Rep:Mod:CT1216
Module: CT1216
Ammonia, NH3
Molecule Properties
Ammonia is a compound of 1 N atom hydrogen bonded to 3 H atoms with the formula of NH3.
Ammonia adopts a trigonal pyramidal shape that results when there are three bonds and one lone pair on the central atom in the molecule. Ammonia has a tetrahedral electron pair geometry and has sp3 hybridization at the central nitrogen.
The optimised N-H bond distance is 1.01798 Å, and optimised H-N-H bond angle is 105.74115°.
The jmol file shown below is an optimised structure of NH3:
Optimised NH3 |
The log file to this structure can be found here: File:CT1216 nh3 1.log.LOG
Summary:
| Summary | ||
|---|---|---|
| Calculation Type | FREQ | |
| Calculation Method | RB3LYP | |
| Basis Set | 6-31G(d,p) | |
| Charge | 0 | |
| Spin | Singlet | |
| E(RB3LYP) | -56.55776873 a.u. | |
| RMS Gradient Norm | 0.00000485 a.u. | |
| Imaginary Freq | 0 | |
| Dipole Moment | 1.8466 | |
| Point Group | C3V | |
The item below shows that the molecule has been fully optimised:
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
Predicted change in Energy=-5.986264D-10
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.018 -DE/DX = 0.0 !
! R2 R(1,3) 1.018 -DE/DX = 0.0 !
! R3 R(1,4) 1.018 -DE/DX = 0.0 !
! A1 A(2,1,3) 105.7412 -DE/DX = 0.0 !
! A2 A(2,1,4) 105.7412 -DE/DX = 0.0 !
! A3 A(3,1,4) 105.7412 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -111.8571 -DE/DX = 0.0 !
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GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
Vibrations
From the 3N-6 rule, we expect ammonia molecule to have 6 (3*4-6) modes of vibrations (as shown using GaussView). Modes 2,3 (1693.95 cm-1) and 5,6 (3589.82 cm-1) are degenerate (have the same energy) as they resonate at the same frequency.
Modes 1 (1089.54 cm-1), 2 and 3 (1693.95 cm-1) are "bending" vibrations.
Modes 4 (3461.29 cm-1), 5 and 6 (3589.82 cm-1) are "bond stretch" vibrations.
Mode 4 (3461.29 cm-1) is highly symmetric.
Mode 1 is a symmetric bend that can be termed the "umbrella mode", as its H-N-H bending motions resemble the opening and closing of an umbrella.
At ~3500 cm-1 the absorption is due to N-H stretchings. The strong peaks at ~1700 cm-1 and ~1000 cm-1 are caused by H-N-H scissoring and N-H wagging, respectively.
Due to some closely degenerate vibrational modes, IR ratios are determined by GaussView to be 145.3814:13.5533:13.5533:1.0608:0.2711:0.2711. We would only expect to see 2 bands in the experimental spectrum of gaseous ammonia as absorption ratios 1.0608 and 0.2711 are too weak.
Analysing the IR spectra produced by Gaussview, it confirms that the literature resonates with experimental values. [1] Only two absorption peaks are observed as IR values 1.0608 and 0.2711 are relatively small. This is because the bond stretch vibrations (mode 4, 5 and 6) do not result in a large enough change in dipole moment.
Charge Analysis
We would expect N-atom to be negatively charged and H-atom to be positively charged. This is because nitrogen is more electronegative compared to hydrogen, and therefore it holds electrons tighter to its nucleus than the three hydrogen atoms. This leaves the nitrogen negatively polarised and the hydrogens positively polarised.
Haber-Bosch Process
The Haber-Bosch process is the industrial means by which nitrogen gas and hydrogen gas are converted to ammonia.
N2 + 3H2 -> 2NH3
Optimised N2 molecule
Optimised N2 |
The log file to this structure can be found here: File:CT1216 N2 OPTF POP.LOG
The N≡N bond length is 1.10550 Å and the optimised N≡N bond angle is 180°.
Summary:
| Summary | ||
|---|---|---|
| Calculation Type | FREQ | |
| Calculation Method | RB3LYP | |
| Basis Set | 6-31G(d,p) | |
| Charge | 0 | |
| Spin | Singlet | |
| E(RB3LYP) | -109.52412868 a.u. | |
| RMS Gradient Norm | 0.00000060 a.u. | |
| Imaginary Freq | 0 | |
| Dipole Moment | 0.0000 | |
| Point Group | D∞h | |
The item of N2 shows that the molecule is fully optimised:
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
Predicted change in Energy=-3.401113D-13
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1055 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
Vibrations
Vibration frequencies = 2457.33 cm-1. There are no negative frequencies, so we can conclude that optimisation was successful.
Optimised H2 molecule
Optimised H2 |
The log file to this structure can be found here: File:CT1216 H2 OPTF POP.LOG
H-H bond length is 0.74279 Å and H-H bond angle is found to be 180 °
Summary:
| Summary | ||
|---|---|---|
| Calculation Type | FREQ | |
| Calculation Method | RB3LYP | |
| Basis Set | 6-31G(d,p) | |
| Charge | 0 | |
| Spin | Singlet | |
| E(RB3LYP) | -1.17853936 a.u. | |
| RMS Gradient Norm | 0.00000017 a.u. | |
| Imaginary Freq | 0 | |
| Dipole Moment | 0.0000 | |
| Point Group | D∞h | |
The item of H2 shows that the molecule is fully optimised:
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
Predicted change in Energy=-1.164080D-13
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 0.7428 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
Vibrations
Vibration frequencies = 4465.68 cm-1. There are no negative frequencies, so we can conclude that optimisation was successful.
Determining the energy for Haber-Bosch Process
Using Hess's Law, we can determine the energy for the reaction between hydrogen gas and nitrogen gas to form ammonia gas.
N2 + 3H2 -> 2NH3
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)]
= -113.1155375-[-109.52359111+(-3.53561808)]
= -0.05579074 a.u. or -146.48 kJ/mol-1
As it is an exothermic reaction, the ammonia product is more thermodynamically stable than the gaseous reactant. The value is significantly different from literature values which shows it to be -46.11 kJ/mol-1. [2]
Cyanide anion, CN-
Molecule properties
Cyanide anion is a molecule that consists of a carbon triple bonded to a nitrogen atom with a formula CN-. The bond lengths and angles have been investigated after the optimisation had been performed: the optimised C≡N bond distance is 1.18409 Å and its optimised bond angle is 180° (linear).
The jmol file shown below is an optimised structure of CN-:
Optimised CN- |
The log file of this structure can be found here: File:CT1216 CN OPTF POP.LOG
Summary:
| Summary | ||
|---|---|---|
| Calculation Type | FREQ | |
| Calculation Method | RB3LYP | |
| Basis Set | 6-31G(d,p) | |
| Charge | -1 | |
| Spin | Singlet | |
| E(RB3LYP) | -92.82453513 a.u. | |
| RMS Gradient Norm | 0.00000704 a.u. | |
| Imaginary Freq | 0 | |
| Dipole Moment | 0.5236 Debye | |
| Point Group | Cv | |
The item of cyanide anion below shows that is has been fully optimised:
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
Predicted change in Energy=-6.593000D-11
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1841 -DE/DX = 0.0 !
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GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
Vibrations
As CN anion adopts a linear conformation, it is subjected to 3N-5 rule. From this, we expect the ion to have 3(2)-5= 1 vibration, which resonates with the result calculated using GaussView. C≡N bond is calculated to absorb at a frequency of 2139.19 cm-1 which is within the literature range of 2210-2260 cm-1 [3] . The frequency that characterizes the stretching vibration of a C≡N bond is proportional to the bond dissociation energy, therefore we can conclude that C≡N triple bond strength is relatively strong.
Diagram below shows the IR spectrum of CN anion:
As predicted, only 1 peak is observed. The mode is IR active as it gives rise to a change in dipole moment.
Charges
Both atoms are negatively charged, C(-0.246) and N(-0.754). Taking into account that the formal charge of a cyanide anion is -1, charges on polyatomic molecules is almost never localized on a single atom, and is typically spread over part of the molecule. As nitrogen is more electronegative than carbon, there is a slightly higher electron density around nitrogen compared to carbon.
Molecular Orbitals
The first 12 molecular orbitals have been modelled using the software Gaussian. I have taken 5 orbitals to investigate further.
The electronic configuration of carbon and nitrogen is 1s2 2s2 2p2 and 1s2 2s2 2p3 respectively. When the carbon and nitrogen triple bond to form a cyanide anion, it is actually the atomic orbitals combining to form molecular orbitals.
I have omitted the explanation for the 1st and 2nd molecular orbitals which arise from the combination of the 1s atomic orbitals of C and N. They are both so deep in energy (-14.00393 and -9.8672) that they do not significantly contribute to the overall bonding of the cyanide ion.
Below shows the 3rd and 4th molecular orbital of cyanide ion, which is the result of an overlap of 2s valance orbitals from carbon and nitrogen. Both MO formed are occupied with electrons. The molecular orbitals are much higher in energy than the first two, hence they play a significant role contributing to the overall bonding.
When the 2s atomic orbitals combine in-phase, a bonding molecular orbital forms. The overlap of the atomic orbitals is so extensive that it almost appears to have a spherical orbital shape. It is a σ molecular orbital and has an energy of -0.56195.
However, when the 2s atomic orbitals combine out-of-phase, an anti-bonding molecular orbital results. It is a σ* molecular orbital and has an energy of -0.10626.
Diagrams above shows the 5th and 6th molecular orbitals which are degenerate. As observed, there are two p orbitals on C and N that are perpendicular to the bond, therefore both bonding orbitals formed are of the exact same energy (-0.01696). As the molecular orbital involves the p orbitals of C and N, the result is a π-bond.
The 7th molecular orbital is the last occupied one, so it is the HOMO. Remember that the cyanide ion has a formal charge of -1, so an extra electron is added to pair with the electron involved in the σ bond. It is a bonding orbital and has an energy of +0.01857, significantly higher than the previous molecular orbitals.
The 8th molecular is the first unoccupied one hence it is termed the LUMO. It is an overall anti-bonding orbital and results from the out-of-phase combination of the π orbitals of C and N. Its energy is +0.35435.
References
- ↑ http://iopscience.iop.org/article/10.1088/0022-3700/5/2/038/pdf
- ↑ Atkins' Physical Chemistry (10th Edition), Peter Atkins and Julio de Paula, Published by Oxford, 2014
- ↑ http://www2.ups.edu/faculty/hanson/Spectroscopy/IR/IRfrequencies.html