ChemWiki - User contributions [en]

MRD:HJW116

2018-05-18T14:35:34Z

Hjw116: /* Polanyi's rules */

== Exercise 1 ==

=== Transition state ===

A potential energy surface graph is gained from a function with two variables, in this case distance of AB, and BC. The transition state is seen at "saddle points" on the plotted graph. These are the maxima and minimas of the energy plot. These occur when the derivatives of each variable is equal to 0.

To determine whether it is a maxima or minima, take the double derivative; a positive value gives a minima, and negative, the maxima.

=== Locating the Transition State ===

[[File:HJW Transition state H2+H.png | thumb | left | 300px | The point where the line AB and BC cross gives the value for the first transition state.]]

[[File:HJW starightline TSthing.png | thumb | centre | 300px | The initial momentum has been set to zero, in order for there not to be enough energy to escape the potential well.]]

In order to maintain a set distance over time, AB and BC were made equal and set to a variety of values; 0.908 giving a straight line (non-changing distance)

=== MEP and Dynamic Calculations ===

The plot of the MEP follows the lowest energy path for the reaction, where the velocity of the molecule is continuously returned to 0 as to remove inertia from making any effect. This is seen on the MEP plot, not the dynamic.

[[File:HJW116 Dyn cont H2.png | thumb | left | Trajectory plot-Dynamics calculation type]]

[[File:HJW116 MEP cont H2.png | thumb | centre | Trajectory plot-MEP calculation type]]

[[File:HJW116 Dyn dis-time H2.png | thumb | left | Distance vs Time graph-Dynamics calculation type]]

[[File:HJW116 MEP dis-time H2.png | thumb | centre | Distance vs Time graph-MEP calculation type]]

=== Reactive and Unreactive Trajectories ===

{| class="wikitable" border="1"
|+ Effect of inertia (Dynamic calculation type)
! p1 !! p2 !! ETotal !! React/Non!!Contour plot !! Discussion
|-
| -1.25 || -2.5 || -99.199 || Reactive || [[File:HJW SP react1b.PNG|315px]] ||Prior to the transition state, the AB molecule does not oscillate (shown by the straight line) Once the minima has been passed, and the BC bond is formed, the bond starts oscillating more. ||
|-
| -1.5 || -2.0 || -100.456 || Unreactive || [[File:HJW SP react2.PNG|315px]] || Despite the bond approaching each other at the start, the momentum of each (AB and C) are not strong enough to overcome the repulsive forces involved.
|-
| -1.5 || -2.5 || -98.956 || Reactive || [[File:HJW SP react3.PNG|315px]] || Simple reaction, AB approach C, whilst vibrating, where BC forms and the strength of vibration continues.
|-
| -2.5 || -5.0 || -84.956 || Uneactive || [[File:HJW SP react4.PNG|315px]] || There is no oscillation at the start whereas, upon contact with C, there is a period of heavy vibrations, that leads to dissociation of the molecule. .||
|-
| -2.5 || -5.2 || -83.416 || Reactive || [[File:HJW SP react5.PNG|315px]] || In a similar way to the reaction above, this gives, upon collision of AB and C, a short lived BC bond that quickly dissociates. However, the reaction continues and a BC molecule is successfully created with strong oscillation.
||
|}

=== Transition state theory ===

A key point to the theory is that the atoms follow the Born-Oppenheimer approximation and ignores the effects of quantum tunneling. It is also assumed that the starting products are equlibrating as according to the energies given by the Boltzmann Distribution. The theory also separates the products and reactants into separate "spaces" with the transition being the middle point of this, where the theoretical product is a mix of the two. Once the state has collapsed and the product is formed, the reaction is irreversible under the same conditions.

My 4th and 5th reaction however, shows the making of product, followed by the state transition back to reactants. Thus breaking the theory. This could be attributed to the calculation being run assuming an isolated system, where as the theory accounts for the external factors as well to determine the equilibrium.

== Exercise 2 ==

As the H-H bond is (-432 kJ/mol), and the F-H is higher in energy (-565 kJ/mol) <ref name="[1]" />, the reaction (F + H2 ⇌ H + HF) is, therefore exothermic, as the energy released from the making of the H-F bond is greater than that taken from the H-H being broken. This can be attributed due to the increased ionic character between the F-H bond due to the change in electronegativity. The reverse direction is therefore endothermic.

