View source for Rep:Mod:lh1316

== NH3 molecule ==

=== Optimization calculation summary ===
 Molecule: NH3
 Calculation Method: RB3LYP
 Basis set: 6-31G(d,p)
 Final energy E(RB3LYP): -56.55776873 a.u.
 RMS gradient: 0.00000485 a.u.
 Point group: C3V
 N-H bond distance: 1.01798 Å
 H-N-H bond angle: 105.741°

In order to check whether the job has optimized successfully, we directly looked the file that Gaussian generates. The following information shows forces and displacements are really converged and smaller than threshold. Since they are the gradient of the potential energy curve, zero value of gradient indicates it is in either the ground state or the transition state. The second derivative of the potential energy is k (force constant of the bond) and frequency is proportional to the value of k. The frequency analysis below indicates frequency is positive and thus it is in the minimum energy state and the optimization has completed.
 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=-5.986278D-10

<jmol><jmolApplet>
  <title> optimized NH3 molecule</title>
  <color>black</color>
  <size>300</size>
  <uploadedFileContents>LH1316_NH3_OPTF_POP.LOG</uploadedFileContents>
  <script>frame 1.16</script>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:LH1316_NH3_OPTF_POP.LOG| here]]

=== Vibration summary ===
[[File:Lh1316_nh3_display_vibrations.PNG]]
[[File:Lh1316_nh3_vibration_spectrum.PNG]]


QUESTIONS & ANSWERS:
<pre>
1.how many modes do you expect from the 3N-6 rule?
  6 modes.
2.which modes are degenerate (ie have the same energy)?
  2 degenerate modes.
  Mode 2 and 3 are degenerate. Mode 5 and 6 are degenerate.
3.which modes are "bending" vibrations and which are "bond stretch" vibrations?
  Mode 1,2 and 3 are bending.
  Mode 4,5 and 6 are bond stretch.  
4.which mode is highly symmetric?
  Mode 1,4 and 6.
5.one mode is known as the "umbrella" mode, which one is this?
  Mode 1.
6.how many bands would you expect to see in an experimental spectrum of gaseous ammonia?
  2 bands. As the vibration picture shows above, mode 4,5 and 6 have small dipole moments
  and thus leading to small intensities. Their bands would disappear in the noise. 
</pre>

=== Charge analysis ===
[[File:Lh1316_nh3_charge_analysis.PNG]]

N-atom should carry negative charge since it is more electronegative and H-atoms should carry positive charge since it is less electronegative.

== N2 molecule ==

=== Optimization calculation summary ===
 
 Molecule: N2
 Calculation Method: RB3LYP
 Basis set: 6-31G(d,p)
 Final energy E(RB3LYP): -109.52412868 a.u.
 RMS gradient: 0.00000060 a.u.
 Point group: D*H
 N-N bond distance: 1.10550 Å

The information in the table below shows forces and displacements are really converged and the optimization has completed.
 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=-3.401090D-13

<jmol><jmolApplet>
  <title> optimized N2 molecule</title>
  <color>grey</color>
  <size>300</size>
  <uploadedFileContents>LH1316_N2_OPTF_POP.LOG</uploadedFileContents>
  <script>frame 1.9</script>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:LH1316_N2_OPTF_POP.LOG| here]]

=== Vibration summary ===
[[File:Lh1316_n2_display_vibrations.PNG]]
[[File:Lh1316_n2_vibration_mode1.PNG | 500px]]

There is no bands in the spectrum because N<sub>2</sub> is symmetric and do not have change in the dipole moment.

== H2 molecule ==

=== Optimization calculation summary ===
 
 Molecule: H2
 Calculation Method: RB3LYP
 Basis set: 6-31G(d,p)
 Final energy E(RB3LYP): -1.17853936 a.u.
 RMS gradient: 0.00000017 a.u.
 Point group: D*H
 H-H bond distance: 0.74279 Å

The information in the table below shows forces and displacements are really converged and the optimization of H2 molecule has completed.
 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

<jmol><jmolApplet>
  <title> optimized H2 molecule</title>
  <color>black</color>
  <size>300</size>
  <uploadedFileContents>LH1316_H2_OPTF_POP.LOG</uploadedFileContents>
  <script>frame 1.10</script>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:LH1316_H2_OPTF_POP.LOG| here]]

=== Vibration summary ===
[[File:Lh1316_h2_display_vibrations.PNG]]
[[File:Lh1316_h2_vibration_mode1.PNG |500px]]

The frequency of H<sub>2</sub> vibration is greater than that of N<sub>2</sub> vibration because the frequency is related to the (k) force constant of the bond and (μ) reduced mass. The greater the mass, the lower the vibration frequency. Hence, H<sub>2</sub> has greater vibration frequency.

== Haber-Bosch reaction energy calculation ==
<pre>
N2+ 3H2 -> 2NH3

E(NH3)= -56.55776873 a.u.
2*E(NH3)= -113.11553746 a.u.

E(N2)= -109.52412868 a.u.

E(H2)= -1.17853936 a.u.
3*E(H2)= -3.53561808 a.u.

