ChemWiki - User contributions [en]

Rep:Mod:HB9151

2016-03-11T14:56:32Z

Hb915: /* Molecular Orbitals */

This is an exploration of molecules and reactions using GaussVeiw in order to understand the importance of computational inorganic chemistry.

Each molecule was draw in GaussVeiw and analysised computationally by solving the Schrödinger equation (EΦ=HΦ) under the Born-Oppenheimer approximation. Firstly the self-consistent field calculation is done for the starting bond lengths and angles giving the electronic wavefunction (Φ) that gives the lowest energy (for the fixed nuclei). The the distance is slightly shortened and the calculation repeated. This is continued until the lowest energy is found and this is the optimized structure. <ref name="olving the Schrödinger equation (EΦ=HΦ) under the Born-Oppenheimer approximation. Firstly the self-consistent field calculation is done for the starting bond lengths and angles giving the electronic wavefunction (Φ) that gives the lowest energy (for the fixed nuclei). The the distance is slightly shortened and the calculation repeated. This is continued until the lowest energy is found and this is the optimized structure." />
<references>
<ref name="olving the Schrödinger equation (EΦ=HΦ) under the Born-Oppenheimer approximation. Firstly the self-consistent field calculation is done for the starting bond lengths and angles giving the electronic wavefunction (Φ) that gives the lowest energy (for the fixed nuclei). The the distance is slightly shortened and the calculation repeated. This is continued until the lowest energy is found and this is the optimized structure.">http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year1/2_understand_opt_nh3.html</ref>
</references>

Once this structure is found the data given by the solutions can be used to explore many properties of the molecule such as the spectrum, molecular orbital and the overall energy of the molecule.

=='''''NH3'''''==
<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 NH3 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 NH3 OPTF POP.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

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=-5.986294D-10
Optimization completed.
-- Stationary point found.

</pre>

There is zero net force and displacement so the optimization has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ NH3 Optimised Information
! !! NH3
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -56.55776873
|-
| RMS gradient / au || 0.00000485
|-
| Point Group || C3V
|-
| H-N bond length / A || 1.01798
|-
| H-N-H bond angle / degrees || 105.741
|}

==='''Molecule Vibrations'''===

[[File:HB915 nh3 optf pop displayvibrations.jpg.png|400px|left]]

''How many modes do you expect from the 3N-6 rule?''

N represents the number of atoms in the molecule. For NH3 there are 4 molecules therefore;
3x4-6=6

''Which modes are degenerate (ie have the same energy)?''

Modes 2-3, and 5-6 are pairs of vibrations with the same energy (equal frequency).

''Which modes are "bending" vibrations and which are "bond stretch" vibrations?''

Modes 1-3 are bending and modes 4-6 are stretching. This is clear both from the animation and because bond stretching vibrations are higher in energy.

''Which mode is highly symmetric?''

Mode 4 is highly symmetric with no change in dipole.

''One mode is known as the "umbrella" mode, which one is this?''

Mode 1

''How many bands would you expect to see in an experimental spectrum of gaseous ammonia?''

There are four different vibrational energies suggesting four different bands. However there is only a minimal change in dipole for modes 4-6 so these would not be visible on a spectrum leaving only two bands.

[[File:HB915 nh3 optf pop spectra.jpg.png|500px|center|left]]

==='''Charge Distribution'''===

Nitrogen has an electronegativity of 3.04 which is comparatively larger than hydrogen with 2.2. Therefore you would expect nitrogen to carry the negative charge. This is supported by the values calculated form the Schrödinger equation shown in the image below.

[[File:HB915 nh3 optf pop charge.jpg.png|300px|center|left]]

=='''''N2'''''==
<jmol><jmolApplet>
<title>N2</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 N2 OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 N2 OPTIMISATION.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

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.

</pre>

There is zero net force and displacement so the optimization has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ N2 Optimised Information
! !! N2
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -109.52412868
|-
| RMS gradient / au || 0.00000365
|-
| Point Group || D*H
|-
| N-N bond length / A || 1.10550
|-
| N-N bond angle / degrees || N/A
|}

==='''Molecule Vibrations'''===

[[File:HB915 n2 optf pop displayvibrations.jpg|400px]]

The 3N-5 rule used for linear molecules gives 3x2-5= 1. This is supported by the frequencies found from computational analysis as seen in the image above. This is due to the simple stretching of the bond.

==='''Charge Distribution'''===

Nitrogen has an electronegativity of 3.04. However when both atoms have the same electronegativity the charge is equally distributed across the molecule.

[[File:HB915 n2 optf pop charge.jpg|300px|center|left]]

=='''''H2'''''==
<jmol><jmolApplet>
<title>H2</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 H2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 H2 OPTF POP.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

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.

</pre>

There is zero net force and displacement so the optimization has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ H2 Optimised Information
! !! H2
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -1.17853930
|-
| RMS gradient / au || 0.00012170
|-
| Point Group || D*H
|-
| H-H bond length / A || 1.10550
|-
| H-H bond angle / degrees || N/A
|}

==='''Molecule Vibrations'''===

[[File:HB915 h2 optf pop displayvibrations.jpg|400px]]

The 3N-5 rule used for linear molecules gives 3x2-5= 1. This is supported by the frequencies found from computational analysis as seen in the image above. This is due to the simple stretching of the bond.

==='''Charge Distribution'''===

Nitrogen has an electronegativity of 2.2. However when both atoms have the same electronegativity the charge is equally distributed across the molecule.

[[File:HB915 h2 optf pop charge.jpg|300px|center|left]]

=='''''Haber-Bosch Process'''''==

==='''Equation of Reaction'''===

N2 + H2 -> NH3

==='''Energy of Reaction'''===

E(NH3)= -56.55776873 au

2*E(NH3)= 2*-56.55776873 = -113.1155375 au

E(N2)= -109.52412868 au

E(H2)= -1.17853930 au

3*E(H2)= 3*-1.17853930 = -3.5356179 au

ΔE = 2*E(NH3)-[E(N2)+3*E(H2)] = -113.1155375-[-109.52412868+-3.5356179]

ΔE = -0.05579092 au

ΔE = -0.05579092*2625.5 = -146.48 kJ/mol to 2.d.p

==='''Stability of Reactants vs Products'''===

ΔE is negative therefore the Haber process is exothermic and the product (NH3) is lower in energy and more stable than the reactants.

=='''''AlCl4-'''''==
<jmol><jmolApplet>
<title>AlCl4-</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 ALCL4- OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 ALCL4- OPTF POP.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000155 0.001800 YES
RMS Displacement 0.000093 0.001200 YES
Predicted change in Energy=-7.051677D-09
Optimization completed.
-- Stationary point found.

</pre>

There is zero net force and displacement so the optimization has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ AlCl4- Optimised Information
! !! AlCl4-
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -2083.61641374
|-
| RMS gradient / au || 0.00001174
|-
| Point Group || TD
|-
| Al-Cl bond length / A || 2.17703
|-
| Cl-Al-Cl bond angle / degrees || 109.471
|}

This is a much higher energy compound than that of N2 and H2.

==='''Molecule Vibrations'''===

[[File:HB915 alcl4- optf pop displayvibrations.jpg]]

The 3N-6 rule gives 3x5-6= 1. This is supported by the frequencies found from computational analysis as seen in the image above. Modes 7-9 are degenerate but in different directions. They are high energy due to the bending character creating a large change in dipole. Modes 3-5 are also degenerate bending vibrations but at a lower energy. Modes 1, 2 and 6 are all symmetrical vibrations that show no change in dipole and are therefore not visible on the spectrum as shown below.

[[File:HB915 alcl4- optf pop spectra.jpg|400px|center|left]]

==='''Charge Distribution'''===

Aluminum has an electronegativity of 1.61 which is comparatively smaller than that of chlorine with 3.16. Therefore you would expect aluminum to carry the positive charge. This is supported by the values calculated form the Schrödinger equation shown in the image below. Also with such a high difference in electronegativity of these two atoms more ionic character will be witnessed.

[[File:HB915 alcl4- optf pop charge.jpg]]

==='''Molecular Orbitals'''===

Images of the molecular orbitals can be visualised by GaussView. They represent each orbital solution to the Schrödinger equation, in other words the Φs, one for each MO energy level.
<ref name="They represent each orbital solution to the Schrödinger equation, in other words the Φs, one for each MO energy level." />
<references>
<ref name="They represent each orbital solution to the Schrödinger equation, in other words the Φs, one for each MO energy level.">http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year1/10_mos_n2.html
</ref>
</references>

There are over 90 orbitals found , 41 of which are occupied, and each can be described by the interactions of the atomic orbitals. Five have been explored here.

[[File:HB915 AlCl4- MO 21.PNG|300px]]

When looking at diatomic molecules the MOs are the simple interaction between the AOs. However when looking at larger molecule you talk about the MO fragments. This is the non-bonding Cl 2 p orbitals. They are too different in energy to interact with the Al orbitals so remain non-bonding. There are 12 with similar energies and shapes that can be attributed to the different orientations and phases of each orbital.

[[File:HB915 AlCl4- MO 26.PNG|300px]]
[[File:HB915 AlCl4- MO 30.PNG|300px]]

These two are a pair of MOs created by interactions between the same AOs; the s Cl fragmant and the s Al. However one is an in-phase interaction (left) which produces a filled bonding orbital and the other out of phase interaction (right) which produced an anti-bonding orbital which is also filled. Both are occupied so these are not the orbitals responsible for bonding in this molecule.

[[File:HB915 AlCl4- MO 31.PNG|300px]]
[[File:HB915 AlCl4- MO 43.PNG|300px]]

This is another bonding (left) and non-bonding (right) pair of MOs. These were caused by the interaction of the 3p Cl fragment and the 3p Al. The bonding is filled and the anti-bonding is empty so it is this orbital that is responsible for the bonds in this molecule.

=='''''S2'''''==
<jmol><jmolApplet>
<title>S2</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 S2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 S2 OPTF POP.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000039 0.000300 YES
Maximum Displacement 0.000067 0.001800 YES
RMS Displacement 0.000095 0.001200 YES
Predicted change in Energy=-2.624039D-09
Optimization completed.
-- Stationary point found.

</pre>

There is zero net force and displacement so the optimization has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ S2 Optimised Information
! !! S2
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -796.32599779
|-
| RMS gradient / au || 0.00002267
|-
| Point Group || D*H
|-
| S-S bond length / A || 1.92952
|-
| S-S bond angle / degrees || N/A
|}

==='''Molecule Vibrations'''===

[[File:HB915 s2 optf pop displayvibrations.jpg]]

The 3N-5 rule used for linear molecules gives 3x2-5= 1. This is supported by the frequencies found from computational analysis as seen in the image above. This is due to the simple stretching of the bond.

==='''Charge Distribution'''===

Sulfur has an electronegativity of 2.58. However when both atoms have the same electronegativity the charge is equally distributed across the molecule.

[[File:HB915 s2 optf pop charge.jpg]]

==='''Molecular Orbitals'''===

Images of the molecular orbitals can be visualised by GaussView. They represent each orbital solution to the Schrödinger equation, in other words the Φs, one for each MO energy level.
<ref name="They represent each orbital solution to the Schrödinger equation, in other words the Φs, one for each MO energy level." />
<references>
<ref name="They represent each orbital solution to the Schrödinger equation, in other words the Φs, one for each MO energy level.">http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year1/10_mos_n2.html
</ref>
</references>

There are over 30 orbitals found , 16 of which are occupied, and each can be described by the interactions of the atomic orbitals. Some examples are given below.

[[File:HB915 S2 MO 11.PNG|300px]]
[[File:HB915 S2 MO 12.PNG|300px]]

3 s orbitals from each Sulfur atom forms a bonding (left), anti-bonding (right) pair of orbitals shown above.

[[File:HB915 S2 MO 15.PNG|300px]]
[[File:HB915 S2 MO 16.PNG|300px]]

The 3px from each sulfur interact to form a bonding (left) and an anti-bonding (right). However both are filled so no bond is formed from these MOs.

[[File:HB915 S2 MO 13.PNG|300px]]
[[File:HB915 S2 MO 18.PNG|300px]]

The 3pz from each sulfur interact to form a filled bonding (left) and a unfilled anti-bonding (right). Therefore this results in a sigma bond being formed between the two sulfur atoms.

[[File:HB915 S2 MO 14.PNG|300px]]
[[File:HB915 S2 MO 17.PNG|300px]]

The 3py from each sulfur interact to form a filled bonding (left) and a unfilled anti-bonding (right). Therefore this results in a pi bond being formed above and below the plane of the two sulfur atoms.

Rep:Mod:HB9151

2016-03-11T14:56:09Z

Hb915: /* Molecular Orbitals */

This is an exploration of molecules and reactions using GaussVeiw in order to understand the importance of computational inorganic chemistry.

Each molecule was draw in GaussVeiw and analysised computationally by solving the Schrödinger equation (EΦ=HΦ) under the Born-Oppenheimer approximation. Firstly the self-consistent field calculation is done for the starting bond lengths and angles giving the electronic wavefunction (Φ) that gives the lowest energy (for the fixed nuclei). The the distance is slightly shortened and the calculation repeated. This is continued until the lowest energy is found and this is the optimized structure. <ref name="olving the Schrödinger equation (EΦ=HΦ) under the Born-Oppenheimer approximation. Firstly the self-consistent field calculation is done for the starting bond lengths and angles giving the electronic wavefunction (Φ) that gives the lowest energy (for the fixed nuclei). The the distance is slightly shortened and the calculation repeated. This is continued until the lowest energy is found and this is the optimized structure." />
<references>
<ref name="olving the Schrödinger equation (EΦ=HΦ) under the Born-Oppenheimer approximation. Firstly the self-consistent field calculation is done for the starting bond lengths and angles giving the electronic wavefunction (Φ) that gives the lowest energy (for the fixed nuclei). The the distance is slightly shortened and the calculation repeated. This is continued until the lowest energy is found and this is the optimized structure.">http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year1/2_understand_opt_nh3.html</ref>
</references>

Once this structure is found the data given by the solutions can be used to explore many properties of the molecule such as the spectrum, molecular orbital and the overall energy of the molecule.

=='''''NH3'''''==
<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 NH3 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 NH3 OPTF POP.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

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=-5.986294D-10
Optimization completed.
-- Stationary point found.

</pre>

There is zero net force and displacement so the optimization has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ NH3 Optimised Information
! !! NH3
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -56.55776873
|-
| RMS gradient / au || 0.00000485
|-
| Point Group || C3V
|-
| H-N bond length / A || 1.01798
|-
| H-N-H bond angle / degrees || 105.741
|}

==='''Molecule Vibrations'''===

[[File:HB915 nh3 optf pop displayvibrations.jpg.png|400px|left]]

''How many modes do you expect from the 3N-6 rule?''

N represents the number of atoms in the molecule. For NH3 there are 4 molecules therefore;
3x4-6=6

''Which modes are degenerate (ie have the same energy)?''

Modes 2-3, and 5-6 are pairs of vibrations with the same energy (equal frequency).

''Which modes are "bending" vibrations and which are "bond stretch" vibrations?''

Modes 1-3 are bending and modes 4-6 are stretching. This is clear both from the animation and because bond stretching vibrations are higher in energy.

''Which mode is highly symmetric?''

Mode 4 is highly symmetric with no change in dipole.

''One mode is known as the "umbrella" mode, which one is this?''

Mode 1

''How many bands would you expect to see in an experimental spectrum of gaseous ammonia?''

There are four different vibrational energies suggesting four different bands. However there is only a minimal change in dipole for modes 4-6 so these would not be visible on a spectrum leaving only two bands.

[[File:HB915 nh3 optf pop spectra.jpg.png|500px|center|left]]

==='''Charge Distribution'''===

Nitrogen has an electronegativity of 3.04 which is comparatively larger than hydrogen with 2.2. Therefore you would expect nitrogen to carry the negative charge. This is supported by the values calculated form the Schrödinger equation shown in the image below.

[[File:HB915 nh3 optf pop charge.jpg.png|300px|center|left]]

=='''''N2'''''==
<jmol><jmolApplet>
<title>N2</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 N2 OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 N2 OPTIMISATION.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

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.

</pre>

There is zero net force and displacement so the optimization has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ N2 Optimised Information
! !! N2
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -109.52412868
|-
| RMS gradient / au || 0.00000365
|-
| Point Group || D*H
|-
| N-N bond length / A || 1.10550
|-
| N-N bond angle / degrees || N/A
|}

==='''Molecule Vibrations'''===

[[File:HB915 n2 optf pop displayvibrations.jpg|400px]]

The 3N-5 rule used for linear molecules gives 3x2-5= 1. This is supported by the frequencies found from computational analysis as seen in the image above. This is due to the simple stretching of the bond.

==='''Charge Distribution'''===

Nitrogen has an electronegativity of 3.04. However when both atoms have the same electronegativity the charge is equally distributed across the molecule.

[[File:HB915 n2 optf pop charge.jpg|300px|center|left]]

=='''''H2'''''==
<jmol><jmolApplet>
<title>H2</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 H2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 H2 OPTF POP.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

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.

</pre>

There is zero net force and displacement so the optimization has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ H2 Optimised Information
! !! H2
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -1.17853930
|-
| RMS gradient / au || 0.00012170
|-
| Point Group || D*H
|-
| H-H bond length / A || 1.10550
|-
| H-H bond angle / degrees || N/A
|}

==='''Molecule Vibrations'''===

[[File:HB915 h2 optf pop displayvibrations.jpg|400px]]

The 3N-5 rule used for linear molecules gives 3x2-5= 1. This is supported by the frequencies found from computational analysis as seen in the image above. This is due to the simple stretching of the bond.

==='''Charge Distribution'''===

Nitrogen has an electronegativity of 2.2. However when both atoms have the same electronegativity the charge is equally distributed across the molecule.

[[File:HB915 h2 optf pop charge.jpg|300px|center|left]]

=='''''Haber-Bosch Process'''''==

==='''Equation of Reaction'''===

N2 + H2 -> NH3

==='''Energy of Reaction'''===

E(NH3)= -56.55776873 au

2*E(NH3)= 2*-56.55776873 = -113.1155375 au

E(N2)= -109.52412868 au

E(H2)= -1.17853930 au

3*E(H2)= 3*-1.17853930 = -3.5356179 au

ΔE = 2*E(NH3)-[E(N2)+3*E(H2)] = -113.1155375-[-109.52412868+-3.5356179]

ΔE = -0.05579092 au

ΔE = -0.05579092*2625.5 = -146.48 kJ/mol to 2.d.p

==='''Stability of Reactants vs Products'''===

ΔE is negative therefore the Haber process is exothermic and the product (NH3) is lower in energy and more stable than the reactants.

=='''''AlCl4-'''''==
<jmol><jmolApplet>
<title>AlCl4-</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 ALCL4- OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 ALCL4- OPTF POP.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000155 0.001800 YES
RMS Displacement 0.000093 0.001200 YES
Predicted change in Energy=-7.051677D-09
Optimization completed.
-- Stationary point found.

</pre>

There is zero net force and displacement so the optimization has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ AlCl4- Optimised Information
! !! AlCl4-
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -2083.61641374
|-
| RMS gradient / au || 0.00001174
|-
| Point Group || TD
|-
| Al-Cl bond length / A || 2.17703
|-
| Cl-Al-Cl bond angle / degrees || 109.471
|}

This is a much higher energy compound than that of N2 and H2.

==='''Molecule Vibrations'''===

[[File:HB915 alcl4- optf pop displayvibrations.jpg]]

The 3N-6 rule gives 3x5-6= 1. This is supported by the frequencies found from computational analysis as seen in the image above. Modes 7-9 are degenerate but in different directions. They are high energy due to the bending character creating a large change in dipole. Modes 3-5 are also degenerate bending vibrations but at a lower energy. Modes 1, 2 and 6 are all symmetrical vibrations that show no change in dipole and are therefore not visible on the spectrum as shown below.

[[File:HB915 alcl4- optf pop spectra.jpg|400px|center|left]]

==='''Charge Distribution'''===

Aluminum has an electronegativity of 1.61 which is comparatively smaller than that of chlorine with 3.16. Therefore you would expect aluminum to carry the positive charge. This is supported by the values calculated form the Schrödinger equation shown in the image below. Also with such a high difference in electronegativity of these two atoms more ionic character will be witnessed.

[[File:HB915 alcl4- optf pop charge.jpg]]

==='''Molecular Orbitals'''===

Images of the molecular orbitals can be visualised by GaussView. They represent each orbital solution to the Schrödinger equation, in other words the Φs, one for each MO energy level.
<ref name="They represent each orbital solution to the Schrödinger equation, in other words the Φs, one for each MO energy level." />
<references>
<ref name="They represent each orbital solution to the Schrödinger equation, in other words the Φs, one for each MO energy level.">http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year1/10_mos_n2.html
</ref>
</references>

There are over 90 orbitals found , 41 of which are occupied, and each can be described by the interactions of the atomic orbitals. Five have been explored here.

[[File:HB915 AlCl4- MO 21.PNG|300px]]

When looking at diatomic molecules the MOs are the simple interaction between the AOs. However when looking at larger molecule you talk about the MO fragments. This is the non-bonding Cl 2 p orbitals. They are too different in energy to interact with the Al orbitals so remain non-bonding. There are 12 with similar energies and shapes that can be attributed to the different orientations and phases of each orbital.

[[File:HB915 AlCl4- MO 26.PNG|300px]]
[[File:HB915 AlCl4- MO 30.PNG|300px]]

These two are a pair of MOs created by interactions between the same AOs; the s Cl fragmant and the s Al. However one is an in-phase interaction (left) which produces a filled bonding orbital and the other out of phase interaction (right) which produced an anti-bonding orbital which is also filled. Both are occupied so these are not the orbitals responsible for bonding in this molecule.

[[File:HB915 AlCl4- MO 31.PNG|300px]]
[[File:HB915 AlCl4- MO 43.PNG|300px]]

This is another bonding (left) and non-bonding (right) pair of MOs. These were caused by the interaction of the 3p Cl fragment and the 3p Al. The bonding is filled and the anti-bonding is empty so it is this orbital that is responsible for the bonds in this molecule.

=='''''S2'''''==
<jmol><jmolApplet>
<title>S2</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 S2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 S2 OPTF POP.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000039 0.000300 YES
Maximum Displacement 0.000067 0.001800 YES
RMS Displacement 0.000095 0.001200 YES
Predicted change in Energy=-2.624039D-09
Optimization completed.
-- Stationary point found.

</pre>

There is zero net force and displacement so the optimization has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ S2 Optimised Information
! !! S2
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -796.32599779
|-
| RMS gradient / au || 0.00002267
|-
| Point Group || D*H
|-
| S-S bond length / A || 1.92952
|-
| S-S bond angle / degrees || N/A
|}

==='''Molecule Vibrations'''===

[[File:HB915 s2 optf pop displayvibrations.jpg]]

The 3N-5 rule used for linear molecules gives 3x2-5= 1. This is supported by the frequencies found from computational analysis as seen in the image above. This is due to the simple stretching of the bond.

==='''Charge Distribution'''===

Sulfur has an electronegativity of 2.58. However when both atoms have the same electronegativity the charge is equally distributed across the molecule.

[[File:HB915 s2 optf pop charge.jpg]]

==='''Molecular Orbitals'''===

Images of the molecular orbitals can be visualised by GaussView. They represent each orbital solution to the Schrödinger equation, in other words the Φs, one for each MO energy level.

There are over 30 orbitals found , 16 of which are occupied, and each can be described by the interactions of the atomic orbitals. Some examples are given below.

[[File:HB915 S2 MO 11.PNG|300px]]
[[File:HB915 S2 MO 12.PNG|300px]]

3 s orbitals from each Sulfur atom forms a bonding (left), anti-bonding (right) pair of orbitals shown above.

[[File:HB915 S2 MO 15.PNG|300px]]
[[File:HB915 S2 MO 16.PNG|300px]]

The 3px from each sulfur interact to form a bonding (left) and an anti-bonding (right). However both are filled so no bond is formed from these MOs.

[[File:HB915 S2 MO 13.PNG|300px]]
[[File:HB915 S2 MO 18.PNG|300px]]

The 3pz from each sulfur interact to form a filled bonding (left) and a unfilled anti-bonding (right). Therefore this results in a sigma bond being formed between the two sulfur atoms.

[[File:HB915 S2 MO 14.PNG|300px]]
[[File:HB915 S2 MO 17.PNG|300px]]

The 3py from each sulfur interact to form a filled bonding (left) and a unfilled anti-bonding (right). Therefore this results in a pi bond being formed above and below the plane of the two sulfur atoms.

Rep:Mod:HB9151

2016-03-11T14:54:50Z

Hb915:

This is an exploration of molecules and reactions using GaussVeiw in order to understand the importance of computational inorganic chemistry.

Each molecule was draw in GaussVeiw and analysised computationally by solving the Schrödinger equation (EΦ=HΦ) under the Born-Oppenheimer approximation. Firstly the self-consistent field calculation is done for the starting bond lengths and angles giving the electronic wavefunction (Φ) that gives the lowest energy (for the fixed nuclei). The the distance is slightly shortened and the calculation repeated. This is continued until the lowest energy is found and this is the optimized structure. <ref name="olving the Schrödinger equation (EΦ=HΦ) under the Born-Oppenheimer approximation. Firstly the self-consistent field calculation is done for the starting bond lengths and angles giving the electronic wavefunction (Φ) that gives the lowest energy (for the fixed nuclei). The the distance is slightly shortened and the calculation repeated. This is continued until the lowest energy is found and this is the optimized structure." />
<references>
<ref name="olving the Schrödinger equation (EΦ=HΦ) under the Born-Oppenheimer approximation. Firstly the self-consistent field calculation is done for the starting bond lengths and angles giving the electronic wavefunction (Φ) that gives the lowest energy (for the fixed nuclei). The the distance is slightly shortened and the calculation repeated. This is continued until the lowest energy is found and this is the optimized structure.">http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year1/2_understand_opt_nh3.html</ref>
</references>

Once this structure is found the data given by the solutions can be used to explore many properties of the molecule such as the spectrum, molecular orbital and the overall energy of the molecule.

=='''''NH3'''''==
<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 NH3 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 NH3 OPTF POP.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

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=-5.986294D-10
Optimization completed.
-- Stationary point found.

</pre>

There is zero net force and displacement so the optimization has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ NH3 Optimised Information
! !! NH3
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -56.55776873
|-
| RMS gradient / au || 0.00000485
|-
| Point Group || C3V
|-
| H-N bond length / A || 1.01798
|-
| H-N-H bond angle / degrees || 105.741
|}

==='''Molecule Vibrations'''===

[[File:HB915 nh3 optf pop displayvibrations.jpg.png|400px|left]]

''How many modes do you expect from the 3N-6 rule?''

N represents the number of atoms in the molecule. For NH3 there are 4 molecules therefore;
3x4-6=6

''Which modes are degenerate (ie have the same energy)?''

Modes 2-3, and 5-6 are pairs of vibrations with the same energy (equal frequency).

''Which modes are "bending" vibrations and which are "bond stretch" vibrations?''

Modes 1-3 are bending and modes 4-6 are stretching. This is clear both from the animation and because bond stretching vibrations are higher in energy.

''Which mode is highly symmetric?''

Mode 4 is highly symmetric with no change in dipole.

''One mode is known as the "umbrella" mode, which one is this?''

Mode 1

''How many bands would you expect to see in an experimental spectrum of gaseous ammonia?''

There are four different vibrational energies suggesting four different bands. However there is only a minimal change in dipole for modes 4-6 so these would not be visible on a spectrum leaving only two bands.

[[File:HB915 nh3 optf pop spectra.jpg.png|500px|center|left]]

==='''Charge Distribution'''===

Nitrogen has an electronegativity of 3.04 which is comparatively larger than hydrogen with 2.2. Therefore you would expect nitrogen to carry the negative charge. This is supported by the values calculated form the Schrödinger equation shown in the image below.

[[File:HB915 nh3 optf pop charge.jpg.png|300px|center|left]]

=='''''N2'''''==
<jmol><jmolApplet>
<title>N2</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 N2 OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 N2 OPTIMISATION.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

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.

</pre>

There is zero net force and displacement so the optimization has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ N2 Optimised Information
! !! N2
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -109.52412868
|-
| RMS gradient / au || 0.00000365
|-
| Point Group || D*H
|-
| N-N bond length / A || 1.10550
|-
| N-N bond angle / degrees || N/A
|}

==='''Molecule Vibrations'''===

[[File:HB915 n2 optf pop displayvibrations.jpg|400px]]

The 3N-5 rule used for linear molecules gives 3x2-5= 1. This is supported by the frequencies found from computational analysis as seen in the image above. This is due to the simple stretching of the bond.

==='''Charge Distribution'''===

Nitrogen has an electronegativity of 3.04. However when both atoms have the same electronegativity the charge is equally distributed across the molecule.

[[File:HB915 n2 optf pop charge.jpg|300px|center|left]]

=='''''H2'''''==
<jmol><jmolApplet>
<title>H2</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 H2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 H2 OPTF POP.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

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.

</pre>

There is zero net force and displacement so the optimization has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ H2 Optimised Information
! !! H2
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -1.17853930
|-
| RMS gradient / au || 0.00012170
|-
| Point Group || D*H
|-
| H-H bond length / A || 1.10550
|-
| H-H bond angle / degrees || N/A
|}

==='''Molecule Vibrations'''===

[[File:HB915 h2 optf pop displayvibrations.jpg|400px]]

The 3N-5 rule used for linear molecules gives 3x2-5= 1. This is supported by the frequencies found from computational analysis as seen in the image above. This is due to the simple stretching of the bond.

==='''Charge Distribution'''===

Nitrogen has an electronegativity of 2.2. However when both atoms have the same electronegativity the charge is equally distributed across the molecule.

[[File:HB915 h2 optf pop charge.jpg|300px|center|left]]

=='''''Haber-Bosch Process'''''==

==='''Equation of Reaction'''===

N2 + H2 -> NH3

==='''Energy of Reaction'''===

E(NH3)= -56.55776873 au

2*E(NH3)= 2*-56.55776873 = -113.1155375 au

E(N2)= -109.52412868 au

E(H2)= -1.17853930 au

3*E(H2)= 3*-1.17853930 = -3.5356179 au

ΔE = 2*E(NH3)-[E(N2)+3*E(H2)] = -113.1155375-[-109.52412868+-3.5356179]

ΔE = -0.05579092 au

ΔE = -0.05579092*2625.5 = -146.48 kJ/mol to 2.d.p

==='''Stability of Reactants vs Products'''===

ΔE is negative therefore the Haber process is exothermic and the product (NH3) is lower in energy and more stable than the reactants.

=='''''AlCl4-'''''==
<jmol><jmolApplet>
<title>AlCl4-</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 ALCL4- OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 ALCL4- OPTF POP.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000155 0.001800 YES
RMS Displacement 0.000093 0.001200 YES
Predicted change in Energy=-7.051677D-09
Optimization completed.
-- Stationary point found.

</pre>

There is zero net force and displacement so the optimization has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ AlCl4- Optimised Information
! !! AlCl4-
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -2083.61641374
|-
| RMS gradient / au || 0.00001174
|-
| Point Group || TD
|-
| Al-Cl bond length / A || 2.17703
|-
| Cl-Al-Cl bond angle / degrees || 109.471
|}

This is a much higher energy compound than that of N2 and H2.

==='''Molecule Vibrations'''===

[[File:HB915 alcl4- optf pop displayvibrations.jpg]]

The 3N-6 rule gives 3x5-6= 1. This is supported by the frequencies found from computational analysis as seen in the image above. Modes 7-9 are degenerate but in different directions. They are high energy due to the bending character creating a large change in dipole. Modes 3-5 are also degenerate bending vibrations but at a lower energy. Modes 1, 2 and 6 are all symmetrical vibrations that show no change in dipole and are therefore not visible on the spectrum as shown below.

[[File:HB915 alcl4- optf pop spectra.jpg|400px|center|left]]

==='''Charge Distribution'''===

Aluminum has an electronegativity of 1.61 which is comparatively smaller than that of chlorine with 3.16. Therefore you would expect aluminum to carry the positive charge. This is supported by the values calculated form the Schrödinger equation shown in the image below. Also with such a high difference in electronegativity of these two atoms more ionic character will be witnessed.

[[File:HB915 alcl4- optf pop charge.jpg]]

==='''Molecular Orbitals'''===

Images of the molecular orbitals can be visualised by GaussView. They represent each orbital solution to the Schrödinger equation, in other words the Φs, one for each MO energy level.

There are over 90 orbitals found , 41 of which are occupied, and each can be described by the interactions of the atomic orbitals. Five have been explored here.

[[File:HB915 AlCl4- MO 21.PNG|300px]]

When looking at diatomic molecules the MOs are the simple interaction between the AOs. However when looking at larger molecule you talk about the MO fragments. This is the non-bonding Cl 2 p orbitals. They are too different in energy to interact with the Al orbitals so remain non-bonding. There are 12 with similar energies and shapes that can be attributed to the different orientations and phases of each orbital.

[[File:HB915 AlCl4- MO 26.PNG|300px]]
[[File:HB915 AlCl4- MO 30.PNG|300px]]

These two are a pair of MOs created by interactions between the same AOs; the s Cl fragmant and the s Al. However one is an in-phase interaction (left) which produces a filled bonding orbital and the other out of phase interaction (right) which produced an anti-bonding orbital which is also filled. Both are occupied so these are not the orbitals responsible for bonding in this molecule.

[[File:HB915 AlCl4- MO 31.PNG|300px]]
[[File:HB915 AlCl4- MO 43.PNG|300px]]

This is another bonding (left) and non-bonding (right) pair of MOs. These were caused by the interaction of the 3p Cl fragment and the 3p Al. The bonding is filled and the anti-bonding is empty so it is this orbital that is responsible for the bonds in this molecule.

=='''''S2'''''==
<jmol><jmolApplet>
<title>S2</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 S2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 S2 OPTF POP.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000039 0.000300 YES
Maximum Displacement 0.000067 0.001800 YES
RMS Displacement 0.000095 0.001200 YES
Predicted change in Energy=-2.624039D-09
Optimization completed.
-- Stationary point found.

</pre>

There is zero net force and displacement so the optimization has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ S2 Optimised Information
! !! S2
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -796.32599779
|-
| RMS gradient / au || 0.00002267
|-
| Point Group || D*H
|-
| S-S bond length / A || 1.92952
|-
| S-S bond angle / degrees || N/A
|}

==='''Molecule Vibrations'''===

[[File:HB915 s2 optf pop displayvibrations.jpg]]

The 3N-5 rule used for linear molecules gives 3x2-5= 1. This is supported by the frequencies found from computational analysis as seen in the image above. This is due to the simple stretching of the bond.

==='''Charge Distribution'''===

Sulfur has an electronegativity of 2.58. However when both atoms have the same electronegativity the charge is equally distributed across the molecule.

[[File:HB915 s2 optf pop charge.jpg]]

==='''Molecular Orbitals'''===

Images of the molecular orbitals can be visualised by GaussView. They represent each orbital solution to the Schrödinger equation, in other words the Φs, one for each MO energy level.

There are over 30 orbitals found , 16 of which are occupied, and each can be described by the interactions of the atomic orbitals. Some examples are given below.

[[File:HB915 S2 MO 11.PNG|300px]]
[[File:HB915 S2 MO 12.PNG|300px]]

3 s orbitals from each Sulfur atom forms a bonding (left), anti-bonding (right) pair of orbitals shown above.

[[File:HB915 S2 MO 15.PNG|300px]]
[[File:HB915 S2 MO 16.PNG|300px]]

The 3px from each sulfur interact to form a bonding (left) and an anti-bonding (right). However both are filled so no bond is formed from these MOs.

[[File:HB915 S2 MO 13.PNG|300px]]
[[File:HB915 S2 MO 18.PNG|300px]]

The 3pz from each sulfur interact to form a filled bonding (left) and a unfilled anti-bonding (right). Therefore this results in a sigma bond being formed between the two sulfur atoms.

[[File:HB915 S2 MO 14.PNG|300px]]
[[File:HB915 S2 MO 17.PNG|300px]]

The 3py from each sulfur interact to form a filled bonding (left) and a unfilled anti-bonding (right). Therefore this results in a pi bond being formed above and below the plane of the two sulfur atoms.

Rep:Mod:HB9151

2016-03-11T14:53:38Z

Hb915:

This is an exploration of molecules and reactions using GaussVeiw in order to understand the importance of computational inorganic chemistry.

Each molecule was draw in GaussVeiw and analysised computationally by solving the Schrödinger equation (EΦ=HΦ) under the Born-Oppenheimer approximation. Firstly the self-consistent field calculation is done for the starting bond lengths and angles giving the electronic wavefunction (Φ) that gives the lowest energy (for the fixed nuclei). The the distance is slightly shortened and the calculation repeated. This is continued until the lowest energy is found and this is the optimized structure. <references>
<ref name="How the calculaiton works">http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year1/2_understand_opt_nh3.html</ref>
</references>

Once this structure is found the data given by the solutions can be used to explore many properties of the molecule such as the spectrum, molecular orbital and the overall energy of the molecule.

=='''''NH3'''''==
<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 NH3 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 NH3 OPTF POP.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

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=-5.986294D-10
Optimization completed.
-- Stationary point found.

