ChemWiki - User contributions [en]

Acc2518

2019-03-04T14:51:43Z

Acc2518: /* Charge analysis */

== NH3 molecule ==
=== Optimisation data ===
{| class="wikitable"
|+ NH3 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-56.55776873 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00000485 (au)
|-
|'''Point group'''
|C3V
|-
|'''Bond length (N-H)'''
|1.02 (Å)
|-
|'''Bond angle (H-N-H)'''
|106(°)
|}
<pre>
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
</pre>

<jmol><jmolApplet>
<title> NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518 NH3 OPTF POP.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>
[[:File:ACC2518 NH3 OPTF POP.LOG|Optimised NH3 .log file (acc2518)]]

=== Vibrations ===
[[File:Acc2518 vibrations screenshot.jpg|The Gaussview "Display Vibrations" window of the optimised ammonia molecule.|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 1090 || 1694
|-
| '''Symmetry''' || A1 || E
|-
| '''Intensity''' (arbitrary units) || 145 || 14
|-
| '''Image'''|| [[File:acc2518VM1.png|250px]] || [[File:acc2518VM2.png|300px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 1694|| 3461
|-
| '''Symmetry''' || E || A1
|-
| '''Intensity''' (arbitrary units) || 14 || 1
|-
| '''Image'''|| [[File:acc2518VM3.png|250px]] || [[File:acc2518VM4.png|275px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 3590|| 3590
|-
| '''Symmetry''' || E || E
|-
| '''Intensity''' (arbitrary units) || 0 || 0
|-
| '''Image'''|| [[File:acc2518VM5.png|275px]] || [[File:acc2518VM6.png|250px]]
|}

Using the 3N-6 rule, where N represents the number of atoms in a molecule, it is expected that ammonia will have six vibrational modes as shown above. There are two pairs of degenerate modes with a frequency of 1694 (cm-1) and 3590 (cm-1). The modes with a frequency of 1090 (cm-1) and 1694 (cm-1) correspond to bending vibrations and the modes with a frequency 3461 (cm-1) and 3590 (cm-1) correspond to bond stretch vibrations. The bond stretch vibration at 3461 (cm-1) is highly symmetric whilst the stretches with a frequency of 3590 (cm-1) are asymmetric. The bending vibration with a frequency of 1090 (cm-1) is known as the umbrella mode. Three bands would be expected to be seen with the two stretches at 3590 (cm-1) being too low in intensity. The bends with a frequency of 1694 (cm-1) are degenerate and only one band will be observed between the two. Hence the three observed bands would be at 1090 (cm-1), 1694 (cm-1) and 3461 (cm-1).

=== Charge analysis ===
[[File:Acc2518 charge analysis.png|The Gaussview generated atomic charges of ammonia.|250px]]

Nitrogen has a greater electronegativity than hydrogen and hence there is greater electron density distributed around the N atom in ammonia relative to hydrogen. This explains the negative charge on N and the positive charge on H.

==N2 molecule==

===Optimisation data===

{| class="wikitable"
|+ N2 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-109.52412868 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00000060 (au)
|-
|'''Point group'''
|D∞h
|-
|'''Bond length (N-N)'''
|1.11 (Å)
|}

<pre>
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
</pre>

<jmol><jmolApplet>
<title> Nitrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518 N2 OPTIMISATION.LOG</uploadedFileContents>
<script>frame 1.10</script>
</jmolApplet></jmol>
[[:File:ACC2518 N2 OPTIMISATION.LOG|Optimised N2 .log file (acc2518)]]

===Vibrations===
[[File:Acc2518 N2vibration.png|Nitrogen display vibrations screenshot|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 2457
|-
| '''Symmetry''' || SGG
|-
| '''Intensity''' (arbitrary units) || 0
|-
| '''Image'''|| [[File:Acc2518NitrogenVM.png|250px]]
|}
Using the 3N-5 rule for linear molecules, Nitrogen can be expected to have one vibrational mode but this mode has an IR intensity of zero since Nitrogen molecules are IR inactive. This is because they have no overall dipole.

===Charge analysis===
[[File:Acc2518nitrogen charges.png]]

Both nitrogen atoms have the same electronegativity so the charge is neutral on both atoms.

===CCDC search===
'''Unique identifier:''' [https://www.ccdc.cam.ac.uk/structures/Search?Ccdcid=VAMQAE&DatabaseToSearch=Published VAMQAE]

'''Deposition number:''' 1530121

The complex linked above contains nitrogen coordinated to cobalt with a N-N bond distance of 1.08 Å which is slightly shorter than the optimised N-N bond length, displayed above, of 1.11 Å (2.d.p). During the optimisation process for nitrogen, assumptions have to be made for the computational process to be carried out. Each assumption made will increase the uncertainty in measurable quantities such as the bond length. Hence, the computationally determined bond length from the optimisation is a model and may not fully reflect the true bond length or the bond length determined by a computational program considering slightly different assumptions.

It should also be considered that the optimisation gave a prediction for the N-N bond length in a nitrogen molecule whereas the molecule linked above contains a nitrogen molecule that is coordinated into a transition metal complex. A lone pair of electrons on one of the nitrogen atoms has been donated to a cobalt ion, this draws electron density away from the donating nitrogen atom and would therefore slightly increase the positive charge on this atom. This may cause the donating nitrogen atom to attract the electrons in the N-N bond more strongly which would then explain the shorter bond in the transition metal complex compared to the nitrogen molecule.

==H2 molecule==

===Optimisation data===
{| class="wikitable"
|+ H2 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-1.17853936 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00000017 (au)
|-
|'''Point group'''
|D∞h
|-
|'''Bond length (H-H)'''
|0.74 (Å)
|}

<pre>
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

</pre>

<jmol><jmolApplet>
<title> Hydrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518 H2 OPTIMISATION.LOG</uploadedFileContents>
<script>frame 1.7</script>
</jmolApplet></jmol>
[[:File:ACC2518 H2 OPTIMISATION.LOG|Optimised H2 .log file (acc2518)]]

===Vibrations===
[[File:Acc2518 H2vibration.png|Hydrogen display vibrations screenshot|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 4466
|-
| '''Symmetry''' || SGG
|-
| '''Intensity''' (arbitrary units) || 0
|-
| '''Image'''|| [[File:Acc2518HydrogenVM.png|250px]]
|}
Using the 3N-5 rule for linear molecules, hydrogen can be expected to have one vibrational mode but this mode has an IR intensity of zero since hydrogen molecules, like nitrogen molecules, are IR inactive.

===Charge analysis===
[[File:Acc2518hydrogen charges.png]]

Both hydrogen atoms have the same electronegativity so the charge is neutral on both atoms.

==The Haber-Bosch process==
N2 + 3H2 -> 2NH3

E(NH3)=-56.55776873

 '''2*E(NH3)''' =2*(-56.55776873)=-113.11553746

 '''E(N2)''' =-109.52412868

E(H2)=-1.17853936

 '''3*E(H2)''' =3*(-1.17853936) =-3.53561808

'''ΔE= 2*E(NH3) -[ E(N2) + 3*E(H2) ]'''= -0.05579069 ≈ -0.05579 au (5.d.p)

'''ΔE=-146.5 kJ/mol (1.d.p)'''

ΔE is negative which indicates that the gaseous reactants are less stable than the ammonia product since the reactants are at a higher energy than the product. Although this process is not necessarily entropically favourable with four reactant gaseous molecules forming two gaseous product molecules, the reaction has a significantly negative enthalpy change which reflects the result calculated above.

== Project molecule (NF3) ==

=== Optimisation data ===
{| class="wikitable"
|+ NF3 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-354.07131058 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00010256 (au)
|-
|'''Point group'''
|C3V
|-
|'''Bond length (N-F)'''
|1.38 (Å)
|-
|'''Bond angle (F-N-F)'''
|102(°)
|}
<pre>
Item Value Threshold Converged?
Maximum Force 0.000164 0.000450 YES
RMS Force 0.000108 0.000300 YES
Maximum Displacement 0.000612 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

<jmol><jmolApplet>
<title> NF3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518_NF3_OPTF_POP.LOG </uploadedFileContents>
<script>frame 1.7</script>
</jmolApplet></jmol>
[[:File:ACC2518_NF3_OPTF_POP.LOG|Optimised NF3 .log file (acc2518)]]

=== Vibrations ===
[[File:Acc2518 NF3 vibrations screenshot.png|The Gaussview "Display Vibrations" window of the optimised nitrogen trifluoride molecule.|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 482 || 482
|-
| '''Symmetry''' || E || E
|-
| '''Intensity''' (arbitrary units) || 1 || 1
|-
| '''Image'''|| [[File:Acc2518 NF3 VM1.png|300px]] || [[File:Acc2518 NF3 VM2.png|300px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 644|| 930
|-
| '''Symmetry''' || A1 || E
|-
| '''Intensity''' (arbitrary units) || 3 || 208
|-
| '''Image'''|| [[File:Acc2518 NF3 VM3.png|300px]] || [[File:Acc2518 NF3 VM4.png|300px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 930|| 1062
|-
| '''Symmetry''' || E || A1
|-
| '''Intensity''' (arbitrary units) || 208 || 40
|-
| '''Image'''|| [[File:Acc2518 NF3 VM5.png|300px]] || [[File:Acc2518 NF3 VM6.png|300px]]
|}

Nitrogen trifluoride has the same number of atoms as ammonia and so six vibrational modes can be predicted from the 3N-6 rule. There are also two pairs of degenerate modes with frequencies of 482 (cm-1) and 930 (cm-1). The modes with a frequency of 482 (cm-1) and 644(cm-1) correspond to bending vibrational modes and the modes with a frequency of 930 (cm-1) and 1062 (cm-1) correspond to stretching vibrational modes. The mode with a frequency of 1062 (cm-1) represents a symmetric stretch whilst the modes with a frequency of 930 (cm-1) represent asymmetric stretches. In contrast to ammonia, the highest frequency bond stretch of nitrogen trifluoride is the symmetric stretch.

Three bands can be expected in the NF3 IR spectrum at frequencies of 644 (cm-1) 930 (cm-1) and 1062 (cm-1). The bends at 482 (cm-1) will be too low in frequency to appear in the spectrum which starts at a frequency of 500 (cm-1). The stretches at 930 (cm-1) are degenerate and hence will only display one band between them. The band as 644 (cm-1) may not be clearly visible due its relative low intensity of 3 arbitrary units.

=== Charge analysis ===
[[File:Acc2518 NF3 charge analysis.png|The Gaussview generated atomic charges of ammonia.|250px]]

Fluorine has a greater electronegativity that nitrogen and therefore there is greater electron density distributed around the three fluorine atoms compared to the nitrogen atom. The three fluorine atoms are treated as equivalent which means that the magnitude of the positive charge on nitrogen is three times the magnitude of the negative charge on a single fluorine atom.

=== Molecular orbitals (MO) ===

The nitrogen atom contributes 7 electrons and each fluorine atom contributes 9 electrons which means that nitrogen trifluoride contains 34 electrons in total and hence 17 electron pairs. In the table below, a molecular orbital number of 1 would denote the molecular orbital that is deepest in energy. Therefore, orbital 17 represents the HOMO and orbital 18 represents the LUMO. All of the molecular orbitals shown below are occupied with the exception of the LUMO.

{| class="wikitable"
!Molecular orbital number
!Image
!Type of molecular orbital
!Energy (au)
!Extra details
|-
|18
|[[File:Acc2518 MO18.png|200px]]
|Antibonding
|0.01947
|There are nodes in the centre of the N-F bonds which indicates that the LUMO is an antibonding orbital with destructive inteference between phases of opposite sign. The nodes in the centre of all four atoms also indicate that this MO was formed from 2p atomic orbitals from both nitrogen and fluorine.
|-
|17
|[[File:Acc2518 MO17.png|200px]]
|Bonding
| -0.35162
| The phase denoted by the green region shows orbital overlap across all three N-H bonds which implies that the HOMO is a bonding orbital. This MO has been formed from 2p orbitals which explains the nodes observed in the centre of the F atoms.
|-
|16
|[[File:Acc2518 MO16.png|200px]]
|Non-bonding
| -0.42224
|There is no electron density along any of the bonds which is the key indicator that this is a non-bonding MO. Since the electron density is localised around the fluorine atoms, this MO appears to show lone electron pairs on these fluorine atoms. There is no electron density being shared between the fluorine atoms which suggests there is destructive interference preventing such an interaction.
|-
|15
|[[File:Acc2518 MO15.png|200px]]
|Bonding
| -0.43590
| As observed in the HOMO, there is electron density along all three bonds which indicates the bonding nature of the MO. However, in contrast to the HOMO, the electron density along the bonds is not in the same phase for each bond. There is also some constructive interference between two of the F atoms which appears to indicate a very partial π character between the two atoms. This also means that this interaction is the product of two 2p atomic orbitals on fluorine overlapping slightly in phase with each other.
|-
|5
|[[File:Acc2518 MO5.png|200px]]
| Bonding
| -1.35870
| This MO contains no nodes at all implying that it is bonding in nature. It is also formed from overlap of 2s orbitals, in phase, on all atoms since the entire molecule is encased in electron density as a result of the constructive interference. It cannot be formed from 1s orbitals which would be far lower in energy and will also only occupy the first 4 MOs since there are 8 1s electrons in NF3.
|}

== Bonus Molecule (CO2) ==

===Optimisation data===

{| class="wikitable"
|+ CO2 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-188.58093945 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00001154 (au)
|-
|'''Point group'''
|D∞h
|-
|'''Bond length (C-O)'''
|1.17 (Å)
|-
|'''Bond angle (C-O-C)'''
|180 (°)
|-
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000017 0.000300 YES
Maximum Displacement 0.000021 0.001800 YES
RMS Displacement 0.000015 0.001200 YES

</pre>

<jmol><jmolApplet>
<title> Carbon dioxide molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518 CO2 OPTF POP.LOG</uploadedFileContents>
<script>frame 1.10</script>
</jmolApplet></jmol>
[[:File:ACC2518 CO2 OPTF POP.LOG|Optimised CO2 .log file (acc2518)]]

===Vibrations===
[[File:Acc2518 CO2vibration.png|Carbon dioxide display vibrations screenshot|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 640|| 640
|-
| '''Symmetry''' || PIU || PIU
|-
| '''Intensity''' (arbitrary units) || 31 || 31
|-
| '''Image'''|| [[File:Acc2518co2VM1.png|200px]] || [[File:Acc2518co2VM2.png|250px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 1372|| 2436
|-
| '''Symmetry''' || SGG || SGU
|-
| '''Intensity''' (arbitrary units) || 0 || 546
|-
| '''Image'''|| [[File:Acc2518co2VM3.png|350px]] || [[File:Acc2518co2VM4.png|300px]]
|}
Using the 3N-5 rule for linear molecules, carbon dioxide can be expected to have 4 vibrational modes. The modes with a frequency of 640 cm-1 correspond to bends and the modes with frequencies of 1372 cm-1 and 2436 cm-1 correspond to stretches. The two modes with a frequency of 640 cm-1 are degenerate and will only produce one IR band between them. The stretch with a frequency of 1372 will not produce an IR band as the stretch is symmetric and has no overall dipole. The asymmetric stretch at 2436 cm-1 will also produce an IR band to give two IR bands overall.

===Charge analysis===
[[File:Acc2518 CO2charges.png]]

Oxygen has a greater electronegativity than carbon which explains the negative charge on each oxygen atom and the positive charge on the central carbon atom.

File:Acc2518 CO2charges.png

2019-03-04T14:50:19Z

Acc2518:

Acc2518

2019-03-04T14:48:30Z

Acc2518: /* Optimisation data */

== NH3 molecule ==
=== Optimisation data ===
{| class="wikitable"
|+ NH3 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-56.55776873 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00000485 (au)
|-
|'''Point group'''
|C3V
|-
|'''Bond length (N-H)'''
|1.02 (Å)
|-
|'''Bond angle (H-N-H)'''
|106(°)
|}
<pre>
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
</pre>

<jmol><jmolApplet>
<title> NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518 NH3 OPTF POP.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>
[[:File:ACC2518 NH3 OPTF POP.LOG|Optimised NH3 .log file (acc2518)]]

=== Vibrations ===
[[File:Acc2518 vibrations screenshot.jpg|The Gaussview "Display Vibrations" window of the optimised ammonia molecule.|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 1090 || 1694
|-
| '''Symmetry''' || A1 || E
|-
| '''Intensity''' (arbitrary units) || 145 || 14
|-
| '''Image'''|| [[File:acc2518VM1.png|250px]] || [[File:acc2518VM2.png|300px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 1694|| 3461
|-
| '''Symmetry''' || E || A1
|-
| '''Intensity''' (arbitrary units) || 14 || 1
|-
| '''Image'''|| [[File:acc2518VM3.png|250px]] || [[File:acc2518VM4.png|275px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 3590|| 3590
|-
| '''Symmetry''' || E || E
|-
| '''Intensity''' (arbitrary units) || 0 || 0
|-
| '''Image'''|| [[File:acc2518VM5.png|275px]] || [[File:acc2518VM6.png|250px]]
|}

Using the 3N-6 rule, where N represents the number of atoms in a molecule, it is expected that ammonia will have six vibrational modes as shown above. There are two pairs of degenerate modes with a frequency of 1694 (cm-1) and 3590 (cm-1). The modes with a frequency of 1090 (cm-1) and 1694 (cm-1) correspond to bending vibrations and the modes with a frequency 3461 (cm-1) and 3590 (cm-1) correspond to bond stretch vibrations. The bond stretch vibration at 3461 (cm-1) is highly symmetric whilst the stretches with a frequency of 3590 (cm-1) are asymmetric. The bending vibration with a frequency of 1090 (cm-1) is known as the umbrella mode. Three bands would be expected to be seen with the two stretches at 3590 (cm-1) being too low in intensity. The bends with a frequency of 1694 (cm-1) are degenerate and only one band will be observed between the two. Hence the three observed bands would be at 1090 (cm-1), 1694 (cm-1) and 3461 (cm-1).

=== Charge analysis ===
[[File:Acc2518 charge analysis.png|The Gaussview generated atomic charges of ammonia.|250px]]

Nitrogen has a greater electronegativity than hydrogen and hence there is greater electron density distributed around the N atom in ammonia relative to hydrogen. This explains the negative charge on N and the positive charge on H.

==N2 molecule==

===Optimisation data===

{| class="wikitable"
|+ N2 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-109.52412868 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00000060 (au)
|-
|'''Point group'''
|D∞h
|-
|'''Bond length (N-N)'''
|1.11 (Å)
|}

<pre>
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
</pre>

<jmol><jmolApplet>
<title> Nitrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518 N2 OPTIMISATION.LOG</uploadedFileContents>
<script>frame 1.10</script>
</jmolApplet></jmol>
[[:File:ACC2518 N2 OPTIMISATION.LOG|Optimised N2 .log file (acc2518)]]

===Vibrations===
[[File:Acc2518 N2vibration.png|Nitrogen display vibrations screenshot|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 2457
|-
| '''Symmetry''' || SGG
|-
| '''Intensity''' (arbitrary units) || 0
|-
| '''Image'''|| [[File:Acc2518NitrogenVM.png|250px]]
|}
Using the 3N-5 rule for linear molecules, Nitrogen can be expected to have one vibrational mode but this mode has an IR intensity of zero since Nitrogen molecules are IR inactive. This is because they have no overall dipole.

===Charge analysis===
[[File:Acc2518nitrogen charges.png]]

Both nitrogen atoms have the same electronegativity so the charge is neutral on both atoms.

===CCDC search===
'''Unique identifier:''' [https://www.ccdc.cam.ac.uk/structures/Search?Ccdcid=VAMQAE&DatabaseToSearch=Published VAMQAE]

'''Deposition number:''' 1530121

The complex linked above contains nitrogen coordinated to cobalt with a N-N bond distance of 1.08 Å which is slightly shorter than the optimised N-N bond length, displayed above, of 1.11 Å (2.d.p). During the optimisation process for nitrogen, assumptions have to be made for the computational process to be carried out. Each assumption made will increase the uncertainty in measurable quantities such as the bond length. Hence, the computationally determined bond length from the optimisation is a model and may not fully reflect the true bond length or the bond length determined by a computational program considering slightly different assumptions.

It should also be considered that the optimisation gave a prediction for the N-N bond length in a nitrogen molecule whereas the molecule linked above contains a nitrogen molecule that is coordinated into a transition metal complex. A lone pair of electrons on one of the nitrogen atoms has been donated to a cobalt ion, this draws electron density away from the donating nitrogen atom and would therefore slightly increase the positive charge on this atom. This may cause the donating nitrogen atom to attract the electrons in the N-N bond more strongly which would then explain the shorter bond in the transition metal complex compared to the nitrogen molecule.

==H2 molecule==

===Optimisation data===
{| class="wikitable"
|+ H2 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-1.17853936 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00000017 (au)
|-
|'''Point group'''
|D∞h
|-
|'''Bond length (H-H)'''
|0.74 (Å)
|}

<pre>
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

</pre>

<jmol><jmolApplet>
<title> Hydrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518 H2 OPTIMISATION.LOG</uploadedFileContents>
<script>frame 1.7</script>
</jmolApplet></jmol>
[[:File:ACC2518 H2 OPTIMISATION.LOG|Optimised H2 .log file (acc2518)]]

===Vibrations===
[[File:Acc2518 H2vibration.png|Hydrogen display vibrations screenshot|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 4466
|-
| '''Symmetry''' || SGG
|-
| '''Intensity''' (arbitrary units) || 0
|-
| '''Image'''|| [[File:Acc2518HydrogenVM.png|250px]]
|}
Using the 3N-5 rule for linear molecules, hydrogen can be expected to have one vibrational mode but this mode has an IR intensity of zero since hydrogen molecules, like nitrogen molecules, are IR inactive.

===Charge analysis===
[[File:Acc2518hydrogen charges.png]]

Both hydrogen atoms have the same electronegativity so the charge is neutral on both atoms.

==The Haber-Bosch process==
N2 + 3H2 -> 2NH3

E(NH3)=-56.55776873

 '''2*E(NH3)''' =2*(-56.55776873)=-113.11553746

 '''E(N2)''' =-109.52412868

E(H2)=-1.17853936

 '''3*E(H2)''' =3*(-1.17853936) =-3.53561808

'''ΔE= 2*E(NH3) -[ E(N2) + 3*E(H2) ]'''= -0.05579069 ≈ -0.05579 au (5.d.p)

'''ΔE=-146.5 kJ/mol (1.d.p)'''

ΔE is negative which indicates that the gaseous reactants are less stable than the ammonia product since the reactants are at a higher energy than the product. Although this process is not necessarily entropically favourable with four reactant gaseous molecules forming two gaseous product molecules, the reaction has a significantly negative enthalpy change which reflects the result calculated above.

== Project molecule (NF3) ==

=== Optimisation data ===
{| class="wikitable"
|+ NF3 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-354.07131058 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00010256 (au)
|-
|'''Point group'''
|C3V
|-
|'''Bond length (N-F)'''
|1.38 (Å)
|-
|'''Bond angle (F-N-F)'''
|102(°)
|}
<pre>
Item Value Threshold Converged?
Maximum Force 0.000164 0.000450 YES
RMS Force 0.000108 0.000300 YES
Maximum Displacement 0.000612 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

<jmol><jmolApplet>
<title> NF3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518_NF3_OPTF_POP.LOG </uploadedFileContents>
<script>frame 1.7</script>
</jmolApplet></jmol>
[[:File:ACC2518_NF3_OPTF_POP.LOG|Optimised NF3 .log file (acc2518)]]

=== Vibrations ===
[[File:Acc2518 NF3 vibrations screenshot.png|The Gaussview "Display Vibrations" window of the optimised nitrogen trifluoride molecule.|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 482 || 482
|-
| '''Symmetry''' || E || E
|-
| '''Intensity''' (arbitrary units) || 1 || 1
|-
| '''Image'''|| [[File:Acc2518 NF3 VM1.png|300px]] || [[File:Acc2518 NF3 VM2.png|300px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 644|| 930
|-
| '''Symmetry''' || A1 || E
|-
| '''Intensity''' (arbitrary units) || 3 || 208
|-
| '''Image'''|| [[File:Acc2518 NF3 VM3.png|300px]] || [[File:Acc2518 NF3 VM4.png|300px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 930|| 1062
|-
| '''Symmetry''' || E || A1
|-
| '''Intensity''' (arbitrary units) || 208 || 40
|-
| '''Image'''|| [[File:Acc2518 NF3 VM5.png|300px]] || [[File:Acc2518 NF3 VM6.png|300px]]
|}

Nitrogen trifluoride has the same number of atoms as ammonia and so six vibrational modes can be predicted from the 3N-6 rule. There are also two pairs of degenerate modes with frequencies of 482 (cm-1) and 930 (cm-1). The modes with a frequency of 482 (cm-1) and 644(cm-1) correspond to bending vibrational modes and the modes with a frequency of 930 (cm-1) and 1062 (cm-1) correspond to stretching vibrational modes. The mode with a frequency of 1062 (cm-1) represents a symmetric stretch whilst the modes with a frequency of 930 (cm-1) represent asymmetric stretches. In contrast to ammonia, the highest frequency bond stretch of nitrogen trifluoride is the symmetric stretch.

Three bands can be expected in the NF3 IR spectrum at frequencies of 644 (cm-1) 930 (cm-1) and 1062 (cm-1). The bends at 482 (cm-1) will be too low in frequency to appear in the spectrum which starts at a frequency of 500 (cm-1). The stretches at 930 (cm-1) are degenerate and hence will only display one band between them. The band as 644 (cm-1) may not be clearly visible due its relative low intensity of 3 arbitrary units.

=== Charge analysis ===
[[File:Acc2518 NF3 charge analysis.png|The Gaussview generated atomic charges of ammonia.|250px]]

Fluorine has a greater electronegativity that nitrogen and therefore there is greater electron density distributed around the three fluorine atoms compared to the nitrogen atom. The three fluorine atoms are treated as equivalent which means that the magnitude of the positive charge on nitrogen is three times the magnitude of the negative charge on a single fluorine atom.

=== Molecular orbitals (MO) ===

The nitrogen atom contributes 7 electrons and each fluorine atom contributes 9 electrons which means that nitrogen trifluoride contains 34 electrons in total and hence 17 electron pairs. In the table below, a molecular orbital number of 1 would denote the molecular orbital that is deepest in energy. Therefore, orbital 17 represents the HOMO and orbital 18 represents the LUMO. All of the molecular orbitals shown below are occupied with the exception of the LUMO.

{| class="wikitable"
!Molecular orbital number
!Image
!Type of molecular orbital
!Energy (au)
!Extra details
|-
|18
|[[File:Acc2518 MO18.png|200px]]
|Antibonding
|0.01947
|There are nodes in the centre of the N-F bonds which indicates that the LUMO is an antibonding orbital with destructive inteference between phases of opposite sign. The nodes in the centre of all four atoms also indicate that this MO was formed from 2p atomic orbitals from both nitrogen and fluorine.
|-
|17
|[[File:Acc2518 MO17.png|200px]]
|Bonding
| -0.35162
| The phase denoted by the green region shows orbital overlap across all three N-H bonds which implies that the HOMO is a bonding orbital. This MO has been formed from 2p orbitals which explains the nodes observed in the centre of the F atoms.
|-
|16
|[[File:Acc2518 MO16.png|200px]]
|Non-bonding
| -0.42224
|There is no electron density along any of the bonds which is the key indicator that this is a non-bonding MO. Since the electron density is localised around the fluorine atoms, this MO appears to show lone electron pairs on these fluorine atoms. There is no electron density being shared between the fluorine atoms which suggests there is destructive interference preventing such an interaction.
|-
|15
|[[File:Acc2518 MO15.png|200px]]
|Bonding
| -0.43590
| As observed in the HOMO, there is electron density along all three bonds which indicates the bonding nature of the MO. However, in contrast to the HOMO, the electron density along the bonds is not in the same phase for each bond. There is also some constructive interference between two of the F atoms which appears to indicate a very partial π character between the two atoms. This also means that this interaction is the product of two 2p atomic orbitals on fluorine overlapping slightly in phase with each other.
|-
|5
|[[File:Acc2518 MO5.png|200px]]
| Bonding
| -1.35870
| This MO contains no nodes at all implying that it is bonding in nature. It is also formed from overlap of 2s orbitals, in phase, on all atoms since the entire molecule is encased in electron density as a result of the constructive interference. It cannot be formed from 1s orbitals which would be far lower in energy and will also only occupy the first 4 MOs since there are 8 1s electrons in NF3.
|}

== Bonus Molecule (CO2) ==

===Optimisation data===

{| class="wikitable"
|+ CO2 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-188.58093945 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00001154 (au)
|-
|'''Point group'''
|D∞h
|-
|'''Bond length (C-O)'''
|1.17 (Å)
|-
|'''Bond angle (C-O-C)'''
|180 (°)
|-
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000017 0.000300 YES
Maximum Displacement 0.000021 0.001800 YES
RMS Displacement 0.000015 0.001200 YES

</pre>

<jmol><jmolApplet>
<title> Carbon dioxide molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518 CO2 OPTF POP.LOG</uploadedFileContents>
<script>frame 1.10</script>
</jmolApplet></jmol>
[[:File:ACC2518 CO2 OPTF POP.LOG|Optimised CO2 .log file (acc2518)]]

===Vibrations===
[[File:Acc2518 CO2vibration.png|Carbon dioxide display vibrations screenshot|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 640|| 640
|-
| '''Symmetry''' || PIU || PIU
|-
| '''Intensity''' (arbitrary units) || 31 || 31
|-
| '''Image'''|| [[File:Acc2518co2VM1.png|200px]] || [[File:Acc2518co2VM2.png|250px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 1372|| 2436
|-
| '''Symmetry''' || SGG || SGU
|-
| '''Intensity''' (arbitrary units) || 0 || 546
|-
| '''Image'''|| [[File:Acc2518co2VM3.png|350px]] || [[File:Acc2518co2VM4.png|300px]]
|}
Using the 3N-5 rule for linear molecules, carbon dioxide can be expected to have 4 vibrational modes. The modes with a frequency of 640 cm-1 correspond to bends and the modes with frequencies of 1372 cm-1 and 2436 cm-1 correspond to stretches. The two modes with a frequency of 640 cm-1 are degenerate and will only produce one IR band between them. The stretch with a frequency of 1372 will not produce an IR band as the stretch is symmetric and has no overall dipole. The asymmetric stretch at 2436 cm-1 will also produce an IR band to give two IR bands overall.

===Charge analysis===
[[File:Acc2518nitrogen charges.png]]

Both nitrogen atoms have the same electronegativity so the charge is neutral on both atoms.

Acc2518

2019-03-04T14:48:10Z

Acc2518: /* Optimisation data */

== NH3 molecule ==
=== Optimisation data ===
{| class="wikitable"
|+ NH3 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-56.55776873 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00000485 (au)
|-
|'''Point group'''
|C3V
|-
|'''Bond length (N-H)'''
|1.02 (Å)
|-
|'''Bond angle (H-N-H)'''
|106(°)
|}
<pre>
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
</pre>

<jmol><jmolApplet>
<title> NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518 NH3 OPTF POP.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>
[[:File:ACC2518 NH3 OPTF POP.LOG|Optimised NH3 .log file (acc2518)]]

=== Vibrations ===
[[File:Acc2518 vibrations screenshot.jpg|The Gaussview "Display Vibrations" window of the optimised ammonia molecule.|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 1090 || 1694
|-
| '''Symmetry''' || A1 || E
|-
| '''Intensity''' (arbitrary units) || 145 || 14
|-
| '''Image'''|| [[File:acc2518VM1.png|250px]] || [[File:acc2518VM2.png|300px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 1694|| 3461
|-
| '''Symmetry''' || E || A1
|-
| '''Intensity''' (arbitrary units) || 14 || 1
|-
| '''Image'''|| [[File:acc2518VM3.png|250px]] || [[File:acc2518VM4.png|275px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 3590|| 3590
|-
| '''Symmetry''' || E || E
|-
| '''Intensity''' (arbitrary units) || 0 || 0
|-
| '''Image'''|| [[File:acc2518VM5.png|275px]] || [[File:acc2518VM6.png|250px]]
|}

Using the 3N-6 rule, where N represents the number of atoms in a molecule, it is expected that ammonia will have six vibrational modes as shown above. There are two pairs of degenerate modes with a frequency of 1694 (cm-1) and 3590 (cm-1). The modes with a frequency of 1090 (cm-1) and 1694 (cm-1) correspond to bending vibrations and the modes with a frequency 3461 (cm-1) and 3590 (cm-1) correspond to bond stretch vibrations. The bond stretch vibration at 3461 (cm-1) is highly symmetric whilst the stretches with a frequency of 3590 (cm-1) are asymmetric. The bending vibration with a frequency of 1090 (cm-1) is known as the umbrella mode. Three bands would be expected to be seen with the two stretches at 3590 (cm-1) being too low in intensity. The bends with a frequency of 1694 (cm-1) are degenerate and only one band will be observed between the two. Hence the three observed bands would be at 1090 (cm-1), 1694 (cm-1) and 3461 (cm-1).

=== Charge analysis ===
[[File:Acc2518 charge analysis.png|The Gaussview generated atomic charges of ammonia.|250px]]

Nitrogen has a greater electronegativity than hydrogen and hence there is greater electron density distributed around the N atom in ammonia relative to hydrogen. This explains the negative charge on N and the positive charge on H.

==N2 molecule==

===Optimisation data===

{| class="wikitable"
|+ N2 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-109.52412868 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00000060 (au)
|-
|'''Point group'''
|D∞h
|-
|'''Bond length (N-N)'''
|1.11 (Å)
|}

<pre>
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
</pre>

<jmol><jmolApplet>
<title> Nitrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518 N2 OPTIMISATION.LOG</uploadedFileContents>
<script>frame 1.10</script>
</jmolApplet></jmol>
[[:File:ACC2518 N2 OPTIMISATION.LOG|Optimised N2 .log file (acc2518)]]

===Vibrations===
[[File:Acc2518 N2vibration.png|Nitrogen display vibrations screenshot|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 2457
|-
| '''Symmetry''' || SGG
|-
| '''Intensity''' (arbitrary units) || 0
|-
| '''Image'''|| [[File:Acc2518NitrogenVM.png|250px]]
|}
Using the 3N-5 rule for linear molecules, Nitrogen can be expected to have one vibrational mode but this mode has an IR intensity of zero since Nitrogen molecules are IR inactive. This is because they have no overall dipole.

===Charge analysis===
[[File:Acc2518nitrogen charges.png]]

Both nitrogen atoms have the same electronegativity so the charge is neutral on both atoms.

===CCDC search===
'''Unique identifier:''' [https://www.ccdc.cam.ac.uk/structures/Search?Ccdcid=VAMQAE&DatabaseToSearch=Published VAMQAE]

'''Deposition number:''' 1530121

The complex linked above contains nitrogen coordinated to cobalt with a N-N bond distance of 1.08 Å which is slightly shorter than the optimised N-N bond length, displayed above, of 1.11 Å (2.d.p). During the optimisation process for nitrogen, assumptions have to be made for the computational process to be carried out. Each assumption made will increase the uncertainty in measurable quantities such as the bond length. Hence, the computationally determined bond length from the optimisation is a model and may not fully reflect the true bond length or the bond length determined by a computational program considering slightly different assumptions.

It should also be considered that the optimisation gave a prediction for the N-N bond length in a nitrogen molecule whereas the molecule linked above contains a nitrogen molecule that is coordinated into a transition metal complex. A lone pair of electrons on one of the nitrogen atoms has been donated to a cobalt ion, this draws electron density away from the donating nitrogen atom and would therefore slightly increase the positive charge on this atom. This may cause the donating nitrogen atom to attract the electrons in the N-N bond more strongly which would then explain the shorter bond in the transition metal complex compared to the nitrogen molecule.

==H2 molecule==

===Optimisation data===
{| class="wikitable"
|+ H2 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-1.17853936 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00000017 (au)
|-
|'''Point group'''
|D∞h
|-
|'''Bond length (H-H)'''
|0.74 (Å)
|}

<pre>
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

</pre>

<jmol><jmolApplet>
<title> Hydrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518 H2 OPTIMISATION.LOG</uploadedFileContents>
<script>frame 1.7</script>
</jmolApplet></jmol>
[[:File:ACC2518 H2 OPTIMISATION.LOG|Optimised H2 .log file (acc2518)]]

===Vibrations===
[[File:Acc2518 H2vibration.png|Hydrogen display vibrations screenshot|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 4466
|-
| '''Symmetry''' || SGG
|-
| '''Intensity''' (arbitrary units) || 0
|-
| '''Image'''|| [[File:Acc2518HydrogenVM.png|250px]]
|}
Using the 3N-5 rule for linear molecules, hydrogen can be expected to have one vibrational mode but this mode has an IR intensity of zero since hydrogen molecules, like nitrogen molecules, are IR inactive.

===Charge analysis===
[[File:Acc2518hydrogen charges.png]]

Both hydrogen atoms have the same electronegativity so the charge is neutral on both atoms.

==The Haber-Bosch process==
N2 + 3H2 -> 2NH3

E(NH3)=-56.55776873

 '''2*E(NH3)''' =2*(-56.55776873)=-113.11553746

 '''E(N2)''' =-109.52412868

E(H2)=-1.17853936

 '''3*E(H2)''' =3*(-1.17853936) =-3.53561808

'''ΔE= 2*E(NH3) -[ E(N2) + 3*E(H2) ]'''= -0.05579069 ≈ -0.05579 au (5.d.p)

'''ΔE=-146.5 kJ/mol (1.d.p)'''

ΔE is negative which indicates that the gaseous reactants are less stable than the ammonia product since the reactants are at a higher energy than the product. Although this process is not necessarily entropically favourable with four reactant gaseous molecules forming two gaseous product molecules, the reaction has a significantly negative enthalpy change which reflects the result calculated above.

== Project molecule (NF3) ==

=== Optimisation data ===
{| class="wikitable"
|+ NF3 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-354.07131058 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00010256 (au)
|-
|'''Point group'''
|C3V
|-
|'''Bond length (N-F)'''
|1.38 (Å)
|-
|'''Bond angle (F-N-F)'''
|102(°)
|}
<pre>
Item Value Threshold Converged?
Maximum Force 0.000164 0.000450 YES
RMS Force 0.000108 0.000300 YES
Maximum Displacement 0.000612 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

<jmol><jmolApplet>
<title> NF3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518_NF3_OPTF_POP.LOG </uploadedFileContents>
<script>frame 1.7</script>
</jmolApplet></jmol>
[[:File:ACC2518_NF3_OPTF_POP.LOG|Optimised NF3 .log file (acc2518)]]

=== Vibrations ===
[[File:Acc2518 NF3 vibrations screenshot.png|The Gaussview "Display Vibrations" window of the optimised nitrogen trifluoride molecule.|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 482 || 482
|-
| '''Symmetry''' || E || E
|-
| '''Intensity''' (arbitrary units) || 1 || 1
|-
| '''Image'''|| [[File:Acc2518 NF3 VM1.png|300px]] || [[File:Acc2518 NF3 VM2.png|300px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 644|| 930
|-
| '''Symmetry''' || A1 || E
|-
| '''Intensity''' (arbitrary units) || 3 || 208
|-
| '''Image'''|| [[File:Acc2518 NF3 VM3.png|300px]] || [[File:Acc2518 NF3 VM4.png|300px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 930|| 1062
|-
| '''Symmetry''' || E || A1
|-
| '''Intensity''' (arbitrary units) || 208 || 40
|-
| '''Image'''|| [[File:Acc2518 NF3 VM5.png|300px]] || [[File:Acc2518 NF3 VM6.png|300px]]
|}

Nitrogen trifluoride has the same number of atoms as ammonia and so six vibrational modes can be predicted from the 3N-6 rule. There are also two pairs of degenerate modes with frequencies of 482 (cm-1) and 930 (cm-1). The modes with a frequency of 482 (cm-1) and 644(cm-1) correspond to bending vibrational modes and the modes with a frequency of 930 (cm-1) and 1062 (cm-1) correspond to stretching vibrational modes. The mode with a frequency of 1062 (cm-1) represents a symmetric stretch whilst the modes with a frequency of 930 (cm-1) represent asymmetric stretches. In contrast to ammonia, the highest frequency bond stretch of nitrogen trifluoride is the symmetric stretch.

Three bands can be expected in the NF3 IR spectrum at frequencies of 644 (cm-1) 930 (cm-1) and 1062 (cm-1). The bends at 482 (cm-1) will be too low in frequency to appear in the spectrum which starts at a frequency of 500 (cm-1). The stretches at 930 (cm-1) are degenerate and hence will only display one band between them. The band as 644 (cm-1) may not be clearly visible due its relative low intensity of 3 arbitrary units.

=== Charge analysis ===
[[File:Acc2518 NF3 charge analysis.png|The Gaussview generated atomic charges of ammonia.|250px]]

Fluorine has a greater electronegativity that nitrogen and therefore there is greater electron density distributed around the three fluorine atoms compared to the nitrogen atom. The three fluorine atoms are treated as equivalent which means that the magnitude of the positive charge on nitrogen is three times the magnitude of the negative charge on a single fluorine atom.

=== Molecular orbitals (MO) ===

The nitrogen atom contributes 7 electrons and each fluorine atom contributes 9 electrons which means that nitrogen trifluoride contains 34 electrons in total and hence 17 electron pairs. In the table below, a molecular orbital number of 1 would denote the molecular orbital that is deepest in energy. Therefore, orbital 17 represents the HOMO and orbital 18 represents the LUMO. All of the molecular orbitals shown below are occupied with the exception of the LUMO.

{| class="wikitable"
!Molecular orbital number
!Image
!Type of molecular orbital
!Energy (au)
!Extra details
|-
|18
|[[File:Acc2518 MO18.png|200px]]
|Antibonding
|0.01947
|There are nodes in the centre of the N-F bonds which indicates that the LUMO is an antibonding orbital with destructive inteference between phases of opposite sign. The nodes in the centre of all four atoms also indicate that this MO was formed from 2p atomic orbitals from both nitrogen and fluorine.
|-
|17
|[[File:Acc2518 MO17.png|200px]]
|Bonding
| -0.35162
| The phase denoted by the green region shows orbital overlap across all three N-H bonds which implies that the HOMO is a bonding orbital. This MO has been formed from 2p orbitals which explains the nodes observed in the centre of the F atoms.
|-
|16
|[[File:Acc2518 MO16.png|200px]]
|Non-bonding
| -0.42224
|There is no electron density along any of the bonds which is the key indicator that this is a non-bonding MO. Since the electron density is localised around the fluorine atoms, this MO appears to show lone electron pairs on these fluorine atoms. There is no electron density being shared between the fluorine atoms which suggests there is destructive interference preventing such an interaction.
|-
|15
|[[File:Acc2518 MO15.png|200px]]
|Bonding
| -0.43590
| As observed in the HOMO, there is electron density along all three bonds which indicates the bonding nature of the MO. However, in contrast to the HOMO, the electron density along the bonds is not in the same phase for each bond. There is also some constructive interference between two of the F atoms which appears to indicate a very partial π character between the two atoms. This also means that this interaction is the product of two 2p atomic orbitals on fluorine overlapping slightly in phase with each other.
|-
|5
|[[File:Acc2518 MO5.png|200px]]
| Bonding
| -1.35870
| This MO contains no nodes at all implying that it is bonding in nature. It is also formed from overlap of 2s orbitals, in phase, on all atoms since the entire molecule is encased in electron density as a result of the constructive interference. It cannot be formed from 1s orbitals which would be far lower in energy and will also only occupy the first 4 MOs since there are 8 1s electrons in NF3.
|}

== Bonus Molecule (CO2) ==

===Optimisation data===

{| class="wikitable"
|+ CO2 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-188.58093945 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00001154 (au)
|-
|'''Point group'''
|D∞h
|-
|'''Bond length (C-O)'''
|1.17 (Å)
|-
|'''Bond angle (C=O=C)'''
|180 (°)
|-
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000017 0.000300 YES
Maximum Displacement 0.000021 0.001800 YES
RMS Displacement 0.000015 0.001200 YES

</pre>

<jmol><jmolApplet>
<title> Carbon dioxide molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518 CO2 OPTF POP.LOG</uploadedFileContents>
<script>frame 1.10</script>
</jmolApplet></jmol>
[[:File:ACC2518 CO2 OPTF POP.LOG|Optimised CO2 .log file (acc2518)]]

===Vibrations===
[[File:Acc2518 CO2vibration.png|Carbon dioxide display vibrations screenshot|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 640|| 640
|-
| '''Symmetry''' || PIU || PIU
|-
| '''Intensity''' (arbitrary units) || 31 || 31
|-
| '''Image'''|| [[File:Acc2518co2VM1.png|200px]] || [[File:Acc2518co2VM2.png|250px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 1372|| 2436
|-
| '''Symmetry''' || SGG || SGU
|-
| '''Intensity''' (arbitrary units) || 0 || 546
|-
| '''Image'''|| [[File:Acc2518co2VM3.png|350px]] || [[File:Acc2518co2VM4.png|300px]]
|}
Using the 3N-5 rule for linear molecules, carbon dioxide can be expected to have 4 vibrational modes. The modes with a frequency of 640 cm-1 correspond to bends and the modes with frequencies of 1372 cm-1 and 2436 cm-1 correspond to stretches. The two modes with a frequency of 640 cm-1 are degenerate and will only produce one IR band between them. The stretch with a frequency of 1372 will not produce an IR band as the stretch is symmetric and has no overall dipole. The asymmetric stretch at 2436 cm-1 will also produce an IR band to give two IR bands overall.

===Charge analysis===
[[File:Acc2518nitrogen charges.png]]

Both nitrogen atoms have the same electronegativity so the charge is neutral on both atoms.

Acc2518

2019-03-04T14:47:27Z

Acc2518: /* Optimisation data */

== NH3 molecule ==
=== Optimisation data ===
{| class="wikitable"
|+ NH3 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-56.55776873 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00000485 (au)
|-
|'''Point group'''
|C3V
|-
|'''Bond length (N-H)'''
|1.02 (Å)
|-
|'''Bond angle (H-N-H)'''
|106(°)
|}
<pre>
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
</pre>

<jmol><jmolApplet>
<title> NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518 NH3 OPTF POP.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>
[[:File:ACC2518 NH3 OPTF POP.LOG|Optimised NH3 .log file (acc2518)]]

=== Vibrations ===
[[File:Acc2518 vibrations screenshot.jpg|The Gaussview "Display Vibrations" window of the optimised ammonia molecule.|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 1090 || 1694
|-
| '''Symmetry''' || A1 || E
|-
| '''Intensity''' (arbitrary units) || 145 || 14
|-
| '''Image'''|| [[File:acc2518VM1.png|250px]] || [[File:acc2518VM2.png|300px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 1694|| 3461
|-
| '''Symmetry''' || E || A1
|-
| '''Intensity''' (arbitrary units) || 14 || 1
|-
| '''Image'''|| [[File:acc2518VM3.png|250px]] || [[File:acc2518VM4.png|275px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 3590|| 3590
|-
| '''Symmetry''' || E || E
|-
| '''Intensity''' (arbitrary units) || 0 || 0
|-
| '''Image'''|| [[File:acc2518VM5.png|275px]] || [[File:acc2518VM6.png|250px]]
|}

Using the 3N-6 rule, where N represents the number of atoms in a molecule, it is expected that ammonia will have six vibrational modes as shown above. There are two pairs of degenerate modes with a frequency of 1694 (cm-1) and 3590 (cm-1). The modes with a frequency of 1090 (cm-1) and 1694 (cm-1) correspond to bending vibrations and the modes with a frequency 3461 (cm-1) and 3590 (cm-1) correspond to bond stretch vibrations. The bond stretch vibration at 3461 (cm-1) is highly symmetric whilst the stretches with a frequency of 3590 (cm-1) are asymmetric. The bending vibration with a frequency of 1090 (cm-1) is known as the umbrella mode. Three bands would be expected to be seen with the two stretches at 3590 (cm-1) being too low in intensity. The bends with a frequency of 1694 (cm-1) are degenerate and only one band will be observed between the two. Hence the three observed bands would be at 1090 (cm-1), 1694 (cm-1) and 3461 (cm-1).

=== Charge analysis ===
[[File:Acc2518 charge analysis.png|The Gaussview generated atomic charges of ammonia.|250px]]

Nitrogen has a greater electronegativity than hydrogen and hence there is greater electron density distributed around the N atom in ammonia relative to hydrogen. This explains the negative charge on N and the positive charge on H.

==N2 molecule==

===Optimisation data===

{| class="wikitable"
|+ N2 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-109.52412868 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00000060 (au)
|-
|'''Point group'''
|D∞h
|-
|'''Bond length (N-N)'''
|1.11 (Å)
|}

<pre>
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
</pre>

<jmol><jmolApplet>
<title> Nitrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518 N2 OPTIMISATION.LOG</uploadedFileContents>
<script>frame 1.10</script>
</jmolApplet></jmol>
[[:File:ACC2518 N2 OPTIMISATION.LOG|Optimised N2 .log file (acc2518)]]

===Vibrations===
[[File:Acc2518 N2vibration.png|Nitrogen display vibrations screenshot|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 2457
|-
| '''Symmetry''' || SGG
|-
| '''Intensity''' (arbitrary units) || 0
|-
| '''Image'''|| [[File:Acc2518NitrogenVM.png|250px]]
|}
Using the 3N-5 rule for linear molecules, Nitrogen can be expected to have one vibrational mode but this mode has an IR intensity of zero since Nitrogen molecules are IR inactive. This is because they have no overall dipole.

===Charge analysis===
[[File:Acc2518nitrogen charges.png]]

Both nitrogen atoms have the same electronegativity so the charge is neutral on both atoms.

===CCDC search===
'''Unique identifier:''' [https://www.ccdc.cam.ac.uk/structures/Search?Ccdcid=VAMQAE&DatabaseToSearch=Published VAMQAE]

'''Deposition number:''' 1530121

The complex linked above contains nitrogen coordinated to cobalt with a N-N bond distance of 1.08 Å which is slightly shorter than the optimised N-N bond length, displayed above, of 1.11 Å (2.d.p). During the optimisation process for nitrogen, assumptions have to be made for the computational process to be carried out. Each assumption made will increase the uncertainty in measurable quantities such as the bond length. Hence, the computationally determined bond length from the optimisation is a model and may not fully reflect the true bond length or the bond length determined by a computational program considering slightly different assumptions.

It should also be considered that the optimisation gave a prediction for the N-N bond length in a nitrogen molecule whereas the molecule linked above contains a nitrogen molecule that is coordinated into a transition metal complex. A lone pair of electrons on one of the nitrogen atoms has been donated to a cobalt ion, this draws electron density away from the donating nitrogen atom and would therefore slightly increase the positive charge on this atom. This may cause the donating nitrogen atom to attract the electrons in the N-N bond more strongly which would then explain the shorter bond in the transition metal complex compared to the nitrogen molecule.

==H2 molecule==

===Optimisation data===
{| class="wikitable"
|+ H2 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-1.17853936 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00000017 (au)
|-
|'''Point group'''
|D∞h
|-
|'''Bond length (H-H)'''
|0.74 (Å)
|}

<pre>
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

</pre>

<jmol><jmolApplet>
<title> Hydrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518 H2 OPTIMISATION.LOG</uploadedFileContents>
<script>frame 1.7</script>
</jmolApplet></jmol>
[[:File:ACC2518 H2 OPTIMISATION.LOG|Optimised H2 .log file (acc2518)]]

===Vibrations===
[[File:Acc2518 H2vibration.png|Hydrogen display vibrations screenshot|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 4466
|-
| '''Symmetry''' || SGG
|-
| '''Intensity''' (arbitrary units) || 0
|-
| '''Image'''|| [[File:Acc2518HydrogenVM.png|250px]]
|}
Using the 3N-5 rule for linear molecules, hydrogen can be expected to have one vibrational mode but this mode has an IR intensity of zero since hydrogen molecules, like nitrogen molecules, are IR inactive.

===Charge analysis===
[[File:Acc2518hydrogen charges.png]]

Both hydrogen atoms have the same electronegativity so the charge is neutral on both atoms.

==The Haber-Bosch process==
N2 + 3H2 -> 2NH3

E(NH3)=-56.55776873

 '''2*E(NH3)''' =2*(-56.55776873)=-113.11553746

 '''E(N2)''' =-109.52412868

E(H2)=-1.17853936

 '''3*E(H2)''' =3*(-1.17853936) =-3.53561808

'''ΔE= 2*E(NH3) -[ E(N2) + 3*E(H2) ]'''= -0.05579069 ≈ -0.05579 au (5.d.p)

'''ΔE=-146.5 kJ/mol (1.d.p)'''

ΔE is negative which indicates that the gaseous reactants are less stable than the ammonia product since the reactants are at a higher energy than the product. Although this process is not necessarily entropically favourable with four reactant gaseous molecules forming two gaseous product molecules, the reaction has a significantly negative enthalpy change which reflects the result calculated above.

