== Exercise 1: H2+H system ==
=== Transition states and minimas ===
The transition state of the triatomic system is defined as the maximum of the minimum energy path on the potential energy surface. This kind of feature is known as a saddle point, and is found by looking at the curvature of the potential energy surface.
For the H2+H system, the total energy gradient for the transition state and for the minimum is 0 for all stationary points, ie ∂V(ri)/∂ri=0.
To differentiate the transition state from a minimum, one must look at the second derivative of the potential energy curve. Derivatives are with respect to three coordinates, the bond lengths of Hb-Hc and Ha-Hb as well as the bond angle between those bonds. The triatomic system considered here is assumed to have a bond angle of 180 degrees and thus we only deal with two out of three degrees of freedom. A saddle point is observed when:

∂f/∂x=0, ∂f/∂y=0 and fxxfyy-fxy2 > 0

=== Locating the Transition state ===
The transition state ought to be on a reactive path between the reactants and products, thus the momenta are fixed to 0 because otherwise the system wouldn't be in the minimum well. A rough estimate of its location is done by looking at the contour plot.
Furthermore, at the transition state, both AB and BC distances should be equal since the system is a symmetric reaction.

[[File:Internuclear time Ex1 mfc16.PNG|thumb|centre|Plot of internuclear distance vs time for the given initial parameters.]]

At the transition state the bonds do not oscillate, the plot should therefore show two horizontal flat lines. This is obtained when r1=r2=0.90755 Å.

[[File:Internuclear TransitionEx1 mfc16.PNG|thumb|centre|Plot of internuclear distance vs time at the transistion state coordinates.]]

=== Differences between dynamics and MEP settings ===
The minimum energy path (mep) is the lowest energy reaction path leading to the formation of products. The variation of potential energyalong the mep is best described as a well rather than a barrier.
==== Contour maps ====

[[File:Dynamics TStrajectory mfc16.PNG|thumb|centre|]]

[[File:MEP contourEx1 mfc16.PNG|thumb|centre|]]

==== Internuclear distance vs time ====
[[File:Internuclear mepTS mfc16.PNG|thumb|centre|]]

[[File:Internuclear time Ex1 mfc16.PNG|thumb|centre|]]

=== Reactive and unreactive trajectories===

{| class="wikitable" border="1"
|+ Effect of momenta on reactivity
! p1 !! p2 !! Total energy !! Type of trajectory !! contour plot !! Description
|-
| -1.25 || -2.5 || -99.119 || Reactive || [[File:Reaction1 contour mc16.png|400px]] || The reaction path heads towards the products minimum region. The A-B molecule starts oscillating slowly, but oscillates faster after the B-C is formed.
|-
| -1.5 || -2.0 || -100.456 || Unreactive ||[[File:Reaction2 contour mfc16.png|400px]] || The A-B bond is oscillating, but the momenta of molecules AB and C combined are not strong enough to overcome repulsion forces and lead to the formation of the BC molecule.
|-
| -1.5 || -2.0 || -98.956 || Reactive ||[[File:Reaction3 contour mfc16.png|400px]] || This trajectory is very similar to the first one, with the main difference being that before formation of the B-C bond, the A-B bond length stretches as C approaches.
|-
| -2.5 || -5.0 || -84.956 || Unreactive || [[File:Reaction4 contour mfc16.png|400px]] || In this reaction, the AC bond does not oscillate initially. However, collision with atom C leads to a strongly vibrating BC bond which then causes the AB bond to stop oscillating. This trajectory is unreactive because the trajectory does not move towards the products since the transition state is isn't high enough in energy.
|-
| -2.5 || -5.2 || -83.416 || Reactive || [[File:Reaction5 contour mfc16.png|400px]] || This plot is very similar to the one before, it even looks like its mirror image but this time the trajectory is in the product channel and has enough energy to lead to the formation of products. The AB product vibrates strongly.
|}

