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Ammonia, NH3

Gaussian Calculation Summary

  • Molecule Name: Ammonia, NH3
  • Calculation Method: RB3LYP
  • Basis set:6-31G(d,p)
  • Final energy E(RB3LYP): -56.55776873 a.u.
  • RMS Gradient: 0.00000485 a.u.
  • The point group of your molecule: C3v
  • H-N-H bond angle:105.7412°
  • H-N bond length: 1.018Å

The optimisation file of NH3 is linked here 

 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=-5.986284D-10

 Optimization completed.

    -- Stationary point found.

                           ----------------------------

                           !   Optimized Parameters   !

                           ! (Angstroms and Degrees)  !

 --------------------------                            --------------------------

 ! Name  Definition              Value          Derivative Info.                !

 --------------------------------------------------------------------------------

 ! R1    R(1,2)                  1.018          -DE/DX =    0.0                 !

 ! R2    R(1,3)                  1.018          -DE/DX =    0.0                 !

 ! R3    R(1,4)                  1.018          -DE/DX =    0.0                 !

 ! A1    A(2,1,3)              105.7412         -DE/DX =    0.0                 !

 ! A2    A(2,1,4)              105.7412         -DE/DX =    0.0                 !

 ! A3    A(3,1,4)              105.7412         -DE/DX =    0.0                 !

 ! D1    D(2,1,4,3)           -111.8571         -DE/DX =    0.0                 !

 --------------------------------------------------------------------------------
NH3 Molecule

Vibration Modes

The animations of the different vibrations modes of the NH3 molecule Mode 1 Mode 2 Mode 3 Mode 4 Mode 5 Mode 6


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

6 Vibration modes.

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

Modes 2 and 3 are degenerate. Also modes 5 and 6 are degenerate.

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

Modes 2 and 3 are "bending" vibrations, mode 4 is symmetrical stretching, modes 5 and 6 are asymmetrical stretching.

Which mode is highly symmetric?

Modes 1 and 4 is highly symmetrical.

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?

2 Bands at 1089.54 cm-1 and 1693.95 cm-1

Charge Distribution

The charge on the Nitrogen atom is expected to be negative and the charge on the Hydrogen atom is expected to be positive as Nitrogen is more electronegative than Hydrogen so the electron density is pulled toward the Nitrogen atom resulting in the negative charge.

Charge Distribution of a NH3 molecule












Charge on the Hydrogen atom: +0.375

Charge on the Nitrogen atom: -1.125

Comparison with Literature Values

The literature values of bond length and bond angles is taken from the [NIST Computational Chemistry Comparison and Benchmark DataBase].

Comparison of Literature values and Calculated values
Property Literature Value Calculated value Difference from the Literature value % Difference compared to the Literature value
H-N-H Bond Angle 106.6700° 105.7412° -0.9288° -0.87%
H-N Bond Length 1.0124Å 1.0180Å +0.0056Å +0.55%

The calculated bond angle and bond length is very close to the literature value. The reason why the values does not match completely is because the basis set is 6-31G(d,p) which only has medium accuracy. This basis set was used so the calculation is quick. For more accurate results, a basis set with higher accuracy should be used however the time taken to complete the calculation would be longer.

Nitrogen, N2

Gaussian Calculation Summary

  • Molecule Name: Nitrogen, N2
  • Calculation Method: RB3LYP
  • Basis set:6-31G(d,p)
  • Final energy E(RB3LYP): -109.52412868 a.u.
  • RMS Gradient: 0.00000217 a.u.
  • The point group of your molecule: D∞h
  • N≡N bond angle: 180°
  • N≡N bond length: 1.1055Å

The optimisation file of N2 is linked here 

 Item                     Value     Threshold  Converged?
 Maximum Force            0.000004     0.000450     YES
 RMS     Force            0.000004     0.000300     YES
 Maximum Displacement     0.000001     0.001800     YES
 RMS     Displacement     0.000002     0.001200     YES
 Predicted change in Energy=-4.428714D-12
 Optimization completed.
    -- Stationary point found.
                           ----------------------------
                           !   Optimized Parameters   !
                           ! (Angstroms and Degrees)  !
 --------------------------                            --------------------------
 ! Name  Definition              Value          Derivative Info.                !
 --------------------------------------------------------------------------------
 ! R1    R(1,2)                  1.1055         -DE/DX =    0.0                 !
 --------------------------------------------------------------------------------

One vibration mode occurs at 2457.34 cm-1

The charge on the two Nitrogen atom is 0. The electrons are distributed evenly since as the two atoms have the same electronegativity as they are the same so there is no net dipole moment.

Hydrogen, H2

Gaussian Calculation Summary

  • Molecule Name: Hydrogen, H2
  • Calculation Method: RB3LYP
  • Basis set:6-31G(d,p)
  • Final energy E(RB3LYP): -1.17853936 a.u.
  • RMS Gradient: 0.00000017 a.u.
  • The point group of your molecule: D∞h
  • H-H bond angle: 180°
  • H-H bond length: 0.7428Å

The optimisation file of H2 is linked here 

 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.
    -- Stationary point found.
                           ----------------------------
                           !   Optimized Parameters   !
                           ! (Angstroms and Degrees)  !
 --------------------------                            --------------------------
 ! Name  Definition              Value          Derivative Info.                !
 --------------------------------------------------------------------------------
 ! R1    R(1,2)                  0.7428         -DE/DX =    0.0                 !
 --------------------------------------------------------------------------------

One vibration mode occurs at 4465.68 cm-1

The charge on the two Hydrogen atom is 0. The electrons are distributed evenly since as the two atoms have the same electronegativity as they are the same so there is no net dipole moment.

Reaction Energy of the Haber-Bosch process

  • 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. = -146.4784828 kJ moɭ -1

ΔE is a negative value which indicated that the gaseous product is more stable.

Methane, CH4

Gaussian Calculation Summary

  • Molecule Name: Methane, CH4
  • Calculation Method: RB3LYP
  • Basis set:6-31G(d,p)
  • Final energy E(RB3LYP): -40.52401404 a.u.
  • RMS Gradient: 0.00003263 a.u.
  • The point group of your molecule: Td
  • H-C-H bond angle:109.4712°
  • C-H bond length: 1.092Å

The optimisation file of CH4 is linked here 

 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=-2.256106D-08
 Optimization completed.
    -- Stationary point found.
                           ----------------------------
                           !   Optimized Parameters   !
                           ! (Angstroms and Degrees)  !
 --------------------------                            --------------------------
 ! Name  Definition              Value          Derivative Info.                !
 --------------------------------------------------------------------------------
 ! R1    R(1,2)                  1.092          -DE/DX =   -0.0001              !
 ! R2    R(1,3)                  1.092          -DE/DX =   -0.0001              !
 ! R3    R(1,4)                  1.092          -DE/DX =   -0.0001              !
 ! R4    R(1,5)                  1.092          -DE/DX =   -0.0001              !
 ! A1    A(2,1,3)              109.4712         -DE/DX =    0.0                 !
 ! A2    A(2,1,4)              109.4712         -DE/DX =    0.0                 !
 ! A3    A(2,1,5)              109.4712         -DE/DX =    0.0                 !
 ! A4    A(3,1,4)              109.4712         -DE/DX =    0.0                 !
 ! A5    A(3,1,5)              109.4712         -DE/DX =    0.0                 !
 ! A6    A(4,1,5)              109.4712         -DE/DX =    0.0                 !
 ! D1    D(2,1,4,3)            120.0            -DE/DX =    0.0                 !
 ! D2    D(2,1,5,3)           -120.0            -DE/DX =    0.0                 !
 ! D3    D(2,1,5,4)            120.0            -DE/DX =    0.0                 !
 ! D4    D(3,1,5,4)           -120.0            -DE/DX =    0.0                 !
 --------------------------------------------------------------------------------
CH4 Molecule

Vibration Modes

Using the 3N-6 rule, the methane molecule is expected to have 9 vibrational modes.

The animations of the different vibrations modes of the CH4 molecule Mode 1 Mode 2 Mode 3 Mode 4 Mode 5 Mode 6 Mode 7 Mode 8 Mode 9

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

̈Modes 1, 2, 3, 4 and 5 are "bending vibrations. Mode 6 is symmetrical stretching. Modes 7 and 8 are asymmetrical stretching.

Charge Distribution

The charge on the Carbon atom is expected to be negative and the charge on the Hydrogen atom is expected to be positive as Carbon is more electronegative than Hydrogen so the electron density is pulled toward the Carbon atom resulting in the negative charge.

Charge Distribution of a CH4 molecule













Charge on the Hydrogen atom: +0.233

Charge on the Carbon atom: -0.930

Molecular Orbital

Molecular orbitals 3, 4 and 5 are degenerate.

Molecular Orbital 1-This is the occupied σ bonding molecular orbital formed by constructive overlap of the 1s atomic orbital of Carbon and the 1s atomic orbital of Hydrogen. This molecular orbital is very deep in energy.
Molecular Orbital 2-This is the occupied σ bonding molecular orbital formed by constructive overlap of the 2s atomic orbital of Carbon and the 1s atomic orbital of Hydrogen
Molecular Orbital 3-This is the occupied σ bonding molecular orbital formed by constructive overlap of the 2s atomic orbital of Carbon and the 2p atomic orbital of Hydrogen
Molecular Orbital 4-This is the occupied σ bonding molecular orbital formed by constructive overlap of the 2s atomic orbital of Carbon and the 2p atomic orbital of Hydrogen
Molecular Orbital 5-This is the occupied σ bonding molecular orbital formed by constructive overlap of the 2s atomic orbital of Carbon and the 2p atomic orbital of Hydrogen. This is the highest occupied energy level (HOMO)
Molecular Orbital 6-This is the unoccupied σ̈* anti-bonding molecular orbital form by destructive overlap of the 2s atomic orbital of Carbon and the 1s atomic orbital of Hydrogen. This is the lowest unoccupied molecular orbital (LUMO)
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