Rep:Mod:IMM2RWL4015
Computational Analysis of an Ammonia Molecule, NH3
Optimising the NH3 Molecule
The following commands were used to calculate the optimal NH3 structure using Gaussian:
| Calculation Type | OPTF |
|---|---|
| Calculation Method | B3LYP |
| Basis Set | 6-31G(d,p) |
The following information about the optimised NH3 molecule was found using the "Summary" window and the "Inquire" tool in GaussView. Experimentally determined values for the N-H bond distance and the H-N-H bond angle were also found and added to the table below:
 | |
| Final Energy, E(RB3LYP) (au) | -56.55776873 |
|---|---|
| RMS Gradient (au) | 0.00000485 |
| Point Group | C3V |
| Optimised N-H Bond Distance (Å) | 1.01798 |
| Experimental N-H Bond Distance (Å) | 1.012[1] |
| Optimised H-N-H Bond Angle (°) | 105.741 |
| Experimental H-N-H Bond Angle (°) | 106.7[1] |
From the "Item" table for the lowest energy molecule shown below, it can be seen that optimisation of the molecule has been performed successfully, with all forces and displacements having converged.
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 link to the *.log file from which the "Item" table is taken is here.
A Jmol dynamic image has been added below to allow the optimised structure of NH3 to be visualised in 3D and magnified and rotated.
Optimised ammonia molecule |
Vibrational Analysis of the NH3 Molecule
The following vibrational modes and their corresponding frequencies and intensities were found for the optimised NH3 molecule:
The absence of any negative frequency values is further evidence that the obtained structure is the fully optimised, lowest energy one.[2]
Using the 3N-6 rule for non-linear molecules, I would expect NH3 to have 6 modes of vibration as 3(4)-6 = 6.[3] The "Display Vibrations" window shows that modes 2 and 3, and 5 and 6 are degenerate, with each pair having the same frequency and therefore the same energy.[3] The vibration animations show that modes 1-3 are "bending" vibrations, while modes 4-6 are "bond stretch" vibrations.[4] Mode 4 in particular vibrates in a highly symmetric manner and mode 1 is known as the "umbrella" mode due to the way this bending vibration occurs and the appearance of the molecule as a result. As the molecule has 4 distinct vibrational modes with different energies, you would expect to see 4 bands in an experimental spectrum of gaseous ammonia, with absorptions occurring at 4 different wavenumbers.[4]
Atomic Charge Analysis of the NH3 Molecule
Since nitrogen is more electronegative than hydrogen (χP values for N and H are 3.04 and 2.20 respectively), I would expect the nitrogen atom to attract electron density in the N-H covalent bonds towards itself, making it negatively charged and leaving the hydrogen atoms positively charged.[5]
The distribution of charge across the NH3 molecule is illustrated below, with charge values for the individual atoms also displayed in the table below.
| Atom | Charge |
|---|---|
| N | -1.125 |
| H | 0.375 |
The overall charge on the molecule is zero and so the charges on the individual atoms must total zero.
Investigating the Haber-Bosch Process
Computational methods are extremely useful in predicting the energy of a reaction and therefore whether the energy is likely to be endothermic or exothermic and how readily it is likely to occur.[6] Here, the reaction between nitrogen gas, N2, and hydrogen gas, H2, to form ammonia, NH3, as part of the Haber-Bosch process is investigated using the previously optimised NH3 molecule and optimising N2 and H2 molecules.
Optimisation Procedure for N2 and H2
The optimised structures of N2 and H2 were obtained using the same commands in Gaussian as for NH3:
| Calculation Type | OPTF |
|---|---|
| Calculation Method | B3LYP |
| Basis Set | 6-31G(d,p) |
Nitrogen, N2
Optimising the N2 Molecule
The following information about the optimised N2 molecule was found:
 | |
| Final Energy, E(RB3LYP) (au) | -109.52412868 |
|---|---|
| RMS Gradient (au) | 0.00000060 |
| Point Group | D∞h |
| Optimised N≡N Bond Distance (Å) | 1.10550 |
The molecule has been optimised successfully, with the "Item" table for the lowest energy molecule indicating that all forces and displacements have converged.
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
The link to the *.log file from which the "Item" table is taken is here.
A Jmol dynamic image has been added below to allow the optimised structure for N2 to be visualised in 3D and magnified and rotated.
