxygen (O2):
Optimized Geometry:
Figure 1: The image shown
above is the optimized geometry of oxygen.
Best Level of Theory:
The
optimization from the 3-21G calculation was chosen as the best
optimized geometry because its bond length was closest to the
referenced bond length for oxygen.
H.O.M.O (Highest Occupied Molecular Orbital):
![HOMO for oxygen](oxygen%20homo.gif)
Figure 2: The
illustration shown above is the HOMO for oxygen. It is
a pi anti-bonding orbital.
Other Calculations:
An additional calculation
that was completed was the vibrational frequency. The vibrational
frequency found for the 3-21G oxygen molecule was 1599.72990
(1/cm). The reference value is 1580 (1/cm). The vibrational
frequency found experimentally was approximately 20 (1/cm) greater than
the reference value, this implies that it has a higher energy.
Potential Energy versus Bond Stretching:
Figure 3: Graph of
PE vs bond stretch for oxygen with three different basis sets (3-21G,
6-31G, and 6-311G).
The potential energy as a function of bond length
has the same form for all of the basis sets. As the number of
functions in the basis set increases, the energy decreases, which
agrees with the variational principle.
Hydrochloric Acid (HCl):
Optimized Geometry:
![Optimization of HCl](optimizedHCl.gif)
Figure 4: The
image shown above is the optimized geometry of
hydrochloric acid.
Best Level of Theory:
The optimization from the
6-311G calculation was chosen as
the best optimized geometry because its bond length was closest to the
referenced bond length for hydrochloric acid.
H.O.M.O (Highest Occupied Molecular Orbital):
![HOMO of HCl](hcl%20homo.gif)
Figure 5: The
illustration shown above is the HOMO for hydrochloric
acid. It is all anti-bonding.
Other Calculations:
An additional calculation
that was completed was the
vibrational frequency. The vibrational frequency found for the
6-311G hydrochloric acid molecule was 3138.320068 (1/cm).
The reference value is 2991
(1/cm). The vibrational frequency found experimentally was
approximately 147 (1/cm) greater than the reference value, this implies
that it has a higher energy.
Potential Energy versus Bond
Stretching:
Figure 6: Graph
of PE vs bond stretch for hydrochloric acid with three different basis
sets (3-21G, 6-31G, and 6-311G).
The potential energy
as a function of bond length has the same form
for all of the basis sets. As the number of functions in the
basis set
increases, the energy decreases, which agrees with the variational
principle.
Phenol (C6H6O):
Optimized Geometry:
![Optimized Geometry of Phenol](optimizedphenol.gif)
Figure 7: The
image shown above is the optimized geometry of phenol.
Best Level of Theory:
The optimization from the
6-31G calculation was chosen as
the best optimized geometry because its average C-C bond length was
closest to the
referenced C-C bond length for phenol.
H.O.M.O (Highest Occupied Molecular Orbital):
Figure 8: The
illustration shown above is the HOMO for phenol. It
shows the pi orbitals.
Other Calculations:
An
additional calculation that was completed was the
vibrational frequency. The vibrational frequencies found for
phenol were calculated using the 6-31G basis set. The values for
the C-C bonds were: 1810.7 (1/cm) and 1798.2 (1/cm). The
values for the C-H bonds were: 3325.8 (1/cm), 3342.8 (1/cm),
3353.4 (1/cm), 3370.0 (1/cm),
and 3378.8 (1/cm). The value for the
O-H bond was 4197.4 (1/cm). On the IR
spectrum from the NIST website, you can find correlations between
the peaks on the spectrum and the values that were calculated.
