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MRD:VFC2398

2019-05-17T12:40:05Z

Vc2217: /* Reaction Dynamics */

=Molecular Dynamics=

==H + H2 system==

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

'''A + B-C -> A-B + C'''

A reactive trajectory can be generated on a potential energy surface measuring the potential energy with respect to the AB and BC inter-atomic distances by applying a set of initial conditions for the positions of the atoms and their momenta. From the potential energy surface the trajectory can be determined by finding the derivate across the whole potential energy surface to find the minima. To find the energy of the transition state, which on the trajectory resembles a saddle point, the derivative of the trajectory must be found but this time to determine the maximum energy. Since the system being observed is symmetric at the maximum ie. transition state, AB and BC inter-atomic distances will be equal as a result can be seen as the point of intersection Figure 1. below of the Internuclear distance against Time graph.

[[File:Vc internuclear part1.PNG|400px]]
Figure 1. Internuclear Distance vs Time for H + H2 reaction. '''RTS ≈ 0.9107 A'''

W= ∫F. ds
E= ∫F. ds
de/ds = F

At the minimum of a potential energy curve, the force is zero so the molecule has no potential energy so it is no longer vibrating this results in the AB and BC to have no vibration so the periodic symmetric vibration wave becomes a straight line due to not having an amplitude as a result of the force on the bond being equal to zero. By inserting different values of '''r2 (AB)= r1 (BC)''' and '''P(AB)=P(BC) = 0''', the transition state bond length can also be determined via trial and error for H + H2 system.

===Trajectories from r1 = rts+δ, r2 = rts===

An MEP shows the mean energy path hence no vibration contributions of the molecules can be seen therefore the trajectory that is depicted on the PES is not wavy but straight, it differs from a dynamics calculation as it does not take the gradient of the potential energy of previous steps into account, only the gradient at the current step is accounted for.A dynamic calculation will display changes in momenta whereas in an MEP there are no changes in the momenta of the atoms/molecules.

'''Determining reactive trajectories'''

The following table shows how changing the momenta p1 (BC) and p2 (AB) within a set of initial conditions with the inter-atomic distances kept constant r1 = 2.0 and r2 = 0.74 can affect the reactivity of a reaction.

{| class="wikitable" border="1"
|+
! p1 (BC) !! p2 (AB) !! Etot !! Reactive? !! Trajectory !! Description of Dynamics
|-
| -1.25 || -2.5 || -99.018 || Yes || [[File:VC 1A TRAJECT.PNG|350px]] || A H atom approaches a H2 molecule, the straight line indicates that there is no vibration until the point of collision where a new H2 vibrating molecule is formed.
|-
| -1.5 || -2.0 || -100.456 || No || [[File:VC 1B TRAJECT.PNG|350px]] || H atom approached a H2 molecule however the energy of the reactants is insufficient to overcome that of the activation energy therefore the product is not formed and the reactants are reformed as it returns to the reactant channel.
|-
| -1.5 || -2.5 || -98.956 || Yes || [[File:VC 1C TRAJECT.PNG|350px]] || This reaction is successful hence the H atom approaches a H2 molecule with enough energy to overcome the activation energy and form the product H2 molecule.
|-
| -2.5 || -5.0 || -84.956 || No || [[File:VC 1D TRAJECT.PNG|350px]] || Reactants have enough energy to overcome the activation barrier to the products, in fact an excess of kinetic energy is observed resulting in the activation energy of the backward reaction being overcome hence the reactants are reformed.
|-
| -2.5 || -5.2 || -83.426 || Yes || [[File:VC 1E TRAJECT.PNG|350px]] || This reaction is successful hence the H atom approaches a H2 molecule with enough energy to overcome the activation energy and form the product H2 molecule.
|-
|}

From this investigation it can be concluded that a reaction is very sensitive to the energy that is supplied to it and that supplying a reaction with enough energy to surpass the activation energy will not necessarily lead to a successful reaction.

===Transition State Theory===
The '''Transition State Theory''' can be used to provide a more accurate measure of the rate constant of a reaction compared to other methods such as the Arrhenius equation. The theory involves treating the transition state as an activated complex in equilibrium with the reactant, therefore the energy of the transition state relative to the reactants determines the Ea of the reaction.1
The reaction can be considered as the following:
A + BC <—> [ABC*] —> AB + C
where ABC* represents the transition state complex

The transition state theory was used to determine that the rate of a reaction by looking at the motion through the saddle point of a potential energy surface.
The assumptions for this theory include:

-The reactants are in equilibrium with the transition state complex

-The energy of the particles follows a Boltzmann distribution during the reaction

-Once the transition state complex is formed, the structure is not converted back to the reactants.

As a result of these assumptions the rate of reaction would be overestimated as it is unable to to describe the scenario of reactions with enough kinetic energy to reform the reactants from the products.

===References===
(1) S. J. Moss and C. J. Coady, Potential-Energy Surfaces and Transition-State Theory, University of Aston in Birmingham, Computer Series

== F - H - H System ==

===PES Inspection===

Literature shows that the H-F bond energy (565kJmol-1)1 is greater than that of H-H(462kJmol-1)1 hence the enthalpy of dissociation of the H-F molecule is greater, this is concordant with the potential energy surface for the F - H - H system. Figure 1. shows that F + H2 -> HF + H is an '''exothermic''' reaction, the potential energy surface shows the products having a lower energy than the reactants. The backward reaction is HF + H -> H2 + F and is therefore '''endothermic''', this reaction has a greater activation energy due to the greater bond enthalpy of the HF molecule requiring more energy for its dissociation.

[[File:VC HF SURFACE.PNG|400px]]
Figure 1. Potential Energy Surface for F-H-H system

By using Hammonds Postulate it can be approximated that the transition state will resemble the either the products or the reactants depending on which is closer in energy. Therefore, in the endothermic reaction the transition state will closely resemble the reactants whereas in an exothermic it closely resembles the products. The idea of Hammonds postulate was used in order to identify the inter-atomic distances at the transition state. For the endothermic reaction the known H-H bond length (0.7445 A) was used as the initial condition and the H-F distance was manipulated to determine the location of the transition state using a graph of the Internuclear distance vs Time to find the optimized H-F distance (1.8311 A) where the force of bond equals zero.

MEP calculations were carried out and a plot of the Energy vs Time was used in order to determine the activation energy of the forward and backward reactions.

[[File:Vc endothermicreaction.png|400px]]
Figure 2. Energy vs Time plot of endothermic reaction showing Ea

HF + H -> H2 + F Activation Energy= 29 kcal/mol

[[File:Vc h2dissociationen.png|400px]]
Figure 3. Energy vs Time plot of exothermic reaction showing Ea

F + H2 -> HF + H Activation Energy= 0.2 kcal/mol

===Reaction Dynamics===

'''Reactive trajectory conditions:'''

R1(H2)= 0.74 A

R2(HF) = 2.30 A

P1 = -1.7

P2 = -2.4

For the reactive trajectory shown in Figures 4 and 5 below of the F + H2 reaction, it can be seen from the Momenta vs Time graph that there is an interconversion between kinetic and potential energy as a fall in potential energy energy is opposed by a rise in kinetic energy, this is in concordance with the law of the conservation of energy. Therefore, for this exothermic reaction the potential energy is converted into kinetic energy giving rise to vibrations of the HF bond that this formed. Infrared spectroscopy can be used to confirm the conversion of energy by calculating the frequency of absorption of the bond.

[[File:VC PART2 REACTIVECONTOUR 2A.PNG|400px]]
Figure 4. Contour Plot of F + H2 reactive trajectory

[[File:VC PART2 ENERGYVSTIME.PNG|400px]]
Figure 5. Energy vs Time of F + H2 reactive trajectory

An investigation into the reaction trajectories was conducted using the initial set of conditions listed below, '''P2 = -0.5''' was kept constant whereas '''P1''' was varied within the range '''X= -3 to 3'''.

R1(H2)= 0.74 A

R2(HF) = 2.30 A

P1 = '''X'''

P2 = -0.5

{| class="wikitable" border="1"
|+
! R1(H2) !! R2(HF) !! P2 !! P1 !! Contour plot of trajectory
|-
| 0.74 || 2.3 || -0.5 || -2.7 || [[File:VC PART2 -2.7MO (1).PNG|350px]]
|-
| 0.74|| 2.3 || -0.5 || -2.1 || [[File:VC PART2B -2.1.PNG|350px]]
|-
| 0.74 || 2.3 || -0.5 || 0.6 || [[File:Vc 0.6mom.PNG|350px]]
|-
| 0.74 || 2.3 || -0.5 || 1.6 || [[File:Vc 1.6mom.PNG|350px]]
|-
| 0.74|| 2.3 || -0.5 || 2.8 || [[File:Vc 2.8mom.PNG|350px]] |
|}

The dynamic calculations show that setting '''P2 = -0.5''' resulted in the reaction being successful at the extremes of the '''P1''' X range, where when the P1 was set close to zero the product was not formed and the momentum was insufficient.

===Polanyi's Rules===

Polanyi's rules state that vibrational energy is more efficient in promoting an endothermic reaction(transition state resembles products) whereas translational energy is more efficient at promoting an exothermic reaction (transition state resembles the reactants).2 For the F-H-H system these rules would suggest that F + H2 -> HF + H being an exothermic reaction has an early transition state and therefore in order for the reaction to be successful translational energy is favoured. This suggests that the vibrational energy of H2 should be low and experience a lower momentum in order for the trajectory to be reactive.

===References===
(1). Huheey, pps. A-21 to A-34; T.L. Cottrell, "The Strengths of Chemical Bonds," 2nd ed., Butterworths, London, 1958; B. deB. Darwent, "National Standard Reference Data Series," National Bureau of Standards, No. 31, Washington, DC, 1970; S.W. Benson, J. Chem. Educ., 42, 502 (1965).

(2.) Polanyi, J. C. Concepts in Reaction Dynamics Acc. Chem. Res. 1972, 5, 161– 168

MRD:VFC2398

2019-05-17T12:34:59Z

Vc2217: /* Polanyi's Rules */

=Molecular Dynamics=

==H + H2 system==

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

'''A + B-C -> A-B + C'''

A reactive trajectory can be generated on a potential energy surface measuring the potential energy with respect to the AB and BC inter-atomic distances by applying a set of initial conditions for the positions of the atoms and their momenta. From the potential energy surface the trajectory can be determined by finding the derivate across the whole potential energy surface to find the minima. To find the energy of the transition state, which on the trajectory resembles a saddle point, the derivative of the trajectory must be found but this time to determine the maximum energy. Since the system being observed is symmetric at the maximum ie. transition state, AB and BC inter-atomic distances will be equal as a result can be seen as the point of intersection Figure 1. below of the Internuclear distance against Time graph.

[[File:Vc internuclear part1.PNG|400px]]
Figure 1. Internuclear Distance vs Time for H + H2 reaction. '''RTS ≈ 0.9107 A'''

W= ∫F. ds
E= ∫F. ds
de/ds = F

At the minimum of a potential energy curve, the force is zero so the molecule has no potential energy so it is no longer vibrating this results in the AB and BC to have no vibration so the periodic symmetric vibration wave becomes a straight line due to not having an amplitude as a result of the force on the bond being equal to zero. By inserting different values of '''r2 (AB)= r1 (BC)''' and '''P(AB)=P(BC) = 0''', the transition state bond length can also be determined via trial and error for H + H2 system.

===Trajectories from r1 = rts+δ, r2 = rts===

An MEP shows the mean energy path hence no vibration contributions of the molecules can be seen therefore the trajectory that is depicted on the PES is not wavy but straight, it differs from a dynamics calculation as it does not take the gradient of the potential energy of previous steps into account, only the gradient at the current step is accounted for.A dynamic calculation will display changes in momenta whereas in an MEP there are no changes in the momenta of the atoms/molecules.

'''Determining reactive trajectories'''

The following table shows how changing the momenta p1 (BC) and p2 (AB) within a set of initial conditions with the inter-atomic distances kept constant r1 = 2.0 and r2 = 0.74 can affect the reactivity of a reaction.

{| class="wikitable" border="1"
|+
! p1 (BC) !! p2 (AB) !! Etot !! Reactive? !! Trajectory !! Description of Dynamics
|-
| -1.25 || -2.5 || -99.018 || Yes || [[File:VC 1A TRAJECT.PNG|350px]] || A H atom approaches a H2 molecule, the straight line indicates that there is no vibration until the point of collision where a new H2 vibrating molecule is formed.
|-
| -1.5 || -2.0 || -100.456 || No || [[File:VC 1B TRAJECT.PNG|350px]] || H atom approached a H2 molecule however the energy of the reactants is insufficient to overcome that of the activation energy therefore the product is not formed and the reactants are reformed as it returns to the reactant channel.
|-
| -1.5 || -2.5 || -98.956 || Yes || [[File:VC 1C TRAJECT.PNG|350px]] || This reaction is successful hence the H atom approaches a H2 molecule with enough energy to overcome the activation energy and form the product H2 molecule.
|-
| -2.5 || -5.0 || -84.956 || No || [[File:VC 1D TRAJECT.PNG|350px]] || Reactants have enough energy to overcome the activation barrier to the products, in fact an excess of kinetic energy is observed resulting in the activation energy of the backward reaction being overcome hence the reactants are reformed.
|-
| -2.5 || -5.2 || -83.426 || Yes || [[File:VC 1E TRAJECT.PNG|350px]] || This reaction is successful hence the H atom approaches a H2 molecule with enough energy to overcome the activation energy and form the product H2 molecule.
|-
|}

From this investigation it can be concluded that a reaction is very sensitive to the energy that is supplied to it and that supplying a reaction with enough energy to surpass the activation energy will not necessarily lead to a successful reaction.

===Transition State Theory===
The '''Transition State Theory''' can be used to provide a more accurate measure of the rate constant of a reaction compared to other methods such as the Arrhenius equation. The theory involves treating the transition state as an activated complex in equilibrium with the reactant, therefore the energy of the transition state relative to the reactants determines the Ea of the reaction.1
The reaction can be considered as the following:
A + BC <—> [ABC*] —> AB + C
where ABC* represents the transition state complex

The transition state theory was used to determine that the rate of a reaction by looking at the motion through the saddle point of a potential energy surface.
The assumptions for this theory include:

-The reactants are in equilibrium with the transition state complex

-The energy of the particles follows a Boltzmann distribution during the reaction

-Once the transition state complex is formed, the structure is not converted back to the reactants.

As a result of these assumptions the rate of reaction would be overestimated as it is unable to to describe the scenario of reactions with enough kinetic energy to reform the reactants from the products.

===References===
(1) S. J. Moss and C. J. Coady, Potential-Energy Surfaces and Transition-State Theory, University of Aston in Birmingham, Computer Series

== F - H - H System ==

===PES Inspection===

Literature shows that the H-F bond energy (565kJmol-1)1 is greater than that of H-H(462kJmol-1)1 hence the enthalpy of dissociation of the H-F molecule is greater, this is concordant with the potential energy surface for the F - H - H system. Figure 1. shows that F + H2 -> HF + H is an '''exothermic''' reaction, the potential energy surface shows the products having a lower energy than the reactants. The backward reaction is HF + H -> H2 + F and is therefore '''endothermic''', this reaction has a greater activation energy due to the greater bond enthalpy of the HF molecule requiring more energy for its dissociation.

[[File:VC HF SURFACE.PNG|400px]]
Figure 1. Potential Energy Surface for F-H-H system

By using Hammonds Postulate it can be approximated that the transition state will resemble the either the products or the reactants depending on which is closer in energy. Therefore, in the endothermic reaction the transition state will closely resemble the reactants whereas in an exothermic it closely resembles the products. The idea of Hammonds postulate was used in order to identify the inter-atomic distances at the transition state. For the endothermic reaction the known H-H bond length (0.7445 A) was used as the initial condition and the H-F distance was manipulated to determine the location of the transition state using a graph of the Internuclear distance vs Time to find the optimized H-F distance (1.8311 A) where the force of bond equals zero.

MEP calculations were carried out and a plot of the Energy vs Time was used in order to determine the activation energy of the forward and backward reactions.

[[File:Vc endothermicreaction.png|400px]]
Figure 2. Energy vs Time plot of endothermic reaction showing Ea

HF + H -> H2 + F Activation Energy= 29 kcal/mol

[[File:Vc h2dissociationen.png|400px]]
Figure 3. Energy vs Time plot of exothermic reaction showing Ea

F + H2 -> HF + H Activation Energy= 0.2 kcal/mol

===Reaction Dynamics===

'''Reactive trajectory conditions:'''

R1(H2)= 0.74 A

R2(HF) = 2.30 A

P1 = -1.7

P2 = -2.4

For the reactive trajectory shown in Figures 4 and 5 below of the F + H2 reaction, it can be seen from the Momenta vs Time graph that there is an interconversion between kinetic and potential energy as a fall in potential energy energy is opposed by a rise in kinetic energy, this is in concordance with the law of the conservation of energy. Therefore, for this exothermic reaction the potential energy is converted into kinetic energy giving rise to vibrations of the HF bond that this formed. Infrared spectroscopy can be used to confirm the conversion of energy by calculating the frequency of absorption of the bond.

[[File:VC PART2 REACTIVECONTOUR 2A.PNG|400px]]
Figure 4. Contour Plot of F + H2 reactive trajectory

[[File:VC PART2 ENERGYVSTIME.PNG|400px]]
Figure 5. Energy vs Time of F + H2 reactive trajectory

An investigation into the reaction trajectories was conducted using the initial set of conditions listed below, '''P2 = -0.5''' was kept constant whereas '''P1''' was varied within the range '''X= -3 to 3'''.

R1(H2)= 0.74 A

R2(HF) = 2.30 A

P1 = '''X'''

P2 = -0.5

{| class="wikitable" border="1"
|+
! R1(H2) !! R2(HF) !! P2 !! P1 !! Contour plot of trajectory
|-
| 0.74 || 2.3 || -0.5 || -2.7 || [[File:VC PART2 -2.7MO (1).PNG|350px]]
|-
| 0.74|| 2.3 || -0.5 || -2.1 || [[File:VC PART2B -2.1.PNG|350px]]
|-
| 0.74 || 2.3 || -0.5 || 0.6 || [[File:Vc 0.6mom.PNG|350px]]
|-
| 0.74 || 2.3 || -0.5 || 1.6 || [[File:Vc 1.6mom.PNG|350px]]
|-
| 0.74|| 2.3 || -0.5 || 2.8 || [[File:Vc 2.8mom.PNG|350px]] |
|}

===Polanyi's Rules===

Polanyi's rules state that vibrational energy is more efficient in promoting an endothermic reaction(transition state resembles products) whereas translational energy is more efficient at promoting an exothermic reaction (transition state resembles the reactants).2 For the F-H-H system these rules would suggest that F + H2 -> HF + H being an exothermic reaction has an early transition state and therefore in order for the reaction to be successful translational energy is favoured. This suggests that the vibrational energy of H2 should be low and experience a lower momentum in order for the trajectory to be reactive.

===References===
(1). Huheey, pps. A-21 to A-34; T.L. Cottrell, "The Strengths of Chemical Bonds," 2nd ed., Butterworths, London, 1958; B. deB. Darwent, "National Standard Reference Data Series," National Bureau of Standards, No. 31, Washington, DC, 1970; S.W. Benson, J. Chem. Educ., 42, 502 (1965).

