MRD:zy1416

2018-05-18T14:09:02Z

Zy1416:

== '''Molecular reaction dynamics''' ==

=== ''EXERCISE 1: H + H2 system'' ===
'''Question 1:''' '''What value do the different components of the gradient of the potential energy surface have at a minimum and at a transition structure? Briefly explain how minima and transition structures can be distinguished using the curvature of the potential energy surface.'''

The gradients of r2 in the potential energy surface at one minimum is zero and the gradient of r1 in another minimum is zero.

The curvatures of both components of the potential energy surface for minima are positive. i.e the second derivative ∂2V(r1)/∂(r1)2 => 0 ∂2V(r2)/∂(r2)2 => 0

At the transition state, the gradients for both components are both zero. But one of the curvatures is negative and one of the curvatures is positive.

 '''Question 2: 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.''' '''<nowiki/>'''
* The transition state position is estimated at r1=r2= 0.908 Å. The “Internuclear Distances vs Time” plot shows two almost flat lines, indicating that the atoms hardly oscillates and are close to an equilibrium. The distance of AB equals to the distance of BC so the two lines overlap.
[[File:Zy1416_transiton_state_estimate.png|400px|center]]

'''Question 3: Comment on how the mep and the trajectory you just calculated differ.'''
* The MEP trajectory reflects the initial part of the dynamics trajectory but occurs at larger time scale.
{| class="wikitable" border="1"
! !! MEP !! Dynamics
|-
! distance
| [[File:Mep_distance_zy1416.png|300px|center]] || [[File:Dynamics_distance_zy1416.png|300px|left]]
|-
! momenta
| [[File:Mep_momenta_zy1416.png|300px|left]] || [[File:Dynamics_distance_zy1416.png|300px|left]]
|}
* Final values of the positions r1(t) r2(t) and the average momenta p1(t) p2(t) at large t:
{| class="wikitable" border="1"
! !! MEP !! Dynamics
|-
! '''r1'''
| 1.72 || 2.76
|-
! '''r2'''
| 0.75 || 0.74
|-
! '''p1'''
| 0 || 0
|-
! '''p2'''
| 2.47 || 1.26
|}

'''Question 4: Complete the table by adding a column with the total energy, and another column reporting if the trajectory is reactive or unreactive. For each set of initial conditions, provide a plot of the trajectory and a small description for what happens along the trajectory.'''

{| class="wikitable" border="1"
! p1 !! p2 !! total energy / kcal mol-1 !! reactivity !! plot !! description
|-
| -1.25 || -2.5 || -99.-018 || reactive || [[File:zy1416_Trajectory_1.png|300px|center]] || trajectory crosses the TS and moves towards the product; r2 decreases in the entrance channel and r1 does not fluctuate; trajectory shows vibration in r2 as r1 increases in the exit channel
|-
| -1.5 || -2.0 || -100.456 || unreactive || [[File:zy1416_Trajectory_2.png|300px|center]] || trajectory does not reach the transition state and moves back towards the initial point in the entrance channel; shows vibration in r1
|-
| -1.5 || -2.5 || -98.956 || reactive || [[File:zy1416_Trajectory_3.png|300px|center]] || trajectory crosses the TS and moves towards the product; slight vibration in r1 as r2 decreases in the entrance channel; vibration in r2 as r1 increases in the exit channel
|-
| -2.5 || -5.0 || -84.956 || unreactive || [[File:zy1416_Trajectory_4.png|300px|center]] || trajectory crosses the transition state region but reverts back to the reactants
|-
| -2.5 || -5.2 || -83.416 || reactive || [[File:zy1416_Trajectory_5.png|300px|center]] || trajectory crosses the transition state and reverts back to the entrance channel and eventually moves towards the products
|}

'''Question 5: 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?'''
* There are three main assumptions made in the transition state theory:
1.The quantum-tunneling effects and the Born-Oppenheimer approximation are ignored.

2.The atoms in the reactant state have energies that are Boltzmann distributed.

3.At the transition state, with a velocity towards the product configuration, it will not re-enter the initial state region again.
* The limitation of the transition state theory is that the quantum-tunneling effect is assumed to be negligible. However, quantum mechanics shows that particles can tunnel through the energy barrier created by the transition state, allowing the reaction to occur. So the experimental values of the reaction rate would be higher than the theoretical values.

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

'''PES inspection'''
'''Question 6: 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?'''
* '''H + HF :'''
[[File:zy1416_Surface_Plot_H2F.png|400px|center]]

It can be seen from the PES plot of this reaction that the products have higher energy than the reactants, indicating an endothermic reaction.
H-F bond is strongly polarisd and has a large ionic component with strong bond strength. The energy required for breaking the H-F bond can not be compensated by the energy gain from the formation of a H-H bond. So overall the reaction is endothermic.
* '''F + H2:'''
[[File:zy1416_Surface_Plot_HHF.png|400px|center]]

The PES plot of F + H2 shows that the reactants have higher energy than the products. This reaction is exothermic. As discussed above, the formation of H-F bond would gain a large enthalpy due to strong bond strength and this energy gain compensates the energy lose for breaking the H-H bond. The overall reaction is exothermic.

 '''Question 7: Locate the approximate position of the transition state.'''
* For H+HF, the reaction is endothermic and the transition state would resemble the product; for the other reaction which is exothermic, the transition state would resemble the reactants which is the products for the first reaction. These two reactions would have the same transition state H--H--F. And the approximate position can be located on the PES plot.

[[File:zy1416_Surface_Plot_transition_state.png|500px|center]]
* The distance between H and H is determined to be 0.745 Å and the distance between H and F is determined to be 1.810 Å. The “Internuclear Distances vs Time” plot confirmed this position. The activation energy for the endothermic reaction is much higher than the exothermic reaction. Because the transition state resembles the H2+F species and they have similar energies.