The broad peak near 3300 (1/cm) corresponds to the O-H bond which we
calculated to be at 4197.4 (1/cm). The sharp peak at
3000 (1/cm) corresponds to the C-H bonds which we calculated to be
between 3325-3379 (1/cm). The small peaks near 1800 (1/cm)
correspond to the aromatic C-C bonds which we calculated to be between
1798-1811 (1/cm). The peaks in the 1100-1800 (1/cm) range appear
to be associated with hydrogen atoms moving in the plane of the
aromatic ring without changing the bond lengths. The peaks in the
700-1100 (1/cm) range appear to be associated with hydrogen atoms
moving perpendicular to the plane of the aromatic ring without changing
the bond lengths. The peaks in the 450-700 (1/cm) range appear to
be associated with changing C-C-C bond angles. The peak near 500
(1/cm) appears to be associated with changes in the C-C-O bond
angle. The peak near 300 (1/cm) appears to be associated with the
motion of H(13) perpendicular to the plane of the aromatic ring.
The values calculated for the O-H and C-H bonds
were much higher than the experimental values, if a larger basis set
was used, we would expect to see these values approach the experimental
values. The values for the aromatic C-C bonds and lower frequency
rotations were closer to experimental values from the spectrum.
This indicates that this basis set is a good approximation for
frequencies of approximately 2000 (1/cm) and smaller.
Another calculation that was done was
the UV-vis transition calculation. Different wavelengths and
oscillator strengths were determined for transitions from ground state
to various excited states. The tables below contain the values
calculated for the two basis sets used.
Excited State
|
Wavelength (nm)
|
Oscillator
Strength
|
1
|
191.5
|
0.054596
|
2
|
180.8
|
0.008093
|
3
|
141.3
|
1.211884
|
4
|
138.3
|
0.993052
|
5
|
133.4
|
0.000113
|
6
|
127.2
|
0.000236
|
Table 1: Wavelengths
calculated from the 3-21G basis set for transitions from
ground state.
Excited State
|
Wavelength (nm)
|
Oscillator Strength
|
1
|
206.8
|
0.056089
|
2
|
197.1
|
0.003337
|
3
|
194.4
|
0.001318
|
4
|
181.2
|
0.016782
|
5
|
173.1
|
0.000639
|
6
|
168.5
|
0.005081
|
Table 2: Wavelengths calculated
from the 6-31G basis set for transitions from ground state.
On the UV-Vis
Spectrum from the NIST website, you can find correlations
between the peaks on the spectrum and the values that were calculated.
The transitions from ground state to the first two excited states
calculated with the 3-21G basis set appear to correspond to the peak on
the spectrum around 270 nm. The transitions from ground state to
excited states three through six appear to correspond to the peak on
the spectrum around 220 nm. The separation of the calculated
peaks is close to the separation of the peaks on the spectrum.
However, the values have much smaller wavelengths
. This is expected from the
variational principle. The better the calculation, the lower the
energy gets and the more closely it approaches the actual value.
The values from the 6-31G basis set were more evenly spread out and
lower energy. There was no noticeable correlation to the peaks
from the spectrum. However, the lower energy is expected from
using a larger basis set. If an even larger basis set was used,
the values would be expected to approach the actual values and would
likely correspond to the spectrum.
Comparison of PE for
Hetero- vs Homo-nuclear Diatomic Molecules
![HCl Pe graph](graphHClpe.gif)
Figure 9: Graph of PE vs bond
stretch for oxygen.
Figure 10: Graph of PE vs bond
stretch for hydrochloric acid.
The potential well
for the homonuclear diatomic (O2)
is deeper than the well for the heteronuclear diatomic (HCl).
This is expected because the double bond of O2
is stronger than the single bond of HCl. It requires more energy
to stretch the stronger double bond than the single bond.
Conclusion:
The computational results are useful in
modeling small inorganic molecules. Computational results do not
hold up for large organic molecules. This system of modeling may
not be useful in saving money in industry, because it does not always
hold up. Companies may spend more money because of invalid
predictions from computational results. Computational results are
another way for students to visualize molecules and may aid in students
understanding of quantum mechanics. Computational
results can also be useful in calculating the peaks in an IR
spectrum. It is also useful in understanding relative bond
strengths between different molecules.