Rep:Mod:hyt215 IMM2
NH3 molecule
Information
|
Click here to view log file. | |||
| Calculation Details | |||
|---|---|---|---|
| Calculation Method | RB3LYP | ||
| Basis Set | 6-31G(d,p) | ||
| Point Group | C3v | ||
| Calculation Results | |||
| Final Energy E(RB3LYP)/a.u. | -56.55776873 | ||
| RMS Gradient/a.u. | 0.00000485 | ||
| Bond Length/Å | 1.01798 | ||
| Bond Angle/° | 37.129 | ||
"Item" Table
Item Value Threshold Converged? Maximum Force 0.000004 0.000450 YES RMS Force 0.000004 0.000300 YES Maximum Displacement 0.000070 0.001800 YES RMS Displacement 0.000033 0.001200 YES
Vibration Modes
The image above shows the screenshot of vibration modes of NH3. As there are no negative frequencies, the energy of the molecule is at its local minima.
| Number of Modes (based on 3N-6 rule) | 6 |
|---|---|
| Degenerate Modes | 2 and 3, 5 and 6 |
| "Bending" Vibrations | 1089.54 Hz (1), 1693.95 Hz (2 and 3) |
| "Bond Stretch" Vibrations | 3461.29 Hz (4), 3589.82 Hz (5 and 6) |
| Highly Symmetric Mode | 4 |
| "Umbrella" Mode | 1 |
| Bands Expected in an Experimental Spectrum | 4 |
Atomic Charge
| Atom | Charge |
|---|---|
| Hydrogen | +0.375 |
| Nitrogen | -1.125 |
Being more electronegative than hydrogen atoms, the nitrogen atom is more electron withdrawing and therefore carries a negative charge. Being less electronegative, the hydrogen atoms carry a positive charge.
N2 molecule
Information
|
Click here to view log file. | |||
| Calculation Details | |||
|---|---|---|---|
| Calculation Method | RB3LYP | ||
| Basis Set | 6-31G(d,p) | ||
| Point Group | D∞h | ||
| Calculation Results | |||
| Final Energy E(RB3LYP)/a.u. | -109.52412868 | ||
| RMS Gradient/a.u. | 0.00000060 | ||
| Bond Length/Å | 1.10550 | ||
"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
Vibration Modes
The image above shows the screenshot of vibration modes of N2. As there are no negative frequencies, the energy of the molecule is at its local minima. Due to the absence of a net dipole moment, there were no IR active vibrational modes present.
Atomic Charge
| Atom | Charge |
|---|---|
| Nitrogen | 0.000 |
As the electronegativity of both atoms are the same, the charge is 0.000.
H2 molecule
Information
|
Click here to view log file. | |||
| Calculation Details | |||
|---|---|---|---|
| Calculation Method | RB3LYP | ||
| Basis Set | 6-31G(d,p) | ||
| Point Group | D∞h | ||
| Calculation Results | |||
| Final Energy E(RB3LYP)/a.u. | -1.17853936 | ||
| RMS Gradient/a.u. | 0.00000222 | ||
| Bond Length/Å | 0.74280 | ||
"Item" Table
Item Value Threshold Converged? Maximum Force 0.000004 0.000450 YES RMS Force 0.000004 0.000300 YES Maximum Displacement 0.000005 0.001800 YES RMS Displacement 0.000007 0.001200 YES
Vibration Modes
The image above shows the screenshot of vibration modes of H2. As there are no negative frequencies, the energy of the molecule is at its local minima. Due to the absence of a net dipole moment, there were no IR active vibrational modes present.
Atomic Charge
| Atom | Charge |
|---|---|
| Hydrogen | 0.000 |
As the electronegativity of both atoms are the same, the charge is 0.000.
Energetics of Haber-Bosch process
N2 + 3H2 → 2NH3
The table below shows the energy of the above reaction in atomic units (a.u.).
| E(NH3) | -56.55776873 |
|---|---|
| 2*E(NH3) | -113.11553746 |
| E(N2) | -109.52412868 |
| E(H2) | -1.17853936 |
| 3*E(H2) | -3.53561808 |
| ΔE=2*E(NH3) - [E(N2) + 3*E(H2)] | -0.05579070 |
The energy change is ΔE= -0.05579070×2625.5= -146.48 kJmol-1. The negative sign of enthalpy change indicates that the reaction is exothermic and energy is released into the surroundings. The decrease in energy indicates that ammonia is more stable than the gaseous reactants.
[AlCl4]- molecule
Information
|
Click here to view log file. | |||
| Calculation Details | |||
|---|---|---|---|
| Calculation Method | RB3LYP | ||
| Basis Set | 6-31G(d,p) | ||
| Point Group | Td | ||
| Calculation Results | |||
| Final Energy E(RB3LYP)/a.u. | -2083.61641374 | ||
| RMS Gradient/a.u. | 0.00000606 | ||
| Bond Length/Å | 2.17690 | ||
| Bond Angle/° | 109.471 | ||
"Item" Table
Item Value Threshold Converged? Maximum Force 0.000012 0.000450 YES RMS Force 0.000006 0.000300 YES Maximum Displacement 0.000080 0.001800 YES RMS Displacement 0.000043 0.001200 YES
Vibration Modes
The image above shows the screenshot of vibration modes of [AlCl4]-. As there are no negative frequencies, the energy of the molecule is at its local minima.
