0MW7FY8

Jacob Forrest

Optimisation of NH3

Molecule - NH₃

the method: B3LYP

the basis set: 6-31G(d,p)

final energy E(RB3LYP) in atomic units: -56.55776873 au

point group : C3_v

Bond length : 1.01798 au

H-N-H bond angle : 105.745 degrees

         Item           Value        Threshold     Converged?
 Maximum Force          0.000006     0.000450         YES
 RMS     Force          0.000004     0.000300         YES
 Maximum Displacement   0.000014     0.001800         YES
 RMS     Displacement   0.000009     0.001200         YES

File:JHF NH3 OPT.LOG

Ammonia

NH₃ bond vibrations

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

  6 because NH3 has 6 modes of vibration

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

  2+3, 5+6 , They are both the two asymmetric stretches(5+6)
  and bends(2+3)

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

  1,2,3 then 4,5,6

which mode is highly symmetric?

  4 because the symmetric stretches do not at all affect the shape or dipoles of the     
  the molecule

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

  1 because the symmetric stretching animation looks similar to the opening and closing        
  of an umbrella

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

  4 because there are 4 vibration modes that create imbalanced dipoles (2,3,5,6)

Charge distribution in NH₃

It is expected for the Nitrogen to have a negative charge as it is more electronegative than hydrogen and therefore will draw the majority of electron density of the molecule to itself this in turn means the hydrogen is expected to be positive and for all of the hydrogen atoms to have the same magnitude of charge as they are all equally electronegative and equally distanced from the nitrogen atom.

Nitrogen charge = -1.125

Hydrogen charge = 0.375

Molecule - N₂

Molecule : N₂

the method: B3LYP

the basis set: 6-31G(d,p)

final energy E(RB3LYP) in atomic units: -109.52412868 au

point group : D∞h

Bond length : 1.10550 A

File:N2 OPTIMISATION.LOG

       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

Vibrations - #Mode:1 // Freq: 2457.33cm^-1

Molecule - H₂

Molecule : H₂

the method: B3LYP

the basis set: 6-31G(d,p)

final energy E(RB3LYP) in atomic units: -1.17835689 au

point group : D∞h

Bond length : 0.74279 A

File:H2 OPTIMISATION.LOG

        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

Vibrations - #Mode:1 // Freq: 4465.68cm^-1

Reaction energy of Haber-Bosch process

   E(NH3)= -56.55776873 au
   2*E(NH3)= -113.11553746 au
   E(N2)=  -109.52412868 au
   E(H2)= -1.17835689 au
   3*E(H2)= -3.53507067 au
   ΔE=2*E(NH3)-[E(N2)+3*E(H2)]= -0.05633811 au
   Therefore in kj/mol = -147.92 (2 d.p)

So the ammonia product is more stable as the forming of the ammonia releases more energy than the separation of the N2 amd H2 molecules; the reaction is exothermic. However this does not mean that N-H bonds individually more stable than the reactants but the overall energy and proportionally the stability of the N-H bonds formed is greater than the energy required to break the N2 and H2 bonds for the formation of the ammonia.

ClF3 optimisation

Vibrations and charges

mode   freq(cm-1)
    1             -43.17
    2             -43.16
    3             416.55
    4             559.35
    5             610.87
    6             610.87

Fluorine charge = -0.396
Chlorine charge = 1.188