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Project Molecule Analysis

The molecules were created using a program called gaussview. Optimisation is carried out on each molecule to ensure the information obtained is as accurate as possible. The energy , charge distribution, molecular structure, bond vibration and molecular orbitals are analysed and discussed.

NH3 molecule

Key Information

The molecules were created and their main properties were observed and analysed using program called gaussview. Optimisation is carried out on each molecule to ensure the information obtained is as accurate as possible.

Gaussian Calculation Summary

Calculation Method = RB3LYP

Basis Set = 6-31G(d,p)

E(RB3LYP) = -56.55776873 a.u.

RMS Gradient Norm = 0.00000176 a.u.

Point Group = C3V

Bond Length of N-H = 1.01798 Angstrom(Å)

Bond Angle of H-N-H = 105.741°


Item Table


         Item               Value     Threshold  Converged?
 Maximum Force            0.000003     0.000450     YES
 RMS     Force            0.000002     0.000300     YES
 Maximum Displacement     0.000028     0.001800     YES
 RMS     Displacement     0.000017     0.001200     YES
 Predicted change in Energy=-1.261292D-10
 Optimization completed.

    -- Stationary point found.
                           


Image of the molecule

Ammonia

Click here for optimisation file.


Display Vibration Window


IR Analysis

From 3N-6 rule, 6 modes are expected from NH3 vibration (N=4)

From the display vibration window, it is observed that there are two degenerate sets of vibration which are mode 2 and 3 as one set and mode 4, 5, and 6 as the other set.

Bending Vibration : mode 1, 2, 3

Stretching Vibration : mode 4, 5, 6

Highly Symmetric Vibration : mode 4

Umbrella Mode : mode 1

In experimental spectrum of gaseous ammonia, only 2 bands are expected to be observed. This is because the intensity of vibration mode 4, 5, and 6 are too low to be detected due to small change in dipole during vibration. Among the detected mode 1, 2, and 3, mode 2 and 3 have similar frequency thus they only show as one band.


IR Spectrum of Molecule


Charge Analysis

Charge on nitrogen(N): -1.125

Charge on hydrogen(H): 0.375

Nitrogen is a more electronegative species compared to hydrogen. Hence, N attracts the electron densities towards itself causing it has slightly negative in charge, leaving the three hydrogen atoms with delta positive charges.


Charges in NH3.


Optimised H2 Molecule

Key Information

Gaussian Calculation Summary

Calculation Method = RB3LYP

Basis Set = 6-31G(d,p)

E(RB3LYP) = -1.17853936 a.u.

RMS Gradient Norm = 0.00000017 a.u.

Point Group = D∞h

Bond Distance of H-H = 0.74279 Å

Bond Angle of H-H = 180°


Item Table

         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.


Image of Molecule

Hydrogen

Click here for optimisation file.

Frequency of H2

The H2 single bond vibration is 4465.68 cm-1. This vibration is IR inactive as there is no change of dipole moment between two similar atoms during bond vibration.


Optimised N2 Molecule

Key Information

Gaussian Calculation Summary

Calculation Method = RB3LYP

Basis Set = 6-31G(d,p)

E(RB3LYP) = -109.52412868 a.u.

RMS Gradient Norm = 0.00000060 a.u.

Point Group = D∞h

Bond Length of N2 = 1.10550 Å

Bond Angle = 180°


Item Table

         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=-3.401023D-13
 Optimization completed.
    -- Stationary point found.


Image of Molecule

Nitrogen

Click here for optimisation file.


Frequency of N2

The N2 single bond vibration is 2457.33 cm-1. This vibration is IR inactive as there is no change of dipole moment between two similar atoms during bond vibration.


Haber-Bosch process

Energy for the reaction of N2 + 3H2 -> 2NH3

E(NH3)= -56.55776873 a.u.

2*E(NH3)= -113.11553746 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)]= -0.0557907 a.u. / -146.82 kJmol-1

Conclusion: The reaction is exothermic as heat energy is released (negative delta E), thus the ammonia product is more stable compared to the gaseous reactants.


Molecule of My Choice : Carbon Monoxide ( CO )

Key Information

Gaussian Calculation Summary

Calculation Method = RB3LYP

Basis Set = 6-31G(d,p)

E(RB3LYP) = -113.30945314 a.u.

RMS Gradient Norm = 0.00000433 a.u.

Point Group = C∞v

Bond Length of CO Triple Bond = 1.13794 Å

Bond Angle of CO = 180° (linear molecule)


Item Table

         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
 Predicted change in Energy=-2.221220D-11
 Optimization completed.
    -- Stationary point found.


Image of the molecule

Carbon Monoxide

Click here for optimisation file.

IR Analysis

From 3N-6 rule, 1 modes are expected from CO triple bond vibration (N=2).

It is observed that there is only one vibration mode available for the CO molecules as it is linear and diatomic.

The vibrational frequency is 2209.01 cm-1 which results from the stretching of bond.


IR Spectrum of Molecule

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Charge Analysis

Charge on Carbon(C): 0.506

Charge on Oxygen(O): -0.506

Oxygen is a more electronegative species compared to hydrogen. Hence, O attract the electron densities towards itself causing it has slightly negative in charge, leaving the carbon with a delta positive charge.


Charges in CO



Molecular Orbital of CO[1]

A MO diagram of carbon monoxide.

From the MO diagram, it is observed that the energy level of 2p σ MO is higher than the two degenerate π bonds. This is because of the mixing of 2s σ and 2p σ which is closed in energy.


Image of the Molecular Orbital

Sigma bond (σ) between 2s orbitals of C and O.

The potential energy of 2s σ MO is -1.15790.

From diagram, it is shown that there is an uneven distribution of electron density between C and O. Since oxygen(O) is more electronegative than carbon, its 2s atomic orbital is located at lower energy level. Thus, O has higher contribution in the sigma bonding MO and it hold greater proportion of electron density.


Sigma* bond (σ*) between 2s orbitals of C and O.

The potential energy of 2s σ* MO is -0.57004.

In the 2s σ* MO, the uneven distribution of electron density between C and O can also be explained due to the difference in atomic orbitals energy levels of C and O. Carbon(C) is less electronegative than carbon, its 2s atomic orbital is located at higher energy level. Thus, C contributes more in the higher energy sigma* bonding MO and it hold greater proportion of electron density.

Cartesian Plane[2]

Cartesian plane to view the orientation of 2px, 2py, 2pz atomic orbitals.


Pi bond (π) between 2p orbitals of C and O.

The potential energy of 2p π MO is -0.46742.

There are 2 π bond formed in the CO molecules due to the side way overlaps of 2 sets of 2p orbitals from C and O, the 2p orbital must be in correct orientation (example : px with px) to overlap. The energy of the two 2π orbitals are degenerates ( see diagram MO energy 5 and 6). The two π MO are orthogonal to each other according to cartesian plane.


This is the 2p sigma (σ) bond which is also the HOMO of CO.

The potential energy of 2p σ MO is -0.37145.

This is the σ bond formed from the heads on overlap between two 2p atomic orbitals from C and O with correct orientation in phase. HOMO stands for highest occupied molecular orbital which is the highest energy molecular orbital that is filled with electron.


This is the 2p pi* bond (π*) which is also the LUMO of CO.

The potential energy of 2p π* MO is -0.02178.

This is the π* bond formed from the side on overlap between two 2p atomic orbitals from C and O with correct orientation out of phase. LUMO stands for lowest unoccupied molecular orbital which is the empty molecular orbital with lowest energy level.

Independence : CH4 Molecule

Key Information

Gaussian Calculation Summary

Calculation Method = RB3LYP

Basis Set = 6-31G(d,p)

E(RB3LYP) = -40.52401404 a.u.

RMS Gradient Norm = 0.00003263 a.u.

Point Group = Td

Bond Length of C-H = 1.09197 Å

Bond Angle of H-C-H = 109.471°


Item Table

Item               Value     Threshold  Converged?
 Maximum Force            0.000063     0.000450     YES
 RMS     Force            0.000034     0.000300     YES
 Maximum Displacement     0.000179     0.001800     YES
 RMS     Displacement     0.000095     0.001200     YES
 Predicted change in Energy=-2.256043D-08
 Optimization completed.
    -- Stationary point found.


Image of the molecule

Methane

Click here for optimisation file.


Display Vibration Window


IR Spectrum of Molecule

IR Spectrum for CH4

Frequency Analysis of CH4

From 3N-6 rule, 9 modes are expected from CH4 vibration (N=5)

However, there are only 2 bands shown from the IR spectrum, which is the C-H bond bending at frequency 1256.2 cm-1 and stretching 3162.33 cm-1 . From the IR spectrum, vibration mode 1 , 2, and 3 are in the same energy so they only show as one peak;whereas vibration mode 7, 8, and 9 are the same energy, thus also show as one peak. There are no peaks show for vibration mode 4, 5, and 6 because there are no change in dipole moment in CH4 to be detected. This is be proved from the zero intensity. Bond stretching is at higher energy than bond bending.

The presence of only two bands in IR spectrum is due to the sp3 hybridisation of the carbon 2s and three 2p orbitals to form 4 degenerate sp3 atomic orbitals. Thus, only one type of C-H bond is observed. This gives CH4 tetrahedral geometry and Td point group with the bond angle of approximate to 109.5°.

sp3 Hybridisation[3]

sp3 hybrid orbital are degenerates and have energy in between 2s and 2p atomic orbitals.

Charge Analysis

Charge on carbon(C) = -0.930

Charge on hydrogen(H) = 0.233

Carbon is more electronegative compared to hydrogen. Hence, C attracts the electron densities towards itself causing it has slightly negative in charge, leaving the four hydrogen atoms with delta positive charges.



Molecular Orbitals of CH4

A1 non-bonding MO of CH4

The potential energy is -10.16707 which is the lowest energy MO.

The electron contribution is only from the 1s2 of C.


Bonding MO of CH4

The potential energy is -0.69041.

The 4 Hs' 1s atomic orbital(AO) overlap contructively with C's 2s AO. The electron density is contributed from the four H's 1s2 and C's 2s2.


HOMO/T2 bonding MO of CH4

The potential energy of HOMO is -0.38831.

This MO is formed from the overlap of C's 2p AO and the four Hs' 1s AO. As C's 2px 2py, 2pz are degenerate and each of the 2p sub-orbital overlap with the four Hs' 1s AO, thus we obtained three 3σ bonding MO with the same energy that are orthogonal to each other.


LUMO/ anti-bonding MO of CH4

The potential energy of LUM0 is 0.11824.

This MO results from the destructive overlap of C's 2s and Hs' 1s AOs.


Reference

[1] Media:http://chem-is-you.blogspot.com/2013/02/fundamentals-of-molecular-bonding.html

[2] Media:http://www.zedism.com/pamelajaeger/defined.html

[3] Media:http://www.chemguide.co.uk/basicorg/bonding/methane.html