NH_3 Molecule

Calculation Method: RCAM-B3LYP

Basis Set: 6-311G(d,p)

E(RB3LYP) = -56.54485793 au

RMS Gradient Norm = 0.00022465

Point Group = C_3v

N-H Bond Length = 1.01400 Å

H-N-H Bond Angle = 107.00922 deg.

Point Group = C_3V

Item Value Threshold Converged?
Maximum Force 0.000349 0.000450 YES
RMS Force 0.000230 0.000300 YES
Maximum Displacement 0.001447 0.001800 YES
RMS Displacement 0.000644 0.001200 YES
Predicted change in Energy=-5.585487D-07
Optimization completed.

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>DARKO_NH3_OPTF_POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

{| class="wikitable"
!Vibrational Symmetry
!A1(1)
!E(2)
!E(3)
!A1(4)
!E(5)
!E(6)
|-
|Frequency (cm**-1)
|1053.9677
|1682.6088
|1682.6088
|3498.1057
|3618.7943
|3618.7944
|-
|IR Intensity (KM/Mole)
|186.4681
|21.3876
|21.3877
|0.1001
|0.3010
|0.3011
|-
|Screenshot
|[[File:Dv818 nh3 vibration 1.jpg|thumb|NH_3, Vibration 1053.97]]
|[[File:Dv818 nh3 vibration 2.jpg|thumb|NH_3, Vibration 1682.61]]
|[[File:Dv818 nh3 vibration 3.jpg|thumb|NH_3, Vibration 1682.61]]
|[[File:Dv818 nh3 vibration 4.jpg|thumb|NH_3, Vibration 3498.11]]
|[[File:Dv818 nh3 vibration 5.jpg|thumb|NH_3, Vibration 3618.79]]
|[[File:Dv818 nh3 vibration 6.jpg|thumb|NH_3, Vibration 3618.79]]
|}
In 3N - 6 number of vibrational modes (nonlinear molecule), N refers to the number of atoms so 6 vibrational modes were expected (as shown by Gaussview). There are two sets of degenerate modes: 2 at frequency = 1682.6088 cm**-1 and 2 at frequency = 3618.7944 cm**-1). The three modes with frequency = 3498.1057 and 3618.7944 are stretching modes (symmetric and 2 asymmetric stretches, respectively) and the three modes with frequency = 1053.9677 (additionally the umbrella mode, with H atoms moving equally forwards/backwards) cm**-1 and 1682.6088 cm**-1 are bending modes (wagging and 2 scissoring, respectively) . Vertical symmetry (σ_h) is observed in A1 (1) at 1053.97 cm**-1cm**-1, horizontal symmetry (σ_v) is observed at 3498.11 cm**-1 (A1) and 3618.79 cm**-1. However, at 3498.11 cm**-1, there is further inversion symmetry (''i''), three perpendicular C_2 axis, and a C_3 rotation (principle axis). An IR spectrum would show 4 distinct peaks since there are two degenerate pairs of vibrations, whilst vibration at 1053.97 cm**-1 would have greatest intensity (186.4681 KM/Mole).

N (charge) = -1.020
H (charge on all) = 0.340
Since N is more electronegative than H, it is to be expected that N carries a partial negative charge and since the overall charge on the molecule must be 0 (neutral molecule), the individual charges must cancel out. The N:H charge ratio is much higher than what would be expected by simply considering the absolute (Mulliken) electronegativities of each element.

N_2 molecule:
Calculation Method: RCAM-B3LYP

Basis Set: 6-31G(d,p)

E(RB3LYP) = -109.52412868 au

RMS Gradient Norm = 0.00000282 au

N-N Bond Length = 1.10550 Å

Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000002 0.001800 YES
RMS Displacement 0.000002 0.001200 YES
Predicted change in Energy=-7.433917D-12
Optimization completed.

<jmol><jmolApplet>
<title>N_2 Optimised</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>DV818_N2_OPTF_POP_T4.LOG</uploadedFileContents>
</jmolApplet></jmol>

{| class="wikitable"
!Vibration
!SGG
|-
|Frequency(cm**-1)
|2457.35
|-
|IR Intensity (KM/Mole)
|0.0000
|-
|Screenshot
|[[File:Dv818 N2 vibration screenshot.jpg|thumb|N_2 Stretching Vibration, Screenshot]]
|}

The Charge Distribution on each Nitrogen atom is 0.000, since it is a diatomic element (equal electronegativities).

H_2 molecule
Calculation Method: RB3LYP

Basis Set: 6-31G(d,p)

E(RB3LYP) = -1.17853936 au

RMS Gradient Norm = 0.00000017

Point Group : D*H

H-H Bondlength = 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.

<jmol><jmolApplet>
<title>N_2 Optimised</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>DV818_H_2_OPTF_POP_T4.LOG</uploadedFileContents>
</jmolApplet></jmol>

{| class="wikitable"
!Vibration
!SGG
|-
|Frequency(cm**-1)
|4465.68
|-
|IR Intensity (KM/Mole)
|0.0000
|-
|Screenshot
|[[File:Dv818_H_2_vibration_screenshot.jpg|thumb|H_2 Stretching Vibration, Screenshot]]
|}

Charge Distribution on H1 = H2 = 0.00000 since equally electronegative.

Mono-metallic Crystal Compound: DAYSUR
N-N bond distance from Gaussian optimisation is 1.10550 Å whilst in DAYSUR it is 1.04 Å. Differences in Bond lengths are due to weak Coloumbic forces present in the crystal structure (a specific chemical environment). Also, presence of neighbouring delta positive Hydrogens could further stabilise the molecule, reducing the bond length.

Haber-Bosch Process Energy Analysis:

E(NH_3)= -56.54485793 au

2*E(NH_3)= -113.08971586 au

E(N_2)= -109.52412868 au

E(H_2)= -1.17853936 au

3*E(H_2)= -3.53561808 au

ΔE=2*E(NH_3)-[E(N_2)+3*E(H_2)]= -0.0299691 au ~ -78.7 kJ/Mol

Since a negative value is obtained, the forward reaction is exothermic suggesting that the product is more stable than the reactants.

CO_2 molecule:

Calculation Method: RB3LYP

Basis Set: 6-31G(d,p)

E(RB3LYP) = -188.58093945

RMS Gradient Norm : 0.00000014

Point Group: D*H

C=O Bond Length = 1.16916 Å

O=C=O Bond Angle = 180.0000 deg

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=-8.124204D-14
Optimization completed.

<jmol><jmolApplet>
<title>CO_2 Optimised</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>DV818_CO_2_OPTF_POP_T1.LOG</uploadedFileContents>
</jmolApplet></jmol>

{| class="wikitable"
!Vibration
!PIU
!PIU
!SGG
!SGG
|-
|Frequency(cm**-1)
|640.03
|640.03
|1372.02
|2436.27
|-
|IR Intensity (KM/Mole)
|30.72
|30.72
|0.00
|545.82
|-
|Screenshot
|[[File:Dv818_CO_2_screenshot1.jpg|thumb|CO_2 Bending Wag, Screenshot]]
|[[File:Dv818_CO_2_screenshot2.jpg|thumb|CO_2 Bending Wag, Screenshot]]
|[[File:Dv818_CO_2_screenshot3.jpg|thumb|CO_2 Symmetric Stretch, Screenshot]]
|[[File:Dv818_CO_2_screenshot4.jpg|thumb|CO_2 Asymmetric Stretch, Screenshot]][
|}

Charge Distribution: O1 = O2 = -0.511 , C = 1.022

{| class="wikitable"
!Molecular Orbital Energy (au)
!(MO=1, Bonding)
!(MO=2, Antibonding)
!(MO=3, Bonding)
!(MO=4, Bonding)
!(MO=6, Antibonding)
!(MO=7, Antibonding)
!(MO=11, HOMO)
!(MO=12, LUMO)
|-
|Energy (au)
|-19.23659
|-19.23658
|-10.38530
|-1.16098
|-0.56234
|-0.51655
|-0.36997
|0.02992
|-
|Gaussview Diagram
|[[File:Dv818_CO_2_MO_1.jpg|thumb|CO_2 MO=1, Screenshot]]
|[[File:Dv818_CO_2_MO_2.jpg|thumb|CO_2 MO=2, Screenshot]]
|[[File:Dv818_CO_2_MO_3.jpg|thumb|CO_2 MO=3, Screenshot]]
|[[File:Dv818_CO_2_MO_4.jpg|thumb|CO_2 MO=4, Screenshot]]
|[[File:Dv818_CO_2_MO_6.jpg ‎|thumb|CO_2 MO=6, Screenshot]]
|[[File:Dv818_CO_2_MO_7.jpg|thumb|CO_2 MO=7, Screenshot]]
|[[File:Dv818_CO_2_MO_11.jpg|thumb|CO_2 MO=11, Screenshot]]
|[[File:Dv818_CO_2_MO_12.jpg|thumb|CO_2 MO=12, Screenshot]][
|}