[[File:Zy1416_Transition_state_distance.png|400px|center]]

'''Question 8: Report the activation energy for both reactions.'''
{| class="wikitable" border=1
! H+HF !! H2+F
|-
| [[File:Zy1416_HHF_Ea.png|300px|center]] || [[File:zy1416_H2F_Ea.png|300px|center]]
|-
| Ea = (-103.785)-(-134.016) = 30.231 kcal/mol || Ea = (-103.752)-(-104.007) = 0.255 kcal/mol
|}

'''Reaction Dynamics'''

'''Question 9: In light of the fact that energy is conserved, discuss the mechanism of release of the reaction energy. How could this be confirmed experimentally?'''

The initial conditions have been set to be rH-H=0.74 Å , rH-F=2.00 Å and momentumH-F=-10. The potential energy released is converted into the kinetic energy of the hydrogen atom. It can be seen from the Momenta vs Time plot that pHH increases after the collision. The kinetic energy would be further convert into thermal energy as the product hydrogen atoms collide with each other. There would be an temperature increase for this exothermic reaction which can be measured experimentally.

[[File:ZZy1416_Momenta_H2F.png|400px|center]]

 '''Questin 10: 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.'''
* '''F+H2'''

With a small momentum of -0.5 for the coming H atom, the reaction would be mostly unsuccessful even the H-H bond has a vibration energy which is significantly larger than the activation energy (0.255 kcal/mol) except for very few values of momenta.

{| class="wikitable" border=1
! pHH !! Contour Plot !! pHH !! Contour Plot !! pHH !! Contour Plot !! {{fontcolor|blue|pHH}} !! {{fontcolor|blue|Contour Plot}}
|-
| -3.0 || [[File:minus3.0_zy1416.png|200px|center]] || -2.9 || [[File:zy1416_minus2.9.png|200px|center]] || -2.0 || [[File:zy1416_minus2.0.png|200px|center]] || {{fontcolor|blue|-2.4}} || [[File:zy1416_minus2.4.png|200px|center]]
|-
| -1.0 || [[File:zy1416_minus1.0.png|200px|center]] || 0.0 || [[File:zy1416_0.png|200px|center]] || 1.0 || [[File:zy1416_minus1.0.png|200px|center]] || {{fontcolor|blue|2.6}} || [[File:Zy1416_2.6.png|200px|center]]
|-
| 2.0 || [[File:zy1416_2.0.png|200px|center]] || 2.9 || [[File:zy1416_2.9.png|200px|center]] || 3.0 || [[File:zy1416_3.0.png|200px|center]] ||
|}

* '''H+HF'''
When the pHH has a large value above the activation energy (30.231 kcal/mol), which was set to be -20. The hydrogen atom collides with the HF molecule and breaks the H-F bond. However, two hydrogen atoms moves apart and do not form a H2 molecule. The reaction is illustrated in the following animation snapshots.
{| class="wikitable" border=1
! [[File:zy1416_HFF_unreactive_animation_0.png|300px|center]] !! [[File:zy1416_HFF_unreactive_animation_1.png|300px|center]] !! [[File:zy1416_HFF_unreactive_animation_2.png|300px|center]]
|}

One reactive trajectory has the conditions of rFH = 0.91 Å, rHH = 2.0 Å, pHF = -0.5 and pHH = -10. The trajectory recrosses the transition state region twice and eventually moves into exit channel, forming products.

[[File:ZY14166_HFF_REACTIVE.png‎|400px|left]]

MRD:zy1416

2018-05-18T14:08:17Z

Zy1416:

== '''Molecular reaction dynamics''' ==

=== ''EXERCISE 1: H + H2 system'' ===
'''Question 1:''' '''What value do the different components of the gradient of the potential energy surface have at a minimum and at a transition structure? Briefly explain how minima and transition structures can be distinguished using the curvature of the potential energy surface.'''

The gradients of r2 in the potential energy surface at one minimum is zero and the gradient of r1 in another minimum is zero.

The curvatures of both components of the potential energy surface for minima are positive. i.e the second derivative ∂2V(r1)/∂(r1)2 => 0 ∂2V(r2)/∂(r2)2 => 0

At the transition state, the gradients for both components are both zero. But one of the curvatures is negative and one of the curvatures is positive.

 '''Question 2: 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.''' '''<nowiki/>'''
* The transition state position is estimated at r1=r2= 0.908 Å. The “Internuclear Distances vs Time” plot shows two almost flat lines, indicating that the atoms hardly oscillates and are close to an equilibrium. The distance of AB equals to the distance of BC so the two lines overlap.
[[File:Zy1416_transiton_state_estimate.png|400px|center]]

'''Question 3: Comment on how the mep and the trajectory you just calculated differ.'''
* The MEP trajectory reflects the initial part of the dynamics trajectory but occurs at larger time scale.
{| class="wikitable" border="1"
! !! MEP !! Dynamics
|-
! distance
| [[File:Mep_distance_zy1416.png|300px|center]] || [[File:Dynamics_distance_zy1416.png|300px|left]]
|-
! momenta
| [[File:Mep_momenta_zy1416.png|300px|left]] || [[File:Dynamics_distance_zy1416.png|300px|left]]
|}
* Final values of the positions r1(t) r2(t) and the average momenta p1(t) p2(t) at large t:
{| class="wikitable" border="1"
! !! MEP !! Dynamics
|-
! '''r1'''
| 1.72 || 2.76
|-
! '''r2'''
| 0.75 || 0.74
|-
! '''p1'''
| 0 || 0
|-
! '''p2'''
| 2.47 || 1.26
|}

'''Question 4: Complete the table by adding a column with the total energy, and another column reporting if the trajectory is reactive or unreactive. For each set of initial conditions, provide a plot of the trajectory and a small description for what happens along the trajectory.'''

