Rep:Mod:HRC115
Molecular Modelling
NH3 Molecule
Key Information
Molecule: NH3
Calculation Method: RB3LYP
Basis Set: 6-31G (d,p)
Final Energy: -56.44397188 a.u
RMS Gradient: 0.05399560 a.u
Point Group: C3V
Bond Length: 1.3 angstrom
Bond Angle: 109.471°
Optimised NH3 Molecule
Key Information
Molecule:NH3
Calculation Method: RB3LYP
Basis Set: 6-31G (d,p)
Final Energy: -56.55776873 a.u
RMS Gradient: 0.00000485 a.u
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=-5.986290D-10
Optimization completed.
-- Stationary point found.
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! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
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! 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 !
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GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
-- Stationary point found.
As seen, the structure has converged.
The optimisation file is liked to here
NH3 Molecule |
Charge on Nitrogen: -1.125
Charge on Hydrogen: 0.375
It is expected that nitrogen would have a negative charge as it has a higher electronegativity than that of hydrogen, so will hold the electrons closer, resulting in an overall negative charge. This means the charge on hydrogen is positive.
Frequency Analysis
From the 3N-6 rule, where N is the number of atoms, 6 vibrational modes are expected to be seen, which is observed in the table. Modes 2 and 3, and 5 and 6, are degenerate as they have the same frequencies. Modes 1-3 are bond bending modes and 4-6 are bond stretching. Mode 4 is highly symmetric. Mode 1 is known as the umbrella mode. In a spectrum of gaseous ammonia, it would be expected that you would see 9 bands.
H2 Molecule
Key Information
Molecule: H2
Calculation Method: RB3LYP
Basis Set: 6-31G (d,p)
RMS Gradient: 0.000000017 a.u
Final Energy: -1.17853936 a.u
Point Group: D∞h
Bond Length: 0.74279 angstroms
Bond Angle: 180°
The optimisation file is liked to here
H2 Molecule |
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. !
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! R1 R(1,2) 0.7428 -DE/DX = 0.0 !
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GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
As seen, the structure has converged.
Frequency Analysis
There are no negative frequencies seen.
N2 Molecule
Key Information
Molecule: N2
Calculation Method: RB3LYP
Basis Set: 6-31G (d,p)
RMS Gradient: 0.00000060 a.u
Final Energy: -109.52412868 a.u
Point Group: D∞h
Bond Length: 1.10550 angstroms
Bond Angle: 180°
The optimisation file is liked to here
N2 Molecule |
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=-3.401045D-13
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
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! R1 R(1,2) 1.1055 -DE/DX = 0.0 !
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GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
As seen, the structure has converged.
There are no negative frequencies seen.
Haber-Bosch Reaction Energy Calculation
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
ΔE=-146.4784829 kJ/mol
The gaseous reactants in the process are favoured.
H2CO Molecule
Key Information
Molecule: H2CO
Calculation Method: RB3LYP
Basis Set: 6-31G (d,p)
RMS Gradient: 0.00007368 a.u
Final Energy: -114.50319933 a.u
Point Group: CS
Bond Length: C=O = 1.20676, C=H = 1.110565
Bond Angle: O=C-H = 122.395, H-C-H = 115.219
The optimisation file is liked to here
H2CO Molecule |
The hydrogen molecules show a charge of 0.150, and carbon of 0.197. Oxygen, however, displays a negative charge at -0.497, due to it having the highest electronegativity, therefore pulling the electrons closer to it.
Item Value Threshold Converged?
Maximum Force 0.000197 0.000450 YES
RMS Force 0.000085 0.000300 YES
Maximum Displacement 0.000232 0.001800 YES
RMS Displacement 0.000149 0.001200 YES
Predicted change in Energy=-3.772186D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
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! R1 R(1,2) 1.2068 -DE/DX = -0.0002 !
! R2 R(2,3) 1.1106 -DE/DX = -0.0001 !
! R3 R(2,4) 1.1106 -DE/DX = -0.0001 !
! A1 A(1,2,3) 122.3859 -DE/DX = 0.0 !
! A2 A(1,2,4) 122.3954 -DE/DX = 0.0 !
! A3 A(3,2,4) 115.2188 -DE/DX = 0.0 !
! D1 D(1,2,4,3) 180.0 -DE/DX = 0.0 !
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GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
As seen, the structure has converged.
Frequency Analysis
Modes 1 and 2 correspond to bond bending, whilst in modes 3 and 4, both bond bending and stretching are seen. In modes 5 and 6, only bond stretching is seen. Again due to 3N-6, it is expected to see 6 vibrational modes, which is what is shown.
H2CO Molecular Orbitals
Shown above are the five lowest energy MO's observed for H2CO. Their respective energies are -19.17003 a.u, -10.28952 a.u, -1.06085 a.u, -0.63678 a.u, and -0.49430 a.u, going from left to right. The first two shown are MO's surrounding oxygen, and then carbon, due to 1s electrons. The next two are a result of the 2s electrons. One shows the bonding orbital completely surrounding the molecule, and the other the bonding and antibonding orbital. There is a big jump in energy when considering the 2s electrons as opposed to just the 1s electrons. In the final picture, the orbitals observed are made from the 2p electrons. The red MO is showing the bonding orbital, and green the antibonding. Here, overlaping p orbitals are shown.