Rep:Mod:01386123

NH3 Molecule

Molecule Name : Ammonia

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

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

NH molecule

The optimisation file is linked here

  NH₃ Display Vibrations

Questions

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

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

  2,3 and 5,6

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

  Bending: 1, 2, 3 & Stretching: 4, 5, 6

4. Which mode is highly symmetric?

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

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

  2 Peaks will be seen in the IR spectra of gaseous ammonia because
  for a peak to occur there must be a change in the dipole moment.
  Modes 4, 5 and 6 do not have a change in dipole so will not be seen
  and 2&3 are degenerate will appear as a singular peak, therefore
  there will be a total of 2 peaks.

Atomic Charges - N has a charge of -1.125 - H has a charge of +0.375

This is what is expected as nitrogen is more electronegative than hydrogen so has a greater electron density.

N2 Molecule

Molecule Name : Nitrogen

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

N-N Bond Angle : 180.000


         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

NH molecule

The optimisation file is linked here

N₂ Display Vibrations

Questions

1. How many modes do you expect from the 3N-5 rule?

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

N/A

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

  Bending: N/A Stretching: 1

4. Which mode is highly symmetric?

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

N/A

6. How many bands would you expect to see in an experimental spectrum of nitrogen?

  No bands will be seen in the experimental spectra because there
  will be no change in the dipole moment of the molecule so it is not
  IR active hence no bands will be seen.

Atomic Charges - Both N atoms have a charge of 0.0

H2 Molecule

Molecule Name : Hydrogen

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

H-H Bond Angle : 180.000


         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

NH molecule

The optimisation file is linked here

  H₂ Display Vibrations

Questions

1. How many modes do you expect from the 3N-5 rule?

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

N/A

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

  Bending: N/A Stretching: 1

4. Which mode is highly symmetric?

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

N/A

6. How many bands would you expect to see in an experimental spectrum of hydrogen?

  No bands will be seen in the experimental spectra because there
  will be no change in the dipole moment of the molecule so it is not
  IR active hence no bands will be seen.

Atomic Charges - Both H atoms have a charge of 0.0

Reaction Energies

E(NH3)= -56.55776873   a.u.
2*E(NH3)= -113.1155375 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)]= -0.0557907 a.u.

-0.0557907 a.u. x 2625.5 = -146.4784829 kJ/mol

Explanation This is an exothermic reaction therefore, the reactants are at a higher energy than the product. As a result, the product are more stable as they are lower in energy.

Literature The value in the literature is -92.2^[1] which is higher than the value that has been calculated above. This difference could be a cause of poor optimization and this is a theoretical value.

Project Molecule - HCl

Molecule Name : Hydrogen Chloride

Calculation Method : RB3LYP

Basis Set : 6-31G(d,p)

Final Energy E(RB3LYP) : -460.80077875 a.u.

RMS Gradient : 0.00005211 a.u.

Point Group : C*V

H-Cl Bond Distance : 1.28599

H-Cl Bond Angle : 180.000


         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

HCl molecule

The optimisation file is linked here

  HCl Display Vibrations

Questions

1. How many modes do you expect from the 3N-5 rule?

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

N/A

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

  Bending: N/A Stretching: 1

4. Which mode is highly symmetric?

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

N/A

6. How many bands would you expect to see in an experimental spectrum of hydrogen chloride?

  1 band will be seen in the experimental spectrum for HCl because
  there is one asymmetric stretch that can be seen. Additionally, the
  difference in electronegativities means that there is a change in
  dipole moment hence this molecule is microwave active.

Atomic Charges - H has a charge of +0.284 - Cl has a charge of -0.284

This is expected as Cl has an electronegativity of 3.16 whilst H has an electronegativity of 2.20. Therefore, there will be a greater distribution of electron density around chlorine thus a negative charge is seen on Cl.

Molecular Orbitals

This is a molecular orbital that has an energy level that is just below that of the HOMO_LUMO region, this means that this is the HOMO. This is going to have a large influence on the bond character as these are valence electrons. It is showing the p orbitals on Cl and is spread across the entirety of the bond.

This molecular orbital is depicting the atomic orbital of a 2p orbital, distinguished by the node. This p orbital is orthogonal to the bond. This is quite deep in energy and is occupied by 2 electrons. It is unlikely that this orbital will contribute to bonding as it is not in the right alignment to overlap with molecular orbitals on the H atom.

Similarly, to the molecular orbital image above this is representing a 2s orbital of chlorine.It is not involved in bonding as it is not interacting with any other orbitals. This is deeper in energy than the p orbitals as it is closer to the nucleus, therefore it is further away from the HOMO-LUMO range.

This image is an atomic orbital and another orientation of the second image. It shows the 2p orbital of chlorine, recognized by the distinctive node. As seen above this orbital is not interacting with anything else so is not impacting the bonding. This is deeper in energy as it is more negative and is also degenerate, has the same energy level as image 2.

This image is depicting a molecular orbital between two s orbitals from H and Cl. This MO is a bonding orbital and it is high in energy as it approaches the HOMO-LUMO range and is occupied by two electrons. As this is high in energy it is likely to have a large effect on bonding.

References

[1]Periodicity, Quantitative Equilibrium and Functional Group Chemistry Nelson Advanced Science Series