Rep:Mod:SFOIA3009
NH3 molecule
Summary of Results
- N-H bond distance = 1.018 Å
- H-N-H bond angle = 105.74°
- Molecule name: Ammonia
- Calculation method: RB3LYP
- Basis set: 6-31G(d,p)
- Final energy E(RB3LYP) in atomic units: -56.55776873 au
- RMS Gradient Norm: 0.00000485 au
- Point group of molecule: C3V
The experimentally determined value of the N-H bond in ammonia is 1.012 Å, which is comparable to the computed value in this report. Moreover, the H-N-H bond angle as per literature is 106.67°, which is close to the computerised value determined here.[1]
Figure 1. Ammonia molecule |
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
Gaussview performs optimisations of molecules by finding the optimum bond lengths and angles that would result in no overall force in the molecule, as well as yield the lowest possible energy and hence the most stable and most likely conformation of the molecule. Gaussview initiates the optimisation process using the input bond length value declared (or set by the software by default) and reccurently varies the distance between nuclei until the potential energy reaches a minimum. This corresponds to the equilibrium positions of the atoms in the bond. To assess whether the optimisation has reached completion it is necessary to verify whether the maximum force (table above) is close to zero, as this suggests that the system is at its most stable state.
The output text file for the optimised molecule can be found here.
Frequency Analysis
The 3N-6 rule dictates that any molecule with N atoms will have 3N-6 vibrational modes. The ammonia molecule (which has four atoms), wold therefore be expected to have 3*4-6 = 6 normal modes of vibration. Out of these, modes 2,3 (vibrational frequency 1693.95) are degenerate and 5,6 (vibrational frequency 3589.82) respectively. Mode numbers 1,2,3 (vibrational frequences 1089.54, 1693.95, 1693.95) are bending vibrations whilst modes 4,5,6 are bond-stretch vibrations. The mode that is highly symmetric is vibration number 4, i.e. frequency 3461.29). Moreover, bending vibrational mode 1 is also called the ''umbrella'' mode. The experimental spectrum of ammonia would only display two bands. These are represented by the infrared amplitudes on 145.3814 (vibrational mode 1) and 13.5533 (vibrational modes 2 and 3, which are degenerate and therefore appear on the spectrum as a single band).
Charge analysis
Charge on the N-atom: -1.125
Charge on the H-atom: +0.375
The expected charge for the nitrogen atom is partially negative whereas the charge of the hydrogen atom should be partially positive due to the electronegativity difference between the two atoms, which is not high enough to give the atoms full charges. This is also reflected in the covalent character of the N-H bonds. The N atom has a higher affinity for electrons, hence rendering its partially negative charge and to H its partially positive charge.
N2
Summary of Results
- N-N bond distance = 1.106 Å
- Molecule name: Nitrogen
- Calculation method: RB3LYP
- Basis set: 6-31G(d,p)
- Final energy E(RB3LYP) in atomic units: -109.52412868 au
- RMS Gradient Norm: 0.00000015 au
- Point group of molecule: D∞
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 output text file for the optimised N2 molecule can be found here.
Frequency Analysis
H2
Summary of Results
- H-H bond distance = 0.743 Å
- Molecule name: Hydrogen
- Calculation method: RB3LYP
- Basis set: 6-31G(d,p)
- Final energy E(RB3LYP) in atomic units (au): -1.17853930
- RMS Gradient Norm: 0.00012170 au
- Point group of molecule: D∞
Item Value Threshold Converged? Maximum Force 0.000211 0.000450 YES RMS Force 0.000211 0.000300 YES Maximum Displacement 0.000278 0.001800 YES RMS Displacement 0.000393 0.001200 YES
The output text file for the optimised H2 molecule can be found here.
Frequency Analysis
Determination of energy change of reaction N2 + 3H2 -> 2NH3
E(NH3)= -56.55776873 au
2*E(NH3)= -113.11553746 au
E(N2)= -109.52412868 au
E(H2)= -1.17853930 au
3*E(H2)= -3.5356179 au
ΔE = 2*E(NH3)-[E(N2)+3*E(H2)] = -113.11553746 - (-109.52412868 - 3.5356179) = -0.05579088 au
ΔE = 2625.5*(-0.05579088) = -146.4789554 kJ/mol
The ammonia product is more stable. The reaction is exothermic hence energy is released when the gases react together, making ammonia more thermodynamically favourable.
Project molecule: ClF3
Summary of results
- Cl-Faxial bond distance = 1.729 Å
- Cl-Fequatorial bond distance = 1.651 Å
- Faxial-Cl-Fequatorial bond angle = 87.14°
- Faxial-Cl-Faxial bond angle = 174.3°
- Molecule name: Chlorine trifluoride
- Calculation method: RB3LYP
- Basis set: 6-31G(d,p)
- Final energy E(RB3LYP) in atomic units: -759.46531688 au
- RMS Gradient Norm: 0.00002465 au
- Point group of molecule: C2V
Figure 5. Chlorine trifluoride |
The literature found values for the axial fluorine - chlorine and the equatorial fluorine - chlorine bonds are 1.698 Å and 1.598 Å respectively. Moreover, the Faxial-Cl-Fequatorial bond angle was found to be 87.48°, which is comparable to the computed value displayed in this report.[2]
Item Value Threshold Converged? Maximum Force 0.000050 0.000450 YES RMS Force 0.000028 0.000300 YES Maximum Displacement 0.000204 0.001800 YES RMS Displacement 0.000134 0.001200 YES
As per the Item table presented above, the maximum force in the optimised molecule is close to zero. This suggests that the optimisation process went to completion as the atoms in the molecule are at their equilibrium state.
The output text file for the optimised ClF3 molecule can be found here.
Frequency analysis
Vibrational frequency is related to the second order derivative of the potential energy vs internuclear distance plot. Therefore, negative frequencies would suggest either the presence of a maximum or a concave curve, hence showing that the system has not reached the minimum of the potential well. Consequently, this would infer that the molecule was not successfully optimised. The fact that all the frequencies displayed in Figure 6 are positive values reinforces that the optimisation of the molecule reached completion.
According to the 3N-6 rule, ClF3 is expected to display 6 vibrations, as shown in Figure 6. However, none of the vibrational modes found for this molecule are degenerate. The experimental spectrum of ClF3 would display four bands (vibrational modes 1,2,5,6). The 3rd and 4th modes would not be displayed as their signals are not strong enough to be detected.
Charge analysis
Charge on the Cl-atom: +1.225
Charge on the equatorial F-atom: -0.316
Charge on the axial F-atom: -0.454
Fluorine is more electronegative than chlorine, so it would be expected for its charge to be more negative than that of Cl, as confirmed by the computationally predicted values reported here.
Molecular Orbitals of ClF3
The MO presented in Figure 7 is a bonding molecular orbital formed from s AOs from the chlorine and the three fluorine atoms. It is occupied by a pair of spin-opposed electrons and it is relatively high in energy compared to lower-lying orbitals, such as the non-bonding MOs coming from 1s atomic orbitals of the three atoms in the molecule. The MO displayed above would be lower in energy than its component atomic orbitals, hence contributing to the stability of the molecule and to bonding.
Figure 8 depicts a MO consisting of a mixture of both bonding and antibonding MOs. s orbitals from the axial fluorine atoms and the chlorine form bonding interactions whereas s orbitals from the equatorial fluorine and the chlorine respectively contribute to a molecular antibonding interaction. The molecular orbital showed in the figure is moderately high in energy and is fully occupied. The bonding interaction encompassed by the MO presented would contribute to the bonding of molecule whereas the antibonding interaction would contribute to the breakdown of the Cl-Fequatorial bond.
The AOs that contribute to the formation of the molecular orbital presented in the figure below are s orbitals on the Cl and F atoms. The MO shown is fully occupied and of antibonding type, being relatively high in energy. The overall effect of this σ* orbital would be towards the breaking of all the bonds comprised in the molecule.
Figure 10 shows a π (bonding) orbital formed by the p orbitals on all the component atoms in the considered molecule. The MO is shallow in energy, suggesting that the position of its electron cloud is further away from the nuclei compared to deeper in energy orbitals, like the one depicted in Figure 2. The molecular orbital is fully occupied and its effect would be to contribute to the lowering in energy and bonding state of the molecule.
Figure 11 below displays the π* (antibonding) orbital comprised from p orbitals on Cl and the three F atoms in the molecule. The MO orbital presented here is the HOMO (highest occupied molecular orbital) of the molecule, and it contains two spin-paired electrons. The effect of this molecular orbital would be to increase the energy of the molecule, hence decreasing its stability and raising its likelihood to break down.
F2
Summary of Results
- F-F bond distance = 1.403 Å
- Molecule name: Fluorine
- Calculation method: RB3LYP
- Basis set: 6-31G(d,p)
- Final energy E(RB3LYP) in atomic units: -199.49825218 au
- RMS Gradient Norm: 0.00007365 au
- Point group of molecule: D∞
Figure 12. Fluorine |
Item Value Threshold Converged? Maximum Force 0.000128 0.000450 YES RMS Force 0.000128 0.000300 YES Maximum Displacement 0.000156 0.001800 YES RMS Displacement 0.000221 0.001200 YES
The output text file for the optimised F2 molecule can be found here.
Frequency Analysis
Charge analysis
Charge on the F-atoms: 0.000
Cl2
Summary of Results
- Cl-Cl bond distance = 2.042 Å
- Molecule name: Chlorine
- Calculation method: RB3LYP
- Basis set: 6-31G(d,p)
- Final energy E(RB3LYP) in atomic units: -920.34987886 au
- RMS Gradient Norm: 0.00002511 au
- Point group of molecule: D∞
Item Value Threshold Converged? Maximum Force 0.000043 0.000450 YES RMS Force 0.000043 0.000300 YES Maximum Displacement 0.000121 0.001800 YES RMS Displacement 0.000172 0.001200 YES
The output text file for the optimised Cl2 molecule can be found here.
Frequency Analysis
Charge analysis
Charge on the Cl-atoms: 0.000
As Cl2 is a homoatomic molecule, the electronegativity difference between its component atoms is close to zero, hence none of them have a charge.
Determination of energy change of reaction 3F2 + Cl2->2ClF3
E(ClF3)= -759.46531688 au
2*E(ClF3)= -1518.930634 au
E(F2)= -199.49825218 au
E(Cl2)= -920.34987886 au
3*E(F2)= -598.4947565 au
ΔE = 2*E(ClF3)-[E(Cl2)+3*E(F2)] = -1518.930634 - (-920.34987886 - 598.4947565) = -0.0859984 au
ΔE = -225.7887992 kJ/mol
The chlorine trifluoride product is more stable than the reactants. The formation ClF3 of is exothermic. Therefore, the energy of the system is lowered as the reaction progresses, making ClF3 the thermodynamical product of the reaction.
References
- ↑ 2. Summary Tables of Calculated and Experimental Parameters of Diatomic, Triatomic, Organic, Silicon, Boron, Aluminium and Organometallic Molecules, Exemplary Results on Condensed Matter Physics, One-Through Twenty-Electron Atoms, Excited States of Helium, g Factor, and Fundamental Particle Masses [Internet]. Millsian. 2017 [cited 24 March 2017]. Available from: http://www.millsian.com/summarytables/SummaryTables022709S.pdf
- ↑ Smith D. The Microwave Spectrum and Structure of Chlorine Trifluoride. The Journal of Chemical Physics. 1953;21(4):609-614.