{| class="wikitable" border="1"
! p1 !! p2 !! total energy / kcal mol-1 !! reactivity !! plot !! description
|-
| -1.25 || -2.5 || -99.-018 || reactive || [[File:zy1416_Trajectory_1.png|300px|center]] || trajectory crosses the TS and moves towards the product; r2 decreases in the entrance channel and r1 does not fluctuate; trajectory shows vibration in r2 as r1 increases in the exit channel
|-
| -1.5 || -2.0 || -100.456 || unreactive || [[File:zy1416_Trajectory_2.png|300px|center]] || trajectory does not reach the transition state and moves back towards the initial point in the entrance channel; shows vibration in r1
|-
| -1.5 || -2.5 || -98.956 || reactive || [[File:zy1416_Trajectory_3.png|300px|center]] || trajectory crosses the TS and moves towards the product; slight vibration in r1 as r2 decreases in the entrance channel; vibration in r2 as r1 increases in the exit channel
|-
| -2.5 || -5.0 || -84.956 || unreactive || [[File:zy1416_Trajectory_4.png|300px|center]] || trajectory crosses the transition state region but reverts back to the reactants
|-
| -2.5 || -5.2 || -83.416 || reactive || [[File:zy1416_Trajectory_5.png|300px|center]] || trajectory crosses the transition state and reverts back to the entrance channel and eventually moves towards the products
|}

'''Question 5: 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?'''
* There are three main assumptions made in the transition state theory:
1.The quantum-tunneling effects and the Born-Oppenheimer approximation are ignored.

2.The atoms in the reactant state have energies that are Boltzmann distributed.

3.At the transition state, with a velocity towards the product configuration, it will not re-enter the initial state region again.
* The limitation of the transition state theory is that the quantum-tunneling effect is assumed to be negligible. However, quantum mechanics shows that particles can tunnel through the energy barrier created by the transition state, allowing the reaction to occur. So the experimental values of the reaction rate would be higher than the theoretical values.

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

'''PES inspection'''
'''Question 6: 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?'''
* '''H + HF :'''
[[File:zy1416_Surface_Plot_H2F.png|400px|center]]

It can be seen from the PES plot of this reaction that the products have higher energy than the reactants, indicating an endothermic reaction.
H-F bond is strongly polarisd and has a large ionic component with strong bond strength. The energy required for breaking the H-F bond can not be compensated by the energy gain from the formation of a H-H bond. So overall the reaction is endothermic.
* '''F + H2:'''
[[File:zy1416_Surface_Plot_HHF.png|400px|center]]

The PES plot of F + H2 shows that the reactants have higher energy than the products. This reaction is exothermic. As discussed above, the formation of H-F bond would gain a large enthalpy due to strong bond strength and this energy gain compensates the energy lose for breaking the H-H bond. The overall reaction is exothermic.

 '''Question 7: Locate the approximate position of the transition state.'''
* For H+HF, the reaction is endothermic and the transition state would resemble the product; for the other reaction which is exothermic, the transition state would resemble the reactants which is the products for the first reaction. These two reactions would have the same transition state H--H--F. And the approximate position can be located on the PES plot.

[[File:zy1416_Surface_Plot_transition_state.png|500px|center]]
* The distance between H and H is determined to be 0.745 Å and the distance between H and F is determined to be 1.810 Å. The “Internuclear Distances vs Time” plot confirmed this position. The activation energy for the endothermic reaction is much higher than the exothermic reaction. Because the transition state resembles the H2+F species and they have similar energies.

[[File:Zy1416_Transition_state_distance.png|400px|center]]

'''Question 8: Report the activation energy for both reactions.'''
{| class="wikitable" border=1
! H+HF !! H2+F
|-
| [[File:Zy1416_HHF_Ea.png|300px|center]] || [[File:zy1416_H2F_Ea.png|300px|center]]
|-
| Ea = (-103.785)-(-134.016) = 30.231 kcal/mol || Ea = (-103.752)-(-104.007) = 0.255 kcal/mol
|}

'''Reaction Dynamics'''

'''Question 9: In light of the fact that energy is conserved, discuss the mechanism of release of the reaction energy. How could this be confirmed experimentally?'''

The initial conditions have been set to be rH-H=0.74 Å , rH-F=2.00 Å and momentumH-F=-10. The potential energy released is converted into the kinetic energy of the hydrogen atom. It can be seen from the Momenta vs Time plot that pHH increases after the collision. The kinetic energy would be further convert into thermal energy as the product hydrogen atoms collide with each other. There would be an temperature increase for this exothermic reaction which can be measured experimentally.

[[File:ZZy1416_Momenta_H2F.png|400px|center]]

 '''Questin 10: 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.'''
* '''F+H2'''

With a small momentum of -0.5 for the coming H atom, the reaction would be mostly unsuccessful even the H-H bond has a vibration energy which is significantly larger than the activation energy (0.255 kcal/mol) except for very few values of momenta.