== Project molecule (NF3) ==

=== Optimisation data ===
{| class="wikitable"
|+ NF3 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-354.07131058 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00010256 (au)
|-
|'''Point group'''
|C3V
|-
|'''Bond length (N-F)'''
|1.38 (Å)
|-
|'''Bond angle (F-N-F)'''
|102(°)
|}
<pre>
Item Value Threshold Converged?
Maximum Force 0.000164 0.000450 YES
RMS Force 0.000108 0.000300 YES
Maximum Displacement 0.000612 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

<jmol><jmolApplet>
<title> NF3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518_NF3_OPTF_POP.LOG </uploadedFileContents>
<script>frame 1.7</script>
</jmolApplet></jmol>
[[:File:ACC2518_NF3_OPTF_POP.LOG|Optimised NF3 .log file (acc2518)]]

=== Vibrations ===
[[File:Acc2518 NF3 vibrations screenshot.png|The Gaussview "Display Vibrations" window of the optimised nitrogen trifluoride molecule.|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 482 || 482
|-
| '''Symmetry''' || E || E
|-
| '''Intensity''' (arbitrary units) || 1 || 1
|-
| '''Image'''|| [[File:Acc2518 NF3 VM1.png|300px]] || [[File:Acc2518 NF3 VM2.png|300px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 644|| 930
|-
| '''Symmetry''' || A1 || E
|-
| '''Intensity''' (arbitrary units) || 3 || 208
|-
| '''Image'''|| [[File:Acc2518 NF3 VM3.png|300px]] || [[File:Acc2518 NF3 VM4.png|300px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 930|| 1062
|-
| '''Symmetry''' || E || A1
|-
| '''Intensity''' (arbitrary units) || 208 || 40
|-
| '''Image'''|| [[File:Acc2518 NF3 VM5.png|300px]] || [[File:Acc2518 NF3 VM6.png|300px]]
|}

Nitrogen trifluoride has the same number of atoms as ammonia and so six vibrational modes can be predicted from the 3N-6 rule. There are also two pairs of degenerate modes with frequencies of 482 (cm-1) and 930 (cm-1). The modes with a frequency of 482 (cm-1) and 644(cm-1) correspond to bending vibrational modes and the modes with a frequency of 930 (cm-1) and 1062 (cm-1) correspond to stretching vibrational modes. The mode with a frequency of 1062 (cm-1) represents a symmetric stretch whilst the modes with a frequency of 930 (cm-1) represent asymmetric stretches. In contrast to ammonia, the highest frequency bond stretch of nitrogen trifluoride is the symmetric stretch.

Three bands can be expected in the NF3 IR spectrum at frequencies of 644 (cm-1) 930 (cm-1) and 1062 (cm-1). The bends at 482 (cm-1) will be too low in frequency to appear in the spectrum which starts at a frequency of 500 (cm-1). The stretches at 930 (cm-1) are degenerate and hence will only display one band between them. The band as 644 (cm-1) may not be clearly visible due its relative low intensity of 3 arbitrary units.

=== Charge analysis ===
[[File:Acc2518 NF3 charge analysis.png|The Gaussview generated atomic charges of ammonia.|250px]]

Fluorine has a greater electronegativity that nitrogen and therefore there is greater electron density distributed around the three fluorine atoms compared to the nitrogen atom. The three fluorine atoms are treated as equivalent which means that the magnitude of the positive charge on nitrogen is three times the magnitude of the negative charge on a single fluorine atom.

=== Molecular orbitals (MO) ===

The nitrogen atom contributes 7 electrons and each fluorine atom contributes 9 electrons which means that nitrogen trifluoride contains 34 electrons in total and hence 17 electron pairs. In the table below, a molecular orbital number of 1 would denote the molecular orbital that is deepest in energy. Therefore, orbital 17 represents the HOMO and orbital 18 represents the LUMO. All of the molecular orbitals shown below are occupied with the exception of the LUMO.

{| class="wikitable"
!Molecular orbital number
!Image
!Type of molecular orbital
!Energy (au)
!Extra details
|-
|18
|[[File:Acc2518 MO18.png|200px]]
|Antibonding
|0.01947
|There are nodes in the centre of the N-F bonds which indicates that the LUMO is an antibonding orbital with destructive inteference between phases of opposite sign. The nodes in the centre of all four atoms also indicate that this MO was formed from 2p atomic orbitals from both nitrogen and fluorine.
|-
|17
|[[File:Acc2518 MO17.png|200px]]
|Bonding
| -0.35162
| The phase denoted by the green region shows orbital overlap across all three N-H bonds which implies that the HOMO is a bonding orbital. This MO has been formed from 2p orbitals which explains the nodes observed in the centre of the F atoms.
|-
|16
|[[File:Acc2518 MO16.png|200px]]
|Non-bonding
| -0.42224
|There is no electron density along any of the bonds which is the key indicator that this is a non-bonding MO. Since the electron density is localised around the fluorine atoms, this MO appears to show lone electron pairs on these fluorine atoms. There is no electron density being shared between the fluorine atoms which suggests there is destructive interference preventing such an interaction.
|-
|15
|[[File:Acc2518 MO15.png|200px]]
|Bonding
| -0.43590
| As observed in the HOMO, there is electron density along all three bonds which indicates the bonding nature of the MO. However, in contrast to the HOMO, the electron density along the bonds is not in the same phase for each bond. There is also some constructive interference between two of the F atoms which appears to indicate a very partial π character between the two atoms. This also means that this interaction is the product of two 2p atomic orbitals on fluorine overlapping slightly in phase with each other.
|-
|5
|[[File:Acc2518 MO5.png|200px]]
| Bonding
| -1.35870
| This MO contains no nodes at all implying that it is bonding in nature. It is also formed from overlap of 2s orbitals, in phase, on all atoms since the entire molecule is encased in electron density as a result of the constructive interference. It cannot be formed from 1s orbitals which would be far lower in energy and will also only occupy the first 4 MOs since there are 8 1s electrons in NF3.
|}

== Bonus Molecule (CO2) ==

===Optimisation data===

{| class="wikitable"
|+ CO2 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-188.58093945 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00001154 (au)
|-
|'''Point group'''
|D∞h
|-
|'''Bond length (C-O)'''
|1.17 (Å)
|-
|'''Bond angle'''
|180 (°)
|-
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000017 0.000300 YES
Maximum Displacement 0.000021 0.001800 YES
RMS Displacement 0.000015 0.001200 YES

</pre>

<jmol><jmolApplet>
<title> Carbon dioxide molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518 CO2 OPTF POP.LOG</uploadedFileContents>
<script>frame 1.10</script>
</jmolApplet></jmol>
[[:File:ACC2518 CO2 OPTF POP.LOG|Optimised CO2 .log file (acc2518)]]

===Vibrations===
[[File:Acc2518 CO2vibration.png|Carbon dioxide display vibrations screenshot|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 640|| 640
|-
| '''Symmetry''' || PIU || PIU
|-
| '''Intensity''' (arbitrary units) || 31 || 31
|-
| '''Image'''|| [[File:Acc2518co2VM1.png|200px]] || [[File:Acc2518co2VM2.png|250px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 1372|| 2436
|-
| '''Symmetry''' || SGG || SGU
|-
| '''Intensity''' (arbitrary units) || 0 || 546
|-
| '''Image'''|| [[File:Acc2518co2VM3.png|350px]] || [[File:Acc2518co2VM4.png|300px]]
|}
Using the 3N-5 rule for linear molecules, carbon dioxide can be expected to have 4 vibrational modes. The modes with a frequency of 640 cm-1 correspond to bends and the modes with frequencies of 1372 cm-1 and 2436 cm-1 correspond to stretches. The two modes with a frequency of 640 cm-1 are degenerate and will only produce one IR band between them. The stretch with a frequency of 1372 will not produce an IR band as the stretch is symmetric and has no overall dipole. The asymmetric stretch at 2436 cm-1 will also produce an IR band to give two IR bands overall.

===Charge analysis===
[[File:Acc2518nitrogen charges.png]]

Both nitrogen atoms have the same electronegativity so the charge is neutral on both atoms.

Acc2518

2019-03-04T14:47:00Z

Acc2518: /* Vibrations */

== NH3 molecule ==
=== Optimisation data ===
{| class="wikitable"
|+ NH3 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-56.55776873 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00000485 (au)
|-
|'''Point group'''
|C3V
|-
|'''Bond length (N-H)'''
|1.02 (Å)
|-
|'''Bond angle (H-N-H)'''
|106(°)
|}
<pre>
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
</pre>

<jmol><jmolApplet>
<title> NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518 NH3 OPTF POP.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>
[[:File:ACC2518 NH3 OPTF POP.LOG|Optimised NH3 .log file (acc2518)]]

=== Vibrations ===
[[File:Acc2518 vibrations screenshot.jpg|The Gaussview "Display Vibrations" window of the optimised ammonia molecule.|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 1090 || 1694
|-
| '''Symmetry''' || A1 || E
|-
| '''Intensity''' (arbitrary units) || 145 || 14
|-
| '''Image'''|| [[File:acc2518VM1.png|250px]] || [[File:acc2518VM2.png|300px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 1694|| 3461
|-
| '''Symmetry''' || E || A1
|-
| '''Intensity''' (arbitrary units) || 14 || 1
|-
| '''Image'''|| [[File:acc2518VM3.png|250px]] || [[File:acc2518VM4.png|275px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 3590|| 3590
|-
| '''Symmetry''' || E || E
|-
| '''Intensity''' (arbitrary units) || 0 || 0
|-
| '''Image'''|| [[File:acc2518VM5.png|275px]] || [[File:acc2518VM6.png|250px]]
|}

Using the 3N-6 rule, where N represents the number of atoms in a molecule, it is expected that ammonia will have six vibrational modes as shown above. There are two pairs of degenerate modes with a frequency of 1694 (cm-1) and 3590 (cm-1). The modes with a frequency of 1090 (cm-1) and 1694 (cm-1) correspond to bending vibrations and the modes with a frequency 3461 (cm-1) and 3590 (cm-1) correspond to bond stretch vibrations. The bond stretch vibration at 3461 (cm-1) is highly symmetric whilst the stretches with a frequency of 3590 (cm-1) are asymmetric. The bending vibration with a frequency of 1090 (cm-1) is known as the umbrella mode. Three bands would be expected to be seen with the two stretches at 3590 (cm-1) being too low in intensity. The bends with a frequency of 1694 (cm-1) are degenerate and only one band will be observed between the two. Hence the three observed bands would be at 1090 (cm-1), 1694 (cm-1) and 3461 (cm-1).

=== Charge analysis ===
[[File:Acc2518 charge analysis.png|The Gaussview generated atomic charges of ammonia.|250px]]

Nitrogen has a greater electronegativity than hydrogen and hence there is greater electron density distributed around the N atom in ammonia relative to hydrogen. This explains the negative charge on N and the positive charge on H.

==N2 molecule==

===Optimisation data===

{| class="wikitable"
|+ N2 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-109.52412868 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00000060 (au)
|-
|'''Point group'''
|D∞h
|-
|'''Bond length (N-N)'''
|1.11 (Å)
|}

<pre>
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
</pre>

<jmol><jmolApplet>
<title> Nitrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518 N2 OPTIMISATION.LOG</uploadedFileContents>
<script>frame 1.10</script>
</jmolApplet></jmol>
[[:File:ACC2518 N2 OPTIMISATION.LOG|Optimised N2 .log file (acc2518)]]

===Vibrations===
[[File:Acc2518 N2vibration.png|Nitrogen display vibrations screenshot|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 2457
|-
| '''Symmetry''' || SGG
|-
| '''Intensity''' (arbitrary units) || 0
|-
| '''Image'''|| [[File:Acc2518NitrogenVM.png|250px]]
|}
Using the 3N-5 rule for linear molecules, Nitrogen can be expected to have one vibrational mode but this mode has an IR intensity of zero since Nitrogen molecules are IR inactive. This is because they have no overall dipole.

===Charge analysis===
[[File:Acc2518nitrogen charges.png]]

Both nitrogen atoms have the same electronegativity so the charge is neutral on both atoms.

===CCDC search===
'''Unique identifier:''' [https://www.ccdc.cam.ac.uk/structures/Search?Ccdcid=VAMQAE&DatabaseToSearch=Published VAMQAE]

'''Deposition number:''' 1530121

The complex linked above contains nitrogen coordinated to cobalt with a N-N bond distance of 1.08 Å which is slightly shorter than the optimised N-N bond length, displayed above, of 1.11 Å (2.d.p). During the optimisation process for nitrogen, assumptions have to be made for the computational process to be carried out. Each assumption made will increase the uncertainty in measurable quantities such as the bond length. Hence, the computationally determined bond length from the optimisation is a model and may not fully reflect the true bond length or the bond length determined by a computational program considering slightly different assumptions.

It should also be considered that the optimisation gave a prediction for the N-N bond length in a nitrogen molecule whereas the molecule linked above contains a nitrogen molecule that is coordinated into a transition metal complex. A lone pair of electrons on one of the nitrogen atoms has been donated to a cobalt ion, this draws electron density away from the donating nitrogen atom and would therefore slightly increase the positive charge on this atom. This may cause the donating nitrogen atom to attract the electrons in the N-N bond more strongly which would then explain the shorter bond in the transition metal complex compared to the nitrogen molecule.

==H2 molecule==

===Optimisation data===
{| class="wikitable"
|+ H2 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-1.17853936 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00000017 (au)
|-
|'''Point group'''
|D∞h
|-
|'''Bond length (N-N)'''
|0.74 (Å)
|}

<pre>
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

</pre>

<jmol><jmolApplet>
<title> Hydrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518 H2 OPTIMISATION.LOG</uploadedFileContents>
<script>frame 1.7</script>
</jmolApplet></jmol>
[[:File:ACC2518 H2 OPTIMISATION.LOG|Optimised H2 .log file (acc2518)]]

===Vibrations===
[[File:Acc2518 H2vibration.png|Hydrogen display vibrations screenshot|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 4466
|-
| '''Symmetry''' || SGG
|-
| '''Intensity''' (arbitrary units) || 0
|-
| '''Image'''|| [[File:Acc2518HydrogenVM.png|250px]]
|}
Using the 3N-5 rule for linear molecules, hydrogen can be expected to have one vibrational mode but this mode has an IR intensity of zero since hydrogen molecules, like nitrogen molecules, are IR inactive.

===Charge analysis===
[[File:Acc2518hydrogen charges.png]]

Both hydrogen atoms have the same electronegativity so the charge is neutral on both atoms.

==The Haber-Bosch process==
N2 + 3H2 -> 2NH3

E(NH3)=-56.55776873

 '''2*E(NH3)''' =2*(-56.55776873)=-113.11553746

 '''E(N2)''' =-109.52412868

E(H2)=-1.17853936

 '''3*E(H2)''' =3*(-1.17853936) =-3.53561808

'''ΔE= 2*E(NH3) -[ E(N2) + 3*E(H2) ]'''= -0.05579069 ≈ -0.05579 au (5.d.p)

'''ΔE=-146.5 kJ/mol (1.d.p)'''

ΔE is negative which indicates that the gaseous reactants are less stable than the ammonia product since the reactants are at a higher energy than the product. Although this process is not necessarily entropically favourable with four reactant gaseous molecules forming two gaseous product molecules, the reaction has a significantly negative enthalpy change which reflects the result calculated above.

== Project molecule (NF3) ==

=== Optimisation data ===
{| class="wikitable"
|+ NF3 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-354.07131058 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00010256 (au)
|-
|'''Point group'''
|C3V
|-
|'''Bond length (N-F)'''
|1.38 (Å)
|-
|'''Bond angle (F-N-F)'''
|102(°)
|}
<pre>
Item Value Threshold Converged?
Maximum Force 0.000164 0.000450 YES
RMS Force 0.000108 0.000300 YES
Maximum Displacement 0.000612 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

<jmol><jmolApplet>
<title> NF3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518_NF3_OPTF_POP.LOG </uploadedFileContents>
<script>frame 1.7</script>
</jmolApplet></jmol>
[[:File:ACC2518_NF3_OPTF_POP.LOG|Optimised NF3 .log file (acc2518)]]

=== Vibrations ===
[[File:Acc2518 NF3 vibrations screenshot.png|The Gaussview "Display Vibrations" window of the optimised nitrogen trifluoride molecule.|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 482 || 482
|-
| '''Symmetry''' || E || E
|-
| '''Intensity''' (arbitrary units) || 1 || 1
|-
| '''Image'''|| [[File:Acc2518 NF3 VM1.png|300px]] || [[File:Acc2518 NF3 VM2.png|300px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 644|| 930
|-
| '''Symmetry''' || A1 || E
|-
| '''Intensity''' (arbitrary units) || 3 || 208
|-
| '''Image'''|| [[File:Acc2518 NF3 VM3.png|300px]] || [[File:Acc2518 NF3 VM4.png|300px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 930|| 1062
|-
| '''Symmetry''' || E || A1
|-
| '''Intensity''' (arbitrary units) || 208 || 40
|-
| '''Image'''|| [[File:Acc2518 NF3 VM5.png|300px]] || [[File:Acc2518 NF3 VM6.png|300px]]
|}

Nitrogen trifluoride has the same number of atoms as ammonia and so six vibrational modes can be predicted from the 3N-6 rule. There are also two pairs of degenerate modes with frequencies of 482 (cm-1) and 930 (cm-1). The modes with a frequency of 482 (cm-1) and 644(cm-1) correspond to bending vibrational modes and the modes with a frequency of 930 (cm-1) and 1062 (cm-1) correspond to stretching vibrational modes. The mode with a frequency of 1062 (cm-1) represents a symmetric stretch whilst the modes with a frequency of 930 (cm-1) represent asymmetric stretches. In contrast to ammonia, the highest frequency bond stretch of nitrogen trifluoride is the symmetric stretch.

Three bands can be expected in the NF3 IR spectrum at frequencies of 644 (cm-1) 930 (cm-1) and 1062 (cm-1). The bends at 482 (cm-1) will be too low in frequency to appear in the spectrum which starts at a frequency of 500 (cm-1). The stretches at 930 (cm-1) are degenerate and hence will only display one band between them. The band as 644 (cm-1) may not be clearly visible due its relative low intensity of 3 arbitrary units.

=== Charge analysis ===
[[File:Acc2518 NF3 charge analysis.png|The Gaussview generated atomic charges of ammonia.|250px]]

Fluorine has a greater electronegativity that nitrogen and therefore there is greater electron density distributed around the three fluorine atoms compared to the nitrogen atom. The three fluorine atoms are treated as equivalent which means that the magnitude of the positive charge on nitrogen is three times the magnitude of the negative charge on a single fluorine atom.

=== Molecular orbitals (MO) ===

The nitrogen atom contributes 7 electrons and each fluorine atom contributes 9 electrons which means that nitrogen trifluoride contains 34 electrons in total and hence 17 electron pairs. In the table below, a molecular orbital number of 1 would denote the molecular orbital that is deepest in energy. Therefore, orbital 17 represents the HOMO and orbital 18 represents the LUMO. All of the molecular orbitals shown below are occupied with the exception of the LUMO.

{| class="wikitable"
!Molecular orbital number
!Image
!Type of molecular orbital
!Energy (au)
!Extra details
|-
|18
|[[File:Acc2518 MO18.png|200px]]
|Antibonding
|0.01947
|There are nodes in the centre of the N-F bonds which indicates that the LUMO is an antibonding orbital with destructive inteference between phases of opposite sign. The nodes in the centre of all four atoms also indicate that this MO was formed from 2p atomic orbitals from both nitrogen and fluorine.
|-
|17
|[[File:Acc2518 MO17.png|200px]]
|Bonding
| -0.35162
| The phase denoted by the green region shows orbital overlap across all three N-H bonds which implies that the HOMO is a bonding orbital. This MO has been formed from 2p orbitals which explains the nodes observed in the centre of the F atoms.
|-
|16
|[[File:Acc2518 MO16.png|200px]]
|Non-bonding
| -0.42224
|There is no electron density along any of the bonds which is the key indicator that this is a non-bonding MO. Since the electron density is localised around the fluorine atoms, this MO appears to show lone electron pairs on these fluorine atoms. There is no electron density being shared between the fluorine atoms which suggests there is destructive interference preventing such an interaction.
|-
|15
|[[File:Acc2518 MO15.png|200px]]
|Bonding
| -0.43590
| As observed in the HOMO, there is electron density along all three bonds which indicates the bonding nature of the MO. However, in contrast to the HOMO, the electron density along the bonds is not in the same phase for each bond. There is also some constructive interference between two of the F atoms which appears to indicate a very partial π character between the two atoms. This also means that this interaction is the product of two 2p atomic orbitals on fluorine overlapping slightly in phase with each other.
|-
|5
|[[File:Acc2518 MO5.png|200px]]
| Bonding
| -1.35870
| This MO contains no nodes at all implying that it is bonding in nature. It is also formed from overlap of 2s orbitals, in phase, on all atoms since the entire molecule is encased in electron density as a result of the constructive interference. It cannot be formed from 1s orbitals which would be far lower in energy and will also only occupy the first 4 MOs since there are 8 1s electrons in NF3.
|}

== Bonus Molecule (CO2) ==

===Optimisation data===

{| class="wikitable"
|+ CO2 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-188.58093945 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00001154 (au)
|-
|'''Point group'''
|D∞h
|-
|'''Bond length (C-O)'''
|1.17 (Å)
|-
|'''Bond angle'''
|180 (°)
|-
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000017 0.000300 YES
Maximum Displacement 0.000021 0.001800 YES
RMS Displacement 0.000015 0.001200 YES

</pre>

<jmol><jmolApplet>
<title> Carbon dioxide molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518 CO2 OPTF POP.LOG</uploadedFileContents>
<script>frame 1.10</script>
</jmolApplet></jmol>
[[:File:ACC2518 CO2 OPTF POP.LOG|Optimised CO2 .log file (acc2518)]]

===Vibrations===
[[File:Acc2518 CO2vibration.png|Carbon dioxide display vibrations screenshot|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 640|| 640
|-
| '''Symmetry''' || PIU || PIU
|-
| '''Intensity''' (arbitrary units) || 31 || 31
|-
| '''Image'''|| [[File:Acc2518co2VM1.png|200px]] || [[File:Acc2518co2VM2.png|250px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 1372|| 2436
|-
| '''Symmetry''' || SGG || SGU
|-
| '''Intensity''' (arbitrary units) || 0 || 546
|-
| '''Image'''|| [[File:Acc2518co2VM3.png|350px]] || [[File:Acc2518co2VM4.png|300px]]
|}
Using the 3N-5 rule for linear molecules, carbon dioxide can be expected to have 4 vibrational modes. The modes with a frequency of 640 cm-1 correspond to bends and the modes with frequencies of 1372 cm-1 and 2436 cm-1 correspond to stretches. The two modes with a frequency of 640 cm-1 are degenerate and will only produce one IR band between them. The stretch with a frequency of 1372 will not produce an IR band as the stretch is symmetric and has no overall dipole. The asymmetric stretch at 2436 cm-1 will also produce an IR band to give two IR bands overall.

===Charge analysis===
[[File:Acc2518nitrogen charges.png]]

Both nitrogen atoms have the same electronegativity so the charge is neutral on both atoms.

Acc2518

2019-03-04T14:41:54Z

Acc2518: /* Vibrations */

== NH3 molecule ==
=== Optimisation data ===
{| class="wikitable"
|+ NH3 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-56.55776873 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00000485 (au)
|-
|'''Point group'''
|C3V
|-
|'''Bond length (N-H)'''
|1.02 (Å)
|-
|'''Bond angle (H-N-H)'''
|106(°)
|}
<pre>
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
</pre>

<jmol><jmolApplet>
<title> NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518 NH3 OPTF POP.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>
[[:File:ACC2518 NH3 OPTF POP.LOG|Optimised NH3 .log file (acc2518)]]

=== Vibrations ===
[[File:Acc2518 vibrations screenshot.jpg|The Gaussview "Display Vibrations" window of the optimised ammonia molecule.|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 1090 || 1694
|-
| '''Symmetry''' || A1 || E
|-
| '''Intensity''' (arbitrary units) || 145 || 14
|-
| '''Image'''|| [[File:acc2518VM1.png|250px]] || [[File:acc2518VM2.png|300px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 1694|| 3461
|-
| '''Symmetry''' || E || A1
|-
| '''Intensity''' (arbitrary units) || 14 || 1
|-
| '''Image'''|| [[File:acc2518VM3.png|250px]] || [[File:acc2518VM4.png|275px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 3590|| 3590
|-
| '''Symmetry''' || E || E
|-
| '''Intensity''' (arbitrary units) || 0 || 0
|-
| '''Image'''|| [[File:acc2518VM5.png|275px]] || [[File:acc2518VM6.png|250px]]
|}

Using the 3N-6 rule, where N represents the number of atoms in a molecule, it is expected that ammonia will have six vibrational modes as shown above. There are two pairs of degenerate modes with a frequency of 1694 (cm-1) and 3590 (cm-1). The modes with a frequency of 1090 (cm-1) and 1694 (cm-1) correspond to bending vibrations and the modes with a frequency 3461 (cm-1) and 3590 (cm-1) correspond to bond stretch vibrations. The bond stretch vibration at 3461 (cm-1) is highly symmetric whilst the stretches with a frequency of 3590 (cm-1) are asymmetric. The bending vibration with a frequency of 1090 (cm-1) is known as the umbrella mode. Three bands would be expected to be seen with the two stretches at 3590 (cm-1) being too low in intensity. The bends with a frequency of 1694 (cm-1) are degenerate and only one band will be observed between the two. Hence the three observed bands would be at 1090 (cm-1), 1694 (cm-1) and 3461 (cm-1).

=== Charge analysis ===
[[File:Acc2518 charge analysis.png|The Gaussview generated atomic charges of ammonia.|250px]]

Nitrogen has a greater electronegativity than hydrogen and hence there is greater electron density distributed around the N atom in ammonia relative to hydrogen. This explains the negative charge on N and the positive charge on H.

==N2 molecule==

===Optimisation data===

{| class="wikitable"
|+ N2 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-109.52412868 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00000060 (au)
|-
|'''Point group'''
|D∞h
|-
|'''Bond length (N-N)'''
|1.11 (Å)
|}

<pre>
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
</pre>

<jmol><jmolApplet>
<title> Nitrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518 N2 OPTIMISATION.LOG</uploadedFileContents>
<script>frame 1.10</script>
</jmolApplet></jmol>
[[:File:ACC2518 N2 OPTIMISATION.LOG|Optimised N2 .log file (acc2518)]]

===Vibrations===
[[File:Acc2518 N2vibration.png|Nitrogen display vibrations screenshot|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 2457
|-
| '''Symmetry''' || SGG
|-
| '''Intensity''' (arbitrary units) || 0
|-
| '''Image'''|| [[File:Acc2518NitrogenVM.png|250px]]
|}
Using the 3N-5 rule for linear molecules, Nitrogen can be expected to have one vibrational mode but this mode has an IR intensity of zero since Nitrogen molecules are IR inactive. This is because they have no overall dipole.

===Charge analysis===
[[File:Acc2518nitrogen charges.png]]

Both nitrogen atoms have the same electronegativity so the charge is neutral on both atoms.

===CCDC search===
'''Unique identifier:''' [https://www.ccdc.cam.ac.uk/structures/Search?Ccdcid=VAMQAE&DatabaseToSearch=Published VAMQAE]

'''Deposition number:''' 1530121

The complex linked above contains nitrogen coordinated to cobalt with a N-N bond distance of 1.08 Å which is slightly shorter than the optimised N-N bond length, displayed above, of 1.11 Å (2.d.p). During the optimisation process for nitrogen, assumptions have to be made for the computational process to be carried out. Each assumption made will increase the uncertainty in measurable quantities such as the bond length. Hence, the computationally determined bond length from the optimisation is a model and may not fully reflect the true bond length or the bond length determined by a computational program considering slightly different assumptions.

It should also be considered that the optimisation gave a prediction for the N-N bond length in a nitrogen molecule whereas the molecule linked above contains a nitrogen molecule that is coordinated into a transition metal complex. A lone pair of electrons on one of the nitrogen atoms has been donated to a cobalt ion, this draws electron density away from the donating nitrogen atom and would therefore slightly increase the positive charge on this atom. This may cause the donating nitrogen atom to attract the electrons in the N-N bond more strongly which would then explain the shorter bond in the transition metal complex compared to the nitrogen molecule.

==H2 molecule==

===Optimisation data===
{| class="wikitable"
|+ H2 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-1.17853936 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00000017 (au)
|-
|'''Point group'''
|D∞h
|-
|'''Bond length (N-N)'''
|0.74 (Å)
|}

<pre>
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

</pre>

<jmol><jmolApplet>
<title> Hydrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518 H2 OPTIMISATION.LOG</uploadedFileContents>
<script>frame 1.7</script>
</jmolApplet></jmol>
[[:File:ACC2518 H2 OPTIMISATION.LOG|Optimised H2 .log file (acc2518)]]

===Vibrations===
[[File:Acc2518 H2vibration.png|Hydrogen display vibrations screenshot|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 4466
|-
| '''Symmetry''' || SGG
|-
| '''Intensity''' (arbitrary units) || 0
|-
| '''Image'''|| [[File:Acc2518HydrogenVM.png|250px]]
|}
Using the 3N-5 rule for linear molecules, hydrogen can be expected to have one vibrational mode but this mode has an IR intensity of zero since hydrogen molecules, like nitrogen molecules, are IR inactive.

===Charge analysis===
[[File:Acc2518hydrogen charges.png]]

Both hydrogen atoms have the same electronegativity so the charge is neutral on both atoms.

==The Haber-Bosch process==
N2 + 3H2 -> 2NH3

E(NH3)=-56.55776873

 '''2*E(NH3)''' =2*(-56.55776873)=-113.11553746

 '''E(N2)''' =-109.52412868

E(H2)=-1.17853936

 '''3*E(H2)''' =3*(-1.17853936) =-3.53561808

'''ΔE= 2*E(NH3) -[ E(N2) + 3*E(H2) ]'''= -0.05579069 ≈ -0.05579 au (5.d.p)

'''ΔE=-146.5 kJ/mol (1.d.p)'''

ΔE is negative which indicates that the gaseous reactants are less stable than the ammonia product since the reactants are at a higher energy than the product. Although this process is not necessarily entropically favourable with four reactant gaseous molecules forming two gaseous product molecules, the reaction has a significantly negative enthalpy change which reflects the result calculated above.

== Project molecule (NF3) ==

=== Optimisation data ===
{| class="wikitable"
|+ NF3 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-354.07131058 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00010256 (au)
|-
|'''Point group'''
|C3V
|-
|'''Bond length (N-F)'''
|1.38 (Å)
|-
|'''Bond angle (F-N-F)'''
|102(°)
|}
<pre>
Item Value Threshold Converged?
Maximum Force 0.000164 0.000450 YES
RMS Force 0.000108 0.000300 YES
Maximum Displacement 0.000612 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

<jmol><jmolApplet>
<title> NF3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518_NF3_OPTF_POP.LOG </uploadedFileContents>
<script>frame 1.7</script>
</jmolApplet></jmol>
[[:File:ACC2518_NF3_OPTF_POP.LOG|Optimised NF3 .log file (acc2518)]]

=== Vibrations ===
[[File:Acc2518 NF3 vibrations screenshot.png|The Gaussview "Display Vibrations" window of the optimised nitrogen trifluoride molecule.|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 482 || 482
|-
| '''Symmetry''' || E || E
|-
| '''Intensity''' (arbitrary units) || 1 || 1
|-
| '''Image'''|| [[File:Acc2518 NF3 VM1.png|300px]] || [[File:Acc2518 NF3 VM2.png|300px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 644|| 930
|-
| '''Symmetry''' || A1 || E
|-
| '''Intensity''' (arbitrary units) || 3 || 208
|-
| '''Image'''|| [[File:Acc2518 NF3 VM3.png|300px]] || [[File:Acc2518 NF3 VM4.png|300px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 930|| 1062
|-
| '''Symmetry''' || E || A1
|-
| '''Intensity''' (arbitrary units) || 208 || 40
|-
| '''Image'''|| [[File:Acc2518 NF3 VM5.png|300px]] || [[File:Acc2518 NF3 VM6.png|300px]]
|}

Nitrogen trifluoride has the same number of atoms as ammonia and so six vibrational modes can be predicted from the 3N-6 rule. There are also two pairs of degenerate modes with frequencies of 482 (cm-1) and 930 (cm-1). The modes with a frequency of 482 (cm-1) and 644(cm-1) correspond to bending vibrational modes and the modes with a frequency of 930 (cm-1) and 1062 (cm-1) correspond to stretching vibrational modes. The mode with a frequency of 1062 (cm-1) represents a symmetric stretch whilst the modes with a frequency of 930 (cm-1) represent asymmetric stretches. In contrast to ammonia, the highest frequency bond stretch of nitrogen trifluoride is the symmetric stretch.

Three bands can be expected in the NF3 IR spectrum at frequencies of 644 (cm-1) 930 (cm-1) and 1062 (cm-1). The bends at 482 (cm-1) will be too low in frequency to appear in the spectrum which starts at a frequency of 500 (cm-1). The stretches at 930 (cm-1) are degenerate and hence will only display one band between them. The band as 644 (cm-1) may not be clearly visible due its relative low intensity of 3 arbitrary units.

=== Charge analysis ===
[[File:Acc2518 NF3 charge analysis.png|The Gaussview generated atomic charges of ammonia.|250px]]

Fluorine has a greater electronegativity that nitrogen and therefore there is greater electron density distributed around the three fluorine atoms compared to the nitrogen atom. The three fluorine atoms are treated as equivalent which means that the magnitude of the positive charge on nitrogen is three times the magnitude of the negative charge on a single fluorine atom.

=== Molecular orbitals (MO) ===

The nitrogen atom contributes 7 electrons and each fluorine atom contributes 9 electrons which means that nitrogen trifluoride contains 34 electrons in total and hence 17 electron pairs. In the table below, a molecular orbital number of 1 would denote the molecular orbital that is deepest in energy. Therefore, orbital 17 represents the HOMO and orbital 18 represents the LUMO. All of the molecular orbitals shown below are occupied with the exception of the LUMO.

{| class="wikitable"
!Molecular orbital number
!Image
!Type of molecular orbital
!Energy (au)
!Extra details
|-
|18
|[[File:Acc2518 MO18.png|200px]]
|Antibonding
|0.01947
|There are nodes in the centre of the N-F bonds which indicates that the LUMO is an antibonding orbital with destructive inteference between phases of opposite sign. The nodes in the centre of all four atoms also indicate that this MO was formed from 2p atomic orbitals from both nitrogen and fluorine.
|-
|17
|[[File:Acc2518 MO17.png|200px]]
|Bonding
| -0.35162
| The phase denoted by the green region shows orbital overlap across all three N-H bonds which implies that the HOMO is a bonding orbital. This MO has been formed from 2p orbitals which explains the nodes observed in the centre of the F atoms.
|-
|16
|[[File:Acc2518 MO16.png|200px]]
|Non-bonding
| -0.42224
|There is no electron density along any of the bonds which is the key indicator that this is a non-bonding MO. Since the electron density is localised around the fluorine atoms, this MO appears to show lone electron pairs on these fluorine atoms. There is no electron density being shared between the fluorine atoms which suggests there is destructive interference preventing such an interaction.
|-
|15
|[[File:Acc2518 MO15.png|200px]]
|Bonding
| -0.43590
| As observed in the HOMO, there is electron density along all three bonds which indicates the bonding nature of the MO. However, in contrast to the HOMO, the electron density along the bonds is not in the same phase for each bond. There is also some constructive interference between two of the F atoms which appears to indicate a very partial π character between the two atoms. This also means that this interaction is the product of two 2p atomic orbitals on fluorine overlapping slightly in phase with each other.
|-
|5
|[[File:Acc2518 MO5.png|200px]]
| Bonding
| -1.35870
| This MO contains no nodes at all implying that it is bonding in nature. It is also formed from overlap of 2s orbitals, in phase, on all atoms since the entire molecule is encased in electron density as a result of the constructive interference. It cannot be formed from 1s orbitals which would be far lower in energy and will also only occupy the first 4 MOs since there are 8 1s electrons in NF3.
|}

== Bonus Molecule (CO2) ==

===Optimisation data===

{| class="wikitable"
|+ CO2 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-188.58093945 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00001154 (au)
|-
|'''Point group'''
|D∞h
|-
|'''Bond length (C-O)'''
|1.17 (Å)
|-
|'''Bond angle'''
|180 (°)
|-
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000017 0.000300 YES
Maximum Displacement 0.000021 0.001800 YES
RMS Displacement 0.000015 0.001200 YES

</pre>

<jmol><jmolApplet>
<title> Carbon dioxide molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518 CO2 OPTF POP.LOG</uploadedFileContents>
<script>frame 1.10</script>
</jmolApplet></jmol>
[[:File:ACC2518 CO2 OPTF POP.LOG|Optimised CO2 .log file (acc2518)]]

===Vibrations===
[[File:Acc2518 CO2vibration.png|Carbon dioxide display vibrations screenshot|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 640|| 640
|-
| '''Symmetry''' || PIU || PIU
|-
| '''Intensity''' (arbitrary units) || 31 || 31
|-
| '''Image'''|| [[File:Acc2518co2VM1.png|200px]] || [[File:Acc2518co2VM2.png|250px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 1372|| 2436
|-
| '''Symmetry''' || SGG || SGU
|-
| '''Intensity''' (arbitrary units) || 0 || 546
|-
| '''Image'''|| [[File:Acc2518co2VM3.png|350px]] || [[File:Acc2518co2VM4.png|300px]]
|}
Using the 3N-5 rule for linear molecules, Nitrogen can be expected to have one vibrational mode but this mode has an IR intensity of zero since Nitrogen molecules are IR inactive. This is because they have no overall dipole.

===Charge analysis===
[[File:Acc2518nitrogen charges.png]]

Both nitrogen atoms have the same electronegativity so the charge is neutral on both atoms.

File:Acc2518co2VM1.png

2019-03-04T14:40:26Z

Acc2518:

File:Acc2518co2VM2.png

2019-03-04T14:40:19Z

Acc2518:

File:Acc2518co2VM3.png

2019-03-04T14:40:11Z

Acc2518:

File:Acc2518co2VM4.png

2019-03-04T14:40:03Z

Acc2518:

Acc2518

2019-03-04T14:33:33Z

Acc2518: /* Vibrations */

== NH3 molecule ==
=== Optimisation data ===
{| class="wikitable"
|+ NH3 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-56.55776873 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00000485 (au)
|-
|'''Point group'''
|C3V
|-
|'''Bond length (N-H)'''
|1.02 (Å)
|-
|'''Bond angle (H-N-H)'''
|106(°)
|}
<pre>
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
</pre>

<jmol><jmolApplet>
<title> NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518 NH3 OPTF POP.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>
[[:File:ACC2518 NH3 OPTF POP.LOG|Optimised NH3 .log file (acc2518)]]

=== Vibrations ===
[[File:Acc2518 vibrations screenshot.jpg|The Gaussview "Display Vibrations" window of the optimised ammonia molecule.|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 1090 || 1694
|-
| '''Symmetry''' || A1 || E
|-
| '''Intensity''' (arbitrary units) || 145 || 14
|-
| '''Image'''|| [[File:acc2518VM1.png|250px]] || [[File:acc2518VM2.png|300px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 1694|| 3461
|-
| '''Symmetry''' || E || A1
|-
| '''Intensity''' (arbitrary units) || 14 || 1
|-
| '''Image'''|| [[File:acc2518VM3.png|250px]] || [[File:acc2518VM4.png|275px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 3590|| 3590
|-
| '''Symmetry''' || E || E
|-
| '''Intensity''' (arbitrary units) || 0 || 0
|-
| '''Image'''|| [[File:acc2518VM5.png|275px]] || [[File:acc2518VM6.png|250px]]
|}

Using the 3N-6 rule, where N represents the number of atoms in a molecule, it is expected that ammonia will have six vibrational modes as shown above. There are two pairs of degenerate modes with a frequency of 1694 (cm-1) and 3590 (cm-1). The modes with a frequency of 1090 (cm-1) and 1694 (cm-1) correspond to bending vibrations and the modes with a frequency 3461 (cm-1) and 3590 (cm-1) correspond to bond stretch vibrations. The bond stretch vibration at 3461 (cm-1) is highly symmetric whilst the stretches with a frequency of 3590 (cm-1) are asymmetric. The bending vibration with a frequency of 1090 (cm-1) is known as the umbrella mode. Three bands would be expected to be seen with the two stretches at 3590 (cm-1) being too low in intensity. The bends with a frequency of 1694 (cm-1) are degenerate and only one band will be observed between the two. Hence the three observed bands would be at 1090 (cm-1), 1694 (cm-1) and 3461 (cm-1).

=== Charge analysis ===
[[File:Acc2518 charge analysis.png|The Gaussview generated atomic charges of ammonia.|250px]]

Nitrogen has a greater electronegativity than hydrogen and hence there is greater electron density distributed around the N atom in ammonia relative to hydrogen. This explains the negative charge on N and the positive charge on H.

==N2 molecule==

===Optimisation data===

{| class="wikitable"
|+ N2 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-109.52412868 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00000060 (au)
|-
|'''Point group'''
|D∞h
|-
|'''Bond length (N-N)'''
|1.11 (Å)
|}

<pre>
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
</pre>

<jmol><jmolApplet>
<title> Nitrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518 N2 OPTIMISATION.LOG</uploadedFileContents>
<script>frame 1.10</script>
</jmolApplet></jmol>
[[:File:ACC2518 N2 OPTIMISATION.LOG|Optimised N2 .log file (acc2518)]]

===Vibrations===
[[File:Acc2518 N2vibration.png|Nitrogen display vibrations screenshot|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 2457
|-
| '''Symmetry''' || SGG
|-
| '''Intensity''' (arbitrary units) || 0
|-
| '''Image'''|| [[File:Acc2518NitrogenVM.png|250px]]
|}
Using the 3N-5 rule for linear molecules, Nitrogen can be expected to have one vibrational mode but this mode has an IR intensity of zero since Nitrogen molecules are IR inactive. This is because they have no overall dipole.

===Charge analysis===
[[File:Acc2518nitrogen charges.png]]

Both nitrogen atoms have the same electronegativity so the charge is neutral on both atoms.

===CCDC search===
'''Unique identifier:''' [https://www.ccdc.cam.ac.uk/structures/Search?Ccdcid=VAMQAE&DatabaseToSearch=Published VAMQAE]

'''Deposition number:''' 1530121

The complex linked above contains nitrogen coordinated to cobalt with a N-N bond distance of 1.08 Å which is slightly shorter than the optimised N-N bond length, displayed above, of 1.11 Å (2.d.p). During the optimisation process for nitrogen, assumptions have to be made for the computational process to be carried out. Each assumption made will increase the uncertainty in measurable quantities such as the bond length. Hence, the computationally determined bond length from the optimisation is a model and may not fully reflect the true bond length or the bond length determined by a computational program considering slightly different assumptions.

It should also be considered that the optimisation gave a prediction for the N-N bond length in a nitrogen molecule whereas the molecule linked above contains a nitrogen molecule that is coordinated into a transition metal complex. A lone pair of electrons on one of the nitrogen atoms has been donated to a cobalt ion, this draws electron density away from the donating nitrogen atom and would therefore slightly increase the positive charge on this atom. This may cause the donating nitrogen atom to attract the electrons in the N-N bond more strongly which would then explain the shorter bond in the transition metal complex compared to the nitrogen molecule.

==H2 molecule==

===Optimisation data===
{| class="wikitable"
|+ H2 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-1.17853936 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00000017 (au)
|-
|'''Point group'''
|D∞h
|-
|'''Bond length (N-N)'''
|0.74 (Å)
|}

<pre>
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

</pre>

<jmol><jmolApplet>
<title> Hydrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518 H2 OPTIMISATION.LOG</uploadedFileContents>
<script>frame 1.7</script>
</jmolApplet></jmol>
[[:File:ACC2518 H2 OPTIMISATION.LOG|Optimised H2 .log file (acc2518)]]

===Vibrations===
[[File:Acc2518 H2vibration.png|Hydrogen display vibrations screenshot|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 4466
|-
| '''Symmetry''' || SGG
|-
| '''Intensity''' (arbitrary units) || 0
|-
| '''Image'''|| [[File:Acc2518HydrogenVM.png|250px]]
|}
Using the 3N-5 rule for linear molecules, hydrogen can be expected to have one vibrational mode but this mode has an IR intensity of zero since hydrogen molecules, like nitrogen molecules, are IR inactive.

===Charge analysis===
[[File:Acc2518hydrogen charges.png]]

Both hydrogen atoms have the same electronegativity so the charge is neutral on both atoms.

==The Haber-Bosch process==
N2 + 3H2 -> 2NH3

E(NH3)=-56.55776873

 '''2*E(NH3)''' =2*(-56.55776873)=-113.11553746

 '''E(N2)''' =-109.52412868

E(H2)=-1.17853936

 '''3*E(H2)''' =3*(-1.17853936) =-3.53561808

'''ΔE= 2*E(NH3) -[ E(N2) + 3*E(H2) ]'''= -0.05579069 ≈ -0.05579 au (5.d.p)

'''ΔE=-146.5 kJ/mol (1.d.p)'''

ΔE is negative which indicates that the gaseous reactants are less stable than the ammonia product since the reactants are at a higher energy than the product. Although this process is not necessarily entropically favourable with four reactant gaseous molecules forming two gaseous product molecules, the reaction has a significantly negative enthalpy change which reflects the result calculated above.

== Project molecule (NF3) ==

=== Optimisation data ===
{| class="wikitable"
|+ NF3 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-354.07131058 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00010256 (au)
|-
|'''Point group'''
|C3V
|-
|'''Bond length (N-F)'''
|1.38 (Å)
|-
|'''Bond angle (F-N-F)'''
|102(°)
|}
<pre>
Item Value Threshold Converged?
Maximum Force 0.000164 0.000450 YES
RMS Force 0.000108 0.000300 YES
Maximum Displacement 0.000612 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

<jmol><jmolApplet>
<title> NF3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518_NF3_OPTF_POP.LOG </uploadedFileContents>
<script>frame 1.7</script>
</jmolApplet></jmol>
[[:File:ACC2518_NF3_OPTF_POP.LOG|Optimised NF3 .log file (acc2518)]]

=== Vibrations ===
[[File:Acc2518 NF3 vibrations screenshot.png|The Gaussview "Display Vibrations" window of the optimised nitrogen trifluoride molecule.|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 482 || 482
|-
| '''Symmetry''' || E || E
|-
| '''Intensity''' (arbitrary units) || 1 || 1
|-
| '''Image'''|| [[File:Acc2518 NF3 VM1.png|300px]] || [[File:Acc2518 NF3 VM2.png|300px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 644|| 930
|-
| '''Symmetry''' || A1 || E
|-
| '''Intensity''' (arbitrary units) || 3 || 208
|-
| '''Image'''|| [[File:Acc2518 NF3 VM3.png|300px]] || [[File:Acc2518 NF3 VM4.png|300px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 930|| 1062
|-
| '''Symmetry''' || E || A1
|-
| '''Intensity''' (arbitrary units) || 208 || 40
|-
| '''Image'''|| [[File:Acc2518 NF3 VM5.png|300px]] || [[File:Acc2518 NF3 VM6.png|300px]]
|}

Nitrogen trifluoride has the same number of atoms as ammonia and so six vibrational modes can be predicted from the 3N-6 rule. There are also two pairs of degenerate modes with frequencies of 482 (cm-1) and 930 (cm-1). The modes with a frequency of 482 (cm-1) and 644(cm-1) correspond to bending vibrational modes and the modes with a frequency of 930 (cm-1) and 1062 (cm-1) correspond to stretching vibrational modes. The mode with a frequency of 1062 (cm-1) represents a symmetric stretch whilst the modes with a frequency of 930 (cm-1) represent asymmetric stretches. In contrast to ammonia, the highest frequency bond stretch of nitrogen trifluoride is the symmetric stretch.

Three bands can be expected in the NF3 IR spectrum at frequencies of 644 (cm-1) 930 (cm-1) and 1062 (cm-1). The bends at 482 (cm-1) will be too low in frequency to appear in the spectrum which starts at a frequency of 500 (cm-1). The stretches at 930 (cm-1) are degenerate and hence will only display one band between them. The band as 644 (cm-1) may not be clearly visible due its relative low intensity of 3 arbitrary units.

=== Charge analysis ===
[[File:Acc2518 NF3 charge analysis.png|The Gaussview generated atomic charges of ammonia.|250px]]

Fluorine has a greater electronegativity that nitrogen and therefore there is greater electron density distributed around the three fluorine atoms compared to the nitrogen atom. The three fluorine atoms are treated as equivalent which means that the magnitude of the positive charge on nitrogen is three times the magnitude of the negative charge on a single fluorine atom.

=== Molecular orbitals (MO) ===

The nitrogen atom contributes 7 electrons and each fluorine atom contributes 9 electrons which means that nitrogen trifluoride contains 34 electrons in total and hence 17 electron pairs. In the table below, a molecular orbital number of 1 would denote the molecular orbital that is deepest in energy. Therefore, orbital 17 represents the HOMO and orbital 18 represents the LUMO. All of the molecular orbitals shown below are occupied with the exception of the LUMO.

{| class="wikitable"
!Molecular orbital number
!Image
!Type of molecular orbital
!Energy (au)
!Extra details
|-
|18
|[[File:Acc2518 MO18.png|200px]]
|Antibonding
|0.01947
|There are nodes in the centre of the N-F bonds which indicates that the LUMO is an antibonding orbital with destructive inteference between phases of opposite sign. The nodes in the centre of all four atoms also indicate that this MO was formed from 2p atomic orbitals from both nitrogen and fluorine.
|-
|17
|[[File:Acc2518 MO17.png|200px]]
|Bonding
| -0.35162
| The phase denoted by the green region shows orbital overlap across all three N-H bonds which implies that the HOMO is a bonding orbital. This MO has been formed from 2p orbitals which explains the nodes observed in the centre of the F atoms.
|-
|16
|[[File:Acc2518 MO16.png|200px]]
|Non-bonding
| -0.42224
|There is no electron density along any of the bonds which is the key indicator that this is a non-bonding MO. Since the electron density is localised around the fluorine atoms, this MO appears to show lone electron pairs on these fluorine atoms. There is no electron density being shared between the fluorine atoms which suggests there is destructive interference preventing such an interaction.
|-
|15
|[[File:Acc2518 MO15.png|200px]]
|Bonding
| -0.43590
| As observed in the HOMO, there is electron density along all three bonds which indicates the bonding nature of the MO. However, in contrast to the HOMO, the electron density along the bonds is not in the same phase for each bond. There is also some constructive interference between two of the F atoms which appears to indicate a very partial π character between the two atoms. This also means that this interaction is the product of two 2p atomic orbitals on fluorine overlapping slightly in phase with each other.
|-
|5
|[[File:Acc2518 MO5.png|200px]]
| Bonding
| -1.35870
| This MO contains no nodes at all implying that it is bonding in nature. It is also formed from overlap of 2s orbitals, in phase, on all atoms since the entire molecule is encased in electron density as a result of the constructive interference. It cannot be formed from 1s orbitals which would be far lower in energy and will also only occupy the first 4 MOs since there are 8 1s electrons in NF3.
|}

== Bonus Molecule (CO2) ==

===Optimisation data===

{| class="wikitable"
|+ CO2 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-188.58093945 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00001154 (au)
|-
|'''Point group'''
|D∞h
|-
|'''Bond length (C-O)'''
|1.17 (Å)
|-
|'''Bond angle'''
|180 (°)
|-
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000017 0.000300 YES
Maximum Displacement 0.000021 0.001800 YES
RMS Displacement 0.000015 0.001200 YES

</pre>

<jmol><jmolApplet>
<title> Carbon dioxide molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518 CO2 OPTF POP.LOG</uploadedFileContents>
<script>frame 1.10</script>
</jmolApplet></jmol>
[[:File:ACC2518 CO2 OPTF POP.LOG|Optimised CO2 .log file (acc2518)]]

===Vibrations===
[[File:Acc2518 CO2vibration.png|Carbon dioxide display vibrations screenshot|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 2457
|-
| '''Symmetry''' || SGG
|-
| '''Intensity''' (arbitrary units) || 0
|-
| '''Image'''|| [[File:Acc2518NitrogenVM.png|250px]]
|}
Using the 3N-5 rule for linear molecules, Nitrogen can be expected to have one vibrational mode but this mode has an IR intensity of zero since Nitrogen molecules are IR inactive. This is because they have no overall dipole.

===Charge analysis===
[[File:Acc2518nitrogen charges.png]]

Both nitrogen atoms have the same electronegativity so the charge is neutral on both atoms.

