ChemWiki - User contributions [en]

Rep:Mod:TBFA2017

2017-03-17T15:42:33Z

Tm1016: /* 3rd and 4th Molecular Orbitals: the 2σg orbitals */

== Molecular Modelling using Gaussian Software ==

Using Gaussview molecules of ammonia, hydrogen and nitrogen were built, optimised and their physical properties were studied.

=== NH3 Optimisation ===

Ammonia has the molecular formula of NH3 and is formed from the reaction between gaseous nitrogen, N2 and hydrogen, H2 in a process known as the Haber Bosch process. The equation for this reaction is:

N2 + 3 H2 → 2 NH3

A molecule of ammonia, NH3 was modelled using Gaussian software. the point group of the molecule was set to C3v. The molecule was then optimised with the calculation method set to RB3LYP and a basis set of 6-31G(d,p). The RMS gradient norm of the optimised product was 0.00000485 a.u. The final energy [E(RB3LYP)] of the ammonia molecule was -56.55776873 atomic units (a.u.). The molecule consists of 1 nitrogen atom covalently bonded to 3 separate hydrogen atoms. The nitrogen to hydrogen bonds are all single bonds with a bond length of 1.01798 angstroms. From the use of gaussian the bond angle of the H-N-H bond in ammonia was determined to be 106.7°C. Ammonia has a triangular planar shape with 3 bonding pairs and 1 lone pair of electrons around the central nitrogen atom. The lone pair of electrons repel more than than the bonding pairs which reduces the bond angle to 106.7°C.

The item table below is taken from the .*log file of the gaussian calculations for optimisation and from it we can see that the forces are all converged. The full optimisation file is liked to [[Media:TMACKIN NH3 OPTF POP.LOG| here]]

<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
</pre>

Below shows a jmol model of the molecule of ammonia built on gaussian:
<jmol><jmolApplet>
<title>Optimization of NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>TMACKIN NH3 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibration Analysis ===

[[File:Tmackin display vibrations optimised nh3.PNG]]

By looking at the second derivative of the potential energy curve for ammonia (ie the curvature of the graph) we can determine the frequencies of the different modes of vibrations of the ammonia molecule.
From the 3N-6 rule, we can expect there to be 6 modes of vibrations. Gaussian confirmed this by giving 6 frequencies of vibrations which are shown in the image above. Modes 2 and 3 have the same frequency of 1693.95 s-1 and modes 5 and 6 also have the same frequency of 3589.82 s-1. Since frequency is proportional to energy, the pairs of modes must also have the same energy. Thus these modes are degenerate. Of the 6 modes, modes 1,2 and 3 are bending vibrations i.e the vibrations cause a change in bond angle. Modes 4, 5 and 6 are examples of bond stretching vibrations which are vibrations which cause the bond length to change. The 4th mode which has a frequency of 3461.29 s-1 is a vibration that causes all the vibrating N-H bonds to stretch out and back in phase with each other and so this mode is highly symmetric.
Mode 1 is a bending vibration and it is known as the umbrella mode.
There are four different frequencies at which the bonds in ammonia vibrate and thus we would expect to see 4 bands in an experimental spectrum of gaseous ammonia, with each band corresponding to one frequency.

=== Charge Analysis ===

Nitrogen is a highly electronegative atom and so can attract the bonding electrons of the N-H bonds towards itself and away from the less electronegative hydrogens. This should result in the nitrogen having a slightly negative charge distribution leaving the electron efficient hydrogens with a slightly positive charge. Using gaussian the charges of the atoms were determined. The nitrogen atom had a charge of -1.125 and on each of the hydrogen atoms the charge was +0.375. These charge distributions are in accordance with our expectations.

== Optimization of N2 ==

Nitrogen, N2 exists as a diatomic molecule with two nitrogen atoms triple bonded covalently to each other. Nitrogen is a linear molecule and thus a bonding angle of 180°C. Below is a Jmol image of a nitrogen molecule:

<jmol><jmolApplet>
<title>Nitrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>TMACKIN N2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

Since it is a linear diatomic nitrogen has D∞ symmetry. the bond length of the triple bond in the nitrogen molecule is 1.10550 angstroms. A molecule of nitrogen was built and optimised with the calculation method set to RB3LYP and a basis set of 6-31G(d,p). The RMS gradient norm of the optimised product was 0.00000060 a.u. The final energy [E(RB3LYP)] of the nitrogen molecule was -109.52412868 atomic units (a.u.).

Below is the item table taken from the full optimisation file which is linked [[Media:TMACKIN N2 OPTF POP.LOG| here]]. The forces are all converged and so optimisation is complete and correct.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000000 0.001800 YES
RMS Displacement 0.000000 0.001200 YES
</pre>

=== Vibration Analysis ===
[[File:Tmackin display vibrations for optimized n2.PNG]]

Nitrogen is diatomic and thus the 3N-6 rule is adapted to 3N-5. Using this rule we can expect nitrogen to have one vibration mode. The frequency of this mode is shown in the image above. This mode is a stretching vibration. The triple bond of the nitrogen molecule stretches and shortens at a frequency of 2457.33 s-1.

=== Charge Analysis ===

Both the nitrogen atoms have zero charge due to the fact that they both have the same electronegativity and so attract the bonding electrons to an equal degree.

== Optimization of Hydrogen molecule ==

Hydrogen is a diatomic molecule that consists of two hydrogen atoms covalently bonded to each other. Below is a jmol image of a hydrogen molecule:
<jmol><jmolApplet>
<title>Hydrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>TMACKIN H2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The bond between the two hydrogens is a single bond with a length of 0.74279 angstroms. the hydrogen molecule is a linear molecule and thus has a bonding angle of 180°C and has a D∞H symmetry. A molecule of hydrogen was built and optimised with the calculation method set to RB3LYP and a basis set of 6-31G(d,p). The RMS gradient norm of the optimised product was 0.00000017 a.u. The final energy [E(RB3LYP)] of the hydrogen molecule was -1.17853936 atomic units (a.u.).

In the item table below taken from the optimisation .*log file (the full file is linked [[Media:TMACKIN H2 OPTF POP.LOG| here]] ) and it tell us that the optimisation was complete as all the forces converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000000 0.001800 YES
RMS Displacement 0.000001 0.001200 YES

</pre>

=== Vibration Analysis ===
[[File:Tmackin vibrations h2 molecule.PNG]]

Applying the 3N-5 rule for diatomic molecules to the hydrogen molecules shows that hydrogen should have one vibration mode. The details of this mode of vibration is shown above. This mode is a stretching vibration. The single covalent bond of the hydrogen molecule stretches and shortens at a frequency of 4465.68 s-1.

=== Charge Analysis ===

Both the hydrogen atoms have zero charge due to the fact that they both have the same electronegativity and so attract the bonding electrons to an equal degree.

== Energy of Haber Bosch process ==

The Haber Bosch process uses nitrogen gas, N2), to produce ammonia, NH3), by reacting it with hydrogen gas, H2). The equation for this reaction is shown at the top of the page. From the energies determined after the optimisation of the ammonia, hydrogen and nitrogen molecules we can calculate the energy change in kJ/mol of the Haber Bosch process:

E(NH3)= -56.55776873 a.u.
2*E(NH3)= -113.1155375 a.u.
E(N2)= -109.52412868 a.u.
E(H2)= -1.17853936 a.u.
3*E(H2)= -3.53561808 a.u.

[E(X) means energy of molecule X]

ΔE=2*E(NH3)-[E(N2))+3*E(H2))]= -113.1155375 -(-109.52412868-3.53561808) = -0.05579074 a.u.

Converting the energy from atomic units change, the energy change of this reaction is -146.4785879 kJ/mol, and for the production of one mole of ammonia is -73.2392935 kJ/mol. this is much higher than the literature value for the energy change of this process which is -45.8 kJ/mol.<ref>https://en.wikipedia.org/wiki/Haber_process</ref>
Gaussian is less accurate for this type of calculation.

Both the reactants and the products in this reaction are highly stable. Nitrogen has a very strong triple bond which requires a lot of energy to break and so has a very high stability, higher than that of ammonia molecules which has only triple bonds in its molecule. Therefore nitrogen, a reactant, is more stable than the product.

== Choice of Own Small Molecule: Fluorine ==

Fluorine is a diatomic molecule that consisted of two fluorine atoms covalently bonded together. The bond is a single bond with a length of 1.40281 angstroms. Fluorine is a linear molecule and thus has a bonding angle of 180°C and has a D∞H. A molecule of hydrogen was built and optimised with the calculation method set to RB3LYP and a basis set of 6-31G(d,p). The RMS gradient norm of the optimised product was 0.00007365 a.u. The final energy [E(RB3LYP)] of the nitrogen molecule was -199.49825218 atomic units (a.u.).

Below is the item table taken from the full optimisation file which is linked [[Media:TMACKIN F2 OPTF POP.LOG| here]]. The forces are all converged and so optimisation is complete and correct.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000128 0.000450 YES
RMS Force 0.000128 0.000300 YES
Maximum Displacement 0.000156 0.001800 YES
RMS Displacement 0.000221 0.001200 YES
</pre>

Here is a Jmol image showing a molecule of fluorine:
<jmol><jmolApplet>
<title>Fluorine molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>TMACKIN F2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibration Analysis ===

[[File:Tmackin display vibrations for optimized f2.PNG]]

Fluorine is diatomic and thus the 3N-6 rule is adapted to 3N-5. Using this rule we can expect fluorine to have one vibration mode. The frequency of this mode is shown in the image above. This mode is a stretching vibration. The single covalent bond of the fluorine molecule stretches and shortens at a frequency of 1065.09 s-1.

=== Charge analysis ===
Both the fluorine atoms have zero charge due to the fact that they both have the same electronegativity and so attract the bonding electrons to an equal degree.

== Molecular Orbitals of Fluorine ==
Fluorine atoms have an electronic configuration of 1s22s22p5. When two fluorine atoms combine to form F2 the atomic orbitals in the atoms combine to from molecular orbitals. Below is the molecular orbital diagram of fluorine:

[[File:Tmackinfluorineorbitals.jpg]]

The screenshot below shows the energy values of each energy level:
[[File:Tmackin f2 mo energy values.PNG]]<ref>https://www.liverpool.ac.uk/~ngreeves/ltfdemo/jmol/orbitalsfluorine.htm</ref>

=== Lowest Occupied Orbital ===

[[File:Tmackin f2 isovalue 0.02 mo1.PNG]]

The first two orbitals are the lowest occupied orbitals and they represent the area where the 1s electrons orbit. These molecular orbitals are the 1s atomic orbital of each fluorine atom combined: the second orbital is the anti-bonding combination and the first is the bonding combination.
These orbitals are held very tightly to the nucleus of each atom and thus are not involved during bonding. The energy of the first orbital is -24.79730 a.u. and the second is -24.79732 a.u.

=== 3rd and 4th Molecular Orbitals: the 2σg orbitals ===
[[File:Tmackin f2 mo3.PNG]]
[[File:Tmackin f2 mo4.PNG]]
The energy of the 3rd molecular orbital is -1.33659a.u. and the energy of the 4th molecular orbital is -1.09047 a.u. These energies are different and thus these orbitals are non degenerate. These molecular orbitals are formed from when the 2s valence atomic orbitals of the fluorine atoms are combined. The 3rd molecular orbital is the bonding combination and the 4th is the anti-bonding combination. There is a lot of overlap in the molecular orbitals and so the energy of these orbitals is higher.

File:Tmackin f2 mo3.PNG

2017-03-17T15:40:57Z

Tm1016:

Rep:Mod:TBFA2017

2017-03-17T15:39:05Z

Tm1016: /* Molecular Orbitals of Fluorine */

== Molecular Modelling using Gaussian Software ==

Using Gaussview molecules of ammonia, hydrogen and nitrogen were built, optimised and their physical properties were studied.

=== NH3 Optimisation ===

Ammonia has the molecular formula of NH3 and is formed from the reaction between gaseous nitrogen, N2 and hydrogen, H2 in a process known as the Haber Bosch process. The equation for this reaction is:

N2 + 3 H2 → 2 NH3

A molecule of ammonia, NH3 was modelled using Gaussian software. the point group of the molecule was set to C3v. The molecule was then optimised with the calculation method set to RB3LYP and a basis set of 6-31G(d,p). The RMS gradient norm of the optimised product was 0.00000485 a.u. The final energy [E(RB3LYP)] of the ammonia molecule was -56.55776873 atomic units (a.u.). The molecule consists of 1 nitrogen atom covalently bonded to 3 separate hydrogen atoms. The nitrogen to hydrogen bonds are all single bonds with a bond length of 1.01798 angstroms. From the use of gaussian the bond angle of the H-N-H bond in ammonia was determined to be 106.7°C. Ammonia has a triangular planar shape with 3 bonding pairs and 1 lone pair of electrons around the central nitrogen atom. The lone pair of electrons repel more than than the bonding pairs which reduces the bond angle to 106.7°C.

The item table below is taken from the .*log file of the gaussian calculations for optimisation and from it we can see that the forces are all converged. The full optimisation file is liked to [[Media:TMACKIN NH3 OPTF POP.LOG| here]]

<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
</pre>

Below shows a jmol model of the molecule of ammonia built on gaussian:
<jmol><jmolApplet>
<title>Optimization of NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>TMACKIN NH3 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibration Analysis ===

[[File:Tmackin display vibrations optimised nh3.PNG]]

By looking at the second derivative of the potential energy curve for ammonia (ie the curvature of the graph) we can determine the frequencies of the different modes of vibrations of the ammonia molecule.
From the 3N-6 rule, we can expect there to be 6 modes of vibrations. Gaussian confirmed this by giving 6 frequencies of vibrations which are shown in the image above. Modes 2 and 3 have the same frequency of 1693.95 s-1 and modes 5 and 6 also have the same frequency of 3589.82 s-1. Since frequency is proportional to energy, the pairs of modes must also have the same energy. Thus these modes are degenerate. Of the 6 modes, modes 1,2 and 3 are bending vibrations i.e the vibrations cause a change in bond angle. Modes 4, 5 and 6 are examples of bond stretching vibrations which are vibrations which cause the bond length to change. The 4th mode which has a frequency of 3461.29 s-1 is a vibration that causes all the vibrating N-H bonds to stretch out and back in phase with each other and so this mode is highly symmetric.
Mode 1 is a bending vibration and it is known as the umbrella mode.
There are four different frequencies at which the bonds in ammonia vibrate and thus we would expect to see 4 bands in an experimental spectrum of gaseous ammonia, with each band corresponding to one frequency.

=== Charge Analysis ===

Nitrogen is a highly electronegative atom and so can attract the bonding electrons of the N-H bonds towards itself and away from the less electronegative hydrogens. This should result in the nitrogen having a slightly negative charge distribution leaving the electron efficient hydrogens with a slightly positive charge. Using gaussian the charges of the atoms were determined. The nitrogen atom had a charge of -1.125 and on each of the hydrogen atoms the charge was +0.375. These charge distributions are in accordance with our expectations.

== Optimization of N2 ==

Nitrogen, N2 exists as a diatomic molecule with two nitrogen atoms triple bonded covalently to each other. Nitrogen is a linear molecule and thus a bonding angle of 180°C. Below is a Jmol image of a nitrogen molecule:

<jmol><jmolApplet>
<title>Nitrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>TMACKIN N2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

Since it is a linear diatomic nitrogen has D∞ symmetry. the bond length of the triple bond in the nitrogen molecule is 1.10550 angstroms. A molecule of nitrogen was built and optimised with the calculation method set to RB3LYP and a basis set of 6-31G(d,p). The RMS gradient norm of the optimised product was 0.00000060 a.u. The final energy [E(RB3LYP)] of the nitrogen molecule was -109.52412868 atomic units (a.u.).

Below is the item table taken from the full optimisation file which is linked [[Media:TMACKIN N2 OPTF POP.LOG| here]]. The forces are all converged and so optimisation is complete and correct.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000000 0.001800 YES
RMS Displacement 0.000000 0.001200 YES
</pre>

=== Vibration Analysis ===
[[File:Tmackin display vibrations for optimized n2.PNG]]

Nitrogen is diatomic and thus the 3N-6 rule is adapted to 3N-5. Using this rule we can expect nitrogen to have one vibration mode. The frequency of this mode is shown in the image above. This mode is a stretching vibration. The triple bond of the nitrogen molecule stretches and shortens at a frequency of 2457.33 s-1.

=== Charge Analysis ===

Both the nitrogen atoms have zero charge due to the fact that they both have the same electronegativity and so attract the bonding electrons to an equal degree.

== Optimization of Hydrogen molecule ==

Hydrogen is a diatomic molecule that consists of two hydrogen atoms covalently bonded to each other. Below is a jmol image of a hydrogen molecule:
<jmol><jmolApplet>
<title>Hydrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>TMACKIN H2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The bond between the two hydrogens is a single bond with a length of 0.74279 angstroms. the hydrogen molecule is a linear molecule and thus has a bonding angle of 180°C and has a D∞H symmetry. A molecule of hydrogen was built and optimised with the calculation method set to RB3LYP and a basis set of 6-31G(d,p). The RMS gradient norm of the optimised product was 0.00000017 a.u. The final energy [E(RB3LYP)] of the hydrogen molecule was -1.17853936 atomic units (a.u.).

In the item table below taken from the optimisation .*log file (the full file is linked [[Media:TMACKIN H2 OPTF POP.LOG| here]] ) and it tell us that the optimisation was complete as all the forces converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000000 0.001800 YES
RMS Displacement 0.000001 0.001200 YES

</pre>

=== Vibration Analysis ===
[[File:Tmackin vibrations h2 molecule.PNG]]

Applying the 3N-5 rule for diatomic molecules to the hydrogen molecules shows that hydrogen should have one vibration mode. The details of this mode of vibration is shown above. This mode is a stretching vibration. The single covalent bond of the hydrogen molecule stretches and shortens at a frequency of 4465.68 s-1.

=== Charge Analysis ===

Both the hydrogen atoms have zero charge due to the fact that they both have the same electronegativity and so attract the bonding electrons to an equal degree.

== Energy of Haber Bosch process ==

The Haber Bosch process uses nitrogen gas, N2), to produce ammonia, NH3), by reacting it with hydrogen gas, H2). The equation for this reaction is shown at the top of the page. From the energies determined after the optimisation of the ammonia, hydrogen and nitrogen molecules we can calculate the energy change in kJ/mol of the Haber Bosch process:

E(NH3)= -56.55776873 a.u.
2*E(NH3)= -113.1155375 a.u.
E(N2)= -109.52412868 a.u.
E(H2)= -1.17853936 a.u.
3*E(H2)= -3.53561808 a.u.

[E(X) means energy of molecule X]

ΔE=2*E(NH3)-[E(N2))+3*E(H2))]= -113.1155375 -(-109.52412868-3.53561808) = -0.05579074 a.u.

Converting the energy from atomic units change, the energy change of this reaction is -146.4785879 kJ/mol, and for the production of one mole of ammonia is -73.2392935 kJ/mol. this is much higher than the literature value for the energy change of this process which is -45.8 kJ/mol.<ref>https://en.wikipedia.org/wiki/Haber_process</ref>
Gaussian is less accurate for this type of calculation.

Both the reactants and the products in this reaction are highly stable. Nitrogen has a very strong triple bond which requires a lot of energy to break and so has a very high stability, higher than that of ammonia molecules which has only triple bonds in its molecule. Therefore nitrogen, a reactant, is more stable than the product.

== Choice of Own Small Molecule: Fluorine ==

Fluorine is a diatomic molecule that consisted of two fluorine atoms covalently bonded together. The bond is a single bond with a length of 1.40281 angstroms. Fluorine is a linear molecule and thus has a bonding angle of 180°C and has a D∞H. A molecule of hydrogen was built and optimised with the calculation method set to RB3LYP and a basis set of 6-31G(d,p). The RMS gradient norm of the optimised product was 0.00007365 a.u. The final energy [E(RB3LYP)] of the nitrogen molecule was -199.49825218 atomic units (a.u.).

Below is the item table taken from the full optimisation file which is linked [[Media:TMACKIN F2 OPTF POP.LOG| here]]. The forces are all converged and so optimisation is complete and correct.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000128 0.000450 YES
RMS Force 0.000128 0.000300 YES
Maximum Displacement 0.000156 0.001800 YES
RMS Displacement 0.000221 0.001200 YES
</pre>

Here is a Jmol image showing a molecule of fluorine:
<jmol><jmolApplet>
<title>Fluorine molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>TMACKIN F2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibration Analysis ===

[[File:Tmackin display vibrations for optimized f2.PNG]]

Fluorine is diatomic and thus the 3N-6 rule is adapted to 3N-5. Using this rule we can expect fluorine to have one vibration mode. The frequency of this mode is shown in the image above. This mode is a stretching vibration. The single covalent bond of the fluorine molecule stretches and shortens at a frequency of 1065.09 s-1.

=== Charge analysis ===
Both the fluorine atoms have zero charge due to the fact that they both have the same electronegativity and so attract the bonding electrons to an equal degree.

== Molecular Orbitals of Fluorine ==
Fluorine atoms have an electronic configuration of 1s22s22p5. When two fluorine atoms combine to form F2 the atomic orbitals in the atoms combine to from molecular orbitals. Below is the molecular orbital diagram of fluorine:

[[File:Tmackinfluorineorbitals.jpg]]

The screenshot below shows the energy values of each energy level:
[[File:Tmackin f2 mo energy values.PNG]]<ref>https://www.liverpool.ac.uk/~ngreeves/ltfdemo/jmol/orbitalsfluorine.htm</ref>

=== Lowest Occupied Orbital ===

[[File:Tmackin f2 isovalue 0.02 mo1.PNG]]

The first two orbitals are the lowest occupied orbitals and they represent the area where the 1s electrons orbit. These molecular orbitals are the 1s atomic orbital of each fluorine atom combined: the second orbital is the anti-bonding combination and the first is the bonding combination.
These orbitals are held very tightly to the nucleus of each atom and thus are not involved during bonding. The energy of the first orbital is -24.79730 a.u. and the second is -24.79732 a.u.