=== Transition state theory ===
The system considered here is a three atom reaction of the form:
A + BC → ABC‡ → AB + C.
The transition state as explained above, can be thought of as a bottleneck on the PES where the reactants have to be if products are to be formed, the theory implies that regions of products and reactants are separate entities.
The assumptions of transition state theory are<ref name="transition state theory" />:
* At fixed themperature, the reactants are in thermal equilibrium, or, at fixed energy, all reactant states are equally accessible.
* Motion along the reaction coordinate (minimum energy path) is seperable from motion orthogonal to it.
* Motion along the reaction coordinate is classical.
* Motion along the minimum energy path is direct.
The first point refers to the fact that starting materials must have energies that obey the Boltzmann distribution, the second one states that the Born-Oppenheimer approximation must be obeyed by each atom in the system, while the third one simply implies that quantum tunneling is no observed. Finally, the last point implies that all trajectories that cross the transition state dividing surface from the reactant side are assumed to go on and form products irreversibly.

However, transition state theory is based on assumptions that cannot be made in some cases. For instance in the 4th reaction tested above, the reactants have enough energy to overcome the activation barrier and get to the transition state, but this doesn't lead to the formation of products and thus goes against the 4th assumption.

== Exercise 2: F-H-H ==
=== PES inspection ===
The reaction F + H2 ⇌ FH + H is an equilibrium reaction, with the forward reaction being exothermic (releases energy to the surroundings) while the reverse reaction is endothermic (absorbs energy from the surroundings). This is explained by the fact that the F-H bond is strong, with a bond energy<ref name="bond energy" /> of 565 kJ/mol, compared to the H-H bond which has a bond energy of 432 kJ/mol.

Settings used :
Atom A: F Atom B: H Atom C: H

The approximate position of the transition state was found to be when:
AB distance = 1.81 Å
BC distance = 0.7456 Å
Both momenta are set to 0 because here we look for the transition state.
This is confirmed by plotting an internuclear distance vs time plot using the dynamics method, where no oscillations are observed meaning that the molecules are at rest which is characteristic of the transition state.

[[File:Ex2 TSlocation mfc16.png]]

In order to find the activation energy, the calculation method is changed from dynamics to MEP and the AB bond distance is varied so that it is displaced from equilibrium at the transition state. By doing so, the molecule is forced to either go back to the reactants or go on to form the product. The Hammond postulate states that exothermic reactions have an early transition state and thus resembles more like the reactants than the products.
*The forward reaction F + H2 → FH + H is exothermic, so the transition state is observed early in the reaction and thus the AB bond length must be increased to find the activation energy.
AB distance is set to 1.91 Å and the number of steps is increased to 10 000.

Energy of the transition state = -103.344 Kcal/mol

Energy of the products = -104.131 Kcal/mol

Activation energy = energy of the transition state - energy of the products = 0.787 Kcal/mol

[[File:Exo activation surface mfc16.PNG|thumb|centre|Surface plot for the exothermic reaction F + H2 → FH + H]]

*The reverse reaction FH + H → F + H2 is endothermic, so the transition state is observed late in the reaction and thus the AB bond length should be decreased to find the activation energy.
AB distance is set to 1.71 Å and the number of steps is increased to 10 000.

Energy of the transition state = -103.618 Kcal/mol

Energy of the products = -131.485 Kcal/mol

Activation energy = energy of the transition state - energy of the products = 27.867 Kcal/mol

[[File:Endo activation surface mfc16.PNG|thumb|centre|Surface plot for the endothermic reaction FH + H → F + H2.]]

=== Reaction dynamics ===
==== Reactive trajectory ====
Let atom A= F atom B= H and atom C= H. Then if:

AB distance = 1.91 Å

BC distance = 0.7455 Å

AB momentum = -1.5

BC momentum = 1.0

[[File:Surface Ex2 Reactivetraj mfc16.png|thumb|centre|Contour plot of a reactive trajectory for the FHH molecule]]

[[File:Internuclearpvst Ex2 mfc16.png|thumb|centre|Internuclear momenta vs time.]]

[[File:Evst Ex2 mfc16.png|thumb|centre|Energy vs time for the reactive trajectory.]]