File:Acc2518 CO2vibration.png

2019-03-04T14:33:01Z

Acc2518:

Acc2518

2019-03-04T14:31:02Z

Acc2518: /* Optimisation data */

== NH3 molecule ==
=== Optimisation data ===
{| class="wikitable"
|+ NH3 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-56.55776873 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00000485 (au)
|-
|'''Point group'''
|C3V
|-
|'''Bond length (N-H)'''
|1.02 (Å)
|-
|'''Bond angle (H-N-H)'''
|106(°)
|}
<pre>
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
</pre>

<jmol><jmolApplet>
<title> NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518 NH3 OPTF POP.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>
[[:File:ACC2518 NH3 OPTF POP.LOG|Optimised NH3 .log file (acc2518)]]

=== Vibrations ===
[[File:Acc2518 vibrations screenshot.jpg|The Gaussview "Display Vibrations" window of the optimised ammonia molecule.|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 1090 || 1694
|-
| '''Symmetry''' || A1 || E
|-
| '''Intensity''' (arbitrary units) || 145 || 14
|-
| '''Image'''|| [[File:acc2518VM1.png|250px]] || [[File:acc2518VM2.png|300px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 1694|| 3461
|-
| '''Symmetry''' || E || A1
|-
| '''Intensity''' (arbitrary units) || 14 || 1
|-
| '''Image'''|| [[File:acc2518VM3.png|250px]] || [[File:acc2518VM4.png|275px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 3590|| 3590
|-
| '''Symmetry''' || E || E
|-
| '''Intensity''' (arbitrary units) || 0 || 0
|-
| '''Image'''|| [[File:acc2518VM5.png|275px]] || [[File:acc2518VM6.png|250px]]
|}

Using the 3N-6 rule, where N represents the number of atoms in a molecule, it is expected that ammonia will have six vibrational modes as shown above. There are two pairs of degenerate modes with a frequency of 1694 (cm-1) and 3590 (cm-1). The modes with a frequency of 1090 (cm-1) and 1694 (cm-1) correspond to bending vibrations and the modes with a frequency 3461 (cm-1) and 3590 (cm-1) correspond to bond stretch vibrations. The bond stretch vibration at 3461 (cm-1) is highly symmetric whilst the stretches with a frequency of 3590 (cm-1) are asymmetric. The bending vibration with a frequency of 1090 (cm-1) is known as the umbrella mode. Three bands would be expected to be seen with the two stretches at 3590 (cm-1) being too low in intensity. The bends with a frequency of 1694 (cm-1) are degenerate and only one band will be observed between the two. Hence the three observed bands would be at 1090 (cm-1), 1694 (cm-1) and 3461 (cm-1).

=== Charge analysis ===
[[File:Acc2518 charge analysis.png|The Gaussview generated atomic charges of ammonia.|250px]]

Nitrogen has a greater electronegativity than hydrogen and hence there is greater electron density distributed around the N atom in ammonia relative to hydrogen. This explains the negative charge on N and the positive charge on H.

==N2 molecule==

===Optimisation data===

{| class="wikitable"
|+ N2 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-109.52412868 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00000060 (au)
|-
|'''Point group'''
|D∞h
|-
|'''Bond length (N-N)'''
|1.11 (Å)
|}

<pre>
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
</pre>

<jmol><jmolApplet>
<title> Nitrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518 N2 OPTIMISATION.LOG</uploadedFileContents>
<script>frame 1.10</script>
</jmolApplet></jmol>
[[:File:ACC2518 N2 OPTIMISATION.LOG|Optimised N2 .log file (acc2518)]]

===Vibrations===
[[File:Acc2518 N2vibration.png|Nitrogen display vibrations screenshot|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 2457
|-
| '''Symmetry''' || SGG
|-
| '''Intensity''' (arbitrary units) || 0
|-
| '''Image'''|| [[File:Acc2518NitrogenVM.png|250px]]
|}
Using the 3N-5 rule for linear molecules, Nitrogen can be expected to have one vibrational mode but this mode has an IR intensity of zero since Nitrogen molecules are IR inactive. This is because they have no overall dipole.

===Charge analysis===
[[File:Acc2518nitrogen charges.png]]

Both nitrogen atoms have the same electronegativity so the charge is neutral on both atoms.

===CCDC search===
'''Unique identifier:''' [https://www.ccdc.cam.ac.uk/structures/Search?Ccdcid=VAMQAE&DatabaseToSearch=Published VAMQAE]

'''Deposition number:''' 1530121

The complex linked above contains nitrogen coordinated to cobalt with a N-N bond distance of 1.08 Å which is slightly shorter than the optimised N-N bond length, displayed above, of 1.11 Å (2.d.p). During the optimisation process for nitrogen, assumptions have to be made for the computational process to be carried out. Each assumption made will increase the uncertainty in measurable quantities such as the bond length. Hence, the computationally determined bond length from the optimisation is a model and may not fully reflect the true bond length or the bond length determined by a computational program considering slightly different assumptions.

It should also be considered that the optimisation gave a prediction for the N-N bond length in a nitrogen molecule whereas the molecule linked above contains a nitrogen molecule that is coordinated into a transition metal complex. A lone pair of electrons on one of the nitrogen atoms has been donated to a cobalt ion, this draws electron density away from the donating nitrogen atom and would therefore slightly increase the positive charge on this atom. This may cause the donating nitrogen atom to attract the electrons in the N-N bond more strongly which would then explain the shorter bond in the transition metal complex compared to the nitrogen molecule.

==H2 molecule==

===Optimisation data===
{| class="wikitable"
|+ H2 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-1.17853936 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00000017 (au)
|-
|'''Point group'''
|D∞h
|-
|'''Bond length (N-N)'''
|0.74 (Å)
|}

<pre>
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

</pre>

<jmol><jmolApplet>
<title> Hydrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518 H2 OPTIMISATION.LOG</uploadedFileContents>
<script>frame 1.7</script>
</jmolApplet></jmol>
[[:File:ACC2518 H2 OPTIMISATION.LOG|Optimised H2 .log file (acc2518)]]

===Vibrations===
[[File:Acc2518 H2vibration.png|Hydrogen display vibrations screenshot|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 4466
|-
| '''Symmetry''' || SGG
|-
| '''Intensity''' (arbitrary units) || 0
|-
| '''Image'''|| [[File:Acc2518HydrogenVM.png|250px]]
|}
Using the 3N-5 rule for linear molecules, hydrogen can be expected to have one vibrational mode but this mode has an IR intensity of zero since hydrogen molecules, like nitrogen molecules, are IR inactive.

===Charge analysis===
[[File:Acc2518hydrogen charges.png]]

Both hydrogen atoms have the same electronegativity so the charge is neutral on both atoms.

==The Haber-Bosch process==
N2 + 3H2 -> 2NH3

E(NH3)=-56.55776873

 '''2*E(NH3)''' =2*(-56.55776873)=-113.11553746

 '''E(N2)''' =-109.52412868

E(H2)=-1.17853936

 '''3*E(H2)''' =3*(-1.17853936) =-3.53561808

'''ΔE= 2*E(NH3) -[ E(N2) + 3*E(H2) ]'''= -0.05579069 ≈ -0.05579 au (5.d.p)

'''ΔE=-146.5 kJ/mol (1.d.p)'''

ΔE is negative which indicates that the gaseous reactants are less stable than the ammonia product since the reactants are at a higher energy than the product. Although this process is not necessarily entropically favourable with four reactant gaseous molecules forming two gaseous product molecules, the reaction has a significantly negative enthalpy change which reflects the result calculated above.

== Project molecule (NF3) ==

=== Optimisation data ===
{| class="wikitable"
|+ NF3 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-354.07131058 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00010256 (au)
|-
|'''Point group'''
|C3V
|-
|'''Bond length (N-F)'''
|1.38 (Å)
|-
|'''Bond angle (F-N-F)'''
|102(°)
|}
<pre>
Item Value Threshold Converged?
Maximum Force 0.000164 0.000450 YES
RMS Force 0.000108 0.000300 YES
Maximum Displacement 0.000612 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

<jmol><jmolApplet>
<title> NF3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518_NF3_OPTF_POP.LOG </uploadedFileContents>
<script>frame 1.7</script>
</jmolApplet></jmol>
[[:File:ACC2518_NF3_OPTF_POP.LOG|Optimised NF3 .log file (acc2518)]]

=== Vibrations ===
[[File:Acc2518 NF3 vibrations screenshot.png|The Gaussview "Display Vibrations" window of the optimised nitrogen trifluoride molecule.|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 482 || 482
|-
| '''Symmetry''' || E || E
|-
| '''Intensity''' (arbitrary units) || 1 || 1
|-
| '''Image'''|| [[File:Acc2518 NF3 VM1.png|300px]] || [[File:Acc2518 NF3 VM2.png|300px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 644|| 930
|-
| '''Symmetry''' || A1 || E
|-
| '''Intensity''' (arbitrary units) || 3 || 208
|-
| '''Image'''|| [[File:Acc2518 NF3 VM3.png|300px]] || [[File:Acc2518 NF3 VM4.png|300px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 930|| 1062
|-
| '''Symmetry''' || E || A1
|-
| '''Intensity''' (arbitrary units) || 208 || 40
|-
| '''Image'''|| [[File:Acc2518 NF3 VM5.png|300px]] || [[File:Acc2518 NF3 VM6.png|300px]]
|}

Nitrogen trifluoride has the same number of atoms as ammonia and so six vibrational modes can be predicted from the 3N-6 rule. There are also two pairs of degenerate modes with frequencies of 482 (cm-1) and 930 (cm-1). The modes with a frequency of 482 (cm-1) and 644(cm-1) correspond to bending vibrational modes and the modes with a frequency of 930 (cm-1) and 1062 (cm-1) correspond to stretching vibrational modes. The mode with a frequency of 1062 (cm-1) represents a symmetric stretch whilst the modes with a frequency of 930 (cm-1) represent asymmetric stretches. In contrast to ammonia, the highest frequency bond stretch of nitrogen trifluoride is the symmetric stretch.

Three bands can be expected in the NF3 IR spectrum at frequencies of 644 (cm-1) 930 (cm-1) and 1062 (cm-1). The bends at 482 (cm-1) will be too low in frequency to appear in the spectrum which starts at a frequency of 500 (cm-1). The stretches at 930 (cm-1) are degenerate and hence will only display one band between them. The band as 644 (cm-1) may not be clearly visible due its relative low intensity of 3 arbitrary units.

=== Charge analysis ===
[[File:Acc2518 NF3 charge analysis.png|The Gaussview generated atomic charges of ammonia.|250px]]

Fluorine has a greater electronegativity that nitrogen and therefore there is greater electron density distributed around the three fluorine atoms compared to the nitrogen atom. The three fluorine atoms are treated as equivalent which means that the magnitude of the positive charge on nitrogen is three times the magnitude of the negative charge on a single fluorine atom.

=== Molecular orbitals (MO) ===

The nitrogen atom contributes 7 electrons and each fluorine atom contributes 9 electrons which means that nitrogen trifluoride contains 34 electrons in total and hence 17 electron pairs. In the table below, a molecular orbital number of 1 would denote the molecular orbital that is deepest in energy. Therefore, orbital 17 represents the HOMO and orbital 18 represents the LUMO. All of the molecular orbitals shown below are occupied with the exception of the LUMO.

{| class="wikitable"
!Molecular orbital number
!Image
!Type of molecular orbital
!Energy (au)
!Extra details
|-
|18
|[[File:Acc2518 MO18.png|200px]]
|Antibonding
|0.01947
|There are nodes in the centre of the N-F bonds which indicates that the LUMO is an antibonding orbital with destructive inteference between phases of opposite sign. The nodes in the centre of all four atoms also indicate that this MO was formed from 2p atomic orbitals from both nitrogen and fluorine.
|-
|17
|[[File:Acc2518 MO17.png|200px]]
|Bonding
| -0.35162
| The phase denoted by the green region shows orbital overlap across all three N-H bonds which implies that the HOMO is a bonding orbital. This MO has been formed from 2p orbitals which explains the nodes observed in the centre of the F atoms.
|-
|16
|[[File:Acc2518 MO16.png|200px]]
|Non-bonding
| -0.42224
|There is no electron density along any of the bonds which is the key indicator that this is a non-bonding MO. Since the electron density is localised around the fluorine atoms, this MO appears to show lone electron pairs on these fluorine atoms. There is no electron density being shared between the fluorine atoms which suggests there is destructive interference preventing such an interaction.
|-
|15
|[[File:Acc2518 MO15.png|200px]]
|Bonding
| -0.43590
| As observed in the HOMO, there is electron density along all three bonds which indicates the bonding nature of the MO. However, in contrast to the HOMO, the electron density along the bonds is not in the same phase for each bond. There is also some constructive interference between two of the F atoms which appears to indicate a very partial π character between the two atoms. This also means that this interaction is the product of two 2p atomic orbitals on fluorine overlapping slightly in phase with each other.
|-
|5
|[[File:Acc2518 MO5.png|200px]]
| Bonding
| -1.35870
| This MO contains no nodes at all implying that it is bonding in nature. It is also formed from overlap of 2s orbitals, in phase, on all atoms since the entire molecule is encased in electron density as a result of the constructive interference. It cannot be formed from 1s orbitals which would be far lower in energy and will also only occupy the first 4 MOs since there are 8 1s electrons in NF3.
|}

== Bonus Molecule (CO2) ==

===Optimisation data===

{| class="wikitable"
|+ CO2 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-188.58093945 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00001154 (au)
|-
|'''Point group'''
|D∞h
|-
|'''Bond length (C-O)'''
|1.17 (Å)
|-
|'''Bond angle'''
|180 (°)
|-
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000017 0.000300 YES
Maximum Displacement 0.000021 0.001800 YES
RMS Displacement 0.000015 0.001200 YES

</pre>

<jmol><jmolApplet>
<title> Carbon dioxide molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518 CO2 OPTF POP.LOG</uploadedFileContents>
<script>frame 1.10</script>
</jmolApplet></jmol>
[[:File:ACC2518 CO2 OPTF POP.LOG|Optimised CO2 .log file (acc2518)]]

===Vibrations===
[[File:Acc2518 N2vibration.png|Nitrogen display vibrations screenshot|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 2457
|-
| '''Symmetry''' || SGG
|-
| '''Intensity''' (arbitrary units) || 0
|-
| '''Image'''|| [[File:Acc2518NitrogenVM.png|250px]]
|}
Using the 3N-5 rule for linear molecules, Nitrogen can be expected to have one vibrational mode but this mode has an IR intensity of zero since Nitrogen molecules are IR inactive. This is because they have no overall dipole.

===Charge analysis===
[[File:Acc2518nitrogen charges.png]]

Both nitrogen atoms have the same electronegativity so the charge is neutral on both atoms.

Acc2518

2019-03-04T14:30:36Z

Acc2518: /* Optimisation data */

== NH3 molecule ==
=== Optimisation data ===
{| class="wikitable"
|+ NH3 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-56.55776873 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00000485 (au)
|-
|'''Point group'''
|C3V
|-
|'''Bond length (N-H)'''
|1.02 (Å)
|-
|'''Bond angle (H-N-H)'''
|106(°)
|}
<pre>
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
</pre>

<jmol><jmolApplet>
<title> NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518 NH3 OPTF POP.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>
[[:File:ACC2518 NH3 OPTF POP.LOG|Optimised NH3 .log file (acc2518)]]

=== Vibrations ===
[[File:Acc2518 vibrations screenshot.jpg|The Gaussview "Display Vibrations" window of the optimised ammonia molecule.|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 1090 || 1694
|-
| '''Symmetry''' || A1 || E
|-
| '''Intensity''' (arbitrary units) || 145 || 14
|-
| '''Image'''|| [[File:acc2518VM1.png|250px]] || [[File:acc2518VM2.png|300px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 1694|| 3461
|-
| '''Symmetry''' || E || A1
|-
| '''Intensity''' (arbitrary units) || 14 || 1
|-
| '''Image'''|| [[File:acc2518VM3.png|250px]] || [[File:acc2518VM4.png|275px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 3590|| 3590
|-
| '''Symmetry''' || E || E
|-
| '''Intensity''' (arbitrary units) || 0 || 0
|-
| '''Image'''|| [[File:acc2518VM5.png|275px]] || [[File:acc2518VM6.png|250px]]
|}

Using the 3N-6 rule, where N represents the number of atoms in a molecule, it is expected that ammonia will have six vibrational modes as shown above. There are two pairs of degenerate modes with a frequency of 1694 (cm-1) and 3590 (cm-1). The modes with a frequency of 1090 (cm-1) and 1694 (cm-1) correspond to bending vibrations and the modes with a frequency 3461 (cm-1) and 3590 (cm-1) correspond to bond stretch vibrations. The bond stretch vibration at 3461 (cm-1) is highly symmetric whilst the stretches with a frequency of 3590 (cm-1) are asymmetric. The bending vibration with a frequency of 1090 (cm-1) is known as the umbrella mode. Three bands would be expected to be seen with the two stretches at 3590 (cm-1) being too low in intensity. The bends with a frequency of 1694 (cm-1) are degenerate and only one band will be observed between the two. Hence the three observed bands would be at 1090 (cm-1), 1694 (cm-1) and 3461 (cm-1).

=== Charge analysis ===
[[File:Acc2518 charge analysis.png|The Gaussview generated atomic charges of ammonia.|250px]]

Nitrogen has a greater electronegativity than hydrogen and hence there is greater electron density distributed around the N atom in ammonia relative to hydrogen. This explains the negative charge on N and the positive charge on H.

==N2 molecule==

===Optimisation data===

{| class="wikitable"
|+ N2 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-109.52412868 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00000060 (au)
|-
|'''Point group'''
|D∞h
|-
|'''Bond length (N-N)'''
|1.11 (Å)
|}

<pre>
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
</pre>

<jmol><jmolApplet>
<title> Nitrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518 N2 OPTIMISATION.LOG</uploadedFileContents>
<script>frame 1.10</script>
</jmolApplet></jmol>
[[:File:ACC2518 N2 OPTIMISATION.LOG|Optimised N2 .log file (acc2518)]]

===Vibrations===
[[File:Acc2518 N2vibration.png|Nitrogen display vibrations screenshot|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 2457
|-
| '''Symmetry''' || SGG
|-
| '''Intensity''' (arbitrary units) || 0
|-
| '''Image'''|| [[File:Acc2518NitrogenVM.png|250px]]
|}
Using the 3N-5 rule for linear molecules, Nitrogen can be expected to have one vibrational mode but this mode has an IR intensity of zero since Nitrogen molecules are IR inactive. This is because they have no overall dipole.

===Charge analysis===
[[File:Acc2518nitrogen charges.png]]

Both nitrogen atoms have the same electronegativity so the charge is neutral on both atoms.

===CCDC search===
'''Unique identifier:''' [https://www.ccdc.cam.ac.uk/structures/Search?Ccdcid=VAMQAE&DatabaseToSearch=Published VAMQAE]

'''Deposition number:''' 1530121

The complex linked above contains nitrogen coordinated to cobalt with a N-N bond distance of 1.08 Å which is slightly shorter than the optimised N-N bond length, displayed above, of 1.11 Å (2.d.p). During the optimisation process for nitrogen, assumptions have to be made for the computational process to be carried out. Each assumption made will increase the uncertainty in measurable quantities such as the bond length. Hence, the computationally determined bond length from the optimisation is a model and may not fully reflect the true bond length or the bond length determined by a computational program considering slightly different assumptions.

It should also be considered that the optimisation gave a prediction for the N-N bond length in a nitrogen molecule whereas the molecule linked above contains a nitrogen molecule that is coordinated into a transition metal complex. A lone pair of electrons on one of the nitrogen atoms has been donated to a cobalt ion, this draws electron density away from the donating nitrogen atom and would therefore slightly increase the positive charge on this atom. This may cause the donating nitrogen atom to attract the electrons in the N-N bond more strongly which would then explain the shorter bond in the transition metal complex compared to the nitrogen molecule.

==H2 molecule==

===Optimisation data===
{| class="wikitable"
|+ H2 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-1.17853936 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00000017 (au)
|-
|'''Point group'''
|D∞h
|-
|'''Bond length (N-N)'''
|0.74 (Å)
|}

<pre>
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

</pre>

<jmol><jmolApplet>
<title> Hydrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518 H2 OPTIMISATION.LOG</uploadedFileContents>
<script>frame 1.7</script>
</jmolApplet></jmol>
[[:File:ACC2518 H2 OPTIMISATION.LOG|Optimised H2 .log file (acc2518)]]

===Vibrations===
[[File:Acc2518 H2vibration.png|Hydrogen display vibrations screenshot|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 4466
|-
| '''Symmetry''' || SGG
|-
| '''Intensity''' (arbitrary units) || 0
|-
| '''Image'''|| [[File:Acc2518HydrogenVM.png|250px]]
|}
Using the 3N-5 rule for linear molecules, hydrogen can be expected to have one vibrational mode but this mode has an IR intensity of zero since hydrogen molecules, like nitrogen molecules, are IR inactive.

===Charge analysis===
[[File:Acc2518hydrogen charges.png]]

Both hydrogen atoms have the same electronegativity so the charge is neutral on both atoms.

==The Haber-Bosch process==
N2 + 3H2 -> 2NH3

E(NH3)=-56.55776873

 '''2*E(NH3)''' =2*(-56.55776873)=-113.11553746

 '''E(N2)''' =-109.52412868

E(H2)=-1.17853936

 '''3*E(H2)''' =3*(-1.17853936) =-3.53561808

'''ΔE= 2*E(NH3) -[ E(N2) + 3*E(H2) ]'''= -0.05579069 ≈ -0.05579 au (5.d.p)

'''ΔE=-146.5 kJ/mol (1.d.p)'''

ΔE is negative which indicates that the gaseous reactants are less stable than the ammonia product since the reactants are at a higher energy than the product. Although this process is not necessarily entropically favourable with four reactant gaseous molecules forming two gaseous product molecules, the reaction has a significantly negative enthalpy change which reflects the result calculated above.

== Project molecule (NF3) ==

=== Optimisation data ===
{| class="wikitable"
|+ NF3 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-354.07131058 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00010256 (au)
|-
|'''Point group'''
|C3V
|-
|'''Bond length (N-F)'''
|1.38 (Å)
|-
|'''Bond angle (F-N-F)'''
|102(°)
|}
<pre>
Item Value Threshold Converged?
Maximum Force 0.000164 0.000450 YES
RMS Force 0.000108 0.000300 YES
Maximum Displacement 0.000612 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

<jmol><jmolApplet>
<title> NF3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518_NF3_OPTF_POP.LOG </uploadedFileContents>
<script>frame 1.7</script>
</jmolApplet></jmol>
[[:File:ACC2518_NF3_OPTF_POP.LOG|Optimised NF3 .log file (acc2518)]]

=== Vibrations ===
[[File:Acc2518 NF3 vibrations screenshot.png|The Gaussview "Display Vibrations" window of the optimised nitrogen trifluoride molecule.|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 482 || 482
|-
| '''Symmetry''' || E || E
|-
| '''Intensity''' (arbitrary units) || 1 || 1
|-
| '''Image'''|| [[File:Acc2518 NF3 VM1.png|300px]] || [[File:Acc2518 NF3 VM2.png|300px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 644|| 930
|-
| '''Symmetry''' || A1 || E
|-
| '''Intensity''' (arbitrary units) || 3 || 208
|-
| '''Image'''|| [[File:Acc2518 NF3 VM3.png|300px]] || [[File:Acc2518 NF3 VM4.png|300px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 930|| 1062
|-
| '''Symmetry''' || E || A1
|-
| '''Intensity''' (arbitrary units) || 208 || 40
|-
| '''Image'''|| [[File:Acc2518 NF3 VM5.png|300px]] || [[File:Acc2518 NF3 VM6.png|300px]]
|}

Nitrogen trifluoride has the same number of atoms as ammonia and so six vibrational modes can be predicted from the 3N-6 rule. There are also two pairs of degenerate modes with frequencies of 482 (cm-1) and 930 (cm-1). The modes with a frequency of 482 (cm-1) and 644(cm-1) correspond to bending vibrational modes and the modes with a frequency of 930 (cm-1) and 1062 (cm-1) correspond to stretching vibrational modes. The mode with a frequency of 1062 (cm-1) represents a symmetric stretch whilst the modes with a frequency of 930 (cm-1) represent asymmetric stretches. In contrast to ammonia, the highest frequency bond stretch of nitrogen trifluoride is the symmetric stretch.

Three bands can be expected in the NF3 IR spectrum at frequencies of 644 (cm-1) 930 (cm-1) and 1062 (cm-1). The bends at 482 (cm-1) will be too low in frequency to appear in the spectrum which starts at a frequency of 500 (cm-1). The stretches at 930 (cm-1) are degenerate and hence will only display one band between them. The band as 644 (cm-1) may not be clearly visible due its relative low intensity of 3 arbitrary units.

=== Charge analysis ===
[[File:Acc2518 NF3 charge analysis.png|The Gaussview generated atomic charges of ammonia.|250px]]

Fluorine has a greater electronegativity that nitrogen and therefore there is greater electron density distributed around the three fluorine atoms compared to the nitrogen atom. The three fluorine atoms are treated as equivalent which means that the magnitude of the positive charge on nitrogen is three times the magnitude of the negative charge on a single fluorine atom.

=== Molecular orbitals (MO) ===

The nitrogen atom contributes 7 electrons and each fluorine atom contributes 9 electrons which means that nitrogen trifluoride contains 34 electrons in total and hence 17 electron pairs. In the table below, a molecular orbital number of 1 would denote the molecular orbital that is deepest in energy. Therefore, orbital 17 represents the HOMO and orbital 18 represents the LUMO. All of the molecular orbitals shown below are occupied with the exception of the LUMO.

{| class="wikitable"
!Molecular orbital number
!Image
!Type of molecular orbital
!Energy (au)
!Extra details
|-
|18
|[[File:Acc2518 MO18.png|200px]]
|Antibonding
|0.01947
|There are nodes in the centre of the N-F bonds which indicates that the LUMO is an antibonding orbital with destructive inteference between phases of opposite sign. The nodes in the centre of all four atoms also indicate that this MO was formed from 2p atomic orbitals from both nitrogen and fluorine.
|-
|17
|[[File:Acc2518 MO17.png|200px]]
|Bonding
| -0.35162
| The phase denoted by the green region shows orbital overlap across all three N-H bonds which implies that the HOMO is a bonding orbital. This MO has been formed from 2p orbitals which explains the nodes observed in the centre of the F atoms.
|-
|16
|[[File:Acc2518 MO16.png|200px]]
|Non-bonding
| -0.42224
|There is no electron density along any of the bonds which is the key indicator that this is a non-bonding MO. Since the electron density is localised around the fluorine atoms, this MO appears to show lone electron pairs on these fluorine atoms. There is no electron density being shared between the fluorine atoms which suggests there is destructive interference preventing such an interaction.
|-
|15
|[[File:Acc2518 MO15.png|200px]]
|Bonding
| -0.43590
| As observed in the HOMO, there is electron density along all three bonds which indicates the bonding nature of the MO. However, in contrast to the HOMO, the electron density along the bonds is not in the same phase for each bond. There is also some constructive interference between two of the F atoms which appears to indicate a very partial π character between the two atoms. This also means that this interaction is the product of two 2p atomic orbitals on fluorine overlapping slightly in phase with each other.
|-
|5
|[[File:Acc2518 MO5.png|200px]]
| Bonding
| -1.35870
| This MO contains no nodes at all implying that it is bonding in nature. It is also formed from overlap of 2s orbitals, in phase, on all atoms since the entire molecule is encased in electron density as a result of the constructive interference. It cannot be formed from 1s orbitals which would be far lower in energy and will also only occupy the first 4 MOs since there are 8 1s electrons in NF3.
|}

== Bonus Molecule (CO2) ==

===Optimisation data===

{| class="wikitable"
|+ CO2 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-188.58093945 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00001154 (au)
|-
|'''Point group'''
|D∞h
|-
|'''Bond length (C-O)'''
|1.17 (Å)
|-
|'''Bond angle'''
|180 (°)
|-
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000017 0.000300 YES
Maximum Displacement 0.000021 0.001800 YES
RMS Displacement 0.000015 0.001200 YES

</pre>

<jmol><jmolApplet>
<title> Carbon dioxide molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518 CO2 OPTF POP.LOG</uploadedFileContents>
<script>frame 1.4</script>
</jmolApplet></jmol>
[[:File:ACC2518 CO2 OPTF POP.LOG|Optimised CO2 .log file (acc2518)]]

===Vibrations===
[[File:Acc2518 N2vibration.png|Nitrogen display vibrations screenshot|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 2457
|-
| '''Symmetry''' || SGG
|-
| '''Intensity''' (arbitrary units) || 0
|-
| '''Image'''|| [[File:Acc2518NitrogenVM.png|250px]]
|}
Using the 3N-5 rule for linear molecules, Nitrogen can be expected to have one vibrational mode but this mode has an IR intensity of zero since Nitrogen molecules are IR inactive. This is because they have no overall dipole.

===Charge analysis===
[[File:Acc2518nitrogen charges.png]]

Both nitrogen atoms have the same electronegativity so the charge is neutral on both atoms.

File:ACC2518 CO2 OPTF POP.LOG

2019-03-04T14:29:44Z

Acc2518:

Acc2518

2019-03-04T14:28:07Z

Acc2518: /* Bonus Molecule (CO2) */

== NH3 molecule ==
=== Optimisation data ===
{| class="wikitable"
|+ NH3 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-56.55776873 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00000485 (au)
|-
|'''Point group'''
|C3V
|-
|'''Bond length (N-H)'''
|1.02 (Å)
|-
|'''Bond angle (H-N-H)'''
|106(°)
|}
<pre>
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
</pre>

<jmol><jmolApplet>
<title> NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518 NH3 OPTF POP.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>
[[:File:ACC2518 NH3 OPTF POP.LOG|Optimised NH3 .log file (acc2518)]]

=== Vibrations ===
[[File:Acc2518 vibrations screenshot.jpg|The Gaussview "Display Vibrations" window of the optimised ammonia molecule.|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 1090 || 1694
|-
| '''Symmetry''' || A1 || E
|-
| '''Intensity''' (arbitrary units) || 145 || 14
|-
| '''Image'''|| [[File:acc2518VM1.png|250px]] || [[File:acc2518VM2.png|300px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 1694|| 3461
|-
| '''Symmetry''' || E || A1
|-
| '''Intensity''' (arbitrary units) || 14 || 1
|-
| '''Image'''|| [[File:acc2518VM3.png|250px]] || [[File:acc2518VM4.png|275px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 3590|| 3590
|-
| '''Symmetry''' || E || E
|-
| '''Intensity''' (arbitrary units) || 0 || 0
|-
| '''Image'''|| [[File:acc2518VM5.png|275px]] || [[File:acc2518VM6.png|250px]]
|}

Using the 3N-6 rule, where N represents the number of atoms in a molecule, it is expected that ammonia will have six vibrational modes as shown above. There are two pairs of degenerate modes with a frequency of 1694 (cm-1) and 3590 (cm-1). The modes with a frequency of 1090 (cm-1) and 1694 (cm-1) correspond to bending vibrations and the modes with a frequency 3461 (cm-1) and 3590 (cm-1) correspond to bond stretch vibrations. The bond stretch vibration at 3461 (cm-1) is highly symmetric whilst the stretches with a frequency of 3590 (cm-1) are asymmetric. The bending vibration with a frequency of 1090 (cm-1) is known as the umbrella mode. Three bands would be expected to be seen with the two stretches at 3590 (cm-1) being too low in intensity. The bends with a frequency of 1694 (cm-1) are degenerate and only one band will be observed between the two. Hence the three observed bands would be at 1090 (cm-1), 1694 (cm-1) and 3461 (cm-1).

=== Charge analysis ===
[[File:Acc2518 charge analysis.png|The Gaussview generated atomic charges of ammonia.|250px]]

Nitrogen has a greater electronegativity than hydrogen and hence there is greater electron density distributed around the N atom in ammonia relative to hydrogen. This explains the negative charge on N and the positive charge on H.

==N2 molecule==

===Optimisation data===

{| class="wikitable"
|+ N2 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-109.52412868 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00000060 (au)
|-
|'''Point group'''
|D∞h
|-
|'''Bond length (N-N)'''
|1.11 (Å)
|}

<pre>
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
</pre>

<jmol><jmolApplet>
<title> Nitrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518 N2 OPTIMISATION.LOG</uploadedFileContents>
<script>frame 1.10</script>
</jmolApplet></jmol>
[[:File:ACC2518 N2 OPTIMISATION.LOG|Optimised N2 .log file (acc2518)]]

===Vibrations===
[[File:Acc2518 N2vibration.png|Nitrogen display vibrations screenshot|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 2457
|-
| '''Symmetry''' || SGG
|-
| '''Intensity''' (arbitrary units) || 0
|-
| '''Image'''|| [[File:Acc2518NitrogenVM.png|250px]]
|}
Using the 3N-5 rule for linear molecules, Nitrogen can be expected to have one vibrational mode but this mode has an IR intensity of zero since Nitrogen molecules are IR inactive. This is because they have no overall dipole.

===Charge analysis===
[[File:Acc2518nitrogen charges.png]]

Both nitrogen atoms have the same electronegativity so the charge is neutral on both atoms.

===CCDC search===
'''Unique identifier:''' [https://www.ccdc.cam.ac.uk/structures/Search?Ccdcid=VAMQAE&DatabaseToSearch=Published VAMQAE]

'''Deposition number:''' 1530121

The complex linked above contains nitrogen coordinated to cobalt with a N-N bond distance of 1.08 Å which is slightly shorter than the optimised N-N bond length, displayed above, of 1.11 Å (2.d.p). During the optimisation process for nitrogen, assumptions have to be made for the computational process to be carried out. Each assumption made will increase the uncertainty in measurable quantities such as the bond length. Hence, the computationally determined bond length from the optimisation is a model and may not fully reflect the true bond length or the bond length determined by a computational program considering slightly different assumptions.

It should also be considered that the optimisation gave a prediction for the N-N bond length in a nitrogen molecule whereas the molecule linked above contains a nitrogen molecule that is coordinated into a transition metal complex. A lone pair of electrons on one of the nitrogen atoms has been donated to a cobalt ion, this draws electron density away from the donating nitrogen atom and would therefore slightly increase the positive charge on this atom. This may cause the donating nitrogen atom to attract the electrons in the N-N bond more strongly which would then explain the shorter bond in the transition metal complex compared to the nitrogen molecule.

==H2 molecule==

===Optimisation data===
{| class="wikitable"
|+ H2 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-1.17853936 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00000017 (au)
|-
|'''Point group'''
|D∞h
|-
|'''Bond length (N-N)'''
|0.74 (Å)
|}

<pre>
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

</pre>

<jmol><jmolApplet>
<title> Hydrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518 H2 OPTIMISATION.LOG</uploadedFileContents>
<script>frame 1.7</script>
</jmolApplet></jmol>
[[:File:ACC2518 H2 OPTIMISATION.LOG|Optimised H2 .log file (acc2518)]]

===Vibrations===
[[File:Acc2518 H2vibration.png|Hydrogen display vibrations screenshot|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 4466
|-
| '''Symmetry''' || SGG
|-
| '''Intensity''' (arbitrary units) || 0
|-
| '''Image'''|| [[File:Acc2518HydrogenVM.png|250px]]
|}
Using the 3N-5 rule for linear molecules, hydrogen can be expected to have one vibrational mode but this mode has an IR intensity of zero since hydrogen molecules, like nitrogen molecules, are IR inactive.

===Charge analysis===
[[File:Acc2518hydrogen charges.png]]

Both hydrogen atoms have the same electronegativity so the charge is neutral on both atoms.

==The Haber-Bosch process==
N2 + 3H2 -> 2NH3

E(NH3)=-56.55776873

 '''2*E(NH3)''' =2*(-56.55776873)=-113.11553746

 '''E(N2)''' =-109.52412868

E(H2)=-1.17853936

 '''3*E(H2)''' =3*(-1.17853936) =-3.53561808

'''ΔE= 2*E(NH3) -[ E(N2) + 3*E(H2) ]'''= -0.05579069 ≈ -0.05579 au (5.d.p)

'''ΔE=-146.5 kJ/mol (1.d.p)'''

ΔE is negative which indicates that the gaseous reactants are less stable than the ammonia product since the reactants are at a higher energy than the product. Although this process is not necessarily entropically favourable with four reactant gaseous molecules forming two gaseous product molecules, the reaction has a significantly negative enthalpy change which reflects the result calculated above.

== Project molecule (NF3) ==

=== Optimisation data ===
{| class="wikitable"
|+ NF3 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-354.07131058 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00010256 (au)
|-
|'''Point group'''
|C3V
|-
|'''Bond length (N-F)'''
|1.38 (Å)
|-
|'''Bond angle (F-N-F)'''
|102(°)
|}
<pre>
Item Value Threshold Converged?
Maximum Force 0.000164 0.000450 YES
RMS Force 0.000108 0.000300 YES
Maximum Displacement 0.000612 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

<jmol><jmolApplet>
<title> NF3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518_NF3_OPTF_POP.LOG </uploadedFileContents>
<script>frame 1.7</script>
</jmolApplet></jmol>
[[:File:ACC2518_NF3_OPTF_POP.LOG|Optimised NF3 .log file (acc2518)]]

=== Vibrations ===
[[File:Acc2518 NF3 vibrations screenshot.png|The Gaussview "Display Vibrations" window of the optimised nitrogen trifluoride molecule.|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 482 || 482
|-
| '''Symmetry''' || E || E
|-
| '''Intensity''' (arbitrary units) || 1 || 1
|-
| '''Image'''|| [[File:Acc2518 NF3 VM1.png|300px]] || [[File:Acc2518 NF3 VM2.png|300px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 644|| 930
|-
| '''Symmetry''' || A1 || E
|-
| '''Intensity''' (arbitrary units) || 3 || 208
|-
| '''Image'''|| [[File:Acc2518 NF3 VM3.png|300px]] || [[File:Acc2518 NF3 VM4.png|300px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 930|| 1062
|-
| '''Symmetry''' || E || A1
|-
| '''Intensity''' (arbitrary units) || 208 || 40
|-
| '''Image'''|| [[File:Acc2518 NF3 VM5.png|300px]] || [[File:Acc2518 NF3 VM6.png|300px]]
|}

Nitrogen trifluoride has the same number of atoms as ammonia and so six vibrational modes can be predicted from the 3N-6 rule. There are also two pairs of degenerate modes with frequencies of 482 (cm-1) and 930 (cm-1). The modes with a frequency of 482 (cm-1) and 644(cm-1) correspond to bending vibrational modes and the modes with a frequency of 930 (cm-1) and 1062 (cm-1) correspond to stretching vibrational modes. The mode with a frequency of 1062 (cm-1) represents a symmetric stretch whilst the modes with a frequency of 930 (cm-1) represent asymmetric stretches. In contrast to ammonia, the highest frequency bond stretch of nitrogen trifluoride is the symmetric stretch.

Three bands can be expected in the NF3 IR spectrum at frequencies of 644 (cm-1) 930 (cm-1) and 1062 (cm-1). The bends at 482 (cm-1) will be too low in frequency to appear in the spectrum which starts at a frequency of 500 (cm-1). The stretches at 930 (cm-1) are degenerate and hence will only display one band between them. The band as 644 (cm-1) may not be clearly visible due its relative low intensity of 3 arbitrary units.

=== Charge analysis ===
[[File:Acc2518 NF3 charge analysis.png|The Gaussview generated atomic charges of ammonia.|250px]]

Fluorine has a greater electronegativity that nitrogen and therefore there is greater electron density distributed around the three fluorine atoms compared to the nitrogen atom. The three fluorine atoms are treated as equivalent which means that the magnitude of the positive charge on nitrogen is three times the magnitude of the negative charge on a single fluorine atom.

=== Molecular orbitals (MO) ===

The nitrogen atom contributes 7 electrons and each fluorine atom contributes 9 electrons which means that nitrogen trifluoride contains 34 electrons in total and hence 17 electron pairs. In the table below, a molecular orbital number of 1 would denote the molecular orbital that is deepest in energy. Therefore, orbital 17 represents the HOMO and orbital 18 represents the LUMO. All of the molecular orbitals shown below are occupied with the exception of the LUMO.

{| class="wikitable"
!Molecular orbital number
!Image
!Type of molecular orbital
!Energy (au)
!Extra details
|-
|18
|[[File:Acc2518 MO18.png|200px]]
|Antibonding
|0.01947
|There are nodes in the centre of the N-F bonds which indicates that the LUMO is an antibonding orbital with destructive inteference between phases of opposite sign. The nodes in the centre of all four atoms also indicate that this MO was formed from 2p atomic orbitals from both nitrogen and fluorine.
|-
|17
|[[File:Acc2518 MO17.png|200px]]
|Bonding
| -0.35162
| The phase denoted by the green region shows orbital overlap across all three N-H bonds which implies that the HOMO is a bonding orbital. This MO has been formed from 2p orbitals which explains the nodes observed in the centre of the F atoms.
|-
|16
|[[File:Acc2518 MO16.png|200px]]
|Non-bonding
| -0.42224
|There is no electron density along any of the bonds which is the key indicator that this is a non-bonding MO. Since the electron density is localised around the fluorine atoms, this MO appears to show lone electron pairs on these fluorine atoms. There is no electron density being shared between the fluorine atoms which suggests there is destructive interference preventing such an interaction.
|-
|15
|[[File:Acc2518 MO15.png|200px]]
|Bonding
| -0.43590
| As observed in the HOMO, there is electron density along all three bonds which indicates the bonding nature of the MO. However, in contrast to the HOMO, the electron density along the bonds is not in the same phase for each bond. There is also some constructive interference between two of the F atoms which appears to indicate a very partial π character between the two atoms. This also means that this interaction is the product of two 2p atomic orbitals on fluorine overlapping slightly in phase with each other.
|-
|5
|[[File:Acc2518 MO5.png|200px]]
| Bonding
| -1.35870
| This MO contains no nodes at all implying that it is bonding in nature. It is also formed from overlap of 2s orbitals, in phase, on all atoms since the entire molecule is encased in electron density as a result of the constructive interference. It cannot be formed from 1s orbitals which would be far lower in energy and will also only occupy the first 4 MOs since there are 8 1s electrons in NF3.
|}

== Bonus Molecule (CO2) ==

===Optimisation data===

{| class="wikitable"
|+ CO2 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-188.58093945 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00001154 (au)
|-
|'''Point group'''
|D∞h
|-
|'''Bond length (C-O)'''
|1.17 (Å)
|-
|'''Bond angle'''
|180 (°)
|-
|}

<pre>
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
</pre>

<jmol><jmolApplet>
<title> Nitrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518 N2 OPTIMISATION.LOG</uploadedFileContents>
<script>frame 1.10</script>
</jmolApplet></jmol>
[[:File:ACC2518 N2 OPTIMISATION.LOG|Optimised N2 .log file (acc2518)]]

===Vibrations===
[[File:Acc2518 N2vibration.png|Nitrogen display vibrations screenshot|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 2457
|-
| '''Symmetry''' || SGG
|-
| '''Intensity''' (arbitrary units) || 0
|-
| '''Image'''|| [[File:Acc2518NitrogenVM.png|250px]]
|}
Using the 3N-5 rule for linear molecules, Nitrogen can be expected to have one vibrational mode but this mode has an IR intensity of zero since Nitrogen molecules are IR inactive. This is because they have no overall dipole.

===Charge analysis===
[[File:Acc2518nitrogen charges.png]]

Both nitrogen atoms have the same electronegativity so the charge is neutral on both atoms.

Acc2518

2019-03-04T14:18:55Z

Acc2518: /* Bonus Molecule (CO2 */

== NH3 molecule ==
=== Optimisation data ===
{| class="wikitable"
|+ NH3 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-56.55776873 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00000485 (au)
|-
|'''Point group'''
|C3V
|-
|'''Bond length (N-H)'''
|1.02 (Å)
|-
|'''Bond angle (H-N-H)'''
|106(°)
|}
<pre>
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
</pre>

<jmol><jmolApplet>
<title> NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518 NH3 OPTF POP.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>
[[:File:ACC2518 NH3 OPTF POP.LOG|Optimised NH3 .log file (acc2518)]]

=== Vibrations ===
[[File:Acc2518 vibrations screenshot.jpg|The Gaussview "Display Vibrations" window of the optimised ammonia molecule.|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 1090 || 1694
|-
| '''Symmetry''' || A1 || E
|-
| '''Intensity''' (arbitrary units) || 145 || 14
|-
| '''Image'''|| [[File:acc2518VM1.png|250px]] || [[File:acc2518VM2.png|300px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 1694|| 3461
|-
| '''Symmetry''' || E || A1
|-
| '''Intensity''' (arbitrary units) || 14 || 1
|-
| '''Image'''|| [[File:acc2518VM3.png|250px]] || [[File:acc2518VM4.png|275px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 3590|| 3590
|-
| '''Symmetry''' || E || E
|-
| '''Intensity''' (arbitrary units) || 0 || 0
|-
| '''Image'''|| [[File:acc2518VM5.png|275px]] || [[File:acc2518VM6.png|250px]]
|}

Using the 3N-6 rule, where N represents the number of atoms in a molecule, it is expected that ammonia will have six vibrational modes as shown above. There are two pairs of degenerate modes with a frequency of 1694 (cm-1) and 3590 (cm-1). The modes with a frequency of 1090 (cm-1) and 1694 (cm-1) correspond to bending vibrations and the modes with a frequency 3461 (cm-1) and 3590 (cm-1) correspond to bond stretch vibrations. The bond stretch vibration at 3461 (cm-1) is highly symmetric whilst the stretches with a frequency of 3590 (cm-1) are asymmetric. The bending vibration with a frequency of 1090 (cm-1) is known as the umbrella mode. Three bands would be expected to be seen with the two stretches at 3590 (cm-1) being too low in intensity. The bends with a frequency of 1694 (cm-1) are degenerate and only one band will be observed between the two. Hence the three observed bands would be at 1090 (cm-1), 1694 (cm-1) and 3461 (cm-1).

=== Charge analysis ===
[[File:Acc2518 charge analysis.png|The Gaussview generated atomic charges of ammonia.|250px]]

Nitrogen has a greater electronegativity than hydrogen and hence there is greater electron density distributed around the N atom in ammonia relative to hydrogen. This explains the negative charge on N and the positive charge on H.

==N2 molecule==

===Optimisation data===

{| class="wikitable"
|+ N2 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-109.52412868 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00000060 (au)
|-
|'''Point group'''
|D∞h
|-
|'''Bond length (N-N)'''
|1.11 (Å)
|}

<pre>
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
</pre>

<jmol><jmolApplet>
<title> Nitrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518 N2 OPTIMISATION.LOG</uploadedFileContents>
<script>frame 1.10</script>
</jmolApplet></jmol>
[[:File:ACC2518 N2 OPTIMISATION.LOG|Optimised N2 .log file (acc2518)]]

===Vibrations===
[[File:Acc2518 N2vibration.png|Nitrogen display vibrations screenshot|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 2457
|-
| '''Symmetry''' || SGG
|-
| '''Intensity''' (arbitrary units) || 0
|-
| '''Image'''|| [[File:Acc2518NitrogenVM.png|250px]]
|}
Using the 3N-5 rule for linear molecules, Nitrogen can be expected to have one vibrational mode but this mode has an IR intensity of zero since Nitrogen molecules are IR inactive. This is because they have no overall dipole.

===Charge analysis===
[[File:Acc2518nitrogen charges.png]]

Both nitrogen atoms have the same electronegativity so the charge is neutral on both atoms.

===CCDC search===
'''Unique identifier:''' [https://www.ccdc.cam.ac.uk/structures/Search?Ccdcid=VAMQAE&DatabaseToSearch=Published VAMQAE]

'''Deposition number:''' 1530121

The complex linked above contains nitrogen coordinated to cobalt with a N-N bond distance of 1.08 Å which is slightly shorter than the optimised N-N bond length, displayed above, of 1.11 Å (2.d.p). During the optimisation process for nitrogen, assumptions have to be made for the computational process to be carried out. Each assumption made will increase the uncertainty in measurable quantities such as the bond length. Hence, the computationally determined bond length from the optimisation is a model and may not fully reflect the true bond length or the bond length determined by a computational program considering slightly different assumptions.

It should also be considered that the optimisation gave a prediction for the N-N bond length in a nitrogen molecule whereas the molecule linked above contains a nitrogen molecule that is coordinated into a transition metal complex. A lone pair of electrons on one of the nitrogen atoms has been donated to a cobalt ion, this draws electron density away from the donating nitrogen atom and would therefore slightly increase the positive charge on this atom. This may cause the donating nitrogen atom to attract the electrons in the N-N bond more strongly which would then explain the shorter bond in the transition metal complex compared to the nitrogen molecule.

==H2 molecule==

===Optimisation data===
{| class="wikitable"
|+ H2 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-1.17853936 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00000017 (au)
|-
|'''Point group'''
|D∞h
|-
|'''Bond length (N-N)'''
|0.74 (Å)
|}

<pre>
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

</pre>

<jmol><jmolApplet>
<title> Hydrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518 H2 OPTIMISATION.LOG</uploadedFileContents>
<script>frame 1.7</script>
</jmolApplet></jmol>
[[:File:ACC2518 H2 OPTIMISATION.LOG|Optimised H2 .log file (acc2518)]]

===Vibrations===
[[File:Acc2518 H2vibration.png|Hydrogen display vibrations screenshot|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 4466
|-
| '''Symmetry''' || SGG
|-
| '''Intensity''' (arbitrary units) || 0
|-
| '''Image'''|| [[File:Acc2518HydrogenVM.png|250px]]
|}
Using the 3N-5 rule for linear molecules, hydrogen can be expected to have one vibrational mode but this mode has an IR intensity of zero since hydrogen molecules, like nitrogen molecules, are IR inactive.

===Charge analysis===
[[File:Acc2518hydrogen charges.png]]

Both hydrogen atoms have the same electronegativity so the charge is neutral on both atoms.

==The Haber-Bosch process==
N2 + 3H2 -> 2NH3

E(NH3)=-56.55776873

 '''2*E(NH3)''' =2*(-56.55776873)=-113.11553746

 '''E(N2)''' =-109.52412868

E(H2)=-1.17853936

 '''3*E(H2)''' =3*(-1.17853936) =-3.53561808

'''ΔE= 2*E(NH3) -[ E(N2) + 3*E(H2) ]'''= -0.05579069 ≈ -0.05579 au (5.d.p)

'''ΔE=-146.5 kJ/mol (1.d.p)'''

ΔE is negative which indicates that the gaseous reactants are less stable than the ammonia product since the reactants are at a higher energy than the product. Although this process is not necessarily entropically favourable with four reactant gaseous molecules forming two gaseous product molecules, the reaction has a significantly negative enthalpy change which reflects the result calculated above.

== Project molecule (NF3) ==

=== Optimisation data ===
{| class="wikitable"
|+ NF3 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-354.07131058 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00010256 (au)
|-
|'''Point group'''
|C3V
|-
|'''Bond length (N-F)'''
|1.38 (Å)
|-
|'''Bond angle (F-N-F)'''
|102(°)
|}
<pre>
Item Value Threshold Converged?
Maximum Force 0.000164 0.000450 YES
RMS Force 0.000108 0.000300 YES
Maximum Displacement 0.000612 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

<jmol><jmolApplet>
<title> NF3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518_NF3_OPTF_POP.LOG </uploadedFileContents>
<script>frame 1.7</script>
</jmolApplet></jmol>
[[:File:ACC2518_NF3_OPTF_POP.LOG|Optimised NF3 .log file (acc2518)]]

=== Vibrations ===
[[File:Acc2518 NF3 vibrations screenshot.png|The Gaussview "Display Vibrations" window of the optimised nitrogen trifluoride molecule.|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 482 || 482
|-
| '''Symmetry''' || E || E
|-
| '''Intensity''' (arbitrary units) || 1 || 1
|-
| '''Image'''|| [[File:Acc2518 NF3 VM1.png|300px]] || [[File:Acc2518 NF3 VM2.png|300px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 644|| 930
|-
| '''Symmetry''' || A1 || E
|-
| '''Intensity''' (arbitrary units) || 3 || 208
|-
| '''Image'''|| [[File:Acc2518 NF3 VM3.png|300px]] || [[File:Acc2518 NF3 VM4.png|300px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 930|| 1062
|-
| '''Symmetry''' || E || A1
|-
| '''Intensity''' (arbitrary units) || 208 || 40
|-
| '''Image'''|| [[File:Acc2518 NF3 VM5.png|300px]] || [[File:Acc2518 NF3 VM6.png|300px]]
|}

Nitrogen trifluoride has the same number of atoms as ammonia and so six vibrational modes can be predicted from the 3N-6 rule. There are also two pairs of degenerate modes with frequencies of 482 (cm-1) and 930 (cm-1). The modes with a frequency of 482 (cm-1) and 644(cm-1) correspond to bending vibrational modes and the modes with a frequency of 930 (cm-1) and 1062 (cm-1) correspond to stretching vibrational modes. The mode with a frequency of 1062 (cm-1) represents a symmetric stretch whilst the modes with a frequency of 930 (cm-1) represent asymmetric stretches. In contrast to ammonia, the highest frequency bond stretch of nitrogen trifluoride is the symmetric stretch.

Three bands can be expected in the NF3 IR spectrum at frequencies of 644 (cm-1) 930 (cm-1) and 1062 (cm-1). The bends at 482 (cm-1) will be too low in frequency to appear in the spectrum which starts at a frequency of 500 (cm-1). The stretches at 930 (cm-1) are degenerate and hence will only display one band between them. The band as 644 (cm-1) may not be clearly visible due its relative low intensity of 3 arbitrary units.

=== Charge analysis ===
[[File:Acc2518 NF3 charge analysis.png|The Gaussview generated atomic charges of ammonia.|250px]]

Fluorine has a greater electronegativity that nitrogen and therefore there is greater electron density distributed around the three fluorine atoms compared to the nitrogen atom. The three fluorine atoms are treated as equivalent which means that the magnitude of the positive charge on nitrogen is three times the magnitude of the negative charge on a single fluorine atom.

=== Molecular orbitals (MO) ===

The nitrogen atom contributes 7 electrons and each fluorine atom contributes 9 electrons which means that nitrogen trifluoride contains 34 electrons in total and hence 17 electron pairs. In the table below, a molecular orbital number of 1 would denote the molecular orbital that is deepest in energy. Therefore, orbital 17 represents the HOMO and orbital 18 represents the LUMO. All of the molecular orbitals shown below are occupied with the exception of the LUMO.

{| class="wikitable"
!Molecular orbital number
!Image
!Type of molecular orbital
!Energy (au)
!Extra details
|-
|18
|[[File:Acc2518 MO18.png|200px]]
|Antibonding
|0.01947
|There are nodes in the centre of the N-F bonds which indicates that the LUMO is an antibonding orbital with destructive inteference between phases of opposite sign. The nodes in the centre of all four atoms also indicate that this MO was formed from 2p atomic orbitals from both nitrogen and fluorine.
|-
|17
|[[File:Acc2518 MO17.png|200px]]
|Bonding
| -0.35162
| The phase denoted by the green region shows orbital overlap across all three N-H bonds which implies that the HOMO is a bonding orbital. This MO has been formed from 2p orbitals which explains the nodes observed in the centre of the F atoms.
|-
|16
|[[File:Acc2518 MO16.png|200px]]
|Non-bonding
| -0.42224
|There is no electron density along any of the bonds which is the key indicator that this is a non-bonding MO. Since the electron density is localised around the fluorine atoms, this MO appears to show lone electron pairs on these fluorine atoms. There is no electron density being shared between the fluorine atoms which suggests there is destructive interference preventing such an interaction.
|-
|15
|[[File:Acc2518 MO15.png|200px]]
|Bonding
| -0.43590
| As observed in the HOMO, there is electron density along all three bonds which indicates the bonding nature of the MO. However, in contrast to the HOMO, the electron density along the bonds is not in the same phase for each bond. There is also some constructive interference between two of the F atoms which appears to indicate a very partial π character between the two atoms. This also means that this interaction is the product of two 2p atomic orbitals on fluorine overlapping slightly in phase with each other.
|-
|5
|[[File:Acc2518 MO5.png|200px]]
| Bonding
| -1.35870
| This MO contains no nodes at all implying that it is bonding in nature. It is also formed from overlap of 2s orbitals, in phase, on all atoms since the entire molecule is encased in electron density as a result of the constructive interference. It cannot be formed from 1s orbitals which would be far lower in energy and will also only occupy the first 4 MOs since there are 8 1s electrons in NF3.
|}

== Bonus Molecule (CO2) ==

a

Acc2518

2019-03-04T14:18:36Z

Acc2518:

== NH3 molecule ==
=== Optimisation data ===
{| class="wikitable"
|+ NH3 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-56.55776873 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00000485 (au)
|-
|'''Point group'''
|C3V
|-
|'''Bond length (N-H)'''
|1.02 (Å)
|-
|'''Bond angle (H-N-H)'''
|106(°)
|}
<pre>
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
</pre>

<jmol><jmolApplet>
<title> NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518 NH3 OPTF POP.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>
[[:File:ACC2518 NH3 OPTF POP.LOG|Optimised NH3 .log file (acc2518)]]

=== Vibrations ===
[[File:Acc2518 vibrations screenshot.jpg|The Gaussview "Display Vibrations" window of the optimised ammonia molecule.|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 1090 || 1694
|-
| '''Symmetry''' || A1 || E
|-
| '''Intensity''' (arbitrary units) || 145 || 14
|-
| '''Image'''|| [[File:acc2518VM1.png|250px]] || [[File:acc2518VM2.png|300px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 1694|| 3461
|-
| '''Symmetry''' || E || A1
|-
| '''Intensity''' (arbitrary units) || 14 || 1
|-
| '''Image'''|| [[File:acc2518VM3.png|250px]] || [[File:acc2518VM4.png|275px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 3590|| 3590
|-
| '''Symmetry''' || E || E
|-
| '''Intensity''' (arbitrary units) || 0 || 0
|-
| '''Image'''|| [[File:acc2518VM5.png|275px]] || [[File:acc2518VM6.png|250px]]
|}

Using the 3N-6 rule, where N represents the number of atoms in a molecule, it is expected that ammonia will have six vibrational modes as shown above. There are two pairs of degenerate modes with a frequency of 1694 (cm-1) and 3590 (cm-1). The modes with a frequency of 1090 (cm-1) and 1694 (cm-1) correspond to bending vibrations and the modes with a frequency 3461 (cm-1) and 3590 (cm-1) correspond to bond stretch vibrations. The bond stretch vibration at 3461 (cm-1) is highly symmetric whilst the stretches with a frequency of 3590 (cm-1) are asymmetric. The bending vibration with a frequency of 1090 (cm-1) is known as the umbrella mode. Three bands would be expected to be seen with the two stretches at 3590 (cm-1) being too low in intensity. The bends with a frequency of 1694 (cm-1) are degenerate and only one band will be observed between the two. Hence the three observed bands would be at 1090 (cm-1), 1694 (cm-1) and 3461 (cm-1).

=== Charge analysis ===
[[File:Acc2518 charge analysis.png|The Gaussview generated atomic charges of ammonia.|250px]]

Nitrogen has a greater electronegativity than hydrogen and hence there is greater electron density distributed around the N atom in ammonia relative to hydrogen. This explains the negative charge on N and the positive charge on H.

==N2 molecule==

===Optimisation data===

{| class="wikitable"
|+ N2 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-109.52412868 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00000060 (au)
|-
|'''Point group'''
|D∞h
|-
|'''Bond length (N-N)'''
|1.11 (Å)
|}

<pre>
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
</pre>

<jmol><jmolApplet>
<title> Nitrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518 N2 OPTIMISATION.LOG</uploadedFileContents>
<script>frame 1.10</script>
</jmolApplet></jmol>
[[:File:ACC2518 N2 OPTIMISATION.LOG|Optimised N2 .log file (acc2518)]]

===Vibrations===
[[File:Acc2518 N2vibration.png|Nitrogen display vibrations screenshot|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 2457
|-
| '''Symmetry''' || SGG
|-
| '''Intensity''' (arbitrary units) || 0
|-
| '''Image'''|| [[File:Acc2518NitrogenVM.png|250px]]
|}
Using the 3N-5 rule for linear molecules, Nitrogen can be expected to have one vibrational mode but this mode has an IR intensity of zero since Nitrogen molecules are IR inactive. This is because they have no overall dipole.

===Charge analysis===
[[File:Acc2518nitrogen charges.png]]

Both nitrogen atoms have the same electronegativity so the charge is neutral on both atoms.

===CCDC search===
'''Unique identifier:''' [https://www.ccdc.cam.ac.uk/structures/Search?Ccdcid=VAMQAE&DatabaseToSearch=Published VAMQAE]

'''Deposition number:''' 1530121

The complex linked above contains nitrogen coordinated to cobalt with a N-N bond distance of 1.08 Å which is slightly shorter than the optimised N-N bond length, displayed above, of 1.11 Å (2.d.p). During the optimisation process for nitrogen, assumptions have to be made for the computational process to be carried out. Each assumption made will increase the uncertainty in measurable quantities such as the bond length. Hence, the computationally determined bond length from the optimisation is a model and may not fully reflect the true bond length or the bond length determined by a computational program considering slightly different assumptions.

It should also be considered that the optimisation gave a prediction for the N-N bond length in a nitrogen molecule whereas the molecule linked above contains a nitrogen molecule that is coordinated into a transition metal complex. A lone pair of electrons on one of the nitrogen atoms has been donated to a cobalt ion, this draws electron density away from the donating nitrogen atom and would therefore slightly increase the positive charge on this atom. This may cause the donating nitrogen atom to attract the electrons in the N-N bond more strongly which would then explain the shorter bond in the transition metal complex compared to the nitrogen molecule.

==H2 molecule==

===Optimisation data===
{| class="wikitable"
|+ H2 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-1.17853936 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00000017 (au)
|-
|'''Point group'''
|D∞h
|-
|'''Bond length (N-N)'''
|0.74 (Å)
|}

<pre>
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

</pre>

<jmol><jmolApplet>
<title> Hydrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518 H2 OPTIMISATION.LOG</uploadedFileContents>
<script>frame 1.7</script>
</jmolApplet></jmol>
[[:File:ACC2518 H2 OPTIMISATION.LOG|Optimised H2 .log file (acc2518)]]

===Vibrations===
[[File:Acc2518 H2vibration.png|Hydrogen display vibrations screenshot|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 4466
|-
| '''Symmetry''' || SGG
|-
| '''Intensity''' (arbitrary units) || 0
|-
| '''Image'''|| [[File:Acc2518HydrogenVM.png|250px]]
|}
Using the 3N-5 rule for linear molecules, hydrogen can be expected to have one vibrational mode but this mode has an IR intensity of zero since hydrogen molecules, like nitrogen molecules, are IR inactive.

===Charge analysis===
[[File:Acc2518hydrogen charges.png]]

Both hydrogen atoms have the same electronegativity so the charge is neutral on both atoms.

==The Haber-Bosch process==
N2 + 3H2 -> 2NH3

E(NH3)=-56.55776873

 '''2*E(NH3)''' =2*(-56.55776873)=-113.11553746

 '''E(N2)''' =-109.52412868

E(H2)=-1.17853936

 '''3*E(H2)''' =3*(-1.17853936) =-3.53561808

'''ΔE= 2*E(NH3) -[ E(N2) + 3*E(H2) ]'''= -0.05579069 ≈ -0.05579 au (5.d.p)

'''ΔE=-146.5 kJ/mol (1.d.p)'''

ΔE is negative which indicates that the gaseous reactants are less stable than the ammonia product since the reactants are at a higher energy than the product. Although this process is not necessarily entropically favourable with four reactant gaseous molecules forming two gaseous product molecules, the reaction has a significantly negative enthalpy change which reflects the result calculated above.

== Project molecule (NF3) ==

=== Optimisation data ===
{| class="wikitable"
|+ NF3 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-354.07131058 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00010256 (au)
|-
|'''Point group'''
|C3V
|-
|'''Bond length (N-F)'''
|1.38 (Å)
|-
|'''Bond angle (F-N-F)'''
|102(°)
|}
<pre>
Item Value Threshold Converged?
Maximum Force 0.000164 0.000450 YES
RMS Force 0.000108 0.000300 YES
Maximum Displacement 0.000612 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

<jmol><jmolApplet>
<title> NF3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518_NF3_OPTF_POP.LOG </uploadedFileContents>
<script>frame 1.7</script>
</jmolApplet></jmol>
[[:File:ACC2518_NF3_OPTF_POP.LOG|Optimised NF3 .log file (acc2518)]]

=== Vibrations ===
[[File:Acc2518 NF3 vibrations screenshot.png|The Gaussview "Display Vibrations" window of the optimised nitrogen trifluoride molecule.|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 482 || 482
|-
| '''Symmetry''' || E || E
|-
| '''Intensity''' (arbitrary units) || 1 || 1
|-
| '''Image'''|| [[File:Acc2518 NF3 VM1.png|300px]] || [[File:Acc2518 NF3 VM2.png|300px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 644|| 930
|-
| '''Symmetry''' || A1 || E
|-
| '''Intensity''' (arbitrary units) || 3 || 208
|-
| '''Image'''|| [[File:Acc2518 NF3 VM3.png|300px]] || [[File:Acc2518 NF3 VM4.png|300px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 930|| 1062
|-
| '''Symmetry''' || E || A1
|-
| '''Intensity''' (arbitrary units) || 208 || 40
|-
| '''Image'''|| [[File:Acc2518 NF3 VM5.png|300px]] || [[File:Acc2518 NF3 VM6.png|300px]]
|}

Nitrogen trifluoride has the same number of atoms as ammonia and so six vibrational modes can be predicted from the 3N-6 rule. There are also two pairs of degenerate modes with frequencies of 482 (cm-1) and 930 (cm-1). The modes with a frequency of 482 (cm-1) and 644(cm-1) correspond to bending vibrational modes and the modes with a frequency of 930 (cm-1) and 1062 (cm-1) correspond to stretching vibrational modes. The mode with a frequency of 1062 (cm-1) represents a symmetric stretch whilst the modes with a frequency of 930 (cm-1) represent asymmetric stretches. In contrast to ammonia, the highest frequency bond stretch of nitrogen trifluoride is the symmetric stretch.

Three bands can be expected in the NF3 IR spectrum at frequencies of 644 (cm-1) 930 (cm-1) and 1062 (cm-1). The bends at 482 (cm-1) will be too low in frequency to appear in the spectrum which starts at a frequency of 500 (cm-1). The stretches at 930 (cm-1) are degenerate and hence will only display one band between them. The band as 644 (cm-1) may not be clearly visible due its relative low intensity of 3 arbitrary units.

=== Charge analysis ===
[[File:Acc2518 NF3 charge analysis.png|The Gaussview generated atomic charges of ammonia.|250px]]

Fluorine has a greater electronegativity that nitrogen and therefore there is greater electron density distributed around the three fluorine atoms compared to the nitrogen atom. The three fluorine atoms are treated as equivalent which means that the magnitude of the positive charge on nitrogen is three times the magnitude of the negative charge on a single fluorine atom.

=== Molecular orbitals (MO) ===

The nitrogen atom contributes 7 electrons and each fluorine atom contributes 9 electrons which means that nitrogen trifluoride contains 34 electrons in total and hence 17 electron pairs. In the table below, a molecular orbital number of 1 would denote the molecular orbital that is deepest in energy. Therefore, orbital 17 represents the HOMO and orbital 18 represents the LUMO. All of the molecular orbitals shown below are occupied with the exception of the LUMO.

{| class="wikitable"
!Molecular orbital number
!Image
!Type of molecular orbital
!Energy (au)
!Extra details
|-
|18
|[[File:Acc2518 MO18.png|200px]]
|Antibonding
|0.01947
|There are nodes in the centre of the N-F bonds which indicates that the LUMO is an antibonding orbital with destructive inteference between phases of opposite sign. The nodes in the centre of all four atoms also indicate that this MO was formed from 2p atomic orbitals from both nitrogen and fluorine.
|-
|17
|[[File:Acc2518 MO17.png|200px]]
|Bonding
| -0.35162
| The phase denoted by the green region shows orbital overlap across all three N-H bonds which implies that the HOMO is a bonding orbital. This MO has been formed from 2p orbitals which explains the nodes observed in the centre of the F atoms.
|-
|16
|[[File:Acc2518 MO16.png|200px]]
|Non-bonding
| -0.42224
|There is no electron density along any of the bonds which is the key indicator that this is a non-bonding MO. Since the electron density is localised around the fluorine atoms, this MO appears to show lone electron pairs on these fluorine atoms. There is no electron density being shared between the fluorine atoms which suggests there is destructive interference preventing such an interaction.
|-
|15
|[[File:Acc2518 MO15.png|200px]]
|Bonding
| -0.43590
| As observed in the HOMO, there is electron density along all three bonds which indicates the bonding nature of the MO. However, in contrast to the HOMO, the electron density along the bonds is not in the same phase for each bond. There is also some constructive interference between two of the F atoms which appears to indicate a very partial π character between the two atoms. This also means that this interaction is the product of two 2p atomic orbitals on fluorine overlapping slightly in phase with each other.
|-
|5
|[[File:Acc2518 MO5.png|200px]]
| Bonding
| -1.35870
| This MO contains no nodes at all implying that it is bonding in nature. It is also formed from overlap of 2s orbitals, in phase, on all atoms since the entire molecule is encased in electron density as a result of the constructive interference. It cannot be formed from 1s orbitals which would be far lower in energy and will also only occupy the first 4 MOs since there are 8 1s electrons in NF3.
|}

== Bonus Molecule (CO2 ==

a

Acc2518

2019-03-04T14:17:48Z

Acc2518: /* Molecular orbitals (MO) */

== NH3 molecule ==
=== Optimisation data ===
{| class="wikitable"
|+ NH3 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-56.55776873 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00000485 (au)
|-
|'''Point group'''
|C3V
|-
|'''Bond length (N-H)'''
|1.02 (Å)
|-
|'''Bond angle (H-N-H)'''
|106(°)
|}
<pre>
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
</pre>

<jmol><jmolApplet>
<title> NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518 NH3 OPTF POP.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>
[[:File:ACC2518 NH3 OPTF POP.LOG|Optimised NH3 .log file (acc2518)]]

=== Vibrations ===
[[File:Acc2518 vibrations screenshot.jpg|The Gaussview "Display Vibrations" window of the optimised ammonia molecule.|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 1090 || 1694
|-
| '''Symmetry''' || A1 || E
|-
| '''Intensity''' (arbitrary units) || 145 || 14
|-
| '''Image'''|| [[File:acc2518VM1.png|250px]] || [[File:acc2518VM2.png|300px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 1694|| 3461
|-
| '''Symmetry''' || E || A1
|-
| '''Intensity''' (arbitrary units) || 14 || 1
|-
| '''Image'''|| [[File:acc2518VM3.png|250px]] || [[File:acc2518VM4.png|275px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 3590|| 3590
|-
| '''Symmetry''' || E || E
|-
| '''Intensity''' (arbitrary units) || 0 || 0
|-
| '''Image'''|| [[File:acc2518VM5.png|275px]] || [[File:acc2518VM6.png|250px]]
|}

Using the 3N-6 rule, where N represents the number of atoms in a molecule, it is expected that ammonia will have six vibrational modes as shown above. There are two pairs of degenerate modes with a frequency of 1694 (cm-1) and 3590 (cm-1). The modes with a frequency of 1090 (cm-1) and 1694 (cm-1) correspond to bending vibrations and the modes with a frequency 3461 (cm-1) and 3590 (cm-1) correspond to bond stretch vibrations. The bond stretch vibration at 3461 (cm-1) is highly symmetric whilst the stretches with a frequency of 3590 (cm-1) are asymmetric. The bending vibration with a frequency of 1090 (cm-1) is known as the umbrella mode. Three bands would be expected to be seen with the two stretches at 3590 (cm-1) being too low in intensity. The bends with a frequency of 1694 (cm-1) are degenerate and only one band will be observed between the two. Hence the three observed bands would be at 1090 (cm-1), 1694 (cm-1) and 3461 (cm-1).

=== Charge analysis ===
[[File:Acc2518 charge analysis.png|The Gaussview generated atomic charges of ammonia.|250px]]

Nitrogen has a greater electronegativity than hydrogen and hence there is greater electron density distributed around the N atom in ammonia relative to hydrogen. This explains the negative charge on N and the positive charge on H.

==N2 molecule==

===Optimisation data===

{| class="wikitable"
|+ N2 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-109.52412868 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00000060 (au)
|-
|'''Point group'''
|D∞h
|-
|'''Bond length (N-N)'''
|1.11 (Å)
|}

<pre>
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
</pre>

<jmol><jmolApplet>
<title> Nitrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518 N2 OPTIMISATION.LOG</uploadedFileContents>
<script>frame 1.10</script>
</jmolApplet></jmol>
[[:File:ACC2518 N2 OPTIMISATION.LOG|Optimised N2 .log file (acc2518)]]

===Vibrations===
[[File:Acc2518 N2vibration.png|Nitrogen display vibrations screenshot|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 2457
|-
| '''Symmetry''' || SGG
|-
| '''Intensity''' (arbitrary units) || 0
|-
| '''Image'''|| [[File:Acc2518NitrogenVM.png|250px]]
|}
Using the 3N-5 rule for linear molecules, Nitrogen can be expected to have one vibrational mode but this mode has an IR intensity of zero since Nitrogen molecules are IR inactive. This is because they have no overall dipole.

===Charge analysis===
[[File:Acc2518nitrogen charges.png]]

Both nitrogen atoms have the same electronegativity so the charge is neutral on both atoms.

===CCDC search===
'''Unique identifier:''' [https://www.ccdc.cam.ac.uk/structures/Search?Ccdcid=VAMQAE&DatabaseToSearch=Published VAMQAE]

'''Deposition number:''' 1530121

The complex linked above contains nitrogen coordinated to cobalt with a N-N bond distance of 1.08 Å which is slightly shorter than the optimised N-N bond length, displayed above, of 1.11 Å (2.d.p). During the optimisation process for nitrogen, assumptions have to be made for the computational process to be carried out. Each assumption made will increase the uncertainty in measurable quantities such as the bond length. Hence, the computationally determined bond length from the optimisation is a model and may not fully reflect the true bond length or the bond length determined by a computational program considering slightly different assumptions.

It should also be considered that the optimisation gave a prediction for the N-N bond length in a nitrogen molecule whereas the molecule linked above contains a nitrogen molecule that is coordinated into a transition metal complex. A lone pair of electrons on one of the nitrogen atoms has been donated to a cobalt ion, this draws electron density away from the donating nitrogen atom and would therefore slightly increase the positive charge on this atom. This may cause the donating nitrogen atom to attract the electrons in the N-N bond more strongly which would then explain the shorter bond in the transition metal complex compared to the nitrogen molecule.

==H2 molecule==

===Optimisation data===
{| class="wikitable"
|+ H2 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-1.17853936 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00000017 (au)
|-
|'''Point group'''
|D∞h
|-
|'''Bond length (N-N)'''
|0.74 (Å)
|}

<pre>
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

</pre>

<jmol><jmolApplet>
<title> Hydrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518 H2 OPTIMISATION.LOG</uploadedFileContents>
<script>frame 1.7</script>
</jmolApplet></jmol>
[[:File:ACC2518 H2 OPTIMISATION.LOG|Optimised H2 .log file (acc2518)]]

===Vibrations===
[[File:Acc2518 H2vibration.png|Hydrogen display vibrations screenshot|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 4466
|-
| '''Symmetry''' || SGG
|-
| '''Intensity''' (arbitrary units) || 0
|-
| '''Image'''|| [[File:Acc2518HydrogenVM.png|250px]]
|}
Using the 3N-5 rule for linear molecules, hydrogen can be expected to have one vibrational mode but this mode has an IR intensity of zero since hydrogen molecules, like nitrogen molecules, are IR inactive.

===Charge analysis===
[[File:Acc2518hydrogen charges.png]]

Both hydrogen atoms have the same electronegativity so the charge is neutral on both atoms.

==The Haber-Bosch process==
N2 + 3H2 -> 2NH3

E(NH3)=-56.55776873

 '''2*E(NH3)''' =2*(-56.55776873)=-113.11553746

 '''E(N2)''' =-109.52412868

E(H2)=-1.17853936

 '''3*E(H2)''' =3*(-1.17853936) =-3.53561808

'''ΔE= 2*E(NH3) -[ E(N2) + 3*E(H2) ]'''= -0.05579069 ≈ -0.05579 au (5.d.p)

'''ΔE=-146.5 kJ/mol (1.d.p)'''

ΔE is negative which indicates that the gaseous reactants are less stable than the ammonia product since the reactants are at a higher energy than the product. Although this process is not necessarily entropically favourable with four reactant gaseous molecules forming two gaseous product molecules, the reaction has a significantly negative enthalpy change which reflects the result calculated above.

== Project molecule (NF3) ==

=== Optimisation data ===
{| class="wikitable"
|+ NF3 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-354.07131058 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00010256 (au)
|-
|'''Point group'''
|C3V
|-
|'''Bond length (N-F)'''
|1.38 (Å)
|-
|'''Bond angle (F-N-F)'''
|102(°)
|}
<pre>
Item Value Threshold Converged?
Maximum Force 0.000164 0.000450 YES
RMS Force 0.000108 0.000300 YES
Maximum Displacement 0.000612 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

<jmol><jmolApplet>
<title> NF3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518_NF3_OPTF_POP.LOG </uploadedFileContents>
<script>frame 1.7</script>
</jmolApplet></jmol>
[[:File:ACC2518_NF3_OPTF_POP.LOG|Optimised NF3 .log file (acc2518)]]

=== Vibrations ===
[[File:Acc2518 NF3 vibrations screenshot.png|The Gaussview "Display Vibrations" window of the optimised nitrogen trifluoride molecule.|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 482 || 482
|-
| '''Symmetry''' || E || E
|-
| '''Intensity''' (arbitrary units) || 1 || 1
|-
| '''Image'''|| [[File:Acc2518 NF3 VM1.png|300px]] || [[File:Acc2518 NF3 VM2.png|300px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 644|| 930
|-
| '''Symmetry''' || A1 || E
|-
| '''Intensity''' (arbitrary units) || 3 || 208
|-
| '''Image'''|| [[File:Acc2518 NF3 VM3.png|300px]] || [[File:Acc2518 NF3 VM4.png|300px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 930|| 1062
|-
| '''Symmetry''' || E || A1
|-
| '''Intensity''' (arbitrary units) || 208 || 40
|-
| '''Image'''|| [[File:Acc2518 NF3 VM5.png|300px]] || [[File:Acc2518 NF3 VM6.png|300px]]
|}

Nitrogen trifluoride has the same number of atoms as ammonia and so six vibrational modes can be predicted from the 3N-6 rule. There are also two pairs of degenerate modes with frequencies of 482 (cm-1) and 930 (cm-1). The modes with a frequency of 482 (cm-1) and 644(cm-1) correspond to bending vibrational modes and the modes with a frequency of 930 (cm-1) and 1062 (cm-1) correspond to stretching vibrational modes. The mode with a frequency of 1062 (cm-1) represents a symmetric stretch whilst the modes with a frequency of 930 (cm-1) represent asymmetric stretches. In contrast to ammonia, the highest frequency bond stretch of nitrogen trifluoride is the symmetric stretch.

Three bands can be expected in the NF3 IR spectrum at frequencies of 644 (cm-1) 930 (cm-1) and 1062 (cm-1). The bends at 482 (cm-1) will be too low in frequency to appear in the spectrum which starts at a frequency of 500 (cm-1). The stretches at 930 (cm-1) are degenerate and hence will only display one band between them. The band as 644 (cm-1) may not be clearly visible due its relative low intensity of 3 arbitrary units.

=== Charge analysis ===
[[File:Acc2518 NF3 charge analysis.png|The Gaussview generated atomic charges of ammonia.|250px]]

Fluorine has a greater electronegativity that nitrogen and therefore there is greater electron density distributed around the three fluorine atoms compared to the nitrogen atom. The three fluorine atoms are treated as equivalent which means that the magnitude of the positive charge on nitrogen is three times the magnitude of the negative charge on a single fluorine atom.

=== Molecular orbitals (MO) ===

The nitrogen atom contributes 7 electrons and each fluorine atom contributes 9 electrons which means that nitrogen trifluoride contains 34 electrons in total and hence 17 electron pairs. In the table below, a molecular orbital number of 1 would denote the molecular orbital that is deepest in energy. Therefore, orbital 17 represents the HOMO and orbital 18 represents the LUMO. All of the molecular orbitals shown below are occupied with the exception of the LUMO.

{| class="wikitable"
!Molecular orbital number
!Image
!Type of molecular orbital
!Energy (au)
!Extra details
|-
|18
|[[File:Acc2518 MO18.png|200px]]
|Antibonding
|0.01947
|There are nodes in the centre of the N-F bonds which indicates that the LUMO is an antibonding orbital with destructive inteference between phases of opposite sign. The nodes in the centre of all four atoms also indicate that this MO was formed from 2p atomic orbitals from both nitrogen and fluorine.
|-
|17
|[[File:Acc2518 MO17.png|200px]]
|Bonding
| -0.35162
| The phase denoted by the green region shows orbital overlap across all three N-H bonds which implies that the HOMO is a bonding orbital. This MO has been formed from 2p orbitals which explains the nodes observed in the centre of the F atoms.
|-
|16
|[[File:Acc2518 MO16.png|200px]]
|Non-bonding
| -0.42224
|There is no electron density along any of the bonds which is the key indicator that this is a non-bonding MO. Since the electron density is localised around the fluorine atoms, this MO appears to show lone electron pairs on these fluorine atoms. There is no electron density being shared between the fluorine atoms which suggests there is destructive interference preventing such an interaction.
|-
|15
|[[File:Acc2518 MO15.png|200px]]
|Bonding
| -0.43590
| As observed in the HOMO, there is electron density along all three bonds which indicates the bonding nature of the MO. However, in contrast to the HOMO, the electron density along the bonds is not in the same phase for each bond. There is also some constructive interference between two of the F atoms which appears to indicate a very partial π character between the two atoms. This also means that this interaction is the product of two 2p atomic orbitals on fluorine overlapping slightly in phase with each other.
|-
|5
|[[File:Acc2518 MO5.png|200px]]
| Bonding
| -1.35870
| This MO contains no nodes at all implying that it is bonding in nature. It is also formed from overlap of 2s orbitals, in phase, on all atoms since the entire molecule is encased in electron density as a result of the constructive interference. It cannot be formed from 1s orbitals which would be far lower in energy and will also only occupy the first 4 MOs since there are 8 1s electrons in NF3.
|}

== Bonus Molecule (CO2 ==

Acc2518

2019-03-04T14:16:00Z

Acc2518: /* Optimisation data */

== NH3 molecule ==
=== Optimisation data ===
{| class="wikitable"
|+ NH3 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-56.55776873 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00000485 (au)
|-
|'''Point group'''
|C3V
|-
|'''Bond length (N-H)'''
|1.02 (Å)
|-
|'''Bond angle (H-N-H)'''
|106(°)
|}
<pre>
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
</pre>

<jmol><jmolApplet>
<title> NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518 NH3 OPTF POP.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>
[[:File:ACC2518 NH3 OPTF POP.LOG|Optimised NH3 .log file (acc2518)]]

=== Vibrations ===
[[File:Acc2518 vibrations screenshot.jpg|The Gaussview "Display Vibrations" window of the optimised ammonia molecule.|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 1090 || 1694
|-
| '''Symmetry''' || A1 || E
|-
| '''Intensity''' (arbitrary units) || 145 || 14
|-
| '''Image'''|| [[File:acc2518VM1.png|250px]] || [[File:acc2518VM2.png|300px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 1694|| 3461
|-
| '''Symmetry''' || E || A1
|-
| '''Intensity''' (arbitrary units) || 14 || 1
|-
| '''Image'''|| [[File:acc2518VM3.png|250px]] || [[File:acc2518VM4.png|275px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 3590|| 3590
|-
| '''Symmetry''' || E || E
|-
| '''Intensity''' (arbitrary units) || 0 || 0
|-
| '''Image'''|| [[File:acc2518VM5.png|275px]] || [[File:acc2518VM6.png|250px]]
|}

Using the 3N-6 rule, where N represents the number of atoms in a molecule, it is expected that ammonia will have six vibrational modes as shown above. There are two pairs of degenerate modes with a frequency of 1694 (cm-1) and 3590 (cm-1). The modes with a frequency of 1090 (cm-1) and 1694 (cm-1) correspond to bending vibrations and the modes with a frequency 3461 (cm-1) and 3590 (cm-1) correspond to bond stretch vibrations. The bond stretch vibration at 3461 (cm-1) is highly symmetric whilst the stretches with a frequency of 3590 (cm-1) are asymmetric. The bending vibration with a frequency of 1090 (cm-1) is known as the umbrella mode. Three bands would be expected to be seen with the two stretches at 3590 (cm-1) being too low in intensity. The bends with a frequency of 1694 (cm-1) are degenerate and only one band will be observed between the two. Hence the three observed bands would be at 1090 (cm-1), 1694 (cm-1) and 3461 (cm-1).

=== Charge analysis ===
[[File:Acc2518 charge analysis.png|The Gaussview generated atomic charges of ammonia.|250px]]

Nitrogen has a greater electronegativity than hydrogen and hence there is greater electron density distributed around the N atom in ammonia relative to hydrogen. This explains the negative charge on N and the positive charge on H.

==N2 molecule==

===Optimisation data===

{| class="wikitable"
|+ N2 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-109.52412868 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00000060 (au)
|-
|'''Point group'''
|D∞h
|-
|'''Bond length (N-N)'''
|1.11 (Å)
|}

<pre>
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
</pre>

<jmol><jmolApplet>
<title> Nitrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518 N2 OPTIMISATION.LOG</uploadedFileContents>
<script>frame 1.10</script>
</jmolApplet></jmol>
[[:File:ACC2518 N2 OPTIMISATION.LOG|Optimised N2 .log file (acc2518)]]

===Vibrations===
[[File:Acc2518 N2vibration.png|Nitrogen display vibrations screenshot|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 2457
|-
| '''Symmetry''' || SGG
|-
| '''Intensity''' (arbitrary units) || 0
|-
| '''Image'''|| [[File:Acc2518NitrogenVM.png|250px]]
|}
Using the 3N-5 rule for linear molecules, Nitrogen can be expected to have one vibrational mode but this mode has an IR intensity of zero since Nitrogen molecules are IR inactive. This is because they have no overall dipole.

===Charge analysis===
[[File:Acc2518nitrogen charges.png]]

Both nitrogen atoms have the same electronegativity so the charge is neutral on both atoms.

===CCDC search===
'''Unique identifier:''' [https://www.ccdc.cam.ac.uk/structures/Search?Ccdcid=VAMQAE&DatabaseToSearch=Published VAMQAE]

'''Deposition number:''' 1530121

The complex linked above contains nitrogen coordinated to cobalt with a N-N bond distance of 1.08 Å which is slightly shorter than the optimised N-N bond length, displayed above, of 1.11 Å (2.d.p). During the optimisation process for nitrogen, assumptions have to be made for the computational process to be carried out. Each assumption made will increase the uncertainty in measurable quantities such as the bond length. Hence, the computationally determined bond length from the optimisation is a model and may not fully reflect the true bond length or the bond length determined by a computational program considering slightly different assumptions.

It should also be considered that the optimisation gave a prediction for the N-N bond length in a nitrogen molecule whereas the molecule linked above contains a nitrogen molecule that is coordinated into a transition metal complex. A lone pair of electrons on one of the nitrogen atoms has been donated to a cobalt ion, this draws electron density away from the donating nitrogen atom and would therefore slightly increase the positive charge on this atom. This may cause the donating nitrogen atom to attract the electrons in the N-N bond more strongly which would then explain the shorter bond in the transition metal complex compared to the nitrogen molecule.

==H2 molecule==

===Optimisation data===
{| class="wikitable"
|+ H2 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-1.17853936 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00000017 (au)
|-
|'''Point group'''
|D∞h
|-
|'''Bond length (N-N)'''
|0.74 (Å)
|}

<pre>
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

</pre>

<jmol><jmolApplet>
<title> Hydrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518 H2 OPTIMISATION.LOG</uploadedFileContents>
<script>frame 1.7</script>
</jmolApplet></jmol>
[[:File:ACC2518 H2 OPTIMISATION.LOG|Optimised H2 .log file (acc2518)]]

===Vibrations===
[[File:Acc2518 H2vibration.png|Hydrogen display vibrations screenshot|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 4466
|-
| '''Symmetry''' || SGG
|-
| '''Intensity''' (arbitrary units) || 0
|-
| '''Image'''|| [[File:Acc2518HydrogenVM.png|250px]]
|}
Using the 3N-5 rule for linear molecules, hydrogen can be expected to have one vibrational mode but this mode has an IR intensity of zero since hydrogen molecules, like nitrogen molecules, are IR inactive.

===Charge analysis===
[[File:Acc2518hydrogen charges.png]]

Both hydrogen atoms have the same electronegativity so the charge is neutral on both atoms.

==The Haber-Bosch process==
N2 + 3H2 -> 2NH3

E(NH3)=-56.55776873

 '''2*E(NH3)''' =2*(-56.55776873)=-113.11553746

 '''E(N2)''' =-109.52412868

E(H2)=-1.17853936

 '''3*E(H2)''' =3*(-1.17853936) =-3.53561808

'''ΔE= 2*E(NH3) -[ E(N2) + 3*E(H2) ]'''= -0.05579069 ≈ -0.05579 au (5.d.p)

'''ΔE=-146.5 kJ/mol (1.d.p)'''

ΔE is negative which indicates that the gaseous reactants are less stable than the ammonia product since the reactants are at a higher energy than the product. Although this process is not necessarily entropically favourable with four reactant gaseous molecules forming two gaseous product molecules, the reaction has a significantly negative enthalpy change which reflects the result calculated above.

== Project molecule (NF3) ==

=== Optimisation data ===
{| class="wikitable"
|+ NF3 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-354.07131058 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00010256 (au)
|-
|'''Point group'''
|C3V
|-
|'''Bond length (N-F)'''
|1.38 (Å)
|-
|'''Bond angle (F-N-F)'''
|102(°)
|}
<pre>
Item Value Threshold Converged?
Maximum Force 0.000164 0.000450 YES
RMS Force 0.000108 0.000300 YES
Maximum Displacement 0.000612 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

<jmol><jmolApplet>
<title> NF3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518_NF3_OPTF_POP.LOG </uploadedFileContents>
<script>frame 1.7</script>
</jmolApplet></jmol>
[[:File:ACC2518_NF3_OPTF_POP.LOG|Optimised NF3 .log file (acc2518)]]

=== Vibrations ===
[[File:Acc2518 NF3 vibrations screenshot.png|The Gaussview "Display Vibrations" window of the optimised nitrogen trifluoride molecule.|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 482 || 482
|-
| '''Symmetry''' || E || E
|-
| '''Intensity''' (arbitrary units) || 1 || 1
|-
| '''Image'''|| [[File:Acc2518 NF3 VM1.png|300px]] || [[File:Acc2518 NF3 VM2.png|300px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 644|| 930
|-
| '''Symmetry''' || A1 || E
|-
| '''Intensity''' (arbitrary units) || 3 || 208
|-
| '''Image'''|| [[File:Acc2518 NF3 VM3.png|300px]] || [[File:Acc2518 NF3 VM4.png|300px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 930|| 1062
|-
| '''Symmetry''' || E || A1
|-
| '''Intensity''' (arbitrary units) || 208 || 40
|-
| '''Image'''|| [[File:Acc2518 NF3 VM5.png|300px]] || [[File:Acc2518 NF3 VM6.png|300px]]
|}

Nitrogen trifluoride has the same number of atoms as ammonia and so six vibrational modes can be predicted from the 3N-6 rule. There are also two pairs of degenerate modes with frequencies of 482 (cm-1) and 930 (cm-1). The modes with a frequency of 482 (cm-1) and 644(cm-1) correspond to bending vibrational modes and the modes with a frequency of 930 (cm-1) and 1062 (cm-1) correspond to stretching vibrational modes. The mode with a frequency of 1062 (cm-1) represents a symmetric stretch whilst the modes with a frequency of 930 (cm-1) represent asymmetric stretches. In contrast to ammonia, the highest frequency bond stretch of nitrogen trifluoride is the symmetric stretch.

Three bands can be expected in the NF3 IR spectrum at frequencies of 644 (cm-1) 930 (cm-1) and 1062 (cm-1). The bends at 482 (cm-1) will be too low in frequency to appear in the spectrum which starts at a frequency of 500 (cm-1). The stretches at 930 (cm-1) are degenerate and hence will only display one band between them. The band as 644 (cm-1) may not be clearly visible due its relative low intensity of 3 arbitrary units.

=== Charge analysis ===
[[File:Acc2518 NF3 charge analysis.png|The Gaussview generated atomic charges of ammonia.|250px]]

Fluorine has a greater electronegativity that nitrogen and therefore there is greater electron density distributed around the three fluorine atoms compared to the nitrogen atom. The three fluorine atoms are treated as equivalent which means that the magnitude of the positive charge on nitrogen is three times the magnitude of the negative charge on a single fluorine atom.

=== Molecular orbitals (MO) ===

The nitrogen atom contributes 7 electrons and each fluorine atom contributes 9 electrons which means that nitrogen trifluoride contains 34 electrons in total and hence 17 electron pairs. In the table below, a molecular orbital number of 1 would denote the molecular orbital that is deepest in energy. Therefore, orbital 17 represents the HOMO and orbital 18 represents the LUMO. All of the molecular orbitals shown below are occupied with the exception of the LUMO.

{| class="wikitable"
!Molecular orbital number
!Image
!Type of molecular orbital
!Energy (au)
!Extra details
|-
|18
|[[File:Acc2518 MO18.png|200px]]
|Antibonding
|0.01947
|There are nodes in the centre of the N-F bonds which indicates that the LUMO is an antibonding orbital with destructive inteference between phases of opposite sign. The nodes in the centre of all four atoms also indicate that this MO was formed from 2p atomic orbitals from both nitrogen and fluorine.
|-
|17
|[[File:Acc2518 MO17.png|200px]]
|Bonding
| -0.35162
| The phase denoted by the green region shows orbital overlap across all three N-H bonds which implies that the HOMO is a bonding orbital. This MO has been formed from 2p orbitals which explains the nodes observed in the centre of the F atoms.
|-
|16
|[[File:Acc2518 MO16.png|200px]]
|Non-bonding
| -0.42224
|There is no electron density along any of the bonds which is the key indicator that this is a non-bonding MO. Since the electron density is localised around the fluorine atoms, this MO appears to show lone electron pairs on these fluorine atoms. There is no electron density being shared between the fluorine atoms which suggests there is destructive interference preventing such an interaction.
|-
|15
|[[File:Acc2518 MO15.png|200px]]
|Bonding
| -0.43590
| As observed in the HOMO, there is electron density along all three bonds which indicates the bonding nature of the MO. However, in contrast to the HOMO, the electron density along the bonds is not in the same phase for each bond. There is also some constructive interference between two of the F atoms which appears to indicate a very partial π character between the two atoms. This also means that this interaction is the product of two 2p atomic orbitals on fluorine overlapping slightly in phase with each other.
|-
|5
|[[File:Acc2518 MO5.png|200px]]
| Bonding
| -1.35870
| This MO contains no nodes at all implying that it is bonding in nature. It is also formed from overlap of 2s orbitals, in phase, on all atoms since the entire molecule is encased in electron density as a result of the constructive interference. It cannot be formed from 1s orbitals which would be far lower in energy and will also only occupy the first 4 MOs since there are 8 1s electrons in NF3.
|}

Acc2518

2019-03-04T14:14:20Z

Acc2518: /* CCDC search */

== NH3 molecule ==
=== Optimisation data ===
{| class="wikitable"
|+ NH3 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-56.55776873 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00000485 (au)
|-
|'''Point group'''
|C3V
|-
|'''Bond length (N-H)'''
|1.02 (Å)
|-
|'''Bond angle (H-N-H)'''
|106(°)
|}
<pre>
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
</pre>

<jmol><jmolApplet>
<title> NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518 NH3 OPTF POP.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>
[[:File:ACC2518 NH3 OPTF POP.LOG|Optimised NH3 .log file (acc2518)]]

=== Vibrations ===
[[File:Acc2518 vibrations screenshot.jpg|The Gaussview "Display Vibrations" window of the optimised ammonia molecule.|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 1090 || 1694
|-
| '''Symmetry''' || A1 || E
|-
| '''Intensity''' (arbitrary units) || 145 || 14
|-
| '''Image'''|| [[File:acc2518VM1.png|250px]] || [[File:acc2518VM2.png|300px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 1694|| 3461
|-
| '''Symmetry''' || E || A1
|-
| '''Intensity''' (arbitrary units) || 14 || 1
|-
| '''Image'''|| [[File:acc2518VM3.png|250px]] || [[File:acc2518VM4.png|275px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 3590|| 3590
|-
| '''Symmetry''' || E || E
|-
| '''Intensity''' (arbitrary units) || 0 || 0
|-
| '''Image'''|| [[File:acc2518VM5.png|275px]] || [[File:acc2518VM6.png|250px]]
|}

Using the 3N-6 rule, where N represents the number of atoms in a molecule, it is expected that ammonia will have six vibrational modes as shown above. There are two pairs of degenerate modes with a frequency of 1694 (cm-1) and 3590 (cm-1). The modes with a frequency of 1090 (cm-1) and 1694 (cm-1) correspond to bending vibrations and the modes with a frequency 3461 (cm-1) and 3590 (cm-1) correspond to bond stretch vibrations. The bond stretch vibration at 3461 (cm-1) is highly symmetric whilst the stretches with a frequency of 3590 (cm-1) are asymmetric. The bending vibration with a frequency of 1090 (cm-1) is known as the umbrella mode. Three bands would be expected to be seen with the two stretches at 3590 (cm-1) being too low in intensity. The bends with a frequency of 1694 (cm-1) are degenerate and only one band will be observed between the two. Hence the three observed bands would be at 1090 (cm-1), 1694 (cm-1) and 3461 (cm-1).

=== Charge analysis ===
[[File:Acc2518 charge analysis.png|The Gaussview generated atomic charges of ammonia.|250px]]

Nitrogen has a greater electronegativity than hydrogen and hence there is greater electron density distributed around the N atom in ammonia relative to hydrogen. This explains the negative charge on N and the positive charge on H.

==N2 molecule==

===Optimisation data===

{| class="wikitable"
|+ N2 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-109.52412868 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00000060 (au)
|-
|'''Point group'''
|D∞h
|-
|'''Bond length (N-N)'''
|1.11 (Å)
|}

<pre>
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
</pre>

<jmol><jmolApplet>
<title> Nitrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518 N2 OPTIMISATION.LOG</uploadedFileContents>
<script>frame 1.10</script>
</jmolApplet></jmol>
[[:File:ACC2518 N2 OPTIMISATION.LOG|Optimised N2 .log file (acc2518)]]

===Vibrations===
[[File:Acc2518 N2vibration.png|Nitrogen display vibrations screenshot|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 2457
|-
| '''Symmetry''' || SGG
|-
| '''Intensity''' (arbitrary units) || 0
|-
| '''Image'''|| [[File:Acc2518NitrogenVM.png|250px]]
|}
Using the 3N-5 rule for linear molecules, Nitrogen can be expected to have one vibrational mode but this mode has an IR intensity of zero since Nitrogen molecules are IR inactive. This is because they have no overall dipole.

===Charge analysis===
[[File:Acc2518nitrogen charges.png]]

Both nitrogen atoms have the same electronegativity so the charge is neutral on both atoms.

===CCDC search===
'''Unique identifier:''' [https://www.ccdc.cam.ac.uk/structures/Search?Ccdcid=VAMQAE&DatabaseToSearch=Published VAMQAE]

'''Deposition number:''' 1530121

The complex linked above contains nitrogen coordinated to cobalt with a N-N bond distance of 1.08 Å which is slightly shorter than the optimised N-N bond length, displayed above, of 1.11 Å (2.d.p). During the optimisation process for nitrogen, assumptions have to be made for the computational process to be carried out. Each assumption made will increase the uncertainty in measurable quantities such as the bond length. Hence, the computationally determined bond length from the optimisation is a model and may not fully reflect the true bond length or the bond length determined by a computational program considering slightly different assumptions.

It should also be considered that the optimisation gave a prediction for the N-N bond length in a nitrogen molecule whereas the molecule linked above contains a nitrogen molecule that is coordinated into a transition metal complex. A lone pair of electrons on one of the nitrogen atoms has been donated to a cobalt ion, this draws electron density away from the donating nitrogen atom and would therefore slightly increase the positive charge on this atom. This may cause the donating nitrogen atom to attract the electrons in the N-N bond more strongly which would then explain the shorter bond in the transition metal complex compared to the nitrogen molecule.

==H2 molecule==

===Optimisation data===
{| class="wikitable"
|+ H2 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-1.17853936 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00000017 (au)
|-
|'''Point group'''
|D∞h
|-
|'''Bond length (N-N)'''
|0.74 (Å)
|}

<pre>
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

</pre>

<jmol><jmolApplet>
<title> Hydrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518 H2 OPTIMISATION.LOG</uploadedFileContents>
<script>frame 1.7</script>
</jmolApplet></jmol>
[[:File:ACC2518 H2 OPTIMISATION.LOG|Optimised H2 .log file (acc2518)]]

===Vibrations===
[[File:Acc2518 H2vibration.png|Hydrogen display vibrations screenshot|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 4466
|-
| '''Symmetry''' || SGG
|-
| '''Intensity''' (arbitrary units) || 0
|-
| '''Image'''|| [[File:Acc2518HydrogenVM.png|250px]]
|}
Using the 3N-5 rule for linear molecules, hydrogen can be expected to have one vibrational mode but this mode has an IR intensity of zero since hydrogen molecules, like nitrogen molecules, are IR inactive.

===Charge analysis===
[[File:Acc2518hydrogen charges.png]]

Both hydrogen atoms have the same electronegativity so the charge is neutral on both atoms.

==The Haber-Bosch process==
N2 + 3H2 -> 2NH3

E(NH3)=-56.55776873

 '''2*E(NH3)''' =2*(-56.55776873)=-113.11553746

 '''E(N2)''' =-109.52412868

E(H2)=-1.17853936

 '''3*E(H2)''' =3*(-1.17853936) =-3.53561808

'''ΔE= 2*E(NH3) -[ E(N2) + 3*E(H2) ]'''= -0.05579069 ≈ -0.05579 au (5.d.p)

'''ΔE=-146.5 kJ/mol (1.d.p)'''

ΔE is negative which indicates that the gaseous reactants are less stable than the ammonia product since the reactants are at a higher energy than the product. Although this process is not necessarily entropically favourable with four reactant gaseous molecules forming two gaseous product molecules, the reaction has a significantly negative enthalpy change which reflects the result calculated above.

== Project molecule (NF3) ==

=== Optimisation data ===
{| class="wikitable"
|+ NF3 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-354.07131058 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00010256 (au)
|-
|'''Point group'''
|C3V
|-
|'''Bond length (N-F)'''
|1.384 (Å)
|-
|'''Bond angle (F-N-F)'''
|102(°)
|}
<pre>
Item Value Threshold Converged?
Maximum Force 0.000164 0.000450 YES
RMS Force 0.000108 0.000300 YES
Maximum Displacement 0.000612 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

<jmol><jmolApplet>
<title> NF3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518_NF3_OPTF_POP.LOG </uploadedFileContents>
<script>frame 1.7</script>
</jmolApplet></jmol>
[[:File:ACC2518_NF3_OPTF_POP.LOG|Optimised NF3 .log file (acc2518)]]

=== Vibrations ===
[[File:Acc2518 NF3 vibrations screenshot.png|The Gaussview "Display Vibrations" window of the optimised nitrogen trifluoride molecule.|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 482 || 482
|-
| '''Symmetry''' || E || E
|-
| '''Intensity''' (arbitrary units) || 1 || 1
|-
| '''Image'''|| [[File:Acc2518 NF3 VM1.png|300px]] || [[File:Acc2518 NF3 VM2.png|300px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 644|| 930
|-
| '''Symmetry''' || A1 || E
|-
| '''Intensity''' (arbitrary units) || 3 || 208
|-
| '''Image'''|| [[File:Acc2518 NF3 VM3.png|300px]] || [[File:Acc2518 NF3 VM4.png|300px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 930|| 1062
|-
| '''Symmetry''' || E || A1
|-
| '''Intensity''' (arbitrary units) || 208 || 40
|-
| '''Image'''|| [[File:Acc2518 NF3 VM5.png|300px]] || [[File:Acc2518 NF3 VM6.png|300px]]
|}

Nitrogen trifluoride has the same number of atoms as ammonia and so six vibrational modes can be predicted from the 3N-6 rule. There are also two pairs of degenerate modes with frequencies of 482 (cm-1) and 930 (cm-1). The modes with a frequency of 482 (cm-1) and 644(cm-1) correspond to bending vibrational modes and the modes with a frequency of 930 (cm-1) and 1062 (cm-1) correspond to stretching vibrational modes. The mode with a frequency of 1062 (cm-1) represents a symmetric stretch whilst the modes with a frequency of 930 (cm-1) represent asymmetric stretches. In contrast to ammonia, the highest frequency bond stretch of nitrogen trifluoride is the symmetric stretch.

Three bands can be expected in the NF3 IR spectrum at frequencies of 644 (cm-1) 930 (cm-1) and 1062 (cm-1). The bends at 482 (cm-1) will be too low in frequency to appear in the spectrum which starts at a frequency of 500 (cm-1). The stretches at 930 (cm-1) are degenerate and hence will only display one band between them. The band as 644 (cm-1) may not be clearly visible due its relative low intensity of 3 arbitrary units.

=== Charge analysis ===
[[File:Acc2518 NF3 charge analysis.png|The Gaussview generated atomic charges of ammonia.|250px]]

Fluorine has a greater electronegativity that nitrogen and therefore there is greater electron density distributed around the three fluorine atoms compared to the nitrogen atom. The three fluorine atoms are treated as equivalent which means that the magnitude of the positive charge on nitrogen is three times the magnitude of the negative charge on a single fluorine atom.

=== Molecular orbitals (MO) ===

The nitrogen atom contributes 7 electrons and each fluorine atom contributes 9 electrons which means that nitrogen trifluoride contains 34 electrons in total and hence 17 electron pairs. In the table below, a molecular orbital number of 1 would denote the molecular orbital that is deepest in energy. Therefore, orbital 17 represents the HOMO and orbital 18 represents the LUMO. All of the molecular orbitals shown below are occupied with the exception of the LUMO.

