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Task one

Optimised NH₃ Molecule

Molecule name: Ammonia

H-N-H bond angle: 105.7

N-H bond length: 1.02 A

Figure 1. A Gaussian image of an optimised NH₃ molecule.

Calculation Method:

Table 1. Optimisation method and optimised parameters.

Item table:

Table 2. Item table for optimised NH₃ molecule.

Vibrations:

Figure 2. Six Vibrations for the optimised NH₃ molecule.

Questions

1. Expected modes : 6

2. Degenerate modes : 2

3. Bending : H-N-H (1693.95^-1) + N-H (1089.54cm^-1)

4. Bond stretch : N-H symmetric (3461.29cm^-1) + 2x asymmetric (3589.82^-1)

6. Umbrella mode: N-H symmetric (3461.29cm^-1)

7. Expected Experimental bands in NH₃(g) : 4

Atomic charges:

Figure 3. Atomic charges within NH₃ molecule

XYZ File:

Figure 4. XYZ file for NH₃.

Jmol file:

JMol of ammonia

Final optimisation file: log file

Optimised N₂ Molecule

Molecule name: Nitrogen

N≡N bond length: 1.11 A

Figure 5. A Gaussian image of an optimised N₂ molecule.

Calculation Method:

Table 3. Optimisation method and optimised parameters.

Item table:

Table 4. Item table for optimised N₂ molecule.

Vibrations:

Figure 6. Six Vibrations for the optimised N₂ molecule.

Atomic charges: Uncharged molecule, symmetrical.

Molecular Orbital:

Figure 7. Occupied orbitals for N₂ molecule.

Final optimisation file: Nitrogen.log

Optimised H₂ Molecule

Molecule name: Hydrogen

H-H bond length: 0.74 A

Figure 8. A Gaussian image of an optimised H₂ molecule.

Calculation Method:

Table 5. Optimisation method and optimised parameters.

Item table:

Table 6. Item table for optimised H₂ molecule.

Vibrations:

Figure 9. Six Vibrations for the optimised H₂ molecule.

Atomic charges: Uncharged molecule, symmetrical.

Molecular Orbital:

Figure 10. Occupied orbitals for H₂ molecule.

Final optimisation file: Hydrogen.log

Energy of Reaction

N₂ + 3H₂ → 2NH₃

•E(NH₃)= -56.55776873

•2*E(NH₃)= -113.11553746

•E(N₂)= -109.25579376

•E(H₂)= -1.16515738

•3*E(H₂)= -3.49547214

•ΔE = 2*E(NH₃) - [E(N₂ )+ 3*E(H₂)] = -0.36427156 a.u

ΔE = -146.5 KJ/mol

Task two

Optimised CH₄ Molecule

Molecule name: Methane

C-H bond length: 1.09 A

Figure 1. A Gaussian image of an optimised CH₄ molecule.

Point group: Td