Rep:Mod:WFBFM
NH3 Molecule
Optimised Structure
Ammonia molecule |
N-H bond distance = 1.018 Å
H-N-H bond angle = 105.74 degrees
Molecule name: Ammonia (NH3)
Calculation method: RB3LYP
Basis Set: 6-31G(d,p)
Type of Calculation: FREQ
Final Energy: Energy=-56.55776873 a.u.
Point group: C3V
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
How many modes do you expect from the 3N-6 rule?
Ammonia is non-linear, so it will have 3N-6 vibrational modes. Expected number of modes = 3x4 - 6 = 12 - 6 = 6
Which modes are degenerate?
Modes 2&3 and modes 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
Which is the umbrella mode?
1
How many bands would you expect to see in an experimental spectrum?
4 bands, as there are 2 degenerate pairs of modes.
Charge distribution of ammonia
Charge on N: -1.125
Charge on H: +0.375
As Nitrogen is more electronegative than Hydrogen, one would expect the Nitrogen to be negatively charged, and the Hydrogens positively charged. The overall charge of the molecule should add up to 0 as ammonia carries no formal charge.
Molecular Orbitals in Ammonia
HOMO
Nitrogen is sp3 hybridised. The HOMO is its lone pair, that sits in an sp3 orbital which does not overlap with the Hydrogen 1s AOs. This orbital is occupied, but does not contribute to bonding.
LUMO
The LUMO in Ammonia is formed by the overlap of 3 Nitrogen sp3 orbitals with 3 out-of-phase Hydrogen 1s orbitals. It is an unoccupied antibonding molecular orbital.
N2 Molecule
Nitrogen molecule |
Nitrogen optimisation log file
Point Group: D∞h
Molecule name: Nitrogen (N2)
Calculation method: RB3LYP
Basis Set: 6-31G(d,p)
Type of Calculation: FREQ
Final Energy: Energy= -109.52359111 a.u.
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 shows that there is only one active vibrational mode - which is what is expected for a diatomic molecule. The active mode is the symmetrical bond stretch.
Nitrogen charge distribution
As expected, the Nitrogen atoms are uncharged: N2 is a homodinuclear molecule and this is the predicted result.
Molecular orbitals in Nitrogen
HOMO
The HOMO in Nitrogen is the 3σg orbital formed by the overlap of two 2pz atomic orbitals. In Nitrogen, the 3σg MO is higher in energy than the 1πu orbital due to MO mixing with the 2σg (since they are of the same symmetry and similar energy, they are able to mix quite strongly).
LUMO
The LUMO in Nitrogen is the 1π*g orbital. Two such orbitals exist, that are degenerate: one MO is formed by the overlap of two 2px atomic orbitals, the other is formed by two 2py atomic orbitals. The picture below shows the 1π*g orbital formed by the 2px orbitals.
H2 Molecule
Hydrogen molecule |
Hydrogen optimisation log file
Point Group: D∞h
Molecule name: Hydrogen (H2)
Calculation method: RB3LYP
Basis Set: 6-31G(d,p)
Type of Calculation: FREQ
Final Energy: Energy = -1.17853936 a.u.
Item table:
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
This shows that there is only one active vibrational mode - which is what is expected for a diatomic molecule. The active mode is the symmetrical bond stretch.
Charge distribution in Hydrogen
Molecular orbitals in Hydrogen
HOMO
The HOMO in Hydrogen is the 1σg orbital formed by the overlap of two in-phase 1s atomic orbitals.
LUMO
The LUMO in Hydrogen is the 1σ*u orbital, formed by the overlap of two out-of-phase 1s atomic orbitals.
Reaction energies
E(NH3)=-56.55776873 a.u. 2*E(NH3)=113.11553746
E(N2)=-109.52359111
E(H2)=-1.17853936
3*E(H2)=3.53561808
ΔE=2*E(NH3)-[E(N2+3*E(H2)]=-0.05632827 a.u.
ΔE=-147.89 kJ/mol
The Ammonia product is more stable.
My choice of small molecule: Cl2
Optimised structure
Chlorine molecule |
Chlorine optimisation log file
Cl-CL Bond length: 2.04163 Å
Point Group: D∞h
Molecule name: Chlorine (Cl2)
Calculation method: RB3LYP
Calculation type: FREQ
Basis Set: 6-31G(d,p)
Type of Calculation: FREQ
Final Energy: Energy= -920.34987887 a.u.
Item table:
Item Value Threshold Converged? Maximum Force 0.000007 0.000450 YES RMS Force 0.000007 0.000300 YES Maximum Displacement 0.000018 0.001800 YES RMS Displacement 0.000026 0.001200 YES
Charge Distribution of Chlorine
Chlorine is a linear, homodinuclear molecule, so we would expect the chlorine atoms to be uncharged and the molecule to be neutral overall. This is indeed what we observe from the optimised structure.
Vibrations
Chlorine is a linear molecule. Using the 3n-5 rule, we would expect 1 mode of vibration. The optimised structure confirms this idea: there is one mode of vibration, at a frequency of 520.46 cm-1. This is the symmetric stretch, as shown in the animation below:
Molecular orbitals in Chlorine
The electron configuration of chlorine is 1s2 2s2 2p6 3s2 3p5. Each chlorine atom has 9 AOs, which overlap to form the 18 MOs in Cl2, the energies of which are shown below:
HOMO
The HOMO in Cl2 is a π* orbital formed by the overlap of two out-of-phase 3px or 3py orbitals. There are two such π* orbitals which are degenerate (MOs 16 and 17 in the picture above). The resultant antibonding orbital formed by the overlap of two out-of-phase 3py orbitals is shown below. These are both filled orbitals that contribute to antibonding in the chlorine molecule.
LUMO
The LUMO in Cl2 is a σ* orbital formed by the overlap of two out-of-phase 3pz orbitals. This MO corresponds to MO 18 in the list. It is the lowest energy unoccupied molecular orbital in chlorine.
π Bonding
Shown below is MO 15: the π bonding orbital formed from the overlap of two in-phase 3py orbitals. MO 14 is a degenerate π bonding orbital formed from the overlap of two in-phase 3px orbitals. It is an occupied orbital that contributes to the bonding in the chlorine molecule.
σ Bonding
MO 13 is a σ bonding orbital formed by the overlap of two in-phase 3pz orbitals. It is filled and lower in energy than the HOMO, contributing to the bonding in the chlorine molecule.
σ* Bonding
MO 12 is a σ* antibonding orbital formed by the overlap of two out-of-phase 3s orbitals. It is filled and lower in energy compared to the HOMO, contributing to the antibonding in the chlorine molecule.
Bibliography
- ↑ This MO Diagram was made in Photoshop by Wikimedia user Tem5psu, uploaded 31 December 2013, 14:00:25