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MRD:sq111714052019

File:Reactive trajectory sq1117.PNG

2019-05-16T20:38:35Z

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2019-05-16T20:37:40Z

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2019-05-16T20:37:28Z

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2019-05-16T20:37:10Z

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2019-05-16T20:36:37Z

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MRD:sq111714052019

2019-05-16T20:28:12Z

Sq1117:

= Molecular Reaction Dynamic Wiki Sicong Qiu =

== Exercise 1 : the H-H-H system. ==

=== 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? ===

It is the point where the second derivatives of both V(r1) and V(r2) are 0. At this point r1 is equal to r2. A local minimum will only have the first derivative of either V(r1) or V(r2) equal to 0, and their second derivative will not be 0.

===Report your best estimate of the transition state position (rts) and explain your reasoning illustrating it with a “Internuclear Distances vs Time” plot for a relevant trajectory.===

The transition state position is approximately 0.908 angstrom. The internuclear distances look to be stabilised, as it is sitting right on the saddle point. The distances of A-B and B-C in the initial simulation also intercept at ~0.91 angstrom.

[[File: HHH_distance_plot1_sq1117.png |thumb|center| Fig 1. The internuclear distances between the 3 H atoms vs time|600px]]

===Comment on how the mep and the dynamic trajectory differ.===

Dynamic graph shows the inertial motion and oscillation of the molecule, which is shown as the internuclear distance is oscillating.

[[File: HHH_dynamic_contour_sq1117.png|thumb|center|Fig 2. A contour graph produced using dynamic calculation type |600px]]

MEP graph shows infinitely slow motion, so the inertial motion and oscillation is ignored. The internuclear distance is a lot more smooth.

[[File: HHH_MEP_contour_sq1117.png|thumb|center|Fig 3. A contour graph produced using MEP calculation type|600px]]

Because momenta is reset to 0 after each step, kinetic energy is lost and the total energy is not conserved. The total energy using dynamic method is -99.119 kcal/mol, and the total energy using MEP method is - 103.869 kcal/mol. The difference is the kinetic energy.

=== Reactive and unreactive trajectory ===

{| class="wikitable" border="1"
|+ Different trajectory
|-
| P1 || P2 || Etot || Reactive? || Description || Illustration
|-
| -1.25 || -2.5 || -99.076 || yes || Atom C approaches with sufficient energy to get through the transition state and forms a bond with B || [[File:HHH_-1.25-2.5_sq1117.png|thumb|Fig 4]]
|-
| -1.5 || -2.0 || -100.028 || no || Atom C approaches without enough energy to get through the TS, it bounces back. || [[File:HHH_-1.5-2.0_sq1117.png|thumb|Fig 5]]
|-
| -1.5 || -2.5 || -98.771 || yes || Atom C approaches with sufficient energy to get through the transition state and forms a bond with B || [[File:HHH_-1.5-2.5_sq1117.png|thumb|Fig 6]]
|-
| -2.5 || -5.0 || -85.000 || no || Atom C approaches with sufficient energy to get through the transition state, but somehow reaction fails and energy is transferred from C to AB || [[File:HHH_-2.5-5.0_sq1117.png|thumb|Fig 7]]
|-
| -2.5 || -5.2 || -83.471 || yes || Atom C has enough energy to get through the transition state, the momentum leaves the molecule in an excited state. || [[File:HHH_-2.5-5.2_sq1117.png|thumb|Fig 8]]
|}

Conclusion

To achieve reaction, the particles must have kinetic energy above a threshold.
However, even with enough energy, there's a chance that energy transfer will happen instead of reaction.

=== Main assumptions in the transition state theory and how they affect the predicted rate in comparison the experimental value. ===

There're a few assumptions being made in the transition state theory1:

1. Nuclear motion and electron motion are separate, similar to the Born-Oppenheimer approximation.

2. Maxwell-Boltzmann distribution is applied to the reactant molecules.

3. Molecules that have crossed the transition state cannot reform reactants.

4. In the transition state, motion along the reaction coordinate may be separated from other motion and treated classically as a translation.

5. Even in the absence of equilibrium between the reactant and the product, the transition states that are becoming the product follows the Maxwell-Boltzmann laws.

However:

1. In our simulations, there're examples that molecules with sufficient energy that have crossed the barrier reform the reactant. With this in mind, the realistic reaction rate is likely to be lower than predicted.

2. For a very short lived transition state, the activated complexes may not have enough time to reach the equilibrium according to Maxwell-Boltzmann laws before turning into products.

3. Particles may behave according to quantum mechanics instead. For a reaction with low energy barrier, particles without sufficient energy may tunnel through the barrier and react.

== Exercise 2: the F-H-H system. ==

=== Energetics and the bond strength of the chemical species. ===

Bond strength in kJ/mol

H-H: 436 H-F: 567

In the F + H2 reaction, a H-H bond is broken and a H-F bond is formed. The reaction is exothermic with -131 kJ/mol.

In the H + HF reaction, a H-F bond is broken and a H-H bond is formed. the reaction is endothermic with 131 kJ/mol.

=== Locating the transition state ===

==== F + H2 system ====

rHF = r1 = 1.810, rHH = r2 = 0.745. At these distances, the internuclear distances can stabilise.

[[File: F_H-H_distance_plot_sq1117.png|thumb|center|Fig 9. The internuclear distances between the F,H,H atoms at transition state vs time|600px]] [[File: F_H-H_contour_sq1117.png|thumb|center|Fig 10. The contour graph of F + H-H system at transition state|600px]]

==== H + H-F system ====

rHH = r1 = 0.745, rHF = r2 = 1.810. At these distances, the internuclear distances can stabilise.

[[File: H_H-F_distance_plot_sq1117.png|thumb|center|Fig 11.The internuclear distances between the H,H,F atoms at transition state vs time|600px]] [[File: H_H-F_contour_plot_sq1117.png|thumb|center|Fig 12. The contour graph of H-F + H system at transition state|600px]]

=== The activation energies ===

A = F, B = H, C = H

By increasing rAB by 0.01 from rts, the reaction is pushed toward the F + H-H side. The activation energy is -103.75-(-103.99) = 0.24 kcal/mol

[[File:Exo_ea_sq1117.png|thumb|center|Fig 13. The energy of the system vs steps when r1 is increased|600px]]

By decreasing rAB by 0.01 from rts, the reaction is pushed toward the H + H-F side. The activation energy is -103.75-(-133.91) = 30.16 kcal/mol

[[File:Endo_ea_sq1117.png|thumb|center|Fig 14. The energy of the system vs steps when r2 is decreased|600px]]

=== Mechanism of the release of energy in the F + H-H reaction and experimental approach ===

The following setup is proved to be a reactive trajectory.

[[File: Reactive_trajectory_sq1117.PNG |thumb|center|Fig 15. The setting of a reactive trajectory of the F + H-H system|600px]] [[File: Reactive_contour_sq1117.png|thumb|center|Fig 16. The contour graph of a reactive trajectory of the F + H-H system|600px]]

It is clear that the initial momentum leaves the product in a hot vibration state, with an increase in momenta and kinetic energy. The momenta and energy vs time graph confirm this. A subsequent drop in potential energy is observed, which makes sure that the total energy is conserved.

[[File: Reactive_momenta_sq1117.png|thumb|center|Fig 17. The momenta vs time graph of a reactive trajectory of the F + H-H system|600px]][[File: Reactive_energy_sq1117.png|thumb|center|Fig 18. The energy vs time graph of a reactive trajectory of the F + H-H system|600px]]

Vibration hot state can be detected using UV-Vis spectroscopy. In an adiabetic environment, the temperature of the system will also increase, which can be measured by a thermometer.

=== The position of the transition state and its relationship with vibration and translation energy. ===

According to Hammond's postulate, because the F + H-H reaction is exothermic, it should have an early transition state that mostly resembles the reactant. On contrary, the H + H-F reaction is endothermic, and its transition state should occur late in terms of reaction coordinates and mostly resemble the product.

The following setup produces a reactive trajectory for the H + H-F reaction.

[[File:Reactive_HHF_setup_sq1117.PNG|thumb|center|Fig 19. The setting of a reactive trajectory of the H + H-F system|600px]][[File: Reactive_HHF_contour_sq1117.png|thumb|center|Fig 20. The contour graph of a reactive trajectory of the H + H-F system|600px]]

In these systems, vibration energy is represented by the intra-molecular momentum of the diatomic, and translation energy is represented by the momentum between the approaching atom and the diatomic.

