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=Short Report on common diatomic gases and compounds that they form together (NH<sub>3</sub> and ClF).=
This wiki contains information on N<sub>2</sub>, H<sub>2</sub>, Cl<sub>2</sub> and F<sub>2</sub> as well as NH<sub>3</sub> and ClF. This report lays out the results of analysis of the above mentioned elements and compounds and offers critical comments where applicable.

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

===<u>General Information</u>===
General information about the H<sub>2</sub> was obtained from analysis using GaussView 5.0.9 (with Gaussian 09W performing all the analysis). The relevant information is presented below:

'''Molecule''' : H<sub>2</sub>

'''Calculation Method''' : RB3LYP

'''Basic Set''' : 6-31G(d,p)

'''Final Energy E(RB3LYP)''' : -1.17853936 a.u.

'''RMS Gradient''' : 0.00000017 a.u.

'''Point Group''' : D<sub>∞h</sub>

'''H-H Bond Length''' : 0.74279 Å

'''Bond Angle''' : 180.00 ° as this is a linear molecule


===<u>"Item" Table for Hydrogen molecule from GaussView 5.0.9</u>===
The "Item" Table allows for the determination of the reliability of the optimisation. As all of the forces and displacements converged, we can assume that the optimisation was completed successfully by Gaussian 09W and that the molecule used for analysis is a suitable representation of the ground-state of molecule in question (H<sub>2</sub> in this case).

<pre>
         Item               Value     Threshold  Converged?
 Maximum Force            0.000000     0.000450     YES
 RMS     Force            0.000000     0.000300     YES
 Maximum Displacement     0.000000     0.001800     YES
 RMS     Displacement     0.000001     0.001200     YES
</pre>

===<u>Interactive model of Hydrogen molecule</u>===
Below is an interactive ball and stick model of the Hydrogen molecule allowing you to visualise the molecule and also explore the symmetry exhibited by the molecule.

We can see that the molecule adopts a linear structure (predicted by Gaussian 09W). This fits with structures predicted by VSEPR for the Hydrogen molecule.<ref name="Atkins" />

<jmol><jmolApplet>
  <title>Hydrogen Molecule</title>
  <color>grey</color>
  <script>frame 1.12</script>
  <size>200</size>
  <uploadedFileContents>EOPOKU H2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

Link to LOG file:[[File:EOPOKU H2 OPTF POP.LOG]]

===<u>Vibrational Modes</u>===
The frequency displayed corresponds to a bond stretch between atoms in the molecule, for which we only expect one as it is a linear diatomic molecule.

The molecule is not infrared-active as there is no change in dipole moment as the bond stretches.

[[File:Vibration modes h2.jpg|thumb|centre|A GaussView window of the vibration modes in the H<sub>2</sub> molecule.]]

===<u>Charge Distribution</u>===
It is expected that there will be an overall even charge distribution over the H<sub>2</sub> molecule as it is a hetero-diatomic molecule and there are is no difference in electronegativity across the two atoms. 

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

===<u>General Information</u>===
General information about the N<sub>2</sub> was obtained from analysis using GaussView 5.0.9 (with Gaussian 09W performing all the analysis). The relevant information is presented below:

'''Molecule''' : N<sub>2</sub>

'''Calculation Method''' : RB3LYP

'''Basic Set''' : 6-31G(d,p)

'''Final Energy E(RB3LYP)''' : -109.52412868 a.u.

'''RMS Gradient''' : 0.00000060 a.u.

'''Point Group''' : D<sub>∞h</sub>

'''N-N Bond Length''' : 1.10550 Å

'''Bond Angle''' : 180.00 ° as it is a linear molecule


===<u>"Item" Table for Nitrogen molecule from GaussView 5.0.9</u>===
The "Item" Table allows for the determination of the reliability of the optimisation. As all of the forces and displacements converged, we can assume that the optimisation was completed successfully by Gaussian 09W and that the molecule used for analysis is a suitable representation of the ground-state of molecule in question (N<sub>2</sub> in this case).
<pre>
         Item               Value     Threshold  Converged?
 Maximum Force            0.000001     0.000450     YES
 RMS     Force            0.000001     0.000300     YES
 Maximum Displacement     0.000000     0.001800     YES
 RMS     Displacement     0.000000     0.001200     YES
</pre>

===<u>Interactive model of Nitrogen molecule</u>===
Below is an interactive ball and stick model of the Nitrogen molecule allowing you to visualise the molecule and also explore the symmetry exhibited by the molecule.

We can see that the molecule adopts a linear structure (predicted by Gaussian 09W). This fits with structures predicted by VSEPR for the Nitrogen molecule.<ref name="Atkins" />
<jmol><jmolApplet>
  <title>Nitrogen Molecule</title>
  <color>grey</color>
  <script>frame 1.10</script>
  <size>200</size>
  <uploadedFileContents>EOPOKU N2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

Link to LOG file:[[File:EOPOKU N2 OPTF POP.LOG]]

===<u>Vibrational Modes</u>===
The frequency displayed corresponds to a bond stretch between atoms in the molecule, for which we only expect one as it is a linear molecule.
[[File:Vibration modes n2.jpg|thumb|centre|A GaussView window of the vibration modes in the N<sub>2</sub> molecule.]]

===<u>Charge Distribution</u>===
It is expected that there will be an overall even charge distribution over the N<sub>2</sub> molecule as it is a hetero-diatomic molecule and there are is no difference in electronegativity across the two atoms, just like in the H<sub>2</sub> molecule above.

==NH<sub>3</sub>==
NH<sub>3</sub> is formed from N<sub>2</sub> and H<sub>2</sub>, and is a very important reaction in industry. Ammonia (NH<sub>3</sub>) is used to produce fertilizers which are essential to the sustenance of an ever increasing population of humans on earth. 

===<u>General Information</u>===
General information about the NH<sub>3</sub> was obtained from analysis using GaussView 5.0.9 (with Gaussian 09W performing all the analysis). The relevant information is presented below:

'''Molecule''' : NH<sub>3</sub>

'''Calculation Method''' : RB3LYP

'''Basic Set''' : 6-31G(d,p)

'''Final Energy E(RB3LYP)''' : -56.55776873 a.u.

'''RMS Gradient''' : 0.00000485 a.u.

'''Point Group''' : C<sub>3v</sub>

'''N-H Bond Length''' : 1.01798 Å

'''H-N-H Bond Angle''' : 105.741 °

===<u>"Item" Table for Ammonia molecule from GaussView 5.0.9</u></u>===

The "Item" Table allows for the determination of the reliability of the optimisation. As all of the forces and displacements converged, we can assume that the optimisation was completed successfully by Gaussian 09W and that the molecule used for analysis is a suitable representation of the ground-state of molecule in question (NH<sub>3</sub> in this case).

<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>


===<u>Interactive model of Ammonia molecule</u>===
Below is an interactive ball and stick model of the Ammonia molecule allowing you to visualise the molecule and also explore the symmetry exhibited by the molecule.

We can see that the molecule adopts a tetrahedral pseudo-structure with the lone pair of electrons on the Nitrogen atom acting to repel any electron density between the hydrogen and the central nitrogen atom - the structure predicted by Gaussian 09W is trigonal pyramidal which fits with structures predicted by VSEPR for the Ammonia molecule.<ref name="Atkins" />

<jmol><jmolApplet>
  <title>Ammonia Molecule</title>
  <color>grey</color>
  <script>frame 1.16</script>
  <size>200</size>
  <uploadedFileContents>EOPOKU NH3 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

Link to LOG file:[[File:EOPOKU NH3 OPTF POP.LOG]]

===<u>Vibrational Modes</u>===
1. We expect to see 6 modes of vibration according to the 3N-6 rule.

2. Vibrational Modes 2 and 3 as well as 5 and 6 are degenerate.

3. Modes 1,2 and 3 are "bending modes" and 4,5 and 6 are "bond stretch vibrations".

4. Vibrational mode 4 is highly symmetric.

5. Vibration mode 1 is known as the "umbrella" mode.

6. 3 bands are expected from an experimental spectrum of gaseous ammonia. From the image below we can deduce that the column titled "Infrared" will be on the y-axis as frequency on an IR Spectrum is on the x-axis. The value for the last three frequencies are relatively small compared to the others and are likely to not show up in an IR Spectrum, thus 3 bands are expected.

[[File:Vibration modes nh3.jpg|thumb|centre|A GaussView window of the vibration modes in the NH<sub>3</sub> molecule.]]

===<u>Charge Distribution</u>===
It is expected for the Nitrogen atom (red) to be negatively charged as it is more electronegative than the Hydrogen and it would attract the bonding electrons towards it more than the Hydrogen atoms (green) would, making the hydrogen atoms carry a slightly positive charge. The charge distribution on the Nitrogen atom is -1.125 and +0.375 on each Hydrogen molecule.

[[File:Charge distribution nh3.jpg|thumb|centre|A GaussView representation of the charge distribution in the NH<sub>3</sub> molecule.]]

==The Haber-Bosch Process (N<sub>2</sub> + H<sub>2</sub>)==

N<sub>2</sub> + 3 H<sub>2</sub> --> 2NH<sub>3</sub>

We can calculate the energy for the above reaction using the energy calculated during the optimisation process.

===<u>Calculating ΔE for the reaction</u>===
'''E(NH3)''' = -56.55776873 a.u.

'''2*E(NH3)''' = -113.11553746 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)]''' = -0.0557907 a.u.

The value of ΔE ≈ '''-146.48 kJ/mol''' suggesting that that ammonia is more stable than the gaseous reactants. This is because there is a negative energy difference between the isolated gaseous reactants compared to that of the ammonia product (accounting for stoichiometry).

This value is very different to the experimentally determined value of '''-91.40 kJ/mol'''. This could be due to the fact that entropic factors weren't considered in the calculations made by Gauss. The calculation would also not have accounted for temperature, pressure and solvation effects which have a say on the final value obtained for ΔE. The fact that the conditions Gauss bases it's calculations on are not the same as those used in this industrial process could also play a part.<ref name="Haber" />

==Cl<sub>2</sub>==

===<u>General Information</u>===
General information about the Cl<sub>2</sub> was obtained from analysis using GaussView 5.0.9 (with Gaussian 09W performing all the analysis). The relevant information is presented below:

'''Molecule''' : Cl<sub>2</sub>

'''Calculation Method''' : RB3LYP

'''Basic Set''' : 6-31G(d,p)

'''Final Energy E(RB3LYP)''' : -920.34987886 a.u.

'''RMS Gradient''' : 0.00002511 a.u.

'''Point Group''' : D<sub>∞h</sub>

'''Cl-Cl Bond Length''' : 2.04174 Å

'''Bond Angle''' : 180.00 ° as this is a linear molecule


===<u>"Item" Table for Chlorine molecule from GaussView 5.0.9</u>===
The "Item" Table allows for the determination of the reliability of the optimisation. As all of the forces and displacements converged, we can assume that the optimisation was completed successfully by Gaussian 09W and that the molecule used for analysis is a suitable representation of the ground-state of molecule in question (Cl<sub>2</sub> in this case).

<pre>
         Item               Value     Threshold  Converged?
 Maximum Force            0.000043     0.000450     YES
 RMS     Force            0.000043     0.000300     YES
 Maximum Displacement     0.000121     0.001800     YES
 RMS     Displacement     0.000172     0.001200     YES
</pre>

===<u>Interactive model of Chlorine molecule</u>===
Below is an interactive ball and stick model of the Chlorine molecule allowing you to visualise the molecule and also explore the symmetry exhibited by the molecule.

We can see that the molecule adopts a linear structure (predicted by Gaussian 09W). This fits with structures predicted by VSEPR for the Chlorine molecule.<ref name="Atkins" />

<jmol><jmolApplet>
  <title>Chlorine Molecule</title>
  <color>grey</color>
  <script>frame 1.10</script>
  <size>200</size>
  <uploadedFileContents>EOPOKU CL2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

Link to LOG file:[[File:EOPOKU CL2 OPTF POP.LOG]]

===<u>Vibrational Modes</u>===
The frequency displayed corresponds to a bond stretch between atoms in the molecule, for which we only expect one as it is a linear diatomic molecule.

The molecule is not infrared-active as there is no change in dipole moment as the bond stretches.

[[File:Vibration modes cl2.jpg|thumb|centre|A GaussView window of the vibration modes in the Cl<sub>2</sub> molecule.]]

===<u>Charge Distribution</u>===
It is expected that there will be an overall even charge distribution over the Cl<sub>2</sub> molecule as it is a hetero-diatomic molecule and there are is no difference in electronegativity across the two atoms.

==F<sub>2</sub>==

===<u>General Information</u>===
General information about the F<sub>2</sub> was obtained from analysis using GaussView 5.0.9 (with Gaussian 09W performing all the analysis). The relevant information is presented below:

'''Molecule''' : F<sub>2</sub>

'''Calculation Method''' : RB3LYP

'''Basic Set''' : 6-31G(d,p)

'''Final Energy E(RB3LYP)''' : -199.49825218 a.u.

'''RMS Gradient''' : 0.00007365 a.u.

'''Point Group''' : D<sub>∞h</sub>

'''F-F Bond Length''' : 1.40281 Å

'''Bond Angle''' : 180.00 ° as this is a linear molecule


===<u>"Item" Table for Chlorine molecule from GaussView 5.0.9</u>===
The "Item" Table allows for the determination of the reliability of the optimisation. As all of the forces and displacements converged, we can assume that the optimisation was completed successfully by Gaussian 09W and that the molecule used for analysis is a suitable representation of the ground-state of molecule in question (F<sub>2</sub> in this case).

<pre>
         Item               Value     Threshold  Converged?
 Maximum Force            0.000128     0.000450     YES
 RMS     Force            0.000128     0.000300     YES
 Maximum Displacement     0.000156     0.001800     YES
 RMS     Displacement     0.000221     0.001200     YES
</pre>

===<u>Interactive model of Fluorine molecule</u>===
Below is an interactive ball and stick model of the Fluorine molecule allowing you to visualise the molecule and also explore the symmetry exhibited by the molecule.

We can see that the molecule adopts a linear structure (predicted by Gaussian 09W). This fits with structures predicted by VSEPR for the Fluorine molecule.<ref name="Atkins" />

<jmol><jmolApplet>
  <title>Fluorine Molecule</title>
  <color>grey</color>
  <script>frame 1.10</script>
  <size>200</size>
  <uploadedFileContents>EOPOKU F2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

Link to LOG file:[[File:EOPOKU F2 OPTF POP.LOG]]

===<u>Vibrational Modes</u>===
The frequency displayed corresponds to a bond stretch between atoms in the molecule, for which we only expect one as it is a linear diatomic molecule.

The molecule is not infrared-active as there is no change in dipole moment as the bond stretches.

[[File:Vibration modes f2.jpg|thumb|centre|A GaussView window of the vibration modes in the F<sub>2</sub> molecule.]]

===<u>Charge Distribution</u>===
It is expected that there will be an overall even charge distribution over the F<sub>2</sub> molecule as it is a hetero-diatomic molecule and there are is no difference in electronegativity across the two atoms.

==ClF==
ClF is formed from F<sub>2</sub> and Cl<sub>2</sub>, and has properties similar to the elements it is made of. It is therefore expected to be quite a reactive compound.

===<u>General Information</u>===
General information about the ClF was obtained from analysis using GaussView 5.0.9 (with Gaussian 09W performing all the analysis). The relevant information is presented below:

'''Molecule''' : ClF

'''Calculation Method''' : RB3LYP

'''Basic Set''' : 6-31G(d,p)

'''Final Energy E(RB3LYP)''' : -559.94269578 a.u.

'''RMS Gradient''' : 0.00014211 a.u.

'''Point Group''' : C<sub>∞v</sub>

'''F-Cl Bond Length''' : 1.66434 Å

'''Bond Angle''' : 180.00 ° as this is a linear molecule

===<u>"Item" Table for Chlorine Monofluoride molecule from GaussView 5.0.9</u>===

The "Item" Table allows for the determination of the reliability of the optimisation. As all of the forces and displacements converged, we can assume that the optimisation was completed successfully by Gaussian 09W and that the molecule used for analysis is a suitable representation of the ground-state of molecule in question (ClF in this case).

<pre>
         Item               Value     Threshold  Converged?
 Maximum Force            0.000246     0.000450     YES
 RMS     Force            0.000246     0.000300     YES
 Maximum Displacement     0.000433     0.001800     YES
 RMS     Displacement     0.000613     0.001200     YES
</pre>


===<u>Interactive model of Chlorine monofluoride molecule</u>===
Below is an interactive ball and stick model of the Chlorine monofluoride molecule allowing you to visualise the molecule and also explore the symmetry exhibited by the molecule. The structure fits with structures predicted by VSEPR for the ClF molecule.<ref name="Atkins" />

'''(The Flourine atom is the smaller, lighter green ball)'''

<jmol><jmolApplet>
  <title>Chlorine monofluoride Molecule</title>
  <color>grey</color>
  <script>frame 1.10</script>
  <size>200</size>
  <uploadedFileContents>EOPOKU CLF OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

Link to LOG file:[[File:EOPOKU CLF OPTF POP.LOG]]

===<u>Vibrational Modes</u>===
One band is expected from an experimental spectrum of the Chlorine monofluoride molecule. From the image below we can see that the molecule is infrared active and this is due to the fact that there is a change in dipole moment when the bond stretches.

[[File:Vibration modes clf.jpg|thumb|centre|A GaussView window of the vibration modes in the ClF molecule.]]

===<u>Charge Distribution</u>===
It is expected for the Flourine atom (red) to be negatively charged as it is the most electronegative atom in the molecule and will attract the bonding electrons towards it more than the Chlorine atom (green) would, making the Chlorine atoms carry a slightly positive charge. The charge distribution on the Fluorine atom is -0.39 and it is 0.39 on the Chlorine.

[[File:Charge distribution clf.jpg|thumb|centre|A GaussView representation of the charge distribution in the ClF molecule.]]

===<u>Molecular Orbitals in ClF</u>===
Using Gaussian 09W to calculate the combination of atomic orbitals(AOs) that produce the molecular orbitals(MOs) present in the ClF molecule.

The electronic configuration for the Cl atom is '''1s<sup>2</sup>,2s<sup>2</sup>,2p<sup>6</sup>,3s<sup>2</sup>,3p<sup>5</sup>''' and '''1s<sup>2</sup>,2s<sup>2</sup>,2p<sup>5</sup>''' for the Fluorine atom.

The table below shows 5 MOs in the molecule (13 filled MOs in total) visualised by GaussView 5.0.9.

{| class="wikitable" border="1"
|+ Five Molecular Orbitals found in ClF Molecule
! Representation of Orbital !! Description of Orbital
|-
|[[File:Clf eo 1s.jpg|thumb|centre|2s orbital from Chlorine atom.]]|| This is the 2s orbital from the Chlorine molecule and it does not have an influence in the bonding between the two atoms. It's energy is quite low (-9.54057 a.u.) and there aren't any other orbitals of a similar energy, thus this orbital has a pure s character and has no effect on bonding. 
|-
|[[File:Clf eo 2p.jpg|thumb|centre|2p orbital from Chlorine atom.]]|| This is the 2p orbital from the Chlorine atom, there are two of these which are degenerate (-7.29213 a.u.). This isn't close in energy to any of the other orbitals and therefore has no effect on the bonding within the molecule. There are 3 2p orbitals that are all non-bonding.
|-
|[[File:Clf eo 2s.jpg|thumb|centre|2s orbital from Fluorine atom and 3s orbital from Chlorine atom.]]|| This is the first bonding orbital where an MO orbital is generated from the combination of a 3s orbital from Chlorine and a 2s orbital from Fluorine. The AOs are in phase and that gives rise to a bonding MO. This MO is relatively higher in energy compared to the other MOs (-1.21864 a.u.). There is more electron density towards the Fluorine which could be attributed to its higher electronegativity.
|-
|[[File:Clf eo homo.jpg|thumb|centre|2p orbital from Fluorine atom and 3p orbital from Chlorine atom.]]|| This MO is the Highest Occupied Molecular Orbital (HOMO) and is degenerate (with energy of -0.32855 a.u.) to another MO with the same shape but with a different orientation in space. These are anti-bonding orbitals resulting from the combination of a 3p orbital from Chlorine(green atom) and a 2p orbital from Fluorine(turquoise). They combine out-of-phase which is represented in the image with oppositely shaded lobes on the MOs. Electrons in this MO are responsible for most behaviour of the molecule when interacting with other molecules. The p character of thee MOs are still evident from the image.
|-
|[[File:Clf eo lumo.jpg|thumb|centre|2p orbital from Fluorine atom and 3p orbital from Chlorine atom.]]|| This MO is the Lowest Unoccupied Molecular Orbital (LUMO) and is not degenerate to any other MO in the molecule. This is an anti-bonding orbital that results from the combination of a 3p orbital from Chlorine(green atom) and a 2p orbital from Fluorine(turquoise). Once again, this is due to an out-of-phase combination which is represented in the image with oppositely shaded lobes on the MOs. If electrons are placed into this high energy (-0.12150 a.u.) MO the bond between the atoms will be inclined to break.
|-
|}

==References==
<references>
<ref name="Atkins">Atkins, P. W., Overton, T., Rourke, Jonathan P., Weller, M. and Armstrong,Shriver & Atkins' Inorganic Chemistry.,ISBN 9780199236176,Oxford, 2010.</ref>
<ref name="Haber">G Austin, Shreve’s Chemical Process Industries, 5th ed., McGraw-HillInternational Editions, New York, 1984.</ref>
</references>