Rep:Mod:JS5315
Computational Lab part 2
Optimisation of NH3 molecule
Molecule: NH3
Calculation Method: RB3LYP
Basis set: 6-31G(d,p)
Final energy E(RB3LYP) in atomic units (au): -56.55776873
RMS gradient: 4.85x10-6
Point group of the molecule: C3V
Bond Length (in Angstroms): 1.01798
Bond Angle (in degrees): 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
NH3 |
Link: https://wiki.ch.ic.ac.uk/wiki/images/e/e6/JSHIMADA_NH3_OPTIMISATION_1.LOG
How many modes do you expect from the 3N-6 rule?
6
Which modes are degenerate (ie have the same energy)?
2&3 are degenerate, as well as 5&6
Which modes are "bending" vibrations and which are "bond stretch" vibrations?
Bending:1,2&3 Stretching: 4,5&6
Which mode is highly symmetric?
1&4 are highly symmetric
One mode is known as the "umbrella" mode, which one is this?
1 is known as the "umbrella" mode
How many bands would you expect to see in an experimental spectrum of gaseous ammonia?
3
Charges
On N: -1.125 On H: 0.375
We expect the charge on N to be negative and H to be positive as N is more electronegative than the surrounding H atoms, thus N attracts the negatively charged electrons towards it.
Optimising N2 and H2
N2
Molecule: N2
Calculation Method: RB3LYP
Basis set: 6-31G(d,p)
Final energy E(RB3LYP) in atomic units (au): -109.52412868
RMS gradient: 4.65x10-6
Point group of the molecule: D*H
Bond Length (in Angstroms): 1.10550
Bond Angle (in degrees): 180
Item Value Threshold Converged? Maximum Force 0.000008 0.000450 YES RMS Force 0.000008 0.000300 YES Maximum Displacement 0.000003 0.001800 YES RMS Displacement 0.000004 0.001200 YES
N2 |
Link:https://wiki.ch.ic.ac.uk/wiki/images/f/f8/JSHIMADA_N2_OPTIMISATION.LOG
Frequencies in Hertz Mode 1: 2457.31
H2
Molecule: H2
Calculation Method: RB3LYP
Basis set: 6-31G(d,p)
Final energy E(RB3LYP) in atomic units (au): -1.17853926
RMS gradient: 1.5955x10-4
Point group of the molecule: D*H
Bond Length (in Angstroms): 0.74241
Bond Angle (in degrees): 180
Item Value Threshold Converged? Maximum Force 0.000276 0.000450 YES RMS Force 0.000276 0.000300 YES Maximum Displacement 0.000362 0.001800 YES RMS Displacement 0.000513 0.001200 YES
H2 |
Link:https://wiki.ch.ic.ac.uk/wiki/images/6/6b/JSHIMADA_H2_OPTIMISATION.LOG
Frequencies in Hertz Mode 1: 4471.18
Haber-Bosch reaction energy calculation
E(NH3)= -56.55776873
2*E(NH3)= -113.1155375
E(N2)= -109.52412868
E(H2)= -1.17853933
3*E(H2)= -3.53561799
ΔE=2*E(NH3)-[E(N2)+3*E(H2)]= -0.05579083 =-146.4788242 kJ/mol
My choice of small molecule - Cl2
Molecule: Cl2
Calculation Method: RB3LYP
Basis set: 6-31G(d,p)
Final energy E(RB3LYP) in atomic units (au): -920.34987887
RMS gradient: 2.397x10-5
Point group of the molecule: D*H
Bond Length (in Angstroms): 2.04173 (Literature value of covalent radius = 1.02 ± 0.04Å) Link: https://en.wikipedia.org/wiki/Chlorine
Bond Angle (in degrees): 180
Item Value Threshold Converged? Maximum Force 0.000042 0.000450 YES RMS Force 0.000042 0.000300 YES Maximum Displacement 0.000116 0.001800 YES RMS Displacement 0.000164 0.001200 YES
Cl2 |
Link:https://wiki.ch.ic.ac.uk/wiki/images/2/27/JSHIMADA_CL2_OPTIMISATION.LOG
Frequency Mode 1: 520.33Hz As the molecule is symmetrical, the charge is distributed evenly. The molecule only has one mode, and it is a stretching mode, parallel to the direction of the bond. It is also highly symmetric. Literature value: "Chlorine (Cl2) has a vibrational frequency of 550 cm^-1" Link: http://www.chegg.com/homework-help/questions-and-answers/chlorine-cl2-vibrational-frequency-550-cm-1-bond-dissociation-energy-240-kj-mol-absorption-q2899998
Molecular Orbitals
This molecular orbital is 6σg. It is filled and is in phase thus overlap head-on to give a sigma bond. It is too deep in energy to contribute to the actual bond. 2p AOs contribute to create this MO.
The MO 10πu is a filled, bonding orbital. However it doesn't contribute much to the actual bonding because it is too deep in energy. As the AOs are in phase, they will overlap sideways to give a pi bond. To generate this MO, the degenerate 2p orbitals that created MO 6 contributes. Thus, the energy levels are very close together (basically degenerate) with E= -7.28592 for MO 6 and E= -7.27043 for this MO.
This is MO 17πg*, the HOMO of Cl2. We can see that it is an occupied anti-bonding MO as stated and also as the p orbitals do not overlap as they are out of phase. Cl 3p orbitals contribute to this MO. AS this is an anti-bonding orbital, it will contribute to separation of the bond, only to be prevented by the unfilled MO 18.
This is MO 18σu*, the LUMO of Cl2. The AOs are not in phase and thus the MO is anti-bonding. This MO is formed from 3p orbitals of both chlorine atoms, but as it is not filled it means that the molecule is stable and does not dissociate on its own.
The MO 30δg is an unfilled bonding orbital. The two delta orbitals are in phase and thus we see overlaps of the four phases seen at 90 degrees to each other. This MO is too high in energy and doesn't contribute to the bond but it is an interesting shape of MO and I have included this here. 4d AOs of both atoms contribute to create this AO. As it is unfilled, it does not affect the bonding.