Rep:Mod:greysmurfy

NH₃ Molecule Analysis

Optimisation Data

Molecule: NH₃

Calculation Method: RB3LYP

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

Final energy: -56.55776873 au

RMS gradient: 0.00000485 au

Point group: C3V

Optimised N-H bond length: 1.01798 Å

Optimised 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

Optimised NH3

The optimisation file is linked to here

Vibrational Analysis of NH₃

Vibrations of the optimised NH3 molecule.

As there are 4 atoms, the 3N-6 rule predicts that we should have 6 modes. The modes 2 and 3 are degenerate, as are modes 5 and 6. Modes 1,2 and 3 are "bending" vibrations, whereas modes 4, 5 and 6 are "bond stretch" vibrations. Mode 4 is highly symmetric, and mode 1 is also known as the "umbrella" mode. We would only expect to see 4 bands in an experimental spectrum of gaseous ammonia however, due to the 2 pairs of degenerate modes.

Charge Analysis of NH₃

The charge on the N atom is -1.125 and the charge on the H atoms are 0.375. Since the N atom is more electronegative than the H atom, we would expect the bonding electrons to be more attracted to the N atom than the H atoms. Hence we expect that the N atom will have a slightly negative charge, and the H atoms will have a slightly positive charge.

N₂ Molecule Analysis

Optimisation Data

Molecule: N₂

Calculation Method: RB3LYP

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

Final energy: -109.52412868 au

RMS gradient: 0.00000060 au

Point group: D*H

Optimised N-N bond length: 1.10550 Å

Optimised N-N bond angle: 180°

        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

Optimised N2

The optimisation file is linked to here

Vibrational Analysis of N₂

Vibrations of the optimised N2 molecule.

Since the molecule is linear and contains only 2 atoms, the 3N-5 rule predicted that there would only be 1 vibrational mode, which turned out to be the case, as seen above.

H₂ Molecule Analysis

Optimisation Data

Molecule: H₂

Calculation Method: RB3LYP

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

Final energy: -1.17853936 au

RMS gradient: 0.00000017 au

Point group: D*H

Optimised H-H bond length: 0.74279 Å

Optimised H-H bond angle: 180°

         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

Optimised H2

The optimisation file is linked to here

Vibrational Analysis of H₂

Vibrations of the optimised H2 molecule.

Since the molecule is linear and contains only 2 atoms, the 3N-5 rule predicted that there would only be 1 vibrational mode, which turned out to be the case, as seen above.

Haber-Bosch Reaction Energy Calculation

E(NH₃) = -56.55776873 au

2*E(NH₃) = -113.11553746 au

E(N₂) = -109.52412868 au

E(H₂) = -1.17853936 au

3*E(H₂) = -3.53561808 au

ΔH = 2*E(NH₃)-[E(N₂)+3*E(H₂)] = -0.0557907 au (-146.47848285 kJ/mol)

In the production of ammonia, the chemical reaction occurring is: N₂ + 3H₂ -> 2NH₃. Hence the calculated value of ΔH above is the energy change for the production of ammonia. Since ΔH is negative, this indicates that the ammonia gas is more stable than the gaseous reactants.

Choice of Small Molecule: H₂CO

Optimisation Data

Molecule: H₂CO

Calculation Method: RB3LYP

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

Final energy: -114.50319933 au

RMS gradient: 0.00007386 au

Point group: CS

Optimised C=O bond length: 1.20676 Å

Optimised C-H bond length: 1.11057 Å

Optimised H-C=O bond angle: 122.386°

Optimised H-C-H bond angle: 115.219°

         Item               Value     Threshold  Converged?
 Maximum Force            0.000197     0.000450     YES
 RMS     Force            0.000085     0.000300     YES
 Maximum Displacement     0.000270     0.001800     YES
 RMS     Displacement     0.000149     0.001200     YES

Optimised H2CO

The optimisation file is linked to here

Vibrational Analysis of H₂CO

Vibrations of the optimised H2CO molecule.

As there are 4 atoms, the 3N-6 rule predicts that we should have 6 modes. Modes 1, 2 and 3 are bending vibrations, and modes 5 and 6 were bond stretch vibrations. Mode 4 was a combination of both bond stretching and bending, with the C=O bond displaying bond stretching, and the C-H bonds displaying bond bending. As none of the modes are degenerate, we would expect to see 4 bands in an experimental spectrum of gaseous methanal.

Charge Analysis of H₂CO

Charge distribution in the H2CO molecule.

The C atom had a charge of 0.221, the O atom had a charge of -0.494 and the H atoms both had a charge of 0.137. This can be explained by the oxygen atom's much greater electronegativity, drawing electrons away from the carbon and hydrogen atoms to form a slightly positive charge on the C and H atoms, with O forming a slightly negative charge.

H₂CO Molecular Orbital (MO) Analysis

Below are a few examples of the molecular orbitals (MO) of H₂CO:

Table of 5 Molecular Orbitals of H₂CO

MO	Energy (au)	Contributing AO	Description
	-19.17003	O: 1s	This is a bonding MO. It has the lowest energy.
	-10.28952	C: 1s	This is an antibonding MO.
	-1.06085	C: 2s, O: 2s	This is a bonding MO.
	-0.44941	C: 2p, O: 2p	This is an antibonding MO.
	-0.26816	C: 2p, O: 2p	This is an antibonding MO. It is the HOMO.