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Rep:Mod:ds3817

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NH3

Bond Length

  • 1.01798 Å

Bond Angle

  • 105.741 °

"Item" table of converged forces and distances for Ammonia.

         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=-3.383793D-13
 Optimization completed.
    -- Stationary point found.

Key information of Ammonia.

Summary
Molecule NH3
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 0
Spin Singlet
E(RB3LYP) -56.55776873 a.u.
RMS Gradient Norm 0.00000485 a.u.
Imaginary Freq 0
Dipole Moment 1.8466 Debye
Point Group C3V

Questions regarding vibration of Ammonia.

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

  • 6.

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

  • 2 and 3; 5 and 6.

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

  • 1-3 is bending; 4-6 is stretching.

Which mode is highly symmetric?

  • Highly Symmetric Bending mode: 1;
  • Highly Symmetric Stretching mode: 4.

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

  • 1

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

  • 2 (4, 5, and 6 are too low in intensity to be seen).

A Gaussview image of an optimised Ammonia molecule.

File:NH3 ds3817.LOG

NH3 molecule

Screenshot of the "Display Vibrations" window.

  • For a spectrum to be seen, a dipole must exist within the molecule. The larger the dipole, the higher the frequency.

Diagram of charge distribution (NBO as the type).

N2

Bond Length

  • 1.105550 Å

Bond Angle

  • 180 °

Vibration Frequency

  • 2457.33 cm-1
  • Only one mode as this is a diatomic.

"Item" table of converged forces and distances for Nitrogen.

         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=-3.383793D-13
 Optimization completed.
    -- Stationary point found.

A Gaussview image of an optimised Nitrogen molecule.

File:N2 new ds3817.LOG

N2 molecule

Key information of Nitrogen.

Summary
Molecule N2
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 0
Spin Singlet
E(RB3LYP) -109.52412868 a.u.
RMS Gradient Norm 0.00000060 a.u.
Imaginary Freq 0
Dipole Moment 0.0000 Debye
Point Group D∞h

H2

Bond Length

  • 0.74279 Å

Bond Angle

  • 180 °

Vibration Frequency

  • 4465.60 cm-1
  • Only one mode as this is a diatomic.

"Item" table of converged forces and distances for Hydrogen.

         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=-1.167770D-13
 Optimization completed.
    -- Stationary point found.

A Gaussview image of an optimised Hydrogen molecule.

File:H2 DS3817.LOG

H2 molecule

Key information of Hydrogen.

Summary
Molecule H2
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 0
Spin Singlet
E(RB3LYP) -1.17853936 a.u.
RMS Gradient Norm 0.00000017 a.u.
Imaginary Freq 0
Dipole Moment 0.0000 Debye
Point Group D∞h

Calculations.

N2 + 3H2 → 2NH3

E(NH3)

  • -56.55776873 a.u.

2*E(NH3)

  • -113.1155375 a.u.

E(N2)

  • -109.5241287 a.u.

E(H2)

  • -1.17853936 a.u.

3*E(H2)

  • -3.53561808 a.u.

ΔE=2*E(NH3)-[E(N2)+3*E(H2)]

  • (-113.1155375) - [(-109.5241287) + (-3.53561808)] = -0.0557907 a.u.
  • -0.0557907 × 2625.5 = -146.48 KJmol-1 (2.d.p)
  • Product (ammonia) is thermodynamically more stable than reactants (hydrogen and nitrogen) because energy is released from the reaction (Negative ΔH), meaning the bonds broken in the reactants are weaker (less stable) than the bonds formed in the products.
  • Literature Value: 92.38 KJmol-1 (2.d.p)[1]
  • The is a difference between the literature value and the value obtained from GaussView.

PH5

Bond Length

  • Axial P–H bond: 1.43316 Å
  • Equatorial P–H bond: 1.48687 Å

Bond Angle

  • 90 °
  • 120 °

"Item" table of converged forces and distances for PH5.

         Item               Value     Threshold  Converged?
 Maximum Force            0.000009     0.000450     YES
 RMS     Force            0.000004     0.000300     YES
 Maximum Displacement     0.000022     0.001800     YES
 RMS     Displacement     0.000009     0.001200     YES
 Predicted change in Energy=-6.688010D-10
 Optimization completed.
    -- Stationary point found.

Key information of PH5.

Summary
Molecule PH5
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 0
Spin Singlet
E(RB3LYP) -344.25491049 a.u.
RMS Gradient Norm 0.00000472 a.u.
Imaginary Freq 0
Dipole Moment 0.0000 Debye
Point Group D3h

Questions regarding vibration of PH5.

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

  • 12.

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

  • 1 and 2; 4 and 5; 6 and 7; 11 and 12.

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

  • 1-7 is bending; 8-12 is stretching.

Which mode is highly symmetric?

