Rep:Mod:5032108

NH3 molecule

The optimisation file is liked to here

Calculation method: RB3LYP

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

Final energy: -56.55776873 a.u

RMS gradient: 0.00000485

Point group: C_3v

N-H bond length: 1.01798

H-N-H bond angle: 105.741

Items table

 
           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=-5.986266D-10
 Optimization completed.
    -- Stationary point found.

Frequency analysis

Six modes are expected from the 3N-6 rule because NH3 is a non-linear molecule and have four atoms.

Modes 2 and 3 are degenerated, modes 5 and 6 are degenerated.

Modes 4,5 and 6 are bond stretch vibrations which have higher energies

Modes 1,2 and 3 are bending vibrations which have lower energies

First mode and fourth mode is highly symmetric

First mode is known as the "umbrella" mode

Four bands are expected to see from an experimental spectrum because there are two pairs of degenerated modes.

Atomic charges


Atom         Atomic charges
Nitrogen     -1.125
Hydrogens     0.375

The numbers on the atoms are atomic charges. Nitrogen atom has negative charge and three hydrogen atoms have positive charges because nitrogen atom is highly electronegative, pull electrons closer to itself.

N2 molecule

The optimisation file is liked to here

Calculation method: RB3LYP

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

Final energy: -109.52412868 a.u

RMS gradient: 0.00000060 a.u

Point group: D_infh

N-N bond length: 1.10550

N-N bond angle: 180.00000

Items table

         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=-3.401122D-13
 Optimization completed.
    -- Stationary point found.

Frequency analysis

Vibration frequency: 2457.33

There is only one vibration mode because It is a linear diatomic molecule. It follows the 3N-5 rule.

H2 molecule

The optimisation file is liked to here

Calculation method: RB3LYP

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

Final energy: -1.17853936 a.u

RMS gradient: 0.00000017 a.u

Point group: D_infh

H-H bond length: 0.74279

H-H bond angle: 180

Items table

         
         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=-1.167770D-13
 Optimization completed.
    -- Stationary point found.

Frequency analysis

Vibration frequency: 4465.68

There is only one vibration mode because It is a linear diatomic molecule. It follows the 3N-5 rule.

Haber-Bosch reaction energies

N2 + 3H2 -> 2NH3

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)]= -0.0557907 a.u = -146.48 kJ/mol

There is a negative value for change in energy which means this reaction is energy favorable because the energy of the product is lower in energy than the total energy in reactants. It is an exothermic reaction.

CH4 molecule

NH3 molecule

The optimisation file is liked to here

Calculation method: RB3LYP

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

Final energy: -40.52401404 a.u

RMS gradient: 0.00003263 a.u

Point group: T_d

C-H bond length: 1.09197

H-C-H bond angle: 109.471

Item table

         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=-2.255980D-08
 Optimization completed.
    -- Stationary point found.

Frequency analysis

CH4 is a non-linear molecule with five atoms. Nine modes are expected from the 3N-6 rule.

The sixth mode is highly symmetric

Modes 1, 2 and 3 are degenerated

Modes 4 and 5 are degenerated

Modes 7 ,8 and 9 are degenerated

Two bands are expected to see from an experimental spectrum because there are two pairs of degenerated modes and there are not change in dipole moment for mode 4,5 and 6 which means it is not observable on the spectrum

Atomic charges

Atom      Atom charges
Carbon    -0.930
Hydrogen   0.233

The carbon atom of methane molecule has a negative charge and four hydrogen atoms have positive charge because the carbon atom is slightly electronegative, pulling the electrons closer to itself.

Molecule Orbitals Analysis

Carbon atom electronic configuration: 1s²2s²2p²

Hydrogen atom electronic configuration: 1s²

The red shaded region on the diagram above is the lowest energy MO. This MO is contributed from the 1s AO of C-atom which is occupied by two electrons form the C-atom. This MO is deep in energy, -10.16707 a.u.

This is the next MO higher in energy. This is the combination of the 2s valence AOs of C-atom and H-atom bonding orbital. These two AOs overlap strongly because there is a larger surface around the molecule on the above diagram. This MO is occupied.

The three diagrams above are interaction between 2p AOs of C-atom and 1s AO of H-atom. These three are HOMO and degenerated. There are three MOs because there are p_x, p_y and p_z AO from C-atom. These three pAOs interact with 1s AO of H-atom.

This is an lowest unoccupied anti-bonding MO. It is high in energy and has a positive energy, +0.11824 a. This is contributed by 2s AO of C-atom and 1s AO of H-atom out of phase overlap.

These three are degenerated unoccupied anti-bonding MOs between pAOs of C-atom and sAOs of H-atom out of phase overlap.