=== 3rd and 4th Molecular Orbitals: the 2σg orbitals ===

[[File:Tmackin f2 mo4.PNG]]
The energy of the 3rd molecular orbital is -1.33659a.u. and the energy of the 4th molecular orbital is -1.09047 a.u. These energies are different and thus these orbitals are non degenerate. These molecular orbitals are formed from when the 2s valence atomic orbitals of the fluorine atoms are combined. The 3rd molecular orbital is the bonding combination and the 4th is the anti-bonding combination. There is a lot of overlap in the molecular orbitals which results in

Now look at MOs 3 and 4, this is the combination of the 2s valence AOs, bonding and antibonding. Notice how they overlap more strongly, the bonding overlap is so extensive that all we see is one extended surface. The energy is also much higher, now in the region of -0.5 to -1.12 au. The energy difference between the bonding and antibonding orbitals is much larger because they overlap better. These are valence orbitals and they are very involved in the chemical bonding.

Molecular orbitals 3 and 4 are non degenerate, with energies of -1.33659 au and -1.09047 au respectively. These correspond the bonding and anti-bonding molecular orbitals of the 2s atomic orbital overlaps leading to the 2σg bonding and the 2σu* anti-bonding MOs. These two orbitals are pictured below

File:Tmackin f2 isovalue 0.02 mo1.PNG

2017-03-17T15:15:39Z

Tm1016:

Rep:Mod:TBFA2017

2017-03-17T15:15:06Z

Tm1016: /* Molecular Orbitals */

== Molecular Modelling using Gaussian Software ==

Using Gaussview molecules of ammonia, hydrogen and nitrogen were built, optimised and their physical properties were studied.

=== NH3 Optimisation ===

Ammonia has the molecular formula of NH3 and is formed from the reaction between gaseous nitrogen, N2 and hydrogen, H2 in a process known as the Haber Bosch process. The equation for this reaction is:

N2 + 3 H2 → 2 NH3

A molecule of ammonia, NH3 was modelled using Gaussian software. the point group of the molecule was set to C3v. The molecule was then optimised with the calculation method set to RB3LYP and a basis set of 6-31G(d,p). The RMS gradient norm of the optimised product was 0.00000485 a.u. The final energy [E(RB3LYP)] of the ammonia molecule was -56.55776873 atomic units (a.u.). The molecule consists of 1 nitrogen atom covalently bonded to 3 separate hydrogen atoms. The nitrogen to hydrogen bonds are all single bonds with a bond length of 1.01798 angstroms. From the use of gaussian the bond angle of the H-N-H bond in ammonia was determined to be 106.7°C. Ammonia has a triangular planar shape with 3 bonding pairs and 1 lone pair of electrons around the central nitrogen atom. The lone pair of electrons repel more than than the bonding pairs which reduces the bond angle to 106.7°C.

The item table below is taken from the .*log file of the gaussian calculations for optimisation and from it we can see that the forces are all converged. The full optimisation file is liked to [[Media:TMACKIN NH3 OPTF POP.LOG| here]]

<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
</pre>

Below shows a jmol model of the molecule of ammonia built on gaussian:
<jmol><jmolApplet>
<title>Optimization of NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>TMACKIN NH3 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibration Analysis ===

[[File:Tmackin display vibrations optimised nh3.PNG]]

By looking at the second derivative of the potential energy curve for ammonia (ie the curvature of the graph) we can determine the frequencies of the different modes of vibrations of the ammonia molecule.
From the 3N-6 rule, we can expect there to be 6 modes of vibrations. Gaussian confirmed this by giving 6 frequencies of vibrations which are shown in the image above. Modes 2 and 3 have the same frequency of 1693.95 s-1 and modes 5 and 6 also have the same frequency of 3589.82 s-1. Since frequency is proportional to energy, the pairs of modes must also have the same energy. Thus these modes are degenerate. Of the 6 modes, modes 1,2 and 3 are bending vibrations i.e the vibrations cause a change in bond angle. Modes 4, 5 and 6 are examples of bond stretching vibrations which are vibrations which cause the bond length to change. The 4th mode which has a frequency of 3461.29 s-1 is a vibration that causes all the vibrating N-H bonds to stretch out and back in phase with each other and so this mode is highly symmetric.
Mode 1 is a bending vibration and it is known as the umbrella mode.
There are four different frequencies at which the bonds in ammonia vibrate and thus we would expect to see 4 bands in an experimental spectrum of gaseous ammonia, with each band corresponding to one frequency.

=== Charge Analysis ===

Nitrogen is a highly electronegative atom and so can attract the bonding electrons of the N-H bonds towards itself and away from the less electronegative hydrogens. This should result in the nitrogen having a slightly negative charge distribution leaving the electron efficient hydrogens with a slightly positive charge. Using gaussian the charges of the atoms were determined. The nitrogen atom had a charge of -1.125 and on each of the hydrogen atoms the charge was +0.375. These charge distributions are in accordance with our expectations.

== Optimization of N2 ==

Nitrogen, N2 exists as a diatomic molecule with two nitrogen atoms triple bonded covalently to each other. Nitrogen is a linear molecule and thus a bonding angle of 180°C. Below is a Jmol image of a nitrogen molecule:

<jmol><jmolApplet>
<title>Nitrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>TMACKIN N2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

Since it is a linear diatomic nitrogen has D∞ symmetry. the bond length of the triple bond in the nitrogen molecule is 1.10550 angstroms. A molecule of nitrogen was built and optimised with the calculation method set to RB3LYP and a basis set of 6-31G(d,p). The RMS gradient norm of the optimised product was 0.00000060 a.u. The final energy [E(RB3LYP)] of the nitrogen molecule was -109.52412868 atomic units (a.u.).

Below is the item table taken from the full optimisation file which is linked [[Media:TMACKIN N2 OPTF POP.LOG| here]]. The forces are all converged and so optimisation is complete and correct.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000000 0.001800 YES
RMS Displacement 0.000000 0.001200 YES
</pre>

=== Vibration Analysis ===
[[File:Tmackin display vibrations for optimized n2.PNG]]

Nitrogen is diatomic and thus the 3N-6 rule is adapted to 3N-5. Using this rule we can expect nitrogen to have one vibration mode. The frequency of this mode is shown in the image above. This mode is a stretching vibration. The triple bond of the nitrogen molecule stretches and shortens at a frequency of 2457.33 s-1.

=== Charge Analysis ===

Both the nitrogen atoms have zero charge due to the fact that they both have the same electronegativity and so attract the bonding electrons to an equal degree.

== Optimization of Hydrogen molecule ==

Hydrogen is a diatomic molecule that consists of two hydrogen atoms covalently bonded to each other. Below is a jmol image of a hydrogen molecule:
<jmol><jmolApplet>
<title>Hydrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>TMACKIN H2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The bond between the two hydrogens is a single bond with a length of 0.74279 angstroms. the hydrogen molecule is a linear molecule and thus has a bonding angle of 180°C and has a D∞H symmetry. A molecule of hydrogen was built and optimised with the calculation method set to RB3LYP and a basis set of 6-31G(d,p). The RMS gradient norm of the optimised product was 0.00000017 a.u. The final energy [E(RB3LYP)] of the hydrogen molecule was -1.17853936 atomic units (a.u.).

In the item table below taken from the optimisation .*log file (the full file is linked [[Media:TMACKIN H2 OPTF POP.LOG| here]] ) and it tell us that the optimisation was complete as all the forces converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000000 0.001800 YES
RMS Displacement 0.000001 0.001200 YES

</pre>

=== Vibration Analysis ===
[[File:Tmackin vibrations h2 molecule.PNG]]

Applying the 3N-5 rule for diatomic molecules to the hydrogen molecules shows that hydrogen should have one vibration mode. The details of this mode of vibration is shown above. This mode is a stretching vibration. The single covalent bond of the hydrogen molecule stretches and shortens at a frequency of 4465.68 s-1.

=== Charge Analysis ===

Both the hydrogen atoms have zero charge due to the fact that they both have the same electronegativity and so attract the bonding electrons to an equal degree.

== Energy of Haber Bosch process ==

The Haber Bosch process uses nitrogen gas, N2), to produce ammonia, NH3), by reacting it with hydrogen gas, H2). The equation for this reaction is shown at the top of the page. From the energies determined after the optimisation of the ammonia, hydrogen and nitrogen molecules we can calculate the energy change in kJ/mol of the Haber Bosch process:

E(NH3)= -56.55776873 a.u.
2*E(NH3)= -113.1155375 a.u.
E(N2)= -109.52412868 a.u.
E(H2)= -1.17853936 a.u.
3*E(H2)= -3.53561808 a.u.

[E(X) means energy of molecule X]

ΔE=2*E(NH3)-[E(N2))+3*E(H2))]= -113.1155375 -(-109.52412868-3.53561808) = -0.05579074 a.u.

Converting the energy from atomic units change, the energy change of this reaction is -146.4785879 kJ/mol, and for the production of one mole of ammonia is -73.2392935 kJ/mol. this is much higher than the literature value for the energy change of this process which is -45.8 kJ/mol.<ref>https://en.wikipedia.org/wiki/Haber_process</ref>
Gaussian is less accurate for this type of calculation.

Both the reactants and the products in this reaction are highly stable. Nitrogen has a very strong triple bond which requires a lot of energy to break and so has a very high stability, higher than that of ammonia molecules which has only triple bonds in its molecule. Therefore nitrogen, a reactant, is more stable than the product.

== Choice of Own Small Molecule: Fluorine ==

Fluorine is a diatomic molecule that consisted of two fluorine atoms covalently bonded together. The bond is a single bond with a length of 1.40281 angstroms. Fluorine is a linear molecule and thus has a bonding angle of 180°C and has a D∞H. A molecule of hydrogen was built and optimised with the calculation method set to RB3LYP and a basis set of 6-31G(d,p). The RMS gradient norm of the optimised product was 0.00007365 a.u. The final energy [E(RB3LYP)] of the nitrogen molecule was -199.49825218 atomic units (a.u.).

Below is the item table taken from the full optimisation file which is linked [[Media:TMACKIN F2 OPTF POP.LOG| here]]. The forces are all converged and so optimisation is complete and correct.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000128 0.000450 YES
RMS Force 0.000128 0.000300 YES
Maximum Displacement 0.000156 0.001800 YES
RMS Displacement 0.000221 0.001200 YES
</pre>

Here is a Jmol image showing a molecule of fluorine:
<jmol><jmolApplet>
<title>Fluorine molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>TMACKIN F2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibration Analysis ===

[[File:Tmackin display vibrations for optimized f2.PNG]]

Fluorine is diatomic and thus the 3N-6 rule is adapted to 3N-5. Using this rule we can expect fluorine to have one vibration mode. The frequency of this mode is shown in the image above. This mode is a stretching vibration. The single covalent bond of the fluorine molecule stretches and shortens at a frequency of 1065.09 s-1.

=== Charge analysis ===
Both the fluorine atoms have zero charge due to the fact that they both have the same electronegativity and so attract the bonding electrons to an equal degree.

== Molecular Orbitals of Fluorine ==
Fluorine atoms have an electronic configuration of 1s22s22p5. When two fluorine atoms combine to form F2 the atomic orbitals in the atoms combine to from molecular orbitals. Fluorine molecules are paramagnetic as all the molecular orbitals are filled. Below is the molecular orbital diagram of fluorine:

[[File:Tmackinfluorineorbitals.jpg]]

The screenshot below shows the energy values of each energy level:
[[File:Tmackin f2 mo energy values.PNG]]

=== Lowest Occupied Orbital ===

=== 2 orbital (4) ===
[[File:Tmackin f2 mo4.PNG]]
=== 6 ===
[[File:Tmackin f2 mo6.PNG]]
=== 8 ===
[[File:Tmackin f2 mo8.PNG]]

File:Tmackin f2 mo8.PNG

2017-03-17T15:13:07Z

Tm1016:

File:Tmackin f2 mo6.PNG

2017-03-17T15:12:50Z

Tm1016:

File:Tmackin f2 mo4.PNG

2017-03-17T15:12:19Z

Tm1016:

File:Tmackinfluorineorbitals.jpg

2017-03-17T15:07:28Z

Tm1016:

File:Tmackin f2 mo energy values.PNG

2017-03-17T14:54:15Z

Tm1016:

Rep:Mod:TBFA2017

2017-03-17T14:50:30Z

Tm1016: /* Choice of Own Small Molecule: Fluorine */

Rep:Mod:TBFA2017

2017-03-17T14:50:13Z

Tm1016: /* optimization of F2 */

== Molecular Modelling using Gaussian Software ==

Using Gaussview molecules of ammonia, hydrogen and nitrogen were built, optimised and their physical properties were studied.

=== NH3 Optimisation ===

Ammonia has the molecular formula of NH3 and is formed from the reaction between gaseous nitrogen, N2 and hydrogen, H2 in a process known as the Haber Bosch process. The equation for this reaction is:

N2 + 3 H2 → 2 NH3

A molecule of ammonia, NH3 was modelled using Gaussian software. the point group of the molecule was set to C3v. The molecule was then optimised with the calculation method set to RB3LYP and a basis set of 6-31G(d,p). The RMS gradient norm of the optimised product was 0.00000485 a.u. The final energy [E(RB3LYP)] of the ammonia molecule was -56.55776873 atomic units (a.u.). The molecule consists of 1 nitrogen atom covalently bonded to 3 separate hydrogen atoms. The nitrogen to hydrogen bonds are all single bonds with a bond length of 1.01798 angstroms. From the use of gaussian the bond angle of the H-N-H bond in ammonia was determined to be 106.7°C. Ammonia has a triangular planar shape with 3 bonding pairs and 1 lone pair of electrons around the central nitrogen atom. The lone pair of electrons repel more than than the bonding pairs which reduces the bond angle to 106.7°C.

The item table below is taken from the .*log file of the gaussian calculations for optimisation and from it we can see that the forces are all converged. The full optimisation file is liked to [[Media:TMACKIN NH3 OPTF POP.LOG| here]]

<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
</pre>

Below shows a jmol model of the molecule of ammonia built on gaussian:
<jmol><jmolApplet>
<title>Optimization of NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>TMACKIN NH3 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibration Analysis ===

[[File:Tmackin display vibrations optimised nh3.PNG]]

By looking at the second derivative of the potential energy curve for ammonia (ie the curvature of the graph) we can determine the frequencies of the different modes of vibrations of the ammonia molecule.
From the 3N-6 rule, we can expect there to be 6 modes of vibrations. Gaussian confirmed this by giving 6 frequencies of vibrations which are shown in the image above. Modes 2 and 3 have the same frequency of 1693.95 s-1 and modes 5 and 6 also have the same frequency of 3589.82 s-1. Since frequency is proportional to energy, the pairs of modes must also have the same energy. Thus these modes are degenerate. Of the 6 modes, modes 1,2 and 3 are bending vibrations i.e the vibrations cause a change in bond angle. Modes 4, 5 and 6 are examples of bond stretching vibrations which are vibrations which cause the bond length to change. The 4th mode which has a frequency of 3461.29 s-1 is a vibration that causes all the vibrating N-H bonds to stretch out and back in phase with each other and so this mode is highly symmetric.
Mode 1 is a bending vibration and it is known as the umbrella mode.
There are four different frequencies at which the bonds in ammonia vibrate and thus we would expect to see 4 bands in an experimental spectrum of gaseous ammonia, with each band corresponding to one frequency.

=== Charge Analysis ===

Nitrogen is a highly electronegative atom and so can attract the bonding electrons of the N-H bonds towards itself and away from the less electronegative hydrogens. This should result in the nitrogen having a slightly negative charge distribution leaving the electron efficient hydrogens with a slightly positive charge. Using gaussian the charges of the atoms were determined. The nitrogen atom had a charge of -1.125 and on each of the hydrogen atoms the charge was +0.375. These charge distributions are in accordance with our expectations.

== Optimization of N2 ==

Nitrogen, N2 exists as a diatomic molecule with two nitrogen atoms triple bonded covalently to each other. Nitrogen is a linear molecule and thus a bonding angle of 180°C. Below is a Jmol image of a nitrogen molecule:

<jmol><jmolApplet>
<title>Nitrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>TMACKIN N2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

Since it is a linear diatomic nitrogen has D∞ symmetry. the bond length of the triple bond in the nitrogen molecule is 1.10550 angstroms. A molecule of nitrogen was built and optimised with the calculation method set to RB3LYP and a basis set of 6-31G(d,p). The RMS gradient norm of the optimised product was 0.00000060 a.u. The final energy [E(RB3LYP)] of the nitrogen molecule was -109.52412868 atomic units (a.u.).

Below is the item table taken from the full optimisation file which is linked [[Media:TMACKIN N2 OPTF POP.LOG| here]]. The forces are all converged and so optimisation is complete and correct.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000000 0.001800 YES
RMS Displacement 0.000000 0.001200 YES
</pre>

=== Vibration Analysis ===
[[File:Tmackin display vibrations for optimized n2.PNG]]

Nitrogen is diatomic and thus the 3N-6 rule is adapted to 3N-5. Using this rule we can expect nitrogen to have one vibration mode. The frequency of this mode is shown in the image above. This mode is a stretching vibration. The triple bond of the nitrogen molecule stretches and shortens at a frequency of 2457.33 s-1.

=== Charge Analysis ===

Both the nitrogen atoms have zero charge due to the fact that they both have the same electronegativity and so attract the bonding electrons to an equal degree.

== Optimization of Hydrogen molecule ==

Hydrogen is a diatomic molecule that consists of two hydrogen atoms covalently bonded to each other. Below is a jmol image of a hydrogen molecule:
<jmol><jmolApplet>
<title>Hydrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>TMACKIN H2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The bond between the two hydrogens is a single bond with a length of 0.74279 angstroms. the hydrogen molecule is a linear molecule and thus has a bonding angle of 180°C and has a D∞H symmetry. A molecule of hydrogen was built and optimised with the calculation method set to RB3LYP and a basis set of 6-31G(d,p). The RMS gradient norm of the optimised product was 0.00000017 a.u. The final energy [E(RB3LYP)] of the hydrogen molecule was -1.17853936 atomic units (a.u.).

In the item table below taken from the optimisation .*log file (the full file is linked [[Media:TMACKIN H2 OPTF POP.LOG| here]] ) and it tell us that the optimisation was complete as all the forces converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000000 0.001800 YES
RMS Displacement 0.000001 0.001200 YES

</pre>

=== Vibration Analysis ===
[[File:Tmackin vibrations h2 molecule.PNG]]

Applying the 3N-5 rule for diatomic molecules to the hydrogen molecules shows that hydrogen should have one vibration mode. The details of this mode of vibration is shown above. This mode is a stretching vibration. The single covalent bond of the hydrogen molecule stretches and shortens at a frequency of 4465.68 s-1.

=== Charge Analysis ===

Both the hydrogen atoms have zero charge due to the fact that they both have the same electronegativity and so attract the bonding electrons to an equal degree.

== Energy of Haber Bosch process ==

The Haber Bosch process uses nitrogen gas, N2), to produce ammonia, NH3), by reacting it with hydrogen gas, H2). The equation for this reaction is shown at the top of the page. From the energies determined after the optimisation of the ammonia, hydrogen and nitrogen molecules we can calculate the energy change in kJ/mol of the Haber Bosch process:

E(NH3)= -56.55776873 a.u.
2*E(NH3)= -113.1155375 a.u.
E(N2)= -109.52412868 a.u.
E(H2)= -1.17853936 a.u.
3*E(H2)= -3.53561808 a.u.

[E(X) means energy of molecule X]

ΔE=2*E(NH3)-[E(N2))+3*E(H2))]= -113.1155375 -(-109.52412868-3.53561808) = -0.05579074 a.u.

Converting the energy from atomic units change, the energy change of this reaction is -146.4785879 kJ/mol, and for the production of one mole of ammonia is -73.2392935 kJ/mol. this is much higher than the literature value for the energy change of this process which is -45.8 kJ/mol.<ref>https://en.wikipedia.org/wiki/Haber_process</ref>
Gaussian is less accurate for this type of calculation.

Both the reactants and the products in this reaction are highly stable. Nitrogen has a very strong triple bond which requires a lot of energy to break and so has a very high stability, higher than that of ammonia molecules which has only triple bonds in its molecule. Therefore nitrogen, a reactant, is more stable than the product.

== Choice of Own Small Molecule: Fluorine ==

Fluorine is a diatomic molecule that consisted of two fluorine atoms covalently bonded together. The bond is a single bond with a length of 1.40281 angstroms. Fluorine is a linear molecule and thus has a bonding angle of 180°C and has a D∞H. A molecule of hydrogen was built and optimised with the calculation method set to RB3LYP and a basis set of 6-31G(d,p). The RMS gradient norm of the optimised product was 0.00007365 a.u. The final energy [E(RB3LYP)] of the nitrogen molecule was -199.49825218 atomic units (a.u.).

Below is the item table taken from the full optimisation file which is linked [[Media:TMACKIN F2 OPTF POP.LOG| here]]. The forces are all converged and so optimisation is complete and correct.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000128 0.000450 YES
RMS Force 0.000128 0.000300 YES
Maximum Displacement 0.000156 0.001800 YES
RMS Displacement 0.000221 0.001200 YES
</pre>

Here is a Jmol image showing a molecule of fluorine:
<jmol><jmolApplet>
<title>Optimization of NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>TMACKIN F2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibration Analysis ===

[[File:Tmackin display vibrations for optimized f2.PNG]]

Fluorine is diatomic and thus the 3N-6 rule is adapted to 3N-5. Using this rule we can expect fluorine to have one vibration mode. The frequency of this mode is shown in the image above. This mode is a stretching vibration. The single covalent bond of the fluorine molecule stretches and shortens at a frequency of 1065.09 s-1.

=== Charge analysis ===
Both the fluorine atoms have zero charge due to the fact that they both have the same electronegativity and so attract the bonding electrons to an equal degree.

=== Molecular Orbitals ===

Rep:Mod:TBFA2017

2017-03-17T14:41:13Z

Tm1016: /* Energy of Haber Bosch process */

== Molecular Modelling using Gaussian Software ==

Using Gaussview molecules of ammonia, hydrogen and nitrogen were built, optimised and their physical properties were studied.

=== NH3 Optimisation ===

Ammonia has the molecular formula of NH3 and is formed from the reaction between gaseous nitrogen, N2 and hydrogen, H2 in a process known as the Haber Bosch process. The equation for this reaction is:

N2 + 3 H2 → 2 NH3

A molecule of ammonia, NH3 was modelled using Gaussian software. the point group of the molecule was set to C3v. The molecule was then optimised with the calculation method set to RB3LYP and a basis set of 6-31G(d,p). The RMS gradient norm of the optimised product was 0.00000485 a.u. The final energy [E(RB3LYP)] of the ammonia molecule was -56.55776873 atomic units (a.u.). The molecule consists of 1 nitrogen atom covalently bonded to 3 separate hydrogen atoms. The nitrogen to hydrogen bonds are all single bonds with a bond length of 1.01798 angstroms. From the use of gaussian the bond angle of the H-N-H bond in ammonia was determined to be 106.7°C. Ammonia has a triangular planar shape with 3 bonding pairs and 1 lone pair of electrons around the central nitrogen atom. The lone pair of electrons repel more than than the bonding pairs which reduces the bond angle to 106.7°C.

The item table below is taken from the .*log file of the gaussian calculations for optimisation and from it we can see that the forces are all converged. The full optimisation file is liked to [[Media:TMACKIN NH3 OPTF POP.LOG| here]]

<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
</pre>

Below shows a jmol model of the molecule of ammonia built on gaussian:
<jmol><jmolApplet>
<title>Optimization of NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>TMACKIN NH3 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibration Analysis ===

[[File:Tmackin display vibrations optimised nh3.PNG]]

By looking at the second derivative of the potential energy curve for ammonia (ie the curvature of the graph) we can determine the frequencies of the different modes of vibrations of the ammonia molecule.
From the 3N-6 rule, we can expect there to be 6 modes of vibrations. Gaussian confirmed this by giving 6 frequencies of vibrations which are shown in the image above. Modes 2 and 3 have the same frequency of 1693.95 s-1 and modes 5 and 6 also have the same frequency of 3589.82 s-1. Since frequency is proportional to energy, the pairs of modes must also have the same energy. Thus these modes are degenerate. Of the 6 modes, modes 1,2 and 3 are bending vibrations i.e the vibrations cause a change in bond angle. Modes 4, 5 and 6 are examples of bond stretching vibrations which are vibrations which cause the bond length to change. The 4th mode which has a frequency of 3461.29 s-1 is a vibration that causes all the vibrating N-H bonds to stretch out and back in phase with each other and so this mode is highly symmetric.
Mode 1 is a bending vibration and it is known as the umbrella mode.
There are four different frequencies at which the bonds in ammonia vibrate and thus we would expect to see 4 bands in an experimental spectrum of gaseous ammonia, with each band corresponding to one frequency.

=== Charge Analysis ===

Nitrogen is a highly electronegative atom and so can attract the bonding electrons of the N-H bonds towards itself and away from the less electronegative hydrogens. This should result in the nitrogen having a slightly negative charge distribution leaving the electron efficient hydrogens with a slightly positive charge. Using gaussian the charges of the atoms were determined. The nitrogen atom had a charge of -1.125 and on each of the hydrogen atoms the charge was +0.375. These charge distributions are in accordance with our expectations.

== Optimization of N2 ==

Nitrogen, N2 exists as a diatomic molecule with two nitrogen atoms triple bonded covalently to each other. Nitrogen is a linear molecule and thus a bonding angle of 180°C. Below is a Jmol image of a nitrogen molecule:

<jmol><jmolApplet>
<title>Nitrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>TMACKIN N2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

Since it is a linear diatomic nitrogen has D∞ symmetry. the bond length of the triple bond in the nitrogen molecule is 1.10550 angstroms. A molecule of nitrogen was built and optimised with the calculation method set to RB3LYP and a basis set of 6-31G(d,p). The RMS gradient norm of the optimised product was 0.00000060 a.u. The final energy [E(RB3LYP)] of the nitrogen molecule was -109.52412868 atomic units (a.u.).

Below is the item table taken from the full optimisation file which is linked [[Media:TMACKIN N2 OPTF POP.LOG| here]]. The forces are all converged and so optimisation is complete and correct.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000000 0.001800 YES
RMS Displacement 0.000000 0.001200 YES
</pre>

=== Vibration Analysis ===
[[File:Tmackin display vibrations for optimized n2.PNG]]

Nitrogen is diatomic and thus the 3N-6 rule is adapted to 3N-5. Using this rule we can expect nitrogen to have one vibration mode. The frequency of this mode is shown in the image above. This mode is a stretching vibration. The triple bond of the nitrogen molecule stretches and shortens at a frequency of 2457.33 s-1.

=== Charge Analysis ===

Both the nitrogen atoms have zero charge due to the fact that they both have the same electronegativity and so attract the bonding electrons to an equal degree.

== Optimization of Hydrogen molecule ==

Hydrogen is a diatomic molecule that consists of two hydrogen atoms covalently bonded to each other. Below is a jmol image of a hydrogen molecule:
<jmol><jmolApplet>
<title>Hydrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>TMACKIN H2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The bond between the two hydrogens is a single bond with a length of 0.74279 angstroms. the hydrogen molecule is a linear molecule and thus has a bonding angle of 180°C and has a D∞H symmetry. A molecule of hydrogen was built and optimised with the calculation method set to RB3LYP and a basis set of 6-31G(d,p). The RMS gradient norm of the optimised product was 0.00000017 a.u. The final energy [E(RB3LYP)] of the hydrogen molecule was -1.17853936 atomic units (a.u.).

In the item table below taken from the optimisation .*log file (the full file is linked [[Media:TMACKIN H2 OPTF POP.LOG| here]] ) and it tell us that the optimisation was complete as all the forces converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000000 0.001800 YES
RMS Displacement 0.000001 0.001200 YES

</pre>

=== Vibration Analysis ===
[[File:Tmackin vibrations h2 molecule.PNG]]

Applying the 3N-5 rule for diatomic molecules to the hydrogen molecules shows that hydrogen should have one vibration mode. The details of this mode of vibration is shown above. This mode is a stretching vibration. The single covalent bond of the hydrogen molecule stretches and shortens at a frequency of 4465.68 s-1.

=== Charge Analysis ===

Both the hydrogen atoms have zero charge due to the fact that they both have the same electronegativity and so attract the bonding electrons to an equal degree.

== Energy of Haber Bosch process ==

The Haber Bosch process uses nitrogen gas, N2), to produce ammonia, NH3), by reacting it with hydrogen gas, H2). The equation for this reaction is shown at the top of the page. From the energies determined after the optimisation of the ammonia, hydrogen and nitrogen molecules we can calculate the energy change in kJ/mol of the Haber Bosch process:

E(NH3)= -56.55776873 a.u.
2*E(NH3)= -113.1155375 a.u.
E(N2)= -109.52412868 a.u.
E(H2)= -1.17853936 a.u.
3*E(H2)= -3.53561808 a.u.

[E(X) means energy of molecule X]

ΔE=2*E(NH3)-[E(N2))+3*E(H2))]= -113.1155375 -(-109.52412868-3.53561808) = -0.05579074 a.u.

Converting the energy from atomic units change, the energy change of this reaction is -146.4785879 kJ/mol, and for the production of one mole of ammonia is -73.2392935 kJ/mol. this is much higher than the literature value for the energy change of this process which is -45.8 kJ/mol.<ref>https://en.wikipedia.org/wiki/Haber_process</ref>
Gaussian is less accurate for this type of calculation.

Both the reactants and the products in this reaction are highly stable. Nitrogen has a very strong triple bond which requires a lot of energy to break and so has a very high stability, higher than that of ammonia molecules which has only triple bonds in its molecule. Therefore nitrogen, a reactant, is more stable than the product.

== optimization of F2 ==

<pre>
Item Value Threshold Converged?
Maximum Force 0.000128 0.000450 YES
RMS Force 0.000128 0.000300 YES
Maximum Displacement 0.000156 0.001800 YES
RMS Displacement 0.000221 0.001200 YES
</pre>

What is the molecule?- fluorine molecule

What is the calculation method? - RB3LYP

What is the basis set? 6-31G(d,p)

What is the final energy E(RB3LYP) in atomic units (au)? -199.49825218 a.u.

What is the RMS gradient? 0.00007365

What is the point group of your molecule? Dinfh

bond angle= 180 (linear)

bond lenght= 1.40281

The optimisation file is liked to [[Media:TMACKIN F2 OPTF POP.LOG| here]]

<jmol><jmolApplet>
<title>Optimization of NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>TMACKIN F2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== vibration analysis ===

[[File:Tmackin display vibrations for optimized f2.PNG]]

how many modes do you expect from the 3N-6 rule? 1

which modes are degenerate (ie have the same energy)?

which modes are "bending" vibrations and which are "bond stretch" vibrations? Stretching

which mode is highly symmetric?

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

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

=== Charge analysis ===
no charge ie both atoms 0.00 charge

=== molecular orbitals ===

Rep:Mod:TBFA2017

2017-03-17T14:40:17Z

Tm1016: /* Energy of Haber Bosch process */

== Molecular Modelling using Gaussian Software ==

Using Gaussview molecules of ammonia, hydrogen and nitrogen were built, optimised and their physical properties were studied.

=== NH3 Optimisation ===

Ammonia has the molecular formula of NH3 and is formed from the reaction between gaseous nitrogen, N2 and hydrogen, H2 in a process known as the Haber Bosch process. The equation for this reaction is:

N2 + 3 H2 → 2 NH3

A molecule of ammonia, NH3 was modelled using Gaussian software. the point group of the molecule was set to C3v. The molecule was then optimised with the calculation method set to RB3LYP and a basis set of 6-31G(d,p). The RMS gradient norm of the optimised product was 0.00000485 a.u. The final energy [E(RB3LYP)] of the ammonia molecule was -56.55776873 atomic units (a.u.). The molecule consists of 1 nitrogen atom covalently bonded to 3 separate hydrogen atoms. The nitrogen to hydrogen bonds are all single bonds with a bond length of 1.01798 angstroms. From the use of gaussian the bond angle of the H-N-H bond in ammonia was determined to be 106.7°C. Ammonia has a triangular planar shape with 3 bonding pairs and 1 lone pair of electrons around the central nitrogen atom. The lone pair of electrons repel more than than the bonding pairs which reduces the bond angle to 106.7°C.

The item table below is taken from the .*log file of the gaussian calculations for optimisation and from it we can see that the forces are all converged. The full optimisation file is liked to [[Media:TMACKIN NH3 OPTF POP.LOG| here]]

<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
</pre>

Below shows a jmol model of the molecule of ammonia built on gaussian:
<jmol><jmolApplet>
<title>Optimization of NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>TMACKIN NH3 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibration Analysis ===

[[File:Tmackin display vibrations optimised nh3.PNG]]

By looking at the second derivative of the potential energy curve for ammonia (ie the curvature of the graph) we can determine the frequencies of the different modes of vibrations of the ammonia molecule.
From the 3N-6 rule, we can expect there to be 6 modes of vibrations. Gaussian confirmed this by giving 6 frequencies of vibrations which are shown in the image above. Modes 2 and 3 have the same frequency of 1693.95 s-1 and modes 5 and 6 also have the same frequency of 3589.82 s-1. Since frequency is proportional to energy, the pairs of modes must also have the same energy. Thus these modes are degenerate. Of the 6 modes, modes 1,2 and 3 are bending vibrations i.e the vibrations cause a change in bond angle. Modes 4, 5 and 6 are examples of bond stretching vibrations which are vibrations which cause the bond length to change. The 4th mode which has a frequency of 3461.29 s-1 is a vibration that causes all the vibrating N-H bonds to stretch out and back in phase with each other and so this mode is highly symmetric.
Mode 1 is a bending vibration and it is known as the umbrella mode.
There are four different frequencies at which the bonds in ammonia vibrate and thus we would expect to see 4 bands in an experimental spectrum of gaseous ammonia, with each band corresponding to one frequency.

=== Charge Analysis ===

Nitrogen is a highly electronegative atom and so can attract the bonding electrons of the N-H bonds towards itself and away from the less electronegative hydrogens. This should result in the nitrogen having a slightly negative charge distribution leaving the electron efficient hydrogens with a slightly positive charge. Using gaussian the charges of the atoms were determined. The nitrogen atom had a charge of -1.125 and on each of the hydrogen atoms the charge was +0.375. These charge distributions are in accordance with our expectations.

== Optimization of N2 ==

Nitrogen, N2 exists as a diatomic molecule with two nitrogen atoms triple bonded covalently to each other. Nitrogen is a linear molecule and thus a bonding angle of 180°C. Below is a Jmol image of a nitrogen molecule:

<jmol><jmolApplet>
<title>Nitrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>TMACKIN N2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

Since it is a linear diatomic nitrogen has D∞ symmetry. the bond length of the triple bond in the nitrogen molecule is 1.10550 angstroms. A molecule of nitrogen was built and optimised with the calculation method set to RB3LYP and a basis set of 6-31G(d,p). The RMS gradient norm of the optimised product was 0.00000060 a.u. The final energy [E(RB3LYP)] of the nitrogen molecule was -109.52412868 atomic units (a.u.).

Below is the item table taken from the full optimisation file which is linked [[Media:TMACKIN N2 OPTF POP.LOG| here]]. The forces are all converged and so optimisation is complete and correct.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000000 0.001800 YES
RMS Displacement 0.000000 0.001200 YES
</pre>

=== Vibration Analysis ===
[[File:Tmackin display vibrations for optimized n2.PNG]]

Nitrogen is diatomic and thus the 3N-6 rule is adapted to 3N-5. Using this rule we can expect nitrogen to have one vibration mode. The frequency of this mode is shown in the image above. This mode is a stretching vibration. The triple bond of the nitrogen molecule stretches and shortens at a frequency of 2457.33 s-1.

=== Charge Analysis ===

Both the nitrogen atoms have zero charge due to the fact that they both have the same electronegativity and so attract the bonding electrons to an equal degree.

== Optimization of Hydrogen molecule ==

Hydrogen is a diatomic molecule that consists of two hydrogen atoms covalently bonded to each other. Below is a jmol image of a hydrogen molecule:
<jmol><jmolApplet>
<title>Hydrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>TMACKIN H2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The bond between the two hydrogens is a single bond with a length of 0.74279 angstroms. the hydrogen molecule is a linear molecule and thus has a bonding angle of 180°C and has a D∞H symmetry. A molecule of hydrogen was built and optimised with the calculation method set to RB3LYP and a basis set of 6-31G(d,p). The RMS gradient norm of the optimised product was 0.00000017 a.u. The final energy [E(RB3LYP)] of the hydrogen molecule was -1.17853936 atomic units (a.u.).

In the item table below taken from the optimisation .*log file (the full file is linked [[Media:TMACKIN H2 OPTF POP.LOG| here]] ) and it tell us that the optimisation was complete as all the forces converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000000 0.001800 YES
RMS Displacement 0.000001 0.001200 YES

</pre>

=== Vibration Analysis ===
[[File:Tmackin vibrations h2 molecule.PNG]]

Applying the 3N-5 rule for diatomic molecules to the hydrogen molecules shows that hydrogen should have one vibration mode. The details of this mode of vibration is shown above. This mode is a stretching vibration. The single covalent bond of the hydrogen molecule stretches and shortens at a frequency of 4465.68 s-1.

=== Charge Analysis ===

Both the hydrogen atoms have zero charge due to the fact that they both have the same electronegativity and so attract the bonding electrons to an equal degree.

== Energy of Haber Bosch process ==

The Haber Bosch process uses nitrogen gas, N2), to produce ammonia, NH3), by reacting it with hydrogen gas, H2). The equation for this reaction is shown at the top of the page. From the energies determined after the optimisation of the ammonia, hydrogen and nitrogen molecules we can calculate the energy change in kJ/mol of the Haber Bosch process:

E(NH3)= -56.55776873 a.u.
2*E(NH3)= -113.1155375 a.u.
E(N2)= -109.52412868 a.u.
E(H2)= -1.17853936 a.u.
3*E(H2)= -3.53561808 a.u.

[E(X) means energy of molecule X]

ΔE=2*E(NH3)-[E(N2))+3*E(H2))]= -113.1155375 -(-109.52412868-3.53561808) = -0.05579074 a.u.

Converting the energy from atomic units change, the energy change of this reaction is -146.4785879 kJ/mol, and for the production of one mole of ammonia is -73.2392935 kJ/mol. this is much higher than the literature value for the energy change of this process which is -45.8 kJ/mol.<ref>https://en.wikipedia.org/wiki/Haber_process</ref>
Gaussian is less accurate for this type of calculation.

Both the reactants and the products in this reaction are highly stable. Nitrogen has a very strong triple bond which requires a lot of energy to break and so has a very high stability, higher than that of ammonia molecules which has only triple bonds in its molecule. Therefore nitrogen, a reactant, is more than the product.

== optimization of F2 ==

<pre>
Item Value Threshold Converged?
Maximum Force 0.000128 0.000450 YES
RMS Force 0.000128 0.000300 YES
Maximum Displacement 0.000156 0.001800 YES
RMS Displacement 0.000221 0.001200 YES
</pre>

What is the molecule?- fluorine molecule

What is the calculation method? - RB3LYP

What is the basis set? 6-31G(d,p)

What is the final energy E(RB3LYP) in atomic units (au)? -199.49825218 a.u.

What is the RMS gradient? 0.00007365

What is the point group of your molecule? Dinfh

bond angle= 180 (linear)

bond lenght= 1.40281

The optimisation file is liked to [[Media:TMACKIN F2 OPTF POP.LOG| here]]

<jmol><jmolApplet>
<title>Optimization of NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>TMACKIN F2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== vibration analysis ===

[[File:Tmackin display vibrations for optimized f2.PNG]]

how many modes do you expect from the 3N-6 rule? 1

which modes are degenerate (ie have the same energy)?

which modes are "bending" vibrations and which are "bond stretch" vibrations? Stretching

which mode is highly symmetric?

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

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

=== Charge analysis ===
no charge ie both atoms 0.00 charge

=== molecular orbitals ===

Rep:Mod:TBFA2017

2017-03-17T14:39:07Z

Tm1016: /* Energy of Haber Bosch process */

== Molecular Modelling using Gaussian Software ==

Using Gaussview molecules of ammonia, hydrogen and nitrogen were built, optimised and their physical properties were studied.

=== NH3 Optimisation ===

Ammonia has the molecular formula of NH3 and is formed from the reaction between gaseous nitrogen, N2 and hydrogen, H2 in a process known as the Haber Bosch process. The equation for this reaction is:

N2 + 3 H2 → 2 NH3

A molecule of ammonia, NH3 was modelled using Gaussian software. the point group of the molecule was set to C3v. The molecule was then optimised with the calculation method set to RB3LYP and a basis set of 6-31G(d,p). The RMS gradient norm of the optimised product was 0.00000485 a.u. The final energy [E(RB3LYP)] of the ammonia molecule was -56.55776873 atomic units (a.u.). The molecule consists of 1 nitrogen atom covalently bonded to 3 separate hydrogen atoms. The nitrogen to hydrogen bonds are all single bonds with a bond length of 1.01798 angstroms. From the use of gaussian the bond angle of the H-N-H bond in ammonia was determined to be 106.7°C. Ammonia has a triangular planar shape with 3 bonding pairs and 1 lone pair of electrons around the central nitrogen atom. The lone pair of electrons repel more than than the bonding pairs which reduces the bond angle to 106.7°C.

The item table below is taken from the .*log file of the gaussian calculations for optimisation and from it we can see that the forces are all converged. The full optimisation file is liked to [[Media:TMACKIN NH3 OPTF POP.LOG| here]]

<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
</pre>

Below shows a jmol model of the molecule of ammonia built on gaussian:
<jmol><jmolApplet>
<title>Optimization of NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>TMACKIN NH3 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibration Analysis ===

[[File:Tmackin display vibrations optimised nh3.PNG]]

By looking at the second derivative of the potential energy curve for ammonia (ie the curvature of the graph) we can determine the frequencies of the different modes of vibrations of the ammonia molecule.
From the 3N-6 rule, we can expect there to be 6 modes of vibrations. Gaussian confirmed this by giving 6 frequencies of vibrations which are shown in the image above. Modes 2 and 3 have the same frequency of 1693.95 s-1 and modes 5 and 6 also have the same frequency of 3589.82 s-1. Since frequency is proportional to energy, the pairs of modes must also have the same energy. Thus these modes are degenerate. Of the 6 modes, modes 1,2 and 3 are bending vibrations i.e the vibrations cause a change in bond angle. Modes 4, 5 and 6 are examples of bond stretching vibrations which are vibrations which cause the bond length to change. The 4th mode which has a frequency of 3461.29 s-1 is a vibration that causes all the vibrating N-H bonds to stretch out and back in phase with each other and so this mode is highly symmetric.
Mode 1 is a bending vibration and it is known as the umbrella mode.
There are four different frequencies at which the bonds in ammonia vibrate and thus we would expect to see 4 bands in an experimental spectrum of gaseous ammonia, with each band corresponding to one frequency.

