View source for MM2 CID:01180527

==Introduction==
Optimisations on an NH<sub>3</sub> molecule were conducted using Gaussian. Key findings and information are presented in subsequent sections.

==Key Data from NH<sub>3</sub> Optimisations==
===Parameters and Derived Information===

{| class="wikitable" border="1"
|-
| Molecule || NH<sub>3</sub>
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d.p)
|-
| Final Energy Type || E(RB3LYP)
|-
| Final Energy Value || -56.55776873 a.u.
|-
| RMS Gradient Norm || 0.00000485 a.u.
|-
| Point Group || C<sub>3v</sub>
|-
| Bond Length || 1.01798Å
|-
| Bond Angle || 37.129<sup>o</sup>
|}
<br>
===Item Table===
         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

The data from the raw *log file can be found [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:TERSHIENANG_NH3_OPTIMISATION_TEST1.LOG#filelinks| here].
<br>
===Optimised Molecule===
<jmol><jmolApplet>
  <title>Ammonia</title>
  <color>gray</color>
  <size>200</size>
  <uploadedFileContents>TERSHIENANG_NH3_OPTIMISATION_TEST1.LOG</uploadedFileContents>
</jmolApplet></jmol>
<br>
===Frequency Analysis & Atomic Charges===

====Frequency Analysis====
[[File:Vibrations_Screenshot.PNG|A screen capture of the different vibrational modes]]

The following answers make reference to the modes presented in the screen capture above (ie: numbers 1-6 representing the different modes as specified above)
{| class="wikitable" border="1"
|-
| colspan="1"| Modes expected || 6
|-
| rowspan="2"| Degenerate Modes
| 2 and 3
|-
| 5 and 6<br>(Asymmetric Stretches)
|-
| Bending Modes || 1, 2, 3
|-
| Stretching Modes || 4, 5, 6
|-
| Symmetric mode || 4
|-
| Umbrella mode || 1
|-
| IR bands expected || 2
|}

Only 2 IR bands are expected despite all 6 modes causing a change in dipole moment because <br>(i) modes 2 and 3 are degenerate so will not produce separate bands<br> (ii) the intensity of the IR bands for modes 4,5,6 are too small to be significantly noticeable on the spectrum

====Atomic Charges====
[[File:Charges.PNG]]

The charges on the NH<sub>3</sub> molecule are as follow: +0.375 on the H atoms and -1.125 on the N atom, in accordance with expected values. Expected charges on N and H would be negative and positive respectively as a result of electronegativity differences causing more electrons to reside towards the N atom in the N-H bond.
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==Reaction Energies==
===N<sub>2</sub> and H<sub>2</sub> Optimisations===
{| class="wikitable" border="1"
|
! N<sub>2</sub> !! H<sub>2</sub>
|-
| Calculation Method || RB3LYP || RB3LYP
|-
| Basis Set || 6-31g(d,p) || 6-31g(d,p)
|-
| Final Energy Value<br>(a.u.) || -109.52412868 || -1.17853936
|-
| RMS Gradient Norm<br>(a.u.) || 0.00000060 || 0.00000017
|-
| Point Group || D<sub>∞h</sub> || D<sub>∞h</sub>
|-
| Bond Length (Å) || 1.10550 || 0.74279
|- 
| Bond Vibrating<br>Frequency || 2457.33 || 4465.68
|}

<br>
N<sub>2</sub> Item Table:
         Item               Value     Threshold  Converged?
 Maximum Force            0.000001     0.000450     YES
 RMS     Force            0.000001     0.000300     YES
 Maximum Displacement     0.000000     0.001800     YES
 RMS     Displacement     0.000000     0.001200     YES

<br>
H<sub>2</sub> Item Table:
         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

<br>
===Calculating Haber-Bosch Reaction Energies===
{| class="wikitable" border="1"
|-
| E(NH<sub>3</sub>) || -56.55776873 a.u.
|-
| 2*E(NH<sub>3</sub>) || -113.11553746 a.u.
|-
| E(N<sub>2</sub>) || -109.52412868 a.u.
|-
| E(H<sub>2</sub>) || -1.17853936 a.u.
|-
| 3*E(H<sub>2</sub>) || -3.53561808 a.u.
|-
| ΔE=2*E(NH3)-[E(N2)+3*E(H2)] || -0.0557907 a.u =<br>-146.48 kJ mol<sup>-1</sup>
|}

Since the reaction is exothermic, this suggests that NH<sub>3</sub> is more stable energetically than the gaseous reactants N<sub>2</sub> and H<sub>2</sub>.
<br>
<br>

==Choice of Small Molecule: F<sub>2</sub>==
===Key Data===

{| class="wikitable" border="1"
|-
| Molecule || F<sub>2</sub>
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d.p)
|-
| Final Energy Type || E(RB3LYP)
|-
| Final Energy Value || -199.49825220 a.u.
|-
| RMS Gradient Norm || 0.00002378 a.u.
|-
| Dipole Moment || None
|-
| Point Group || D<sub>∞h</sub>
|-
| Bond Length || 1.40293Å
|}

===Item Table===
         Item               Value     Threshold  Converged?
 Maximum Force            0.000041     0.000450     YES
 RMS     Force            0.000041     0.000300     YES
 Maximum Displacement     0.000051     0.001800     YES
 RMS     Displacement     0.000071     0.001200     YES

The data from the raw *log file can be found [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:TSA_F2_OPTIMISATION.LOG#file| here]
<br>

===Interactive Molecule Image===
<jmol><jmolApplet>
  <title>Fluorine</title>
  <color>gray</color>
  <size>200</size>
  <uploadedFileContents>TSA F2 OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet></jmol>
<br>

===Frequency Analysis & Atomic Charges===

====Frequency Analysis====
[[File:F2_Vibrations_Screenshot.PNG|A screen capture of the Fluorine molecule's vibrational mode]]

The vibrational mode shown is a symmetric stretch; no other vibrational modes are present since F<sub>2</sub> is a linear diatomic molecule, hence there are only 3N-5 = 3(2)-5 = 1 mode.

However, as the vibration does not cause a change in dipole moment of the F<sub>2</sub> molecule, hence no IR bands are expected in an IR spectrum since the molecule is IR-inactive by Gross Selection Rule.
<br>
====Atomic Charge Distribution====
[[File:F2_Charge_Distribution.PNG]]

As expected, charges on each F atom in F<sub>2</sub> are 0. This is because both F atoms on the bond are equal in electronegativity hence electron distribution in the F<sub>2</sub> bond is equal despite F being the most electronegative element. The equal electron distribution results in no charge being created. The molecule is also non-polar as a result.
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<br>

===Molecular Orbitals===

====Highest Occupied Molecular Orbitals (HOMO)====
[[File:F2_HOMO.PNG]]

The HOMO of F<sub>2</sub> are the π* (pi anti-bonding) orbitals - one formed from interaction between the 2p<sub>x</sub> orbitals and another from 2p<sub>y</sub> orbitals of the constituent F atoms. The HOMO is high is energy and in the HOMO-LUMO energy region.

====Lowest Occupied Molecular Orbitals (LUMO)====
[[File:F2_LUMO.PNG]]

The LUMO of F<sub>2</sub> is the σ* orbital formed from interaction between the 2p<sub>z</sub> orbitals of the constituent F atoms. The LUMO is high is energy and in the HOMO-LUMO energy region.

====A selection of other MOs====
[[File:F2_MO3.PNG]]<br>
The above MO is the σ bonding MO formed from the interaction between 2s orbitals of the constituent F atoms. This MO is deep in energy. Since it is a bonding MO, it has a positive effect on bonding and is occupied by electrons.
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[[File:F2_MO5.PNG]]<br>
The above MO is the σ bonding MO formed from the interaction between 2p<sub>z</sub> orbitals of the constituent F atoms. This MO is deep in energy. Since it is a bonding MO, it has a positive effect on bonding and is occupied by electrons.
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[[File:F2_MO6.PNG]]<br>
The above MO is the π bonding MO formed from the interaction between 2p<sub>y</sub> orbitals of the constituent F atoms. It could also be formed from the 2p<sub>x</sub> orbitals since both resulting π MOs are degenerate; it depends on how the cartesian axes are defined. This MO is deep in energy. Since it is a bonding MO, it has a positive effect on bonding and is occupied by electrons.


==Independent Study on H<sub>2</sub>SiO==
===Key Data===

{| class="wikitable" border="1"
|-
| Molecule || H<sub>2</sub>SiO
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d.p)
|-
| Final Energy Type || E(RB3LYP)
|-
| Final Energy Value || -365.90001391 a.u.
|-
| RMS Gradient Norm || 0.00009788 a.u.
|-
| Dipole Moment || 3.4344 Debyes
|-
| Bond Length (Si-H) || 1.48651Å
|-
| Bond Length (Si-O) || 1.53146Å
|-
| Bond Angle (H-Si-H) || 111.732<sup>o</sup>
|-
| Bond Angle (H-Si-O) || 124.135<sup>o</sup>
|}

===Item Table===
         Item               Value     Threshold  Converged?
 Maximum Force            0.000271     0.000450     YES
 RMS     Force            0.000111     0.000300     YES
 Maximum Displacement     0.000816     0.001800     YES
 RMS     Displacement     0.000575     0.001200     YES

===Interactive Molecule Image===
<jmol><jmolApplet>
  <title>H2SiO</title>
  <color>gray</color>
  <size>200</size>
  <uploadedFileContents>TERSHIENANG_H2SIO_OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet></jmol>
<br>

===Frequency Analysis===
[[File:H2SiO_Vibrations_Screenshot.PNG]]<br>
Shown above is the different vibrational modes exhibited by H<sub>2</sub>SiO. Modes 1, 2 and 3 are purely bending modes. Mode 4 is a combination of a stretch and a bend. Mode 5 and 6 are purely stretching modes. Since H<sub>2</sub>SiO is a non-linear molecule, hence it has 3N-6 = 3(4)- = 6 modes, and the result is as expected. Since all the vibrations result in a change in the molecule's dipole moment, hence they are all IR active and 6 IR bands are expected. The predicted IR spectrum is shown below.
[[File:H2SiO_Predicted_IR_Spectrum.PNG]]
<br>
===Atomic Charges===
[[File:H2SiO_Atomic_Charges.PNG]]<br>
Electronegativities of the elements in H<sub>2</sub>SiO increases in the order Si<H<O, hence we would expect the charges to decrease (become more negative) in the same order. Therefore the result is as expected.

===Molecular Orbitals===
[[File:H2SiO_LUMO.PNG]]<br>
Shown above is the LUMO of H<sub>2</sub>SiO. It is unoccupied and anti-bonding.
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[[File:H2SiO_HOMO.PNG]]<br>
Shown above is the HOMO of H<sub>2</sub>SiO. It is occupied and anti-bonding.