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==NH<sub>3</sub> molecule==
===property of NH<sub>3</sub>===

bond length of N-H is 1.01798 Angstrom

Bond angle of NH<sub>3</sub> is 105.741 degrees

<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.
</pre>

{| class="wikitable" border="1"
|+ colspan="2" style="text-align: center;"| NH<sub>3</sub> 
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| RMS Gradient Norm|| 0.00000485 a.u
|-
|  final energy E(RB3LYP) || -56.55776873 a.u
|-
| Point Group || C<sub>3V</sub>
|}

<jmol><jmolApplet>
  <title>NH3 molecule</title>
  <color>black</color>
  <size>200</size>
  <uploadedFileContents>JIANCHEN_NH3_OPTF_POP.LOG</uploadedFileContents>
  <script>frame 1.16</script>
</jmolApplet></jmol>

[[Media:JIANCHEN_NH3_OPTF_POP.LOG]]

===vibration of NH<sub>3</sub> molecule===
[[File:nh3_screenshot.png]]

there are 6 type of vibration of NH<sub>3</sub>.

The mode 2 and mode 3 have same bending frequency at 1693.95 cm-1. The mode 5 and mode 6 have same stretching frequency at 3589.82 cm-1.Thus, there are degenerate.

The mode 1, mode 2 and mode 3 are bending vibration and mode 4, mode 5 and mode 6 are bond stretch vibration. 

The mode 1 and mode 4 are the symmetrical vibration. The mode 1 is the umbrella mode.

There are 4 different energy levels in the vibration mode. Therefore, there 4 bands in the vibration spectrum.

=== atomic charges of NH<sub>3</sub> molecule===

[[File:Nh3_charge.png]]

The Nitrogen has -1.125 charges and Hydrogen has +0.375 charges 

The Nitrogen has higher electronegativity than Hydrogen. Thus, the Nitrogen withdraw electron density from Hydrogen.

==H<sub>2</sub>==
===property of H<sub>2</sub>===
bond length of H-H is 0.74247 Angstrom

The H<sub>2</sub> is a linear molecular, which the bond angle is 180 degrees.

<pre>
        Item               Value     Threshold  Converged?
 Maximum Force            0.000232     0.000450     YES
 RMS     Force            0.000232     0.000300     YES
 Maximum Displacement     0.000305     0.001800     YES
 RMS     Displacement     0.000431     0.001200     YES
 Predicted change in Energy=-7.091616D-08
 Optimization completed.
    -- Stationary point found.
</pre>

{| class="wikitable" border="1"
|+ colspan="2" style="text-align: center;"|  H<sub>2</sub>
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| RMS Gradient Norm|| 0.00013423 a.u
|-
|  final energy E(RB3LYP) || -1.17853929 a.u
|-
| Point Group || D<sub>*h</sub>
|}

<jmol><jmolApplet>
  <title>H2 molecule</title>
  <color>black</color>
  <size>200</size>
  <uploadedFileContents>JIANCHEN_H2_OPTF_POP.LOG</uploadedFileContents>
  <script> frame 1.10 </script>
</jmolApplet></jmol>

[[Media:JIANCHEN_H2_OPTF_POP.LOG]]

===vibration of H<sub>2</sub>===

[[File:jianchen_h2_screenshot.png]]

There is only one symmetrical vibration in the H<sub>2</sub> molecule at 4470.30cm-1.
There are no band in the infra red.

===atmoic charges of H<sub>2</sub>===

[[File:jianchen_h2_charges.png]]

There is no charges between two hydrogen atoms due to the same electronegativity of two same atoms.

==N<sub>2</sub> molecule==
===property of N<sub>2</sub> molecule===
bond length of N-N is 1.10555 Angstrom

The N<sub>2</sub> is a linear molecular, which the bond angle is 180 degrees.

<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>

{| class="wikitable" border="1"
|+ colspan="2" style="text-align: center;"|  H<sub>2</sub>
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| RMS Gradient Norm|| 0.00008380 a.u
|-
|  final energy E(RB3LYP) || -109.52412867 a.u
|-
| Point Group || D<sub>*h</sub>
|}

<jmol><jmolApplet>
  <title>N2 molecule</title>
  <color>black</color>
  <size>200</size>
  <uploadedFileContents>JIANCHEN_N2_OPTF_POP.LOG</uploadedFileContents>
  <script> frame 1.10 </script>
</jmolApplet></jmol>

[[Media:JIANCHEN_N2_OPTF_POP.LOG]]

===vibration of N<sub>2</sub>===
[[File:jianchen_n2_screenshot.png]]

There is only one symmetrical vibration occur at 2456.91cm-1.
There are no band in the infra red.

===atomic charges of N<sub>2</sub>===
[[File:jianchen_n2_charges.png]]

There is no charge difference between two same atoms dur to the same electronegativity

==Reaction energy of Haber Process==
===Haber Process is N<sub>2</sub> + 3H<sub>2</sub> -> 2NH<sub>3</sub>===
E(NH<sub>3</sub>)= -148492.4331122 KJ/mol

2*E(NH<sub>3</sub>)= -296984.8662KJ/mol

E(N<sub>2</sub>)= -287555.62172791 KJ/mol

E(H<sub>2</sub>)= -3094.2551416 KJ/mol

3*E(H<sub>2</sub>)= -9282.765425 KJ/mol

ΔE=2*E(NH<sub>3</sub>)-[E(N<sub>2</sub)+3*E(H<sub>2</sub>)]=-296984.8662 + 296838.38715291 = -146.48 KJ/mol

The enthalpy of the reaction is exothermic. Thus, the ammoina product is more stable than the gaseous product.<ref name="BH" />

==CH<sub>4</sub>==

===property of CH<sub>4</sub> molecule===

bond length of C-H is 1.09179 Angstrom

The bong angle of C-H-C is 109.471 degrees

<pre>
        Item               Value     Threshold  Converged?
 Maximum Force            0.000057     0.000450     YES
 RMS     Force            0.000030     0.000300     YES
 Maximum Displacement     0.000161     0.001800     YES
 RMS     Displacement     0.000086     0.001200     YES
 Predicted change in Energy=-1.829380D-08
 Optimization completed.
    -- Stationary point found.
</pre>

{| class="wikitable" border="1"
|+ colspan="2" style="text-align: center;"|  CH<sub>4</sub>
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| RMS Gradient Norm|| 0.00002940 a.u
|-
|  final energy E(RB3LYP) || -40.52401404 a.u
|-
| Point Group || T<sub>d</sub>
|}


<jmol><jmolApplet>
  <title>CH4 molecule</title>
  <color>black</color>
  <size>200</size>
  <uploadedFileContents>JIANCHEN_CH4_OPTF_POP.LOG</uploadedFileContents>
  <script> frame 1.8 </script>
</jmolApplet></jmol>


[[Media:JIANCHEN_CH4_OPTF_POP.LOG]]

===vibration of CH<sub>4</sub>molecule===
[[File:jianchen_ch4_screenshot.png]]

There are 9 modes of the vibration in the CH<sub>4</sub>molecule.

However, mode1, mode2 and mode3 are degenerate due to the same frequency at 1355.84cm-1.
Mode1, mode2, mode3, mode4 and mode5 is bending vibration.

Mode6, mode7, mode8 and mode9 is streching vibration.

Moreoer, mode4 and mode5 are degenerate, which have the same vibration frequency at 1578.46cm-1 and mode7, mode8 and mode 9 are degenerate, which have same viation frequnecy at 3163.98cm-1.

Mode4, mode5 and mode6 are the symmetrical vibration that do not form the dipole moments.
There are only 2 band will be showed on the infra red.

=== atomic charges of CH<sub>4</sub>molecule===

[[File:jianchen_ch4_charges.png]]

The charges on the carbon is -0.930 this is because the electronegativity of carbon (2.55)  is sightly higher then Hydrogen (2.2). Thus, the charges on Hydrogen is +0.233. 

===Molecular orbital of CH<sub>4</sub>molecule===

{| class="wikitable" border="1"
|+ colspan="2" style="text-align: center;"| CH<sub>4</sub>molecular Orbital
|-
| [[File:Jianchen_ch4_1smo.PNG | 700px | thumb| MO 1]] || This energy level (-10.167 a.u.) of the CH<sub>4</sub>molecule orbital will not interact with other molecular orbital due to the deep energy. 
Therefore, it does not hybridized with other atomic orbitals and it will not interact with the molecular orbital due to the electrons hold by the nuclear too tightly.
Moreover, it do not give any bonding affect to the CH<sub>4</sub>molecule

|-
| [[File:Jianchen_ch4_2smo.PNG | 700px | thumb| MO 2 ]] ||  This is σ-bonding Molecular orbital,that 2s Carbon atomic orbital hybridized with 1s Hydrogen atomic orbital to gives a relatively low energy level compare with MO3,MO4 and MO5.
It contribute the bonding effect to the CH<sub>4</sub>molecule
|-
| [[File:Jianchen_ch4_2pzmo.PNG |700px | thumb| MO 3 ]] ||  This is π-bonding Molecular orbital, that the 2px Carbon atomic orbital hybridized with 1s Hydrogen atomic orbital to gives a energy level at -0.38834 a.u. It degenerated with MO4 and MO5.
It contribute the bonding effect to the CH<sub>4</sub>molecule
|-
| [[File:Jianchen_ch4_mo4.PNG | 700px | thumb | MO4]] || This is π-bonding Molecular orbital, that the 2py Carbon atomic orbital hybridized with 1s Hydrogen atomic orbital to gives a energy level at -0.38834 a.u. It degenerated with MO3 and MO5.
It contribute the bonding effect to the CH<sub>4</sub>molecule
|-
| [[File:Jianchen_ch4_2pymo.PNG |  700px | thumb| MO 5]] || This is π-bonding Molecular orbital, that is the 2pz Carbon atomic orbital hybridized with 1s Hydrogen atomic orbital to gives a energy level at -0.38834 a.u. It degenerated with MO3 and MO4.
It is the HOMO of CH<sub>4</sub>molecule.
It contribute the bonding effect to the CH<sub>4</sub>molecule
|-
|  [[File:Jianchen_ch4_3smo.PNG |  700px | thumb| MO 6]]|| This Molecular orbital is the anti-bonding orbital of 2s Carbon atomic orbital hybridized with 1s Hydrogen atomic orbital to gives a energy level at 0.11828 a.u. 
It is the LUMO of CH<sub>4</sub>molecule.
It  σ-antibonding molecular orbital.
It not contribute the bonding effect to the CH<sub>4</sub>molecule.
|}

==Reference==
<references> 


<ref name="BH"> http://www.chemguide.co.uk/physical/equilibria/haber.html (Accessed March 2018) </ref>


</references>