Rep:Mod:krb15MolecLab
Section 1: Optimisation
NH3 Molecule
Key Information
| Molecule Name | Ammonia, NH3 |
| Calculation Method | RB3LYP |
| Basis Set | 6-31G(d,p) |
| Final Energy, E(RB3LYP) | -56.55776873 au |
| Point Group | C3v |
| RMS Gradient | 0.00000485 |
Bond Lengths and Angles
N-H Bond Length = 1.01798 Å
H-N-H Bond Angle = 105.741°
'Item' Table
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
Dynamic Image
Ammonia Molecule |
The optimisation file for NH3 is liked to here
Optimisation Graphs
Section 2: Vibrations and Charges
Vibrational Modes
Questions
How many modes do you expect from the 3N-6 rule?
Based on the 3N-6 rule, which applies to non-linear molecules, there would be 6 vibrational modes expected (3X4 - 6).
Which modes are degenerate (ie have the same energy)?
There are two pairs of degenerate modes, 2 and 3 at frequency 1693.95 cm-1 and 5 and 6 at frequency 3589.82 cm-1.
Which modes are "bending" vibrations and which are "bond stretch" vibrations?
Modes 1, 2 and 3 are bending vibrations, so appear at a lower frequency than modes 4, 5 and 6 which are the stretching vibrational modes.
Which mode is highly symmetric?
Mode 4 is a highly symmetric stretching mode, as all of the bonds are changing length at the same time with the same rate.
One mode is known as the "umbrella" mode, which one is this?
Mode 1 is the most likely to be known as the 'umbrella' mode.
How many bands would you expect to see in an experimental spectrum of gaseous ammonia?
You would expect to see 4 bands in the spectrum, as there are 4 distinct vibrational modes for the molecule. However,as you can see by the final column of the vibrations window, the two stretching modes occur at too low an intensity to be visible in the spectrum. This is because the stretching modes have a much smaller effect on the overall dipole moment of the molecule, so will appear at a lower intensity.
Charge Analysis
The charge on the hydrogen atoms is 0.375, and the charge on the nitrogen atom is -1.125. This follows what we would expect, as the nitrogen is more electronegative than hydrogen so attracts the bonding electrons more strongly, hence the slight negative charge it experiences. In addition, the charges all add up to 0, which is what we would expect, given that ammonia is neutral.
Section 3: Reactions and Orbitals
N2 Analysis
Key Information
| Molecule Name | Nitrogen, N2 |
| Calculation Method | RB3LYP |
| Basis Set | 6-31G(d,p) |
| Final Energy, E(RB3LYP) | -109.52412868 au |
| Point Group | D∞h |
| RMS Gradient | 0.00000060 |
This table summarises some of the important information about the optimisation, including the final energy of the optimised molecule, which can be useful for calculations, and the point group of the optimised molecule, which describes the symmetry of the molecule.
Bond Lengths and Angles
N-N Bond Length: 1.10550 Å
Bond Angle: 180° (linear molecule)
'Item' Table
Item Value Threshold Converged? Maximum Force 0.000001 0.000450 YES RMS Force 0.000001 0.000300 YES Maximum Displacement 0.000000 0.001800 YES RMS Displacement 0.000000 0.001200 YES
This table is taken directly from the .log file that Gaussian produces, and shows that both the maximum and average forces are below the threshold required for convergence, and therefore the molecule is optimised.
Dynamic Image
Nitrogen Molecule |
This is a dynamic, 3D representation of the Nitrogen molecule, note that the triple bond has not been depicted in full.
The optimisation file for N2 is liked to here
Vibrational Modes
This is the only vibrational mode for N2 and appears a a frequency of 2457.33 cm-1. This is at a lower frequency than the N-H bond stretches in NH3 because the atoms in the N-N bond are heavier, and therefore have a greater reduced mass and will vibrate at a lower frequency.
H2 Analysis
Key Information
| Molecule Name | Hydrogen, H2 |
| Calculation Method | RB3LYP |
| Basis Set | 6-31G(d,p) |
| Final Energy, E(RB3LYP) | -1.17853936 au |
| Point Group | D∞h |
| RMS Gradient | 0.00000017 |
This table summarises some of the important information about the optimisation. Note that the final energy of the hydrogen molecule is significantly lower in magnitude than that of the nitrogen molecule, and that the point groups are identical.
Bond Lengths and Angles
H-H Bond Length: 0.74279 Å
Bond Angle: 180° (linear molecule)
'Item' Table
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
This table is taken directly from the .log file generated by Gaussian, and shows that the maximum and average forces are below the threshold required for optimisation.
Dynamic Image
Hydrogen Molecule |
This is a dynamic, 3D representation of the H2 molecule.
The optimisation file for H2 is liked to here
Vibrational Modes
This is the only vibrational mode of the hydrogen molecule and it appears at the frequency 4465.68 cm-1. It appears at a much greater frequency than the N-N stretching mode because the hydrogen atoms are much lighter so will vibrate at a higher frequency.
Reactions Energies
Determining the energy of reaction for the following: N2 + 3H2 ----> 2NH3
| Energy Type | Value (Atomic Units) |
|---|---|
| E(NH3) | -56.55776873 |
| 2 X E(NH3) | -113.1155375 |
| E(N2) | -109.52412868 |
| E(H2) | -1.17853936 |
| 3 X E(H2 | -3.53561808 |
| ΔE = 2*E(NH3)-[E(N2)+3*E(H2)] | -0.05579074 |
This energy change is equal to -146.48 kJmol-1, which is the enthalpy change of the reaction based on the energies provided by Gaussian. This enthalpy change is negative so the reaction is classed as exothermic, meaning there is energy given out during the process. Therefore, the ammonia product is lower in energy than the gaseous reactants so is more stable.
Own Molecule Analysis: NO+
Key Information Table
| Molecule Name | NO+ |
| Calculation Method | RB3LYP |
| Basis Set | 6-31G(d,p) |
| Charge | +1 |
| Final Energy, E(RB3LYP) | -129.52978899 au |
| Point Group | C∞v |
| RMS Gradient | 0.000105005 |
This table shows some important information from the optimisation, the RMS gradient is signifiantly higher than for previous optimisations, but this is only an indicator of how far the molecule was optimised. It is still small enough for the molecule to be considered optimised.
Bond Lengths and Angles
N-O Bond Length: 1.07289 Å
Bond Angle: 180° (linear molecule)
'Item' Table
Item Value Threshold Converged? Maximum Force 0.000260 0.000450 YES RMS Force 0.000260 0.000300 YES Maximum Displacement 0.000075 0.001800 YES RMS Displacement 0.000106 0.001200 YES
This is the data taken directly from the .log file generated during the optimisation. The values of the maximum and RMS forces are greater than they were for previous optimisations, but they are still below the threshold required for convergence. This has no significant impact on the optimisation, as it only indicates the point at which the parameters fell below the threshold.
Dynamic Image
NO+ Molecule |
This is a dynamic, 3D representation of the NO+ molecule. Note that the bond has been represented as a single bond by the programme.
The optimisation file for NO+ is liked to here
Charge Distribution
Both of these charges are positive, because the molecule has an overall charge of +1. The oxygen has a much lower charge because it is the more electronegative element, so attracts the electrons more strongly, so the positive charge it carries is reduced. The nitrogen has a greater charge because it is less electronegative, so it's positive charge is greater.
Vibrational Modes
This is the only vibrational mode for the molecule and occurs at a frequency of 2480.06 cm-1. This is very similar to the frequency of the N-N bond stretching frequency because the weight of the atoms is very similar, and the bond order is the same, so they are likely to be of similar strength.
Molecular Orbitals
These two orbitals are non-bonding and correspond to the 1s orbitals of both atoms. The 1s orbital of the oxygen atom is lower in energy than that of the nitrogen because oxygen is the more electronegative element so will attract its electrons more strongly, therefore having a more stable orbital.
There are two degenerate forms of this orbital, along two of the axes. The third axis is where the σ overlap of the remaining p orbitals occurs. This molecular orbital is larger on the side of the oxygen atom because there is a greater contribution from the 2p orbitals of the oxygen, because it is more electronegative and therefore its 2p orbitals are closer in energy to the molecular orbital formed.
The HOMO is not the shape we would expect, this is likely to be due to further mixing of the orbitals that have the same symmetry and are close in energy. This could also have effected the distribution of the orbital, as it is not what we would expect to see. The LUMO is unoccupied and is an anti-bonding orbital. It is larger on the side of the nitrogen because it is the less electronegative element so will contribute more to the anti-bonding molecular orbitals. This is because its atomic orbitals are higher in energy than the equivalent atomic orbitals in oxygen, so will be closer in energy to the anti-bonding molecular orbitals.