ChemWiki - User contributions [en]

MRD:sp2416

2018-05-18T14:19:56Z

Sp2416: /* Reaction Dynamics */

==H + H2==

===Transition State ===

The transition state is defined at the maximum on the minimum energy path linking reactants and products. Both minima and transition states are saddle points on the potential energy surface. On the potential energy surface diagram of H + H2 analysed, the gradient of both the transition state and minimum are found to be zero (∂V(ri)/∂ri=0). Minima and transition structures can be distinguished by taking the second derivative of the gradient. For transition state this will be negative and positive, while for minima the answer to this will be positive.

===Locating the Transition State===

[[File:Internucleardistancesp2416.PNG|thumb|centre|Internuclear Distance vs Time plot for H + H2]]

On the first graph the Transition state is where the A-B and B-C lines cross.

To locate the Transition state the momenta are changed to 0, (as a transition state is a saddle point) and then the distances AB and BC are adjusted so as to get an Internuclear Distance graph where both distances are stationary. This distance is found to be stationary when both AB and BC are set to be 0.90755.

[[File:InternucleardistanceTSsp2416.PNG|thumb|centre|Internuclear Distance vs Time plot for H + H2 Transition state]]

===Dynamic and MEP Calculation types===

The following results were obtained when the AB distance was changed to 0.90855 and the BC distance was maintained at 0.09755 (transition state position)

[[File:Trajectory_plot_dynamics_sp2416.PNG|thumb|centre|Trajectory plot using Dynamics calculation type]]

[[File:Trajectory_plot_mep_sp2416.PNG|thumb|centre|Trajectory plot using mep calculation type]]

[[File:Distance_time_dynamics_sp2416.PNG|thumb|centre|Internuclear Distance vs Time graph using Dynamics calculation type]]

[[File:Distance_time_mep_sp2416.PNG|thumb|centre|Internuclear Distance vs Time graph using mep calculation type]]

===Reactive and Unreactive Trajectories===

{| class="wikitable" border="1"
|+ Effect of different momenta on reactivity (Dynamic Calculation Type)
! p1 !! p2 !! Total Energy!!Type of Trajectory!!Contour plot!!Description
|-
| -1.25 || -2.5 || -99.199 || Reactive || [[File:Contour1_sp2416.PNG|320px]] ||The reaction starts with a minorly oscillating AB-molecule, which is shown by a straight line plot at the start. Post the transition state occurring, and the BC-bond has been formed the molecule starts oscillating stronger. ||
|-
| -1.5 || -2.0 || -100.456 || Uneactive || [[File:Contour2_sp2416.PNG|320px]] || The A-B bond is oscillating at the beginning. However, both momenta of AB and C together are not strong enough to overcome the repulsion force and build the BC molecule. The particles however do approach each other, but the reaction does not go to completion. ||
|-
| -1.5 || -2.5 || -98.956 || Reactive || [[File:Contour3_sp2416.PNG|320px]] || Very similar to the first reaction, the only difference being that the A-B bond oscillates from the beginning as C is approaching.||
|-
| -2.5 || -5.0 || -84.956 || Uneactive || [[File:Contour4_sp2416.PNG|320px]] || The A-B bond does not oscillate. The impact with atom C leads to a brief period of time where B and C can be observed vibrating strongly, before it dissociates again.||
|-
| -2.5 || -5.2 || -83.416 || Reactive || [[File:Contour5_sp2416.PNG|320px]] || This plot can be considered as the mirror image of the previous plot as it starts with a non-oscillating A-B bond. Collision with C give a short-lived BC bond, which dissociates back to A-B. However, the reaction goes back to a B-C molecule.
||
|}

===Transition State Theory===

Transition State theory separates reaction systems into the reactant-space and the product-space region. In the reactant-space the starting material has not reacted yet and the product-space region is entered after the reaction occurs. The border between these two systems is defined as the transition state. As soon as the transition state is overcomed and the products are produced, the reaction cannot be reveresed and the reactant-space cannot be entered again.

The theory assumes that the atoms obey the Born-Oppenheimer approximation and that quantum-tunneling effects do not occur. Also, the atoms of the starting material obey the Boltzmann Distribution and hence we assume that the system has enough time to equilibrate at the beginning.

However, upon consideration of the above calculations for the 4th reaction, it can be observed that the reactants are actually able to enter the product space and dissociate back to the starting material. Hence the theory cannot be applied here. The reason for this is because the calculations performed by the program are assuming isolation of the reactant system, while the theory takes the surrounding and the possible energy exchange with neighbouring molecules into account, in order to achieve equilibrium.

==F - H - H ==

=== PES Inspection ===

The equilibrium reaction F + H2 ⇌ H + HF is exothermic when it goes forward releasing energy, whilst the backward reaction is endothermic, taking energy in. <ref name="[1]" /> The H-H bond is -432 kJ/mol and the H-F bond is -565 kj/mol <ref name="[2]" />. This means that more energy is needed to break the H-F than the energy gained by forming the H-H bond, and hence the forward reaction is exothermic (and the backward endothermic).

 Locating the Transition Stateː 

Applying the following settingsː

Atom A: F

Atom B: H

Atom C: H

AB distance: 1.81 Å

BC distance: 0.7455 Å

Both momenta are set to 0.

These settings were applied using the Dynamics Calculation type and visualising the Internuclear Distance vs Time plot. Trial and error values were used until all the distances (A-B, B-C and A-C) produce straight lines, as shown in the figure below.

[[File:Distance_time_1_sp2416.PNG|thumb|centre|Internuclear Distance vs Time graph using Dynamics calculation type for F-H-H]]

 Reporting the Activation Energyː 

To find the activation energy, the type of calculation used is MEP and the AB distance is displaced slightly (form 1.81 is changed to 1.83) in order to force the reaction to go to either direction of the equilibrium - right hand side or left hand side.

The forward reaction in the equilibrium F + H2 ⇌ H + HF is exothermic. Hammond's postulate states that the transition state resembles more the reactants than the products in an exothermic reaction. Hence, the activation energy is obtained when the A-B distance is displaced in this calculation.

Energy of the transition state = -103.752 kcal/mol

Energy of products = -133.466 kcal/mol

Activation energy of the reaction = 29.714 cal/mol

[[File:Activationenergysp2416.PNG|thumb|centre|Finding the activation energy]]

=== Reaction Dynamics ===

Reactive Trajectory 

Atom A : F

Atom B : H

Atom C : H

AB distance = 1.91 Å

BC distance = 0.7455 Å

AB momentum = -1.5

BC momentum = 1.0

[[File:Reactivetrajsp2416.png|thumb|centre|Reactive Trajectory]]

[[File:Momentasp2416.png|thumb|centre|Internuclear Momenta vs Time]]

An increased and vigorous oscillation of the resulting molecule can be seen from the Momentum vs Time plot. This means that the energy released during this exothermic reaction is converted into vibrational energy.

[[File:Energyplotsp2416.png|thumb|centre|Energy vs Time]]

The Energy vs Time plot shows an increased oscillation in the kinetic energy of the molecule.

Investigating the effect of changing the momentum of AB

Atom A : F

Atom B : H

Atom C : H

AB distance = 1.91 Å

BC distance = 0.7455 Å

AB momentum = -3 to 3

BC momentum = -0.5

As soon as the AB momentum reaches 0, no more reaction can be observed. Increasing the value in the positive direction only results in a change of the oscillation strength of the A-B bond.

[[File:Figure1sp2416.png|thumb|centre|AB-momentum = -2, reaction occurs]]

[[File:Figure2sp2416.png|thumb|centre|AB-momentum = 0, no reaction, reaction occurs]]

[[File:Figure3sp2416.png|thumb|centre|B-momentum = 3, large oscillation]]

=== Polanyi's rules ===

The different motions (e.g. vibrational and rotational) on a reaction are discussed by Polanyi Rules.

As the forward reaction in F + H2 ⇌ H + HF is exothermic, the transition state resembles the reactants and occurs early, and therefore is promoted by translational motion. This motion is resembled by the momentum corresponding to the molecules which initially are further apart (in this case the AB momentum), as this momentum is responsible for the strength of the collision.

In the backward reaction which is endothermic, the transition state is late and is hence promoted by a high initial vibrational energy of the starting material. The momentum of the initially bonded molecule represents this energy.

Thus, it depends on the reaction monitored which momentum leads to a promotion of which reaction.

The reaction examined above corresponds to the endothermic one, which explains why an increase in the AB-momentum results in no reaction.

== References ==

<references>
<ref name="[1]">J.C. Polanyi, D.C. Tardy, 1969, J. Chem. Phys., Vol.51 "Energy Distribution in the Exothermic Reaction F + H2 , and the Endothermic Reaction HF + H", p.255-321.</ref>

<ref name="[2]">http://www.wiredchemist.com/chemistry/data/bond_energies_lengths.html (Assessed on 15/05/2018 17ː10).</ref>
</references>

File:Figure3sp2416.png

2018-05-18T14:19:34Z

Sp2416:

File:Figure2sp2416.png

2018-05-18T14:18:19Z

Sp2416:

File:Figure1sp2416.png

2018-05-18T14:16:06Z

Sp2416:

MRD:sp2416

2018-05-16T15:55:20Z

Sp2416: /* Reaction Dynamics */

==H + H2==

===Transition State ===

The transition state is defined at the maximum on the minimum energy path linking reactants and products. Both minima and transition states are saddle points on the potential energy surface. On the potential energy surface diagram of H + H2 analysed, the gradient of both the transition state and minimum are found to be zero (∂V(ri)/∂ri=0). Minima and transition structures can be distinguished by taking the second derivative of the gradient. For transition state this will be negative and positive, while for minima the answer to this will be positive.

===Locating the Transition State===

[[File:Internucleardistancesp2416.PNG|thumb|centre|Internuclear Distance vs Time plot for H + H2]]

On the first graph the Transition state is where the A-B and B-C lines cross.

To locate the Transition state the momenta are changed to 0, (as a transition state is a saddle point) and then the distances AB and BC are adjusted so as to get an Internuclear Distance graph where both distances are stationary. This distance is found to be stationary when both AB and BC are set to be 0.90755.

[[File:InternucleardistanceTSsp2416.PNG|thumb|centre|Internuclear Distance vs Time plot for H + H2 Transition state]]

===Dynamic and MEP Calculation types===

The following results were obtained when the AB distance was changed to 0.90855 and the BC distance was maintained at 0.09755 (transition state position)

[[File:Trajectory_plot_dynamics_sp2416.PNG|thumb|centre|Trajectory plot using Dynamics calculation type]]

[[File:Trajectory_plot_mep_sp2416.PNG|thumb|centre|Trajectory plot using mep calculation type]]

[[File:Distance_time_dynamics_sp2416.PNG|thumb|centre|Internuclear Distance vs Time graph using Dynamics calculation type]]

[[File:Distance_time_mep_sp2416.PNG|thumb|centre|Internuclear Distance vs Time graph using mep calculation type]]

===Reactive and Unreactive Trajectories===

{| class="wikitable" border="1"
|+ Effect of different momenta on reactivity (Dynamic Calculation Type)
! p1 !! p2 !! Total Energy!!Type of Trajectory!!Contour plot!!Description
|-
| -1.25 || -2.5 || -99.199 || Reactive || [[File:Contour1_sp2416.PNG|320px]] ||The reaction starts with a minorly oscillating AB-molecule, which is shown by a straight line plot at the start. Post the transition state occurring, and the BC-bond has been formed the molecule starts oscillating stronger. ||
|-
| -1.5 || -2.0 || -100.456 || Uneactive || [[File:Contour2_sp2416.PNG|320px]] || The A-B bond is oscillating at the beginning. However, both momenta of AB and C together are not strong enough to overcome the repulsion force and build the BC molecule. The particles however do approach each other, but the reaction does not go to completion. ||
|-
| -1.5 || -2.5 || -98.956 || Reactive || [[File:Contour3_sp2416.PNG|320px]] || Very similar to the first reaction, the only difference being that the A-B bond oscillates from the beginning as C is approaching.||
|-
| -2.5 || -5.0 || -84.956 || Uneactive || [[File:Contour4_sp2416.PNG|320px]] || The A-B bond does not oscillate. The impact with atom C leads to a brief period of time where B and C can be observed vibrating strongly, before it dissociates again.||
|-
| -2.5 || -5.2 || -83.416 || Reactive || [[File:Contour5_sp2416.PNG|320px]] || This plot can be considered as the mirror image of the previous plot as it starts with a non-oscillating A-B bond. Collision with C give a short-lived BC bond, which dissociates back to A-B. However, the reaction goes back to a B-C molecule.
||
|}

===Transition State Theory===

Transition State theory separates reaction systems into the reactant-space and the product-space region. In the reactant-space the starting material has not reacted yet and the product-space region is entered after the reaction occurs. The border between these two systems is defined as the transition state. As soon as the transition state is overcomed and the products are produced, the reaction cannot be reveresed and the reactant-space cannot be entered again.

The theory assumes that the atoms obey the Born-Oppenheimer approximation and that quantum-tunneling effects do not occur. Also, the atoms of the starting material obey the Boltzmann Distribution and hence we assume that the system has enough time to equilibrate at the beginning.

However, upon consideration of the above calculations for the 4th reaction, it can be observed that the reactants are actually able to enter the product space and dissociate back to the starting material. Hence the theory cannot be applied here. The reason for this is because the calculations performed by the program are assuming isolation of the reactant system, while the theory takes the surrounding and the possible energy exchange with neighbouring molecules into account, in order to achieve equilibrium.

==F - H - H ==

=== PES Inspection ===

The equilibrium reaction F + H2 ⇌ H + HF is exothermic when it goes forward releasing energy, whilst the backward reaction is endothermic, taking energy in. <ref name="[1]" /> The H-H bond is -432 kJ/mol and the H-F bond is -565 kj/mol <ref name="[2]" />. This means that more energy is needed to break the H-F than the energy gained by forming the H-H bond, and hence the forward reaction is exothermic (and the backward endothermic).

 Locating the Transition Stateː 

Applying the following settingsː

Atom A: F

Atom B: H

Atom C: H

AB distance: 1.81 Å

BC distance: 0.7455 Å

Both momenta are set to 0.

These settings were applied using the Dynamics Calculation type and visualising the Internuclear Distance vs Time plot. Trial and error values were used until all the distances (A-B, B-C and A-C) produce straight lines, as shown in the figure below.

[[File:Distance_time_1_sp2416.PNG|thumb|centre|Internuclear Distance vs Time graph using Dynamics calculation type for F-H-H]]

 Reporting the Activation Energyː 

To find the activation energy, the type of calculation used is MEP and the AB distance is displaced slightly (form 1.81 is changed to 1.83) in order to force the reaction to go to either direction of the equilibrium - right hand side or left hand side.

The forward reaction in the equilibrium F + H2 ⇌ H + HF is exothermic. Hammond's postulate states that the transition state resembles more the reactants than the products in an exothermic reaction. Hence, the activation energy is obtained when the A-B distance is displaced in this calculation.

Energy of the transition state = -103.752 kJ/mol

Energy of products = -133.466 kJ/mol

Activation energy of the reaction = 29.714 kJ/mol

[[File:Activationenergysp2416.PNG|thumb|centre|Finding the activation energy]]

=== Reaction Dynamics ===

Reactive Trajectory 

Atom A : F

Atom B : H

Atom C : H

AB distance = 1.91 Å

BC distance = 0.7455 Å

AB momentum = -1.5

BC momentum = 1.0

[[File:Reactivetrajsp2416.png|thumb|centre|Reactive Trajectory]]

[[File:Momentasp2416.png|thumb|centre|Internuclear Momenta vs Time]]

An increased and vigorous oscillation of the resulting molecule can be seen from the Momentum vs Time plot. This means that the energy released during this exothermic reaction is converted into vibrational energy.

[[File:Energyplotsp2416.png|thumb|centre|Energy vs Time]]

The Energy vs Time plot shows an increased oscillation in the kinetic energy of the molecule.

Investigating the effect of changing the momentum of AB

Atom A : F

Atom B : H

Atom C : H

AB distance = 1.91 Å

BC distance = 0.7455 Å

AB momentum = -3 to 3

BC momentum = -0.5

=== Polanyi's rules ===

The different motions (e.g. vibrational and rotational) on a reaction are discussed by Polanyi Rules.

As the forward reaction in F + H2 ⇌ H + HF is exothermic, the transition state resembles the reactants and occurs early, and therefore is promoted by translational motion. This motion is resembled by the momentum corresponding to the molecules which initially are further apart (in this case the AB momentum), as this momentum is responsible for the strength of the collision.

In the backward reaction which is endothermic, the transition state is late and is hence promoted by a high initial vibrational energy of the starting material. The momentum of the initially bonded molecule represents this energy.

Thus, it depends on the reaction monitored which momentum leads to a promotion of which reaction.

The reaction examined above corresponds to the endothermic one, which explains why an increase in the AB-momentum results in no reaction.

== References ==

<references>
<ref name="[1]">J.C. Polanyi, D.C. Tardy, 1969, J. Chem. Phys., Vol.51 "Energy Distribution in the Exothermic Reaction F + H2 , and the Endothermic Reaction HF + H", p.255-321.</ref>

<ref name="[2]">http://www.wiredchemist.com/chemistry/data/bond_energies_lengths.html (Assessed on 15/05/2018 17ː10).</ref>
</references>

MRD:sp2416

2018-05-16T15:54:44Z

Sp2416: /* Reaction Dynamics */

==H + H2==

===Transition State ===

The transition state is defined at the maximum on the minimum energy path linking reactants and products. Both minima and transition states are saddle points on the potential energy surface. On the potential energy surface diagram of H + H2 analysed, the gradient of both the transition state and minimum are found to be zero (∂V(ri)/∂ri=0). Minima and transition structures can be distinguished by taking the second derivative of the gradient. For transition state this will be negative and positive, while for minima the answer to this will be positive.

===Locating the Transition State===

[[File:Internucleardistancesp2416.PNG|thumb|centre|Internuclear Distance vs Time plot for H + H2]]

On the first graph the Transition state is where the A-B and B-C lines cross.

To locate the Transition state the momenta are changed to 0, (as a transition state is a saddle point) and then the distances AB and BC are adjusted so as to get an Internuclear Distance graph where both distances are stationary. This distance is found to be stationary when both AB and BC are set to be 0.90755.

[[File:InternucleardistanceTSsp2416.PNG|thumb|centre|Internuclear Distance vs Time plot for H + H2 Transition state]]

===Dynamic and MEP Calculation types===

The following results were obtained when the AB distance was changed to 0.90855 and the BC distance was maintained at 0.09755 (transition state position)

[[File:Trajectory_plot_dynamics_sp2416.PNG|thumb|centre|Trajectory plot using Dynamics calculation type]]

[[File:Trajectory_plot_mep_sp2416.PNG|thumb|centre|Trajectory plot using mep calculation type]]

[[File:Distance_time_dynamics_sp2416.PNG|thumb|centre|Internuclear Distance vs Time graph using Dynamics calculation type]]

[[File:Distance_time_mep_sp2416.PNG|thumb|centre|Internuclear Distance vs Time graph using mep calculation type]]

===Reactive and Unreactive Trajectories===

{| class="wikitable" border="1"
|+ Effect of different momenta on reactivity (Dynamic Calculation Type)
! p1 !! p2 !! Total Energy!!Type of Trajectory!!Contour plot!!Description
|-
| -1.25 || -2.5 || -99.199 || Reactive || [[File:Contour1_sp2416.PNG|320px]] ||The reaction starts with a minorly oscillating AB-molecule, which is shown by a straight line plot at the start. Post the transition state occurring, and the BC-bond has been formed the molecule starts oscillating stronger. ||
|-
| -1.5 || -2.0 || -100.456 || Uneactive || [[File:Contour2_sp2416.PNG|320px]] || The A-B bond is oscillating at the beginning. However, both momenta of AB and C together are not strong enough to overcome the repulsion force and build the BC molecule. The particles however do approach each other, but the reaction does not go to completion. ||
|-
| -1.5 || -2.5 || -98.956 || Reactive || [[File:Contour3_sp2416.PNG|320px]] || Very similar to the first reaction, the only difference being that the A-B bond oscillates from the beginning as C is approaching.||
|-
| -2.5 || -5.0 || -84.956 || Uneactive || [[File:Contour4_sp2416.PNG|320px]] || The A-B bond does not oscillate. The impact with atom C leads to a brief period of time where B and C can be observed vibrating strongly, before it dissociates again.||
|-
| -2.5 || -5.2 || -83.416 || Reactive || [[File:Contour5_sp2416.PNG|320px]] || This plot can be considered as the mirror image of the previous plot as it starts with a non-oscillating A-B bond. Collision with C give a short-lived BC bond, which dissociates back to A-B. However, the reaction goes back to a B-C molecule.
||
|}

===Transition State Theory===

Transition State theory separates reaction systems into the reactant-space and the product-space region. In the reactant-space the starting material has not reacted yet and the product-space region is entered after the reaction occurs. The border between these two systems is defined as the transition state. As soon as the transition state is overcomed and the products are produced, the reaction cannot be reveresed and the reactant-space cannot be entered again.

The theory assumes that the atoms obey the Born-Oppenheimer approximation and that quantum-tunneling effects do not occur. Also, the atoms of the starting material obey the Boltzmann Distribution and hence we assume that the system has enough time to equilibrate at the beginning.

However, upon consideration of the above calculations for the 4th reaction, it can be observed that the reactants are actually able to enter the product space and dissociate back to the starting material. Hence the theory cannot be applied here. The reason for this is because the calculations performed by the program are assuming isolation of the reactant system, while the theory takes the surrounding and the possible energy exchange with neighbouring molecules into account, in order to achieve equilibrium.

==F - H - H ==

=== PES Inspection ===

The equilibrium reaction F + H2 ⇌ H + HF is exothermic when it goes forward releasing energy, whilst the backward reaction is endothermic, taking energy in. <ref name="[1]" /> The H-H bond is -432 kJ/mol and the H-F bond is -565 kj/mol <ref name="[2]" />. This means that more energy is needed to break the H-F than the energy gained by forming the H-H bond, and hence the forward reaction is exothermic (and the backward endothermic).

 Locating the Transition Stateː 

Applying the following settingsː

Atom A: F

Atom B: H

Atom C: H

AB distance: 1.81 Å

BC distance: 0.7455 Å

Both momenta are set to 0.

These settings were applied using the Dynamics Calculation type and visualising the Internuclear Distance vs Time plot. Trial and error values were used until all the distances (A-B, B-C and A-C) produce straight lines, as shown in the figure below.

[[File:Distance_time_1_sp2416.PNG|thumb|centre|Internuclear Distance vs Time graph using Dynamics calculation type for F-H-H]]

 Reporting the Activation Energyː 

To find the activation energy, the type of calculation used is MEP and the AB distance is displaced slightly (form 1.81 is changed to 1.83) in order to force the reaction to go to either direction of the equilibrium - right hand side or left hand side.

The forward reaction in the equilibrium F + H2 ⇌ H + HF is exothermic. Hammond's postulate states that the transition state resembles more the reactants than the products in an exothermic reaction. Hence, the activation energy is obtained when the A-B distance is displaced in this calculation.

Energy of the transition state = -103.752 kJ/mol

Energy of products = -133.466 kJ/mol

Activation energy of the reaction = 29.714 kJ/mol

[[File:Activationenergysp2416.PNG|thumb|centre|Finding the activation energy]]

=== Reaction Dynamics ===

Reactive Trajectory 

Atom A : F

Atom B : H

Atom C : H

AB distance = 1.91 Å

BC distance = 0.7455 Å

AB momentum = -1.5

BC momentum = 1.0

[[File:Reactivetrajsp2416.png|thumb|centre|Reactive Trajectory]]

[[File:Momentasp2416.png|thumb|centre|Internuclear Momenta vs Time]]

An increased and vigorous oscillation of the resulting molecule can be seen from the Momentum vs Time plot. This means that the energy released during this exothermic reaction is converted into vibrational energy.

[[File:Energyplotsp2416.png|thumb|centre|Energy vs Time]]

The Energy vs Time plot shows an increased oscillation in the kinetic energy of the molecule.

Investigating the effect of changing the momentum of AB

Atom A : F

Atom B : H

Atom C : H

AB distance = 1.91

BC distance = 0.7455

AB momentum = -3 to 3

BC momentum = -0.5

=== Polanyi's rules ===

The different motions (e.g. vibrational and rotational) on a reaction are discussed by Polanyi Rules.

As the forward reaction in F + H2 ⇌ H + HF is exothermic, the transition state resembles the reactants and occurs early, and therefore is promoted by translational motion. This motion is resembled by the momentum corresponding to the molecules which initially are further apart (in this case the AB momentum), as this momentum is responsible for the strength of the collision.

In the backward reaction which is endothermic, the transition state is late and is hence promoted by a high initial vibrational energy of the starting material. The momentum of the initially bonded molecule represents this energy.

Thus, it depends on the reaction monitored which momentum leads to a promotion of which reaction.

The reaction examined above corresponds to the endothermic one, which explains why an increase in the AB-momentum results in no reaction.

== References ==

<references>
<ref name="[1]">J.C. Polanyi, D.C. Tardy, 1969, J. Chem. Phys., Vol.51 "Energy Distribution in the Exothermic Reaction F + H2 , and the Endothermic Reaction HF + H", p.255-321.</ref>

<ref name="[2]">http://www.wiredchemist.com/chemistry/data/bond_energies_lengths.html (Assessed on 15/05/2018 17ː10).</ref>
</references>

MRD:sp2416

2018-05-16T15:52:31Z

Sp2416: /* Reactive and Unreactive Trajectories */

==H + H2==

===Transition State ===

The transition state is defined at the maximum on the minimum energy path linking reactants and products. Both minima and transition states are saddle points on the potential energy surface. On the potential energy surface diagram of H + H2 analysed, the gradient of both the transition state and minimum are found to be zero (∂V(ri)/∂ri=0). Minima and transition structures can be distinguished by taking the second derivative of the gradient. For transition state this will be negative and positive, while for minima the answer to this will be positive.

===Locating the Transition State===

[[File:Internucleardistancesp2416.PNG|thumb|centre|Internuclear Distance vs Time plot for H + H2]]

On the first graph the Transition state is where the A-B and B-C lines cross.

To locate the Transition state the momenta are changed to 0, (as a transition state is a saddle point) and then the distances AB and BC are adjusted so as to get an Internuclear Distance graph where both distances are stationary. This distance is found to be stationary when both AB and BC are set to be 0.90755.

