MRD:mco218

2020-05-15T10:06:50Z

Mco218: /* F-H + H Reaction */

== '''Molecular Reaction Dynamics 2020''' ==

=== Exercise 1: H + H2→H2 + H ===

A Potential Energy Surface (PES) describes the potential energy of the system when molecular species react depending on the distance between the reacting species. The Transition State (TS) is mathematically defined as the saddle point on the PES. It is located at the maximum along the reaction trajectory which is the minimum energy path taken by the reactants. At the TS the derivative of the energy path is equal to zero, ∂V('''ri''')/∂'''ri'''=0. The TS can be identified by a configuration such that its trajectory proceeds to react to form products1. [[File:TS potential energy.png|thumb|left|alt=Fig.1.|Fig. 1 Potential energy diagram of the TS represented by a red cross.]] Most trajectories on PESs don't travel directly over the saddle point meaning they must acquire a total energy higher than the TS energy. Hence, the experimentally calculated activation energy is often higher than the actual saddle point energy. The TS can be distinguished from the local minimum in the PES by examining the second derivatives of both peaks. The TS is at the local maximum meaning its second derivative must be less than zero whereas the local minimum has a second derivative above zero.

<nowiki> </nowiki>By examining the instance of the TS, the bond distances between each of the three molecules can be considered equal as the H atom approaches collinearly. The reason its line of attack is collinear is the potential energy barrier is lowest at this trajectory and the overall reaction rate is higher than other angles. The bond distance between HA and HB & HB and HC at the TS can be labelled rts. As mentioned above, the TS occurs at the maximum of the minimum energy path, shown in Fig. 1 as a red cross when rts is 90.775 pm.

Here H and H2 have zero momentum, meaning zero force, 0 kJ mol-1.pm-1 is acting on the system and the species cannot fall towards either the reactants or products. The red cross indicates the maximum in potential energy of which the reactants must obtain to transform into products. The internuclear distances vs time graph illustrate the motion of each reactive species in Fig. 2. The B-C and A-C distances display a horizontal, constant behaviour meaning the bond distances remain the same through out the TS.
[[File:TS internuclear distances.png|thumb|centre|alt=Fig.2.|Fig. 2 Internuclear Distances vs Time at the TS.]]

==== Trajectories of r1=rts+δ , r2=rts ====
Whilst looking at the trajectory of the reactants when r1 is slightly longer than r2, the reactants can turn into the products H2 + H. The trajectory follows the PES floor as indicated by a black line in Fig. 3 and Fig. 4. Using a Minimum Energy Path (MEP) simulation, the trajectory is a smooth line suggesting there is no vibrational energy obtained by the products. In a Dynamics simulation, there is a non-linear line with sinusoidal behaviour indicating that the products are in a vibrationally excited state.
[[File:MEP_path_mco.png|thumb|left|alt=Fig.3.|Fig. 3 MEP simulation representation of the trajectory taken by the reactants on the PES.]]
[[File:Dynamics_Path_mco.png|thumb|centre|alt=Fig.4.|Fig. 4 . Dynamics simulation representation of the trajectory taken by the reactants on the PES.]]

==== Reactive and Unreactive Trajectories ====
Reaction 1

HAHB + HC → HA + HBHC

In the trajectories below, AB distance refers to the distance between HA and HB and BC distance refers to the distance between HB and HC. The initial positions were AB = 74 pm and BC = 200 pm.
{| class="wikitable"
!Situation
!p1/g.mol-1.pm.fs-1
!p2/g.mol-1.pm.fs-1
!Etot/kJ mol-1
!Reactive?
!Description of dynamics
!Illustration of the Trajectory
|-
|'''1)'''
|<nowiki>-2.56</nowiki>
|<nowiki>-5.1</nowiki>
|<nowiki>-414.280</nowiki>
|Yes
|[[File:P2_-5.1_p1_-2.56.png|thumb|alt=Trajectory 1|Fig. 5 Trajectory for p1=-2.56, p2=-5.1.]]
|This reaction is reactive since the trajectory displays the reactants through the saddle point and following the MEP towards the products. The majority of the energy before reaction is translational kinetic energy by observing the smooth line along the left hand side of the contour map. The products display a vibrationally excited trajectory after the reaction suggesting some of the initial translational energy was transformed into vibrational energy during the reaction.
|-
|'''2)'''
|<nowiki>-3.1</nowiki>
|<nowiki>-4.1</nowiki>
|<nowiki>-420.077</nowiki>
|No
|[[File:P2_-4.1.png|thumb|alt=Trajectory 2|Fig. 6 Trajectory for p1=-3.1, p2=-4.1.]]
|This process is un-reactive. The reactants begin in an excited vibrational state demonstrated by the sinusoidal-type trajectory. However, just before the saddle point, the trajectory rebounds on itself. This is because the reactants didn't have sufficient energy to overcome the potential energy barrier at the saddle point. The trajectory travels off the contour map highlighting how the BC distance continues to increase indefinitely.
|-
|'''3)'''
|<nowiki>-3.1</nowiki>
|<nowiki>-5.1</nowiki>
|<nowiki>-413.977</nowiki>
|Yes
|[[File:P2_-5.1_p1_-3.1.png|thumb|alt=Trajectory 3|Fig. 7 Trajectory for p1=-3.1, p2=-5.1.]]
|This reaction is reactive. The reactants display some vibrational energy from the HAHB molecule. The trajectory follows the MEP through the saddle point and towards the reactants which again have vibrational energy.
|-
|'''4)'''
|<nowiki>-5.1</nowiki>
|<nowiki>-10.1</nowiki>
|<nowiki>-357.277</nowiki>
|No
|[[File:P2_-10.1.png|thumb|alt=Trajectory 4|Fig. 8 Trajectory for p1=-5.1, p2=-10.1.]]
|This reaction is surprisingly un-reactive. Although HC has a much higher velocity magnitude than before, the reaction doesn't go to completion. The trajectory does not go through the saddle point but instead travels up and down the sides of the steep potential surface walls meaning it would require even more energy to get to the products having followed this path.
|-
|'''5)'''
|<nowiki>-5.1</nowiki>
|<nowiki>-10.6</nowiki>
|<nowiki>-349.477</nowiki>
|Yes
|[[File:P2_-10.6.png|thumb|alt=Trajectory 5|Fig. 9 Trajectory for p1=-5.1, p2=-10.6.]]
|This reaction goes to completion and is the highest in energy. The reactants don't go through the MEP instead it travels up the sides of the potential wall. However, unlike in the above case, this reaction has more energy to overcome the activation energy and form the products which have significantly more vibrational energy between HB and HC.
|}
Table 1. Exploring different cases where the momenta of the reactant species in reaction 1 are altered.