</pre>

There is zero net force and displacement so the optimization has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ NH3 Optimised Information
! !! NH3
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -56.55776873
|-
| RMS gradient / au || 0.00000485
|-
| Point Group || C3V
|-
| H-N bond length / A || 1.01798
|-
| H-N-H bond angle / degrees || 105.741
|}

==='''Molecule Vibrations'''===

[[File:HB915 nh3 optf pop displayvibrations.jpg.png|400px|left]]

''How many modes do you expect from the 3N-6 rule?''

N represents the number of atoms in the molecule. For NH3 there are 4 molecules therefore;
3x4-6=6

''Which modes are degenerate (ie have the same energy)?''

Modes 2-3, and 5-6 are pairs of vibrations with the same energy (equal frequency).

''Which modes are "bending" vibrations and which are "bond stretch" vibrations?''

Modes 1-3 are bending and modes 4-6 are stretching. This is clear both from the animation and because bond stretching vibrations are higher in energy.

''Which mode is highly symmetric?''

Mode 4 is highly symmetric with no change in dipole.

''One mode is known as the "umbrella" mode, which one is this?''

Mode 1

''How many bands would you expect to see in an experimental spectrum of gaseous ammonia?''

There are four different vibrational energies suggesting four different bands. However there is only a minimal change in dipole for modes 4-6 so these would not be visible on a spectrum leaving only two bands.

[[File:HB915 nh3 optf pop spectra.jpg.png|500px|center|left]]

==='''Charge Distribution'''===

Nitrogen has an electronegativity of 3.04 which is comparatively larger than hydrogen with 2.2. Therefore you would expect nitrogen to carry the negative charge. This is supported by the values calculated form the Schrödinger equation shown in the image below.

[[File:HB915 nh3 optf pop charge.jpg.png|300px|center|left]]

=='''''N2'''''==
<jmol><jmolApplet>
<title>N2</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 N2 OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 N2 OPTIMISATION.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

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.

</pre>

There is zero net force and displacement so the optimization has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ N2 Optimised Information
! !! N2
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -109.52412868
|-
| RMS gradient / au || 0.00000365
|-
| Point Group || D*H
|-
| N-N bond length / A || 1.10550
|-
| N-N bond angle / degrees || N/A
|}

==='''Molecule Vibrations'''===

[[File:HB915 n2 optf pop displayvibrations.jpg|400px]]

The 3N-5 rule used for linear molecules gives 3x2-5= 1. This is supported by the frequencies found from computational analysis as seen in the image above. This is due to the simple stretching of the bond.

==='''Charge Distribution'''===

Nitrogen has an electronegativity of 3.04. However when both atoms have the same electronegativity the charge is equally distributed across the molecule.

[[File:HB915 n2 optf pop charge.jpg|300px|center|left]]

=='''''H2'''''==
<jmol><jmolApplet>
<title>H2</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 H2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 H2 OPTF POP.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

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.

</pre>

There is zero net force and displacement so the optimization has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ H2 Optimised Information
! !! H2
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -1.17853930
|-
| RMS gradient / au || 0.00012170
|-
| Point Group || D*H
|-
| H-H bond length / A || 1.10550
|-
| H-H bond angle / degrees || N/A
|}

==='''Molecule Vibrations'''===

[[File:HB915 h2 optf pop displayvibrations.jpg|400px]]

The 3N-5 rule used for linear molecules gives 3x2-5= 1. This is supported by the frequencies found from computational analysis as seen in the image above. This is due to the simple stretching of the bond.

==='''Charge Distribution'''===

Nitrogen has an electronegativity of 2.2. However when both atoms have the same electronegativity the charge is equally distributed across the molecule.

[[File:HB915 h2 optf pop charge.jpg|300px|center|left]]

=='''''Haber-Bosch Process'''''==

==='''Equation of Reaction'''===

N2 + H2 -> NH3

==='''Energy of Reaction'''===

E(NH3)= -56.55776873 au

2*E(NH3)= 2*-56.55776873 = -113.1155375 au

E(N2)= -109.52412868 au

E(H2)= -1.17853930 au

3*E(H2)= 3*-1.17853930 = -3.5356179 au

ΔE = 2*E(NH3)-[E(N2)+3*E(H2)] = -113.1155375-[-109.52412868+-3.5356179]

ΔE = -0.05579092 au

ΔE = -0.05579092*2625.5 = -146.48 kJ/mol to 2.d.p

==='''Stability of Reactants vs Products'''===

ΔE is negative therefore the Haber process is exothermic and the product (NH3) is lower in energy and more stable than the reactants.

=='''''AlCl4-'''''==
<jmol><jmolApplet>
<title>AlCl4-</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 ALCL4- OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 ALCL4- OPTF POP.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000155 0.001800 YES
RMS Displacement 0.000093 0.001200 YES
Predicted change in Energy=-7.051677D-09
Optimization completed.
-- Stationary point found.

</pre>

There is zero net force and displacement so the optimization has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ AlCl4- Optimised Information
! !! AlCl4-
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -2083.61641374
|-
| RMS gradient / au || 0.00001174
|-
| Point Group || TD
|-
| Al-Cl bond length / A || 2.17703
|-
| Cl-Al-Cl bond angle / degrees || 109.471
|}

This is a much higher energy compound than that of N2 and H2.

==='''Molecule Vibrations'''===

[[File:HB915 alcl4- optf pop displayvibrations.jpg]]

The 3N-6 rule gives 3x5-6= 1. This is supported by the frequencies found from computational analysis as seen in the image above. Modes 7-9 are degenerate but in different directions. They are high energy due to the bending character creating a large change in dipole. Modes 3-5 are also degenerate bending vibrations but at a lower energy. Modes 1, 2 and 6 are all symmetrical vibrations that show no change in dipole and are therefore not visible on the spectrum as shown below.

[[File:HB915 alcl4- optf pop spectra.jpg|400px|center|left]]

==='''Charge Distribution'''===

Aluminum has an electronegativity of 1.61 which is comparatively smaller than that of chlorine with 3.16. Therefore you would expect aluminum to carry the positive charge. This is supported by the values calculated form the Schrödinger equation shown in the image below. Also with such a high difference in electronegativity of these two atoms more ionic character will be witnessed.

[[File:HB915 alcl4- optf pop charge.jpg]]

==='''Molecular Orbitals'''===

Images of the molecular orbitals can be visualised by GaussView. They represent each orbital solution to the Schrödinger equation, in other words the Φs, one for each MO energy level.

There are over 90 orbitals found , 41 of which are occupied, and each can be described by the interactions of the atomic orbitals. Five have been explored here.

[[File:HB915 AlCl4- MO 21.PNG|300px]]

When looking at diatomic molecules the MOs are the simple interaction between the AOs. However when looking at larger molecule you talk about the MO fragments. This is the non-bonding Cl 2 p orbitals. They are too different in energy to interact with the Al orbitals so remain non-bonding. There are 12 with similar energies and shapes that can be attributed to the different orientations and phases of each orbital.

[[File:HB915 AlCl4- MO 26.PNG|300px]]
[[File:HB915 AlCl4- MO 30.PNG|300px]]

These two are a pair of MOs created by interactions between the same AOs; the s Cl fragmant and the s Al. However one is an in-phase interaction (left) which produces a filled bonding orbital and the other out of phase interaction (right) which produced an anti-bonding orbital which is also filled. Both are occupied so these are not the orbitals responsible for bonding in this molecule.

[[File:HB915 AlCl4- MO 31.PNG|300px]]
[[File:HB915 AlCl4- MO 43.PNG|300px]]

This is another bonding (left) and non-bonding (right) pair of MOs. These were caused by the interaction of the 3p Cl fragment and the 3p Al. The bonding is filled and the anti-bonding is empty so it is this orbital that is responsible for the bonds in this molecule.

=='''''S2'''''==
<jmol><jmolApplet>
<title>S2</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 S2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 S2 OPTF POP.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000039 0.000300 YES
Maximum Displacement 0.000067 0.001800 YES
RMS Displacement 0.000095 0.001200 YES
Predicted change in Energy=-2.624039D-09
Optimization completed.
-- Stationary point found.

</pre>

There is zero net force and displacement so the optimization has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ S2 Optimised Information
! !! S2
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -796.32599779
|-
| RMS gradient / au || 0.00002267
|-
| Point Group || D*H
|-
| S-S bond length / A || 1.92952
|-
| S-S bond angle / degrees || N/A
|}

==='''Molecule Vibrations'''===

[[File:HB915 s2 optf pop displayvibrations.jpg]]

The 3N-5 rule used for linear molecules gives 3x2-5= 1. This is supported by the frequencies found from computational analysis as seen in the image above. This is due to the simple stretching of the bond.

==='''Charge Distribution'''===

Sulfur has an electronegativity of 2.58. However when both atoms have the same electronegativity the charge is equally distributed across the molecule.

[[File:HB915 s2 optf pop charge.jpg]]

==='''Molecular Orbitals'''===

Images of the molecular orbitals can be visualised by GaussView. They represent each orbital solution to the Schrödinger equation, in other words the Φs, one for each MO energy level.

There are over 30 orbitals found , 16 of which are occupied, and each can be described by the interactions of the atomic orbitals. Some examples are given below.

[[File:HB915 S2 MO 11.PNG|300px]]
[[File:HB915 S2 MO 12.PNG|300px]]

3 s orbitals from each Sulfur atom forms a bonding (left), anti-bonding (right) pair of orbitals shown above.

[[File:HB915 S2 MO 15.PNG|300px]]
[[File:HB915 S2 MO 16.PNG|300px]]

The 3px from each sulfur interact to form a bonding (left) and an anti-bonding (right). However both are filled so no bond is formed from these MOs.

[[File:HB915 S2 MO 13.PNG|300px]]
[[File:HB915 S2 MO 18.PNG|300px]]

The 3pz from each sulfur interact to form a filled bonding (left) and a unfilled anti-bonding (right). Therefore this results in a sigma bond being formed between the two sulfur atoms.

[[File:HB915 S2 MO 14.PNG|300px]]
[[File:HB915 S2 MO 17.PNG|300px]]

The 3py from each sulfur interact to form a filled bonding (left) and a unfilled anti-bonding (right). Therefore this results in a pi bond being formed above and below the plane of the two sulfur atoms.

Rep:Mod:HB9151

2016-03-11T14:50:44Z

Hb915: /* Molecular Orbitals */

This is an exploration of molecules and reactions using GaussVeiw in order to understand the importance of computational inorganic chemistry.

Each molecule was draw in GaussVeiw and analysised computationally by solving the Schrödinger equation (EΦ=HΦ) under the Born-Oppenheimer approximation. Firstly the self-consistent field calculation is done for the starting bond lengths and angles giving the electronic wavefunction (Φ) that gives the lowest energy (for the fixed nuclei). The the distance is slightly shortened and the calculation repeated. This is continued until the lowest energy is found and this is the optimized structure.

Once this structure is found the data given by the solutions can be used to explore many properties of the molecule such as the spectrum, molecular orbital and the overall energy of the molecule.

=='''''NH3'''''==
<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 NH3 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 NH3 OPTF POP.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

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=-5.986294D-10
Optimization completed.
-- Stationary point found.

</pre>

There is zero net force and displacement so the optimization has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ NH3 Optimised Information
! !! NH3
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -56.55776873
|-
| RMS gradient / au || 0.00000485
|-
| Point Group || C3V
|-
| H-N bond length / A || 1.01798
|-
| H-N-H bond angle / degrees || 105.741
|}

==='''Molecule Vibrations'''===

[[File:HB915 nh3 optf pop displayvibrations.jpg.png|400px|left]]

''How many modes do you expect from the 3N-6 rule?''

N represents the number of atoms in the molecule. For NH3 there are 4 molecules therefore;
3x4-6=6

''Which modes are degenerate (ie have the same energy)?''

Modes 2-3, and 5-6 are pairs of vibrations with the same energy (equal frequency).

''Which modes are "bending" vibrations and which are "bond stretch" vibrations?''

Modes 1-3 are bending and modes 4-6 are stretching. This is clear both from the animation and because bond stretching vibrations are higher in energy.

''Which mode is highly symmetric?''

Mode 4 is highly symmetric with no change in dipole.

''One mode is known as the "umbrella" mode, which one is this?''

Mode 1

''How many bands would you expect to see in an experimental spectrum of gaseous ammonia?''

There are four different vibrational energies suggesting four different bands. However there is only a minimal change in dipole for modes 4-6 so these would not be visible on a spectrum leaving only two bands.

[[File:HB915 nh3 optf pop spectra.jpg.png|500px|center|left]]

==='''Charge Distribution'''===

Nitrogen has an electronegativity of 3.04 which is comparatively larger than hydrogen with 2.2. Therefore you would expect nitrogen to carry the negative charge. This is supported by the values calculated form the Schrödinger equation shown in the image below.

[[File:HB915 nh3 optf pop charge.jpg.png|300px|center|left]]

=='''''N2'''''==
<jmol><jmolApplet>
<title>N2</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 N2 OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 N2 OPTIMISATION.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

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.

</pre>

There is zero net force and displacement so the optimization has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ N2 Optimised Information
! !! N2
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -109.52412868
|-
| RMS gradient / au || 0.00000365
|-
| Point Group || D*H
|-
| N-N bond length / A || 1.10550
|-
| N-N bond angle / degrees || N/A
|}

==='''Molecule Vibrations'''===

[[File:HB915 n2 optf pop displayvibrations.jpg|400px]]

The 3N-5 rule used for linear molecules gives 3x2-5= 1. This is supported by the frequencies found from computational analysis as seen in the image above. This is due to the simple stretching of the bond.

==='''Charge Distribution'''===

Nitrogen has an electronegativity of 3.04. However when both atoms have the same electronegativity the charge is equally distributed across the molecule.

[[File:HB915 n2 optf pop charge.jpg|300px|center|left]]

=='''''H2'''''==
<jmol><jmolApplet>
<title>H2</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 H2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 H2 OPTF POP.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

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.

</pre>

There is zero net force and displacement so the optimization has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ H2 Optimised Information
! !! H2
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -1.17853930
|-
| RMS gradient / au || 0.00012170
|-
| Point Group || D*H
|-
| H-H bond length / A || 1.10550
|-
| H-H bond angle / degrees || N/A
|}

==='''Molecule Vibrations'''===

[[File:HB915 h2 optf pop displayvibrations.jpg|400px]]

The 3N-5 rule used for linear molecules gives 3x2-5= 1. This is supported by the frequencies found from computational analysis as seen in the image above. This is due to the simple stretching of the bond.

==='''Charge Distribution'''===

Nitrogen has an electronegativity of 2.2. However when both atoms have the same electronegativity the charge is equally distributed across the molecule.

[[File:HB915 h2 optf pop charge.jpg|300px|center|left]]

=='''''Haber-Bosch Process'''''==

==='''Equation of Reaction'''===

N2 + H2 -> NH3

==='''Energy of Reaction'''===

E(NH3)= -56.55776873 au

2*E(NH3)= 2*-56.55776873 = -113.1155375 au

E(N2)= -109.52412868 au

E(H2)= -1.17853930 au

3*E(H2)= 3*-1.17853930 = -3.5356179 au

ΔE = 2*E(NH3)-[E(N2)+3*E(H2)] = -113.1155375-[-109.52412868+-3.5356179]

ΔE = -0.05579092 au

ΔE = -0.05579092*2625.5 = -146.48 kJ/mol to 2.d.p

==='''Stability of Reactants vs Products'''===

ΔE is negative therefore the Haber process is exothermic and the product (NH3) is lower in energy and more stable than the reactants.

=='''''AlCl4-'''''==
<jmol><jmolApplet>
<title>AlCl4-</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 ALCL4- OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 ALCL4- OPTF POP.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000155 0.001800 YES
RMS Displacement 0.000093 0.001200 YES
Predicted change in Energy=-7.051677D-09
Optimization completed.
-- Stationary point found.

</pre>

There is zero net force and displacement so the optimization has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ AlCl4- Optimised Information
! !! AlCl4-
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -2083.61641374
|-
| RMS gradient / au || 0.00001174
|-
| Point Group || TD
|-
| Al-Cl bond length / A || 2.17703
|-
| Cl-Al-Cl bond angle / degrees || 109.471
|}

This is a much higher energy compound than that of N2 and H2.

==='''Molecule Vibrations'''===

[[File:HB915 alcl4- optf pop displayvibrations.jpg]]

The 3N-6 rule gives 3x5-6= 1. This is supported by the frequencies found from computational analysis as seen in the image above. Modes 7-9 are degenerate but in different directions. They are high energy due to the bending character creating a large change in dipole. Modes 3-5 are also degenerate bending vibrations but at a lower energy. Modes 1, 2 and 6 are all symmetrical vibrations that show no change in dipole and are therefore not visible on the spectrum as shown below.

[[File:HB915 alcl4- optf pop spectra.jpg|400px|center|left]]

==='''Charge Distribution'''===

Aluminum has an electronegativity of 1.61 which is comparatively smaller than that of chlorine with 3.16. Therefore you would expect aluminum to carry the positive charge. This is supported by the values calculated form the Schrödinger equation shown in the image below. Also with such a high difference in electronegativity of these two atoms more ionic character will be witnessed.

[[File:HB915 alcl4- optf pop charge.jpg]]

==='''Molecular Orbitals'''===

Images of the molecular orbitals can be visualised by GaussView. They represent each orbital solution to the Schrödinger equation, in other words the Φs, one for each MO energy level.

There are over 90 orbitals found , 41 of which are occupied, and each can be described by the interactions of the atomic orbitals. Five have been explored here.

[[File:HB915 AlCl4- MO 21.PNG|300px]]

When looking at diatomic molecules the MOs are the simple interaction between the AOs. However when looking at larger molecule you talk about the MO fragments. This is the non-bonding Cl 2 p orbitals. They are too different in energy to interact with the Al orbitals so remain non-bonding. There are 12 with similar energies and shapes that can be attributed to the different orientations and phases of each orbital.

[[File:HB915 AlCl4- MO 26.PNG|300px]]
[[File:HB915 AlCl4- MO 30.PNG|300px]]

These two are a pair of MOs created by interactions between the same AOs; the s Cl fragmant and the s Al. However one is an in-phase interaction (left) which produces a filled bonding orbital and the other out of phase interaction (right) which produced an anti-bonding orbital which is also filled. Both are occupied so these are not the orbitals responsible for bonding in this molecule.

[[File:HB915 AlCl4- MO 31.PNG|300px]]
[[File:HB915 AlCl4- MO 43.PNG|300px]]

This is another bonding (left) and non-bonding (right) pair of MOs. These were caused by the interaction of the 3p Cl fragment and the 3p Al. The bonding is filled and the anti-bonding is empty so it is this orbital that is responsible for the bonds in this molecule.

=='''''S2'''''==
<jmol><jmolApplet>
<title>S2</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 S2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 S2 OPTF POP.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000039 0.000300 YES
Maximum Displacement 0.000067 0.001800 YES
RMS Displacement 0.000095 0.001200 YES
Predicted change in Energy=-2.624039D-09
Optimization completed.
-- Stationary point found.

</pre>

There is zero net force and displacement so the optimization has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ S2 Optimised Information
! !! S2
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -796.32599779
|-
| RMS gradient / au || 0.00002267
|-
| Point Group || D*H
|-
| S-S bond length / A || 1.92952
|-
| S-S bond angle / degrees || N/A
|}

==='''Molecule Vibrations'''===

[[File:HB915 s2 optf pop displayvibrations.jpg]]

The 3N-5 rule used for linear molecules gives 3x2-5= 1. This is supported by the frequencies found from computational analysis as seen in the image above. This is due to the simple stretching of the bond.

==='''Charge Distribution'''===

Sulfur has an electronegativity of 2.58. However when both atoms have the same electronegativity the charge is equally distributed across the molecule.

[[File:HB915 s2 optf pop charge.jpg]]

==='''Molecular Orbitals'''===

Images of the molecular orbitals can be visualised by GaussView. They represent each orbital solution to the Schrödinger equation, in other words the Φs, one for each MO energy level.

There are over 30 orbitals found , 16 of which are occupied, and each can be described by the interactions of the atomic orbitals. Some examples are given below.

[[File:HB915 S2 MO 11.PNG|300px]]
[[File:HB915 S2 MO 12.PNG|300px]]

3 s orbitals from each Sulfur atom forms a bonding (left), anti-bonding (right) pair of orbitals shown above.

[[File:HB915 S2 MO 15.PNG|300px]]
[[File:HB915 S2 MO 16.PNG|300px]]

The 3px from each sulfur interact to form a bonding (left) and an anti-bonding (right). However both are filled so no bond is formed from these MOs.

[[File:HB915 S2 MO 13.PNG|300px]]
[[File:HB915 S2 MO 18.PNG|300px]]

The 3pz from each sulfur interact to form a filled bonding (left) and a unfilled anti-bonding (right). Therefore this results in a sigma bond being formed between the two sulfur atoms.

[[File:HB915 S2 MO 14.PNG|300px]]
[[File:HB915 S2 MO 17.PNG|300px]]

The 3py from each sulfur interact to form a filled bonding (left) and a unfilled anti-bonding (right). Therefore this results in a pi bond being formed above and below the plane of the two sulfur atoms.

Rep:Mod:HB9151

2016-03-11T14:49:47Z

Hb915: /* Molecular Orbitals */

This is an exploration of molecules and reactions using GaussVeiw in order to understand the importance of computational inorganic chemistry.

Each molecule was draw in GaussVeiw and analysised computationally by solving the Schrödinger equation (EΦ=HΦ) under the Born-Oppenheimer approximation. Firstly the self-consistent field calculation is done for the starting bond lengths and angles giving the electronic wavefunction (Φ) that gives the lowest energy (for the fixed nuclei). The the distance is slightly shortened and the calculation repeated. This is continued until the lowest energy is found and this is the optimized structure.

Once this structure is found the data given by the solutions can be used to explore many properties of the molecule such as the spectrum, molecular orbital and the overall energy of the molecule.

=='''''NH3'''''==
<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 NH3 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 NH3 OPTF POP.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

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=-5.986294D-10
Optimization completed.
-- Stationary point found.

</pre>

There is zero net force and displacement so the optimization has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ NH3 Optimised Information
! !! NH3
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -56.55776873
|-
| RMS gradient / au || 0.00000485
|-
| Point Group || C3V
|-
| H-N bond length / A || 1.01798
|-
| H-N-H bond angle / degrees || 105.741
|}

==='''Molecule Vibrations'''===

[[File:HB915 nh3 optf pop displayvibrations.jpg.png|400px|left]]

''How many modes do you expect from the 3N-6 rule?''

N represents the number of atoms in the molecule. For NH3 there are 4 molecules therefore;
3x4-6=6

''Which modes are degenerate (ie have the same energy)?''

Modes 2-3, and 5-6 are pairs of vibrations with the same energy (equal frequency).

''Which modes are "bending" vibrations and which are "bond stretch" vibrations?''

Modes 1-3 are bending and modes 4-6 are stretching. This is clear both from the animation and because bond stretching vibrations are higher in energy.

''Which mode is highly symmetric?''

Mode 4 is highly symmetric with no change in dipole.

''One mode is known as the "umbrella" mode, which one is this?''

Mode 1

''How many bands would you expect to see in an experimental spectrum of gaseous ammonia?''

There are four different vibrational energies suggesting four different bands. However there is only a minimal change in dipole for modes 4-6 so these would not be visible on a spectrum leaving only two bands.

[[File:HB915 nh3 optf pop spectra.jpg.png|500px|center|left]]

==='''Charge Distribution'''===

Nitrogen has an electronegativity of 3.04 which is comparatively larger than hydrogen with 2.2. Therefore you would expect nitrogen to carry the negative charge. This is supported by the values calculated form the Schrödinger equation shown in the image below.

[[File:HB915 nh3 optf pop charge.jpg.png|300px|center|left]]

=='''''N2'''''==
<jmol><jmolApplet>
<title>N2</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 N2 OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 N2 OPTIMISATION.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

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.

</pre>

There is zero net force and displacement so the optimization has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ N2 Optimised Information
! !! N2
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -109.52412868
|-
| RMS gradient / au || 0.00000365
|-
| Point Group || D*H
|-
| N-N bond length / A || 1.10550
|-
| N-N bond angle / degrees || N/A
|}

==='''Molecule Vibrations'''===

[[File:HB915 n2 optf pop displayvibrations.jpg|400px]]

The 3N-5 rule used for linear molecules gives 3x2-5= 1. This is supported by the frequencies found from computational analysis as seen in the image above. This is due to the simple stretching of the bond.

==='''Charge Distribution'''===

Nitrogen has an electronegativity of 3.04. However when both atoms have the same electronegativity the charge is equally distributed across the molecule.

[[File:HB915 n2 optf pop charge.jpg|300px|center|left]]

=='''''H2'''''==
<jmol><jmolApplet>
<title>H2</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 H2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 H2 OPTF POP.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

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.

</pre>

There is zero net force and displacement so the optimization has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ H2 Optimised Information
! !! H2
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -1.17853930
|-
| RMS gradient / au || 0.00012170
|-
| Point Group || D*H
|-
| H-H bond length / A || 1.10550
|-
| H-H bond angle / degrees || N/A
|}

==='''Molecule Vibrations'''===

[[File:HB915 h2 optf pop displayvibrations.jpg|400px]]

The 3N-5 rule used for linear molecules gives 3x2-5= 1. This is supported by the frequencies found from computational analysis as seen in the image above. This is due to the simple stretching of the bond.

==='''Charge Distribution'''===

Nitrogen has an electronegativity of 2.2. However when both atoms have the same electronegativity the charge is equally distributed across the molecule.

[[File:HB915 h2 optf pop charge.jpg|300px|center|left]]

=='''''Haber-Bosch Process'''''==

==='''Equation of Reaction'''===

N2 + H2 -> NH3

==='''Energy of Reaction'''===

E(NH3)= -56.55776873 au

2*E(NH3)= 2*-56.55776873 = -113.1155375 au

E(N2)= -109.52412868 au

E(H2)= -1.17853930 au

3*E(H2)= 3*-1.17853930 = -3.5356179 au

ΔE = 2*E(NH3)-[E(N2)+3*E(H2)] = -113.1155375-[-109.52412868+-3.5356179]

ΔE = -0.05579092 au

ΔE = -0.05579092*2625.5 = -146.48 kJ/mol to 2.d.p

==='''Stability of Reactants vs Products'''===

ΔE is negative therefore the Haber process is exothermic and the product (NH3) is lower in energy and more stable than the reactants.

=='''''AlCl4-'''''==
<jmol><jmolApplet>
<title>AlCl4-</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 ALCL4- OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 ALCL4- OPTF POP.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000155 0.001800 YES
RMS Displacement 0.000093 0.001200 YES
Predicted change in Energy=-7.051677D-09
Optimization completed.
-- Stationary point found.

</pre>

There is zero net force and displacement so the optimization has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ AlCl4- Optimised Information
! !! AlCl4-
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -2083.61641374
|-
| RMS gradient / au || 0.00001174
|-
| Point Group || TD
|-
| Al-Cl bond length / A || 2.17703
|-
| Cl-Al-Cl bond angle / degrees || 109.471
|}

This is a much higher energy compound than that of N2 and H2.

==='''Molecule Vibrations'''===

[[File:HB915 alcl4- optf pop displayvibrations.jpg]]

The 3N-6 rule gives 3x5-6= 1. This is supported by the frequencies found from computational analysis as seen in the image above. Modes 7-9 are degenerate but in different directions. They are high energy due to the bending character creating a large change in dipole. Modes 3-5 are also degenerate bending vibrations but at a lower energy. Modes 1, 2 and 6 are all symmetrical vibrations that show no change in dipole and are therefore not visible on the spectrum as shown below.

[[File:HB915 alcl4- optf pop spectra.jpg|400px|center|left]]

==='''Charge Distribution'''===

Aluminum has an electronegativity of 1.61 which is comparatively smaller than that of chlorine with 3.16. Therefore you would expect aluminum to carry the positive charge. This is supported by the values calculated form the Schrödinger equation shown in the image below. Also with such a high difference in electronegativity of these two atoms more ionic character will be witnessed.

[[File:HB915 alcl4- optf pop charge.jpg]]

==='''Molecular Orbitals'''===

Images of the molecular orbitals can be visualised by GaussView. They represent each orbital solution to the Schrödinger equation, in other words the Φs, one for each MO energy level.

There are over 90 orbitals found , 41 of which are occupied, and each can be described by the interactions of the atomic orbitals. Five have been explored here.

[[File:HB915 AlCl4- MO 21.PNG|300px]]

When looking at diatomic molecules the MOs are the simple interaction between the AOs. However when looking at larger molecule you talk about the MO fragments. This is the non-bonding Cl 2 p orbitals. They are too different in energy to interact with the Al orbitals so remain non-bonding. There are 12 with similar energies and shapes that can be attributed to the different orientations and phases of each orbital.

[[File:HB915 AlCl4- MO 26.PNG|300px]]
[[File:HB915 AlCl4- MO 30.PNG|300px]]

These two are a pair of MOs created by interactions between the same AOs; the s Cl fragmant and the s Al. However one is an in-phase interaction (left) which produces a filled bonding orbital and the other out of phase interaction (right) which produced an anti-bonding orbital which is also filled. Both are occupied so these are not the orbitals responsible for bonding in this molecule.

[[File:HB915 AlCl4- MO 31.PNG|300px]]
[[File:HB915 AlCl4- MO 43.PNG|300px]]

This is another bonding (left) and non-bonding (right) pair of MOs. These were caused by the interaction of the 3p Cl fragment and the 3p Al. The bonding is filled and the anti-bonding is empty so it is this orbital that is responsible for the bonds in this molecule.

=='''''S2'''''==
<jmol><jmolApplet>
<title>S2</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 S2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 S2 OPTF POP.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000039 0.000300 YES
Maximum Displacement 0.000067 0.001800 YES
RMS Displacement 0.000095 0.001200 YES
Predicted change in Energy=-2.624039D-09
Optimization completed.
-- Stationary point found.

</pre>

There is zero net force and displacement so the optimization has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ S2 Optimised Information
! !! S2
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -796.32599779
|-
| RMS gradient / au || 0.00002267
|-
| Point Group || D*H
|-
| S-S bond length / A || 1.92952
|-
| S-S bond angle / degrees || N/A
|}

==='''Molecule Vibrations'''===

[[File:HB915 s2 optf pop displayvibrations.jpg]]

The 3N-5 rule used for linear molecules gives 3x2-5= 1. This is supported by the frequencies found from computational analysis as seen in the image above. This is due to the simple stretching of the bond.

==='''Charge Distribution'''===

Sulfur has an electronegativity of 2.58. However when both atoms have the same electronegativity the charge is equally distributed across the molecule.

[[File:HB915 s2 optf pop charge.jpg]]

==='''Molecular Orbitals'''===

Images of the molecular orbitals can be visualised by GaussView. They represent each orbital solution to the Schrödinger equation, in other words the Φs, one for each MO energy level.

There are over 30 orbitals found , 16 of which are occupied, and each can be described by the interactions of the atomic orbitals. Some examples are given below.

[[File:HB915 S2 MO 11.PNG|300px]]
[[File:HB915 S2 MO 12.PNG|300px]]

3 s orbitals from each Sulfur atom forms a bonding (left), non-bonding (right) pair of orbitals shown above.

[[File:HB915 S2 MO 15.PNG|300px]]
[[File:HB915 S2 MO 16.PNG|300px]]

The 3px from each sulfur interact to form a bonding (left) and an anti-bonding (right). However both are filled so no bond is formed from these MOs.

[[File:HB915 S2 MO 13.PNG|300px]]
[[File:HB915 S2 MO 18.PNG|300px]]

The 3pz from each sulfur interact to form a filled bonding (left) and a unfilled anti-bonding (right). Therefore this results in a sigma bond being formed between the two sulfur atoms.

[[File:HB915 S2 MO 14.PNG|300px]]
[[File:HB915 S2 MO 17.PNG|300px]]

The 3py from each sulfur interact to form a filled bonding (left) and a unfilled anti-bonding (right). Therefore this results in a pi bond being formed above and below the plane of the two sulfur atoms.

Rep:Mod:HB9151

2016-03-11T14:49:21Z

Hb915: /* Molecule Vibrations */

This is an exploration of molecules and reactions using GaussVeiw in order to understand the importance of computational inorganic chemistry.

Each molecule was draw in GaussVeiw and analysised computationally by solving the Schrödinger equation (EΦ=HΦ) under the Born-Oppenheimer approximation. Firstly the self-consistent field calculation is done for the starting bond lengths and angles giving the electronic wavefunction (Φ) that gives the lowest energy (for the fixed nuclei). The the distance is slightly shortened and the calculation repeated. This is continued until the lowest energy is found and this is the optimized structure.

Once this structure is found the data given by the solutions can be used to explore many properties of the molecule such as the spectrum, molecular orbital and the overall energy of the molecule.

=='''''NH3'''''==
<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 NH3 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 NH3 OPTF POP.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

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=-5.986294D-10
Optimization completed.
-- Stationary point found.

</pre>

There is zero net force and displacement so the optimization has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ NH3 Optimised Information
! !! NH3
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -56.55776873
|-
| RMS gradient / au || 0.00000485
|-
| Point Group || C3V
|-
| H-N bond length / A || 1.01798
|-
| H-N-H bond angle / degrees || 105.741
|}

==='''Molecule Vibrations'''===

[[File:HB915 nh3 optf pop displayvibrations.jpg.png|400px|left]]

''How many modes do you expect from the 3N-6 rule?''

N represents the number of atoms in the molecule. For NH3 there are 4 molecules therefore;
3x4-6=6

''Which modes are degenerate (ie have the same energy)?''

Modes 2-3, and 5-6 are pairs of vibrations with the same energy (equal frequency).

''Which modes are "bending" vibrations and which are "bond stretch" vibrations?''

Modes 1-3 are bending and modes 4-6 are stretching. This is clear both from the animation and because bond stretching vibrations are higher in energy.

''Which mode is highly symmetric?''

Mode 4 is highly symmetric with no change in dipole.

''One mode is known as the "umbrella" mode, which one is this?''

Mode 1

''How many bands would you expect to see in an experimental spectrum of gaseous ammonia?''

There are four different vibrational energies suggesting four different bands. However there is only a minimal change in dipole for modes 4-6 so these would not be visible on a spectrum leaving only two bands.

[[File:HB915 nh3 optf pop spectra.jpg.png|500px|center|left]]

==='''Charge Distribution'''===

Nitrogen has an electronegativity of 3.04 which is comparatively larger than hydrogen with 2.2. Therefore you would expect nitrogen to carry the negative charge. This is supported by the values calculated form the Schrödinger equation shown in the image below.

[[File:HB915 nh3 optf pop charge.jpg.png|300px|center|left]]

=='''''N2'''''==
<jmol><jmolApplet>
<title>N2</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 N2 OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 N2 OPTIMISATION.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

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.

</pre>

There is zero net force and displacement so the optimization has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ N2 Optimised Information
! !! N2
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -109.52412868
|-
| RMS gradient / au || 0.00000365
|-
| Point Group || D*H
|-
| N-N bond length / A || 1.10550
|-
| N-N bond angle / degrees || N/A
|}

==='''Molecule Vibrations'''===

[[File:HB915 n2 optf pop displayvibrations.jpg|400px]]

The 3N-5 rule used for linear molecules gives 3x2-5= 1. This is supported by the frequencies found from computational analysis as seen in the image above. This is due to the simple stretching of the bond.

==='''Charge Distribution'''===

Nitrogen has an electronegativity of 3.04. However when both atoms have the same electronegativity the charge is equally distributed across the molecule.

[[File:HB915 n2 optf pop charge.jpg|300px|center|left]]

=='''''H2'''''==
<jmol><jmolApplet>
<title>H2</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 H2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 H2 OPTF POP.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

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.

</pre>

There is zero net force and displacement so the optimization has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ H2 Optimised Information
! !! H2
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -1.17853930
|-
| RMS gradient / au || 0.00012170
|-
| Point Group || D*H
|-
| H-H bond length / A || 1.10550
|-
| H-H bond angle / degrees || N/A
|}

==='''Molecule Vibrations'''===

[[File:HB915 h2 optf pop displayvibrations.jpg|400px]]

The 3N-5 rule used for linear molecules gives 3x2-5= 1. This is supported by the frequencies found from computational analysis as seen in the image above. This is due to the simple stretching of the bond.

==='''Charge Distribution'''===

Nitrogen has an electronegativity of 2.2. However when both atoms have the same electronegativity the charge is equally distributed across the molecule.

[[File:HB915 h2 optf pop charge.jpg|300px|center|left]]

=='''''Haber-Bosch Process'''''==

==='''Equation of Reaction'''===

N2 + H2 -> NH3

==='''Energy of Reaction'''===

E(NH3)= -56.55776873 au

2*E(NH3)= 2*-56.55776873 = -113.1155375 au

E(N2)= -109.52412868 au

E(H2)= -1.17853930 au

3*E(H2)= 3*-1.17853930 = -3.5356179 au

ΔE = 2*E(NH3)-[E(N2)+3*E(H2)] = -113.1155375-[-109.52412868+-3.5356179]

ΔE = -0.05579092 au

ΔE = -0.05579092*2625.5 = -146.48 kJ/mol to 2.d.p

==='''Stability of Reactants vs Products'''===

ΔE is negative therefore the Haber process is exothermic and the product (NH3) is lower in energy and more stable than the reactants.

=='''''AlCl4-'''''==
<jmol><jmolApplet>
<title>AlCl4-</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 ALCL4- OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 ALCL4- OPTF POP.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000155 0.001800 YES
RMS Displacement 0.000093 0.001200 YES
Predicted change in Energy=-7.051677D-09
Optimization completed.
-- Stationary point found.

</pre>

There is zero net force and displacement so the optimization has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ AlCl4- Optimised Information
! !! AlCl4-
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -2083.61641374
|-
| RMS gradient / au || 0.00001174
|-
| Point Group || TD
|-
| Al-Cl bond length / A || 2.17703
|-
| Cl-Al-Cl bond angle / degrees || 109.471
|}

This is a much higher energy compound than that of N2 and H2.

==='''Molecule Vibrations'''===

[[File:HB915 alcl4- optf pop displayvibrations.jpg]]

The 3N-6 rule gives 3x5-6= 1. This is supported by the frequencies found from computational analysis as seen in the image above. Modes 7-9 are degenerate but in different directions. They are high energy due to the bending character creating a large change in dipole. Modes 3-5 are also degenerate bending vibrations but at a lower energy. Modes 1, 2 and 6 are all symmetrical vibrations that show no change in dipole and are therefore not visible on the spectrum as shown below.

[[File:HB915 alcl4- optf pop spectra.jpg|400px|center|left]]

==='''Charge Distribution'''===

Aluminum has an electronegativity of 1.61 which is comparatively smaller than that of chlorine with 3.16. Therefore you would expect aluminum to carry the positive charge. This is supported by the values calculated form the Schrödinger equation shown in the image below. Also with such a high difference in electronegativity of these two atoms more ionic character will be witnessed.

[[File:HB915 alcl4- optf pop charge.jpg]]

==='''Molecular Orbitals'''===

Images of the molecular orbitals can be visualised by GaussView. They represent each orbital solution to the Schrödinger equation, in other words the Φs, one for each MO energy level.

There are over 90 orbitals found , 41 of which are occupied, and each can be described by the interactions of the atomic orbitals. Five have been explored here.

[[File:HB915 AlCl4- MO 21.PNG|300px]]

When looking at diatomic molecules the MOs are the simple interaction between the AOs. However when looking at larger molecule you talk about the MO fragments. This is the non-bonding Cl 2 p orbitals. They are too different in energy to interact with the Al orbitals so remain non-bonding. There are 12 with similar energies and shapes that can be attributed to the different orientations and phases of each orbital.

[[File:HB915 AlCl4- MO 26.PNG|300px]]
[[File:HB915 AlCl4- MO 30.PNG|300px]]

These two are a pair of MOs created by interactions between the same AOs; the s Cl fragrant and the s Al. However one is an in-phase interaction (left) which produces a filled bonding orbital and the other out of phase interaction (right) which produced an anti-bonding orbital which is also filled. Both are occupied so these are not the orbitals responsible for bonding in this molecule.

[[File:HB915 AlCl4- MO 31.PNG|300px]]
[[File:HB915 AlCl4- MO 43.PNG|300px]]

This is another bonding (left) and non-bonding (right) pair of MOs. These were caused by the interaction of the 3p Cl fragment and the 3p Al. The bonding is filled and the anti-bonding is empty so it is this orbital that is responsible for the bonds in this molecule.

=='''''S2'''''==
<jmol><jmolApplet>
<title>S2</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 S2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 S2 OPTF POP.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000039 0.000300 YES
Maximum Displacement 0.000067 0.001800 YES
RMS Displacement 0.000095 0.001200 YES
Predicted change in Energy=-2.624039D-09
Optimization completed.
-- Stationary point found.

</pre>

There is zero net force and displacement so the optimization has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ S2 Optimised Information
! !! S2
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -796.32599779
|-
| RMS gradient / au || 0.00002267
|-
| Point Group || D*H
|-
| S-S bond length / A || 1.92952
|-
| S-S bond angle / degrees || N/A
|}

==='''Molecule Vibrations'''===

[[File:HB915 s2 optf pop displayvibrations.jpg]]

The 3N-5 rule used for linear molecules gives 3x2-5= 1. This is supported by the frequencies found from computational analysis as seen in the image above. This is due to the simple stretching of the bond.

==='''Charge Distribution'''===

Sulfur has an electronegativity of 2.58. However when both atoms have the same electronegativity the charge is equally distributed across the molecule.

[[File:HB915 s2 optf pop charge.jpg]]

==='''Molecular Orbitals'''===

Images of the molecular orbitals can be visualised by GaussView. They represent each orbital solution to the Schrödinger equation, in other words the Φs, one for each MO energy level.

There are over 30 orbitals found , 16 of which are occupied, and each can be described by the interactions of the atomic orbitals. Some examples are given below.

[[File:HB915 S2 MO 11.PNG|300px]]
[[File:HB915 S2 MO 12.PNG|300px]]

3 s orbitals from each Sulfur atom forms a bonding (left), non-bonding (right) pair of orbitals shown above.

[[File:HB915 S2 MO 15.PNG|300px]]
[[File:HB915 S2 MO 16.PNG|300px]]

The 3px from each sulfur interact to form a bonding (left) and an anti-bonding (right). However both are filled so no bond is formed from these MOs.

[[File:HB915 S2 MO 13.PNG|300px]]
[[File:HB915 S2 MO 18.PNG|300px]]

The 3pz from each sulfur interact to form a filled bonding (left) and a unfilled anti-bonding (right). Therefore this results in a sigma bond being formed between the two sulfur atoms.

[[File:HB915 S2 MO 14.PNG|300px]]
[[File:HB915 S2 MO 17.PNG|300px]]

The 3py from each sulfur interact to form a filled bonding (left) and a unfilled anti-bonding (right). Therefore this results in a pi bond being formed above and below the plane of the two sulfur atoms.

Rep:Mod:HB9151

2016-03-11T14:35:41Z

Hb915: /* Molecule Vibrations */

This is an exploration of molecules and reactions using GaussVeiw in order to understand the importance of computational inorganic chemistry.

Each molecule was draw in GaussVeiw and analysised computationally by solving the Schrödinger equation (EΦ=HΦ) under the Born-Oppenheimer approximation. Firstly the self-consistent field calculation is done for the starting bond lengths and angles giving the electronic wavefunction (Φ) that gives the lowest energy (for the fixed nuclei). The the distance is slightly shortened and the calculation repeated. This is continued until the lowest energy is found and this is the optimized structure.

Once this structure is found the data given by the solutions can be used to explore many properties of the molecule such as the spectrum, molecular orbital and the overall energy of the molecule.

=='''''NH3'''''==
<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 NH3 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 NH3 OPTF POP.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

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=-5.986294D-10
Optimization completed.
-- Stationary point found.

</pre>

There is zero net force and displacement so the optimization has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ NH3 Optimised Information
! !! NH3
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -56.55776873
|-
| RMS gradient / au || 0.00000485
|-
| Point Group || C3V
|-
| H-N bond length / A || 1.01798
|-
| H-N-H bond angle / degrees || 105.741
|}

==='''Molecule Vibrations'''===

[[File:HB915 nh3 optf pop displayvibrations.jpg.png|400px|left]]

''How many modes do you expect from the 3N-6 rule?''

N represents the number of atoms in the molecule. For NH3 there are 4 molecules therefore;
3x4-6=6

''Which modes are degenerate (ie have the same energy)?''

Modes 2 and 3 and 5 and 6 have the same energy (equal frequency).

''Which modes are "bending" vibrations and which are "bond stretch" vibrations?''

Modes 1-3 are bending and modes 4-6 are stretching. This is clear both from the animation and because bond stretching vibrations are higher in energy.

''Which mode is highly symmetric?''

Mode 4 is highly symmetric with no change in dipole.

''One mode is known as the "umbrella" mode, which one is this?''

Mode 1

''How many bands would you expect to see in an experimental spectrum of gaseous ammonia?''

There are four different vibrational energies suggesting four different bands. However there is only a minimal change in dipole for modes 4-6 so these would not be visible on a spectrum leaving only two bands.

[[File:HB915 nh3 optf pop spectra.jpg.png|500px|center|left]]

==='''Charge Distribution'''===

Nitrogen has an electronegativity of 3.04 which is comparatively larger than hydrogen with 2.2. Therefore you would expect nitrogen to carry the negative charge. This is supported by the values calculated form the Schrödinger equation shown in the image below.

[[File:HB915 nh3 optf pop charge.jpg.png|300px|center|left]]

=='''''N2'''''==
<jmol><jmolApplet>
<title>N2</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 N2 OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 N2 OPTIMISATION.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

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.

</pre>

There is zero net force and displacement so the optimization has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ N2 Optimised Information
! !! N2
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -109.52412868
|-
| RMS gradient / au || 0.00000365
|-
| Point Group || D*H
|-
| N-N bond length / A || 1.10550
|-
| N-N bond angle / degrees || N/A
|}

==='''Molecule Vibrations'''===

[[File:HB915 n2 optf pop displayvibrations.jpg|400px]]

The 3N-5 rule used for linear molecules gives 3x2-5= 1. This is supported by the frequencies found from computational analysis as seen in the image above. This is due to the simple stretching of the bond.

==='''Charge Distribution'''===

Nitrogen has an electronegativity of 3.04. However when both atoms have the same electronegativity the charge is equally distributed across the molecule.

[[File:HB915 n2 optf pop charge.jpg|300px|center|left]]

=='''''H2'''''==
<jmol><jmolApplet>
<title>H2</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 H2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 H2 OPTF POP.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

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.

</pre>

There is zero net force and displacement so the optimization has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ H2 Optimised Information
! !! H2
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -1.17853930
|-
| RMS gradient / au || 0.00012170
|-
| Point Group || D*H
|-
| H-H bond length / A || 1.10550
|-
| H-H bond angle / degrees || N/A
|}

==='''Molecule Vibrations'''===

[[File:HB915 h2 optf pop displayvibrations.jpg|400px]]

The 3N-5 rule used for linear molecules gives 3x2-5= 1. This is supported by the frequencies found from computational analysis as seen in the image above. This is due to the simple stretching of the bond.

==='''Charge Distribution'''===

Nitrogen has an electronegativity of 2.2. However when both atoms have the same electronegativity the charge is equally distributed across the molecule.

[[File:HB915 h2 optf pop charge.jpg|300px|center|left]]

=='''''Haber-Bosch Process'''''==

==='''Equation of Reaction'''===

N2 + H2 -> NH3

==='''Energy of Reaction'''===

E(NH3)= -56.55776873 au

2*E(NH3)= 2*-56.55776873 = -113.1155375 au

E(N2)= -109.52412868 au

E(H2)= -1.17853930 au

3*E(H2)= 3*-1.17853930 = -3.5356179 au

ΔE = 2*E(NH3)-[E(N2)+3*E(H2)] = -113.1155375-[-109.52412868+-3.5356179]

ΔE = -0.05579092 au

ΔE = -0.05579092*2625.5 = -146.48 kJ/mol to 2.d.p

==='''Stability of Reactants vs Products'''===

ΔE is negative therefore the Haber process is exothermic and the product (NH3) is lower in energy and more stable than the reactants.

=='''''AlCl4-'''''==
<jmol><jmolApplet>
<title>AlCl4-</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 ALCL4- OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 ALCL4- OPTF POP.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000155 0.001800 YES
RMS Displacement 0.000093 0.001200 YES
Predicted change in Energy=-7.051677D-09
Optimization completed.
-- Stationary point found.

</pre>

There is zero net force and displacement so the optimization has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ AlCl4- Optimised Information
! !! AlCl4-
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -2083.61641374
|-
| RMS gradient / au || 0.00001174
|-
| Point Group || TD
|-
| Al-Cl bond length / A || 2.17703
|-
| Cl-Al-Cl bond angle / degrees || 109.471
|}

This is a much higher energy compound than that of N2 and H2.

==='''Molecule Vibrations'''===

[[File:HB915 alcl4- optf pop displayvibrations.jpg]]

The 3N-6 rule gives 3x5-6= 1. This is supported by the frequencies found from computational analysis as seen in the image above. Modes 7-9 are degenerate but in different directions. They are high energy due to the bending character creating a large change in dipole. Modes 3-5 are also degenerate bending vibrations but at a lower energy. Modes 1, 2 and 6 are all symmetrical vibrations that show no change in dipole and are therefore not visible on the spectrum as shown below.

[[File:HB915 alcl4- optf pop spectra.jpg|400px|center|left]]

==='''Charge Distribution'''===

Aluminum has an electronegativity of 1.61 which is comparatively smaller than that of chlorine with 3.16. Therefore you would expect aluminum to carry the positive charge. This is supported by the values calculated form the Schrödinger equation shown in the image below. Also with such a high difference in electronegativity of these two atoms more ionic character will be witnessed.

[[File:HB915 alcl4- optf pop charge.jpg]]

==='''Molecular Orbitals'''===

Images of the molecular orbitals can be visualised by GaussView. They represent each orbital solution to the Schrödinger equation, in other words the Φs, one for each MO energy level.

There are over 90 orbitals found , 41 of which are occupied, and each can be described by the interactions of the atomic orbitals. Five have been explored here.

[[File:HB915 AlCl4- MO 21.PNG|300px]]

When looking at diatomic molecules the MOs are the simple interaction between the AOs. However when looking at larger molecule you talk about the MO fragments. This is the non-bonding Cl 2 p orbitals. They are too different in energy to interact with the Al orbitals so remain non-bonding. There are 12 with similar energies and shapes that can be attributed to the different orientations and phases of each orbital.

[[File:HB915 AlCl4- MO 26.PNG|300px]]
[[File:HB915 AlCl4- MO 30.PNG|300px]]

These two are a pair of MOs created by interactions between the same AOs; the s Cl fragrant and the s Al. However one is an in-phase interaction (left) which produces a filled bonding orbital and the other out of phase interaction (right) which produced an anti-bonding orbital which is also filled. Both are occupied so these are not the orbitals responsible for bonding in this molecule.

[[File:HB915 AlCl4- MO 31.PNG|300px]]
[[File:HB915 AlCl4- MO 43.PNG|300px]]

This is another bonding (left) and non-bonding (right) pair of MOs. These were caused by the interaction of the 3p Cl fragment and the 3p Al. The bonding is filled and the anti-bonding is empty so it is this orbital that is responsible for the bonds in this molecule.

=='''''S2'''''==
<jmol><jmolApplet>
<title>S2</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 S2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 S2 OPTF POP.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000039 0.000300 YES
Maximum Displacement 0.000067 0.001800 YES
RMS Displacement 0.000095 0.001200 YES
Predicted change in Energy=-2.624039D-09
Optimization completed.
-- Stationary point found.

</pre>

There is zero net force and displacement so the optimization has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ S2 Optimised Information
! !! S2
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -796.32599779
|-
| RMS gradient / au || 0.00002267
|-
| Point Group || D*H
|-
| S-S bond length / A || 1.92952
|-
| S-S bond angle / degrees || N/A
|}

==='''Molecule Vibrations'''===

[[File:HB915 s2 optf pop displayvibrations.jpg]]

The 3N-5 rule used for linear molecules gives 3x2-5= 1. This is supported by the frequencies found from computational analysis as seen in the image above. This is due to the simple stretching of the bond.

==='''Charge Distribution'''===

Sulfur has an electronegativity of 2.58. However when both atoms have the same electronegativity the charge is equally distributed across the molecule.

[[File:HB915 s2 optf pop charge.jpg]]

==='''Molecular Orbitals'''===

Images of the molecular orbitals can be visualised by GaussView. They represent each orbital solution to the Schrödinger equation, in other words the Φs, one for each MO energy level.

There are over 30 orbitals found , 16 of which are occupied, and each can be described by the interactions of the atomic orbitals. Some examples are given below.

[[File:HB915 S2 MO 11.PNG|300px]]
[[File:HB915 S2 MO 12.PNG|300px]]

3 s orbitals from each Sulfur atom forms a bonding (left), non-bonding (right) pair of orbitals shown above.

[[File:HB915 S2 MO 15.PNG|300px]]
[[File:HB915 S2 MO 16.PNG|300px]]

The 3px from each sulfur interact to form a bonding (left) and an anti-bonding (right). However both are filled so no bond is formed from these MOs.

[[File:HB915 S2 MO 13.PNG|300px]]
[[File:HB915 S2 MO 18.PNG|300px]]

The 3pz from each sulfur interact to form a filled bonding (left) and a unfilled anti-bonding (right). Therefore this results in a sigma bond being formed between the two sulfur atoms.

[[File:HB915 S2 MO 14.PNG|300px]]
[[File:HB915 S2 MO 17.PNG|300px]]

The 3py from each sulfur interact to form a filled bonding (left) and a unfilled anti-bonding (right). Therefore this results in a pi bond being formed above and below the plane of the two sulfur atoms.

Rep:Mod:HB9151

2016-03-11T14:35:23Z

Hb915: /* Molecule Vibrations */

This is an exploration of molecules and reactions using GaussVeiw in order to understand the importance of computational inorganic chemistry.

Each molecule was draw in GaussVeiw and analysised computationally by solving the Schrödinger equation (EΦ=HΦ) under the Born-Oppenheimer approximation. Firstly the self-consistent field calculation is done for the starting bond lengths and angles giving the electronic wavefunction (Φ) that gives the lowest energy (for the fixed nuclei). The the distance is slightly shortened and the calculation repeated. This is continued until the lowest energy is found and this is the optimized structure.

Once this structure is found the data given by the solutions can be used to explore many properties of the molecule such as the spectrum, molecular orbital and the overall energy of the molecule.

=='''''NH3'''''==
<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 NH3 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 NH3 OPTF POP.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

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=-5.986294D-10
Optimization completed.
-- Stationary point found.

</pre>

There is zero net force and displacement so the optimization has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ NH3 Optimised Information
! !! NH3
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -56.55776873
|-
| RMS gradient / au || 0.00000485
|-
| Point Group || C3V
|-
| H-N bond length / A || 1.01798
|-
| H-N-H bond angle / degrees || 105.741
|}

==='''Molecule Vibrations'''===

[[File:HB915 nh3 optf pop displayvibrations.jpg.png|400px|left]]

''How many modes do you expect from the 3N-6 rule?''

N represents the number of atoms in the molecule. For NH3 there are 4 molecules therefore;
3x4-6=6

''Which modes are degenerate (ie have the same energy)?''

Modes 2 and 3 and 5 and 6 have the same energy (equal frequency).

''Which modes are "bending" vibrations and which are "bond stretch" vibrations?''

Modes 1-3 are bending and modes 4-6 are stretching. This is clear both from the animation and because bond stretching vibrations are higher in energy.

''Which mode is highly symmetric?''

Mode 4 is highly symmetric with no change in dipole.

''One mode is known as the "umbrella" mode, which one is this?''

Mode 1

''How many bands would you expect to see in an experimental spectrum of gaseous ammonia?''

There are four different vibrational energies suggesting four different bands. However there is only a minimal change in dipole for modes 4-6 so these would not be visible on a spectrum leaving only two bands.

[[File:HB915 nh3 optf pop spectra.jpg.png|500px|center|left]]

==='''Charge Distribution'''===

Nitrogen has an electronegativity of 3.04 which is comparatively larger than hydrogen with 2.2. Therefore you would expect nitrogen to carry the negative charge. This is supported by the values calculated form the Schrödinger equation shown in the image below.

[[File:HB915 nh3 optf pop charge.jpg.png|300px|center|left]]

=='''''N2'''''==
<jmol><jmolApplet>
<title>N2</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 N2 OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 N2 OPTIMISATION.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

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.

</pre>

There is zero net force and displacement so the optimization has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ N2 Optimised Information
! !! N2
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -109.52412868
|-
| RMS gradient / au || 0.00000365
|-
| Point Group || D*H
|-
| N-N bond length / A || 1.10550
|-
| N-N bond angle / degrees || N/A
|}

==='''Molecule Vibrations'''===

[[File:HB915 n2 optf pop displayvibrations.jpg|400px|center|left]]

The 3N-5 rule used for linear molecules gives 3x2-5= 1. This is supported by the frequencies found from computational analysis as seen in the image above. This is due to the simple stretching of the bond.

==='''Charge Distribution'''===

Nitrogen has an electronegativity of 3.04. However when both atoms have the same electronegativity the charge is equally distributed across the molecule.

[[File:HB915 n2 optf pop charge.jpg|300px|center|left]]

=='''''H2'''''==
<jmol><jmolApplet>
<title>H2</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 H2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 H2 OPTF POP.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

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.

</pre>

There is zero net force and displacement so the optimization has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ H2 Optimised Information
! !! H2
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -1.17853930
|-
| RMS gradient / au || 0.00012170
|-
| Point Group || D*H
|-
| H-H bond length / A || 1.10550
|-
| H-H bond angle / degrees || N/A
|}

==='''Molecule Vibrations'''===

[[File:HB915 h2 optf pop displayvibrations.jpg|400px]]

The 3N-5 rule used for linear molecules gives 3x2-5= 1. This is supported by the frequencies found from computational analysis as seen in the image above. This is due to the simple stretching of the bond.

==='''Charge Distribution'''===

Nitrogen has an electronegativity of 2.2. However when both atoms have the same electronegativity the charge is equally distributed across the molecule.

[[File:HB915 h2 optf pop charge.jpg|300px|center|left]]

=='''''Haber-Bosch Process'''''==

==='''Equation of Reaction'''===

N2 + H2 -> NH3

==='''Energy of Reaction'''===

E(NH3)= -56.55776873 au

2*E(NH3)= 2*-56.55776873 = -113.1155375 au

E(N2)= -109.52412868 au

E(H2)= -1.17853930 au

3*E(H2)= 3*-1.17853930 = -3.5356179 au

ΔE = 2*E(NH3)-[E(N2)+3*E(H2)] = -113.1155375-[-109.52412868+-3.5356179]

ΔE = -0.05579092 au

ΔE = -0.05579092*2625.5 = -146.48 kJ/mol to 2.d.p

==='''Stability of Reactants vs Products'''===

ΔE is negative therefore the Haber process is exothermic and the product (NH3) is lower in energy and more stable than the reactants.

=='''''AlCl4-'''''==
<jmol><jmolApplet>
<title>AlCl4-</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 ALCL4- OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 ALCL4- OPTF POP.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000155 0.001800 YES
RMS Displacement 0.000093 0.001200 YES
Predicted change in Energy=-7.051677D-09
Optimization completed.
-- Stationary point found.

</pre>

There is zero net force and displacement so the optimization has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ AlCl4- Optimised Information
! !! AlCl4-
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -2083.61641374
|-
| RMS gradient / au || 0.00001174
|-
| Point Group || TD
|-
| Al-Cl bond length / A || 2.17703
|-
| Cl-Al-Cl bond angle / degrees || 109.471
|}

This is a much higher energy compound than that of N2 and H2.

==='''Molecule Vibrations'''===

[[File:HB915 alcl4- optf pop displayvibrations.jpg]]

The 3N-6 rule gives 3x5-6= 1. This is supported by the frequencies found from computational analysis as seen in the image above. Modes 7-9 are degenerate but in different directions. They are high energy due to the bending character creating a large change in dipole. Modes 3-5 are also degenerate bending vibrations but at a lower energy. Modes 1, 2 and 6 are all symmetrical vibrations that show no change in dipole and are therefore not visible on the spectrum as shown below.

[[File:HB915 alcl4- optf pop spectra.jpg|400px|center|left]]

==='''Charge Distribution'''===

Aluminum has an electronegativity of 1.61 which is comparatively smaller than that of chlorine with 3.16. Therefore you would expect aluminum to carry the positive charge. This is supported by the values calculated form the Schrödinger equation shown in the image below. Also with such a high difference in electronegativity of these two atoms more ionic character will be witnessed.

[[File:HB915 alcl4- optf pop charge.jpg]]

==='''Molecular Orbitals'''===

Images of the molecular orbitals can be visualised by GaussView. They represent each orbital solution to the Schrödinger equation, in other words the Φs, one for each MO energy level.

There are over 90 orbitals found , 41 of which are occupied, and each can be described by the interactions of the atomic orbitals. Five have been explored here.

[[File:HB915 AlCl4- MO 21.PNG|300px]]

When looking at diatomic molecules the MOs are the simple interaction between the AOs. However when looking at larger molecule you talk about the MO fragments. This is the non-bonding Cl 2 p orbitals. They are too different in energy to interact with the Al orbitals so remain non-bonding. There are 12 with similar energies and shapes that can be attributed to the different orientations and phases of each orbital.

[[File:HB915 AlCl4- MO 26.PNG|300px]]
[[File:HB915 AlCl4- MO 30.PNG|300px]]

These two are a pair of MOs created by interactions between the same AOs; the s Cl fragrant and the s Al. However one is an in-phase interaction (left) which produces a filled bonding orbital and the other out of phase interaction (right) which produced an anti-bonding orbital which is also filled. Both are occupied so these are not the orbitals responsible for bonding in this molecule.

[[File:HB915 AlCl4- MO 31.PNG|300px]]
[[File:HB915 AlCl4- MO 43.PNG|300px]]

This is another bonding (left) and non-bonding (right) pair of MOs. These were caused by the interaction of the 3p Cl fragment and the 3p Al. The bonding is filled and the anti-bonding is empty so it is this orbital that is responsible for the bonds in this molecule.

=='''''S2'''''==
<jmol><jmolApplet>
<title>S2</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 S2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 S2 OPTF POP.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000039 0.000300 YES
Maximum Displacement 0.000067 0.001800 YES
RMS Displacement 0.000095 0.001200 YES
Predicted change in Energy=-2.624039D-09
Optimization completed.
-- Stationary point found.

</pre>

There is zero net force and displacement so the optimization has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ S2 Optimised Information
! !! S2
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -796.32599779
|-
| RMS gradient / au || 0.00002267
|-
| Point Group || D*H
|-
| S-S bond length / A || 1.92952
|-
| S-S bond angle / degrees || N/A
|}

==='''Molecule Vibrations'''===

[[File:HB915 s2 optf pop displayvibrations.jpg]]

The 3N-5 rule used for linear molecules gives 3x2-5= 1. This is supported by the frequencies found from computational analysis as seen in the image above. This is due to the simple stretching of the bond.

==='''Charge Distribution'''===

Sulfur has an electronegativity of 2.58. However when both atoms have the same electronegativity the charge is equally distributed across the molecule.

[[File:HB915 s2 optf pop charge.jpg]]

==='''Molecular Orbitals'''===

Images of the molecular orbitals can be visualised by GaussView. They represent each orbital solution to the Schrödinger equation, in other words the Φs, one for each MO energy level.

There are over 30 orbitals found , 16 of which are occupied, and each can be described by the interactions of the atomic orbitals. Some examples are given below.

[[File:HB915 S2 MO 11.PNG|300px]]
[[File:HB915 S2 MO 12.PNG|300px]]

3 s orbitals from each Sulfur atom forms a bonding (left), non-bonding (right) pair of orbitals shown above.

[[File:HB915 S2 MO 15.PNG|300px]]
[[File:HB915 S2 MO 16.PNG|300px]]

The 3px from each sulfur interact to form a bonding (left) and an anti-bonding (right). However both are filled so no bond is formed from these MOs.

[[File:HB915 S2 MO 13.PNG|300px]]
[[File:HB915 S2 MO 18.PNG|300px]]

The 3pz from each sulfur interact to form a filled bonding (left) and a unfilled anti-bonding (right). Therefore this results in a sigma bond being formed between the two sulfur atoms.

[[File:HB915 S2 MO 14.PNG|300px]]
[[File:HB915 S2 MO 17.PNG|300px]]

The 3py from each sulfur interact to form a filled bonding (left) and a unfilled anti-bonding (right). Therefore this results in a pi bond being formed above and below the plane of the two sulfur atoms.

Rep:Mod:HB9151

2016-03-11T14:35:07Z

Hb915: /* Molecule Vibrations */

This is an exploration of molecules and reactions using GaussVeiw in order to understand the importance of computational inorganic chemistry.

Each molecule was draw in GaussVeiw and analysised computationally by solving the Schrödinger equation (EΦ=HΦ) under the Born-Oppenheimer approximation. Firstly the self-consistent field calculation is done for the starting bond lengths and angles giving the electronic wavefunction (Φ) that gives the lowest energy (for the fixed nuclei). The the distance is slightly shortened and the calculation repeated. This is continued until the lowest energy is found and this is the optimized structure.

Once this structure is found the data given by the solutions can be used to explore many properties of the molecule such as the spectrum, molecular orbital and the overall energy of the molecule.

=='''''NH3'''''==
<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 NH3 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 NH3 OPTF POP.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

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=-5.986294D-10
Optimization completed.
-- Stationary point found.

</pre>

There is zero net force and displacement so the optimization has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ NH3 Optimised Information
! !! NH3
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -56.55776873
|-
| RMS gradient / au || 0.00000485
|-
| Point Group || C3V
|-
| H-N bond length / A || 1.01798
|-
| H-N-H bond angle / degrees || 105.741
|}

==='''Molecule Vibrations'''===

[[File:HB915 nh3 optf pop displayvibrations.jpg.png|400px|left]]

''How many modes do you expect from the 3N-6 rule?''

N represents the number of atoms in the molecule. For NH3 there are 4 molecules therefore;
3x4-6=6

''Which modes are degenerate (ie have the same energy)?''

Modes 2 and 3 and 5 and 6 have the same energy (equal frequency).

''Which modes are "bending" vibrations and which are "bond stretch" vibrations?''

Modes 1-3 are bending and modes 4-6 are stretching. This is clear both from the animation and because bond stretching vibrations are higher in energy.

''Which mode is highly symmetric?''

Mode 4 is highly symmetric with no change in dipole.

''One mode is known as the "umbrella" mode, which one is this?''

Mode 1

''How many bands would you expect to see in an experimental spectrum of gaseous ammonia?''

There are four different vibrational energies suggesting four different bands. However there is only a minimal change in dipole for modes 4-6 so these would not be visible on a spectrum leaving only two bands.

[[File:HB915 nh3 optf pop spectra.jpg.png|500px|center|left]]

==='''Charge Distribution'''===

Nitrogen has an electronegativity of 3.04 which is comparatively larger than hydrogen with 2.2. Therefore you would expect nitrogen to carry the negative charge. This is supported by the values calculated form the Schrödinger equation shown in the image below.

[[File:HB915 nh3 optf pop charge.jpg.png|300px|center|left]]

=='''''N2'''''==
<jmol><jmolApplet>
<title>N2</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 N2 OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 N2 OPTIMISATION.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

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.

</pre>

There is zero net force and displacement so the optimization has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ N2 Optimised Information
! !! N2
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -109.52412868
|-
| RMS gradient / au || 0.00000365
|-
| Point Group || D*H
|-
| N-N bond length / A || 1.10550
|-
| N-N bond angle / degrees || N/A
|}

==='''Molecule Vibrations'''===

[[File:HB915 n2 optf pop displayvibrations.jpg|400px|center|left]]

The 3N-5 rule used for linear molecules gives 3x2-5= 1. This is supported by the frequencies found from computational analysis as seen in the image above. This is due to the simple stretching of the bond.

==='''Charge Distribution'''===

Nitrogen has an electronegativity of 3.04. However when both atoms have the same electronegativity the charge is equally distributed across the molecule.

[[File:HB915 n2 optf pop charge.jpg|300px|center|left]]

=='''''H2'''''==
<jmol><jmolApplet>
<title>H2</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 H2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 H2 OPTF POP.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

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.

</pre>

There is zero net force and displacement so the optimization has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ H2 Optimised Information
! !! H2
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -1.17853930
|-
| RMS gradient / au || 0.00012170
|-
| Point Group || D*H
|-
| H-H bond length / A || 1.10550
|-
| H-H bond angle / degrees || N/A
|}

==='''Molecule Vibrations'''===

[[File:HB915 h2 optf pop displayvibrations.jpg|400px|left]]

The 3N-5 rule used for linear molecules gives 3x2-5= 1. This is supported by the frequencies found from computational analysis as seen in the image above. This is due to the simple stretching of the bond.

==='''Charge Distribution'''===

Nitrogen has an electronegativity of 2.2. However when both atoms have the same electronegativity the charge is equally distributed across the molecule.

[[File:HB915 h2 optf pop charge.jpg|300px|center|left]]

=='''''Haber-Bosch Process'''''==

==='''Equation of Reaction'''===

N2 + H2 -> NH3

==='''Energy of Reaction'''===

E(NH3)= -56.55776873 au

2*E(NH3)= 2*-56.55776873 = -113.1155375 au

E(N2)= -109.52412868 au

E(H2)= -1.17853930 au

3*E(H2)= 3*-1.17853930 = -3.5356179 au

ΔE = 2*E(NH3)-[E(N2)+3*E(H2)] = -113.1155375-[-109.52412868+-3.5356179]

ΔE = -0.05579092 au

ΔE = -0.05579092*2625.5 = -146.48 kJ/mol to 2.d.p

==='''Stability of Reactants vs Products'''===

ΔE is negative therefore the Haber process is exothermic and the product (NH3) is lower in energy and more stable than the reactants.

=='''''AlCl4-'''''==
<jmol><jmolApplet>
<title>AlCl4-</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 ALCL4- OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 ALCL4- OPTF POP.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000155 0.001800 YES
RMS Displacement 0.000093 0.001200 YES
Predicted change in Energy=-7.051677D-09
Optimization completed.
-- Stationary point found.

</pre>

There is zero net force and displacement so the optimization has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ AlCl4- Optimised Information
! !! AlCl4-
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -2083.61641374
|-
| RMS gradient / au || 0.00001174
|-
| Point Group || TD
|-
| Al-Cl bond length / A || 2.17703
|-
| Cl-Al-Cl bond angle / degrees || 109.471
|}

This is a much higher energy compound than that of N2 and H2.

==='''Molecule Vibrations'''===

[[File:HB915 alcl4- optf pop displayvibrations.jpg]]

The 3N-6 rule gives 3x5-6= 1. This is supported by the frequencies found from computational analysis as seen in the image above. Modes 7-9 are degenerate but in different directions. They are high energy due to the bending character creating a large change in dipole. Modes 3-5 are also degenerate bending vibrations but at a lower energy. Modes 1, 2 and 6 are all symmetrical vibrations that show no change in dipole and are therefore not visible on the spectrum as shown below.

[[File:HB915 alcl4- optf pop spectra.jpg|400px|center|left]]

==='''Charge Distribution'''===

Aluminum has an electronegativity of 1.61 which is comparatively smaller than that of chlorine with 3.16. Therefore you would expect aluminum to carry the positive charge. This is supported by the values calculated form the Schrödinger equation shown in the image below. Also with such a high difference in electronegativity of these two atoms more ionic character will be witnessed.

[[File:HB915 alcl4- optf pop charge.jpg]]

==='''Molecular Orbitals'''===

Images of the molecular orbitals can be visualised by GaussView. They represent each orbital solution to the Schrödinger equation, in other words the Φs, one for each MO energy level.

There are over 90 orbitals found , 41 of which are occupied, and each can be described by the interactions of the atomic orbitals. Five have been explored here.

[[File:HB915 AlCl4- MO 21.PNG|300px]]

When looking at diatomic molecules the MOs are the simple interaction between the AOs. However when looking at larger molecule you talk about the MO fragments. This is the non-bonding Cl 2 p orbitals. They are too different in energy to interact with the Al orbitals so remain non-bonding. There are 12 with similar energies and shapes that can be attributed to the different orientations and phases of each orbital.

[[File:HB915 AlCl4- MO 26.PNG|300px]]
[[File:HB915 AlCl4- MO 30.PNG|300px]]

These two are a pair of MOs created by interactions between the same AOs; the s Cl fragrant and the s Al. However one is an in-phase interaction (left) which produces a filled bonding orbital and the other out of phase interaction (right) which produced an anti-bonding orbital which is also filled. Both are occupied so these are not the orbitals responsible for bonding in this molecule.

[[File:HB915 AlCl4- MO 31.PNG|300px]]
[[File:HB915 AlCl4- MO 43.PNG|300px]]

This is another bonding (left) and non-bonding (right) pair of MOs. These were caused by the interaction of the 3p Cl fragment and the 3p Al. The bonding is filled and the anti-bonding is empty so it is this orbital that is responsible for the bonds in this molecule.

=='''''S2'''''==
<jmol><jmolApplet>
<title>S2</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 S2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 S2 OPTF POP.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000039 0.000300 YES
Maximum Displacement 0.000067 0.001800 YES
RMS Displacement 0.000095 0.001200 YES
Predicted change in Energy=-2.624039D-09
Optimization completed.
-- Stationary point found.

</pre>

There is zero net force and displacement so the optimization has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ S2 Optimised Information
! !! S2
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -796.32599779
|-
| RMS gradient / au || 0.00002267
|-
| Point Group || D*H
|-
| S-S bond length / A || 1.92952
|-
| S-S bond angle / degrees || N/A
|}

==='''Molecule Vibrations'''===

[[File:HB915 s2 optf pop displayvibrations.jpg]]

The 3N-5 rule used for linear molecules gives 3x2-5= 1. This is supported by the frequencies found from computational analysis as seen in the image above. This is due to the simple stretching of the bond.

==='''Charge Distribution'''===

Sulfur has an electronegativity of 2.58. However when both atoms have the same electronegativity the charge is equally distributed across the molecule.

[[File:HB915 s2 optf pop charge.jpg]]

==='''Molecular Orbitals'''===

Images of the molecular orbitals can be visualised by GaussView. They represent each orbital solution to the Schrödinger equation, in other words the Φs, one for each MO energy level.

There are over 30 orbitals found , 16 of which are occupied, and each can be described by the interactions of the atomic orbitals. Some examples are given below.

[[File:HB915 S2 MO 11.PNG|300px]]
[[File:HB915 S2 MO 12.PNG|300px]]

3 s orbitals from each Sulfur atom forms a bonding (left), non-bonding (right) pair of orbitals shown above.

[[File:HB915 S2 MO 15.PNG|300px]]
[[File:HB915 S2 MO 16.PNG|300px]]

The 3px from each sulfur interact to form a bonding (left) and an anti-bonding (right). However both are filled so no bond is formed from these MOs.

[[File:HB915 S2 MO 13.PNG|300px]]
[[File:HB915 S2 MO 18.PNG|300px]]

The 3pz from each sulfur interact to form a filled bonding (left) and a unfilled anti-bonding (right). Therefore this results in a sigma bond being formed between the two sulfur atoms.

[[File:HB915 S2 MO 14.PNG|300px]]
[[File:HB915 S2 MO 17.PNG|300px]]

The 3py from each sulfur interact to form a filled bonding (left) and a unfilled anti-bonding (right). Therefore this results in a pi bond being formed above and below the plane of the two sulfur atoms.

Rep:Mod:HB9151

2016-03-11T14:34:32Z

Hb915: /* Proof of Structure Convergence */

This is an exploration of molecules and reactions using GaussVeiw in order to understand the importance of computational inorganic chemistry.

Each molecule was draw in GaussVeiw and analysised computationally by solving the Schrödinger equation (EΦ=HΦ) under the Born-Oppenheimer approximation. Firstly the self-consistent field calculation is done for the starting bond lengths and angles giving the electronic wavefunction (Φ) that gives the lowest energy (for the fixed nuclei). The the distance is slightly shortened and the calculation repeated. This is continued until the lowest energy is found and this is the optimized structure.

Once this structure is found the data given by the solutions can be used to explore many properties of the molecule such as the spectrum, molecular orbital and the overall energy of the molecule.

=='''''NH3'''''==
<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 NH3 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 NH3 OPTF POP.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

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=-5.986294D-10
Optimization completed.
-- Stationary point found.

</pre>

There is zero net force and displacement so the optimization has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ NH3 Optimised Information
! !! NH3
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -56.55776873
|-
| RMS gradient / au || 0.00000485
|-
| Point Group || C3V
|-
| H-N bond length / A || 1.01798
|-
| H-N-H bond angle / degrees || 105.741
|}

==='''Molecule Vibrations'''===

[[File:HB915 nh3 optf pop displayvibrations.jpg.png|400px|left]]

''How many modes do you expect from the 3N-6 rule?''

N represents the number of atoms in the molecule. For NH3 there are 4 molecules therefore;
3x4-6=6

''Which modes are degenerate (ie have the same energy)?''

Modes 2 and 3 and 5 and 6 have the same energy (equal frequency).

''Which modes are "bending" vibrations and which are "bond stretch" vibrations?''

Modes 1-3 are bending and modes 4-6 are stretching. This is clear both from the animation and because bond stretching vibrations are higher in energy.

''Which mode is highly symmetric?''

Mode 4 is highly symmetric with no change in dipole.

''One mode is known as the "umbrella" mode, which one is this?''

Mode 1

''How many bands would you expect to see in an experimental spectrum of gaseous ammonia?''

There are four different vibrational energies suggesting four different bands. However there is only a minimal change in dipole for modes 4-6 so these would not be visible on a spectrum leaving only two bands.

[[File:HB915 nh3 optf pop spectra.jpg.png|500px|center|left]]

==='''Charge Distribution'''===

Nitrogen has an electronegativity of 3.04 which is comparatively larger than hydrogen with 2.2. Therefore you would expect nitrogen to carry the negative charge. This is supported by the values calculated form the Schrödinger equation shown in the image below.

[[File:HB915 nh3 optf pop charge.jpg.png|300px|center|left]]

=='''''N2'''''==
<jmol><jmolApplet>
<title>N2</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 N2 OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 N2 OPTIMISATION.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

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.

</pre>

There is zero net force and displacement so the optimization has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ N2 Optimised Information
! !! N2
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -109.52412868
|-
| RMS gradient / au || 0.00000365
|-
| Point Group || D*H
|-
| N-N bond length / A || 1.10550
|-
| N-N bond angle / degrees || N/A
|}

==='''Molecule Vibrations'''===

[[File:HB915 n2 optf pop displayvibrations.jpg|400px|center|left]]

The 3N-5 rule used for linear molecules gives 3x2-5= 1. This is supported by the frequencies found from computational analysis as seen in the image above. This is due to the simple stretching of the bond.

==='''Charge Distribution'''===

Nitrogen has an electronegativity of 3.04. However when both atoms have the same electronegativity the charge is equally distributed across the molecule.

[[File:HB915 n2 optf pop charge.jpg|300px|center|left]]

=='''''H2'''''==
<jmol><jmolApplet>
<title>H2</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 H2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 H2 OPTF POP.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

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.

</pre>

There is zero net force and displacement so the optimization has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ H2 Optimised Information
! !! H2
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -1.17853930
|-
| RMS gradient / au || 0.00012170
|-
| Point Group || D*H
|-
| H-H bond length / A || 1.10550
|-
| H-H bond angle / degrees || N/A
|}

==='''Molecule Vibrations'''===

Image of frequencies

[[File:HB915 h2 optf pop displayvibrations.jpg|400px|left]]

The 3N-5 rule used for linear molecules gives 3x2-5= 1. This is supported by the frequencies found from computational analysis as seen in the image above. This is due to the simple stretching of the bond.

==='''Charge Distribution'''===

Nitrogen has an electronegativity of 2.2. However when both atoms have the same electronegativity the charge is equally distributed across the molecule.

[[File:HB915 h2 optf pop charge.jpg|300px|center|left]]

=='''''Haber-Bosch Process'''''==

==='''Equation of Reaction'''===

N2 + H2 -> NH3

==='''Energy of Reaction'''===

E(NH3)= -56.55776873 au

2*E(NH3)= 2*-56.55776873 = -113.1155375 au

E(N2)= -109.52412868 au

E(H2)= -1.17853930 au

3*E(H2)= 3*-1.17853930 = -3.5356179 au

ΔE = 2*E(NH3)-[E(N2)+3*E(H2)] = -113.1155375-[-109.52412868+-3.5356179]

ΔE = -0.05579092 au

ΔE = -0.05579092*2625.5 = -146.48 kJ/mol to 2.d.p

==='''Stability of Reactants vs Products'''===

ΔE is negative therefore the Haber process is exothermic and the product (NH3) is lower in energy and more stable than the reactants.

=='''''AlCl4-'''''==
<jmol><jmolApplet>
<title>AlCl4-</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 ALCL4- OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 ALCL4- OPTF POP.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000155 0.001800 YES
RMS Displacement 0.000093 0.001200 YES
Predicted change in Energy=-7.051677D-09
Optimization completed.
-- Stationary point found.

</pre>

There is zero net force and displacement so the optimization has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ AlCl4- Optimised Information
! !! AlCl4-
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -2083.61641374
|-
| RMS gradient / au || 0.00001174
|-
| Point Group || TD
|-
| Al-Cl bond length / A || 2.17703
|-
| Cl-Al-Cl bond angle / degrees || 109.471
|}

This is a much higher energy compound than that of N2 and H2.

==='''Molecule Vibrations'''===

[[File:HB915 alcl4- optf pop displayvibrations.jpg]]

The 3N-6 rule gives 3x5-6= 1. This is supported by the frequencies found from computational analysis as seen in the image above. Modes 7-9 are degenerate but in different directions. They are high energy due to the bending character creating a large change in dipole. Modes 3-5 are also degenerate bending vibrations but at a lower energy. Modes 1, 2 and 6 are all symmetrical vibrations that show no change in dipole and are therefore not visible on the spectrum as shown below.

[[File:HB915 alcl4- optf pop spectra.jpg|400px|center|left]]

==='''Charge Distribution'''===

Aluminum has an electronegativity of 1.61 which is comparatively smaller than that of chlorine with 3.16. Therefore you would expect aluminum to carry the positive charge. This is supported by the values calculated form the Schrödinger equation shown in the image below. Also with such a high difference in electronegativity of these two atoms more ionic character will be witnessed.

[[File:HB915 alcl4- optf pop charge.jpg]]

==='''Molecular Orbitals'''===

Images of the molecular orbitals can be visualised by GaussView. They represent each orbital solution to the Schrödinger equation, in other words the Φs, one for each MO energy level.

There are over 90 orbitals found , 41 of which are occupied, and each can be described by the interactions of the atomic orbitals. Five have been explored here.

[[File:HB915 AlCl4- MO 21.PNG|300px]]

When looking at diatomic molecules the MOs are the simple interaction between the AOs. However when looking at larger molecule you talk about the MO fragments. This is the non-bonding Cl 2 p orbitals. They are too different in energy to interact with the Al orbitals so remain non-bonding. There are 12 with similar energies and shapes that can be attributed to the different orientations and phases of each orbital.

[[File:HB915 AlCl4- MO 26.PNG|300px]]
[[File:HB915 AlCl4- MO 30.PNG|300px]]

These two are a pair of MOs created by interactions between the same AOs; the s Cl fragrant and the s Al. However one is an in-phase interaction (left) which produces a filled bonding orbital and the other out of phase interaction (right) which produced an anti-bonding orbital which is also filled. Both are occupied so these are not the orbitals responsible for bonding in this molecule.

[[File:HB915 AlCl4- MO 31.PNG|300px]]
[[File:HB915 AlCl4- MO 43.PNG|300px]]

This is another bonding (left) and non-bonding (right) pair of MOs. These were caused by the interaction of the 3p Cl fragment and the 3p Al. The bonding is filled and the anti-bonding is empty so it is this orbital that is responsible for the bonds in this molecule.

=='''''S2'''''==
<jmol><jmolApplet>
<title>S2</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 S2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 S2 OPTF POP.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000039 0.000300 YES
Maximum Displacement 0.000067 0.001800 YES
RMS Displacement 0.000095 0.001200 YES
Predicted change in Energy=-2.624039D-09
Optimization completed.
-- Stationary point found.

</pre>

There is zero net force and displacement so the optimization has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ S2 Optimised Information
! !! S2
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -796.32599779
|-
| RMS gradient / au || 0.00002267
|-
| Point Group || D*H
|-
| S-S bond length / A || 1.92952
|-
| S-S bond angle / degrees || N/A
|}

==='''Molecule Vibrations'''===

[[File:HB915 s2 optf pop displayvibrations.jpg]]

The 3N-5 rule used for linear molecules gives 3x2-5= 1. This is supported by the frequencies found from computational analysis as seen in the image above. This is due to the simple stretching of the bond.

==='''Charge Distribution'''===

Sulfur has an electronegativity of 2.58. However when both atoms have the same electronegativity the charge is equally distributed across the molecule.

[[File:HB915 s2 optf pop charge.jpg]]

==='''Molecular Orbitals'''===

Images of the molecular orbitals can be visualised by GaussView. They represent each orbital solution to the Schrödinger equation, in other words the Φs, one for each MO energy level.

There are over 30 orbitals found , 16 of which are occupied, and each can be described by the interactions of the atomic orbitals. Some examples are given below.

[[File:HB915 S2 MO 11.PNG|300px]]
[[File:HB915 S2 MO 12.PNG|300px]]

3 s orbitals from each Sulfur atom forms a bonding (left), non-bonding (right) pair of orbitals shown above.

[[File:HB915 S2 MO 15.PNG|300px]]
[[File:HB915 S2 MO 16.PNG|300px]]

The 3px from each sulfur interact to form a bonding (left) and an anti-bonding (right). However both are filled so no bond is formed from these MOs.

[[File:HB915 S2 MO 13.PNG|300px]]
[[File:HB915 S2 MO 18.PNG|300px]]

The 3pz from each sulfur interact to form a filled bonding (left) and a unfilled anti-bonding (right). Therefore this results in a sigma bond being formed between the two sulfur atoms.

[[File:HB915 S2 MO 14.PNG|300px]]
[[File:HB915 S2 MO 17.PNG|300px]]

The 3py from each sulfur interact to form a filled bonding (left) and a unfilled anti-bonding (right). Therefore this results in a pi bond being formed above and below the plane of the two sulfur atoms.

Rep:Mod:HB9151

2016-03-11T14:34:06Z

Hb915: /* Proof of Structure Convergence */

This is an exploration of molecules and reactions using GaussVeiw in order to understand the importance of computational inorganic chemistry.

Each molecule was draw in GaussVeiw and analysised computationally by solving the Schrödinger equation (EΦ=HΦ) under the Born-Oppenheimer approximation. Firstly the self-consistent field calculation is done for the starting bond lengths and angles giving the electronic wavefunction (Φ) that gives the lowest energy (for the fixed nuclei). The the distance is slightly shortened and the calculation repeated. This is continued until the lowest energy is found and this is the optimized structure.

Once this structure is found the data given by the solutions can be used to explore many properties of the molecule such as the spectrum, molecular orbital and the overall energy of the molecule.

=='''''NH3'''''==
<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 NH3 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 NH3 OPTF POP.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

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=-5.986294D-10
Optimization completed.
-- Stationary point found.

</pre>

There is zero net force and displacement so the optimization has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ NH3 Optimised Information
! !! NH3
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -56.55776873
|-
| RMS gradient / au || 0.00000485
|-
| Point Group || C3V
|-
| H-N bond length / A || 1.01798
|-
| H-N-H bond angle / degrees || 105.741
|}

==='''Molecule Vibrations'''===

[[File:HB915 nh3 optf pop displayvibrations.jpg.png|400px|left]]

''How many modes do you expect from the 3N-6 rule?''

N represents the number of atoms in the molecule. For NH3 there are 4 molecules therefore;
3x4-6=6

''Which modes are degenerate (ie have the same energy)?''

Modes 2 and 3 and 5 and 6 have the same energy (equal frequency).

''Which modes are "bending" vibrations and which are "bond stretch" vibrations?''

Modes 1-3 are bending and modes 4-6 are stretching. This is clear both from the animation and because bond stretching vibrations are higher in energy.

''Which mode is highly symmetric?''

Mode 4 is highly symmetric with no change in dipole.

''One mode is known as the "umbrella" mode, which one is this?''

Mode 1

''How many bands would you expect to see in an experimental spectrum of gaseous ammonia?''

There are four different vibrational energies suggesting four different bands. However there is only a minimal change in dipole for modes 4-6 so these would not be visible on a spectrum leaving only two bands.

[[File:HB915 nh3 optf pop spectra.jpg.png|500px|center|left]]

==='''Charge Distribution'''===

Nitrogen has an electronegativity of 3.04 which is comparatively larger than hydrogen with 2.2. Therefore you would expect nitrogen to carry the negative charge. This is supported by the values calculated form the Schrödinger equation shown in the image below.

[[File:HB915 nh3 optf pop charge.jpg.png|300px|center|left]]

=='''''N2'''''==
<jmol><jmolApplet>
<title>N2</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 N2 OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 N2 OPTIMISATION.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

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.

</pre>

There is zero net force and displacement so the optimization has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ N2 Optimised Information
! !! N2
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -109.52412868
|-
| RMS gradient / au || 0.00000365
|-
| Point Group || D*H
|-
| N-N bond length / A || 1.10550
|-
| N-N bond angle / degrees || N/A
|}

==='''Molecule Vibrations'''===

[[File:HB915 n2 optf pop displayvibrations.jpg|400px|center|left]]

The 3N-5 rule used for linear molecules gives 3x2-5= 1. This is supported by the frequencies found from computational analysis as seen in the image above. This is due to the simple stretching of the bond.

==='''Charge Distribution'''===

Nitrogen has an electronegativity of 3.04. However when both atoms have the same electronegativity the charge is equally distributed across the molecule.

[[File:HB915 n2 optf pop charge.jpg|300px|center|left]]

=='''''H2'''''==
<jmol><jmolApplet>
<title>H2</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 H2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 H2 OPTF POP.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

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.

</pre>

There is zero net force and displacement so the optimization has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ H2 Optimised Information
! !! H2
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -1.17853930
|-
| RMS gradient / au || 0.00012170
|-
| Point Group || D*H
|-
| H-H bond length / A || 1.10550
|-
| H-H bond angle / degrees || N/A
|}

==='''Molecule Vibrations'''===

Image of frequencies

[[File:HB915 h2 optf pop displayvibrations.jpg|400px|left]]

The 3N-5 rule used for linear molecules gives 3x2-5= 1. This is supported by the frequencies found from computational analysis as seen in the image above. This is due to the simple stretching of the bond.

==='''Charge Distribution'''===

Nitrogen has an electronegativity of 2.2. However when both atoms have the same electronegativity the charge is equally distributed across the molecule.

[[File:HB915 h2 optf pop charge.jpg|300px|center|left]]

=='''''Haber-Bosch Process'''''==

==='''Equation of Reaction'''===

N2 + H2 -> NH3

==='''Energy of Reaction'''===

E(NH3)= -56.55776873 au

2*E(NH3)= 2*-56.55776873 = -113.1155375 au

E(N2)= -109.52412868 au

E(H2)= -1.17853930 au

3*E(H2)= 3*-1.17853930 = -3.5356179 au

ΔE = 2*E(NH3)-[E(N2)+3*E(H2)] = -113.1155375-[-109.52412868+-3.5356179]

ΔE = -0.05579092 au

ΔE = -0.05579092*2625.5 = -146.48 kJ/mol to 2.d.p

==='''Stability of Reactants vs Products'''===

ΔE is negative therefore the Haber process is exothermic and the product (NH3) is lower in energy and more stable than the reactants.

=='''''AlCl4-'''''==
<jmol><jmolApplet>
<title>AlCl4-</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 ALCL4- OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 ALCL4- OPTF POP.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000155 0.001800 YES
RMS Displacement 0.000093 0.001200 YES
Predicted change in Energy=-7.051677D-09
Optimization completed.
-- Stationary point found.

</pre>

There is zero net force and displacement so the optimization has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ AlCl4- Optimised Information
! !! AlCl4-
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -2083.61641374
|-
| RMS gradient / au || 0.00001174
|-
| Point Group || TD
|-
| Al-Cl bond length / A || 2.17703
|-
| Cl-Al-Cl bond angle / degrees || 109.471
|}

This is a much higher energy compound than that of N2 and H2.

==='''Molecule Vibrations'''===

[[File:HB915 alcl4- optf pop displayvibrations.jpg]]

The 3N-6 rule gives 3x5-6= 1. This is supported by the frequencies found from computational analysis as seen in the image above. Modes 7-9 are degenerate but in different directions. They are high energy due to the bending character creating a large change in dipole. Modes 3-5 are also degenerate bending vibrations but at a lower energy. Modes 1, 2 and 6 are all symmetrical vibrations that show no change in dipole and are therefore not visible on the spectrum as shown below.

[[File:HB915 alcl4- optf pop spectra.jpg|400px|center|left]]

==='''Charge Distribution'''===

Aluminum has an electronegativity of 1.61 which is comparatively smaller than that of chlorine with 3.16. Therefore you would expect aluminum to carry the positive charge. This is supported by the values calculated form the Schrödinger equation shown in the image below. Also with such a high difference in electronegativity of these two atoms more ionic character will be witnessed.

[[File:HB915 alcl4- optf pop charge.jpg]]

==='''Molecular Orbitals'''===

Images of the molecular orbitals can be visualised by GaussView. They represent each orbital solution to the Schrödinger equation, in other words the Φs, one for each MO energy level.

There are over 90 orbitals found , 41 of which are occupied, and each can be described by the interactions of the atomic orbitals. Five have been explored here.

[[File:HB915 AlCl4- MO 21.PNG|300px]]

When looking at diatomic molecules the MOs are the simple interaction between the AOs. However when looking at larger molecule you talk about the MO fragments. This is the non-bonding Cl 2 p orbitals. They are too different in energy to interact with the Al orbitals so remain non-bonding. There are 12 with similar energies and shapes that can be attributed to the different orientations and phases of each orbital.

[[File:HB915 AlCl4- MO 26.PNG|300px]]
[[File:HB915 AlCl4- MO 30.PNG|300px]]

These two are a pair of MOs created by interactions between the same AOs; the s Cl fragrant and the s Al. However one is an in-phase interaction (left) which produces a filled bonding orbital and the other out of phase interaction (right) which produced an anti-bonding orbital which is also filled. Both are occupied so these are not the orbitals responsible for bonding in this molecule.

[[File:HB915 AlCl4- MO 31.PNG|300px]]
[[File:HB915 AlCl4- MO 43.PNG|300px]]

This is another bonding (left) and non-bonding (right) pair of MOs. These were caused by the interaction of the 3p Cl fragment and the 3p Al. The bonding is filled and the anti-bonding is empty so it is this orbital that is responsible for the bonds in this molecule.

=='''''S2'''''==
<jmol><jmolApplet>
<title>S2</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 S2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 S2 OPTF POP.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000039 0.000300 YES
Maximum Displacement 0.000067 0.001800 YES
RMS Displacement 0.000095 0.001200 YES
Predicted change in Energy=-2.624039D-09
Optimization completed.
-- Stationary point found.

</pre>

There is zero net force and displacement so the optimizstion has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ S2 Optimised Information
! !! S2
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -796.32599779
|-
| RMS gradient / au || 0.00002267
|-
| Point Group || D*H
|-
| S-S bond length / A || 1.92952
|-
| S-S bond angle / degrees || N/A
|}

==='''Molecule Vibrations'''===

[[File:HB915 s2 optf pop displayvibrations.jpg]]

The 3N-5 rule used for linear molecules gives 3x2-5= 1. This is supported by the frequencies found from computational analysis as seen in the image above. This is due to the simple stretching of the bond.

==='''Charge Distribution'''===

Sulfur has an electronegativity of 2.58. However when both atoms have the same electronegativity the charge is equally distributed across the molecule.

[[File:HB915 s2 optf pop charge.jpg]]

==='''Molecular Orbitals'''===

Images of the molecular orbitals can be visualised by GaussView. They represent each orbital solution to the Schrödinger equation, in other words the Φs, one for each MO energy level.

There are over 30 orbitals found , 16 of which are occupied, and each can be described by the interactions of the atomic orbitals. Some examples are given below.

[[File:HB915 S2 MO 11.PNG|300px]]
[[File:HB915 S2 MO 12.PNG|300px]]

3 s orbitals from each Sulfur atom forms a bonding (left), non-bonding (right) pair of orbitals shown above.

[[File:HB915 S2 MO 15.PNG|300px]]
[[File:HB915 S2 MO 16.PNG|300px]]

The 3px from each sulfur interact to form a bonding (left) and an anti-bonding (right). However both are filled so no bond is formed from these MOs.

[[File:HB915 S2 MO 13.PNG|300px]]
[[File:HB915 S2 MO 18.PNG|300px]]

The 3pz from each sulfur interact to form a filled bonding (left) and a unfilled anti-bonding (right). Therefore this results in a sigma bond being formed between the two sulfur atoms.

[[File:HB915 S2 MO 14.PNG|300px]]
[[File:HB915 S2 MO 17.PNG|300px]]

The 3py from each sulfur interact to form a filled bonding (left) and a unfilled anti-bonding (right). Therefore this results in a pi bond being formed above and below the plane of the two sulfur atoms.

Rep:Mod:HB9151

2016-03-11T14:33:53Z

Hb915: /* Proof of Structure Convergence */

This is an exploration of molecules and reactions using GaussVeiw in order to understand the importance of computational inorganic chemistry.

Each molecule was draw in GaussVeiw and analysised computationally by solving the Schrödinger equation (EΦ=HΦ) under the Born-Oppenheimer approximation. Firstly the self-consistent field calculation is done for the starting bond lengths and angles giving the electronic wavefunction (Φ) that gives the lowest energy (for the fixed nuclei). The the distance is slightly shortened and the calculation repeated. This is continued until the lowest energy is found and this is the optimized structure.

Once this structure is found the data given by the solutions can be used to explore many properties of the molecule such as the spectrum, molecular orbital and the overall energy of the molecule.

=='''''NH3'''''==
<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 NH3 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 NH3 OPTF POP.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

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=-5.986294D-10
Optimization completed.
-- Stationary point found.

</pre>

There is zero net force and displacement so the optimization has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ NH3 Optimised Information
! !! NH3
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -56.55776873
|-
| RMS gradient / au || 0.00000485
|-
| Point Group || C3V
|-
| H-N bond length / A || 1.01798
|-
| H-N-H bond angle / degrees || 105.741
|}

==='''Molecule Vibrations'''===

[[File:HB915 nh3 optf pop displayvibrations.jpg.png|400px|left]]

''How many modes do you expect from the 3N-6 rule?''

N represents the number of atoms in the molecule. For NH3 there are 4 molecules therefore;
3x4-6=6

''Which modes are degenerate (ie have the same energy)?''

Modes 2 and 3 and 5 and 6 have the same energy (equal frequency).

''Which modes are "bending" vibrations and which are "bond stretch" vibrations?''

Modes 1-3 are bending and modes 4-6 are stretching. This is clear both from the animation and because bond stretching vibrations are higher in energy.

''Which mode is highly symmetric?''

Mode 4 is highly symmetric with no change in dipole.

''One mode is known as the "umbrella" mode, which one is this?''

Mode 1

''How many bands would you expect to see in an experimental spectrum of gaseous ammonia?''

There are four different vibrational energies suggesting four different bands. However there is only a minimal change in dipole for modes 4-6 so these would not be visible on a spectrum leaving only two bands.

[[File:HB915 nh3 optf pop spectra.jpg.png|500px|center|left]]

==='''Charge Distribution'''===

Nitrogen has an electronegativity of 3.04 which is comparatively larger than hydrogen with 2.2. Therefore you would expect nitrogen to carry the negative charge. This is supported by the values calculated form the Schrödinger equation shown in the image below.

[[File:HB915 nh3 optf pop charge.jpg.png|300px|center|left]]

=='''''N2'''''==
<jmol><jmolApplet>
<title>N2</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 N2 OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 N2 OPTIMISATION.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

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.

</pre>

There is zero net force and displacement so the optimization has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ N2 Optimised Information
! !! N2
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -109.52412868
|-
| RMS gradient / au || 0.00000365
|-
| Point Group || D*H
|-
| N-N bond length / A || 1.10550
|-
| N-N bond angle / degrees || N/A
|}

==='''Molecule Vibrations'''===

[[File:HB915 n2 optf pop displayvibrations.jpg|400px|center|left]]

The 3N-5 rule used for linear molecules gives 3x2-5= 1. This is supported by the frequencies found from computational analysis as seen in the image above. This is due to the simple stretching of the bond.

==='''Charge Distribution'''===

Nitrogen has an electronegativity of 3.04. However when both atoms have the same electronegativity the charge is equally distributed across the molecule.

[[File:HB915 n2 optf pop charge.jpg|300px|center|left]]

=='''''H2'''''==
<jmol><jmolApplet>
<title>H2</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 H2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 H2 OPTF POP.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

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.

</pre>

There is zero net force and displacement so the optimization has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ H2 Optimised Information
! !! H2
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -1.17853930
|-
| RMS gradient / au || 0.00012170
|-
| Point Group || D*H
|-
| H-H bond length / A || 1.10550
|-
| H-H bond angle / degrees || N/A
|}

==='''Molecule Vibrations'''===

Image of frequencies

[[File:HB915 h2 optf pop displayvibrations.jpg|400px|left]]

The 3N-5 rule used for linear molecules gives 3x2-5= 1. This is supported by the frequencies found from computational analysis as seen in the image above. This is due to the simple stretching of the bond.

==='''Charge Distribution'''===

Nitrogen has an electronegativity of 2.2. However when both atoms have the same electronegativity the charge is equally distributed across the molecule.

[[File:HB915 h2 optf pop charge.jpg|300px|center|left]]

=='''''Haber-Bosch Process'''''==

==='''Equation of Reaction'''===

N2 + H2 -> NH3

==='''Energy of Reaction'''===

E(NH3)= -56.55776873 au

2*E(NH3)= 2*-56.55776873 = -113.1155375 au

E(N2)= -109.52412868 au

E(H2)= -1.17853930 au

3*E(H2)= 3*-1.17853930 = -3.5356179 au

ΔE = 2*E(NH3)-[E(N2)+3*E(H2)] = -113.1155375-[-109.52412868+-3.5356179]

ΔE = -0.05579092 au

ΔE = -0.05579092*2625.5 = -146.48 kJ/mol to 2.d.p

==='''Stability of Reactants vs Products'''===

ΔE is negative therefore the Haber process is exothermic and the product (NH3) is lower in energy and more stable than the reactants.

=='''''AlCl4-'''''==
<jmol><jmolApplet>
<title>AlCl4-</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 ALCL4- OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 ALCL4- OPTF POP.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000155 0.001800 YES
RMS Displacement 0.000093 0.001200 YES
Predicted change in Energy=-7.051677D-09
Optimization completed.
-- Stationary point found.

</pre>

There is zero net force and displacement so the optimizstion has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ AlCl4- Optimised Information
! !! AlCl4-
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -2083.61641374
|-
| RMS gradient / au || 0.00001174
|-
| Point Group || TD
|-
| Al-Cl bond length / A || 2.17703
|-
| Cl-Al-Cl bond angle / degrees || 109.471
|}

This is a much higher energy compound than that of N2 and H2.

==='''Molecule Vibrations'''===

[[File:HB915 alcl4- optf pop displayvibrations.jpg]]

The 3N-6 rule gives 3x5-6= 1. This is supported by the frequencies found from computational analysis as seen in the image above. Modes 7-9 are degenerate but in different directions. They are high energy due to the bending character creating a large change in dipole. Modes 3-5 are also degenerate bending vibrations but at a lower energy. Modes 1, 2 and 6 are all symmetrical vibrations that show no change in dipole and are therefore not visible on the spectrum as shown below.

[[File:HB915 alcl4- optf pop spectra.jpg|400px|center|left]]

==='''Charge Distribution'''===

Aluminum has an electronegativity of 1.61 which is comparatively smaller than that of chlorine with 3.16. Therefore you would expect aluminum to carry the positive charge. This is supported by the values calculated form the Schrödinger equation shown in the image below. Also with such a high difference in electronegativity of these two atoms more ionic character will be witnessed.

[[File:HB915 alcl4- optf pop charge.jpg]]

==='''Molecular Orbitals'''===

Images of the molecular orbitals can be visualised by GaussView. They represent each orbital solution to the Schrödinger equation, in other words the Φs, one for each MO energy level.

There are over 90 orbitals found , 41 of which are occupied, and each can be described by the interactions of the atomic orbitals. Five have been explored here.

[[File:HB915 AlCl4- MO 21.PNG|300px]]

When looking at diatomic molecules the MOs are the simple interaction between the AOs. However when looking at larger molecule you talk about the MO fragments. This is the non-bonding Cl 2 p orbitals. They are too different in energy to interact with the Al orbitals so remain non-bonding. There are 12 with similar energies and shapes that can be attributed to the different orientations and phases of each orbital.

[[File:HB915 AlCl4- MO 26.PNG|300px]]
[[File:HB915 AlCl4- MO 30.PNG|300px]]

These two are a pair of MOs created by interactions between the same AOs; the s Cl fragrant and the s Al. However one is an in-phase interaction (left) which produces a filled bonding orbital and the other out of phase interaction (right) which produced an anti-bonding orbital which is also filled. Both are occupied so these are not the orbitals responsible for bonding in this molecule.

[[File:HB915 AlCl4- MO 31.PNG|300px]]
[[File:HB915 AlCl4- MO 43.PNG|300px]]

This is another bonding (left) and non-bonding (right) pair of MOs. These were caused by the interaction of the 3p Cl fragment and the 3p Al. The bonding is filled and the anti-bonding is empty so it is this orbital that is responsible for the bonds in this molecule.

=='''''S2'''''==
<jmol><jmolApplet>
<title>S2</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 S2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 S2 OPTF POP.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000039 0.000300 YES
Maximum Displacement 0.000067 0.001800 YES
RMS Displacement 0.000095 0.001200 YES
Predicted change in Energy=-2.624039D-09
Optimization completed.
-- Stationary point found.

</pre>

There is zero net force and displacement so the optimizstion has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ S2 Optimised Information
! !! S2
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -796.32599779
|-
| RMS gradient / au || 0.00002267
|-
| Point Group || D*H
|-
| S-S bond length / A || 1.92952
|-
| S-S bond angle / degrees || N/A
|}

==='''Molecule Vibrations'''===

[[File:HB915 s2 optf pop displayvibrations.jpg]]

The 3N-5 rule used for linear molecules gives 3x2-5= 1. This is supported by the frequencies found from computational analysis as seen in the image above. This is due to the simple stretching of the bond.

==='''Charge Distribution'''===

Sulfur has an electronegativity of 2.58. However when both atoms have the same electronegativity the charge is equally distributed across the molecule.

[[File:HB915 s2 optf pop charge.jpg]]

==='''Molecular Orbitals'''===

Images of the molecular orbitals can be visualised by GaussView. They represent each orbital solution to the Schrödinger equation, in other words the Φs, one for each MO energy level.

There are over 30 orbitals found , 16 of which are occupied, and each can be described by the interactions of the atomic orbitals. Some examples are given below.

[[File:HB915 S2 MO 11.PNG|300px]]
[[File:HB915 S2 MO 12.PNG|300px]]

3 s orbitals from each Sulfur atom forms a bonding (left), non-bonding (right) pair of orbitals shown above.

[[File:HB915 S2 MO 15.PNG|300px]]
[[File:HB915 S2 MO 16.PNG|300px]]

The 3px from each sulfur interact to form a bonding (left) and an anti-bonding (right). However both are filled so no bond is formed from these MOs.

[[File:HB915 S2 MO 13.PNG|300px]]
[[File:HB915 S2 MO 18.PNG|300px]]

The 3pz from each sulfur interact to form a filled bonding (left) and a unfilled anti-bonding (right). Therefore this results in a sigma bond being formed between the two sulfur atoms.

[[File:HB915 S2 MO 14.PNG|300px]]
[[File:HB915 S2 MO 17.PNG|300px]]

The 3py from each sulfur interact to form a filled bonding (left) and a unfilled anti-bonding (right). Therefore this results in a pi bond being formed above and below the plane of the two sulfur atoms.

Rep:Mod:HB9151

2016-03-11T14:33:08Z

Hb915: /* Proof of Structure Convergence */

This is an exploration of molecules and reactions using GaussVeiw in order to understand the importance of computational inorganic chemistry.

Each molecule was draw in GaussVeiw and analysised computationally by solving the Schrödinger equation (EΦ=HΦ) under the Born-Oppenheimer approximation. Firstly the self-consistent field calculation is done for the starting bond lengths and angles giving the electronic wavefunction (Φ) that gives the lowest energy (for the fixed nuclei). The the distance is slightly shortened and the calculation repeated. This is continued until the lowest energy is found and this is the optimized structure.

Once this structure is found the data given by the solutions can be used to explore many properties of the molecule such as the spectrum, molecular orbital and the overall energy of the molecule.

=='''''NH3'''''==
<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 NH3 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 NH3 OPTF POP.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

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=-5.986294D-10
Optimization completed.
-- Stationary point found.

</pre>

There is zero net force and displacement so the optimization has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ NH3 Optimised Information
! !! NH3
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -56.55776873
|-
| RMS gradient / au || 0.00000485
|-
| Point Group || C3V
|-
| H-N bond length / A || 1.01798
|-
| H-N-H bond angle / degrees || 105.741
|}

==='''Molecule Vibrations'''===

[[File:HB915 nh3 optf pop displayvibrations.jpg.png|400px|left]]

''How many modes do you expect from the 3N-6 rule?''

N represents the number of atoms in the molecule. For NH3 there are 4 molecules therefore;
3x4-6=6

''Which modes are degenerate (ie have the same energy)?''

Modes 2 and 3 and 5 and 6 have the same energy (equal frequency).

''Which modes are "bending" vibrations and which are "bond stretch" vibrations?''

Modes 1-3 are bending and modes 4-6 are stretching. This is clear both from the animation and because bond stretching vibrations are higher in energy.

''Which mode is highly symmetric?''

Mode 4 is highly symmetric with no change in dipole.

''One mode is known as the "umbrella" mode, which one is this?''

Mode 1

''How many bands would you expect to see in an experimental spectrum of gaseous ammonia?''

There are four different vibrational energies suggesting four different bands. However there is only a minimal change in dipole for modes 4-6 so these would not be visible on a spectrum leaving only two bands.

[[File:HB915 nh3 optf pop spectra.jpg.png|500px|center|left]]

==='''Charge Distribution'''===

Nitrogen has an electronegativity of 3.04 which is comparatively larger than hydrogen with 2.2. Therefore you would expect nitrogen to carry the negative charge. This is supported by the values calculated form the Schrödinger equation shown in the image below.

[[File:HB915 nh3 optf pop charge.jpg.png|300px|center|left]]

=='''''N2'''''==
<jmol><jmolApplet>
<title>N2</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 N2 OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 N2 OPTIMISATION.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

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.

</pre>

There is zero net force and displacement so the optimization has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ N2 Optimised Information
! !! N2
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -109.52412868
|-
| RMS gradient / au || 0.00000365
|-
| Point Group || D*H
|-
| N-N bond length / A || 1.10550
|-
| N-N bond angle / degrees || N/A
|}

==='''Molecule Vibrations'''===

[[File:HB915 n2 optf pop displayvibrations.jpg|400px|center|left]]

The 3N-5 rule used for linear molecules gives 3x2-5= 1. This is supported by the frequencies found from computational analysis as seen in the image above. This is due to the simple stretching of the bond.

==='''Charge Distribution'''===

Nitrogen has an electronegativity of 3.04. However when both atoms have the same electronegativity the charge is equally distributed across the molecule.

[[File:HB915 n2 optf pop charge.jpg|300px|center|left]]

=='''''H2'''''==
<jmol><jmolApplet>
<title>H2</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 H2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 H2 OPTF POP.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

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.

</pre>

There is zero net force and displacement so the optimizstion has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ H2 Optimised Information
! !! H2
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -1.17853930
|-
| RMS gradient / au || 0.00012170
|-
| Point Group || D*H
|-
| H-H bond length / A || 1.10550
|-
| H-H bond angle / degrees || N/A
|}

==='''Molecule Vibrations'''===

Image of frequencies

[[File:HB915 h2 optf pop displayvibrations.jpg|400px|left]]

The 3N-5 rule used for linear molecules gives 3x2-5= 1. This is supported by the frequencies found from computational analysis as seen in the image above. This is due to the simple stretching of the bond.

==='''Charge Distribution'''===

Nitrogen has an electronegativity of 2.2. However when both atoms have the same electronegativity the charge is equally distributed across the molecule.

[[File:HB915 h2 optf pop charge.jpg|300px|center|left]]

=='''''Haber-Bosch Process'''''==

==='''Equation of Reaction'''===

N2 + H2 -> NH3

==='''Energy of Reaction'''===

E(NH3)= -56.55776873 au

2*E(NH3)= 2*-56.55776873 = -113.1155375 au

E(N2)= -109.52412868 au

E(H2)= -1.17853930 au

3*E(H2)= 3*-1.17853930 = -3.5356179 au

ΔE = 2*E(NH3)-[E(N2)+3*E(H2)] = -113.1155375-[-109.52412868+-3.5356179]

ΔE = -0.05579092 au

ΔE = -0.05579092*2625.5 = -146.48 kJ/mol to 2.d.p

==='''Stability of Reactants vs Products'''===

ΔE is negative therefore the Haber process is exothermic and the product (NH3) is lower in energy and more stable than the reactants.

=='''''AlCl4-'''''==
<jmol><jmolApplet>
<title>AlCl4-</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 ALCL4- OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 ALCL4- OPTF POP.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000155 0.001800 YES
RMS Displacement 0.000093 0.001200 YES
Predicted change in Energy=-7.051677D-09
Optimization completed.
-- Stationary point found.

</pre>

There is zero net force and displacement so the optimizstion has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ AlCl4- Optimised Information
! !! AlCl4-
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -2083.61641374
|-
| RMS gradient / au || 0.00001174
|-
| Point Group || TD
|-
| Al-Cl bond length / A || 2.17703
|-
| Cl-Al-Cl bond angle / degrees || 109.471
|}

This is a much higher energy compound than that of N2 and H2.

==='''Molecule Vibrations'''===

[[File:HB915 alcl4- optf pop displayvibrations.jpg]]

The 3N-6 rule gives 3x5-6= 1. This is supported by the frequencies found from computational analysis as seen in the image above. Modes 7-9 are degenerate but in different directions. They are high energy due to the bending character creating a large change in dipole. Modes 3-5 are also degenerate bending vibrations but at a lower energy. Modes 1, 2 and 6 are all symmetrical vibrations that show no change in dipole and are therefore not visible on the spectrum as shown below.

[[File:HB915 alcl4- optf pop spectra.jpg|400px|center|left]]

==='''Charge Distribution'''===

Aluminum has an electronegativity of 1.61 which is comparatively smaller than that of chlorine with 3.16. Therefore you would expect aluminum to carry the positive charge. This is supported by the values calculated form the Schrödinger equation shown in the image below. Also with such a high difference in electronegativity of these two atoms more ionic character will be witnessed.

[[File:HB915 alcl4- optf pop charge.jpg]]

==='''Molecular Orbitals'''===

Images of the molecular orbitals can be visualised by GaussView. They represent each orbital solution to the Schrödinger equation, in other words the Φs, one for each MO energy level.

There are over 90 orbitals found , 41 of which are occupied, and each can be described by the interactions of the atomic orbitals. Five have been explored here.

[[File:HB915 AlCl4- MO 21.PNG|300px]]

When looking at diatomic molecules the MOs are the simple interaction between the AOs. However when looking at larger molecule you talk about the MO fragments. This is the non-bonding Cl 2 p orbitals. They are too different in energy to interact with the Al orbitals so remain non-bonding. There are 12 with similar energies and shapes that can be attributed to the different orientations and phases of each orbital.

[[File:HB915 AlCl4- MO 26.PNG|300px]]
[[File:HB915 AlCl4- MO 30.PNG|300px]]

These two are a pair of MOs created by interactions between the same AOs; the s Cl fragrant and the s Al. However one is an in-phase interaction (left) which produces a filled bonding orbital and the other out of phase interaction (right) which produced an anti-bonding orbital which is also filled. Both are occupied so these are not the orbitals responsible for bonding in this molecule.

[[File:HB915 AlCl4- MO 31.PNG|300px]]
[[File:HB915 AlCl4- MO 43.PNG|300px]]

This is another bonding (left) and non-bonding (right) pair of MOs. These were caused by the interaction of the 3p Cl fragment and the 3p Al. The bonding is filled and the anti-bonding is empty so it is this orbital that is responsible for the bonds in this molecule.

=='''''S2'''''==
<jmol><jmolApplet>
<title>S2</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 S2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 S2 OPTF POP.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000039 0.000300 YES
Maximum Displacement 0.000067 0.001800 YES
RMS Displacement 0.000095 0.001200 YES
Predicted change in Energy=-2.624039D-09
Optimization completed.
-- Stationary point found.

</pre>

There is zero net force and displacement so the optimizstion has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ S2 Optimised Information
! !! S2
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -796.32599779
|-
| RMS gradient / au || 0.00002267
|-
| Point Group || D*H
|-
| S-S bond length / A || 1.92952
|-
| S-S bond angle / degrees || N/A
|}

==='''Molecule Vibrations'''===

[[File:HB915 s2 optf pop displayvibrations.jpg]]

The 3N-5 rule used for linear molecules gives 3x2-5= 1. This is supported by the frequencies found from computational analysis as seen in the image above. This is due to the simple stretching of the bond.

==='''Charge Distribution'''===

Sulfur has an electronegativity of 2.58. However when both atoms have the same electronegativity the charge is equally distributed across the molecule.

[[File:HB915 s2 optf pop charge.jpg]]

==='''Molecular Orbitals'''===

Images of the molecular orbitals can be visualised by GaussView. They represent each orbital solution to the Schrödinger equation, in other words the Φs, one for each MO energy level.

There are over 30 orbitals found , 16 of which are occupied, and each can be described by the interactions of the atomic orbitals. Some examples are given below.

[[File:HB915 S2 MO 11.PNG|300px]]
[[File:HB915 S2 MO 12.PNG|300px]]

3 s orbitals from each Sulfur atom forms a bonding (left), non-bonding (right) pair of orbitals shown above.

[[File:HB915 S2 MO 15.PNG|300px]]
[[File:HB915 S2 MO 16.PNG|300px]]

The 3px from each sulfur interact to form a bonding (left) and an anti-bonding (right). However both are filled so no bond is formed from these MOs.

[[File:HB915 S2 MO 13.PNG|300px]]
[[File:HB915 S2 MO 18.PNG|300px]]

The 3pz from each sulfur interact to form a filled bonding (left) and a unfilled anti-bonding (right). Therefore this results in a sigma bond being formed between the two sulfur atoms.

[[File:HB915 S2 MO 14.PNG|300px]]
[[File:HB915 S2 MO 17.PNG|300px]]

The 3py from each sulfur interact to form a filled bonding (left) and a unfilled anti-bonding (right). Therefore this results in a pi bond being formed above and below the plane of the two sulfur atoms.

Rep:Mod:HB9151

2016-03-11T14:32:55Z

Hb915: /* Proof of Structure Convergence */

This is an exploration of molecules and reactions using GaussVeiw in order to understand the importance of computational inorganic chemistry.

Each molecule was draw in GaussVeiw and analysised computationally by solving the Schrödinger equation (EΦ=HΦ) under the Born-Oppenheimer approximation. Firstly the self-consistent field calculation is done for the starting bond lengths and angles giving the electronic wavefunction (Φ) that gives the lowest energy (for the fixed nuclei). The the distance is slightly shortened and the calculation repeated. This is continued until the lowest energy is found and this is the optimized structure.

Once this structure is found the data given by the solutions can be used to explore many properties of the molecule such as the spectrum, molecular orbital and the overall energy of the molecule.

=='''''NH3'''''==
<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 NH3 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 NH3 OPTF POP.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

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=-5.986294D-10
Optimization completed.
-- Stationary point found.

</pre>

There is zero net force and displacement so the optimizstion has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ NH3 Optimised Information
! !! NH3
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -56.55776873
|-
| RMS gradient / au || 0.00000485
|-
| Point Group || C3V
|-
| H-N bond length / A || 1.01798
|-
| H-N-H bond angle / degrees || 105.741
|}

==='''Molecule Vibrations'''===

[[File:HB915 nh3 optf pop displayvibrations.jpg.png|400px|left]]

''How many modes do you expect from the 3N-6 rule?''

N represents the number of atoms in the molecule. For NH3 there are 4 molecules therefore;
3x4-6=6

''Which modes are degenerate (ie have the same energy)?''

Modes 2 and 3 and 5 and 6 have the same energy (equal frequency).

''Which modes are "bending" vibrations and which are "bond stretch" vibrations?''

Modes 1-3 are bending and modes 4-6 are stretching. This is clear both from the animation and because bond stretching vibrations are higher in energy.

''Which mode is highly symmetric?''

Mode 4 is highly symmetric with no change in dipole.

''One mode is known as the "umbrella" mode, which one is this?''

Mode 1

''How many bands would you expect to see in an experimental spectrum of gaseous ammonia?''

There are four different vibrational energies suggesting four different bands. However there is only a minimal change in dipole for modes 4-6 so these would not be visible on a spectrum leaving only two bands.

[[File:HB915 nh3 optf pop spectra.jpg.png|500px|center|left]]

==='''Charge Distribution'''===

Nitrogen has an electronegativity of 3.04 which is comparatively larger than hydrogen with 2.2. Therefore you would expect nitrogen to carry the negative charge. This is supported by the values calculated form the Schrödinger equation shown in the image below.

[[File:HB915 nh3 optf pop charge.jpg.png|300px|center|left]]

=='''''N2'''''==
<jmol><jmolApplet>
<title>N2</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 N2 OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 N2 OPTIMISATION.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

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.

</pre>

There is zero net force and displacement so the optimization has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ N2 Optimised Information
! !! N2
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -109.52412868
|-
| RMS gradient / au || 0.00000365
|-
| Point Group || D*H
|-
| N-N bond length / A || 1.10550
|-
| N-N bond angle / degrees || N/A
|}

==='''Molecule Vibrations'''===

[[File:HB915 n2 optf pop displayvibrations.jpg|400px|center|left]]

The 3N-5 rule used for linear molecules gives 3x2-5= 1. This is supported by the frequencies found from computational analysis as seen in the image above. This is due to the simple stretching of the bond.

==='''Charge Distribution'''===

Nitrogen has an electronegativity of 3.04. However when both atoms have the same electronegativity the charge is equally distributed across the molecule.

[[File:HB915 n2 optf pop charge.jpg|300px|center|left]]

=='''''H2'''''==
<jmol><jmolApplet>
<title>H2</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 H2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 H2 OPTF POP.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

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.

</pre>

There is zero net force and displacement so the optimizstion has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ H2 Optimised Information
! !! H2
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -1.17853930
|-
| RMS gradient / au || 0.00012170
|-
| Point Group || D*H
|-
| H-H bond length / A || 1.10550
|-
| H-H bond angle / degrees || N/A
|}

==='''Molecule Vibrations'''===

Image of frequencies

[[File:HB915 h2 optf pop displayvibrations.jpg|400px|left]]

The 3N-5 rule used for linear molecules gives 3x2-5= 1. This is supported by the frequencies found from computational analysis as seen in the image above. This is due to the simple stretching of the bond.

==='''Charge Distribution'''===

Nitrogen has an electronegativity of 2.2. However when both atoms have the same electronegativity the charge is equally distributed across the molecule.

[[File:HB915 h2 optf pop charge.jpg|300px|center|left]]

=='''''Haber-Bosch Process'''''==

==='''Equation of Reaction'''===

N2 + H2 -> NH3

==='''Energy of Reaction'''===

E(NH3)= -56.55776873 au

2*E(NH3)= 2*-56.55776873 = -113.1155375 au

E(N2)= -109.52412868 au

E(H2)= -1.17853930 au

3*E(H2)= 3*-1.17853930 = -3.5356179 au

ΔE = 2*E(NH3)-[E(N2)+3*E(H2)] = -113.1155375-[-109.52412868+-3.5356179]

ΔE = -0.05579092 au

ΔE = -0.05579092*2625.5 = -146.48 kJ/mol to 2.d.p

==='''Stability of Reactants vs Products'''===

ΔE is negative therefore the Haber process is exothermic and the product (NH3) is lower in energy and more stable than the reactants.

=='''''AlCl4-'''''==
<jmol><jmolApplet>
<title>AlCl4-</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 ALCL4- OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 ALCL4- OPTF POP.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000155 0.001800 YES
RMS Displacement 0.000093 0.001200 YES
Predicted change in Energy=-7.051677D-09
Optimization completed.
-- Stationary point found.

</pre>

There is zero net force and displacement so the optimizstion has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ AlCl4- Optimised Information
! !! AlCl4-
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -2083.61641374
|-
| RMS gradient / au || 0.00001174
|-
| Point Group || TD
|-
| Al-Cl bond length / A || 2.17703
|-
| Cl-Al-Cl bond angle / degrees || 109.471
|}

This is a much higher energy compound than that of N2 and H2.

==='''Molecule Vibrations'''===

[[File:HB915 alcl4- optf pop displayvibrations.jpg]]

The 3N-6 rule gives 3x5-6= 1. This is supported by the frequencies found from computational analysis as seen in the image above. Modes 7-9 are degenerate but in different directions. They are high energy due to the bending character creating a large change in dipole. Modes 3-5 are also degenerate bending vibrations but at a lower energy. Modes 1, 2 and 6 are all symmetrical vibrations that show no change in dipole and are therefore not visible on the spectrum as shown below.

[[File:HB915 alcl4- optf pop spectra.jpg|400px|center|left]]

==='''Charge Distribution'''===

Aluminum has an electronegativity of 1.61 which is comparatively smaller than that of chlorine with 3.16. Therefore you would expect aluminum to carry the positive charge. This is supported by the values calculated form the Schrödinger equation shown in the image below. Also with such a high difference in electronegativity of these two atoms more ionic character will be witnessed.

[[File:HB915 alcl4- optf pop charge.jpg]]

==='''Molecular Orbitals'''===

Images of the molecular orbitals can be visualised by GaussView. They represent each orbital solution to the Schrödinger equation, in other words the Φs, one for each MO energy level.

There are over 90 orbitals found , 41 of which are occupied, and each can be described by the interactions of the atomic orbitals. Five have been explored here.

[[File:HB915 AlCl4- MO 21.PNG|300px]]

When looking at diatomic molecules the MOs are the simple interaction between the AOs. However when looking at larger molecule you talk about the MO fragments. This is the non-bonding Cl 2 p orbitals. They are too different in energy to interact with the Al orbitals so remain non-bonding. There are 12 with similar energies and shapes that can be attributed to the different orientations and phases of each orbital.

[[File:HB915 AlCl4- MO 26.PNG|300px]]
[[File:HB915 AlCl4- MO 30.PNG|300px]]

These two are a pair of MOs created by interactions between the same AOs; the s Cl fragrant and the s Al. However one is an in-phase interaction (left) which produces a filled bonding orbital and the other out of phase interaction (right) which produced an anti-bonding orbital which is also filled. Both are occupied so these are not the orbitals responsible for bonding in this molecule.

[[File:HB915 AlCl4- MO 31.PNG|300px]]
[[File:HB915 AlCl4- MO 43.PNG|300px]]

This is another bonding (left) and non-bonding (right) pair of MOs. These were caused by the interaction of the 3p Cl fragment and the 3p Al. The bonding is filled and the anti-bonding is empty so it is this orbital that is responsible for the bonds in this molecule.

=='''''S2'''''==
<jmol><jmolApplet>
<title>S2</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 S2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 S2 OPTF POP.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000039 0.000300 YES
Maximum Displacement 0.000067 0.001800 YES
RMS Displacement 0.000095 0.001200 YES
Predicted change in Energy=-2.624039D-09
Optimization completed.
-- Stationary point found.

</pre>

There is zero net force and displacement so the optimizstion has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ S2 Optimised Information
! !! S2
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -796.32599779
|-
| RMS gradient / au || 0.00002267
|-
| Point Group || D*H
|-
| S-S bond length / A || 1.92952
|-
| S-S bond angle / degrees || N/A
|}

==='''Molecule Vibrations'''===

[[File:HB915 s2 optf pop displayvibrations.jpg]]

The 3N-5 rule used for linear molecules gives 3x2-5= 1. This is supported by the frequencies found from computational analysis as seen in the image above. This is due to the simple stretching of the bond.

==='''Charge Distribution'''===

Sulfur has an electronegativity of 2.58. However when both atoms have the same electronegativity the charge is equally distributed across the molecule.

[[File:HB915 s2 optf pop charge.jpg]]

==='''Molecular Orbitals'''===

Images of the molecular orbitals can be visualised by GaussView. They represent each orbital solution to the Schrödinger equation, in other words the Φs, one for each MO energy level.

There are over 30 orbitals found , 16 of which are occupied, and each can be described by the interactions of the atomic orbitals. Some examples are given below.

[[File:HB915 S2 MO 11.PNG|300px]]
[[File:HB915 S2 MO 12.PNG|300px]]

3 s orbitals from each Sulfur atom forms a bonding (left), non-bonding (right) pair of orbitals shown above.

[[File:HB915 S2 MO 15.PNG|300px]]
[[File:HB915 S2 MO 16.PNG|300px]]

The 3px from each sulfur interact to form a bonding (left) and an anti-bonding (right). However both are filled so no bond is formed from these MOs.

[[File:HB915 S2 MO 13.PNG|300px]]
[[File:HB915 S2 MO 18.PNG|300px]]

The 3pz from each sulfur interact to form a filled bonding (left) and a unfilled anti-bonding (right). Therefore this results in a sigma bond being formed between the two sulfur atoms.

[[File:HB915 S2 MO 14.PNG|300px]]
[[File:HB915 S2 MO 17.PNG|300px]]

The 3py from each sulfur interact to form a filled bonding (left) and a unfilled anti-bonding (right). Therefore this results in a pi bond being formed above and below the plane of the two sulfur atoms.

Rep:Mod:HB9151

2016-03-11T14:32:03Z

Hb915: /* Molecule Vibrations */

This is an exploration of molecules and reactions using GaussVeiw in order to understand the importance of computational inorganic chemistry.

Each molecule was draw in GaussVeiw and analysised computationally by solving the Schrödinger equation (EΦ=HΦ) under the Born-Oppenheimer approximation. Firstly the self-consistent field calculation is done for the starting bond lengths and angles giving the electronic wavefunction (Φ) that gives the lowest energy (for the fixed nuclei). The the distance is slightly shortened and the calculation repeated. This is continued until the lowest energy is found and this is the optimized structure.

Once this structure is found the data given by the solutions can be used to explore many properties of the molecule such as the spectrum, molecular orbital and the overall energy of the molecule.

=='''''NH3'''''==
<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 NH3 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 NH3 OPTF POP.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

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=-5.986294D-10
Optimization completed.
-- Stationary point found.

</pre>

There is zero net force and displacement so the optimizstion has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ NH3 Optimised Information
! !! NH3
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -56.55776873
|-
| RMS gradient / au || 0.00000485
|-
| Point Group || C3V
|-
| H-N bond length / A || 1.01798
|-
| H-N-H bond angle / degrees || 105.741
|}

==='''Molecule Vibrations'''===

[[File:HB915 nh3 optf pop displayvibrations.jpg.png|400px|left]]

''How many modes do you expect from the 3N-6 rule?''

N represents the number of atoms in the molecule. For NH3 there are 4 molecules therefore;
3x4-6=6

''Which modes are degenerate (ie have the same energy)?''

Modes 2 and 3 and 5 and 6 have the same energy (equal frequency).

''Which modes are "bending" vibrations and which are "bond stretch" vibrations?''

Modes 1-3 are bending and modes 4-6 are stretching. This is clear both from the animation and because bond stretching vibrations are higher in energy.

''Which mode is highly symmetric?''

Mode 4 is highly symmetric with no change in dipole.

''One mode is known as the "umbrella" mode, which one is this?''

Mode 1

''How many bands would you expect to see in an experimental spectrum of gaseous ammonia?''

There are four different vibrational energies suggesting four different bands. However there is only a minimal change in dipole for modes 4-6 so these would not be visible on a spectrum leaving only two bands.

[[File:HB915 nh3 optf pop spectra.jpg.png|500px|center|left]]

==='''Charge Distribution'''===

Nitrogen has an electronegativity of 3.04 which is comparatively larger than hydrogen with 2.2. Therefore you would expect nitrogen to carry the negative charge. This is supported by the values calculated form the Schrödinger equation shown in the image below.

[[File:HB915 nh3 optf pop charge.jpg.png|300px|center|left]]

=='''''N2'''''==
<jmol><jmolApplet>
<title>N2</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 N2 OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 N2 OPTIMISATION.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

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.

</pre>

There is zero net force and displacement so the optimizstion has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ N2 Optimised Information
! !! N2
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -109.52412868
|-
| RMS gradient / au || 0.00000365
|-
| Point Group || D*H
|-
| N-N bond length / A || 1.10550
|-
| N-N bond angle / degrees || N/A
|}

==='''Molecule Vibrations'''===

[[File:HB915 n2 optf pop displayvibrations.jpg|400px|center|left]]

The 3N-5 rule used for linear molecules gives 3x2-5= 1. This is supported by the frequencies found from computational analysis as seen in the image above. This is due to the simple stretching of the bond.

==='''Charge Distribution'''===

Nitrogen has an electronegativity of 3.04. However when both atoms have the same electronegativity the charge is equally distributed across the molecule.

[[File:HB915 n2 optf pop charge.jpg|300px|center|left]]

=='''''H2'''''==
<jmol><jmolApplet>
<title>H2</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 H2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 H2 OPTF POP.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

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.

</pre>

There is zero net force and displacement so the optimizstion has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ H2 Optimised Information
! !! H2
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -1.17853930
|-
| RMS gradient / au || 0.00012170
|-
| Point Group || D*H
|-
| H-H bond length / A || 1.10550
|-
| H-H bond angle / degrees || N/A
|}

==='''Molecule Vibrations'''===

Image of frequencies

[[File:HB915 h2 optf pop displayvibrations.jpg|400px|left]]

The 3N-5 rule used for linear molecules gives 3x2-5= 1. This is supported by the frequencies found from computational analysis as seen in the image above. This is due to the simple stretching of the bond.

==='''Charge Distribution'''===

Nitrogen has an electronegativity of 2.2. However when both atoms have the same electronegativity the charge is equally distributed across the molecule.

[[File:HB915 h2 optf pop charge.jpg|300px|center|left]]

=='''''Haber-Bosch Process'''''==

==='''Equation of Reaction'''===

N2 + H2 -> NH3

==='''Energy of Reaction'''===

E(NH3)= -56.55776873 au

2*E(NH3)= 2*-56.55776873 = -113.1155375 au

E(N2)= -109.52412868 au

E(H2)= -1.17853930 au

3*E(H2)= 3*-1.17853930 = -3.5356179 au

ΔE = 2*E(NH3)-[E(N2)+3*E(H2)] = -113.1155375-[-109.52412868+-3.5356179]

ΔE = -0.05579092 au

ΔE = -0.05579092*2625.5 = -146.48 kJ/mol to 2.d.p

==='''Stability of Reactants vs Products'''===

ΔE is negative therefore the Haber process is exothermic and the product (NH3) is lower in energy and more stable than the reactants.

=='''''AlCl4-'''''==
<jmol><jmolApplet>
<title>AlCl4-</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 ALCL4- OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 ALCL4- OPTF POP.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000155 0.001800 YES
RMS Displacement 0.000093 0.001200 YES
Predicted change in Energy=-7.051677D-09
Optimization completed.
-- Stationary point found.

</pre>

There is zero net force and displacement so the optimizstion has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ AlCl4- Optimised Information
! !! AlCl4-
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -2083.61641374
|-
| RMS gradient / au || 0.00001174
|-
| Point Group || TD
|-
| Al-Cl bond length / A || 2.17703
|-
| Cl-Al-Cl bond angle / degrees || 109.471
|}

This is a much higher energy compound than that of N2 and H2.

==='''Molecule Vibrations'''===

[[File:HB915 alcl4- optf pop displayvibrations.jpg]]

The 3N-6 rule gives 3x5-6= 1. This is supported by the frequencies found from computational analysis as seen in the image above. Modes 7-9 are degenerate but in different directions. They are high energy due to the bending character creating a large change in dipole. Modes 3-5 are also degenerate bending vibrations but at a lower energy. Modes 1, 2 and 6 are all symmetrical vibrations that show no change in dipole and are therefore not visible on the spectrum as shown below.

[[File:HB915 alcl4- optf pop spectra.jpg|400px|center|left]]

==='''Charge Distribution'''===

Aluminum has an electronegativity of 1.61 which is comparatively smaller than that of chlorine with 3.16. Therefore you would expect aluminum to carry the positive charge. This is supported by the values calculated form the Schrödinger equation shown in the image below. Also with such a high difference in electronegativity of these two atoms more ionic character will be witnessed.

[[File:HB915 alcl4- optf pop charge.jpg]]

==='''Molecular Orbitals'''===

Images of the molecular orbitals can be visualised by GaussView. They represent each orbital solution to the Schrödinger equation, in other words the Φs, one for each MO energy level.

There are over 90 orbitals found , 41 of which are occupied, and each can be described by the interactions of the atomic orbitals. Five have been explored here.

[[File:HB915 AlCl4- MO 21.PNG|300px]]

When looking at diatomic molecules the MOs are the simple interaction between the AOs. However when looking at larger molecule you talk about the MO fragments. This is the non-bonding Cl 2 p orbitals. They are too different in energy to interact with the Al orbitals so remain non-bonding. There are 12 with similar energies and shapes that can be attributed to the different orientations and phases of each orbital.

[[File:HB915 AlCl4- MO 26.PNG|300px]]
[[File:HB915 AlCl4- MO 30.PNG|300px]]

These two are a pair of MOs created by interactions between the same AOs; the s Cl fragrant and the s Al. However one is an in-phase interaction (left) which produces a filled bonding orbital and the other out of phase interaction (right) which produced an anti-bonding orbital which is also filled. Both are occupied so these are not the orbitals responsible for bonding in this molecule.

[[File:HB915 AlCl4- MO 31.PNG|300px]]
[[File:HB915 AlCl4- MO 43.PNG|300px]]

This is another bonding (left) and non-bonding (right) pair of MOs. These were caused by the interaction of the 3p Cl fragment and the 3p Al. The bonding is filled and the anti-bonding is empty so it is this orbital that is responsible for the bonds in this molecule.

=='''''S2'''''==
<jmol><jmolApplet>
<title>S2</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 S2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 S2 OPTF POP.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000039 0.000300 YES
Maximum Displacement 0.000067 0.001800 YES
RMS Displacement 0.000095 0.001200 YES
Predicted change in Energy=-2.624039D-09
Optimization completed.
-- Stationary point found.

</pre>

There is zero net force and displacement so the optimizstion has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ S2 Optimised Information
! !! S2
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -796.32599779
|-
| RMS gradient / au || 0.00002267
|-
| Point Group || D*H
|-
| S-S bond length / A || 1.92952
|-
| S-S bond angle / degrees || N/A
|}

==='''Molecule Vibrations'''===

[[File:HB915 s2 optf pop displayvibrations.jpg]]

The 3N-5 rule used for linear molecules gives 3x2-5= 1. This is supported by the frequencies found from computational analysis as seen in the image above. This is due to the simple stretching of the bond.

==='''Charge Distribution'''===

Sulfur has an electronegativity of 2.58. However when both atoms have the same electronegativity the charge is equally distributed across the molecule.

[[File:HB915 s2 optf pop charge.jpg]]

==='''Molecular Orbitals'''===

Images of the molecular orbitals can be visualised by GaussView. They represent each orbital solution to the Schrödinger equation, in other words the Φs, one for each MO energy level.

There are over 30 orbitals found , 16 of which are occupied, and each can be described by the interactions of the atomic orbitals. Some examples are given below.

[[File:HB915 S2 MO 11.PNG|300px]]
[[File:HB915 S2 MO 12.PNG|300px]]

3 s orbitals from each Sulfur atom forms a bonding (left), non-bonding (right) pair of orbitals shown above.

[[File:HB915 S2 MO 15.PNG|300px]]
[[File:HB915 S2 MO 16.PNG|300px]]

The 3px from each sulfur interact to form a bonding (left) and an anti-bonding (right). However both are filled so no bond is formed from these MOs.

[[File:HB915 S2 MO 13.PNG|300px]]
[[File:HB915 S2 MO 18.PNG|300px]]

The 3pz from each sulfur interact to form a filled bonding (left) and a unfilled anti-bonding (right). Therefore this results in a sigma bond being formed between the two sulfur atoms.

[[File:HB915 S2 MO 14.PNG|300px]]
[[File:HB915 S2 MO 17.PNG|300px]]

The 3py from each sulfur interact to form a filled bonding (left) and a unfilled anti-bonding (right). Therefore this results in a pi bond being formed above and below the plane of the two sulfur atoms.

Rep:Mod:HB9151

2016-03-11T14:31:42Z

Hb915: /* Molecule Vibrations */

This is an exploration of molecules and reactions using GaussVeiw in order to understand the importance of computational inorganic chemistry.

Each molecule was draw in GaussVeiw and analysised computationally by solving the Schrödinger equation (EΦ=HΦ) under the Born-Oppenheimer approximation. Firstly the self-consistent field calculation is done for the starting bond lengths and angles giving the electronic wavefunction (Φ) that gives the lowest energy (for the fixed nuclei). The the distance is slightly shortened and the calculation repeated. This is continued until the lowest energy is found and this is the optimized structure.

Once this structure is found the data given by the solutions can be used to explore many properties of the molecule such as the spectrum, molecular orbital and the overall energy of the molecule.

=='''''NH3'''''==
<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 NH3 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 NH3 OPTF POP.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

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=-5.986294D-10
Optimization completed.
-- Stationary point found.

</pre>

There is zero net force and displacement so the optimizstion has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ NH3 Optimised Information
! !! NH3
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -56.55776873
|-
| RMS gradient / au || 0.00000485
|-
| Point Group || C3V
|-
| H-N bond length / A || 1.01798
|-
| H-N-H bond angle / degrees || 105.741
|}

==='''Molecule Vibrations'''===

[[File:HB915 nh3 optf pop displayvibrations.jpg.png|400px|left]]

''How many modes do you expect from the 3N-6 rule?''

N represents the number of atoms in the molecule. For NH3 there are 4 molecules therefore;
3x4-6=6

''Which modes are degenerate (ie have the same energy)?''

Modes 2 and 3 and 5 and 6 have the same energy (equal frequency).

''Which modes are "bending" vibrations and which are "bond stretch" vibrations?''

Modes 1-3 are bending and modes 4-6 are stretching. This is clear both from the animation and because bond stretching vibrations are higher in energy.

''Which mode is highly symmetric?''

Mode 4 is highly symmetric with no change in dipole.

''One mode is known as the "umbrella" mode, which one is this?''

Mode 1

''How many bands would you expect to see in an experimental spectrum of gaseous ammonia?''

There are four different vibrational energies suggesting four different bands. However there is only a minimal change in dipole for modes 4-6 so these would not be visible on a spectrum leaving only two bands.

[[File:HB915 nh3 optf pop spectra.jpg.png|500px|center|left]]

==='''Charge Distribution'''===

Nitrogen has an electronegativity of 3.04 which is comparatively larger than hydrogen with 2.2. Therefore you would expect nitrogen to carry the negative charge. This is supported by the values calculated form the Schrödinger equation shown in the image below.

[[File:HB915 nh3 optf pop charge.jpg.png|300px|center|left]]

=='''''N2'''''==
<jmol><jmolApplet>
<title>N2</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 N2 OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 N2 OPTIMISATION.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

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.

</pre>

There is zero net force and displacement so the optimizstion has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ N2 Optimised Information
! !! N2
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -109.52412868
|-
| RMS gradient / au || 0.00000365
|-
| Point Group || D*H
|-
| N-N bond length / A || 1.10550
|-
| N-N bond angle / degrees || N/A
|}

==='''Molecule Vibrations'''===

[[File:HB915 n2 optf pop displayvibrations.jpg|400px|center|left]]

The 3N-5 rule used for linear molecules gives 3x2-5= 1. This is supported by the frequencies found from computational analysis as seen in the image above. This is due to the simple stretching of the bond.

==='''Charge Distribution'''===

Nitrogen has an electronegativity of 3.04. However when both atoms have the same electronegativity the charge is equally distributed across the molecule.

[[File:HB915 n2 optf pop charge.jpg|300px|center|left]]

=='''''H2'''''==
<jmol><jmolApplet>
<title>H2</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 H2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 H2 OPTF POP.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

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.

</pre>

There is zero net force and displacement so the optimizstion has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ H2 Optimised Information
! !! H2
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -1.17853930
|-
| RMS gradient / au || 0.00012170
|-
| Point Group || D*H
|-
| H-H bond length / A || 1.10550
|-
| H-H bond angle / degrees || N/A
|}

==='''Molecule Vibrations'''===

Image of frequencies

[[File:HB915 h2 optf pop displayvibrations.jpg|400px|left]]

The 3N-5 rule used for linear molecules gives 3x2-5= 1. This is supported by the frequencies found from computational analysis as seen in the image above. This is due to the simple stretching of the bond.

==='''Charge Distribution'''===

Nitrogen has an electronegativity of 2.2. However when both atoms have the same electronegativity the charge is equally distributed across the molecule.

[[File:HB915 h2 optf pop charge.jpg|300px|center|left]]

=='''''Haber-Bosch Process'''''==

==='''Equation of Reaction'''===

N2 + H2 -> NH3

==='''Energy of Reaction'''===

E(NH3)= -56.55776873 au

2*E(NH3)= 2*-56.55776873 = -113.1155375 au

E(N2)= -109.52412868 au

E(H2)= -1.17853930 au

3*E(H2)= 3*-1.17853930 = -3.5356179 au

ΔE = 2*E(NH3)-[E(N2)+3*E(H2)] = -113.1155375-[-109.52412868+-3.5356179]

ΔE = -0.05579092 au

ΔE = -0.05579092*2625.5 = -146.48 kJ/mol to 2.d.p

==='''Stability of Reactants vs Products'''===

ΔE is negative therefore the Haber process is exothermic and the product (NH3) is lower in energy and more stable than the reactants.

=='''''AlCl4-'''''==
<jmol><jmolApplet>
<title>AlCl4-</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 ALCL4- OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 ALCL4- OPTF POP.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000155 0.001800 YES
RMS Displacement 0.000093 0.001200 YES
Predicted change in Energy=-7.051677D-09
Optimization completed.
-- Stationary point found.

</pre>

There is zero net force and displacement so the optimizstion has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ AlCl4- Optimised Information
! !! AlCl4-
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -2083.61641374
|-
| RMS gradient / au || 0.00001174
|-
| Point Group || TD
|-
| Al-Cl bond length / A || 2.17703
|-
| Cl-Al-Cl bond angle / degrees || 109.471
|}

This is a much higher energy compound than that of N2 and H2.

==='''Molecule Vibrations'''===

[[File:HB915 alcl4- optf pop displayvibrations.jpg]]

The 3N-6 rule gives 3x5-6= 1. This is supported by the frequencies found from computational analysis as seen in the image above. Modes 7-9 are degenerate but in different directions. They are high energy due to the bending character creating a large change in dipole. Modes 3-5 are also degenerate bending vibrations but at a lower energy. Modes 1, 2 and 6 are all symmetrical vibrations that show no change in dipole and are therefore not visible on the spectrum as shown below.

[[File:HB915 alcl4- optf pop spectra.jpg|400px|center|left]]

==='''Charge Distribution'''===

Aluminum has an electronegativity of 1.61 which is comparatively smaller than that of chlorine with 3.16. Therefore you would expect aluminum to carry the positive charge. This is supported by the values calculated form the Schrödinger equation shown in the image below. Also with such a high difference in electronegativity of these two atoms more ionic character will be witnessed.

[[File:HB915 alcl4- optf pop charge.jpg]]

==='''Molecular Orbitals'''===

Images of the molecular orbitals can be visualised by GaussView. They represent each orbital solution to the Schrödinger equation, in other words the Φs, one for each MO energy level.

There are over 90 orbitals found , 41 of which are occupied, and each can be described by the interactions of the atomic orbitals. Five have been explored here.

[[File:HB915 AlCl4- MO 21.PNG|300px]]

When looking at diatomic molecules the MOs are the simple interaction between the AOs. However when looking at larger molecule you talk about the MO fragments. This is the non-bonding Cl 2 p orbitals. They are too different in energy to interact with the Al orbitals so remain non-bonding. There are 12 with similar energies and shapes that can be attributed to the different orientations and phases of each orbital.

[[File:HB915 AlCl4- MO 26.PNG|300px]]
[[File:HB915 AlCl4- MO 30.PNG|300px]]

These two are a pair of MOs created by interactions between the same AOs; the s Cl fragrant and the s Al. However one is an in-phase interaction (left) which produces a filled bonding orbital and the other out of phase interaction (right) which produced an anti-bonding orbital which is also filled. Both are occupied so these are not the orbitals responsible for bonding in this molecule.

[[File:HB915 AlCl4- MO 31.PNG|300px]]
[[File:HB915 AlCl4- MO 43.PNG|300px]]

This is another bonding (left) and non-bonding (right) pair of MOs. These were caused by the interaction of the 3p Cl fragment and the 3p Al. The bonding is filled and the anti-bonding is empty so it is this orbital that is responsible for the bonds in this molecule.

=='''''S2'''''==
<jmol><jmolApplet>
<title>S2</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 S2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 S2 OPTF POP.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000039 0.000300 YES
Maximum Displacement 0.000067 0.001800 YES
RMS Displacement 0.000095 0.001200 YES
Predicted change in Energy=-2.624039D-09
Optimization completed.
-- Stationary point found.

</pre>

There is zero net force and displacement so the optimizstion has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ S2 Optimised Information
! !! S2
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -796.32599779
|-
| RMS gradient / au || 0.00002267
|-
| Point Group || D*H
|-
| S-S bond length / A || 1.92952
|-
| S-S bond angle / degrees || N/A
|}

==='''Molecule Vibrations'''===

[[File:HB915 s2 optf pop displayvibrations.jpg]]

The 3N-5 rule used for linear molecules gives 3x2-5= 1. This is supported by the frequencies found from computational analysis as seen in the image above. This is due to the simple stretching of the bond.

==='''Charge Distribution'''===

Sulfur has an electronegativity of 2.58. However when both atoms have the same electronegativity the charge is equally distributed across the molecule.

[[File:HB915 s2 optf pop charge.jpg]]

==='''Molecular Orbitals'''===

Images of the molecular orbitals can be visualised by GaussView. They represent each orbital solution to the Schrödinger equation, in other words the Φs, one for each MO energy level.

There are over 30 orbitals found , 16 of which are occupied, and each can be described by the interactions of the atomic orbitals. Some examples are given below.

[[File:HB915 S2 MO 11.PNG|300px]]
[[File:HB915 S2 MO 12.PNG|300px]]

3 s orbitals from each Sulfur atom forms a bonding (left), non-bonding (right) pair of orbitals shown above.

[[File:HB915 S2 MO 15.PNG|300px]]
[[File:HB915 S2 MO 16.PNG|300px]]

The 3px from each sulfur interact to form a bonding (left) and an anti-bonding (right). However both are filled so no bond is formed from these MOs.

[[File:HB915 S2 MO 13.PNG|300px]]
[[File:HB915 S2 MO 18.PNG|300px]]

The 3pz from each sulfur interact to form a filled bonding (left) and a unfilled anti-bonding (right). Therefore this results in a sigma bond being formed between the two sulfur atoms.

[[File:HB915 S2 MO 14.PNG|300px]]
[[File:HB915 S2 MO 17.PNG|300px]]

The 3py from each sulfur interact to form a filled bonding (left) and a unfilled anti-bonding (right). Therefore this results in a pi bond being formed above and below the plane of the two sulfur atoms.

Rep:Mod:HB9151

2016-03-11T14:31:18Z

Hb915: /* Molecule Vibrations */

This is an exploration of molecules and reactions using GaussVeiw in order to understand the importance of computational inorganic chemistry.

Each molecule was draw in GaussVeiw and analysised computationally by solving the Schrödinger equation (EΦ=HΦ) under the Born-Oppenheimer approximation. Firstly the self-consistent field calculation is done for the starting bond lengths and angles giving the electronic wavefunction (Φ) that gives the lowest energy (for the fixed nuclei). The the distance is slightly shortened and the calculation repeated. This is continued until the lowest energy is found and this is the optimized structure.

Once this structure is found the data given by the solutions can be used to explore many properties of the molecule such as the spectrum, molecular orbital and the overall energy of the molecule.

=='''''NH3'''''==
<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 NH3 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 NH3 OPTF POP.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

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=-5.986294D-10
Optimization completed.
-- Stationary point found.

</pre>

There is zero net force and displacement so the optimizstion has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ NH3 Optimised Information
! !! NH3
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -56.55776873
|-
| RMS gradient / au || 0.00000485
|-
| Point Group || C3V
|-
| H-N bond length / A || 1.01798
|-
| H-N-H bond angle / degrees || 105.741
|}

==='''Molecule Vibrations'''===

[[File:HB915 nh3 optf pop displayvibrations.jpg.png|400px|left]]

''How many modes do you expect from the 3N-6 rule?''

N represents the number of atoms in the molecule. For NH3 there are 4 molecules therefore;
3x4-6=6

''Which modes are degenerate (ie have the same energy)?''

Modes 2 and 3 and 5 and 6 have the same energy (equal frequency).

''Which modes are "bending" vibrations and which are "bond stretch" vibrations?''

Modes 1-3 are bending and modes 4-6 are stretching. This is clear both from the animation and because bond stretching vibrations are higher in energy.

''Which mode is highly symmetric?''

Mode 4 is highly symmetric with no change in dipole.

''One mode is known as the "umbrella" mode, which one is this?''

Mode 1

''How many bands would you expect to see in an experimental spectrum of gaseous ammonia?''

There are four different vibrational energies suggesting four different bands. However there is only a minimal change in dipole for modes 4-6 so these would not be visible on a spectrum leaving only two bands.

[[File:HB915 nh3 optf pop spectra.jpg.png|500px|center|left]]

==='''Charge Distribution'''===

Nitrogen has an electronegativity of 3.04 which is comparatively larger than hydrogen with 2.2. Therefore you would expect nitrogen to carry the negative charge. This is supported by the values calculated form the Schrödinger equation shown in the image below.

[[File:HB915 nh3 optf pop charge.jpg.png|300px|center|left]]

=='''''N2'''''==
<jmol><jmolApplet>
<title>N2</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 N2 OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 N2 OPTIMISATION.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

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.

</pre>

There is zero net force and displacement so the optimizstion has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ N2 Optimised Information
! !! N2
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -109.52412868
|-
| RMS gradient / au || 0.00000365
|-
| Point Group || D*H
|-
| N-N bond length / A || 1.10550
|-
| N-N bond angle / degrees || N/A
|}

==='''Molecule Vibrations'''===

[[File:HB915 n2 optf pop displayvibrations.jpg|400px|center|left]]

The 3N-5 rule used for linear molecules gives 3x2-5= 1. This is supported by the frequencies found from computational analysis as seen in the image above. This is due to the simple stretching of the bond.

==='''Charge Distribution'''===

Nitrogen has an electronegativity of 3.04. However when both atoms have the same electronegativity the charge is equally distributed across the molecule.

[[File:HB915 n2 optf pop charge.jpg|300px|center|left]]

=='''''H2'''''==
<jmol><jmolApplet>
<title>H2</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 H2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 H2 OPTF POP.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

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.

</pre>

There is zero net force and displacement so the optimizstion has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ H2 Optimised Information
! !! H2
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -1.17853930
|-
| RMS gradient / au || 0.00012170
|-
| Point Group || D*H
|-
| H-H bond length / A || 1.10550
|-
| H-H bond angle / degrees || N/A
|}

==='''Molecule Vibrations'''===

Image of frequencies

[[File:HB915 h2 optf pop displayvibrations.jpg|400px|left]]

The 3N-5 rule used for linear molecules gives 3x2-5= 1. This is supported by the frequencies found from computational analysis as seen in the image above. This is due to the simple stretching of the bond.

==='''Charge Distribution'''===

Nitrogen has an electronegativity of 2.2. However when both atoms have the same electronegativity the charge is equally distributed across the molecule.

[[File:HB915 h2 optf pop charge.jpg|300px|center|left]]

=='''''Haber-Bosch Process'''''==

==='''Equation of Reaction'''===

N2 + H2 -> NH3

==='''Energy of Reaction'''===

E(NH3)= -56.55776873 au

2*E(NH3)= 2*-56.55776873 = -113.1155375 au

E(N2)= -109.52412868 au

E(H2)= -1.17853930 au

3*E(H2)= 3*-1.17853930 = -3.5356179 au

ΔE = 2*E(NH3)-[E(N2)+3*E(H2)] = -113.1155375-[-109.52412868+-3.5356179]

ΔE = -0.05579092 au

ΔE = -0.05579092*2625.5 = -146.48 kJ/mol to 2.d.p

==='''Stability of Reactants vs Products'''===

ΔE is negative therefore the Haber process is exothermic and the product (NH3) is lower in energy and more stable than the reactants.

=='''''AlCl4-'''''==
<jmol><jmolApplet>
<title>AlCl4-</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 ALCL4- OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 ALCL4- OPTF POP.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000155 0.001800 YES
RMS Displacement 0.000093 0.001200 YES
Predicted change in Energy=-7.051677D-09
Optimization completed.
-- Stationary point found.

</pre>

There is zero net force and displacement so the optimizstion has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ AlCl4- Optimised Information
! !! AlCl4-
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -2083.61641374
|-
| RMS gradient / au || 0.00001174
|-
| Point Group || TD
|-
| Al-Cl bond length / A || 2.17703
|-
| Cl-Al-Cl bond angle / degrees || 109.471
|}

This is a much higher energy compound than that of N2 and H2.

==='''Molecule Vibrations'''===

[[File:HB915 alcl4- optf pop displayvibrations.jpg]]

The 3N-6 rule gives 3x5-6= 1. This is supported by the frequencies found from computational analysis as seen in the image above. Modes 7-9 are degenerate but in different directions. They are high energy due to the bending character creating a large change in dipole. Modes 3-5 are also degenerate bending vibrations but at a lower energy. Modes 1, 2 and 6 are all symmetrical vibrations that show no change in dipole and are therefore not visible on the spectrum as shown below.

[[File:HB915 alcl4- optf pop spectra.jpg|400px|center|left]]

==='''Charge Distribution'''===

Aluminum has an electronegativity of 1.61 which is comparatively smaller than that of chlorine with 3.16. Therefore you would expect aluminum to carry the positive charge. This is supported by the values calculated form the Schrödinger equation shown in the image below. Also with such a high difference in electronegativity of these two atoms more ionic character will be witnessed.

[[File:HB915 alcl4- optf pop charge.jpg]]

==='''Molecular Orbitals'''===

Images of the molecular orbitals can be visualised by GaussView. They represent each orbital solution to the Schrödinger equation, in other words the Φs, one for each MO energy level.

There are over 90 orbitals found , 41 of which are occupied, and each can be described by the interactions of the atomic orbitals. Five have been explored here.

[[File:HB915 AlCl4- MO 21.PNG|300px]]

When looking at diatomic molecules the MOs are the simple interaction between the AOs. However when looking at larger molecule you talk about the MO fragments. This is the non-bonding Cl 2 p orbitals. They are too different in energy to interact with the Al orbitals so remain non-bonding. There are 12 with similar energies and shapes that can be attributed to the different orientations and phases of each orbital.

[[File:HB915 AlCl4- MO 26.PNG|300px]]
[[File:HB915 AlCl4- MO 30.PNG|300px]]

These two are a pair of MOs created by interactions between the same AOs; the s Cl fragrant and the s Al. However one is an in-phase interaction (left) which produces a filled bonding orbital and the other out of phase interaction (right) which produced an anti-bonding orbital which is also filled. Both are occupied so these are not the orbitals responsible for bonding in this molecule.

[[File:HB915 AlCl4- MO 31.PNG|300px]]
[[File:HB915 AlCl4- MO 43.PNG|300px]]

This is another bonding (left) and non-bonding (right) pair of MOs. These were caused by the interaction of the 3p Cl fragment and the 3p Al. The bonding is filled and the anti-bonding is empty so it is this orbital that is responsible for the bonds in this molecule.

=='''''S2'''''==
<jmol><jmolApplet>
<title>S2</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 S2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 S2 OPTF POP.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000039 0.000300 YES
Maximum Displacement 0.000067 0.001800 YES
RMS Displacement 0.000095 0.001200 YES
Predicted change in Energy=-2.624039D-09
Optimization completed.
-- Stationary point found.

</pre>

There is zero net force and displacement so the optimizstion has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ S2 Optimised Information
! !! S2
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -796.32599779
|-
| RMS gradient / au || 0.00002267
|-
| Point Group || D*H
|-
| S-S bond length / A || 1.92952
|-
| S-S bond angle / degrees || N/A
|}

==='''Molecule Vibrations'''===

[[File:HB915 s2 optf pop displayvibrations.jpg]]

The 3N-5 rule used for linear molecules gives 3x2-5= 1. This is supported by the frequencies found from computational analysis as seen in the image above. This is due to the simple stretching of the bond.

==='''Charge Distribution'''===

Sulfur has an electronegativity of 2.58. However when both atoms have the same electronegativity the charge is equally distributed across the molecule.

[[File:HB915 s2 optf pop charge.jpg]]

==='''Molecular Orbitals'''===

Images of the molecular orbitals can be visualised by GaussView. They represent each orbital solution to the Schrödinger equation, in other words the Φs, one for each MO energy level.

There are over 30 orbitals found , 16 of which are occupied, and each can be described by the interactions of the atomic orbitals. Some examples are given below.

[[File:HB915 S2 MO 11.PNG|300px]]
[[File:HB915 S2 MO 12.PNG|300px]]

3 s orbitals from each Sulfur atom forms a bonding (left), non-bonding (right) pair of orbitals shown above.

[[File:HB915 S2 MO 15.PNG|300px]]
[[File:HB915 S2 MO 16.PNG|300px]]

The 3px from each sulfur interact to form a bonding (left) and an anti-bonding (right). However both are filled so no bond is formed from these MOs.

[[File:HB915 S2 MO 13.PNG|300px]]
[[File:HB915 S2 MO 18.PNG|300px]]

The 3pz from each sulfur interact to form a filled bonding (left) and a unfilled anti-bonding (right). Therefore this results in a sigma bond being formed between the two sulfur atoms.

[[File:HB915 S2 MO 14.PNG|300px]]
[[File:HB915 S2 MO 17.PNG|300px]]

The 3py from each sulfur interact to form a filled bonding (left) and a unfilled anti-bonding (right). Therefore this results in a pi bond being formed above and below the plane of the two sulfur atoms.

Rep:Mod:HB9151

2016-03-11T14:31:05Z

Hb915: /* Molecule Vibrations */

This is an exploration of molecules and reactions using GaussVeiw in order to understand the importance of computational inorganic chemistry.

Each molecule was draw in GaussVeiw and analysised computationally by solving the Schrödinger equation (EΦ=HΦ) under the Born-Oppenheimer approximation. Firstly the self-consistent field calculation is done for the starting bond lengths and angles giving the electronic wavefunction (Φ) that gives the lowest energy (for the fixed nuclei). The the distance is slightly shortened and the calculation repeated. This is continued until the lowest energy is found and this is the optimized structure.

Once this structure is found the data given by the solutions can be used to explore many properties of the molecule such as the spectrum, molecular orbital and the overall energy of the molecule.

=='''''NH3'''''==
<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 NH3 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 NH3 OPTF POP.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

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=-5.986294D-10
Optimization completed.
-- Stationary point found.

</pre>

There is zero net force and displacement so the optimizstion has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ NH3 Optimised Information
! !! NH3
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -56.55776873
|-
| RMS gradient / au || 0.00000485
|-
| Point Group || C3V
|-
| H-N bond length / A || 1.01798
|-
| H-N-H bond angle / degrees || 105.741
|}

==='''Molecule Vibrations'''===

[[File:HB915 nh3 optf pop displayvibrations.jpg.png|400px|center|left]]

''How many modes do you expect from the 3N-6 rule?''

N represents the number of atoms in the molecule. For NH3 there are 4 molecules therefore;
3x4-6=6

''Which modes are degenerate (ie have the same energy)?''

Modes 2 and 3 and 5 and 6 have the same energy (equal frequency).

''Which modes are "bending" vibrations and which are "bond stretch" vibrations?''

Modes 1-3 are bending and modes 4-6 are stretching. This is clear both from the animation and because bond stretching vibrations are higher in energy.

''Which mode is highly symmetric?''

Mode 4 is highly symmetric with no change in dipole.

''One mode is known as the "umbrella" mode, which one is this?''

Mode 1

''How many bands would you expect to see in an experimental spectrum of gaseous ammonia?''

There are four different vibrational energies suggesting four different bands. However there is only a minimal change in dipole for modes 4-6 so these would not be visible on a spectrum leaving only two bands.

[[File:HB915 nh3 optf pop spectra.jpg.png|500px|center|left]]

==='''Charge Distribution'''===

Nitrogen has an electronegativity of 3.04 which is comparatively larger than hydrogen with 2.2. Therefore you would expect nitrogen to carry the negative charge. This is supported by the values calculated form the Schrödinger equation shown in the image below.

[[File:HB915 nh3 optf pop charge.jpg.png|300px|center|left]]

=='''''N2'''''==
<jmol><jmolApplet>
<title>N2</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 N2 OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 N2 OPTIMISATION.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

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.

</pre>

There is zero net force and displacement so the optimizstion has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ N2 Optimised Information
! !! N2
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -109.52412868
|-
| RMS gradient / au || 0.00000365
|-
| Point Group || D*H
|-
| N-N bond length / A || 1.10550
|-
| N-N bond angle / degrees || N/A
|}

==='''Molecule Vibrations'''===

[[File:HB915 n2 optf pop displayvibrations.jpg|400px|center|left]]

The 3N-5 rule used for linear molecules gives 3x2-5= 1. This is supported by the frequencies found from computational analysis as seen in the image above. This is due to the simple stretching of the bond.

==='''Charge Distribution'''===

Nitrogen has an electronegativity of 3.04. However when both atoms have the same electronegativity the charge is equally distributed across the molecule.

[[File:HB915 n2 optf pop charge.jpg|300px|center|left]]

=='''''H2'''''==
<jmol><jmolApplet>
<title>H2</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 H2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 H2 OPTF POP.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

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.

</pre>

There is zero net force and displacement so the optimizstion has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ H2 Optimised Information
! !! H2
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -1.17853930
|-
| RMS gradient / au || 0.00012170
|-
| Point Group || D*H
|-
| H-H bond length / A || 1.10550
|-
| H-H bond angle / degrees || N/A
|}

==='''Molecule Vibrations'''===

Image of frequencies

[[File:HB915 h2 optf pop displayvibrations.jpg|400px|left]]

The 3N-5 rule used for linear molecules gives 3x2-5= 1. This is supported by the frequencies found from computational analysis as seen in the image above. This is due to the simple stretching of the bond.

==='''Charge Distribution'''===

Nitrogen has an electronegativity of 2.2. However when both atoms have the same electronegativity the charge is equally distributed across the molecule.

[[File:HB915 h2 optf pop charge.jpg|300px|center|left]]

=='''''Haber-Bosch Process'''''==

==='''Equation of Reaction'''===

N2 + H2 -> NH3

==='''Energy of Reaction'''===

E(NH3)= -56.55776873 au

2*E(NH3)= 2*-56.55776873 = -113.1155375 au

E(N2)= -109.52412868 au

E(H2)= -1.17853930 au

3*E(H2)= 3*-1.17853930 = -3.5356179 au

ΔE = 2*E(NH3)-[E(N2)+3*E(H2)] = -113.1155375-[-109.52412868+-3.5356179]

ΔE = -0.05579092 au

ΔE = -0.05579092*2625.5 = -146.48 kJ/mol to 2.d.p

==='''Stability of Reactants vs Products'''===

ΔE is negative therefore the Haber process is exothermic and the product (NH3) is lower in energy and more stable than the reactants.

=='''''AlCl4-'''''==
<jmol><jmolApplet>
<title>AlCl4-</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 ALCL4- OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 ALCL4- OPTF POP.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000155 0.001800 YES
RMS Displacement 0.000093 0.001200 YES
Predicted change in Energy=-7.051677D-09
Optimization completed.
-- Stationary point found.

</pre>

There is zero net force and displacement so the optimizstion has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ AlCl4- Optimised Information
! !! AlCl4-
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -2083.61641374
|-
| RMS gradient / au || 0.00001174
|-
| Point Group || TD
|-
| Al-Cl bond length / A || 2.17703
|-
| Cl-Al-Cl bond angle / degrees || 109.471
|}

This is a much higher energy compound than that of N2 and H2.

==='''Molecule Vibrations'''===

[[File:HB915 alcl4- optf pop displayvibrations.jpg]]

The 3N-6 rule gives 3x5-6= 1. This is supported by the frequencies found from computational analysis as seen in the image above. Modes 7-9 are degenerate but in different directions. They are high energy due to the bending character creating a large change in dipole. Modes 3-5 are also degenerate bending vibrations but at a lower energy. Modes 1, 2 and 6 are all symmetrical vibrations that show no change in dipole and are therefore not visible on the spectrum as shown below.

[[File:HB915 alcl4- optf pop spectra.jpg|400px|center|left]]

==='''Charge Distribution'''===

Aluminum has an electronegativity of 1.61 which is comparatively smaller than that of chlorine with 3.16. Therefore you would expect aluminum to carry the positive charge. This is supported by the values calculated form the Schrödinger equation shown in the image below. Also with such a high difference in electronegativity of these two atoms more ionic character will be witnessed.

[[File:HB915 alcl4- optf pop charge.jpg]]

==='''Molecular Orbitals'''===

Images of the molecular orbitals can be visualised by GaussView. They represent each orbital solution to the Schrödinger equation, in other words the Φs, one for each MO energy level.

There are over 90 orbitals found , 41 of which are occupied, and each can be described by the interactions of the atomic orbitals. Five have been explored here.

[[File:HB915 AlCl4- MO 21.PNG|300px]]

When looking at diatomic molecules the MOs are the simple interaction between the AOs. However when looking at larger molecule you talk about the MO fragments. This is the non-bonding Cl 2 p orbitals. They are too different in energy to interact with the Al orbitals so remain non-bonding. There are 12 with similar energies and shapes that can be attributed to the different orientations and phases of each orbital.

[[File:HB915 AlCl4- MO 26.PNG|300px]]
[[File:HB915 AlCl4- MO 30.PNG|300px]]

These two are a pair of MOs created by interactions between the same AOs; the s Cl fragrant and the s Al. However one is an in-phase interaction (left) which produces a filled bonding orbital and the other out of phase interaction (right) which produced an anti-bonding orbital which is also filled. Both are occupied so these are not the orbitals responsible for bonding in this molecule.

[[File:HB915 AlCl4- MO 31.PNG|300px]]
[[File:HB915 AlCl4- MO 43.PNG|300px]]

This is another bonding (left) and non-bonding (right) pair of MOs. These were caused by the interaction of the 3p Cl fragment and the 3p Al. The bonding is filled and the anti-bonding is empty so it is this orbital that is responsible for the bonds in this molecule.

=='''''S2'''''==
<jmol><jmolApplet>
<title>S2</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 S2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 S2 OPTF POP.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000039 0.000300 YES
Maximum Displacement 0.000067 0.001800 YES
RMS Displacement 0.000095 0.001200 YES
Predicted change in Energy=-2.624039D-09
Optimization completed.
-- Stationary point found.

</pre>

There is zero net force and displacement so the optimizstion has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ S2 Optimised Information
! !! S2
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -796.32599779
|-
| RMS gradient / au || 0.00002267
|-
| Point Group || D*H
|-
| S-S bond length / A || 1.92952
|-
| S-S bond angle / degrees || N/A
|}

==='''Molecule Vibrations'''===

[[File:HB915 s2 optf pop displayvibrations.jpg]]

The 3N-5 rule used for linear molecules gives 3x2-5= 1. This is supported by the frequencies found from computational analysis as seen in the image above. This is due to the simple stretching of the bond.

==='''Charge Distribution'''===

Sulfur has an electronegativity of 2.58. However when both atoms have the same electronegativity the charge is equally distributed across the molecule.

[[File:HB915 s2 optf pop charge.jpg]]

==='''Molecular Orbitals'''===

Images of the molecular orbitals can be visualised by GaussView. They represent each orbital solution to the Schrödinger equation, in other words the Φs, one for each MO energy level.

There are over 30 orbitals found , 16 of which are occupied, and each can be described by the interactions of the atomic orbitals. Some examples are given below.

[[File:HB915 S2 MO 11.PNG|300px]]
[[File:HB915 S2 MO 12.PNG|300px]]

3 s orbitals from each Sulfur atom forms a bonding (left), non-bonding (right) pair of orbitals shown above.

[[File:HB915 S2 MO 15.PNG|300px]]
[[File:HB915 S2 MO 16.PNG|300px]]

The 3px from each sulfur interact to form a bonding (left) and an anti-bonding (right). However both are filled so no bond is formed from these MOs.

[[File:HB915 S2 MO 13.PNG|300px]]
[[File:HB915 S2 MO 18.PNG|300px]]

The 3pz from each sulfur interact to form a filled bonding (left) and a unfilled anti-bonding (right). Therefore this results in a sigma bond being formed between the two sulfur atoms.

[[File:HB915 S2 MO 14.PNG|300px]]
[[File:HB915 S2 MO 17.PNG|300px]]

The 3py from each sulfur interact to form a filled bonding (left) and a unfilled anti-bonding (right). Therefore this results in a pi bond being formed above and below the plane of the two sulfur atoms.

Rep:Mod:HB9151

2016-03-11T14:29:32Z

Hb915: /* Molecular Orbitals */

This is an exploration of molecules and reactions using GaussVeiw in order to understand the importance of computational inorganic chemistry.

Each molecule was draw in GaussVeiw and analysised computationally by solving the Schrödinger equation (EΦ=HΦ) under the Born-Oppenheimer approximation. Firstly the self-consistent field calculation is done for the starting bond lengths and angles giving the electronic wavefunction (Φ) that gives the lowest energy (for the fixed nuclei). The the distance is slightly shortened and the calculation repeated. This is continued until the lowest energy is found and this is the optimized structure.

Once this structure is found the data given by the solutions can be used to explore many properties of the molecule such as the spectrum, molecular orbital and the overall energy of the molecule.

=='''''NH3'''''==
<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 NH3 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 NH3 OPTF POP.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

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=-5.986294D-10
Optimization completed.
-- Stationary point found.

</pre>

There is zero net force and displacement so the optimizstion has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ NH3 Optimised Information
! !! NH3
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -56.55776873
|-
| RMS gradient / au || 0.00000485
|-
| Point Group || C3V
|-
| H-N bond length / A || 1.01798
|-
| H-N-H bond angle / degrees || 105.741
|}

==='''Molecule Vibrations'''===

[[File:HB915 nh3 optf pop displayvibrations.jpg.png|400px|center|left]]

''How many modes do you expect from the 3N-6 rule?''

N represents the number of atoms in the molecule. For NH3 there are 4 molecules therefore;
3x4-6=6

''Which modes are degenerate (ie have the same energy)?''

Modes 2 and 3 and 5 and 6 have the same energy (equal frequency).

''Which modes are "bending" vibrations and which are "bond stretch" vibrations?''

Modes 1-3 are bending and modes 4-6 are stretching. This is clear both from the animation and because bond stretching vibrations are higher in energy.

''Which mode is highly symmetric?''

Mode 4 is highly symmetric with no change in dipole.

''One mode is known as the "umbrella" mode, which one is this?''

Mode 1

''How many bands would you expect to see in an experimental spectrum of gaseous ammonia?''

There are four different vibrational energies suggesting four different bands. However there is only a minimal change in dipole for modes 4-6 so these would not be visible on a spectrum leaving only two bands.

[[File:HB915 nh3 optf pop spectra.jpg.png|500px|center|left]]

==='''Charge Distribution'''===

Nitrogen has an electronegativity of 3.04 which is comparatively larger than hydrogen with 2.2. Therefore you would expect nitrogen to carry the negative charge. This is supported by the values calculated form the Schrödinger equation shown in the image below.

[[File:HB915 nh3 optf pop charge.jpg.png|300px|center|left]]

=='''''N2'''''==
<jmol><jmolApplet>
<title>N2</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 N2 OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 N2 OPTIMISATION.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

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.

</pre>

There is zero net force and displacement so the optimizstion has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ N2 Optimised Information
! !! N2
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -109.52412868
|-
| RMS gradient / au || 0.00000365
|-
| Point Group || D*H
|-
| N-N bond length / A || 1.10550
|-
| N-N bond angle / degrees || N/A
|}

==='''Molecule Vibrations'''===

[[File:HB915 n2 optf pop displayvibrations.jpg|400px|center|left]]

The 3N-5 rule used for linear molecules gives 3x2-5= 1. This is supported by the frequencies found from computational analysis as seen in the image above. This is due to the simple stretching of the bond.

==='''Charge Distribution'''===

Nitrogen has an electronegativity of 3.04. However when both atoms have the same electronegativity the charge is equally distributed across the molecule.

[[File:HB915 n2 optf pop charge.jpg|300px|center|left]]

=='''''H2'''''==
<jmol><jmolApplet>
<title>H2</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 H2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 H2 OPTF POP.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

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.

</pre>

There is zero net force and displacement so the optimizstion has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ H2 Optimised Information
! !! H2
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -1.17853930
|-
| RMS gradient / au || 0.00012170
|-
| Point Group || D*H
|-
| H-H bond length / A || 1.10550
|-
| H-H bond angle / degrees || N/A
|}

==='''Molecule Vibrations'''===

Image of frequencies

[[File:HB915 h2 optf pop displayvibrations.jpg|400px|center|left]]

The 3N-5 rule used for linear molecules gives 3x2-5= 1. This is supported by the frequencies found from computational analysis as seen in the image above. This is due to the simple stretching of the bond.

==='''Charge Distribution'''===

Nitrogen has an electronegativity of 2.2. However when both atoms have the same electronegativity the charge is equally distributed across the molecule.

[[File:HB915 h2 optf pop charge.jpg|300px|center|left]]

=='''''Haber-Bosch Process'''''==

==='''Equation of Reaction'''===

N2 + H2 -> NH3

==='''Energy of Reaction'''===

E(NH3)= -56.55776873 au

2*E(NH3)= 2*-56.55776873 = -113.1155375 au

E(N2)= -109.52412868 au

E(H2)= -1.17853930 au

3*E(H2)= 3*-1.17853930 = -3.5356179 au

ΔE = 2*E(NH3)-[E(N2)+3*E(H2)] = -113.1155375-[-109.52412868+-3.5356179]

ΔE = -0.05579092 au

ΔE = -0.05579092*2625.5 = -146.48 kJ/mol to 2.d.p

==='''Stability of Reactants vs Products'''===

ΔE is negative therefore the Haber process is exothermic and the product (NH3) is lower in energy and more stable than the reactants.

=='''''AlCl4-'''''==
<jmol><jmolApplet>
<title>AlCl4-</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 ALCL4- OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 ALCL4- OPTF POP.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000155 0.001800 YES
RMS Displacement 0.000093 0.001200 YES
Predicted change in Energy=-7.051677D-09
Optimization completed.
-- Stationary point found.

</pre>

There is zero net force and displacement so the optimizstion has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ AlCl4- Optimised Information
! !! AlCl4-
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -2083.61641374
|-
| RMS gradient / au || 0.00001174
|-
| Point Group || TD
|-
| Al-Cl bond length / A || 2.17703
|-
| Cl-Al-Cl bond angle / degrees || 109.471
|}

This is a much higher energy compound than that of N2 and H2.

==='''Molecule Vibrations'''===

[[File:HB915 alcl4- optf pop displayvibrations.jpg]]

The 3N-6 rule gives 3x5-6= 1. This is supported by the frequencies found from computational analysis as seen in the image above. Modes 7-9 are degenerate but in different directions. They are high energy due to the bending character creating a large change in dipole. Modes 3-5 are also degenerate bending vibrations but at a lower energy. Modes 1, 2 and 6 are all symmetrical vibrations that show no change in dipole and are therefore not visible on the spectrum as shown below.

[[File:HB915 alcl4- optf pop spectra.jpg|400px|center|left]]

==='''Charge Distribution'''===

Aluminum has an electronegativity of 1.61 which is comparatively smaller than that of chlorine with 3.16. Therefore you would expect aluminum to carry the positive charge. This is supported by the values calculated form the Schrödinger equation shown in the image below. Also with such a high difference in electronegativity of these two atoms more ionic character will be witnessed.

[[File:HB915 alcl4- optf pop charge.jpg]]

==='''Molecular Orbitals'''===

Images of the molecular orbitals can be visualised by GaussView. They represent each orbital solution to the Schrödinger equation, in other words the Φs, one for each MO energy level.

There are over 90 orbitals found , 41 of which are occupied, and each can be described by the interactions of the atomic orbitals. Five have been explored here.

[[File:HB915 AlCl4- MO 21.PNG|300px]]

When looking at diatomic molecules the MOs are the simple interaction between the AOs. However when looking at larger molecule you talk about the MO fragments. This is the non-bonding Cl 2 p orbitals. They are too different in energy to interact with the Al orbitals so remain non-bonding. There are 12 with similar energies and shapes that can be attributed to the different orientations and phases of each orbital.

[[File:HB915 AlCl4- MO 26.PNG|300px]]
[[File:HB915 AlCl4- MO 30.PNG|300px]]

These two are a pair of MOs created by interactions between the same AOs; the s Cl fragrant and the s Al. However one is an in-phase interaction (left) which produces a filled bonding orbital and the other out of phase interaction (right) which produced an anti-bonding orbital which is also filled. Both are occupied so these are not the orbitals responsible for bonding in this molecule.

[[File:HB915 AlCl4- MO 31.PNG|300px]]
[[File:HB915 AlCl4- MO 43.PNG|300px]]

This is another bonding (left) and non-bonding (right) pair of MOs. These were caused by the interaction of the 3p Cl fragment and the 3p Al. The bonding is filled and the anti-bonding is empty so it is this orbital that is responsible for the bonds in this molecule.

=='''''S2'''''==
<jmol><jmolApplet>
<title>S2</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 S2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 S2 OPTF POP.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000039 0.000300 YES
Maximum Displacement 0.000067 0.001800 YES
RMS Displacement 0.000095 0.001200 YES
Predicted change in Energy=-2.624039D-09
Optimization completed.
-- Stationary point found.

</pre>

There is zero net force and displacement so the optimizstion has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ S2 Optimised Information
! !! S2
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -796.32599779
|-
| RMS gradient / au || 0.00002267
|-
| Point Group || D*H
|-
| S-S bond length / A || 1.92952
|-
| S-S bond angle / degrees || N/A
|}

==='''Molecule Vibrations'''===

[[File:HB915 s2 optf pop displayvibrations.jpg]]

The 3N-5 rule used for linear molecules gives 3x2-5= 1. This is supported by the frequencies found from computational analysis as seen in the image above. This is due to the simple stretching of the bond.

==='''Charge Distribution'''===

Sulfur has an electronegativity of 2.58. However when both atoms have the same electronegativity the charge is equally distributed across the molecule.

[[File:HB915 s2 optf pop charge.jpg]]

==='''Molecular Orbitals'''===

Images of the molecular orbitals can be visualised by GaussView. They represent each orbital solution to the Schrödinger equation, in other words the Φs, one for each MO energy level.

There are over 30 orbitals found , 16 of which are occupied, and each can be described by the interactions of the atomic orbitals. Some examples are given below.

[[File:HB915 S2 MO 11.PNG|300px]]
[[File:HB915 S2 MO 12.PNG|300px]]

3 s orbitals from each Sulfur atom forms a bonding (left), non-bonding (right) pair of orbitals shown above.

[[File:HB915 S2 MO 15.PNG|300px]]
[[File:HB915 S2 MO 16.PNG|300px]]

The 3px from each sulfur interact to form a bonding (left) and an anti-bonding (right). However both are filled so no bond is formed from these MOs.

[[File:HB915 S2 MO 13.PNG|300px]]
[[File:HB915 S2 MO 18.PNG|300px]]

The 3pz from each sulfur interact to form a filled bonding (left) and a unfilled anti-bonding (right). Therefore this results in a sigma bond being formed between the two sulfur atoms.

[[File:HB915 S2 MO 14.PNG|300px]]
[[File:HB915 S2 MO 17.PNG|300px]]

The 3py from each sulfur interact to form a filled bonding (left) and a unfilled anti-bonding (right). Therefore this results in a pi bond being formed above and below the plane of the two sulfur atoms.

File:HB915 S2 MO 18.PNG

2016-03-11T14:28:30Z

Hb915:

File:HB915 S2 MO 17.PNG

2016-03-11T14:28:21Z

Hb915:

File:HB915 S2 MO 16.PNG

2016-03-11T14:28:06Z

Hb915:

File:HB915 S2 MO 15.PNG

2016-03-11T14:27:55Z

Hb915:

File:HB915 S2 MO 14.PNG

2016-03-11T14:27:45Z

Hb915:

File:HB915 S2 MO 13.PNG

2016-03-11T14:27:34Z

Hb915:

File:HB915 S2 MO 12.PNG

2016-03-11T14:27:24Z

Hb915:

File:HB915 S2 MO 11.PNG

2016-03-11T14:27:10Z

Hb915:

Rep:Mod:HB9151

2016-03-11T14:27:00Z

Hb915: /* Molecular Orbitals */

This is an exploration of molecules and reactions using GaussVeiw in order to understand the importance of computational inorganic chemistry.

Each molecule was draw in GaussVeiw and analysised computationally by solving the Schrödinger equation (EΦ=HΦ) under the Born-Oppenheimer approximation. Firstly the self-consistent field calculation is done for the starting bond lengths and angles giving the electronic wavefunction (Φ) that gives the lowest energy (for the fixed nuclei). The the distance is slightly shortened and the calculation repeated. This is continued until the lowest energy is found and this is the optimized structure.

Once this structure is found the data given by the solutions can be used to explore many properties of the molecule such as the spectrum, molecular orbital and the overall energy of the molecule.

=='''''NH3'''''==
<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 NH3 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 NH3 OPTF POP.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

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=-5.986294D-10
Optimization completed.
-- Stationary point found.

</pre>

There is zero net force and displacement so the optimizstion has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ NH3 Optimised Information
! !! NH3
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -56.55776873
|-
| RMS gradient / au || 0.00000485
|-
| Point Group || C3V
|-
| H-N bond length / A || 1.01798
|-
| H-N-H bond angle / degrees || 105.741
|}

==='''Molecule Vibrations'''===

[[File:HB915 nh3 optf pop displayvibrations.jpg.png|400px|center|left]]

''How many modes do you expect from the 3N-6 rule?''

N represents the number of atoms in the molecule. For NH3 there are 4 molecules therefore;
3x4-6=6

''Which modes are degenerate (ie have the same energy)?''

Modes 2 and 3 and 5 and 6 have the same energy (equal frequency).

''Which modes are "bending" vibrations and which are "bond stretch" vibrations?''

Modes 1-3 are bending and modes 4-6 are stretching. This is clear both from the animation and because bond stretching vibrations are higher in energy.

''Which mode is highly symmetric?''

Mode 4 is highly symmetric with no change in dipole.

''One mode is known as the "umbrella" mode, which one is this?''

Mode 1

''How many bands would you expect to see in an experimental spectrum of gaseous ammonia?''

There are four different vibrational energies suggesting four different bands. However there is only a minimal change in dipole for modes 4-6 so these would not be visible on a spectrum leaving only two bands.

[[File:HB915 nh3 optf pop spectra.jpg.png|500px|center|left]]

==='''Charge Distribution'''===

Nitrogen has an electronegativity of 3.04 which is comparatively larger than hydrogen with 2.2. Therefore you would expect nitrogen to carry the negative charge. This is supported by the values calculated form the Schrödinger equation shown in the image below.

[[File:HB915 nh3 optf pop charge.jpg.png|300px|center|left]]

=='''''N2'''''==
<jmol><jmolApplet>
<title>N2</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 N2 OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 N2 OPTIMISATION.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

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.

</pre>

There is zero net force and displacement so the optimizstion has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ N2 Optimised Information
! !! N2
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -109.52412868
|-
| RMS gradient / au || 0.00000365
|-
| Point Group || D*H
|-
| N-N bond length / A || 1.10550
|-
| N-N bond angle / degrees || N/A
|}

==='''Molecule Vibrations'''===

[[File:HB915 n2 optf pop displayvibrations.jpg|400px|center|left]]

The 3N-5 rule used for linear molecules gives 3x2-5= 1. This is supported by the frequencies found from computational analysis as seen in the image above. This is due to the simple stretching of the bond.

==='''Charge Distribution'''===

Nitrogen has an electronegativity of 3.04. However when both atoms have the same electronegativity the charge is equally distributed across the molecule.

[[File:HB915 n2 optf pop charge.jpg|300px|center|left]]

=='''''H2'''''==
<jmol><jmolApplet>
<title>H2</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 H2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 H2 OPTF POP.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

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.

</pre>

There is zero net force and displacement so the optimizstion has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ H2 Optimised Information
! !! H2
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -1.17853930
|-
| RMS gradient / au || 0.00012170
|-
| Point Group || D*H
|-
| H-H bond length / A || 1.10550
|-
| H-H bond angle / degrees || N/A
|}

==='''Molecule Vibrations'''===

Image of frequencies

[[File:HB915 h2 optf pop displayvibrations.jpg|400px|center|left]]

The 3N-5 rule used for linear molecules gives 3x2-5= 1. This is supported by the frequencies found from computational analysis as seen in the image above. This is due to the simple stretching of the bond.

==='''Charge Distribution'''===

Nitrogen has an electronegativity of 2.2. However when both atoms have the same electronegativity the charge is equally distributed across the molecule.

[[File:HB915 h2 optf pop charge.jpg|300px|center|left]]

=='''''Haber-Bosch Process'''''==

==='''Equation of Reaction'''===

N2 + H2 -> NH3

==='''Energy of Reaction'''===

E(NH3)= -56.55776873 au

2*E(NH3)= 2*-56.55776873 = -113.1155375 au

E(N2)= -109.52412868 au

E(H2)= -1.17853930 au

3*E(H2)= 3*-1.17853930 = -3.5356179 au

ΔE = 2*E(NH3)-[E(N2)+3*E(H2)] = -113.1155375-[-109.52412868+-3.5356179]

ΔE = -0.05579092 au

ΔE = -0.05579092*2625.5 = -146.48 kJ/mol to 2.d.p

==='''Stability of Reactants vs Products'''===

ΔE is negative therefore the Haber process is exothermic and the product (NH3) is lower in energy and more stable than the reactants.

=='''''AlCl4-'''''==
<jmol><jmolApplet>
<title>AlCl4-</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 ALCL4- OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 ALCL4- OPTF POP.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000155 0.001800 YES
RMS Displacement 0.000093 0.001200 YES
Predicted change in Energy=-7.051677D-09
Optimization completed.
-- Stationary point found.

</pre>

There is zero net force and displacement so the optimizstion has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ AlCl4- Optimised Information
! !! AlCl4-
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -2083.61641374
|-
| RMS gradient / au || 0.00001174
|-
| Point Group || TD
|-
| Al-Cl bond length / A || 2.17703
|-
| Cl-Al-Cl bond angle / degrees || 109.471
|}

This is a much higher energy compound than that of N2 and H2.

==='''Molecule Vibrations'''===

[[File:HB915 alcl4- optf pop displayvibrations.jpg]]

The 3N-6 rule gives 3x5-6= 1. This is supported by the frequencies found from computational analysis as seen in the image above. Modes 7-9 are degenerate but in different directions. They are high energy due to the bending character creating a large change in dipole. Modes 3-5 are also degenerate bending vibrations but at a lower energy. Modes 1, 2 and 6 are all symmetrical vibrations that show no change in dipole and are therefore not visible on the spectrum as shown below.

[[File:HB915 alcl4- optf pop spectra.jpg|400px|center|left]]

==='''Charge Distribution'''===

Aluminum has an electronegativity of 1.61 which is comparatively smaller than that of chlorine with 3.16. Therefore you would expect aluminum to carry the positive charge. This is supported by the values calculated form the Schrödinger equation shown in the image below. Also with such a high difference in electronegativity of these two atoms more ionic character will be witnessed.

[[File:HB915 alcl4- optf pop charge.jpg]]

==='''Molecular Orbitals'''===

Images of the molecular orbitals can be visualised by GaussView. They represent each orbital solution to the Schrödinger equation, in other words the Φs, one for each MO energy level.

There are over 90 orbitals found , 41 of which are occupied, and each can be described by the interactions of the atomic orbitals. Five have been explored here.

[[File:HB915 AlCl4- MO 21.PNG|300px]]

When looking at diatomic molecules the MOs are the simple interaction between the AOs. However when looking at larger molecule you talk about the MO fragments. This is the non-bonding Cl 2 p orbitals. They are too different in energy to interact with the Al orbitals so remain non-bonding. There are 12 with similar energies and shapes that can be attributed to the different orientations and phases of each orbital.

[[File:HB915 AlCl4- MO 26.PNG|300px]]
[[File:HB915 AlCl4- MO 30.PNG|300px]]

These two are a pair of MOs created by interactions between the same AOs; the s Cl fragrant and the s Al. However one is an in-phase interaction (left) which produces a filled bonding orbital and the other out of phase interaction (right) which produced an anti-bonding orbital which is also filled. Both are occupied so these are not the orbitals responsible for bonding in this molecule.

[[File:HB915 AlCl4- MO 31.PNG|300px]]
[[File:HB915 AlCl4- MO 43.PNG|300px]]

This is another bonding (left) and non-bonding (right) pair of MOs. These were caused by the interaction of the 3p Cl fragment and the 3p Al. The bonding is filled and the anti-bonding is empty so it is this orbital that is responsible for the bonds in this molecule.

=='''''S2'''''==
<jmol><jmolApplet>
<title>S2</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 S2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 S2 OPTF POP.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000039 0.000300 YES
Maximum Displacement 0.000067 0.001800 YES
RMS Displacement 0.000095 0.001200 YES
Predicted change in Energy=-2.624039D-09
Optimization completed.
-- Stationary point found.

</pre>

There is zero net force and displacement so the optimizstion has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ S2 Optimised Information
! !! S2
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -796.32599779
|-
| RMS gradient / au || 0.00002267
|-
| Point Group || D*H
|-
| S-S bond length / A || 1.92952
|-
| S-S bond angle / degrees || N/A
|}

==='''Molecule Vibrations'''===

[[File:HB915 s2 optf pop displayvibrations.jpg]]

The 3N-5 rule used for linear molecules gives 3x2-5= 1. This is supported by the frequencies found from computational analysis as seen in the image above. This is due to the simple stretching of the bond.

==='''Charge Distribution'''===

Sulfur has an electronegativity of 2.58. However when both atoms have the same electronegativity the charge is equally distributed across the molecule.

[[File:HB915 s2 optf pop charge.jpg]]

==='''Molecular Orbitals'''===

Images of the molecular orbitals can be visualised by GaussView. They represent each orbital solution to the Schrödinger equation, in other words the Φs, one for each MO energy level.

There are over 30 orbitals found , 16 of which are occupied, and each can be described by the interactions of the atomic orbitals. Some examples are given below.

[[File:HB915 AlCl4- MO 11.PNG|300px]]
[[File:HB915 AlCl4- MO 12.PNG|300px]]

3 s orbitals from each Sulfur atom forms a bonding (left), non-bonding (right) pair of orbitals shown above.

[[File:HB915 AlCl4- MO 15.PNG|300px]]
[[File:HB915 AlCl4- MO 16.PNG|300px]]

The 3px from each sulfur interact to form a bonding (left) and an anti-bonding (right). However both are filled so no bond is formed from these MOs.

[[File:HB915 AlCl4- MO 13.PNG|300px]]
[[File:HB915 AlCl4- MO 18.PNG|300px]]

The 3pz from each sulfur interact to form a filled bonding (left) and a unfilled anti-bonding (right). Therefore this results in a sigma bond being formed between the two sulfur atoms.

[[File:HB915 AlCl4- MO 14.PNG|300px]]
[[File:HB915 AlCl4- MO 17.PNG|300px]]

The 3py from each sulfur interact to form a filled bonding (left) and a unfilled anti-bonding (right). Therefore this results in a pi bond being formed above and below the plane of the two sulfur atoms.

Rep:Mod:HB9151

2016-03-11T14:26:02Z

Hb915: /* Molecular Orbitals */

This is an exploration of molecules and reactions using GaussVeiw in order to understand the importance of computational inorganic chemistry.

Each molecule was draw in GaussVeiw and analysised computationally by solving the Schrödinger equation (EΦ=HΦ) under the Born-Oppenheimer approximation. Firstly the self-consistent field calculation is done for the starting bond lengths and angles giving the electronic wavefunction (Φ) that gives the lowest energy (for the fixed nuclei). The the distance is slightly shortened and the calculation repeated. This is continued until the lowest energy is found and this is the optimized structure.

Once this structure is found the data given by the solutions can be used to explore many properties of the molecule such as the spectrum, molecular orbital and the overall energy of the molecule.

=='''''NH3'''''==
<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 NH3 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 NH3 OPTF POP.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

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=-5.986294D-10
Optimization completed.
-- Stationary point found.

</pre>

There is zero net force and displacement so the optimizstion has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ NH3 Optimised Information
! !! NH3
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -56.55776873
|-
| RMS gradient / au || 0.00000485
|-
| Point Group || C3V
|-
| H-N bond length / A || 1.01798
|-
| H-N-H bond angle / degrees || 105.741
|}

==='''Molecule Vibrations'''===

[[File:HB915 nh3 optf pop displayvibrations.jpg.png|400px|center|left]]

''How many modes do you expect from the 3N-6 rule?''

N represents the number of atoms in the molecule. For NH3 there are 4 molecules therefore;
3x4-6=6

''Which modes are degenerate (ie have the same energy)?''

Modes 2 and 3 and 5 and 6 have the same energy (equal frequency).

''Which modes are "bending" vibrations and which are "bond stretch" vibrations?''

Modes 1-3 are bending and modes 4-6 are stretching. This is clear both from the animation and because bond stretching vibrations are higher in energy.

''Which mode is highly symmetric?''

Mode 4 is highly symmetric with no change in dipole.

''One mode is known as the "umbrella" mode, which one is this?''

Mode 1

''How many bands would you expect to see in an experimental spectrum of gaseous ammonia?''

There are four different vibrational energies suggesting four different bands. However there is only a minimal change in dipole for modes 4-6 so these would not be visible on a spectrum leaving only two bands.

[[File:HB915 nh3 optf pop spectra.jpg.png|500px|center|left]]

==='''Charge Distribution'''===

Nitrogen has an electronegativity of 3.04 which is comparatively larger than hydrogen with 2.2. Therefore you would expect nitrogen to carry the negative charge. This is supported by the values calculated form the Schrödinger equation shown in the image below.

[[File:HB915 nh3 optf pop charge.jpg.png|300px|center|left]]

=='''''N2'''''==
<jmol><jmolApplet>
<title>N2</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 N2 OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 N2 OPTIMISATION.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

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.

</pre>

There is zero net force and displacement so the optimizstion has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ N2 Optimised Information
! !! N2
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -109.52412868
|-
| RMS gradient / au || 0.00000365
|-
| Point Group || D*H
|-
| N-N bond length / A || 1.10550
|-
| N-N bond angle / degrees || N/A
|}

==='''Molecule Vibrations'''===

[[File:HB915 n2 optf pop displayvibrations.jpg|400px|center|left]]

The 3N-5 rule used for linear molecules gives 3x2-5= 1. This is supported by the frequencies found from computational analysis as seen in the image above. This is due to the simple stretching of the bond.

==='''Charge Distribution'''===

Nitrogen has an electronegativity of 3.04. However when both atoms have the same electronegativity the charge is equally distributed across the molecule.

[[File:HB915 n2 optf pop charge.jpg|300px|center|left]]

=='''''H2'''''==
<jmol><jmolApplet>
<title>H2</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 H2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 H2 OPTF POP.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

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.

</pre>

There is zero net force and displacement so the optimizstion has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ H2 Optimised Information
! !! H2
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -1.17853930
|-
| RMS gradient / au || 0.00012170
|-
| Point Group || D*H
|-
| H-H bond length / A || 1.10550
|-
| H-H bond angle / degrees || N/A
|}

==='''Molecule Vibrations'''===

Image of frequencies

[[File:HB915 h2 optf pop displayvibrations.jpg|400px|center|left]]

The 3N-5 rule used for linear molecules gives 3x2-5= 1. This is supported by the frequencies found from computational analysis as seen in the image above. This is due to the simple stretching of the bond.

==='''Charge Distribution'''===

Nitrogen has an electronegativity of 2.2. However when both atoms have the same electronegativity the charge is equally distributed across the molecule.

[[File:HB915 h2 optf pop charge.jpg|300px|center|left]]

=='''''Haber-Bosch Process'''''==

==='''Equation of Reaction'''===

N2 + H2 -> NH3

==='''Energy of Reaction'''===

E(NH3)= -56.55776873 au

2*E(NH3)= 2*-56.55776873 = -113.1155375 au

E(N2)= -109.52412868 au

E(H2)= -1.17853930 au

3*E(H2)= 3*-1.17853930 = -3.5356179 au

ΔE = 2*E(NH3)-[E(N2)+3*E(H2)] = -113.1155375-[-109.52412868+-3.5356179]

ΔE = -0.05579092 au

ΔE = -0.05579092*2625.5 = -146.48 kJ/mol to 2.d.p

==='''Stability of Reactants vs Products'''===

ΔE is negative therefore the Haber process is exothermic and the product (NH3) is lower in energy and more stable than the reactants.

=='''''AlCl4-'''''==
<jmol><jmolApplet>
<title>AlCl4-</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 ALCL4- OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 ALCL4- OPTF POP.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000155 0.001800 YES
RMS Displacement 0.000093 0.001200 YES
Predicted change in Energy=-7.051677D-09
Optimization completed.
-- Stationary point found.

</pre>

There is zero net force and displacement so the optimizstion has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ AlCl4- Optimised Information
! !! AlCl4-
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -2083.61641374
|-
| RMS gradient / au || 0.00001174
|-
| Point Group || TD
|-
| Al-Cl bond length / A || 2.17703
|-
| Cl-Al-Cl bond angle / degrees || 109.471
|}

This is a much higher energy compound than that of N2 and H2.

==='''Molecule Vibrations'''===

[[File:HB915 alcl4- optf pop displayvibrations.jpg]]

The 3N-6 rule gives 3x5-6= 1. This is supported by the frequencies found from computational analysis as seen in the image above. Modes 7-9 are degenerate but in different directions. They are high energy due to the bending character creating a large change in dipole. Modes 3-5 are also degenerate bending vibrations but at a lower energy. Modes 1, 2 and 6 are all symmetrical vibrations that show no change in dipole and are therefore not visible on the spectrum as shown below.

[[File:HB915 alcl4- optf pop spectra.jpg|400px|center|left]]

==='''Charge Distribution'''===

Aluminum has an electronegativity of 1.61 which is comparatively smaller than that of chlorine with 3.16. Therefore you would expect aluminum to carry the positive charge. This is supported by the values calculated form the Schrödinger equation shown in the image below. Also with such a high difference in electronegativity of these two atoms more ionic character will be witnessed.

[[File:HB915 alcl4- optf pop charge.jpg]]

==='''Molecular Orbitals'''===

Images of the molecular orbitals can be visualised by GaussView. They represent each orbital solution to the Schrödinger equation, in other words the Φs, one for each MO energy level.

There are over 90 orbitals found , 41 of which are occupied, and each can be described by the interactions of the atomic orbitals. Five have been explored here.

[[File:HB915 AlCl4- MO 21.PNG|300px]]

When looking at diatomic molecules the MOs are the simple interaction between the AOs. However when looking at larger molecule you talk about the MO fragments. This is the non-bonding Cl 2 p orbitals. They are too different in energy to interact with the Al orbitals so remain non-bonding. There are 12 with similar energies and shapes that can be attributed to the different orientations and phases of each orbital.

[[File:HB915 AlCl4- MO 26.PNG|300px]]
[[File:HB915 AlCl4- MO 30.PNG|300px]]

These two are a pair of MOs created by interactions between the same AOs; the s Cl fragrant and the s Al. However one is an in-phase interaction (left) which produces a filled bonding orbital and the other out of phase interaction (right) which produced an anti-bonding orbital which is also filled. Both are occupied so these are not the orbitals responsible for bonding in this molecule.

[[File:HB915 AlCl4- MO 31.PNG|300px]]
[[File:HB915 AlCl4- MO 43.PNG|300px]]

This is another bonding (left) and non-bonding (right) pair of MOs. These were caused by the interaction of the 3p Cl fragment and the 3p Al. The bonding is filled and the anti-bonding is empty so it is this orbital that is responsible for the bonds in this molecule.

=='''''S2'''''==
<jmol><jmolApplet>
<title>S2</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 S2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 S2 OPTF POP.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000039 0.000300 YES
Maximum Displacement 0.000067 0.001800 YES
RMS Displacement 0.000095 0.001200 YES
Predicted change in Energy=-2.624039D-09
Optimization completed.
-- Stationary point found.

</pre>

There is zero net force and displacement so the optimizstion has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ S2 Optimised Information
! !! S2
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -796.32599779
|-
| RMS gradient / au || 0.00002267
|-
| Point Group || D*H
|-
| S-S bond length / A || 1.92952
|-
| S-S bond angle / degrees || N/A
|}

==='''Molecule Vibrations'''===

[[File:HB915 s2 optf pop displayvibrations.jpg]]

The 3N-5 rule used for linear molecules gives 3x2-5= 1. This is supported by the frequencies found from computational analysis as seen in the image above. This is due to the simple stretching of the bond.

==='''Charge Distribution'''===

Sulfur has an electronegativity of 2.58. However when both atoms have the same electronegativity the charge is equally distributed across the molecule.

[[File:HB915 s2 optf pop charge.jpg]]

==='''Molecular Orbitals'''===

Images of the molecular orbitals can be visualised by GaussView. They represent each orbital solution to the Schrödinger equation, in other words the Φs, one for each MO energy level.

There are over 90 orbitals found , 41 of which are occupied, and each can be described by the interactions of the atomic orbitals. Five have been explored here.

[[File:HB915 AlCl4- MO 11.PNG|300px]]
[[File:HB915 AlCl4- MO 12.PNG|300px]]

3 s orbitals from each Sulfur atom forms a bonding (left), non-bonding (right) pair of orbitals shown above.

[[File:HB915 AlCl4- MO 15.PNG|300px]]
[[File:HB915 AlCl4- MO 16.PNG|300px]]

The 3px from each sulfur interact to form a bonding (left) and an anti-bonding (right). However both are filled so no bond is formed from these MOs.

[[File:HB915 AlCl4- MO 13.PNG|300px]]
[[File:HB915 AlCl4- MO 18.PNG|300px]]

The 3pz from each sulfur interact to form a filled bonding (left) and a unfilled anti-bonding (right). Therefore this results in a sigma bond being formed between the two sulfur atoms.

[[File:HB915 AlCl4- MO 14.PNG|300px]]
[[File:HB915 AlCl4- MO 17.PNG|300px]]

The 3py from each sulfur interact to form a filled bonding (left) and a unfilled anti-bonding (right). Therefore this results in a pi bond being formed above and below the plane of the two sulfur atoms.

Rep:Mod:HB9151

2016-03-11T14:04:29Z

Hb915: /* Summary Information */

This is an exploration of molecules and reactions using GaussVeiw in order to understand the importance of computational inorganic chemistry.

Each molecule was draw in GaussVeiw and analysised computationally by solving the Schrödinger equation (EΦ=HΦ) under the Born-Oppenheimer approximation. Firstly the self-consistent field calculation is done for the starting bond lengths and angles giving the electronic wavefunction (Φ) that gives the lowest energy (for the fixed nuclei). The the distance is slightly shortened and the calculation repeated. This is continued until the lowest energy is found and this is the optimized structure.

Once this structure is found the data given by the solutions can be used to explore many properties of the molecule such as the spectrum, molecular orbital and the overall energy of the molecule.

=='''''NH3'''''==
<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 NH3 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 NH3 OPTF POP.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

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=-5.986294D-10
Optimization completed.
-- Stationary point found.

</pre>

There is zero net force and displacement so the optimizstion has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ NH3 Optimised Information
! !! NH3
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -56.55776873
|-
| RMS gradient / au || 0.00000485
|-
| Point Group || C3V
|-
| H-N bond length / A || 1.01798
|-
| H-N-H bond angle / degrees || 105.741
|}

==='''Molecule Vibrations'''===

[[File:HB915 nh3 optf pop displayvibrations.jpg.png|400px|center|left]]

''How many modes do you expect from the 3N-6 rule?''

N represents the number of atoms in the molecule. For NH3 there are 4 molecules therefore;
3x4-6=6

''Which modes are degenerate (ie have the same energy)?''

Modes 2 and 3 and 5 and 6 have the same energy (equal frequency).

''Which modes are "bending" vibrations and which are "bond stretch" vibrations?''

Modes 1-3 are bending and modes 4-6 are stretching. This is clear both from the animation and because bond stretching vibrations are higher in energy.

''Which mode is highly symmetric?''

Mode 4 is highly symmetric with no change in dipole.

''One mode is known as the "umbrella" mode, which one is this?''

Mode 1

''How many bands would you expect to see in an experimental spectrum of gaseous ammonia?''

There are four different vibrational energies suggesting four different bands. However there is only a minimal change in dipole for modes 4-6 so these would not be visible on a spectrum leaving only two bands.

[[File:HB915 nh3 optf pop spectra.jpg.png|500px|center|left]]

==='''Charge Distribution'''===

Nitrogen has an electronegativity of 3.04 which is comparatively larger than hydrogen with 2.2. Therefore you would expect nitrogen to carry the negative charge. This is supported by the values calculated form the Schrödinger equation shown in the image below.

[[File:HB915 nh3 optf pop charge.jpg.png|300px|center|left]]

=='''''N2'''''==
<jmol><jmolApplet>
<title>N2</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 N2 OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 N2 OPTIMISATION.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

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.

</pre>

There is zero net force and displacement so the optimizstion has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ N2 Optimised Information
! !! N2
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -109.52412868
|-
| RMS gradient / au || 0.00000365
|-
| Point Group || D*H
|-
| N-N bond length / A || 1.10550
|-
| N-N bond angle / degrees || N/A
|}

==='''Molecule Vibrations'''===

[[File:HB915 n2 optf pop displayvibrations.jpg|400px|center|left]]

The 3N-5 rule used for linear molecules gives 3x2-5= 1. This is supported by the frequencies found from computational analysis as seen in the image above. This is due to the simple stretching of the bond.

==='''Charge Distribution'''===

Nitrogen has an electronegativity of 3.04. However when both atoms have the same electronegativity the charge is equally distributed across the molecule.

[[File:HB915 n2 optf pop charge.jpg|300px|center|left]]

=='''''H2'''''==
<jmol><jmolApplet>
<title>H2</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 H2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 H2 OPTF POP.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

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.

</pre>

There is zero net force and displacement so the optimizstion has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ H2 Optimised Information
! !! H2
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -1.17853930
|-
| RMS gradient / au || 0.00012170
|-
| Point Group || D*H
|-
| H-H bond length / A || 1.10550
|-
| H-H bond angle / degrees || N/A
|}

==='''Molecule Vibrations'''===

Image of frequencies

[[File:HB915 h2 optf pop displayvibrations.jpg|400px|center|left]]

The 3N-5 rule used for linear molecules gives 3x2-5= 1. This is supported by the frequencies found from computational analysis as seen in the image above. This is due to the simple stretching of the bond.

==='''Charge Distribution'''===

Nitrogen has an electronegativity of 2.2. However when both atoms have the same electronegativity the charge is equally distributed across the molecule.

[[File:HB915 h2 optf pop charge.jpg|300px|center|left]]

=='''''Haber-Bosch Process'''''==

==='''Equation of Reaction'''===

N2 + H2 -> NH3

==='''Energy of Reaction'''===

E(NH3)= -56.55776873 au

2*E(NH3)= 2*-56.55776873 = -113.1155375 au

E(N2)= -109.52412868 au

E(H2)= -1.17853930 au

3*E(H2)= 3*-1.17853930 = -3.5356179 au

ΔE = 2*E(NH3)-[E(N2)+3*E(H2)] = -113.1155375-[-109.52412868+-3.5356179]

ΔE = -0.05579092 au

ΔE = -0.05579092*2625.5 = -146.48 kJ/mol to 2.d.p

==='''Stability of Reactants vs Products'''===

ΔE is negative therefore the Haber process is exothermic and the product (NH3) is lower in energy and more stable than the reactants.

=='''''AlCl4-'''''==
<jmol><jmolApplet>
<title>AlCl4-</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 ALCL4- OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 ALCL4- OPTF POP.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000155 0.001800 YES
RMS Displacement 0.000093 0.001200 YES
Predicted change in Energy=-7.051677D-09
Optimization completed.
-- Stationary point found.

</pre>

There is zero net force and displacement so the optimizstion has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ AlCl4- Optimised Information
! !! AlCl4-
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -2083.61641374
|-
| RMS gradient / au || 0.00001174
|-
| Point Group || TD
|-
| Al-Cl bond length / A || 2.17703
|-
| Cl-Al-Cl bond angle / degrees || 109.471
|}

This is a much higher energy compound than that of N2 and H2.

==='''Molecule Vibrations'''===

[[File:HB915 alcl4- optf pop displayvibrations.jpg]]

The 3N-6 rule gives 3x5-6= 1. This is supported by the frequencies found from computational analysis as seen in the image above. Modes 7-9 are degenerate but in different directions. They are high energy due to the bending character creating a large change in dipole. Modes 3-5 are also degenerate bending vibrations but at a lower energy. Modes 1, 2 and 6 are all symmetrical vibrations that show no change in dipole and are therefore not visible on the spectrum as shown below.

[[File:HB915 alcl4- optf pop spectra.jpg|400px|center|left]]

==='''Charge Distribution'''===

Aluminum has an electronegativity of 1.61 which is comparatively smaller than that of chlorine with 3.16. Therefore you would expect aluminum to carry the positive charge. This is supported by the values calculated form the Schrödinger equation shown in the image below. Also with such a high difference in electronegativity of these two atoms more ionic character will be witnessed.

[[File:HB915 alcl4- optf pop charge.jpg]]

==='''Molecular Orbitals'''===

Images of the molecular orbitals can be visualised by GaussView. They represent each orbital solution to the Schrödinger equation, in other words the Φs, one for each MO energy level.

There are over 90 orbitals found , 41 of which are occupied, and each can be described by the interactions of the atomic orbitals. Five have been explored here.

[[File:HB915 AlCl4- MO 21.PNG|300px]]

When looking at diatomic molecules the MOs are the simple interaction between the AOs. However when looking at larger molecule you talk about the MO fragments. This is the non-bonding Cl 2 p orbitals. They are too different in energy to interact with the Al orbitals so remain non-bonding. There are 12 with similar energies and shapes that can be attributed to the different orientations and phases of each orbital.

[[File:HB915 AlCl4- MO 26.PNG|300px]]
[[File:HB915 AlCl4- MO 30.PNG|300px]]

These two are a pair of MOs created by interactions between the same AOs; the s Cl fragrant and the s Al. However one is an in-phase interaction (left) which produces a filled bonding orbital and the other out of phase interaction (right) which produced an anti-bonding orbital which is also filled. Both are occupied so these are not the orbitals responsible for bonding in this molecule.

[[File:HB915 AlCl4- MO 31.PNG|300px]]
[[File:HB915 AlCl4- MO 43.PNG|300px]]

This is another bonding (left) and non-bonding (right) pair of MOs. These were caused by the interaction of the 3p Cl fragment and the 3p Al. The bonding is filled and the anti-bonding is empty so it is this orbital that is responsible for the bonds in this molecule.

=='''''S2'''''==
<jmol><jmolApplet>
<title>S2</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 S2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 S2 OPTF POP.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000039 0.000300 YES
Maximum Displacement 0.000067 0.001800 YES
RMS Displacement 0.000095 0.001200 YES
Predicted change in Energy=-2.624039D-09
Optimization completed.
-- Stationary point found.

</pre>

There is zero net force and displacement so the optimizstion has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ S2 Optimised Information
! !! S2
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -796.32599779
|-
| RMS gradient / au || 0.00002267
|-
| Point Group || D*H
|-
| S-S bond length / A || 1.92952
|-
| S-S bond angle / degrees || N/A
|}

==='''Molecule Vibrations'''===

[[File:HB915 s2 optf pop displayvibrations.jpg]]

The 3N-5 rule used for linear molecules gives 3x2-5= 1. This is supported by the frequencies found from computational analysis as seen in the image above. This is due to the simple stretching of the bond.

==='''Charge Distribution'''===

Sulfur has an electronegativity of 2.58. However when both atoms have the same electronegativity the charge is equally distributed across the molecule.

[[File:HB915 s2 optf pop charge.jpg]]

==='''Molecular Orbitals'''===

Images of the molecular orbitals can be visualised by GaussView. They represent each orbital solution to the Schrödinger equation, in other words the Φs, one for each MO energy level.

File:HB915 s2 optf pop displayvibrations.jpg

2016-03-11T14:03:47Z

Hb915:

File:HB915 s2 optf pop charge.jpg

2016-03-11T14:03:36Z

Hb915:

File:HB915 S2 OPTF POP.LOG

2016-03-11T14:03:20Z

Hb915:

Rep:Mod:HB9151

2016-03-11T14:00:40Z

Hb915:

This is an exploration of molecules and reactions using GaussVeiw in order to understand the importance of computational inorganic chemistry.

Each molecule was draw in GaussVeiw and analysised computationally by solving the Schrödinger equation (EΦ=HΦ) under the Born-Oppenheimer approximation. Firstly the self-consistent field calculation is done for the starting bond lengths and angles giving the electronic wavefunction (Φ) that gives the lowest energy (for the fixed nuclei). The the distance is slightly shortened and the calculation repeated. This is continued until the lowest energy is found and this is the optimized structure.

Once this structure is found the data given by the solutions can be used to explore many properties of the molecule such as the spectrum, molecular orbital and the overall energy of the molecule.

=='''''NH3'''''==
<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 NH3 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 NH3 OPTF POP.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

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=-5.986294D-10
Optimization completed.
-- Stationary point found.

</pre>

There is zero net force and displacement so the optimizstion has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ NH3 Optimised Information
! !! NH3
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -56.55776873
|-
| RMS gradient / au || 0.00000485
|-
| Point Group || C3V
|-
| H-N bond length / A || 1.01798
|-
| H-N-H bond angle / degrees || 105.741
|}

==='''Molecule Vibrations'''===

[[File:HB915 nh3 optf pop displayvibrations.jpg.png|400px|center|left]]

''How many modes do you expect from the 3N-6 rule?''

N represents the number of atoms in the molecule. For NH3 there are 4 molecules therefore;
3x4-6=6

''Which modes are degenerate (ie have the same energy)?''

Modes 2 and 3 and 5 and 6 have the same energy (equal frequency).

''Which modes are "bending" vibrations and which are "bond stretch" vibrations?''

Modes 1-3 are bending and modes 4-6 are stretching. This is clear both from the animation and because bond stretching vibrations are higher in energy.

''Which mode is highly symmetric?''

Mode 4 is highly symmetric with no change in dipole.

''One mode is known as the "umbrella" mode, which one is this?''

Mode 1

''How many bands would you expect to see in an experimental spectrum of gaseous ammonia?''

There are four different vibrational energies suggesting four different bands. However there is only a minimal change in dipole for modes 4-6 so these would not be visible on a spectrum leaving only two bands.

[[File:HB915 nh3 optf pop spectra.jpg.png|500px|center|left]]

==='''Charge Distribution'''===

Nitrogen has an electronegativity of 3.04 which is comparatively larger than hydrogen with 2.2. Therefore you would expect nitrogen to carry the negative charge. This is supported by the values calculated form the Schrödinger equation shown in the image below.

[[File:HB915 nh3 optf pop charge.jpg.png|300px|center|left]]

=='''''N2'''''==
<jmol><jmolApplet>
<title>N2</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 N2 OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 N2 OPTIMISATION.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

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.

</pre>

There is zero net force and displacement so the optimizstion has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ N2 Optimised Information
! !! N2
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -109.52412868
|-
| RMS gradient / au || 0.00000365
|-
| Point Group || D*H
|-
| N-N bond length / A || 1.10550
|-
| N-N bond angle / degrees || N/A
|}

==='''Molecule Vibrations'''===

[[File:HB915 n2 optf pop displayvibrations.jpg|400px|center|left]]

The 3N-5 rule used for linear molecules gives 3x2-5= 1. This is supported by the frequencies found from computational analysis as seen in the image above. This is due to the simple stretching of the bond.

==='''Charge Distribution'''===

Nitrogen has an electronegativity of 3.04. However when both atoms have the same electronegativity the charge is equally distributed across the molecule.

[[File:HB915 n2 optf pop charge.jpg|300px|center|left]]

=='''''H2'''''==
<jmol><jmolApplet>
<title>H2</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 H2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 H2 OPTF POP.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

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.

</pre>

There is zero net force and displacement so the optimizstion has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ H2 Optimised Information
! !! H2
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -1.17853930
|-
| RMS gradient / au || 0.00012170
|-
| Point Group || D*H
|-
| H-H bond length / A || 1.10550
|-
| H-H bond angle / degrees || N/A
|}

==='''Molecule Vibrations'''===

Image of frequencies

[[File:HB915 h2 optf pop displayvibrations.jpg|400px|center|left]]

The 3N-5 rule used for linear molecules gives 3x2-5= 1. This is supported by the frequencies found from computational analysis as seen in the image above. This is due to the simple stretching of the bond.

==='''Charge Distribution'''===

Nitrogen has an electronegativity of 2.2. However when both atoms have the same electronegativity the charge is equally distributed across the molecule.

[[File:HB915 h2 optf pop charge.jpg|300px|center|left]]

=='''''Haber-Bosch Process'''''==

==='''Equation of Reaction'''===

N2 + H2 -> NH3

==='''Energy of Reaction'''===

E(NH3)= -56.55776873 au

2*E(NH3)= 2*-56.55776873 = -113.1155375 au

E(N2)= -109.52412868 au

E(H2)= -1.17853930 au

3*E(H2)= 3*-1.17853930 = -3.5356179 au

ΔE = 2*E(NH3)-[E(N2)+3*E(H2)] = -113.1155375-[-109.52412868+-3.5356179]

ΔE = -0.05579092 au

ΔE = -0.05579092*2625.5 = -146.48 kJ/mol to 2.d.p

==='''Stability of Reactants vs Products'''===

ΔE is negative therefore the Haber process is exothermic and the product (NH3) is lower in energy and more stable than the reactants.

=='''''AlCl4-'''''==
<jmol><jmolApplet>
<title>AlCl4-</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 ALCL4- OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 ALCL4- OPTF POP.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000155 0.001800 YES
RMS Displacement 0.000093 0.001200 YES
Predicted change in Energy=-7.051677D-09
Optimization completed.
-- Stationary point found.

</pre>

There is zero net force and displacement so the optimizstion has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ AlCl4- Optimised Information
! !! AlCl4-
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -2083.61641374
|-
| RMS gradient / au || 0.00001174
|-
| Point Group || TD
|-
| Al-Cl bond length / A || 2.17703
|-
| Cl-Al-Cl bond angle / degrees || 109.471
|}

This is a much higher energy compound than that of N2 and H2.

==='''Molecule Vibrations'''===

[[File:HB915 alcl4- optf pop displayvibrations.jpg]]

The 3N-6 rule gives 3x5-6= 1. This is supported by the frequencies found from computational analysis as seen in the image above. Modes 7-9 are degenerate but in different directions. They are high energy due to the bending character creating a large change in dipole. Modes 3-5 are also degenerate bending vibrations but at a lower energy. Modes 1, 2 and 6 are all symmetrical vibrations that show no change in dipole and are therefore not visible on the spectrum as shown below.

[[File:HB915 alcl4- optf pop spectra.jpg|400px|center|left]]

==='''Charge Distribution'''===

Aluminum has an electronegativity of 1.61 which is comparatively smaller than that of chlorine with 3.16. Therefore you would expect aluminum to carry the positive charge. This is supported by the values calculated form the Schrödinger equation shown in the image below. Also with such a high difference in electronegativity of these two atoms more ionic character will be witnessed.

[[File:HB915 alcl4- optf pop charge.jpg]]

==='''Molecular Orbitals'''===

Images of the molecular orbitals can be visualised by GaussView. They represent each orbital solution to the Schrödinger equation, in other words the Φs, one for each MO energy level.

There are over 90 orbitals found , 41 of which are occupied, and each can be described by the interactions of the atomic orbitals. Five have been explored here.

[[File:HB915 AlCl4- MO 21.PNG|300px]]

When looking at diatomic molecules the MOs are the simple interaction between the AOs. However when looking at larger molecule you talk about the MO fragments. This is the non-bonding Cl 2 p orbitals. They are too different in energy to interact with the Al orbitals so remain non-bonding. There are 12 with similar energies and shapes that can be attributed to the different orientations and phases of each orbital.

[[File:HB915 AlCl4- MO 26.PNG|300px]]
[[File:HB915 AlCl4- MO 30.PNG|300px]]

These two are a pair of MOs created by interactions between the same AOs; the s Cl fragrant and the s Al. However one is an in-phase interaction (left) which produces a filled bonding orbital and the other out of phase interaction (right) which produced an anti-bonding orbital which is also filled. Both are occupied so these are not the orbitals responsible for bonding in this molecule.

[[File:HB915 AlCl4- MO 31.PNG|300px]]
[[File:HB915 AlCl4- MO 43.PNG|300px]]

This is another bonding (left) and non-bonding (right) pair of MOs. These were caused by the interaction of the 3p Cl fragment and the 3p Al. The bonding is filled and the anti-bonding is empty so it is this orbital that is responsible for the bonds in this molecule.

=='''''S2'''''==
<jmol><jmolApplet>
<title>S2</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 S2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 S2 OPTF POP.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000039 0.000300 YES
Maximum Displacement 0.000067 0.001800 YES
RMS Displacement 0.000095 0.001200 YES
Predicted change in Energy=-2.624039D-09
Optimization completed.
-- Stationary point found.

</pre>

There is zero net force and displacement so the optimizstion has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ S2 Optimised Information
! !! S2
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -796.32599779
|-
| RMS gradient / au || 0.00002267
|-
| Point Group || D*H
|-
| S-S bond length / A || 1.92952
|-
| S-S bond angle / degrees || 109.471
|}

==='''Molecule Vibrations'''===

[[File:HB915 s2 optf pop displayvibrations.jpg]]

The 3N-5 rule used for linear molecules gives 3x2-5= 1. This is supported by the frequencies found from computational analysis as seen in the image above. This is due to the simple stretching of the bond.

==='''Charge Distribution'''===

Sulfur has an electronegativity of 2.58. However when both atoms have the same electronegativity the charge is equally distributed across the molecule.

[[File:HB915 s2 optf pop charge.jpg]]

==='''Molecular Orbitals'''===

Images of the molecular orbitals can be visualised by GaussView. They represent each orbital solution to the Schrödinger equation, in other words the Φs, one for each MO energy level.

Rep:Mod:HB9151

2016-03-11T13:54:41Z

Hb915: /* Molecule Vibrations */

This is an exploration of molecules and reactions using GaussVeiw in order to understand the importance of computational inorganic chemistry.

Each molecule was draw in GaussVeiw and analysised computationally by solving the Schrödinger equation (EΦ=HΦ) under the Born-Oppenheimer approximation. Firstly the self-consistent field calculation is done for the starting bond lengths and angles giving the electronic wavefunction (Φ) that gives the lowest energy (for the fixed nuclei). The the distance is slightly shortened and the calculation repeated. This is continued until the lowest energy is found and this is the optimized structure.

Once this structure is found the data given by the solutions can be used to explore many properties of the molecule such as the spectrum, molecular orbital and the overall energy of the molecule.

=='''''NH3'''''==
<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 NH3 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 NH3 OPTF POP.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

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=-5.986294D-10
Optimization completed.
-- Stationary point found.

</pre>

There is zero net force and displacement so the optimizstion has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ NH3 Optimised Information
! !! NH3
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -56.55776873
|-
| RMS gradient / au || 0.00000485
|-
| Point Group || C3V
|-
| H-N bond length / A || 1.01798
|-
| H-N-H bond angle / degrees || 105.741
|}

==='''Molecule Vibrations'''===

[[File:HB915 nh3 optf pop displayvibrations.jpg.png|400px|center|left]]

''How many modes do you expect from the 3N-6 rule?''

N represents the number of atoms in the molecule. For NH3 there are 4 molecules therefore;
3x4-6=6

''Which modes are degenerate (ie have the same energy)?''

Modes 2 and 3 and 5 and 6 have the same energy (equal frequency).

''Which modes are "bending" vibrations and which are "bond stretch" vibrations?''

Modes 1-3 are bending and modes 4-6 are stretching. This is clear both from the animation and because bond stretching vibrations are higher in energy.

''Which mode is highly symmetric?''

Mode 4 is highly symmetric with no change in dipole.

''One mode is known as the "umbrella" mode, which one is this?''

Mode 1

''How many bands would you expect to see in an experimental spectrum of gaseous ammonia?''

There are four different vibrational energies suggesting four different bands. However there is only a minimal change in dipole for modes 4-6 so these would not be visible on a spectrum leaving only two bands.

[[File:HB915 nh3 optf pop spectra.jpg.png|500px|center|left]]

==='''Charge Distribution'''===

Nitrogen has an electronegativity of 3.04 which is comparatively larger than hydrogen with 2.2. Therefore you would expect nitrogen to carry the negative charge. This is supported by the values calculated form the Schrödinger equation shown in the image below.

[[File:HB915 nh3 optf pop charge.jpg.png|300px|center|left]]

=='''''N2'''''==
<jmol><jmolApplet>
<title>N2</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 N2 OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 N2 OPTIMISATION.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

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.

</pre>

There is zero net force and displacement so the optimizstion has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ N2 Optimised Information
! !! N2
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -109.52412868
|-
| RMS gradient / au || 0.00000365
|-
| Point Group || D*H
|-
| N-N bond length / A || 1.10550
|-
| N-N bond angle / degrees || N/A
|}

==='''Molecule Vibrations'''===

[[File:HB915 n2 optf pop displayvibrations.jpg|400px|center|left]]

The 3N-5 rule used for linear molecules gives 3x2-5= 1. This is supported by the frequencies found from computational analysis as seen in the image above. This is due to the simple stretching of the bond.

==='''Charge Distribution'''===

Nitrogen has an electronegativity of 3.04. However when both atoms have the same electronegativity the charge is equally distributed across the molecule.

[[File:HB915 n2 optf pop charge.jpg|300px|center|left]]

=='''''H2'''''==
<jmol><jmolApplet>
<title>H2</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 H2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 H2 OPTF POP.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

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.

</pre>

There is zero net force and displacement so the optimizstion has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ H2 Optimised Information
! !! H2
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -1.17853930
|-
| RMS gradient / au || 0.00012170
|-
| Point Group || D*H
|-
| H-H bond length / A || 1.10550
|-
| H-H bond angle / degrees || N/A
|}

==='''Molecule Vibrations'''===

Image of frequencies

[[File:HB915 h2 optf pop displayvibrations.jpg|400px|center|left]]

The 3N-5 rule used for linear molecules gives 3x2-5= 1. This is supported by the frequencies found from computational analysis as seen in the image above. This is due to the simple stretching of the bond.

==='''Charge Distribution'''===

Nitrogen has an electronegativity of 2.2. However when both atoms have the same electronegativity the charge is equally distributed across the molecule.

[[File:HB915 h2 optf pop charge.jpg|300px|center|left]]

=='''''Haber-Bosch Process'''''==

==='''Equation of Reaction'''===

N2 + H2 -> NH3

==='''Energy of Reaction'''===

E(NH3)= -56.55776873 au

2*E(NH3)= 2*-56.55776873 = -113.1155375 au

E(N2)= -109.52412868 au

E(H2)= -1.17853930 au

3*E(H2)= 3*-1.17853930 = -3.5356179 au

ΔE = 2*E(NH3)-[E(N2)+3*E(H2)] = -113.1155375-[-109.52412868+-3.5356179]

ΔE = -0.05579092 au

ΔE = -0.05579092*2625.5 = -146.48 kJ/mol to 2.d.p

==='''Stability of Reactants vs Products'''===

ΔE is negative therefore the Haber process is exothermic and the product (NH3) is lower in energy and more stable than the reactants.

=='''''AlCl4-'''''==
<jmol><jmolApplet>
<title>AlCl4-</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 ALCL4- OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 ALCL4- OPTF POP.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000155 0.001800 YES
RMS Displacement 0.000093 0.001200 YES
Predicted change in Energy=-7.051677D-09
Optimization completed.
-- Stationary point found.

</pre>

There is zero net force and displacement so the optimizstion has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ AlCl4- Optimised Information
! !! AlCl4-
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -2083.61641374
|-
| RMS gradient / au || 0.00001174
|-
| Point Group || TD
|-
| Al-Cl bond length / A || 2.17703
|-
| Cl-Al-Cl bond angle / degrees || 109.471
|}

This is a much higher energy compound than that of N2 and H2.

==='''Molecule Vibrations'''===

[[File:HB915 alcl4- optf pop displayvibrations.jpg]]

The 3N-6 rule gives 3x5-6= 1. This is supported by the frequencies found from computational analysis as seen in the image above. Modes 7-9 are degenerate but in different directions. They are high energy due to the bending character creating a large change in dipole. Modes 3-5 are also degenerate bending vibrations but at a lower energy. Modes 1, 2 and 6 are all symmetrical vibrations that show no change in dipole and are therefore not visible on the spectrum as shown below.

[[File:HB915 alcl4- optf pop spectra.jpg|400px|center|left]]

==='''Charge Distribution'''===

Aluminum has an electronegativity of 1.61 which is comparatively smaller than that of chlorine with 3.16. Therefore you would expect aluminum to carry the positive charge. This is supported by the values calculated form the Schrödinger equation shown in the image below. Also with such a high difference in electronegativity of these two atoms more ionic character will be witnessed.

[[File:HB915 alcl4- optf pop charge.jpg]]

==='''Molecular Orbitals'''===

Images of the molecular orbitals can be visualised by GaussView. They represent each orbital solution to the Schrödinger equation, in other words the Φs, one for each MO energy level.

There are over 90 orbitals found , 41 of which are occupied, and each can be described by the interactions of the atomic orbitals. Five have been explored here.

[[File:HB915 AlCl4- MO 21.PNG|300px]]

When looking at diatomic molecules the MOs are the simple interaction between the AOs. However when looking at larger molecule you talk about the MO fragments. This is the non-bonding Cl 2 p orbitals. They are too different in energy to interact with the Al orbitals so remain non-bonding. There are 12 with similar energies and shapes that can be attributed to the different orientations and phases of each orbital.

[[File:HB915 AlCl4- MO 26.PNG|300px]]
[[File:HB915 AlCl4- MO 30.PNG|300px]]

These two are a pair of MOs created by interactions between the same AOs; the s Cl fragrant and the s Al. However one is an in-phase interaction (left) which produces a filled bonding orbital and the other out of phase interaction (right) which produced an anti-bonding orbital which is also filled. Both are occupied so these are not the orbitals responsible for bonding in this molecule.

[[File:HB915 AlCl4- MO 31.PNG|300px]]
[[File:HB915 AlCl4- MO 43.PNG|300px]]

This is another bonding (left) and non-bonding (right) pair of MOs. These were caused by the interaction of the 3p Cl fragment and the 3p Al. The bonding is filled and the anti-bonding is empty so it is this orbital that is responsible for the bonds in this molecule.

Rep:Mod:HB9151

2016-03-11T13:49:40Z

Hb915: /* Molecule Vibrations */

This is an exploration of molecules and reactions using GaussVeiw in order to understand the importance of computational inorganic chemistry.

Each molecule was draw in GaussVeiw and analysised computationally by solving the Schrödinger equation (EΦ=HΦ) under the Born-Oppenheimer approximation. Firstly the self-consistent field calculation is done for the starting bond lengths and angles giving the electronic wavefunction (Φ) that gives the lowest energy (for the fixed nuclei). The the distance is slightly shortened and the calculation repeated. This is continued until the lowest energy is found and this is the optimized structure.

Once this structure is found the data given by the solutions can be used to explore many properties of the molecule such as the spectrum, molecular orbital and the overall energy of the molecule.

=='''''NH3'''''==
<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 NH3 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 NH3 OPTF POP.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

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=-5.986294D-10
Optimization completed.
-- Stationary point found.

</pre>

There is zero net force and displacement so the optimizstion has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ NH3 Optimised Information
! !! NH3
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -56.55776873
|-
| RMS gradient / au || 0.00000485
|-
| Point Group || C3V
|-
| H-N bond length / A || 1.01798
|-
| H-N-H bond angle / degrees || 105.741
|}

==='''Molecule Vibrations'''===

[[File:HB915 nh3 optf pop displayvibrations.jpg.png|400px|center|left]]

''How many modes do you expect from the 3N-6 rule?''

N represents the number of atoms in the molecule. For NH3 there are 4 molecules therefore;
3x4-6=6

''Which modes are degenerate (ie have the same energy)?''

Modes 2 and 3 and 5 and 6 have the same energy (equal frequency).

''Which modes are "bending" vibrations and which are "bond stretch" vibrations?''

Modes 1-3 are bending and modes 4-6 are stretching. This is clear both from the animation and because bond stretching vibrations are higher in energy.

''Which mode is highly symmetric?''

Mode 4 is highly symmetric with no change in dipole.

''One mode is known as the "umbrella" mode, which one is this?''

Mode 1

''How many bands would you expect to see in an experimental spectrum of gaseous ammonia?''

There are four different vibrational energies suggesting four different bands. However there is only a minimal change in dipole for modes 4-6 so these would not be visible on a spectrum leaving only two bands.

[[File:HB915 nh3 optf pop spectra.jpg.png|500px|center|left]]

==='''Charge Distribution'''===

Nitrogen has an electronegativity of 3.04 which is comparatively larger than hydrogen with 2.2. Therefore you would expect nitrogen to carry the negative charge. This is supported by the values calculated form the Schrödinger equation shown in the image below.

[[File:HB915 nh3 optf pop charge.jpg.png|300px|center|left]]

=='''''N2'''''==
<jmol><jmolApplet>
<title>N2</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 N2 OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 N2 OPTIMISATION.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

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.

</pre>

There is zero net force and displacement so the optimizstion has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ N2 Optimised Information
! !! N2
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -109.52412868
|-
| RMS gradient / au || 0.00000365
|-
| Point Group || D*H
|-
| N-N bond length / A || 1.10550
|-
| N-N bond angle / degrees || N/A
|}

==='''Molecule Vibrations'''===

[[File:HB915 n2 optf pop displayvibrations.jpg|400px|center|left]]

The 3N-5 rule used for linear molecules gives 3x2-5= 1. This is supported by the frequencies found from computational analysis as seen in the image above. This is due to the simple stretching of the bond.

==='''Charge Distribution'''===

Nitrogen has an electronegativity of 3.04. However when both atoms have the same electronegativity the charge is equally distributed across the molecule.

[[File:HB915 n2 optf pop charge.jpg|300px|center|left]]

=='''''H2'''''==
<jmol><jmolApplet>
<title>H2</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 H2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 H2 OPTF POP.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

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.

</pre>

There is zero net force and displacement so the optimizstion has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ H2 Optimised Information
! !! H2
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -1.17853930
|-
| RMS gradient / au || 0.00012170
|-
| Point Group || D*H
|-
| H-H bond length / A || 1.10550
|-
| H-H bond angle / degrees || N/A
|}

==='''Molecule Vibrations'''===

Image of frequencies

[[File:HB915 h2 optf pop displayvibrations.jpg|400px|center|left]]

The 3N-5 rule used for linear molecules gives 3x2-5= 1. This is supported by the frequencies found from computational analysis as seen in the image above. This is due to the simple stretching of the bond.

==='''Charge Distribution'''===

Nitrogen has an electronegativity of 2.2. However when both atoms have the same electronegativity the charge is equally distributed across the molecule.

[[File:HB915 h2 optf pop charge.jpg|300px|center|left]]

=='''''Haber-Bosch Process'''''==

==='''Equation of Reaction'''===

N2 + H2 -> NH3

==='''Energy of Reaction'''===

E(NH3)= -56.55776873 au

2*E(NH3)= 2*-56.55776873 = -113.1155375 au

E(N2)= -109.52412868 au

E(H2)= -1.17853930 au

3*E(H2)= 3*-1.17853930 = -3.5356179 au

ΔE = 2*E(NH3)-[E(N2)+3*E(H2)] = -113.1155375-[-109.52412868+-3.5356179]

ΔE = -0.05579092 au

ΔE = -0.05579092*2625.5 = -146.48 kJ/mol to 2.d.p

==='''Stability of Reactants vs Products'''===

ΔE is negative therefore the Haber process is exothermic and the product (NH3) is lower in energy and more stable than the reactants.

=='''''AlCl4-'''''==
<jmol><jmolApplet>
<title>AlCl4-</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 ALCL4- OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 ALCL4- OPTF POP.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000155 0.001800 YES
RMS Displacement 0.000093 0.001200 YES
Predicted change in Energy=-7.051677D-09
Optimization completed.
-- Stationary point found.

</pre>

There is zero net force and displacement so the optimizstion has successfully converged and is complete.

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ AlCl4- Optimised Information
! !! AlCl4-
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -2083.61641374
|-
| RMS gradient / au || 0.00001174
|-
| Point Group || TD
|-
| Al-Cl bond length / A || 2.17703
|-
| Cl-Al-Cl bond angle / degrees || 109.471
|}

This is a much higher energy compound than that of N2 and H2.

==='''Molecule Vibrations'''===

[[File:HB915 alcl4- optf pop displayvibrations.jpg]]

Modes 7-9 are degenerate but in different directions. They are high energy due to the bending character creating a large change in dipole. Modes 3-5 are also degenerate bending vibrations but at a lower energy. Modes 1, 2 and 6 are all symmetrical vibrations that show no change in dipole and are therefore not visible on the spectrum as shown below.

[[File:HB915 alcl4- optf pop spectra.jpg|400px|center|left]]

==='''Charge Distribution'''===

Aluminum has an electronegativity of 1.61 which is comparatively smaller than that of chlorine with 3.16. Therefore you would expect aluminum to carry the positive charge. This is supported by the values calculated form the Schrödinger equation shown in the image below. Also with such a high difference in electronegativity of these two atoms more ionic character will be witnessed.

[[File:HB915 alcl4- optf pop charge.jpg]]

==='''Molecular Orbitals'''===

Images of the molecular orbitals can be visualised by GaussView. They represent each orbital solution to the Schrödinger equation, in other words the Φs, one for each MO energy level.

There are over 90 orbitals found , 41 of which are occupied, and each can be described by the interactions of the atomic orbitals. Five have been explored here.

[[File:HB915 AlCl4- MO 21.PNG|300px]]

When looking at diatomic molecules the MOs are the simple interaction between the AOs. However when looking at larger molecule you talk about the MO fragments. This is the non-bonding Cl 2 p orbitals. They are too different in energy to interact with the Al orbitals so remain non-bonding. There are 12 with similar energies and shapes that can be attributed to the different orientations and phases of each orbital.

[[File:HB915 AlCl4- MO 26.PNG|300px]]
[[File:HB915 AlCl4- MO 30.PNG|300px]]

These two are a pair of MOs created by interactions between the same AOs; the s Cl fragrant and the s Al. However one is an in-phase interaction (left) which produces a filled bonding orbital and the other out of phase interaction (right) which produced an anti-bonding orbital which is also filled. Both are occupied so these are not the orbitals responsible for bonding in this molecule.

[[File:HB915 AlCl4- MO 31.PNG|300px]]
[[File:HB915 AlCl4- MO 43.PNG|300px]]

This is another bonding (left) and non-bonding (right) pair of MOs. These were caused by the interaction of the 3p Cl fragment and the 3p Al. The bonding is filled and the anti-bonding is empty so it is this orbital that is responsible for the bonds in this molecule.

Rep:Mod:HB9151

2016-03-11T13:49:16Z

Hb915: /* Molecule Vibrations */

Rep:Mod:HB9151

2016-03-11T13:45:09Z

Hb915: /* Molecule Vibrations */

Rep:Mod:HB9151

2016-03-11T13:42:09Z

Hb915: /* Proof of Structure Convergence */

Rep:Mod:HB9151

2016-03-11T13:41:45Z

Hb915: /* Proof of Structure Convergence */

Rep:Mod:HB9151

2016-03-11T13:41:08Z

Hb915: /* Proof of Structure Convergence */

Rep:Mod:HB9151

2016-03-11T13:40:54Z

Hb915: /* Proof of Structure Convergence */

Rep:Mod:HB9151

2016-03-11T13:38:55Z

Hb915: /* Molecular Orbitals */

Rep:Mod:HB9151

2016-03-11T13:15:31Z

Hb915:

File:HB915 AlCl4- MO 21.PNG

2016-03-10T16:48:13Z

Hb915:

Rep:Mod:HB9151

2016-03-10T16:47:47Z

Hb915: /* Molecular Orbitals */

This is an exploration of molecules and reactions using GaussVeiw in order to understand the importance of computational inorganic chemistry.

=='''''NH3'''''==
<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 NH3 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 NH3 OPTF POP.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

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=-5.986294D-10
Optimization completed.
-- Stationary point found.

</pre>

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ NH3 Optimised Information
! !! NH3
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -56.55776873
|-
| RMS gradient / au || 0.00000485
|-
| Point Group || C3V
|-
| H-N bond length / A || 1.01798
|-
| H-N-H bond angle / degrees || 105.741
|}

==='''Molecule Vibrations'''===

[[File:HB915 nh3 optf pop displayvibrations.jpg.png|400px|center|left]]

''How many modes do you expect from the 3N-6 rule?''

N represents the number of atoms in the molecule. For NH3 there are 4 molecules therefore;
3x4-6=6

''Which modes are degenerate (ie have the same energy)?''

Modes 2 and 3 and 5 and 6 have the same energy (equal frequency).

''Which modes are "bending" vibrations and which are "bond stretch" vibrations?''

Modes 1-3 are bending and modes 4-6 are stretching. This is clear both from the animation and because bond stretching vibrations are higher in energy.

''Which mode is highly symmetric?''

Mode 4 is highly symmetric with no change in dipole.

''One mode is known as the "umbrella" mode, which one is this?''

Mode 1

''How many bands would you expect to see in an experimental spectrum of gaseous ammonia?''

There are four different vibrational energies suggesting four different bands. However there is only a minimal change in dipole for modes 4-6 so these would not be visible on a spectrum leaving only two bands.

[[File:HB915 nh3 optf pop spectra.jpg.png|500px|center|left]]

==='''Charge Distribution'''===

Nitrogen has an electronegativity of 3.04 which is comparatively larger than hydrogen with 2.2. Therefore you would expect nitrogen to carry the negative charge. This is supported by the values calculated form the Schrödinger equation shown in the image below.

[[File:HB915 nh3 optf pop charge.jpg.png|300px|center|left]]

=='''''N2'''''==
<jmol><jmolApplet>
<title>N2</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 N2 OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 N2 OPTIMISATION.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

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.

</pre>

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ N2 Optimised Information
! !! N2
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -109.52412868
|-
| RMS gradient / au || 0.00000365
|-
| Point Group || D*H
|-
| N-N bond length / A || 1.10550
|-
| N-N bond angle / degrees || N/A
|}

==='''Molecule Vibrations'''===

Image of frequencies

[[File:HB915 n2 optf pop displayvibrations.jpg|400px|center|left]]

==='''Charge Distribution'''===

Nitrogen has an electronegativity of 3.04. However when both atoms have the same electronegativity the charge is equally distributed across the molecule.

[[File:HB915 n2 optf pop charge.jpg|300px|center|left]]

=='''''H2'''''==
<jmol><jmolApplet>
<title>H2</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 H2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 H2 OPTF POP.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

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.

</pre>

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ H2 Optimised Information
! !! H2
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -1.17853930
|-
| RMS gradient / au || 0.00012170
|-
| Point Group || D*H
|-
| H-H bond length / A || 1.10550
|-
| H-H bond angle / degrees || N/A
|}

==='''Molecule Vibrations'''===

Image of frequencies

[[File:HB915 h2 optf pop displayvibrations.jpg|400px|center|left]]

==='''Charge Distribution'''===

Nitrogen has an electronegativity of 2.2. However when both atoms have the same electronegativity the charge is equally distributed across the molecule.

[[File:HB915 h2 optf pop charge.jpg|300px|center|left]]

=='''''Haber-Bosch Process'''''==

==='''Equation of Reaction'''===

N2 + H2 -> NH3

==='''Energy of Reaction'''===

E(NH3)= -56.55776873 au

2*E(NH3)= 2*-56.55776873 = -113.1155375 au

E(N2)= -109.52412868 au

E(H2)= -1.17853930 au

3*E(H2)= 3*-1.17853930 = -3.5356179 au

ΔE = 2*E(NH3)-[E(N2)+3*E(H2)] = -113.1155375-[-109.52412868+-3.5356179]

ΔE = -0.05579092 au

ΔE = -0.05579092*2625.5 = -146.48 kJ/mol to 2.d.p

==='''Stability of Reactants vs Products'''===

ΔE is negative therefore the Haber process is exothermic and the product (NH3) is lower in energy and more stable than the reactants.

=='''''AlCl4-'''''==
<jmol><jmolApplet>
<title>AlCl4-</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 ALCL4- OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 ALCL4- OPTF POP.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000155 0.001800 YES
RMS Displacement 0.000093 0.001200 YES
Predicted change in Energy=-7.051677D-09
Optimization completed.
-- Stationary point found.

</pre>

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ AlCl4- Optimised Information
! !! AlCl4-
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -2083.61641374
|-
| RMS gradient / au || 0.00001174
|-
| Point Group || TD
|-
| Al-Cl bond length / A || 2.17703
|-
| Cl-Al-Cl bond angle / degrees || 109.471
|}

This is a much higher energy compound than that of N2 and H2.

==='''Molecule Vibrations'''===

[[File:HB915 alcl4- optf pop displayvibrations.jpg]]

Modes 7-9 are degenerate but in different directions. They are high energy due to the bending character creating a large change in dipole. Modes 3-5 are also degenerate bending vibrations but at a lower energy. Modes 1, 2 and 6 are all symmetrical vibrations that show no change in dipole and are therefore not visible on the spectrum as shown below.

[[File:HB915 alcl4- optf pop spectra.jpg|400px|center|left]]

==='''Charge Distribution'''===

Aluminum has an electronegativity of 1.61 which is comparatively smaller than that of chlorine with 3.16. Therefore you would expect aluminum to carry the positive charge. This is supported by the values calculated form the Schrödinger equation shown in the image below. Also with such a high difference in electronegativity of these two atoms more ionic character will be witnessed.

[[File:HB915 alcl4- optf pop charge.jpg]]

==='''Molecular Orbitals'''===

[[File:HB915 AlCl4- MO 21.PNG|300px]]

[[File:HB915 AlCl4- MO 26.PNG|300px]]
[[File:HB915 AlCl4- MO 30.PNG|300px]]

[[File:HB915 AlCl4- MO 31.PNG|300px]]
[[File:HB915 AlCl4- MO 43.PNG|300px]]

Rep:Mod:HB9151

2016-03-10T16:41:43Z

Hb915: /* Molecular Orbitals */

This is an exploration of molecules and reactions using GaussVeiw in order to understand the importance of computational inorganic chemistry.

=='''''NH3'''''==
<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 NH3 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 NH3 OPTF POP.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

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=-5.986294D-10
Optimization completed.
-- Stationary point found.

</pre>

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ NH3 Optimised Information
! !! NH3
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -56.55776873
|-
| RMS gradient / au || 0.00000485
|-
| Point Group || C3V
|-
| H-N bond length / A || 1.01798
|-
| H-N-H bond angle / degrees || 105.741
|}

==='''Molecule Vibrations'''===

[[File:HB915 nh3 optf pop displayvibrations.jpg.png|400px|center|left]]

''How many modes do you expect from the 3N-6 rule?''

N represents the number of atoms in the molecule. For NH3 there are 4 molecules therefore;
3x4-6=6

''Which modes are degenerate (ie have the same energy)?''

Modes 2 and 3 and 5 and 6 have the same energy (equal frequency).

''Which modes are "bending" vibrations and which are "bond stretch" vibrations?''

Modes 1-3 are bending and modes 4-6 are stretching. This is clear both from the animation and because bond stretching vibrations are higher in energy.

''Which mode is highly symmetric?''

Mode 4 is highly symmetric with no change in dipole.

''One mode is known as the "umbrella" mode, which one is this?''

Mode 1

''How many bands would you expect to see in an experimental spectrum of gaseous ammonia?''

There are four different vibrational energies suggesting four different bands. However there is only a minimal change in dipole for modes 4-6 so these would not be visible on a spectrum leaving only two bands.

[[File:HB915 nh3 optf pop spectra.jpg.png|500px|center|left]]

==='''Charge Distribution'''===

Nitrogen has an electronegativity of 3.04 which is comparatively larger than hydrogen with 2.2. Therefore you would expect nitrogen to carry the negative charge. This is supported by the values calculated form the Schrödinger equation shown in the image below.

[[File:HB915 nh3 optf pop charge.jpg.png|300px|center|left]]

=='''''N2'''''==
<jmol><jmolApplet>
<title>N2</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 N2 OPTIMISATION.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 N2 OPTIMISATION.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

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.

</pre>

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ N2 Optimised Information
! !! N2
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -109.52412868
|-
| RMS gradient / au || 0.00000365
|-
| Point Group || D*H
|-
| N-N bond length / A || 1.10550
|-
| N-N bond angle / degrees || N/A
|}

==='''Molecule Vibrations'''===

Image of frequencies

[[File:HB915 n2 optf pop displayvibrations.jpg|400px|center|left]]

==='''Charge Distribution'''===

Nitrogen has an electronegativity of 3.04. However when both atoms have the same electronegativity the charge is equally distributed across the molecule.

[[File:HB915 n2 optf pop charge.jpg|300px|center|left]]

=='''''H2'''''==
<jmol><jmolApplet>
<title>H2</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 H2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 H2 OPTF POP.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

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.

</pre>

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ H2 Optimised Information
! !! H2
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -1.17853930
|-
| RMS gradient / au || 0.00012170
|-
| Point Group || D*H
|-
| H-H bond length / A || 1.10550
|-
| H-H bond angle / degrees || N/A
|}

==='''Molecule Vibrations'''===

Image of frequencies

[[File:HB915 h2 optf pop displayvibrations.jpg|400px|center|left]]

==='''Charge Distribution'''===

Nitrogen has an electronegativity of 2.2. However when both atoms have the same electronegativity the charge is equally distributed across the molecule.

[[File:HB915 h2 optf pop charge.jpg|300px|center|left]]

=='''''Haber-Bosch Process'''''==

==='''Equation of Reaction'''===

N2 + H2 -> NH3

==='''Energy of Reaction'''===

E(NH3)= -56.55776873 au

2*E(NH3)= 2*-56.55776873 = -113.1155375 au

E(N2)= -109.52412868 au

E(H2)= -1.17853930 au

3*E(H2)= 3*-1.17853930 = -3.5356179 au

ΔE = 2*E(NH3)-[E(N2)+3*E(H2)] = -113.1155375-[-109.52412868+-3.5356179]

ΔE = -0.05579092 au

ΔE = -0.05579092*2625.5 = -146.48 kJ/mol to 2.d.p

==='''Stability of Reactants vs Products'''===

ΔE is negative therefore the Haber process is exothermic and the product (NH3) is lower in energy and more stable than the reactants.

=='''''AlCl4-'''''==
<jmol><jmolApplet>
<title>AlCl4-</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HB915 ALCL4- OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file is liked to [[Media:HB915 ALCL4- OPTF POP.LOG| here]]

==='''Proof of Structure Convergence'''===
<pre>

Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000155 0.001800 YES
RMS Displacement 0.000093 0.001200 YES
Predicted change in Energy=-7.051677D-09
Optimization completed.
-- Stationary point found.

</pre>

==='''Summary Information'''===
{| class="wikitable" border="1"
|+ AlCl4- Optimised Information
! !! AlCl4-
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| E(RB3LYP)/ au || -2083.61641374
|-
| RMS gradient / au || 0.00001174
|-
| Point Group || TD
|-
| Al-Cl bond length / A || 2.17703
|-
| Cl-Al-Cl bond angle / degrees || 109.471
|}

This is a much higher energy compound than that of N2 and H2.

==='''Molecule Vibrations'''===

[[File:HB915 alcl4- optf pop displayvibrations.jpg]]

Modes 7-9 are degenerate but in different directions. They are high energy due to the bending character creating a large change in dipole. Modes 3-5 are also degenerate bending vibrations but at a lower energy. Modes 1, 2 and 6 are all symmetrical vibrations that show no change in dipole and are therefore not visible on the spectrum as shown below.

[[File:HB915 alcl4- optf pop spectra.jpg|400px|center|left]]

==='''Charge Distribution'''===

Aluminum has an electronegativity of 1.61 which is comparatively smaller than that of chlorine with 3.16. Therefore you would expect aluminum to carry the positive charge. This is supported by the values calculated form the Schrödinger equation shown in the image below. Also with such a high difference in electronegativity of these two atoms more ionic character will be witnessed.

[[File:HB915 alcl4- optf pop charge.jpg]]

==='''Molecular Orbitals'''===

[[File:HB915 AlCl4- MO 26.PNG|150px]]
[[File:HB915 AlCl4- MO 30.PNG|150px]]

[[File:HB915 AlCl4- MO 31.PNG|150px]]
[[File:HB915 AlCl4- MO 43.PNG|150px]]

File:HB915 AlCl4- MO 43.PNG

2016-03-10T16:40:57Z

Hb915:

File:HB915 AlCl4- MO 31.PNG

2016-03-10T16:40:46Z

Hb915: