Rep:Mod:jl7816

NH₃

Information of NH₃

A Gaussview image of an optimised NH₃ molecule.

Image of NH3 molecule

NH₃ optimisaion

Molecule Name	NH3
Calculation Method	RB3LYP
Basic Set	6-31G(d.p)
E(RB3LYP)	-56.55776873a.u.
RMS Gradient Norm	0.00000485a.u.
Point Group	C3V
N-H Bond Length	1.30Å
H-N-H Bond Angle	109.471

Item Table

 Item               Value     Threshold  Converged?
 Maximum Force            0.000004     0.000450     YES
 RMS     Force            0.000004     0.000300     YES
 Maximum Displacement     0.000070     0.001800     YES
 RMS     Displacement     0.000033     0.001200     YES
 Predicted change in Energy=-5.785197D-10

The optimisation file is liked to log file link

Display Vibration Modes of NH₃

A screenshot of the display vibrations window.

How many modes do you expect from the 3N-6 rule?

3x4-6= 6 modes

Which modes are degenerate (ie have the same energy)?

Modes 2 and 3 are degenerated, and modes 5 and 6 are degenerated.

Which modes are "bending" vibrations and which are "bond stretch" vibrations?

Modes 1,2 and 3 are "bending" vibrations, modes 4,5 and 6 are "bond stretch" vibrations.

Which mode is highly symmetric?

Mode 4 is highly symmetric.

One mode is known as the "umbrella" mode, which one is this?

Mode 1.

How many bands would you expect to see in an experimental spectrum of gaseous ammonia?

Four.

Charge Analysis of NH₃

A screenshot of the charge analysis.

The charge on N is -1.125 and the charge on H is 0.375.

The N atom would be expected to be negatively charged and H atom would be expected to be positively charged, because nitrogen atom is more electronegative than hydrogen atom.

N₂

Information of N₂

A Gaussview image of an optimised N₂ molecule.

Image of N2 molecule

N₂ optimisaion

Molecule Name	N2
Calculation Method	RB3LYP
Basic Set	6-31G(d.p)
E(RB3LYP)	-109.52412868a.u.
RMS Gradient Norm	0.00000003a.u.
Point Group	D∞h

Item Table

 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     0.000000     0.001200     YES

The optimisation file is liked to log file link

Display Vibration Modes of N₂

A screenshot of the display vibrations window.

H₂

Information of H₂

A Gaussview image of an optimised H₂ molecule.

Image of H2 molecule

H₂ optimisaion

Molecule Name	H2
Calculation Method	RB3LYP
Basic Set	6-31G(d.p)
E(RB3LYP)	-1.17853936a.u.
RMS Gradient Norm	0.00002276a.u.
Point Group	D∞h

Item Table

 Item               Value     Threshold  Converged?
 Maximum Force            0.000039     0.000450     YES
 RMS     Force            0.000039     0.000300     YES
 Maximum Displacement     0.000052     0.001800     YES
 RMS     Displacement     0.000073     0.001200     YES

The optimisation file is liked to log file link

Display Vibration Modes of H₂

A screenshot of the display vibrations window.

Determining the energy in a.u. for the Haber-Bosch reaction (N₂ + 3H₂ → 2NH₃)

Energy

E(NH3)= ''-56.55776873''
2*E(NH3)= ''-113.11553746''
E(N2)=''-109.52412868''
E(H2)=''-1.17853936''
3*E(H2)=''-3.53561808''
ΔE=2*E(NH3)-[E(N2)+3*E(H2)]=''-0.05579070''

Energy difference in kJ/mol

ΔE=-146.47848285

The product is more stable as it is an exothermic reaction, energy is released. Therefore, the product has a lower energy than the reactants.

The literature value of the energy change is -92.0kJ/mol.^[1] Percentage error= (146.4785-92.0)/92.0= 59.2%. This %error is very large, which means the ΔE we have calculated is not accurate.

F₂

Information of F₂

A Gaussview image of an optimised F₂ molecule.

Image of F2 molecule

F₂ optimisaion

Molecule Name	F2
Calculation Method	RB3LYP
Basic Set	6-31G(d.p)
E(RB3LYP)	-199.49825220a.u.
RMS Gradient Norm	0.00000019a.u.
Point Group	D∞h
F-F Bond Length	1.40298Å

Item Table

 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=-1.347388D-13

The optimisation file is liked to log file link

Display Vibration Modes of F₂

A screenshot of the display vibrations window.

Charge Analysis of F₂

A screenshot of the charge analysis.

The charges on both F atom are 0 as they are non-polar and have the same electronegativity.

Molecular Orbitals of F2

This is an image of 1σg MO, it is MO bonding. The MO bonding is formed by 1s-1s orbital interaction. It is deep in energy and occupied.	This is an image of 2σg MO, it is MO bonding. The MO bonding is formed by 2s-2s orbital interaction. It is deep in energy and occupied.	This is an image of 3σg MO, it is MO bonding. The MO bonding is formed by 2pz-2pz orbital interaction. It is deep in energy and occupied.
This is an image of 1πu MO, it is MO bonding. The MO bonding is formed by 2px-2px orbital interaction. It is deep in energy and occupied.	This is an image of 2πg* MO, it is MO anti-bonding. The MO bonding is formed by 2px-2px orbital interaction. It is in the HOMO energy level region and occupied.

References

[1]Literature value: https://chem.libretexts.org/Core/Physical_and_Theoretical_Chemistry/Equilibria/Case_Studies/Haber_Process