  • Highly Symmetric Stretching mode: 8 and 10.

How many bands would you expect to see in an experimental spectrum of gaseous PH5?

  • 5.

A Gaussview image of an optimised PH5.

File:PH5 DS3817.LOG

PH5 molecule

Screenshot of the "Display Vibrations" window.

Diagram of charge distribution (NBO as the type).

Snapshot of 5 MOs.

Second MO of PH5

What AOs contribute to the MO?
  • Only AO from Phosphorus contribute to the MO.
  • Strong 2s orbital contribution from the phosphorus AO only. Little to no contributions from 1s AO of hydrogen because the energy differences between the 1s orbital of hydrogen and 2s orbital of phosphorus is too large.
Is the MO bonding, antibonding or a mixture.
  • MO is non-bonding.
Is the MO deep in energy, in the HOMO/LUMO region or high in energy?
  • MO is deep in energy.
Is the MO occupied or unoccupied? What effect will your MOs have on bonding?
  • MO is occupied.
  • MOs have little to no effect on bonding.

Fifth MO of PH5

What AOs contribute to the MO?
  • Only AO from Phosphorus contribute to the MO.
  • Strong 2pz orbital contribution from the phosphorus AO only. Little to no contributions from 1s AO of hydrogen because the energy differences between the 1s orbital of hydrogen and 2pz orbital of phosphorus is too large.
Is the MO bonding, antibonding or a mixture.
  • MO is non-bonding.
Is the MO deep in energy, in the HOMO/LUMO region or high in energy?
  • MO is deep in energy.
Is the MO occupied or unoccupied? What effect will your MOs have on bonding?
  • MO is occupied.
  • MOs have little to no effect on bonding.

Sixth MO of PH5

What AOs contribute to the MO?
  • Both AOs from Phosphorus and Hydrogen contribute to the MO.
  • Mainly 3s and 2s AO of Phosphorus and 1s AO of Hydrogen and the final MO is formed by the partial positive contribution of the AOs.
Is the MO bondng, antibonding or a mixture.
  • MO is bonding.
Is the MO deep in energy, in the HOMO/LUMO region or high in energy?
  • MO low in energy.
Is the MO occupied or unoccupied? What effect will your MOs have on bonding?
  • MO is occupied.
  • MOs are bonding, which implies extra stability, so molecule is not reactive.

Ninth MO of PH5

What AOs contribute to the MO?
  • Both AOs from Phosphorus and Hydrogen contribute to the MO.
  • Strong 3pz AOs and partial 2pz of Phosphorus AOs and 1s AOs of the axial hydrogen due to the partial positive contribution of the AOs.
Is the MO bondng, antibonding or a mixture.
  • MO is bonding.
Is the MO deep in energy, in the HOMO/LUMO region or high in energy?
  • MO low in energy.
Is the MO occupied or unoccupied? What effect will your MOs have on bonding?
  • MO is occupied.
  • MOs infer extra stability, so molecule is not reactive.

Tenth MO of PH5

What AOs contribute to the MO?
  • Both AOs from Phosphorus and Hydrogen contribute to the MO.
  • Mainly 5dz2 orbital and partially 4s orbital of Phosphorus and positive contribution from the 2s AOs of the axial Hydrogens and negative contribution from 2s AO of the equatorial Hydrogens.
  • Final MO is formed from the partial contribution of all AOs.
Is the MO bondng, antibonding or a mixture.
  • MO is bonding.
Is the MO deep in energy, in the HOMO/LUMO region or high in energy?
  • MO in HOMO region.
Is the MO occupied or unoccupied? What effect will your MOs have on bonding?
  • MO is occupied.
  • MOs are bonding, which implies extra stability, so molecule is not reactive.

Extra Small molecule - Chlorine.

Bond Length

  • 2.04174 Å

Bond Angle

  • 180 °

Vibration Frequency

  • 520.32 cm-1

"Item" table of converged forces and distances for Chlorine.

         Item               Value     Threshold  Converged?
 Maximum Force            0.000043     0.000450     YES
 RMS     Force            0.000043     0.000300     YES
 Maximum Displacement     0.000121     0.001800     YES
 RMS     Displacement     0.000172     0.001200     YES
 Predicted change in Energy=-4.911243D-09
 Optimization completed.
    -- Stationary point found.

Key information of Chlorine.

Summary
Molecule Cl2
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 0
Spin Singlet
E(RB3LYP) -920.34987886 a.u.
RMS Gradient Norm 0.00002510 a.u.
Imaginary Freq 0
Dipole Moment 0.0000 Debye
Point Group C3V

A Gaussview image of an optimised Chlorine molecule.

File:CL2 DS3817.LOG

Cl2 molecule

References

  1. ↑ https://www.ohio.edu/mechanical/thermo/property_tables/combustion/Enth_Formation.html
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