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MRD:ahp3018

2020-05-15T22:54:56Z

Ahp3018: /* Release of energy */

== Molecular Reaction Dynamics: Applications to Triatomic Systems ==
== H + H2 System ==

=== Dynamics from the transition state region ===
On a potential energy surface diagram, the transition state is mathematically defined as the point at which dV(ri)/dri=0 is true. This can be described as the maximum point on the minimum reactive trajectory (minimum energy path linking reactants and products).

The transition state appears as a saddle point in the potential energy surface (PES) - i.e. in one direction, the point is a maximum point in the graph and in the other direction, it is a minimum. See Figure 1.

If a trajectory is started at the transition state, no change will occur if there is no initial momentum supplied. However, if the system has momentum in the direction of the products, it will roll towards the products (likewise in the opposite direction for the reactants). If a trajectory is started at a local minimum of the PES, it will not move from there even if it has momentum.

=== Locating the transition state ===
As the H + H2 surface is symmetrical, the bond lengths in the transition state must be equal (r1=r2=rts). The best estimate for rts from the software is rts=90.5 pm. See Figures 2 and 3.

This is a good estimate for the bond length in the transition state as Figure 2 shows the system stably remaining in one place (the red cross is directly on top of the black dot). Figure 3 shows the internuclear distances remaining roughly constant and equal to each other.

[[File:Ahp3018_contour90.5|Figure 2: Contour Plot for PES at r=90.5 pm]]
[[File:Ahp3018Internuclear_distances_at_ts.png|Figure 3: Internuclear distances vs Time at r=90.5 pm]]

=== Trajectories and minimum energy path ===
The minimum energy path (or reaction path) is a trajectory that corresponds to infinitely slow motion. It can be calculated by putting r1=rts+d where d=1 pm, keeping r2=rts and p1=p2=0 g.mol-1pm.fs-1. This was calculated for both a gaseous system (MEP calculation) a more realistic system (Dynamics calculation).

[[File:Ahp3018Contour_plot_mep.png|Figure 4: Contour plot (MEP)]]
[[File:Ahp3018Surface_plot_mep.png|Figure 5: Surface plot (MEP)]]
[[File:Ahp3018Contour_plot_dynamic.png|Figure 6: Contour plot (Dynamics)]]
[[File:Ahp3018Surface_plot_dynamic.png|Figure 7: Surface plot (Dynamics)]]

Figures 4 and 5 show the contour plot and surface plot for the gaseous system. Figures 6 and 7 show them for the more realistic system. These latter plots show the oscillations of the atoms, i.e. the internuclear distance oscillating, whereas the MEP plots do not.

The table below shows the internuclear distance-time plots and momenta-time plots for dynamics systems with varying r1 and r2.

{| class="wikitable"
!r1=rts+d , r2=rts
!r2=rts+d , r1=rts
|-
|[[File:Ahp3018R1=+1distance-time dynamics.png|400px|Figure 8: Internuclear distance-time plot]]
|[[File:Ahp3018R2=+1distance-time dynamics.png|400px|Figure 9: Internuclear distance-time plot]]
|-
|[[File:Ahp3018R1=+1momenta-time dynamics.png|400px|Figure 10: Momenta-time plot]]
|[[File:Ahp3018R2=+1momenta-time dynamics.png|400px|Figure 11: Momenta-time plot]]
|}

Switching r1 (BC) and r2 (AB) in the parameters simply switches the A-B and B-C lines in all plots.

=== Reactive and unreactive trajectories ===

{| class="wikitable"
!p1/g.mol-1pm.fs-1
!p2/g.mol-1pm.fs-1
!Etot/kJ.mol-1
!Reactive?
!Description of the dynamics
!Illustration of the trajectory
|-
| -2.56
| -5.1
| -414.3
|yes
|Reactants collide with enough energy to form the products - there is the right amount of energy in the system
|[[File:Ahp3018Traj1.png|thumb]]
|-
| -3.1
| -4.1
| -420.1
|no
|The reactants do not have enough momentum to collide and therefore cannot form the products
|[[File:Ahp3018Traj2.png|thumb]]
|-
| -3.1
| -5.1
| -414.0
|yes
|Reactants collide with enough energy to form the products - there is the right amount of energy in the system
|[[File:Ahp3018Traj3.png|thumb]]
|-
| -5.1
| -10.1
| -357.3
|no
|Reactants collide but there is not enough energy for the reaction to take place
|[[File:Ahp3018Traj4.png|thumb]]
|-
| -5.1
| -10.6
| -349.5
|yes
|The reactants collide and the products are formed
|[[File:Ahp3018Traj5.png|thumb]]
|}

=== Transition state theory ===

Transition state theory uses the properties of the reactants and the transition state to rationalise and calculate the rate of chemical reactions. However, some assumptions are made, reducing its accuracy:
* all collisions with the required kinetic energy (activation energy) will result in a reaction - this ignores the possibility of the energy being distributed incorrectly
* once the collision occurs and the trajectory passes the reaction barrier, it cannot turn back into the reactants, i.e. the reaction is irreversible
In conclusion, these assumptions lead to transition state theory over-estimating the reaction rates.