Considering MO=1 (E=-19.23659 au), the 1s Atomic Orbitals (AOs) contribute to the Molecular Orbital (MO); as such electrons are core and not valence, the overlap is small (almost negligible) as exemplified by MO=2 ,the Anti-bonding MO which is almost identical in energy. MO=3 (E= -10.38530 au) shows the sigma framework within CO_2 whilst MO=4 (E= -1.16098 au) shows the pi and sigma overlap (double bond) leading to a higher energy. M=11 (E= -0.36997 au) is the HOMO and an orbital resulting from mixing. M=12 (E = 0.02992 au) is the LUMO, thus has positive energy as there are no valence electrons that experience Coulomb forces of attraction.

Additional O_2 Molecule:

Calculation Method: RB3LYP

Basis Set: 6-31G(d,p)

E(RB3LYP) = -150.25742434 au

RMS Gradient Norm = 0.00007502

Point Group: D*H

O=O Bond Length = 1.21602 Å

Item Value Threshold Converged?
Maximum Force 0.000130 0.000450 YES
RMS Force 0.000130 0.000300 YES
Maximum Displacement 0.000080 0.001800 YES
RMS Displacement 0.000113 0.001200 YES
Predicted change in Energy=-1.033738D-08
Optimization completed.

<jmol><jmolApplet>
<title>CO_2 Optimised</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>DV818_O_2_OPTF_POP_T1.LOG</uploadedFileContents>
</jmolApplet></jmol>

{| class="wikitable"
!Vibration
!SGG
|-
|Frequency(cm**-1)
|1642.74
|-
|IR Intensity (KM/Mole)
| 0.0000
|-
|Screenshot
|[[File:Dv818_O_2_Vibration.jpg|thumb|H_2 Stretching Vibration, Screenshot]]
|}

File:Dv818 O 2 Vibration.jpg

2019-03-08T17:09:54Z

Dv818:

Rep:Mod:dv818

2019-03-08T17:05:37Z

Dv818:

NH_3 Molecule

Calculation Method: RCAM-B3LYP

Basis Set: 6-311G(d,p)

E(RB3LYP) = -56.54485793 au

RMS Gradient Norm = 0.00022465

Point Group = C_3v

N-H Bond Length = 1.01400 Å

H-N-H Bond Angle = 107.00922 deg.

Point Group = C_3V

Item Value Threshold Converged?
Maximum Force 0.000349 0.000450 YES
RMS Force 0.000230 0.000300 YES
Maximum Displacement 0.001447 0.001800 YES
RMS Displacement 0.000644 0.001200 YES
Predicted change in Energy=-5.585487D-07
Optimization completed.

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>DARKO_NH3_OPTF_POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

{| class="wikitable"
!Vibrational Symmetry
!A1(1)
!E(2)
!E(3)
!A1(4)
!E(5)
!E(6)
|-
|Frequency (cm**-1)
|1053.9677
|1682.6088
|1682.6088
|3498.1057
|3618.7943
|3618.7944
|-
|IR Intensity (KM/Mole)
|186.4681
|21.3876
|21.3877
|0.1001
|0.3010
|0.3011
|-
|Screenshot
|[[File:Dv818 nh3 vibration 1.jpg|thumb|NH_3, Vibration 1053.97]]
|[[File:Dv818 nh3 vibration 2.jpg|thumb|NH_3, Vibration 1682.61]]
|[[File:Dv818 nh3 vibration 3.jpg|thumb|NH_3, Vibration 1682.61]]
|[[File:Dv818 nh3 vibration 4.jpg|thumb|NH_3, Vibration 3498.11]]
|[[File:Dv818 nh3 vibration 5.jpg|thumb|NH_3, Vibration 3618.79]]
|[[File:Dv818 nh3 vibration 6.jpg|thumb|NH_3, Vibration 3618.79]]
|}
In 3N - 6 number of vibrational modes (nonlinear molecule), N refers to the number of atoms so 6 vibrational modes were expected (as shown by Gaussview). There are two sets of degenerate modes: 2 at frequency = 1682.6088 cm**-1 and 2 at frequency = 3618.7944 cm**-1). The three modes with frequency = 3498.1057 and 3618.7944 are stretching modes (symmetric and 2 asymmetric stretches, respectively) and the three modes with frequency = 1053.9677 (additionally the umbrella mode, with H atoms moving equally forwards/backwards) cm**-1 and 1682.6088 cm**-1 are bending modes (wagging and 2 scissoring, respectively) . Vertical symmetry (σ_h) is observed in A1 (1) at 1053.97 cm**-1cm**-1, horizontal symmetry (σ_v) is observed at 3498.11 cm**-1 (A1) and 3618.79 cm**-1. However, at 3498.11 cm**-1, there is further inversion symmetry (''i''), three perpendicular C_2 axis, and a C_3 rotation (principle axis). An IR spectrum would show 4 distinct peaks since there are two degenerate pairs of vibrations, whilst vibration at 1053.97 cm**-1 would have greatest intensity (186.4681 KM/Mole).

N (charge) = -1.020
H (charge on all) = 0.340
Since N is more electronegative than H, it is to be expected that N carries a partial negative charge and since the overall charge on the molecule must be 0 (neutral molecule), the individual charges must cancel out. The N:H charge ratio is much higher than what would be expected by simply considering the absolute (Mulliken) electronegativities of each element.

N_2 molecule:
Calculation Method: RCAM-B3LYP

Basis Set: 6-31G(d,p)

E(RB3LYP) = -109.52412868 au

RMS Gradient Norm = 0.00000282 au

N-N Bond Length = 1.10550 Å

Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000002 0.001800 YES
RMS Displacement 0.000002 0.001200 YES
Predicted change in Energy=-7.433917D-12
Optimization completed.

<jmol><jmolApplet>
<title>N_2 Optimised</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>DV818_N2_OPTF_POP_T4.LOG</uploadedFileContents>
</jmolApplet></jmol>

{| class="wikitable"
!Vibration
!SGG
|-
|Frequency(cm**-1)
|2457.35
|-
|IR Intensity (KM/Mole)
|0.0000
|-
|Screenshot
|[[File:Dv818 N2 vibration screenshot.jpg|thumb|N_2 Stretching Vibration, Screenshot]]
|}

The Charge Distribution on each Nitrogen atom is 0.000, since it is a diatomic element (equal electronegativities).

H_2 molecule
Calculation Method: RB3LYP

Basis Set: 6-31G(d,p)

E(RB3LYP) = -1.17853936 au

RMS Gradient Norm = 0.00000017

Point Group : D*H

H-H Bondlength = 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.

<jmol><jmolApplet>
<title>N_2 Optimised</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>DV818_H_2_OPTF_POP_T4.LOG</uploadedFileContents>
</jmolApplet></jmol>

{| class="wikitable"
!Vibration
!SGG
!
!
|-
|Frequency(cm**-1)
|4465.68
|
|
|-
|IR Intensity (KM/Mole)
|0.0000
|
|
|-
|Screenshot
|[[File:Dv818_H_2_vibration_screenshot.jpg|thumb|H_2 Stretching Vibration, Screenshot]]
|
|
|}

Charge Distribution on H1 = H2 = 0.00000 since equally electronegative.

Mono-metallic Crystal Compound: DAYSUR
N-N bond distance from Gaussian optimisation is 1.10550 Å whilst in DAYSUR it is 1.04 Å. Differences in Bond lengths are due to weak Coloumbic forces present in the crystal structure (a specific chemical environment). Also, presence of neighbouring delta positive Hydrogens could further stabilise the molecule, reducing the bond length.

Haber-Bosch Process Energy Analysis:

E(NH_3)= -56.54485793 au

2*E(NH_3)= -113.08971586 au

E(N_2)= -109.52412868 au

E(H_2)= -1.17853936 au

3*E(H_2)= -3.53561808 au

ΔE=2*E(NH_3)-[E(N_2)+3*E(H_2)]= -0.0299691 au ~ -78.7 kJ/Mol

Since a negative value is obtained, the forward reaction is exothermic suggesting that the product is more stable than the reactants.

CO_2 molecule:

Calculation Method: RB3LYP

Basis Set: 6-31G(d,p)

E(RB3LYP) = -188.58093945

RMS Gradient Norm : 0.00000014

Point Group: D*H

C=O Bond Length = 1.16916 Å

O=C=O Bond Angle = 180.0000 deg

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=-8.124204D-14
Optimization completed.

