Do261717991799

NH₃ Molecule

Summary Data

Calculation Method	RB3LYP
Basis Set	6-31G(d,p)
Final energy(au)	-56.55776873 a.u
RMS Gradient	0.00000485
Point Group	C3v
N-H Bond Length	1.3 Å
H-N-H bond angle	109.471°

Optimisation Results

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

   

NH3 Molecule

Here is a link to my NH3 file: here

Vibrations

A table showing the vibration frequencies for NH3.

Clicking on the image will take you to the uploaded file page for the image.

- The number of nodes for a non-linear molecule =3N-6, so for NH3, we expect to see 6 nodes

- Modes 2 and 3 are degenerate as well as modes 5 and 6

- Modes 4,5 and 6 are bond stretching and modes 1, 2 and 3 are bond bending vibrations

- Mode 4 is highly symmetric

- Mode 1 is the umbrella mode

- 4 bands would be seen in the experimental spectrum of gaseous NH3

Atomic Charges

- The charge on the Nitrogen atom is -1.125 and on each Hydrogen atom +0.375

- Nitrogen is more electronegative than hydrogen so it is expected that nitrogen has a negative charge

N₂ Molecule

Summary Data

Calculation Method	RB3LYP
Basis Set	6-31G(d,p)
Final energy(au)	-109.52412868 a.u
RMS Gradient	0.00000060 a.u
Point Group	D*H
N≡N Bond Length	1.10550 Å

Optimisation results

 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

As seen by the table above, all items did converge.

Vibrations

A table showing the vibration frequency for N2.

- Clicking on the image will take you to the uploaded file page for the image.

- As seen, the molecule is infrared inactive due to there being no permanent dipole in the molecule.

H₂ Molecule

Summary Data

Calculation Method	RB3LYP
Basis Set	6-31G(d,p)
Final energy(au)	-1.17853936 a.u
RMS Gradient	0.00000017 a.u
Point Group	D*H
H-H Bond Length	0.74279 Å

Optimisation results

 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

As seen by the table above, all items did converge.

Vibrations

A table showing the vibration frequency for H2.

- Clicking on the image will take you to the uploaded file page for the image.

- As seen, the molecule is infrared inactive due to there being no permanent dipole in the molecule.

Energy of reaction for the Haber-Bosch process

- Overall the reaction is: N₂ + 3H₂ → 2NH₃

E(NH3)	-56.55776873 a.u
2*E(NH3)	-113.11553750 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)] = [-113.11553750 a.u] - [-109.52412868 a.u + -3.53561808 a.u] = -0.05579070 a.u

- Converting from a.u to KJ/mol, ΔE = -0.05579070 a.u × 2625.5 = -146.48 KJ/mol (2 d.p)

- As ΔH=-ve, the reaction is exothermic, and as such, on an energy diagram, the products (ammonia) will be lower in energy and therefore more stable.

Cl₂

Summary Data

Calculation Method	RB3LYP
Basis Set	6-31G(d.p)
Final energy(au)	-920.34987886 a.u
RMS Gradient	0.00002510
Point Group	D*H
Cl-Cl Bond Length(Angstroms)	2.04174

Optimisation Results

 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

- As seen by the table above, all items did converge.

Vibrations

A table showing the vibration frequency for Cl₂ .

- Clicking on the image will take you to the uploaded file page for the image.

- As seen, the molecule is infrared inactive due to there being no permanent dipole in the molecule.

Atomic Charges

An image showing the charges on each Cl atom for a molecule of Cl₂

- Clicking on the image will take you to the uploaded file page for the image.

- The Cl₂ molecule has no permanent dipole because both atoms both have the same electronegativity. This means no atom has an overall charge.

Cl₂ Molecular Orbitals

Molecular Orbital	Orbital energy(au)	Description
	-9.51829	This image shows the occupied bonding orbital as a result of the combination of two 2s orbitals; one from each Cl atom. As seen in the image, the two separate orbitals do not overlap, which is due to the high penetrating power of s-orbitals. The 2s orbital is held close to the nucleus, deep in energy and is therefore not involved in chemical bonding. Due to being deep in energy, it has no bonding contribution.
	-0.47392	This image shows the overlap between two occupied 3p bonding orbitals; one on each Cl atom. That produces this resultant sigma molecular orbital. This MO is involved in chemical bonding. It has a positive bonding contribution.
	-0.93313	This image shows the bonding orbital between two occupied 3s orbitals; one from each Cl atom. The orbital energy is much greater in this s-orbital compared to the orbital energy of the 2s orbital. This means that the orbital is held less closely to the nuclei and are not as deep in energy. This means that they are able to overlap and become involved in chemical bonding. It has a positive contribution to bonding.
	-0.40695	This image shows the occupied bonding MO consisting of the overlap of 2 3p orbitals; one from each Cl atom. There are however two p-orbitals on each Cl atom. The two p-orbitals are orthogonal to each other. As such, when the other set of p-orbitals overlap, they produce another degenerate molecular orbital. The two sets of p-orbitals are exactly the same, so when they overlap, they produce two degenerate MOs. The MO is high in energy, near the HOMO LUMO region. This has a positive contribution to bonding.
	-0.31361	This shows an anti-bonding occupied molecular orbital which has a negative contribution to bonding, and consists of a p-orbital from each chlorine in the molecule. H2O Summary Data Calculation Method RB3LYP Basis Set 6-31G(d,p) Final energy(au) -76.41973740 a.u RMS Gradient 0.00006276 a.u Point Group D*H H-O Bond Length 0.96522 Å H-O-H bond angle 103.745° Optimisation results Item Value Threshold Converged? Maximum Force 0.000099 0.000450 YES RMS Force 0.000081 0.000300 YES Maximum Displacement 0.000115 0.001800 YES RMS Displacement 0.000120 0.001200 YES As seen by the table above, all items did converge. Vibrations A table showing the vibration frequency for H2. - Clicking on the image will take you to the uploaded file page for the image. - As seen, the molecule is infrared active are there is a dipole between the H and O atoms.