Rep:Mod:93221633
Computational Chemistry Lab Exercises
Ammonia
| Information | |||
|---|---|---|---|
| |||
| Ammonia, NH3 | |||
| Calculation Details | |||
| Calculation method | RB3LYP | ||
| Basis set | 6-31G(d,p) | ||
| Calculation Results | |||
| Final energy | -56.55776873 au | ||
| RMS gradient | 0.00000485 au | ||
| Point Group | C3v | ||
| Optimised N-H bond distance | 1.01798Å | ||
| Optimised H-N-H bond angle | 105.741° | ||
Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000072 0.001800 YES
RMS Displacement 0.000035 0.001200 YES
Predicted change in Energy=-5.986275D-10
Optimization completed.
-- Stationary point found.
The optimisation file is linked to here
Vibrations
| Mode | Frequency / cm-1 | Intensity |
|---|---|---|
| 1 | 1089.54 | 145.3814 |
| 2 | 1693.95 | 13.5533 |
| 3 | 1693.95 | 13.5533 |
| 4 | 3461.29 | 1.0608 |
| 5 | 3589.82 | 0.2711 |
| 6 | 3589.82 | 0.2711 |
Since Ammonia consists of 4 atoms, a total of 3(4)-6 = 6 vibrations is expected. This is confirmed to be true as 6 vibrations are computed using the GaussView program.
There are two different degenerate vibrations - one at 1693.95 cm-1 (modes 2 and 3) and the other at 3589.82 cm-1 (modes 5 and 6). Modes 1 to 3 are bending vibrations and modes 4 to 6 are stretching vibrations. This is also reflected in their frequencies as the frequencies of the stretching vibrations are higher than that of bending. Mode 4 is highly symmetric and mode 1 is known as the "umbrella" mode as the three H atoms are moving out in a motion akin to opening an umbrella. In an experimental spectrum of gaseous ammonia, 3 bands would be expected as there are 3 different frequency values computed. However, only two bands would be clearly visible, this is due to the intensity of the higher energy vibrations which is very low.
This can be confirmed when looking at the actual experimental IR gas phase spectrum of Ammonia, where there are 3 different broad bands of frequencies.
Charge Distribution
| Atom | Charge |
|---|---|
| Charge on N | -1.125 |
| Charge on H | 0.375 |
It is to be expected that N would bear the negative charge and H the positive as N is the more electronegative atom (3.04 for N to 2.20 for H). This means that N is more likely to draw the electrons in the bonding orbital towards itself, hence leading to it bearing a negative charge.
Nitrogen
| Information | |||
|---|---|---|---|
| |||
| Nitrogen, N2 | |||
| Calculation Details | |||
| Calculation method | RB3LYP | ||
| Basis set | 6-31G(d,p) | ||
| Calculation Results | |||
| Final energy | -109.52412868 au | ||
| RMS gradient | 0.00000096 au | ||
| Point Group | D∞h | ||
| Optimised N-N bond distance | 1.10550Å | ||
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000001 0.001800 YES
RMS Displacement 0.000001 0.001200 YES
Predicted change in Energy=-8.657069D-13
Optimization completed.
-- Stationary point found.
The optimisation file is linked to here
Vibrations
| Mode | Frequency / cm-1 | Intensity |
|---|---|---|
| 1 | 2457.33 | 0.0000 |
Nitrogen only shows one vibrational mode, and this is predicted using the 3N-5 rule for linear molecules. This vibrational mode corresponds to the symmetric stretch of the N≡N bond. However, this vibrational mode is IR inactive (0 on the intensity scale) as there is no change in dipole moment associated with the stretch.
Charge Distribution
There is no charge distribution in nitrogen as it is a homodinuclear neutral molecule. It can form instantaneous dipoles, but overall on average the nitrogen atoms do not bear any charge.
Hydrogen
| Information | |||
|---|---|---|---|
| |||
| Hydrogen, H2 | |||
| Calculation Details | |||
| Calculation method | RB3LYP | ||
| Basis set | 6-31G(d,p) | ||
| Calculation Results | |||
| Final energy | -1.17853936 au | ||
| RMS gradient | 0.00000017 au | ||
| Point Group | D∞h | ||
| Optimised H-H bond distance | 0.74279Å | ||
Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000000 0.001800 YES
RMS Displacement 0.000001 0.001200 YES
Predicted change in Energy=-1.164080D-13
Optimization completed.
-- Stationary point found.
The optimisation file is linked to here
Vibrations
| Mode | Frequency / cm-1 | Intensity |
|---|---|---|
| 1 | 4465.68 | 0.0000 |
Hydrogen only shows one vibrational mode, and this is predicted using the 3N-5 rule for linear molecules. This vibrational mode corresponds to the symmetric stretch of the H-H bond. However, this vibrational mode is IR inactive (0 on the intensity scale) as there is no change in dipole moment associated with the stretch.
Charge Distribution
Similar to nitrogen, there is no charge distribution in hydrogen as well since it is a homodinuclear neutral molecule.
Reaction Energy
Using the energy values of ammonia, nitrogen and hydrogen, simple calculations can be made to determine the reaction enthalpy of synthesising ammonia from nitrogen and hydrogen, otherwise known as the Haber-Bosch process.
Energy for Haber-Bosch process
E(NH3) = -56.55776873 au
2*E(NH3) = -113.11553746
E(N2) = -109.52412868 au
E(H2) = -1.17853936 au
3*E(H2) = -3.53561808 au
ΔE=2*E(NH3)-[E(N2)+3*E(H2)] = -0.0557907 au
ΔE = -146.48 kJmol-1
In the reaction of hydrogen and nitrogen to form ammonia, the product, ammonia is more stable as the energy difference is negative, indicating that energy has been released in the process.