== F-H-H System ==
=== Transition states and enthalpy of the reaction ===
[[File:Ahp3018Surface Plot.png|thumb|right|Figure 12: PES of F + H2, showing the early transition state]]
The two reactions in this system can be analysed using their PESs. Using Polanyi's rules and Hammond's postulate, we can use the transition state position to determine if the reaction is exo- or endothermic.
Polanyi's rules state that an early barrier means that the transition state lies closer to the reactants while a late barrier corresponds to a transition state closer to the products. In the former scenario, translational energy is more efficient to complete the reaction whereas when the transition state is late, vibrational energy is more efficient.
Hammond's postulate shows that an early transition state (resembling the reactants) gives an exothermic reaction and a late transition state (resembling the products) gives an endothermic reaction.

Thus, using its PES (Figure 12), it can be seen that F + H2 has an early transition state and is therefore an exothermic reaction. Conversely, HF + F shows a late transition state, indicating an endothermic reaction.

More energy is needed to break the F-H bond (therfore causing the late transition state of the second reaction) than to break the H-H bond, showing the F-H bond is stronger than the H-H bond.

=== Location of the transition states===
[[File:Ahp3018F+h2.png|thumb|left|Figure 13: Transition state of F + H2]]

The location of the transition state for one of these reactions would have the coordinates opposite and equal to the other reaction's transition state.
For F + H2, its early transition state means the F-H length is longer than the H-H distance, which was found in the previous H + H2 system to be 74 pm. Therefore, the internuclear distances for this reaction were found to be F-H=181.5 pm and H-H=74 pm. See Figure 13 to see its structure.
The transition state for HF = H reaction would have coordinates of H-F=181.5 pm and H-H=74 pm.

=== Activation energies ===

A resonable estimate was found by performing an MEP calculation with 1500 steps and 0.1 step size from a structure neighbouring the transition state, i.e. r1=rts+d , r2=rts.

The activation energy for the F + H2 reaction was found by finding the difference between the energy of the transition state (-433.942 kJ.mol-1) and the energy of a system with maximum displacement between the reactants (F-H=750 pm, energy=-435.100 kJ.mol-1). This gives an activation energy of 1.158 kJ.mol-1.

The activation energy for the HF + H reaction was found by finding the difference between the energy of the transition state (-433.942 kJ.mol-1) and that of the reactant path (-551.535 kJ.mol-1), giving an activation of 117.593 kJ.mol-1.

=== Release of energy ===
There are two mechanisms for the release of energy in a reaction - the release of translational kinetic energy and the release of vibrational kinetic energy. One method of measuring energy release is through calorimetry.
Vibrational energy can emit IR radiation, however it is possible for IR radiation to be reabsorbed by the walls of a bomb calorimeter therefore preventing the differentiation between the two energy release mechanisms by this method.

=== Modes of energy distribution ===

When the system is relaxed, the ground state energy is populated the most. Once excited, electrons can be promoted from the ground state to the first energy level, and from the first energy level to the second.

In an early transition state reaction, translational energy is more efficient to complete the reaction, whereas when the transition state is late, vibrational energy is more efficient.

MRD:ahp3018

2020-05-15T22:53:40Z

Ahp3018: /* Location of the transition states */

== Molecular Reaction Dynamics: Applications to Triatomic Systems ==
== H + H2 System ==

=== Dynamics from the transition state region ===
On a potential energy surface diagram, the transition state is mathematically defined as the point at which dV(ri)/dri=0 is true. This can be described as the maximum point on the minimum reactive trajectory (minimum energy path linking reactants and products).

The transition state appears as a saddle point in the potential energy surface (PES) - i.e. in one direction, the point is a maximum point in the graph and in the other direction, it is a minimum. See Figure 1.

If a trajectory is started at the transition state, no change will occur if there is no initial momentum supplied. However, if the system has momentum in the direction of the products, it will roll towards the products (likewise in the opposite direction for the reactants). If a trajectory is started at a local minimum of the PES, it will not move from there even if it has momentum.

=== Locating the transition state ===
As the H + H2 surface is symmetrical, the bond lengths in the transition state must be equal (r1=r2=rts). The best estimate for rts from the software is rts=90.5 pm. See Figures 2 and 3.

This is a good estimate for the bond length in the transition state as Figure 2 shows the system stably remaining in one place (the red cross is directly on top of the black dot). Figure 3 shows the internuclear distances remaining roughly constant and equal to each other.

[[File:Ahp3018_contour90.5|Figure 2: Contour Plot for PES at r=90.5 pm]]
[[File:Ahp3018Internuclear_distances_at_ts.png|Figure 3: Internuclear distances vs Time at r=90.5 pm]]

=== Trajectories and minimum energy path ===
The minimum energy path (or reaction path) is a trajectory that corresponds to infinitely slow motion. It can be calculated by putting r1=rts+d where d=1 pm, keeping r2=rts and p1=p2=0 g.mol-1pm.fs-1. This was calculated for both a gaseous system (MEP calculation) a more realistic system (Dynamics calculation).

[[File:Ahp3018Contour_plot_mep.png|Figure 4: Contour plot (MEP)]]
[[File:Ahp3018Surface_plot_mep.png|Figure 5: Surface plot (MEP)]]
[[File:Ahp3018Contour_plot_dynamic.png|Figure 6: Contour plot (Dynamics)]]
[[File:Ahp3018Surface_plot_dynamic.png|Figure 7: Surface plot (Dynamics)]]

Figures 4 and 5 show the contour plot and surface plot for the gaseous system. Figures 6 and 7 show them for the more realistic system. These latter plots show the oscillations of the atoms, i.e. the internuclear distance oscillating, whereas the MEP plots do not.

The table below shows the internuclear distance-time plots and momenta-time plots for dynamics systems with varying r1 and r2.

{| class="wikitable"
!r1=rts+d , r2=rts
!r2=rts+d , r1=rts
|-
|[[File:Ahp3018R1=+1distance-time dynamics.png|400px|Figure 8: Internuclear distance-time plot]]
|[[File:Ahp3018R2=+1distance-time dynamics.png|400px|Figure 9: Internuclear distance-time plot]]
|-
|[[File:Ahp3018R1=+1momenta-time dynamics.png|400px|Figure 10: Momenta-time plot]]
|[[File:Ahp3018R2=+1momenta-time dynamics.png|400px|Figure 11: Momenta-time plot]]
|}

Switching r1 (BC) and r2 (AB) in the parameters simply switches the A-B and B-C lines in all plots.

=== Reactive and unreactive trajectories ===

{| class="wikitable"
!p1/g.mol-1pm.fs-1
!p2/g.mol-1pm.fs-1
!Etot/kJ.mol-1
!Reactive?
!Description of the dynamics
!Illustration of the trajectory
|-
| -2.56
| -5.1
| -414.3
|yes
|Reactants collide with enough energy to form the products - there is the right amount of energy in the system
|[[File:Ahp3018Traj1.png|thumb]]
|-
| -3.1
| -4.1
| -420.1
|no
|The reactants do not have enough momentum to collide and therefore cannot form the products
|[[File:Ahp3018Traj2.png|thumb]]
|-
| -3.1
| -5.1
| -414.0
|yes
|Reactants collide with enough energy to form the products - there is the right amount of energy in the system
|[[File:Ahp3018Traj3.png|thumb]]
|-
| -5.1
| -10.1
| -357.3
|no
|Reactants collide but there is not enough energy for the reaction to take place
|[[File:Ahp3018Traj4.png|thumb]]
|-
| -5.1
| -10.6
| -349.5
|yes
|The reactants collide and the products are formed
|[[File:Ahp3018Traj5.png|thumb]]
|}

=== Transition state theory ===

Transition state theory uses the properties of the reactants and the transition state to rationalise and calculate the rate of chemical reactions. However, some assumptions are made, reducing its accuracy:
* all collisions with the required kinetic energy (activation energy) will result in a reaction - this ignores the possibility of the energy being distributed incorrectly
* once the collision occurs and the trajectory passes the reaction barrier, it cannot turn back into the reactants, i.e. the reaction is irreversible
In conclusion, these assumptions lead to transition state theory over-estimating the reaction rates.

== F-H-H System ==
=== Transition states and enthalpy of the reaction ===
[[File:Ahp3018Surface Plot.png|thumb|right|Figure 12: PES of F + H2, showing the early transition state]]
The two reactions in this system can be analysed using their PESs. Using Polanyi's rules and Hammond's postulate, we can use the transition state position to determine if the reaction is exo- or endothermic.
Polanyi's rules state that an early barrier means that the transition state lies closer to the reactants while a late barrier corresponds to a transition state closer to the products. In the former scenario, translational energy is more efficient to complete the reaction whereas when the transition state is late, vibrational energy is more efficient.
Hammond's postulate shows that an early transition state (resembling the reactants) gives an exothermic reaction and a late transition state (resembling the products) gives an endothermic reaction.

Thus, using its PES (Figure 12), it can be seen that F + H2 has an early transition state and is therefore an exothermic reaction. Conversely, HF + F shows a late transition state, indicating an endothermic reaction.

More energy is needed to break the F-H bond (therfore causing the late transition state of the second reaction) than to break the H-H bond, showing the F-H bond is stronger than the H-H bond.

=== Location of the transition states===
[[File:Ahp3018F+h2.png|thumb|left|Figure 13: Transition state of F + H2]]

The location of the transition state for one of these reactions would have the coordinates opposite and equal to the other reaction's transition state.
For F + H2, its early transition state means the F-H length is longer than the H-H distance, which was found in the previous H + H2 system to be 74 pm. Therefore, the internuclear distances for this reaction were found to be F-H=181.5 pm and H-H=74 pm. See Figure 13 to see its structure.
The transition state for HF = H reaction would have coordinates of H-F=181.5 pm and H-H=74 pm.

=== Activation energies ===

A resonable estimate was found by performing an MEP calculation with 1500 steps and 0.1 step size from a structure neighbouring the transition state, i.e. r1=rts+d , r2=rts.

The activation energy for the F + H2 reaction was found by finding the difference between the energy of the transition state (-433.942 kJ.mol-1) and the energy of a system with maximum displacement between the reactants (F-H=750 pm, energy=-435.100 kJ.mol-1). This gives an activation energy of 1.158 kJ.mol-1.

The activation energy for the HF + H reaction was found by finding the difference between the energy of the transition state (-433.942 kJ.mol-1) and that of the reactant path (-551.535 kJ.mol-1), giving an activation of 117.593 kJ.mol-1.

=== Release of energy ===
There are two mechanisms for the release of energy in a reaction - the release of translational kinetic energy and the release of vibrational kinetic energy. One method of measuring energy release is through calorimetry.
Vibration energy can emit IR radiation, however IR radiation can be reabsorbed by the walls of a bomb calorimeter therefore preventing the differentiation between the two energy release mechanisms.

=== Modes of energy distribution ===

When the system is relaxed, the ground state energy is populated the most. Once excited, electrons can be promoted from the ground state to the first energy level, and from the first energy level to the second.

In an early transition state reaction, translational energy is more efficient to complete the reaction, whereas when the transition state is late, vibrational energy is more efficient.

MRD:ahp3018

2020-05-15T22:53:10Z

Ahp3018: /* Reactive and unreactive trajectories */

== Molecular Reaction Dynamics: Applications to Triatomic Systems ==
== H + H2 System ==

=== Dynamics from the transition state region ===
On a potential energy surface diagram, the transition state is mathematically defined as the point at which dV(ri)/dri=0 is true. This can be described as the maximum point on the minimum reactive trajectory (minimum energy path linking reactants and products).

The transition state appears as a saddle point in the potential energy surface (PES) - i.e. in one direction, the point is a maximum point in the graph and in the other direction, it is a minimum. See Figure 1.

If a trajectory is started at the transition state, no change will occur if there is no initial momentum supplied. However, if the system has momentum in the direction of the products, it will roll towards the products (likewise in the opposite direction for the reactants). If a trajectory is started at a local minimum of the PES, it will not move from there even if it has momentum.

=== Locating the transition state ===
As the H + H2 surface is symmetrical, the bond lengths in the transition state must be equal (r1=r2=rts). The best estimate for rts from the software is rts=90.5 pm. See Figures 2 and 3.

This is a good estimate for the bond length in the transition state as Figure 2 shows the system stably remaining in one place (the red cross is directly on top of the black dot). Figure 3 shows the internuclear distances remaining roughly constant and equal to each other.

[[File:Ahp3018_contour90.5|Figure 2: Contour Plot for PES at r=90.5 pm]]
[[File:Ahp3018Internuclear_distances_at_ts.png|Figure 3: Internuclear distances vs Time at r=90.5 pm]]

=== Trajectories and minimum energy path ===
The minimum energy path (or reaction path) is a trajectory that corresponds to infinitely slow motion. It can be calculated by putting r1=rts+d where d=1 pm, keeping r2=rts and p1=p2=0 g.mol-1pm.fs-1. This was calculated for both a gaseous system (MEP calculation) a more realistic system (Dynamics calculation).

[[File:Ahp3018Contour_plot_mep.png|Figure 4: Contour plot (MEP)]]
[[File:Ahp3018Surface_plot_mep.png|Figure 5: Surface plot (MEP)]]
[[File:Ahp3018Contour_plot_dynamic.png|Figure 6: Contour plot (Dynamics)]]
[[File:Ahp3018Surface_plot_dynamic.png|Figure 7: Surface plot (Dynamics)]]

Figures 4 and 5 show the contour plot and surface plot for the gaseous system. Figures 6 and 7 show them for the more realistic system. These latter plots show the oscillations of the atoms, i.e. the internuclear distance oscillating, whereas the MEP plots do not.

The table below shows the internuclear distance-time plots and momenta-time plots for dynamics systems with varying r1 and r2.

{| class="wikitable"
!r1=rts+d , r2=rts
!r2=rts+d , r1=rts
|-
|[[File:Ahp3018R1=+1distance-time dynamics.png|400px|Figure 8: Internuclear distance-time plot]]
|[[File:Ahp3018R2=+1distance-time dynamics.png|400px|Figure 9: Internuclear distance-time plot]]
|-
|[[File:Ahp3018R1=+1momenta-time dynamics.png|400px|Figure 10: Momenta-time plot]]
|[[File:Ahp3018R2=+1momenta-time dynamics.png|400px|Figure 11: Momenta-time plot]]
|}

Switching r1 (BC) and r2 (AB) in the parameters simply switches the A-B and B-C lines in all plots.

=== Reactive and unreactive trajectories ===

{| class="wikitable"
!p1/g.mol-1pm.fs-1
!p2/g.mol-1pm.fs-1
!Etot/kJ.mol-1
!Reactive?
!Description of the dynamics
!Illustration of the trajectory
|-
| -2.56
| -5.1
| -414.3
|yes
|Reactants collide with enough energy to form the products - there is the right amount of energy in the system
|[[File:Ahp3018Traj1.png|thumb]]
|-
| -3.1
| -4.1
| -420.1
|no
|The reactants do not have enough momentum to collide and therefore cannot form the products
|[[File:Ahp3018Traj2.png|thumb]]
|-
| -3.1
| -5.1
| -414.0
|yes
|Reactants collide with enough energy to form the products - there is the right amount of energy in the system
|[[File:Ahp3018Traj3.png|thumb]]
|-
| -5.1
| -10.1
| -357.3
|no
|Reactants collide but there is not enough energy for the reaction to take place
|[[File:Ahp3018Traj4.png|thumb]]
|-
| -5.1
| -10.6
| -349.5
|yes
|The reactants collide and the products are formed
|[[File:Ahp3018Traj5.png|thumb]]
|}

=== Transition state theory ===

Transition state theory uses the properties of the reactants and the transition state to rationalise and calculate the rate of chemical reactions. However, some assumptions are made, reducing its accuracy:
* all collisions with the required kinetic energy (activation energy) will result in a reaction - this ignores the possibility of the energy being distributed incorrectly
* once the collision occurs and the trajectory passes the reaction barrier, it cannot turn back into the reactants, i.e. the reaction is irreversible
In conclusion, these assumptions lead to transition state theory over-estimating the reaction rates.

== F-H-H System ==
=== Transition states and enthalpy of the reaction ===
[[File:Ahp3018Surface Plot.png|thumb|right|Figure 12: PES of F + H2, showing the early transition state]]
The two reactions in this system can be analysed using their PESs. Using Polanyi's rules and Hammond's postulate, we can use the transition state position to determine if the reaction is exo- or endothermic.
Polanyi's rules state that an early barrier means that the transition state lies closer to the reactants while a late barrier corresponds to a transition state closer to the products. In the former scenario, translational energy is more efficient to complete the reaction whereas when the transition state is late, vibrational energy is more efficient.
Hammond's postulate shows that an early transition state (resembling the reactants) gives an exothermic reaction and a late transition state (resembling the products) gives an endothermic reaction.

Thus, using its PES (Figure 12), it can be seen that F + H2 has an early transition state and is therefore an exothermic reaction. Conversely, HF + F shows a late transition state, indicating an endothermic reaction.

More energy is needed to break the F-H bond (therfore causing the late transition state of the second reaction) than to break the H-H bond, showing the F-H bond is stronger than the H-H bond.

=== Location of the transition states===
[[File:Ahp3018F+h2.png|thumb|left|Figure 12: Figure 13: Transition state of F + H2]]

The location of the transition state for one of these reactions would have the coordinates opposite and equal to the other reaction's transition state.
For F + H2, its early transition state means the F-H length is longer than the H-H distance, which was found in the previous H + H2 system to be 74 pm. Therefore, the internuclear distances for this reaction were found to be F-H=181.5 pm and H-H=74 pm. See Figure 13 to see its structure.
The transition state for HF = H reaction would have coordinates of H-F=181.5 pm and H-H=74 pm.

=== Activation energies ===

A resonable estimate was found by performing an MEP calculation with 1500 steps and 0.1 step size from a structure neighbouring the transition state, i.e. r1=rts+d , r2=rts.

The activation energy for the F + H2 reaction was found by finding the difference between the energy of the transition state (-433.942 kJ.mol-1) and the energy of a system with maximum displacement between the reactants (F-H=750 pm, energy=-435.100 kJ.mol-1). This gives an activation energy of 1.158 kJ.mol-1.

The activation energy for the HF + H reaction was found by finding the difference between the energy of the transition state (-433.942 kJ.mol-1) and that of the reactant path (-551.535 kJ.mol-1), giving an activation of 117.593 kJ.mol-1.

=== Release of energy ===
There are two mechanisms for the release of energy in a reaction - the release of translational kinetic energy and the release of vibrational kinetic energy. One method of measuring energy release is through calorimetry.
Vibration energy can emit IR radiation, however IR radiation can be reabsorbed by the walls of a bomb calorimeter therefore preventing the differentiation between the two energy release mechanisms.

=== Modes of energy distribution ===

When the system is relaxed, the ground state energy is populated the most. Once excited, electrons can be promoted from the ground state to the first energy level, and from the first energy level to the second.

In an early transition state reaction, translational energy is more efficient to complete the reaction, whereas when the transition state is late, vibrational energy is more efficient.

