Rep:Mod:REN29

NH₃ molecule

NH3 molecule

The optimisation file is linked here

Optimisation results

Calculation method	RB3LYP
Basis set	6-31G(d,p)
Final energy (RB3LYP)	-56.55776873 a.u.
RMS Gradient	0.00000485 a.u.
Point group	C3v
N-H bond distance	1.01798 Å
H-N-H bond angle	105.741°

Item table

         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 

Vibrational modes

We expect to see 6 vibrational modes. (3N-6)

Modes 2 and 3 are degenerate, as are 5 and 6.

1, 2 and 3 are bending modes.

4, 5 and 6 are stretching modes.

4 is a highly symmetric mode.

1 is the umbrella mode.

Mode 5 and 6 would not be seen on the IR spectrum of ammonia as it has a very low intensity. Modes 2 and 3 are degenerate. Because of these two factors we would expect to see 3 bands in an experimental spectrum of gaseous ammonia.

Charge Analysis

The charge on the N-atom is found to be -1.125.

The charge on the H-atoms is 0.375.

I would expect N to have a negative charge as it has a lone pair of electrons.

N is more electronegative than H, and thus draws electron density away towards itself.

H is more electropositive than N and therefore I would expect it to have a positive charge.

N₂ molecule

N2 molecule

The optimisation file is linked here

Optimisation results

Calculation method	RB3LYP
Basis set	6-31G(d,p)
Final energy (RB3LYP)	-109.52412868 a.u.
RMS Gradient	0.00000060 a.u.
Point group	D∞h
N-N bond distance	1.10550 Å

Item table

         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

Vibrational modes

H₂ molecule

H2 molecule

The optimisation file is liked to here

Optimisation results

Calculation method	RB3LYP
Basis set	6-31G(d,p)
Final energy (RB3LYP)	-1.17853936 a.u.
RMS Gradient	0.00000017 a.u.
Point group	D∞h
H-H bond distance	0.74279 Å

Item table

         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

Vibrational modes

The Haber-Bosch process

N2 + 3H2 -> 2NH3

E(NH3)= -56.55776873 a.u.

2*E(NH3)= -113.11553746 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)] = -0.0557907 a.u.

ΔE= -146.48 kJ/mol

The forward reaction is exothermic.

The ammonia product is more stable than the gaseous reactants.

F₂ molecule

F2 molecule

The optimisation file is linked here

Optimisation results

Calculation method	RB3LYP
Basis set	6-31G(d,p)
Final energy (RB3LYP)	-199.49825218 a.u.
RMS Gradient	0.00007365 a.u.
Point group	D∞h
F-F bond distance	1.40281 Å

Item table

         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

Vibrational modes

One vibrational mode is observed which is as we would expect from 3N-5.

The F₂ molecule is not IR active because it is homodinuclear it will have no change in dipole moment.

The two F atoms have no net charge.

The molecule is homodinuclear, and therefore the bond is non-polar.

Molecular orbitals

This image shows the molecular orbital formed by the two in phase 1s orbitals.

These are very deep in energy due to the large electronegativity of F.

Much of the electron density can been seen close the F nuclei.

There is little electron density along the internuclear axis and therefore this molecular orbital is not relevant for bonding.

This molecular orbital is the 1σ_g and is occupied by two electrons.

This image shows the molecular orbital formed by the two out of phase 1s orbitals.

Again, these orbitals are non-bonding as they are very deep in energy.

This molecular orbital is occupied by two electrons and it is called the 1σ_u* orbital.

This image shows the 3σ_g orbital, which is occupied by two electrons.

This bonding orbital is formed by the overlap of the in phase 2p_z orbital of each F atom.

Two nodal planes are seen, one at each nucleus.

This image shows one of the HOMOs.

There are two HOMOs which are degenerate.

One is formed by the out of phase 2p_x atomic orbitals.

The other is formed by the overlap of the 2p_y atomic orbitals when they are out of phase.

Four electrons occupy these antibonding orbitals, with two electrons occupying each one.

These molecular orbitals are named the 1π_g* orbitals.

There are two nodal planes to be seen, one of which bisects the internuclear axis and the other which runs along the internuclear axis.

This image depicts the LUMO - the 3σ_u* orbital.

This unoccupied anti-bonding orbital is formed by the out of phase 2p_z atomic orbitals.

There are three nodal planes - one along the internuclear axis and one at each of the F nuclei.

H₂SiO molecule

H2SiO molecule

The optimisation file is linked here

Optimisation results

Calculation method	RB3LYP
Basis set	6-31G(d,p)
Final energy (RB3LYP)	-365.90001403 a.u.
RMS Gradient	0.00000941 a.u.
Point group	Cs
Si=O bond distance	1.53172 Å
Si-H bond distance	1.48652 Å
H-Si-O bond angle	124.158°
H-Si-H bond angle	111.686°

The above values differ from experimentally determined values for the Si=O bond length, which was found to be 1.515 Å, and for the Si—H bond it was measured as 1.472 Å.

Item table

        Item             Value        Threshold    Converged?
Maximum Force            0.000023     0.000450     YES
RMS     Force            0.000009     0.000300     YES
Maximum Displacement     0.000023     0.001800     YES
RMS     Displacement     0.000017     0.001200     YES

Charge Analysis

The Si atom has a +1.472 charge.

The O atom has a -1.001 charge.

The H atoms each have a charge of -0.236.

O and H are both more electronegative than Si.

The Si-O bond is strongly polarised due to the large electronegativity difference between O and Si.

The makes this molecule highly unstable and reactive.