NH₃, also known as ammonia, is a major compound of our curernt society, from its use in agriculture, in refrigeration... In the following sections, the main characteristics of ammonia, H₂, N₂ are investigated in order to study the Haber-Bosch process and why it is energetically favoured.

Finally, a comparison of cyanide [CN]^- and hydrogen cyanide HCN is carried out, in order to find the most table structure between the base and the acid.

NH₃ molecule

Optimization

Molecule name : NH₃

Calculation method : RB3LYP

Basis set : 6-31G(d.p)

Final energy : E(RB3LYP) = -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

NH3 molecule

Recorded optimized N-H bond length : r_NH = 1.018 Å

Recorded optimized H-N-H bond angle : θ = 105°

The optimization file can be accessed here.

Vibration and Charges

Vibration

NH₃ vibrational modes
Wavenumber cm^-1	1089	1693	1693	3461	3589	3589
Symmetry	A1	E	E	A1	E	E
Intensity arbitrary units	145	14	14	1	0	0
Image

From the 3N-6 rule, 6 vibrational modes are to be expected. On the table, it is shown that 4 modes are degenerate (2 of them have a frequency of 1693 cm^-1, and two others have a frequency of 3589 cm^-1).

The first three vibrational modes (in the table) correspond to bending, while the last three correspond to streching vibrations. The vibrational mode with a frequency 3461 cm^-1, also called the symmetric strech, is the most symmetric vibration. The vibration with the smallest frequency is known as the umbrella mode.

From the degeneracy of the modes, 4 peaks should be expected in an experimental spectrum of gaseous ammonia. However, the last two signals have very low intensity and for this reason, only 2 peaks can be observed in an IR spectrum of NH₃ (1089 and 1693 cm^-1).

Charge

As expected, the calculations show a negative charge on the N atom, while positive chrges can be observed on the H atoms. Futhermore, it can be noted that q_N = -3q_H as the overall charge of the molecule Q = q_N +3q_H = 0.

N₂ molecule

Molecule optimization

Molecule name : N₂

Calculation method : RB3LYP

Basis set : 6-31G(d.p)

Final energy : E(RB3LYP) = -109.52412868 a.u.

RMS gradient = 0.00000060 a.u.

Point group : 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 molecule

Recorded N-N bond length : r_N2 = 1.106 Å

Please note that N₂ is a linear diatomic molecule, therefore no optimzed angle is recorded.

The optimization file can be accessed here.

Vibrations and Charges

Vibrations

Here the table shows the only vibration in N₂ has a frequency of 2457 cm^-1, not shown in the IR spectrum (as its intensity is predicted to be 0). This can be explained by the fact that symmetrical vibrations are not IR active.

Charge

As, N₂ is a symmetric diatomic molecule, it comes to no surprise that no charge can be observed on either of the atoms, as it is displayed in the modelisation below.

H₂ molecule

Molecule optimization

Molecule name : H₂

Calculation method : RB3LYP

Basis set : 6-31G(d.p)

Final energy : E(RB3LYP) = -1.17853936 a.u.

RMS gradient = 0.00000908 a.u.

Point group : D_∞h

         Item               Value     Threshold  Converged?
 Maximum Force            0.000016     0.000450     YES
 RMS     Force            0.000016     0.000300     YES
 Maximum Displacement     0.000021     0.001800     YES
 RMS     Displacement     0.000029     0.001200     YES

H2 molecule

Recorded N-N bond length : r_H2 = 0.743 Å

Please note that H₂ is a linear diatomic molecule, therefore no optimzed angle is recorded.

The optimization file can be accessed here.

Vibrations and Charges

Vibrations

Here the table shows the only vibration in H₂ has a frequency of 4466 cm^-1, not shown in the IR spectrum ( as its intensity is predicted to be 0). This can be explained by the fact that symmetrical vibrations are not IR active.

