Amonia

Key Information

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

Final energy E(RB3LYP): -56.55776873 a.u.

RMS gradient norm: 0.00000485 a.u.

Point group: C_3v

Geometric Information

Optimized N-H bond distance: 0.01798Å

Optimized H-N-H bond angle: 105.741°

Summary Table

Item Table

 Item                     Value        Threshold  Converged?
 Maximum Force            0.000007     0.000450      YES
 RMS     Force            0.000006     0.000300      YES
 Maximum Displacement     0.000112     0.001800      YES
 RMS     Displacement     0.000053     0.001200      YES

Jmol Dynamic Image

test molecule

Link to the final file of the optimisation/frequency

Vibration

3N-6 rule says: in general, a non-linear molecule with N atoms has 3N-6 normal modes of vibration. In our NH₃ molecule, there are 4 atoms, so there are 3x4-6=6 vibrational modes:

Vibrational Modes
Mode number	frequency (cm^-1)	Infrared
1	1090	145
2	1694	14
3	1694	14
4	3461	1
5	3589	0
6	3589	0

Modes are degenerate when they have the same energy. In this case, mode 2 and mode 3, which have the same frequency of 1694.20 cm^-1 thus the same energy, are degenerate. Both mode 5 and mode 6 have frequency of 3589.43 cm^-1 so they are degenerate as well.

Mode 1, 2 and 3 are "bending" vibrations, while mode 4, 5 and 6 are "stretching" vibrations. Mode 1 is known as the "umbrella" mode.

Symmetry and Intensity
Wavenumber(cm^-1)	Symmetry	Intensity(arbitrary units)
1090	A1	145
1694	E	14
1694	E	14
3461	A1	1
3589	E	0
3589	E	0

The Fourth mode (the mode with wavenumber 3461cm^-1) is the most highly symmetric.

Experimental Spectrum

According to the table in the last section, there are 4 different wavenumbers. Although the intensities for the last two wavenumbers are round to zero, they are not completely zero. So, there is still a peak for them. Therefore, it is expected that there are totally 4 peaks in an experimental spectrum of gaseous ammonia.

Charge Distribution

Charge on nitrogen atom: -1.125

Charge on hydrogen atom: +0.375

The charge on the nitrogen atom is expected to be negative while the charge on the hydrogen atom is expected to be positive because nitrogen is much more electronegative than hydrogen.

Nitrogen

Key Information

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

Final energy E(RB3LYP): -109.52412868 a.u.

RMS gradient norm: 0.00000060 a.u.

Point group: D_∞h

Geometric Information

Optimized N-N bond distance: 1.10550Å

Optimized N-N bond angle: 180°

Summary Table

Item Table

 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

Jmol Dynamic Image

test molecule

Link to the final file of the optimisation/frequency

Charge Distribution

Charge on both atoms: 0

Vibration

3N-5 rule says: in general, a linear molecule with N atoms has 3N-5 normal modes of vibration. In our N₂ molecule, there are 2 atoms, so there is 3x2-5=1 vibrational mode:

Vibrational Modes
Mode number	frequency (cm^-1)	Infrared
1	2457	0.0000

Mono-metallic TM Complex

DAMSUG:

N-N bond distance in this crystal structure: 1.128(4) Å and 1.134(5) Å

Link to more information: [Link to CSD Entry: DAMSUG]

Optimised N-N distance: 1.10550Å

N-N bond distance in DAMSUG crystal structure is longer than the optimised N-N distance. Explaination is that: in DAMSUG crystal structure, one of the nitrogen in is forming four bonds, while in the gaseous nitrogen structure, there is only a triple bond. When one of the nitrogen is forming four bonds, it becomes partially positive because its lone pair is shared with the other atom (in this case, the W atom). The electrons in the triple bond would delocalised to stabilise the partially positive nitrogen atom, forming a resonant form with double bond between two nitrogen atoms. Double bond is longer than the triple bond.

Haber-Bosch Process

N₂ + 3H₂ → 2NH₃

E(NH₃)= -55.55776862 a.u.

2*E(NH₃)= 2*(-55.55776862)= -111.1155372 a.u.

E(N₂)= -109.52412868 a.u.

E(H₂)= -1.17853936 a.u.

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

ΔE=2*E(NH₃)-[E(N₂)+3*E(H₂)]= -111.1155372-[(-109.52412868)+(-3.53561808)]= +1.94420956 a.u.

Unit conversion: ΔE=+1.94420956*2625.5= +5104.5222 kJ/mol

Hydrogen

Key Information

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

Final energy E(RB3LYP): -1.17853936 a.u.

RMS gradient norm: 0.00000017 a.u.

Point group: D_∞h

Geometric Information

Optimized H-H bond distance: 0.74279Å

Optimized H-H bond angle: 180°

Summary Table

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

Jmol Dynamic Image

test molecule

Link to the final file of the optimisation/frequency

Charge Distribution

Charge on both atoms: 0

Vibration

3N-5 rule says: in general, a linear molecule with N atoms has 3N-5 normal modes of vibration. In our H₂ molecule, there are 2 atoms, so there is 3x2-5=1 vibrational mode:

Vibrational Modes
Mode number	frequency (cm^-1)	Infrared
1	4466	0.0000

Hydrogen Sulfide

Key Information

Calculation method: RB3LYP

Basis set: 6-31G(d.p)

Final energy E(RB3LYP): -399.39162414 a.u.

RMS gradient norm: 0.00012068 a.u.

