View source for IMM2 : Jae Eun Lee CID : 01076523

== NH3 molecule ==

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

==== Key information about NH<sub>3</sub> molecule ====

<b>Molecule Name</b> : Ammonia(NH<sub>3</sub>)

<b>Calculation method</b> : RB3LYP

<b>Basis set</b> : 6-31G(d.p)

<b>Final energy E(RB3LYP) in atomic units (au)</b> : -56.55776873

<b>RMS gradient in atomic units (au)</b> : 0.00000323

<b>The point group of the molecule</b> : C<sub>3</sub>V

<b>N-H bond distance</b> = 1.01798 Å

<b>H-N-H bond angle</b> = 105.745 °

==== Item table of NH<sub>3</sub> molecule ====

The optimisation file is linked to [[Media:JAE NH3 OPTF POP.LOG| here]]

<pre>

         Item             Value        Threshold  Converged?
 Maximum Force            0.000006     0.000450      YES
 RMS     Force            0.000004     0.000300      YES
 Maximum Displacement     0.000014     0.001800      YES
 RMS     Displacement     0.000009     0.001200      YES
 Predicted change in Energy=-1.141685D-10
 Optimization 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)              105.7446         -DE/DX =    0.0                 !
 ! A2    A(2,1,4)              105.7446         -DE/DX =    0.0                 !
 ! A3    A(3,1,4)              105.7446         -DE/DX =    0.0                 !
 ! D1    D(2,1,4,3)           -111.8637         -DE/DX =    0.0                 !
 --------------------------------------------------------------------------------
</pre>
<i> Table 1. Item table of NH<sub>3</sub> molecule</i>

The table above shows that the energy of the NH<sub>3</sub> molecule is the minimum and therefore the structure of the NH<sub>3</sub> is optimised.

==== Jmol dynamic image of NH<sub>3</sub> molecule ====

<jmol><jmolApplet>
  <title> Figure 1. NH3 Molecule at the lowest energy state CID : 01076523</title>
  <color>black</color>
  <size>200</size>  
  <script>frame 1.12</script>
  <position>center</position>
<uploadedFileContents>JAE NH3 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Animating the Vibrations ===

==== Image of display vibrations of NH<sub>3</sub> molecule ==== 

[[File:JaeEunLee NH3 Display Vibration.jpg|thumb|center|Figure 2. An image of the 'Display Vibreations' of NH<sub>3</sub> molecule. CID : 01076523]]

==== Q&A ====


<b>Q1</b> : How many modes do you expect from the 3N-6 rule?

<b>A</b>  : Number of modes = 3(4) - 6 = 6 modes.


<b>Q2</b> : Which modes are degenerate?

<b>A</b>  : mode 2 and 3 (frequency = 1693.94 cm<sup>-1</sup>), and mode 5 and 6 (frequency = 3589.86 cm<sup>-1</sup>) are degenerate.


<b>Q3</b> : Which modes are 'bending' vibrations and which are 'bond stretch' vibrations?

<b>A</b>  : mode 1, 2 and 3 are bending vibrations and mode 4, 5 and 6 are bond stretch vibrations.


<b>Q4</b> : Which mode is highly symmetric?

<b>A</b>  : Mode 4 is highly symmetric (symmetric stretching of N-H bond).


<b>Q5</b> : One mode is known as the 'umbrella' mode, which one is this?

<b>A</b>  : Mode 1 is known as the 'umbrella' mode (symmetric bending of N-H bond).


<b>Q6</b> : How many bands would you expect to see in an experimental spectrum of gaseous ammonia?

<b>A</b>  : There are two peaks in the experimental spectrum of gaseous ammonia. The intensity of the peaks is dependent on the change of the dipole moment of the molecule. The intensity of the peak of mode 1 is much higher than other modes because the symmetric bending vibrations lead to a large change of dipole moment. However, the other modes have much smaller change of dipole moment and this leads to lower intensity of the peaks. Mode 2 and 3 have less symmetric bending vibrations and this minimizes the change in dipole moment. The stretching vibrations of mode 4, 5 and 6 lead to insignificant change in dipole moment and therefore the intensities of the peaks are insignificant such that they not observable on the spectrum. 


=== Charge Analysis === 

<b>Charge of the N-atom</b> : - 1.125


<b>Charge of the H-atom</b> : + 0.375


<b>Expectation of the charges of the N and H atoms</b> :

The charge of the N atom would be negative and the charge of the H atom would be positive. It is because the N atom is more electronegative than the H atom. Since NH<sub>3</sub> is a neutral atom the sum of the charges is equal to 0.

 
=== Reactivity ===

==== H2 molecule ====

===== Key information about H<sub>2</sub> molecule =====

<b>Molecule Name</b> : Hydrogen molecule(H<sub>2</sub>)

<b>Calculation method</b> : RB3LYP

<b>Basis set</b> : 6-31G(d.p)

<b>Final energy E(RB3LYP) in atomic units (au)</b> : -1.17853936

<b>RMS gradient in atomic units (au)</b> : 0.00000017

<b>The point group of the molecule</b> : D<sub>∞</sub>H

===== Item table of H<sub>2</sub> molecule =====

The optimisation file is linked to [[Media:JAEEUNLEE H2 OPTF POP.LOG| here]]

<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>
<i> Table 2. Item table of H<sub>2</sub> molecule</i>

The table above shows that the energy of the H<sub>2</sub> molecule is the minimum and therefore the structure of the H<sub>2</sub> is optimised.

===== Jmol dynamic image of NH<sub>3</sub> molecule =====

<jmol><jmolApplet>
  <title> Figure 3. H2 Molecule CID : 01076523</title>
  <color>black</color>
  <size>200</size>  
  <script>frame 1.11</script>
  <position>center</position>
<uploadedFileContents>JAEEUNLEE H2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

===== Image of display vibrations of H<sub>2</sub> molecule =====

[[File:JaeEunLee H2 Display Vibration.jpg|thumb|center|Figure 4. An image of the 'Display Vibreations' of H<sub>2</sub> molecule. CID : 01076523]]

frequency : 4465.68 cm<sup>-1</sup>

There is only one frequency because a diatomic molecule has only one mode of vibration.

The intensity of the H<sub>2</sub> molecule is zero because there is no dipole moment for the H<sub>2</sub> molecule.

==== N2 molecule ====

===== Key information about N<sub>2</sub> molecule =====

<b>Molecule Name</b> : Nitrogen molecule(N<sub>2</sub>)

<b>Calculation method</b> : RB3LYP

<b>Basis set</b> : 6-31G(d.p)

<b>Final energy E(RB3LYP) in atomic units (au)</b> : -109.52412868

<b>RMS gradient in atomic units (au)</b> : 0.00000060

<b>The point group of the molecule</b> : D<sub>∞</sub>H

===== Item table of N<sub>2</sub> molecule =====

The optimisation file is linked to [[Media:JAEEUNLEE N2 OPTF POP.LOG| here]]

<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=-3.401007D-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                 !
 --------------------------------------------------------------------------------
 RMS     Displacement     0.000000     0.001200      YES
</pre>
<i> Table 3. Item table of N<sub>2</sub> molecule </i>


The table above shows that the energy of the N<sub>2</sub> molecule is the minimum and therefore the structure of the N<sub>2</sub> is optimised.


===== Jmol dynamic image of N<sub>2</sub> molecule =====

<jmol><jmolApplet>
  <title> Figure 5. N2 Molecule CID : 01076523</title>
  <color>black</color>
  <size>200</size>  
  <script>frame 1.9</script>
  <position>center</position>
<uploadedFileContents>JAEEUNLEE N2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

===== Image of display vibrations of N<sub>2</sub> molecule =====

[[File:JaeEunLee N2 Display Vibration.jpg|thumb|center|Figure 6. An image of the 'Display Vibreations' of N<sub>2</sub> molecule. CID : 01076523]]

frequency : 2457.33 cm<sup>-1</sup>

There is only one frequency because a diatomic molecule has only one mode of vibration.

The intensity of the peak of the N<sub>2</sub> molecule is zero because there is no dipole moment for the stretching vibration of the N<sub>2</sub> molecule.

==== Calculating the energy of the reaction ====

<b>E(NH<sub>3</sub>)</b> = -56.55776873 au

<b>2*(NH<sub>3</sub>)</b> = -113.11553746 au

<b>E(N<sub>2</sub>)</b> = -109.52412868 au

<b>E(H<sub>2</sub>)</b> = -1.17853936 au

<b>3*E(H<sub>2</sub>)</b> = - 3.53561808 au

<b>ΔE</b> = 2*(NH<sub>3</sub>)-[E(N<sub>2</sub>)+3*E(H<sub>2</sub>)] = -0.0557907 au

By converting the energy difference into KJ/mol,

<b>ΔE</b> = -0.0557907 * 2625.5 = -146.47848285 KJ/mol = -146.48 KJ/mol.

<b>Q</b> : Identify whether the gaseous reactants are more stable or the ammonia product is more stable.

<b>A</b> :  The ammonia product is more stable than the gaseous reactants because the energy is released when the ammonia product is formed. Thus, the ammonia product has lower energy compared to the gaseous reactants. Therefore the ammonia product is more stable.

== Choosing my own molecule : HCl ==

=== Key information about HCl molecule ===

<b>Molecule Name</b> : Hydrogen Chloride molecule(HCl)

<b>Calculation method</b> : RB3LYP

<b>Basis set</b> : 6-31G(d.p)

<b>Final energy E(RB3LYP) in atomic units (au)</b> : -460.80077875

<b>RMS gradient in atomic units (au)</b> : 0.00005211

<b>The point group of the molecule</b> : C<sub>∞</sub>V


==== Item table of HCl molecule ====

The optimisation file is linked to [[Media:JAEEUNLEE_HCL_OPTF_POP.LOG| here]]

<pre>
        
         Item             Value        Threshold  Converged?
 Maximum Force            0.000090     0.000450      YES
 RMS     Force            0.000090     0.000300      YES
 Maximum Displacement     0.000139     0.001800      YES
 RMS     Displacement     0.000197     0.001200      YES
 Predicted change in Energy=-1.256951D-08
 Optimization completed.
    -- Stationary point found.
                           ----------------------------
                           !   Optimized Parameters   !
                           ! (Angstroms and Degrees)  !
 --------------------------                            --------------------------
 ! Name  Definition              Value          Derivative Info.                !
 --------------------------------------------------------------------------------
 ! R1    R(1,2)                  1.286          -DE/DX =    0.0001              !
 --------------------------------------------------------------------------------
</pre>
<i> Table 4. Item table of HCl molecule </i>

The table above shows that the energy of the HCl molecule is the minimum and therefore the structure of the HCl is optimised.


==== Jmol dynamic image of HCl molecule ====

<jmol><jmolApplet>
  <title> Figure 7. HCl Molecule at the lowest energy state CID : 01076523</title>
  <color>black</color>
  <size>200</size>  
  <script>frame 1.7</script>
  <position>center</position>
<uploadedFileContents>JAEEUNLEE_HCL_OPTF_POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Vibrations of N<sub>2</sub> molecule ====

[[File:JaeEunLee_HCl_Display_Vibration.jpg|thumb|center|Figure 8. An image of the 'Display Vibreations' of HCl molecule. CID : 01076523]]


[[File:JaeEunLee_HCl_IR_Spectrum.jpg|thumb|center|Figure 9. An image of IR Spectrum of HCl molecule. CID : 01076523]]

<b>Analysis</b>

HCl has 1 mode of vibration based on the calculation below.

Number of modes = 3N - 5 = 3(2)- 5 = 1 mode.

Diatomic molecules such as HCl have only one mode of vibration because only stretching vibration is possible for linear diatomic molecules.

Based on Figure 8, the stretching vibration of HCl molecule has the absorption frequency at 2956.80 cm<sup>-1</sup>.

Figure 9 shows the IR spectrum of the HCl molecule. It has only one peak because it has only one stretching vibration at 2956.80 cm<sup>-1</sup>. The broad absorption band is observed due to the hydrogen bonding formed between the HCl molecules. The extent of hydrogen bonding between HCl molecules varies in the sample and as a result, IR absorption occurs at slightly different frequencies. Different extents of absorption broaden the peak of the HCl molecule in the IR spectrum.

Unlike N<sub>2</sub> and H<sub>2</sub> molecules, HCl has a dipole moment due to different electronegativities of H atom and Cl atom. Thus, the peak is observed.

<b>Comparing with the literature value</b>

The literature value of the frequency of the HCl peak is 2990.946 cm<sup>-1</sup>. Since the frequency determined by using Gaussview is 2956.80 cm<sup>-1</sup>, the value is accurate.
 
==== Atomic charges of HCl ====

[[File:JaeEunLee_HCl_Charge.jpg|thumb|center|An image of charges of the atoms in CH<sub>3</sub>OH molecule. CID : 01076523]]

<b>Analysis</b>

The charge on the H atom is positive while the charge on the Cl atom is negative because the Cl atom is more electronegative compared to the H atom. Since HCl is a neutral molecule, the sum of the charges of the H and Cl atom is equal to zero.


==== Molecular Orbitals of HCl molecule ====

[[File:JaeEunLee_HCl_MO_4.jpg|thumb|center|Figure 10. 2p non-bonding molecular orbital of HCl. CID : 01076523]]

<b>Analysis</b>

The inner 1s, 2s and 2p orbitals of Cl atom do not interact with 1s orbital of H atom because they are tightly bounded to the nucleus of Cl atom. As a result, they remain as non-bonding orbitals in HCl molecular orbital. Since they are tightly bounded, they have much lower energies than 3s and 3p orbitals. 


[[File:JaeEunLee_HCl_MO_1.jpg|thumb|center|Figure 11. 3s bonding molecular orbital of HCl. CID : 01076523]]

<b>Analysis</b>

3s orbital of Cl atom is large enough to interact with 1s orbital of H atom. In this case, both 1s orbital of H and 3s orbital of Cl are in-phase such that they have a constructive overlap of orbitals to form a bonding orbital.


[[File:JaeEunLee_HCl_MO_2.jpg|thumb|center|Figure 12. 3σ bonding molecular orbital of HCl . CID : 01076523]]

<b>Analysis</b>

In this case, the 1s orbital of H atom is out of phase and the 3p<sub>z</sub> orbital of Cl atom is in the right orientation and phase to interact with the out of phase H atom. Thus, it forms the sigma bond.



[[File:JaeEunLee_HCl_MO_3.jpg|thumb|center|Figure 13. 3p non-bonding molecular orbital of HCl. CID : 01076523]]


<b>Analysis</b>

The 3p<sub>x</sub> and 3p<sub>y</sub> orbitals are orientated in such a way that they are not able to overlap with 1s orbital of the H atom. Thus, those 3p orbitals remain as non-bonding molecular orbitals.


[[File:JaeEunLee_HCl_MO_5.jpg|thumb|center|Figure 14. 3σ<sup>*</sup> anti-bonding molecular orbital of HCl. CID : 01076523]]

<b>Analysis</b>

In this case, the 1s orbital of H atom is in-phase but the side of 3p<sub>z</sub> orbital that overlaps with the 1s orbital of the H atom is out of phase. As a result it forms an anti-bonding molecular orbital.