In order to determine the transition state the saddle state was needed. This was, again, determined via the maximum of an MEP graph of IN distance vs Time (derivative = 0). Through trial and error, this gave values of AB=1.812 Å and BC=0.745 Å in which A is Flourine, and B,C are both Hydrogen. (Momenta was set to zero.) This gave a straight line graph, thus showing the correct value had been obtained.

=== Activation Energy ===

By slight alteration of the equilibrium settings (AB being changed to 1.91 Å) we can force the reaction to one side. In this case, due to the extended bond length, towards the F + H2 side.

Using an MEP (Energy vs Time) graph the activation energy was seen to be to be 29.16 kcal/mol (121.99 kJ/mol).

[[File:H2 F energydiagram.PNG| thumb | left | 320px | MEP Energy vs time]]

==== Dynamics ====

From the graph it was seen the AB distance, for determining the trajectory, was 1.81 Å and BC was 0.75 Å, with momenta of -0.5 and 0.8 kg.m/sec respectively. The contour plot of which is shown:

[[File:HJW116 FHreaction traj.PNG | thumb | 300px | left | Reaction trajectory]]
[[File:HJW116 FHreaction momentavstime.PNG | thumb | 300px | centre | Momentum vs Time]]
[[File:HJW116 FHreaction energyvstime.PNG | thumb | 300px | left | Energy vs Time]]

From the contour and momenta graphs, it can be seen the high level of vibrational energy, showing the energy released form the exothermic process is being transferred into kinetic vibrations. The energy plot clearly shows the conservation of energy, as the kinetic rises, the potential falls et vice versa.

=== Polanyi's rules ===

When a transition state is seen, it can mimic the products or reactants; these rules follow the effects of vibrational, and translational, vibrations have on this. <ref name="[2]" /> It is seen that high vibrational energy leads to an late Ts, with the early Ts being highly disfavoured. Exothermic reactions are late transition states, therefore has products with increased amount of vibrational energy, and lower translational as energy must be conserved. <ref name="[3]" /> For an endothermic reaction, this is simply reversed.

A set up of AB=1.8 and BC=0.78 were used to see the rules for our exothermic reaction. The momenta were set to -0.55 and 0.15 respectively, followed by a run of the inverse of this. Run 1 showed product being formed, however run 2 showed no product being formed, mainly due to it's initial momentum being in the wrong direction. This being the exothermic part of the reversible reaction, it has a late transition state, therefore the vibrational energy is seen to show the best efficacy towards driving the reaction on.

[[File:HJW116 Prules run1.PNG | thumb | left | 300px | Run 1]]

[[File:HJW116 Prules run2.PNG | thumb | centre | 300px | Run 2]]

== References ==

<references>
<ref name="[1]">http://www.wiredchemist.com/chemistry/data/bond_energies_lengths.html (Assessed on 16/05/2018 18ː53).</ref>

<ref name="[2]">Evans, M. G.; Polanyi, M., J. Chem. Soc., Faraday Trans., 1936, 32, 1340.</ref>

<ref name="[3]">Z. Zhang et al, J.Phys. Chem. Lett., 2012, "Theoretical Study of the Validity of the Polanyi Rules for the Late-Barrier Cl + CHD3 Reaction", Vol. 3 (23) p.3416–3419.</ref>
</references>

MRD:HJW116

2018-05-18T14:35:05Z

Hjw116: /* Polanyi's rules */

== Exercise 1 ==

=== Transition state ===

A potential energy surface graph is gained from a function with two variables, in this case distance of AB, and BC. The transition state is seen at "saddle points" on the plotted graph. These are the maxima and minimas of the energy plot. These occur when the derivatives of each variable is equal to 0.

To determine whether it is a maxima or minima, take the double derivative; a positive value gives a minima, and negative, the maxima.

=== Locating the Transition State ===

[[File:HJW Transition state H2+H.png | thumb | left | 300px | The point where the line AB and BC cross gives the value for the first transition state.]]

[[File:HJW starightline TSthing.png | thumb | centre | 300px | The initial momentum has been set to zero, in order for there not to be enough energy to escape the potential well.]]