Point group: C_2v

Geometric Information

Optimized S-H bond distance: 1.34737Å

Optimized H-S-H bond angle: 92.681°

Summary Table

Item Table

 Item                     Value        Threshold  Converged?
 Maximum Force            0.000175     0.000450      YES
 RMS     Force            0.000145     0.000300      YES
 Maximum Displacement     0.000386     0.001800      YES
 RMS     Displacement     0.000386     0.001200      YES

Jmol Dynamic Image

test molecule

Link to the final file of the optimisation/frequency

Charge Distribution

Charge on sulfur atom: -0.312

Charge on hydrogen atom: +0.156

The charge on the sulfur atom is expected to be negative while the charge on the hydrogen atom is expected to be positive because sulfur is more electronegative than hydrogen.

Vibration

3N-6 rule says: in general, a non-linear molecule with N atoms has 3N-6 normal modes of vibration. In our SH₂ molecule, there are 3 atoms, so there are 3x3-6=3 vibrational modes:

Vibrational Modes
Mode number	frequency (cm^-1)	Infrared
1	1224	5
2	2692	7
3	2712	9

There is no degenerate level because all three modes have different frequencies thus different energies.

Mode 1 is "bending" vibration, while mode 2 and 3 are "stretching" vibrations.

Symmetry and Intensity
Wavenumber(cm^-1)	Symmetry	Intensity(arbitrary units)
1224	A1	5
2692	A1	7
2712	B2	9

Molecular Orbitals

MO 2:

What AOs contribute to this MO?

s orbitals

Is that MO occupied or unoccupied?

Occupied

Bonding or Anti-bonding or Mixture?

Bonding orbital

What is the enrgy of this MO?

-7.95115 a.u.

Is this MO deep in energy, in the HOMO/LUMO region or High in energy?

Deep in energy

MO 6:

What AOs contribute to this MO?

s orbitals

Is that MO occupied or unoccupied?

Occupied

Bonding or Anti-bonding or Mixture?

Bonding orbital

What is the enrgy of this MO?

-0.74654 a.u.

Is this MO deep in energy, in the HOMO/LUMO region or High in energy?

In the HOMO/LUMO region

MO 7:

What AOs contribute to this MO?

s and p orbitals

Is that MO occupied or unoccupied?

Occupied

Bonding or Anti-bonding or Mixture?

Mixture

What is the enrgy of this MO?

-0.0.44963 a.u.

Is this MO deep in energy, in the HOMO/LUMO region or High in energy?

In the HOMO/LUMO region

MO 10:

What AOs contribute to this MO?

p orbitals

Is that MO occupied or unoccupied?

Unoccupied

Bonding or Anti-bonding or Mixture?

Anti-bonding orbital

What is the enrgy of this MO?

+0.02126 a.u.

Is this MO deep in energy, in the HOMO/LUMO region or High in energy?

In the HOMO/LUMO region

MO 11:

What AOs contribute to this MO?

s and p orbitals

Is that MO occupied or unoccupied?

Unoccupied

Bonding or Anti-bonding or Mixture?

Mixture

What is the enrgy of this MO?

+0.05780 a.u.

Is this MO deep in energy, in the HOMO/LUMO region or High in energy?

In the HOMO/LUMO region

Marking

Note: All grades and comments are provisional and subjecct to change until your grades are officially returned via blackboard. Please do not contact anyone about anything to do with the marking of this lab until you have recieved your grade from blackboard.

Wiki structure and presentation 1/1

Is your wiki page clear and easy to follow, with consistent formatting?

YES

Do you effectively use tables, figures and subheadings to communicate your work?

YES

NH3 1/1

Have you completed the calculation and given a link to the file?

YES

Have you included summary and item tables in your wiki?

YES

Have you included a 3d jmol file or an image of the finished structure?

YES

Have you included the bond lengths and angles asked for?

YES

Have you included the “display vibrations” table?

YES

Have you added a table to your wiki listing the wavenumber and intensity of each vibration?

YES

Did you do the optional extra of adding images of the vibrations?

YES

Have you included answers to the questions about vibrations and charges in the lab script?

YES, however due to their low intensities stretching modes are not observed in experimental spectra of gaseous NH3 which reduces the number of bands to 2.

N2 and H2 0/0.5

Have you completed the calculations and included all relevant information? (summary, item table, structural information, jmol image, vibrations and charges)

YES, you could have explained that the charges are 0 as the electronegativities are equal.

You stated a bond angle for H2 and N2. To define a bond angle a minimum of 3 atoms is needed!

Crystal structure comparison 0.5/0.5

Have you included a link to a structure from the CCDC that includes a coordinated N2 or H2 molecule?

YES

Have you compared your optimised bond distance to the crystal structure bond distance?

YES

Haber-Bosch reaction energy calculation 0/1

Have you correctly calculated the energies asked for? ΔE=2*E(NH3)-[E(N2)+3*E(H2)]

No - you extracted the correct values for the total energies of the ducts and products. However your final calculation of the reaction energy is incorrect.

Have you reported your answers to the correct number of decimal places?

NO - Energies should be reported with 1 decimal place if they are given in kJ/mol.

Do your energies have the correct +/- sign?

NO

Have you answered the question, Identify which is more stable the gaseous reactants or the ammonia product?

NO

Your choice of small molecule 3.5/5

Have you completed the calculation and included all relevant information?

YES

Have you added information about MOs and charges on atoms?

You have done a good job of presenting this information, well done! You could have included more precise information on the Mos involved in building the MOs. You identified their shape correctly correctly but information on their principal quantum numbers are missing. MO2 is a non-bonding MO since the s orbital on S does not interact with any Mos on the Hs. MO7 is not a mixture of bonding and anti bonding orbitals. The node does not make it anti-bonding at all. It is a bonding orbital.

Independence 0/1

If you have finished everything else and have spare time in the lab you could: Check one of your results against the literature, or Do an extra calculation on another small molecule, or Do some deeper analysis on your results so far

NO - no independent work was identified