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A Gaussview image of an optimised benzene molecule.

A Gaussview image of an optimised benzene molecule.

test molecule

The optimisation file is liked to here

The quick brown fox jumps over the lazy dog.

caption

heading	heading
cell	cell
cell	cell

The table's caption

Cell 1	Cell 2	Cell 3
Cell A	Cell B	Cell C

caption

Information
More Info
Column 1	Column 2	Column 3
A	B
	C	D
	E
F
G

Ammonia, NH₃

test molecule

Properties

NH₃ optimised bond length= 1.01798 Angstroms

NH₃ optimised bond angle=105.741 degrees

Calculation type=FREQ

Calculation method=RB3LYP

Point group=C_3v

E(RB3LYP)= -56.55776873au

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

         Item               Value     Threshold  Converged?
 Maximum Force            0.000004     0.000450     YES
 RMS     Force            0.000004     0.000300     YES
 Maximum Displacement     0.000070     0.001800     YES
 RMS     Displacement     0.000033     0.001200     YES
 RMS     Displacement     0.000824     0.001200     YES

The optimisation file is linked to SAMUELJONES NH3 OPT COMPPHYS.log

Vibrations

Vibrational modes

Using the 3N-6 rule, I would expect ammonia to have 6 modes ((3x4)-6), which it does. Modes 2 and 3 and modes 5 and 6 are degenerate, as they have the same frequency of vibration.

Mode 4 is highly symmetric, as it is a symmetric stretch of all 3 N-H bonds. The umbrella mode is probably mode 1, as the molecule looks like it turns inside-out, like an umbrella in the wind. I would expect to see 4 bands in an IR spectrum of NH_3(g), as 2 pairs of vibrational modes are degenerate.

Charges and charge distribution

On the N atom, there is a charge of -1.125 and on each H, there is a charge of 0.375. I would have expected a charge of zero on both if the bond was truly covalent, but I know that N has a higher electronegativity than H, so it will draw electron density towards itself.

N₂

Information

Bond length= 1.10550 Angstroms

         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

Point group=D_∞h

Vibrational modes for ammonia

Mode	Type of vibration
1	Symmetric bend
2	Asymmetric bend
3	Asymmetric bend
4	Symmetric stretch
5	Asymmetric stretch
6	Asymmetric stretch

From the 3N-5 rule, I expected there to be 1 vibrational mode (3x2)-5=1 vibrational mode (and there was). The optimisation file is linked to SamuelJones N2 opt.log

H₂

Bond length= 0.74279 Angstroms

Point group=D_∞h

Vibrational modes for nitrogen

Mode	Type of vibration	Frequency/Hz
1	Symmetric stretch	2457.33

From the 3N-5 rule, I expected there to be 1 vibrational mode (and there was). The optimisation file is linked to SAMUELJONES H2 OPT.log

The Haber Process

N_2(g)+3H_2(g)--->2NH_3(g)

Energy of reaction/au

E(NH_3(g))=

2E(NH_3(g))=

E(N_2(g))=

E(H_2(g))=

3E(H_3(g))=

ΔE=2E(NH_3(g))-[E(N_2(g))-3E(H_2(g))]=

Energy of reaction/kJmol^-1

E(NH_3(g))=

2E(NH_3(g))=

E(N_2(g))=

E(H_2(g))=

3E(H_3(g))=

ΔE=2E(NH_3(g))-[E(N_2(g))-3E(H_2(g))]=

The products are more stable, as the enthalpy change of the reaction is negative, which means that the bonds formed are stronger than those broken to form them.

Molecule of my choice

CO_2(g)

Information

Linear Point group=D_∞h Optimisation

Vibrational modes

Based on the 3N-5 rule, I expected there to be 4 vibrational modes ((3x3)-5), which there were.

Energy change of formation

C_(s)(graphite)+O_2(g)--->CO_2(g)

E(C_(s))(graphite))=

E(O_2(g))=

E(CO_2(g))=

ΔE=E(CO_2(g))-(E(O_2(g))+E(C_(s))(graphite)))

Extra molecule

Information

Vibrational modes for hydrogen

Mode	Type of vibration	Frequency/Hz
1	Symmetric stretch	4465.68