=== Charge Analysis ===

Nitrogen is a highly electronegative atom and so can attract the bonding electrons of the N-H bonds towards itself and away from the less electronegative hydrogens. This should result in the nitrogen having a slightly negative charge distribution leaving the electron efficient hydrogens with a slightly positive charge. Using gaussian the charges of the atoms were determined. The nitrogen atom had a charge of -1.125 and on each of the hydrogen atoms the charge was +0.375. These charge distributions are in accordance with our expectations.

== Optimization of N2 ==

Nitrogen, N2 exists as a diatomic molecule with two nitrogen atoms triple bonded covalently to each other. Nitrogen is a linear molecule and thus a bonding angle of 180°C. Below is a Jmol image of a nitrogen molecule:

<jmol><jmolApplet>
<title>Nitrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>TMACKIN N2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

Since it is a linear diatomic nitrogen has D∞ symmetry. the bond length of the triple bond in the nitrogen molecule is 1.10550 angstroms. A molecule of nitrogen was built and optimised with the calculation method set to RB3LYP and a basis set of 6-31G(d,p). The RMS gradient norm of the optimised product was 0.00000060 a.u. The final energy [E(RB3LYP)] of the nitrogen molecule was -109.52412868 atomic units (a.u.).

Below is the item table taken from the full optimisation file which is linked [[Media:TMACKIN N2 OPTF POP.LOG| here]]. The forces are all converged and so optimisation is complete and correct.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000000 0.001800 YES
RMS Displacement 0.000000 0.001200 YES
</pre>

=== Vibration Analysis ===
[[File:Tmackin display vibrations for optimized n2.PNG]]

Nitrogen is diatomic and thus the 3N-6 rule is adapted to 3N-5. Using this rule we can expect nitrogen to have one vibration mode. The frequency of this mode is shown in the image above. This mode is a stretching vibration. The triple bond of the nitrogen molecule stretches and shortens at a frequency of 2457.33 s-1.

=== Charge Analysis ===

Both the nitrogen atoms have zero charge due to the fact that they both have the same electronegativity and so attract the bonding electrons to an equal degree.

== Optimization of Hydrogen molecule ==

Hydrogen is a diatomic molecule that consists of two hydrogen atoms covalently bonded to each other. Below is a jmol image of a hydrogen molecule:
<jmol><jmolApplet>
<title>Hydrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>TMACKIN H2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The bond between the two hydrogens is a single bond with a length of 0.74279 angstroms. the hydrogen molecule is a linear molecule and thus has a bonding angle of 180°C and has a D∞H symmetry. A molecule of hydrogen was built and optimised with the calculation method set to RB3LYP and a basis set of 6-31G(d,p). The RMS gradient norm of the optimised product was 0.00000017 a.u. The final energy [E(RB3LYP)] of the hydrogen molecule was -1.17853936 atomic units (a.u.).

In the item table below taken from the optimisation .*log file (the full file is linked [[Media:TMACKIN H2 OPTF POP.LOG| here]] ) and it tell us that the optimisation was complete as all the forces converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000000 0.001800 YES
RMS Displacement 0.000001 0.001200 YES

</pre>

=== Vibration Analysis ===
[[File:Tmackin vibrations h2 molecule.PNG]]

Applying the 3N-5 rule for diatomic molecules to the hydrogen molecules shows that hydrogen should have one vibration mode. The details of this mode of vibration is shown above. This mode is a stretching vibration. The single covalent bond of the hydrogen molecule stretches and shortens at a frequency of 4465.68 s-1.

=== Charge Analysis ===

Both the hydrogen atoms have zero charge due to the fact that they both have the same electronegativity and so attract the bonding electrons to an equal degree.

== Energy of Haber Bosch process ==

The Haber Bosch process uses nitrogen gas, N2), to produce ammonia, NH3), by reacting it with hydrogen gas, H2). The equation for this reaction is shown at the top of the page. From the energies determined after the optimisation of the ammonia, hydrogen and nitrogen molecules we can calculate the energy change in kJ/mol of the Haber Bosch process:

E(NH3)= -56.55776873 a.u.
2*E(NH3)= -113.1155375 a.u.
E(N2)= -109.52412868 a.u.
E(H2)= -1.17853936 a.u.
3*E(H2)= -3.53561808 a.u.

[E(X) means energy of molecule X]

ΔE=2*E(NH3)-[E(N2))+3*E(H2))]= -113.1155375 -(-109.52412868-3.53561808) = -0.05579074 a.u.

Converting the energy from atomic units change, the energy change of this reaction is -146.4785879 kJ/mol, and for the production of one mole of ammonia is -73.2392935 kJ/mol. this is much higher than the literature value for the energy change of this process which is -45.8 kJ/mol.<ref>1</ref><div class="references-small">https://en.wikipedia.org/wiki/Haber_process</div>. Gaussian is less accurate for this type of calculation.

Both the reactants and the products in this reaction are highly stable. Nitrogen has a very strong triple bond which requires a lot of energy to break and so has a very high stability, higher than that of ammonia molecules which has only triple bonds in its molecule. Therefore nitrogen, a reactant, is more than the product.

== optimization of F2 ==

<pre>
Item Value Threshold Converged?
Maximum Force 0.000128 0.000450 YES
RMS Force 0.000128 0.000300 YES
Maximum Displacement 0.000156 0.001800 YES
RMS Displacement 0.000221 0.001200 YES
</pre>

What is the molecule?- fluorine molecule

What is the calculation method? - RB3LYP

What is the basis set? 6-31G(d,p)

What is the final energy E(RB3LYP) in atomic units (au)? -199.49825218 a.u.

What is the RMS gradient? 0.00007365

What is the point group of your molecule? Dinfh

bond angle= 180 (linear)

bond lenght= 1.40281

The optimisation file is liked to [[Media:TMACKIN F2 OPTF POP.LOG| here]]

<jmol><jmolApplet>
<title>Optimization of NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>TMACKIN F2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== vibration analysis ===

[[File:Tmackin display vibrations for optimized f2.PNG]]

how many modes do you expect from the 3N-6 rule? 1

which modes are degenerate (ie have the same energy)?

which modes are "bending" vibrations and which are "bond stretch" vibrations? Stretching

which mode is highly symmetric?

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

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

=== Charge analysis ===
no charge ie both atoms 0.00 charge

=== molecular orbitals ===

Rep:Mod:TBFA2017

2017-03-17T14:16:11Z

Tm1016: /* Optimization of Hydrogen molecule */

== Molecular Modelling using Gaussian Software ==

Using Gaussview molecules of ammonia, hydrogen and nitrogen were built, optimised and their physical properties were studied.

=== NH3 Optimisation ===

Ammonia has the molecular formula of NH3 and is formed from the reaction between gaseous nitrogen, N2 and hydrogen, H2 in a process known as the Haber Bosch process. The equation for this reaction is:

N2 + 3 H2 → 2 NH3

A molecule of ammonia, NH3 was modelled using Gaussian software. the point group of the molecule was set to C3v. The molecule was then optimised with the calculation method set to RB3LYP and a basis set of 6-31G(d,p). The RMS gradient norm of the optimised product was 0.00000485 a.u. The final energy [E(RB3LYP)] of the ammonia molecule was -56.55776873 atomic units (a.u.). The molecule consists of 1 nitrogen atom covalently bonded to 3 separate hydrogen atoms. The nitrogen to hydrogen bonds are all single bonds with a bond length of 1.01798 angstroms. From the use of gaussian the bond angle of the H-N-H bond in ammonia was determined to be 106.7°C. Ammonia has a triangular planar shape with 3 bonding pairs and 1 lone pair of electrons around the central nitrogen atom. The lone pair of electrons repel more than than the bonding pairs which reduces the bond angle to 106.7°C.

The item table below is taken from the .*log file of the gaussian calculations for optimisation and from it we can see that the forces are all converged. The full optimisation file is liked to [[Media:TMACKIN NH3 OPTF POP.LOG| here]]

<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
</pre>

Below shows a jmol model of the molecule of ammonia built on gaussian:
<jmol><jmolApplet>
<title>Optimization of NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>TMACKIN NH3 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibration Analysis ===

[[File:Tmackin display vibrations optimised nh3.PNG]]

By looking at the second derivative of the potential energy curve for ammonia (ie the curvature of the graph) we can determine the frequencies of the different modes of vibrations of the ammonia molecule.
From the 3N-6 rule, we can expect there to be 6 modes of vibrations. Gaussian confirmed this by giving 6 frequencies of vibrations which are shown in the image above. Modes 2 and 3 have the same frequency of 1693.95 s-1 and modes 5 and 6 also have the same frequency of 3589.82 s-1. Since frequency is proportional to energy, the pairs of modes must also have the same energy. Thus these modes are degenerate. Of the 6 modes, modes 1,2 and 3 are bending vibrations i.e the vibrations cause a change in bond angle. Modes 4, 5 and 6 are examples of bond stretching vibrations which are vibrations which cause the bond length to change. The 4th mode which has a frequency of 3461.29 s-1 is a vibration that causes all the vibrating N-H bonds to stretch out and back in phase with each other and so this mode is highly symmetric.
Mode 1 is a bending vibration and it is known as the umbrella mode.
There are four different frequencies at which the bonds in ammonia vibrate and thus we would expect to see 4 bands in an experimental spectrum of gaseous ammonia, with each band corresponding to one frequency.

=== Charge Analysis ===

Nitrogen is a highly electronegative atom and so can attract the bonding electrons of the N-H bonds towards itself and away from the less electronegative hydrogens. This should result in the nitrogen having a slightly negative charge distribution leaving the electron efficient hydrogens with a slightly positive charge. Using gaussian the charges of the atoms were determined. The nitrogen atom had a charge of -1.125 and on each of the hydrogen atoms the charge was +0.375. These charge distributions are in accordance with our expectations.

== Optimization of N2 ==

Nitrogen, N2 exists as a diatomic molecule with two nitrogen atoms triple bonded covalently to each other. Nitrogen is a linear molecule and thus a bonding angle of 180°C. Below is a Jmol image of a nitrogen molecule:

<jmol><jmolApplet>
<title>Nitrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>TMACKIN N2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

Since it is a linear diatomic nitrogen has D∞ symmetry. the bond length of the triple bond in the nitrogen molecule is 1.10550 angstroms. A molecule of nitrogen was built and optimised with the calculation method set to RB3LYP and a basis set of 6-31G(d,p). The RMS gradient norm of the optimised product was 0.00000060 a.u. The final energy [E(RB3LYP)] of the nitrogen molecule was -109.52412868 atomic units (a.u.).

Below is the item table taken from the full optimisation file which is linked [[Media:TMACKIN N2 OPTF POP.LOG| here]]. The forces are all converged and so optimisation is complete and correct.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000000 0.001800 YES
RMS Displacement 0.000000 0.001200 YES
</pre>

=== Vibration Analysis ===
[[File:Tmackin display vibrations for optimized n2.PNG]]

Nitrogen is diatomic and thus the 3N-6 rule is adapted to 3N-5. Using this rule we can expect nitrogen to have one vibration mode. The frequency of this mode is shown in the image above. This mode is a stretching vibration. The triple bond of the nitrogen molecule stretches and shortens at a frequency of 2457.33 s-1.

=== Charge Analysis ===

Both the nitrogen atoms have zero charge due to the fact that they both have the same electronegativity and so attract the bonding electrons to an equal degree.

== Optimization of Hydrogen molecule ==

Hydrogen is a diatomic molecule that consists of two hydrogen atoms covalently bonded to each other. Below is a jmol image of a hydrogen molecule:
<jmol><jmolApplet>
<title>Hydrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>TMACKIN H2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The bond between the two hydrogens is a single bond with a length of 0.74279 angstroms. the hydrogen molecule is a linear molecule and thus has a bonding angle of 180°C and has a D∞H symmetry. A molecule of hydrogen was built and optimised with the calculation method set to RB3LYP and a basis set of 6-31G(d,p). The RMS gradient norm of the optimised product was 0.00000017 a.u. The final energy [E(RB3LYP)] of the hydrogen molecule was -1.17853936 atomic units (a.u.).

In the item table below taken from the optimisation .*log file (the full file is linked [[Media:TMACKIN H2 OPTF POP.LOG| here]] ) and it tell us that the optimisation was complete as all the forces converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000000 0.001800 YES
RMS Displacement 0.000001 0.001200 YES

</pre>

=== Vibration Analysis ===
[[File:Tmackin vibrations h2 molecule.PNG]]

Applying the 3N-5 rule for diatomic molecules to the hydrogen molecules shows that hydrogen should have one vibration mode. The details of this mode of vibration is shown above. This mode is a stretching vibration. The single covalent bond of the hydrogen molecule stretches and shortens at a frequency of 4465.68 s-1.

=== Charge Analysis ===

Both the hydrogen atoms have zero charge due to the fact that they both have the same electronegativity and so attract the bonding electrons to an equal degree.

== Energy of Haber Bosch process ==

E(NH3)= -56.55776873
2*E(NH3)= -113.1155375
E(N2)= -109.52412868
E(H2)= -1.17853936
3*E(H2)= -3.53561808
ΔE=2*E(NH3)-[E(N2)+3*E(H2)]= -113.1155375 -(-109.52412868-3.53561808) = -0.05579074 a.u.

energy change = -146.4785879 kJ/mol ---- this is wrong!

Identify which is more stable the gaseous reactants or the ammonia product?

== optimization of F2 ==

<pre>
Item Value Threshold Converged?
Maximum Force 0.000128 0.000450 YES
RMS Force 0.000128 0.000300 YES
Maximum Displacement 0.000156 0.001800 YES
RMS Displacement 0.000221 0.001200 YES
</pre>

What is the molecule?- fluorine molecule

What is the calculation method? - RB3LYP

What is the basis set? 6-31G(d,p)

What is the final energy E(RB3LYP) in atomic units (au)? -199.49825218 a.u.

What is the RMS gradient? 0.00007365

What is the point group of your molecule? Dinfh

bond angle= 180 (linear)

bond lenght= 1.40281

The optimisation file is liked to [[Media:TMACKIN F2 OPTF POP.LOG| here]]

<jmol><jmolApplet>
<title>Optimization of NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>TMACKIN F2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== vibration analysis ===

[[File:Tmackin display vibrations for optimized f2.PNG]]

how many modes do you expect from the 3N-6 rule? 1

which modes are degenerate (ie have the same energy)?

which modes are "bending" vibrations and which are "bond stretch" vibrations? Stretching

which mode is highly symmetric?

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

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

=== Charge analysis ===
no charge ie both atoms 0.00 charge

=== molecular orbitals ===

Rep:Mod:TBFA2017

2017-03-17T14:15:56Z

Tm1016: /* Optimization of Hydrogen molecule */

== Molecular Modelling using Gaussian Software ==

Using Gaussview molecules of ammonia, hydrogen and nitrogen were built, optimised and their physical properties were studied.

=== NH3 Optimisation ===

Ammonia has the molecular formula of NH3 and is formed from the reaction between gaseous nitrogen, N2 and hydrogen, H2 in a process known as the Haber Bosch process. The equation for this reaction is:

N2 + 3 H2 → 2 NH3

A molecule of ammonia, NH3 was modelled using Gaussian software. the point group of the molecule was set to C3v. The molecule was then optimised with the calculation method set to RB3LYP and a basis set of 6-31G(d,p). The RMS gradient norm of the optimised product was 0.00000485 a.u. The final energy [E(RB3LYP)] of the ammonia molecule was -56.55776873 atomic units (a.u.). The molecule consists of 1 nitrogen atom covalently bonded to 3 separate hydrogen atoms. The nitrogen to hydrogen bonds are all single bonds with a bond length of 1.01798 angstroms. From the use of gaussian the bond angle of the H-N-H bond in ammonia was determined to be 106.7°C. Ammonia has a triangular planar shape with 3 bonding pairs and 1 lone pair of electrons around the central nitrogen atom. The lone pair of electrons repel more than than the bonding pairs which reduces the bond angle to 106.7°C.

The item table below is taken from the .*log file of the gaussian calculations for optimisation and from it we can see that the forces are all converged. The full optimisation file is liked to [[Media:TMACKIN NH3 OPTF POP.LOG| here]]

<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
</pre>

Below shows a jmol model of the molecule of ammonia built on gaussian:
<jmol><jmolApplet>
<title>Optimization of NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>TMACKIN NH3 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibration Analysis ===

[[File:Tmackin display vibrations optimised nh3.PNG]]

By looking at the second derivative of the potential energy curve for ammonia (ie the curvature of the graph) we can determine the frequencies of the different modes of vibrations of the ammonia molecule.
From the 3N-6 rule, we can expect there to be 6 modes of vibrations. Gaussian confirmed this by giving 6 frequencies of vibrations which are shown in the image above. Modes 2 and 3 have the same frequency of 1693.95 s-1 and modes 5 and 6 also have the same frequency of 3589.82 s-1. Since frequency is proportional to energy, the pairs of modes must also have the same energy. Thus these modes are degenerate. Of the 6 modes, modes 1,2 and 3 are bending vibrations i.e the vibrations cause a change in bond angle. Modes 4, 5 and 6 are examples of bond stretching vibrations which are vibrations which cause the bond length to change. The 4th mode which has a frequency of 3461.29 s-1 is a vibration that causes all the vibrating N-H bonds to stretch out and back in phase with each other and so this mode is highly symmetric.
Mode 1 is a bending vibration and it is known as the umbrella mode.
There are four different frequencies at which the bonds in ammonia vibrate and thus we would expect to see 4 bands in an experimental spectrum of gaseous ammonia, with each band corresponding to one frequency.

=== Charge Analysis ===

Nitrogen is a highly electronegative atom and so can attract the bonding electrons of the N-H bonds towards itself and away from the less electronegative hydrogens. This should result in the nitrogen having a slightly negative charge distribution leaving the electron efficient hydrogens with a slightly positive charge. Using gaussian the charges of the atoms were determined. The nitrogen atom had a charge of -1.125 and on each of the hydrogen atoms the charge was +0.375. These charge distributions are in accordance with our expectations.

== Optimization of N2 ==

Nitrogen, N2 exists as a diatomic molecule with two nitrogen atoms triple bonded covalently to each other. Nitrogen is a linear molecule and thus a bonding angle of 180°C. Below is a Jmol image of a nitrogen molecule:

<jmol><jmolApplet>
<title>Nitrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>TMACKIN N2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

Since it is a linear diatomic nitrogen has D∞ symmetry. the bond length of the triple bond in the nitrogen molecule is 1.10550 angstroms. A molecule of nitrogen was built and optimised with the calculation method set to RB3LYP and a basis set of 6-31G(d,p). The RMS gradient norm of the optimised product was 0.00000060 a.u. The final energy [E(RB3LYP)] of the nitrogen molecule was -109.52412868 atomic units (a.u.).

Below is the item table taken from the full optimisation file which is linked [[Media:TMACKIN N2 OPTF POP.LOG| here]]. The forces are all converged and so optimisation is complete and correct.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000000 0.001800 YES
RMS Displacement 0.000000 0.001200 YES
</pre>

=== Vibration Analysis ===
[[File:Tmackin display vibrations for optimized n2.PNG]]

Nitrogen is diatomic and thus the 3N-6 rule is adapted to 3N-5. Using this rule we can expect nitrogen to have one vibration mode. The frequency of this mode is shown in the image above. This mode is a stretching vibration. The triple bond of the nitrogen molecule stretches and shortens at a frequency of 2457.33 s-1.

=== Charge Analysis ===

Both the nitrogen atoms have zero charge due to the fact that they both have the same electronegativity and so attract the bonding electrons to an equal degree.

== Optimization of Hydrogen molecule ==

Hydrogen is a diatomic molecule that consists of two hydrogen atoms covalently bonded to each other. Below is a jmol image of a hydrogen molecule:
<jmol><jmolApplet>
<title>Hydrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>TMACKIN H2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>
</jmolApplet></jmol>

The bond between the two hydrogens is a single bond with a length of 0.74279 angstroms. the hydrogen molecule is a linear molecule and thus has a bonding angle of 180°C and has a D∞H symmetry. A molecule of hydrogen was built and optimised with the calculation method set to RB3LYP and a basis set of 6-31G(d,p). The RMS gradient norm of the optimised product was 0.00000017 a.u. The final energy [E(RB3LYP)] of the hydrogen molecule was -1.17853936 atomic units (a.u.).

In the item table below taken from the optimisation .*log file (the full file is linked [[Media:TMACKIN H2 OPTF POP.LOG| here]] ) and it tell us that the optimisation was complete as all the forces converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000000 0.001800 YES
RMS Displacement 0.000001 0.001200 YES

</pre>

=== Vibration Analysis ===
[[File:Tmackin vibrations h2 molecule.PNG]]

Applying the 3N-5 rule for diatomic molecules to the hydrogen molecules shows that hydrogen should have one vibration mode. The details of this mode of vibration is shown above. This mode is a stretching vibration. The single covalent bond of the hydrogen molecule stretches and shortens at a frequency of 4465.68 s-1.

=== Charge Analysis ===

Both the hydrogen atoms have zero charge due to the fact that they both have the same electronegativity and so attract the bonding electrons to an equal degree.

== Energy of Haber Bosch process ==

E(NH3)= -56.55776873
2*E(NH3)= -113.1155375
E(N2)= -109.52412868
E(H2)= -1.17853936
3*E(H2)= -3.53561808
ΔE=2*E(NH3)-[E(N2)+3*E(H2)]= -113.1155375 -(-109.52412868-3.53561808) = -0.05579074 a.u.

energy change = -146.4785879 kJ/mol ---- this is wrong!

Identify which is more stable the gaseous reactants or the ammonia product?

== optimization of F2 ==

<pre>
Item Value Threshold Converged?
Maximum Force 0.000128 0.000450 YES
RMS Force 0.000128 0.000300 YES
Maximum Displacement 0.000156 0.001800 YES
RMS Displacement 0.000221 0.001200 YES
</pre>

What is the molecule?- fluorine molecule

What is the calculation method? - RB3LYP

What is the basis set? 6-31G(d,p)

What is the final energy E(RB3LYP) in atomic units (au)? -199.49825218 a.u.

