ChemWiki - User contributions [en]

Sam Young Reaction Dynamics

2018-05-18T14:27:20Z

Sly116: /* Q1 - Energetics */

= H + H2 System =
== Q1 - Transition State Gradients ==
[[File:Sly-Saddle.png|thumb|upright=0.8|centre|Figure 1 - Potential Energy Surface Plot of H2 + H System, with initial conditions A-B distance = 0.74, B-C distance = 2.30, AB momentum = 0 & BC momentum = 2.7]]

The minimum energy surface, shown running along the bottom of figure one obeys the derivative; ∂V/∂(rx) = ∂V/∂(ry) = 0, with rx and ry run parallel to their respective gradients. However, the saddle point where the transition state lies is located along the minimum energy surface at the maximum point. Therefore, it can be found by taking the second derivative, as the two orthogonal gradients have different signs, with one along the potential energy minimum being negative and the other orthogonal graident being positive.

∂2V/∂(rx)2 > 0

∂2V/∂(ry)2 < 0

== Q2 - Transition State Estimate ==

By making the momentum of the whole system equal to zero, it was possible to put the AB distance = BC distance and alter this value to obtain a result for the rts, which was found to be approximately 0.9077Å (one value due to the system being completely symmetric), which gave figure 2. This number was found by taking the intersect of the AB and BC lines from the internuclear plot with the same initial conditions given above, and optimising this value to give constant distances. Due to the gradient of potential energy at the transition state being zero, the system has no kinetic energy, only potential energy. Therefore, there is no oscillation and the plot of internuclear distance against time shows constant interatomic distances.

[[File:Sly_Q2.png|thumb|upright=0.80|centre|Figure 2 - Internucleur Distance]]

== Q3 - MEP ==

The MEP is the minimum energy pathway followed for the reaction H2 + H to take place, although it can be seen in figures 4 and 5 that it differs from the dynamic trajectory due to the masses of the atoms, and therefore the bond oscillations along the trajectory causing deviations from the mep. This is shown by the wavy black line on figure 5. Both figures illustrate the reaction path (represented by the black line) starting at the transition state point, with the dynamic reaction going to the complete formation of a H2 product, while the mep plot shows it going only slightly towards the product formation.

'''change with + - 0.01 and discuss'''

[[File:Sly_MEP2.png|thumb|upright=0.80|centre|Figure 4 - Minimum Energy Pathway]] [[File:newdynamicsam.png|thumb|upright=0.80|centre|Figure 5 - Dynamic Trajectory]]

== Q4 - Reactive and Unreactive Trajectories==

{| class="wikitable" border=1
! p1 !! p2 !! Total Energy !! Reactive or Unreactive !! Trajectory Plot !! Discussion
|-
| -1.25 || -2.5 || -99.018 || [[File:SY-1.png|frameless|upright=0.80]] || Reactive || The reactivity of the trajectory is shown as the reaction path progresses towards the prodcut H2. Upon forming, the new bond vibrates.
|-
| -1.5 || -2.0 || -100.456 || [[File:SY-2.png|frameless|upright=0.80]] || Unreactive || This figure represents an unreactive system due to the approaching H atom not having enough energy to overcome the activation barrier for the reaction. This results in the reaction trajectory returning to the original H2 bond oscillating back towards its energy minimum.
|-
| -1.5 || -2.5 || -98.956 || [[File:SY-3.png|frameless|upright=0.80]] || Reactive || This model shows a very simimlar picture to the first in the table, although due to p1 being slightly higher, the original H2 bond oscillates with higher energy.
|-
| -2.5 || -5.0 || -84.956 || [[File:SLY4.png|frameless|upright=0.80]] || Unreactive || Here one H atom aproaches the H2 molecule and the transition state complex H-H-H forms, however due to a lack of energy, the trajectory path is unable to continue to form the products so returns to the original reactants.
|-
| -2.5 || -5.2 || -83.416 ||[[File:SY5.png|frameless|upright=0.80]] || Reactive || The case has a high enough energy to form the transition state complex and to continue to overcome the energy barrier to obtain the products.
|}

== Q5 - Transition State Theory ==

Transition state theory focusses on the activated complexes formed at a transition state of the reaction, therefore by examining the transition state of a potential surface plot (found at the saddle point) one can obtain the rate of a reaction, due to the activated complex's quasi-equilibrium with the reactants. It assumes that if the collision is of sufficient energy to overcome the transition state, the products will form. This is based on the assumption that molecules react according to the classical picture, and does not take quantum mechanics into account, leading to limitations when considering phenomena such as tunnelling, whereby the reaction path bypasses a low activation energy. Furthermore the transition state theory does not account for reactions recrossing the activation barrier to return to the products as shown above. As a result, this theory would give a higher rate to the real situation, where the product can recross the transition state to return to the reactant (as shown in Part 2 Q5).

= F H H System =

== Q1 - Energetics ==

F + H2
This reaction is shown to be exothermic (i.e. the system releases energy upon reacting, ΔH < 0) from the plot due to the energy minimum of the FH bond being lower in energy than the HH bond, therefore more stable. This is due to the large electronegativity difference between F (3.98) and H (2.20), as opposed to the non polar HH bond. As a result, the reaction of FH + H is therefore endothermic for the same reasons, due to the FH bond dissociation energy being larger than the HH bond formation enthalpy.

[[File:SLYFH.png|thumb|upright=0.80|centre|Figure 6 - Potential energy surface plot of the F + H2 reaction]]

== Q2 - Position of the Transition State ==

The transition state can be found at the point where the internuclear distances of the atoms does not change over time. This is the same point on the graph for both the forward and reverse reactions. By using Hammond's postulate, that the activated intermediate complex at the transition state should resemble the state that it is closest in energy to, therefore similar to an HF + H model. As a result, it was possible to look at the surface plot and optimise the bond distances around where the transition state was roughly located. It was found that the approximate internuclear distances at this transition state are H-F : 1.810 and H-H : 0.746.

[[File:tshighlight.png|thumb|none|Figure 7 - Potential energy surface plot showing the transition state]] [[File:transstatesly.png|thumb|upright=0.80|none|Figure 8 - Internuclear distance vs time]]

== Q3 - Activation Energy ==

By finding the equilibrium bond length of both reactants and products, and knowing the location of the transition state, it was possible to obtain energies for all of these positions, and therefore calculate the energy of activation.

Energy at HF minimum -133.586 AB 2.3 BC 0.9

Energy at HH minimum -103.33 AB 0.7 BC 2.3

Energy at transition state -103.742 AB 0.75 BC 1.81

ΔE = E(transition state) - E(reactants)

''ΔEFH + H‡ = (-103.742) - (-133.586) = 29.844 Kcalmol-1''

''ΔEH2 + F‡ = (-103.742) - (-103.330) = 0.412 Kcalmol-1''

== Q4 - Mechanism of Release of the Activation Energy ==

F + H2

This plot shows the reaction of initial conditions FH distance = 2.0Å HH distance = 0.74Å FH momentm = -0.5 HH momentum = -2.0, resulting in a successful reaction. Due to the exothermic nature of this reaction, it releases energy as the products have a lower potential energy than the reactants, and from the plot of internuclear distance vs. time, it is clear that this energy is converted to kinetic energy in the form of an oscillating F-H bond, which oscillates at a much higher energy than the original H-H bond. This could be confirmed experimentally by IR which would show the vibrationally excited state of the H-F bond, or energy can be measured by calorimetry inorder to prove that it is conserved.

[[File:samlyoungvibvib.png|thumb|upright=0.80|centre|Figure 9 - Internuclear Momenta vs Time plot]]

== Q5 - Efficiency of Reaction ==

Figures 10-14 clearly show the effect of varying the translaitonal and vibrational contributions to the reaction trajectory of both the endothermic and exothermic reactions. For the exothermic F + H2 reaction, the momentum of the translaitonal approach of the F atom was kept constant while the momentum of the H-H oscillation was varied between 3kgms-1 and -3kgms-1. The result clearly shows that for this early transition state reaction, a higher vibration energy causes the reaction path to overcome the transition state but it recrosses this barrier to return to the initial state due to too much energy. The limit (to 2 d.p.)of the vibrational energy was found to be -2.49kgms-1 in order for the reaction to be successful. A higher energy would cause the recrossing.
This case is the opposite for the endothermic reaction, with a late transition state, whereby if the translational energy is too high the reaction will cross then recross the transition state to return to the products, resulting in an unsuccessful reaction. The limit of translational energy for this reaction was found to be -0.61kgms-1.

To conclude, the success of an early transition state reaction depends on the vibrational energy, while the success of the late transition state depends on the translational energy, with both rebounding back to reactants with of the energy is too high because it still has enough energy to overcome the reverse reaction due to it being energetically excited.

{| class="wikitable" border=1
! !! !!
|-
| [[File:fh2highvibworks.png|thumb|upright=0.80|centre|Figure 10 - Reaction of H2 + F (H-H = 0.74Å, H-F = 2.Å, pHH = -3.0kgms-1, pHF = -0.5kgms-1)]] || [[File:lowvibsamyoung.png|thumb|upright=0.80|centre|Figure 11 - Reaction of H2 + F (H-H = 0.74Å, H-F = 2.0Å, pHH = -0.5kgms-1, pHF = -0.5kgms-1)]] || [[File:samlyounglimit2.png|thumb|upright=0.80|centre|Figure 12 - Reaction of H2 + F (H-H = 0.74Å, H-F = 2.0Å, pHH = -2.49kgms-1, pHF = -0.5kgms-1)]]
|-
| [[File:fhhidealsly.png|thumb|upright=0.80|centre|Figure 13 - Reaction of H2 + F (H-H = 2Å, H-F = 0.74Å, pHH = -0.61kgms-1, pHF = -0.5kgms-1)]] || [[File:slylowtrans.png|thumb|upright=0.80|centre|Figure 13 - Reaction of H2 + F (H-H = 2Å, H-F = 0.74Å, pHH = -0.1kgms-1, pHF = -0.5kgms-1)]]|| [[File:translationalsamsam.png|thumb|upright=0.80|centre|Figure 14 - Reaction of H2 + F (H-H = 2Å, H-F = 0.74Å, pHH = -3.0kgms-1, pHF = -0.5kgms-1)]]

|}

= Bibliography =

Electronegativity values : https://sciencenotes.org/list-of-electronegativity-values-of-the-elements/

Physical Chemistry, Ninth Edition, Peter Atkins & Julio De Paula , Oxford University Press

Sam Young Reaction Dynamics

2018-05-18T14:26:47Z

Sly116: /* Q2 - Position of the Transition State */

= H + H2 System =
== Q1 - Transition State Gradients ==
[[File:Sly-Saddle.png|thumb|upright=0.8|centre|Figure 1 - Potential Energy Surface Plot of H2 + H System, with initial conditions A-B distance = 0.74, B-C distance = 2.30, AB momentum = 0 & BC momentum = 2.7]]

The minimum energy surface, shown running along the bottom of figure one obeys the derivative; ∂V/∂(rx) = ∂V/∂(ry) = 0, with rx and ry run parallel to their respective gradients. However, the saddle point where the transition state lies is located along the minimum energy surface at the maximum point. Therefore, it can be found by taking the second derivative, as the two orthogonal gradients have different signs, with one along the potential energy minimum being negative and the other orthogonal graident being positive.

∂2V/∂(rx)2 > 0

∂2V/∂(ry)2 < 0

== Q2 - Transition State Estimate ==

By making the momentum of the whole system equal to zero, it was possible to put the AB distance = BC distance and alter this value to obtain a result for the rts, which was found to be approximately 0.9077Å (one value due to the system being completely symmetric), which gave figure 2. This number was found by taking the intersect of the AB and BC lines from the internuclear plot with the same initial conditions given above, and optimising this value to give constant distances. Due to the gradient of potential energy at the transition state being zero, the system has no kinetic energy, only potential energy. Therefore, there is no oscillation and the plot of internuclear distance against time shows constant interatomic distances.

[[File:Sly_Q2.png|thumb|upright=0.80|centre|Figure 2 - Internucleur Distance]]

== Q3 - MEP ==

The MEP is the minimum energy pathway followed for the reaction H2 + H to take place, although it can be seen in figures 4 and 5 that it differs from the dynamic trajectory due to the masses of the atoms, and therefore the bond oscillations along the trajectory causing deviations from the mep. This is shown by the wavy black line on figure 5. Both figures illustrate the reaction path (represented by the black line) starting at the transition state point, with the dynamic reaction going to the complete formation of a H2 product, while the mep plot shows it going only slightly towards the product formation.

'''change with + - 0.01 and discuss'''

[[File:Sly_MEP2.png|thumb|upright=0.80|centre|Figure 4 - Minimum Energy Pathway]] [[File:newdynamicsam.png|thumb|upright=0.80|centre|Figure 5 - Dynamic Trajectory]]

== Q4 - Reactive and Unreactive Trajectories==

{| class="wikitable" border=1
! p1 !! p2 !! Total Energy !! Reactive or Unreactive !! Trajectory Plot !! Discussion
|-
| -1.25 || -2.5 || -99.018 || [[File:SY-1.png|frameless|upright=0.80]] || Reactive || The reactivity of the trajectory is shown as the reaction path progresses towards the prodcut H2. Upon forming, the new bond vibrates.
|-
| -1.5 || -2.0 || -100.456 || [[File:SY-2.png|frameless|upright=0.80]] || Unreactive || This figure represents an unreactive system due to the approaching H atom not having enough energy to overcome the activation barrier for the reaction. This results in the reaction trajectory returning to the original H2 bond oscillating back towards its energy minimum.
|-
| -1.5 || -2.5 || -98.956 || [[File:SY-3.png|frameless|upright=0.80]] || Reactive || This model shows a very simimlar picture to the first in the table, although due to p1 being slightly higher, the original H2 bond oscillates with higher energy.
|-
| -2.5 || -5.0 || -84.956 || [[File:SLY4.png|frameless|upright=0.80]] || Unreactive || Here one H atom aproaches the H2 molecule and the transition state complex H-H-H forms, however due to a lack of energy, the trajectory path is unable to continue to form the products so returns to the original reactants.
|-
| -2.5 || -5.2 || -83.416 ||[[File:SY5.png|frameless|upright=0.80]] || Reactive || The case has a high enough energy to form the transition state complex and to continue to overcome the energy barrier to obtain the products.
|}

== Q5 - Transition State Theory ==

Transition state theory focusses on the activated complexes formed at a transition state of the reaction, therefore by examining the transition state of a potential surface plot (found at the saddle point) one can obtain the rate of a reaction, due to the activated complex's quasi-equilibrium with the reactants. It assumes that if the collision is of sufficient energy to overcome the transition state, the products will form. This is based on the assumption that molecules react according to the classical picture, and does not take quantum mechanics into account, leading to limitations when considering phenomena such as tunnelling, whereby the reaction path bypasses a low activation energy. Furthermore the transition state theory does not account for reactions recrossing the activation barrier to return to the products as shown above. As a result, this theory would give a higher rate to the real situation, where the product can recross the transition state to return to the reactant (as shown in Part 2 Q5).

= F H H System =

== Q1 - Energetics ==

F + H2
This reaction is shown to be exothermic (i.e. the system releases energy upon reacting, ΔH < 0) from the plot due to the energy minimum of the FH bond being lower in energy than the HH bond, therefore more stable. This is due to the large electronegativity difference between F (3.98) and H (2.20), as opposed to the non polar HH bond. As a result, the reaction of FH + H is therefore endothermic for the same reasons, due to the FH bond dissociation energy being larger than the HH bond formation enthalpy.

[[File:SLYFH.png|thumb|upright=0.80|centre|Figure 6]]

== Q2 - Position of the Transition State ==

The transition state can be found at the point where the internuclear distances of the atoms does not change over time. This is the same point on the graph for both the forward and reverse reactions. By using Hammond's postulate, that the activated intermediate complex at the transition state should resemble the state that it is closest in energy to, therefore similar to an HF + H model. As a result, it was possible to look at the surface plot and optimise the bond distances around where the transition state was roughly located. It was found that the approximate internuclear distances at this transition state are H-F : 1.810 and H-H : 0.746.

[[File:tshighlight.png|thumb|none|Figure 7 - Potential energy surface plot showing the transition state]] [[File:transstatesly.png|thumb|upright=0.80|none|Figure 8 - Internuclear distance vs time]]

== Q3 - Activation Energy ==

By finding the equilibrium bond length of both reactants and products, and knowing the location of the transition state, it was possible to obtain energies for all of these positions, and therefore calculate the energy of activation.

Energy at HF minimum -133.586 AB 2.3 BC 0.9

Energy at HH minimum -103.33 AB 0.7 BC 2.3

Energy at transition state -103.742 AB 0.75 BC 1.81

ΔE = E(transition state) - E(reactants)

''ΔEFH + H‡ = (-103.742) - (-133.586) = 29.844 Kcalmol-1''

''ΔEH2 + F‡ = (-103.742) - (-103.330) = 0.412 Kcalmol-1''

== Q4 - Mechanism of Release of the Activation Energy ==

F + H2

This plot shows the reaction of initial conditions FH distance = 2.0Å HH distance = 0.74Å FH momentm = -0.5 HH momentum = -2.0, resulting in a successful reaction. Due to the exothermic nature of this reaction, it releases energy as the products have a lower potential energy than the reactants, and from the plot of internuclear distance vs. time, it is clear that this energy is converted to kinetic energy in the form of an oscillating F-H bond, which oscillates at a much higher energy than the original H-H bond. This could be confirmed experimentally by IR which would show the vibrationally excited state of the H-F bond, or energy can be measured by calorimetry inorder to prove that it is conserved.

[[File:samlyoungvibvib.png|thumb|upright=0.80|centre|Figure 9 - Internuclear Momenta vs Time plot]]

== Q5 - Efficiency of Reaction ==

Figures 10-14 clearly show the effect of varying the translaitonal and vibrational contributions to the reaction trajectory of both the endothermic and exothermic reactions. For the exothermic F + H2 reaction, the momentum of the translaitonal approach of the F atom was kept constant while the momentum of the H-H oscillation was varied between 3kgms-1 and -3kgms-1. The result clearly shows that for this early transition state reaction, a higher vibration energy causes the reaction path to overcome the transition state but it recrosses this barrier to return to the initial state due to too much energy. The limit (to 2 d.p.)of the vibrational energy was found to be -2.49kgms-1 in order for the reaction to be successful. A higher energy would cause the recrossing.
This case is the opposite for the endothermic reaction, with a late transition state, whereby if the translational energy is too high the reaction will cross then recross the transition state to return to the products, resulting in an unsuccessful reaction. The limit of translational energy for this reaction was found to be -0.61kgms-1.

To conclude, the success of an early transition state reaction depends on the vibrational energy, while the success of the late transition state depends on the translational energy, with both rebounding back to reactants with of the energy is too high because it still has enough energy to overcome the reverse reaction due to it being energetically excited.

{| class="wikitable" border=1
! !! !!
|-
| [[File:fh2highvibworks.png|thumb|upright=0.80|centre|Figure 10 - Reaction of H2 + F (H-H = 0.74Å, H-F = 2.Å, pHH = -3.0kgms-1, pHF = -0.5kgms-1)]] || [[File:lowvibsamyoung.png|thumb|upright=0.80|centre|Figure 11 - Reaction of H2 + F (H-H = 0.74Å, H-F = 2.0Å, pHH = -0.5kgms-1, pHF = -0.5kgms-1)]] || [[File:samlyounglimit2.png|thumb|upright=0.80|centre|Figure 12 - Reaction of H2 + F (H-H = 0.74Å, H-F = 2.0Å, pHH = -2.49kgms-1, pHF = -0.5kgms-1)]]
|-
| [[File:fhhidealsly.png|thumb|upright=0.80|centre|Figure 13 - Reaction of H2 + F (H-H = 2Å, H-F = 0.74Å, pHH = -0.61kgms-1, pHF = -0.5kgms-1)]] || [[File:slylowtrans.png|thumb|upright=0.80|centre|Figure 13 - Reaction of H2 + F (H-H = 2Å, H-F = 0.74Å, pHH = -0.1kgms-1, pHF = -0.5kgms-1)]]|| [[File:translationalsamsam.png|thumb|upright=0.80|centre|Figure 14 - Reaction of H2 + F (H-H = 2Å, H-F = 0.74Å, pHH = -3.0kgms-1, pHF = -0.5kgms-1)]]

|}

= Bibliography =

Electronegativity values : https://sciencenotes.org/list-of-electronegativity-values-of-the-elements/

Physical Chemistry, Ninth Edition, Peter Atkins & Julio De Paula , Oxford University Press

Sam Young Reaction Dynamics

2018-05-18T14:26:28Z

Sly116: /* Q2 - Position of the Transition State */

= H + H2 System =
== Q1 - Transition State Gradients ==
[[File:Sly-Saddle.png|thumb|upright=0.8|centre|Figure 1 - Potential Energy Surface Plot of H2 + H System, with initial conditions A-B distance = 0.74, B-C distance = 2.30, AB momentum = 0 & BC momentum = 2.7]]

The minimum energy surface, shown running along the bottom of figure one obeys the derivative; ∂V/∂(rx) = ∂V/∂(ry) = 0, with rx and ry run parallel to their respective gradients. However, the saddle point where the transition state lies is located along the minimum energy surface at the maximum point. Therefore, it can be found by taking the second derivative, as the two orthogonal gradients have different signs, with one along the potential energy minimum being negative and the other orthogonal graident being positive.

∂2V/∂(rx)2 > 0

∂2V/∂(ry)2 < 0

== Q2 - Transition State Estimate ==

By making the momentum of the whole system equal to zero, it was possible to put the AB distance = BC distance and alter this value to obtain a result for the rts, which was found to be approximately 0.9077Å (one value due to the system being completely symmetric), which gave figure 2. This number was found by taking the intersect of the AB and BC lines from the internuclear plot with the same initial conditions given above, and optimising this value to give constant distances. Due to the gradient of potential energy at the transition state being zero, the system has no kinetic energy, only potential energy. Therefore, there is no oscillation and the plot of internuclear distance against time shows constant interatomic distances.

[[File:Sly_Q2.png|thumb|upright=0.80|centre|Figure 2 - Internucleur Distance]]

== Q3 - MEP ==

The MEP is the minimum energy pathway followed for the reaction H2 + H to take place, although it can be seen in figures 4 and 5 that it differs from the dynamic trajectory due to the masses of the atoms, and therefore the bond oscillations along the trajectory causing deviations from the mep. This is shown by the wavy black line on figure 5. Both figures illustrate the reaction path (represented by the black line) starting at the transition state point, with the dynamic reaction going to the complete formation of a H2 product, while the mep plot shows it going only slightly towards the product formation.

'''change with + - 0.01 and discuss'''

[[File:Sly_MEP2.png|thumb|upright=0.80|centre|Figure 4 - Minimum Energy Pathway]] [[File:newdynamicsam.png|thumb|upright=0.80|centre|Figure 5 - Dynamic Trajectory]]

== Q4 - Reactive and Unreactive Trajectories==

{| class="wikitable" border=1
! p1 !! p2 !! Total Energy !! Reactive or Unreactive !! Trajectory Plot !! Discussion
|-
| -1.25 || -2.5 || -99.018 || [[File:SY-1.png|frameless|upright=0.80]] || Reactive || The reactivity of the trajectory is shown as the reaction path progresses towards the prodcut H2. Upon forming, the new bond vibrates.
|-
| -1.5 || -2.0 || -100.456 || [[File:SY-2.png|frameless|upright=0.80]] || Unreactive || This figure represents an unreactive system due to the approaching H atom not having enough energy to overcome the activation barrier for the reaction. This results in the reaction trajectory returning to the original H2 bond oscillating back towards its energy minimum.
|-
| -1.5 || -2.5 || -98.956 || [[File:SY-3.png|frameless|upright=0.80]] || Reactive || This model shows a very simimlar picture to the first in the table, although due to p1 being slightly higher, the original H2 bond oscillates with higher energy.
|-
| -2.5 || -5.0 || -84.956 || [[File:SLY4.png|frameless|upright=0.80]] || Unreactive || Here one H atom aproaches the H2 molecule and the transition state complex H-H-H forms, however due to a lack of energy, the trajectory path is unable to continue to form the products so returns to the original reactants.
|-
| -2.5 || -5.2 || -83.416 ||[[File:SY5.png|frameless|upright=0.80]] || Reactive || The case has a high enough energy to form the transition state complex and to continue to overcome the energy barrier to obtain the products.
|}

== Q5 - Transition State Theory ==

Transition state theory focusses on the activated complexes formed at a transition state of the reaction, therefore by examining the transition state of a potential surface plot (found at the saddle point) one can obtain the rate of a reaction, due to the activated complex's quasi-equilibrium with the reactants. It assumes that if the collision is of sufficient energy to overcome the transition state, the products will form. This is based on the assumption that molecules react according to the classical picture, and does not take quantum mechanics into account, leading to limitations when considering phenomena such as tunnelling, whereby the reaction path bypasses a low activation energy. Furthermore the transition state theory does not account for reactions recrossing the activation barrier to return to the products as shown above. As a result, this theory would give a higher rate to the real situation, where the product can recross the transition state to return to the reactant (as shown in Part 2 Q5).

= F H H System =

== Q1 - Energetics ==

F + H2
This reaction is shown to be exothermic (i.e. the system releases energy upon reacting, ΔH < 0) from the plot due to the energy minimum of the FH bond being lower in energy than the HH bond, therefore more stable. This is due to the large electronegativity difference between F (3.98) and H (2.20), as opposed to the non polar HH bond. As a result, the reaction of FH + H is therefore endothermic for the same reasons, due to the FH bond dissociation energy being larger than the HH bond formation enthalpy.

[[File:SLYFH.png|thumb|upright=0.80|centre|Figure 6]]

== Q2 - Position of the Transition State ==

The transition state can be found at the point where the internuclear distances of the atoms does not change over time. This is the same point on the graph for both the forward and reverse reactions. By using Hammond's postulate, that the activated intermediate complex at the transition state should resemble the state that it is closest in energy to, therefore similar to an HF + H model. As a result, it was possible to look at the surface plot and optimise the bond distances around where the transition state was roughly located. It was found that the approximate internuclear distances at this transition state are H-F : 1.810 and H-H : 0.746.

[[File:tshighlight.png|thumb|none|Figure 7 - Potential energy surface plot showing the transition state]] [[File:transstatesly.png|thumb|upright=0.80|none|Figure 8]]

== Q3 - Activation Energy ==

By finding the equilibrium bond length of both reactants and products, and knowing the location of the transition state, it was possible to obtain energies for all of these positions, and therefore calculate the energy of activation.

Energy at HF minimum -133.586 AB 2.3 BC 0.9

Energy at HH minimum -103.33 AB 0.7 BC 2.3

Energy at transition state -103.742 AB 0.75 BC 1.81

ΔE = E(transition state) - E(reactants)

''ΔEFH + H‡ = (-103.742) - (-133.586) = 29.844 Kcalmol-1''

''ΔEH2 + F‡ = (-103.742) - (-103.330) = 0.412 Kcalmol-1''

== Q4 - Mechanism of Release of the Activation Energy ==

F + H2

This plot shows the reaction of initial conditions FH distance = 2.0Å HH distance = 0.74Å FH momentm = -0.5 HH momentum = -2.0, resulting in a successful reaction. Due to the exothermic nature of this reaction, it releases energy as the products have a lower potential energy than the reactants, and from the plot of internuclear distance vs. time, it is clear that this energy is converted to kinetic energy in the form of an oscillating F-H bond, which oscillates at a much higher energy than the original H-H bond. This could be confirmed experimentally by IR which would show the vibrationally excited state of the H-F bond, or energy can be measured by calorimetry inorder to prove that it is conserved.

[[File:samlyoungvibvib.png|thumb|upright=0.80|centre|Figure 9 - Internuclear Momenta vs Time plot]]

== Q5 - Efficiency of Reaction ==

Figures 10-14 clearly show the effect of varying the translaitonal and vibrational contributions to the reaction trajectory of both the endothermic and exothermic reactions. For the exothermic F + H2 reaction, the momentum of the translaitonal approach of the F atom was kept constant while the momentum of the H-H oscillation was varied between 3kgms-1 and -3kgms-1. The result clearly shows that for this early transition state reaction, a higher vibration energy causes the reaction path to overcome the transition state but it recrosses this barrier to return to the initial state due to too much energy. The limit (to 2 d.p.)of the vibrational energy was found to be -2.49kgms-1 in order for the reaction to be successful. A higher energy would cause the recrossing.
This case is the opposite for the endothermic reaction, with a late transition state, whereby if the translational energy is too high the reaction will cross then recross the transition state to return to the products, resulting in an unsuccessful reaction. The limit of translational energy for this reaction was found to be -0.61kgms-1.

To conclude, the success of an early transition state reaction depends on the vibrational energy, while the success of the late transition state depends on the translational energy, with both rebounding back to reactants with of the energy is too high because it still has enough energy to overcome the reverse reaction due to it being energetically excited.

{| class="wikitable" border=1
! !! !!
|-
| [[File:fh2highvibworks.png|thumb|upright=0.80|centre|Figure 10 - Reaction of H2 + F (H-H = 0.74Å, H-F = 2.Å, pHH = -3.0kgms-1, pHF = -0.5kgms-1)]] || [[File:lowvibsamyoung.png|thumb|upright=0.80|centre|Figure 11 - Reaction of H2 + F (H-H = 0.74Å, H-F = 2.0Å, pHH = -0.5kgms-1, pHF = -0.5kgms-1)]] || [[File:samlyounglimit2.png|thumb|upright=0.80|centre|Figure 12 - Reaction of H2 + F (H-H = 0.74Å, H-F = 2.0Å, pHH = -2.49kgms-1, pHF = -0.5kgms-1)]]
|-
| [[File:fhhidealsly.png|thumb|upright=0.80|centre|Figure 13 - Reaction of H2 + F (H-H = 2Å, H-F = 0.74Å, pHH = -0.61kgms-1, pHF = -0.5kgms-1)]] || [[File:slylowtrans.png|thumb|upright=0.80|centre|Figure 13 - Reaction of H2 + F (H-H = 2Å, H-F = 0.74Å, pHH = -0.1kgms-1, pHF = -0.5kgms-1)]]|| [[File:translationalsamsam.png|thumb|upright=0.80|centre|Figure 14 - Reaction of H2 + F (H-H = 2Å, H-F = 0.74Å, pHH = -3.0kgms-1, pHF = -0.5kgms-1)]]

|}

= Bibliography =

Electronegativity values : https://sciencenotes.org/list-of-electronegativity-values-of-the-elements/

Physical Chemistry, Ninth Edition, Peter Atkins & Julio De Paula , Oxford University Press

Sam Young Reaction Dynamics

2018-05-18T14:25:57Z

Sly116: /* Q4 - Mechanism of Release of the Activation Energy */

= H + H2 System =
== Q1 - Transition State Gradients ==
[[File:Sly-Saddle.png|thumb|upright=0.8|centre|Figure 1 - Potential Energy Surface Plot of H2 + H System, with initial conditions A-B distance = 0.74, B-C distance = 2.30, AB momentum = 0 & BC momentum = 2.7]]

The minimum energy surface, shown running along the bottom of figure one obeys the derivative; ∂V/∂(rx) = ∂V/∂(ry) = 0, with rx and ry run parallel to their respective gradients. However, the saddle point where the transition state lies is located along the minimum energy surface at the maximum point. Therefore, it can be found by taking the second derivative, as the two orthogonal gradients have different signs, with one along the potential energy minimum being negative and the other orthogonal graident being positive.

∂2V/∂(rx)2 > 0

∂2V/∂(ry)2 < 0

== Q2 - Transition State Estimate ==

By making the momentum of the whole system equal to zero, it was possible to put the AB distance = BC distance and alter this value to obtain a result for the rts, which was found to be approximately 0.9077Å (one value due to the system being completely symmetric), which gave figure 2. This number was found by taking the intersect of the AB and BC lines from the internuclear plot with the same initial conditions given above, and optimising this value to give constant distances. Due to the gradient of potential energy at the transition state being zero, the system has no kinetic energy, only potential energy. Therefore, there is no oscillation and the plot of internuclear distance against time shows constant interatomic distances.

[[File:Sly_Q2.png|thumb|upright=0.80|centre|Figure 2 - Internucleur Distance]]

== Q3 - MEP ==

The MEP is the minimum energy pathway followed for the reaction H2 + H to take place, although it can be seen in figures 4 and 5 that it differs from the dynamic trajectory due to the masses of the atoms, and therefore the bond oscillations along the trajectory causing deviations from the mep. This is shown by the wavy black line on figure 5. Both figures illustrate the reaction path (represented by the black line) starting at the transition state point, with the dynamic reaction going to the complete formation of a H2 product, while the mep plot shows it going only slightly towards the product formation.

'''change with + - 0.01 and discuss'''

[[File:Sly_MEP2.png|thumb|upright=0.80|centre|Figure 4 - Minimum Energy Pathway]] [[File:newdynamicsam.png|thumb|upright=0.80|centre|Figure 5 - Dynamic Trajectory]]

== Q4 - Reactive and Unreactive Trajectories==

{| class="wikitable" border=1
! p1 !! p2 !! Total Energy !! Reactive or Unreactive !! Trajectory Plot !! Discussion
|-
| -1.25 || -2.5 || -99.018 || [[File:SY-1.png|frameless|upright=0.80]] || Reactive || The reactivity of the trajectory is shown as the reaction path progresses towards the prodcut H2. Upon forming, the new bond vibrates.
|-
| -1.5 || -2.0 || -100.456 || [[File:SY-2.png|frameless|upright=0.80]] || Unreactive || This figure represents an unreactive system due to the approaching H atom not having enough energy to overcome the activation barrier for the reaction. This results in the reaction trajectory returning to the original H2 bond oscillating back towards its energy minimum.
|-
| -1.5 || -2.5 || -98.956 || [[File:SY-3.png|frameless|upright=0.80]] || Reactive || This model shows a very simimlar picture to the first in the table, although due to p1 being slightly higher, the original H2 bond oscillates with higher energy.
|-
| -2.5 || -5.0 || -84.956 || [[File:SLY4.png|frameless|upright=0.80]] || Unreactive || Here one H atom aproaches the H2 molecule and the transition state complex H-H-H forms, however due to a lack of energy, the trajectory path is unable to continue to form the products so returns to the original reactants.
|-
| -2.5 || -5.2 || -83.416 ||[[File:SY5.png|frameless|upright=0.80]] || Reactive || The case has a high enough energy to form the transition state complex and to continue to overcome the energy barrier to obtain the products.
|}

== Q5 - Transition State Theory ==

Transition state theory focusses on the activated complexes formed at a transition state of the reaction, therefore by examining the transition state of a potential surface plot (found at the saddle point) one can obtain the rate of a reaction, due to the activated complex's quasi-equilibrium with the reactants. It assumes that if the collision is of sufficient energy to overcome the transition state, the products will form. This is based on the assumption that molecules react according to the classical picture, and does not take quantum mechanics into account, leading to limitations when considering phenomena such as tunnelling, whereby the reaction path bypasses a low activation energy. Furthermore the transition state theory does not account for reactions recrossing the activation barrier to return to the products as shown above. As a result, this theory would give a higher rate to the real situation, where the product can recross the transition state to return to the reactant (as shown in Part 2 Q5).

= F H H System =

== Q1 - Energetics ==

F + H2
This reaction is shown to be exothermic (i.e. the system releases energy upon reacting, ΔH < 0) from the plot due to the energy minimum of the FH bond being lower in energy than the HH bond, therefore more stable. This is due to the large electronegativity difference between F (3.98) and H (2.20), as opposed to the non polar HH bond. As a result, the reaction of FH + H is therefore endothermic for the same reasons, due to the FH bond dissociation energy being larger than the HH bond formation enthalpy.

[[File:SLYFH.png|thumb|upright=0.80|centre|Figure 6]]

== Q2 - Position of the Transition State ==

The transition state can be found at the point where the internuclear distances of the atoms does not change over time. This is the same point on the graph for both the forward and reverse reactions. By using Hammond's postulate, that the activated intermediate complex at the transition state should resemble the state that it is closest in energy to, therefore similar to an HF + H model. As a result, it was possible to look at the surface plot and optimise the bond distances around where the transition state was roughly located. It was found that the approximate internuclear distances at this transition state are H-F : 1.810 and H-H : 0.746.

[[File:tshighlight.png|thumb|none|Figure 7]] [[File:transstatesly.png|thumb|upright=0.80|none|Figure 8]]

== Q3 - Activation Energy ==

By finding the equilibrium bond length of both reactants and products, and knowing the location of the transition state, it was possible to obtain energies for all of these positions, and therefore calculate the energy of activation.

Energy at HF minimum -133.586 AB 2.3 BC 0.9

Energy at HH minimum -103.33 AB 0.7 BC 2.3

Energy at transition state -103.742 AB 0.75 BC 1.81

ΔE = E(transition state) - E(reactants)

''ΔEFH + H‡ = (-103.742) - (-133.586) = 29.844 Kcalmol-1''

''ΔEH2 + F‡ = (-103.742) - (-103.330) = 0.412 Kcalmol-1''

== Q4 - Mechanism of Release of the Activation Energy ==

F + H2

This plot shows the reaction of initial conditions FH distance = 2.0Å HH distance = 0.74Å FH momentm = -0.5 HH momentum = -2.0, resulting in a successful reaction. Due to the exothermic nature of this reaction, it releases energy as the products have a lower potential energy than the reactants, and from the plot of internuclear distance vs. time, it is clear that this energy is converted to kinetic energy in the form of an oscillating F-H bond, which oscillates at a much higher energy than the original H-H bond. This could be confirmed experimentally by IR which would show the vibrationally excited state of the H-F bond, or energy can be measured by calorimetry inorder to prove that it is conserved.

[[File:samlyoungvibvib.png|thumb|upright=0.80|centre|Figure 9 - Internuclear Momenta vs Time plot]]

== Q5 - Efficiency of Reaction ==

Figures 10-14 clearly show the effect of varying the translaitonal and vibrational contributions to the reaction trajectory of both the endothermic and exothermic reactions. For the exothermic F + H2 reaction, the momentum of the translaitonal approach of the F atom was kept constant while the momentum of the H-H oscillation was varied between 3kgms-1 and -3kgms-1. The result clearly shows that for this early transition state reaction, a higher vibration energy causes the reaction path to overcome the transition state but it recrosses this barrier to return to the initial state due to too much energy. The limit (to 2 d.p.)of the vibrational energy was found to be -2.49kgms-1 in order for the reaction to be successful. A higher energy would cause the recrossing.
This case is the opposite for the endothermic reaction, with a late transition state, whereby if the translational energy is too high the reaction will cross then recross the transition state to return to the products, resulting in an unsuccessful reaction. The limit of translational energy for this reaction was found to be -0.61kgms-1.

To conclude, the success of an early transition state reaction depends on the vibrational energy, while the success of the late transition state depends on the translational energy, with both rebounding back to reactants with of the energy is too high because it still has enough energy to overcome the reverse reaction due to it being energetically excited.

{| class="wikitable" border=1
! !! !!
|-
| [[File:fh2highvibworks.png|thumb|upright=0.80|centre|Figure 10 - Reaction of H2 + F (H-H = 0.74Å, H-F = 2.Å, pHH = -3.0kgms-1, pHF = -0.5kgms-1)]] || [[File:lowvibsamyoung.png|thumb|upright=0.80|centre|Figure 11 - Reaction of H2 + F (H-H = 0.74Å, H-F = 2.0Å, pHH = -0.5kgms-1, pHF = -0.5kgms-1)]] || [[File:samlyounglimit2.png|thumb|upright=0.80|centre|Figure 12 - Reaction of H2 + F (H-H = 0.74Å, H-F = 2.0Å, pHH = -2.49kgms-1, pHF = -0.5kgms-1)]]
|-
| [[File:fhhidealsly.png|thumb|upright=0.80|centre|Figure 13 - Reaction of H2 + F (H-H = 2Å, H-F = 0.74Å, pHH = -0.61kgms-1, pHF = -0.5kgms-1)]] || [[File:slylowtrans.png|thumb|upright=0.80|centre|Figure 13 - Reaction of H2 + F (H-H = 2Å, H-F = 0.74Å, pHH = -0.1kgms-1, pHF = -0.5kgms-1)]]|| [[File:translationalsamsam.png|thumb|upright=0.80|centre|Figure 14 - Reaction of H2 + F (H-H = 2Å, H-F = 0.74Å, pHH = -3.0kgms-1, pHF = -0.5kgms-1)]]

|}

= Bibliography =

Electronegativity values : https://sciencenotes.org/list-of-electronegativity-values-of-the-elements/

Physical Chemistry, Ninth Edition, Peter Atkins & Julio De Paula , Oxford University Press

Sam Young Reaction Dynamics

2018-05-18T14:25:00Z

Sly116: /* Q4 - Mechanism of Release of the Activation Energy */

= H + H2 System =
== Q1 - Transition State Gradients ==
[[File:Sly-Saddle.png|thumb|upright=0.8|centre|Figure 1 - Potential Energy Surface Plot of H2 + H System, with initial conditions A-B distance = 0.74, B-C distance = 2.30, AB momentum = 0 & BC momentum = 2.7]]

The minimum energy surface, shown running along the bottom of figure one obeys the derivative; ∂V/∂(rx) = ∂V/∂(ry) = 0, with rx and ry run parallel to their respective gradients. However, the saddle point where the transition state lies is located along the minimum energy surface at the maximum point. Therefore, it can be found by taking the second derivative, as the two orthogonal gradients have different signs, with one along the potential energy minimum being negative and the other orthogonal graident being positive.

∂2V/∂(rx)2 > 0

∂2V/∂(ry)2 < 0

== Q2 - Transition State Estimate ==

By making the momentum of the whole system equal to zero, it was possible to put the AB distance = BC distance and alter this value to obtain a result for the rts, which was found to be approximately 0.9077Å (one value due to the system being completely symmetric), which gave figure 2. This number was found by taking the intersect of the AB and BC lines from the internuclear plot with the same initial conditions given above, and optimising this value to give constant distances. Due to the gradient of potential energy at the transition state being zero, the system has no kinetic energy, only potential energy. Therefore, there is no oscillation and the plot of internuclear distance against time shows constant interatomic distances.

[[File:Sly_Q2.png|thumb|upright=0.80|centre|Figure 2 - Internucleur Distance]]

== Q3 - MEP ==

The MEP is the minimum energy pathway followed for the reaction H2 + H to take place, although it can be seen in figures 4 and 5 that it differs from the dynamic trajectory due to the masses of the atoms, and therefore the bond oscillations along the trajectory causing deviations from the mep. This is shown by the wavy black line on figure 5. Both figures illustrate the reaction path (represented by the black line) starting at the transition state point, with the dynamic reaction going to the complete formation of a H2 product, while the mep plot shows it going only slightly towards the product formation.