{| class="wikitable"
!Molecular orbital number
!Image
!Type of molecular orbital
!Energy (au)
!Extra details
|-
|18
|[[File:Acc2518 MO18.png|200px]]
|Antibonding
|0.01947
|There are nodes in the centre of the N-F bonds which indicates that the LUMO is an antibonding orbital with destructive inteference between phases of opposite sign. The nodes in the centre of all four atoms also indicate that this MO was formed from 2p atomic orbitals from both nitrogen and fluorine.
|-
|17
|[[File:Acc2518 MO17.png|200px]]
|Bonding
| -0.35162
| The phase denoted by the green region shows orbital overlap across all three N-H bonds which implies that the HOMO is a bonding orbital. This MO has been formed from 2p orbitals which explains the nodes observed in the centre of the F atoms.
|-
|16
|[[File:Acc2518 MO16.png|200px]]
|Non-bonding
| -0.42224
|There is no electron density along any of the bonds which is the key indicator that this is a non-bonding MO. Since the electron density is localised around the fluorine atoms, this MO appears to show lone electron pairs on these fluorine atoms. There is no electron density being shared between the fluorine atoms which suggests there is destructive interference preventing such an interaction.
|-
|15
|[[File:Acc2518 MO15.png|200px]]
|Bonding
| -0.43590
| As observed in the HOMO, there is electron density along all three bonds which indicates the bonding nature of the MO. However, in contrast to the HOMO, the electron density along the bonds is not in the same phase for each bond. There is also some constructive interference between two of the F atoms which appears to indicate a very partial π character between the two atoms. This also means that this interaction is the product of two 2p atomic orbitals on fluorine overlapping slightly in phase with each other.
|-
|5
|[[File:Acc2518 MO5.png|200px]]
| Bonding
| -1.35870
| This MO contains no nodes at all implying that it is bonding in nature. It is also formed from overlap of 2s orbitals, in phase, on all atoms since the entire molecule is encased in electron density as a result of the constructive interference. It cannot be formed from 1s orbitals which would be far lower in energy and will also only occupy the first 4 MOs since there are 8 1s electrons in NF3.
|}

Acc2518

2019-03-04T14:13:46Z

Acc2518: /* Optimisation data */

== NH3 molecule ==
=== Optimisation data ===
{| class="wikitable"
|+ NH3 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-56.55776873 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00000485 (au)
|-
|'''Point group'''
|C3V
|-
|'''Bond length (N-H)'''
|1.02 (Å)
|-
|'''Bond angle (H-N-H)'''
|106(°)
|}
<pre>
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
</pre>

<jmol><jmolApplet>
<title> NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518 NH3 OPTF POP.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>
[[:File:ACC2518 NH3 OPTF POP.LOG|Optimised NH3 .log file (acc2518)]]

=== Vibrations ===
[[File:Acc2518 vibrations screenshot.jpg|The Gaussview "Display Vibrations" window of the optimised ammonia molecule.|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 1090 || 1694
|-
| '''Symmetry''' || A1 || E
|-
| '''Intensity''' (arbitrary units) || 145 || 14
|-
| '''Image'''|| [[File:acc2518VM1.png|250px]] || [[File:acc2518VM2.png|300px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 1694|| 3461
|-
| '''Symmetry''' || E || A1
|-
| '''Intensity''' (arbitrary units) || 14 || 1
|-
| '''Image'''|| [[File:acc2518VM3.png|250px]] || [[File:acc2518VM4.png|275px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 3590|| 3590
|-
| '''Symmetry''' || E || E
|-
| '''Intensity''' (arbitrary units) || 0 || 0
|-
| '''Image'''|| [[File:acc2518VM5.png|275px]] || [[File:acc2518VM6.png|250px]]
|}

Using the 3N-6 rule, where N represents the number of atoms in a molecule, it is expected that ammonia will have six vibrational modes as shown above. There are two pairs of degenerate modes with a frequency of 1694 (cm-1) and 3590 (cm-1). The modes with a frequency of 1090 (cm-1) and 1694 (cm-1) correspond to bending vibrations and the modes with a frequency 3461 (cm-1) and 3590 (cm-1) correspond to bond stretch vibrations. The bond stretch vibration at 3461 (cm-1) is highly symmetric whilst the stretches with a frequency of 3590 (cm-1) are asymmetric. The bending vibration with a frequency of 1090 (cm-1) is known as the umbrella mode. Three bands would be expected to be seen with the two stretches at 3590 (cm-1) being too low in intensity. The bends with a frequency of 1694 (cm-1) are degenerate and only one band will be observed between the two. Hence the three observed bands would be at 1090 (cm-1), 1694 (cm-1) and 3461 (cm-1).

=== Charge analysis ===
[[File:Acc2518 charge analysis.png|The Gaussview generated atomic charges of ammonia.|250px]]

Nitrogen has a greater electronegativity than hydrogen and hence there is greater electron density distributed around the N atom in ammonia relative to hydrogen. This explains the negative charge on N and the positive charge on H.

==N2 molecule==

===Optimisation data===

{| class="wikitable"
|+ N2 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-109.52412868 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00000060 (au)
|-
|'''Point group'''
|D∞h
|-
|'''Bond length (N-N)'''
|1.11 (Å)
|}

<pre>
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
</pre>

<jmol><jmolApplet>
<title> Nitrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518 N2 OPTIMISATION.LOG</uploadedFileContents>
<script>frame 1.10</script>
</jmolApplet></jmol>
[[:File:ACC2518 N2 OPTIMISATION.LOG|Optimised N2 .log file (acc2518)]]

===Vibrations===
[[File:Acc2518 N2vibration.png|Nitrogen display vibrations screenshot|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 2457
|-
| '''Symmetry''' || SGG
|-
| '''Intensity''' (arbitrary units) || 0
|-
| '''Image'''|| [[File:Acc2518NitrogenVM.png|250px]]
|}
Using the 3N-5 rule for linear molecules, Nitrogen can be expected to have one vibrational mode but this mode has an IR intensity of zero since Nitrogen molecules are IR inactive. This is because they have no overall dipole.

===Charge analysis===
[[File:Acc2518nitrogen charges.png]]

Both nitrogen atoms have the same electronegativity so the charge is neutral on both atoms.

===CCDC search===
'''Unique identifier:''' [https://www.ccdc.cam.ac.uk/structures/Search?Ccdcid=VAMQAE&DatabaseToSearch=Published VAMQAE]

'''Deposition number:''' 1530121

The complex linked above contains nitrogen coordinated to cobalt with a N-N bond distance of 1.08 Å which is slightly shorter than the optimised N-N bond length, displayed above, of 1.11 Å (3.s.f). During the optimisation process for nitrogen, assumptions have to be made for the computational process to be carried out. Each assumption made will increase the uncertainty in measurable quantities such as the bond length. Hence, the computationally determined bond length from the optimisation is a model and may not fully reflect the true bond length or the bond length determined by a computational program considering slightly different assumptions.

It should also be considered that the optimisation gave a prediction for the N-N bond length in a nitrogen molecule whereas the molecule linked above contains a nitrogen molecule that is coordinated into a transition metal complex. A lone pair of electrons on one of the nitrogen atoms has been donated to a cobalt ion, this draws electron density away from the donating nitrogen atom and would therefore slightly increase the positive charge on this atom. This may cause the donating nitrogen atom to attract the electrons in the N-N bond more strongly which would then explain the shorter bond in the transition metal complex compared to the nitrogen molecule.

==H2 molecule==

===Optimisation data===
{| class="wikitable"
|+ H2 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-1.17853936 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00000017 (au)
|-
|'''Point group'''
|D∞h
|-
|'''Bond length (N-N)'''
|0.74 (Å)
|}

<pre>
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

</pre>

<jmol><jmolApplet>
<title> Hydrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518 H2 OPTIMISATION.LOG</uploadedFileContents>
<script>frame 1.7</script>
</jmolApplet></jmol>
[[:File:ACC2518 H2 OPTIMISATION.LOG|Optimised H2 .log file (acc2518)]]

===Vibrations===
[[File:Acc2518 H2vibration.png|Hydrogen display vibrations screenshot|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 4466
|-
| '''Symmetry''' || SGG
|-
| '''Intensity''' (arbitrary units) || 0
|-
| '''Image'''|| [[File:Acc2518HydrogenVM.png|250px]]
|}
Using the 3N-5 rule for linear molecules, hydrogen can be expected to have one vibrational mode but this mode has an IR intensity of zero since hydrogen molecules, like nitrogen molecules, are IR inactive.

===Charge analysis===
[[File:Acc2518hydrogen charges.png]]

Both hydrogen atoms have the same electronegativity so the charge is neutral on both atoms.

==The Haber-Bosch process==
N2 + 3H2 -> 2NH3

E(NH3)=-56.55776873

 '''2*E(NH3)''' =2*(-56.55776873)=-113.11553746

 '''E(N2)''' =-109.52412868

E(H2)=-1.17853936

 '''3*E(H2)''' =3*(-1.17853936) =-3.53561808

'''ΔE= 2*E(NH3) -[ E(N2) + 3*E(H2) ]'''= -0.05579069 ≈ -0.05579 au (5.d.p)

'''ΔE=-146.5 kJ/mol (1.d.p)'''

ΔE is negative which indicates that the gaseous reactants are less stable than the ammonia product since the reactants are at a higher energy than the product. Although this process is not necessarily entropically favourable with four reactant gaseous molecules forming two gaseous product molecules, the reaction has a significantly negative enthalpy change which reflects the result calculated above.

== Project molecule (NF3) ==

=== Optimisation data ===
{| class="wikitable"
|+ NF3 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-354.07131058 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00010256 (au)
|-
|'''Point group'''
|C3V
|-
|'''Bond length (N-F)'''
|1.384 (Å)
|-
|'''Bond angle (F-N-F)'''
|102(°)
|}
<pre>
Item Value Threshold Converged?
Maximum Force 0.000164 0.000450 YES
RMS Force 0.000108 0.000300 YES
Maximum Displacement 0.000612 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

<jmol><jmolApplet>
<title> NF3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518_NF3_OPTF_POP.LOG </uploadedFileContents>
<script>frame 1.7</script>
</jmolApplet></jmol>
[[:File:ACC2518_NF3_OPTF_POP.LOG|Optimised NF3 .log file (acc2518)]]

=== Vibrations ===
[[File:Acc2518 NF3 vibrations screenshot.png|The Gaussview "Display Vibrations" window of the optimised nitrogen trifluoride molecule.|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 482 || 482
|-
| '''Symmetry''' || E || E
|-
| '''Intensity''' (arbitrary units) || 1 || 1
|-
| '''Image'''|| [[File:Acc2518 NF3 VM1.png|300px]] || [[File:Acc2518 NF3 VM2.png|300px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 644|| 930
|-
| '''Symmetry''' || A1 || E
|-
| '''Intensity''' (arbitrary units) || 3 || 208
|-
| '''Image'''|| [[File:Acc2518 NF3 VM3.png|300px]] || [[File:Acc2518 NF3 VM4.png|300px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 930|| 1062
|-
| '''Symmetry''' || E || A1
|-
| '''Intensity''' (arbitrary units) || 208 || 40
|-
| '''Image'''|| [[File:Acc2518 NF3 VM5.png|300px]] || [[File:Acc2518 NF3 VM6.png|300px]]
|}

Nitrogen trifluoride has the same number of atoms as ammonia and so six vibrational modes can be predicted from the 3N-6 rule. There are also two pairs of degenerate modes with frequencies of 482 (cm-1) and 930 (cm-1). The modes with a frequency of 482 (cm-1) and 644(cm-1) correspond to bending vibrational modes and the modes with a frequency of 930 (cm-1) and 1062 (cm-1) correspond to stretching vibrational modes. The mode with a frequency of 1062 (cm-1) represents a symmetric stretch whilst the modes with a frequency of 930 (cm-1) represent asymmetric stretches. In contrast to ammonia, the highest frequency bond stretch of nitrogen trifluoride is the symmetric stretch.

Three bands can be expected in the NF3 IR spectrum at frequencies of 644 (cm-1) 930 (cm-1) and 1062 (cm-1). The bends at 482 (cm-1) will be too low in frequency to appear in the spectrum which starts at a frequency of 500 (cm-1). The stretches at 930 (cm-1) are degenerate and hence will only display one band between them. The band as 644 (cm-1) may not be clearly visible due its relative low intensity of 3 arbitrary units.

=== Charge analysis ===
[[File:Acc2518 NF3 charge analysis.png|The Gaussview generated atomic charges of ammonia.|250px]]

Fluorine has a greater electronegativity that nitrogen and therefore there is greater electron density distributed around the three fluorine atoms compared to the nitrogen atom. The three fluorine atoms are treated as equivalent which means that the magnitude of the positive charge on nitrogen is three times the magnitude of the negative charge on a single fluorine atom.

=== Molecular orbitals (MO) ===

The nitrogen atom contributes 7 electrons and each fluorine atom contributes 9 electrons which means that nitrogen trifluoride contains 34 electrons in total and hence 17 electron pairs. In the table below, a molecular orbital number of 1 would denote the molecular orbital that is deepest in energy. Therefore, orbital 17 represents the HOMO and orbital 18 represents the LUMO. All of the molecular orbitals shown below are occupied with the exception of the LUMO.

{| class="wikitable"
!Molecular orbital number
!Image
!Type of molecular orbital
!Energy (au)
!Extra details
|-
|18
|[[File:Acc2518 MO18.png|200px]]
|Antibonding
|0.01947
|There are nodes in the centre of the N-F bonds which indicates that the LUMO is an antibonding orbital with destructive inteference between phases of opposite sign. The nodes in the centre of all four atoms also indicate that this MO was formed from 2p atomic orbitals from both nitrogen and fluorine.
|-
|17
|[[File:Acc2518 MO17.png|200px]]
|Bonding
| -0.35162
| The phase denoted by the green region shows orbital overlap across all three N-H bonds which implies that the HOMO is a bonding orbital. This MO has been formed from 2p orbitals which explains the nodes observed in the centre of the F atoms.
|-
|16
|[[File:Acc2518 MO16.png|200px]]
|Non-bonding
| -0.42224
|There is no electron density along any of the bonds which is the key indicator that this is a non-bonding MO. Since the electron density is localised around the fluorine atoms, this MO appears to show lone electron pairs on these fluorine atoms. There is no electron density being shared between the fluorine atoms which suggests there is destructive interference preventing such an interaction.
|-
|15
|[[File:Acc2518 MO15.png|200px]]
|Bonding
| -0.43590
| As observed in the HOMO, there is electron density along all three bonds which indicates the bonding nature of the MO. However, in contrast to the HOMO, the electron density along the bonds is not in the same phase for each bond. There is also some constructive interference between two of the F atoms which appears to indicate a very partial π character between the two atoms. This also means that this interaction is the product of two 2p atomic orbitals on fluorine overlapping slightly in phase with each other.
|-
|5
|[[File:Acc2518 MO5.png|200px]]
| Bonding
| -1.35870
| This MO contains no nodes at all implying that it is bonding in nature. It is also formed from overlap of 2s orbitals, in phase, on all atoms since the entire molecule is encased in electron density as a result of the constructive interference. It cannot be formed from 1s orbitals which would be far lower in energy and will also only occupy the first 4 MOs since there are 8 1s electrons in NF3.
|}

Acc2518

2019-03-04T14:13:31Z

Acc2518: /* Optimisation data */

== NH3 molecule ==
=== Optimisation data ===
{| class="wikitable"
|+ NH3 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-56.55776873 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00000485 (au)
|-
|'''Point group'''
|C3V
|-
|'''Bond length (N-H)'''
|1.02 (Å)
|-
|'''Bond angle (H-N-H)'''
|106(°)
|}
<pre>
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
</pre>

<jmol><jmolApplet>
<title> NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518 NH3 OPTF POP.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>
[[:File:ACC2518 NH3 OPTF POP.LOG|Optimised NH3 .log file (acc2518)]]

=== Vibrations ===
[[File:Acc2518 vibrations screenshot.jpg|The Gaussview "Display Vibrations" window of the optimised ammonia molecule.|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 1090 || 1694
|-
| '''Symmetry''' || A1 || E
|-
| '''Intensity''' (arbitrary units) || 145 || 14
|-
| '''Image'''|| [[File:acc2518VM1.png|250px]] || [[File:acc2518VM2.png|300px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 1694|| 3461
|-
| '''Symmetry''' || E || A1
|-
| '''Intensity''' (arbitrary units) || 14 || 1
|-
| '''Image'''|| [[File:acc2518VM3.png|250px]] || [[File:acc2518VM4.png|275px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 3590|| 3590
|-
| '''Symmetry''' || E || E
|-
| '''Intensity''' (arbitrary units) || 0 || 0
|-
| '''Image'''|| [[File:acc2518VM5.png|275px]] || [[File:acc2518VM6.png|250px]]
|}

Using the 3N-6 rule, where N represents the number of atoms in a molecule, it is expected that ammonia will have six vibrational modes as shown above. There are two pairs of degenerate modes with a frequency of 1694 (cm-1) and 3590 (cm-1). The modes with a frequency of 1090 (cm-1) and 1694 (cm-1) correspond to bending vibrations and the modes with a frequency 3461 (cm-1) and 3590 (cm-1) correspond to bond stretch vibrations. The bond stretch vibration at 3461 (cm-1) is highly symmetric whilst the stretches with a frequency of 3590 (cm-1) are asymmetric. The bending vibration with a frequency of 1090 (cm-1) is known as the umbrella mode. Three bands would be expected to be seen with the two stretches at 3590 (cm-1) being too low in intensity. The bends with a frequency of 1694 (cm-1) are degenerate and only one band will be observed between the two. Hence the three observed bands would be at 1090 (cm-1), 1694 (cm-1) and 3461 (cm-1).

=== Charge analysis ===
[[File:Acc2518 charge analysis.png|The Gaussview generated atomic charges of ammonia.|250px]]

Nitrogen has a greater electronegativity than hydrogen and hence there is greater electron density distributed around the N atom in ammonia relative to hydrogen. This explains the negative charge on N and the positive charge on H.

==N2 molecule==

===Optimisation data===

{| class="wikitable"
|+ N2 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-109.52412868 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00000060 (au)
|-
|'''Point group'''
|D∞h
|-
|'''Bond length (N-N)'''
|1.106 (Å)
|}

<pre>
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
</pre>

<jmol><jmolApplet>
<title> Nitrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518 N2 OPTIMISATION.LOG</uploadedFileContents>
<script>frame 1.10</script>
</jmolApplet></jmol>
[[:File:ACC2518 N2 OPTIMISATION.LOG|Optimised N2 .log file (acc2518)]]

===Vibrations===
[[File:Acc2518 N2vibration.png|Nitrogen display vibrations screenshot|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 2457
|-
| '''Symmetry''' || SGG
|-
| '''Intensity''' (arbitrary units) || 0
|-
| '''Image'''|| [[File:Acc2518NitrogenVM.png|250px]]
|}
Using the 3N-5 rule for linear molecules, Nitrogen can be expected to have one vibrational mode but this mode has an IR intensity of zero since Nitrogen molecules are IR inactive. This is because they have no overall dipole.

===Charge analysis===
[[File:Acc2518nitrogen charges.png]]

Both nitrogen atoms have the same electronegativity so the charge is neutral on both atoms.

===CCDC search===
'''Unique identifier:''' [https://www.ccdc.cam.ac.uk/structures/Search?Ccdcid=VAMQAE&DatabaseToSearch=Published VAMQAE]

'''Deposition number:''' 1530121

The complex linked above contains nitrogen coordinated to cobalt with a N-N bond distance of 1.08 Å which is slightly shorter than the optimised N-N bond length, displayed above, of 1.11 Å (3.s.f). During the optimisation process for nitrogen, assumptions have to be made for the computational process to be carried out. Each assumption made will increase the uncertainty in measurable quantities such as the bond length. Hence, the computationally determined bond length from the optimisation is a model and may not fully reflect the true bond length or the bond length determined by a computational program considering slightly different assumptions.

It should also be considered that the optimisation gave a prediction for the N-N bond length in a nitrogen molecule whereas the molecule linked above contains a nitrogen molecule that is coordinated into a transition metal complex. A lone pair of electrons on one of the nitrogen atoms has been donated to a cobalt ion, this draws electron density away from the donating nitrogen atom and would therefore slightly increase the positive charge on this atom. This may cause the donating nitrogen atom to attract the electrons in the N-N bond more strongly which would then explain the shorter bond in the transition metal complex compared to the nitrogen molecule.

==H2 molecule==

===Optimisation data===
{| class="wikitable"
|+ H2 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-1.17853936 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00000017 (au)
|-
|'''Point group'''
|D∞h
|-
|'''Bond length (N-N)'''
|0.74 (Å)
|}

<pre>
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

</pre>

<jmol><jmolApplet>
<title> Hydrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518 H2 OPTIMISATION.LOG</uploadedFileContents>
<script>frame 1.7</script>
</jmolApplet></jmol>
[[:File:ACC2518 H2 OPTIMISATION.LOG|Optimised H2 .log file (acc2518)]]

===Vibrations===
[[File:Acc2518 H2vibration.png|Hydrogen display vibrations screenshot|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 4466
|-
| '''Symmetry''' || SGG
|-
| '''Intensity''' (arbitrary units) || 0
|-
| '''Image'''|| [[File:Acc2518HydrogenVM.png|250px]]
|}
Using the 3N-5 rule for linear molecules, hydrogen can be expected to have one vibrational mode but this mode has an IR intensity of zero since hydrogen molecules, like nitrogen molecules, are IR inactive.

===Charge analysis===
[[File:Acc2518hydrogen charges.png]]

Both hydrogen atoms have the same electronegativity so the charge is neutral on both atoms.

==The Haber-Bosch process==
N2 + 3H2 -> 2NH3

E(NH3)=-56.55776873

 '''2*E(NH3)''' =2*(-56.55776873)=-113.11553746

 '''E(N2)''' =-109.52412868

E(H2)=-1.17853936

 '''3*E(H2)''' =3*(-1.17853936) =-3.53561808

'''ΔE= 2*E(NH3) -[ E(N2) + 3*E(H2) ]'''= -0.05579069 ≈ -0.05579 au (5.d.p)

'''ΔE=-146.5 kJ/mol (1.d.p)'''

ΔE is negative which indicates that the gaseous reactants are less stable than the ammonia product since the reactants are at a higher energy than the product. Although this process is not necessarily entropically favourable with four reactant gaseous molecules forming two gaseous product molecules, the reaction has a significantly negative enthalpy change which reflects the result calculated above.

== Project molecule (NF3) ==

=== Optimisation data ===
{| class="wikitable"
|+ NF3 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-354.07131058 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00010256 (au)
|-
|'''Point group'''
|C3V
|-
|'''Bond length (N-F)'''
|1.384 (Å)
|-
|'''Bond angle (F-N-F)'''
|102(°)
|}
<pre>
Item Value Threshold Converged?
Maximum Force 0.000164 0.000450 YES
RMS Force 0.000108 0.000300 YES
Maximum Displacement 0.000612 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

<jmol><jmolApplet>
<title> NF3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518_NF3_OPTF_POP.LOG </uploadedFileContents>
<script>frame 1.7</script>
</jmolApplet></jmol>
[[:File:ACC2518_NF3_OPTF_POP.LOG|Optimised NF3 .log file (acc2518)]]

=== Vibrations ===
[[File:Acc2518 NF3 vibrations screenshot.png|The Gaussview "Display Vibrations" window of the optimised nitrogen trifluoride molecule.|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 482 || 482
|-
| '''Symmetry''' || E || E
|-
| '''Intensity''' (arbitrary units) || 1 || 1
|-
| '''Image'''|| [[File:Acc2518 NF3 VM1.png|300px]] || [[File:Acc2518 NF3 VM2.png|300px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 644|| 930
|-
| '''Symmetry''' || A1 || E
|-
| '''Intensity''' (arbitrary units) || 3 || 208
|-
| '''Image'''|| [[File:Acc2518 NF3 VM3.png|300px]] || [[File:Acc2518 NF3 VM4.png|300px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 930|| 1062
|-
| '''Symmetry''' || E || A1
|-
| '''Intensity''' (arbitrary units) || 208 || 40
|-
| '''Image'''|| [[File:Acc2518 NF3 VM5.png|300px]] || [[File:Acc2518 NF3 VM6.png|300px]]
|}

Nitrogen trifluoride has the same number of atoms as ammonia and so six vibrational modes can be predicted from the 3N-6 rule. There are also two pairs of degenerate modes with frequencies of 482 (cm-1) and 930 (cm-1). The modes with a frequency of 482 (cm-1) and 644(cm-1) correspond to bending vibrational modes and the modes with a frequency of 930 (cm-1) and 1062 (cm-1) correspond to stretching vibrational modes. The mode with a frequency of 1062 (cm-1) represents a symmetric stretch whilst the modes with a frequency of 930 (cm-1) represent asymmetric stretches. In contrast to ammonia, the highest frequency bond stretch of nitrogen trifluoride is the symmetric stretch.

Three bands can be expected in the NF3 IR spectrum at frequencies of 644 (cm-1) 930 (cm-1) and 1062 (cm-1). The bends at 482 (cm-1) will be too low in frequency to appear in the spectrum which starts at a frequency of 500 (cm-1). The stretches at 930 (cm-1) are degenerate and hence will only display one band between them. The band as 644 (cm-1) may not be clearly visible due its relative low intensity of 3 arbitrary units.

=== Charge analysis ===
[[File:Acc2518 NF3 charge analysis.png|The Gaussview generated atomic charges of ammonia.|250px]]

Fluorine has a greater electronegativity that nitrogen and therefore there is greater electron density distributed around the three fluorine atoms compared to the nitrogen atom. The three fluorine atoms are treated as equivalent which means that the magnitude of the positive charge on nitrogen is three times the magnitude of the negative charge on a single fluorine atom.

=== Molecular orbitals (MO) ===

The nitrogen atom contributes 7 electrons and each fluorine atom contributes 9 electrons which means that nitrogen trifluoride contains 34 electrons in total and hence 17 electron pairs. In the table below, a molecular orbital number of 1 would denote the molecular orbital that is deepest in energy. Therefore, orbital 17 represents the HOMO and orbital 18 represents the LUMO. All of the molecular orbitals shown below are occupied with the exception of the LUMO.

{| class="wikitable"
!Molecular orbital number
!Image
!Type of molecular orbital
!Energy (au)
!Extra details
|-
|18
|[[File:Acc2518 MO18.png|200px]]
|Antibonding
|0.01947
|There are nodes in the centre of the N-F bonds which indicates that the LUMO is an antibonding orbital with destructive inteference between phases of opposite sign. The nodes in the centre of all four atoms also indicate that this MO was formed from 2p atomic orbitals from both nitrogen and fluorine.
|-
|17
|[[File:Acc2518 MO17.png|200px]]
|Bonding
| -0.35162
| The phase denoted by the green region shows orbital overlap across all three N-H bonds which implies that the HOMO is a bonding orbital. This MO has been formed from 2p orbitals which explains the nodes observed in the centre of the F atoms.
|-
|16
|[[File:Acc2518 MO16.png|200px]]
|Non-bonding
| -0.42224
|There is no electron density along any of the bonds which is the key indicator that this is a non-bonding MO. Since the electron density is localised around the fluorine atoms, this MO appears to show lone electron pairs on these fluorine atoms. There is no electron density being shared between the fluorine atoms which suggests there is destructive interference preventing such an interaction.
|-
|15
|[[File:Acc2518 MO15.png|200px]]
|Bonding
| -0.43590
| As observed in the HOMO, there is electron density along all three bonds which indicates the bonding nature of the MO. However, in contrast to the HOMO, the electron density along the bonds is not in the same phase for each bond. There is also some constructive interference between two of the F atoms which appears to indicate a very partial π character between the two atoms. This also means that this interaction is the product of two 2p atomic orbitals on fluorine overlapping slightly in phase with each other.
|-
|5
|[[File:Acc2518 MO5.png|200px]]
| Bonding
| -1.35870
| This MO contains no nodes at all implying that it is bonding in nature. It is also formed from overlap of 2s orbitals, in phase, on all atoms since the entire molecule is encased in electron density as a result of the constructive interference. It cannot be formed from 1s orbitals which would be far lower in energy and will also only occupy the first 4 MOs since there are 8 1s electrons in NF3.
|}

Acc2518

2019-03-04T14:13:17Z

Acc2518: /* Optimisation data */

== NH3 molecule ==
=== Optimisation data ===
{| class="wikitable"
|+ NH3 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-56.55776873 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00000485 (au)
|-
|'''Point group'''
|C3V
|-
|'''Bond length (N-H)'''
|1.018 (Å)
|-
|'''Bond angle (H-N-H)'''
|106(°)
|}
<pre>
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
</pre>

<jmol><jmolApplet>
<title> NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518 NH3 OPTF POP.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>
[[:File:ACC2518 NH3 OPTF POP.LOG|Optimised NH3 .log file (acc2518)]]

=== Vibrations ===
[[File:Acc2518 vibrations screenshot.jpg|The Gaussview "Display Vibrations" window of the optimised ammonia molecule.|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 1090 || 1694
|-
| '''Symmetry''' || A1 || E
|-
| '''Intensity''' (arbitrary units) || 145 || 14
|-
| '''Image'''|| [[File:acc2518VM1.png|250px]] || [[File:acc2518VM2.png|300px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 1694|| 3461
|-
| '''Symmetry''' || E || A1
|-
| '''Intensity''' (arbitrary units) || 14 || 1
|-
| '''Image'''|| [[File:acc2518VM3.png|250px]] || [[File:acc2518VM4.png|275px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 3590|| 3590
|-
| '''Symmetry''' || E || E
|-
| '''Intensity''' (arbitrary units) || 0 || 0
|-
| '''Image'''|| [[File:acc2518VM5.png|275px]] || [[File:acc2518VM6.png|250px]]
|}

Using the 3N-6 rule, where N represents the number of atoms in a molecule, it is expected that ammonia will have six vibrational modes as shown above. There are two pairs of degenerate modes with a frequency of 1694 (cm-1) and 3590 (cm-1). The modes with a frequency of 1090 (cm-1) and 1694 (cm-1) correspond to bending vibrations and the modes with a frequency 3461 (cm-1) and 3590 (cm-1) correspond to bond stretch vibrations. The bond stretch vibration at 3461 (cm-1) is highly symmetric whilst the stretches with a frequency of 3590 (cm-1) are asymmetric. The bending vibration with a frequency of 1090 (cm-1) is known as the umbrella mode. Three bands would be expected to be seen with the two stretches at 3590 (cm-1) being too low in intensity. The bends with a frequency of 1694 (cm-1) are degenerate and only one band will be observed between the two. Hence the three observed bands would be at 1090 (cm-1), 1694 (cm-1) and 3461 (cm-1).

=== Charge analysis ===
[[File:Acc2518 charge analysis.png|The Gaussview generated atomic charges of ammonia.|250px]]

Nitrogen has a greater electronegativity than hydrogen and hence there is greater electron density distributed around the N atom in ammonia relative to hydrogen. This explains the negative charge on N and the positive charge on H.

==N2 molecule==

===Optimisation data===

{| class="wikitable"
|+ N2 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-109.52412868 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00000060 (au)
|-
|'''Point group'''
|D∞h
|-
|'''Bond length (N-N)'''
|1.106 (Å)
|}

<pre>
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
</pre>

<jmol><jmolApplet>
<title> Nitrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518 N2 OPTIMISATION.LOG</uploadedFileContents>
<script>frame 1.10</script>
</jmolApplet></jmol>
[[:File:ACC2518 N2 OPTIMISATION.LOG|Optimised N2 .log file (acc2518)]]

===Vibrations===
[[File:Acc2518 N2vibration.png|Nitrogen display vibrations screenshot|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 2457
|-
| '''Symmetry''' || SGG
|-
| '''Intensity''' (arbitrary units) || 0
|-
| '''Image'''|| [[File:Acc2518NitrogenVM.png|250px]]
|}
Using the 3N-5 rule for linear molecules, Nitrogen can be expected to have one vibrational mode but this mode has an IR intensity of zero since Nitrogen molecules are IR inactive. This is because they have no overall dipole.

===Charge analysis===
[[File:Acc2518nitrogen charges.png]]

Both nitrogen atoms have the same electronegativity so the charge is neutral on both atoms.

===CCDC search===
'''Unique identifier:''' [https://www.ccdc.cam.ac.uk/structures/Search?Ccdcid=VAMQAE&DatabaseToSearch=Published VAMQAE]

'''Deposition number:''' 1530121

The complex linked above contains nitrogen coordinated to cobalt with a N-N bond distance of 1.08 Å which is slightly shorter than the optimised N-N bond length, displayed above, of 1.11 Å (3.s.f). During the optimisation process for nitrogen, assumptions have to be made for the computational process to be carried out. Each assumption made will increase the uncertainty in measurable quantities such as the bond length. Hence, the computationally determined bond length from the optimisation is a model and may not fully reflect the true bond length or the bond length determined by a computational program considering slightly different assumptions.

It should also be considered that the optimisation gave a prediction for the N-N bond length in a nitrogen molecule whereas the molecule linked above contains a nitrogen molecule that is coordinated into a transition metal complex. A lone pair of electrons on one of the nitrogen atoms has been donated to a cobalt ion, this draws electron density away from the donating nitrogen atom and would therefore slightly increase the positive charge on this atom. This may cause the donating nitrogen atom to attract the electrons in the N-N bond more strongly which would then explain the shorter bond in the transition metal complex compared to the nitrogen molecule.

==H2 molecule==

===Optimisation data===
{| class="wikitable"
|+ H2 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-1.17853936 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00000017 (au)
|-
|'''Point group'''
|D∞h
|-
|'''Bond length (N-N)'''
|0.74 (Å)
|}

<pre>
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

</pre>

<jmol><jmolApplet>
<title> Hydrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518 H2 OPTIMISATION.LOG</uploadedFileContents>
<script>frame 1.7</script>
</jmolApplet></jmol>
[[:File:ACC2518 H2 OPTIMISATION.LOG|Optimised H2 .log file (acc2518)]]

===Vibrations===
[[File:Acc2518 H2vibration.png|Hydrogen display vibrations screenshot|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 4466
|-
| '''Symmetry''' || SGG
|-
| '''Intensity''' (arbitrary units) || 0
|-
| '''Image'''|| [[File:Acc2518HydrogenVM.png|250px]]
|}
Using the 3N-5 rule for linear molecules, hydrogen can be expected to have one vibrational mode but this mode has an IR intensity of zero since hydrogen molecules, like nitrogen molecules, are IR inactive.

===Charge analysis===
[[File:Acc2518hydrogen charges.png]]

Both hydrogen atoms have the same electronegativity so the charge is neutral on both atoms.

==The Haber-Bosch process==
N2 + 3H2 -> 2NH3

E(NH3)=-56.55776873

 '''2*E(NH3)''' =2*(-56.55776873)=-113.11553746

 '''E(N2)''' =-109.52412868

E(H2)=-1.17853936

 '''3*E(H2)''' =3*(-1.17853936) =-3.53561808

'''ΔE= 2*E(NH3) -[ E(N2) + 3*E(H2) ]'''= -0.05579069 ≈ -0.05579 au (5.d.p)

'''ΔE=-146.5 kJ/mol (1.d.p)'''

ΔE is negative which indicates that the gaseous reactants are less stable than the ammonia product since the reactants are at a higher energy than the product. Although this process is not necessarily entropically favourable with four reactant gaseous molecules forming two gaseous product molecules, the reaction has a significantly negative enthalpy change which reflects the result calculated above.

== Project molecule (NF3) ==

=== Optimisation data ===
{| class="wikitable"
|+ NF3 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-354.07131058 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00010256 (au)
|-
|'''Point group'''
|C3V
|-
|'''Bond length (N-F)'''
|1.384 (Å)
|-
|'''Bond angle (F-N-F)'''
|102(°)
|}
<pre>
Item Value Threshold Converged?
Maximum Force 0.000164 0.000450 YES
RMS Force 0.000108 0.000300 YES
Maximum Displacement 0.000612 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

<jmol><jmolApplet>
<title> NF3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518_NF3_OPTF_POP.LOG </uploadedFileContents>
<script>frame 1.7</script>
</jmolApplet></jmol>
[[:File:ACC2518_NF3_OPTF_POP.LOG|Optimised NF3 .log file (acc2518)]]

=== Vibrations ===
[[File:Acc2518 NF3 vibrations screenshot.png|The Gaussview "Display Vibrations" window of the optimised nitrogen trifluoride molecule.|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 482 || 482
|-
| '''Symmetry''' || E || E
|-
| '''Intensity''' (arbitrary units) || 1 || 1
|-
| '''Image'''|| [[File:Acc2518 NF3 VM1.png|300px]] || [[File:Acc2518 NF3 VM2.png|300px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 644|| 930
|-
| '''Symmetry''' || A1 || E
|-
| '''Intensity''' (arbitrary units) || 3 || 208
|-
| '''Image'''|| [[File:Acc2518 NF3 VM3.png|300px]] || [[File:Acc2518 NF3 VM4.png|300px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 930|| 1062
|-
| '''Symmetry''' || E || A1
|-
| '''Intensity''' (arbitrary units) || 208 || 40
|-
| '''Image'''|| [[File:Acc2518 NF3 VM5.png|300px]] || [[File:Acc2518 NF3 VM6.png|300px]]
|}

Nitrogen trifluoride has the same number of atoms as ammonia and so six vibrational modes can be predicted from the 3N-6 rule. There are also two pairs of degenerate modes with frequencies of 482 (cm-1) and 930 (cm-1). The modes with a frequency of 482 (cm-1) and 644(cm-1) correspond to bending vibrational modes and the modes with a frequency of 930 (cm-1) and 1062 (cm-1) correspond to stretching vibrational modes. The mode with a frequency of 1062 (cm-1) represents a symmetric stretch whilst the modes with a frequency of 930 (cm-1) represent asymmetric stretches. In contrast to ammonia, the highest frequency bond stretch of nitrogen trifluoride is the symmetric stretch.

Three bands can be expected in the NF3 IR spectrum at frequencies of 644 (cm-1) 930 (cm-1) and 1062 (cm-1). The bends at 482 (cm-1) will be too low in frequency to appear in the spectrum which starts at a frequency of 500 (cm-1). The stretches at 930 (cm-1) are degenerate and hence will only display one band between them. The band as 644 (cm-1) may not be clearly visible due its relative low intensity of 3 arbitrary units.

=== Charge analysis ===
[[File:Acc2518 NF3 charge analysis.png|The Gaussview generated atomic charges of ammonia.|250px]]

Fluorine has a greater electronegativity that nitrogen and therefore there is greater electron density distributed around the three fluorine atoms compared to the nitrogen atom. The three fluorine atoms are treated as equivalent which means that the magnitude of the positive charge on nitrogen is three times the magnitude of the negative charge on a single fluorine atom.

=== Molecular orbitals (MO) ===

The nitrogen atom contributes 7 electrons and each fluorine atom contributes 9 electrons which means that nitrogen trifluoride contains 34 electrons in total and hence 17 electron pairs. In the table below, a molecular orbital number of 1 would denote the molecular orbital that is deepest in energy. Therefore, orbital 17 represents the HOMO and orbital 18 represents the LUMO. All of the molecular orbitals shown below are occupied with the exception of the LUMO.

{| class="wikitable"
!Molecular orbital number
!Image
!Type of molecular orbital
!Energy (au)
!Extra details
|-
|18
|[[File:Acc2518 MO18.png|200px]]
|Antibonding
|0.01947
|There are nodes in the centre of the N-F bonds which indicates that the LUMO is an antibonding orbital with destructive inteference between phases of opposite sign. The nodes in the centre of all four atoms also indicate that this MO was formed from 2p atomic orbitals from both nitrogen and fluorine.
|-
|17
|[[File:Acc2518 MO17.png|200px]]
|Bonding
| -0.35162
| The phase denoted by the green region shows orbital overlap across all three N-H bonds which implies that the HOMO is a bonding orbital. This MO has been formed from 2p orbitals which explains the nodes observed in the centre of the F atoms.
|-
|16
|[[File:Acc2518 MO16.png|200px]]
|Non-bonding
| -0.42224
|There is no electron density along any of the bonds which is the key indicator that this is a non-bonding MO. Since the electron density is localised around the fluorine atoms, this MO appears to show lone electron pairs on these fluorine atoms. There is no electron density being shared between the fluorine atoms which suggests there is destructive interference preventing such an interaction.
|-
|15
|[[File:Acc2518 MO15.png|200px]]
|Bonding
| -0.43590
| As observed in the HOMO, there is electron density along all three bonds which indicates the bonding nature of the MO. However, in contrast to the HOMO, the electron density along the bonds is not in the same phase for each bond. There is also some constructive interference between two of the F atoms which appears to indicate a very partial π character between the two atoms. This also means that this interaction is the product of two 2p atomic orbitals on fluorine overlapping slightly in phase with each other.
|-
|5
|[[File:Acc2518 MO5.png|200px]]
| Bonding
| -1.35870
| This MO contains no nodes at all implying that it is bonding in nature. It is also formed from overlap of 2s orbitals, in phase, on all atoms since the entire molecule is encased in electron density as a result of the constructive interference. It cannot be formed from 1s orbitals which would be far lower in energy and will also only occupy the first 4 MOs since there are 8 1s electrons in NF3.
|}

Acc2518

2019-03-04T14:09:44Z

Acc2518: /* Optimisation data */

== NH3 molecule ==
=== Optimisation data ===
{| class="wikitable"
|+ NH3 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-56.55776873 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00000485 (au)
|-
|'''Point group'''
|C3V
|-
|'''Bond length (N-H)'''
|1.018 (Å)
|-
|'''Bond angle (H-N-H)'''
|106(°)
|}
<pre>
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
</pre>

<jmol><jmolApplet>
<title> NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518 NH3 OPTF POP.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>
[[:File:ACC2518 NH3 OPTF POP.LOG|Optimised NH3 .log file (acc2518)]]

=== Vibrations ===
[[File:Acc2518 vibrations screenshot.jpg|The Gaussview "Display Vibrations" window of the optimised ammonia molecule.|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 1090 || 1694
|-
| '''Symmetry''' || A1 || E
|-
| '''Intensity''' (arbitrary units) || 145 || 14
|-
| '''Image'''|| [[File:acc2518VM1.png|250px]] || [[File:acc2518VM2.png|300px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 1694|| 3461
|-
| '''Symmetry''' || E || A1
|-
| '''Intensity''' (arbitrary units) || 14 || 1
|-
| '''Image'''|| [[File:acc2518VM3.png|250px]] || [[File:acc2518VM4.png|275px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 3590|| 3590
|-
| '''Symmetry''' || E || E
|-
| '''Intensity''' (arbitrary units) || 0 || 0
|-
| '''Image'''|| [[File:acc2518VM5.png|275px]] || [[File:acc2518VM6.png|250px]]
|}

Using the 3N-6 rule, where N represents the number of atoms in a molecule, it is expected that ammonia will have six vibrational modes as shown above. There are two pairs of degenerate modes with a frequency of 1694 (cm-1) and 3590 (cm-1). The modes with a frequency of 1090 (cm-1) and 1694 (cm-1) correspond to bending vibrations and the modes with a frequency 3461 (cm-1) and 3590 (cm-1) correspond to bond stretch vibrations. The bond stretch vibration at 3461 (cm-1) is highly symmetric whilst the stretches with a frequency of 3590 (cm-1) are asymmetric. The bending vibration with a frequency of 1090 (cm-1) is known as the umbrella mode. Three bands would be expected to be seen with the two stretches at 3590 (cm-1) being too low in intensity. The bends with a frequency of 1694 (cm-1) are degenerate and only one band will be observed between the two. Hence the three observed bands would be at 1090 (cm-1), 1694 (cm-1) and 3461 (cm-1).

=== Charge analysis ===
[[File:Acc2518 charge analysis.png|The Gaussview generated atomic charges of ammonia.|250px]]

Nitrogen has a greater electronegativity than hydrogen and hence there is greater electron density distributed around the N atom in ammonia relative to hydrogen. This explains the negative charge on N and the positive charge on H.

==N2 molecule==

===Optimisation data===

{| class="wikitable"
|+ N2 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-109.52412868 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00000060 (au)
|-
|'''Point group'''
|D∞h
|-
|'''Bond length (N-N)'''
|1.106 (Å)
|}

<pre>
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
</pre>

<jmol><jmolApplet>
<title> Nitrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518 N2 OPTIMISATION.LOG</uploadedFileContents>
<script>frame 1.10</script>
</jmolApplet></jmol>
[[:File:ACC2518 N2 OPTIMISATION.LOG|Optimised N2 .log file (acc2518)]]

===Vibrations===
[[File:Acc2518 N2vibration.png|Nitrogen display vibrations screenshot|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 2457
|-
| '''Symmetry''' || SGG
|-
| '''Intensity''' (arbitrary units) || 0
|-
| '''Image'''|| [[File:Acc2518NitrogenVM.png|250px]]
|}
Using the 3N-5 rule for linear molecules, Nitrogen can be expected to have one vibrational mode but this mode has an IR intensity of zero since Nitrogen molecules are IR inactive. This is because they have no overall dipole.

===Charge analysis===
[[File:Acc2518nitrogen charges.png]]

Both nitrogen atoms have the same electronegativity so the charge is neutral on both atoms.

===CCDC search===
'''Unique identifier:''' [https://www.ccdc.cam.ac.uk/structures/Search?Ccdcid=VAMQAE&DatabaseToSearch=Published VAMQAE]

'''Deposition number:''' 1530121

The complex linked above contains nitrogen coordinated to cobalt with a N-N bond distance of 1.08 Å which is slightly shorter than the optimised N-N bond length, displayed above, of 1.11 Å (3.s.f). During the optimisation process for nitrogen, assumptions have to be made for the computational process to be carried out. Each assumption made will increase the uncertainty in measurable quantities such as the bond length. Hence, the computationally determined bond length from the optimisation is a model and may not fully reflect the true bond length or the bond length determined by a computational program considering slightly different assumptions.

It should also be considered that the optimisation gave a prediction for the N-N bond length in a nitrogen molecule whereas the molecule linked above contains a nitrogen molecule that is coordinated into a transition metal complex. A lone pair of electrons on one of the nitrogen atoms has been donated to a cobalt ion, this draws electron density away from the donating nitrogen atom and would therefore slightly increase the positive charge on this atom. This may cause the donating nitrogen atom to attract the electrons in the N-N bond more strongly which would then explain the shorter bond in the transition metal complex compared to the nitrogen molecule.

==H2 molecule==

===Optimisation data===
{| class="wikitable"
|+ H2 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-1.17853936 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00000017 (au)
|-
|'''Point group'''
|D∞h
|-
|'''Bond length (N-N)'''
|0.74279 (Å)
|}

<pre>
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

</pre>

<jmol><jmolApplet>
<title> Hydrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518 H2 OPTIMISATION.LOG</uploadedFileContents>
<script>frame 1.7</script>
</jmolApplet></jmol>
[[:File:ACC2518 H2 OPTIMISATION.LOG|Optimised H2 .log file (acc2518)]]

===Vibrations===
[[File:Acc2518 H2vibration.png|Hydrogen display vibrations screenshot|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 4466
|-
| '''Symmetry''' || SGG
|-
| '''Intensity''' (arbitrary units) || 0
|-
| '''Image'''|| [[File:Acc2518HydrogenVM.png|250px]]
|}
Using the 3N-5 rule for linear molecules, hydrogen can be expected to have one vibrational mode but this mode has an IR intensity of zero since hydrogen molecules, like nitrogen molecules, are IR inactive.

===Charge analysis===
[[File:Acc2518hydrogen charges.png]]

Both hydrogen atoms have the same electronegativity so the charge is neutral on both atoms.

==The Haber-Bosch process==
N2 + 3H2 -> 2NH3

E(NH3)=-56.55776873

 '''2*E(NH3)''' =2*(-56.55776873)=-113.11553746

 '''E(N2)''' =-109.52412868

E(H2)=-1.17853936

 '''3*E(H2)''' =3*(-1.17853936) =-3.53561808

'''ΔE= 2*E(NH3) -[ E(N2) + 3*E(H2) ]'''= -0.05579069 ≈ -0.05579 au (5.d.p)

'''ΔE=-146.5 kJ/mol (1.d.p)'''

ΔE is negative which indicates that the gaseous reactants are less stable than the ammonia product since the reactants are at a higher energy than the product. Although this process is not necessarily entropically favourable with four reactant gaseous molecules forming two gaseous product molecules, the reaction has a significantly negative enthalpy change which reflects the result calculated above.

== Project molecule (NF3) ==

=== Optimisation data ===
{| class="wikitable"
|+ NF3 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-354.07131058 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00010256 (au)
|-
|'''Point group'''
|C3V
|-
|'''Bond length (N-F)'''
|1.384 (Å)
|-
|'''Bond angle (F-N-F)'''
|102(°)
|}
<pre>
Item Value Threshold Converged?
Maximum Force 0.000164 0.000450 YES
RMS Force 0.000108 0.000300 YES
Maximum Displacement 0.000612 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

<jmol><jmolApplet>
<title> NF3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518_NF3_OPTF_POP.LOG </uploadedFileContents>
<script>frame 1.7</script>
</jmolApplet></jmol>
[[:File:ACC2518_NF3_OPTF_POP.LOG|Optimised NF3 .log file (acc2518)]]

=== Vibrations ===
[[File:Acc2518 NF3 vibrations screenshot.png|The Gaussview "Display Vibrations" window of the optimised nitrogen trifluoride molecule.|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 482 || 482
|-
| '''Symmetry''' || E || E
|-
| '''Intensity''' (arbitrary units) || 1 || 1
|-
| '''Image'''|| [[File:Acc2518 NF3 VM1.png|300px]] || [[File:Acc2518 NF3 VM2.png|300px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 644|| 930
|-
| '''Symmetry''' || A1 || E
|-
| '''Intensity''' (arbitrary units) || 3 || 208
|-
| '''Image'''|| [[File:Acc2518 NF3 VM3.png|300px]] || [[File:Acc2518 NF3 VM4.png|300px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 930|| 1062
|-
| '''Symmetry''' || E || A1
|-
| '''Intensity''' (arbitrary units) || 208 || 40
|-
| '''Image'''|| [[File:Acc2518 NF3 VM5.png|300px]] || [[File:Acc2518 NF3 VM6.png|300px]]
|}

Nitrogen trifluoride has the same number of atoms as ammonia and so six vibrational modes can be predicted from the 3N-6 rule. There are also two pairs of degenerate modes with frequencies of 482 (cm-1) and 930 (cm-1). The modes with a frequency of 482 (cm-1) and 644(cm-1) correspond to bending vibrational modes and the modes with a frequency of 930 (cm-1) and 1062 (cm-1) correspond to stretching vibrational modes. The mode with a frequency of 1062 (cm-1) represents a symmetric stretch whilst the modes with a frequency of 930 (cm-1) represent asymmetric stretches. In contrast to ammonia, the highest frequency bond stretch of nitrogen trifluoride is the symmetric stretch.

Three bands can be expected in the NF3 IR spectrum at frequencies of 644 (cm-1) 930 (cm-1) and 1062 (cm-1). The bends at 482 (cm-1) will be too low in frequency to appear in the spectrum which starts at a frequency of 500 (cm-1). The stretches at 930 (cm-1) are degenerate and hence will only display one band between them. The band as 644 (cm-1) may not be clearly visible due its relative low intensity of 3 arbitrary units.

=== Charge analysis ===
[[File:Acc2518 NF3 charge analysis.png|The Gaussview generated atomic charges of ammonia.|250px]]

Fluorine has a greater electronegativity that nitrogen and therefore there is greater electron density distributed around the three fluorine atoms compared to the nitrogen atom. The three fluorine atoms are treated as equivalent which means that the magnitude of the positive charge on nitrogen is three times the magnitude of the negative charge on a single fluorine atom.

=== Molecular orbitals (MO) ===

The nitrogen atom contributes 7 electrons and each fluorine atom contributes 9 electrons which means that nitrogen trifluoride contains 34 electrons in total and hence 17 electron pairs. In the table below, a molecular orbital number of 1 would denote the molecular orbital that is deepest in energy. Therefore, orbital 17 represents the HOMO and orbital 18 represents the LUMO. All of the molecular orbitals shown below are occupied with the exception of the LUMO.

