2019-03-22T06:24:57Z

Ck4918:

==NH3==
<pre>
Molecule: ammonia

Calculation method: RB3LYP

Basis set: 6-31G(d,p)

Final energy E(RB3LYP):-56.55776873 au

RMS gradient: 0.00000485 au

Point group: C3V

N-H bond length: 1.02 Angstroms

H-N-H bond angle: 106°
</pre>

<jmol><jmolApplet>
<title>Interactive ammonia molecule</title>
<color>black</color>
<size>400</size>
<uploadedFileContents>CKERWIN_NH3_OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:optimised nh3 image.png|400px|thumb|left|Optimised ammonia structure]]

<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>

[[File:vibrational table.png|600px|thumb|left|Initial table displaying the vibrational modes data for ammonia]]

{| class="wikitable" border="1"
|+ Vibrational frequencies of NH3
! Vibration number !! Frequency (cm-1) !! Intensity (arbitrary units) !! Symmetry !! Image
|-
| 1 || 1090 || 145 || A1 || [[File:Vibration image 1.png|200px|thumb|left|]]
|-
| 2 || 1694 || 14 || E || [[File:Vibration image 2.png|200px|thumb|left|]]
|-
| 3 || 1694 || 14 || E || [[File:Vibration image 3.png|200px|thumb|left|]]
|-
| 4 || 3461 || 1 || A1 || [[File:Vibrational image 4.png|200px|thumb|left|]]
|-
| 5 || 3590 || 0 || E || [[File:Vibrational image 5.png|200px|thumb|left|]]
|-
| 6 || 3590 || 0 || E || [[File:Vibrational image 6.png|200px|thumb|left|]]
|}

<pre>
Using the 3N-6 rule, 6 vibrational modes are expected, as 3(4)-6=6.
There are two sets of degenerate modes; one set is at 1694 wavenumbers (modes 2 & 3) and the other set is at 3590 wavenumbers (modes 5 & 6)
The modes at 1090 wavenumbers and 1694 wavenumbers (modes 1, 2 & 3) are bending vibrations and the modes at 3461 wavenumbers and 3590 wavenumbers (modes 4, 5 & 6) are stretching.
The mode at 3461 wavenumbers (mode 4) is highly symmetric.
The "umbrella" mode is at 1090 wavenumbers (mode 1)
Two bands would be observed in an experimental spectrum of gaseous ammonia - although four different frequencies are observed in total, the stretching frequencies are of much lower intensity, therefore meaning only
two bands would be observed.
</pre>

[[File:ammonia charge image 2.png|600px|thumb|centre|Image displaying the charge distribution on an ammonia molecule]]

<pre>
Shown above is an image of the charge distribution on an ammonia molecule. It is expected that the nitrogen is negatively charged and the hydrogens are positively charged - this is because nitrogen is much more
electronegative than hydrogen, therefore nitrogen pulls the electron density towards itself.
</pre>
Optimisation file can be found here [[File:CKERWIN_NH3_OPTIMISATION.LOG]]

==N2==

<pre>
Molecule: nitrogen

Calculation method: RB3LYP

Basis set: 6-31G(d,p)

Final energy E(RB3LYP): -109.52359111 au

RMS gradient: 0.02473091 au

Point group: D∞H

N-N bond length: 1.11 Angstroms
N-N bond angle: 180°

</pre>

<jmol><jmolApplet>
<title>Interactive nitrogen molecule</title>
<color>black</color>
<size>400</size>
<uploadedFileContents>CKERWIN_N2_OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:n2 optimised image.png|400px|thumb|left|Optimised nitrogen structure]]

<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>

[[File:vibrations table n2.png|600px|thumb|left|Initial table displaying the vibrational modes data for nitrogen]]

The optimisation file can be found here [[File:CKERWIN_N2_OPTIMISATION.LOG]]

==H2==

<pre>
Molecule: hydrogen

Calculation method: RB3LYP

Basis set: 6-31G(d,p)

Final energy E(RB3LYP): -1.17853936 au

RMS gradient: 0.00000017 au

Point group: D∞H

H-H bond length: 0.74 Angstroms
H-H bond angle: 180°

</pre>

<jmol><jmolApplet>
<title>Interactive hydrogen molecule</title>
<color>black</color>
<size>400</size>
<uploadedFileContents>CKERWIN_H2_OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:h2 optimised image.png|400px|thumb|left|Optimised hydrogen structure]]

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

[[File:h2 vibrational table.png|600px|thumb|left|Initial table displaying the vibrational modes data for hydrogen]]

The optimisation file can be found here [[File:CKERWIN_H2_OPTIMISATION.LOG]]

==Haber Bosch Process==
<pre>
The Haber Bosch Process is a process in which ammonia is formed from nitrogen and hydrogen. The equation for the reaction is shown below:

N2 +3H2 --> 2NH3
E(NH3)= -56.55776873 au
2*E(NH3)= -113.1155375 au
E(N2)= -109.52359111 au
E(H2)= -1.17853936 au
3*E(H2)= -3.53561808
ΔE=2*E(NH3)-[E(N2)+3*E(H2)]= -0.05632831 au
ΔE=-147.9kJ/mol
This process is exothermic, meaning the product (ammonia) is more stable as it is at a lower energy.
</pre>

==CH4==
<pre>
Molecule: methane

Calculation method: RB3LYP

Basis set: 6-31G(d,p)

Final energy E(RB3LYP):-40.52401404 au

RMS gradient: 0.00003263 au

Point group: Td

C-H bond length: 1.09 Angstroms

H-C-H bond angle: 109°
</pre>

<jmol><jmolApplet>
<title>Interactive methane molecule</title>
<color>black</color>
<size>400</size>
<uploadedFileContents>CKERWIN_CH4_OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:ch4 optimised image.png|400px|thumb|left|Optimised methane structure]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000063 0.000450 YES
RMS Force 0.000034 0.000300 YES
Maximum Displacement 0.000179 0.001800 YES
RMS Displacement 0.000095 0.001200 YES
</pre>

[[File:ch4 vibrations table.png|600px|thumb|left|Initial table displaying the vibrational modes data for methane]]

{| class="wikitable" border="1"
|+ Vibrational frequencies of CH4
! Vibration number !! Frequency (cm-1) !! Intensity (arbitrary units) !! Symmetry !! Image
|-
| 1 || 1356 || 14 || T2 || [[File:ch4 vibration 1.png|200px|thumb|left|]]
|-
| 2 || 1356 || 14 || T2 || [[File:ch4 vibration 2.png|200px|thumb|left|]]
|-
| 3 || 1356 || 14 || T2 || [[File:ch4 vibration 3.png|200px|thumb|left|]]
|-
| 4 || 1579 || 0 || E || [[File:ch4 vibration 4.png|200px|thumb|left|]]
|-
| 5 || 1579 || 0 || E || [[File:ch4 vibration 5.png|200px|thumb|left|]]
|-
| 6 || 3046 || 0 || A1 || [[File:ch4 vibration 6.png|200px|thumb|left|]]
|-
| 7 || 3162 || 25 || T2 || [[File:ch4 vibration 4.png|200px|thumb|left|]]
|-
| 8 || 3162 || 25 || T2 || [[File:ch4 vibration 5.png|200px|thumb|left|]]
|-
| 9 || 3162 || 25 || T2 || [[File:ch4 vibration 6.png|200px|thumb|left|]]
|}

[[File:ch4 charge image.png|400px|thumb|left|Charge distribution of methane]]

<pre>
This charge distribution is as expected, as carbon is more electronegative than hydrogen and therefore pulls the electron density towards itself, creating a negative charge on the carbon and a positive charge
on the hydrogen atoms.
</pre>

====Molecular orbitals of CH4====

File:Ch4 charge image.png

2019-03-22T06:22:46Z

Ck4918:

Mod01559535

2019-03-22T06:10:27Z

Ck4918:

==NH3==
<pre>
Molecule: ammonia

Calculation method: RB3LYP

Basis set: 6-31G(d,p)

Final energy E(RB3LYP):-56.55776873 au

RMS gradient: 0.00000485 au

Point group: C3V

N-H bond length: 1.02 Angstroms

H-N-H bond angle: 106°
</pre>

<jmol><jmolApplet>
<title>Interactive ammonia molecule</title>
<color>black</color>
<size>400</size>
<uploadedFileContents>CKERWIN_NH3_OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:optimised nh3 image.png|400px|thumb|left|Optimised ammonia structure]]

<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>

[[File:vibrational table.png|600px|thumb|left|Initial table displaying the vibrational modes data for ammonia]]

{| class="wikitable" border="1"
|+ Vibrational frequencies of NH3
! Vibration number !! Frequency (cm-1) !! Intensity (arbitrary units) !! Symmetry !! Image
|-
| 1 || 1090 || 145 || A1 || [[File:Vibration image 1.png|200px|thumb|left|]]
|-
| 2 || 1694 || 14 || E || [[File:Vibration image 2.png|200px|thumb|left|]]
|-
| 3 || 1694 || 14 || E || [[File:Vibration image 3.png|200px|thumb|left|]]
|-
| 4 || 3461 || 1 || A1 || [[File:Vibrational image 4.png|200px|thumb|left|]]
|-
| 5 || 3590 || 0 || E || [[File:Vibrational image 5.png|200px|thumb|left|]]
|-
| 6 || 3590 || 0 || E || [[File:Vibrational image 6.png|200px|thumb|left|]]
|}

<pre>
Using the 3N-6 rule, 6 vibrational modes are expected, as 3(4)-6=6.
There are two sets of degenerate modes; one set is at 1694 wavenumbers (modes 2 & 3) and the other set is at 3590 wavenumbers (modes 5 & 6)
The modes at 1090 wavenumbers and 1694 wavenumbers (modes 1, 2 & 3) are bending vibrations and the modes at 3461 wavenumbers and 3590 wavenumbers (modes 4, 5 & 6) are stretching.
The mode at 3461 wavenumbers (mode 4) is highly symmetric.
The "umbrella" mode is at 1090 wavenumbers (mode 1)
Two bands would be observed in an experimental spectrum of gaseous ammonia - although four different frequencies are observed in total, the stretching frequencies are of much lower intensity, therefore meaning only
two bands would be observed.
</pre>

[[File:ammonia charge image 2.png|600px|thumb|centre|Image displaying the charge distribution on an ammonia molecule]]

<pre>
Shown above is an image of the charge distribution on an ammonia molecule. It is expected that the nitrogen is negatively charged and the hydrogens are positively charged - this is because nitrogen is much more
electronegative than hydrogen, therefore nitrogen pulls the electron density towards itself.
</pre>
Optimisation file can be found here [[File:CKERWIN_NH3_OPTIMISATION.LOG]]

==N2==

<pre>
Molecule: nitrogen

Calculation method: RB3LYP

Basis set: 6-31G(d,p)

Final energy E(RB3LYP): -109.52359111 au

RMS gradient: 0.02473091 au

Point group: D∞H

N-N bond length: 1.11 Angstroms
N-N bond angle: 180°

</pre>

<jmol><jmolApplet>
<title>Interactive nitrogen molecule</title>
<color>black</color>
<size>400</size>
<uploadedFileContents>CKERWIN_N2_OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:n2 optimised image.png|400px|thumb|left|Optimised nitrogen structure]]

<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>

[[File:vibrations table n2.png|600px|thumb|left|Initial table displaying the vibrational modes data for nitrogen]]

The optimisation file can be found here [[File:CKERWIN_N2_OPTIMISATION.LOG]]

==H2==

<pre>
Molecule: hydrogen

Calculation method: RB3LYP

Basis set: 6-31G(d,p)

Final energy E(RB3LYP): -1.17853936 au

RMS gradient: 0.00000017 au

Point group: D∞H

H-H bond length: 0.74 Angstroms
H-H bond angle: 180°

</pre>

<jmol><jmolApplet>
<title>Interactive hydrogen molecule</title>
<color>black</color>
<size>400</size>
<uploadedFileContents>CKERWIN_H2_OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:h2 optimised image.png|400px|thumb|left|Optimised hydrogen structure]]

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

[[File:h2 vibrational table.png|600px|thumb|left|Initial table displaying the vibrational modes data for hydrogen]]

The optimisation file can be found here [[File:CKERWIN_H2_OPTIMISATION.LOG]]

==Haber Bosch Process==
<pre>
The Haber Bosch Process is a process in which ammonia is formed from nitrogen and hydrogen. The equation for the reaction is shown below:

N2 +3H2 --> 2NH3
E(NH3)= -56.55776873 au
2*E(NH3)= -113.1155375 au
E(N2)= -109.52359111 au
E(H2)= -1.17853936 au
3*E(H2)= -3.53561808
ΔE=2*E(NH3)-[E(N2)+3*E(H2)]= -0.05632831 au
ΔE=-147.9kJ/mol
This process is exothermic, meaning the product (ammonia) is more stable as it is at a lower energy.
</pre>

==CH4==
<pre>
Molecule: methane

Calculation method: RB3LYP

Basis set: 6-31G(d,p)

Final energy E(RB3LYP):-40.52401404 au

RMS gradient: 0.00003263 au

Point group: Td

C-H bond length: 1.09 Angstroms

H-C-H bond angle: 109°
</pre>

<jmol><jmolApplet>
<title>Interactive methane molecule</title>
<color>black</color>
<size>400</size>
<uploadedFileContents>CKERWIN_CH4_OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:ch4 optimised image.png|400px|thumb|left|Optimised methane structure]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000063 0.000450 YES
RMS Force 0.000034 0.000300 YES
Maximum Displacement 0.000179 0.001800 YES
RMS Displacement 0.000095 0.001200 YES
</pre>

[[File:ch4 vibrations table.png|600px|thumb|left|Initial table displaying the vibrational modes data for methane]]

{| class="wikitable" border="1"
|+ Vibrational frequencies of CH4
! Vibration number !! Frequency (cm-1) !! Intensity (arbitrary units) !! Symmetry !! Image
|-
| 1 || 1356 || 14 || T2 || [[File:ch4 vibration 1.png|200px|thumb|left|]]
|-
| 2 || 1356 || 14 || T2 || [[File:ch4 vibration 2.png|200px|thumb|left|]]
|-
| 3 || 1356 || 14 || T2 || [[File:ch4 vibration 3.png|200px|thumb|left|]]
|-
| 4 || 1579 || 0 || E || [[File:ch4 vibration 4.png|200px|thumb|left|]]
|-
| 5 || 1579 || 0 || E || [[File:ch4 vibration 5.png|200px|thumb|left|]]
|-
| 6 || 3046 || 0 || A1 || [[File:ch4 vibration 6.png|200px|thumb|left|]]
|-
| 7 || 3162 || 25 || T2 || [[File:ch4 vibration 4.png|200px|thumb|left|]]
|-
| 8 || 3162 || 25 || T2 || [[File:ch4 vibration 5.png|200px|thumb|left|]]
|-
| 9 || 3162 || 25 || T2 || [[File:ch4 vibration 6.png|200px|thumb|left|]]
|}

====Molecular orbitals of CH4====