Ammonia Molecule

Summary of NH3

After optimisation of structure of ammonia, we can measure the N-H bond length and H-N-H bond angle:

N-H bond length=1.01798 Å

H-N-H bond angle=105.741

        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

It's easy to find that the structure of NH3 is optimized because the force is nearly zero which means it's the lowest energy form of ammonia.

calculation method:RB3LYP
basis set:6-31G(d,p)
final energy E(RB3LYP):-56.55776873au
point group:C3V

test molecule

The optimisation file is liked to here

Vibration display of NH3

how many modes do you expect from the 3N-6 rule?

Answer:6

which modes are degenerate (ie have the same energy)?

Answer:mode2and3, mode5and6

which modes are "bending" vibrations and which are "bond stretch" vibrations?

Answer:"bending" vibrations:mode1,2,3/"bond stretch" vibrations:mode4,5,6

which mode is highly symmetric?

Answer:mode4

one mode is known as the "umbrella" mode, which one is this?

Answer:mode 1

It has the highest intensity because of largest change in dipole moment.

how many bands would you expect to see in an experimental spectrum of gaseous ammonia?

Answer:2

Since there are four different vibration frequency, four bands are expected to to be seen in the spectrum. However, only two peaks are observed because the change in dipole moment of mode 4, mode 5 and mode 6 is very small and the intensity is too low.

charge distribution of NH3

N is expected to be negatively charged, and H is expected to possess positive charges because N has larger electronegativity than H.

H2 molecule

summary of H2

         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.

Structure is optimised when force equals zero.

calculation method:RB3LYP
basis set:6-31G(d,p)
final energy E(RB3LYP):-1.17853936au
point group: D∞h

Vibration display of H2

Intensity is zero because there is no change in dipole moment.

charge distribution of H2

No charge was expected on H because no difference between electronegativity

N2 molecule

summary of N2

calculation method:RB3LYP
basis set:6-31G(d,p)
final energy E(RB3LYP):-109.52412868au
point group: D∞h

         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=-3.401002D-13

Vibration display of N2

Intensity is zero because there is no change in dipole moment.

charge distribution of N2

No charge was expected on N because no difference between electronegativity

Enthalpy change of formation of NH3

N2 + 3H2 -> 2NH3

E(NH3)=-56.55776873au

2*E(NH3)=-113.1155375au

E(N2)=-109.52412868au

E(H2)=-1.17853936au

3*E(H2)=-3.53561808au

ΔE=2*E(NH3)-[E(N2)+3*E(H2)]=-0.05579074au=-146.478599028 KJ/mol

The enthalpy change is negative, therefore exothermic reaction and the ammonia product is favoured.

HCL Molecule

Vibration display of HCL

Intensity is not zero because there is change in dipole moment.

Charge Distribution of HCL

Cl atom is negatively charged due to higher electronegativity than H, and H atom is positively charged.

Molecular Orbital of HCl

This is the 1π molecular orbital of HCl which is occupied by 2 electrons and deep in energy(-7.22836au). It is contributed by 2py atomic orbital of Cl. It is a non-bonding orbital.

This is the 3σ molecular orbital of HCl which is occupied by 2 electrons and deep in energy(-7.23847au). It is contributed by 2pz atomic orbital of Cl. It has lower energy than 1pi as a result of mixing with 1s orbital of H because of same symmetry. It is a non-bonding orbital.

This is the 4σ molecular orbital of HCl which is occupied by 2 electrons and deep in energy(-0.84773au). It is formed by mixing 3s atomic orbital of Cl and 1s orbital of H. It is a bonding orbital.

This is the 5σ molecular orbital of HCl which is occupied by 2 electrons and deep in energy(-0.47433au). It is formed by mixing 3sp atomic orbital of Cl and 1s orbital of H . It is a bonding orbital.

This is the 6σ* molecular orbital of HCl which is the lowest unoccupied molecular orbital (0.01366au). It is formed by mixing 3sp atomic orbital of Cl and 1s orbital of H . It is an anti-bonding orbital.