ChemWiki - User contributions [en]

MRD:IGE15

2018-05-22T13:05:01Z

Ige15: /* H + H-F */

= Molecular Reaction Dynamics: Applications to Triatomic systems =
Chemical reactions can be modeled using Newtonian mechanics, ignoring quantum mechanical phenomena. Presented here is the study of 2 systems based on the linear collision of a single atom into a diatomic molecule.

== H - H - H System ==
=== Potential Energy Surfaces ===
==== What value do the different components of the gradient of the potential energy surface have at a minimum and at a transition structure? Briefly explain how minima and transition structures can be distinguished using the curvature of the potential energy surface. ====
The reaction path that links reactants to products follows a minimum energy. The highest energy point along this path is a saddle point known as the transition state. At this location, the two components of the gradient equal to zero, however, a deviation from the path will cause an increase in energy while movement along the path will cause a decrease in energy i.e. the second derivative in the direction along the path is negative and the second derivative perpendicular to the path is positive. In contrast, movement in any direction at the minima (reactants/products) will result in an increase in energy, the second derivative in both directions is positive.

==== 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. ====
[[File:Internuclear Distance IGE.PNG|thumb|700px|center|Internuclear distance at r,sub.ts]]
Given the symmetric nature of the triatomic Hydrogen system, in the transition state, r1 is expected to equal r2. Furthermore, at the transition state, the gradient in both directions is zero and so there should be no resultant momentum. Modifying the internuclear separation with r1 = r2 to minimise internuclear momentum yields an approximate value for the transition state at rts = 0.90774 Å. This seems a reasonable value for a state between bond formation and breaking. It is larger than the H-H bond length, but smaller than the combined Van der Waals radii of 2 H atoms.

=== Reaction Path Trajectories ===
==== Comment on how the mep and the trajectory you just calculated differ. ====
{| border="1" align="center"
|-
| [[File:MEP contour IGE.png|350px|thumb|center| Reaction path using MEP calculation ]] ||
[[File:Dynamics contour IGE.png|350px|thumb|center| Reaction path using dynamics calculation]]
|}
In the minimum energy path calculation, the system's velocities are reset to 0 after each iteration and so the atoms move infinitely slowly. As a result, the trajectory follows the path of lowest energy without deviation. In the dynamic calculation, the velocity is conserved, manifesting as an oscillation in internuclear distance i.e. a molecular vibration. 
In this case, r1 is displaced to rts + 0.01 and so the atoms form the product (A + BC). When r2 is displaced and r1 set to rts, the atoms move to the reactants (AB + C).

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

{| class="wikitable" border=1
! p1 !! p2 !! Total E /kcalmol-1 !! Trajectory !! Plot !! Description
|-
| -1.25 || -2.5 || -99.018 || Reactive || [[File:IGE Trajectory1.png|250px]] || C approaches AB with enough momentum to react (pass through the transition state), producing molecular BC and atomic A.
|-
| -1.5 || -2.0 || -100.456 || Unreactive || [[File:IGE Trajectory2.png|250px]] || C does not approach AB with enough momentum to get over the energetic barrier and so is repelled without reaction.
|-
| -1.5 || -2.5 || -98.956 || Reactive || [[File:IGE Trajectory3.png|250px]] || Another successfully reactive trajectory. The larger difference in momentum results in slightly larger oscillation post-reaction and so a higher total energy.
|-
| -2.5 || -5.0 || -84.956 || Unreactive || [[File:IGE Trajectory4.png|250px]] || C has enough energy to pass through the transition state and form a temporary bond, however it moves so close to B that coulombic repulsion between the atoms launches it back and no reaction occurs. This is an example of "barrier recrossing", wherein the system passes through the transition state multiple times.
|-
| -2.5 || -5.2 || -83.416 || Reactive || [[File:IGE Trajectory5.png|250px]] || BC passes through the transition state 3 times, another example of barrier recrossing. The BC bond is formed then broken to induce large enough vibration in AB to break the bond, before subsequently reforming the to produce the reactants.
|}
===Transition State Theory===
====State what are the main assumptions of Transition State Theory. Given the results you have obtained, how will Transition State Theory predictions for reaction rate values compare with experimental values?====

It is assumed that: 
1. Chemical reactions can be predicted using the Newtonian interactions of atoms and ignoring quantum mechanical effects. 
2. Activated complexes near the transition state are in equilibrium with the reactant molecules and can be converted into the products. 
3. Each time the transition state is crossed, a reaction goes to completion. 

At mild temperatures, Transition State Theory (TST) will fairly accurately predict the rate of reaction. Once the temperature is elevated enough to allow for barrier recrossing however, the rate will be overestimated compared to experiment. Additionally, at lower temperatures, TST does not account for the ability of particles to undergo quantum tunneling and bypass the transition state energy barrier to react at a lower energy. Therefore, the rate of reaction may be underestimated compared to experiment.

== H - H - F System ==
=== PES Inspection ===
====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?====

[[File:HHF surface IGE.png|thumb|700px|center|Surface plot of H H F system.]]

Entropic effects can be considered negligible in comparison to enthalpy as both products and reactants involve 2 species, one monatomic and one diatomic. The depth of valleys indicate a total energy of -104 kcalmol-1 for H-H + F and -134 kcalmol-1 for H + H-F, hence the reaction of F with H2 is exothermic and the reaction of H with HF is endothermic.

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

{| border="1" align="center"
|-
| [[File:HHF distance TS IGE.png|350px|thumb|center| Internuclear distance for H H F at transition state. ]] ||
[[File:HHF TS contour IGE.png|350px|thumb|center| Location of H H F transition state.]]
|}

By changing r1 and r2 to minimise internuclear momenta, the transition state can be located. By using Hammond's postulate, one can assume that the transition state more closely resembles F + H-H as it is closer in energy to this configuration. The resulting values are rHH = 0.744888 Å and rHF = 1.810748 Å.

==== Report the activation energy for both reactions.====
{| border="1" align="center"
|-
| [[File:Activationenergy HH IGE.png|350px|thumb|center| E vs t plot of MEP trajectory from TS to H-H + F ]] ||
[[File:Activationenergy HF IGE.png|350px|thumb|center| E vs t plot of MEP trajectory from TS to H + H-F]]
|}

The energy of the TS was found to be -103.752 kcalmol-1. The energy at the minimum H + H-F was -134.025 kcalmol-1 and hence the activation energy for the reaction of H with H-F is 30.273 kcalmol-1. The energy at the minimum H-H + F was -103.995 kcalmol-1 and so the activation energy for the reaction of H-H with F is 0.243 kcalmol-1.

=== Reaction Dynamics ===

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

[[File:Reaction momenta IGE.png|350px|thumb|center| Momentum vs time plot for the reaction of H-H with F.]]

The loss of potential energy in the exothermic reaction of H-H + F to form H and H-F is converted into kinetic energy in the form of vibrational and translational motion of the atoms. This energy is subsequently dissipated to other molecules in a reaction vessel when this is carried out on a macroscopic scale. The result of this is an increase in temperature of the reaction mixture, which can be observed and measured to confirm the magnitude of temperature change is equivalent to the loss of potential energy.

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

===== F + H-H =====

Given the initial positions rHH = 0.74 Å and rHF = 2.00 Å, the following results were obtained when varying the initial momenta:

{| class="wikitable" border=1
! pHF !! pHH !! Reactivity !! Plot !! Follows Polanyi's Rules?
|-
| -0.5 || -3.0 || Unreactive || [[File:IGE HH reaction1.png|250px]] || Yes
|-
| -0.5 || -1.5 || Reactive || [[File:IGE HH reaction2.png|250px]] || -
|-
| -0.5 || 0.0 || Reactive || [[File:IGE HH reaction3.png|250px]] || Yes
|-
| -0.5 || 1.5 || Unreactive || [[File:IGE HH reaction4.png|250px]] || -
|-
| -0.5 || 3.0 || Unreactive || [[File:IGE HH reaction5.png|250px]] || Yes
|-
| -0.8 ||-0.1 || Reactive || [[File:IGE HH reaction6.png|250px]] || Yes
|-
| -0.2 ||-4.0 || Reactive || [[File:IGE HH reaction7.png|250px]] || No
|}

===== H + H-F =====

Given the initial positions rHF = 0.92 Å and rHH = 2.00 Å, the following results were obtained when varying the initial momenta:

{| class="wikitable" border=1
! pHF !! pHH !! Reactivity !! Plot !! Follows Polanyi's Rules?
|-
| -1.00 || -11.00 || Reactive || [[File:IGE HF reaction1.png|250px]] || Yes
|-
| -0.10 || -11.00 || Reactive || [[File:IGE HF reaction3.png|250px]] || Yes
|-
| -0.01 || -11.00 || Reactive || [[File:IGE HF reaction4.png|250px]] || Yes
|-
| -0.01 || -8.00 || Reactive || [[File:IGE HF reaction5.png|250px]] || Yes
|-
| -11.00 || -1.00 || Unreactive || [[File:IGE HF reaction6.png|250px]] || Yes
|-
| -11.00 || -0.10 || Unreactive || [[File:IGE HF reaction8.png|250px]] || Yes
|-
| -8.00 || -0.01 || Unreactive || [[File:IGE HF reaction7.png|250px]] || Yes
|-
| -10.00 || -1.00 || Reactive || [[File:IGE HF reaction2.png|250px]] || No
|}

=====Discussion=====

Polanyi's rules state that an early transition state requires translational energy for reaction efficiency, while a late transition state requires vibrational energy.<ref>R. D. Levine Molecular Reaction Dynamics, Cambridge University Press, 2005</ref> We can apply this to the H H F system as follows: the H-H + F reaction is exothermic, therefore has an early transition state and so should require translational energy. This can be seen in the first table above: the simulations with high vibrational energy often fail. When this is reduced, however, the tendency to react increases. 

In the case of H + H-F, the rules indicate that high vibrational energy is necessary. Indeed, with a high H-F vibrational energy, the reaction proceeds easily and when given equivalent translational energies and low vibrational energy, it fails. 

These rules are in reality only guidelines however. The opposite case of low vibrational energy and high translational energy may also yield a successful reaction of H and H-F as in the final case above. Alternatively, in the reaction of H-H with F, a high vibrational energy and low translational energy can also yield a successful reaction.

File:IGE HF reaction1.png

2018-05-22T13:03:56Z

Ige15: Ige15 uploaded a new version of File:IGE HF reaction1.png

File:IGE HF reaction1.png

2018-05-22T13:02:42Z

Ige15: Ige15 uploaded a new version of File:IGE HF reaction1.png

File:IGE HF reaction1.png

2018-05-22T13:02:13Z

Ige15: Ige15 uploaded a new version of File:IGE HF reaction1.png

MRD:IGE15

2018-05-22T13:00:00Z

Ige15: /* H + H-F */

= Molecular Reaction Dynamics: Applications to Triatomic systems =
Chemical reactions can be modeled using Newtonian mechanics, ignoring quantum mechanical phenomena. Presented here is the study of 2 systems based on the linear collision of a single atom into a diatomic molecule.

== H - H - H System ==
=== Potential Energy Surfaces ===
==== What value do the different components of the gradient of the potential energy surface have at a minimum and at a transition structure? Briefly explain how minima and transition structures can be distinguished using the curvature of the potential energy surface. ====
The reaction path that links reactants to products follows a minimum energy. The highest energy point along this path is a saddle point known as the transition state. At this location, the two components of the gradient equal to zero, however, a deviation from the path will cause an increase in energy while movement along the path will cause a decrease in energy i.e. the second derivative in the direction along the path is negative and the second derivative perpendicular to the path is positive. In contrast, movement in any direction at the minima (reactants/products) will result in an increase in energy, the second derivative in both directions is positive.

==== 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. ====
[[File:Internuclear Distance IGE.PNG|thumb|700px|center|Internuclear distance at r,sub.ts]]
Given the symmetric nature of the triatomic Hydrogen system, in the transition state, r1 is expected to equal r2. Furthermore, at the transition state, the gradient in both directions is zero and so there should be no resultant momentum. Modifying the internuclear separation with r1 = r2 to minimise internuclear momentum yields an approximate value for the transition state at rts = 0.90774 Å. This seems a reasonable value for a state between bond formation and breaking. It is larger than the H-H bond length, but smaller than the combined Van der Waals radii of 2 H atoms.

=== Reaction Path Trajectories ===
==== Comment on how the mep and the trajectory you just calculated differ. ====
{| border="1" align="center"
|-
| [[File:MEP contour IGE.png|350px|thumb|center| Reaction path using MEP calculation ]] ||
[[File:Dynamics contour IGE.png|350px|thumb|center| Reaction path using dynamics calculation]]
|}
In the minimum energy path calculation, the system's velocities are reset to 0 after each iteration and so the atoms move infinitely slowly. As a result, the trajectory follows the path of lowest energy without deviation. In the dynamic calculation, the velocity is conserved, manifesting as an oscillation in internuclear distance i.e. a molecular vibration. 
In this case, r1 is displaced to rts + 0.01 and so the atoms form the product (A + BC). When r2 is displaced and r1 set to rts, the atoms move to the reactants (AB + C).

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

{| class="wikitable" border=1
! p1 !! p2 !! Total E /kcalmol-1 !! Trajectory !! Plot !! Description
|-
| -1.25 || -2.5 || -99.018 || Reactive || [[File:IGE Trajectory1.png|250px]] || C approaches AB with enough momentum to react (pass through the transition state), producing molecular BC and atomic A.
|-
| -1.5 || -2.0 || -100.456 || Unreactive || [[File:IGE Trajectory2.png|250px]] || C does not approach AB with enough momentum to get over the energetic barrier and so is repelled without reaction.
|-
| -1.5 || -2.5 || -98.956 || Reactive || [[File:IGE Trajectory3.png|250px]] || Another successfully reactive trajectory. The larger difference in momentum results in slightly larger oscillation post-reaction and so a higher total energy.
|-
| -2.5 || -5.0 || -84.956 || Unreactive || [[File:IGE Trajectory4.png|250px]] || C has enough energy to pass through the transition state and form a temporary bond, however it moves so close to B that coulombic repulsion between the atoms launches it back and no reaction occurs. This is an example of "barrier recrossing", wherein the system passes through the transition state multiple times.
|-
| -2.5 || -5.2 || -83.416 || Reactive || [[File:IGE Trajectory5.png|250px]] || BC passes through the transition state 3 times, another example of barrier recrossing. The BC bond is formed then broken to induce large enough vibration in AB to break the bond, before subsequently reforming the to produce the reactants.
|}
===Transition State Theory===
====State what are the main assumptions of Transition State Theory. Given the results you have obtained, how will Transition State Theory predictions for reaction rate values compare with experimental values?====

It is assumed that: 
1. Chemical reactions can be predicted using the Newtonian interactions of atoms and ignoring quantum mechanical effects. 
2. Activated complexes near the transition state are in equilibrium with the reactant molecules and can be converted into the products. 
3. Each time the transition state is crossed, a reaction goes to completion. 

At mild temperatures, Transition State Theory (TST) will fairly accurately predict the rate of reaction. Once the temperature is elevated enough to allow for barrier recrossing however, the rate will be overestimated compared to experiment. Additionally, at lower temperatures, TST does not account for the ability of particles to undergo quantum tunneling and bypass the transition state energy barrier to react at a lower energy. Therefore, the rate of reaction may be underestimated compared to experiment.

== H - H - F System ==
=== PES Inspection ===
====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?====

[[File:HHF surface IGE.png|thumb|700px|center|Surface plot of H H F system.]]

Entropic effects can be considered negligible in comparison to enthalpy as both products and reactants involve 2 species, one monatomic and one diatomic. The depth of valleys indicate a total energy of -104 kcalmol-1 for H-H + F and -134 kcalmol-1 for H + H-F, hence the reaction of F with H2 is exothermic and the reaction of H with HF is endothermic.

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

{| border="1" align="center"
|-
| [[File:HHF distance TS IGE.png|350px|thumb|center| Internuclear distance for H H F at transition state. ]] ||
[[File:HHF TS contour IGE.png|350px|thumb|center| Location of H H F transition state.]]
|}

By changing r1 and r2 to minimise internuclear momenta, the transition state can be located. By using Hammond's postulate, one can assume that the transition state more closely resembles F + H-H as it is closer in energy to this configuration. The resulting values are rHH = 0.744888 Å and rHF = 1.810748 Å.

==== Report the activation energy for both reactions.====
{| border="1" align="center"
|-
| [[File:Activationenergy HH IGE.png|350px|thumb|center| E vs t plot of MEP trajectory from TS to H-H + F ]] ||
[[File:Activationenergy HF IGE.png|350px|thumb|center| E vs t plot of MEP trajectory from TS to H + H-F]]
|}

The energy of the TS was found to be -103.752 kcalmol-1. The energy at the minimum H + H-F was -134.025 kcalmol-1 and hence the activation energy for the reaction of H with H-F is 30.273 kcalmol-1. The energy at the minimum H-H + F was -103.995 kcalmol-1 and so the activation energy for the reaction of H-H with F is 0.243 kcalmol-1.

=== Reaction Dynamics ===

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

[[File:Reaction momenta IGE.png|350px|thumb|center| Momentum vs time plot for the reaction of H-H with F.]]

The loss of potential energy in the exothermic reaction of H-H + F to form H and H-F is converted into kinetic energy in the form of vibrational and translational motion of the atoms. This energy is subsequently dissipated to other molecules in a reaction vessel when this is carried out on a macroscopic scale. The result of this is an increase in temperature of the reaction mixture, which can be observed and measured to confirm the magnitude of temperature change is equivalent to the loss of potential energy.

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

===== F + H-H =====

Given the initial positions rHH = 0.74 Å and rHF = 2.00 Å, the following results were obtained when varying the initial momenta:

{| class="wikitable" border=1
! pHF !! pHH !! Reactivity !! Plot !! Follows Polanyi's Rules?
|-
| -0.5 || -3.0 || Unreactive || [[File:IGE HH reaction1.png|250px]] || Yes
|-
| -0.5 || -1.5 || Reactive || [[File:IGE HH reaction2.png|250px]] || -
|-
| -0.5 || 0.0 || Reactive || [[File:IGE HH reaction3.png|250px]] || Yes
|-
| -0.5 || 1.5 || Unreactive || [[File:IGE HH reaction4.png|250px]] || -
|-
| -0.5 || 3.0 || Unreactive || [[File:IGE HH reaction5.png|250px]] || Yes
|-
| -0.8 ||-0.1 || Reactive || [[File:IGE HH reaction6.png|250px]] || Yes
|-
| -0.2 ||-4.0 || Reactive || [[File:IGE HH reaction7.png|250px]] || No
|}

===== H + H-F =====

With initial positions rHF = 0.92 Å and rHH = 2.00 Å, the following results were obtained when varying initial momenta:

{| class="wikitable" border=1
! pHF !! pHH !! Reactivity !! Plot !! Follows Polanyi's Rules?
|-
| -1.00 || -11.00 || Reactive || [[File:IGE HF reaction1.png|250px]] || Yes
|-
| -0.10 || -11.00 || Reactive || [[File:IGE HF reaction3.png|250px]] || Yes
|-
| -0.01 || -11.00 || Reactive || [[File:IGE HF reaction4.png|250px]] || Yes
|-
| -0.01 || -8.00 || Reactive || [[File:IGE HF reaction5.png|250px]] || Yes
|-
| -11.00 || -1.00 || Unreactive || [[File:IGE HF reaction6.png|250px]] || Yes
|-
| -11.00 || -0.10 || Unreactive || [[File:IGE HF reaction8.png|250px]] || Yes
|-
| -8.00 || -0.01 || Unreactive || [[File:IGE HF reaction7.png|250px]] || Yes
|-
| -10.00 || -1.00 || Reactive || [[File:IGE HF reaction2.png|250px]] || No
|}

=====Discussion=====

Polanyi's rules state that an early transition state requires translational energy for reaction efficiency, while a late transition state requires vibrational energy.<ref>R. D. Levine Molecular Reaction Dynamics, Cambridge University Press, 2005</ref> We can apply this to the H H F system as follows: the H-H + F reaction is exothermic, therefore has an early transition state and so should require translational energy. This can be seen in the first table above: the simulations with high vibrational energy often fail. When this is reduced, however, the tendency to react increases. 

In the case of H + H-F, the rules indicate that high vibrational energy is necessary. Indeed, with a high H-F vibrational energy, the reaction proceeds easily and when given equivalent translational energies and low vibrational energy, it fails. 

These rules are in reality only guidelines however. The opposite case of low vibrational energy and high translational energy may also yield a successful reaction of H and H-F as in the final case above. Alternatively, in the reaction of H-H with F, a high vibrational energy and low translational energy can also yield a successful reaction.

2018-05-21T17:38:56Z

Ige15: Ige15 uploaded a new version of File:IGE HF reaction6.png

MRD:IGE15

2018-05-21T17:37:52Z

Ige15: /* F + H-H */

== Introduction ==
Chemical reactions can be modeled using Newtonian mechanics and ignoring quantum mechanical phenomena. I will be studying systems based on the collision of a single atom into a diatomic molecule by calculating potential energy surfaces. All distances are given in Ångstroms.

== H - H - H System ==

==== What value do the different components of the gradient of the potential energy surface have at a minimum and at a transition structure? Briefly explain how minima and transition structures can be distinguished using the curvature of the potential energy surface. ====
The reaction path that links reactants to products is a minimum energy. The highest energy point along this path is a saddle point known as the transition state. At this location, the two components of the gradient equal to zero, however, a deviation from the path will cause an increase in energy while movement along the path will cause a decrease in energy i.e. the second derivative in the direction along the path is negative and the second derivative perpendicular to the path is positive. In contrast, movement in any direction at the minima (reactants/products) will result in an increase in energy, the second derivative in both directions is positive.

==== 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. ====
[[File:Internuclear Distance IGE.PNG|thumb|700px|center|Internuclear distance at r,sub.ts]]
Modifying the internuclear separation with r1 = r2 to minimise internuclear momentum yields an approximate value for the transition state at rts = 0.90774 Å.

==== Comment on how the mep and the trajectory you just calculated differ. ====
{| border="1" align="center"
|-
| [[File:MEP contour IGE.png|350px|thumb|center| Reaction path using MEP calculation ]] ||
[[File:Dynamics contour IGE.png|350px|thumb|center| Reaction path using dynamics calculation]]
|}
Using the minimum energy path calculation, the atoms move infinitely slow, as a result, the trajectory follows the path of lowest energy without deviation. Under a dynamic calculation, the velocity is retained after each step, manifesting as an oscillation in internuclear distance i.e. a molecular vibration. 
In this case, r1 is displaced to rts + 0.01 and so the atoms form the product (A + BC). When r2 is displaced and r1 set to rts, the atoms move to the reactants (AB + C).

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

{| class="wikitable" border=1
! p1 !! p2 !! Total E /kcalmol-1 !! Trajectory !! Plot !! Description
|-
| -1.25 || -2.5 || -99.018 || Reactive || [[File:IGE Trajectory1.png|250px]] || C approaches AB with enough momentum to react (pass through the transition state), producing molecular BC and atomic A.
|-
| -1.5 || -2.0 || -100.456 || Unreactive || [[File:IGE Trajectory2.png|250px]] || C does not approach AB with enough momentum to get over the energetic barrier and so is repelled without reaction.
|-
| -1.5 || -2.5 || -98.956 || Reactive || [[File:IGE Trajectory3.png|250px]] || Another successfully reactive trajectory. The larger difference in momentum results in slightly larger oscillation post-reaction and so a higher total energy.
|-
| -2.5 || -5.0 || -84.956 || Unreactive || [[File:IGE Trajectory4.png|250px]] || C has enough energy to pass through the transition state and form a temporary bond, however it moves so close to B that coulombic repulsion between the atoms launches it back and no reaction occurs. This is an example of "barrier recrossing", wherein the system passes through the transition state multiple times.
|-
| -2.5 || -5.2 || -83.416 || Reactive || [[File:IGE Trajectory5.png|250px]] || BC passes through the transition state 3 times, another example of barrier recrossing. The BC bond is formed then broken to induce large enough vibration in AB to break the bond, before subsequently reforming the to produce the reactants.
|}

====State what are the main assumptions of Transition State Theory. Given the results you have obtained, how will Transition State Theory predictions for reaction rate values compare with experimental values?====

It is assumed that: 
1. Chemical reactions can be predicted using the Newtonian interactions of atoms and ignoring quantum mechanical effects. 
2. Activated complexes near the transition state are in equilibrium with the reactant molecules and can be converted into the products. 
3. Each time the transition state is crossed, a reaction occurs. 

At mild temperatures, Transition State Theory (TST) will fairly accurately predict the rate of reaction. Once the temperature is elevated enough to allow for barrier recrossing however, the rate will be overestimated compared to experiment. Additionally, at lower temperatures, TST does not account for the ability of particles to undergo quantum tunneling and bypass the transition state energy barrier to react at a lower energy. Therefore, the rate of reaction may be underestimated compared to experiment.

== H - H - F System ==
====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?====

[[File:HHF surface IGE.png|thumb|700px|center|Surface plot of H H F system.]]

Entropic effects can be considered negligible in comparison to enthalpy as both products and reactants involve 2 species, one monatomic and one diatomic. The depth of valleys indicate a total energy of -104 kcalmol-1 for H-H + F and -134 kcalmol-1 for H + H-F, hence the reaction of F with H2 is exothermic and the reaction of H with HF is endothermic.

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

{| border="1" align="center"
|-
| [[File:HHF distance TS IGE.png|350px|thumb|center| Internuclear distance for H H F at transition state. ]] ||
[[File:HHF TS contour IGE.png|350px|thumb|center| Location of H H F transition state.]]
|}

By changing r1 and r2 to minimise internuclear momenta, the transition state can be located. By using Hammond's postulate, one can assume that the transition state more closely resembles F + H-H as it is closer in energy to this configuration. The resulting values are rHH = 0.744888 Å and rHF = 1.810748 Å.

==== Report the activation energy for both reactions.====
{| border="1" align="center"
|-
| [[File:Activationenergy HH IGE.png|350px|thumb|center| E vs t plot of MEP trajectory from TS to H-H + F ]] ||
[[File:Activationenergy HF IGE.png|350px|thumb|center| E vs t plot of MEP trajectory from TS to H + H-F]]
|}

The energy of the TS was found to be -103.752 kcalmol-1. The energy at the minimum H + H-F was -134.025 kcalmol-1 and hence the activation energy for the reaction of H with H-F is 30.273 kcalmol-1. The energy at the minimum H-H + F was -103.995 kcalmol-1 and so the activation energy for the reaction of H-H with F is 0.243 kcalmol-1.

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

[[File:Reaction momenta IGE.png|350px|thumb|center| Momentum vs time plot for the reaction of H-H with F.]]

The loss of potential energy in the exothermic reaction of H-H + F to form H and H-F is converted into kinetic energy in the form of vibrational and translational motion of the atoms. This energy is subsequently dissipated to other molecules in a reaction vessel when this is carried out on a macroscopic scale. The result of this is an increase in temperature of the reaction mixture. This can be observed and would indicate that the reaction is exothermic.

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

===== F + H-H =====

Given the initial positions rHH = 0.74 Å and rHF = 2.00 Å, the following results were obtained when varying the initial momenta:

{| class="wikitable" border=1
! pHF !! pHH !! Reactivity !! Plot !! Follows Polanyi's Rules?
|-
| -0.5 || -3.0 || Unreactive || [[File:IGE HH reaction1.png|250px]] || Yes
|-
| -0.5 || -1.5 || Reactive || [[File:IGE HH reaction2.png|250px]] || -
|-
| -0.5 || 0.0 || Reactive || [[File:IGE HH reaction3.png|250px]] || Yes
|-
| -0.5 || 1.5 || Unreactive || [[File:IGE HH reaction4.png|250px]] || -
|-
| -0.5 || 3.0 || Unreactive || [[File:IGE HH reaction5.png|250px]] || Yes
|-
| -0.8 ||-0.1 || Reactive || [[File:IGE HH reaction6.png|250px]] || Yes
|-
| -0.2 ||-4.0 || Reactive || [[File:IGE HH reaction7.png|250px]] || No
|}

===== H + H-F =====

With initial positions rHF = 0.92 Å and rHH = 5.00 Å, the following results were obtained when varying initial momenta:

{| class="wikitable" border=1
! pHF !! pHH !! Reactivity !! Plot
|-
| -1 || -11 || Reactive || [[File:IGE HF reaction1.png|250px]]
|-
| -0.1 || -11 || Reactive || [[File:IGE HF reaction3.png|250px]]
|-
| -0.01 || -11 || Reactive || [[File:IGE HF reaction4.png|250px]]
|-
| -0.01 || -8 || Reactive || [[File:IGE HF reaction5.png|250px]]
|-
| -10 || -0.1 || Unreactive || [[File:IGE HF reaction6.png|250px]]
|-
| -8 || -0.01 || Unreactive || [[File:IGE HF reaction7.png|250px]]
|-
| -11 || -0.1 || Unreactive || [[File:IGE HF reaction8.png|250px]]
|-
| -10 || -1 || Reactive || [[File:IGE HF reaction2.png|250px]]
|}

=====Discussion=====

Polanyi's rules state that an early transition state requires translational energy for reaction efficiency, while a late transition state requires vibrational energy. Applying this, to the H H F system, the H-H + F reaction is exothermic, has an early transition state and so should require translational energy. This can be seen in first table above, the simulations with high vibrational energy often fail, however when this is reduced, the tendency to react increases. 

In the case of H + H-F, the rules imply that high vibrational energy is necessary. Indeed, with a high H-F vibrational energy, the reaction proceeds easily. These rules are in reality only guidelines however. The opposite case of low vibrational energy and high translational energy may also yield a successful reaction as in the final case above. Additionally, in the reaction of H-H with F, a high vibrational energy and low translational energy can also yield a successful reaction.

MRD:IGE15

2018-05-21T17:35:10Z

MRD:IGE15

2018-05-21T17:28:50Z

2018-05-21T16:37:01Z

Ige15:

MRD:IGE15

2018-05-21T16:26:17Z

Ige15: /* H - H - F System */