[[File:InternucleardistanceTSsp2416.PNG|thumb|centre|Internuclear Distance vs Time plot for H + H2 Transition state]]

===Dynamic and MEP Calculation types===

The following results were obtained when the AB distance was changed to 0.90855 and the BC distance was maintained at 0.09755 (transition state position)

[[File:Trajectory_plot_dynamics_sp2416.PNG|thumb|centre|Trajectory plot using Dynamics calculation type]]

[[File:Trajectory_plot_mep_sp2416.PNG|thumb|centre|Trajectory plot using mep calculation type]]

[[File:Distance_time_dynamics_sp2416.PNG|thumb|centre|Internuclear Distance vs Time graph using Dynamics calculation type]]

[[File:Distance_time_mep_sp2416.PNG|thumb|centre|Internuclear Distance vs Time graph using mep calculation type]]

===Reactive and Unreactive Trajectories===

{| class="wikitable" border="1"
|+ Effect of different momenta on reactivity (Dynamic Calculation Type)
! p1 !! p2 !! Total Energy!!Type of Trajectory!!Contour plot!!Description
|-
| -1.25 || -2.5 || -99.199 || Reactive || [[File:Contour1_sp2416.PNG|320px]] ||The reaction starts with a minorly oscillating AB-molecule, which is shown by a straight line plot at the start. Post the transition state occurring, and the BC-bond has been formed the molecule starts oscillating stronger. ||
|-
| -1.5 || -2.0 || -100.456 || Uneactive || [[File:Contour2_sp2416.PNG|320px]] || The A-B bond is oscillating at the beginning. However, both momenta of AB and C together are not strong enough to overcome the repulsion force and build the BC molecule. The particles however do approach each other, but the reaction does not go to completion. ||
|-
| -1.5 || -2.5 || -98.956 || Reactive || [[File:Contour3_sp2416.PNG|320px]] || Very similar to the first reaction, the only difference being that the A-B bond oscillates from the beginning as C is approaching.||
|-
| -2.5 || -5.0 || -84.956 || Uneactive || [[File:Contour4_sp2416.PNG|320px]] || The A-B bond does not oscillate. The impact with atom C leads to a brief period of time where B and C can be observed vibrating strongly, before it dissociates again.||
|-
| -2.5 || -5.2 || -83.416 || Reactive || [[File:Contour5_sp2416.PNG|320px]] || This plot can be considered as the mirror image of the previous plot as it starts with a non-oscillating A-B bond. Collision with C give a short-lived BC bond, which dissociates back to A-B. However, the reaction goes back to a B-C molecule.
||
|}

===Transition State Theory===

Transition State theory separates reaction systems into the reactant-space and the product-space region. In the reactant-space the starting material has not reacted yet and the product-space region is entered after the reaction occurs. The border between these two systems is defined as the transition state. As soon as the transition state is overcomed and the products are produced, the reaction cannot be reveresed and the reactant-space cannot be entered again.

The theory assumes that the atoms obey the Born-Oppenheimer approximation and that quantum-tunneling effects do not occur. Also, the atoms of the starting material obey the Boltzmann Distribution and hence we assume that the system has enough time to equilibrate at the beginning.

However, upon consideration of the above calculations for the 4th reaction, it can be observed that the reactants are actually able to enter the product space and dissociate back to the starting material. Hence the theory cannot be applied here. The reason for this is because the calculations performed by the program are assuming isolation of the reactant system, while the theory takes the surrounding and the possible energy exchange with neighbouring molecules into account, in order to achieve equilibrium.

==F - H - H ==

=== PES Inspection ===

The equilibrium reaction F + H2 ⇌ H + HF is exothermic when it goes forward releasing energy, whilst the backward reaction is endothermic, taking energy in. <ref name="[1]" /> The H-H bond is -432 kJ/mol and the H-F bond is -565 kj/mol <ref name="[2]" />. This means that more energy is needed to break the H-F than the energy gained by forming the H-H bond, and hence the forward reaction is exothermic (and the backward endothermic).

 Locating the Transition Stateː 

Applying the following settingsː

Atom A: F

Atom B: H

Atom C: H

AB distance: 1.81 Å

BC distance: 0.7455 Å

Both momenta are set to 0.

These settings were applied using the Dynamics Calculation type and visualising the Internuclear Distance vs Time plot. Trial and error values were used until all the distances (A-B, B-C and A-C) produce straight lines, as shown in the figure below.

[[File:Distance_time_1_sp2416.PNG|thumb|centre|Internuclear Distance vs Time graph using Dynamics calculation type for F-H-H]]

 Reporting the Activation Energyː 

To find the activation energy, the type of calculation used is MEP and the AB distance is displaced slightly (form 1.81 is changed to 1.83) in order to force the reaction to go to either direction of the equilibrium - right hand side or left hand side.

The forward reaction in the equilibrium F + H2 ⇌ H + HF is exothermic. Hammond's postulate states that the transition state resembles more the reactants than the products in an exothermic reaction. Hence, the activation energy is obtained when the A-B distance is displaced in this calculation.

Energy of the transition state = -103.752 kJ/mol

Energy of products = -133.466 kJ/mol

Activation energy of the reaction = 29.714 kJ/mol

[[File:Activationenergysp2416.PNG|thumb|centre|Finding the activation energy]]

=== Reaction Dynamics ===

Reactive Trajectory 

Atom A : F

Atom B : H

Atom C : H

AB distance = 1.91

BC distance = 0.7455

AB momentum = -1.5

BC momentum = 1.0

[[File:Reactivetrajsp2416.png|thumb|centre|Reactive Trajectory]]

[[File:Momentasp2416.png|thumb|centre|Internuclear Momenta vs Time]]

An increased and vigorous oscillation of the resulting molecule can be seen from the Momentum vs Time plot. This means that the energy released during this exothermic reaction is converted into vibrational energy.

[[File:Energyplotsp2416.png|thumb|centre|Energy vs Time]]

The Energy vs Time plot shows an increased oscillation in the kinetic energy of the molecule.

Investigating the effect of changing the momentum of AB

Atom A : F

Atom B : H

Atom C : H

AB distance = 1.91

BC distance = 0.7455

AB momentum = -3 to 3

BC momentum = -0.5

=== Polanyi's rules ===

The different motions (e.g. vibrational and rotational) on a reaction are discussed by Polanyi Rules.

As the forward reaction in F + H2 ⇌ H + HF is exothermic, the transition state resembles the reactants and occurs early, and therefore is promoted by translational motion. This motion is resembled by the momentum corresponding to the molecules which initially are further apart (in this case the AB momentum), as this momentum is responsible for the strength of the collision.

In the backward reaction which is endothermic, the transition state is late and is hence promoted by a high initial vibrational energy of the starting material. The momentum of the initially bonded molecule represents this energy.

Thus, it depends on the reaction monitored which momentum leads to a promotion of which reaction.

The reaction examined above corresponds to the endothermic one, which explains why an increase in the AB-momentum results in no reaction.

== References ==

<references>
<ref name="[1]">J.C. Polanyi, D.C. Tardy, 1969, J. Chem. Phys., Vol.51 "Energy Distribution in the Exothermic Reaction F + H2 , and the Endothermic Reaction HF + H", p.255-321.</ref>

<ref name="[2]">http://www.wiredchemist.com/chemistry/data/bond_energies_lengths.html (Assessed on 15/05/2018 17ː10).</ref>
</references>

MRD:sp2416

2018-05-16T15:51:03Z

Sp2416: /* Transition State Theory */

==H + H2==

===Transition State ===

The transition state is defined at the maximum on the minimum energy path linking reactants and products. Both minima and transition states are saddle points on the potential energy surface. On the potential energy surface diagram of H + H2 analysed, the gradient of both the transition state and minimum are found to be zero (∂V(ri)/∂ri=0). Minima and transition structures can be distinguished by taking the second derivative of the gradient. For transition state this will be negative and positive, while for minima the answer to this will be positive.

===Locating the Transition State===

[[File:Internucleardistancesp2416.PNG|thumb|centre|Internuclear Distance vs Time plot for H + H2]]

On the first graph the Transition state is where the A-B and B-C lines cross.

To locate the Transition state the momenta are changed to 0, (as a transition state is a saddle point) and then the distances AB and BC are adjusted so as to get an Internuclear Distance graph where both distances are stationary. This distance is found to be stationary when both AB and BC are set to be 0.90755.

[[File:InternucleardistanceTSsp2416.PNG|thumb|centre|Internuclear Distance vs Time plot for H + H2 Transition state]]

===Dynamic and MEP Calculation types===

The following results were obtained when the AB distance was changed to 0.90855 and the BC distance was maintained at 0.09755 (transition state position)

[[File:Trajectory_plot_dynamics_sp2416.PNG|thumb|centre|Trajectory plot using Dynamics calculation type]]

[[File:Trajectory_plot_mep_sp2416.PNG|thumb|centre|Trajectory plot using mep calculation type]]

[[File:Distance_time_dynamics_sp2416.PNG|thumb|centre|Internuclear Distance vs Time graph using Dynamics calculation type]]

[[File:Distance_time_mep_sp2416.PNG|thumb|centre|Internuclear Distance vs Time graph using mep calculation type]]

===Reactive and Unreactive Trajectories===

{| class="wikitable" border="1"
|+ Effect of different momenta on reactivity
! p1 !! p2 !! Total Energy!!Type of Trajectory!!Contour plot!!Description
|-
| -1.25 || -2.5 || -99.199 || Reactive || [[File:Contour1_sp2416.PNG|320px]] ||The reaction starts with a minorly oscillating AB-molecule, which is shown by a straight line plot at the start. Post the transition state occurring, and the BC-bond has been formed the molecule starts oscillating stronger. ||
|-
| -1.5 || -2.0 || -100.456 || Uneactive || [[File:Contour2_sp2416.PNG|320px]] || The A-B bond is oscillating at the beginning. However, both momenta of AB and C together are not strong enough to overcome the repulsion force and build the BC molecule. The particles however do approach each other, but the reaction does not go to completion. ||
|-
| -1.5 || -2.5 || -98.956 || Reactive || [[File:Contour3_sp2416.PNG|320px]] || Very similar to the first reaction, the only difference being that the A-B bond oscillates from the beginning as C is approaching.||
|-
| -2.5 || -5.0 || -84.956 || Uneactive || [[File:Contour4_sp2416.PNG|320px]] || The A-B bond does not oscillate. The impact with atom C leads to a brief period of time where B and C can be observed vibrating strongly, before it dissociates again.||
|-
| -2.5 || -5.2 || -83.416 || Reactive || [[File:Contour5_sp2416.PNG|320px]] || This plot can be considered as the mirror image of the previous plot as it starts with a non-oscillating A-B bond. Collision with C give a short-lived BC bond, which dissociates back to A-B. However, the reaction goes back to a B-C molecule.
||
|}

===Transition State Theory===

Transition State theory separates reaction systems into the reactant-space and the product-space region. In the reactant-space the starting material has not reacted yet and the product-space region is entered after the reaction occurs. The border between these two systems is defined as the transition state. As soon as the transition state is overcomed and the products are produced, the reaction cannot be reveresed and the reactant-space cannot be entered again.

The theory assumes that the atoms obey the Born-Oppenheimer approximation and that quantum-tunneling effects do not occur. Also, the atoms of the starting material obey the Boltzmann Distribution and hence we assume that the system has enough time to equilibrate at the beginning.

However, upon consideration of the above calculations for the 4th reaction, it can be observed that the reactants are actually able to enter the product space and dissociate back to the starting material. Hence the theory cannot be applied here. The reason for this is because the calculations performed by the program are assuming isolation of the reactant system, while the theory takes the surrounding and the possible energy exchange with neighbouring molecules into account, in order to achieve equilibrium.

==F - H - H ==

=== PES Inspection ===

The equilibrium reaction F + H2 ⇌ H + HF is exothermic when it goes forward releasing energy, whilst the backward reaction is endothermic, taking energy in. <ref name="[1]" /> The H-H bond is -432 kJ/mol and the H-F bond is -565 kj/mol <ref name="[2]" />. This means that more energy is needed to break the H-F than the energy gained by forming the H-H bond, and hence the forward reaction is exothermic (and the backward endothermic).

 Locating the Transition Stateː 

Applying the following settingsː

Atom A: F

Atom B: H

Atom C: H

AB distance: 1.81 Å

BC distance: 0.7455 Å

Both momenta are set to 0.

These settings were applied using the Dynamics Calculation type and visualising the Internuclear Distance vs Time plot. Trial and error values were used until all the distances (A-B, B-C and A-C) produce straight lines, as shown in the figure below.

[[File:Distance_time_1_sp2416.PNG|thumb|centre|Internuclear Distance vs Time graph using Dynamics calculation type for F-H-H]]

 Reporting the Activation Energyː 

To find the activation energy, the type of calculation used is MEP and the AB distance is displaced slightly (form 1.81 is changed to 1.83) in order to force the reaction to go to either direction of the equilibrium - right hand side or left hand side.

The forward reaction in the equilibrium F + H2 ⇌ H + HF is exothermic. Hammond's postulate states that the transition state resembles more the reactants than the products in an exothermic reaction. Hence, the activation energy is obtained when the A-B distance is displaced in this calculation.

Energy of the transition state = -103.752 kJ/mol

Energy of products = -133.466 kJ/mol

Activation energy of the reaction = 29.714 kJ/mol

[[File:Activationenergysp2416.PNG|thumb|centre|Finding the activation energy]]

=== Reaction Dynamics ===

Reactive Trajectory 

Atom A : F

Atom B : H

Atom C : H

AB distance = 1.91

BC distance = 0.7455

AB momentum = -1.5

BC momentum = 1.0

[[File:Reactivetrajsp2416.png|thumb|centre|Reactive Trajectory]]

[[File:Momentasp2416.png|thumb|centre|Internuclear Momenta vs Time]]

An increased and vigorous oscillation of the resulting molecule can be seen from the Momentum vs Time plot. This means that the energy released during this exothermic reaction is converted into vibrational energy.

[[File:Energyplotsp2416.png|thumb|centre|Energy vs Time]]

The Energy vs Time plot shows an increased oscillation in the kinetic energy of the molecule.

Investigating the effect of changing the momentum of AB

Atom A : F

Atom B : H

Atom C : H

AB distance = 1.91

BC distance = 0.7455

AB momentum = -3 to 3

BC momentum = -0.5

=== Polanyi's rules ===

The different motions (e.g. vibrational and rotational) on a reaction are discussed by Polanyi Rules.

As the forward reaction in F + H2 ⇌ H + HF is exothermic, the transition state resembles the reactants and occurs early, and therefore is promoted by translational motion. This motion is resembled by the momentum corresponding to the molecules which initially are further apart (in this case the AB momentum), as this momentum is responsible for the strength of the collision.

In the backward reaction which is endothermic, the transition state is late and is hence promoted by a high initial vibrational energy of the starting material. The momentum of the initially bonded molecule represents this energy.

Thus, it depends on the reaction monitored which momentum leads to a promotion of which reaction.

The reaction examined above corresponds to the endothermic one, which explains why an increase in the AB-momentum results in no reaction.

== References ==

<references>
<ref name="[1]">J.C. Polanyi, D.C. Tardy, 1969, J. Chem. Phys., Vol.51 "Energy Distribution in the Exothermic Reaction F + H2 , and the Endothermic Reaction HF + H", p.255-321.</ref>

<ref name="[2]">http://www.wiredchemist.com/chemistry/data/bond_energies_lengths.html (Assessed on 15/05/2018 17ː10).</ref>
</references>

MRD:sp2416

2018-05-16T15:13:03Z

Sp2416: /* Reactive and Unreactive Trajectories */

==H + H2==

===Transition State ===

The transition state is defined at the maximum on the minimum energy path linking reactants and products. Both minima and transition states are saddle points on the potential energy surface. On the potential energy surface diagram of H + H2 analysed, the gradient of both the transition state and minimum are found to be zero (∂V(ri)/∂ri=0). Minima and transition structures can be distinguished by taking the second derivative of the gradient. For transition state this will be negative and positive, while for minima the answer to this will be positive.

===Locating the Transition State===

[[File:Internucleardistancesp2416.PNG|thumb|centre|Internuclear Distance vs Time plot for H + H2]]

On the first graph the Transition state is where the A-B and B-C lines cross.

To locate the Transition state the momenta are changed to 0, (as a transition state is a saddle point) and then the distances AB and BC are adjusted so as to get an Internuclear Distance graph where both distances are stationary. This distance is found to be stationary when both AB and BC are set to be 0.90755.

[[File:InternucleardistanceTSsp2416.PNG|thumb|centre|Internuclear Distance vs Time plot for H + H2 Transition state]]

===Dynamic and MEP Calculation types===

The following results were obtained when the AB distance was changed to 0.90855 and the BC distance was maintained at 0.09755 (transition state position)

[[File:Trajectory_plot_dynamics_sp2416.PNG|thumb|centre|Trajectory plot using Dynamics calculation type]]

[[File:Trajectory_plot_mep_sp2416.PNG|thumb|centre|Trajectory plot using mep calculation type]]

[[File:Distance_time_dynamics_sp2416.PNG|thumb|centre|Internuclear Distance vs Time graph using Dynamics calculation type]]

[[File:Distance_time_mep_sp2416.PNG|thumb|centre|Internuclear Distance vs Time graph using mep calculation type]]

===Reactive and Unreactive Trajectories===

{| class="wikitable" border="1"
|+ Effect of different momenta on reactivity
! p1 !! p2 !! Total Energy!!Type of Trajectory!!Contour plot!!Description
|-
| -1.25 || -2.5 || -99.199 || Reactive || [[File:Contour1_sp2416.PNG|320px]] ||The reaction starts with a minorly oscillating AB-molecule, which is shown by a straight line plot at the start. Post the transition state occurring, and the BC-bond has been formed the molecule starts oscillating stronger. ||
|-
| -1.5 || -2.0 || -100.456 || Uneactive || [[File:Contour2_sp2416.PNG|320px]] || The A-B bond is oscillating at the beginning. However, both momenta of AB and C together are not strong enough to overcome the repulsion force and build the BC molecule. The particles however do approach each other, but the reaction does not go to completion. ||
|-
| -1.5 || -2.5 || -98.956 || Reactive || [[File:Contour3_sp2416.PNG|320px]] || Very similar to the first reaction, the only difference being that the A-B bond oscillates from the beginning as C is approaching.||
|-
| -2.5 || -5.0 || -84.956 || Uneactive || [[File:Contour4_sp2416.PNG|320px]] || The A-B bond does not oscillate. The impact with atom C leads to a brief period of time where B and C can be observed vibrating strongly, before it dissociates again.||
|-
| -2.5 || -5.2 || -83.416 || Reactive || [[File:Contour5_sp2416.PNG|320px]] || This plot can be considered as the mirror image of the previous plot as it starts with a non-oscillating A-B bond. Collision with C give a short-lived BC bond, which dissociates back to A-B. However, the reaction goes back to a B-C molecule.
||
|}

===Transition State Theory===

Complete

==F - H - H ==

=== PES Inspection ===

The equilibrium reaction F + H2 ⇌ H + HF is exothermic when it goes forward releasing energy, whilst the backward reaction is endothermic, taking energy in. <ref name="[1]" /> The H-H bond is -432 kJ/mol and the H-F bond is -565 kj/mol <ref name="[2]" />. This means that more energy is needed to break the H-F than the energy gained by forming the H-H bond, and hence the forward reaction is exothermic (and the backward endothermic).

 Locating the Transition Stateː 

Applying the following settingsː

Atom A: F

Atom B: H

Atom C: H

AB distance: 1.81 Å

BC distance: 0.7455 Å

Both momenta are set to 0.

These settings were applied using the Dynamics Calculation type and visualising the Internuclear Distance vs Time plot. Trial and error values were used until all the distances (A-B, B-C and A-C) produce straight lines, as shown in the figure below.

[[File:Distance_time_1_sp2416.PNG|thumb|centre|Internuclear Distance vs Time graph using Dynamics calculation type for F-H-H]]

 Reporting the Activation Energyː 

To find the activation energy, the type of calculation used is MEP and the AB distance is displaced slightly (form 1.81 is changed to 1.83) in order to force the reaction to go to either direction of the equilibrium - right hand side or left hand side.

The forward reaction in the equilibrium F + H2 ⇌ H + HF is exothermic. Hammond's postulate states that the transition state resembles more the reactants than the products in an exothermic reaction. Hence, the activation energy is obtained when the A-B distance is displaced in this calculation.

Energy of the transition state = -103.752 kJ/mol

Energy of products = -133.466 kJ/mol

Activation energy of the reaction = 29.714 kJ/mol

[[File:Activationenergysp2416.PNG|thumb|centre|Finding the activation energy]]

=== Reaction Dynamics ===

Reactive Trajectory 

Atom A : F

Atom B : H

Atom C : H

AB distance = 1.91

BC distance = 0.7455

AB momentum = -1.5

BC momentum = 1.0

[[File:Reactivetrajsp2416.png|thumb|centre|Reactive Trajectory]]

[[File:Momentasp2416.png|thumb|centre|Internuclear Momenta vs Time]]

An increased and vigorous oscillation of the resulting molecule can be seen from the Momentum vs Time plot. This means that the energy released during this exothermic reaction is converted into vibrational energy.

[[File:Energyplotsp2416.png|thumb|centre|Energy vs Time]]

The Energy vs Time plot shows an increased oscillation in the kinetic energy of the molecule.

Investigating the effect of changing the momentum of AB

Atom A : F

Atom B : H

Atom C : H

AB distance = 1.91

BC distance = 0.7455

AB momentum = -3 to 3

BC momentum = -0.5

=== Polanyi's rules ===

The different motions (e.g. vibrational and rotational) on a reaction are discussed by Polanyi Rules.

As the forward reaction in F + H2 ⇌ H + HF is exothermic, the transition state resembles the reactants and occurs early, and therefore is promoted by translational motion. This motion is resembled by the momentum corresponding to the molecules which initially are further apart (in this case the AB momentum), as this momentum is responsible for the strength of the collision.

In the backward reaction which is endothermic, the transition state is late and is hence promoted by a high initial vibrational energy of the starting material. The momentum of the initially bonded molecule represents this energy.

Thus, it depends on the reaction monitored which momentum leads to a promotion of which reaction.

The reaction examined above corresponds to the endothermic one, which explains why an increase in the AB-momentum results in no reaction.

== References ==

<references>
<ref name="[1]">J.C. Polanyi, D.C. Tardy, 1969, J. Chem. Phys., Vol.51 "Energy Distribution in the Exothermic Reaction F + H2 , and the Endothermic Reaction HF + H", p.255-321.</ref>

<ref name="[2]">http://www.wiredchemist.com/chemistry/data/bond_energies_lengths.html (Assessed on 15/05/2018 17ː10).</ref>
</references>

MRD:sp2416

2018-05-16T14:21:57Z

Sp2416: /* Reactive and Unreactive Trajectories */

==H + H2==

===Transition State ===

The transition state is defined at the maximum on the minimum energy path linking reactants and products. Both minima and transition states are saddle points on the potential energy surface. On the potential energy surface diagram of H + H2 analysed, the gradient of both the transition state and minimum are found to be zero (∂V(ri)/∂ri=0). Minima and transition structures can be distinguished by taking the second derivative of the gradient. For transition state this will be negative and positive, while for minima the answer to this will be positive.

===Locating the Transition State===

[[File:Internucleardistancesp2416.PNG|thumb|centre|Internuclear Distance vs Time plot for H + H2]]

On the first graph the Transition state is where the A-B and B-C lines cross.

To locate the Transition state the momenta are changed to 0, (as a transition state is a saddle point) and then the distances AB and BC are adjusted so as to get an Internuclear Distance graph where both distances are stationary. This distance is found to be stationary when both AB and BC are set to be 0.90755.

[[File:InternucleardistanceTSsp2416.PNG|thumb|centre|Internuclear Distance vs Time plot for H + H2 Transition state]]

===Dynamic and MEP Calculation types===

The following results were obtained when the AB distance was changed to 0.90855 and the BC distance was maintained at 0.09755 (transition state position)

[[File:Trajectory_plot_dynamics_sp2416.PNG|thumb|centre|Trajectory plot using Dynamics calculation type]]

[[File:Trajectory_plot_mep_sp2416.PNG|thumb|centre|Trajectory plot using mep calculation type]]

[[File:Distance_time_dynamics_sp2416.PNG|thumb|centre|Internuclear Distance vs Time graph using Dynamics calculation type]]

[[File:Distance_time_mep_sp2416.PNG|thumb|centre|Internuclear Distance vs Time graph using mep calculation type]]

===Reactive and Unreactive Trajectories===

{| class="wikitable" border="1"
|+ Effect of different momenta on reactivity
! p1 !! p2 !! Total Energy!!Type of Trajectory!!Contour plot!!Description
|-
| -1.25 || -2.5 || -99.199 || Reactive || [[File:Contour1_sp2416.PNG|320px]] || cell ||
|-
| -1.5 || -2.0 || -100.456 || Uneactive || [[File:Contour2_sp2416.PNG|320px]] || cell ||
|-
| -1.5 || -2.5 || -98.956 || Reactive || [[File:Contour3_sp2416.PNG|320px]] || cell ||
|-
| -2.5 || -5.0 || -84.956 || Uneactive || [[File:Contour4_sp2416.PNG|320px]] || cell ||
|-
| -2.5 || -5.2 || -83.416 || Reactive || [[File:Contour5_sp2416.PNG|320px]] || cell ||
|}

===Transition State Theory===

Complete

==F - H - H ==

=== PES Inspection ===

The equilibrium reaction F + H2 ⇌ H + HF is exothermic when it goes forward releasing energy, whilst the backward reaction is endothermic, taking energy in. <ref name="[1]" /> The H-H bond is -432 kJ/mol and the H-F bond is -565 kj/mol <ref name="[2]" />. This means that more energy is needed to break the H-F than the energy gained by forming the H-H bond, and hence the forward reaction is exothermic (and the backward endothermic).

 Locating the Transition Stateː 

Applying the following settingsː

Atom A: F

Atom B: H

Atom C: H

AB distance: 1.81 Å

BC distance: 0.7455 Å

Both momenta are set to 0.

These settings were applied using the Dynamics Calculation type and visualising the Internuclear Distance vs Time plot. Trial and error values were used until all the distances (A-B, B-C and A-C) produce straight lines, as shown in the figure below.

[[File:Distance_time_1_sp2416.PNG|thumb|centre|Internuclear Distance vs Time graph using Dynamics calculation type for F-H-H]]

 Reporting the Activation Energyː 

To find the activation energy, the type of calculation used is MEP and the AB distance is displaced slightly (form 1.81 is changed to 1.83) in order to force the reaction to go to either direction of the equilibrium - right hand side or left hand side.