{| class="wikitable" border=1
! pHH !! Contour Plot !! pHH !! Contour Plot !! pHH !! Contour Plot !! pHH !! Contour Plot
|-
| -3.0 || [[File:minus3.0_zy1416.png|200px|center]] || -2.9 || [[File:zy1416_minus2.9.png|200px|center]] || -2.0 || [[File:zy1416_minus2.0.png|200px|center]] || {{fontcolor|red|-2.4}} || [[File:zy1416_minus2.4.png|200px|center]]
|-
| -1.0 || [[File:zy1416_minus1.0.png|200px|center]] || 0.0 || [[File:zy1416_0.png|200px|center]] || 1.0 || [[File:zy1416_minus1.0.png|200px|center]] || {{fontcolor|red|2.6}} || [[File:Zy1416_2.6.png|200px|center]]
|-
| 2.0 || [[File:zy1416_2.0.png|200px|center]] || 2.9 || [[File:zy1416_2.9.png|200px|center]] || 3.0 || [[File:zy1416_3.0.png|200px|center]] ||
|}

* '''H+HF'''
When the pHH has a large value above the activation energy (30.231 kcal/mol), which was set to be -20. The hydrogen atom collides with the HF molecule and breaks the H-F bond. However, two hydrogen atoms moves apart and do not form a H2 molecule. The reaction is illustrated in the following animation snapshots.
{| class="wikitable" border=1
! [[File:zy1416_HFF_unreactive_animation_0.png|300px|center]] !! [[File:zy1416_HFF_unreactive_animation_1.png|300px|center]] !! [[File:zy1416_HFF_unreactive_animation_2.png|300px|center]]
|}

One reactive trajectory has the conditions of rFH = 0.91 Å, rHH = 2.0 Å, pHF = -0.5 and pHH = -10. The trajectory recrosses the transition state region twice and eventually moves into exit channel, forming products.

[[File:ZY14166_HFF_REACTIVE.png‎|400px|left]]

MRD:zy1416

2018-05-18T14:06:12Z

Zy1416:

== '''Molecular reaction dynamics''' ==

=== ''EXERCISE 1: H + H2 system'' ===
'''Question 1:''' '''What value do the different components of the gradient of the potential energy surface have at a minimum and at a transition structure? Briefly explain how minima and transition structures can be distinguished using the curvature of the potential energy surface.'''

The gradients of r2 in the potential energy surface at one minimum is zero and the gradient of r1 in another minimum is zero.

The curvatures of both components of the potential energy surface for minima are positive. i.e the second derivative ∂2V(r1)/∂(r1)2 => 0 ∂2V(r2)/∂(r2)2 => 0

At the transition state, the gradients for both components are both zero. But one of the curvatures is negative and one of the curvatures is positive.

 '''Question 2: 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.''' '''<nowiki/>'''
* The transition state position is estimated at r1=r2= 0.908 Å. The “Internuclear Distances vs Time” plot shows two almost flat lines, indicating that the atoms hardly oscillates and are close to an equilibrium. The distance of AB equals to the distance of BC so the two lines overlap.
[[File:Zy1416_transiton_state_estimate.png|400px|center]]

'''Question 3: Comment on how the mep and the trajectory you just calculated differ.'''
* The MEP trajectory reflects the initial part of the dynamics trajectory but occurs at larger time scale.
{| class="wikitable" border="1"
! !! MEP !! Dynamics
|-
! distance
| [[File:Mep_distance_zy1416.png|300px|center]] || [[File:Dynamics_distance_zy1416.png|300px|left]]
|-
! momenta
| [[File:Mep_momenta_zy1416.png|300px|left]] || [[File:Dynamics_distance_zy1416.png|300px|left]]
|}
* Final values of the positions r1(t) r2(t) and the average momenta p1(t) p2(t) at large t:
{| class="wikitable" border="1"
! !! MEP !! Dynamics
|-
! '''r1'''
| 1.72 || 2.76
|-
! '''r2'''
| 0.75 || 0.74
|-
! '''p1'''
| 0 || 0
|-
! '''p2'''
| 2.47 || 1.26
|}

'''Question 4: Complete the table by adding a column with the total energy, and another column reporting if the trajectory is reactive or unreactive. For each set of initial conditions, provide a plot of the trajectory and a small description for what happens along the trajectory.'''

{| class="wikitable" border="1"
! p1 !! p2 !! total energy / kcal mol-1 !! reactivity !! plot !! description
|-
| -1.25 || -2.5 || -99.-018 || reactive || [[File:zy1416_Trajectory_1.png|300px|center]] || trajectory crosses the TS and moves towards the product; r2 decreases in the entrance channel and r1 does not fluctuate; trajectory shows vibration in r2 as r1 increases in the exit channel
|-
| -1.5 || -2.0 || -100.456 || unreactive || [[File:zy1416_Trajectory_2.png|300px|center]] || trajectory does not reach the transition state and moves back towards the initial point in the entrance channel; shows vibration in r1
|-
| -1.5 || -2.5 || -98.956 || reactive || [[File:zy1416_Trajectory_3.png|300px|center]] || trajectory crosses the TS and moves towards the product; slight vibration in r1 as r2 decreases in the entrance channel; vibration in r2 as r1 increases in the exit channel
|-
| -2.5 || -5.0 || -84.956 || unreactive || [[File:zy1416_Trajectory_4.png|300px|center]] || trajectory crosses the transition state region but reverts back to the reactants
|-
| -2.5 || -5.2 || -83.416 || reactive || [[File:zy1416_Trajectory_5.png|300px|center]] || trajectory crosses the transition state and reverts back to the entrance channel and eventually moves towards the products
|}

'''Question 5: 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?'''
* There are three main assumptions made in the transition state theory:
1.The quantum-tunneling effects and the Born-Oppenheimer approximation are ignored.

2.The atoms in the reactant state have energies that are Boltzmann distributed.

3.At the transition state, with a velocity towards the product configuration, it will not re-enter the initial state region again.
* The limitation of the transition state theory is that the quantum-tunneling effect is assumed to be negligible. However, quantum mechanics shows that particles can tunnel through the energy barrier created by the transition state, allowing the reaction to occur. So the experimental values of the reaction rate would be higher than the theoretical values.

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

'''PES inspection'''
'''Question 6: 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?'''
* '''H + HF :'''
[[File:zy1416_Surface_Plot_H2F.png|400px|center]]

It can be seen from the PES plot of this reaction that the products have higher energy than the reactants, indicating an endothermic reaction.
H-F bond is strongly polarisd and has a large ionic component with strong bond strength. The energy required for breaking the H-F bond can not be compensated by the energy gain from the formation of a H-H bond. So overall the reaction is endothermic.
* '''F + H2:'''
[[File:zy1416_Surface_Plot_HHF.png|400px|center]]

The PES plot of F + H2 shows that the reactants have higher energy than the products. This reaction is exothermic. As discussed above, the formation of H-F bond would gain a large enthalpy due to strong bond strength and this energy gain compensates the energy lose for breaking the H-H bond. The overall reaction is exothermic.

 '''Question 7: Locate the approximate position of the transition state.'''
* For H+HF, the reaction is endothermic and the transition state would resemble the product; for the other reaction which is exothermic, the transition state would resemble the reactants which is the products for the first reaction. These two reactions would have the same transition state H--H--F. And the approximate position can be located on the PES plot.

[[File:zy1416_Surface_Plot_transition_state.png|500px|center]]
* The distance between H and H is determined to be 0.745 Å and the distance between H and F is determined to be 1.810 Å. The “Internuclear Distances vs Time” plot confirmed this position. The activation energy for the endothermic reaction is much higher than the exothermic reaction. Because the transition state resembles the H2+F species and they have similar energies.

[[File:Zy1416_Transition_state_distance.png|400px|center]]

'''Question 8: Report the activation energy for both reactions.'''
{| class="wikitable" border=1
! H+HF !! H2+F
|-
| [[File:Zy1416_HHF_Ea.png|300px|center]] || [[File:zy1416_H2F_Ea.png|300px|center]]
|-
| Ea = (-103.785)-(-134.016) = 30.231 kcal/mol || Ea = (-103.752)-(-104.007) = 0.255 kcal/mol
|}

'''Reaction Dynamics'''

'''Question 9: In light of the fact that energy is conserved, discuss the mechanism of release of the reaction energy. How could this be confirmed experimentally?'''

The initial conditions have been set to be rH-H=0.74 Å , rH-F=2.00 Å and momentumH-F=-10. The potential energy released is converted into the kinetic energy of the hydrogen atom. It can be seen from the Momenta vs Time plot that pHH increases after the collision. The kinetic energy would be further convert into thermal energy as the product hydrogen atoms collide with each other. There would be an temperature increase for this exothermic reaction which can be measured experimentally.

[[File:ZZy1416_Momenta_H2F.png|400px|center]]

 '''Questin 10: 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.'''
* '''F+H2'''

With a small momentum of -0.5 for the coming H atom, the reaction would be mostly unsuccessful even the H-H bond has a vibration energy which is significantly larger than the activation energy (0.255 kcal/mol) except for very few values of momenta.

{| class="wikitable" border=1
! pHH !! Contour Plot !! pHH !! Contour Plot !! pHH !! Contour Plot !! pHH !! Contour Plot
|-
| -3.0 || [[File:minus3.0_zy1416.png|200px|center]] || -2.9 || [[File:zy1416_minus2.9.png|200px|center]] || -2.0 || [[File:zy1416_minus2.0.png|200px|center]] || -2.4 || [[File:zy1416_minus2.4.png|200px|center]]
|-
| -1.0 || [[File:zy1416_minus1.0.png|200px|center]] || 0.0 || [[File:zy1416_0.png|200px|center]] || 1.0 || [[File:zy1416_minus1.0.png|200px|center]] || 2.6 || [[File:Zy1416_2.6.png|200px|center]]
|-
| 2.0 || [[File:zy1416_2.0.png|200px|center]] || 2.9 || [[File:zy1416_2.9.png|200px|center]] || 3.0 || [[File:zy1416_3.0.png|200px|center]] ||
|}

* '''H+HF'''
When the pHH has a large value above the activation energy (30.231 kcal/mol), which was set to be -20. The hydrogen atom collides with the HF molecule and breaks the H-F bond. However, two hydrogen atoms moves apart and do not form a H2 molecule. The reaction is illustrated in the following animation snapshots.
{| class="wikitable" border=1
! [[File:zy1416_HFF_unreactive_animation_0.png|300px|center]] !! [[File:zy1416_HFF_unreactive_animation_1.png|300px|center]] !! [[File:zy1416_HFF_unreactive_animation_2.png|300px|center]]
|}

One reactive trajectory has the conditions of rFH = 0.91 Å, rHH = 2.0 Å, pHF = -0.5 and pHH = -10. The trajectory recrosses the transition state region twice and eventually moves into exit channel, forming products.

[[File:ZY14166_HFF_REACTIVE.png‎|400px|left]]

MRD:zy1416

2018-05-18T14:05:21Z

Zy1416:

== '''Molecular reaction dynamics''' ==

=== ''EXERCISE 1: H + H2 system'' ===
'''Question 1:''' '''What value do the different components of the gradient of the potential energy surface have at a minimum and at a transition structure? Briefly explain how minima and transition structures can be distinguished using the curvature of the potential energy surface.'''

The gradients of r2 in the potential energy surface at one minimum is zero and the gradient of r1 in another minimum is zero.

The curvatures of both components of the potential energy surface for minima are positive. i.e the second derivative ∂2V(r1)/∂(r1)2 => 0 ∂2V(r2)/∂(r2)2 => 0

At the transition state, the gradients for both components are both zero. But one of the curvatures is negative and one of the curvatures is positive.

 '''Question 2: 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.''' '''<nowiki/>'''
* The transition state position is estimated at r1=r2= 0.908 Å. The “Internuclear Distances vs Time” plot shows two almost flat lines, indicating that the atoms hardly oscillates and are close to an equilibrium. The distance of AB equals to the distance of BC so the two lines overlap.
[[File:Zy1416_transiton_state_estimate.png|400px|center]]

'''Question 3: Comment on how the mep and the trajectory you just calculated differ.'''
* The MEP trajectory reflects the initial part of the dynamics trajectory but occurs at larger time scale.
{| class="wikitable" border="1"
! !! MEP !! Dynamics
|-
! distance
| [[File:Mep_distance_zy1416.png|300px|center]] || [[File:Dynamics_distance_zy1416.png|300px|left]]
|-
! momenta
| [[File:Mep_momenta_zy1416.png|300px|left]] || [[File:Dynamics_distance_zy1416.png|300px|left]]
|}
* Final values of the positions r1(t) r2(t) and the average momenta p1(t) p2(t) at large t:
{| class="wikitable" border="1"
! !! MEP !! Dynamics
|-
! '''r1'''
| 1.72 || 2.76
|-
! '''r2'''
| 0.75 || 0.74
|-
! '''p1'''
| 0 || 0
|-
! '''p2'''
| 2.47 || 1.26
|}

'''Question 4: Complete the table by adding a column with the total energy, and another column reporting if the trajectory is reactive or unreactive. For each set of initial conditions, provide a plot of the trajectory and a small description for what happens along the trajectory.'''

{| class="wikitable" border="1"
! p1 !! p2 !! total energy / kcal mol-1 !! reactivity !! plot !! description
|-
| -1.25 || -2.5 || -99.-018 || reactive || [[File:zy1416_Trajectory_1.png|300px|center]] || trajectory crosses the TS and moves towards the product; r2 decreases in the entrance channel and r1 does not fluctuate; trajectory shows vibration in r2 as r1 increases in the exit channel
|-
| -1.5 || -2.0 || -100.456 || unreactive || [[File:zy1416_Trajectory_2.png|300px|center]] || trajectory does not reach the transition state and moves back towards the initial point in the entrance channel; shows vibration in r1
|-
| -1.5 || -2.5 || -98.956 || reactive || [[File:zy1416_Trajectory_3.png|300px|center]] || trajectory crosses the TS and moves towards the product; slight vibration in r1 as r2 decreases in the entrance channel; vibration in r2 as r1 increases in the exit channel
|-
| -2.5 || -5.0 || -84.956 || unreactive || [[File:zy1416_Trajectory_4.png|300px|center]] || trajectory crosses the transition state region but reverts back to the reactants
|-
| -2.5 || -5.2 || -83.416 || reactive || [[File:zy1416_Trajectory_5.png|300px|center]] || trajectory crosses the transition state and reverts back to the entrance channel and eventually moves towards the products
|}

'''Question 5: 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?'''
* There are three main assumptions made in the transition state theory:
1.The quantum-tunneling effects and the Born-Oppenheimer approximation are ignored.

2.The atoms in the reactant state have energies that are Boltzmann distributed.

3.At the transition state, with a velocity towards the product configuration, it will not re-enter the initial state region again.
* The limitation of the transition state theory is that the quantum-tunneling effect is assumed to be negligible. However, quantum mechanics shows that particles can tunnel through the energy barrier created by the transition state, allowing the reaction to occur. So the experimental values of the reaction rate would be higher than the theoretical values.

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

'''PES inspection'''
'''Question 6: 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?'''
* '''H + HF :'''
[[File:zy1416_Surface_Plot_H2F.png|400px|center]]

It can be seen from the PES plot of this reaction that the products have higher energy than the reactants, indicating an endothermic reaction.
H-F bond is strongly polarisd and has a large ionic component with strong bond strength. The energy required for breaking the H-F bond can not be compensated by the energy gain from the formation of a H-H bond. So overall the reaction is endothermic.
* '''F + H2:'''
[[File:zy1416_Surface_Plot_HHF.png|400px|center]]

The PES plot of F + H2 shows that the reactants have higher energy than the products. This reaction is exothermic. As discussed above, the formation of H-F bond would gain a large enthalpy due to strong bond strength and this energy gain compensates the energy lose for breaking the H-H bond. The overall reaction is exothermic.

 '''Question 7: Locate the approximate position of the transition state.'''
* For H+HF, the reaction is endothermic and the transition state would resemble the product; for the other reaction which is exothermic, the transition state would resemble the reactants which is the products for the first reaction. These two reactions would have the same transition state H--H--F. And the approximate position can be located on the PES plot.

[[File:zy1416_Surface_Plot_transition_state.png|500px|center]]
* The distance between H and H is determined to be 0.745 Å and the distance between H and F is determined to be 1.810 Å. The “Internuclear Distances vs Time” plot confirmed this position. The activation energy for the endothermic reaction is much higher than the exothermic reaction. Because the transition state resembles the H2+F species and they have similar energies.

[[File:Zy1416_Transition_state_distance.png|400px|center]]

'''Question 8: Report the activation energy for both reactions.'''
{| class="wikitable" border=1
! H+HF !! H2+F
|-
| [[File:Zy1416_HHF_Ea.png|300px|center]] || [[File:zy1416_H2F_Ea.png|300px|center]]
|-
| Ea = (-103.785)-(-134.016) = 30.231 kcal/mol || Ea = (-103.752)-(-104.007) = 0.255 kcal/mol
|}

'''Reaction Dynamics'''

'''Question 9: In light of the fact that energy is conserved, discuss the mechanism of release of the reaction energy. How could this be confirmed experimentally?'''

The initial conditions have been set to be rH-H=0.74 Å , rH-F=2.00 Å and momentumH-F=-10. The potential energy released is converted into the kinetic energy of the hydrogen atom. It can be seen from the Momenta vs Time plot that pHH increases after the collision. The kinetic energy would be further convert into thermal energy as the product hydrogen atoms collide with each other. There would be an temperature increase for this exothermic reaction which can be measured experimentally.

[[File:ZZy1416_Momenta_H2F.png|400px|center]]

 '''Questin 10: 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.'''
* '''F+H2'''

With a small momentum of -0.5 for the coming H atom, the reaction would be mostly unsuccessful even the H-H bond has a vibration energy which is significantly larger than the activation energy (0.255 kcal/mol) except for very few values of momenta.

{| class="wikitable" border=1
! pHH !! Contour Plot !! pHH !! Contour Plot !! pHH !! Contour Plot !! pHH !! Contour Plot
|-
| -3.0 || [[File:minus3.0_zy1416.png|200px|center]] || -2.9 || [[File:zy1416_minus2.9.png|200px|center]] || -2.0 || [[File:zy1416_minus2.0.png|200px|center]] || -2.4 || [[File:zy1416_minus2.4.png|200px|center]]
|-
| -1.0 || [[File:zy1416_minus1.0.png|200px|center]] || 0.0 || [[File:zy1416_0.png|200px|center]] || 1.0 || [[File:zy1416_minus1.0.png|200px|center]] || [[File:Zy1416_2.6.png|200px|center]]
|-
| 2.0 || [[File:zy1416_2.0.png|200px|center]] || 2.9 || [[File:zy1416_2.9.png|200px|center]] || 3.0 || [[File:zy1416_3.0.png|200px|center]] ||
|}

* '''H+HF'''
When the pHH has a large value above the activation energy (30.231 kcal/mol), which was set to be -20. The hydrogen atom collides with the HF molecule and breaks the H-F bond. However, two hydrogen atoms moves apart and do not form a H2 molecule. The reaction is illustrated in the following animation snapshots.
{| class="wikitable" border=1
! [[File:zy1416_HFF_unreactive_animation_0.png|300px|center]] !! [[File:zy1416_HFF_unreactive_animation_1.png|300px|center]] !! [[File:zy1416_HFF_unreactive_animation_2.png|300px|center]]
|}

One reactive trajectory has the conditions of rFH = 0.91 Å, rHH = 2.0 Å, pHF = -0.5 and pHH = -10. The trajectory recrosses the transition state region twice and eventually moves into exit channel, forming products.

[[File:ZY14166_HFF_REACTIVE.png‎|400px|left]]

File:Zy1416 2.6.png

2018-05-18T14:04:48Z

Zy1416: Zy1416 uploaded a new version of File:Zy1416 2.6.png

File:Zy1416 minus2.4.png

2018-05-18T14:03:38Z

Zy1416:

2018-05-17T21:33:59Z

Zy1416:

MRD:zy1416

2018-05-17T21:32:37Z

Zy1416:

== '''Molecular reaction dynamics''' ==

=== ''EXERCISE 1: H + H2 system'' ===
'''Question 1:''' '''What value do the different components of the gradient of the potential energy surface have at a minimum and at a transition structure? Briefly explain how minima and transition structures can be distinguished using the curvature of the potential energy surface.'''

The gradients of r2 in the potential energy surface at one minimum and the gradient of r1 in another minimum.

At the transition state, the gradients for both components are both zero.

The curvatures of the potential energy surface for minima are positive

i.e the second derivative ∂2V(r1)/∂(r1)2=∂2V(r2)/∂(r2)2 => 0

At the transition states, one of the curvature is negative and one of the curvature is positive.

 '''Question 2: 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.''' '''<nowiki/>'''
* The transition state position is estimated at r1=r2= 0.908 Å. The “Internuclear Distances vs Time” plot shows two almost flat lines, indicating that the atoms hardly oscillates and are close to an equilibrium. The distance of AB equals to the distance of BC so the two lines overlap.
[[File:Zy1416_transiton_state_estimate.png|400px|center]]

'''Question 3: Comment on how the mep and the trajectory you just calculated differ.'''
* The MEP trajectory reflects the initial part of the dynamics trajectory but occurs at larger time scale.
{| class="wikitable" border="1"
! !! MEP !! Dynamics
|-
! distance
| [[File:Mep_distance_zy1416.png|300px|center]] || [[File:Dynamics_distance_zy1416.png|300px|left]]
|-
! momenta
| [[File:Mep_momenta_zy1416.png|300px|left]] || [[File:Dynamics_distance_zy1416.png|300px|left]]
|}
* Final values of the positions r1(t) r2(t) and the average momenta p1(t) p2(t) at large t:
{| class="wikitable" border="1"
! !! MEP !! Dynamics
|-
! '''r1'''
| 1.72 || 2.76
|-
! '''r2'''
| 0.75 || 0.74
|-
! '''p1'''
| 0 || 0
|-
! '''p2'''
| 2.47 || 1.26
|}

'''Question 4: Complete the table by adding a column with the total energy, and another column reporting if the trajectory is reactive or unreactive. For each set of initial conditions, provide a plot of the trajectory and a small description for what happens along the trajectory.'''
{| class="wikitable" border="1"
! p1 !! p2 !! total energy / kcal mol-1 !! reactivity !! plot !! description
|-
| -1.25 || -2.5 || -99.-018 || reactive || [[File:zy1416_Trajectory_1.png|300px|center]] || trajectory crosses the TS and moves towards the product; r2 decreases in the entrance channel and r1 does not fluctuate; trajectory shows vibration in r2 as r1 increases in the exit channel
|-
| -1.5 || -2.0 || -100.456 || unreactive || [[File:zy1416_Trajectory_2.png|300px|center]] || trajectory does not reach the transition state and moves back towards the initial point in the entrance channel; shows vibration in r1
|-
| -1.5 || -2.5 || -98.956 || reactive || [[File:zy1416_Trajectory_3.png|300px|center]] || trajectory crosses the TS and moves towards the product; slight vibration in r1 as r2 decreases in the entrance channel; vibration in r2 as r1 increases in the exit channel
|-
| -2.5 || -5.0 || -84.956 || unreactive || [[File:zy1416_Trajectory_4.png|300px|center]] || trajectory crosses the transition state region but reverts back to the reactants
|-
| -2.5 || -5.2 || -83.416 || reactive || [[File:zy1416_Trajectory_5.png|300px|center]] || trajectory crosses the transition state and reverts back to the entrance channel and eventually moves towards the products
|}

'''Question 5: 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?'''
* There are three main assumptions made in the transition state theory:
1.The quantum-tunneling effects and the Born-Oppenheimer approximation are ignored.