==== The effects of varying the momentum of AB ====
AB distance = 1.914 Å
BC distance= 0.74 Å
AB momentum= -3 to 3
BC momentum= -0.5

*In the case where pHH =-3 the molecules is strongly oscillating and leads to the formation of products.
[[File:Pof-3 contour mfc16.png|thumb|centre|Contour map in the case where pHH=-3.]]

*In the case where pHH =-0.5
[[File:Pof-0.5 contour mfc16.png|thumb|centre|Contour map in the case where pHH=-0.5.]]

*In the case where pHH =3

[[File:P=3 contour mfc16.png|thumb|centre|Contour map in the case where pHH =3.]]

=== Polanyi's empirical rules ===
The different distribution of energy between different modes (translational and vibrational) have an impact on the type of transition state in a reaction. This was investigated by Polanyi who came up with a set of rules used to describe this relationship and was first illustrated using the same triatomic equilibrium system discussed here. The rules state that vibrational energy is more efficient in promoting a late barrier reaction (endothermic) than translational energy, and the reverse is true for early-barrier reaction (exothermic).

In the case studied here, the F + H2 → FH + H is exothermic and thus the rules would predict that a higher distribution of energy in the translational energy mode would promote the reaction. This is illustrated

== References ==
<references>
<ref name="transition state theory">M. Brouard, 1998, Reaction dynamics, "chapter 2 Potential energy surfaces" p13</ref>
<ref name="bond energy"> http://www.wiredchemist.com/chemistry/data/bond_energies_lengths.htm</ref>
</references>

MRD:mfc16

2018-05-17T14:04:23Z

Mfc16: /* The effects of varying the momentum of AB */

== Exercise 1: H2+H system ==
=== Transition states and minimas ===
The transition state of the triatomic system is defined as the maximum of the minimum energy path on the potential energy surface. This kind of feature is known as a saddle point, and is found by looking at the curvature of the potential energy surface.
For the H2+H system, the total energy gradient for the transition state and for the minimum is 0 for all stationary points, ie ∂V(ri)/∂ri=0.
To differentiate the transition state from a minimum, one must look at the second derivative of the potential energy curve. Derivatives are with respect to three coordinates, the bond lengths of Hb-Hc and Ha-Hb as well as the bond angle between those bonds. The triatomic system considered here is assumed to have a bond angle of 180 degrees and thus we only deal with two out of three degrees of freedom. A saddle point is observed when:

∂f/∂x=0, ∂f/∂y=0 and fxxfyy-fxy2 > 0

=== Locating the Transition state ===
The transition state ought to be on a reactive path between the reactants and products, thus the momenta are fixed to 0 because otherwise the system wouldn't be in the minimum well. A rough estimate of its location is done by looking at the contour plot.
Furthermore, at the transition state, both AB and BC distances should be equal since the system is a symmetric reaction.

[[File:Internuclear time Ex1 mfc16.PNG|thumb|centre|Plot of internuclear distance vs time for the given initial parameters.]]

At the transition state the bonds do not oscillate, the plot should therefore show two horizontal flat lines. This is obtained when r1=r2=0.90755 Å.

[[File:Internuclear TransitionEx1 mfc16.PNG|thumb|centre|Plot of internuclear distance vs time at the transistion state coordinates.]]

=== Differences between dynamics and MEP settings ===
The minimum energy path (mep) is the lowest energy reaction path leading to the formation of products. The variation of potential energyalong the mep is best described as a well rather than a barrier.
==== Contour maps ====

[[File:Dynamics TStrajectory mfc16.PNG|thumb|centre|]]

[[File:MEP contourEx1 mfc16.PNG|thumb|centre|]]

==== Internuclear distance vs time ====
[[File:Internuclear mepTS mfc16.PNG|thumb|centre|]]

[[File:Internuclear time Ex1 mfc16.PNG|thumb|centre|]]