The forward reaction in the equilibrium F + H2 ⇌ H + HF is exothermic. Hammond's postulate states that the transition state resembles more the reactants than the products in an exothermic reaction. Hence, the activation energy is obtained when the A-B distance is displaced in this calculation.

Energy of the transition state = -103.752 kJ/mol

Energy of products = -133.466 kJ/mol

Activation energy of the reaction = 29.714 kJ/mol

[[File:Activationenergysp2416.PNG|thumb|centre|Finding the activation energy]]

=== Reaction Dynamics ===

Reactive Trajectory 

Atom A : F

Atom B : H

Atom C : H

AB distance = 1.91

BC distance = 0.7455

AB momentum = -1.5

BC momentum = 1.0

[[File:Reactivetrajsp2416.png|thumb|centre|Reactive Trajectory]]

[[File:Momentasp2416.png|thumb|centre|Internuclear Momenta vs Time]]

An increased and vigorous oscillation of the resulting molecule can be seen from the Momentum vs Time plot. This means that the energy released during this exothermic reaction is converted into vibrational energy.

[[File:Energyplotsp2416.png|thumb|centre|Energy vs Time]]

The Energy vs Time plot shows an increased oscillation in the kinetic energy of the molecule.

Investigating the effect of changing the momentum of AB

Atom A : F

Atom B : H

Atom C : H

AB distance = 1.91

BC distance = 0.7455

AB momentum = -3 to 3

BC momentum = -0.5

=== Polanyi's rules ===

The different motions (e.g. vibrational and rotational) on a reaction are discussed by Polanyi Rules.

As the forward reaction in F + H2 ⇌ H + HF is exothermic, the transition state resembles the reactants and occurs early, and therefore is promoted by translational motion. This motion is resembled by the momentum corresponding to the molecules which initially are further apart (in this case the AB momentum), as this momentum is responsible for the strength of the collision.

In the backward reaction which is endothermic, the transition state is late and is hence promoted by a high initial vibrational energy of the starting material. The momentum of the initially bonded molecule represents this energy.

Thus, it depends on the reaction monitored which momentum leads to a promotion of which reaction.

The reaction examined above corresponds to the endothermic one, which explains why an increase in the AB-momentum results in no reaction.

== References ==

<references>
<ref name="[1]">J.C. Polanyi, D.C. Tardy, 1969, J. Chem. Phys., Vol.51 "Energy Distribution in the Exothermic Reaction F + H2 , and the Endothermic Reaction HF + H", p.255-321.</ref>

<ref name="[2]">http://www.wiredchemist.com/chemistry/data/bond_energies_lengths.html (Assessed on 15/05/2018 17ː10).</ref>
</references>

MRD:sp2416

2018-05-16T14:21:34Z

Sp2416: /* Dynamic and MEP Calculation types */

==H + H2==

===Transition State ===

The transition state is defined at the maximum on the minimum energy path linking reactants and products. Both minima and transition states are saddle points on the potential energy surface. On the potential energy surface diagram of H + H2 analysed, the gradient of both the transition state and minimum are found to be zero (∂V(ri)/∂ri=0). Minima and transition structures can be distinguished by taking the second derivative of the gradient. For transition state this will be negative and positive, while for minima the answer to this will be positive.

===Locating the Transition State===

[[File:Internucleardistancesp2416.PNG|thumb|centre|Internuclear Distance vs Time plot for H + H2]]

On the first graph the Transition state is where the A-B and B-C lines cross.

To locate the Transition state the momenta are changed to 0, (as a transition state is a saddle point) and then the distances AB and BC are adjusted so as to get an Internuclear Distance graph where both distances are stationary. This distance is found to be stationary when both AB and BC are set to be 0.90755.

[[File:InternucleardistanceTSsp2416.PNG|thumb|centre|Internuclear Distance vs Time plot for H + H2 Transition state]]

===Dynamic and MEP Calculation types===

The following results were obtained when the AB distance was changed to 0.90855 and the BC distance was maintained at 0.09755 (transition state position)

[[File:Trajectory_plot_dynamics_sp2416.PNG|thumb|centre|Trajectory plot using Dynamics calculation type]]

[[File:Trajectory_plot_mep_sp2416.PNG|thumb|centre|Trajectory plot using mep calculation type]]

[[File:Distance_time_dynamics_sp2416.PNG|thumb|centre|Internuclear Distance vs Time graph using Dynamics calculation type]]

[[File:Distance_time_mep_sp2416.PNG|thumb|centre|Internuclear Distance vs Time graph using mep calculation type]]

===Reactive and Unreactive Trajectories===

{| class="wikitable" border="1"
|+ Effect of different momenta on reactivity
! p1 !! p2 !! Total Energy!!Type of Trajectory!!Contour plot!!Description
|-
| -1.25 || -2.5 || -99.199 || Reactive || [[File:Contour1_sp2416.PNG|320px]] || cell ||
|-
| -1.5 || -2.0 || -100.456 || Uneactive || [[File:Contour2_sp2416.PNG|320px]] || cell ||
|-
| -1.5 || -2.5 || -98.956 || Reactive || [[File:Contour3_sp2416.PNG|320px]] || cell ||
|-
| -2.5 || -5.0 || -84.956 || Uneactive || [[File:Contour4_sp2416.PNG|320px]] || cell ||
|-
| -2.5 || -5.2 || -83.416 || Reactive || [[File:Contour5_sp2416.PNG|320px]] || cell ||
|}

===Transition State Theory===

Complete

==F - H - H ==

=== PES Inspection ===

The equilibrium reaction F + H2 ⇌ H + HF is exothermic when it goes forward releasing energy, whilst the backward reaction is endothermic, taking energy in. <ref name="[1]" /> The H-H bond is -432 kJ/mol and the H-F bond is -565 kj/mol <ref name="[2]" />. This means that more energy is needed to break the H-F than the energy gained by forming the H-H bond, and hence the forward reaction is exothermic (and the backward endothermic).

 Locating the Transition Stateː 

Applying the following settingsː

Atom A: F

Atom B: H

Atom C: H

AB distance: 1.81 Å

BC distance: 0.7455 Å

Both momenta are set to 0.

These settings were applied using the Dynamics Calculation type and visualising the Internuclear Distance vs Time plot. Trial and error values were used until all the distances (A-B, B-C and A-C) produce straight lines, as shown in the figure below.

[[File:Distance_time_1_sp2416.PNG|thumb|centre|Internuclear Distance vs Time graph using Dynamics calculation type for F-H-H]]

 Reporting the Activation Energyː 

To find the activation energy, the type of calculation used is MEP and the AB distance is displaced slightly (form 1.81 is changed to 1.83) in order to force the reaction to go to either direction of the equilibrium - right hand side or left hand side.

The forward reaction in the equilibrium F + H2 ⇌ H + HF is exothermic. Hammond's postulate states that the transition state resembles more the reactants than the products in an exothermic reaction. Hence, the activation energy is obtained when the A-B distance is displaced in this calculation.

Energy of the transition state = -103.752 kJ/mol

Energy of products = -133.466 kJ/mol

Activation energy of the reaction = 29.714 kJ/mol

[[File:Activationenergysp2416.PNG|thumb|centre|Finding the activation energy]]

=== Reaction Dynamics ===

Reactive Trajectory 

Atom A : F

Atom B : H

Atom C : H

AB distance = 1.91

BC distance = 0.7455

AB momentum = -1.5

BC momentum = 1.0

[[File:Reactivetrajsp2416.png|thumb|centre|Reactive Trajectory]]

[[File:Momentasp2416.png|thumb|centre|Internuclear Momenta vs Time]]

An increased and vigorous oscillation of the resulting molecule can be seen from the Momentum vs Time plot. This means that the energy released during this exothermic reaction is converted into vibrational energy.

[[File:Energyplotsp2416.png|thumb|centre|Energy vs Time]]

The Energy vs Time plot shows an increased oscillation in the kinetic energy of the molecule.

Investigating the effect of changing the momentum of AB

Atom A : F

Atom B : H

Atom C : H

AB distance = 1.91

BC distance = 0.7455

AB momentum = -3 to 3

BC momentum = -0.5

=== Polanyi's rules ===

The different motions (e.g. vibrational and rotational) on a reaction are discussed by Polanyi Rules.

As the forward reaction in F + H2 ⇌ H + HF is exothermic, the transition state resembles the reactants and occurs early, and therefore is promoted by translational motion. This motion is resembled by the momentum corresponding to the molecules which initially are further apart (in this case the AB momentum), as this momentum is responsible for the strength of the collision.

In the backward reaction which is endothermic, the transition state is late and is hence promoted by a high initial vibrational energy of the starting material. The momentum of the initially bonded molecule represents this energy.

Thus, it depends on the reaction monitored which momentum leads to a promotion of which reaction.

The reaction examined above corresponds to the endothermic one, which explains why an increase in the AB-momentum results in no reaction.

== References ==

<references>
<ref name="[1]">J.C. Polanyi, D.C. Tardy, 1969, J. Chem. Phys., Vol.51 "Energy Distribution in the Exothermic Reaction F + H2 , and the Endothermic Reaction HF + H", p.255-321.</ref>

<ref name="[2]">http://www.wiredchemist.com/chemistry/data/bond_energies_lengths.html (Assessed on 15/05/2018 17ː10).</ref>
</references>

MRD:sp2416

2018-05-16T14:20:35Z

Sp2416: /* Dynamic and MEP Calculation types */

==H + H2==

===Transition State ===

The transition state is defined at the maximum on the minimum energy path linking reactants and products. Both minima and transition states are saddle points on the potential energy surface. On the potential energy surface diagram of H + H2 analysed, the gradient of both the transition state and minimum are found to be zero (∂V(ri)/∂ri=0). Minima and transition structures can be distinguished by taking the second derivative of the gradient. For transition state this will be negative and positive, while for minima the answer to this will be positive.

===Locating the Transition State===

[[File:Internucleardistancesp2416.PNG|thumb|centre|Internuclear Distance vs Time plot for H + H2]]

On the first graph the Transition state is where the A-B and B-C lines cross.

To locate the Transition state the momenta are changed to 0, (as a transition state is a saddle point) and then the distances AB and BC are adjusted so as to get an Internuclear Distance graph where both distances are stationary. This distance is found to be stationary when both AB and BC are set to be 0.90755.

[[File:InternucleardistanceTSsp2416.PNG|thumb|centre|Internuclear Distance vs Time plot for H + H2 Transition state]]

===Dynamic and MEP Calculation types===

The following results were obtained when the AB distance was changed to 0.90855 and the BC distance was maintained at 0.09755 (transition state position)

[[File:Trajectory_plot_dynamics_sp2416.PNG|thumb|Trajectory plot using Dynamics calculation type]]

[[File:Trajectory_plot_mep_sp2416.PNG|thumb|Trajectory plot using mep calculation type]]

[[File:Distance_time_dynamics_sp2416.PNG|thumb|Internuclear Distance vs Time graph using Dynamics calculation type]]

[[File:Distance_time_mep_sp2416.PNG|thumb|Internuclear Distance vs Time graph using mep calculation type]]

===Reactive and Unreactive Trajectories===

{| class="wikitable" border="1"
|+ Effect of different momenta on reactivity
! p1 !! p2 !! Total Energy!!Type of Trajectory!!Contour plot!!Description
|-
| -1.25 || -2.5 || -99.199 || Reactive || [[File:Contour1_sp2416.PNG|320px]] || cell ||
|-
| -1.5 || -2.0 || -100.456 || Uneactive || [[File:Contour2_sp2416.PNG|320px]] || cell ||
|-
| -1.5 || -2.5 || -98.956 || Reactive || [[File:Contour3_sp2416.PNG|320px]] || cell ||
|-
| -2.5 || -5.0 || -84.956 || Uneactive || [[File:Contour4_sp2416.PNG|320px]] || cell ||
|-
| -2.5 || -5.2 || -83.416 || Reactive || [[File:Contour5_sp2416.PNG|320px]] || cell ||
|}

===Transition State Theory===

Complete

==F - H - H ==

=== PES Inspection ===

The equilibrium reaction F + H2 ⇌ H + HF is exothermic when it goes forward releasing energy, whilst the backward reaction is endothermic, taking energy in. <ref name="[1]" /> The H-H bond is -432 kJ/mol and the H-F bond is -565 kj/mol <ref name="[2]" />. This means that more energy is needed to break the H-F than the energy gained by forming the H-H bond, and hence the forward reaction is exothermic (and the backward endothermic).

 Locating the Transition Stateː 

Applying the following settingsː

Atom A: F

Atom B: H

Atom C: H

AB distance: 1.81 Å

BC distance: 0.7455 Å

Both momenta are set to 0.

These settings were applied using the Dynamics Calculation type and visualising the Internuclear Distance vs Time plot. Trial and error values were used until all the distances (A-B, B-C and A-C) produce straight lines, as shown in the figure below.

[[File:Distance_time_1_sp2416.PNG|thumb|centre|Internuclear Distance vs Time graph using Dynamics calculation type for F-H-H]]

 Reporting the Activation Energyː 

To find the activation energy, the type of calculation used is MEP and the AB distance is displaced slightly (form 1.81 is changed to 1.83) in order to force the reaction to go to either direction of the equilibrium - right hand side or left hand side.

The forward reaction in the equilibrium F + H2 ⇌ H + HF is exothermic. Hammond's postulate states that the transition state resembles more the reactants than the products in an exothermic reaction. Hence, the activation energy is obtained when the A-B distance is displaced in this calculation.

Energy of the transition state = -103.752 kJ/mol

Energy of products = -133.466 kJ/mol

Activation energy of the reaction = 29.714 kJ/mol

[[File:Activationenergysp2416.PNG|thumb|centre|Finding the activation energy]]

=== Reaction Dynamics ===

Reactive Trajectory 

Atom A : F

Atom B : H

Atom C : H

AB distance = 1.91

BC distance = 0.7455

AB momentum = -1.5

BC momentum = 1.0

[[File:Reactivetrajsp2416.png|thumb|centre|Reactive Trajectory]]

[[File:Momentasp2416.png|thumb|centre|Internuclear Momenta vs Time]]

An increased and vigorous oscillation of the resulting molecule can be seen from the Momentum vs Time plot. This means that the energy released during this exothermic reaction is converted into vibrational energy.

[[File:Energyplotsp2416.png|thumb|centre|Energy vs Time]]

The Energy vs Time plot shows an increased oscillation in the kinetic energy of the molecule.

Investigating the effect of changing the momentum of AB

Atom A : F

Atom B : H

Atom C : H

AB distance = 1.91

BC distance = 0.7455

AB momentum = -3 to 3

BC momentum = -0.5

=== Polanyi's rules ===

The different motions (e.g. vibrational and rotational) on a reaction are discussed by Polanyi Rules.

As the forward reaction in F + H2 ⇌ H + HF is exothermic, the transition state resembles the reactants and occurs early, and therefore is promoted by translational motion. This motion is resembled by the momentum corresponding to the molecules which initially are further apart (in this case the AB momentum), as this momentum is responsible for the strength of the collision.

In the backward reaction which is endothermic, the transition state is late and is hence promoted by a high initial vibrational energy of the starting material. The momentum of the initially bonded molecule represents this energy.

Thus, it depends on the reaction monitored which momentum leads to a promotion of which reaction.

The reaction examined above corresponds to the endothermic one, which explains why an increase in the AB-momentum results in no reaction.

== References ==

<references>
<ref name="[1]">J.C. Polanyi, D.C. Tardy, 1969, J. Chem. Phys., Vol.51 "Energy Distribution in the Exothermic Reaction F + H2 , and the Endothermic Reaction HF + H", p.255-321.</ref>

<ref name="[2]">http://www.wiredchemist.com/chemistry/data/bond_energies_lengths.html (Assessed on 15/05/2018 17ː10).</ref>
</references>

MRD:sp2416

2018-05-16T14:20:00Z

Sp2416: /* Dynamic and MEP Calculation types */

==H + H2==

===Transition State ===

The transition state is defined at the maximum on the minimum energy path linking reactants and products. Both minima and transition states are saddle points on the potential energy surface. On the potential energy surface diagram of H + H2 analysed, the gradient of both the transition state and minimum are found to be zero (∂V(ri)/∂ri=0). Minima and transition structures can be distinguished by taking the second derivative of the gradient. For transition state this will be negative and positive, while for minima the answer to this will be positive.

===Locating the Transition State===

[[File:Internucleardistancesp2416.PNG|thumb|centre|Internuclear Distance vs Time plot for H + H2]]

On the first graph the Transition state is where the A-B and B-C lines cross.

To locate the Transition state the momenta are changed to 0, (as a transition state is a saddle point) and then the distances AB and BC are adjusted so as to get an Internuclear Distance graph where both distances are stationary. This distance is found to be stationary when both AB and BC are set to be 0.90755.

[[File:InternucleardistanceTSsp2416.PNG|thumb|centre|Internuclear Distance vs Time plot for H + H2 Transition state]]

===Dynamic and MEP Calculation types===

The following results were obtained when the AB distance was changed to 0.90855 and the BC distance was maintained at 0.09755 (transition state position)

[[File:Trajectory_plot_dynamics_sp2416.PNG|thumb|left|Trajectory plot using Dynamics calculation type]]

[[File:Trajectory_plot_mep_sp2416.PNG|thumb|right|Trajectory plot using mep calculation type]]

[[File:Distance_time_dynamics_sp2416.PNG|thumb|left|Internuclear Distance vs Time graph using Dynamics calculation type]]

[[File:Distance_time_mep_sp2416.PNG|thumb|right|Internuclear Distance vs Time graph using mep calculation type]]

===Reactive and Unreactive Trajectories===

{| class="wikitable" border="1"
|+ Effect of different momenta on reactivity
! p1 !! p2 !! Total Energy!!Type of Trajectory!!Contour plot!!Description
|-
| -1.25 || -2.5 || -99.199 || Reactive || [[File:Contour1_sp2416.PNG|320px]] || cell ||
|-
| -1.5 || -2.0 || -100.456 || Uneactive || [[File:Contour2_sp2416.PNG|320px]] || cell ||
|-
| -1.5 || -2.5 || -98.956 || Reactive || [[File:Contour3_sp2416.PNG|320px]] || cell ||
|-
| -2.5 || -5.0 || -84.956 || Uneactive || [[File:Contour4_sp2416.PNG|320px]] || cell ||
|-
| -2.5 || -5.2 || -83.416 || Reactive || [[File:Contour5_sp2416.PNG|320px]] || cell ||
|}

===Transition State Theory===

Complete

==F - H - H ==

=== PES Inspection ===

The equilibrium reaction F + H2 ⇌ H + HF is exothermic when it goes forward releasing energy, whilst the backward reaction is endothermic, taking energy in. <ref name="[1]" /> The H-H bond is -432 kJ/mol and the H-F bond is -565 kj/mol <ref name="[2]" />. This means that more energy is needed to break the H-F than the energy gained by forming the H-H bond, and hence the forward reaction is exothermic (and the backward endothermic).

 Locating the Transition Stateː 

Applying the following settingsː

Atom A: F

Atom B: H

Atom C: H

AB distance: 1.81 Å

BC distance: 0.7455 Å

Both momenta are set to 0.

These settings were applied using the Dynamics Calculation type and visualising the Internuclear Distance vs Time plot. Trial and error values were used until all the distances (A-B, B-C and A-C) produce straight lines, as shown in the figure below.

[[File:Distance_time_1_sp2416.PNG|thumb|centre|Internuclear Distance vs Time graph using Dynamics calculation type for F-H-H]]

 Reporting the Activation Energyː 

To find the activation energy, the type of calculation used is MEP and the AB distance is displaced slightly (form 1.81 is changed to 1.83) in order to force the reaction to go to either direction of the equilibrium - right hand side or left hand side.

The forward reaction in the equilibrium F + H2 ⇌ H + HF is exothermic. Hammond's postulate states that the transition state resembles more the reactants than the products in an exothermic reaction. Hence, the activation energy is obtained when the A-B distance is displaced in this calculation.

Energy of the transition state = -103.752 kJ/mol

Energy of products = -133.466 kJ/mol

Activation energy of the reaction = 29.714 kJ/mol

[[File:Activationenergysp2416.PNG|thumb|centre|Finding the activation energy]]

=== Reaction Dynamics ===

Reactive Trajectory 

Atom A : F

Atom B : H

Atom C : H

AB distance = 1.91

BC distance = 0.7455

AB momentum = -1.5

BC momentum = 1.0

[[File:Reactivetrajsp2416.png|thumb|centre|Reactive Trajectory]]

[[File:Momentasp2416.png|thumb|centre|Internuclear Momenta vs Time]]

An increased and vigorous oscillation of the resulting molecule can be seen from the Momentum vs Time plot. This means that the energy released during this exothermic reaction is converted into vibrational energy.

[[File:Energyplotsp2416.png|thumb|centre|Energy vs Time]]

The Energy vs Time plot shows an increased oscillation in the kinetic energy of the molecule.

Investigating the effect of changing the momentum of AB

Atom A : F

Atom B : H

Atom C : H

AB distance = 1.91

BC distance = 0.7455

AB momentum = -3 to 3

BC momentum = -0.5

=== Polanyi's rules ===

The different motions (e.g. vibrational and rotational) on a reaction are discussed by Polanyi Rules.

As the forward reaction in F + H2 ⇌ H + HF is exothermic, the transition state resembles the reactants and occurs early, and therefore is promoted by translational motion. This motion is resembled by the momentum corresponding to the molecules which initially are further apart (in this case the AB momentum), as this momentum is responsible for the strength of the collision.

In the backward reaction which is endothermic, the transition state is late and is hence promoted by a high initial vibrational energy of the starting material. The momentum of the initially bonded molecule represents this energy.

Thus, it depends on the reaction monitored which momentum leads to a promotion of which reaction.

The reaction examined above corresponds to the endothermic one, which explains why an increase in the AB-momentum results in no reaction.

== References ==

<references>
<ref name="[1]">J.C. Polanyi, D.C. Tardy, 1969, J. Chem. Phys., Vol.51 "Energy Distribution in the Exothermic Reaction F + H2 , and the Endothermic Reaction HF + H", p.255-321.</ref>

<ref name="[2]">http://www.wiredchemist.com/chemistry/data/bond_energies_lengths.html (Assessed on 15/05/2018 17ː10).</ref>
</references>

MRD:sp2416

2018-05-16T14:18:40Z

Sp2416: /* Dynamic and mep Calculation types */

==H + H2==

===Transition State ===

The transition state is defined at the maximum on the minimum energy path linking reactants and products. Both minima and transition states are saddle points on the potential energy surface. On the potential energy surface diagram of H + H2 analysed, the gradient of both the transition state and minimum are found to be zero (∂V(ri)/∂ri=0). Minima and transition structures can be distinguished by taking the second derivative of the gradient. For transition state this will be negative and positive, while for minima the answer to this will be positive.

===Locating the Transition State===

[[File:Internucleardistancesp2416.PNG|thumb|centre|Internuclear Distance vs Time plot for H + H2]]

On the first graph the Transition state is where the A-B and B-C lines cross.

To locate the Transition state the momenta are changed to 0, (as a transition state is a saddle point) and then the distances AB and BC are adjusted so as to get an Internuclear Distance graph where both distances are stationary. This distance is found to be stationary when both AB and BC are set to be 0.90755.

[[File:InternucleardistanceTSsp2416.PNG|thumb|centre|Internuclear Distance vs Time plot for H + H2 Transition state]]

===Dynamic and MEP Calculation types===

The following results were obtained when the AB distance was changed to 0.90855 and the BC distance was maintained at 0.09755 (transition state position)

[[File:Trajectory_plot_dynamics_sp2416.PNG|thumb|centre|Trajectory plot using Dynamics calculation type]]

[[File:Trajectory_plot_mep_sp2416.PNG|thumb|centre|Trajectory plot using mep calculation type]]

[[File:Distance_time_dynamics_sp2416.PNG|thumb|centre|Internuclear Distance vs Time graph using Dynamics calculation type]]

[[File:Distance_time_mep_sp2416.PNG|thumb|centre|Internuclear Distance vs Time graph using mep calculation type]]

===Reactive and Unreactive Trajectories===

{| class="wikitable" border="1"
|+ Effect of different momenta on reactivity
! p1 !! p2 !! Total Energy!!Type of Trajectory!!Contour plot!!Description
|-
| -1.25 || -2.5 || -99.199 || Reactive || [[File:Contour1_sp2416.PNG|320px]] || cell ||
|-
| -1.5 || -2.0 || -100.456 || Uneactive || [[File:Contour2_sp2416.PNG|320px]] || cell ||
|-
| -1.5 || -2.5 || -98.956 || Reactive || [[File:Contour3_sp2416.PNG|320px]] || cell ||
|-
| -2.5 || -5.0 || -84.956 || Uneactive || [[File:Contour4_sp2416.PNG|320px]] || cell ||
|-
| -2.5 || -5.2 || -83.416 || Reactive || [[File:Contour5_sp2416.PNG|320px]] || cell ||
|}

===Transition State Theory===

Complete

==F - H - H ==

=== PES Inspection ===

The equilibrium reaction F + H2 ⇌ H + HF is exothermic when it goes forward releasing energy, whilst the backward reaction is endothermic, taking energy in. <ref name="[1]" /> The H-H bond is -432 kJ/mol and the H-F bond is -565 kj/mol <ref name="[2]" />. This means that more energy is needed to break the H-F than the energy gained by forming the H-H bond, and hence the forward reaction is exothermic (and the backward endothermic).

 Locating the Transition Stateː 

Applying the following settingsː

Atom A: F

Atom B: H

Atom C: H

AB distance: 1.81 Å

BC distance: 0.7455 Å

Both momenta are set to 0.

These settings were applied using the Dynamics Calculation type and visualising the Internuclear Distance vs Time plot. Trial and error values were used until all the distances (A-B, B-C and A-C) produce straight lines, as shown in the figure below.

[[File:Distance_time_1_sp2416.PNG|thumb|centre|Internuclear Distance vs Time graph using Dynamics calculation type for F-H-H]]

 Reporting the Activation Energyː 

To find the activation energy, the type of calculation used is MEP and the AB distance is displaced slightly (form 1.81 is changed to 1.83) in order to force the reaction to go to either direction of the equilibrium - right hand side or left hand side.

The forward reaction in the equilibrium F + H2 ⇌ H + HF is exothermic. Hammond's postulate states that the transition state resembles more the reactants than the products in an exothermic reaction. Hence, the activation energy is obtained when the A-B distance is displaced in this calculation.

Energy of the transition state = -103.752 kJ/mol

Energy of products = -133.466 kJ/mol

Activation energy of the reaction = 29.714 kJ/mol

[[File:Activationenergysp2416.PNG|thumb|centre|Finding the activation energy]]

=== Reaction Dynamics ===

Reactive Trajectory 

Atom A : F

Atom B : H

Atom C : H

AB distance = 1.91

BC distance = 0.7455

AB momentum = -1.5

BC momentum = 1.0

[[File:Reactivetrajsp2416.png|thumb|centre|Reactive Trajectory]]

[[File:Momentasp2416.png|thumb|centre|Internuclear Momenta vs Time]]

An increased and vigorous oscillation of the resulting molecule can be seen from the Momentum vs Time plot. This means that the energy released during this exothermic reaction is converted into vibrational energy.

[[File:Energyplotsp2416.png|thumb|centre|Energy vs Time]]

The Energy vs Time plot shows an increased oscillation in the kinetic energy of the molecule.

Investigating the effect of changing the momentum of AB

Atom A : F

Atom B : H

Atom C : H

AB distance = 1.91

BC distance = 0.7455

AB momentum = -3 to 3

BC momentum = -0.5

=== Polanyi's rules ===

The different motions (e.g. vibrational and rotational) on a reaction are discussed by Polanyi Rules.

As the forward reaction in F + H2 ⇌ H + HF is exothermic, the transition state resembles the reactants and occurs early, and therefore is promoted by translational motion. This motion is resembled by the momentum corresponding to the molecules which initially are further apart (in this case the AB momentum), as this momentum is responsible for the strength of the collision.

In the backward reaction which is endothermic, the transition state is late and is hence promoted by a high initial vibrational energy of the starting material. The momentum of the initially bonded molecule represents this energy.

Thus, it depends on the reaction monitored which momentum leads to a promotion of which reaction.

The reaction examined above corresponds to the endothermic one, which explains why an increase in the AB-momentum results in no reaction.

== References ==

<references>
<ref name="[1]">J.C. Polanyi, D.C. Tardy, 1969, J. Chem. Phys., Vol.51 "Energy Distribution in the Exothermic Reaction F + H2 , and the Endothermic Reaction HF + H", p.255-321.</ref>

<ref name="[2]">http://www.wiredchemist.com/chemistry/data/bond_energies_lengths.html (Assessed on 15/05/2018 17ː10).</ref>
</references>

MRD:sp2416

2018-05-16T14:12:27Z

Sp2416: /* Polanyi's rules */

==H + H2==

===Transition State ===

The transition state is defined at the maximum on the minimum energy path linking reactants and products. Both minima and transition states are saddle points on the potential energy surface. On the potential energy surface diagram of H + H2 analysed, the gradient of both the transition state and minimum are found to be zero (∂V(ri)/∂ri=0). Minima and transition structures can be distinguished by taking the second derivative of the gradient. For transition state this will be negative and positive, while for minima the answer to this will be positive.

===Locating the Transition State===

[[File:Internucleardistancesp2416.PNG|thumb|centre|Internuclear Distance vs Time plot for H + H2]]

On the first graph the Transition state is where the A-B and B-C lines cross.

To locate the Transition state the momenta are changed to 0, (as a transition state is a saddle point) and then the distances AB and BC are adjusted so as to get an Internuclear Distance graph where both distances are stationary. This distance is found to be stationary when both AB and BC are set to be 0.90755.

[[File:InternucleardistanceTSsp2416.PNG|thumb|centre|Internuclear Distance vs Time plot for H + H2 Transition state]]

===Dynamic and mep Calculation types===

The following results were obtained when the AB distance was changed to 0.90855 and the BC distance was maintained at 0.09755 (transition state position)

[[File:Trajectory_plot_dynamics_sp2416.PNG|thumb|centre|Trajectory plot using Dynamics calculation type]]

[[File:Trajectory_plot_mep_sp2416.PNG|thumb|centre|Trajectory plot using mep calculation type]]

[[File:Distance_time_dynamics_sp2416.PNG|thumb|centre|Internuclear Distance vs Time graph using Dynamics calculation type]]

[[File:Distance_time_mep_sp2416.PNG|thumb|centre|Internuclear Distance vs Time graph using mep calculation type]]

===Reactive and Unreactive Trajectories===

{| class="wikitable" border="1"
|+ Effect of different momenta on reactivity
! p1 !! p2 !! Total Energy!!Type of Trajectory!!Contour plot!!Description
|-
| -1.25 || -2.5 || -99.199 || Reactive || [[File:Contour1_sp2416.PNG|320px]] || cell ||
|-
| -1.5 || -2.0 || -100.456 || Uneactive || [[File:Contour2_sp2416.PNG|320px]] || cell ||
|-
| -1.5 || -2.5 || -98.956 || Reactive || [[File:Contour3_sp2416.PNG|320px]] || cell ||
|-
| -2.5 || -5.0 || -84.956 || Uneactive || [[File:Contour4_sp2416.PNG|320px]] || cell ||
|-
| -2.5 || -5.2 || -83.416 || Reactive || [[File:Contour5_sp2416.PNG|320px]] || cell ||
|}

===Transition State Theory===

Complete

==F - H - H ==

=== PES Inspection ===

The equilibrium reaction F + H2 ⇌ H + HF is exothermic when it goes forward releasing energy, whilst the backward reaction is endothermic, taking energy in. <ref name="[1]" /> The H-H bond is -432 kJ/mol and the H-F bond is -565 kj/mol <ref name="[2]" />. This means that more energy is needed to break the H-F than the energy gained by forming the H-H bond, and hence the forward reaction is exothermic (and the backward endothermic).

 Locating the Transition Stateː 

Applying the following settingsː

Atom A: F

Atom B: H

Atom C: H

AB distance: 1.81 Å

BC distance: 0.7455 Å

Both momenta are set to 0.

These settings were applied using the Dynamics Calculation type and visualising the Internuclear Distance vs Time plot. Trial and error values were used until all the distances (A-B, B-C and A-C) produce straight lines, as shown in the figure below.

[[File:Distance_time_1_sp2416.PNG|thumb|centre|Internuclear Distance vs Time graph using Dynamics calculation type for F-H-H]]

 Reporting the Activation Energyː 

To find the activation energy, the type of calculation used is MEP and the AB distance is displaced slightly (form 1.81 is changed to 1.83) in order to force the reaction to go to either direction of the equilibrium - right hand side or left hand side.

The forward reaction in the equilibrium F + H2 ⇌ H + HF is exothermic. Hammond's postulate states that the transition state resembles more the reactants than the products in an exothermic reaction. Hence, the activation energy is obtained when the A-B distance is displaced in this calculation.

Energy of the transition state = -103.752 kJ/mol

Energy of products = -133.466 kJ/mol

Activation energy of the reaction = 29.714 kJ/mol

[[File:Activationenergysp2416.PNG|thumb|centre|Finding the activation energy]]

=== Reaction Dynamics ===

Reactive Trajectory 

Atom A : F

Atom B : H

Atom C : H

AB distance = 1.91

BC distance = 0.7455

AB momentum = -1.5

BC momentum = 1.0

[[File:Reactivetrajsp2416.png|thumb|centre|Reactive Trajectory]]

[[File:Momentasp2416.png|thumb|centre|Internuclear Momenta vs Time]]

An increased and vigorous oscillation of the resulting molecule can be seen from the Momentum vs Time plot. This means that the energy released during this exothermic reaction is converted into vibrational energy.

[[File:Energyplotsp2416.png|thumb|centre|Energy vs Time]]

The Energy vs Time plot shows an increased oscillation in the kinetic energy of the molecule.

Investigating the effect of changing the momentum of AB

Atom A : F

Atom B : H

Atom C : H

AB distance = 1.91

BC distance = 0.7455

AB momentum = -3 to 3

BC momentum = -0.5

=== Polanyi's rules ===

The different motions (e.g. vibrational and rotational) on a reaction are discussed by Polanyi Rules.

As the forward reaction in F + H2 ⇌ H + HF is exothermic, the transition state resembles the reactants and occurs early, and therefore is promoted by translational motion. This motion is resembled by the momentum corresponding to the molecules which initially are further apart (in this case the AB momentum), as this momentum is responsible for the strength of the collision.

In the backward reaction which is endothermic, the transition state is late and is hence promoted by a high initial vibrational energy of the starting material. The momentum of the initially bonded molecule represents this energy.

Thus, it depends on the reaction monitored which momentum leads to a promotion of which reaction.

The reaction examined above corresponds to the endothermic one, which explains why an increase in the AB-momentum results in no reaction.

== References ==

<references>
<ref name="[1]">J.C. Polanyi, D.C. Tardy, 1969, J. Chem. Phys., Vol.51 "Energy Distribution in the Exothermic Reaction F + H2 , and the Endothermic Reaction HF + H", p.255-321.</ref>

<ref name="[2]">http://www.wiredchemist.com/chemistry/data/bond_energies_lengths.html (Assessed on 15/05/2018 17ː10).</ref>
</references>

MRD:sp2416

2018-05-16T14:12:08Z

Sp2416: /* Polanyi's rules */

==H + H2==

===Transition State ===

The transition state is defined at the maximum on the minimum energy path linking reactants and products. Both minima and transition states are saddle points on the potential energy surface. On the potential energy surface diagram of H + H2 analysed, the gradient of both the transition state and minimum are found to be zero (∂V(ri)/∂ri=0). Minima and transition structures can be distinguished by taking the second derivative of the gradient. For transition state this will be negative and positive, while for minima the answer to this will be positive.

===Locating the Transition State===

[[File:Internucleardistancesp2416.PNG|thumb|centre|Internuclear Distance vs Time plot for H + H2]]

On the first graph the Transition state is where the A-B and B-C lines cross.

To locate the Transition state the momenta are changed to 0, (as a transition state is a saddle point) and then the distances AB and BC are adjusted so as to get an Internuclear Distance graph where both distances are stationary. This distance is found to be stationary when both AB and BC are set to be 0.90755.

[[File:InternucleardistanceTSsp2416.PNG|thumb|centre|Internuclear Distance vs Time plot for H + H2 Transition state]]

===Dynamic and mep Calculation types===

The following results were obtained when the AB distance was changed to 0.90855 and the BC distance was maintained at 0.09755 (transition state position)

[[File:Trajectory_plot_dynamics_sp2416.PNG|thumb|centre|Trajectory plot using Dynamics calculation type]]

[[File:Trajectory_plot_mep_sp2416.PNG|thumb|centre|Trajectory plot using mep calculation type]]

[[File:Distance_time_dynamics_sp2416.PNG|thumb|centre|Internuclear Distance vs Time graph using Dynamics calculation type]]

[[File:Distance_time_mep_sp2416.PNG|thumb|centre|Internuclear Distance vs Time graph using mep calculation type]]

===Reactive and Unreactive Trajectories===

{| class="wikitable" border="1"
|+ Effect of different momenta on reactivity
! p1 !! p2 !! Total Energy!!Type of Trajectory!!Contour plot!!Description
|-
| -1.25 || -2.5 || -99.199 || Reactive || [[File:Contour1_sp2416.PNG|320px]] || cell ||
|-
| -1.5 || -2.0 || -100.456 || Uneactive || [[File:Contour2_sp2416.PNG|320px]] || cell ||
|-
| -1.5 || -2.5 || -98.956 || Reactive || [[File:Contour3_sp2416.PNG|320px]] || cell ||
|-
| -2.5 || -5.0 || -84.956 || Uneactive || [[File:Contour4_sp2416.PNG|320px]] || cell ||
|-
| -2.5 || -5.2 || -83.416 || Reactive || [[File:Contour5_sp2416.PNG|320px]] || cell ||
|}

===Transition State Theory===

Complete

==F - H - H ==

=== PES Inspection ===

The equilibrium reaction F + H2 ⇌ H + HF is exothermic when it goes forward releasing energy, whilst the backward reaction is endothermic, taking energy in. <ref name="[1]" /> The H-H bond is -432 kJ/mol and the H-F bond is -565 kj/mol <ref name="[2]" />. This means that more energy is needed to break the H-F than the energy gained by forming the H-H bond, and hence the forward reaction is exothermic (and the backward endothermic).

 Locating the Transition Stateː 

Applying the following settingsː

Atom A: F

Atom B: H

Atom C: H

AB distance: 1.81 Å

BC distance: 0.7455 Å

Both momenta are set to 0.

These settings were applied using the Dynamics Calculation type and visualising the Internuclear Distance vs Time plot. Trial and error values were used until all the distances (A-B, B-C and A-C) produce straight lines, as shown in the figure below.

[[File:Distance_time_1_sp2416.PNG|thumb|centre|Internuclear Distance vs Time graph using Dynamics calculation type for F-H-H]]

 Reporting the Activation Energyː 

To find the activation energy, the type of calculation used is MEP and the AB distance is displaced slightly (form 1.81 is changed to 1.83) in order to force the reaction to go to either direction of the equilibrium - right hand side or left hand side.

The forward reaction in the equilibrium F + H2 ⇌ H + HF is exothermic. Hammond's postulate states that the transition state resembles more the reactants than the products in an exothermic reaction. Hence, the activation energy is obtained when the A-B distance is displaced in this calculation.

Energy of the transition state = -103.752 kJ/mol

Energy of products = -133.466 kJ/mol

Activation energy of the reaction = 29.714 kJ/mol

[[File:Activationenergysp2416.PNG|thumb|centre|Finding the activation energy]]

=== Reaction Dynamics ===

Reactive Trajectory 

Atom A : F

Atom B : H

Atom C : H

AB distance = 1.91

BC distance = 0.7455

AB momentum = -1.5

BC momentum = 1.0

[[File:Reactivetrajsp2416.png|thumb|centre|Reactive Trajectory]]

[[File:Momentasp2416.png|thumb|centre|Internuclear Momenta vs Time]]

An increased and vigorous oscillation of the resulting molecule can be seen from the Momentum vs Time plot. This means that the energy released during this exothermic reaction is converted into vibrational energy.

[[File:Energyplotsp2416.png|thumb|centre|Energy vs Time]]

The Energy vs Time plot shows an increased oscillation in the kinetic energy of the molecule.

Investigating the effect of changing the momentum of AB

Atom A : F

Atom B : H

Atom C : H

AB distance = 1.91

BC distance = 0.7455

AB momentum = -3 to 3

BC momentum = -0.5

=== Polanyi's rules ===

The different motions (e.g. vibrational and rotational) on a reaction are discussed by Polanyi Rules.

As the forward reaction in F + H2 ⇌ H + HF is exothermic, the transition state resembles the reactants and occurs early, and therefore is promoted by translational motion. This motion is resembled by the momentum corresponding to the molecules which initially are further apart (in this case the AB momentum), as this momentum is responsible for the strength of the collision.

In the backward reaction which is endothermic, the transition state is late and is hence promoted by a high initial vibrational energy of the starting material. The momentum of the initially bonded molecule represents this energy.

Thus, it depends on the reaction monitored which momentum leads to a promotion of which reaction.

The reaction examined above corresponds to the endothermic one, which explains why an increase in the AB-momentum results in no reaction.

== References ==

<references>
<ref name="[1]">J.C. Polanyi, D.C. Tardy, 1969, J. Chem. Phys., Vol.51 "Energy Distribution in the Exothermic Reaction F + H2 , and the Endothermic Reaction HF + H", p.255-321.</ref>

<ref name="[2]">http://www.wiredchemist.com/chemistry/data/bond_energies_lengths.html (Assessed on 15/05/2018 17ː10).</ref>
</references>

MRD:sp2416

2018-05-16T13:27:11Z

Sp2416: /* Reaction Dynamics */

MRD:sp2416

2018-05-16T13:23:54Z

Sp2416: /* Transition State */

MRD:sp2416

2018-05-15T17:31:38Z

Sp2416: /* Reaction Dynamics */

==H + H2==

===Transition State ===

The transition state is defined a the maximum on the minimum energy path linking reactants and products. Both minima and transition states are saddle points on the potential energy surface. On the potential energy surface diagram of H + H2 analysed, the gradient of both the transition state and minimum are found to be zero (∂V(ri)/∂ri=0). Minima and transition structures can be distinguished by taking the second derivative of the gradient. For transition state this will be negative and positive, while for minima the answer to this will be positive.

===Locating the Transition State===

[[File:Internucleardistancesp2416.PNG|thumb|centre|Internuclear Distance vs Time plot for H + H2]]

On the first graph the Transition state is where the A-B and B-C lines cross.

To locate the Transition state the momenta are changed to 0, (as a transition state is a saddle point) and then the distances AB and BC are adjusted so as to get an Internuclear Distance graph where both distances are stationary. This distance is found to be stationary when both AB and BC are set to be 0.90755.

[[File:InternucleardistanceTSsp2416.PNG|thumb|centre|Internuclear Distance vs Time plot for H + H2 Transition state]]

===Dynamic and mep Calculation types===

The following results were obtained when the AB distance was changed to 0.90855 and the BC distance was maintained at 0.09755 (transition state position)

[[File:Trajectory_plot_dynamics_sp2416.PNG|thumb|centre|Trajectory plot using Dynamics calculation type]]

[[File:Trajectory_plot_mep_sp2416.PNG|thumb|centre|Trajectory plot using mep calculation type]]

[[File:Distance_time_dynamics_sp2416.PNG|thumb|centre|Internuclear Distance vs Time graph using Dynamics calculation type]]

[[File:Distance_time_mep_sp2416.PNG|thumb|centre|Internuclear Distance vs Time graph using mep calculation type]]

===Reactive and Unreactive Trajectories===

{| class="wikitable" border="1"
|+ Effect of different momenta on reactivity
! p1 !! p2 !! Total Energy!!Type of Trajectory!!Contour plot!!Description
|-
| -1.25 || -2.5 || -99.199 || Reactive || [[File:Contour1_sp2416.PNG|320px]] || cell ||
|-
| -1.5 || -2.0 || -100.456 || Uneactive || [[File:Contour2_sp2416.PNG|320px]] || cell ||
|-
| -1.5 || -2.5 || -98.956 || Reactive || [[File:Contour3_sp2416.PNG|320px]] || cell ||
|-
| -2.5 || -5.0 || -84.956 || Uneactive || [[File:Contour4_sp2416.PNG|320px]] || cell ||
|-
| -2.5 || -5.2 || -83.416 || Reactive || [[File:Contour5_sp2416.PNG|320px]] || cell ||
|}

===Transition State Theory===

Complete

==F - H - H ==

=== PES Inspection ===

The equilibrium reaction F + H2 ⇌ H + HF is exothermic when it goes forward releasing energy, whilst the backward reaction is endothermic, taking energy in. <ref name="[1]" /> The H-H bond is -432 kJ/mol and the H-F bond is -565 kj/mol <ref name="[2]" />. This means that more energy is needed to break the H-F than the energy gained by forming the H-H bond, and hence the forward reaction is exothermic (and the backward endothermic).

 Locating the Transition Stateː 

Applying the following settingsː

Atom A: F

Atom B: H

Atom C: H

AB distance: 1.81 Å

BC distance: 0.7455 Å

Both momenta are set to 0.

These settings were applied using the Dynamics Calculation type and visualising the Internuclear Distance vs Time plot. Trial and error values were used until all the distances (A-B, B-C and A-C) produce straight lines, as shown in the figure below.

[[File:Distance_time_1_sp2416.PNG|thumb|centre|Internuclear Distance vs Time graph using Dynamics calculation type for F-H-H]]

 Reporting the Activation Energyː 

To find the activation energy, the type of calculation used is MEP and the AB distance is displaced slightly (form 1.81 is changed to 1.83) in order to force the reaction to go to either direction of the equilibrium - right hand side or left hand side.

The forward reaction in the equilibrium F + H2 ⇌ H + HF is exothermic. Hammond's postulate states that the transition state resembles more the reactants than the products in an exothermic reaction. Hence, the activation energy is obtained when the A-B distance is displaced in this calculation.

Energy of the transition state = -103.752 kJ/mol

Energy of products = -133.466 kJ/mol

Activation energy of the reaction = 29.714 kJ/mol

[[File:Activationenergysp2416.PNG|thumb|centre|Finding the activation energy]]

=== Reaction Dynamics ===

Reactive Trajectory 

Atom A : F

Atom B : H

Atom C : H

AB distance = 1.91

BC distance = 0.7455

AB momentum = -1.5

BC momentum = 1.0

[[File:Reactivetrajsp2416.png|thumb|centre|Reactive Trajectory]]

[[File:Momentasp2416.png|thumb|centre|Internuclear Momenta vs Time]]

An increased and vigorous oscillation of the resulting molecule can be seen from the Momentum vs Time plot. This means that the energy released during this exothermic reaction is converted into vibrational energy.

[[File:Energyplotsp2416.png|thumb|centre|Energy vs Time]]

The Energy vs Time plot shows an increased oscillation in the kinetic energy of the molecule.

Investigating the effect of changing the momentum of AB

Atom A : F

Atom B : H

Atom C : H

AB distance = 1.91

BC distance = 0.7455

AB momentum = -3 to 3

BC momentum = -0.5

== References ==

<references>
<ref name="[1]">J.C. Polanyi, D.C. Tardy, 1969, J. Chem. Phys., Vol.51 "Energy Distribution in the Exothermic Reaction F + H2 , and the Endothermic Reaction HF + H", p.255-321.</ref>

<ref name="[2]">http://www.wiredchemist.com/chemistry/data/bond_energies_lengths.html (Assessed on 15/05/2018 17ː10).</ref>
</references>

MRD:sp2416

2018-05-15T17:26:32Z

Sp2416: /* Reaction Dynamics */

==H + H2==

===Transition State ===

The transition state is defined a the maximum on the minimum energy path linking reactants and products. Both minima and transition states are saddle points on the potential energy surface. On the potential energy surface diagram of H + H2 analysed, the gradient of both the transition state and minimum are found to be zero (∂V(ri)/∂ri=0). Minima and transition structures can be distinguished by taking the second derivative of the gradient. For transition state this will be negative and positive, while for minima the answer to this will be positive.

===Locating the Transition State===

[[File:Internucleardistancesp2416.PNG|thumb|centre|Internuclear Distance vs Time plot for H + H2]]

On the first graph the Transition state is where the A-B and B-C lines cross.

To locate the Transition state the momenta are changed to 0, (as a transition state is a saddle point) and then the distances AB and BC are adjusted so as to get an Internuclear Distance graph where both distances are stationary. This distance is found to be stationary when both AB and BC are set to be 0.90755.

[[File:InternucleardistanceTSsp2416.PNG|thumb|centre|Internuclear Distance vs Time plot for H + H2 Transition state]]

===Dynamic and mep Calculation types===

The following results were obtained when the AB distance was changed to 0.90855 and the BC distance was maintained at 0.09755 (transition state position)

[[File:Trajectory_plot_dynamics_sp2416.PNG|thumb|centre|Trajectory plot using Dynamics calculation type]]

[[File:Trajectory_plot_mep_sp2416.PNG|thumb|centre|Trajectory plot using mep calculation type]]

[[File:Distance_time_dynamics_sp2416.PNG|thumb|centre|Internuclear Distance vs Time graph using Dynamics calculation type]]

[[File:Distance_time_mep_sp2416.PNG|thumb|centre|Internuclear Distance vs Time graph using mep calculation type]]

===Reactive and Unreactive Trajectories===

{| class="wikitable" border="1"
|+ Effect of different momenta on reactivity
! p1 !! p2 !! Total Energy!!Type of Trajectory!!Contour plot!!Description
|-
| -1.25 || -2.5 || -99.199 || Reactive || [[File:Contour1_sp2416.PNG|320px]] || cell ||
|-
| -1.5 || -2.0 || -100.456 || Uneactive || [[File:Contour2_sp2416.PNG|320px]] || cell ||
|-
| -1.5 || -2.5 || -98.956 || Reactive || [[File:Contour3_sp2416.PNG|320px]] || cell ||
|-
| -2.5 || -5.0 || -84.956 || Uneactive || [[File:Contour4_sp2416.PNG|320px]] || cell ||
|-
| -2.5 || -5.2 || -83.416 || Reactive || [[File:Contour5_sp2416.PNG|320px]] || cell ||
|}

===Transition State Theory===

Complete

==F - H - H ==

=== PES Inspection ===

The equilibrium reaction F + H2 ⇌ H + HF is exothermic when it goes forward releasing energy, whilst the backward reaction is endothermic, taking energy in. <ref name="[1]" /> The H-H bond is -432 kJ/mol and the H-F bond is -565 kj/mol <ref name="[2]" />. This means that more energy is needed to break the H-F than the energy gained by forming the H-H bond, and hence the forward reaction is exothermic (and the backward endothermic).

 Locating the Transition Stateː 

Applying the following settingsː

Atom A: F

Atom B: H

Atom C: H

AB distance: 1.81 Å

BC distance: 0.7455 Å

Both momenta are set to 0.

These settings were applied using the Dynamics Calculation type and visualising the Internuclear Distance vs Time plot. Trial and error values were used until all the distances (A-B, B-C and A-C) produce straight lines, as shown in the figure below.

[[File:Distance_time_1_sp2416.PNG|thumb|centre|Internuclear Distance vs Time graph using Dynamics calculation type for F-H-H]]

 Reporting the Activation Energyː 

To find the activation energy, the type of calculation used is MEP and the AB distance is displaced slightly (form 1.81 is changed to 1.83) in order to force the reaction to go to either direction of the equilibrium - right hand side or left hand side.

The forward reaction in the equilibrium F + H2 ⇌ H + HF is exothermic. Hammond's postulate states that the transition state resembles more the reactants than the products in an exothermic reaction. Hence, the activation energy is obtained when the A-B distance is displaced in this calculation.

Energy of the transition state = -103.752 kJ/mol

Energy of products = -133.466 kJ/mol

Activation energy of the reaction = 29.714 kJ/mol

[[File:Activationenergysp2416.PNG|thumb|centre|Finding the activation energy]]

=== Reaction Dynamics ===

Reactive Trajectory 

Atom A : F

Atom B : H

Atom C : H

AB distance = 1.91

BC distance = 0.7455

AB momentum = -1.5

BC momentum = 1.0

[[File:Reactivetrajsp2416.png|thumb|centre|Reactive Trajectory]]

[[File:Momentasp2416.png|thumb|centre|Internuclear Momenta vs Time]]

An increased and vigorous oscillation of the resulting molecule can be seen from the Momentum vs Time plot. This means that the energy released during this exothermic reaction is converted into vibrational energy.

[[File:Energyplotsp2416.png|thumb|centre|Energy vs Time]]

The Energy vs Time plot shows an increased oscillation in the kinetic energy of the molecule.

== References ==

<references>
<ref name="[1]">J.C. Polanyi, D.C. Tardy, 1969, J. Chem. Phys., Vol.51 "Energy Distribution in the Exothermic Reaction F + H2 , and the Endothermic Reaction HF + H", p.255-321.</ref>

<ref name="[2]">http://www.wiredchemist.com/chemistry/data/bond_energies_lengths.html (Assessed on 15/05/2018 17ː10).</ref>
</references>

MRD:sp2416

2018-05-15T17:26:08Z

Sp2416: /* Reaction Dynamics */

==H + H2==

===Transition State ===

The transition state is defined a the maximum on the minimum energy path linking reactants and products. Both minima and transition states are saddle points on the potential energy surface. On the potential energy surface diagram of H + H2 analysed, the gradient of both the transition state and minimum are found to be zero (∂V(ri)/∂ri=0). Minima and transition structures can be distinguished by taking the second derivative of the gradient. For transition state this will be negative and positive, while for minima the answer to this will be positive.

===Locating the Transition State===

[[File:Internucleardistancesp2416.PNG|thumb|centre|Internuclear Distance vs Time plot for H + H2]]

On the first graph the Transition state is where the A-B and B-C lines cross.

To locate the Transition state the momenta are changed to 0, (as a transition state is a saddle point) and then the distances AB and BC are adjusted so as to get an Internuclear Distance graph where both distances are stationary. This distance is found to be stationary when both AB and BC are set to be 0.90755.

[[File:InternucleardistanceTSsp2416.PNG|thumb|centre|Internuclear Distance vs Time plot for H + H2 Transition state]]

===Dynamic and mep Calculation types===

The following results were obtained when the AB distance was changed to 0.90855 and the BC distance was maintained at 0.09755 (transition state position)

[[File:Trajectory_plot_dynamics_sp2416.PNG|thumb|centre|Trajectory plot using Dynamics calculation type]]

[[File:Trajectory_plot_mep_sp2416.PNG|thumb|centre|Trajectory plot using mep calculation type]]

[[File:Distance_time_dynamics_sp2416.PNG|thumb|centre|Internuclear Distance vs Time graph using Dynamics calculation type]]

[[File:Distance_time_mep_sp2416.PNG|thumb|centre|Internuclear Distance vs Time graph using mep calculation type]]

===Reactive and Unreactive Trajectories===

{| class="wikitable" border="1"
|+ Effect of different momenta on reactivity
! p1 !! p2 !! Total Energy!!Type of Trajectory!!Contour plot!!Description
|-
| -1.25 || -2.5 || -99.199 || Reactive || [[File:Contour1_sp2416.PNG|320px]] || cell ||
|-
| -1.5 || -2.0 || -100.456 || Uneactive || [[File:Contour2_sp2416.PNG|320px]] || cell ||
|-
| -1.5 || -2.5 || -98.956 || Reactive || [[File:Contour3_sp2416.PNG|320px]] || cell ||
|-
| -2.5 || -5.0 || -84.956 || Uneactive || [[File:Contour4_sp2416.PNG|320px]] || cell ||
|-
| -2.5 || -5.2 || -83.416 || Reactive || [[File:Contour5_sp2416.PNG|320px]] || cell ||
|}

===Transition State Theory===

Complete

==F - H - H ==

=== PES Inspection ===

The equilibrium reaction F + H2 ⇌ H + HF is exothermic when it goes forward releasing energy, whilst the backward reaction is endothermic, taking energy in. <ref name="[1]" /> The H-H bond is -432 kJ/mol and the H-F bond is -565 kj/mol <ref name="[2]" />. This means that more energy is needed to break the H-F than the energy gained by forming the H-H bond, and hence the forward reaction is exothermic (and the backward endothermic).

 Locating the Transition Stateː 

Applying the following settingsː

Atom A: F

Atom B: H

Atom C: H

AB distance: 1.81 Å

BC distance: 0.7455 Å

Both momenta are set to 0.

These settings were applied using the Dynamics Calculation type and visualising the Internuclear Distance vs Time plot. Trial and error values were used until all the distances (A-B, B-C and A-C) produce straight lines, as shown in the figure below.

[[File:Distance_time_1_sp2416.PNG|thumb|centre|Internuclear Distance vs Time graph using Dynamics calculation type for F-H-H]]

 Reporting the Activation Energyː 

To find the activation energy, the type of calculation used is MEP and the AB distance is displaced slightly (form 1.81 is changed to 1.83) in order to force the reaction to go to either direction of the equilibrium - right hand side or left hand side.

The forward reaction in the equilibrium F + H2 ⇌ H + HF is exothermic. Hammond's postulate states that the transition state resembles more the reactants than the products in an exothermic reaction. Hence, the activation energy is obtained when the A-B distance is displaced in this calculation.

Energy of the transition state = -103.752 kJ/mol

Energy of products = -133.466 kJ/mol

Activation energy of the reaction = 29.714 kJ/mol

[[File:Activationenergysp2416.PNG|thumb|centre|Finding the activation energy]]

=== Reaction Dynamics ===

Reactive Trajectory 

Atom A : F

Atom B : H

Atom C : H

AB distance = 1.91

BC distance = 0.7455

AB momentum = -1.5

BC momentum = 1.0

An increased and vigorous oscillation of the resulting molecule can be seen from the Momentum vs Time plot. This means that the energy released during this exothermic reaction is converted into vibrational energy.

The Energy vs Time plot shows an increased oscillation in the kinetic energy of the molecule.

[[File:Reactivetrajsp2416.png|thumb|centre|Reactive Trajectory]]

[[File:Momentasp2416.png|thumb|centre|Internuclear Momenta vs Time]]

[[File:Energyplotsp2416.png|thumb|centre|Energy vs Time]]

== References ==

<references>
<ref name="[1]">J.C. Polanyi, D.C. Tardy, 1969, J. Chem. Phys., Vol.51 "Energy Distribution in the Exothermic Reaction F + H2 , and the Endothermic Reaction HF + H", p.255-321.</ref>

<ref name="[2]">http://www.wiredchemist.com/chemistry/data/bond_energies_lengths.html (Assessed on 15/05/2018 17ː10).</ref>
</references>

MRD:sp2416

2018-05-15T17:22:32Z

Sp2416: /* Reaction Dynamics */

==H + H2==

===Transition State ===

The transition state is defined a the maximum on the minimum energy path linking reactants and products. Both minima and transition states are saddle points on the potential energy surface. On the potential energy surface diagram of H + H2 analysed, the gradient of both the transition state and minimum are found to be zero (∂V(ri)/∂ri=0). Minima and transition structures can be distinguished by taking the second derivative of the gradient. For transition state this will be negative and positive, while for minima the answer to this will be positive.

===Locating the Transition State===

[[File:Internucleardistancesp2416.PNG|thumb|centre|Internuclear Distance vs Time plot for H + H2]]

On the first graph the Transition state is where the A-B and B-C lines cross.

To locate the Transition state the momenta are changed to 0, (as a transition state is a saddle point) and then the distances AB and BC are adjusted so as to get an Internuclear Distance graph where both distances are stationary. This distance is found to be stationary when both AB and BC are set to be 0.90755.

[[File:InternucleardistanceTSsp2416.PNG|thumb|centre|Internuclear Distance vs Time plot for H + H2 Transition state]]

===Dynamic and mep Calculation types===

The following results were obtained when the AB distance was changed to 0.90855 and the BC distance was maintained at 0.09755 (transition state position)

[[File:Trajectory_plot_dynamics_sp2416.PNG|thumb|centre|Trajectory plot using Dynamics calculation type]]

[[File:Trajectory_plot_mep_sp2416.PNG|thumb|centre|Trajectory plot using mep calculation type]]

[[File:Distance_time_dynamics_sp2416.PNG|thumb|centre|Internuclear Distance vs Time graph using Dynamics calculation type]]

[[File:Distance_time_mep_sp2416.PNG|thumb|centre|Internuclear Distance vs Time graph using mep calculation type]]

===Reactive and Unreactive Trajectories===

{| class="wikitable" border="1"
|+ Effect of different momenta on reactivity
! p1 !! p2 !! Total Energy!!Type of Trajectory!!Contour plot!!Description
|-
| -1.25 || -2.5 || -99.199 || Reactive || [[File:Contour1_sp2416.PNG|320px]] || cell ||
|-
| -1.5 || -2.0 || -100.456 || Uneactive || [[File:Contour2_sp2416.PNG|320px]] || cell ||
|-
| -1.5 || -2.5 || -98.956 || Reactive || [[File:Contour3_sp2416.PNG|320px]] || cell ||
|-
| -2.5 || -5.0 || -84.956 || Uneactive || [[File:Contour4_sp2416.PNG|320px]] || cell ||
|-
| -2.5 || -5.2 || -83.416 || Reactive || [[File:Contour5_sp2416.PNG|320px]] || cell ||
|}

===Transition State Theory===

Complete

==F - H - H ==

=== PES Inspection ===

The equilibrium reaction F + H2 ⇌ H + HF is exothermic when it goes forward releasing energy, whilst the backward reaction is endothermic, taking energy in. <ref name="[1]" /> The H-H bond is -432 kJ/mol and the H-F bond is -565 kj/mol <ref name="[2]" />. This means that more energy is needed to break the H-F than the energy gained by forming the H-H bond, and hence the forward reaction is exothermic (and the backward endothermic).

 Locating the Transition Stateː 

Applying the following settingsː

Atom A: F

Atom B: H

Atom C: H

AB distance: 1.81 Å

BC distance: 0.7455 Å

Both momenta are set to 0.

These settings were applied using the Dynamics Calculation type and visualising the Internuclear Distance vs Time plot. Trial and error values were used until all the distances (A-B, B-C and A-C) produce straight lines, as shown in the figure below.

[[File:Distance_time_1_sp2416.PNG|thumb|centre|Internuclear Distance vs Time graph using Dynamics calculation type for F-H-H]]

 Reporting the Activation Energyː 

To find the activation energy, the type of calculation used is MEP and the AB distance is displaced slightly (form 1.81 is changed to 1.83) in order to force the reaction to go to either direction of the equilibrium - right hand side or left hand side.

The forward reaction in the equilibrium F + H2 ⇌ H + HF is exothermic. Hammond's postulate states that the transition state resembles more the reactants than the products in an exothermic reaction. Hence, the activation energy is obtained when the A-B distance is displaced in this calculation.

Energy of the transition state = -103.752 kJ/mol

Energy of products = -133.466 kJ/mol

Activation energy of the reaction = 29.714 kJ/mol

[[File:Activationenergysp2416.PNG|thumb|centre|Finding the activation energy]]

=== Reaction Dynamics ===

Reactive Trajectory 

Atom A : F

Atom B : H

Atom C : H

AB distance = 1.91

BC distance = 0.7455

AB momentum = -1.5

BC momentum = 1.0

[[File:Reactivetrajsp2416.png|thumb|centre|Reactive Trajectory]]

[[File:Momentasp2416.png|thumb|centre|Internuclear Momenta vs Time]]

[[File:Energyplotsp2416.png|thumb|centre|Energy vs Time]]

== References ==

<references>
<ref name="[1]">J.C. Polanyi, D.C. Tardy, 1969, J. Chem. Phys., Vol.51 "Energy Distribution in the Exothermic Reaction F + H2 , and the Endothermic Reaction HF + H", p.255-321.</ref>

<ref name="[2]">http://www.wiredchemist.com/chemistry/data/bond_energies_lengths.html (Assessed on 15/05/2018 17ː10).</ref>
</references>

File:Energyplotsp2416.png

2018-05-15T17:22:08Z

Sp2416:

MRD:sp2416

2018-05-15T17:20:19Z

Sp2416: /* Reaction Dynamics */

==H + H2==

===Transition State ===

The transition state is defined a the maximum on the minimum energy path linking reactants and products. Both minima and transition states are saddle points on the potential energy surface. On the potential energy surface diagram of H + H2 analysed, the gradient of both the transition state and minimum are found to be zero (∂V(ri)/∂ri=0). Minima and transition structures can be distinguished by taking the second derivative of the gradient. For transition state this will be negative and positive, while for minima the answer to this will be positive.

===Locating the Transition State===

[[File:Internucleardistancesp2416.PNG|thumb|centre|Internuclear Distance vs Time plot for H + H2]]

On the first graph the Transition state is where the A-B and B-C lines cross.

To locate the Transition state the momenta are changed to 0, (as a transition state is a saddle point) and then the distances AB and BC are adjusted so as to get an Internuclear Distance graph where both distances are stationary. This distance is found to be stationary when both AB and BC are set to be 0.90755.

[[File:InternucleardistanceTSsp2416.PNG|thumb|centre|Internuclear Distance vs Time plot for H + H2 Transition state]]

===Dynamic and mep Calculation types===

The following results were obtained when the AB distance was changed to 0.90855 and the BC distance was maintained at 0.09755 (transition state position)

[[File:Trajectory_plot_dynamics_sp2416.PNG|thumb|centre|Trajectory plot using Dynamics calculation type]]

[[File:Trajectory_plot_mep_sp2416.PNG|thumb|centre|Trajectory plot using mep calculation type]]

[[File:Distance_time_dynamics_sp2416.PNG|thumb|centre|Internuclear Distance vs Time graph using Dynamics calculation type]]

[[File:Distance_time_mep_sp2416.PNG|thumb|centre|Internuclear Distance vs Time graph using mep calculation type]]

===Reactive and Unreactive Trajectories===

{| class="wikitable" border="1"
|+ Effect of different momenta on reactivity
! p1 !! p2 !! Total Energy!!Type of Trajectory!!Contour plot!!Description
|-
| -1.25 || -2.5 || -99.199 || Reactive || [[File:Contour1_sp2416.PNG|320px]] || cell ||
|-
| -1.5 || -2.0 || -100.456 || Uneactive || [[File:Contour2_sp2416.PNG|320px]] || cell ||
|-
| -1.5 || -2.5 || -98.956 || Reactive || [[File:Contour3_sp2416.PNG|320px]] || cell ||
|-
| -2.5 || -5.0 || -84.956 || Uneactive || [[File:Contour4_sp2416.PNG|320px]] || cell ||
|-
| -2.5 || -5.2 || -83.416 || Reactive || [[File:Contour5_sp2416.PNG|320px]] || cell ||
|}

===Transition State Theory===

Complete

==F - H - H ==

=== PES Inspection ===

The equilibrium reaction F + H2 ⇌ H + HF is exothermic when it goes forward releasing energy, whilst the backward reaction is endothermic, taking energy in. <ref name="[1]" /> The H-H bond is -432 kJ/mol and the H-F bond is -565 kj/mol <ref name="[2]" />. This means that more energy is needed to break the H-F than the energy gained by forming the H-H bond, and hence the forward reaction is exothermic (and the backward endothermic).

 Locating the Transition Stateː 

Applying the following settingsː

Atom A: F

Atom B: H

Atom C: H

AB distance: 1.81 Å

BC distance: 0.7455 Å

Both momenta are set to 0.

These settings were applied using the Dynamics Calculation type and visualising the Internuclear Distance vs Time plot. Trial and error values were used until all the distances (A-B, B-C and A-C) produce straight lines, as shown in the figure below.

[[File:Distance_time_1_sp2416.PNG|thumb|centre|Internuclear Distance vs Time graph using Dynamics calculation type for F-H-H]]

 Reporting the Activation Energyː 

To find the activation energy, the type of calculation used is MEP and the AB distance is displaced slightly (form 1.81 is changed to 1.83) in order to force the reaction to go to either direction of the equilibrium - right hand side or left hand side.

The forward reaction in the equilibrium F + H2 ⇌ H + HF is exothermic. Hammond's postulate states that the transition state resembles more the reactants than the products in an exothermic reaction. Hence, the activation energy is obtained when the A-B distance is displaced in this calculation.

Energy of the transition state = -103.752 kJ/mol

Energy of products = -133.466 kJ/mol

Activation energy of the reaction = 29.714 kJ/mol

[[File:Activationenergysp2416.PNG|thumb|centre|Finding the activation energy]]

=== Reaction Dynamics ===

Reactive Trajectory 

Atom A : F

Atom B : H

Atom C : H

AB distance = 1.91

BC distance = 0.7455

AB momentum = -1.5

BC momentum = 1.0

[[File:Reactivetrajsp2416.png|thumb|centre|Reactive Trajectory]]

[[File:Momentasp2416.png|thumb|centre|Internuclear Momenta vs Time]]

== References ==

<references>
<ref name="[1]">J.C. Polanyi, D.C. Tardy, 1969, J. Chem. Phys., Vol.51 "Energy Distribution in the Exothermic Reaction F + H2 , and the Endothermic Reaction HF + H", p.255-321.</ref>

<ref name="[2]">http://www.wiredchemist.com/chemistry/data/bond_energies_lengths.html (Assessed on 15/05/2018 17ː10).</ref>
</references>

MRD:sp2416

2018-05-15T17:20:01Z

Sp2416: /* Reaction Dynamics */

==H + H2==

===Transition State ===

The transition state is defined a the maximum on the minimum energy path linking reactants and products. Both minima and transition states are saddle points on the potential energy surface. On the potential energy surface diagram of H + H2 analysed, the gradient of both the transition state and minimum are found to be zero (∂V(ri)/∂ri=0). Minima and transition structures can be distinguished by taking the second derivative of the gradient. For transition state this will be negative and positive, while for minima the answer to this will be positive.

===Locating the Transition State===

[[File:Internucleardistancesp2416.PNG|thumb|centre|Internuclear Distance vs Time plot for H + H2]]

On the first graph the Transition state is where the A-B and B-C lines cross.

To locate the Transition state the momenta are changed to 0, (as a transition state is a saddle point) and then the distances AB and BC are adjusted so as to get an Internuclear Distance graph where both distances are stationary. This distance is found to be stationary when both AB and BC are set to be 0.90755.

[[File:InternucleardistanceTSsp2416.PNG|thumb|centre|Internuclear Distance vs Time plot for H + H2 Transition state]]

===Dynamic and mep Calculation types===

The following results were obtained when the AB distance was changed to 0.90855 and the BC distance was maintained at 0.09755 (transition state position)

[[File:Trajectory_plot_dynamics_sp2416.PNG|thumb|centre|Trajectory plot using Dynamics calculation type]]

[[File:Trajectory_plot_mep_sp2416.PNG|thumb|centre|Trajectory plot using mep calculation type]]

[[File:Distance_time_dynamics_sp2416.PNG|thumb|centre|Internuclear Distance vs Time graph using Dynamics calculation type]]

[[File:Distance_time_mep_sp2416.PNG|thumb|centre|Internuclear Distance vs Time graph using mep calculation type]]

===Reactive and Unreactive Trajectories===

{| class="wikitable" border="1"
|+ Effect of different momenta on reactivity
! p1 !! p2 !! Total Energy!!Type of Trajectory!!Contour plot!!Description
|-
| -1.25 || -2.5 || -99.199 || Reactive || [[File:Contour1_sp2416.PNG|320px]] || cell ||
|-
| -1.5 || -2.0 || -100.456 || Uneactive || [[File:Contour2_sp2416.PNG|320px]] || cell ||
|-
| -1.5 || -2.5 || -98.956 || Reactive || [[File:Contour3_sp2416.PNG|320px]] || cell ||
|-
| -2.5 || -5.0 || -84.956 || Uneactive || [[File:Contour4_sp2416.PNG|320px]] || cell ||
|-
| -2.5 || -5.2 || -83.416 || Reactive || [[File:Contour5_sp2416.PNG|320px]] || cell ||
|}

===Transition State Theory===

Complete

==F - H - H ==

=== PES Inspection ===

The equilibrium reaction F + H2 ⇌ H + HF is exothermic when it goes forward releasing energy, whilst the backward reaction is endothermic, taking energy in. <ref name="[1]" /> The H-H bond is -432 kJ/mol and the H-F bond is -565 kj/mol <ref name="[2]" />. This means that more energy is needed to break the H-F than the energy gained by forming the H-H bond, and hence the forward reaction is exothermic (and the backward endothermic).

 Locating the Transition Stateː 

Applying the following settingsː

Atom A: F

Atom B: H

Atom C: H

AB distance: 1.81 Å

BC distance: 0.7455 Å

Both momenta are set to 0.

These settings were applied using the Dynamics Calculation type and visualising the Internuclear Distance vs Time plot. Trial and error values were used until all the distances (A-B, B-C and A-C) produce straight lines, as shown in the figure below.

[[File:Distance_time_1_sp2416.PNG|thumb|centre|Internuclear Distance vs Time graph using Dynamics calculation type for F-H-H]]

 Reporting the Activation Energyː 

To find the activation energy, the type of calculation used is MEP and the AB distance is displaced slightly (form 1.81 is changed to 1.83) in order to force the reaction to go to either direction of the equilibrium - right hand side or left hand side.

The forward reaction in the equilibrium F + H2 ⇌ H + HF is exothermic. Hammond's postulate states that the transition state resembles more the reactants than the products in an exothermic reaction. Hence, the activation energy is obtained when the A-B distance is displaced in this calculation.

Energy of the transition state = -103.752 kJ/mol

Energy of products = -133.466 kJ/mol

Activation energy of the reaction = 29.714 kJ/mol

[[File:Activationenergysp2416.PNG|thumb|centre|Finding the activation energy]]

=== Reaction Dynamics ===

Reactive Trajectory 

Atom A : F

Atom B : H

Atom C : H

AB distance = 1.91

BC distance = 0.7455

AB momentum = -1.5

BC momentum = 1.0

[[File:Reactivetrajsp2416.png|thumb|centre|Reactive Trajectory]]

[[File:Momentasp2416.png|thumb|centre|Reactive Trajectory]]

== References ==

<references>
<ref name="[1]">J.C. Polanyi, D.C. Tardy, 1969, J. Chem. Phys., Vol.51 "Energy Distribution in the Exothermic Reaction F + H2 , and the Endothermic Reaction HF + H", p.255-321.</ref>

<ref name="[2]">http://www.wiredchemist.com/chemistry/data/bond_energies_lengths.html (Assessed on 15/05/2018 17ː10).</ref>
</references>

File:Momentasp2416.png

2018-05-15T17:19:37Z

Sp2416:

MRD:sp2416

2018-05-15T17:13:42Z

Sp2416: /* Reaction Dynamics */

==H + H2==

===Transition State ===

The transition state is defined a the maximum on the minimum energy path linking reactants and products. Both minima and transition states are saddle points on the potential energy surface. On the potential energy surface diagram of H + H2 analysed, the gradient of both the transition state and minimum are found to be zero (∂V(ri)/∂ri=0). Minima and transition structures can be distinguished by taking the second derivative of the gradient. For transition state this will be negative and positive, while for minima the answer to this will be positive.

===Locating the Transition State===

[[File:Internucleardistancesp2416.PNG|thumb|centre|Internuclear Distance vs Time plot for H + H2]]

On the first graph the Transition state is where the A-B and B-C lines cross.

To locate the Transition state the momenta are changed to 0, (as a transition state is a saddle point) and then the distances AB and BC are adjusted so as to get an Internuclear Distance graph where both distances are stationary. This distance is found to be stationary when both AB and BC are set to be 0.90755.

[[File:InternucleardistanceTSsp2416.PNG|thumb|centre|Internuclear Distance vs Time plot for H + H2 Transition state]]

===Dynamic and mep Calculation types===

The following results were obtained when the AB distance was changed to 0.90855 and the BC distance was maintained at 0.09755 (transition state position)

[[File:Trajectory_plot_dynamics_sp2416.PNG|thumb|centre|Trajectory plot using Dynamics calculation type]]

[[File:Trajectory_plot_mep_sp2416.PNG|thumb|centre|Trajectory plot using mep calculation type]]

[[File:Distance_time_dynamics_sp2416.PNG|thumb|centre|Internuclear Distance vs Time graph using Dynamics calculation type]]

[[File:Distance_time_mep_sp2416.PNG|thumb|centre|Internuclear Distance vs Time graph using mep calculation type]]

===Reactive and Unreactive Trajectories===

{| class="wikitable" border="1"
|+ Effect of different momenta on reactivity
! p1 !! p2 !! Total Energy!!Type of Trajectory!!Contour plot!!Description
|-
| -1.25 || -2.5 || -99.199 || Reactive || [[File:Contour1_sp2416.PNG|320px]] || cell ||
|-
| -1.5 || -2.0 || -100.456 || Uneactive || [[File:Contour2_sp2416.PNG|320px]] || cell ||
|-
| -1.5 || -2.5 || -98.956 || Reactive || [[File:Contour3_sp2416.PNG|320px]] || cell ||
|-
| -2.5 || -5.0 || -84.956 || Uneactive || [[File:Contour4_sp2416.PNG|320px]] || cell ||
|-
| -2.5 || -5.2 || -83.416 || Reactive || [[File:Contour5_sp2416.PNG|320px]] || cell ||
|}

===Transition State Theory===

Complete

==F - H - H ==

=== PES Inspection ===

The equilibrium reaction F + H2 ⇌ H + HF is exothermic when it goes forward releasing energy, whilst the backward reaction is endothermic, taking energy in. <ref name="[1]" /> The H-H bond is -432 kJ/mol and the H-F bond is -565 kj/mol <ref name="[2]" />. This means that more energy is needed to break the H-F than the energy gained by forming the H-H bond, and hence the forward reaction is exothermic (and the backward endothermic).

 Locating the Transition Stateː 

Applying the following settingsː

Atom A: F

Atom B: H

Atom C: H

AB distance: 1.81 Å

BC distance: 0.7455 Å

Both momenta are set to 0.

These settings were applied using the Dynamics Calculation type and visualising the Internuclear Distance vs Time plot. Trial and error values were used until all the distances (A-B, B-C and A-C) produce straight lines, as shown in the figure below.

[[File:Distance_time_1_sp2416.PNG|thumb|centre|Internuclear Distance vs Time graph using Dynamics calculation type for F-H-H]]

 Reporting the Activation Energyː 

To find the activation energy, the type of calculation used is MEP and the AB distance is displaced slightly (form 1.81 is changed to 1.83) in order to force the reaction to go to either direction of the equilibrium - right hand side or left hand side.

The forward reaction in the equilibrium F + H2 ⇌ H + HF is exothermic. Hammond's postulate states that the transition state resembles more the reactants than the products in an exothermic reaction. Hence, the activation energy is obtained when the A-B distance is displaced in this calculation.

Energy of the transition state = -103.752 kJ/mol

Energy of products = -133.466 kJ/mol

Activation energy of the reaction = 29.714 kJ/mol

[[File:Activationenergysp2416.PNG|thumb|centre|Finding the activation energy]]

=== Reaction Dynamics ===

Reactive Trajectory 

Atom A : F

Atom B : H

Atom C : H

AB distance = 1.91

BC distance = 0.7455

AB momentum = -1.5

BC momentum = 1.0

[[File:Reactivetrajsp2416.png|thumb|centre|Reactive Trajectory]]

== References ==

<references>
<ref name="[1]">J.C. Polanyi, D.C. Tardy, 1969, J. Chem. Phys., Vol.51 "Energy Distribution in the Exothermic Reaction F + H2 , and the Endothermic Reaction HF + H", p.255-321.</ref>

<ref name="[2]">http://www.wiredchemist.com/chemistry/data/bond_energies_lengths.html (Assessed on 15/05/2018 17ː10).</ref>
</references>

MRD:sp2416

2018-05-15T17:12:54Z

Sp2416: /* PES Inspection */

==H + H2==

===Transition State ===

The transition state is defined a the maximum on the minimum energy path linking reactants and products. Both minima and transition states are saddle points on the potential energy surface. On the potential energy surface diagram of H + H2 analysed, the gradient of both the transition state and minimum are found to be zero (∂V(ri)/∂ri=0). Minima and transition structures can be distinguished by taking the second derivative of the gradient. For transition state this will be negative and positive, while for minima the answer to this will be positive.

===Locating the Transition State===

[[File:Internucleardistancesp2416.PNG|thumb|centre|Internuclear Distance vs Time plot for H + H2]]

On the first graph the Transition state is where the A-B and B-C lines cross.

To locate the Transition state the momenta are changed to 0, (as a transition state is a saddle point) and then the distances AB and BC are adjusted so as to get an Internuclear Distance graph where both distances are stationary. This distance is found to be stationary when both AB and BC are set to be 0.90755.

[[File:InternucleardistanceTSsp2416.PNG|thumb|centre|Internuclear Distance vs Time plot for H + H2 Transition state]]

===Dynamic and mep Calculation types===

The following results were obtained when the AB distance was changed to 0.90855 and the BC distance was maintained at 0.09755 (transition state position)

[[File:Trajectory_plot_dynamics_sp2416.PNG|thumb|centre|Trajectory plot using Dynamics calculation type]]

[[File:Trajectory_plot_mep_sp2416.PNG|thumb|centre|Trajectory plot using mep calculation type]]

[[File:Distance_time_dynamics_sp2416.PNG|thumb|centre|Internuclear Distance vs Time graph using Dynamics calculation type]]

[[File:Distance_time_mep_sp2416.PNG|thumb|centre|Internuclear Distance vs Time graph using mep calculation type]]

===Reactive and Unreactive Trajectories===

{| class="wikitable" border="1"
|+ Effect of different momenta on reactivity
! p1 !! p2 !! Total Energy!!Type of Trajectory!!Contour plot!!Description
|-
| -1.25 || -2.5 || -99.199 || Reactive || [[File:Contour1_sp2416.PNG|320px]] || cell ||
|-
| -1.5 || -2.0 || -100.456 || Uneactive || [[File:Contour2_sp2416.PNG|320px]] || cell ||
|-
| -1.5 || -2.5 || -98.956 || Reactive || [[File:Contour3_sp2416.PNG|320px]] || cell ||
|-
| -2.5 || -5.0 || -84.956 || Uneactive || [[File:Contour4_sp2416.PNG|320px]] || cell ||
|-
| -2.5 || -5.2 || -83.416 || Reactive || [[File:Contour5_sp2416.PNG|320px]] || cell ||
|}

===Transition State Theory===

Complete

==F - H - H ==

=== PES Inspection ===

The equilibrium reaction F + H2 ⇌ H + HF is exothermic when it goes forward releasing energy, whilst the backward reaction is endothermic, taking energy in. <ref name="[1]" /> The H-H bond is -432 kJ/mol and the H-F bond is -565 kj/mol <ref name="[2]" />. This means that more energy is needed to break the H-F than the energy gained by forming the H-H bond, and hence the forward reaction is exothermic (and the backward endothermic).

 Locating the Transition Stateː 

Applying the following settingsː

Atom A: F

Atom B: H

Atom C: H

AB distance: 1.81 Å

BC distance: 0.7455 Å

Both momenta are set to 0.

These settings were applied using the Dynamics Calculation type and visualising the Internuclear Distance vs Time plot. Trial and error values were used until all the distances (A-B, B-C and A-C) produce straight lines, as shown in the figure below.

[[File:Distance_time_1_sp2416.PNG|thumb|centre|Internuclear Distance vs Time graph using Dynamics calculation type for F-H-H]]

 Reporting the Activation Energyː 

To find the activation energy, the type of calculation used is MEP and the AB distance is displaced slightly (form 1.81 is changed to 1.83) in order to force the reaction to go to either direction of the equilibrium - right hand side or left hand side.

The forward reaction in the equilibrium F + H2 ⇌ H + HF is exothermic. Hammond's postulate states that the transition state resembles more the reactants than the products in an exothermic reaction. Hence, the activation energy is obtained when the A-B distance is displaced in this calculation.

Energy of the transition state = -103.752 kJ/mol

Energy of products = -133.466 kJ/mol

Activation energy of the reaction = 29.714 kJ/mol

[[File:Activationenergysp2416.PNG|thumb|centre|Finding the activation energy]]

=== Reaction Dynamics ===

Reactive Trajectory 

Atom A : F

Atom B : H

Atom C : H

AB distance = 1.91

BC distance = 0.7455

AB momentum = -1.5

BC momentum = 1.0

[[File:Reactivetrajsp2416.png]]

== References ==

<references>
<ref name="[1]">J.C. Polanyi, D.C. Tardy, 1969, J. Chem. Phys., Vol.51 "Energy Distribution in the Exothermic Reaction F + H2 , and the Endothermic Reaction HF + H", p.255-321.</ref>

<ref name="[2]">http://www.wiredchemist.com/chemistry/data/bond_energies_lengths.html (Assessed on 15/05/2018 17ː10).</ref>
</references>

MRD:sp2416

2018-05-15T17:12:01Z

Sp2416: /* PES Inspection */

==H + H2==

===Transition State ===

The transition state is defined a the maximum on the minimum energy path linking reactants and products. Both minima and transition states are saddle points on the potential energy surface. On the potential energy surface diagram of H + H2 analysed, the gradient of both the transition state and minimum are found to be zero (∂V(ri)/∂ri=0). Minima and transition structures can be distinguished by taking the second derivative of the gradient. For transition state this will be negative and positive, while for minima the answer to this will be positive.

===Locating the Transition State===

[[File:Internucleardistancesp2416.PNG|thumb|centre|Internuclear Distance vs Time plot for H + H2]]

On the first graph the Transition state is where the A-B and B-C lines cross.

To locate the Transition state the momenta are changed to 0, (as a transition state is a saddle point) and then the distances AB and BC are adjusted so as to get an Internuclear Distance graph where both distances are stationary. This distance is found to be stationary when both AB and BC are set to be 0.90755.

[[File:InternucleardistanceTSsp2416.PNG|thumb|centre|Internuclear Distance vs Time plot for H + H2 Transition state]]

===Dynamic and mep Calculation types===

The following results were obtained when the AB distance was changed to 0.90855 and the BC distance was maintained at 0.09755 (transition state position)

[[File:Trajectory_plot_dynamics_sp2416.PNG|thumb|centre|Trajectory plot using Dynamics calculation type]]

[[File:Trajectory_plot_mep_sp2416.PNG|thumb|centre|Trajectory plot using mep calculation type]]

[[File:Distance_time_dynamics_sp2416.PNG|thumb|centre|Internuclear Distance vs Time graph using Dynamics calculation type]]

[[File:Distance_time_mep_sp2416.PNG|thumb|centre|Internuclear Distance vs Time graph using mep calculation type]]

===Reactive and Unreactive Trajectories===

{| class="wikitable" border="1"
|+ Effect of different momenta on reactivity
! p1 !! p2 !! Total Energy!!Type of Trajectory!!Contour plot!!Description
|-
| -1.25 || -2.5 || -99.199 || Reactive || [[File:Contour1_sp2416.PNG|320px]] || cell ||
|-
| -1.5 || -2.0 || -100.456 || Uneactive || [[File:Contour2_sp2416.PNG|320px]] || cell ||
|-
| -1.5 || -2.5 || -98.956 || Reactive || [[File:Contour3_sp2416.PNG|320px]] || cell ||
|-
| -2.5 || -5.0 || -84.956 || Uneactive || [[File:Contour4_sp2416.PNG|320px]] || cell ||
|-
| -2.5 || -5.2 || -83.416 || Reactive || [[File:Contour5_sp2416.PNG|320px]] || cell ||
|}

===Transition State Theory===

Complete

==F - H - H ==

=== PES Inspection ===

The equilibrium reaction F + H2 ⇌ H + HF is exothermic when it goes forward releasing energy, whilst the backward reaction is endothermic, taking energy in. <ref name="[1]" /> The H-H bond is -432 kJ/mol and the H-F bond is -565 kj/mol <ref name="[2]" />. This means that more energy is needed to break the H-F than the energy gained by forming the H-H bond, and hence the forward reaction is exothermic (and the backward endothermic).

 Locating the Transition Stateː 

Applying the following settingsː

Atom A: F

Atom B: H

Atom C: H

AB distance: 1.81 Å

BC distance: 0.7455 Å

Both momenta are set to 0.

These settings were applied using the Dynamics Calculation type and visualising the Internuclear Distance vs Time plot. Trial and error values were used until all the distances (A-B, B-C and A-C) produce straight lines, as shown in the figure below.

[[File:Distance_time_1_sp2416.PNG|thumb|centre|Internuclear Distance vs Time graph using Dynamics calculation type for F-H-H]]

 Reporting the Activation Energyː 

To find the activation energy, the type of calculation used is MEP and the AB distance is displaced slightly (form 1.81 is changed to 1.83) in order to force the reaction to go to either direction of the equilibrium - right hand side or left hand side.

The forward reaction in the equilibrium F + H2 ⇌ H + HF is exothermic. Hammond's postulate states that the transition state resembles more the reactants than the products in an exothermic reaction. Hence, the activation energy is obtained when the A-B distance is displaced in this calculation.

Energy of the transition state = -103.752 kJ/mol

Energy of products = -133.466 kJ/mol

Activation energy of the reaction = 29.714 kJ/mol

[[File:Activationenergysp2416.PNG|thumb|centre|Reactive Trajectory]]

=== Reaction Dynamics ===

Reactive Trajectory 

Atom A : F

Atom B : H

Atom C : H

AB distance = 1.91

BC distance = 0.7455

AB momentum = -1.5

BC momentum = 1.0

[[File:Reactivetrajsp2416.png]]

== References ==

<references>
<ref name="[1]">J.C. Polanyi, D.C. Tardy, 1969, J. Chem. Phys., Vol.51 "Energy Distribution in the Exothermic Reaction F + H2 , and the Endothermic Reaction HF + H", p.255-321.</ref>

<ref name="[2]">http://www.wiredchemist.com/chemistry/data/bond_energies_lengths.html (Assessed on 15/05/2018 17ː10).</ref>
</references>

MRD:sp2416

2018-05-15T17:11:21Z

Sp2416: /* Reaction Dynamics */

==H + H2==

===Transition State ===

The transition state is defined a the maximum on the minimum energy path linking reactants and products. Both minima and transition states are saddle points on the potential energy surface. On the potential energy surface diagram of H + H2 analysed, the gradient of both the transition state and minimum are found to be zero (∂V(ri)/∂ri=0). Minima and transition structures can be distinguished by taking the second derivative of the gradient. For transition state this will be negative and positive, while for minima the answer to this will be positive.

===Locating the Transition State===

[[File:Internucleardistancesp2416.PNG|thumb|centre|Internuclear Distance vs Time plot for H + H2]]

On the first graph the Transition state is where the A-B and B-C lines cross.

To locate the Transition state the momenta are changed to 0, (as a transition state is a saddle point) and then the distances AB and BC are adjusted so as to get an Internuclear Distance graph where both distances are stationary. This distance is found to be stationary when both AB and BC are set to be 0.90755.

[[File:InternucleardistanceTSsp2416.PNG|thumb|centre|Internuclear Distance vs Time plot for H + H2 Transition state]]

===Dynamic and mep Calculation types===

The following results were obtained when the AB distance was changed to 0.90855 and the BC distance was maintained at 0.09755 (transition state position)

[[File:Trajectory_plot_dynamics_sp2416.PNG|thumb|centre|Trajectory plot using Dynamics calculation type]]

[[File:Trajectory_plot_mep_sp2416.PNG|thumb|centre|Trajectory plot using mep calculation type]]

[[File:Distance_time_dynamics_sp2416.PNG|thumb|centre|Internuclear Distance vs Time graph using Dynamics calculation type]]

[[File:Distance_time_mep_sp2416.PNG|thumb|centre|Internuclear Distance vs Time graph using mep calculation type]]

===Reactive and Unreactive Trajectories===

{| class="wikitable" border="1"
|+ Effect of different momenta on reactivity
! p1 !! p2 !! Total Energy!!Type of Trajectory!!Contour plot!!Description
|-
| -1.25 || -2.5 || -99.199 || Reactive || [[File:Contour1_sp2416.PNG|320px]] || cell ||
|-
| -1.5 || -2.0 || -100.456 || Uneactive || [[File:Contour2_sp2416.PNG|320px]] || cell ||
|-
| -1.5 || -2.5 || -98.956 || Reactive || [[File:Contour3_sp2416.PNG|320px]] || cell ||
|-
| -2.5 || -5.0 || -84.956 || Uneactive || [[File:Contour4_sp2416.PNG|320px]] || cell ||
|-
| -2.5 || -5.2 || -83.416 || Reactive || [[File:Contour5_sp2416.PNG|320px]] || cell ||
|}

===Transition State Theory===

Complete

==F - H - H ==

=== PES Inspection ===

The equilibrium reaction F + H2 ⇌ H + HF is exothermic when it goes forward releasing energy, whilst the backward reaction is endothermic, taking energy in. <ref name="[1]" /> The H-H bond is -432 kJ/mol and the H-F bond is -565 kj/mol <ref name="[2]" />. This means that more energy is needed to break the H-F than the energy gained by forming the H-H bond, and hence the forward reaction is exothermic (and the backward endothermic).

 Locating the Transition Stateː 

Applying the following settingsː

Atom A: F

Atom B: H

Atom C: H

AB distance: 1.81 Å

BC distance: 0.7455 Å

Both momenta are set to 0.

These settings were applied using the Dynamics Calculation type and visualising the Internuclear Distance vs Time plot. Trial and error values were used until all the distances (A-B, B-C and A-C) produce straight lines, as shown in the figure below.

[[File:Distance_time_1_sp2416.PNG|thumb|centre|Internuclear Distance vs Time graph using Dynamics calculation type for F-H-H]]

 Reporting the Activation Energyː 

To find the activation energy, the type of calculation used is MEP and the AB distance is displaced slightly (form 1.81 is changed to 1.83) in order to force the reaction to go to either direction of the equilibrium - right hand side or left hand side.

The forward reaction in the equilibrium F + H2 ⇌ H + HF is exothermic. Hammond's postulate states that the transition state resembles more the reactants than the products in an exothermic reaction. Hence, the activation energy is obtained when the A-B distance is displaced in this calculation.

Energy of the transition state = -103.752 kJ/mol

Energy of products = -133.466 kJ/mol

Activation energy of the reaction = 29.714 kJ/mol

[[File:Activationenergysp2416.PNG|thumb|centre|Calculation of the activation energy]]

=== Reaction Dynamics ===

Reactive Trajectory 

Atom A : F

Atom B : H

Atom C : H

AB distance = 1.91

BC distance = 0.7455

AB momentum = -1.5

BC momentum = 1.0

[[File:Reactivetrajsp2416.png]]

== References ==

<references>
<ref name="[1]">J.C. Polanyi, D.C. Tardy, 1969, J. Chem. Phys., Vol.51 "Energy Distribution in the Exothermic Reaction F + H2 , and the Endothermic Reaction HF + H", p.255-321.</ref>

<ref name="[2]">http://www.wiredchemist.com/chemistry/data/bond_energies_lengths.html (Assessed on 15/05/2018 17ː10).</ref>
</references>

File:Reactivetrajsp2416.png

2018-05-15T17:11:08Z

Sp2416:

File:Activationenergysp2416.PNG

2018-05-15T17:10:51Z

Sp2416: Sp2416 uploaded a new version of File:Activationenergysp2416.PNG

MRD:sp2416

2018-05-15T17:09:37Z

Sp2416: /* Reaction Dynamics */

==H + H2==

===Transition State ===

The transition state is defined a the maximum on the minimum energy path linking reactants and products. Both minima and transition states are saddle points on the potential energy surface. On the potential energy surface diagram of H + H2 analysed, the gradient of both the transition state and minimum are found to be zero (∂V(ri)/∂ri=0). Minima and transition structures can be distinguished by taking the second derivative of the gradient. For transition state this will be negative and positive, while for minima the answer to this will be positive.

===Locating the Transition State===

[[File:Internucleardistancesp2416.PNG|thumb|centre|Internuclear Distance vs Time plot for H + H2]]

On the first graph the Transition state is where the A-B and B-C lines cross.

To locate the Transition state the momenta are changed to 0, (as a transition state is a saddle point) and then the distances AB and BC are adjusted so as to get an Internuclear Distance graph where both distances are stationary. This distance is found to be stationary when both AB and BC are set to be 0.90755.

[[File:InternucleardistanceTSsp2416.PNG|thumb|centre|Internuclear Distance vs Time plot for H + H2 Transition state]]

===Dynamic and mep Calculation types===

The following results were obtained when the AB distance was changed to 0.90855 and the BC distance was maintained at 0.09755 (transition state position)

[[File:Trajectory_plot_dynamics_sp2416.PNG|thumb|centre|Trajectory plot using Dynamics calculation type]]

[[File:Trajectory_plot_mep_sp2416.PNG|thumb|centre|Trajectory plot using mep calculation type]]

[[File:Distance_time_dynamics_sp2416.PNG|thumb|centre|Internuclear Distance vs Time graph using Dynamics calculation type]]

[[File:Distance_time_mep_sp2416.PNG|thumb|centre|Internuclear Distance vs Time graph using mep calculation type]]

===Reactive and Unreactive Trajectories===

{| class="wikitable" border="1"
|+ Effect of different momenta on reactivity
! p1 !! p2 !! Total Energy!!Type of Trajectory!!Contour plot!!Description
|-
| -1.25 || -2.5 || -99.199 || Reactive || [[File:Contour1_sp2416.PNG|320px]] || cell ||
|-
| -1.5 || -2.0 || -100.456 || Uneactive || [[File:Contour2_sp2416.PNG|320px]] || cell ||
|-
| -1.5 || -2.5 || -98.956 || Reactive || [[File:Contour3_sp2416.PNG|320px]] || cell ||
|-
| -2.5 || -5.0 || -84.956 || Uneactive || [[File:Contour4_sp2416.PNG|320px]] || cell ||
|-
| -2.5 || -5.2 || -83.416 || Reactive || [[File:Contour5_sp2416.PNG|320px]] || cell ||
|}

===Transition State Theory===

Complete

==F - H - H ==

=== PES Inspection ===

The equilibrium reaction F + H2 ⇌ H + HF is exothermic when it goes forward releasing energy, whilst the backward reaction is endothermic, taking energy in. <ref name="[1]" /> The H-H bond is -432 kJ/mol and the H-F bond is -565 kj/mol <ref name="[2]" />. This means that more energy is needed to break the H-F than the energy gained by forming the H-H bond, and hence the forward reaction is exothermic (and the backward endothermic).

 Locating the Transition Stateː 

Applying the following settingsː

Atom A: F

Atom B: H

Atom C: H

AB distance: 1.81 Å

BC distance: 0.7455 Å

Both momenta are set to 0.

These settings were applied using the Dynamics Calculation type and visualising the Internuclear Distance vs Time plot. Trial and error values were used until all the distances (A-B, B-C and A-C) produce straight lines, as shown in the figure below.

[[File:Distance_time_1_sp2416.PNG|thumb|centre|Internuclear Distance vs Time graph using Dynamics calculation type for F-H-H]]

 Reporting the Activation Energyː 

To find the activation energy, the type of calculation used is MEP and the AB distance is displaced slightly (form 1.81 is changed to 1.83) in order to force the reaction to go to either direction of the equilibrium - right hand side or left hand side.

The forward reaction in the equilibrium F + H2 ⇌ H + HF is exothermic. Hammond's postulate states that the transition state resembles more the reactants than the products in an exothermic reaction. Hence, the activation energy is obtained when the A-B distance is displaced in this calculation.

Energy of the transition state = -103.752 kJ/mol

Energy of products = -133.466 kJ/mol

Activation energy of the reaction = 29.714 kJ/mol

[[File:Activationenergysp2416.PNG|thumb|centre|Calculation of the activation energy]]

=== Reaction Dynamics ===

Reactive Trajectory 

Atom A : F

Atom B : H

Atom C : H

AB distance = 1.91

BC distance = 0.7455

AB momentum = -1.5

BC momentum = 1.0

== References ==

<references>
<ref name="[1]">J.C. Polanyi, D.C. Tardy, 1969, J. Chem. Phys., Vol.51 "Energy Distribution in the Exothermic Reaction F + H2 , and the Endothermic Reaction HF + H", p.255-321.</ref>

<ref name="[2]">http://www.wiredchemist.com/chemistry/data/bond_energies_lengths.html (Assessed on 15/05/2018 17ː10).</ref>
</references>

MRD:sp2416

2018-05-15T17:05:09Z

Sp2416: /* Reaction Dynamics */

==H + H2==

===Transition State ===

The transition state is defined a the maximum on the minimum energy path linking reactants and products. Both minima and transition states are saddle points on the potential energy surface. On the potential energy surface diagram of H + H2 analysed, the gradient of both the transition state and minimum are found to be zero (∂V(ri)/∂ri=0). Minima and transition structures can be distinguished by taking the second derivative of the gradient. For transition state this will be negative and positive, while for minima the answer to this will be positive.

===Locating the Transition State===

[[File:Internucleardistancesp2416.PNG|thumb|centre|Internuclear Distance vs Time plot for H + H2]]

On the first graph the Transition state is where the A-B and B-C lines cross.

To locate the Transition state the momenta are changed to 0, (as a transition state is a saddle point) and then the distances AB and BC are adjusted so as to get an Internuclear Distance graph where both distances are stationary. This distance is found to be stationary when both AB and BC are set to be 0.90755.

[[File:InternucleardistanceTSsp2416.PNG|thumb|centre|Internuclear Distance vs Time plot for H + H2 Transition state]]

===Dynamic and mep Calculation types===

The following results were obtained when the AB distance was changed to 0.90855 and the BC distance was maintained at 0.09755 (transition state position)

[[File:Trajectory_plot_dynamics_sp2416.PNG|thumb|centre|Trajectory plot using Dynamics calculation type]]

[[File:Trajectory_plot_mep_sp2416.PNG|thumb|centre|Trajectory plot using mep calculation type]]

[[File:Distance_time_dynamics_sp2416.PNG|thumb|centre|Internuclear Distance vs Time graph using Dynamics calculation type]]

[[File:Distance_time_mep_sp2416.PNG|thumb|centre|Internuclear Distance vs Time graph using mep calculation type]]

===Reactive and Unreactive Trajectories===

{| class="wikitable" border="1"
|+ Effect of different momenta on reactivity
! p1 !! p2 !! Total Energy!!Type of Trajectory!!Contour plot!!Description
|-
| -1.25 || -2.5 || -99.199 || Reactive || [[File:Contour1_sp2416.PNG|320px]] || cell ||
|-
| -1.5 || -2.0 || -100.456 || Uneactive || [[File:Contour2_sp2416.PNG|320px]] || cell ||
|-
| -1.5 || -2.5 || -98.956 || Reactive || [[File:Contour3_sp2416.PNG|320px]] || cell ||
|-
| -2.5 || -5.0 || -84.956 || Uneactive || [[File:Contour4_sp2416.PNG|320px]] || cell ||
|-
| -2.5 || -5.2 || -83.416 || Reactive || [[File:Contour5_sp2416.PNG|320px]] || cell ||
|}

===Transition State Theory===

Complete

==F - H - H ==

=== PES Inspection ===

The equilibrium reaction F + H2 ⇌ H + HF is exothermic when it goes forward releasing energy, whilst the backward reaction is endothermic, taking energy in. <ref name="[1]" /> The H-H bond is -432 kJ/mol and the H-F bond is -565 kj/mol <ref name="[2]" />. This means that more energy is needed to break the H-F than the energy gained by forming the H-H bond, and hence the forward reaction is exothermic (and the backward endothermic).

 Locating the Transition Stateː 

Applying the following settingsː

Atom A: F

Atom B: H

Atom C: H

AB distance: 1.81 Å

BC distance: 0.7455 Å

Both momenta are set to 0.

These settings were applied using the Dynamics Calculation type and visualising the Internuclear Distance vs Time plot. Trial and error values were used until all the distances (A-B, B-C and A-C) produce straight lines, as shown in the figure below.

[[File:Distance_time_1_sp2416.PNG|thumb|centre|Internuclear Distance vs Time graph using Dynamics calculation type for F-H-H]]

 Reporting the Activation Energyː 

To find the activation energy, the type of calculation used is MEP and the AB distance is displaced slightly (form 1.81 is changed to 1.83) in order to force the reaction to go to either direction of the equilibrium - right hand side or left hand side.

The forward reaction in the equilibrium F + H2 ⇌ H + HF is exothermic. Hammond's postulate states that the transition state resembles more the reactants than the products in an exothermic reaction. Hence, the activation energy is obtained when the A-B distance is displaced in this calculation.

Energy of the transition state = -103.752 kJ/mol

Energy of products = -133.466 kJ/mol

Activation energy of the reaction = 29.714 kJ/mol

[[File:Activationenergysp2416.PNG|thumb|centre|Calculation of the activation energy]]

=== Reaction Dynamics ===

Reactive Trajectory 

Atom A : F

Atom B : H

Atom C : H

AB distance = 1.92

BC distance = 0.7455

AB momentum = -1.5

BC momentum = 1.0

== References ==

<references>
<ref name="[1]">J.C. Polanyi, D.C. Tardy, 1969, J. Chem. Phys., Vol.51 "Energy Distribution in the Exothermic Reaction F + H2 , and the Endothermic Reaction HF + H", p.255-321.</ref>

<ref name="[2]">http://www.wiredchemist.com/chemistry/data/bond_energies_lengths.html (Assessed on 15/05/2018 17ː10).</ref>
</references>

MRD:sp2416

2018-05-15T17:05:01Z

Sp2416: /* Reaction Dynamics */

==H + H2==

===Transition State ===

The transition state is defined a the maximum on the minimum energy path linking reactants and products. Both minima and transition states are saddle points on the potential energy surface. On the potential energy surface diagram of H + H2 analysed, the gradient of both the transition state and minimum are found to be zero (∂V(ri)/∂ri=0). Minima and transition structures can be distinguished by taking the second derivative of the gradient. For transition state this will be negative and positive, while for minima the answer to this will be positive.

===Locating the Transition State===

[[File:Internucleardistancesp2416.PNG|thumb|centre|Internuclear Distance vs Time plot for H + H2]]

On the first graph the Transition state is where the A-B and B-C lines cross.

To locate the Transition state the momenta are changed to 0, (as a transition state is a saddle point) and then the distances AB and BC are adjusted so as to get an Internuclear Distance graph where both distances are stationary. This distance is found to be stationary when both AB and BC are set to be 0.90755.

[[File:InternucleardistanceTSsp2416.PNG|thumb|centre|Internuclear Distance vs Time plot for H + H2 Transition state]]

===Dynamic and mep Calculation types===

The following results were obtained when the AB distance was changed to 0.90855 and the BC distance was maintained at 0.09755 (transition state position)

[[File:Trajectory_plot_dynamics_sp2416.PNG|thumb|centre|Trajectory plot using Dynamics calculation type]]

[[File:Trajectory_plot_mep_sp2416.PNG|thumb|centre|Trajectory plot using mep calculation type]]

[[File:Distance_time_dynamics_sp2416.PNG|thumb|centre|Internuclear Distance vs Time graph using Dynamics calculation type]]

[[File:Distance_time_mep_sp2416.PNG|thumb|centre|Internuclear Distance vs Time graph using mep calculation type]]

===Reactive and Unreactive Trajectories===

{| class="wikitable" border="1"
|+ Effect of different momenta on reactivity
! p1 !! p2 !! Total Energy!!Type of Trajectory!!Contour plot!!Description
|-
| -1.25 || -2.5 || -99.199 || Reactive || [[File:Contour1_sp2416.PNG|320px]] || cell ||
|-
| -1.5 || -2.0 || -100.456 || Uneactive || [[File:Contour2_sp2416.PNG|320px]] || cell ||
|-
| -1.5 || -2.5 || -98.956 || Reactive || [[File:Contour3_sp2416.PNG|320px]] || cell ||
|-
| -2.5 || -5.0 || -84.956 || Uneactive || [[File:Contour4_sp2416.PNG|320px]] || cell ||
|-
| -2.5 || -5.2 || -83.416 || Reactive || [[File:Contour5_sp2416.PNG|320px]] || cell ||
|}

===Transition State Theory===

Complete

==F - H - H ==

=== PES Inspection ===

The equilibrium reaction F + H2 ⇌ H + HF is exothermic when it goes forward releasing energy, whilst the backward reaction is endothermic, taking energy in. <ref name="[1]" /> The H-H bond is -432 kJ/mol and the H-F bond is -565 kj/mol <ref name="[2]" />. This means that more energy is needed to break the H-F than the energy gained by forming the H-H bond, and hence the forward reaction is exothermic (and the backward endothermic).

 Locating the Transition Stateː 

Applying the following settingsː

Atom A: F

Atom B: H

Atom C: H

AB distance: 1.81 Å

BC distance: 0.7455 Å

Both momenta are set to 0.

These settings were applied using the Dynamics Calculation type and visualising the Internuclear Distance vs Time plot. Trial and error values were used until all the distances (A-B, B-C and A-C) produce straight lines, as shown in the figure below.

[[File:Distance_time_1_sp2416.PNG|thumb|centre|Internuclear Distance vs Time graph using Dynamics calculation type for F-H-H]]

 Reporting the Activation Energyː 

To find the activation energy, the type of calculation used is MEP and the AB distance is displaced slightly (form 1.81 is changed to 1.83) in order to force the reaction to go to either direction of the equilibrium - right hand side or left hand side.

The forward reaction in the equilibrium F + H2 ⇌ H + HF is exothermic. Hammond's postulate states that the transition state resembles more the reactants than the products in an exothermic reaction. Hence, the activation energy is obtained when the A-B distance is displaced in this calculation.

Energy of the transition state = -103.752 kJ/mol

Energy of products = -133.466 kJ/mol

Activation energy of the reaction = 29.714 kJ/mol

[[File:Activationenergysp2416.PNG|thumb|centre|Calculation of the activation energy]]

=== Reaction Dynamics ===

Reactive Trajectory 

Atom A : F
Atom B : H
Atom C : H

AB distance = 1.92

BC distance = 0.7455

AB momentum = -1.5

BC momentum = 1.0

== References ==

<references>
<ref name="[1]">J.C. Polanyi, D.C. Tardy, 1969, J. Chem. Phys., Vol.51 "Energy Distribution in the Exothermic Reaction F + H2 , and the Endothermic Reaction HF + H", p.255-321.</ref>

<ref name="[2]">http://www.wiredchemist.com/chemistry/data/bond_energies_lengths.html (Assessed on 15/05/2018 17ː10).</ref>
</references>

MRD:sp2416

2018-05-15T17:04:55Z

Sp2416: /* Reaction Dynamics */

==H + H2==

===Transition State ===

The transition state is defined a the maximum on the minimum energy path linking reactants and products. Both minima and transition states are saddle points on the potential energy surface. On the potential energy surface diagram of H + H2 analysed, the gradient of both the transition state and minimum are found to be zero (∂V(ri)/∂ri=0). Minima and transition structures can be distinguished by taking the second derivative of the gradient. For transition state this will be negative and positive, while for minima the answer to this will be positive.

===Locating the Transition State===

[[File:Internucleardistancesp2416.PNG|thumb|centre|Internuclear Distance vs Time plot for H + H2]]

On the first graph the Transition state is where the A-B and B-C lines cross.

To locate the Transition state the momenta are changed to 0, (as a transition state is a saddle point) and then the distances AB and BC are adjusted so as to get an Internuclear Distance graph where both distances are stationary. This distance is found to be stationary when both AB and BC are set to be 0.90755.

[[File:InternucleardistanceTSsp2416.PNG|thumb|centre|Internuclear Distance vs Time plot for H + H2 Transition state]]

===Dynamic and mep Calculation types===

The following results were obtained when the AB distance was changed to 0.90855 and the BC distance was maintained at 0.09755 (transition state position)

[[File:Trajectory_plot_dynamics_sp2416.PNG|thumb|centre|Trajectory plot using Dynamics calculation type]]

[[File:Trajectory_plot_mep_sp2416.PNG|thumb|centre|Trajectory plot using mep calculation type]]

[[File:Distance_time_dynamics_sp2416.PNG|thumb|centre|Internuclear Distance vs Time graph using Dynamics calculation type]]

[[File:Distance_time_mep_sp2416.PNG|thumb|centre|Internuclear Distance vs Time graph using mep calculation type]]

===Reactive and Unreactive Trajectories===

{| class="wikitable" border="1"
|+ Effect of different momenta on reactivity
! p1 !! p2 !! Total Energy!!Type of Trajectory!!Contour plot!!Description
|-
| -1.25 || -2.5 || -99.199 || Reactive || [[File:Contour1_sp2416.PNG|320px]] || cell ||
|-
| -1.5 || -2.0 || -100.456 || Uneactive || [[File:Contour2_sp2416.PNG|320px]] || cell ||
|-
| -1.5 || -2.5 || -98.956 || Reactive || [[File:Contour3_sp2416.PNG|320px]] || cell ||
|-
| -2.5 || -5.0 || -84.956 || Uneactive || [[File:Contour4_sp2416.PNG|320px]] || cell ||
|-
| -2.5 || -5.2 || -83.416 || Reactive || [[File:Contour5_sp2416.PNG|320px]] || cell ||
|}

===Transition State Theory===

Complete

==F - H - H ==

=== PES Inspection ===

The equilibrium reaction F + H2 ⇌ H + HF is exothermic when it goes forward releasing energy, whilst the backward reaction is endothermic, taking energy in. <ref name="[1]" /> The H-H bond is -432 kJ/mol and the H-F bond is -565 kj/mol <ref name="[2]" />. This means that more energy is needed to break the H-F than the energy gained by forming the H-H bond, and hence the forward reaction is exothermic (and the backward endothermic).

 Locating the Transition Stateː 

Applying the following settingsː

Atom A: F

Atom B: H

Atom C: H

AB distance: 1.81 Å

BC distance: 0.7455 Å

Both momenta are set to 0.

These settings were applied using the Dynamics Calculation type and visualising the Internuclear Distance vs Time plot. Trial and error values were used until all the distances (A-B, B-C and A-C) produce straight lines, as shown in the figure below.

[[File:Distance_time_1_sp2416.PNG|thumb|centre|Internuclear Distance vs Time graph using Dynamics calculation type for F-H-H]]

 Reporting the Activation Energyː 

To find the activation energy, the type of calculation used is MEP and the AB distance is displaced slightly (form 1.81 is changed to 1.83) in order to force the reaction to go to either direction of the equilibrium - right hand side or left hand side.

The forward reaction in the equilibrium F + H2 ⇌ H + HF is exothermic. Hammond's postulate states that the transition state resembles more the reactants than the products in an exothermic reaction. Hence, the activation energy is obtained when the A-B distance is displaced in this calculation.

Energy of the transition state = -103.752 kJ/mol

Energy of products = -133.466 kJ/mol

Activation energy of the reaction = 29.714 kJ/mol

[[File:Activationenergysp2416.PNG|thumb|centre|Calculation of the activation energy]]

=== Reaction Dynamics ===

Reactive Trajectory 

Atom A : F
Atom B : H
Atom C : H

AB distance = 1.92
BC distance = 0.7455
AB momentum = -1.5
BC momentum = 1.0

== References ==

<references>
<ref name="[1]">J.C. Polanyi, D.C. Tardy, 1969, J. Chem. Phys., Vol.51 "Energy Distribution in the Exothermic Reaction F + H2 , and the Endothermic Reaction HF + H", p.255-321.</ref>

<ref name="[2]">http://www.wiredchemist.com/chemistry/data/bond_energies_lengths.html (Assessed on 15/05/2018 17ː10).</ref>
</references>

MRD:sp2416

2018-05-15T17:04:43Z

Sp2416: /* Reaction Dynamics */

==H + H2==

===Transition State ===

The transition state is defined a the maximum on the minimum energy path linking reactants and products. Both minima and transition states are saddle points on the potential energy surface. On the potential energy surface diagram of H + H2 analysed, the gradient of both the transition state and minimum are found to be zero (∂V(ri)/∂ri=0). Minima and transition structures can be distinguished by taking the second derivative of the gradient. For transition state this will be negative and positive, while for minima the answer to this will be positive.

===Locating the Transition State===

[[File:Internucleardistancesp2416.PNG|thumb|centre|Internuclear Distance vs Time plot for H + H2]]

On the first graph the Transition state is where the A-B and B-C lines cross.

To locate the Transition state the momenta are changed to 0, (as a transition state is a saddle point) and then the distances AB and BC are adjusted so as to get an Internuclear Distance graph where both distances are stationary. This distance is found to be stationary when both AB and BC are set to be 0.90755.

[[File:InternucleardistanceTSsp2416.PNG|thumb|centre|Internuclear Distance vs Time plot for H + H2 Transition state]]

===Dynamic and mep Calculation types===

The following results were obtained when the AB distance was changed to 0.90855 and the BC distance was maintained at 0.09755 (transition state position)

[[File:Trajectory_plot_dynamics_sp2416.PNG|thumb|centre|Trajectory plot using Dynamics calculation type]]

[[File:Trajectory_plot_mep_sp2416.PNG|thumb|centre|Trajectory plot using mep calculation type]]

[[File:Distance_time_dynamics_sp2416.PNG|thumb|centre|Internuclear Distance vs Time graph using Dynamics calculation type]]

[[File:Distance_time_mep_sp2416.PNG|thumb|centre|Internuclear Distance vs Time graph using mep calculation type]]

===Reactive and Unreactive Trajectories===

{| class="wikitable" border="1"
|+ Effect of different momenta on reactivity
! p1 !! p2 !! Total Energy!!Type of Trajectory!!Contour plot!!Description
|-
| -1.25 || -2.5 || -99.199 || Reactive || [[File:Contour1_sp2416.PNG|320px]] || cell ||
|-
| -1.5 || -2.0 || -100.456 || Uneactive || [[File:Contour2_sp2416.PNG|320px]] || cell ||
|-
| -1.5 || -2.5 || -98.956 || Reactive || [[File:Contour3_sp2416.PNG|320px]] || cell ||
|-
| -2.5 || -5.0 || -84.956 || Uneactive || [[File:Contour4_sp2416.PNG|320px]] || cell ||
|-
| -2.5 || -5.2 || -83.416 || Reactive || [[File:Contour5_sp2416.PNG|320px]] || cell ||
|}

===Transition State Theory===

Complete

==F - H - H ==

=== PES Inspection ===

The equilibrium reaction F + H2 ⇌ H + HF is exothermic when it goes forward releasing energy, whilst the backward reaction is endothermic, taking energy in. <ref name="[1]" /> The H-H bond is -432 kJ/mol and the H-F bond is -565 kj/mol <ref name="[2]" />. This means that more energy is needed to break the H-F than the energy gained by forming the H-H bond, and hence the forward reaction is exothermic (and the backward endothermic).

 Locating the Transition Stateː 

Applying the following settingsː

Atom A: F

Atom B: H

Atom C: H

AB distance: 1.81 Å

BC distance: 0.7455 Å

Both momenta are set to 0.

These settings were applied using the Dynamics Calculation type and visualising the Internuclear Distance vs Time plot. Trial and error values were used until all the distances (A-B, B-C and A-C) produce straight lines, as shown in the figure below.

[[File:Distance_time_1_sp2416.PNG|thumb|centre|Internuclear Distance vs Time graph using Dynamics calculation type for F-H-H]]

 Reporting the Activation Energyː 

To find the activation energy, the type of calculation used is MEP and the AB distance is displaced slightly (form 1.81 is changed to 1.83) in order to force the reaction to go to either direction of the equilibrium - right hand side or left hand side.

The forward reaction in the equilibrium F + H2 ⇌ H + HF is exothermic. Hammond's postulate states that the transition state resembles more the reactants than the products in an exothermic reaction. Hence, the activation energy is obtained when the A-B distance is displaced in this calculation.

Energy of the transition state = -103.752 kJ/mol

Energy of products = -133.466 kJ/mol

Activation energy of the reaction = 29.714 kJ/mol

[[File:Activationenergysp2416.PNG|thumb|centre|Calculation of the activation energy]]

=== Reaction Dynamics ===

Reactive Trajectory 

Atom A : F

Atom B : H

Atom C : H

AB distance = 1.92

BC distance = 0.7455

AB momentum = -1.5

BC momentum = 1.0

== References ==

<references>
<ref name="[1]">J.C. Polanyi, D.C. Tardy, 1969, J. Chem. Phys., Vol.51 "Energy Distribution in the Exothermic Reaction F + H2 , and the Endothermic Reaction HF + H", p.255-321.</ref>

<ref name="[2]">http://www.wiredchemist.com/chemistry/data/bond_energies_lengths.html (Assessed on 15/05/2018 17ː10).</ref>
</references>

MRD:sp2416

2018-05-15T17:00:19Z

Sp2416: /* PES Inspection */

==H + H2==

===Transition State ===

The transition state is defined a the maximum on the minimum energy path linking reactants and products. Both minima and transition states are saddle points on the potential energy surface. On the potential energy surface diagram of H + H2 analysed, the gradient of both the transition state and minimum are found to be zero (∂V(ri)/∂ri=0). Minima and transition structures can be distinguished by taking the second derivative of the gradient. For transition state this will be negative and positive, while for minima the answer to this will be positive.

===Locating the Transition State===

[[File:Internucleardistancesp2416.PNG|thumb|centre|Internuclear Distance vs Time plot for H + H2]]

On the first graph the Transition state is where the A-B and B-C lines cross.

To locate the Transition state the momenta are changed to 0, (as a transition state is a saddle point) and then the distances AB and BC are adjusted so as to get an Internuclear Distance graph where both distances are stationary. This distance is found to be stationary when both AB and BC are set to be 0.90755.

[[File:InternucleardistanceTSsp2416.PNG|thumb|centre|Internuclear Distance vs Time plot for H + H2 Transition state]]

===Dynamic and mep Calculation types===

The following results were obtained when the AB distance was changed to 0.90855 and the BC distance was maintained at 0.09755 (transition state position)

[[File:Trajectory_plot_dynamics_sp2416.PNG|thumb|centre|Trajectory plot using Dynamics calculation type]]

[[File:Trajectory_plot_mep_sp2416.PNG|thumb|centre|Trajectory plot using mep calculation type]]

[[File:Distance_time_dynamics_sp2416.PNG|thumb|centre|Internuclear Distance vs Time graph using Dynamics calculation type]]

[[File:Distance_time_mep_sp2416.PNG|thumb|centre|Internuclear Distance vs Time graph using mep calculation type]]

===Reactive and Unreactive Trajectories===

{| class="wikitable" border="1"
|+ Effect of different momenta on reactivity
! p1 !! p2 !! Total Energy!!Type of Trajectory!!Contour plot!!Description
|-
| -1.25 || -2.5 || -99.199 || Reactive || [[File:Contour1_sp2416.PNG|320px]] || cell ||
|-
| -1.5 || -2.0 || -100.456 || Uneactive || [[File:Contour2_sp2416.PNG|320px]] || cell ||
|-
| -1.5 || -2.5 || -98.956 || Reactive || [[File:Contour3_sp2416.PNG|320px]] || cell ||
|-
| -2.5 || -5.0 || -84.956 || Uneactive || [[File:Contour4_sp2416.PNG|320px]] || cell ||
|-
| -2.5 || -5.2 || -83.416 || Reactive || [[File:Contour5_sp2416.PNG|320px]] || cell ||
|}

===Transition State Theory===

Complete

==F - H - H ==

=== PES Inspection ===

The equilibrium reaction F + H2 ⇌ H + HF is exothermic when it goes forward releasing energy, whilst the backward reaction is endothermic, taking energy in. <ref name="[1]" /> The H-H bond is -432 kJ/mol and the H-F bond is -565 kj/mol <ref name="[2]" />. This means that more energy is needed to break the H-F than the energy gained by forming the H-H bond, and hence the forward reaction is exothermic (and the backward endothermic).

 Locating the Transition Stateː 

Applying the following settingsː

Atom A: F

Atom B: H

Atom C: H

AB distance: 1.81 Å

BC distance: 0.7455 Å

Both momenta are set to 0.

These settings were applied using the Dynamics Calculation type and visualising the Internuclear Distance vs Time plot. Trial and error values were used until all the distances (A-B, B-C and A-C) produce straight lines, as shown in the figure below.

[[File:Distance_time_1_sp2416.PNG|thumb|centre|Internuclear Distance vs Time graph using Dynamics calculation type for F-H-H]]

 Reporting the Activation Energyː 

To find the activation energy, the type of calculation used is MEP and the AB distance is displaced slightly (form 1.81 is changed to 1.83) in order to force the reaction to go to either direction of the equilibrium - right hand side or left hand side.

The forward reaction in the equilibrium F + H2 ⇌ H + HF is exothermic. Hammond's postulate states that the transition state resembles more the reactants than the products in an exothermic reaction. Hence, the activation energy is obtained when the A-B distance is displaced in this calculation.

Energy of the transition state = -103.752 kJ/mol

Energy of products = -133.466 kJ/mol

Activation energy of the reaction = 29.714 kJ/mol

[[File:Activationenergysp2416.PNG|thumb|centre|Calculation of the activation energy]]

=== Reaction Dynamics ===

== References ==

<references>
<ref name="[1]">J.C. Polanyi, D.C. Tardy, 1969, J. Chem. Phys., Vol.51 "Energy Distribution in the Exothermic Reaction F + H2 , and the Endothermic Reaction HF + H", p.255-321.</ref>

<ref name="[2]">http://www.wiredchemist.com/chemistry/data/bond_energies_lengths.html (Assessed on 15/05/2018 17ː10).</ref>
</references>

MRD:sp2416

2018-05-15T16:58:34Z

Sp2416: /* PES Inspection */

==H + H2==

===Transition State ===

The transition state is defined a the maximum on the minimum energy path linking reactants and products. Both minima and transition states are saddle points on the potential energy surface. On the potential energy surface diagram of H + H2 analysed, the gradient of both the transition state and minimum are found to be zero (∂V(ri)/∂ri=0). Minima and transition structures can be distinguished by taking the second derivative of the gradient. For transition state this will be negative and positive, while for minima the answer to this will be positive.

===Locating the Transition State===

[[File:Internucleardistancesp2416.PNG|thumb|centre|Internuclear Distance vs Time plot for H + H2]]

On the first graph the Transition state is where the A-B and B-C lines cross.

To locate the Transition state the momenta are changed to 0, (as a transition state is a saddle point) and then the distances AB and BC are adjusted so as to get an Internuclear Distance graph where both distances are stationary. This distance is found to be stationary when both AB and BC are set to be 0.90755.

[[File:InternucleardistanceTSsp2416.PNG|thumb|centre|Internuclear Distance vs Time plot for H + H2 Transition state]]

===Dynamic and mep Calculation types===

The following results were obtained when the AB distance was changed to 0.90855 and the BC distance was maintained at 0.09755 (transition state position)

[[File:Trajectory_plot_dynamics_sp2416.PNG|thumb|centre|Trajectory plot using Dynamics calculation type]]

[[File:Trajectory_plot_mep_sp2416.PNG|thumb|centre|Trajectory plot using mep calculation type]]

[[File:Distance_time_dynamics_sp2416.PNG|thumb|centre|Internuclear Distance vs Time graph using Dynamics calculation type]]

[[File:Distance_time_mep_sp2416.PNG|thumb|centre|Internuclear Distance vs Time graph using mep calculation type]]

===Reactive and Unreactive Trajectories===

{| class="wikitable" border="1"
|+ Effect of different momenta on reactivity
! p1 !! p2 !! Total Energy!!Type of Trajectory!!Contour plot!!Description
|-
| -1.25 || -2.5 || -99.199 || Reactive || [[File:Contour1_sp2416.PNG|320px]] || cell ||
|-
| -1.5 || -2.0 || -100.456 || Uneactive || [[File:Contour2_sp2416.PNG|320px]] || cell ||
|-
| -1.5 || -2.5 || -98.956 || Reactive || [[File:Contour3_sp2416.PNG|320px]] || cell ||
|-
| -2.5 || -5.0 || -84.956 || Uneactive || [[File:Contour4_sp2416.PNG|320px]] || cell ||
|-
| -2.5 || -5.2 || -83.416 || Reactive || [[File:Contour5_sp2416.PNG|320px]] || cell ||
|}

===Transition State Theory===

Complete

==F - H - H ==

=== PES Inspection ===

The equilibrium reaction F + H2 ⇌ H + HF is exothermic when it goes forward releasing energy, whilst the backward reaction is endothermic, taking energy in. <ref name="[1]" /> The H-H bond is -432 kJ/mol and the H-F bond is -565 kj/mol <ref name="[2]" />. This means that more energy is needed to break the H-F than the energy gained by forming the H-H bond, and hence the forward reaction is exothermic (and the backward endothermic).

 Locating the Transition Stateː 

Applying the following settingsː

Atom A: F

Atom B: H

Atom C: H

AB distance: 1.81 Å

BC distance: 0.7455 Å

Both momenta are set to 0.

These settings were applied using the Dynamics Calculation type and visualising the Internuclear Distance vs Time plot. Trial and error values were used until all the distances (A-B, B-C and A-C) produce straight lines, as shown in the figure below.

[[File:Distance_time_1_sp2416.PNG|thumb|centre|Internuclear Distance vs Time graph using Dynamics calculation type for F-H-H]]

 Reporting the Activation Energyː 

To find the activation energy, the type of calculation used is MEP and the AB distance is displaced slightly (form 1.81 is changed to 1.83) in order to force the reaction to go to either direction of the equilibrium - right hand side or left hand side.

The forward reaction in the equilibrium F + H2 ⇌ H + HF is exothermic. Hammond's postulate states that the transition state resembles more the reactants than the products in an exothermic reaction. Hence, the activation energy is obtained when the A-B distance is displaced in this calculation.

Energy of the transition state = -103.752 kJ/mol

Energy of products = -133.466 kJ/mol

Activation energy of the reaction = 29.714 kJ/mol

[[File:Activationenergysp2416.PNG|thumb|centre|Calculation of the activation energy]]

== References ==

<references>
<ref name="[1]">J.C. Polanyi, D.C. Tardy, 1969, J. Chem. Phys., Vol.51 "Energy Distribution in the Exothermic Reaction F + H2 , and the Endothermic Reaction HF + H", p.255-321.</ref>

<ref name="[2]">http://www.wiredchemist.com/chemistry/data/bond_energies_lengths.html (Assessed on 15/05/2018 17ː10).</ref>
</references>

MRD:sp2416

2018-05-15T16:56:35Z

Sp2416: /* PES Inspection */

==H + H2==

===Transition State ===

The transition state is defined a the maximum on the minimum energy path linking reactants and products. Both minima and transition states are saddle points on the potential energy surface. On the potential energy surface diagram of H + H2 analysed, the gradient of both the transition state and minimum are found to be zero (∂V(ri)/∂ri=0). Minima and transition structures can be distinguished by taking the second derivative of the gradient. For transition state this will be negative and positive, while for minima the answer to this will be positive.

===Locating the Transition State===

[[File:Internucleardistancesp2416.PNG|thumb|centre|Internuclear Distance vs Time plot for H + H2]]

On the first graph the Transition state is where the A-B and B-C lines cross.

To locate the Transition state the momenta are changed to 0, (as a transition state is a saddle point) and then the distances AB and BC are adjusted so as to get an Internuclear Distance graph where both distances are stationary. This distance is found to be stationary when both AB and BC are set to be 0.90755.

[[File:InternucleardistanceTSsp2416.PNG|thumb|centre|Internuclear Distance vs Time plot for H + H2 Transition state]]

===Dynamic and mep Calculation types===

The following results were obtained when the AB distance was changed to 0.90855 and the BC distance was maintained at 0.09755 (transition state position)

[[File:Trajectory_plot_dynamics_sp2416.PNG|thumb|centre|Trajectory plot using Dynamics calculation type]]

[[File:Trajectory_plot_mep_sp2416.PNG|thumb|centre|Trajectory plot using mep calculation type]]

[[File:Distance_time_dynamics_sp2416.PNG|thumb|centre|Internuclear Distance vs Time graph using Dynamics calculation type]]

[[File:Distance_time_mep_sp2416.PNG|thumb|centre|Internuclear Distance vs Time graph using mep calculation type]]

===Reactive and Unreactive Trajectories===

{| class="wikitable" border="1"
|+ Effect of different momenta on reactivity
! p1 !! p2 !! Total Energy!!Type of Trajectory!!Contour plot!!Description
|-
| -1.25 || -2.5 || -99.199 || Reactive || [[File:Contour1_sp2416.PNG|320px]] || cell ||
|-
| -1.5 || -2.0 || -100.456 || Uneactive || [[File:Contour2_sp2416.PNG|320px]] || cell ||
|-
| -1.5 || -2.5 || -98.956 || Reactive || [[File:Contour3_sp2416.PNG|320px]] || cell ||
|-
| -2.5 || -5.0 || -84.956 || Uneactive || [[File:Contour4_sp2416.PNG|320px]] || cell ||
|-
| -2.5 || -5.2 || -83.416 || Reactive || [[File:Contour5_sp2416.PNG|320px]] || cell ||
|}

===Transition State Theory===

Complete

==F - H - H ==

=== PES Inspection ===

The equilibrium reaction F + H2 ⇌ H + HF is exothermic when it goes forward releasing energy, whilst the backward reaction is endothermic, taking energy in. <ref name="[1]" /> The H-H bond is -432 kJ/mol and the H-F bond is -565 kj/mol <ref name="[2]" />. This means that more energy is needed to break the H-F than the energy gained by forming the H-H bond, and hence the forward reaction is exothermic (and the backward endothermic).

 Locating the Transition Stateː 

Applying the following settingsː

Atom A: F

Atom B: H

Atom C: H

AB distance: 1.81 Å

BC distance: 0.7455 Å

Both momenta are set to 0.

These settings were applied using the Dynamics Calculation type and visualising the Internuclear Distance vs Time plot. Trial and error values were used until all the distances (A-B, B-C and A-C) produce straight lines, as shown in the figure below.

[[File:Distance_time_1_sp2416.PNG|thumb|centre|Internuclear Distance vs Time graph using Dynamics calculation type for F-H-H]]

 Reporting the Activation Energyː 

To find the activation energy, the type of calculation used is MEP and the AB distance is displaced slightly (form 1.81 is changed to 1.83) in order to force the reaction to go to either direction of the equilibrium - right hand side or left hand side.

The forward reaction in the equilibrium F + H2 ⇌ H + HF is exothermic. Hammond's postulate states that the transition state resembles more the reactants than the products in an exothermic reaction. Hence, the activation energy is obtained when the A-B distance is displaced in this calculation.

Energy of the transition state = -103.752 kJ/mol

Energy of products = -133.466 kJ/mol

Activation energy of the reaction = 29.714 kJ/mol

Activationenergysp2416.PNG

[[File:Activationenergysp2416.PNG|thumb|centre|Calculation of the activation energy]]

== References ==

<references>
<ref name="[1]">J.C. Polanyi, D.C. Tardy, 1969, J. Chem. Phys., Vol.51 "Energy Distribution in the Exothermic Reaction F + H2 , and the Endothermic Reaction HF + H", p.255-321.</ref>

<ref name="[2]">http://www.wiredchemist.com/chemistry/data/bond_energies_lengths.html (Assessed on 15/05/2018 17ː10).</ref>
</references>

File:Activationenergysp2416.PNG

2018-05-15T16:55:33Z

Sp2416:

MRD:sp2416

2018-05-15T16:53:04Z

Sp2416: /* PES Inspection */

==H + H2==

===Transition State ===

The transition state is defined a the maximum on the minimum energy path linking reactants and products. Both minima and transition states are saddle points on the potential energy surface. On the potential energy surface diagram of H + H2 analysed, the gradient of both the transition state and minimum are found to be zero (∂V(ri)/∂ri=0). Minima and transition structures can be distinguished by taking the second derivative of the gradient. For transition state this will be negative and positive, while for minima the answer to this will be positive.

===Locating the Transition State===

[[File:Internucleardistancesp2416.PNG|thumb|centre|Internuclear Distance vs Time plot for H + H2]]

On the first graph the Transition state is where the A-B and B-C lines cross.

To locate the Transition state the momenta are changed to 0, (as a transition state is a saddle point) and then the distances AB and BC are adjusted so as to get an Internuclear Distance graph where both distances are stationary. This distance is found to be stationary when both AB and BC are set to be 0.90755.

[[File:InternucleardistanceTSsp2416.PNG|thumb|centre|Internuclear Distance vs Time plot for H + H2 Transition state]]

===Dynamic and mep Calculation types===

The following results were obtained when the AB distance was changed to 0.90855 and the BC distance was maintained at 0.09755 (transition state position)

[[File:Trajectory_plot_dynamics_sp2416.PNG|thumb|centre|Trajectory plot using Dynamics calculation type]]

[[File:Trajectory_plot_mep_sp2416.PNG|thumb|centre|Trajectory plot using mep calculation type]]

[[File:Distance_time_dynamics_sp2416.PNG|thumb|centre|Internuclear Distance vs Time graph using Dynamics calculation type]]

[[File:Distance_time_mep_sp2416.PNG|thumb|centre|Internuclear Distance vs Time graph using mep calculation type]]

===Reactive and Unreactive Trajectories===

{| class="wikitable" border="1"
|+ Effect of different momenta on reactivity
! p1 !! p2 !! Total Energy!!Type of Trajectory!!Contour plot!!Description
|-
| -1.25 || -2.5 || -99.199 || Reactive || [[File:Contour1_sp2416.PNG|320px]] || cell ||
|-
| -1.5 || -2.0 || -100.456 || Uneactive || [[File:Contour2_sp2416.PNG|320px]] || cell ||
|-
| -1.5 || -2.5 || -98.956 || Reactive || [[File:Contour3_sp2416.PNG|320px]] || cell ||
|-
| -2.5 || -5.0 || -84.956 || Uneactive || [[File:Contour4_sp2416.PNG|320px]] || cell ||
|-
| -2.5 || -5.2 || -83.416 || Reactive || [[File:Contour5_sp2416.PNG|320px]] || cell ||
|}

===Transition State Theory===

Complete

==F - H - H ==

=== PES Inspection ===

The equilibrium reaction F + H2 ⇌ H + HF is exothermic when it goes forward releasing energy, whilst the backward reaction is endothermic, taking energy in. <ref name="[1]" /> The H-H bond is -432 kJ/mol and the H-F bond is -565 kj/mol <ref name="[2]" />. This means that more energy is needed to break the H-F than the energy gained by forming the H-H bond, and hence the forward reaction is exothermic (and the backward endothermic).

 Locating the Transition Stateː 

Applying the following settingsː

Atom A: F

Atom B: H

Atom C: H

AB distance: 1.81 Å

BC distance: 0.7455 Å

Both momenta are set to 0.

These settings were applied using the Dynamics Calculation type and visualising the Internuclear Distance vs Time plot. Trial and error values were used until all the distances (A-B, B-C and A-C) produce straight lines, as shown in the figure below.

[[File:Distance_time_1_sp2416.PNG|thumb|centre|Internuclear Distance vs Time graph using Dynamics calculation type for F-H-H]]

 Reporting the Activation Energyː 

To find the activation energy, the type of calculation used is MEP and the AB distance is displaced slightly (form 1.81 is changed to 1.83) in order to force the reaction to go to either direction of the equilibrium - right hand side or left hand side.

The forward reaction in the equilibrium F + H2 ⇌ H + HF is exothermic. Hammond's postulate states that the transition state resembles more the reactants than the products in an exothermic reaction. Hence, the activation energy is obtained when the A-B distance is displaced in this calculation.

Energy of the transition state = -103.752 kJ/mol

Energy of products = -133.466 kJ/mol

Activation energy of the reaction = 29.714 kJ/mol

== References ==

<references>
<ref name="[1]">J.C. Polanyi, D.C. Tardy, 1969, J. Chem. Phys., Vol.51 "Energy Distribution in the Exothermic Reaction F + H2 , and the Endothermic Reaction HF + H", p.255-321.</ref>

<ref name="[2]">http://www.wiredchemist.com/chemistry/data/bond_energies_lengths.html (Assessed on 15/05/2018 17ː10).</ref>
</references>

MRD:sp2416

2018-05-15T16:44:20Z

Sp2416: /* PES Inspection */

==H + H2==

===Transition State ===

The transition state is defined a the maximum on the minimum energy path linking reactants and products. Both minima and transition states are saddle points on the potential energy surface. On the potential energy surface diagram of H + H2 analysed, the gradient of both the transition state and minimum are found to be zero (∂V(ri)/∂ri=0). Minima and transition structures can be distinguished by taking the second derivative of the gradient. For transition state this will be negative and positive, while for minima the answer to this will be positive.

===Locating the Transition State===

[[File:Internucleardistancesp2416.PNG|thumb|centre|Internuclear Distance vs Time plot for H + H2]]

On the first graph the Transition state is where the A-B and B-C lines cross.

To locate the Transition state the momenta are changed to 0, (as a transition state is a saddle point) and then the distances AB and BC are adjusted so as to get an Internuclear Distance graph where both distances are stationary. This distance is found to be stationary when both AB and BC are set to be 0.90755.

[[File:InternucleardistanceTSsp2416.PNG|thumb|centre|Internuclear Distance vs Time plot for H + H2 Transition state]]

===Dynamic and mep Calculation types===

The following results were obtained when the AB distance was changed to 0.90855 and the BC distance was maintained at 0.09755 (transition state position)

[[File:Trajectory_plot_dynamics_sp2416.PNG|thumb|centre|Trajectory plot using Dynamics calculation type]]

[[File:Trajectory_plot_mep_sp2416.PNG|thumb|centre|Trajectory plot using mep calculation type]]

[[File:Distance_time_dynamics_sp2416.PNG|thumb|centre|Internuclear Distance vs Time graph using Dynamics calculation type]]

[[File:Distance_time_mep_sp2416.PNG|thumb|centre|Internuclear Distance vs Time graph using mep calculation type]]

===Reactive and Unreactive Trajectories===

{| class="wikitable" border="1"
|+ Effect of different momenta on reactivity
! p1 !! p2 !! Total Energy!!Type of Trajectory!!Contour plot!!Description
|-
| -1.25 || -2.5 || -99.199 || Reactive || [[File:Contour1_sp2416.PNG|320px]] || cell ||
|-
| -1.5 || -2.0 || -100.456 || Uneactive || [[File:Contour2_sp2416.PNG|320px]] || cell ||
|-
| -1.5 || -2.5 || -98.956 || Reactive || [[File:Contour3_sp2416.PNG|320px]] || cell ||
|-
| -2.5 || -5.0 || -84.956 || Uneactive || [[File:Contour4_sp2416.PNG|320px]] || cell ||
|-
| -2.5 || -5.2 || -83.416 || Reactive || [[File:Contour5_sp2416.PNG|320px]] || cell ||
|}

===Transition State Theory===

Complete

==F - H - H ==

=== PES Inspection ===

The equilibrium reaction F + H2 ⇌ H + HF is exothermic when it goes forward releasing energy, whilst the backward reaction is endothermic, taking energy in. <ref name="[1]" /> The H-H bond is -432 kJ/mol and the H-F bond is -565 kj/mol <ref name="[2]" />. This means that more energy is needed to break the H-F than the energy gained by forming the H-H bond, and hence the forward reaction is exothermic (and the backward endothermic).

 Locating the Transition Stateː 

Applying the following settingsː

Atom A: F

Atom B: H

Atom C: H

AB distance: 1.81 Å

BC distance: 0.7455 Å

Both momenta are set to 0.

These settings were applied using the Dynamics Calculation type and visualising the Internuclear Distance vs Time plot. Trial and error values were used until all the distances (A-B, B-C and A-C) produce straight lines, as shown in the figure below.

[[File:Distance_time_1_sp2416.PNG|thumb|centre|Internuclear Distance vs Time graph using Dynamics calculation type for F-H-H]]

 Reporting the Activation Energyː 

To find the activation energy, the type of calculation used is MEP and the AB distance is displaced slightly (form 1.81 is changed to 1.83) in order to force the reaction to go to either direction of the equilibrium - right hand side or left hand side.

The forward reaction in the equilibrium F + H2 ⇌ H + HF is exothermic. Hammond's postulate states that the transition state resembles more the reactants than the products in an exothermic reaction. Hence, the activation energy is obtained when the A-B distance is displaced in this calculation.

Energy of the transition state = -103.752

Energy of products =

Activation energy of the reaction =

== References ==

<references>
<ref name="[1]">J.C. Polanyi, D.C. Tardy, 1969, J. Chem. Phys., Vol.51 "Energy Distribution in the Exothermic Reaction F + H2 , and the Endothermic Reaction HF + H", p.255-321.</ref>

<ref name="[2]">http://www.wiredchemist.com/chemistry/data/bond_energies_lengths.html (Assessed on 15/05/2018 17ː10).</ref>
</references>

MRD:sp2416

2018-05-15T16:31:29Z

Sp2416: /* PES Inspection */

==H + H2==

===Transition State ===

The transition state is defined a the maximum on the minimum energy path linking reactants and products. Both minima and transition states are saddle points on the potential energy surface. On the potential energy surface diagram of H + H2 analysed, the gradient of both the transition state and minimum are found to be zero (∂V(ri)/∂ri=0). Minima and transition structures can be distinguished by taking the second derivative of the gradient. For transition state this will be negative and positive, while for minima the answer to this will be positive.

===Locating the Transition State===

[[File:Internucleardistancesp2416.PNG|thumb|centre|Internuclear Distance vs Time plot for H + H2]]

On the first graph the Transition state is where the A-B and B-C lines cross.

To locate the Transition state the momenta are changed to 0, (as a transition state is a saddle point) and then the distances AB and BC are adjusted so as to get an Internuclear Distance graph where both distances are stationary. This distance is found to be stationary when both AB and BC are set to be 0.90755.

[[File:InternucleardistanceTSsp2416.PNG|thumb|centre|Internuclear Distance vs Time plot for H + H2 Transition state]]

===Dynamic and mep Calculation types===

The following results were obtained when the AB distance was changed to 0.90855 and the BC distance was maintained at 0.09755 (transition state position)

[[File:Trajectory_plot_dynamics_sp2416.PNG|thumb|centre|Trajectory plot using Dynamics calculation type]]

[[File:Trajectory_plot_mep_sp2416.PNG|thumb|centre|Trajectory plot using mep calculation type]]

[[File:Distance_time_dynamics_sp2416.PNG|thumb|centre|Internuclear Distance vs Time graph using Dynamics calculation type]]

[[File:Distance_time_mep_sp2416.PNG|thumb|centre|Internuclear Distance vs Time graph using mep calculation type]]

===Reactive and Unreactive Trajectories===

{| class="wikitable" border="1"
|+ Effect of different momenta on reactivity
! p1 !! p2 !! Total Energy!!Type of Trajectory!!Contour plot!!Description
|-
| -1.25 || -2.5 || -99.199 || Reactive || [[File:Contour1_sp2416.PNG|320px]] || cell ||
|-
| -1.5 || -2.0 || -100.456 || Uneactive || [[File:Contour2_sp2416.PNG|320px]] || cell ||
|-
| -1.5 || -2.5 || -98.956 || Reactive || [[File:Contour3_sp2416.PNG|320px]] || cell ||
|-
| -2.5 || -5.0 || -84.956 || Uneactive || [[File:Contour4_sp2416.PNG|320px]] || cell ||
|-
| -2.5 || -5.2 || -83.416 || Reactive || [[File:Contour5_sp2416.PNG|320px]] || cell ||
|}

===Transition State Theory===

Complete

==F - H - H ==

=== PES Inspection ===

The equilibrium reaction F + H2 ⇌ H + HF is exothermic when it goes forward releasing energy, whilst the backward reaction is endothermic, taking energy in. <ref name="[1]" /> The H-H bond is -432 kJ/mol and the H-F bond is -565 kj/mol <ref name="[2]" />. This means that more energy is needed to break the H-F than the energy gained by forming the H-H bond, and hence the forward reaction is exothermic (and the backward endothermic).

 Locating the Transition Stateː 

Applying the following settingsː

Atom A: F

Atom B: H

Atom C: H

AB distance: 1.81

BC distance: 0.7455

Both momenta are set to 0.

These settings were applied using the Dynamics Calculation type and visualising the Internuclear Distance vs Time plot. Trial and error values were used until all the distances (A-B, B-C and A-C) produce straight lines, as shown in the figure below.

[[File:Distance_time_1_sp2416.PNG|thumb|centre|Internuclear Distance vs Time graph using Dynamics calculation type for F-H-H]]

 Reporting the Activation Energyː 

To find the activation energy, the type of calculation used is MEP and the AB distance is displaced slightly (form 1.81 is changed to 1.83) in order to force the reaction to go to either direction of the equilibrium - right hand side or left hand side.

The forward reaction in the equilibrium F + H2 ⇌ H + HF is exothermic. Hammond's postulate states that the transition state resembles more the reactants than the products in an exothermic reaction. Hence, the activation energy is obtained when the A-B distance is displaced in this calculation.

Energy of the transition state = -103.752

Energy of products =

Activation energy of the reaction =

== References ==

<references>
<ref name="[1]">J.C. Polanyi, D.C. Tardy, 1969, J. Chem. Phys., Vol.51 "Energy Distribution in the Exothermic Reaction F + H2 , and the Endothermic Reaction HF + H", p.255-321.</ref>

<ref name="[2]">http://www.wiredchemist.com/chemistry/data/bond_energies_lengths.html (Assessed on 15/05/2018 17ː10).</ref>
</references>

MRD:sp2416

2018-05-15T16:31:16Z

Sp2416: /* PES Inspection */

==H + H2==

===Transition State ===

The transition state is defined a the maximum on the minimum energy path linking reactants and products. Both minima and transition states are saddle points on the potential energy surface. On the potential energy surface diagram of H + H2 analysed, the gradient of both the transition state and minimum are found to be zero (∂V(ri)/∂ri=0). Minima and transition structures can be distinguished by taking the second derivative of the gradient. For transition state this will be negative and positive, while for minima the answer to this will be positive.

===Locating the Transition State===

[[File:Internucleardistancesp2416.PNG|thumb|centre|Internuclear Distance vs Time plot for H + H2]]

On the first graph the Transition state is where the A-B and B-C lines cross.

To locate the Transition state the momenta are changed to 0, (as a transition state is a saddle point) and then the distances AB and BC are adjusted so as to get an Internuclear Distance graph where both distances are stationary. This distance is found to be stationary when both AB and BC are set to be 0.90755.

[[File:InternucleardistanceTSsp2416.PNG|thumb|centre|Internuclear Distance vs Time plot for H + H2 Transition state]]

===Dynamic and mep Calculation types===

The following results were obtained when the AB distance was changed to 0.90855 and the BC distance was maintained at 0.09755 (transition state position)

[[File:Trajectory_plot_dynamics_sp2416.PNG|thumb|centre|Trajectory plot using Dynamics calculation type]]

[[File:Trajectory_plot_mep_sp2416.PNG|thumb|centre|Trajectory plot using mep calculation type]]

[[File:Distance_time_dynamics_sp2416.PNG|thumb|centre|Internuclear Distance vs Time graph using Dynamics calculation type]]

[[File:Distance_time_mep_sp2416.PNG|thumb|centre|Internuclear Distance vs Time graph using mep calculation type]]

===Reactive and Unreactive Trajectories===

{| class="wikitable" border="1"
|+ Effect of different momenta on reactivity
! p1 !! p2 !! Total Energy!!Type of Trajectory!!Contour plot!!Description
|-
| -1.25 || -2.5 || -99.199 || Reactive || [[File:Contour1_sp2416.PNG|320px]] || cell ||
|-
| -1.5 || -2.0 || -100.456 || Uneactive || [[File:Contour2_sp2416.PNG|320px]] || cell ||
|-
| -1.5 || -2.5 || -98.956 || Reactive || [[File:Contour3_sp2416.PNG|320px]] || cell ||
|-
| -2.5 || -5.0 || -84.956 || Uneactive || [[File:Contour4_sp2416.PNG|320px]] || cell ||
|-
| -2.5 || -5.2 || -83.416 || Reactive || [[File:Contour5_sp2416.PNG|320px]] || cell ||
|}

===Transition State Theory===

Complete

==F - H - H ==

=== PES Inspection ===

The equilibrium reaction F + H2 ⇌ H + HF is exothermic when it goes forward releasing energy, whilst the backward reaction is endothermic, taking energy in. <ref name="[1]" /> The H-H bond is -432 kJ/mol and the H-F bond is -565 kj/mol <ref name="[2]" />. This means that more energy is needed to break the H-F than the energy gained by forming the H-H bond, and hence the forward reaction is exothermic (and the backward endothermic).

 Locating the Transition Stateː 

Applying the following settingsː

Atom A: F

Atom B: H

Atom C: H

AB distance: 1.81

BC distance: 0.7455

Both momenta are set to 0.

These settings were applied using the Dynamics Calculation type and visualising the Internuclear Distance vs Time plot. Trial and error values were used until all the distances (A-B, B-C and A-C) produce straight lines, as shown in the figure below.

[[File:Distance_time_1_sp2416.PNG|thumb|centre|Internuclear Distance vs Time graph using Dynamics calculation type for F-H-H]]

 Reporting the Activation Energyː 

To find the activation energy, the type of calculation used is MEP and the AB distance is displaced slightly (form 1.81 is changed to 1.83) in order to force the reaction to go to either direction of the equilibrium - right hand side or left hand side.

The forward reaction in the equilibrium F + H2 ⇌ H + HF is exothermic. Hammond's postulate states that the transition state resembles more the reactants than the products in an exothermic reaction. Hence, the activation energy is obtained when the A-B distance is displaced in this calculation.

Energy of the transition state = -103.752

Energy of products = -104.005

Activation energy of the reaction = 0.253

== References ==

<references>
<ref name="[1]">J.C. Polanyi, D.C. Tardy, 1969, J. Chem. Phys., Vol.51 "Energy Distribution in the Exothermic Reaction F + H2 , and the Endothermic Reaction HF + H", p.255-321.</ref>

<ref name="[2]">http://www.wiredchemist.com/chemistry/data/bond_energies_lengths.html (Assessed on 15/05/2018 17ː10).</ref>
</references>

MRD:sp2416

2018-05-15T16:19:24Z

Sp2416: /* PES Inspection */

==H + H2==

===Transition State ===

The transition state is defined a the maximum on the minimum energy path linking reactants and products. Both minima and transition states are saddle points on the potential energy surface. On the potential energy surface diagram of H + H2 analysed, the gradient of both the transition state and minimum are found to be zero (∂V(ri)/∂ri=0). Minima and transition structures can be distinguished by taking the second derivative of the gradient. For transition state this will be negative and positive, while for minima the answer to this will be positive.

===Locating the Transition State===

[[File:Internucleardistancesp2416.PNG|thumb|centre|Internuclear Distance vs Time plot for H + H2]]

On the first graph the Transition state is where the A-B and B-C lines cross.

To locate the Transition state the momenta are changed to 0, (as a transition state is a saddle point) and then the distances AB and BC are adjusted so as to get an Internuclear Distance graph where both distances are stationary. This distance is found to be stationary when both AB and BC are set to be 0.90755.

[[File:InternucleardistanceTSsp2416.PNG|thumb|centre|Internuclear Distance vs Time plot for H + H2 Transition state]]

===Dynamic and mep Calculation types===

The following results were obtained when the AB distance was changed to 0.90855 and the BC distance was maintained at 0.09755 (transition state position)

[[File:Trajectory_plot_dynamics_sp2416.PNG|thumb|centre|Trajectory plot using Dynamics calculation type]]

[[File:Trajectory_plot_mep_sp2416.PNG|thumb|centre|Trajectory plot using mep calculation type]]

[[File:Distance_time_dynamics_sp2416.PNG|thumb|centre|Internuclear Distance vs Time graph using Dynamics calculation type]]

[[File:Distance_time_mep_sp2416.PNG|thumb|centre|Internuclear Distance vs Time graph using mep calculation type]]

===Reactive and Unreactive Trajectories===

{| class="wikitable" border="1"
|+ Effect of different momenta on reactivity
! p1 !! p2 !! Total Energy!!Type of Trajectory!!Contour plot!!Description
|-
| -1.25 || -2.5 || -99.199 || Reactive || [[File:Contour1_sp2416.PNG|320px]] || cell ||
|-
| -1.5 || -2.0 || -100.456 || Uneactive || [[File:Contour2_sp2416.PNG|320px]] || cell ||
|-
| -1.5 || -2.5 || -98.956 || Reactive || [[File:Contour3_sp2416.PNG|320px]] || cell ||
|-
| -2.5 || -5.0 || -84.956 || Uneactive || [[File:Contour4_sp2416.PNG|320px]] || cell ||
|-
| -2.5 || -5.2 || -83.416 || Reactive || [[File:Contour5_sp2416.PNG|320px]] || cell ||
|}

===Transition State Theory===

Complete

==F - H - H ==

=== PES Inspection ===

The equilibrium reaction F + H2 ⇌ H + HF is exothermic when it goes forward releasing energy, whilst the backward reaction is endothermic, taking energy in. <ref name="[1]" /> The H-H bond is -432 kJ/mol and the H-F bond is -565 kj/mol <ref name="[2]" />. This means that more energy is needed to break the H-F than the energy gained by forming the H-H bond, and hence the forward reaction is exothermic (and the backward endothermic).

 Locating the Transition Stateː 

Applying the following settingsː

Atom A: F
Atom B: H
Atom C: H

AB distance: 1.81
BC distance: 0.7456

Both momenta are set to 0.

These settings were applied using the Dynamics Calculation type and visualising the Internuclear Distance vs Time plot. Trial and error values were used until all the distances (A-B, B-C and A-C) produce straight lines, as shown in the figure below.

[[File:Distance_time_1_sp2416.PNG|thumb|centre|Internuclear Distance vs Time graph using Dynamics calculation type for F-H-H]]

== References ==

<references>
<ref name="[1]">J.C. Polanyi, D.C. Tardy, 1969, J. Chem. Phys., Vol.51 "Energy Distribution in the Exothermic Reaction F + H2 , and the Endothermic Reaction HF + H", p.255-321.</ref>

<ref name="[2]">http://www.wiredchemist.com/chemistry/data/bond_energies_lengths.html (Assessed on 15/05/2018 17ː10).</ref>
</references>

MRD:sp2416

2018-05-15T16:18:42Z

Sp2416: /* Dynamic and mep Calculation types */

MRD:sp2416

2018-05-15T16:18:33Z

Sp2416: /* PES Inspection */

File:Distance time 1 sp2416.PNG

2018-05-15T16:18:31Z

Sp2416:

MRD:sp2416

2018-05-15T16:16:03Z

Sp2416: /* PES Inspection */