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:

    Optimized Geometry of Oxygen

    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

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:

PE vs Bond Stretch of Oxygen    

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

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

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:

PE vs Bond Stretch HCl

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

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):

Phenol HOMO

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 wavelengthsThis 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

Oxygen PE graph           HCl Pe graph

                       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.