ChemWiki - User contributions [en]

Rep:Mod:WSL1819

2018-03-16T17:57:28Z

Wsl1917: /* Charge Analysis of Optimised H2 */

== Optimisation of NH3 ==

=== General Information of Optimised NH3 ===

From the 'Summary' table (Figure 1.1), the following general information about the optimisation calculation is obtained: the molecule optimised is ammonia, NH3, the calculation method is RB3LYP; the basis set is 6-31G(d,p); the final energy E(RB3LYP) is -56.44397188 a.u.; the RMS gradient is 0.05399560 a.u.; and the point group of NH3 is C3v.

[[File:Nh3_summary.jpg|400px|thumb|center|Figure 1.1: Summary Table of optimised NH3]]

=== Geometric Information of Optimised NH3 ===

Optimised bond length: 1.01798 Å ≈ 1.018 Å

Optimised bond angle: 105.741 o ≈ 105.7 o

=== Verification of Successful Optimisation of NH3 ===

The 'Item' table (Figure 1.2) shows that the final set of forces and displacements are converged and that the forces are approximately zero; since force is the gradient of a potential energy vs distance graph, this indicates that the structure obtained is at equilibrium, demonstrating successful optimisation of NH3.

<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>

Figure 1.2: Item Table of optimised NH3

Moreover, successful optimisation of NH3 is indicated by the last structure having the most negative energy and the smallest gradient (Figure 1.3).

[[File:Nh3 optimisation.jpg|400px|thumb|center|Figure 1.3: Optimisation plots of NH3]]

=== Dynamic Image of Optimised NH3 ===

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ZOEYWAISUMLUNG_NH3_OPTF_POP.LOG</uploadedFileContents>
<script>frame 1.7</script>
</jmolApplet></jmol>
Figure 1.4: A 3D jmol file of optimised NH3

The optimisation file is linked to [[Media:ZOEYWAISUMLUNG_NH3_OPTF_POP.LOG| here]]

=== Vibrational Analysis of Optimised NH3 ===

From Figure 1.5 in vibrational analysis, there are 6 modes as expected, modes 2 and 3 and modes 5 and 6 are degenerate as they have the same frequency of 1693.95 cm-1 and 3589.82 cm-1 respectively; modes 1, 2 and 3 are "bending" vibrations and modes 4, 5 and 6 are "bond stretch" vibrations; mode 4 is highly symmetric ; mode 1 is the "umbrella" mode and 2 bands in the experimental spectrum (Figure 1.6) of gaseous ammonia as expected.

2 bands in the experimental spectrum are expected firstly because modes 4, 5 and 6 have very small intensities due to small rate of change of dipole moment and since its an experimental spectrum, the noise is great enough to cover such small intensities and secondly because modes 2 and 3, though with significant intensities, are degenerate.

[[File:Nh3 vibrations 1.jpg ‎|400px|thumb|centre|Figure 1.5: Vibrational Table of optimised NH3]]

[[File:Nh3_spectrum.jpg ‎|400px|thumb|centre|Figure 1.6: Spectrum of optimised NH3]]

=== Charge Analysis of Optimised NH3 ===

Charge analysis (Figure 1.7) shows the charge on the nitrogen atom is -1.125 whilst that of the hydrogen atoms is +0.375. This result where nitrogen has a negative charge with a larger magnitude and hydrogen has a positive charge with a smaller magnitude is expected, since nitrogen is more electronegative than hydrogen, nitrogen should withdraw more electron density from each of the three N-H bonds.

[[File:Nh3_charge.jpg ‎|400px|thumb|centre|Figure 1.7: Charge Analysis of optimised NH3]]

== Optimisation of N2 ==

=== General Information of Optimised N2 ===

From the 'Summary' table (Figure 2.1), the following general information about the optimisation calculation is obtained: the molecule optimised is nitrogen, N2, the calculation method is RB3LYP; the basis set is 6-31G(d,p); the final energy E(RB3LYP) is -109.52412868 a.u.; the RMS gradient is 0.00000011 a.u.; and the point group of N2 is D∞h.

[[File:N2 summary 2.jpg|400px|thumb|center|Figure 2.1: Summary Table of optimised N2]]

=== Geometric Information of Optimised N2 ===

Optimised bond length: 1.10550 Å ≈ 1.106 Å

=== Verification of Successful Optimisation of N2 ===

The 'Item' table (Figure 2.2) shows that the final set of forces and displacements are converged and that the forces are zero; since force is the gradient of a potential energy vs distance graph, this indicates that the structure obtained is at equilibrium, demonstrating successful optimisation of N2.

<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 0.000000 0.001200 YES
</pre>

Figure 2.2: Item Table of optimised N2

Moreover, successful optimisation of N2 is indicated by the last structure having the most negative energy and the smallest gradient (Figure 2.3).

[[File:N2 optimisation.jpg|400px|thumb|center|Figure 2.3: Optimisation plots of N2]]

=== Dynamic Image of Optimised N2 ===

<jmol><jmolApplet>
<title>Figure 2.4: Optimised nitrogen</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ZOEYWAISUMLUNG_N2_OPTF_POP.LOG</uploadedFileContents>
<script>frame 1.4</script>
</jmolApplet></jmol>

The optimisation file is linked to [[Media:ZOEYWAISUMLUNG_N2_OPTF_POP.LOG| here]]

=== Vibrational Analysis of Optimised N2 ===

From Figure 2.5 in vibrational analysis, there are 0 modes as expected, and 0 bands in the experimental spectrum (Figure 2.6) of gaseous nitrogen as expected.

No bands are expected to be seen in the experimental spectrum because nitrogen is a linear molecule there is no dipole moment hence no change in dipole moment in a linear molecule.

[[File:N2 vibrations.jpg ‎|400px|thumb|centre|Figure 2.5: Vibrational Table of optimised N2]]

[[File:N2 spectrum.jpg ‎|400px|thumb|centre|Figure 2.6: Spectrum of optimised N2]]

=== Charge Analysis of Optimised N2 ===

Charge analysis (Figure 2.7) shows the charge on both nitrogen atoms is 0.000. This result is expected because both atoms of the lienar bond are the same so there are no expected differences in electronegativity therefore electron density is shared equally between the nitrogen atoms. Note that the atoms are colored by charge, a charge of 0.000 is represented by the color black and the numbers are written in black therefore they cannot be seen here.

[[File:N2 charge.jpg ‎|400px|thumb|centre|Figure 2.7: Charge Analysis of optimised N2]]

== Optimisation of H2 ==

=== General Information of Optimised H2 ===

From the 'Summary' table (Figure 3.1), the following general information about the optimisation calculation is obtained: the molecule optimised is hydrogen, H2, the calculation method is RB3LYP; the basis set is 6-31G(d,p); the final energy E(RB3LYP) is -1.17853936 a.u.; the RMS gradient is 0.00002276 a.u.; and the point group of H2 is D∞h.

[[File:H2 summary.jpg|400px|thumb|center|Figure 3.1: Summary Table of optimised H2]]

=== Geometric Information of Optimised H2 ===

Optimised bond length: 0.74274 Å ≈ 0.7427 Å

=== Verification of Successful Optimisation of H2 ===

The 'Item' table (Figure 3.2) shows that the final set of forces and displacements are converged and that the forces are zero; since force is the gradient of a potential energy vs distance graph, this indicates that the structure obtained is at equilibrium, demonstrating successful optimisation of H2.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000039 0.000300 YES
Maximum Displacement 0.000052 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
</pre>

Figure 3.2: Item Table of optimised H2

Moreover, successful optimisation of H2 is indicated by the last structure having the most negative energy and the smallest gradient (Figure 3.3).

[[File:H2 optimisation.jpg|400px|thumb|center|Figure 3.3: Optimisation plots of H2]]

=== Dynamic Image of Optimised H2 ===

<jmol><jmolApplet>
<title>Figure 3.4: Optimised hydrogen</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ZOEYWAISUMLUNG_H2_OPTF_POP.LOG</uploadedFileContents>
<script>frame 1.3</script>
</jmolApplet></jmol>

The optimisation file is linked to [[Media:ZOEYWAISUMLUNG_H2_OPTF_POP.LOG| here]]

=== Vibrational Analysis of Optimised H2 ===

From Figure 3.5 in vibrational analysis, there are 0 modes as expected, and 0 bands in the experimental spectrum (Figure 3.6) of gaseous hydrogen as expected.

No bands are expected to be seen in the experimental spectrum because hydrogen is a linear molecule there is no dipole moment hence no change in dipole moment in a linear molecule.

[[File:H2 vibrations.jpg ‎|400px|thumb|centre|Figure 3.5: Vibrational Table of optimised H2]]

[[File:H2 spectrum.jpg ‎|400px|thumb|centre|Figure 3.6: Spectrum of optimised H2]]

=== Charge Analysis of Optimised H2 ===

Charge analysis (Figure 3.7) shows the charge on both hydrogen atoms is 0.000. This result is expected because both atoms of the linear bond are the same so there are no expected differences in electronegativity therefore electron density is shared equally between the hydrogen atoms. If a higher basis set is used, a single bond would likely to be displayed.

[[File:H2 charge.jpg ‎|400px|thumb|centre|Figure 2.7: Charge Analysis of optimised H2]]

== Energy Analysis ==

E(NH3) = -56.44397188 a.u.
2*E(NH3)= -112.88794376 a.u.
E(N2)= -109.52412868 a.u.
E(H2)= -1.17853936 a.u.
3*E(H2)= -3.53561808 a.u.
ΔE=2*E(NH3)-[E(N2)+3*E(H2)]= -112.88794376 a.u. - (-109.52412868 a.u. + -3.53561808 a.u.) = -112.88794376 a.u. -(-113.05974676) a.u. = + 0.171803 a.u. = +451.0687765 kJ/mol = +451.07 kJ/mol

However, the forward reaction is supposed to be exothermic, further optimisation would be needed.

== Optimisation of S2 ==

=== General Information of Optimised S2 ===

From the 'Summary' table (Figure 4.1), the following general information about the optimisation calculation is obtained: the molecule optimised is sulphur, S2, the calculation method is RB3LYP; the basis set is 6-31G(d,p); the final energy E(RB3LYP) is -796.32599779 a.u.; the RMS gradient is 0.00000905 a.u.; and the point group of S2 is D∞h.

[[File:S2 summary.jpg|400px|thumb|center|Figure 4.1: Summary Table of optimised S2]]

=== Geometric Information of Optimised S2 ===

Optimised bond length: 1.92947 Å ≈ 1.929 Å

=== Verification of Successful Optimisation of S2 ===

The 'Item' table (Figure 4.2) shows that the final set of forces and displacements are converged and that the forces are approximately zero; since force is the gradient of a potential energy vs distance graph, this indicates that the structure obtained is at equilibrium, demonstrating successful optimisation of S2.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.000027 0.001800 YES
RMS Displacement 0.000038 0.001200 YES
</pre>

Figure 4.2: Item Table of optimised S2

Moreover, successful optimisation of S2 is indicated by the last structure having the most negative energy and the smallest gradient (Figure 4.3).

[[File:S2 optimisation.jpg|400px|thumb|center|Figure 4.3: Optimisation plots of S2]]

=== Dynamic Image of Optimised S2 ===

<jmol><jmolApplet>
<title>Figure 4.4: Optimised sulphur</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ZOEYWAISUMLUNG_S2_OPTF_POP.LOG</uploadedFileContents>
<script>frame 1.4</script>
</jmolApplet></jmol>

The optimisation file is linked to [[Media:ZOEYWAISUMLUNG_S2_OPTF_POP.LOG| here]]

=== Vibrational Analysis of Optimised S2 ===

From Figure 4.5 in vibrational analysis, there are 0 modes as expected, and 0 bands in the experimental spectrum (Figure 4.6) of gaseous sulphur as expected.

No bands are expected to be seen in the experimental spectrum because sulphur is a linear molecule there is no dipole moment hence no change in dipole moment in a linear molecule.

[[File:S2 vibrations.jpg ‎|400px|thumb|centre|Figure 4.5: Vibrational Table of optimised S2]]

[[File:S2 spectrum.jpg ‎|400px|thumb|centre|Figure 4.6: Spectrum of optimised S2]]

=== Charge Analysis of Optimised S2 ===

Charge analysis (Figure 4.7) shows the charge on both sulphur atoms is 0.000. This result is expected because both atoms of the linear bond are the same so there are no expected differences in electronegativity therefore electron density is shared equally between the sulphur atoms. A single bond instead of a double bond is displayed however this would most likely not be the case if a higher basis set is used for optimisation.

[[File:S2 charge.jpg ‎|400px|thumb|centre|Figure 2.7: Charge Analysis of optimised H2]]

=== Molecular Orbitals of Optimised S2 ===

{| class="wikitable" border="1"
|+ caption
! heading !! heading
|-
| [[File:1s sigma orbital 1.JPG ‎|300px|thumb|centre]] || The two 1s AOs form a non-bonding σ MO. The energy of the MO formed is -88.93663 a.u. The MOs cannot be visualised and there is minimal if no interaction between the orbitals because the AOs are so concentrated within each of the individual respective nuclei and they are so small.
|-
| [[File:1s sigma orbital 2.JPG ‎|300px|thumb|centre]] || The two 1s AOs form a non-bonding σ* MO. The energy of the MO formed is -88.93661 a.u. The MOs cannot be visualised and there is minimal if no interaction between the orbitals because the AOs are so concentrated within each of the individual respective nuclei and they are so small.
|-
| [[File:2s sigma orbital 2.JPG ‎|300px|thumb|centre]]|| The two 2s AOs form a non-bonding σ MO. The energy of the MO formed is -7.99779 a.u.
|-
| [[File:2s sigma orbital 1.JPG ‎|300px|thumb|centre]] || The two 2s AOs form a non-bonding σ* MO. The energy of the MO formed is -7.99769 a.u.
|-
| [[File:2p pi orbital 1.JPG ‎|300px|thumb|centre]] [[File:2p pi orbital 2.JPG ‎|300px|thumb|centre]] || The two 2px and two 2py AOs form two non-bonding π MOs. These two orbitals are degenerate- the energies of the MOs are -5.96349 a.u. and -5.94946 a.u. respectively.
|-
| [[File:2p pi orbital 3.JPG ‎|300px|thumb|centre]] [[File:2p pi orbital 4.JPG ‎|300px|thumb|centre]] || The two 2px and two 2py AOs form two non-bonding π* MOs. These two orbitals are degenerate- the energies of the MOs are -5.96135 a.u.
|-
| [[File:2p pi orbital 5.JPG ‎|300px|thumb|centre]] || The two 2pz AOs form one non-bonding σ MO. The energy of the MO is -5.96135 a.u.
|-
| [[File:2p pi orbital 6.JPG ‎|300px|thumb|centre]] || The two 2pz AOs form one non-bonding σ * MOs. The energy of the MO is -5.96078 a.u.
|-
| [[File:3s sigma orbital 1.JPG ‎|300px|thumb|centre]] || The two 3s AOs overlap constructively head=on to form a bonding σ MO. The energy of the MO formed is -0.83212 a.u.
|-
| [[File:3s sigma orbital 2.JPG ‎|300px|thumb|centre]] || The two 3s AOs overlap destructively to form an anti-bonding σ* MO. The energy of the MO formed is -0.61535 a.u.
|-
| [[File:3p sigma orbital 1.JPG ‎|300px|thumb|centre]] || The two 3pz AOs overlap constructively head-on to form a bonding σ MO. The energy of this bonding MO is -0.39516 a.u. The energy of this MO is lower in energy than the bonding MOs formed from the overlap of the two 2px and the two 2py orbitals because the head-on interaction is much stronger than the lateral interactions.
|-
| [[File:3p pi orbital 1.JPG ‎|300px|thumb|centre]] [[File:3p pi orbital 2.JPG ‎|300px|thumb|centre]] || The two 3px and the two 3py AOs overlap constructively laterally to form two bonding π MOs of relatively the same energy of -0.36283 a.u. and -0.34958 a.u. respectively.
|-
| [[File:3p pi orbital 3.JPG ‎|300px|thumb|centre]] [[File:3p pi orbital 4.JPG ‎|300px|thumb|centre]] || The two 3px and the two 3py AOs overlap destructively laterally to form two anti-bonding π* MOs of relatively the same energy of -0.21843 a.u. and -0.18463 a.u. respectively. It is important to note that these two anti-bonding π* MOs formed are the HOMO and LUMO respectively of sulphur, meaning that all reactions would react with the sulphur-sulphur pi-bond and not the sigma bond of the double bond.
|-
| [[File:3p sigma orbital 2.JPG ‎|300px|thumb|centre]] || The two 3pz AOs overlap destructively head-on to form an anti-bonding σ* MO. The energy of this bonding MO is -0.01307 a.u.
|}

Rep:Mod:WSL1819

2018-03-16T17:47:19Z

Wsl1917: /* Molecular Orbitals of Optimised S2 */

== Optimisation of NH3 ==

=== General Information of Optimised NH3 ===

From the 'Summary' table (Figure 1.1), the following general information about the optimisation calculation is obtained: the molecule optimised is ammonia, NH3, the calculation method is RB3LYP; the basis set is 6-31G(d,p); the final energy E(RB3LYP) is -56.44397188 a.u.; the RMS gradient is 0.05399560 a.u.; and the point group of NH3 is C3v.

[[File:Nh3_summary.jpg|400px|thumb|center|Figure 1.1: Summary Table of optimised NH3]]

=== Geometric Information of Optimised NH3 ===

Optimised bond length: 1.01798 Å ≈ 1.018 Å

Optimised bond angle: 105.741 o ≈ 105.7 o

=== Verification of Successful Optimisation of NH3 ===

The 'Item' table (Figure 1.2) shows that the final set of forces and displacements are converged and that the forces are approximately zero; since force is the gradient of a potential energy vs distance graph, this indicates that the structure obtained is at equilibrium, demonstrating successful optimisation of NH3.

<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>

Figure 1.2: Item Table of optimised NH3

Moreover, successful optimisation of NH3 is indicated by the last structure having the most negative energy and the smallest gradient (Figure 1.3).

[[File:Nh3 optimisation.jpg|400px|thumb|center|Figure 1.3: Optimisation plots of NH3]]

=== Dynamic Image of Optimised NH3 ===

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ZOEYWAISUMLUNG_NH3_OPTF_POP.LOG</uploadedFileContents>
<script>frame 1.7</script>
</jmolApplet></jmol>
Figure 1.4: A 3D jmol file of optimised NH3

The optimisation file is linked to [[Media:ZOEYWAISUMLUNG_NH3_OPTF_POP.LOG| here]]

=== Vibrational Analysis of Optimised NH3 ===

From Figure 1.5 in vibrational analysis, there are 6 modes as expected, modes 2 and 3 and modes 5 and 6 are degenerate as they have the same frequency of 1693.95 cm-1 and 3589.82 cm-1 respectively; modes 1, 2 and 3 are "bending" vibrations and modes 4, 5 and 6 are "bond stretch" vibrations; mode 4 is highly symmetric ; mode 1 is the "umbrella" mode and 2 bands in the experimental spectrum (Figure 1.6) of gaseous ammonia as expected.

2 bands in the experimental spectrum are expected firstly because modes 4, 5 and 6 have very small intensities due to small rate of change of dipole moment and since its an experimental spectrum, the noise is great enough to cover such small intensities and secondly because modes 2 and 3, though with significant intensities, are degenerate.

[[File:Nh3 vibrations 1.jpg ‎|400px|thumb|centre|Figure 1.5: Vibrational Table of optimised NH3]]

[[File:Nh3_spectrum.jpg ‎|400px|thumb|centre|Figure 1.6: Spectrum of optimised NH3]]

=== Charge Analysis of Optimised NH3 ===

Charge analysis (Figure 1.7) shows the charge on the nitrogen atom is -1.125 whilst that of the hydrogen atoms is +0.375. This result where nitrogen has a negative charge with a larger magnitude and hydrogen has a positive charge with a smaller magnitude is expected, since nitrogen is more electronegative than hydrogen, nitrogen should withdraw more electron density from each of the three N-H bonds.

[[File:Nh3_charge.jpg ‎|400px|thumb|centre|Figure 1.7: Charge Analysis of optimised NH3]]

== Optimisation of N2 ==

=== General Information of Optimised N2 ===

From the 'Summary' table (Figure 2.1), the following general information about the optimisation calculation is obtained: the molecule optimised is nitrogen, N2, the calculation method is RB3LYP; the basis set is 6-31G(d,p); the final energy E(RB3LYP) is -109.52412868 a.u.; the RMS gradient is 0.00000011 a.u.; and the point group of N2 is D∞h.

[[File:N2 summary 2.jpg|400px|thumb|center|Figure 2.1: Summary Table of optimised N2]]

=== Geometric Information of Optimised N2 ===

Optimised bond length: 1.10550 Å ≈ 1.106 Å

=== Verification of Successful Optimisation of N2 ===

The 'Item' table (Figure 2.2) shows that the final set of forces and displacements are converged and that the forces are zero; since force is the gradient of a potential energy vs distance graph, this indicates that the structure obtained is at equilibrium, demonstrating successful optimisation of N2.

<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 0.000000 0.001200 YES
</pre>

Figure 2.2: Item Table of optimised N2

Moreover, successful optimisation of N2 is indicated by the last structure having the most negative energy and the smallest gradient (Figure 2.3).

[[File:N2 optimisation.jpg|400px|thumb|center|Figure 2.3: Optimisation plots of N2]]

=== Dynamic Image of Optimised N2 ===

<jmol><jmolApplet>
<title>Figure 2.4: Optimised nitrogen</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ZOEYWAISUMLUNG_N2_OPTF_POP.LOG</uploadedFileContents>
<script>frame 1.4</script>
</jmolApplet></jmol>

The optimisation file is linked to [[Media:ZOEYWAISUMLUNG_N2_OPTF_POP.LOG| here]]

=== Vibrational Analysis of Optimised N2 ===

From Figure 2.5 in vibrational analysis, there are 0 modes as expected, and 0 bands in the experimental spectrum (Figure 2.6) of gaseous nitrogen as expected.

No bands are expected to be seen in the experimental spectrum because nitrogen is a linear molecule there is no dipole moment hence no change in dipole moment in a linear molecule.

[[File:N2 vibrations.jpg ‎|400px|thumb|centre|Figure 2.5: Vibrational Table of optimised N2]]

[[File:N2 spectrum.jpg ‎|400px|thumb|centre|Figure 2.6: Spectrum of optimised N2]]

=== Charge Analysis of Optimised N2 ===

Charge analysis (Figure 2.7) shows the charge on both nitrogen atoms is 0.000. This result is expected because both atoms of the lienar bond are the same so there are no expected differences in electronegativity therefore electron density is shared equally between the nitrogen atoms. Note that the atoms are colored by charge, a charge of 0.000 is represented by the color black and the numbers are written in black therefore they cannot be seen here.

[[File:N2 charge.jpg ‎|400px|thumb|centre|Figure 2.7: Charge Analysis of optimised N2]]

== Optimisation of H2 ==

=== General Information of Optimised H2 ===

From the 'Summary' table (Figure 3.1), the following general information about the optimisation calculation is obtained: the molecule optimised is hydrogen, H2, the calculation method is RB3LYP; the basis set is 6-31G(d,p); the final energy E(RB3LYP) is -1.17853936 a.u.; the RMS gradient is 0.00002276 a.u.; and the point group of H2 is D∞h.

[[File:H2 summary.jpg|400px|thumb|center|Figure 3.1: Summary Table of optimised H2]]

=== Geometric Information of Optimised H2 ===

Optimised bond length: 0.74274 Å ≈ 0.7427 Å

=== Verification of Successful Optimisation of H2 ===

The 'Item' table (Figure 3.2) shows that the final set of forces and displacements are converged and that the forces are zero; since force is the gradient of a potential energy vs distance graph, this indicates that the structure obtained is at equilibrium, demonstrating successful optimisation of H2.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000039 0.000300 YES
Maximum Displacement 0.000052 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
</pre>

Figure 3.2: Item Table of optimised H2

Moreover, successful optimisation of H2 is indicated by the last structure having the most negative energy and the smallest gradient (Figure 3.3).

[[File:H2 optimisation.jpg|400px|thumb|center|Figure 3.3: Optimisation plots of H2]]

=== Dynamic Image of Optimised H2 ===

<jmol><jmolApplet>
<title>Figure 3.4: Optimised hydrogen</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ZOEYWAISUMLUNG_H2_OPTF_POP.LOG</uploadedFileContents>
<script>frame 1.3</script>
</jmolApplet></jmol>

The optimisation file is linked to [[Media:ZOEYWAISUMLUNG_H2_OPTF_POP.LOG| here]]

=== Vibrational Analysis of Optimised H2 ===

From Figure 3.5 in vibrational analysis, there are 0 modes as expected, and 0 bands in the experimental spectrum (Figure 3.6) of gaseous hydrogen as expected.

No bands are expected to be seen in the experimental spectrum because hydrogen is a linear molecule there is no dipole moment hence no change in dipole moment in a linear molecule.

[[File:H2 vibrations.jpg ‎|400px|thumb|centre|Figure 3.5: Vibrational Table of optimised H2]]

[[File:H2 spectrum.jpg ‎|400px|thumb|centre|Figure 3.6: Spectrum of optimised H2]]

=== Charge Analysis of Optimised H2 ===

Charge analysis (Figure 3.7) shows the charge on both hydrogen atoms is 0.000. This result is expected because both atoms of the linear bond are the same so there are no expected differences in electronegativity therefore electron density is shared equally between the hydrogen atoms. If a higher basis set is used, a single bond would likely to be displayed.

[[File:H2 charge.jpg ‎|400px|thumb|centre|Figure 2.7: Charge Analysis of optimised H2]]

== Optimisation of S2 ==

=== General Information of Optimised S2 ===

From the 'Summary' table (Figure 4.1), the following general information about the optimisation calculation is obtained: the molecule optimised is sulphur, S2, the calculation method is RB3LYP; the basis set is 6-31G(d,p); the final energy E(RB3LYP) is -796.32599779 a.u.; the RMS gradient is 0.00000905 a.u.; and the point group of S2 is D∞h.

[[File:S2 summary.jpg|400px|thumb|center|Figure 4.1: Summary Table of optimised S2]]

=== Geometric Information of Optimised S2 ===

Optimised bond length: 1.92947 Å ≈ 1.929 Å

=== Verification of Successful Optimisation of S2 ===

The 'Item' table (Figure 4.2) shows that the final set of forces and displacements are converged and that the forces are approximately zero; since force is the gradient of a potential energy vs distance graph, this indicates that the structure obtained is at equilibrium, demonstrating successful optimisation of S2.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.000027 0.001800 YES
RMS Displacement 0.000038 0.001200 YES
</pre>

Figure 4.2: Item Table of optimised S2

Moreover, successful optimisation of S2 is indicated by the last structure having the most negative energy and the smallest gradient (Figure 4.3).

[[File:S2 optimisation.jpg|400px|thumb|center|Figure 4.3: Optimisation plots of S2]]

=== Dynamic Image of Optimised S2 ===

<jmol><jmolApplet>
<title>Figure 4.4: Optimised sulphur</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ZOEYWAISUMLUNG_S2_OPTF_POP.LOG</uploadedFileContents>
<script>frame 1.4</script>
</jmolApplet></jmol>

The optimisation file is linked to [[Media:ZOEYWAISUMLUNG_S2_OPTF_POP.LOG| here]]

=== Vibrational Analysis of Optimised S2 ===

From Figure 4.5 in vibrational analysis, there are 0 modes as expected, and 0 bands in the experimental spectrum (Figure 4.6) of gaseous sulphur as expected.

No bands are expected to be seen in the experimental spectrum because sulphur is a linear molecule there is no dipole moment hence no change in dipole moment in a linear molecule.

[[File:S2 vibrations.jpg ‎|400px|thumb|centre|Figure 4.5: Vibrational Table of optimised S2]]

[[File:S2 spectrum.jpg ‎|400px|thumb|centre|Figure 4.6: Spectrum of optimised S2]]

=== Charge Analysis of Optimised S2 ===

Charge analysis (Figure 4.7) shows the charge on both sulphur atoms is 0.000. This result is expected because both atoms of the linear bond are the same so there are no expected differences in electronegativity therefore electron density is shared equally between the sulphur atoms. A single bond instead of a double bond is displayed however this would most likely not be the case if a higher basis set is used for optimisation.

[[File:S2 charge.jpg ‎|400px|thumb|centre|Figure 2.7: Charge Analysis of optimised H2]]

=== Molecular Orbitals of Optimised S2 ===

{| class="wikitable" border="1"
|+ caption
! heading !! heading
|-
| [[File:1s sigma orbital 1.JPG ‎|300px|thumb|centre]] || The two 1s AOs form a non-bonding σ MO. The energy of the MO formed is -88.93663 a.u. The MOs cannot be visualised and there is minimal if no interaction between the orbitals because the AOs are so concentrated within each of the individual respective nuclei and they are so small.
|-
| [[File:1s sigma orbital 2.JPG ‎|300px|thumb|centre]] || The two 1s AOs form a non-bonding σ* MO. The energy of the MO formed is -88.93661 a.u. The MOs cannot be visualised and there is minimal if no interaction between the orbitals because the AOs are so concentrated within each of the individual respective nuclei and they are so small.
|-
| [[File:2s sigma orbital 2.JPG ‎|300px|thumb|centre]]|| The two 2s AOs form a non-bonding σ MO. The energy of the MO formed is -7.99779 a.u.
|-
| [[File:2s sigma orbital 1.JPG ‎|300px|thumb|centre]] || The two 2s AOs form a non-bonding σ* MO. The energy of the MO formed is -7.99769 a.u.
|-
| [[File:2p pi orbital 1.JPG ‎|300px|thumb|centre]] [[File:2p pi orbital 2.JPG ‎|300px|thumb|centre]] || The two 2px and two 2py AOs form two non-bonding π MOs. These two orbitals are degenerate- the energies of the MOs are -5.96349 a.u. and -5.94946 a.u. respectively.
|-
| [[File:2p pi orbital 3.JPG ‎|300px|thumb|centre]] [[File:2p pi orbital 4.JPG ‎|300px|thumb|centre]] || The two 2px and two 2py AOs form two non-bonding π* MOs. These two orbitals are degenerate- the energies of the MOs are -5.96135 a.u.
|-
| [[File:2p pi orbital 5.JPG ‎|300px|thumb|centre]] || The two 2pz AOs form one non-bonding σ MO. The energy of the MO is -5.96135 a.u.
|-
| [[File:2p pi orbital 6.JPG ‎|300px|thumb|centre]] || The two 2pz AOs form one non-bonding σ * MOs. The energy of the MO is -5.96078 a.u.
|-
| [[File:3s sigma orbital 1.JPG ‎|300px|thumb|centre]] || The two 3s AOs overlap constructively head=on to form a bonding σ MO. The energy of the MO formed is -0.83212 a.u.
|-
| [[File:3s sigma orbital 2.JPG ‎|300px|thumb|centre]] || The two 3s AOs overlap destructively to form an anti-bonding σ* MO. The energy of the MO formed is -0.61535 a.u.
|-
| [[File:3p sigma orbital 1.JPG ‎|300px|thumb|centre]] || The two 3pz AOs overlap constructively head-on to form a bonding σ MO. The energy of this bonding MO is -0.39516 a.u. The energy of this MO is lower in energy than the bonding MOs formed from the overlap of the two 2px and the two 2py orbitals because the head-on interaction is much stronger than the lateral interactions.
|-
| [[File:3p pi orbital 1.JPG ‎|300px|thumb|centre]] [[File:3p pi orbital 2.JPG ‎|300px|thumb|centre]] || The two 3px and the two 3py AOs overlap constructively laterally to form two bonding π MOs of relatively the same energy of -0.36283 a.u. and -0.34958 a.u. respectively.
|-
| [[File:3p pi orbital 3.JPG ‎|300px|thumb|centre]] [[File:3p pi orbital 4.JPG ‎|300px|thumb|centre]] || The two 3px and the two 3py AOs overlap destructively laterally to form two anti-bonding π* MOs of relatively the same energy of -0.21843 a.u. and -0.18463 a.u. respectively. It is important to note that these two anti-bonding π* MOs formed are the HOMO and LUMO respectively of sulphur, meaning that all reactions would react with the sulphur-sulphur pi-bond and not the sigma bond of the double bond.
|-
| [[File:3p sigma orbital 2.JPG ‎|300px|thumb|centre]] || The two 3pz AOs overlap destructively head-on to form an anti-bonding σ* MO. The energy of this bonding MO is -0.01307 a.u.
|}

File:3p sigma orbital 2.JPG

2018-03-16T17:43:59Z

Wsl1917:

File:3p pi orbital 4.JPG

2018-03-16T17:43:37Z

Wsl1917:

File:3p pi orbital 3.JPG

2018-03-16T17:43:16Z

Wsl1917:

Rep:Mod:WSL1819

2018-03-16T17:42:57Z

Wsl1917: /* Molecular Orbitals of Optimised S2 */

== Optimisation of NH3 ==

=== General Information of Optimised NH3 ===

From the 'Summary' table (Figure 1.1), the following general information about the optimisation calculation is obtained: the molecule optimised is ammonia, NH3, the calculation method is RB3LYP; the basis set is 6-31G(d,p); the final energy E(RB3LYP) is -56.44397188 a.u.; the RMS gradient is 0.05399560 a.u.; and the point group of NH3 is C3v.

[[File:Nh3_summary.jpg|400px|thumb|center|Figure 1.1: Summary Table of optimised NH3]]

=== Geometric Information of Optimised NH3 ===

Optimised bond length: 1.01798 Å ≈ 1.018 Å

Optimised bond angle: 105.741 o ≈ 105.7 o

=== Verification of Successful Optimisation of NH3 ===

The 'Item' table (Figure 1.2) shows that the final set of forces and displacements are converged and that the forces are approximately zero; since force is the gradient of a potential energy vs distance graph, this indicates that the structure obtained is at equilibrium, demonstrating successful optimisation of NH3.

<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>

Figure 1.2: Item Table of optimised NH3

Moreover, successful optimisation of NH3 is indicated by the last structure having the most negative energy and the smallest gradient (Figure 1.3).

[[File:Nh3 optimisation.jpg|400px|thumb|center|Figure 1.3: Optimisation plots of NH3]]

=== Dynamic Image of Optimised NH3 ===

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ZOEYWAISUMLUNG_NH3_OPTF_POP.LOG</uploadedFileContents>
<script>frame 1.7</script>
</jmolApplet></jmol>
Figure 1.4: A 3D jmol file of optimised NH3

The optimisation file is linked to [[Media:ZOEYWAISUMLUNG_NH3_OPTF_POP.LOG| here]]

=== Vibrational Analysis of Optimised NH3 ===

From Figure 1.5 in vibrational analysis, there are 6 modes as expected, modes 2 and 3 and modes 5 and 6 are degenerate as they have the same frequency of 1693.95 cm-1 and 3589.82 cm-1 respectively; modes 1, 2 and 3 are "bending" vibrations and modes 4, 5 and 6 are "bond stretch" vibrations; mode 4 is highly symmetric ; mode 1 is the "umbrella" mode and 2 bands in the experimental spectrum (Figure 1.6) of gaseous ammonia as expected.

2 bands in the experimental spectrum are expected firstly because modes 4, 5 and 6 have very small intensities due to small rate of change of dipole moment and since its an experimental spectrum, the noise is great enough to cover such small intensities and secondly because modes 2 and 3, though with significant intensities, are degenerate.

[[File:Nh3 vibrations 1.jpg ‎|400px|thumb|centre|Figure 1.5: Vibrational Table of optimised NH3]]

[[File:Nh3_spectrum.jpg ‎|400px|thumb|centre|Figure 1.6: Spectrum of optimised NH3]]

=== Charge Analysis of Optimised NH3 ===

Charge analysis (Figure 1.7) shows the charge on the nitrogen atom is -1.125 whilst that of the hydrogen atoms is +0.375. This result where nitrogen has a negative charge with a larger magnitude and hydrogen has a positive charge with a smaller magnitude is expected, since nitrogen is more electronegative than hydrogen, nitrogen should withdraw more electron density from each of the three N-H bonds.

[[File:Nh3_charge.jpg ‎|400px|thumb|centre|Figure 1.7: Charge Analysis of optimised NH3]]

== Optimisation of N2 ==

=== General Information of Optimised N2 ===

From the 'Summary' table (Figure 2.1), the following general information about the optimisation calculation is obtained: the molecule optimised is nitrogen, N2, the calculation method is RB3LYP; the basis set is 6-31G(d,p); the final energy E(RB3LYP) is -109.52412868 a.u.; the RMS gradient is 0.00000011 a.u.; and the point group of N2 is D∞h.

[[File:N2 summary 2.jpg|400px|thumb|center|Figure 2.1: Summary Table of optimised N2]]

=== Geometric Information of Optimised N2 ===

Optimised bond length: 1.10550 Å ≈ 1.106 Å

=== Verification of Successful Optimisation of N2 ===

The 'Item' table (Figure 2.2) shows that the final set of forces and displacements are converged and that the forces are zero; since force is the gradient of a potential energy vs distance graph, this indicates that the structure obtained is at equilibrium, demonstrating successful optimisation of N2.

<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 0.000000 0.001200 YES
</pre>

Figure 2.2: Item Table of optimised N2

Moreover, successful optimisation of N2 is indicated by the last structure having the most negative energy and the smallest gradient (Figure 2.3).

[[File:N2 optimisation.jpg|400px|thumb|center|Figure 2.3: Optimisation plots of N2]]

=== Dynamic Image of Optimised N2 ===

<jmol><jmolApplet>
<title>Figure 2.4: Optimised nitrogen</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ZOEYWAISUMLUNG_N2_OPTF_POP.LOG</uploadedFileContents>
<script>frame 1.4</script>
</jmolApplet></jmol>

The optimisation file is linked to [[Media:ZOEYWAISUMLUNG_N2_OPTF_POP.LOG| here]]

=== Vibrational Analysis of Optimised N2 ===

From Figure 2.5 in vibrational analysis, there are 0 modes as expected, and 0 bands in the experimental spectrum (Figure 2.6) of gaseous nitrogen as expected.

No bands are expected to be seen in the experimental spectrum because nitrogen is a linear molecule there is no dipole moment hence no change in dipole moment in a linear molecule.

[[File:N2 vibrations.jpg ‎|400px|thumb|centre|Figure 2.5: Vibrational Table of optimised N2]]

[[File:N2 spectrum.jpg ‎|400px|thumb|centre|Figure 2.6: Spectrum of optimised N2]]

=== Charge Analysis of Optimised N2 ===

Charge analysis (Figure 2.7) shows the charge on both nitrogen atoms is 0.000. This result is expected because both atoms of the lienar bond are the same so there are no expected differences in electronegativity therefore electron density is shared equally between the nitrogen atoms. Note that the atoms are colored by charge, a charge of 0.000 is represented by the color black and the numbers are written in black therefore they cannot be seen here.

[[File:N2 charge.jpg ‎|400px|thumb|centre|Figure 2.7: Charge Analysis of optimised N2]]

== Optimisation of H2 ==

=== General Information of Optimised H2 ===

From the 'Summary' table (Figure 3.1), the following general information about the optimisation calculation is obtained: the molecule optimised is hydrogen, H2, the calculation method is RB3LYP; the basis set is 6-31G(d,p); the final energy E(RB3LYP) is -1.17853936 a.u.; the RMS gradient is 0.00002276 a.u.; and the point group of H2 is D∞h.

[[File:H2 summary.jpg|400px|thumb|center|Figure 3.1: Summary Table of optimised H2]]

=== Geometric Information of Optimised H2 ===

Optimised bond length: 0.74274 Å ≈ 0.7427 Å

=== Verification of Successful Optimisation of H2 ===

The 'Item' table (Figure 3.2) shows that the final set of forces and displacements are converged and that the forces are zero; since force is the gradient of a potential energy vs distance graph, this indicates that the structure obtained is at equilibrium, demonstrating successful optimisation of H2.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000039 0.000300 YES
Maximum Displacement 0.000052 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
</pre>

Figure 3.2: Item Table of optimised H2

Moreover, successful optimisation of H2 is indicated by the last structure having the most negative energy and the smallest gradient (Figure 3.3).

[[File:H2 optimisation.jpg|400px|thumb|center|Figure 3.3: Optimisation plots of H2]]

=== Dynamic Image of Optimised H2 ===

<jmol><jmolApplet>
<title>Figure 3.4: Optimised hydrogen</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ZOEYWAISUMLUNG_H2_OPTF_POP.LOG</uploadedFileContents>
<script>frame 1.3</script>
</jmolApplet></jmol>

The optimisation file is linked to [[Media:ZOEYWAISUMLUNG_H2_OPTF_POP.LOG| here]]

=== Vibrational Analysis of Optimised H2 ===

From Figure 3.5 in vibrational analysis, there are 0 modes as expected, and 0 bands in the experimental spectrum (Figure 3.6) of gaseous hydrogen as expected.

No bands are expected to be seen in the experimental spectrum because hydrogen is a linear molecule there is no dipole moment hence no change in dipole moment in a linear molecule.

[[File:H2 vibrations.jpg ‎|400px|thumb|centre|Figure 3.5: Vibrational Table of optimised H2]]

[[File:H2 spectrum.jpg ‎|400px|thumb|centre|Figure 3.6: Spectrum of optimised H2]]

=== Charge Analysis of Optimised H2 ===

Charge analysis (Figure 3.7) shows the charge on both hydrogen atoms is 0.000. This result is expected because both atoms of the linear bond are the same so there are no expected differences in electronegativity therefore electron density is shared equally between the hydrogen atoms. If a higher basis set is used, a single bond would likely to be displayed.

[[File:H2 charge.jpg ‎|400px|thumb|centre|Figure 2.7: Charge Analysis of optimised H2]]

== Optimisation of S2 ==

=== General Information of Optimised S2 ===

From the 'Summary' table (Figure 4.1), the following general information about the optimisation calculation is obtained: the molecule optimised is sulphur, S2, the calculation method is RB3LYP; the basis set is 6-31G(d,p); the final energy E(RB3LYP) is -796.32599779 a.u.; the RMS gradient is 0.00000905 a.u.; and the point group of S2 is D∞h.

[[File:S2 summary.jpg|400px|thumb|center|Figure 4.1: Summary Table of optimised S2]]

=== Geometric Information of Optimised S2 ===

Optimised bond length: 1.92947 Å ≈ 1.929 Å

=== Verification of Successful Optimisation of S2 ===

The 'Item' table (Figure 4.2) shows that the final set of forces and displacements are converged and that the forces are approximately zero; since force is the gradient of a potential energy vs distance graph, this indicates that the structure obtained is at equilibrium, demonstrating successful optimisation of S2.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.000027 0.001800 YES
RMS Displacement 0.000038 0.001200 YES
</pre>

Figure 4.2: Item Table of optimised S2

Moreover, successful optimisation of S2 is indicated by the last structure having the most negative energy and the smallest gradient (Figure 4.3).

[[File:S2 optimisation.jpg|400px|thumb|center|Figure 4.3: Optimisation plots of S2]]

=== Dynamic Image of Optimised S2 ===

<jmol><jmolApplet>
<title>Figure 4.4: Optimised sulphur</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ZOEYWAISUMLUNG_S2_OPTF_POP.LOG</uploadedFileContents>
<script>frame 1.4</script>
</jmolApplet></jmol>

The optimisation file is linked to [[Media:ZOEYWAISUMLUNG_S2_OPTF_POP.LOG| here]]

=== Vibrational Analysis of Optimised S2 ===

From Figure 4.5 in vibrational analysis, there are 0 modes as expected, and 0 bands in the experimental spectrum (Figure 4.6) of gaseous sulphur as expected.

No bands are expected to be seen in the experimental spectrum because sulphur is a linear molecule there is no dipole moment hence no change in dipole moment in a linear molecule.

[[File:S2 vibrations.jpg ‎|400px|thumb|centre|Figure 4.5: Vibrational Table of optimised S2]]

[[File:S2 spectrum.jpg ‎|400px|thumb|centre|Figure 4.6: Spectrum of optimised S2]]

=== Charge Analysis of Optimised S2 ===

Charge analysis (Figure 4.7) shows the charge on both sulphur atoms is 0.000. This result is expected because both atoms of the linear bond are the same so there are no expected differences in electronegativity therefore electron density is shared equally between the sulphur atoms. A single bond instead of a double bond is displayed however this would most likely not be the case if a higher basis set is used for optimisation.

[[File:S2 charge.jpg ‎|400px|thumb|centre|Figure 2.7: Charge Analysis of optimised H2]]

=== Molecular Orbitals of Optimised S2 ===

{| class="wikitable" border="1"
|+ caption
! heading !! heading
|-
| [[File:1s sigma orbital 1.JPG ‎|300px|thumb|centre]]
|| The two 1s AOs form a non-bonding σ MO. The energy of the MO formed is -88.93663 a.u.
|-
| [[File:1s sigma orbital 2.JPG ‎|300px|thumb|centre]] || The two 1s AOs form a non-bonding σ* MO. The energy of the MO formed is -88.93661 a.u.
|-
| [[File:2s sigma orbital 2.JPG ‎|300px|thumb|centre]]|| The two 2s AOs overlap constructively to form a non-bonding σ MO. The energy of the MO formed is -7.99779 a.u.
|-
| [[File:2s sigma orbital 1.JPG ‎|300px|thumb|centre]] || The two 2s AOs form a non-bonding σ* MO. The energy of the MO formed is -7.99769 a.u.
|-
| [[File:2p pi orbital 1.JPG ‎|300px|thumb|centre]] [[File:2p pi orbital 2.JPG ‎|300px|thumb|centre]] || The two 2px and two 2py AOs form two non-bonding π MOs. These two orbitals are degenerate- the energies of the MOs are -5.96349 a.u. and -5.94946 a.u. respectively.
|-
| [[File:2p pi orbital 3.JPG ‎|300px|thumb|centre]] [[File:2p pi orbital 4.JPG ‎|300px|thumb|centre]] || The two 2px and two 2py AOs form two non-bonding π* MOs. These two orbitals are degenerate- the energies of the MOs are -5.96135 a.u.
|-
| [[File:2p pi orbital 5.JPG ‎|300px|thumb|centre]] || The two 2pz AOs form one non-bonding σ MO. The energy of the MO is -5.96135 a.u.
|-
| [[File:2p pi orbital 6.JPG ‎|300px|thumb|centre]] || The two 2pz AOs form one non-bonding σ * MOs. The energy of the MO is -5.96078 a.u.
|-
| [[File:3s sigma orbital 1.JPG ‎|300px|thumb|centre]] || The two 3s AOs overlap constructively head=on to form a bonding σ MO. The energy of the MO formed is -0.83212 a.u.
|-
| [[File:3s sigma orbital 2.JPG ‎|300px|thumb|centre]] || The two 3s AOs overlap destructively to form an anti-bonding σ* MO. The energy of the MO formed is -0.61535 a.u.
|-
| [[File:3p sigma orbital 1.JPG ‎|300px|thumb|centre]] || The two 3pz AOs overlap constructively head-on to form a bonding σ MO. The energy of this bonding MO is -0.39516 a.u. The energy of this MO is lower in energy than the bonding MOs formed from the overlap of the two 2px and the two 2py orbitals because the head-on interaction is much stronger than the lateral interactions.
|-
| [[File:3p pi orbital 1.JPG ‎|300px|thumb|centre]] [[File:3p pi orbital 2.JPG ‎|300px|thumb|centre]] || The two 2px and the two 2py AOs overlap constructively laterally to form two bonding π MOs of relatively the same energy of -0.36283 a.u. and -0.34958 a.u. respectively.
|-
| [[File:3p pi orbital 3.JPG ‎|300px|thumb|centre]] [[File:3p pi orbital 4.JPG ‎|300px|thumb|centre]] || The two 2px and the two 2py AOs overlap destructively laterally to form two anti-bonding π* MOs of relatively the same energy of -0.21843 a.u. and -0.18463 a.u. respectively. It is important to note that these two anti-bonding π* MOs formed are the HOMO and LUMO respectively of sulphur, meaning that all reactions would react with the sulphur-sulphur pi-bond and not the sigma bond of the double bond.
| [[File:3p sigma orbital 2.JPG ‎|300px|thumb|centre]] || The two 3pz AOs overlap destructively head-on to form an anti-bonding σ* MO. The energy of this bonding MO is -0.01307 a.u.
|}

File:3p sigma orbital 1.JPG

2018-03-16T17:35:09Z

Wsl1917:

File:3p pi orbital 2.JPG

2018-03-16T17:34:06Z

Wsl1917:

File:3p pi orbital 1.JPG

2018-03-16T17:33:20Z

Wsl1917:

Rep:Mod:WSL1819

2018-03-16T17:32:55Z

Wsl1917: /* Molecular Orbitals of Optimised S2 */

== Optimisation of NH3 ==

=== General Information of Optimised NH3 ===

From the 'Summary' table (Figure 1.1), the following general information about the optimisation calculation is obtained: the molecule optimised is ammonia, NH3, the calculation method is RB3LYP; the basis set is 6-31G(d,p); the final energy E(RB3LYP) is -56.44397188 a.u.; the RMS gradient is 0.05399560 a.u.; and the point group of NH3 is C3v.

[[File:Nh3_summary.jpg|400px|thumb|center|Figure 1.1: Summary Table of optimised NH3]]

=== Geometric Information of Optimised NH3 ===

Optimised bond length: 1.01798 Å ≈ 1.018 Å

Optimised bond angle: 105.741 o ≈ 105.7 o

=== Verification of Successful Optimisation of NH3 ===

The 'Item' table (Figure 1.2) shows that the final set of forces and displacements are converged and that the forces are approximately zero; since force is the gradient of a potential energy vs distance graph, this indicates that the structure obtained is at equilibrium, demonstrating successful optimisation of NH3.

<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>

Figure 1.2: Item Table of optimised NH3

Moreover, successful optimisation of NH3 is indicated by the last structure having the most negative energy and the smallest gradient (Figure 1.3).

[[File:Nh3 optimisation.jpg|400px|thumb|center|Figure 1.3: Optimisation plots of NH3]]

=== Dynamic Image of Optimised NH3 ===

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ZOEYWAISUMLUNG_NH3_OPTF_POP.LOG</uploadedFileContents>
<script>frame 1.7</script>
</jmolApplet></jmol>
Figure 1.4: A 3D jmol file of optimised NH3

The optimisation file is linked to [[Media:ZOEYWAISUMLUNG_NH3_OPTF_POP.LOG| here]]

=== Vibrational Analysis of Optimised NH3 ===

From Figure 1.5 in vibrational analysis, there are 6 modes as expected, modes 2 and 3 and modes 5 and 6 are degenerate as they have the same frequency of 1693.95 cm-1 and 3589.82 cm-1 respectively; modes 1, 2 and 3 are "bending" vibrations and modes 4, 5 and 6 are "bond stretch" vibrations; mode 4 is highly symmetric ; mode 1 is the "umbrella" mode and 2 bands in the experimental spectrum (Figure 1.6) of gaseous ammonia as expected.

2 bands in the experimental spectrum are expected firstly because modes 4, 5 and 6 have very small intensities due to small rate of change of dipole moment and since its an experimental spectrum, the noise is great enough to cover such small intensities and secondly because modes 2 and 3, though with significant intensities, are degenerate.

[[File:Nh3 vibrations 1.jpg ‎|400px|thumb|centre|Figure 1.5: Vibrational Table of optimised NH3]]

[[File:Nh3_spectrum.jpg ‎|400px|thumb|centre|Figure 1.6: Spectrum of optimised NH3]]

=== Charge Analysis of Optimised NH3 ===

Charge analysis (Figure 1.7) shows the charge on the nitrogen atom is -1.125 whilst that of the hydrogen atoms is +0.375. This result where nitrogen has a negative charge with a larger magnitude and hydrogen has a positive charge with a smaller magnitude is expected, since nitrogen is more electronegative than hydrogen, nitrogen should withdraw more electron density from each of the three N-H bonds.

[[File:Nh3_charge.jpg ‎|400px|thumb|centre|Figure 1.7: Charge Analysis of optimised NH3]]

== Optimisation of N2 ==

=== General Information of Optimised N2 ===

From the 'Summary' table (Figure 2.1), the following general information about the optimisation calculation is obtained: the molecule optimised is nitrogen, N2, the calculation method is RB3LYP; the basis set is 6-31G(d,p); the final energy E(RB3LYP) is -109.52412868 a.u.; the RMS gradient is 0.00000011 a.u.; and the point group of N2 is D∞h.

[[File:N2 summary 2.jpg|400px|thumb|center|Figure 2.1: Summary Table of optimised N2]]

=== Geometric Information of Optimised N2 ===

Optimised bond length: 1.10550 Å ≈ 1.106 Å

=== Verification of Successful Optimisation of N2 ===

The 'Item' table (Figure 2.2) shows that the final set of forces and displacements are converged and that the forces are zero; since force is the gradient of a potential energy vs distance graph, this indicates that the structure obtained is at equilibrium, demonstrating successful optimisation of N2.

<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 0.000000 0.001200 YES
</pre>

Figure 2.2: Item Table of optimised N2

Moreover, successful optimisation of N2 is indicated by the last structure having the most negative energy and the smallest gradient (Figure 2.3).

[[File:N2 optimisation.jpg|400px|thumb|center|Figure 2.3: Optimisation plots of N2]]

=== Dynamic Image of Optimised N2 ===

<jmol><jmolApplet>
<title>Figure 2.4: Optimised nitrogen</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ZOEYWAISUMLUNG_N2_OPTF_POP.LOG</uploadedFileContents>
<script>frame 1.4</script>
</jmolApplet></jmol>

The optimisation file is linked to [[Media:ZOEYWAISUMLUNG_N2_OPTF_POP.LOG| here]]

=== Vibrational Analysis of Optimised N2 ===

From Figure 2.5 in vibrational analysis, there are 0 modes as expected, and 0 bands in the experimental spectrum (Figure 2.6) of gaseous nitrogen as expected.

No bands are expected to be seen in the experimental spectrum because nitrogen is a linear molecule there is no dipole moment hence no change in dipole moment in a linear molecule.

[[File:N2 vibrations.jpg ‎|400px|thumb|centre|Figure 2.5: Vibrational Table of optimised N2]]

[[File:N2 spectrum.jpg ‎|400px|thumb|centre|Figure 2.6: Spectrum of optimised N2]]

=== Charge Analysis of Optimised N2 ===

Charge analysis (Figure 2.7) shows the charge on both nitrogen atoms is 0.000. This result is expected because both atoms of the lienar bond are the same so there are no expected differences in electronegativity therefore electron density is shared equally between the nitrogen atoms. Note that the atoms are colored by charge, a charge of 0.000 is represented by the color black and the numbers are written in black therefore they cannot be seen here.

[[File:N2 charge.jpg ‎|400px|thumb|centre|Figure 2.7: Charge Analysis of optimised N2]]

== Optimisation of H2 ==

=== General Information of Optimised H2 ===

From the 'Summary' table (Figure 3.1), the following general information about the optimisation calculation is obtained: the molecule optimised is hydrogen, H2, the calculation method is RB3LYP; the basis set is 6-31G(d,p); the final energy E(RB3LYP) is -1.17853936 a.u.; the RMS gradient is 0.00002276 a.u.; and the point group of H2 is D∞h.

[[File:H2 summary.jpg|400px|thumb|center|Figure 3.1: Summary Table of optimised H2]]

=== Geometric Information of Optimised H2 ===

Optimised bond length: 0.74274 Å ≈ 0.7427 Å

=== Verification of Successful Optimisation of H2 ===

The 'Item' table (Figure 3.2) shows that the final set of forces and displacements are converged and that the forces are zero; since force is the gradient of a potential energy vs distance graph, this indicates that the structure obtained is at equilibrium, demonstrating successful optimisation of H2.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000039 0.000300 YES
Maximum Displacement 0.000052 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
</pre>

Figure 3.2: Item Table of optimised H2

Moreover, successful optimisation of H2 is indicated by the last structure having the most negative energy and the smallest gradient (Figure 3.3).

[[File:H2 optimisation.jpg|400px|thumb|center|Figure 3.3: Optimisation plots of H2]]

=== Dynamic Image of Optimised H2 ===

<jmol><jmolApplet>
<title>Figure 3.4: Optimised hydrogen</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ZOEYWAISUMLUNG_H2_OPTF_POP.LOG</uploadedFileContents>
<script>frame 1.3</script>
</jmolApplet></jmol>

The optimisation file is linked to [[Media:ZOEYWAISUMLUNG_H2_OPTF_POP.LOG| here]]

=== Vibrational Analysis of Optimised H2 ===

From Figure 3.5 in vibrational analysis, there are 0 modes as expected, and 0 bands in the experimental spectrum (Figure 3.6) of gaseous hydrogen as expected.

No bands are expected to be seen in the experimental spectrum because hydrogen is a linear molecule there is no dipole moment hence no change in dipole moment in a linear molecule.

[[File:H2 vibrations.jpg ‎|400px|thumb|centre|Figure 3.5: Vibrational Table of optimised H2]]

[[File:H2 spectrum.jpg ‎|400px|thumb|centre|Figure 3.6: Spectrum of optimised H2]]

=== Charge Analysis of Optimised H2 ===

Charge analysis (Figure 3.7) shows the charge on both hydrogen atoms is 0.000. This result is expected because both atoms of the linear bond are the same so there are no expected differences in electronegativity therefore electron density is shared equally between the hydrogen atoms. If a higher basis set is used, a single bond would likely to be displayed.

[[File:H2 charge.jpg ‎|400px|thumb|centre|Figure 2.7: Charge Analysis of optimised H2]]

== Optimisation of S2 ==

=== General Information of Optimised S2 ===

From the 'Summary' table (Figure 4.1), the following general information about the optimisation calculation is obtained: the molecule optimised is sulphur, S2, the calculation method is RB3LYP; the basis set is 6-31G(d,p); the final energy E(RB3LYP) is -796.32599779 a.u.; the RMS gradient is 0.00000905 a.u.; and the point group of S2 is D∞h.

[[File:S2 summary.jpg|400px|thumb|center|Figure 4.1: Summary Table of optimised S2]]

=== Geometric Information of Optimised S2 ===

Optimised bond length: 1.92947 Å ≈ 1.929 Å

=== Verification of Successful Optimisation of S2 ===

The 'Item' table (Figure 4.2) shows that the final set of forces and displacements are converged and that the forces are approximately zero; since force is the gradient of a potential energy vs distance graph, this indicates that the structure obtained is at equilibrium, demonstrating successful optimisation of S2.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.000027 0.001800 YES
RMS Displacement 0.000038 0.001200 YES
</pre>

Figure 4.2: Item Table of optimised S2

Moreover, successful optimisation of S2 is indicated by the last structure having the most negative energy and the smallest gradient (Figure 4.3).

[[File:S2 optimisation.jpg|400px|thumb|center|Figure 4.3: Optimisation plots of S2]]

=== Dynamic Image of Optimised S2 ===

<jmol><jmolApplet>
<title>Figure 4.4: Optimised sulphur</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ZOEYWAISUMLUNG_S2_OPTF_POP.LOG</uploadedFileContents>
<script>frame 1.4</script>
</jmolApplet></jmol>

The optimisation file is linked to [[Media:ZOEYWAISUMLUNG_S2_OPTF_POP.LOG| here]]

=== Vibrational Analysis of Optimised S2 ===

From Figure 4.5 in vibrational analysis, there are 0 modes as expected, and 0 bands in the experimental spectrum (Figure 4.6) of gaseous sulphur as expected.

No bands are expected to be seen in the experimental spectrum because sulphur is a linear molecule there is no dipole moment hence no change in dipole moment in a linear molecule.

[[File:S2 vibrations.jpg ‎|400px|thumb|centre|Figure 4.5: Vibrational Table of optimised S2]]

[[File:S2 spectrum.jpg ‎|400px|thumb|centre|Figure 4.6: Spectrum of optimised S2]]

=== Charge Analysis of Optimised S2 ===

Charge analysis (Figure 4.7) shows the charge on both sulphur atoms is 0.000. This result is expected because both atoms of the linear bond are the same so there are no expected differences in electronegativity therefore electron density is shared equally between the sulphur atoms. A single bond instead of a double bond is displayed however this would most likely not be the case if a higher basis set is used for optimisation.

[[File:S2 charge.jpg ‎|400px|thumb|centre|Figure 2.7: Charge Analysis of optimised H2]]

=== Molecular Orbitals of Optimised S2 ===

{| class="wikitable" border="1"
|+ caption
! heading !! heading
|-
| [[File:1s sigma orbital 1.JPG ‎|300px|thumb|centre]]
|| The two 1s AOs form a non-bonding σ MO. The energy of the MO formed is -88.93663 a.u.
|-
| [[File:1s sigma orbital 2.JPG ‎|300px|thumb|centre]] || The two 1s AOs form a non-bonding σ* MO. The energy of the MO formed is -88.93661 a.u.
|-
| [[File:2s sigma orbital 2.JPG ‎|300px|thumb|centre]]|| The two 2s AOs overlap constructively to form a non-bonding σ MO. The energy of the MO formed is -7.99779 a.u.
|-
| [[File:2s sigma orbital 1.JPG ‎|300px|thumb|centre]] || The two 2s AOs form a non-bonding σ* MO. The energy of the MO formed is -7.99769 a.u.
|-
| [[File:2p pi orbital 1.JPG ‎|300px|thumb|centre]] [[File:2p pi orbital 2.JPG ‎|300px|thumb|centre]] || The two 2px and two 2py AOs form two non-bonding π MOs. These two orbitals are degenerate- the energies of the MOs are -5.96349 a.u. and -5.94946 a.u. respectively.
|-
| [[File:2p pi orbital 3.JPG ‎|300px|thumb|centre]] [[File:2p pi orbital 4.JPG ‎|300px|thumb|centre]] || The two 2px and two 2py AOs form two non-bonding π* MOs. These two orbitals are degenerate- the energies of the MOs are -5.96135 a.u.
|-
| [[File:2p pi orbital 5.JPG ‎|300px|thumb|centre]] || The two 2pz AOs form one non-bonding σ MO. The energy of the MO is -5.96135 a.u.
|-
| [[File:2p pi orbital 6.JPG ‎|300px|thumb|centre]] || The two 2pz AOs form one non-bonding σ * MOs. The energy of the MO is -5.96078 a.u.
|-
| [[File:3s sigma orbital 1.JPG ‎|300px|thumb|centre]] || The two 3s AOs overlap constructively head=on to form a bonding σ MO. The energy of the MO formed is -0.83212 a.u.
|-
| [[File:3s sigma orbital 2.JPG ‎|300px|thumb|centre]] || The two 3s AOs overlap destructively to form an anti-bonding σ* MO. The energy of the MO formed is -0.61535 a.u.
|-
| [[File:3p sigma orbital 1.JPG ‎|300px|thumb|centre]] || The two 3pz AOs overlap constructively head-on to form a bonding π MO. The energy of this bonding MO is -0.39516 a.u. The energy of this MO is lower in energy than the bonding MOs formed from the overlap of the two 2px and the two 2py orbitals because the head-on interaction is much stronger than the lateral interactions.
|-
| [[File:3p pi orbital 1.JPG ‎|300px|thumb|centre]] [[File:3p pi orbital 2.JPG ‎|300px|thumb|centre]] || The two 2px and the two 2py AOs overlap constructively laterally to form two bonding MOs of relatively the same energy of -0.36283 a.u. and -0.34958 a.u. respectively.

|}

Rep:Mod:WSL1819

2018-03-16T17:21:57Z

Wsl1917: /* Molecular Orbitals of Optimised S2 */

== Optimisation of NH3 ==

=== General Information of Optimised NH3 ===

From the 'Summary' table (Figure 1.1), the following general information about the optimisation calculation is obtained: the molecule optimised is ammonia, NH3, the calculation method is RB3LYP; the basis set is 6-31G(d,p); the final energy E(RB3LYP) is -56.44397188 a.u.; the RMS gradient is 0.05399560 a.u.; and the point group of NH3 is C3v.

[[File:Nh3_summary.jpg|400px|thumb|center|Figure 1.1: Summary Table of optimised NH3]]

=== Geometric Information of Optimised NH3 ===

Optimised bond length: 1.01798 Å ≈ 1.018 Å

Optimised bond angle: 105.741 o ≈ 105.7 o

=== Verification of Successful Optimisation of NH3 ===

The 'Item' table (Figure 1.2) shows that the final set of forces and displacements are converged and that the forces are approximately zero; since force is the gradient of a potential energy vs distance graph, this indicates that the structure obtained is at equilibrium, demonstrating successful optimisation of NH3.

<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>

Figure 1.2: Item Table of optimised NH3

Moreover, successful optimisation of NH3 is indicated by the last structure having the most negative energy and the smallest gradient (Figure 1.3).

[[File:Nh3 optimisation.jpg|400px|thumb|center|Figure 1.3: Optimisation plots of NH3]]

=== Dynamic Image of Optimised NH3 ===

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ZOEYWAISUMLUNG_NH3_OPTF_POP.LOG</uploadedFileContents>
<script>frame 1.7</script>
</jmolApplet></jmol>
Figure 1.4: A 3D jmol file of optimised NH3

The optimisation file is linked to [[Media:ZOEYWAISUMLUNG_NH3_OPTF_POP.LOG| here]]

=== Vibrational Analysis of Optimised NH3 ===

From Figure 1.5 in vibrational analysis, there are 6 modes as expected, modes 2 and 3 and modes 5 and 6 are degenerate as they have the same frequency of 1693.95 cm-1 and 3589.82 cm-1 respectively; modes 1, 2 and 3 are "bending" vibrations and modes 4, 5 and 6 are "bond stretch" vibrations; mode 4 is highly symmetric ; mode 1 is the "umbrella" mode and 2 bands in the experimental spectrum (Figure 1.6) of gaseous ammonia as expected.

2 bands in the experimental spectrum are expected firstly because modes 4, 5 and 6 have very small intensities due to small rate of change of dipole moment and since its an experimental spectrum, the noise is great enough to cover such small intensities and secondly because modes 2 and 3, though with significant intensities, are degenerate.

[[File:Nh3 vibrations 1.jpg ‎|400px|thumb|centre|Figure 1.5: Vibrational Table of optimised NH3]]

[[File:Nh3_spectrum.jpg ‎|400px|thumb|centre|Figure 1.6: Spectrum of optimised NH3]]

=== Charge Analysis of Optimised NH3 ===

Charge analysis (Figure 1.7) shows the charge on the nitrogen atom is -1.125 whilst that of the hydrogen atoms is +0.375. This result where nitrogen has a negative charge with a larger magnitude and hydrogen has a positive charge with a smaller magnitude is expected, since nitrogen is more electronegative than hydrogen, nitrogen should withdraw more electron density from each of the three N-H bonds.

[[File:Nh3_charge.jpg ‎|400px|thumb|centre|Figure 1.7: Charge Analysis of optimised NH3]]

== Optimisation of N2 ==

=== General Information of Optimised N2 ===

From the 'Summary' table (Figure 2.1), the following general information about the optimisation calculation is obtained: the molecule optimised is nitrogen, N2, the calculation method is RB3LYP; the basis set is 6-31G(d,p); the final energy E(RB3LYP) is -109.52412868 a.u.; the RMS gradient is 0.00000011 a.u.; and the point group of N2 is D∞h.

[[File:N2 summary 2.jpg|400px|thumb|center|Figure 2.1: Summary Table of optimised N2]]

=== Geometric Information of Optimised N2 ===

Optimised bond length: 1.10550 Å ≈ 1.106 Å

=== Verification of Successful Optimisation of N2 ===

The 'Item' table (Figure 2.2) shows that the final set of forces and displacements are converged and that the forces are zero; since force is the gradient of a potential energy vs distance graph, this indicates that the structure obtained is at equilibrium, demonstrating successful optimisation of N2.

<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 0.000000 0.001200 YES
</pre>

Figure 2.2: Item Table of optimised N2

Moreover, successful optimisation of N2 is indicated by the last structure having the most negative energy and the smallest gradient (Figure 2.3).

[[File:N2 optimisation.jpg|400px|thumb|center|Figure 2.3: Optimisation plots of N2]]

=== Dynamic Image of Optimised N2 ===

<jmol><jmolApplet>
<title>Figure 2.4: Optimised nitrogen</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ZOEYWAISUMLUNG_N2_OPTF_POP.LOG</uploadedFileContents>
<script>frame 1.4</script>
</jmolApplet></jmol>

The optimisation file is linked to [[Media:ZOEYWAISUMLUNG_N2_OPTF_POP.LOG| here]]

=== Vibrational Analysis of Optimised N2 ===

From Figure 2.5 in vibrational analysis, there are 0 modes as expected, and 0 bands in the experimental spectrum (Figure 2.6) of gaseous nitrogen as expected.

No bands are expected to be seen in the experimental spectrum because nitrogen is a linear molecule there is no dipole moment hence no change in dipole moment in a linear molecule.

[[File:N2 vibrations.jpg ‎|400px|thumb|centre|Figure 2.5: Vibrational Table of optimised N2]]

[[File:N2 spectrum.jpg ‎|400px|thumb|centre|Figure 2.6: Spectrum of optimised N2]]

=== Charge Analysis of Optimised N2 ===

Charge analysis (Figure 2.7) shows the charge on both nitrogen atoms is 0.000. This result is expected because both atoms of the lienar bond are the same so there are no expected differences in electronegativity therefore electron density is shared equally between the nitrogen atoms. Note that the atoms are colored by charge, a charge of 0.000 is represented by the color black and the numbers are written in black therefore they cannot be seen here.

[[File:N2 charge.jpg ‎|400px|thumb|centre|Figure 2.7: Charge Analysis of optimised N2]]

== Optimisation of H2 ==

=== General Information of Optimised H2 ===

From the 'Summary' table (Figure 3.1), the following general information about the optimisation calculation is obtained: the molecule optimised is hydrogen, H2, the calculation method is RB3LYP; the basis set is 6-31G(d,p); the final energy E(RB3LYP) is -1.17853936 a.u.; the RMS gradient is 0.00002276 a.u.; and the point group of H2 is D∞h.

[[File:H2 summary.jpg|400px|thumb|center|Figure 3.1: Summary Table of optimised H2]]

=== Geometric Information of Optimised H2 ===

Optimised bond length: 0.74274 Å ≈ 0.7427 Å

=== Verification of Successful Optimisation of H2 ===

The 'Item' table (Figure 3.2) shows that the final set of forces and displacements are converged and that the forces are zero; since force is the gradient of a potential energy vs distance graph, this indicates that the structure obtained is at equilibrium, demonstrating successful optimisation of H2.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000039 0.000300 YES
Maximum Displacement 0.000052 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
</pre>

Figure 3.2: Item Table of optimised H2

Moreover, successful optimisation of H2 is indicated by the last structure having the most negative energy and the smallest gradient (Figure 3.3).

[[File:H2 optimisation.jpg|400px|thumb|center|Figure 3.3: Optimisation plots of H2]]

=== Dynamic Image of Optimised H2 ===

<jmol><jmolApplet>
<title>Figure 3.4: Optimised hydrogen</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ZOEYWAISUMLUNG_H2_OPTF_POP.LOG</uploadedFileContents>
<script>frame 1.3</script>
</jmolApplet></jmol>

The optimisation file is linked to [[Media:ZOEYWAISUMLUNG_H2_OPTF_POP.LOG| here]]

=== Vibrational Analysis of Optimised H2 ===

From Figure 3.5 in vibrational analysis, there are 0 modes as expected, and 0 bands in the experimental spectrum (Figure 3.6) of gaseous hydrogen as expected.

No bands are expected to be seen in the experimental spectrum because hydrogen is a linear molecule there is no dipole moment hence no change in dipole moment in a linear molecule.

[[File:H2 vibrations.jpg ‎|400px|thumb|centre|Figure 3.5: Vibrational Table of optimised H2]]

[[File:H2 spectrum.jpg ‎|400px|thumb|centre|Figure 3.6: Spectrum of optimised H2]]

=== Charge Analysis of Optimised H2 ===

Charge analysis (Figure 3.7) shows the charge on both hydrogen atoms is 0.000. This result is expected because both atoms of the linear bond are the same so there are no expected differences in electronegativity therefore electron density is shared equally between the hydrogen atoms. If a higher basis set is used, a single bond would likely to be displayed.

[[File:H2 charge.jpg ‎|400px|thumb|centre|Figure 2.7: Charge Analysis of optimised H2]]

== Optimisation of S2 ==

=== General Information of Optimised S2 ===

From the 'Summary' table (Figure 4.1), the following general information about the optimisation calculation is obtained: the molecule optimised is sulphur, S2, the calculation method is RB3LYP; the basis set is 6-31G(d,p); the final energy E(RB3LYP) is -796.32599779 a.u.; the RMS gradient is 0.00000905 a.u.; and the point group of S2 is D∞h.

[[File:S2 summary.jpg|400px|thumb|center|Figure 4.1: Summary Table of optimised S2]]

=== Geometric Information of Optimised S2 ===

Optimised bond length: 1.92947 Å ≈ 1.929 Å

=== Verification of Successful Optimisation of S2 ===

The 'Item' table (Figure 4.2) shows that the final set of forces and displacements are converged and that the forces are approximately zero; since force is the gradient of a potential energy vs distance graph, this indicates that the structure obtained is at equilibrium, demonstrating successful optimisation of S2.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.000027 0.001800 YES
RMS Displacement 0.000038 0.001200 YES
</pre>

Figure 4.2: Item Table of optimised S2

Moreover, successful optimisation of S2 is indicated by the last structure having the most negative energy and the smallest gradient (Figure 4.3).

[[File:S2 optimisation.jpg|400px|thumb|center|Figure 4.3: Optimisation plots of S2]]

=== Dynamic Image of Optimised S2 ===

<jmol><jmolApplet>
<title>Figure 4.4: Optimised sulphur</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ZOEYWAISUMLUNG_S2_OPTF_POP.LOG</uploadedFileContents>
<script>frame 1.4</script>
</jmolApplet></jmol>

The optimisation file is linked to [[Media:ZOEYWAISUMLUNG_S2_OPTF_POP.LOG| here]]

=== Vibrational Analysis of Optimised S2 ===

From Figure 4.5 in vibrational analysis, there are 0 modes as expected, and 0 bands in the experimental spectrum (Figure 4.6) of gaseous sulphur as expected.

No bands are expected to be seen in the experimental spectrum because sulphur is a linear molecule there is no dipole moment hence no change in dipole moment in a linear molecule.

[[File:S2 vibrations.jpg ‎|400px|thumb|centre|Figure 4.5: Vibrational Table of optimised S2]]

[[File:S2 spectrum.jpg ‎|400px|thumb|centre|Figure 4.6: Spectrum of optimised S2]]

=== Charge Analysis of Optimised S2 ===

Charge analysis (Figure 4.7) shows the charge on both sulphur atoms is 0.000. This result is expected because both atoms of the linear bond are the same so there are no expected differences in electronegativity therefore electron density is shared equally between the sulphur atoms. A single bond instead of a double bond is displayed however this would most likely not be the case if a higher basis set is used for optimisation.

[[File:S2 charge.jpg ‎|400px|thumb|centre|Figure 2.7: Charge Analysis of optimised H2]]

=== Molecular Orbitals of Optimised S2 ===

{| class="wikitable" border="1"
|+ caption
! heading !! heading
|-
| [[File:1s sigma orbital 1.JPG ‎|300px|thumb|centre]]
|| The two 1s AOs form a non-bonding σ MO. The energy of the MO formed is -88.93663.
|-
| [[File:1s sigma orbital 2.JPG ‎|300px|thumb|centre]] || The two 1s AOs form a non-bonding σ* MO. The energy of the MO formed is -88.93661.
|-
| [[File:2s sigma orbital 2.JPG ‎|300px|thumb|centre]]|| The two 2s AOs overlap constructively to form a non-bonding σ MO. The energy of the MO formed is -7.99779.
|-
| [[File:2s sigma orbital 1.JPG ‎|300px|thumb|centre]] || The two 2s AOs form a non-bonding σ* MO. The energy of the MO formed is -7.99769.
|-
| [[File:2p pi orbital 1.JPG ‎|300px|thumb|centre]] [[File:2p pi orbital 2.JPG ‎|300px|thumb|centre]] || The two 2px and two 2py AOs form two non-bonding π MOs. These two orbitals are degenerate- the energies of the MOs are -5.96349 and -5.94946 respectively.
|-
| [[File:2p pi orbital 3.JPG ‎|300px|thumb|centre]] [[File:2p pi orbital 4.JPG ‎|300px|thumb|centre]] || The two 2px and two 2py AOs form two non-bonding π* MOs. These two orbitals are degenerate- the energies of the MOs are -5.96135.
|-
| [[File:2p pi orbital 5.JPG ‎|300px|thumb|centre]] || The two 2pz AOs overlap constructively head-on to form one non-bonding σ MO. The energy of the MO is -5.96135.
|-
| [[File:2p pi orbital 6.JPG ‎|300px|thumb|centre]] || The two 2pz AOs form one non-bonding σ * MOs. The energy of the MO is -5.96078 .
|-
| [[File:3s sigma orbital 1.JPG ‎|300px|thumb|centre]] || The two 3s AOs overlap constructively head=on to form a bonding σ MO. The energy of the MO formed is -0.83212.
|-
| [[File:3s sigma orbital 2.JPG ‎|300px|thumb|centre]] || The two 3s AOs also overlap destructively to form an anti-bonding σ* MO. The energy of the MO formed is -0.61535.
|}

Rep:Mod:WSL1819

2018-03-16T17:18:27Z

Wsl1917: /* Vibrational Analysis of Optimised S2 */

== Optimisation of NH3 ==

=== General Information of Optimised NH3 ===

From the 'Summary' table (Figure 1.1), the following general information about the optimisation calculation is obtained: the molecule optimised is ammonia, NH3, the calculation method is RB3LYP; the basis set is 6-31G(d,p); the final energy E(RB3LYP) is -56.44397188 a.u.; the RMS gradient is 0.05399560 a.u.; and the point group of NH3 is C3v.

[[File:Nh3_summary.jpg|400px|thumb|center|Figure 1.1: Summary Table of optimised NH3]]

=== Geometric Information of Optimised NH3 ===

Optimised bond length: 1.01798 Å ≈ 1.018 Å

Optimised bond angle: 105.741 o ≈ 105.7 o

=== Verification of Successful Optimisation of NH3 ===

The 'Item' table (Figure 1.2) shows that the final set of forces and displacements are converged and that the forces are approximately zero; since force is the gradient of a potential energy vs distance graph, this indicates that the structure obtained is at equilibrium, demonstrating successful optimisation of NH3.

<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>

Figure 1.2: Item Table of optimised NH3

Moreover, successful optimisation of NH3 is indicated by the last structure having the most negative energy and the smallest gradient (Figure 1.3).

[[File:Nh3 optimisation.jpg|400px|thumb|center|Figure 1.3: Optimisation plots of NH3]]

=== Dynamic Image of Optimised NH3 ===

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ZOEYWAISUMLUNG_NH3_OPTF_POP.LOG</uploadedFileContents>
<script>frame 1.7</script>
</jmolApplet></jmol>
Figure 1.4: A 3D jmol file of optimised NH3

The optimisation file is linked to [[Media:ZOEYWAISUMLUNG_NH3_OPTF_POP.LOG| here]]

=== Vibrational Analysis of Optimised NH3 ===

From Figure 1.5 in vibrational analysis, there are 6 modes as expected, modes 2 and 3 and modes 5 and 6 are degenerate as they have the same frequency of 1693.95 cm-1 and 3589.82 cm-1 respectively; modes 1, 2 and 3 are "bending" vibrations and modes 4, 5 and 6 are "bond stretch" vibrations; mode 4 is highly symmetric ; mode 1 is the "umbrella" mode and 2 bands in the experimental spectrum (Figure 1.6) of gaseous ammonia as expected.

2 bands in the experimental spectrum are expected firstly because modes 4, 5 and 6 have very small intensities due to small rate of change of dipole moment and since its an experimental spectrum, the noise is great enough to cover such small intensities and secondly because modes 2 and 3, though with significant intensities, are degenerate.

[[File:Nh3 vibrations 1.jpg ‎|400px|thumb|centre|Figure 1.5: Vibrational Table of optimised NH3]]

[[File:Nh3_spectrum.jpg ‎|400px|thumb|centre|Figure 1.6: Spectrum of optimised NH3]]

=== Charge Analysis of Optimised NH3 ===

Charge analysis (Figure 1.7) shows the charge on the nitrogen atom is -1.125 whilst that of the hydrogen atoms is +0.375. This result where nitrogen has a negative charge with a larger magnitude and hydrogen has a positive charge with a smaller magnitude is expected, since nitrogen is more electronegative than hydrogen, nitrogen should withdraw more electron density from each of the three N-H bonds.

[[File:Nh3_charge.jpg ‎|400px|thumb|centre|Figure 1.7: Charge Analysis of optimised NH3]]

== Optimisation of N2 ==

=== General Information of Optimised N2 ===

From the 'Summary' table (Figure 2.1), the following general information about the optimisation calculation is obtained: the molecule optimised is nitrogen, N2, the calculation method is RB3LYP; the basis set is 6-31G(d,p); the final energy E(RB3LYP) is -109.52412868 a.u.; the RMS gradient is 0.00000011 a.u.; and the point group of N2 is D∞h.

[[File:N2 summary 2.jpg|400px|thumb|center|Figure 2.1: Summary Table of optimised N2]]

=== Geometric Information of Optimised N2 ===

Optimised bond length: 1.10550 Å ≈ 1.106 Å

=== Verification of Successful Optimisation of N2 ===

The 'Item' table (Figure 2.2) shows that the final set of forces and displacements are converged and that the forces are zero; since force is the gradient of a potential energy vs distance graph, this indicates that the structure obtained is at equilibrium, demonstrating successful optimisation of N2.

<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 0.000000 0.001200 YES
</pre>

Figure 2.2: Item Table of optimised N2

Moreover, successful optimisation of N2 is indicated by the last structure having the most negative energy and the smallest gradient (Figure 2.3).

[[File:N2 optimisation.jpg|400px|thumb|center|Figure 2.3: Optimisation plots of N2]]

=== Dynamic Image of Optimised N2 ===

<jmol><jmolApplet>
<title>Figure 2.4: Optimised nitrogen</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ZOEYWAISUMLUNG_N2_OPTF_POP.LOG</uploadedFileContents>
<script>frame 1.4</script>
</jmolApplet></jmol>

The optimisation file is linked to [[Media:ZOEYWAISUMLUNG_N2_OPTF_POP.LOG| here]]

=== Vibrational Analysis of Optimised N2 ===

From Figure 2.5 in vibrational analysis, there are 0 modes as expected, and 0 bands in the experimental spectrum (Figure 2.6) of gaseous nitrogen as expected.

No bands are expected to be seen in the experimental spectrum because nitrogen is a linear molecule there is no dipole moment hence no change in dipole moment in a linear molecule.

[[File:N2 vibrations.jpg ‎|400px|thumb|centre|Figure 2.5: Vibrational Table of optimised N2]]

[[File:N2 spectrum.jpg ‎|400px|thumb|centre|Figure 2.6: Spectrum of optimised N2]]

=== Charge Analysis of Optimised N2 ===

Charge analysis (Figure 2.7) shows the charge on both nitrogen atoms is 0.000. This result is expected because both atoms of the lienar bond are the same so there are no expected differences in electronegativity therefore electron density is shared equally between the nitrogen atoms. Note that the atoms are colored by charge, a charge of 0.000 is represented by the color black and the numbers are written in black therefore they cannot be seen here.

[[File:N2 charge.jpg ‎|400px|thumb|centre|Figure 2.7: Charge Analysis of optimised N2]]

== Optimisation of H2 ==

=== General Information of Optimised H2 ===

From the 'Summary' table (Figure 3.1), the following general information about the optimisation calculation is obtained: the molecule optimised is hydrogen, H2, the calculation method is RB3LYP; the basis set is 6-31G(d,p); the final energy E(RB3LYP) is -1.17853936 a.u.; the RMS gradient is 0.00002276 a.u.; and the point group of H2 is D∞h.

[[File:H2 summary.jpg|400px|thumb|center|Figure 3.1: Summary Table of optimised H2]]

=== Geometric Information of Optimised H2 ===

Optimised bond length: 0.74274 Å ≈ 0.7427 Å

=== Verification of Successful Optimisation of H2 ===

The 'Item' table (Figure 3.2) shows that the final set of forces and displacements are converged and that the forces are zero; since force is the gradient of a potential energy vs distance graph, this indicates that the structure obtained is at equilibrium, demonstrating successful optimisation of H2.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000039 0.000300 YES
Maximum Displacement 0.000052 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
</pre>

Figure 3.2: Item Table of optimised H2

Moreover, successful optimisation of H2 is indicated by the last structure having the most negative energy and the smallest gradient (Figure 3.3).

[[File:H2 optimisation.jpg|400px|thumb|center|Figure 3.3: Optimisation plots of H2]]

=== Dynamic Image of Optimised H2 ===

<jmol><jmolApplet>
<title>Figure 3.4: Optimised hydrogen</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ZOEYWAISUMLUNG_H2_OPTF_POP.LOG</uploadedFileContents>
<script>frame 1.3</script>
</jmolApplet></jmol>

The optimisation file is linked to [[Media:ZOEYWAISUMLUNG_H2_OPTF_POP.LOG| here]]

=== Vibrational Analysis of Optimised H2 ===

From Figure 3.5 in vibrational analysis, there are 0 modes as expected, and 0 bands in the experimental spectrum (Figure 3.6) of gaseous hydrogen as expected.

No bands are expected to be seen in the experimental spectrum because hydrogen is a linear molecule there is no dipole moment hence no change in dipole moment in a linear molecule.

[[File:H2 vibrations.jpg ‎|400px|thumb|centre|Figure 3.5: Vibrational Table of optimised H2]]

[[File:H2 spectrum.jpg ‎|400px|thumb|centre|Figure 3.6: Spectrum of optimised H2]]

=== Charge Analysis of Optimised H2 ===

Charge analysis (Figure 3.7) shows the charge on both hydrogen atoms is 0.000. This result is expected because both atoms of the linear bond are the same so there are no expected differences in electronegativity therefore electron density is shared equally between the hydrogen atoms. If a higher basis set is used, a single bond would likely to be displayed.

[[File:H2 charge.jpg ‎|400px|thumb|centre|Figure 2.7: Charge Analysis of optimised H2]]

== Optimisation of S2 ==

=== General Information of Optimised S2 ===

From the 'Summary' table (Figure 4.1), the following general information about the optimisation calculation is obtained: the molecule optimised is sulphur, S2, the calculation method is RB3LYP; the basis set is 6-31G(d,p); the final energy E(RB3LYP) is -796.32599779 a.u.; the RMS gradient is 0.00000905 a.u.; and the point group of S2 is D∞h.

[[File:S2 summary.jpg|400px|thumb|center|Figure 4.1: Summary Table of optimised S2]]

=== Geometric Information of Optimised S2 ===

Optimised bond length: 1.92947 Å ≈ 1.929 Å

=== Verification of Successful Optimisation of S2 ===

The 'Item' table (Figure 4.2) shows that the final set of forces and displacements are converged and that the forces are approximately zero; since force is the gradient of a potential energy vs distance graph, this indicates that the structure obtained is at equilibrium, demonstrating successful optimisation of S2.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.000027 0.001800 YES
RMS Displacement 0.000038 0.001200 YES
</pre>

Figure 4.2: Item Table of optimised S2

Moreover, successful optimisation of S2 is indicated by the last structure having the most negative energy and the smallest gradient (Figure 4.3).

[[File:S2 optimisation.jpg|400px|thumb|center|Figure 4.3: Optimisation plots of S2]]

=== Dynamic Image of Optimised S2 ===

<jmol><jmolApplet>
<title>Figure 4.4: Optimised sulphur</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ZOEYWAISUMLUNG_S2_OPTF_POP.LOG</uploadedFileContents>
<script>frame 1.4</script>
</jmolApplet></jmol>

The optimisation file is linked to [[Media:ZOEYWAISUMLUNG_S2_OPTF_POP.LOG| here]]

=== Vibrational Analysis of Optimised S2 ===

From Figure 4.5 in vibrational analysis, there are 0 modes as expected, and 0 bands in the experimental spectrum (Figure 4.6) of gaseous sulphur as expected.

No bands are expected to be seen in the experimental spectrum because sulphur is a linear molecule there is no dipole moment hence no change in dipole moment in a linear molecule.

[[File:S2 vibrations.jpg ‎|400px|thumb|centre|Figure 4.5: Vibrational Table of optimised S2]]

[[File:S2 spectrum.jpg ‎|400px|thumb|centre|Figure 4.6: Spectrum of optimised S2]]

=== Charge Analysis of Optimised S2 ===

Charge analysis (Figure 4.7) shows the charge on both sulphur atoms is 0.000. This result is expected because both atoms of the linear bond are the same so there are no expected differences in electronegativity therefore electron density is shared equally between the sulphur atoms. A single bond instead of a double bond is displayed however this would most likely not be the case if a higher basis set is used for optimisation.

[[File:S2 charge.jpg ‎|400px|thumb|centre|Figure 2.7: Charge Analysis of optimised H2]]

=== Molecular Orbitals of Optimised S2 ===

{| class="wikitable" border="1"
|+ caption
! heading !! heading
|-
| [[File:1s sigma orbital 1.JPG ‎|300px|thumb|centre]]
|| The two 1s AOs overlap constructively to form a non-bonding σ MO. The energy of the MO formed is -88.93663.
|-
| [[File:1s sigma orbital 2.JPG ‎|300px|thumb|centre]] || The two 1s AOs also overlap destructively to form a non-bonding σ* MO. The energy of the MO formed is -88.93661.
|-
| [[File:2s sigma orbital 2.JPG ‎|300px|thumb|centre]]|| The two 2s AOs overlap constructively to form a non-bonding σ MO. The energy of the MO formed is -7.99779.
|-
| [[File:2s sigma orbital 1.JPG ‎|300px|thumb|centre]] || The two 2s AOs also overlap destructively to form a non-bonding σ* MO. The energy of the MO formed is -7.99769.
|-
| [[File:2p pi orbital 1.JPG ‎|300px|thumb|centre]] [[File:2p pi orbital 2.JPG ‎|300px|thumb|centre]] || The 2px and 2py AOs overlap constructively laterally to form two non-bonding π MOs. These two orbitals are degenerate- the energies of the MOs are -5.96349 and -5.94946 respectively.
|-
| [[File:2p pi orbital 3.JPG ‎|300px|thumb|centre]] [[File:2p pi orbital 4.JPG ‎|300px|thumb|centre]] || The 2px and 2py AOs overlap destructively laterally to form two non-bonding π* MOs. These two orbitals are degenerate- the energies of the MOs are -5.96135.
|-
| [[File:2p pi orbital 5.JPG ‎|300px|thumb|centre]] || The 2pz AOs overlap constructively head-on to form one non-bonding σ MO. The energy of the MO is -5.96135.
|-
| [[File:2p pi orbital 6.JPG ‎|300px|thumb|centre]] || The 2pz AOs overlap destructively head-on to form one non-bonding σ * MOs. The energy of the MO is -5.96078 .
|-
| [[File:3s sigma orbital 1.JPG ‎|300px|thumb|centre]] || The two 3s AOs overlap constructively head=on to form a bonding σ MO. The energy of the MO formed is -0.83212.
|-
| [[File:3s sigma orbital 2.JPG ‎|300px|thumb|centre]] || The two 3s AOs also overlap destructively to form an anti-bonding σ* MO. The energy of the MO formed is -0.61535.
|}

Rep:Mod:WSL1819

2018-03-16T17:18:00Z

Wsl1917: /* Vibrational Analysis of Optimised H2 */

== Optimisation of NH3 ==

=== General Information of Optimised NH3 ===

From the 'Summary' table (Figure 1.1), the following general information about the optimisation calculation is obtained: the molecule optimised is ammonia, NH3, the calculation method is RB3LYP; the basis set is 6-31G(d,p); the final energy E(RB3LYP) is -56.44397188 a.u.; the RMS gradient is 0.05399560 a.u.; and the point group of NH3 is C3v.

[[File:Nh3_summary.jpg|400px|thumb|center|Figure 1.1: Summary Table of optimised NH3]]

=== Geometric Information of Optimised NH3 ===

Optimised bond length: 1.01798 Å ≈ 1.018 Å

Optimised bond angle: 105.741 o ≈ 105.7 o

=== Verification of Successful Optimisation of NH3 ===

The 'Item' table (Figure 1.2) shows that the final set of forces and displacements are converged and that the forces are approximately zero; since force is the gradient of a potential energy vs distance graph, this indicates that the structure obtained is at equilibrium, demonstrating successful optimisation of NH3.

<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>

Figure 1.2: Item Table of optimised NH3

Moreover, successful optimisation of NH3 is indicated by the last structure having the most negative energy and the smallest gradient (Figure 1.3).

[[File:Nh3 optimisation.jpg|400px|thumb|center|Figure 1.3: Optimisation plots of NH3]]

=== Dynamic Image of Optimised NH3 ===

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ZOEYWAISUMLUNG_NH3_OPTF_POP.LOG</uploadedFileContents>
<script>frame 1.7</script>
</jmolApplet></jmol>
Figure 1.4: A 3D jmol file of optimised NH3

The optimisation file is linked to [[Media:ZOEYWAISUMLUNG_NH3_OPTF_POP.LOG| here]]

=== Vibrational Analysis of Optimised NH3 ===

From Figure 1.5 in vibrational analysis, there are 6 modes as expected, modes 2 and 3 and modes 5 and 6 are degenerate as they have the same frequency of 1693.95 cm-1 and 3589.82 cm-1 respectively; modes 1, 2 and 3 are "bending" vibrations and modes 4, 5 and 6 are "bond stretch" vibrations; mode 4 is highly symmetric ; mode 1 is the "umbrella" mode and 2 bands in the experimental spectrum (Figure 1.6) of gaseous ammonia as expected.

2 bands in the experimental spectrum are expected firstly because modes 4, 5 and 6 have very small intensities due to small rate of change of dipole moment and since its an experimental spectrum, the noise is great enough to cover such small intensities and secondly because modes 2 and 3, though with significant intensities, are degenerate.

[[File:Nh3 vibrations 1.jpg ‎|400px|thumb|centre|Figure 1.5: Vibrational Table of optimised NH3]]

[[File:Nh3_spectrum.jpg ‎|400px|thumb|centre|Figure 1.6: Spectrum of optimised NH3]]

=== Charge Analysis of Optimised NH3 ===

Charge analysis (Figure 1.7) shows the charge on the nitrogen atom is -1.125 whilst that of the hydrogen atoms is +0.375. This result where nitrogen has a negative charge with a larger magnitude and hydrogen has a positive charge with a smaller magnitude is expected, since nitrogen is more electronegative than hydrogen, nitrogen should withdraw more electron density from each of the three N-H bonds.

[[File:Nh3_charge.jpg ‎|400px|thumb|centre|Figure 1.7: Charge Analysis of optimised NH3]]

== Optimisation of N2 ==

=== General Information of Optimised N2 ===

From the 'Summary' table (Figure 2.1), the following general information about the optimisation calculation is obtained: the molecule optimised is nitrogen, N2, the calculation method is RB3LYP; the basis set is 6-31G(d,p); the final energy E(RB3LYP) is -109.52412868 a.u.; the RMS gradient is 0.00000011 a.u.; and the point group of N2 is D∞h.

[[File:N2 summary 2.jpg|400px|thumb|center|Figure 2.1: Summary Table of optimised N2]]

=== Geometric Information of Optimised N2 ===

Optimised bond length: 1.10550 Å ≈ 1.106 Å

=== Verification of Successful Optimisation of N2 ===

The 'Item' table (Figure 2.2) shows that the final set of forces and displacements are converged and that the forces are zero; since force is the gradient of a potential energy vs distance graph, this indicates that the structure obtained is at equilibrium, demonstrating successful optimisation of N2.

<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 0.000000 0.001200 YES
</pre>

Figure 2.2: Item Table of optimised N2

Moreover, successful optimisation of N2 is indicated by the last structure having the most negative energy and the smallest gradient (Figure 2.3).

[[File:N2 optimisation.jpg|400px|thumb|center|Figure 2.3: Optimisation plots of N2]]

=== Dynamic Image of Optimised N2 ===

<jmol><jmolApplet>
<title>Figure 2.4: Optimised nitrogen</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ZOEYWAISUMLUNG_N2_OPTF_POP.LOG</uploadedFileContents>
<script>frame 1.4</script>
</jmolApplet></jmol>

The optimisation file is linked to [[Media:ZOEYWAISUMLUNG_N2_OPTF_POP.LOG| here]]

=== Vibrational Analysis of Optimised N2 ===

From Figure 2.5 in vibrational analysis, there are 0 modes as expected, and 0 bands in the experimental spectrum (Figure 2.6) of gaseous nitrogen as expected.

No bands are expected to be seen in the experimental spectrum because nitrogen is a linear molecule there is no dipole moment hence no change in dipole moment in a linear molecule.

[[File:N2 vibrations.jpg ‎|400px|thumb|centre|Figure 2.5: Vibrational Table of optimised N2]]

[[File:N2 spectrum.jpg ‎|400px|thumb|centre|Figure 2.6: Spectrum of optimised N2]]

=== Charge Analysis of Optimised N2 ===

Charge analysis (Figure 2.7) shows the charge on both nitrogen atoms is 0.000. This result is expected because both atoms of the lienar bond are the same so there are no expected differences in electronegativity therefore electron density is shared equally between the nitrogen atoms. Note that the atoms are colored by charge, a charge of 0.000 is represented by the color black and the numbers are written in black therefore they cannot be seen here.

[[File:N2 charge.jpg ‎|400px|thumb|centre|Figure 2.7: Charge Analysis of optimised N2]]

== Optimisation of H2 ==

=== General Information of Optimised H2 ===

From the 'Summary' table (Figure 3.1), the following general information about the optimisation calculation is obtained: the molecule optimised is hydrogen, H2, the calculation method is RB3LYP; the basis set is 6-31G(d,p); the final energy E(RB3LYP) is -1.17853936 a.u.; the RMS gradient is 0.00002276 a.u.; and the point group of H2 is D∞h.

[[File:H2 summary.jpg|400px|thumb|center|Figure 3.1: Summary Table of optimised H2]]

=== Geometric Information of Optimised H2 ===

Optimised bond length: 0.74274 Å ≈ 0.7427 Å

=== Verification of Successful Optimisation of H2 ===

The 'Item' table (Figure 3.2) shows that the final set of forces and displacements are converged and that the forces are zero; since force is the gradient of a potential energy vs distance graph, this indicates that the structure obtained is at equilibrium, demonstrating successful optimisation of H2.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000039 0.000300 YES
Maximum Displacement 0.000052 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
</pre>

Figure 3.2: Item Table of optimised H2

Moreover, successful optimisation of H2 is indicated by the last structure having the most negative energy and the smallest gradient (Figure 3.3).

[[File:H2 optimisation.jpg|400px|thumb|center|Figure 3.3: Optimisation plots of H2]]

=== Dynamic Image of Optimised H2 ===

<jmol><jmolApplet>
<title>Figure 3.4: Optimised hydrogen</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ZOEYWAISUMLUNG_H2_OPTF_POP.LOG</uploadedFileContents>
<script>frame 1.3</script>
</jmolApplet></jmol>

The optimisation file is linked to [[Media:ZOEYWAISUMLUNG_H2_OPTF_POP.LOG| here]]

=== Vibrational Analysis of Optimised H2 ===

From Figure 3.5 in vibrational analysis, there are 0 modes as expected, and 0 bands in the experimental spectrum (Figure 3.6) of gaseous hydrogen as expected.

No bands are expected to be seen in the experimental spectrum because hydrogen is a linear molecule there is no dipole moment hence no change in dipole moment in a linear molecule.

[[File:H2 vibrations.jpg ‎|400px|thumb|centre|Figure 3.5: Vibrational Table of optimised H2]]

[[File:H2 spectrum.jpg ‎|400px|thumb|centre|Figure 3.6: Spectrum of optimised H2]]

=== Charge Analysis of Optimised H2 ===

Charge analysis (Figure 3.7) shows the charge on both hydrogen atoms is 0.000. This result is expected because both atoms of the linear bond are the same so there are no expected differences in electronegativity therefore electron density is shared equally between the hydrogen atoms. If a higher basis set is used, a single bond would likely to be displayed.

[[File:H2 charge.jpg ‎|400px|thumb|centre|Figure 2.7: Charge Analysis of optimised H2]]

== Optimisation of S2 ==

=== General Information of Optimised S2 ===

From the 'Summary' table (Figure 4.1), the following general information about the optimisation calculation is obtained: the molecule optimised is sulphur, S2, the calculation method is RB3LYP; the basis set is 6-31G(d,p); the final energy E(RB3LYP) is -796.32599779 a.u.; the RMS gradient is 0.00000905 a.u.; and the point group of S2 is D∞h.

[[File:S2 summary.jpg|400px|thumb|center|Figure 4.1: Summary Table of optimised S2]]

=== Geometric Information of Optimised S2 ===

Optimised bond length: 1.92947 Å ≈ 1.929 Å

=== Verification of Successful Optimisation of S2 ===

The 'Item' table (Figure 4.2) shows that the final set of forces and displacements are converged and that the forces are approximately zero; since force is the gradient of a potential energy vs distance graph, this indicates that the structure obtained is at equilibrium, demonstrating successful optimisation of S2.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.000027 0.001800 YES
RMS Displacement 0.000038 0.001200 YES
</pre>

Figure 4.2: Item Table of optimised S2

Moreover, successful optimisation of S2 is indicated by the last structure having the most negative energy and the smallest gradient (Figure 4.3).

[[File:S2 optimisation.jpg|400px|thumb|center|Figure 4.3: Optimisation plots of S2]]

=== Dynamic Image of Optimised S2 ===

<jmol><jmolApplet>
<title>Figure 4.4: Optimised sulphur</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ZOEYWAISUMLUNG_S2_OPTF_POP.LOG</uploadedFileContents>
<script>frame 1.4</script>
</jmolApplet></jmol>

The optimisation file is linked to [[Media:ZOEYWAISUMLUNG_S2_OPTF_POP.LOG| here]]

=== Vibrational Analysis of Optimised S2 ===

From Figure 4.5 in vibrational analysis, there are 0 modes as expected, and 0 bands in the experimental spectrum (Figure 4.6) of gaseous sulphur as expected.

[[File:S2 vibrations.jpg ‎|400px|thumb|centre|Figure 4.5: Vibrational Table of optimised S2]]

[[File:S2 spectrum.jpg ‎|400px|thumb|centre|Figure 4.6: Spectrum of optimised S2]]

=== Charge Analysis of Optimised S2 ===

Charge analysis (Figure 4.7) shows the charge on both sulphur atoms is 0.000. This result is expected because both atoms of the linear bond are the same so there are no expected differences in electronegativity therefore electron density is shared equally between the sulphur atoms. A single bond instead of a double bond is displayed however this would most likely not be the case if a higher basis set is used for optimisation.

[[File:S2 charge.jpg ‎|400px|thumb|centre|Figure 2.7: Charge Analysis of optimised H2]]

=== Molecular Orbitals of Optimised S2 ===

{| class="wikitable" border="1"
|+ caption
! heading !! heading
|-
| [[File:1s sigma orbital 1.JPG ‎|300px|thumb|centre]]
|| The two 1s AOs overlap constructively to form a non-bonding σ MO. The energy of the MO formed is -88.93663.
|-
| [[File:1s sigma orbital 2.JPG ‎|300px|thumb|centre]] || The two 1s AOs also overlap destructively to form a non-bonding σ* MO. The energy of the MO formed is -88.93661.
|-
| [[File:2s sigma orbital 2.JPG ‎|300px|thumb|centre]]|| The two 2s AOs overlap constructively to form a non-bonding σ MO. The energy of the MO formed is -7.99779.
|-
| [[File:2s sigma orbital 1.JPG ‎|300px|thumb|centre]] || The two 2s AOs also overlap destructively to form a non-bonding σ* MO. The energy of the MO formed is -7.99769.
|-
| [[File:2p pi orbital 1.JPG ‎|300px|thumb|centre]] [[File:2p pi orbital 2.JPG ‎|300px|thumb|centre]] || The 2px and 2py AOs overlap constructively laterally to form two non-bonding π MOs. These two orbitals are degenerate- the energies of the MOs are -5.96349 and -5.94946 respectively.
|-
| [[File:2p pi orbital 3.JPG ‎|300px|thumb|centre]] [[File:2p pi orbital 4.JPG ‎|300px|thumb|centre]] || The 2px and 2py AOs overlap destructively laterally to form two non-bonding π* MOs. These two orbitals are degenerate- the energies of the MOs are -5.96135.
|-
| [[File:2p pi orbital 5.JPG ‎|300px|thumb|centre]] || The 2pz AOs overlap constructively head-on to form one non-bonding σ MO. The energy of the MO is -5.96135.
|-
| [[File:2p pi orbital 6.JPG ‎|300px|thumb|centre]] || The 2pz AOs overlap destructively head-on to form one non-bonding σ * MOs. The energy of the MO is -5.96078 .
|-
| [[File:3s sigma orbital 1.JPG ‎|300px|thumb|centre]] || The two 3s AOs overlap constructively head=on to form a bonding σ MO. The energy of the MO formed is -0.83212.
|-
| [[File:3s sigma orbital 2.JPG ‎|300px|thumb|centre]] || The two 3s AOs also overlap destructively to form an anti-bonding σ* MO. The energy of the MO formed is -0.61535.
|}

Rep:Mod:WSL1819

2018-03-16T17:17:44Z

Wsl1917: /* Vibrational Analysis of Optimised N2 */

== Optimisation of NH3 ==

=== General Information of Optimised NH3 ===

From the 'Summary' table (Figure 1.1), the following general information about the optimisation calculation is obtained: the molecule optimised is ammonia, NH3, the calculation method is RB3LYP; the basis set is 6-31G(d,p); the final energy E(RB3LYP) is -56.44397188 a.u.; the RMS gradient is 0.05399560 a.u.; and the point group of NH3 is C3v.

[[File:Nh3_summary.jpg|400px|thumb|center|Figure 1.1: Summary Table of optimised NH3]]

=== Geometric Information of Optimised NH3 ===

Optimised bond length: 1.01798 Å ≈ 1.018 Å

Optimised bond angle: 105.741 o ≈ 105.7 o

=== Verification of Successful Optimisation of NH3 ===

The 'Item' table (Figure 1.2) shows that the final set of forces and displacements are converged and that the forces are approximately zero; since force is the gradient of a potential energy vs distance graph, this indicates that the structure obtained is at equilibrium, demonstrating successful optimisation of NH3.

<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>

Figure 1.2: Item Table of optimised NH3

Moreover, successful optimisation of NH3 is indicated by the last structure having the most negative energy and the smallest gradient (Figure 1.3).

[[File:Nh3 optimisation.jpg|400px|thumb|center|Figure 1.3: Optimisation plots of NH3]]

=== Dynamic Image of Optimised NH3 ===

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ZOEYWAISUMLUNG_NH3_OPTF_POP.LOG</uploadedFileContents>
<script>frame 1.7</script>
</jmolApplet></jmol>
Figure 1.4: A 3D jmol file of optimised NH3

The optimisation file is linked to [[Media:ZOEYWAISUMLUNG_NH3_OPTF_POP.LOG| here]]

=== Vibrational Analysis of Optimised NH3 ===

From Figure 1.5 in vibrational analysis, there are 6 modes as expected, modes 2 and 3 and modes 5 and 6 are degenerate as they have the same frequency of 1693.95 cm-1 and 3589.82 cm-1 respectively; modes 1, 2 and 3 are "bending" vibrations and modes 4, 5 and 6 are "bond stretch" vibrations; mode 4 is highly symmetric ; mode 1 is the "umbrella" mode and 2 bands in the experimental spectrum (Figure 1.6) of gaseous ammonia as expected.

2 bands in the experimental spectrum are expected firstly because modes 4, 5 and 6 have very small intensities due to small rate of change of dipole moment and since its an experimental spectrum, the noise is great enough to cover such small intensities and secondly because modes 2 and 3, though with significant intensities, are degenerate.

[[File:Nh3 vibrations 1.jpg ‎|400px|thumb|centre|Figure 1.5: Vibrational Table of optimised NH3]]

[[File:Nh3_spectrum.jpg ‎|400px|thumb|centre|Figure 1.6: Spectrum of optimised NH3]]

=== Charge Analysis of Optimised NH3 ===

Charge analysis (Figure 1.7) shows the charge on the nitrogen atom is -1.125 whilst that of the hydrogen atoms is +0.375. This result where nitrogen has a negative charge with a larger magnitude and hydrogen has a positive charge with a smaller magnitude is expected, since nitrogen is more electronegative than hydrogen, nitrogen should withdraw more electron density from each of the three N-H bonds.

[[File:Nh3_charge.jpg ‎|400px|thumb|centre|Figure 1.7: Charge Analysis of optimised NH3]]

== Optimisation of N2 ==

=== General Information of Optimised N2 ===

From the 'Summary' table (Figure 2.1), the following general information about the optimisation calculation is obtained: the molecule optimised is nitrogen, N2, the calculation method is RB3LYP; the basis set is 6-31G(d,p); the final energy E(RB3LYP) is -109.52412868 a.u.; the RMS gradient is 0.00000011 a.u.; and the point group of N2 is D∞h.

[[File:N2 summary 2.jpg|400px|thumb|center|Figure 2.1: Summary Table of optimised N2]]

=== Geometric Information of Optimised N2 ===

Optimised bond length: 1.10550 Å ≈ 1.106 Å

=== Verification of Successful Optimisation of N2 ===

The 'Item' table (Figure 2.2) shows that the final set of forces and displacements are converged and that the forces are zero; since force is the gradient of a potential energy vs distance graph, this indicates that the structure obtained is at equilibrium, demonstrating successful optimisation of N2.

<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 0.000000 0.001200 YES
</pre>

Figure 2.2: Item Table of optimised N2

Moreover, successful optimisation of N2 is indicated by the last structure having the most negative energy and the smallest gradient (Figure 2.3).

[[File:N2 optimisation.jpg|400px|thumb|center|Figure 2.3: Optimisation plots of N2]]

=== Dynamic Image of Optimised N2 ===

<jmol><jmolApplet>
<title>Figure 2.4: Optimised nitrogen</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ZOEYWAISUMLUNG_N2_OPTF_POP.LOG</uploadedFileContents>
<script>frame 1.4</script>
</jmolApplet></jmol>

The optimisation file is linked to [[Media:ZOEYWAISUMLUNG_N2_OPTF_POP.LOG| here]]

=== Vibrational Analysis of Optimised N2 ===

From Figure 2.5 in vibrational analysis, there are 0 modes as expected, and 0 bands in the experimental spectrum (Figure 2.6) of gaseous nitrogen as expected.

No bands are expected to be seen in the experimental spectrum because nitrogen is a linear molecule there is no dipole moment hence no change in dipole moment in a linear molecule.

[[File:N2 vibrations.jpg ‎|400px|thumb|centre|Figure 2.5: Vibrational Table of optimised N2]]

[[File:N2 spectrum.jpg ‎|400px|thumb|centre|Figure 2.6: Spectrum of optimised N2]]

=== Charge Analysis of Optimised N2 ===

Charge analysis (Figure 2.7) shows the charge on both nitrogen atoms is 0.000. This result is expected because both atoms of the lienar bond are the same so there are no expected differences in electronegativity therefore electron density is shared equally between the nitrogen atoms. Note that the atoms are colored by charge, a charge of 0.000 is represented by the color black and the numbers are written in black therefore they cannot be seen here.

[[File:N2 charge.jpg ‎|400px|thumb|centre|Figure 2.7: Charge Analysis of optimised N2]]

== Optimisation of H2 ==

=== General Information of Optimised H2 ===

From the 'Summary' table (Figure 3.1), the following general information about the optimisation calculation is obtained: the molecule optimised is hydrogen, H2, the calculation method is RB3LYP; the basis set is 6-31G(d,p); the final energy E(RB3LYP) is -1.17853936 a.u.; the RMS gradient is 0.00002276 a.u.; and the point group of H2 is D∞h.

[[File:H2 summary.jpg|400px|thumb|center|Figure 3.1: Summary Table of optimised H2]]

=== Geometric Information of Optimised H2 ===

Optimised bond length: 0.74274 Å ≈ 0.7427 Å

=== Verification of Successful Optimisation of H2 ===

The 'Item' table (Figure 3.2) shows that the final set of forces and displacements are converged and that the forces are zero; since force is the gradient of a potential energy vs distance graph, this indicates that the structure obtained is at equilibrium, demonstrating successful optimisation of H2.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000039 0.000300 YES
Maximum Displacement 0.000052 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
</pre>

Figure 3.2: Item Table of optimised H2

Moreover, successful optimisation of H2 is indicated by the last structure having the most negative energy and the smallest gradient (Figure 3.3).

[[File:H2 optimisation.jpg|400px|thumb|center|Figure 3.3: Optimisation plots of H2]]

=== Dynamic Image of Optimised H2 ===

<jmol><jmolApplet>
<title>Figure 3.4: Optimised hydrogen</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ZOEYWAISUMLUNG_H2_OPTF_POP.LOG</uploadedFileContents>
<script>frame 1.3</script>
</jmolApplet></jmol>

The optimisation file is linked to [[Media:ZOEYWAISUMLUNG_H2_OPTF_POP.LOG| here]]

=== Vibrational Analysis of Optimised H2 ===

From Figure 3.5 in vibrational analysis, there are 0 modes as expected, and 0 bands in the experimental spectrum (Figure 3.6) of gaseous hydrogen as expected.

[[File:H2 vibrations.jpg ‎|400px|thumb|centre|Figure 3.5: Vibrational Table of optimised H2]]

[[File:H2 spectrum.jpg ‎|400px|thumb|centre|Figure 3.6: Spectrum of optimised H2]]

=== Charge Analysis of Optimised H2 ===

Charge analysis (Figure 3.7) shows the charge on both hydrogen atoms is 0.000. This result is expected because both atoms of the linear bond are the same so there are no expected differences in electronegativity therefore electron density is shared equally between the hydrogen atoms. If a higher basis set is used, a single bond would likely to be displayed.

[[File:H2 charge.jpg ‎|400px|thumb|centre|Figure 2.7: Charge Analysis of optimised H2]]

== Optimisation of S2 ==

=== General Information of Optimised S2 ===

From the 'Summary' table (Figure 4.1), the following general information about the optimisation calculation is obtained: the molecule optimised is sulphur, S2, the calculation method is RB3LYP; the basis set is 6-31G(d,p); the final energy E(RB3LYP) is -796.32599779 a.u.; the RMS gradient is 0.00000905 a.u.; and the point group of S2 is D∞h.

[[File:S2 summary.jpg|400px|thumb|center|Figure 4.1: Summary Table of optimised S2]]

=== Geometric Information of Optimised S2 ===

Optimised bond length: 1.92947 Å ≈ 1.929 Å

=== Verification of Successful Optimisation of S2 ===

The 'Item' table (Figure 4.2) shows that the final set of forces and displacements are converged and that the forces are approximately zero; since force is the gradient of a potential energy vs distance graph, this indicates that the structure obtained is at equilibrium, demonstrating successful optimisation of S2.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.000027 0.001800 YES
RMS Displacement 0.000038 0.001200 YES
</pre>

Figure 4.2: Item Table of optimised S2

Moreover, successful optimisation of S2 is indicated by the last structure having the most negative energy and the smallest gradient (Figure 4.3).

[[File:S2 optimisation.jpg|400px|thumb|center|Figure 4.3: Optimisation plots of S2]]

=== Dynamic Image of Optimised S2 ===

<jmol><jmolApplet>
<title>Figure 4.4: Optimised sulphur</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ZOEYWAISUMLUNG_S2_OPTF_POP.LOG</uploadedFileContents>
<script>frame 1.4</script>
</jmolApplet></jmol>

The optimisation file is linked to [[Media:ZOEYWAISUMLUNG_S2_OPTF_POP.LOG| here]]

=== Vibrational Analysis of Optimised S2 ===

From Figure 4.5 in vibrational analysis, there are 0 modes as expected, and 0 bands in the experimental spectrum (Figure 4.6) of gaseous sulphur as expected.

[[File:S2 vibrations.jpg ‎|400px|thumb|centre|Figure 4.5: Vibrational Table of optimised S2]]

[[File:S2 spectrum.jpg ‎|400px|thumb|centre|Figure 4.6: Spectrum of optimised S2]]

=== Charge Analysis of Optimised S2 ===

Charge analysis (Figure 4.7) shows the charge on both sulphur atoms is 0.000. This result is expected because both atoms of the linear bond are the same so there are no expected differences in electronegativity therefore electron density is shared equally between the sulphur atoms. A single bond instead of a double bond is displayed however this would most likely not be the case if a higher basis set is used for optimisation.

[[File:S2 charge.jpg ‎|400px|thumb|centre|Figure 2.7: Charge Analysis of optimised H2]]

=== Molecular Orbitals of Optimised S2 ===

{| class="wikitable" border="1"
|+ caption
! heading !! heading
|-
| [[File:1s sigma orbital 1.JPG ‎|300px|thumb|centre]]
|| The two 1s AOs overlap constructively to form a non-bonding σ MO. The energy of the MO formed is -88.93663.
|-
| [[File:1s sigma orbital 2.JPG ‎|300px|thumb|centre]] || The two 1s AOs also overlap destructively to form a non-bonding σ* MO. The energy of the MO formed is -88.93661.
|-
| [[File:2s sigma orbital 2.JPG ‎|300px|thumb|centre]]|| The two 2s AOs overlap constructively to form a non-bonding σ MO. The energy of the MO formed is -7.99779.
|-
| [[File:2s sigma orbital 1.JPG ‎|300px|thumb|centre]] || The two 2s AOs also overlap destructively to form a non-bonding σ* MO. The energy of the MO formed is -7.99769.
|-
| [[File:2p pi orbital 1.JPG ‎|300px|thumb|centre]] [[File:2p pi orbital 2.JPG ‎|300px|thumb|centre]] || The 2px and 2py AOs overlap constructively laterally to form two non-bonding π MOs. These two orbitals are degenerate- the energies of the MOs are -5.96349 and -5.94946 respectively.
|-
| [[File:2p pi orbital 3.JPG ‎|300px|thumb|centre]] [[File:2p pi orbital 4.JPG ‎|300px|thumb|centre]] || The 2px and 2py AOs overlap destructively laterally to form two non-bonding π* MOs. These two orbitals are degenerate- the energies of the MOs are -5.96135.
|-
| [[File:2p pi orbital 5.JPG ‎|300px|thumb|centre]] || The 2pz AOs overlap constructively head-on to form one non-bonding σ MO. The energy of the MO is -5.96135.
|-
| [[File:2p pi orbital 6.JPG ‎|300px|thumb|centre]] || The 2pz AOs overlap destructively head-on to form one non-bonding σ * MOs. The energy of the MO is -5.96078 .
|-
| [[File:3s sigma orbital 1.JPG ‎|300px|thumb|centre]] || The two 3s AOs overlap constructively head=on to form a bonding σ MO. The energy of the MO formed is -0.83212.
|-
| [[File:3s sigma orbital 2.JPG ‎|300px|thumb|centre]] || The two 3s AOs also overlap destructively to form an anti-bonding σ* MO. The energy of the MO formed is -0.61535.
|}

Rep:Mod:WSL1819

2018-03-16T17:17:09Z

Wsl1917: /* Vibrational Analysis of Optimised NH3 */

== Optimisation of NH3 ==

=== General Information of Optimised NH3 ===

From the 'Summary' table (Figure 1.1), the following general information about the optimisation calculation is obtained: the molecule optimised is ammonia, NH3, the calculation method is RB3LYP; the basis set is 6-31G(d,p); the final energy E(RB3LYP) is -56.44397188 a.u.; the RMS gradient is 0.05399560 a.u.; and the point group of NH3 is C3v.

[[File:Nh3_summary.jpg|400px|thumb|center|Figure 1.1: Summary Table of optimised NH3]]

=== Geometric Information of Optimised NH3 ===

Optimised bond length: 1.01798 Å ≈ 1.018 Å

Optimised bond angle: 105.741 o ≈ 105.7 o

=== Verification of Successful Optimisation of NH3 ===

The 'Item' table (Figure 1.2) shows that the final set of forces and displacements are converged and that the forces are approximately zero; since force is the gradient of a potential energy vs distance graph, this indicates that the structure obtained is at equilibrium, demonstrating successful optimisation of NH3.

<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>

Figure 1.2: Item Table of optimised NH3

Moreover, successful optimisation of NH3 is indicated by the last structure having the most negative energy and the smallest gradient (Figure 1.3).

[[File:Nh3 optimisation.jpg|400px|thumb|center|Figure 1.3: Optimisation plots of NH3]]

=== Dynamic Image of Optimised NH3 ===

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ZOEYWAISUMLUNG_NH3_OPTF_POP.LOG</uploadedFileContents>
<script>frame 1.7</script>
</jmolApplet></jmol>
Figure 1.4: A 3D jmol file of optimised NH3

The optimisation file is linked to [[Media:ZOEYWAISUMLUNG_NH3_OPTF_POP.LOG| here]]

=== Vibrational Analysis of Optimised NH3 ===

From Figure 1.5 in vibrational analysis, there are 6 modes as expected, modes 2 and 3 and modes 5 and 6 are degenerate as they have the same frequency of 1693.95 cm-1 and 3589.82 cm-1 respectively; modes 1, 2 and 3 are "bending" vibrations and modes 4, 5 and 6 are "bond stretch" vibrations; mode 4 is highly symmetric ; mode 1 is the "umbrella" mode and 2 bands in the experimental spectrum (Figure 1.6) of gaseous ammonia as expected.

2 bands in the experimental spectrum are expected firstly because modes 4, 5 and 6 have very small intensities due to small rate of change of dipole moment and since its an experimental spectrum, the noise is great enough to cover such small intensities and secondly because modes 2 and 3, though with significant intensities, are degenerate.

[[File:Nh3 vibrations 1.jpg ‎|400px|thumb|centre|Figure 1.5: Vibrational Table of optimised NH3]]

[[File:Nh3_spectrum.jpg ‎|400px|thumb|centre|Figure 1.6: Spectrum of optimised NH3]]

=== Charge Analysis of Optimised NH3 ===

Charge analysis (Figure 1.7) shows the charge on the nitrogen atom is -1.125 whilst that of the hydrogen atoms is +0.375. This result where nitrogen has a negative charge with a larger magnitude and hydrogen has a positive charge with a smaller magnitude is expected, since nitrogen is more electronegative than hydrogen, nitrogen should withdraw more electron density from each of the three N-H bonds.

[[File:Nh3_charge.jpg ‎|400px|thumb|centre|Figure 1.7: Charge Analysis of optimised NH3]]

== Optimisation of N2 ==

=== General Information of Optimised N2 ===

From the 'Summary' table (Figure 2.1), the following general information about the optimisation calculation is obtained: the molecule optimised is nitrogen, N2, the calculation method is RB3LYP; the basis set is 6-31G(d,p); the final energy E(RB3LYP) is -109.52412868 a.u.; the RMS gradient is 0.00000011 a.u.; and the point group of N2 is D∞h.

[[File:N2 summary 2.jpg|400px|thumb|center|Figure 2.1: Summary Table of optimised N2]]

=== Geometric Information of Optimised N2 ===

Optimised bond length: 1.10550 Å ≈ 1.106 Å

=== Verification of Successful Optimisation of N2 ===

The 'Item' table (Figure 2.2) shows that the final set of forces and displacements are converged and that the forces are zero; since force is the gradient of a potential energy vs distance graph, this indicates that the structure obtained is at equilibrium, demonstrating successful optimisation of N2.

<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 0.000000 0.001200 YES
</pre>

Figure 2.2: Item Table of optimised N2

Moreover, successful optimisation of N2 is indicated by the last structure having the most negative energy and the smallest gradient (Figure 2.3).

[[File:N2 optimisation.jpg|400px|thumb|center|Figure 2.3: Optimisation plots of N2]]

=== Dynamic Image of Optimised N2 ===

<jmol><jmolApplet>
<title>Figure 2.4: Optimised nitrogen</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ZOEYWAISUMLUNG_N2_OPTF_POP.LOG</uploadedFileContents>
<script>frame 1.4</script>
</jmolApplet></jmol>

The optimisation file is linked to [[Media:ZOEYWAISUMLUNG_N2_OPTF_POP.LOG| here]]

=== Vibrational Analysis of Optimised N2 ===

From Figure 2.5 in vibrational analysis, there are 0 modes as expected, and 0 bands in the experimental spectrum (Figure 2.6) of gaseous nitrogen as expected.

No bands are expected to be seen in the experimental spectrum because there is no dipole moment in a linear molecule.

[[File:N2 vibrations.jpg ‎|400px|thumb|centre|Figure 2.5: Vibrational Table of optimised N2]]

[[File:N2 spectrum.jpg ‎|400px|thumb|centre|Figure 2.6: Spectrum of optimised N2]]

=== Charge Analysis of Optimised N2 ===

Charge analysis (Figure 2.7) shows the charge on both nitrogen atoms is 0.000. This result is expected because both atoms of the lienar bond are the same so there are no expected differences in electronegativity therefore electron density is shared equally between the nitrogen atoms. Note that the atoms are colored by charge, a charge of 0.000 is represented by the color black and the numbers are written in black therefore they cannot be seen here.

[[File:N2 charge.jpg ‎|400px|thumb|centre|Figure 2.7: Charge Analysis of optimised N2]]

== Optimisation of H2 ==

=== General Information of Optimised H2 ===

From the 'Summary' table (Figure 3.1), the following general information about the optimisation calculation is obtained: the molecule optimised is hydrogen, H2, the calculation method is RB3LYP; the basis set is 6-31G(d,p); the final energy E(RB3LYP) is -1.17853936 a.u.; the RMS gradient is 0.00002276 a.u.; and the point group of H2 is D∞h.

[[File:H2 summary.jpg|400px|thumb|center|Figure 3.1: Summary Table of optimised H2]]

=== Geometric Information of Optimised H2 ===

Optimised bond length: 0.74274 Å ≈ 0.7427 Å

=== Verification of Successful Optimisation of H2 ===

The 'Item' table (Figure 3.2) shows that the final set of forces and displacements are converged and that the forces are zero; since force is the gradient of a potential energy vs distance graph, this indicates that the structure obtained is at equilibrium, demonstrating successful optimisation of H2.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000039 0.000300 YES
Maximum Displacement 0.000052 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
</pre>

Figure 3.2: Item Table of optimised H2

Moreover, successful optimisation of H2 is indicated by the last structure having the most negative energy and the smallest gradient (Figure 3.3).

[[File:H2 optimisation.jpg|400px|thumb|center|Figure 3.3: Optimisation plots of H2]]

=== Dynamic Image of Optimised H2 ===

<jmol><jmolApplet>
<title>Figure 3.4: Optimised hydrogen</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ZOEYWAISUMLUNG_H2_OPTF_POP.LOG</uploadedFileContents>
<script>frame 1.3</script>
</jmolApplet></jmol>

The optimisation file is linked to [[Media:ZOEYWAISUMLUNG_H2_OPTF_POP.LOG| here]]

=== Vibrational Analysis of Optimised H2 ===

From Figure 3.5 in vibrational analysis, there are 0 modes as expected, and 0 bands in the experimental spectrum (Figure 3.6) of gaseous hydrogen as expected.

[[File:H2 vibrations.jpg ‎|400px|thumb|centre|Figure 3.5: Vibrational Table of optimised H2]]

[[File:H2 spectrum.jpg ‎|400px|thumb|centre|Figure 3.6: Spectrum of optimised H2]]

=== Charge Analysis of Optimised H2 ===

Charge analysis (Figure 3.7) shows the charge on both hydrogen atoms is 0.000. This result is expected because both atoms of the linear bond are the same so there are no expected differences in electronegativity therefore electron density is shared equally between the hydrogen atoms. If a higher basis set is used, a single bond would likely to be displayed.

[[File:H2 charge.jpg ‎|400px|thumb|centre|Figure 2.7: Charge Analysis of optimised H2]]

== Optimisation of S2 ==

=== General Information of Optimised S2 ===

From the 'Summary' table (Figure 4.1), the following general information about the optimisation calculation is obtained: the molecule optimised is sulphur, S2, the calculation method is RB3LYP; the basis set is 6-31G(d,p); the final energy E(RB3LYP) is -796.32599779 a.u.; the RMS gradient is 0.00000905 a.u.; and the point group of S2 is D∞h.

[[File:S2 summary.jpg|400px|thumb|center|Figure 4.1: Summary Table of optimised S2]]

=== Geometric Information of Optimised S2 ===

Optimised bond length: 1.92947 Å ≈ 1.929 Å

=== Verification of Successful Optimisation of S2 ===

The 'Item' table (Figure 4.2) shows that the final set of forces and displacements are converged and that the forces are approximately zero; since force is the gradient of a potential energy vs distance graph, this indicates that the structure obtained is at equilibrium, demonstrating successful optimisation of S2.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.000027 0.001800 YES
RMS Displacement 0.000038 0.001200 YES
</pre>

Figure 4.2: Item Table of optimised S2

Moreover, successful optimisation of S2 is indicated by the last structure having the most negative energy and the smallest gradient (Figure 4.3).

[[File:S2 optimisation.jpg|400px|thumb|center|Figure 4.3: Optimisation plots of S2]]

=== Dynamic Image of Optimised S2 ===

<jmol><jmolApplet>
<title>Figure 4.4: Optimised sulphur</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ZOEYWAISUMLUNG_S2_OPTF_POP.LOG</uploadedFileContents>
<script>frame 1.4</script>
</jmolApplet></jmol>

The optimisation file is linked to [[Media:ZOEYWAISUMLUNG_S2_OPTF_POP.LOG| here]]

=== Vibrational Analysis of Optimised S2 ===

From Figure 4.5 in vibrational analysis, there are 0 modes as expected, and 0 bands in the experimental spectrum (Figure 4.6) of gaseous sulphur as expected.

[[File:S2 vibrations.jpg ‎|400px|thumb|centre|Figure 4.5: Vibrational Table of optimised S2]]

[[File:S2 spectrum.jpg ‎|400px|thumb|centre|Figure 4.6: Spectrum of optimised S2]]

=== Charge Analysis of Optimised S2 ===

Charge analysis (Figure 4.7) shows the charge on both sulphur atoms is 0.000. This result is expected because both atoms of the linear bond are the same so there are no expected differences in electronegativity therefore electron density is shared equally between the sulphur atoms. A single bond instead of a double bond is displayed however this would most likely not be the case if a higher basis set is used for optimisation.

[[File:S2 charge.jpg ‎|400px|thumb|centre|Figure 2.7: Charge Analysis of optimised H2]]

=== Molecular Orbitals of Optimised S2 ===

{| class="wikitable" border="1"
|+ caption
! heading !! heading
|-
| [[File:1s sigma orbital 1.JPG ‎|300px|thumb|centre]]
|| The two 1s AOs overlap constructively to form a non-bonding σ MO. The energy of the MO formed is -88.93663.
|-
| [[File:1s sigma orbital 2.JPG ‎|300px|thumb|centre]] || The two 1s AOs also overlap destructively to form a non-bonding σ* MO. The energy of the MO formed is -88.93661.
|-
| [[File:2s sigma orbital 2.JPG ‎|300px|thumb|centre]]|| The two 2s AOs overlap constructively to form a non-bonding σ MO. The energy of the MO formed is -7.99779.
|-
| [[File:2s sigma orbital 1.JPG ‎|300px|thumb|centre]] || The two 2s AOs also overlap destructively to form a non-bonding σ* MO. The energy of the MO formed is -7.99769.
|-
| [[File:2p pi orbital 1.JPG ‎|300px|thumb|centre]] [[File:2p pi orbital 2.JPG ‎|300px|thumb|centre]] || The 2px and 2py AOs overlap constructively laterally to form two non-bonding π MOs. These two orbitals are degenerate- the energies of the MOs are -5.96349 and -5.94946 respectively.
|-
| [[File:2p pi orbital 3.JPG ‎|300px|thumb|centre]] [[File:2p pi orbital 4.JPG ‎|300px|thumb|centre]] || The 2px and 2py AOs overlap destructively laterally to form two non-bonding π* MOs. These two orbitals are degenerate- the energies of the MOs are -5.96135.
|-
| [[File:2p pi orbital 5.JPG ‎|300px|thumb|centre]] || The 2pz AOs overlap constructively head-on to form one non-bonding σ MO. The energy of the MO is -5.96135.
|-
| [[File:2p pi orbital 6.JPG ‎|300px|thumb|centre]] || The 2pz AOs overlap destructively head-on to form one non-bonding σ * MOs. The energy of the MO is -5.96078 .
|-
| [[File:3s sigma orbital 1.JPG ‎|300px|thumb|centre]] || The two 3s AOs overlap constructively head=on to form a bonding σ MO. The energy of the MO formed is -0.83212.
|-
| [[File:3s sigma orbital 2.JPG ‎|300px|thumb|centre]] || The two 3s AOs also overlap destructively to form an anti-bonding σ* MO. The energy of the MO formed is -0.61535.
|}

Rep:Mod:WSL1819

2018-03-16T17:16:31Z

Wsl1917: /* Vibrational Analysis of Optimised N2 */

== Optimisation of NH3 ==

=== General Information of Optimised NH3 ===

From the 'Summary' table (Figure 1.1), the following general information about the optimisation calculation is obtained: the molecule optimised is ammonia, NH3, the calculation method is RB3LYP; the basis set is 6-31G(d,p); the final energy E(RB3LYP) is -56.44397188 a.u.; the RMS gradient is 0.05399560 a.u.; and the point group of NH3 is C3v.

[[File:Nh3_summary.jpg|400px|thumb|center|Figure 1.1: Summary Table of optimised NH3]]

=== Geometric Information of Optimised NH3 ===

Optimised bond length: 1.01798 Å ≈ 1.018 Å

Optimised bond angle: 105.741 o ≈ 105.7 o

=== Verification of Successful Optimisation of NH3 ===

The 'Item' table (Figure 1.2) shows that the final set of forces and displacements are converged and that the forces are approximately zero; since force is the gradient of a potential energy vs distance graph, this indicates that the structure obtained is at equilibrium, demonstrating successful optimisation of NH3.

<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>

Figure 1.2: Item Table of optimised NH3

Moreover, successful optimisation of NH3 is indicated by the last structure having the most negative energy and the smallest gradient (Figure 1.3).

[[File:Nh3 optimisation.jpg|400px|thumb|center|Figure 1.3: Optimisation plots of NH3]]

=== Dynamic Image of Optimised NH3 ===

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ZOEYWAISUMLUNG_NH3_OPTF_POP.LOG</uploadedFileContents>
<script>frame 1.7</script>
</jmolApplet></jmol>
Figure 1.4: A 3D jmol file of optimised NH3

The optimisation file is linked to [[Media:ZOEYWAISUMLUNG_NH3_OPTF_POP.LOG| here]]

=== Vibrational Analysis of Optimised NH3 ===

From Figure 1.5 in vibrational analysis, there are 6 modes as expected, modes 2 and 3 and modes 5 and 6 are degenerate as they have the same frequency of 1693.95 cm-1 and 3589.82 cm-1 respectively; modes 1, 2 and 3 are "bending" vibrations and modes 4, 5 and 6 are "bond stretch" vibrations; mode 4 is highly symmetric ; mode 1 is the "umbrella" mode and 2 bands in the experimental spectrum (Figure 1.6) of gaseous ammonia as expected.

2 bands in the experimental spectrum are expected because modes 4, 5 and 6 have very small intensities due to small rate of change of dipole moment and because modes 2 and 3, though with significant intensities, are degenerate.

[[File:Nh3 vibrations 1.jpg ‎|400px|thumb|centre|Figure 1.5: Vibrational Table of optimised NH3]]

[[File:Nh3_spectrum.jpg ‎|400px|thumb|centre|Figure 1.6: Spectrum of optimised NH3]]

=== Charge Analysis of Optimised NH3 ===

Charge analysis (Figure 1.7) shows the charge on the nitrogen atom is -1.125 whilst that of the hydrogen atoms is +0.375. This result where nitrogen has a negative charge with a larger magnitude and hydrogen has a positive charge with a smaller magnitude is expected, since nitrogen is more electronegative than hydrogen, nitrogen should withdraw more electron density from each of the three N-H bonds.

[[File:Nh3_charge.jpg ‎|400px|thumb|centre|Figure 1.7: Charge Analysis of optimised NH3]]

== Optimisation of N2 ==

=== General Information of Optimised N2 ===

From the 'Summary' table (Figure 2.1), the following general information about the optimisation calculation is obtained: the molecule optimised is nitrogen, N2, the calculation method is RB3LYP; the basis set is 6-31G(d,p); the final energy E(RB3LYP) is -109.52412868 a.u.; the RMS gradient is 0.00000011 a.u.; and the point group of N2 is D∞h.

[[File:N2 summary 2.jpg|400px|thumb|center|Figure 2.1: Summary Table of optimised N2]]

=== Geometric Information of Optimised N2 ===

Optimised bond length: 1.10550 Å ≈ 1.106 Å

=== Verification of Successful Optimisation of N2 ===

The 'Item' table (Figure 2.2) shows that the final set of forces and displacements are converged and that the forces are zero; since force is the gradient of a potential energy vs distance graph, this indicates that the structure obtained is at equilibrium, demonstrating successful optimisation of N2.

<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 0.000000 0.001200 YES
</pre>

Figure 2.2: Item Table of optimised N2

Moreover, successful optimisation of N2 is indicated by the last structure having the most negative energy and the smallest gradient (Figure 2.3).

[[File:N2 optimisation.jpg|400px|thumb|center|Figure 2.3: Optimisation plots of N2]]

=== Dynamic Image of Optimised N2 ===

<jmol><jmolApplet>
<title>Figure 2.4: Optimised nitrogen</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ZOEYWAISUMLUNG_N2_OPTF_POP.LOG</uploadedFileContents>
<script>frame 1.4</script>
</jmolApplet></jmol>

The optimisation file is linked to [[Media:ZOEYWAISUMLUNG_N2_OPTF_POP.LOG| here]]

=== Vibrational Analysis of Optimised N2 ===

From Figure 2.5 in vibrational analysis, there are 0 modes as expected, and 0 bands in the experimental spectrum (Figure 2.6) of gaseous nitrogen as expected.

No bands are expected to be seen in the experimental spectrum because there is no dipole moment in a linear molecule.

[[File:N2 vibrations.jpg ‎|400px|thumb|centre|Figure 2.5: Vibrational Table of optimised N2]]

[[File:N2 spectrum.jpg ‎|400px|thumb|centre|Figure 2.6: Spectrum of optimised N2]]

=== Charge Analysis of Optimised N2 ===

Charge analysis (Figure 2.7) shows the charge on both nitrogen atoms is 0.000. This result is expected because both atoms of the lienar bond are the same so there are no expected differences in electronegativity therefore electron density is shared equally between the nitrogen atoms. Note that the atoms are colored by charge, a charge of 0.000 is represented by the color black and the numbers are written in black therefore they cannot be seen here.

[[File:N2 charge.jpg ‎|400px|thumb|centre|Figure 2.7: Charge Analysis of optimised N2]]

== Optimisation of H2 ==

=== General Information of Optimised H2 ===

From the 'Summary' table (Figure 3.1), the following general information about the optimisation calculation is obtained: the molecule optimised is hydrogen, H2, the calculation method is RB3LYP; the basis set is 6-31G(d,p); the final energy E(RB3LYP) is -1.17853936 a.u.; the RMS gradient is 0.00002276 a.u.; and the point group of H2 is D∞h.

[[File:H2 summary.jpg|400px|thumb|center|Figure 3.1: Summary Table of optimised H2]]

=== Geometric Information of Optimised H2 ===

Optimised bond length: 0.74274 Å ≈ 0.7427 Å

=== Verification of Successful Optimisation of H2 ===

The 'Item' table (Figure 3.2) shows that the final set of forces and displacements are converged and that the forces are zero; since force is the gradient of a potential energy vs distance graph, this indicates that the structure obtained is at equilibrium, demonstrating successful optimisation of H2.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000039 0.000300 YES
Maximum Displacement 0.000052 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
</pre>

Figure 3.2: Item Table of optimised H2

Moreover, successful optimisation of H2 is indicated by the last structure having the most negative energy and the smallest gradient (Figure 3.3).

[[File:H2 optimisation.jpg|400px|thumb|center|Figure 3.3: Optimisation plots of H2]]

=== Dynamic Image of Optimised H2 ===

<jmol><jmolApplet>
<title>Figure 3.4: Optimised hydrogen</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ZOEYWAISUMLUNG_H2_OPTF_POP.LOG</uploadedFileContents>
<script>frame 1.3</script>
</jmolApplet></jmol>

The optimisation file is linked to [[Media:ZOEYWAISUMLUNG_H2_OPTF_POP.LOG| here]]

=== Vibrational Analysis of Optimised H2 ===

From Figure 3.5 in vibrational analysis, there are 0 modes as expected, and 0 bands in the experimental spectrum (Figure 3.6) of gaseous hydrogen as expected.

[[File:H2 vibrations.jpg ‎|400px|thumb|centre|Figure 3.5: Vibrational Table of optimised H2]]

[[File:H2 spectrum.jpg ‎|400px|thumb|centre|Figure 3.6: Spectrum of optimised H2]]

=== Charge Analysis of Optimised H2 ===

Charge analysis (Figure 3.7) shows the charge on both hydrogen atoms is 0.000. This result is expected because both atoms of the linear bond are the same so there are no expected differences in electronegativity therefore electron density is shared equally between the hydrogen atoms. If a higher basis set is used, a single bond would likely to be displayed.

[[File:H2 charge.jpg ‎|400px|thumb|centre|Figure 2.7: Charge Analysis of optimised H2]]

== Optimisation of S2 ==

=== General Information of Optimised S2 ===

From the 'Summary' table (Figure 4.1), the following general information about the optimisation calculation is obtained: the molecule optimised is sulphur, S2, the calculation method is RB3LYP; the basis set is 6-31G(d,p); the final energy E(RB3LYP) is -796.32599779 a.u.; the RMS gradient is 0.00000905 a.u.; and the point group of S2 is D∞h.

[[File:S2 summary.jpg|400px|thumb|center|Figure 4.1: Summary Table of optimised S2]]

=== Geometric Information of Optimised S2 ===

Optimised bond length: 1.92947 Å ≈ 1.929 Å

=== Verification of Successful Optimisation of S2 ===

The 'Item' table (Figure 4.2) shows that the final set of forces and displacements are converged and that the forces are approximately zero; since force is the gradient of a potential energy vs distance graph, this indicates that the structure obtained is at equilibrium, demonstrating successful optimisation of S2.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.000027 0.001800 YES
RMS Displacement 0.000038 0.001200 YES
</pre>

Figure 4.2: Item Table of optimised S2

Moreover, successful optimisation of S2 is indicated by the last structure having the most negative energy and the smallest gradient (Figure 4.3).

[[File:S2 optimisation.jpg|400px|thumb|center|Figure 4.3: Optimisation plots of S2]]

=== Dynamic Image of Optimised S2 ===

<jmol><jmolApplet>
<title>Figure 4.4: Optimised sulphur</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ZOEYWAISUMLUNG_S2_OPTF_POP.LOG</uploadedFileContents>
<script>frame 1.4</script>
</jmolApplet></jmol>

The optimisation file is linked to [[Media:ZOEYWAISUMLUNG_S2_OPTF_POP.LOG| here]]

=== Vibrational Analysis of Optimised S2 ===

From Figure 4.5 in vibrational analysis, there are 0 modes as expected, and 0 bands in the experimental spectrum (Figure 4.6) of gaseous sulphur as expected.

[[File:S2 vibrations.jpg ‎|400px|thumb|centre|Figure 4.5: Vibrational Table of optimised S2]]

[[File:S2 spectrum.jpg ‎|400px|thumb|centre|Figure 4.6: Spectrum of optimised S2]]

=== Charge Analysis of Optimised S2 ===

Charge analysis (Figure 4.7) shows the charge on both sulphur atoms is 0.000. This result is expected because both atoms of the linear bond are the same so there are no expected differences in electronegativity therefore electron density is shared equally between the sulphur atoms. A single bond instead of a double bond is displayed however this would most likely not be the case if a higher basis set is used for optimisation.

[[File:S2 charge.jpg ‎|400px|thumb|centre|Figure 2.7: Charge Analysis of optimised H2]]

=== Molecular Orbitals of Optimised S2 ===

{| class="wikitable" border="1"
|+ caption
! heading !! heading
|-
| [[File:1s sigma orbital 1.JPG ‎|300px|thumb|centre]]
|| The two 1s AOs overlap constructively to form a non-bonding σ MO. The energy of the MO formed is -88.93663.
|-
| [[File:1s sigma orbital 2.JPG ‎|300px|thumb|centre]] || The two 1s AOs also overlap destructively to form a non-bonding σ* MO. The energy of the MO formed is -88.93661.
|-
| [[File:2s sigma orbital 2.JPG ‎|300px|thumb|centre]]|| The two 2s AOs overlap constructively to form a non-bonding σ MO. The energy of the MO formed is -7.99779.
|-
| [[File:2s sigma orbital 1.JPG ‎|300px|thumb|centre]] || The two 2s AOs also overlap destructively to form a non-bonding σ* MO. The energy of the MO formed is -7.99769.
|-
| [[File:2p pi orbital 1.JPG ‎|300px|thumb|centre]] [[File:2p pi orbital 2.JPG ‎|300px|thumb|centre]] || The 2px and 2py AOs overlap constructively laterally to form two non-bonding π MOs. These two orbitals are degenerate- the energies of the MOs are -5.96349 and -5.94946 respectively.
|-
| [[File:2p pi orbital 3.JPG ‎|300px|thumb|centre]] [[File:2p pi orbital 4.JPG ‎|300px|thumb|centre]] || The 2px and 2py AOs overlap destructively laterally to form two non-bonding π* MOs. These two orbitals are degenerate- the energies of the MOs are -5.96135.
|-
| [[File:2p pi orbital 5.JPG ‎|300px|thumb|centre]] || The 2pz AOs overlap constructively head-on to form one non-bonding σ MO. The energy of the MO is -5.96135.
|-
| [[File:2p pi orbital 6.JPG ‎|300px|thumb|centre]] || The 2pz AOs overlap destructively head-on to form one non-bonding σ * MOs. The energy of the MO is -5.96078 .
|-
| [[File:3s sigma orbital 1.JPG ‎|300px|thumb|centre]] || The two 3s AOs overlap constructively head=on to form a bonding σ MO. The energy of the MO formed is -0.83212.
|-
| [[File:3s sigma orbital 2.JPG ‎|300px|thumb|centre]] || The two 3s AOs also overlap destructively to form an anti-bonding σ* MO. The energy of the MO formed is -0.61535.
|}

Rep:Mod:WSL1819

2018-03-16T17:15:47Z

Wsl1917: /* Optimisation of NH3 */

== Optimisation of NH3 ==

=== General Information of Optimised NH3 ===

From the 'Summary' table (Figure 1.1), the following general information about the optimisation calculation is obtained: the molecule optimised is ammonia, NH3, the calculation method is RB3LYP; the basis set is 6-31G(d,p); the final energy E(RB3LYP) is -56.44397188 a.u.; the RMS gradient is 0.05399560 a.u.; and the point group of NH3 is C3v.

[[File:Nh3_summary.jpg|400px|thumb|center|Figure 1.1: Summary Table of optimised NH3]]

=== Geometric Information of Optimised NH3 ===

Optimised bond length: 1.01798 Å ≈ 1.018 Å

Optimised bond angle: 105.741 o ≈ 105.7 o

=== Verification of Successful Optimisation of NH3 ===

The 'Item' table (Figure 1.2) shows that the final set of forces and displacements are converged and that the forces are approximately zero; since force is the gradient of a potential energy vs distance graph, this indicates that the structure obtained is at equilibrium, demonstrating successful optimisation of NH3.

<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>

Figure 1.2: Item Table of optimised NH3

Moreover, successful optimisation of NH3 is indicated by the last structure having the most negative energy and the smallest gradient (Figure 1.3).

[[File:Nh3 optimisation.jpg|400px|thumb|center|Figure 1.3: Optimisation plots of NH3]]

=== Dynamic Image of Optimised NH3 ===

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ZOEYWAISUMLUNG_NH3_OPTF_POP.LOG</uploadedFileContents>
<script>frame 1.7</script>
</jmolApplet></jmol>
Figure 1.4: A 3D jmol file of optimised NH3

The optimisation file is linked to [[Media:ZOEYWAISUMLUNG_NH3_OPTF_POP.LOG| here]]

=== Vibrational Analysis of Optimised NH3 ===

From Figure 1.5 in vibrational analysis, there are 6 modes as expected, modes 2 and 3 and modes 5 and 6 are degenerate as they have the same frequency of 1693.95 cm-1 and 3589.82 cm-1 respectively; modes 1, 2 and 3 are "bending" vibrations and modes 4, 5 and 6 are "bond stretch" vibrations; mode 4 is highly symmetric ; mode 1 is the "umbrella" mode and 2 bands in the experimental spectrum (Figure 1.6) of gaseous ammonia as expected.

2 bands in the experimental spectrum are expected because modes 4, 5 and 6 have very small intensities due to small rate of change of dipole moment and because modes 2 and 3, though with significant intensities, are degenerate.

[[File:Nh3 vibrations 1.jpg ‎|400px|thumb|centre|Figure 1.5: Vibrational Table of optimised NH3]]

[[File:Nh3_spectrum.jpg ‎|400px|thumb|centre|Figure 1.6: Spectrum of optimised NH3]]

=== Charge Analysis of Optimised NH3 ===

Charge analysis (Figure 1.7) shows the charge on the nitrogen atom is -1.125 whilst that of the hydrogen atoms is +0.375. This result where nitrogen has a negative charge with a larger magnitude and hydrogen has a positive charge with a smaller magnitude is expected, since nitrogen is more electronegative than hydrogen, nitrogen should withdraw more electron density from each of the three N-H bonds.

[[File:Nh3_charge.jpg ‎|400px|thumb|centre|Figure 1.7: Charge Analysis of optimised NH3]]

== Optimisation of N2 ==

=== General Information of Optimised N2 ===

From the 'Summary' table (Figure 2.1), the following general information about the optimisation calculation is obtained: the molecule optimised is nitrogen, N2, the calculation method is RB3LYP; the basis set is 6-31G(d,p); the final energy E(RB3LYP) is -109.52412868 a.u.; the RMS gradient is 0.00000011 a.u.; and the point group of N2 is D∞h.

[[File:N2 summary 2.jpg|400px|thumb|center|Figure 2.1: Summary Table of optimised N2]]

=== Geometric Information of Optimised N2 ===

Optimised bond length: 1.10550 Å ≈ 1.106 Å

=== Verification of Successful Optimisation of N2 ===

The 'Item' table (Figure 2.2) shows that the final set of forces and displacements are converged and that the forces are zero; since force is the gradient of a potential energy vs distance graph, this indicates that the structure obtained is at equilibrium, demonstrating successful optimisation of N2.

<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 0.000000 0.001200 YES
</pre>

Figure 2.2: Item Table of optimised N2

Moreover, successful optimisation of N2 is indicated by the last structure having the most negative energy and the smallest gradient (Figure 2.3).

[[File:N2 optimisation.jpg|400px|thumb|center|Figure 2.3: Optimisation plots of N2]]

=== Dynamic Image of Optimised N2 ===

<jmol><jmolApplet>
<title>Figure 2.4: Optimised nitrogen</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ZOEYWAISUMLUNG_N2_OPTF_POP.LOG</uploadedFileContents>
<script>frame 1.4</script>
</jmolApplet></jmol>

The optimisation file is linked to [[Media:ZOEYWAISUMLUNG_N2_OPTF_POP.LOG| here]]

=== Vibrational Analysis of Optimised N2 ===

From Figure 2.5 in vibrational analysis, there are 0 modes as expected, and 0 bands in the experimental spectrum (Figure 2.6) of gaseous nitrogen as expected.

[[File:N2 vibrations.jpg ‎|400px|thumb|centre|Figure 2.5: Vibrational Table of optimised N2]]

[[File:N2 spectrum.jpg ‎|400px|thumb|centre|Figure 2.6: Spectrum of optimised N2]]

=== Charge Analysis of Optimised N2 ===

Charge analysis (Figure 2.7) shows the charge on both nitrogen atoms is 0.000. This result is expected because both atoms of the lienar bond are the same so there are no expected differences in electronegativity therefore electron density is shared equally between the nitrogen atoms. Note that the atoms are colored by charge, a charge of 0.000 is represented by the color black and the numbers are written in black therefore they cannot be seen here.

[[File:N2 charge.jpg ‎|400px|thumb|centre|Figure 2.7: Charge Analysis of optimised N2]]

== Optimisation of H2 ==

=== General Information of Optimised H2 ===

From the 'Summary' table (Figure 3.1), the following general information about the optimisation calculation is obtained: the molecule optimised is hydrogen, H2, the calculation method is RB3LYP; the basis set is 6-31G(d,p); the final energy E(RB3LYP) is -1.17853936 a.u.; the RMS gradient is 0.00002276 a.u.; and the point group of H2 is D∞h.

[[File:H2 summary.jpg|400px|thumb|center|Figure 3.1: Summary Table of optimised H2]]

=== Geometric Information of Optimised H2 ===

Optimised bond length: 0.74274 Å ≈ 0.7427 Å

=== Verification of Successful Optimisation of H2 ===

The 'Item' table (Figure 3.2) shows that the final set of forces and displacements are converged and that the forces are zero; since force is the gradient of a potential energy vs distance graph, this indicates that the structure obtained is at equilibrium, demonstrating successful optimisation of H2.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000039 0.000300 YES
Maximum Displacement 0.000052 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
</pre>

Figure 3.2: Item Table of optimised H2

Moreover, successful optimisation of H2 is indicated by the last structure having the most negative energy and the smallest gradient (Figure 3.3).

[[File:H2 optimisation.jpg|400px|thumb|center|Figure 3.3: Optimisation plots of H2]]

=== Dynamic Image of Optimised H2 ===

<jmol><jmolApplet>
<title>Figure 3.4: Optimised hydrogen</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ZOEYWAISUMLUNG_H2_OPTF_POP.LOG</uploadedFileContents>
<script>frame 1.3</script>
</jmolApplet></jmol>

The optimisation file is linked to [[Media:ZOEYWAISUMLUNG_H2_OPTF_POP.LOG| here]]

=== Vibrational Analysis of Optimised H2 ===

From Figure 3.5 in vibrational analysis, there are 0 modes as expected, and 0 bands in the experimental spectrum (Figure 3.6) of gaseous hydrogen as expected.

[[File:H2 vibrations.jpg ‎|400px|thumb|centre|Figure 3.5: Vibrational Table of optimised H2]]

[[File:H2 spectrum.jpg ‎|400px|thumb|centre|Figure 3.6: Spectrum of optimised H2]]

=== Charge Analysis of Optimised H2 ===

Charge analysis (Figure 3.7) shows the charge on both hydrogen atoms is 0.000. This result is expected because both atoms of the linear bond are the same so there are no expected differences in electronegativity therefore electron density is shared equally between the hydrogen atoms. If a higher basis set is used, a single bond would likely to be displayed.

[[File:H2 charge.jpg ‎|400px|thumb|centre|Figure 2.7: Charge Analysis of optimised H2]]

== Optimisation of S2 ==

=== General Information of Optimised S2 ===

From the 'Summary' table (Figure 4.1), the following general information about the optimisation calculation is obtained: the molecule optimised is sulphur, S2, the calculation method is RB3LYP; the basis set is 6-31G(d,p); the final energy E(RB3LYP) is -796.32599779 a.u.; the RMS gradient is 0.00000905 a.u.; and the point group of S2 is D∞h.

[[File:S2 summary.jpg|400px|thumb|center|Figure 4.1: Summary Table of optimised S2]]

=== Geometric Information of Optimised S2 ===

Optimised bond length: 1.92947 Å ≈ 1.929 Å

=== Verification of Successful Optimisation of S2 ===

The 'Item' table (Figure 4.2) shows that the final set of forces and displacements are converged and that the forces are approximately zero; since force is the gradient of a potential energy vs distance graph, this indicates that the structure obtained is at equilibrium, demonstrating successful optimisation of S2.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.000027 0.001800 YES
RMS Displacement 0.000038 0.001200 YES
</pre>

Figure 4.2: Item Table of optimised S2

Moreover, successful optimisation of S2 is indicated by the last structure having the most negative energy and the smallest gradient (Figure 4.3).

[[File:S2 optimisation.jpg|400px|thumb|center|Figure 4.3: Optimisation plots of S2]]

=== Dynamic Image of Optimised S2 ===

<jmol><jmolApplet>
<title>Figure 4.4: Optimised sulphur</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ZOEYWAISUMLUNG_S2_OPTF_POP.LOG</uploadedFileContents>
<script>frame 1.4</script>
</jmolApplet></jmol>

The optimisation file is linked to [[Media:ZOEYWAISUMLUNG_S2_OPTF_POP.LOG| here]]

=== Vibrational Analysis of Optimised S2 ===

From Figure 4.5 in vibrational analysis, there are 0 modes as expected, and 0 bands in the experimental spectrum (Figure 4.6) of gaseous sulphur as expected.

[[File:S2 vibrations.jpg ‎|400px|thumb|centre|Figure 4.5: Vibrational Table of optimised S2]]

[[File:S2 spectrum.jpg ‎|400px|thumb|centre|Figure 4.6: Spectrum of optimised S2]]

=== Charge Analysis of Optimised S2 ===

Charge analysis (Figure 4.7) shows the charge on both sulphur atoms is 0.000. This result is expected because both atoms of the linear bond are the same so there are no expected differences in electronegativity therefore electron density is shared equally between the sulphur atoms. A single bond instead of a double bond is displayed however this would most likely not be the case if a higher basis set is used for optimisation.

[[File:S2 charge.jpg ‎|400px|thumb|centre|Figure 2.7: Charge Analysis of optimised H2]]

=== Molecular Orbitals of Optimised S2 ===

{| class="wikitable" border="1"
|+ caption
! heading !! heading
|-
| [[File:1s sigma orbital 1.JPG ‎|300px|thumb|centre]]
|| The two 1s AOs overlap constructively to form a non-bonding σ MO. The energy of the MO formed is -88.93663.
|-
| [[File:1s sigma orbital 2.JPG ‎|300px|thumb|centre]] || The two 1s AOs also overlap destructively to form a non-bonding σ* MO. The energy of the MO formed is -88.93661.
|-
| [[File:2s sigma orbital 2.JPG ‎|300px|thumb|centre]]|| The two 2s AOs overlap constructively to form a non-bonding σ MO. The energy of the MO formed is -7.99779.
|-
| [[File:2s sigma orbital 1.JPG ‎|300px|thumb|centre]] || The two 2s AOs also overlap destructively to form a non-bonding σ* MO. The energy of the MO formed is -7.99769.
|-
| [[File:2p pi orbital 1.JPG ‎|300px|thumb|centre]] [[File:2p pi orbital 2.JPG ‎|300px|thumb|centre]] || The 2px and 2py AOs overlap constructively laterally to form two non-bonding π MOs. These two orbitals are degenerate- the energies of the MOs are -5.96349 and -5.94946 respectively.
|-
| [[File:2p pi orbital 3.JPG ‎|300px|thumb|centre]] [[File:2p pi orbital 4.JPG ‎|300px|thumb|centre]] || The 2px and 2py AOs overlap destructively laterally to form two non-bonding π* MOs. These two orbitals are degenerate- the energies of the MOs are -5.96135.
|-
| [[File:2p pi orbital 5.JPG ‎|300px|thumb|centre]] || The 2pz AOs overlap constructively head-on to form one non-bonding σ MO. The energy of the MO is -5.96135.
|-
| [[File:2p pi orbital 6.JPG ‎|300px|thumb|centre]] || The 2pz AOs overlap destructively head-on to form one non-bonding σ * MOs. The energy of the MO is -5.96078 .
|-
| [[File:3s sigma orbital 1.JPG ‎|300px|thumb|centre]] || The two 3s AOs overlap constructively head=on to form a bonding σ MO. The energy of the MO formed is -0.83212.
|-
| [[File:3s sigma orbital 2.JPG ‎|300px|thumb|centre]] || The two 3s AOs also overlap destructively to form an anti-bonding σ* MO. The energy of the MO formed is -0.61535.
|}

File:2p pi orbital 6.JPG

2018-03-16T11:53:19Z

Wsl1917:

File:2p pi orbital 5.JPG

2018-03-16T11:53:09Z

Wsl1917:

File:2p pi orbital 4.JPG

2018-03-16T11:52:38Z

Wsl1917:

File:2p pi orbital 3.JPG

2018-03-16T11:52:12Z

Wsl1917:

Rep:Mod:WSL1819

2018-03-16T11:51:56Z

Wsl1917: /* Molecular Orbitals of Optimised S2 */

== Optimisation of NH3 ==

=== General Information of Optimised NH3 ===

From the 'Summary' table (Figure 1.1), the following general information about the optimisation calculation is obtained: the molecule optimised is ammonia, NH3, the calculation method is RB3LYP; the basis set is 6-31G(d,p); the final energy E(RB3LYP) is -56.44397188 a.u.; the RMS gradient is 0.05399560 a.u.; and the point group of NH3 is C3v.

[[File:Nh3_summary.jpg|400px|thumb|center|Figure 1.1: Summary Table of optimised NH3]]

=== Geometric Information of Optimised NH3 ===

Optimised bond length: 1.01798 Å ≈ 1.018 Å

Optimised bond angle: 105.741 o ≈ 105.7 o

=== Verification of Successful Optimisation of NH3 ===

The 'Item' table (Figure 1.2) shows that the final set of forces and displacements are converged and that the forces are approximately zero; since force is the gradient of a potential energy vs distance graph, this indicates that the structure obtained is at equilibrium, demonstrating successful optimisation of NH3.

<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>

Figure 1.2: Item Table of optimised NH3

Moreover, successful optimisation of NH3 is indicated by the last structure having the most negative energy and the smallest gradient (Figure 1.3).

[[File:Nh3 optimisation.jpg|400px|thumb|center|Figure 1.3: Optimisation plots of NH3]]

=== Dynamic Image of Optimised NH3 ===

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ZOEYWAISUMLUNG_NH3_OPTF_POP.LOG</uploadedFileContents>
<script>frame 1.7</script>
</jmolApplet></jmol>
Figure 1.4: A 3D jmol file of optimised NH3

The optimisation file is linked to [[Media:ZOEYWAISUMLUNG_NH3_OPTF_POP.LOG| here]]

=== Vibrational Analysis of Optimised NH3 ===

From Figure 1.5 in vibrational analysis, there are 6 modes as expected, modes 2 and 3 and modes 5 and 6 are degenerate as they have the same frequency of 1693.95 cm-1 and 3589.82 cm-1 respectively; modes 1, 2 and 3 are "bending" vibrations and modes 4, 5 and 6 are "bond stretch" vibrations; mode 4 is highly symmetric ; mode 1 is the "umbrella" mode and 2 bands in the experimental spectrum (Figure 1.6) of gaseous ammonia as expected.

[[File:Nh3 vibrations 1.jpg ‎|400px|thumb|centre|Figure 1.5: Vibrational Table of optimised NH3]]

[[File:Nh3_spectrum.jpg ‎|400px|thumb|centre|Figure 1.6: Spectrum of optimised NH3]]

=== Charge Analysis of Optimised NH3 ===

Charge analysis (Figure 1.7) shows the charge on the nitrogen atom is -1.125 whilst that of the hydrogen atoms is +0.375. This result where nitrogen has a negative charge with a larger magnitude and hydrogen has a positive charge with a smaller magnitude is expected, since nitrogen is more electronegative than hydrogen, nitrogen should withdraw more electron density from each of the three N-H bonds.

[[File:Nh3_charge.jpg ‎|400px|thumb|centre|Figure 1.7: Charge Analysis of optimised NH3]]

== Optimisation of N2 ==

=== General Information of Optimised N2 ===

From the 'Summary' table (Figure 2.1), the following general information about the optimisation calculation is obtained: the molecule optimised is nitrogen, N2, the calculation method is RB3LYP; the basis set is 6-31G(d,p); the final energy E(RB3LYP) is -109.52412868 a.u.; the RMS gradient is 0.00000011 a.u.; and the point group of N2 is D∞h.

[[File:N2 summary 2.jpg|400px|thumb|center|Figure 2.1: Summary Table of optimised N2]]

=== Geometric Information of Optimised N2 ===

Optimised bond length: 1.10550 Å ≈ 1.106 Å

=== Verification of Successful Optimisation of N2 ===

The 'Item' table (Figure 2.2) shows that the final set of forces and displacements are converged and that the forces are zero; since force is the gradient of a potential energy vs distance graph, this indicates that the structure obtained is at equilibrium, demonstrating successful optimisation of N2.

<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 0.000000 0.001200 YES
</pre>

Figure 2.2: Item Table of optimised N2

Moreover, successful optimisation of N2 is indicated by the last structure having the most negative energy and the smallest gradient (Figure 2.3).

[[File:N2 optimisation.jpg|400px|thumb|center|Figure 2.3: Optimisation plots of N2]]

=== Dynamic Image of Optimised N2 ===

<jmol><jmolApplet>
<title>Figure 2.4: Optimised nitrogen</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ZOEYWAISUMLUNG_N2_OPTF_POP.LOG</uploadedFileContents>
<script>frame 1.4</script>
</jmolApplet></jmol>

The optimisation file is linked to [[Media:ZOEYWAISUMLUNG_N2_OPTF_POP.LOG| here]]

=== Vibrational Analysis of Optimised N2 ===

From Figure 2.5 in vibrational analysis, there are 0 modes as expected, and 0 bands in the experimental spectrum (Figure 2.6) of gaseous nitrogen as expected.

[[File:N2 vibrations.jpg ‎|400px|thumb|centre|Figure 2.5: Vibrational Table of optimised N2]]

[[File:N2 spectrum.jpg ‎|400px|thumb|centre|Figure 2.6: Spectrum of optimised N2]]

=== Charge Analysis of Optimised N2 ===

Charge analysis (Figure 2.7) shows the charge on both nitrogen atoms is 0.000. This result is expected because both atoms of the lienar bond are the same so there are no expected differences in electronegativity therefore electron density is shared equally between the nitrogen atoms. Note that the atoms are colored by charge, a charge of 0.000 is represented by the color black and the numbers are written in black therefore they cannot be seen here.

[[File:N2 charge.jpg ‎|400px|thumb|centre|Figure 2.7: Charge Analysis of optimised N2]]

== Optimisation of H2 ==

=== General Information of Optimised H2 ===

From the 'Summary' table (Figure 3.1), the following general information about the optimisation calculation is obtained: the molecule optimised is hydrogen, H2, the calculation method is RB3LYP; the basis set is 6-31G(d,p); the final energy E(RB3LYP) is -1.17853936 a.u.; the RMS gradient is 0.00002276 a.u.; and the point group of H2 is D∞h.

[[File:H2 summary.jpg|400px|thumb|center|Figure 3.1: Summary Table of optimised H2]]

=== Geometric Information of Optimised H2 ===

Optimised bond length: 0.74274 Å ≈ 0.7427 Å

=== Verification of Successful Optimisation of H2 ===

The 'Item' table (Figure 3.2) shows that the final set of forces and displacements are converged and that the forces are zero; since force is the gradient of a potential energy vs distance graph, this indicates that the structure obtained is at equilibrium, demonstrating successful optimisation of H2.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000039 0.000300 YES
Maximum Displacement 0.000052 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
</pre>

Figure 3.2: Item Table of optimised H2

Moreover, successful optimisation of H2 is indicated by the last structure having the most negative energy and the smallest gradient (Figure 3.3).

[[File:H2 optimisation.jpg|400px|thumb|center|Figure 3.3: Optimisation plots of H2]]

=== Dynamic Image of Optimised H2 ===

<jmol><jmolApplet>
<title>Figure 3.4: Optimised hydrogen</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ZOEYWAISUMLUNG_H2_OPTF_POP.LOG</uploadedFileContents>
<script>frame 1.3</script>
</jmolApplet></jmol>

The optimisation file is linked to [[Media:ZOEYWAISUMLUNG_H2_OPTF_POP.LOG| here]]

=== Vibrational Analysis of Optimised H2 ===

From Figure 3.5 in vibrational analysis, there are 0 modes as expected, and 0 bands in the experimental spectrum (Figure 3.6) of gaseous hydrogen as expected.

[[File:H2 vibrations.jpg ‎|400px|thumb|centre|Figure 3.5: Vibrational Table of optimised H2]]

[[File:H2 spectrum.jpg ‎|400px|thumb|centre|Figure 3.6: Spectrum of optimised H2]]

=== Charge Analysis of Optimised H2 ===

Charge analysis (Figure 3.7) shows the charge on both hydrogen atoms is 0.000. This result is expected because both atoms of the linear bond are the same so there are no expected differences in electronegativity therefore electron density is shared equally between the hydrogen atoms. If a higher basis set is used, a single bond would likely to be displayed.

[[File:H2 charge.jpg ‎|400px|thumb|centre|Figure 2.7: Charge Analysis of optimised H2]]

== Optimisation of S2 ==

=== General Information of Optimised S2 ===

From the 'Summary' table (Figure 4.1), the following general information about the optimisation calculation is obtained: the molecule optimised is sulphur, S2, the calculation method is RB3LYP; the basis set is 6-31G(d,p); the final energy E(RB3LYP) is -796.32599779 a.u.; the RMS gradient is 0.00000905 a.u.; and the point group of S2 is D∞h.

[[File:S2 summary.jpg|400px|thumb|center|Figure 4.1: Summary Table of optimised S2]]

=== Geometric Information of Optimised S2 ===

Optimised bond length: 1.92947 Å ≈ 1.929 Å

=== Verification of Successful Optimisation of S2 ===

The 'Item' table (Figure 4.2) shows that the final set of forces and displacements are converged and that the forces are approximately zero; since force is the gradient of a potential energy vs distance graph, this indicates that the structure obtained is at equilibrium, demonstrating successful optimisation of S2.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.000027 0.001800 YES
RMS Displacement 0.000038 0.001200 YES
</pre>

Figure 4.2: Item Table of optimised S2

Moreover, successful optimisation of S2 is indicated by the last structure having the most negative energy and the smallest gradient (Figure 4.3).

[[File:S2 optimisation.jpg|400px|thumb|center|Figure 4.3: Optimisation plots of S2]]

=== Dynamic Image of Optimised S2 ===

<jmol><jmolApplet>
<title>Figure 4.4: Optimised sulphur</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ZOEYWAISUMLUNG_S2_OPTF_POP.LOG</uploadedFileContents>
<script>frame 1.4</script>
</jmolApplet></jmol>

The optimisation file is linked to [[Media:ZOEYWAISUMLUNG_S2_OPTF_POP.LOG| here]]

=== Vibrational Analysis of Optimised S2 ===

From Figure 4.5 in vibrational analysis, there are 0 modes as expected, and 0 bands in the experimental spectrum (Figure 4.6) of gaseous sulphur as expected.

[[File:S2 vibrations.jpg ‎|400px|thumb|centre|Figure 4.5: Vibrational Table of optimised S2]]

[[File:S2 spectrum.jpg ‎|400px|thumb|centre|Figure 4.6: Spectrum of optimised S2]]

=== Charge Analysis of Optimised S2 ===

Charge analysis (Figure 4.7) shows the charge on both sulphur atoms is 0.000. This result is expected because both atoms of the linear bond are the same so there are no expected differences in electronegativity therefore electron density is shared equally between the sulphur atoms. A single bond instead of a double bond is displayed however this would most likely not be the case if a higher basis set is used for optimisation.

[[File:S2 charge.jpg ‎|400px|thumb|centre|Figure 2.7: Charge Analysis of optimised H2]]

=== Molecular Orbitals of Optimised S2 ===

{| class="wikitable" border="1"
|+ caption
! heading !! heading
|-
| [[File:1s sigma orbital 1.JPG ‎|300px|thumb|centre]]
|| The two 1s AOs overlap constructively to form a non-bonding σ MO. The energy of the MO formed is -88.93663.
|-
| [[File:1s sigma orbital 2.JPG ‎|300px|thumb|centre]] || The two 1s AOs also overlap destructively to form a non-bonding σ* MO. The energy of the MO formed is -88.93661.
|-
| [[File:2s sigma orbital 2.JPG ‎|300px|thumb|centre]]|| The two 2s AOs overlap constructively to form a non-bonding σ MO. The energy of the MO formed is -7.99779.
|-
| [[File:2s sigma orbital 1.JPG ‎|300px|thumb|centre]] || The two 2s AOs also overlap destructively to form a non-bonding σ* MO. The energy of the MO formed is -7.99769.
|-
| [[File:2p pi orbital 1.JPG ‎|300px|thumb|centre]] [[File:2p pi orbital 2.JPG ‎|300px|thumb|centre]] || The 2px and 2py AOs overlap constructively laterally to form two non-bonding π MOs. These two orbitals are degenerate- the energies of the MOs are -5.96349 and -5.94946 respectively.
|-
| [[File:2p pi orbital 3.JPG ‎|300px|thumb|centre]] [[File:2p pi orbital 4.JPG ‎|300px|thumb|centre]] || The 2px and 2py AOs overlap destructively laterally to form two non-bonding π* MOs. These two orbitals are degenerate- the energies of the MOs are -5.96135.
|-
| [[File:2p pi orbital 5.JPG ‎|300px|thumb|centre]] || The 2pz AOs overlap constructively head-on to form one non-bonding σ MO. The energy of the MO is -5.96135.
|-
| [[File:2p pi orbital 6.JPG ‎|300px|thumb|centre]] || The 2pz AOs overlap destructively head-on to form one non-bonding σ * MOs. The energy of the MO is -5.96078 .
|-
| [[File:3s sigma orbital 1.JPG ‎|300px|thumb|centre]] || The two 3s AOs overlap constructively head=on to form a bonding σ MO. The energy of the MO formed is -0.83212.
|-
| [[File:3s sigma orbital 2.JPG ‎|300px|thumb|centre]] || The two 3s AOs also overlap destructively to form an anti-bonding σ* MO. The energy of the MO formed is -0.61535.
|}

File:3s sigma orbital 1.JPG

2018-03-16T11:51:23Z

Wsl1917: Wsl1917 uploaded a new version of File:3s sigma orbital 1.JPG

File:3s sigma orbital 1.JPG

2018-03-16T11:50:18Z

Wsl1917: Wsl1917 uploaded a new version of File:3s sigma orbital 1.JPG

Rep:Mod:WSL1819

2018-03-16T11:49:23Z

Wsl1917: /* Molecular Orbitals of Optimised S2 */

== Optimisation of NH3 ==

=== General Information of Optimised NH3 ===

From the 'Summary' table (Figure 1.1), the following general information about the optimisation calculation is obtained: the molecule optimised is ammonia, NH3, the calculation method is RB3LYP; the basis set is 6-31G(d,p); the final energy E(RB3LYP) is -56.44397188 a.u.; the RMS gradient is 0.05399560 a.u.; and the point group of NH3 is C3v.

[[File:Nh3_summary.jpg|400px|thumb|center|Figure 1.1: Summary Table of optimised NH3]]

=== Geometric Information of Optimised NH3 ===

Optimised bond length: 1.01798 Å ≈ 1.018 Å

Optimised bond angle: 105.741 o ≈ 105.7 o

=== Verification of Successful Optimisation of NH3 ===

The 'Item' table (Figure 1.2) shows that the final set of forces and displacements are converged and that the forces are approximately zero; since force is the gradient of a potential energy vs distance graph, this indicates that the structure obtained is at equilibrium, demonstrating successful optimisation of NH3.

<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>

Figure 1.2: Item Table of optimised NH3

Moreover, successful optimisation of NH3 is indicated by the last structure having the most negative energy and the smallest gradient (Figure 1.3).

[[File:Nh3 optimisation.jpg|400px|thumb|center|Figure 1.3: Optimisation plots of NH3]]

=== Dynamic Image of Optimised NH3 ===

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ZOEYWAISUMLUNG_NH3_OPTF_POP.LOG</uploadedFileContents>
<script>frame 1.7</script>
</jmolApplet></jmol>
Figure 1.4: A 3D jmol file of optimised NH3

The optimisation file is linked to [[Media:ZOEYWAISUMLUNG_NH3_OPTF_POP.LOG| here]]

=== Vibrational Analysis of Optimised NH3 ===

From Figure 1.5 in vibrational analysis, there are 6 modes as expected, modes 2 and 3 and modes 5 and 6 are degenerate as they have the same frequency of 1693.95 cm-1 and 3589.82 cm-1 respectively; modes 1, 2 and 3 are "bending" vibrations and modes 4, 5 and 6 are "bond stretch" vibrations; mode 4 is highly symmetric ; mode 1 is the "umbrella" mode and 2 bands in the experimental spectrum (Figure 1.6) of gaseous ammonia as expected.

[[File:Nh3 vibrations 1.jpg ‎|400px|thumb|centre|Figure 1.5: Vibrational Table of optimised NH3]]

[[File:Nh3_spectrum.jpg ‎|400px|thumb|centre|Figure 1.6: Spectrum of optimised NH3]]

=== Charge Analysis of Optimised NH3 ===

Charge analysis (Figure 1.7) shows the charge on the nitrogen atom is -1.125 whilst that of the hydrogen atoms is +0.375. This result where nitrogen has a negative charge with a larger magnitude and hydrogen has a positive charge with a smaller magnitude is expected, since nitrogen is more electronegative than hydrogen, nitrogen should withdraw more electron density from each of the three N-H bonds.

[[File:Nh3_charge.jpg ‎|400px|thumb|centre|Figure 1.7: Charge Analysis of optimised NH3]]

== Optimisation of N2 ==

=== General Information of Optimised N2 ===

From the 'Summary' table (Figure 2.1), the following general information about the optimisation calculation is obtained: the molecule optimised is nitrogen, N2, the calculation method is RB3LYP; the basis set is 6-31G(d,p); the final energy E(RB3LYP) is -109.52412868 a.u.; the RMS gradient is 0.00000011 a.u.; and the point group of N2 is D∞h.

[[File:N2 summary 2.jpg|400px|thumb|center|Figure 2.1: Summary Table of optimised N2]]

=== Geometric Information of Optimised N2 ===

Optimised bond length: 1.10550 Å ≈ 1.106 Å

=== Verification of Successful Optimisation of N2 ===

The 'Item' table (Figure 2.2) shows that the final set of forces and displacements are converged and that the forces are zero; since force is the gradient of a potential energy vs distance graph, this indicates that the structure obtained is at equilibrium, demonstrating successful optimisation of N2.

<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 0.000000 0.001200 YES
</pre>

Figure 2.2: Item Table of optimised N2

Moreover, successful optimisation of N2 is indicated by the last structure having the most negative energy and the smallest gradient (Figure 2.3).

[[File:N2 optimisation.jpg|400px|thumb|center|Figure 2.3: Optimisation plots of N2]]

=== Dynamic Image of Optimised N2 ===

<jmol><jmolApplet>
<title>Figure 2.4: Optimised nitrogen</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ZOEYWAISUMLUNG_N2_OPTF_POP.LOG</uploadedFileContents>
<script>frame 1.4</script>
</jmolApplet></jmol>

The optimisation file is linked to [[Media:ZOEYWAISUMLUNG_N2_OPTF_POP.LOG| here]]

=== Vibrational Analysis of Optimised N2 ===

From Figure 2.5 in vibrational analysis, there are 0 modes as expected, and 0 bands in the experimental spectrum (Figure 2.6) of gaseous nitrogen as expected.

[[File:N2 vibrations.jpg ‎|400px|thumb|centre|Figure 2.5: Vibrational Table of optimised N2]]

[[File:N2 spectrum.jpg ‎|400px|thumb|centre|Figure 2.6: Spectrum of optimised N2]]

=== Charge Analysis of Optimised N2 ===

Charge analysis (Figure 2.7) shows the charge on both nitrogen atoms is 0.000. This result is expected because both atoms of the lienar bond are the same so there are no expected differences in electronegativity therefore electron density is shared equally between the nitrogen atoms. Note that the atoms are colored by charge, a charge of 0.000 is represented by the color black and the numbers are written in black therefore they cannot be seen here.

[[File:N2 charge.jpg ‎|400px|thumb|centre|Figure 2.7: Charge Analysis of optimised N2]]

== Optimisation of H2 ==

=== General Information of Optimised H2 ===

From the 'Summary' table (Figure 3.1), the following general information about the optimisation calculation is obtained: the molecule optimised is hydrogen, H2, the calculation method is RB3LYP; the basis set is 6-31G(d,p); the final energy E(RB3LYP) is -1.17853936 a.u.; the RMS gradient is 0.00002276 a.u.; and the point group of H2 is D∞h.

[[File:H2 summary.jpg|400px|thumb|center|Figure 3.1: Summary Table of optimised H2]]

=== Geometric Information of Optimised H2 ===

Optimised bond length: 0.74274 Å ≈ 0.7427 Å

=== Verification of Successful Optimisation of H2 ===

The 'Item' table (Figure 3.2) shows that the final set of forces and displacements are converged and that the forces are zero; since force is the gradient of a potential energy vs distance graph, this indicates that the structure obtained is at equilibrium, demonstrating successful optimisation of H2.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000039 0.000300 YES
Maximum Displacement 0.000052 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
</pre>

Figure 3.2: Item Table of optimised H2

Moreover, successful optimisation of H2 is indicated by the last structure having the most negative energy and the smallest gradient (Figure 3.3).

[[File:H2 optimisation.jpg|400px|thumb|center|Figure 3.3: Optimisation plots of H2]]

=== Dynamic Image of Optimised H2 ===

<jmol><jmolApplet>
<title>Figure 3.4: Optimised hydrogen</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ZOEYWAISUMLUNG_H2_OPTF_POP.LOG</uploadedFileContents>
<script>frame 1.3</script>
</jmolApplet></jmol>

The optimisation file is linked to [[Media:ZOEYWAISUMLUNG_H2_OPTF_POP.LOG| here]]

=== Vibrational Analysis of Optimised H2 ===

From Figure 3.5 in vibrational analysis, there are 0 modes as expected, and 0 bands in the experimental spectrum (Figure 3.6) of gaseous hydrogen as expected.

[[File:H2 vibrations.jpg ‎|400px|thumb|centre|Figure 3.5: Vibrational Table of optimised H2]]

[[File:H2 spectrum.jpg ‎|400px|thumb|centre|Figure 3.6: Spectrum of optimised H2]]

=== Charge Analysis of Optimised H2 ===

Charge analysis (Figure 3.7) shows the charge on both hydrogen atoms is 0.000. This result is expected because both atoms of the linear bond are the same so there are no expected differences in electronegativity therefore electron density is shared equally between the hydrogen atoms. If a higher basis set is used, a single bond would likely to be displayed.

[[File:H2 charge.jpg ‎|400px|thumb|centre|Figure 2.7: Charge Analysis of optimised H2]]

== Optimisation of S2 ==

=== General Information of Optimised S2 ===

From the 'Summary' table (Figure 4.1), the following general information about the optimisation calculation is obtained: the molecule optimised is sulphur, S2, the calculation method is RB3LYP; the basis set is 6-31G(d,p); the final energy E(RB3LYP) is -796.32599779 a.u.; the RMS gradient is 0.00000905 a.u.; and the point group of S2 is D∞h.

[[File:S2 summary.jpg|400px|thumb|center|Figure 4.1: Summary Table of optimised S2]]

=== Geometric Information of Optimised S2 ===

Optimised bond length: 1.92947 Å ≈ 1.929 Å

=== Verification of Successful Optimisation of S2 ===

The 'Item' table (Figure 4.2) shows that the final set of forces and displacements are converged and that the forces are approximately zero; since force is the gradient of a potential energy vs distance graph, this indicates that the structure obtained is at equilibrium, demonstrating successful optimisation of S2.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.000027 0.001800 YES
RMS Displacement 0.000038 0.001200 YES
</pre>

Figure 4.2: Item Table of optimised S2

Moreover, successful optimisation of S2 is indicated by the last structure having the most negative energy and the smallest gradient (Figure 4.3).

[[File:S2 optimisation.jpg|400px|thumb|center|Figure 4.3: Optimisation plots of S2]]

=== Dynamic Image of Optimised S2 ===

<jmol><jmolApplet>
<title>Figure 4.4: Optimised sulphur</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ZOEYWAISUMLUNG_S2_OPTF_POP.LOG</uploadedFileContents>
<script>frame 1.4</script>
</jmolApplet></jmol>

The optimisation file is linked to [[Media:ZOEYWAISUMLUNG_S2_OPTF_POP.LOG| here]]

=== Vibrational Analysis of Optimised S2 ===

From Figure 4.5 in vibrational analysis, there are 0 modes as expected, and 0 bands in the experimental spectrum (Figure 4.6) of gaseous sulphur as expected.

[[File:S2 vibrations.jpg ‎|400px|thumb|centre|Figure 4.5: Vibrational Table of optimised S2]]

[[File:S2 spectrum.jpg ‎|400px|thumb|centre|Figure 4.6: Spectrum of optimised S2]]

=== Charge Analysis of Optimised S2 ===

Charge analysis (Figure 4.7) shows the charge on both sulphur atoms is 0.000. This result is expected because both atoms of the linear bond are the same so there are no expected differences in electronegativity therefore electron density is shared equally between the sulphur atoms. A single bond instead of a double bond is displayed however this would most likely not be the case if a higher basis set is used for optimisation.

[[File:S2 charge.jpg ‎|400px|thumb|centre|Figure 2.7: Charge Analysis of optimised H2]]

=== Molecular Orbitals of Optimised S2 ===

{| class="wikitable" border="1"
|+ caption
! heading !! heading
|-
| [[File:1s sigma orbital 1.JPG ‎|300px|thumb|centre]]
|| The two 1s AOs overlap constructively to form a non-bonding σ MO. The energy of the MO formed is -88.93663.
|-
| [[File:1s sigma orbital 2.JPG ‎|300px|thumb|centre]] || The two 1s AOs also overlap destructively to form a non-bonding σ* MO. The energy of the MO formed is -88.93661.
|-
| [[File:2s sigma orbital 2.JPG ‎|300px|thumb|centre]]|| The two 2s AOs overlap constructively to form a non-bonding σ MO. The energy of the MO formed is -7.99779.
|-
| [[File:2s sigma orbital 1.JPG ‎|300px|thumb|centre]] || The two 2s AOs also overlap destructively to form a non-bonding σ* MO. The energy of the MO formed is -7.99769.
|-
| [[File:2p pi orbital 1.JPG ‎|300px|thumb|centre]] [[File:2p pi orbital 2.JPG ‎|300px|thumb|centre]] || The 2px and 2py AOs overlap constructively laterally to form two non-bonding π MOs. These two orbitals are degenerate- the energies of the MOs are -5.96349 and -5.94946 respectively.
|-
| [[File:2p pi orbital 3.JPG ‎|300px|thumb|centre]] [[File:2p pi orbital 4.JPG ‎|300px|thumb|centre]] || The 2px and 2py AOs overlap destructively laterally to form two non-bonding π* MOs. These two orbitals are degenerate- the energies of the MOs are -5.96135.
|-
| [[File:2p pi orbital 5.JPG ‎|300px|thumb|centre]] || The 2pz AOs overlap constructively head-on to form one non-bonding σ MO. The energy of the MO is -5.96135.
|-
| [[File:2p pi orbital 6.JPG ‎|300px|thumb|centre]] || The 2pz AOs overlap destructively head-on to form one non-bonding σ * MOs. The energy of the MO is -5.96078 .
|-
| [[File:3s sigma orbital 1.JPG ‎|300px|thumb|centre]] || The two 3s AOs overlap constructively head=on to form a bonding σ MO. The energy of the MO formed is -0.83212.
|-
| [[File:3s sigma orbital 1.JPG ‎|300px|thumb|centre]] || The two 3s AOs also overlap destructively to form an anti-bonding σ* MO. The energy of the MO formed is -0.61535.
|}

File:3s sigma orbital 2.JPG

2018-03-16T11:49:15Z

Wsl1917:

File:3s sigma orbital 1.JPG

2018-03-16T11:49:06Z

Wsl1917:

Rep:Mod:WSL1819

2018-03-16T11:42:48Z

Wsl1917: /* Molecular Orbitals of Optimised S2 */

== Optimisation of NH3 ==

=== General Information of Optimised NH3 ===

From the 'Summary' table (Figure 1.1), the following general information about the optimisation calculation is obtained: the molecule optimised is ammonia, NH3, the calculation method is RB3LYP; the basis set is 6-31G(d,p); the final energy E(RB3LYP) is -56.44397188 a.u.; the RMS gradient is 0.05399560 a.u.; and the point group of NH3 is C3v.

[[File:Nh3_summary.jpg|400px|thumb|center|Figure 1.1: Summary Table of optimised NH3]]

=== Geometric Information of Optimised NH3 ===

Optimised bond length: 1.01798 Å ≈ 1.018 Å

Optimised bond angle: 105.741 o ≈ 105.7 o

=== Verification of Successful Optimisation of NH3 ===

The 'Item' table (Figure 1.2) shows that the final set of forces and displacements are converged and that the forces are approximately zero; since force is the gradient of a potential energy vs distance graph, this indicates that the structure obtained is at equilibrium, demonstrating successful optimisation of NH3.

<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>

Figure 1.2: Item Table of optimised NH3

Moreover, successful optimisation of NH3 is indicated by the last structure having the most negative energy and the smallest gradient (Figure 1.3).

[[File:Nh3 optimisation.jpg|400px|thumb|center|Figure 1.3: Optimisation plots of NH3]]

=== Dynamic Image of Optimised NH3 ===

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ZOEYWAISUMLUNG_NH3_OPTF_POP.LOG</uploadedFileContents>
<script>frame 1.7</script>
</jmolApplet></jmol>
Figure 1.4: A 3D jmol file of optimised NH3

The optimisation file is linked to [[Media:ZOEYWAISUMLUNG_NH3_OPTF_POP.LOG| here]]

=== Vibrational Analysis of Optimised NH3 ===

From Figure 1.5 in vibrational analysis, there are 6 modes as expected, modes 2 and 3 and modes 5 and 6 are degenerate as they have the same frequency of 1693.95 cm-1 and 3589.82 cm-1 respectively; modes 1, 2 and 3 are "bending" vibrations and modes 4, 5 and 6 are "bond stretch" vibrations; mode 4 is highly symmetric ; mode 1 is the "umbrella" mode and 2 bands in the experimental spectrum (Figure 1.6) of gaseous ammonia as expected.

[[File:Nh3 vibrations 1.jpg ‎|400px|thumb|centre|Figure 1.5: Vibrational Table of optimised NH3]]

[[File:Nh3_spectrum.jpg ‎|400px|thumb|centre|Figure 1.6: Spectrum of optimised NH3]]

=== Charge Analysis of Optimised NH3 ===

Charge analysis (Figure 1.7) shows the charge on the nitrogen atom is -1.125 whilst that of the hydrogen atoms is +0.375. This result where nitrogen has a negative charge with a larger magnitude and hydrogen has a positive charge with a smaller magnitude is expected, since nitrogen is more electronegative than hydrogen, nitrogen should withdraw more electron density from each of the three N-H bonds.

[[File:Nh3_charge.jpg ‎|400px|thumb|centre|Figure 1.7: Charge Analysis of optimised NH3]]

== Optimisation of N2 ==

=== General Information of Optimised N2 ===

From the 'Summary' table (Figure 2.1), the following general information about the optimisation calculation is obtained: the molecule optimised is nitrogen, N2, the calculation method is RB3LYP; the basis set is 6-31G(d,p); the final energy E(RB3LYP) is -109.52412868 a.u.; the RMS gradient is 0.00000011 a.u.; and the point group of N2 is D∞h.

[[File:N2 summary 2.jpg|400px|thumb|center|Figure 2.1: Summary Table of optimised N2]]

=== Geometric Information of Optimised N2 ===

Optimised bond length: 1.10550 Å ≈ 1.106 Å

=== Verification of Successful Optimisation of N2 ===

The 'Item' table (Figure 2.2) shows that the final set of forces and displacements are converged and that the forces are zero; since force is the gradient of a potential energy vs distance graph, this indicates that the structure obtained is at equilibrium, demonstrating successful optimisation of N2.

<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 0.000000 0.001200 YES
</pre>

Figure 2.2: Item Table of optimised N2

Moreover, successful optimisation of N2 is indicated by the last structure having the most negative energy and the smallest gradient (Figure 2.3).

[[File:N2 optimisation.jpg|400px|thumb|center|Figure 2.3: Optimisation plots of N2]]

=== Dynamic Image of Optimised N2 ===

<jmol><jmolApplet>
<title>Figure 2.4: Optimised nitrogen</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ZOEYWAISUMLUNG_N2_OPTF_POP.LOG</uploadedFileContents>
<script>frame 1.4</script>
</jmolApplet></jmol>

The optimisation file is linked to [[Media:ZOEYWAISUMLUNG_N2_OPTF_POP.LOG| here]]

=== Vibrational Analysis of Optimised N2 ===

From Figure 2.5 in vibrational analysis, there are 0 modes as expected, and 0 bands in the experimental spectrum (Figure 2.6) of gaseous nitrogen as expected.

[[File:N2 vibrations.jpg ‎|400px|thumb|centre|Figure 2.5: Vibrational Table of optimised N2]]

[[File:N2 spectrum.jpg ‎|400px|thumb|centre|Figure 2.6: Spectrum of optimised N2]]

=== Charge Analysis of Optimised N2 ===

Charge analysis (Figure 2.7) shows the charge on both nitrogen atoms is 0.000. This result is expected because both atoms of the lienar bond are the same so there are no expected differences in electronegativity therefore electron density is shared equally between the nitrogen atoms. Note that the atoms are colored by charge, a charge of 0.000 is represented by the color black and the numbers are written in black therefore they cannot be seen here.

[[File:N2 charge.jpg ‎|400px|thumb|centre|Figure 2.7: Charge Analysis of optimised N2]]

== Optimisation of H2 ==

=== General Information of Optimised H2 ===

From the 'Summary' table (Figure 3.1), the following general information about the optimisation calculation is obtained: the molecule optimised is hydrogen, H2, the calculation method is RB3LYP; the basis set is 6-31G(d,p); the final energy E(RB3LYP) is -1.17853936 a.u.; the RMS gradient is 0.00002276 a.u.; and the point group of H2 is D∞h.

[[File:H2 summary.jpg|400px|thumb|center|Figure 3.1: Summary Table of optimised H2]]

=== Geometric Information of Optimised H2 ===

Optimised bond length: 0.74274 Å ≈ 0.7427 Å

=== Verification of Successful Optimisation of H2 ===

The 'Item' table (Figure 3.2) shows that the final set of forces and displacements are converged and that the forces are zero; since force is the gradient of a potential energy vs distance graph, this indicates that the structure obtained is at equilibrium, demonstrating successful optimisation of H2.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000039 0.000300 YES
Maximum Displacement 0.000052 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
</pre>

Figure 3.2: Item Table of optimised H2

Moreover, successful optimisation of H2 is indicated by the last structure having the most negative energy and the smallest gradient (Figure 3.3).

[[File:H2 optimisation.jpg|400px|thumb|center|Figure 3.3: Optimisation plots of H2]]

=== Dynamic Image of Optimised H2 ===

<jmol><jmolApplet>
<title>Figure 3.4: Optimised hydrogen</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ZOEYWAISUMLUNG_H2_OPTF_POP.LOG</uploadedFileContents>
<script>frame 1.3</script>
</jmolApplet></jmol>

The optimisation file is linked to [[Media:ZOEYWAISUMLUNG_H2_OPTF_POP.LOG| here]]

=== Vibrational Analysis of Optimised H2 ===

From Figure 3.5 in vibrational analysis, there are 0 modes as expected, and 0 bands in the experimental spectrum (Figure 3.6) of gaseous hydrogen as expected.

[[File:H2 vibrations.jpg ‎|400px|thumb|centre|Figure 3.5: Vibrational Table of optimised H2]]

[[File:H2 spectrum.jpg ‎|400px|thumb|centre|Figure 3.6: Spectrum of optimised H2]]

=== Charge Analysis of Optimised H2 ===

Charge analysis (Figure 3.7) shows the charge on both hydrogen atoms is 0.000. This result is expected because both atoms of the linear bond are the same so there are no expected differences in electronegativity therefore electron density is shared equally between the hydrogen atoms. If a higher basis set is used, a single bond would likely to be displayed.

[[File:H2 charge.jpg ‎|400px|thumb|centre|Figure 2.7: Charge Analysis of optimised H2]]

== Optimisation of S2 ==

=== General Information of Optimised S2 ===

From the 'Summary' table (Figure 4.1), the following general information about the optimisation calculation is obtained: the molecule optimised is sulphur, S2, the calculation method is RB3LYP; the basis set is 6-31G(d,p); the final energy E(RB3LYP) is -796.32599779 a.u.; the RMS gradient is 0.00000905 a.u.; and the point group of S2 is D∞h.

[[File:S2 summary.jpg|400px|thumb|center|Figure 4.1: Summary Table of optimised S2]]

=== Geometric Information of Optimised S2 ===

Optimised bond length: 1.92947 Å ≈ 1.929 Å

=== Verification of Successful Optimisation of S2 ===

The 'Item' table (Figure 4.2) shows that the final set of forces and displacements are converged and that the forces are approximately zero; since force is the gradient of a potential energy vs distance graph, this indicates that the structure obtained is at equilibrium, demonstrating successful optimisation of S2.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.000027 0.001800 YES
RMS Displacement 0.000038 0.001200 YES
</pre>

Figure 4.2: Item Table of optimised S2

Moreover, successful optimisation of S2 is indicated by the last structure having the most negative energy and the smallest gradient (Figure 4.3).

[[File:S2 optimisation.jpg|400px|thumb|center|Figure 4.3: Optimisation plots of S2]]

=== Dynamic Image of Optimised S2 ===

<jmol><jmolApplet>
<title>Figure 4.4: Optimised sulphur</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ZOEYWAISUMLUNG_S2_OPTF_POP.LOG</uploadedFileContents>
<script>frame 1.4</script>
</jmolApplet></jmol>

The optimisation file is linked to [[Media:ZOEYWAISUMLUNG_S2_OPTF_POP.LOG| here]]

=== Vibrational Analysis of Optimised S2 ===

From Figure 4.5 in vibrational analysis, there are 0 modes as expected, and 0 bands in the experimental spectrum (Figure 4.6) of gaseous sulphur as expected.

[[File:S2 vibrations.jpg ‎|400px|thumb|centre|Figure 4.5: Vibrational Table of optimised S2]]

[[File:S2 spectrum.jpg ‎|400px|thumb|centre|Figure 4.6: Spectrum of optimised S2]]

=== Charge Analysis of Optimised S2 ===

Charge analysis (Figure 4.7) shows the charge on both sulphur atoms is 0.000. This result is expected because both atoms of the linear bond are the same so there are no expected differences in electronegativity therefore electron density is shared equally between the sulphur atoms. A single bond instead of a double bond is displayed however this would most likely not be the case if a higher basis set is used for optimisation.

[[File:S2 charge.jpg ‎|400px|thumb|centre|Figure 2.7: Charge Analysis of optimised H2]]

=== Molecular Orbitals of Optimised S2 ===

{| class="wikitable" border="1"
|+ caption
! heading !! heading
|-
| [[File:1s sigma orbital 1.JPG ‎|300px|thumb|centre]]
|| The two 1s AOs overlap constructively to form a non-bonding σ MO. The energy of the MO formed is -88.93663.
|-
| [[File:1s sigma orbital 2.JPG ‎|300px|thumb|centre]] || The two 1s AOs also overlap destructively to form a non-bonding σ* MO. The energy of the MO formed is -88.93661.
|-
| [[File:2s sigma orbital 2.JPG ‎|300px|thumb|centre]]|| The two 2s AOs overlap constructively to form a non-bonding σ MO. The energy of the MO formed is -7.99779.
|-
| [[File:2s sigma orbital 1.JPG ‎|300px|thumb|centre]] || The two 2s AOs also overlap destructively to form a non-bonding σ* MO. The energy of the MO formed is -7.99769.
|-
| [[File:2p pi orbital 1.JPG ‎|300px|thumb|centre]] [[File:2p pi orbital 2.JPG ‎|300px|thumb|centre]] || The 2px and 2py AOs overlap constructively laterally to form two non-bonding π MOs. These two orbitals are degenerate- the energies of the MOs are -5.96349 and -5.94946 respectively.
|-
| [[File:2p pi orbital 3.JPG ‎|300px|thumb|centre]] [[File:2p pi orbital 4.JPG ‎|300px|thumb|centre]] || The 2px and 2py AOs overlap destructively laterally to form two non-bonding π* MOs. These two orbitals are degenerate- the energies of the MOs are -5.96349 and -5.94945 respectively.
|-
| [[File:2p pi orbital 5.JPG ‎|300px|thumb|centre]] || The two 3s AOs overlap constructively head=on to form a bonding σ MO. The energy of the MO formed is -0.83212.
|-
| [[File:2p pi orbital 6.JPG ‎|300px|thumb|centre]] || The two 3s AOs also overlap destructively to form an anti-bonding σ* MO. The energy of the MO formed is -0.61535.
|-
| [[File:1s sigma orbital 1.JPG ‎|300px|thumb|centre]] || cell
|}

Rep:Mod:WSL1819

2018-03-16T11:36:13Z

Wsl1917: /* Molecular Orbitals of Optimised S2 */

== Optimisation of NH3 ==

=== General Information of Optimised NH3 ===

From the 'Summary' table (Figure 1.1), the following general information about the optimisation calculation is obtained: the molecule optimised is ammonia, NH3, the calculation method is RB3LYP; the basis set is 6-31G(d,p); the final energy E(RB3LYP) is -56.44397188 a.u.; the RMS gradient is 0.05399560 a.u.; and the point group of NH3 is C3v.

[[File:Nh3_summary.jpg|400px|thumb|center|Figure 1.1: Summary Table of optimised NH3]]

=== Geometric Information of Optimised NH3 ===

Optimised bond length: 1.01798 Å ≈ 1.018 Å

Optimised bond angle: 105.741 o ≈ 105.7 o

=== Verification of Successful Optimisation of NH3 ===

The 'Item' table (Figure 1.2) shows that the final set of forces and displacements are converged and that the forces are approximately zero; since force is the gradient of a potential energy vs distance graph, this indicates that the structure obtained is at equilibrium, demonstrating successful optimisation of NH3.

<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>

Figure 1.2: Item Table of optimised NH3

Moreover, successful optimisation of NH3 is indicated by the last structure having the most negative energy and the smallest gradient (Figure 1.3).

[[File:Nh3 optimisation.jpg|400px|thumb|center|Figure 1.3: Optimisation plots of NH3]]

=== Dynamic Image of Optimised NH3 ===

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ZOEYWAISUMLUNG_NH3_OPTF_POP.LOG</uploadedFileContents>
<script>frame 1.7</script>
</jmolApplet></jmol>
Figure 1.4: A 3D jmol file of optimised NH3

The optimisation file is linked to [[Media:ZOEYWAISUMLUNG_NH3_OPTF_POP.LOG| here]]

=== Vibrational Analysis of Optimised NH3 ===

From Figure 1.5 in vibrational analysis, there are 6 modes as expected, modes 2 and 3 and modes 5 and 6 are degenerate as they have the same frequency of 1693.95 cm-1 and 3589.82 cm-1 respectively; modes 1, 2 and 3 are "bending" vibrations and modes 4, 5 and 6 are "bond stretch" vibrations; mode 4 is highly symmetric ; mode 1 is the "umbrella" mode and 2 bands in the experimental spectrum (Figure 1.6) of gaseous ammonia as expected.

[[File:Nh3 vibrations 1.jpg ‎|400px|thumb|centre|Figure 1.5: Vibrational Table of optimised NH3]]

[[File:Nh3_spectrum.jpg ‎|400px|thumb|centre|Figure 1.6: Spectrum of optimised NH3]]

=== Charge Analysis of Optimised NH3 ===

Charge analysis (Figure 1.7) shows the charge on the nitrogen atom is -1.125 whilst that of the hydrogen atoms is +0.375. This result where nitrogen has a negative charge with a larger magnitude and hydrogen has a positive charge with a smaller magnitude is expected, since nitrogen is more electronegative than hydrogen, nitrogen should withdraw more electron density from each of the three N-H bonds.

[[File:Nh3_charge.jpg ‎|400px|thumb|centre|Figure 1.7: Charge Analysis of optimised NH3]]

== Optimisation of N2 ==

=== General Information of Optimised N2 ===

From the 'Summary' table (Figure 2.1), the following general information about the optimisation calculation is obtained: the molecule optimised is nitrogen, N2, the calculation method is RB3LYP; the basis set is 6-31G(d,p); the final energy E(RB3LYP) is -109.52412868 a.u.; the RMS gradient is 0.00000011 a.u.; and the point group of N2 is D∞h.

[[File:N2 summary 2.jpg|400px|thumb|center|Figure 2.1: Summary Table of optimised N2]]

=== Geometric Information of Optimised N2 ===

Optimised bond length: 1.10550 Å ≈ 1.106 Å

=== Verification of Successful Optimisation of N2 ===

The 'Item' table (Figure 2.2) shows that the final set of forces and displacements are converged and that the forces are zero; since force is the gradient of a potential energy vs distance graph, this indicates that the structure obtained is at equilibrium, demonstrating successful optimisation of N2.

<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 0.000000 0.001200 YES
</pre>

Figure 2.2: Item Table of optimised N2

Moreover, successful optimisation of N2 is indicated by the last structure having the most negative energy and the smallest gradient (Figure 2.3).

[[File:N2 optimisation.jpg|400px|thumb|center|Figure 2.3: Optimisation plots of N2]]

=== Dynamic Image of Optimised N2 ===

<jmol><jmolApplet>
<title>Figure 2.4: Optimised nitrogen</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ZOEYWAISUMLUNG_N2_OPTF_POP.LOG</uploadedFileContents>
<script>frame 1.4</script>
</jmolApplet></jmol>

The optimisation file is linked to [[Media:ZOEYWAISUMLUNG_N2_OPTF_POP.LOG| here]]

=== Vibrational Analysis of Optimised N2 ===

From Figure 2.5 in vibrational analysis, there are 0 modes as expected, and 0 bands in the experimental spectrum (Figure 2.6) of gaseous nitrogen as expected.

[[File:N2 vibrations.jpg ‎|400px|thumb|centre|Figure 2.5: Vibrational Table of optimised N2]]

[[File:N2 spectrum.jpg ‎|400px|thumb|centre|Figure 2.6: Spectrum of optimised N2]]

=== Charge Analysis of Optimised N2 ===

Charge analysis (Figure 2.7) shows the charge on both nitrogen atoms is 0.000. This result is expected because both atoms of the lienar bond are the same so there are no expected differences in electronegativity therefore electron density is shared equally between the nitrogen atoms. Note that the atoms are colored by charge, a charge of 0.000 is represented by the color black and the numbers are written in black therefore they cannot be seen here.

[[File:N2 charge.jpg ‎|400px|thumb|centre|Figure 2.7: Charge Analysis of optimised N2]]

== Optimisation of H2 ==

=== General Information of Optimised H2 ===

From the 'Summary' table (Figure 3.1), the following general information about the optimisation calculation is obtained: the molecule optimised is hydrogen, H2, the calculation method is RB3LYP; the basis set is 6-31G(d,p); the final energy E(RB3LYP) is -1.17853936 a.u.; the RMS gradient is 0.00002276 a.u.; and the point group of H2 is D∞h.

[[File:H2 summary.jpg|400px|thumb|center|Figure 3.1: Summary Table of optimised H2]]

=== Geometric Information of Optimised H2 ===

Optimised bond length: 0.74274 Å ≈ 0.7427 Å

=== Verification of Successful Optimisation of H2 ===

The 'Item' table (Figure 3.2) shows that the final set of forces and displacements are converged and that the forces are zero; since force is the gradient of a potential energy vs distance graph, this indicates that the structure obtained is at equilibrium, demonstrating successful optimisation of H2.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000039 0.000300 YES
Maximum Displacement 0.000052 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
</pre>

Figure 3.2: Item Table of optimised H2

Moreover, successful optimisation of H2 is indicated by the last structure having the most negative energy and the smallest gradient (Figure 3.3).

[[File:H2 optimisation.jpg|400px|thumb|center|Figure 3.3: Optimisation plots of H2]]

=== Dynamic Image of Optimised H2 ===

<jmol><jmolApplet>
<title>Figure 3.4: Optimised hydrogen</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ZOEYWAISUMLUNG_H2_OPTF_POP.LOG</uploadedFileContents>
<script>frame 1.3</script>
</jmolApplet></jmol>

The optimisation file is linked to [[Media:ZOEYWAISUMLUNG_H2_OPTF_POP.LOG| here]]

=== Vibrational Analysis of Optimised H2 ===

From Figure 3.5 in vibrational analysis, there are 0 modes as expected, and 0 bands in the experimental spectrum (Figure 3.6) of gaseous hydrogen as expected.

[[File:H2 vibrations.jpg ‎|400px|thumb|centre|Figure 3.5: Vibrational Table of optimised H2]]

[[File:H2 spectrum.jpg ‎|400px|thumb|centre|Figure 3.6: Spectrum of optimised H2]]

=== Charge Analysis of Optimised H2 ===

Charge analysis (Figure 3.7) shows the charge on both hydrogen atoms is 0.000. This result is expected because both atoms of the linear bond are the same so there are no expected differences in electronegativity therefore electron density is shared equally between the hydrogen atoms. If a higher basis set is used, a single bond would likely to be displayed.

[[File:H2 charge.jpg ‎|400px|thumb|centre|Figure 2.7: Charge Analysis of optimised H2]]

== Optimisation of S2 ==

=== General Information of Optimised S2 ===

From the 'Summary' table (Figure 4.1), the following general information about the optimisation calculation is obtained: the molecule optimised is sulphur, S2, the calculation method is RB3LYP; the basis set is 6-31G(d,p); the final energy E(RB3LYP) is -796.32599779 a.u.; the RMS gradient is 0.00000905 a.u.; and the point group of S2 is D∞h.

[[File:S2 summary.jpg|400px|thumb|center|Figure 4.1: Summary Table of optimised S2]]

=== Geometric Information of Optimised S2 ===

Optimised bond length: 1.92947 Å ≈ 1.929 Å

=== Verification of Successful Optimisation of S2 ===

The 'Item' table (Figure 4.2) shows that the final set of forces and displacements are converged and that the forces are approximately zero; since force is the gradient of a potential energy vs distance graph, this indicates that the structure obtained is at equilibrium, demonstrating successful optimisation of S2.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.000027 0.001800 YES
RMS Displacement 0.000038 0.001200 YES
</pre>

Figure 4.2: Item Table of optimised S2

Moreover, successful optimisation of S2 is indicated by the last structure having the most negative energy and the smallest gradient (Figure 4.3).

[[File:S2 optimisation.jpg|400px|thumb|center|Figure 4.3: Optimisation plots of S2]]

=== Dynamic Image of Optimised S2 ===

<jmol><jmolApplet>
<title>Figure 4.4: Optimised sulphur</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ZOEYWAISUMLUNG_S2_OPTF_POP.LOG</uploadedFileContents>
<script>frame 1.4</script>
</jmolApplet></jmol>

The optimisation file is linked to [[Media:ZOEYWAISUMLUNG_S2_OPTF_POP.LOG| here]]

=== Vibrational Analysis of Optimised S2 ===

From Figure 4.5 in vibrational analysis, there are 0 modes as expected, and 0 bands in the experimental spectrum (Figure 4.6) of gaseous sulphur as expected.

[[File:S2 vibrations.jpg ‎|400px|thumb|centre|Figure 4.5: Vibrational Table of optimised S2]]

[[File:S2 spectrum.jpg ‎|400px|thumb|centre|Figure 4.6: Spectrum of optimised S2]]

=== Charge Analysis of Optimised S2 ===

Charge analysis (Figure 4.7) shows the charge on both sulphur atoms is 0.000. This result is expected because both atoms of the linear bond are the same so there are no expected differences in electronegativity therefore electron density is shared equally between the sulphur atoms. A single bond instead of a double bond is displayed however this would most likely not be the case if a higher basis set is used for optimisation.

[[File:S2 charge.jpg ‎|400px|thumb|centre|Figure 2.7: Charge Analysis of optimised H2]]

=== Molecular Orbitals of Optimised S2 ===

{| class="wikitable" border="1"
|+ caption
! heading !! heading
|-
| [[File:1s sigma orbital 1.JPG ‎|300px|thumb|centre]]
|| The two 1s AOs overlap constructively to form a non-bonding σ MO. The energy of the MO formed is -88.93663.
|-
| [[File:1s sigma orbital 2.JPG ‎|300px|thumb|centre]] || The two 1s AOs also overlap destructively to form a non-bonding σ* MO. The energy of the MO formed is -88.93661. The energy of the two MOs formed from the two 1s AOs are very similar and hence degenerate.
|-
| [[File:2s sigma orbital 2.JPG ‎|300px|thumb|centre]]|| The two 2s AOs overlap constructively to form a non-bonding σ MO. The energy of the MO formed is -7.99779.
|-
| [[File:2s sigma orbital 1.JPG ‎|300px|thumb|centre]] || The two 2s AOs also overlap destructively to form a non-bonding σ* MO. The energy of the MO formed is -7.99769. The energy of the two MOs formed from the two 2s AOs are very similar and hence degenerate.
|-
| [[File:2p pi orbital 1.JPG ‎|300px|thumb|centre]] [[File:2p pi orbital 2.JPG ‎|300px|thumb|centre]] || The 2px and 2py AOs overlap constructively to form two non-bonding π* MOs. These two orbitals are degenerate- the energies of the MOs are -5.96349 and -5.94946 respectively.
|-
| [[File:1s sigma orbital 1.JPG ‎|300px|thumb|centre]] || cell
|-
| [[File:1s sigma orbital 1.JPG ‎|300px|thumb|centre]] || cell
|-
| [[File:1s sigma orbital 1.JPG ‎|300px|thumb|centre]] || cell
|-
| [[File:1s sigma orbital 1.JPG ‎|300px|thumb|centre]] || cell
|}

Rep:Mod:WSL1819

2018-03-16T11:35:34Z

Wsl1917: /* Molecular Orbitals of Optimised S2 */

== Optimisation of NH3 ==

=== General Information of Optimised NH3 ===

From the 'Summary' table (Figure 1.1), the following general information about the optimisation calculation is obtained: the molecule optimised is ammonia, NH3, the calculation method is RB3LYP; the basis set is 6-31G(d,p); the final energy E(RB3LYP) is -56.44397188 a.u.; the RMS gradient is 0.05399560 a.u.; and the point group of NH3 is C3v.

[[File:Nh3_summary.jpg|400px|thumb|center|Figure 1.1: Summary Table of optimised NH3]]

=== Geometric Information of Optimised NH3 ===

Optimised bond length: 1.01798 Å ≈ 1.018 Å

Optimised bond angle: 105.741 o ≈ 105.7 o

=== Verification of Successful Optimisation of NH3 ===

The 'Item' table (Figure 1.2) shows that the final set of forces and displacements are converged and that the forces are approximately zero; since force is the gradient of a potential energy vs distance graph, this indicates that the structure obtained is at equilibrium, demonstrating successful optimisation of NH3.

<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>

Figure 1.2: Item Table of optimised NH3

Moreover, successful optimisation of NH3 is indicated by the last structure having the most negative energy and the smallest gradient (Figure 1.3).

[[File:Nh3 optimisation.jpg|400px|thumb|center|Figure 1.3: Optimisation plots of NH3]]

=== Dynamic Image of Optimised NH3 ===

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ZOEYWAISUMLUNG_NH3_OPTF_POP.LOG</uploadedFileContents>
<script>frame 1.7</script>
</jmolApplet></jmol>
Figure 1.4: A 3D jmol file of optimised NH3

The optimisation file is linked to [[Media:ZOEYWAISUMLUNG_NH3_OPTF_POP.LOG| here]]

=== Vibrational Analysis of Optimised NH3 ===

From Figure 1.5 in vibrational analysis, there are 6 modes as expected, modes 2 and 3 and modes 5 and 6 are degenerate as they have the same frequency of 1693.95 cm-1 and 3589.82 cm-1 respectively; modes 1, 2 and 3 are "bending" vibrations and modes 4, 5 and 6 are "bond stretch" vibrations; mode 4 is highly symmetric ; mode 1 is the "umbrella" mode and 2 bands in the experimental spectrum (Figure 1.6) of gaseous ammonia as expected.

[[File:Nh3 vibrations 1.jpg ‎|400px|thumb|centre|Figure 1.5: Vibrational Table of optimised NH3]]

[[File:Nh3_spectrum.jpg ‎|400px|thumb|centre|Figure 1.6: Spectrum of optimised NH3]]

=== Charge Analysis of Optimised NH3 ===

Charge analysis (Figure 1.7) shows the charge on the nitrogen atom is -1.125 whilst that of the hydrogen atoms is +0.375. This result where nitrogen has a negative charge with a larger magnitude and hydrogen has a positive charge with a smaller magnitude is expected, since nitrogen is more electronegative than hydrogen, nitrogen should withdraw more electron density from each of the three N-H bonds.

[[File:Nh3_charge.jpg ‎|400px|thumb|centre|Figure 1.7: Charge Analysis of optimised NH3]]

== Optimisation of N2 ==

=== General Information of Optimised N2 ===

From the 'Summary' table (Figure 2.1), the following general information about the optimisation calculation is obtained: the molecule optimised is nitrogen, N2, the calculation method is RB3LYP; the basis set is 6-31G(d,p); the final energy E(RB3LYP) is -109.52412868 a.u.; the RMS gradient is 0.00000011 a.u.; and the point group of N2 is D∞h.

[[File:N2 summary 2.jpg|400px|thumb|center|Figure 2.1: Summary Table of optimised N2]]

=== Geometric Information of Optimised N2 ===

Optimised bond length: 1.10550 Å ≈ 1.106 Å

=== Verification of Successful Optimisation of N2 ===

The 'Item' table (Figure 2.2) shows that the final set of forces and displacements are converged and that the forces are zero; since force is the gradient of a potential energy vs distance graph, this indicates that the structure obtained is at equilibrium, demonstrating successful optimisation of N2.

<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 0.000000 0.001200 YES
</pre>

Figure 2.2: Item Table of optimised N2

Moreover, successful optimisation of N2 is indicated by the last structure having the most negative energy and the smallest gradient (Figure 2.3).

[[File:N2 optimisation.jpg|400px|thumb|center|Figure 2.3: Optimisation plots of N2]]

=== Dynamic Image of Optimised N2 ===

<jmol><jmolApplet>
<title>Figure 2.4: Optimised nitrogen</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ZOEYWAISUMLUNG_N2_OPTF_POP.LOG</uploadedFileContents>
<script>frame 1.4</script>
</jmolApplet></jmol>

The optimisation file is linked to [[Media:ZOEYWAISUMLUNG_N2_OPTF_POP.LOG| here]]

=== Vibrational Analysis of Optimised N2 ===

From Figure 2.5 in vibrational analysis, there are 0 modes as expected, and 0 bands in the experimental spectrum (Figure 2.6) of gaseous nitrogen as expected.

[[File:N2 vibrations.jpg ‎|400px|thumb|centre|Figure 2.5: Vibrational Table of optimised N2]]

[[File:N2 spectrum.jpg ‎|400px|thumb|centre|Figure 2.6: Spectrum of optimised N2]]

=== Charge Analysis of Optimised N2 ===

Charge analysis (Figure 2.7) shows the charge on both nitrogen atoms is 0.000. This result is expected because both atoms of the lienar bond are the same so there are no expected differences in electronegativity therefore electron density is shared equally between the nitrogen atoms. Note that the atoms are colored by charge, a charge of 0.000 is represented by the color black and the numbers are written in black therefore they cannot be seen here.

[[File:N2 charge.jpg ‎|400px|thumb|centre|Figure 2.7: Charge Analysis of optimised N2]]

== Optimisation of H2 ==

=== General Information of Optimised H2 ===

From the 'Summary' table (Figure 3.1), the following general information about the optimisation calculation is obtained: the molecule optimised is hydrogen, H2, the calculation method is RB3LYP; the basis set is 6-31G(d,p); the final energy E(RB3LYP) is -1.17853936 a.u.; the RMS gradient is 0.00002276 a.u.; and the point group of H2 is D∞h.

[[File:H2 summary.jpg|400px|thumb|center|Figure 3.1: Summary Table of optimised H2]]

=== Geometric Information of Optimised H2 ===

Optimised bond length: 0.74274 Å ≈ 0.7427 Å

=== Verification of Successful Optimisation of H2 ===

The 'Item' table (Figure 3.2) shows that the final set of forces and displacements are converged and that the forces are zero; since force is the gradient of a potential energy vs distance graph, this indicates that the structure obtained is at equilibrium, demonstrating successful optimisation of H2.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000039 0.000300 YES
Maximum Displacement 0.000052 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
</pre>

Figure 3.2: Item Table of optimised H2

Moreover, successful optimisation of H2 is indicated by the last structure having the most negative energy and the smallest gradient (Figure 3.3).

[[File:H2 optimisation.jpg|400px|thumb|center|Figure 3.3: Optimisation plots of H2]]

=== Dynamic Image of Optimised H2 ===

<jmol><jmolApplet>
<title>Figure 3.4: Optimised hydrogen</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ZOEYWAISUMLUNG_H2_OPTF_POP.LOG</uploadedFileContents>
<script>frame 1.3</script>
</jmolApplet></jmol>

The optimisation file is linked to [[Media:ZOEYWAISUMLUNG_H2_OPTF_POP.LOG| here]]

=== Vibrational Analysis of Optimised H2 ===

From Figure 3.5 in vibrational analysis, there are 0 modes as expected, and 0 bands in the experimental spectrum (Figure 3.6) of gaseous hydrogen as expected.

[[File:H2 vibrations.jpg ‎|400px|thumb|centre|Figure 3.5: Vibrational Table of optimised H2]]

[[File:H2 spectrum.jpg ‎|400px|thumb|centre|Figure 3.6: Spectrum of optimised H2]]

=== Charge Analysis of Optimised H2 ===

Charge analysis (Figure 3.7) shows the charge on both hydrogen atoms is 0.000. This result is expected because both atoms of the linear bond are the same so there are no expected differences in electronegativity therefore electron density is shared equally between the hydrogen atoms. If a higher basis set is used, a single bond would likely to be displayed.

[[File:H2 charge.jpg ‎|400px|thumb|centre|Figure 2.7: Charge Analysis of optimised H2]]

== Optimisation of S2 ==

=== General Information of Optimised S2 ===

From the 'Summary' table (Figure 4.1), the following general information about the optimisation calculation is obtained: the molecule optimised is sulphur, S2, the calculation method is RB3LYP; the basis set is 6-31G(d,p); the final energy E(RB3LYP) is -796.32599779 a.u.; the RMS gradient is 0.00000905 a.u.; and the point group of S2 is D∞h.

[[File:S2 summary.jpg|400px|thumb|center|Figure 4.1: Summary Table of optimised S2]]

=== Geometric Information of Optimised S2 ===

Optimised bond length: 1.92947 Å ≈ 1.929 Å

=== Verification of Successful Optimisation of S2 ===

The 'Item' table (Figure 4.2) shows that the final set of forces and displacements are converged and that the forces are approximately zero; since force is the gradient of a potential energy vs distance graph, this indicates that the structure obtained is at equilibrium, demonstrating successful optimisation of S2.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.000027 0.001800 YES
RMS Displacement 0.000038 0.001200 YES
</pre>

Figure 4.2: Item Table of optimised S2

Moreover, successful optimisation of S2 is indicated by the last structure having the most negative energy and the smallest gradient (Figure 4.3).

[[File:S2 optimisation.jpg|400px|thumb|center|Figure 4.3: Optimisation plots of S2]]

=== Dynamic Image of Optimised S2 ===

<jmol><jmolApplet>
<title>Figure 4.4: Optimised sulphur</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ZOEYWAISUMLUNG_S2_OPTF_POP.LOG</uploadedFileContents>
<script>frame 1.4</script>
</jmolApplet></jmol>

The optimisation file is linked to [[Media:ZOEYWAISUMLUNG_S2_OPTF_POP.LOG| here]]

=== Vibrational Analysis of Optimised S2 ===

From Figure 4.5 in vibrational analysis, there are 0 modes as expected, and 0 bands in the experimental spectrum (Figure 4.6) of gaseous sulphur as expected.

[[File:S2 vibrations.jpg ‎|400px|thumb|centre|Figure 4.5: Vibrational Table of optimised S2]]

[[File:S2 spectrum.jpg ‎|400px|thumb|centre|Figure 4.6: Spectrum of optimised S2]]

=== Charge Analysis of Optimised S2 ===

Charge analysis (Figure 4.7) shows the charge on both sulphur atoms is 0.000. This result is expected because both atoms of the linear bond are the same so there are no expected differences in electronegativity therefore electron density is shared equally between the sulphur atoms. A single bond instead of a double bond is displayed however this would most likely not be the case if a higher basis set is used for optimisation.

[[File:S2 charge.jpg ‎|400px|thumb|centre|Figure 2.7: Charge Analysis of optimised H2]]

=== Molecular Orbitals of Optimised S2 ===

{| class="wikitable" border="1"
|+ caption
! heading !! heading
|-
| [[File:1s sigma orbital 1.JPG ‎|300px|thumb|centre]]
|| The two 1s AOs overlap constructively to form a non-bonding σ MO. The energy of the MO formed is -88.93663.
|-
| [[File:1s sigma orbital 2.JPG ‎|300px|thumb|centre]] || The two 1s AOs also overlap destructively to form a non-bonding σ* MO. The energy of the MO formed is -88.93661. The energy of the two MOs formed from the two 1s AOs are very similar and hence degenerate.
|-
| [[File:2s sigma orbital 2.JPG ‎|300px|thumb|centre]]|| The two 2s AOs overlap constructively to form a non-bonding σ MO. The energy of the MO formed is -7.99779.
|-
| [[File:2s sigma orbital 1.JPG ‎|300px|thumb|centre]] || The two 2s AOs also overlap destructively to form a non-bonding σ* MO. The energy of the MO formed is -7.99769. The energy of the two MOs formed from the two 2s AOs are very similar and hence degenerate.
|-
| [[File:2p pi orbital 1.JPG ‎|300px|thumb]] [[File:2p pi orbital 2.JPG ‎|300px|thumb|centre]] || The 2px and 2py AOs overlap constructively to form two non-bonding π* MOs. These two orbitals are degenerate- the energies of the MOs are -5.96349 and -5.94946 respectively.
|-
| [[File:1s sigma orbital 1.JPG ‎|300px|thumb|centre]] || cell
|-
| [[File:1s sigma orbital 1.JPG ‎|300px|thumb|centre]] || cell
|-
| [[File:1s sigma orbital 1.JPG ‎|300px|thumb|centre]] || cell
|-
| [[File:1s sigma orbital 1.JPG ‎|300px|thumb|centre]] || cell
|}

Rep:Mod:WSL1819

2018-03-16T11:35:09Z

Wsl1917: /* Molecular Orbitals of Optimised S2 */

== Optimisation of NH3 ==

=== General Information of Optimised NH3 ===

From the 'Summary' table (Figure 1.1), the following general information about the optimisation calculation is obtained: the molecule optimised is ammonia, NH3, the calculation method is RB3LYP; the basis set is 6-31G(d,p); the final energy E(RB3LYP) is -56.44397188 a.u.; the RMS gradient is 0.05399560 a.u.; and the point group of NH3 is C3v.

[[File:Nh3_summary.jpg|400px|thumb|center|Figure 1.1: Summary Table of optimised NH3]]

=== Geometric Information of Optimised NH3 ===

Optimised bond length: 1.01798 Å ≈ 1.018 Å

Optimised bond angle: 105.741 o ≈ 105.7 o

=== Verification of Successful Optimisation of NH3 ===

The 'Item' table (Figure 1.2) shows that the final set of forces and displacements are converged and that the forces are approximately zero; since force is the gradient of a potential energy vs distance graph, this indicates that the structure obtained is at equilibrium, demonstrating successful optimisation of NH3.

<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>

Figure 1.2: Item Table of optimised NH3

Moreover, successful optimisation of NH3 is indicated by the last structure having the most negative energy and the smallest gradient (Figure 1.3).

[[File:Nh3 optimisation.jpg|400px|thumb|center|Figure 1.3: Optimisation plots of NH3]]

=== Dynamic Image of Optimised NH3 ===

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ZOEYWAISUMLUNG_NH3_OPTF_POP.LOG</uploadedFileContents>
<script>frame 1.7</script>
</jmolApplet></jmol>
Figure 1.4: A 3D jmol file of optimised NH3

The optimisation file is linked to [[Media:ZOEYWAISUMLUNG_NH3_OPTF_POP.LOG| here]]

=== Vibrational Analysis of Optimised NH3 ===

From Figure 1.5 in vibrational analysis, there are 6 modes as expected, modes 2 and 3 and modes 5 and 6 are degenerate as they have the same frequency of 1693.95 cm-1 and 3589.82 cm-1 respectively; modes 1, 2 and 3 are "bending" vibrations and modes 4, 5 and 6 are "bond stretch" vibrations; mode 4 is highly symmetric ; mode 1 is the "umbrella" mode and 2 bands in the experimental spectrum (Figure 1.6) of gaseous ammonia as expected.

[[File:Nh3 vibrations 1.jpg ‎|400px|thumb|centre|Figure 1.5: Vibrational Table of optimised NH3]]

[[File:Nh3_spectrum.jpg ‎|400px|thumb|centre|Figure 1.6: Spectrum of optimised NH3]]

=== Charge Analysis of Optimised NH3 ===

Charge analysis (Figure 1.7) shows the charge on the nitrogen atom is -1.125 whilst that of the hydrogen atoms is +0.375. This result where nitrogen has a negative charge with a larger magnitude and hydrogen has a positive charge with a smaller magnitude is expected, since nitrogen is more electronegative than hydrogen, nitrogen should withdraw more electron density from each of the three N-H bonds.

[[File:Nh3_charge.jpg ‎|400px|thumb|centre|Figure 1.7: Charge Analysis of optimised NH3]]

== Optimisation of N2 ==

=== General Information of Optimised N2 ===

From the 'Summary' table (Figure 2.1), the following general information about the optimisation calculation is obtained: the molecule optimised is nitrogen, N2, the calculation method is RB3LYP; the basis set is 6-31G(d,p); the final energy E(RB3LYP) is -109.52412868 a.u.; the RMS gradient is 0.00000011 a.u.; and the point group of N2 is D∞h.

[[File:N2 summary 2.jpg|400px|thumb|center|Figure 2.1: Summary Table of optimised N2]]

=== Geometric Information of Optimised N2 ===

Optimised bond length: 1.10550 Å ≈ 1.106 Å

=== Verification of Successful Optimisation of N2 ===

The 'Item' table (Figure 2.2) shows that the final set of forces and displacements are converged and that the forces are zero; since force is the gradient of a potential energy vs distance graph, this indicates that the structure obtained is at equilibrium, demonstrating successful optimisation of N2.

<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 0.000000 0.001200 YES
</pre>

Figure 2.2: Item Table of optimised N2

Moreover, successful optimisation of N2 is indicated by the last structure having the most negative energy and the smallest gradient (Figure 2.3).

[[File:N2 optimisation.jpg|400px|thumb|center|Figure 2.3: Optimisation plots of N2]]

=== Dynamic Image of Optimised N2 ===

<jmol><jmolApplet>
<title>Figure 2.4: Optimised nitrogen</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ZOEYWAISUMLUNG_N2_OPTF_POP.LOG</uploadedFileContents>
<script>frame 1.4</script>
</jmolApplet></jmol>

The optimisation file is linked to [[Media:ZOEYWAISUMLUNG_N2_OPTF_POP.LOG| here]]

=== Vibrational Analysis of Optimised N2 ===

From Figure 2.5 in vibrational analysis, there are 0 modes as expected, and 0 bands in the experimental spectrum (Figure 2.6) of gaseous nitrogen as expected.

[[File:N2 vibrations.jpg ‎|400px|thumb|centre|Figure 2.5: Vibrational Table of optimised N2]]

[[File:N2 spectrum.jpg ‎|400px|thumb|centre|Figure 2.6: Spectrum of optimised N2]]

=== Charge Analysis of Optimised N2 ===

Charge analysis (Figure 2.7) shows the charge on both nitrogen atoms is 0.000. This result is expected because both atoms of the lienar bond are the same so there are no expected differences in electronegativity therefore electron density is shared equally between the nitrogen atoms. Note that the atoms are colored by charge, a charge of 0.000 is represented by the color black and the numbers are written in black therefore they cannot be seen here.

[[File:N2 charge.jpg ‎|400px|thumb|centre|Figure 2.7: Charge Analysis of optimised N2]]

== Optimisation of H2 ==

=== General Information of Optimised H2 ===

From the 'Summary' table (Figure 3.1), the following general information about the optimisation calculation is obtained: the molecule optimised is hydrogen, H2, the calculation method is RB3LYP; the basis set is 6-31G(d,p); the final energy E(RB3LYP) is -1.17853936 a.u.; the RMS gradient is 0.00002276 a.u.; and the point group of H2 is D∞h.

[[File:H2 summary.jpg|400px|thumb|center|Figure 3.1: Summary Table of optimised H2]]

=== Geometric Information of Optimised H2 ===

Optimised bond length: 0.74274 Å ≈ 0.7427 Å

=== Verification of Successful Optimisation of H2 ===

The 'Item' table (Figure 3.2) shows that the final set of forces and displacements are converged and that the forces are zero; since force is the gradient of a potential energy vs distance graph, this indicates that the structure obtained is at equilibrium, demonstrating successful optimisation of H2.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000039 0.000300 YES
Maximum Displacement 0.000052 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
</pre>

Figure 3.2: Item Table of optimised H2

Moreover, successful optimisation of H2 is indicated by the last structure having the most negative energy and the smallest gradient (Figure 3.3).

[[File:H2 optimisation.jpg|400px|thumb|center|Figure 3.3: Optimisation plots of H2]]

=== Dynamic Image of Optimised H2 ===

<jmol><jmolApplet>
<title>Figure 3.4: Optimised hydrogen</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ZOEYWAISUMLUNG_H2_OPTF_POP.LOG</uploadedFileContents>
<script>frame 1.3</script>
</jmolApplet></jmol>

The optimisation file is linked to [[Media:ZOEYWAISUMLUNG_H2_OPTF_POP.LOG| here]]

=== Vibrational Analysis of Optimised H2 ===

From Figure 3.5 in vibrational analysis, there are 0 modes as expected, and 0 bands in the experimental spectrum (Figure 3.6) of gaseous hydrogen as expected.

[[File:H2 vibrations.jpg ‎|400px|thumb|centre|Figure 3.5: Vibrational Table of optimised H2]]

[[File:H2 spectrum.jpg ‎|400px|thumb|centre|Figure 3.6: Spectrum of optimised H2]]

=== Charge Analysis of Optimised H2 ===

Charge analysis (Figure 3.7) shows the charge on both hydrogen atoms is 0.000. This result is expected because both atoms of the linear bond are the same so there are no expected differences in electronegativity therefore electron density is shared equally between the hydrogen atoms. If a higher basis set is used, a single bond would likely to be displayed.

[[File:H2 charge.jpg ‎|400px|thumb|centre|Figure 2.7: Charge Analysis of optimised H2]]

== Optimisation of S2 ==

=== General Information of Optimised S2 ===

From the 'Summary' table (Figure 4.1), the following general information about the optimisation calculation is obtained: the molecule optimised is sulphur, S2, the calculation method is RB3LYP; the basis set is 6-31G(d,p); the final energy E(RB3LYP) is -796.32599779 a.u.; the RMS gradient is 0.00000905 a.u.; and the point group of S2 is D∞h.

[[File:S2 summary.jpg|400px|thumb|center|Figure 4.1: Summary Table of optimised S2]]

=== Geometric Information of Optimised S2 ===

Optimised bond length: 1.92947 Å ≈ 1.929 Å

=== Verification of Successful Optimisation of S2 ===

The 'Item' table (Figure 4.2) shows that the final set of forces and displacements are converged and that the forces are approximately zero; since force is the gradient of a potential energy vs distance graph, this indicates that the structure obtained is at equilibrium, demonstrating successful optimisation of S2.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.000027 0.001800 YES
RMS Displacement 0.000038 0.001200 YES
</pre>

Figure 4.2: Item Table of optimised S2

Moreover, successful optimisation of S2 is indicated by the last structure having the most negative energy and the smallest gradient (Figure 4.3).

[[File:S2 optimisation.jpg|400px|thumb|center|Figure 4.3: Optimisation plots of S2]]

=== Dynamic Image of Optimised S2 ===

<jmol><jmolApplet>
<title>Figure 4.4: Optimised sulphur</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ZOEYWAISUMLUNG_S2_OPTF_POP.LOG</uploadedFileContents>
<script>frame 1.4</script>
</jmolApplet></jmol>

The optimisation file is linked to [[Media:ZOEYWAISUMLUNG_S2_OPTF_POP.LOG| here]]

=== Vibrational Analysis of Optimised S2 ===

From Figure 4.5 in vibrational analysis, there are 0 modes as expected, and 0 bands in the experimental spectrum (Figure 4.6) of gaseous sulphur as expected.

[[File:S2 vibrations.jpg ‎|400px|thumb|centre|Figure 4.5: Vibrational Table of optimised S2]]

[[File:S2 spectrum.jpg ‎|400px|thumb|centre|Figure 4.6: Spectrum of optimised S2]]

=== Charge Analysis of Optimised S2 ===

Charge analysis (Figure 4.7) shows the charge on both sulphur atoms is 0.000. This result is expected because both atoms of the linear bond are the same so there are no expected differences in electronegativity therefore electron density is shared equally between the sulphur atoms. A single bond instead of a double bond is displayed however this would most likely not be the case if a higher basis set is used for optimisation.

[[File:S2 charge.jpg ‎|400px|thumb|centre|Figure 2.7: Charge Analysis of optimised H2]]

=== Molecular Orbitals of Optimised S2 ===

{| class="wikitable" border="1"
|+ caption
! heading !! heading
|-
| [[File:1s sigma orbital 1.JPG ‎|300px|thumb|centre]]
|| The two 1s AOs overlap constructively to form a non-bonding σ MO. The energy of the MO formed is -88.93663.
|-
| [[File:1s sigma orbital 2.JPG ‎|300px|thumb|centre]] || The two 1s AOs also overlap destructively to form a non-bonding σ* MO. The energy of the MO formed is -88.93661. The energy of the two MOs formed from the two 1s AOs are very similar and hence degenerate.
|-
| [[File:2s sigma orbital 2.JPG ‎|300px|thumb|centre]]|| The two 2s AOs overlap constructively to form a non-bonding σ MO. The energy of the MO formed is -7.99779.
|-
| [[File:2s sigma orbital 1.JPG ‎|300px|thumb|centre]] || The two 2s AOs also overlap destructively to form a non-bonding σ* MO. The energy of the MO formed is -7.99769. The energy of the two MOs formed from the two 2s AOs are very similar and hence degenerate.
|-
| [[File:2p pi orbital 1.JPG ‎|300px|thumb|centre]] [[File:2p pi orbital 2.JPG ‎|300px|thumb|centre]] || The 2px and 2py AOs overlap constructively to form two non-bonding π* MOs. These two orbitals are degenerate- the energies of the MOs are -5.96349 and -5.94946 respectively.
|-
| [[File:1s sigma orbital 1.JPG ‎|300px|thumb|centre]] || cell
|-
| [[File:1s sigma orbital 1.JPG ‎|300px|thumb|centre]] || cell
|-
| [[File:1s sigma orbital 1.JPG ‎|300px|thumb|centre]] || cell
|-
| [[File:1s sigma orbital 1.JPG ‎|300px|thumb|centre]] || cell
|}

File:2p pi orbital 2.JPG

2018-03-16T11:35:04Z

Wsl1917:

File:2p pi orbital 1.JPG

2018-03-16T11:34:49Z

Wsl1917:

Rep:Mod:WSL1819

2018-03-16T11:29:32Z

Wsl1917: /* Molecular Orbitals of Optimised S2 */

== Optimisation of NH3 ==

=== General Information of Optimised NH3 ===

From the 'Summary' table (Figure 1.1), the following general information about the optimisation calculation is obtained: the molecule optimised is ammonia, NH3, the calculation method is RB3LYP; the basis set is 6-31G(d,p); the final energy E(RB3LYP) is -56.44397188 a.u.; the RMS gradient is 0.05399560 a.u.; and the point group of NH3 is C3v.

[[File:Nh3_summary.jpg|400px|thumb|center|Figure 1.1: Summary Table of optimised NH3]]

=== Geometric Information of Optimised NH3 ===

Optimised bond length: 1.01798 Å ≈ 1.018 Å

Optimised bond angle: 105.741 o ≈ 105.7 o

=== Verification of Successful Optimisation of NH3 ===

The 'Item' table (Figure 1.2) shows that the final set of forces and displacements are converged and that the forces are approximately zero; since force is the gradient of a potential energy vs distance graph, this indicates that the structure obtained is at equilibrium, demonstrating successful optimisation of NH3.

<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>

Figure 1.2: Item Table of optimised NH3

Moreover, successful optimisation of NH3 is indicated by the last structure having the most negative energy and the smallest gradient (Figure 1.3).

[[File:Nh3 optimisation.jpg|400px|thumb|center|Figure 1.3: Optimisation plots of NH3]]

=== Dynamic Image of Optimised NH3 ===

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ZOEYWAISUMLUNG_NH3_OPTF_POP.LOG</uploadedFileContents>
<script>frame 1.7</script>
</jmolApplet></jmol>
Figure 1.4: A 3D jmol file of optimised NH3

The optimisation file is linked to [[Media:ZOEYWAISUMLUNG_NH3_OPTF_POP.LOG| here]]

=== Vibrational Analysis of Optimised NH3 ===

From Figure 1.5 in vibrational analysis, there are 6 modes as expected, modes 2 and 3 and modes 5 and 6 are degenerate as they have the same frequency of 1693.95 cm-1 and 3589.82 cm-1 respectively; modes 1, 2 and 3 are "bending" vibrations and modes 4, 5 and 6 are "bond stretch" vibrations; mode 4 is highly symmetric ; mode 1 is the "umbrella" mode and 2 bands in the experimental spectrum (Figure 1.6) of gaseous ammonia as expected.

[[File:Nh3 vibrations 1.jpg ‎|400px|thumb|centre|Figure 1.5: Vibrational Table of optimised NH3]]

[[File:Nh3_spectrum.jpg ‎|400px|thumb|centre|Figure 1.6: Spectrum of optimised NH3]]

=== Charge Analysis of Optimised NH3 ===

Charge analysis (Figure 1.7) shows the charge on the nitrogen atom is -1.125 whilst that of the hydrogen atoms is +0.375. This result where nitrogen has a negative charge with a larger magnitude and hydrogen has a positive charge with a smaller magnitude is expected, since nitrogen is more electronegative than hydrogen, nitrogen should withdraw more electron density from each of the three N-H bonds.

[[File:Nh3_charge.jpg ‎|400px|thumb|centre|Figure 1.7: Charge Analysis of optimised NH3]]

== Optimisation of N2 ==

=== General Information of Optimised N2 ===

From the 'Summary' table (Figure 2.1), the following general information about the optimisation calculation is obtained: the molecule optimised is nitrogen, N2, the calculation method is RB3LYP; the basis set is 6-31G(d,p); the final energy E(RB3LYP) is -109.52412868 a.u.; the RMS gradient is 0.00000011 a.u.; and the point group of N2 is D∞h.

[[File:N2 summary 2.jpg|400px|thumb|center|Figure 2.1: Summary Table of optimised N2]]

=== Geometric Information of Optimised N2 ===

Optimised bond length: 1.10550 Å ≈ 1.106 Å

=== Verification of Successful Optimisation of N2 ===

The 'Item' table (Figure 2.2) shows that the final set of forces and displacements are converged and that the forces are zero; since force is the gradient of a potential energy vs distance graph, this indicates that the structure obtained is at equilibrium, demonstrating successful optimisation of N2.

<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 0.000000 0.001200 YES
</pre>

Figure 2.2: Item Table of optimised N2

Moreover, successful optimisation of N2 is indicated by the last structure having the most negative energy and the smallest gradient (Figure 2.3).

[[File:N2 optimisation.jpg|400px|thumb|center|Figure 2.3: Optimisation plots of N2]]

=== Dynamic Image of Optimised N2 ===

<jmol><jmolApplet>
<title>Figure 2.4: Optimised nitrogen</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ZOEYWAISUMLUNG_N2_OPTF_POP.LOG</uploadedFileContents>
<script>frame 1.4</script>
</jmolApplet></jmol>

The optimisation file is linked to [[Media:ZOEYWAISUMLUNG_N2_OPTF_POP.LOG| here]]

=== Vibrational Analysis of Optimised N2 ===

From Figure 2.5 in vibrational analysis, there are 0 modes as expected, and 0 bands in the experimental spectrum (Figure 2.6) of gaseous nitrogen as expected.

[[File:N2 vibrations.jpg ‎|400px|thumb|centre|Figure 2.5: Vibrational Table of optimised N2]]

[[File:N2 spectrum.jpg ‎|400px|thumb|centre|Figure 2.6: Spectrum of optimised N2]]

=== Charge Analysis of Optimised N2 ===

Charge analysis (Figure 2.7) shows the charge on both nitrogen atoms is 0.000. This result is expected because both atoms of the lienar bond are the same so there are no expected differences in electronegativity therefore electron density is shared equally between the nitrogen atoms. Note that the atoms are colored by charge, a charge of 0.000 is represented by the color black and the numbers are written in black therefore they cannot be seen here.

[[File:N2 charge.jpg ‎|400px|thumb|centre|Figure 2.7: Charge Analysis of optimised N2]]

== Optimisation of H2 ==

=== General Information of Optimised H2 ===

From the 'Summary' table (Figure 3.1), the following general information about the optimisation calculation is obtained: the molecule optimised is hydrogen, H2, the calculation method is RB3LYP; the basis set is 6-31G(d,p); the final energy E(RB3LYP) is -1.17853936 a.u.; the RMS gradient is 0.00002276 a.u.; and the point group of H2 is D∞h.

[[File:H2 summary.jpg|400px|thumb|center|Figure 3.1: Summary Table of optimised H2]]

=== Geometric Information of Optimised H2 ===

Optimised bond length: 0.74274 Å ≈ 0.7427 Å

=== Verification of Successful Optimisation of H2 ===

The 'Item' table (Figure 3.2) shows that the final set of forces and displacements are converged and that the forces are zero; since force is the gradient of a potential energy vs distance graph, this indicates that the structure obtained is at equilibrium, demonstrating successful optimisation of H2.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000039 0.000300 YES
Maximum Displacement 0.000052 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
</pre>

Figure 3.2: Item Table of optimised H2

Moreover, successful optimisation of H2 is indicated by the last structure having the most negative energy and the smallest gradient (Figure 3.3).

[[File:H2 optimisation.jpg|400px|thumb|center|Figure 3.3: Optimisation plots of H2]]

=== Dynamic Image of Optimised H2 ===

<jmol><jmolApplet>
<title>Figure 3.4: Optimised hydrogen</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ZOEYWAISUMLUNG_H2_OPTF_POP.LOG</uploadedFileContents>
<script>frame 1.3</script>
</jmolApplet></jmol>

The optimisation file is linked to [[Media:ZOEYWAISUMLUNG_H2_OPTF_POP.LOG| here]]

=== Vibrational Analysis of Optimised H2 ===

From Figure 3.5 in vibrational analysis, there are 0 modes as expected, and 0 bands in the experimental spectrum (Figure 3.6) of gaseous hydrogen as expected.

[[File:H2 vibrations.jpg ‎|400px|thumb|centre|Figure 3.5: Vibrational Table of optimised H2]]

[[File:H2 spectrum.jpg ‎|400px|thumb|centre|Figure 3.6: Spectrum of optimised H2]]

=== Charge Analysis of Optimised H2 ===

Charge analysis (Figure 3.7) shows the charge on both hydrogen atoms is 0.000. This result is expected because both atoms of the linear bond are the same so there are no expected differences in electronegativity therefore electron density is shared equally between the hydrogen atoms. If a higher basis set is used, a single bond would likely to be displayed.

[[File:H2 charge.jpg ‎|400px|thumb|centre|Figure 2.7: Charge Analysis of optimised H2]]

== Optimisation of S2 ==

=== General Information of Optimised S2 ===

From the 'Summary' table (Figure 4.1), the following general information about the optimisation calculation is obtained: the molecule optimised is sulphur, S2, the calculation method is RB3LYP; the basis set is 6-31G(d,p); the final energy E(RB3LYP) is -796.32599779 a.u.; the RMS gradient is 0.00000905 a.u.; and the point group of S2 is D∞h.

[[File:S2 summary.jpg|400px|thumb|center|Figure 4.1: Summary Table of optimised S2]]

=== Geometric Information of Optimised S2 ===

Optimised bond length: 1.92947 Å ≈ 1.929 Å

=== Verification of Successful Optimisation of S2 ===

The 'Item' table (Figure 4.2) shows that the final set of forces and displacements are converged and that the forces are approximately zero; since force is the gradient of a potential energy vs distance graph, this indicates that the structure obtained is at equilibrium, demonstrating successful optimisation of S2.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.000027 0.001800 YES
RMS Displacement 0.000038 0.001200 YES
</pre>

Figure 4.2: Item Table of optimised S2

Moreover, successful optimisation of S2 is indicated by the last structure having the most negative energy and the smallest gradient (Figure 4.3).

[[File:S2 optimisation.jpg|400px|thumb|center|Figure 4.3: Optimisation plots of S2]]

=== Dynamic Image of Optimised S2 ===

<jmol><jmolApplet>
<title>Figure 4.4: Optimised sulphur</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ZOEYWAISUMLUNG_S2_OPTF_POP.LOG</uploadedFileContents>
<script>frame 1.4</script>
</jmolApplet></jmol>

The optimisation file is linked to [[Media:ZOEYWAISUMLUNG_S2_OPTF_POP.LOG| here]]

=== Vibrational Analysis of Optimised S2 ===

From Figure 4.5 in vibrational analysis, there are 0 modes as expected, and 0 bands in the experimental spectrum (Figure 4.6) of gaseous sulphur as expected.

[[File:S2 vibrations.jpg ‎|400px|thumb|centre|Figure 4.5: Vibrational Table of optimised S2]]

[[File:S2 spectrum.jpg ‎|400px|thumb|centre|Figure 4.6: Spectrum of optimised S2]]

=== Charge Analysis of Optimised S2 ===

Charge analysis (Figure 4.7) shows the charge on both sulphur atoms is 0.000. This result is expected because both atoms of the linear bond are the same so there are no expected differences in electronegativity therefore electron density is shared equally between the sulphur atoms. A single bond instead of a double bond is displayed however this would most likely not be the case if a higher basis set is used for optimisation.

[[File:S2 charge.jpg ‎|400px|thumb|centre|Figure 2.7: Charge Analysis of optimised H2]]

=== Molecular Orbitals of Optimised S2 ===

{| class="wikitable" border="1"
|+ caption
! heading !! heading
|-
| [[File:1s sigma orbital 1.JPG ‎|300px|thumb|centre]]
|| The two 1s AOs overlap constructively to form a non-bonding σ MO. The energy of the MO formed is -88.93663.
|-
| [[File:1s sigma orbital 2.JPG ‎|300px|thumb|centre]] || The two 1s AOs also overlap destructively to form a non-bonding σ* MO. The energy of the MO formed is -88.93661. The energy of the two MOs formed from the two 1s AOs are very similar and hence degenerate.
|-
| [[File:2s sigma orbital 2.JPG ‎|300px|thumb|centre]]|| The two 2s AOs overlap constructively to form a non-bonding σ MO. The energy of the MO formed is -7.99779.
|-
| [[File:1s sigma orbital 1.JPG ‎|300px|thumb|centre]] || The two 2s AOs also overlap destructively to form a non-bonding σ* MO. The energy of the MO formed is -7.99769. The energy of the two MOs formed from the two 2s AOs are very similar and hence degenerate.
|-
| [[File:1s sigma orbital 1.JPG ‎|300px|thumb|centre]] || cell
|-
| [[File:1s sigma orbital 1.JPG ‎|300px|thumb|centre]] || cell
|-
| [[File:1s sigma orbital 1.JPG ‎|300px|thumb|centre]] || cell
|-
| [[File:1s sigma orbital 1.JPG ‎|300px|thumb|centre]] || cell
|-
| [[File:1s sigma orbital 1.JPG ‎|300px|thumb|centre]] || cell
|}

Rep:Mod:WSL1819

2018-03-16T11:29:11Z

Wsl1917: /* Molecular Orbitals of Optimised S2 */

== Optimisation of NH3 ==

=== General Information of Optimised NH3 ===

From the 'Summary' table (Figure 1.1), the following general information about the optimisation calculation is obtained: the molecule optimised is ammonia, NH3, the calculation method is RB3LYP; the basis set is 6-31G(d,p); the final energy E(RB3LYP) is -56.44397188 a.u.; the RMS gradient is 0.05399560 a.u.; and the point group of NH3 is C3v.

[[File:Nh3_summary.jpg|400px|thumb|center|Figure 1.1: Summary Table of optimised NH3]]

=== Geometric Information of Optimised NH3 ===

Optimised bond length: 1.01798 Å ≈ 1.018 Å

Optimised bond angle: 105.741 o ≈ 105.7 o

=== Verification of Successful Optimisation of NH3 ===

The 'Item' table (Figure 1.2) shows that the final set of forces and displacements are converged and that the forces are approximately zero; since force is the gradient of a potential energy vs distance graph, this indicates that the structure obtained is at equilibrium, demonstrating successful optimisation of NH3.

<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>

Figure 1.2: Item Table of optimised NH3

Moreover, successful optimisation of NH3 is indicated by the last structure having the most negative energy and the smallest gradient (Figure 1.3).

[[File:Nh3 optimisation.jpg|400px|thumb|center|Figure 1.3: Optimisation plots of NH3]]

=== Dynamic Image of Optimised NH3 ===

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ZOEYWAISUMLUNG_NH3_OPTF_POP.LOG</uploadedFileContents>
<script>frame 1.7</script>
</jmolApplet></jmol>
Figure 1.4: A 3D jmol file of optimised NH3

The optimisation file is linked to [[Media:ZOEYWAISUMLUNG_NH3_OPTF_POP.LOG| here]]

=== Vibrational Analysis of Optimised NH3 ===

From Figure 1.5 in vibrational analysis, there are 6 modes as expected, modes 2 and 3 and modes 5 and 6 are degenerate as they have the same frequency of 1693.95 cm-1 and 3589.82 cm-1 respectively; modes 1, 2 and 3 are "bending" vibrations and modes 4, 5 and 6 are "bond stretch" vibrations; mode 4 is highly symmetric ; mode 1 is the "umbrella" mode and 2 bands in the experimental spectrum (Figure 1.6) of gaseous ammonia as expected.

[[File:Nh3 vibrations 1.jpg ‎|400px|thumb|centre|Figure 1.5: Vibrational Table of optimised NH3]]

[[File:Nh3_spectrum.jpg ‎|400px|thumb|centre|Figure 1.6: Spectrum of optimised NH3]]

=== Charge Analysis of Optimised NH3 ===

Charge analysis (Figure 1.7) shows the charge on the nitrogen atom is -1.125 whilst that of the hydrogen atoms is +0.375. This result where nitrogen has a negative charge with a larger magnitude and hydrogen has a positive charge with a smaller magnitude is expected, since nitrogen is more electronegative than hydrogen, nitrogen should withdraw more electron density from each of the three N-H bonds.

[[File:Nh3_charge.jpg ‎|400px|thumb|centre|Figure 1.7: Charge Analysis of optimised NH3]]

== Optimisation of N2 ==

=== General Information of Optimised N2 ===

From the 'Summary' table (Figure 2.1), the following general information about the optimisation calculation is obtained: the molecule optimised is nitrogen, N2, the calculation method is RB3LYP; the basis set is 6-31G(d,p); the final energy E(RB3LYP) is -109.52412868 a.u.; the RMS gradient is 0.00000011 a.u.; and the point group of N2 is D∞h.

[[File:N2 summary 2.jpg|400px|thumb|center|Figure 2.1: Summary Table of optimised N2]]

=== Geometric Information of Optimised N2 ===

Optimised bond length: 1.10550 Å ≈ 1.106 Å

=== Verification of Successful Optimisation of N2 ===

The 'Item' table (Figure 2.2) shows that the final set of forces and displacements are converged and that the forces are zero; since force is the gradient of a potential energy vs distance graph, this indicates that the structure obtained is at equilibrium, demonstrating successful optimisation of N2.

<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 0.000000 0.001200 YES
</pre>

Figure 2.2: Item Table of optimised N2

Moreover, successful optimisation of N2 is indicated by the last structure having the most negative energy and the smallest gradient (Figure 2.3).

[[File:N2 optimisation.jpg|400px|thumb|center|Figure 2.3: Optimisation plots of N2]]

=== Dynamic Image of Optimised N2 ===

<jmol><jmolApplet>
<title>Figure 2.4: Optimised nitrogen</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ZOEYWAISUMLUNG_N2_OPTF_POP.LOG</uploadedFileContents>
<script>frame 1.4</script>
</jmolApplet></jmol>

The optimisation file is linked to [[Media:ZOEYWAISUMLUNG_N2_OPTF_POP.LOG| here]]

=== Vibrational Analysis of Optimised N2 ===

From Figure 2.5 in vibrational analysis, there are 0 modes as expected, and 0 bands in the experimental spectrum (Figure 2.6) of gaseous nitrogen as expected.

[[File:N2 vibrations.jpg ‎|400px|thumb|centre|Figure 2.5: Vibrational Table of optimised N2]]

[[File:N2 spectrum.jpg ‎|400px|thumb|centre|Figure 2.6: Spectrum of optimised N2]]

=== Charge Analysis of Optimised N2 ===

Charge analysis (Figure 2.7) shows the charge on both nitrogen atoms is 0.000. This result is expected because both atoms of the lienar bond are the same so there are no expected differences in electronegativity therefore electron density is shared equally between the nitrogen atoms. Note that the atoms are colored by charge, a charge of 0.000 is represented by the color black and the numbers are written in black therefore they cannot be seen here.

[[File:N2 charge.jpg ‎|400px|thumb|centre|Figure 2.7: Charge Analysis of optimised N2]]

== Optimisation of H2 ==

=== General Information of Optimised H2 ===

From the 'Summary' table (Figure 3.1), the following general information about the optimisation calculation is obtained: the molecule optimised is hydrogen, H2, the calculation method is RB3LYP; the basis set is 6-31G(d,p); the final energy E(RB3LYP) is -1.17853936 a.u.; the RMS gradient is 0.00002276 a.u.; and the point group of H2 is D∞h.

[[File:H2 summary.jpg|400px|thumb|center|Figure 3.1: Summary Table of optimised H2]]

=== Geometric Information of Optimised H2 ===

Optimised bond length: 0.74274 Å ≈ 0.7427 Å

=== Verification of Successful Optimisation of H2 ===

The 'Item' table (Figure 3.2) shows that the final set of forces and displacements are converged and that the forces are zero; since force is the gradient of a potential energy vs distance graph, this indicates that the structure obtained is at equilibrium, demonstrating successful optimisation of H2.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000039 0.000300 YES
Maximum Displacement 0.000052 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
</pre>

Figure 3.2: Item Table of optimised H2

Moreover, successful optimisation of H2 is indicated by the last structure having the most negative energy and the smallest gradient (Figure 3.3).

[[File:H2 optimisation.jpg|400px|thumb|center|Figure 3.3: Optimisation plots of H2]]

=== Dynamic Image of Optimised H2 ===

<jmol><jmolApplet>
<title>Figure 3.4: Optimised hydrogen</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ZOEYWAISUMLUNG_H2_OPTF_POP.LOG</uploadedFileContents>
<script>frame 1.3</script>
</jmolApplet></jmol>

The optimisation file is linked to [[Media:ZOEYWAISUMLUNG_H2_OPTF_POP.LOG| here]]

=== Vibrational Analysis of Optimised H2 ===

From Figure 3.5 in vibrational analysis, there are 0 modes as expected, and 0 bands in the experimental spectrum (Figure 3.6) of gaseous hydrogen as expected.

[[File:H2 vibrations.jpg ‎|400px|thumb|centre|Figure 3.5: Vibrational Table of optimised H2]]

[[File:H2 spectrum.jpg ‎|400px|thumb|centre|Figure 3.6: Spectrum of optimised H2]]

=== Charge Analysis of Optimised H2 ===

Charge analysis (Figure 3.7) shows the charge on both hydrogen atoms is 0.000. This result is expected because both atoms of the linear bond are the same so there are no expected differences in electronegativity therefore electron density is shared equally between the hydrogen atoms. If a higher basis set is used, a single bond would likely to be displayed.

[[File:H2 charge.jpg ‎|400px|thumb|centre|Figure 2.7: Charge Analysis of optimised H2]]

== Optimisation of S2 ==

=== General Information of Optimised S2 ===

From the 'Summary' table (Figure 4.1), the following general information about the optimisation calculation is obtained: the molecule optimised is sulphur, S2, the calculation method is RB3LYP; the basis set is 6-31G(d,p); the final energy E(RB3LYP) is -796.32599779 a.u.; the RMS gradient is 0.00000905 a.u.; and the point group of S2 is D∞h.

[[File:S2 summary.jpg|400px|thumb|center|Figure 4.1: Summary Table of optimised S2]]

=== Geometric Information of Optimised S2 ===

Optimised bond length: 1.92947 Å ≈ 1.929 Å

=== Verification of Successful Optimisation of S2 ===

The 'Item' table (Figure 4.2) shows that the final set of forces and displacements are converged and that the forces are approximately zero; since force is the gradient of a potential energy vs distance graph, this indicates that the structure obtained is at equilibrium, demonstrating successful optimisation of S2.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.000027 0.001800 YES
RMS Displacement 0.000038 0.001200 YES
</pre>

Figure 4.2: Item Table of optimised S2

Moreover, successful optimisation of S2 is indicated by the last structure having the most negative energy and the smallest gradient (Figure 4.3).

[[File:S2 optimisation.jpg|400px|thumb|center|Figure 4.3: Optimisation plots of S2]]

=== Dynamic Image of Optimised S2 ===

<jmol><jmolApplet>
<title>Figure 4.4: Optimised sulphur</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ZOEYWAISUMLUNG_S2_OPTF_POP.LOG</uploadedFileContents>
<script>frame 1.4</script>
</jmolApplet></jmol>

The optimisation file is linked to [[Media:ZOEYWAISUMLUNG_S2_OPTF_POP.LOG| here]]

=== Vibrational Analysis of Optimised S2 ===

From Figure 4.5 in vibrational analysis, there are 0 modes as expected, and 0 bands in the experimental spectrum (Figure 4.6) of gaseous sulphur as expected.

[[File:S2 vibrations.jpg ‎|400px|thumb|centre|Figure 4.5: Vibrational Table of optimised S2]]

[[File:S2 spectrum.jpg ‎|400px|thumb|centre|Figure 4.6: Spectrum of optimised S2]]

=== Charge Analysis of Optimised S2 ===

Charge analysis (Figure 4.7) shows the charge on both sulphur atoms is 0.000. This result is expected because both atoms of the linear bond are the same so there are no expected differences in electronegativity therefore electron density is shared equally between the sulphur atoms. A single bond instead of a double bond is displayed however this would most likely not be the case if a higher basis set is used for optimisation.

[[File:S2 charge.jpg ‎|400px|thumb|centre|Figure 2.7: Charge Analysis of optimised H2]]

=== Molecular Orbitals of Optimised S2 ===

{| class="wikitable" border="1"
|+ caption
! heading !! heading
|-
| [[File:1s sigma orbital 1.JPG ‎|100px|thumb|centre]]
|| The two 1s AOs overlap constructively to form a non-bonding σ MO. The energy of the MO formed is -88.93663.
|-
| [[File:1s sigma orbital 2.JPG ‎|100px|thumb|centre]] || The two 1s AOs also overlap destructively to form a non-bonding σ* MO. The energy of the MO formed is -88.93661. The energy of the two MOs formed from the two 1s AOs are very similar and hence degenerate.
|-
| [[File:2s sigma orbital 2.JPG ‎|100px|thumb|centre]]|| The two 2s AOs overlap constructively to form a non-bonding σ MO. The energy of the MO formed is -7.99779.
|-
| [[File:1s sigma orbital 1.JPG ‎|100px|thumb|centre]] || The two 2s AOs also overlap destructively to form a non-bonding σ* MO. The energy of the MO formed is -7.99769. The energy of the two MOs formed from the two 2s AOs are very similar and hence degenerate.
|-
| [[File:1s sigma orbital 1.JPG ‎|300px|thumb|centre]] || cell
|-
| [[File:1s sigma orbital 1.JPG ‎|300px|thumb|centre]] || cell
|-
| [[File:1s sigma orbital 1.JPG ‎|300px|thumb|centre]] || cell
|-
| [[File:1s sigma orbital 1.JPG ‎|300px|thumb|centre]] || cell
|-
| [[File:1s sigma orbital 1.JPG ‎|300px|thumb|centre]] || cell
|}

Rep:Mod:WSL1819

2018-03-16T11:28:50Z

Wsl1917: /* Molecular Orbitals of Optimised S2 */

== Optimisation of NH3 ==

=== General Information of Optimised NH3 ===

From the 'Summary' table (Figure 1.1), the following general information about the optimisation calculation is obtained: the molecule optimised is ammonia, NH3, the calculation method is RB3LYP; the basis set is 6-31G(d,p); the final energy E(RB3LYP) is -56.44397188 a.u.; the RMS gradient is 0.05399560 a.u.; and the point group of NH3 is C3v.

[[File:Nh3_summary.jpg|400px|thumb|center|Figure 1.1: Summary Table of optimised NH3]]

=== Geometric Information of Optimised NH3 ===

Optimised bond length: 1.01798 Å ≈ 1.018 Å

Optimised bond angle: 105.741 o ≈ 105.7 o

=== Verification of Successful Optimisation of NH3 ===

The 'Item' table (Figure 1.2) shows that the final set of forces and displacements are converged and that the forces are approximately zero; since force is the gradient of a potential energy vs distance graph, this indicates that the structure obtained is at equilibrium, demonstrating successful optimisation of NH3.

<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>

Figure 1.2: Item Table of optimised NH3

Moreover, successful optimisation of NH3 is indicated by the last structure having the most negative energy and the smallest gradient (Figure 1.3).

[[File:Nh3 optimisation.jpg|400px|thumb|center|Figure 1.3: Optimisation plots of NH3]]

=== Dynamic Image of Optimised NH3 ===

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ZOEYWAISUMLUNG_NH3_OPTF_POP.LOG</uploadedFileContents>
<script>frame 1.7</script>
</jmolApplet></jmol>
Figure 1.4: A 3D jmol file of optimised NH3

The optimisation file is linked to [[Media:ZOEYWAISUMLUNG_NH3_OPTF_POP.LOG| here]]

=== Vibrational Analysis of Optimised NH3 ===

From Figure 1.5 in vibrational analysis, there are 6 modes as expected, modes 2 and 3 and modes 5 and 6 are degenerate as they have the same frequency of 1693.95 cm-1 and 3589.82 cm-1 respectively; modes 1, 2 and 3 are "bending" vibrations and modes 4, 5 and 6 are "bond stretch" vibrations; mode 4 is highly symmetric ; mode 1 is the "umbrella" mode and 2 bands in the experimental spectrum (Figure 1.6) of gaseous ammonia as expected.

[[File:Nh3 vibrations 1.jpg ‎|400px|thumb|centre|Figure 1.5: Vibrational Table of optimised NH3]]

[[File:Nh3_spectrum.jpg ‎|400px|thumb|centre|Figure 1.6: Spectrum of optimised NH3]]

=== Charge Analysis of Optimised NH3 ===

Charge analysis (Figure 1.7) shows the charge on the nitrogen atom is -1.125 whilst that of the hydrogen atoms is +0.375. This result where nitrogen has a negative charge with a larger magnitude and hydrogen has a positive charge with a smaller magnitude is expected, since nitrogen is more electronegative than hydrogen, nitrogen should withdraw more electron density from each of the three N-H bonds.

[[File:Nh3_charge.jpg ‎|400px|thumb|centre|Figure 1.7: Charge Analysis of optimised NH3]]

== Optimisation of N2 ==

=== General Information of Optimised N2 ===

From the 'Summary' table (Figure 2.1), the following general information about the optimisation calculation is obtained: the molecule optimised is nitrogen, N2, the calculation method is RB3LYP; the basis set is 6-31G(d,p); the final energy E(RB3LYP) is -109.52412868 a.u.; the RMS gradient is 0.00000011 a.u.; and the point group of N2 is D∞h.

[[File:N2 summary 2.jpg|400px|thumb|center|Figure 2.1: Summary Table of optimised N2]]

=== Geometric Information of Optimised N2 ===

Optimised bond length: 1.10550 Å ≈ 1.106 Å

=== Verification of Successful Optimisation of N2 ===

The 'Item' table (Figure 2.2) shows that the final set of forces and displacements are converged and that the forces are zero; since force is the gradient of a potential energy vs distance graph, this indicates that the structure obtained is at equilibrium, demonstrating successful optimisation of N2.

<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 0.000000 0.001200 YES
</pre>

Figure 2.2: Item Table of optimised N2

Moreover, successful optimisation of N2 is indicated by the last structure having the most negative energy and the smallest gradient (Figure 2.3).

[[File:N2 optimisation.jpg|400px|thumb|center|Figure 2.3: Optimisation plots of N2]]

=== Dynamic Image of Optimised N2 ===

<jmol><jmolApplet>
<title>Figure 2.4: Optimised nitrogen</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ZOEYWAISUMLUNG_N2_OPTF_POP.LOG</uploadedFileContents>
<script>frame 1.4</script>
</jmolApplet></jmol>

The optimisation file is linked to [[Media:ZOEYWAISUMLUNG_N2_OPTF_POP.LOG| here]]

=== Vibrational Analysis of Optimised N2 ===

From Figure 2.5 in vibrational analysis, there are 0 modes as expected, and 0 bands in the experimental spectrum (Figure 2.6) of gaseous nitrogen as expected.

[[File:N2 vibrations.jpg ‎|400px|thumb|centre|Figure 2.5: Vibrational Table of optimised N2]]

[[File:N2 spectrum.jpg ‎|400px|thumb|centre|Figure 2.6: Spectrum of optimised N2]]

=== Charge Analysis of Optimised N2 ===

Charge analysis (Figure 2.7) shows the charge on both nitrogen atoms is 0.000. This result is expected because both atoms of the lienar bond are the same so there are no expected differences in electronegativity therefore electron density is shared equally between the nitrogen atoms. Note that the atoms are colored by charge, a charge of 0.000 is represented by the color black and the numbers are written in black therefore they cannot be seen here.

[[File:N2 charge.jpg ‎|400px|thumb|centre|Figure 2.7: Charge Analysis of optimised N2]]

== Optimisation of H2 ==

=== General Information of Optimised H2 ===

From the 'Summary' table (Figure 3.1), the following general information about the optimisation calculation is obtained: the molecule optimised is hydrogen, H2, the calculation method is RB3LYP; the basis set is 6-31G(d,p); the final energy E(RB3LYP) is -1.17853936 a.u.; the RMS gradient is 0.00002276 a.u.; and the point group of H2 is D∞h.

[[File:H2 summary.jpg|400px|thumb|center|Figure 3.1: Summary Table of optimised H2]]

=== Geometric Information of Optimised H2 ===

Optimised bond length: 0.74274 Å ≈ 0.7427 Å

=== Verification of Successful Optimisation of H2 ===

The 'Item' table (Figure 3.2) shows that the final set of forces and displacements are converged and that the forces are zero; since force is the gradient of a potential energy vs distance graph, this indicates that the structure obtained is at equilibrium, demonstrating successful optimisation of H2.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000039 0.000300 YES
Maximum Displacement 0.000052 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
</pre>

Figure 3.2: Item Table of optimised H2

Moreover, successful optimisation of H2 is indicated by the last structure having the most negative energy and the smallest gradient (Figure 3.3).

[[File:H2 optimisation.jpg|400px|thumb|center|Figure 3.3: Optimisation plots of H2]]

=== Dynamic Image of Optimised H2 ===

<jmol><jmolApplet>
<title>Figure 3.4: Optimised hydrogen</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ZOEYWAISUMLUNG_H2_OPTF_POP.LOG</uploadedFileContents>
<script>frame 1.3</script>
</jmolApplet></jmol>

The optimisation file is linked to [[Media:ZOEYWAISUMLUNG_H2_OPTF_POP.LOG| here]]

=== Vibrational Analysis of Optimised H2 ===

From Figure 3.5 in vibrational analysis, there are 0 modes as expected, and 0 bands in the experimental spectrum (Figure 3.6) of gaseous hydrogen as expected.

[[File:H2 vibrations.jpg ‎|400px|thumb|centre|Figure 3.5: Vibrational Table of optimised H2]]

[[File:H2 spectrum.jpg ‎|400px|thumb|centre|Figure 3.6: Spectrum of optimised H2]]

=== Charge Analysis of Optimised H2 ===

Charge analysis (Figure 3.7) shows the charge on both hydrogen atoms is 0.000. This result is expected because both atoms of the linear bond are the same so there are no expected differences in electronegativity therefore electron density is shared equally between the hydrogen atoms. If a higher basis set is used, a single bond would likely to be displayed.

[[File:H2 charge.jpg ‎|400px|thumb|centre|Figure 2.7: Charge Analysis of optimised H2]]

== Optimisation of S2 ==

=== General Information of Optimised S2 ===

From the 'Summary' table (Figure 4.1), the following general information about the optimisation calculation is obtained: the molecule optimised is sulphur, S2, the calculation method is RB3LYP; the basis set is 6-31G(d,p); the final energy E(RB3LYP) is -796.32599779 a.u.; the RMS gradient is 0.00000905 a.u.; and the point group of S2 is D∞h.

[[File:S2 summary.jpg|400px|thumb|center|Figure 4.1: Summary Table of optimised S2]]

=== Geometric Information of Optimised S2 ===

Optimised bond length: 1.92947 Å ≈ 1.929 Å

=== Verification of Successful Optimisation of S2 ===

The 'Item' table (Figure 4.2) shows that the final set of forces and displacements are converged and that the forces are approximately zero; since force is the gradient of a potential energy vs distance graph, this indicates that the structure obtained is at equilibrium, demonstrating successful optimisation of S2.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.000027 0.001800 YES
RMS Displacement 0.000038 0.001200 YES
</pre>

Figure 4.2: Item Table of optimised S2

Moreover, successful optimisation of S2 is indicated by the last structure having the most negative energy and the smallest gradient (Figure 4.3).

[[File:S2 optimisation.jpg|400px|thumb|center|Figure 4.3: Optimisation plots of S2]]

=== Dynamic Image of Optimised S2 ===

<jmol><jmolApplet>
<title>Figure 4.4: Optimised sulphur</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ZOEYWAISUMLUNG_S2_OPTF_POP.LOG</uploadedFileContents>
<script>frame 1.4</script>
</jmolApplet></jmol>

The optimisation file is linked to [[Media:ZOEYWAISUMLUNG_S2_OPTF_POP.LOG| here]]

=== Vibrational Analysis of Optimised S2 ===

From Figure 4.5 in vibrational analysis, there are 0 modes as expected, and 0 bands in the experimental spectrum (Figure 4.6) of gaseous sulphur as expected.

[[File:S2 vibrations.jpg ‎|400px|thumb|centre|Figure 4.5: Vibrational Table of optimised S2]]

[[File:S2 spectrum.jpg ‎|400px|thumb|centre|Figure 4.6: Spectrum of optimised S2]]

=== Charge Analysis of Optimised S2 ===

Charge analysis (Figure 4.7) shows the charge on both sulphur atoms is 0.000. This result is expected because both atoms of the linear bond are the same so there are no expected differences in electronegativity therefore electron density is shared equally between the sulphur atoms. A single bond instead of a double bond is displayed however this would most likely not be the case if a higher basis set is used for optimisation.

[[File:S2 charge.jpg ‎|400px|thumb|centre|Figure 2.7: Charge Analysis of optimised H2]]

=== Molecular Orbitals of Optimised S2 ===

{| class="wikitable" border="1"
|+ caption
! heading !! heading
|-
| [[File:1s sigma orbital 1.JPG ‎|100px|thumb|centre]]
|| The two 1s AOs overlap constructively to form a non-bonding σ MO. The energy of the MO formed is -88.93663.
|-
| [[File:1s sigma orbital 2.JPG ‎|100px|thumb|centre]] || The two 1s AOs also overlap destructively to form a non-bonding σ* MO. The energy of the MO formed is -88.93661. The energy of the two MOs formed from the two 1s AOs are very similar and hence degenerate.
|-
| [[File:2s sigma orbital 2.JPG ‎|100px|thumb|centre]]|| The two 2s AOs overlap constructively to form a non-bonding σ MO. The energy of the MO formed is -7.99779.
|-
| [[File:1s sigma orbital 1.JPG ‎|300px|thumb|centre]] || The two 2s AOs also overlap destructively to form a non-bonding σ* MO. The energy of the MO formed is -7.99769. The energy of the two MOs formed from the two 2s AOs are very similar and hence degenerate.
|-
| [[File:1s sigma orbital 1.JPG ‎|300px|thumb|centre]] || cell
|-
| [[File:1s sigma orbital 1.JPG ‎|300px|thumb|centre]] || cell
|-
| [[File:1s sigma orbital 1.JPG ‎|300px|thumb|centre]] || cell
|-
| [[File:1s sigma orbital 1.JPG ‎|300px|thumb|centre]] || cell
|-
| [[File:1s sigma orbital 1.JPG ‎|300px|thumb|centre]] || cell
|}

File:2s sigma orbital 2.JPG

2018-03-16T11:28:43Z

Wsl1917:

File:2s sigma orbital 1.JPG

2018-03-16T11:27:05Z

Wsl1917:

Rep:Mod:WSL1819

2018-03-16T11:24:14Z

Wsl1917: /* Molecular Orbitals of Optimised S2 */

== Optimisation of NH3 ==

=== General Information of Optimised NH3 ===

From the 'Summary' table (Figure 1.1), the following general information about the optimisation calculation is obtained: the molecule optimised is ammonia, NH3, the calculation method is RB3LYP; the basis set is 6-31G(d,p); the final energy E(RB3LYP) is -56.44397188 a.u.; the RMS gradient is 0.05399560 a.u.; and the point group of NH3 is C3v.

[[File:Nh3_summary.jpg|400px|thumb|center|Figure 1.1: Summary Table of optimised NH3]]

=== Geometric Information of Optimised NH3 ===

Optimised bond length: 1.01798 Å ≈ 1.018 Å

Optimised bond angle: 105.741 o ≈ 105.7 o

=== Verification of Successful Optimisation of NH3 ===

The 'Item' table (Figure 1.2) shows that the final set of forces and displacements are converged and that the forces are approximately zero; since force is the gradient of a potential energy vs distance graph, this indicates that the structure obtained is at equilibrium, demonstrating successful optimisation of NH3.

<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>

Figure 1.2: Item Table of optimised NH3

Moreover, successful optimisation of NH3 is indicated by the last structure having the most negative energy and the smallest gradient (Figure 1.3).

[[File:Nh3 optimisation.jpg|400px|thumb|center|Figure 1.3: Optimisation plots of NH3]]

=== Dynamic Image of Optimised NH3 ===

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ZOEYWAISUMLUNG_NH3_OPTF_POP.LOG</uploadedFileContents>
<script>frame 1.7</script>
</jmolApplet></jmol>
Figure 1.4: A 3D jmol file of optimised NH3

The optimisation file is linked to [[Media:ZOEYWAISUMLUNG_NH3_OPTF_POP.LOG| here]]

=== Vibrational Analysis of Optimised NH3 ===

From Figure 1.5 in vibrational analysis, there are 6 modes as expected, modes 2 and 3 and modes 5 and 6 are degenerate as they have the same frequency of 1693.95 cm-1 and 3589.82 cm-1 respectively; modes 1, 2 and 3 are "bending" vibrations and modes 4, 5 and 6 are "bond stretch" vibrations; mode 4 is highly symmetric ; mode 1 is the "umbrella" mode and 2 bands in the experimental spectrum (Figure 1.6) of gaseous ammonia as expected.

[[File:Nh3 vibrations 1.jpg ‎|400px|thumb|centre|Figure 1.5: Vibrational Table of optimised NH3]]

[[File:Nh3_spectrum.jpg ‎|400px|thumb|centre|Figure 1.6: Spectrum of optimised NH3]]

=== Charge Analysis of Optimised NH3 ===

Charge analysis (Figure 1.7) shows the charge on the nitrogen atom is -1.125 whilst that of the hydrogen atoms is +0.375. This result where nitrogen has a negative charge with a larger magnitude and hydrogen has a positive charge with a smaller magnitude is expected, since nitrogen is more electronegative than hydrogen, nitrogen should withdraw more electron density from each of the three N-H bonds.

[[File:Nh3_charge.jpg ‎|400px|thumb|centre|Figure 1.7: Charge Analysis of optimised NH3]]

== Optimisation of N2 ==

=== General Information of Optimised N2 ===

From the 'Summary' table (Figure 2.1), the following general information about the optimisation calculation is obtained: the molecule optimised is nitrogen, N2, the calculation method is RB3LYP; the basis set is 6-31G(d,p); the final energy E(RB3LYP) is -109.52412868 a.u.; the RMS gradient is 0.00000011 a.u.; and the point group of N2 is D∞h.

[[File:N2 summary 2.jpg|400px|thumb|center|Figure 2.1: Summary Table of optimised N2]]

=== Geometric Information of Optimised N2 ===

Optimised bond length: 1.10550 Å ≈ 1.106 Å

=== Verification of Successful Optimisation of N2 ===

The 'Item' table (Figure 2.2) shows that the final set of forces and displacements are converged and that the forces are zero; since force is the gradient of a potential energy vs distance graph, this indicates that the structure obtained is at equilibrium, demonstrating successful optimisation of N2.

<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 0.000000 0.001200 YES
</pre>

Figure 2.2: Item Table of optimised N2

Moreover, successful optimisation of N2 is indicated by the last structure having the most negative energy and the smallest gradient (Figure 2.3).

[[File:N2 optimisation.jpg|400px|thumb|center|Figure 2.3: Optimisation plots of N2]]

=== Dynamic Image of Optimised N2 ===

<jmol><jmolApplet>
<title>Figure 2.4: Optimised nitrogen</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ZOEYWAISUMLUNG_N2_OPTF_POP.LOG</uploadedFileContents>
<script>frame 1.4</script>
</jmolApplet></jmol>

The optimisation file is linked to [[Media:ZOEYWAISUMLUNG_N2_OPTF_POP.LOG| here]]

=== Vibrational Analysis of Optimised N2 ===

From Figure 2.5 in vibrational analysis, there are 0 modes as expected, and 0 bands in the experimental spectrum (Figure 2.6) of gaseous nitrogen as expected.

[[File:N2 vibrations.jpg ‎|400px|thumb|centre|Figure 2.5: Vibrational Table of optimised N2]]

[[File:N2 spectrum.jpg ‎|400px|thumb|centre|Figure 2.6: Spectrum of optimised N2]]

=== Charge Analysis of Optimised N2 ===

Charge analysis (Figure 2.7) shows the charge on both nitrogen atoms is 0.000. This result is expected because both atoms of the lienar bond are the same so there are no expected differences in electronegativity therefore electron density is shared equally between the nitrogen atoms. Note that the atoms are colored by charge, a charge of 0.000 is represented by the color black and the numbers are written in black therefore they cannot be seen here.

[[File:N2 charge.jpg ‎|400px|thumb|centre|Figure 2.7: Charge Analysis of optimised N2]]

== Optimisation of H2 ==

=== General Information of Optimised H2 ===

From the 'Summary' table (Figure 3.1), the following general information about the optimisation calculation is obtained: the molecule optimised is hydrogen, H2, the calculation method is RB3LYP; the basis set is 6-31G(d,p); the final energy E(RB3LYP) is -1.17853936 a.u.; the RMS gradient is 0.00002276 a.u.; and the point group of H2 is D∞h.

[[File:H2 summary.jpg|400px|thumb|center|Figure 3.1: Summary Table of optimised H2]]

=== Geometric Information of Optimised H2 ===

Optimised bond length: 0.74274 Å ≈ 0.7427 Å

=== Verification of Successful Optimisation of H2 ===

The 'Item' table (Figure 3.2) shows that the final set of forces and displacements are converged and that the forces are zero; since force is the gradient of a potential energy vs distance graph, this indicates that the structure obtained is at equilibrium, demonstrating successful optimisation of H2.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000039 0.000300 YES
Maximum Displacement 0.000052 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
</pre>

Figure 3.2: Item Table of optimised H2

Moreover, successful optimisation of H2 is indicated by the last structure having the most negative energy and the smallest gradient (Figure 3.3).

[[File:H2 optimisation.jpg|400px|thumb|center|Figure 3.3: Optimisation plots of H2]]

=== Dynamic Image of Optimised H2 ===

<jmol><jmolApplet>
<title>Figure 3.4: Optimised hydrogen</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ZOEYWAISUMLUNG_H2_OPTF_POP.LOG</uploadedFileContents>
<script>frame 1.3</script>
</jmolApplet></jmol>

The optimisation file is linked to [[Media:ZOEYWAISUMLUNG_H2_OPTF_POP.LOG| here]]

=== Vibrational Analysis of Optimised H2 ===

From Figure 3.5 in vibrational analysis, there are 0 modes as expected, and 0 bands in the experimental spectrum (Figure 3.6) of gaseous hydrogen as expected.

[[File:H2 vibrations.jpg ‎|400px|thumb|centre|Figure 3.5: Vibrational Table of optimised H2]]

[[File:H2 spectrum.jpg ‎|400px|thumb|centre|Figure 3.6: Spectrum of optimised H2]]

=== Charge Analysis of Optimised H2 ===

Charge analysis (Figure 3.7) shows the charge on both hydrogen atoms is 0.000. This result is expected because both atoms of the linear bond are the same so there are no expected differences in electronegativity therefore electron density is shared equally between the hydrogen atoms. If a higher basis set is used, a single bond would likely to be displayed.

[[File:H2 charge.jpg ‎|400px|thumb|centre|Figure 2.7: Charge Analysis of optimised H2]]

== Optimisation of S2 ==

=== General Information of Optimised S2 ===

From the 'Summary' table (Figure 4.1), the following general information about the optimisation calculation is obtained: the molecule optimised is sulphur, S2, the calculation method is RB3LYP; the basis set is 6-31G(d,p); the final energy E(RB3LYP) is -796.32599779 a.u.; the RMS gradient is 0.00000905 a.u.; and the point group of S2 is D∞h.

[[File:S2 summary.jpg|400px|thumb|center|Figure 4.1: Summary Table of optimised S2]]

=== Geometric Information of Optimised S2 ===

Optimised bond length: 1.92947 Å ≈ 1.929 Å

=== Verification of Successful Optimisation of S2 ===

The 'Item' table (Figure 4.2) shows that the final set of forces and displacements are converged and that the forces are approximately zero; since force is the gradient of a potential energy vs distance graph, this indicates that the structure obtained is at equilibrium, demonstrating successful optimisation of S2.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.000027 0.001800 YES
RMS Displacement 0.000038 0.001200 YES
</pre>

Figure 4.2: Item Table of optimised S2

Moreover, successful optimisation of S2 is indicated by the last structure having the most negative energy and the smallest gradient (Figure 4.3).

[[File:S2 optimisation.jpg|400px|thumb|center|Figure 4.3: Optimisation plots of S2]]

=== Dynamic Image of Optimised S2 ===

<jmol><jmolApplet>
<title>Figure 4.4: Optimised sulphur</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ZOEYWAISUMLUNG_S2_OPTF_POP.LOG</uploadedFileContents>
<script>frame 1.4</script>
</jmolApplet></jmol>

The optimisation file is linked to [[Media:ZOEYWAISUMLUNG_S2_OPTF_POP.LOG| here]]

=== Vibrational Analysis of Optimised S2 ===

From Figure 4.5 in vibrational analysis, there are 0 modes as expected, and 0 bands in the experimental spectrum (Figure 4.6) of gaseous sulphur as expected.

[[File:S2 vibrations.jpg ‎|400px|thumb|centre|Figure 4.5: Vibrational Table of optimised S2]]

[[File:S2 spectrum.jpg ‎|400px|thumb|centre|Figure 4.6: Spectrum of optimised S2]]

=== Charge Analysis of Optimised S2 ===

Charge analysis (Figure 4.7) shows the charge on both sulphur atoms is 0.000. This result is expected because both atoms of the linear bond are the same so there are no expected differences in electronegativity therefore electron density is shared equally between the sulphur atoms. A single bond instead of a double bond is displayed however this would most likely not be the case if a higher basis set is used for optimisation.

[[File:S2 charge.jpg ‎|400px|thumb|centre|Figure 2.7: Charge Analysis of optimised H2]]

=== Molecular Orbitals of Optimised S2 ===

{| class="wikitable" border="1"
|+ caption
! heading !! heading
|-
| [[File:1s sigma orbital 1.JPG ‎|300px|thumb|centre]]
|| The two 1s AOs overlap to form a non-bonding σ MO. The energy of the MO formed is -88.93663.
|-
| [[File:1s sigma orbital 2.JPG ‎|300px|thumb|centre]] || The two 1s AOs also overlap to form a non-bonding σ* MO. The energy of the MO formed is -88.93661. The energy of the two MOs formed from the two 1s AOs are very similar and hence degenerate.
|-
| cell || cell
|-
| cell || cell
|-
| cell || cell
|-
| cell || cell
|-
| cell || cell
|-
| cell || cell
|-
| cell || cell
|}

File:1s sigma orbital 2.JPG

2018-03-16T11:23:49Z

Wsl1917:

Rep:Mod:WSL1819

2018-03-16T11:21:11Z

Wsl1917: /* Molecular Orbitals of Optimised S2 */

== Optimisation of NH3 ==

=== General Information of Optimised NH3 ===

From the 'Summary' table (Figure 1.1), the following general information about the optimisation calculation is obtained: the molecule optimised is ammonia, NH3, the calculation method is RB3LYP; the basis set is 6-31G(d,p); the final energy E(RB3LYP) is -56.44397188 a.u.; the RMS gradient is 0.05399560 a.u.; and the point group of NH3 is C3v.

[[File:Nh3_summary.jpg|400px|thumb|center|Figure 1.1: Summary Table of optimised NH3]]

=== Geometric Information of Optimised NH3 ===

Optimised bond length: 1.01798 Å ≈ 1.018 Å

Optimised bond angle: 105.741 o ≈ 105.7 o

=== Verification of Successful Optimisation of NH3 ===

The 'Item' table (Figure 1.2) shows that the final set of forces and displacements are converged and that the forces are approximately zero; since force is the gradient of a potential energy vs distance graph, this indicates that the structure obtained is at equilibrium, demonstrating successful optimisation of NH3.

<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>

Figure 1.2: Item Table of optimised NH3

Moreover, successful optimisation of NH3 is indicated by the last structure having the most negative energy and the smallest gradient (Figure 1.3).

[[File:Nh3 optimisation.jpg|400px|thumb|center|Figure 1.3: Optimisation plots of NH3]]

=== Dynamic Image of Optimised NH3 ===

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ZOEYWAISUMLUNG_NH3_OPTF_POP.LOG</uploadedFileContents>
<script>frame 1.7</script>
</jmolApplet></jmol>
Figure 1.4: A 3D jmol file of optimised NH3

The optimisation file is linked to [[Media:ZOEYWAISUMLUNG_NH3_OPTF_POP.LOG| here]]

=== Vibrational Analysis of Optimised NH3 ===

From Figure 1.5 in vibrational analysis, there are 6 modes as expected, modes 2 and 3 and modes 5 and 6 are degenerate as they have the same frequency of 1693.95 cm-1 and 3589.82 cm-1 respectively; modes 1, 2 and 3 are "bending" vibrations and modes 4, 5 and 6 are "bond stretch" vibrations; mode 4 is highly symmetric ; mode 1 is the "umbrella" mode and 2 bands in the experimental spectrum (Figure 1.6) of gaseous ammonia as expected.

[[File:Nh3 vibrations 1.jpg ‎|400px|thumb|centre|Figure 1.5: Vibrational Table of optimised NH3]]

[[File:Nh3_spectrum.jpg ‎|400px|thumb|centre|Figure 1.6: Spectrum of optimised NH3]]

=== Charge Analysis of Optimised NH3 ===

Charge analysis (Figure 1.7) shows the charge on the nitrogen atom is -1.125 whilst that of the hydrogen atoms is +0.375. This result where nitrogen has a negative charge with a larger magnitude and hydrogen has a positive charge with a smaller magnitude is expected, since nitrogen is more electronegative than hydrogen, nitrogen should withdraw more electron density from each of the three N-H bonds.

[[File:Nh3_charge.jpg ‎|400px|thumb|centre|Figure 1.7: Charge Analysis of optimised NH3]]

== Optimisation of N2 ==

=== General Information of Optimised N2 ===

From the 'Summary' table (Figure 2.1), the following general information about the optimisation calculation is obtained: the molecule optimised is nitrogen, N2, the calculation method is RB3LYP; the basis set is 6-31G(d,p); the final energy E(RB3LYP) is -109.52412868 a.u.; the RMS gradient is 0.00000011 a.u.; and the point group of N2 is D∞h.

[[File:N2 summary 2.jpg|400px|thumb|center|Figure 2.1: Summary Table of optimised N2]]

=== Geometric Information of Optimised N2 ===

Optimised bond length: 1.10550 Å ≈ 1.106 Å

=== Verification of Successful Optimisation of N2 ===

The 'Item' table (Figure 2.2) shows that the final set of forces and displacements are converged and that the forces are zero; since force is the gradient of a potential energy vs distance graph, this indicates that the structure obtained is at equilibrium, demonstrating successful optimisation of N2.

<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 0.000000 0.001200 YES
</pre>

Figure 2.2: Item Table of optimised N2

Moreover, successful optimisation of N2 is indicated by the last structure having the most negative energy and the smallest gradient (Figure 2.3).

[[File:N2 optimisation.jpg|400px|thumb|center|Figure 2.3: Optimisation plots of N2]]

=== Dynamic Image of Optimised N2 ===

<jmol><jmolApplet>
<title>Figure 2.4: Optimised nitrogen</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ZOEYWAISUMLUNG_N2_OPTF_POP.LOG</uploadedFileContents>
<script>frame 1.4</script>
</jmolApplet></jmol>

The optimisation file is linked to [[Media:ZOEYWAISUMLUNG_N2_OPTF_POP.LOG| here]]

=== Vibrational Analysis of Optimised N2 ===

From Figure 2.5 in vibrational analysis, there are 0 modes as expected, and 0 bands in the experimental spectrum (Figure 2.6) of gaseous nitrogen as expected.

[[File:N2 vibrations.jpg ‎|400px|thumb|centre|Figure 2.5: Vibrational Table of optimised N2]]

[[File:N2 spectrum.jpg ‎|400px|thumb|centre|Figure 2.6: Spectrum of optimised N2]]

=== Charge Analysis of Optimised N2 ===

Charge analysis (Figure 2.7) shows the charge on both nitrogen atoms is 0.000. This result is expected because both atoms of the lienar bond are the same so there are no expected differences in electronegativity therefore electron density is shared equally between the nitrogen atoms. Note that the atoms are colored by charge, a charge of 0.000 is represented by the color black and the numbers are written in black therefore they cannot be seen here.

[[File:N2 charge.jpg ‎|400px|thumb|centre|Figure 2.7: Charge Analysis of optimised N2]]

== Optimisation of H2 ==

=== General Information of Optimised H2 ===

From the 'Summary' table (Figure 3.1), the following general information about the optimisation calculation is obtained: the molecule optimised is hydrogen, H2, the calculation method is RB3LYP; the basis set is 6-31G(d,p); the final energy E(RB3LYP) is -1.17853936 a.u.; the RMS gradient is 0.00002276 a.u.; and the point group of H2 is D∞h.

[[File:H2 summary.jpg|400px|thumb|center|Figure 3.1: Summary Table of optimised H2]]

=== Geometric Information of Optimised H2 ===

Optimised bond length: 0.74274 Å ≈ 0.7427 Å

=== Verification of Successful Optimisation of H2 ===

The 'Item' table (Figure 3.2) shows that the final set of forces and displacements are converged and that the forces are zero; since force is the gradient of a potential energy vs distance graph, this indicates that the structure obtained is at equilibrium, demonstrating successful optimisation of H2.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000039 0.000300 YES
Maximum Displacement 0.000052 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
</pre>

Figure 3.2: Item Table of optimised H2

Moreover, successful optimisation of H2 is indicated by the last structure having the most negative energy and the smallest gradient (Figure 3.3).

[[File:H2 optimisation.jpg|400px|thumb|center|Figure 3.3: Optimisation plots of H2]]

=== Dynamic Image of Optimised H2 ===

<jmol><jmolApplet>
<title>Figure 3.4: Optimised hydrogen</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ZOEYWAISUMLUNG_H2_OPTF_POP.LOG</uploadedFileContents>
<script>frame 1.3</script>
</jmolApplet></jmol>

The optimisation file is linked to [[Media:ZOEYWAISUMLUNG_H2_OPTF_POP.LOG| here]]

=== Vibrational Analysis of Optimised H2 ===

From Figure 3.5 in vibrational analysis, there are 0 modes as expected, and 0 bands in the experimental spectrum (Figure 3.6) of gaseous hydrogen as expected.

[[File:H2 vibrations.jpg ‎|400px|thumb|centre|Figure 3.5: Vibrational Table of optimised H2]]

[[File:H2 spectrum.jpg ‎|400px|thumb|centre|Figure 3.6: Spectrum of optimised H2]]

=== Charge Analysis of Optimised H2 ===

Charge analysis (Figure 3.7) shows the charge on both hydrogen atoms is 0.000. This result is expected because both atoms of the linear bond are the same so there are no expected differences in electronegativity therefore electron density is shared equally between the hydrogen atoms. If a higher basis set is used, a single bond would likely to be displayed.

[[File:H2 charge.jpg ‎|400px|thumb|centre|Figure 2.7: Charge Analysis of optimised H2]]

== Optimisation of S2 ==

=== General Information of Optimised S2 ===

From the 'Summary' table (Figure 4.1), the following general information about the optimisation calculation is obtained: the molecule optimised is sulphur, S2, the calculation method is RB3LYP; the basis set is 6-31G(d,p); the final energy E(RB3LYP) is -796.32599779 a.u.; the RMS gradient is 0.00000905 a.u.; and the point group of S2 is D∞h.

[[File:S2 summary.jpg|400px|thumb|center|Figure 4.1: Summary Table of optimised S2]]

=== Geometric Information of Optimised S2 ===

Optimised bond length: 1.92947 Å ≈ 1.929 Å

=== Verification of Successful Optimisation of S2 ===

The 'Item' table (Figure 4.2) shows that the final set of forces and displacements are converged and that the forces are approximately zero; since force is the gradient of a potential energy vs distance graph, this indicates that the structure obtained is at equilibrium, demonstrating successful optimisation of S2.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.000027 0.001800 YES
RMS Displacement 0.000038 0.001200 YES
</pre>

Figure 4.2: Item Table of optimised S2

Moreover, successful optimisation of S2 is indicated by the last structure having the most negative energy and the smallest gradient (Figure 4.3).

[[File:S2 optimisation.jpg|400px|thumb|center|Figure 4.3: Optimisation plots of S2]]

=== Dynamic Image of Optimised S2 ===

<jmol><jmolApplet>
<title>Figure 4.4: Optimised sulphur</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ZOEYWAISUMLUNG_S2_OPTF_POP.LOG</uploadedFileContents>
<script>frame 1.4</script>
</jmolApplet></jmol>

The optimisation file is linked to [[Media:ZOEYWAISUMLUNG_S2_OPTF_POP.LOG| here]]

=== Vibrational Analysis of Optimised S2 ===

From Figure 4.5 in vibrational analysis, there are 0 modes as expected, and 0 bands in the experimental spectrum (Figure 4.6) of gaseous sulphur as expected.

[[File:S2 vibrations.jpg ‎|400px|thumb|centre|Figure 4.5: Vibrational Table of optimised S2]]

[[File:S2 spectrum.jpg ‎|400px|thumb|centre|Figure 4.6: Spectrum of optimised S2]]

=== Charge Analysis of Optimised S2 ===

Charge analysis (Figure 4.7) shows the charge on both sulphur atoms is 0.000. This result is expected because both atoms of the linear bond are the same so there are no expected differences in electronegativity therefore electron density is shared equally between the sulphur atoms. A single bond instead of a double bond is displayed however this would most likely not be the case if a higher basis set is used for optimisation.

[[File:S2 charge.jpg ‎|400px|thumb|centre|Figure 2.7: Charge Analysis of optimised H2]]

=== Molecular Orbitals of Optimised S2 ===

{| class="wikitable" border="1"
|+ caption
! heading !! heading
|-
| [[File:1s sigma orbital 1.JPG ‎|300px|thumb|centre]]
|| The two 1s AOs overlap to form a non-bonding σ MO. The energy of the MO formed is -88.93663.
|-
| cell || cell
|-
| cell || cell
|-
| cell || cell
|-
| cell || cell
|-
| cell || cell
|-
| cell || cell
|-
| cell || cell
|-
| cell || cell
|}

Rep:Mod:WSL1819

2018-03-16T11:20:57Z

Wsl1917: /* Molecular Orbitals of Optimised S2 */

== Optimisation of NH3 ==

=== General Information of Optimised NH3 ===

From the 'Summary' table (Figure 1.1), the following general information about the optimisation calculation is obtained: the molecule optimised is ammonia, NH3, the calculation method is RB3LYP; the basis set is 6-31G(d,p); the final energy E(RB3LYP) is -56.44397188 a.u.; the RMS gradient is 0.05399560 a.u.; and the point group of NH3 is C3v.

[[File:Nh3_summary.jpg|400px|thumb|center|Figure 1.1: Summary Table of optimised NH3]]

=== Geometric Information of Optimised NH3 ===

Optimised bond length: 1.01798 Å ≈ 1.018 Å

Optimised bond angle: 105.741 o ≈ 105.7 o

=== Verification of Successful Optimisation of NH3 ===

The 'Item' table (Figure 1.2) shows that the final set of forces and displacements are converged and that the forces are approximately zero; since force is the gradient of a potential energy vs distance graph, this indicates that the structure obtained is at equilibrium, demonstrating successful optimisation of NH3.

<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>

Figure 1.2: Item Table of optimised NH3

Moreover, successful optimisation of NH3 is indicated by the last structure having the most negative energy and the smallest gradient (Figure 1.3).

[[File:Nh3 optimisation.jpg|400px|thumb|center|Figure 1.3: Optimisation plots of NH3]]

=== Dynamic Image of Optimised NH3 ===

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ZOEYWAISUMLUNG_NH3_OPTF_POP.LOG</uploadedFileContents>
<script>frame 1.7</script>
</jmolApplet></jmol>
Figure 1.4: A 3D jmol file of optimised NH3

The optimisation file is linked to [[Media:ZOEYWAISUMLUNG_NH3_OPTF_POP.LOG| here]]

=== Vibrational Analysis of Optimised NH3 ===

From Figure 1.5 in vibrational analysis, there are 6 modes as expected, modes 2 and 3 and modes 5 and 6 are degenerate as they have the same frequency of 1693.95 cm-1 and 3589.82 cm-1 respectively; modes 1, 2 and 3 are "bending" vibrations and modes 4, 5 and 6 are "bond stretch" vibrations; mode 4 is highly symmetric ; mode 1 is the "umbrella" mode and 2 bands in the experimental spectrum (Figure 1.6) of gaseous ammonia as expected.

[[File:Nh3 vibrations 1.jpg ‎|400px|thumb|centre|Figure 1.5: Vibrational Table of optimised NH3]]

[[File:Nh3_spectrum.jpg ‎|400px|thumb|centre|Figure 1.6: Spectrum of optimised NH3]]

=== Charge Analysis of Optimised NH3 ===

Charge analysis (Figure 1.7) shows the charge on the nitrogen atom is -1.125 whilst that of the hydrogen atoms is +0.375. This result where nitrogen has a negative charge with a larger magnitude and hydrogen has a positive charge with a smaller magnitude is expected, since nitrogen is more electronegative than hydrogen, nitrogen should withdraw more electron density from each of the three N-H bonds.

[[File:Nh3_charge.jpg ‎|400px|thumb|centre|Figure 1.7: Charge Analysis of optimised NH3]]

== Optimisation of N2 ==

=== General Information of Optimised N2 ===

From the 'Summary' table (Figure 2.1), the following general information about the optimisation calculation is obtained: the molecule optimised is nitrogen, N2, the calculation method is RB3LYP; the basis set is 6-31G(d,p); the final energy E(RB3LYP) is -109.52412868 a.u.; the RMS gradient is 0.00000011 a.u.; and the point group of N2 is D∞h.

[[File:N2 summary 2.jpg|400px|thumb|center|Figure 2.1: Summary Table of optimised N2]]

=== Geometric Information of Optimised N2 ===

Optimised bond length: 1.10550 Å ≈ 1.106 Å

=== Verification of Successful Optimisation of N2 ===

The 'Item' table (Figure 2.2) shows that the final set of forces and displacements are converged and that the forces are zero; since force is the gradient of a potential energy vs distance graph, this indicates that the structure obtained is at equilibrium, demonstrating successful optimisation of N2.

<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 0.000000 0.001200 YES
</pre>

Figure 2.2: Item Table of optimised N2

Moreover, successful optimisation of N2 is indicated by the last structure having the most negative energy and the smallest gradient (Figure 2.3).

[[File:N2 optimisation.jpg|400px|thumb|center|Figure 2.3: Optimisation plots of N2]]

=== Dynamic Image of Optimised N2 ===

<jmol><jmolApplet>
<title>Figure 2.4: Optimised nitrogen</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ZOEYWAISUMLUNG_N2_OPTF_POP.LOG</uploadedFileContents>
<script>frame 1.4</script>
</jmolApplet></jmol>

The optimisation file is linked to [[Media:ZOEYWAISUMLUNG_N2_OPTF_POP.LOG| here]]

=== Vibrational Analysis of Optimised N2 ===

From Figure 2.5 in vibrational analysis, there are 0 modes as expected, and 0 bands in the experimental spectrum (Figure 2.6) of gaseous nitrogen as expected.

[[File:N2 vibrations.jpg ‎|400px|thumb|centre|Figure 2.5: Vibrational Table of optimised N2]]

[[File:N2 spectrum.jpg ‎|400px|thumb|centre|Figure 2.6: Spectrum of optimised N2]]

=== Charge Analysis of Optimised N2 ===

Charge analysis (Figure 2.7) shows the charge on both nitrogen atoms is 0.000. This result is expected because both atoms of the lienar bond are the same so there are no expected differences in electronegativity therefore electron density is shared equally between the nitrogen atoms. Note that the atoms are colored by charge, a charge of 0.000 is represented by the color black and the numbers are written in black therefore they cannot be seen here.

[[File:N2 charge.jpg ‎|400px|thumb|centre|Figure 2.7: Charge Analysis of optimised N2]]

== Optimisation of H2 ==

=== General Information of Optimised H2 ===

From the 'Summary' table (Figure 3.1), the following general information about the optimisation calculation is obtained: the molecule optimised is hydrogen, H2, the calculation method is RB3LYP; the basis set is 6-31G(d,p); the final energy E(RB3LYP) is -1.17853936 a.u.; the RMS gradient is 0.00002276 a.u.; and the point group of H2 is D∞h.

[[File:H2 summary.jpg|400px|thumb|center|Figure 3.1: Summary Table of optimised H2]]

=== Geometric Information of Optimised H2 ===

Optimised bond length: 0.74274 Å ≈ 0.7427 Å

=== Verification of Successful Optimisation of H2 ===

The 'Item' table (Figure 3.2) shows that the final set of forces and displacements are converged and that the forces are zero; since force is the gradient of a potential energy vs distance graph, this indicates that the structure obtained is at equilibrium, demonstrating successful optimisation of H2.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000039 0.000300 YES
Maximum Displacement 0.000052 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
</pre>

Figure 3.2: Item Table of optimised H2

Moreover, successful optimisation of H2 is indicated by the last structure having the most negative energy and the smallest gradient (Figure 3.3).

[[File:H2 optimisation.jpg|400px|thumb|center|Figure 3.3: Optimisation plots of H2]]

=== Dynamic Image of Optimised H2 ===

<jmol><jmolApplet>
<title>Figure 3.4: Optimised hydrogen</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ZOEYWAISUMLUNG_H2_OPTF_POP.LOG</uploadedFileContents>
<script>frame 1.3</script>
</jmolApplet></jmol>

The optimisation file is linked to [[Media:ZOEYWAISUMLUNG_H2_OPTF_POP.LOG| here]]

=== Vibrational Analysis of Optimised H2 ===

From Figure 3.5 in vibrational analysis, there are 0 modes as expected, and 0 bands in the experimental spectrum (Figure 3.6) of gaseous hydrogen as expected.

[[File:H2 vibrations.jpg ‎|400px|thumb|centre|Figure 3.5: Vibrational Table of optimised H2]]

[[File:H2 spectrum.jpg ‎|400px|thumb|centre|Figure 3.6: Spectrum of optimised H2]]

=== Charge Analysis of Optimised H2 ===

Charge analysis (Figure 3.7) shows the charge on both hydrogen atoms is 0.000. This result is expected because both atoms of the linear bond are the same so there are no expected differences in electronegativity therefore electron density is shared equally between the hydrogen atoms. If a higher basis set is used, a single bond would likely to be displayed.

[[File:H2 charge.jpg ‎|400px|thumb|centre|Figure 2.7: Charge Analysis of optimised H2]]

== Optimisation of S2 ==

=== General Information of Optimised S2 ===

From the 'Summary' table (Figure 4.1), the following general information about the optimisation calculation is obtained: the molecule optimised is sulphur, S2, the calculation method is RB3LYP; the basis set is 6-31G(d,p); the final energy E(RB3LYP) is -796.32599779 a.u.; the RMS gradient is 0.00000905 a.u.; and the point group of S2 is D∞h.

[[File:S2 summary.jpg|400px|thumb|center|Figure 4.1: Summary Table of optimised S2]]

=== Geometric Information of Optimised S2 ===

Optimised bond length: 1.92947 Å ≈ 1.929 Å

=== Verification of Successful Optimisation of S2 ===

The 'Item' table (Figure 4.2) shows that the final set of forces and displacements are converged and that the forces are approximately zero; since force is the gradient of a potential energy vs distance graph, this indicates that the structure obtained is at equilibrium, demonstrating successful optimisation of S2.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.000027 0.001800 YES
RMS Displacement 0.000038 0.001200 YES
</pre>

Figure 4.2: Item Table of optimised S2

Moreover, successful optimisation of S2 is indicated by the last structure having the most negative energy and the smallest gradient (Figure 4.3).

[[File:S2 optimisation.jpg|400px|thumb|center|Figure 4.3: Optimisation plots of S2]]

=== Dynamic Image of Optimised S2 ===

<jmol><jmolApplet>
<title>Figure 4.4: Optimised sulphur</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ZOEYWAISUMLUNG_S2_OPTF_POP.LOG</uploadedFileContents>
<script>frame 1.4</script>
</jmolApplet></jmol>

The optimisation file is linked to [[Media:ZOEYWAISUMLUNG_S2_OPTF_POP.LOG| here]]

=== Vibrational Analysis of Optimised S2 ===

From Figure 4.5 in vibrational analysis, there are 0 modes as expected, and 0 bands in the experimental spectrum (Figure 4.6) of gaseous sulphur as expected.

[[File:S2 vibrations.jpg ‎|400px|thumb|centre|Figure 4.5: Vibrational Table of optimised S2]]

[[File:S2 spectrum.jpg ‎|400px|thumb|centre|Figure 4.6: Spectrum of optimised S2]]

=== Charge Analysis of Optimised S2 ===

Charge analysis (Figure 4.7) shows the charge on both sulphur atoms is 0.000. This result is expected because both atoms of the linear bond are the same so there are no expected differences in electronegativity therefore electron density is shared equally between the sulphur atoms. A single bond instead of a double bond is displayed however this would most likely not be the case if a higher basis set is used for optimisation.

[[File:S2 charge.jpg ‎|400px|thumb|centre|Figure 2.7: Charge Analysis of optimised H2]]

=== Molecular Orbitals of Optimised S2 ===

{| class="wikitable" border="1"
|+ caption
! heading !! heading
|-
| [[File:1s sigma orbital 1.JPG ‎|400px|thumb|centre]]
|| The two 1s AOs overlap to form a non-bonding σ MO. The energy of the MO formed is -88.93663.
|-
| cell || cell
|-
| cell || cell
|-
| cell || cell
|-
| cell || cell
|-
| cell || cell
|-
| cell || cell
|-
| cell || cell
|-
| cell || cell
|}

Rep:Mod:WSL1819

2018-03-16T11:18:21Z

Wsl1917: /* Molecular Orbitals of Optimised S2 */

== Optimisation of NH3 ==

=== General Information of Optimised NH3 ===

From the 'Summary' table (Figure 1.1), the following general information about the optimisation calculation is obtained: the molecule optimised is ammonia, NH3, the calculation method is RB3LYP; the basis set is 6-31G(d,p); the final energy E(RB3LYP) is -56.44397188 a.u.; the RMS gradient is 0.05399560 a.u.; and the point group of NH3 is C3v.

[[File:Nh3_summary.jpg|400px|thumb|center|Figure 1.1: Summary Table of optimised NH3]]

=== Geometric Information of Optimised NH3 ===

Optimised bond length: 1.01798 Å ≈ 1.018 Å

Optimised bond angle: 105.741 o ≈ 105.7 o

=== Verification of Successful Optimisation of NH3 ===

The 'Item' table (Figure 1.2) shows that the final set of forces and displacements are converged and that the forces are approximately zero; since force is the gradient of a potential energy vs distance graph, this indicates that the structure obtained is at equilibrium, demonstrating successful optimisation of NH3.

<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>

Figure 1.2: Item Table of optimised NH3

Moreover, successful optimisation of NH3 is indicated by the last structure having the most negative energy and the smallest gradient (Figure 1.3).

[[File:Nh3 optimisation.jpg|400px|thumb|center|Figure 1.3: Optimisation plots of NH3]]

=== Dynamic Image of Optimised NH3 ===

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ZOEYWAISUMLUNG_NH3_OPTF_POP.LOG</uploadedFileContents>
<script>frame 1.7</script>
</jmolApplet></jmol>
Figure 1.4: A 3D jmol file of optimised NH3

The optimisation file is linked to [[Media:ZOEYWAISUMLUNG_NH3_OPTF_POP.LOG| here]]

=== Vibrational Analysis of Optimised NH3 ===

From Figure 1.5 in vibrational analysis, there are 6 modes as expected, modes 2 and 3 and modes 5 and 6 are degenerate as they have the same frequency of 1693.95 cm-1 and 3589.82 cm-1 respectively; modes 1, 2 and 3 are "bending" vibrations and modes 4, 5 and 6 are "bond stretch" vibrations; mode 4 is highly symmetric ; mode 1 is the "umbrella" mode and 2 bands in the experimental spectrum (Figure 1.6) of gaseous ammonia as expected.

[[File:Nh3 vibrations 1.jpg ‎|400px|thumb|centre|Figure 1.5: Vibrational Table of optimised NH3]]

[[File:Nh3_spectrum.jpg ‎|400px|thumb|centre|Figure 1.6: Spectrum of optimised NH3]]

=== Charge Analysis of Optimised NH3 ===

Charge analysis (Figure 1.7) shows the charge on the nitrogen atom is -1.125 whilst that of the hydrogen atoms is +0.375. This result where nitrogen has a negative charge with a larger magnitude and hydrogen has a positive charge with a smaller magnitude is expected, since nitrogen is more electronegative than hydrogen, nitrogen should withdraw more electron density from each of the three N-H bonds.

[[File:Nh3_charge.jpg ‎|400px|thumb|centre|Figure 1.7: Charge Analysis of optimised NH3]]

== Optimisation of N2 ==

=== General Information of Optimised N2 ===

From the 'Summary' table (Figure 2.1), the following general information about the optimisation calculation is obtained: the molecule optimised is nitrogen, N2, the calculation method is RB3LYP; the basis set is 6-31G(d,p); the final energy E(RB3LYP) is -109.52412868 a.u.; the RMS gradient is 0.00000011 a.u.; and the point group of N2 is D∞h.

[[File:N2 summary 2.jpg|400px|thumb|center|Figure 2.1: Summary Table of optimised N2]]

=== Geometric Information of Optimised N2 ===

Optimised bond length: 1.10550 Å ≈ 1.106 Å

=== Verification of Successful Optimisation of N2 ===

The 'Item' table (Figure 2.2) shows that the final set of forces and displacements are converged and that the forces are zero; since force is the gradient of a potential energy vs distance graph, this indicates that the structure obtained is at equilibrium, demonstrating successful optimisation of N2.

<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 0.000000 0.001200 YES
</pre>

Figure 2.2: Item Table of optimised N2

Moreover, successful optimisation of N2 is indicated by the last structure having the most negative energy and the smallest gradient (Figure 2.3).

[[File:N2 optimisation.jpg|400px|thumb|center|Figure 2.3: Optimisation plots of N2]]

=== Dynamic Image of Optimised N2 ===

<jmol><jmolApplet>
<title>Figure 2.4: Optimised nitrogen</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ZOEYWAISUMLUNG_N2_OPTF_POP.LOG</uploadedFileContents>
<script>frame 1.4</script>
</jmolApplet></jmol>

The optimisation file is linked to [[Media:ZOEYWAISUMLUNG_N2_OPTF_POP.LOG| here]]

=== Vibrational Analysis of Optimised N2 ===

From Figure 2.5 in vibrational analysis, there are 0 modes as expected, and 0 bands in the experimental spectrum (Figure 2.6) of gaseous nitrogen as expected.

[[File:N2 vibrations.jpg ‎|400px|thumb|centre|Figure 2.5: Vibrational Table of optimised N2]]

[[File:N2 spectrum.jpg ‎|400px|thumb|centre|Figure 2.6: Spectrum of optimised N2]]

=== Charge Analysis of Optimised N2 ===

Charge analysis (Figure 2.7) shows the charge on both nitrogen atoms is 0.000. This result is expected because both atoms of the lienar bond are the same so there are no expected differences in electronegativity therefore electron density is shared equally between the nitrogen atoms. Note that the atoms are colored by charge, a charge of 0.000 is represented by the color black and the numbers are written in black therefore they cannot be seen here.

[[File:N2 charge.jpg ‎|400px|thumb|centre|Figure 2.7: Charge Analysis of optimised N2]]

== Optimisation of H2 ==

=== General Information of Optimised H2 ===

From the 'Summary' table (Figure 3.1), the following general information about the optimisation calculation is obtained: the molecule optimised is hydrogen, H2, the calculation method is RB3LYP; the basis set is 6-31G(d,p); the final energy E(RB3LYP) is -1.17853936 a.u.; the RMS gradient is 0.00002276 a.u.; and the point group of H2 is D∞h.

[[File:H2 summary.jpg|400px|thumb|center|Figure 3.1: Summary Table of optimised H2]]

=== Geometric Information of Optimised H2 ===

Optimised bond length: 0.74274 Å ≈ 0.7427 Å

=== Verification of Successful Optimisation of H2 ===

The 'Item' table (Figure 3.2) shows that the final set of forces and displacements are converged and that the forces are zero; since force is the gradient of a potential energy vs distance graph, this indicates that the structure obtained is at equilibrium, demonstrating successful optimisation of H2.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000039 0.000300 YES
Maximum Displacement 0.000052 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
</pre>

Figure 3.2: Item Table of optimised H2

Moreover, successful optimisation of H2 is indicated by the last structure having the most negative energy and the smallest gradient (Figure 3.3).

[[File:H2 optimisation.jpg|400px|thumb|center|Figure 3.3: Optimisation plots of H2]]

=== Dynamic Image of Optimised H2 ===

<jmol><jmolApplet>
<title>Figure 3.4: Optimised hydrogen</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ZOEYWAISUMLUNG_H2_OPTF_POP.LOG</uploadedFileContents>
<script>frame 1.3</script>
</jmolApplet></jmol>

The optimisation file is linked to [[Media:ZOEYWAISUMLUNG_H2_OPTF_POP.LOG| here]]

=== Vibrational Analysis of Optimised H2 ===

From Figure 3.5 in vibrational analysis, there are 0 modes as expected, and 0 bands in the experimental spectrum (Figure 3.6) of gaseous hydrogen as expected.

[[File:H2 vibrations.jpg ‎|400px|thumb|centre|Figure 3.5: Vibrational Table of optimised H2]]

[[File:H2 spectrum.jpg ‎|400px|thumb|centre|Figure 3.6: Spectrum of optimised H2]]

=== Charge Analysis of Optimised H2 ===

Charge analysis (Figure 3.7) shows the charge on both hydrogen atoms is 0.000. This result is expected because both atoms of the linear bond are the same so there are no expected differences in electronegativity therefore electron density is shared equally between the hydrogen atoms. If a higher basis set is used, a single bond would likely to be displayed.

[[File:H2 charge.jpg ‎|400px|thumb|centre|Figure 2.7: Charge Analysis of optimised H2]]

== Optimisation of S2 ==

=== General Information of Optimised S2 ===

From the 'Summary' table (Figure 4.1), the following general information about the optimisation calculation is obtained: the molecule optimised is sulphur, S2, the calculation method is RB3LYP; the basis set is 6-31G(d,p); the final energy E(RB3LYP) is -796.32599779 a.u.; the RMS gradient is 0.00000905 a.u.; and the point group of S2 is D∞h.

[[File:S2 summary.jpg|400px|thumb|center|Figure 4.1: Summary Table of optimised S2]]

=== Geometric Information of Optimised S2 ===

Optimised bond length: 1.92947 Å ≈ 1.929 Å

=== Verification of Successful Optimisation of S2 ===

The 'Item' table (Figure 4.2) shows that the final set of forces and displacements are converged and that the forces are approximately zero; since force is the gradient of a potential energy vs distance graph, this indicates that the structure obtained is at equilibrium, demonstrating successful optimisation of S2.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.000027 0.001800 YES
RMS Displacement 0.000038 0.001200 YES
</pre>

Figure 4.2: Item Table of optimised S2

Moreover, successful optimisation of S2 is indicated by the last structure having the most negative energy and the smallest gradient (Figure 4.3).

[[File:S2 optimisation.jpg|400px|thumb|center|Figure 4.3: Optimisation plots of S2]]

=== Dynamic Image of Optimised S2 ===

<jmol><jmolApplet>
<title>Figure 4.4: Optimised sulphur</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ZOEYWAISUMLUNG_S2_OPTF_POP.LOG</uploadedFileContents>
<script>frame 1.4</script>
</jmolApplet></jmol>

The optimisation file is linked to [[Media:ZOEYWAISUMLUNG_S2_OPTF_POP.LOG| here]]

=== Vibrational Analysis of Optimised S2 ===

From Figure 4.5 in vibrational analysis, there are 0 modes as expected, and 0 bands in the experimental spectrum (Figure 4.6) of gaseous sulphur as expected.

[[File:S2 vibrations.jpg ‎|400px|thumb|centre|Figure 4.5: Vibrational Table of optimised S2]]

[[File:S2 spectrum.jpg ‎|400px|thumb|centre|Figure 4.6: Spectrum of optimised S2]]

=== Charge Analysis of Optimised S2 ===

Charge analysis (Figure 4.7) shows the charge on both sulphur atoms is 0.000. This result is expected because both atoms of the linear bond are the same so there are no expected differences in electronegativity therefore electron density is shared equally between the sulphur atoms. A single bond instead of a double bond is displayed however this would most likely not be the case if a higher basis set is used for optimisation.

[[File:S2 charge.jpg ‎|400px|thumb|centre|Figure 2.7: Charge Analysis of optimised H2]]

=== Molecular Orbitals of Optimised S2 ===

{| class="wikitable" border="1"
|+ caption
! heading !! heading
|-
| [[File:1s sigma orbital 1.JPG ‎|400px|thumb|centre]]
|| cell
|-
| cell || cell
|-
| cell || cell
|-
| cell || cell
|-
| cell || cell
|-
| cell || cell
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| cell || cell
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File:1s sigma orbital 1.JPG

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