<jmol><jmolApplet>
<title>CO_2 Optimised</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>DV818_CO_2_OPTF_POP_T1.LOG</uploadedFileContents>
</jmolApplet></jmol>

{| class="wikitable"
!Vibration
!PIU
!PIU
!SGG
!SGG
|-
|Frequency(cm**-1)
|640.03
|640.03
|1372.02
|2436.27
|-
|IR Intensity (KM/Mole)
|30.72
|30.72
|0.00
|545.82
|-
|Screenshot
|[[File:Dv818_CO_2_screenshot1.jpg|thumb|CO_2 Bending Wag, Screenshot]]
|[[File:Dv818_CO_2_screenshot2.jpg|thumb|CO_2 Bending Wag, Screenshot]]
|[[File:Dv818_CO_2_screenshot3.jpg|thumb|CO_2 Symmetric Stretch, Screenshot]]
|[[File:Dv818_CO_2_screenshot4.jpg|thumb|CO_2 Asymmetric Stretch, Screenshot]][
|}

Charge Distribution: O1 = O2 = -0.511 , C = 1.022

{| class="wikitable"
!Molecular Orbital Energy (au)
!(MO=1, Bonding)
!(MO=2, Antibonding)
!(MO=3, Bonding)
!(MO=4, Bonding)
!(MO=6, Antibonding)
!(MO=7, Antibonding)
!(MO=11, HOMO)
!(MO=12, LUMO)
|-
|Energy (au)
|-19.23659
|-19.23658
|-10.38530
|-1.16098
|-0.56234
|-0.51655
|-0.36997
|0.02992
|-
|Gaussview Diagram
|[[File:Dv818_CO_2_MO_1.jpg|thumb|CO_2 MO=1, Screenshot]]
|[[File:Dv818_CO_2_MO_2.jpg|thumb|CO_2 MO=2, Screenshot]]
|[[File:Dv818_CO_2_MO_3.jpg|thumb|CO_2 MO=3, Screenshot]]
|[[File:Dv818_CO_2_MO_4.jpg|thumb|CO_2 MO=4, Screenshot]]
|[[File:Dv818_CO_2_MO_6.jpg ‎|thumb|CO_2 MO=6, Screenshot]]
|[[File:Dv818_CO_2_MO_7.jpg|thumb|CO_2 MO=7, Screenshot]]
|[[File:Dv818_CO_2_MO_11.jpg|thumb|CO_2 MO=11, Screenshot]]
|[[File:Dv818_CO_2_MO_12.jpg|thumb|CO_2 MO=12, Screenshot]][
|}

Considering MO=1 (E=-19.23659 au), the 1s Atomic Orbitals (AOs) contribute to the Molecular Orbital (MO); as such electrons are core and not valence, the overlap is small (almost negligible) as exemplified by MO=2 ,the Anti-bonding MO which is almost identical in energy. MO=3 (E= -10.38530 au) shows the sigma framework within CO_2 whilst MO=4 (E= -1.16098 au) shows the pi and sigma overlap (double bond) leading to a higher energy. M=11 (E= -0.36997 au) is the HOMO and an orbital resulting from mixing. M=12 (E = 0.02992 au) is the LUMO, thus has positive energy as there are no valence electrons that experience Coulomb forces of attraction.

Additional O_2 Molecule:

Calculation Method: RB3LYP

Basis Set: 6-31G(d,p)

E(RB3LYP) = -150.25742434 au

RMS Gradient Norm = 0.00007502

Point Group: D*H

O=O Bond Length = 1.21602 Å

Item Value Threshold Converged?
Maximum Force 0.000130 0.000450 YES
RMS Force 0.000130 0.000300 YES
Maximum Displacement 0.000080 0.001800 YES
RMS Displacement 0.000113 0.001200 YES
Predicted change in Energy=-1.033738D-08
Optimization completed.

<jmol><jmolApplet>
<title>CO_2 Optimised</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>DV818_O_2_OPTF_POP_T1.LOG</uploadedFileContents>
</jmolApplet></jmol>

2019-03-08T16:09:02Z

Dv818:

Rep:Mod:dv818

2019-03-08T16:08:45Z

File:Dv818 CO 2 MO 12.jpg

2019-03-08T15:58:20Z

Dv818:

File:Dv818 CO 2 MO 11.jpg

2019-03-08T15:58:10Z

Dv818:

2019-03-08T14:47:11Z

Dv818: Dv818 uploaded a new version of File:Dv818 CO 2 screenshot1.jpg

Rep:Mod:dv818

2019-03-08T14:46:51Z

Dv818:

NH_3 Molecule

Calculation Method: RCAM-B3LYP

Basis Set: 6-311G(d,p)

E(RB3LYP) = -56.54485793 au

RMS Gradient Norm = 0.00022465

Point Group = C_3v

N-H Bond Length = 1.01400 Å
H-N-H Bond Angle = 107.00922 deg.

