Rep:Mod:mm2wp216

NH₃ Molecule

Optimisation

Calculation Method	RB3LYP
Basis Set	6-31G(d,p)
E(RB3LYP), FINAL ENERGY	-56.55776873 a.u.
RMS Gradient	0.00000485 a.u.
Point Group	C3V

  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

N-H bond length = 1.01798 angstroms

H-N-H bond angle = 105.741 degrees

NH3

The optimisation file is liked to here

Frequency Analysis

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

6

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

2 and 3, 5 and 6.

3. Which modes are "bending" vibrations and which are "bond stretch" vibrations?

1,2,3 are bending vibrations, 4,5,6 are bond stretching vibrations.

4. Which mode is highly symmetric?

Mode 4

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

Mode 1

6. How many bands would you expect to see in an experimental spectrum of gaseous ammonia?

4 bands

Nitrogen is more electronegative than hydrogen and is therefore expected to be negatively charged (hydrogen = positive)

Nitrogen charge: -1.125 Hydrogen charge: +0.375

N₂ Molecule

Optimisation

Calculation Method	RB3LYP
Basis Set	6-31G(d,p)
E(RB3LYP), FINAL ENERGY	-109.52412868 a.u.
RMS Gradient	0.00000060 a.u.
Point Group	Dinfh

         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

N2

The optimisation file is liked to here

Frequency Analysis

H₂ Molecule

Optimisation

Calculation Method	RB3LYP
Basis Set	6-31G(d,p)
E(RB3LYP), FINAL ENERGY	-1.15928020 a.u.
RMS Gradient	0.09719500 a.u.
Point Group	Dinfh

         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

H2

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Frequency Analysis

Reactivity (Haber-Bosch Process)

E(NH3)= -56.55776873 a.u.

2*E(NH3)= -113.1155375 a.u.

E(N2)= -109.52412868 a.u.

E(H2)= -1.15928020 a.u.

3*E(H2)= -3.4778406 a.u.

ΔE=2*E(NH3)-[E(N2)+3*E(H2)]= -20.11356922 a.u.=-52808.18 kJ/mol

F₂ Molecule

Optimisation

Calculation Method	RB3LYP
Basis Set	6-31G(d,p)
E(RB3LYP), FINAL ENERGY	-199.49825218 a.u.
RMS Gradient	0.00007365 a.u.
Point Group	Dinfh

 Item               Value     Threshold  Converged?
 Maximum Force            0.000128     0.000450     YES
 RMS     Force            0.000128     0.000300     YES
 Maximum Displacement     0.000156     0.001800     YES
 RMS     Displacement     0.000221     0.001200     YES

F-F bond length = 1.40 angstrom

F2

The optimisation file is liked to here

Frequency Analysis

There is no change in dipole moment in F2 (not charged); the molecule is not IR active. No peak in IR spectrum.

F2 Molecular Orbitals

MO	AOs	Bonding/Antibonding	Filled?	Energy
	2s	Bonding	Yes
	2s	Antibonding	Yes
	2p	Antibonding	Yes
	2p	Bonding	Yes
	2p	Antibonding	No	LUMO