Charge

As, H₂ is a symmetric diatomic molecule, it comes to no surprise that no charge can be observed, as it is the case for N₂.

Reaction and orbitals

Structure and reactivity

Mono-metallic transition metal complex

A search in ConQuest permits to find that Molybdenum compound coordinates N₂: cis-bis(1-(diethylphosphino)-N-((diethylphosphino)methyl)-N-(2,6-difluorobenzyl)methanamine)-bis(dinitrogen)-molybdenum. Its unique identifier is AQEZED, and more information about the compound can be found |here.

The recorded bond length in that molecule are r₁ = 1.117 Å and r₂ = 1.113 Å. Those values are higher than the predicted bond length calculated on Gaussian. This can be explained by the fact that the first N atom also shares a bond with the Mo atom, leading to a more diffuse distribution of the electrons around that nitrogen atom (formal positive charge), hence the difference between the computed and experimental bonds.

Haber-Bosch process

E(NH₃) = -56.55776873 a.u.

2*E(NH₃)= -113.1155375 a.u.

E(N2)= -109.52412868 a.u.

E(H2)= -1.17853936 a.u.

3*E(H2)= -3.53561808 a.u.

ΔE=2*E(NH3)-[E(N2)+3*E(H2)]= -0.05579074 a.u. = -146.5 kJ.mol^-1 (tp 1 d.p.)

ΔE is negative, indicating that the product (ammonia) is more stable than the reactants (nitrogen and hydrogen).

Cyanide

In this part, we will be intersted in the [CN]^- molecule, a very harmful substance to living beings, yet impressively useful molecule at a catalysist or base in different reactions.

[CN]^- molecule

Molecule optimization

Molecule name : [CN]^-

Calculation method : RB3LYP

Basis set : 6-31G(d.p)

Charge : q = -1

Final energy : E(RB3LYP) = -92.82453153 a.u.

RMS gradient = 0.00000704 a.u.

Point group : 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]- molecule

Recorded bond length : r_CN = 1.184 Å

[CN]^- being a linear diatomic molecule, no optimized angle was calculated.

The optimization file can be accessed here.

Vibrations and charges

Vibrations

[CN]^- being a diatomic molecule, it only shows one vibration mode : the C-N stretch, and thus its IR spectrum will be composed of a unique peak at 2139 cm^-1, and of intensity 7 (in arbitrary units). This vibration is illustrated by the figure below.

Charge

[CN]^- is an anion with a charge q = -1, which is, in theory, on the C atom. However, according to computed calculations, the strong electronegative nature of the nitrogen atom results on a distribtion of the negative charge throughout the molecule, with a great portion of it still on the C atom. This is can be illustrated by the picture below:

HCN molecule

The negative charge on [CN]^{-</sup< can be neutralized when the carbon atom bonds with a Hydrogen atom, forming a HCN molecule. Let us study this new molecule.}

Molecule optimization

Molecule name : HCN

Calculation method : RB3LYP

Basis set : 6-31G(d.p)

Final energy : E(RB3LYP) = -93.42458132 a.u.

RMS gradient = 0.00017006 a.u.

Point group : 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 molecule

Recorded C-H bond length : r_C-H = 1.069 Å

Recorded C-N bond length : r_C-N = 1.157 Å

Recorded bond angle : θ = 180°

The optimization file can be accessed here.

Vibrations and Charges

Vibrations

HCN vibrational modes
Wavenumber cm^-1	766	766	2214	3479
Symmetry	PI	PI	SG	SG
Intensity arbitrary units	35	35	2	57
Image

Here the table shows the different vibration modes of HCN. It can be observed that the first two vibration modes are degenerate, i.e. have the same energy. The high symmetrical nature of the third onehas a very low intensity, implying that the spectrum will only show two peaks.

Charge

The Nitrogen atom is known to be highly electronegative compared to C and H, which explains its partial negative charge, while the Carbon and Hydrogen atom positive charges sum up to compensate this negative charge.

Molecular orbitals

HCN molecular orbitals
Molecular orbital	2σ_g	3σ_g	3σ^*_u	1π_u	1π^*_g
Energy a. u.	-0.92	-0.61	-0.38	-0.36	0.02
Contributing atomic orbitals	H (1s) and C (sp)	C (sp) and N (2p_z)	C (sp) and N (2p_z)	C (2p_x) and N (2p_x)	C (2p_x) and N (2p_x)
Bonding and filling	bonding, occupied	bonding, occupied	antibonding, unoccupied	bonding, occupied	antibonding, unoccupied
Image

Above is displayed a table showing five of the molecular orbitals that constitute HCN.

The first orbital chosen, bond between the H and C atoms, helps illustrating the mixing between and s and a p orbital in the C atom. The second one, 3σ_g, is interesting because it is part of the C-N triple bond. Its corresponding antibonding orbital should be studied as it shows, again, the mixing of the carbon atomic orbitals. Here, on the π molecular orbitals were displayed to allow to understand the degeneracy of those orbitals which also consitute the triple bond, and allows us to comprehend that the bond strength is mainly due to the efficient overlap between the 2p orbitals of the same size (as they belong to the same period). It is also the HOMO. Finally, its corresponding aintibonding orbital is shown here for similar reasons, and also because it is the LUMO.

Analytical comparison

The point of this section is to analyse the effect of the addition of a proton on the cyanide molecule.

The first point of comparison to take into consideration is the bond length of the C-N triple bond. It should be noted that the diffrence between the two bonds is :

Δr = r_CN - r_HCN = 1.184 - 1.157 = 0.024 Å

The bond is shorter in HCN, and thus it can be concluded that the bond is strengthened by the addition of hydrogen. This can be explained bt the fact that in [CN]^-, the lone pair of electrons it very repulsive – more repulsive than a potential C-H bond, and therefore weakens the C-N bond.

HCN, more stable than [CN]^- (due to the stabilising of the negative charge), has a pKa = 9.1 in water ^[1]. As the carbon loses its lone pair, the molecule cannot react as a base anymore, but behaves as an acid in aqueous conditions (with a pH < 9.1), as it is the case in the reaction shown below:

In this reaction, HCN reacts with H₂C=O to form hydroxyacetonitrile. The reagent used is H₂SO₄. This example helps see clearly how the addition of hydrogen to cyanide makes it an efficient acid. ^[2]. However, it should be noted that HCn is rarely used because of its highly poisonous character, and substitutes such as KCN, or NaCN are often used.

References

↑ Oleg A, Reutov, Russian Chemical Reviews, Equilibrium acidity of carbohydrogen bonds in organic compounds, 1974, Vol. 43(1), pp. 17-31.
↑ Tian Xi, Xie Yifeng, Wu Xingwei, Industrial perparation method of hydroxyacetonitrile, Assignee Fushun Shunte, 2018.

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 - only in the first sentence there are some poorly formatted words.

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 - you could have included a electronegativity argument to explain the charges.

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 4/5

Have you completed the calculation and included all relevant information?

YES

Have you added information about MOs and charges on atoms?

YES

The third displayed MO is a bonding orbital rather than anti-bonding. Besides that you correctly described the MOs. You could have explained and discussed the relative orbital energies.

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

YES - however the link to the .log file of the CN- ion is not working, therefore the achievable mark is lowered by 1 for this section. But you had a very good and unique idea for this section of the lab!

Do some deeper analysis on your results so far

[pKa-1] Oleg A, Reutov, Russian Chemical Reviews, Equilibrium acidity of carbohydrogen bonds in organic compounds, 1974, Vol. 43(1), pp. 17-31.

[Reaction-2] Tian Xi, Xie Yifeng, Wu Xingwei, Industrial perparation method of hydroxyacetonitrile, Assignee Fushun Shunte, 2018.

[1]

[2]