However, the value of -146.48 kJmol-1 is far greater than the experimental reaction enthalpy determined which is -92.4 kJmol-1. This indicates that the methods used to calculate the energies of the molecules may not be very accurate.
Molecular Orbitals
Molecular Orbitals of N2
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Using the GaussView program, the molecular orbitals of Nitrogen were computed by solving for the wavefunctions of the Schrödinger equation.
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Small molecule of my choice
Methanol
| Information | |||
|---|---|---|---|
| |||
| Methanol, CH3OH | |||
| Calculation Details | |||
| Calculation method | RB3LYP | ||
| Basis set | 6-31G(d,p) | ||
| Calculation Results | |||
| Final energy | -115.72396421 au | ||
| RMS gradient | 0.00001482 au | ||
| Point Group | Cs | ||
| Optimised C-H bond distance | 1.09301Å | ||
| Optimised C-O bond distance | 1.41811Å | ||
| Optimised O-H bond distance | 0.96520Å | ||
| Optimised H-C-H bond angle | 107.899° | ||
| Optimised H-C-O bond angle | 106.904° | ||
| Optimised C-O-H bond angle | 107.737° | ||
Item Value Threshold Converged?
Maximum Force 0.000038 0.000450 YES
RMS Force 0.000020 0.000300 YES
Maximum Displacement 0.000382 0.001800 YES
RMS Displacement 0.000147 0.001200 YES
Predicted change in Energy=-1.415779D-08
Optimization completed.
-- Stationary point found.
The optimisation file is linked to here
Vibrations
| Mode | Frequency / cm-1 | Intensity |
|---|---|---|
| 1 | 337.02 | 124.5852 |
| 2 | 1061.57 | 118.5957 |
| 3 | 1094.70 | 4.2776 |
| 4 | 1178.99 | 0.5661 |
| 5 | 1385.22 | 27.5494 |
| 6 | 1499.67 | 6.9556 |
| 7 | 1508.65 | 1.5034 |
| 8 | 1526.57 | 4.2553 |
| 9 | 2988.36 | 63.9619 |
| 10 | 3033.94 | 82.7288 |
| 11 | 3122.14 | 34.2158 |
| 12 | 3824.78 | 13.2212 |
The molecular vibrations of methanol calculated using GaussView shows 12 different modes, all of which are non-degenerate. However, the actual IR spectra of methanol shows only 4 bands of frequencies shown. This can be explained by the fact that some of the vibrations calculated have a very low intensity and would hence not be easily detected. The different vibrational modes that can be detected are shown below.
The small peak shown around 2100 cm-1 is likely to be an overtone of the C-O stretch.
 C-O stretch (1061.57 cm-1) |
 C-O-H scissoring (1385.82 cm-1) |
 C-H symmetric stretch (2988.36 cm-1) |
 C-H asymmetric stretch (3033.94 cm-1) |
 C-H asymmetric stretch (3122.14 cm-1) |
 O-H stretch 3824.78 cm-1) |
Charge Distribution
| Atom | Charge |
|---|---|
| O | -0.747 |
| H (bonded to O) | 0.473 |
| C | -0.317 |
| H (bonded to C) | 0.188, 0.215 |
The charge distribution in methanol can again be explained using the different electronegativities of the atoms. Oxygen, being the most electronegative atom among the three atoms, will bear the most negative charge. The H bonded to O will therefore have the most positive charge as well, since O is drawing the charge density towards itself in the O-H bond. C also bears a small negative charge even though it is bonded to O. This is because it is also bonded to 3 other H atoms, which are less electronegative than C and hence would bear a positive charge while C would bear a negative charge.
Molecular Orbitals
As CH3OH is a slightly more complex molecule, the molecular orbitals that have been calculated are not as simple as that of homodinuclear or heterodinuclear molecules. However, using a simplified MO diagram of CH3OH, the different MOs can be distinguished based on their energy levels. It is important to note that the electrons in methanol only occupy the bonding and non-bonding MOS, and not the high energy anti-bonding MOs which would destabilise the molecule.
| MO1, E = -19.14032 au This is a very low energy non-bonding orbital that is associated with the 1s orbital of the oxygen molecule. This MO is visually similar to MO2, except that in MO2 the MO is surrounding the carbon atom instead. | 
|
| MO7, E = -0.41891 au This is a bonding MO, associated with the C-H σ orbital. | 
|
| MO9, E = -0.26493 au This is a non-bonding HOMO, associated with the lone pair of oxygen. It resembles MO8 as there are two lone pairs of electrons in oxygen. | 
|
| MO10, E = 0.07706 au This is an anti-bonding LUMO, associated with the C-H σ* orbital. | 
|
| MO14, E = 0.20629 au This is another anti-bonding orbital, this time associated with the C-O σ* orbital. | 
|
References
- ↑ Ammonia. "IR spectrum of Ammonia", National Institute of Standards and Technology, Retrieved on 29 February 2016.
- ↑ ChemTube3D. "Molecular Orbitals in Nitrogen", University of Liverpool, Retrieved on 27 February 2016.
- ↑ Methyl Alcohol. "IR spectrum of Methanol", National Institute of Standards and Technology, Retrieved on 29 February 2016.
- ↑ Simple Molecular Orbitals - Sigma and Pi Bonds in Molecules http://www.cpp.edu/~psbeauchamp/pdf/314_supp_2_hybrid_MO.pdf, California State Polytechnic University, Pomona, Retrieved on 4 March 2016.