ChemWiki - User contributions [en]

MRD:01531254

2020-05-08T10:47:58Z

Aa6718: /* Exercise 2: F - H - H system */

== Molecular Reaction Dynamics Lab ==

The objectives of this exercise are to study the reactivity of triatomic systems, where an atom and a diatomic molecule collide, through calculating Molecular Dynamics trajectories.

=== Exercise 1: H + H2 system ===

==== Dynamics from the transition state region ====

{{fontcolor1|blue| On a potential energy surface diagram, how is the transition state mathematically defined? How can the transition state be identified, and how can it be distinguished from a local minimum of the potential energy surface? }}

The transition state is defined as the maximum on the minimum energy path linking reactants and the products. The transition point can be identified on a potential energy surface as being at a saddle point, where the reactive trajectory is at its highest point and the gradient of the potential energy surface is zero. Saddle points have a local maximum in one direction and a local minimum in the other. They can be mathematically defined using their gradient: the partial derivative of the gradient, fx, equals zero, indicating that the gradient is zero at this point. Furthermore, saddle points are distinguished from local minima in that the result of the second partial derivative test, fxxfyy-fxy2, is larger than zero. <ref name="Reference 111" />

[[File:MRD_111_figure1.png|thumb|center|A PES with the transition state region highlighted.|400px]]

==== Trajectories from r1 = r2: locating the transition state ====

{{fontcolor1|blue| 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. }}

Since the H + H2 surface is symmetric, the transition state must have r1 = r2. In trajectories from r1 = r2 the trajectory oscillates on the ridge; this can be used to locate the transition state geometry.

When testing different initial conditions with r1 = r2, and p1 = p2 = 0.0 g.mol-1.pm.fs-1, it can be seen that the system undergoes a periodic symmetric vibration.

[[File:Y2C10.png|center|400px]]

For example, the Internuclear Distances vs Time plot for r1 = r2 = 100 pm , p1 = p2 = 0.0 g.mol-1.pm.fs-1 is shown below ,and clear oscillation can be seen.

[[File:MRD_112_figure1.png|thumb|center|The Internuclear Distances vs Time plot for r1 = r2 = 100 pm.|400px]]

However, when r1 = r2 is set to 91, the vibration is very minimal. This is a good estimate for the transition state because when a trajectory starts at the transition state, with no initial momentum, it stays there forever.

[[File:MRD_112_figure2.png|thumb|center|The Internuclear Distances vs Time plot for r1 = r2 = 91 pm.|400px]]

==== Calculating the reaction path and trajectories from r1 = rts+δ, r2 = rts ====

{{fontcolor1|blue| Comment on how the mep and the trajectory differ. }}

The minimum energy path (or mep) is a very special trajectory that corresponds to infinitely slow motion. This can be tested with initial conditions r1 = rts + 1 and r1 = rts, and p1 = p2 = 0.0 g.mol-1.pm.fs-1 and the calculation type as 'MEP'. With r1 set at 92 and r2 set at 91, it can be seen that the trajectory simply follows the valley floor to H1 + H2 - H3.

[[File:MRD_113_figure1.png|thumb|center|A PES with the mep trajectory highlighted.|400px]]

However, mep doesn't provide a realistic account of the motion of atoms during a reaction because it doesn't account for the mass of the atoms. When the same reaction is repeated with the calculation type as 'Dynamics' rather than 'MEP', the inertial motion of the atoms is indicated by the oscillation of the BC distance caused by the masses interacting.

[[File:MRD_113_figure2.png|thumb|center|A PES with the reaction path highlighted.|400px]]

==== Reactive and unreactive trajectories ====

{{fontcolor1|blue| Complete the table by adding the total energy, whether the trajectory is reactive or unreactive, and provide a plot of the trajectory and a small description for what happens along the trajectory. What can you conclude from the table? }}

[[File:Y2C1.png|center|500px]]

Initial positions r1 = 74 pm and r2 = 200 pm:

{| class="wikitable" border=1
! p1 / g.mol-1.pm.fs-1 !! p2 / g.mol-1.pm.fs-1 !! Etot / kJ.mol-1 !! Reactive? !! Description of the dynamics !! Illustration of the trajectory
|-
| -2.56 || -5.1 || -414.280 || Yes || m1 and m2-m3 collide and react to form m1-m2 and m3 || [[File:MRD_114_figure1.png|center|200px]]
|-
| -3.1 || -4.1 || -420.077 || No || m1 and m2-m3 do not collide so no reaction occurs || [[File:MRD_114_figure2.png|center|200px]]
|-
| -3.1 || -5.1 || -413.977 || Yes || m1 and m2-m3 collide and react to form m1-m2 and m3 || [[File:MRD_114_figure3.png|center|200px]]
|-
| -5.1 || -10.1 || -357.277 || No || m1 and m2-m3 collide and r1 oscillates but m2-m3 remains intact so no reaction occurs. This is a case of barrier recrossing: the system crosses the transition state region, the bond in the product forms, but then the system reverts back to the reactants. || [[File:MRD_114_figure4.png|center|200px]]
|-
| -5.1 || -10.6 || -349.477 || Yes || m1 and m2-m3 collide, and though r2 oscillates they ultimately react to form m1-m2 and m3|| [[File:MRD_114_figure5.png|center|200px]]
|}

==== Transition State Theory ====

{{fontcolor1|blue| Given the results you have obtained, how will Transition State Theory predictions for reaction rate values compare with experimental values? }}

A powerful theory to rationalise and calculate the rate of chemical reactions based on the properties of the reactants and the transitions state structure is Transition State Theory. It predicts that the rate constant for a generic bimolecular reaction <math>\mathcal{A+B}\rightarrow\mathcal{P}</math> is:

<math>k_{TST}=R_{cl}\frac{Q_{\ddagger}'/V}{(Q_{\mathcal{A}}/V)(Q_{\mathcal{B}}/V)}e^{-\frac{E_0}{k_B T}}</math>

A crucial assumption of Transition State Theory in estimating ''Rcl'' is that all trajectories with a kinetic energy along the reaction coordinate greater than the activation energy will be reactive. By further assuming that the kinetic energy along the reaction coordinate follows the Boltzmann distribution, one obtain the conventional Transition State Theory rate constant expression:

<math>k_{TST}=\frac{k_B T}{h} \frac{Q_{\ddagger}'/V}{(Q_{\mathcal{A}}/V)(Q_{\mathcal{B}}/V)}e^{-\frac{E_0}{k_B T}}</math>

In Transition State Theory motion is treated by classical mechanics, and it is assumed that this motion always leads to products without recrossings of the saddle point. This is incorrect as quantum mechanical tunneling allows barrier crossing to take place when the total energy is less than the potential energy at the top of the barrier.<ref name="Reference 115"/> Barrier recrossing is seento occur in the calculated experiment values, for example:

[[File:MRD_114_figure4.png|center|thumb|The PES of a reaction where barrier crossing occurs.|400px]]

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

==== PES inspection: F + H2 ====

{{fontcolor1|blue| By inspecting the potential energy surfaces, classify the F + H2 and H + HF reactions according to their energetics (endothermic or exothermic). How does this relate to the bond strength of the chemical species involved? Locate the approximate position of the transition state. Report the activation energy for both reactions. }}

[[File:MRD_121_figure3.png|center|500px]]

F + H2 is an exothermic reaction as characterised by the fact that the transition state occurs early in the reaction coordinate on its potential energy surface, i.e. it is an attractive surface.<ref name="Reference 121"/> This relates to the bond strengths involved as a relatively weak H-H bond is broken while a strong H-F bond is formed; bond making is an exothermic process, so the formation of a bond with high bond enthalpy makes the overall reaction exothermic.<ref name="Reference 121"/>

[[File:MRD_121_figure1.png|center|thumb|The contour plot of F + H2 with the transition state region highlighted.|400px]]

The approximate position of the transition state is where the F---H gap is 125 pm and the H---H gap is 96 pm. This is reflected in the Internuclear Distances vs Time plot where this position is set at this position with p1 = p2 = 0.0 g.mol-1.pm.fs-1; the system undergoes a periodic symmetric vibration but does not move from the spot. This structure is consistent with Hammond's postulate, where the transition state in an exothermic reaction is close in structure to the reactants.<ref name="Reference 121 1"/>

[[File:MRD_121_figure2.png|center|thumb|The Internuclear Distances vs Time plot of F + H2 at the position r1 = 125 pm and r2 = 96 pm.|400px]]

Part of the Energy vs Time plot is shown from the reaction, depicting the potential energy of the products, transition states and reactants. From this the activation energy can be calculated to be 59 kJ/mol for this reaction.

[[File:MRD_121_figure4.png|center|thumb|The beginning of the Energy vs Time plot of F + H2.|400px]]

==== PES inspection: H + HF ====

{{fontcolor1|blue| By inspecting the potential energy surfaces, classify the F + H2 and H + HF reactions according to their energetics (endothermic or exothermic). How does this relate to the bond strength of the chemical species involved? Locate the approximate position of the transition state. Report the activation energy for both reactions. }}

[[File:MRD_122_figure3.png|center|500px]]

H + HF is an endothermic reaction as characterised by the fact that the transition state occurs late in the reaction coordinate on its potential energy surface, i.e. it is an repulsive surface.<ref name="Reference 121"/> This relates to the bond strengths involved as a strong H-F bond is broken while a weaker H-H bond is formed; bond breaking is an endothermic process, so the breakage of a bond with high bond enthalpy makes the overall reaction endothermic.<ref name="Reference 121"/>

[[File:MRD_122_figure1.png|center|thumb|The contour plot of H + HF with the transition state region highlighted.|400px]]

The approximate position of the transition state is where the F---H gap is 125 pm and the H---H gap is 96 pm. This is reflected in the Internuclear Distances vs Time plot where this position is set at this position with p1 = p2 = 0.0 g.mol-1.pm.fs-1; the system undergoes a periodic symmetric vibration but does not move from the spot. This structure is consistent with Hammond's postulate, where the transition state in an endothermic reaction is close in structure to the products.<ref name="Reference 121 1"/>

[[File:MRD_121_figure2.png|center|thumb|The Internuclear Distances vs Time plot of H + HF at the position r1 = 129 pm and r2 = 90 pm.|400px]]

Part of the Energy vs Time plot is shown from the reaction, depicting the potential energy of the products, transition states and reactants. From this the activation energy can be calculated to be 160 kJ/mol for this reaction.

[[File:MRD_122_figure4.png|center|thumb|The beginning of the Energy vs Time plot of H + HF.|400px]]

==== Reaction dynamics: F + H2 ====

{{fontcolor1|blue| In light of the fact that energy is conserved, discuss the mechanism of release of the reaction energy. Explain how this could be confirmed experimentally. }}

One set of initial conditions that results in a reactive trajectory for F + H2 is r1 = 140 pm, r2 = 74 pm, p1 = 0 g.mol-1.pm.fs-1 and p2 = -5 g.mol-1.pm.fs-1. By considering the animation and Momenta vs Time plot, the mechanism can be examined. As H2 approaches F the momentum of its bond increases; after the transition state, where H1 bonds with F and the other H moves away from the new product, the H-F bond oscillates.

[[File:MRD_123_figure1.png|center|thumb|The Momenta vs Time plot of F + H2.|400px]]

The hydrogen molecule could be polaried by the electronegative fluoride and form a bond in the transition state via an SN2 mechanism. It could be possible to determine the order of the reaction experimentally, which should correspond to a SN2 rate law involving the concentrations of both the species in the reaction.

==== Reaction dynamics: Polanyi ====

{{fontcolor1|blue| 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. }}

Polanyi's empirical rules explain and predict the effect of translational and vibrational energy in driving reactions. They state that for reactions with an early transition state / reactant-like transition state, translational energy is most effective in driving the reaction; for reactions with a late transition state / product-like transition state, vibrational energy is most effective in driving the reaction.<ref name="Reference 124"/> These rules can be demonstated through different case studies: F + H2 falls into the first category, so is most affected by translational energy, and H + HF falls into the second category, so is most affected by vibrational energy. Consider the following examples:

{| class="wikitable" border=1
! rFH !! rHH !! pFH !! pHH !! Description !! Diagram
|-
| 160 || 74 || -1 || -6.1 || [[File:MRD_121_figure3.png|center|400px]] The H2 molecule has a high amount of energy on the H-H vibration. The system undergoes barrier recrossing but does not react because for systems with an early transition state translational energy is more effective. || [[File:MRD_124_figure1.png|center|200px]]
|-
| 160 || 74 || -1 || 6.1 || [[File:MRD_121_figure3.png|center|400px]] The H2 molecule has a high amount of energy on the H-H vibration. The system undergoes barrier recrossing but does not react because for systems with an early transition state translational energy is more effective. || [[File:MRD_124_figure2.png|center|200px]]
|-
| 160 || 74 || -1.6 || 0.2 || [[File:MRD_121_figure3.png|center|400px]] The H2 molecule has a low amount of vibrational energy. The system reacts successfully because for systems with an early transition state translational energy is more effective. || [[File:MRD_124_figure3.png|center|200px]]
|-
| 94 || 150 || 0 || 21 || [[File:MRD_122_figure3.png|center|400px]] The HF molecule has a low amount of vibrational energy. The system molecules collide but do not react successfully because for systems with a late transition state vibrational energy is more effective. || [[File:MRD_124_figure4.png|center|200px]]
|-
| 94 || 150 || 21 || 0 || [[File:MRD_122_figure3.png|center|400px]] The HF molecule has a high amount of energy on the H-F vibration. The molecules collide and react successfully because for systems with a late transition state vibrational energy is more effective. || [[File:MRD_124_figure5.png|center|200px]]
|}

=== References ===

<references>

<ref name="Reference 111"> https://www.khanacademy.org/math/multivariable-calculus/applications-of-multivariable-derivatives/optimizing-multivariable-functions/a/maximums-minimums-and-saddle-points </ref>

<ref name="Reference 115"> N. E. Henriksen and F. Y. Hansen Theories of Molecular Reaction Dynamics 2nd ed., OUP, 2019 </ref>

<ref name="Reference 121"> Atkins, de Paula, Keeler: Physical Chemistry, 11th Edition </ref>

<ref name="Reference 121 1"> Clayden, Greeves, Warren: Organic Chemistry, 2nd Edition </ref>

<ref name="Reference 124"> Guo, Liu: Control of chemical reactivity by transition-state and beyond </ref>

</references>

File:MRD 122 figure4.png

2020-05-07T16:20:23Z

Aa6718:

File:MRD 121 figure4.png

2020-05-07T16:20:12Z

Aa6718:

MRD:01531254

2020-05-07T16:19:54Z

Aa6718: /* Exercise 2: F - H - H system */

== Molecular Reaction Dynamics Lab ==

The objectives of this exercise are to study the reactivity of triatomic systems, where an atom and a diatomic molecule collide, through calculating Molecular Dynamics trajectories.

=== Exercise 1: H + H2 system ===

==== Dynamics from the transition state region ====

{{fontcolor1|blue| On a potential energy surface diagram, how is the transition state mathematically defined? How can the transition state be identified, and how can it be distinguished from a local minimum of the potential energy surface? }}

The transition state is defined as the maximum on the minimum energy path linking reactants and the products. The transition point can be identified on a potential energy surface as being at a saddle point, where the reactive trajectory is at its highest point and the gradient of the potential energy surface is zero. Saddle points have a local maximum in one direction and a local minimum in the other. They can be mathematically defined using their gradient: the partial derivative of the gradient, fx, equals zero, indicating that the gradient is zero at this point. Furthermore, saddle points are distinguished from local minima in that the result of the second partial derivative test, fxxfyy-fxy2, is larger than zero. <ref name="Reference 111" />

[[File:MRD_111_figure1.png|thumb|center|A PES with the transition state region highlighted.|400px]]

==== Trajectories from r1 = r2: locating the transition state ====

{{fontcolor1|blue| 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. }}

Since the H + H2 surface is symmetric, the transition state must have r1 = r2. In trajectories from r1 = r2 the trajectory oscillates on the ridge; this can be used to locate the transition state geometry.

When testing different initial conditions with r1 = r2, and p1 = p2 = 0.0 g.mol-1.pm.fs-1, it can be seen that the system undergoes a periodic symmetric vibration.

[[File:Y2C10.png|center|400px]]

For example, the Internuclear Distances vs Time plot for r1 = r2 = 100 pm , p1 = p2 = 0.0 g.mol-1.pm.fs-1 is shown below ,and clear oscillation can be seen.

[[File:MRD_112_figure1.png|thumb|center|The Internuclear Distances vs Time plot for r1 = r2 = 100 pm.|400px]]

However, when r1 = r2 is set to 91, the vibration is very minimal. This is a good estimate for the transition state because when a trajectory starts at the transition state, with no initial momentum, it stays there forever.

[[File:MRD_112_figure2.png|thumb|center|The Internuclear Distances vs Time plot for r1 = r2 = 91 pm.|400px]]

==== Calculating the reaction path and trajectories from r1 = rts+δ, r2 = rts ====

{{fontcolor1|blue| Comment on how the mep and the trajectory differ. }}

The minimum energy path (or mep) is a very special trajectory that corresponds to infinitely slow motion. This can be tested with initial conditions r1 = rts + 1 and r1 = rts, and p1 = p2 = 0.0 g.mol-1.pm.fs-1 and the calculation type as 'MEP'. With r1 set at 92 and r2 set at 91, it can be seen that the trajectory simply follows the valley floor to H1 + H2 - H3.

[[File:MRD_113_figure1.png|thumb|center|A PES with the mep trajectory highlighted.|400px]]

However, mep doesn't provide a realistic account of the motion of atoms during a reaction because it doesn't account for the mass of the atoms. When the same reaction is repeated with the calculation type as 'Dynamics' rather than 'MEP', the inertial motion of the atoms is indicated by the oscillation of the BC distance caused by the masses interacting.