ΔE=2*E(NH3)-[E(N2)+3*E(H2)]= -0.0557909 a.u. = -146.47848285 kJ/mol
</pre>

The enthalpy change of formation of NH3 is -73.24 kJ/mol. Since the reaction is exothermic, the ammonia product is more stable than the gaseous reactants.

The literature value of the energy change is -92.0kJ/mol.<ref name=" -92.0kJ/mol" /> 

We used the optimized structure to calculate the reaction energy hence it is common to have difference between theoretical and practical value.

== Choice of small molecule (ClF3) ==

=== Optimization calculation summary ===
 Molecule: ClF3
 Calculation Method: RB3LYP
 Basis set: 6-31G(d,p)
 Final energy E(RB3LYP): -759.46531688 a.u.
 RMS gradient: 0.00002465 a.u.
 Point group: C3V
 Cl-F bond distance (equatorial): 1.65143 Å
 Cl-F bond distance (axial): 1.72863 Å
 F-Cl-F bond angle (equatorial-axial): 87.140°
 F-Cl-F bond angle (axial-axial):174.281°

The information in the table below shows forces and displacements are really converged and the optimization of H2 molecule has completed.
 Item                     Value        Threshold    Converged?
 Maximum Force            0.000050     0.000450     YES
 RMS     Force            0.000028     0.000300     YES
 Maximum Displacement     0.000204     0.001800     YES
 RMS     Displacement     0.000134     0.001200     YES
 Predicted change in Energy=-1.250218D-08


<jmol><jmolApplet>
  <title> optimized CLF3 molecule</title>
  <color>black</color>
  <size>300</size>
  <uploadedFileContents>LH1316_CLF3_OPTF_POP.LOG</uploadedFileContents>
  <script>frame 1.14</script>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:LH1316_CLF3_OPTF_POP.LOG| here]]

=== Vibration summary ===
[[File:Lh1316_clf3_display_vibrations.PNG]]
[[File:Lh1316_clf3_vibration_spectrum.PNG]]

Vibrational modes 1 and 2 are degenerate modes. But the frequency is a little different because of the imperfect T-shape structure of ClF3.
 
There are 3 bands in the spectrum. The vibration frequencies are low because of heavier F and Cl atoms.  As the vibration picture shows above, mode 3 and 4 have small dipole moments and thus leading to small intensities. Thus their bands would disappear in the noise. Since the intensities of mode 1 and 2 are extremely close, only one peak appears.

=== Charge analysis ===
[[File:Lh1316_clf3_charge_analysis.PNG]]

Cl-atom carrys positive charge since it is less electronegative and F-atoms carry negative charge since they are more electronegative. F atoms have different charges due to different molecular orbitals overlapped with Cl atom.

=== Molecular orbitals ===

[[File:Lh1316_clf3_MO4.PNG]]

'''2p orbital of Cl'''

MO7, 8 and 9 are formed by degenerate 2p orbitals of Cl atoms. 

The small difference in energy is due to different orientation and hence different repulsion with F atom.


[[File:Lh1316_clf3_MO1.PNG]]

'''Occupied MO bonding'''

MO9 is the sigma bonding between one 3s orbital of Cl atom and three 2s orbital of F atoms.

The enegy of MO9 is 6.2 a.u. higher than that of MO8 because MO8 is non-bonding and the electrons are held tightly to the respective nuclei.




[[File:Lh1316_clf3_MO2.PNG]]

'''Occupied MO mixture'''

One 3s orbital of Cl atom and two 2s orbital of F atoms in MO10 form sigma bonding.

The 2s orbital of equatorial F atom is out of phase with the left three atoms.

The energy of MO10 is 0.11 a.u. higher than that of bonding MO9. 


[[File:Lh1316_clf3_MO3.PNG]]

'''Occupied MO antibonding'''

In MO12, The 3s orbital of Cl atom is out of phase with all three 2s orbital of F atoms.

MO12 is higher in energy than the bonding MO9. The energy difference between the bonding and antibonding orbitals is much larger because they overlap better. These are valence orbitals and they are very involved in the chemical bonding.



[[File:Lh1316_clf3_MO5.PNG]]

'''Occupied MO antibonding'''

In MO22, 3p orbital of Cl atom is out of phase with 2p orbitals of all three F atoms.

MO 22 is HOMO(highest occupied molecular orbital).


=== Haber-Bosch reaction energy calculation ===

<pre>
Cl2 + 3F2 -> 2ClF3

E(ClF3)= -759.46531688 a.u.
2*E(ClF3)= -1518.93063376 a.u.

E(Cl2)= -920.34987886 au

E(F2)= -199.49825218a.u.
3*E(F2)= -598.49475654 a.u.

ΔE=2*E(ClF3)-[E(Cl2)+3*E(F2)]= -0.08599836 a.u. = -225.79 kJ/mol
</pre>

The enthalpy change of formation of ClF3 is -112.89 kJ/mol. Since the reaction is exothermic, the product ClF3 is more stable than gaseous reactants.


== Reference ==
<references>
<ref name=" -92.0kJ/mol" >  https://chem.libretexts.org/Core/Physical_and_Theoretical_Chemistry/Equilibria/Case_Studies/Haber_Process</ref>
</references>