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== NH<sub>3</sub> Analysis ==

===<u>NH<sub>3</sub> Summary</u>===

{| class="wikitable" border="1"
|+ NH<sub>3</sub> Summary
! Calculation Method !! Basis Set !! Final Energy !! RMS Gradient !! Point Group
|-
| RB3LYP || 6-31G(d,p) || -56.55776873 au || 0.00000485 || C3v 
|}

Optimised bond length= <b>1.01798</b>

Bond angle= <b>105.7</b>

===<u>Item table</u>===

<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
 Predicted change in Energy=-5.986279D-10
 Optimization completed.
    -- Stationary point found.
</pre>

[[File:NH3 OPTIMISATION pop.LOG]]

===<u>Jmol NH<sub>3</sub></u>===

<jmol><jmolApplet>
  <title>test molecule</title>
  <color>black</color>
  <size>200</size>
  <uploadedFileContents>NH3_OPTIMISATION_pop.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>

This Molecule is the most stable for ammonia

===<u>NH<sub>3</sub> Vibrations</u>===

{| class="wikitable" border="1"
|+ NH<sub>3</sub> Vibrations
! Number of modes !! Degenerate modes !! Modes that bend !! Modes that stretch!! Which is symmetric
|-
| 6 || 5 and 6, 2 and 3 || 1,2 and 3 || 4,5 and 6 || 1 and 4
|}


Umbrella mode= <b>1</b>

expected bands in an experimental spectrum of gaseous ammonia?= <b>2</b>

[[File:NH3_display_vibrations.png|thumb|centre|350px|Vibrational analysis of NH<sub>3</sub>]]

===<u>NH<sub>3</sub> Charge Distribution</u>===

Nitrogen (red)= <b>-1.25</b>
Hydrogen (green)= <b>0.375</b>

[[File:NH3_charge_analysis.PNG|250px]]


== <u>N<sub>2</sub></u>==

===<u>Summary</u>===

{| class="wikitable" border="1"
|+ N<sub>2</sub> Summary
! Calculation Method !! Basis Set !! Final Energy !! RMS Gradient !! Point Group
|-
| RB3LYP || 6-31G(d,p) || -109.52412868 au || 0.00000060 || D*H
|}


Optmised bond length= <b>1.1055 A</b>

Bond angle= <b>180</b>

Frequency= <b>2457.33</b>, IR= <b>0</b>

===<u>Item table</u>===

<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
 Predicted change in Energy=-3.401116D-13
 Optimization completed.
    -- Stationary point found.
</pre>

[[File:N2 OPTIMISATION.LOG]]

<jmol><jmolApplet>
  <title>test molecule</title>
  <color>black</color>
  <size>200</size>
  <uploadedFileContents>N2_OPTIMISATION.LOG</uploadedFileContents>
<script>frame 1.12</script>
</jmolApplet></jmol>

===N<sub>2</sub> Vibrations===

[[File:N2_vibrations.PNG|250px]]

===N<sub>2</sub> Charge Distribution===

[[File:N2_charge_distribution.PNG|250px]]

Diatomic with same atoms of equal negativity, hence no charges

==<u>H<sub>2</sub></u>==

===<u>H<sub>2</sub> Summary</u>===

{| class="wikitable" border="1"
|+ H<sub>2</sub> Summary
! Calculation Method !! Basis Set !! Final Energy !! RMS Gradient !! Point Group
|-
| RB3LYP || 6-31G(d,p) || -1.17853936 au || 0.00000017 || D*H
|}


Optimised bond length <b>0.74279 A</b>

Bond angle=<b>180</b>

===<u>Item table</u>===

<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
 Predicted change in Energy=-1.164080D-13
 Optimization completed.
    -- Stationary point found.
</pre>

[[File:H2 OPTIMISATION.LOG]]


===<u>Jmol H<sub>2</sub></u>===

<jmol><jmolApplet>
  <title>test molecule</title>
  <color>black</color>
  <size>200</size>
  <uploadedFileContents>H2_OPTIMISATION.LOG</uploadedFileContents>
<script>frame 1.12</script>
</jmolApplet></jmol>


===<u>Vibrations H<sub>2</sub></u>===

Frequency= <b>4464.68</b> , IR=<b>0</b>


===<u> H<sub>2</sub> Charge Distribution</u> ===

[[File:H2_charge_distribution.PNG|thumb|centre||250px|Charge Distribution of H<sub>2</sub>]]

Diatomic with same atoms of equal negativity, hence no charges

==<u>Haber-Bosch reaction</u>==


N2 + 3H2 -> 2NH3

{| class="wikitable" border="1"
|+ NH<sub>3</sub> Energies of species
! E(NH<sub>3</sub>) !! 2*E(NH<sub>3</sub>) !! E(N<sub>2</sub>) !! E(H<sub>2</sub>) !! 3*E(H<sub>2</sub>)
|-
| -56.55776873 au || -113.115537 au || -109.52412868 au || -1.17853936 au || -3.53561808 au 
|}

Change in energy= 2*E(NH3)-[E(N2)+3*E(H2)]=<b>- 0.005579024 au = -146.47727512 KJ/mol</b>

<b>reactants are less stable</b>

==CH4==

===<u>Summary</u>===

{| class="wikitable" border="1"
|+ N<sub>2</sub> Summary
! Calculation Method !! Basis Set !! Final Energy !! RMS Gradient !! Point Group
|-
| RB3LYP || 6-31G(d,p) || -40.52401404 au || 0.00003263 || TD
|}


Optimised bond length= <b>1.09197 A</b>
Bond angle= <b>109.47</b>

===<u>Item table</u>===

<pre>
       Item               Value     Threshold  Converged?
 Maximum Force            0.000063     0.000450     YES
 RMS     Force            0.000034     0.000300     YES
 Maximum Displacement     0.000179     0.001800     YES
 RMS     Displacement     0.000095     0.001200     YES
 Predicted change in Energy=-2.256043D-08
 Optimization completed.
    -- Stationary point found.
</pre>

[[File:CH4_OPTIMISATION.LOG]]

===<u>Jmol CH<sub>4</sub></u>===

<jmol><jmolApplet>
  <title>test molecule</title>
  <color>black</color>
  <size>200</size>
  <uploadedFileContents>CH4_OPTIMISATION.LOG </uploadedFileContents>
<script>frame 1.8</script>
</jmolApplet></jmol>

This is the most stable form of methane

===<u>Vibrations</u>===

{| class="wikitable" border="1"
|+ CH<sub>4</sub> Vibrations
! Number of modes !! Degenerate modes !! Modes that bend !! Modes that stretch!! Which is symmetric
|-
| 0 || 1,2 and 3;4 and 5; 7,8 and 9) || 1,2,3 and 4 || 5,6,7,8 and 9 || 6,5 and 4
|}



expected bands in an experimental spectrum?= <b>2</b>

[[File:CH4_vibrations.PNG|350px]]

===<u>Charge Distribution</u>===

[[File:CH4_charge_distribution.PNG|350px|centre]]

===<u>CH<sub>4</sub> Bending</u>===

[[FILE:CH4_bending.PNG|350px|centre]]

===<u><b>CH<sub>4</sub> MO's</b></u>===

<b>MO 1</b>

[[FILE:CH4_MO_1s.PNG|350px|centre]] 

This occupied orbital is very deep in energy with -10.17 au. This 1s from the carbon, which does not contribute towards bonding, makes up the MO. Its small size and stability is due to its proximity to the carbon nucleus and large attractive forces. Very little overlap is seen with the Hydrogens.

<b>MO 2</b>

[[FILE:CH4_symmetrical.PNG|350px|centre]]

The contribution from each AO is from each atom, to form the MO. Contribution of 2s from Carbon and 1s from each hydrogen atom. There is a large degree of mixing. Quite deep in energy and more than MO 3, however, there is also contribution from the 2p Carbon orbitals. This is a bonding orbital. Its energy is found as -0.69041 au.

<b>MO 3- sp<sub>3</sub></b>

[[FILE:CH4_sp3.PNG|350px|centre]]

This is the bonding HOMO, given that MO 3,4 and 5 are all degenerate. Three AO P orbitals of Carbon; px, py, pz hybridise with its 2s to bond to to each 1s Hydrogen orbital.Its energy is found to be -0.38831 auand is higher than MO 2 due to the energy of the orbitals involved- being further away from the nucleus.

<b>MO 4-LUMO</b>

[[FILE:CH4_LUMO.PNG|350px|centre]]

This orbital is unoccupied and the lowest-unoccupied molecular orbital- it is anti-bonding 1s orbital from Carbon.  Its energy is positive as 0.11824 au,  and is lower in energy than the anti-bonding hybridised MO.

<b>MO 5</b>

[[FILE:CH4_antibonding_hybridised.PNG|350px|centre]]

This anti-bonding orbital related to the anti bonding of the hybridised Carbon sp<sub>3</sub> and the 1s on each Hydrogen. Higher in energy than the LUMO. Its energy is 0.17677 au and has of course, 2 other MO's that are degenerate to it- MO 8 and 9.

==<u>Water</u>==

===<u>Summary</u>===

{| class="wikitable" border="1"
|+ H<sub>2</sub>O Summary
! Calculation Method !! Basis Set !! Final Energy !! RMS Gradient !! Point Group
|-
| RB3LYP || 6-31G(d,p) || -76.41973740 au || 0.00006276 || C2V
|}

Optimised bond length= <b>0.96522</b>

Bond angle= <b>103.7</b>


===<u> Item Table </u>===


Item               Value     Threshold  Converged?
 Maximum Force            0.000099     0.000450     YES
 RMS     Force            0.000081     0.000300     YES
 Maximum Displacement     0.000115     0.001800     YES
 RMS     Displacement     0.000120     0.001200     YES
 Predicted change in Energy=-1.939669D-08
 Optimization completed.
    -- Stationary point found.

[[File:H2O_OPTIMISATION.LOG]]

===<u> Jmol H<sub>2</sub>O </u>===

<jmol><jmolApplet>
  <title>test molecule</title>
  <color>black</color>
  <size>200</size>
  <uploadedFileContents>H2O_OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet></jmol>


This Jmol shows the most stable form of the molecule

===<u>H<sub>2</sub>O Vibrations</u>===
{| class="wikitable" border="1"
|+ CH<sub>4</sub> Vibrations
! Number of modes !! Degenerate modes !! Modes that bend !! Modes that stretch!! Which is symmetric
|-
| 3 || 0 || 0 || 3 || 1 and 2
|}

[[File:H2O_vibrations.PNG|350px]]