Point Group = C3V

Item Value Threshold Converged?
Maximum Force 0.000349 0.000450 YES
RMS Force 0.000230 0.000300 YES
Maximum Displacement 0.001447 0.001800 YES
RMS Displacement 0.000644 0.001200 YES
Predicted change in Energy=-5.585487D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.014 -DE/DX = -0.0003 !
! R2 R(1,3) 1.014 -DE/DX = -0.0003 !
! R3 R(1,4) 1.014 -DE/DX = -0.0003 !
! A1 A(2,1,3) 107.0092 -DE/DX = 0.0 !
! A2 A(2,1,4) 107.0092 -DE/DX = 0.0 !
! A3 A(3,1,4) 107.0092 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -114.4235 -DE/DX = 0.0 !
--------------------------------------------------------------------------------

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>DARKO_NH3_OPTF_POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:Dv818 screenshot 1.jpg|thumb|NH_3 (optimised), Vibrations Display, screenshot ]
|}
{| class="wikitable"
!Vibrational Symmetry
!A1(1)
!E(2)
!E(3)
!A1(4)
!E(5)
!E(6)
|-
|Frequency (cm**-1)
|1053.9677
|1682.6088
|1682.6088
|3498.1057
|3618.7943
|3618.7944
|-
|IR Intensity (KM/Mole)
|186.4681
|21.3876
|21.3877
|0.1001
|0.3010
|0.3011
|-
|Screenshot
|[[File:Dv818 nh3 vibration 1.jpg|thumb|NH_3, Vibration 1053.97]]
|[[File:Dv818 nh3 vibration 2.jpg|thumb|NH_3, Vibration 1682.61]]
|[[File:Dv818 nh3 vibration 3.jpg|thumb|NH_3, Vibration 1682.61]]
|[[File:Dv818 nh3 vibration 4.jpg|thumb|NH_3, Vibration 3498.11]]
|[[File:Dv818 nh3 vibration 5.jpg|thumb|NH_3, Vibration 3618.79]]
|[[File:Dv818 nh3 vibration 6.jpg|thumb|NH_3, Vibration 3618.79]]
|}
In 3N - 6 number of vibrational modes (nonlinear molecule), N refers to the number of atoms so 6 vibrational modes were expected (as shown by Gaussview). There are two sets of degenerate modes: 2 at frequency = 1682.6088 cm**-1 and 2 at frequency = 3618.7944 cm**-1). The three modes with frequency = 3498.1057 and 3618.7944 are stretching modes (symmetric and 2 asymmetric stretches, respectively) and the three modes with frequency = 1053.9677 (additionally the umbrella mode, with H atoms moving equally forwards/backwards) cm**-1 and 1682.6088 cm**-1 are bending modes (wagging and 2 scissoring, respectively) . Vertical symmetry (σ_h) is observed in A1 (1) at 1053.97 cm**-1cm**-1, horizontal symmetry (σ_v) is observed at 3498.11 cm**-1 (A1) and 3618.79 cm**-1. However, at 3498.11 cm**-1, there is further inversion symmetry (''i''), three perpendicular C_2 axis, and a C_3 rotation (principle axis). An IR spectrum would show 4 distinct peaks since there are two degenerate pairs of vibrations, whilst vibration at 1053.97 cm**-1 would have greatest intensity (186.4681 KM/Mole).

N (charge) = -1.020
H (charge on all) = 0.340
Since N is more electronegative than H, it is to be expected that N carries a partial negative charge and since the overall charge on the molecule must be 0 (neutral molecule), the individual charges must cancel out. The N:H charge ratio is much higher than what would be expected by simply considering the absolute (Mulliken) electronegativities of each element.

N_2 molecule:
Calculation Method: RCAM-B3LYP

Basis Set: 6-31G(d,p)

E(RB3LYP) = -109.52412868 au

RMS Gradient Norm = 0.00000282 au

N-N Bond Length = 1.10550 Å

Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000002 0.001800 YES
RMS Displacement 0.000002 0.001200 YES
Predicted change in Energy=-7.433917D-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 !
--------------------------------------------------------------------------------

<jmol><jmolApplet>
<title>N_2 Optimised</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>DV818_N2_OPTF_POP_T4.LOG</uploadedFileContents>
</jmolApplet></jmol>
|
|
|}
{| class="wikitable"
!Vibration
!SGG
!
!
|-
|Frequency(cm**-1)
|2457.35
|
|
|-
|IR Intensity (KM/Mole)
|0.0000
|
|
|-
|Screenshot
|[[File:Dv818 N2 vibration screenshot.jpg|thumb|N_2 Stretching Vibration, Screenshot]]
|
|
|}

The Charge Distribution on each Nitrogen atom is 0.000, since it is a diatomic element (equal electronegativities).

H_2 molecule
Calculation Method: RB3LYP
Basis Set: 6-31G(d,p)
E(RB3LYP) = -1.17853936 au
RMS Gradient Norm = 0.00000017
Point Group : D*H
H-H Bondlength = 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.

<jmol><jmolApplet>
<title>N_2 Optimised</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>DV818_H_2_OPTF_POP_T4.LOG</uploadedFileContents>
</jmolApplet></jmol>

|
|
|}
{| class="wikitable"
!Vibration
!SGG
!
!
|-
|Frequency(cm**-1)
|4465.68
|
|
|-
|IR Intensity (KM/Mole)
|0.0000
|
|
|-
|Screenshot
|[[File:Dv818_H_2_vibration_screenshot.jpg|thumb|H_2 Stretching Vibration, Screenshot]]
|
|
|}

Charge Distribution on H1 = H2 = 0.00000 since equally electronegative.

Mono-metallic Crystal Compound: DAYSUR
N-N bond distance from Gaussian optimisation is 1.10550 Å whilst in DAYSUR it is 1.04 Å. Differences in Bond lengths are due to weak Coloumbic forces present in the crystal structure (a specific chemical environment). Also, presence of neighbouring delta positive Hydrogens could further stabilise the molecule, reducing the bond length.

Haber-Bosch Process Energy Analysis:
E(NH_3)= -56.54485793 au
2*E(NH_3)= -113.08971586 au
E(N_2)= -109.52412868 au
E(H_2)= -1.17853936 au
3*E(H_2)= -3.53561808 au
ΔE=2*E(NH_3)-[E(N_2)+3*E(H_2)]= -0.0299691 au ~ -78.7 kJ/Mol
Since a negative value is obtained, the forward reaction is exothermic suggesting that the product is more stable than the reactants.

CO_2 molecule:

Calculation Method: RB3LYP
Basis Set: 6-31G(d,p)
E(RB3LYP) = -188.58093945
RMS Gradient Norm : 0.00000014
Point Group: D*H

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=-8.124204D-14
Optimization completed.

<jmol><jmolApplet>
<title>CO_2 Optimised</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>DV818_CO_2_OPTF_POP_T1.LOG</uploadedFileContents>
</jmolApplet></jmol>

|
|
|}
{| class="wikitable"
!Vibration
!PIU
!PIU
!SGG
!SGG
|-
|Frequency(cm**-1)
|640.03
|640.03
|1372.02
|2436.27
|-
|IR Intensity (KM/Mole)
|30.72
|30.72
|0.00
|545.82
|-
|Screenshot
|[[File:Dv818 N2 vibration screenshot.jpg|thumb|N_2 Stretching Vibration, Screenshot]]
|[[File:Dv818 N2 vibration screenshot.jpg|thumb|N_2 Stretching Vibration, Screenshot]]
|[[File:Dv818 N2 vibration screenshot.jpg|thumb|N_2 Stretching Vibration, Screenshot]]
|[[File:Dv818 N2 vibration screenshot.jpg|thumb|N_2 Stretching Vibration, Screenshot]][
|}

File:Dv818 CO 2 screenshot4.jpg

2019-03-08T14:45:56Z

Dv818:

File:Dv818 CO 2 screenshot3.jpg

2019-03-08T14:44:21Z

Dv818:

File:Dv818 CO 2 screenshot2.jpg

2019-03-08T14:42:46Z

Dv818:

File:Dv818 CO 2 screenshot1.jpg

2019-03-08T14:41:22Z

Dv818: