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MRD:FMJ17

2019-05-24T14:58:39Z

Fmj17: /* State what are the main assumptions of Transition State Theory. Given the results you have obtained, how will Transition State Theory predictions for reaction rate values compare with experimental values? */

=Exercise 1=
===On a potential energy surface diagram, how is the transition state mathematically defined? How can the transition state be identified, and how can it be distinguished from a local minimum of the potential energy surface?===
The transition state is defined as the point at which the potential gradient is zero, δV(ri)/δ(ri)=0. Contrary to local minima in the enrgy surface, the transition state will be at the point along the reaction path where the energy is maximum.
===Trajectories from r1 = r2: locating the transition state===
transition state position, rts=0.90775 Å
====Internuclear Dictances vs Time Plot====
[[File:Int_nuc_1_fmj.PNG]]
The straight lines indicate no vibrations. This indicates that the momenta are zero, confirming that the point corresponds to the transition state.
===Calculating the Reaction Path===
====Minimum Energy Pathway Calculation====
The figure below shows a surface plot obtained using the MEP calculation type. The black line illustrates the reaction path (from the transition state to the products).
[[File:Surface_Plot_mep_fmj.png]]

Below is the contour plot, showing the same reaction path. (black line)

[[File:Contour_plot_mep_fmj.png]]

====Comparing Dynamics and MEP Calculation Types====
Below is a surface plot obtained by using the dynamics calculation type.
[[File:Surface_Plot_dyn_fmj.png]]

Again, the black line shows the the reaction path (from the transition state to the products). This calculation was made using the same initial conditions as the MEP calculation above.

The two trajectories calculated using the two calculation types are different. The dynamic calculation indicates vibrations (curves on the line), while the MEP calculation does not (no curves).

===Reactive and unreactive trajectories===

{| class="wikitable" border=1
! p1 !! p2 !! Etot !! Reactive? !! Description of the dynamics !! Illustration of the trajectory
|-
| -1.25 || -2.5 ||-99.018 ||Yes||The hydrogen atom collides with the hydrogen molecule, the transition state forms. Eventually, the original H-H bond breaks and a new one is formed.||[[File:Contour_1_fmj.png|150px]]
|-
| -1.5 || -2.0 ||-100.456 ||No ||The hydrogen atom collides with the hydrogen molecule, the transition state does not form. The atom and the molecule bounce off each other and move in opposite directions. ||[[File:Contour_2_fmj.png|150px]]
|-
| -1.5 || -2.5 ||-98.956 ||Yes ||The hydrogen atom collides with the hydrogen molecule, the transition state forms. Eventually, the original H-H bond breaks and a new one is formed. ||[[File:Contour_3_fmj.png|150px]]
|-
| -2.5 || -5.0 ||-84.956 ||No ||The hydrogen atom collides with the hydrogen molecule, the transition state forms, but the original bond does not break. Instead, the molecule and the atom move away from each other. ||[[File:Contour_4_fmj.png|150px]]
|-
| -2.5 || -5.2 ||-83.416 ||Yes ||The hydrogen atom collides with the hydrogen molecule, the transition state forms, then break downs back into lower energy structures. It is then formed again, followed by the products. ||[[File:Contour_5_fmj.png|150px]]
|}

=Exercise 2=
===Potential Energy Surface inspection of F-H-H system===
Below is a surface plot for the F-H-H system.
[[File:H2_f_surface_potential_fmj.png]]
It shows H-H and F as being more energetic than F-H and H. This indicates that the reaction between H-H and F is exothermic and that the H-F bond is stronger than the H-H bond. It also indicates that the reaction between H-F and H is endothermic, again because the H-F bond is stronger than the H-H bond.

====Transition State====
Below is a surface plot showing the position of the transition state (black dot) of the H-H + F reaction.
[[File:F_h_TS_fmj.png]]

====Activation Energy====
The activation energy for the H-H + F reaction is 30 kcal/mol.

[[File:Activation_energy.png]]

The activation energy for the H-F + H reaction is 0.15 kcal/mol.

[[File:Act_energy_2_fmj.png]]

===Reaction dynamics===
A set of initial conditions which result in a reaction is shown below.

[[File:In_con_fmj.PNG]]

This is the momentum vs Time graph for the reaction trajectory resulting from the initial conditions above.

[[File:Momenta_time_fh_fmj.png]]

==== In light of the fact that energy is conserved, discuss the mechanism of release of the reaction energy. Explain how this could be confirmed experimentally.====
The formation of HF is an exothermic process. The formation of the H-F bond releases more energy than is used to break the H-H bond. This can be confirmed by observing an increase in temperature corresponding to the release of energy.

{| class="wikitable" border=1
! pFH !! pHH !! Reactive? !! Comments !! Plots
|-
| -0.5 || -3.0 ||Yes||The graph shows that the H-H distance increases with time and the H-F distance initially decreases, but then maintains a constant equilibrium value. This indicates the formation of the F-H bond ||[[File:Mom_1_fmj.png|150px]]
|-
| -0.5 || -2.8 ||Yes ||The graph now shows a reactive trajectory. ||[[File:Plot_2_fmj.png|150px]]
|-
| -0.5 || -2.0 ||No ||The graph shows that the H-H distance maintains a constant equilibrium value with time and the H-F distance initially decreases, but increases with time. This indicates that the F-H bond did not form. ||[[File:Plot2_fmj.png|150px]]
|-
| -0.5 || -1.0 ||No ||The graph shows that the H-H distance maintains a constant equilibrium value with time and the H-F distance initially decreases, but increases with time. This indicates that the F-H bond did not form. ||[[File:Plot3_fmj.png|150px]]
|-
| -0.5 || 0 ||No||The graph shows that the H-H distance maintains a constant equilibrium value with time and the H-F distance initially decreases, but increases with time. This indicates that the F-H bond did not form. ||[[File:Plot4_fmj.png|150px]]
|-
| -0.5 || 1.0 ||No ||The graph shows that the H-H distance maintains a constant equilibrium value with time and the H-F distance initially decreases, but increases with time. This indicates that the F-H bond did not form. ||[[File:Plot5_fmj.png|150px]]
|-
| -0.5 || 2.0 ||Yes ||The graph shows that the H-H distance increases with time and the H-F distance initially decreases, but then maintains a constant equilibrium value. This indicates the formation of the F-H bond ||[[File:Plot6_fmj.png|150px]]
|-
| -0.5 || 2.8 ||No ||The graph shows that the H-H distance maintains a constant equilibrium value with time and the H-F distance initially decreases, but increases with time. This indicates that the F-H bond did not form. ||[[File:Plot7_fmj.png |150px]]
|-
| -0.5 || 3.0 ||No ||The graph shows that the H-H distance maintains a constant equilibrium value with time and the H-F distance initially decreases, but increases with time. This indicates that the F-H bond did not form. ||[[File:Plot8_fmj.png|150px]]
|-
| -0.8 || 0.1 ||Yes||The graph shows that the H-H distance increases with time and the H-F distance initially decreases, but then maintains a constant equilibrium value. This indicates the formation of the F-H bond ||[[File:Plot9_fmj.png|150px]]
|-
|}

===Polanyi's Empirical Rules===
For a reaction with a late transition state, that is the transition state is closer in structure to the products than it is to the reactants, it's success will depend more on the vibrational energy of the reactant molecule than it will on the translational energy of said molecules. For a reaction with an early transition state, the opposite is true; translational energy will be at the main promoter of the reaction.

MRD:FMJ17

2019-05-24T14:57:49Z

Fmj17: /* Polanyi's Empirical Rules */

=Exercise 1=
===On a potential energy surface diagram, how is the transition state mathematically defined? How can the transition state be identified, and how can it be distinguished from a local minimum of the potential energy surface?===
The transition state is defined as the point at which the potential gradient is zero, δV(ri)/δ(ri)=0. Contrary to local minima in the enrgy surface, the transition state will be at the point along the reaction path where the energy is maximum.
===Trajectories from r1 = r2: locating the transition state===
transition state position, rts=0.90775 Å
====Internuclear Dictances vs Time Plot====
[[File:Int_nuc_1_fmj.PNG]]
The straight lines indicate no vibrations. This indicates that the momenta are zero, confirming that the point corresponds to the transition state.
===Calculating the Reaction Path===
====Minimum Energy Pathway Calculation====
The figure below shows a surface plot obtained using the MEP calculation type. The black line illustrates the reaction path (from the transition state to the products).
[[File:Surface_Plot_mep_fmj.png]]

Below is the contour plot, showing the same reaction path. (black line)

[[File:Contour_plot_mep_fmj.png]]

====Comparing Dynamics and MEP Calculation Types====
Below is a surface plot obtained by using the dynamics calculation type.
[[File:Surface_Plot_dyn_fmj.png]]

Again, the black line shows the the reaction path (from the transition state to the products). This calculation was made using the same initial conditions as the MEP calculation above.

The two trajectories calculated using the two calculation types are different. The dynamic calculation indicates vibrations (curves on the line), while the MEP calculation does not (no curves).

===Reactive and unreactive trajectories===

{| class="wikitable" border=1
! p1 !! p2 !! Etot !! Reactive? !! Description of the dynamics !! Illustration of the trajectory
|-
| -1.25 || -2.5 ||-99.018 ||Yes||The hydrogen atom collides with the hydrogen molecule, the transition state forms. Eventually, the original H-H bond breaks and a new one is formed.||[[File:Contour_1_fmj.png|150px]]
|-
| -1.5 || -2.0 ||-100.456 ||No ||The hydrogen atom collides with the hydrogen molecule, the transition state does not form. The atom and the molecule bounce off each other and move in opposite directions. ||[[File:Contour_2_fmj.png|150px]]
|-
| -1.5 || -2.5 ||-98.956 ||Yes ||The hydrogen atom collides with the hydrogen molecule, the transition state forms. Eventually, the original H-H bond breaks and a new one is formed. ||[[File:Contour_3_fmj.png|150px]]
|-
| -2.5 || -5.0 ||-84.956 ||No ||The hydrogen atom collides with the hydrogen molecule, the transition state forms, but the original bond does not break. Instead, the molecule and the atom move away from each other. ||[[File:Contour_4_fmj.png|150px]]
|-
| -2.5 || -5.2 ||-83.416 ||Yes ||The hydrogen atom collides with the hydrogen molecule, the transition state forms, then break downs back into lower energy structures. It is then formed again, followed by the products. ||[[File:Contour_5_fmj.png|150px]]
|}

