View source for Rep:Mod:rum123

== NH<sub>3</sub> molecule ==
The molecule is a nitrogen molecule bonded covalently to three hydrogen atoms, forming and NH<sub>3</sub> molecule knows as ammonia.

The optimised structure of ammonia can be caluculated using the programme Gaussview. Calculations made can be seen below. 
<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=-5.986266D-10
 Optimisation completed.
    -- Stationary point found.
                           ----------------------------
                           !   Optimized Parameters   !
                           ! (Angstroms and Degrees)  !
 --------------------------                            --------------------------
 ! Name  Definition              Value          Derivative Info.                !
 --------------------------------------------------------------------------------
 ! R1    R(1,2)                  1.018          -DE/DX =    0.0                 !
 ! R2    R(1,3)                  1.018          -DE/DX =    0.0                 !
 ! R3    R(1,4)                  1.018          -DE/DX =    0.0                 !
 ! A1    A(2,1,3)              105.7412         -DE/DX =    0.0                 !
 ! A2    A(2,1,4)              105.7412         -DE/DX =    0.0                 !
 ! A3    A(3,1,4)              105.7412         -DE/DX =    0.0                 !
 ! D1    D(2,1,4,3)           -111.8571         -DE/DX =    0.0                 !
 --------------------------------------------------------------------------------
</pre>
Optimised values can be seen below
{| class="wikitable" border="1"
|+ Optimised values for NH<sub>3</sub>
! Type !! Value
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Final energy || -56.557au
|-
| RMS Gradient Norm || 0.00000485
|-
| Point group || C3v
|}


<jmol><jmolApplet>
  <title>NH3 molecule</title>
  <color>black</color>
  <size>200</size>
  <uploadedFileContents>Aa516_nh3.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[Media:Aa516_nh3.LOG|Nh3 log file link]]

=== Vibrations of NH<sub>3</sub> ===

From the 3N-6 rule we expect to have 6 vibration modes. Here we expect the stretching vibrations seen in modes 5 and 6 to have degenerate energies, as well as bending vibrations from modes 2 and 3. 
Modes 1 and 4 can be seen to be highly symmetric. Mode 1, is also known as the umbrella mode.

Due to degenerate energies, 4 bands can be observed in the infrared spectrum of gaseous ammonia.

The charges on the atoms of an ammonia can be seen to be -1.125au and +0.375au for nitrogen and hydrogen respectively. This is due to the high  electronegativity  of nitrogen, this allows the nitrogen atom to attract the electrons in the bonds towards itself, resulting in the fomentation of a polarized bond. A image of this can be seen below.

[[file:Charge-dis.png|300px]]

==== N<sub>2</sub> and H<sub>2</sub> ====
Furthermore both N<sub>2</sub> and H<sub>2</sub> have the point groups D∞h due to them being linear molecules.
<jmol><jmolApplet>
  <title>N2 molecule</title>
  <color>black</color>
  <size>200</size>
  <uploadedFileContents>Aa516_N2.LOG</uploadedFileContents>
</jmolApplet></jmol>

The bond length of N<sub>2</sub> was found to be 1.09Å,the optimization of N<sub>2</sub> can be seen below. 
<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=-3.400973D-13
 Optimization completed.
    -- Stationary point found.
                           ----------------------------
                           !   Optimized Parameters   !
                           ! (Angstroms and Degrees)  !
 --------------------------                            --------------------------
 ! Name  Definition              Value          Derivative Info.                !
 --------------------------------------------------------------------------------
 ! R1    R(1,2)                  1.1055         -DE/DX =    0.0                 !
 --------------------------------------------------------------------------------

</pre>

{| class="wikitable" border="1"
|+ Optimised values for N<sub>2</sub>
! Type !! Value
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Final energy || -109.52412868au
|-
| RMS Gradient Norm || 0.00000060au

|}



For H<sub>2</sub> the optimized bond length was found to be 0.743Å, the optimization can be seen below.
<jmol><jmolApplet>
  <title>H2 molecule</title>
  <color>black</color>
  <size>200</size>
  <uploadedFileContents>Aa516HYDROGEN_OPTI.LOG</uploadedFileContents>
</jmolApplet></jmol>

<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.
                           ----------------------------
                           !   Optimized Parameters   !
                           ! (Angstroms and Degrees)  !
 --------------------------                            --------------------------
 ! Name  Definition              Value          Derivative Info.                !
 --------------------------------------------------------------------------------
 ! R1    R(1,2)                  0.7428         -DE/DX =    0.0                 !
 --------------------------------------------------------------------------------
</pre>

{| class="wikitable" border="1"
|+ Optimised values for H<sub>2</sub>
! Type !! Value
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Final energy || -1.17853936au
|-
| RMS Gradient Norm || 0.00000017au

|}

The balanced symbol equation of the formation of NH<sub>3</sub>, with their corresponding energies, can be sen below. 
 N<sub>2</sub> + 3H<sub>2</sub> -> 2NH<sub>3</sub>
{| class="wikitable" border="1"
|+ Energy values<sub>2</sub>
! Molecule!! energy value
|-
| E(NH3) || -56.55776873 au
|-
| 2*E(NH3) || -113.11553746 au
|-
| E(N2) || -109.52412868 au
|-
| E(H2) || -1.17853936 au
|-
| 3*E(H2) || -3.53561808 au
|-
| ΔE=2*E(NH3)-[E(N2)+3*E(H2)] || -146 kJ/mol
|}


Due a negative difference of energy, the products are more stable than the reactants.

== F<sub>2</sub> molecule ==
As fluorine is the most electrnegative atom, it is also the most reactive. The atom has 7 valence electrons and can form strong covelant bonds with other atoms.
A structure for the F<sub>2</sub> molecule was optimised, the calculation for this and the optimised values can be seen here.
<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
 Predicted change in Energy=-1.995025D-08
 Optimization completed.
    -- Stationary point found.
                           ----------------------------
                           !   Optimized Parameters   !
                           ! (Angstroms and Degrees)  !
 --------------------------                            --------------------------
 ! Name  Definition              Value          Derivative Info.                !
 --------------------------------------------------------------------------------
 ! R1    R(1,2)                  1.4028         -DE/DX =    0.0001              !
 --------------------------------------------------------------------------------
</pre>

{| class="wikitable" border="1"
|+ Optimised values for F<sub>2</sub>
! Type !! Value
|-
| Basis Set || 6-31G(d,p)
|-
| Charge || 0
|-
| Bond energy || -199.49825218 KJ/mol
|-
| RMS Gradient Norm || 0.00007365

|}

The high bond energy reflects the strength of the bond formed by the molecule.
As the molecule is linear, only a single stretch vibration can be seen. This is estimated to occur at a frequency of 1065.09Hz. Furthermore literature values of the bond energy can be found to be -154.39 <ref name="f2-energy" />, this is comparable to our calculated value of -199KJ/mol.

<jmol><jmolApplet>
  <title>F2 molecule</title>
  <color>black</color>
  <size>200</size>
  <uploadedFileContents>F22.LOG</uploadedFileContents>
</jmolApplet></jmol>


Molecular orbitals for F2 consist of 2s and 2p orbitals, combining in and out of phase to form σ and π orbitals.
{| class="wikitable" border="1"
|+ 
|-
| [[file:Aa516-sigma-2s.png|200px]]|| Here two 2s orbitals which are in phase overlap to form a 2σg bonding orbital. The energy of this orbital is -1.34ev.
|-
| [[file:Aa516-sigma-anti.png|200px]] || This is the anti-bonding orbital formed from the overlap of two 2s orbitals which are out of phase. This can be classified as a 2σu*, and has an energy of -1.09ev
|-
| [[file:Aa516-sigma-2p-bonding.png|200px]] || 2p orbitals on adjacent atoms can also overlap to form a 3σg bonding orbital. This has a energy of -0.588ev.
|-
| [[file:Aa516_f2_pi-bond.png|200px]] || The overlap of two in phase 2p orbitals leads to the formation of a 1πu bonding orbital. This has a energy of -0.523ev.
|-
| [[file:Aa516_f2_PI-anti.png|200px]] || Furthermore the overlap of two out of phase 2p orbitals results in the formation of 1πg*. This has a energy of -0.392ev

|}

<references>
<ref name="f2-energy">Why is the F2 bond so weak? A bond energy decomposition analysis. <i>Linnea E. Forslund and Nikolas Kaltsoyannis</i> (2003) .</ref>