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Rep:Mod:01358709

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Molecules

NH3

General information

Property Value
Calculation method RB3LYP
Basis set 6-31G(d,p)
Final energy -56.5577683 a.u.
RMS gradient 0.00000485 a.u.
Point group C3v
N-H bond length 1.01798 Å
H-N-H bond angle 105.741˚
Charge(N) -1.125
Charge(H) 0.375

N has negative charge and H has positive which is to be expected since N is a more electronegative element. 

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=-5.986272D-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                 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

[| NH3 optimization]

File:KERLI TALI NH3 OPTIMIZATION.LOG

Optimized NH3 molecule

Vibrations

Vibrations for NH3 molecule

From 3N-6 rule I would expect 3×4-6=6 vibrations, which is how many there are in the table. 1-3 in the table are bending vibrations and 4-6 are stretching vibrations. Modes 2,3 and 5,6 are degenerate. Mode 4 is highly symmetric. Vibration 1 is called the umbrella mode. I would expect to see 3 bands in an experimental spectrum of gaseous ammonia (mode 1, 2&3, 4) because modes 5 and 6 have a very low frequency and these are not likely to be visible due to noise.












N2

Property Value
Calculation method RB3LYP
Basis set 6-31G(d,p)
Final energy -109.52412868 a.u.
RMS gradient 0.00000365 a.u.
Point group D*H
Bond length 1.10550 Å

IR spectra of N2 will not show any bands because N2 is a linear molecule without dipole moment so there is not a vibration that it could undergo that would generate dipole moment. 

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.
                          ----------------------------
                          !   Optimized Parameters   !
                          ! (Angstroms and Degrees)  !
--------------------------                            --------------------------
! Name  Definition              Value          Derivative Info.                !
--------------------------------------------------------------------------------
! R1    R(1,2)                  1.1055         -DE/DX =    0.0                 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

[| N2 optimization]

File:N2OPTKTALI1.LOG

Optimized N2 molecule


H2

Property Value
Calculation method RB3LYP
Basis set 6-31G(d,p)
Final energy -1.17853864 a.u.
RMS gradient 0.00000204 a.u.
Point group D*H
Bond length 0.74279 Å

IR spectra of H2 will not show any bands because H2 is a linear molecule without dipole moment so there is not a vibration that it could undergo that would generate dipole moment. 


Item               Value     Threshold  Converged?
Maximum Force            0.000004     0.000450     YES
RMS     Force            0.000004     0.000300     YES
Maximum Displacement     0.000005     0.001800     YES
RMS     Displacement     0.000007     0.001200     YES
Predicted change in Energy=-1.634290D-11
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                 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

[| H2 optimization]

File:H2OPTKTALI3.LOG

Optimized H2 molecule


H2S

General information

Property Value !
Calculation method RB3LYP
Basis set 6-31G(d,p)
Final energy -399.39162414 a.u.
RMS gradient 0.00012068 a.u.
Point group C2v
Dipole moment 1.3993 Debye
H-S bond length 1.34737 Å
H-S-H bond angle 92.681˚
Charge(S) -0.312
Charge(H) 0.156


Charge is positive on H and negative on S which I would expect since S is a more electronegative element. 


     Item               Value     Threshold  Converged?
Maximum Force            0.000175     0.000450     YES
RMS     Force            0.000145     0.000300     YES
Maximum Displacement     0.000472     0.001800     YES
RMS     Displacement     0.000386     0.001200     YES
Predicted change in Energy=-1.208488D-07
Optimization completed.
   -- Stationary point found.
                          ----------------------------
                          !   Optimized Parameters   !
                          ! (Angstroms and Degrees)  !
--------------------------                            --------------------------
! Name  Definition              Value          Derivative Info.                !
--------------------------------------------------------------------------------
! R1    R(1,2)                  1.3474         -DE/DX =    0.0002              !
! R2    R(1,3)                  1.3474         -DE/DX =    0.0002              !
! A1    A(2,1,3)               92.681          -DE/DX =    0.0                 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

[| H2S optimization]


File:H2SOPTKTALI.LOG

Optimized H2S molecule

Vibrations

Vibrations for H2S

Mode 1 is a bending vibration and 2,3 are bond stretch vibrations. I would expect to see 3 peaks in IR spectra as none of the modes are degenerate.














Molecular orbitals

1s(H) and 2p(S) atomic orbitals contribute to the MO. MO is occupied and bonding. It is quite deep in energy compared to valence shell MOs so does not contribute to chemical bonding.
|
1s(H) and 3s(S) atomic orbitals contribute to MO. It is occupied, bonding and valence shell orbital so involved in the bonding.
1s(H) and 3p(S) atomic orbitals contribute to MO. MO is occupied, bonding, second-highest occupied molecular orbital so involved in bonding.
1s(H) and 3p(S) atomic orbitals contribute to MO. MO is occupied, antibonding and HOMO.
1s(H) and 3p(S) atomic orbitals contribute to MO. MO is unoccupied, antibonding, LUMO.

BH3

General information

Property Value
Calculation method RB3LYP
Basis set 6-31G(d,p)
Final energy -26.61532362 a.u.
RMS gradient 0.00003234 a.u.
Point group D3H
B-H bond length 1.19219 Å
H-B-H bond angle 120.000˚
Charge(B) 0.297
Charge(H) -0.099 
 Item               Value     Threshold  Converged?
Maximum Force            0.000065     0.000450     YES
RMS     Force            0.000042     0.000300     YES
Maximum Displacement     0.000254     0.001800     YES
RMS     Displacement     0.000166     0.001200     YES
Predicted change in Energy=-2.465372D-08
Optimization completed.
   -- Stationary point found.
                          ----------------------------
                          !   Optimized Parameters   !
                          ! (Angstroms and Degrees)  !
--------------------------                            --------------------------
! Name  Definition              Value          Derivative Info.                !
--------------------------------------------------------------------------------
! R1    R(1,2)                  1.1922         -DE/DX =    0.0001              !
! R2    R(1,3)                  1.1922         -DE/DX =    0.0001              !
! R3    R(1,4)                  1.1922         -DE/DX =    0.0001              !
! A1    A(2,1,3)              120.0            -DE/DX =    0.0                 !
! A2    A(2,1,4)              120.0            -DE/DX =    0.0                 !
! A3    A(3,1,4)              120.0            -DE/DX =    0.0                 !
! D1    D(2,1,4,3)            180.0            -DE/DX =    0.0                 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

[| BH3 optimization]

File:BH3OPTKTALI.LOG

Optimized BH3 molecule

Vibrations

BH3 vibrations

From 3N-6 rule I would expect 6 modes. 1-3 are bending vibrational modes and 4-6 are stretching vibrational modes. 2,3 and 5,6 mode are degenerate. In the experimental spectrum I would expect to see 3 modes (1,2&3,5&6) since mode 4 will not show in IR (no dipole moment change).















Haber-Bosch process

Reaction for Haber-Bosch process is N2 + 3H2 → 2NH3

Molecule Energy (a.u.)
E(NH3) -56.5577683
2*E(NH3) -113.1155366
E(H2) -1.17853864
3*E(H2) -3.53561592
E(N2) -109.52412868
ΔE=2*E(NH3)-[E(N2)+3*E(H2)] -0.0557921

ΔE=-146.48 kJ/mol

According to this energy difference, ammonia is more stable than the gaseous reactants.

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