What is the RMS gradient? 0.00007365

What is the point group of your molecule? Dinfh

bond angle= 180 (linear)

bond lenght= 1.40281

The optimisation file is liked to [[Media:TMACKIN F2 OPTF POP.LOG| here]]

<jmol><jmolApplet>
<title>Optimization of NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>TMACKIN F2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== vibration analysis ===

[[File:Tmackin display vibrations for optimized f2.PNG]]

how many modes do you expect from the 3N-6 rule? 1

which modes are degenerate (ie have the same energy)?

which modes are "bending" vibrations and which are "bond stretch" vibrations? Stretching

which mode is highly symmetric?

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

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

=== Charge analysis ===
no charge ie both atoms 0.00 charge

=== molecular orbitals ===

Rep:Mod:TBFA2017

2017-03-17T14:15:35Z

Tm1016: /* Optimization of N2 */

== Molecular Modelling using Gaussian Software ==

Using Gaussview molecules of ammonia, hydrogen and nitrogen were built, optimised and their physical properties were studied.

=== NH3 Optimisation ===

Ammonia has the molecular formula of NH3 and is formed from the reaction between gaseous nitrogen, N2 and hydrogen, H2 in a process known as the Haber Bosch process. The equation for this reaction is:

N2 + 3 H2 → 2 NH3

A molecule of ammonia, NH3 was modelled using Gaussian software. the point group of the molecule was set to C3v. The molecule was then optimised with the calculation method set to RB3LYP and a basis set of 6-31G(d,p). The RMS gradient norm of the optimised product was 0.00000485 a.u. The final energy [E(RB3LYP)] of the ammonia molecule was -56.55776873 atomic units (a.u.). The molecule consists of 1 nitrogen atom covalently bonded to 3 separate hydrogen atoms. The nitrogen to hydrogen bonds are all single bonds with a bond length of 1.01798 angstroms. From the use of gaussian the bond angle of the H-N-H bond in ammonia was determined to be 106.7°C. Ammonia has a triangular planar shape with 3 bonding pairs and 1 lone pair of electrons around the central nitrogen atom. The lone pair of electrons repel more than than the bonding pairs which reduces the bond angle to 106.7°C.

The item table below is taken from the .*log file of the gaussian calculations for optimisation and from it we can see that the forces are all converged. The full optimisation file is liked to [[Media:TMACKIN NH3 OPTF POP.LOG| here]]

<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
</pre>

Below shows a jmol model of the molecule of ammonia built on gaussian:
<jmol><jmolApplet>
<title>Optimization of NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>TMACKIN NH3 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibration Analysis ===

[[File:Tmackin display vibrations optimised nh3.PNG]]

By looking at the second derivative of the potential energy curve for ammonia (ie the curvature of the graph) we can determine the frequencies of the different modes of vibrations of the ammonia molecule.
From the 3N-6 rule, we can expect there to be 6 modes of vibrations. Gaussian confirmed this by giving 6 frequencies of vibrations which are shown in the image above. Modes 2 and 3 have the same frequency of 1693.95 s-1 and modes 5 and 6 also have the same frequency of 3589.82 s-1. Since frequency is proportional to energy, the pairs of modes must also have the same energy. Thus these modes are degenerate. Of the 6 modes, modes 1,2 and 3 are bending vibrations i.e the vibrations cause a change in bond angle. Modes 4, 5 and 6 are examples of bond stretching vibrations which are vibrations which cause the bond length to change. The 4th mode which has a frequency of 3461.29 s-1 is a vibration that causes all the vibrating N-H bonds to stretch out and back in phase with each other and so this mode is highly symmetric.
Mode 1 is a bending vibration and it is known as the umbrella mode.
There are four different frequencies at which the bonds in ammonia vibrate and thus we would expect to see 4 bands in an experimental spectrum of gaseous ammonia, with each band corresponding to one frequency.

=== Charge Analysis ===

Nitrogen is a highly electronegative atom and so can attract the bonding electrons of the N-H bonds towards itself and away from the less electronegative hydrogens. This should result in the nitrogen having a slightly negative charge distribution leaving the electron efficient hydrogens with a slightly positive charge. Using gaussian the charges of the atoms were determined. The nitrogen atom had a charge of -1.125 and on each of the hydrogen atoms the charge was +0.375. These charge distributions are in accordance with our expectations.

== Optimization of N2 ==

Nitrogen, N2 exists as a diatomic molecule with two nitrogen atoms triple bonded covalently to each other. Nitrogen is a linear molecule and thus a bonding angle of 180°C. Below is a Jmol image of a nitrogen molecule:

<jmol><jmolApplet>
<title>Nitrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>TMACKIN N2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

Since it is a linear diatomic nitrogen has D∞ symmetry. the bond length of the triple bond in the nitrogen molecule is 1.10550 angstroms. A molecule of nitrogen was built and optimised with the calculation method set to RB3LYP and a basis set of 6-31G(d,p). The RMS gradient norm of the optimised product was 0.00000060 a.u. The final energy [E(RB3LYP)] of the nitrogen molecule was -109.52412868 atomic units (a.u.).

Below is the item table taken from the full optimisation file which is linked [[Media:TMACKIN N2 OPTF POP.LOG| here]]. The forces are all converged and so optimisation is complete and correct.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000000 0.001800 YES
RMS Displacement 0.000000 0.001200 YES
</pre>

=== Vibration Analysis ===
[[File:Tmackin display vibrations for optimized n2.PNG]]

Nitrogen is diatomic and thus the 3N-6 rule is adapted to 3N-5. Using this rule we can expect nitrogen to have one vibration mode. The frequency of this mode is shown in the image above. This mode is a stretching vibration. The triple bond of the nitrogen molecule stretches and shortens at a frequency of 2457.33 s-1.

=== Charge Analysis ===

Both the nitrogen atoms have zero charge due to the fact that they both have the same electronegativity and so attract the bonding electrons to an equal degree.

== Optimization of Hydrogen molecule ==

Hydrogen is a diatomic molecule that consists of two hydrogen atoms covalently bonded to each other. Below is a jmol image of a hydrogen molecule:
<jmol><jmolApplet>
<title>Optimization of NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>TMACKIN H2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>
</jmolApplet></jmol>

The bond between the two hydrogens is a single bond with a length of 0.74279 angstroms. the hydrogen molecule is a linear molecule and thus has a bonding angle of 180°C and has a D∞H symmetry. A molecule of hydrogen was built and optimised with the calculation method set to RB3LYP and a basis set of 6-31G(d,p). The RMS gradient norm of the optimised product was 0.00000017 a.u. The final energy [E(RB3LYP)] of the hydrogen molecule was -1.17853936 atomic units (a.u.).

In the item table below taken from the optimisation .*log file (the full file is linked [[Media:TMACKIN H2 OPTF POP.LOG| here]] ) and it tell us that the optimisation was complete as all the forces converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000000 0.001800 YES
RMS Displacement 0.000001 0.001200 YES

</pre>

Below is a jmol image of a hydrogen molecule.
<jmol><jmolApplet>
<title>Optimization of NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>TMACKIN H2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibration Analysis ===
[[File:Tmackin vibrations h2 molecule.PNG]]

Applying the 3N-5 rule for diatomic molecules to the hydrogen molecules shows that hydrogen should have one vibration mode. The details of this mode of vibration is shown above. This mode is a stretching vibration. The single covalent bond of the hydrogen molecule stretches and shortens at a frequency of 4465.68 s-1.

=== Charge Analysis ===

Both the hydrogen atoms have zero charge due to the fact that they both have the same electronegativity and so attract the bonding electrons to an equal degree.

== Energy of Haber Bosch process ==

E(NH3)= -56.55776873
2*E(NH3)= -113.1155375
E(N2)= -109.52412868
E(H2)= -1.17853936
3*E(H2)= -3.53561808
ΔE=2*E(NH3)-[E(N2)+3*E(H2)]= -113.1155375 -(-109.52412868-3.53561808) = -0.05579074 a.u.

energy change = -146.4785879 kJ/mol ---- this is wrong!

Identify which is more stable the gaseous reactants or the ammonia product?

== optimization of F2 ==

<pre>
Item Value Threshold Converged?
Maximum Force 0.000128 0.000450 YES
RMS Force 0.000128 0.000300 YES
Maximum Displacement 0.000156 0.001800 YES
RMS Displacement 0.000221 0.001200 YES
</pre>

What is the molecule?- fluorine molecule

What is the calculation method? - RB3LYP

What is the basis set? 6-31G(d,p)

What is the final energy E(RB3LYP) in atomic units (au)? -199.49825218 a.u.

What is the RMS gradient? 0.00007365

What is the point group of your molecule? Dinfh

bond angle= 180 (linear)

bond lenght= 1.40281

The optimisation file is liked to [[Media:TMACKIN F2 OPTF POP.LOG| here]]

<jmol><jmolApplet>
<title>Optimization of NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>TMACKIN F2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== vibration analysis ===

[[File:Tmackin display vibrations for optimized f2.PNG]]

how many modes do you expect from the 3N-6 rule? 1

which modes are degenerate (ie have the same energy)?

which modes are "bending" vibrations and which are "bond stretch" vibrations? Stretching

which mode is highly symmetric?

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

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

=== Charge analysis ===
no charge ie both atoms 0.00 charge

=== molecular orbitals ===

Rep:Mod:TBFA2017

2017-03-17T14:14:23Z

Tm1016: /* Optimization of Hydrogen molecule */

== Molecular Modelling using Gaussian Software ==

Using Gaussview molecules of ammonia, hydrogen and nitrogen were built, optimised and their physical properties were studied.

=== NH3 Optimisation ===

Ammonia has the molecular formula of NH3 and is formed from the reaction between gaseous nitrogen, N2 and hydrogen, H2 in a process known as the Haber Bosch process. The equation for this reaction is:

N2 + 3 H2 → 2 NH3

A molecule of ammonia, NH3 was modelled using Gaussian software. the point group of the molecule was set to C3v. The molecule was then optimised with the calculation method set to RB3LYP and a basis set of 6-31G(d,p). The RMS gradient norm of the optimised product was 0.00000485 a.u. The final energy [E(RB3LYP)] of the ammonia molecule was -56.55776873 atomic units (a.u.). The molecule consists of 1 nitrogen atom covalently bonded to 3 separate hydrogen atoms. The nitrogen to hydrogen bonds are all single bonds with a bond length of 1.01798 angstroms. From the use of gaussian the bond angle of the H-N-H bond in ammonia was determined to be 106.7°C. Ammonia has a triangular planar shape with 3 bonding pairs and 1 lone pair of electrons around the central nitrogen atom. The lone pair of electrons repel more than than the bonding pairs which reduces the bond angle to 106.7°C.

The item table below is taken from the .*log file of the gaussian calculations for optimisation and from it we can see that the forces are all converged. The full optimisation file is liked to [[Media:TMACKIN NH3 OPTF POP.LOG| here]]

<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
</pre>

Below shows a jmol model of the molecule of ammonia built on gaussian:
<jmol><jmolApplet>
<title>Optimization of NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>TMACKIN NH3 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibration Analysis ===

[[File:Tmackin display vibrations optimised nh3.PNG]]

By looking at the second derivative of the potential energy curve for ammonia (ie the curvature of the graph) we can determine the frequencies of the different modes of vibrations of the ammonia molecule.
From the 3N-6 rule, we can expect there to be 6 modes of vibrations. Gaussian confirmed this by giving 6 frequencies of vibrations which are shown in the image above. Modes 2 and 3 have the same frequency of 1693.95 s-1 and modes 5 and 6 also have the same frequency of 3589.82 s-1. Since frequency is proportional to energy, the pairs of modes must also have the same energy. Thus these modes are degenerate. Of the 6 modes, modes 1,2 and 3 are bending vibrations i.e the vibrations cause a change in bond angle. Modes 4, 5 and 6 are examples of bond stretching vibrations which are vibrations which cause the bond length to change. The 4th mode which has a frequency of 3461.29 s-1 is a vibration that causes all the vibrating N-H bonds to stretch out and back in phase with each other and so this mode is highly symmetric.
Mode 1 is a bending vibration and it is known as the umbrella mode.
There are four different frequencies at which the bonds in ammonia vibrate and thus we would expect to see 4 bands in an experimental spectrum of gaseous ammonia, with each band corresponding to one frequency.

=== Charge Analysis ===

Nitrogen is a highly electronegative atom and so can attract the bonding electrons of the N-H bonds towards itself and away from the less electronegative hydrogens. This should result in the nitrogen having a slightly negative charge distribution leaving the electron efficient hydrogens with a slightly positive charge. Using gaussian the charges of the atoms were determined. The nitrogen atom had a charge of -1.125 and on each of the hydrogen atoms the charge was +0.375. These charge distributions are in accordance with our expectations.

== Optimization of N2 ==

Nitrogen, N2 exists as a diatomic molecule with two nitrogen atoms triple bonded covalently to each other. Nitrogen is a linear molecule and thus a bonding angle of 180°C. Below is a Jmol image of a nitrogen molecule:

<jmol><jmolApplet>
<title>Optimization of NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>TMACKIN N2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

Since it is a linear diatomic nitrogen has D∞ symmetry. the bond length of the triple bond in the nitrogen molecule is 1.10550 angstroms. A molecule of nitrogen was built and optimised with the calculation method set to RB3LYP and a basis set of 6-31G(d,p). The RMS gradient norm of the optimised product was 0.00000060 a.u. The final energy [E(RB3LYP)] of the nitrogen molecule was -109.52412868 atomic units (a.u.).

Below is the item table taken from the full optimisation file which is linked [[Media:TMACKIN N2 OPTF POP.LOG| here]]. The forces are all converged and so optimisation is complete and correct.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000000 0.001800 YES
RMS Displacement 0.000000 0.001200 YES
</pre>

=== Vibration Analysis ===
[[File:Tmackin display vibrations for optimized n2.PNG]]

Nitrogen is diatomic and thus the 3N-6 rule is adapted to 3N-5. Using this rule we can expect nitrogen to have one vibration mode. The frequency of this mode is shown in the image above. This mode is a stretching vibration. The triple bond of the nitrogen molecule stretches and shortens at a frequency of 2457.33 s-1.

=== Charge Analysis ===

Both the nitrogen atoms have zero charge due to the fact that they both have the same electronegativity and so attract the bonding electrons to an equal degree.

== Optimization of Hydrogen molecule ==

Hydrogen is a diatomic molecule that consists of two hydrogen atoms covalently bonded to each other. Below is a jmol image of a hydrogen molecule:
<jmol><jmolApplet>
<title>Optimization of NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>TMACKIN H2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>
</jmolApplet></jmol>

The bond between the two hydrogens is a single bond with a length of 0.74279 angstroms. the hydrogen molecule is a linear molecule and thus has a bonding angle of 180°C and has a D∞H symmetry. A molecule of hydrogen was built and optimised with the calculation method set to RB3LYP and a basis set of 6-31G(d,p). The RMS gradient norm of the optimised product was 0.00000017 a.u. The final energy [E(RB3LYP)] of the hydrogen molecule was -1.17853936 atomic units (a.u.).

In the item table below taken from the optimisation .*log file (the full file is linked [[Media:TMACKIN H2 OPTF POP.LOG| here]] ) and it tell us that the optimisation was complete as all the forces converged.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000000 0.001800 YES
RMS Displacement 0.000001 0.001200 YES

</pre>

Below is a jmol image of a hydrogen molecule.
<jmol><jmolApplet>
<title>Optimization of NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>TMACKIN H2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibration Analysis ===
[[File:Tmackin vibrations h2 molecule.PNG]]

Applying the 3N-5 rule for diatomic molecules to the hydrogen molecules shows that hydrogen should have one vibration mode. The details of this mode of vibration is shown above. This mode is a stretching vibration. The single covalent bond of the hydrogen molecule stretches and shortens at a frequency of 4465.68 s-1.

=== Charge Analysis ===

Both the hydrogen atoms have zero charge due to the fact that they both have the same electronegativity and so attract the bonding electrons to an equal degree.

== Energy of Haber Bosch process ==

E(NH3)= -56.55776873
2*E(NH3)= -113.1155375
E(N2)= -109.52412868
E(H2)= -1.17853936
3*E(H2)= -3.53561808
ΔE=2*E(NH3)-[E(N2)+3*E(H2)]= -113.1155375 -(-109.52412868-3.53561808) = -0.05579074 a.u.

energy change = -146.4785879 kJ/mol ---- this is wrong!

Identify which is more stable the gaseous reactants or the ammonia product?

== optimization of F2 ==

<pre>
Item Value Threshold Converged?
Maximum Force 0.000128 0.000450 YES
RMS Force 0.000128 0.000300 YES
Maximum Displacement 0.000156 0.001800 YES
RMS Displacement 0.000221 0.001200 YES
</pre>

What is the molecule?- fluorine molecule

What is the calculation method? - RB3LYP

What is the basis set? 6-31G(d,p)

What is the final energy E(RB3LYP) in atomic units (au)? -199.49825218 a.u.

What is the RMS gradient? 0.00007365

What is the point group of your molecule? Dinfh

bond angle= 180 (linear)

bond lenght= 1.40281

The optimisation file is liked to [[Media:TMACKIN F2 OPTF POP.LOG| here]]

<jmol><jmolApplet>
<title>Optimization of NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>TMACKIN F2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== vibration analysis ===

[[File:Tmackin display vibrations for optimized f2.PNG]]

how many modes do you expect from the 3N-6 rule? 1

which modes are degenerate (ie have the same energy)?

which modes are "bending" vibrations and which are "bond stretch" vibrations? Stretching

which mode is highly symmetric?

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

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

=== Charge analysis ===
no charge ie both atoms 0.00 charge

=== molecular orbitals ===

Rep:Mod:TBFA2017

2017-03-17T13:52:31Z

Tm1016: /* Optimization of N2 */

Rep:Mod:TBFA2017

2017-03-17T13:31:44Z

Tm1016: /* Charge Analysis */

Rep:Mod:TBFA2017

2017-03-17T13:21:13Z

Tm1016: /* Vibrations */

Rep:Mod:TBFA2017

2017-03-17T12:54:23Z

Tm1016: /* Optimization of Ammonia, NH3 */

Rep:Mod:TBFA2017

2017-03-17T10:58:46Z

Tm1016: /* NH3 optimization */

== Optimization of Ammonia, NH3 ==

=== NH3 optimization ===
molecule name= ammonia, NH3
calculation method= RB3LYP
basis set=6-31G(d,p)
final energy E(RB3LYP) in atomic units (au)= -56.55776873
the point group of your molecule= C3V
bond length= 1.01798(N1-H4)
bond angle=37.129
<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
</pre>

<jmol><jmolApplet>
<title>Optimization of NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>TMACKIN NH3 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

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

Using Gaussview molecules of ammonia, hydrogen and nitrogen were built, optimised and their physical properties were studied.

=== Vibrations ===

[[File:Tmackin display vibrations optimised nh3.PNG]]

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

which modes are degenerate (ie have the same energy)? - ''2 and 3 have the same energy and 5 and 6 have the same energy''

which modes are "bending" vibrations and which are "bond stretch" vibrations? - ''bending=1,2,3 stretching=4,5,6
''

which mode is highly symmetric? ''4''

one mode is known as the "umbrella" mode, which one is this? ''1 is the umbrella mode''

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

=== Charge Analysis ===

charge on nitrogen atom= -1.125 charge on nitrogen atoms= +0.375

'''''

When carrying out calculations it is always good to check your results against your expectations. Write a sentence saying what charge (positive or negative) you would expect for N and H and why?'''''

== Optimization of N2 ==

What is the molecule?- nitrogen molecule

What is the calculation method? - RB3LYP

What is the basis set? 6-31G(d,p)

What is the final energy E(RB3LYP) in atomic units (au)? -109.52412868

What is the RMS gradient? 0.00000060

What is the point group of your molecule? Dinfh

bond angle= 180

bond lenght= 1.10550 (N1-N2)

<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000000 0.001800 YES
RMS Displacement 0.000000 0.001200 YES
</pre>

The optimisation file is liked to [[Media:TMACKIN N2 OPTF POP.LOG| here]]

<jmol><jmolApplet>
<title>Optimization of NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>TMACKIN N2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== vibration analysis ===
[[File:Tmackin display vibrations for optimized n2.PNG]]

how many modes do you expect from the 3N-6 rule? - use the 3n-5 rule so 1 vibration

which modes are degenerate (ie have the same energy)? ----------

which modes are "bending" vibrations and which are "bond stretch" vibrations? the 1 vibration is a stretching vibration

which mode is highly symmetric?--

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

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

=== Charge Analysis ===

both nitrogen atoms have 0.00 charge

== Optimization of Hydrogen molecule ==

<pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000000 0.001800 YES
RMS Displacement 0.000001 0.001200 YES

</pre>

What is the molecule? -hydrogen molecule

What is the calculation method?
RB3LYP

What is the basis set?
6-31G(d,p)

What is the final energy E(RB3LYP) in atomic units (au)?
-1.17853936 a.u

What is the RMS gradient?
0.00000017 a.u.

What is the point group of your molecule?
DinfH

bond length- 0.74279

bond angle- linear so 180 C

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

<jmol><jmolApplet>
<title>Optimization of NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>TMACKIN H2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibration analysis ===
[[File:Tmackin vibrations h2 molecule.PNG]]

how many modes do you expect from the 3N-6 rule?- linear 3n-5 rule hence 1 mode

which modes are degenerate (ie have the same energy)?----

which modes are "bending" vibrations and which are "bond stretch" vibrations? stretching vibration

which mode is highly symmetric?