[[File:MRD_113_figure2.png|thumb|center|A PES with the reaction path highlighted.|400px]]

==== Reactive and unreactive trajectories ====

{{fontcolor1|blue| Complete the table by adding the total energy, whether the trajectory is reactive or unreactive, and provide a plot of the trajectory and a small description for what happens along the trajectory. What can you conclude from the table? }}

[[File:Y2C1.png|center|500px]]

Initial positions r1 = 74 pm and r2 = 200 pm:

{| class="wikitable" border=1
! p1 / g.mol-1.pm.fs-1 !! p2 / g.mol-1.pm.fs-1 !! Etot / kJ.mol-1 !! Reactive? !! Description of the dynamics !! Illustration of the trajectory
|-
| -2.56 || -5.1 || -414.280 || Yes || m1 and m2-m3 collide and react to form m1-m2 and m3 || [[File:MRD_114_figure1.png|center|200px]]
|-
| -3.1 || -4.1 || -420.077 || No || m1 and m2-m3 do not collide so no reaction occurs || [[File:MRD_114_figure2.png|center|200px]]
|-
| -3.1 || -5.1 || -413.977 || Yes || m1 and m2-m3 collide and react to form m1-m2 and m3 || [[File:MRD_114_figure3.png|center|200px]]
|-
| -5.1 || -10.1 || -357.277 || No || m1 and m2-m3 collide and r1 oscillates but m2-m3 remains intact so no reaction occurs. This is a case of barrier recrossing: the system crosses the transition state region, the bond in the product forms, but then the system reverts back to the reactants. || [[File:MRD_114_figure4.png|center|200px]]
|-
| -5.1 || -10.6 || -349.477 || Yes || m1 and m2-m3 collide, and though r2 oscillates they ultimately react to form m1-m2 and m3|| [[File:MRD_114_figure5.png|center|200px]]
|}

==== Transition State Theory ====

{{fontcolor1|blue| Given the results you have obtained, how will Transition State Theory predictions for reaction rate values compare with experimental values? }}

A powerful theory to rationalise and calculate the rate of chemical reactions based on the properties of the reactants and the transitions state structure is Transition State Theory. It predicts that the rate constant for a generic bimolecular reaction <math>\mathcal{A+B}\rightarrow\mathcal{P}</math> is:

<math>k_{TST}=R_{cl}\frac{Q_{\ddagger}'/V}{(Q_{\mathcal{A}}/V)(Q_{\mathcal{B}}/V)}e^{-\frac{E_0}{k_B T}}</math>

A crucial assumption of Transition State Theory in estimating ''Rcl'' is that all trajectories with a kinetic energy along the reaction coordinate greater than the activation energy will be reactive. By further assuming that the kinetic energy along the reaction coordinate follows the Boltzmann distribution, one obtain the conventional Transition State Theory rate constant expression:

<math>k_{TST}=\frac{k_B T}{h} \frac{Q_{\ddagger}'/V}{(Q_{\mathcal{A}}/V)(Q_{\mathcal{B}}/V)}e^{-\frac{E_0}{k_B T}}</math>

In Transition State Theory motion is treated by classical mechanics, and it is assumed that this motion always leads to products without recrossings of the saddle point. This is incorrect as quantum mechanical tunneling allows barrier crossing to take place when the total energy is less than the potential energy at the top of the barrier.<ref name="Reference 115"/> Barrier recrossing is seento occur in the calculated experiment values, for example:

[[File:MRD_114_figure4.png|center|thumb|The PES of a reaction where barrier crossing occurs.|400px]]

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

==== PES inspection: F + H2 ====

{{fontcolor1|blue| By inspecting the potential energy surfaces, classify the F + H2 and H + HF reactions according to their energetics (endothermic or exothermic). How does this relate to the bond strength of the chemical species involved? Locate the approximate position of the transition state. Report the activation energy for both reactions. }}

[[File:MRD_121_figure3.png|center|500px]]

F + H2 is an exothermic reaction as characterised by the fact that the transition state occurs early in the reaction coordinate on its potential energy surface, i.e. it is an attractive surface.<ref name="Reference 121"/> This relates to the bond strengths involved as a relatively weak H-H bond is broken while a strong H-F bond is formed; bond making is an exothermic process, so the formation of a bond with high bond enthalpy makes the overall reaction exothermic.<ref name="Reference 121"/>

[[File:MRD_121_figure1.png|center|thumb|The contour plot of F + H2 with the transition state region highlighted.|400px]]

The approximate position of the transition state is where the F---H gap is 125 pm and the H---H gap is 96 pm. This is reflected in the Internuclear Distances vs Time plot where this position is set at this position with p1 = p2 = 0.0 g.mol-1.pm.fs-1; the system undergoes a periodic symmetric vibration but does not move from the spot. This structure is consistent with Hammond's postulate, where the transition state in an exothermic reaction is close in structure to the reactants.<ref name="Reference 121 1"/>

[[File:MRD_121_figure2.png|center|thumb|The Internuclear Distances vs Time plot of F + H2 at the position r1 = 125 pm and r2 = 96 pm.|400px]]

Part of the Energy vs Time plot is shown from the reaction, depicting the potential energy of the products, transition states and reactants. From this the activation energy can be calculated to be 59 kJ/mol for this reaction.

[[File:MRD_121_figure4.png|center|thumb|The beginning of the Energy vs Time plot of F + H2.|400px]]

==== PES inspection: H + HF ====

{{fontcolor1|blue| By inspecting the potential energy surfaces, classify the F + H2 and H + HF reactions according to their energetics (endothermic or exothermic). How does this relate to the bond strength of the chemical species involved? Locate the approximate position of the transition state. Report the activation energy for both reactions. }}

[[File:MRD_122_figure3.png|center|500px]]

H + HF is an endothermic reaction as characterised by the fact that the transition state occurs late in the reaction coordinate on its potential energy surface, i.e. it is an repulsive surface.<ref name="Reference 121"/> This relates to the bond strengths involved as a strong H-F bond is broken while a weaker H-H bond is formed; bond breaking is an endothermic process, so the breakage of a bond with high bond enthalpy makes the overall reaction endothermic.<ref name="Reference 121"/>

[[File:MRD_122_figure1.png|center|thumb|The contour plot of H + HF with the transition state region highlighted.|400px]]

The approximate position of the transition state is where the F---H gap is 129 pm and the H---H gap is 90 pm. This is reflected in the Internuclear Distances vs Time plot where this position is set at this position with p1 = p2 = 0.0 g.mol-1.pm.fs-1; the system undergoes a periodic symmetric vibration but does not move from the spot. This structure is consistent with Hammond's postulate, where the transition state in an endothermic reaction is close in structure to the products.<ref name="Reference 121 1"/>

[[File:MRD_122_figure2.png|center|thumb|The Internuclear Distances vs Time plot of H + HF at the position r1 = 129 pm and r2 = 90 pm.|400px]]

Part of the Energy vs Time plot is shown from the reaction, depicting the potential energy of the products, transition states and reactants. From this the activation energy can be calculated to be 160 kJ/mol for this reaction.

[[File:MRD_122_figure4.png|center|thumb|The beginning of the Energy vs Time plot of H + HF.|400px]]

==== Reaction dynamics: F + H2 ====

{{fontcolor1|blue| In light of the fact that energy is conserved, discuss the mechanism of release of the reaction energy. Explain how this could be confirmed experimentally. }}

One set of initial conditions that results in a reactive trajectory for F + H2 is r1 = 140 pm, r2 = 74 pm, p1 = 0 g.mol-1.pm.fs-1 and p2 = -5 g.mol-1.pm.fs-1. By considering the animation and Momenta vs Time plot, the mechanism can be examined. As H2 approaches F the momentum of its bond increases; after the transition state, where H1 bonds with F and the other H moves away from the new product, the H-F bond oscillates.

[[File:MRD_123_figure1.png|center|thumb|The Momenta vs Time plot of F + H2.|400px]]

The hydrogen molecule could be polaried by the electronegative fluoride and form a bond in the transition state via an SN2 mechanism. It could be possible to determine the order of the reaction experimentally, which should correspond to a SN2 rate law involving the concentrations of both the species in the reaction.

==== Reaction dynamics: Polanyi ====

{{fontcolor1|blue| 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. }}

Polanyi's empirical rules explain and predict the effect of translational and vibrational energy in driving reactions. They state that for reactions with an early transition state / reactant-like transition state, translational energy is most effective in driving the reaction; for reactions with a late transition state / product-like transition state, vibrational energy is most effective in driving the reaction.<ref name="Reference 124"/> These rules can be demonstated through different case studies: F + H2 falls into the first category, so is most affected by translational energy, and H + HF falls into the second category, so is most affected by vibrational energy. Consider the following examples:

{| class="wikitable" border=1
! rFH !! rHH !! pFH !! pHH !! Description !! Diagram
|-
| 160 || 74 || -1 || -6.1 || [[File:MRD_121_figure3.png|center|400px]] The H2 molecule has a high amount of energy on the H-H vibration. The system undergoes barrier recrossing but does not react because for systems with an early transition state translational energy is more effective. || [[File:MRD_124_figure1.png|center|200px]]
|-
| 160 || 74 || -1 || 6.1 || [[File:MRD_121_figure3.png|center|400px]] The H2 molecule has a high amount of energy on the H-H vibration. The system undergoes barrier recrossing but does not react because for systems with an early transition state translational energy is more effective. || [[File:MRD_124_figure2.png|center|200px]]
|-
| 160 || 74 || -1.6 || 0.2 || [[File:MRD_121_figure3.png|center|400px]] The H2 molecule has a low amount of vibrational energy. The system reacts successfully because for systems with an early transition state translational energy is more effective. || [[File:MRD_124_figure3.png|center|200px]]
|-
| 94 || 150 || 0 || 21 || [[File:MRD_122_figure3.png|center|400px]] The HF molecule has a low amount of vibrational energy. The system molecules collide but do not react successfully because for systems with a late transition state vibrational energy is more effective. || [[File:MRD_124_figure4.png|center|200px]]
|-
| 94 || 150 || 21 || 0 || [[File:MRD_122_figure3.png|center|400px]] The HF molecule has a high amount of energy on the H-F vibration. The molecules collide and react successfully because for systems with a late transition state vibrational energy is more effective. || [[File:MRD_124_figure5.png|center|200px]]
|}

=== References ===

<references>

<ref name="Reference 111"> https://www.khanacademy.org/math/multivariable-calculus/applications-of-multivariable-derivatives/optimizing-multivariable-functions/a/maximums-minimums-and-saddle-points </ref>

<ref name="Reference 115"> N. E. Henriksen and F. Y. Hansen Theories of Molecular Reaction Dynamics 2nd ed., OUP, 2019 </ref>

<ref name="Reference 121"> Atkins, de Paula, Keeler: Physical Chemistry, 11th Edition </ref>

<ref name="Reference 121 1"> Clayden, Greeves, Warren: Organic Chemistry, 2nd Edition </ref>

<ref name="Reference 124"> Guo, Liu: Control of chemical reactivity by transition-state and beyond </ref>

</references>

MRD:01531254

2020-05-07T15:45:21Z

Aa6718: /* PES inspection: H + HF */

== Molecular Reaction Dynamics Lab ==

The objectives of this exercise are to study the reactivity of triatomic systems, where an atom and a diatomic molecule collide, through calculating Molecular Dynamics trajectories.

=== Exercise 1: H + H2 system ===

==== Dynamics from the transition state region ====

{{fontcolor1|blue| On a potential energy surface diagram, how is the transition state mathematically defined? How can the transition state be identified, and how can it be distinguished from a local minimum of the potential energy surface? }}

The transition state is defined as the maximum on the minimum energy path linking reactants and the products. The transition point can be identified on a potential energy surface as being at a saddle point, where the reactive trajectory is at its highest point and the gradient of the potential energy surface is zero. Saddle points have a local maximum in one direction and a local minimum in the other. They can be mathematically defined using their gradient: the partial derivative of the gradient, dy/dx, equals zero, indicating that the gradient is zero at this point. Furthermore, saddle points are distinguished from local minima in that their second partial derivative, d2y/dx2, is larger than zero. <ref name="Reference 111" />

[[File:MRD_111_figure1.png|thumb|center|A PES with the transition state region highlighted.|400px]]

==== Trajectories from r1 = r2: locating the transition state ====

{{fontcolor1|blue| 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. }}

Since the H + H2 surface is symmetric, the transition state must have r1 = r2. In trajectories from r1 = r2 the trajectory oscillates on the ridge; this can be used to locate the transition state geometry.

When testing different initial conditions with r1 = r2, and p1 = p2 = 0.0 g.mol-1.pm.fs-1, it can be seen that the system undergoes a periodic symmetric vibration.

[[File:Y2C10.png|center|400px]]

For example, the Internuclear Distances vs Time plot for r1 = r2 = 100 pm , p1 = p2 = 0.0 g.mol-1.pm.fs-1 is shown below ,and clear oscillation can be seen.

[[File:MRD_112_figure1.png|thumb|center|The Internuclear Distances vs Time plot for r1 = r2 = 100 pm.|400px]]

However, when r1 = r2 is set to 91, the vibration is very minimal. This is a good estimate for the transition state because when a trajectory starts at the transition state, with no initial momentum, it stays there forever.

[[File:MRD_112_figure2.png|thumb|center|The Internuclear Distances vs Time plot for r1 = r2 = 91 pm.|400px]]

==== Calculating the reaction path and trajectories from r1 = rts+δ, r2 = rts ====

{{fontcolor1|blue| Comment on how the mep and the trajectory differ. }}

The minimum energy path (or mep) is a very special trajectory that corresponds to infinitely slow motion. This wan be tested with initial conditions r1 = rts + 1 and r1 = rts, and p1 = p2 = 0.0 g.mol-1.pm.fs-1 and the calculation type as 'MEP'. With r1 set at 92 and r2 set at 91, it can be seen that the trajectory simply follows the valley floor to H1 + H2 - H3.

[[File:MRD_113_figure1.png|thumb|center|A PES with the mep trajectory highlighted.|400px]]

However, mep doesn't provide a realistic account of the motion of atoms during a reaction because it doesn't account for the mass of the atoms. When the same reaction is repeated with the calculation type as 'Dynamics' rather than 'MEP', the inertial motion of the atoms is indicated by the oscillation of the BC distance caused by the masses interacting.

[[File:MRD_113_figure2.png|thumb|center|A PES with the reaction path highlighted.|400px]]

==== Reactive and unreactive trajectories ====

{{fontcolor1|blue| Complete the table by adding the total energy, whether the trajectory is reactive or unreactive, and provide a plot of the trajectory and a small description for what happens along the trajectory. What can you conclude from the table? }}

[[File:Y2C1.png|center|500px]]

Initial positions r1 = 74 pm and r2 = 200 pm:

{| class="wikitable" border=1
! p1 / g.mol-1.pm.fs-1 !! p2 / g.mol-1.pm.fs-1 !! Etot / kJ.mol-1 !! Reactive? !! Description of the dynamics !! Illustration of the trajectory
|-
| -2.56 || -5.1 || -414.280 || Yes || m1 and m2-m3 collide and react to form m1-m2 and m3 || [[File:MRD_114_figure1.png|center|200px]]
|-
| -3.1 || -4.1 || -420.077 || No || m1 and m2-m3 do not collide so no reaction occurs || [[File:MRD_114_figure2.png|center|200px]]
|-
| -3.1 || -5.1 || -413.977 || Yes || m1 and m2-m3 collide and react to form m1-m2 and m3 || [[File:MRD_114_figure3.png|center|200px]]
|-
| -5.1 || -10.1 || -357.277 || No || m1 and m2-m3 collide and r1 oscillates but m2-m3 remains intact so no reaction occurs. This is a case of barrier recrossing: the system crosses the transition state region, the bond in the product forms, but then the system reverts back to the reactants. || [[File:MRD_114_figure4.png|center|200px]]
|-
| -5.1 || -10.6 || -349.477 || Yes || m1 and m2-m3 collide, and though r2 oscillates they ultimately react to form m1-m2 and m3|| [[File:MRD_114_figure5.png|center|200px]]
|}

==== Transition State Theory ====

{{fontcolor1|blue| Given the results you have obtained, how will Transition State Theory predictions for reaction rate values compare with experimental values? }}

A powerful theory to rationalise and calculate the rate of chemical reactions based on the properties of the reactants and the transitions state structure is Transition State Theory. It predicts that the rate constant for a generic bimolecular reaction <math>\mathcal{A+B}\rightarrow\mathcal{P}</math> is:

<math>k_{TST}=R_{cl}\frac{Q_{\ddagger}'/V}{(Q_{\mathcal{A}}/V)(Q_{\mathcal{B}}/V)}e^{-\frac{E_0}{k_B T}}</math>

A crucial assumption of Transition State Theory in estimating ''Rcl'' is that all trajectories with a kinetic energy along the reaction coordinate greater than the activation energy will be reactive. By further assuming that the kinetic energy along the reaction coordinate follows the Boltzmann distribution, one obtain the conventional Transition State Theory rate constant expression:

<math>k_{TST}=\frac{k_B T}{h} \frac{Q_{\ddagger}'/V}{(Q_{\mathcal{A}}/V)(Q_{\mathcal{B}}/V)}e^{-\frac{E_0}{k_B T}}</math>

In Transition State Theory motion is treated by classical mechanics, and it is assumed that this motion always leads to products without recrossings of the saddle point. This is incorrect as quantum mechanical tunneling allows barrier crossing to take place when the total energy is less than the potential energy at the top of the barrier.<ref name="Reference 115"/> Barrier recrossing is seento occur in the calculated experiment values, for example:

[[File:MRD_114_figure4.png|center|thumb|The PES of a reaction where barrier crossing occurs.|400px]]

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

==== PES inspection: F + H2 ====

{{fontcolor1|blue| By inspecting the potential energy surfaces, classify the F + H2 and H + HF reactions according to their energetics (endothermic or exothermic). How does this relate to the bond strength of the chemical species involved? Locate the approximate position of the transition state. Report the activation energy for both reactions. }}

[[File:MRD_121_figure3.png|center|500px]]

F + H2 is an exothermic reaction as characterised by the fact that the transition state occurs early in the reaction coordinate on its potential energy surface, i.e. it is an attractive surface.<ref name="Reference 121"/> This relates to the bond strengths involved as a relatively weak H-H bond is broken while a strong H-F bond is formed; bond making is an exothermic process, so the formation of a bond with high bond enthalpy makes the overall reaction exothermic.<ref name="Reference 121"/>

[[File:MRD_121_figure1.png|center|thumb|The contour plot of F + H2 with the transition state region highlighted.|400px]]

The approximate position of the transition state is where the F---H gap is 125 pm and the H---H gap is 96 pm. This is reflected in the Internuclear Distances vs Time plot where this position is set at this position with p1 = p2 = 0.0 g.mol-1.pm.fs-1; the system undergoes a periodic symmetric vibration but does not move from the spot.