{| class="wikitable"
!Molecular orbital number
!Image
!Type of molecular orbital
!Energy (au)
!Extra details
|-
|18
|[[File:Acc2518 MO18.png|200px]]
|Antibonding
|0.01947
|There are nodes in the centre of the N-F bonds which indicates that the LUMO is an antibonding orbital with destructive inteference between phases of opposite sign. The nodes in the centre of all four atoms also indicate that this MO was formed from 2p atomic orbitals from both nitrogen and fluorine.
|-
|17
|[[File:Acc2518 MO17.png|200px]]
|Bonding
| -0.35162
| The phase denoted by the green region shows orbital overlap across all three N-H bonds which implies that the HOMO is a bonding orbital. This MO has been formed from 2p orbitals which explains the nodes observed in the centre of the F atoms.
|-
|16
|[[File:Acc2518 MO16.png|200px]]
|Non-bonding
| -0.42224
|There is no electron density along any of the bonds which is the key indicator that this is a non-bonding MO. Since the electron density is localised around the fluorine atoms, this MO appears to show lone electron pairs on these fluorine atoms. There is no electron density being shared between the fluorine atoms which suggests there is destructive interference preventing such an interaction.
|-
|15
|[[File:Acc2518 MO15.png|200px]]
|Bonding
| -0.43590
| As observed in the HOMO, there is electron density along all three bonds which indicates the bonding nature of the MO. However, in contrast to the HOMO, the electron density along the bonds is not in the same phase for each bond. There is also some constructive interference between two of the F atoms which appears to indicate a very partial π character between the two atoms. This also means that this interaction is the product of two 2p atomic orbitals on fluorine overlapping slightly in phase with each other.
|-
|5
|[[File:Acc2518 MO5.png|200px]]
| Bonding
| -1.35870
| This MO contains no nodes at all implying that it is bonding in nature. It is also formed from overlap of 2s orbitals, in phase, on all atoms since the entire molecule is encased in electron density as a result of the constructive interference. It cannot be formed from 1s orbitals which would be far lower in energy and will also only occupy the first 4 MOs since there are 8 1s electrons in NF3.
|}

File:Acc2518 MO5.png

2019-03-04T14:06:01Z

Acc2518:

Acc2518

2019-03-04T14:05:51Z

Acc2518: /* Molecular orbitals */

== NH3 molecule ==
=== Optimisation data ===
{| class="wikitable"
|+ NH3 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-56.55776873 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00000485 (au)
|-
|'''Point group'''
|C3V
|-
|'''Bond length (N-H)'''
|1.018 (Å)
|-
|'''Bond angle (H-N-H)'''
|106(°)
|}
<pre>
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
</pre>

<jmol><jmolApplet>
<title> NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518 NH3 OPTF POP.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>
[[:File:ACC2518 NH3 OPTF POP.LOG|Optimised NH3 .log file (acc2518)]]

=== Vibrations ===
[[File:Acc2518 vibrations screenshot.jpg|The Gaussview "Display Vibrations" window of the optimised ammonia molecule.|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 1090 || 1694
|-
| '''Symmetry''' || A1 || E
|-
| '''Intensity''' (arbitrary units) || 145 || 14
|-
| '''Image'''|| [[File:acc2518VM1.png|250px]] || [[File:acc2518VM2.png|300px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 1694|| 3461
|-
| '''Symmetry''' || E || A1
|-
| '''Intensity''' (arbitrary units) || 14 || 1
|-
| '''Image'''|| [[File:acc2518VM3.png|250px]] || [[File:acc2518VM4.png|275px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 3590|| 3590
|-
| '''Symmetry''' || E || E
|-
| '''Intensity''' (arbitrary units) || 0 || 0
|-
| '''Image'''|| [[File:acc2518VM5.png|275px]] || [[File:acc2518VM6.png|250px]]
|}

Using the 3N-6 rule, where N represents the number of atoms in a molecule, it is expected that ammonia will have six vibrational modes as shown above. There are two pairs of degenerate modes with a frequency of 1694 (cm-1) and 3590 (cm-1). The modes with a frequency of 1090 (cm-1) and 1694 (cm-1) correspond to bending vibrations and the modes with a frequency 3461 (cm-1) and 3590 (cm-1) correspond to bond stretch vibrations. The bond stretch vibration at 3461 (cm-1) is highly symmetric whilst the stretches with a frequency of 3590 (cm-1) are asymmetric. The bending vibration with a frequency of 1090 (cm-1) is known as the umbrella mode. Three bands would be expected to be seen with the two stretches at 3590 (cm-1) being too low in intensity. The bends with a frequency of 1694 (cm-1) are degenerate and only one band will be observed between the two. Hence the three observed bands would be at 1090 (cm-1), 1694 (cm-1) and 3461 (cm-1).

=== Charge analysis ===
[[File:Acc2518 charge analysis.png|The Gaussview generated atomic charges of ammonia.|250px]]

Nitrogen has a greater electronegativity than hydrogen and hence there is greater electron density distributed around the N atom in ammonia relative to hydrogen. This explains the negative charge on N and the positive charge on H.

==N2 molecule==

===Optimisation data===

{| class="wikitable"
|+ N2 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-109.52412868 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00000060 (au)
|-
|'''Point group'''
|D∞h
|-
|'''Bond length (N-N)'''
|1.10550 (Å)
|}

<pre>
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
</pre>

<jmol><jmolApplet>
<title> Nitrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518 N2 OPTIMISATION.LOG</uploadedFileContents>
<script>frame 1.10</script>
</jmolApplet></jmol>
[[:File:ACC2518 N2 OPTIMISATION.LOG|Optimised N2 .log file (acc2518)]]

===Vibrations===
[[File:Acc2518 N2vibration.png|Nitrogen display vibrations screenshot|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 2457
|-
| '''Symmetry''' || SGG
|-
| '''Intensity''' (arbitrary units) || 0
|-
| '''Image'''|| [[File:Acc2518NitrogenVM.png|250px]]
|}
Using the 3N-5 rule for linear molecules, Nitrogen can be expected to have one vibrational mode but this mode has an IR intensity of zero since Nitrogen molecules are IR inactive. This is because they have no overall dipole.

===Charge analysis===
[[File:Acc2518nitrogen charges.png]]

Both nitrogen atoms have the same electronegativity so the charge is neutral on both atoms.

===CCDC search===
'''Unique identifier:''' [https://www.ccdc.cam.ac.uk/structures/Search?Ccdcid=VAMQAE&DatabaseToSearch=Published VAMQAE]

'''Deposition number:''' 1530121

The complex linked above contains nitrogen coordinated to cobalt with a N-N bond distance of 1.08 Å which is slightly shorter than the optimised N-N bond length, displayed above, of 1.11 Å (3.s.f). During the optimisation process for nitrogen, assumptions have to be made for the computational process to be carried out. Each assumption made will increase the uncertainty in measurable quantities such as the bond length. Hence, the computationally determined bond length from the optimisation is a model and may not fully reflect the true bond length or the bond length determined by a computational program considering slightly different assumptions.

It should also be considered that the optimisation gave a prediction for the N-N bond length in a nitrogen molecule whereas the molecule linked above contains a nitrogen molecule that is coordinated into a transition metal complex. A lone pair of electrons on one of the nitrogen atoms has been donated to a cobalt ion, this draws electron density away from the donating nitrogen atom and would therefore slightly increase the positive charge on this atom. This may cause the donating nitrogen atom to attract the electrons in the N-N bond more strongly which would then explain the shorter bond in the transition metal complex compared to the nitrogen molecule.

==H2 molecule==

===Optimisation data===
{| class="wikitable"
|+ H2 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-1.17853936 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00000017 (au)
|-
|'''Point group'''
|D∞h
|-
|'''Bond length (N-N)'''
|0.74279 (Å)
|}

<pre>
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

</pre>

<jmol><jmolApplet>
<title> Hydrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518 H2 OPTIMISATION.LOG</uploadedFileContents>
<script>frame 1.7</script>
</jmolApplet></jmol>
[[:File:ACC2518 H2 OPTIMISATION.LOG|Optimised H2 .log file (acc2518)]]

===Vibrations===
[[File:Acc2518 H2vibration.png|Hydrogen display vibrations screenshot|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 4466
|-
| '''Symmetry''' || SGG
|-
| '''Intensity''' (arbitrary units) || 0
|-
| '''Image'''|| [[File:Acc2518HydrogenVM.png|250px]]
|}
Using the 3N-5 rule for linear molecules, hydrogen can be expected to have one vibrational mode but this mode has an IR intensity of zero since hydrogen molecules, like nitrogen molecules, are IR inactive.

===Charge analysis===
[[File:Acc2518hydrogen charges.png]]

Both hydrogen atoms have the same electronegativity so the charge is neutral on both atoms.

==The Haber-Bosch process==
N2 + 3H2 -> 2NH3

E(NH3)=-56.55776873

 '''2*E(NH3)''' =2*(-56.55776873)=-113.11553746

 '''E(N2)''' =-109.52412868

E(H2)=-1.17853936

 '''3*E(H2)''' =3*(-1.17853936) =-3.53561808

'''ΔE= 2*E(NH3) -[ E(N2) + 3*E(H2) ]'''= -0.05579069 ≈ -0.05579 au (5.d.p)

'''ΔE=-146.5 kJ/mol (1.d.p)'''

ΔE is negative which indicates that the gaseous reactants are less stable than the ammonia product since the reactants are at a higher energy than the product. Although this process is not necessarily entropically favourable with four reactant gaseous molecules forming two gaseous product molecules, the reaction has a significantly negative enthalpy change which reflects the result calculated above.

== Project molecule (NF3) ==

=== Optimisation data ===
{| class="wikitable"
|+ NF3 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-354.07131058 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00010256 (au)
|-
|'''Point group'''
|C3V
|-
|'''Bond length (N-F)'''
|1.384 (Å)
|-
|'''Bond angle (F-N-F)'''
|102(°)
|}
<pre>
Item Value Threshold Converged?
Maximum Force 0.000164 0.000450 YES
RMS Force 0.000108 0.000300 YES
Maximum Displacement 0.000612 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

<jmol><jmolApplet>
<title> NF3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518_NF3_OPTF_POP.LOG </uploadedFileContents>
<script>frame 1.7</script>
</jmolApplet></jmol>
[[:File:ACC2518_NF3_OPTF_POP.LOG|Optimised NF3 .log file (acc2518)]]

=== Vibrations ===
[[File:Acc2518 NF3 vibrations screenshot.png|The Gaussview "Display Vibrations" window of the optimised nitrogen trifluoride molecule.|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 482 || 482
|-
| '''Symmetry''' || E || E
|-
| '''Intensity''' (arbitrary units) || 1 || 1
|-
| '''Image'''|| [[File:Acc2518 NF3 VM1.png|300px]] || [[File:Acc2518 NF3 VM2.png|300px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 644|| 930
|-
| '''Symmetry''' || A1 || E
|-
| '''Intensity''' (arbitrary units) || 3 || 208
|-
| '''Image'''|| [[File:Acc2518 NF3 VM3.png|300px]] || [[File:Acc2518 NF3 VM4.png|300px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 930|| 1062
|-
| '''Symmetry''' || E || A1
|-
| '''Intensity''' (arbitrary units) || 208 || 40
|-
| '''Image'''|| [[File:Acc2518 NF3 VM5.png|300px]] || [[File:Acc2518 NF3 VM6.png|300px]]
|}

Nitrogen trifluoride has the same number of atoms as ammonia and so six vibrational modes can be predicted from the 3N-6 rule. There are also two pairs of degenerate modes with frequencies of 482 (cm-1) and 930 (cm-1). The modes with a frequency of 482 (cm-1) and 644(cm-1) correspond to bending vibrational modes and the modes with a frequency of 930 (cm-1) and 1062 (cm-1) correspond to stretching vibrational modes. The mode with a frequency of 1062 (cm-1) represents a symmetric stretch whilst the modes with a frequency of 930 (cm-1) represent asymmetric stretches. In contrast to ammonia, the highest frequency bond stretch of nitrogen trifluoride is the symmetric stretch.

Three bands can be expected in the NF3 IR spectrum at frequencies of 644 (cm-1) 930 (cm-1) and 1062 (cm-1). The bends at 482 (cm-1) will be too low in frequency to appear in the spectrum which starts at a frequency of 500 (cm-1). The stretches at 930 (cm-1) are degenerate and hence will only display one band between them. The band as 644 (cm-1) may not be clearly visible due its relative low intensity of 3 arbitrary units.

=== Charge analysis ===
[[File:Acc2518 NF3 charge analysis.png|The Gaussview generated atomic charges of ammonia.|250px]]

Fluorine has a greater electronegativity that nitrogen and therefore there is greater electron density distributed around the three fluorine atoms compared to the nitrogen atom. The three fluorine atoms are treated as equivalent which means that the magnitude of the positive charge on nitrogen is three times the magnitude of the negative charge on a single fluorine atom.

=== Molecular orbitals (MO) ===

The nitrogen atom contributes 7 electrons and each fluorine atom contributes 9 electrons which means that nitrogen trifluoride contains 34 electrons in total and hence 17 electron pairs. In the table below, a molecular orbital number of 1 would denote the molecular orbital that is deepest in energy. Therefore, orbital 17 represents the HOMO and orbital 18 represents the LUMO. All of the molecular orbitals shown below are occupied with the exception of the LUMO.

{| class="wikitable"
!Molecular orbital number
!Image
!Type of molecular orbital
!Energy (au)
!Extra details
|-
|18
|[[File:Acc2518 MO18.png|200px]]
|Antibonding
|0.01947
|There are nodes in the centre of the N-F bonds which indicates that the LUMO is an antibonding orbital with destructive inteference between phases of opposite sign. The nodes in the centre of all four atoms also indicate that this MO was formed from 2p atomic orbitals from both nitrogen and fluorine.
|-
|17
|[[File:Acc2518 MO17.png|200px]]
|Bonding
| -0.35162
| The phase denoted by the green region shows orbital overlap across all three N-H bonds which implies that the HOMO is a bonding orbital. This MO has been formed from 2p orbitals which explains the nodes observed in the centre of the F atoms.
|-
|16
|[[File:Acc2518 MO16.png|200px]]
|Non-bonding
| -0.42224
|There is no electron density along any of the bonds which is the key indicator that this is a non-bonding MO. Since the electron density is localised around the fluorine atoms, this MO appears to show lone electron pairs on these fluorine atoms. There is no electron density being shared between the fluorine atoms which suggests there is destructive interference preventing such an interaction.
|-
|15
|[[File:Acc2518 MO15.png|200px]]
|Bonding
| -0.43590
| As observed in the HOMO, there is electron density along all three bonds which indicates the bonding nature of the MO. However, in contrast to the HOMO, the electron density along the bonds is not in the same phase for each bond. There is also some constructive interference between two of the F atoms which appears to indicate a very partial π character between the two atoms. This also means that this interaction is the product of two 2p atomic orbitals on fluorine overlapping slightly in phase with each other.
|-
|5
|[[File:Acc2518 MO5.png|200px]]
| Bonding
| -1.35870
| This MO contains no nodes at all implying that it is bonding in nature. It is also formed from overlap of 2s orbitals, in phase, on all atoms since the entire molecule is encased in electron density as a result of the constructive interference. It cannot be formed from 1s orbitals which would be far lower in energy and will also only occupy the first 4 MOs since there are 8 1s electrons in NF3.
|}

File:Acc2518 MO15.png

2019-03-04T13:56:10Z

Acc2518:

Acc2518

2019-03-04T13:48:42Z

Acc2518: /* Molecular orbitals */

== NH3 molecule ==
=== Optimisation data ===
{| class="wikitable"
|+ NH3 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-56.55776873 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00000485 (au)
|-
|'''Point group'''
|C3V
|-
|'''Bond length (N-H)'''
|1.018 (Å)
|-
|'''Bond angle (H-N-H)'''
|106(°)
|}
<pre>
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
</pre>

<jmol><jmolApplet>
<title> NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518 NH3 OPTF POP.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>
[[:File:ACC2518 NH3 OPTF POP.LOG|Optimised NH3 .log file (acc2518)]]

=== Vibrations ===
[[File:Acc2518 vibrations screenshot.jpg|The Gaussview "Display Vibrations" window of the optimised ammonia molecule.|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 1090 || 1694
|-
| '''Symmetry''' || A1 || E
|-
| '''Intensity''' (arbitrary units) || 145 || 14
|-
| '''Image'''|| [[File:acc2518VM1.png|250px]] || [[File:acc2518VM2.png|300px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 1694|| 3461
|-
| '''Symmetry''' || E || A1
|-
| '''Intensity''' (arbitrary units) || 14 || 1
|-
| '''Image'''|| [[File:acc2518VM3.png|250px]] || [[File:acc2518VM4.png|275px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 3590|| 3590
|-
| '''Symmetry''' || E || E
|-
| '''Intensity''' (arbitrary units) || 0 || 0
|-
| '''Image'''|| [[File:acc2518VM5.png|275px]] || [[File:acc2518VM6.png|250px]]
|}

Using the 3N-6 rule, where N represents the number of atoms in a molecule, it is expected that ammonia will have six vibrational modes as shown above. There are two pairs of degenerate modes with a frequency of 1694 (cm-1) and 3590 (cm-1). The modes with a frequency of 1090 (cm-1) and 1694 (cm-1) correspond to bending vibrations and the modes with a frequency 3461 (cm-1) and 3590 (cm-1) correspond to bond stretch vibrations. The bond stretch vibration at 3461 (cm-1) is highly symmetric whilst the stretches with a frequency of 3590 (cm-1) are asymmetric. The bending vibration with a frequency of 1090 (cm-1) is known as the umbrella mode. Three bands would be expected to be seen with the two stretches at 3590 (cm-1) being too low in intensity. The bends with a frequency of 1694 (cm-1) are degenerate and only one band will be observed between the two. Hence the three observed bands would be at 1090 (cm-1), 1694 (cm-1) and 3461 (cm-1).

=== Charge analysis ===
[[File:Acc2518 charge analysis.png|The Gaussview generated atomic charges of ammonia.|250px]]

Nitrogen has a greater electronegativity than hydrogen and hence there is greater electron density distributed around the N atom in ammonia relative to hydrogen. This explains the negative charge on N and the positive charge on H.

==N2 molecule==

===Optimisation data===

{| class="wikitable"
|+ N2 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-109.52412868 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00000060 (au)
|-
|'''Point group'''
|D∞h
|-
|'''Bond length (N-N)'''
|1.10550 (Å)
|}

<pre>
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
</pre>

<jmol><jmolApplet>
<title> Nitrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518 N2 OPTIMISATION.LOG</uploadedFileContents>
<script>frame 1.10</script>
</jmolApplet></jmol>
[[:File:ACC2518 N2 OPTIMISATION.LOG|Optimised N2 .log file (acc2518)]]

===Vibrations===
[[File:Acc2518 N2vibration.png|Nitrogen display vibrations screenshot|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 2457
|-
| '''Symmetry''' || SGG
|-
| '''Intensity''' (arbitrary units) || 0
|-
| '''Image'''|| [[File:Acc2518NitrogenVM.png|250px]]
|}
Using the 3N-5 rule for linear molecules, Nitrogen can be expected to have one vibrational mode but this mode has an IR intensity of zero since Nitrogen molecules are IR inactive. This is because they have no overall dipole.

===Charge analysis===
[[File:Acc2518nitrogen charges.png]]

Both nitrogen atoms have the same electronegativity so the charge is neutral on both atoms.

===CCDC search===
'''Unique identifier:''' [https://www.ccdc.cam.ac.uk/structures/Search?Ccdcid=VAMQAE&DatabaseToSearch=Published VAMQAE]

'''Deposition number:''' 1530121

The complex linked above contains nitrogen coordinated to cobalt with a N-N bond distance of 1.08 Å which is slightly shorter than the optimised N-N bond length, displayed above, of 1.11 Å (3.s.f). During the optimisation process for nitrogen, assumptions have to be made for the computational process to be carried out. Each assumption made will increase the uncertainty in measurable quantities such as the bond length. Hence, the computationally determined bond length from the optimisation is a model and may not fully reflect the true bond length or the bond length determined by a computational program considering slightly different assumptions.

It should also be considered that the optimisation gave a prediction for the N-N bond length in a nitrogen molecule whereas the molecule linked above contains a nitrogen molecule that is coordinated into a transition metal complex. A lone pair of electrons on one of the nitrogen atoms has been donated to a cobalt ion, this draws electron density away from the donating nitrogen atom and would therefore slightly increase the positive charge on this atom. This may cause the donating nitrogen atom to attract the electrons in the N-N bond more strongly which would then explain the shorter bond in the transition metal complex compared to the nitrogen molecule.

==H2 molecule==

===Optimisation data===
{| class="wikitable"
|+ H2 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-1.17853936 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00000017 (au)
|-
|'''Point group'''
|D∞h
|-
|'''Bond length (N-N)'''
|0.74279 (Å)
|}

<pre>
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

</pre>

<jmol><jmolApplet>
<title> Hydrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518 H2 OPTIMISATION.LOG</uploadedFileContents>
<script>frame 1.7</script>
</jmolApplet></jmol>
[[:File:ACC2518 H2 OPTIMISATION.LOG|Optimised H2 .log file (acc2518)]]

===Vibrations===
[[File:Acc2518 H2vibration.png|Hydrogen display vibrations screenshot|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 4466
|-
| '''Symmetry''' || SGG
|-
| '''Intensity''' (arbitrary units) || 0
|-
| '''Image'''|| [[File:Acc2518HydrogenVM.png|250px]]
|}
Using the 3N-5 rule for linear molecules, hydrogen can be expected to have one vibrational mode but this mode has an IR intensity of zero since hydrogen molecules, like nitrogen molecules, are IR inactive.

===Charge analysis===
[[File:Acc2518hydrogen charges.png]]

Both hydrogen atoms have the same electronegativity so the charge is neutral on both atoms.

==The Haber-Bosch process==
N2 + 3H2 -> 2NH3

E(NH3)=-56.55776873

 '''2*E(NH3)''' =2*(-56.55776873)=-113.11553746

 '''E(N2)''' =-109.52412868

E(H2)=-1.17853936

 '''3*E(H2)''' =3*(-1.17853936) =-3.53561808

'''ΔE= 2*E(NH3) -[ E(N2) + 3*E(H2) ]'''= -0.05579069 ≈ -0.05579 au (5.d.p)

'''ΔE=-146.5 kJ/mol (1.d.p)'''

ΔE is negative which indicates that the gaseous reactants are less stable than the ammonia product since the reactants are at a higher energy than the product. Although this process is not necessarily entropically favourable with four reactant gaseous molecules forming two gaseous product molecules, the reaction has a significantly negative enthalpy change which reflects the result calculated above.

== Project molecule (NF3) ==

=== Optimisation data ===
{| class="wikitable"
|+ NF3 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-354.07131058 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00010256 (au)
|-
|'''Point group'''
|C3V
|-
|'''Bond length (N-F)'''
|1.384 (Å)
|-
|'''Bond angle (F-N-F)'''
|102(°)
|}
<pre>
Item Value Threshold Converged?
Maximum Force 0.000164 0.000450 YES
RMS Force 0.000108 0.000300 YES
Maximum Displacement 0.000612 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

<jmol><jmolApplet>
<title> NF3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518_NF3_OPTF_POP.LOG </uploadedFileContents>
<script>frame 1.7</script>
</jmolApplet></jmol>
[[:File:ACC2518_NF3_OPTF_POP.LOG|Optimised NF3 .log file (acc2518)]]

=== Vibrations ===
[[File:Acc2518 NF3 vibrations screenshot.png|The Gaussview "Display Vibrations" window of the optimised nitrogen trifluoride molecule.|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 482 || 482
|-
| '''Symmetry''' || E || E
|-
| '''Intensity''' (arbitrary units) || 1 || 1
|-
| '''Image'''|| [[File:Acc2518 NF3 VM1.png|300px]] || [[File:Acc2518 NF3 VM2.png|300px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 644|| 930
|-
| '''Symmetry''' || A1 || E
|-
| '''Intensity''' (arbitrary units) || 3 || 208
|-
| '''Image'''|| [[File:Acc2518 NF3 VM3.png|300px]] || [[File:Acc2518 NF3 VM4.png|300px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 930|| 1062
|-
| '''Symmetry''' || E || A1
|-
| '''Intensity''' (arbitrary units) || 208 || 40
|-
| '''Image'''|| [[File:Acc2518 NF3 VM5.png|300px]] || [[File:Acc2518 NF3 VM6.png|300px]]
|}

Nitrogen trifluoride has the same number of atoms as ammonia and so six vibrational modes can be predicted from the 3N-6 rule. There are also two pairs of degenerate modes with frequencies of 482 (cm-1) and 930 (cm-1). The modes with a frequency of 482 (cm-1) and 644(cm-1) correspond to bending vibrational modes and the modes with a frequency of 930 (cm-1) and 1062 (cm-1) correspond to stretching vibrational modes. The mode with a frequency of 1062 (cm-1) represents a symmetric stretch whilst the modes with a frequency of 930 (cm-1) represent asymmetric stretches. In contrast to ammonia, the highest frequency bond stretch of nitrogen trifluoride is the symmetric stretch.

Three bands can be expected in the NF3 IR spectrum at frequencies of 644 (cm-1) 930 (cm-1) and 1062 (cm-1). The bends at 482 (cm-1) will be too low in frequency to appear in the spectrum which starts at a frequency of 500 (cm-1). The stretches at 930 (cm-1) are degenerate and hence will only display one band between them. The band as 644 (cm-1) may not be clearly visible due its relative low intensity of 3 arbitrary units.

=== Charge analysis ===
[[File:Acc2518 NF3 charge analysis.png|The Gaussview generated atomic charges of ammonia.|250px]]

Fluorine has a greater electronegativity that nitrogen and therefore there is greater electron density distributed around the three fluorine atoms compared to the nitrogen atom. The three fluorine atoms are treated as equivalent which means that the magnitude of the positive charge on nitrogen is three times the magnitude of the negative charge on a single fluorine atom.

=== Molecular orbitals ===

The nitrogen atom contributes 7 electrons and each fluorine atom contributes 9 electrons which means that nitrogen trifluoride contains 34 electrons in total and hence 17 electron pairs. In the table below, a molecular orbital number of 1 would denote the molecular orbital that is deepest in energy. Therefore, orbital 17 represents the HOMO and orbital 18 represents the LUMO. All of the molecular orbitals shown below are occupied with the exception of the LUMO.

{| class="wikitable"
!Molecular orbital number
!Image
!Type of molecular orbital
!Energy (au)
!Extra details
|-
|18
|[[File:Acc2518 MO18.png|200px]]
|Antibonding
|0.01947
|There are nodes in the centre of the N-F bonds which indicates that the LUMO is an antibonding orbital with destructive inteference between phases of opposite sign. The nodes in the centre of all four atoms also indicate that this molecular orbital was formed from 2p atomic orbitals from both nitrogen and fluorine.
|-
|17
|[[File:Acc2518 MO17.png|200px]]
|Bonding
| -0.35162
| The phase denoted by the green region shows orbital overlap across all three N-H bonds which implies that the HOMO is a bonding orbital. This molecular orbital has been formed from 2p orbitals which explains the nodes observed in the centre of the F atoms.
|-
|16
|[[File:Acc2518 MO16.png|200px]]
|Non-bonding
| -0.42224
|There is no electron density along any of the bonds which is the key indicator that this is a non-bonding molecular orbital. Since the electron density is localised around the fluorine atoms, this molecular orbital appears to show lone electron pairs on these fluorine atoms. There is no electron density being shared between the fluorine atoms which suggests there is destructive interference preventing such an interaction.
|-
|15
|
|
|
|
|-
|
|
|
|
|
|}

Acc2518

2019-03-04T13:47:22Z

Acc2518: /* Molecular orbitals */

== NH3 molecule ==
=== Optimisation data ===
{| class="wikitable"
|+ NH3 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-56.55776873 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00000485 (au)
|-
|'''Point group'''
|C3V
|-
|'''Bond length (N-H)'''
|1.018 (Å)
|-
|'''Bond angle (H-N-H)'''
|106(°)
|}
<pre>
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
</pre>

<jmol><jmolApplet>
<title> NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518 NH3 OPTF POP.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>
[[:File:ACC2518 NH3 OPTF POP.LOG|Optimised NH3 .log file (acc2518)]]

=== Vibrations ===
[[File:Acc2518 vibrations screenshot.jpg|The Gaussview "Display Vibrations" window of the optimised ammonia molecule.|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 1090 || 1694
|-
| '''Symmetry''' || A1 || E
|-
| '''Intensity''' (arbitrary units) || 145 || 14
|-
| '''Image'''|| [[File:acc2518VM1.png|250px]] || [[File:acc2518VM2.png|300px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 1694|| 3461
|-
| '''Symmetry''' || E || A1
|-
| '''Intensity''' (arbitrary units) || 14 || 1
|-
| '''Image'''|| [[File:acc2518VM3.png|250px]] || [[File:acc2518VM4.png|275px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 3590|| 3590
|-
| '''Symmetry''' || E || E
|-
| '''Intensity''' (arbitrary units) || 0 || 0
|-
| '''Image'''|| [[File:acc2518VM5.png|275px]] || [[File:acc2518VM6.png|250px]]
|}

Using the 3N-6 rule, where N represents the number of atoms in a molecule, it is expected that ammonia will have six vibrational modes as shown above. There are two pairs of degenerate modes with a frequency of 1694 (cm-1) and 3590 (cm-1). The modes with a frequency of 1090 (cm-1) and 1694 (cm-1) correspond to bending vibrations and the modes with a frequency 3461 (cm-1) and 3590 (cm-1) correspond to bond stretch vibrations. The bond stretch vibration at 3461 (cm-1) is highly symmetric whilst the stretches with a frequency of 3590 (cm-1) are asymmetric. The bending vibration with a frequency of 1090 (cm-1) is known as the umbrella mode. Three bands would be expected to be seen with the two stretches at 3590 (cm-1) being too low in intensity. The bends with a frequency of 1694 (cm-1) are degenerate and only one band will be observed between the two. Hence the three observed bands would be at 1090 (cm-1), 1694 (cm-1) and 3461 (cm-1).

=== Charge analysis ===
[[File:Acc2518 charge analysis.png|The Gaussview generated atomic charges of ammonia.|250px]]

Nitrogen has a greater electronegativity than hydrogen and hence there is greater electron density distributed around the N atom in ammonia relative to hydrogen. This explains the negative charge on N and the positive charge on H.

==N2 molecule==

===Optimisation data===

{| class="wikitable"
|+ N2 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-109.52412868 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00000060 (au)
|-
|'''Point group'''
|D∞h
|-
|'''Bond length (N-N)'''
|1.10550 (Å)
|}

<pre>
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
</pre>

<jmol><jmolApplet>
<title> Nitrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518 N2 OPTIMISATION.LOG</uploadedFileContents>
<script>frame 1.10</script>
</jmolApplet></jmol>
[[:File:ACC2518 N2 OPTIMISATION.LOG|Optimised N2 .log file (acc2518)]]

===Vibrations===
[[File:Acc2518 N2vibration.png|Nitrogen display vibrations screenshot|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 2457
|-
| '''Symmetry''' || SGG
|-
| '''Intensity''' (arbitrary units) || 0
|-
| '''Image'''|| [[File:Acc2518NitrogenVM.png|250px]]
|}
Using the 3N-5 rule for linear molecules, Nitrogen can be expected to have one vibrational mode but this mode has an IR intensity of zero since Nitrogen molecules are IR inactive. This is because they have no overall dipole.

===Charge analysis===
[[File:Acc2518nitrogen charges.png]]

Both nitrogen atoms have the same electronegativity so the charge is neutral on both atoms.

===CCDC search===
'''Unique identifier:''' [https://www.ccdc.cam.ac.uk/structures/Search?Ccdcid=VAMQAE&DatabaseToSearch=Published VAMQAE]

'''Deposition number:''' 1530121

The complex linked above contains nitrogen coordinated to cobalt with a N-N bond distance of 1.08 Å which is slightly shorter than the optimised N-N bond length, displayed above, of 1.11 Å (3.s.f). During the optimisation process for nitrogen, assumptions have to be made for the computational process to be carried out. Each assumption made will increase the uncertainty in measurable quantities such as the bond length. Hence, the computationally determined bond length from the optimisation is a model and may not fully reflect the true bond length or the bond length determined by a computational program considering slightly different assumptions.

It should also be considered that the optimisation gave a prediction for the N-N bond length in a nitrogen molecule whereas the molecule linked above contains a nitrogen molecule that is coordinated into a transition metal complex. A lone pair of electrons on one of the nitrogen atoms has been donated to a cobalt ion, this draws electron density away from the donating nitrogen atom and would therefore slightly increase the positive charge on this atom. This may cause the donating nitrogen atom to attract the electrons in the N-N bond more strongly which would then explain the shorter bond in the transition metal complex compared to the nitrogen molecule.

==H2 molecule==

===Optimisation data===
{| class="wikitable"
|+ H2 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-1.17853936 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00000017 (au)
|-
|'''Point group'''
|D∞h
|-
|'''Bond length (N-N)'''
|0.74279 (Å)
|}

<pre>
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

</pre>

<jmol><jmolApplet>
<title> Hydrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518 H2 OPTIMISATION.LOG</uploadedFileContents>
<script>frame 1.7</script>
</jmolApplet></jmol>
[[:File:ACC2518 H2 OPTIMISATION.LOG|Optimised H2 .log file (acc2518)]]

===Vibrations===
[[File:Acc2518 H2vibration.png|Hydrogen display vibrations screenshot|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 4466
|-
| '''Symmetry''' || SGG
|-
| '''Intensity''' (arbitrary units) || 0
|-
| '''Image'''|| [[File:Acc2518HydrogenVM.png|250px]]
|}
Using the 3N-5 rule for linear molecules, hydrogen can be expected to have one vibrational mode but this mode has an IR intensity of zero since hydrogen molecules, like nitrogen molecules, are IR inactive.

===Charge analysis===
[[File:Acc2518hydrogen charges.png]]

Both hydrogen atoms have the same electronegativity so the charge is neutral on both atoms.

==The Haber-Bosch process==
N2 + 3H2 -> 2NH3

E(NH3)=-56.55776873

 '''2*E(NH3)''' =2*(-56.55776873)=-113.11553746

 '''E(N2)''' =-109.52412868

E(H2)=-1.17853936

 '''3*E(H2)''' =3*(-1.17853936) =-3.53561808

'''ΔE= 2*E(NH3) -[ E(N2) + 3*E(H2) ]'''= -0.05579069 ≈ -0.05579 au (5.d.p)

'''ΔE=-146.5 kJ/mol (1.d.p)'''

ΔE is negative which indicates that the gaseous reactants are less stable than the ammonia product since the reactants are at a higher energy than the product. Although this process is not necessarily entropically favourable with four reactant gaseous molecules forming two gaseous product molecules, the reaction has a significantly negative enthalpy change which reflects the result calculated above.

== Project molecule (NF3) ==

=== Optimisation data ===
{| class="wikitable"
|+ NF3 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-354.07131058 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00010256 (au)
|-
|'''Point group'''
|C3V
|-
|'''Bond length (N-F)'''
|1.384 (Å)
|-
|'''Bond angle (F-N-F)'''
|102(°)
|}
<pre>
Item Value Threshold Converged?
Maximum Force 0.000164 0.000450 YES
RMS Force 0.000108 0.000300 YES
Maximum Displacement 0.000612 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

<jmol><jmolApplet>
<title> NF3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518_NF3_OPTF_POP.LOG </uploadedFileContents>
<script>frame 1.7</script>
</jmolApplet></jmol>
[[:File:ACC2518_NF3_OPTF_POP.LOG|Optimised NF3 .log file (acc2518)]]

=== Vibrations ===
[[File:Acc2518 NF3 vibrations screenshot.png|The Gaussview "Display Vibrations" window of the optimised nitrogen trifluoride molecule.|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 482 || 482
|-
| '''Symmetry''' || E || E
|-
| '''Intensity''' (arbitrary units) || 1 || 1
|-
| '''Image'''|| [[File:Acc2518 NF3 VM1.png|300px]] || [[File:Acc2518 NF3 VM2.png|300px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 644|| 930
|-
| '''Symmetry''' || A1 || E
|-
| '''Intensity''' (arbitrary units) || 3 || 208
|-
| '''Image'''|| [[File:Acc2518 NF3 VM3.png|300px]] || [[File:Acc2518 NF3 VM4.png|300px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 930|| 1062
|-
| '''Symmetry''' || E || A1
|-
| '''Intensity''' (arbitrary units) || 208 || 40
|-
| '''Image'''|| [[File:Acc2518 NF3 VM5.png|300px]] || [[File:Acc2518 NF3 VM6.png|300px]]
|}

Nitrogen trifluoride has the same number of atoms as ammonia and so six vibrational modes can be predicted from the 3N-6 rule. There are also two pairs of degenerate modes with frequencies of 482 (cm-1) and 930 (cm-1). The modes with a frequency of 482 (cm-1) and 644(cm-1) correspond to bending vibrational modes and the modes with a frequency of 930 (cm-1) and 1062 (cm-1) correspond to stretching vibrational modes. The mode with a frequency of 1062 (cm-1) represents a symmetric stretch whilst the modes with a frequency of 930 (cm-1) represent asymmetric stretches. In contrast to ammonia, the highest frequency bond stretch of nitrogen trifluoride is the symmetric stretch.

Three bands can be expected in the NF3 IR spectrum at frequencies of 644 (cm-1) 930 (cm-1) and 1062 (cm-1). The bends at 482 (cm-1) will be too low in frequency to appear in the spectrum which starts at a frequency of 500 (cm-1). The stretches at 930 (cm-1) are degenerate and hence will only display one band between them. The band as 644 (cm-1) may not be clearly visible due its relative low intensity of 3 arbitrary units.

=== Charge analysis ===
[[File:Acc2518 NF3 charge analysis.png|The Gaussview generated atomic charges of ammonia.|250px]]

Fluorine has a greater electronegativity that nitrogen and therefore there is greater electron density distributed around the three fluorine atoms compared to the nitrogen atom. The three fluorine atoms are treated as equivalent which means that the magnitude of the positive charge on nitrogen is three times the magnitude of the negative charge on a single fluorine atom.

=== Molecular orbitals ===

The nitrogen atom contributes 7 electrons and each fluorine atom contributes 9 electrons which means that nitrogen trifluoride contains 34 electrons in total and hence 17 electron pairs. In the table below, a molecular orbital number of 1 would denote the molecular orbital that is deepest in energy. Therefore, orbital 17 represents the HOMO and orbital 18 represents the LUMO.

{| class="wikitable"
!Molecular orbital number
!Image
!Type of molecular orbital
!Energy (au)
!Extra details
|-
|18
|[[File:Acc2518 MO18.png|200px]]
|Antibonding
|0.01947
|There are nodes in the centre of the N-F bonds which indicates that the LUMO is an antibonding orbital with destructive inteference between phases of opposite sign. The nodes in the centre of all four atoms also indicate that this molecular orbital was formed from 2p atomic orbitals from both nitrogen and fluorine.
|-
|17
|[[File:Acc2518 MO17.png|200px]]
|Bonding
| -0.35162
| The phase denoted by the green region shows orbital overlap across all three N-H bonds which implies that the HOMO is a bonding orbital. This molecular orbital has been formed from 2p orbitals which explains the nodes observed in the centre of the F atoms.
|-
|16
|[[File:Acc2518 MO16.png|200px]]
|Non-bonding
| -0.42224
|There is no electron density along any of the bonds which is the key indicator that this is a non-bonding molecular orbital. Since the electron density is localised around the fluorine atoms, this molecular orbital appears to show lone electron pairs on these fluorine atoms. There is no electron density being shared between the fluorine atoms which suggests there is destructive interference preventing such an interaction.
|-
|
|
|
|
|
|-
|
|
|
|
|
|}

Acc2518

2019-03-04T13:40:05Z

Acc2518: /* Molecular orbitals */

== NH3 molecule ==
=== Optimisation data ===
{| class="wikitable"
|+ NH3 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-56.55776873 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00000485 (au)
|-
|'''Point group'''
|C3V
|-
|'''Bond length (N-H)'''
|1.018 (Å)
|-
|'''Bond angle (H-N-H)'''
|106(°)
|}
<pre>
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
</pre>

<jmol><jmolApplet>
<title> NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518 NH3 OPTF POP.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>
[[:File:ACC2518 NH3 OPTF POP.LOG|Optimised NH3 .log file (acc2518)]]

=== Vibrations ===
[[File:Acc2518 vibrations screenshot.jpg|The Gaussview "Display Vibrations" window of the optimised ammonia molecule.|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 1090 || 1694
|-
| '''Symmetry''' || A1 || E
|-
| '''Intensity''' (arbitrary units) || 145 || 14
|-
| '''Image'''|| [[File:acc2518VM1.png|250px]] || [[File:acc2518VM2.png|300px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 1694|| 3461
|-
| '''Symmetry''' || E || A1
|-
| '''Intensity''' (arbitrary units) || 14 || 1
|-
| '''Image'''|| [[File:acc2518VM3.png|250px]] || [[File:acc2518VM4.png|275px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 3590|| 3590
|-
| '''Symmetry''' || E || E
|-
| '''Intensity''' (arbitrary units) || 0 || 0
|-
| '''Image'''|| [[File:acc2518VM5.png|275px]] || [[File:acc2518VM6.png|250px]]
|}

Using the 3N-6 rule, where N represents the number of atoms in a molecule, it is expected that ammonia will have six vibrational modes as shown above. There are two pairs of degenerate modes with a frequency of 1694 (cm-1) and 3590 (cm-1). The modes with a frequency of 1090 (cm-1) and 1694 (cm-1) correspond to bending vibrations and the modes with a frequency 3461 (cm-1) and 3590 (cm-1) correspond to bond stretch vibrations. The bond stretch vibration at 3461 (cm-1) is highly symmetric whilst the stretches with a frequency of 3590 (cm-1) are asymmetric. The bending vibration with a frequency of 1090 (cm-1) is known as the umbrella mode. Three bands would be expected to be seen with the two stretches at 3590 (cm-1) being too low in intensity. The bends with a frequency of 1694 (cm-1) are degenerate and only one band will be observed between the two. Hence the three observed bands would be at 1090 (cm-1), 1694 (cm-1) and 3461 (cm-1).

=== Charge analysis ===
[[File:Acc2518 charge analysis.png|The Gaussview generated atomic charges of ammonia.|250px]]

Nitrogen has a greater electronegativity than hydrogen and hence there is greater electron density distributed around the N atom in ammonia relative to hydrogen. This explains the negative charge on N and the positive charge on H.

==N2 molecule==

===Optimisation data===

{| class="wikitable"
|+ N2 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-109.52412868 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00000060 (au)
|-
|'''Point group'''
|D∞h
|-
|'''Bond length (N-N)'''
|1.10550 (Å)
|}

<pre>
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
</pre>

<jmol><jmolApplet>
<title> Nitrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518 N2 OPTIMISATION.LOG</uploadedFileContents>
<script>frame 1.10</script>
</jmolApplet></jmol>
[[:File:ACC2518 N2 OPTIMISATION.LOG|Optimised N2 .log file (acc2518)]]

===Vibrations===
[[File:Acc2518 N2vibration.png|Nitrogen display vibrations screenshot|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 2457
|-
| '''Symmetry''' || SGG
|-
| '''Intensity''' (arbitrary units) || 0
|-
| '''Image'''|| [[File:Acc2518NitrogenVM.png|250px]]
|}
Using the 3N-5 rule for linear molecules, Nitrogen can be expected to have one vibrational mode but this mode has an IR intensity of zero since Nitrogen molecules are IR inactive. This is because they have no overall dipole.

===Charge analysis===
[[File:Acc2518nitrogen charges.png]]

Both nitrogen atoms have the same electronegativity so the charge is neutral on both atoms.

===CCDC search===
'''Unique identifier:''' [https://www.ccdc.cam.ac.uk/structures/Search?Ccdcid=VAMQAE&DatabaseToSearch=Published VAMQAE]

'''Deposition number:''' 1530121

The complex linked above contains nitrogen coordinated to cobalt with a N-N bond distance of 1.08 Å which is slightly shorter than the optimised N-N bond length, displayed above, of 1.11 Å (3.s.f). During the optimisation process for nitrogen, assumptions have to be made for the computational process to be carried out. Each assumption made will increase the uncertainty in measurable quantities such as the bond length. Hence, the computationally determined bond length from the optimisation is a model and may not fully reflect the true bond length or the bond length determined by a computational program considering slightly different assumptions.

It should also be considered that the optimisation gave a prediction for the N-N bond length in a nitrogen molecule whereas the molecule linked above contains a nitrogen molecule that is coordinated into a transition metal complex. A lone pair of electrons on one of the nitrogen atoms has been donated to a cobalt ion, this draws electron density away from the donating nitrogen atom and would therefore slightly increase the positive charge on this atom. This may cause the donating nitrogen atom to attract the electrons in the N-N bond more strongly which would then explain the shorter bond in the transition metal complex compared to the nitrogen molecule.

==H2 molecule==

===Optimisation data===
{| class="wikitable"
|+ H2 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-1.17853936 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00000017 (au)
|-
|'''Point group'''
|D∞h
|-
|'''Bond length (N-N)'''
|0.74279 (Å)
|}

<pre>
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

</pre>

<jmol><jmolApplet>
<title> Hydrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518 H2 OPTIMISATION.LOG</uploadedFileContents>
<script>frame 1.7</script>
</jmolApplet></jmol>
[[:File:ACC2518 H2 OPTIMISATION.LOG|Optimised H2 .log file (acc2518)]]

===Vibrations===
[[File:Acc2518 H2vibration.png|Hydrogen display vibrations screenshot|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 4466
|-
| '''Symmetry''' || SGG
|-
| '''Intensity''' (arbitrary units) || 0
|-
| '''Image'''|| [[File:Acc2518HydrogenVM.png|250px]]
|}
Using the 3N-5 rule for linear molecules, hydrogen can be expected to have one vibrational mode but this mode has an IR intensity of zero since hydrogen molecules, like nitrogen molecules, are IR inactive.

===Charge analysis===
[[File:Acc2518hydrogen charges.png]]

Both hydrogen atoms have the same electronegativity so the charge is neutral on both atoms.

==The Haber-Bosch process==
N2 + 3H2 -> 2NH3

E(NH3)=-56.55776873

 '''2*E(NH3)''' =2*(-56.55776873)=-113.11553746

 '''E(N2)''' =-109.52412868

E(H2)=-1.17853936

 '''3*E(H2)''' =3*(-1.17853936) =-3.53561808

'''ΔE= 2*E(NH3) -[ E(N2) + 3*E(H2) ]'''= -0.05579069 ≈ -0.05579 au (5.d.p)

'''ΔE=-146.5 kJ/mol (1.d.p)'''

ΔE is negative which indicates that the gaseous reactants are less stable than the ammonia product since the reactants are at a higher energy than the product. Although this process is not necessarily entropically favourable with four reactant gaseous molecules forming two gaseous product molecules, the reaction has a significantly negative enthalpy change which reflects the result calculated above.

== Project molecule (NF3) ==

=== Optimisation data ===
{| class="wikitable"
|+ NF3 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-354.07131058 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00010256 (au)
|-
|'''Point group'''
|C3V
|-
|'''Bond length (N-F)'''
|1.384 (Å)
|-
|'''Bond angle (F-N-F)'''
|102(°)
|}
<pre>
Item Value Threshold Converged?
Maximum Force 0.000164 0.000450 YES
RMS Force 0.000108 0.000300 YES
Maximum Displacement 0.000612 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

<jmol><jmolApplet>
<title> NF3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518_NF3_OPTF_POP.LOG </uploadedFileContents>
<script>frame 1.7</script>
</jmolApplet></jmol>
[[:File:ACC2518_NF3_OPTF_POP.LOG|Optimised NF3 .log file (acc2518)]]

=== Vibrations ===
[[File:Acc2518 NF3 vibrations screenshot.png|The Gaussview "Display Vibrations" window of the optimised nitrogen trifluoride molecule.|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 482 || 482
|-
| '''Symmetry''' || E || E
|-
| '''Intensity''' (arbitrary units) || 1 || 1
|-
| '''Image'''|| [[File:Acc2518 NF3 VM1.png|300px]] || [[File:Acc2518 NF3 VM2.png|300px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 644|| 930
|-
| '''Symmetry''' || A1 || E
|-
| '''Intensity''' (arbitrary units) || 3 || 208
|-
| '''Image'''|| [[File:Acc2518 NF3 VM3.png|300px]] || [[File:Acc2518 NF3 VM4.png|300px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 930|| 1062
|-
| '''Symmetry''' || E || A1
|-
| '''Intensity''' (arbitrary units) || 208 || 40
|-
| '''Image'''|| [[File:Acc2518 NF3 VM5.png|300px]] || [[File:Acc2518 NF3 VM6.png|300px]]
|}

Nitrogen trifluoride has the same number of atoms as ammonia and so six vibrational modes can be predicted from the 3N-6 rule. There are also two pairs of degenerate modes with frequencies of 482 (cm-1) and 930 (cm-1). The modes with a frequency of 482 (cm-1) and 644(cm-1) correspond to bending vibrational modes and the modes with a frequency of 930 (cm-1) and 1062 (cm-1) correspond to stretching vibrational modes. The mode with a frequency of 1062 (cm-1) represents a symmetric stretch whilst the modes with a frequency of 930 (cm-1) represent asymmetric stretches. In contrast to ammonia, the highest frequency bond stretch of nitrogen trifluoride is the symmetric stretch.

Three bands can be expected in the NF3 IR spectrum at frequencies of 644 (cm-1) 930 (cm-1) and 1062 (cm-1). The bends at 482 (cm-1) will be too low in frequency to appear in the spectrum which starts at a frequency of 500 (cm-1). The stretches at 930 (cm-1) are degenerate and hence will only display one band between them. The band as 644 (cm-1) may not be clearly visible due its relative low intensity of 3 arbitrary units.

=== Charge analysis ===
[[File:Acc2518 NF3 charge analysis.png|The Gaussview generated atomic charges of ammonia.|250px]]

Fluorine has a greater electronegativity that nitrogen and therefore there is greater electron density distributed around the three fluorine atoms compared to the nitrogen atom. The three fluorine atoms are treated as equivalent which means that the magnitude of the positive charge on nitrogen is three times the magnitude of the negative charge on a single fluorine atom.

=== Molecular orbitals ===

The nitrogen atom contributes 7 electrons and each fluorine atom contributes 9 electrons which means that nitrogen trifluoride contains 34 electrons in total and hence 17 electron pairs. In the table below, a molecular orbital number of 1 would denote the molecular orbital that is deepest in energy. Therefore, orbital 17 represents the HOMO and orbital 18 represents the LUMO.

{| class="wikitable"
!Molecular orbital number
!Image
!Type of molecular orbital
!Energy (au)
!Extra details
|-
|18
|[[File:Acc2518 MO18.png|200px]]
|Antibonding
|0.01947
|There are nodes in the centre of the N-F bonds which indicates that the LUMO is an antibonding orbital with destructive inteference between phases of opposite sign. The nodes in the centre of all four atoms also indicate that this molecular orbital was formed from 2p atomic orbitals from both nitrogen and fluorine.
|-
|17
|[[File:Acc2518 MO17.png|200px]]
|Bonding
| -0.35162
| The phase denoted by the green region shows orbital overlap across all three N-H bonds which implies that the HOMO is a bonding orbital. This molecular orbital has been formed from 2p orbitals which explains the nodes observed in the centre of the F atoms.
|-
|
|
|
|
|
|-
|
|
|
|
|
|-
|
|
|
|
|
|}

File:Acc2518 MO16.png

2019-03-04T13:37:12Z

Acc2518:

Acc2518

2019-03-04T13:33:16Z

Acc2518: /* Molecular orbitals */

== NH3 molecule ==
=== Optimisation data ===
{| class="wikitable"
|+ NH3 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-56.55776873 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00000485 (au)
|-
|'''Point group'''
|C3V
|-
|'''Bond length (N-H)'''
|1.018 (Å)
|-
|'''Bond angle (H-N-H)'''
|106(°)
|}
<pre>
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
</pre>

<jmol><jmolApplet>
<title> NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518 NH3 OPTF POP.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>
[[:File:ACC2518 NH3 OPTF POP.LOG|Optimised NH3 .log file (acc2518)]]

=== Vibrations ===
[[File:Acc2518 vibrations screenshot.jpg|The Gaussview "Display Vibrations" window of the optimised ammonia molecule.|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 1090 || 1694
|-
| '''Symmetry''' || A1 || E
|-
| '''Intensity''' (arbitrary units) || 145 || 14
|-
| '''Image'''|| [[File:acc2518VM1.png|250px]] || [[File:acc2518VM2.png|300px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 1694|| 3461
|-
| '''Symmetry''' || E || A1
|-
| '''Intensity''' (arbitrary units) || 14 || 1
|-
| '''Image'''|| [[File:acc2518VM3.png|250px]] || [[File:acc2518VM4.png|275px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 3590|| 3590
|-
| '''Symmetry''' || E || E
|-
| '''Intensity''' (arbitrary units) || 0 || 0
|-
| '''Image'''|| [[File:acc2518VM5.png|275px]] || [[File:acc2518VM6.png|250px]]
|}

Using the 3N-6 rule, where N represents the number of atoms in a molecule, it is expected that ammonia will have six vibrational modes as shown above. There are two pairs of degenerate modes with a frequency of 1694 (cm-1) and 3590 (cm-1). The modes with a frequency of 1090 (cm-1) and 1694 (cm-1) correspond to bending vibrations and the modes with a frequency 3461 (cm-1) and 3590 (cm-1) correspond to bond stretch vibrations. The bond stretch vibration at 3461 (cm-1) is highly symmetric whilst the stretches with a frequency of 3590 (cm-1) are asymmetric. The bending vibration with a frequency of 1090 (cm-1) is known as the umbrella mode. Three bands would be expected to be seen with the two stretches at 3590 (cm-1) being too low in intensity. The bends with a frequency of 1694 (cm-1) are degenerate and only one band will be observed between the two. Hence the three observed bands would be at 1090 (cm-1), 1694 (cm-1) and 3461 (cm-1).

=== Charge analysis ===
[[File:Acc2518 charge analysis.png|The Gaussview generated atomic charges of ammonia.|250px]]

Nitrogen has a greater electronegativity than hydrogen and hence there is greater electron density distributed around the N atom in ammonia relative to hydrogen. This explains the negative charge on N and the positive charge on H.

==N2 molecule==

===Optimisation data===

{| class="wikitable"
|+ N2 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-109.52412868 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00000060 (au)
|-
|'''Point group'''
|D∞h
|-
|'''Bond length (N-N)'''
|1.10550 (Å)
|}

<pre>
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
</pre>

<jmol><jmolApplet>
<title> Nitrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518 N2 OPTIMISATION.LOG</uploadedFileContents>
<script>frame 1.10</script>
</jmolApplet></jmol>
[[:File:ACC2518 N2 OPTIMISATION.LOG|Optimised N2 .log file (acc2518)]]

===Vibrations===
[[File:Acc2518 N2vibration.png|Nitrogen display vibrations screenshot|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 2457
|-
| '''Symmetry''' || SGG
|-
| '''Intensity''' (arbitrary units) || 0
|-
| '''Image'''|| [[File:Acc2518NitrogenVM.png|250px]]
|}
Using the 3N-5 rule for linear molecules, Nitrogen can be expected to have one vibrational mode but this mode has an IR intensity of zero since Nitrogen molecules are IR inactive. This is because they have no overall dipole.

===Charge analysis===
[[File:Acc2518nitrogen charges.png]]

Both nitrogen atoms have the same electronegativity so the charge is neutral on both atoms.

===CCDC search===
'''Unique identifier:''' [https://www.ccdc.cam.ac.uk/structures/Search?Ccdcid=VAMQAE&DatabaseToSearch=Published VAMQAE]

'''Deposition number:''' 1530121

The complex linked above contains nitrogen coordinated to cobalt with a N-N bond distance of 1.08 Å which is slightly shorter than the optimised N-N bond length, displayed above, of 1.11 Å (3.s.f). During the optimisation process for nitrogen, assumptions have to be made for the computational process to be carried out. Each assumption made will increase the uncertainty in measurable quantities such as the bond length. Hence, the computationally determined bond length from the optimisation is a model and may not fully reflect the true bond length or the bond length determined by a computational program considering slightly different assumptions.

It should also be considered that the optimisation gave a prediction for the N-N bond length in a nitrogen molecule whereas the molecule linked above contains a nitrogen molecule that is coordinated into a transition metal complex. A lone pair of electrons on one of the nitrogen atoms has been donated to a cobalt ion, this draws electron density away from the donating nitrogen atom and would therefore slightly increase the positive charge on this atom. This may cause the donating nitrogen atom to attract the electrons in the N-N bond more strongly which would then explain the shorter bond in the transition metal complex compared to the nitrogen molecule.

==H2 molecule==

===Optimisation data===
{| class="wikitable"
|+ H2 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-1.17853936 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00000017 (au)
|-
|'''Point group'''
|D∞h
|-
|'''Bond length (N-N)'''
|0.74279 (Å)
|}

<pre>
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

</pre>

<jmol><jmolApplet>
<title> Hydrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518 H2 OPTIMISATION.LOG</uploadedFileContents>
<script>frame 1.7</script>
</jmolApplet></jmol>
[[:File:ACC2518 H2 OPTIMISATION.LOG|Optimised H2 .log file (acc2518)]]

===Vibrations===
[[File:Acc2518 H2vibration.png|Hydrogen display vibrations screenshot|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 4466
|-
| '''Symmetry''' || SGG
|-
| '''Intensity''' (arbitrary units) || 0
|-
| '''Image'''|| [[File:Acc2518HydrogenVM.png|250px]]
|}
Using the 3N-5 rule for linear molecules, hydrogen can be expected to have one vibrational mode but this mode has an IR intensity of zero since hydrogen molecules, like nitrogen molecules, are IR inactive.

===Charge analysis===
[[File:Acc2518hydrogen charges.png]]

Both hydrogen atoms have the same electronegativity so the charge is neutral on both atoms.

==The Haber-Bosch process==
N2 + 3H2 -> 2NH3

E(NH3)=-56.55776873

 '''2*E(NH3)''' =2*(-56.55776873)=-113.11553746

 '''E(N2)''' =-109.52412868

E(H2)=-1.17853936

 '''3*E(H2)''' =3*(-1.17853936) =-3.53561808

'''ΔE= 2*E(NH3) -[ E(N2) + 3*E(H2) ]'''= -0.05579069 ≈ -0.05579 au (5.d.p)

'''ΔE=-146.5 kJ/mol (1.d.p)'''

ΔE is negative which indicates that the gaseous reactants are less stable than the ammonia product since the reactants are at a higher energy than the product. Although this process is not necessarily entropically favourable with four reactant gaseous molecules forming two gaseous product molecules, the reaction has a significantly negative enthalpy change which reflects the result calculated above.

== Project molecule (NF3) ==

=== Optimisation data ===
{| class="wikitable"
|+ NF3 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-354.07131058 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00010256 (au)
|-
|'''Point group'''
|C3V
|-
|'''Bond length (N-F)'''
|1.384 (Å)
|-
|'''Bond angle (F-N-F)'''
|102(°)
|}
<pre>
Item Value Threshold Converged?
Maximum Force 0.000164 0.000450 YES
RMS Force 0.000108 0.000300 YES
Maximum Displacement 0.000612 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

<jmol><jmolApplet>
<title> NF3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518_NF3_OPTF_POP.LOG </uploadedFileContents>
<script>frame 1.7</script>
</jmolApplet></jmol>
[[:File:ACC2518_NF3_OPTF_POP.LOG|Optimised NF3 .log file (acc2518)]]

=== Vibrations ===
[[File:Acc2518 NF3 vibrations screenshot.png|The Gaussview "Display Vibrations" window of the optimised nitrogen trifluoride molecule.|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 482 || 482
|-
| '''Symmetry''' || E || E
|-
| '''Intensity''' (arbitrary units) || 1 || 1
|-
| '''Image'''|| [[File:Acc2518 NF3 VM1.png|300px]] || [[File:Acc2518 NF3 VM2.png|300px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 644|| 930
|-
| '''Symmetry''' || A1 || E
|-
| '''Intensity''' (arbitrary units) || 3 || 208
|-
| '''Image'''|| [[File:Acc2518 NF3 VM3.png|300px]] || [[File:Acc2518 NF3 VM4.png|300px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 930|| 1062
|-
| '''Symmetry''' || E || A1
|-
| '''Intensity''' (arbitrary units) || 208 || 40
|-
| '''Image'''|| [[File:Acc2518 NF3 VM5.png|300px]] || [[File:Acc2518 NF3 VM6.png|300px]]
|}

Nitrogen trifluoride has the same number of atoms as ammonia and so six vibrational modes can be predicted from the 3N-6 rule. There are also two pairs of degenerate modes with frequencies of 482 (cm-1) and 930 (cm-1). The modes with a frequency of 482 (cm-1) and 644(cm-1) correspond to bending vibrational modes and the modes with a frequency of 930 (cm-1) and 1062 (cm-1) correspond to stretching vibrational modes. The mode with a frequency of 1062 (cm-1) represents a symmetric stretch whilst the modes with a frequency of 930 (cm-1) represent asymmetric stretches. In contrast to ammonia, the highest frequency bond stretch of nitrogen trifluoride is the symmetric stretch.

Three bands can be expected in the NF3 IR spectrum at frequencies of 644 (cm-1) 930 (cm-1) and 1062 (cm-1). The bends at 482 (cm-1) will be too low in frequency to appear in the spectrum which starts at a frequency of 500 (cm-1). The stretches at 930 (cm-1) are degenerate and hence will only display one band between them. The band as 644 (cm-1) may not be clearly visible due its relative low intensity of 3 arbitrary units.

=== Charge analysis ===
[[File:Acc2518 NF3 charge analysis.png|The Gaussview generated atomic charges of ammonia.|250px]]

Fluorine has a greater electronegativity that nitrogen and therefore there is greater electron density distributed around the three fluorine atoms compared to the nitrogen atom. The three fluorine atoms are treated as equivalent which means that the magnitude of the positive charge on nitrogen is three times the magnitude of the negative charge on a single fluorine atom.

=== Molecular orbitals ===

The nitrogen atom contributes 7 electrons and each fluorine atom contributes 9 electrons which means that nitrogen trifluoride contains 34 electrons in total and hence 17 electron pairs. In the table below, a molecular orbital number of 1 would denote the molecular orbital that is deepest in energy. Therefore, orbital 17 represents the HOMO and orbital 18 represents the LUMO.

{| class="wikitable"
!Molecular orbital number
!Image
!Bonding/Antibonding
!Energy (au)
!Extra details
|-
|18
|[[File:Acc2518 MO18.png|300px]]
|Antibonding
|0.01947
|
|-
|17
|[[File:Acc2518 MO17.png|300px]]
|Bonding
|-0.35162
|The phase denoted by the green region shows orbital overlap across all three N-H bonds which implies that the HOMO is a bonding orbital. This molecular orbital has been formed from 2p orbitals which explains the nodes observed in the centre of the F atoms.
|-
|
|
|
|
|
|-
|
|
|
|
|
|-
|
|
|
|
|
|}

File:Acc2518 MO18.png

2019-03-04T13:21:45Z

Acc2518:

File:Acc2518 MO17.png

2019-03-04T13:21:30Z

Acc2518:

Acc2518

2019-03-04T11:18:32Z

Acc2518: /* Molecular orbitals */

== NH3 molecule ==
=== Optimisation data ===
{| class="wikitable"
|+ NH3 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-56.55776873 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00000485 (au)
|-
|'''Point group'''
|C3V
|-
|'''Bond length (N-H)'''
|1.018 (Å)
|-
|'''Bond angle (H-N-H)'''
|106(°)
|}
<pre>
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
</pre>

<jmol><jmolApplet>
<title> NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518 NH3 OPTF POP.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>
[[:File:ACC2518 NH3 OPTF POP.LOG|Optimised NH3 .log file (acc2518)]]

=== Vibrations ===
[[File:Acc2518 vibrations screenshot.jpg|The Gaussview "Display Vibrations" window of the optimised ammonia molecule.|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 1090 || 1694
|-
| '''Symmetry''' || A1 || E
|-
| '''Intensity''' (arbitrary units) || 145 || 14
|-
| '''Image'''|| [[File:acc2518VM1.png|250px]] || [[File:acc2518VM2.png|300px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 1694|| 3461
|-
| '''Symmetry''' || E || A1
|-
| '''Intensity''' (arbitrary units) || 14 || 1
|-
| '''Image'''|| [[File:acc2518VM3.png|250px]] || [[File:acc2518VM4.png|275px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 3590|| 3590
|-
| '''Symmetry''' || E || E
|-
| '''Intensity''' (arbitrary units) || 0 || 0
|-
| '''Image'''|| [[File:acc2518VM5.png|275px]] || [[File:acc2518VM6.png|250px]]
|}

Using the 3N-6 rule, where N represents the number of atoms in a molecule, it is expected that ammonia will have six vibrational modes as shown above. There are two pairs of degenerate modes with a frequency of 1694 (cm-1) and 3590 (cm-1). The modes with a frequency of 1090 (cm-1) and 1694 (cm-1) correspond to bending vibrations and the modes with a frequency 3461 (cm-1) and 3590 (cm-1) correspond to bond stretch vibrations. The bond stretch vibration at 3461 (cm-1) is highly symmetric whilst the stretches with a frequency of 3590 (cm-1) are asymmetric. The bending vibration with a frequency of 1090 (cm-1) is known as the umbrella mode. Three bands would be expected to be seen with the two stretches at 3590 (cm-1) being too low in intensity. The bends with a frequency of 1694 (cm-1) are degenerate and only one band will be observed between the two. Hence the three observed bands would be at 1090 (cm-1), 1694 (cm-1) and 3461 (cm-1).

=== Charge analysis ===
[[File:Acc2518 charge analysis.png|The Gaussview generated atomic charges of ammonia.|250px]]

Nitrogen has a greater electronegativity than hydrogen and hence there is greater electron density distributed around the N atom in ammonia relative to hydrogen. This explains the negative charge on N and the positive charge on H.

==N2 molecule==

===Optimisation data===

{| class="wikitable"
|+ N2 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-109.52412868 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00000060 (au)
|-
|'''Point group'''
|D∞h
|-
|'''Bond length (N-N)'''
|1.10550 (Å)
|}

<pre>
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
</pre>

<jmol><jmolApplet>
<title> Nitrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518 N2 OPTIMISATION.LOG</uploadedFileContents>
<script>frame 1.10</script>
</jmolApplet></jmol>
[[:File:ACC2518 N2 OPTIMISATION.LOG|Optimised N2 .log file (acc2518)]]

===Vibrations===
[[File:Acc2518 N2vibration.png|Nitrogen display vibrations screenshot|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 2457
|-
| '''Symmetry''' || SGG
|-
| '''Intensity''' (arbitrary units) || 0
|-
| '''Image'''|| [[File:Acc2518NitrogenVM.png|250px]]
|}
Using the 3N-5 rule for linear molecules, Nitrogen can be expected to have one vibrational mode but this mode has an IR intensity of zero since Nitrogen molecules are IR inactive. This is because they have no overall dipole.

===Charge analysis===
[[File:Acc2518nitrogen charges.png]]

Both nitrogen atoms have the same electronegativity so the charge is neutral on both atoms.

===CCDC search===
'''Unique identifier:''' [https://www.ccdc.cam.ac.uk/structures/Search?Ccdcid=VAMQAE&DatabaseToSearch=Published VAMQAE]

'''Deposition number:''' 1530121

The complex linked above contains nitrogen coordinated to cobalt with a N-N bond distance of 1.08 Å which is slightly shorter than the optimised N-N bond length, displayed above, of 1.11 Å (3.s.f). During the optimisation process for nitrogen, assumptions have to be made for the computational process to be carried out. Each assumption made will increase the uncertainty in measurable quantities such as the bond length. Hence, the computationally determined bond length from the optimisation is a model and may not fully reflect the true bond length or the bond length determined by a computational program considering slightly different assumptions.

It should also be considered that the optimisation gave a prediction for the N-N bond length in a nitrogen molecule whereas the molecule linked above contains a nitrogen molecule that is coordinated into a transition metal complex. A lone pair of electrons on one of the nitrogen atoms has been donated to a cobalt ion, this draws electron density away from the donating nitrogen atom and would therefore slightly increase the positive charge on this atom. This may cause the donating nitrogen atom to attract the electrons in the N-N bond more strongly which would then explain the shorter bond in the transition metal complex compared to the nitrogen molecule.

==H2 molecule==

===Optimisation data===
{| class="wikitable"
|+ H2 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-1.17853936 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00000017 (au)
|-
|'''Point group'''
|D∞h
|-
|'''Bond length (N-N)'''
|0.74279 (Å)
|}

<pre>
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

</pre>

<jmol><jmolApplet>
<title> Hydrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518 H2 OPTIMISATION.LOG</uploadedFileContents>
<script>frame 1.7</script>
</jmolApplet></jmol>
[[:File:ACC2518 H2 OPTIMISATION.LOG|Optimised H2 .log file (acc2518)]]

===Vibrations===
[[File:Acc2518 H2vibration.png|Hydrogen display vibrations screenshot|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 4466
|-
| '''Symmetry''' || SGG
|-
| '''Intensity''' (arbitrary units) || 0
|-
| '''Image'''|| [[File:Acc2518HydrogenVM.png|250px]]
|}
Using the 3N-5 rule for linear molecules, hydrogen can be expected to have one vibrational mode but this mode has an IR intensity of zero since hydrogen molecules, like nitrogen molecules, are IR inactive.

===Charge analysis===
[[File:Acc2518hydrogen charges.png]]

Both hydrogen atoms have the same electronegativity so the charge is neutral on both atoms.

==The Haber-Bosch process==
N2 + 3H2 -> 2NH3

E(NH3)=-56.55776873

 '''2*E(NH3)''' =2*(-56.55776873)=-113.11553746

 '''E(N2)''' =-109.52412868

E(H2)=-1.17853936

 '''3*E(H2)''' =3*(-1.17853936) =-3.53561808

'''ΔE= 2*E(NH3) -[ E(N2) + 3*E(H2) ]'''= -0.05579069 ≈ -0.05579 au (5.d.p)

'''ΔE=-146.5 kJ/mol (1.d.p)'''

ΔE is negative which indicates that the gaseous reactants are less stable than the ammonia product since the reactants are at a higher energy than the product. Although this process is not necessarily entropically favourable with four reactant gaseous molecules forming two gaseous product molecules, the reaction has a significantly negative enthalpy change which reflects the result calculated above.

== Project molecule (NF3) ==

=== Optimisation data ===
{| class="wikitable"
|+ NF3 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-354.07131058 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00010256 (au)
|-
|'''Point group'''
|C3V
|-
|'''Bond length (N-F)'''
|1.384 (Å)
|-
|'''Bond angle (F-N-F)'''
|102(°)
|}
<pre>
Item Value Threshold Converged?
Maximum Force 0.000164 0.000450 YES
RMS Force 0.000108 0.000300 YES
Maximum Displacement 0.000612 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

<jmol><jmolApplet>
<title> NF3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518_NF3_OPTF_POP.LOG </uploadedFileContents>
<script>frame 1.7</script>
</jmolApplet></jmol>
[[:File:ACC2518_NF3_OPTF_POP.LOG|Optimised NF3 .log file (acc2518)]]

=== Vibrations ===
[[File:Acc2518 NF3 vibrations screenshot.png|The Gaussview "Display Vibrations" window of the optimised nitrogen trifluoride molecule.|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 482 || 482
|-
| '''Symmetry''' || E || E
|-
| '''Intensity''' (arbitrary units) || 1 || 1
|-
| '''Image'''|| [[File:Acc2518 NF3 VM1.png|300px]] || [[File:Acc2518 NF3 VM2.png|300px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 644|| 930
|-
| '''Symmetry''' || A1 || E
|-
| '''Intensity''' (arbitrary units) || 3 || 208
|-
| '''Image'''|| [[File:Acc2518 NF3 VM3.png|300px]] || [[File:Acc2518 NF3 VM4.png|300px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 930|| 1062
|-
| '''Symmetry''' || E || A1
|-
| '''Intensity''' (arbitrary units) || 208 || 40
|-
| '''Image'''|| [[File:Acc2518 NF3 VM5.png|300px]] || [[File:Acc2518 NF3 VM6.png|300px]]
|}

Nitrogen trifluoride has the same number of atoms as ammonia and so six vibrational modes can be predicted from the 3N-6 rule. There are also two pairs of degenerate modes with frequencies of 482 (cm-1) and 930 (cm-1). The modes with a frequency of 482 (cm-1) and 644(cm-1) correspond to bending vibrational modes and the modes with a frequency of 930 (cm-1) and 1062 (cm-1) correspond to stretching vibrational modes. The mode with a frequency of 1062 (cm-1) represents a symmetric stretch whilst the modes with a frequency of 930 (cm-1) represent asymmetric stretches. In contrast to ammonia, the highest frequency bond stretch of nitrogen trifluoride is the symmetric stretch.

Three bands can be expected in the NF3 IR spectrum at frequencies of 644 (cm-1) 930 (cm-1) and 1062 (cm-1). The bends at 482 (cm-1) will be too low in frequency to appear in the spectrum which starts at a frequency of 500 (cm-1). The stretches at 930 (cm-1) are degenerate and hence will only display one band between them. The band as 644 (cm-1) may not be clearly visible due its relative low intensity of 3 arbitrary units.

=== Charge analysis ===
[[File:Acc2518 NF3 charge analysis.png|The Gaussview generated atomic charges of ammonia.|250px]]

Fluorine has a greater electronegativity that nitrogen and therefore there is greater electron density distributed around the three fluorine atoms compared to the nitrogen atom. The three fluorine atoms are treated as equivalent which means that the magnitude of the positive charge on nitrogen is three times the magnitude of the negative charge on a single fluorine atom.

=== Molecular orbitals ===

{| class="wikitable"
!Molecular orbital number
!Image
!Type
!Extra details
|-
|a
|b
|c
|d
|-
|
|
|
|
|-
|
|
|
|
|-
|
|
|
|
|-
|
|
|
|
|}

Acc2518

2019-03-04T11:18:18Z

Acc2518:

== NH3 molecule ==
=== Optimisation data ===
{| class="wikitable"
|+ NH3 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-56.55776873 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00000485 (au)
|-
|'''Point group'''
|C3V
|-
|'''Bond length (N-H)'''
|1.018 (Å)
|-
|'''Bond angle (H-N-H)'''
|106(°)
|}
<pre>
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
</pre>

<jmol><jmolApplet>
<title> NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518 NH3 OPTF POP.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>
[[:File:ACC2518 NH3 OPTF POP.LOG|Optimised NH3 .log file (acc2518)]]

=== Vibrations ===
[[File:Acc2518 vibrations screenshot.jpg|The Gaussview "Display Vibrations" window of the optimised ammonia molecule.|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 1090 || 1694
|-
| '''Symmetry''' || A1 || E
|-
| '''Intensity''' (arbitrary units) || 145 || 14
|-
| '''Image'''|| [[File:acc2518VM1.png|250px]] || [[File:acc2518VM2.png|300px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 1694|| 3461
|-
| '''Symmetry''' || E || A1
|-
| '''Intensity''' (arbitrary units) || 14 || 1
|-
| '''Image'''|| [[File:acc2518VM3.png|250px]] || [[File:acc2518VM4.png|275px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 3590|| 3590
|-
| '''Symmetry''' || E || E
|-
| '''Intensity''' (arbitrary units) || 0 || 0
|-
| '''Image'''|| [[File:acc2518VM5.png|275px]] || [[File:acc2518VM6.png|250px]]
|}

Using the 3N-6 rule, where N represents the number of atoms in a molecule, it is expected that ammonia will have six vibrational modes as shown above. There are two pairs of degenerate modes with a frequency of 1694 (cm-1) and 3590 (cm-1). The modes with a frequency of 1090 (cm-1) and 1694 (cm-1) correspond to bending vibrations and the modes with a frequency 3461 (cm-1) and 3590 (cm-1) correspond to bond stretch vibrations. The bond stretch vibration at 3461 (cm-1) is highly symmetric whilst the stretches with a frequency of 3590 (cm-1) are asymmetric. The bending vibration with a frequency of 1090 (cm-1) is known as the umbrella mode. Three bands would be expected to be seen with the two stretches at 3590 (cm-1) being too low in intensity. The bends with a frequency of 1694 (cm-1) are degenerate and only one band will be observed between the two. Hence the three observed bands would be at 1090 (cm-1), 1694 (cm-1) and 3461 (cm-1).

=== Charge analysis ===
[[File:Acc2518 charge analysis.png|The Gaussview generated atomic charges of ammonia.|250px]]

Nitrogen has a greater electronegativity than hydrogen and hence there is greater electron density distributed around the N atom in ammonia relative to hydrogen. This explains the negative charge on N and the positive charge on H.

==N2 molecule==

===Optimisation data===

{| class="wikitable"
|+ N2 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-109.52412868 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00000060 (au)
|-
|'''Point group'''
|D∞h
|-
|'''Bond length (N-N)'''
|1.10550 (Å)
|}

<pre>
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
</pre>

<jmol><jmolApplet>
<title> Nitrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518 N2 OPTIMISATION.LOG</uploadedFileContents>
<script>frame 1.10</script>
</jmolApplet></jmol>
[[:File:ACC2518 N2 OPTIMISATION.LOG|Optimised N2 .log file (acc2518)]]

===Vibrations===
[[File:Acc2518 N2vibration.png|Nitrogen display vibrations screenshot|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 2457
|-
| '''Symmetry''' || SGG
|-
| '''Intensity''' (arbitrary units) || 0
|-
| '''Image'''|| [[File:Acc2518NitrogenVM.png|250px]]
|}
Using the 3N-5 rule for linear molecules, Nitrogen can be expected to have one vibrational mode but this mode has an IR intensity of zero since Nitrogen molecules are IR inactive. This is because they have no overall dipole.

===Charge analysis===
[[File:Acc2518nitrogen charges.png]]

Both nitrogen atoms have the same electronegativity so the charge is neutral on both atoms.

===CCDC search===
'''Unique identifier:''' [https://www.ccdc.cam.ac.uk/structures/Search?Ccdcid=VAMQAE&DatabaseToSearch=Published VAMQAE]

'''Deposition number:''' 1530121

The complex linked above contains nitrogen coordinated to cobalt with a N-N bond distance of 1.08 Å which is slightly shorter than the optimised N-N bond length, displayed above, of 1.11 Å (3.s.f). During the optimisation process for nitrogen, assumptions have to be made for the computational process to be carried out. Each assumption made will increase the uncertainty in measurable quantities such as the bond length. Hence, the computationally determined bond length from the optimisation is a model and may not fully reflect the true bond length or the bond length determined by a computational program considering slightly different assumptions.

It should also be considered that the optimisation gave a prediction for the N-N bond length in a nitrogen molecule whereas the molecule linked above contains a nitrogen molecule that is coordinated into a transition metal complex. A lone pair of electrons on one of the nitrogen atoms has been donated to a cobalt ion, this draws electron density away from the donating nitrogen atom and would therefore slightly increase the positive charge on this atom. This may cause the donating nitrogen atom to attract the electrons in the N-N bond more strongly which would then explain the shorter bond in the transition metal complex compared to the nitrogen molecule.

==H2 molecule==

===Optimisation data===
{| class="wikitable"
|+ H2 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-1.17853936 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00000017 (au)
|-
|'''Point group'''
|D∞h
|-
|'''Bond length (N-N)'''
|0.74279 (Å)
|}

<pre>
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

</pre>

<jmol><jmolApplet>
<title> Hydrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518 H2 OPTIMISATION.LOG</uploadedFileContents>
<script>frame 1.7</script>
</jmolApplet></jmol>
[[:File:ACC2518 H2 OPTIMISATION.LOG|Optimised H2 .log file (acc2518)]]

===Vibrations===
[[File:Acc2518 H2vibration.png|Hydrogen display vibrations screenshot|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 4466
|-
| '''Symmetry''' || SGG
|-
| '''Intensity''' (arbitrary units) || 0
|-
| '''Image'''|| [[File:Acc2518HydrogenVM.png|250px]]
|}
Using the 3N-5 rule for linear molecules, hydrogen can be expected to have one vibrational mode but this mode has an IR intensity of zero since hydrogen molecules, like nitrogen molecules, are IR inactive.

===Charge analysis===
[[File:Acc2518hydrogen charges.png]]

Both hydrogen atoms have the same electronegativity so the charge is neutral on both atoms.

==The Haber-Bosch process==
N2 + 3H2 -> 2NH3

E(NH3)=-56.55776873

 '''2*E(NH3)''' =2*(-56.55776873)=-113.11553746

 '''E(N2)''' =-109.52412868

E(H2)=-1.17853936

 '''3*E(H2)''' =3*(-1.17853936) =-3.53561808

'''ΔE= 2*E(NH3) -[ E(N2) + 3*E(H2) ]'''= -0.05579069 ≈ -0.05579 au (5.d.p)

'''ΔE=-146.5 kJ/mol (1.d.p)'''

ΔE is negative which indicates that the gaseous reactants are less stable than the ammonia product since the reactants are at a higher energy than the product. Although this process is not necessarily entropically favourable with four reactant gaseous molecules forming two gaseous product molecules, the reaction has a significantly negative enthalpy change which reflects the result calculated above.

== Project molecule (NF3) ==

=== Optimisation data ===
{| class="wikitable"
|+ NF3 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-354.07131058 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00010256 (au)
|-
|'''Point group'''
|C3V
|-
|'''Bond length (N-F)'''
|1.384 (Å)
|-
|'''Bond angle (F-N-F)'''
|102(°)
|}
<pre>
Item Value Threshold Converged?
Maximum Force 0.000164 0.000450 YES
RMS Force 0.000108 0.000300 YES
Maximum Displacement 0.000612 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

<jmol><jmolApplet>
<title> NF3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518_NF3_OPTF_POP.LOG </uploadedFileContents>
<script>frame 1.7</script>
</jmolApplet></jmol>
[[:File:ACC2518_NF3_OPTF_POP.LOG|Optimised NF3 .log file (acc2518)]]

=== Vibrations ===
[[File:Acc2518 NF3 vibrations screenshot.png|The Gaussview "Display Vibrations" window of the optimised nitrogen trifluoride molecule.|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 482 || 482
|-
| '''Symmetry''' || E || E
|-
| '''Intensity''' (arbitrary units) || 1 || 1
|-
| '''Image'''|| [[File:Acc2518 NF3 VM1.png|300px]] || [[File:Acc2518 NF3 VM2.png|300px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 644|| 930
|-
| '''Symmetry''' || A1 || E
|-
| '''Intensity''' (arbitrary units) || 3 || 208
|-
| '''Image'''|| [[File:Acc2518 NF3 VM3.png|300px]] || [[File:Acc2518 NF3 VM4.png|300px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 930|| 1062
|-
| '''Symmetry''' || E || A1
|-
| '''Intensity''' (arbitrary units) || 208 || 40
|-
| '''Image'''|| [[File:Acc2518 NF3 VM5.png|300px]] || [[File:Acc2518 NF3 VM6.png|300px]]
|}

Nitrogen trifluoride has the same number of atoms as ammonia and so six vibrational modes can be predicted from the 3N-6 rule. There are also two pairs of degenerate modes with frequencies of 482 (cm-1) and 930 (cm-1). The modes with a frequency of 482 (cm-1) and 644(cm-1) correspond to bending vibrational modes and the modes with a frequency of 930 (cm-1) and 1062 (cm-1) correspond to stretching vibrational modes. The mode with a frequency of 1062 (cm-1) represents a symmetric stretch whilst the modes with a frequency of 930 (cm-1) represent asymmetric stretches. In contrast to ammonia, the highest frequency bond stretch of nitrogen trifluoride is the symmetric stretch.

Three bands can be expected in the NF3 IR spectrum at frequencies of 644 (cm-1) 930 (cm-1) and 1062 (cm-1). The bends at 482 (cm-1) will be too low in frequency to appear in the spectrum which starts at a frequency of 500 (cm-1). The stretches at 930 (cm-1) are degenerate and hence will only display one band between them. The band as 644 (cm-1) may not be clearly visible due its relative low intensity of 3 arbitrary units.

=== Charge analysis ===
[[File:Acc2518 NF3 charge analysis.png|The Gaussview generated atomic charges of ammonia.|250px]]

Fluorine has a greater electronegativity that nitrogen and therefore there is greater electron density distributed around the three fluorine atoms compared to the nitrogen atom. The three fluorine atoms are treated as equivalent which means that the magnitude of the positive charge on nitrogen is three times the magnitude of the negative charge on a single fluorine atom.

=== Molecular orbitals ===

{| class="wikitable"
!Molecular orbital number
!Image
!Type
!Extra details
|-
|
|
|
|
|-
|
|
|
|
|-
|
|
|
|
|-
|
|
|
|
|-
|
|
|
|
|}

Acc2518

2019-03-04T11:17:58Z

Acc2518:

== NH3 molecule ==
=== Optimisation data ===
{| class="wikitable"
|+ NH3 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-56.55776873 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00000485 (au)
|-
|'''Point group'''
|C3V
|-
|'''Bond length (N-H)'''
|1.018 (Å)
|-
|'''Bond angle (H-N-H)'''
|106(°)
|}
<pre>
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
</pre>

<jmol><jmolApplet>
<title> NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518 NH3 OPTF POP.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>
[[:File:ACC2518 NH3 OPTF POP.LOG|Optimised NH3 .log file (acc2518)]]

=== Vibrations ===
[[File:Acc2518 vibrations screenshot.jpg|The Gaussview "Display Vibrations" window of the optimised ammonia molecule.|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 1090 || 1694
|-
| '''Symmetry''' || A1 || E
|-
| '''Intensity''' (arbitrary units) || 145 || 14
|-
| '''Image'''|| [[File:acc2518VM1.png|250px]] || [[File:acc2518VM2.png|300px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 1694|| 3461
|-
| '''Symmetry''' || E || A1
|-
| '''Intensity''' (arbitrary units) || 14 || 1
|-
| '''Image'''|| [[File:acc2518VM3.png|250px]] || [[File:acc2518VM4.png|275px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 3590|| 3590
|-
| '''Symmetry''' || E || E
|-
| '''Intensity''' (arbitrary units) || 0 || 0
|-
| '''Image'''|| [[File:acc2518VM5.png|275px]] || [[File:acc2518VM6.png|250px]]
|}

Using the 3N-6 rule, where N represents the number of atoms in a molecule, it is expected that ammonia will have six vibrational modes as shown above. There are two pairs of degenerate modes with a frequency of 1694 (cm-1) and 3590 (cm-1). The modes with a frequency of 1090 (cm-1) and 1694 (cm-1) correspond to bending vibrations and the modes with a frequency 3461 (cm-1) and 3590 (cm-1) correspond to bond stretch vibrations. The bond stretch vibration at 3461 (cm-1) is highly symmetric whilst the stretches with a frequency of 3590 (cm-1) are asymmetric. The bending vibration with a frequency of 1090 (cm-1) is known as the umbrella mode. Three bands would be expected to be seen with the two stretches at 3590 (cm-1) being too low in intensity. The bends with a frequency of 1694 (cm-1) are degenerate and only one band will be observed between the two. Hence the three observed bands would be at 1090 (cm-1), 1694 (cm-1) and 3461 (cm-1).

=== Charge analysis ===
[[File:Acc2518 charge analysis.png|The Gaussview generated atomic charges of ammonia.|250px]]

Nitrogen has a greater electronegativity than hydrogen and hence there is greater electron density distributed around the N atom in ammonia relative to hydrogen. This explains the negative charge on N and the positive charge on H.

==N2 molecule==

===Optimisation data===

{| class="wikitable"
|+ N2 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-109.52412868 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00000060 (au)
|-
|'''Point group'''
|D∞h
|-
|'''Bond length (N-N)'''
|1.10550 (Å)
|}

<pre>
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
</pre>

<jmol><jmolApplet>
<title> Nitrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518 N2 OPTIMISATION.LOG</uploadedFileContents>
<script>frame 1.10</script>
</jmolApplet></jmol>
[[:File:ACC2518 N2 OPTIMISATION.LOG|Optimised N2 .log file (acc2518)]]

===Vibrations===
[[File:Acc2518 N2vibration.png|Nitrogen display vibrations screenshot|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 2457
|-
| '''Symmetry''' || SGG
|-
| '''Intensity''' (arbitrary units) || 0
|-
| '''Image'''|| [[File:Acc2518NitrogenVM.png|250px]]
|}
Using the 3N-5 rule for linear molecules, Nitrogen can be expected to have one vibrational mode but this mode has an IR intensity of zero since Nitrogen molecules are IR inactive. This is because they have no overall dipole.

===Charge analysis===
[[File:Acc2518nitrogen charges.png]]

Both nitrogen atoms have the same electronegativity so the charge is neutral on both atoms.

===CCDC search===
'''Unique identifier:''' [https://www.ccdc.cam.ac.uk/structures/Search?Ccdcid=VAMQAE&DatabaseToSearch=Published VAMQAE]

'''Deposition number:''' 1530121

The complex linked above contains nitrogen coordinated to cobalt with a N-N bond distance of 1.08 Å which is slightly shorter than the optimised N-N bond length, displayed above, of 1.11 Å (3.s.f). During the optimisation process for nitrogen, assumptions have to be made for the computational process to be carried out. Each assumption made will increase the uncertainty in measurable quantities such as the bond length. Hence, the computationally determined bond length from the optimisation is a model and may not fully reflect the true bond length or the bond length determined by a computational program considering slightly different assumptions.

It should also be considered that the optimisation gave a prediction for the N-N bond length in a nitrogen molecule whereas the molecule linked above contains a nitrogen molecule that is coordinated into a transition metal complex. A lone pair of electrons on one of the nitrogen atoms has been donated to a cobalt ion, this draws electron density away from the donating nitrogen atom and would therefore slightly increase the positive charge on this atom. This may cause the donating nitrogen atom to attract the electrons in the N-N bond more strongly which would then explain the shorter bond in the transition metal complex compared to the nitrogen molecule.

==H2 molecule==

===Optimisation data===
{| class="wikitable"
|+ H2 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-1.17853936 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00000017 (au)
|-
|'''Point group'''
|D∞h
|-
|'''Bond length (N-N)'''
|0.74279 (Å)
|}

<pre>
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

</pre>

<jmol><jmolApplet>
<title> Hydrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518 H2 OPTIMISATION.LOG</uploadedFileContents>
<script>frame 1.7</script>
</jmolApplet></jmol>
[[:File:ACC2518 H2 OPTIMISATION.LOG|Optimised H2 .log file (acc2518)]]

===Vibrations===
[[File:Acc2518 H2vibration.png|Hydrogen display vibrations screenshot|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 4466
|-
| '''Symmetry''' || SGG
|-
| '''Intensity''' (arbitrary units) || 0
|-
| '''Image'''|| [[File:Acc2518HydrogenVM.png|250px]]
|}
Using the 3N-5 rule for linear molecules, hydrogen can be expected to have one vibrational mode but this mode has an IR intensity of zero since hydrogen molecules, like nitrogen molecules, are IR inactive.

===Charge analysis===
[[File:Acc2518hydrogen charges.png]]

Both hydrogen atoms have the same electronegativity so the charge is neutral on both atoms.

==The Haber-Bosch process==
N2 + 3H2 -> 2NH3

E(NH3)=-56.55776873

 '''2*E(NH3)''' =2*(-56.55776873)=-113.11553746

 '''E(N2)''' =-109.52412868

E(H2)=-1.17853936

 '''3*E(H2)''' =3*(-1.17853936) =-3.53561808

'''ΔE= 2*E(NH3) -[ E(N2) + 3*E(H2) ]'''= -0.05579069 ≈ -0.05579 au (5.d.p)

'''ΔE=-146.5 kJ/mol (1.d.p)'''

ΔE is negative which indicates that the gaseous reactants are less stable than the ammonia product since the reactants are at a higher energy than the product. Although this process is not necessarily entropically favourable with four reactant gaseous molecules forming two gaseous product molecules, the reaction has a significantly negative enthalpy change which reflects the result calculated above.

== Project molecule (NF3) ==

=== Optimisation data ===
{| class="wikitable"
|+ NF3 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-354.07131058 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00010256 (au)
|-
|'''Point group'''
|C3V
|-
|'''Bond length (N-F)'''
|1.384 (Å)
|-
|'''Bond angle (F-N-F)'''
|102(°)
|}
<pre>
Item Value Threshold Converged?
Maximum Force 0.000164 0.000450 YES
RMS Force 0.000108 0.000300 YES
Maximum Displacement 0.000612 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

<jmol><jmolApplet>
<title> NF3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518_NF3_OPTF_POP.LOG </uploadedFileContents>
<script>frame 1.7</script>
</jmolApplet></jmol>
[[:File:ACC2518_NF3_OPTF_POP.LOG|Optimised NF3 .log file (acc2518)]]

=== Vibrations ===
[[File:Acc2518 NF3 vibrations screenshot.png|The Gaussview "Display Vibrations" window of the optimised nitrogen trifluoride molecule.|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 482 || 482
|-
| '''Symmetry''' || E || E
|-
| '''Intensity''' (arbitrary units) || 1 || 1
|-
| '''Image'''|| [[File:Acc2518 NF3 VM1.png|300px]] || [[File:Acc2518 NF3 VM2.png|300px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 644|| 930
|-
| '''Symmetry''' || A1 || E
|-
| '''Intensity''' (arbitrary units) || 3 || 208
|-
| '''Image'''|| [[File:Acc2518 NF3 VM3.png|300px]] || [[File:Acc2518 NF3 VM4.png|300px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 930|| 1062
|-
| '''Symmetry''' || E || A1
|-
| '''Intensity''' (arbitrary units) || 208 || 40
|-
| '''Image'''|| [[File:Acc2518 NF3 VM5.png|300px]] || [[File:Acc2518 NF3 VM6.png|300px]]
|}

Nitrogen trifluoride has the same number of atoms as ammonia and so six vibrational modes can be predicted from the 3N-6 rule. There are also two pairs of degenerate modes with frequencies of 482 (cm-1) and 930 (cm-1). The modes with a frequency of 482 (cm-1) and 644(cm-1) correspond to bending vibrational modes and the modes with a frequency of 930 (cm-1) and 1062 (cm-1) correspond to stretching vibrational modes. The mode with a frequency of 1062 (cm-1) represents a symmetric stretch whilst the modes with a frequency of 930 (cm-1) represent asymmetric stretches. In contrast to ammonia, the highest frequency bond stretch of nitrogen trifluoride is the symmetric stretch.

Three bands can be expected in the NF3 IR spectrum at frequencies of 644 (cm-1) 930 (cm-1) and 1062 (cm-1). The bends at 482 (cm-1) will be too low in frequency to appear in the spectrum which starts at a frequency of 500 (cm-1). The stretches at 930 (cm-1) are degenerate and hence will only display one band between them. The band as 644 (cm-1) may not be clearly visible due its relative low intensity of 3 arbitrary units.

=== Charge analysis ===
[[File:Acc2518 NF3 charge analysis.png|The Gaussview generated atomic charges of ammonia.|250px]]

Fluorine has a greater electronegativity that nitrogen and therefore there is greater electron density distributed around the three fluorine atoms compared to the nitrogen atom. The three fluorine atoms are treated as equivalent which means that the magnitude of the positive charge on nitrogen is three times the magnitude of the negative charge on a single fluorine atom.

=== Molecular orbitals ===

Acc2518

2019-03-04T11:17:08Z

Acc2518: /* Project molecule (NF3) */

== NH3 molecule ==
=== Optimisation data ===
{| class="wikitable"
|+ NH3 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-56.55776873 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00000485 (au)
|-
|'''Point group'''
|C3V
|-
|'''Bond length (N-H)'''
|1.018 (Å)
|-
|'''Bond angle (H-N-H)'''
|106(°)
|}
<pre>
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
</pre>

<jmol><jmolApplet>
<title> NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518 NH3 OPTF POP.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>
[[:File:ACC2518 NH3 OPTF POP.LOG|Optimised NH3 .log file (acc2518)]]

=== Vibrations ===
[[File:Acc2518 vibrations screenshot.jpg|The Gaussview "Display Vibrations" window of the optimised ammonia molecule.|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 1090 || 1694
|-
| '''Symmetry''' || A1 || E
|-
| '''Intensity''' (arbitrary units) || 145 || 14
|-
| '''Image'''|| [[File:acc2518VM1.png|250px]] || [[File:acc2518VM2.png|300px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 1694|| 3461
|-
| '''Symmetry''' || E || A1
|-
| '''Intensity''' (arbitrary units) || 14 || 1
|-
| '''Image'''|| [[File:acc2518VM3.png|250px]] || [[File:acc2518VM4.png|275px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 3590|| 3590
|-
| '''Symmetry''' || E || E
|-
| '''Intensity''' (arbitrary units) || 0 || 0
|-
| '''Image'''|| [[File:acc2518VM5.png|275px]] || [[File:acc2518VM6.png|250px]]
|}

Using the 3N-6 rule, where N represents the number of atoms in a molecule, it is expected that ammonia will have six vibrational modes as shown above. There are two pairs of degenerate modes with a frequency of 1694 (cm-1) and 3590 (cm-1). The modes with a frequency of 1090 (cm-1) and 1694 (cm-1) correspond to bending vibrations and the modes with a frequency 3461 (cm-1) and 3590 (cm-1) correspond to bond stretch vibrations. The bond stretch vibration at 3461 (cm-1) is highly symmetric whilst the stretches with a frequency of 3590 (cm-1) are asymmetric. The bending vibration with a frequency of 1090 (cm-1) is known as the umbrella mode. Three bands would be expected to be seen with the two stretches at 3590 (cm-1) being too low in intensity. The bends with a frequency of 1694 (cm-1) are degenerate and only one band will be observed between the two. Hence the three observed bands would be at 1090 (cm-1), 1694 (cm-1) and 3461 (cm-1).

=== Charge analysis ===
[[File:Acc2518 charge analysis.png|The Gaussview generated atomic charges of ammonia.|250px]]

Nitrogen has a greater electronegativity than hydrogen and hence there is greater electron density distributed around the N atom in ammonia relative to hydrogen. This explains the negative charge on N and the positive charge on H.

==N2 molecule==

===Optimisation data===

{| class="wikitable"
|+ N2 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-109.52412868 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00000060 (au)
|-
|'''Point group'''
|D∞h
|-
|'''Bond length (N-N)'''
|1.10550 (Å)
|}

<pre>
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
</pre>

<jmol><jmolApplet>
<title> Nitrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518 N2 OPTIMISATION.LOG</uploadedFileContents>
<script>frame 1.10</script>
</jmolApplet></jmol>
[[:File:ACC2518 N2 OPTIMISATION.LOG|Optimised N2 .log file (acc2518)]]

===Vibrations===
[[File:Acc2518 N2vibration.png|Nitrogen display vibrations screenshot|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 2457
|-
| '''Symmetry''' || SGG
|-
| '''Intensity''' (arbitrary units) || 0
|-
| '''Image'''|| [[File:Acc2518NitrogenVM.png|250px]]
|}
Using the 3N-5 rule for linear molecules, Nitrogen can be expected to have one vibrational mode but this mode has an IR intensity of zero since Nitrogen molecules are IR inactive. This is because they have no overall dipole.

===Charge analysis===
[[File:Acc2518nitrogen charges.png]]

Both nitrogen atoms have the same electronegativity so the charge is neutral on both atoms.

===CCDC search===
'''Unique identifier:''' [https://www.ccdc.cam.ac.uk/structures/Search?Ccdcid=VAMQAE&DatabaseToSearch=Published VAMQAE]

'''Deposition number:''' 1530121

The complex linked above contains nitrogen coordinated to cobalt with a N-N bond distance of 1.08 Å which is slightly shorter than the optimised N-N bond length, displayed above, of 1.11 Å (3.s.f). During the optimisation process for nitrogen, assumptions have to be made for the computational process to be carried out. Each assumption made will increase the uncertainty in measurable quantities such as the bond length. Hence, the computationally determined bond length from the optimisation is a model and may not fully reflect the true bond length or the bond length determined by a computational program considering slightly different assumptions.

It should also be considered that the optimisation gave a prediction for the N-N bond length in a nitrogen molecule whereas the molecule linked above contains a nitrogen molecule that is coordinated into a transition metal complex. A lone pair of electrons on one of the nitrogen atoms has been donated to a cobalt ion, this draws electron density away from the donating nitrogen atom and would therefore slightly increase the positive charge on this atom. This may cause the donating nitrogen atom to attract the electrons in the N-N bond more strongly which would then explain the shorter bond in the transition metal complex compared to the nitrogen molecule.

==H2 molecule==

===Optimisation data===
{| class="wikitable"
|+ H2 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-1.17853936 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00000017 (au)
|-
|'''Point group'''
|D∞h
|-
|'''Bond length (N-N)'''
|0.74279 (Å)
|}

<pre>
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

</pre>

<jmol><jmolApplet>
<title> Hydrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518 H2 OPTIMISATION.LOG</uploadedFileContents>
<script>frame 1.7</script>
</jmolApplet></jmol>
[[:File:ACC2518 H2 OPTIMISATION.LOG|Optimised H2 .log file (acc2518)]]

===Vibrations===
[[File:Acc2518 H2vibration.png|Hydrogen display vibrations screenshot|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 4466
|-
| '''Symmetry''' || SGG
|-
| '''Intensity''' (arbitrary units) || 0
|-
| '''Image'''|| [[File:Acc2518HydrogenVM.png|250px]]
|}
Using the 3N-5 rule for linear molecules, hydrogen can be expected to have one vibrational mode but this mode has an IR intensity of zero since hydrogen molecules, like nitrogen molecules, are IR inactive.

===Charge analysis===
[[File:Acc2518hydrogen charges.png]]

Both hydrogen atoms have the same electronegativity so the charge is neutral on both atoms.

==The Haber-Bosch process==
N2 + 3H2 -> 2NH3

E(NH3)=-56.55776873

 '''2*E(NH3)''' =2*(-56.55776873)=-113.11553746

 '''E(N2)''' =-109.52412868

E(H2)=-1.17853936

 '''3*E(H2)''' =3*(-1.17853936) =-3.53561808

'''ΔE= 2*E(NH3) -[ E(N2) + 3*E(H2) ]'''= -0.05579069 ≈ -0.05579 au (5.d.p)

'''ΔE=-146.5 kJ/mol (1.d.p)'''

ΔE is negative which indicates that the gaseous reactants are less stable than the ammonia product since the reactants are at a higher energy than the product. Although this process is not necessarily entropically favourable with four reactant gaseous molecules forming two gaseous product molecules, the reaction has a significantly negative enthalpy change which reflects the result calculated above.

== Project molecule (NF3) ==

=== Optimisation data ===
{| class="wikitable"
|+ NF3 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-354.07131058 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00010256 (au)
|-
|'''Point group'''
|C3V
|-
|'''Bond length (N-F)'''
|1.384 (Å)
|-
|'''Bond angle (F-N-F)'''
|102(°)
|}
<pre>
Item Value Threshold Converged?
Maximum Force 0.000164 0.000450 YES
RMS Force 0.000108 0.000300 YES
Maximum Displacement 0.000612 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

<jmol><jmolApplet>
<title> NF3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518_NF3_OPTF_POP.LOG </uploadedFileContents>
<script>frame 1.7</script>
</jmolApplet></jmol>
[[:File:ACC2518_NF3_OPTF_POP.LOG|Optimised NF3 .log file (acc2518)]]

=== Vibrations ===
[[File:Acc2518 NF3 vibrations screenshot.png|The Gaussview "Display Vibrations" window of the optimised nitrogen trifluoride molecule.|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 482 || 482
|-
| '''Symmetry''' || E || E
|-
| '''Intensity''' (arbitrary units) || 1 || 1
|-
| '''Image'''|| [[File:Acc2518 NF3 VM1.png|300px]] || [[File:Acc2518 NF3 VM2.png|300px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 644|| 930
|-
| '''Symmetry''' || A1 || E
|-
| '''Intensity''' (arbitrary units) || 3 || 208
|-
| '''Image'''|| [[File:Acc2518 NF3 VM3.png|300px]] || [[File:Acc2518 NF3 VM4.png|300px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 930|| 1062
|-
| '''Symmetry''' || E || A1
|-
| '''Intensity''' (arbitrary units) || 208 || 40
|-
| '''Image'''|| [[File:Acc2518 NF3 VM5.png|300px]] || [[File:Acc2518 NF3 VM6.png|300px]]
|}

Nitrogen trifluoride has the same number of atoms as ammonia and so six vibrational modes can be predicted from the 3N-6 rule. There are also two pairs of degenerate modes with frequencies of 482 (cm-1) and 930 (cm-1). The modes with a frequency of 482 (cm-1) and 644(cm-1) correspond to bending vibrational modes and the modes with a frequency of 930 (cm-1) and 1062 (cm-1) correspond to stretching vibrational modes. The mode with a frequency of 1062 (cm-1) represents a symmetric stretch whilst the modes with a frequency of 930 (cm-1) represent asymmetric stretches. In contrast to ammonia, the highest frequency bond stretch of nitrogen trifluoride is the symmetric stretch.

Three bands can be expected in the NF3 IR spectrum at frequencies of 644 (cm-1) 930 (cm-1) and 1062 (cm-1). The bends at 482 (cm-1) will be too low in frequency to appear in the spectrum which starts at a frequency of 500 (cm-1). The stretches at 930 (cm-1) are degenerate and hence will only display one band between them. The band as 644 (cm-1) may not be clearly visible due its relative low intensity of 3 arbitrary units.

=== Charge analysis ===
[[File:Acc2518 NF3 charge analysis.png|The Gaussview generated atomic charges of ammonia.|250px]]

Fluorine has a greater electronegativity that nitrogen and therefore there is greater electron density distributed around the three fluorine atoms compared to the nitrogen atom. The three fluorine atoms are treated as equivalent which means that the magnitude of the positive charge on nitrogen is three times the magnitude of the negative charge on a single fluorine atom.

=== Molecular orbital===

Acc2518test

2019-03-04T11:15:30Z

Acc2518: Created page with "{| class="wikitable" !Molecular orbital number !Image !Type !Extra details |- | | | | |- | | | | |- | | | | |- | | | | |- | | | | |}"

{| class="wikitable"
!Molecular orbital number
!Image
!Type
!Extra details
|-
|
|
|
|
|-
|
|
|
|
|-
|
|
|
|
|-
|
|
|
|
|-
|
|
|
|
|}

Acc2518

2019-03-04T11:04:07Z

Acc2518: /* Vibrations */

== NH3 molecule ==
=== Optimisation data ===
{| class="wikitable"
|+ NH3 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-56.55776873 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00000485 (au)
|-
|'''Point group'''
|C3V
|-
|'''Bond length (N-H)'''
|1.018 (Å)
|-
|'''Bond angle (H-N-H)'''
|106(°)
|}
<pre>
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
</pre>

<jmol><jmolApplet>
<title> NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518 NH3 OPTF POP.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>
[[:File:ACC2518 NH3 OPTF POP.LOG|Optimised NH3 .log file (acc2518)]]

=== Vibrations ===
[[File:Acc2518 vibrations screenshot.jpg|The Gaussview "Display Vibrations" window of the optimised ammonia molecule.|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 1090 || 1694
|-
| '''Symmetry''' || A1 || E
|-
| '''Intensity''' (arbitrary units) || 145 || 14
|-
| '''Image'''|| [[File:acc2518VM1.png|250px]] || [[File:acc2518VM2.png|300px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 1694|| 3461
|-
| '''Symmetry''' || E || A1
|-
| '''Intensity''' (arbitrary units) || 14 || 1
|-
| '''Image'''|| [[File:acc2518VM3.png|250px]] || [[File:acc2518VM4.png|275px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 3590|| 3590
|-
| '''Symmetry''' || E || E
|-
| '''Intensity''' (arbitrary units) || 0 || 0
|-
| '''Image'''|| [[File:acc2518VM5.png|275px]] || [[File:acc2518VM6.png|250px]]
|}

Using the 3N-6 rule, where N represents the number of atoms in a molecule, it is expected that ammonia will have six vibrational modes as shown above. There are two pairs of degenerate modes with a frequency of 1694 (cm-1) and 3590 (cm-1). The modes with a frequency of 1090 (cm-1) and 1694 (cm-1) correspond to bending vibrations and the modes with a frequency 3461 (cm-1) and 3590 (cm-1) correspond to bond stretch vibrations. The bond stretch vibration at 3461 (cm-1) is highly symmetric whilst the stretches with a frequency of 3590 (cm-1) are asymmetric. The bending vibration with a frequency of 1090 (cm-1) is known as the umbrella mode. Three bands would be expected to be seen with the two stretches at 3590 (cm-1) being too low in intensity. The bends with a frequency of 1694 (cm-1) are degenerate and only one band will be observed between the two. Hence the three observed bands would be at 1090 (cm-1), 1694 (cm-1) and 3461 (cm-1).

=== Charge analysis ===
[[File:Acc2518 charge analysis.png|The Gaussview generated atomic charges of ammonia.|250px]]

Nitrogen has a greater electronegativity than hydrogen and hence there is greater electron density distributed around the N atom in ammonia relative to hydrogen. This explains the negative charge on N and the positive charge on H.

==N2 molecule==

===Optimisation data===

{| class="wikitable"
|+ N2 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-109.52412868 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00000060 (au)
|-
|'''Point group'''
|D∞h
|-
|'''Bond length (N-N)'''
|1.10550 (Å)
|}

<pre>
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
</pre>

<jmol><jmolApplet>
<title> Nitrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518 N2 OPTIMISATION.LOG</uploadedFileContents>
<script>frame 1.10</script>
</jmolApplet></jmol>
[[:File:ACC2518 N2 OPTIMISATION.LOG|Optimised N2 .log file (acc2518)]]

===Vibrations===
[[File:Acc2518 N2vibration.png|Nitrogen display vibrations screenshot|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 2457
|-
| '''Symmetry''' || SGG
|-
| '''Intensity''' (arbitrary units) || 0
|-
| '''Image'''|| [[File:Acc2518NitrogenVM.png|250px]]
|}
Using the 3N-5 rule for linear molecules, Nitrogen can be expected to have one vibrational mode but this mode has an IR intensity of zero since Nitrogen molecules are IR inactive. This is because they have no overall dipole.

===Charge analysis===
[[File:Acc2518nitrogen charges.png]]

Both nitrogen atoms have the same electronegativity so the charge is neutral on both atoms.

===CCDC search===
'''Unique identifier:''' [https://www.ccdc.cam.ac.uk/structures/Search?Ccdcid=VAMQAE&DatabaseToSearch=Published VAMQAE]

'''Deposition number:''' 1530121

The complex linked above contains nitrogen coordinated to cobalt with a N-N bond distance of 1.08 Å which is slightly shorter than the optimised N-N bond length, displayed above, of 1.11 Å (3.s.f). During the optimisation process for nitrogen, assumptions have to be made for the computational process to be carried out. Each assumption made will increase the uncertainty in measurable quantities such as the bond length. Hence, the computationally determined bond length from the optimisation is a model and may not fully reflect the true bond length or the bond length determined by a computational program considering slightly different assumptions.

It should also be considered that the optimisation gave a prediction for the N-N bond length in a nitrogen molecule whereas the molecule linked above contains a nitrogen molecule that is coordinated into a transition metal complex. A lone pair of electrons on one of the nitrogen atoms has been donated to a cobalt ion, this draws electron density away from the donating nitrogen atom and would therefore slightly increase the positive charge on this atom. This may cause the donating nitrogen atom to attract the electrons in the N-N bond more strongly which would then explain the shorter bond in the transition metal complex compared to the nitrogen molecule.

==H2 molecule==

===Optimisation data===
{| class="wikitable"
|+ H2 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-1.17853936 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00000017 (au)
|-
|'''Point group'''
|D∞h
|-
|'''Bond length (N-N)'''
|0.74279 (Å)
|}

<pre>
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

</pre>

<jmol><jmolApplet>
<title> Hydrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518 H2 OPTIMISATION.LOG</uploadedFileContents>
<script>frame 1.7</script>
</jmolApplet></jmol>
[[:File:ACC2518 H2 OPTIMISATION.LOG|Optimised H2 .log file (acc2518)]]

===Vibrations===
[[File:Acc2518 H2vibration.png|Hydrogen display vibrations screenshot|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 4466
|-
| '''Symmetry''' || SGG
|-
| '''Intensity''' (arbitrary units) || 0
|-
| '''Image'''|| [[File:Acc2518HydrogenVM.png|250px]]
|}
Using the 3N-5 rule for linear molecules, hydrogen can be expected to have one vibrational mode but this mode has an IR intensity of zero since hydrogen molecules, like nitrogen molecules, are IR inactive.

===Charge analysis===
[[File:Acc2518hydrogen charges.png]]

Both hydrogen atoms have the same electronegativity so the charge is neutral on both atoms.

==The Haber-Bosch process==
N2 + 3H2 -> 2NH3

E(NH3)=-56.55776873

 '''2*E(NH3)''' =2*(-56.55776873)=-113.11553746

 '''E(N2)''' =-109.52412868

E(H2)=-1.17853936

 '''3*E(H2)''' =3*(-1.17853936) =-3.53561808

'''ΔE= 2*E(NH3) -[ E(N2) + 3*E(H2) ]'''= -0.05579069 ≈ -0.05579 au (5.d.p)

'''ΔE=-146.5 kJ/mol (1.d.p)'''

ΔE is negative which indicates that the gaseous reactants are less stable than the ammonia product since the reactants are at a higher energy than the product. Although this process is not necessarily entropically favourable with four reactant gaseous molecules forming two gaseous product molecules, the reaction has a significantly negative enthalpy change which reflects the result calculated above.

== Project molecule (NF3) ==

=== Optimisation data ===
{| class="wikitable"
|+ NF3 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-354.07131058 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00010256 (au)
|-
|'''Point group'''
|C3V
|-
|'''Bond length (N-F)'''
|1.384 (Å)
|-
|'''Bond angle (F-N-F)'''
|102(°)
|}
<pre>
Item Value Threshold Converged?
Maximum Force 0.000164 0.000450 YES
RMS Force 0.000108 0.000300 YES
Maximum Displacement 0.000612 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

<jmol><jmolApplet>
<title> NF3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518_NF3_OPTF_POP.LOG </uploadedFileContents>
<script>frame 1.7</script>
</jmolApplet></jmol>
[[:File:ACC2518_NF3_OPTF_POP.LOG|Optimised NF3 .log file (acc2518)]]

=== Vibrations ===
[[File:Acc2518 NF3 vibrations screenshot.png|The Gaussview "Display Vibrations" window of the optimised nitrogen trifluoride molecule.|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 482 || 482
|-
| '''Symmetry''' || E || E
|-
| '''Intensity''' (arbitrary units) || 1 || 1
|-
| '''Image'''|| [[File:Acc2518 NF3 VM1.png|300px]] || [[File:Acc2518 NF3 VM2.png|300px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 644|| 930
|-
| '''Symmetry''' || A1 || E
|-
| '''Intensity''' (arbitrary units) || 3 || 208
|-
| '''Image'''|| [[File:Acc2518 NF3 VM3.png|300px]] || [[File:Acc2518 NF3 VM4.png|300px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 930|| 1062
|-
| '''Symmetry''' || E || A1
|-
| '''Intensity''' (arbitrary units) || 208 || 40
|-
| '''Image'''|| [[File:Acc2518 NF3 VM5.png|300px]] || [[File:Acc2518 NF3 VM6.png|300px]]
|}

Nitrogen trifluoride has the same number of atoms as ammonia and so six vibrational modes can be predicted from the 3N-6 rule. There are also two pairs of degenerate modes with frequencies of 482 (cm-1) and 930 (cm-1). The modes with a frequency of 482 (cm-1) and 644(cm-1) correspond to bending vibrational modes and the modes with a frequency of 930 (cm-1) and 1062 (cm-1) correspond to stretching vibrational modes. The mode with a frequency of 1062 (cm-1) represents a symmetric stretch whilst the modes with a frequency of 930 (cm-1) represent asymmetric stretches. In contrast to ammonia, the highest frequency bond stretch of nitrogen trifluoride is the symmetric stretch.

Three bands can be expected in the NF3 IR spectrum at frequencies of 644 (cm-1) 930 (cm-1) and 1062 (cm-1). The bends at 482 (cm-1) will be too low in frequency to appear in the spectrum which starts at a frequency of 500 (cm-1). The stretches at 930 (cm-1) are degenerate and hence will only display one band between them. The band as 644 (cm-1) may not be clearly visible due its relative low intensity of 3 arbitrary units.

=== Charge analysis ===
[[File:Acc2518 NF3 charge analysis.png|The Gaussview generated atomic charges of ammonia.|250px]]

Fluorine has a greater electronegativity that nitrogen and therefore there is greater electron density distributed around the three fluorine atoms compared to the nitrogen atom. The three fluorine atoms are treated as equivalent which means that the magnitude of the positive charge on nitrogen is three times the magnitude of the negative charge on a single fluorine atom.

Acc2518

2019-03-04T10:50:26Z

Acc2518: /* H2 molecule */

== NH3 molecule ==
=== Optimisation data ===
{| class="wikitable"
|+ NH3 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-56.55776873 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00000485 (au)
|-
|'''Point group'''
|C3V
|-
|'''Bond length (N-H)'''
|1.018 (Å)
|-
|'''Bond angle (H-N-H)'''
|106(°)
|}
<pre>
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
</pre>

<jmol><jmolApplet>
<title> NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518 NH3 OPTF POP.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>
[[:File:ACC2518 NH3 OPTF POP.LOG|Optimised NH3 .log file (acc2518)]]

=== Vibrations ===
[[File:Acc2518 vibrations screenshot.jpg|The Gaussview "Display Vibrations" window of the optimised ammonia molecule.|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 1090 || 1694
|-
| '''Symmetry''' || A1 || E
|-
| '''Intensity''' (arbitrary units) || 145 || 14
|-
| '''Image'''|| [[File:acc2518VM1.png|250px]] || [[File:acc2518VM2.png|300px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 1694|| 3461
|-
| '''Symmetry''' || E || A1
|-
| '''Intensity''' (arbitrary units) || 14 || 1
|-
| '''Image'''|| [[File:acc2518VM3.png|250px]] || [[File:acc2518VM4.png|275px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 3590|| 3590
|-
| '''Symmetry''' || E || E
|-
| '''Intensity''' (arbitrary units) || 0 || 0
|-
| '''Image'''|| [[File:acc2518VM5.png|275px]] || [[File:acc2518VM6.png|250px]]
|}

Using the 3N-6 rule, where N represents the number of atoms in a molecule, it is expected that ammonia will have six vibrational modes as shown above. There are two pairs of degenerate modes with a frequency of 1694 (cm-1) and 3590 (cm-1). The modes with a frequency of 1090 (cm-1) and 1694 (cm-1) correspond to bending vibrations and the modes with a frequency 3461 (cm-1) and 3590 (cm-1) correspond to bond stretch vibrations. The bond stretch vibration at 3461 (cm-1) is highly symmetric whilst the stretches with a frequency of 3590 (cm-1) are asymmetric. The bending vibration with a frequency of 1090 (cm-1) is known as the umbrella mode. Three bands would be expected to be seen with the two stretches at 3590 (cm-1) being too low in intensity. The bends with a frequency of 1694 (cm-1) are degenerate and only one band will be observed between the two. Hence the three observed bands would be at 1090 (cm-1), 1694 (cm-1) and 3461 (cm-1).

=== Charge analysis ===
[[File:Acc2518 charge analysis.png|The Gaussview generated atomic charges of ammonia.|250px]]

Nitrogen has a greater electronegativity than hydrogen and hence there is greater electron density distributed around the N atom in ammonia relative to hydrogen. This explains the negative charge on N and the positive charge on H.

==N2 molecule==

===Optimisation data===

{| class="wikitable"
|+ N2 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-109.52412868 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00000060 (au)
|-
|'''Point group'''
|D∞h
|-
|'''Bond length (N-N)'''
|1.10550 (Å)
|}

<pre>
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
</pre>

<jmol><jmolApplet>
<title> Nitrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518 N2 OPTIMISATION.LOG</uploadedFileContents>
<script>frame 1.10</script>
</jmolApplet></jmol>
[[:File:ACC2518 N2 OPTIMISATION.LOG|Optimised N2 .log file (acc2518)]]

===Vibrations===
[[File:Acc2518 N2vibration.png|Nitrogen display vibrations screenshot|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 2457
|-
| '''Symmetry''' || SGG
|-
| '''Intensity''' (arbitrary units) || 0
|-
| '''Image'''|| [[File:Acc2518NitrogenVM.png|250px]]
|}
Using the 3N-5 rule for linear molecules, Nitrogen can be expected to have one vibrational mode but this mode has an IR intensity of zero since Nitrogen molecules are IR inactive. This is because they have no overall dipole.

===Charge analysis===
[[File:Acc2518nitrogen charges.png]]

Both nitrogen atoms have the same electronegativity so the charge is neutral on both atoms.

===CCDC search===
'''Unique identifier:''' [https://www.ccdc.cam.ac.uk/structures/Search?Ccdcid=VAMQAE&DatabaseToSearch=Published VAMQAE]

'''Deposition number:''' 1530121

The complex linked above contains nitrogen coordinated to cobalt with a N-N bond distance of 1.08 Å which is slightly shorter than the optimised N-N bond length, displayed above, of 1.11 Å (3.s.f). During the optimisation process for nitrogen, assumptions have to be made for the computational process to be carried out. Each assumption made will increase the uncertainty in measurable quantities such as the bond length. Hence, the computationally determined bond length from the optimisation is a model and may not fully reflect the true bond length or the bond length determined by a computational program considering slightly different assumptions.

It should also be considered that the optimisation gave a prediction for the N-N bond length in a nitrogen molecule whereas the molecule linked above contains a nitrogen molecule that is coordinated into a transition metal complex. A lone pair of electrons on one of the nitrogen atoms has been donated to a cobalt ion, this draws electron density away from the donating nitrogen atom and would therefore slightly increase the positive charge on this atom. This may cause the donating nitrogen atom to attract the electrons in the N-N bond more strongly which would then explain the shorter bond in the transition metal complex compared to the nitrogen molecule.

==H2 molecule==

===Optimisation data===
{| class="wikitable"
|+ H2 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-1.17853936 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00000017 (au)
|-
|'''Point group'''
|D∞h
|-
|'''Bond length (N-N)'''
|0.74279 (Å)
|}

<pre>
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

</pre>

<jmol><jmolApplet>
<title> Hydrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518 H2 OPTIMISATION.LOG</uploadedFileContents>
<script>frame 1.7</script>
</jmolApplet></jmol>
[[:File:ACC2518 H2 OPTIMISATION.LOG|Optimised H2 .log file (acc2518)]]

===Vibrations===
[[File:Acc2518 H2vibration.png|Hydrogen display vibrations screenshot|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 4466
|-
| '''Symmetry''' || SGG
|-
| '''Intensity''' (arbitrary units) || 0
|-
| '''Image'''|| [[File:Acc2518HydrogenVM.png|250px]]
|}
Using the 3N-5 rule for linear molecules, hydrogen can be expected to have one vibrational mode but this mode has an IR intensity of zero since hydrogen molecules, like nitrogen molecules, are IR inactive.

===Charge analysis===
[[File:Acc2518hydrogen charges.png]]

Both hydrogen atoms have the same electronegativity so the charge is neutral on both atoms.

==The Haber-Bosch process==
N2 + 3H2 -> 2NH3

E(NH3)=-56.55776873

 '''2*E(NH3)''' =2*(-56.55776873)=-113.11553746

 '''E(N2)''' =-109.52412868

E(H2)=-1.17853936

 '''3*E(H2)''' =3*(-1.17853936) =-3.53561808

'''ΔE= 2*E(NH3) -[ E(N2) + 3*E(H2) ]'''= -0.05579069 ≈ -0.05579 au (5.d.p)

'''ΔE=-146.5 kJ/mol (1.d.p)'''

ΔE is negative which indicates that the gaseous reactants are less stable than the ammonia product since the reactants are at a higher energy than the product. Although this process is not necessarily entropically favourable with four reactant gaseous molecules forming two gaseous product molecules, the reaction has a significantly negative enthalpy change which reflects the result calculated above.

== Project molecule (NF3) ==

=== Optimisation data ===
{| class="wikitable"
|+ NF3 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-354.07131058 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00010256 (au)
|-
|'''Point group'''
|C3V
|-
|'''Bond length (N-F)'''
|1.384 (Å)
|-
|'''Bond angle (F-N-F)'''
|102(°)
|}
<pre>
Item Value Threshold Converged?
Maximum Force 0.000164 0.000450 YES
RMS Force 0.000108 0.000300 YES
Maximum Displacement 0.000612 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

<jmol><jmolApplet>
<title> NF3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518_NF3_OPTF_POP.LOG </uploadedFileContents>
<script>frame 1.7</script>
</jmolApplet></jmol>
[[:File:ACC2518_NF3_OPTF_POP.LOG|Optimised NF3 .log file (acc2518)]]

=== Vibrations ===
[[File:Acc2518 NF3 vibrations screenshot.png|The Gaussview "Display Vibrations" window of the optimised nitrogen trifluoride molecule.|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 482 || 482
|-
| '''Symmetry''' || E || E
|-
| '''Intensity''' (arbitrary units) || 1 || 1
|-
| '''Image'''|| [[File:Acc2518 NF3 VM1.png|300px]] || [[File:Acc2518 NF3 VM2.png|300px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 644|| 930
|-
| '''Symmetry''' || A1 || E
|-
| '''Intensity''' (arbitrary units) || 3 || 208
|-
| '''Image'''|| [[File:Acc2518 NF3 VM3.png|300px]] || [[File:Acc2518 NF3 VM4.png|300px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 930|| 1062
|-
| '''Symmetry''' || E || A1
|-
| '''Intensity''' (arbitrary units) || 208 || 40
|-
| '''Image'''|| [[File:Acc2518 NF3 VM5.png|300px]] || [[File:Acc2518 NF3 VM6.png|300px]]
|}

Nitrogen trifluoride has the same number of atoms as ammonia and so six vibrational modes can be predicted from the 3N-6 rule. There are also two pairs of degenerate modes with frequencies of 482 (cm-1) and 930 (cm-1). The modes with a frequency of 482 (cm-1) and 644(cm-1) correspond to bending vibrational modes and the modes with a frequency of 930 (cm-1) and 1062 (cm-1) correspond to stretching vibrational modes. The mode with a frequency of 1062 (cm-1) represents a symmetric stretch whilst the modes with a frequency of 930 (cm-1) represent asymmetric stretches. In contrast to ammonia, the highest frequency bond stretch of nitrogen trifluoride is the symmetric stretch.

Using the 3N-6 rule, where N represents the number of atoms in a molecule, it is expected that ammonia will have six vibrational modes as shown above. There are two pairs of degenerate modes with frequencies of 1694 (cm-1) and 3590 (cm-1). The modes of frequency 1090 (cm-1) and 1694 (cm-1) correspond to bending vibrations and the modes of frequency 3461 (cm-1) and 3590 (cm-1) correspond to bond stretch vibrations. The bond stretch vibration at 3461 (cm-1) is highly symmetric whilst the other stretches are asymmetric. The bending vibration at 1090 (cm-1) is known as the umbrella mode. Three bands would be expected to be seen with the two stretches at 3590 (cm-1) being too low in intensity. The bends with a frequency of 1694 (cm-1) are degenerate and only one band will be observed between the two. Hence the three observed bands would be at 1090 (cm-1), 1694 (cm-1) and 3461 (cm-1).

=== Charge analysis ===
[[File:Acc2518 NF3 charge analysis.png|The Gaussview generated atomic charges of ammonia.|250px]]

Fluorine has a greater electronegativity that nitrogen and therefore there is greater electron density distributed around the three fluorine atoms compared to the nitrogen atom. The three fluorine atoms are treated as equivalent which means that the magnitude of the positive charge on nitrogen is three times the magnitude of the negative charge on a single fluorine atom.

Acc2518

2019-03-04T10:49:56Z

Acc2518: /* Optiimisation */

== NH3 molecule ==
=== Optimisation data ===
{| class="wikitable"
|+ NH3 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-56.55776873 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00000485 (au)
|-
|'''Point group'''
|C3V
|-
|'''Bond length (N-H)'''
|1.018 (Å)
|-
|'''Bond angle (H-N-H)'''
|106(°)
|}
<pre>
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
</pre>

<jmol><jmolApplet>
<title> NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518 NH3 OPTF POP.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>
[[:File:ACC2518 NH3 OPTF POP.LOG|Optimised NH3 .log file (acc2518)]]

=== Vibrations ===
[[File:Acc2518 vibrations screenshot.jpg|The Gaussview "Display Vibrations" window of the optimised ammonia molecule.|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 1090 || 1694
|-
| '''Symmetry''' || A1 || E
|-
| '''Intensity''' (arbitrary units) || 145 || 14
|-
| '''Image'''|| [[File:acc2518VM1.png|250px]] || [[File:acc2518VM2.png|300px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 1694|| 3461
|-
| '''Symmetry''' || E || A1
|-
| '''Intensity''' (arbitrary units) || 14 || 1
|-
| '''Image'''|| [[File:acc2518VM3.png|250px]] || [[File:acc2518VM4.png|275px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 3590|| 3590
|-
| '''Symmetry''' || E || E
|-
| '''Intensity''' (arbitrary units) || 0 || 0
|-
| '''Image'''|| [[File:acc2518VM5.png|275px]] || [[File:acc2518VM6.png|250px]]
|}

Using the 3N-6 rule, where N represents the number of atoms in a molecule, it is expected that ammonia will have six vibrational modes as shown above. There are two pairs of degenerate modes with a frequency of 1694 (cm-1) and 3590 (cm-1). The modes with a frequency of 1090 (cm-1) and 1694 (cm-1) correspond to bending vibrations and the modes with a frequency 3461 (cm-1) and 3590 (cm-1) correspond to bond stretch vibrations. The bond stretch vibration at 3461 (cm-1) is highly symmetric whilst the stretches with a frequency of 3590 (cm-1) are asymmetric. The bending vibration with a frequency of 1090 (cm-1) is known as the umbrella mode. Three bands would be expected to be seen with the two stretches at 3590 (cm-1) being too low in intensity. The bends with a frequency of 1694 (cm-1) are degenerate and only one band will be observed between the two. Hence the three observed bands would be at 1090 (cm-1), 1694 (cm-1) and 3461 (cm-1).

=== Charge analysis ===
[[File:Acc2518 charge analysis.png|The Gaussview generated atomic charges of ammonia.|250px]]

Nitrogen has a greater electronegativity than hydrogen and hence there is greater electron density distributed around the N atom in ammonia relative to hydrogen. This explains the negative charge on N and the positive charge on H.

==N2 molecule==

===Optimisation data===

{| class="wikitable"
|+ N2 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-109.52412868 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00000060 (au)
|-
|'''Point group'''
|D∞h
|-
|'''Bond length (N-N)'''
|1.10550 (Å)
|}

<pre>
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
</pre>

<jmol><jmolApplet>
<title> Nitrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518 N2 OPTIMISATION.LOG</uploadedFileContents>
<script>frame 1.10</script>
</jmolApplet></jmol>
[[:File:ACC2518 N2 OPTIMISATION.LOG|Optimised N2 .log file (acc2518)]]

===Vibrations===
[[File:Acc2518 N2vibration.png|Nitrogen display vibrations screenshot|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 2457
|-
| '''Symmetry''' || SGG
|-
| '''Intensity''' (arbitrary units) || 0
|-
| '''Image'''|| [[File:Acc2518NitrogenVM.png|250px]]
|}
Using the 3N-5 rule for linear molecules, Nitrogen can be expected to have one vibrational mode but this mode has an IR intensity of zero since Nitrogen molecules are IR inactive. This is because they have no overall dipole.

===Charge analysis===
[[File:Acc2518nitrogen charges.png]]

Both nitrogen atoms have the same electronegativity so the charge is neutral on both atoms.

===CCDC search===
'''Unique identifier:''' [https://www.ccdc.cam.ac.uk/structures/Search?Ccdcid=VAMQAE&DatabaseToSearch=Published VAMQAE]

'''Deposition number:''' 1530121

The complex linked above contains nitrogen coordinated to cobalt with a N-N bond distance of 1.08 Å which is slightly shorter than the optimised N-N bond length, displayed above, of 1.11 Å (3.s.f). During the optimisation process for nitrogen, assumptions have to be made for the computational process to be carried out. Each assumption made will increase the uncertainty in measurable quantities such as the bond length. Hence, the computationally determined bond length from the optimisation is a model and may not fully reflect the true bond length or the bond length determined by a computational program considering slightly different assumptions.

It should also be considered that the optimisation gave a prediction for the N-N bond length in a nitrogen molecule whereas the molecule linked above contains a nitrogen molecule that is coordinated into a transition metal complex. A lone pair of electrons on one of the nitrogen atoms has been donated to a cobalt ion, this draws electron density away from the donating nitrogen atom and would therefore slightly increase the positive charge on this atom. This may cause the donating nitrogen atom to attract the electrons in the N-N bond more strongly which would then explain the shorter bond in the transition metal complex compared to the nitrogen molecule.

==H2 molecule==
{| class="wikitable"
|+ H2 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-1.17853936 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00000017 (au)
|-
|'''Point group'''
|D∞h
|-
|'''Bond length (N-N)'''
|0.74279 (Å)
|}

<pre>
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

</pre>

<jmol><jmolApplet>
<title> Hydrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518 H2 OPTIMISATION.LOG</uploadedFileContents>
<script>frame 1.7</script>
</jmolApplet></jmol>
[[:File:ACC2518 H2 OPTIMISATION.LOG|Optimised H2 .log file (acc2518)]]

===Vibrations===
[[File:Acc2518 H2vibration.png|Hydrogen display vibrations screenshot|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 4466
|-
| '''Symmetry''' || SGG
|-
| '''Intensity''' (arbitrary units) || 0
|-
| '''Image'''|| [[File:Acc2518HydrogenVM.png|250px]]
|}
Using the 3N-5 rule for linear molecules, hydrogen can be expected to have one vibrational mode but this mode has an IR intensity of zero since hydrogen molecules, like nitrogen molecules, are IR inactive.

===Charge analysis===
[[File:Acc2518hydrogen charges.png]]

Both hydrogen atoms have the same electronegativity so the charge is neutral on both atoms.

==The Haber-Bosch process==
N2 + 3H2 -> 2NH3

E(NH3)=-56.55776873

 '''2*E(NH3)''' =2*(-56.55776873)=-113.11553746

 '''E(N2)''' =-109.52412868

E(H2)=-1.17853936

 '''3*E(H2)''' =3*(-1.17853936) =-3.53561808

'''ΔE= 2*E(NH3) -[ E(N2) + 3*E(H2) ]'''= -0.05579069 ≈ -0.05579 au (5.d.p)

'''ΔE=-146.5 kJ/mol (1.d.p)'''

ΔE is negative which indicates that the gaseous reactants are less stable than the ammonia product since the reactants are at a higher energy than the product. Although this process is not necessarily entropically favourable with four reactant gaseous molecules forming two gaseous product molecules, the reaction has a significantly negative enthalpy change which reflects the result calculated above.

== Project molecule (NF3) ==

=== Optimisation data ===
{| class="wikitable"
|+ NF3 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-354.07131058 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00010256 (au)
|-
|'''Point group'''
|C3V
|-
|'''Bond length (N-F)'''
|1.384 (Å)
|-
|'''Bond angle (F-N-F)'''
|102(°)
|}
<pre>
Item Value Threshold Converged?
Maximum Force 0.000164 0.000450 YES
RMS Force 0.000108 0.000300 YES
Maximum Displacement 0.000612 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

<jmol><jmolApplet>
<title> NF3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518_NF3_OPTF_POP.LOG </uploadedFileContents>
<script>frame 1.7</script>
</jmolApplet></jmol>
[[:File:ACC2518_NF3_OPTF_POP.LOG|Optimised NF3 .log file (acc2518)]]

=== Vibrations ===
[[File:Acc2518 NF3 vibrations screenshot.png|The Gaussview "Display Vibrations" window of the optimised nitrogen trifluoride molecule.|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 482 || 482
|-
| '''Symmetry''' || E || E
|-
| '''Intensity''' (arbitrary units) || 1 || 1
|-
| '''Image'''|| [[File:Acc2518 NF3 VM1.png|300px]] || [[File:Acc2518 NF3 VM2.png|300px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 644|| 930
|-
| '''Symmetry''' || A1 || E
|-
| '''Intensity''' (arbitrary units) || 3 || 208
|-
| '''Image'''|| [[File:Acc2518 NF3 VM3.png|300px]] || [[File:Acc2518 NF3 VM4.png|300px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 930|| 1062
|-
| '''Symmetry''' || E || A1
|-
| '''Intensity''' (arbitrary units) || 208 || 40
|-
| '''Image'''|| [[File:Acc2518 NF3 VM5.png|300px]] || [[File:Acc2518 NF3 VM6.png|300px]]
|}

Nitrogen trifluoride has the same number of atoms as ammonia and so six vibrational modes can be predicted from the 3N-6 rule. There are also two pairs of degenerate modes with frequencies of 482 (cm-1) and 930 (cm-1). The modes with a frequency of 482 (cm-1) and 644(cm-1) correspond to bending vibrational modes and the modes with a frequency of 930 (cm-1) and 1062 (cm-1) correspond to stretching vibrational modes. The mode with a frequency of 1062 (cm-1) represents a symmetric stretch whilst the modes with a frequency of 930 (cm-1) represent asymmetric stretches. In contrast to ammonia, the highest frequency bond stretch of nitrogen trifluoride is the symmetric stretch.

Using the 3N-6 rule, where N represents the number of atoms in a molecule, it is expected that ammonia will have six vibrational modes as shown above. There are two pairs of degenerate modes with frequencies of 1694 (cm-1) and 3590 (cm-1). The modes of frequency 1090 (cm-1) and 1694 (cm-1) correspond to bending vibrations and the modes of frequency 3461 (cm-1) and 3590 (cm-1) correspond to bond stretch vibrations. The bond stretch vibration at 3461 (cm-1) is highly symmetric whilst the other stretches are asymmetric. The bending vibration at 1090 (cm-1) is known as the umbrella mode. Three bands would be expected to be seen with the two stretches at 3590 (cm-1) being too low in intensity. The bends with a frequency of 1694 (cm-1) are degenerate and only one band will be observed between the two. Hence the three observed bands would be at 1090 (cm-1), 1694 (cm-1) and 3461 (cm-1).

=== Charge analysis ===
[[File:Acc2518 NF3 charge analysis.png|The Gaussview generated atomic charges of ammonia.|250px]]

Fluorine has a greater electronegativity that nitrogen and therefore there is greater electron density distributed around the three fluorine atoms compared to the nitrogen atom. The three fluorine atoms are treated as equivalent which means that the magnitude of the positive charge on nitrogen is three times the magnitude of the negative charge on a single fluorine atom.

Acc2518

2019-03-04T10:49:36Z

Acc2518: /* N2 molecule */

== NH3 molecule ==
=== Optimisation data ===
{| class="wikitable"
|+ NH3 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-56.55776873 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00000485 (au)
|-
|'''Point group'''
|C3V
|-
|'''Bond length (N-H)'''
|1.018 (Å)
|-
|'''Bond angle (H-N-H)'''
|106(°)
|}
<pre>
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
</pre>

<jmol><jmolApplet>
<title> NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518 NH3 OPTF POP.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>
[[:File:ACC2518 NH3 OPTF POP.LOG|Optimised NH3 .log file (acc2518)]]

=== Vibrations ===
[[File:Acc2518 vibrations screenshot.jpg|The Gaussview "Display Vibrations" window of the optimised ammonia molecule.|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 1090 || 1694
|-
| '''Symmetry''' || A1 || E
|-
| '''Intensity''' (arbitrary units) || 145 || 14
|-
| '''Image'''|| [[File:acc2518VM1.png|250px]] || [[File:acc2518VM2.png|300px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 1694|| 3461
|-
| '''Symmetry''' || E || A1
|-
| '''Intensity''' (arbitrary units) || 14 || 1
|-
| '''Image'''|| [[File:acc2518VM3.png|250px]] || [[File:acc2518VM4.png|275px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 3590|| 3590
|-
| '''Symmetry''' || E || E
|-
| '''Intensity''' (arbitrary units) || 0 || 0
|-
| '''Image'''|| [[File:acc2518VM5.png|275px]] || [[File:acc2518VM6.png|250px]]
|}

Using the 3N-6 rule, where N represents the number of atoms in a molecule, it is expected that ammonia will have six vibrational modes as shown above. There are two pairs of degenerate modes with a frequency of 1694 (cm-1) and 3590 (cm-1). The modes with a frequency of 1090 (cm-1) and 1694 (cm-1) correspond to bending vibrations and the modes with a frequency 3461 (cm-1) and 3590 (cm-1) correspond to bond stretch vibrations. The bond stretch vibration at 3461 (cm-1) is highly symmetric whilst the stretches with a frequency of 3590 (cm-1) are asymmetric. The bending vibration with a frequency of 1090 (cm-1) is known as the umbrella mode. Three bands would be expected to be seen with the two stretches at 3590 (cm-1) being too low in intensity. The bends with a frequency of 1694 (cm-1) are degenerate and only one band will be observed between the two. Hence the three observed bands would be at 1090 (cm-1), 1694 (cm-1) and 3461 (cm-1).

=== Charge analysis ===
[[File:Acc2518 charge analysis.png|The Gaussview generated atomic charges of ammonia.|250px]]

Nitrogen has a greater electronegativity than hydrogen and hence there is greater electron density distributed around the N atom in ammonia relative to hydrogen. This explains the negative charge on N and the positive charge on H.

==N2 molecule==

===Optiimisation===

{| class="wikitable"
|+ N2 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-109.52412868 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00000060 (au)
|-
|'''Point group'''
|D∞h
|-
|'''Bond length (N-N)'''
|1.10550 (Å)
|}

<pre>
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
</pre>

<jmol><jmolApplet>
<title> Nitrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518 N2 OPTIMISATION.LOG</uploadedFileContents>
<script>frame 1.10</script>
</jmolApplet></jmol>
[[:File:ACC2518 N2 OPTIMISATION.LOG|Optimised N2 .log file (acc2518)]]

===Vibrations===
[[File:Acc2518 N2vibration.png|Nitrogen display vibrations screenshot|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 2457
|-
| '''Symmetry''' || SGG
|-
| '''Intensity''' (arbitrary units) || 0
|-
| '''Image'''|| [[File:Acc2518NitrogenVM.png|250px]]
|}
Using the 3N-5 rule for linear molecules, Nitrogen can be expected to have one vibrational mode but this mode has an IR intensity of zero since Nitrogen molecules are IR inactive. This is because they have no overall dipole.

===Charge analysis===
[[File:Acc2518nitrogen charges.png]]

Both nitrogen atoms have the same electronegativity so the charge is neutral on both atoms.

===CCDC search===
'''Unique identifier:''' [https://www.ccdc.cam.ac.uk/structures/Search?Ccdcid=VAMQAE&DatabaseToSearch=Published VAMQAE]

'''Deposition number:''' 1530121

The complex linked above contains nitrogen coordinated to cobalt with a N-N bond distance of 1.08 Å which is slightly shorter than the optimised N-N bond length, displayed above, of 1.11 Å (3.s.f). During the optimisation process for nitrogen, assumptions have to be made for the computational process to be carried out. Each assumption made will increase the uncertainty in measurable quantities such as the bond length. Hence, the computationally determined bond length from the optimisation is a model and may not fully reflect the true bond length or the bond length determined by a computational program considering slightly different assumptions.

It should also be considered that the optimisation gave a prediction for the N-N bond length in a nitrogen molecule whereas the molecule linked above contains a nitrogen molecule that is coordinated into a transition metal complex. A lone pair of electrons on one of the nitrogen atoms has been donated to a cobalt ion, this draws electron density away from the donating nitrogen atom and would therefore slightly increase the positive charge on this atom. This may cause the donating nitrogen atom to attract the electrons in the N-N bond more strongly which would then explain the shorter bond in the transition metal complex compared to the nitrogen molecule.

==H2 molecule==
{| class="wikitable"
|+ H2 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-1.17853936 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00000017 (au)
|-
|'''Point group'''
|D∞h
|-
|'''Bond length (N-N)'''
|0.74279 (Å)
|}

<pre>
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

</pre>

<jmol><jmolApplet>
<title> Hydrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518 H2 OPTIMISATION.LOG</uploadedFileContents>
<script>frame 1.7</script>
</jmolApplet></jmol>
[[:File:ACC2518 H2 OPTIMISATION.LOG|Optimised H2 .log file (acc2518)]]

===Vibrations===
[[File:Acc2518 H2vibration.png|Hydrogen display vibrations screenshot|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 4466
|-
| '''Symmetry''' || SGG
|-
| '''Intensity''' (arbitrary units) || 0
|-
| '''Image'''|| [[File:Acc2518HydrogenVM.png|250px]]
|}
Using the 3N-5 rule for linear molecules, hydrogen can be expected to have one vibrational mode but this mode has an IR intensity of zero since hydrogen molecules, like nitrogen molecules, are IR inactive.

===Charge analysis===
[[File:Acc2518hydrogen charges.png]]

Both hydrogen atoms have the same electronegativity so the charge is neutral on both atoms.

==The Haber-Bosch process==
N2 + 3H2 -> 2NH3

E(NH3)=-56.55776873

 '''2*E(NH3)''' =2*(-56.55776873)=-113.11553746

 '''E(N2)''' =-109.52412868

E(H2)=-1.17853936

 '''3*E(H2)''' =3*(-1.17853936) =-3.53561808

'''ΔE= 2*E(NH3) -[ E(N2) + 3*E(H2) ]'''= -0.05579069 ≈ -0.05579 au (5.d.p)

'''ΔE=-146.5 kJ/mol (1.d.p)'''

ΔE is negative which indicates that the gaseous reactants are less stable than the ammonia product since the reactants are at a higher energy than the product. Although this process is not necessarily entropically favourable with four reactant gaseous molecules forming two gaseous product molecules, the reaction has a significantly negative enthalpy change which reflects the result calculated above.

== Project molecule (NF3) ==

=== Optimisation data ===
{| class="wikitable"
|+ NF3 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-354.07131058 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00010256 (au)
|-
|'''Point group'''
|C3V
|-
|'''Bond length (N-F)'''
|1.384 (Å)
|-
|'''Bond angle (F-N-F)'''
|102(°)
|}
<pre>
Item Value Threshold Converged?
Maximum Force 0.000164 0.000450 YES
RMS Force 0.000108 0.000300 YES
Maximum Displacement 0.000612 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

<jmol><jmolApplet>
<title> NF3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518_NF3_OPTF_POP.LOG </uploadedFileContents>
<script>frame 1.7</script>
</jmolApplet></jmol>
[[:File:ACC2518_NF3_OPTF_POP.LOG|Optimised NF3 .log file (acc2518)]]

=== Vibrations ===
[[File:Acc2518 NF3 vibrations screenshot.png|The Gaussview "Display Vibrations" window of the optimised nitrogen trifluoride molecule.|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 482 || 482
|-
| '''Symmetry''' || E || E
|-
| '''Intensity''' (arbitrary units) || 1 || 1
|-
| '''Image'''|| [[File:Acc2518 NF3 VM1.png|300px]] || [[File:Acc2518 NF3 VM2.png|300px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 644|| 930
|-
| '''Symmetry''' || A1 || E
|-
| '''Intensity''' (arbitrary units) || 3 || 208
|-
| '''Image'''|| [[File:Acc2518 NF3 VM3.png|300px]] || [[File:Acc2518 NF3 VM4.png|300px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 930|| 1062
|-
| '''Symmetry''' || E || A1
|-
| '''Intensity''' (arbitrary units) || 208 || 40
|-
| '''Image'''|| [[File:Acc2518 NF3 VM5.png|300px]] || [[File:Acc2518 NF3 VM6.png|300px]]
|}

Nitrogen trifluoride has the same number of atoms as ammonia and so six vibrational modes can be predicted from the 3N-6 rule. There are also two pairs of degenerate modes with frequencies of 482 (cm-1) and 930 (cm-1). The modes with a frequency of 482 (cm-1) and 644(cm-1) correspond to bending vibrational modes and the modes with a frequency of 930 (cm-1) and 1062 (cm-1) correspond to stretching vibrational modes. The mode with a frequency of 1062 (cm-1) represents a symmetric stretch whilst the modes with a frequency of 930 (cm-1) represent asymmetric stretches. In contrast to ammonia, the highest frequency bond stretch of nitrogen trifluoride is the symmetric stretch.

Using the 3N-6 rule, where N represents the number of atoms in a molecule, it is expected that ammonia will have six vibrational modes as shown above. There are two pairs of degenerate modes with frequencies of 1694 (cm-1) and 3590 (cm-1). The modes of frequency 1090 (cm-1) and 1694 (cm-1) correspond to bending vibrations and the modes of frequency 3461 (cm-1) and 3590 (cm-1) correspond to bond stretch vibrations. The bond stretch vibration at 3461 (cm-1) is highly symmetric whilst the other stretches are asymmetric. The bending vibration at 1090 (cm-1) is known as the umbrella mode. Three bands would be expected to be seen with the two stretches at 3590 (cm-1) being too low in intensity. The bends with a frequency of 1694 (cm-1) are degenerate and only one band will be observed between the two. Hence the three observed bands would be at 1090 (cm-1), 1694 (cm-1) and 3461 (cm-1).

=== Charge analysis ===
[[File:Acc2518 NF3 charge analysis.png|The Gaussview generated atomic charges of ammonia.|250px]]

Fluorine has a greater electronegativity that nitrogen and therefore there is greater electron density distributed around the three fluorine atoms compared to the nitrogen atom. The three fluorine atoms are treated as equivalent which means that the magnitude of the positive charge on nitrogen is three times the magnitude of the negative charge on a single fluorine atom.

Acc2518

2019-03-04T10:48:12Z

Acc2518: /* CCDC search */

== NH3 molecule ==
=== Optimisation data ===
{| class="wikitable"
|+ NH3 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-56.55776873 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00000485 (au)
|-
|'''Point group'''
|C3V
|-
|'''Bond length (N-H)'''
|1.018 (Å)
|-
|'''Bond angle (H-N-H)'''
|106(°)
|}
<pre>
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
</pre>

<jmol><jmolApplet>
<title> NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518 NH3 OPTF POP.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>
[[:File:ACC2518 NH3 OPTF POP.LOG|Optimised NH3 .log file (acc2518)]]

=== Vibrations ===
[[File:Acc2518 vibrations screenshot.jpg|The Gaussview "Display Vibrations" window of the optimised ammonia molecule.|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 1090 || 1694
|-
| '''Symmetry''' || A1 || E
|-
| '''Intensity''' (arbitrary units) || 145 || 14
|-
| '''Image'''|| [[File:acc2518VM1.png|250px]] || [[File:acc2518VM2.png|300px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 1694|| 3461
|-
| '''Symmetry''' || E || A1
|-
| '''Intensity''' (arbitrary units) || 14 || 1
|-
| '''Image'''|| [[File:acc2518VM3.png|250px]] || [[File:acc2518VM4.png|275px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 3590|| 3590
|-
| '''Symmetry''' || E || E
|-
| '''Intensity''' (arbitrary units) || 0 || 0
|-
| '''Image'''|| [[File:acc2518VM5.png|275px]] || [[File:acc2518VM6.png|250px]]
|}

Using the 3N-6 rule, where N represents the number of atoms in a molecule, it is expected that ammonia will have six vibrational modes as shown above. There are two pairs of degenerate modes with a frequency of 1694 (cm-1) and 3590 (cm-1). The modes with a frequency of 1090 (cm-1) and 1694 (cm-1) correspond to bending vibrations and the modes with a frequency 3461 (cm-1) and 3590 (cm-1) correspond to bond stretch vibrations. The bond stretch vibration at 3461 (cm-1) is highly symmetric whilst the stretches with a frequency of 3590 (cm-1) are asymmetric. The bending vibration with a frequency of 1090 (cm-1) is known as the umbrella mode. Three bands would be expected to be seen with the two stretches at 3590 (cm-1) being too low in intensity. The bends with a frequency of 1694 (cm-1) are degenerate and only one band will be observed between the two. Hence the three observed bands would be at 1090 (cm-1), 1694 (cm-1) and 3461 (cm-1).

=== Charge analysis ===
[[File:Acc2518 charge analysis.png|The Gaussview generated atomic charges of ammonia.|250px]]

Nitrogen has a greater electronegativity than hydrogen and hence there is greater electron density distributed around the N atom in ammonia relative to hydrogen. This explains the negative charge on N and the positive charge on H.

==N2 molecule==
{| class="wikitable"
|+ N2 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-109.52412868 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00000060 (au)
|-
|'''Point group'''
|D∞h
|-
|'''Bond length (N-N)'''
|1.10550 (Å)
|}

<pre>
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
</pre>

<jmol><jmolApplet>
<title> Nitrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518 N2 OPTIMISATION.LOG</uploadedFileContents>
<script>frame 1.10</script>
</jmolApplet></jmol>
[[:File:ACC2518 N2 OPTIMISATION.LOG|Optimised N2 .log file (acc2518)]]

===Vibrations===
[[File:Acc2518 N2vibration.png|Nitrogen display vibrations screenshot|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 2457
|-
| '''Symmetry''' || SGG
|-
| '''Intensity''' (arbitrary units) || 0
|-
| '''Image'''|| [[File:Acc2518NitrogenVM.png|250px]]
|}
Using the 3N-5 rule for linear molecules, Nitrogen can be expected to have one vibrational mode but this mode has an IR intensity of zero since Nitrogen molecules are IR inactive. This is because they have no overall dipole.

===Charge analysis===
[[File:Acc2518nitrogen charges.png]]

Both nitrogen atoms have the same electronegativity so the charge is neutral on both atoms.

===CCDC search===
'''Unique identifier:''' [https://www.ccdc.cam.ac.uk/structures/Search?Ccdcid=VAMQAE&DatabaseToSearch=Published VAMQAE]

'''Deposition number:''' 1530121

The complex linked above contains nitrogen coordinated to cobalt with a N-N bond distance of 1.08 Å which is slightly shorter than the optimised N-N bond length, displayed above, of 1.11 Å (3.s.f). During the optimisation process for nitrogen, assumptions have to be made for the computational process to be carried out. Each assumption made will increase the uncertainty in measurable quantities such as the bond length. Hence, the computationally determined bond length from the optimisation is a model and may not fully reflect the true bond length or the bond length determined by a computational program considering slightly different assumptions.

It should also be considered that the optimisation gave a prediction for the N-N bond length in a nitrogen molecule whereas the molecule linked above contains a nitrogen molecule that is coordinated into a transition metal complex. A lone pair of electrons on one of the nitrogen atoms has been donated to a cobalt ion, this draws electron density away from the donating nitrogen atom and would therefore slightly increase the positive charge on this atom. This may cause the donating nitrogen atom to attract the electrons in the N-N bond more strongly which would then explain the shorter bond in the transition metal complex compared to the nitrogen molecule.

==H2 molecule==
{| class="wikitable"
|+ H2 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-1.17853936 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00000017 (au)
|-
|'''Point group'''
|D∞h
|-
|'''Bond length (N-N)'''
|0.74279 (Å)
|}

<pre>
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

</pre>

<jmol><jmolApplet>
<title> Hydrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518 H2 OPTIMISATION.LOG</uploadedFileContents>
<script>frame 1.7</script>
</jmolApplet></jmol>
[[:File:ACC2518 H2 OPTIMISATION.LOG|Optimised H2 .log file (acc2518)]]

===Vibrations===
[[File:Acc2518 H2vibration.png|Hydrogen display vibrations screenshot|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 4466
|-
| '''Symmetry''' || SGG
|-
| '''Intensity''' (arbitrary units) || 0
|-
| '''Image'''|| [[File:Acc2518HydrogenVM.png|250px]]
|}
Using the 3N-5 rule for linear molecules, hydrogen can be expected to have one vibrational mode but this mode has an IR intensity of zero since hydrogen molecules, like nitrogen molecules, are IR inactive.

===Charge analysis===
[[File:Acc2518hydrogen charges.png]]

Both hydrogen atoms have the same electronegativity so the charge is neutral on both atoms.

==The Haber-Bosch process==
N2 + 3H2 -> 2NH3

E(NH3)=-56.55776873

 '''2*E(NH3)''' =2*(-56.55776873)=-113.11553746

 '''E(N2)''' =-109.52412868

E(H2)=-1.17853936

 '''3*E(H2)''' =3*(-1.17853936) =-3.53561808

'''ΔE= 2*E(NH3) -[ E(N2) + 3*E(H2) ]'''= -0.05579069 ≈ -0.05579 au (5.d.p)

'''ΔE=-146.5 kJ/mol (1.d.p)'''

ΔE is negative which indicates that the gaseous reactants are less stable than the ammonia product since the reactants are at a higher energy than the product. Although this process is not necessarily entropically favourable with four reactant gaseous molecules forming two gaseous product molecules, the reaction has a significantly negative enthalpy change which reflects the result calculated above.

== Project molecule (NF3) ==

=== Optimisation data ===
{| class="wikitable"
|+ NF3 optimisation
|'''Calculation method'''
|RB3LYP
|-
|'''Basis set'''
|6-31G(d.p)
|-
|'''Final energy E(RB3LYP)'''
|<nowiki>-354.07131058 (au)</nowiki>
|-
|'''RMS gradient'''
|0.00010256 (au)
|-
|'''Point group'''
|C3V
|-
|'''Bond length (N-F)'''
|1.384 (Å)
|-
|'''Bond angle (F-N-F)'''
|102(°)
|}
<pre>
Item Value Threshold Converged?
Maximum Force 0.000164 0.000450 YES
RMS Force 0.000108 0.000300 YES
Maximum Displacement 0.000612 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

<jmol><jmolApplet>
<title> NF3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ACC2518_NF3_OPTF_POP.LOG </uploadedFileContents>
<script>frame 1.7</script>
</jmolApplet></jmol>
[[:File:ACC2518_NF3_OPTF_POP.LOG|Optimised NF3 .log file (acc2518)]]

=== Vibrations ===
[[File:Acc2518 NF3 vibrations screenshot.png|The Gaussview "Display Vibrations" window of the optimised nitrogen trifluoride molecule.|350px]]

{| class="wikitable" border="1"
|+ IR vibration data
|-
| '''Wavenumber''' (cm-1) || 482 || 482
|-
| '''Symmetry''' || E || E
|-
| '''Intensity''' (arbitrary units) || 1 || 1
|-
| '''Image'''|| [[File:Acc2518 NF3 VM1.png|300px]] || [[File:Acc2518 NF3 VM2.png|300px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 644|| 930
|-
| '''Symmetry''' || A1 || E
|-
| '''Intensity''' (arbitrary units) || 3 || 208
|-
| '''Image'''|| [[File:Acc2518 NF3 VM3.png|300px]] || [[File:Acc2518 NF3 VM4.png|300px]]
|-
! colspan="3" style="text-align: centre;"|
|-
| '''Wavenumber''' (cm-1) || 930|| 1062
|-
| '''Symmetry''' || E || A1
|-
| '''Intensity''' (arbitrary units) || 208 || 40
|-
| '''Image'''|| [[File:Acc2518 NF3 VM5.png|300px]] || [[File:Acc2518 NF3 VM6.png|300px]]
|}

Nitrogen trifluoride has the same number of atoms as ammonia and so six vibrational modes can be predicted from the 3N-6 rule. There are also two pairs of degenerate modes with frequencies of 482 (cm-1) and 930 (cm-1). The modes with a frequency of 482 (cm-1) and 644(cm-1) correspond to bending vibrational modes and the modes with a frequency of 930 (cm-1) and 1062 (cm-1) correspond to stretching vibrational modes. The mode with a frequency of 1062 (cm-1) represents a symmetric stretch whilst the modes with a frequency of 930 (cm-1) represent asymmetric stretches. In contrast to ammonia, the highest frequency bond stretch of nitrogen trifluoride is the symmetric stretch.

Using the 3N-6 rule, where N represents the number of atoms in a molecule, it is expected that ammonia will have six vibrational modes as shown above. There are two pairs of degenerate modes with frequencies of 1694 (cm-1) and 3590 (cm-1). The modes of frequency 1090 (cm-1) and 1694 (cm-1) correspond to bending vibrations and the modes of frequency 3461 (cm-1) and 3590 (cm-1) correspond to bond stretch vibrations. The bond stretch vibration at 3461 (cm-1) is highly symmetric whilst the other stretches are asymmetric. The bending vibration at 1090 (cm-1) is known as the umbrella mode. Three bands would be expected to be seen with the two stretches at 3590 (cm-1) being too low in intensity. The bends with a frequency of 1694 (cm-1) are degenerate and only one band will be observed between the two. Hence the three observed bands would be at 1090 (cm-1), 1694 (cm-1) and 3461 (cm-1).

=== Charge analysis ===
[[File:Acc2518 NF3 charge analysis.png|The Gaussview generated atomic charges of ammonia.|250px]]

Fluorine has a greater electronegativity that nitrogen and therefore there is greater electron density distributed around the three fluorine atoms compared to the nitrogen atom. The three fluorine atoms are treated as equivalent which means that the magnitude of the positive charge on nitrogen is three times the magnitude of the negative charge on a single fluorine atom.

Acc2518

2019-03-04T10:30:33Z

Acc2518: /* Vibrations */

Acc2518

2019-03-04T10:28:46Z

Acc2518: /* Vibrations */

Acc2518

2019-03-04T10:24:59Z

Acc2518: /* Vibrations */

Acc2518

2019-03-04T10:17:47Z

Acc2518: /* Vibrations */