Rep:Mod:AMZ1470

NH₃ Molecule

Key Information

N-H bond length = 1.01798 A

H-N-H bond angle = 105.74115 degrees

Calculation Method: RB3LYP

Basis Set: 6-31G(d,p)

Final Energy: -56.55776873 au

RMS Gradient: 0.00000485 au

Point Group: C3V


         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=-5.986259D-10

test molecule

Link to optimized file: File:Sk4915 NH3 optf pop.log

Vibration

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

6

Which modes are degenerate (i.e have the same energy)?

Modes 2 & 3 are degenerate. Modes 5 & 6 also are degenerate.

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

Modes 1, 2 & 3 are bending vibrations and modes 4, 5 & 6 are bond stretch vibrations.

Which mode is highly symmetric?

Mode 4.

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

Mode 1.

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

Two bands.

Charge Distribution

Charge on the N-atom: -1.125

Charge on the H-atoms: 0.375

These charges match expectations as Nitrogen is the most electronegative atom in this molecule and so more strongly attracts the bonding electrons, pulling the electrons further away from the Hydrogen atoms. Therefore, there is a slight negative charge on the Nitrogen and slight positive charges on the Hydrogen atoms.

H₂ Molecule

Key Information

H-H bond length = 0.74279 A

Calculation Method: RB3LYP

Basis Set: 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
 Predicted change in Energy=-1.164080D-13

test molecule

Link to optimized file: File:SK4915 H2.LOG

Vibration

Vibrational modes in an H2 molecule.

Charge Distribution

Charge on the H-atoms: 0.00 C

Both atoms in this molecule are identical so there is no dipole.

N₂ Molecule

Key Information

N-N bond length = 1.09200 A

Calculation Method: RB3LYP

Basis Set: 6-31G(d,p)

Final Energy: -109.52359111 au

RMS Gradient: 0.02473091 au

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=-3.400935D-13

test molecule

Link to optimized file: File:SK4915 N2.LOG

Vibration

Vibrational modes in an N2 molecule.

Charge Distribution

Charge on the N-atom: 0.00 C

Both atoms in this molecule are identical so there is no dipole.

Energy Calculations

Reaction:

N₂ + 3H₂ -> 2NH₃

E(NH₃) = -56.55776873 au

2*E(NH₃) = -113.1155375 au

E(N₂) = -109.52359111 au

E(H₂) = -1.17853936 au

3*E(H₂) = -3.53561808 au

ΔE = 2*E(NH₃) - [E(N₂) + E(H₂)] = -0.05632827 au

= -147.890 kJmol^-1

The Ammonia product is more stable than the gaseous reactants.

CH₄ Molecule

Key Information

C-H bond length = 1.07000 A

H-C-H bond angle = 109.47122 degrees

Calculation Method: RB3LYP

Basis Set: 6-31G(d,p)

Final Energy: -40.52401404 au

RMS Gradient: 0.00003263 au

Point Group: TD


         Item               Value     Threshold  Converged?
 Maximum Force            0.000063     0.000450     YES
 RMS     Force            0.000034     0.000300     YES
 Maximum Displacement     0.000179     0.001800     YES
 RMS     Displacement     0.000095     0.001200     YES
 Predicted change in Energy=-2.256038D-08

test molecule

Link to optimized file: File:SK4915 CH4.LOG

Vibration

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

9

Which modes are degenerate (i.e have the same energy)?

Modes 1, 2 & 3, modes 4 & 5 and modes 7, 8 & 9 are degenerate.

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

Modes 1, 2, 3, 4 & 5 are bending vibrations and modes 6, 7, 8 & 9 are bond stretch vibrations.

Which mode is highly symmetric?

Mode 6.

Charge Distribution

Charge on the C-atom: -0.930

Charge on the H-atoms: 0.233

These charges match expectations as Carbon is the most electronegative atom in this molecule and so more strongly attracts the bonding electrons, pulling the electrons further away from the Hydrogen atoms. Therefore, there is a slight negative charge on the Carbon and slight positive charges on the Hydrogen atoms.