====State what are the main assumptions of Transition State Theory. Given the results you have obtained, how will Transition State Theory predictions for reaction rate values compare with experimental values?====
The main assumptions are

=Exercise 2=
===Potential Energy Surface inspection of F-H-H system===
Below is a surface plot for the F-H-H system.
[[File:H2_f_surface_potential_fmj.png]]
It shows H-H and F as being more energetic than F-H and H. This indicates that the reaction between H-H and F is exothermic and that the H-F bond is stronger than the H-H bond. It also indicates that the reaction between H-F and H is endothermic, again because the H-F bond is stronger than the H-H bond.

====Transition State====
Below is a surface plot showing the position of the transition state (black dot) of the H-H + F reaction.
[[File:F_h_TS_fmj.png]]

====Activation Energy====
The activation energy for the H-H + F reaction is 30 kcal/mol.

[[File:Activation_energy.png]]

The activation energy for the H-F + H reaction is 0.15 kcal/mol.

[[File:Act_energy_2_fmj.png]]

===Reaction dynamics===
A set of initial conditions which result in a reaction is shown below.

[[File:In_con_fmj.PNG]]

This is the momentum vs Time graph for the reaction trajectory resulting from the initial conditions above.

[[File:Momenta_time_fh_fmj.png]]

==== In light of the fact that energy is conserved, discuss the mechanism of release of the reaction energy. Explain how this could be confirmed experimentally.====
The formation of HF is an exothermic process. The formation of the H-F bond releases more energy than is used to break the H-H bond. This can be confirmed by observing an increase in temperature corresponding to the release of energy.

{| class="wikitable" border=1
! pFH !! pHH !! Reactive? !! Comments !! Plots
|-
| -0.5 || -3.0 ||Yes||The graph shows that the H-H distance increases with time and the H-F distance initially decreases, but then maintains a constant equilibrium value. This indicates the formation of the F-H bond ||[[File:Mom_1_fmj.png|150px]]
|-
| -0.5 || -2.8 ||Yes ||The graph now shows a reactive trajectory. ||[[File:Plot_2_fmj.png|150px]]
|-
| -0.5 || -2.0 ||No ||The graph shows that the H-H distance maintains a constant equilibrium value with time and the H-F distance initially decreases, but increases with time. This indicates that the F-H bond did not form. ||[[File:Plot2_fmj.png|150px]]
|-
| -0.5 || -1.0 ||No ||The graph shows that the H-H distance maintains a constant equilibrium value with time and the H-F distance initially decreases, but increases with time. This indicates that the F-H bond did not form. ||[[File:Plot3_fmj.png|150px]]
|-
| -0.5 || 0 ||No||The graph shows that the H-H distance maintains a constant equilibrium value with time and the H-F distance initially decreases, but increases with time. This indicates that the F-H bond did not form. ||[[File:Plot4_fmj.png|150px]]
|-
| -0.5 || 1.0 ||No ||The graph shows that the H-H distance maintains a constant equilibrium value with time and the H-F distance initially decreases, but increases with time. This indicates that the F-H bond did not form. ||[[File:Plot5_fmj.png|150px]]
|-
| -0.5 || 2.0 ||Yes ||The graph shows that the H-H distance increases with time and the H-F distance initially decreases, but then maintains a constant equilibrium value. This indicates the formation of the F-H bond ||[[File:Plot6_fmj.png|150px]]
|-
| -0.5 || 2.8 ||No ||The graph shows that the H-H distance maintains a constant equilibrium value with time and the H-F distance initially decreases, but increases with time. This indicates that the F-H bond did not form. ||[[File:Plot7_fmj.png |150px]]
|-
| -0.5 || 3.0 ||No ||The graph shows that the H-H distance maintains a constant equilibrium value with time and the H-F distance initially decreases, but increases with time. This indicates that the F-H bond did not form. ||[[File:Plot8_fmj.png|150px]]
|-
| -0.8 || 0.1 ||Yes||The graph shows that the H-H distance increases with time and the H-F distance initially decreases, but then maintains a constant equilibrium value. This indicates the formation of the F-H bond ||[[File:Plot9_fmj.png|150px]]
|-
|}

===Polanyi's Empirical Rules===
For a reaction with a late transition state, that is the transition state is closer in structure to the products than it is to the reactants, it's success will depend more on the vibrational energy of the reactant molecule than it will on the translational energy of said molecules. For a reaction with an early transition state, the opposite is true; translational energy will be at the main promoter of the reaction.

MRD:FMJ17

2019-05-24T14:46:04Z

Fmj17: /* Reaction dynamics */

=Exercise 1=
===On a potential energy surface diagram, how is the transition state mathematically defined? How can the transition state be identified, and how can it be distinguished from a local minimum of the potential energy surface?===
The transition state is defined as the point at which the potential gradient is zero, δV(ri)/δ(ri)=0. Contrary to local minima in the enrgy surface, the transition state will be at the point along the reaction path where the energy is maximum.
===Trajectories from r1 = r2: locating the transition state===
transition state position, rts=0.90775 Å
====Internuclear Dictances vs Time Plot====
[[File:Int_nuc_1_fmj.PNG]]
The straight lines indicate no vibrations. This indicates that the momenta are zero, confirming that the point corresponds to the transition state.
===Calculating the Reaction Path===
====Minimum Energy Pathway Calculation====
The figure below shows a surface plot obtained using the MEP calculation type. The black line illustrates the reaction path (from the transition state to the products).
[[File:Surface_Plot_mep_fmj.png]]

Below is the contour plot, showing the same reaction path. (black line)

[[File:Contour_plot_mep_fmj.png]]

====Comparing Dynamics and MEP Calculation Types====
Below is a surface plot obtained by using the dynamics calculation type.
[[File:Surface_Plot_dyn_fmj.png]]

Again, the black line shows the the reaction path (from the transition state to the products). This calculation was made using the same initial conditions as the MEP calculation above.

The two trajectories calculated using the two calculation types are different. The dynamic calculation indicates vibrations (curves on the line), while the MEP calculation does not (no curves).

===Reactive and unreactive trajectories===

{| class="wikitable" border=1
! p1 !! p2 !! Etot !! Reactive? !! Description of the dynamics !! Illustration of the trajectory
|-
| -1.25 || -2.5 ||-99.018 ||Yes||The hydrogen atom collides with the hydrogen molecule, the transition state forms. Eventually, the original H-H bond breaks and a new one is formed.||[[File:Contour_1_fmj.png|150px]]
|-
| -1.5 || -2.0 ||-100.456 ||No ||The hydrogen atom collides with the hydrogen molecule, the transition state does not form. The atom and the molecule bounce off each other and move in opposite directions. ||[[File:Contour_2_fmj.png|150px]]
|-
| -1.5 || -2.5 ||-98.956 ||Yes ||The hydrogen atom collides with the hydrogen molecule, the transition state forms. Eventually, the original H-H bond breaks and a new one is formed. ||[[File:Contour_3_fmj.png|150px]]
|-
| -2.5 || -5.0 ||-84.956 ||No ||The hydrogen atom collides with the hydrogen molecule, the transition state forms, but the original bond does not break. Instead, the molecule and the atom move away from each other. ||[[File:Contour_4_fmj.png|150px]]
|-
| -2.5 || -5.2 ||-83.416 ||Yes ||The hydrogen atom collides with the hydrogen molecule, the transition state forms, then break downs back into lower energy structures. It is then formed again, followed by the products. ||[[File:Contour_5_fmj.png|150px]]
|}

====State what are the main assumptions of Transition State Theory. Given the results you have obtained, how will Transition State Theory predictions for reaction rate values compare with experimental values?====
The main assumptions are

=Exercise 2=
===Potential Energy Surface inspection of F-H-H system===
Below is a surface plot for the F-H-H system.
[[File:H2_f_surface_potential_fmj.png]]
It shows H-H and F as being more energetic than F-H and H. This indicates that the reaction between H-H and F is exothermic and that the H-F bond is stronger than the H-H bond. It also indicates that the reaction between H-F and H is endothermic, again because the H-F bond is stronger than the H-H bond.

====Transition State====
Below is a surface plot showing the position of the transition state (black dot) of the H-H + F reaction.
[[File:F_h_TS_fmj.png]]

====Activation Energy====
The activation energy for the H-H + F reaction is 30 kcal/mol.

[[File:Activation_energy.png]]

The activation energy for the H-F + H reaction is 0.15 kcal/mol.

[[File:Act_energy_2_fmj.png]]

===Reaction dynamics===
A set of initial conditions which result in a reaction is shown below.

[[File:In_con_fmj.PNG]]

This is the momentum vs Time graph for the reaction trajectory resulting from the initial conditions above.

[[File:Momenta_time_fh_fmj.png]]

==== In light of the fact that energy is conserved, discuss the mechanism of release of the reaction energy. Explain how this could be confirmed experimentally.====
The formation of HF is an exothermic process. The formation of the H-F bond releases more energy than is used to break the H-H bond. This can be confirmed by observing an increase in temperature corresponding to the release of energy.

{| class="wikitable" border=1
! pFH !! pHH !! Reactive? !! Comments !! Plots
|-
| -0.5 || -3.0 ||Yes||The graph shows that the H-H distance increases with time and the H-F distance initially decreases, but then maintains a constant equilibrium value. This indicates the formation of the F-H bond ||[[File:Mom_1_fmj.png|150px]]
|-
| -0.5 || -2.8 ||Yes ||The graph now shows a reactive trajectory. ||[[File:Plot_2_fmj.png|150px]]
|-
| -0.5 || -2.0 ||No ||The graph shows that the H-H distance maintains a constant equilibrium value with time and the H-F distance initially decreases, but increases with time. This indicates that the F-H bond did not form. ||[[File:Plot2_fmj.png|150px]]
|-
| -0.5 || -1.0 ||No ||The graph shows that the H-H distance maintains a constant equilibrium value with time and the H-F distance initially decreases, but increases with time. This indicates that the F-H bond did not form. ||[[File:Plot3_fmj.png|150px]]
|-
| -0.5 || 0 ||No||The graph shows that the H-H distance maintains a constant equilibrium value with time and the H-F distance initially decreases, but increases with time. This indicates that the F-H bond did not form. ||[[File:Plot4_fmj.png|150px]]
|-
| -0.5 || 1.0 ||No ||The graph shows that the H-H distance maintains a constant equilibrium value with time and the H-F distance initially decreases, but increases with time. This indicates that the F-H bond did not form. ||[[File:Plot5_fmj.png|150px]]
|-
| -0.5 || 2.0 ||Yes ||The graph shows that the H-H distance increases with time and the H-F distance initially decreases, but then maintains a constant equilibrium value. This indicates the formation of the F-H bond ||[[File:Plot6_fmj.png|150px]]
|-
| -0.5 || 2.8 ||No ||The graph shows that the H-H distance maintains a constant equilibrium value with time and the H-F distance initially decreases, but increases with time. This indicates that the F-H bond did not form. ||[[File:Plot7_fmj.png |150px]]
|-
| -0.5 || 3.0 ||No ||The graph shows that the H-H distance maintains a constant equilibrium value with time and the H-F distance initially decreases, but increases with time. This indicates that the F-H bond did not form. ||[[File:Plot8_fmj.png|150px]]
|-
| -0.8 || 0.1 ||Yes||The graph shows that the H-H distance increases with time and the H-F distance initially decreases, but then maintains a constant equilibrium value. This indicates the formation of the F-H bond ||[[File:Plot9_fmj.png|150px]]
|-
|}

===Polanyi's Empirical Rules===

MRD:FMJ17

2019-05-24T14:41:39Z

=Exercise 1=
===On a potential energy surface diagram, how is the transition state mathematically defined? How can the transition state be identified, and how can it be distinguished from a local minimum of the potential energy surface?===
The transition state is defined as the point at which the potential gradient is zero, δV(ri)/δ(ri)=0. Contrary to local minima in the enrgy surface, the transition state will be at the point along the reaction path where the energy is maximum.
===Trajectories from r1 = r2: locating the transition state===
transition state position, rts=0.90775 Å
====Internuclear Dictances vs Time Plot====
[[File:Int_nuc_1_fmj.PNG]]
The straight lines indicate no vibrations. This indicates that the momenta are zero, confirming that the point corresponds to the transition state.
===Calculating the Reaction Path===
====Minimum Energy Pathway Calculation====
The figure below shows a surface plot obtained using the MEP calculation type. The black line illustrates the reaction path (from the transition state to the products).
[[File:Surface_Plot_mep_fmj.png]]

Below is the contour plot, showing the same reaction path. (black line)

[[File:Contour_plot_mep_fmj.png]]

====Comparing Dynamics and MEP Calculation Types====
Below is a surface plot obtained by using the dynamics calculation type.
[[File:Surface_Plot_dyn_fmj.png]]

Again, the black line shows the the reaction path (from the transition state to the products). This calculation was made using the same initial conditions as the MEP calculation above.

The two trajectories calculated using the two calculation types are different. The dynamic calculation indicates vibrations (curves on the line), while the MEP calculation does not (no curves).

===Reactive and unreactive trajectories===

{| class="wikitable" border=1
! p1 !! p2 !! Etot !! Reactive? !! Description of the dynamics !! Illustration of the trajectory
|-
| -1.25 || -2.5 ||-99.018 ||Yes||The hydrogen atom collides with the hydrogen molecule, the transition state forms. Eventually, the original H-H bond breaks and a new one is formed.||[[File:Contour_1_fmj.png|150px]]
|-
| -1.5 || -2.0 ||-100.456 ||No ||The hydrogen atom collides with the hydrogen molecule, the transition state does not form. The atom and the molecule bounce off each other and move in opposite directions. ||[[File:Contour_2_fmj.png|150px]]
|-
| -1.5 || -2.5 ||-98.956 ||Yes ||The hydrogen atom collides with the hydrogen molecule, the transition state forms. Eventually, the original H-H bond breaks and a new one is formed. ||[[File:Contour_3_fmj.png|150px]]
|-
| -2.5 || -5.0 ||-84.956 ||No ||The hydrogen atom collides with the hydrogen molecule, the transition state forms, but the original bond does not break. Instead, the molecule and the atom move away from each other. ||[[File:Contour_4_fmj.png|150px]]
|-
| -2.5 || -5.2 ||-83.416 ||Yes ||The hydrogen atom collides with the hydrogen molecule, the transition state forms, then break downs back into lower energy structures. It is then formed again, followed by the products. ||[[File:Contour_5_fmj.png|150px]]
|}

====State what are the main assumptions of Transition State Theory. Given the results you have obtained, how will Transition State Theory predictions for reaction rate values compare with experimental values?====
The main assumptions are

=Exercise 2=
===Potential Energy Surface inspection of F-H-H system===
Below is a surface plot for the F-H-H system.
[[File:H2_f_surface_potential_fmj.png]]
It shows H-H and F as being more energetic than F-H and H. This indicates that the reaction between H-H and F is exothermic and that the H-F bond is stronger than the H-H bond. It also indicates that the reaction between H-F and H is endothermic, again because the H-F bond is stronger than the H-H bond.

====Transition State====
Below is a surface plot showing the position of the transition state (black dot) of the H-H + F reaction.
[[File:F_h_TS_fmj.png]]

====Activation Energy====
The activation energy for the H-H + F reaction is 30 kcal/mol.

[[File:Activation_energy.png]]

The activation energy for the H-F + H reaction is 0.15 kcal/mol.

[[File:Act_energy_2_fmj.png]]

===Reaction dynamics===
A set of initial conditions which result in a reaction is shown below.

[[File:In_con_fmj.PNG]]

This is the momentum vs Time graph for the reaction trajectory resulting from the initial conditions above.

[[File:Momenta_time_fh_fmj.png]]

explain something here

{| class="wikitable" border=1
! pFH !! pHH !! Reactive? !! Comments !! Plots
|-
| -0.5 || -3.0 ||Yes||The graph shows that the H-H distance increases with time and the H-F distance initially decreases, but then maintains a constant equilibrium value. This indicates the formation of the F-H bond ||[[File:Mom_1_fmj.png|150px]]
|-
| -0.5 || -2.8 ||Yes ||The graph now shows a reactive trajectory. ||[[File:Plot_2_fmj.png|150px]]
|-
| -0.5 || -2.0 ||No ||The graph shows that the H-H distance maintains a constant equilibrium value with time and the H-F distance initially decreases, but increases with time. This indicates that the F-H bond did not form. ||[[File:Plot2_fmj.png|150px]]
|-
| -0.5 || -1.0 ||No ||The graph shows that the H-H distance maintains a constant equilibrium value with time and the H-F distance initially decreases, but increases with time. This indicates that the F-H bond did not form. ||[[File:Plot3_fmj.png|150px]]
|-
| -0.5 || 0 ||No||The graph shows that the H-H distance maintains a constant equilibrium value with time and the H-F distance initially decreases, but increases with time. This indicates that the F-H bond did not form. ||[[File:Plot4_fmj.png|150px]]
|-
| -0.5 || 1.0 ||No ||The graph shows that the H-H distance maintains a constant equilibrium value with time and the H-F distance initially decreases, but increases with time. This indicates that the F-H bond did not form. ||[[File:Plot5_fmj.png|150px]]
|-
| -0.5 || 2.0 ||Yes ||The graph shows that the H-H distance increases with time and the H-F distance initially decreases, but then maintains a constant equilibrium value. This indicates the formation of the F-H bond ||[[File:Plot6_fmj.png|150px]]
|-
| -0.5 || 2.8 ||No ||The graph shows that the H-H distance maintains a constant equilibrium value with time and the H-F distance initially decreases, but increases with time. This indicates that the F-H bond did not form. ||[[File:Plot7_fmj.png |150px]]
|-
| -0.5 || 3.0 ||No ||The graph shows that the H-H distance maintains a constant equilibrium value with time and the H-F distance initially decreases, but increases with time. This indicates that the F-H bond did not form. ||[[File:Plot8_fmj.png|150px]]
|-
| -0.8 || 0.1 ||Yes||The graph shows that the H-H distance increases with time and the H-F distance initially decreases, but then maintains a constant equilibrium value. This indicates the formation of the F-H bond ||[[File:Plot9_fmj.png|150px]]
|-
|}

===Polanyi's Empirical Rules===

MRD:FMJ17

2019-05-24T14:26:03Z

Fmj17: /* Reaction dynamics */

=Exercise 1=
===On a potential energy surface diagram, how is the transition state mathematically defined? How can the transition state be identified, and how can it be distinguished from a local minimum of the potential energy surface?===
The transition state is defined as the point at which the potential gradient is zero, δV(ri)/δ(ri)=0. Contrary to local minima in the enrgy surface, the transition state will be at the point along the reaction path where the energy is maximum.
===Trajectories from r1 = r2: locating the transition state===
transition state position, rts=0.90775 Å
====Internuclear Dictances vs Time Plot====
[[File:Int_nuc_1_fmj.PNG]]
The straight lines indicate no vibrations. This indicates that the momenta are zero, confirming that the point corresponds to the transition state.
===Calculating the Reaction Path===
====Minimum Energy Pathway Calculation====
The figure below shows a surface plot obtained using the MEP calculation type. The black line illustrates the reaction path (from the transition state to the products).
[[File:Surface_Plot_mep_fmj.png]]

Below is the contour plot, showing the same reaction path. (black line)

[[File:Contour_plot_mep_fmj.png]]

====Comparing Dynamics and MEP Calculation Types====
Below is a surface plot obtained by using the dynamics calculation type.
[[File:Surface_Plot_dyn_fmj.png]]

Again, the black line shows the the reaction path (from the transition state to the products). This calculation was made using the same initial conditions as the MEP calculation above.

The two trajectories calculated using the two calculation types are different. The dynamic calculation indicates vibrations (curves on the line), while the MEP calculation does not (no curves).

===Reactive and unreactive trajectories===

{| class="wikitable" border=1
! p1 !! p2 !! Etot !! Reactive? !! Description of the dynamics !! Illustration of the trajectory
|-
| -1.25 || -2.5 ||-99.018 ||Yes||The hydrogen atom collides with the hydrogen molecule, the transition state forms. Eventually, the original H-H bond breaks and a new one is formed.||[[File:Contour_1_fmj.png|150px]]
|-
| -1.5 || -2.0 ||-100.456 ||No ||The hydrogen atom collides with the hydrogen molecule, the transition state does not form. The atom and the molecule bounce off each other and move in opposite directions. ||[[File:Contour_2_fmj.png|150px]]
|-
| -1.5 || -2.5 ||-98.956 ||Yes ||The hydrogen atom collides with the hydrogen molecule, the transition state forms. Eventually, the original H-H bond breaks and a new one is formed. ||[[File:Contour_3_fmj.png|150px]]
|-
| -2.5 || -5.0 ||-84.956 ||No ||The hydrogen atom collides with the hydrogen molecule, the transition state forms, but the original bond does not break. Instead, the molecule and the atom move away from each other. ||[[File:Contour_4_fmj.png|150px]]
|-
| -2.5 || -5.2 ||-83.416 ||Yes ||The hydrogen atom collides with the hydrogen molecule, the transition state forms, then break downs back into lower energy structures. It is then formed again, followed by the products. ||[[File:Contour_5_fmj.png|150px]]
|}

====State what are the main assumptions of Transition State Theory. Given the results you have obtained, how will Transition State Theory predictions for reaction rate values compare with experimental values?====
The main assumptions are:
1) The momentum is zero
2) pakner

=Exercise 2=
===Potential Energy Surface inspection of F-H-H system===
Below is a surface plot for the F-H-H system.
[[File:H2_f_surface_potential_fmj.png]]
It shows H-H and F as being more energetic than F-H and H. This indicates that the reaction between H-H and F is exothermic and that the H-F bond is stronger than the H-H bond. It also indicates that the reaction between H-F and H is endothermic, again because the H-F bond is stronger than the H-H bond.

====Transition State====
Below is a surface plot showing the position of the transition state (black dot) of the H-H + F reaction.
[[File:F_h_TS_fmj.png]]

====Activation Energy====
The activation energy for the H-H + F reaction is 30 kcal/mol.

[[File:Activation_energy.png]]

The activation energy for the H-F + H reaction is 0.15 kcal/mol.

[[File:Act_energy_2_fmj.png]]

===Reaction dynamics===
A set of initial conditions which result in a reaction is shown below.

[[File:In_con_fmj.PNG]]

This is the momentum vs Time graph for the reaction trajectory resulting from the initial conditions above.

[[File:Momenta_time_fh_fmj.png]]

explain something here

{| class="wikitable" border=1
! pFH !! pHH !! Reactive? !! Comments !! Plots
|-
| -0.5 || -3.0 ||Yes||The graph shows that the H-H distance increases with time and the H-F distance initially decreases, but then maintains a constant equilibrium value. This indicates the formation of the F-H bond ||[[File:Mom_1_fmj.png|150px]]
|-
| -0.5 || -2.8 ||Yes ||The graph now shows a reactive trajectory. ||[[File:Plot_2_fmj.png|150px]]
|-
| -0.5 || -2.0 ||No ||The graph shows that the H-H distance maintains a constant equilibrium value with time and the H-F distance initially decreases, but increases with time. This indicates that the F-H bond did not form. ||[[File:Plot2_fmj.png|150px]]
|-
| -0.5 || -1.0 ||No ||The graph shows that the H-H distance maintains a constant equilibrium value with time and the H-F distance initially decreases, but increases with time. This indicates that the F-H bond did not form. ||[[File:Plot3_fmj.png|150px]]
|-
| -0.5 || 0 ||No||The graph shows that the H-H distance maintains a constant equilibrium value with time and the H-F distance initially decreases, but increases with time. This indicates that the F-H bond did not form. ||[[File:Plot4_fmj.png|150px]]
|-
| -0.5 || 1.0 ||No ||The graph shows that the H-H distance maintains a constant equilibrium value with time and the H-F distance initially decreases, but increases with time. This indicates that the F-H bond did not form. ||[[File:Plot5_fmj.png|150px]]
|-
| -0.5 || 2.0 ||Yes ||The graph shows that the H-H distance increases with time and the H-F distance initially decreases, but then maintains a constant equilibrium value. This indicates the formation of the F-H bond ||[[File:Plot6_fmj.png|150px]]
|-
| -0.5 || 2.8 ||No ||The graph shows that the H-H distance maintains a constant equilibrium value with time and the H-F distance initially decreases, but increases with time. This indicates that the F-H bond did not form. ||[[File:Plot7_fmj.png |150px]]
|-
| -0.5 || 3.0 ||No ||The graph shows that the H-H distance maintains a constant equilibrium value with time and the H-F distance initially decreases, but increases with time. This indicates that the F-H bond did not form. ||[[File:Plot8_fmj.png|150px]]
|-
| -0.8 || 0.1 ||Yes||The graph shows that the H-H distance increases with time and the H-F distance initially decreases, but then maintains a constant equilibrium value. This indicates the formation of the F-H bond ||[[File:Plot9_fmj.png|150px]]
|-
|}

