Rep:Mod:KJH0608

NH₃

Summary Information

• Calculation Method: RB3LYP
• Basis Set: 6-31G(d,p)
• Final energy E(RB3LYP): -56.55776873 a.u.
• RMS gradient: 0.00000485 a.u.
• Point group: C3V
• N-H bond length: 1.01865Å
• H-N-H bond angle: 105.7412

        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

Optimised Molecule of Ammonia

Link to .log file: File:01363227 PHUNT NH3 OPTF POP.LOG

Vibrational Analysis

A Gaussview image of the vibrations of an optimised ammonia molecule

• Using 3N-6, 6 vibrational modes are expected
• Vibrational modes 2 and 3, and 5 and 6, are degenerate
• Vibrational modes 1-3 are bending vibrations and modes 4-6 are stretching vibrations
• Vibrational mode 4 is highly symmetric
• Vibrational mode 1 is the "umbrella" mode
• 2 bands are expected to be seen in an experimental spectrum of gaseous ammonia. There are 4 non-dengenerate vibrational modes, of which 2 have relatively too low of a peak to show up on the experimental spectrum

Charge Analysis

• The charge on the N-atom = -1.125e
• The charge on the H-atom = 0.375e

N is expected to have a negative charge and H is expected to have a positive charge, as N is more electronegative than H.

N₂

Summary Information

• Calculation Method: RB3LYP
• Basis Set: 6-31G(d,p)
• Final energy E(RB3LYP): -109.52412868 a.u.
• RMS gradient: 0.00000060 a.u.
• Point group: D*H
• N-N bond length: 1.1.550Å

        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

Optimised Molecule of Nitrogen

Link to .log file: File:01363227 PHUNT N2 OPTF POP.LOG

Vibrational Analysis

A Gaussview image of the vibrations of an optimised nitrogen molecule

• The band will not show on a vibrational spectrum as the molecules does not have a change in dipole moment as the bond vibrates.
• The literature value of the vibrational frequency is found to be 2358.07cm^-1.

H₂

Summary Information

• Calculation Method: RB3LYP
• Basis Set: 6-31G(d,p)
• Final energy E(RB3LYP): -1.17853936 a.u.
• RMS gradient: 0.00000017 a.u.
• Point group: D*H
• H-H bond length: 0.74279Å

         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

Optimised Molecule of Hydrogen

Link to .log file: File:01363227 PHUNT H2 OPTF POP2.LOG

Vibrational Analysis

A Gaussview image of the vibrations of an optimised hydrogen molecule

• The band will not show on a vibrational spectrum as the molecules does not have a change in dipole moment as the bond vibrates.
• The literature value of the vibrational frequency is found to be 4400.39cm^-1.

Reaction Energy

N₂ + 3H₂ -> 2NH₃
E(NH₃)= -56.557769
2*E(NH₃)= -113.115538
E(N₂)= -109.524129
E(H₂)= -1.178539
3*E(H₂)= -3.535617
ΔE=2*E(NH₃)-[E(N₂)+3*E(H₂)]= -0.55792 a.u. = -146.48 kJ/mol
The products are more stable as the energy change is negative, which means the products are lower in energy than the reactants.

HCl

Summary Information

• Calculation Method: RB3LYP
• Basis Set: 6-31G(d,p)
• Final energy E(RB3LYP): -460.80077875 a.u.
• RMS gradient: 0.00005211 a.u.
• Point group: C*V
• H-Cl bond length: 1.28599Å

         Item               Value     Threshold  Converged?
 Maximum Force            0.000090     0.000450     YES
 RMS     Force            0.000090     0.000300     YES
 Maximum Displacement     0.000139     0.001800     YES
 RMS     Displacement     0.000197     0.001200     YES

Optimised Molecule of Hydrogen Chloride

Link to .log file: File:01363227 PHUNT HCL OPTF POP.LOG

Vibrational Analysis

A Gaussview image of the vibrations of an optimised hydrogen chloride molecule

• Using 3N-5, 1 vibrational mode is expected
• 1 band isexpected to be seen in an experimental spectrum of hydrogen chloride as there is only one vibrational mode.
• The literature value of the vibrational frequency is found to be 2828cm^-1. This is because the vibrational frequency calculated is at 0K, whereas the literature value does not give the vibrational frequency at 0K.

Charge Analysis

• The charge on the Cl-atom = -0.284 a.u.
• The charge on the H-atom = 0.284 a.u.

Cl is expected to have a negative charge and H is expected to have a positive charge, as Cl is more electronegative than H.

Molecular Orbitals

(*)The z-axis goes along the bond of the molecule, the x- and y- axes are perpendicular to the bond of the molecule.
(*)The size of the molecule has not been changed in the images, so the MO sizes can be compared to each other.

Molecular Orbitals of HCl

Molecular Orbital	Description
	The 1s orbitals of H and Cl contribute to the MO. It is non-bonding as it is deep in energy. The MO is occupied. The MO has σ symmetry.
	The 1s orbital of H and 2s orbital of Cl contribute to the MO. It is non-bonding as it is deep in energy. The MO is occupied. The MO has σ symmetry.
	The 1s orbital of H and 2pz orbital of Cl contribute to the MO. It is non-bonding as it is deep in energy. The MO is occupied. The MO has σ symmetry.
	The 1s orbitals of H and 2px,2py orbitals of Cl contribute to the two degenerate MOs. They are non-bonding as they are deep in energy. The MOs are occupied. The MOs have π symmetry.
	The 1s orbital of H and 3s orbital of Cl contribute to the MO. It is non-bonding as the Cl 3s orbital is not high enough in energy to interact with the 1s orbital of H. The MO is occupied.The MO has σ symmetry.
	The 1s orbital of H and 3pz orbital of Cl contribute to the MO. It is bonding as the Cl 3pz orbital is high enough in energy to interact with the 1s orbital of H. The MO is occupied. The MO has σ symmetry.
	The 1s orbitals of H and 3px,3py orbitals of Cl contribute to the two degenerate MO. They are non-bonding as one bonding orbital has already been formed, and H only has one available electron. The MOs are occupied. The two degenerate orbitals are the HOMO of HCl.The MO has π symmetry.
	The 1s orbital of H and 3pz orbital of Cl contribute to the MO. It is anti-bonding as the Cl 3pz orbital interacts out of phase with the 1s orbital of H. The MO is unoccupied. This orbital is the LUMO of HCl. The MO has σ* symmetry.

The molecular orbitals of hydrogen chloride