Rep:Mod:myfirstwikipage
NH3
Summary Information
Molecule: NH3
Calculation Method: RB3LYP
Basis Set: 6-31G(d.p)
Final Energy: -56.55776873 a.u.
RMS Gradient: 0.000000485 a.u.
Point Group: C3V
H-N-H Bond Angle: 105.74115o
N-H Bond Length: 1.01798 Å
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=-5.986292D-10 Optimization completed. -- Stationary point found.
! 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 |
Vibrations
1) N = 4 , so the number of modes = 3 x 4 - 6 = 6. One would expect 6 vibrational modes.
2) Modes 2 and 3 and modes 5 and 6 are degenerate.
3) Bending vibrations: modes 1,2 and 3 Bond stretches: modes 4,5 and 6
4) Mode 4
5) Mode 1
6) 5 bands. Mode 4 would not produce a band as it is a symmetric stretch and there is no change in dipole.
Charge Distribution
Charge on N-atom: -1.125
Charge on each H-atom: +0.375
We would expect the partial charge on the N-atom to be negative, as nitrogen is more electronegative than hydrogen. Hence, the expected partial charge on the H-atoms of ammonia are expected to be positive. This agrees with the partial charges computed by Gaussview.
N2
Summary Information
Molecule: N2
Calculation Method: RB3LYP
Basis Set: 6-31G(d.p)
Final Energy: - 109.52412868 a.u.
RMS Gradient: 0.00000060 a.u.
Point Group: D*H
N-N Bond Angle: 180o
N-N Bond Length: 1.10550 Å
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=-3.401146D-13
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 |
Vibrations
No negative frequencies
H2
Summary Information
Molecule: H2
Calculation Method: RB3LYP
Basis Set: 6-31G(d.p)
Final Energy: -1.17853936 a.u.
RMS Gradient: 0.00000017 a.u.
Point Group: D*H
H-H Bond Angle: 180o
H-H Bond Length: 0.74279 Å
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.
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! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
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H2 molecule |
Vibrations
No negative frequencies
Haber-Bosch Reaction
N2 + H2 -> NH3
E(NH3)= -56.55776873 a.u.
2*E(NH3)= -113.1155375 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)]= -113.1155375 - ( - 109.52412868 + -3.53561808) = -0.05579074 a.u.
ΔE= -0.05579074 a.u. = -0.05579074*2625.5 kJ/mol = -146.48 kJ/mol
HCl
Summary Information
Molecule: HCl
Calculation Method: RB3LYP
Basis Set: 6-31G(d.p)
Final Energy: -460.80077875 a.u.
RMS Gradient: 0.00005211 a.u.
Point Group: C*V
H-Cl Bond Angle: 180o
H-Cl Bond Length: 1.28599 Å
Item Value Threshold Converged?
Maximum Force 0.000090 0.000450 YES
RMS Force 0.000090 0.000300 YES
Maximum Displacement 0.000139 0.001800 YES
RMS Displacement 0.000197 0.001200 YES
Predicted change in Energy=-1.256951D-08
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) 1.286 -DE/DX = 0.0001 !
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HCl molecule |
Vibrations
Number of vibrational modes: 1. This the number of modes one would anticipate, as 3*(2)-5 = 1 (according to the 3N-5 rule for linear molecules).
Charge Distribution
Charge on H-atom: +0.185
Charge on Cl-atom: -0.185
Charge distribution is equal and opposite, as expected, as the molecule is neutral overall. As anticipated, the more electronegative carries the negative partial charge.
Molecular Bonding
[1]
MO energy diagram of HCl (for n=3)
The image shows one the two non-bonding 2p-orbitals (from the Cl-atom). The energy of this orbital is -7.22836 a.u. . These two orbitals do not contribute to the bonding at all.
The image illustrates the σ3pz bonding orbital. This bonding σ-orbital is formed by the overlap of the H-atom's 1s-orbital and the Cl-atom's 3pz-orbital. The energy of the orbital is -0.47433 a.u. . It is evident, that the Cl-atom contributes more to the bonding than the H-atom, as the overall shape of the bonding orbital resembles a slightly rounded dumbbell. The dumbbell shape is similar to the 3pz-orbital form the Cl-atom involved in the bonding.
Each image shows one of the two non-bonding 3p-orbitals (3px and 3py)from the Cl-atom. Both orbitals are degenerate at an energy of -0.33163 a.u. . Each 3p-MO is occupied with two lone pair electrons. Both of these filled 3p-orbitals are degenerate HOMOs (highest occupied molecular orbitals). These two non-bonding orbitals do not contribute to the bonding at all.
The picture displays the anitbonding σ*pz orbital. This orbital is the LUMO (lowest unoccupied molecular orbital), which is unfilled, containing no electrons. The energy of this antibonding orbital is 0.01366 a.u. .
Independent Work: Cl2
Summary Information
Molecule: Cl2
Calculation Method: RB3LYP
Basis Set: 6-31G(d.p)
Final Energy: -920.34987886 a.u.
RMS Gradient: 0.00002510 a.u.
Point Group: D*H
Cl-Cl Bond Angle: 180o
Cl-Cl Bond Length: 2.04174 Å
Item Value Threshold Converged? Maximum Force 0.000043 0.000450 YES RMS Force 0.000043 0.000300 YES Maximum Displacement 0.000121 0.001800 YES RMS Displacement 0.000172 0.001200 YES Predicted change in Energy=-5.277179D-09 Optimization completed. -- Stationary point found.
Vibrations
No negative frequencies
Charge Distribution
There is no charge on any of the two Cl-atoms, as expected. Each Cl-atom has an equal attraction for the shared pair of electrons in the covalent bond.