Molecular modelling

Ammonia

Molecule of Ammonia

The molecule of NH₃ was modelled and then optimised using calculation method B3LYP and basis set 6-31G(d,p). The results are shown in the table below.

Results
Final energy E(RB3LYP)	-56.55776873 au
RMS gradient	0.00000485 au
Point group	C3V
N-H bond length	1.02 Å
H-N-H bond angle	105°

         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

The optimisation file of ammonia is linked to here

Vibrational Analysis

From the 3N-6 rule 6 vibrational modes were expected, what was confirmed by computational analysis. The mode 1 and mode 2 and also mode 5 and 6 are degenerate with corresponding wavenumbers 1693.95 and 3589.82. Modes 1, 2 and 3 are bending vibrations and modes 4, 5 and 6 are bond stretch vibrations. The most highly symmetric mode is mode 4. The mode 1 is also know as umbrella mode. In total the ammonia has 6 vibrational modes from witch two pairs are degenerate. Based on this we can expect to see 4 bands in a spectrum, but mode 4 and modes 5 and 6 have very low intensity so only two bands are possible to see.

Results
	mode 1	mode 2	mode 3	mode 4	mode 5	mode 6
wavenumber [cm^-1]	1089.54	1693.95	1693.95	3461.29	3589.82	3589.82
symmetry	A1	E	E	A1	E	E
intensity [arbitrary units]	145.4	13.6	13.6	1.1	0.3	0.3
image

Charge distribution

The electronegativity by Puling scale of nitrogen is 3.0 and hydrogen 2.2. As the nitrogen is more electonegative, the partial negative charge on nitrogen and partial positive charges on hydrogens are expected.

Nitrogen

Molecule of Nitrogen

The B3LYP calculation method was used for calculations with basis set 6-31G(d,p).

Results
Final energy E(RB3LYP)	-109.52412867 au
RMS gradient	0.00008380 au
Point group	D_{inf h}
N-N bond length	1.11 Å

         Item               Value     Threshold  Converged?
 Maximum Force            0.000145     0.000450     YES
 RMS     Force            0.000145     0.000300     YES
 Maximum Displacement     0.000045     0.001800     YES
 RMS     Displacement     0.000064     0.001200     YES

The optimisation file of nitrogen is linked to here

Vibrational analysis

Results
	mode 1
wavenumber [cm^-1]	2456.91
intensity [arbitrary units]	0.0
image

Charge distribution

The molecule of nitrogen is composed from two identical atoms which have same electronegativity. Therefore the charge on each atom was expected to be zero.

Hydrogen

Molecule of Hydrogen

The B3LYP calculation method was used for calculations with basis set 6-31G(d,p).

Results
Final energy E(RB3LYP)	-1.17853936 au
RMS gradient	0.00000017 au
Point group	D_{inf h}
H-H bond length	0.74 Å

         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

The optimisation file of hydrogen is linked to here

Vibrational analysis

Results
	mode 1
wavenumber [cm^-1]	4465.68
intensity [arbitrary units]	0.0
image

Charge distribution

The molecule of hydrogen is composed from two identical atoms which have same electronegativity. Therefore the charge on each atom was expected to be zero.

TM complex

The trans-bis(Dinitrogen)-bis(1,2-bis(bis(4-ethylphenyl)phosphino)ethane)-molybdenum toluene is compound with two molecules of nitrogen bonded to the molybdenum. The two N-N bond lengths are 1.117 au and 1.116 au. Refcode of the compound is DAMSOA. [[1]].

Haber-Bosch reaction

E(NH₃)=-56.55776873 au

2*E(NH₃)=-113.1155375 au

E(N₂)=-109.52412867 au

E(H₂)=-1.17853936 au

3*E(H₂)=-3.53561808 au

ΔE=2*E(NH₃)-[E(N₂)+3*E(H₂)]=-0.05579071 au = -146.47 KJ/mol

The nitrogen is lower in energy than hydrogen and ammonia on their own, but ammonia (the product) is overall more stable than gaseous reactants.

Silane

Molecule of Silane

The B3LYP calculation method was used for calculations with basis set 6-31G(d,p).

Results
Final energy E(RB3LYP)	-291.88802760 au
RMS gradient	0.00000002 au
Point group	T_d
Si-H bond length	1.485 Å
H-Si-H bond angle	109.5°

         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     0.000000     0.001200     YES

The optimisation file of silane is linked to here

Vibrational analysis

Results
	mode 1	mode 2	mode 3	mode 4	mode 5	mode 6	mode 7	mode 8	mode 9
wavenumber [cm^-1]	919.21	919.21	919.21	0.0	0.0	0.0	143.3961	143.3961	143.3961
symmetry	T2	T2	T2	E	E	A1	T2	T2	T2
intensity [arbitrary units]	136.1485	136.1485	136.1485	1.1	0.3	0.3	1.1	0.3	0.3
bending/stretching	bending	bending	bending	bending	bending	stretching	stretching	stretching	stretching
image

Charge distribution

The carbon is more electronegative than hydrogen in contrast with silicon, which is less elecronegative. This results in the reverse charge distribution in silane molecule compared to the methane.

Molecular orbitals

Results
				HOMO	LUMO
Bonding?	non-bonding	nonbonding	bonding	bonding	bonding
Occupied?	occupied	occupied	occupied	occupied	unccupied
Energy [au]	-5.28056	-3.63858	-0.54726	-0.35184	0.05053
contributing AOs	Si 2s	Si 2p_z	Si 3s, 4s and 3 x H 1s	Si 3p_y, 2 x H 2s and 2 x H -2s	Si 4p_y,3p_y, 2 x H 2s and 2 x H -2s
image

Marking

Note: All grades and comments are provisional and subject to change until your grades are officially returned via blackboard. Please do not contact anyone about anything to do with the marking of this lab until you have received your grade from blackboard.

Wiki structure and presentation 1/1

Is your wiki page clear and easy to follow, with consistent formatting?

YES

Do you effectively use tables, figures and subheadings to communicate your work?

YES

NH3 1/1

Have you completed the calculation and given a link to the file?

YES

Have you included summary and item tables in your wiki?

YES

Have you included a 3d jmol file or an image of the finished structure?

YES

Have you included the bond lengths and angles asked for?

YES

Have you included the “display vibrations” table?

YES

Have you added a table to your wiki listing the wavenumber and intensity of each vibration?

YES

Did you do the optional extra of adding images of the vibrations?

YES

Have you included answers to the questions about vibrations and charges in the lab script?

YES

N2 and H2 0.5/0.5

Have you completed the calculations and included all relevant information? (summary, item table, structural information, jmol image, vibrations and charges)

YES

Crystal structure comparison 0/0.5

Have you included a link to a structure from the CCDC that includes a coordinated N2 or H2 molecule?

YES - well done on this part.

Have you compared your optimised bond distance to the crystal structure bond distance?

You didn't attempt to discuss the difference between your own calculated value and the crystal structure value.

Haber-Bosch reaction energy calculation 1/1

Have you correctly calculated the energies asked for? ΔE=2*E(NH3)-[E(N2)+3*E(H2)]

YES

Have you reported your answers to the correct number of decimal places?

YES

Do your energies have the correct +/- sign?

YES

Have you answered the question, Identify which is more stable the gaseous reactants or the ammonia product?

YES

Your choice of small molecule 4/5

Have you completed the calculation and included all relevant information?

YES

Have you added information about MOs and charges on atoms?

YES - overall good explanations throughout your wiki. However with your MOs a few sentences would have been be appreciated! The LUMO is actually the antibonding counterpart to the HOMO - please see included image.

Independence 0/1

If you have finished everything else and have spare time in the lab you could: Check one of your results against the literature, or Do an extra calculation on another small molecule, or Do some deeper analysis on your results so far