=== Reactive and unreactive trajectories===

{| class="wikitable" border="1"
|+ Effect of momenta on reactivity
! p1 !! p2 !! Total energy !! Type of trajectory !! contour plot !! Description
|-
| -1.25 || -2.5 || -99.119 || Reactive || [[File:Reaction1 contour mc16.png|400px]] || The reaction path heads towards the products minimum region. The A-B molecule starts oscillating slowly, but oscillates faster after the B-C is formed.
|-
| -1.5 || -2.0 || -100.456 || Unreactive ||[[File:Reaction2 contour mfc16.png|400px]] || The A-B bond is oscillating, but the momenta of molecules AB and C combined are not strong enough to overcome repulsion forces and lead to the formation of the BC molecule.
|-
| -1.5 || -2.0 || -98.956 || Reactive ||[[File:Reaction3 contour mfc16.png|400px]] || This trajectory is very similar to the first one, with the main difference being that before formation of the B-C bond, the A-B bond length stretches as C approaches.
|-
| -2.5 || -5.0 || -84.956 || Unreactive || [[File:Reaction4 contour mfc16.png|400px]] || In this reaction, the AC bond does not oscillate initially. However, collision with atom C leads to a strongly vibrating BC bond which then causes the AB bond to stop oscillating. This trajectory is unreactive because the trajectory does not move towards the products since the transition state is isn't high enough in energy.
|-
| -2.5 || -5.2 || -83.416 || Reactive || [[File:Reaction5 contour mfc16.png|400px]] || This plot is very similar to the one before, it even looks like its mirror image but this time the trajectory is in the product channel and has enough energy to lead to the formation of products. The AB product vibrates strongly.
|}

=== Transition state theory ===
The system considered here is a three atom reaction of the form:
A + BC → ABC‡ → AB + C.
The transition state as explained above, can be thought of as a bottleneck on the PES where the reactants have to be if products are to be formed, the theory implies that regions of products and reactants are separate entities.
The assumptions of transition state theory are<ref name="transition state theory" />:
* At fixed themperature, the reactants are in thermal equilibrium, or, at fixed energy, all reactant states are equally accessible.
* Motion along the reaction coordinate (minimum energy path) is seperable from motion orthogonal to it.
* Motion along the reaction coordinate is classical.
* Motion along the minimum energy path is direct.
The first point refers to the fact that starting materials must have energies that obey the Boltzmann distribution, the second one states that the Born-Oppenheimer approximation must be obeyed by each atom in the system, while the third one simply implies that quantum tunneling is no observed. Finally, the last point implies that all trajectories that cross the transition state dividing surface from the reactant side are assumed to go on and form products irreversibly.

However, transition state theory is based on assumptions that cannot be made in some cases. For instance in the 4th reaction tested above, the reactants have enough energy to overcome the activation barrier and get to the transition state, but this doesn't lead to the formation of products and thus goes against the 4th assumption.

== Exercise 2: F-H-H ==
=== PES inspection ===
The reaction F + H2 ⇌ FH + H is an equilibrium reaction, with the forward reaction being exothermic (releases energy to the surroundings) while the reverse reaction is endothermic (absorbs energy from the surroundings). This is explained by the fact that the F-H bond is strong, with a bond energy<ref name="bond energy" /> of 565 kJ/mol, compared to the H-H bond which has a bond energy of 432 kJ/mol.

Settings used :
Atom A: F Atom B: H Atom C: H

The approximate position of the transition state was found to be when:
AB distance = 1.81 Å
BC distance = 0.7456 Å
Both momenta are set to 0 because here we look for the transition state.
This is confirmed by plotting an internuclear distance vs time plot using the dynamics method, where no oscillations are observed meaning that the molecules are at rest which is characteristic of the transition state.

[[File:Ex2 TSlocation mfc16.png]]

In order to find the activation energy, the calculation method is changed from dynamics to MEP and the AB bond distance is varied so that it is displaced from equilibrium at the transition state. By doing so, the molecule is forced to either go back to the reactants or go on to form the product. The Hammond postulate states that exothermic reactions have an early transition state and thus resembles more like the reactants than the products.
*The forward reaction F + H2 → FH + H is exothermic, so the transition state is observed early in the reaction and thus the AB bond length must be increased to find the activation energy.
AB distance is set to 1.91 Å and the number of steps is increased to 10 000.

Energy of the transition state = -103.344 Kcal/mol

Energy of the products = -132.936 Kcal/mol

Activation energy = energy of the transition state - energy of the reactants = Kcal/mol

[[File:Exo activation surface mfc16.PNG|thumb|centre|Surface plot for the exothermic reaction F + H2 → FH + H]]

*The reverse reaction FH + H → F + H2 is endothermic, so the transition state is observed late in the reaction and thus the AB bond length should be decreased to find the activation energy.
AB distance is set to 1.71 Å and the number of steps is increased to 10 000.

Energy of the transition state = -103.618 Kcal/mol

Energy of the products = -104.485 Kcal/mol

Activation energy = energy of the transition state - energy of the reactants = Kcal/mol

[[File:Endo activation surface mfc16.PNG|thumb|centre|Surface plot for the endothermic reaction FH + H → F + H2.]]

=== Reaction dynamics ===
==== Reactive trajectory ====
Let atom A= F atom B= H and atom C= H. Then if:

AB distance = 1.91 Å

BC distance = 0.7455 Å

AB momentum = -1.5

BC momentum = 1.0

[[File:Surface Ex2 Reactivetraj mfc16.png|thumb|centre|Contour plot of a reactive trajectory for the FHH molecule]]

[[File:Internuclearpvst Ex2 mfc16.png|thumb|centre|Internuclear momenta vs time.]]

[[File:Evst Ex2 mfc16.png|thumb|centre|Energy vs time for the reactive trajectory.]]

==== The effects of varying the momentum of AB ====
AB distance = 1.914 Å
BC distance= 0.74 Å
AB momentum= -3 to 3
BC momentum= -0.5

*In the case where pHH =-3 the molecules is strongly oscillating and leads to the formation of products.
[[File:Pof-3 contour mfc16.png|thumb|centre|Contour map in the case where pHH=-3.]]

*In the case where pHH =-0.5
[[File:Pof-0.5 contour mfc16.png|thumb|centre|Contour map in the case where pHH=-0.5.]]

*In the case where pHH =3

[[File:P=3 contour mfc16.png|thumb|centre|Contour map in the case where pHH =3.]]

=== Polanyi's empirical rules ===
The different distribution of energy between different modes (translational and vibrational)

== References ==
<references>
<ref name="transition state theory">M. Brouard, 1998, Reaction dynamics, "chapter 2 Potential energy surfaces" p13</ref>
<ref name="bond energy"> http://www.wiredchemist.com/chemistry/data/bond_energies_lengths.htm</ref>
</references>

File:P=3 contour mfc16.png

2018-05-17T14:03:40Z

Mfc16:

MRD:mfc16

2018-05-17T14:01:54Z

Mfc16: /* Exercise 2: F-H-H */

== Exercise 1: H2+H system ==
=== Transition states and minimas ===
The transition state of the triatomic system is defined as the maximum of the minimum energy path on the potential energy surface. This kind of feature is known as a saddle point, and is found by looking at the curvature of the potential energy surface.
For the H2+H system, the total energy gradient for the transition state and for the minimum is 0 for all stationary points, ie ∂V(ri)/∂ri=0.
To differentiate the transition state from a minimum, one must look at the second derivative of the potential energy curve. Derivatives are with respect to three coordinates, the bond lengths of Hb-Hc and Ha-Hb as well as the bond angle between those bonds. The triatomic system considered here is assumed to have a bond angle of 180 degrees and thus we only deal with two out of three degrees of freedom. A saddle point is observed when:

∂f/∂x=0, ∂f/∂y=0 and fxxfyy-fxy2 > 0

=== Locating the Transition state ===
The transition state ought to be on a reactive path between the reactants and products, thus the momenta are fixed to 0 because otherwise the system wouldn't be in the minimum well. A rough estimate of its location is done by looking at the contour plot.
Furthermore, at the transition state, both AB and BC distances should be equal since the system is a symmetric reaction.

[[File:Internuclear time Ex1 mfc16.PNG|thumb|centre|Plot of internuclear distance vs time for the given initial parameters.]]

At the transition state the bonds do not oscillate, the plot should therefore show two horizontal flat lines. This is obtained when r1=r2=0.90755 Å.

[[File:Internuclear TransitionEx1 mfc16.PNG|thumb|centre|Plot of internuclear distance vs time at the transistion state coordinates.]]

=== Differences between dynamics and MEP settings ===
The minimum energy path (mep) is the lowest energy reaction path leading to the formation of products. The variation of potential energyalong the mep is best described as a well rather than a barrier.
==== Contour maps ====

[[File:Dynamics TStrajectory mfc16.PNG|thumb|centre|]]

[[File:MEP contourEx1 mfc16.PNG|thumb|centre|]]

==== Internuclear distance vs time ====
[[File:Internuclear mepTS mfc16.PNG|thumb|centre|]]

[[File:Internuclear time Ex1 mfc16.PNG|thumb|centre|]]

=== Reactive and unreactive trajectories===

{| class="wikitable" border="1"
|+ Effect of momenta on reactivity
! p1 !! p2 !! Total energy !! Type of trajectory !! contour plot !! Description
|-
| -1.25 || -2.5 || -99.119 || Reactive || [[File:Reaction1 contour mc16.png|400px]] || The reaction path heads towards the products minimum region. The A-B molecule starts oscillating slowly, but oscillates faster after the B-C is formed.
|-
| -1.5 || -2.0 || -100.456 || Unreactive ||[[File:Reaction2 contour mfc16.png|400px]] || The A-B bond is oscillating, but the momenta of molecules AB and C combined are not strong enough to overcome repulsion forces and lead to the formation of the BC molecule.
|-
| -1.5 || -2.0 || -98.956 || Reactive ||[[File:Reaction3 contour mfc16.png|400px]] || This trajectory is very similar to the first one, with the main difference being that before formation of the B-C bond, the A-B bond length stretches as C approaches.
|-
| -2.5 || -5.0 || -84.956 || Unreactive || [[File:Reaction4 contour mfc16.png|400px]] || In this reaction, the AC bond does not oscillate initially. However, collision with atom C leads to a strongly vibrating BC bond which then causes the AB bond to stop oscillating. This trajectory is unreactive because the trajectory does not move towards the products since the transition state is isn't high enough in energy.
|-
| -2.5 || -5.2 || -83.416 || Reactive || [[File:Reaction5 contour mfc16.png|400px]] || This plot is very similar to the one before, it even looks like its mirror image but this time the trajectory is in the product channel and has enough energy to lead to the formation of products. The AB product vibrates strongly.
|}

=== Transition state theory ===
The system considered here is a three atom reaction of the form:
A + BC → ABC‡ → AB + C.
The transition state as explained above, can be thought of as a bottleneck on the PES where the reactants have to be if products are to be formed, the theory implies that regions of products and reactants are separate entities.
The assumptions of transition state theory are<ref name="transition state theory" />:
* At fixed themperature, the reactants are in thermal equilibrium, or, at fixed energy, all reactant states are equally accessible.
* Motion along the reaction coordinate (minimum energy path) is seperable from motion orthogonal to it.
* Motion along the reaction coordinate is classical.
* Motion along the minimum energy path is direct.
The first point refers to the fact that starting materials must have energies that obey the Boltzmann distribution, the second one states that the Born-Oppenheimer approximation must be obeyed by each atom in the system, while the third one simply implies that quantum tunneling is no observed. Finally, the last point implies that all trajectories that cross the transition state dividing surface from the reactant side are assumed to go on and form products irreversibly.

However, transition state theory is based on assumptions that cannot be made in some cases. For instance in the 4th reaction tested above, the reactants have enough energy to overcome the activation barrier and get to the transition state, but this doesn't lead to the formation of products and thus goes against the 4th assumption.