[[File:MRD_121_figure2.png|center|thumb|The Internuclear Distances vs Time plot of F + H2 at the position r1 = 125 pm and r2 = 96 pm.|400px]]

==== PES inspection: H + HF ====

{{fontcolor1|blue| By inspecting the potential energy surfaces, classify the F + H2 and H + HF reactions according to their energetics (endothermic or exothermic). How does this relate to the bond strength of the chemical species involved? Locate the approximate position of the transition state. Report the activation energy for both reactions. }}

[[File:MRD_122_figure3.png|center|500px]]

H + HF is an endothermic reaction as characterised by the fact that the transition state occurs late in the reaction coordinate on its potential energy surface, i.e. it is an repulsive surface.<ref name="Reference 121"/> This relates to the bond strengths involved as a strong H-F bond is broken while a weaker H-H bond is formed; bond breaking is an endothermic process, so the breakage of a bond with high bond enthalpy makes the overall reaction endothermic.<ref name="Reference 121"/>

[[File:MRD_122_figure1.png|center|thumb|The contour plot of H + HF with the transition state region highlighted.|400px]]

The approximate position of the transition state is where the F---H gap is 129 pm and the H---H gap is 90 pm. This is reflected in the Internuclear Distances vs Time plot where this position is set at this position with p1 = p2 = 0.0 g.mol-1.pm.fs-1; the system undergoes a periodic symmetric vibration but does not move from the spot. This structure is consistent with Hammond's postulate, where the transition state in an endothermic reaction is close in structure to the reactants.<ref name="Reference 121 2"/>

[[File:MRD_122_figure2.png|center|thumb|The Internuclear Distances vs Time plot of F + H2 at the position r1 = 129 pm and r2 = 90 pm.|400px]]

==== Reaction dynamics ====

{{fontcolor1|blue| In light of the fact that energy is conserved, discuss the mechanism of release of the reaction energy. Explain how this could be confirmed experimentally. }}

==== Reaction dynamics: reverse reaction ====

{{fontcolor1|blue| 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. }}

=== References ===

<references>

<ref name="Reference 111"> https://www.khanacademy.org/math/multivariable-calculus/applications-of-multivariable-derivatives/optimizing-multivariable-functions/a/maximums-minimums-and-saddle-points </ref>

<ref name="Reference 115"> N. E. Henriksen and F. Y. Hansen Theories of Molecular Reaction Dynamics 2nd ed., OUP, 2019 </ref>

<ref name="Reference 121"> Atkins, de Paula, Keeler: Physical Chemistry, 11th Edition </ref>

</references>

File:MRD 122 figure1.png

2020-05-07T09:40:11Z

Aa6718: Aa6718 uploaded a new version of File:MRD 122 figure1.png

File:MRD 121 figure1.png

2020-05-07T09:39:55Z

Aa6718: Aa6718 uploaded a new version of File:MRD 121 figure1.png

MRD:01531254

2020-05-07T09:38:38Z

Aa6718: /* Exercise 2: F - H - H system */

== Molecular Reaction Dynamics Lab ==

The objectives of this exercise are to study the reactivity of triatomic systems, where an atom and a diatomic molecule collide, through calculating Molecular Dynamics trajectories.

=== Exercise 1: H + H2 system ===

==== Dynamics from the transition state region ====

{{fontcolor1|blue| On a potential energy surface diagram, how is the transition state mathematically defined? How can the transition state be identified, and how can it be distinguished from a local minimum of the potential energy surface? }}

The transition state is defined as the maximum on the minimum energy path linking reactants and the products. The transition point can be identified on a potential energy surface as being at a saddle point, where the reactive trajectory is at its highest point and the gradient of the potential energy surface is zero. Saddle points have a local maximum in one direction and a local minimum in the other. They can be mathematically defined using their gradient: the partial derivative of the gradient, dy/dx, equals zero, indicating that the gradient is zero at this point. Furthermore, saddle points are distinguished from local minima in that their second partial derivative, d2y/dx2, is larger than zero. <ref name="Reference 111" />

[[File:MRD_111_figure1.png|thumb|center|A PES with the transition state region highlighted.|400px]]

==== Trajectories from r1 = r2: locating the transition state ====

{{fontcolor1|blue| 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. }}

Since the H + H2 surface is symmetric, the transition state must have r1 = r2. In trajectories from r1 = r2 the trajectory oscillates on the ridge; this can be used to locate the transition state geometry.

When testing different initial conditions with r1 = r2, and p1 = p2 = 0.0 g.mol-1.pm.fs-1, it can be seen that the system undergoes a periodic symmetric vibration.

[[File:Y2C10.png|center|400px]]

For example, the Internuclear Distances vs Time plot for r1 = r2 = 100 pm , p1 = p2 = 0.0 g.mol-1.pm.fs-1 is shown below ,and clear oscillation can be seen.

[[File:MRD_112_figure1.png|thumb|center|The Internuclear Distances vs Time plot for r1 = r2 = 100 pm.|400px]]

However, when r1 = r2 is set to 91, the vibration is very minimal. This is a good estimate for the transition state because when a trajectory starts at the transition state, with no initial momentum, it stays there forever.

[[File:MRD_112_figure2.png|thumb|center|The Internuclear Distances vs Time plot for r1 = r2 = 91 pm.|400px]]

==== Calculating the reaction path and trajectories from r1 = rts+δ, r2 = rts ====

{{fontcolor1|blue| Comment on how the mep and the trajectory differ. }}

The minimum energy path (or mep) is a very special trajectory that corresponds to infinitely slow motion. This wan be tested with initial conditions r1 = rts + 1 and r1 = rts, and p1 = p2 = 0.0 g.mol-1.pm.fs-1 and the calculation type as 'MEP'. With r1 set at 92 and r2 set at 91, it can be seen that the trajectory simply follows the valley floor to H1 + H2 - H3.

[[File:MRD_113_figure1.png|thumb|center|A PES with the mep trajectory highlighted.|400px]]

However, mep doesn't provide a realistic account of the motion of atoms during a reaction because it doesn't account for the mass of the atoms. When the same reaction is repeated with the calculation type as 'Dynamics' rather than 'MEP', the inertial motion of the atoms is indicated by the oscillation of the BC distance caused by the masses interacting.

