IMM2 MS
Ammonia - NH3
Optimisation Data
| Optimisation Data | Value |
|---|---|
| Calculation Method | RB3LYP |
| Basis Set | 6-31G(d.p) |
| Final Energy (E(RB3LYP)) | -56.55776873 a.u. |
| RMS Gradient | 0.00000485 a.u. |
| Point Group | C3v |
| N-H Bond Length | 1.01798 Å |
| 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=-5.986293D-10
Optimization completed.
-- Stationary point found.
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! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
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! R1 R(1,2) 1.018 -DE/DX = 0.0 !
! R2 R(1,3) 1.018 -DE/DX = 0.0 !
! R3 R(1,4) 1.018 -DE/DX = 0.0 !
! A1 A(2,1,3) 105.7412 -DE/DX = 0.0 !
! A2 A(2,1,4) 105.7412 -DE/DX = 0.0 !
! A3 A(3,1,4) 105.7412 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -111.8571 -DE/DX = 0.0 !
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Ammonia Molecule |
The optimisation file is linked to here
"Display Vibrations" Window
Questions
Expected number of modes => (3x4)-6 = 12-6 = 6 modes
Degenerate Modes => Modes 2 & 3 and 5 & 6 are degenerate frequency mode pairs
Mode Vibration => Modes 1,2 and 3 are 'bending' vibrations, Modes 4,5 and 6 are 'streching' vibrations
Highly Symmetric Mode => Mode 4 is highly symmetric
"Umbrella" Mode =>Mode 1 is the "Umbrella" mode
Expected Bands => The data shows that a spectrum will have 2 bands at 1089.54 cm-1 and 1693.95 cm-1, for mode 1 and modes 2 & 3 respectively. modes 4, 5 and 6 have no bands as these modes don't have a change in dipole moment and so are IR inactive.
Charge Distribution
| Atom | Charge |
|---|---|
| N | -1.125 |
| H | 0.375 |
It would be expected for the Nitrogen atom to carry a negative charge as N is more electronegative than Hydrogen, which is also why a positive charge is expected on the H atoms.
Nitrogen - N2
Optimisation Data
| Optimisation Data | Value |
|---|---|
| Calculation Method | RB3LYP |
| Basis Set | 6-31G(d.p) |
| Final Energy (E(RB3LYP)) | -109.52412868 a.u. |
| RMS Gradient | 0.00000060 a.u. |
| Point Group | C∞h |
| N-N Bond Length | 1.10550 Å |
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
Predicted change in Energy=-3.401033D-13
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
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! R1 R(1,2) 1.1055 -DE/DX = 0.0 !
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Nitrogen Molecule |
The optimisation file is linked to here
"Display Vibrations" Window
1 Mode of Vibration - no negative frequencies. The vibration is IR inactive as there is no change in dipole moment (molecule is homo-nuclear diatomic).
Hydrogen - H2
Optimisation Data
| Optimisation Data | Value |
|---|---|
| Calculation Method | RB3LYP |
| Basis Set | 6-31G(d.p) |
| Final Energy (E(RB3LYP)) | -1.17853935 a.u. |
| RMS Gradient | 0.00005349 a.u. |
| Point Group | C∞h |
| H-H Bond Length | 0.74292 Å |
Item Value Threshold Converged?
Maximum Force 0.000093 0.000450 YES
RMS Force 0.000093 0.000300 YES
Maximum Displacement 0.000122 0.001800 YES
RMS Displacement 0.000172 0.001200 YES
Predicted change in Energy=-1.129292D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 0.7429 -DE/DX = -0.0001 !
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Hydrogen Molecule |
The optimisation file is linked to here
"Display Vibrations" Window
1 Mode of Vibration, no negative frequencies. The vibration is IR inactive as there is no change in dipole moment (molecule is homo-nuclear diatomic).
Reaction Energies
E(NH3)= -56.55776873 a.u.
2*(NH3)= -113.11553746 a.u.
E(N2)= -109.52412868 a.u
E(H2)= -1.17853935 a.u.
3*(H2)= -3.53561805 a.u.
ΔE=2*(NH3)-[E(N2)+3*(H2)]= -113.11553746-[-113.05974673] = -0.05579073 a.u.
ΔE (kJ/mol)= -0.05579073*2625.5 =-146.478561615 kJ/mol
Energy change is negative, therefore the product (Ammonia Gas) is more stable than the reactant gases.
Molecule of Choice - Cyanide CN-
| Optimisation Data | Value |
|---|---|
| Calculation Method | RB3LYP |
| Basis Set | 6-31G(d.p) |
| Final Energy (E(RB3LYP)) | -92.82453153 a.u. |
| RMS Gradient | 0.00000704 a.u. |
| Point Group | C∞v |
| C-N Bond Length | 1.18409 Å |
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000005 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-6.650386D-11
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
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! R1 R(1,2) 1.1841 -DE/DX = 0.0 !
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Cyanide Ion |
The optimisation file is linked to here
"Display Vibrations" Window
1 Mode of Vibration, no negative frequencies. The vibration is IR active, this is because the molecule is a hetero-nuclear diatomic, during vibration there is a change in dipole moment.
Charge Distribution
| Atom | Charge |
|---|---|
| N | -0.754 |
| C | -0.246 |
Both atoms carry a negative charge as the overall charge of the ion is -1. As nitrogen is more electronegative it has a more negative charge than the carbon.
Molecular Orbitals
| MO Pair | Images (Bonding (Left) + Anti-bonding (Right)) | Comments |
|---|---|---|
| 3 & 4 |  |
The two orbitals correspond to the 2sσ and 2sσ* orbitals. Both of these orbitals are occupied, so as they cancel each other out they have no overall contribution to the bond order of the molecule. The 2s AO of the Nitrogen atom contributes more to the bonding MO, while the Carbon 2s AO contributes more to the anti-bonding MO. As can be seen in the MO energy list, both these MOs are deeper in energy than orbitals 5 and above, with MO 4 (-0.10626 a.u.) being about 1 order of magnitude deeper than MO 5 (-0.01696 a.u.), and MO 3 (-0.56195) being even deeper than this. This means the electron density of the MO is pulled in more than the orbitals higher in energy. |
| 5 & 8 |  |
These two correspond to one of the 2pπ and 2pπ* bonding-antibonding MOs. The 2p orbitals that contribute to these MOs are orthogonal to the plane of the bond and so form π-bonds instead of σ-bonds. Unlike MOs 3&4, only the bonding MO is occupied, meaning the bonding orbital contributes to the bond order. The Carbon 2p AO contributes more to the anti-bonding MO, as the picture demonstrates larger regions of density about the Carbon, the Nitrogen contributes more to the bonding MO, as Nitrogen is more elctronegative. MO 5 is negative in energy, while MO 8 is positive. MO 8 is also the LUMO for the ion. |
| 6 & 9 |  |
This pair is degenerate to MOs 5&8, they have contribution from the other 2p orbitals orthogonal to the bond. As such they both have the same energy and features, just a different orientation in space. It is therefore fair to say that MO 9 can also be considered the LUMO of the ion. Again the bonding MO is occupied while the anti-bonding MO isn't, meaning that the bonding MO contributes to the bond order. |
| 7 & 10 |  |
This pair corresponds to the 2pσ and 2pσ* MOs, these have contribution from the 2p AOs that are parallel to the bond and so form a σ-bond. The bonding orbital is occupied and the anti-bonding is unoccupied, so the bonding MO contributes to the bond order. From this it is shown that the bond order is 3, explain why CN- has a triple bond. Again the Nitrogen 2p AO contributes more to the bonding character of the bonding MO, while the Carbon contributes more to anti-bonding character, this is due to Nitrogen being more electronegative than Carbon. |
Literature Comparison
The calculated value of the CN bond length is 1.18409 Å, this compares well to a literature value of 1.1554 Å[1], the calculated value is slightly larger, but not by a dramatic amount.
References
- ↑ Tables of Interatomic Distances and Configuration in Molecules and Ions, L.E. Sutton, ed., London: The Chemical Society, 1958.