Rep:Mod:htl116

Ammonia

Result Summary

Record:

• molecule name: Ammonia NH₃
• calculation method: RB3LYP
• basis set: 6-31G(d,p)
• final energy E(RB3LYP) in atomic units (au): -56.55776873 a.u.
• the point group of your molecule: C₃V

Optimized Bond Length and Angle

Optimized Bond Length: 1.01798 armstrong

Optimized Bond Angle: 105.741 degree

         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

 Predicted change in Energy=-5.986260D-10

 Optimization completed.

Ammonia

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

which modes are degenerate (ie have the same energy)? ANS: mode 2 &3. mode 5&6

which modes are "bending" vibrations and which are "bond stretch" vibrations? ANS: bond stretch vibrations are mode 1 &4, bending vibrations are mode 2,3,5,6

which mode is highly symmetric? ANS: mode 1& 4

one mode is known as the "umbrella" mode, which one is this? ANS: mode 1

how many bands would you expect to see in an experimental spectrum of gaseous ammonia? ANS: 4 bands

Charge of N atom = -1.125

Charge of H atom = 0.375

Charge of N atom is expected to have a negative value because N is more electronegative than H atom.

Charge of H atom is expected to have a positive value because H is more electropositive than N atom.

Hydrogen

Result Summary

Record:

• molecule name: Hydrogen H₂
• calculation method: RB3LYP
• basis set: 6-31G(d,p)
• final energy E(RB3LYP) in atomic units (au): -1.17853936 a.u.
• the point group of your molecule:  D_∞h

Optimized Bond Length and Angle

Optimized Bond Length: 0.74279 armstrong

         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.

Vibration frequency = 4465.68

Nitrogen

Result Summary

Record:

• molecule name: Nitrogen N₂
• calculation method: RB3LYP
• basis set: 6-31G(d,p)
• final energy E(RB3LYP) in atomic units (au): -109.52412868 a.u.
• the point group of your molecule:  D_∞h

Optimized Bond Length and Angle

Optimized Bond Length: 1.10550 armstrong

         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=-3.401020D-13
 Optimization completed.

Vibration frequency = 2457.33

Energy Calculation of ammonia formation

• 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)]= -0.05579070 a.u.

In terms of KJ/mol: ΔE = -146.47848285 KJ/mol

Own Choice of Small Molecule = Fluorine

Result Summary

Record:

• molecule name: Fluorine F₂
• calculation method: RB3LYP
• basis set: 6-31G(d,p)
• final energy E(RB3LYP) in atomic units (au): -199.49825220 a.u.
• the point group of your molecule:  D_∞h

Optimized Bond Length and Angle

Optimized Bond Length: 1.40297 armstrong

The optimized bond length is compared to literature value of 1.42 armstrong, the reason that the optimized bond length is smaller than the actual bond length is electron repulsion exist in real molecules hence it is not optimized in reality

         Item               Value     Threshold  Converged?
 Maximum Force            0.000003     0.000450     YES
 RMS     Force            0.000003     0.000300     YES
 Maximum Displacement     0.000004     0.001800     YES
 RMS     Displacement     0.000006     0.001200     YES
 Predicted change in Energy=-1.355555D-11
 Optimization completed.

Vibration Frequency = 1064.58

Charge on F atoms = 0.00000

Fluorine

Molecular Orbitals

2s σ bonding molecular orbital formed from overlapping of two 2s atomic orbital from two fluorine atoms
2p σ bonding molecular orbital formed from overlapping of two 2pz atomic orbital from two fluorine atoms
2p π bonding molecular orbital formed from side-on overlapping of two 2py atomic orbital from two fluorine atoms
2p π anti-bonding molecular orbital formed from two 2py atomic orbital from two fluorine atoms. This orbital is the highest-occupied-molecular-orbital (HOMO).
2p σ anti-bonding molecular orbital formed from two 2pz atomic orbital from two fluorine atoms. This orbital is the Lowest-occupied-molecular-orbital (LUMO)