[[File:MRD_113_figure2.png|thumb|center|A PES with the reaction path highlighted.|400px]]

==== Reactive and unreactive trajectories ====

{{fontcolor1|blue| Complete the table by adding the total energy, whether the trajectory is reactive or unreactive, and provide a plot of the trajectory and a small description for what happens along the trajectory. What can you conclude from the table? }}

[[File:Y2C1.png|center|500px]]

Initial positions r1 = 74 pm and r2 = 200 pm:

{| class="wikitable" border=1
! p1 / g.mol-1.pm.fs-1 !! p2 / g.mol-1.pm.fs-1 !! Etot / kJ.mol-1 !! Reactive? !! Description of the dynamics !! Illustration of the trajectory
|-
| -2.56 || -5.1 || -414.280 || Yes || m1 and m2-m3 collide and react to form m1-m2 and m3 || [[File:MRD_114_figure1.png|center|200px]]
|-
| -3.1 || -4.1 || -420.077 || No || m1 and m2-m3 do not collide so no reaction occurs || [[File:MRD_114_figure2.png|center|200px]]
|-
| -3.1 || -5.1 || -413.977 || Yes || m1 and m2-m3 collide and react to form m1-m2 and m3 || [[File:MRD_114_figure3.png|center|200px]]
|-
| -5.1 || -10.1 || -357.277 || No || m1 and m2-m3 collide and r1 oscillates but m2-m3 remains intact so no reaction occurs. This is a case of barrier recrossing: the system crosses the transition state region, the bond in the product forms, but then the system reverts back to the reactants. || [[File:MRD_114_figure4.png|center|200px]]
|-
| -5.1 || -10.6 || -349.477 || Yes || m1 and m2-m3 collide, and though r2 oscillates they ultimately react to form m1-m2 and m3|| [[File:MRD_114_figure5.png|center|200px]]
|}

==== Transition State Theory ====

{{fontcolor1|blue| Given the results you have obtained, how will Transition State Theory predictions for reaction rate values compare with experimental values? }}

A powerful theory to rationalise and calculate the rate of chemical reactions based on the properties of the reactants and the transitions state structure is Transition State Theory. It predicts that the rate constant for a generic bimolecular reaction <math>\mathcal{A+B}\rightarrow\mathcal{P}</math> is:

<math>k_{TST}=R_{cl}\frac{Q_{\ddagger}'/V}{(Q_{\mathcal{A}}/V)(Q_{\mathcal{B}}/V)}e^{-\frac{E_0}{k_B T}}</math>

A crucial assumption of Transition State Theory in estimating ''Rcl'' is that all trajectories with a kinetic energy along the reaction coordinate greater than the activation energy will be reactive. By further assuming that the kinetic energy along the reaction coordinate follows the Boltzmann distribution, one obtain the conventional Transition State Theory rate constant expression:

<math>k_{TST}=\frac{k_B T}{h} \frac{Q_{\ddagger}'/V}{(Q_{\mathcal{A}}/V)(Q_{\mathcal{B}}/V)}e^{-\frac{E_0}{k_B T}}</math>

In Transition State Theory motion is treated by classical mechanics, and it is assumed that this motion always leads to products without recrossings of the saddle point. This is incorrect as quantum mechanical tunneling allows barrier crossing to take place when the total energy is less than the potential energy at the top of the barrier.<ref name="Reference 115"/> Barrier recrossing is seento occur in the calculated experiment values, for example:

[[File:MRD_114_figure4.png|center|thumb|The PES of a reaction where barrier crossing occurs.|400px]]

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

==== PES inspection: F + H2 ====

{{fontcolor1|blue| By inspecting the potential energy surfaces, classify the F + H2 and H + HF reactions according to their energetics (endothermic or exothermic). How does this relate to the bond strength of the chemical species involved? Locate the approximate position of the transition state. Report the activation energy for both reactions. }}

[[File:MRD_121_figure3.png|center|500px]]

F + H2 is an exothermic reaction as characterised by the fact that the transition state occurs early in the reaction coordinate on its potential energy surface, i.e. it is an attractive surface.<ref name="Reference 121"/> This relates to the bond strengths involved as a relatively weak H-H bond is broken while a strong H-F bond is formed; bond making is an exothermic process, so the formation of a bond with high bond enthalpy makes the overall reaction exothermic.<ref name="Reference 121"/>

[[File:MRD_121_figure1.png|center|thumb|The contour plot of F + H2 with the transition state region highlighted.|400px]]

The approximate position of the transition state is where the F---H gap is 125 pm and the H---H gap is 96 pm. This is reflected in the Internuclear Distances vs Time plot where this position is set at this position with p1 = p2 = 0.0 g.mol-1.pm.fs-1; the system undergoes a periodic symmetric vibration but does not move from the spot.

[[File:MRD_121_figure2.png|center|thumb|The Internuclear Distances vs Time plot of F + H2 at the position r1 = 125 pm and r2 = 96 pm.|400px]]

==== PES inspection: H + HF ====

{{fontcolor1|blue| By inspecting the potential energy surfaces, classify the F + H2 and H + HF reactions according to their energetics (endothermic or exothermic). How does this relate to the bond strength of the chemical species involved? Locate the approximate position of the transition state. Report the activation energy for both reactions. }}

[[File:MRD_122_figure3.png|center|500px]]

H + HF is an endothermic reaction as characterised by the fact that the transition state occurs late in the reaction coordinate on its potential energy surface, i.e. it is an repulsive surface.<ref name="Reference 121"/> This relates to the bond strengths involved as a strong H-F bond is broken while a weaker H-H bond is formed; bond breaking is an endothermic process, so the breakage of a bond with high bond enthalpy makes the overall reaction endothermic.<ref name="Reference 121"/>

[[File:MRD_122_figure1.png|center|thumb|The contour plot of H + HF with the transition state region highlighted.|400px]]

The approximate position of the transition state is where the F---H gap is 129 pm and the H---H gap is 90 pm. This is reflected in the Internuclear Distances vs Time plot where this position is set at this position with p1 = p2 = 0.0 g.mol-1.pm.fs-1; the system undergoes a periodic symmetric vibration but does not move from the spot.

[[File:MRD_122_figure2.png|center|thumb|The Internuclear Distances vs Time plot of F + H2 at the position r1 = 129 pm and r2 = 90 pm.|400px]]

==== Reaction dynamics ====

{{fontcolor1|blue| In light of the fact that energy is conserved, discuss the mechanism of release of the reaction energy. Explain how this could be confirmed experimentally. }}

==== Reaction dynamics: reverse reaction ====

{{fontcolor1|blue| 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. }}

=== References ===

<references>

<ref name="Reference 111"> https://www.khanacademy.org/math/multivariable-calculus/applications-of-multivariable-derivatives/optimizing-multivariable-functions/a/maximums-minimums-and-saddle-points </ref>

<ref name="Reference 115"> N. E. Henriksen and F. Y. Hansen Theories of Molecular Reaction Dynamics 2nd ed., OUP, 2019 </ref>

<ref name="Reference 121"> Atkins, de Paula, Keeler: Physical Chemistry, 11th Edition </ref>

</references>

File:MRD 122 figure2.png

2020-05-07T09:37:16Z

Aa6718:

2020-05-07T08:40:55Z

Aa6718: /* Exercise 2: F - H - H system */