By analysing the different scenarios from the above table, I can conclude that the distribution of energy in the reacting species needs to be at a certain configuration for the reaction to happen. In situtation 2, the reactants are vibrationally excited however there is insufficient translational kinetic energy available for the reaction to form products. In situation 4, the colliding atom has excess translational energy however the HAHC lacks vibrational energy to react. In situation 5, the total energy of the system is more than 10 kJ mol-1 higher than in situation 4. This provides the additional energy needed to overcome the higher potential barrier by not proceeding through the saddle point.

==== How Transition State Theory (TST) predictions compare with experimental values ====
TST states many assumptions when examining PESs. TST assumes that once the reactant trajectory passes over the TS the trajectory cannot go back to the reactants but instead form the products. This assumption is contradicted in many chemical reactions as shown in Fig. 8. The trajectory overcomes the potential energy barrier but fails to produce products and rebounds towards its initial starting point. Another assumption is that all collisions with a kinetic energy higher than the activation energy will result in a reaction. However, even when high amounts of energy is given to a system, the reactants fail to make products as seen in Fig. 8. This eludes to the conclusion that the distribution of energy in a system between modes other than translational, such as vibrational, determines whether the reaction will go to completion. TST is a classical theory where quantum effects such as quantum tunnelling are not involved.

By experimenting with different reactive and un-reactive reactions, it is clear that many trajectories on PESs don't travel directly over a saddle point but instead partially climb the walls of the potential well. In order for the reaction to go to completion, the reactants in these situations must acquire a total energy significantly higher than the saddle point energy. As a result of this, the experimentally determined activation energy for reactions are commonly higher than the TST energy barrier predictions. In reality, with a higher energy barrier this would suggest that the rate of reaction is higher in TST rate predictions than in experimental values.

=== Exercise 2: F-H-H System ===

==== Energetics of F + H2 and H + HF ====
Reaction 2.1

<nowiki> </nowiki>F + HAHB → FHA + HB

Reaction 2.2

<nowiki> </nowiki>HA + HBF → HAHB + F
{| class="wikitable"
!
!Reaction
!Initial distances / pm
!Momenta / g.mol-1.pm.fs-1
!Total Energy / kJ mol-1
!Transition State Position
!Forces at TS / kJ mol-1
!Activation Energy kJ mol-1
|-
|'''2.1)'''
|F + HAHB
|F - HA = 200
HA - HB = 74
|AB = -2.5
BC = -5.1
|<nowiki>-417.591 </nowiki>
|F - HA = ~98 pm
HA - HB = ~104 pm
|along AB = -1.197
along BC = +1.140

Net Force = -0.057 '''AB'''
|0.006 (Exothermic)
|-
|'''2.2)'''
|HA + HBF
|HA - HB = 200
HB - F = 92
|AB = -23.0
BC = -10.0
|<nowiki>-207.717</nowiki>
|HA - HB = ~103 pm
HB - F = ~98 pm
|along AB = +1.197
along BC = -1.133

Net Force = +0.064 '''AB'''
|1.171 (Endothermic)
|}
Table 2. The total energy of each reacting system.

Reaction 2.1 is lower in energy, -417.591 kJ mol-1, than reaction 2.2 at -207.717 kJ mol-1. This suggests that reaction 2.1 is a more energetically favourable reaction. Reaction 2.2 is higher in energy and unstable requiring energy from the surroundings to react as demonstrated by the larger activation energy in table 2. This implies that the new H-F bond formed is stronger than the H-H bond and more energetically favourable. As reaction 2.2 is more endothermic, it requires energy from its surroundings to form the H-H bond again meaning it is a weaker, less stable bond than H-F.

[[File:EA_reaction2.1.png]]

Fig. 10 Activation energy required to form F-H + H in reaction 2.1.

[[File:AE_reaction2.2.png]]

Fig. 11 Activation energy required to create H2 + F in reaction 2.2.

=== Reaction Dynamics ===

==== F + H2 Reaction ====
{| class="wikitable"
|[[File:p1(-1)p2(-3)r2.1.png|thumb|alt=fig12|Fig. 12. PES contour plot of the trajectory of reaction 2.1. P1 = -1, p2 = -3.]]
|[[File:p1(-1)p2(-5.9)r2.1_SP.png|thumb|alt=fig13|Fig. 13 . PES 3D map of the potential well and trajectory taken by the reactants. P1 = -1, p2 = -5.9.]]
|-
|[[File:p1(-1)p2(5.9)r2.1.png|thumb|alt=fig14|Fig. 14. PES contour map of the trajectory of reactants in reaction 2.1. P1 = -1, p2 = 5.9.]]
|[[File:p1(-1.6)p2(0.2)r2.1.png|thumb|alt=fig15|Fig. 15. PES contour map for reaction 2.1. P1 = -1.6, p2 = 0.2.]]
|}
Table 3. Contour and Surface plots of reaction 2.1 with various initial momenta settings whilst initial internuclear distances remain constant.

<nowiki> </nowiki>As shown in the table 3., varying amounts of energy are given to reaction 2.1 by altering the initial momenta. The energy provided exceeds the activation energy yet not all of the reactions in Fig. 12 - 15 are reactive. In Fig. 12, the reactants trajectory travels through the reactants channel whilst oscillating up and down the sides of the potential wall. The reactants overcome the energy barrier but rebound back towards the reactants channel, meaning the reactants don't have sufficient energy distribution in both translational and vibrational modes. This is similar to the trajectory in Fig. 15. Both trajectories in Fig. 13 and 14 showcase successfully reactive reactions. The reactants travel through the transition state towards the products. The reactants appear to obtain a significant amount of vibrational energy suggesting the H2 molecule is in a vibrationally excited state.

By examining Polanyi's Rules2, since reaction 2.1 is more exothermic, it has an earlier TS. This leads to an earlier energy barrier in the entrance channel of the potential well, nearer the reactants. To overcome this barrier, the reaction is more effective if the reactants have a higher amount of translational energy than vibrational. If there is more vibrational energy in the reactants, the trajectory can travel up the sides of the repulsive potential well and lose energy in the process meaning they cannot travel over the potential energy barrier at the TS. In Fig. 14, the reactants may have some vibrational energy but have a significant amount of translational energy due to the higher initial momentum of the incoming atom. Whereas in Fig. 15 the reactants have lower translational energy and cannot reach the products, hence it is unreactive.

==== F-H + H Reaction ====
Reaction 2.2 is more endothermic when compared to reaction 2.1 as the H-F is broken in the process which is a stronger bond. In Fig. 18, the reactants are given a high translational kinetic energy as demonstrated by the relatively linear trajectory in the reactants channel. The reaction in Fig. 18 is reactive as it overcomes the energy barrier towards the products. However, the reaction in Fig. 19 is un-reactive and the reactant trajectory rebounds once it reaches the TS energy barrier. In this trajectory, the reactants have more vibrational energy than in Fig. 18 whilst the reactants in Fig. 18 have more translational motion.

[[File:reaction2.2_endothermic_reactive.png]]

Fig. 18 A successful reaction trajectory of reaction 2.2.

[[File:reaction2.2_unsuccessful.png]]

Fig. 19 An un-reactive trajectory of reaction 2.2.

By appreciating Polanyi's Rules2, the reason behind the reactivity of the trajectories in Fig. 18 and 19 can be solved. The endothermic reaction 2.2 means it has an later TS which resembles the structure of the products. When a reaction has a late TS, the potential energy barrier is located in the exit channel. Reactants which have more vibrational energy are able to overcome the earlier TS barrier, Fig. 18, whereas reactants with high translational energy collide against the repulsive potential energy walls before even reaching the energy barrier, Fig. 19 and hence lose energy in the process.

== Bibliography ==
1 Atkins ___

2020-05-14T16:54:25Z

Mco218: /* Bibliography */

== '''Molecular Reaction Dynamics 2020''' ==

=== Exercise 1: H + H2→H2 + H ===

A Potential Energy Surface (PES) describes the potential energy of the system when molecular species react depending on the distance between the reacting species. The Transition State (TS) is mathematically defined as the saddle point on the PES. It is located at the maximum along the reaction trajectory which is the minimum energy path taken by the reactants. At the TS the derivative of the energy path is equal to zero, ∂V('''ri''')/∂'''ri'''=0. The TS can be identified by a configuration such that its trajectory proceeds to react to form products1. [[File:TS potential energy.png|thumb|left|alt=Fig.1.|Fig. 1 Potential energy diagram of the TS represented by a red cross.]] Most trajectories on PESs don't travel directly over the saddle point meaning they must acquire a total energy higher than the TS energy. Hence, the experimentally calculated activation energy is often higher than the actual saddle point energy. The TS can be distinguished from the local minimum in the PES by examining the second derivatives of both peaks. The TS is at the local maximum meaning its second derivative must be less than zero whereas the local minimum has a second derivative above zero.

<nowiki> </nowiki>By examining the instance of the TS, the bond distances between each of the three molecules can be considered equal as the H atom approaches collinearly. The reason its line of attack is collinear is the potential energy barrier is lowest at this trajectory and the overall reaction rate is higher than other angles. The bond distance between HA and HB & HB and HC at the TS can be labelled rts. As mentioned above, the TS occurs at the maximum of the minimum energy path, shown in Fig. 1 as a red cross when rts is 90.775 pm.

Here H and H2 have zero momentum, meaning zero force, 0 kJ mol-1.pm-1 is acting on the system and the species cannot fall towards either the reactants or products. The red cross indicates the maximum in potential energy of which the reactants must obtain to transform into products. The internuclear distances vs time graph illustrate the motion of each reactive species in Fig. 2. The B-C and A-C distances display a horizontal, constant behaviour meaning the bond distances remain the same through out the TS.
[[File:TS internuclear distances.png|thumb|centre|alt=Fig.2.|Fig. 2 Internuclear Distances vs Time at the TS.]]

==== Trajectories of r1=rts+δ , r2=rts ====
Whilst looking at the trajectory of the reactants when r1 is slightly longer than r2, the reactants can turn into the products H2 + H. The trajectory follows the PES floor as indicated by a black line in Fig. 3 and Fig. 4. Using a Minimum Energy Path (MEP) simulation, the trajectory is a smooth line suggesting there is no vibrational energy obtained by the products. In a Dynamics simulation, there is a non-linear line with sinusoidal behaviour indicating that the products are in a vibrationally excited state.
[[File:MEP_path_mco.png|thumb|left|alt=Fig.3.|Fig. 3 MEP simulation representation of the trajectory taken by the reactants on the PES.]]
[[File:Dynamics_Path_mco.png|thumb|centre|alt=Fig.4.|Fig. 4 . Dynamics simulation representation of the trajectory taken by the reactants on the PES.]]

==== Reactive and Unreactive Trajectories ====
Reaction 1

HAHB + HC → HA + HBHC

In the trajectories below, AB distance refers to the distance between HA and HB and BC distance refers to the distance between HB and HC. The initial positions were AB = 74 pm and BC = 200 pm.
{| class="wikitable"
!Situation
!p1/g.mol-1.pm.fs-1
!p2/g.mol-1.pm.fs-1
!Etot/kJ mol-1
!Reactive?
!Description of dynamics
!Illustration of the Trajectory
|-
|'''1)'''
|<nowiki>-2.56</nowiki>
|<nowiki>-5.1</nowiki>
|<nowiki>-414.280</nowiki>
|Yes
|[[File:P2_-5.1_p1_-2.56.png|thumb|alt=Trajectory 1|Fig. 5 Trajectory for p1=-2.56, p2=-5.1.]]
|This reaction is reactive since the trajectory displays the reactants through the saddle point and following the MEP towards the products. The majority of the energy before reaction is translational kinetic energy by observing the smooth line along the left hand side of the contour map. The products display a vibrationally excited trajectory after the reaction suggesting some of the initial translational energy was transformed into vibrational energy during the reaction.
|-
|'''2)'''
|<nowiki>-3.1</nowiki>
|<nowiki>-4.1</nowiki>
|<nowiki>-420.077</nowiki>
|No
|[[File:P2_-4.1.png|thumb|alt=Trajectory 2|Fig. 6 Trajectory for p1=-3.1, p2=-4.1.]]
|This process is un-reactive. The reactants begin in an excited vibrational state demonstrated by the sinusoidal-type trajectory. However, just before the saddle point, the trajectory rebounds on itself. This is because the reactants didn't have sufficient energy to overcome the potential energy barrier at the saddle point. The trajectory travels off the contour map highlighting how the BC distance continues to increase indefinitely.
|-
|'''3)'''
|<nowiki>-3.1</nowiki>
|<nowiki>-5.1</nowiki>
|<nowiki>-413.977</nowiki>
|Yes
|[[File:P2_-5.1_p1_-3.1.png|thumb|alt=Trajectory 3|Fig. 7 Trajectory for p1=-3.1, p2=-5.1.]]
|This reaction is reactive. The reactants display some vibrational energy from the HAHB molecule. The trajectory follows the MEP through the saddle point and towards the reactants which again have vibrational energy.
|-
|'''4)'''
|<nowiki>-5.1</nowiki>
|<nowiki>-10.1</nowiki>
|<nowiki>-357.277</nowiki>
|No
|[[File:P2_-10.1.png|thumb|alt=Trajectory 4|Fig. 8 Trajectory for p1=-5.1, p2=-10.1.]]
|This reaction is surprisingly un-reactive. Although HC has a much higher velocity magnitude than before, the reaction doesn't go to completion. The trajectory does not go through the saddle point but instead travels up and down the sides of the steep potential surface walls meaning it would require even more energy to get to the products having followed this path.
|-
|'''5)'''
|<nowiki>-5.1</nowiki>
|<nowiki>-10.6</nowiki>
|<nowiki>-349.477</nowiki>
|Yes
|[[File:P2_-10.6.png|thumb|alt=Trajectory 5|Fig. 9 Trajectory for p1=-5.1, p2=-10.6.]]
|This reaction goes to completion and is the highest in energy. The reactants don't go through the MEP instead it travels up the sides of the potential wall. However, unlike in the above case, this reaction has more energy to overcome the activation energy and form the products which have significantly more vibrational energy between HB and HC.
|}
Table 1. Exploring different cases where the momenta of the reactant species in reaction 1 are altered.

By analysing the different scenarios from the above table, I can conclude that the distribution of energy in the reacting species needs to be at a certain configuration for the reaction to happen. In situtation 2, the reactants are vibrationally excited however there is insufficient translational kinetic energy available for the reaction to form products. In situation 4, the colliding atom has excess translational energy however the HAHC lacks vibrational energy to react. In situation 5, the total energy of the system is more than 10 kJ mol-1 higher than in situation 4. This provides the additional energy needed to overcome the higher potential barrier by not proceeding through the saddle point.

==== How Transition State Theory (TST) predictions compare with experimental values ====
TST states many assumptions when examining PESs. TST assumes that once the reactant trajectory passes over the TS the trajectory cannot go back to the reactants but instead form the products. This assumption is contradicted in many chemical reactions as shown in Fig. 8. The trajectory overcomes the potential energy barrier but fails to produce products and rebounds towards its initial starting point. Another assumption is that all collisions with a kinetic energy higher than the activation energy will result in a reaction. However, even when high amounts of energy is given to a system, the reactants fail to make products as seen in Fig. 8. This eludes to the conclusion that the distribution of energy in a system between modes other than translational, such as vibrational, determines whether the reaction will go to completion. TST is a classical theory where quantum effects such as quantum tunnelling are not involved.

By experimenting with different reactive and un-reactive reactions, it is clear that many trajectories on PESs don't travel directly over a saddle point but instead partially climb the walls of the potential well. In order for the reaction to go to completion, the reactants in these situations must acquire a total energy significantly higher than the saddle point energy. As a result of this, the experimentally determined activation energy for reactions are commonly higher than the TST energy barrier predictions. In reality, with a higher energy barrier this would suggest that the rate of reaction is higher in TST rate predictions than in experimental values.

=== Exercise 2: F-H-H System ===

==== Energetics of F + H2 and H + HF ====
Reaction 2.1

<nowiki> </nowiki>F + HAHB → FHA + HB

Reaction 2.2

<nowiki> </nowiki>HA + HBF → HAHB + F
{| class="wikitable"
!
!Reaction
!Initial distances / pm
!Momenta / g.mol-1.pm.fs-1
!Total Energy / kJ mol-1
!Transition State Position
!Forces at TS / kJ mol-1
!Activation Energy kJ mol-1
|-
|'''2.1)'''
|F + HAHB
|F - HA = 200
HA - HB = 74
|AB = -2.5
BC = -5.1
|<nowiki>-417.591</nowiki>
|F - HA = ~98 pm
HA - HB = ~104 pm
|along AB = -1.197
along BC = +1.140

Net Force = -0.057 '''AB'''
|0.006
|-
|'''2.2)'''
|HA + HBF
|HA - HB = 200
HB - F = 92
|AB = -23.0
BC = -10.0
|<nowiki>-207.717</nowiki>
|HA - HB = ~103 pm
HB - F = ~98 pm
|along AB = +1.197
along BC = -1.133

Net Force = +0.064 '''AB'''
|1.171
|}
Table 2. The total energy of each reacting system.

The F + H2 reaction is lower in energy, -417.591 kJ mol-1, than H + HF at -206.638 kJ mol-1. This suggests that reaction 2.1 is more energetically favourable and hence exothermic. Reaction 2.2 is higher in energy and unstable, hence it is endothermic, requiring energy from the surroundings to react. Since reaction 2.1 is more exothermic this implies that the new H-F bond formed is stronger than the H-H bond and more energetically favourable. As reaction 2.2 is more endothermic, it requires energy from its surroundings to form the H-H bond again meaning it is a weaker, less stable bond than H-F.

[[File:EA_reaction2.1.png]]

Fig. 10 Activation energy required to form F-H + H in reaction 2.1.

[[File:AE_reaction2.2.png]]

Fig. 11 Activation energy required to create H2 + F in reaction 2.2.

=== Reaction Dynamics ===

==== F + H2 Reaction ====
{| class="wikitable"
|[[File:p1(-1)p2(-3)r2.1.png|thumb|alt=fig12|Fig. 12. PES contour plot of the trajectory of reaction 2.1. P1 = -1, p2 = -3.]]
|[[File:p1(-1)p2(-5.9)r2.1_SP.png|thumb|alt=fig13|Fig. 13 . PES 3D map of the potential well and trajectory taken by the reactants. P1 = -1, p2 = -5.9.]]
|-
|[[File:p1(-1)p2(5.9)r2.1.png|thumb|alt=fig14|Fig. 14. PES contour map of the trajectory of reactants in reaction 2.1. P1 = -1, p2 = 5.9.]]
|[[File:p1(-1.6)p2(0.2)r2.1.png|thumb|alt=fig15|Fig. 15. PES contour map for reaction 2.1. P1 = -1.6, p2 = 0.2.]]
|}
Table 3. Contour and Surface plots of reaction 2.1 with various initial momenta settings whilst initial internuclear distances remain constant.

<nowiki> </nowiki>As shown in the table 3., varying amounts of energy are given to reaction 2.1 by altering the initial momenta. The energy provided exceeds the activation energy yet not all of the reactions in Fig. 12 - 15 are reactive. In Fig. 12, the reactants trajectory travels through the reactants channel whilst oscillating up and down the sides of the potential wall. The reactants overcome the energy barrier but rebound back towards the reactants channel, meaning the reactants don't have sufficient energy distribution in both translational and vibrational modes. This is similar to the trajectory in Fig. 15. Both trajectories in Fig. 13 and 14 showcase successfully reactive reactions. The reactants travel through the transition state towards the products. The reactants appear to obtain a significant amount of vibrational energy suggesting the H2 molecule is in a vibrationally excited state.

The vibrational energy of the reactants in a reactive process in Fig. 14 can be compared to those in an un-reactive reaction in Fig. 15.
{| class="wikitable"
!
!Potential/Kinetic Energy

as a function of time
|-
|Fig. 14 Trajectory
|[[File:PE_p1(-1).png|thumb|alt=fig 16|Fig. 16 Energy vs Time graph for Fig. 14 reaction.]]
|-
|Fig. 15 Trajectory
|[[File:PE_p1(-1.6).png|thumb|alt=fig 17|Fig. 17 Energy vs Time graph for Fig. 15 reaction.]]
|}
Table 4. Energy vs Time graphs for an un-reactive and reactive version of reaction 2.1.

By observing table 4., there is a clear difference in the modes of kinetic energy of the reactants before the TS. In Fig. 16 the graph showcases the vibrational energy of the reactants with the sinusoidal type line. Whereas, in Fig. 17, there is a straight horizontal line for the energy of reactants highlighting the absence of sufficient vibrational energy which is required for the reaction to be successful. The displacement of the curve in Fig. 16 appears to change once the reaction has occurred. The amplitude of the potential energy curve depends on the force constant, k, of the vibrating bond, U=1/2kx2 in a simple harmonic oscillator. This suggests that the products have a higher force constant due to the larger amplitude of the curve, hence the vibrating bond formed in the reaction is stronger than the vibrating bond in the reactants. This proves that the H-F bond has a higher bond strength than H-H and explains why the activation energy for reaction 2.1 is much lower than that for reaction 2.2.

==== FH + H Reaction ====
As shown in table 2., reaction 2.2 is more endothermic when compared to reaction 2.1. In Fig. 18, the reactants are given a high translational kinetic energy as demonstrated by the relatively linear trajectory in the reactants channel. The reaction in Fig. 18 is reactive as it overcomes the energy barrier towards the products. However, the reaction in Fig. 19 is un-reactive and the reactant trajectory rebounds once it reaches the TS energy barrier. In this trajectory, the reactants have more vibrational energy than in Fig. 18 whilst the reactants in Fig. 18 have more translational motion.

[[File:reaction2.2_successful.png]]

Fig. 18 A successful reaction trajectory of reaction 2.2.

[[File:reaction2.2_unsuccessful.png]]

Fig. 19 An un-reactive trajectory of reaction 2.2.

By appreciating Polanyi's Rules2, the reason behind the reactivity of the trajectories in Fig. 18 and 19 can be solved. The endothermic reaction 2.2 means it has a later TS which resembles the structure of the products. When a reaction has a late TS, the potential energy barrier is located in the exit channel. Reactants which have more vibrational energy are able to overcome the late TS barrier, Fig. 18, whereas reactants with high translation energy collide against the repulsive potential energy walls before even reaching the energy barrier, Fig. 19.

== Bibliography ==
1 Atkins ___

File:Reaction2.2 unsuccessful.png

2020-05-14T16:40:54Z

Mco218:

2020-05-14T15:48:22Z

Mco218: /* Bibliography */

== '''Molecular Reaction Dynamics 2020''' ==

=== Exercise 1: H + H2→H2 + H ===

A Potential Energy Surface (PES) describes the potential energy of the system when molecular species react depending on the distance between the reacting species. The Transition State (TS) is mathematically defined as the saddle point on the PES. It is located at the maximum along the reaction trajectory which is the minimum energy path taken by the reactants. At the TS the derivative of the energy path is equal to zero, ∂V('''ri''')/∂'''ri'''=0. The TS can be identified by a configuration such that its trajectory proceeds to react to form products1. [[File:TS potential energy.png|thumb|left|alt=Fig.1.|Fig. 1 Potential energy diagram of the TS represented by a red cross.]] Most trajectories on PESs don't travel directly over the saddle point meaning they must acquire a total energy higher than the TS energy. Hence, the experimentally calculated activation energy is often higher than the actual saddle point energy. The TS can be distinguished from the local minimum in the PES by examining the second derivatives of both peaks. The TS is at the local maximum meaning its second derivative must be less than zero whereas the local minimum has a second derivative above zero.

<nowiki> </nowiki>By examining the instance of the TS, the bond distances between each of the three molecules can be considered equal as the H atom approaches collinearly. The reason its line of attack is collinear is the potential energy barrier is lowest at this trajectory and the overall reaction rate is higher than other angles. The bond distance between HA and HB & HB and HC at the TS can be labelled rts. As mentioned above, the TS occurs at the maximum of the minimum energy path, shown in Fig. 1 as a red cross when rts is 90.775 pm.

Here H and H2 have zero momentum, meaning zero force, 0 kJ mol-1.pm-1 is acting on the system and the species cannot fall towards either the reactants or products. The red cross indicates the maximum in potential energy of which the reactants must obtain to transform into products. The internuclear distances vs time graph illustrate the motion of each reactive species in Fig. 2. The B-C and A-C distances display a horizontal, constant behaviour meaning the bond distances remain the same through out the TS.
[[File:TS internuclear distances.png|thumb|centre|alt=Fig.2.|Fig. 2 Internuclear Distances vs Time at the TS.]]

==== Trajectories of r1=rts+δ , r2=rts ====
Whilst looking at the trajectory of the reactants when r1 is slightly longer than r2, the reactants can turn into the products H2 + H. The trajectory follows the PES floor as indicated by a black line in Fig. 3 and Fig. 4. Using a Minimum Energy Path (MEP) simulation, the trajectory is a smooth line suggesting there is no vibrational energy obtained by the products. In a Dynamics simulation, there is a non-linear line with sinusoidal behaviour indicating that the products are in a vibrationally excited state.
[[File:MEP_path_mco.png|thumb|left|alt=Fig.3.|Fig. 3 MEP simulation representation of the trajectory taken by the reactants on the PES.]]
[[File:Dynamics_Path_mco.png|thumb|centre|alt=Fig.4.|Fig. 4 . Dynamics simulation representation of the trajectory taken by the reactants on the PES.]]

==== Reactive and Unreactive Trajectories ====
Reaction 1

HAHB + HC → HA + HBHC

In the trajectories below, AB distance refers to the distance between HA and HB and BC distance refers to the distance between HB and HC. The initial positions were AB = 74 pm and BC = 200 pm.
{| class="wikitable"
!Situation
!p1/g.mol-1.pm.fs-1
!p2/g.mol-1.pm.fs-1
!Etot/kJ mol-1
!Reactive?
!Description of dynamics
!Illustration of the Trajectory
|-
|'''1)'''
|<nowiki>-2.56</nowiki>
|<nowiki>-5.1</nowiki>
|<nowiki>-414.280</nowiki>
|Yes
|[[File:P2_-5.1_p1_-2.56.png|thumb|alt=Trajectory 1|Fig. 5 Trajectory for p1=-2.56, p2=-5.1.]]
|This reaction is reactive since the trajectory displays the reactants through the saddle point and following the MEP towards the products. The majority of the energy before reaction is translational kinetic energy by observing the smooth line along the left hand side of the contour map. The products display a vibrationally excited trajectory after the reaction suggesting some of the initial translational energy was transformed into vibrational energy during the reaction.
|-
|'''2)'''
|<nowiki>-3.1</nowiki>
|<nowiki>-4.1</nowiki>
|<nowiki>-420.077</nowiki>
|No
|[[File:P2_-4.1.png|thumb|alt=Trajectory 2|Fig. 6 Trajectory for p1=-3.1, p2=-4.1.]]
|This process is un-reactive. The reactants begin in an excited vibrational state demonstrated by the sinusoidal-type trajectory. However, just before the saddle point, the trajectory rebounds on itself. This is because the reactants didn't have sufficient energy to overcome the potential energy barrier at the saddle point. The trajectory travels off the contour map highlighting how the BC distance continues to increase indefinitely.
|-
|'''3)'''
|<nowiki>-3.1</nowiki>
|<nowiki>-5.1</nowiki>
|<nowiki>-413.977</nowiki>
|Yes
|[[File:P2_-5.1_p1_-3.1.png|thumb|alt=Trajectory 3|Fig. 7 Trajectory for p1=-3.1, p2=-5.1.]]
|This reaction is reactive. The reactants display some vibrational energy from the HAHB molecule. The trajectory follows the MEP through the saddle point and towards the reactants which again have vibrational energy.
|-
|'''4)'''
|<nowiki>-5.1</nowiki>
|<nowiki>-10.1</nowiki>
|<nowiki>-357.277</nowiki>
|No
|[[File:P2_-10.1.png|thumb|alt=Trajectory 4|Fig. 8 Trajectory for p1=-5.1, p2=-10.1.]]
|This reaction is surprisingly un-reactive. Although HC has a much higher velocity magnitude than before, the reaction doesn't go to completion. The trajectory does not go through the saddle point but instead travels up and down the sides of the steep potential surface walls meaning it would require even more energy to get to the products having followed this path.
|-
|'''5)'''
|<nowiki>-5.1</nowiki>
|<nowiki>-10.6</nowiki>
|<nowiki>-349.477</nowiki>
|Yes
|[[File:P2_-10.6.png|thumb|alt=Trajectory 5|Fig. 9 Trajectory for p1=-5.1, p2=-10.6.]]
|This reaction goes to completion and is the highest in energy. The reactants don't go through the MEP instead it travels up the sides of the potential wall. However, unlike in the above case, this reaction has more energy to overcome the activation energy and form the products which have significantly more vibrational energy between HB and HC.
|}
Table 1. Exploring different cases where the momenta of the reactant species in reaction 1 are altered.

By analysing the different scenarios from the above table, I can conclude that the distribution of energy in the reacting species needs to be at a certain configuration for the reaction to happen. In situtation 2, the reactants are vibrationally excited however there is insufficient translational kinetic energy available for the reaction to form products. In situation 4, the colliding atom has excess translational energy however the HAHC lacks vibrational energy to react. In situation 5, the total energy of the system is more than 10 kJ mol-1 higher than in situation 4. This provides the additional energy needed to overcome the higher potential barrier by not proceeding through the saddle point.

==== How Transition State Theory (TST) predictions compare with experimental values ====
TST states many assumptions when examining PESs. TST assumes that once the reactant trajectory passes over the TS the trajectory cannot go back to the reactants but instead form the products. This assumption is contradicted in many chemical reactions as shown in Fig. 8. The trajectory overcomes the potential energy barrier but fails to produce products and rebounds towards its initial starting point. Another assumption is that all collisions with a kinetic energy higher than the activation energy will result in a reaction. However, even when high amounts of energy is given to a system, the reactants fail to make products as seen in Fig. 8. This eludes to the conclusion that the distribution of energy in a system between modes other than translational, such as vibrational, determines whether the reaction will go to completion. TST is a classical theory where quantum effects such as quantum tunnelling are not involved.

By experimenting with different reactive and un-reactive reactions, it is clear that many trajectories on PESs don't travel directly over a saddle point but instead partially climb the walls of the potential well. In order for the reaction to go to completion, the reactants in these situations must acquire a total energy significantly higher than the saddle point energy. As a result of this, the experimentally determined activation energy for reactions are commonly higher than the TST energy barrier predictions. In reality, with a higher energy barrier this would suggest that the rate of reaction is higher in TST rate predictions than in experimental values.

=== Exercise 2: F-H-H System ===

==== Energetics of F + H2 and H + HF ====
Reaction 2.1

<nowiki> </nowiki>F + HAHB → FHA + HB

Reaction 2.2

<nowiki> </nowiki>HA + HBF → HAHB + F
{| class="wikitable"
!
!Reaction
!Initial distances / pm
!Momenta / g.mol-1.pm.fs-1
!Total Energy / kJ mol-1
!Transition State Position
!Forces at TS / kJ mol-1
!Activation Energy kJ mol-1
|-
|'''2.1)'''
|F + HAHB
|F - HA = 200
HA - HB = 74
|AB = -2.5
BC = -5.1
|<nowiki>-417.591</nowiki>
|F - HA = ~98 pm
HA - HB = ~104 pm
|along AB = -1.197
along BC = +1.140

Net Force = -0.057 '''AB'''
|0.006
|-
|'''2.2)'''
|HA + HBF
|HA - HB = 200
HB - F = 92
|AB = -23.0
BC = -10.0
|<nowiki>-207.717</nowiki>
|HA - HB = ~103 pm
HB - F = ~98 pm
|along AB = +1.197
along BC = -1.133

Net Force = +0.064 '''AB'''
|1.171
|}
Table 2. The total energy of each reacting system.

The F + H2 reaction is lower in energy, -417.591 kJ mol-1, than H + HF at -206.638 kJ mol-1. This suggests that reaction 2.1 is more energetically favourable and hence exothermic. Reaction 2.2 is higher in energy and unstable, hence it is endothermic, requiring energy from the surroundings to react. Since reaction 2.1 is more exothermic this implies that the new H-F bond formed is stronger than the H-H bond and more energetically favourable. As reaction 2.2 is more endothermic, it requires energy from its surroundings to form the H-H bond again meaning it is a weaker, less stable bond than H-F.

[[File:EA_reaction2.1.png]]

Fig. 10 Activation energy required to form F-H + H in reaction 2.1.

[[File:AE_reaction2.2.png]]

Fig. 11 Activation energy required to create H2 + F in reaction 2.2.

=== Reaction Dynamics ===

==== F + H2 Reaction ====
{| class="wikitable"
|[[File:p1(-1)p2(-3)r2.1.png|thumb|alt=fig12|Fig. 12. PES contour plot of the trajectory of reaction 2.1. P1 = -1, p2 = -3.]]
|[[File:p1(-1)p2(-5.9)r2.1_SP.png|thumb|alt=fig13|Fig. 13 . PES 3D map of the potential well and trajectory taken by the reactants. P1 = -1, p2 = -5.9.]]
|-
|[[File:p1(-1)p2(5.9)r2.1.png|thumb|alt=fig14|Fig. 14. PES contour map of the trajectory of reactants in reaction 2.1. P1 = -1, p2 = 5.9.]]
|[[File:p1(-1.6)p2(0.2)r2.1.png|thumb|alt=fig15|Fig. 15. PES contour map for reaction 2.1. P1 = -1.6, p2 = 0.2.]]
|}
As shown in the table 3., varying amounts of energy are given to reaction 2.1 by altering the initial momenta. The energy provided exceeds the activation energy yet not all of the reactions in Fig. 12 - 15 are reactive. In Fig. 12, the reactants trajectory travels through the reactants channel whilst oscillating up and down the sides of the potential wall. The reactants overcome the energy barrier but rebound back towards the reactants channel, meaning the reactants don't have sufficient energy distribution in both translational and vibrational modes. This is similar to the trajectory in Fig. 15. Both trajectories in Fig. 13 and 14 showcase successfully reactive reactions. The reactants travel through the transition state towards the products. The reactants appear to obtain a significant amount of vibrational energy suggesting the H2 molecule is in a vibrationally excited state.

The vibrational energy of the reactants in a reactive process in Fig. 14 can be compared to those in an un-reactive reaction in Fig. 15.
{| class="wikitable"
!
!Potential/Kinetic Energy

as a function of time
|-
|Fig. 14 Trajectory
|fig 14
|-
|Fig. 15 Trajectory
|fig 15
|}

PE_p1(-1).png

PE_p1(-1.6).png

== Bibliography ==
1 Atkins ___

File:PE p1(-1).png

2020-05-14T15:46:35Z

Mco218:

2020-05-14T12:38:32Z

Mco218: /* Molecular Reaction Dynamics 2020 */