'''change with + - 0.01 and discuss'''

[[File:Sly_MEP2.png|thumb|upright=0.80|centre|Figure 4 - Minimum Energy Pathway]] [[File:newdynamicsam.png|thumb|upright=0.80|centre|Figure 5 - Dynamic Trajectory]]

== Q4 - Reactive and Unreactive Trajectories==

{| class="wikitable" border=1
! p1 !! p2 !! Total Energy !! Reactive or Unreactive !! Trajectory Plot !! Discussion
|-
| -1.25 || -2.5 || -99.018 || [[File:SY-1.png|frameless|upright=0.80]] || Reactive || The reactivity of the trajectory is shown as the reaction path progresses towards the prodcut H2. Upon forming, the new bond vibrates.
|-
| -1.5 || -2.0 || -100.456 || [[File:SY-2.png|frameless|upright=0.80]] || Unreactive || This figure represents an unreactive system due to the approaching H atom not having enough energy to overcome the activation barrier for the reaction. This results in the reaction trajectory returning to the original H2 bond oscillating back towards its energy minimum.
|-
| -1.5 || -2.5 || -98.956 || [[File:SY-3.png|frameless|upright=0.80]] || Reactive || This model shows a very simimlar picture to the first in the table, although due to p1 being slightly higher, the original H2 bond oscillates with higher energy.
|-
| -2.5 || -5.0 || -84.956 || [[File:SLY4.png|frameless|upright=0.80]] || Unreactive || Here one H atom aproaches the H2 molecule and the transition state complex H-H-H forms, however due to a lack of energy, the trajectory path is unable to continue to form the products so returns to the original reactants.
|-
| -2.5 || -5.2 || -83.416 ||[[File:SY5.png|frameless|upright=0.80]] || Reactive || The case has a high enough energy to form the transition state complex and to continue to overcome the energy barrier to obtain the products.
|}

== Q5 - Transition State Theory ==

Transition state theory focusses on the activated complexes formed at a transition state of the reaction, therefore by examining the transition state of a potential surface plot (found at the saddle point) one can obtain the rate of a reaction, due to the activated complex's quasi-equilibrium with the reactants. It assumes that if the collision is of sufficient energy to overcome the transition state, the products will form. This is based on the assumption that molecules react according to the classical picture, and does not take quantum mechanics into account, leading to limitations when considering phenomena such as tunnelling, whereby the reaction path bypasses a low activation energy. Furthermore the transition state theory does not account for reactions recrossing the activation barrier to return to the products as shown above. As a result, this theory would give a higher rate to the real situation, where the product can recross the transition state to return to the reactant (as shown in Part 2 Q5).

= F H H System =

== Q1 - Energetics ==

F + H2
This reaction is shown to be exothermic (i.e. the system releases energy upon reacting, ΔH < 0) from the plot due to the energy minimum of the FH bond being lower in energy than the HH bond, therefore more stable. This is due to the large electronegativity difference between F (3.98) and H (2.20), as opposed to the non polar HH bond. As a result, the reaction of FH + H is therefore endothermic for the same reasons, due to the FH bond dissociation energy being larger than the HH bond formation enthalpy.

[[File:SLYFH.png|thumb|upright=0.80|centre|Figure 6]]

== Q2 - Position of the Transition State ==

The transition state can be found at the point where the internuclear distances of the atoms does not change over time. This is the same point on the graph for both the forward and reverse reactions. By using Hammond's postulate, that the activated intermediate complex at the transition state should resemble the state that it is closest in energy to, therefore similar to an HF + H model. As a result, it was possible to look at the surface plot and optimise the bond distances around where the transition state was roughly located. It was found that the approximate internuclear distances at this transition state are H-F : 1.810 and H-H : 0.746.

[[File:tshighlight.png|thumb|none|Figure 7]] [[File:transstatesly.png|thumb|upright=0.80|none|Figure 8]]

== Q3 - Activation Energy ==

By finding the equilibrium bond length of both reactants and products, and knowing the location of the transition state, it was possible to obtain energies for all of these positions, and therefore calculate the energy of activation.

Energy at HF minimum -133.586 AB 2.3 BC 0.9

Energy at HH minimum -103.33 AB 0.7 BC 2.3

Energy at transition state -103.742 AB 0.75 BC 1.81

ΔE = E(transition state) - E(reactants)

''ΔEFH + H‡ = (-103.742) - (-133.586) = 29.844 Kcalmol-1''

''ΔEH2 + F‡ = (-103.742) - (-103.330) = 0.412 Kcalmol-1''

== Q4 - Mechanism of Release of the Activation Energy ==

F + H2

This plot shows the reaction of initial conditions FH distance = 2.0Å HH distance = 0.74Å FH momentm = -0.5 HH momentum = -2.0, resulting in a successful reaction. Due to the exothermic nature of this reaction, it releases energy as the products have a lower potential energy than the reactants, and from the plot of internuclear distance vs. time, it is clear that this energy is converted to kinetic energy in the form of an oscillating F-H bond, which oscillates at a much higher energy than the original H-H bond. This could be confirmed experimentally by IR which would show the vibrationally excited state of the H-F bond, or energy can be measured by calorimetry.

[[File:samlyoungvibvib.png|thumb|upright=0.80|centre|Figure 9 - Internuclear Momenta vs Time plot]]

== Q5 - Efficiency of Reaction ==

Figures 10-14 clearly show the effect of varying the translaitonal and vibrational contributions to the reaction trajectory of both the endothermic and exothermic reactions. For the exothermic F + H2 reaction, the momentum of the translaitonal approach of the F atom was kept constant while the momentum of the H-H oscillation was varied between 3kgms-1 and -3kgms-1. The result clearly shows that for this early transition state reaction, a higher vibration energy causes the reaction path to overcome the transition state but it recrosses this barrier to return to the initial state due to too much energy. The limit (to 2 d.p.)of the vibrational energy was found to be -2.49kgms-1 in order for the reaction to be successful. A higher energy would cause the recrossing.
This case is the opposite for the endothermic reaction, with a late transition state, whereby if the translational energy is too high the reaction will cross then recross the transition state to return to the products, resulting in an unsuccessful reaction. The limit of translational energy for this reaction was found to be -0.61kgms-1.

To conclude, the success of an early transition state reaction depends on the vibrational energy, while the success of the late transition state depends on the translational energy, with both rebounding back to reactants with of the energy is too high because it still has enough energy to overcome the reverse reaction due to it being energetically excited.

{| class="wikitable" border=1
! !! !!
|-
| [[File:fh2highvibworks.png|thumb|upright=0.80|centre|Figure 10 - Reaction of H2 + F (H-H = 0.74Å, H-F = 2.Å, pHH = -3.0kgms-1, pHF = -0.5kgms-1)]] || [[File:lowvibsamyoung.png|thumb|upright=0.80|centre|Figure 11 - Reaction of H2 + F (H-H = 0.74Å, H-F = 2.0Å, pHH = -0.5kgms-1, pHF = -0.5kgms-1)]] || [[File:samlyounglimit2.png|thumb|upright=0.80|centre|Figure 12 - Reaction of H2 + F (H-H = 0.74Å, H-F = 2.0Å, pHH = -2.49kgms-1, pHF = -0.5kgms-1)]]
|-
| [[File:fhhidealsly.png|thumb|upright=0.80|centre|Figure 13 - Reaction of H2 + F (H-H = 2Å, H-F = 0.74Å, pHH = -0.61kgms-1, pHF = -0.5kgms-1)]] || [[File:slylowtrans.png|thumb|upright=0.80|centre|Figure 13 - Reaction of H2 + F (H-H = 2Å, H-F = 0.74Å, pHH = -0.1kgms-1, pHF = -0.5kgms-1)]]|| [[File:translationalsamsam.png|thumb|upright=0.80|centre|Figure 14 - Reaction of H2 + F (H-H = 2Å, H-F = 0.74Å, pHH = -3.0kgms-1, pHF = -0.5kgms-1)]]

|}

= Bibliography =

Electronegativity values : https://sciencenotes.org/list-of-electronegativity-values-of-the-elements/

Physical Chemistry, Ninth Edition, Peter Atkins & Julio De Paula , Oxford University Press

File:Samlyoungvibvib.png

2018-05-18T14:23:11Z

Sly116:

Sam Young Reaction Dynamics

2018-05-18T14:23:01Z

Sly116: /* Q4 - Mechanism of Release of the Activation Energy */

= H + H2 System =
== Q1 - Transition State Gradients ==
[[File:Sly-Saddle.png|thumb|upright=0.8|centre|Figure 1 - Potential Energy Surface Plot of H2 + H System, with initial conditions A-B distance = 0.74, B-C distance = 2.30, AB momentum = 0 & BC momentum = 2.7]]

The minimum energy surface, shown running along the bottom of figure one obeys the derivative; ∂V/∂(rx) = ∂V/∂(ry) = 0, with rx and ry run parallel to their respective gradients. However, the saddle point where the transition state lies is located along the minimum energy surface at the maximum point. Therefore, it can be found by taking the second derivative, as the two orthogonal gradients have different signs, with one along the potential energy minimum being negative and the other orthogonal graident being positive.

∂2V/∂(rx)2 > 0

∂2V/∂(ry)2 < 0

== Q2 - Transition State Estimate ==

By making the momentum of the whole system equal to zero, it was possible to put the AB distance = BC distance and alter this value to obtain a result for the rts, which was found to be approximately 0.9077Å (one value due to the system being completely symmetric), which gave figure 2. This number was found by taking the intersect of the AB and BC lines from the internuclear plot with the same initial conditions given above, and optimising this value to give constant distances. Due to the gradient of potential energy at the transition state being zero, the system has no kinetic energy, only potential energy. Therefore, there is no oscillation and the plot of internuclear distance against time shows constant interatomic distances.

[[File:Sly_Q2.png|thumb|upright=0.80|centre|Figure 2 - Internucleur Distance]]

== Q3 - MEP ==

The MEP is the minimum energy pathway followed for the reaction H2 + H to take place, although it can be seen in figures 4 and 5 that it differs from the dynamic trajectory due to the masses of the atoms, and therefore the bond oscillations along the trajectory causing deviations from the mep. This is shown by the wavy black line on figure 5. Both figures illustrate the reaction path (represented by the black line) starting at the transition state point, with the dynamic reaction going to the complete formation of a H2 product, while the mep plot shows it going only slightly towards the product formation.

'''change with + - 0.01 and discuss'''

[[File:Sly_MEP2.png|thumb|upright=0.80|centre|Figure 4 - Minimum Energy Pathway]] [[File:newdynamicsam.png|thumb|upright=0.80|centre|Figure 5 - Dynamic Trajectory]]

== Q4 - Reactive and Unreactive Trajectories==

{| class="wikitable" border=1
! p1 !! p2 !! Total Energy !! Reactive or Unreactive !! Trajectory Plot !! Discussion
|-
| -1.25 || -2.5 || -99.018 || [[File:SY-1.png|frameless|upright=0.80]] || Reactive || The reactivity of the trajectory is shown as the reaction path progresses towards the prodcut H2. Upon forming, the new bond vibrates.
|-
| -1.5 || -2.0 || -100.456 || [[File:SY-2.png|frameless|upright=0.80]] || Unreactive || This figure represents an unreactive system due to the approaching H atom not having enough energy to overcome the activation barrier for the reaction. This results in the reaction trajectory returning to the original H2 bond oscillating back towards its energy minimum.
|-
| -1.5 || -2.5 || -98.956 || [[File:SY-3.png|frameless|upright=0.80]] || Reactive || This model shows a very simimlar picture to the first in the table, although due to p1 being slightly higher, the original H2 bond oscillates with higher energy.
|-
| -2.5 || -5.0 || -84.956 || [[File:SLY4.png|frameless|upright=0.80]] || Unreactive || Here one H atom aproaches the H2 molecule and the transition state complex H-H-H forms, however due to a lack of energy, the trajectory path is unable to continue to form the products so returns to the original reactants.
|-
| -2.5 || -5.2 || -83.416 ||[[File:SY5.png|frameless|upright=0.80]] || Reactive || The case has a high enough energy to form the transition state complex and to continue to overcome the energy barrier to obtain the products.
|}

== Q5 - Transition State Theory ==

Transition state theory focusses on the activated complexes formed at a transition state of the reaction, therefore by examining the transition state of a potential surface plot (found at the saddle point) one can obtain the rate of a reaction, due to the activated complex's quasi-equilibrium with the reactants. It assumes that if the collision is of sufficient energy to overcome the transition state, the products will form. This is based on the assumption that molecules react according to the classical picture, and does not take quantum mechanics into account, leading to limitations when considering phenomena such as tunnelling, whereby the reaction path bypasses a low activation energy. Furthermore the transition state theory does not account for reactions recrossing the activation barrier to return to the products as shown above. As a result, this theory would give a higher rate to the real situation, where the product can recross the transition state to return to the reactant (as shown in Part 2 Q5).

= F H H System =

== Q1 - Energetics ==

F + H2
This reaction is shown to be exothermic (i.e. the system releases energy upon reacting, ΔH < 0) from the plot due to the energy minimum of the FH bond being lower in energy than the HH bond, therefore more stable. This is due to the large electronegativity difference between F (3.98) and H (2.20), as opposed to the non polar HH bond. As a result, the reaction of FH + H is therefore endothermic for the same reasons, due to the FH bond dissociation energy being larger than the HH bond formation enthalpy.

[[File:SLYFH.png|thumb|upright=0.80|centre|Figure 6]]

== Q2 - Position of the Transition State ==

The transition state can be found at the point where the internuclear distances of the atoms does not change over time. This is the same point on the graph for both the forward and reverse reactions. By using Hammond's postulate, that the activated intermediate complex at the transition state should resemble the state that it is closest in energy to, therefore similar to an HF + H model. As a result, it was possible to look at the surface plot and optimise the bond distances around where the transition state was roughly located. It was found that the approximate internuclear distances at this transition state are H-F : 1.810 and H-H : 0.746.

[[File:tshighlight.png|thumb|none|Figure 7]] [[File:transstatesly.png|thumb|upright=0.80|none|Figure 8]]

== Q3 - Activation Energy ==

By finding the equilibrium bond length of both reactants and products, and knowing the location of the transition state, it was possible to obtain energies for all of these positions, and therefore calculate the energy of activation.

Energy at HF minimum -133.586 AB 2.3 BC 0.9

Energy at HH minimum -103.33 AB 0.7 BC 2.3

Energy at transition state -103.742 AB 0.75 BC 1.81

ΔE = E(transition state) - E(reactants)

''ΔEFH + H‡ = (-103.742) - (-133.586) = 29.844 Kcalmol-1''

''ΔEH2 + F‡ = (-103.742) - (-103.330) = 0.412 Kcalmol-1''

== Q4 - Mechanism of Release of the Activation Energy ==

F + H2

This plot shows the reaction of initial conditions FH distance = 2.30Å HH distance = 0.85Å FH momentm = -7.0 HH momentum = -1.0, resulting in a successful reaction. Due to the exothermic nature of this reaction, it releases energy as the products have a lower potential energy than the reactants, and from the plot of internuclear distance vs. time, it is clear that this energy is converted to kinetic energy in the form of an oscillating F-H bond, which oscillates at a much higher energy than the original H-H bond. This could be confirmed experimentally by IR which would show the vibrationally excited state of the H-F bond, or energy can be measured by calorimetry.

[[File:vibratingsam.png|thumb|upright=0.80|centre|Figure 9]]
[[File:samlyoungvibvib.png]]

== Q5 - Efficiency of Reaction ==

Figures 10-14 clearly show the effect of varying the translaitonal and vibrational contributions to the reaction trajectory of both the endothermic and exothermic reactions. For the exothermic F + H2 reaction, the momentum of the translaitonal approach of the F atom was kept constant while the momentum of the H-H oscillation was varied between 3kgms-1 and -3kgms-1. The result clearly shows that for this early transition state reaction, a higher vibration energy causes the reaction path to overcome the transition state but it recrosses this barrier to return to the initial state due to too much energy. The limit (to 2 d.p.)of the vibrational energy was found to be -2.49kgms-1 in order for the reaction to be successful. A higher energy would cause the recrossing.
This case is the opposite for the endothermic reaction, with a late transition state, whereby if the translational energy is too high the reaction will cross then recross the transition state to return to the products, resulting in an unsuccessful reaction. The limit of translational energy for this reaction was found to be -0.61kgms-1.

To conclude, the success of an early transition state reaction depends on the vibrational energy, while the success of the late transition state depends on the translational energy, with both rebounding back to reactants with of the energy is too high because it still has enough energy to overcome the reverse reaction due to it being energetically excited.

{| class="wikitable" border=1
! !! !!
|-
| [[File:fh2highvibworks.png|thumb|upright=0.80|centre|Figure 10 - Reaction of H2 + F (H-H = 0.74Å, H-F = 2.Å, pHH = -3.0kgms-1, pHF = -0.5kgms-1)]] || [[File:lowvibsamyoung.png|thumb|upright=0.80|centre|Figure 11 - Reaction of H2 + F (H-H = 0.74Å, H-F = 2.0Å, pHH = -0.5kgms-1, pHF = -0.5kgms-1)]] || [[File:samlyounglimit2.png|thumb|upright=0.80|centre|Figure 12 - Reaction of H2 + F (H-H = 0.74Å, H-F = 2.0Å, pHH = -2.49kgms-1, pHF = -0.5kgms-1)]]
|-
| [[File:fhhidealsly.png|thumb|upright=0.80|centre|Figure 13 - Reaction of H2 + F (H-H = 2Å, H-F = 0.74Å, pHH = -0.61kgms-1, pHF = -0.5kgms-1)]] || [[File:slylowtrans.png|thumb|upright=0.80|centre|Figure 13 - Reaction of H2 + F (H-H = 2Å, H-F = 0.74Å, pHH = -0.1kgms-1, pHF = -0.5kgms-1)]]|| [[File:translationalsamsam.png|thumb|upright=0.80|centre|Figure 14 - Reaction of H2 + F (H-H = 2Å, H-F = 0.74Å, pHH = -3.0kgms-1, pHF = -0.5kgms-1)]]

|}

= Bibliography =

Electronegativity values : https://sciencenotes.org/list-of-electronegativity-values-of-the-elements/

Physical Chemistry, Ninth Edition, Peter Atkins & Julio De Paula , Oxford University Press

File:Vibratingsam.png

2018-05-18T14:22:18Z

Sly116:

Sam Young Reaction Dynamics

2018-05-18T14:22:07Z

Sly116: /* Q4 - Mechanism of Release of the Activation Energy */

= H + H2 System =
== Q1 - Transition State Gradients ==
[[File:Sly-Saddle.png|thumb|upright=0.8|centre|Figure 1 - Potential Energy Surface Plot of H2 + H System, with initial conditions A-B distance = 0.74, B-C distance = 2.30, AB momentum = 0 & BC momentum = 2.7]]

The minimum energy surface, shown running along the bottom of figure one obeys the derivative; ∂V/∂(rx) = ∂V/∂(ry) = 0, with rx and ry run parallel to their respective gradients. However, the saddle point where the transition state lies is located along the minimum energy surface at the maximum point. Therefore, it can be found by taking the second derivative, as the two orthogonal gradients have different signs, with one along the potential energy minimum being negative and the other orthogonal graident being positive.

∂2V/∂(rx)2 > 0

∂2V/∂(ry)2 < 0

== Q2 - Transition State Estimate ==

By making the momentum of the whole system equal to zero, it was possible to put the AB distance = BC distance and alter this value to obtain a result for the rts, which was found to be approximately 0.9077Å (one value due to the system being completely symmetric), which gave figure 2. This number was found by taking the intersect of the AB and BC lines from the internuclear plot with the same initial conditions given above, and optimising this value to give constant distances. Due to the gradient of potential energy at the transition state being zero, the system has no kinetic energy, only potential energy. Therefore, there is no oscillation and the plot of internuclear distance against time shows constant interatomic distances.

[[File:Sly_Q2.png|thumb|upright=0.80|centre|Figure 2 - Internucleur Distance]]

== Q3 - MEP ==

The MEP is the minimum energy pathway followed for the reaction H2 + H to take place, although it can be seen in figures 4 and 5 that it differs from the dynamic trajectory due to the masses of the atoms, and therefore the bond oscillations along the trajectory causing deviations from the mep. This is shown by the wavy black line on figure 5. Both figures illustrate the reaction path (represented by the black line) starting at the transition state point, with the dynamic reaction going to the complete formation of a H2 product, while the mep plot shows it going only slightly towards the product formation.

'''change with + - 0.01 and discuss'''

[[File:Sly_MEP2.png|thumb|upright=0.80|centre|Figure 4 - Minimum Energy Pathway]] [[File:newdynamicsam.png|thumb|upright=0.80|centre|Figure 5 - Dynamic Trajectory]]

== Q4 - Reactive and Unreactive Trajectories==

{| class="wikitable" border=1
! p1 !! p2 !! Total Energy !! Reactive or Unreactive !! Trajectory Plot !! Discussion
|-
| -1.25 || -2.5 || -99.018 || [[File:SY-1.png|frameless|upright=0.80]] || Reactive || The reactivity of the trajectory is shown as the reaction path progresses towards the prodcut H2. Upon forming, the new bond vibrates.
|-
| -1.5 || -2.0 || -100.456 || [[File:SY-2.png|frameless|upright=0.80]] || Unreactive || This figure represents an unreactive system due to the approaching H atom not having enough energy to overcome the activation barrier for the reaction. This results in the reaction trajectory returning to the original H2 bond oscillating back towards its energy minimum.
|-
| -1.5 || -2.5 || -98.956 || [[File:SY-3.png|frameless|upright=0.80]] || Reactive || This model shows a very simimlar picture to the first in the table, although due to p1 being slightly higher, the original H2 bond oscillates with higher energy.
|-
| -2.5 || -5.0 || -84.956 || [[File:SLY4.png|frameless|upright=0.80]] || Unreactive || Here one H atom aproaches the H2 molecule and the transition state complex H-H-H forms, however due to a lack of energy, the trajectory path is unable to continue to form the products so returns to the original reactants.
|-
| -2.5 || -5.2 || -83.416 ||[[File:SY5.png|frameless|upright=0.80]] || Reactive || The case has a high enough energy to form the transition state complex and to continue to overcome the energy barrier to obtain the products.
|}

== Q5 - Transition State Theory ==

Transition state theory focusses on the activated complexes formed at a transition state of the reaction, therefore by examining the transition state of a potential surface plot (found at the saddle point) one can obtain the rate of a reaction, due to the activated complex's quasi-equilibrium with the reactants. It assumes that if the collision is of sufficient energy to overcome the transition state, the products will form. This is based on the assumption that molecules react according to the classical picture, and does not take quantum mechanics into account, leading to limitations when considering phenomena such as tunnelling, whereby the reaction path bypasses a low activation energy. Furthermore the transition state theory does not account for reactions recrossing the activation barrier to return to the products as shown above. As a result, this theory would give a higher rate to the real situation, where the product can recross the transition state to return to the reactant (as shown in Part 2 Q5).

= F H H System =

== Q1 - Energetics ==

F + H2
This reaction is shown to be exothermic (i.e. the system releases energy upon reacting, ΔH < 0) from the plot due to the energy minimum of the FH bond being lower in energy than the HH bond, therefore more stable. This is due to the large electronegativity difference between F (3.98) and H (2.20), as opposed to the non polar HH bond. As a result, the reaction of FH + H is therefore endothermic for the same reasons, due to the FH bond dissociation energy being larger than the HH bond formation enthalpy.

[[File:SLYFH.png|thumb|upright=0.80|centre|Figure 6]]

== Q2 - Position of the Transition State ==

The transition state can be found at the point where the internuclear distances of the atoms does not change over time. This is the same point on the graph for both the forward and reverse reactions. By using Hammond's postulate, that the activated intermediate complex at the transition state should resemble the state that it is closest in energy to, therefore similar to an HF + H model. As a result, it was possible to look at the surface plot and optimise the bond distances around where the transition state was roughly located. It was found that the approximate internuclear distances at this transition state are H-F : 1.810 and H-H : 0.746.

[[File:tshighlight.png|thumb|none|Figure 7]] [[File:transstatesly.png|thumb|upright=0.80|none|Figure 8]]

== Q3 - Activation Energy ==

By finding the equilibrium bond length of both reactants and products, and knowing the location of the transition state, it was possible to obtain energies for all of these positions, and therefore calculate the energy of activation.

Energy at HF minimum -133.586 AB 2.3 BC 0.9

Energy at HH minimum -103.33 AB 0.7 BC 2.3

Energy at transition state -103.742 AB 0.75 BC 1.81

ΔE = E(transition state) - E(reactants)

''ΔEFH + H‡ = (-103.742) - (-133.586) = 29.844 Kcalmol-1''

''ΔEH2 + F‡ = (-103.742) - (-103.330) = 0.412 Kcalmol-1''

== Q4 - Mechanism of Release of the Activation Energy ==

F + H2

This plot shows the reaction of initial conditions FH distance = 2.30Å HH distance = 0.85Å FH momentm = -7.0 HH momentum = -1.0, resulting in a successful reaction. Due to the exothermic nature of this reaction, it releases energy as the products have a lower potential energy than the reactants, and from the plot of internuclear distance vs. time, it is clear that this energy is converted to kinetic energy in the form of an oscillating F-H bond, which oscillates at a much higher energy than the original H-H bond. This could be confirmed experimentally by IR which would show the vibrationally excited state of the H-F bond, or energy can be measured by calorimetry.

[[File:vibratingsam.png|thumb|upright=0.80|centre|Figure 9]]

== Q5 - Efficiency of Reaction ==

Figures 10-14 clearly show the effect of varying the translaitonal and vibrational contributions to the reaction trajectory of both the endothermic and exothermic reactions. For the exothermic F + H2 reaction, the momentum of the translaitonal approach of the F atom was kept constant while the momentum of the H-H oscillation was varied between 3kgms-1 and -3kgms-1. The result clearly shows that for this early transition state reaction, a higher vibration energy causes the reaction path to overcome the transition state but it recrosses this barrier to return to the initial state due to too much energy. The limit (to 2 d.p.)of the vibrational energy was found to be -2.49kgms-1 in order for the reaction to be successful. A higher energy would cause the recrossing.
This case is the opposite for the endothermic reaction, with a late transition state, whereby if the translational energy is too high the reaction will cross then recross the transition state to return to the products, resulting in an unsuccessful reaction. The limit of translational energy for this reaction was found to be -0.61kgms-1.

To conclude, the success of an early transition state reaction depends on the vibrational energy, while the success of the late transition state depends on the translational energy, with both rebounding back to reactants with of the energy is too high because it still has enough energy to overcome the reverse reaction due to it being energetically excited.

{| class="wikitable" border=1
! !! !!
|-
| [[File:fh2highvibworks.png|thumb|upright=0.80|centre|Figure 10 - Reaction of H2 + F (H-H = 0.74Å, H-F = 2.Å, pHH = -3.0kgms-1, pHF = -0.5kgms-1)]] || [[File:lowvibsamyoung.png|thumb|upright=0.80|centre|Figure 11 - Reaction of H2 + F (H-H = 0.74Å, H-F = 2.0Å, pHH = -0.5kgms-1, pHF = -0.5kgms-1)]] || [[File:samlyounglimit2.png|thumb|upright=0.80|centre|Figure 12 - Reaction of H2 + F (H-H = 0.74Å, H-F = 2.0Å, pHH = -2.49kgms-1, pHF = -0.5kgms-1)]]
|-
| [[File:fhhidealsly.png|thumb|upright=0.80|centre|Figure 13 - Reaction of H2 + F (H-H = 2Å, H-F = 0.74Å, pHH = -0.61kgms-1, pHF = -0.5kgms-1)]] || [[File:slylowtrans.png|thumb|upright=0.80|centre|Figure 13 - Reaction of H2 + F (H-H = 2Å, H-F = 0.74Å, pHH = -0.1kgms-1, pHF = -0.5kgms-1)]]|| [[File:translationalsamsam.png|thumb|upright=0.80|centre|Figure 14 - Reaction of H2 + F (H-H = 2Å, H-F = 0.74Å, pHH = -3.0kgms-1, pHF = -0.5kgms-1)]]

|}

= Bibliography =

Electronegativity values : https://sciencenotes.org/list-of-electronegativity-values-of-the-elements/

Physical Chemistry, Ninth Edition, Peter Atkins & Julio De Paula , Oxford University Press

Sam Young Reaction Dynamics

2018-05-18T14:16:55Z

Sly116: /* Bibliography */

= H + H2 System =
== Q1 - Transition State Gradients ==
[[File:Sly-Saddle.png|thumb|upright=0.8|centre|Figure 1 - Potential Energy Surface Plot of H2 + H System, with initial conditions A-B distance = 0.74, B-C distance = 2.30, AB momentum = 0 & BC momentum = 2.7]]

The minimum energy surface, shown running along the bottom of figure one obeys the derivative; ∂V/∂(rx) = ∂V/∂(ry) = 0, with rx and ry run parallel to their respective gradients. However, the saddle point where the transition state lies is located along the minimum energy surface at the maximum point. Therefore, it can be found by taking the second derivative, as the two orthogonal gradients have different signs, with one along the potential energy minimum being negative and the other orthogonal graident being positive.

∂2V/∂(rx)2 > 0

∂2V/∂(ry)2 < 0

== Q2 - Transition State Estimate ==

By making the momentum of the whole system equal to zero, it was possible to put the AB distance = BC distance and alter this value to obtain a result for the rts, which was found to be approximately 0.9077Å (one value due to the system being completely symmetric), which gave figure 2. This number was found by taking the intersect of the AB and BC lines from the internuclear plot with the same initial conditions given above, and optimising this value to give constant distances. Due to the gradient of potential energy at the transition state being zero, the system has no kinetic energy, only potential energy. Therefore, there is no oscillation and the plot of internuclear distance against time shows constant interatomic distances.

[[File:Sly_Q2.png|thumb|upright=0.80|centre|Figure 2 - Internucleur Distance]]

== Q3 - MEP ==

The MEP is the minimum energy pathway followed for the reaction H2 + H to take place, although it can be seen in figures 4 and 5 that it differs from the dynamic trajectory due to the masses of the atoms, and therefore the bond oscillations along the trajectory causing deviations from the mep. This is shown by the wavy black line on figure 5. Both figures illustrate the reaction path (represented by the black line) starting at the transition state point, with the dynamic reaction going to the complete formation of a H2 product, while the mep plot shows it going only slightly towards the product formation.

'''change with + - 0.01 and discuss'''

[[File:Sly_MEP2.png|thumb|upright=0.80|centre|Figure 4 - Minimum Energy Pathway]] [[File:newdynamicsam.png|thumb|upright=0.80|centre|Figure 5 - Dynamic Trajectory]]

== Q4 - Reactive and Unreactive Trajectories==

{| class="wikitable" border=1
! p1 !! p2 !! Total Energy !! Reactive or Unreactive !! Trajectory Plot !! Discussion
|-
| -1.25 || -2.5 || -99.018 || [[File:SY-1.png|frameless|upright=0.80]] || Reactive || The reactivity of the trajectory is shown as the reaction path progresses towards the prodcut H2. Upon forming, the new bond vibrates.
|-
| -1.5 || -2.0 || -100.456 || [[File:SY-2.png|frameless|upright=0.80]] || Unreactive || This figure represents an unreactive system due to the approaching H atom not having enough energy to overcome the activation barrier for the reaction. This results in the reaction trajectory returning to the original H2 bond oscillating back towards its energy minimum.
|-
| -1.5 || -2.5 || -98.956 || [[File:SY-3.png|frameless|upright=0.80]] || Reactive || This model shows a very simimlar picture to the first in the table, although due to p1 being slightly higher, the original H2 bond oscillates with higher energy.
|-
| -2.5 || -5.0 || -84.956 || [[File:SLY4.png|frameless|upright=0.80]] || Unreactive || Here one H atom aproaches the H2 molecule and the transition state complex H-H-H forms, however due to a lack of energy, the trajectory path is unable to continue to form the products so returns to the original reactants.
|-
| -2.5 || -5.2 || -83.416 ||[[File:SY5.png|frameless|upright=0.80]] || Reactive || The case has a high enough energy to form the transition state complex and to continue to overcome the energy barrier to obtain the products.
|}

== Q5 - Transition State Theory ==

Transition state theory focusses on the activated complexes formed at a transition state of the reaction, therefore by examining the transition state of a potential surface plot (found at the saddle point) one can obtain the rate of a reaction, due to the activated complex's quasi-equilibrium with the reactants. It assumes that if the collision is of sufficient energy to overcome the transition state, the products will form. This is based on the assumption that molecules react according to the classical picture, and does not take quantum mechanics into account, leading to limitations when considering phenomena such as tunnelling, whereby the reaction path bypasses a low activation energy. Furthermore the transition state theory does not account for reactions recrossing the activation barrier to return to the products as shown above. As a result, this theory would give a higher rate to the real situation, where the product can recross the transition state to return to the reactant (as shown in Part 2 Q5).

= F H H System =

== Q1 - Energetics ==

F + H2
This reaction is shown to be exothermic (i.e. the system releases energy upon reacting, ΔH < 0) from the plot due to the energy minimum of the FH bond being lower in energy than the HH bond, therefore more stable. This is due to the large electronegativity difference between F (3.98) and H (2.20), as opposed to the non polar HH bond. As a result, the reaction of FH + H is therefore endothermic for the same reasons, due to the FH bond dissociation energy being larger than the HH bond formation enthalpy.

[[File:SLYFH.png|thumb|upright=0.80|centre|Figure 6]]

== Q2 - Position of the Transition State ==

The transition state can be found at the point where the internuclear distances of the atoms does not change over time. This is the same point on the graph for both the forward and reverse reactions. By using Hammond's postulate, that the activated intermediate complex at the transition state should resemble the state that it is closest in energy to, therefore similar to an HF + H model. As a result, it was possible to look at the surface plot and optimise the bond distances around where the transition state was roughly located. It was found that the approximate internuclear distances at this transition state are H-F : 1.810 and H-H : 0.746.

[[File:tshighlight.png|thumb|none|Figure 7]] [[File:transstatesly.png|thumb|upright=0.80|none|Figure 8]]

== Q3 - Activation Energy ==

By finding the equilibrium bond length of both reactants and products, and knowing the location of the transition state, it was possible to obtain energies for all of these positions, and therefore calculate the energy of activation.

Energy at HF minimum -133.586 AB 2.3 BC 0.9

Energy at HH minimum -103.33 AB 0.7 BC 2.3

Energy at transition state -103.742 AB 0.75 BC 1.81

ΔE = E(transition state) - E(reactants)

''ΔEFH + H‡ = (-103.742) - (-133.586) = 29.844 Kcalmol-1''

''ΔEH2 + F‡ = (-103.742) - (-103.330) = 0.412 Kcalmol-1''

== Q4 - Mechanism of Release of the Activation Energy ==

F + H2

This plot shows the reaction of initial conditions FH distance = 2.30Å HH distance = 0.85Å FH momentm = -7.0 HH momentum = -1.0, resulting in a successful reaction. Due to the exothermic nature of this reaction, it releases energy as the products have a lower potential energy than the reactants, and from the plot of internuclear distance vs. time, it is clear that this energy is converted to kinetic energy in the form of an oscillating F-H bond, which oscillates at a much higher energy than the original H-H bond. This could be confirmed experimentally by IR which would show the vibrationally excited state of the H-F bond, or energy can be measured by calorimetry.

[[File:slyreactive.png|thumb|upright=0.80|centre|Figure 9]]

== Q5 - Efficiency of Reaction ==

Figures 10-14 clearly show the effect of varying the translaitonal and vibrational contributions to the reaction trajectory of both the endothermic and exothermic reactions. For the exothermic F + H2 reaction, the momentum of the translaitonal approach of the F atom was kept constant while the momentum of the H-H oscillation was varied between 3kgms-1 and -3kgms-1. The result clearly shows that for this early transition state reaction, a higher vibration energy causes the reaction path to overcome the transition state but it recrosses this barrier to return to the initial state due to too much energy. The limit (to 2 d.p.)of the vibrational energy was found to be -2.49kgms-1 in order for the reaction to be successful. A higher energy would cause the recrossing.
This case is the opposite for the endothermic reaction, with a late transition state, whereby if the translational energy is too high the reaction will cross then recross the transition state to return to the products, resulting in an unsuccessful reaction. The limit of translational energy for this reaction was found to be -0.61kgms-1.

To conclude, the success of an early transition state reaction depends on the vibrational energy, while the success of the late transition state depends on the translational energy, with both rebounding back to reactants with of the energy is too high because it still has enough energy to overcome the reverse reaction due to it being energetically excited.

{| class="wikitable" border=1
! !! !!
|-
| [[File:fh2highvibworks.png|thumb|upright=0.80|centre|Figure 10 - Reaction of H2 + F (H-H = 0.74Å, H-F = 2.Å, pHH = -3.0kgms-1, pHF = -0.5kgms-1)]] || [[File:lowvibsamyoung.png|thumb|upright=0.80|centre|Figure 11 - Reaction of H2 + F (H-H = 0.74Å, H-F = 2.0Å, pHH = -0.5kgms-1, pHF = -0.5kgms-1)]] || [[File:samlyounglimit2.png|thumb|upright=0.80|centre|Figure 12 - Reaction of H2 + F (H-H = 0.74Å, H-F = 2.0Å, pHH = -2.49kgms-1, pHF = -0.5kgms-1)]]
|-
| [[File:fhhidealsly.png|thumb|upright=0.80|centre|Figure 13 - Reaction of H2 + F (H-H = 2Å, H-F = 0.74Å, pHH = -0.61kgms-1, pHF = -0.5kgms-1)]] || [[File:slylowtrans.png|thumb|upright=0.80|centre|Figure 13 - Reaction of H2 + F (H-H = 2Å, H-F = 0.74Å, pHH = -0.1kgms-1, pHF = -0.5kgms-1)]]|| [[File:translationalsamsam.png|thumb|upright=0.80|centre|Figure 14 - Reaction of H2 + F (H-H = 2Å, H-F = 0.74Å, pHH = -3.0kgms-1, pHF = -0.5kgms-1)]]

|}

= Bibliography =

Electronegativity values : https://sciencenotes.org/list-of-electronegativity-values-of-the-elements/

Physical Chemistry, Ninth Edition, Peter Atkins & Julio De Paula , Oxford University Press

Sam Young Reaction Dynamics

2018-05-18T14:14:50Z

Sly116: /* Q5 - Transition State Theory */

= H + H2 System =
== Q1 - Transition State Gradients ==
[[File:Sly-Saddle.png|thumb|upright=0.8|centre|Figure 1 - Potential Energy Surface Plot of H2 + H System, with initial conditions A-B distance = 0.74, B-C distance = 2.30, AB momentum = 0 & BC momentum = 2.7]]

The minimum energy surface, shown running along the bottom of figure one obeys the derivative; ∂V/∂(rx) = ∂V/∂(ry) = 0, with rx and ry run parallel to their respective gradients. However, the saddle point where the transition state lies is located along the minimum energy surface at the maximum point. Therefore, it can be found by taking the second derivative, as the two orthogonal gradients have different signs, with one along the potential energy minimum being negative and the other orthogonal graident being positive.

∂2V/∂(rx)2 > 0

∂2V/∂(ry)2 < 0

== Q2 - Transition State Estimate ==

By making the momentum of the whole system equal to zero, it was possible to put the AB distance = BC distance and alter this value to obtain a result for the rts, which was found to be approximately 0.9077Å (one value due to the system being completely symmetric), which gave figure 2. This number was found by taking the intersect of the AB and BC lines from the internuclear plot with the same initial conditions given above, and optimising this value to give constant distances. Due to the gradient of potential energy at the transition state being zero, the system has no kinetic energy, only potential energy. Therefore, there is no oscillation and the plot of internuclear distance against time shows constant interatomic distances.

[[File:Sly_Q2.png|thumb|upright=0.80|centre|Figure 2 - Internucleur Distance]]

== Q3 - MEP ==

The MEP is the minimum energy pathway followed for the reaction H2 + H to take place, although it can be seen in figures 4 and 5 that it differs from the dynamic trajectory due to the masses of the atoms, and therefore the bond oscillations along the trajectory causing deviations from the mep. This is shown by the wavy black line on figure 5. Both figures illustrate the reaction path (represented by the black line) starting at the transition state point, with the dynamic reaction going to the complete formation of a H2 product, while the mep plot shows it going only slightly towards the product formation.

'''change with + - 0.01 and discuss'''

[[File:Sly_MEP2.png|thumb|upright=0.80|centre|Figure 4 - Minimum Energy Pathway]] [[File:newdynamicsam.png|thumb|upright=0.80|centre|Figure 5 - Dynamic Trajectory]]

== Q4 - Reactive and Unreactive Trajectories==

{| class="wikitable" border=1
! p1 !! p2 !! Total Energy !! Reactive or Unreactive !! Trajectory Plot !! Discussion
|-
| -1.25 || -2.5 || -99.018 || [[File:SY-1.png|frameless|upright=0.80]] || Reactive || The reactivity of the trajectory is shown as the reaction path progresses towards the prodcut H2. Upon forming, the new bond vibrates.
|-
| -1.5 || -2.0 || -100.456 || [[File:SY-2.png|frameless|upright=0.80]] || Unreactive || This figure represents an unreactive system due to the approaching H atom not having enough energy to overcome the activation barrier for the reaction. This results in the reaction trajectory returning to the original H2 bond oscillating back towards its energy minimum.
|-
| -1.5 || -2.5 || -98.956 || [[File:SY-3.png|frameless|upright=0.80]] || Reactive || This model shows a very simimlar picture to the first in the table, although due to p1 being slightly higher, the original H2 bond oscillates with higher energy.
|-
| -2.5 || -5.0 || -84.956 || [[File:SLY4.png|frameless|upright=0.80]] || Unreactive || Here one H atom aproaches the H2 molecule and the transition state complex H-H-H forms, however due to a lack of energy, the trajectory path is unable to continue to form the products so returns to the original reactants.
|-
| -2.5 || -5.2 || -83.416 ||[[File:SY5.png|frameless|upright=0.80]] || Reactive || The case has a high enough energy to form the transition state complex and to continue to overcome the energy barrier to obtain the products.
|}

== Q5 - Transition State Theory ==

Transition state theory focusses on the activated complexes formed at a transition state of the reaction, therefore by examining the transition state of a potential surface plot (found at the saddle point) one can obtain the rate of a reaction, due to the activated complex's quasi-equilibrium with the reactants. It assumes that if the collision is of sufficient energy to overcome the transition state, the products will form. This is based on the assumption that molecules react according to the classical picture, and does not take quantum mechanics into account, leading to limitations when considering phenomena such as tunnelling, whereby the reaction path bypasses a low activation energy. Furthermore the transition state theory does not account for reactions recrossing the activation barrier to return to the products as shown above. As a result, this theory would give a higher rate to the real situation, where the product can recross the transition state to return to the reactant (as shown in Part 2 Q5).

= F H H System =

== Q1 - Energetics ==

F + H2
This reaction is shown to be exothermic (i.e. the system releases energy upon reacting, ΔH < 0) from the plot due to the energy minimum of the FH bond being lower in energy than the HH bond, therefore more stable. This is due to the large electronegativity difference between F (3.98) and H (2.20), as opposed to the non polar HH bond. As a result, the reaction of FH + H is therefore endothermic for the same reasons, due to the FH bond dissociation energy being larger than the HH bond formation enthalpy.

[[File:SLYFH.png|thumb|upright=0.80|centre|Figure 6]]

== Q2 - Position of the Transition State ==

The transition state can be found at the point where the internuclear distances of the atoms does not change over time. This is the same point on the graph for both the forward and reverse reactions. By using Hammond's postulate, that the activated intermediate complex at the transition state should resemble the state that it is closest in energy to, therefore similar to an HF + H model. As a result, it was possible to look at the surface plot and optimise the bond distances around where the transition state was roughly located. It was found that the approximate internuclear distances at this transition state are H-F : 1.810 and H-H : 0.746.

[[File:tshighlight.png|thumb|none|Figure 7]] [[File:transstatesly.png|thumb|upright=0.80|none|Figure 8]]

== Q3 - Activation Energy ==

By finding the equilibrium bond length of both reactants and products, and knowing the location of the transition state, it was possible to obtain energies for all of these positions, and therefore calculate the energy of activation.

Energy at HF minimum -133.586 AB 2.3 BC 0.9

Energy at HH minimum -103.33 AB 0.7 BC 2.3

Energy at transition state -103.742 AB 0.75 BC 1.81

ΔE = E(transition state) - E(reactants)

''ΔEFH + H‡ = (-103.742) - (-133.586) = 29.844 Kcalmol-1''

''ΔEH2 + F‡ = (-103.742) - (-103.330) = 0.412 Kcalmol-1''

== Q4 - Mechanism of Release of the Activation Energy ==

F + H2

This plot shows the reaction of initial conditions FH distance = 2.30Å HH distance = 0.85Å FH momentm = -7.0 HH momentum = -1.0, resulting in a successful reaction. Due to the exothermic nature of this reaction, it releases energy as the products have a lower potential energy than the reactants, and from the plot of internuclear distance vs. time, it is clear that this energy is converted to kinetic energy in the form of an oscillating F-H bond, which oscillates at a much higher energy than the original H-H bond. This could be confirmed experimentally by IR which would show the vibrationally excited state of the H-F bond, or energy can be measured by calorimetry.

[[File:slyreactive.png|thumb|upright=0.80|centre|Figure 9]]

== Q5 - Efficiency of Reaction ==

Figures 10-14 clearly show the effect of varying the translaitonal and vibrational contributions to the reaction trajectory of both the endothermic and exothermic reactions. For the exothermic F + H2 reaction, the momentum of the translaitonal approach of the F atom was kept constant while the momentum of the H-H oscillation was varied between 3kgms-1 and -3kgms-1. The result clearly shows that for this early transition state reaction, a higher vibration energy causes the reaction path to overcome the transition state but it recrosses this barrier to return to the initial state due to too much energy. The limit (to 2 d.p.)of the vibrational energy was found to be -2.49kgms-1 in order for the reaction to be successful. A higher energy would cause the recrossing.
This case is the opposite for the endothermic reaction, with a late transition state, whereby if the translational energy is too high the reaction will cross then recross the transition state to return to the products, resulting in an unsuccessful reaction. The limit of translational energy for this reaction was found to be -0.61kgms-1.

To conclude, the success of an early transition state reaction depends on the vibrational energy, while the success of the late transition state depends on the translational energy, with both rebounding back to reactants with of the energy is too high because it still has enough energy to overcome the reverse reaction due to it being energetically excited.

{| class="wikitable" border=1
! !! !!
|-
| [[File:fh2highvibworks.png|thumb|upright=0.80|centre|Figure 10 - Reaction of H2 + F (H-H = 0.74Å, H-F = 2.Å, pHH = -3.0kgms-1, pHF = -0.5kgms-1)]] || [[File:lowvibsamyoung.png|thumb|upright=0.80|centre|Figure 11 - Reaction of H2 + F (H-H = 0.74Å, H-F = 2.0Å, pHH = -0.5kgms-1, pHF = -0.5kgms-1)]] || [[File:samlyounglimit2.png|thumb|upright=0.80|centre|Figure 12 - Reaction of H2 + F (H-H = 0.74Å, H-F = 2.0Å, pHH = -2.49kgms-1, pHF = -0.5kgms-1)]]
|-
| [[File:fhhidealsly.png|thumb|upright=0.80|centre|Figure 13 - Reaction of H2 + F (H-H = 2Å, H-F = 0.74Å, pHH = -0.61kgms-1, pHF = -0.5kgms-1)]] || [[File:slylowtrans.png|thumb|upright=0.80|centre|Figure 13 - Reaction of H2 + F (H-H = 2Å, H-F = 0.74Å, pHH = -0.1kgms-1, pHF = -0.5kgms-1)]]|| [[File:translationalsamsam.png|thumb|upright=0.80|centre|Figure 14 - Reaction of H2 + F (H-H = 2Å, H-F = 0.74Å, pHH = -3.0kgms-1, pHF = -0.5kgms-1)]]

|}

= Bibliography =

Electronegativity values : https://sciencenotes.org/list-of-electronegativity-values-of-the-elements/

Sam Young Reaction Dynamics

2018-05-18T14:12:57Z

Sly116: /* Q1 - Energetics */

= H + H2 System =
== Q1 - Transition State Gradients ==
[[File:Sly-Saddle.png|thumb|upright=0.8|centre|Figure 1 - Potential Energy Surface Plot of H2 + H System, with initial conditions A-B distance = 0.74, B-C distance = 2.30, AB momentum = 0 & BC momentum = 2.7]]

The minimum energy surface, shown running along the bottom of figure one obeys the derivative; ∂V/∂(rx) = ∂V/∂(ry) = 0, with rx and ry run parallel to their respective gradients. However, the saddle point where the transition state lies is located along the minimum energy surface at the maximum point. Therefore, it can be found by taking the second derivative, as the two orthogonal gradients have different signs, with one along the potential energy minimum being negative and the other orthogonal graident being positive.

∂2V/∂(rx)2 > 0

∂2V/∂(ry)2 < 0

== Q2 - Transition State Estimate ==

By making the momentum of the whole system equal to zero, it was possible to put the AB distance = BC distance and alter this value to obtain a result for the rts, which was found to be approximately 0.9077Å (one value due to the system being completely symmetric), which gave figure 2. This number was found by taking the intersect of the AB and BC lines from the internuclear plot with the same initial conditions given above, and optimising this value to give constant distances. Due to the gradient of potential energy at the transition state being zero, the system has no kinetic energy, only potential energy. Therefore, there is no oscillation and the plot of internuclear distance against time shows constant interatomic distances.

[[File:Sly_Q2.png|thumb|upright=0.80|centre|Figure 2 - Internucleur Distance]]

== Q3 - MEP ==

The MEP is the minimum energy pathway followed for the reaction H2 + H to take place, although it can be seen in figures 4 and 5 that it differs from the dynamic trajectory due to the masses of the atoms, and therefore the bond oscillations along the trajectory causing deviations from the mep. This is shown by the wavy black line on figure 5. Both figures illustrate the reaction path (represented by the black line) starting at the transition state point, with the dynamic reaction going to the complete formation of a H2 product, while the mep plot shows it going only slightly towards the product formation.

'''change with + - 0.01 and discuss'''

[[File:Sly_MEP2.png|thumb|upright=0.80|centre|Figure 4 - Minimum Energy Pathway]] [[File:newdynamicsam.png|thumb|upright=0.80|centre|Figure 5 - Dynamic Trajectory]]

== Q4 - Reactive and Unreactive Trajectories==

{| class="wikitable" border=1
! p1 !! p2 !! Total Energy !! Reactive or Unreactive !! Trajectory Plot !! Discussion
|-
| -1.25 || -2.5 || -99.018 || [[File:SY-1.png|frameless|upright=0.80]] || Reactive || The reactivity of the trajectory is shown as the reaction path progresses towards the prodcut H2. Upon forming, the new bond vibrates.
|-
| -1.5 || -2.0 || -100.456 || [[File:SY-2.png|frameless|upright=0.80]] || Unreactive || This figure represents an unreactive system due to the approaching H atom not having enough energy to overcome the activation barrier for the reaction. This results in the reaction trajectory returning to the original H2 bond oscillating back towards its energy minimum.
|-
| -1.5 || -2.5 || -98.956 || [[File:SY-3.png|frameless|upright=0.80]] || Reactive || This model shows a very simimlar picture to the first in the table, although due to p1 being slightly higher, the original H2 bond oscillates with higher energy.
|-
| -2.5 || -5.0 || -84.956 || [[File:SLY4.png|frameless|upright=0.80]] || Unreactive || Here one H atom aproaches the H2 molecule and the transition state complex H-H-H forms, however due to a lack of energy, the trajectory path is unable to continue to form the products so returns to the original reactants.
|-
| -2.5 || -5.2 || -83.416 ||[[File:SY5.png|frameless|upright=0.80]] || Reactive || The case has a high enough energy to form the transition state complex and to continue to overcome the energy barrier to obtain the products.
|}

== Q5 - Transition State Theory ==

Transition state theory focusses on the activated complexes formed at a transition state of the reaction, therefore by examining the transition state of a potential surface plot (found at the saddle point) one can obtain the rate of a reaction, due to the activated complex's quasi-equilibrium with the reactants. It assumes that if the collision is of sufficient energy to overcome the transition state, the products will form. This is based on the assumption that molecules react according to the classical picture, and does not take quantum mechanics into account, leading to limitations when considering phenomena such as tunnelling, whereby the reaction path bypasses a low activation energy. Furthermore the transition state theory does not account for reactions recrossing the activation barrier to return to the products as shown above. As a result, this theory would give a higher rate to the real situation.

= F H H System =

== Q1 - Energetics ==

F + H2
This reaction is shown to be exothermic (i.e. the system releases energy upon reacting, ΔH < 0) from the plot due to the energy minimum of the FH bond being lower in energy than the HH bond, therefore more stable. This is due to the large electronegativity difference between F (3.98) and H (2.20), as opposed to the non polar HH bond. As a result, the reaction of FH + H is therefore endothermic for the same reasons, due to the FH bond dissociation energy being larger than the HH bond formation enthalpy.

[[File:SLYFH.png|thumb|upright=0.80|centre|Figure 6]]

== Q2 - Position of the Transition State ==

The transition state can be found at the point where the internuclear distances of the atoms does not change over time. This is the same point on the graph for both the forward and reverse reactions. By using Hammond's postulate, that the activated intermediate complex at the transition state should resemble the state that it is closest in energy to, therefore similar to an HF + H model. As a result, it was possible to look at the surface plot and optimise the bond distances around where the transition state was roughly located. It was found that the approximate internuclear distances at this transition state are H-F : 1.810 and H-H : 0.746.

[[File:tshighlight.png|thumb|none|Figure 7]] [[File:transstatesly.png|thumb|upright=0.80|none|Figure 8]]

== Q3 - Activation Energy ==

By finding the equilibrium bond length of both reactants and products, and knowing the location of the transition state, it was possible to obtain energies for all of these positions, and therefore calculate the energy of activation.

Energy at HF minimum -133.586 AB 2.3 BC 0.9

Energy at HH minimum -103.33 AB 0.7 BC 2.3

Energy at transition state -103.742 AB 0.75 BC 1.81

ΔE = E(transition state) - E(reactants)

''ΔEFH + H‡ = (-103.742) - (-133.586) = 29.844 Kcalmol-1''

''ΔEH2 + F‡ = (-103.742) - (-103.330) = 0.412 Kcalmol-1''

== Q4 - Mechanism of Release of the Activation Energy ==

F + H2

This plot shows the reaction of initial conditions FH distance = 2.30Å HH distance = 0.85Å FH momentm = -7.0 HH momentum = -1.0, resulting in a successful reaction. Due to the exothermic nature of this reaction, it releases energy as the products have a lower potential energy than the reactants, and from the plot of internuclear distance vs. time, it is clear that this energy is converted to kinetic energy in the form of an oscillating F-H bond, which oscillates at a much higher energy than the original H-H bond. This could be confirmed experimentally by IR which would show the vibrationally excited state of the H-F bond, or energy can be measured by calorimetry.

[[File:slyreactive.png|thumb|upright=0.80|centre|Figure 9]]

== Q5 - Efficiency of Reaction ==

Figures 10-14 clearly show the effect of varying the translaitonal and vibrational contributions to the reaction trajectory of both the endothermic and exothermic reactions. For the exothermic F + H2 reaction, the momentum of the translaitonal approach of the F atom was kept constant while the momentum of the H-H oscillation was varied between 3kgms-1 and -3kgms-1. The result clearly shows that for this early transition state reaction, a higher vibration energy causes the reaction path to overcome the transition state but it recrosses this barrier to return to the initial state due to too much energy. The limit (to 2 d.p.)of the vibrational energy was found to be -2.49kgms-1 in order for the reaction to be successful. A higher energy would cause the recrossing.
This case is the opposite for the endothermic reaction, with a late transition state, whereby if the translational energy is too high the reaction will cross then recross the transition state to return to the products, resulting in an unsuccessful reaction. The limit of translational energy for this reaction was found to be -0.61kgms-1.

To conclude, the success of an early transition state reaction depends on the vibrational energy, while the success of the late transition state depends on the translational energy, with both rebounding back to reactants with of the energy is too high because it still has enough energy to overcome the reverse reaction due to it being energetically excited.

{| class="wikitable" border=1
! !! !!
|-
| [[File:fh2highvibworks.png|thumb|upright=0.80|centre|Figure 10 - Reaction of H2 + F (H-H = 0.74Å, H-F = 2.Å, pHH = -3.0kgms-1, pHF = -0.5kgms-1)]] || [[File:lowvibsamyoung.png|thumb|upright=0.80|centre|Figure 11 - Reaction of H2 + F (H-H = 0.74Å, H-F = 2.0Å, pHH = -0.5kgms-1, pHF = -0.5kgms-1)]] || [[File:samlyounglimit2.png|thumb|upright=0.80|centre|Figure 12 - Reaction of H2 + F (H-H = 0.74Å, H-F = 2.0Å, pHH = -2.49kgms-1, pHF = -0.5kgms-1)]]
|-
| [[File:fhhidealsly.png|thumb|upright=0.80|centre|Figure 13 - Reaction of H2 + F (H-H = 2Å, H-F = 0.74Å, pHH = -0.61kgms-1, pHF = -0.5kgms-1)]] || [[File:slylowtrans.png|thumb|upright=0.80|centre|Figure 13 - Reaction of H2 + F (H-H = 2Å, H-F = 0.74Å, pHH = -0.1kgms-1, pHF = -0.5kgms-1)]]|| [[File:translationalsamsam.png|thumb|upright=0.80|centre|Figure 14 - Reaction of H2 + F (H-H = 2Å, H-F = 0.74Å, pHH = -3.0kgms-1, pHF = -0.5kgms-1)]]

|}

= Bibliography =

Electronegativity values : https://sciencenotes.org/list-of-electronegativity-values-of-the-elements/

Sam Young Reaction Dynamics

2018-05-18T14:12:11Z

Sly116: /* Q1 - Energetics */

= H + H2 System =
== Q1 - Transition State Gradients ==
[[File:Sly-Saddle.png|thumb|upright=0.8|centre|Figure 1 - Potential Energy Surface Plot of H2 + H System, with initial conditions A-B distance = 0.74, B-C distance = 2.30, AB momentum = 0 & BC momentum = 2.7]]

The minimum energy surface, shown running along the bottom of figure one obeys the derivative; ∂V/∂(rx) = ∂V/∂(ry) = 0, with rx and ry run parallel to their respective gradients. However, the saddle point where the transition state lies is located along the minimum energy surface at the maximum point. Therefore, it can be found by taking the second derivative, as the two orthogonal gradients have different signs, with one along the potential energy minimum being negative and the other orthogonal graident being positive.

∂2V/∂(rx)2 > 0

∂2V/∂(ry)2 < 0

== Q2 - Transition State Estimate ==

By making the momentum of the whole system equal to zero, it was possible to put the AB distance = BC distance and alter this value to obtain a result for the rts, which was found to be approximately 0.9077Å (one value due to the system being completely symmetric), which gave figure 2. This number was found by taking the intersect of the AB and BC lines from the internuclear plot with the same initial conditions given above, and optimising this value to give constant distances. Due to the gradient of potential energy at the transition state being zero, the system has no kinetic energy, only potential energy. Therefore, there is no oscillation and the plot of internuclear distance against time shows constant interatomic distances.

[[File:Sly_Q2.png|thumb|upright=0.80|centre|Figure 2 - Internucleur Distance]]

== Q3 - MEP ==

The MEP is the minimum energy pathway followed for the reaction H2 + H to take place, although it can be seen in figures 4 and 5 that it differs from the dynamic trajectory due to the masses of the atoms, and therefore the bond oscillations along the trajectory causing deviations from the mep. This is shown by the wavy black line on figure 5. Both figures illustrate the reaction path (represented by the black line) starting at the transition state point, with the dynamic reaction going to the complete formation of a H2 product, while the mep plot shows it going only slightly towards the product formation.

'''change with + - 0.01 and discuss'''

[[File:Sly_MEP2.png|thumb|upright=0.80|centre|Figure 4 - Minimum Energy Pathway]] [[File:newdynamicsam.png|thumb|upright=0.80|centre|Figure 5 - Dynamic Trajectory]]

== Q4 - Reactive and Unreactive Trajectories==

{| class="wikitable" border=1
! p1 !! p2 !! Total Energy !! Reactive or Unreactive !! Trajectory Plot !! Discussion
|-
| -1.25 || -2.5 || -99.018 || [[File:SY-1.png|frameless|upright=0.80]] || Reactive || The reactivity of the trajectory is shown as the reaction path progresses towards the prodcut H2. Upon forming, the new bond vibrates.
|-
| -1.5 || -2.0 || -100.456 || [[File:SY-2.png|frameless|upright=0.80]] || Unreactive || This figure represents an unreactive system due to the approaching H atom not having enough energy to overcome the activation barrier for the reaction. This results in the reaction trajectory returning to the original H2 bond oscillating back towards its energy minimum.
|-
| -1.5 || -2.5 || -98.956 || [[File:SY-3.png|frameless|upright=0.80]] || Reactive || This model shows a very simimlar picture to the first in the table, although due to p1 being slightly higher, the original H2 bond oscillates with higher energy.
|-
| -2.5 || -5.0 || -84.956 || [[File:SLY4.png|frameless|upright=0.80]] || Unreactive || Here one H atom aproaches the H2 molecule and the transition state complex H-H-H forms, however due to a lack of energy, the trajectory path is unable to continue to form the products so returns to the original reactants.
|-
| -2.5 || -5.2 || -83.416 ||[[File:SY5.png|frameless|upright=0.80]] || Reactive || The case has a high enough energy to form the transition state complex and to continue to overcome the energy barrier to obtain the products.
|}

== Q5 - Transition State Theory ==

Transition state theory focusses on the activated complexes formed at a transition state of the reaction, therefore by examining the transition state of a potential surface plot (found at the saddle point) one can obtain the rate of a reaction, due to the activated complex's quasi-equilibrium with the reactants. It assumes that if the collision is of sufficient energy to overcome the transition state, the products will form. This is based on the assumption that molecules react according to the classical picture, and does not take quantum mechanics into account, leading to limitations when considering phenomena such as tunnelling, whereby the reaction path bypasses a low activation energy. Furthermore the transition state theory does not account for reactions recrossing the activation barrier to return to the products as shown above. As a result, this theory would give a higher rate to the real situation.

= F H H System =

== Q1 - Energetics ==

F + H2
This reaction is shown to be exothermic (i.e. the system releases energy upon reacting, ΔH < 0) from the plot due to the energy minimum of the FH bond being lower in energy than the HH bond, therefore more stable. This is due to the large electronegativity difference between F (3.98) and H (2.20), as opposed to the non polar HH bond. As a result, the reaction of FH + H is therefore endothermic for the same reasons, due to the FH bond enthalpy

[[File:SLYFH.png|thumb|upright=0.80|centre|Figure 6]]

== Q2 - Position of the Transition State ==

The transition state can be found at the point where the internuclear distances of the atoms does not change over time. This is the same point on the graph for both the forward and reverse reactions. By using Hammond's postulate, that the activated intermediate complex at the transition state should resemble the state that it is closest in energy to, therefore similar to an HF + H model. As a result, it was possible to look at the surface plot and optimise the bond distances around where the transition state was roughly located. It was found that the approximate internuclear distances at this transition state are H-F : 1.810 and H-H : 0.746.

[[File:tshighlight.png|thumb|none|Figure 7]] [[File:transstatesly.png|thumb|upright=0.80|none|Figure 8]]

== Q3 - Activation Energy ==

By finding the equilibrium bond length of both reactants and products, and knowing the location of the transition state, it was possible to obtain energies for all of these positions, and therefore calculate the energy of activation.

Energy at HF minimum -133.586 AB 2.3 BC 0.9

Energy at HH minimum -103.33 AB 0.7 BC 2.3

Energy at transition state -103.742 AB 0.75 BC 1.81

ΔE = E(transition state) - E(reactants)

''ΔEFH + H‡ = (-103.742) - (-133.586) = 29.844 Kcalmol-1''

''ΔEH2 + F‡ = (-103.742) - (-103.330) = 0.412 Kcalmol-1''

== Q4 - Mechanism of Release of the Activation Energy ==

F + H2

This plot shows the reaction of initial conditions FH distance = 2.30Å HH distance = 0.85Å FH momentm = -7.0 HH momentum = -1.0, resulting in a successful reaction. Due to the exothermic nature of this reaction, it releases energy as the products have a lower potential energy than the reactants, and from the plot of internuclear distance vs. time, it is clear that this energy is converted to kinetic energy in the form of an oscillating F-H bond, which oscillates at a much higher energy than the original H-H bond. This could be confirmed experimentally by IR which would show the vibrationally excited state of the H-F bond, or energy can be measured by calorimetry.

[[File:slyreactive.png|thumb|upright=0.80|centre|Figure 9]]

== Q5 - Efficiency of Reaction ==

Figures 10-14 clearly show the effect of varying the translaitonal and vibrational contributions to the reaction trajectory of both the endothermic and exothermic reactions. For the exothermic F + H2 reaction, the momentum of the translaitonal approach of the F atom was kept constant while the momentum of the H-H oscillation was varied between 3kgms-1 and -3kgms-1. The result clearly shows that for this early transition state reaction, a higher vibration energy causes the reaction path to overcome the transition state but it recrosses this barrier to return to the initial state due to too much energy. The limit (to 2 d.p.)of the vibrational energy was found to be -2.49kgms-1 in order for the reaction to be successful. A higher energy would cause the recrossing.
This case is the opposite for the endothermic reaction, with a late transition state, whereby if the translational energy is too high the reaction will cross then recross the transition state to return to the products, resulting in an unsuccessful reaction. The limit of translational energy for this reaction was found to be -0.61kgms-1.

To conclude, the success of an early transition state reaction depends on the vibrational energy, while the success of the late transition state depends on the translational energy, with both rebounding back to reactants with of the energy is too high because it still has enough energy to overcome the reverse reaction due to it being energetically excited.

{| class="wikitable" border=1
! !! !!
|-
| [[File:fh2highvibworks.png|thumb|upright=0.80|centre|Figure 10 - Reaction of H2 + F (H-H = 0.74Å, H-F = 2.Å, pHH = -3.0kgms-1, pHF = -0.5kgms-1)]] || [[File:lowvibsamyoung.png|thumb|upright=0.80|centre|Figure 11 - Reaction of H2 + F (H-H = 0.74Å, H-F = 2.0Å, pHH = -0.5kgms-1, pHF = -0.5kgms-1)]] || [[File:samlyounglimit2.png|thumb|upright=0.80|centre|Figure 12 - Reaction of H2 + F (H-H = 0.74Å, H-F = 2.0Å, pHH = -2.49kgms-1, pHF = -0.5kgms-1)]]
|-
| [[File:fhhidealsly.png|thumb|upright=0.80|centre|Figure 13 - Reaction of H2 + F (H-H = 2Å, H-F = 0.74Å, pHH = -0.61kgms-1, pHF = -0.5kgms-1)]] || [[File:slylowtrans.png|thumb|upright=0.80|centre|Figure 13 - Reaction of H2 + F (H-H = 2Å, H-F = 0.74Å, pHH = -0.1kgms-1, pHF = -0.5kgms-1)]]|| [[File:translationalsamsam.png|thumb|upright=0.80|centre|Figure 14 - Reaction of H2 + F (H-H = 2Å, H-F = 0.74Å, pHH = -3.0kgms-1, pHF = -0.5kgms-1)]]

|}

= Bibliography =

Electronegativity values : https://sciencenotes.org/list-of-electronegativity-values-of-the-elements/

Sam Young Reaction Dynamics

2018-05-18T14:10:58Z

Sly116: /* Q5 - Efficiency of Reaction */

= H + H2 System =
== Q1 - Transition State Gradients ==
[[File:Sly-Saddle.png|thumb|upright=0.8|centre|Figure 1 - Potential Energy Surface Plot of H2 + H System, with initial conditions A-B distance = 0.74, B-C distance = 2.30, AB momentum = 0 & BC momentum = 2.7]]

The minimum energy surface, shown running along the bottom of figure one obeys the derivative; ∂V/∂(rx) = ∂V/∂(ry) = 0, with rx and ry run parallel to their respective gradients. However, the saddle point where the transition state lies is located along the minimum energy surface at the maximum point. Therefore, it can be found by taking the second derivative, as the two orthogonal gradients have different signs, with one along the potential energy minimum being negative and the other orthogonal graident being positive.

∂2V/∂(rx)2 > 0

∂2V/∂(ry)2 < 0

== Q2 - Transition State Estimate ==

By making the momentum of the whole system equal to zero, it was possible to put the AB distance = BC distance and alter this value to obtain a result for the rts, which was found to be approximately 0.9077Å (one value due to the system being completely symmetric), which gave figure 2. This number was found by taking the intersect of the AB and BC lines from the internuclear plot with the same initial conditions given above, and optimising this value to give constant distances. Due to the gradient of potential energy at the transition state being zero, the system has no kinetic energy, only potential energy. Therefore, there is no oscillation and the plot of internuclear distance against time shows constant interatomic distances.

[[File:Sly_Q2.png|thumb|upright=0.80|centre|Figure 2 - Internucleur Distance]]

== Q3 - MEP ==

The MEP is the minimum energy pathway followed for the reaction H2 + H to take place, although it can be seen in figures 4 and 5 that it differs from the dynamic trajectory due to the masses of the atoms, and therefore the bond oscillations along the trajectory causing deviations from the mep. This is shown by the wavy black line on figure 5. Both figures illustrate the reaction path (represented by the black line) starting at the transition state point, with the dynamic reaction going to the complete formation of a H2 product, while the mep plot shows it going only slightly towards the product formation.

'''change with + - 0.01 and discuss'''

[[File:Sly_MEP2.png|thumb|upright=0.80|centre|Figure 4 - Minimum Energy Pathway]] [[File:newdynamicsam.png|thumb|upright=0.80|centre|Figure 5 - Dynamic Trajectory]]

== Q4 - Reactive and Unreactive Trajectories==

{| class="wikitable" border=1
! p1 !! p2 !! Total Energy !! Reactive or Unreactive !! Trajectory Plot !! Discussion
|-
| -1.25 || -2.5 || -99.018 || [[File:SY-1.png|frameless|upright=0.80]] || Reactive || The reactivity of the trajectory is shown as the reaction path progresses towards the prodcut H2. Upon forming, the new bond vibrates.
|-
| -1.5 || -2.0 || -100.456 || [[File:SY-2.png|frameless|upright=0.80]] || Unreactive || This figure represents an unreactive system due to the approaching H atom not having enough energy to overcome the activation barrier for the reaction. This results in the reaction trajectory returning to the original H2 bond oscillating back towards its energy minimum.
|-
| -1.5 || -2.5 || -98.956 || [[File:SY-3.png|frameless|upright=0.80]] || Reactive || This model shows a very simimlar picture to the first in the table, although due to p1 being slightly higher, the original H2 bond oscillates with higher energy.
|-
| -2.5 || -5.0 || -84.956 || [[File:SLY4.png|frameless|upright=0.80]] || Unreactive || Here one H atom aproaches the H2 molecule and the transition state complex H-H-H forms, however due to a lack of energy, the trajectory path is unable to continue to form the products so returns to the original reactants.
|-
| -2.5 || -5.2 || -83.416 ||[[File:SY5.png|frameless|upright=0.80]] || Reactive || The case has a high enough energy to form the transition state complex and to continue to overcome the energy barrier to obtain the products.
|}

== Q5 - Transition State Theory ==

Transition state theory focusses on the activated complexes formed at a transition state of the reaction, therefore by examining the transition state of a potential surface plot (found at the saddle point) one can obtain the rate of a reaction, due to the activated complex's quasi-equilibrium with the reactants. It assumes that if the collision is of sufficient energy to overcome the transition state, the products will form. This is based on the assumption that molecules react according to the classical picture, and does not take quantum mechanics into account, leading to limitations when considering phenomena such as tunnelling, whereby the reaction path bypasses a low activation energy. Furthermore the transition state theory does not account for reactions recrossing the activation barrier to return to the products as shown above. As a result, this theory would give a higher rate to the real situation.

= F H H System =

== Q1 - Energetics ==

F + H2
This reaction is shown to be exothermic (i.e. the system releases energy upon reacting, ΔH < 0) from the plot due to the energy minimum of the FH bond being lower in energy than the HH bond, therefore more stable. This is due to the large electronegativity difference between F (3.98) and H (2.20), as opposed to the non polar HH bond. As a result, the reaction of FH + H is therefore endothermic for the same reasons.

'''Talk about enthalpies of formation/dissociation'''

[[File:SLYFH.png|thumb|upright=0.80|centre|Figure 6]]

== Q2 - Position of the Transition State ==

The transition state can be found at the point where the internuclear distances of the atoms does not change over time. This is the same point on the graph for both the forward and reverse reactions. By using Hammond's postulate, that the activated intermediate complex at the transition state should resemble the state that it is closest in energy to, therefore similar to an HF + H model. As a result, it was possible to look at the surface plot and optimise the bond distances around where the transition state was roughly located. It was found that the approximate internuclear distances at this transition state are H-F : 1.810 and H-H : 0.746.

[[File:tshighlight.png|thumb|none|Figure 7]] [[File:transstatesly.png|thumb|upright=0.80|none|Figure 8]]

== Q3 - Activation Energy ==

By finding the equilibrium bond length of both reactants and products, and knowing the location of the transition state, it was possible to obtain energies for all of these positions, and therefore calculate the energy of activation.

Energy at HF minimum -133.586 AB 2.3 BC 0.9

Energy at HH minimum -103.33 AB 0.7 BC 2.3

Energy at transition state -103.742 AB 0.75 BC 1.81

ΔE = E(transition state) - E(reactants)

''ΔEFH + H‡ = (-103.742) - (-133.586) = 29.844 Kcalmol-1''

''ΔEH2 + F‡ = (-103.742) - (-103.330) = 0.412 Kcalmol-1''

== Q4 - Mechanism of Release of the Activation Energy ==

F + H2

This plot shows the reaction of initial conditions FH distance = 2.30Å HH distance = 0.85Å FH momentm = -7.0 HH momentum = -1.0, resulting in a successful reaction. Due to the exothermic nature of this reaction, it releases energy as the products have a lower potential energy than the reactants, and from the plot of internuclear distance vs. time, it is clear that this energy is converted to kinetic energy in the form of an oscillating F-H bond, which oscillates at a much higher energy than the original H-H bond. This could be confirmed experimentally by IR which would show the vibrationally excited state of the H-F bond, or energy can be measured by calorimetry.

[[File:slyreactive.png|thumb|upright=0.80|centre|Figure 9]]

== Q5 - Efficiency of Reaction ==

Figures 10-14 clearly show the effect of varying the translaitonal and vibrational contributions to the reaction trajectory of both the endothermic and exothermic reactions. For the exothermic F + H2 reaction, the momentum of the translaitonal approach of the F atom was kept constant while the momentum of the H-H oscillation was varied between 3kgms-1 and -3kgms-1. The result clearly shows that for this early transition state reaction, a higher vibration energy causes the reaction path to overcome the transition state but it recrosses this barrier to return to the initial state due to too much energy. The limit (to 2 d.p.)of the vibrational energy was found to be -2.49kgms-1 in order for the reaction to be successful. A higher energy would cause the recrossing.
This case is the opposite for the endothermic reaction, with a late transition state, whereby if the translational energy is too high the reaction will cross then recross the transition state to return to the products, resulting in an unsuccessful reaction. The limit of translational energy for this reaction was found to be -0.61kgms-1.

To conclude, the success of an early transition state reaction depends on the vibrational energy, while the success of the late transition state depends on the translational energy, with both rebounding back to reactants with of the energy is too high because it still has enough energy to overcome the reverse reaction due to it being energetically excited.

{| class="wikitable" border=1
! !! !!
|-
| [[File:fh2highvibworks.png|thumb|upright=0.80|centre|Figure 10 - Reaction of H2 + F (H-H = 0.74Å, H-F = 2.Å, pHH = -3.0kgms-1, pHF = -0.5kgms-1)]] || [[File:lowvibsamyoung.png|thumb|upright=0.80|centre|Figure 11 - Reaction of H2 + F (H-H = 0.74Å, H-F = 2.0Å, pHH = -0.5kgms-1, pHF = -0.5kgms-1)]] || [[File:samlyounglimit2.png|thumb|upright=0.80|centre|Figure 12 - Reaction of H2 + F (H-H = 0.74Å, H-F = 2.0Å, pHH = -2.49kgms-1, pHF = -0.5kgms-1)]]
|-
| [[File:fhhidealsly.png|thumb|upright=0.80|centre|Figure 13 - Reaction of H2 + F (H-H = 2Å, H-F = 0.74Å, pHH = -0.61kgms-1, pHF = -0.5kgms-1)]] || [[File:slylowtrans.png|thumb|upright=0.80|centre|Figure 13 - Reaction of H2 + F (H-H = 2Å, H-F = 0.74Å, pHH = -0.1kgms-1, pHF = -0.5kgms-1)]]|| [[File:translationalsamsam.png|thumb|upright=0.80|centre|Figure 14 - Reaction of H2 + F (H-H = 2Å, H-F = 0.74Å, pHH = -3.0kgms-1, pHF = -0.5kgms-1)]]

|}

= Bibliography =

Electronegativity values : https://sciencenotes.org/list-of-electronegativity-values-of-the-elements/

Sam Young Reaction Dynamics

2018-05-18T14:10:15Z

Sly116: /* Q5 - Efficiency of Reaction */

= H + H2 System =
== Q1 - Transition State Gradients ==
[[File:Sly-Saddle.png|thumb|upright=0.8|centre|Figure 1 - Potential Energy Surface Plot of H2 + H System, with initial conditions A-B distance = 0.74, B-C distance = 2.30, AB momentum = 0 & BC momentum = 2.7]]

The minimum energy surface, shown running along the bottom of figure one obeys the derivative; ∂V/∂(rx) = ∂V/∂(ry) = 0, with rx and ry run parallel to their respective gradients. However, the saddle point where the transition state lies is located along the minimum energy surface at the maximum point. Therefore, it can be found by taking the second derivative, as the two orthogonal gradients have different signs, with one along the potential energy minimum being negative and the other orthogonal graident being positive.

∂2V/∂(rx)2 > 0

∂2V/∂(ry)2 < 0

== Q2 - Transition State Estimate ==

By making the momentum of the whole system equal to zero, it was possible to put the AB distance = BC distance and alter this value to obtain a result for the rts, which was found to be approximately 0.9077Å (one value due to the system being completely symmetric), which gave figure 2. This number was found by taking the intersect of the AB and BC lines from the internuclear plot with the same initial conditions given above, and optimising this value to give constant distances. Due to the gradient of potential energy at the transition state being zero, the system has no kinetic energy, only potential energy. Therefore, there is no oscillation and the plot of internuclear distance against time shows constant interatomic distances.

[[File:Sly_Q2.png|thumb|upright=0.80|centre|Figure 2 - Internucleur Distance]]

== Q3 - MEP ==

The MEP is the minimum energy pathway followed for the reaction H2 + H to take place, although it can be seen in figures 4 and 5 that it differs from the dynamic trajectory due to the masses of the atoms, and therefore the bond oscillations along the trajectory causing deviations from the mep. This is shown by the wavy black line on figure 5. Both figures illustrate the reaction path (represented by the black line) starting at the transition state point, with the dynamic reaction going to the complete formation of a H2 product, while the mep plot shows it going only slightly towards the product formation.

'''change with + - 0.01 and discuss'''

[[File:Sly_MEP2.png|thumb|upright=0.80|centre|Figure 4 - Minimum Energy Pathway]] [[File:newdynamicsam.png|thumb|upright=0.80|centre|Figure 5 - Dynamic Trajectory]]

== Q4 - Reactive and Unreactive Trajectories==

{| class="wikitable" border=1
! p1 !! p2 !! Total Energy !! Reactive or Unreactive !! Trajectory Plot !! Discussion
|-
| -1.25 || -2.5 || -99.018 || [[File:SY-1.png|frameless|upright=0.80]] || Reactive || The reactivity of the trajectory is shown as the reaction path progresses towards the prodcut H2. Upon forming, the new bond vibrates.
|-
| -1.5 || -2.0 || -100.456 || [[File:SY-2.png|frameless|upright=0.80]] || Unreactive || This figure represents an unreactive system due to the approaching H atom not having enough energy to overcome the activation barrier for the reaction. This results in the reaction trajectory returning to the original H2 bond oscillating back towards its energy minimum.
|-
| -1.5 || -2.5 || -98.956 || [[File:SY-3.png|frameless|upright=0.80]] || Reactive || This model shows a very simimlar picture to the first in the table, although due to p1 being slightly higher, the original H2 bond oscillates with higher energy.
|-
| -2.5 || -5.0 || -84.956 || [[File:SLY4.png|frameless|upright=0.80]] || Unreactive || Here one H atom aproaches the H2 molecule and the transition state complex H-H-H forms, however due to a lack of energy, the trajectory path is unable to continue to form the products so returns to the original reactants.
|-
| -2.5 || -5.2 || -83.416 ||[[File:SY5.png|frameless|upright=0.80]] || Reactive || The case has a high enough energy to form the transition state complex and to continue to overcome the energy barrier to obtain the products.
|}

== Q5 - Transition State Theory ==

Transition state theory focusses on the activated complexes formed at a transition state of the reaction, therefore by examining the transition state of a potential surface plot (found at the saddle point) one can obtain the rate of a reaction, due to the activated complex's quasi-equilibrium with the reactants. It assumes that if the collision is of sufficient energy to overcome the transition state, the products will form. This is based on the assumption that molecules react according to the classical picture, and does not take quantum mechanics into account, leading to limitations when considering phenomena such as tunnelling, whereby the reaction path bypasses a low activation energy. Furthermore the transition state theory does not account for reactions recrossing the activation barrier to return to the products as shown above. As a result, this theory would give a higher rate to the real situation.

= F H H System =

== Q1 - Energetics ==

F + H2
This reaction is shown to be exothermic (i.e. the system releases energy upon reacting, ΔH < 0) from the plot due to the energy minimum of the FH bond being lower in energy than the HH bond, therefore more stable. This is due to the large electronegativity difference between F (3.98) and H (2.20), as opposed to the non polar HH bond. As a result, the reaction of FH + H is therefore endothermic for the same reasons.

'''Talk about enthalpies of formation/dissociation'''

[[File:SLYFH.png|thumb|upright=0.80|centre|Figure 6]]

== Q2 - Position of the Transition State ==

The transition state can be found at the point where the internuclear distances of the atoms does not change over time. This is the same point on the graph for both the forward and reverse reactions. By using Hammond's postulate, that the activated intermediate complex at the transition state should resemble the state that it is closest in energy to, therefore similar to an HF + H model. As a result, it was possible to look at the surface plot and optimise the bond distances around where the transition state was roughly located. It was found that the approximate internuclear distances at this transition state are H-F : 1.810 and H-H : 0.746.

[[File:tshighlight.png|thumb|none|Figure 7]] [[File:transstatesly.png|thumb|upright=0.80|none|Figure 8]]

== Q3 - Activation Energy ==

By finding the equilibrium bond length of both reactants and products, and knowing the location of the transition state, it was possible to obtain energies for all of these positions, and therefore calculate the energy of activation.

Energy at HF minimum -133.586 AB 2.3 BC 0.9

Energy at HH minimum -103.33 AB 0.7 BC 2.3

Energy at transition state -103.742 AB 0.75 BC 1.81

ΔE = E(transition state) - E(reactants)

''ΔEFH + H‡ = (-103.742) - (-133.586) = 29.844 Kcalmol-1''

''ΔEH2 + F‡ = (-103.742) - (-103.330) = 0.412 Kcalmol-1''

== Q4 - Mechanism of Release of the Activation Energy ==

F + H2

This plot shows the reaction of initial conditions FH distance = 2.30Å HH distance = 0.85Å FH momentm = -7.0 HH momentum = -1.0, resulting in a successful reaction. Due to the exothermic nature of this reaction, it releases energy as the products have a lower potential energy than the reactants, and from the plot of internuclear distance vs. time, it is clear that this energy is converted to kinetic energy in the form of an oscillating F-H bond, which oscillates at a much higher energy than the original H-H bond. This could be confirmed experimentally by IR which would show the vibrationally excited state of the H-F bond, or energy can be measured by calorimetry.

[[File:slyreactive.png|thumb|upright=0.80|centre|Figure 9]]

== Q5 - Efficiency of Reaction ==

Figures 10-14 clearly show the effect of varying the translaitonal and vibrational contributions to the reaction trajectory of both the endothermic and exothermic reactions. For the exothermic F + H2 reaction, the momentum of the translaitonal approach of the F atom was kept constant while the momentum of the H-H oscillation was varied between 3kgms-1 and -3kgms-1. The result clearly shows that for this early transition state reaction, a higher vibration energy causes the reaction path to overcome the transition state but it recrosses this barrier to return to the initial state due to too much energy. The limit (to 2 d.p.)of the vibrational energy was found to be -2.49kgms-1 in order for the reaction to be successful. A higher energy would cause the recrossing.
This case is the opposite for the endothermic reaction, with a late transition state, whereby if the translational energy is too high the reaction will cross then recross the transition state to return to the products, resulting in an unsuccessful reaction. The limit of translational energy for this reaction was found to be -0.61kgms-1.

To conclude, the success of an early transition state reaction depends on the vibrational energy, while the success of the late transition state depends on the translational energy, with both rebounding back to reactants with of the energy is too high because it still has enough energy to overcome the reverse reaction.

{| class="wikitable" border=1
! !! !!
|-
| [[File:fh2highvibworks.png|thumb|upright=0.80|centre|Figure 10 - Reaction of H2 + F (H-H = 0.74Å, H-F = 2.Å, pHH = -3.0kgms-1, pHF = -0.5kgms-1)]] || [[File:lowvibsamyoung.png|thumb|upright=0.80|centre|Figure 11 - Reaction of H2 + F (H-H = 0.74Å, H-F = 2.0Å, pHH = -0.5kgms-1, pHF = -0.5kgms-1)]] || [[File:samlyounglimit2.png|thumb|upright=0.80|centre|Figure 12 - Reaction of H2 + F (H-H = 0.74Å, H-F = 2.0Å, pHH = -2.49kgms-1, pHF = -0.5kgms-1)]]
|-
| [[File:fhhidealsly.png|thumb|upright=0.80|centre|Figure 13 - Reaction of H2 + F (H-H = 2Å, H-F = 0.74Å, pHH = -0.61kgms-1, pHF = -0.5kgms-1)]] || [[File:slylowtrans.png|thumb|upright=0.80|centre|Figure 13 - Reaction of H2 + F (H-H = 2Å, H-F = 0.74Å, pHH = -0.1kgms-1, pHF = -0.5kgms-1)]]|| [[File:translationalsamsam.png|thumb|upright=0.80|centre|Figure 14 - Reaction of H2 + F (H-H = 2Å, H-F = 0.74Å, pHH = -3.0kgms-1, pHF = -0.5kgms-1)]]

|}

= Bibliography =

Electronegativity values : https://sciencenotes.org/list-of-electronegativity-values-of-the-elements/

Sam Young Reaction Dynamics

2018-05-18T14:01:44Z

Sly116: /* Q5 - Efficiency of Reaction */

= H + H2 System =
== Q1 - Transition State Gradients ==
[[File:Sly-Saddle.png|thumb|upright=0.8|centre|Figure 1 - Potential Energy Surface Plot of H2 + H System, with initial conditions A-B distance = 0.74, B-C distance = 2.30, AB momentum = 0 & BC momentum = 2.7]]

The minimum energy surface, shown running along the bottom of figure one obeys the derivative; ∂V/∂(rx) = ∂V/∂(ry) = 0, with rx and ry run parallel to their respective gradients. However, the saddle point where the transition state lies is located along the minimum energy surface at the maximum point. Therefore, it can be found by taking the second derivative, as the two orthogonal gradients have different signs, with one along the potential energy minimum being negative and the other orthogonal graident being positive.

∂2V/∂(rx)2 > 0

∂2V/∂(ry)2 < 0

== Q2 - Transition State Estimate ==

By making the momentum of the whole system equal to zero, it was possible to put the AB distance = BC distance and alter this value to obtain a result for the rts, which was found to be approximately 0.9077Å (one value due to the system being completely symmetric), which gave figure 2. This number was found by taking the intersect of the AB and BC lines from the internuclear plot with the same initial conditions given above, and optimising this value to give constant distances. Due to the gradient of potential energy at the transition state being zero, the system has no kinetic energy, only potential energy. Therefore, there is no oscillation and the plot of internuclear distance against time shows constant interatomic distances.

[[File:Sly_Q2.png|thumb|upright=0.80|centre|Figure 2 - Internucleur Distance]]

== Q3 - MEP ==

The MEP is the minimum energy pathway followed for the reaction H2 + H to take place, although it can be seen in figures 4 and 5 that it differs from the dynamic trajectory due to the masses of the atoms, and therefore the bond oscillations along the trajectory causing deviations from the mep. This is shown by the wavy black line on figure 5. Both figures illustrate the reaction path (represented by the black line) starting at the transition state point, with the dynamic reaction going to the complete formation of a H2 product, while the mep plot shows it going only slightly towards the product formation.

'''change with + - 0.01 and discuss'''

[[File:Sly_MEP2.png|thumb|upright=0.80|centre|Figure 4 - Minimum Energy Pathway]] [[File:newdynamicsam.png|thumb|upright=0.80|centre|Figure 5 - Dynamic Trajectory]]

== Q4 - Reactive and Unreactive Trajectories==

{| class="wikitable" border=1
! p1 !! p2 !! Total Energy !! Reactive or Unreactive !! Trajectory Plot !! Discussion
|-
| -1.25 || -2.5 || -99.018 || [[File:SY-1.png|frameless|upright=0.80]] || Reactive || The reactivity of the trajectory is shown as the reaction path progresses towards the prodcut H2. Upon forming, the new bond vibrates.
|-
| -1.5 || -2.0 || -100.456 || [[File:SY-2.png|frameless|upright=0.80]] || Unreactive || This figure represents an unreactive system due to the approaching H atom not having enough energy to overcome the activation barrier for the reaction. This results in the reaction trajectory returning to the original H2 bond oscillating back towards its energy minimum.
|-
| -1.5 || -2.5 || -98.956 || [[File:SY-3.png|frameless|upright=0.80]] || Reactive || This model shows a very simimlar picture to the first in the table, although due to p1 being slightly higher, the original H2 bond oscillates with higher energy.
|-
| -2.5 || -5.0 || -84.956 || [[File:SLY4.png|frameless|upright=0.80]] || Unreactive || Here one H atom aproaches the H2 molecule and the transition state complex H-H-H forms, however due to a lack of energy, the trajectory path is unable to continue to form the products so returns to the original reactants.
|-
| -2.5 || -5.2 || -83.416 ||[[File:SY5.png|frameless|upright=0.80]] || Reactive || The case has a high enough energy to form the transition state complex and to continue to overcome the energy barrier to obtain the products.
|}

== Q5 - Transition State Theory ==

Transition state theory focusses on the activated complexes formed at a transition state of the reaction, therefore by examining the transition state of a potential surface plot (found at the saddle point) one can obtain the rate of a reaction, due to the activated complex's quasi-equilibrium with the reactants. It assumes that if the collision is of sufficient energy to overcome the transition state, the products will form. This is based on the assumption that molecules react according to the classical picture, and does not take quantum mechanics into account, leading to limitations when considering phenomena such as tunnelling, whereby the reaction path bypasses a low activation energy. Furthermore the transition state theory does not account for reactions recrossing the activation barrier to return to the products as shown above. As a result, this theory would give a higher rate to the real situation.

= F H H System =

== Q1 - Energetics ==

F + H2
This reaction is shown to be exothermic (i.e. the system releases energy upon reacting, ΔH < 0) from the plot due to the energy minimum of the FH bond being lower in energy than the HH bond, therefore more stable. This is due to the large electronegativity difference between F (3.98) and H (2.20), as opposed to the non polar HH bond. As a result, the reaction of FH + H is therefore endothermic for the same reasons.

'''Talk about enthalpies of formation/dissociation'''

[[File:SLYFH.png|thumb|upright=0.80|centre|Figure 6]]

== Q2 - Position of the Transition State ==

The transition state can be found at the point where the internuclear distances of the atoms does not change over time. This is the same point on the graph for both the forward and reverse reactions. By using Hammond's postulate, that the activated intermediate complex at the transition state should resemble the state that it is closest in energy to, therefore similar to an HF + H model. As a result, it was possible to look at the surface plot and optimise the bond distances around where the transition state was roughly located. It was found that the approximate internuclear distances at this transition state are H-F : 1.810 and H-H : 0.746.

[[File:tshighlight.png|thumb|none|Figure 7]] [[File:transstatesly.png|thumb|upright=0.80|none|Figure 8]]

== Q3 - Activation Energy ==

By finding the equilibrium bond length of both reactants and products, and knowing the location of the transition state, it was possible to obtain energies for all of these positions, and therefore calculate the energy of activation.

Energy at HF minimum -133.586 AB 2.3 BC 0.9

Energy at HH minimum -103.33 AB 0.7 BC 2.3

Energy at transition state -103.742 AB 0.75 BC 1.81

ΔE = E(transition state) - E(reactants)

''ΔEFH + H‡ = (-103.742) - (-133.586) = 29.844 Kcalmol-1''

''ΔEH2 + F‡ = (-103.742) - (-103.330) = 0.412 Kcalmol-1''

== Q4 - Mechanism of Release of the Activation Energy ==

F + H2

This plot shows the reaction of initial conditions FH distance = 2.30Å HH distance = 0.85Å FH momentm = -7.0 HH momentum = -1.0, resulting in a successful reaction. Due to the exothermic nature of this reaction, it releases energy as the products have a lower potential energy than the reactants, and from the plot of internuclear distance vs. time, it is clear that this energy is converted to kinetic energy in the form of an oscillating F-H bond, which oscillates at a much higher energy than the original H-H bond. This could be confirmed experimentally by IR which would show the vibrationally excited state of the H-F bond, or energy can be measured by calorimetry.

[[File:slyreactive.png|thumb|upright=0.80|centre|Figure 9]]

== Q5 - Efficiency of Reaction ==

Figures 10-14 clearly show the effect of varying the translaitonal and vibrational contributions to the reaction trajectory of both the endothermic and exothermic reactions. For the exothermic F + H2 reaction, the momentum of the translaitonal approach of the F atom was kept constant while the momentum of the H-H oscillation was varied between 3kgms-1 and -3kgms-1. The result clearly shows that for this early transition state reaction, a higher vibration energy causes the reaction path to overcome the transition state but it recrosses this barrier to return to the initial state due to too much energy. The limit (to 2 d.p.)of the vibrational energy was found to be -2.49kgms-1 in order for the reaction to be successful. A higher energy would cause the recrossing.
This case is the opposite for the endothermic reaction, with a late transition state, whereby if the translational energy is too high the reaction will cross then recross the transition state to return to the products, resulting in an unsuccessful reaction. The limit of translational energy for this reaction was found to be -0.61kgms-1.

To conclude, the success of an early transition state reaction depends on the vibrational energy, while the success of the late transition state depends on the translational energy.

{| class="wikitable" border=1
! !! !!
|-
| [[File:fh2highvibworks.png|thumb|upright=0.80|centre|Figure 10 - Reaction of H2 + F (H-H = 0.74Å, H-F = 2.Å, pHH = -3.0kgms-1, pHF = -0.5kgms-1)]] || [[File:lowvibsamyoung.png|thumb|upright=0.80|centre|Figure 11 - Reaction of H2 + F (H-H = 0.74Å, H-F = 2.0Å, pHH = -0.5kgms-1, pHF = -0.5kgms-1)]] || [[File:samlyounglimit2.png|thumb|upright=0.80|centre|Figure 12 - Reaction of H2 + F (H-H = 0.74Å, H-F = 2.0Å, pHH = -2.49kgms-1, pHF = -0.5kgms-1)]]
|-
| [[File:fhhidealsly.png|thumb|upright=0.80|centre|Figure 13 - Reaction of H2 + F (H-H = 2Å, H-F = 0.74Å, pHH = -0.61kgms-1, pHF = -0.5kgms-1)]] || [[File:slylowtrans.png|thumb|upright=0.80|centre|Figure 13 - Reaction of H2 + F (H-H = 2Å, H-F = 0.74Å, pHH = -0.1kgms-1, pHF = -0.5kgms-1)]]|| [[File:translationalsamsam.png|thumb|upright=0.80|centre|Figure 14 - Reaction of H2 + F (H-H = 2Å, H-F = 0.74Å, pHH = -3.0kgms-1, pHF = -0.5kgms-1)]]

|}

= Bibliography =

Electronegativity values : https://sciencenotes.org/list-of-electronegativity-values-of-the-elements/

Sam Young Reaction Dynamics

2018-05-18T14:00:01Z

Sly116: /* Q5 - Efficiency of Reaction */

= H + H2 System =
== Q1 - Transition State Gradients ==
[[File:Sly-Saddle.png|thumb|upright=0.8|centre|Figure 1 - Potential Energy Surface Plot of H2 + H System, with initial conditions A-B distance = 0.74, B-C distance = 2.30, AB momentum = 0 & BC momentum = 2.7]]

The minimum energy surface, shown running along the bottom of figure one obeys the derivative; ∂V/∂(rx) = ∂V/∂(ry) = 0, with rx and ry run parallel to their respective gradients. However, the saddle point where the transition state lies is located along the minimum energy surface at the maximum point. Therefore, it can be found by taking the second derivative, as the two orthogonal gradients have different signs, with one along the potential energy minimum being negative and the other orthogonal graident being positive.

∂2V/∂(rx)2 > 0

∂2V/∂(ry)2 < 0

== Q2 - Transition State Estimate ==

By making the momentum of the whole system equal to zero, it was possible to put the AB distance = BC distance and alter this value to obtain a result for the rts, which was found to be approximately 0.9077Å (one value due to the system being completely symmetric), which gave figure 2. This number was found by taking the intersect of the AB and BC lines from the internuclear plot with the same initial conditions given above, and optimising this value to give constant distances. Due to the gradient of potential energy at the transition state being zero, the system has no kinetic energy, only potential energy. Therefore, there is no oscillation and the plot of internuclear distance against time shows constant interatomic distances.

[[File:Sly_Q2.png|thumb|upright=0.80|centre|Figure 2 - Internucleur Distance]]

== Q3 - MEP ==

The MEP is the minimum energy pathway followed for the reaction H2 + H to take place, although it can be seen in figures 4 and 5 that it differs from the dynamic trajectory due to the masses of the atoms, and therefore the bond oscillations along the trajectory causing deviations from the mep. This is shown by the wavy black line on figure 5. Both figures illustrate the reaction path (represented by the black line) starting at the transition state point, with the dynamic reaction going to the complete formation of a H2 product, while the mep plot shows it going only slightly towards the product formation.

'''change with + - 0.01 and discuss'''

[[File:Sly_MEP2.png|thumb|upright=0.80|centre|Figure 4 - Minimum Energy Pathway]] [[File:newdynamicsam.png|thumb|upright=0.80|centre|Figure 5 - Dynamic Trajectory]]

== Q4 - Reactive and Unreactive Trajectories==

{| class="wikitable" border=1
! p1 !! p2 !! Total Energy !! Reactive or Unreactive !! Trajectory Plot !! Discussion
|-
| -1.25 || -2.5 || -99.018 || [[File:SY-1.png|frameless|upright=0.80]] || Reactive || The reactivity of the trajectory is shown as the reaction path progresses towards the prodcut H2. Upon forming, the new bond vibrates.
|-
| -1.5 || -2.0 || -100.456 || [[File:SY-2.png|frameless|upright=0.80]] || Unreactive || This figure represents an unreactive system due to the approaching H atom not having enough energy to overcome the activation barrier for the reaction. This results in the reaction trajectory returning to the original H2 bond oscillating back towards its energy minimum.
|-
| -1.5 || -2.5 || -98.956 || [[File:SY-3.png|frameless|upright=0.80]] || Reactive || This model shows a very simimlar picture to the first in the table, although due to p1 being slightly higher, the original H2 bond oscillates with higher energy.
|-
| -2.5 || -5.0 || -84.956 || [[File:SLY4.png|frameless|upright=0.80]] || Unreactive || Here one H atom aproaches the H2 molecule and the transition state complex H-H-H forms, however due to a lack of energy, the trajectory path is unable to continue to form the products so returns to the original reactants.
|-
| -2.5 || -5.2 || -83.416 ||[[File:SY5.png|frameless|upright=0.80]] || Reactive || The case has a high enough energy to form the transition state complex and to continue to overcome the energy barrier to obtain the products.
|}

== Q5 - Transition State Theory ==

Transition state theory focusses on the activated complexes formed at a transition state of the reaction, therefore by examining the transition state of a potential surface plot (found at the saddle point) one can obtain the rate of a reaction, due to the activated complex's quasi-equilibrium with the reactants. It assumes that if the collision is of sufficient energy to overcome the transition state, the products will form. This is based on the assumption that molecules react according to the classical picture, and does not take quantum mechanics into account, leading to limitations when considering phenomena such as tunnelling, whereby the reaction path bypasses a low activation energy. Furthermore the transition state theory does not account for reactions recrossing the activation barrier to return to the products as shown above. As a result, this theory would give a higher rate to the real situation.

= F H H System =

== Q1 - Energetics ==

F + H2
This reaction is shown to be exothermic (i.e. the system releases energy upon reacting, ΔH < 0) from the plot due to the energy minimum of the FH bond being lower in energy than the HH bond, therefore more stable. This is due to the large electronegativity difference between F (3.98) and H (2.20), as opposed to the non polar HH bond. As a result, the reaction of FH + H is therefore endothermic for the same reasons.

'''Talk about enthalpies of formation/dissociation'''

[[File:SLYFH.png|thumb|upright=0.80|centre|Figure 6]]

== Q2 - Position of the Transition State ==

The transition state can be found at the point where the internuclear distances of the atoms does not change over time. This is the same point on the graph for both the forward and reverse reactions. By using Hammond's postulate, that the activated intermediate complex at the transition state should resemble the state that it is closest in energy to, therefore similar to an HF + H model. As a result, it was possible to look at the surface plot and optimise the bond distances around where the transition state was roughly located. It was found that the approximate internuclear distances at this transition state are H-F : 1.810 and H-H : 0.746.

[[File:tshighlight.png|thumb|none|Figure 7]] [[File:transstatesly.png|thumb|upright=0.80|none|Figure 8]]

== Q3 - Activation Energy ==

By finding the equilibrium bond length of both reactants and products, and knowing the location of the transition state, it was possible to obtain energies for all of these positions, and therefore calculate the energy of activation.

Energy at HF minimum -133.586 AB 2.3 BC 0.9

Energy at HH minimum -103.33 AB 0.7 BC 2.3

Energy at transition state -103.742 AB 0.75 BC 1.81

ΔE = E(transition state) - E(reactants)

''ΔEFH + H‡ = (-103.742) - (-133.586) = 29.844 Kcalmol-1''

''ΔEH2 + F‡ = (-103.742) - (-103.330) = 0.412 Kcalmol-1''

== Q4 - Mechanism of Release of the Activation Energy ==

F + H2

This plot shows the reaction of initial conditions FH distance = 2.30Å HH distance = 0.85Å FH momentm = -7.0 HH momentum = -1.0, resulting in a successful reaction. Due to the exothermic nature of this reaction, it releases energy as the products have a lower potential energy than the reactants, and from the plot of internuclear distance vs. time, it is clear that this energy is converted to kinetic energy in the form of an oscillating F-H bond, which oscillates at a much higher energy than the original H-H bond. This could be confirmed experimentally by IR which would show the vibrationally excited state of the H-F bond, or energy can be measured by calorimetry.

[[File:slyreactive.png|thumb|upright=0.80|centre|Figure 9]]

== Q5 - Efficiency of Reaction ==

Figures 10-14 clearly show the effect of varying the translaitonal and vibrational contributions to the reaction trajectory of both the endothermic and exothermic reactions. For the exothermic F + H2 reaction, the momentum of the translaitonal approach of the F atom was kept constant while the momentum of the H-H oscillation was varied between 3kgms-1 and -3kgms-1. The result clearly shows that for this early transition state reaction, a higher vibration energy causes the reaction path to overcome the transition state but it recrosses this barrier to return to the initial state due to too much energy. The limit (to 2 d.p.)of the vibrational energy was found to be -2.49kgms-1 in order for the reaction to be successful. A higher energy would cause the recrossing.
This case is the opposite for the endothermic reaction, with a late transition state, whereby if the translational energy is too high the reaction will cross then recross the transition state to return to the products, resulting in an unsuccessful reaction. The limit of translational energy for this reaction was found to be -0.61kgms-1.

{| class="wikitable" border=1
! !! !!
|-
| [[File:fh2highvibworks.png|thumb|upright=0.80|centre|Figure 10 - Reaction of H2 + F (H-H = 0.74Å, H-F = 2.Å, pHH = -3.0kgms-1, pHF = -0.5kgms-1)]] || [[File:lowvibsamyoung.png|thumb|upright=0.80|centre|Figure 11 - Reaction of H2 + F (H-H = 0.74Å, H-F = 2.0Å, pHH = -0.5kgms-1, pHF = -0.5kgms-1)]] || [[File:samlyounglimit2.png|thumb|upright=0.80|centre|Figure 12 - Reaction of H2 + F (H-H = 0.74Å, H-F = 2.0Å, pHH = -2.49kgms-1, pHF = -0.5kgms-1)]]
|-
| [[File:fhhidealsly.png|thumb|upright=0.80|centre|Figure 13 - Reaction of H2 + F (H-H = 2Å, H-F = 0.74Å, pHH = -0.61kgms-1, pHF = -0.5kgms-1)]] || [[File:slylowtrans.png|thumb|upright=0.80|centre|Figure 13 - Reaction of H2 + F (H-H = 2Å, H-F = 0.74Å, pHH = -0.1kgms-1, pHF = -0.5kgms-1)]]|| [[File:translationalsamsam.png|thumb|upright=0.80|centre|Figure 14 - Reaction of H2 + F (H-H = 2Å, H-F = 0.74Å, pHH = -3.0kgms-1, pHF = -0.5kgms-1)]]

|}

= Bibliography =

Electronegativity values : https://sciencenotes.org/list-of-electronegativity-values-of-the-elements/

Sam Young Reaction Dynamics

2018-05-18T13:59:19Z

Sly116: /* Q5 - Efficiency of Reaction */

= H + H2 System =
== Q1 - Transition State Gradients ==
[[File:Sly-Saddle.png|thumb|upright=0.8|centre|Figure 1 - Potential Energy Surface Plot of H2 + H System, with initial conditions A-B distance = 0.74, B-C distance = 2.30, AB momentum = 0 & BC momentum = 2.7]]

The minimum energy surface, shown running along the bottom of figure one obeys the derivative; ∂V/∂(rx) = ∂V/∂(ry) = 0, with rx and ry run parallel to their respective gradients. However, the saddle point where the transition state lies is located along the minimum energy surface at the maximum point. Therefore, it can be found by taking the second derivative, as the two orthogonal gradients have different signs, with one along the potential energy minimum being negative and the other orthogonal graident being positive.

∂2V/∂(rx)2 > 0

∂2V/∂(ry)2 < 0

== Q2 - Transition State Estimate ==

By making the momentum of the whole system equal to zero, it was possible to put the AB distance = BC distance and alter this value to obtain a result for the rts, which was found to be approximately 0.9077Å (one value due to the system being completely symmetric), which gave figure 2. This number was found by taking the intersect of the AB and BC lines from the internuclear plot with the same initial conditions given above, and optimising this value to give constant distances. Due to the gradient of potential energy at the transition state being zero, the system has no kinetic energy, only potential energy. Therefore, there is no oscillation and the plot of internuclear distance against time shows constant interatomic distances.

[[File:Sly_Q2.png|thumb|upright=0.80|centre|Figure 2 - Internucleur Distance]]

== Q3 - MEP ==

The MEP is the minimum energy pathway followed for the reaction H2 + H to take place, although it can be seen in figures 4 and 5 that it differs from the dynamic trajectory due to the masses of the atoms, and therefore the bond oscillations along the trajectory causing deviations from the mep. This is shown by the wavy black line on figure 5. Both figures illustrate the reaction path (represented by the black line) starting at the transition state point, with the dynamic reaction going to the complete formation of a H2 product, while the mep plot shows it going only slightly towards the product formation.

'''change with + - 0.01 and discuss'''

[[File:Sly_MEP2.png|thumb|upright=0.80|centre|Figure 4 - Minimum Energy Pathway]] [[File:newdynamicsam.png|thumb|upright=0.80|centre|Figure 5 - Dynamic Trajectory]]

== Q4 - Reactive and Unreactive Trajectories==

{| class="wikitable" border=1
! p1 !! p2 !! Total Energy !! Reactive or Unreactive !! Trajectory Plot !! Discussion
|-
| -1.25 || -2.5 || -99.018 || [[File:SY-1.png|frameless|upright=0.80]] || Reactive || The reactivity of the trajectory is shown as the reaction path progresses towards the prodcut H2. Upon forming, the new bond vibrates.
|-
| -1.5 || -2.0 || -100.456 || [[File:SY-2.png|frameless|upright=0.80]] || Unreactive || This figure represents an unreactive system due to the approaching H atom not having enough energy to overcome the activation barrier for the reaction. This results in the reaction trajectory returning to the original H2 bond oscillating back towards its energy minimum.
|-
| -1.5 || -2.5 || -98.956 || [[File:SY-3.png|frameless|upright=0.80]] || Reactive || This model shows a very simimlar picture to the first in the table, although due to p1 being slightly higher, the original H2 bond oscillates with higher energy.
|-
| -2.5 || -5.0 || -84.956 || [[File:SLY4.png|frameless|upright=0.80]] || Unreactive || Here one H atom aproaches the H2 molecule and the transition state complex H-H-H forms, however due to a lack of energy, the trajectory path is unable to continue to form the products so returns to the original reactants.
|-
| -2.5 || -5.2 || -83.416 ||[[File:SY5.png|frameless|upright=0.80]] || Reactive || The case has a high enough energy to form the transition state complex and to continue to overcome the energy barrier to obtain the products.
|}

== Q5 - Transition State Theory ==

Transition state theory focusses on the activated complexes formed at a transition state of the reaction, therefore by examining the transition state of a potential surface plot (found at the saddle point) one can obtain the rate of a reaction, due to the activated complex's quasi-equilibrium with the reactants. It assumes that if the collision is of sufficient energy to overcome the transition state, the products will form. This is based on the assumption that molecules react according to the classical picture, and does not take quantum mechanics into account, leading to limitations when considering phenomena such as tunnelling, whereby the reaction path bypasses a low activation energy. Furthermore the transition state theory does not account for reactions recrossing the activation barrier to return to the products as shown above. As a result, this theory would give a higher rate to the real situation.

= F H H System =

== Q1 - Energetics ==

F + H2
This reaction is shown to be exothermic (i.e. the system releases energy upon reacting, ΔH < 0) from the plot due to the energy minimum of the FH bond being lower in energy than the HH bond, therefore more stable. This is due to the large electronegativity difference between F (3.98) and H (2.20), as opposed to the non polar HH bond. As a result, the reaction of FH + H is therefore endothermic for the same reasons.

'''Talk about enthalpies of formation/dissociation'''

[[File:SLYFH.png|thumb|upright=0.80|centre|Figure 6]]

== Q2 - Position of the Transition State ==

The transition state can be found at the point where the internuclear distances of the atoms does not change over time. This is the same point on the graph for both the forward and reverse reactions. By using Hammond's postulate, that the activated intermediate complex at the transition state should resemble the state that it is closest in energy to, therefore similar to an HF + H model. As a result, it was possible to look at the surface plot and optimise the bond distances around where the transition state was roughly located. It was found that the approximate internuclear distances at this transition state are H-F : 1.810 and H-H : 0.746.

[[File:tshighlight.png|thumb|none|Figure 7]] [[File:transstatesly.png|thumb|upright=0.80|none|Figure 8]]

== Q3 - Activation Energy ==

By finding the equilibrium bond length of both reactants and products, and knowing the location of the transition state, it was possible to obtain energies for all of these positions, and therefore calculate the energy of activation.

Energy at HF minimum -133.586 AB 2.3 BC 0.9

Energy at HH minimum -103.33 AB 0.7 BC 2.3

Energy at transition state -103.742 AB 0.75 BC 1.81

ΔE = E(transition state) - E(reactants)

''ΔEFH + H‡ = (-103.742) - (-133.586) = 29.844 Kcalmol-1''

''ΔEH2 + F‡ = (-103.742) - (-103.330) = 0.412 Kcalmol-1''

== Q4 - Mechanism of Release of the Activation Energy ==

F + H2

This plot shows the reaction of initial conditions FH distance = 2.30Å HH distance = 0.85Å FH momentm = -7.0 HH momentum = -1.0, resulting in a successful reaction. Due to the exothermic nature of this reaction, it releases energy as the products have a lower potential energy than the reactants, and from the plot of internuclear distance vs. time, it is clear that this energy is converted to kinetic energy in the form of an oscillating F-H bond, which oscillates at a much higher energy than the original H-H bond. This could be confirmed experimentally by IR which would show the vibrationally excited state of the H-F bond, or energy can be measured by calorimetry.

[[File:slyreactive.png|thumb|upright=0.80|centre|Figure 9]]

== Q5 - Efficiency of Reaction ==

Figures 10-14 clearly show the effect of varying the translaitonal and vibrational contributions to the reaction trajectory of both the endothermic and exothermic reactions. For the exothermic F + H2 reaction, the momentum of the translaitonal approach of the F atom was kept constant while the momentum of the H-H oscillation was varied between 3kgms-1 and -3kgms-1. The result clearly shows that for this early transition state reaction, a higher vibration energy causes the reaction path to overcome the transition state but it recrosses this barrier to return to the initial state due to too much energy. The limit of the vibrational energy was found to be -2.49kgms-1 in order for the reaction to be successful. A higher energy would cause the recrossing.
This case is the opposite for the endothermic reaction, with a late transition state, whereby if the translational energy is too high the reaction will cross then recross the transition state to return to the products, resulting in an unsuccessful reaction. The limit of translational energy for this reaction was found to be -0.61kgms-1

{| class="wikitable" border=1
! !! !!
|-
| [[File:fh2highvibworks.png|thumb|upright=0.80|centre|Figure 10 - Reaction of H2 + F (H-H = 0.74Å, H-F = 2.Å, pHH = -3.0kgms-1, pHF = -0.5kgms-1)]] || [[File:lowvibsamyoung.png|thumb|upright=0.80|centre|Figure 11 - Reaction of H2 + F (H-H = 0.74Å, H-F = 2.0Å, pHH = -0.5kgms-1, pHF = -0.5kgms-1)]] || [[File:samlyounglimit2.png|thumb|upright=0.80|centre|Figure 12 - Reaction of H2 + F (H-H = 0.74Å, H-F = 2.0Å, pHH = -2.49kgms-1, pHF = -0.5kgms-1)]]
|-
| [[File:fhhidealsly.png|thumb|upright=0.80|centre|Figure 13 - Reaction of H2 + F (H-H = 2Å, H-F = 0.74Å, pHH = -0.61kgms-1, pHF = -0.5kgms-1)]] || [[File:slylowtrans.png|thumb|upright=0.80|centre|Figure 13 - Reaction of H2 + F (H-H = 2Å, H-F = 0.74Å, pHH = -0.1kgms-1, pHF = -0.5kgms-1)]]|| [[File:translationalsamsam.png|thumb|upright=0.80|centre|Figure 14 - Reaction of H2 + F (H-H = 2Å, H-F = 0.74Å, pHH = -3.0kgms-1, pHF = -0.5kgms-1)]]

|}

= Bibliography =

Electronegativity values : https://sciencenotes.org/list-of-electronegativity-values-of-the-elements/

Sam Young Reaction Dynamics

2018-05-18T13:54:32Z

Sly116: /* Q5 - Efficiency of Reaction */

= H + H2 System =
== Q1 - Transition State Gradients ==
[[File:Sly-Saddle.png|thumb|upright=0.8|centre|Figure 1 - Potential Energy Surface Plot of H2 + H System, with initial conditions A-B distance = 0.74, B-C distance = 2.30, AB momentum = 0 & BC momentum = 2.7]]

The minimum energy surface, shown running along the bottom of figure one obeys the derivative; ∂V/∂(rx) = ∂V/∂(ry) = 0, with rx and ry run parallel to their respective gradients. However, the saddle point where the transition state lies is located along the minimum energy surface at the maximum point. Therefore, it can be found by taking the second derivative, as the two orthogonal gradients have different signs, with one along the potential energy minimum being negative and the other orthogonal graident being positive.

∂2V/∂(rx)2 > 0

∂2V/∂(ry)2 < 0

== Q2 - Transition State Estimate ==

By making the momentum of the whole system equal to zero, it was possible to put the AB distance = BC distance and alter this value to obtain a result for the rts, which was found to be approximately 0.9077Å (one value due to the system being completely symmetric), which gave figure 2. This number was found by taking the intersect of the AB and BC lines from the internuclear plot with the same initial conditions given above, and optimising this value to give constant distances. Due to the gradient of potential energy at the transition state being zero, the system has no kinetic energy, only potential energy. Therefore, there is no oscillation and the plot of internuclear distance against time shows constant interatomic distances.

[[File:Sly_Q2.png|thumb|upright=0.80|centre|Figure 2 - Internucleur Distance]]

== Q3 - MEP ==

The MEP is the minimum energy pathway followed for the reaction H2 + H to take place, although it can be seen in figures 4 and 5 that it differs from the dynamic trajectory due to the masses of the atoms, and therefore the bond oscillations along the trajectory causing deviations from the mep. This is shown by the wavy black line on figure 5. Both figures illustrate the reaction path (represented by the black line) starting at the transition state point, with the dynamic reaction going to the complete formation of a H2 product, while the mep plot shows it going only slightly towards the product formation.

'''change with + - 0.01 and discuss'''

[[File:Sly_MEP2.png|thumb|upright=0.80|centre|Figure 4 - Minimum Energy Pathway]] [[File:newdynamicsam.png|thumb|upright=0.80|centre|Figure 5 - Dynamic Trajectory]]

== Q4 - Reactive and Unreactive Trajectories==

{| class="wikitable" border=1
! p1 !! p2 !! Total Energy !! Reactive or Unreactive !! Trajectory Plot !! Discussion
|-
| -1.25 || -2.5 || -99.018 || [[File:SY-1.png|frameless|upright=0.80]] || Reactive || The reactivity of the trajectory is shown as the reaction path progresses towards the prodcut H2. Upon forming, the new bond vibrates.
|-
| -1.5 || -2.0 || -100.456 || [[File:SY-2.png|frameless|upright=0.80]] || Unreactive || This figure represents an unreactive system due to the approaching H atom not having enough energy to overcome the activation barrier for the reaction. This results in the reaction trajectory returning to the original H2 bond oscillating back towards its energy minimum.
|-
| -1.5 || -2.5 || -98.956 || [[File:SY-3.png|frameless|upright=0.80]] || Reactive || This model shows a very simimlar picture to the first in the table, although due to p1 being slightly higher, the original H2 bond oscillates with higher energy.
|-
| -2.5 || -5.0 || -84.956 || [[File:SLY4.png|frameless|upright=0.80]] || Unreactive || Here one H atom aproaches the H2 molecule and the transition state complex H-H-H forms, however due to a lack of energy, the trajectory path is unable to continue to form the products so returns to the original reactants.
|-
| -2.5 || -5.2 || -83.416 ||[[File:SY5.png|frameless|upright=0.80]] || Reactive || The case has a high enough energy to form the transition state complex and to continue to overcome the energy barrier to obtain the products.
|}

== Q5 - Transition State Theory ==

Transition state theory focusses on the activated complexes formed at a transition state of the reaction, therefore by examining the transition state of a potential surface plot (found at the saddle point) one can obtain the rate of a reaction, due to the activated complex's quasi-equilibrium with the reactants. It assumes that if the collision is of sufficient energy to overcome the transition state, the products will form. This is based on the assumption that molecules react according to the classical picture, and does not take quantum mechanics into account, leading to limitations when considering phenomena such as tunnelling, whereby the reaction path bypasses a low activation energy. Furthermore the transition state theory does not account for reactions recrossing the activation barrier to return to the products as shown above. As a result, this theory would give a higher rate to the real situation.

= F H H System =

== Q1 - Energetics ==

F + H2
This reaction is shown to be exothermic (i.e. the system releases energy upon reacting, ΔH < 0) from the plot due to the energy minimum of the FH bond being lower in energy than the HH bond, therefore more stable. This is due to the large electronegativity difference between F (3.98) and H (2.20), as opposed to the non polar HH bond. As a result, the reaction of FH + H is therefore endothermic for the same reasons.

'''Talk about enthalpies of formation/dissociation'''

[[File:SLYFH.png|thumb|upright=0.80|centre|Figure 6]]

== Q2 - Position of the Transition State ==

The transition state can be found at the point where the internuclear distances of the atoms does not change over time. This is the same point on the graph for both the forward and reverse reactions. By using Hammond's postulate, that the activated intermediate complex at the transition state should resemble the state that it is closest in energy to, therefore similar to an HF + H model. As a result, it was possible to look at the surface plot and optimise the bond distances around where the transition state was roughly located. It was found that the approximate internuclear distances at this transition state are H-F : 1.810 and H-H : 0.746.

[[File:tshighlight.png|thumb|none|Figure 7]] [[File:transstatesly.png|thumb|upright=0.80|none|Figure 8]]

== Q3 - Activation Energy ==

By finding the equilibrium bond length of both reactants and products, and knowing the location of the transition state, it was possible to obtain energies for all of these positions, and therefore calculate the energy of activation.

Energy at HF minimum -133.586 AB 2.3 BC 0.9

Energy at HH minimum -103.33 AB 0.7 BC 2.3

Energy at transition state -103.742 AB 0.75 BC 1.81

ΔE = E(transition state) - E(reactants)

''ΔEFH + H‡ = (-103.742) - (-133.586) = 29.844 Kcalmol-1''

''ΔEH2 + F‡ = (-103.742) - (-103.330) = 0.412 Kcalmol-1''

== Q4 - Mechanism of Release of the Activation Energy ==

F + H2

This plot shows the reaction of initial conditions FH distance = 2.30Å HH distance = 0.85Å FH momentm = -7.0 HH momentum = -1.0, resulting in a successful reaction. Due to the exothermic nature of this reaction, it releases energy as the products have a lower potential energy than the reactants, and from the plot of internuclear distance vs. time, it is clear that this energy is converted to kinetic energy in the form of an oscillating F-H bond, which oscillates at a much higher energy than the original H-H bond. This could be confirmed experimentally by IR which would show the vibrationally excited state of the H-F bond, or energy can be measured by calorimetry.

[[File:slyreactive.png|thumb|upright=0.80|centre|Figure 9]]

== Q5 - Efficiency of Reaction ==

Figures 10-14 clearly show the effect of varying the translaitonal and vibrational contributions to the reaction trajectory of both the endothermic and exothermic reactions. For the exothermic F + H2 reaction, the momentum of the translaitonal approach of the F atom was kept constant while the momentum of the H-H oscillation was varied between 3 and -3. The result clearly shows that for this early transition state reaction, a higher vibration energy causes the reaction path to overcome the transition state but it recrosses this barrier to return to the initial state due to too much energy. The limit of the vibrational energy was found to be -2.49

{| class="wikitable" border=1
! !! !!
|-
| [[File:fh2highvibworks.png|thumb|upright=0.80|centre|Figure 10 - Reaction of H2 + F (H-H = 0.74Å, H-F = 2.Å, pHH = -3.0, pHF = -0.5)]] || [[File:lowvibsamyoung.png|thumb|upright=0.80|centre|Figure 11 - Reaction of H2 + F (H-H = 0.74Å, H-F = 2.0Å, pHH = -0.5, pHF = -0.5)]] || [[File:samlyounglimit2.png|thumb|upright=0.80|centre|Figure 12 - Reaction of H2 + F (H-H = 0.74Å, H-F = 2.0Å, pHH = -2.49, pHF = -0.5)]]
|-
| [[File:fhhidealsly.png|thumb|upright=0.80|centre|Figure 13 - Reaction of H2 + F (H-H = 2Å, H-F = 0.74Å, pHH = -0.61, pHF = -0.5)]] || [[File:slylowtrans.png|thumb|upright=0.80|centre|Figure 13 - Reaction of H2 + F (H-H = 2Å, H-F = 0.74Å, pHH = -0.1, pHF = -0.5)]]|| [[File:translationalsamsam.png|thumb|upright=0.80|centre|Figure 14 - Reaction of H2 + F (H-H = 2Å, H-F = 0.74Å, pHH = -3.0, pHF = -0.5)]]

|}

= Bibliography =

Electronegativity values : https://sciencenotes.org/list-of-electronegativity-values-of-the-elements/

Sam Young Reaction Dynamics

2018-05-18T13:54:01Z

Sly116: /* Q5 - Efficiency of Reaction */

= H + H2 System =
== Q1 - Transition State Gradients ==
[[File:Sly-Saddle.png|thumb|upright=0.8|centre|Figure 1 - Potential Energy Surface Plot of H2 + H System, with initial conditions A-B distance = 0.74, B-C distance = 2.30, AB momentum = 0 & BC momentum = 2.7]]

The minimum energy surface, shown running along the bottom of figure one obeys the derivative; ∂V/∂(rx) = ∂V/∂(ry) = 0, with rx and ry run parallel to their respective gradients. However, the saddle point where the transition state lies is located along the minimum energy surface at the maximum point. Therefore, it can be found by taking the second derivative, as the two orthogonal gradients have different signs, with one along the potential energy minimum being negative and the other orthogonal graident being positive.

∂2V/∂(rx)2 > 0

∂2V/∂(ry)2 < 0

== Q2 - Transition State Estimate ==

By making the momentum of the whole system equal to zero, it was possible to put the AB distance = BC distance and alter this value to obtain a result for the rts, which was found to be approximately 0.9077Å (one value due to the system being completely symmetric), which gave figure 2. This number was found by taking the intersect of the AB and BC lines from the internuclear plot with the same initial conditions given above, and optimising this value to give constant distances. Due to the gradient of potential energy at the transition state being zero, the system has no kinetic energy, only potential energy. Therefore, there is no oscillation and the plot of internuclear distance against time shows constant interatomic distances.

[[File:Sly_Q2.png|thumb|upright=0.80|centre|Figure 2 - Internucleur Distance]]

== Q3 - MEP ==

The MEP is the minimum energy pathway followed for the reaction H2 + H to take place, although it can be seen in figures 4 and 5 that it differs from the dynamic trajectory due to the masses of the atoms, and therefore the bond oscillations along the trajectory causing deviations from the mep. This is shown by the wavy black line on figure 5. Both figures illustrate the reaction path (represented by the black line) starting at the transition state point, with the dynamic reaction going to the complete formation of a H2 product, while the mep plot shows it going only slightly towards the product formation.

'''change with + - 0.01 and discuss'''

[[File:Sly_MEP2.png|thumb|upright=0.80|centre|Figure 4 - Minimum Energy Pathway]] [[File:newdynamicsam.png|thumb|upright=0.80|centre|Figure 5 - Dynamic Trajectory]]

== Q4 - Reactive and Unreactive Trajectories==

{| class="wikitable" border=1
! p1 !! p2 !! Total Energy !! Reactive or Unreactive !! Trajectory Plot !! Discussion
|-
| -1.25 || -2.5 || -99.018 || [[File:SY-1.png|frameless|upright=0.80]] || Reactive || The reactivity of the trajectory is shown as the reaction path progresses towards the prodcut H2. Upon forming, the new bond vibrates.
|-
| -1.5 || -2.0 || -100.456 || [[File:SY-2.png|frameless|upright=0.80]] || Unreactive || This figure represents an unreactive system due to the approaching H atom not having enough energy to overcome the activation barrier for the reaction. This results in the reaction trajectory returning to the original H2 bond oscillating back towards its energy minimum.
|-
| -1.5 || -2.5 || -98.956 || [[File:SY-3.png|frameless|upright=0.80]] || Reactive || This model shows a very simimlar picture to the first in the table, although due to p1 being slightly higher, the original H2 bond oscillates with higher energy.
|-
| -2.5 || -5.0 || -84.956 || [[File:SLY4.png|frameless|upright=0.80]] || Unreactive || Here one H atom aproaches the H2 molecule and the transition state complex H-H-H forms, however due to a lack of energy, the trajectory path is unable to continue to form the products so returns to the original reactants.
|-
| -2.5 || -5.2 || -83.416 ||[[File:SY5.png|frameless|upright=0.80]] || Reactive || The case has a high enough energy to form the transition state complex and to continue to overcome the energy barrier to obtain the products.
|}

== Q5 - Transition State Theory ==

Transition state theory focusses on the activated complexes formed at a transition state of the reaction, therefore by examining the transition state of a potential surface plot (found at the saddle point) one can obtain the rate of a reaction, due to the activated complex's quasi-equilibrium with the reactants. It assumes that if the collision is of sufficient energy to overcome the transition state, the products will form. This is based on the assumption that molecules react according to the classical picture, and does not take quantum mechanics into account, leading to limitations when considering phenomena such as tunnelling, whereby the reaction path bypasses a low activation energy. Furthermore the transition state theory does not account for reactions recrossing the activation barrier to return to the products as shown above. As a result, this theory would give a higher rate to the real situation.

= F H H System =

== Q1 - Energetics ==

F + H2
This reaction is shown to be exothermic (i.e. the system releases energy upon reacting, ΔH < 0) from the plot due to the energy minimum of the FH bond being lower in energy than the HH bond, therefore more stable. This is due to the large electronegativity difference between F (3.98) and H (2.20), as opposed to the non polar HH bond. As a result, the reaction of FH + H is therefore endothermic for the same reasons.

'''Talk about enthalpies of formation/dissociation'''

[[File:SLYFH.png|thumb|upright=0.80|centre|Figure 6]]

== Q2 - Position of the Transition State ==

The transition state can be found at the point where the internuclear distances of the atoms does not change over time. This is the same point on the graph for both the forward and reverse reactions. By using Hammond's postulate, that the activated intermediate complex at the transition state should resemble the state that it is closest in energy to, therefore similar to an HF + H model. As a result, it was possible to look at the surface plot and optimise the bond distances around where the transition state was roughly located. It was found that the approximate internuclear distances at this transition state are H-F : 1.810 and H-H : 0.746.

[[File:tshighlight.png|thumb|none|Figure 7]] [[File:transstatesly.png|thumb|upright=0.80|none|Figure 8]]

== Q3 - Activation Energy ==

By finding the equilibrium bond length of both reactants and products, and knowing the location of the transition state, it was possible to obtain energies for all of these positions, and therefore calculate the energy of activation.

Energy at HF minimum -133.586 AB 2.3 BC 0.9

Energy at HH minimum -103.33 AB 0.7 BC 2.3

Energy at transition state -103.742 AB 0.75 BC 1.81

ΔE = E(transition state) - E(reactants)

''ΔEFH + H‡ = (-103.742) - (-133.586) = 29.844 Kcalmol-1''

''ΔEH2 + F‡ = (-103.742) - (-103.330) = 0.412 Kcalmol-1''

== Q4 - Mechanism of Release of the Activation Energy ==

F + H2

This plot shows the reaction of initial conditions FH distance = 2.30Å HH distance = 0.85Å FH momentm = -7.0 HH momentum = -1.0, resulting in a successful reaction. Due to the exothermic nature of this reaction, it releases energy as the products have a lower potential energy than the reactants, and from the plot of internuclear distance vs. time, it is clear that this energy is converted to kinetic energy in the form of an oscillating F-H bond, which oscillates at a much higher energy than the original H-H bond. This could be confirmed experimentally by IR which would show the vibrationally excited state of the H-F bond, or energy can be measured by calorimetry.

[[File:slyreactive.png|thumb|upright=0.80|centre|Figure 9]]

== Q5 - Efficiency of Reaction ==

Figures 10-14 clearly show the effect of varying the translaitonal and vibrational contributions to the reaction trajectory of both the endothermic and exothermic reactions. For the exothermic F + H2 reaction, the momentum of the translaitonal approach of the F atom was kept constant while the momentum of the H-H oscillation was varied between 3 and -3. The result clearly shows that for this early transition state reaction, a higher vibration energy causes the reaction path to overcome the transition state but it recrosses this barrier to return to the initial state due to too much energy. The limit of the vibrational energy was found to be -2.49

[[File:fh2highvibworks.png|thumb|upright=0.80|centre|Figure 10 - Reaction of H2 + F (H-H = 0.74Å, H-F = 2.Å, pHH = -3.0, pHF = -0.5)]][[File:lowvibsamyoung.png|thumb|upright=0.80|centre|Figure 11 - Reaction of H2 + F (H-H = 0.74Å, H-F = 2.0Å, pHH = -0.5, pHF = -0.5)]][[File:samlyounglimit2.png|thumb|upright=0.80|centre|Figure 12 - Reaction of H2 + F (H-H = 0.74Å, H-F = 2.0Å, pHH = -2.49, pHF = -0.5)]]
[[File:fhhidealsly.png|thumb|upright=0.80|centre|Figure 13 - Reaction of H2 + F (H-H = 2Å, H-F = 0.74Å, pHH = -0.61, pHF = -0.5)]][[File:slylowtrans.png|thumb|upright=0.80|centre|Figure 13 - Reaction of H2 + F (H-H = 2Å, H-F = 0.74Å, pHH = -0.1, pHF = -0.5)]][[File:translationalsamsam.png|thumb|upright=0.80|centre|Figure 14 - Reaction of H2 + F (H-H = 2Å, H-F = 0.74Å, pHH = -3.0, pHF = -0.5)]]

{| class="wikitable" border=1
! p1 !! p2 !! Total Energy
|-
| [[File:fh2highvibworks.png|thumb|upright=0.80|centre|Figure 10 - Reaction of H2 + F (H-H = 0.74Å, H-F = 2.Å, pHH = -3.0, pHF = -0.5)]] || [[File:lowvibsamyoung.png|thumb|upright=0.80|centre|Figure 11 - Reaction of H2 + F (H-H = 0.74Å, H-F = 2.0Å, pHH = -0.5, pHF = -0.5)]] || [[File:samlyounglimit2.png|thumb|upright=0.80|centre|Figure 12 - Reaction of H2 + F (H-H = 0.74Å, H-F = 2.0Å, pHH = -2.49, pHF = -0.5)]]
|-
| [[File:fhhidealsly.png|thumb|upright=0.80|centre|Figure 13 - Reaction of H2 + F (H-H = 2Å, H-F = 0.74Å, pHH = -0.61, pHF = -0.5)]] || [[File:slylowtrans.png|thumb|upright=0.80|centre|Figure 13 - Reaction of H2 + F (H-H = 2Å, H-F = 0.74Å, pHH = -0.1, pHF = -0.5)]]|| [[File:translationalsamsam.png|thumb|upright=0.80|centre|Figure 14 - Reaction of H2 + F (H-H = 2Å, H-F = 0.74Å, pHH = -3.0, pHF = -0.5)]]

|}

= Bibliography =

Electronegativity values : https://sciencenotes.org/list-of-electronegativity-values-of-the-elements/

Sam Young Reaction Dynamics

2018-05-18T13:51:18Z

Sly116: /* Q5 - Efficiency of Reaction */

= H + H2 System =
== Q1 - Transition State Gradients ==
[[File:Sly-Saddle.png|thumb|upright=0.8|centre|Figure 1 - Potential Energy Surface Plot of H2 + H System, with initial conditions A-B distance = 0.74, B-C distance = 2.30, AB momentum = 0 & BC momentum = 2.7]]

The minimum energy surface, shown running along the bottom of figure one obeys the derivative; ∂V/∂(rx) = ∂V/∂(ry) = 0, with rx and ry run parallel to their respective gradients. However, the saddle point where the transition state lies is located along the minimum energy surface at the maximum point. Therefore, it can be found by taking the second derivative, as the two orthogonal gradients have different signs, with one along the potential energy minimum being negative and the other orthogonal graident being positive.

∂2V/∂(rx)2 > 0

∂2V/∂(ry)2 < 0

== Q2 - Transition State Estimate ==

By making the momentum of the whole system equal to zero, it was possible to put the AB distance = BC distance and alter this value to obtain a result for the rts, which was found to be approximately 0.9077Å (one value due to the system being completely symmetric), which gave figure 2. This number was found by taking the intersect of the AB and BC lines from the internuclear plot with the same initial conditions given above, and optimising this value to give constant distances. Due to the gradient of potential energy at the transition state being zero, the system has no kinetic energy, only potential energy. Therefore, there is no oscillation and the plot of internuclear distance against time shows constant interatomic distances.

[[File:Sly_Q2.png|thumb|upright=0.80|centre|Figure 2 - Internucleur Distance]]

== Q3 - MEP ==

The MEP is the minimum energy pathway followed for the reaction H2 + H to take place, although it can be seen in figures 4 and 5 that it differs from the dynamic trajectory due to the masses of the atoms, and therefore the bond oscillations along the trajectory causing deviations from the mep. This is shown by the wavy black line on figure 5. Both figures illustrate the reaction path (represented by the black line) starting at the transition state point, with the dynamic reaction going to the complete formation of a H2 product, while the mep plot shows it going only slightly towards the product formation.

'''change with + - 0.01 and discuss'''

[[File:Sly_MEP2.png|thumb|upright=0.80|centre|Figure 4 - Minimum Energy Pathway]] [[File:newdynamicsam.png|thumb|upright=0.80|centre|Figure 5 - Dynamic Trajectory]]

== Q4 - Reactive and Unreactive Trajectories==

{| class="wikitable" border=1
! p1 !! p2 !! Total Energy !! Reactive or Unreactive !! Trajectory Plot !! Discussion
|-
| -1.25 || -2.5 || -99.018 || [[File:SY-1.png|frameless|upright=0.80]] || Reactive || The reactivity of the trajectory is shown as the reaction path progresses towards the prodcut H2. Upon forming, the new bond vibrates.
|-
| -1.5 || -2.0 || -100.456 || [[File:SY-2.png|frameless|upright=0.80]] || Unreactive || This figure represents an unreactive system due to the approaching H atom not having enough energy to overcome the activation barrier for the reaction. This results in the reaction trajectory returning to the original H2 bond oscillating back towards its energy minimum.
|-
| -1.5 || -2.5 || -98.956 || [[File:SY-3.png|frameless|upright=0.80]] || Reactive || This model shows a very simimlar picture to the first in the table, although due to p1 being slightly higher, the original H2 bond oscillates with higher energy.
|-
| -2.5 || -5.0 || -84.956 || [[File:SLY4.png|frameless|upright=0.80]] || Unreactive || Here one H atom aproaches the H2 molecule and the transition state complex H-H-H forms, however due to a lack of energy, the trajectory path is unable to continue to form the products so returns to the original reactants.
|-
| -2.5 || -5.2 || -83.416 ||[[File:SY5.png|frameless|upright=0.80]] || Reactive || The case has a high enough energy to form the transition state complex and to continue to overcome the energy barrier to obtain the products.
|}

== Q5 - Transition State Theory ==

Transition state theory focusses on the activated complexes formed at a transition state of the reaction, therefore by examining the transition state of a potential surface plot (found at the saddle point) one can obtain the rate of a reaction, due to the activated complex's quasi-equilibrium with the reactants. It assumes that if the collision is of sufficient energy to overcome the transition state, the products will form. This is based on the assumption that molecules react according to the classical picture, and does not take quantum mechanics into account, leading to limitations when considering phenomena such as tunnelling, whereby the reaction path bypasses a low activation energy. Furthermore the transition state theory does not account for reactions recrossing the activation barrier to return to the products as shown above. As a result, this theory would give a higher rate to the real situation.

= F H H System =

== Q1 - Energetics ==

F + H2
This reaction is shown to be exothermic (i.e. the system releases energy upon reacting, ΔH < 0) from the plot due to the energy minimum of the FH bond being lower in energy than the HH bond, therefore more stable. This is due to the large electronegativity difference between F (3.98) and H (2.20), as opposed to the non polar HH bond. As a result, the reaction of FH + H is therefore endothermic for the same reasons.

'''Talk about enthalpies of formation/dissociation'''

[[File:SLYFH.png|thumb|upright=0.80|centre|Figure 6]]

== Q2 - Position of the Transition State ==

The transition state can be found at the point where the internuclear distances of the atoms does not change over time. This is the same point on the graph for both the forward and reverse reactions. By using Hammond's postulate, that the activated intermediate complex at the transition state should resemble the state that it is closest in energy to, therefore similar to an HF + H model. As a result, it was possible to look at the surface plot and optimise the bond distances around where the transition state was roughly located. It was found that the approximate internuclear distances at this transition state are H-F : 1.810 and H-H : 0.746.

[[File:tshighlight.png|thumb|none|Figure 7]] [[File:transstatesly.png|thumb|upright=0.80|none|Figure 8]]

== Q3 - Activation Energy ==

By finding the equilibrium bond length of both reactants and products, and knowing the location of the transition state, it was possible to obtain energies for all of these positions, and therefore calculate the energy of activation.

Energy at HF minimum -133.586 AB 2.3 BC 0.9

Energy at HH minimum -103.33 AB 0.7 BC 2.3

Energy at transition state -103.742 AB 0.75 BC 1.81

ΔE = E(transition state) - E(reactants)

''ΔEFH + H‡ = (-103.742) - (-133.586) = 29.844 Kcalmol-1''

''ΔEH2 + F‡ = (-103.742) - (-103.330) = 0.412 Kcalmol-1''

== Q4 - Mechanism of Release of the Activation Energy ==

F + H2

This plot shows the reaction of initial conditions FH distance = 2.30Å HH distance = 0.85Å FH momentm = -7.0 HH momentum = -1.0, resulting in a successful reaction. Due to the exothermic nature of this reaction, it releases energy as the products have a lower potential energy than the reactants, and from the plot of internuclear distance vs. time, it is clear that this energy is converted to kinetic energy in the form of an oscillating F-H bond, which oscillates at a much higher energy than the original H-H bond. This could be confirmed experimentally by IR which would show the vibrationally excited state of the H-F bond, or energy can be measured by calorimetry.

[[File:slyreactive.png|thumb|upright=0.80|centre|Figure 9]]

== Q5 - Efficiency of Reaction ==

Figures 10-14 clearly show the effect of varying the translaitonal and vibrational contributions to the reaction trajectory of both the endothermic and exothermic reactions. For the exothermic F + H2 reaction, the momentum of the translaitonal approach of the F atom was kept constant while the momentum of the H-H oscillation was varied between 3 and -3. The result clearly shows that for this early transition state reaction, a higher vibration energy causes the reaction path to overcome the transition state but it recrosses this barrier to return to the initial state due to too much energy. The limit of the vibrational energy was found to be -2.49

[[File:fh2highvibworks.png|thumb|upright=0.80|centre|Figure 10 - Reaction of H2 + F (H-H = 0.74Å, H-F = 2.Å, pHH = -3.0, pHF = -0.5)]][[File:lowvibsamyoung.png|thumb|upright=0.80|centre|Figure 11 - Reaction of H2 + F (H-H = 0.74Å, H-F = 2.0Å, pHH = -0.5, pHF = -0.5)]][[File:samlyounglimit2.png|thumb|upright=0.80|centre|Figure 12 - Reaction of H2 + F (H-H = 0.74Å, H-F = 2.0Å, pHH = -2.49, pHF = -0.5)]]
[[File:fhhidealsly.png|thumb|upright=0.80|centre|Figure 13 - Reaction of H2 + F (H-H = 2Å, H-F = 0.74Å, pHH = -0.61, pHF = -0.5)]][[File:slylowtrans.png|thumb|upright=0.80|centre|Figure 13 - Reaction of H2 + F (H-H = 2Å, H-F = 0.74Å, pHH = -0.1, pHF = -0.5)]][[File:translationalsamsam.png|thumb|upright=0.80|centre|Figure 14 - Reaction of H2 + F (H-H = 2Å, H-F = 0.74Å, pHH = -3.0, pHF = -0.5)]]

= Bibliography =

Electronegativity values : https://sciencenotes.org/list-of-electronegativity-values-of-the-elements/

Sam Young Reaction Dynamics

2018-05-18T13:41:08Z

Sly116: /* Q5 - Efficiency of Reaction */

= H + H2 System =
== Q1 - Transition State Gradients ==
[[File:Sly-Saddle.png|thumb|upright=0.8|centre|Figure 1 - Potential Energy Surface Plot of H2 + H System, with initial conditions A-B distance = 0.74, B-C distance = 2.30, AB momentum = 0 & BC momentum = 2.7]]

The minimum energy surface, shown running along the bottom of figure one obeys the derivative; ∂V/∂(rx) = ∂V/∂(ry) = 0, with rx and ry run parallel to their respective gradients. However, the saddle point where the transition state lies is located along the minimum energy surface at the maximum point. Therefore, it can be found by taking the second derivative, as the two orthogonal gradients have different signs, with one along the potential energy minimum being negative and the other orthogonal graident being positive.

∂2V/∂(rx)2 > 0

∂2V/∂(ry)2 < 0

== Q2 - Transition State Estimate ==

By making the momentum of the whole system equal to zero, it was possible to put the AB distance = BC distance and alter this value to obtain a result for the rts, which was found to be approximately 0.9077Å (one value due to the system being completely symmetric), which gave figure 2. This number was found by taking the intersect of the AB and BC lines from the internuclear plot with the same initial conditions given above, and optimising this value to give constant distances. Due to the gradient of potential energy at the transition state being zero, the system has no kinetic energy, only potential energy. Therefore, there is no oscillation and the plot of internuclear distance against time shows constant interatomic distances.

[[File:Sly_Q2.png|thumb|upright=0.80|centre|Figure 2 - Internucleur Distance]]

== Q3 - MEP ==

The MEP is the minimum energy pathway followed for the reaction H2 + H to take place, although it can be seen in figures 4 and 5 that it differs from the dynamic trajectory due to the masses of the atoms, and therefore the bond oscillations along the trajectory causing deviations from the mep. This is shown by the wavy black line on figure 5. Both figures illustrate the reaction path (represented by the black line) starting at the transition state point, with the dynamic reaction going to the complete formation of a H2 product, while the mep plot shows it going only slightly towards the product formation.

'''change with + - 0.01 and discuss'''

[[File:Sly_MEP2.png|thumb|upright=0.80|centre|Figure 4 - Minimum Energy Pathway]] [[File:newdynamicsam.png|thumb|upright=0.80|centre|Figure 5 - Dynamic Trajectory]]

== Q4 - Reactive and Unreactive Trajectories==

{| class="wikitable" border=1
! p1 !! p2 !! Total Energy !! Reactive or Unreactive !! Trajectory Plot !! Discussion
|-
| -1.25 || -2.5 || -99.018 || [[File:SY-1.png|frameless|upright=0.80]] || Reactive || The reactivity of the trajectory is shown as the reaction path progresses towards the prodcut H2. Upon forming, the new bond vibrates.
|-
| -1.5 || -2.0 || -100.456 || [[File:SY-2.png|frameless|upright=0.80]] || Unreactive || This figure represents an unreactive system due to the approaching H atom not having enough energy to overcome the activation barrier for the reaction. This results in the reaction trajectory returning to the original H2 bond oscillating back towards its energy minimum.
|-
| -1.5 || -2.5 || -98.956 || [[File:SY-3.png|frameless|upright=0.80]] || Reactive || This model shows a very simimlar picture to the first in the table, although due to p1 being slightly higher, the original H2 bond oscillates with higher energy.
|-
| -2.5 || -5.0 || -84.956 || [[File:SLY4.png|frameless|upright=0.80]] || Unreactive || Here one H atom aproaches the H2 molecule and the transition state complex H-H-H forms, however due to a lack of energy, the trajectory path is unable to continue to form the products so returns to the original reactants.
|-
| -2.5 || -5.2 || -83.416 ||[[File:SY5.png|frameless|upright=0.80]] || Reactive || The case has a high enough energy to form the transition state complex and to continue to overcome the energy barrier to obtain the products.
|}

== Q5 - Transition State Theory ==

Transition state theory focusses on the activated complexes formed at a transition state of the reaction, therefore by examining the transition state of a potential surface plot (found at the saddle point) one can obtain the rate of a reaction, due to the activated complex's quasi-equilibrium with the reactants. It assumes that if the collision is of sufficient energy to overcome the transition state, the products will form. This is based on the assumption that molecules react according to the classical picture, and does not take quantum mechanics into account, leading to limitations when considering phenomena such as tunnelling, whereby the reaction path bypasses a low activation energy. Furthermore the transition state theory does not account for reactions recrossing the activation barrier to return to the products as shown above. As a result, this theory would give a higher rate to the real situation.

= F H H System =

== Q1 - Energetics ==

F + H2
This reaction is shown to be exothermic (i.e. the system releases energy upon reacting, ΔH < 0) from the plot due to the energy minimum of the FH bond being lower in energy than the HH bond, therefore more stable. This is due to the large electronegativity difference between F (3.98) and H (2.20), as opposed to the non polar HH bond. As a result, the reaction of FH + H is therefore endothermic for the same reasons.

'''Talk about enthalpies of formation/dissociation'''

[[File:SLYFH.png|thumb|upright=0.80|centre|Figure 6]]

== Q2 - Position of the Transition State ==

The transition state can be found at the point where the internuclear distances of the atoms does not change over time. This is the same point on the graph for both the forward and reverse reactions. By using Hammond's postulate, that the activated intermediate complex at the transition state should resemble the state that it is closest in energy to, therefore similar to an HF + H model. As a result, it was possible to look at the surface plot and optimise the bond distances around where the transition state was roughly located. It was found that the approximate internuclear distances at this transition state are H-F : 1.810 and H-H : 0.746.

[[File:tshighlight.png|thumb|none|Figure 7]] [[File:transstatesly.png|thumb|upright=0.80|none|Figure 8]]

== Q3 - Activation Energy ==

By finding the equilibrium bond length of both reactants and products, and knowing the location of the transition state, it was possible to obtain energies for all of these positions, and therefore calculate the energy of activation.

Energy at HF minimum -133.586 AB 2.3 BC 0.9

Energy at HH minimum -103.33 AB 0.7 BC 2.3

Energy at transition state -103.742 AB 0.75 BC 1.81

ΔE = E(transition state) - E(reactants)

''ΔEFH + H‡ = (-103.742) - (-133.586) = 29.844 Kcalmol-1''

''ΔEH2 + F‡ = (-103.742) - (-103.330) = 0.412 Kcalmol-1''

== Q4 - Mechanism of Release of the Activation Energy ==

F + H2

This plot shows the reaction of initial conditions FH distance = 2.30Å HH distance = 0.85Å FH momentm = -7.0 HH momentum = -1.0, resulting in a successful reaction. Due to the exothermic nature of this reaction, it releases energy as the products have a lower potential energy than the reactants, and from the plot of internuclear distance vs. time, it is clear that this energy is converted to kinetic energy in the form of an oscillating F-H bond, which oscillates at a much higher energy than the original H-H bond. This could be confirmed experimentally by IR which would show the vibrationally excited state of the H-F bond, or energy can be measured by calorimetry.

[[File:slyreactive.png|thumb|upright=0.80|centre|Figure 9]]

== Q5 - Efficiency of Reaction ==

[[File:fh2highvibworks.png|thumb|upright=0.80|centre|Figure 10 - Reaction of H2 + F (H-H = 0.74Å, H-F = 2.Å, pHH = -3.0, pHF = -0.5)]][[File:lowvibsamyoung.png|thumb|upright=0.80|centre|Figure 11 - Reaction of H2 + F (H-H = 0.74Å, H-F = 2.0Å, pHH = -0.5, pHF = -0.5)]][[File:samlyounglimit2.png|thumb|upright=0.80|centre|Figure 12 - Reaction of H2 + F (H-H = 0.74Å, H-F = 2.0Å, pHH = -2.49, pHF = -0.5)]]
[[File:fhhidealsly.png|thumb|upright=0.80|centre|Figure 13 - Reaction of H2 + F (H-H = 2Å, H-F = 0.74Å, pHH = -0.61, pHF = -0.5)]][[File:slylowtrans.png|thumb|upright=0.80|centre|Figure 13 - Reaction of H2 + F (H-H = 2Å, H-F = 0.74Å, pHH = -0.1, pHF = -0.5)]][[File:translationalsamsam.png|thumb|upright=0.80|centre|Figure 10 - Reaction of H2 + F (H-H = 2Å, H-F = 0.74Å, pHH = -3.0, pHF = -0.5)]]

= Bibliography =

Electronegativity values : https://sciencenotes.org/list-of-electronegativity-values-of-the-elements/

Sam Young Reaction Dynamics

2018-05-18T13:40:38Z

Sly116: /* Q5 - Efficiency of Reaction */

= H + H2 System =
== Q1 - Transition State Gradients ==
[[File:Sly-Saddle.png|thumb|upright=0.8|centre|Figure 1 - Potential Energy Surface Plot of H2 + H System, with initial conditions A-B distance = 0.74, B-C distance = 2.30, AB momentum = 0 & BC momentum = 2.7]]

The minimum energy surface, shown running along the bottom of figure one obeys the derivative; ∂V/∂(rx) = ∂V/∂(ry) = 0, with rx and ry run parallel to their respective gradients. However, the saddle point where the transition state lies is located along the minimum energy surface at the maximum point. Therefore, it can be found by taking the second derivative, as the two orthogonal gradients have different signs, with one along the potential energy minimum being negative and the other orthogonal graident being positive.

∂2V/∂(rx)2 > 0

∂2V/∂(ry)2 < 0

== Q2 - Transition State Estimate ==

By making the momentum of the whole system equal to zero, it was possible to put the AB distance = BC distance and alter this value to obtain a result for the rts, which was found to be approximately 0.9077Å (one value due to the system being completely symmetric), which gave figure 2. This number was found by taking the intersect of the AB and BC lines from the internuclear plot with the same initial conditions given above, and optimising this value to give constant distances. Due to the gradient of potential energy at the transition state being zero, the system has no kinetic energy, only potential energy. Therefore, there is no oscillation and the plot of internuclear distance against time shows constant interatomic distances.

[[File:Sly_Q2.png|thumb|upright=0.80|centre|Figure 2 - Internucleur Distance]]

== Q3 - MEP ==

The MEP is the minimum energy pathway followed for the reaction H2 + H to take place, although it can be seen in figures 4 and 5 that it differs from the dynamic trajectory due to the masses of the atoms, and therefore the bond oscillations along the trajectory causing deviations from the mep. This is shown by the wavy black line on figure 5. Both figures illustrate the reaction path (represented by the black line) starting at the transition state point, with the dynamic reaction going to the complete formation of a H2 product, while the mep plot shows it going only slightly towards the product formation.

'''change with + - 0.01 and discuss'''

[[File:Sly_MEP2.png|thumb|upright=0.80|centre|Figure 4 - Minimum Energy Pathway]] [[File:newdynamicsam.png|thumb|upright=0.80|centre|Figure 5 - Dynamic Trajectory]]

== Q4 - Reactive and Unreactive Trajectories==

{| class="wikitable" border=1
! p1 !! p2 !! Total Energy !! Reactive or Unreactive !! Trajectory Plot !! Discussion
|-
| -1.25 || -2.5 || -99.018 || [[File:SY-1.png|frameless|upright=0.80]] || Reactive || The reactivity of the trajectory is shown as the reaction path progresses towards the prodcut H2. Upon forming, the new bond vibrates.
|-
| -1.5 || -2.0 || -100.456 || [[File:SY-2.png|frameless|upright=0.80]] || Unreactive || This figure represents an unreactive system due to the approaching H atom not having enough energy to overcome the activation barrier for the reaction. This results in the reaction trajectory returning to the original H2 bond oscillating back towards its energy minimum.
|-
| -1.5 || -2.5 || -98.956 || [[File:SY-3.png|frameless|upright=0.80]] || Reactive || This model shows a very simimlar picture to the first in the table, although due to p1 being slightly higher, the original H2 bond oscillates with higher energy.
|-
| -2.5 || -5.0 || -84.956 || [[File:SLY4.png|frameless|upright=0.80]] || Unreactive || Here one H atom aproaches the H2 molecule and the transition state complex H-H-H forms, however due to a lack of energy, the trajectory path is unable to continue to form the products so returns to the original reactants.
|-
| -2.5 || -5.2 || -83.416 ||[[File:SY5.png|frameless|upright=0.80]] || Reactive || The case has a high enough energy to form the transition state complex and to continue to overcome the energy barrier to obtain the products.
|}

== Q5 - Transition State Theory ==

Transition state theory focusses on the activated complexes formed at a transition state of the reaction, therefore by examining the transition state of a potential surface plot (found at the saddle point) one can obtain the rate of a reaction, due to the activated complex's quasi-equilibrium with the reactants. It assumes that if the collision is of sufficient energy to overcome the transition state, the products will form. This is based on the assumption that molecules react according to the classical picture, and does not take quantum mechanics into account, leading to limitations when considering phenomena such as tunnelling, whereby the reaction path bypasses a low activation energy. Furthermore the transition state theory does not account for reactions recrossing the activation barrier to return to the products as shown above. As a result, this theory would give a higher rate to the real situation.

= F H H System =

== Q1 - Energetics ==

F + H2
This reaction is shown to be exothermic (i.e. the system releases energy upon reacting, ΔH < 0) from the plot due to the energy minimum of the FH bond being lower in energy than the HH bond, therefore more stable. This is due to the large electronegativity difference between F (3.98) and H (2.20), as opposed to the non polar HH bond. As a result, the reaction of FH + H is therefore endothermic for the same reasons.

'''Talk about enthalpies of formation/dissociation'''

[[File:SLYFH.png|thumb|upright=0.80|centre|Figure 6]]

== Q2 - Position of the Transition State ==

The transition state can be found at the point where the internuclear distances of the atoms does not change over time. This is the same point on the graph for both the forward and reverse reactions. By using Hammond's postulate, that the activated intermediate complex at the transition state should resemble the state that it is closest in energy to, therefore similar to an HF + H model. As a result, it was possible to look at the surface plot and optimise the bond distances around where the transition state was roughly located. It was found that the approximate internuclear distances at this transition state are H-F : 1.810 and H-H : 0.746.

[[File:tshighlight.png|thumb|none|Figure 7]] [[File:transstatesly.png|thumb|upright=0.80|none|Figure 8]]

== Q3 - Activation Energy ==

By finding the equilibrium bond length of both reactants and products, and knowing the location of the transition state, it was possible to obtain energies for all of these positions, and therefore calculate the energy of activation.

Energy at HF minimum -133.586 AB 2.3 BC 0.9

Energy at HH minimum -103.33 AB 0.7 BC 2.3

Energy at transition state -103.742 AB 0.75 BC 1.81

ΔE = E(transition state) - E(reactants)

''ΔEFH + H‡ = (-103.742) - (-133.586) = 29.844 Kcalmol-1''

''ΔEH2 + F‡ = (-103.742) - (-103.330) = 0.412 Kcalmol-1''

== Q4 - Mechanism of Release of the Activation Energy ==

F + H2

This plot shows the reaction of initial conditions FH distance = 2.30Å HH distance = 0.85Å FH momentm = -7.0 HH momentum = -1.0, resulting in a successful reaction. Due to the exothermic nature of this reaction, it releases energy as the products have a lower potential energy than the reactants, and from the plot of internuclear distance vs. time, it is clear that this energy is converted to kinetic energy in the form of an oscillating F-H bond, which oscillates at a much higher energy than the original H-H bond. This could be confirmed experimentally by IR which would show the vibrationally excited state of the H-F bond, or energy can be measured by calorimetry.

[[File:slyreactive.png|thumb|upright=0.80|centre|Figure 9]]

== Q5 - Efficiency of Reaction ==

[[File:fh2highvibworks.png|thumb|upright=0.80|left|Figure 10 - Reaction of H2 + F (H-H = 0.74Å, H-F = 2.Å, pHH = -3.0, pHF = -0.5)]][[File:lowvibsamyoung.png|thumb|upright=0.80|centre|Figure 11 - Reaction of H2 + F (H-H = 0.74Å, H-F = 2.0Å, pHH = -0.5, pHF = -0.5)]][[File:samlyounglimit2.png|thumb|upright=0.80|left|Figure 12 - Reaction of H2 + F (H-H = 0.74Å, H-F = 2.0Å, pHH = -2.49, pHF = -0.5)]]
[[File:fhhidealsly.png|thumb|upright=0.80|centre|Figure 13 - Reaction of H2 + F (H-H = 2Å, H-F = 0.74Å, pHH = -0.61, pHF = -0.5)]][[File:slylowtrans.png|thumb|upright=0.80|left|Figure 13 - Reaction of H2 + F (H-H = 2Å, H-F = 0.74Å, pHH = -0.1, pHF = -0.5)]][[File:translationalsamsam.png|thumb|upright=0.80|centre|Figure 10 - Reaction of H2 + F (H-H = 2Å, H-F = 0.74Å, pHH = -3.0, pHF = -0.5)]]

= Bibliography =

Electronegativity values : https://sciencenotes.org/list-of-electronegativity-values-of-the-elements/

Sam Young Reaction Dynamics

2018-05-18T13:39:56Z

Sly116: /* Q5 - Efficiency of Reaction */

= H + H2 System =
== Q1 - Transition State Gradients ==
[[File:Sly-Saddle.png|thumb|upright=0.8|centre|Figure 1 - Potential Energy Surface Plot of H2 + H System, with initial conditions A-B distance = 0.74, B-C distance = 2.30, AB momentum = 0 & BC momentum = 2.7]]

The minimum energy surface, shown running along the bottom of figure one obeys the derivative; ∂V/∂(rx) = ∂V/∂(ry) = 0, with rx and ry run parallel to their respective gradients. However, the saddle point where the transition state lies is located along the minimum energy surface at the maximum point. Therefore, it can be found by taking the second derivative, as the two orthogonal gradients have different signs, with one along the potential energy minimum being negative and the other orthogonal graident being positive.

∂2V/∂(rx)2 > 0

∂2V/∂(ry)2 < 0

== Q2 - Transition State Estimate ==

By making the momentum of the whole system equal to zero, it was possible to put the AB distance = BC distance and alter this value to obtain a result for the rts, which was found to be approximately 0.9077Å (one value due to the system being completely symmetric), which gave figure 2. This number was found by taking the intersect of the AB and BC lines from the internuclear plot with the same initial conditions given above, and optimising this value to give constant distances. Due to the gradient of potential energy at the transition state being zero, the system has no kinetic energy, only potential energy. Therefore, there is no oscillation and the plot of internuclear distance against time shows constant interatomic distances.

[[File:Sly_Q2.png|thumb|upright=0.80|centre|Figure 2 - Internucleur Distance]]

== Q3 - MEP ==

The MEP is the minimum energy pathway followed for the reaction H2 + H to take place, although it can be seen in figures 4 and 5 that it differs from the dynamic trajectory due to the masses of the atoms, and therefore the bond oscillations along the trajectory causing deviations from the mep. This is shown by the wavy black line on figure 5. Both figures illustrate the reaction path (represented by the black line) starting at the transition state point, with the dynamic reaction going to the complete formation of a H2 product, while the mep plot shows it going only slightly towards the product formation.

'''change with + - 0.01 and discuss'''

[[File:Sly_MEP2.png|thumb|upright=0.80|centre|Figure 4 - Minimum Energy Pathway]] [[File:newdynamicsam.png|thumb|upright=0.80|centre|Figure 5 - Dynamic Trajectory]]

== Q4 - Reactive and Unreactive Trajectories==

{| class="wikitable" border=1
! p1 !! p2 !! Total Energy !! Reactive or Unreactive !! Trajectory Plot !! Discussion
|-
| -1.25 || -2.5 || -99.018 || [[File:SY-1.png|frameless|upright=0.80]] || Reactive || The reactivity of the trajectory is shown as the reaction path progresses towards the prodcut H2. Upon forming, the new bond vibrates.
|-
| -1.5 || -2.0 || -100.456 || [[File:SY-2.png|frameless|upright=0.80]] || Unreactive || This figure represents an unreactive system due to the approaching H atom not having enough energy to overcome the activation barrier for the reaction. This results in the reaction trajectory returning to the original H2 bond oscillating back towards its energy minimum.
|-
| -1.5 || -2.5 || -98.956 || [[File:SY-3.png|frameless|upright=0.80]] || Reactive || This model shows a very simimlar picture to the first in the table, although due to p1 being slightly higher, the original H2 bond oscillates with higher energy.
|-
| -2.5 || -5.0 || -84.956 || [[File:SLY4.png|frameless|upright=0.80]] || Unreactive || Here one H atom aproaches the H2 molecule and the transition state complex H-H-H forms, however due to a lack of energy, the trajectory path is unable to continue to form the products so returns to the original reactants.
|-
| -2.5 || -5.2 || -83.416 ||[[File:SY5.png|frameless|upright=0.80]] || Reactive || The case has a high enough energy to form the transition state complex and to continue to overcome the energy barrier to obtain the products.
|}

== Q5 - Transition State Theory ==

Transition state theory focusses on the activated complexes formed at a transition state of the reaction, therefore by examining the transition state of a potential surface plot (found at the saddle point) one can obtain the rate of a reaction, due to the activated complex's quasi-equilibrium with the reactants. It assumes that if the collision is of sufficient energy to overcome the transition state, the products will form. This is based on the assumption that molecules react according to the classical picture, and does not take quantum mechanics into account, leading to limitations when considering phenomena such as tunnelling, whereby the reaction path bypasses a low activation energy. Furthermore the transition state theory does not account for reactions recrossing the activation barrier to return to the products as shown above. As a result, this theory would give a higher rate to the real situation.

= F H H System =

== Q1 - Energetics ==

F + H2
This reaction is shown to be exothermic (i.e. the system releases energy upon reacting, ΔH < 0) from the plot due to the energy minimum of the FH bond being lower in energy than the HH bond, therefore more stable. This is due to the large electronegativity difference between F (3.98) and H (2.20), as opposed to the non polar HH bond. As a result, the reaction of FH + H is therefore endothermic for the same reasons.

'''Talk about enthalpies of formation/dissociation'''

[[File:SLYFH.png|thumb|upright=0.80|centre|Figure 6]]

== Q2 - Position of the Transition State ==

The transition state can be found at the point where the internuclear distances of the atoms does not change over time. This is the same point on the graph for both the forward and reverse reactions. By using Hammond's postulate, that the activated intermediate complex at the transition state should resemble the state that it is closest in energy to, therefore similar to an HF + H model. As a result, it was possible to look at the surface plot and optimise the bond distances around where the transition state was roughly located. It was found that the approximate internuclear distances at this transition state are H-F : 1.810 and H-H : 0.746.

[[File:tshighlight.png|thumb|none|Figure 7]] [[File:transstatesly.png|thumb|upright=0.80|none|Figure 8]]

== Q3 - Activation Energy ==

By finding the equilibrium bond length of both reactants and products, and knowing the location of the transition state, it was possible to obtain energies for all of these positions, and therefore calculate the energy of activation.

Energy at HF minimum -133.586 AB 2.3 BC 0.9

Energy at HH minimum -103.33 AB 0.7 BC 2.3

Energy at transition state -103.742 AB 0.75 BC 1.81

ΔE = E(transition state) - E(reactants)

''ΔEFH + H‡ = (-103.742) - (-133.586) = 29.844 Kcalmol-1''

''ΔEH2 + F‡ = (-103.742) - (-103.330) = 0.412 Kcalmol-1''

== Q4 - Mechanism of Release of the Activation Energy ==

F + H2

This plot shows the reaction of initial conditions FH distance = 2.30Å HH distance = 0.85Å FH momentm = -7.0 HH momentum = -1.0, resulting in a successful reaction. Due to the exothermic nature of this reaction, it releases energy as the products have a lower potential energy than the reactants, and from the plot of internuclear distance vs. time, it is clear that this energy is converted to kinetic energy in the form of an oscillating F-H bond, which oscillates at a much higher energy than the original H-H bond. This could be confirmed experimentally by IR which would show the vibrationally excited state of the H-F bond, or energy can be measured by calorimetry.

[[File:slyreactive.png|thumb|upright=0.80|centre|Figure 9]]

== Q5 - Efficiency of Reaction ==

[[File:fh2highvibworks.png|thumb|upright=0.80|left|Figure 10 - Reaction of H2 + F (H-H = 0.74Å, H-F = 2.Å, pHH = -3.0, pHF = -0.5)]][[File:lowvibsamyoung.png|thumb|upright=0.80|centre|Figure 11 - Reaction of H2 + F (H-H = 0.74Å, H-F = 2.0Å, pHH = -0.5, pHF = -0.5)]][[File:samlyounglimit2.png|thumb|upright=0.80|left|Figure 12 - Reaction of H2 + F (H-H = 0.74Å, H-F = 2.0Å, pHH = -2.49, pHF = -0.5)]]
[[File:fhhidealsly.png|thumb|upright=0.80|centre|Figure 13 - Reaction of H2 + F (H-H = 2Å, H-F = 0.74Å, pHH = -0.61, pHF = -0.5)]][[File:slylowtrans.png|thumb|upright=0.80|left|Figure 13 - Reaction of H2 + F (H-H = 2Å, H-F = 0.74Å, pHH = -0.1, pHF = -0.5)]][[File:translationalsamsam.png|thumb|upright=0.80|centre|Figure 10 - Reaction of H2 + F (H-H = 2Å, H-F = 0.74Å, pHH = -3.0, pHF = -0.5)]]

= Bibliography =

Electronegativity values : https://sciencenotes.org/list-of-electronegativity-values-of-the-elements/

Sam Young Reaction Dynamics

2018-05-18T13:39:05Z

Sly116: /* Q5 - Efficiency of Reaction */

= H + H2 System =
== Q1 - Transition State Gradients ==
[[File:Sly-Saddle.png|thumb|upright=0.8|centre|Figure 1 - Potential Energy Surface Plot of H2 + H System, with initial conditions A-B distance = 0.74, B-C distance = 2.30, AB momentum = 0 & BC momentum = 2.7]]

The minimum energy surface, shown running along the bottom of figure one obeys the derivative; ∂V/∂(rx) = ∂V/∂(ry) = 0, with rx and ry run parallel to their respective gradients. However, the saddle point where the transition state lies is located along the minimum energy surface at the maximum point. Therefore, it can be found by taking the second derivative, as the two orthogonal gradients have different signs, with one along the potential energy minimum being negative and the other orthogonal graident being positive.

∂2V/∂(rx)2 > 0

∂2V/∂(ry)2 < 0

== Q2 - Transition State Estimate ==

By making the momentum of the whole system equal to zero, it was possible to put the AB distance = BC distance and alter this value to obtain a result for the rts, which was found to be approximately 0.9077Å (one value due to the system being completely symmetric), which gave figure 2. This number was found by taking the intersect of the AB and BC lines from the internuclear plot with the same initial conditions given above, and optimising this value to give constant distances. Due to the gradient of potential energy at the transition state being zero, the system has no kinetic energy, only potential energy. Therefore, there is no oscillation and the plot of internuclear distance against time shows constant interatomic distances.

[[File:Sly_Q2.png|thumb|upright=0.80|centre|Figure 2 - Internucleur Distance]]

== Q3 - MEP ==

The MEP is the minimum energy pathway followed for the reaction H2 + H to take place, although it can be seen in figures 4 and 5 that it differs from the dynamic trajectory due to the masses of the atoms, and therefore the bond oscillations along the trajectory causing deviations from the mep. This is shown by the wavy black line on figure 5. Both figures illustrate the reaction path (represented by the black line) starting at the transition state point, with the dynamic reaction going to the complete formation of a H2 product, while the mep plot shows it going only slightly towards the product formation.

'''change with + - 0.01 and discuss'''

[[File:Sly_MEP2.png|thumb|upright=0.80|centre|Figure 4 - Minimum Energy Pathway]] [[File:newdynamicsam.png|thumb|upright=0.80|centre|Figure 5 - Dynamic Trajectory]]

== Q4 - Reactive and Unreactive Trajectories==

{| class="wikitable" border=1
! p1 !! p2 !! Total Energy !! Reactive or Unreactive !! Trajectory Plot !! Discussion
|-
| -1.25 || -2.5 || -99.018 || [[File:SY-1.png|frameless|upright=0.80]] || Reactive || The reactivity of the trajectory is shown as the reaction path progresses towards the prodcut H2. Upon forming, the new bond vibrates.
|-
| -1.5 || -2.0 || -100.456 || [[File:SY-2.png|frameless|upright=0.80]] || Unreactive || This figure represents an unreactive system due to the approaching H atom not having enough energy to overcome the activation barrier for the reaction. This results in the reaction trajectory returning to the original H2 bond oscillating back towards its energy minimum.
|-
| -1.5 || -2.5 || -98.956 || [[File:SY-3.png|frameless|upright=0.80]] || Reactive || This model shows a very simimlar picture to the first in the table, although due to p1 being slightly higher, the original H2 bond oscillates with higher energy.
|-
| -2.5 || -5.0 || -84.956 || [[File:SLY4.png|frameless|upright=0.80]] || Unreactive || Here one H atom aproaches the H2 molecule and the transition state complex H-H-H forms, however due to a lack of energy, the trajectory path is unable to continue to form the products so returns to the original reactants.
|-
| -2.5 || -5.2 || -83.416 ||[[File:SY5.png|frameless|upright=0.80]] || Reactive || The case has a high enough energy to form the transition state complex and to continue to overcome the energy barrier to obtain the products.
|}

== Q5 - Transition State Theory ==

Transition state theory focusses on the activated complexes formed at a transition state of the reaction, therefore by examining the transition state of a potential surface plot (found at the saddle point) one can obtain the rate of a reaction, due to the activated complex's quasi-equilibrium with the reactants. It assumes that if the collision is of sufficient energy to overcome the transition state, the products will form. This is based on the assumption that molecules react according to the classical picture, and does not take quantum mechanics into account, leading to limitations when considering phenomena such as tunnelling, whereby the reaction path bypasses a low activation energy. Furthermore the transition state theory does not account for reactions recrossing the activation barrier to return to the products as shown above. As a result, this theory would give a higher rate to the real situation.

= F H H System =

== Q1 - Energetics ==

F + H2
This reaction is shown to be exothermic (i.e. the system releases energy upon reacting, ΔH < 0) from the plot due to the energy minimum of the FH bond being lower in energy than the HH bond, therefore more stable. This is due to the large electronegativity difference between F (3.98) and H (2.20), as opposed to the non polar HH bond. As a result, the reaction of FH + H is therefore endothermic for the same reasons.

'''Talk about enthalpies of formation/dissociation'''

[[File:SLYFH.png|thumb|upright=0.80|centre|Figure 6]]

== Q2 - Position of the Transition State ==

The transition state can be found at the point where the internuclear distances of the atoms does not change over time. This is the same point on the graph for both the forward and reverse reactions. By using Hammond's postulate, that the activated intermediate complex at the transition state should resemble the state that it is closest in energy to, therefore similar to an HF + H model. As a result, it was possible to look at the surface plot and optimise the bond distances around where the transition state was roughly located. It was found that the approximate internuclear distances at this transition state are H-F : 1.810 and H-H : 0.746.

[[File:tshighlight.png|thumb|none|Figure 7]] [[File:transstatesly.png|thumb|upright=0.80|none|Figure 8]]

== Q3 - Activation Energy ==

By finding the equilibrium bond length of both reactants and products, and knowing the location of the transition state, it was possible to obtain energies for all of these positions, and therefore calculate the energy of activation.

Energy at HF minimum -133.586 AB 2.3 BC 0.9

Energy at HH minimum -103.33 AB 0.7 BC 2.3

Energy at transition state -103.742 AB 0.75 BC 1.81

ΔE = E(transition state) - E(reactants)

''ΔEFH + H‡ = (-103.742) - (-133.586) = 29.844 Kcalmol-1''

''ΔEH2 + F‡ = (-103.742) - (-103.330) = 0.412 Kcalmol-1''

== Q4 - Mechanism of Release of the Activation Energy ==

F + H2

This plot shows the reaction of initial conditions FH distance = 2.30Å HH distance = 0.85Å FH momentm = -7.0 HH momentum = -1.0, resulting in a successful reaction. Due to the exothermic nature of this reaction, it releases energy as the products have a lower potential energy than the reactants, and from the plot of internuclear distance vs. time, it is clear that this energy is converted to kinetic energy in the form of an oscillating F-H bond, which oscillates at a much higher energy than the original H-H bond. This could be confirmed experimentally by IR which would show the vibrationally excited state of the H-F bond, or energy can be measured by calorimetry.

[[File:slyreactive.png|thumb|upright=0.80|centre|Figure 9]]

== Q5 - Efficiency of Reaction ==

[[File:fh2highvibworks.png|thumb|upright=0.80|centre|Figure 10 - Reaction of H2 + F (H-H = 0.74Å, H-F = 2.Å, pHH = -3.0, pHF = -0.5)]]

[[File:lowvibsamyoung.png|thumb|upright=0.80|centre|Figure 11 - Reaction of H2 + F (H-H = 0.74Å, H-F = 2.0Å, pHH = -0.5, pHF = -0.5)]]

[[File:samlyounglimit2.png|thumb|upright=0.80|centre|Figure 12 - Reaction of H2 + F (H-H = 0.74Å, H-F = 2.0Å, pHH = -2.49, pHF = -0.5)]]

[[File:fhhidealsly.png|thumb|upright=0.80|left|Figure 13 - Reaction of H2 + F (H-H = 2Å, H-F = 0.74Å, pHH = -0.61, pHF = -0.5)]][[File:slylowtrans.png|thumb|upright=0.80|centre|Figure 13 - Reaction of H2 + F (H-H = 2Å, H-F = 0.74Å, pHH = -0.1, pHF = -0.5)]][[File:translationalsamsam.png|thumb|upright=0.80|right|Figure 10 - Reaction of H2 + F (H-H = 2Å, H-F = 0.74Å, pHH = -3.0, pHF = -0.5)]]

= Bibliography =

Electronegativity values : https://sciencenotes.org/list-of-electronegativity-values-of-the-elements/

Sam Young Reaction Dynamics

2018-05-18T13:37:22Z

Sly116: /* Q5 - Efficiency of Reaction */

= H + H2 System =
== Q1 - Transition State Gradients ==
[[File:Sly-Saddle.png|thumb|upright=0.8|centre|Figure 1 - Potential Energy Surface Plot of H2 + H System, with initial conditions A-B distance = 0.74, B-C distance = 2.30, AB momentum = 0 & BC momentum = 2.7]]

The minimum energy surface, shown running along the bottom of figure one obeys the derivative; ∂V/∂(rx) = ∂V/∂(ry) = 0, with rx and ry run parallel to their respective gradients. However, the saddle point where the transition state lies is located along the minimum energy surface at the maximum point. Therefore, it can be found by taking the second derivative, as the two orthogonal gradients have different signs, with one along the potential energy minimum being negative and the other orthogonal graident being positive.

∂2V/∂(rx)2 > 0

∂2V/∂(ry)2 < 0

== Q2 - Transition State Estimate ==

By making the momentum of the whole system equal to zero, it was possible to put the AB distance = BC distance and alter this value to obtain a result for the rts, which was found to be approximately 0.9077Å (one value due to the system being completely symmetric), which gave figure 2. This number was found by taking the intersect of the AB and BC lines from the internuclear plot with the same initial conditions given above, and optimising this value to give constant distances. Due to the gradient of potential energy at the transition state being zero, the system has no kinetic energy, only potential energy. Therefore, there is no oscillation and the plot of internuclear distance against time shows constant interatomic distances.

[[File:Sly_Q2.png|thumb|upright=0.80|centre|Figure 2 - Internucleur Distance]]

== Q3 - MEP ==

The MEP is the minimum energy pathway followed for the reaction H2 + H to take place, although it can be seen in figures 4 and 5 that it differs from the dynamic trajectory due to the masses of the atoms, and therefore the bond oscillations along the trajectory causing deviations from the mep. This is shown by the wavy black line on figure 5. Both figures illustrate the reaction path (represented by the black line) starting at the transition state point, with the dynamic reaction going to the complete formation of a H2 product, while the mep plot shows it going only slightly towards the product formation.

'''change with + - 0.01 and discuss'''

[[File:Sly_MEP2.png|thumb|upright=0.80|centre|Figure 4 - Minimum Energy Pathway]] [[File:newdynamicsam.png|thumb|upright=0.80|centre|Figure 5 - Dynamic Trajectory]]

== Q4 - Reactive and Unreactive Trajectories==

{| class="wikitable" border=1
! p1 !! p2 !! Total Energy !! Reactive or Unreactive !! Trajectory Plot !! Discussion
|-
| -1.25 || -2.5 || -99.018 || [[File:SY-1.png|frameless|upright=0.80]] || Reactive || The reactivity of the trajectory is shown as the reaction path progresses towards the prodcut H2. Upon forming, the new bond vibrates.
|-
| -1.5 || -2.0 || -100.456 || [[File:SY-2.png|frameless|upright=0.80]] || Unreactive || This figure represents an unreactive system due to the approaching H atom not having enough energy to overcome the activation barrier for the reaction. This results in the reaction trajectory returning to the original H2 bond oscillating back towards its energy minimum.
|-
| -1.5 || -2.5 || -98.956 || [[File:SY-3.png|frameless|upright=0.80]] || Reactive || This model shows a very simimlar picture to the first in the table, although due to p1 being slightly higher, the original H2 bond oscillates with higher energy.
|-
| -2.5 || -5.0 || -84.956 || [[File:SLY4.png|frameless|upright=0.80]] || Unreactive || Here one H atom aproaches the H2 molecule and the transition state complex H-H-H forms, however due to a lack of energy, the trajectory path is unable to continue to form the products so returns to the original reactants.
|-
| -2.5 || -5.2 || -83.416 ||[[File:SY5.png|frameless|upright=0.80]] || Reactive || The case has a high enough energy to form the transition state complex and to continue to overcome the energy barrier to obtain the products.
|}

== Q5 - Transition State Theory ==

Transition state theory focusses on the activated complexes formed at a transition state of the reaction, therefore by examining the transition state of a potential surface plot (found at the saddle point) one can obtain the rate of a reaction, due to the activated complex's quasi-equilibrium with the reactants. It assumes that if the collision is of sufficient energy to overcome the transition state, the products will form. This is based on the assumption that molecules react according to the classical picture, and does not take quantum mechanics into account, leading to limitations when considering phenomena such as tunnelling, whereby the reaction path bypasses a low activation energy. Furthermore the transition state theory does not account for reactions recrossing the activation barrier to return to the products as shown above. As a result, this theory would give a higher rate to the real situation.

= F H H System =

== Q1 - Energetics ==

F + H2
This reaction is shown to be exothermic (i.e. the system releases energy upon reacting, ΔH < 0) from the plot due to the energy minimum of the FH bond being lower in energy than the HH bond, therefore more stable. This is due to the large electronegativity difference between F (3.98) and H (2.20), as opposed to the non polar HH bond. As a result, the reaction of FH + H is therefore endothermic for the same reasons.

'''Talk about enthalpies of formation/dissociation'''

[[File:SLYFH.png|thumb|upright=0.80|centre|Figure 6]]

== Q2 - Position of the Transition State ==

The transition state can be found at the point where the internuclear distances of the atoms does not change over time. This is the same point on the graph for both the forward and reverse reactions. By using Hammond's postulate, that the activated intermediate complex at the transition state should resemble the state that it is closest in energy to, therefore similar to an HF + H model. As a result, it was possible to look at the surface plot and optimise the bond distances around where the transition state was roughly located. It was found that the approximate internuclear distances at this transition state are H-F : 1.810 and H-H : 0.746.

[[File:tshighlight.png|thumb|none|Figure 7]] [[File:transstatesly.png|thumb|upright=0.80|none|Figure 8]]

== Q3 - Activation Energy ==

By finding the equilibrium bond length of both reactants and products, and knowing the location of the transition state, it was possible to obtain energies for all of these positions, and therefore calculate the energy of activation.

Energy at HF minimum -133.586 AB 2.3 BC 0.9

Energy at HH minimum -103.33 AB 0.7 BC 2.3

Energy at transition state -103.742 AB 0.75 BC 1.81

ΔE = E(transition state) - E(reactants)

''ΔEFH + H‡ = (-103.742) - (-133.586) = 29.844 Kcalmol-1''

''ΔEH2 + F‡ = (-103.742) - (-103.330) = 0.412 Kcalmol-1''

== Q4 - Mechanism of Release of the Activation Energy ==

F + H2

This plot shows the reaction of initial conditions FH distance = 2.30Å HH distance = 0.85Å FH momentm = -7.0 HH momentum = -1.0, resulting in a successful reaction. Due to the exothermic nature of this reaction, it releases energy as the products have a lower potential energy than the reactants, and from the plot of internuclear distance vs. time, it is clear that this energy is converted to kinetic energy in the form of an oscillating F-H bond, which oscillates at a much higher energy than the original H-H bond. This could be confirmed experimentally by IR which would show the vibrationally excited state of the H-F bond, or energy can be measured by calorimetry.

[[File:slyreactive.png|thumb|upright=0.80|centre|Figure 9]]

== Q5 - Efficiency of Reaction ==

[[File:fh2highvibworks.png|thumb|upright=0.80|centre|Figure 10 - Reaction of H2 + F (H-H = 0.74Å, H-F = 2.Å, pHH = -3.0, pHF = -0.5)]]

[[File:lowvibsamyoung.png|thumb|upright=0.80|centre|Figure 11 - Reaction of H2 + F (H-H = 0.74Å, H-F = 2.0Å, pHH = -0.5, pHF = -0.5)]]

[[File:samlyounglimit2.png|thumb|upright=0.80|centre|Figure 12 - Reaction of H2 + F (H-H = 0.74Å, H-F = 2.0Å, pHH = -2.49, pHF = -0.5)]]

[[File:fhhidealsly.png|thumb|upright=0.80|centre|Figure 13 - Reaction of H2 + F (H-H = 2Å, H-F = 0.74Å, pHH = -0.61, pHF = -0.5)]]

[[File:slylowtrans.png|thumb|upright=0.80|centre|Figure 13 - Reaction of H2 + F (H-H = 2Å, H-F = 0.74Å, pHH = -0.1, pHF = -0.5)]]

[[File:translationalsamsam.png|thumb|upright=0.80|centre|Figure 10 - Reaction of H2 + F (H-H = 2Å, H-F = 0.74Å, pHH = -3.0, pHF = -0.5)]]

= Bibliography =

Electronegativity values : https://sciencenotes.org/list-of-electronegativity-values-of-the-elements/

File:Translationalsamsam.png

2018-05-18T13:36:51Z

Sly116:

Sam Young Reaction Dynamics

2018-05-18T13:36:40Z

Sly116: /* Q5 - Efficiency of Reaction */

= H + H2 System =
== Q1 - Transition State Gradients ==
[[File:Sly-Saddle.png|thumb|upright=0.8|centre|Figure 1 - Potential Energy Surface Plot of H2 + H System, with initial conditions A-B distance = 0.74, B-C distance = 2.30, AB momentum = 0 & BC momentum = 2.7]]

The minimum energy surface, shown running along the bottom of figure one obeys the derivative; ∂V/∂(rx) = ∂V/∂(ry) = 0, with rx and ry run parallel to their respective gradients. However, the saddle point where the transition state lies is located along the minimum energy surface at the maximum point. Therefore, it can be found by taking the second derivative, as the two orthogonal gradients have different signs, with one along the potential energy minimum being negative and the other orthogonal graident being positive.

∂2V/∂(rx)2 > 0

∂2V/∂(ry)2 < 0

== Q2 - Transition State Estimate ==

By making the momentum of the whole system equal to zero, it was possible to put the AB distance = BC distance and alter this value to obtain a result for the rts, which was found to be approximately 0.9077Å (one value due to the system being completely symmetric), which gave figure 2. This number was found by taking the intersect of the AB and BC lines from the internuclear plot with the same initial conditions given above, and optimising this value to give constant distances. Due to the gradient of potential energy at the transition state being zero, the system has no kinetic energy, only potential energy. Therefore, there is no oscillation and the plot of internuclear distance against time shows constant interatomic distances.

[[File:Sly_Q2.png|thumb|upright=0.80|centre|Figure 2 - Internucleur Distance]]

== Q3 - MEP ==

The MEP is the minimum energy pathway followed for the reaction H2 + H to take place, although it can be seen in figures 4 and 5 that it differs from the dynamic trajectory due to the masses of the atoms, and therefore the bond oscillations along the trajectory causing deviations from the mep. This is shown by the wavy black line on figure 5. Both figures illustrate the reaction path (represented by the black line) starting at the transition state point, with the dynamic reaction going to the complete formation of a H2 product, while the mep plot shows it going only slightly towards the product formation.

'''change with + - 0.01 and discuss'''

[[File:Sly_MEP2.png|thumb|upright=0.80|centre|Figure 4 - Minimum Energy Pathway]] [[File:newdynamicsam.png|thumb|upright=0.80|centre|Figure 5 - Dynamic Trajectory]]

== Q4 - Reactive and Unreactive Trajectories==

{| class="wikitable" border=1
! p1 !! p2 !! Total Energy !! Reactive or Unreactive !! Trajectory Plot !! Discussion
|-
| -1.25 || -2.5 || -99.018 || [[File:SY-1.png|frameless|upright=0.80]] || Reactive || The reactivity of the trajectory is shown as the reaction path progresses towards the prodcut H2. Upon forming, the new bond vibrates.
|-
| -1.5 || -2.0 || -100.456 || [[File:SY-2.png|frameless|upright=0.80]] || Unreactive || This figure represents an unreactive system due to the approaching H atom not having enough energy to overcome the activation barrier for the reaction. This results in the reaction trajectory returning to the original H2 bond oscillating back towards its energy minimum.
|-
| -1.5 || -2.5 || -98.956 || [[File:SY-3.png|frameless|upright=0.80]] || Reactive || This model shows a very simimlar picture to the first in the table, although due to p1 being slightly higher, the original H2 bond oscillates with higher energy.
|-
| -2.5 || -5.0 || -84.956 || [[File:SLY4.png|frameless|upright=0.80]] || Unreactive || Here one H atom aproaches the H2 molecule and the transition state complex H-H-H forms, however due to a lack of energy, the trajectory path is unable to continue to form the products so returns to the original reactants.
|-
| -2.5 || -5.2 || -83.416 ||[[File:SY5.png|frameless|upright=0.80]] || Reactive || The case has a high enough energy to form the transition state complex and to continue to overcome the energy barrier to obtain the products.
|}

== Q5 - Transition State Theory ==

Transition state theory focusses on the activated complexes formed at a transition state of the reaction, therefore by examining the transition state of a potential surface plot (found at the saddle point) one can obtain the rate of a reaction, due to the activated complex's quasi-equilibrium with the reactants. It assumes that if the collision is of sufficient energy to overcome the transition state, the products will form. This is based on the assumption that molecules react according to the classical picture, and does not take quantum mechanics into account, leading to limitations when considering phenomena such as tunnelling, whereby the reaction path bypasses a low activation energy. Furthermore the transition state theory does not account for reactions recrossing the activation barrier to return to the products as shown above. As a result, this theory would give a higher rate to the real situation.

= F H H System =

== Q1 - Energetics ==

F + H2
This reaction is shown to be exothermic (i.e. the system releases energy upon reacting, ΔH < 0) from the plot due to the energy minimum of the FH bond being lower in energy than the HH bond, therefore more stable. This is due to the large electronegativity difference between F (3.98) and H (2.20), as opposed to the non polar HH bond. As a result, the reaction of FH + H is therefore endothermic for the same reasons.

'''Talk about enthalpies of formation/dissociation'''

[[File:SLYFH.png|thumb|upright=0.80|centre|Figure 6]]

== Q2 - Position of the Transition State ==

The transition state can be found at the point where the internuclear distances of the atoms does not change over time. This is the same point on the graph for both the forward and reverse reactions. By using Hammond's postulate, that the activated intermediate complex at the transition state should resemble the state that it is closest in energy to, therefore similar to an HF + H model. As a result, it was possible to look at the surface plot and optimise the bond distances around where the transition state was roughly located. It was found that the approximate internuclear distances at this transition state are H-F : 1.810 and H-H : 0.746.

[[File:tshighlight.png|thumb|none|Figure 7]] [[File:transstatesly.png|thumb|upright=0.80|none|Figure 8]]

== Q3 - Activation Energy ==

By finding the equilibrium bond length of both reactants and products, and knowing the location of the transition state, it was possible to obtain energies for all of these positions, and therefore calculate the energy of activation.

Energy at HF minimum -133.586 AB 2.3 BC 0.9

Energy at HH minimum -103.33 AB 0.7 BC 2.3

Energy at transition state -103.742 AB 0.75 BC 1.81

ΔE = E(transition state) - E(reactants)

''ΔEFH + H‡ = (-103.742) - (-133.586) = 29.844 Kcalmol-1''

''ΔEH2 + F‡ = (-103.742) - (-103.330) = 0.412 Kcalmol-1''

== Q4 - Mechanism of Release of the Activation Energy ==

F + H2

This plot shows the reaction of initial conditions FH distance = 2.30Å HH distance = 0.85Å FH momentm = -7.0 HH momentum = -1.0, resulting in a successful reaction. Due to the exothermic nature of this reaction, it releases energy as the products have a lower potential energy than the reactants, and from the plot of internuclear distance vs. time, it is clear that this energy is converted to kinetic energy in the form of an oscillating F-H bond, which oscillates at a much higher energy than the original H-H bond. This could be confirmed experimentally by IR which would show the vibrationally excited state of the H-F bond, or energy can be measured by calorimetry.

[[File:slyreactive.png|thumb|upright=0.80|centre|Figure 9]]

== Q5 - Efficiency of Reaction ==

[[File:fh2highvibworks.png|thumb|upright=0.80|centre|Figure 10 - Reaction of H2 + F (H-H = 0.74Å, H-F = 2.Å, pHH = -3.0, pHF = -0.5)]]

[[File:lowvibsamyoung.png|thumb|upright=0.80|centre|Figure 11 - Reaction of H2 + F (H-H = 0.74Å, H-F = 2.0Å, pHH = -0.5, pHF = -0.5)]]

[[File:samlyounglimit2.png|thumb|upright=0.80|centre|Figure 12 - Reaction of H2 + F (H-H = 0.74Å, H-F = 2.0Å, pHH = -2.49, pHF = -0.5)]]

[[File:fhhidealsly.png|thumb|upright=0.80|centre|Figure 13 - Reaction of H2 + F (H-H = 2Å, H-F = 0.74Å, pHH = -0.61, pHF = -0.5)]]

[[File:slylowtrans.png|thumb|upright=0.80|centre|Figure 13 - Reaction of H2 + F (H-H = 2Å, H-F = 0.74Å, pHH = -0.1, pHF = -0.5)]]

[[File:translationalsamsam.png]]

= Bibliography =

Electronegativity values : https://sciencenotes.org/list-of-electronegativity-values-of-the-elements/

File:Samsamtrans.png

2018-05-18T13:35:46Z

Sly116:

Sam Young Reaction Dynamics

2018-05-18T13:35:37Z

Sly116: /* Q5 - Efficiency of Reaction */

= H + H2 System =
== Q1 - Transition State Gradients ==
[[File:Sly-Saddle.png|thumb|upright=0.8|centre|Figure 1 - Potential Energy Surface Plot of H2 + H System, with initial conditions A-B distance = 0.74, B-C distance = 2.30, AB momentum = 0 & BC momentum = 2.7]]

The minimum energy surface, shown running along the bottom of figure one obeys the derivative; ∂V/∂(rx) = ∂V/∂(ry) = 0, with rx and ry run parallel to their respective gradients. However, the saddle point where the transition state lies is located along the minimum energy surface at the maximum point. Therefore, it can be found by taking the second derivative, as the two orthogonal gradients have different signs, with one along the potential energy minimum being negative and the other orthogonal graident being positive.

∂2V/∂(rx)2 > 0

∂2V/∂(ry)2 < 0

== Q2 - Transition State Estimate ==

By making the momentum of the whole system equal to zero, it was possible to put the AB distance = BC distance and alter this value to obtain a result for the rts, which was found to be approximately 0.9077Å (one value due to the system being completely symmetric), which gave figure 2. This number was found by taking the intersect of the AB and BC lines from the internuclear plot with the same initial conditions given above, and optimising this value to give constant distances. Due to the gradient of potential energy at the transition state being zero, the system has no kinetic energy, only potential energy. Therefore, there is no oscillation and the plot of internuclear distance against time shows constant interatomic distances.

[[File:Sly_Q2.png|thumb|upright=0.80|centre|Figure 2 - Internucleur Distance]]

== Q3 - MEP ==

The MEP is the minimum energy pathway followed for the reaction H2 + H to take place, although it can be seen in figures 4 and 5 that it differs from the dynamic trajectory due to the masses of the atoms, and therefore the bond oscillations along the trajectory causing deviations from the mep. This is shown by the wavy black line on figure 5. Both figures illustrate the reaction path (represented by the black line) starting at the transition state point, with the dynamic reaction going to the complete formation of a H2 product, while the mep plot shows it going only slightly towards the product formation.

'''change with + - 0.01 and discuss'''

[[File:Sly_MEP2.png|thumb|upright=0.80|centre|Figure 4 - Minimum Energy Pathway]] [[File:newdynamicsam.png|thumb|upright=0.80|centre|Figure 5 - Dynamic Trajectory]]

== Q4 - Reactive and Unreactive Trajectories==

{| class="wikitable" border=1
! p1 !! p2 !! Total Energy !! Reactive or Unreactive !! Trajectory Plot !! Discussion
|-
| -1.25 || -2.5 || -99.018 || [[File:SY-1.png|frameless|upright=0.80]] || Reactive || The reactivity of the trajectory is shown as the reaction path progresses towards the prodcut H2. Upon forming, the new bond vibrates.
|-
| -1.5 || -2.0 || -100.456 || [[File:SY-2.png|frameless|upright=0.80]] || Unreactive || This figure represents an unreactive system due to the approaching H atom not having enough energy to overcome the activation barrier for the reaction. This results in the reaction trajectory returning to the original H2 bond oscillating back towards its energy minimum.
|-
| -1.5 || -2.5 || -98.956 || [[File:SY-3.png|frameless|upright=0.80]] || Reactive || This model shows a very simimlar picture to the first in the table, although due to p1 being slightly higher, the original H2 bond oscillates with higher energy.
|-
| -2.5 || -5.0 || -84.956 || [[File:SLY4.png|frameless|upright=0.80]] || Unreactive || Here one H atom aproaches the H2 molecule and the transition state complex H-H-H forms, however due to a lack of energy, the trajectory path is unable to continue to form the products so returns to the original reactants.
|-
| -2.5 || -5.2 || -83.416 ||[[File:SY5.png|frameless|upright=0.80]] || Reactive || The case has a high enough energy to form the transition state complex and to continue to overcome the energy barrier to obtain the products.
|}

== Q5 - Transition State Theory ==

Transition state theory focusses on the activated complexes formed at a transition state of the reaction, therefore by examining the transition state of a potential surface plot (found at the saddle point) one can obtain the rate of a reaction, due to the activated complex's quasi-equilibrium with the reactants. It assumes that if the collision is of sufficient energy to overcome the transition state, the products will form. This is based on the assumption that molecules react according to the classical picture, and does not take quantum mechanics into account, leading to limitations when considering phenomena such as tunnelling, whereby the reaction path bypasses a low activation energy. Furthermore the transition state theory does not account for reactions recrossing the activation barrier to return to the products as shown above. As a result, this theory would give a higher rate to the real situation.

= F H H System =

== Q1 - Energetics ==

F + H2
This reaction is shown to be exothermic (i.e. the system releases energy upon reacting, ΔH < 0) from the plot due to the energy minimum of the FH bond being lower in energy than the HH bond, therefore more stable. This is due to the large electronegativity difference between F (3.98) and H (2.20), as opposed to the non polar HH bond. As a result, the reaction of FH + H is therefore endothermic for the same reasons.

'''Talk about enthalpies of formation/dissociation'''

[[File:SLYFH.png|thumb|upright=0.80|centre|Figure 6]]

== Q2 - Position of the Transition State ==

The transition state can be found at the point where the internuclear distances of the atoms does not change over time. This is the same point on the graph for both the forward and reverse reactions. By using Hammond's postulate, that the activated intermediate complex at the transition state should resemble the state that it is closest in energy to, therefore similar to an HF + H model. As a result, it was possible to look at the surface plot and optimise the bond distances around where the transition state was roughly located. It was found that the approximate internuclear distances at this transition state are H-F : 1.810 and H-H : 0.746.

[[File:tshighlight.png|thumb|none|Figure 7]] [[File:transstatesly.png|thumb|upright=0.80|none|Figure 8]]

== Q3 - Activation Energy ==

By finding the equilibrium bond length of both reactants and products, and knowing the location of the transition state, it was possible to obtain energies for all of these positions, and therefore calculate the energy of activation.

Energy at HF minimum -133.586 AB 2.3 BC 0.9

Energy at HH minimum -103.33 AB 0.7 BC 2.3

Energy at transition state -103.742 AB 0.75 BC 1.81

ΔE = E(transition state) - E(reactants)

''ΔEFH + H‡ = (-103.742) - (-133.586) = 29.844 Kcalmol-1''

''ΔEH2 + F‡ = (-103.742) - (-103.330) = 0.412 Kcalmol-1''

== Q4 - Mechanism of Release of the Activation Energy ==

F + H2

This plot shows the reaction of initial conditions FH distance = 2.30Å HH distance = 0.85Å FH momentm = -7.0 HH momentum = -1.0, resulting in a successful reaction. Due to the exothermic nature of this reaction, it releases energy as the products have a lower potential energy than the reactants, and from the plot of internuclear distance vs. time, it is clear that this energy is converted to kinetic energy in the form of an oscillating F-H bond, which oscillates at a much higher energy than the original H-H bond. This could be confirmed experimentally by IR which would show the vibrationally excited state of the H-F bond, or energy can be measured by calorimetry.

[[File:slyreactive.png|thumb|upright=0.80|centre|Figure 9]]

== Q5 - Efficiency of Reaction ==

[[File:fh2highvibworks.png|thumb|upright=0.80|centre|Figure 10 - Reaction of H2 + F (H-H = 0.74Å, H-F = 2.Å, pHH = -3.0, pHF = -0.5)]]

[[File:lowvibsamyoung.png|thumb|upright=0.80|centre|Figure 11 - Reaction of H2 + F (H-H = 0.74Å, H-F = 2.0Å, pHH = -0.5, pHF = -0.5)]]

[[File:samlyounglimit2.png|thumb|upright=0.80|centre|Figure 12 - Reaction of H2 + F (H-H = 0.74Å, H-F = 2.0Å, pHH = -2.49, pHF = -0.5)]]

[[File:fhhidealsly.png|thumb|upright=0.80|centre|Figure 13 - Reaction of H2 + F (H-H = 2Å, H-F = 0.74Å, pHH = -0.61, pHF = -0.5)]]

[[File:slylowtrans.png|thumb|upright=0.80|centre|Figure 13 - Reaction of H2 + F (H-H = 2Å, H-F = 0.74Å, pHH = -0.1, pHF = -0.5)]]

[[File:samsamtrans.png|thumb|upright=0.80|centre|Figure 13 - Reaction of H2 + F (H-H = 2Å, H-F = 0.74Å, pHH = -3.0, pHF = -0.5)]]

= Bibliography =

Electronegativity values : https://sciencenotes.org/list-of-electronegativity-values-of-the-elements/

Sam Young Reaction Dynamics

2018-05-18T13:34:44Z

Sly116: /* Q5 - Efficiency of Reaction */

= H + H2 System =
== Q1 - Transition State Gradients ==
[[File:Sly-Saddle.png|thumb|upright=0.8|centre|Figure 1 - Potential Energy Surface Plot of H2 + H System, with initial conditions A-B distance = 0.74, B-C distance = 2.30, AB momentum = 0 & BC momentum = 2.7]]

The minimum energy surface, shown running along the bottom of figure one obeys the derivative; ∂V/∂(rx) = ∂V/∂(ry) = 0, with rx and ry run parallel to their respective gradients. However, the saddle point where the transition state lies is located along the minimum energy surface at the maximum point. Therefore, it can be found by taking the second derivative, as the two orthogonal gradients have different signs, with one along the potential energy minimum being negative and the other orthogonal graident being positive.

∂2V/∂(rx)2 > 0

∂2V/∂(ry)2 < 0

== Q2 - Transition State Estimate ==

By making the momentum of the whole system equal to zero, it was possible to put the AB distance = BC distance and alter this value to obtain a result for the rts, which was found to be approximately 0.9077Å (one value due to the system being completely symmetric), which gave figure 2. This number was found by taking the intersect of the AB and BC lines from the internuclear plot with the same initial conditions given above, and optimising this value to give constant distances. Due to the gradient of potential energy at the transition state being zero, the system has no kinetic energy, only potential energy. Therefore, there is no oscillation and the plot of internuclear distance against time shows constant interatomic distances.

[[File:Sly_Q2.png|thumb|upright=0.80|centre|Figure 2 - Internucleur Distance]]

== Q3 - MEP ==

The MEP is the minimum energy pathway followed for the reaction H2 + H to take place, although it can be seen in figures 4 and 5 that it differs from the dynamic trajectory due to the masses of the atoms, and therefore the bond oscillations along the trajectory causing deviations from the mep. This is shown by the wavy black line on figure 5. Both figures illustrate the reaction path (represented by the black line) starting at the transition state point, with the dynamic reaction going to the complete formation of a H2 product, while the mep plot shows it going only slightly towards the product formation.

'''change with + - 0.01 and discuss'''

[[File:Sly_MEP2.png|thumb|upright=0.80|centre|Figure 4 - Minimum Energy Pathway]] [[File:newdynamicsam.png|thumb|upright=0.80|centre|Figure 5 - Dynamic Trajectory]]

== Q4 - Reactive and Unreactive Trajectories==

{| class="wikitable" border=1
! p1 !! p2 !! Total Energy !! Reactive or Unreactive !! Trajectory Plot !! Discussion
|-
| -1.25 || -2.5 || -99.018 || [[File:SY-1.png|frameless|upright=0.80]] || Reactive || The reactivity of the trajectory is shown as the reaction path progresses towards the prodcut H2. Upon forming, the new bond vibrates.
|-
| -1.5 || -2.0 || -100.456 || [[File:SY-2.png|frameless|upright=0.80]] || Unreactive || This figure represents an unreactive system due to the approaching H atom not having enough energy to overcome the activation barrier for the reaction. This results in the reaction trajectory returning to the original H2 bond oscillating back towards its energy minimum.
|-
| -1.5 || -2.5 || -98.956 || [[File:SY-3.png|frameless|upright=0.80]] || Reactive || This model shows a very simimlar picture to the first in the table, although due to p1 being slightly higher, the original H2 bond oscillates with higher energy.
|-
| -2.5 || -5.0 || -84.956 || [[File:SLY4.png|frameless|upright=0.80]] || Unreactive || Here one H atom aproaches the H2 molecule and the transition state complex H-H-H forms, however due to a lack of energy, the trajectory path is unable to continue to form the products so returns to the original reactants.
|-
| -2.5 || -5.2 || -83.416 ||[[File:SY5.png|frameless|upright=0.80]] || Reactive || The case has a high enough energy to form the transition state complex and to continue to overcome the energy barrier to obtain the products.
|}

== Q5 - Transition State Theory ==

Transition state theory focusses on the activated complexes formed at a transition state of the reaction, therefore by examining the transition state of a potential surface plot (found at the saddle point) one can obtain the rate of a reaction, due to the activated complex's quasi-equilibrium with the reactants. It assumes that if the collision is of sufficient energy to overcome the transition state, the products will form. This is based on the assumption that molecules react according to the classical picture, and does not take quantum mechanics into account, leading to limitations when considering phenomena such as tunnelling, whereby the reaction path bypasses a low activation energy. Furthermore the transition state theory does not account for reactions recrossing the activation barrier to return to the products as shown above. As a result, this theory would give a higher rate to the real situation.

= F H H System =

== Q1 - Energetics ==

F + H2
This reaction is shown to be exothermic (i.e. the system releases energy upon reacting, ΔH < 0) from the plot due to the energy minimum of the FH bond being lower in energy than the HH bond, therefore more stable. This is due to the large electronegativity difference between F (3.98) and H (2.20), as opposed to the non polar HH bond. As a result, the reaction of FH + H is therefore endothermic for the same reasons.

'''Talk about enthalpies of formation/dissociation'''

[[File:SLYFH.png|thumb|upright=0.80|centre|Figure 6]]

== Q2 - Position of the Transition State ==

The transition state can be found at the point where the internuclear distances of the atoms does not change over time. This is the same point on the graph for both the forward and reverse reactions. By using Hammond's postulate, that the activated intermediate complex at the transition state should resemble the state that it is closest in energy to, therefore similar to an HF + H model. As a result, it was possible to look at the surface plot and optimise the bond distances around where the transition state was roughly located. It was found that the approximate internuclear distances at this transition state are H-F : 1.810 and H-H : 0.746.

[[File:tshighlight.png|thumb|none|Figure 7]] [[File:transstatesly.png|thumb|upright=0.80|none|Figure 8]]

== Q3 - Activation Energy ==

By finding the equilibrium bond length of both reactants and products, and knowing the location of the transition state, it was possible to obtain energies for all of these positions, and therefore calculate the energy of activation.

Energy at HF minimum -133.586 AB 2.3 BC 0.9

Energy at HH minimum -103.33 AB 0.7 BC 2.3

Energy at transition state -103.742 AB 0.75 BC 1.81

ΔE = E(transition state) - E(reactants)

''ΔEFH + H‡ = (-103.742) - (-133.586) = 29.844 Kcalmol-1''

''ΔEH2 + F‡ = (-103.742) - (-103.330) = 0.412 Kcalmol-1''

== Q4 - Mechanism of Release of the Activation Energy ==

F + H2

This plot shows the reaction of initial conditions FH distance = 2.30Å HH distance = 0.85Å FH momentm = -7.0 HH momentum = -1.0, resulting in a successful reaction. Due to the exothermic nature of this reaction, it releases energy as the products have a lower potential energy than the reactants, and from the plot of internuclear distance vs. time, it is clear that this energy is converted to kinetic energy in the form of an oscillating F-H bond, which oscillates at a much higher energy than the original H-H bond. This could be confirmed experimentally by IR which would show the vibrationally excited state of the H-F bond, or energy can be measured by calorimetry.

[[File:slyreactive.png|thumb|upright=0.80|centre|Figure 9]]

== Q5 - Efficiency of Reaction ==

[[File:fh2highvibworks.png|thumb|upright=0.80|centre|Figure 10 - Reaction of H2 + F (H-H = 0.74Å, H-F = 2.Å, pHH = -3.0, pHF = -0.5)]]

[[File:lowvibsamyoung.png|thumb|upright=0.80|centre|Figure 11 - Reaction of H2 + F (H-H = 0.74Å, H-F = 2.0Å, pHH = -0.5, pHF = -0.5)]]

[[File:samlyounglimit2.png|thumb|upright=0.80|centre|Figure 12 - Reaction of H2 + F (H-H = 0.74Å, H-F = 2.0Å, pHH = -2.49, pHF = -0.5)]]

[[File:fhhidealsly.png|thumb|upright=0.80|centre|Figure 13 - Reaction of H2 + F (H-H = 2Å, H-F = 0.74Å, pHH = -0.61, pHF = -0.5)]]

[[File:slylowtrans.png|thumb|upright=0.80|centre|Figure 13 - Reaction of H2 + F (H-H = 2Å, H-F = 0.74Å, pHH = -0.1, pHF = -0.5)]]

[[File:samlyounghightrans.png|thumb|upright=0.80|centre|Figure 13 - Reaction of H2 + F (H-H = 2Å, H-F = 0.74Å, pHH = -3.0, pHF = -0.5)]]

= Bibliography =

Electronegativity values : https://sciencenotes.org/list-of-electronegativity-values-of-the-elements/

Sam Young Reaction Dynamics

2018-05-18T13:34:05Z

Sly116: /* Q5 - Efficiency of Reaction */

= H + H2 System =
== Q1 - Transition State Gradients ==
[[File:Sly-Saddle.png|thumb|upright=0.8|centre|Figure 1 - Potential Energy Surface Plot of H2 + H System, with initial conditions A-B distance = 0.74, B-C distance = 2.30, AB momentum = 0 & BC momentum = 2.7]]

The minimum energy surface, shown running along the bottom of figure one obeys the derivative; ∂V/∂(rx) = ∂V/∂(ry) = 0, with rx and ry run parallel to their respective gradients. However, the saddle point where the transition state lies is located along the minimum energy surface at the maximum point. Therefore, it can be found by taking the second derivative, as the two orthogonal gradients have different signs, with one along the potential energy minimum being negative and the other orthogonal graident being positive.

∂2V/∂(rx)2 > 0

∂2V/∂(ry)2 < 0

== Q2 - Transition State Estimate ==

By making the momentum of the whole system equal to zero, it was possible to put the AB distance = BC distance and alter this value to obtain a result for the rts, which was found to be approximately 0.9077Å (one value due to the system being completely symmetric), which gave figure 2. This number was found by taking the intersect of the AB and BC lines from the internuclear plot with the same initial conditions given above, and optimising this value to give constant distances. Due to the gradient of potential energy at the transition state being zero, the system has no kinetic energy, only potential energy. Therefore, there is no oscillation and the plot of internuclear distance against time shows constant interatomic distances.

[[File:Sly_Q2.png|thumb|upright=0.80|centre|Figure 2 - Internucleur Distance]]

== Q3 - MEP ==

The MEP is the minimum energy pathway followed for the reaction H2 + H to take place, although it can be seen in figures 4 and 5 that it differs from the dynamic trajectory due to the masses of the atoms, and therefore the bond oscillations along the trajectory causing deviations from the mep. This is shown by the wavy black line on figure 5. Both figures illustrate the reaction path (represented by the black line) starting at the transition state point, with the dynamic reaction going to the complete formation of a H2 product, while the mep plot shows it going only slightly towards the product formation.

'''change with + - 0.01 and discuss'''

[[File:Sly_MEP2.png|thumb|upright=0.80|centre|Figure 4 - Minimum Energy Pathway]] [[File:newdynamicsam.png|thumb|upright=0.80|centre|Figure 5 - Dynamic Trajectory]]

== Q4 - Reactive and Unreactive Trajectories==

{| class="wikitable" border=1
! p1 !! p2 !! Total Energy !! Reactive or Unreactive !! Trajectory Plot !! Discussion
|-
| -1.25 || -2.5 || -99.018 || [[File:SY-1.png|frameless|upright=0.80]] || Reactive || The reactivity of the trajectory is shown as the reaction path progresses towards the prodcut H2. Upon forming, the new bond vibrates.
|-
| -1.5 || -2.0 || -100.456 || [[File:SY-2.png|frameless|upright=0.80]] || Unreactive || This figure represents an unreactive system due to the approaching H atom not having enough energy to overcome the activation barrier for the reaction. This results in the reaction trajectory returning to the original H2 bond oscillating back towards its energy minimum.
|-
| -1.5 || -2.5 || -98.956 || [[File:SY-3.png|frameless|upright=0.80]] || Reactive || This model shows a very simimlar picture to the first in the table, although due to p1 being slightly higher, the original H2 bond oscillates with higher energy.
|-
| -2.5 || -5.0 || -84.956 || [[File:SLY4.png|frameless|upright=0.80]] || Unreactive || Here one H atom aproaches the H2 molecule and the transition state complex H-H-H forms, however due to a lack of energy, the trajectory path is unable to continue to form the products so returns to the original reactants.
|-
| -2.5 || -5.2 || -83.416 ||[[File:SY5.png|frameless|upright=0.80]] || Reactive || The case has a high enough energy to form the transition state complex and to continue to overcome the energy barrier to obtain the products.
|}

== Q5 - Transition State Theory ==

Transition state theory focusses on the activated complexes formed at a transition state of the reaction, therefore by examining the transition state of a potential surface plot (found at the saddle point) one can obtain the rate of a reaction, due to the activated complex's quasi-equilibrium with the reactants. It assumes that if the collision is of sufficient energy to overcome the transition state, the products will form. This is based on the assumption that molecules react according to the classical picture, and does not take quantum mechanics into account, leading to limitations when considering phenomena such as tunnelling, whereby the reaction path bypasses a low activation energy. Furthermore the transition state theory does not account for reactions recrossing the activation barrier to return to the products as shown above. As a result, this theory would give a higher rate to the real situation.

= F H H System =

== Q1 - Energetics ==

F + H2
This reaction is shown to be exothermic (i.e. the system releases energy upon reacting, ΔH < 0) from the plot due to the energy minimum of the FH bond being lower in energy than the HH bond, therefore more stable. This is due to the large electronegativity difference between F (3.98) and H (2.20), as opposed to the non polar HH bond. As a result, the reaction of FH + H is therefore endothermic for the same reasons.

'''Talk about enthalpies of formation/dissociation'''

[[File:SLYFH.png|thumb|upright=0.80|centre|Figure 6]]

== Q2 - Position of the Transition State ==

The transition state can be found at the point where the internuclear distances of the atoms does not change over time. This is the same point on the graph for both the forward and reverse reactions. By using Hammond's postulate, that the activated intermediate complex at the transition state should resemble the state that it is closest in energy to, therefore similar to an HF + H model. As a result, it was possible to look at the surface plot and optimise the bond distances around where the transition state was roughly located. It was found that the approximate internuclear distances at this transition state are H-F : 1.810 and H-H : 0.746.

[[File:tshighlight.png|thumb|none|Figure 7]] [[File:transstatesly.png|thumb|upright=0.80|none|Figure 8]]

== Q3 - Activation Energy ==

By finding the equilibrium bond length of both reactants and products, and knowing the location of the transition state, it was possible to obtain energies for all of these positions, and therefore calculate the energy of activation.

Energy at HF minimum -133.586 AB 2.3 BC 0.9

Energy at HH minimum -103.33 AB 0.7 BC 2.3

Energy at transition state -103.742 AB 0.75 BC 1.81

ΔE = E(transition state) - E(reactants)

''ΔEFH + H‡ = (-103.742) - (-133.586) = 29.844 Kcalmol-1''

''ΔEH2 + F‡ = (-103.742) - (-103.330) = 0.412 Kcalmol-1''

== Q4 - Mechanism of Release of the Activation Energy ==

F + H2

This plot shows the reaction of initial conditions FH distance = 2.30Å HH distance = 0.85Å FH momentm = -7.0 HH momentum = -1.0, resulting in a successful reaction. Due to the exothermic nature of this reaction, it releases energy as the products have a lower potential energy than the reactants, and from the plot of internuclear distance vs. time, it is clear that this energy is converted to kinetic energy in the form of an oscillating F-H bond, which oscillates at a much higher energy than the original H-H bond. This could be confirmed experimentally by IR which would show the vibrationally excited state of the H-F bond, or energy can be measured by calorimetry.

[[File:slyreactive.png|thumb|upright=0.80|centre|Figure 9]]

== Q5 - Efficiency of Reaction ==

[[File:fh2highvibworks.png|thumb|upright=0.80|centre|Figure 10 - Reaction of H2 + F (H-H = 0.74Å, H-F = 2.Å, pHH = -3.0, pHF = -0.5)]]

[[File:lowvibsamyoung.png|thumb|upright=0.80|centre|Figure 11 - Reaction of H2 + F (H-H = 0.74Å, H-F = 2.0Å, pHH = -0.5, pHF = -0.5)]]

[[File:samlyounglimit2.png|thumb|upright=0.80|centre|Figure 12 - Reaction of H2 + F (H-H = 0.74Å, H-F = 2.0Å, pHH = -2.49, pHF = -0.5)]]

[[File:fhhidealsly.png|thumb|upright=0.80|centre|Figure 13 - Reaction of H2 + F (H-H = 2Å, H-F = 0.74Å, pHH = -0.61, pHF = -0.5)]]

[[File:slylowtrans.png|thumb|upright=0.80|centre|Figure 13 - Reaction of H2 + F (H-H = 2Å, H-F = 0.74Å, pHH = -0.1, pHF = -0.5)]]

[[File:slyhightrans2.png|thumb|upright=0.80|centre|Figure 13 - Reaction of H2 + F (H-H = 2Å, H-F = 0.74Å, pHH = -3.0, pHF = -0.5)]]

= Bibliography =

Electronegativity values : https://sciencenotes.org/list-of-electronegativity-values-of-the-elements/

File:Slyhightrans.png

2018-05-18T13:32:26Z

Sly116:

Sam Young Reaction Dynamics

2018-05-18T13:31:50Z

Sly116: /* Q5 - Efficiency of Reaction */

= H + H2 System =
== Q1 - Transition State Gradients ==
[[File:Sly-Saddle.png|thumb|upright=0.8|centre|Figure 1 - Potential Energy Surface Plot of H2 + H System, with initial conditions A-B distance = 0.74, B-C distance = 2.30, AB momentum = 0 & BC momentum = 2.7]]

The minimum energy surface, shown running along the bottom of figure one obeys the derivative; ∂V/∂(rx) = ∂V/∂(ry) = 0, with rx and ry run parallel to their respective gradients. However, the saddle point where the transition state lies is located along the minimum energy surface at the maximum point. Therefore, it can be found by taking the second derivative, as the two orthogonal gradients have different signs, with one along the potential energy minimum being negative and the other orthogonal graident being positive.

∂2V/∂(rx)2 > 0

∂2V/∂(ry)2 < 0

== Q2 - Transition State Estimate ==

By making the momentum of the whole system equal to zero, it was possible to put the AB distance = BC distance and alter this value to obtain a result for the rts, which was found to be approximately 0.9077Å (one value due to the system being completely symmetric), which gave figure 2. This number was found by taking the intersect of the AB and BC lines from the internuclear plot with the same initial conditions given above, and optimising this value to give constant distances. Due to the gradient of potential energy at the transition state being zero, the system has no kinetic energy, only potential energy. Therefore, there is no oscillation and the plot of internuclear distance against time shows constant interatomic distances.

[[File:Sly_Q2.png|thumb|upright=0.80|centre|Figure 2 - Internucleur Distance]]

== Q3 - MEP ==

The MEP is the minimum energy pathway followed for the reaction H2 + H to take place, although it can be seen in figures 4 and 5 that it differs from the dynamic trajectory due to the masses of the atoms, and therefore the bond oscillations along the trajectory causing deviations from the mep. This is shown by the wavy black line on figure 5. Both figures illustrate the reaction path (represented by the black line) starting at the transition state point, with the dynamic reaction going to the complete formation of a H2 product, while the mep plot shows it going only slightly towards the product formation.

'''change with + - 0.01 and discuss'''

[[File:Sly_MEP2.png|thumb|upright=0.80|centre|Figure 4 - Minimum Energy Pathway]] [[File:newdynamicsam.png|thumb|upright=0.80|centre|Figure 5 - Dynamic Trajectory]]

== Q4 - Reactive and Unreactive Trajectories==

{| class="wikitable" border=1
! p1 !! p2 !! Total Energy !! Reactive or Unreactive !! Trajectory Plot !! Discussion
|-
| -1.25 || -2.5 || -99.018 || [[File:SY-1.png|frameless|upright=0.80]] || Reactive || The reactivity of the trajectory is shown as the reaction path progresses towards the prodcut H2. Upon forming, the new bond vibrates.
|-
| -1.5 || -2.0 || -100.456 || [[File:SY-2.png|frameless|upright=0.80]] || Unreactive || This figure represents an unreactive system due to the approaching H atom not having enough energy to overcome the activation barrier for the reaction. This results in the reaction trajectory returning to the original H2 bond oscillating back towards its energy minimum.
|-
| -1.5 || -2.5 || -98.956 || [[File:SY-3.png|frameless|upright=0.80]] || Reactive || This model shows a very simimlar picture to the first in the table, although due to p1 being slightly higher, the original H2 bond oscillates with higher energy.
|-
| -2.5 || -5.0 || -84.956 || [[File:SLY4.png|frameless|upright=0.80]] || Unreactive || Here one H atom aproaches the H2 molecule and the transition state complex H-H-H forms, however due to a lack of energy, the trajectory path is unable to continue to form the products so returns to the original reactants.
|-
| -2.5 || -5.2 || -83.416 ||[[File:SY5.png|frameless|upright=0.80]] || Reactive || The case has a high enough energy to form the transition state complex and to continue to overcome the energy barrier to obtain the products.
|}

== Q5 - Transition State Theory ==

Transition state theory focusses on the activated complexes formed at a transition state of the reaction, therefore by examining the transition state of a potential surface plot (found at the saddle point) one can obtain the rate of a reaction, due to the activated complex's quasi-equilibrium with the reactants. It assumes that if the collision is of sufficient energy to overcome the transition state, the products will form. This is based on the assumption that molecules react according to the classical picture, and does not take quantum mechanics into account, leading to limitations when considering phenomena such as tunnelling, whereby the reaction path bypasses a low activation energy. Furthermore the transition state theory does not account for reactions recrossing the activation barrier to return to the products as shown above. As a result, this theory would give a higher rate to the real situation.

= F H H System =

== Q1 - Energetics ==

F + H2
This reaction is shown to be exothermic (i.e. the system releases energy upon reacting, ΔH < 0) from the plot due to the energy minimum of the FH bond being lower in energy than the HH bond, therefore more stable. This is due to the large electronegativity difference between F (3.98) and H (2.20), as opposed to the non polar HH bond. As a result, the reaction of FH + H is therefore endothermic for the same reasons.

'''Talk about enthalpies of formation/dissociation'''

[[File:SLYFH.png|thumb|upright=0.80|centre|Figure 6]]

== Q2 - Position of the Transition State ==

The transition state can be found at the point where the internuclear distances of the atoms does not change over time. This is the same point on the graph for both the forward and reverse reactions. By using Hammond's postulate, that the activated intermediate complex at the transition state should resemble the state that it is closest in energy to, therefore similar to an HF + H model. As a result, it was possible to look at the surface plot and optimise the bond distances around where the transition state was roughly located. It was found that the approximate internuclear distances at this transition state are H-F : 1.810 and H-H : 0.746.

[[File:tshighlight.png|thumb|none|Figure 7]] [[File:transstatesly.png|thumb|upright=0.80|none|Figure 8]]

== Q3 - Activation Energy ==

By finding the equilibrium bond length of both reactants and products, and knowing the location of the transition state, it was possible to obtain energies for all of these positions, and therefore calculate the energy of activation.

Energy at HF minimum -133.586 AB 2.3 BC 0.9

Energy at HH minimum -103.33 AB 0.7 BC 2.3

Energy at transition state -103.742 AB 0.75 BC 1.81

ΔE = E(transition state) - E(reactants)

''ΔEFH + H‡ = (-103.742) - (-133.586) = 29.844 Kcalmol-1''

''ΔEH2 + F‡ = (-103.742) - (-103.330) = 0.412 Kcalmol-1''

== Q4 - Mechanism of Release of the Activation Energy ==

F + H2

This plot shows the reaction of initial conditions FH distance = 2.30Å HH distance = 0.85Å FH momentm = -7.0 HH momentum = -1.0, resulting in a successful reaction. Due to the exothermic nature of this reaction, it releases energy as the products have a lower potential energy than the reactants, and from the plot of internuclear distance vs. time, it is clear that this energy is converted to kinetic energy in the form of an oscillating F-H bond, which oscillates at a much higher energy than the original H-H bond. This could be confirmed experimentally by IR which would show the vibrationally excited state of the H-F bond, or energy can be measured by calorimetry.

[[File:slyreactive.png|thumb|upright=0.80|centre|Figure 9]]

== Q5 - Efficiency of Reaction ==

[[File:fh2highvibworks.png|thumb|upright=0.80|centre|Figure 10 - Reaction of H2 + F (H-H = 0.74Å, H-F = 2.Å, pHH = -3.0, pHF = -0.5)]]

[[File:lowvibsamyoung.png|thumb|upright=0.80|centre|Figure 11 - Reaction of H2 + F (H-H = 0.74Å, H-F = 2.0Å, pHH = -0.5, pHF = -0.5)]]

[[File:samlyounglimit2.png|thumb|upright=0.80|centre|Figure 12 - Reaction of H2 + F (H-H = 0.74Å, H-F = 2.0Å, pHH = -2.49, pHF = -0.5)]]

[[File:fhhidealsly.png|thumb|upright=0.80|centre|Figure 13 - Reaction of H2 + F (H-H = 2Å, H-F = 0.74Å, pHH = -0.61, pHF = -0.5)]]

[[File:slylowtrans.png|thumb|upright=0.80|centre|Figure 13 - Reaction of H2 + F (H-H = 2Å, H-F = 0.74Å, pHH = -0.1, pHF = -0.5)]]

[[File:slyhightrans.png|thumb|upright=0.80|centre|Figure 13 - Reaction of H2 + F (H-H = 2Å, H-F = 0.74Å, pHH = -3.0, pHF = -0.5)]]

= Bibliography =

Electronegativity values : https://sciencenotes.org/list-of-electronegativity-values-of-the-elements/

File:Slylowtrans.png

2018-05-18T13:31:21Z

Sly116:

Sam Young Reaction Dynamics

2018-05-18T13:31:12Z

Sly116: /* Q5 - Efficiency of Reaction */

= H + H2 System =
== Q1 - Transition State Gradients ==
[[File:Sly-Saddle.png|thumb|upright=0.8|centre|Figure 1 - Potential Energy Surface Plot of H2 + H System, with initial conditions A-B distance = 0.74, B-C distance = 2.30, AB momentum = 0 & BC momentum = 2.7]]

The minimum energy surface, shown running along the bottom of figure one obeys the derivative; ∂V/∂(rx) = ∂V/∂(ry) = 0, with rx and ry run parallel to their respective gradients. However, the saddle point where the transition state lies is located along the minimum energy surface at the maximum point. Therefore, it can be found by taking the second derivative, as the two orthogonal gradients have different signs, with one along the potential energy minimum being negative and the other orthogonal graident being positive.

∂2V/∂(rx)2 > 0

∂2V/∂(ry)2 < 0

== Q2 - Transition State Estimate ==

By making the momentum of the whole system equal to zero, it was possible to put the AB distance = BC distance and alter this value to obtain a result for the rts, which was found to be approximately 0.9077Å (one value due to the system being completely symmetric), which gave figure 2. This number was found by taking the intersect of the AB and BC lines from the internuclear plot with the same initial conditions given above, and optimising this value to give constant distances. Due to the gradient of potential energy at the transition state being zero, the system has no kinetic energy, only potential energy. Therefore, there is no oscillation and the plot of internuclear distance against time shows constant interatomic distances.

[[File:Sly_Q2.png|thumb|upright=0.80|centre|Figure 2 - Internucleur Distance]]

== Q3 - MEP ==

The MEP is the minimum energy pathway followed for the reaction H2 + H to take place, although it can be seen in figures 4 and 5 that it differs from the dynamic trajectory due to the masses of the atoms, and therefore the bond oscillations along the trajectory causing deviations from the mep. This is shown by the wavy black line on figure 5. Both figures illustrate the reaction path (represented by the black line) starting at the transition state point, with the dynamic reaction going to the complete formation of a H2 product, while the mep plot shows it going only slightly towards the product formation.

'''change with + - 0.01 and discuss'''

[[File:Sly_MEP2.png|thumb|upright=0.80|centre|Figure 4 - Minimum Energy Pathway]] [[File:newdynamicsam.png|thumb|upright=0.80|centre|Figure 5 - Dynamic Trajectory]]

== Q4 - Reactive and Unreactive Trajectories==

{| class="wikitable" border=1
! p1 !! p2 !! Total Energy !! Reactive or Unreactive !! Trajectory Plot !! Discussion
|-
| -1.25 || -2.5 || -99.018 || [[File:SY-1.png|frameless|upright=0.80]] || Reactive || The reactivity of the trajectory is shown as the reaction path progresses towards the prodcut H2. Upon forming, the new bond vibrates.
|-
| -1.5 || -2.0 || -100.456 || [[File:SY-2.png|frameless|upright=0.80]] || Unreactive || This figure represents an unreactive system due to the approaching H atom not having enough energy to overcome the activation barrier for the reaction. This results in the reaction trajectory returning to the original H2 bond oscillating back towards its energy minimum.
|-
| -1.5 || -2.5 || -98.956 || [[File:SY-3.png|frameless|upright=0.80]] || Reactive || This model shows a very simimlar picture to the first in the table, although due to p1 being slightly higher, the original H2 bond oscillates with higher energy.
|-
| -2.5 || -5.0 || -84.956 || [[File:SLY4.png|frameless|upright=0.80]] || Unreactive || Here one H atom aproaches the H2 molecule and the transition state complex H-H-H forms, however due to a lack of energy, the trajectory path is unable to continue to form the products so returns to the original reactants.
|-
| -2.5 || -5.2 || -83.416 ||[[File:SY5.png|frameless|upright=0.80]] || Reactive || The case has a high enough energy to form the transition state complex and to continue to overcome the energy barrier to obtain the products.
|}

== Q5 - Transition State Theory ==

Transition state theory focusses on the activated complexes formed at a transition state of the reaction, therefore by examining the transition state of a potential surface plot (found at the saddle point) one can obtain the rate of a reaction, due to the activated complex's quasi-equilibrium with the reactants. It assumes that if the collision is of sufficient energy to overcome the transition state, the products will form. This is based on the assumption that molecules react according to the classical picture, and does not take quantum mechanics into account, leading to limitations when considering phenomena such as tunnelling, whereby the reaction path bypasses a low activation energy. Furthermore the transition state theory does not account for reactions recrossing the activation barrier to return to the products as shown above. As a result, this theory would give a higher rate to the real situation.

= F H H System =

== Q1 - Energetics ==

F + H2
This reaction is shown to be exothermic (i.e. the system releases energy upon reacting, ΔH < 0) from the plot due to the energy minimum of the FH bond being lower in energy than the HH bond, therefore more stable. This is due to the large electronegativity difference between F (3.98) and H (2.20), as opposed to the non polar HH bond. As a result, the reaction of FH + H is therefore endothermic for the same reasons.

'''Talk about enthalpies of formation/dissociation'''

[[File:SLYFH.png|thumb|upright=0.80|centre|Figure 6]]

== Q2 - Position of the Transition State ==

The transition state can be found at the point where the internuclear distances of the atoms does not change over time. This is the same point on the graph for both the forward and reverse reactions. By using Hammond's postulate, that the activated intermediate complex at the transition state should resemble the state that it is closest in energy to, therefore similar to an HF + H model. As a result, it was possible to look at the surface plot and optimise the bond distances around where the transition state was roughly located. It was found that the approximate internuclear distances at this transition state are H-F : 1.810 and H-H : 0.746.

[[File:tshighlight.png|thumb|none|Figure 7]] [[File:transstatesly.png|thumb|upright=0.80|none|Figure 8]]

== Q3 - Activation Energy ==

By finding the equilibrium bond length of both reactants and products, and knowing the location of the transition state, it was possible to obtain energies for all of these positions, and therefore calculate the energy of activation.

Energy at HF minimum -133.586 AB 2.3 BC 0.9

Energy at HH minimum -103.33 AB 0.7 BC 2.3

Energy at transition state -103.742 AB 0.75 BC 1.81

ΔE = E(transition state) - E(reactants)

''ΔEFH + H‡ = (-103.742) - (-133.586) = 29.844 Kcalmol-1''

''ΔEH2 + F‡ = (-103.742) - (-103.330) = 0.412 Kcalmol-1''

== Q4 - Mechanism of Release of the Activation Energy ==

F + H2

This plot shows the reaction of initial conditions FH distance = 2.30Å HH distance = 0.85Å FH momentm = -7.0 HH momentum = -1.0, resulting in a successful reaction. Due to the exothermic nature of this reaction, it releases energy as the products have a lower potential energy than the reactants, and from the plot of internuclear distance vs. time, it is clear that this energy is converted to kinetic energy in the form of an oscillating F-H bond, which oscillates at a much higher energy than the original H-H bond. This could be confirmed experimentally by IR which would show the vibrationally excited state of the H-F bond, or energy can be measured by calorimetry.

[[File:slyreactive.png|thumb|upright=0.80|centre|Figure 9]]

== Q5 - Efficiency of Reaction ==

[[File:fh2highvibworks.png|thumb|upright=0.80|centre|Figure 10 - Reaction of H2 + F (H-H = 0.74Å, H-F = 2.Å, pHH = -3.0, pHF = -0.5)]]

[[File:lowvibsamyoung.png|thumb|upright=0.80|centre|Figure 11 - Reaction of H2 + F (H-H = 0.74Å, H-F = 2.0Å, pHH = -0.5, pHF = -0.5)]]

[[File:samlyounglimit2.png|thumb|upright=0.80|centre|Figure 12 - Reaction of H2 + F (H-H = 0.74Å, H-F = 2.0Å, pHH = -2.49, pHF = -0.5)]]

[[File:fhhidealsly.png|thumb|upright=0.80|centre|Figure 13 - Reaction of H2 + F (H-H = 2Å, H-F = 0.74Å, pHH = -0.61, pHF = -0.5)]]

[[File:slylowtrans.png|thumb|upright=0.80|centre|Figure 13 - Reaction of H2 + F (H-H = 2Å, H-F = 0.74Å, pHH = -0.1, pHF = -0.5)]]

= Bibliography =

Electronegativity values : https://sciencenotes.org/list-of-electronegativity-values-of-the-elements/

File:Fhhidealsly.png

2018-05-18T13:29:36Z

Sly116:

Sam Young Reaction Dynamics

2018-05-18T13:29:27Z

Sly116: /* Q5 - Efficiency of Reaction */

= H + H2 System =
== Q1 - Transition State Gradients ==
[[File:Sly-Saddle.png|thumb|upright=0.8|centre|Figure 1 - Potential Energy Surface Plot of H2 + H System, with initial conditions A-B distance = 0.74, B-C distance = 2.30, AB momentum = 0 & BC momentum = 2.7]]

The minimum energy surface, shown running along the bottom of figure one obeys the derivative; ∂V/∂(rx) = ∂V/∂(ry) = 0, with rx and ry run parallel to their respective gradients. However, the saddle point where the transition state lies is located along the minimum energy surface at the maximum point. Therefore, it can be found by taking the second derivative, as the two orthogonal gradients have different signs, with one along the potential energy minimum being negative and the other orthogonal graident being positive.

∂2V/∂(rx)2 > 0

∂2V/∂(ry)2 < 0

== Q2 - Transition State Estimate ==

By making the momentum of the whole system equal to zero, it was possible to put the AB distance = BC distance and alter this value to obtain a result for the rts, which was found to be approximately 0.9077Å (one value due to the system being completely symmetric), which gave figure 2. This number was found by taking the intersect of the AB and BC lines from the internuclear plot with the same initial conditions given above, and optimising this value to give constant distances. Due to the gradient of potential energy at the transition state being zero, the system has no kinetic energy, only potential energy. Therefore, there is no oscillation and the plot of internuclear distance against time shows constant interatomic distances.

[[File:Sly_Q2.png|thumb|upright=0.80|centre|Figure 2 - Internucleur Distance]]

== Q3 - MEP ==

The MEP is the minimum energy pathway followed for the reaction H2 + H to take place, although it can be seen in figures 4 and 5 that it differs from the dynamic trajectory due to the masses of the atoms, and therefore the bond oscillations along the trajectory causing deviations from the mep. This is shown by the wavy black line on figure 5. Both figures illustrate the reaction path (represented by the black line) starting at the transition state point, with the dynamic reaction going to the complete formation of a H2 product, while the mep plot shows it going only slightly towards the product formation.

'''change with + - 0.01 and discuss'''

[[File:Sly_MEP2.png|thumb|upright=0.80|centre|Figure 4 - Minimum Energy Pathway]] [[File:newdynamicsam.png|thumb|upright=0.80|centre|Figure 5 - Dynamic Trajectory]]

== Q4 - Reactive and Unreactive Trajectories==

{| class="wikitable" border=1
! p1 !! p2 !! Total Energy !! Reactive or Unreactive !! Trajectory Plot !! Discussion
|-
| -1.25 || -2.5 || -99.018 || [[File:SY-1.png|frameless|upright=0.80]] || Reactive || The reactivity of the trajectory is shown as the reaction path progresses towards the prodcut H2. Upon forming, the new bond vibrates.
|-
| -1.5 || -2.0 || -100.456 || [[File:SY-2.png|frameless|upright=0.80]] || Unreactive || This figure represents an unreactive system due to the approaching H atom not having enough energy to overcome the activation barrier for the reaction. This results in the reaction trajectory returning to the original H2 bond oscillating back towards its energy minimum.
|-
| -1.5 || -2.5 || -98.956 || [[File:SY-3.png|frameless|upright=0.80]] || Reactive || This model shows a very simimlar picture to the first in the table, although due to p1 being slightly higher, the original H2 bond oscillates with higher energy.
|-
| -2.5 || -5.0 || -84.956 || [[File:SLY4.png|frameless|upright=0.80]] || Unreactive || Here one H atom aproaches the H2 molecule and the transition state complex H-H-H forms, however due to a lack of energy, the trajectory path is unable to continue to form the products so returns to the original reactants.
|-
| -2.5 || -5.2 || -83.416 ||[[File:SY5.png|frameless|upright=0.80]] || Reactive || The case has a high enough energy to form the transition state complex and to continue to overcome the energy barrier to obtain the products.
|}

== Q5 - Transition State Theory ==

Transition state theory focusses on the activated complexes formed at a transition state of the reaction, therefore by examining the transition state of a potential surface plot (found at the saddle point) one can obtain the rate of a reaction, due to the activated complex's quasi-equilibrium with the reactants. It assumes that if the collision is of sufficient energy to overcome the transition state, the products will form. This is based on the assumption that molecules react according to the classical picture, and does not take quantum mechanics into account, leading to limitations when considering phenomena such as tunnelling, whereby the reaction path bypasses a low activation energy. Furthermore the transition state theory does not account for reactions recrossing the activation barrier to return to the products as shown above. As a result, this theory would give a higher rate to the real situation.

= F H H System =

== Q1 - Energetics ==

F + H2
This reaction is shown to be exothermic (i.e. the system releases energy upon reacting, ΔH < 0) from the plot due to the energy minimum of the FH bond being lower in energy than the HH bond, therefore more stable. This is due to the large electronegativity difference between F (3.98) and H (2.20), as opposed to the non polar HH bond. As a result, the reaction of FH + H is therefore endothermic for the same reasons.

'''Talk about enthalpies of formation/dissociation'''

[[File:SLYFH.png|thumb|upright=0.80|centre|Figure 6]]

== Q2 - Position of the Transition State ==

The transition state can be found at the point where the internuclear distances of the atoms does not change over time. This is the same point on the graph for both the forward and reverse reactions. By using Hammond's postulate, that the activated intermediate complex at the transition state should resemble the state that it is closest in energy to, therefore similar to an HF + H model. As a result, it was possible to look at the surface plot and optimise the bond distances around where the transition state was roughly located. It was found that the approximate internuclear distances at this transition state are H-F : 1.810 and H-H : 0.746.

[[File:tshighlight.png|thumb|none|Figure 7]] [[File:transstatesly.png|thumb|upright=0.80|none|Figure 8]]

== Q3 - Activation Energy ==

By finding the equilibrium bond length of both reactants and products, and knowing the location of the transition state, it was possible to obtain energies for all of these positions, and therefore calculate the energy of activation.

Energy at HF minimum -133.586 AB 2.3 BC 0.9

Energy at HH minimum -103.33 AB 0.7 BC 2.3

Energy at transition state -103.742 AB 0.75 BC 1.81

ΔE = E(transition state) - E(reactants)

''ΔEFH + H‡ = (-103.742) - (-133.586) = 29.844 Kcalmol-1''

''ΔEH2 + F‡ = (-103.742) - (-103.330) = 0.412 Kcalmol-1''

== Q4 - Mechanism of Release of the Activation Energy ==

F + H2

This plot shows the reaction of initial conditions FH distance = 2.30Å HH distance = 0.85Å FH momentm = -7.0 HH momentum = -1.0, resulting in a successful reaction. Due to the exothermic nature of this reaction, it releases energy as the products have a lower potential energy than the reactants, and from the plot of internuclear distance vs. time, it is clear that this energy is converted to kinetic energy in the form of an oscillating F-H bond, which oscillates at a much higher energy than the original H-H bond. This could be confirmed experimentally by IR which would show the vibrationally excited state of the H-F bond, or energy can be measured by calorimetry.

[[File:slyreactive.png|thumb|upright=0.80|centre|Figure 9]]

== Q5 - Efficiency of Reaction ==

[[File:fh2highvibworks.png|thumb|upright=0.80|centre|Figure 10 - Reaction of H2 + F (H-H = 0.74Å, H-F = 2.Å, pHH = -3.0, pHF = -0.5)]]

[[File:lowvibsamyoung.png|thumb|upright=0.80|centre|Figure 11 - Reaction of H2 + F (H-H = 0.74Å, H-F = 2.0Å, pHH = -0.5, pHF = -0.5)]]

[[File:samlyounglimit2.png|thumb|upright=0.80|centre|Figure 12 - Reaction of H2 + F (H-H = 0.74Å, H-F = 2.0Å, pHH = -2.49, pHF = -0.5)]]

[[File:fhhidealsly.png|thumb|upright=0.80|centre|Figure 13 - Reaction of H2 + F (H-H = 2Å, H-F = 0.74Å, pHH = -0.61, pHF = -0.5)]]

= Bibliography =

Electronegativity values : https://sciencenotes.org/list-of-electronegativity-values-of-the-elements/

Sam Young Reaction Dynamics

2018-05-18T13:25:09Z

Sly116: /* Q5 - Efficiency of Reaction */

= H + H2 System =
== Q1 - Transition State Gradients ==
[[File:Sly-Saddle.png|thumb|upright=0.8|centre|Figure 1 - Potential Energy Surface Plot of H2 + H System, with initial conditions A-B distance = 0.74, B-C distance = 2.30, AB momentum = 0 & BC momentum = 2.7]]

The minimum energy surface, shown running along the bottom of figure one obeys the derivative; ∂V/∂(rx) = ∂V/∂(ry) = 0, with rx and ry run parallel to their respective gradients. However, the saddle point where the transition state lies is located along the minimum energy surface at the maximum point. Therefore, it can be found by taking the second derivative, as the two orthogonal gradients have different signs, with one along the potential energy minimum being negative and the other orthogonal graident being positive.

∂2V/∂(rx)2 > 0

∂2V/∂(ry)2 < 0

== Q2 - Transition State Estimate ==

By making the momentum of the whole system equal to zero, it was possible to put the AB distance = BC distance and alter this value to obtain a result for the rts, which was found to be approximately 0.9077Å (one value due to the system being completely symmetric), which gave figure 2. This number was found by taking the intersect of the AB and BC lines from the internuclear plot with the same initial conditions given above, and optimising this value to give constant distances. Due to the gradient of potential energy at the transition state being zero, the system has no kinetic energy, only potential energy. Therefore, there is no oscillation and the plot of internuclear distance against time shows constant interatomic distances.

[[File:Sly_Q2.png|thumb|upright=0.80|centre|Figure 2 - Internucleur Distance]]

== Q3 - MEP ==

The MEP is the minimum energy pathway followed for the reaction H2 + H to take place, although it can be seen in figures 4 and 5 that it differs from the dynamic trajectory due to the masses of the atoms, and therefore the bond oscillations along the trajectory causing deviations from the mep. This is shown by the wavy black line on figure 5. Both figures illustrate the reaction path (represented by the black line) starting at the transition state point, with the dynamic reaction going to the complete formation of a H2 product, while the mep plot shows it going only slightly towards the product formation.

'''change with + - 0.01 and discuss'''

[[File:Sly_MEP2.png|thumb|upright=0.80|centre|Figure 4 - Minimum Energy Pathway]] [[File:newdynamicsam.png|thumb|upright=0.80|centre|Figure 5 - Dynamic Trajectory]]

== Q4 - Reactive and Unreactive Trajectories==

{| class="wikitable" border=1
! p1 !! p2 !! Total Energy !! Reactive or Unreactive !! Trajectory Plot !! Discussion
|-
| -1.25 || -2.5 || -99.018 || [[File:SY-1.png|frameless|upright=0.80]] || Reactive || The reactivity of the trajectory is shown as the reaction path progresses towards the prodcut H2. Upon forming, the new bond vibrates.
|-
| -1.5 || -2.0 || -100.456 || [[File:SY-2.png|frameless|upright=0.80]] || Unreactive || This figure represents an unreactive system due to the approaching H atom not having enough energy to overcome the activation barrier for the reaction. This results in the reaction trajectory returning to the original H2 bond oscillating back towards its energy minimum.
|-
| -1.5 || -2.5 || -98.956 || [[File:SY-3.png|frameless|upright=0.80]] || Reactive || This model shows a very simimlar picture to the first in the table, although due to p1 being slightly higher, the original H2 bond oscillates with higher energy.
|-
| -2.5 || -5.0 || -84.956 || [[File:SLY4.png|frameless|upright=0.80]] || Unreactive || Here one H atom aproaches the H2 molecule and the transition state complex H-H-H forms, however due to a lack of energy, the trajectory path is unable to continue to form the products so returns to the original reactants.
|-
| -2.5 || -5.2 || -83.416 ||[[File:SY5.png|frameless|upright=0.80]] || Reactive || The case has a high enough energy to form the transition state complex and to continue to overcome the energy barrier to obtain the products.
|}

== Q5 - Transition State Theory ==

Transition state theory focusses on the activated complexes formed at a transition state of the reaction, therefore by examining the transition state of a potential surface plot (found at the saddle point) one can obtain the rate of a reaction, due to the activated complex's quasi-equilibrium with the reactants. It assumes that if the collision is of sufficient energy to overcome the transition state, the products will form. This is based on the assumption that molecules react according to the classical picture, and does not take quantum mechanics into account, leading to limitations when considering phenomena such as tunnelling, whereby the reaction path bypasses a low activation energy. Furthermore the transition state theory does not account for reactions recrossing the activation barrier to return to the products as shown above. As a result, this theory would give a higher rate to the real situation.

= F H H System =

== Q1 - Energetics ==

F + H2
This reaction is shown to be exothermic (i.e. the system releases energy upon reacting, ΔH < 0) from the plot due to the energy minimum of the FH bond being lower in energy than the HH bond, therefore more stable. This is due to the large electronegativity difference between F (3.98) and H (2.20), as opposed to the non polar HH bond. As a result, the reaction of FH + H is therefore endothermic for the same reasons.

'''Talk about enthalpies of formation/dissociation'''

[[File:SLYFH.png|thumb|upright=0.80|centre|Figure 6]]

== Q2 - Position of the Transition State ==

The transition state can be found at the point where the internuclear distances of the atoms does not change over time. This is the same point on the graph for both the forward and reverse reactions. By using Hammond's postulate, that the activated intermediate complex at the transition state should resemble the state that it is closest in energy to, therefore similar to an HF + H model. As a result, it was possible to look at the surface plot and optimise the bond distances around where the transition state was roughly located. It was found that the approximate internuclear distances at this transition state are H-F : 1.810 and H-H : 0.746.

[[File:tshighlight.png|thumb|none|Figure 7]] [[File:transstatesly.png|thumb|upright=0.80|none|Figure 8]]

== Q3 - Activation Energy ==

By finding the equilibrium bond length of both reactants and products, and knowing the location of the transition state, it was possible to obtain energies for all of these positions, and therefore calculate the energy of activation.

Energy at HF minimum -133.586 AB 2.3 BC 0.9

Energy at HH minimum -103.33 AB 0.7 BC 2.3

Energy at transition state -103.742 AB 0.75 BC 1.81

ΔE = E(transition state) - E(reactants)

''ΔEFH + H‡ = (-103.742) - (-133.586) = 29.844 Kcalmol-1''

''ΔEH2 + F‡ = (-103.742) - (-103.330) = 0.412 Kcalmol-1''

== Q4 - Mechanism of Release of the Activation Energy ==

F + H2

This plot shows the reaction of initial conditions FH distance = 2.30Å HH distance = 0.85Å FH momentm = -7.0 HH momentum = -1.0, resulting in a successful reaction. Due to the exothermic nature of this reaction, it releases energy as the products have a lower potential energy than the reactants, and from the plot of internuclear distance vs. time, it is clear that this energy is converted to kinetic energy in the form of an oscillating F-H bond, which oscillates at a much higher energy than the original H-H bond. This could be confirmed experimentally by IR which would show the vibrationally excited state of the H-F bond, or energy can be measured by calorimetry.

[[File:slyreactive.png|thumb|upright=0.80|centre|Figure 9]]

== Q5 - Efficiency of Reaction ==

[[File:fh2highvibworks.png|thumb|upright=0.80|centre|Figure 10 - Reaction of H2 + F (H-H = 0.74Å, H-F = 2.Å, pHH = -3.0, pHF = -0.5)]]

[[File:lowvibsamyoung.png|thumb|upright=0.80|centre|Figure 11 - Reaction of H2 + F (H-H = 0.74Å, H-F = 2.0Å, pHH = -0.5, pHF = -0.5)]]

[[File:samlyounglimit2.png|thumb|upright=0.80|centre|Figure 12 - Reaction of H2 + F (H-H = 0.74Å, H-F = 2.0Å, pHH = -2.49, pHF = -0.5)]]

= Bibliography =

Electronegativity values : https://sciencenotes.org/list-of-electronegativity-values-of-the-elements/

File:Samlyounglimit2.png

2018-05-18T13:24:50Z

Sly116:

Sam Young Reaction Dynamics

2018-05-18T13:24:41Z

Sly116: /* Q5 - Efficiency of Reaction */

= H + H2 System =
== Q1 - Transition State Gradients ==
[[File:Sly-Saddle.png|thumb|upright=0.8|centre|Figure 1 - Potential Energy Surface Plot of H2 + H System, with initial conditions A-B distance = 0.74, B-C distance = 2.30, AB momentum = 0 & BC momentum = 2.7]]

The minimum energy surface, shown running along the bottom of figure one obeys the derivative; ∂V/∂(rx) = ∂V/∂(ry) = 0, with rx and ry run parallel to their respective gradients. However, the saddle point where the transition state lies is located along the minimum energy surface at the maximum point. Therefore, it can be found by taking the second derivative, as the two orthogonal gradients have different signs, with one along the potential energy minimum being negative and the other orthogonal graident being positive.

∂2V/∂(rx)2 > 0

∂2V/∂(ry)2 < 0

== Q2 - Transition State Estimate ==

By making the momentum of the whole system equal to zero, it was possible to put the AB distance = BC distance and alter this value to obtain a result for the rts, which was found to be approximately 0.9077Å (one value due to the system being completely symmetric), which gave figure 2. This number was found by taking the intersect of the AB and BC lines from the internuclear plot with the same initial conditions given above, and optimising this value to give constant distances. Due to the gradient of potential energy at the transition state being zero, the system has no kinetic energy, only potential energy. Therefore, there is no oscillation and the plot of internuclear distance against time shows constant interatomic distances.

[[File:Sly_Q2.png|thumb|upright=0.80|centre|Figure 2 - Internucleur Distance]]

== Q3 - MEP ==

The MEP is the minimum energy pathway followed for the reaction H2 + H to take place, although it can be seen in figures 4 and 5 that it differs from the dynamic trajectory due to the masses of the atoms, and therefore the bond oscillations along the trajectory causing deviations from the mep. This is shown by the wavy black line on figure 5. Both figures illustrate the reaction path (represented by the black line) starting at the transition state point, with the dynamic reaction going to the complete formation of a H2 product, while the mep plot shows it going only slightly towards the product formation.

'''change with + - 0.01 and discuss'''

[[File:Sly_MEP2.png|thumb|upright=0.80|centre|Figure 4 - Minimum Energy Pathway]] [[File:newdynamicsam.png|thumb|upright=0.80|centre|Figure 5 - Dynamic Trajectory]]

== Q4 - Reactive and Unreactive Trajectories==

{| class="wikitable" border=1
! p1 !! p2 !! Total Energy !! Reactive or Unreactive !! Trajectory Plot !! Discussion
|-
| -1.25 || -2.5 || -99.018 || [[File:SY-1.png|frameless|upright=0.80]] || Reactive || The reactivity of the trajectory is shown as the reaction path progresses towards the prodcut H2. Upon forming, the new bond vibrates.
|-
| -1.5 || -2.0 || -100.456 || [[File:SY-2.png|frameless|upright=0.80]] || Unreactive || This figure represents an unreactive system due to the approaching H atom not having enough energy to overcome the activation barrier for the reaction. This results in the reaction trajectory returning to the original H2 bond oscillating back towards its energy minimum.
|-
| -1.5 || -2.5 || -98.956 || [[File:SY-3.png|frameless|upright=0.80]] || Reactive || This model shows a very simimlar picture to the first in the table, although due to p1 being slightly higher, the original H2 bond oscillates with higher energy.
|-
| -2.5 || -5.0 || -84.956 || [[File:SLY4.png|frameless|upright=0.80]] || Unreactive || Here one H atom aproaches the H2 molecule and the transition state complex H-H-H forms, however due to a lack of energy, the trajectory path is unable to continue to form the products so returns to the original reactants.
|-
| -2.5 || -5.2 || -83.416 ||[[File:SY5.png|frameless|upright=0.80]] || Reactive || The case has a high enough energy to form the transition state complex and to continue to overcome the energy barrier to obtain the products.
|}

== Q5 - Transition State Theory ==

Transition state theory focusses on the activated complexes formed at a transition state of the reaction, therefore by examining the transition state of a potential surface plot (found at the saddle point) one can obtain the rate of a reaction, due to the activated complex's quasi-equilibrium with the reactants. It assumes that if the collision is of sufficient energy to overcome the transition state, the products will form. This is based on the assumption that molecules react according to the classical picture, and does not take quantum mechanics into account, leading to limitations when considering phenomena such as tunnelling, whereby the reaction path bypasses a low activation energy. Furthermore the transition state theory does not account for reactions recrossing the activation barrier to return to the products as shown above. As a result, this theory would give a higher rate to the real situation.

