Rep:Mod:Harry3105
Computational analysis of NH3
Key information on the optimised NH3 molecule
| Name | Ammonia |
| Calculation method | RB3LYP |
| Basis set | 6-31G(d.p) |
| Final energy | -56.558 a.u. |
| RMS Gradient Norm | 0.000005 a.u. |
| Point Group | C3V |
N-H bond length: 1.01798 Å
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=-5.986276D-10
Ammonia molecule |
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Vibrations and charges
Vibrations of NH3 molecule
-How many modes do you expect from the 3N-6 rule?
Ammonia (NH3) is a non-linear molecule. Therefore by applying the 3N-6 rule (N is the number of atoms in the molecule):
3x4-6=6
6 different modes are expected to be observed.
-Which modes are degenerate (ie have the same energy)?
Mode 2 and 3 (Frequency= 1693.95 Hz) and modes 5 and 6 (Frequency= 3589.82 Hz) are degenerate.
-Which modes are "bending" vibrations and which are "bond stretch" vibrations?
Bending modes: 1; 2; 3.
Stretching modes: 4; 5; 6.
-Which mode is highly symmetric?
Mode 1 is highly symmetrical.
-One mode is known as the "umbrella" mode, which one is this?
The umbrella mode is mode 1.
-How many bands would you expect to see in an experimental spectrum of gaseous ammonia?
As there are 4 different frequencies for the 6 different vibrations of ammonia, we would expect 4 bands in the spectrum.
Charge of NH3 molecule
Nitrogen is more electronegative than hydrogen. In consequence, we can predict that the nitrogen atom will be as negatively charged as the 3 hydrogen atoms are positively charged.
Charge of Nitrogen atom: -1.125 a.u.
Charged of each Hydrogen atom: 0.375 a.u.
Reactions and Orbitals
Reactivity
N2 molecule
| Name | Nitrogen |
| Calculation method | RB3LYP |
| Basis set | 6-31G(d.p) |
| Final energy | -109.52412868 a.u. |
| RMS Gradient Norm | 0.00000060 a.u. |
| Point Group | d∞h |
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Frequency of H2: 4465.68 Hz
The frequency is positive.
H2 molecule
| Name | Hydrogen |
| Calculation method | RB3LYP |
| Basis set | 6-31G(d.p) |
| Final energy | -1.17853936 a.u. |
| RMS Gradient Norm | 0.0000017 a.u. |
| Point Group | d∞h |
The optimisation file is liked to here
Frequency of N2: 2457.33 Hz
The frequency is positive.
Reaction energy
Reaction: 3H2+N2-> 2NH3
E(NH3)= -56.55776873 a.u.
2*E(NH3)= -113.1155375 a.u.
E(N2)= -109.52412868 a.u.
E(H2)= -1.17853936 a.u.
3*E(H2)= -3.53561808 a.u.
The total change is energy during the reaction is :ΔE=2*E(NH3)-[E(N2)+3*E(H2)]= -0.05579074 a.u.
ΔE= -0.05579074 x 2625.5 = -146.4785879 kJ/mol.
When converting nitrogen and hydrogen into ammonia, -146.4785879 kJ/mol is released. Therefore ammonia is more stable than a mix of hydrogen and nitrogen gas.
Orbitals of Nitrogen
Computational analysis of CH4
Key information on optimised CH4 molecule
| Name | Methane |
| Calculation method | RB3LYP |
| Basis set | 6-31G(d.p) |
| Final energy | -40.524 a.u. |
| RMS Gradient Norm | 0.00003263 a.u. |
| Point Group | TD |
C-H bond length: 1.09197 Å
Bond angle: 109.471°
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=-5.986276D-10
Methane molecule |
The optimisation file is liked to here
Vibrations, charges and orbitals
Vibrations of CH4 molecule
Methane(CH4) is a non-linear molecule. Therefore by applying the 3N-6 rule (N is the number of atoms in the molecule):
3x5-6=9
9 different modes are expected to be observed.
Mode 1, 2 and 3 (Frequency= 1356.20 Hz), modes 4 and 5 (Frequency= 1578.58 Hz) and mode 7, 8 and 9 (Frequency= 3162.33 Hz) are degenerate.
Bending modes: 1; 2; 3; 4 and 5.
Stretching modes: 6; 7; 8 and 9.
Mode 4, 5, and 6 is highly symmetrical.
As there are 4 different frequencies for the 9 different vibrations of methane, we would expect 4 bands in the spectrum.
Charge of CH4 molecule
Carbon is more electronegative than hydrogen. In consequence, we can predict that the carbon atom will be as negatively charged as the 4 hydrogen atoms are positively charged.
Charge of Carbon atom: -0.930 a.u.
Charged of each Hydrogen atom: 0.233 a.u.
Orbitals
The 1s orbital of the carbon is too low in energy to interact with the 1s orbital of the hydrogen. This orbital is not analysed in the table following.
| Molecular Orbital | Energy | Number | Description |
 |
-0.69 a.u. | 1 | This is a σ bonding molecular orbital. In order to create the first bond (i.e. one of the four C-H bonds) the 2s orbital of the carbon combines with the 1s orbital of one of the carbons. This is proven by a lower energy than the other ofbital, resulting from a 2s orbital of the carbon and not a 2p. |
 |
-0.39 a.u. | 2 | This is a σ bonding molecular orbital. It is formed by combining a 2p orbital from the carbon and a 1s orbital from the hydrogen. Therefore it will be higher in energy than the previously formed orbital, and identical energy and the two other similar bonds formed by mixing the same atomic orbitals. |
 |
-0.39 a.u. | 3 | This is also a σ bonding orbital. It is formed in the same way as the previous molecular orbital. Higher in energy as the molecular orbital first formed by combining the 2s of carbon with 1s of hydrogen. But the energy difference is so small that actually a tetrahedral carbon undergoes hybridization, there all the 4 molecular orbital s are degenerate. |
 |
-0.39 a.u. | 4 | This is also a σ bonding orbital and is formed identically as the previous one. |
 |
-0.12 a.u. | 5 | This is a σ* antibonding orbital. As it is the lowest in energy, it is the antibonding orbital correspond to bonding molecular orbital nb.1. This is the Lowest unoccupied molecular orbital (LUMO). There is a node around the carbon atom. |