In the exothermic F + H-H system, converting translation energy into vibration energy results in a failed trajectory, while having more translation energy and less vibration energy do not hinder the reaction.

[[File:FHH_high_ts_low_vb_good_sq1117.png|thumb|center|Fig 21. For exothermic reaction, having more translation energy makes a trajectory goes forward.(ptrans=-1.6, pvb=-0.3)|600px]]

[[File:FHH_low_ts_high_vb_fail_sq1117.png|thumb|center|Fig 22. Increasing vibration energy at the cost of translation energy results in a failed exothermic reaction. (ptrans=-0.3, pvb=-1.6)|600px]]

In the endothermic H + H-F system, it is the opposite. Vibration energy is preferred over translation energy.

[[File:

2019-05-16T19:17:49Z

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File:Reactive HHF contour sq1117.png

2019-05-16T19:17:01Z

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File:Reactive HHF setup sq1117.PNG

2019-05-16T19:14:55Z

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File:Reactive HHF setup sq1117.PNG

2019-05-16T19:14:25Z

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File:Reactive HHF setup sq1117.PNG

2019-05-16T19:13:29Z

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MRD:sq111714052019

2019-05-16T18:54:43Z

Sq1117:

= Molecular Reaction Dynamic Wiki Sicong Qiu =

== Exercise 1 : the H-H-H system. ==

=== 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? ===

It is the point where the second derivatives of both V(r1) and V(r2) are 0. At this point r1 is equal to r2. A local minimum will only have the first derivative of either V(r1) or V(r2) equal to 0, and their second derivative will not be 0.

===Report your best estimate of the transition state position (rts) and explain your reasoning illustrating it with a “Internuclear Distances vs Time” plot for a relevant trajectory.===

The transition state position is approximately 0.908 angstrom. The internuclear distances look to be stabilised, as it is sitting right on the saddle point. The distances of A-B and B-C in the initial simulation also intercept at ~0.91 angstrom.

[[File: HHH_distance_plot1_sq1117.png |thumb|center| Fig 1. The internuclear distances between the 3 H atoms vs time|600px]]

===Comment on how the mep and the dynamic trajectory differ.===

Dynamic graph shows the inertial motion and oscillation of the molecule, which is shown as the internuclear distance is oscillating.

[[File: HHH_dynamic_contour_sq1117.png|thumb|center|Fig 2. A contour graph produced using dynamic calculation type |600px]]

MEP graph shows infinitely slow motion, so the inertial motion and oscillation is ignored. The internuclear distance is a lot more smooth.

[[File: HHH_MEP_contour_sq1117.png|thumb|center|Fig 3. A contour graph produced using MEP calculation type|600px]]

Because momenta is reset to 0 after each step, kinetic energy is lost and the total energy is not conserved. The total energy using dynamic method is -99.119 kcal/mol, and the total energy using MEP method is - 103.869 kcal/mol. The difference is the kinetic energy.

=== Reactive and unreactive trajectory ===

{| class="wikitable" border="1"
|+ Different trajectory
|-
| P1 || P2 || Etot || Reactive? || Description || Illustration
|-
| -1.25 || -2.5 || -99.076 || yes || Atom C approaches with sufficient energy to get through the transition state and forms a bond with B || [[File:HHH_-1.25-2.5_sq1117.png|thumb|Fig 4]]
|-
| -1.5 || -2.0 || -100.028 || no || Atom C approaches without enough energy to get through the TS, it bounces back. || [[File:HHH_-1.5-2.0_sq1117.png|thumb|Fig 5]]
|-
| -1.5 || -2.5 || -98.771 || yes || Atom C approaches with sufficient energy to get through the transition state and forms a bond with B || [[File:HHH_-1.5-2.5_sq1117.png|thumb|Fig 6]]
|-
| -2.5 || -5.0 || -85.000 || no || Atom C approaches with sufficient energy to get through the transition state, but somehow reaction fails and energy is transferred from C to AB || [[File:HHH_-2.5-5.0_sq1117.png|thumb|Fig 7]]
|-
| -2.5 || -5.2 || -83.471 || yes || Atom C has enough energy to get through the transition state, the momentum leaves the molecule in an excited state. || [[File:HHH_-2.5-5.2_sq1117.png|thumb|Fig 8]]
|}

Conclusion

To achieve reaction, the particles must have kinetic energy above a threshold.
However, even with enough energy, there's a chance that energy transfer will happen instead of reaction.

=== Main assumptions in the transition state theory and how they affect the predicted rate in comparison the experimental value. ===

There're a few assumptions being made in the transition state theory1:

1. Nuclear motion and electron motion are separate, similar to the Born-Oppenheimer approximation.

2. Maxwell-Boltzmann distribution is applied to the reactant molecules.

3. Molecules that have crossed the transition state cannot reform reactants.

4. In the transition state, motion along the reaction coordinate may be separated from other motion and treated classically as a translation.

5. Even in the absence of equilibrium between the reactant and the product, the transition states that are becoming the product follows the Maxwell-Boltzmann laws.

However:

1. In our simulations, there're examples that molecules with sufficient energy that have crossed the barrier reform the reactant. With this in mind, the realistic reaction rate is likely to be lower than predicted.

2. For a very short lived transition state, the activated complexes may not have enough time to reach the equilibrium according to Maxwell-Boltzmann laws before turning into products.

3. Particles may behave according to quantum mechanics instead. For a reaction with low energy barrier, particles without sufficient energy may tunnel through the barrier and react.

== Exercise 2: the F-H-H system. ==

=== Energetics and the bond strength of the chemical species. ===

Bond strength in kJ/mol

H-H: 436 H-F: 567

In the F + H2 reaction, a H-H bond is broken and a H-F bond is formed. The reaction is exothermic with -131 kJ/mol.

In the H + HF reaction, a H-F bond is broken and a H-H bond is formed. the reaction is endothermic with 131 kJ/mol.

=== Locating the transition state ===

==== F + H2 system ====

rHF = r1 = 1.810, rHH = r2 = 0.745. At these distances, the internuclear distances can stabilise.

[[File: F_H-H_distance_plot_sq1117.png|thumb|center|Fig 9. The internuclear distances between the F,H,H atoms at transition state vs time|600px]] [[File: F_H-H_contour_sq1117.png|thumb|center|Fig 10. The contour graph of F + H-H system at transition state|600px]]

==== H + H-F system ====

rHH = r1 = 0.745, rHF = r2 = 1.810. At these distances, the internuclear distances can stabilise.

[[File: H_H-F_distance_plot_sq1117.png|thumb|center|Fig 11.The internuclear distances between the H,H,F atoms at transition state vs time|600px]] [[File: H_H-F_contour_plot_sq1117.png|thumb|center|Fig 12. The contour graph of H-F + H system at transition state|600px]]

=== The activation energies ===

A = F, B = H, C = H

By increasing rAB by 0.01 from rts, the reaction is pushed toward the F + H-H side. The activation energy is -103.75-(-103.99) = 0.24 kcal/mol

[[File:Exo_ea_sq1117.png|thumb|center|Fig 13. The energy of the system vs steps when r1 is increased|600px]]

By decreasing rAB by 0.01 from rts, the reaction is pushed toward the H + H-F side. The activation energy is -103.75-(-133.91) = 30.16 kcal/mol

[[File:Endo_ea_sq1117.png|thumb|center|Fig 14. The energy of the system vs steps when r2 is decreased|600px]]

=== Mechanism of the release of energy in the F + H-H reaction and experimental approach ===

The following setup is proved to be a reactive trajectory.

[[File: Reactive_trajectory_sq1117.PNG |thumb|center|Fig 15. The setting of a reactive trajectory of the F + H-H system|600px]] [[File: Reactive_contour_sq1117.png|thumb|center|Fig 16. The contour graph of a reactive trajectory of the F + H-H system|600px]]

It is clear that the initial momentum leaves the product in a hot vibration state, with an increase in momenta and kinetic energy. The momenta and energy vs time graph confirm this. A subsequent drop in potential energy is observed, which makes sure that the total energy is conserved.

[[File: Reactive_momenta_sq1117.png|thumb|center|Fig 17. The momenta vs time graph of a reactive trajectory of the F + H-H system|600px]][[File: Reactive_energy_sq1117.png|thumb|center|Fig 18. The energy vs time graph of a reactive trajectory of the F + H-H system|600px]]

Vibration hot state can be detected using UV-Vis spectroscopy. In an adiabetic environment, the temperature of the system will also increase, which can be measured by a thermometer.

=== The position of the transition state and its relationship with vibration and translation energy. ===

According to Hammond's postulate, because the F + H-H reaction is exothermic, it should have an early transition state that mostly resembles the reactant. On contrary, the H + H-F reaction is endothermic, and its transition state should occur late in terms of reaction coordinates and mostly resemble the product.

The following setup produces a reactive trajectory for the H + H-F reaction.

[[File:Reactive_HHF_setup_sq1117.PNG|thumb|center|Fig 19. The setting of a reactive trajectory of the H + H-F system|600px]][[File: Reactive_HHF_contour_sq1117.png|thumb|center|Fig 20. The contour graph of a reactive trajectory of the H + H-F system|600px]]

In these systems, vibration energy is represented by the intra-molecular momentum of the diatomic, and translation energy is represented by the momentum between the approaching atom and the diatomic.

MRD:sq111714052019

2019-05-16T18:51:14Z

Sq1117:

= Molecular Reaction Dynamic Wiki Sicong Qiu =

== Exercise 1 : the H-H-H system. ==

=== 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? ===

It is the point where the second derivatives of both V(r1) and V(r2) are 0. At this point r1 is equal to r2. A local minimum will only have the first derivative of either V(r1) or V(r2) equal to 0, and their second derivative will not be 0.

===Report your best estimate of the transition state position (rts) and explain your reasoning illustrating it with a “Internuclear Distances vs Time” plot for a relevant trajectory.===

The transition state position is approximately 0.908 angstrom. The internuclear distances look to be stabilised, as it is sitting right on the saddle point. The distances of A-B and B-C in the initial simulation also intercept at ~0.91 angstrom.

[[File: HHH_distance_plot1_sq1117.png |thumb|center| Fig 1. The internuclear distances between the 3 H atoms vs time|600px]]

===Comment on how the mep and the dynamic trajectory differ.===

Dynamic graph shows the inertial motion and oscillation of the molecule, which is shown as the internuclear distance is oscillating.

[[File: HHH_dynamic_contour_sq1117.png|thumb|center|Fig 2. A contour graph produced using dynamic calculation type |600px]]

MEP graph shows infinitely slow motion, so the inertial motion and oscillation is ignored. The internuclear distance is a lot more smooth.

[[File: HHH_MEP_contour_sq1117.png|thumb|center|Fig 3. A contour graph produced using MEP calculation type|600px]]

Because momenta is reset to 0 after each step, kinetic energy is lost and the total energy is not conserved. The total energy using dynamic method is -99.119 kcal/mol, and the total energy using MEP method is - 103.869 kcal/mol. The difference is the kinetic energy.

=== Reactive and unreactive trajectory ===

{| class="wikitable" border="1"
|+ Different trajectory
|-
| P1 || P2 || Etot || Reactive? || Description || Illustration
|-
| -1.25 || -2.5 || -99.076 || yes || Atom C approaches with sufficient energy to get through the transition state and forms a bond with B || [[File:HHH_-1.25-2.5_sq1117.png|thumb|Fig 4]]
|-
| -1.5 || -2.0 || -100.028 || no || Atom C approaches without enough energy to get through the TS, it bounces back. || [[File:HHH_-1.5-2.0_sq1117.png|thumb|Fig 5]]
|-
| -1.5 || -2.5 || -98.771 || yes || Atom C approaches with sufficient energy to get through the transition state and forms a bond with B || [[File:HHH_-1.5-2.5_sq1117.png|thumb|Fig 6]]
|-
| -2.5 || -5.0 || -85.000 || no || Atom C approaches with sufficient energy to get through the transition state, but somehow reaction fails and energy is transferred from C to AB || [[File:HHH_-2.5-5.0_sq1117.png|thumb|Fig 7]]
|-
| -2.5 || -5.2 || -83.471 || yes || Atom C has enough energy to get through the transition state, the momentum leaves the molecule in an excited state. || [[File:HHH_-2.5-5.2_sq1117.png|thumb|Fig 8]]
|}

Conclusion

To achieve reaction, the particles must have kinetic energy above a threshold.
However, even with enough energy, there's a chance that energy transfer will happen instead of reaction.

=== Main assumptions in the transition state theory and how they affect the predicted rate in comparison the experimental value. ===

There're a few assumptions being made in the transition state theory1:

1. Nuclear motion and electron motion are separate, similar to the Born-Oppenheimer approximation.

2. Maxwell-Boltzmann distribution is applied to the reactant molecules.

3. Molecules that have crossed the transition state cannot reform reactants.

4. In the transition state, motion along the reaction coordinate may be separated from other motion and treated classically as a translation.

5. Even in the absence of equilibrium between the reactant and the product, the transition states that are becoming the product follows the Maxwell-Boltzmann laws.

However:

1. In our simulations, there're examples that molecules with sufficient energy that have crossed the barrier reform the reactant. With this in mind, the realistic reaction rate is likely to be lower than predicted.

2. For a very short lived transition state, the activated complexes may not have enough time to reach the equilibrium according to Maxwell-Boltzmann laws before turning into products.

3. Particles may behave according to quantum mechanics instead. For a reaction with low energy barrier, particles without sufficient energy may tunnel through the barrier and react.

== Exercise 2: the F-H-H system. ==

=== Energetics and the bond strength of the chemical species. ===

Bond strength in kJ/mol

H-H: 436 H-F: 567

In the F + H2 reaction, a H-H bond is broken and a H-F bond is formed. The reaction is exothermic with -131 kJ/mol.

In the H + HF reaction, a H-F bond is broken and a H-H bond is formed. the reaction is endothermic with 131 kJ/mol.

=== Locating the transition state ===

==== F + H2 system ====

rHF = r1 = 1.810, rHH = r2 = 0.745. At these distances, the internuclear distances can stabilise.

[[File: F_H-H_distance_plot_sq1117.png|thumb|center|Fig 9. The internuclear distances between the F,H,H atoms at transition state vs time|600px]] [[File: F_H-H_contour_sq1117.png|thumb|center|Fig 10. The contour graph of F + H-H system at transition state|600px]]

==== H + H-F system ====

rHH = r1 = 0.745, rHF = r2 = 1.810. At these distances, the internuclear distances can stabilise.

[[File: H_H-F_distance_plot_sq1117.png|thumb|center|Fig 11.The internuclear distances between the H,H,F atoms at transition state vs time|600px]] [[File: H_H-F_contour_plot_sq1117.png|thumb|center|Fig 12. The contour graph of H-F + H system at transition state|600px]]

=== The activation energies ===

A = F, B = H, C = H

By increasing rAB by 0.01 from rts, the reaction is pushed toward the F + H-H side. The activation energy is -103.75-(-103.99) = 0.24 kcal/mol

[[File:Exo_ea_sq1117.png|thumb|center|Fig 13. The energy of the system vs steps when r1 is increased|600px]]

By decreasing rAB by 0.01 from rts, the reaction is pushed toward the H + H-F side. The activation energy is -103.75-(-133.91) = 30.16 kcal/mol

[[File:Endo_ea_sq1117.png|thumb|center|Fig 14. The energy of the system vs steps when r2 is decreased|600px]]

=== Mechanism of the release of energy in the F + H-H reaction and experimental approach ===

The following setup is proved to be a reactive trajectory.

[[File: Reactive_trajectory_sq1117.PNG |thumb|center|Fig 15. The setting of a reactive trajectory of the F + H-H system|600px]] [[File: Reactive_contour_sq1117.png|thumb|center|Fig 16. The contour graph of a reactive trajectory of the F + H-H system|600px]]

It is clear that the initial momentum leaves the product in a hot vibration state, with an increase in momenta and kinetic energy. The momenta and energy vs time graph confirm this. A subsequent drop in potential energy is observed, which makes sure that the total energy is conserved.

[[File: Reactive_momenta_sq1117.png|thumb|center|Fig 17. The momenta vs time graph of a reactive trajectory of the F + H-H system|600px]][[File: Reactive_energy_sq1117.png|thumb|center|Fig 18. The energy vs time graph of a reactive trajectory of the F + H-H system|600px]]

Vibration hot state can be detected using UV-Vis spectroscopy. In an adiabetic environment, the temperature of the system will also increase, which can be measured by a thermometer.

=== The position of the transition state and its relationship with vibration and translation energy. ===

According to Hammond's postulate, because the F + H-H reaction is exothermic, it should have an early transition state that mostly resembles the reactant. On contrary, the H + H-F reaction is endothermic, and its transition state should occur late in terms of reaction coordinates and mostly resemble the product.

The following setup produces a reactive trajectory for the H + H-F reaction.

[[File:Reactive_HHF_setup_sq1117.PNG|thumb|center|Fig 19. The setting of a reactive trajectory of the H + H-F system|600px]][[File: Reactive_HHF_contour_sq1117.png|thumb|center|Fig 20. The contour graph of a reactive trajectory of the H + H-F system|600px]]

MRD:sq111714052019

2019-05-16T18:50:22Z

Sq1117:

= Molecular Reaction Dynamic Wiki Sicong Qiu =

== Exercise 1 : the H-H-H system. ==

=== 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? ===

It is the point where the second derivatives of both V(r1) and V(r2) are 0. At this point r1 is equal to r2. A local minimum will only have the first derivative of either V(r1) or V(r2) equal to 0, and their second derivative will not be 0.

===Report your best estimate of the transition state position (rts) and explain your reasoning illustrating it with a “Internuclear Distances vs Time” plot for a relevant trajectory.===

The transition state position is approximately 0.908 angstrom. The internuclear distances look to be stabilised, as it is sitting right on the saddle point. The distances of A-B and B-C in the initial simulation also intercept at ~0.91 angstrom.

[[File: HHH_distance_plot1_sq1117.png |thumb|center| Fig 1. The internuclear distances between the 3 H atoms vs time|600px]]

===Comment on how the mep and the dynamic trajectory differ.===

Dynamic graph shows the inertial motion and oscillation of the molecule, which is shown as the internuclear distance is oscillating.

[[File: HHH_dynamic_contour_sq1117.png|thumb|center|Fig 2. A contour graph produced using dynamic calculation type |600px]]

MEP graph shows infinitely slow motion, so the inertial motion and oscillation is ignored. The internuclear distance is a lot more smooth.

[[File: HHH_MEP_contour_sq1117.png|thumb|center|Fig 3. A contour graph produced using MEP calculation type|600px]]

Because momenta is reset to 0 after each step, kinetic energy is lost and the total energy is not conserved. The total energy using dynamic method is -99.119 kcal/mol, and the total energy using MEP method is - 103.869 kcal/mol. The difference is the kinetic energy.

=== Reactive and unreactive trajectory ===

{| class="wikitable" border="1"
|+ Different trajectory
|-
| P1 || P2 || Etot || Reactive? || Description || Illustration
|-
| -1.25 || -2.5 || -99.076 || yes || Atom C approaches with sufficient energy to get through the transition state and forms a bond with B || [[File:HHH_-1.25-2.5_sq1117.png|thumb|Fig 4]]
|-
| -1.5 || -2.0 || -100.028 || no || Atom C approaches without enough energy to get through the TS, it bounces back. || [[File:HHH_-1.5-2.0_sq1117.png|thumb|Fig 5]]
|-
| -1.5 || -2.5 || -98.771 || yes || Atom C approaches with sufficient energy to get through the transition state and forms a bond with B || [[File:HHH_-1.5-2.5_sq1117.png|thumb|Fig 6]]
|-
| -2.5 || -5.0 || -85.000 || no || Atom C approaches with sufficient energy to get through the transition state, but somehow reaction fails and energy is transferred from C to AB || [[File:HHH_-2.5-5.0_sq1117.png|thumb|Fig 7]]
|-
| -2.5 || -5.2 || -83.471 || yes || Atom C has enough energy to get through the transition state, the momentum leaves the molecule in an excited state. || [[File:HHH_-2.5-5.2_sq1117.png|thumb|Fig 8]]
|}

Conclusion

To achieve reaction, the particles must have kinetic energy above a threshold.
However, even with enough energy, there's a chance that energy transfer will happen instead of reaction.

=== Main assumptions in the transition state theory and how they affect the predicted rate in comparison the experimental value. ===

There're a few assumptions being made in the transition state theory1:

1. Nuclear motion and electron motion are separate, similar to the Born-Oppenheimer approximation.

2. Maxwell-Boltzmann distribution is applied to the reactant molecules.

3. Molecules that have crossed the transition state cannot reform reactants.

4. In the transition state, motion along the reaction coordinate may be separated from other motion and treated classically as a translation.

5. Even in the absence of equilibrium between the reactant and the product, the transition states that are becoming the product follows the Maxwell-Boltzmann laws.