= F H H System =

== Q1 - Energetics ==

F + H2
This reaction is shown to be exothermic (i.e. the system releases energy upon reacting, ΔH < 0) from the plot due to the energy minimum of the FH bond being lower in energy than the HH bond, therefore more stable. This is due to the large electronegativity difference between F (3.98) and H (2.20), as opposed to the non polar HH bond. As a result, the reaction of FH + H is therefore endothermic for the same reasons.

'''Talk about enthalpies of formation/dissociation'''

[[File:SLYFH.png|thumb|upright=0.80|centre|Figure 6]]

== Q2 - Position of the Transition State ==

The transition state can be found at the point where the internuclear distances of the atoms does not change over time. This is the same point on the graph for both the forward and reverse reactions. By using Hammond's postulate, that the activated intermediate complex at the transition state should resemble the state that it is closest in energy to, therefore similar to an HF + H model. As a result, it was possible to look at the surface plot and optimise the bond distances around where the transition state was roughly located. It was found that the approximate internuclear distances at this transition state are H-F : 1.810 and H-H : 0.746.

[[File:tshighlight.png|thumb|none|Figure 7]] [[File:transstatesly.png|thumb|upright=0.80|none|Figure 8]]

== Q3 - Activation Energy ==

By finding the equilibrium bond length of both reactants and products, and knowing the location of the transition state, it was possible to obtain energies for all of these positions, and therefore calculate the energy of activation.

Energy at HF minimum -133.586 AB 2.3 BC 0.9

Energy at HH minimum -103.33 AB 0.7 BC 2.3

Energy at transition state -103.742 AB 0.75 BC 1.81

ΔE = E(transition state) - E(reactants)

''ΔEFH + H‡ = (-103.742) - (-133.586) = 29.844 Kcalmol-1''

''ΔEH2 + F‡ = (-103.742) - (-103.330) = 0.412 Kcalmol-1''

== Q4 - Mechanism of Release of the Activation Energy ==

F + H2

This plot shows the reaction of initial conditions FH distance = 2.30Å HH distance = 0.85Å FH momentm = -7.0 HH momentum = -1.0, resulting in a successful reaction. Due to the exothermic nature of this reaction, it releases energy as the products have a lower potential energy than the reactants, and from the plot of internuclear distance vs. time, it is clear that this energy is converted to kinetic energy in the form of an oscillating F-H bond, which oscillates at a much higher energy than the original H-H bond. This could be confirmed experimentally by IR which would show the vibrationally excited state of the H-F bond, or energy can be measured by calorimetry.

[[File:slyreactive.png|thumb|upright=0.80|centre|Figure 9]]

== Q5 - Efficiency of Reaction ==

[[File:fh2highvibworks.png|thumb|upright=0.80|centre|Figure 10 - Reaction of H2 + F (H-H = 0.74Å, H-F = 2.Å, pHH = -3.0, pHF = -0.5)]]

[[File:lowvibsamyoung.png|thumb|upright=0.80|centre|Figure 11 - Reaction of H2 + F (H-H = 0.74Å, H-F = 2.0Å, pHH = -0.5, pHF = -0.5)]]

[[File:samlyounglimit2.png|thumb|upright=0.80|centre|Figure 11 - Reaction of H2 + F (H-H = 0.74Å, H-F = 2.0Å, pHH = -2.49, pHF = -0.5)]]

= Bibliography =

Electronegativity values : https://sciencenotes.org/list-of-electronegativity-values-of-the-elements/

File:Limitsamyoung.png

2018-05-18T13:24:10Z

Sly116:

Sam Young Reaction Dynamics

2018-05-18T13:24:00Z

Sly116: /* Q5 - Efficiency of Reaction */

= H + H2 System =
== Q1 - Transition State Gradients ==
[[File:Sly-Saddle.png|thumb|upright=0.8|centre|Figure 1 - Potential Energy Surface Plot of H2 + H System, with initial conditions A-B distance = 0.74, B-C distance = 2.30, AB momentum = 0 & BC momentum = 2.7]]

The minimum energy surface, shown running along the bottom of figure one obeys the derivative; ∂V/∂(rx) = ∂V/∂(ry) = 0, with rx and ry run parallel to their respective gradients. However, the saddle point where the transition state lies is located along the minimum energy surface at the maximum point. Therefore, it can be found by taking the second derivative, as the two orthogonal gradients have different signs, with one along the potential energy minimum being negative and the other orthogonal graident being positive.

∂2V/∂(rx)2 > 0

∂2V/∂(ry)2 < 0

== Q2 - Transition State Estimate ==

By making the momentum of the whole system equal to zero, it was possible to put the AB distance = BC distance and alter this value to obtain a result for the rts, which was found to be approximately 0.9077Å (one value due to the system being completely symmetric), which gave figure 2. This number was found by taking the intersect of the AB and BC lines from the internuclear plot with the same initial conditions given above, and optimising this value to give constant distances. Due to the gradient of potential energy at the transition state being zero, the system has no kinetic energy, only potential energy. Therefore, there is no oscillation and the plot of internuclear distance against time shows constant interatomic distances.

[[File:Sly_Q2.png|thumb|upright=0.80|centre|Figure 2 - Internucleur Distance]]

== Q3 - MEP ==

The MEP is the minimum energy pathway followed for the reaction H2 + H to take place, although it can be seen in figures 4 and 5 that it differs from the dynamic trajectory due to the masses of the atoms, and therefore the bond oscillations along the trajectory causing deviations from the mep. This is shown by the wavy black line on figure 5. Both figures illustrate the reaction path (represented by the black line) starting at the transition state point, with the dynamic reaction going to the complete formation of a H2 product, while the mep plot shows it going only slightly towards the product formation.

'''change with + - 0.01 and discuss'''

[[File:Sly_MEP2.png|thumb|upright=0.80|centre|Figure 4 - Minimum Energy Pathway]] [[File:newdynamicsam.png|thumb|upright=0.80|centre|Figure 5 - Dynamic Trajectory]]

== Q4 - Reactive and Unreactive Trajectories==

{| class="wikitable" border=1
! p1 !! p2 !! Total Energy !! Reactive or Unreactive !! Trajectory Plot !! Discussion
|-
| -1.25 || -2.5 || -99.018 || [[File:SY-1.png|frameless|upright=0.80]] || Reactive || The reactivity of the trajectory is shown as the reaction path progresses towards the prodcut H2. Upon forming, the new bond vibrates.
|-
| -1.5 || -2.0 || -100.456 || [[File:SY-2.png|frameless|upright=0.80]] || Unreactive || This figure represents an unreactive system due to the approaching H atom not having enough energy to overcome the activation barrier for the reaction. This results in the reaction trajectory returning to the original H2 bond oscillating back towards its energy minimum.
|-
| -1.5 || -2.5 || -98.956 || [[File:SY-3.png|frameless|upright=0.80]] || Reactive || This model shows a very simimlar picture to the first in the table, although due to p1 being slightly higher, the original H2 bond oscillates with higher energy.
|-
| -2.5 || -5.0 || -84.956 || [[File:SLY4.png|frameless|upright=0.80]] || Unreactive || Here one H atom aproaches the H2 molecule and the transition state complex H-H-H forms, however due to a lack of energy, the trajectory path is unable to continue to form the products so returns to the original reactants.
|-
| -2.5 || -5.2 || -83.416 ||[[File:SY5.png|frameless|upright=0.80]] || Reactive || The case has a high enough energy to form the transition state complex and to continue to overcome the energy barrier to obtain the products.
|}

== Q5 - Transition State Theory ==

Transition state theory focusses on the activated complexes formed at a transition state of the reaction, therefore by examining the transition state of a potential surface plot (found at the saddle point) one can obtain the rate of a reaction, due to the activated complex's quasi-equilibrium with the reactants. It assumes that if the collision is of sufficient energy to overcome the transition state, the products will form. This is based on the assumption that molecules react according to the classical picture, and does not take quantum mechanics into account, leading to limitations when considering phenomena such as tunnelling, whereby the reaction path bypasses a low activation energy. Furthermore the transition state theory does not account for reactions recrossing the activation barrier to return to the products as shown above. As a result, this theory would give a higher rate to the real situation.

= F H H System =

== Q1 - Energetics ==

F + H2
This reaction is shown to be exothermic (i.e. the system releases energy upon reacting, ΔH < 0) from the plot due to the energy minimum of the FH bond being lower in energy than the HH bond, therefore more stable. This is due to the large electronegativity difference between F (3.98) and H (2.20), as opposed to the non polar HH bond. As a result, the reaction of FH + H is therefore endothermic for the same reasons.

'''Talk about enthalpies of formation/dissociation'''

[[File:SLYFH.png|thumb|upright=0.80|centre|Figure 6]]

== Q2 - Position of the Transition State ==

The transition state can be found at the point where the internuclear distances of the atoms does not change over time. This is the same point on the graph for both the forward and reverse reactions. By using Hammond's postulate, that the activated intermediate complex at the transition state should resemble the state that it is closest in energy to, therefore similar to an HF + H model. As a result, it was possible to look at the surface plot and optimise the bond distances around where the transition state was roughly located. It was found that the approximate internuclear distances at this transition state are H-F : 1.810 and H-H : 0.746.

[[File:tshighlight.png|thumb|none|Figure 7]] [[File:transstatesly.png|thumb|upright=0.80|none|Figure 8]]

== Q3 - Activation Energy ==

By finding the equilibrium bond length of both reactants and products, and knowing the location of the transition state, it was possible to obtain energies for all of these positions, and therefore calculate the energy of activation.

Energy at HF minimum -133.586 AB 2.3 BC 0.9

Energy at HH minimum -103.33 AB 0.7 BC 2.3

Energy at transition state -103.742 AB 0.75 BC 1.81

ΔE = E(transition state) - E(reactants)

''ΔEFH + H‡ = (-103.742) - (-133.586) = 29.844 Kcalmol-1''

''ΔEH2 + F‡ = (-103.742) - (-103.330) = 0.412 Kcalmol-1''

== Q4 - Mechanism of Release of the Activation Energy ==

F + H2

This plot shows the reaction of initial conditions FH distance = 2.30Å HH distance = 0.85Å FH momentm = -7.0 HH momentum = -1.0, resulting in a successful reaction. Due to the exothermic nature of this reaction, it releases energy as the products have a lower potential energy than the reactants, and from the plot of internuclear distance vs. time, it is clear that this energy is converted to kinetic energy in the form of an oscillating F-H bond, which oscillates at a much higher energy than the original H-H bond. This could be confirmed experimentally by IR which would show the vibrationally excited state of the H-F bond, or energy can be measured by calorimetry.

[[File:slyreactive.png|thumb|upright=0.80|centre|Figure 9]]

== Q5 - Efficiency of Reaction ==

[[File:fh2highvibworks.png|thumb|upright=0.80|centre|Figure 10 - Reaction of H2 + F (H-H = 0.74Å, H-F = 2.Å, pHH = -3.0, pHF = -0.5)]]

[[File:lowvibsamyoung.png|thumb|upright=0.80|centre|Figure 11 - Reaction of H2 + F (H-H = 0.74Å, H-F = 2.0Å, pHH = -0.5, pHF = -0.5)]]

[[File:limitsamyoung.png|thumb|upright=0.80|centre|Figure 11 - Reaction of H2 + F (H-H = 0.74Å, H-F = 2.0Å, pHH = -2.49, pHF = -0.5)]]

= Bibliography =

Electronegativity values : https://sciencenotes.org/list-of-electronegativity-values-of-the-elements/

Sam Young Reaction Dynamics

2018-05-18T13:22:21Z

Sly116: /* Q5 - Efficiency of Reaction */

= H + H2 System =
== Q1 - Transition State Gradients ==
[[File:Sly-Saddle.png|thumb|upright=0.8|centre|Figure 1 - Potential Energy Surface Plot of H2 + H System, with initial conditions A-B distance = 0.74, B-C distance = 2.30, AB momentum = 0 & BC momentum = 2.7]]

The minimum energy surface, shown running along the bottom of figure one obeys the derivative; ∂V/∂(rx) = ∂V/∂(ry) = 0, with rx and ry run parallel to their respective gradients. However, the saddle point where the transition state lies is located along the minimum energy surface at the maximum point. Therefore, it can be found by taking the second derivative, as the two orthogonal gradients have different signs, with one along the potential energy minimum being negative and the other orthogonal graident being positive.

∂2V/∂(rx)2 > 0

∂2V/∂(ry)2 < 0

== Q2 - Transition State Estimate ==

By making the momentum of the whole system equal to zero, it was possible to put the AB distance = BC distance and alter this value to obtain a result for the rts, which was found to be approximately 0.9077Å (one value due to the system being completely symmetric), which gave figure 2. This number was found by taking the intersect of the AB and BC lines from the internuclear plot with the same initial conditions given above, and optimising this value to give constant distances. Due to the gradient of potential energy at the transition state being zero, the system has no kinetic energy, only potential energy. Therefore, there is no oscillation and the plot of internuclear distance against time shows constant interatomic distances.

[[File:Sly_Q2.png|thumb|upright=0.80|centre|Figure 2 - Internucleur Distance]]

== Q3 - MEP ==

The MEP is the minimum energy pathway followed for the reaction H2 + H to take place, although it can be seen in figures 4 and 5 that it differs from the dynamic trajectory due to the masses of the atoms, and therefore the bond oscillations along the trajectory causing deviations from the mep. This is shown by the wavy black line on figure 5. Both figures illustrate the reaction path (represented by the black line) starting at the transition state point, with the dynamic reaction going to the complete formation of a H2 product, while the mep plot shows it going only slightly towards the product formation.

'''change with + - 0.01 and discuss'''

[[File:Sly_MEP2.png|thumb|upright=0.80|centre|Figure 4 - Minimum Energy Pathway]] [[File:newdynamicsam.png|thumb|upright=0.80|centre|Figure 5 - Dynamic Trajectory]]

== Q4 - Reactive and Unreactive Trajectories==

{| class="wikitable" border=1
! p1 !! p2 !! Total Energy !! Reactive or Unreactive !! Trajectory Plot !! Discussion
|-
| -1.25 || -2.5 || -99.018 || [[File:SY-1.png|frameless|upright=0.80]] || Reactive || The reactivity of the trajectory is shown as the reaction path progresses towards the prodcut H2. Upon forming, the new bond vibrates.
|-
| -1.5 || -2.0 || -100.456 || [[File:SY-2.png|frameless|upright=0.80]] || Unreactive || This figure represents an unreactive system due to the approaching H atom not having enough energy to overcome the activation barrier for the reaction. This results in the reaction trajectory returning to the original H2 bond oscillating back towards its energy minimum.
|-
| -1.5 || -2.5 || -98.956 || [[File:SY-3.png|frameless|upright=0.80]] || Reactive || This model shows a very simimlar picture to the first in the table, although due to p1 being slightly higher, the original H2 bond oscillates with higher energy.
|-
| -2.5 || -5.0 || -84.956 || [[File:SLY4.png|frameless|upright=0.80]] || Unreactive || Here one H atom aproaches the H2 molecule and the transition state complex H-H-H forms, however due to a lack of energy, the trajectory path is unable to continue to form the products so returns to the original reactants.
|-
| -2.5 || -5.2 || -83.416 ||[[File:SY5.png|frameless|upright=0.80]] || Reactive || The case has a high enough energy to form the transition state complex and to continue to overcome the energy barrier to obtain the products.
|}

== Q5 - Transition State Theory ==

Transition state theory focusses on the activated complexes formed at a transition state of the reaction, therefore by examining the transition state of a potential surface plot (found at the saddle point) one can obtain the rate of a reaction, due to the activated complex's quasi-equilibrium with the reactants. It assumes that if the collision is of sufficient energy to overcome the transition state, the products will form. This is based on the assumption that molecules react according to the classical picture, and does not take quantum mechanics into account, leading to limitations when considering phenomena such as tunnelling, whereby the reaction path bypasses a low activation energy. Furthermore the transition state theory does not account for reactions recrossing the activation barrier to return to the products as shown above. As a result, this theory would give a higher rate to the real situation.

= F H H System =

== Q1 - Energetics ==

F + H2
This reaction is shown to be exothermic (i.e. the system releases energy upon reacting, ΔH < 0) from the plot due to the energy minimum of the FH bond being lower in energy than the HH bond, therefore more stable. This is due to the large electronegativity difference between F (3.98) and H (2.20), as opposed to the non polar HH bond. As a result, the reaction of FH + H is therefore endothermic for the same reasons.

'''Talk about enthalpies of formation/dissociation'''

[[File:SLYFH.png|thumb|upright=0.80|centre|Figure 6]]

== Q2 - Position of the Transition State ==

The transition state can be found at the point where the internuclear distances of the atoms does not change over time. This is the same point on the graph for both the forward and reverse reactions. By using Hammond's postulate, that the activated intermediate complex at the transition state should resemble the state that it is closest in energy to, therefore similar to an HF + H model. As a result, it was possible to look at the surface plot and optimise the bond distances around where the transition state was roughly located. It was found that the approximate internuclear distances at this transition state are H-F : 1.810 and H-H : 0.746.

[[File:tshighlight.png|thumb|none|Figure 7]] [[File:transstatesly.png|thumb|upright=0.80|none|Figure 8]]

== Q3 - Activation Energy ==

By finding the equilibrium bond length of both reactants and products, and knowing the location of the transition state, it was possible to obtain energies for all of these positions, and therefore calculate the energy of activation.

Energy at HF minimum -133.586 AB 2.3 BC 0.9

Energy at HH minimum -103.33 AB 0.7 BC 2.3

Energy at transition state -103.742 AB 0.75 BC 1.81

ΔE = E(transition state) - E(reactants)

''ΔEFH + H‡ = (-103.742) - (-133.586) = 29.844 Kcalmol-1''

''ΔEH2 + F‡ = (-103.742) - (-103.330) = 0.412 Kcalmol-1''

== Q4 - Mechanism of Release of the Activation Energy ==

F + H2

This plot shows the reaction of initial conditions FH distance = 2.30Å HH distance = 0.85Å FH momentm = -7.0 HH momentum = -1.0, resulting in a successful reaction. Due to the exothermic nature of this reaction, it releases energy as the products have a lower potential energy than the reactants, and from the plot of internuclear distance vs. time, it is clear that this energy is converted to kinetic energy in the form of an oscillating F-H bond, which oscillates at a much higher energy than the original H-H bond. This could be confirmed experimentally by IR which would show the vibrationally excited state of the H-F bond, or energy can be measured by calorimetry.

[[File:slyreactive.png|thumb|upright=0.80|centre|Figure 9]]

== Q5 - Efficiency of Reaction ==

[[File:fh2highvibworks.png|thumb|upright=0.80|centre|Figure 10 - Reaction of H2 + F (H-H = 0.74Å, H-F = 2.Å, pHH = -3.0, pHF = -0.5)]]

[[File:lowvibsamyoung.png|thumb|upright=0.80|centre|Figure 11 - Reaction of H2 + F (H-H = 0.74Å, H-F = 2.0Å, pHH = -0.5, pHF = -0.5)]]

= Bibliography =

Electronegativity values : https://sciencenotes.org/list-of-electronegativity-values-of-the-elements/

File:Lowvibsamyoung.png

2018-05-18T13:22:07Z

Sly116:

Sam Young Reaction Dynamics

2018-05-18T13:21:59Z

Sly116: /* Q5 - Efficiency of Reaction */

= H + H2 System =
== Q1 - Transition State Gradients ==
[[File:Sly-Saddle.png|thumb|upright=0.8|centre|Figure 1 - Potential Energy Surface Plot of H2 + H System, with initial conditions A-B distance = 0.74, B-C distance = 2.30, AB momentum = 0 & BC momentum = 2.7]]

The minimum energy surface, shown running along the bottom of figure one obeys the derivative; ∂V/∂(rx) = ∂V/∂(ry) = 0, with rx and ry run parallel to their respective gradients. However, the saddle point where the transition state lies is located along the minimum energy surface at the maximum point. Therefore, it can be found by taking the second derivative, as the two orthogonal gradients have different signs, with one along the potential energy minimum being negative and the other orthogonal graident being positive.

∂2V/∂(rx)2 > 0

∂2V/∂(ry)2 < 0

== Q2 - Transition State Estimate ==

By making the momentum of the whole system equal to zero, it was possible to put the AB distance = BC distance and alter this value to obtain a result for the rts, which was found to be approximately 0.9077Å (one value due to the system being completely symmetric), which gave figure 2. This number was found by taking the intersect of the AB and BC lines from the internuclear plot with the same initial conditions given above, and optimising this value to give constant distances. Due to the gradient of potential energy at the transition state being zero, the system has no kinetic energy, only potential energy. Therefore, there is no oscillation and the plot of internuclear distance against time shows constant interatomic distances.

[[File:Sly_Q2.png|thumb|upright=0.80|centre|Figure 2 - Internucleur Distance]]

== Q3 - MEP ==

The MEP is the minimum energy pathway followed for the reaction H2 + H to take place, although it can be seen in figures 4 and 5 that it differs from the dynamic trajectory due to the masses of the atoms, and therefore the bond oscillations along the trajectory causing deviations from the mep. This is shown by the wavy black line on figure 5. Both figures illustrate the reaction path (represented by the black line) starting at the transition state point, with the dynamic reaction going to the complete formation of a H2 product, while the mep plot shows it going only slightly towards the product formation.

'''change with + - 0.01 and discuss'''

[[File:Sly_MEP2.png|thumb|upright=0.80|centre|Figure 4 - Minimum Energy Pathway]] [[File:newdynamicsam.png|thumb|upright=0.80|centre|Figure 5 - Dynamic Trajectory]]

== Q4 - Reactive and Unreactive Trajectories==

{| class="wikitable" border=1
! p1 !! p2 !! Total Energy !! Reactive or Unreactive !! Trajectory Plot !! Discussion
|-
| -1.25 || -2.5 || -99.018 || [[File:SY-1.png|frameless|upright=0.80]] || Reactive || The reactivity of the trajectory is shown as the reaction path progresses towards the prodcut H2. Upon forming, the new bond vibrates.
|-
| -1.5 || -2.0 || -100.456 || [[File:SY-2.png|frameless|upright=0.80]] || Unreactive || This figure represents an unreactive system due to the approaching H atom not having enough energy to overcome the activation barrier for the reaction. This results in the reaction trajectory returning to the original H2 bond oscillating back towards its energy minimum.
|-
| -1.5 || -2.5 || -98.956 || [[File:SY-3.png|frameless|upright=0.80]] || Reactive || This model shows a very simimlar picture to the first in the table, although due to p1 being slightly higher, the original H2 bond oscillates with higher energy.
|-
| -2.5 || -5.0 || -84.956 || [[File:SLY4.png|frameless|upright=0.80]] || Unreactive || Here one H atom aproaches the H2 molecule and the transition state complex H-H-H forms, however due to a lack of energy, the trajectory path is unable to continue to form the products so returns to the original reactants.
|-
| -2.5 || -5.2 || -83.416 ||[[File:SY5.png|frameless|upright=0.80]] || Reactive || The case has a high enough energy to form the transition state complex and to continue to overcome the energy barrier to obtain the products.
|}

== Q5 - Transition State Theory ==

Transition state theory focusses on the activated complexes formed at a transition state of the reaction, therefore by examining the transition state of a potential surface plot (found at the saddle point) one can obtain the rate of a reaction, due to the activated complex's quasi-equilibrium with the reactants. It assumes that if the collision is of sufficient energy to overcome the transition state, the products will form. This is based on the assumption that molecules react according to the classical picture, and does not take quantum mechanics into account, leading to limitations when considering phenomena such as tunnelling, whereby the reaction path bypasses a low activation energy. Furthermore the transition state theory does not account for reactions recrossing the activation barrier to return to the products as shown above. As a result, this theory would give a higher rate to the real situation.

= F H H System =

== Q1 - Energetics ==

F + H2
This reaction is shown to be exothermic (i.e. the system releases energy upon reacting, ΔH < 0) from the plot due to the energy minimum of the FH bond being lower in energy than the HH bond, therefore more stable. This is due to the large electronegativity difference between F (3.98) and H (2.20), as opposed to the non polar HH bond. As a result, the reaction of FH + H is therefore endothermic for the same reasons.

'''Talk about enthalpies of formation/dissociation'''

[[File:SLYFH.png|thumb|upright=0.80|centre|Figure 6]]

== Q2 - Position of the Transition State ==

The transition state can be found at the point where the internuclear distances of the atoms does not change over time. This is the same point on the graph for both the forward and reverse reactions. By using Hammond's postulate, that the activated intermediate complex at the transition state should resemble the state that it is closest in energy to, therefore similar to an HF + H model. As a result, it was possible to look at the surface plot and optimise the bond distances around where the transition state was roughly located. It was found that the approximate internuclear distances at this transition state are H-F : 1.810 and H-H : 0.746.

[[File:tshighlight.png|thumb|none|Figure 7]] [[File:transstatesly.png|thumb|upright=0.80|none|Figure 8]]

== Q3 - Activation Energy ==

By finding the equilibrium bond length of both reactants and products, and knowing the location of the transition state, it was possible to obtain energies for all of these positions, and therefore calculate the energy of activation.

Energy at HF minimum -133.586 AB 2.3 BC 0.9

Energy at HH minimum -103.33 AB 0.7 BC 2.3

Energy at transition state -103.742 AB 0.75 BC 1.81

ΔE = E(transition state) - E(reactants)

''ΔEFH + H‡ = (-103.742) - (-133.586) = 29.844 Kcalmol-1''

''ΔEH2 + F‡ = (-103.742) - (-103.330) = 0.412 Kcalmol-1''

== Q4 - Mechanism of Release of the Activation Energy ==

F + H2

This plot shows the reaction of initial conditions FH distance = 2.30Å HH distance = 0.85Å FH momentm = -7.0 HH momentum = -1.0, resulting in a successful reaction. Due to the exothermic nature of this reaction, it releases energy as the products have a lower potential energy than the reactants, and from the plot of internuclear distance vs. time, it is clear that this energy is converted to kinetic energy in the form of an oscillating F-H bond, which oscillates at a much higher energy than the original H-H bond. This could be confirmed experimentally by IR which would show the vibrationally excited state of the H-F bond, or energy can be measured by calorimetry.

[[File:slyreactive.png|thumb|upright=0.80|centre|Figure 9]]

== Q5 - Efficiency of Reaction ==

[[File:fh2highvibworks.png|thumb|upright=0.80|centre|Figure 10 - Reaction of H2 + F (H-H = 0.74Å, H-F = 2.Å, pHH = -3.0, pHF = -0.5)]]

[[File:lowvibsamyoung.png|thumb|upright=0.80|centre|Figure 11 - Reaction of H2 + F (H-H = 0.74Å, H-F = 2.3Å, pHH = -0.2, pHF = -0.5)]]

= Bibliography =

Electronegativity values : https://sciencenotes.org/list-of-electronegativity-values-of-the-elements/

Sam Young Reaction Dynamics

2018-05-18T13:20:15Z

Sly116: /* Q5 - Efficiency of Reaction */

= H + H2 System =
== Q1 - Transition State Gradients ==
[[File:Sly-Saddle.png|thumb|upright=0.8|centre|Figure 1 - Potential Energy Surface Plot of H2 + H System, with initial conditions A-B distance = 0.74, B-C distance = 2.30, AB momentum = 0 & BC momentum = 2.7]]

The minimum energy surface, shown running along the bottom of figure one obeys the derivative; ∂V/∂(rx) = ∂V/∂(ry) = 0, with rx and ry run parallel to their respective gradients. However, the saddle point where the transition state lies is located along the minimum energy surface at the maximum point. Therefore, it can be found by taking the second derivative, as the two orthogonal gradients have different signs, with one along the potential energy minimum being negative and the other orthogonal graident being positive.

∂2V/∂(rx)2 > 0

∂2V/∂(ry)2 < 0

== Q2 - Transition State Estimate ==

By making the momentum of the whole system equal to zero, it was possible to put the AB distance = BC distance and alter this value to obtain a result for the rts, which was found to be approximately 0.9077Å (one value due to the system being completely symmetric), which gave figure 2. This number was found by taking the intersect of the AB and BC lines from the internuclear plot with the same initial conditions given above, and optimising this value to give constant distances. Due to the gradient of potential energy at the transition state being zero, the system has no kinetic energy, only potential energy. Therefore, there is no oscillation and the plot of internuclear distance against time shows constant interatomic distances.

[[File:Sly_Q2.png|thumb|upright=0.80|centre|Figure 2 - Internucleur Distance]]

== Q3 - MEP ==

The MEP is the minimum energy pathway followed for the reaction H2 + H to take place, although it can be seen in figures 4 and 5 that it differs from the dynamic trajectory due to the masses of the atoms, and therefore the bond oscillations along the trajectory causing deviations from the mep. This is shown by the wavy black line on figure 5. Both figures illustrate the reaction path (represented by the black line) starting at the transition state point, with the dynamic reaction going to the complete formation of a H2 product, while the mep plot shows it going only slightly towards the product formation.

'''change with + - 0.01 and discuss'''

[[File:Sly_MEP2.png|thumb|upright=0.80|centre|Figure 4 - Minimum Energy Pathway]] [[File:newdynamicsam.png|thumb|upright=0.80|centre|Figure 5 - Dynamic Trajectory]]

== Q4 - Reactive and Unreactive Trajectories==

{| class="wikitable" border=1
! p1 !! p2 !! Total Energy !! Reactive or Unreactive !! Trajectory Plot !! Discussion
|-
| -1.25 || -2.5 || -99.018 || [[File:SY-1.png|frameless|upright=0.80]] || Reactive || The reactivity of the trajectory is shown as the reaction path progresses towards the prodcut H2. Upon forming, the new bond vibrates.
|-
| -1.5 || -2.0 || -100.456 || [[File:SY-2.png|frameless|upright=0.80]] || Unreactive || This figure represents an unreactive system due to the approaching H atom not having enough energy to overcome the activation barrier for the reaction. This results in the reaction trajectory returning to the original H2 bond oscillating back towards its energy minimum.
|-
| -1.5 || -2.5 || -98.956 || [[File:SY-3.png|frameless|upright=0.80]] || Reactive || This model shows a very simimlar picture to the first in the table, although due to p1 being slightly higher, the original H2 bond oscillates with higher energy.
|-
| -2.5 || -5.0 || -84.956 || [[File:SLY4.png|frameless|upright=0.80]] || Unreactive || Here one H atom aproaches the H2 molecule and the transition state complex H-H-H forms, however due to a lack of energy, the trajectory path is unable to continue to form the products so returns to the original reactants.
|-
| -2.5 || -5.2 || -83.416 ||[[File:SY5.png|frameless|upright=0.80]] || Reactive || The case has a high enough energy to form the transition state complex and to continue to overcome the energy barrier to obtain the products.
|}

== Q5 - Transition State Theory ==

Transition state theory focusses on the activated complexes formed at a transition state of the reaction, therefore by examining the transition state of a potential surface plot (found at the saddle point) one can obtain the rate of a reaction, due to the activated complex's quasi-equilibrium with the reactants. It assumes that if the collision is of sufficient energy to overcome the transition state, the products will form. This is based on the assumption that molecules react according to the classical picture, and does not take quantum mechanics into account, leading to limitations when considering phenomena such as tunnelling, whereby the reaction path bypasses a low activation energy. Furthermore the transition state theory does not account for reactions recrossing the activation barrier to return to the products as shown above. As a result, this theory would give a higher rate to the real situation.

= F H H System =

== Q1 - Energetics ==

F + H2
This reaction is shown to be exothermic (i.e. the system releases energy upon reacting, ΔH < 0) from the plot due to the energy minimum of the FH bond being lower in energy than the HH bond, therefore more stable. This is due to the large electronegativity difference between F (3.98) and H (2.20), as opposed to the non polar HH bond. As a result, the reaction of FH + H is therefore endothermic for the same reasons.

'''Talk about enthalpies of formation/dissociation'''

[[File:SLYFH.png|thumb|upright=0.80|centre|Figure 6]]

== Q2 - Position of the Transition State ==

The transition state can be found at the point where the internuclear distances of the atoms does not change over time. This is the same point on the graph for both the forward and reverse reactions. By using Hammond's postulate, that the activated intermediate complex at the transition state should resemble the state that it is closest in energy to, therefore similar to an HF + H model. As a result, it was possible to look at the surface plot and optimise the bond distances around where the transition state was roughly located. It was found that the approximate internuclear distances at this transition state are H-F : 1.810 and H-H : 0.746.

[[File:tshighlight.png|thumb|none|Figure 7]] [[File:transstatesly.png|thumb|upright=0.80|none|Figure 8]]

== Q3 - Activation Energy ==

By finding the equilibrium bond length of both reactants and products, and knowing the location of the transition state, it was possible to obtain energies for all of these positions, and therefore calculate the energy of activation.

Energy at HF minimum -133.586 AB 2.3 BC 0.9

Energy at HH minimum -103.33 AB 0.7 BC 2.3

Energy at transition state -103.742 AB 0.75 BC 1.81

ΔE = E(transition state) - E(reactants)

''ΔEFH + H‡ = (-103.742) - (-133.586) = 29.844 Kcalmol-1''

''ΔEH2 + F‡ = (-103.742) - (-103.330) = 0.412 Kcalmol-1''

== Q4 - Mechanism of Release of the Activation Energy ==

F + H2

This plot shows the reaction of initial conditions FH distance = 2.30Å HH distance = 0.85Å FH momentm = -7.0 HH momentum = -1.0, resulting in a successful reaction. Due to the exothermic nature of this reaction, it releases energy as the products have a lower potential energy than the reactants, and from the plot of internuclear distance vs. time, it is clear that this energy is converted to kinetic energy in the form of an oscillating F-H bond, which oscillates at a much higher energy than the original H-H bond. This could be confirmed experimentally by IR which would show the vibrationally excited state of the H-F bond, or energy can be measured by calorimetry.

[[File:slyreactive.png|thumb|upright=0.80|centre|Figure 9]]

== Q5 - Efficiency of Reaction ==

[[File:fh2highvibworks.png|thumb|upright=0.80|centre|Figure 10 - Reaction of H2 + F (H-H = 0.74Å, H-F = 2.Å, pHH = -3.0, pHF = -0.5)]]

[[File:fh2lowvibsam2.png|thumb|upright=0.80|centre|Figure 11 - Reaction of H2 + F (H-H = 0.74Å, H-F = 2.3Å, pHH = -0.2, pHF = -0.5)]]

= Bibliography =

Electronegativity values : https://sciencenotes.org/list-of-electronegativity-values-of-the-elements/

File:Fh2lowvibsam.png

2018-05-18T13:19:57Z

Sly116:

Sam Young Reaction Dynamics

2018-05-18T13:19:48Z

Sly116: /* Q5 - Efficiency of Reaction */

= H + H2 System =
== Q1 - Transition State Gradients ==
[[File:Sly-Saddle.png|thumb|upright=0.8|centre|Figure 1 - Potential Energy Surface Plot of H2 + H System, with initial conditions A-B distance = 0.74, B-C distance = 2.30, AB momentum = 0 & BC momentum = 2.7]]

The minimum energy surface, shown running along the bottom of figure one obeys the derivative; ∂V/∂(rx) = ∂V/∂(ry) = 0, with rx and ry run parallel to their respective gradients. However, the saddle point where the transition state lies is located along the minimum energy surface at the maximum point. Therefore, it can be found by taking the second derivative, as the two orthogonal gradients have different signs, with one along the potential energy minimum being negative and the other orthogonal graident being positive.

∂2V/∂(rx)2 > 0

∂2V/∂(ry)2 < 0

== Q2 - Transition State Estimate ==

By making the momentum of the whole system equal to zero, it was possible to put the AB distance = BC distance and alter this value to obtain a result for the rts, which was found to be approximately 0.9077Å (one value due to the system being completely symmetric), which gave figure 2. This number was found by taking the intersect of the AB and BC lines from the internuclear plot with the same initial conditions given above, and optimising this value to give constant distances. Due to the gradient of potential energy at the transition state being zero, the system has no kinetic energy, only potential energy. Therefore, there is no oscillation and the plot of internuclear distance against time shows constant interatomic distances.

[[File:Sly_Q2.png|thumb|upright=0.80|centre|Figure 2 - Internucleur Distance]]

== Q3 - MEP ==

The MEP is the minimum energy pathway followed for the reaction H2 + H to take place, although it can be seen in figures 4 and 5 that it differs from the dynamic trajectory due to the masses of the atoms, and therefore the bond oscillations along the trajectory causing deviations from the mep. This is shown by the wavy black line on figure 5. Both figures illustrate the reaction path (represented by the black line) starting at the transition state point, with the dynamic reaction going to the complete formation of a H2 product, while the mep plot shows it going only slightly towards the product formation.

'''change with + - 0.01 and discuss'''

[[File:Sly_MEP2.png|thumb|upright=0.80|centre|Figure 4 - Minimum Energy Pathway]] [[File:newdynamicsam.png|thumb|upright=0.80|centre|Figure 5 - Dynamic Trajectory]]

== Q4 - Reactive and Unreactive Trajectories==

{| class="wikitable" border=1
! p1 !! p2 !! Total Energy !! Reactive or Unreactive !! Trajectory Plot !! Discussion
|-
| -1.25 || -2.5 || -99.018 || [[File:SY-1.png|frameless|upright=0.80]] || Reactive || The reactivity of the trajectory is shown as the reaction path progresses towards the prodcut H2. Upon forming, the new bond vibrates.
|-
| -1.5 || -2.0 || -100.456 || [[File:SY-2.png|frameless|upright=0.80]] || Unreactive || This figure represents an unreactive system due to the approaching H atom not having enough energy to overcome the activation barrier for the reaction. This results in the reaction trajectory returning to the original H2 bond oscillating back towards its energy minimum.
|-
| -1.5 || -2.5 || -98.956 || [[File:SY-3.png|frameless|upright=0.80]] || Reactive || This model shows a very simimlar picture to the first in the table, although due to p1 being slightly higher, the original H2 bond oscillates with higher energy.
|-
| -2.5 || -5.0 || -84.956 || [[File:SLY4.png|frameless|upright=0.80]] || Unreactive || Here one H atom aproaches the H2 molecule and the transition state complex H-H-H forms, however due to a lack of energy, the trajectory path is unable to continue to form the products so returns to the original reactants.
|-
| -2.5 || -5.2 || -83.416 ||[[File:SY5.png|frameless|upright=0.80]] || Reactive || The case has a high enough energy to form the transition state complex and to continue to overcome the energy barrier to obtain the products.
|}

== Q5 - Transition State Theory ==

Transition state theory focusses on the activated complexes formed at a transition state of the reaction, therefore by examining the transition state of a potential surface plot (found at the saddle point) one can obtain the rate of a reaction, due to the activated complex's quasi-equilibrium with the reactants. It assumes that if the collision is of sufficient energy to overcome the transition state, the products will form. This is based on the assumption that molecules react according to the classical picture, and does not take quantum mechanics into account, leading to limitations when considering phenomena such as tunnelling, whereby the reaction path bypasses a low activation energy. Furthermore the transition state theory does not account for reactions recrossing the activation barrier to return to the products as shown above. As a result, this theory would give a higher rate to the real situation.

= F H H System =

== Q1 - Energetics ==

F + H2
This reaction is shown to be exothermic (i.e. the system releases energy upon reacting, ΔH < 0) from the plot due to the energy minimum of the FH bond being lower in energy than the HH bond, therefore more stable. This is due to the large electronegativity difference between F (3.98) and H (2.20), as opposed to the non polar HH bond. As a result, the reaction of FH + H is therefore endothermic for the same reasons.

'''Talk about enthalpies of formation/dissociation'''

[[File:SLYFH.png|thumb|upright=0.80|centre|Figure 6]]

== Q2 - Position of the Transition State ==

The transition state can be found at the point where the internuclear distances of the atoms does not change over time. This is the same point on the graph for both the forward and reverse reactions. By using Hammond's postulate, that the activated intermediate complex at the transition state should resemble the state that it is closest in energy to, therefore similar to an HF + H model. As a result, it was possible to look at the surface plot and optimise the bond distances around where the transition state was roughly located. It was found that the approximate internuclear distances at this transition state are H-F : 1.810 and H-H : 0.746.

[[File:tshighlight.png|thumb|none|Figure 7]] [[File:transstatesly.png|thumb|upright=0.80|none|Figure 8]]

== Q3 - Activation Energy ==

By finding the equilibrium bond length of both reactants and products, and knowing the location of the transition state, it was possible to obtain energies for all of these positions, and therefore calculate the energy of activation.

Energy at HF minimum -133.586 AB 2.3 BC 0.9

Energy at HH minimum -103.33 AB 0.7 BC 2.3

Energy at transition state -103.742 AB 0.75 BC 1.81

ΔE = E(transition state) - E(reactants)

''ΔEFH + H‡ = (-103.742) - (-133.586) = 29.844 Kcalmol-1''

''ΔEH2 + F‡ = (-103.742) - (-103.330) = 0.412 Kcalmol-1''

== Q4 - Mechanism of Release of the Activation Energy ==

F + H2

This plot shows the reaction of initial conditions FH distance = 2.30Å HH distance = 0.85Å FH momentm = -7.0 HH momentum = -1.0, resulting in a successful reaction. Due to the exothermic nature of this reaction, it releases energy as the products have a lower potential energy than the reactants, and from the plot of internuclear distance vs. time, it is clear that this energy is converted to kinetic energy in the form of an oscillating F-H bond, which oscillates at a much higher energy than the original H-H bond. This could be confirmed experimentally by IR which would show the vibrationally excited state of the H-F bond, or energy can be measured by calorimetry.

[[File:slyreactive.png|thumb|upright=0.80|centre|Figure 9]]

== Q5 - Efficiency of Reaction ==

[[File:fh2highvibworks.png|thumb|upright=0.80|centre|Figure 10 - Reaction of H2 + F (H-H = 0.74Å, H-F = 2.Å, pHH = -3.0, pHF = -0.5)]]

[[File:fh2lowvibsam.png|thumb|upright=0.80|centre|Figure 11 - Reaction of H2 + F (H-H = 0.74Å, H-F = 2.3Å, pHH = -0.2, pHF = -0.5)]]

= Bibliography =

Electronegativity values : https://sciencenotes.org/list-of-electronegativity-values-of-the-elements/

File:Fh2highvibworks.png

2018-05-18T13:18:53Z

Sly116: