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The Haber Process

N2 + 3H2 -> 2NH3

The combination of nitrogen a gas that is in surplus in our atmosphere and hydrogen results in the production of ammonia, this vital process allows for the industrial production of fertilizers.

NH3 Optimization

Ammonia
Optimisation Results
Calculation method RB3LYP
Basis set 6-31G(d,p)
Final Energy (au) -56.55776873
RMS Gradient 0.00000485
Point Group C3V
N-H Bond Length 1.01798
H-N-H Bond Angle 105.741° 


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=-5.986273D-10
 Optimization completed.

Media:VIRGINIA_NH3_OPTIMIZATION.LOG ‎

Vibrations

  • From the 3N-6 rule 6 modes are expected
  • Degenerate modes: 2&3, 5&6 as both pairs of modes have the same energy
  • Bending vibrations: 1,2,3
  • Bond stretch vibrations: 4,5,6
  • 4 is a highly symmetric mode as all of the atoms move in the same direction
  • The "umbrella" mode is mode 1
  • You would expect to see 3 bands in the spectrum as the symmetric stretch does not result in a change in dipole hence would not show a band. However, only 2 can clearly be

seen in the spectra as the others that are degenerate (5&6) have very low intensities.

Charges

A negative charge was expected on the N atom and a more positive on the H atoms because Nitrogen is more electronegative than hydrogen hence it withdraws electron density towards itself.


N2 Optimization

Nitrogen Molecule
Optimisation Results
Calculation method RB3LYP
Basis set 6-31G(d,p)
Final Energy (au) -109.52412868
RMS Gradient 0.00000060
Point Group DinfH
N-H Bond Length 1.10550 
          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=-3.400996D-13
 Optimization completed.


Media:VIRGINIA_N2_OPTIMIZATION.LOG ‎

Vibrations

  • No band can be seen in the IR spectrum as the bond is not IR-active due to the molecule not having a dipole moment

Charges

  • No charge on N atoms
  • Identical atoms hence both have the same electronegativity
  • No dipole moment

H2 Optimization

Hydrogen Molecule
Optimisation Results
Calculation method RB3LYP
Basis set 6-31G(d,p)
Final Energy (au) -1.17853936
RMS Gradient 0.00000017
Point Group DinfH
H-H Bond Length 0.74279 


          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.

Vibrations

  • No band can be seen in the IR spectrum as the bond is not IR-active due to the molecule not having a dipole moment

Charges

  • No charge on H atoms
  • Identical atoms hence both have the same electronegativity
  • No dipole moment


Media:VIRGINIA_H2_OPTIMIZATION.LOG ‎

Energy Calculation

Energy Calculation
E(NH3)= -56.55776873
2*E(NH3)= -113.1155375
E(N2)= -109.52412868
E(H2)= -1.17853936
3*E(H2) -3.53561808
ΔE=2*E(NH3)-[E(N2)+3*E(H2)]= -0.05579074

ΔE = -146.478599028 kJmol-1

The Ammonia product is more stable than the gaseous reactants, this is because the change in energy for the conversion of the gases into ammonia is quite negative, hence a lot of energy is gained from the conversion, so the product is energetically more favourable.

Hydrogen Sulfide

Hydrogen Sulfide Molecule

Optimization

Optimisation Results
Calculation method RB3LYP
Basis set 6-31G(d,p)
Final Energy (au) -339.39162414
RMS Gradient 0.00012068
Point Group C2v
S-H Bond Length 1.34737
H-S-H Bond Angle 92.681° 


           Item               Value     Threshold  Converged?
 Maximum Force            0.000175     0.000450     YES
 RMS     Force            0.000145     0.000300     YES
 Maximum Displacement     0.000472     0.001800     YES
 RMS     Displacement     0.000386     0.001200     YES
 Predicted change in Energy=-1.208488D-07


Vibrations


  • From the 3N-6 rule 3 modes are expected
  • Degenerate modes: None
  • Bending vibrations: 1
  • Bond stretch vibrations: 2&3
  • 2 is a highly symmetric mode as all of the atoms move in the same direction
  • You would expect to see 2 bands in the spectrum as the symmetric stretch (Mode 2) does not result in a change in dipole hence would not show a band

Charges

A negative charge was expected on the S atom and a more positive on the H atoms because Sulfur is more electronegative than hydrogen hence it withdraws electron density towards itself.

Molecular Orbitals

1s

  • Energy : -88.88741 au
  • 1s Sulfur atom orbital
  • Very deep in energy compared to valence electrons
  • Cannot be seen as this orbital is too low in energy to be involved in chemical bonding
  • Non Bonding

2s

  • Energy: -7.9515
  • 2s Orbital of sulfur
  • Still quite low in energy and is not involved in chemical bonding
  • Non Bonding

2Py

  • Energy: -5.91588
  • 2py orbital of S
  • Non Bonding

2Pz

  • Energy: -5.912688
  • 2pz orbital of S
  • Non Bonding

2Px

  • Energy: -5.90552
  • 2px orbital of S
  • Non Bonding

3s-1s

  • Energy: -0.74654
  • 3s orbital of S combined with 1s orbital of H
  • Bonding

3py-1s

  • Energy: -0.44963
  • 3py orbital of S combined with 1s orbital of H
  • Bonding

3pz-1s

  • Energy: -0.36725
  • 3pz orbital of S combined with 1s orbital of H
  • Bonding

Highest Occupied Molecular Orbital

  • Energy: -0.26181
  • HOMO
  • Non Bonding
  • Contains Lone Pair from 3px orbital of the S atom

Lowest Unoccupied Molecular orbital

  • Energy: -0.02126
  • LUMO
  • 3py AO of S and 1s AO of H atom
  • Antibonding
  • Unoccuppied




Media:VIRGINIA_FINAL_H2S_OPTIMIZATION.LOG ‎


Borane

Borane Molecule

Optimization

Optimisation Results
Calculation method RB3LYP
Basis set 6-31G(d,p)
Final Energy (au) -26.61532364
RMS Gradient 0.00000211
Point Group D3h
B-H Bond Length 1.19232
H-B-H Bond Angle 120° 


  Item               Value     Threshold  Converged?
 Maximum Force            0.000004     0.000450     YES
 RMS     Force            0.000003     0.000300     YES
 Maximum Displacement     0.000017     0.001800     YES
 RMS     Displacement     0.000011     0.001200     YES
 Predicted change in Energy=-1.053682D-10
 Optimization completed.

Vibrations

  • From the 3N-6 rule 6 modes are expected
  • Degenerate modes: 2&3, 5&6 as both pairs of modes have the same energy
  • Bending vibrations: 1,2,3
  • Bond stretch vibrations: 4,5,6
  • 4 is a highly symmetric mode as all of the atoms move in the same direction
  • The "umbrella" mode is mode 1
  • You would expect to see 3 bands in the spectrum due to the degenerate modes and because the symmetric stretch does not result in a change in dipole hence would not show a band. This can be seen in the IR spectrum.

Charges

  • Charge on Boron = 0.297
  • Charge on Hydrogen atoms= -0.099

This is expected as hydrogen is more electronegative than Boron, this can be seen from their electronegativity literature values.

Literature Values:

Electonegativity of Boron (Pauling units): 2.04 [1]

Electonegativity of Hydrogen (Pauling units): 2.20 [2]


Media:VIRGINIA_FINAL_BH3_OPTIMIZATION.LOG

  1. ↑ https://www.webelements.com/boron/electronegativity.html
  2. ↑ https://www.webelements.com/hydrogen/electronegativity.html
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