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

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

=== Charge Analysis ===
charge on both atoms is 0.000
'''
When carrying out calculations it is always good to check your results against your expectations. Write a sentence saying what charge (positive or negative) you would expect for N and H and why'''

== Energy of Haber Bosch process ==

E(NH3)= -56.55776873
2*E(NH3)= -113.1155375
E(N2)= -109.52412868
E(H2)= -1.17853936
3*E(H2)= -3.53561808
ΔE=2*E(NH3)-[E(N2)+3*E(H2)]= -113.1155375 -(-109.52412868-3.53561808) = -0.05579074 a.u.

energy change = -146.4785879 kJ/mol ---- this is wrong!

Identify which is more stable the gaseous reactants or the ammonia product?

== optimization of F2 ==

<pre>
Item Value Threshold Converged?
Maximum Force 0.000128 0.000450 YES
RMS Force 0.000128 0.000300 YES
Maximum Displacement 0.000156 0.001800 YES
RMS Displacement 0.000221 0.001200 YES
</pre>

What is the molecule?- fluorine molecule

What is the calculation method? - RB3LYP

What is the basis set? 6-31G(d,p)

What is the final energy E(RB3LYP) in atomic units (au)? -199.49825218 a.u.

What is the RMS gradient? 0.00007365

What is the point group of your molecule? Dinfh

bond angle= 180 (linear)

bond lenght= 1.40281

The optimisation file is liked to [[Media:TMACKIN F2 OPTF POP.LOG| here]]

<jmol><jmolApplet>
<title>Optimization of NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>TMACKIN F2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== vibration analysis ===

[[File:Tmackin display vibrations for optimized f2.PNG]]

how many modes do you expect from the 3N-6 rule? 1

which modes are degenerate (ie have the same energy)?

which modes are "bending" vibrations and which are "bond stretch" vibrations? Stretching

which mode is highly symmetric?

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

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

=== Charge analysis ===
no charge ie both atoms 0.00 charge

=== molecular orbitals ===

Rep:Mod:TBFA2017

2017-03-17T10:55:18Z

Tm1016: /* Chlorine TriFluoride */

== Optimization of Ammonia, NH3 ==

=== NH3 optimization ===
molecule name= ammonia, NH3
calculation method= RB3LYP
basis set=6-31G(d,p)
final energy E(RB3LYP) in atomic units (au)= -56.55776873
the point group of your molecule= C3V
bond length= 1.01798(N1-H4)
bond angle=37.129
<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
</pre>

<jmol><jmolApplet>
<title>Optimization of NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>TMACKIN NH3 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

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

using Gaussview

=== Vibrations ===

[[File:Tmackin display vibrations optimised nh3.PNG]]

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

which modes are degenerate (ie have the same energy)? - ''2 and 3 have the same energy and 5 and 6 have the same energy''

which modes are "bending" vibrations and which are "bond stretch" vibrations? - ''bending=1,2,3 stretching=4,5,6
''

which mode is highly symmetric? ''4''

one mode is known as the "umbrella" mode, which one is this? ''1 is the umbrella mode''

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

=== Charge Analysis ===

charge on nitrogen atom= -1.125 charge on nitrogen atoms= +0.375

'''''

When carrying out calculations it is always good to check your results against your expectations. Write a sentence saying what charge (positive or negative) you would expect for N and H and why?'''''

== Optimization of N2 ==

What is the molecule?- nitrogen molecule

What is the calculation method? - RB3LYP

What is the basis set? 6-31G(d,p)

What is the final energy E(RB3LYP) in atomic units (au)? -109.52412868

What is the RMS gradient? 0.00000060

What is the point group of your molecule? Dinfh

bond angle= 180

bond lenght= 1.10550 (N1-N2)

<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000000 0.001800 YES
RMS Displacement 0.000000 0.001200 YES
</pre>

The optimisation file is liked to [[Media:TMACKIN N2 OPTF POP.LOG| here]]

<jmol><jmolApplet>
<title>Optimization of NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>TMACKIN N2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== vibration analysis ===
[[File:Tmackin display vibrations for optimized n2.PNG]]

how many modes do you expect from the 3N-6 rule? - use the 3n-5 rule so 1 vibration

which modes are degenerate (ie have the same energy)? ----------

which modes are "bending" vibrations and which are "bond stretch" vibrations? the 1 vibration is a stretching vibration

which mode is highly symmetric?--

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

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

=== Charge Analysis ===

both nitrogen atoms have 0.00 charge

== Optimization of Hydrogen molecule ==

<pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000000 0.001800 YES
RMS Displacement 0.000001 0.001200 YES

</pre>

What is the molecule? -hydrogen molecule

What is the calculation method?
RB3LYP

What is the basis set?
6-31G(d,p)

What is the final energy E(RB3LYP) in atomic units (au)?
-1.17853936 a.u

What is the RMS gradient?
0.00000017 a.u.

What is the point group of your molecule?
DinfH

bond length- 0.74279

bond angle- linear so 180 C

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

<jmol><jmolApplet>
<title>Optimization of NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>TMACKIN H2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibration analysis ===
[[File:Tmackin vibrations h2 molecule.PNG]]

how many modes do you expect from the 3N-6 rule?- linear 3n-5 rule hence 1 mode

which modes are degenerate (ie have the same energy)?----

which modes are "bending" vibrations and which are "bond stretch" vibrations? stretching vibration

which mode is highly symmetric?

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

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

=== Charge Analysis ===
charge on both atoms is 0.000
'''
When carrying out calculations it is always good to check your results against your expectations. Write a sentence saying what charge (positive or negative) you would expect for N and H and why'''

== Energy of Haber Bosch process ==

E(NH3)= -56.55776873
2*E(NH3)= -113.1155375
E(N2)= -109.52412868
E(H2)= -1.17853936
3*E(H2)= -3.53561808
ΔE=2*E(NH3)-[E(N2)+3*E(H2)]= -113.1155375 -(-109.52412868-3.53561808) = -0.05579074 a.u.

energy change = -146.4785879 kJ/mol ---- this is wrong!

Identify which is more stable the gaseous reactants or the ammonia product?

== optimization of F2 ==

<pre>
Item Value Threshold Converged?
Maximum Force 0.000128 0.000450 YES
RMS Force 0.000128 0.000300 YES
Maximum Displacement 0.000156 0.001800 YES
RMS Displacement 0.000221 0.001200 YES
</pre>

What is the molecule?- fluorine molecule

What is the calculation method? - RB3LYP

What is the basis set? 6-31G(d,p)

What is the final energy E(RB3LYP) in atomic units (au)? -199.49825218 a.u.

What is the RMS gradient? 0.00007365

What is the point group of your molecule? Dinfh

bond angle= 180 (linear)

bond lenght= 1.40281

The optimisation file is liked to [[Media:TMACKIN F2 OPTF POP.LOG| here]]

<jmol><jmolApplet>
<title>Optimization of NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>TMACKIN F2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== vibration analysis ===

[[File:Tmackin display vibrations for optimized f2.PNG]]

how many modes do you expect from the 3N-6 rule? 1

which modes are degenerate (ie have the same energy)?

which modes are "bending" vibrations and which are "bond stretch" vibrations? Stretching

which mode is highly symmetric?

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

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

=== Charge analysis ===
no charge ie both atoms 0.00 charge

=== molecular orbitals ===

Rep:Mod:TBFA2017

2017-03-16T22:04:14Z

Tm1016: /* NH3 optimization */

== Optimization of Ammonia, NH3 ==

=== NH3 optimization ===
molecule name= ammonia, NH3
calculation method= RB3LYP
basis set=6-31G(d,p)
final energy E(RB3LYP) in atomic units (au)= -56.55776873
the point group of your molecule= C3V
bond length= 1.01798(N1-H4)
bond angle=37.129
<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
</pre>

<jmol><jmolApplet>
<title>Optimization of NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>TMACKIN NH3 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

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

using Gaussview

=== Vibrations ===

[[File:Tmackin display vibrations optimised nh3.PNG]]

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

which modes are degenerate (ie have the same energy)? - ''2 and 3 have the same energy and 5 and 6 have the same energy''

which modes are "bending" vibrations and which are "bond stretch" vibrations? - ''bending=1,2,3 stretching=4,5,6
''

which mode is highly symmetric? ''4''

one mode is known as the "umbrella" mode, which one is this? ''1 is the umbrella mode''

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

=== Charge Analysis ===

charge on nitrogen atom= -1.125 charge on nitrogen atoms= +0.375

'''''

When carrying out calculations it is always good to check your results against your expectations. Write a sentence saying what charge (positive or negative) you would expect for N and H and why?'''''

== Optimization of N2 ==

What is the molecule?- nitrogen molecule

What is the calculation method? - RB3LYP

What is the basis set? 6-31G(d,p)

What is the final energy E(RB3LYP) in atomic units (au)? -109.52412868

What is the RMS gradient? 0.00000060

What is the point group of your molecule? Dinfh

bond angle= 180

bond lenght= 1.10550 (N1-N2)

<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000000 0.001800 YES
RMS Displacement 0.000000 0.001200 YES
</pre>

The optimisation file is liked to [[Media:TMACKIN N2 OPTF POP.LOG| here]]

<jmol><jmolApplet>
<title>Optimization of NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>TMACKIN N2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== vibration analysis ===
[[File:Tmackin display vibrations for optimized n2.PNG]]

how many modes do you expect from the 3N-6 rule? - use the 3n-5 rule so 1 vibration

which modes are degenerate (ie have the same energy)? ----------

which modes are "bending" vibrations and which are "bond stretch" vibrations? the 1 vibration is a stretching vibration

which mode is highly symmetric?--

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

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

=== Charge Analysis ===

both nitrogen atoms have 0.00 charge

== Optimization of Hydrogen molecule ==

<pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000000 0.001800 YES
RMS Displacement 0.000001 0.001200 YES

</pre>

What is the molecule? -hydrogen molecule

What is the calculation method?
RB3LYP

What is the basis set?
6-31G(d,p)

What is the final energy E(RB3LYP) in atomic units (au)?
-1.17853936 a.u

What is the RMS gradient?
0.00000017 a.u.

What is the point group of your molecule?
DinfH

bond length- 0.74279

bond angle- linear so 180 C

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

<jmol><jmolApplet>
<title>Optimization of NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>TMACKIN H2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibration analysis ===
[[File:Tmackin vibrations h2 molecule.PNG]]

how many modes do you expect from the 3N-6 rule?- linear 3n-5 rule hence 1 mode

which modes are degenerate (ie have the same energy)?----

which modes are "bending" vibrations and which are "bond stretch" vibrations? stretching vibration

which mode is highly symmetric?

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

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

=== Charge Analysis ===
charge on both atoms is 0.000
'''
When carrying out calculations it is always good to check your results against your expectations. Write a sentence saying what charge (positive or negative) you would expect for N and H and why'''

== Energy of Haber Bosch process ==

E(NH3)= -56.55776873
2*E(NH3)= -113.1155375
E(N2)= -109.52412868
E(H2)= -1.17853936
3*E(H2)= -3.53561808
ΔE=2*E(NH3)-[E(N2)+3*E(H2)]= -113.1155375 -(-109.52412868-3.53561808) = -0.05579074 a.u.

energy change = -146.4785879 kJ/mol ---- this is wrong!

Identify which is more stable the gaseous reactants or the ammonia product?

== optimization of F2 ==

<pre>
Item Value Threshold Converged?
Maximum Force 0.000128 0.000450 YES
RMS Force 0.000128 0.000300 YES
Maximum Displacement 0.000156 0.001800 YES
RMS Displacement 0.000221 0.001200 YES
</pre>

What is the molecule?- fluorine molecule

What is the calculation method? - RB3LYP

What is the basis set? 6-31G(d,p)

What is the final energy E(RB3LYP) in atomic units (au)? -199.49825218 a.u.

What is the RMS gradient? 0.00007365

What is the point group of your molecule? Dinfh

bond angle= 180 (linear)

bond lenght= 1.40281

The optimisation file is liked to [[Media:TMACKIN F2 OPTF POP.LOG| here]]

<jmol><jmolApplet>
<title>Optimization of NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>TMACKIN F2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== vibration analysis ===

[[File:Tmackin display vibrations for optimized f2.PNG]]

how many modes do you expect from the 3N-6 rule? 1

which modes are degenerate (ie have the same energy)?

which modes are "bending" vibrations and which are "bond stretch" vibrations? Stretching

which mode is highly symmetric?

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

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

=== Charge analysis ===
no charge ie both atoms 0.00 charge

=== molecular orbitals ===

== Chlorine TriFluoride ==

used C2v point group symmetry [http://www.chembio.uoguelph.ca/educmat/chm364_preuss/5_6%20MO%20Theory_VB%20vs%20MO.pdf]

What is the molecule?- ClF3

What is the calculation method?

What is the basis set?

What is the final energy E(RB3LYP) in atomic units (au)?

What is the RMS gradient?

What is the point group of your molecule?

Rep:Mod:TBFA2017

2017-03-16T22:03:13Z

Tm1016: /* Optimization of Ammonia, NH3 */

== Optimization of Ammonia, NH3 ==

=== NH3 optimization ===
molecule name= ammonia, NH3
calculation method= RB3LYP
basis set=6-31G(d,p)
final energy E(RB3LYP) in atomic units (au)= -56.55776873
the point group of your molecule= C3V
bond length= 1.01798(N1-H4)
bond angle=37.129
<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
</pre>

<jmol><jmolApplet>
<title>Optimization of NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>TMACKIN NH3 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

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

using Gaussview

=== Vibrations ===

[[File:Tmackin display vibrations optimised nh3.PNG]]

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

which modes are degenerate (ie have the same energy)? - ''2 and 3 have the same energy and 5 and 6 have the same energy''

which modes are "bending" vibrations and which are "bond stretch" vibrations? - ''bending=1,2,3 stretching=4,5,6
''

which mode is highly symmetric? ''4''

one mode is known as the "umbrella" mode, which one is this? ''1 is the umbrella mode''

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

=== Charge Analysis ===

charge on nitrogen atom= -1.125 charge on nitrogen atoms= +0.375

'''''

When carrying out calculations it is always good to check your results against your expectations. Write a sentence saying what charge (positive or negative) you would expect for N and H and why?'''''

== Optimization of N2 ==

What is the molecule?- nitrogen molecule

What is the calculation method? - RB3LYP

What is the basis set? 6-31G(d,p)

What is the final energy E(RB3LYP) in atomic units (au)? -109.52412868

What is the RMS gradient? 0.00000060

What is the point group of your molecule? Dinfh

bond angle= 180

bond lenght= 1.10550 (N1-N2)

<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000000 0.001800 YES
RMS Displacement 0.000000 0.001200 YES
</pre>

The optimisation file is liked to [[Media:TMACKIN N2 OPTF POP.LOG| here]]

<jmol><jmolApplet>
<title>Optimization of NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>TMACKIN N2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== vibration analysis ===
[[File:Tmackin display vibrations for optimized n2.PNG]]

how many modes do you expect from the 3N-6 rule? - use the 3n-5 rule so 1 vibration

which modes are degenerate (ie have the same energy)? ----------

which modes are "bending" vibrations and which are "bond stretch" vibrations? the 1 vibration is a stretching vibration

which mode is highly symmetric?--

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

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

=== Charge Analysis ===

both nitrogen atoms have 0.00 charge

== Optimization of Hydrogen molecule ==

<pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000000 0.001800 YES
RMS Displacement 0.000001 0.001200 YES

</pre>

What is the molecule? -hydrogen molecule

What is the calculation method?
RB3LYP

What is the basis set?
6-31G(d,p)

What is the final energy E(RB3LYP) in atomic units (au)?
-1.17853936 a.u

What is the RMS gradient?
0.00000017 a.u.

What is the point group of your molecule?
DinfH

bond length- 0.74279

bond angle- linear so 180 C

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

<jmol><jmolApplet>
<title>Optimization of NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>TMACKIN H2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibration analysis ===
[[File:Tmackin vibrations h2 molecule.PNG]]

how many modes do you expect from the 3N-6 rule?- linear 3n-5 rule hence 1 mode

which modes are degenerate (ie have the same energy)?----

which modes are "bending" vibrations and which are "bond stretch" vibrations? stretching vibration

which mode is highly symmetric?

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

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

=== Charge Analysis ===
charge on both atoms is 0.000
'''
When carrying out calculations it is always good to check your results against your expectations. Write a sentence saying what charge (positive or negative) you would expect for N and H and why'''

== Energy of Haber Bosch process ==

E(NH3)= -56.55776873
2*E(NH3)= -113.1155375
E(N2)= -109.52412868
E(H2)= -1.17853936
3*E(H2)= -3.53561808
ΔE=2*E(NH3)-[E(N2)+3*E(H2)]= -113.1155375 -(-109.52412868-3.53561808) = -0.05579074 a.u.

energy change = -146.4785879 kJ/mol ---- this is wrong!

Identify which is more stable the gaseous reactants or the ammonia product?

== optimization of F2 ==

<pre>
Item Value Threshold Converged?
Maximum Force 0.000128 0.000450 YES
RMS Force 0.000128 0.000300 YES
Maximum Displacement 0.000156 0.001800 YES
RMS Displacement 0.000221 0.001200 YES
</pre>

What is the molecule?- fluorine molecule

What is the calculation method? - RB3LYP

What is the basis set? 6-31G(d,p)

What is the final energy E(RB3LYP) in atomic units (au)? -199.49825218 a.u.

What is the RMS gradient? 0.00007365

What is the point group of your molecule? Dinfh

bond angle= 180 (linear)

bond lenght= 1.40281

The optimisation file is liked to [[Media:TMACKIN F2 OPTF POP.LOG| here]]

<jmol><jmolApplet>
<title>Optimization of NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>TMACKIN F2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== vibration analysis ===

[[File:Tmackin display vibrations for optimized f2.PNG]]

how many modes do you expect from the 3N-6 rule? 1

which modes are degenerate (ie have the same energy)?

which modes are "bending" vibrations and which are "bond stretch" vibrations? Stretching

which mode is highly symmetric?

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

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

=== Charge analysis ===
no charge ie both atoms 0.00 charge

=== molecular orbitals ===

== Chlorine TriFluoride ==

used C2v point group symmetry [http://www.chembio.uoguelph.ca/educmat/chm364_preuss/5_6%20MO%20Theory_VB%20vs%20MO.pdf]

What is the molecule?- ClF3

What is the calculation method?

What is the basis set?

What is the final energy E(RB3LYP) in atomic units (au)?

What is the RMS gradient?

What is the point group of your molecule?

Rep:Mod:TBFA2017

2017-03-16T15:34:05Z

Tm1016: /* NH3 optimization */

== Optimization of Ammonia, NH3 ==

=== NH3 optimization ===
molecule name= ammonia, NH3
calculation method= RB3LYP
basis set=6-31G(d,p)
final energy E(RB3LYP) in atomic units (au)= -56.55776873
the point group of your molecule= C3V
bond length= 1.01798(N1-H4)
bond angle=37.129
<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
</pre>

<jmol><jmolApplet>
<title>Optimization of NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>TMACKIN NH3 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

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

using Gaussview

=== Vibrations ===

[[File:Tmackin display vibrations optimised nh3.PNG]]

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

which modes are degenerate (ie have the same energy)? - ''2 and 3 have the same energy and 5 and 6 have the same energy''

which modes are "bending" vibrations and which are "bond stretch" vibrations? - ''bending=1,2,3 stretching=4,5,6
''

which mode is highly symmetric? ''4''

one mode is known as the "umbrella" mode, which one is this? ''1 is the umbrella mode''

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

=== Charge Analysis ===

charge on nitrogen atom= -1.125 charge on nitrogen atoms= +0.375

'''''

When carrying out calculations it is always good to check your results against your expectations. Write a sentence saying what charge (positive or negative) you would expect for N and H and why?'''''

== Optimization of N2 ==

What is the molecule?- nitrogen molecule

What is the calculation method? - RB3LYP

What is the basis set? 6-31G(d,p)

What is the final energy E(RB3LYP) in atomic units (au)? -109.52412868

What is the RMS gradient? 0.00000060

What is the point group of your molecule? Dinfh

bond angle= 180

bond lenght= 1.10550 (N1-N2)

<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000000 0.001800 YES
RMS Displacement 0.000000 0.001200 YES
</pre>

The optimisation file is liked to [[Media:TMACKIN N2 OPTF POP.LOG| here]]

<jmol><jmolApplet>
<title>Optimization of NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>TMACKIN N2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== vibration analysis ===
[[File:Tmackin display vibrations for optimized n2.PNG]]

how many modes do you expect from the 3N-6 rule? - use the 3n-5 rule so 1 vibration

which modes are degenerate (ie have the same energy)? ----------

which modes are "bending" vibrations and which are "bond stretch" vibrations? the 1 vibration is a stretching vibration

which mode is highly symmetric?--

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

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

=== Charge Analysis ===

both nitrogen atoms have 0.00 charge

== Optimization of Hydrogen molecule ==

<pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000000 0.001800 YES
RMS Displacement 0.000001 0.001200 YES

</pre>

What is the molecule? -hydrogen molecule

What is the calculation method?
RB3LYP

What is the basis set?
6-31G(d,p)

What is the final energy E(RB3LYP) in atomic units (au)?
-1.17853936 a.u

What is the RMS gradient?
0.00000017 a.u.

What is the point group of your molecule?
DinfH

bond length- 0.74279

bond angle- linear so 180 C

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

<jmol><jmolApplet>
<title>Optimization of NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>TMACKIN H2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibration analysis ===
[[File:Tmackin vibrations h2 molecule.PNG]]

how many modes do you expect from the 3N-6 rule?- linear 3n-5 rule hence 1 mode

which modes are degenerate (ie have the same energy)?----

which modes are "bending" vibrations and which are "bond stretch" vibrations? stretching vibration

which mode is highly symmetric?

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

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

=== Charge Analysis ===
charge on both atoms is 0.000
'''
When carrying out calculations it is always good to check your results against your expectations. Write a sentence saying what charge (positive or negative) you would expect for N and H and why'''

== Energy of Haber Bosch process ==

E(NH3)= -56.55776873
2*E(NH3)= -113.1155375
E(N2)= -109.52412868
E(H2)= -1.17853936
3*E(H2)= -3.53561808
ΔE=2*E(NH3)-[E(N2)+3*E(H2)]= -113.1155375 -(-109.52412868-3.53561808) = -0.05579074 a.u.

energy change = -146.4785879 kJ/mol ---- this is wrong!

Identify which is more stable the gaseous reactants or the ammonia product?

== optimization of F2 ==

<pre>
Item Value Threshold Converged?
Maximum Force 0.000128 0.000450 YES
RMS Force 0.000128 0.000300 YES
Maximum Displacement 0.000156 0.001800 YES
RMS Displacement 0.000221 0.001200 YES
</pre>

What is the molecule?- fluorine molecule

What is the calculation method? - RB3LYP

What is the basis set? 6-31G(d,p)

What is the final energy E(RB3LYP) in atomic units (au)? -199.49825218 a.u.

What is the RMS gradient? 0.00007365

What is the point group of your molecule? Dinfh

bond angle= 180 (linear)

bond lenght= 1.40281

The optimisation file is liked to [[Media:TMACKIN F2 OPTF POP.LOG| here]]

<jmol><jmolApplet>
<title>Optimization of NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>TMACKIN F2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== vibration analysis ===

[[File:Tmackin display vibrations for optimized f2.PNG]]

how many modes do you expect from the 3N-6 rule? 1

which modes are degenerate (ie have the same energy)?

which modes are "bending" vibrations and which are "bond stretch" vibrations? Stretching

which mode is highly symmetric?

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

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

=== Charge analysis ===
no charge ie both atoms 0.00 charge

=== molecular orbitals ===

== Chlorine TriFluoride ==

used C2v point group symmetry [http://www.chembio.uoguelph.ca/educmat/chm364_preuss/5_6%20MO%20Theory_VB%20vs%20MO.pdf]

What is the molecule?- ClF3

What is the calculation method?

What is the basis set?

What is the final energy E(RB3LYP) in atomic units (au)?

What is the RMS gradient?

What is the point group of your molecule?

Rep:Mod:TBFA2017

2017-03-16T11:31:05Z

Tm1016: /* molecular orbitals */

== Optimization of Ammonia, NH3 ==

=== NH3 optimization ===

molecule name= TMackin_nh3_optf_pop
calculation method= RB3LYP
basis set=6-31G(d,p)
final energy E(RB3LYP) in atomic units (au)= -56.55776873
the point group of your molecule= C3V
bond length= 1.01798(N1-H4)
bond angle=37.129
<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
</pre>

<jmol><jmolApplet>
<title>Optimization of NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>TMACKIN NH3 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

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

=== Vibrations ===

[[File:Tmackin display vibrations optimised nh3.PNG]]

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

which modes are degenerate (ie have the same energy)? - ''2 and 3 have the same energy and 5 and 6 have the same energy''

which modes are "bending" vibrations and which are "bond stretch" vibrations? - ''bending=1,2,3 stretching=4,5,6
''

which mode is highly symmetric? ''4''

one mode is known as the "umbrella" mode, which one is this? ''1 is the umbrella mode''

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

=== Charge Analysis ===

charge on nitrogen atom= -1.125 charge on nitrogen atoms= +0.375

'''''

When carrying out calculations it is always good to check your results against your expectations. Write a sentence saying what charge (positive or negative) you would expect for N and H and why?'''''

== Optimization of N2 ==

What is the molecule?- nitrogen molecule

What is the calculation method? - RB3LYP

What is the basis set? 6-31G(d,p)

What is the final energy E(RB3LYP) in atomic units (au)? -109.52412868

What is the RMS gradient? 0.00000060

What is the point group of your molecule? Dinfh

bond angle= 180

bond lenght= 1.10550 (N1-N2)

<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000000 0.001800 YES
RMS Displacement 0.000000 0.001200 YES
</pre>

The optimisation file is liked to [[Media:TMACKIN N2 OPTF POP.LOG| here]]

<jmol><jmolApplet>
<title>Optimization of NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>TMACKIN N2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== vibration analysis ===
[[File:Tmackin display vibrations for optimized n2.PNG]]

how many modes do you expect from the 3N-6 rule? - use the 3n-5 rule so 1 vibration

which modes are degenerate (ie have the same energy)? ----------

which modes are "bending" vibrations and which are "bond stretch" vibrations? the 1 vibration is a stretching vibration

which mode is highly symmetric?--

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

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

=== Charge Analysis ===

both nitrogen atoms have 0.00 charge

== Optimization of Hydrogen molecule ==

<pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000000 0.001800 YES
RMS Displacement 0.000001 0.001200 YES

</pre>

What is the molecule? -hydrogen molecule

What is the calculation method?
RB3LYP

What is the basis set?
6-31G(d,p)

What is the final energy E(RB3LYP) in atomic units (au)?
-1.17853936 a.u

What is the RMS gradient?
0.00000017 a.u.

What is the point group of your molecule?
DinfH

bond length- 0.74279

bond angle- linear so 180 C

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

<jmol><jmolApplet>
<title>Optimization of NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>TMACKIN H2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibration analysis ===
[[File:Tmackin vibrations h2 molecule.PNG]]

how many modes do you expect from the 3N-6 rule?- linear 3n-5 rule hence 1 mode

which modes are degenerate (ie have the same energy)?----

which modes are "bending" vibrations and which are "bond stretch" vibrations? stretching vibration

which mode is highly symmetric?

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

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

=== Charge Analysis ===
charge on both atoms is 0.000
'''
When carrying out calculations it is always good to check your results against your expectations. Write a sentence saying what charge (positive or negative) you would expect for N and H and why'''

== Energy of Haber Bosch process ==

E(NH3)= -56.55776873
2*E(NH3)= -113.1155375
E(N2)= -109.52412868
E(H2)= -1.17853936
3*E(H2)= -3.53561808
ΔE=2*E(NH3)-[E(N2)+3*E(H2)]= -113.1155375 -(-109.52412868-3.53561808) = -0.05579074 a.u.

energy change = -146.4785879 kJ/mol ---- this is wrong!

Identify which is more stable the gaseous reactants or the ammonia product?

== optimization of F2 ==

<pre>
Item Value Threshold Converged?
Maximum Force 0.000128 0.000450 YES
RMS Force 0.000128 0.000300 YES
Maximum Displacement 0.000156 0.001800 YES
RMS Displacement 0.000221 0.001200 YES
</pre>

What is the molecule?- fluorine molecule

What is the calculation method? - RB3LYP

What is the basis set? 6-31G(d,p)

What is the final energy E(RB3LYP) in atomic units (au)? -199.49825218 a.u.

What is the RMS gradient? 0.00007365

What is the point group of your molecule? Dinfh

bond angle= 180 (linear)

bond lenght= 1.40281

The optimisation file is liked to [[Media:TMACKIN F2 OPTF POP.LOG| here]]

<jmol><jmolApplet>
<title>Optimization of NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>TMACKIN F2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== vibration analysis ===

[[File:Tmackin display vibrations for optimized f2.PNG]]

how many modes do you expect from the 3N-6 rule? 1

which modes are degenerate (ie have the same energy)?

which modes are "bending" vibrations and which are "bond stretch" vibrations? Stretching

which mode is highly symmetric?

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

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

=== Charge analysis ===
no charge ie both atoms 0.00 charge

=== molecular orbitals ===

== Chlorine TriFluoride ==

used C2v point group symmetry [http://www.chembio.uoguelph.ca/educmat/chm364_preuss/5_6%20MO%20Theory_VB%20vs%20MO.pdf]

What is the molecule?- ClF3

What is the calculation method?

What is the basis set?

What is the final energy E(RB3LYP) in atomic units (au)?

What is the RMS gradient?

What is the point group of your molecule?

Rep:Mod:TBFA2017

2017-03-16T11:10:37Z

Tm1016: /* optimization of F2 */

Rep:Mod:TBFA2017

2017-03-16T11:10:14Z

Tm1016: /* Optimization of Hydrogen molecule */

== Optimization of Ammonia, NH3 ==

=== NH3 optimization ===

molecule name= TMackin_nh3_optf_pop
calculation method= RB3LYP
basis set=6-31G(d,p)
final energy E(RB3LYP) in atomic units (au)= -56.55776873
the point group of your molecule= C3V
bond length= 1.01798(N1-H4)
bond angle=37.129
<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
</pre>

<jmol><jmolApplet>
<title>Optimization of NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>TMACKIN NH3 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

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

=== Vibrations ===

[[File:Tmackin display vibrations optimised nh3.PNG]]

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

which modes are degenerate (ie have the same energy)? - ''2 and 3 have the same energy and 5 and 6 have the same energy''

which modes are "bending" vibrations and which are "bond stretch" vibrations? - ''bending=1,2,3 stretching=4,5,6
''

which mode is highly symmetric? ''4''

one mode is known as the "umbrella" mode, which one is this? ''1 is the umbrella mode''

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

=== Charge Analysis ===

charge on nitrogen atom= -1.125 charge on nitrogen atoms= +0.375

'''''

When carrying out calculations it is always good to check your results against your expectations. Write a sentence saying what charge (positive or negative) you would expect for N and H and why?'''''

== Optimization of N2 ==

What is the molecule?- nitrogen molecule

What is the calculation method? - RB3LYP

What is the basis set? 6-31G(d,p)

What is the final energy E(RB3LYP) in atomic units (au)? -109.52412868

What is the RMS gradient? 0.00000060

What is the point group of your molecule? Dinfh

bond angle= 180

bond lenght= 1.10550 (N1-N2)

<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000000 0.001800 YES
RMS Displacement 0.000000 0.001200 YES
</pre>

The optimisation file is liked to [[Media:TMACKIN N2 OPTF POP.LOG| here]]

<jmol><jmolApplet>
<title>Optimization of NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>TMACKIN N2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== vibration analysis ===
[[File:Tmackin display vibrations for optimized n2.PNG]]

how many modes do you expect from the 3N-6 rule? - use the 3n-5 rule so 1 vibration

which modes are degenerate (ie have the same energy)? ----------

which modes are "bending" vibrations and which are "bond stretch" vibrations? the 1 vibration is a stretching vibration

which mode is highly symmetric?--

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

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

=== Charge Analysis ===

both nitrogen atoms have 0.00 charge

== Optimization of Hydrogen molecule ==

<pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000000 0.001800 YES
RMS Displacement 0.000001 0.001200 YES

</pre>

What is the molecule? -hydrogen molecule

What is the calculation method?
RB3LYP

What is the basis set?
6-31G(d,p)

What is the final energy E(RB3LYP) in atomic units (au)?
-1.17853936 a.u

What is the RMS gradient?
0.00000017 a.u.

What is the point group of your molecule?
DinfH

bond length- 0.74279

bond angle- linear so 180 C

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

<jmol><jmolApplet>
<title>Optimization of NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>TMACKIN H2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibration analysis ===
[[File:Tmackin vibrations h2 molecule.PNG]]

how many modes do you expect from the 3N-6 rule?- linear 3n-5 rule hence 1 mode

which modes are degenerate (ie have the same energy)?----

which modes are "bending" vibrations and which are "bond stretch" vibrations? stretching vibration

which mode is highly symmetric?

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

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

=== Charge Analysis ===
charge on both atoms is 0.000
'''
When carrying out calculations it is always good to check your results against your expectations. Write a sentence saying what charge (positive or negative) you would expect for N and H and why'''

== Energy of Haber Bosch process ==

E(NH3)= -56.55776873
2*E(NH3)= -113.1155375
E(N2)= -109.52412868
E(H2)= -1.17853936
3*E(H2)= -3.53561808
ΔE=2*E(NH3)-[E(N2)+3*E(H2)]= -113.1155375 -(-109.52412868-3.53561808) = -0.05579074 a.u.

energy change = -146.4785879 kJ/mol ---- this is wrong!

Identify which is more stable the gaseous reactants or the ammonia product?

== optimization of F2 ==

<pre>
Item Value Threshold Converged?
Maximum Force 0.000128 0.000450 YES
RMS Force 0.000128 0.000300 YES
Maximum Displacement 0.000156 0.001800 YES
RMS Displacement 0.000221 0.001200 YES
</pre>

What is the molecule?- fluorine molecule

What is the calculation method? - RB3LYP

What is the basis set? 6-31G(d,p)

What is the final energy E(RB3LYP) in atomic units (au)? -199.49825218 a.u.

What is the RMS gradient? 0.00007365

What is the point group of your molecule? Dinfh

bond angle= 180 (linear)

bond lenght= 1.40281

The optimisation file is liked to [[Media:TMACKIN F2 OPTF POP.LOG| here]]

=== vibration analysis ===

[[File:Tmackin display vibrations for optimized f2.PNG]]

how many modes do you expect from the 3N-6 rule? 1

which modes are degenerate (ie have the same energy)?

which modes are "bending" vibrations and which are "bond stretch" vibrations? Stretching

which mode is highly symmetric?

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

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

=== Charge analysis ===
no charge ie both atoms 0.00 charge

=== molecular orbitals ===

Rep:Mod:TBFA2017

2017-03-16T11:09:38Z

Tm1016: /* Optimization of N2 */

== Optimization of Ammonia, NH3 ==

=== NH3 optimization ===

molecule name= TMackin_nh3_optf_pop
calculation method= RB3LYP
basis set=6-31G(d,p)
final energy E(RB3LYP) in atomic units (au)= -56.55776873
the point group of your molecule= C3V
bond length= 1.01798(N1-H4)
bond angle=37.129
<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
</pre>

<jmol><jmolApplet>
<title>Optimization of NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>TMACKIN NH3 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

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

=== Vibrations ===

[[File:Tmackin display vibrations optimised nh3.PNG]]

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

which modes are degenerate (ie have the same energy)? - ''2 and 3 have the same energy and 5 and 6 have the same energy''

which modes are "bending" vibrations and which are "bond stretch" vibrations? - ''bending=1,2,3 stretching=4,5,6
''

which mode is highly symmetric? ''4''

one mode is known as the "umbrella" mode, which one is this? ''1 is the umbrella mode''

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

=== Charge Analysis ===

charge on nitrogen atom= -1.125 charge on nitrogen atoms= +0.375

'''''

When carrying out calculations it is always good to check your results against your expectations. Write a sentence saying what charge (positive or negative) you would expect for N and H and why?'''''

== Optimization of N2 ==

What is the molecule?- nitrogen molecule

What is the calculation method? - RB3LYP

What is the basis set? 6-31G(d,p)

What is the final energy E(RB3LYP) in atomic units (au)? -109.52412868

What is the RMS gradient? 0.00000060

What is the point group of your molecule? Dinfh

bond angle= 180

bond lenght= 1.10550 (N1-N2)

<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000000 0.001800 YES
RMS Displacement 0.000000 0.001200 YES
</pre>

The optimisation file is liked to [[Media:TMACKIN N2 OPTF POP.LOG| here]]

<jmol><jmolApplet>
<title>Optimization of NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>TMACKIN N2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== vibration analysis ===
[[File:Tmackin display vibrations for optimized n2.PNG]]

how many modes do you expect from the 3N-6 rule? - use the 3n-5 rule so 1 vibration

which modes are degenerate (ie have the same energy)? ----------

which modes are "bending" vibrations and which are "bond stretch" vibrations? the 1 vibration is a stretching vibration

which mode is highly symmetric?--

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

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

=== Charge Analysis ===

both nitrogen atoms have 0.00 charge

== Optimization of Hydrogen molecule ==

<pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000000 0.001800 YES
RMS Displacement 0.000001 0.001200 YES

</pre>

What is the molecule? -hydrogen molecule

What is the calculation method?
RB3LYP

What is the basis set?
6-31G(d,p)

What is the final energy E(RB3LYP) in atomic units (au)?
-1.17853936 a.u

What is the RMS gradient?
0.00000017 a.u.

What is the point group of your molecule?
DinfH

bond length- 0.74279

bond angle- linear so 180 C

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

=== Vibration analysis ===
[[File:Tmackin vibrations h2 molecule.PNG]]

how many modes do you expect from the 3N-6 rule?- linear 3n-5 rule hence 1 mode

which modes are degenerate (ie have the same energy)?----

which modes are "bending" vibrations and which are "bond stretch" vibrations? stretching vibration

which mode is highly symmetric?

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

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

=== Charge Analysis ===
charge on both atoms is 0.000
'''
When carrying out calculations it is always good to check your results against your expectations. Write a sentence saying what charge (positive or negative) you would expect for N and H and why'''

== Energy of Haber Bosch process ==

E(NH3)= -56.55776873
2*E(NH3)= -113.1155375
E(N2)= -109.52412868
E(H2)= -1.17853936
3*E(H2)= -3.53561808
ΔE=2*E(NH3)-[E(N2)+3*E(H2)]= -113.1155375 -(-109.52412868-3.53561808) = -0.05579074 a.u.

energy change = -146.4785879 kJ/mol ---- this is wrong!

Identify which is more stable the gaseous reactants or the ammonia product?

== optimization of F2 ==

<pre>
Item Value Threshold Converged?
Maximum Force 0.000128 0.000450 YES
RMS Force 0.000128 0.000300 YES
Maximum Displacement 0.000156 0.001800 YES
RMS Displacement 0.000221 0.001200 YES
</pre>

What is the molecule?- fluorine molecule

What is the calculation method? - RB3LYP

What is the basis set? 6-31G(d,p)

What is the final energy E(RB3LYP) in atomic units (au)? -199.49825218 a.u.

What is the RMS gradient? 0.00007365

What is the point group of your molecule? Dinfh

bond angle= 180 (linear)

bond lenght= 1.40281

The optimisation file is liked to [[Media:TMACKIN F2 OPTF POP.LOG| here]]

=== vibration analysis ===

[[File:Tmackin display vibrations for optimized f2.PNG]]

how many modes do you expect from the 3N-6 rule? 1

which modes are degenerate (ie have the same energy)?

which modes are "bending" vibrations and which are "bond stretch" vibrations? Stretching

which mode is highly symmetric?

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

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

=== Charge analysis ===
no charge ie both atoms 0.00 charge

=== molecular orbitals ===

Rep:Mod:TBFA2017

2017-03-16T10:57:06Z

Tm1016: /* Charge analysis */

== Optimization of Ammonia, NH3 ==

=== NH3 optimization ===

molecule name= TMackin_nh3_optf_pop
calculation method= RB3LYP
basis set=6-31G(d,p)
final energy E(RB3LYP) in atomic units (au)= -56.55776873
the point group of your molecule= C3V
bond length= 1.01798(N1-H4)
bond angle=37.129
<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
</pre>

<jmol><jmolApplet>
<title>Optimization of NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>TMACKIN NH3 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

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

=== Vibrations ===

[[File:Tmackin display vibrations optimised nh3.PNG]]

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

which modes are degenerate (ie have the same energy)? - ''2 and 3 have the same energy and 5 and 6 have the same energy''

which modes are "bending" vibrations and which are "bond stretch" vibrations? - ''bending=1,2,3 stretching=4,5,6
''

which mode is highly symmetric? ''4''

one mode is known as the "umbrella" mode, which one is this? ''1 is the umbrella mode''

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

=== Charge Analysis ===

charge on nitrogen atom= -1.125 charge on nitrogen atoms= +0.375

'''''

When carrying out calculations it is always good to check your results against your expectations. Write a sentence saying what charge (positive or negative) you would expect for N and H and why?'''''

== Optimization of N2 ==

What is the molecule?- nitrogen molecule

What is the calculation method? - RB3LYP

What is the basis set? 6-31G(d,p)

What is the final energy E(RB3LYP) in atomic units (au)? -109.52412868

What is the RMS gradient? 0.00000060

What is the point group of your molecule? Dinfh

bond angle= 180

bond lenght= 1.10550 (N1-N2)

<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000000 0.001800 YES
RMS Displacement 0.000000 0.001200 YES
</pre>

The optimisation file is liked to [[Media:TMACKIN N2 OPTF POP.LOG| here]]

=== vibration analysis ===
[[File:Tmackin display vibrations for optimized n2.PNG]]

how many modes do you expect from the 3N-6 rule? - use the 3n-5 rule so 1 vibration

which modes are degenerate (ie have the same energy)? ----------

which modes are "bending" vibrations and which are "bond stretch" vibrations? the 1 vibration is a stretching vibration

which mode is highly symmetric?--

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

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

=== Charge Analysis ===

both nitrogen atoms have 0.00 charge

== Optimization of Hydrogen molecule ==

<pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000000 0.001800 YES
RMS Displacement 0.000001 0.001200 YES

</pre>

What is the molecule? -hydrogen molecule

What is the calculation method?
RB3LYP

What is the basis set?
6-31G(d,p)

What is the final energy E(RB3LYP) in atomic units (au)?
-1.17853936 a.u

What is the RMS gradient?
0.00000017 a.u.

What is the point group of your molecule?
DinfH

bond length- 0.74279

bond angle- linear so 180 C

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

=== Vibration analysis ===
[[File:Tmackin vibrations h2 molecule.PNG]]

how many modes do you expect from the 3N-6 rule?- linear 3n-5 rule hence 1 mode

which modes are degenerate (ie have the same energy)?----

which modes are "bending" vibrations and which are "bond stretch" vibrations? stretching vibration

which mode is highly symmetric?

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

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

=== Charge Analysis ===
charge on both atoms is 0.000
'''
When carrying out calculations it is always good to check your results against your expectations. Write a sentence saying what charge (positive or negative) you would expect for N and H and why'''

== Energy of Haber Bosch process ==

E(NH3)= -56.55776873
2*E(NH3)= -113.1155375
E(N2)= -109.52412868
E(H2)= -1.17853936
3*E(H2)= -3.53561808
ΔE=2*E(NH3)-[E(N2)+3*E(H2)]= -113.1155375 -(-109.52412868-3.53561808) = -0.05579074 a.u.

energy change = -146.4785879 kJ/mol ---- this is wrong!

Identify which is more stable the gaseous reactants or the ammonia product?

== optimization of F2 ==

<pre>
Item Value Threshold Converged?
Maximum Force 0.000128 0.000450 YES
RMS Force 0.000128 0.000300 YES
Maximum Displacement 0.000156 0.001800 YES
RMS Displacement 0.000221 0.001200 YES
</pre>

What is the molecule?- fluorine molecule

What is the calculation method? - RB3LYP

What is the basis set? 6-31G(d,p)

What is the final energy E(RB3LYP) in atomic units (au)? -199.49825218 a.u.

What is the RMS gradient? 0.00007365

What is the point group of your molecule? Dinfh

bond angle= 180 (linear)

bond lenght= 1.40281

The optimisation file is liked to [[Media:TMACKIN F2 OPTF POP.LOG| here]]

=== vibration analysis ===

[[File:Tmackin display vibrations for optimized f2.PNG]]

how many modes do you expect from the 3N-6 rule? 1

which modes are degenerate (ie have the same energy)?

which modes are "bending" vibrations and which are "bond stretch" vibrations? Stretching

which mode is highly symmetric?

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

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

=== Charge analysis ===
no charge ie both atoms 0.00 charge

=== molecular orbitals ===

Rep:Mod:TBFA2017

2017-03-16T10:56:44Z

Tm1016: /* vibration analysis */

== Optimization of Ammonia, NH3 ==

=== NH3 optimization ===

molecule name= TMackin_nh3_optf_pop
calculation method= RB3LYP
basis set=6-31G(d,p)
final energy E(RB3LYP) in atomic units (au)= -56.55776873
the point group of your molecule= C3V
bond length= 1.01798(N1-H4)
bond angle=37.129
<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
</pre>

<jmol><jmolApplet>
<title>Optimization of NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>TMACKIN NH3 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

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

=== Vibrations ===

[[File:Tmackin display vibrations optimised nh3.PNG]]

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

which modes are degenerate (ie have the same energy)? - ''2 and 3 have the same energy and 5 and 6 have the same energy''

which modes are "bending" vibrations and which are "bond stretch" vibrations? - ''bending=1,2,3 stretching=4,5,6
''

which mode is highly symmetric? ''4''

one mode is known as the "umbrella" mode, which one is this? ''1 is the umbrella mode''

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

=== Charge Analysis ===

charge on nitrogen atom= -1.125 charge on nitrogen atoms= +0.375

'''''

When carrying out calculations it is always good to check your results against your expectations. Write a sentence saying what charge (positive or negative) you would expect for N and H and why?'''''

== Optimization of N2 ==

What is the molecule?- nitrogen molecule

What is the calculation method? - RB3LYP

What is the basis set? 6-31G(d,p)

What is the final energy E(RB3LYP) in atomic units (au)? -109.52412868

What is the RMS gradient? 0.00000060

What is the point group of your molecule? Dinfh

bond angle= 180

bond lenght= 1.10550 (N1-N2)

<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000000 0.001800 YES
RMS Displacement 0.000000 0.001200 YES
</pre>

The optimisation file is liked to [[Media:TMACKIN N2 OPTF POP.LOG| here]]

=== vibration analysis ===
[[File:Tmackin display vibrations for optimized n2.PNG]]

how many modes do you expect from the 3N-6 rule? - use the 3n-5 rule so 1 vibration

which modes are degenerate (ie have the same energy)? ----------

which modes are "bending" vibrations and which are "bond stretch" vibrations? the 1 vibration is a stretching vibration

which mode is highly symmetric?--

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

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

=== Charge Analysis ===

both nitrogen atoms have 0.00 charge

== Optimization of Hydrogen molecule ==

<pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000000 0.001800 YES
RMS Displacement 0.000001 0.001200 YES

</pre>

What is the molecule? -hydrogen molecule

What is the calculation method?
RB3LYP

What is the basis set?
6-31G(d,p)

What is the final energy E(RB3LYP) in atomic units (au)?
-1.17853936 a.u

What is the RMS gradient?
0.00000017 a.u.

What is the point group of your molecule?
DinfH

bond length- 0.74279

bond angle- linear so 180 C

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

=== Vibration analysis ===
[[File:Tmackin vibrations h2 molecule.PNG]]

how many modes do you expect from the 3N-6 rule?- linear 3n-5 rule hence 1 mode

which modes are degenerate (ie have the same energy)?----

which modes are "bending" vibrations and which are "bond stretch" vibrations? stretching vibration

which mode is highly symmetric?

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

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

=== Charge Analysis ===
charge on both atoms is 0.000
'''
When carrying out calculations it is always good to check your results against your expectations. Write a sentence saying what charge (positive or negative) you would expect for N and H and why'''

== Energy of Haber Bosch process ==

E(NH3)= -56.55776873
2*E(NH3)= -113.1155375
E(N2)= -109.52412868
E(H2)= -1.17853936
3*E(H2)= -3.53561808
ΔE=2*E(NH3)-[E(N2)+3*E(H2)]= -113.1155375 -(-109.52412868-3.53561808) = -0.05579074 a.u.

energy change = -146.4785879 kJ/mol ---- this is wrong!

Identify which is more stable the gaseous reactants or the ammonia product?

== optimization of F2 ==

<pre>
Item Value Threshold Converged?
Maximum Force 0.000128 0.000450 YES
RMS Force 0.000128 0.000300 YES
Maximum Displacement 0.000156 0.001800 YES
RMS Displacement 0.000221 0.001200 YES
</pre>

What is the molecule?- fluorine molecule

What is the calculation method? - RB3LYP

What is the basis set? 6-31G(d,p)

What is the final energy E(RB3LYP) in atomic units (au)? -199.49825218 a.u.

What is the RMS gradient? 0.00007365

What is the point group of your molecule? Dinfh

bond angle= 180 (linear)

bond lenght= 1.40281

The optimisation file is liked to [[Media:TMACKIN F2 OPTF POP.LOG| here]]

=== vibration analysis ===

[[File:Tmackin display vibrations for optimized f2.PNG]]

how many modes do you expect from the 3N-6 rule? 1

which modes are degenerate (ie have the same energy)?

which modes are "bending" vibrations and which are "bond stretch" vibrations? Stretching

which mode is highly symmetric?

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

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

=== Charge analysis ===
no charge ie both atoms 0.00 charge

Rep:Mod:TBFA2017

2017-03-16T10:55:11Z

Tm1016: /* vibration analysis */

== Optimization of Ammonia, NH3 ==

=== NH3 optimization ===

molecule name= TMackin_nh3_optf_pop
calculation method= RB3LYP
basis set=6-31G(d,p)
final energy E(RB3LYP) in atomic units (au)= -56.55776873
the point group of your molecule= C3V
bond length= 1.01798(N1-H4)
bond angle=37.129
<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
</pre>

<jmol><jmolApplet>
<title>Optimization of NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>TMACKIN NH3 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

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

=== Vibrations ===

[[File:Tmackin display vibrations optimised nh3.PNG]]

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

which modes are degenerate (ie have the same energy)? - ''2 and 3 have the same energy and 5 and 6 have the same energy''

which modes are "bending" vibrations and which are "bond stretch" vibrations? - ''bending=1,2,3 stretching=4,5,6
''

which mode is highly symmetric? ''4''

one mode is known as the "umbrella" mode, which one is this? ''1 is the umbrella mode''

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

=== Charge Analysis ===

charge on nitrogen atom= -1.125 charge on nitrogen atoms= +0.375

'''''

When carrying out calculations it is always good to check your results against your expectations. Write a sentence saying what charge (positive or negative) you would expect for N and H and why?'''''

== Optimization of N2 ==

What is the molecule?- nitrogen molecule

What is the calculation method? - RB3LYP

What is the basis set? 6-31G(d,p)

What is the final energy E(RB3LYP) in atomic units (au)? -109.52412868

What is the RMS gradient? 0.00000060

What is the point group of your molecule? Dinfh

bond angle= 180

bond lenght= 1.10550 (N1-N2)

<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000000 0.001800 YES
RMS Displacement 0.000000 0.001200 YES
</pre>

The optimisation file is liked to [[Media:TMACKIN N2 OPTF POP.LOG| here]]

=== vibration analysis ===
[[File:Tmackin display vibrations for optimized n2.PNG]]

how many modes do you expect from the 3N-6 rule? - use the 3n-5 rule so 1 vibration

which modes are degenerate (ie have the same energy)? ----------

which modes are "bending" vibrations and which are "bond stretch" vibrations? the 1 vibration is a stretching vibration

which mode is highly symmetric?--

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

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

=== Charge Analysis ===

both nitrogen atoms have 0.00 charge

== Optimization of Hydrogen molecule ==

<pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000000 0.001800 YES
RMS Displacement 0.000001 0.001200 YES

</pre>

What is the molecule? -hydrogen molecule

What is the calculation method?
RB3LYP

What is the basis set?
6-31G(d,p)

What is the final energy E(RB3LYP) in atomic units (au)?
-1.17853936 a.u

What is the RMS gradient?
0.00000017 a.u.

What is the point group of your molecule?
DinfH

bond length- 0.74279

bond angle- linear so 180 C

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

=== Vibration analysis ===
[[File:Tmackin vibrations h2 molecule.PNG]]

how many modes do you expect from the 3N-6 rule?- linear 3n-5 rule hence 1 mode

which modes are degenerate (ie have the same energy)?----

which modes are "bending" vibrations and which are "bond stretch" vibrations? stretching vibration

which mode is highly symmetric?

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

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

=== Charge Analysis ===
charge on both atoms is 0.000
'''
When carrying out calculations it is always good to check your results against your expectations. Write a sentence saying what charge (positive or negative) you would expect for N and H and why'''

== Energy of Haber Bosch process ==

E(NH3)= -56.55776873
2*E(NH3)= -113.1155375
E(N2)= -109.52412868
E(H2)= -1.17853936
3*E(H2)= -3.53561808
ΔE=2*E(NH3)-[E(N2)+3*E(H2)]= -113.1155375 -(-109.52412868-3.53561808) = -0.05579074 a.u.

energy change = -146.4785879 kJ/mol ---- this is wrong!

Identify which is more stable the gaseous reactants or the ammonia product?

== optimization of F2 ==

<pre>
Item Value Threshold Converged?
Maximum Force 0.000128 0.000450 YES
RMS Force 0.000128 0.000300 YES
Maximum Displacement 0.000156 0.001800 YES
RMS Displacement 0.000221 0.001200 YES
</pre>

What is the molecule?- fluorine molecule

What is the calculation method? - RB3LYP

What is the basis set? 6-31G(d,p)

What is the final energy E(RB3LYP) in atomic units (au)? -199.49825218 a.u.

What is the RMS gradient? 0.00007365

What is the point group of your molecule? Dinfh

bond angle= 180 (linear)

bond lenght= 1.40281

The optimisation file is liked to [[Media:TMACKIN F2 OPTF POP.LOG| here]]

=== vibration analysis ===

[[File:Tmackin display vibrations for optimized f2.PNG]]

how many modes do you expect from the 3N-6 rule? 1

which modes are degenerate (ie have the same energy)?

which modes are "bending" vibrations and which are "bond stretch" vibrations? Stretching

which mode is highly symmetric?

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

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

Rep:Mod:TBFA2017

2017-03-16T10:53:50Z

Tm1016: /* optimization of F2 */

== Optimization of Ammonia, NH3 ==

=== NH3 optimization ===

molecule name= TMackin_nh3_optf_pop
calculation method= RB3LYP
basis set=6-31G(d,p)
final energy E(RB3LYP) in atomic units (au)= -56.55776873
the point group of your molecule= C3V
bond length= 1.01798(N1-H4)
bond angle=37.129
<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
</pre>

<jmol><jmolApplet>
<title>Optimization of NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>TMACKIN NH3 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

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

=== Vibrations ===

[[File:Tmackin display vibrations optimised nh3.PNG]]

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

which modes are degenerate (ie have the same energy)? - ''2 and 3 have the same energy and 5 and 6 have the same energy''

which modes are "bending" vibrations and which are "bond stretch" vibrations? - ''bending=1,2,3 stretching=4,5,6
''

which mode is highly symmetric? ''4''

one mode is known as the "umbrella" mode, which one is this? ''1 is the umbrella mode''

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

=== Charge Analysis ===

charge on nitrogen atom= -1.125 charge on nitrogen atoms= +0.375

'''''

When carrying out calculations it is always good to check your results against your expectations. Write a sentence saying what charge (positive or negative) you would expect for N and H and why?'''''

== Optimization of N2 ==

What is the molecule?- nitrogen molecule

What is the calculation method? - RB3LYP

What is the basis set? 6-31G(d,p)

What is the final energy E(RB3LYP) in atomic units (au)? -109.52412868

What is the RMS gradient? 0.00000060

What is the point group of your molecule? Dinfh

bond angle= 180

bond lenght= 1.10550 (N1-N2)

<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000000 0.001800 YES
RMS Displacement 0.000000 0.001200 YES
</pre>

The optimisation file is liked to [[Media:TMACKIN N2 OPTF POP.LOG| here]]

=== vibration analysis ===
[[File:Tmackin display vibrations for optimized n2.PNG]]

how many modes do you expect from the 3N-6 rule? - use the 3n-5 rule so 1 vibration

which modes are degenerate (ie have the same energy)? ----------

which modes are "bending" vibrations and which are "bond stretch" vibrations? the 1 vibration is a stretching vibration

which mode is highly symmetric?--

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

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

=== Charge Analysis ===

both nitrogen atoms have 0.00 charge

== Optimization of Hydrogen molecule ==

<pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000000 0.001800 YES
RMS Displacement 0.000001 0.001200 YES

</pre>

What is the molecule? -hydrogen molecule

What is the calculation method?
RB3LYP

What is the basis set?
6-31G(d,p)

What is the final energy E(RB3LYP) in atomic units (au)?
-1.17853936 a.u

What is the RMS gradient?
0.00000017 a.u.

What is the point group of your molecule?
DinfH

bond length- 0.74279

bond angle- linear so 180 C

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

=== Vibration analysis ===
[[File:Tmackin vibrations h2 molecule.PNG]]

how many modes do you expect from the 3N-6 rule?- linear 3n-5 rule hence 1 mode

which modes are degenerate (ie have the same energy)?----

which modes are "bending" vibrations and which are "bond stretch" vibrations? stretching vibration

which mode is highly symmetric?

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

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

=== Charge Analysis ===
charge on both atoms is 0.000
'''
When carrying out calculations it is always good to check your results against your expectations. Write a sentence saying what charge (positive or negative) you would expect for N and H and why'''

== Energy of Haber Bosch process ==

E(NH3)= -56.55776873
2*E(NH3)= -113.1155375
E(N2)= -109.52412868
E(H2)= -1.17853936
3*E(H2)= -3.53561808
ΔE=2*E(NH3)-[E(N2)+3*E(H2)]= -113.1155375 -(-109.52412868-3.53561808) = -0.05579074 a.u.

energy change = -146.4785879 kJ/mol ---- this is wrong!

Identify which is more stable the gaseous reactants or the ammonia product?

== optimization of F2 ==

<pre>
Item Value Threshold Converged?
Maximum Force 0.000128 0.000450 YES
RMS Force 0.000128 0.000300 YES
Maximum Displacement 0.000156 0.001800 YES
RMS Displacement 0.000221 0.001200 YES
</pre>

What is the molecule?- fluorine molecule

What is the calculation method? - RB3LYP

What is the basis set? 6-31G(d,p)

What is the final energy E(RB3LYP) in atomic units (au)? -199.49825218 a.u.

What is the RMS gradient? 0.00007365

What is the point group of your molecule? Dinfh

bond angle= 180 (linear)

bond lenght= 1.40281

The optimisation file is liked to [[Media:TMACKIN F2 OPTF POP.LOG| here]]

=== vibration analysis ===

[[File:Tmackin display vibrations for optimized f2.PNG]]

File:TMACKIN F2 OPTF POP.LOG

2017-03-16T10:53:13Z

Tm1016:

Rep:Mod:TBFA2017

2017-03-16T10:52:34Z

Tm1016: /* Energy of Haber Bosch process */

== Optimization of Ammonia, NH3 ==

=== NH3 optimization ===

molecule name= TMackin_nh3_optf_pop
calculation method= RB3LYP
basis set=6-31G(d,p)
final energy E(RB3LYP) in atomic units (au)= -56.55776873
the point group of your molecule= C3V
bond length= 1.01798(N1-H4)
bond angle=37.129
<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
</pre>

<jmol><jmolApplet>
<title>Optimization of NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>TMACKIN NH3 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

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

=== Vibrations ===

[[File:Tmackin display vibrations optimised nh3.PNG]]

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

which modes are degenerate (ie have the same energy)? - ''2 and 3 have the same energy and 5 and 6 have the same energy''

which modes are "bending" vibrations and which are "bond stretch" vibrations? - ''bending=1,2,3 stretching=4,5,6
''

which mode is highly symmetric? ''4''

one mode is known as the "umbrella" mode, which one is this? ''1 is the umbrella mode''

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

=== Charge Analysis ===

charge on nitrogen atom= -1.125 charge on nitrogen atoms= +0.375

'''''

When carrying out calculations it is always good to check your results against your expectations. Write a sentence saying what charge (positive or negative) you would expect for N and H and why?'''''

== Optimization of N2 ==

What is the molecule?- nitrogen molecule

What is the calculation method? - RB3LYP

What is the basis set? 6-31G(d,p)

What is the final energy E(RB3LYP) in atomic units (au)? -109.52412868

What is the RMS gradient? 0.00000060

What is the point group of your molecule? Dinfh

bond angle= 180

bond lenght= 1.10550 (N1-N2)

<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000000 0.001800 YES
RMS Displacement 0.000000 0.001200 YES
</pre>

The optimisation file is liked to [[Media:TMACKIN N2 OPTF POP.LOG| here]]

=== vibration analysis ===
[[File:Tmackin display vibrations for optimized n2.PNG]]

how many modes do you expect from the 3N-6 rule? - use the 3n-5 rule so 1 vibration

which modes are degenerate (ie have the same energy)? ----------

which modes are "bending" vibrations and which are "bond stretch" vibrations? the 1 vibration is a stretching vibration

which mode is highly symmetric?--

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

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

=== Charge Analysis ===

both nitrogen atoms have 0.00 charge

== Optimization of Hydrogen molecule ==

<pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000000 0.001800 YES
RMS Displacement 0.000001 0.001200 YES

</pre>

What is the molecule? -hydrogen molecule

What is the calculation method?
RB3LYP

What is the basis set?
6-31G(d,p)

What is the final energy E(RB3LYP) in atomic units (au)?
-1.17853936 a.u

What is the RMS gradient?
0.00000017 a.u.

What is the point group of your molecule?
DinfH

bond length- 0.74279

bond angle- linear so 180 C

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

=== Vibration analysis ===
[[File:Tmackin vibrations h2 molecule.PNG]]

how many modes do you expect from the 3N-6 rule?- linear 3n-5 rule hence 1 mode

which modes are degenerate (ie have the same energy)?----

which modes are "bending" vibrations and which are "bond stretch" vibrations? stretching vibration

which mode is highly symmetric?

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

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

=== Charge Analysis ===
charge on both atoms is 0.000
'''
When carrying out calculations it is always good to check your results against your expectations. Write a sentence saying what charge (positive or negative) you would expect for N and H and why'''

== Energy of Haber Bosch process ==

E(NH3)= -56.55776873
2*E(NH3)= -113.1155375
E(N2)= -109.52412868
E(H2)= -1.17853936
3*E(H2)= -3.53561808
ΔE=2*E(NH3)-[E(N2)+3*E(H2)]= -113.1155375 -(-109.52412868-3.53561808) = -0.05579074 a.u.

energy change = -146.4785879 kJ/mol ---- this is wrong!

Identify which is more stable the gaseous reactants or the ammonia product?

== optimization of F2 ==

<pre>
Item Value Threshold Converged?
Maximum Force 0.000128 0.000450 YES
RMS Force 0.000128 0.000300 YES
Maximum Displacement 0.000156 0.001800 YES
RMS Displacement 0.000221 0.001200 YES
</pre>

What is the molecule?- fluorine molecule

What is the calculation method? - RB3LYP

What is the basis set? 6-31G(d,p)

What is the final energy E(RB3LYP) in atomic units (au)? -199.49825218 a.u.

What is the RMS gradient? 0.00007365

What is the point group of your molecule? Dinfh

bond angle= 180 (linear)

bond lenght= 1.40281

=== vibration analysis ===

[[File:Tmackin display vibrations for optimized f2.PNG]]

File:Tmackin display vibrations for optimized f2.PNG

2017-03-16T10:52:20Z

Tm1016:

Rep:Mod:TBFA2017

2017-03-16T09:56:19Z

Tm1016: /* Charge Analysis */

Rep:Mod:TBFA2017

2017-03-16T09:36:30Z

Tm1016: /* Vibration analysis */

Rep:Mod:TBFA2017

2017-03-16T09:32:00Z

Tm1016: /* vibration analysis */

Rep:Mod:TBFA2017

2017-03-16T09:31:35Z

Tm1016: /* Optimization of Hydrogen molecule */

File:Tmackin vibrations h2 molecule.PNG

2017-03-16T09:31:21Z

Tm1016:

Rep:Mod:TBFA2017

2017-03-16T09:29:31Z

Tm1016: /* Optimization of Hydrogen molecule */

Rep:Mod:TBFA2017

2017-03-16T09:28:38Z

Tm1016: /* Optimization of Ammonia, NH3 */

Rep:Mod:TBFA2017

2017-03-16T09:28:17Z

Tm1016: /* Charge Analysis */

File:TMACKIN H2 OPTF POP.LOG

2017-03-16T09:27:54Z

Tm1016:

Rep:Mod:TBFA2017

2017-03-13T12:09:11Z

Tm1016: /* vibration analysis */

File:Tmackin display vibrations for optimized n2.PNG

2017-03-13T12:03:59Z

Tm1016: