Rep:Mod:CLR110
NH3 Molecule
General Information
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.
Symmetry=C3v
Geometric Information
For Optimised Structure
Bond Distance (N-H): 1.01798Å
Bond Angle (H-N-H): 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
Predicted change in Energy=-5.986258D-10
Optimization completed.
-- Stationary point found.
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! Optimized Parameters !
! (Angstroms and Degrees) !
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! 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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NH3 Molecule |
The optimisation file is liked to here
Vibrational Analysis
From the 3N-6 Rule, we should expect NH3 to have 6 vibrational modes. From the table above, it is clear that Mode 2 and 3 are degenerate, and Mode 5 and 6 are degenerate; this suggests that we can expect to see 4 bands in the experimental spectrum of gaseous ammonia. Modes 1, 2 and 3 are "bending" vibrations and Modes 4, 5 and 6 are "bond stretch" vibrations, with Mode 4 being highly symmetric. Mode 1 is known as the "umbrella mode".
Charge Analysis
Since nitrogen is an electronegative atom, we can expect its charge to be negative. We can also expect the charge on a hydrogen atom to be positive.
Charge on N-atom = -1.125C
Charge on H-atom = 0.375C
N2 Molecule
General Information
Name: Nitrogen (N2)
Calculation Method:RB3LYP
Basis Set: 6-31G(d,p)
Final Energy [E(RB3LYP)] = -109.52412868 a.u.
RMS Gradient = 0.00000365 a.u.
Symmetry=D∞h
Geometric Information
For Optimised Structure
Bond Distance (N-N): 1.10550Å
Bond Angle (N-N): 180°
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 0.000003 0.001200 YES
Predicted change in Energy=-1.248809D-11
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) 1.1055 -DE/DX = 0.0 !
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N2 Molecule |
The optimisation file is liked to here
Vibrational Analysis
The table shows that a nitrogen molecule has one vibrational mode. This mode is a "bond stretch" vibration which is highly symmetric.
H2 Molecule
General Information
Name: Hydrogen (H2)
Calculation Method:RB3LYP
Basis Set: 6-31G(d,p)
Final Energy [E(RB3LYP)] = -1.17853930 a.u.
RMS Gradient = 0.00012170 a.u.
Symmetry=D∞h
Geometric Information
For Optimised Structure
Bond Distance (H-H): 0.74309Å
Bond Angle (H-H): 180°
Item Value Threshold Converged?
Maximum Force 0.000211 0.000450 YES
RMS Force 0.000211 0.000300 YES
Maximum Displacement 0.000278 0.001800 YES
RMS Displacement 0.000393 0.001200 YES
Predicted change in Energy=-5.852867D-08
Optimization completed.
-- Stationary point found.
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! Optimized Parameters !
! (Angstroms and Degrees) !
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! Name Definition Value Derivative Info. !
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! R1 R(1,2) 0.7431 -DE/DX = -0.0002 !
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H2 Molecule |
The optimisation file is liked to here
Vibrational Analysis
The table shows that a hydrogen molecule has one vibrational mode. This mode is a "bond stretch" vibration which is highly symmetric. It is of a very high vibrational frequency because H atoms have a very low atomic mass.
Reaction of N2 with H2
E(NH3)= -56.55776873 a.u.
2*E(NH3)= -113.11537460 a.u.
E(N2)= -109.52412868 a.u.
E(H2)= -1.17853930 a.u.
3*E(H2)= -3.53561790 a.u.
ΔE=2*E(NH3)-[E(N2)+3*E(H2)]= -0.0556281 a.u. = -146.0515765kJ/mol = -146.05kJ/mol (2dp)
The energy of the reactants is higher than the energy of the products, showing that the ammonia product is more stable than the gaseous reactants.
Project Molecule - HCl Molecule
General Information
Name: HCl
Calculation Method:RB3LYP
Basis Set: 6-31G(d,p)
Final Energy [E(RB3LYP)] = -460.80077876 a.u.
RMS Gradient = 0.00000004 a.u.
Symmetry=C∞v
Geometric Information
For Optimised Structure
Bond Distance (H-Cl): 1.28613Å
Bond Angle (H-Cl): 180°
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 0.000000 0.001200 YES
Predicted change in Energy=-9.317109D-15
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) 1.2861 -DE/DX = 0.0 !
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HCl Molecule |
The optimisation file is liked to here
Vibrational Analysis
The table shows that HCl has one vibrational mode which is a "bond stretch". This is highly symmetric.
Charge Analysis
Chlorine is an electronegative atom so we can expect its charge to be negative. We can also expect the charge on the hydrogen atom to be positive.
Charge on Cl-atom = -0.284C
Charge on H-atom = 0.284C
Molecular Orbitals
The figure above shows the non-bonding molecular orbital of HCl. This molecular orbital has complete s character since it has contribution solely from the 3s atomic orbital of the Cl atom. It is a low energy molecular orbital.
The figure on the left shows the σ3pz bonding molecular orbital of HCl. It has 50:50 s to p character since it is made from the linear combination of the 1s atomic orbital from H and the 3pz atomic orbital from Cl - each of these atomic orbitals contributes one electron. This is also the HOMO (highest energy occupied molecular orbital).
The figures on the right and the centre show non-bonding molecular orbitals of HCl. They have 100% p character since their electrons come from the 3px and 3py atomic orbitals of Cl. They are both degenerate and are higher energy than the σ3pz orbital (because they are non bonding and are therefore less stable).
The figure above shows the antibonding molecular orbital of HCl (which is part of the bonding/antibonding pair with the σ3pz molecular orbital). It is generated from the linear combination (out of phase) of the 1s atomic orbital from H and the 3pz atomic orbital from Cl. This orbital is the LUMO (lowest energy unoccupied molecular orbital).