Johnslara

Comments

You've done a great job overall especially with the formatting and communication—everything is clear and well-presented. If you have any queries or want more detailed feedback on your computational lab, please contact Prof. Hunt. Well done!

NH₃ molecule

Calculation Data

Name of submitted log file	LJohns_NH3_optf_pop_8_04_2025.log
Method	RB3LYP
Basis set	6-31G(d,p)
Final energy	-56.557769
RMS gradient	0.000000
Point group	C3v

Convergence

Below is the table confirming displacements and forces have converged.

         Item               Value     Threshold  Converged?
 Maximum Force            0.000000     0.000015     YES
 RMS     Force            0.000000     0.000010     YES
 Maximum Displacement     0.000003     0.000060     YES
 RMS     Displacement     0.000001     0.000040     YES

This confirms a minimum has been reached and the optimisation was complete.

 Low frequencies ---   -5.6864   -3.6131   -3.6124    0.0017    0.0048    0.0162
 Low frequencies --- 1089.3674 1693.9284 1693.9284

Optimised molecule

Logfile: Media:LJohns_NH3_optf_pop_8_04_2025.log

Static image:

Jmol rotateable molecule:

Optimised NH3 molecule

Geometric parameters

Optimised bond distance and angle for NH₃:

Coord	Value
r(N-H)	1.02Â
θ	106°

Vibrations

Table of vibrations:

Mode	1	2	3	4	5	6
Wavenumber (cm-1)	1089	1694	1694	3461	3590	3590
Symmetry	A1	E	E	A1	E	E
Intensity (arbitary units)	145	14	14	1	0	0

IR spectrum obtained from GaussView:

The following questions were not required, however have been answered for understanding purposes.

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

N is the number of atoms in the NH₃ molecule, which is 4. This means that 3*(4)-6=6 modes are expected. This is indeed what was found through the Gaussian optimisation.

• How many bands do we see in the computed spectrum of gaseous ammonia?
  

2 bands are observed in this spectrum, which makes sense as all vibrations are calculated.

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

Modes 2 and 3, at 1694 cm^-1, and modes 5 and 6, at 3590 cm^-1, are degenerate.

• Some modes have essentially no intensity, which ones?
  

Modes 4, 5, and 6 have basically no intensity. These are the A₁ 3461 cm^-1 and E 3590 cm^-1 vibrations, which indicates that they do not involve a dipole moment change.

• What is the selection rule for IR vibrations?
  

A change in dipole moment is required to absorb IR radiation, hence producing a peak in the spectrum.

• Why are there fewer modes than we expect from the 3N-6 rule?

Degenerate modes appear as a single peak as they have the same energy (so wavenumber). This reduces the modes from 6 to 4 different ones. 2 of the vibrations also have little to no dipole moment change, hence removing 2 more modes from the spectrum and ending up with 2 peaks.

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

Stretch vibrations are higher energy vibrations, so modes 4, 5, and 6. Bending vibrations are those of lower energy, hence modes 1, 2, and 3. This was checked using the animation feature on GaussView.

• Which mode is highly symmetric?
  

Mode 4 is highly symmetric. This is the 3-way stretching vibration of the H nuclei away from the central N atom.

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

The umbrella mode is mode 1, as it looks like one.

• Why is the umbrella mode so intense?
  

Because it causes a large change in the dipole moment.

Charges

Image of NBO charges colour coded red for negative and green for positive. The charge range is ±1.125e.

Table of NH₃ charges:

Atom	Charge
N	-1.13
H	+0.38

Molecular Orbitals

These were included to set up the formatting for the project molecule.

Actual 2a1 MO	Predicted LCAO MO

N₂F₂ molecule

Calculation Data

Name of submitted log file	LJOHNS_N2F2_OPTF_POP_8_04_2025.LOG
Method	RB3LYP
Basis set	6-31G(d,p)
Final energy	-309.012413
RMS gradient	0.000000
Point group	C2v

Convergence

Below is the table confirming displacements and forces have converged.

         Item               Value     Threshold  Converged?
 Maximum Force            0.000001     0.000015     YES
 RMS     Force            0.000000     0.000010     YES
 Maximum Displacement     0.000001     0.000060     YES
 RMS     Displacement     0.000001     0.000040     YES

This confirms a minimum has been reached and the optimisation was complete.

 Low frequencies ---   -0.0019    0.0002    0.0008    3.2225    4.3532    5.1001
 Low frequencies ---  347.8772  561.2472  771.6105

Optimised molecule

Logfile: Media:LJOHNS_N2F2_OPTF_POP_8_04_2025.LOG

Static image:

Jmol rotateable molecule:

Optimised N2F2 molecule

• Why does the static image from the log file show the molecule without bonds between the F and N atoms?

GaussView only draws bonds depending on the distance between the nuclei in the molecule. The optimised molecule appears without drawn N-F bonds as the optimal bond distance calculated is greater than the pre-determined value GuassView stops drawing bonds at. They exist however are just not drawn by the software.

Geometric parameters

Optimised bond distance and angle for N₂F₂:

Coord	Value
r(N-F)	1.39Â
r(N=N)	1.22Â
θ(F-N=N)	114°
θ(F-N=N-F)	0°

Vibrations

Table of vibrations:

Mode	1	2	3	4	5	6
Wavenumber (cm-1)	348	561	772	949	987	1637
Symmetry	A1	A2	B2	A1	B2	A1
Intensity (arbitary units)	1	0	75	75	81	21

IR spectrum obtained from GaussView:

• How many vibrations are expected from the 3N-6 rule?

N is the number of atoms in the N₂F₂ molecule, which is 4. This means that 3*(4)-6=6 modes are expected. This is indeed what was found through the Gaussian optimisation.

• Why are there only 4 peaks in the IR spectrum?

Modes 1, at 348 cm^-1, and 2, at 561 cm^-1, both have a negligible intensity, hence will not be observed in the IR spectrum. These vibrations cause little to no change in the dipole moment of the molecule. A change in dipole moment is required to absorb IR radiation, hence producing a peak in the spectrum. This leaves 4 observable peaks of modes 3, 4, 5, and 6.

• Which vibration is the asymmetric N-F stretch?

Mode 3, at 772 cm^-1, is the asymmetric N-F stretch vibration. It should be noted that Mode 5, at 987 cm^-1, also involves asymmetric stretching of the N-F bonds due to the N=N bending vibration, however the N=N bending vibration is the relatively dominant vibration of this mode.

• What is the nature of the highest energy vibration?

The highest energy vibration mode 6, at 1637 cm^-1, is the N=N bond stretching vibration.

Charges

Image of NBO charges colour coded red for negative and green for positive. The charge range is ±0.215e.

Table of N₂F₂ charges:

Atom	Charge
N	+0.22
F	-0.22

Molecular Orbitals

• What are the core orbital MOs?

MOs 1-4 are the core orbital MOs as they are not involved in the bonding of the molecule. This is shown by the fact that they have no electron density overlapping with the bonds, they are just held tightly around their individual nuclei.

Actual MO 9	Predicted LCAO MO 9