In order to maintain a set distance over time, AB and BC were made equal and set to a variety of values; 0.908 giving a straight line (non-changing distance)

=== MEP and Dynamic Calculations ===

The plot of the MEP follows the lowest energy path for the reaction, where the velocity of the molecule is continuously returned to 0 as to remove inertia from making any effect. This is seen on the MEP plot, not the dynamic.

[[File:HJW116 Dyn cont H2.png | thumb | left | Trajectory plot-Dynamics calculation type]]

[[File:HJW116 MEP cont H2.png | thumb | centre | Trajectory plot-MEP calculation type]]

[[File:HJW116 Dyn dis-time H2.png | thumb | left | Distance vs Time graph-Dynamics calculation type]]

[[File:HJW116 MEP dis-time H2.png | thumb | centre | Distance vs Time graph-MEP calculation type]]

=== Reactive and Unreactive Trajectories ===

{| class="wikitable" border="1"
|+ Effect of inertia (Dynamic calculation type)
! p1 !! p2 !! ETotal !! React/Non!!Contour plot !! Discussion
|-
| -1.25 || -2.5 || -99.199 || Reactive || [[File:HJW SP react1b.PNG|315px]] ||Prior to the transition state, the AB molecule does not oscillate (shown by the straight line) Once the minima has been passed, and the BC bond is formed, the bond starts oscillating more. ||
|-
| -1.5 || -2.0 || -100.456 || Unreactive || [[File:HJW SP react2.PNG|315px]] || Despite the bond approaching each other at the start, the momentum of each (AB and C) are not strong enough to overcome the repulsive forces involved.
|-
| -1.5 || -2.5 || -98.956 || Reactive || [[File:HJW SP react3.PNG|315px]] || Simple reaction, AB approach C, whilst vibrating, where BC forms and the strength of vibration continues.
|-
| -2.5 || -5.0 || -84.956 || Uneactive || [[File:HJW SP react4.PNG|315px]] || There is no oscillation at the start whereas, upon contact with C, there is a period of heavy vibrations, that leads to dissociation of the molecule. .||
|-
| -2.5 || -5.2 || -83.416 || Reactive || [[File:HJW SP react5.PNG|315px]] || In a similar way to the reaction above, this gives, upon collision of AB and C, a short lived BC bond that quickly dissociates. However, the reaction continues and a BC molecule is successfully created with strong oscillation.
||
|}

=== Transition state theory ===

A key point to the theory is that the atoms follow the Born-Oppenheimer approximation and ignores the effects of quantum tunneling. It is also assumed that the starting products are equlibrating as according to the energies given by the Boltzmann Distribution. The theory also separates the products and reactants into separate "spaces" with the transition being the middle point of this, where the theoretical product is a mix of the two. Once the state has collapsed and the product is formed, the reaction is irreversible under the same conditions.

My 4th and 5th reaction however, shows the making of product, followed by the state transition back to reactants. Thus breaking the theory. This could be attributed to the calculation being run assuming an isolated system, where as the theory accounts for the external factors as well to determine the equilibrium.

== Exercise 2 ==

As the H-H bond is (-432 kJ/mol), and the F-H is higher in energy (-565 kJ/mol) <ref name="[1]" />, the reaction (F + H2 ⇌ H + HF) is, therefore exothermic, as the energy released from the making of the H-F bond is greater than that taken from the H-H being broken. This can be attributed due to the increased ionic character between the F-H bond due to the change in electronegativity. The reverse direction is therefore endothermic.

In order to determine the transition state the saddle state was needed. This was, again, determined via the maximum of an MEP graph of IN distance vs Time (derivative = 0). Through trial and error, this gave values of AB=1.812 Å and BC=0.745 Å in which A is Flourine, and B,C are both Hydrogen. (Momenta was set to zero.) This gave a straight line graph, thus showing the correct value had been obtained.

=== Activation Energy ===

By slight alteration of the equilibrium settings (AB being changed to 1.91 Å) we can force the reaction to one side. In this case, due to the extended bond length, towards the F + H2 side.

Using an MEP (Energy vs Time) graph the activation energy was seen to be to be 29.16 kcal/mol (121.99 kJ/mol).

[[File:H2 F energydiagram.PNG| thumb | left | 320px | MEP Energy vs time]]

==== Dynamics ====

From the graph it was seen the AB distance, for determining the trajectory, was 1.81 Å and BC was 0.75 Å, with momenta of -0.5 and 0.8 kg.m/sec respectively. The contour plot of which is shown:

[[File:HJW116 FHreaction traj.PNG | thumb | 300px | left | Reaction trajectory]]
[[File:HJW116 FHreaction momentavstime.PNG | thumb | 300px | centre | Momentum vs Time]]
[[File:HJW116 FHreaction energyvstime.PNG | thumb | 300px | left | Energy vs Time]]

From the contour and momenta graphs, it can be seen the high level of vibrational energy, showing the energy released form the exothermic process is being transferred into kinetic vibrations. The energy plot clearly shows the conservation of energy, as the kinetic rises, the potential falls et vice versa.

=== Polanyi's rules ===

When a transition state is seen, it can mimic the products or reactants; these rules follow the effects of vibrational, and translational, vibrations have on this. <ref name="[2]" /> It is seen that high vibrational energy leads to an late Ts, with the early Ts being highly disfavoured. Exothermic reactions are late transition states, therefore has products with increased amount of vibrational energy, and lower translational as energy must be conserved. <ref name="[3]" /> For an endothermic reaction, this is simply reversed.

A set up of AB=1.8 and BC=0.78 were used to see the rules for our exothermic reaction. The momenta were set to -0.55 and 0.15 respectively, followed by a run of the inverse of this. Run 1 showed product being formed, however run 2 showed no product being formed, mainly due to it's initial momentum being in the wrong direction. This being the exothermic part of the reversible reaction, it has a late transition state, therefore the vibrational energy is seen to show the best efficacy towards driving the reaction on.

[File:HJW116 Prules run1.PNG | thumb | left | 300px | Run 1]]

[File:HJW116 Prules run2.PNG | thumb | centre | 300px | Run 2]]

== References ==

<references>
<ref name="[1]">http://www.wiredchemist.com/chemistry/data/bond_energies_lengths.html (Assessed on 16/05/2018 18ː53).</ref>

<ref name="[2]">Evans, M. G.; Polanyi, M., J. Chem. Soc., Faraday Trans., 1936, 32, 1340.</ref>

<ref name="[3]">Z. Zhang et al, J.Phys. Chem. Lett., 2012, "Theoretical Study of the Validity of the Polanyi Rules for the Late-Barrier Cl + CHD3 Reaction", Vol. 3 (23) p.3416–3419.</ref>
</references>

File:HJW116 Prules run2.PNG

2018-05-18T14:26:46Z

Hjw116:

2018-05-17T14:36:06Z

Hjw116:

File:HJW116 FHreaction momentavstime.PNG

2018-05-17T14:35:33Z

Hjw116:

File:HJW116 FHreaction traj.PNG

2018-05-17T14:34:51Z

Hjw116:

MRD:HJW116

2018-05-17T14:26:17Z

Hjw116: /* Activation Energy */

== Exercise 1 ==

=== Transition state ===

A potential energy surface graph is gained from a function with two variables, in this case distance of AB, and BC. The transition state is seen at "saddle points" on the plotted graph. These are the maxima and minimas of the energy plot. These occur when the derivatives of each variable is equal to 0.

To determine whether it is a maxima or minima, take the double derivative; a positive value gives a minima, and negative, the maxima.

=== Locating the Transition State ===

[[File:HJW Transition state H2+H.png | thumb | left | 200px | The point where the line AB and BC cross gives the value for the first transition state.]]

[[File:HJW starightline TSthing.png | thumb | right | 200px | The initial momentum has been set to zero, in order for there not to be enough energy to escape the potential well.]]

In order to maintain a set distance over time, AB and BC were made equal and set to a variety of values; 0.908 giving a straight line (non-changing distance)

=== MEP and Dynamic Calculations ===

The plot of the MEP follows the lowest energy path for the reaction, where the velocity of the molecule is continuously returned to 0 as to remove inertia from making any effect. This is seen on the MEP plot, not the dynamic.

[[File:HJW116 Dyn cont H2.png | thumb | left | Trajectory plot-Dynamics calculation type]]

[[File:HJW116 MEP cont H2.png | thumb | centre | Trajectory plot-MEP calculation type]]

[[File:HJW116 Dyn dis-time H2.png | thumb | left | Distance vs Time graph-Dynamics calculation type]]

[[File:HJW116 MEP dis-time H2.png | thumb | centre | Distance vs Time graph-MEP calculation type]]

=== Reactive and Unreactive Trajectories ===

{| class="wikitable" border="1"
|+ Effect of inertia (Dynamic calculation type)
! p1 !! p2 !! ETotal !! React/Non!!Contour plot !! Discussion
|-
| -1.25 || -2.5 || -99.199 || Reactive || [[File:HJW SP react1b.PNG|315px]] ||Prior to the transition state, the AB molecule does not oscillate (shown by the straight line) Once the minima has been passed, and the BC bond is formed, the bond starts oscillating more. ||
|-
| -1.5 || -2.0 || -100.456 || Unreactive || [[File:HJW SP react2.PNG|315px]] || Despite the bond approaching each other at the start, the momentum of each (AB and C) are not strong enough to overcome the repulsive forces involved.
|-
| -1.5 || -2.5 || -98.956 || Reactive || [[File:HJW SP react3.PNG|315px]] || Simple reaction, AB approach C, whilst vibrating, where BC forms and the strength of vibration continues.
|-
| -2.5 || -5.0 || -84.956 || Uneactive || [[File:HJW SP react4.PNG|315px]] || There is no oscillation at the start whereas, upon contact with C, there is a period of heavy vibrations, that leads to dissociation of the molecule. .||
|-
| -2.5 || -5.2 || -83.416 || Reactive || [[File:HJW SP react5.PNG|315px]] || In a similar way to the reaction above, this gives, upon collision of AB and C, a short lived BC bond that quickly dissociates. However, the reaction continues and a BC molecule is successfully created with strong oscillation.
||
|}

=== Transition state theory ===

A key point to the theory is that the atoms follow the Born-Oppenheimer approximation and ignores the effects of quantum tunneling. It is also assumed that the starting products are equlibrating as according to the energies given by the Boltzmann Distribution. The theory also separates the products and reactants into separate "spaces" with the transition being the middle point of this, where the theoretical product is a mix of the two. Once the state has collapsed and the product is formed, the reaction is irreversible under the same conditions.

My 4th and 5th reaction however, shows the making of product, followed by the state transition back to reactants. Thus breaking the theory. This could be attributed to the calculation being run assuming an isolated system, where as the theory accounts for the external factors as well to determine the equilibrium.

== Exercise 2 ==

As the H-H bond is (-432 kJ/mol), and the F-H is higher in energy (-565 kJ/mol) <ref name="[1]" />, the reaction (F + H2 ⇌ H + HF) is, therefore exothermic, as the energy released from the making of the H-F bond is greater than that taken from the H-H being broken. This can be attributed due to the increased ionic character between the F-H bond due to the change in electronegativity. The reverse direction is therefore endothermic.

In order to determine the transition state the saddle state was needed. This was, again, determined via the maximum of an MEP graph of IN distance vs Time (derivative = 0). Through trial and error, this gave values of AB=1.812 Å and BC=0.745 Å in which A is Flourine, and B,C are both Hydrogen. (Momenta was set to zero.) This gave a straight line graph, thus showing the correct value had been obtained.

=== Activation Energy ===

By slight alteration of the equilibrium settings (AB being changed to 1.91 Å) we can force the reaction to one side. In this case, due to the extended bond length, towards the F + H2 side.

Using an MEP (Energy vs Time) graph the activation energy was seen to be to be 29.16 kcal/mol (121.99 kJ/mol).

[[File:H2 F energydiagram.PNG| thumb | left | 320px | MEP Energy vs time]]

==== Dynamics ====

== References ==

<references>
<ref name="[1]">http://www.wiredchemist.com/chemistry/data/bond_energies_lengths.html (Assessed on 16/05/2018 18ː53).</ref>
</references>

MRD:sp2416

2018-05-17T14:25:05Z

2018-05-16T17:50:20Z

Hjw116: /* Exercise 2 */