View source for CompLab:ZCJ17

==NH<sub>3</sub>== 
<pre>   
Calculation Type	FREQ
Calculation Method	RB3LYP
Basis Set	        6-31G(d,p)
E(RB3LYP)	        -56.55776873 a.u.
RMS Gradient Norm	0.00000485 a.u.
Point Group	        C3V

</pre>
<pre>
          Item               Value     Threshold  Converged?
 Maximum Force            0.000004     0.000450     YES
 RMS     Force            0.000004     0.000300     YES
 Maximum Displacement     0.000072     0.001800     YES
 RMS     Displacement     0.000035     0.001200     YES

 Predicted change in Energy=-5.986277D-10
 Optimization completed.
    -- Stationary point found.
</pre>

<jmol><jmolApplet>
  <title>NH3</title>
  <color>black</color>
  <size>200</size>
  <uploadedFileContents>ZJEFFERS NH3 OPT POP.LOG </uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is linked to [https://wiki.ch.ic.ac.uk/wiki/images/a/a1/ZJEFFERS_NH3_OPT_POP.LOG here]

<b>Vibrations</b>

[[File:ZjeffersNH3vibration.PNG]]

From the 3N-6 rule, you would expect there to be (3*4)-6 = 12-6 =6 vibrations. 
This is consistent with the vibrations outputted by Gaussian.

Modes 2 and 3 are degenerate (1693.95) as well as modes 5 and 6 (3589.82).

The first three modes are bend vibrations. The final three are stretch vibrations.
Mode 4 is highly symmetric
Mode 1 is known as the umbrella mode
In an experimental spectrum there would be four bands, as two pairs of modes are degenerate. 

{| class="wikitable" border="1"
|+ Charges
! Atom !! Charge (a.u.)
|-
| N || -1.125
|-
| H || 0.375
|}

This is approximately what is expected as the Nitrogen has an electronegativity of 3.04.<ref name="Atkins" />, whereas the electronagtivity of hydrogen is 2.2.<ref name="Atkins" />. This means the Nitrogen is holding the electrons closer, therefore has more negative charge. The bond angle is 107 degrees.

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

Calculation Type	FREQ
Calculation Method	RB3LYP
Basis Set	        6-31G(d,p)
E(RB3LYP)	        -109.52412868	 a.u.
RMS Gradient Norm	0.00000060	 a.u.
Point Group	        D*H
Bond Length             1.10550 Angstrom
</pre>

<pre>
Item                      Value        Threshold  Converged?
Maximum  Force            0.000001     0.000450     YES
RMS      Force            0.000001     0.000300     YES
Maximum  Displacement     0.000000     0.001800     YES
RMS      Displacement     0.000000     0.001200     YES
 
Predicted change in Energy=-3.401075D-13

Optimization completed.

Stationary point found.
</pre>
<jmol><jmolApplet>
  <title>N2</title>
  <color>black</color>
  <size>200</size>
  <uploadedFileContents>ZJEFFERS N2 OPT POP.LOG </uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [https://wiki.ch.ic.ac.uk/wiki/images/0/02/ZJEFFERSN2OPTPOP.LOG here]

<b>Vibrations</b>

[[File:ZjeffersN2vibration.PNG]]
There are no negative vibrations

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

Calculation Type	FREQ
Calculation Method	RB3LYP
Basis Set	        6-31G(d,p)
E(RB3LYP)	        -1.17853936	 a.u.
RMS Gradient Norm	0.00000017	 a.u.
Point Group	        D*H
Bond Length             0.74279          Angstrom
</pre>

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

Predicted change in Energy=-1.164080D-13

Optimization completed.

Stationary point found.

</pre>
<jmol><jmolApplet>
  <title>H2</title>
  <color>black</color>
  <size>200</size>
  <uploadedFileContents>ZJEFFERS H2 OPT POP.LOG </uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is linked to [https://wiki.ch.ic.ac.uk/wiki/images/2/2c/ZJEFFERSH2OPTPOP.LOG here]

<b>Vibrations</b>

[[File:ZjeffersH2vibration.PNG]]
There are no negative vibrations

==Reaction Energy Calculations==


E(NH<sub>3</sub>)   = -56.55776873      a.u.

2*E(NH<sub>3</sub>) = -113.11553746     a.u.

E(N<sub>2</sub>)    = -109.52412868	 a.u.

E(H<sub>2</sub>)    = -1.17853936	 a.u.

3*E(H<sub>2</sub>)  = -3.53561808        a.u.


ΔE= 2*E(NH<sub>3</sub>) - [E(N<sub>2</sub>) + 3*E(H<sub>2</sub>)]
 
= -113.11553746 - [ -109.52412868 + (-3.53561808 )]

= -113.11553746 - [ -113.05974676]
 
= -0.05579070 a.u.

= -146.49 kJ/mol

The reaction is exothermic and gives out energy, so therefore the products are more stable as they are of lower energy.

==S<sub>2</sub>==
<pre>

Calculation Type	FREQ
Calculation Method	RB3LYP
Basis Set	        6-31G(d,p)
E(RB3LYP)	        -796.32599779	 a.u.
RMS Gradient Norm	0.00000372	 a.u.
Point Group	        D*H
Bond Length             1.92943          Angstrom
</pre>

<pre>
Item                      Value        Threshold  Converged?
Maximum  Force            0.000006     0.000450     YES
RMS      Force            0.000006     0.000300     YES
Maximum  Displacement     0.000011     0.001800     YES
RMS      Displacement     0.000016     0.001200     YES

Predicted change in Energy=-7.077703D-11

Optimization completed.

Stationary point found.
</pre>
<jmol><jmolApplet>
  <title>S2</title>
  <color>black</color>
  <size>200</size>
  <uploadedFileContents>ZJEFFERS S2 OPT POP.LOG </uploadedFileContents>
</jmolApplet></jmol>

As it is a diatomic molecule there is no charge on either of the atoms.

The optimisation file is linked [https://wiki.ch.ic.ac.uk/wiki/images/2/2f/ZJEFFERS%2AS2OPTPOP.LOG here]

<b>Vibrations</b>

[[File:ZjeffersS2vibration.PNG]]
There are no negative vibrations


<b>Molecular Orbitals</b>

The electronic configuration of a Sulfur atom is
1s<sup>2</sup> 2s<sup>2</sup> 2p<sup>6</sup> 3s<sup>2</sup> 3p<sup>4</sup>

[[File:ZjeffersS2MO1.PNG]]

This is the first molecular orbital. It contains two electrons, but they are pulled very deep in energy (-88.93663 a.u./-233503.13985 kJ/mol) so they are not involved in bonding. 


[[File:ZjeffersS2MO11peanut.PNG]]

This is the 11th molecular orbital. It was formed by combiing 2 3s orbitals and contains two electrons


[[File:ZjeffersS2MO15pi.PNG]]

This is the fifteenth molecular orbital. It contains two electrons and is a pi orbital. It is involved in bonding as there is a very good overlap. 
 

[[File:ZjeffersS2homo.PNG]]

This is the HOMO- the Highest Occupied Molecular Orbital. It is an antibonding orbital and contains two electrons 

[[File:ZjeffersS2lumo.PNG]]

This is the LUMO- the Lowest Unoccupied Molecular Orbital. It is not involved in bonding and contains no electrons

==Comparison of Gaussian vs Literature Values==

Literature Values taken From Atkins
{| class="wikitable" border="1"
|+ Gaussian vs Literature
! Atom!! Property!! Gausssian!!Literature.<ref name="Atkins" />
|-
| N <sub>2</sub>||Bond Length ||1.10550 Angstrom||1.0976 Angstrom
|-
| H <sub>2</sub>|||Bond Length|| 0.74279 Angstrom||0.74138 Angstrom
|}

This shows that Gaussian produces results very close to the accepted values.

==References==
<references>
<ref name="Atkins"> Physical Chemistry 9th Edition, Oxford University Press (ISBN 978-0-19-969740-3.</ref>
</references>