Ammonia NH₃

Structure

Optimisation of of NH₃
Calculation Method	Basis Set	Final Energy E / a.u.	Point Group
RB3LYP	631G(d,p)	-56.55776873	C_3V

         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

NH3

Optimised N-H bond length (Angstrom): 1.02 ± 0.01

Optimised H-N-H bond angle (Degrees): 106 ± 1

Charge on N: +0.375

Charge on H: -1.125

(Dipole Moment: 1.8466 Db)

Opt file here

Vibrational Modes

Vibrational Modes of NH₃
Wavenumber / cm^-1	Symmetry	Intensity	Bend or Stretch
1090	A1	145.4	Bend
1694	E	13.6
1694	E	13.6
3461	A1	1.1	Stretch
3590	E	0.3
3590	E	0.3

Number of expected vibrational modes: $3 N - 6 = 3 * 4 - 6 = 6$

Two pairs of degenerate vibrational modes, one pair at 1694 cm^-1, the other at 3590 cm^-1.

The vibrations at 1090 cm^-1 and 3461 cm^-1 are highly symmetric.

The 1090 cm^-1 is known as the "umbrella" mode due to its resemblance to an opening and closing umbrella.

In an IR spectrum of gaseous ammonia, four bands would be predicted since there are vibrational modes at four different frequencies.

Haber-Bosch Process

Molecular Nitrogen N₂

Structure

Optimisation of of N₂
Calculation Method	Basis Set	Final Energy E / a.u.	Point Group
RB3LYP	631G(d,p)	-109.52412868	D_∞h

         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

Optimised N≡N bond length (Angstrom): 1.11 ± 0.01

Charge on each N: 0

(Dipole moment: 0 Db)

The molecule (dinitrogen)-(2,2',2' '-(phosphanetriyl)tris(1-(diphenylphosphanyl)-3-methyl-1H-indole))-ruthenium tetrahydrofuran solvate (refcode DEKFUX) has a reported N≡N bond length of 1.086(6) Angstrom. In dinitrogen complexes, one of the nitrogens donates its lone pair, which exists in an sp orbital, to the metal to form a dative covalent bond. Consequently, the electron density around the donor nitrogen decreases, causing it to attract the electrons in the N≡N pi-bond more strongly since the effective nuclear charge they experience increases. Because the electrons move closer to the bonded nitrogen, so too does the second nitrogen; this results in a shorter equilibrium bond length. In pure diatomic molecular nitrogen gas, both atoms are electronically equal, but when coordinated with a metal there is an imbalance in electron density.

Opt file here

Vibrational Modes

Vibrational Modes of N₂
Wavenumber / cm^-1	Symmetry	Intensity	Bend or Stretch	Image
2457	SGG	0.0 (IR inactive)	Stretch

Number of expected vibrational modes: $3 N - 5 = 3 * 2 - 5 = 1$

Molecular Hydrogen H₂

Structure

Optimisation of of H₂
Calculation Method	Basis Set	Final Energy E / a.u.	Point Group
RB3LYP	631G(d,p)	-1.17853936	D_∞h

         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

Optimised H-H bond length (Angstrom): 0.74 ± 0.01

Charge on each H: 0

(Dipole moment: 0 Db)

Opt file here

Vibrational Modes

Vibrational Modes of H₂
Wavenumber / cm^-1	Symmetry	Intensity	Bend or Stretch	Image
4466	SGG	0.0 (IR Inactive)	Stretch

Number of expected vibrational modes: $3 N - 5 = 3 * 2 - 5 = 1$

Energy Calculations

$E (N H_{3}) = - 56.55777$

$2 * E (N H_{3}) = - 113.11554$

$E (N_{2}) = - 109.52413$

$E (H_{2}) = - 1.17854$

$3 * E (H_{2}) = - 3.53562$

$Δ E = 2 * E (N H_{3}) - [E (N_{2}) + 3 * E (H_{2})] = - 113.11554 - (- 109.52413 - 3.53562) = - 0.0557905 a . u . = - 146.5 k J m o l^{- 1}$

Hence ΔE = -146.5 kJ mol^-1 < 0

So the reaction is exothermic, and thus the ammonia product is more stable than the reactants. However, entropy greatly favours the reverse reaction.

Sulfur Tetrafluoride SF₄

Structure

Optimisation of of SF₄
Calculation Method	Basis Set	Final Energy E / a.u.	Point Group
RB3LYP	631G(d,p)	-797.45952460	C_2v

         Item               Value     Threshold  Converged?
 Maximum Force            0.000148     0.000450     YES
 RMS     Force            0.000065     0.000300     YES
 Maximum Displacement     0.000570     0.001800     YES
 RMS     Displacement     0.000281     0.001200     YES

SF4

Optimised S-F_ax bond length (Angstrom): 1.67 ± 0.01

Optimised S-F_eq bond length (Angstrom): 1.59 ± 0.01

Optimised F_ax-S-F_ax bond angle (Degrees): 171 ± 1

Optimised F_eq-S-F_eq bond angle (Degrees): 102 ± 1

Optimised F_ax-S-F_eq bond angle (Degrees): 87 ± 1

Charge on S: +1.983

Charge on F_ax: -0.537

Charge on F_eq: -0.455

(Dipole moment: 0.8849 Db)

Opt file here

Vibrational Modes

Vibrational Modes of SF₄
Wavenumber / cm^-1	Symmetry	Intensity	Bend or Stretch
189	A1	0.5	Bend
330	B1	9.9
435	A2	0.0 (IR inactive)
488	A1	20.5
496	B2	2.1
584	A1	2.7	Stretch
807	B2	508.8
852	B1	149.9
867	A1	100.8

Number of expected vibrational modes: $3 N - 6 = 3 * 5 - 6 = 9$

Molecular Orbitals

Molecular Orbitals of SF₄
Orbital Number	Energy / eV	Orbital type	Occupied?
9	-6.17183	Non-bonding	Yes
10	-1.32222	Bonding	Yes
13	-1.17960	Primarily bonding	Yes
14	-0.78968	Primatily antionding	Yes
26 (HOMO)	-0.34280	Primarily bonding	Yes
27 (LUMO)	-0.07939	Primarily antibonding	No

Orbitals 1-9 are very deep in energy and are therefore inaccessible; these are made from the core electrons of the constituent atoms. However, subsequent MOs are much higher-lying, with all MOs above the 14^th having E > -1 eV. Overall the molecule has no pi bonds, therefore for every filled bonding orbital with pi character there must be an equal amount of pi antibonding character. Due to the number of atomic orbitals contributing to the molecular orbitals, none of the higher-lying orbitals can be considered to be purely bonding or purely antibonding. The electron distribution for the orbitals may lie between one pair of atoms, but produce a node between another pair. S-character can be observed in the shape of orbital 14, whilst the large rear lobe(s) of orbitals 26 and 27 (the HOMO and LUMO) indicate contribution from a d orbital.

Independence Task - other small molecules

Carbon Monoxide CO

Structure

Optimisation of of CO
Calculation Method	Basis Set	Final Energy E / a.u.	Point Group
RB3LYP	631G(d,p)	-113.30945314	C_∞v

         Item               Value     Threshold  Converged?
 Maximum Force            0.000007     0.000450     YES
 RMS     Force            0.000007     0.000300     YES
 Maximum Displacement     0.000003     0.001800     YES
 RMS     Displacement     0.000004     0.001200     YES

CO

Optimised C-O bond length (Angstrom): 1.14 ± 0.01

Charge on C: +0.506

Charge on O: -0.506

(Dipole moment: 0.0599 Db)

Opt file here

Vibrational Modes

Vibrational Modes of CO
Wavenumber / cm^-1	Symmetry	Intensity	Bend or Stretch	Image
2209	SG	68.0	Stretch

Number of expected vibrational modes: $3 N - 5 = 3 * 2 - 5 = 1$

Cyanide CN^-

Structure

Optimisation of of CN^-
Calculation Method	Basis Set	Final Energy E / a.u.	Point Group
RB3LYP	631G(d,p)	-92.82453153	C_∞v

         Item               Value     Threshold  Converged?
 Maximum Force            0.000012     0.000450     YES
 RMS     Force            0.000012     0.000300     YES
 Maximum Displacement     0.000005     0.001800     YES
 RMS     Displacement     0.000008     0.001200     YES

CN-

Optimised C-N bond length (Angstrom): 1.18 ± 0.01

Charge on C: -0.246

Charge on N: -0.754

(Dipole moment: 0.5236 Db)

Opt file here

Vibrational Modes

Vibrational Modes of CN^-
Wavenumber / cm^-1	Symmetry	Intensity	Bend or Stretch	Image
2139	SG	7.8	Stretch

Number of expected vibrational modes: $3 N - 5 = 3 * 2 - 5 = 1$

Hydrogen Cyanide HCN

Structure

Optimisation of of HCN
Calculation Method	Basis Set	Final Energy E / a.u.	Point Group
RB3LYP	631G(d,p)	-93.42458132	C_∞v

         Item               Value     Threshold  Converged?
 Maximum Force            0.000370     0.000450     YES
 RMS     Force            0.000255     0.000300     YES
 Maximum Displacement     0.000676     0.001800     YES
 RMS     Displacement     0.000427     0.001200     YES

HCN

Optimised C-N bond length (Angstrom): 1.07 ± 0.01

Optimised H-C bond length (Angstrom): 1.16 ± 0.01

Charge on H: +0.234

Charge on C: +0.073

Charge on N: -0.308

(Dipole moment: 2.8933 Db)

Opt file here

Vibrational Modes

Vibrational Modes of HCN
Wavenumber / cm^-1	Symmetry	Intensity	Bend or Stretch
767	PI	35.3	Bend
767	PI	35.3	Bend
2215	SG	2.0	Stretch
3480	SG	57.3	Stretch

Number of expected vibrational modes: $3 N - 5 = 3 * 3 - 5 = 4$

Pair of degenerate vibrational modes at 767 cm^-1

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 0.5/1

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, most answers are correct. However there are only 2 visible peaks in the spectra of NH3, due to the low intensity of the other 2 peaks. (See infrared column in vibrations table.)

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 0.5/0.5

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

YES

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

YES

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 3/5

Have you completed the calculation and included all relevant information?

YES

Have you added information about MOs and charges on atoms?

YES, you added all the necessary information, well done! To improve you could have explain the charges in terms of electronegativity, and added more details on the individual MOs such as which AOs are contributing to each. The explanation of the MOs overall was good though.

Independence 1/1

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

You did several extra calculations, with analysis, well done!

Ammonia NH3

Structure

Vibrational Modes

Haber-Bosch Process

Molecular Nitrogen N2

Structure

Vibrational Modes

Molecular Hydrogen H2

Structure

Vibrational Modes

Energy Calculations

Sulfur Tetrafluoride SF4

Structure

Vibrational Modes

Molecular Orbitals

Independence Task - other small molecules

Carbon Monoxide CO

Structure

Vibrational Modes

Cyanide CN-

Structure

Vibrational Modes

Hydrogen Cyanide HCN

Structure

Vibrational Modes

Marking

Wiki structure and presentation 1/1

NH3 0.5/1

N2 and H2 0.5/0.5

Crystal structure comparison 0.5/0.5

Haber-Bosch reaction energy calculation 1/1

Your choice of small molecule 3/5

Independence 1/1

Ammonia NH₃

Molecular Nitrogen N₂

Molecular Hydrogen H₂

Sulfur Tetrafluoride SF₄

Cyanide CN^-