== Exercise 2: F-H-H ==
=== PES inspection ===
The reaction F + H2 ⇌ FH + H is an equilibrium reaction, with the forward reaction being exothermic (releases energy to the surroundings) while the reverse reaction is endothermic (absorbs energy from the surroundings). This is explained by the fact that the F-H bond is strong, with a bond energy<ref name="bond energy" /> of 565 kJ/mol, compared to the H-H bond which has a bond energy of 432 kJ/mol.

Settings used :
Atom A: F Atom B: H Atom C: H

The approximate position of the transition state was found to be when:
AB distance = 1.81 Å
BC distance = 0.7456 Å
Both momenta are set to 0 because here we look for the transition state.
This is confirmed by plotting an internuclear distance vs time plot using the dynamics method, where no oscillations are observed meaning that the molecules are at rest which is characteristic of the transition state.

[[File:Ex2 TSlocation mfc16.png]]

In order to find the activation energy, the calculation method is changed from dynamics to MEP and the AB bond distance is varied so that it is displaced from equilibrium at the transition state. By doing so, the molecule is forced to either go back to the reactants or go on to form the product. The Hammond postulate states that exothermic reactions have an early transition state and thus resembles more like the reactants than the products.
*The forward reaction F + H2 → FH + H is exothermic, so the transition state is observed early in the reaction and thus the AB bond length must be increased to find the activation energy.
AB distance is set to 1.91 Å and the number of steps is increased to 10 000.

Energy of the transition state = -103.344 Kcal/mol

Energy of the products = -132.936 Kcal/mol

Activation energy = energy of the transition state - energy of the reactants = Kcal/mol

[[File:Exo activation surface mfc16.PNG|thumb|centre|Surface plot for the exothermic reaction F + H2 → FH + H]]

*The reverse reaction FH + H → F + H2 is endothermic, so the transition state is observed late in the reaction and thus the AB bond length should be decreased to find the activation energy.
AB distance is set to 1.71 Å and the number of steps is increased to 10 000.

Energy of the transition state = -103.618 Kcal/mol

Energy of the products = -104.485 Kcal/mol

Activation energy = energy of the transition state - energy of the reactants = Kcal/mol

[[File:Endo activation surface mfc16.PNG|thumb|centre|Surface plot for the endothermic reaction FH + H → F + H2.]]

=== Reaction dynamics ===
==== Reactive trajectory ====
Let atom A= F atom B= H and atom C= H. Then if:

AB distance = 1.91 Å

BC distance = 0.7455 Å

AB momentum = -1.5

BC momentum = 1.0

[[File:Surface Ex2 Reactivetraj mfc16.png|thumb|centre|Contour plot of a reactive trajectory for the FHH molecule]]

[[File:Internuclearpvst Ex2 mfc16.png|thumb|centre|Internuclear momenta vs time.]]

[[File:Evst Ex2 mfc16.png|thumb|centre|Energy vs time for the reactive trajectory.]]

==== The effects of varying the momentum of AB ====
AB distance = 1.914 Å
BC distance= 0.74 Å
AB momentum= -3 to 3
BC momentum= -0.5

*In the case where pHH=-3 the molecules is strongly oscillating and leads to the formation of products.
[[File:Pof-3 contour mfc16.png|thumb|centre|Contour map in the case where pHH=-3.]]

*In the case where pHH=-0.5
[[File:Pof-0.5 contour mfc16.png|thumb|centre|Contour map in the case where pHH=-0.5.]]

*In the case where pHH=3

[[

=== Polanyi's empirical rules ===
The different distribution of energy between different modes (translational and vibrational)

== References ==
<references>
<ref name="transition state theory">M. Brouard, 1998, Reaction dynamics, "chapter 2 Potential energy surfaces" p13</ref>
<ref name="bond energy"> http://www.wiredchemist.com/chemistry/data/bond_energies_lengths.htm</ref>
</references>

MRD:mfc16

MRD:mfc16

2018-05-16T14:12:13Z

Mfc16: /* Transition state theory */