View source for Nattan Yeshitila 1343100

== <b>NH3 Optimisation</b> ==
=== Summary Results ===
* Molecule: NH<sub>3</sub>
* Calculation Method: RB3LYP
* Basis Set: 6-31G(d.p)
* E(RB3LYP): -56.55776873 a.u.
* RMS Gradient: 0.00000485 a.u.
* Point Group: C<sub>3</sub>V
* Bond Length: 1.01798 A
* Bond Angle: 105.741<sup>0</sup>

=== Item Table ===
<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=-5.986277D-10
 Optimization completed.
    -- Stationary point found.
                           ----------------------------
                           !   Optimized Parameters   !
                           ! (Angstroms and Degrees)  !
 --------------------------                            --------------------------
 ! Name  Definition              Value          Derivative Info.                !
 --------------------------------------------------------------------------------
 ! R1    R(1,2)                  1.018          -DE/DX =    0.0                 !
 ! R2    R(1,3)                  1.018          -DE/DX =    0.0                 !
 ! R3    R(1,4)                  1.018          -DE/DX =    0.0                 !
 ! A1    A(2,1,3)              105.7412         -DE/DX =    0.0                 !
 ! A2    A(2,1,4)              105.7412         -DE/DX =    0.0                 !
 ! A3    A(3,1,4)              105.7412         -DE/DX =    0.0                 !
 ! D1    D(2,1,4,3)           -111.8571         -DE/DX =    0.0                 !
 --------------------------------------------------------------------------------
 GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

=== Dynamic Image ===
<jmol><jmolApplet>
  <title>NH3</title>
  <color>black</color>
  <size>200</size>
  <uploadedFileContents>NY517_NH3_OPTIMISATION_1.LOG</uploadedFileContents>
<script>frame x.y</script>
</jmolApplet></jmol>

This image can be found ([[File:NY517_NH3_OPTIMISATION_3.LOG]])

=== Vibrational and Frequency Analysis ===
[[File:NY517_Display Vibrations_2.png|300px]]

==== <u>''Questions''</u> ====

Since NH<sub>3</sub> is a non-linear molecule, the number of nodes should follow the 3N-6 rule where N represents the number of atoms. As a result, I would expect the molecule to have 6 nodes which is what was produced.

Modes 2&3 and 5&6 are degenerate because they have the same frequency and hence the same energy. The frequency of their vibrations are the same because the vibrations have the same motion but occur on different bonds in the opposite directions.

Modes 1-3 are bending vibrations and modes 4-6 are stretching vibrations. This could have been predicted since stretching vibrations are generally a higher energy than bending vibrations.

Mode 4 is highly symmetric because the bonds stretch in and out simultaneously and therefore maintain their symmetry through the the central atom. This is called a symmetric stretch.

Mode 1 is the umbrella mode due to the bending vibration of the bonds up and down simultaneously.

I would expect to see four bands in an experimental spectrum where the peaks at 3461.30 and 3589.86 would be so small that they are unlikely to be spotted clearly in the spectrum.

==== Charges ====
Nitrogen atom: -1.125                                 Hydrogen atoms: +0.375

I would have expected nitrogen to be negatively charged and hydrogen to be positively charged because nitrogen is more electronegative than hydrogen. Also, the total charge of the molecule is zero which is expected since it is a neutral molecule.

==‍ '''Haber-Bosch Process ''(N<sub>2</sub> & H<sub>2</sub>)'''''==

=== N<sub>2</sub> ===
=== Summary Results ===
* Molecule: N<sub>2</sub>
* Calculation Method: RB3LYP
* Basis Set: 6-31G(d.p)
* E(RB3LYP): -109.52412868 a.u.
* RMS Gradient: 0.00000060 a.u.
* Point Group: D<sup>*</sup>H
* Bond Length: 1.10550 A
* Bond Angle: 180<sup>0</sup>

=== Item Table ===
<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=-3.401007D-13
 Optimization completed.
    -- Stationary point found.
                           ----------------------------
                           !   Optimized Parameters   !
                           ! (Angstroms and Degrees)  !
 --------------------------                            --------------------------
 ! Name  Definition              Value          Derivative Info.                !
 --------------------------------------------------------------------------------
 ! R1    R(1,2)                  1.1055         -DE/DX =    0.0                 !
 --------------------------------------------------------------------------------
 GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

=== Dynamic Image ===
<jmol><jmolApplet>
  <title>N2</title>
  <color>black</color>
  <size>200</size>
  <uploadedFileContents>NY517 N2 OPTIMISATION.LOG</uploadedFileContents>
<script>frame x.y</script>
</jmolApplet></jmol>

This image can be found ([[File:NY517 N2 OPTIMISATION.LOG]])


=== Vibrational and Frequency Analysis ===
[[File:NY517 vibrations N2 2.png|600px]]


=== H<sub>2</sub> ===
=== Summary Results ===
* Molecule: H<sub>2</sub>
* Calculation Method: RB3LYP
* Basis Set: 6-31G(d.p)
* E(RB3LYP): -1.17853936 a.u.
* RMS Gradient: 0.00000017 a.u.
* Point Group: D<sup>*</sup>H
* Bond Length: 0.74279 A
* Bond Angle: 180<sup>0</sup>

=== Item Table ===
<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.
                           ----------------------------
                           !   Optimized Parameters   !
                           ! (Angstroms and Degrees)  !
 --------------------------                            --------------------------
 ! Name  Definition              Value          Derivative Info.                !
 --------------------------------------------------------------------------------
 ! R1    R(1,2)                  0.7428         -DE/DX =    0.0                 !
 --------------------------------------------------------------------------------
 GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

=== Dynamic Image ===
<jmol><jmolApplet>
  <title>H2</title>
  <color>black</color>
  <size>200</size>
  <uploadedFileContents>NY517 H2 OPTIMISATION.LOG</uploadedFileContents>
<script>frame x.y</script>
</jmolApplet></jmol>

This image can be found ([[File:NY517 H2 OPTIMISATION.LOG]])


=== Vibrational and Frequency Analysis ===
[[File:NY517 Vibrations H2.png|300px]]

=== Energy Values (au) ===

* E(NH3)= -56.55776873
* 2*E(NH3)= -113.11553746
* E(N2)= -109.52412868
* E(H2)= -1.17853936
* 3*E(H2)= -3.53561808
* ΔE=2*E(NH3)-[E(N2)+3*E(H2)]= -0.05579070= '''-146.48 kJ mol<sup>-1</sup>'''
The formula for ΔE in this reaction is applicable because 2 moles of NH<sub>3</sub> are formed when 1 mole of N<sub>2</sub> reacts with 3 moles of H<sub>2</sub>. Hence why the energy in bold is the energy for converting hydrogen and nitrogen gas to ammonia. Ammonia is more stable than the gaseous reactants because it has a lower energy structure.

== <b>O<sub>2</sub> Optimisation</b> ==
=== Summary Results ===
* Molecule: O<sub>2</sub>
* Calculation Method: RB3LYP
* Basis Set: 6-31G(d.p)
* E(RB3LYP): -150.25742434 a.u.
* RMS Gradient: 0.00007502 a.u.
* Point Group: D<sup>*</sup>H
* Bond Length: 1.01798 A
* Bond Angle: 105.745<sup>0</sup>

=== Item Table ===
<pre>    Item               Value     Threshold  Converged?
 Maximum Force            0.000130     0.000450     YES
 RMS     Force            0.000130     0.000300     YES
 Maximum Displacement     0.000080     0.001800     YES
 RMS     Displacement     0.000113     0.001200     YES
 Predicted change in Energy=-1.033738D-08
 Optimization completed.
    -- Stationary point found.
                           ----------------------------
                           !   Optimized Parameters   !
                           ! (Angstroms and Degrees)  !
 --------------------------                            --------------------------
 ! Name  Definition              Value          Derivative Info.                !
 --------------------------------------------------------------------------------
 ! R1    R(1,2)                  1.216          -DE/DX =   -0.0001              !
 --------------------------------------------------------------------------------
 GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>

=== Dynamic Image ===
<jmol><jmolApplet>
  <title>O2</title>
  <color>black</color>
  <size>200</size>
  <uploadedFileContents>NY517 O2 OPTIMISATION.LOG</uploadedFileContents>
<script>frame x.y</script>
</jmolApplet></jmol>

This image can be found here ([[File:NY517_O2_OPTIMISATION.LOG|here]])

=== Vibrational and Frequency Analysis ===
[[File:NY517 Vibrations O2.png|300px]]

=== Molecular Orbitals ===
[[File:NY517 2nd orbital.png|200px]]

This is a '''σ*s''' orbital formed from the combination of 2s orbitals from both atoms out of phase. It has a node in the middle resulting in a positive and negative phase. It is an anitbonding orbital deep in energy (at -0.798 au) and is fully occupied. This orbital does not really affect reactivity due to its very low energy.


[[File:NY517 3rd orbital.png|200px]]

This is a '''σp<sub>z</sub>''' orbital formed from the overlap of 2p<sub>z</sub> orbitals from both oxygen atoms. It has two nodes caused by the overlapping of the p-orbitals and the fact that p-orbitals already have a node. It is a bonding orbital that is fully occupied and has an energy of -0.532 au. sp mixing occurs between this orbital and the πp orbitals due to them being similar in energy and the orientations of the orbitals being slightly aligned for overlapping. 


[[File:NY517 4th orbital.png|200px]]

Depending on the axis, this could be a '''πp<sub>x</sub>''' or '''πp<sub>y</sub>''' orbital. They have identical shapes but just in a different orientation. It has one node formed from the orthogonal overlapping of p<sub>x</sub> or p<sub>y</sub> degenerate orbitals hence why it has a different shape to the σp<sub>z</sub> orbital. Despite being formed from degenerate orbitals, their energies are very slightly different most likely due to the different levels of sp mixing. This is a bonding orbital that is fully occupied in the x and y orientations.


[[File:NY517 5th orbital.png|200px]]

Once again, depending on the axis, this could be a '''πp<sub>x</sub>*''' or '''πp<sub>y</sub>*''' orbital. This has four nodes caused by the of degenerate p-orbitals. This was once again an orthogonal overlap but is now an antibonding orbital hence why the shape is different to that of p<sub>x</sub> and p<sub>y</sub>. It results in more nodes and more more changes in phase. These represent the HOMO orbital and since they are only half full, any addition of electrons will be added to these orbitals and so they are very reactive. If an electron was to be excited, it would be excited from these orbitals to the LUMO.


[[File:NY517 6th orbital.png|200px]]


This is a '''σp<sub>z</sub>*''' orbital formed from the out of phase overlap from 2p<sub>z</sub> orbitals. There are four different phases in this despite even though only two would be predicted. This is due to the sp mixing with causing these extra nodes. This is an antibonding orbital that is unfilled and is hence the LUMO. The HOMO-LUMO is fairly small therefore an excitation can be likely with relatively low energy.