Optimised nitrogen molecule |
Vibrational Analysis of the N2 Molecule
As expected using the 3N-5 rule for linear molcules, a single vibrational mode was found for the optimised N2 molecule:[3]
Again, the absence of any negative frequency values provides further evidence of a fully optimised, lowest-energy structure.[2] Note that the infrared intensity value for the vibration is zero due to N2 being homonuclear and symmetric and therefore not having a dipole moment and being IR inactive.[5]
Hydrogen, H2
Optimising the H2 Molecule
The following information about the optimised H2 molecule was found:
 | |
| Final Energy, E(RB3LYP) (au) | -1.17853936 |
|---|---|
| RMS Gradient (au) | 0.00000017 |
| Point Group | D∞h |
| Optimised H-H Bond Distance (Å) | 0.74279 |
The molecule has been optimised successfully, with the "Item" table for the lowest energy molecule indicating that all forces and displacements have converged.
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 link to the *.log file from which the "Item" table is taken is here.
A magnifiable and rotatable Jmol dynamic image of the optimised H2 structure in 3D is shown below:
Optimised hydrogen molecule |
Vibrational Analysis of the H2 Molecule
As with N2, the 3N-5 rule for linear molcules predicts a single vibrational mode for the optimised H2 molecule:[3]
Since the frequency is positive, the optimisation process has been successful.[2] Again, the absence of a dipole moment results in an infrared intensity of zero.[5]
Determining the Energy of the Haber-Bosch Process
The following energy values were used to calculate the energy for the reaction between nitrogen and hydrogen gas to form ammonia, N2 (g) + 3H2 (g) → 2NH3 (g) :[7]
| Energy, E(RB3LYP) (au) | |
|---|---|
| E(NH3) | -56.55776873 |
| 2E(NH3) | -113.1155375 |
| E(N2) | -109.52412868 |
| E(H2) | -1.17853936 |
| 3E(H2) | -3.53561808 |
| ΔE | -0.05579074 |
Note that ΔE = 2E(NH3) - [E(N2) + 3E(H2)].[2]
The energy difference, ΔE, can be expressed in kJ mol-1 as follows:
ΔE = -0.05579074 au × 2625.5 = -146.48 kJ mol-1
A negative ΔE value indicates that the reaction is exothermic and so the release of energy results in the ammonia, NH3 product being energetically more stable than the hydrogen, H2 and nitrogen, N2 reactants from which it is formed.[3]
Computational Analysis of a Cyanide Anion, CN-
Optimising the CN- Anion
The following commands were used to calculate the optimised CN- structure using Gaussian:
| Calculation Type | OPTF |
|---|---|
| Calculation Method | B3LYP |
| Basis Set | 6-31G(d,p) |
The following information about the optimised CN- anion was found using the "Summary" window and the "Inquire" tool in GaussView:
 | |
| Final Energy, E(RB3LYP) (au) | -92.82453153 |
|---|---|
| RMS Gradient (au) | 0.00000704 |
| Point Group | C∞v |
| Optimised C≡N Bond Distance (Å) | 1.18409 |
As shown by the "Item" table below, the forces and the displacements are converged. Optimisation has therefore been successful.
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
The link to the *.log file from which the "Item" table is taken is here.
A Jmol dynamic image of the optimised structure of CN- can be found below:
Optimised cyanide anion |
Vibrational Analysis of the CN- Anion
The following vibrational modes and their corresponding frequencies and intensities were found for the optimised CN- molecule:
The presence of only 1 vibrational mode matches the prediction from the 3N-5 rule for linear molecules.[3]
The absence of any negative frequency values is again evidence that the obtained structure is the fully optimised, lowest energy one.[2] There is also a non-zero intensity as CN- is heteronuclear and asymmetric and so has a dipole moment.[5]
Atomic Charge Analysis of the CN- Anion
Since nitrogen is more electronegative than carbon, I would expect the nitrogen atom to attract electron density in the C≡N covalent bonds towards itself, making it negatively charged and leaving the hydrogen atoms positively charged.[5]
The distribution of charge across the CN- anion is illustrated and the charge values for the individual atoms are tabulated below:
| Atom | Charge |
|---|---|
| C | -0.246 |
| N | -0.754 |
Since the overall charge on the anion is -1, the individual charges must add up to -1.
Molecular Orbital Analysis of the CN- Anion
The shapes and energies of the molecular orbitals of the CN- anion were investigated using GaussView.
The energies for the first 12 molecular orbitals CN- are displayed below:
| MO | Energy (au) | Electrons |
|---|---|---|
| 1 | -14.00393 | ↿⇂ |
| 2 | -9.86720 | ↿⇂ |
| 3 | -0.56195 | ↿⇂ |
| 4 | -0.10626 | ↿⇂ |
| 5 | -0.01696 | ↿⇂ |
| 6 | -0.01696 | ↿⇂ |
| 7 | 0.01859 | ↿⇂ |
| 8 | 0.35435 | |
| 9 | 0.35435 | |
| 10 | 0.59206 | |
| 11 | 0.84601 | |
| 12 | 0.84601 |
The shapes of 5 CN- molecular orbitals are depicted below:
| MO Number | 3 | 4 | 5 | 7 | 8 |
|---|---|---|---|---|---|
| Image from GaussView |  |
 |
 |
 |
 |
Molecular orbital 3 (3σ) is occupied by a pair of electrons and is formed from the overlap of the 2s atomic orbitals, which are both in the same phase, on the carbon and the nitrogen atoms. Note that the nitrogen atom has a greater electron density around it due to its greater electronegativity relative to carbon as well as the decreased Zeff due to the extra electron on the carbon atom.[5] Although this MO is a combination of valence AOs, it sits deep in energy, indicated by a negative energy value.
Molecular orbital 4 (4σ*) is also occupied by a pair of electrons. However, since the two atomic orbitals are out-of-phase and destructive interference occurs,, indicated by the differently coloured electron density clouds, the MO is the σ* antibonding orbital and has a higher energy.[5] Again, the electron density is skewed towards the more electronegative nitrogen atom and the extra electron associated with the carbon atom.
Molecular orbital 5 (1π) is formed from the in-phase overlap of the occupied 2p atomic orbitals, with the same orientation, on the carbon and nitrogen atoms, resulting in constructive the formation of a π-bond.[5] Note that the AOs are both perpendicular to the bond formed. The overlapping AOs are larger and so the electrons are further from the nuclei, hence a higher energy.
Molecular orbital 7 (5σ) is the highest occupied molecular orbital, HOMO, and has a distorted shape due to mixing and is the bonding molecular orbital formed by the overlap of the 2p atomic orbitals parallel to the σ-bond formed.[2]
Molecular orbital 8 (2π*) is the lowest unoccupied molecular orbital, LUMO, and is the π* antibonding orbital formed by the out-of-phase overlap of the perpendicular 2p orbitals.[5] This MO has the highest energy of the MOs discussed here.
Computational Analysis of a Borohydride Ion, BH4-
Optimising the BH4- Anion
The following commands were used to calculate the optimised BH4- structure using Gaussian:
| Calculation Type | OPTF |
|---|---|
| Calculation Method | B3LYP |
| Basis Set | 6-31G(d,p) |
The following information about the optimised BH4- anion was found using the "Summary" window and the "Inquire" tool in GaussView:
 | |
| Final Energy, E(RB3LYP) (au) | -27.24992701 |
|---|---|
| RMS Gradient (au) | 0.00000671 |
| Point Group | Td |
| Optimised B-H Bond Distance (Å) | 1.23933 |
| Optimised H-B-H Bond Angle (°) | 109.471 |
As shown by the "Item" table below, convergence has occurred for all parameters and so optimisation has been successful.
Item Value Threshold Converged? Maximum Force 0.000013 0.000450 YES RMS Force 0.000007 0.000300 YES Maximum Displacement 0.000065 0.001800 YES RMS Displacement 0.000035 0.001200 YES
The link to the *.log file from which the "Item" table is taken is here.
A Jmol dynamic image of the optimised BH4- structure can be found below:
Optimised borohydride anion |
Vibrational Analysis of the BH4- Anion
Borohydride is formed of 5 atoms. According to the 3N-6 rule, I would expect there to be 9 vibrational modes.[3]
The following vibrational modes and their corresponding frequencies and intensities were found for the optimised BH4- anion:
All the frequency values are positive and so BH4- has been successfully optimised.[2] The tetrahedral structure results in BH4- being symmetrical and therefore not having a dipole moment.[5] As observed, the symmetrical vibrational modes therefore have an infrared intensity of zero.
Atomic Charge Analysis of the BH4- Anion
Since boron is much more electronegative than hydrogen, a large proportion of the electron density would be attracted towards the boron atom, resulting in it having a greater negative charge than the hydrogen atoms.[5]
The distribution of charge as well as the charge values associated with the individual atoms making up the BH4- anion are shown below.
| Atom | Charge |
|---|---|
| B | -0.615 |
| H | -0.096 |
Again, the overall charge on the anion is -1 and so the total charge that can be distributed across the individual atoms is -1.
Molecular Orbital Analysis of the BH4- Anion
The shapes and energies of the molecular orbitals of the BH4- anion were investigated using GaussView.
The energies for the first 12 molecular orbitals of BH4- are displayed below:
| MO | Energy (au) | Electrons |
|---|---|---|
| 1 | -6.42128 | ↿⇂ |
| 2 | -0.22587 | ↿⇂ |
| 3 | -0.03183 | ↿⇂ |
| 4 | -0.03183 | ↿⇂ |
| 5 | -0.03183 | ↿⇂ |
| 6 | 0.41617 | |
| 7 | 0.41617 | |
| 8 | 0.41617 | |
| 9 | 0.43601 | |
| 10 | 0.67306 | |
| 11 | 0.67306 | |
| 12 | 0.67306 |
The shapes of 5 BH4- molecular orbitals are depicted below:
| MO Number | 1 | 2 | 3 | 4 | 9 |
|---|---|---|---|---|---|
| Image from GaussView |  |
 |
 |
 |
 |
Molecular orbital 1 is very deep in energy, having an extremely large negative energy in comparison to the other molecular orbitals. Since the pair of electrons in this very small orbital take no part in bonding and are held very tightly to the boron atom, with no overlap with the orbitals of the hydrogen atoms, this MO is described as non-bonding.[5]
Molecular orbital 2 (σg) is a bonding orbital occupied by a pair of electrons and is formed from the overlap of the 2s orbital on the central boron atom with the 1s orbitals of the hydrogen atoms to form 4 sigma bonds.[5]
Molecular orbitals 3 and 4 (σg) are also bonding orbitals occupied by electrons but in this case are formed from the overlap of the 2p orbital on the boron atom and the 1s orbitals of the hydrogen atoms and have a slightly higher energy than molecular orbital 2. The two orbitals have the same shape, being formed by the 2p orbital in different orientations and so are degenerate, being 2 of the 3 degenerate MOs for each of the 3 possible orientations of the 2p atomic orbital.[5] The different phases on the p orbital and the bonding nature of the MO gives rise to the formation of a nodal plane through the centre of the boron atom.[5]
Molecular orbital 9 (σg*) is very high in energy, having a positive value, and is therefore unoccupied. This MO is the antibonding MO that corresponds to molecular orbital 1 and is the result of the out-of-phase overlap of the 2s atomic orbital on boron and the 1s orbitals on the 4 hydrogen atoms, with all 4 hydrogen AOs having the same phase in this case.
References
- ↑ 1.0 1.1 M. R. Chacon-Taylor and M. I. McCarthy, J. Phys. Chem., 2011, 115, 7610-7616.
- ↑ 2.0 2.1 2.2 2.3 2.4 2.5 2.6 Hunt Research Group, http://www.huntresearchgroup.org.uk/teaching/year1_lab_start.html, (accessed March 2017).
- ↑ 3.0 3.1 3.2 3.3 3.4 3.5 3.6 P. Atkins and J. de Paula, Elements of Physical Chemistry, Oxford University Press, Oxford, 7th edn., 2017.
- ↑ 4.0 4.1 Chemguide, http://www.chemguide.co.uk/analysis/ir/background.html, (accessed March 2017).
- ↑ 5.00 5.01 5.02 5.03 5.04 5.05 5.06 5.07 5.08 5.09 5.10 5.11 5.12 5.13 5.14 D. Shriver et al., Inorganic Chemistry, Oxford University Press, Oxford, 6th edn., 2014.
- ↑ Y. Lan et al., J. Phys. Chem. A, 2011, 115, 13906-13920.
- ↑ T. Kandemir et al., Angew. Chem. Int. Ed., 2013, 52, 12723-12726.