The table below shows the vibrations of the molecule. As [AlCl4]- is non-linear, there are 3(5)-6=9 vibrational modes, given by the equation 3N-6 where N is the number of atoms.
| Mode | Frequency/cm-1 | Infared Intensity | Vibrations | Remarks |
|---|---|---|---|---|
| 1 | 113.14 | 0.0000 | 
|
Due to the presence of symmetric bending, there are no net dipole moments for these two degenerate vibrational modes. This vibrational mode is IR inactive. |
| 2 | 113.14 | 0.0000 | 
| |
| 3 | 176.10 | 7.2635 | 
|
Due to the presence of assymmetric bending, these three degenerate bending modes are IR active. |
| 4 | 176.10 | 7.2635 | 
| |
| 5 | 176.10 | 7.2635 | 
| |
| 6 | 333.01 | 0.0000 | 
|
Due to the presence of symmetric stretching, there are no net dipole moments. This vibrational mode is IR inactive. |
| 7 | 492.30 | 186.2173 | 
|
Due to the presence of asymmetric stretching, these three degenerate vibrational modes are IR active. |
| 8 | 492.30 | 186.2173 | 
| |
| 9 | 492.30 | 186.2173 | 
|
The image above shows the predicted IR spectra for [AlCl4]-. As there are two energy levels at which [AlCl4]- are IR active, there are two peaks in the spectrum at 176.10 cm-1 and 492.30 cm-1.
Atomic Charge
| Atom | Charge |
|---|---|
| Aluminium | +1.415 |
| Chlorine | -0.604 |
Being more electronegative than aluminium, chlorine atoms are more electron withdrawing and therefore carries a negative charge. Being less electronegative, the aluminium atoms carry a positive charge.
Molecular Orbitals
A molecular orbital diagram was calculated using GaussView with a degeneracy threshold of 0.00001. A small degeneracy threshold was chosen to allow for small differences in energy to be visibly shown.
The table below describes some of the MOs shown above.
| MO | Image | Energy/a.u. | Contributing AOs | Bonding/Non-bonding/Antibonding | Energy (deep, high, HOMO/LUMO) | MO occupied or unoccupied |
|---|---|---|---|---|---|---|
| 1 | 
|
-101.36438 | 1s orbitals of chlorine. There are four degenerate molecular orbitals. | Non-bonding. The atomic orbitals are too small and far apart to interact with each other. | Deep. This is the lowest energy level, probably due to the strong electrostatic forces of attraction between the nucleus and the electrons. As chlorine has more protons than aluminium, the forces of attraction are lower and therefore holds the 1s orbital more closely to the nucleus than that of aluminium. | Occupied |
| 23 | 
|
-2.29204 | 2p orbital of aluminium | Non-bonding. As the energy gap between this orbital and others is large, there are no interactions between this orbital and other orbitals | Deep. Though significantly higher than that of chlorine, it is still rather low compared to other orbitals | Occupied |
| 26 | 
|
-0.65623 | 3s orbital of aluminium and 3s bonding fragment orbital of chlorine | Bonding. There are orbital overlaps between the energy levels of aluminium and chlorine as the orbitals are of the right orientation. | Deep. As this orientation is favourable, the energy level is low. | Occupied |
| 30 | 
|
-0.28838 | 3s orbital of aluminium and 3s bonding fragment orbital of chlorine | Antibonding (of MO26) | This MO is stabilised by mixing with MO42 (3p orbitals of chlorine). Due to the orientation of orbitals, the favorable interactions lowers the energy of this MO. | Occupied |
| 36 | 
|
-0.16663 | 3p orbitals of chlorine | Non-bonding. There are no favorable interactions between the molecular orbitals. | High. This is near the HOMO/LUMO region due to the lack of stabilising interactions between the atomic orbitals. | Occupied |
| 42 | 
|
+0.16534 | 3p orbitals of chlorine interacts with MO30 | Anti-bonding | LUMO. Due to mixing with MO30, the energy level of this molecular orbital is raised such that there are no electrons in this orbital. | Unoccupied |
AlCl3 molecule
Information
|
Click here to view log file. | |||
| Calculation Details | |||
|---|---|---|---|
| Calculation Method | RB3LYP | ||
| Basis Set | 6-31G(d,p) | ||
| Point Group | D3h | ||
| Calculation Results | |||
| Final Energy E(RB3LYP)/a.u. | -244.20693747 | ||
| RMS Gradient/a.u. | 0.00005838 | ||
| Bond Length/Å | 1.58678 | ||
| Bond Angle/° | 120 | ||
"Item" Table
Item Value Threshold Converged? Maximum Force 0.000117 0.000450 YES RMS Force 0.000076 0.000300 YES Maximum Displacement 0.000825 0.001800 YES RMS Displacement 0.000540 0.001200 YES
Vibration Modes
The image above shows the screenshot of vibration modes of AlCl3. As there are no negative frequencies, the energy of the molecule is at its local minima.
Atomic Charge
| Atom | Charge |
|---|---|
| Aluminium | +1.135 |
| Chlorine | -0.378 |
Being more electronegative than aluminium, chlorine atoms are more electron withdrawing and therefore carries a negative charge. Being less electronegative, the aluminium atoms carry a positive charge.