2.The atoms in the reactant state have energies that are Boltzmann distributed.

3.At the transition state, with a velocity towards the product configuration, it will not re-enter the initial state region again.
* The limitation of the transition state theory is that the quantum-tunneling effect is assumed to be negligible. However, quantum mechanics shows that particles can tunnel through the energy barrier created by the transition state, allowing the reaction to occur. So the experimental values of the reaction rate would be higher than the theoretical values.

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

=== '''PES inspection''' ===
'''Question 6: 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?'''
* '''H + HF :'''
[[File:zy1416_Surface_Plot_H2F.png|400px|center]]

It can be seen from the PES plot of this reaction that the products have higher energy than the reactants, indicating an endothermic reaction.
H-F bond is strongly polarisd and has a large ionic component with strong bond strength. The energy required for breaking the H-F bond can not be compensated by the energy gain from the formation of a H-H bond. So overall the reaction is endothermic.
* '''F + H2:'''
[[File:zy1416_Surface_Plot_HHF.png|400px|center]]

The PES plot of F + H2 shows that the reactants have higher energy than the products. This reaction is exothermic. As discussed above, the formation of H-F bond would gain a large enthalpy due to strong bond strength and this energy gain compensates the energy lose for breaking the H-H bond. The overall reaction is exothermic.

 '''Question 7: Locate the approximate position of the transition state.'''
* For H+HF, the reaction is endothermic and the transition state would resemble the product; for the other reaction which is exothermic, the transition state would resemble the reactants which is the products for the first reaction. These two reactions would have the same transition state H--H--F. And the approximate position can be located on the PES plot.

[[File:zy1416_Surface_Plot_transition_state.png|500px|center]]
* The distance between H and H is determined to be 0.745 Å and the distance between H and F is determined to be 1.810 Å. The “Internuclear Distances vs Time” plot confirmed this position. The activation energy for the endothermic reaction is much higher than the exothermic reaction. Because the transition state resembles the H2+F species and they have similar energies.

[[File:Zy1416_Transition_state_distance.png|400px|center]]

'''Question 8: Report the activation energy for both reactions.'''
{| class="wikitable" border=1
! H+HF !! H2+F
|-
| [[File:Zy1416_HHF_Ea.png|300px|center]] || [[File:zy1416_H2F_Ea.png|300px|center]]
|-
| Ea = (-103.785)-(-134.016) = 30.231 kcal/mol || Ea = (-103.752)-(-104.007) = 0.255 kcal/mol
|}

'''Question 9: In light of the fact that energy is conserved, discuss the mechanism of release of the reaction energy. How could this be confirmed experimentally?'''

The initial conditions have been set to be rH-H=0.74 Å , rH-F=2.00 Å and momentumH-F=-10. The potential energy released is converted into the kinetic energy of the hydrogen atom. It can be seen from the Momenta vs Time plot that pHH increases after the collision. The kinetic energy would be further convert into thermal energy as the product hydrogen atoms collide with each other. There would be an temperature increase for this exothermic reaction which can be measured experimentally.

[[File:ZZy1416_Momenta_H2F.png|400px|center]]

 '''Questin 10: 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.'''
* '''F+H2'''

{| class="wikitable" border=1
! pHH !! 0.1(pHF=-0.8) !! 0.1
|-
| Contour Plot || [[File:zy1416_Reducingoverall.png|300px|center]] || [[File:zy1416_0.1.png|300px|center]]
|-
| Feasibility || reactive || reactive
|}

reactive 2.90 2.94 2.95 2.89 2.87 2.86 2.85 2.84 2.83 2.82 2.81 2.79 2.78 2.77 2.73 2.72
unreactive 3.00 2.99 2.98 2.97 2.96 2.93 2.92 2.91 2.88 2.80 2.76 2.75 2.74 2.71 2.70

* '''H+HF'''
When the pHH has a large value above the activation energy (30.231 kcal/mol), which was set to be -20. The hydrogen atom collides with the HF molecule and breaks the H-F bond. However, two hydrogen atoms moves apart and do not form a H2 molecule. The reaction is illustrated in the following animation snapshots.
{| class="wikitable" border=1
! [[File:zy1416_HFF_unreactive_animation_0.png|300px|center]] !! [[File:zy1416_HFF_unreactive_animation_1.png|300px|center]] !! [[File:zy1416_HFF_unreactive_animation_2.png|300px|center]]
|}

One reactive trajectory has the conditions of rFH = 0.91 Å, rHH = 2.0 Å, pHF = -0.5 and pHH = -10. The trajectory recrosses the transition state region twice and eventually moves into exit channel, forming products.

[[File:Zy1416_HFF_REACTIVE.png ‎|400px|left]]

File:Zy1416 HFF unreactive animation 2.png

2018-05-17T21:32:35Z

Zy1416:

File:Zy1416 HFF unreactive animation 1.png

2018-05-17T21:32:21Z

Zy1416: