Rep:Mod:7317

Introduction To Molecular Modelling 2

NH₃ Molecule

• Molecule= NH₃
• Calculation Method=RB3LYP
• Basis Step= 6-31G(d,p)
• Final energy E(RB3LYP)= -56.55776873 a.u.
• RMS gradient= 0.00000485 a.u.
• Point Group= C3V
• N-H Bond Distance= 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

NH₃ Animation

test molecule

Vibrational Modes of NH3 molecule

• From the 3N-6 rule, I would expect 6 nodes for a molecule of NH3.
• The 2nd and 3rd, and the 5th and 6th vibrational modes are degenerate with respect to each other.
• The 1st,2nd and 3rd modes are bending vibrations, while the 4th,5th and 6th modes are stretching.
• The 4th vibrational mode is highly symmetric.
• The 1st vibrational mode is known as the 'umbrella mode'.
• I would expect to see 2 bands in an experimental spectrum of gaseous ammonia- the 1st vibrational mode, and the 2nd and 3rd which are degenerate. This is because the 4th,5th and 6th vibrational modes have a very low intensity compared to the first 3 vibrational modes so wouldn't be seen in the experimental spectrum.

Charge Distribution of NH3 molecule

• The charge on the nitrogen atom is -1.125
• The charge on the hydrogen atoms is +0.375.
• I would have expected that the charge of the nitrogen atom would be negative, while the charge on the hydrogen atoms would be positive. This charge distribution has agreed with my expectations.

H₂ Molecule

• Calculation Method- RB3LYP
• Basis Step- 6-31G(d,p)
• Final Energy- -1.17853936 au
• RMS Gradient- 0.00000017 au
• Point Group- D*H

        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

• There is one vibrational mode at a frequency of 4465.68 cm-1

N₂ molecule

• Calculation Method- RB3LYP
• Basis Step- 6-31G(d,p)
• Final Energy- -109.52412868 au
• RMS gradient- 0.000000326 au
• Point Group- D*H

        Item               Value     Threshold  Converged?
Maximum Force            0.000006     0.000450     YES
RMS     Force            0.000006     0.000300     YES
Maximum Displacement     0.000002     0.001800     YES
RMS     Displacement     0.000002     0.001200     YES

• There is one vibrational mode at a frequency of 2457.35 cm-1

Calculating the Energy Change for the Haber process

• E(NH3)= -56.55776873 au
• 2*E(NH3)= -113.1155375 au
• E(N2)= -109.52412868 au
• E(H2)= -1.17853936 au
• 3*E(H2)= -3.53561808 au
• ΔE=2*E(NH3)-[E(N2)+3*E(H2)]= -0.05579074au = -146.48 kJ/mol

• The ammonia product is more stable than the gaseous reactants.

Project Molecule[CN^-]

Optimization Information

• Calculation Method- RB3LYP
• Basis Step- 6-31G(d,p)
• Final Energy- -92.82453153 au
• RMS Gradient- 0.00001661 au
• Point Group- C*V

        Item               Value     Threshold  Converged?
Maximum Force            0.000029     0.000450     YES
RMS     Force            0.000029     0.000300     YES
Maximum Displacement     0.000013     0.001800     YES
RMS     Displacement     0.000018     0.001200     YES

CN^- Animation

test molecule

Vibrational Modes

• There is only one vibrational mode for CN^-, which occurs at a frequency of 2139.14 cm^-1. This is a bond stretch vibration.

Charge Distribution in CN^- molecule

• The charge on the carbon atom is -0.246.
• The charge on the nitrogen atom is -0.754.
• I expected that the charge on the nitrogen atom would be more negative than on the carbon atom, as it is a more electronegative atom. The calculated charges confirm my expectations.

Molecular Orbitals

• This bonding molecular orbital (σ bond) is formed from two 2s atomic orbitals, combining in the same phase. It is occupied and deep in energy.
• It has a node near the carbon atom because the 2s orbitals are slightly hybridised with 2p orbitals, which influence the electron density.

• This anti-bonding molecular orbital (σ* bond) is formed from two 2s atomic orbitals, combining out of phasse. It is occupied and deep in energy.
• It has a node near the nitrogen atom because of the influence of 2p orbitals.

• This anti-bonding molecular orbital (π* orbital) is formed from two P_y or two P_z orbitals, combining out of phase. It is the LUMO.

• This bonding molecular orbital (σ bond) is formed from two 2P_x orbitals, combining in phase. It is the HOMO.

• This bonding molecular orbital (π bond) is formed from two P_y or two P_z orbitals, combining in phase. It is occupied and deep in energy.