(2.) Polanyi, J. C. Concepts in Reaction Dynamics Acc. Chem. Res. 1972, 5, 161– 168

MRD:VFC2398

2019-05-17T12:31:30Z

Vc2217: /* Reaction Dynamics */

=Molecular Dynamics=

==H + H2 system==

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

'''A + B-C -> A-B + C'''

A reactive trajectory can be generated on a potential energy surface measuring the potential energy with respect to the AB and BC inter-atomic distances by applying a set of initial conditions for the positions of the atoms and their momenta. From the potential energy surface the trajectory can be determined by finding the derivate across the whole potential energy surface to find the minima. To find the energy of the transition state, which on the trajectory resembles a saddle point, the derivative of the trajectory must be found but this time to determine the maximum energy. Since the system being observed is symmetric at the maximum ie. transition state, AB and BC inter-atomic distances will be equal as a result can be seen as the point of intersection Figure 1. below of the Internuclear distance against Time graph.

[[File:Vc internuclear part1.PNG|400px]]
Figure 1. Internuclear Distance vs Time for H + H2 reaction. '''RTS ≈ 0.9107 A'''

W= ∫F. ds
E= ∫F. ds
de/ds = F

At the minimum of a potential energy curve, the force is zero so the molecule has no potential energy so it is no longer vibrating this results in the AB and BC to have no vibration so the periodic symmetric vibration wave becomes a straight line due to not having an amplitude as a result of the force on the bond being equal to zero. By inserting different values of '''r2 (AB)= r1 (BC)''' and '''P(AB)=P(BC) = 0''', the transition state bond length can also be determined via trial and error for H + H2 system.

===Trajectories from r1 = rts+δ, r2 = rts===

An MEP shows the mean energy path hence no vibration contributions of the molecules can be seen therefore the trajectory that is depicted on the PES is not wavy but straight, it differs from a dynamics calculation as it does not take the gradient of the potential energy of previous steps into account, only the gradient at the current step is accounted for.A dynamic calculation will display changes in momenta whereas in an MEP there are no changes in the momenta of the atoms/molecules.

'''Determining reactive trajectories'''

The following table shows how changing the momenta p1 (BC) and p2 (AB) within a set of initial conditions with the inter-atomic distances kept constant r1 = 2.0 and r2 = 0.74 can affect the reactivity of a reaction.

{| class="wikitable" border="1"
|+
! p1 (BC) !! p2 (AB) !! Etot !! Reactive? !! Trajectory !! Description of Dynamics
|-
| -1.25 || -2.5 || -99.018 || Yes || [[File:VC 1A TRAJECT.PNG|350px]] || A H atom approaches a H2 molecule, the straight line indicates that there is no vibration until the point of collision where a new H2 vibrating molecule is formed.
|-
| -1.5 || -2.0 || -100.456 || No || [[File:VC 1B TRAJECT.PNG|350px]] || H atom approached a H2 molecule however the energy of the reactants is insufficient to overcome that of the activation energy therefore the product is not formed and the reactants are reformed as it returns to the reactant channel.
|-
| -1.5 || -2.5 || -98.956 || Yes || [[File:VC 1C TRAJECT.PNG|350px]] || This reaction is successful hence the H atom approaches a H2 molecule with enough energy to overcome the activation energy and form the product H2 molecule.
|-
| -2.5 || -5.0 || -84.956 || No || [[File:VC 1D TRAJECT.PNG|350px]] || Reactants have enough energy to overcome the activation barrier to the products, in fact an excess of kinetic energy is observed resulting in the activation energy of the backward reaction being overcome hence the reactants are reformed.
|-
| -2.5 || -5.2 || -83.426 || Yes || [[File:VC 1E TRAJECT.PNG|350px]] || This reaction is successful hence the H atom approaches a H2 molecule with enough energy to overcome the activation energy and form the product H2 molecule.
|-
|}

From this investigation it can be concluded that a reaction is very sensitive to the energy that is supplied to it and that supplying a reaction with enough energy to surpass the activation energy will not necessarily lead to a successful reaction.

===Transition State Theory===
The '''Transition State Theory''' can be used to provide a more accurate measure of the rate constant of a reaction compared to other methods such as the Arrhenius equation. The theory involves treating the transition state as an activated complex in equilibrium with the reactant, therefore the energy of the transition state relative to the reactants determines the Ea of the reaction.1
The reaction can be considered as the following:
A + BC <—> [ABC*] —> AB + C
where ABC* represents the transition state complex

The transition state theory was used to determine that the rate of a reaction by looking at the motion through the saddle point of a potential energy surface.
The assumptions for this theory include:

-The reactants are in equilibrium with the transition state complex

-The energy of the particles follows a Boltzmann distribution during the reaction

-Once the transition state complex is formed, the structure is not converted back to the reactants.

As a result of these assumptions the rate of reaction would be overestimated as it is unable to to describe the scenario of reactions with enough kinetic energy to reform the reactants from the products.

===References===
(1) S. J. Moss and C. J. Coady, Potential-Energy Surfaces and Transition-State Theory, University of Aston in Birmingham, Computer Series

== F - H - H System ==

===PES Inspection===

Literature shows that the H-F bond energy (565kJmol-1)1 is greater than that of H-H(462kJmol-1)1 hence the enthalpy of dissociation of the H-F molecule is greater, this is concordant with the potential energy surface for the F - H - H system. Figure 1. shows that F + H2 -> HF + H is an '''exothermic''' reaction, the potential energy surface shows the products having a lower energy than the reactants. The backward reaction is HF + H -> H2 + F and is therefore '''endothermic''', this reaction has a greater activation energy due to the greater bond enthalpy of the HF molecule requiring more energy for its dissociation.

[[File:VC HF SURFACE.PNG|400px]]
Figure 1. Potential Energy Surface for F-H-H system

By using Hammonds Postulate it can be approximated that the transition state will resemble the either the products or the reactants depending on which is closer in energy. Therefore, in the endothermic reaction the transition state will closely resemble the reactants whereas in an exothermic it closely resembles the products. The idea of Hammonds postulate was used in order to identify the inter-atomic distances at the transition state. For the endothermic reaction the known H-H bond length (0.7445 A) was used as the initial condition and the H-F distance was manipulated to determine the location of the transition state using a graph of the Internuclear distance vs Time to find the optimized H-F distance (1.8311 A) where the force of bond equals zero.

MEP calculations were carried out and a plot of the Energy vs Time was used in order to determine the activation energy of the forward and backward reactions.

[[File:Vc endothermicreaction.png|400px]]
Figure 2. Energy vs Time plot of endothermic reaction showing Ea

HF + H -> H2 + F Activation Energy= 29 kcal/mol

[[File:Vc h2dissociationen.png|400px]]
Figure 3. Energy vs Time plot of exothermic reaction showing Ea

F + H2 -> HF + H Activation Energy= 0.2 kcal/mol

===Reaction Dynamics===

'''Reactive trajectory conditions:'''

R1(H2)= 0.74 A

R2(HF) = 2.30 A

P1 = -1.7

P2 = -2.4

For the reactive trajectory shown in Figures 4 and 5 below of the F + H2 reaction, it can be seen from the Momenta vs Time graph that there is an interconversion between kinetic and potential energy as a fall in potential energy energy is opposed by a rise in kinetic energy, this is in concordance with the law of the conservation of energy. Therefore, for this exothermic reaction the potential energy is converted into kinetic energy giving rise to vibrations of the HF bond that this formed. Infrared spectroscopy can be used to confirm the conversion of energy by calculating the frequency of absorption of the bond.

[[File:VC PART2 REACTIVECONTOUR 2A.PNG|400px]]
Figure 4. Contour Plot of F + H2 reactive trajectory

[[File:VC PART2 ENERGYVSTIME.PNG|400px]]
Figure 5. Energy vs Time of F + H2 reactive trajectory

An investigation into the reaction trajectories was conducted using the initial set of conditions listed below, '''P2 = -0.5''' was kept constant whereas '''P1''' was varied within the range '''X= -3 to 3'''.

R1(H2)= 0.74 A

R2(HF) = 2.30 A

P1 = '''X'''

P2 = -0.5

{| class="wikitable" border="1"
|+
! R1(H2) !! R2(HF) !! P2 !! P1 !! Contour plot of trajectory
|-
| 0.74 || 2.3 || -0.5 || -2.7 || [[File:VC PART2 -2.7MO (1).PNG|350px]]
|-
| 0.74|| 2.3 || -0.5 || -2.1 || [[File:VC PART2B -2.1.PNG|350px]]
|-
| 0.74 || 2.3 || -0.5 || 0.6 || [[File:Vc 0.6mom.PNG|350px]]
|-
| 0.74 || 2.3 || -0.5 || 1.6 || [[File:Vc 1.6mom.PNG|350px]]
|-
| 0.74|| 2.3 || -0.5 || 2.8 || [[File:Vc 2.8mom.PNG|350px]] |
|}

===Polanyi's Rules===

Polanyi's rules state that vibrational energy is more efficient in promoting an endothermic reaction(transition state resembles products) whereas translational energy is more efficient at promoting an exothermic reaction (transition state resembles the reactants).2 For the F-H-H system these rules would suggest that F + H2 -> HF + H being an exothermic reaction has an early transition state and therefore in order for the reaction to be successful translational energy is favoured. This suggests that the vibrational energy of H2 should be low and experience a lower momentum in order for the trajectory to be reactive.

===References===
(1). Huheey, pps. A-21 to A-34; T.L. Cottrell, "The Strengths of Chemical Bonds," 2nd ed., Butterworths, London, 1958; B. deB. Darwent, "National Standard Reference Data Series," National Bureau of Standards, No. 31, Washington, DC, 1970; S.W. Benson, J. Chem. Educ., 42, 502 (1965).

(2.) Polanyi, J. C. Concepts in Reaction Dynamics Acc. Chem. Res. 1972, 5, 161– 168

MRD:VFC2398

2019-05-17T12:30:19Z

Vc2217: /* PES Inspection */

=Molecular Dynamics=

==H + H2 system==

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

'''A + B-C -> A-B + C'''

A reactive trajectory can be generated on a potential energy surface measuring the potential energy with respect to the AB and BC inter-atomic distances by applying a set of initial conditions for the positions of the atoms and their momenta. From the potential energy surface the trajectory can be determined by finding the derivate across the whole potential energy surface to find the minima. To find the energy of the transition state, which on the trajectory resembles a saddle point, the derivative of the trajectory must be found but this time to determine the maximum energy. Since the system being observed is symmetric at the maximum ie. transition state, AB and BC inter-atomic distances will be equal as a result can be seen as the point of intersection Figure 1. below of the Internuclear distance against Time graph.

[[File:Vc internuclear part1.PNG|400px]]
Figure 1. Internuclear Distance vs Time for H + H2 reaction. '''RTS ≈ 0.9107 A'''

W= ∫F. ds
E= ∫F. ds
de/ds = F

At the minimum of a potential energy curve, the force is zero so the molecule has no potential energy so it is no longer vibrating this results in the AB and BC to have no vibration so the periodic symmetric vibration wave becomes a straight line due to not having an amplitude as a result of the force on the bond being equal to zero. By inserting different values of '''r2 (AB)= r1 (BC)''' and '''P(AB)=P(BC) = 0''', the transition state bond length can also be determined via trial and error for H + H2 system.

===Trajectories from r1 = rts+δ, r2 = rts===

An MEP shows the mean energy path hence no vibration contributions of the molecules can be seen therefore the trajectory that is depicted on the PES is not wavy but straight, it differs from a dynamics calculation as it does not take the gradient of the potential energy of previous steps into account, only the gradient at the current step is accounted for.A dynamic calculation will display changes in momenta whereas in an MEP there are no changes in the momenta of the atoms/molecules.

'''Determining reactive trajectories'''

The following table shows how changing the momenta p1 (BC) and p2 (AB) within a set of initial conditions with the inter-atomic distances kept constant r1 = 2.0 and r2 = 0.74 can affect the reactivity of a reaction.

{| class="wikitable" border="1"
|+
! p1 (BC) !! p2 (AB) !! Etot !! Reactive? !! Trajectory !! Description of Dynamics
|-
| -1.25 || -2.5 || -99.018 || Yes || [[File:VC 1A TRAJECT.PNG|350px]] || A H atom approaches a H2 molecule, the straight line indicates that there is no vibration until the point of collision where a new H2 vibrating molecule is formed.
|-
| -1.5 || -2.0 || -100.456 || No || [[File:VC 1B TRAJECT.PNG|350px]] || H atom approached a H2 molecule however the energy of the reactants is insufficient to overcome that of the activation energy therefore the product is not formed and the reactants are reformed as it returns to the reactant channel.
|-
| -1.5 || -2.5 || -98.956 || Yes || [[File:VC 1C TRAJECT.PNG|350px]] || This reaction is successful hence the H atom approaches a H2 molecule with enough energy to overcome the activation energy and form the product H2 molecule.
|-
| -2.5 || -5.0 || -84.956 || No || [[File:VC 1D TRAJECT.PNG|350px]] || Reactants have enough energy to overcome the activation barrier to the products, in fact an excess of kinetic energy is observed resulting in the activation energy of the backward reaction being overcome hence the reactants are reformed.
|-
| -2.5 || -5.2 || -83.426 || Yes || [[File:VC 1E TRAJECT.PNG|350px]] || This reaction is successful hence the H atom approaches a H2 molecule with enough energy to overcome the activation energy and form the product H2 molecule.
|-
|}

From this investigation it can be concluded that a reaction is very sensitive to the energy that is supplied to it and that supplying a reaction with enough energy to surpass the activation energy will not necessarily lead to a successful reaction.

===Transition State Theory===
The '''Transition State Theory''' can be used to provide a more accurate measure of the rate constant of a reaction compared to other methods such as the Arrhenius equation. The theory involves treating the transition state as an activated complex in equilibrium with the reactant, therefore the energy of the transition state relative to the reactants determines the Ea of the reaction.1
The reaction can be considered as the following:
A + BC <—> [ABC*] —> AB + C
where ABC* represents the transition state complex

The transition state theory was used to determine that the rate of a reaction by looking at the motion through the saddle point of a potential energy surface.
The assumptions for this theory include:

-The reactants are in equilibrium with the transition state complex

-The energy of the particles follows a Boltzmann distribution during the reaction

-Once the transition state complex is formed, the structure is not converted back to the reactants.

As a result of these assumptions the rate of reaction would be overestimated as it is unable to to describe the scenario of reactions with enough kinetic energy to reform the reactants from the products.

===References===
(1) S. J. Moss and C. J. Coady, Potential-Energy Surfaces and Transition-State Theory, University of Aston in Birmingham, Computer Series

== F - H - H System ==

===PES Inspection===

Literature shows that the H-F bond energy (565kJmol-1)1 is greater than that of H-H(462kJmol-1)1 hence the enthalpy of dissociation of the H-F molecule is greater, this is concordant with the potential energy surface for the F - H - H system. Figure 1. shows that F + H2 -> HF + H is an '''exothermic''' reaction, the potential energy surface shows the products having a lower energy than the reactants. The backward reaction is HF + H -> H2 + F and is therefore '''endothermic''', this reaction has a greater activation energy due to the greater bond enthalpy of the HF molecule requiring more energy for its dissociation.

[[File:VC HF SURFACE.PNG|400px]]
Figure 1. Potential Energy Surface for F-H-H system

By using Hammonds Postulate it can be approximated that the transition state will resemble the either the products or the reactants depending on which is closer in energy. Therefore, in the endothermic reaction the transition state will closely resemble the reactants whereas in an exothermic it closely resembles the products. The idea of Hammonds postulate was used in order to identify the inter-atomic distances at the transition state. For the endothermic reaction the known H-H bond length (0.7445 A) was used as the initial condition and the H-F distance was manipulated to determine the location of the transition state using a graph of the Internuclear distance vs Time to find the optimized H-F distance (1.8311 A) where the force of bond equals zero.

MEP calculations were carried out and a plot of the Energy vs Time was used in order to determine the activation energy of the forward and backward reactions.

[[File:Vc endothermicreaction.png|400px]]
Figure 2. Energy vs Time plot of endothermic reaction showing Ea

HF + H -> H2 + F Activation Energy= 29 kcal/mol

[[File:Vc h2dissociationen.png|400px]]
Figure 3. Energy vs Time plot of exothermic reaction showing Ea

F + H2 -> HF + H Activation Energy= 0.2 kcal/mol

===Reaction Dynamics===

'''Reactive trajectory conditions:'''

R1(H2)= 0.74 A

R2(HF) = 2.30 A

P1 = -1.7

P2 = -2.4

[[File:VC PART2 REACTIVECONTOUR 2A.PNG|400px]]
Figure 4. Contour Plot of F + H2 reactive trajectory

[[File:VC PART2 ENERGYVSTIME.PNG|400px]]
Figure 5. Energy vs Time of F + H2 reactive trajectory

For the reactive trajectory shown in Figures above of the F + H2 reaction, it can be seen from the Momenta vs Time graph that there is an interconversion between kinetic and potential energy as a fall in potential energy energy is opposed by a rise in kinetic energy, this is in concordance with the law of the conservation of energy. Therefore, for this exothermic reaction the potential energy is converted into kinetic energy giving rise to vibrations of the HF bond that this formed. Infrared spectroscopy can be used to confirm the conversion of energy by calculating the frequency of absorption of the bond.

An investigation into the reaction trajectories was conducted using the initial set of conditions listed below, '''P2 = -0.5''' was kept constant whereas '''P1''' was varied within the range '''X= -3 to 3'''.

R1(H2)= 0.74 A

R2(HF) = 2.30 A

P1 = '''X'''

P2 = -0.5

{| class="wikitable" border="1"
|+
! R1(H2) !! R2(HF) !! P2 !! P1 !! Contour plot of trajectory
|-
| 0.74 || 2.3 || -0.5 || -2.7 || [[File:VC PART2 -2.7MO (1).PNG|350px]]
|-
| 0.74|| 2.3 || -0.5 || -2.1 || [[File:VC PART2B -2.1.PNG|350px]]
|-
| 0.74 || 2.3 || -0.5 || 0.6 || [[File:Vc 0.6mom.PNG|350px]]
|-
| 0.74 || 2.3 || -0.5 || 1.6 || [[File:Vc 1.6mom.PNG|350px]]
|-
| 0.74|| 2.3 || -0.5 || 2.8 || [[File:Vc 2.8mom.PNG|350px]] |
|}

===Polanyi's Rules===

Polanyi's rules state that vibrational energy is more efficient in promoting an endothermic reaction(transition state resembles products) whereas translational energy is more efficient at promoting an exothermic reaction (transition state resembles the reactants).2 For the F-H-H system these rules would suggest that F + H2 -> HF + H being an exothermic reaction has an early transition state and therefore in order for the reaction to be successful translational energy is favoured. This suggests that the vibrational energy of H2 should be low and experience a lower momentum in order for the trajectory to be reactive.

===References===
(1). Huheey, pps. A-21 to A-34; T.L. Cottrell, "The Strengths of Chemical Bonds," 2nd ed., Butterworths, London, 1958; B. deB. Darwent, "National Standard Reference Data Series," National Bureau of Standards, No. 31, Washington, DC, 1970; S.W. Benson, J. Chem. Educ., 42, 502 (1965).