===Polanyi's Empirical Rules===

MRD:FMJ17

2019-05-24T14:11:30Z

Fmj17: /* Activation Energy */

MRD:FMJ17

2019-05-24T14:11:08Z

Fmj17: /* Reactive and unreactive trajectories */

File:Contour 4 fmj.png

2019-05-24T14:03:15Z

Fmj17:

MRD:FMJ17

2019-05-24T13:48:02Z

Fmj17: /* Exercise 2 */

MRD:FMJ17

2019-05-24T13:46:27Z

Fmj17: /* Reaction dynamics */

MRD:FMJ17

2019-05-24T13:45:49Z

Fmj17: /* Reaction dynamics */

MRD:FMJ17

2019-05-24T13:45:36Z

Fmj17: /* Reaction dynamics */

MRD:FMJ17

2019-05-24T13:35:06Z

Fmj17: /* Reaction dynamics */

File:Plot9 fmj.png

2019-05-24T13:33:27Z

Fmj17:

MRD:FMJ17

2019-05-24T13:28:48Z

Fmj17: /* Reaction dynamics */

File:Plot8 fmj.png

2019-05-24T13:28:15Z

Fmj17:

File:Plot7 fmj.png

2019-05-24T13:27:06Z

Fmj17:

File:Plot6 fmj.png

2019-05-24T13:25:53Z

Fmj17:

File:Plot5 fmj.png

2019-05-24T13:24:12Z

Fmj17:

File:Plot4 fmj.png

2019-05-24T13:22:10Z

Fmj17:

File:Plot3 fmj.png

2019-05-24T13:20:23Z

Fmj17:

File:Plot2 fmj.png

2019-05-24T13:18:18Z

Fmj17:

File:Plot 2 fmj.png

2019-05-24T13:16:29Z

Fmj17:

File:Mom 1 fmj.png

2019-05-24T13:12:12Z

Fmj17:

MRD:FMJ17

2019-05-24T13:05:14Z

Fmj17: /* Activation Energy */

File:Act energy 2 fmj.png

2019-05-24T13:04:49Z

Fmj17:

File:Activation energy.png

2019-05-24T13:00:33Z

Fmj17:

MRD:FMJ17

2019-05-23T15:32:49Z

Fmj17: /* Exercise 2 */

MRD:FMJ17

2019-05-23T15:25:56Z

Fmj17: /* Exercise 2 */

File:Momenta time fh fmj.png

2019-05-23T15:17:11Z

Fmj17:

File:In con fmj.PNG

2019-05-23T15:11:51Z

Fmj17:

MRD:FMJ17

2019-05-23T15:01:34Z

Fmj17: /* Activation Energy */

MRD:FMJ17

2019-05-23T14:28:25Z

Fmj17: /* Potential Energy Surface inspection of F-H-H system */

MRD:FMJ17

2019-05-23T14:21:52Z

Fmj17: /* Exercise 2 */

MRD:FMJ17

2019-05-23T14:19:08Z

Fmj17:

File:F h TS fmj.png

2019-05-23T14:17:33Z

Fmj17:

File:H2 f surface potential fmj.png

2019-05-23T13:32:38Z

Fmj17:

MRD:FMJ17

2019-05-21T15:51:41Z

Fmj17: /* Reactive and unreactive trajectories */

MRD:FMJ17

2019-05-21T15:32:06Z

Fmj17: /* Reactive and unreactive trajectories */

File:Contour 5 fmj.png

2019-05-21T15:30:34Z

Fmj17:

MRD:FMJ17

2019-05-21T15:26:59Z

Fmj17: /* Reactive and unreactive trajectories */

File:Contour 3 fmj.png

2019-05-21T15:26:22Z

Fmj17:

File:Contour 2 fmj.png

2019-05-21T15:24:01Z

Fmj17:

MRD:FMJ17

2019-05-21T15:21:11Z

Fmj17: /* Reactive and unreactive trajectories */

MRD:FMJ17

2019-05-21T15:20:24Z

Fmj17: /* Exercise 1 */

File:Contour 1 fmj.png

2019-05-21T15:20:06Z

Fmj17:

MRD:FMJ17

2019-05-21T14:53:47Z

Fmj17: /* Comparing Dynamics and MEP Calculation Types */

MRD:FMJ17

2019-05-21T14:53:18Z

Fmj17: /* Calculating the Reaction Path */

File:Surface Plot dyn fmj.png

2019-05-21T14:47:15Z

Fmj17:

MRD:FMJ17

2019-05-21T14:43:26Z

Fmj17: /* Minimum Energy Pathway Calculation */