MRD:ahp3018

2020-05-15T22:52:33Z

Ahp3018:

== Molecular Reaction Dynamics: Applications to Triatomic Systems ==
== H + H2 System ==

=== Dynamics from the transition state region ===
On a potential energy surface diagram, the transition state is mathematically defined as the point at which dV(ri)/dri=0 is true. This can be described as the maximum point on the minimum reactive trajectory (minimum energy path linking reactants and products).

The transition state appears as a saddle point in the potential energy surface (PES) - i.e. in one direction, the point is a maximum point in the graph and in the other direction, it is a minimum. See Figure 1.

If a trajectory is started at the transition state, no change will occur if there is no initial momentum supplied. However, if the system has momentum in the direction of the products, it will roll towards the products (likewise in the opposite direction for the reactants). If a trajectory is started at a local minimum of the PES, it will not move from there even if it has momentum.

=== Locating the transition state ===
As the H + H2 surface is symmetrical, the bond lengths in the transition state must be equal (r1=r2=rts). The best estimate for rts from the software is rts=90.5 pm. See Figures 2 and 3.

This is a good estimate for the bond length in the transition state as Figure 2 shows the system stably remaining in one place (the red cross is directly on top of the black dot). Figure 3 shows the internuclear distances remaining roughly constant and equal to each other.

[[File:Ahp3018_contour90.5|Figure 2: Contour Plot for PES at r=90.5 pm]]
[[File:Ahp3018Internuclear_distances_at_ts.png|Figure 3: Internuclear distances vs Time at r=90.5 pm]]

=== Trajectories and minimum energy path ===
The minimum energy path (or reaction path) is a trajectory that corresponds to infinitely slow motion. It can be calculated by putting r1=rts+d where d=1 pm, keeping r2=rts and p1=p2=0 g.mol-1pm.fs-1. This was calculated for both a gaseous system (MEP calculation) a more realistic system (Dynamics calculation).

[[File:Ahp3018Contour_plot_mep.png|Figure 4: Contour plot (MEP)]]
[[File:Ahp3018Surface_plot_mep.png|Figure 5: Surface plot (MEP)]]
[[File:Ahp3018Contour_plot_dynamic.png|Figure 6: Contour plot (Dynamics)]]
[[File:Ahp3018Surface_plot_dynamic.png|Figure 7: Surface plot (Dynamics)]]

Figures 4 and 5 show the contour plot and surface plot for the gaseous system. Figures 6 and 7 show them for the more realistic system. These latter plots show the oscillations of the atoms, i.e. the internuclear distance oscillating, whereas the MEP plots do not.

The table below shows the internuclear distance-time plots and momenta-time plots for dynamics systems with varying r1 and r2.

{| class="wikitable"
!r1=rts+d , r2=rts
!r2=rts+d , r1=rts
|-
|[[File:Ahp3018R1=+1distance-time dynamics.png|400px|Figure 8: Internuclear distance-time plot]]
|[[File:Ahp3018R2=+1distance-time dynamics.png|400px|Figure 9: Internuclear distance-time plot]]
|-
|[[File:Ahp3018R1=+1momenta-time dynamics.png|400px|Figure 10: Momenta-time plot]]
|[[File:Ahp3018R2=+1momenta-time dynamics.png|400px|Figure 11: Momenta-time plot]]
|}

Switching r1 (BC) and r2 (AB) in the parameters simply switches the A-B and B-C lines in all plots.

=== Reactive and unreactive trajectories ===

{| class="wikitable"
!p1/g.mol-1pm.fs-1
!p2/g.mol-1pm.fs-1
!Etot/kJ.mol-1
!Reactive?
!Description of the dynamics
!Illustration of the trajectory
|-
| -2.56
| -5.1
| -414.3
|yes
|Reactants collide with enough energy to form the products - there is the right amount of energy in the system
|[[File:Ahp3018Traj1.png|thumb]]
|-
| -3.1
| -4.1
| -420.1
|no
|The reactants do not have enough momentum to collide and therefore cannot form the products
|[[FFile:Ahp3018Traj2.png|thumb]]
|-
| -3.1
| -5.1
| -414.0
|yes
|Reactants collide with enough energy to form the products - there is the right amount of energy in the system
|[[File:Ahp3018Traj3.png|thumb]]
|-
| -5.1
| -10.1
| -357.3
|no
|Reactants collide but there is not enough energy for the reaction to take place
|[[File:Ahp3018Traj4.png|thumb]]
|-
| -5.1
| -10.6
| -349.5
|yes
|The reactants collide and the products are formed
|[[File:Ahp3018Traj5.png|thumb]]
|}

=== Transition state theory ===

Transition state theory uses the properties of the reactants and the transition state to rationalise and calculate the rate of chemical reactions. However, some assumptions are made, reducing its accuracy:
* all collisions with the required kinetic energy (activation energy) will result in a reaction - this ignores the possibility of the energy being distributed incorrectly
* once the collision occurs and the trajectory passes the reaction barrier, it cannot turn back into the reactants, i.e. the reaction is irreversible
In conclusion, these assumptions lead to transition state theory over-estimating the reaction rates.

== F-H-H System ==
=== Transition states and enthalpy of the reaction ===
[[File:Ahp3018Surface Plot.png|thumb|right|Figure 12: PES of F + H2, showing the early transition state]]
The two reactions in this system can be analysed using their PESs. Using Polanyi's rules and Hammond's postulate, we can use the transition state position to determine if the reaction is exo- or endothermic.
Polanyi's rules state that an early barrier means that the transition state lies closer to the reactants while a late barrier corresponds to a transition state closer to the products. In the former scenario, translational energy is more efficient to complete the reaction whereas when the transition state is late, vibrational energy is more efficient.
Hammond's postulate shows that an early transition state (resembling the reactants) gives an exothermic reaction and a late transition state (resembling the products) gives an endothermic reaction.

Thus, using its PES (Figure 12), it can be seen that F + H2 has an early transition state and is therefore an exothermic reaction. Conversely, HF + F shows a late transition state, indicating an endothermic reaction.

More energy is needed to break the F-H bond (therfore causing the late transition state of the second reaction) than to break the H-H bond, showing the F-H bond is stronger than the H-H bond.

=== Location of the transition states===
[[File:Ahp3018F+h2.png|thumb|left|Figure 12: Figure 13: Transition state of F + H2]]

The location of the transition state for one of these reactions would have the coordinates opposite and equal to the other reaction's transition state.
For F + H2, its early transition state means the F-H length is longer than the H-H distance, which was found in the previous H + H2 system to be 74 pm. Therefore, the internuclear distances for this reaction were found to be F-H=181.5 pm and H-H=74 pm. See Figure 13 to see its structure.
The transition state for HF = H reaction would have coordinates of H-F=181.5 pm and H-H=74 pm.

=== Activation energies ===

A resonable estimate was found by performing an MEP calculation with 1500 steps and 0.1 step size from a structure neighbouring the transition state, i.e. r1=rts+d , r2=rts.

The activation energy for the F + H2 reaction was found by finding the difference between the energy of the transition state (-433.942 kJ.mol-1) and the energy of a system with maximum displacement between the reactants (F-H=750 pm, energy=-435.100 kJ.mol-1). This gives an activation energy of 1.158 kJ.mol-1.

The activation energy for the HF + H reaction was found by finding the difference between the energy of the transition state (-433.942 kJ.mol-1) and that of the reactant path (-551.535 kJ.mol-1), giving an activation of 117.593 kJ.mol-1.

=== Release of energy ===
There are two mechanisms for the release of energy in a reaction - the release of translational kinetic energy and the release of vibrational kinetic energy. One method of measuring energy release is through calorimetry.
Vibration energy can emit IR radiation, however IR radiation can be reabsorbed by the walls of a bomb calorimeter therefore preventing the differentiation between the two energy release mechanisms.

=== Modes of energy distribution ===

When the system is relaxed, the ground state energy is populated the most. Once excited, electrons can be promoted from the ground state to the first energy level, and from the first energy level to the second.

In an early transition state reaction, translational energy is more efficient to complete the reaction, whereas when the transition state is late, vibrational energy is more efficient.

File:Ahp3018F+h2.png

2020-05-15T21:55:57Z

Ahp3018: Ahp3018 uploaded a new version of File:Ahp3018F+h2.png

MRD:ahp3018

2020-05-15T21:50:15Z

Ahp3018: /* F-H-H System */

== Molecular Reaction Dynamics: Applications to Triatomic Systems ==
== H + H2 System ==

=== Dynamics from the transition state region ===
On a potential energy surface diagram, the transition state is mathematically defined as the point at which dV(ri)/dri=0 is true. This can be described as the maximum point on the minimum reactive trajectory (minimum energy path linking reactants and products).

The transition state appears as a saddle point in the potential energy surface (PES) - i.e. in one direction, the point is a maximum point in the graph and in the other direction, it is a minimum. See Figure 1.

If a trajectory is started at the transition state, no change will occur if there is no initial momentum supplied. However, if the system has momentum in the direction of the products, it will roll towards the products (likewise in the opposite direction for the reactants). If a trajectory is started at a local minimum of the PES, it will not move from there even if it has momentum.

=== Locating the transition state ===
As the H + H2 surface is symmetrical, the bond lengths in the transition state must be equal (r1=r2=rts). The best estimate for rts from the software is rts=90.5 pm. See Figures 2 and 3.

This is a good estimate for the bond length in the transition state as Figure 2 shows the system stably remaining in one place (the red cross is directly on top of the black dot). Figure 3 shows the internuclear distances remaining roughly constant and equal to each other.

[[File:Ahp3018_contour90.5|Figure 2: Contour Plot for PES at r=90.5 pm]]
[[File:Ahp3018Internuclear_distances_at_ts.png|Figure 3: Internuclear distances vs Time at r=90.5 pm]]

=== Trajectories and minimum energy path ===
The minimum energy path (or reaction path) is a trajectory that corresponds to infinitely slow motion. It can be calculated by putting r1=rts+d where d=1 pm, keeping r2=rts and p1=p2=0 g.mol-1pm.fs-1. This was calculated for both a gaseous system (MEP calculation) a more realistic system (Dynamics calculation).

[[File:Ahp3018Contour_plot_mep.png|Figure 4: Contour plot (MEP)]]
[[File:Ahp3018Surface_plot_mep.png|Figure 5: Surface plot (MEP)]]
[[File:Ahp3018Contour_plot_dynamic.png|Figure 6: Contour plot (Dynamics)]]
[[File:Ahp3018Surface_plot_dynamic.png|Figure 7: Surface plot (Dynamics)]]

Figures 4 and 5 show the contour plot and surface plot for the gaseous system. Figures 6 and 7 show them for the more realistic system. These latter plots show the oscillations of the atoms, i.e. the internuclear distance oscillating, whereas the MEP plots do not.

The table below shows the internuclear distance-time plots and momenta-time plots for dynamics systems with varying r1 and r2.

{| class="wikitable"
!r1=rts+d , r2=rts
!r2=rts+d , r1=rts
|-
|[[File:Ahp3018R1=+1distance-time dynamics.png|400px|Figure 8: Internuclear distance-time plot]]
|[[File:Ahp3018R2=+1distance-time dynamics.png|400px|Figure 9: Internuclear distance-time plot]]
|-
|[[File:Ahp3018R1=+1momenta-time dynamics.png|400px|Figure 10: Momenta-time plot]]
|[[File:Ahp3018R2=+1momenta-time dynamics.png|400px|Figure 11: Momenta-time plot]]
|}

Switching r1 (BC) and r2 (AB) in the parameters simply switches the A-B and B-C lines in all plots.

=== Reactive and unreactive trajectories ===

{| class="wikitable"
!p1/g.mol-1pm.fs-1
!p2/g.mol-1pm.fs-1
!Etot/kJ.mol-1
!Reactive?
!Description of the dynamics
!Illustration of the trajectory
|-
| -2.56
| -5.1
| -414.3
|yes
|Reactants collide with enough energy to form the products - there is the right amount of energy in the system
|[[File:Ahp3018Traj1.png|thumb]]
|-
| -3.1
| -4.1
| -420.1
|no
|The reactants do not have enough momentum to collide and therefore cannot form the products
|[[FFile:Ahp3018Traj2.png|thumb]]
|-
| -3.1
| -5.1
| -414.0
|yes
|Reactants collide with enough energy to form the products - there is the right amount of energy in the system
|[[File:Ahp3018Traj3.png|thumb]]
|-
| -5.1
| -10.1
| -357.3
|no
|Reactants collide but there is not enough energy for the reaction to take place
|[[File:Ahp3018Traj4.png|thumb]]
|-
| -5.1
| -10.6
| -349.5
|yes
|The reactants collide and the products are formed
|[[File:Ahp3018Traj5.png|thumb]]
|}

=== Transition state theory ===

Transition state theory uses the properties of the reactants and the transition state to rationalise and calculate the rate of chemical reactions. However, some assumptions are made, reducing its accuracy:
* all collisions with the required kinetic energy (activation energy) will result in a reaction - this ignores the possibility of the energy being distributed incorrectly
* once the collision occurs and the trajectory passes the reaction barrier, it cannot turn back into the reactants, i.e. the reaction is irreversible
In conclusion, these assumptions lead to transition state theory over-estimating the reaction rates.

== F-H-H System ==
[[File:Ahp3018Surface Plot.png|thumb|right|Figure 12: PES of F + H2, showing the early transition state]]
The two reactions in this system can be analysed using their PESs. Using Polanyi's rules and Hammond's postulate, we can use the transition state position to determine if the reaction is exo- or endothermic.
Polanyi's rules state that an early barrier means that the transition state lies closer to the reactants while a late barrier corresponds to a transition state closer to the products. In the former scenario, translational energy is more efficient to complete the reaction whereas when the transition state is late, vibrational energy is more efficient.
Hammond's postulate shows that an early transition state (resembling the reactants) gives an exothermic reaction and a late transition state (resembling the products) gives an endothermic reaction.

Thus, using its PES (Figure 12), it can be seen that F + H2 has an early transition state and is therefore an exothermic reaction. Conversely, HF + F shows a late transition state, indicating an endothermic reaction.

More energy is needed to break the F-H bond (therfore causing the late transition state of the second reaction) than to break the H-H bond, showing the F-H bond is stronger than the H-H bond.

MRD:ahp3018

2020-05-15T21:49:50Z

MRD:ahp3018

2020-05-15T18:02:55Z

Ahp3018: /* Locating the transition state */