Rep:Mod:gab116

NH₃ Molecule

Molecule	NH3
Calculation method	RB3LYP
Basis set	6-31G(d,p)
Final energy E(RB3LYP)/au	-56.57603584
RMS gradient	0.00000431
Point group of molecule	C3V

N-H bond distance/Angstrom= 1.01579

H-N-H bond angle/degrees= 106.451

         Item             Value        Threshold    Converged?
 Maximum Force            0.000005     0.000450     YES
 RMS     Force            0.000003     0.000300     YES
 Maximum Displacement     0.000075     0.001800     YES
 RMS     Displacement     0.000037     0.001200     YES

[NH₃ optimisation .log file]

NH3 Molecule

Questions on vibrations

How many modes do you expect from the 3N-6 rule? 3*4-6=12-6=6.

Which modes are degenerate (ie have the same energy)? Mode numbers 2 and 3 and numbers 5 and 6.

Which modes are "bending" vibrations and which are "bond stretch" vibrations? Mode numbers 1, 2 and 3 are bending and numbers 4, 5 and 6 are stretching vibrations.

Which mode is highly symmetric? Mode number 4.

One mode is known as the "umbrella" mode, which one is this? Mode number 1.

How many bands would you expect to see in an experimental spectrum of gaseous ammonia? 4 bands

NH3 molecule's vibrational modes displayed.

Charge on the N-atom= -1.008

Charge on the H-atoms= 0.336

This is the expected result as nitrogen is more electronegative than hydrogen and draws the bonding electrons closer and so nitrogen is negatively charged.

N₂ Molecule

Molecule	N2
Calculation method	RB3LYP
Basis set	6-31G(d,p)
Final energy E(RB3LYP)/au	-109.52412868
RMS gradient	0.00000060
Point group of molecule	D*H

N-N bond distance/Angstrom= 1.10550

N-N bond angle/degrees= 120

         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 optimisation .log file]

N2 Molecule

N2 molecule's vibrational modes displayed.

H₂ Molecule

Molecule	H2
Calculation method	RB3LYP
Basis set	6-31G(d,p)
Final energy E(RB3LYP)/au	-1.17853936
RMS gradient	0.00000017
Point group of molecule	D*H

H-H bond distance/Angstrom= 0.74279

H-H bond angle/degrees= 120

         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 optimisation .log file]

H2 Molecule

H2 molecule's vibrational modes displayed.

Reactivity Questions

E(NH3)=-56.57603584 au

2*E(NH3)=-113.1520717 au

E(N2)=-109.52412868 au

E(H2)=-1.17853936 au

3*E(H2)=-3.53561808 au

ΔE=2*E(NH3)-[E(N2)+3*E(H2)]=-0.09232494 au

The energy change for converting hydrogen and nitrogen gas into ammonia gas is -242.40 kJ/mol (to 2 d.p.) and so the ammonia product is more stable.

F₂ Molecule

Molecule	F2
Calculation method	RB3LYP
Basis set	6-31G(d,p)
Final energy E(RB3LYP)/au	-199.49825218
RMS gradient	0.00007365
Point group of molecule	D*H

F-F bond distance/Angstrom= 1.40281

F-F bond angle/degrees= 120

          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

[F₂ optimisation .log file]

F2 Molecule

F2 molecule's vibrational modes displayed.

Charge on the F-atoms= 0.0000

Molecular Orbitals

This MO is formed from 2 2s AOs and is a bonding orbital. The MO is deep in energy and is occupied but has little effect on bonding.

This MO is formed from 2 2p AOs and is a bonding orbital. The MO is relatively deep in energy and is occupied.

This MO is formed from 2 2p AOs and is the antibonding orbital of the above MO. The MO relatively high in energy and is the LUMO.

This MO is formed from 2 2p AOs and is a bonding orbital. There are two degenerate MOs which share this same appearance. Both MOs are just below the HOMO/LUMO region and are occupied.

This MO is formed from 2 2p AOs and is the antibonding orbital of the above MO. As above, there are two degenerate MOs which share this same appearance. These MOs are both HOMOs.