(2.) Polanyi, J. C. Concepts in Reaction Dynamics Acc. Chem. Res. 1972, 5, 161– 168

MRD:VFC2398

2019-05-17T12:29:16Z

Vc2217: /* Dynamics from the transition state region */

=Molecular Dynamics=

==H + H2 system==

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

'''A + B-C -> A-B + C'''

A reactive trajectory can be generated on a potential energy surface measuring the potential energy with respect to the AB and BC inter-atomic distances by applying a set of initial conditions for the positions of the atoms and their momenta. From the potential energy surface the trajectory can be determined by finding the derivate across the whole potential energy surface to find the minima. To find the energy of the transition state, which on the trajectory resembles a saddle point, the derivative of the trajectory must be found but this time to determine the maximum energy. Since the system being observed is symmetric at the maximum ie. transition state, AB and BC inter-atomic distances will be equal as a result can be seen as the point of intersection Figure 1. below of the Internuclear distance against Time graph.

[[File:Vc internuclear part1.PNG|400px]]
Figure 1. Internuclear Distance vs Time for H + H2 reaction. '''RTS ≈ 0.9107 A'''

W= ∫F. ds
E= ∫F. ds
de/ds = F

At the minimum of a potential energy curve, the force is zero so the molecule has no potential energy so it is no longer vibrating this results in the AB and BC to have no vibration so the periodic symmetric vibration wave becomes a straight line due to not having an amplitude as a result of the force on the bond being equal to zero. By inserting different values of '''r2 (AB)= r1 (BC)''' and '''P(AB)=P(BC) = 0''', the transition state bond length can also be determined via trial and error for H + H2 system.

===Trajectories from r1 = rts+δ, r2 = rts===

An MEP shows the mean energy path hence no vibration contributions of the molecules can be seen therefore the trajectory that is depicted on the PES is not wavy but straight, it differs from a dynamics calculation as it does not take the gradient of the potential energy of previous steps into account, only the gradient at the current step is accounted for.A dynamic calculation will display changes in momenta whereas in an MEP there are no changes in the momenta of the atoms/molecules.

'''Determining reactive trajectories'''

The following table shows how changing the momenta p1 (BC) and p2 (AB) within a set of initial conditions with the inter-atomic distances kept constant r1 = 2.0 and r2 = 0.74 can affect the reactivity of a reaction.

{| class="wikitable" border="1"
|+
! p1 (BC) !! p2 (AB) !! Etot !! Reactive? !! Trajectory !! Description of Dynamics
|-
| -1.25 || -2.5 || -99.018 || Yes || [[File:VC 1A TRAJECT.PNG|350px]] || A H atom approaches a H2 molecule, the straight line indicates that there is no vibration until the point of collision where a new H2 vibrating molecule is formed.
|-
| -1.5 || -2.0 || -100.456 || No || [[File:VC 1B TRAJECT.PNG|350px]] || H atom approached a H2 molecule however the energy of the reactants is insufficient to overcome that of the activation energy therefore the product is not formed and the reactants are reformed as it returns to the reactant channel.
|-
| -1.5 || -2.5 || -98.956 || Yes || [[File:VC 1C TRAJECT.PNG|350px]] || This reaction is successful hence the H atom approaches a H2 molecule with enough energy to overcome the activation energy and form the product H2 molecule.
|-
| -2.5 || -5.0 || -84.956 || No || [[File:VC 1D TRAJECT.PNG|350px]] || Reactants have enough energy to overcome the activation barrier to the products, in fact an excess of kinetic energy is observed resulting in the activation energy of the backward reaction being overcome hence the reactants are reformed.
|-
| -2.5 || -5.2 || -83.426 || Yes || [[File:VC 1E TRAJECT.PNG|350px]] || This reaction is successful hence the H atom approaches a H2 molecule with enough energy to overcome the activation energy and form the product H2 molecule.
|-
|}

From this investigation it can be concluded that a reaction is very sensitive to the energy that is supplied to it and that supplying a reaction with enough energy to surpass the activation energy will not necessarily lead to a successful reaction.

===Transition State Theory===
The '''Transition State Theory''' can be used to provide a more accurate measure of the rate constant of a reaction compared to other methods such as the Arrhenius equation. The theory involves treating the transition state as an activated complex in equilibrium with the reactant, therefore the energy of the transition state relative to the reactants determines the Ea of the reaction.1
The reaction can be considered as the following:
A + BC <—> [ABC*] —> AB + C
where ABC* represents the transition state complex

The transition state theory was used to determine that the rate of a reaction by looking at the motion through the saddle point of a potential energy surface.
The assumptions for this theory include:

-The reactants are in equilibrium with the transition state complex

-The energy of the particles follows a Boltzmann distribution during the reaction

-Once the transition state complex is formed, the structure is not converted back to the reactants.

As a result of these assumptions the rate of reaction would be overestimated as it is unable to to describe the scenario of reactions with enough kinetic energy to reform the reactants from the products.

===References===
(1) S. J. Moss and C. J. Coady, Potential-Energy Surfaces and Transition-State Theory, University of Aston in Birmingham, Computer Series

== F - H - H System ==

===PES Inspection===

Literature shows that the H-F bond energy (565kJmol-1)1 is greater than that of H-H(462kJmol-1)1 hence the enthalpy of dissociation of the H-F molecule is greater, this is concordant with the potential energy surface for the F - H - H system. Figure 1. shows that F + H2 -> HF + H is an '''exothermic''' reaction, the potential energy surface shows the products having a lower energy than the reactants. The backward reaction is HF + H -> H2 + F and is therefore '''endothermic''', this reaction has a greater activation energy due to the greater bond enthalpy of the HF molecule requiring more energy for its dissociation.

[[File:VC HF SURFACE.PNG|400px]]
Figure 1. Potential Energy Surface for F-H-H system

By using Hammonds Postulate it can be approximated that the transition state will resemble the either the products or the reactants depending on which is closer in energy. Therefore, in the endothermic reaction the transition state will closely resemble the reactants whereas in an exothermic it closely resembles the products. The idea of Hammonds postulate was used in order to identify the inter-atomic distances at the transition state. For the endothermic reaction the known H-H bond length (0.7445 A) was used as the initial condition and the H-F distance was manipulated to determine the location of the transition state using a graph of the Internuclear distance vs Time to find the optimized H-F distance (1.8311 A) where the force of bond equals zero.

MEP calculations were carried out and a plot of the Energy vs Time was used in order to determine the activation energy of the forward and backward reactions.

[[File:Vc endothermicreaction.png|400px]]
Figure 2. Energy vs Time plot of endothermic reaction showing Ea

HF + H -> H2 + F Activation Energy= 29 kcal/mol

[[File:Vc h2dissociationen.png|400px]]
Figure 3. Energy vs Time plot of exothermic reaction showing Ea

F + H2 -> HF + H Activation Energy= 0.2 kcal/mol

===Reaction Dynamics===

'''Reactive trajectory conditions:'''

R1(H2)= 0.74 A

R2(HF) = 2.30 A

P1 = -1.7

P2 = -2.4

[[File:VC PART2 REACTIVECONTOUR 2A.PNG|400px]]
Figure 4. Contour Plot of F + H2 reactive trajectory

[[File:VC PART2 ENERGYVSTIME.PNG|400px]]
Figure 5. Energy vs Time of F + H2 reactive trajectory

For the reactive trajectory shown in Figures above of the F + H2 reaction, it can be seen from the Momenta vs Time graph that there is an interconversion between kinetic and potential energy as a fall in potential energy energy is opposed by a rise in kinetic energy, this is in concordance with the law of the conservation of energy. Therefore, for this exothermic reaction the potential energy is converted into kinetic energy giving rise to vibrations of the HF bond that this formed. Infrared spectroscopy can be used to confirm the conversion of energy by calculating the frequency of absorption of the bond.

An investigation into the reaction trajectories was conducted using the initial set of conditions listed below, '''P2 = -0.5''' was kept constant whereas '''P1''' was varied within the range '''X= -3 to 3'''.

R1(H2)= 0.74 A

R2(HF) = 2.30 A

P1 = '''X'''

P2 = -0.5

{| class="wikitable" border="1"
|+
! R1(H2) !! R2(HF) !! P2 !! P1 !! Contour plot of trajectory
|-
| 0.74 || 2.3 || -0.5 || -2.7 || [[File:VC PART2 -2.7MO (1).PNG|350px]]
|-
| 0.74|| 2.3 || -0.5 || -2.1 || [[File:VC PART2B -2.1.PNG|350px]]
|-
| 0.74 || 2.3 || -0.5 || 0.6 || [[File:Vc 0.6mom.PNG|350px]]
|-
| 0.74 || 2.3 || -0.5 || 1.6 || [[File:Vc 1.6mom.PNG|350px]]
|-
| 0.74|| 2.3 || -0.5 || 2.8 || [[File:Vc 2.8mom.PNG|350px]] |
|}

===Polanyi's Rules===

Polanyi's rules state that vibrational energy is more efficient in promoting an endothermic reaction(transition state resembles products) whereas translational energy is more efficient at promoting an exothermic reaction (transition state resembles the reactants).2 For the F-H-H system these rules would suggest that F + H2 -> HF + H being an exothermic reaction has an early transition state and therefore in order for the reaction to be successful translational energy is favoured. This suggests that the vibrational energy of H2 should be low and experience a lower momentum in order for the trajectory to be reactive.

===References===
(1). Huheey, pps. A-21 to A-34; T.L. Cottrell, "The Strengths of Chemical Bonds," 2nd ed., Butterworths, London, 1958; B. deB. Darwent, "National Standard Reference Data Series," National Bureau of Standards, No. 31, Washington, DC, 1970; S.W. Benson, J. Chem. Educ., 42, 502 (1965).

(2.) Polanyi, J. C. Concepts in Reaction Dynamics Acc. Chem. Res. 1972, 5, 161– 168

MRD:VFC2398

2019-05-17T12:27:23Z

Vc2217:

=Molecular Dynamics=

==H + H2 system==

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

'''A + B-C -> A-B + C'''

A reactive trajectory can be generated on a potential energy surface measuring the potential energy with respect to the AB and BC inter-atomic distances by applying a set of initial conditions for the positions of the atoms and their momenta. From the potential energy surface the trajectory can be determined by finding the derivate across the whole potential energy surface to find the minima. To find the energy of the transition state, which on the trajectory resembles a saddle point, the derivative of the trajectory must be found but this time to determine the maximum energy. Since the system being observed is symmetric at the maximum ie. transition state, AB and BC inter-atomic distances will be equal as a result can be seen as the point of intersection Figure 1. below of the Internuclear distance against Time graph.

[[File:Vc internuclear part1.PNG]]
Figure 1. Internuclear Distance vs Time for H + H2 reaction. RTS ≈ 0.9107 A

W= ∫F. ds
E= ∫F. ds
de/ds = F

At the minimum of a potential energy curve, the force is zero so the molecule has no potential energy so it is no longer vibrating this results in the AB and BC to have no vibration so the periodic symmetric vibration wave becomes a straight line due to not having an amplitude as a result of the force on the bond being equal to zero. By inserting different values of '''r2 (AB)= r1 (BC)''' and '''P(AB)=P(BC) = 0''', the transition state bond length can also be determined via trial and error for H + H2 system.

[[File:VC LOCATINGTS.PNG]]
Figure 2. Internuclear Distance vs Time showing force = 0

===Trajectories from r1 = rts+δ, r2 = rts===

An MEP shows the mean energy path hence no vibration contributions of the molecules can be seen therefore the trajectory that is depicted on the PES is not wavy but straight, it differs from a dynamics calculation as it does not take the gradient of the potential energy of previous steps into account, only the gradient at the current step is accounted for.A dynamic calculation will display changes in momenta whereas in an MEP there are no changes in the momenta of the atoms/molecules.

'''Determining reactive trajectories'''

The following table shows how changing the momenta p1 (BC) and p2 (AB) within a set of initial conditions with the inter-atomic distances kept constant r1 = 2.0 and r2 = 0.74 can affect the reactivity of a reaction.

{| class="wikitable" border="1"
|+
! p1 (BC) !! p2 (AB) !! Etot !! Reactive? !! Trajectory !! Description of Dynamics
|-
| -1.25 || -2.5 || -99.018 || Yes || [[File:VC 1A TRAJECT.PNG|350px]] || A H atom approaches a H2 molecule, the straight line indicates that there is no vibration until the point of collision where a new H2 vibrating molecule is formed.
|-
| -1.5 || -2.0 || -100.456 || No || [[File:VC 1B TRAJECT.PNG|350px]] || H atom approached a H2 molecule however the energy of the reactants is insufficient to overcome that of the activation energy therefore the product is not formed and the reactants are reformed as it returns to the reactant channel.
|-
| -1.5 || -2.5 || -98.956 || Yes || [[File:VC 1C TRAJECT.PNG|350px]] || This reaction is successful hence the H atom approaches a H2 molecule with enough energy to overcome the activation energy and form the product H2 molecule.
|-
| -2.5 || -5.0 || -84.956 || No || [[File:VC 1D TRAJECT.PNG|350px]] || Reactants have enough energy to overcome the activation barrier to the products, in fact an excess of kinetic energy is observed resulting in the activation energy of the backward reaction being overcome hence the reactants are reformed.
|-
| -2.5 || -5.2 || -83.426 || Yes || [[File:VC 1E TRAJECT.PNG|350px]] || This reaction is successful hence the H atom approaches a H2 molecule with enough energy to overcome the activation energy and form the product H2 molecule.
|-
|}

From this investigation it can be concluded that a reaction is very sensitive to the energy that is supplied to it and that supplying a reaction with enough energy to surpass the activation energy will not necessarily lead to a successful reaction.

===Transition State Theory===
The '''Transition State Theory''' can be used to provide a more accurate measure of the rate constant of a reaction compared to other methods such as the Arrhenius equation. The theory involves treating the transition state as an activated complex in equilibrium with the reactant, therefore the energy of the transition state relative to the reactants determines the Ea of the reaction.1
The reaction can be considered as the following:
A + BC <—> [ABC*] —> AB + C
where ABC* represents the transition state complex

The transition state theory was used to determine that the rate of a reaction by looking at the motion through the saddle point of a potential energy surface.
The assumptions for this theory include:

-The reactants are in equilibrium with the transition state complex

-The energy of the particles follows a Boltzmann distribution during the reaction

-Once the transition state complex is formed, the structure is not converted back to the reactants.

As a result of these assumptions the rate of reaction would be overestimated as it is unable to to describe the scenario of reactions with enough kinetic energy to reform the reactants from the products.

===References===
(1) S. J. Moss and C. J. Coady, Potential-Energy Surfaces and Transition-State Theory, University of Aston in Birmingham, Computer Series

== F - H - H System ==

===PES Inspection===

Literature shows that the H-F bond energy (565kJmol-1)1 is greater than that of H-H(462kJmol-1)1 hence the enthalpy of dissociation of the H-F molecule is greater, this is concordant with the potential energy surface for the F - H - H system. Figure 1. shows that F + H2 -> HF + H is an '''exothermic''' reaction, the potential energy surface shows the products having a lower energy than the reactants. The backward reaction is HF + H -> H2 + F and is therefore '''endothermic''', this reaction has a greater activation energy due to the greater bond enthalpy of the HF molecule requiring more energy for its dissociation.

[[File:VC HF SURFACE.PNG|400px]]
Figure 1. Potential Energy Surface for F-H-H system

By using Hammonds Postulate it can be approximated that the transition state will resemble the either the products or the reactants depending on which is closer in energy. Therefore, in the endothermic reaction the transition state will closely resemble the reactants whereas in an exothermic it closely resembles the products. The idea of Hammonds postulate was used in order to identify the inter-atomic distances at the transition state. For the endothermic reaction the known H-H bond length (0.7445 A) was used as the initial condition and the H-F distance was manipulated to determine the location of the transition state using a graph of the Internuclear distance vs Time to find the optimized H-F distance (1.8311 A) where the force of bond equals zero.

MEP calculations were carried out and a plot of the Energy vs Time was used in order to determine the activation energy of the forward and backward reactions.

[[File:Vc endothermicreaction.png|400px]]
Figure 2. Energy vs Time plot of endothermic reaction showing Ea

HF + H -> H2 + F Activation Energy= 29 kcal/mol

[[File:Vc h2dissociationen.png|400px]]
Figure 3. Energy vs Time plot of exothermic reaction showing Ea

F + H2 -> HF + H Activation Energy= 0.2 kcal/mol

===Reaction Dynamics===

'''Reactive trajectory conditions:'''

R1(H2)= 0.74 A

R2(HF) = 2.30 A

P1 = -1.7

P2 = -2.4

[[File:VC PART2 REACTIVECONTOUR 2A.PNG|400px]]
Figure 4. Contour Plot of F + H2 reactive trajectory

[[File:VC PART2 ENERGYVSTIME.PNG|400px]]
Figure 5. Energy vs Time of F + H2 reactive trajectory

For the reactive trajectory shown in Figures above of the F + H2 reaction, it can be seen from the Momenta vs Time graph that there is an interconversion between kinetic and potential energy as a fall in potential energy energy is opposed by a rise in kinetic energy, this is in concordance with the law of the conservation of energy. Therefore, for this exothermic reaction the potential energy is converted into kinetic energy giving rise to vibrations of the HF bond that this formed. Infrared spectroscopy can be used to confirm the conversion of energy by calculating the frequency of absorption of the bond.

An investigation into the reaction trajectories was conducted using the initial set of conditions listed below, '''P2 = -0.5''' was kept constant whereas '''P1''' was varied within the range '''X= -3 to 3'''.

R1(H2)= 0.74 A

R2(HF) = 2.30 A

P1 = '''X'''

P2 = -0.5

{| class="wikitable" border="1"
|+
! R1(H2) !! R2(HF) !! P2 !! P1 !! Contour plot of trajectory
|-
| 0.74 || 2.3 || -0.5 || -2.7 || [[File:VC PART2 -2.7MO (1).PNG|350px]]
|-
| 0.74|| 2.3 || -0.5 || -2.1 || [[File:VC PART2B -2.1.PNG|350px]]
|-
| 0.74 || 2.3 || -0.5 || 0.6 || [[File:Vc 0.6mom.PNG|350px]]
|-
| 0.74 || 2.3 || -0.5 || 1.6 || [[File:Vc 1.6mom.PNG|350px]]
|-
| 0.74|| 2.3 || -0.5 || 2.8 || [[File:Vc 2.8mom.PNG|350px]] |
|}

===Polanyi's Rules===

Polanyi's rules state that vibrational energy is more efficient in promoting an endothermic reaction(transition state resembles products) whereas translational energy is more efficient at promoting an exothermic reaction (transition state resembles the reactants).2 For the F-H-H system these rules would suggest that F + H2 -> HF + H being an exothermic reaction has an early transition state and therefore in order for the reaction to be successful translational energy is favoured. This suggests that the vibrational energy of H2 should be low and experience a lower momentum in order for the trajectory to be reactive.

===References===
(1). Huheey, pps. A-21 to A-34; T.L. Cottrell, "The Strengths of Chemical Bonds," 2nd ed., Butterworths, London, 1958; B. deB. Darwent, "National Standard Reference Data Series," National Bureau of Standards, No. 31, Washington, DC, 1970; S.W. Benson, J. Chem. Educ., 42, 502 (1965).

(2.) Polanyi, J. C. Concepts in Reaction Dynamics Acc. Chem. Res. 1972, 5, 161– 168

MRD:VFC2398

2019-05-17T10:56:33Z

Vc2217: /* F - H - H System */

=Molecular Dynamics=

==H + H2 system==

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

'''A + B-C -> A-B + C'''

A reactive trajectory can be generated on a potential energy surface measuring the potential energy with respect to the AB and BC inter-atomic distances by applying a set of initial conditions for the positions of the atoms and their momenta. From the potential energy surface the trajectory can be determined by finding the derivate across the whole potential energy surface to find the minima. To find the energy of the transition state, which on the trajectory resembles a saddle point, the derivative of the trajectory must be found but this time to determine the maximum energy. Since the system being observed is symmetric at the maximum ie. transition state, AB and BC inter-atomic distances will be equal as a result can be seen as the point of intersection Figure X. on the Internuclear distance against Time graph.

Graphs depicting "Internuclear Distances vs Time" can also be used to determine the energy of a transition state.

W= ∫F. ds
E= ∫F. ds
de/ds = F

At the minimum of a potential energy curve, the force is zero so the molecule has no potential energy so it is no longer vibrating this results in the AB and BC to have no vibration so the periodic symmetric vibration wave becomes a straight line due to not having an amplitude as a result of the force on the bond being equal to zero. By inserting different values of '''r2 (AB)= r1 (BC)''' and '''P(AB)=P(BC) = 0''', the transition state bond length can be determined via trial and error for H + H2 system.

[[File:VC LOCATINGTS.PNG]]

===Trajectories from r1 = rts+δ, r2 = rts===

An MEP shows the mean energy path hence no vibration contributions of the molecules can be seen therefore the trajectory that is depicted on the PES is not wavy but straight, it differs from a dynamics calculation as it does not take the gradient of the potential energy of previous steps into account, only the gradient at the current step is accounted for.A dynamic calculation will display changes in momenta whereas in an MEP there are no changes in the momenta of the atoms/molecules.

'''Determining reactive trajectories'''

The following table shows how changing the momenta p1 (BC) and p2 (AB) within a set of initial conditions with the inter-atomic distances kept constant r1 = 2.0 and r2 = 0.74 can affect the reactivity of a reaction.

{| class="wikitable" border="1"
|+
! p1 (BC) !! p2 (AB) !! Etot !! Reactive? !! Trajectory !! Description of Dynamics
|-
| -1.25 || -2.5 || -99.018 || Yes || [[File:VC 1A TRAJECT.PNG|350px]] || A H atom approaches a H2 molecule, the straight line indicates that there is no vibration until the point of collision where a new H2 vibrating molecule is formed.
|-
| -1.5 || -2.0 || -100.456 || No || [[File:VC 1B TRAJECT.PNG|350px]] || H atom approached a H2 molecule however the energy of the reactants is insufficient to overcome that of the activation energy therefore the product is not formed and the reactants are reformed as it returns to the reactant channel.
|-
| -1.5 || -2.5 || -98.956 || Yes || [[File:VC 1C TRAJECT.PNG|350px]] || This reaction is successful hence the H atom approaches a H2 molecule with enough energy to overcome the activation energy and form the product H2 molecule.
|-
| -2.5 || -5.0 || -84.956 || No || [[File:VC 1D TRAJECT.PNG|350px]] || Reactants have enough energy to overcome the activation barrier to the products, in fact an excess of kinetic energy is observed resulting in the activation energy of the backward reaction being overcome hence the reactants are reformed.
|-
| -2.5 || -5.2 || -83.426 || Yes || [[File:VC 1E TRAJECT.PNG|350px]] || This reaction is successful hence the H atom approaches a H2 molecule with enough energy to overcome the activation energy and form the product H2 molecule.
|-
|}

From this investigation it can be concluded that a reaction is very sensitive to the energy that is supplied to it and that supplying a reaction with enough energy to surpass the activation energy will not necessarily lead to a successful reaction.

===Transition State Theory===
The '''Transition State Theory''' can be used to provide a more accurate measure of the rate constant of a reaction compared to other methods such as the Arrhenius equation. The theory involves treating the transition state as an activated complex in equilibrium with the reactant, therefore the energy of the transition state relative to the reactants determines the Ea of the reaction.1
The reaction can be considered as the following:
A + BC <—> [ABC*] —> AB + C
where ABC* represents the transition state complex

The transition state theory was used to determine that the rate of a reaction by looking at the motion through the saddle point of a potential energy surface.
The assumptions for this theory include:

-The reactants are in equilibrium with the transition state complex

-The energy of the particles follows a Boltzmann distribution during the reaction

-Once the transition state complex is formed, the structure is not converted back to the reactants.

As a result of these assumptions the rate of reaction would be overestimated as it is unable to to describe the scenario of reactions with enough kinetic energy to reform the reactants from the products.

===References===
(1) S. J. Moss and C. J. Coady, Potential-Energy Surfaces and Transition-State Theory, University of Aston in Birmingham, Computer Series

== F - H - H System ==

===PES Inspection===

Literature shows that the H-F bond energy (565kJmol-1)1 is greater than that of H-H(462kJmol-1)1 hence the enthalpy of dissociation of the H-F molecule is greater, this is concordant with the potential energy surface for the F - H - H system. Figure X shows that F + H2 -> HF + H is an '''exothermic''' reaction, the potential energy surface shows the products having a lower energy than the reactants. The backward reaction is HF + H -> H2 + F and is therefore '''endothermic''', this reaction has a greater activation energy due to the greater bond enthalpy of the HF molecule requiring more energy for its dissociation.

[[File:VC HF SURFACE.PNG|400px]]

By using Hammonds Postulate it can be approximated that the transition state will resemble the either the products or the reactants depending on which is closer in energy. Therefore, in the endothermic reaction the transition state will closely resemble the reactants whereas in an exothermic it closely resembles the products. The idea of Hammonds postulate was used in order to identify the inter-atomic distances at the transition state. For the endothermic reaction the known H-H bond length (0.7445 A) was used as the initial condition and the H-F distance was manipulated to determine the location of the transition state using a graph of the Internuclear distance vs Time to find the optimized H-F distance (1.8311 A) where the force of bond equals zero.

MEP calculations were carried out and a plot of the Energy vs Time was used in order to determine the activation energy of the forward and backward reactions.

[[File:Vc endothermicreaction.png|400px]]

HF + H -> H2 + F Activation Energy= 29 kcal/mol

[[File:Vc h2dissociationen.png|400px]]

F + H2 -> HF + H Activation Energy= 0.2 kcal/mol

===Reaction Dynamics===

'''Reactive trajectory conditions:'''

R1(H2)= 0.74 A

R2(HF) = 2.30 A

P1 = -1.7

P2 = -2.4

[[File:VC PART2 REACTIVECONTOUR 2A.PNG|400px]] [[File:VC PART2 ENERGYVSTIME.PNG|400px]]

For the reactive trajectory shown in Figures above of the F + H2 reaction, it can be seen from the Momenta vs Time graph that there is an interconversion between kinetic and potential energy as a fall in potential energy energy is opposed by a rise in kinetic energy, this is in concordance with the law of the conservation of energy. Therefore, for this exothermic reaction the potential energy is converted into kinetic energy giving rise to vibrations of the HF bond that this formed. Infrared spectroscopy can be used to confirm the conversion of energy by calculating the frequency of absorption of the bond.

An investigation into the reaction trajectories was conducted using the initial set of conditions listed below, '''P2 = -0.5''' was kept constant whereas '''P1''' was varied within the range '''X= -3 to 3'''.

R1(H2)= 0.74 A

R2(HF) = 2.30 A

P1 = '''X'''

P2 = -0.5

{| class="wikitable" border="1"
|+
! R1(H2) !! R2(HF) !! P2 !! P1 !! Contour plot of trajectory
|-
| 0.74 || 2.3 || -0.5 || -2.7 || [[File:VC PART2 -2.7MO (1).PNG|350px]]
|-
| 0.74|| 2.3 || -0.5 || -2.1 || [[File:VC PART2B -2.1.PNG|350px]]
|-
| 0.74 || 2.3 || -0.5 || 0.6 || [[File:Vc 0.6mom.PNG|350px]]
|-
| 0.74 || 2.3 || -0.5 || 1.6 || [[File:Vc 1.6mom.PNG|350px]]
|-
| 0.74|| 2.3 || -0.5 || 2.8 || [[File:Vc 2.8mom.PNG|350px]] |
|}

===Polanyi's Rules===

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

===References===
(1). Huheey, pps. A-21 to A-34; T.L. Cottrell, "The Strengths of Chemical Bonds," 2nd ed., Butterworths, London, 1958; B. deB. Darwent, "National Standard Reference Data Series," National Bureau of Standards, No. 31, Washington, DC, 1970; S.W. Benson, J. Chem. Educ., 42, 502 (1965).

File:Vc internuclear part1.PNG

2019-05-17T10:48:26Z

Vc2217:

File:VC HF SURFACE.PNG

2019-05-17T10:47:30Z

Vc2217:

File:Vc h2dissociationen.png

2019-05-17T10:45:38Z

Vc2217:

MRD:VFC2398

2019-05-17T07:43:30Z

Vc2217: /* Transition State Theory */

=Molecular Dynamics=

==H + H2 system==

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

'''A + B-C -> A-B + C'''

A reactive trajectory can be generated on a potential energy surface measuring the potential energy with respect to the AB and BC inter-atomic distances by applying a set of initial conditions for the positions of the atoms and their momenta. From the potential energy surface the trajectory can be determined by finding the derivate across the whole potential energy surface to find the minima. To find the energy of the transition state, which on the trajectory resembles a saddle point, the derivative of the trajectory must be found but this time to determine the maximum energy. Since the system being observed is symmetric at the maximum ie. transition state, AB and BC inter-atomic distances will be equal as a result can be seen as the point of intersection Figure X. on the Internuclear distance against Time graph.

Graphs depicting "Internuclear Distances vs Time" can also be used to determine the energy of a transition state.

W= ∫F. ds
E= ∫F. ds
de/ds = F

At the minimum of a potential energy curve, the force is zero so the molecule has no potential energy so it is no longer vibrating this results in the AB and BC to have no vibration so the periodic symmetric vibration wave becomes a straight line due to not having an amplitude as a result of the force on the bond being equal to zero. By inserting different values of '''r2 (AB)= r1 (BC)''' and '''P(AB)=P(BC) = 0''', the transition state bond length can be determined via trial and error for H + H2 system.

[[File:VC LOCATINGTS.PNG]]

===Trajectories from r1 = rts+δ, r2 = rts===

An MEP shows the mean energy path hence no vibration contributions of the molecules can be seen therefore the trajectory that is depicted on the PES is not wavy but straight, it differs from a dynamics calculation as it does not take the gradient of the potential energy of previous steps into account, only the gradient at the current step is accounted for.A dynamic calculation will display changes in momenta whereas in an MEP there are no changes in the momenta of the atoms/molecules.

'''Determining reactive trajectories'''

The following table shows how changing the momenta p1 (BC) and p2 (AB) within a set of initial conditions with the inter-atomic distances kept constant r1 = 2.0 and r2 = 0.74 can affect the reactivity of a reaction.

{| class="wikitable" border="1"
|+
! p1 (BC) !! p2 (AB) !! Etot !! Reactive? !! Trajectory !! Description of Dynamics
|-
| -1.25 || -2.5 || -99.018 || Yes || [[File:VC 1A TRAJECT.PNG|350px]] || A H atom approaches a H2 molecule, the straight line indicates that there is no vibration until the point of collision where a new H2 vibrating molecule is formed.
|-
| -1.5 || -2.0 || -100.456 || No || [[File:VC 1B TRAJECT.PNG|350px]] || H atom approached a H2 molecule however the energy of the reactants is insufficient to overcome that of the activation energy therefore the product is not formed and the reactants are reformed as it returns to the reactant channel.
|-
| -1.5 || -2.5 || -98.956 || Yes || [[File:VC 1C TRAJECT.PNG|350px]] || This reaction is successful hence the H atom approaches a H2 molecule with enough energy to overcome the activation energy and form the product H2 molecule.
|-
| -2.5 || -5.0 || -84.956 || No || [[File:VC 1D TRAJECT.PNG|350px]] || Reactants have enough energy to overcome the activation barrier to the products, in fact an excess of kinetic energy is observed resulting in the activation energy of the backward reaction being overcome hence the reactants are reformed.
|-
| -2.5 || -5.2 || -83.426 || Yes || [[File:VC 1E TRAJECT.PNG|350px]] || This reaction is successful hence the H atom approaches a H2 molecule with enough energy to overcome the activation energy and form the product H2 molecule.
|-
|}

From this investigation it can be concluded that a reaction is very sensitive to the energy that is supplied to it and that supplying a reaction with enough energy to surpass the activation energy will not necessarily lead to a successful reaction.

===Transition State Theory===
The '''Transition State Theory''' can be used to provide a more accurate measure of the rate constant of a reaction compared to other methods such as the Arrhenius equation. The theory involves treating the transition state as an activated complex in equilibrium with the reactant, therefore the energy of the transition state relative to the reactants determines the Ea of the reaction.1
The reaction can be considered as the following:
A + BC <—> [ABC*] —> AB + C
where ABC* represents the transition state complex

The transition state theory was used to determine that the rate of a reaction by looking at the motion through the saddle point of a potential energy surface.
The assumptions for this theory include:

-The reactants are in equilibrium with the transition state complex

-The energy of the particles follows a Boltzmann distribution during the reaction

-Once the transition state complex is formed, the structure is not converted back to the reactants.

As a result of these assumptions the rate of reaction would be overestimated as it is unable to to describe the scenario of reactions with enough kinetic energy to reform the reactants from the products.

===References===
(1) S. J. Moss and C. J. Coady, Potential-Energy Surfaces and Transition-State Theory, University of Aston in Birmingham, Computer Series

== F - H - H System ==

===PES Inspection===

Literature shows that the H-F bond energy (565kJmol-1)1 is greater than that of H-H(462kJmol-1)1 hence the enthalpy of dissociation of the H-F molecule is greater, this is concordant with the potential energy surface for the F - H - H system. Figure X shows that F + H2 -> HF + H is an '''exothermic''' reaction, the potential energy surface shows the products having a lower energy than the reactants. The backward reaction is HF + H -> H2 + F and is therefore '''endothermic''', this reaction has a greater activation energy due to the greater bond enthalpy of the HF molecule requiring more energy for its dissociation.

By using Hammonds Postulate it can be approximated that the transition state will resemble the either the products or the reactants depending on which is closer in energy. Therefore, in the endothermic reaction the transition state will closely resemble the reactants whereas in an exothermic it closely resembles the products. The idea of Hammonds postulate was used in order to identify the inter-atomic distances at the transition state. For the endothermic reaction the known H-H bond length (0.744 A) was used as the initial condition and the H-F distance was manipulated to determine the location of the transition state using a graph of the Internuclear distance vs Time to find the optimized H-F distance (1.8311 A) where the force of bond equals zero.

MEP calculations were carried out and a plot of the Energy vs Time was used in order to determine the activation energy of the forward and backward reactions.

[[File:Vc endothermicreaction.png|400px]]

HF + H -> H2 + F Activation Energy= 29 kcal/mol

F + H2 -> HF + H Activation Energy=

===Reaction Dynamics===

'''Reactive trajectory conditions:'''

R1(H2)= 0.74 A

R2(HF) = 2.30 A

P1 = -1.7

P2 = -2.4

[[File:VC PART2 REACTIVECONTOUR 2A.PNG|400px]] [[File:VC PART2 ENERGYVSTIME.PNG|400px]]

For the reactive trajectory shown in Figures above of the F + H2 reaction, it can be seen from the Momenta vs Time graph that there is an interconversion between kinetic and potential energy as a fall in potential energy energy is opposed by a rise in kinetic energy, this is in concordance with the law of the conservation of energy. Therefore, for this exothermic reaction the potential energy is converted into kinetic energy giving rise to vibrations of the HF bond that this formed. Infrared spectroscopy can be used to confirm the conversion of energy by calculating the frequency of absorption of the bond.

An investigation into the reaction trajectories was conducted using the initial set of conditions listed below, '''P2 = -0.5''' was kept constant whereas '''P1''' was varied within the range '''X= -3 to 3'''.

R1(H2)= 0.74 A

R2(HF) = 2.30 A

P1 = '''X'''

P2 = -0.5

{| class="wikitable" border="1"
|+
! R1(H2) !! R2(HF) !! P2 !! P1 !! Contour plot of trajectory
|-
| 0.74 || 2.3 || -0.5 || -2.7 || [[File:VC PART2 -2.7MO (1).PNG|350px]]
|-
| 0.74|| 2.3 || -0.5 || -2.1 || [[File:VC PART2B -2.1.PNG|350px]]
|-
| 0.74 || 2.3 || -0.5 || 0.6 || [[File:Vc 0.6mom.PNG|350px]]
|-
| 0.74 || 2.3 || -0.5 || 1.6 || [[File:Vc 1.6mom.PNG|350px]]
|-
| 0.74|| 2.3 || -0.5 || 2.8 || [[File:Vc 2.8mom.PNG|350px]] |
|}

===Polanyi's Rules===

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

===References===
(1). Huheey, pps. A-21 to A-34; T.L. Cottrell, "The Strengths of Chemical Bonds," 2nd ed., Butterworths, London, 1958; B. deB. Darwent, "National Standard Reference Data Series," National Bureau of Standards, No. 31, Washington, DC, 1970; S.W. Benson, J. Chem. Educ., 42, 502 (1965).

MRD:VFC2398

2019-05-17T07:39:12Z

Vc2217: /* Molecular Dynamics */

=Molecular Dynamics=

==H + H2 system==

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

'''A + B-C -> A-B + C'''

A reactive trajectory can be generated on a potential energy surface measuring the potential energy with respect to the AB and BC inter-atomic distances by applying a set of initial conditions for the positions of the atoms and their momenta. From the potential energy surface the trajectory can be determined by finding the derivate across the whole potential energy surface to find the minima. To find the energy of the transition state, which on the trajectory resembles a saddle point, the derivative of the trajectory must be found but this time to determine the maximum energy. Since the system being observed is symmetric at the maximum ie. transition state, AB and BC inter-atomic distances will be equal as a result can be seen as the point of intersection Figure X. on the Internuclear distance against Time graph.

Graphs depicting "Internuclear Distances vs Time" can also be used to determine the energy of a transition state.

W= ∫F. ds
E= ∫F. ds
de/ds = F

At the minimum of a potential energy curve, the force is zero so the molecule has no potential energy so it is no longer vibrating this results in the AB and BC to have no vibration so the periodic symmetric vibration wave becomes a straight line due to not having an amplitude as a result of the force on the bond being equal to zero. By inserting different values of '''r2 (AB)= r1 (BC)''' and '''P(AB)=P(BC) = 0''', the transition state bond length can be determined via trial and error for H + H2 system.

[[File:VC LOCATINGTS.PNG]]

===Trajectories from r1 = rts+δ, r2 = rts===

An MEP shows the mean energy path hence no vibration contributions of the molecules can be seen therefore the trajectory that is depicted on the PES is not wavy but straight, it differs from a dynamics calculation as it does not take the gradient of the potential energy of previous steps into account, only the gradient at the current step is accounted for.A dynamic calculation will display changes in momenta whereas in an MEP there are no changes in the momenta of the atoms/molecules.

'''Determining reactive trajectories'''

The following table shows how changing the momenta p1 (BC) and p2 (AB) within a set of initial conditions with the inter-atomic distances kept constant r1 = 2.0 and r2 = 0.74 can affect the reactivity of a reaction.

{| class="wikitable" border="1"
|+
! p1 (BC) !! p2 (AB) !! Etot !! Reactive? !! Trajectory !! Description of Dynamics
|-
| -1.25 || -2.5 || -99.018 || Yes || [[File:VC 1A TRAJECT.PNG|350px]] || A H atom approaches a H2 molecule, the straight line indicates that there is no vibration until the point of collision where a new H2 vibrating molecule is formed.
|-
| -1.5 || -2.0 || -100.456 || No || [[File:VC 1B TRAJECT.PNG|350px]] || H atom approached a H2 molecule however the energy of the reactants is insufficient to overcome that of the activation energy therefore the product is not formed and the reactants are reformed as it returns to the reactant channel.
|-
| -1.5 || -2.5 || -98.956 || Yes || [[File:VC 1C TRAJECT.PNG|350px]] || This reaction is successful hence the H atom approaches a H2 molecule with enough energy to overcome the activation energy and form the product H2 molecule.
|-
| -2.5 || -5.0 || -84.956 || No || [[File:VC 1D TRAJECT.PNG|350px]] || Reactants have enough energy to overcome the activation barrier to the products, in fact an excess of kinetic energy is observed resulting in the activation energy of the backward reaction being overcome hence the reactants are reformed.
|-
| -2.5 || -5.2 || -83.426 || Yes || [[File:VC 1E TRAJECT.PNG|350px]] || This reaction is successful hence the H atom approaches a H2 molecule with enough energy to overcome the activation energy and form the product H2 molecule.
|-
|}

From this investigation it can be concluded that a reaction is very sensitive to the energy that is supplied to it and that supplying a reaction with enough energy to surpass the activation energy will not necessarily lead to a successful reaction.

===Transition State Theory===
The '''Transition State Theory''' can be used to provide a more accurate measure of the rate constant of a reaction compared to other methods such as the Arrhenius equation. The theory involves treating the transition state as an activated complex in equilibrium with the reactant, therefore the energy of the transition state relative to the reactants determines the Ea of the reaction.1
The reaction can be considered as the following:
A + BC <—> [ABC*] —> AB + C
where ABC* represents the transition state complex

The transition state theory was used to determine that the rate of a reaction by looking at the motion through the saddle point of a potential energy surface.
The assumptions for this theory include:

-The reactants are in equilibrium with the transition state complex

-The energy of the particles follows a Boltzmann distribution during the reaction

-Once the transition state complex is formed, the structure does not collapse back to the reactants.

As a result of these assumptions the rate of reaction would be overestimated as it is unable to to describe the scenario of reactions with enough kinetic energy to reform the reactants from the products.

===References===
(1) S. J. Moss and C. J. Coady, Potential-Energy Surfaces and Transition-State Theory, University of Aston in Birmingham, Computer Series

== F - H - H System ==

===PES Inspection===

Literature shows that the H-F bond energy (565kJmol-1)1 is greater than that of H-H(462kJmol-1)1 hence the enthalpy of dissociation of the H-F molecule is greater, this is concordant with the potential energy surface for the F - H - H system. Figure X shows that F + H2 -> HF + H is an '''exothermic''' reaction, the potential energy surface shows the products having a lower energy than the reactants. The backward reaction is HF + H -> H2 + F and is therefore '''endothermic''', this reaction has a greater activation energy due to the greater bond enthalpy of the HF molecule requiring more energy for its dissociation.

By using Hammonds Postulate it can be approximated that the transition state will resemble the either the products or the reactants depending on which is closer in energy. Therefore, in the endothermic reaction the transition state will closely resemble the reactants whereas in an exothermic it closely resembles the products. The idea of Hammonds postulate was used in order to identify the inter-atomic distances at the transition state. For the endothermic reaction the known H-H bond length (0.744 A) was used as the initial condition and the H-F distance was manipulated to determine the location of the transition state using a graph of the Internuclear distance vs Time to find the optimized H-F distance (1.8311 A) where the force of bond equals zero.

MEP calculations were carried out and a plot of the Energy vs Time was used in order to determine the activation energy of the forward and backward reactions.

[[File:Vc endothermicreaction.png|400px]]

HF + H -> H2 + F Activation Energy= 29 kcal/mol

F + H2 -> HF + H Activation Energy=

===Reaction Dynamics===

'''Reactive trajectory conditions:'''

R1(H2)= 0.74 A

R2(HF) = 2.30 A

P1 = -1.7

P2 = -2.4

[[File:VC PART2 REACTIVECONTOUR 2A.PNG|400px]] [[File:VC PART2 ENERGYVSTIME.PNG|400px]]

For the reactive trajectory shown in Figures above of the F + H2 reaction, it can be seen from the Momenta vs Time graph that there is an interconversion between kinetic and potential energy as a fall in potential energy energy is opposed by a rise in kinetic energy, this is in concordance with the law of the conservation of energy. Therefore, for this exothermic reaction the potential energy is converted into kinetic energy giving rise to vibrations of the HF bond that this formed. Infrared spectroscopy can be used to confirm the conversion of energy by calculating the frequency of absorption of the bond.

An investigation into the reaction trajectories was conducted using the initial set of conditions listed below, '''P2 = -0.5''' was kept constant whereas '''P1''' was varied within the range '''X= -3 to 3'''.

R1(H2)= 0.74 A

R2(HF) = 2.30 A

P1 = '''X'''

P2 = -0.5

{| class="wikitable" border="1"
|+
! R1(H2) !! R2(HF) !! P2 !! P1 !! Contour plot of trajectory
|-
| 0.74 || 2.3 || -0.5 || -2.7 || [[File:VC PART2 -2.7MO (1).PNG|350px]]
|-
| 0.74|| 2.3 || -0.5 || -2.1 || [[File:VC PART2B -2.1.PNG|350px]]
|-
| 0.74 || 2.3 || -0.5 || 0.6 || [[File:Vc 0.6mom.PNG|350px]]
|-
| 0.74 || 2.3 || -0.5 || 1.6 || [[File:Vc 1.6mom.PNG|350px]]
|-
| 0.74|| 2.3 || -0.5 || 2.8 || [[File:Vc 2.8mom.PNG|350px]] |
|}

===Polanyi's Rules===

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

===References===
(1). Huheey, pps. A-21 to A-34; T.L. Cottrell, "The Strengths of Chemical Bonds," 2nd ed., Butterworths, London, 1958; B. deB. Darwent, "National Standard Reference Data Series," National Bureau of Standards, No. 31, Washington, DC, 1970; S.W. Benson, J. Chem. Educ., 42, 502 (1965).

MRD:VFC2398

2019-05-16T21:20:02Z

Vc2217: /* Trajectories from r1 = rts+δ, r2 = rts */

=Molecular Dynamics=

==H + H2 system==

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

A reactive trajectory can be generated on a potential energy surface measuring the potential energy with respect to the AB and BC inter-atomic distances by applying a set of initial conditions for the positions of the atoms and their momenta. From the potential energy surface the trajectory can be determined by differentiating across the whole potential energy surface to find the minima. To find the energy of the transition state, the trajectory would be differentiated to find the maximum energy. At the maximum AB and BC inter-atomic distances will be equal.

Graphs depicting "Internuclear Distances vs Time" can also be used to determine the energy of a transition state.
W= ∫F. ds
E= ∫F. ds
de/ds = F

At the minimum of a potential energy curve, the force is zero so the molecule has no potential energy so it is no longer vibrating this results in the AB and BC to have no vibration so the periodic symmetric vibration wave becomes a straight line due to not having an amplitude as a result of the force on the bond being equal to zero. By inserting different values of '''r2 (AB)= r1 (BC)''' and '''P(AB)=P(BC) = 0''', the transition state bond length can be determined via trial and error for H + H2 system.

[[File:VC LOCATINGTS.PNG]]

===Trajectories from r1 = rts+δ, r2 = rts===

An MEP shows the mean energy path hence no vibration contributions of the molecules can be seen, it differs from a dynamics calculation as it does not take the gradient of the potential energy of previous steps into account, only the gradient at the current step is accounted for.

{| class="wikitable" border="1"
|+
! p1 (BC) !! p2 (AB) !! Etot !! Reactive? !! Trajectory !! Description of Dynamics
|-
| -1.25 || -2.5 || -99.018 || Yes || [[File:VC 1A TRAJECT.PNG|350px]] || A H atom approaches a H2 molecule, the straight line indicates that there is no vibration until the point of collision where a new H2 vibrating molecule is formed.
|-
| -1.5 || -2.0 || -100.456 || No || [[File:VC 1B TRAJECT.PNG|350px]] || H atom approached a H2 molecule however the energy of the reactants is insufficient to overcome that of the activation energy therefore the product is not formed and the reactants are reformed as it returns to the reactant channel.
|-
| -1.5 || -2.5 || -98.956 || Yes || [[File:VC 1C TRAJECT.PNG|350px]] || This reaction is successful hence the H atom approaches a H2 molecule with enough energy to overcome the activation energy and form the product H2 molecule.
|-
| -2.5 || -5.0 || -84.956 || No || [[File:VC 1D TRAJECT.PNG|350px]] || Reactants have enough energy to overcome the activation barrier to the products, in fact an excess of kinetic energy is observed resulting in the activation energy of the backward reaction being overcome hence the reactants are reformed.
|-
| -2.5 || -5.2 || -83.426 || Yes || [[File:VC 1E TRAJECT.PNG|350px]] || This reaction is successful hence the H atom approaches a H2 molecule with enough energy to overcome the activation energy and form the product H2 molecule.
|-
|}

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

== F - H - H System ==

===PES Inspection===

Literature shows that the H-F bond energy (565kJmol-1)1 is greater than that of H-H(462kJmol-1)1 hence the enthalpy of dissociation of the H-F molecule is greater, this is concordant with the potential energy surface for the F - H - H system. Figure X shows that F + H2 -> HF + H is an '''exothermic''' reaction, the potential energy surface shows the products having a lower energy than the reactants. The backward reaction is HF + H -> H2 + F and is therefore '''endothermic''', this reaction has a greater activation energy due to the greater bond enthalpy of the HF molecule requiring more energy for its dissociation.

By using Hammonds Postulate it can be approximated that the transition state will resemble the either the products or the reactants depending on which is closer in energy. Therefore, in the endothermic reaction the transition state will closely resemble the reactants whereas in an exothermic it closely resembles the products. The idea of Hammonds postulate was used in order to identify the inter-atomic distances at the transition state. For the endothermic reaction the known H-H bond length (0.744 A) was used as the initial condition and the H-F distance was manipulated to determine the location of the transition state using a graph of the Internuclear distance vs Time to find the optimized H-F distance (1.8311 A) where the force of bond equals zero.

MEP calculations were carried out and a plot of the Energy vs Time was used in order to determine the activation energy of the forward and backward reactions.

[[File:Vc endothermicreaction.png|400px]]

HF + H -> H2 + F Activation Energy= 29 kcal/mol

F + H2 -> HF + H Activation Energy=

===Reaction Dynamics===

'''Reactive trajectory conditions:'''

R1(H2)= 0.74 A

R2(HF) = 2.30 A

P1 = -1.7

P2 = -2.4

[[File:VC PART2 REACTIVECONTOUR 2A.PNG|400px]] [[File:VC PART2 ENERGYVSTIME.PNG|400px]]

For the reactive trajectory shown in Figures above of the F + H2 reaction, it can be seen from the Momenta vs Time graph that there is an interconversion between kinetic and potential energy as a fall in potential energy energy is opposed by a rise in kinetic energy, this is in concordance with the law of the conservation of energy. Therefore, for this exothermic reaction the potential energy is converted into kinetic energy giving rise to vibrations of the HF bond that this formed. Infrared spectroscopy can be used to confirm the conversion of energy by calculating the frequency of absorption of the bond.

An investigation into the reaction trajectories was conducted using the initial set of conditions listed below, '''P2 = -0.5''' was kept constant whereas '''P1''' was varied within the range '''X= -3 to 3'''.

R1(H2)= 0.74 A

R2(HF) = 2.30 A

P1 = '''X'''

P2 = -0.5

{| class="wikitable" border="1"
|+
! R1(H2) !! R2(HF) !! P2 !! P1 !! Contour plot of trajectory
|-
| 0.74 || 2.3 || -0.5 || -2.7 || [[File:VC PART2 -2.7MO (1).PNG|350px]]
|-
| 0.74|| 2.3 || -0.5 || -2.1 || [[File:VC PART2B -2.1.PNG|350px]]
|-
| 0.74 || 2.3 || -0.5 || 0.6 || [[File:Vc 0.6mom.PNG|350px]]
|-
| 0.74 || 2.3 || -0.5 || 1.6 || [[File:Vc 1.6mom.PNG|350px]]
|-
| 0.74|| 2.3 || -0.5 || 2.8 || [[File:Vc 2.8mom.PNG|350px]] |
|}

===References===
(1). Huheey, pps. A-21 to A-34; T.L. Cottrell, "The Strengths of Chemical Bonds," 2nd ed., Butterworths, London, 1958; B. deB. Darwent, "National Standard Reference Data Series," National Bureau of Standards, No. 31, Washington, DC, 1970; S.W. Benson, J. Chem. Educ., 42, 502 (1965).

MRD:VFC2398

2019-05-16T21:08:49Z

Vc2217: /* Trajectories from r1 = rts+δ, r2 = rts */

=Molecular Dynamics=

==H + H2 system==

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

A reactive trajectory can be generated on a potential energy surface measuring the potential energy with respect to the AB and BC inter-atomic distances by applying a set of initial conditions for the positions of the atoms and their momenta. From the potential energy surface the trajectory can be determined by differentiating across the whole potential energy surface to find the minima. To find the energy of the transition state, the trajectory would be differentiated to find the maximum energy. At the maximum AB and BC inter-atomic distances will be equal.

Graphs depicting "Internuclear Distances vs Time" can also be used to determine the energy of a transition state.
W= ∫F. ds
E= ∫F. ds
de/ds = F

At the minimum of a potential energy curve, the force is zero so the molecule has no potential energy so it is no longer vibrating this results in the AB and BC to have no vibration so the periodic symmetric vibration wave becomes a straight line due to not having an amplitude as a result of the force on the bond being equal to zero. By inserting different values of '''r2 (AB)= r1 (BC)''' and '''P(AB)=P(BC) = 0''', the transition state bond length can be determined via trial and error for H + H2 system.

[[File:VC LOCATINGTS.PNG]]

===Trajectories from r1 = rts+δ, r2 = rts===

An MEP shows the mean energy path hence no vibration contributions of the molecules can be seen, it differs from a dynamics calculation as it does not take the gradient of the potential energy of previous steps into account, only the gradient at the current step is accounted for.

{| class="wikitable" border="1"
|+
! p1 (BC) !! p2 (AB) !! Etot !! Reactive? !! Trajectory !! Description of Dynamics
|-
| -1.25 || -2.5 || -99.018 || Yes || [[File:VC 1A TRAJECT.PNG|350px]] || A H atom approaches a H2 molecule, the straight line indicates that there is no vibration until the point of collision where a new H2 vibrating molecule is formed.
|-
| -1.5 || -2.0 || -100.456 || No || [[File:VC 1B TRAJECT.PNG|350px]] || cell
|-
| -1.5 || -2.5 || -98.956 || Yes || [[File:VC 1C TRAJECT.PNG|350px]] || cell
|-
| -2.5 || -5.0 || -84.956 || No || [[File:VC 1D TRAJECT.PNG|350px]] || cell
|-
| -2.5 || -5.2 || -83.426 || Yes || [[File:VC 1E TRAJECT.PNG|350px]] || cell
|}

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

== F - H - H System ==

===PES Inspection===

Literature shows that the H-F bond energy (565kJmol-1)1 is greater than that of H-H(462kJmol-1)1 hence the enthalpy of dissociation of the H-F molecule is greater, this is concordant with the potential energy surface for the F - H - H system. Figure X shows that F + H2 -> HF + H is an '''exothermic''' reaction, the potential energy surface shows the products having a lower energy than the reactants. The backward reaction is HF + H -> H2 + F and is therefore '''endothermic''', this reaction has a greater activation energy due to the greater bond enthalpy of the HF molecule requiring more energy for its dissociation.

By using Hammonds Postulate it can be approximated that the transition state will resemble the either the products or the reactants depending on which is closer in energy. Therefore, in the endothermic reaction the transition state will closely resemble the reactants whereas in an exothermic it closely resembles the products. The idea of Hammonds postulate was used in order to identify the inter-atomic distances at the transition state. For the endothermic reaction the known H-H bond length (0.744 A) was used as the initial condition and the H-F distance was manipulated to determine the location of the transition state using a graph of the Internuclear distance vs Time to find the optimized H-F distance (1.8311 A) where the force of bond equals zero.

MEP calculations were carried out and a plot of the Energy vs Time was used in order to determine the activation energy of the forward and backward reactions.

[[File:Vc endothermicreaction.png|400px]]

HF + H -> H2 + F Activation Energy= 29 kcal/mol

F + H2 -> HF + H Activation Energy=

===Reaction Dynamics===

'''Reactive trajectory conditions:'''

R1(H2)= 0.74 A

R2(HF) = 2.30 A

P1 = -1.7

P2 = -2.4

[[File:VC PART2 REACTIVECONTOUR 2A.PNG|400px]] [[File:VC PART2 ENERGYVSTIME.PNG|400px]]

For the reactive trajectory shown in Figures above of the F + H2 reaction, it can be seen from the Momenta vs Time graph that there is an interconversion between kinetic and potential energy as a fall in potential energy energy is opposed by a rise in kinetic energy, this is in concordance with the law of the conservation of energy. Therefore, for this exothermic reaction the potential energy is converted into kinetic energy giving rise to vibrations of the HF bond that this formed. Infrared spectroscopy can be used to confirm the conversion of energy by calculating the frequency of absorption of the bond.

An investigation into the reaction trajectories was conducted using the initial set of conditions listed below, '''P2 = -0.5''' was kept constant whereas '''P1''' was varied within the range '''X= -3 to 3'''.

R1(H2)= 0.74 A

R2(HF) = 2.30 A

P1 = '''X'''

P2 = -0.5

{| class="wikitable" border="1"
|+
! R1(H2) !! R2(HF) !! P2 !! P1 !! Contour plot of trajectory
|-
| 0.74 || 2.3 || -0.5 || -2.7 || [[File:VC PART2 -2.7MO (1).PNG|350px]]
|-
| 0.74|| 2.3 || -0.5 || -2.1 || [[File:VC PART2B -2.1.PNG|350px]]
|-
| 0.74 || 2.3 || -0.5 || 0.6 || [[File:Vc 0.6mom.PNG|350px]]
|-
| 0.74 || 2.3 || -0.5 || 1.6 || [[File:Vc 1.6mom.PNG|350px]]
|-
| 0.74|| 2.3 || -0.5 || 2.8 || [[File:Vc 2.8mom.PNG|350px]] |
|}

===References===
(1). Huheey, pps. A-21 to A-34; T.L. Cottrell, "The Strengths of Chemical Bonds," 2nd ed., Butterworths, London, 1958; B. deB. Darwent, "National Standard Reference Data Series," National Bureau of Standards, No. 31, Washington, DC, 1970; S.W. Benson, J. Chem. Educ., 42, 502 (1965).

MRD:VFC2398

2019-05-16T20:31:53Z

Vc2217: /* PES Inspection */

=Molecular Dynamics=

==H + H2 system==

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

A reactive trajectory can be generated on a potential energy surface measuring the potential energy with respect to the AB and BC inter-atomic distances by applying a set of initial conditions for the positions of the atoms and their momenta. From the potential energy surface the trajectory can be determined by differentiating across the whole potential energy surface to find the minima. To find the energy of the transition state, the trajectory would be differentiated to find the maximum energy. At the maximum AB and BC inter-atomic distances will be equal.

Graphs depicting "Internuclear Distances vs Time" can also be used to determine the energy of a transition state.
W= ∫F. ds
E= ∫F. ds
de/ds = F

At the minimum of a potential energy curve, the force is zero so the molecule has no potential energy so it is no longer vibrating this results in the AB and BC to have no vibration so the periodic symmetric vibration wave becomes a straight line due to not having an amplitude as a result of the force on the bond being equal to zero. By inserting different values of '''r2 (AB)= r1 (BC)''' and '''P(AB)=P(BC) = 0''', the transition state bond length can be determined via trial and error for H + H2 system.

[[File:VC LOCATINGTS.PNG]]

===Trajectories from r1 = rts+δ, r2 = rts===

An MEP shows the mean energy path hence no vibration contributions of the molecules can be seen, it differs from a dynamics calculation as it does not take the gradient of the potential energy of previous steps into account, only the gradient at the current step is accounted for.

{| class="wikitable" border="1"
|+
! p1 (BC) !! p2 (AB) !! Etot !! Reactive? !! Trajectory !! Description of Dynamics
|-
| -1.25 || -2.5 || -99.018 || Yes || [[File:VC 1A TRAJECT.PNG|350px]] || cell
|-
| -1.5 || -2.0 || -100.456 || No || [[File:VC 1B TRAJECT.PNG|350px]] || cell
|-
| -1.5 || -2.5 || -98.956 || Yes || [[File:VC 1C TRAJECT.PNG|350px]] || cell
|-
| -2.5 || -5.0 || -84.956 || No || [[File:VC 1D TRAJECT.PNG|350px]] || cell
|-
| -2.5 || -5.2 || -83.426 || Yes || [[File:VC 1E TRAJECT.PNG|350px]] || cell
|}

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

== F - H - H System ==

===PES Inspection===

Literature shows that the H-F bond energy (565kJmol-1)1 is greater than that of H-H(462kJmol-1)1 hence the enthalpy of dissociation of the H-F molecule is greater, this is concordant with the potential energy surface for the F - H - H system. Figure X shows that F + H2 -> HF + H is an '''exothermic''' reaction, the potential energy surface shows the products having a lower energy than the reactants. The backward reaction is HF + H -> H2 + F and is therefore '''endothermic''', this reaction has a greater activation energy due to the greater bond enthalpy of the HF molecule requiring more energy for its dissociation.

By using Hammonds Postulate it can be approximated that the transition state will resemble the either the products or the reactants depending on which is closer in energy. Therefore, in the endothermic reaction the transition state will closely resemble the reactants whereas in an exothermic it closely resembles the products. The idea of Hammonds postulate was used in order to identify the inter-atomic distances at the transition state. For the endothermic reaction the known H-H bond length (0.744 A) was used as the initial condition and the H-F distance was manipulated to determine the location of the transition state using a graph of the Internuclear distance vs Time to find the optimized H-F distance (1.8311 A) where the force of bond equals zero.

MEP calculations were carried out and a plot of the Energy vs Time was used in order to determine the activation energy of the forward and backward reactions.

[[File:Vc endothermicreaction.png|400px]]

HF + H -> H2 + F Activation Energy= 29 kcal/mol

F + H2 -> HF + H Activation Energy=

===Reaction Dynamics===

'''Reactive trajectory conditions:'''

R1(H2)= 0.74 A

R2(HF) = 2.30 A

P1 = -1.7

P2 = -2.4

[[File:VC PART2 REACTIVECONTOUR 2A.PNG|400px]] [[File:VC PART2 ENERGYVSTIME.PNG|400px]]

For the reactive trajectory shown in Figures above of the F + H2 reaction, it can be seen from the Momenta vs Time graph that there is an interconversion between kinetic and potential energy as a fall in potential energy energy is opposed by a rise in kinetic energy, this is in concordance with the law of the conservation of energy. Therefore, for this exothermic reaction the potential energy is converted into kinetic energy giving rise to vibrations of the HF bond that this formed. Infrared spectroscopy can be used to confirm the conversion of energy by calculating the frequency of absorption of the bond.

An investigation into the reaction trajectories was conducted using the initial set of conditions listed below, '''P2 = -0.5''' was kept constant whereas '''P1''' was varied within the range '''X= -3 to 3'''.

R1(H2)= 0.74 A

R2(HF) = 2.30 A

P1 = '''X'''

P2 = -0.5

{| class="wikitable" border="1"
|+
! R1(H2) !! R2(HF) !! P2 !! P1 !! Contour plot of trajectory
|-
| 0.74 || 2.3 || -0.5 || -2.7 || [[File:VC PART2 -2.7MO (1).PNG|350px]]
|-
| 0.74|| 2.3 || -0.5 || -2.1 || [[File:VC PART2B -2.1.PNG|350px]]
|-
| 0.74 || 2.3 || -0.5 || 0.6 || [[File:Vc 0.6mom.PNG|350px]]
|-
| 0.74 || 2.3 || -0.5 || 1.6 || [[File:Vc 1.6mom.PNG|350px]]
|-
| 0.74|| 2.3 || -0.5 || 2.8 || [[File:Vc 2.8mom.PNG|350px]] |
|}

===References===
(1). Huheey, pps. A-21 to A-34; T.L. Cottrell, "The Strengths of Chemical Bonds," 2nd ed., Butterworths, London, 1958; B. deB. Darwent, "National Standard Reference Data Series," National Bureau of Standards, No. 31, Washington, DC, 1970; S.W. Benson, J. Chem. Educ., 42, 502 (1965).

MRD:VFC2398

2019-05-16T20:31:12Z

Vc2217: /* Reaction Dynamics */

=Molecular Dynamics=

==H + H2 system==

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

A reactive trajectory can be generated on a potential energy surface measuring the potential energy with respect to the AB and BC inter-atomic distances by applying a set of initial conditions for the positions of the atoms and their momenta. From the potential energy surface the trajectory can be determined by differentiating across the whole potential energy surface to find the minima. To find the energy of the transition state, the trajectory would be differentiated to find the maximum energy. At the maximum AB and BC inter-atomic distances will be equal.

Graphs depicting "Internuclear Distances vs Time" can also be used to determine the energy of a transition state.
W= ∫F. ds
E= ∫F. ds
de/ds = F

At the minimum of a potential energy curve, the force is zero so the molecule has no potential energy so it is no longer vibrating this results in the AB and BC to have no vibration so the periodic symmetric vibration wave becomes a straight line due to not having an amplitude as a result of the force on the bond being equal to zero. By inserting different values of '''r2 (AB)= r1 (BC)''' and '''P(AB)=P(BC) = 0''', the transition state bond length can be determined via trial and error for H + H2 system.

[[File:VC LOCATINGTS.PNG]]

===Trajectories from r1 = rts+δ, r2 = rts===

An MEP shows the mean energy path hence no vibration contributions of the molecules can be seen, it differs from a dynamics calculation as it does not take the gradient of the potential energy of previous steps into account, only the gradient at the current step is accounted for.

{| class="wikitable" border="1"
|+
! p1 (BC) !! p2 (AB) !! Etot !! Reactive? !! Trajectory !! Description of Dynamics
|-
| -1.25 || -2.5 || -99.018 || Yes || [[File:VC 1A TRAJECT.PNG|350px]] || cell
|-
| -1.5 || -2.0 || -100.456 || No || [[File:VC 1B TRAJECT.PNG|350px]] || cell
|-
| -1.5 || -2.5 || -98.956 || Yes || [[File:VC 1C TRAJECT.PNG|350px]] || cell
|-
| -2.5 || -5.0 || -84.956 || No || [[File:VC 1D TRAJECT.PNG|350px]] || cell
|-
| -2.5 || -5.2 || -83.426 || Yes || [[File:VC 1E TRAJECT.PNG|350px]] || cell
|}

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

== F - H - H System ==

===PES Inspection===

Literature shows that the H-F bond energy (565kJmol-1)1 is greater than that of H-H(462kJmol-1)1 hence the enthalpy of dissociation of the H-F molecule is greater, this is concordant with the potential energy surface for the F - H - H system. Figure X shows that F + H2 -> HF + H is an '''exothermic''' reaction, the potential energy surface shows the products having a lower energy than the reactants. The backward reaction is HF + H -> H2 + F and is therefore '''endothermic''', this reaction has a greater activation energy due to the greater bond enthalpy of the HF molecule requiring more energy for its dissociation.

By using Hammonds Postulate it can be approximated that the transition state will resemble the either the products or the reactants depending on which is closer in energy. Therefore, in the endothermic reaction the transition state will closely resemble the reactants whereas in an exothermic it closely resembles the products. The idea of Hammonds postulate was used in order to identify the inter-atomic distances at the transition state. For the endothermic reaction the known H-H bond length (0.744 A) was used as the initial condition and the H-F distance was manipulated to determine the location of the transition state using a graph of the Internuclear distance vs Time to find the optimized H-F distance (1.8311 A) where the force of bond equals zero.

MEP calculations were carried out and a plot of the Energy vs Time was used in order to determine the activation of the forward and backward reactions.

[[File:Vc endothermicreaction.png|400px]]

HF + H -> H2 + F Activation Energy= 29 kcal/mol

F + H2 -> HF + H Activation Energy=

===Reaction Dynamics===

'''Reactive trajectory conditions:'''

R1(H2)= 0.74 A

R2(HF) = 2.30 A

P1 = -1.7

P2 = -2.4

[[File:VC PART2 REACTIVECONTOUR 2A.PNG|400px]] [[File:VC PART2 ENERGYVSTIME.PNG|400px]]

For the reactive trajectory shown in Figures above of the F + H2 reaction, it can be seen from the Momenta vs Time graph that there is an interconversion between kinetic and potential energy as a fall in potential energy energy is opposed by a rise in kinetic energy, this is in concordance with the law of the conservation of energy. Therefore, for this exothermic reaction the potential energy is converted into kinetic energy giving rise to vibrations of the HF bond that this formed. Infrared spectroscopy can be used to confirm the conversion of energy by calculating the frequency of absorption of the bond.

An investigation into the reaction trajectories was conducted using the initial set of conditions listed below, '''P2 = -0.5''' was kept constant whereas '''P1''' was varied within the range '''X= -3 to 3'''.

R1(H2)= 0.74 A

R2(HF) = 2.30 A

P1 = '''X'''

P2 = -0.5

{| class="wikitable" border="1"
|+
! R1(H2) !! R2(HF) !! P2 !! P1 !! Contour plot of trajectory
|-
| 0.74 || 2.3 || -0.5 || -2.7 || [[File:VC PART2 -2.7MO (1).PNG|350px]]
|-
| 0.74|| 2.3 || -0.5 || -2.1 || [[File:VC PART2B -2.1.PNG|350px]]
|-
| 0.74 || 2.3 || -0.5 || 0.6 || [[File:Vc 0.6mom.PNG|350px]]
|-
| 0.74 || 2.3 || -0.5 || 1.6 || [[File:Vc 1.6mom.PNG|350px]]
|-
| 0.74|| 2.3 || -0.5 || 2.8 || [[File:Vc 2.8mom.PNG|350px]] |
|}

===References===
(1). Huheey, pps. A-21 to A-34; T.L. Cottrell, "The Strengths of Chemical Bonds," 2nd ed., Butterworths, London, 1958; B. deB. Darwent, "National Standard Reference Data Series," National Bureau of Standards, No. 31, Washington, DC, 1970; S.W. Benson, J. Chem. Educ., 42, 502 (1965).

MRD:VFC2398

2019-05-16T20:30:39Z

Vc2217: /* Molecular Dynamics */

=Molecular Dynamics=

==H + H2 system==

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

A reactive trajectory can be generated on a potential energy surface measuring the potential energy with respect to the AB and BC inter-atomic distances by applying a set of initial conditions for the positions of the atoms and their momenta. From the potential energy surface the trajectory can be determined by differentiating across the whole potential energy surface to find the minima. To find the energy of the transition state, the trajectory would be differentiated to find the maximum energy. At the maximum AB and BC inter-atomic distances will be equal.

Graphs depicting "Internuclear Distances vs Time" can also be used to determine the energy of a transition state.
W= ∫F. ds
E= ∫F. ds
de/ds = F

At the minimum of a potential energy curve, the force is zero so the molecule has no potential energy so it is no longer vibrating this results in the AB and BC to have no vibration so the periodic symmetric vibration wave becomes a straight line due to not having an amplitude as a result of the force on the bond being equal to zero. By inserting different values of '''r2 (AB)= r1 (BC)''' and '''P(AB)=P(BC) = 0''', the transition state bond length can be determined via trial and error for H + H2 system.

[[File:VC LOCATINGTS.PNG]]

===Trajectories from r1 = rts+δ, r2 = rts===

An MEP shows the mean energy path hence no vibration contributions of the molecules can be seen, it differs from a dynamics calculation as it does not take the gradient of the potential energy of previous steps into account, only the gradient at the current step is accounted for.

{| class="wikitable" border="1"
|+
! p1 (BC) !! p2 (AB) !! Etot !! Reactive? !! Trajectory !! Description of Dynamics
|-
| -1.25 || -2.5 || -99.018 || Yes || [[File:VC 1A TRAJECT.PNG|350px]] || cell
|-
| -1.5 || -2.0 || -100.456 || No || [[File:VC 1B TRAJECT.PNG|350px]] || cell
|-
| -1.5 || -2.5 || -98.956 || Yes || [[File:VC 1C TRAJECT.PNG|350px]] || cell
|-
| -2.5 || -5.0 || -84.956 || No || [[File:VC 1D TRAJECT.PNG|350px]] || cell
|-
| -2.5 || -5.2 || -83.426 || Yes || [[File:VC 1E TRAJECT.PNG|350px]] || cell
|}

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

== F - H - H System ==

===PES Inspection===

Literature shows that the H-F bond energy (565kJmol-1)1 is greater than that of H-H(462kJmol-1)1 hence the enthalpy of dissociation of the H-F molecule is greater, this is concordant with the potential energy surface for the F - H - H system. Figure X shows that F + H2 -> HF + H is an '''exothermic''' reaction, the potential energy surface shows the products having a lower energy than the reactants. The backward reaction is HF + H -> H2 + F and is therefore '''endothermic''', this reaction has a greater activation energy due to the greater bond enthalpy of the HF molecule requiring more energy for its dissociation.

By using Hammonds Postulate it can be approximated that the transition state will resemble the either the products or the reactants depending on which is closer in energy. Therefore, in the endothermic reaction the transition state will closely resemble the reactants whereas in an exothermic it closely resembles the products. The idea of Hammonds postulate was used in order to identify the inter-atomic distances at the transition state. For the endothermic reaction the known H-H bond length (0.744 A) was used as the initial condition and the H-F distance was manipulated to determine the location of the transition state using a graph of the Internuclear distance vs Time to find the optimized H-F distance (1.8311 A) where the force of bond equals zero.

MEP calculations were carried out and a plot of the Energy vs Time was used in order to determine the activation of the forward and backward reactions.

[[File:Vc endothermicreaction.png|400px]]

HF + H -> H2 + F Activation Energy= 29 kcal/mol

F + H2 -> HF + H Activation Energy=

===Reaction Dynamics===

'''Reactive trajectory conditions:'''

R1(H2)= 0.74 A

R2(HF) = 2.30 A

P1 = -1.7

P2 = -2.4

[[File:VC PART2 REACTIVECONTOUR 2A.PNG|400px]] [[File:VC PART2 ENERGYVSTIME.PNG|400px]]

For the reactive trajectory shown in Figures above of the F + H2 reaction, it can be seen from the Momenta vs Time graph that there is an interconversion between kinetic and potential energy as a fall in potential energy energy is opposed by a rise in kinetic energy, this is in concordance with the law of the conservation of energy. Therefore, for this exothermic reaction the potential energy is converted into kinetic energy giving rise to vibrations of the HF bond that this formed. Infrared spectroscopy can be used to confirm the conversion of energy by calculating the frequency of absorption of the bond.

An investigation into the reaction trajectories was conducted using the initial set of conditions listed below, '''P2 = -0.5''' was kept constant whereas '''P1''' was varied within the range '''X= -3 to 3'''.

R1(H2)= 0.74 A

R2(HF) = 2.30 A

P1 = '''X'''

P2 = -0.5

{| class="wikitable" border="1"
|+
! R1(H2) !! R2(HF) !! P2 !! P1 !! Contour plot of trajectory
| 0.74 || 2.3 || -0.5 || -2.7 || [[File:VC PART2 -2.7MO (1).PNG|350px]]
|-
| 0.74|| 2.3 || -0.5 || -2.1 || [[File:VC PART2B -2.1.PNG|350px]]
|-
| 0.74 || 2.3 || -0.5 || 0.6 || [[File:Vc 0.6mom.PNG|350px]]
|-
| 0.74 || 2.3 || -0.5 || 1.6 || [[File:Vc 1.6mom.PNG|350px]]
|-
| 0.74|| 2.3 || -0.5 || 2.8 || [[File:Vc 2.8mom.PNG|350px]] |
|}

===References===
(1). Huheey, pps. A-21 to A-34; T.L. Cottrell, "The Strengths of Chemical Bonds," 2nd ed., Butterworths, London, 1958; B. deB. Darwent, "National Standard Reference Data Series," National Bureau of Standards, No. 31, Washington, DC, 1970; S.W. Benson, J. Chem. Educ., 42, 502 (1965).

File:Vc 2.8mom.PNG

2019-05-16T20:30:22Z

Vc2217:

File:Vc 1.6mom.PNG

2019-05-16T20:29:51Z

Vc2217:

File:Vc 0.6mom.PNG

2019-05-16T20:29:00Z

Vc2217:

File:VC PART2B -2.1.PNG

2019-05-16T20:28:12Z

Vc2217:

File:VC PART2 -2.7MO (1).PNG

2019-05-16T20:27:26Z

Vc2217:

MRD:VFC2398

2019-05-16T20:20:22Z

Vc2217: /* Reaction Dynamics */

=Molecular Dynamics=

==H + H2 system==

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

A reactive trajectory can be generated on a potential energy surface measuring the potential energy with respect to the AB and BC inter-atomic distances by applying a set of initial conditions for the positions of the atoms and their momenta. From the potential energy surface the trajectory can be determined by differentiating across the whole potential energy surface to find the minima. To find the energy of the transition state, the trajectory would be differentiated to find the maximum energy. At the maximum AB and BC inter-atomic distances will be equal.

Graphs depicting "Internuclear Distances vs Time" can also be used to determine the energy of a transition state.
W= ∫F. ds
E= ∫F. ds
de/ds = F

At the minimum of a potential energy curve, the force is zero so the molecule has no potential energy so it is no longer vibrating this results in the AB and BC to have no vibration so the periodic symmetric vibration wave becomes a straight line due to not having an amplitude as a result of the force on the bond being equal to zero. By inserting different values of '''r2 (AB)= r1 (BC)''' and '''P(AB)=P(BC) = 0''', the transition state bond length can be determined via trial and error for H + H2 system.

[[File:VC LOCATINGTS.PNG]]

===Trajectories from r1 = rts+δ, r2 = rts===

An MEP shows the mean energy path hence no vibration contributions of the molecules can be seen, it differs from a dynamics calculation as it does not take the gradient of the potential energy of previous steps into account, only the gradient at the current step is accounted for.

{| class="wikitable" border="1"
|+
! p1 (BC) !! p2 (AB) !! Etot !! Reactive? !! Trajectory !! Description of Dynamics
|-
| -1.25 || -2.5 || -99.018 || Yes || [[File:VC 1A TRAJECT.PNG|350px]] || cell
|-
| -1.5 || -2.0 || -100.456 || No || [[File:VC 1B TRAJECT.PNG|350px]] || cell
|-
| -1.5 || -2.5 || -98.956 || Yes || [[File:VC 1C TRAJECT.PNG|350px]] || cell
|-
| -2.5 || -5.0 || -84.956 || No || [[File:VC 1D TRAJECT.PNG|350px]] || cell
|-
| -2.5 || -5.2 || -83.426 || Yes || [[File:VC 1E TRAJECT.PNG|350px]] || cell
|}

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

== F - H - H System ==

===PES Inspection===

Literature shows that the H-F bond energy (565kJmol-1)1 is greater than that of H-H(462kJmol-1)1 hence the enthalpy of dissociation of the H-F molecule is greater, this is concordant with the potential energy surface for the F - H - H system. Figure X shows that F + H2 -> HF + H is an '''exothermic''' reaction, the potential energy surface shows the products having a lower energy than the reactants. The backward reaction is HF + H -> H2 + F and is therefore '''endothermic''', this reaction has a greater activation energy due to the greater bond enthalpy of the HF molecule requiring more energy for its dissociation.

By using Hammonds Postulate it can be approximated that the transition state will resemble the either the products or the reactants depending on which is closer in energy. Therefore, in the endothermic reaction the transition state will closely resemble the reactants whereas in an exothermic it closely resembles the products. The idea of Hammonds postulate was used in order to identify the inter-atomic distances at the transition state. For the endothermic reaction the known H-H bond length (0.744A) was used as the initial condition and the H-F distance was manipulated to determine the location of the transition state using a graph of the Internuclear distance vs Time to find the optimized H-F distance (1.8311 A) where the force of bond equals zero.

MEP calculations were carried out and a plot of the Energy vs Time was used in order to determine the activation of the forward and backward reactions.

[[File:Vc endothermicreaction.png|400px]]

HF + H -> H2 + F Activation Energy= 29 kcal/mol

F + H2 -> HF + H Activation Energy=

===Reaction Dynamics===

'''Reactive trajectory conditions:'''

R1(H2)= 0.74 A

R2(HF) = 2.30 A

P1 = -1.7

P2 = -2.4

[[File:VC PART2 REACTIVECONTOUR 2A.PNG|400px]] [[File:VC PART2 ENERGYVSTIME.PNG|400px]]

For the reactive trajectory shown in Figures above of the F + H2 reaction, it can be seen from the Momenta vs Time graph that there is an interconversion between kinetic and potential energy as a fall in potential energy energy is opposed by a rise in kinetic energy, this is in concordance with the law of the conservation of energy. Therefore, for this exothermic reaction the potential energy is converted into kinetic energy giving rise to vibrations of the HF bond that this formed. Infrared spectroscopy can be used to confirm the conversion of energy by calculating the frequency of absorption of the bond.

An investigation into the reaction trajectories was conducted using the initial set of conditions listed below, '''P2 = -0.5''' was kept constant whereas '''P1''' was varied with the range '''X= -3 to 3'''.

R1(H2)= 0.74 A

R2(HF) = 2.30 A

P1 = '''X'''

P2 = -0.5

===References===
(1). Huheey, pps. A-21 to A-34; T.L. Cottrell, "The Strengths of Chemical Bonds," 2nd ed., Butterworths, London, 1958; B. deB. Darwent, "National Standard Reference Data Series," National Bureau of Standards, No. 31, Washington, DC, 1970; S.W. Benson, J. Chem. Educ., 42, 502 (1965).

MRD:VFC2398

2019-05-16T20:19:10Z

Vc2217: /* Reaction Dynamics */

=Molecular Dynamics=

==H + H2 system==

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

A reactive trajectory can be generated on a potential energy surface measuring the potential energy with respect to the AB and BC inter-atomic distances by applying a set of initial conditions for the positions of the atoms and their momenta. From the potential energy surface the trajectory can be determined by differentiating across the whole potential energy surface to find the minima. To find the energy of the transition state, the trajectory would be differentiated to find the maximum energy. At the maximum AB and BC inter-atomic distances will be equal.

Graphs depicting "Internuclear Distances vs Time" can also be used to determine the energy of a transition state.
W= ∫F. ds
E= ∫F. ds
de/ds = F

At the minimum of a potential energy curve, the force is zero so the molecule has no potential energy so it is no longer vibrating this results in the AB and BC to have no vibration so the periodic symmetric vibration wave becomes a straight line due to not having an amplitude as a result of the force on the bond being equal to zero. By inserting different values of '''r2 (AB)= r1 (BC)''' and '''P(AB)=P(BC) = 0''', the transition state bond length can be determined via trial and error for H + H2 system.

[[File:VC LOCATINGTS.PNG]]

===Trajectories from r1 = rts+δ, r2 = rts===

An MEP shows the mean energy path hence no vibration contributions of the molecules can be seen, it differs from a dynamics calculation as it does not take the gradient of the potential energy of previous steps into account, only the gradient at the current step is accounted for.

{| class="wikitable" border="1"
|+
! p1 (BC) !! p2 (AB) !! Etot !! Reactive? !! Trajectory !! Description of Dynamics
|-
| -1.25 || -2.5 || -99.018 || Yes || [[File:VC 1A TRAJECT.PNG|350px]] || cell
|-
| -1.5 || -2.0 || -100.456 || No || [[File:VC 1B TRAJECT.PNG|350px]] || cell
|-
| -1.5 || -2.5 || -98.956 || Yes || [[File:VC 1C TRAJECT.PNG|350px]] || cell
|-
| -2.5 || -5.0 || -84.956 || No || [[File:VC 1D TRAJECT.PNG|350px]] || cell
|-
| -2.5 || -5.2 || -83.426 || Yes || [[File:VC 1E TRAJECT.PNG|350px]] || cell
|}

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

== F - H - H System ==

===PES Inspection===

Literature shows that the H-F bond energy (565kJmol-1)1 is greater than that of H-H(462kJmol-1)1 hence the enthalpy of dissociation of the H-F molecule is greater, this is concordant with the potential energy surface for the F - H - H system. Figure X shows that F + H2 -> HF + H is an '''exothermic''' reaction, the potential energy surface shows the products having a lower energy than the reactants. The backward reaction is HF + H -> H2 + F and is therefore '''endothermic''', this reaction has a greater activation energy due to the greater bond enthalpy of the HF molecule requiring more energy for its dissociation.

By using Hammonds Postulate it can be approximated that the transition state will resemble the either the products or the reactants depending on which is closer in energy. Therefore, in the endothermic reaction the transition state will closely resemble the reactants whereas in an exothermic it closely resembles the products. The idea of Hammonds postulate was used in order to identify the inter-atomic distances at the transition state. For the endothermic reaction the known H-H bond length (0.744A) was used as the initial condition and the H-F distance was manipulated to determine the location of the transition state using a graph of the Internuclear distance vs Time to find the optimized H-F distance (1.8311 A) where the force of bond equals zero.

MEP calculations were carried out and a plot of the Energy vs Time was used in order to determine the activation of the forward and backward reactions.

[[File:Vc endothermicreaction.png|400px]]

HF + H -> H2 + F Activation Energy= 29 kcal/mol

F + H2 -> HF + H Activation Energy=

===Reaction Dynamics===

'''Reactive trajectory conditions:'''

R1(H2)= 0.74 A

R2(HF) = 2.30 A

P1 = -1.7

P2 = -2.4

[[File:VC PART2 REACTIVECONTOUR 2A.PNG|400px]] [[File:VC PART2 ENERGYVSTIME.PNG|400px]]

For the reactive trajectory shown in Figures ... of the F + H2, it can be seen from the Momenta vs Time graph that there is an interconversion between kinetic and potential energy as a fall in potential energy energy is opposed by a rise in kinetic energy, this is in concordance with the law of the conservation of energy. Therefore, for this exothermic reaction the potential energy is converted into kinetic energy giving rise to vibrations of the HF bond that this formed. Infrared spectroscopy can be used to confirm the conversion of energy by calculating the frequency of absorption of the bond.

An investigation into the reaction trajectories was conducted using the initial set of conditions listed below, '''P2 = -0.5''' was kept constant whereas '''P1''' was varied with the range X= -3 to 3.

R1(H2)= 0.74 A

R2(HF) = 2.30 A

P1 = X

P2 = -0.5

===References===
(1). Huheey, pps. A-21 to A-34; T.L. Cottrell, "The Strengths of Chemical Bonds," 2nd ed., Butterworths, London, 1958; B. deB. Darwent, "National Standard Reference Data Series," National Bureau of Standards, No. 31, Washington, DC, 1970; S.W. Benson, J. Chem. Educ., 42, 502 (1965).

MRD:VFC2398

2019-05-16T20:10:55Z

Vc2217: /* Reaction Dynamics */

=Molecular Dynamics=

==H + H2 system==

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

A reactive trajectory can be generated on a potential energy surface measuring the potential energy with respect to the AB and BC inter-atomic distances by applying a set of initial conditions for the positions of the atoms and their momenta. From the potential energy surface the trajectory can be determined by differentiating across the whole potential energy surface to find the minima. To find the energy of the transition state, the trajectory would be differentiated to find the maximum energy. At the maximum AB and BC inter-atomic distances will be equal.

Graphs depicting "Internuclear Distances vs Time" can also be used to determine the energy of a transition state.
W= ∫F. ds
E= ∫F. ds
de/ds = F

At the minimum of a potential energy curve, the force is zero so the molecule has no potential energy so it is no longer vibrating this results in the AB and BC to have no vibration so the periodic symmetric vibration wave becomes a straight line due to not having an amplitude as a result of the force on the bond being equal to zero. By inserting different values of '''r2 (AB)= r1 (BC)''' and '''P(AB)=P(BC) = 0''', the transition state bond length can be determined via trial and error for H + H2 system.

[[File:VC LOCATINGTS.PNG]]

===Trajectories from r1 = rts+δ, r2 = rts===

An MEP shows the mean energy path hence no vibration contributions of the molecules can be seen, it differs from a dynamics calculation as it does not take the gradient of the potential energy of previous steps into account, only the gradient at the current step is accounted for.

{| class="wikitable" border="1"
|+
! p1 (BC) !! p2 (AB) !! Etot !! Reactive? !! Trajectory !! Description of Dynamics
|-
| -1.25 || -2.5 || -99.018 || Yes || [[File:VC 1A TRAJECT.PNG|350px]] || cell
|-
| -1.5 || -2.0 || -100.456 || No || [[File:VC 1B TRAJECT.PNG|350px]] || cell
|-
| -1.5 || -2.5 || -98.956 || Yes || [[File:VC 1C TRAJECT.PNG|350px]] || cell
|-
| -2.5 || -5.0 || -84.956 || No || [[File:VC 1D TRAJECT.PNG|350px]] || cell
|-
| -2.5 || -5.2 || -83.426 || Yes || [[File:VC 1E TRAJECT.PNG|350px]] || cell
|}

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

== F - H - H System ==

===PES Inspection===

Literature shows that the H-F bond energy (565kJmol-1)1 is greater than that of H-H(462kJmol-1)1 hence the enthalpy of dissociation of the H-F molecule is greater, this is concordant with the potential energy surface for the F - H - H system. Figure X shows that F + H2 -> HF + H is an '''exothermic''' reaction, the potential energy surface shows the products having a lower energy than the reactants. The backward reaction is HF + H -> H2 + F and is therefore '''endothermic''', this reaction has a greater activation energy due to the greater bond enthalpy of the HF molecule requiring more energy for its dissociation.

By using Hammonds Postulate it can be approximated that the transition state will resemble the either the products or the reactants depending on which is closer in energy. Therefore, in the endothermic reaction the transition state will closely resemble the reactants whereas in an exothermic it closely resembles the products. The idea of Hammonds postulate was used in order to identify the inter-atomic distances at the transition state. For the endothermic reaction the known H-H bond length (0.744A) was used as the initial condition and the H-F distance was manipulated to determine the location of the transition state using a graph of the Internuclear distance vs Time to find the optimized H-F distance (1.8311 A) where the force of bond equals zero.

MEP calculations were carried out and a plot of the Energy vs Time was used in order to determine the activation of the forward and backward reactions.

[[File:Vc endothermicreaction.png|400px]]

HF + H -> H2 + F Activation Energy= 29 kcal/mol

F + H2 -> HF + H Activation Energy=

===Reaction Dynamics===

'''Reactive trajectory conditions:'''

R1(H2)= 0.74 A

R2(HF) = 2.30 A

P1 = -1.7

P1 = -2.4

[[File:VC PART2 REACTIVECONTOUR 2A.PNG|400px]]

[[File:VC PART2 ENERGYVSTIME.PNG|400px]]

For the reactive trajectory shown in Figures ... of the F + H2, it can be seen from the Momenta vs Time graph that there is an interconversion between kinetic and potential energy as a fall in potential energy energy is opposed by a rise in kinetic energy, this is in concordance with the law of the conservation of energy. Therefore, for this exothermic reaction the potential energy is converted into kinetic energy giving rise to vibrations of the HF bond that this formed. Infrared spectroscopy can be used to confirm the conversion of energy by calculating the frequency of absorption of the bond.

Setup a calculation starting on the side of the reactants of F + H2, at the bottom of the well rHH = 0.74, with a momentum pFH = -0.5, and explore several values of pHH in the range -3 to 3 (explore values also close to these limits). What do you observe? Note that we are putting a significant amount of energy (much more than the activation energy) into the system on the H - H vibration.

===References===
(1). Huheey, pps. A-21 to A-34; T.L. Cottrell, "The Strengths of Chemical Bonds," 2nd ed., Butterworths, London, 1958; B. deB. Darwent, "National Standard Reference Data Series," National Bureau of Standards, No. 31, Washington, DC, 1970; S.W. Benson, J. Chem. Educ., 42, 502 (1965).

MRD:VFC2398

2019-05-16T20:00:02Z

Vc2217: /* PES Inspection */

=Molecular Dynamics=

==H + H2 system==

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

A reactive trajectory can be generated on a potential energy surface measuring the potential energy with respect to the AB and BC inter-atomic distances by applying a set of initial conditions for the positions of the atoms and their momenta. From the potential energy surface the trajectory can be determined by differentiating across the whole potential energy surface to find the minima. To find the energy of the transition state, the trajectory would be differentiated to find the maximum energy. At the maximum AB and BC inter-atomic distances will be equal.

Graphs depicting "Internuclear Distances vs Time" can also be used to determine the energy of a transition state.
W= ∫F. ds
E= ∫F. ds
de/ds = F

At the minimum of a potential energy curve, the force is zero so the molecule has no potential energy so it is no longer vibrating this results in the AB and BC to have no vibration so the periodic symmetric vibration wave becomes a straight line due to not having an amplitude as a result of the force on the bond being equal to zero. By inserting different values of '''r2 (AB)= r1 (BC)''' and '''P(AB)=P(BC) = 0''', the transition state bond length can be determined via trial and error for H + H2 system.

[[File:VC LOCATINGTS.PNG]]

===Trajectories from r1 = rts+δ, r2 = rts===

An MEP shows the mean energy path hence no vibration contributions of the molecules can be seen, it differs from a dynamics calculation as it does not take the gradient of the potential energy of previous steps into account, only the gradient at the current step is accounted for.

{| class="wikitable" border="1"
|+
! p1 (BC) !! p2 (AB) !! Etot !! Reactive? !! Trajectory !! Description of Dynamics
|-
| -1.25 || -2.5 || -99.018 || Yes || [[File:VC 1A TRAJECT.PNG|350px]] || cell
|-
| -1.5 || -2.0 || -100.456 || No || [[File:VC 1B TRAJECT.PNG|350px]] || cell
|-
| -1.5 || -2.5 || -98.956 || Yes || [[File:VC 1C TRAJECT.PNG|350px]] || cell
|-
| -2.5 || -5.0 || -84.956 || No || [[File:VC 1D TRAJECT.PNG|350px]] || cell
|-
| -2.5 || -5.2 || -83.426 || Yes || [[File:VC 1E TRAJECT.PNG|350px]] || cell
|}

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

== F - H - H System ==

===PES Inspection===

Literature shows that the H-F bond energy (565kJmol-1)1 is greater than that of H-H(462kJmol-1)1 hence the enthalpy of dissociation of the H-F molecule is greater, this is concordant with the potential energy surface for the F - H - H system. Figure X shows that F + H2 -> HF + H is an '''exothermic''' reaction, the potential energy surface shows the products having a lower energy than the reactants. The backward reaction is HF + H -> H2 + F and is therefore '''endothermic''', this reaction has a greater activation energy due to the greater bond enthalpy of the HF molecule requiring more energy for its dissociation.

By using Hammonds Postulate it can be approximated that the transition state will resemble the either the products or the reactants depending on which is closer in energy. Therefore, in the endothermic reaction the transition state will closely resemble the reactants whereas in an exothermic it closely resembles the products. The idea of Hammonds postulate was used in order to identify the inter-atomic distances at the transition state. For the endothermic reaction the known H-H bond length (0.744A) was used as the initial condition and the H-F distance was manipulated to determine the location of the transition state using a graph of the Internuclear distance vs Time to find the optimized H-F distance (1.8311 A) where the force of bond equals zero.

MEP calculations were carried out and a plot of the Energy vs Time was used in order to determine the activation of the forward and backward reactions.

[[File:Vc endothermicreaction.png|400px]]

HF + H -> H2 + F Activation Energy= 29 kcal/mol

F + H2 -> HF + H Activation Energy=

===Reaction Dynamics===

'''Reactive trajectory conditions:'''

R1(H2)= 0.74 A

R2(HF) = 2.30 A

P1 = -1.7

P1 = -2.4

[[File:VC PART2 REACTIVECONTOUR 2A.PNG|400px]]

[[File:VC PART2 ENERGYVSTIME.PNG|400px]]

For the reactive trajectory shown in Figures ... of the F + H2, it can be seen that the

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

Setup a calculation starting on the side of the reactants of F + H2, at the bottom of the well rHH = 0.74, with a momentum pFH = -0.5, and explore several values of pHH in the range -3 to 3 (explore values also close to these limits). What do you observe? Note that we are putting a significant amount of energy (much more than the activation energy) into the system on the H - H vibration.

===References===
(1). Huheey, pps. A-21 to A-34; T.L. Cottrell, "The Strengths of Chemical Bonds," 2nd ed., Butterworths, London, 1958; B. deB. Darwent, "National Standard Reference Data Series," National Bureau of Standards, No. 31, Washington, DC, 1970; S.W. Benson, J. Chem. Educ., 42, 502 (1965).

MRD:VFC2398

2019-05-16T19:59:35Z

Vc2217: /* F - H - H System */

=Molecular Dynamics=

==H + H2 system==

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

A reactive trajectory can be generated on a potential energy surface measuring the potential energy with respect to the AB and BC inter-atomic distances by applying a set of initial conditions for the positions of the atoms and their momenta. From the potential energy surface the trajectory can be determined by differentiating across the whole potential energy surface to find the minima. To find the energy of the transition state, the trajectory would be differentiated to find the maximum energy. At the maximum AB and BC inter-atomic distances will be equal.

Graphs depicting "Internuclear Distances vs Time" can also be used to determine the energy of a transition state.
W= ∫F. ds
E= ∫F. ds
de/ds = F

At the minimum of a potential energy curve, the force is zero so the molecule has no potential energy so it is no longer vibrating this results in the AB and BC to have no vibration so the periodic symmetric vibration wave becomes a straight line due to not having an amplitude as a result of the force on the bond being equal to zero. By inserting different values of '''r2 (AB)= r1 (BC)''' and '''P(AB)=P(BC) = 0''', the transition state bond length can be determined via trial and error for H + H2 system.

[[File:VC LOCATINGTS.PNG]]

===Trajectories from r1 = rts+δ, r2 = rts===

An MEP shows the mean energy path hence no vibration contributions of the molecules can be seen, it differs from a dynamics calculation as it does not take the gradient of the potential energy of previous steps into account, only the gradient at the current step is accounted for.

{| class="wikitable" border="1"
|+
! p1 (BC) !! p2 (AB) !! Etot !! Reactive? !! Trajectory !! Description of Dynamics
|-
| -1.25 || -2.5 || -99.018 || Yes || [[File:VC 1A TRAJECT.PNG|350px]] || cell
|-
| -1.5 || -2.0 || -100.456 || No || [[File:VC 1B TRAJECT.PNG|350px]] || cell
|-
| -1.5 || -2.5 || -98.956 || Yes || [[File:VC 1C TRAJECT.PNG|350px]] || cell
|-
| -2.5 || -5.0 || -84.956 || No || [[File:VC 1D TRAJECT.PNG|350px]] || cell
|-
| -2.5 || -5.2 || -83.426 || Yes || [[File:VC 1E TRAJECT.PNG|350px]] || cell
|}

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

== F - H - H System ==

===PES Inspection===

Literature shows that the H-F bond energy (565kJmol-1)-1 is greater than that of H-H(462kJmol-1)-1 hence the enthalpy of dissociation of the H-F molecule is greater, this is concordant with the potential energy surface for the F - H - H system. Figure X shows that F + H2 -> HF + H is an '''exothermic''' reaction, the potential energy surface shows the products having a lower energy than the reactants. The backward reaction is HF + H -> H2 + F and is therefore '''endothermic''', this reaction has a greater activation energy due to the greater bond enthalpy of the HF molecule requiring more energy for its dissociation.

By using Hammonds Postulate it can be approximated that the transition state will resemble the either the products or the reactants depending on which is closer in energy. Therefore, in the endothermic reaction the transition state will closely resemble the reactants whereas in an exothermic it closely resembles the products. The idea of Hammonds postulate was used in order to identify the inter-atomic distances at the transition state. For the endothermic reaction the known H-H bond length (0.744A) was used as the initial condition and the H-F distance was manipulated to determine the location of the transition state using a graph of the Internuclear distance vs Time to find the optimized H-F distance (1.8311 A) where the force of bond equals zero.

MEP calculations were carried out and a plot of the Energy vs Time was used in order to determine the activation of the forward and backward reactions.

[[File:Vc endothermicreaction.png|400px]]

HF + H -> H2 + F Activation Energy= 29 kcal/mol

F + H2 -> HF + H Activation Energy=

===Reaction Dynamics===

'''Reactive trajectory conditions:'''

R1(H2)= 0.74 A

R2(HF) = 2.30 A

P1 = -1.7

P1 = -2.4

[[File:VC PART2 REACTIVECONTOUR 2A.PNG|400px]]

[[File:VC PART2 ENERGYVSTIME.PNG|400px]]

For the reactive trajectory shown in Figures ... of the F + H2, it can be seen that the

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

Setup a calculation starting on the side of the reactants of F + H2, at the bottom of the well rHH = 0.74, with a momentum pFH = -0.5, and explore several values of pHH in the range -3 to 3 (explore values also close to these limits). What do you observe? Note that we are putting a significant amount of energy (much more than the activation energy) into the system on the H - H vibration.

===References===
(1). Huheey, pps. A-21 to A-34; T.L. Cottrell, "The Strengths of Chemical Bonds," 2nd ed., Butterworths, London, 1958; B. deB. Darwent, "National Standard Reference Data Series," National Bureau of Standards, No. 31, Washington, DC, 1970; S.W. Benson, J. Chem. Educ., 42, 502 (1965).

File:VC PART2 ENERGYVSTIME.PNG

2019-05-16T19:55:37Z

Vc2217:

File:VC PART2 REACTIVECONTOUR 2A.PNG

2019-05-16T19:55:01Z

Vc2217:

MRD:VFC2398

2019-05-16T19:39:52Z

Vc2217: /* F - H - H System */

MRD:VFC2398

2019-05-16T19:03:37Z

Vc2217: /* Molecular Dynamics */

File:Vc endothermicreaction.png

2019-05-16T18:39:50Z

Vc2217:

File:Vc endothermic.png

2019-05-16T18:38:09Z

Vc2217:

MRD:VFC2398

2019-05-16T16:00:52Z

Vc2217: /* Molecular Dynamics */

MRD:VFC2398

2019-05-15T11:02:20Z

Vc2217: /* Trajectories from r1 = rts+δ, r2 = rts */

MRD:VFC2398

2019-05-15T11:00:28Z

Vc2217: /* Dynamics from the transition state region */

MRD:VFC2398

2019-05-15T11:00:09Z

Vc2217: /* H + H2 system */

MRD:VFC2398

2019-05-15T10:57:01Z

Vc2217: /* Trajectories from r1 = rts+δ, r2 = rt s */

=Molecular Dynamics=

==H + H2 system==

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

A reactive trajectory can be generated on a potential energy surface measuring the potential energy with respect to the AB and BC inter-atomic distances by applying a set of initial conditions for the positions of the atoms and their momenta. From the potential energy surface the trajectory can be determined by differentiating across the whole potential energy surface to find the minima. To find the energy of the transition state, the trajectory would be differentiated to find the maximum energy. At the maximum AB and BC inter-atomic distances will be equal.

Graphs depicting "Internuclear Distances vs Time" can also be used to determine the energy of a transition state.
W= ∫F. ds
E= ∫F. ds
de/ds = F

At the minimum of a potential energy curve, the force is zero so the molecule has no potential energy so it is no longer vibrating this results in the AB and BC to have no vibration so the periodic symmetric vibration wave becomes a straight line due to not having an amplitude as a result of the force on the bond being equal to zero. By inserting different values of AB=BC and P(AB)=P(BC) = 0, the transition state bond length can be determined via trial and error for H + H2 system.

[[File:VC LOCATINGTS.PNG]]

===Trajectories from r1 = rts+δ, r2 = rt s===

An MEP shows the mean energy path hence no vibration contributions of the molecules can be seen, it differs from a dynamics calculation as it does not take the gradient of the potential energy of previous steps into account, only the gradient at the current step is accounted for.

{| class="wikitable" border="1"
|
! p1 (BC) !! p2 (AB) !! Etot !! Reactive? !! Trajectory !! Description of Dynamics
|-
| -1.25 || -2.5 || -99.018 || Yes || [[File:VC 1A TRAJECT.PNG|350px]] || cell
|-
| -1.5 || -2.0 || -100.456 || No || [[File:VC 1B TRAJECT.PNG|350px]] || cell
|-
| -1.5 || -2.5 || -98.956 || Yes || [[File:VC 1C TRAJECT.PNG|350px]] || cell
|-
| -2.5 || -5.0 || -84.956 || No || [[File:VC 1D TRAJECT.PNG|350px]] || cell
|-
| -2.5 || -5.2 || -83.426 || Yes || [[File:VC 1E TRAJECT.PNG|350px]] || cell
|}

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

== F - H - H System ==

MRD:VFC2398

2019-05-15T10:36:55Z

Vc2217: /* Molecular Dynamics */

=Molecular Dynamics=

==H + H2 system==

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

A reactive trajectory can be generated on a potential energy surface measuring the potential energy with respect to the AB and BC inter-atomic distances by applying a set of initial conditions for the positions of the atoms and their momenta. From the potential energy surface the trajectory can be determined by differentiating across the whole potential energy surface to find the minima. To find the energy of the transition state, the trajectory would be differentiated to find the maximum energy. At the maximum AB and BC inter-atomic distances will be equal.

Graphs depicting "Internuclear Distances vs Time" can also be used to determine the energy of a transition state.
W= ∫F. ds
E= ∫F. ds
de/ds = F

At the minimum of a potential energy curve, the force is zero so the molecule has no potential energy so it is no longer vibrating this results in the AB and BC to have no vibration so the periodic symmetric vibration wave becomes a straight line due to not having an amplitude as a result of the force on the bond being equal to zero. By inserting different values of AB=BC and P(AB)=P(BC) = 0, the transition state bond length can be determined via trial and error for H + H2 system.

[[File:VC LOCATINGTS.PNG]]

===Trajectories from r1 = rts+δ, r2 = rt s===

An MEP shows the mean energy path hence no vibration contributions of the molecules can be seen, it differs from a dynamics calculation as it does not take the gradient of the potential energy of previous steps into account, only the gradient at the current step is accounted for.

{| class="wikitable" border="1"
|+ caption
! p1 !! p2 !! Etot !! Reactive? !! Trajectory !! Description of Dynamics
|-
| -1.25 || -2.5 || -99.018 || Yes || [[File:VC 1A TRAJECT.PNG|350px]] || cell
|-
| -1.5 || -2.0 || -100.456 || No || [[File:VC 1B TRAJECT.PNG|350px]] || cell
|-
| -1.5 || -2.5 || -98.956 || Yes || [[File:VC 1C TRAJECT.PNG|350px]] || cell
|-
| -2.5 || -5.0 || -84.956 || No || [[File:VC 1D TRAJECT.PNG|350px]] || cell
|-
| -2.5 || -5.2 || -83.426 || Yes || [[File:VC 1E TRAJECT.PNG|350px]] || cell
|}

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

== F - H - H System ==

MRD:VFC2398

2019-05-15T10:35:33Z

Vc2217: /* Molecular Dynamics */

=Molecular Dynamics=

==H + H2 system==

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

A reactive trajectory can be generated on a potential energy surface measuring the potential energy with respect to the AB and BC inter-atomic distances by applying a set of initial conditions for the positions of the atoms and their momenta. From the potential energy surface the trajectory can be determined by differentiating across the whole potential energy surface to find the minima. To find the energy of the transition state, the trajectory would be differentiated to find the maximum energy. At the maximum AB and BC inter-atomic distances will be equal.

Graphs depicting "Internuclear Distances vs Time" can also be used to determine the energy of a transition state.
W= ∫F. ds
E= ∫F. ds
de/ds = F

At the minimum of a potential energy curve, the force is zero so the molecule has no potential energy so it is no longer vibrating this results in the AB and BC to have no vibration so the periodic symmetric vibration wave becomes a straight line due to not having an amplitude as a result of the force on the bond being equal to zero. By inserting different values of AB=BC and P(AB)=P(BC) = 0, the transition state bond length can be determined via trial and error for H + H2 system.

[[File:VC LOCATINGTS.PNG]]

===Trajectories from r1 = rts+δ, r2 = rt s===

An MEP shows the mean energy path hence no vibration contributions of the molecules can be seen, it differs from a dynamics calculation as it does not take the gradient of the potential energy of previous steps into account, only the gradient at the current step is accounted for.

{| class="wikitable" border="1"
|+ caption
! p1 !! p2 !! Etot !! Reactive? !! Trajectory !! Description of Dynamics
|-
| -1.25 || -2.5 || -99.018 || Yes || [[File:VC 1A TRAJECT.PNG|350px]] || cell
|-
| -1.5 || -2.0 || -100.456 || No || [[File:VC 1B TRAJECT.PNG|350px]] || cell
|-
| -1.5 || -2.5 || -98.956 || Yes || [[File:VC 1C TRAJECT.PNG|350px]] || cell
|-
| -2.5 || -5.0 || -84.956 || No || [[File:VC 1D TRAJECT.PNG|350px]] || cell
|-
| -2.5 || -5.2 || -83.426 || Yes || [[File:VC 1E TRAJECT.PNG|350px]] || cell
|}

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

MRD:VFC2398

2019-05-15T10:34:12Z

Vc2217: /* Molecular Dynamics */

=Molecular Dynamics=

==H + H2 system==

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

A reactive trajectory can be generated on a potential energy surface measuring the potential energy with respect to the AB and BC inter-atomic distances by applying a set of initial conditions for the positions of the atoms and their momenta. From the potential energy surface the trajectory can be determined by differentiating across the whole potential energy surface to find the minima. To find the energy of the transition state, the trajectory would be differentiated to find the maximum energy. At the maximum AB and BC inter-atomic distances will be equal.

Graphs depicting "Internuclear Distances vs Time" can also be used to determine the energy of a transition state.
W= ∫F. ds
E= ∫F. ds
de/ds = F

At the minimum of a potential energy curve, the force is zero so the molecule has no potential energy so it is no longer vibrating this results in the AB and BC to have no vibration so the periodic symmetric vibration wave becomes a straight line due to not having an amplitude as a result of the force on the bond being equal to zero. By inserting different values of AB=BC and P(AB)=P(BC) = 0, the transition state bond length can be determined via trial and error for H + H2 system.

[[File:VC LOCATINGTS.PNG]]

===Trajectories from r1 = rts+δ, r2 = rt s===

An MEP shows the mean energy path hence no vibration contributions of the molecules can be seen, it differs from a dynamics calculation as it does not take the gradient of the potential energy of previous steps into account, only the gradient at the current step is accounted for.

{| class="wikitable" border="1"
|+ caption
! p1 !! p2 !! Etot !! Reactive? !! Trajectory !! Description of Dynamics
|-
| -1.25 || -2.5 || -99.018 || Yes || [[File:VC 1A TRAJECT.PNG|350px]] || cell
|-
| -1.5 || -2.0 || -100.456 || No || [[File:VC 1B TRAJECT.PNG|350px]] || cell
|-
| -1.5 || -2.5 || -98.956 || Yes || [[File:VC 1C TRAJECT.PNG|350px]] || cell
|-
| -2.5 || -5.0 || -84.956 || No || [[File:VC 1D TRAJECT.PNG|350px]] || cell
|-
| -2.5 || -5.2 || -83.426 || Yes || [[File:VC 1E TRAJECT.PNG|350px]] || cell
|}

MRD:VFC2398

2019-05-15T10:33:55Z

Vc2217: /* Molecular Dynamics */

=Molecular Dynamics=

==H + H2 system==

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

A reactive trajectory can be generated on a potential energy surface measuring the potential energy with respect to the AB and BC inter-atomic distances by applying a set of initial conditions for the positions of the atoms and their momenta. From the potential energy surface the trajectory can be determined by differentiating across the whole potential energy surface to find the minima. To find the energy of the transition state, the trajectory would be differentiated to find the maximum energy. At the maximum AB and BC inter-atomic distances will be equal.

Graphs depicting "Internuclear Distances vs Time" can also be used to determine the energy of a transition state.
W= ∫F. ds
E= ∫F. ds
de/ds = F

At the minimum of a potential energy curve, the force is zero so the molecule has no potential energy so it is no longer vibrating this results in the AB and BC to have no vibration so the periodic symmetric vibration wave becomes a straight line due to not having an amplitude as a result of the force on the bond being equal to zero. By inserting different values of AB=BC and P(AB)=P(BC) = 0, the transition state bond length can be determined via trial and error for H + H2 system.

[[File:VC LOCATINGTS.PNG]]

===Trajectories from r1 = rts+δ, r2 = rt s===

An MEP shows the mean energy path hence no vibration contributions of the molecules can be seen, it differs from a dynamics calculation as it does not take the gradient of the potential energy of previous steps into account, only the gradient at the current step is accounted for.
-1.25 -2.5
-1.5 -2.0
-1.5 -2.5
-2.5 -5.0
-2.5 -5.2

{| class="wikitable" border="1"
|+ caption
! p1 !! p2 !! Etot !! Reactive? !! Trajectory !! Description of Dynamics
|-
| -1.25 || -2.5 || -99.018 || Yes || [[File:VC 1A TRAJECT.PNG|350px]] || cell
|-
| -1.5 || -2.0 || -100.456 || No || [[File:VC 1B TRAJECT.PNG|350px]] || cell
|-
| -1.5 || -2.5 || -98.956 || Yes || [[File:VC 1C TRAJECT.PNG|350px]] || cell
|-
| -2.5 || -5.0 || -84.956 || No || [[File:VC 1D TRAJECT.PNG|350px]] || cell
|-
| -2.5 || -5.2 || -83.426 || Yes || [[File:VC 1E TRAJECT.PNG|350px]] || cell
|}

File:VC 1E TRAJECT.PNG

2019-05-15T10:33:22Z

Vc2217:

File:VC 1D TRAJECT.PNG

2019-05-15T10:32:27Z

Vc2217:

File:VC 1C TRAJECT.PNG

2019-05-15T10:31:22Z

Vc2217:

File:VC 1B TRAJECT.PNG

2019-05-15T10:29:54Z

Vc2217:

File:VC 1A TRAJECT.PNG

2019-05-15T10:26:29Z

Vc2217:

File:VC LOCATINGTS.PNG

2019-05-15T10:11:38Z

Vc2217: Vc2217 uploaded a new version of File:VC LOCATINGTS.PNG

File:VC LOCATINGTS.PNG

2019-05-15T10:10:21Z

Vc2217:

MRD:VFC2398

2019-05-15T09:50:21Z

Vc2217: Created page with "=Molecular Dynamics= ==H + H2 system== ===Dynamics from the transition state region=== A reactive trajectory can be generated on a potential energy surface measuring the po..."