However:

1. In our simulations, there're examples that molecules with sufficient energy that have crossed the barrier reform the reactant. With this in mind, the realistic reaction rate is likely to be lower than predicted.

2. For a very short lived transition state, the activated complexes may not have enough time to reach the equilibrium according to Maxwell-Boltzmann laws before turning into products.

3. Particles may behave according to quantum mechanics instead. For a reaction with low energy barrier, particles without sufficient energy may tunnel through the barrier and react.

== Exercise 2: the F-H-H system. ==

=== Energetics and the bond strength of the chemical species. ===

Bond strength in kJ/mol

H-H: 436 H-F: 567

In the F + H2 reaction, a H-H bond is broken and a H-F bond is formed. The reaction is exothermic with -131 kJ/mol.

In the H + HF reaction, a H-F bond is broken and a H-H bond is formed. the reaction is endothermic with 131 kJ/mol.

=== Locating the transition state ===

==== F + H2 system ====

rHF = r1 = 1.810, rHH = r2 = 0.745. At these distances, the internuclear distances can stabilise.

[[File: F_H-H_distance_plot_sq1117.png|thumb|center|Fig 9. The internuclear distances between the F,H,H atoms at transition state vs time|600px]] [[File: F_H-H_contour_sq1117.png|thumb|center|Fig 10. The contour graph of F + H-H system at transition state|600px]]

==== H + H-F system ====

rHH = r1 = 0.745, rHF = r2 = 1.810. At these distances, the internuclear distances can stabilise.

[[File: H_H-F_distance_plot_sq1117.png|thumb|center|Fig 11.The internuclear distances between the H,H,F atoms at transition state vs time|600px]] [[File: H_H-F_contour_plot_sq1117.png|thumb|center|Fig 12. The contour graph of H-F + H system at transition state|600px]]

=== The activation energies ===

A = F, B = H, C = H

By increasing rAB by 0.01 from rts, the reaction is pushed toward the F + H-H side. The activation energy is -103.75-(-103.99) = 0.24 kcal/mol

[[File:Exo_ea_sq1117.png|thumb|center|Fig 13. The energy of the system vs steps when r1 is increased|600px]]

By decreasing rAB by 0.01 from rts, the reaction is pushed toward the H + H-F side. The activation energy is -103.75-(-133.91) = 30.16 kcal/mol

[[File:Endo_ea_sq1117.png|thumb|center|Fig 14. The energy of the system vs steps when r2 is decreased|600px]]

=== Mechanism of the release of energy in the F + H-H reaction and experimental approach ===

The following setup is proved to be a reactive trajectory.

[[File: Reactive_trajectory_sq1117.PNG |thumb|center|Fig 15. The setting of a reactive trajectory of the F + H-H system|600px]] [[File: Reactive_contour_sq1117.png|thumb|center|Fig 16. The contour graph of a reactive trajectory of the F + H-H system|600px]]

It is clear that the initial momentum leaves the product in a hot vibration state, with an increase in momenta and kinetic energy. The momenta and energy vs time graph confirm this. A subsequent drop in potential energy is observed, which makes sure that the total energy is conserved.

[[File: Reactive_momenta_sq1117.png|thumb|center|Fig 17. The momenta vs time graph of a reactive trajectory of the F + H-H system|600px]][[File: Reactive_energy_sq1117.png|thumb|center|Fig 18. The energy vs time graph of a reactive trajectory of the F + H-H system|600px]]

Vibration hot state can be detected using UV-Vis spectroscopy. In an adiabetic environment, the temperature of the system will also increase, which can be measured by a thermometer.

=== The position of the transition state and its relationship with vibration and translation energy. ===

According to Hammond's postulate, because the F + H-H reaction is exothermic, it should have an early transition state that mostly resembles the reactant. On contrary, the H + H-F reaction is endothermic, and its transition state should occur late in terms of reaction coordinates and mostly resemble the product.

The following setup produces a reactive trajectory for the H + H-F reaction.

[[File:Reactive_HHF_setup_sq1117.PNG|thumb|center|Fig 19. The setting of a reactive trajectory of the H + H-F system|600px]][[File: [[File: Reactive_HHF_contour_sq1117.png|thumb|center|Fig 20. The contour graph of a reactive trajectory of the H + H-F system|600px]]

File:Reactive HHF contour sq1117.png

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