== Basic Theory ==

===Transition State Theory ==

== EXERCISE 1: H + H2 system ==

=== Q1. 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 the maximum in energy (saddle point) along the reaction pathway. On the potential energy surface diagram, the saddle point is minimum when viewing potential against r1/r2. However, it is maximum for the angle orthogonal to it. Mathematically, the maximum can be defined using first and second derivative. The first derivative equals to zero, and the second derivative should be a negative value.

=== Q2. 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. ===

If the system starts at the transition state with no momentum, there will be no force acting on the atom, so the atom will not oscillate. So if there are two horizontal straight lines on the internuclear distance vs time plot, that means the atoms are not move at all. The best estimate of the transition state position is 90.775 pm.

=== Q3. Comment on how the mep and the trajectory you just calculated differ. ===

Under the same condition ( r1 = rts+δ, r2 = rts), the potential energy equals to the total energy, where the kinetic energy keeps zero all the time and there is no vibrational energy on mep calculation, and the total energy is not constant in mep. However, on the dynamics calculation, the atoms vibrate, and total energy conserves.

=== Q4. Complete the table above by adding the total energy, whether the trajectory is reactive or unreactive, and provide a plot of the trajectory and a small description for what happens along the trajectory. What can you conclude from the table? ===

{| class="wikitable" border=1
! p1/ g.mol-1.pm.fs-1 !! p2/ g.mol-1.pm.fs-1 !! Etot !! Reactive? !! Description of the dynamics !! Illustration of the trajectory
|-
| -2.56 || -5.1 || -414.280 || reactive || The H atom and H2 molecule approach to each other, and the system has enough energy to across the energy barrier and form the product. || [[File:0149685_t1.png|180px]]
|-
| -3.1 || -4.1 || -420.077 || unreactive || The atom is approaching to the molecule, then they separate again since they don't have enough energy to overcome the activation energy. || [[File:01499685_t2.png|180px]]
|-
| -3.1 || -5.1 || -413.977|| reactive ||The atom is going to react with the molecule and the gives the product. || [[File:01499685_t3.png|180px]]
|-
| -5.1 || -10.1 || -357.277 || unreactive || The reactants just collide with each other, they don't have enough energy to across the energy barrier. ||[[File:01499685_t4.png|180px]]
|-
| -5.1 || -10.6 || -349.477|| unreactive || They collide with each other and unable to form the transition state. ||[[File:01499685_t5.png|180px]]
|}

=== Q5.Given the results you have obtained, how will Transition State Theory predictions for reaction rate values compare with experimental values? ===

The Transition State Theory prediction underestimate the reaction rate values compare with experimental values. Because the transition state theory assumes that once the reactant across the energy barrier and it cannot back to reactant. However, in the actual experiment, the reactants can go across the transition state and form products, then reform the reactants.

== EXERCISE 2: F - H - H system ==

=== Q1. By inspecting the potential energy surfaces, classify the F + H2 and H + HF reactions according to their energetics (endothermic or exothermic). How does this relate to the bond strength of the chemical species involved? ===

It is an exothermic reaction. Since H can form a stronger bond with F, it will release more energy when forming the new H-F bond. It only needs a little energy to break the H-H bond and reach the transition state. Overall, it is an exothermic reaction.

=== Q2. Locate the approximate position of the transition state. ===

Since this reaction of F + H2 is an exothermic reaction, the transition state has a energy closer to the reactant. Based on the Hammond's Postulate, the structure of the transition state will resemble the structure of reactant. This type of transition state is defined as early transition state. In this case, early barrier and translational energy are more efficient.In the F-H-H system, the H-H bond will not be elongated too much, so the bond length is 74 pm. Then set the momentum zero, and by testing the different value of the distance between F and H, the approximate position of the transition is around 182 pm.

activation energy

=== Q3. Report the activation energy for both reactions.===

===Q4. 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.===

=== Q5. Discuss how the distribution of energy between different modes (translation and vibration) affect the efficiency of the reaction, and how this is influenced by the position of the transition state.===

MRD:01499685

2020-05-15T14:07:06Z

Yw21318:

== Basic Theory ==

===Transition State Theory ==

== EXERCISE 1: H + H2 system ==

=== Q1. 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 the maximum in energy (saddle point) along the reaction pathway. On the potential energy surface diagram, the saddle point is minimum when viewing potential against r1/r2. However, it is maximum for the angle orthogonal to it. Mathematically, the maximum can be defined using first and second derivative. The first derivative equals to zero, and the second derivative should be a negative value.

=== Q2. 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. ===

If the system starts at the transition state with no momentum, there will be no force acting on the atom, so the atom will not oscillate. So if there are two horizontal straight lines on the internuclear distance vs time plot, that means the atoms are not move at all. The best estimate of the transition state position is 90.775 pm.

=== Q3. Comment on how the mep and the trajectory you just calculated differ. ===

Under the same condition ( r1 = rts+δ, r2 = rts), the potential energy equals to the total energy, where the kinetic energy keeps zero all the time and there is no vibrational energy on mep calculation, and the total energy is not constant in mep. However, on the dynamics calculation, the atoms vibrate, and total energy conserves.

=== Q4. Complete the table above by adding the total energy, whether the trajectory is reactive or unreactive, and provide a plot of the trajectory and a small description for what happens along the trajectory. What can you conclude from the table? ===

{| class="wikitable" border=1
! p1/ g.mol-1.pm.fs-1 !! p2/ g.mol-1.pm.fs-1 !! Etot !! Reactive? !! Description of the dynamics !! Illustration of the trajectory
|-
| -2.56 || -5.1 || -414.280 || reactive || The H atom and H2 molecule approach to each other, and the system has enough energy to across the energy barrier and form the product. || [[File:0149685_t1.png|150px]]
|-
| -3.1 || -4.1 || -420.077 || unreactive || The atom is approaching to the molecule, then they separate again since they don't have enough energy to overcome the activation energy. || [[File:01499685_t2.png|150px]]
|-
| -3.1 || -5.1 || -413.977|| reactive ||The atom is going to react with the molecule and the gives the product. || [[File:01499685_t3.png|150px]]
|-
| -5.1 || -10.1 || -357.277 || unreactive || The reactants just collide with each other, they don't have enough energy to across the energy barrier. ||[[File:01499685_t4.png|150px]]
|-
| -5.1 || -10.6 || -349.477|| unreactive || They collide with each other and unable to form the transition state. ||[[File:01499685_t5.png|150px]]
|}

=== Q5.Given the results you have obtained, how will Transition State Theory predictions for reaction rate values compare with experimental values? ===

The Transition State Theory prediction underestimate the reaction rate values compare with experimental values. Because the transition state theory assumes that once the reactant across the energy barrier and it cannot back to reactant. However, in the actual experiment, the reactants can go across the transition state and form products, then reform the reactants.

== EXERCISE 2: F - H - H system ==

=== Q1. By inspecting the potential energy surfaces, classify the F + H2 and H + HF reactions according to their energetics (endothermic or exothermic). How does this relate to the bond strength of the chemical species involved? ===

It is an exothermic reaction. Since H can form a stronger bond with F, it will release more energy when forming the new H-F bond. It only needs a little energy to break the H-H bond and reach the transition state. Overall, it is an exothermic reaction.

=== Q2. Locate the approximate position of the transition state. ===

Since this reaction of F + H2 is an exothermic reaction, the transition state has a energy closer to the reactant. Based on the Hammond's Postulate, the structure of the transition state will resemble the structure of reactant. This type of transition state is defined as early transition state. In this case, early barrier and translational energy are more efficient.In the F-H-H system, the H-H bond will not be elongated too much, so the bond length is 74 pm. Then set the momentum zero, and by testing the different value of the distance between F and H, the approximate position of the transition is around 182 pm.

activation energy

=== Q3. Report the activation energy for both reactions.===

===Q4. 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.===

=== Q5. Discuss how the distribution of energy between different modes (translation and vibration) affect the efficiency of the reaction, and how this is influenced by the position of the transition state.===

MRD:01499685

2020-05-15T12:36:36Z

Yw21318:

MRD:01499685

2020-05-15T12:15:06Z

Yw21318:

File:01499685 t5.png

2020-05-14T12:15:26Z

Yw21318:

MRD:01499685

2020-05-14T12:12:55Z

Yw21318: