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MRD:sm6416

2018-05-25T16:41:49Z

Sm6416: /* Reaction Dynamics */

==H2 + H Exercise 1==

===Transition State Dynamics===

The transition state is the stage in a reaction coordinate that must be passed through in order for a reaction to occur and occurs at a saddle point, as shown by the numerous surface plots on this page. The first derivative highlights the positions along the reaction coordinate where the gradient equals zero. However, in order to determine if a saddle point ensues, the second derivative of the gradient must be taken. A saddle point is only present if the second derivative > 0.

Another way to think of the transition state is by thinking of the tangent that can be formed at the transition state itself. This tangent will follow the reaction coordinate profile and therefore is expected to be a maximum, where the gradient = 0. A line can be drawn to the normal of the tangent at the selected transition state. This path would show a minimum, where the gradient again = 0, at the intersection of the tangent with normal if the transition state has been correctly identified. It is only in this scenario that a transition state can be determined as one.

===Locating the Transition State===

The transition state was determined through iterations of both r1 and r2 which resulted in the smallest displacement of momenta along with no displacement as shown by the contour plot. This method determined at rts = 0.907743.

[[File:sm6416_Transition_State_Contour.png|thumb|none|350px|Contour plot demonstrating rts = 0.907743 as a result of no fluctuations from the initial input, hence the complex is at the transition state.]]

[[File:sm6416_Transition_State_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating minimum, and almost zero, momentum at rts = 0.907743.]]

[[File:sm6416_Transition_State_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot demonstrating no fluctuations in distance and hence rts = 0.907743.]]

===Reaction Path===

The minimum energy path (MEP) is defined as the lowest path the reaction must follow to form the products and is the downhill motion from the transition state. It can be applied in both directions in the case in question. The MEP views the system as static as it resets the velocity to zero at each step. Whereas the trajectory is very much dynamic and the momenta is accounted for, this is reflected in the vibrational oscillation of the molecule as it passes along the minimum well towards the products.

====MEP====

Initial conditions of r1 = rts + 0.01 = 0.917743, r2 = rts = 0.907743 and p1 = p2 = 0 for the MEP simulation.

[[File:sm6416_MEP_Surface.png|thumb|none|350px|Surface plot highlighting the minimum energy path (MEP), as the reaction returns to the reactants without fully passing through the transition state.]]

[[File:sm6416_MEP_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating zero momentum, as inputted, and more importantly not change in momentum with running the simulation.]]

[[File:sm6416_MEP_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot showing that the reactants reach the transition state at the interception of r1 = r2. r1 quickly reaches a constant value, namely the equilibrium bond length of the reactant molecule. r2 increases logarithmically as time progresses, this represents an increasing distance of Ha from Hb-Hc and a continuing loss of momentum.]]

Final values from the MEP simulation.

r1 = 2.76195

r2 = 0.75883

These values reflect the minimum trajectory for a successful reaction.

p1 = p2 = 0

====Dynamic====

[[File:sm6416_Dynamic_Surface.png|thumb|none|350px|Surface plot highlighting the minimum energy path (MEP) with oscillation of the reactants, as the reaction returns to the reactants without fully passing through the transition state. It is therefore evident that the momentum as a result of the vibrational oscillation does not provide enough energy to proceed to the products.]]

[[File:sm6416_Dynamic_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating the momenta associated with the oscillating reactants.]]

[[File:sm6416_Dynamic_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot showing that the reactants reach the transition state at the interception of r1 = r2. r1 quickly decreases and oscillates about a constant value, namely the equilibrium bond length of the reactant molecule. r2 increases linearly as time progresses, this represents an increasing distance of Ha from Hb-Hc with a constant momentum.]]

Dynamic simulation final values

r1 = 10.0045

r2 = 0.75883

p1 = 2.48523

p2 = 1.29898

p(average) = 1.90409

With r1 = rts and r2 = rts + 0.01 would simply produce the same answer however the values would be flipped to the other distance. In other words r1 = 0.75883 and r2 = 10.0045 would be the output values.

Maintaining the final trajectories as calculated from the dynamic simulation and reversing the sign of the momenta, the reaction proceeds in the reverse direction to the products.

===Reactivity of Trajectories===

These simulations are restricted by the number of steps the program can handle, however a sound understanding of the reaction can be appreciated and the reactivity of each scenario can be determined appropriately.

{| class="wikitable" border=2
! Simulation !! p1 !! p2 !! Energy (kcal/mol) !! Reactivity !! Evidence !! Description
|-
| 1 || -1.25 || -2.5 || 5.03500 || Reactive || [[File:sm6416_MEP_Figure1.png|thumb|none|350px]] || The reactants proceed through the transition state and to the products. The r2 distance decreases to the equilibrium bond length, whilst r1 simultaneously exhibits dissociation and increases beyond the scope of the graph. The small momenta attributed to the reactants is reflected in the vibrationally oscillating products, with a small amplitude.
|-
| 2 || -1.5 || -2.0 || 3.62879 || Unreactive || [[File:sm6416_MEP_Figure2.png|thumb|none|350px]] || This is unreactive as the oscillating reactants reach the transition state point and r1 immediately returns to the initial bond length, whilst r2 continues to increase as it moves away from the H2 molecule.
|-
| 3 || -1.5 || -2.5 || 5.13738 || Reactive || [[File:sm6416_MEP_Figure3.png|thumb|none|350px]] || This simulation shows a reactive pathway that is very similar to simulation 1, however due to the greater momenta associated with the reactants, as inputted, vibrational oscillations with a greater amplitude can be observed.
|-
| 4 || -2.5 || -5.0 || 9.86678 || Unreactive || [[File:sm6416_MEP_Figure4.png|thumb|none|350px]] || Initially seen here are oscillating reactants with a very large amplitude. However, this simulation is unreactive despite the reactants going through the transition state and towards the product, they return to the initial reactants.
|-
| 5 || -2.5 || -5.2 || 11.80780 || Reactive || [[File:sm6416_MEP_Figure5.png|thumb|none|350px]] || Like simulation 4, this simulation shows a large oscillating amplitude, whereas in this scenario after passing through the transition state, the products are completely obtained. The slight increase in the p2 momentum can be seen to result in the products.
|}

====Transition State Theory====

Transition State Theory (TST) assumes a quasi-equilibrium between reactants and the transition state. The reaction between the transition state and products is irreversible and therefore is unable to return to the reactants, however many of the surface plots on this page show the complete antithesis of this highlighting a dichotomy between theory and experimental. TST further assumes that fluctuation as to whether the transition complexes go towards reactants or products are independent of each other and hence the rate of one can not be determined by the other.

TST is an excellent qualitative tool and can identify the enthalpy, standard entropy and standard Gibbs energy of activation. Despite this, it the method is unable to accurately determine these true values in line with experimental results as doing so would require a deep understanding of the potential energy surface of each reaction. Therefore, TST under estimates the reaction rate in comparison to the experimental values. When TST was developed in 1935 a lack of adequate computer software to accurately map potential energy surfaces with the relative quantum mechanical contributions to determine the distribution of electron density, unlike there is today. Hence resulting in a less accurate and longer method to map these surfaces for each reaction.

==F-H-H System Exercise 2==
===Potential Energy Surface Inspection===
====Energetics====

F + H2 is an exothermic reaction as can be seen from the surface plot, the reaction progresses from a small H-H distance to a longer one, whilst H-F simultaneously equilibriates about the F-H bond length. It can be seen that the products are lower, and hence more stable, in energy than the reactants.

F-H + H is simply the reverse reaction that passes through the same transition state, hence this reaction is endothermic with the products being higher in energy than the reactants. There is an overall gain of energy.

With this information in mind, the F-H bond is more stable and thus stronger than the H-H bond. The main factors to this argument is the greater electronegativity of F leading to a stronger contribution to the bond than the molecular orbitals. Hence the overlap of molecular orbitals is a weaker factor in the bond strength.

[[File:sm6416_FHH_Surface.png|thumb|none|350px|Surface plot highlighting the energetics of the F-H-H system.]]

[[File:sm6416_HHF_Surface.png|thumb|none|350px|Surface plot highlighting the energetics of the H-H-F system.]]

====Transition State====

Hammond's postulate aids in finding the transition state; it relates the composition of the transition complex to either the reactants or products for an early or late transition state respectively. In the scenario under investigation for F + H2 an early transition state is present as the reaction is exothermic in this direction, hence the transition state resembles the reactants more.

This guidance proved useful in determining the transition state complex at r1 = F-H = 1.810076 Angstrom and r2 = H-H = 0.74634 Angstrom, as can be seen from the surface and contour plots below showing the absence of displacement to either reactants or products. Furthermore the Momenta vs Time plot indicates a very small momenta of the overall system, without any deviation or substantial change in the momenta.

[[File:sm6416_FHH_Transition_State_Contour.png|thumb|none|350px|Contour plot demonstrating rts as a result of no fluctuations from the initial input, hence the complex is metaphorically sitting on the transition state.]]

[[File:sm6416_FHH_Transition_State_Momenta_Time.png|thumb|none|350px|Momenta vs Time plot demonstrating minimum, and almost zero, momentum at rts.]]

[[File:sm6416_FHH_Transition_State_Surface.png|thumb|none|350px]]

====Activation Energy====

The activation energy for the exothermic reaction was calculated through a 500000 step MEP simulation with input values of r1 = 1.820076, r2 = 0.74634 and p1 = p2 = 0. It was required that after following the minimum energy path, the gradient of the line signifying the reactants was constant.

The activation energy is reported at +0.258 kcal/mol for the exothermic process.

[[File:sm6416_FHH_Activation_Energy_1.png|thumb|none|350px|Energy vs Time graph highlighting the activation energy of the exothermic reaction.]]

The activation energy for the endothermic process was determined with the following parameters: r1 = 1.800076, r2 = 0.74634, p1 = p2 = 0 with 250000 steps. These parameters 'tipped' the reaction towards the FH + H reactants. The reported activation energy was +30.277 kcal/mol.

[[File:sm6416_FHH_Activation_Energy_2.png|thumb|none|350px|Energy vs Time graph highlighting the activation energy of the endothermic reaction.]]

It can hence be seen that the exothermic reaction of F + H2 --> F-H + H only requires a small activation energy as the products are substantially more thermodynamically stable than the reactants.

===Reaction Dynamics===

In this exothermic reaction, the potential energy is mainly converted into vibrational energy of the FH bond, along with heat. As a result of this vibrational energy in the FH bond, vibrational levels above the ground state will become partially populated. In this manner, by recording an IR spectrum of the products, the main F-H will be observed alongside an overtone, with the intensity of this overtone relating to the population of this vibrationally excited state, which can then be used to determine the vibrational energy in the bond itself.

In this same vein, IR chemiluminescence can be employed to yield the same result by measuring the wavelength, and subsequent vibrational energy of the FH bond, of the infrared light that is irradiated from the products and being excited with incident light.

Calorimetry is not a suitable method to measure the vibrational energy of the bond, as this method merely takes an average of both translational and vibrational energies present in the system.

As the momentum closes towards the boundaries of -3 < p < +3, the system passes through transition state but returns to reactant well. This shows that the excess momentum of the system in the product well is sufficient to overcome the high activation energy and return to the thermodynamically unfavourable reactants.

The following parameters were employed for all simulations rFH = 2.3, rHH = 0.74 with 500 steps calculated.

{| class="wikitable" border=2
! Simulation !! pHH !! pFH !! Surface Plot !! Momenta vs Time Plot !! Observations !!
|-
| 1 || -2.5 || -1.5 || [[File:sm6416_Trajectory_1_Surface.png|thumb|none|350px]] ||[[File:sm6416_Trajectory_1_Momenta.png|thumb|none|350px]] || This trajectory results in a successful reaction as seen from the surface plot; the reactants proceed through the transition state and continue into the product well, whilst continually oscillating as a result of the momentum gained.
|-
| 2 || -0.5 || -0.5 || [[File:sm6416_Trajectory_2_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_2_Momenta.png|thumb|none|350px]] || This momentum does not proceed to a reaction. Through the dynamic animation it can be seen that the HH molecule does not possess enough momentum to translate towards F. Therefore the system does not translate out of the reactant well, as seen in the surface plot, since there is not enough energy to overcome the activation energy. The momenta plot simply shows a small up trend, this is expected due to the long range electrostatic force of attraction between F and HH, resulting in a slight increase in the HH vibration velocity. There is no drastic change in the momenta of either F or HH that would otherwise indicate the occurrence of a reaction, as seen in simulation 1 above.
|-
| 3 || +0.5 || -0.5 || [[File:sm6416_Trajectory_3_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_3_Momenta.png|thumb|none|350px]] || This simulation shows an unreactive path, as can be seen from the surface plot, the system remains in the reactant well as it does not overcome the small activation energy for the exothermic reaction to proceed. As in simulation 2, the momentum amplitude of the oscillating HH remains constant however the overall momenta of the system increases due to a slight translation towards F, thus increasing electrostatic attraction forces resulting in this slight overall momenta increase.
|-
| 4 || -1.6 || -0.5 || [[File:sm6416_Trajectory_4_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_4_Momenta.png|thumb|none|350px]] || This simulation is very similar to simulations 2 & 3 in that the system remains in the reactant well as there is not sufficient energy to overcome the activation energy. However as a result of the greater HH momentum, the oscillation amplitude is greater than both simulation 1 & 2.
|-
| 5 || +1.6 || -0.5 || [[File:sm6416_Trajectory_5_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_5_Momenta.png|thumb|none|350px]] || Firstly, this simulation is unreactive as can be seen from the surface plot. In comparison to simulation 4, HH momentum sign has been changed and as a result this has led to not only a greater oscillating amplitude but also a larger translation towards F. So much so in the latter than the Momenta vs Time plot shows an increase in FH oscillation momentum as the electrostatic forces of attraction dominate due to the reduction in internuclear distance.
|-
| 6 || -2.9 || -0.5 || [[File:sm6416_Trajectory_6_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_6_Momenta.png|thumb|none|350px]] || This is the first reactive simulation observed, as can be seen from the surface plot and the drastic change in the momentum of FH. Evidently, there is sufficient energy to pass through the transition state complex and towards the reactants.
|-
| 7 || +2.9 || -0.5 || [[File:sm6416_Trajectory_7_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_7_Momenta.png|thumb|none|350px]] || This simulation is indeed similar to that of simulation 6 however, the change of sign for the HH momentum again results in a greater translation towards F and consequently the system passes through the transition complex shown by the surface plot and Momenta vs Time plot. However after a single oscillation, FH dissociates and the system returns to the reactant well with HH possessing a greater momentum. This scenario could be as a result of the HH momentum being too high and thus providing sufficient activation energy to proceed in the endothermic direction. This is surprising as the exothermic reaction elucidates more thermodynamically stable products.
|-
| 8 || +0.1 || -0.8 || [[File:sm6416_Trajectory_8_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_8_Momenta.png|thumb|none|350px]] || With a mere 60% change in FH momentum and a minimum HH momentum, the system can be seen to react fully, without returning through the transition state. The Momenta vs Time plot further shows a noticeable change in the AB momentum, which corresponds to FH. Despite the oscillations not being regular, it can be noted that the amplitudes are relatively of the same size and show no signs of regressing. This information highlights that the overall the FH momentum dominates the reactivity of the system and has a large weighting to overcoming the activation energy. It can be thought that the increase in momentum aids in allowing a closer distance of F & H, where electrostatic attraction forces will prevail.
|}

====Polyani's Empirical Rules====

The reactive trajectory for the FH + H was determined with the following parameters: rFH = 0.9, rHH = 2.3, pFH = 6.5, pHH = -1.5. The plots below highlight that these parameters lead to a reactive trajectory.

[[File:sm6416_FHH_Reactive_Trajectory_1_Surface.png|thumb|none|350px|Surface plot showing the reactants pass through the transition state and enter the product well without returning through the transition complex. This trajectory is therefore reactive.]]
[[File:sm6416_FHH_Reactive_Trajectory_1_Momenta.png|thumb|none|350px|Momenta vs Time plot indicating the substantial loss of momentum of FH, indicating dissociation, with the simultaneous gain in momentum of HH, indicated by the orange line.]]
[[File:sm6416_FHH_Reactive_Trajectory_1_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot showing a successful reaction. The HH distance vibrationally oscillates about the equilibrium bond distance, whereas the F-H distance increases linearly as a result of F translating away from H2.]]
[[File:sm6416_FHH_Reactive_Trajectory_1_Contour.png|thumb|none|350px|Contour plot highlighting similar information to the surface plot above in that the system stably occupies the product well without returning through the transition complex.]]

In order to react, a system must overcome the activation energy, the energy to achieve this is supplied by either translational or vibrational energy. As reported by Polanyi's Empirical Rules, a late transition state, one that resembles the products more as stated through Hammond's Postulate, is achieved through a greater contribution from vibrational energy enabling the activation energy to be overcome. The opposite is true for an early transition state which is promoted by a greater contribution from translational energy.

The F + H2 system is exothermic, thus an early transition state is present. Therefore this is promoted with higher translational energy being able to overcome the activation energy, hence pFH would contribute to the translational energy whereas pHH relates to the vibrational energy of the HH bond.

On the other hand, the FH + H system is endothermic and relates to a late transition state as dictated by Hammond's Postulate, requiring high vibrational energy of the FH bond to overcome the activation energy. In this scenario, pFH refers to the vibrational energy and pHH the translational energy.

MRD:sm6416

2018-05-25T16:37:54Z

Sm6416: /* Transition State */

==H2 + H Exercise 1==

===Transition State Dynamics===

The transition state is the stage in a reaction coordinate that must be passed through in order for a reaction to occur and occurs at a saddle point, as shown by the numerous surface plots on this page. The first derivative highlights the positions along the reaction coordinate where the gradient equals zero. However, in order to determine if a saddle point ensues, the second derivative of the gradient must be taken. A saddle point is only present if the second derivative > 0.

Another way to think of the transition state is by thinking of the tangent that can be formed at the transition state itself. This tangent will follow the reaction coordinate profile and therefore is expected to be a maximum, where the gradient = 0. A line can be drawn to the normal of the tangent at the selected transition state. This path would show a minimum, where the gradient again = 0, at the intersection of the tangent with normal if the transition state has been correctly identified. It is only in this scenario that a transition state can be determined as one.

===Locating the Transition State===

The transition state was determined through iterations of both r1 and r2 which resulted in the smallest displacement of momenta along with no displacement as shown by the contour plot. This method determined at rts = 0.907743.

[[File:sm6416_Transition_State_Contour.png|thumb|none|350px|Contour plot demonstrating rts = 0.907743 as a result of no fluctuations from the initial input, hence the complex is at the transition state.]]

[[File:sm6416_Transition_State_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating minimum, and almost zero, momentum at rts = 0.907743.]]

[[File:sm6416_Transition_State_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot demonstrating no fluctuations in distance and hence rts = 0.907743.]]

===Reaction Path===

The minimum energy path (MEP) is defined as the lowest path the reaction must follow to form the products and is the downhill motion from the transition state. It can be applied in both directions in the case in question. The MEP views the system as static as it resets the velocity to zero at each step. Whereas the trajectory is very much dynamic and the momenta is accounted for, this is reflected in the vibrational oscillation of the molecule as it passes along the minimum well towards the products.

====MEP====

Initial conditions of r1 = rts + 0.01 = 0.917743, r2 = rts = 0.907743 and p1 = p2 = 0 for the MEP simulation.

[[File:sm6416_MEP_Surface.png|thumb|none|350px|Surface plot highlighting the minimum energy path (MEP), as the reaction returns to the reactants without fully passing through the transition state.]]

[[File:sm6416_MEP_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating zero momentum, as inputted, and more importantly not change in momentum with running the simulation.]]

[[File:sm6416_MEP_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot showing that the reactants reach the transition state at the interception of r1 = r2. r1 quickly reaches a constant value, namely the equilibrium bond length of the reactant molecule. r2 increases logarithmically as time progresses, this represents an increasing distance of Ha from Hb-Hc and a continuing loss of momentum.]]

Final values from the MEP simulation.

r1 = 2.76195

r2 = 0.75883

These values reflect the minimum trajectory for a successful reaction.

p1 = p2 = 0

====Dynamic====

[[File:sm6416_Dynamic_Surface.png|thumb|none|350px|Surface plot highlighting the minimum energy path (MEP) with oscillation of the reactants, as the reaction returns to the reactants without fully passing through the transition state. It is therefore evident that the momentum as a result of the vibrational oscillation does not provide enough energy to proceed to the products.]]

[[File:sm6416_Dynamic_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating the momenta associated with the oscillating reactants.]]

[[File:sm6416_Dynamic_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot showing that the reactants reach the transition state at the interception of r1 = r2. r1 quickly decreases and oscillates about a constant value, namely the equilibrium bond length of the reactant molecule. r2 increases linearly as time progresses, this represents an increasing distance of Ha from Hb-Hc with a constant momentum.]]

Dynamic simulation final values

r1 = 10.0045

r2 = 0.75883

p1 = 2.48523

p2 = 1.29898

p(average) = 1.90409

With r1 = rts and r2 = rts + 0.01 would simply produce the same answer however the values would be flipped to the other distance. In other words r1 = 0.75883 and r2 = 10.0045 would be the output values.

Maintaining the final trajectories as calculated from the dynamic simulation and reversing the sign of the momenta, the reaction proceeds in the reverse direction to the products.

===Reactivity of Trajectories===

These simulations are restricted by the number of steps the program can handle, however a sound understanding of the reaction can be appreciated and the reactivity of each scenario can be determined appropriately.

{| class="wikitable" border=2
! Simulation !! p1 !! p2 !! Energy (kcal/mol) !! Reactivity !! Evidence !! Description
|-
| 1 || -1.25 || -2.5 || 5.03500 || Reactive || [[File:sm6416_MEP_Figure1.png|thumb|none|350px]] || The reactants proceed through the transition state and to the products. The r2 distance decreases to the equilibrium bond length, whilst r1 simultaneously exhibits dissociation and increases beyond the scope of the graph. The small momenta attributed to the reactants is reflected in the vibrationally oscillating products, with a small amplitude.
|-
| 2 || -1.5 || -2.0 || 3.62879 || Unreactive || [[File:sm6416_MEP_Figure2.png|thumb|none|350px]] || This is unreactive as the oscillating reactants reach the transition state point and r1 immediately returns to the initial bond length, whilst r2 continues to increase as it moves away from the H2 molecule.
|-
| 3 || -1.5 || -2.5 || 5.13738 || Reactive || [[File:sm6416_MEP_Figure3.png|thumb|none|350px]] || This simulation shows a reactive pathway that is very similar to simulation 1, however due to the greater momenta associated with the reactants, as inputted, vibrational oscillations with a greater amplitude can be observed.
|-
| 4 || -2.5 || -5.0 || 9.86678 || Unreactive || [[File:sm6416_MEP_Figure4.png|thumb|none|350px]] || Initially seen here are oscillating reactants with a very large amplitude. However, this simulation is unreactive despite the reactants going through the transition state and towards the product, they return to the initial reactants.
|-
| 5 || -2.5 || -5.2 || 11.80780 || Reactive || [[File:sm6416_MEP_Figure5.png|thumb|none|350px]] || Like simulation 4, this simulation shows a large oscillating amplitude, whereas in this scenario after passing through the transition state, the products are completely obtained. The slight increase in the p2 momentum can be seen to result in the products.
|}

====Transition State Theory====

Transition State Theory (TST) assumes a quasi-equilibrium between reactants and the transition state. The reaction between the transition state and products is irreversible and therefore is unable to return to the reactants, however many of the surface plots on this page show the complete antithesis of this highlighting a dichotomy between theory and experimental. TST further assumes that fluctuation as to whether the transition complexes go towards reactants or products are independent of each other and hence the rate of one can not be determined by the other.

TST is an excellent qualitative tool and can identify the enthalpy, standard entropy and standard Gibbs energy of activation. Despite this, it the method is unable to accurately determine these true values in line with experimental results as doing so would require a deep understanding of the potential energy surface of each reaction. Therefore, TST under estimates the reaction rate in comparison to the experimental values. When TST was developed in 1935 a lack of adequate computer software to accurately map potential energy surfaces with the relative quantum mechanical contributions to determine the distribution of electron density, unlike there is today. Hence resulting in a less accurate and longer method to map these surfaces for each reaction.

==F-H-H System Exercise 2==
===Potential Energy Surface Inspection===
====Energetics====

F + H2 is an exothermic reaction as can be seen from the surface plot, the reaction progresses from a small H-H distance to a longer one, whilst H-F simultaneously equilibriates about the F-H bond length. It can be seen that the products are lower, and hence more stable, in energy than the reactants.

F-H + H is simply the reverse reaction that passes through the same transition state, hence this reaction is endothermic with the products being higher in energy than the reactants. There is an overall gain of energy.

With this information in mind, the F-H bond is more stable and thus stronger than the H-H bond. The main factors to this argument is the greater electronegativity of F leading to a stronger contribution to the bond than the molecular orbitals. Hence the overlap of molecular orbitals is a weaker factor in the bond strength.

[[File:sm6416_FHH_Surface.png|thumb|none|350px|Surface plot highlighting the energetics of the F-H-H system.]]

[[File:sm6416_HHF_Surface.png|thumb|none|350px|Surface plot highlighting the energetics of the H-H-F system.]]

====Transition State====

Hammond's postulate aids in finding the transition state; it relates the composition of the transition complex to either the reactants or products for an early or late transition state respectively. In the scenario under investigation for F + H2 an early transition state is present as the reaction is exothermic in this direction, hence the transition state resembles the reactants more.

This guidance proved useful in determining the transition state complex at r1 = F-H = 1.810076 Angstrom and r2 = H-H = 0.74634 Angstrom, as can be seen from the surface and contour plots below showing the absence of displacement to either reactants or products. Furthermore the Momenta vs Time plot indicates a very small momenta of the overall system, without any deviation or substantial change in the momenta.

[[File:sm6416_FHH_Transition_State_Contour.png|thumb|none|350px|Contour plot demonstrating rts as a result of no fluctuations from the initial input, hence the complex is metaphorically sitting on the transition state.]]

[[File:sm6416_FHH_Transition_State_Momenta_Time.png|thumb|none|350px|Momenta vs Time plot demonstrating minimum, and almost zero, momentum at rts.]]

[[File:sm6416_FHH_Transition_State_Surface.png|thumb|none|350px]]

====Activation Energy====

The activation energy for the exothermic reaction was calculated through a 500000 step MEP simulation with input values of r1 = 1.820076, r2 = 0.74634 and p1 = p2 = 0. It was required that after following the minimum energy path, the gradient of the line signifying the reactants was constant.

The activation energy is reported at +0.258 kcal/mol for the exothermic process.

[[File:sm6416_FHH_Activation_Energy_1.png|thumb|none|350px|Energy vs Time graph highlighting the activation energy of the exothermic reaction.]]

The activation energy for the endothermic process was determined with the following parameters: r1 = 1.800076, r2 = 0.74634, p1 = p2 = 0 with 250000 steps. These parameters 'tipped' the reaction towards the FH + H reactants. The reported activation energy was +30.277 kcal/mol.

[[File:sm6416_FHH_Activation_Energy_2.png|thumb|none|350px|Energy vs Time graph highlighting the activation energy of the endothermic reaction.]]

It can hence be seen that the exothermic reaction of F + H2 --> F-H + H only requires a small activation energy as the products are substantially more thermodynamically stable than the reactants.

===Reaction Dynamics===

In this exothermic reaction, the potential energy is mainly converted into vibrational energy of the FH bond, along with heat. As a result of this vibrational energy in the FH bond, vibrational levels above the ground state will become partially populated. In this manner, by recording an IR spectrum of the products, the main F-H will be observed alongside an overtone, with the intensity of this overtone relating to the population of this vibrationally excited state, which can then be used to determine the vibrational energy in the bond itself.

In this same vein, IR chemiluminescence can be employed to yield the same result by measuring the wavelength, and subsequent vibrational energy of the FH bond, of the infrared light that is irradiated from the products and being excited with incident light.

As the momentum closes towards the boundaries of -3 < p < +3, the system passes through transition state but returns to reactant well. This shows that the excess momentum of the system in the product well is sufficient to overcome the high activation energy and return to the thermodynamically unfavourable reactants.

The following parameters were employed for all simulations rFH = 2.3, rHH = 0.74 with 500 steps calculated.

{| class="wikitable" border=2
! Simulation !! pHH !! pFH !! Surface Plot !! Momenta vs Time Plot !! Observations !!
|-
| 1 || -2.5 || -1.5 || [[File:sm6416_Trajectory_1_Surface.png|thumb|none|350px]] ||[[File:sm6416_Trajectory_1_Momenta.png|thumb|none|350px]] || This trajectory results in a successful reaction as seen from the surface plot; the reactants proceed through the transition state and continue into the product well, whilst continually oscillating as a result of the momentum gained.
|-
| 2 || -0.5 || -0.5 || [[File:sm6416_Trajectory_2_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_2_Momenta.png|thumb|none|350px]] || This momentum does not proceed to a reaction. Through the dynamic animation it can be seen that the HH molecule does not possess enough momentum to translate towards F. Therefore the system does not translate out of the reactant well, as seen in the surface plot, since there is not enough energy to overcome the activation energy. The momenta plot simply shows a small up trend, this is expected due to the long range electrostatic force of attraction between F and HH, resulting in a slight increase in the HH vibration velocity. There is no drastic change in the momenta of either F or HH that would otherwise indicate the occurrence of a reaction, as seen in simulation 1 above.
|-
| 3 || +0.5 || -0.5 || [[File:sm6416_Trajectory_3_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_3_Momenta.png|thumb|none|350px]] || This simulation shows an unreactive path, as can be seen from the surface plot, the system remains in the reactant well as it does not overcome the small activation energy for the exothermic reaction to proceed. As in simulation 2, the momentum amplitude of the oscillating HH remains constant however the overall momenta of the system increases due to a slight translation towards F, thus increasing electrostatic attraction forces resulting in this slight overall momenta increase.
|-
| 4 || -1.6 || -0.5 || [[File:sm6416_Trajectory_4_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_4_Momenta.png|thumb|none|350px]] || This simulation is very similar to simulations 2 & 3 in that the system remains in the reactant well as there is not sufficient energy to overcome the activation energy. However as a result of the greater HH momentum, the oscillation amplitude is greater than both simulation 1 & 2.
|-
| 5 || +1.6 || -0.5 || [[File:sm6416_Trajectory_5_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_5_Momenta.png|thumb|none|350px]] || Firstly, this simulation is unreactive as can be seen from the surface plot. In comparison to simulation 4, HH momentum sign has been changed and as a result this has led to not only a greater oscillating amplitude but also a larger translation towards F. So much so in the latter than the Momenta vs Time plot shows an increase in FH oscillation momentum as the electrostatic forces of attraction dominate due to the reduction in internuclear distance.
|-
| 6 || -2.9 || -0.5 || [[File:sm6416_Trajectory_6_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_6_Momenta.png|thumb|none|350px]] || This is the first reactive simulation observed, as can be seen from the surface plot and the drastic change in the momentum of FH. Evidently, there is sufficient energy to pass through the transition state complex and towards the reactants.
|-
| 7 || +2.9 || -0.5 || [[File:sm6416_Trajectory_7_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_7_Momenta.png|thumb|none|350px]] || This simulation is indeed similar to that of simulation 6 however, the change of sign for the HH momentum again results in a greater translation towards F and consequently the system passes through the transition complex shown by the surface plot and Momenta vs Time plot. However after a single oscillation, FH dissociates and the system returns to the reactant well with HH possessing a greater momentum. This scenario could be as a result of the HH momentum being too high and thus providing sufficient activation energy to proceed in the endothermic direction. This is surprising as the exothermic reaction elucidates more thermodynamically stable products.
|-
| 8 || +0.1 || -0.8 || [[File:sm6416_Trajectory_8_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_8_Momenta.png|thumb|none|350px]] || With a mere 60% change in FH momentum and a minimum HH momentum, the system can be seen to react fully, without returning through the transition state. The Momenta vs Time plot further shows a noticeable change in the AB momentum, which corresponds to FH. Despite the oscillations not being regular, it can be noted that the amplitudes are relatively of the same size and show no signs of regressing. This information highlights that the overall the FH momentum dominates the reactivity of the system and has a large weighting to overcoming the activation energy. It can be thought that the increase in momentum aids in allowing a closer distance of F & H, where electrostatic attraction forces will prevail.
|}

====Polyani's Empirical Rules====

The reactive trajectory for the FH + H was determined with the following parameters: rFH = 0.9, rHH = 2.3, pFH = 6.5, pHH = -1.5. The plots below highlight that these parameters lead to a reactive trajectory.

[[File:sm6416_FHH_Reactive_Trajectory_1_Surface.png|thumb|none|350px|Surface plot showing the reactants pass through the transition state and enter the product well without returning through the transition complex. This trajectory is therefore reactive.]]
[[File:sm6416_FHH_Reactive_Trajectory_1_Momenta.png|thumb|none|350px|Momenta vs Time plot indicating the substantial loss of momentum of FH, indicating dissociation, with the simultaneous gain in momentum of HH, indicated by the orange line.]]
[[File:sm6416_FHH_Reactive_Trajectory_1_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot showing a successful reaction. The HH distance vibrationally oscillates about the equilibrium bond distance, whereas the F-H distance increases linearly as a result of F translating away from H2.]]
[[File:sm6416_FHH_Reactive_Trajectory_1_Contour.png|thumb|none|350px|Contour plot highlighting similar information to the surface plot above in that the system stably occupies the product well without returning through the transition complex.]]

In order to react, a system must overcome the activation energy, the energy to achieve this is supplied by either translational or vibrational energy. As reported by Polanyi's Empirical Rules, a late transition state, one that resembles the products more as stated through Hammond's Postulate, is achieved through a greater contribution from vibrational energy enabling the activation energy to be overcome. The opposite is true for an early transition state which is promoted by a greater contribution from translational energy.

The F + H2 system is exothermic, thus an early transition state is present. Therefore this is promoted with higher translational energy being able to overcome the activation energy, hence pFH would contribute to the translational energy whereas pHH relates to the vibrational energy of the HH bond.

On the other hand, the FH + H system is endothermic and relates to a late transition state as dictated by Hammond's Postulate, requiring high vibrational energy of the FH bond to overcome the activation energy. In this scenario, pFH refers to the vibrational energy and pHH the translational energy.

MRD:sm6416

2018-05-25T16:37:11Z

Sm6416: /* Transition State Theory */

==H2 + H Exercise 1==

===Transition State Dynamics===

The transition state is the stage in a reaction coordinate that must be passed through in order for a reaction to occur and occurs at a saddle point, as shown by the numerous surface plots on this page. The first derivative highlights the positions along the reaction coordinate where the gradient equals zero. However, in order to determine if a saddle point ensues, the second derivative of the gradient must be taken. A saddle point is only present if the second derivative > 0.

Another way to think of the transition state is by thinking of the tangent that can be formed at the transition state itself. This tangent will follow the reaction coordinate profile and therefore is expected to be a maximum, where the gradient = 0. A line can be drawn to the normal of the tangent at the selected transition state. This path would show a minimum, where the gradient again = 0, at the intersection of the tangent with normal if the transition state has been correctly identified. It is only in this scenario that a transition state can be determined as one.

===Locating the Transition State===

The transition state was determined through iterations of both r1 and r2 which resulted in the smallest displacement of momenta along with no displacement as shown by the contour plot. This method determined at rts = 0.907743.

[[File:sm6416_Transition_State_Contour.png|thumb|none|350px|Contour plot demonstrating rts = 0.907743 as a result of no fluctuations from the initial input, hence the complex is at the transition state.]]

[[File:sm6416_Transition_State_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating minimum, and almost zero, momentum at rts = 0.907743.]]

[[File:sm6416_Transition_State_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot demonstrating no fluctuations in distance and hence rts = 0.907743.]]

===Reaction Path===

The minimum energy path (MEP) is defined as the lowest path the reaction must follow to form the products and is the downhill motion from the transition state. It can be applied in both directions in the case in question. The MEP views the system as static as it resets the velocity to zero at each step. Whereas the trajectory is very much dynamic and the momenta is accounted for, this is reflected in the vibrational oscillation of the molecule as it passes along the minimum well towards the products.

====MEP====

Initial conditions of r1 = rts + 0.01 = 0.917743, r2 = rts = 0.907743 and p1 = p2 = 0 for the MEP simulation.

[[File:sm6416_MEP_Surface.png|thumb|none|350px|Surface plot highlighting the minimum energy path (MEP), as the reaction returns to the reactants without fully passing through the transition state.]]

[[File:sm6416_MEP_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating zero momentum, as inputted, and more importantly not change in momentum with running the simulation.]]

[[File:sm6416_MEP_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot showing that the reactants reach the transition state at the interception of r1 = r2. r1 quickly reaches a constant value, namely the equilibrium bond length of the reactant molecule. r2 increases logarithmically as time progresses, this represents an increasing distance of Ha from Hb-Hc and a continuing loss of momentum.]]

Final values from the MEP simulation.

r1 = 2.76195

r2 = 0.75883

These values reflect the minimum trajectory for a successful reaction.

p1 = p2 = 0

====Dynamic====

[[File:sm6416_Dynamic_Surface.png|thumb|none|350px|Surface plot highlighting the minimum energy path (MEP) with oscillation of the reactants, as the reaction returns to the reactants without fully passing through the transition state. It is therefore evident that the momentum as a result of the vibrational oscillation does not provide enough energy to proceed to the products.]]

[[File:sm6416_Dynamic_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating the momenta associated with the oscillating reactants.]]

[[File:sm6416_Dynamic_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot showing that the reactants reach the transition state at the interception of r1 = r2. r1 quickly decreases and oscillates about a constant value, namely the equilibrium bond length of the reactant molecule. r2 increases linearly as time progresses, this represents an increasing distance of Ha from Hb-Hc with a constant momentum.]]

Dynamic simulation final values

r1 = 10.0045

r2 = 0.75883

p1 = 2.48523

p2 = 1.29898

p(average) = 1.90409

With r1 = rts and r2 = rts + 0.01 would simply produce the same answer however the values would be flipped to the other distance. In other words r1 = 0.75883 and r2 = 10.0045 would be the output values.

Maintaining the final trajectories as calculated from the dynamic simulation and reversing the sign of the momenta, the reaction proceeds in the reverse direction to the products.

===Reactivity of Trajectories===

These simulations are restricted by the number of steps the program can handle, however a sound understanding of the reaction can be appreciated and the reactivity of each scenario can be determined appropriately.

{| class="wikitable" border=2
! Simulation !! p1 !! p2 !! Energy (kcal/mol) !! Reactivity !! Evidence !! Description
|-
| 1 || -1.25 || -2.5 || 5.03500 || Reactive || [[File:sm6416_MEP_Figure1.png|thumb|none|350px]] || The reactants proceed through the transition state and to the products. The r2 distance decreases to the equilibrium bond length, whilst r1 simultaneously exhibits dissociation and increases beyond the scope of the graph. The small momenta attributed to the reactants is reflected in the vibrationally oscillating products, with a small amplitude.
|-
| 2 || -1.5 || -2.0 || 3.62879 || Unreactive || [[File:sm6416_MEP_Figure2.png|thumb|none|350px]] || This is unreactive as the oscillating reactants reach the transition state point and r1 immediately returns to the initial bond length, whilst r2 continues to increase as it moves away from the H2 molecule.
|-
| 3 || -1.5 || -2.5 || 5.13738 || Reactive || [[File:sm6416_MEP_Figure3.png|thumb|none|350px]] || This simulation shows a reactive pathway that is very similar to simulation 1, however due to the greater momenta associated with the reactants, as inputted, vibrational oscillations with a greater amplitude can be observed.
|-
| 4 || -2.5 || -5.0 || 9.86678 || Unreactive || [[File:sm6416_MEP_Figure4.png|thumb|none|350px]] || Initially seen here are oscillating reactants with a very large amplitude. However, this simulation is unreactive despite the reactants going through the transition state and towards the product, they return to the initial reactants.
|-
| 5 || -2.5 || -5.2 || 11.80780 || Reactive || [[File:sm6416_MEP_Figure5.png|thumb|none|350px]] || Like simulation 4, this simulation shows a large oscillating amplitude, whereas in this scenario after passing through the transition state, the products are completely obtained. The slight increase in the p2 momentum can be seen to result in the products.
|}

====Transition State Theory====

Transition State Theory (TST) assumes a quasi-equilibrium between reactants and the transition state. The reaction between the transition state and products is irreversible and therefore is unable to return to the reactants, however many of the surface plots on this page show the complete antithesis of this highlighting a dichotomy between theory and experimental. TST further assumes that fluctuation as to whether the transition complexes go towards reactants or products are independent of each other and hence the rate of one can not be determined by the other.

TST is an excellent qualitative tool and can identify the enthalpy, standard entropy and standard Gibbs energy of activation. Despite this, it the method is unable to accurately determine these true values in line with experimental results as doing so would require a deep understanding of the potential energy surface of each reaction. Therefore, TST under estimates the reaction rate in comparison to the experimental values. When TST was developed in 1935 a lack of adequate computer software to accurately map potential energy surfaces with the relative quantum mechanical contributions to determine the distribution of electron density, unlike there is today. Hence resulting in a less accurate and longer method to map these surfaces for each reaction.

==F-H-H System Exercise 2==
===Potential Energy Surface Inspection===
====Energetics====

F + H2 is an exothermic reaction as can be seen from the surface plot, the reaction progresses from a small H-H distance to a longer one, whilst H-F simultaneously equilibriates about the F-H bond length. It can be seen that the products are lower, and hence more stable, in energy than the reactants.

F-H + H is simply the reverse reaction that passes through the same transition state, hence this reaction is endothermic with the products being higher in energy than the reactants. There is an overall gain of energy.

With this information in mind, the F-H bond is more stable and thus stronger than the H-H bond. The main factors to this argument is the greater electronegativity of F leading to a stronger contribution to the bond than the molecular orbitals. Hence the overlap of molecular orbitals is a weaker factor in the bond strength.

[[File:sm6416_FHH_Surface.png|thumb|none|350px|Surface plot highlighting the energetics of the F-H-H system.]]

[[File:sm6416_HHF_Surface.png|thumb|none|350px|Surface plot highlighting the energetics of the H-H-F system.]]

====Transition State====

Hammond's postulate aids in finding the transition state; it relates the composition of the transition complex to either the reactants or products for an early or late transition state respectively. In the scenario under investigation for F +H2 an early transition state is present as the reaction is exothermic in this direction, hence the transition state resembles the reactants more.

This guidance proved useful in determining the transition state complex at r1 = F-H = 1.810076 Angstrom and r2 = H-H = 0.74634 Angstrom, as can be seen from the surface and contour plots below showing the absence of displacement to either reactants or products. Furthermore the Momenta vs Time plot indicates a very small momenta of the overall system, without any deviation or substantial change in the momenta.

[[File:sm6416_FHH_Transition_State_Contour.png|thumb|none|350px|Contour plot demonstrating rts as a result of no fluctuations from the initial input, hence the complex is metaphorically sitting on the transition state.]]

[[File:sm6416_FHH_Transition_State_Momenta_Time.png|thumb|none|350px|Momenta vs Time plot demonstrating minimum, and almost zero, momentum at rts.]]

[[File:sm6416_FHH_Transition_State_Surface.png|thumb|none|350px]]

====Activation Energy====

The activation energy for the exothermic reaction was calculated through a 500000 step MEP simulation with input values of r1 = 1.820076, r2 = 0.74634 and p1 = p2 = 0. It was required that after following the minimum energy path, the gradient of the line signifying the reactants was constant.

The activation energy is reported at +0.258 kcal/mol for the exothermic process.

[[File:sm6416_FHH_Activation_Energy_1.png|thumb|none|350px|Energy vs Time graph highlighting the activation energy of the exothermic reaction.]]

The activation energy for the endothermic process was determined with the following parameters: r1 = 1.800076, r2 = 0.74634, p1 = p2 = 0 with 250000 steps. These parameters 'tipped' the reaction towards the FH + H reactants. The reported activation energy was +30.277 kcal/mol.

[[File:sm6416_FHH_Activation_Energy_2.png|thumb|none|350px|Energy vs Time graph highlighting the activation energy of the endothermic reaction.]]

It can hence be seen that the exothermic reaction of F + H2 --> F-H + H only requires a small activation energy as the products are substantially more thermodynamically stable than the reactants.

===Reaction Dynamics===

In this exothermic reaction, the potential energy is mainly converted into vibrational energy of the FH bond, along with heat. As a result of this vibrational energy in the FH bond, vibrational levels above the ground state will become partially populated. In this manner, by recording an IR spectrum of the products, the main F-H will be observed alongside an overtone, with the intensity of this overtone relating to the population of this vibrationally excited state, which can then be used to determine the vibrational energy in the bond itself.

In this same vein, IR chemiluminescence can be employed to yield the same result by measuring the wavelength, and subsequent vibrational energy of the FH bond, of the infrared light that is irradiated from the products and being excited with incident light.

As the momentum closes towards the boundaries of -3 < p < +3, the system passes through transition state but returns to reactant well. This shows that the excess momentum of the system in the product well is sufficient to overcome the high activation energy and return to the thermodynamically unfavourable reactants.

The following parameters were employed for all simulations rFH = 2.3, rHH = 0.74 with 500 steps calculated.

{| class="wikitable" border=2
! Simulation !! pHH !! pFH !! Surface Plot !! Momenta vs Time Plot !! Observations !!
|-
| 1 || -2.5 || -1.5 || [[File:sm6416_Trajectory_1_Surface.png|thumb|none|350px]] ||[[File:sm6416_Trajectory_1_Momenta.png|thumb|none|350px]] || This trajectory results in a successful reaction as seen from the surface plot; the reactants proceed through the transition state and continue into the product well, whilst continually oscillating as a result of the momentum gained.
|-
| 2 || -0.5 || -0.5 || [[File:sm6416_Trajectory_2_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_2_Momenta.png|thumb|none|350px]] || This momentum does not proceed to a reaction. Through the dynamic animation it can be seen that the HH molecule does not possess enough momentum to translate towards F. Therefore the system does not translate out of the reactant well, as seen in the surface plot, since there is not enough energy to overcome the activation energy. The momenta plot simply shows a small up trend, this is expected due to the long range electrostatic force of attraction between F and HH, resulting in a slight increase in the HH vibration velocity. There is no drastic change in the momenta of either F or HH that would otherwise indicate the occurrence of a reaction, as seen in simulation 1 above.
|-
| 3 || +0.5 || -0.5 || [[File:sm6416_Trajectory_3_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_3_Momenta.png|thumb|none|350px]] || This simulation shows an unreactive path, as can be seen from the surface plot, the system remains in the reactant well as it does not overcome the small activation energy for the exothermic reaction to proceed. As in simulation 2, the momentum amplitude of the oscillating HH remains constant however the overall momenta of the system increases due to a slight translation towards F, thus increasing electrostatic attraction forces resulting in this slight overall momenta increase.
|-
| 4 || -1.6 || -0.5 || [[File:sm6416_Trajectory_4_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_4_Momenta.png|thumb|none|350px]] || This simulation is very similar to simulations 2 & 3 in that the system remains in the reactant well as there is not sufficient energy to overcome the activation energy. However as a result of the greater HH momentum, the oscillation amplitude is greater than both simulation 1 & 2.
|-
| 5 || +1.6 || -0.5 || [[File:sm6416_Trajectory_5_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_5_Momenta.png|thumb|none|350px]] || Firstly, this simulation is unreactive as can be seen from the surface plot. In comparison to simulation 4, HH momentum sign has been changed and as a result this has led to not only a greater oscillating amplitude but also a larger translation towards F. So much so in the latter than the Momenta vs Time plot shows an increase in FH oscillation momentum as the electrostatic forces of attraction dominate due to the reduction in internuclear distance.
|-
| 6 || -2.9 || -0.5 || [[File:sm6416_Trajectory_6_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_6_Momenta.png|thumb|none|350px]] || This is the first reactive simulation observed, as can be seen from the surface plot and the drastic change in the momentum of FH. Evidently, there is sufficient energy to pass through the transition state complex and towards the reactants.
|-
| 7 || +2.9 || -0.5 || [[File:sm6416_Trajectory_7_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_7_Momenta.png|thumb|none|350px]] || This simulation is indeed similar to that of simulation 6 however, the change of sign for the HH momentum again results in a greater translation towards F and consequently the system passes through the transition complex shown by the surface plot and Momenta vs Time plot. However after a single oscillation, FH dissociates and the system returns to the reactant well with HH possessing a greater momentum. This scenario could be as a result of the HH momentum being too high and thus providing sufficient activation energy to proceed in the endothermic direction. This is surprising as the exothermic reaction elucidates more thermodynamically stable products.
|-
| 8 || +0.1 || -0.8 || [[File:sm6416_Trajectory_8_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_8_Momenta.png|thumb|none|350px]] || With a mere 60% change in FH momentum and a minimum HH momentum, the system can be seen to react fully, without returning through the transition state. The Momenta vs Time plot further shows a noticeable change in the AB momentum, which corresponds to FH. Despite the oscillations not being regular, it can be noted that the amplitudes are relatively of the same size and show no signs of regressing. This information highlights that the overall the FH momentum dominates the reactivity of the system and has a large weighting to overcoming the activation energy. It can be thought that the increase in momentum aids in allowing a closer distance of F & H, where electrostatic attraction forces will prevail.
|}

====Polyani's Empirical Rules====

The reactive trajectory for the FH + H was determined with the following parameters: rFH = 0.9, rHH = 2.3, pFH = 6.5, pHH = -1.5. The plots below highlight that these parameters lead to a reactive trajectory.

[[File:sm6416_FHH_Reactive_Trajectory_1_Surface.png|thumb|none|350px|Surface plot showing the reactants pass through the transition state and enter the product well without returning through the transition complex. This trajectory is therefore reactive.]]
[[File:sm6416_FHH_Reactive_Trajectory_1_Momenta.png|thumb|none|350px|Momenta vs Time plot indicating the substantial loss of momentum of FH, indicating dissociation, with the simultaneous gain in momentum of HH, indicated by the orange line.]]
[[File:sm6416_FHH_Reactive_Trajectory_1_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot showing a successful reaction. The HH distance vibrationally oscillates about the equilibrium bond distance, whereas the F-H distance increases linearly as a result of F translating away from H2.]]
[[File:sm6416_FHH_Reactive_Trajectory_1_Contour.png|thumb|none|350px|Contour plot highlighting similar information to the surface plot above in that the system stably occupies the product well without returning through the transition complex.]]

In order to react, a system must overcome the activation energy, the energy to achieve this is supplied by either translational or vibrational energy. As reported by Polanyi's Empirical Rules, a late transition state, one that resembles the products more as stated through Hammond's Postulate, is achieved through a greater contribution from vibrational energy enabling the activation energy to be overcome. The opposite is true for an early transition state which is promoted by a greater contribution from translational energy.

The F + H2 system is exothermic, thus an early transition state is present. Therefore this is promoted with higher translational energy being able to overcome the activation energy, hence pFH would contribute to the translational energy whereas pHH relates to the vibrational energy of the HH bond.

On the other hand, the FH + H system is endothermic and relates to a late transition state as dictated by Hammond's Postulate, requiring high vibrational energy of the FH bond to overcome the activation energy. In this scenario, pFH refers to the vibrational energy and pHH the translational energy.

MRD:sm6416

2018-05-25T16:36:37Z

Sm6416: /* Transition State Theory */

==H2 + H Exercise 1==

===Transition State Dynamics===

The transition state is the stage in a reaction coordinate that must be passed through in order for a reaction to occur and occurs at a saddle point, as shown by the numerous surface plots on this page. The first derivative highlights the positions along the reaction coordinate where the gradient equals zero. However, in order to determine if a saddle point ensues, the second derivative of the gradient must be taken. A saddle point is only present if the second derivative > 0.

Another way to think of the transition state is by thinking of the tangent that can be formed at the transition state itself. This tangent will follow the reaction coordinate profile and therefore is expected to be a maximum, where the gradient = 0. A line can be drawn to the normal of the tangent at the selected transition state. This path would show a minimum, where the gradient again = 0, at the intersection of the tangent with normal if the transition state has been correctly identified. It is only in this scenario that a transition state can be determined as one.

===Locating the Transition State===

The transition state was determined through iterations of both r1 and r2 which resulted in the smallest displacement of momenta along with no displacement as shown by the contour plot. This method determined at rts = 0.907743.

[[File:sm6416_Transition_State_Contour.png|thumb|none|350px|Contour plot demonstrating rts = 0.907743 as a result of no fluctuations from the initial input, hence the complex is at the transition state.]]

[[File:sm6416_Transition_State_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating minimum, and almost zero, momentum at rts = 0.907743.]]

[[File:sm6416_Transition_State_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot demonstrating no fluctuations in distance and hence rts = 0.907743.]]

===Reaction Path===

The minimum energy path (MEP) is defined as the lowest path the reaction must follow to form the products and is the downhill motion from the transition state. It can be applied in both directions in the case in question. The MEP views the system as static as it resets the velocity to zero at each step. Whereas the trajectory is very much dynamic and the momenta is accounted for, this is reflected in the vibrational oscillation of the molecule as it passes along the minimum well towards the products.

====MEP====

Initial conditions of r1 = rts + 0.01 = 0.917743, r2 = rts = 0.907743 and p1 = p2 = 0 for the MEP simulation.

[[File:sm6416_MEP_Surface.png|thumb|none|350px|Surface plot highlighting the minimum energy path (MEP), as the reaction returns to the reactants without fully passing through the transition state.]]

[[File:sm6416_MEP_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating zero momentum, as inputted, and more importantly not change in momentum with running the simulation.]]

[[File:sm6416_MEP_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot showing that the reactants reach the transition state at the interception of r1 = r2. r1 quickly reaches a constant value, namely the equilibrium bond length of the reactant molecule. r2 increases logarithmically as time progresses, this represents an increasing distance of Ha from Hb-Hc and a continuing loss of momentum.]]

Final values from the MEP simulation.

r1 = 2.76195

r2 = 0.75883

These values reflect the minimum trajectory for a successful reaction.

p1 = p2 = 0

====Dynamic====

[[File:sm6416_Dynamic_Surface.png|thumb|none|350px|Surface plot highlighting the minimum energy path (MEP) with oscillation of the reactants, as the reaction returns to the reactants without fully passing through the transition state. It is therefore evident that the momentum as a result of the vibrational oscillation does not provide enough energy to proceed to the products.]]

[[File:sm6416_Dynamic_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating the momenta associated with the oscillating reactants.]]

[[File:sm6416_Dynamic_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot showing that the reactants reach the transition state at the interception of r1 = r2. r1 quickly decreases and oscillates about a constant value, namely the equilibrium bond length of the reactant molecule. r2 increases linearly as time progresses, this represents an increasing distance of Ha from Hb-Hc with a constant momentum.]]

Dynamic simulation final values

r1 = 10.0045

r2 = 0.75883

p1 = 2.48523

p2 = 1.29898

p(average) = 1.90409

With r1 = rts and r2 = rts + 0.01 would simply produce the same answer however the values would be flipped to the other distance. In other words r1 = 0.75883 and r2 = 10.0045 would be the output values.

Maintaining the final trajectories as calculated from the dynamic simulation and reversing the sign of the momenta, the reaction proceeds in the reverse direction to the products.

===Reactivity of Trajectories===

These simulations are restricted by the number of steps the program can handle, however a sound understanding of the reaction can be appreciated and the reactivity of each scenario can be determined appropriately.

{| class="wikitable" border=2
! Simulation !! p1 !! p2 !! Energy (kcal/mol) !! Reactivity !! Evidence !! Description
|-
| 1 || -1.25 || -2.5 || 5.03500 || Reactive || [[File:sm6416_MEP_Figure1.png|thumb|none|350px]] || The reactants proceed through the transition state and to the products. The r2 distance decreases to the equilibrium bond length, whilst r1 simultaneously exhibits dissociation and increases beyond the scope of the graph. The small momenta attributed to the reactants is reflected in the vibrationally oscillating products, with a small amplitude.
|-
| 2 || -1.5 || -2.0 || 3.62879 || Unreactive || [[File:sm6416_MEP_Figure2.png|thumb|none|350px]] || This is unreactive as the oscillating reactants reach the transition state point and r1 immediately returns to the initial bond length, whilst r2 continues to increase as it moves away from the H2 molecule.
|-
| 3 || -1.5 || -2.5 || 5.13738 || Reactive || [[File:sm6416_MEP_Figure3.png|thumb|none|350px]] || This simulation shows a reactive pathway that is very similar to simulation 1, however due to the greater momenta associated with the reactants, as inputted, vibrational oscillations with a greater amplitude can be observed.
|-
| 4 || -2.5 || -5.0 || 9.86678 || Unreactive || [[File:sm6416_MEP_Figure4.png|thumb|none|350px]] || Initially seen here are oscillating reactants with a very large amplitude. However, this simulation is unreactive despite the reactants going through the transition state and towards the product, they return to the initial reactants.
|-
| 5 || -2.5 || -5.2 || 11.80780 || Reactive || [[File:sm6416_MEP_Figure5.png|thumb|none|350px]] || Like simulation 4, this simulation shows a large oscillating amplitude, whereas in this scenario after passing through the transition state, the products are completely obtained. The slight increase in the p2 momentum can be seen to result in the products.
|}

====Transition State Theory====

Transition State Theory (TST) assumes a quasi-equilibrium between reactants and the transition state. The reaction between the transition state and products is irreversible and therefore is unable to return to the reactants, however many of the surface plots on this page show the complete antithesis of this highlighting a dichotomy between theory and experimental. TST further assumes that fluctuation as to whether the transition complexes go towards reactants or products are independent of each other and hence the rate of one can not be determined by the other.

TST is an excellent qualitative tool and can identify the enthalpy, standard entropy and standard Gibbs energy of activation. Despite this, it the method is unable to accurately determine these true values in line with experimental results as doing so would require a deep understanding of the potential energy surface of each reaction. Therefore, TST under estimates the reaction rate in comparison to the experimental values. When TST was developed in 1935 a lack of adequate computer software to accurately map potential energy surfaces with the relative quantum chemical contributions, unlike there is today. Hence resulting in a less accurate and longer method to map these surfaces for each reaction.

==F-H-H System Exercise 2==
===Potential Energy Surface Inspection===
====Energetics====

F + H2 is an exothermic reaction as can be seen from the surface plot, the reaction progresses from a small H-H distance to a longer one, whilst H-F simultaneously equilibriates about the F-H bond length. It can be seen that the products are lower, and hence more stable, in energy than the reactants.

F-H + H is simply the reverse reaction that passes through the same transition state, hence this reaction is endothermic with the products being higher in energy than the reactants. There is an overall gain of energy.

With this information in mind, the F-H bond is more stable and thus stronger than the H-H bond. The main factors to this argument is the greater electronegativity of F leading to a stronger contribution to the bond than the molecular orbitals. Hence the overlap of molecular orbitals is a weaker factor in the bond strength.

[[File:sm6416_FHH_Surface.png|thumb|none|350px|Surface plot highlighting the energetics of the F-H-H system.]]

[[File:sm6416_HHF_Surface.png|thumb|none|350px|Surface plot highlighting the energetics of the H-H-F system.]]

====Transition State====

Hammond's postulate aids in finding the transition state; it relates the composition of the transition complex to either the reactants or products for an early or late transition state respectively. In the scenario under investigation for F +H2 an early transition state is present as the reaction is exothermic in this direction, hence the transition state resembles the reactants more.

This guidance proved useful in determining the transition state complex at r1 = F-H = 1.810076 Angstrom and r2 = H-H = 0.74634 Angstrom, as can be seen from the surface and contour plots below showing the absence of displacement to either reactants or products. Furthermore the Momenta vs Time plot indicates a very small momenta of the overall system, without any deviation or substantial change in the momenta.

[[File:sm6416_FHH_Transition_State_Contour.png|thumb|none|350px|Contour plot demonstrating rts as a result of no fluctuations from the initial input, hence the complex is metaphorically sitting on the transition state.]]

[[File:sm6416_FHH_Transition_State_Momenta_Time.png|thumb|none|350px|Momenta vs Time plot demonstrating minimum, and almost zero, momentum at rts.]]

[[File:sm6416_FHH_Transition_State_Surface.png|thumb|none|350px]]

====Activation Energy====

The activation energy for the exothermic reaction was calculated through a 500000 step MEP simulation with input values of r1 = 1.820076, r2 = 0.74634 and p1 = p2 = 0. It was required that after following the minimum energy path, the gradient of the line signifying the reactants was constant.

The activation energy is reported at +0.258 kcal/mol for the exothermic process.

[[File:sm6416_FHH_Activation_Energy_1.png|thumb|none|350px|Energy vs Time graph highlighting the activation energy of the exothermic reaction.]]

The activation energy for the endothermic process was determined with the following parameters: r1 = 1.800076, r2 = 0.74634, p1 = p2 = 0 with 250000 steps. These parameters 'tipped' the reaction towards the FH + H reactants. The reported activation energy was +30.277 kcal/mol.

[[File:sm6416_FHH_Activation_Energy_2.png|thumb|none|350px|Energy vs Time graph highlighting the activation energy of the endothermic reaction.]]

It can hence be seen that the exothermic reaction of F + H2 --> F-H + H only requires a small activation energy as the products are substantially more thermodynamically stable than the reactants.

===Reaction Dynamics===

In this exothermic reaction, the potential energy is mainly converted into vibrational energy of the FH bond, along with heat. As a result of this vibrational energy in the FH bond, vibrational levels above the ground state will become partially populated. In this manner, by recording an IR spectrum of the products, the main F-H will be observed alongside an overtone, with the intensity of this overtone relating to the population of this vibrationally excited state, which can then be used to determine the vibrational energy in the bond itself.

In this same vein, IR chemiluminescence can be employed to yield the same result by measuring the wavelength, and subsequent vibrational energy of the FH bond, of the infrared light that is irradiated from the products and being excited with incident light.

As the momentum closes towards the boundaries of -3 < p < +3, the system passes through transition state but returns to reactant well. This shows that the excess momentum of the system in the product well is sufficient to overcome the high activation energy and return to the thermodynamically unfavourable reactants.

The following parameters were employed for all simulations rFH = 2.3, rHH = 0.74 with 500 steps calculated.

{| class="wikitable" border=2
! Simulation !! pHH !! pFH !! Surface Plot !! Momenta vs Time Plot !! Observations !!
|-
| 1 || -2.5 || -1.5 || [[File:sm6416_Trajectory_1_Surface.png|thumb|none|350px]] ||[[File:sm6416_Trajectory_1_Momenta.png|thumb|none|350px]] || This trajectory results in a successful reaction as seen from the surface plot; the reactants proceed through the transition state and continue into the product well, whilst continually oscillating as a result of the momentum gained.
|-
| 2 || -0.5 || -0.5 || [[File:sm6416_Trajectory_2_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_2_Momenta.png|thumb|none|350px]] || This momentum does not proceed to a reaction. Through the dynamic animation it can be seen that the HH molecule does not possess enough momentum to translate towards F. Therefore the system does not translate out of the reactant well, as seen in the surface plot, since there is not enough energy to overcome the activation energy. The momenta plot simply shows a small up trend, this is expected due to the long range electrostatic force of attraction between F and HH, resulting in a slight increase in the HH vibration velocity. There is no drastic change in the momenta of either F or HH that would otherwise indicate the occurrence of a reaction, as seen in simulation 1 above.
|-
| 3 || +0.5 || -0.5 || [[File:sm6416_Trajectory_3_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_3_Momenta.png|thumb|none|350px]] || This simulation shows an unreactive path, as can be seen from the surface plot, the system remains in the reactant well as it does not overcome the small activation energy for the exothermic reaction to proceed. As in simulation 2, the momentum amplitude of the oscillating HH remains constant however the overall momenta of the system increases due to a slight translation towards F, thus increasing electrostatic attraction forces resulting in this slight overall momenta increase.
|-
| 4 || -1.6 || -0.5 || [[File:sm6416_Trajectory_4_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_4_Momenta.png|thumb|none|350px]] || This simulation is very similar to simulations 2 & 3 in that the system remains in the reactant well as there is not sufficient energy to overcome the activation energy. However as a result of the greater HH momentum, the oscillation amplitude is greater than both simulation 1 & 2.
|-
| 5 || +1.6 || -0.5 || [[File:sm6416_Trajectory_5_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_5_Momenta.png|thumb|none|350px]] || Firstly, this simulation is unreactive as can be seen from the surface plot. In comparison to simulation 4, HH momentum sign has been changed and as a result this has led to not only a greater oscillating amplitude but also a larger translation towards F. So much so in the latter than the Momenta vs Time plot shows an increase in FH oscillation momentum as the electrostatic forces of attraction dominate due to the reduction in internuclear distance.
|-
| 6 || -2.9 || -0.5 || [[File:sm6416_Trajectory_6_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_6_Momenta.png|thumb|none|350px]] || This is the first reactive simulation observed, as can be seen from the surface plot and the drastic change in the momentum of FH. Evidently, there is sufficient energy to pass through the transition state complex and towards the reactants.
|-
| 7 || +2.9 || -0.5 || [[File:sm6416_Trajectory_7_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_7_Momenta.png|thumb|none|350px]] || This simulation is indeed similar to that of simulation 6 however, the change of sign for the HH momentum again results in a greater translation towards F and consequently the system passes through the transition complex shown by the surface plot and Momenta vs Time plot. However after a single oscillation, FH dissociates and the system returns to the reactant well with HH possessing a greater momentum. This scenario could be as a result of the HH momentum being too high and thus providing sufficient activation energy to proceed in the endothermic direction. This is surprising as the exothermic reaction elucidates more thermodynamically stable products.
|-
| 8 || +0.1 || -0.8 || [[File:sm6416_Trajectory_8_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_8_Momenta.png|thumb|none|350px]] || With a mere 60% change in FH momentum and a minimum HH momentum, the system can be seen to react fully, without returning through the transition state. The Momenta vs Time plot further shows a noticeable change in the AB momentum, which corresponds to FH. Despite the oscillations not being regular, it can be noted that the amplitudes are relatively of the same size and show no signs of regressing. This information highlights that the overall the FH momentum dominates the reactivity of the system and has a large weighting to overcoming the activation energy. It can be thought that the increase in momentum aids in allowing a closer distance of F & H, where electrostatic attraction forces will prevail.
|}

====Polyani's Empirical Rules====

The reactive trajectory for the FH + H was determined with the following parameters: rFH = 0.9, rHH = 2.3, pFH = 6.5, pHH = -1.5. The plots below highlight that these parameters lead to a reactive trajectory.

[[File:sm6416_FHH_Reactive_Trajectory_1_Surface.png|thumb|none|350px|Surface plot showing the reactants pass through the transition state and enter the product well without returning through the transition complex. This trajectory is therefore reactive.]]
[[File:sm6416_FHH_Reactive_Trajectory_1_Momenta.png|thumb|none|350px|Momenta vs Time plot indicating the substantial loss of momentum of FH, indicating dissociation, with the simultaneous gain in momentum of HH, indicated by the orange line.]]
[[File:sm6416_FHH_Reactive_Trajectory_1_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot showing a successful reaction. The HH distance vibrationally oscillates about the equilibrium bond distance, whereas the F-H distance increases linearly as a result of F translating away from H2.]]
[[File:sm6416_FHH_Reactive_Trajectory_1_Contour.png|thumb|none|350px|Contour plot highlighting similar information to the surface plot above in that the system stably occupies the product well without returning through the transition complex.]]

In order to react, a system must overcome the activation energy, the energy to achieve this is supplied by either translational or vibrational energy. As reported by Polanyi's Empirical Rules, a late transition state, one that resembles the products more as stated through Hammond's Postulate, is achieved through a greater contribution from vibrational energy enabling the activation energy to be overcome. The opposite is true for an early transition state which is promoted by a greater contribution from translational energy.

The F + H2 system is exothermic, thus an early transition state is present. Therefore this is promoted with higher translational energy being able to overcome the activation energy, hence pFH would contribute to the translational energy whereas pHH relates to the vibrational energy of the HH bond.

On the other hand, the FH + H system is endothermic and relates to a late transition state as dictated by Hammond's Postulate, requiring high vibrational energy of the FH bond to overcome the activation energy. In this scenario, pFH refers to the vibrational energy and pHH the translational energy.

MRD:sm6416

2018-05-25T16:36:03Z

Sm6416: /* Transition State Theory */

==H2 + H Exercise 1==

===Transition State Dynamics===

The transition state is the stage in a reaction coordinate that must be passed through in order for a reaction to occur and occurs at a saddle point, as shown by the numerous surface plots on this page. The first derivative highlights the positions along the reaction coordinate where the gradient equals zero. However, in order to determine if a saddle point ensues, the second derivative of the gradient must be taken. A saddle point is only present if the second derivative > 0.

Another way to think of the transition state is by thinking of the tangent that can be formed at the transition state itself. This tangent will follow the reaction coordinate profile and therefore is expected to be a maximum, where the gradient = 0. A line can be drawn to the normal of the tangent at the selected transition state. This path would show a minimum, where the gradient again = 0, at the intersection of the tangent with normal if the transition state has been correctly identified. It is only in this scenario that a transition state can be determined as one.

===Locating the Transition State===

The transition state was determined through iterations of both r1 and r2 which resulted in the smallest displacement of momenta along with no displacement as shown by the contour plot. This method determined at rts = 0.907743.

[[File:sm6416_Transition_State_Contour.png|thumb|none|350px|Contour plot demonstrating rts = 0.907743 as a result of no fluctuations from the initial input, hence the complex is at the transition state.]]

[[File:sm6416_Transition_State_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating minimum, and almost zero, momentum at rts = 0.907743.]]

[[File:sm6416_Transition_State_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot demonstrating no fluctuations in distance and hence rts = 0.907743.]]

===Reaction Path===

The minimum energy path (MEP) is defined as the lowest path the reaction must follow to form the products and is the downhill motion from the transition state. It can be applied in both directions in the case in question. The MEP views the system as static as it resets the velocity to zero at each step. Whereas the trajectory is very much dynamic and the momenta is accounted for, this is reflected in the vibrational oscillation of the molecule as it passes along the minimum well towards the products.

====MEP====

Initial conditions of r1 = rts + 0.01 = 0.917743, r2 = rts = 0.907743 and p1 = p2 = 0 for the MEP simulation.

[[File:sm6416_MEP_Surface.png|thumb|none|350px|Surface plot highlighting the minimum energy path (MEP), as the reaction returns to the reactants without fully passing through the transition state.]]

[[File:sm6416_MEP_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating zero momentum, as inputted, and more importantly not change in momentum with running the simulation.]]

[[File:sm6416_MEP_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot showing that the reactants reach the transition state at the interception of r1 = r2. r1 quickly reaches a constant value, namely the equilibrium bond length of the reactant molecule. r2 increases logarithmically as time progresses, this represents an increasing distance of Ha from Hb-Hc and a continuing loss of momentum.]]

Final values from the MEP simulation.

r1 = 2.76195

r2 = 0.75883

These values reflect the minimum trajectory for a successful reaction.

p1 = p2 = 0

====Dynamic====

[[File:sm6416_Dynamic_Surface.png|thumb|none|350px|Surface plot highlighting the minimum energy path (MEP) with oscillation of the reactants, as the reaction returns to the reactants without fully passing through the transition state. It is therefore evident that the momentum as a result of the vibrational oscillation does not provide enough energy to proceed to the products.]]

[[File:sm6416_Dynamic_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating the momenta associated with the oscillating reactants.]]

[[File:sm6416_Dynamic_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot showing that the reactants reach the transition state at the interception of r1 = r2. r1 quickly decreases and oscillates about a constant value, namely the equilibrium bond length of the reactant molecule. r2 increases linearly as time progresses, this represents an increasing distance of Ha from Hb-Hc with a constant momentum.]]

Dynamic simulation final values

r1 = 10.0045

r2 = 0.75883

p1 = 2.48523

p2 = 1.29898

p(average) = 1.90409

With r1 = rts and r2 = rts + 0.01 would simply produce the same answer however the values would be flipped to the other distance. In other words r1 = 0.75883 and r2 = 10.0045 would be the output values.

Maintaining the final trajectories as calculated from the dynamic simulation and reversing the sign of the momenta, the reaction proceeds in the reverse direction to the products.

===Reactivity of Trajectories===

These simulations are restricted by the number of steps the program can handle, however a sound understanding of the reaction can be appreciated and the reactivity of each scenario can be determined appropriately.

{| class="wikitable" border=2
! Simulation !! p1 !! p2 !! Energy (kcal/mol) !! Reactivity !! Evidence !! Description
|-
| 1 || -1.25 || -2.5 || 5.03500 || Reactive || [[File:sm6416_MEP_Figure1.png|thumb|none|350px]] || The reactants proceed through the transition state and to the products. The r2 distance decreases to the equilibrium bond length, whilst r1 simultaneously exhibits dissociation and increases beyond the scope of the graph. The small momenta attributed to the reactants is reflected in the vibrationally oscillating products, with a small amplitude.
|-
| 2 || -1.5 || -2.0 || 3.62879 || Unreactive || [[File:sm6416_MEP_Figure2.png|thumb|none|350px]] || This is unreactive as the oscillating reactants reach the transition state point and r1 immediately returns to the initial bond length, whilst r2 continues to increase as it moves away from the H2 molecule.
|-
| 3 || -1.5 || -2.5 || 5.13738 || Reactive || [[File:sm6416_MEP_Figure3.png|thumb|none|350px]] || This simulation shows a reactive pathway that is very similar to simulation 1, however due to the greater momenta associated with the reactants, as inputted, vibrational oscillations with a greater amplitude can be observed.
|-
| 4 || -2.5 || -5.0 || 9.86678 || Unreactive || [[File:sm6416_MEP_Figure4.png|thumb|none|350px]] || Initially seen here are oscillating reactants with a very large amplitude. However, this simulation is unreactive despite the reactants going through the transition state and towards the product, they return to the initial reactants.
|-
| 5 || -2.5 || -5.2 || 11.80780 || Reactive || [[File:sm6416_MEP_Figure5.png|thumb|none|350px]] || Like simulation 4, this simulation shows a large oscillating amplitude, whereas in this scenario after passing through the transition state, the products are completely obtained. The slight increase in the p2 momentum can be seen to result in the products.
|}

====Transition State Theory====

Transition State Theory (TST) assumes a quasi-equilibrium between reactants and the transition state. The reaction between the transition state and products is irreversible and therefore is unable to return to the reactants, however many of the surface plots on this page show the complete antithesis of this highlighting a dichotomy between theory and experimental. TST further assumes that fluctuation as to whether the transition complexes go towards reactants or products are independent of each other and hence the rate of one can not be determined by the other.

TST is an excellent qualitative tool and can identify the enthalpy, standard entropy and standard Gibbs energy of activation. Despite this, it the method is unable to accurately determine these true values in line with experimental results as doing so would require a deep understanding of the potential energy surface of each reaction. Therefore, TST under estimates the reaction rate in comparison to the experimental values. When TST was developed in 1935 a lack of adequate computer software to accurately map potential energy surfaces, unlike there is today. Hence resulting in a less accurate and longer method to map these surfaces for each reaction.

==F-H-H System Exercise 2==
===Potential Energy Surface Inspection===
====Energetics====

F + H2 is an exothermic reaction as can be seen from the surface plot, the reaction progresses from a small H-H distance to a longer one, whilst H-F simultaneously equilibriates about the F-H bond length. It can be seen that the products are lower, and hence more stable, in energy than the reactants.

F-H + H is simply the reverse reaction that passes through the same transition state, hence this reaction is endothermic with the products being higher in energy than the reactants. There is an overall gain of energy.

With this information in mind, the F-H bond is more stable and thus stronger than the H-H bond. The main factors to this argument is the greater electronegativity of F leading to a stronger contribution to the bond than the molecular orbitals. Hence the overlap of molecular orbitals is a weaker factor in the bond strength.

[[File:sm6416_FHH_Surface.png|thumb|none|350px|Surface plot highlighting the energetics of the F-H-H system.]]

[[File:sm6416_HHF_Surface.png|thumb|none|350px|Surface plot highlighting the energetics of the H-H-F system.]]

====Transition State====

Hammond's postulate aids in finding the transition state; it relates the composition of the transition complex to either the reactants or products for an early or late transition state respectively. In the scenario under investigation for F +H2 an early transition state is present as the reaction is exothermic in this direction, hence the transition state resembles the reactants more.

This guidance proved useful in determining the transition state complex at r1 = F-H = 1.810076 Angstrom and r2 = H-H = 0.74634 Angstrom, as can be seen from the surface and contour plots below showing the absence of displacement to either reactants or products. Furthermore the Momenta vs Time plot indicates a very small momenta of the overall system, without any deviation or substantial change in the momenta.

[[File:sm6416_FHH_Transition_State_Contour.png|thumb|none|350px|Contour plot demonstrating rts as a result of no fluctuations from the initial input, hence the complex is metaphorically sitting on the transition state.]]

[[File:sm6416_FHH_Transition_State_Momenta_Time.png|thumb|none|350px|Momenta vs Time plot demonstrating minimum, and almost zero, momentum at rts.]]

[[File:sm6416_FHH_Transition_State_Surface.png|thumb|none|350px]]

====Activation Energy====

The activation energy for the exothermic reaction was calculated through a 500000 step MEP simulation with input values of r1 = 1.820076, r2 = 0.74634 and p1 = p2 = 0. It was required that after following the minimum energy path, the gradient of the line signifying the reactants was constant.

The activation energy is reported at +0.258 kcal/mol for the exothermic process.

[[File:sm6416_FHH_Activation_Energy_1.png|thumb|none|350px|Energy vs Time graph highlighting the activation energy of the exothermic reaction.]]

The activation energy for the endothermic process was determined with the following parameters: r1 = 1.800076, r2 = 0.74634, p1 = p2 = 0 with 250000 steps. These parameters 'tipped' the reaction towards the FH + H reactants. The reported activation energy was +30.277 kcal/mol.

[[File:sm6416_FHH_Activation_Energy_2.png|thumb|none|350px|Energy vs Time graph highlighting the activation energy of the endothermic reaction.]]

It can hence be seen that the exothermic reaction of F + H2 --> F-H + H only requires a small activation energy as the products are substantially more thermodynamically stable than the reactants.

===Reaction Dynamics===

In this exothermic reaction, the potential energy is mainly converted into vibrational energy of the FH bond, along with heat. As a result of this vibrational energy in the FH bond, vibrational levels above the ground state will become partially populated. In this manner, by recording an IR spectrum of the products, the main F-H will be observed alongside an overtone, with the intensity of this overtone relating to the population of this vibrationally excited state, which can then be used to determine the vibrational energy in the bond itself.

In this same vein, IR chemiluminescence can be employed to yield the same result by measuring the wavelength, and subsequent vibrational energy of the FH bond, of the infrared light that is irradiated from the products and being excited with incident light.

As the momentum closes towards the boundaries of -3 < p < +3, the system passes through transition state but returns to reactant well. This shows that the excess momentum of the system in the product well is sufficient to overcome the high activation energy and return to the thermodynamically unfavourable reactants.

The following parameters were employed for all simulations rFH = 2.3, rHH = 0.74 with 500 steps calculated.

{| class="wikitable" border=2
! Simulation !! pHH !! pFH !! Surface Plot !! Momenta vs Time Plot !! Observations !!
|-
| 1 || -2.5 || -1.5 || [[File:sm6416_Trajectory_1_Surface.png|thumb|none|350px]] ||[[File:sm6416_Trajectory_1_Momenta.png|thumb|none|350px]] || This trajectory results in a successful reaction as seen from the surface plot; the reactants proceed through the transition state and continue into the product well, whilst continually oscillating as a result of the momentum gained.
|-
| 2 || -0.5 || -0.5 || [[File:sm6416_Trajectory_2_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_2_Momenta.png|thumb|none|350px]] || This momentum does not proceed to a reaction. Through the dynamic animation it can be seen that the HH molecule does not possess enough momentum to translate towards F. Therefore the system does not translate out of the reactant well, as seen in the surface plot, since there is not enough energy to overcome the activation energy. The momenta plot simply shows a small up trend, this is expected due to the long range electrostatic force of attraction between F and HH, resulting in a slight increase in the HH vibration velocity. There is no drastic change in the momenta of either F or HH that would otherwise indicate the occurrence of a reaction, as seen in simulation 1 above.
|-
| 3 || +0.5 || -0.5 || [[File:sm6416_Trajectory_3_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_3_Momenta.png|thumb|none|350px]] || This simulation shows an unreactive path, as can be seen from the surface plot, the system remains in the reactant well as it does not overcome the small activation energy for the exothermic reaction to proceed. As in simulation 2, the momentum amplitude of the oscillating HH remains constant however the overall momenta of the system increases due to a slight translation towards F, thus increasing electrostatic attraction forces resulting in this slight overall momenta increase.
|-
| 4 || -1.6 || -0.5 || [[File:sm6416_Trajectory_4_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_4_Momenta.png|thumb|none|350px]] || This simulation is very similar to simulations 2 & 3 in that the system remains in the reactant well as there is not sufficient energy to overcome the activation energy. However as a result of the greater HH momentum, the oscillation amplitude is greater than both simulation 1 & 2.
|-
| 5 || +1.6 || -0.5 || [[File:sm6416_Trajectory_5_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_5_Momenta.png|thumb|none|350px]] || Firstly, this simulation is unreactive as can be seen from the surface plot. In comparison to simulation 4, HH momentum sign has been changed and as a result this has led to not only a greater oscillating amplitude but also a larger translation towards F. So much so in the latter than the Momenta vs Time plot shows an increase in FH oscillation momentum as the electrostatic forces of attraction dominate due to the reduction in internuclear distance.
|-
| 6 || -2.9 || -0.5 || [[File:sm6416_Trajectory_6_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_6_Momenta.png|thumb|none|350px]] || This is the first reactive simulation observed, as can be seen from the surface plot and the drastic change in the momentum of FH. Evidently, there is sufficient energy to pass through the transition state complex and towards the reactants.
|-
| 7 || +2.9 || -0.5 || [[File:sm6416_Trajectory_7_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_7_Momenta.png|thumb|none|350px]] || This simulation is indeed similar to that of simulation 6 however, the change of sign for the HH momentum again results in a greater translation towards F and consequently the system passes through the transition complex shown by the surface plot and Momenta vs Time plot. However after a single oscillation, FH dissociates and the system returns to the reactant well with HH possessing a greater momentum. This scenario could be as a result of the HH momentum being too high and thus providing sufficient activation energy to proceed in the endothermic direction. This is surprising as the exothermic reaction elucidates more thermodynamically stable products.
|-
| 8 || +0.1 || -0.8 || [[File:sm6416_Trajectory_8_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_8_Momenta.png|thumb|none|350px]] || With a mere 60% change in FH momentum and a minimum HH momentum, the system can be seen to react fully, without returning through the transition state. The Momenta vs Time plot further shows a noticeable change in the AB momentum, which corresponds to FH. Despite the oscillations not being regular, it can be noted that the amplitudes are relatively of the same size and show no signs of regressing. This information highlights that the overall the FH momentum dominates the reactivity of the system and has a large weighting to overcoming the activation energy. It can be thought that the increase in momentum aids in allowing a closer distance of F & H, where electrostatic attraction forces will prevail.
|}

====Polyani's Empirical Rules====

The reactive trajectory for the FH + H was determined with the following parameters: rFH = 0.9, rHH = 2.3, pFH = 6.5, pHH = -1.5. The plots below highlight that these parameters lead to a reactive trajectory.

[[File:sm6416_FHH_Reactive_Trajectory_1_Surface.png|thumb|none|350px|Surface plot showing the reactants pass through the transition state and enter the product well without returning through the transition complex. This trajectory is therefore reactive.]]
[[File:sm6416_FHH_Reactive_Trajectory_1_Momenta.png|thumb|none|350px|Momenta vs Time plot indicating the substantial loss of momentum of FH, indicating dissociation, with the simultaneous gain in momentum of HH, indicated by the orange line.]]
[[File:sm6416_FHH_Reactive_Trajectory_1_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot showing a successful reaction. The HH distance vibrationally oscillates about the equilibrium bond distance, whereas the F-H distance increases linearly as a result of F translating away from H2.]]
[[File:sm6416_FHH_Reactive_Trajectory_1_Contour.png|thumb|none|350px|Contour plot highlighting similar information to the surface plot above in that the system stably occupies the product well without returning through the transition complex.]]

In order to react, a system must overcome the activation energy, the energy to achieve this is supplied by either translational or vibrational energy. As reported by Polanyi's Empirical Rules, a late transition state, one that resembles the products more as stated through Hammond's Postulate, is achieved through a greater contribution from vibrational energy enabling the activation energy to be overcome. The opposite is true for an early transition state which is promoted by a greater contribution from translational energy.

The F + H2 system is exothermic, thus an early transition state is present. Therefore this is promoted with higher translational energy being able to overcome the activation energy, hence pFH would contribute to the translational energy whereas pHH relates to the vibrational energy of the HH bond.

On the other hand, the FH + H system is endothermic and relates to a late transition state as dictated by Hammond's Postulate, requiring high vibrational energy of the FH bond to overcome the activation energy. In this scenario, pFH refers to the vibrational energy and pHH the translational energy.

MRD:sm6416

2018-05-25T16:35:30Z

Sm6416: /* Reactivity of Trajectories */

==H2 + H Exercise 1==

===Transition State Dynamics===

The transition state is the stage in a reaction coordinate that must be passed through in order for a reaction to occur and occurs at a saddle point, as shown by the numerous surface plots on this page. The first derivative highlights the positions along the reaction coordinate where the gradient equals zero. However, in order to determine if a saddle point ensues, the second derivative of the gradient must be taken. A saddle point is only present if the second derivative > 0.

Another way to think of the transition state is by thinking of the tangent that can be formed at the transition state itself. This tangent will follow the reaction coordinate profile and therefore is expected to be a maximum, where the gradient = 0. A line can be drawn to the normal of the tangent at the selected transition state. This path would show a minimum, where the gradient again = 0, at the intersection of the tangent with normal if the transition state has been correctly identified. It is only in this scenario that a transition state can be determined as one.

===Locating the Transition State===

The transition state was determined through iterations of both r1 and r2 which resulted in the smallest displacement of momenta along with no displacement as shown by the contour plot. This method determined at rts = 0.907743.

[[File:sm6416_Transition_State_Contour.png|thumb|none|350px|Contour plot demonstrating rts = 0.907743 as a result of no fluctuations from the initial input, hence the complex is at the transition state.]]

[[File:sm6416_Transition_State_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating minimum, and almost zero, momentum at rts = 0.907743.]]

[[File:sm6416_Transition_State_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot demonstrating no fluctuations in distance and hence rts = 0.907743.]]

===Reaction Path===

The minimum energy path (MEP) is defined as the lowest path the reaction must follow to form the products and is the downhill motion from the transition state. It can be applied in both directions in the case in question. The MEP views the system as static as it resets the velocity to zero at each step. Whereas the trajectory is very much dynamic and the momenta is accounted for, this is reflected in the vibrational oscillation of the molecule as it passes along the minimum well towards the products.

====MEP====

Initial conditions of r1 = rts + 0.01 = 0.917743, r2 = rts = 0.907743 and p1 = p2 = 0 for the MEP simulation.

[[File:sm6416_MEP_Surface.png|thumb|none|350px|Surface plot highlighting the minimum energy path (MEP), as the reaction returns to the reactants without fully passing through the transition state.]]

[[File:sm6416_MEP_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating zero momentum, as inputted, and more importantly not change in momentum with running the simulation.]]

[[File:sm6416_MEP_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot showing that the reactants reach the transition state at the interception of r1 = r2. r1 quickly reaches a constant value, namely the equilibrium bond length of the reactant molecule. r2 increases logarithmically as time progresses, this represents an increasing distance of Ha from Hb-Hc and a continuing loss of momentum.]]

Final values from the MEP simulation.

r1 = 2.76195

r2 = 0.75883

These values reflect the minimum trajectory for a successful reaction.

p1 = p2 = 0

====Dynamic====

[[File:sm6416_Dynamic_Surface.png|thumb|none|350px|Surface plot highlighting the minimum energy path (MEP) with oscillation of the reactants, as the reaction returns to the reactants without fully passing through the transition state. It is therefore evident that the momentum as a result of the vibrational oscillation does not provide enough energy to proceed to the products.]]

[[File:sm6416_Dynamic_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating the momenta associated with the oscillating reactants.]]

[[File:sm6416_Dynamic_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot showing that the reactants reach the transition state at the interception of r1 = r2. r1 quickly decreases and oscillates about a constant value, namely the equilibrium bond length of the reactant molecule. r2 increases linearly as time progresses, this represents an increasing distance of Ha from Hb-Hc with a constant momentum.]]

Dynamic simulation final values

r1 = 10.0045

r2 = 0.75883

p1 = 2.48523

p2 = 1.29898

p(average) = 1.90409

With r1 = rts and r2 = rts + 0.01 would simply produce the same answer however the values would be flipped to the other distance. In other words r1 = 0.75883 and r2 = 10.0045 would be the output values.

Maintaining the final trajectories as calculated from the dynamic simulation and reversing the sign of the momenta, the reaction proceeds in the reverse direction to the products.

===Reactivity of Trajectories===

These simulations are restricted by the number of steps the program can handle, however a sound understanding of the reaction can be appreciated and the reactivity of each scenario can be determined appropriately.

{| class="wikitable" border=2
! Simulation !! p1 !! p2 !! Energy (kcal/mol) !! Reactivity !! Evidence !! Description
|-
| 1 || -1.25 || -2.5 || 5.03500 || Reactive || [[File:sm6416_MEP_Figure1.png|thumb|none|350px]] || The reactants proceed through the transition state and to the products. The r2 distance decreases to the equilibrium bond length, whilst r1 simultaneously exhibits dissociation and increases beyond the scope of the graph. The small momenta attributed to the reactants is reflected in the vibrationally oscillating products, with a small amplitude.
|-
| 2 || -1.5 || -2.0 || 3.62879 || Unreactive || [[File:sm6416_MEP_Figure2.png|thumb|none|350px]] || This is unreactive as the oscillating reactants reach the transition state point and r1 immediately returns to the initial bond length, whilst r2 continues to increase as it moves away from the H2 molecule.
|-
| 3 || -1.5 || -2.5 || 5.13738 || Reactive || [[File:sm6416_MEP_Figure3.png|thumb|none|350px]] || This simulation shows a reactive pathway that is very similar to simulation 1, however due to the greater momenta associated with the reactants, as inputted, vibrational oscillations with a greater amplitude can be observed.
|-
| 4 || -2.5 || -5.0 || 9.86678 || Unreactive || [[File:sm6416_MEP_Figure4.png|thumb|none|350px]] || Initially seen here are oscillating reactants with a very large amplitude. However, this simulation is unreactive despite the reactants going through the transition state and towards the product, they return to the initial reactants.
|-
| 5 || -2.5 || -5.2 || 11.80780 || Reactive || [[File:sm6416_MEP_Figure5.png|thumb|none|350px]] || Like simulation 4, this simulation shows a large oscillating amplitude, whereas in this scenario after passing through the transition state, the products are completely obtained. The slight increase in the p2 momentum can be seen to result in the products.
|}

====Transition State Theory====

Transition State Theory (TST) assumes a quasi-equilibrium between reactants and the transition state. The reaction between the transition state and products is irreversible and therefore is unable to return to the reactants, however many of the surface plots on this page show the complete antithesis of this highlighting a dichotomy between theory and experimental. TST further assumes that fluctuation as to whether the transition complexes go towards reactants or products are independent of each other and hence the rate of one can not be determined by the other.

TST is excellent qualitative tool and can identify the enthalpy, standard entropy and standard Gibbs energy of activation. Despite this, it the method is unable to accurately determine these true values in line with experimental results as doing so would require a deep understanding of the potential energy surface of each reaction. Therefore, TST under estimates the reaction rate in comparison to the experimental values. When TST was developed in 1935 a lack of adequate computer software to accurately map potential energy surfaces, unlike there is today. Hence resulting in a less accurate and longer method to map these surfaces for each reaction.

==F-H-H System Exercise 2==
===Potential Energy Surface Inspection===
====Energetics====

F + H2 is an exothermic reaction as can be seen from the surface plot, the reaction progresses from a small H-H distance to a longer one, whilst H-F simultaneously equilibriates about the F-H bond length. It can be seen that the products are lower, and hence more stable, in energy than the reactants.

F-H + H is simply the reverse reaction that passes through the same transition state, hence this reaction is endothermic with the products being higher in energy than the reactants. There is an overall gain of energy.

With this information in mind, the F-H bond is more stable and thus stronger than the H-H bond. The main factors to this argument is the greater electronegativity of F leading to a stronger contribution to the bond than the molecular orbitals. Hence the overlap of molecular orbitals is a weaker factor in the bond strength.

[[File:sm6416_FHH_Surface.png|thumb|none|350px|Surface plot highlighting the energetics of the F-H-H system.]]

[[File:sm6416_HHF_Surface.png|thumb|none|350px|Surface plot highlighting the energetics of the H-H-F system.]]

====Transition State====

Hammond's postulate aids in finding the transition state; it relates the composition of the transition complex to either the reactants or products for an early or late transition state respectively. In the scenario under investigation for F +H2 an early transition state is present as the reaction is exothermic in this direction, hence the transition state resembles the reactants more.

This guidance proved useful in determining the transition state complex at r1 = F-H = 1.810076 Angstrom and r2 = H-H = 0.74634 Angstrom, as can be seen from the surface and contour plots below showing the absence of displacement to either reactants or products. Furthermore the Momenta vs Time plot indicates a very small momenta of the overall system, without any deviation or substantial change in the momenta.

[[File:sm6416_FHH_Transition_State_Contour.png|thumb|none|350px|Contour plot demonstrating rts as a result of no fluctuations from the initial input, hence the complex is metaphorically sitting on the transition state.]]

[[File:sm6416_FHH_Transition_State_Momenta_Time.png|thumb|none|350px|Momenta vs Time plot demonstrating minimum, and almost zero, momentum at rts.]]

[[File:sm6416_FHH_Transition_State_Surface.png|thumb|none|350px]]

====Activation Energy====

The activation energy for the exothermic reaction was calculated through a 500000 step MEP simulation with input values of r1 = 1.820076, r2 = 0.74634 and p1 = p2 = 0. It was required that after following the minimum energy path, the gradient of the line signifying the reactants was constant.

The activation energy is reported at +0.258 kcal/mol for the exothermic process.

[[File:sm6416_FHH_Activation_Energy_1.png|thumb|none|350px|Energy vs Time graph highlighting the activation energy of the exothermic reaction.]]

The activation energy for the endothermic process was determined with the following parameters: r1 = 1.800076, r2 = 0.74634, p1 = p2 = 0 with 250000 steps. These parameters 'tipped' the reaction towards the FH + H reactants. The reported activation energy was +30.277 kcal/mol.

[[File:sm6416_FHH_Activation_Energy_2.png|thumb|none|350px|Energy vs Time graph highlighting the activation energy of the endothermic reaction.]]

It can hence be seen that the exothermic reaction of F + H2 --> F-H + H only requires a small activation energy as the products are substantially more thermodynamically stable than the reactants.

===Reaction Dynamics===

In this exothermic reaction, the potential energy is mainly converted into vibrational energy of the FH bond, along with heat. As a result of this vibrational energy in the FH bond, vibrational levels above the ground state will become partially populated. In this manner, by recording an IR spectrum of the products, the main F-H will be observed alongside an overtone, with the intensity of this overtone relating to the population of this vibrationally excited state, which can then be used to determine the vibrational energy in the bond itself.

In this same vein, IR chemiluminescence can be employed to yield the same result by measuring the wavelength, and subsequent vibrational energy of the FH bond, of the infrared light that is irradiated from the products and being excited with incident light.

As the momentum closes towards the boundaries of -3 < p < +3, the system passes through transition state but returns to reactant well. This shows that the excess momentum of the system in the product well is sufficient to overcome the high activation energy and return to the thermodynamically unfavourable reactants.

The following parameters were employed for all simulations rFH = 2.3, rHH = 0.74 with 500 steps calculated.

{| class="wikitable" border=2
! Simulation !! pHH !! pFH !! Surface Plot !! Momenta vs Time Plot !! Observations !!
|-
| 1 || -2.5 || -1.5 || [[File:sm6416_Trajectory_1_Surface.png|thumb|none|350px]] ||[[File:sm6416_Trajectory_1_Momenta.png|thumb|none|350px]] || This trajectory results in a successful reaction as seen from the surface plot; the reactants proceed through the transition state and continue into the product well, whilst continually oscillating as a result of the momentum gained.
|-
| 2 || -0.5 || -0.5 || [[File:sm6416_Trajectory_2_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_2_Momenta.png|thumb|none|350px]] || This momentum does not proceed to a reaction. Through the dynamic animation it can be seen that the HH molecule does not possess enough momentum to translate towards F. Therefore the system does not translate out of the reactant well, as seen in the surface plot, since there is not enough energy to overcome the activation energy. The momenta plot simply shows a small up trend, this is expected due to the long range electrostatic force of attraction between F and HH, resulting in a slight increase in the HH vibration velocity. There is no drastic change in the momenta of either F or HH that would otherwise indicate the occurrence of a reaction, as seen in simulation 1 above.
|-
| 3 || +0.5 || -0.5 || [[File:sm6416_Trajectory_3_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_3_Momenta.png|thumb|none|350px]] || This simulation shows an unreactive path, as can be seen from the surface plot, the system remains in the reactant well as it does not overcome the small activation energy for the exothermic reaction to proceed. As in simulation 2, the momentum amplitude of the oscillating HH remains constant however the overall momenta of the system increases due to a slight translation towards F, thus increasing electrostatic attraction forces resulting in this slight overall momenta increase.
|-
| 4 || -1.6 || -0.5 || [[File:sm6416_Trajectory_4_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_4_Momenta.png|thumb|none|350px]] || This simulation is very similar to simulations 2 & 3 in that the system remains in the reactant well as there is not sufficient energy to overcome the activation energy. However as a result of the greater HH momentum, the oscillation amplitude is greater than both simulation 1 & 2.
|-
| 5 || +1.6 || -0.5 || [[File:sm6416_Trajectory_5_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_5_Momenta.png|thumb|none|350px]] || Firstly, this simulation is unreactive as can be seen from the surface plot. In comparison to simulation 4, HH momentum sign has been changed and as a result this has led to not only a greater oscillating amplitude but also a larger translation towards F. So much so in the latter than the Momenta vs Time plot shows an increase in FH oscillation momentum as the electrostatic forces of attraction dominate due to the reduction in internuclear distance.
|-
| 6 || -2.9 || -0.5 || [[File:sm6416_Trajectory_6_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_6_Momenta.png|thumb|none|350px]] || This is the first reactive simulation observed, as can be seen from the surface plot and the drastic change in the momentum of FH. Evidently, there is sufficient energy to pass through the transition state complex and towards the reactants.
|-
| 7 || +2.9 || -0.5 || [[File:sm6416_Trajectory_7_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_7_Momenta.png|thumb|none|350px]] || This simulation is indeed similar to that of simulation 6 however, the change of sign for the HH momentum again results in a greater translation towards F and consequently the system passes through the transition complex shown by the surface plot and Momenta vs Time plot. However after a single oscillation, FH dissociates and the system returns to the reactant well with HH possessing a greater momentum. This scenario could be as a result of the HH momentum being too high and thus providing sufficient activation energy to proceed in the endothermic direction. This is surprising as the exothermic reaction elucidates more thermodynamically stable products.
|-
| 8 || +0.1 || -0.8 || [[File:sm6416_Trajectory_8_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_8_Momenta.png|thumb|none|350px]] || With a mere 60% change in FH momentum and a minimum HH momentum, the system can be seen to react fully, without returning through the transition state. The Momenta vs Time plot further shows a noticeable change in the AB momentum, which corresponds to FH. Despite the oscillations not being regular, it can be noted that the amplitudes are relatively of the same size and show no signs of regressing. This information highlights that the overall the FH momentum dominates the reactivity of the system and has a large weighting to overcoming the activation energy. It can be thought that the increase in momentum aids in allowing a closer distance of F & H, where electrostatic attraction forces will prevail.
|}

====Polyani's Empirical Rules====

The reactive trajectory for the FH + H was determined with the following parameters: rFH = 0.9, rHH = 2.3, pFH = 6.5, pHH = -1.5. The plots below highlight that these parameters lead to a reactive trajectory.

[[File:sm6416_FHH_Reactive_Trajectory_1_Surface.png|thumb|none|350px|Surface plot showing the reactants pass through the transition state and enter the product well without returning through the transition complex. This trajectory is therefore reactive.]]
[[File:sm6416_FHH_Reactive_Trajectory_1_Momenta.png|thumb|none|350px|Momenta vs Time plot indicating the substantial loss of momentum of FH, indicating dissociation, with the simultaneous gain in momentum of HH, indicated by the orange line.]]
[[File:sm6416_FHH_Reactive_Trajectory_1_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot showing a successful reaction. The HH distance vibrationally oscillates about the equilibrium bond distance, whereas the F-H distance increases linearly as a result of F translating away from H2.]]
[[File:sm6416_FHH_Reactive_Trajectory_1_Contour.png|thumb|none|350px|Contour plot highlighting similar information to the surface plot above in that the system stably occupies the product well without returning through the transition complex.]]

In order to react, a system must overcome the activation energy, the energy to achieve this is supplied by either translational or vibrational energy. As reported by Polanyi's Empirical Rules, a late transition state, one that resembles the products more as stated through Hammond's Postulate, is achieved through a greater contribution from vibrational energy enabling the activation energy to be overcome. The opposite is true for an early transition state which is promoted by a greater contribution from translational energy.

The F + H2 system is exothermic, thus an early transition state is present. Therefore this is promoted with higher translational energy being able to overcome the activation energy, hence pFH would contribute to the translational energy whereas pHH relates to the vibrational energy of the HH bond.

On the other hand, the FH + H system is endothermic and relates to a late transition state as dictated by Hammond's Postulate, requiring high vibrational energy of the FH bond to overcome the activation energy. In this scenario, pFH refers to the vibrational energy and pHH the translational energy.

MRD:sm6416

2018-05-25T16:31:00Z

Sm6416: /* H2 H Exercise 1 */

==H2 + H Exercise 1==

===Transition State Dynamics===

The transition state is the stage in a reaction coordinate that must be passed through in order for a reaction to occur and occurs at a saddle point, as shown by the numerous surface plots on this page. The first derivative highlights the positions along the reaction coordinate where the gradient equals zero. However, in order to determine if a saddle point ensues, the second derivative of the gradient must be taken. A saddle point is only present if the second derivative > 0.

Another way to think of the transition state is by thinking of the tangent that can be formed at the transition state itself. This tangent will follow the reaction coordinate profile and therefore is expected to be a maximum, where the gradient = 0. A line can be drawn to the normal of the tangent at the selected transition state. This path would show a minimum, where the gradient again = 0, at the intersection of the tangent with normal if the transition state has been correctly identified. It is only in this scenario that a transition state can be determined as one.

===Locating the Transition State===

The transition state was determined through iterations of both r1 and r2 which resulted in the smallest displacement of momenta along with no displacement as shown by the contour plot. This method determined at rts = 0.907743.

[[File:sm6416_Transition_State_Contour.png|thumb|none|350px|Contour plot demonstrating rts = 0.907743 as a result of no fluctuations from the initial input, hence the complex is at the transition state.]]

[[File:sm6416_Transition_State_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating minimum, and almost zero, momentum at rts = 0.907743.]]

[[File:sm6416_Transition_State_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot demonstrating no fluctuations in distance and hence rts = 0.907743.]]

===Reaction Path===

The minimum energy path (MEP) is defined as the lowest path the reaction must follow to form the products and is the downhill motion from the transition state. It can be applied in both directions in the case in question. The MEP views the system as static as it resets the velocity to zero at each step. Whereas the trajectory is very much dynamic and the momenta is accounted for, this is reflected in the vibrational oscillation of the molecule as it passes along the minimum well towards the products.

====MEP====

Initial conditions of r1 = rts + 0.01 = 0.917743, r2 = rts = 0.907743 and p1 = p2 = 0 for the MEP simulation.

[[File:sm6416_MEP_Surface.png|thumb|none|350px|Surface plot highlighting the minimum energy path (MEP), as the reaction returns to the reactants without fully passing through the transition state.]]

[[File:sm6416_MEP_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating zero momentum, as inputted, and more importantly not change in momentum with running the simulation.]]

[[File:sm6416_MEP_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot showing that the reactants reach the transition state at the interception of r1 = r2. r1 quickly reaches a constant value, namely the equilibrium bond length of the reactant molecule. r2 increases logarithmically as time progresses, this represents an increasing distance of Ha from Hb-Hc and a continuing loss of momentum.]]

Final values from the MEP simulation.

r1 = 2.76195

r2 = 0.75883

These values reflect the minimum trajectory for a successful reaction.

p1 = p2 = 0

====Dynamic====

[[File:sm6416_Dynamic_Surface.png|thumb|none|350px|Surface plot highlighting the minimum energy path (MEP) with oscillation of the reactants, as the reaction returns to the reactants without fully passing through the transition state. It is therefore evident that the momentum as a result of the vibrational oscillation does not provide enough energy to proceed to the products.]]

[[File:sm6416_Dynamic_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating the momenta associated with the oscillating reactants.]]

[[File:sm6416_Dynamic_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot showing that the reactants reach the transition state at the interception of r1 = r2. r1 quickly decreases and oscillates about a constant value, namely the equilibrium bond length of the reactant molecule. r2 increases linearly as time progresses, this represents an increasing distance of Ha from Hb-Hc with a constant momentum.]]

Dynamic simulation final values

r1 = 10.0045

r2 = 0.75883

p1 = 2.48523

p2 = 1.29898

p(average) = 1.90409

With r1 = rts and r2 = rts + 0.01 would simply produce the same answer however the values would be flipped to the other distance. In other words r1 = 0.75883 and r2 = 10.0045 would be the output values.

Maintaining the final trajectories as calculated from the dynamic simulation and reversing the sign of the momenta, the reaction proceeds in the reverse direction to the products.

===Reactivity of Trajectories===

These simulations are restricted by the number of steps the program can handle, however a sound understanding of the reaction can be appreciated and the reactivity of each scenario can be determined appropriately.

{| class="wikitable" border=2
! Simulation !! p1 !! p2 !! Energy (kcal/mol) !! Reactivity !! Evidence !! Description
|-
| 1 || -1.25 || -2.5 || 5.03500 || Reactive || [[File:sm6416_MEP_Figure1.png|thumb|none|350px]] || Simulation 1: The reactants proceed through the transition state and to the products. The r2 distance decreases to the equilibrium bond length, whilst r1 simultaneously exhibits dissociation and increases beyond the scope of the graph. The small momenta attributed to the reactants is reflected in the vibrationally oscillating products, with a small amplitude.
|-
| 2 || -1.5 || -2.0 || 3.62879 || Unreactive || [[File:sm6416_MEP_Figure2.png|thumb|none|350px]] || Simulation 2: This is unreactive as the oscillating reactants reach the transition state point and r1 immediately returns to the initial bond length, whilst r2 continues to increase as it moves away from the H2 molecule.
|-
| 3 || -1.5 || -2.5 || 5.13738 || Reactive || [[File:sm6416_MEP_Figure3.png|thumb|none|350px]] || Simulation 3: This simulation shows a reactive pathway that is very similar to simulation 1, however due to the greater momenta associated with the reactants, as inputted, vibrational oscillations with a greater amplitude can be observed.
|-
| 4 || -2.5 || -5.0 || 9.86678 || Unreactive || [[File:sm6416_MEP_Figure4.png|thumb|none|350px]] || Simulation 4: Initially seen here are oscillating reactants with a very large amplitude. However, this simulation is unreactive despite the reactants going through the transition state and towards the product, they return to the initial reactants.
|-
| 5 || -2.5 || -5.2 || 11.80780 || Reactive || [[File:sm6416_MEP_Figure5.png|thumb|none|350px]] || Simulation 5: Like simulation 4, this simulation shows a large oscillating amplitude, whereas in this scenario after passing through the transition state, the products are completely obtained. The slight increase in the p2 momentum can be seen to result in the products.
|}

====Transition State Theory====

Transition State Theory (TST) assumes a quasi-equilibrium between reactants and the transition state. The reaction between the transition state and products is irreversible and therefore is unable to return to the reactants, however many of the surface plots on this page show the complete antithesis of this highlighting a dichotomy between theory and experimental. TST further assumes that fluctuation as to whether the transition complexes go towards reactants or products are independent of each other and hence the rate of one can not be determined by the other.

TST is excellent qualitative tool and can identify the enthalpy, standard entropy and standard Gibbs energy of activation. Despite this, it the method is unable to accurately determine these true values in line with experimental results as doing so would require a deep understanding of the potential energy surface of each reaction. Therefore, TST under estimates the reaction rate in comparison to the experimental values. When TST was developed in 1935 a lack of adequate computer software to accurately map potential energy surfaces, unlike there is today. Hence resulting in a less accurate and longer method to map these surfaces for each reaction.

==F-H-H System Exercise 2==
===Potential Energy Surface Inspection===
====Energetics====

F + H2 is an exothermic reaction as can be seen from the surface plot, the reaction progresses from a small H-H distance to a longer one, whilst H-F simultaneously equilibriates about the F-H bond length. It can be seen that the products are lower, and hence more stable, in energy than the reactants.

F-H + H is simply the reverse reaction that passes through the same transition state, hence this reaction is endothermic with the products being higher in energy than the reactants. There is an overall gain of energy.

With this information in mind, the F-H bond is more stable and thus stronger than the H-H bond. The main factors to this argument is the greater electronegativity of F leading to a stronger contribution to the bond than the molecular orbitals. Hence the overlap of molecular orbitals is a weaker factor in the bond strength.

[[File:sm6416_FHH_Surface.png|thumb|none|350px|Surface plot highlighting the energetics of the F-H-H system.]]

[[File:sm6416_HHF_Surface.png|thumb|none|350px|Surface plot highlighting the energetics of the H-H-F system.]]

====Transition State====

Hammond's postulate aids in finding the transition state; it relates the composition of the transition complex to either the reactants or products for an early or late transition state respectively. In the scenario under investigation for F +H2 an early transition state is present as the reaction is exothermic in this direction, hence the transition state resembles the reactants more.

This guidance proved useful in determining the transition state complex at r1 = F-H = 1.810076 Angstrom and r2 = H-H = 0.74634 Angstrom, as can be seen from the surface and contour plots below showing the absence of displacement to either reactants or products. Furthermore the Momenta vs Time plot indicates a very small momenta of the overall system, without any deviation or substantial change in the momenta.

[[File:sm6416_FHH_Transition_State_Contour.png|thumb|none|350px|Contour plot demonstrating rts as a result of no fluctuations from the initial input, hence the complex is metaphorically sitting on the transition state.]]

[[File:sm6416_FHH_Transition_State_Momenta_Time.png|thumb|none|350px|Momenta vs Time plot demonstrating minimum, and almost zero, momentum at rts.]]

[[File:sm6416_FHH_Transition_State_Surface.png|thumb|none|350px]]

====Activation Energy====

The activation energy for the exothermic reaction was calculated through a 500000 step MEP simulation with input values of r1 = 1.820076, r2 = 0.74634 and p1 = p2 = 0. It was required that after following the minimum energy path, the gradient of the line signifying the reactants was constant.

The activation energy is reported at +0.258 kcal/mol for the exothermic process.

[[File:sm6416_FHH_Activation_Energy_1.png|thumb|none|350px|Energy vs Time graph highlighting the activation energy of the exothermic reaction.]]

The activation energy for the endothermic process was determined with the following parameters: r1 = 1.800076, r2 = 0.74634, p1 = p2 = 0 with 250000 steps. These parameters 'tipped' the reaction towards the FH + H reactants. The reported activation energy was +30.277 kcal/mol.

[[File:sm6416_FHH_Activation_Energy_2.png|thumb|none|350px|Energy vs Time graph highlighting the activation energy of the endothermic reaction.]]

It can hence be seen that the exothermic reaction of F + H2 --> F-H + H only requires a small activation energy as the products are substantially more thermodynamically stable than the reactants.

===Reaction Dynamics===

In this exothermic reaction, the potential energy is mainly converted into vibrational energy of the FH bond, along with heat. As a result of this vibrational energy in the FH bond, vibrational levels above the ground state will become partially populated. In this manner, by recording an IR spectrum of the products, the main F-H will be observed alongside an overtone, with the intensity of this overtone relating to the population of this vibrationally excited state, which can then be used to determine the vibrational energy in the bond itself.

In this same vein, IR chemiluminescence can be employed to yield the same result by measuring the wavelength, and subsequent vibrational energy of the FH bond, of the infrared light that is irradiated from the products and being excited with incident light.

As the momentum closes towards the boundaries of -3 < p < +3, the system passes through transition state but returns to reactant well. This shows that the excess momentum of the system in the product well is sufficient to overcome the high activation energy and return to the thermodynamically unfavourable reactants.

The following parameters were employed for all simulations rFH = 2.3, rHH = 0.74 with 500 steps calculated.

{| class="wikitable" border=2
! Simulation !! pHH !! pFH !! Surface Plot !! Momenta vs Time Plot !! Observations !!
|-
| 1 || -2.5 || -1.5 || [[File:sm6416_Trajectory_1_Surface.png|thumb|none|350px]] ||[[File:sm6416_Trajectory_1_Momenta.png|thumb|none|350px]] || This trajectory results in a successful reaction as seen from the surface plot; the reactants proceed through the transition state and continue into the product well, whilst continually oscillating as a result of the momentum gained.
|-
| 2 || -0.5 || -0.5 || [[File:sm6416_Trajectory_2_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_2_Momenta.png|thumb|none|350px]] || This momentum does not proceed to a reaction. Through the dynamic animation it can be seen that the HH molecule does not possess enough momentum to translate towards F. Therefore the system does not translate out of the reactant well, as seen in the surface plot, since there is not enough energy to overcome the activation energy. The momenta plot simply shows a small up trend, this is expected due to the long range electrostatic force of attraction between F and HH, resulting in a slight increase in the HH vibration velocity. There is no drastic change in the momenta of either F or HH that would otherwise indicate the occurrence of a reaction, as seen in simulation 1 above.
|-
| 3 || +0.5 || -0.5 || [[File:sm6416_Trajectory_3_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_3_Momenta.png|thumb|none|350px]] || This simulation shows an unreactive path, as can be seen from the surface plot, the system remains in the reactant well as it does not overcome the small activation energy for the exothermic reaction to proceed. As in simulation 2, the momentum amplitude of the oscillating HH remains constant however the overall momenta of the system increases due to a slight translation towards F, thus increasing electrostatic attraction forces resulting in this slight overall momenta increase.
|-
| 4 || -1.6 || -0.5 || [[File:sm6416_Trajectory_4_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_4_Momenta.png|thumb|none|350px]] || This simulation is very similar to simulations 2 & 3 in that the system remains in the reactant well as there is not sufficient energy to overcome the activation energy. However as a result of the greater HH momentum, the oscillation amplitude is greater than both simulation 1 & 2.
|-
| 5 || +1.6 || -0.5 || [[File:sm6416_Trajectory_5_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_5_Momenta.png|thumb|none|350px]] || Firstly, this simulation is unreactive as can be seen from the surface plot. In comparison to simulation 4, HH momentum sign has been changed and as a result this has led to not only a greater oscillating amplitude but also a larger translation towards F. So much so in the latter than the Momenta vs Time plot shows an increase in FH oscillation momentum as the electrostatic forces of attraction dominate due to the reduction in internuclear distance.
|-
| 6 || -2.9 || -0.5 || [[File:sm6416_Trajectory_6_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_6_Momenta.png|thumb|none|350px]] || This is the first reactive simulation observed, as can be seen from the surface plot and the drastic change in the momentum of FH. Evidently, there is sufficient energy to pass through the transition state complex and towards the reactants.
|-
| 7 || +2.9 || -0.5 || [[File:sm6416_Trajectory_7_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_7_Momenta.png|thumb|none|350px]] || This simulation is indeed similar to that of simulation 6 however, the change of sign for the HH momentum again results in a greater translation towards F and consequently the system passes through the transition complex shown by the surface plot and Momenta vs Time plot. However after a single oscillation, FH dissociates and the system returns to the reactant well with HH possessing a greater momentum. This scenario could be as a result of the HH momentum being too high and thus providing sufficient activation energy to proceed in the endothermic direction. This is surprising as the exothermic reaction elucidates more thermodynamically stable products.
|-
| 8 || +0.1 || -0.8 || [[File:sm6416_Trajectory_8_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_8_Momenta.png|thumb|none|350px]] || With a mere 60% change in FH momentum and a minimum HH momentum, the system can be seen to react fully, without returning through the transition state. The Momenta vs Time plot further shows a noticeable change in the AB momentum, which corresponds to FH. Despite the oscillations not being regular, it can be noted that the amplitudes are relatively of the same size and show no signs of regressing. This information highlights that the overall the FH momentum dominates the reactivity of the system and has a large weighting to overcoming the activation energy. It can be thought that the increase in momentum aids in allowing a closer distance of F & H, where electrostatic attraction forces will prevail.
|}

====Polyani's Empirical Rules====

The reactive trajectory for the FH + H was determined with the following parameters: rFH = 0.9, rHH = 2.3, pFH = 6.5, pHH = -1.5. The plots below highlight that these parameters lead to a reactive trajectory.

[[File:sm6416_FHH_Reactive_Trajectory_1_Surface.png|thumb|none|350px|Surface plot showing the reactants pass through the transition state and enter the product well without returning through the transition complex. This trajectory is therefore reactive.]]
[[File:sm6416_FHH_Reactive_Trajectory_1_Momenta.png|thumb|none|350px|Momenta vs Time plot indicating the substantial loss of momentum of FH, indicating dissociation, with the simultaneous gain in momentum of HH, indicated by the orange line.]]
[[File:sm6416_FHH_Reactive_Trajectory_1_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot showing a successful reaction. The HH distance vibrationally oscillates about the equilibrium bond distance, whereas the F-H distance increases linearly as a result of F translating away from H2.]]
[[File:sm6416_FHH_Reactive_Trajectory_1_Contour.png|thumb|none|350px|Contour plot highlighting similar information to the surface plot above in that the system stably occupies the product well without returning through the transition complex.]]

In order to react, a system must overcome the activation energy, the energy to achieve this is supplied by either translational or vibrational energy. As reported by Polanyi's Empirical Rules, a late transition state, one that resembles the products more as stated through Hammond's Postulate, is achieved through a greater contribution from vibrational energy enabling the activation energy to be overcome. The opposite is true for an early transition state which is promoted by a greater contribution from translational energy.

The F + H2 system is exothermic, thus an early transition state is present. Therefore this is promoted with higher translational energy being able to overcome the activation energy, hence pFH would contribute to the translational energy whereas pHH relates to the vibrational energy of the HH bond.

On the other hand, the FH + H system is endothermic and relates to a late transition state as dictated by Hammond's Postulate, requiring high vibrational energy of the FH bond to overcome the activation energy. In this scenario, pFH refers to the vibrational energy and pHH the translational energy.

MRD:sm6416

2018-05-25T16:30:45Z

Sm6416: /* Polyani's Empirical Rules */

==H2 H Exercise 1==

===Transition State Dynamics===

The transition state is the stage in a reaction coordinate that must be passed through in order for a reaction to occur and occurs at a saddle point, as shown by the numerous surface plots on this page. The first derivative highlights the positions along the reaction coordinate where the gradient equals zero. However, in order to determine if a saddle point ensues, the second derivative of the gradient must be taken. A saddle point is only present if the second derivative > 0.

Another way to think of the transition state is by thinking of the tangent that can be formed at the transition state itself. This tangent will follow the reaction coordinate profile and therefore is expected to be a maximum, where the gradient = 0. A line can be drawn to the normal of the tangent at the selected transition state. This path would show a minimum, where the gradient again = 0, at the intersection of the tangent with normal if the transition state has been correctly identified. It is only in this scenario that a transition state can be determined as one.

===Locating the Transition State===

The transition state was determined through iterations of both r1 and r2 which resulted in the smallest displacement of momenta along with no displacement as shown by the contour plot. This method determined at rts = 0.907743.

[[File:sm6416_Transition_State_Contour.png|thumb|none|350px|Contour plot demonstrating rts = 0.907743 as a result of no fluctuations from the initial input, hence the complex is at the transition state.]]

[[File:sm6416_Transition_State_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating minimum, and almost zero, momentum at rts = 0.907743.]]

[[File:sm6416_Transition_State_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot demonstrating no fluctuations in distance and hence rts = 0.907743.]]

===Reaction Path===

The minimum energy path (MEP) is defined as the lowest path the reaction must follow to form the products and is the downhill motion from the transition state. It can be applied in both directions in the case in question. The MEP views the system as static as it resets the velocity to zero at each step. Whereas the trajectory is very much dynamic and the momenta is accounted for, this is reflected in the vibrational oscillation of the molecule as it passes along the minimum well towards the products.

====MEP====

Initial conditions of r1 = rts + 0.01 = 0.917743, r2 = rts = 0.907743 and p1 = p2 = 0 for the MEP simulation.

[[File:sm6416_MEP_Surface.png|thumb|none|350px|Surface plot highlighting the minimum energy path (MEP), as the reaction returns to the reactants without fully passing through the transition state.]]

[[File:sm6416_MEP_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating zero momentum, as inputted, and more importantly not change in momentum with running the simulation.]]

[[File:sm6416_MEP_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot showing that the reactants reach the transition state at the interception of r1 = r2. r1 quickly reaches a constant value, namely the equilibrium bond length of the reactant molecule. r2 increases logarithmically as time progresses, this represents an increasing distance of Ha from Hb-Hc and a continuing loss of momentum.]]

Final values from the MEP simulation.

r1 = 2.76195

r2 = 0.75883

These values reflect the minimum trajectory for a successful reaction.

p1 = p2 = 0

====Dynamic====

[[File:sm6416_Dynamic_Surface.png|thumb|none|350px|Surface plot highlighting the minimum energy path (MEP) with oscillation of the reactants, as the reaction returns to the reactants without fully passing through the transition state. It is therefore evident that the momentum as a result of the vibrational oscillation does not provide enough energy to proceed to the products.]]

[[File:sm6416_Dynamic_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating the momenta associated with the oscillating reactants.]]

[[File:sm6416_Dynamic_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot showing that the reactants reach the transition state at the interception of r1 = r2. r1 quickly decreases and oscillates about a constant value, namely the equilibrium bond length of the reactant molecule. r2 increases linearly as time progresses, this represents an increasing distance of Ha from Hb-Hc with a constant momentum.]]

Dynamic simulation final values

r1 = 10.0045

r2 = 0.75883

p1 = 2.48523

p2 = 1.29898

p(average) = 1.90409

With r1 = rts and r2 = rts + 0.01 would simply produce the same answer however the values would be flipped to the other distance. In other words r1 = 0.75883 and r2 = 10.0045 would be the output values.

Maintaining the final trajectories as calculated from the dynamic simulation and reversing the sign of the momenta, the reaction proceeds in the reverse direction to the products.

===Reactivity of Trajectories===

These simulations are restricted by the number of steps the program can handle, however a sound understanding of the reaction can be appreciated and the reactivity of each scenario can be determined appropriately.

{| class="wikitable" border=2
! Simulation !! p1 !! p2 !! Energy (kcal/mol) !! Reactivity !! Evidence !! Description
|-
| 1 || -1.25 || -2.5 || 5.03500 || Reactive || [[File:sm6416_MEP_Figure1.png|thumb|none|350px]] || Simulation 1: The reactants proceed through the transition state and to the products. The r2 distance decreases to the equilibrium bond length, whilst r1 simultaneously exhibits dissociation and increases beyond the scope of the graph. The small momenta attributed to the reactants is reflected in the vibrationally oscillating products, with a small amplitude.
|-
| 2 || -1.5 || -2.0 || 3.62879 || Unreactive || [[File:sm6416_MEP_Figure2.png|thumb|none|350px]] || Simulation 2: This is unreactive as the oscillating reactants reach the transition state point and r1 immediately returns to the initial bond length, whilst r2 continues to increase as it moves away from the H2 molecule.
|-
| 3 || -1.5 || -2.5 || 5.13738 || Reactive || [[File:sm6416_MEP_Figure3.png|thumb|none|350px]] || Simulation 3: This simulation shows a reactive pathway that is very similar to simulation 1, however due to the greater momenta associated with the reactants, as inputted, vibrational oscillations with a greater amplitude can be observed.
|-
| 4 || -2.5 || -5.0 || 9.86678 || Unreactive || [[File:sm6416_MEP_Figure4.png|thumb|none|350px]] || Simulation 4: Initially seen here are oscillating reactants with a very large amplitude. However, this simulation is unreactive despite the reactants going through the transition state and towards the product, they return to the initial reactants.
|-
| 5 || -2.5 || -5.2 || 11.80780 || Reactive || [[File:sm6416_MEP_Figure5.png|thumb|none|350px]] || Simulation 5: Like simulation 4, this simulation shows a large oscillating amplitude, whereas in this scenario after passing through the transition state, the products are completely obtained. The slight increase in the p2 momentum can be seen to result in the products.
|}

====Transition State Theory====

Transition State Theory (TST) assumes a quasi-equilibrium between reactants and the transition state. The reaction between the transition state and products is irreversible and therefore is unable to return to the reactants, however many of the surface plots on this page show the complete antithesis of this highlighting a dichotomy between theory and experimental. TST further assumes that fluctuation as to whether the transition complexes go towards reactants or products are independent of each other and hence the rate of one can not be determined by the other.

TST is excellent qualitative tool and can identify the enthalpy, standard entropy and standard Gibbs energy of activation. Despite this, it the method is unable to accurately determine these true values in line with experimental results as doing so would require a deep understanding of the potential energy surface of each reaction. Therefore, TST under estimates the reaction rate in comparison to the experimental values. When TST was developed in 1935 a lack of adequate computer software to accurately map potential energy surfaces, unlike there is today. Hence resulting in a less accurate and longer method to map these surfaces for each reaction.

==F-H-H System Exercise 2==
===Potential Energy Surface Inspection===
====Energetics====

F + H2 is an exothermic reaction as can be seen from the surface plot, the reaction progresses from a small H-H distance to a longer one, whilst H-F simultaneously equilibriates about the F-H bond length. It can be seen that the products are lower, and hence more stable, in energy than the reactants.

F-H + H is simply the reverse reaction that passes through the same transition state, hence this reaction is endothermic with the products being higher in energy than the reactants. There is an overall gain of energy.

With this information in mind, the F-H bond is more stable and thus stronger than the H-H bond. The main factors to this argument is the greater electronegativity of F leading to a stronger contribution to the bond than the molecular orbitals. Hence the overlap of molecular orbitals is a weaker factor in the bond strength.

[[File:sm6416_FHH_Surface.png|thumb|none|350px|Surface plot highlighting the energetics of the F-H-H system.]]

[[File:sm6416_HHF_Surface.png|thumb|none|350px|Surface plot highlighting the energetics of the H-H-F system.]]

====Transition State====

Hammond's postulate aids in finding the transition state; it relates the composition of the transition complex to either the reactants or products for an early or late transition state respectively. In the scenario under investigation for F +H2 an early transition state is present as the reaction is exothermic in this direction, hence the transition state resembles the reactants more.

This guidance proved useful in determining the transition state complex at r1 = F-H = 1.810076 Angstrom and r2 = H-H = 0.74634 Angstrom, as can be seen from the surface and contour plots below showing the absence of displacement to either reactants or products. Furthermore the Momenta vs Time plot indicates a very small momenta of the overall system, without any deviation or substantial change in the momenta.

[[File:sm6416_FHH_Transition_State_Contour.png|thumb|none|350px|Contour plot demonstrating rts as a result of no fluctuations from the initial input, hence the complex is metaphorically sitting on the transition state.]]

[[File:sm6416_FHH_Transition_State_Momenta_Time.png|thumb|none|350px|Momenta vs Time plot demonstrating minimum, and almost zero, momentum at rts.]]

[[File:sm6416_FHH_Transition_State_Surface.png|thumb|none|350px]]

====Activation Energy====

The activation energy for the exothermic reaction was calculated through a 500000 step MEP simulation with input values of r1 = 1.820076, r2 = 0.74634 and p1 = p2 = 0. It was required that after following the minimum energy path, the gradient of the line signifying the reactants was constant.

The activation energy is reported at +0.258 kcal/mol for the exothermic process.

[[File:sm6416_FHH_Activation_Energy_1.png|thumb|none|350px|Energy vs Time graph highlighting the activation energy of the exothermic reaction.]]

The activation energy for the endothermic process was determined with the following parameters: r1 = 1.800076, r2 = 0.74634, p1 = p2 = 0 with 250000 steps. These parameters 'tipped' the reaction towards the FH + H reactants. The reported activation energy was +30.277 kcal/mol.

[[File:sm6416_FHH_Activation_Energy_2.png|thumb|none|350px|Energy vs Time graph highlighting the activation energy of the endothermic reaction.]]

It can hence be seen that the exothermic reaction of F + H2 --> F-H + H only requires a small activation energy as the products are substantially more thermodynamically stable than the reactants.

===Reaction Dynamics===

In this exothermic reaction, the potential energy is mainly converted into vibrational energy of the FH bond, along with heat. As a result of this vibrational energy in the FH bond, vibrational levels above the ground state will become partially populated. In this manner, by recording an IR spectrum of the products, the main F-H will be observed alongside an overtone, with the intensity of this overtone relating to the population of this vibrationally excited state, which can then be used to determine the vibrational energy in the bond itself.

In this same vein, IR chemiluminescence can be employed to yield the same result by measuring the wavelength, and subsequent vibrational energy of the FH bond, of the infrared light that is irradiated from the products and being excited with incident light.

As the momentum closes towards the boundaries of -3 < p < +3, the system passes through transition state but returns to reactant well. This shows that the excess momentum of the system in the product well is sufficient to overcome the high activation energy and return to the thermodynamically unfavourable reactants.

The following parameters were employed for all simulations rFH = 2.3, rHH = 0.74 with 500 steps calculated.

{| class="wikitable" border=2
! Simulation !! pHH !! pFH !! Surface Plot !! Momenta vs Time Plot !! Observations !!
|-
| 1 || -2.5 || -1.5 || [[File:sm6416_Trajectory_1_Surface.png|thumb|none|350px]] ||[[File:sm6416_Trajectory_1_Momenta.png|thumb|none|350px]] || This trajectory results in a successful reaction as seen from the surface plot; the reactants proceed through the transition state and continue into the product well, whilst continually oscillating as a result of the momentum gained.
|-
| 2 || -0.5 || -0.5 || [[File:sm6416_Trajectory_2_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_2_Momenta.png|thumb|none|350px]] || This momentum does not proceed to a reaction. Through the dynamic animation it can be seen that the HH molecule does not possess enough momentum to translate towards F. Therefore the system does not translate out of the reactant well, as seen in the surface plot, since there is not enough energy to overcome the activation energy. The momenta plot simply shows a small up trend, this is expected due to the long range electrostatic force of attraction between F and HH, resulting in a slight increase in the HH vibration velocity. There is no drastic change in the momenta of either F or HH that would otherwise indicate the occurrence of a reaction, as seen in simulation 1 above.
|-
| 3 || +0.5 || -0.5 || [[File:sm6416_Trajectory_3_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_3_Momenta.png|thumb|none|350px]] || This simulation shows an unreactive path, as can be seen from the surface plot, the system remains in the reactant well as it does not overcome the small activation energy for the exothermic reaction to proceed. As in simulation 2, the momentum amplitude of the oscillating HH remains constant however the overall momenta of the system increases due to a slight translation towards F, thus increasing electrostatic attraction forces resulting in this slight overall momenta increase.
|-
| 4 || -1.6 || -0.5 || [[File:sm6416_Trajectory_4_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_4_Momenta.png|thumb|none|350px]] || This simulation is very similar to simulations 2 & 3 in that the system remains in the reactant well as there is not sufficient energy to overcome the activation energy. However as a result of the greater HH momentum, the oscillation amplitude is greater than both simulation 1 & 2.
|-
| 5 || +1.6 || -0.5 || [[File:sm6416_Trajectory_5_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_5_Momenta.png|thumb|none|350px]] || Firstly, this simulation is unreactive as can be seen from the surface plot. In comparison to simulation 4, HH momentum sign has been changed and as a result this has led to not only a greater oscillating amplitude but also a larger translation towards F. So much so in the latter than the Momenta vs Time plot shows an increase in FH oscillation momentum as the electrostatic forces of attraction dominate due to the reduction in internuclear distance.
|-
| 6 || -2.9 || -0.5 || [[File:sm6416_Trajectory_6_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_6_Momenta.png|thumb|none|350px]] || This is the first reactive simulation observed, as can be seen from the surface plot and the drastic change in the momentum of FH. Evidently, there is sufficient energy to pass through the transition state complex and towards the reactants.
|-
| 7 || +2.9 || -0.5 || [[File:sm6416_Trajectory_7_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_7_Momenta.png|thumb|none|350px]] || This simulation is indeed similar to that of simulation 6 however, the change of sign for the HH momentum again results in a greater translation towards F and consequently the system passes through the transition complex shown by the surface plot and Momenta vs Time plot. However after a single oscillation, FH dissociates and the system returns to the reactant well with HH possessing a greater momentum. This scenario could be as a result of the HH momentum being too high and thus providing sufficient activation energy to proceed in the endothermic direction. This is surprising as the exothermic reaction elucidates more thermodynamically stable products.
|-
| 8 || +0.1 || -0.8 || [[File:sm6416_Trajectory_8_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_8_Momenta.png|thumb|none|350px]] || With a mere 60% change in FH momentum and a minimum HH momentum, the system can be seen to react fully, without returning through the transition state. The Momenta vs Time plot further shows a noticeable change in the AB momentum, which corresponds to FH. Despite the oscillations not being regular, it can be noted that the amplitudes are relatively of the same size and show no signs of regressing. This information highlights that the overall the FH momentum dominates the reactivity of the system and has a large weighting to overcoming the activation energy. It can be thought that the increase in momentum aids in allowing a closer distance of F & H, where electrostatic attraction forces will prevail.
|}

====Polyani's Empirical Rules====

The reactive trajectory for the FH + H was determined with the following parameters: rFH = 0.9, rHH = 2.3, pFH = 6.5, pHH = -1.5. The plots below highlight that these parameters lead to a reactive trajectory.

[[File:sm6416_FHH_Reactive_Trajectory_1_Surface.png|thumb|none|350px|Surface plot showing the reactants pass through the transition state and enter the product well without returning through the transition complex. This trajectory is therefore reactive.]]
[[File:sm6416_FHH_Reactive_Trajectory_1_Momenta.png|thumb|none|350px|Momenta vs Time plot indicating the substantial loss of momentum of FH, indicating dissociation, with the simultaneous gain in momentum of HH, indicated by the orange line.]]
[[File:sm6416_FHH_Reactive_Trajectory_1_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot showing a successful reaction. The HH distance vibrationally oscillates about the equilibrium bond distance, whereas the F-H distance increases linearly as a result of F translating away from H2.]]
[[File:sm6416_FHH_Reactive_Trajectory_1_Contour.png|thumb|none|350px|Contour plot highlighting similar information to the surface plot above in that the system stably occupies the product well without returning through the transition complex.]]

In order to react, a system must overcome the activation energy, the energy to achieve this is supplied by either translational or vibrational energy. As reported by Polanyi's Empirical Rules, a late transition state, one that resembles the products more as stated through Hammond's Postulate, is achieved through a greater contribution from vibrational energy enabling the activation energy to be overcome. The opposite is true for an early transition state which is promoted by a greater contribution from translational energy.

The F + H2 system is exothermic, thus an early transition state is present. Therefore this is promoted with higher translational energy being able to overcome the activation energy, hence pFH would contribute to the translational energy whereas pHH relates to the vibrational energy of the HH bond.

On the other hand, the FH + H system is endothermic and relates to a late transition state as dictated by Hammond's Postulate, requiring high vibrational energy of the FH bond to overcome the activation energy. In this scenario, pFH refers to the vibrational energy and pHH the translational energy.

MRD:sm6416

2018-05-25T16:21:55Z

Sm6416: /* Polyani's Empirical Rules */

==H2 H Exercise 1==

===Transition State Dynamics===

The transition state is the stage in a reaction coordinate that must be passed through in order for a reaction to occur and occurs at a saddle point, as shown by the numerous surface plots on this page. The first derivative highlights the positions along the reaction coordinate where the gradient equals zero. However, in order to determine if a saddle point ensues, the second derivative of the gradient must be taken. A saddle point is only present if the second derivative > 0.

Another way to think of the transition state is by thinking of the tangent that can be formed at the transition state itself. This tangent will follow the reaction coordinate profile and therefore is expected to be a maximum, where the gradient = 0. A line can be drawn to the normal of the tangent at the selected transition state. This path would show a minimum, where the gradient again = 0, at the intersection of the tangent with normal if the transition state has been correctly identified. It is only in this scenario that a transition state can be determined as one.

===Locating the Transition State===

The transition state was determined through iterations of both r1 and r2 which resulted in the smallest displacement of momenta along with no displacement as shown by the contour plot. This method determined at rts = 0.907743.

[[File:sm6416_Transition_State_Contour.png|thumb|none|350px|Contour plot demonstrating rts = 0.907743 as a result of no fluctuations from the initial input, hence the complex is at the transition state.]]

[[File:sm6416_Transition_State_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating minimum, and almost zero, momentum at rts = 0.907743.]]

[[File:sm6416_Transition_State_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot demonstrating no fluctuations in distance and hence rts = 0.907743.]]

===Reaction Path===

The minimum energy path (MEP) is defined as the lowest path the reaction must follow to form the products and is the downhill motion from the transition state. It can be applied in both directions in the case in question. The MEP views the system as static as it resets the velocity to zero at each step. Whereas the trajectory is very much dynamic and the momenta is accounted for, this is reflected in the vibrational oscillation of the molecule as it passes along the minimum well towards the products.

====MEP====

Initial conditions of r1 = rts + 0.01 = 0.917743, r2 = rts = 0.907743 and p1 = p2 = 0 for the MEP simulation.

[[File:sm6416_MEP_Surface.png|thumb|none|350px|Surface plot highlighting the minimum energy path (MEP), as the reaction returns to the reactants without fully passing through the transition state.]]

[[File:sm6416_MEP_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating zero momentum, as inputted, and more importantly not change in momentum with running the simulation.]]

[[File:sm6416_MEP_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot showing that the reactants reach the transition state at the interception of r1 = r2. r1 quickly reaches a constant value, namely the equilibrium bond length of the reactant molecule. r2 increases logarithmically as time progresses, this represents an increasing distance of Ha from Hb-Hc and a continuing loss of momentum.]]

Final values from the MEP simulation.

r1 = 2.76195

r2 = 0.75883

These values reflect the minimum trajectory for a successful reaction.

p1 = p2 = 0

====Dynamic====

[[File:sm6416_Dynamic_Surface.png|thumb|none|350px|Surface plot highlighting the minimum energy path (MEP) with oscillation of the reactants, as the reaction returns to the reactants without fully passing through the transition state. It is therefore evident that the momentum as a result of the vibrational oscillation does not provide enough energy to proceed to the products.]]

[[File:sm6416_Dynamic_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating the momenta associated with the oscillating reactants.]]

[[File:sm6416_Dynamic_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot showing that the reactants reach the transition state at the interception of r1 = r2. r1 quickly decreases and oscillates about a constant value, namely the equilibrium bond length of the reactant molecule. r2 increases linearly as time progresses, this represents an increasing distance of Ha from Hb-Hc with a constant momentum.]]

Dynamic simulation final values

r1 = 10.0045

r2 = 0.75883

p1 = 2.48523

p2 = 1.29898

p(average) = 1.90409

With r1 = rts and r2 = rts + 0.01 would simply produce the same answer however the values would be flipped to the other distance. In other words r1 = 0.75883 and r2 = 10.0045 would be the output values.

Maintaining the final trajectories as calculated from the dynamic simulation and reversing the sign of the momenta, the reaction proceeds in the reverse direction to the products.

===Reactivity of Trajectories===

These simulations are restricted by the number of steps the program can handle, however a sound understanding of the reaction can be appreciated and the reactivity of each scenario can be determined appropriately.

{| class="wikitable" border=2
! Simulation !! p1 !! p2 !! Energy (kcal/mol) !! Reactivity !! Evidence !! Description
|-
| 1 || -1.25 || -2.5 || 5.03500 || Reactive || [[File:sm6416_MEP_Figure1.png|thumb|none|350px]] || Simulation 1: The reactants proceed through the transition state and to the products. The r2 distance decreases to the equilibrium bond length, whilst r1 simultaneously exhibits dissociation and increases beyond the scope of the graph. The small momenta attributed to the reactants is reflected in the vibrationally oscillating products, with a small amplitude.
|-
| 2 || -1.5 || -2.0 || 3.62879 || Unreactive || [[File:sm6416_MEP_Figure2.png|thumb|none|350px]] || Simulation 2: This is unreactive as the oscillating reactants reach the transition state point and r1 immediately returns to the initial bond length, whilst r2 continues to increase as it moves away from the H2 molecule.
|-
| 3 || -1.5 || -2.5 || 5.13738 || Reactive || [[File:sm6416_MEP_Figure3.png|thumb|none|350px]] || Simulation 3: This simulation shows a reactive pathway that is very similar to simulation 1, however due to the greater momenta associated with the reactants, as inputted, vibrational oscillations with a greater amplitude can be observed.
|-
| 4 || -2.5 || -5.0 || 9.86678 || Unreactive || [[File:sm6416_MEP_Figure4.png|thumb|none|350px]] || Simulation 4: Initially seen here are oscillating reactants with a very large amplitude. However, this simulation is unreactive despite the reactants going through the transition state and towards the product, they return to the initial reactants.
|-
| 5 || -2.5 || -5.2 || 11.80780 || Reactive || [[File:sm6416_MEP_Figure5.png|thumb|none|350px]] || Simulation 5: Like simulation 4, this simulation shows a large oscillating amplitude, whereas in this scenario after passing through the transition state, the products are completely obtained. The slight increase in the p2 momentum can be seen to result in the products.
|}

====Transition State Theory====

Transition State Theory (TST) assumes a quasi-equilibrium between reactants and the transition state. The reaction between the transition state and products is irreversible and therefore is unable to return to the reactants, however many of the surface plots on this page show the complete antithesis of this highlighting a dichotomy between theory and experimental. TST further assumes that fluctuation as to whether the transition complexes go towards reactants or products are independent of each other and hence the rate of one can not be determined by the other.

TST is excellent qualitative tool and can identify the enthalpy, standard entropy and standard Gibbs energy of activation. Despite this, it the method is unable to accurately determine these true values in line with experimental results as doing so would require a deep understanding of the potential energy surface of each reaction. Therefore, TST under estimates the reaction rate in comparison to the experimental values. When TST was developed in 1935 a lack of adequate computer software to accurately map potential energy surfaces, unlike there is today. Hence resulting in a less accurate and longer method to map these surfaces for each reaction.

==F-H-H System Exercise 2==
===Potential Energy Surface Inspection===
====Energetics====

F + H2 is an exothermic reaction as can be seen from the surface plot, the reaction progresses from a small H-H distance to a longer one, whilst H-F simultaneously equilibriates about the F-H bond length. It can be seen that the products are lower, and hence more stable, in energy than the reactants.

F-H + H is simply the reverse reaction that passes through the same transition state, hence this reaction is endothermic with the products being higher in energy than the reactants. There is an overall gain of energy.

With this information in mind, the F-H bond is more stable and thus stronger than the H-H bond. The main factors to this argument is the greater electronegativity of F leading to a stronger contribution to the bond than the molecular orbitals. Hence the overlap of molecular orbitals is a weaker factor in the bond strength.

[[File:sm6416_FHH_Surface.png|thumb|none|350px|Surface plot highlighting the energetics of the F-H-H system.]]

[[File:sm6416_HHF_Surface.png|thumb|none|350px|Surface plot highlighting the energetics of the H-H-F system.]]

====Transition State====

Hammond's postulate aids in finding the transition state; it relates the composition of the transition complex to either the reactants or products for an early or late transition state respectively. In the scenario under investigation for F +H2 an early transition state is present as the reaction is exothermic in this direction, hence the transition state resembles the reactants more.

This guidance proved useful in determining the transition state complex at r1 = F-H = 1.810076 Angstrom and r2 = H-H = 0.74634 Angstrom, as can be seen from the surface and contour plots below showing the absence of displacement to either reactants or products. Furthermore the Momenta vs Time plot indicates a very small momenta of the overall system, without any deviation or substantial change in the momenta.

[[File:sm6416_FHH_Transition_State_Contour.png|thumb|none|350px|Contour plot demonstrating rts as a result of no fluctuations from the initial input, hence the complex is metaphorically sitting on the transition state.]]

[[File:sm6416_FHH_Transition_State_Momenta_Time.png|thumb|none|350px|Momenta vs Time plot demonstrating minimum, and almost zero, momentum at rts.]]

[[File:sm6416_FHH_Transition_State_Surface.png|thumb|none|350px]]

====Activation Energy====

The activation energy for the exothermic reaction was calculated through a 500000 step MEP simulation with input values of r1 = 1.820076, r2 = 0.74634 and p1 = p2 = 0. It was required that after following the minimum energy path, the gradient of the line signifying the reactants was constant.

The activation energy is reported at +0.258 kcal/mol for the exothermic process.

[[File:sm6416_FHH_Activation_Energy_1.png|thumb|none|350px|Energy vs Time graph highlighting the activation energy of the exothermic reaction.]]

The activation energy for the endothermic process was determined with the following parameters: r1 = 1.800076, r2 = 0.74634, p1 = p2 = 0 with 250000 steps. These parameters 'tipped' the reaction towards the FH + H reactants. The reported activation energy was +30.277 kcal/mol.

[[File:sm6416_FHH_Activation_Energy_2.png|thumb|none|350px|Energy vs Time graph highlighting the activation energy of the endothermic reaction.]]

It can hence be seen that the exothermic reaction of F + H2 --> F-H + H only requires a small activation energy as the products are substantially more thermodynamically stable than the reactants.

===Reaction Dynamics===

In this exothermic reaction, the potential energy is mainly converted into vibrational energy of the FH bond, along with heat. As a result of this vibrational energy in the FH bond, vibrational levels above the ground state will become partially populated. In this manner, by recording an IR spectrum of the products, the main F-H will be observed alongside an overtone, with the intensity of this overtone relating to the population of this vibrationally excited state, which can then be used to determine the vibrational energy in the bond itself.

In this same vein, IR chemiluminescence can be employed to yield the same result by measuring the wavelength, and subsequent vibrational energy of the FH bond, of the infrared light that is irradiated from the products and being excited with incident light.

As the momentum closes towards the boundaries of -3 < p < +3, the system passes through transition state but returns to reactant well. This shows that the excess momentum of the system in the product well is sufficient to overcome the high activation energy and return to the thermodynamically unfavourable reactants.

The following parameters were employed for all simulations rFH = 2.3, rHH = 0.74 with 500 steps calculated.

{| class="wikitable" border=2
! Simulation !! pHH !! pFH !! Surface Plot !! Momenta vs Time Plot !! Observations !!
|-
| 1 || -2.5 || -1.5 || [[File:sm6416_Trajectory_1_Surface.png|thumb|none|350px]] ||[[File:sm6416_Trajectory_1_Momenta.png|thumb|none|350px]] || This trajectory results in a successful reaction as seen from the surface plot; the reactants proceed through the transition state and continue into the product well, whilst continually oscillating as a result of the momentum gained.
|-
| 2 || -0.5 || -0.5 || [[File:sm6416_Trajectory_2_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_2_Momenta.png|thumb|none|350px]] || This momentum does not proceed to a reaction. Through the dynamic animation it can be seen that the HH molecule does not possess enough momentum to translate towards F. Therefore the system does not translate out of the reactant well, as seen in the surface plot, since there is not enough energy to overcome the activation energy. The momenta plot simply shows a small up trend, this is expected due to the long range electrostatic force of attraction between F and HH, resulting in a slight increase in the HH vibration velocity. There is no drastic change in the momenta of either F or HH that would otherwise indicate the occurrence of a reaction, as seen in simulation 1 above.
|-
| 3 || +0.5 || -0.5 || [[File:sm6416_Trajectory_3_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_3_Momenta.png|thumb|none|350px]] || This simulation shows an unreactive path, as can be seen from the surface plot, the system remains in the reactant well as it does not overcome the small activation energy for the exothermic reaction to proceed. As in simulation 2, the momentum amplitude of the oscillating HH remains constant however the overall momenta of the system increases due to a slight translation towards F, thus increasing electrostatic attraction forces resulting in this slight overall momenta increase.
|-
| 4 || -1.6 || -0.5 || [[File:sm6416_Trajectory_4_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_4_Momenta.png|thumb|none|350px]] || This simulation is very similar to simulations 2 & 3 in that the system remains in the reactant well as there is not sufficient energy to overcome the activation energy. However as a result of the greater HH momentum, the oscillation amplitude is greater than both simulation 1 & 2.
|-
| 5 || +1.6 || -0.5 || [[File:sm6416_Trajectory_5_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_5_Momenta.png|thumb|none|350px]] || Firstly, this simulation is unreactive as can be seen from the surface plot. In comparison to simulation 4, HH momentum sign has been changed and as a result this has led to not only a greater oscillating amplitude but also a larger translation towards F. So much so in the latter than the Momenta vs Time plot shows an increase in FH oscillation momentum as the electrostatic forces of attraction dominate due to the reduction in internuclear distance.
|-
| 6 || -2.9 || -0.5 || [[File:sm6416_Trajectory_6_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_6_Momenta.png|thumb|none|350px]] || This is the first reactive simulation observed, as can be seen from the surface plot and the drastic change in the momentum of FH. Evidently, there is sufficient energy to pass through the transition state complex and towards the reactants.
|-
| 7 || +2.9 || -0.5 || [[File:sm6416_Trajectory_7_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_7_Momenta.png|thumb|none|350px]] || This simulation is indeed similar to that of simulation 6 however, the change of sign for the HH momentum again results in a greater translation towards F and consequently the system passes through the transition complex shown by the surface plot and Momenta vs Time plot. However after a single oscillation, FH dissociates and the system returns to the reactant well with HH possessing a greater momentum. This scenario could be as a result of the HH momentum being too high and thus providing sufficient activation energy to proceed in the endothermic direction. This is surprising as the exothermic reaction elucidates more thermodynamically stable products.
|-
| 8 || +0.1 || -0.8 || [[File:sm6416_Trajectory_8_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_8_Momenta.png|thumb|none|350px]] || With a mere 60% change in FH momentum and a minimum HH momentum, the system can be seen to react fully, without returning through the transition state. The Momenta vs Time plot further shows a noticeable change in the AB momentum, which corresponds to FH. Despite the oscillations not being regular, it can be noted that the amplitudes are relatively of the same size and show no signs of regressing. This information highlights that the overall the FH momentum dominates the reactivity of the system and has a large weighting to overcoming the activation energy. It can be thought that the increase in momentum aids in allowing a closer distance of F & H, where electrostatic attraction forces will prevail.
|}

====Polyani's Empirical Rules====

The reactive trajectory for the FH + H was determined with the following parameters: rFH = 0.9, rHH = 2.3, pFH = 6.5, pHH = -1.5. The plots below highlight that these parameters lead to a reactive trajectory.

[[File:sm6416_FHH_Reactive_Trajectory_1_Surface.png|thumb|none|350px]]
[[File:sm6416_FHH_Reactive_Trajectory_1_Momenta.png|thumb|none|350px]]
[[File:sm6416_FHH_Reactive_Trajectory_1_Distance.png|thumb|none|350px]]
[[File:sm6416_FHH_Reactive_Trajectory_1_Contour.png|thumb|none|350px]]

In order to react, a system must overcome the activation energy, the energy to achieve this is supplied by either translational or vibrational energy. As reported by Polanyi's Empirical Rules, a late transition state, one that resembles the products more as stated through Hammond's Postulate, is achieved through a greater contribution from vibrational energy enabling the activation energy to be overcome. The opposite is true for an early transition state which is promoted by a greater contribution from translational energy.

The F + H2 system is exothermic, thus an early transition state is present. Therefore this is promoted with higher translational energy being able to overcome the activation energy, hence pFH would contribute to the translational energy whereas pHH relates to the vibrational energy of the HH bond.

On the other hand, the FH + H system is endothermic and relates to a late transition state as dictated by Hammond's Postulate, requiring high vibrational energy of the FH bond to overcome the activation energy. In this scenario, pFH refers to the vibrational energy and pHH the translational energy.

MRD:sm6416

2018-05-25T16:14:02Z

Sm6416: /* Polyani's Empirical Rules */

==H2 H Exercise 1==

===Transition State Dynamics===

The transition state is the stage in a reaction coordinate that must be passed through in order for a reaction to occur and occurs at a saddle point, as shown by the numerous surface plots on this page. The first derivative highlights the positions along the reaction coordinate where the gradient equals zero. However, in order to determine if a saddle point ensues, the second derivative of the gradient must be taken. A saddle point is only present if the second derivative > 0.

Another way to think of the transition state is by thinking of the tangent that can be formed at the transition state itself. This tangent will follow the reaction coordinate profile and therefore is expected to be a maximum, where the gradient = 0. A line can be drawn to the normal of the tangent at the selected transition state. This path would show a minimum, where the gradient again = 0, at the intersection of the tangent with normal if the transition state has been correctly identified. It is only in this scenario that a transition state can be determined as one.

===Locating the Transition State===

The transition state was determined through iterations of both r1 and r2 which resulted in the smallest displacement of momenta along with no displacement as shown by the contour plot. This method determined at rts = 0.907743.

[[File:sm6416_Transition_State_Contour.png|thumb|none|350px|Contour plot demonstrating rts = 0.907743 as a result of no fluctuations from the initial input, hence the complex is at the transition state.]]

[[File:sm6416_Transition_State_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating minimum, and almost zero, momentum at rts = 0.907743.]]

[[File:sm6416_Transition_State_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot demonstrating no fluctuations in distance and hence rts = 0.907743.]]

===Reaction Path===

The minimum energy path (MEP) is defined as the lowest path the reaction must follow to form the products and is the downhill motion from the transition state. It can be applied in both directions in the case in question. The MEP views the system as static as it resets the velocity to zero at each step. Whereas the trajectory is very much dynamic and the momenta is accounted for, this is reflected in the vibrational oscillation of the molecule as it passes along the minimum well towards the products.

====MEP====

Initial conditions of r1 = rts + 0.01 = 0.917743, r2 = rts = 0.907743 and p1 = p2 = 0 for the MEP simulation.

[[File:sm6416_MEP_Surface.png|thumb|none|350px|Surface plot highlighting the minimum energy path (MEP), as the reaction returns to the reactants without fully passing through the transition state.]]

[[File:sm6416_MEP_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating zero momentum, as inputted, and more importantly not change in momentum with running the simulation.]]

[[File:sm6416_MEP_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot showing that the reactants reach the transition state at the interception of r1 = r2. r1 quickly reaches a constant value, namely the equilibrium bond length of the reactant molecule. r2 increases logarithmically as time progresses, this represents an increasing distance of Ha from Hb-Hc and a continuing loss of momentum.]]

Final values from the MEP simulation.

r1 = 2.76195

r2 = 0.75883

These values reflect the minimum trajectory for a successful reaction.

p1 = p2 = 0

====Dynamic====

[[File:sm6416_Dynamic_Surface.png|thumb|none|350px|Surface plot highlighting the minimum energy path (MEP) with oscillation of the reactants, as the reaction returns to the reactants without fully passing through the transition state. It is therefore evident that the momentum as a result of the vibrational oscillation does not provide enough energy to proceed to the products.]]

[[File:sm6416_Dynamic_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating the momenta associated with the oscillating reactants.]]

[[File:sm6416_Dynamic_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot showing that the reactants reach the transition state at the interception of r1 = r2. r1 quickly decreases and oscillates about a constant value, namely the equilibrium bond length of the reactant molecule. r2 increases linearly as time progresses, this represents an increasing distance of Ha from Hb-Hc with a constant momentum.]]

Dynamic simulation final values

r1 = 10.0045

r2 = 0.75883

p1 = 2.48523

p2 = 1.29898

p(average) = 1.90409

With r1 = rts and r2 = rts + 0.01 would simply produce the same answer however the values would be flipped to the other distance. In other words r1 = 0.75883 and r2 = 10.0045 would be the output values.

Maintaining the final trajectories as calculated from the dynamic simulation and reversing the sign of the momenta, the reaction proceeds in the reverse direction to the products.

===Reactivity of Trajectories===

These simulations are restricted by the number of steps the program can handle, however a sound understanding of the reaction can be appreciated and the reactivity of each scenario can be determined appropriately.

{| class="wikitable" border=2
! Simulation !! p1 !! p2 !! Energy (kcal/mol) !! Reactivity !! Evidence !! Description
|-
| 1 || -1.25 || -2.5 || 5.03500 || Reactive || [[File:sm6416_MEP_Figure1.png|thumb|none|350px]] || Simulation 1: The reactants proceed through the transition state and to the products. The r2 distance decreases to the equilibrium bond length, whilst r1 simultaneously exhibits dissociation and increases beyond the scope of the graph. The small momenta attributed to the reactants is reflected in the vibrationally oscillating products, with a small amplitude.
|-
| 2 || -1.5 || -2.0 || 3.62879 || Unreactive || [[File:sm6416_MEP_Figure2.png|thumb|none|350px]] || Simulation 2: This is unreactive as the oscillating reactants reach the transition state point and r1 immediately returns to the initial bond length, whilst r2 continues to increase as it moves away from the H2 molecule.
|-
| 3 || -1.5 || -2.5 || 5.13738 || Reactive || [[File:sm6416_MEP_Figure3.png|thumb|none|350px]] || Simulation 3: This simulation shows a reactive pathway that is very similar to simulation 1, however due to the greater momenta associated with the reactants, as inputted, vibrational oscillations with a greater amplitude can be observed.
|-
| 4 || -2.5 || -5.0 || 9.86678 || Unreactive || [[File:sm6416_MEP_Figure4.png|thumb|none|350px]] || Simulation 4: Initially seen here are oscillating reactants with a very large amplitude. However, this simulation is unreactive despite the reactants going through the transition state and towards the product, they return to the initial reactants.
|-
| 5 || -2.5 || -5.2 || 11.80780 || Reactive || [[File:sm6416_MEP_Figure5.png|thumb|none|350px]] || Simulation 5: Like simulation 4, this simulation shows a large oscillating amplitude, whereas in this scenario after passing through the transition state, the products are completely obtained. The slight increase in the p2 momentum can be seen to result in the products.
|}

====Transition State Theory====

Transition State Theory (TST) assumes a quasi-equilibrium between reactants and the transition state. The reaction between the transition state and products is irreversible and therefore is unable to return to the reactants, however many of the surface plots on this page show the complete antithesis of this highlighting a dichotomy between theory and experimental. TST further assumes that fluctuation as to whether the transition complexes go towards reactants or products are independent of each other and hence the rate of one can not be determined by the other.

TST is excellent qualitative tool and can identify the enthalpy, standard entropy and standard Gibbs energy of activation. Despite this, it the method is unable to accurately determine these true values in line with experimental results as doing so would require a deep understanding of the potential energy surface of each reaction. Therefore, TST under estimates the reaction rate in comparison to the experimental values. When TST was developed in 1935 a lack of adequate computer software to accurately map potential energy surfaces, unlike there is today. Hence resulting in a less accurate and longer method to map these surfaces for each reaction.

==F-H-H System Exercise 2==
===Potential Energy Surface Inspection===
====Energetics====

F + H2 is an exothermic reaction as can be seen from the surface plot, the reaction progresses from a small H-H distance to a longer one, whilst H-F simultaneously equilibriates about the F-H bond length. It can be seen that the products are lower, and hence more stable, in energy than the reactants.

F-H + H is simply the reverse reaction that passes through the same transition state, hence this reaction is endothermic with the products being higher in energy than the reactants. There is an overall gain of energy.

With this information in mind, the F-H bond is more stable and thus stronger than the H-H bond. The main factors to this argument is the greater electronegativity of F leading to a stronger contribution to the bond than the molecular orbitals. Hence the overlap of molecular orbitals is a weaker factor in the bond strength.

[[File:sm6416_FHH_Surface.png|thumb|none|350px|Surface plot highlighting the energetics of the F-H-H system.]]

[[File:sm6416_HHF_Surface.png|thumb|none|350px|Surface plot highlighting the energetics of the H-H-F system.]]

====Transition State====

Hammond's postulate aids in finding the transition state; it relates the composition of the transition complex to either the reactants or products for an early or late transition state respectively. In the scenario under investigation for F +H2 an early transition state is present as the reaction is exothermic in this direction, hence the transition state resembles the reactants more.

This guidance proved useful in determining the transition state complex at r1 = F-H = 1.810076 Angstrom and r2 = H-H = 0.74634 Angstrom, as can be seen from the surface and contour plots below showing the absence of displacement to either reactants or products. Furthermore the Momenta vs Time plot indicates a very small momenta of the overall system, without any deviation or substantial change in the momenta.

[[File:sm6416_FHH_Transition_State_Contour.png|thumb|none|350px|Contour plot demonstrating rts as a result of no fluctuations from the initial input, hence the complex is metaphorically sitting on the transition state.]]

[[File:sm6416_FHH_Transition_State_Momenta_Time.png|thumb|none|350px|Momenta vs Time plot demonstrating minimum, and almost zero, momentum at rts.]]

[[File:sm6416_FHH_Transition_State_Surface.png|thumb|none|350px]]

====Activation Energy====

The activation energy for the exothermic reaction was calculated through a 500000 step MEP simulation with input values of r1 = 1.820076, r2 = 0.74634 and p1 = p2 = 0. It was required that after following the minimum energy path, the gradient of the line signifying the reactants was constant.

The activation energy is reported at +0.258 kcal/mol for the exothermic process.

[[File:sm6416_FHH_Activation_Energy_1.png|thumb|none|350px|Energy vs Time graph highlighting the activation energy of the exothermic reaction.]]

The activation energy for the endothermic process was determined with the following parameters: r1 = 1.800076, r2 = 0.74634, p1 = p2 = 0 with 250000 steps. These parameters 'tipped' the reaction towards the FH + H reactants. The reported activation energy was +30.277 kcal/mol.

[[File:sm6416_FHH_Activation_Energy_2.png|thumb|none|350px|Energy vs Time graph highlighting the activation energy of the endothermic reaction.]]

It can hence be seen that the exothermic reaction of F + H2 --> F-H + H only requires a small activation energy as the products are substantially more thermodynamically stable than the reactants.

===Reaction Dynamics===

In this exothermic reaction, the potential energy is mainly converted into vibrational energy of the FH bond, along with heat. As a result of this vibrational energy in the FH bond, vibrational levels above the ground state will become partially populated. In this manner, by recording an IR spectrum of the products, the main F-H will be observed alongside an overtone, with the intensity of this overtone relating to the population of this vibrationally excited state, which can then be used to determine the vibrational energy in the bond itself.

In this same vein, IR chemiluminescence can be employed to yield the same result by measuring the wavelength, and subsequent vibrational energy of the FH bond, of the infrared light that is irradiated from the products and being excited with incident light.

As the momentum closes towards the boundaries of -3 < p < +3, the system passes through transition state but returns to reactant well. This shows that the excess momentum of the system in the product well is sufficient to overcome the high activation energy and return to the thermodynamically unfavourable reactants.

The following parameters were employed for all simulations rFH = 2.3, rHH = 0.74 with 500 steps calculated.

{| class="wikitable" border=2
! Simulation !! pHH !! pFH !! Surface Plot !! Momenta vs Time Plot !! Observations !!
|-
| 1 || -2.5 || -1.5 || [[File:sm6416_Trajectory_1_Surface.png|thumb|none|350px]] ||[[File:sm6416_Trajectory_1_Momenta.png|thumb|none|350px]] || This trajectory results in a successful reaction as seen from the surface plot; the reactants proceed through the transition state and continue into the product well, whilst continually oscillating as a result of the momentum gained.
|-
| 2 || -0.5 || -0.5 || [[File:sm6416_Trajectory_2_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_2_Momenta.png|thumb|none|350px]] || This momentum does not proceed to a reaction. Through the dynamic animation it can be seen that the HH molecule does not possess enough momentum to translate towards F. Therefore the system does not translate out of the reactant well, as seen in the surface plot, since there is not enough energy to overcome the activation energy. The momenta plot simply shows a small up trend, this is expected due to the long range electrostatic force of attraction between F and HH, resulting in a slight increase in the HH vibration velocity. There is no drastic change in the momenta of either F or HH that would otherwise indicate the occurrence of a reaction, as seen in simulation 1 above.
|-
| 3 || +0.5 || -0.5 || [[File:sm6416_Trajectory_3_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_3_Momenta.png|thumb|none|350px]] || This simulation shows an unreactive path, as can be seen from the surface plot, the system remains in the reactant well as it does not overcome the small activation energy for the exothermic reaction to proceed. As in simulation 2, the momentum amplitude of the oscillating HH remains constant however the overall momenta of the system increases due to a slight translation towards F, thus increasing electrostatic attraction forces resulting in this slight overall momenta increase.
|-
| 4 || -1.6 || -0.5 || [[File:sm6416_Trajectory_4_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_4_Momenta.png|thumb|none|350px]] || This simulation is very similar to simulations 2 & 3 in that the system remains in the reactant well as there is not sufficient energy to overcome the activation energy. However as a result of the greater HH momentum, the oscillation amplitude is greater than both simulation 1 & 2.
|-
| 5 || +1.6 || -0.5 || [[File:sm6416_Trajectory_5_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_5_Momenta.png|thumb|none|350px]] || Firstly, this simulation is unreactive as can be seen from the surface plot. In comparison to simulation 4, HH momentum sign has been changed and as a result this has led to not only a greater oscillating amplitude but also a larger translation towards F. So much so in the latter than the Momenta vs Time plot shows an increase in FH oscillation momentum as the electrostatic forces of attraction dominate due to the reduction in internuclear distance.
|-
| 6 || -2.9 || -0.5 || [[File:sm6416_Trajectory_6_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_6_Momenta.png|thumb|none|350px]] || This is the first reactive simulation observed, as can be seen from the surface plot and the drastic change in the momentum of FH. Evidently, there is sufficient energy to pass through the transition state complex and towards the reactants.
|-
| 7 || +2.9 || -0.5 || [[File:sm6416_Trajectory_7_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_7_Momenta.png|thumb|none|350px]] || This simulation is indeed similar to that of simulation 6 however, the change of sign for the HH momentum again results in a greater translation towards F and consequently the system passes through the transition complex shown by the surface plot and Momenta vs Time plot. However after a single oscillation, FH dissociates and the system returns to the reactant well with HH possessing a greater momentum. This scenario could be as a result of the HH momentum being too high and thus providing sufficient activation energy to proceed in the endothermic direction. This is surprising as the exothermic reaction elucidates more thermodynamically stable products.
|-
| 8 || +0.1 || -0.8 || [[File:sm6416_Trajectory_8_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_8_Momenta.png|thumb|none|350px]] || With a mere 60% change in FH momentum and a minimum HH momentum, the system can be seen to react fully, without returning through the transition state. The Momenta vs Time plot further shows a noticeable change in the AB momentum, which corresponds to FH. Despite the oscillations not being regular, it can be noted that the amplitudes are relatively of the same size and show no signs of regressing. This information highlights that the overall the FH momentum dominates the reactivity of the system and has a large weighting to overcoming the activation energy. It can be thought that the increase in momentum aids in allowing a closer distance of F & H, where electrostatic attraction forces will prevail.
|}

====Polyani's Empirical Rules====

The reactive trajectory for the FH + H was determined with the following parameters: rFH = 0.9, rHH = 2.3, pFH = 6.5, pHH = -1.5

Discuss relative translational and vibrational energies required to match the transition state for each endo/exothermic reaction relating to Hammond's postulate.

In order to react, a system must overcome the activation energy, the energy to achieve this is supplied by either translational or vibrational energy. As reported by Polanyi's Empirical Rules, a late transition state, one that resembles the products more as stated through Hammond's Postulate, is achieved through a greater contribution from vibrational energy enabling the activation energy to be overcome. The opposite is true for an early transition state which is promoted by a greater contribution from translational energy.

[[File:sm6416_FHH_Reactive_Trajectory_1_Surface.png|thumb|none|350px]]
[[File:sm6416_FHH_Reactive_Trajectory_1_Momenta.png|thumb|none|350px]]
[[File:sm6416_FHH_Reactive_Trajectory_1_Distance.png|thumb|none|350px]]
[[File:sm6416_FHH_Reactive_Trajectory_1_Contour.png|thumb|none|350px]]

MRD:sm6416

2018-05-25T16:03:00Z

Sm6416: /* Polyani's Empirical Rules */

==H2 H Exercise 1==

===Transition State Dynamics===

The transition state is the stage in a reaction coordinate that must be passed through in order for a reaction to occur and occurs at a saddle point, as shown by the numerous surface plots on this page. The first derivative highlights the positions along the reaction coordinate where the gradient equals zero. However, in order to determine if a saddle point ensues, the second derivative of the gradient must be taken. A saddle point is only present if the second derivative > 0.

Another way to think of the transition state is by thinking of the tangent that can be formed at the transition state itself. This tangent will follow the reaction coordinate profile and therefore is expected to be a maximum, where the gradient = 0. A line can be drawn to the normal of the tangent at the selected transition state. This path would show a minimum, where the gradient again = 0, at the intersection of the tangent with normal if the transition state has been correctly identified. It is only in this scenario that a transition state can be determined as one.

===Locating the Transition State===

The transition state was determined through iterations of both r1 and r2 which resulted in the smallest displacement of momenta along with no displacement as shown by the contour plot. This method determined at rts = 0.907743.

[[File:sm6416_Transition_State_Contour.png|thumb|none|350px|Contour plot demonstrating rts = 0.907743 as a result of no fluctuations from the initial input, hence the complex is at the transition state.]]

[[File:sm6416_Transition_State_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating minimum, and almost zero, momentum at rts = 0.907743.]]

[[File:sm6416_Transition_State_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot demonstrating no fluctuations in distance and hence rts = 0.907743.]]

===Reaction Path===

The minimum energy path (MEP) is defined as the lowest path the reaction must follow to form the products and is the downhill motion from the transition state. It can be applied in both directions in the case in question. The MEP views the system as static as it resets the velocity to zero at each step. Whereas the trajectory is very much dynamic and the momenta is accounted for, this is reflected in the vibrational oscillation of the molecule as it passes along the minimum well towards the products.

====MEP====

Initial conditions of r1 = rts + 0.01 = 0.917743, r2 = rts = 0.907743 and p1 = p2 = 0 for the MEP simulation.

[[File:sm6416_MEP_Surface.png|thumb|none|350px|Surface plot highlighting the minimum energy path (MEP), as the reaction returns to the reactants without fully passing through the transition state.]]

[[File:sm6416_MEP_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating zero momentum, as inputted, and more importantly not change in momentum with running the simulation.]]

[[File:sm6416_MEP_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot showing that the reactants reach the transition state at the interception of r1 = r2. r1 quickly reaches a constant value, namely the equilibrium bond length of the reactant molecule. r2 increases logarithmically as time progresses, this represents an increasing distance of Ha from Hb-Hc and a continuing loss of momentum.]]

Final values from the MEP simulation.

r1 = 2.76195

r2 = 0.75883

These values reflect the minimum trajectory for a successful reaction.

p1 = p2 = 0

====Dynamic====

[[File:sm6416_Dynamic_Surface.png|thumb|none|350px|Surface plot highlighting the minimum energy path (MEP) with oscillation of the reactants, as the reaction returns to the reactants without fully passing through the transition state. It is therefore evident that the momentum as a result of the vibrational oscillation does not provide enough energy to proceed to the products.]]

[[File:sm6416_Dynamic_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating the momenta associated with the oscillating reactants.]]

[[File:sm6416_Dynamic_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot showing that the reactants reach the transition state at the interception of r1 = r2. r1 quickly decreases and oscillates about a constant value, namely the equilibrium bond length of the reactant molecule. r2 increases linearly as time progresses, this represents an increasing distance of Ha from Hb-Hc with a constant momentum.]]

Dynamic simulation final values

r1 = 10.0045

r2 = 0.75883

p1 = 2.48523

p2 = 1.29898

p(average) = 1.90409

With r1 = rts and r2 = rts + 0.01 would simply produce the same answer however the values would be flipped to the other distance. In other words r1 = 0.75883 and r2 = 10.0045 would be the output values.

Maintaining the final trajectories as calculated from the dynamic simulation and reversing the sign of the momenta, the reaction proceeds in the reverse direction to the products.

===Reactivity of Trajectories===

These simulations are restricted by the number of steps the program can handle, however a sound understanding of the reaction can be appreciated and the reactivity of each scenario can be determined appropriately.

{| class="wikitable" border=2
! Simulation !! p1 !! p2 !! Energy (kcal/mol) !! Reactivity !! Evidence !! Description
|-
| 1 || -1.25 || -2.5 || 5.03500 || Reactive || [[File:sm6416_MEP_Figure1.png|thumb|none|350px]] || Simulation 1: The reactants proceed through the transition state and to the products. The r2 distance decreases to the equilibrium bond length, whilst r1 simultaneously exhibits dissociation and increases beyond the scope of the graph. The small momenta attributed to the reactants is reflected in the vibrationally oscillating products, with a small amplitude.
|-
| 2 || -1.5 || -2.0 || 3.62879 || Unreactive || [[File:sm6416_MEP_Figure2.png|thumb|none|350px]] || Simulation 2: This is unreactive as the oscillating reactants reach the transition state point and r1 immediately returns to the initial bond length, whilst r2 continues to increase as it moves away from the H2 molecule.
|-
| 3 || -1.5 || -2.5 || 5.13738 || Reactive || [[File:sm6416_MEP_Figure3.png|thumb|none|350px]] || Simulation 3: This simulation shows a reactive pathway that is very similar to simulation 1, however due to the greater momenta associated with the reactants, as inputted, vibrational oscillations with a greater amplitude can be observed.
|-
| 4 || -2.5 || -5.0 || 9.86678 || Unreactive || [[File:sm6416_MEP_Figure4.png|thumb|none|350px]] || Simulation 4: Initially seen here are oscillating reactants with a very large amplitude. However, this simulation is unreactive despite the reactants going through the transition state and towards the product, they return to the initial reactants.
|-
| 5 || -2.5 || -5.2 || 11.80780 || Reactive || [[File:sm6416_MEP_Figure5.png|thumb|none|350px]] || Simulation 5: Like simulation 4, this simulation shows a large oscillating amplitude, whereas in this scenario after passing through the transition state, the products are completely obtained. The slight increase in the p2 momentum can be seen to result in the products.
|}

====Transition State Theory====

Transition State Theory (TST) assumes a quasi-equilibrium between reactants and the transition state. The reaction between the transition state and products is irreversible and therefore is unable to return to the reactants, however many of the surface plots on this page show the complete antithesis of this highlighting a dichotomy between theory and experimental. TST further assumes that fluctuation as to whether the transition complexes go towards reactants or products are independent of each other and hence the rate of one can not be determined by the other.

TST is excellent qualitative tool and can identify the enthalpy, standard entropy and standard Gibbs energy of activation. Despite this, it the method is unable to accurately determine these true values in line with experimental results as doing so would require a deep understanding of the potential energy surface of each reaction. Therefore, TST under estimates the reaction rate in comparison to the experimental values. When TST was developed in 1935 a lack of adequate computer software to accurately map potential energy surfaces, unlike there is today. Hence resulting in a less accurate and longer method to map these surfaces for each reaction.

==F-H-H System Exercise 2==
===Potential Energy Surface Inspection===
====Energetics====

F + H2 is an exothermic reaction as can be seen from the surface plot, the reaction progresses from a small H-H distance to a longer one, whilst H-F simultaneously equilibriates about the F-H bond length. It can be seen that the products are lower, and hence more stable, in energy than the reactants.

F-H + H is simply the reverse reaction that passes through the same transition state, hence this reaction is endothermic with the products being higher in energy than the reactants. There is an overall gain of energy.

With this information in mind, the F-H bond is more stable and thus stronger than the H-H bond. The main factors to this argument is the greater electronegativity of F leading to a stronger contribution to the bond than the molecular orbitals. Hence the overlap of molecular orbitals is a weaker factor in the bond strength.

[[File:sm6416_FHH_Surface.png|thumb|none|350px|Surface plot highlighting the energetics of the F-H-H system.]]

[[File:sm6416_HHF_Surface.png|thumb|none|350px|Surface plot highlighting the energetics of the H-H-F system.]]

====Transition State====

Hammond's postulate aids in finding the transition state; it relates the composition of the transition complex to either the reactants or products for an early or late transition state respectively. In the scenario under investigation for F +H2 an early transition state is present as the reaction is exothermic in this direction, hence the transition state resembles the reactants more.

This guidance proved useful in determining the transition state complex at r1 = F-H = 1.810076 Angstrom and r2 = H-H = 0.74634 Angstrom, as can be seen from the surface and contour plots below showing the absence of displacement to either reactants or products. Furthermore the Momenta vs Time plot indicates a very small momenta of the overall system, without any deviation or substantial change in the momenta.

[[File:sm6416_FHH_Transition_State_Contour.png|thumb|none|350px|Contour plot demonstrating rts as a result of no fluctuations from the initial input, hence the complex is metaphorically sitting on the transition state.]]

[[File:sm6416_FHH_Transition_State_Momenta_Time.png|thumb|none|350px|Momenta vs Time plot demonstrating minimum, and almost zero, momentum at rts.]]

[[File:sm6416_FHH_Transition_State_Surface.png|thumb|none|350px]]

====Activation Energy====

The activation energy for the exothermic reaction was calculated through a 500000 step MEP simulation with input values of r1 = 1.820076, r2 = 0.74634 and p1 = p2 = 0. It was required that after following the minimum energy path, the gradient of the line signifying the reactants was constant.

The activation energy is reported at +0.258 kcal/mol for the exothermic process.

[[File:sm6416_FHH_Activation_Energy_1.png|thumb|none|350px|Energy vs Time graph highlighting the activation energy of the exothermic reaction.]]

The activation energy for the endothermic process was determined with the following parameters: r1 = 1.800076, r2 = 0.74634, p1 = p2 = 0 with 250000 steps. These parameters 'tipped' the reaction towards the FH + H reactants. The reported activation energy was +30.277 kcal/mol.

[[File:sm6416_FHH_Activation_Energy_2.png|thumb|none|350px|Energy vs Time graph highlighting the activation energy of the endothermic reaction.]]

It can hence be seen that the exothermic reaction of F + H2 --> F-H + H only requires a small activation energy as the products are substantially more thermodynamically stable than the reactants.

===Reaction Dynamics===

In this exothermic reaction, the potential energy is mainly converted into vibrational energy of the FH bond, along with heat. As a result of this vibrational energy in the FH bond, vibrational levels above the ground state will become partially populated. In this manner, by recording an IR spectrum of the products, the main F-H will be observed alongside an overtone, with the intensity of this overtone relating to the population of this vibrationally excited state, which can then be used to determine the vibrational energy in the bond itself.

In this same vein, IR chemiluminescence can be employed to yield the same result by measuring the wavelength, and subsequent vibrational energy of the FH bond, of the infrared light that is irradiated from the products and being excited with incident light.

As the momentum closes towards the boundaries of -3 < p < +3, the system passes through transition state but returns to reactant well. This shows that the excess momentum of the system in the product well is sufficient to overcome the high activation energy and return to the thermodynamically unfavourable reactants.

The following parameters were employed for all simulations rFH = 2.3, rHH = 0.74 with 500 steps calculated.

{| class="wikitable" border=2
! Simulation !! pHH !! pFH !! Surface Plot !! Momenta vs Time Plot !! Observations !!
|-
| 1 || -2.5 || -1.5 || [[File:sm6416_Trajectory_1_Surface.png|thumb|none|350px]] ||[[File:sm6416_Trajectory_1_Momenta.png|thumb|none|350px]] || This trajectory results in a successful reaction as seen from the surface plot; the reactants proceed through the transition state and continue into the product well, whilst continually oscillating as a result of the momentum gained.
|-
| 2 || -0.5 || -0.5 || [[File:sm6416_Trajectory_2_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_2_Momenta.png|thumb|none|350px]] || This momentum does not proceed to a reaction. Through the dynamic animation it can be seen that the HH molecule does not possess enough momentum to translate towards F. Therefore the system does not translate out of the reactant well, as seen in the surface plot, since there is not enough energy to overcome the activation energy. The momenta plot simply shows a small up trend, this is expected due to the long range electrostatic force of attraction between F and HH, resulting in a slight increase in the HH vibration velocity. There is no drastic change in the momenta of either F or HH that would otherwise indicate the occurrence of a reaction, as seen in simulation 1 above.
|-
| 3 || +0.5 || -0.5 || [[File:sm6416_Trajectory_3_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_3_Momenta.png|thumb|none|350px]] || This simulation shows an unreactive path, as can be seen from the surface plot, the system remains in the reactant well as it does not overcome the small activation energy for the exothermic reaction to proceed. As in simulation 2, the momentum amplitude of the oscillating HH remains constant however the overall momenta of the system increases due to a slight translation towards F, thus increasing electrostatic attraction forces resulting in this slight overall momenta increase.
|-
| 4 || -1.6 || -0.5 || [[File:sm6416_Trajectory_4_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_4_Momenta.png|thumb|none|350px]] || This simulation is very similar to simulations 2 & 3 in that the system remains in the reactant well as there is not sufficient energy to overcome the activation energy. However as a result of the greater HH momentum, the oscillation amplitude is greater than both simulation 1 & 2.
|-
| 5 || +1.6 || -0.5 || [[File:sm6416_Trajectory_5_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_5_Momenta.png|thumb|none|350px]] || Firstly, this simulation is unreactive as can be seen from the surface plot. In comparison to simulation 4, HH momentum sign has been changed and as a result this has led to not only a greater oscillating amplitude but also a larger translation towards F. So much so in the latter than the Momenta vs Time plot shows an increase in FH oscillation momentum as the electrostatic forces of attraction dominate due to the reduction in internuclear distance.
|-
| 6 || -2.9 || -0.5 || [[File:sm6416_Trajectory_6_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_6_Momenta.png|thumb|none|350px]] || This is the first reactive simulation observed, as can be seen from the surface plot and the drastic change in the momentum of FH. Evidently, there is sufficient energy to pass through the transition state complex and towards the reactants.
|-
| 7 || +2.9 || -0.5 || [[File:sm6416_Trajectory_7_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_7_Momenta.png|thumb|none|350px]] || This simulation is indeed similar to that of simulation 6 however, the change of sign for the HH momentum again results in a greater translation towards F and consequently the system passes through the transition complex shown by the surface plot and Momenta vs Time plot. However after a single oscillation, FH dissociates and the system returns to the reactant well with HH possessing a greater momentum. This scenario could be as a result of the HH momentum being too high and thus providing sufficient activation energy to proceed in the endothermic direction. This is surprising as the exothermic reaction elucidates more thermodynamically stable products.
|-
| 8 || +0.1 || -0.8 || [[File:sm6416_Trajectory_8_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_8_Momenta.png|thumb|none|350px]] || With a mere 60% change in FH momentum and a minimum HH momentum, the system can be seen to react fully, without returning through the transition state. The Momenta vs Time plot further shows a noticeable change in the AB momentum, which corresponds to FH. Despite the oscillations not being regular, it can be noted that the amplitudes are relatively of the same size and show no signs of regressing. This information highlights that the overall the FH momentum dominates the reactivity of the system and has a large weighting to overcoming the activation energy. It can be thought that the increase in momentum aids in allowing a closer distance of F & H, where electrostatic attraction forces will prevail.
|}

====Polyani's Empirical Rules====

The reactive trajectory for the FH + H was determined with the following parameters: rFH = 0.9, rHH = 2.3, pFH = 6.5, pHH = -1.5

Discuss relative translational and vibrational energies required to match the transition state for each endo/exothermic reaction relating to Hammond's postulate.

Cite reference

[[File:sm6416_FHH_Reactive_Trajectory_1_Surface.png|thumb|none|350px]]
[[File:sm6416_FHH_Reactive_Trajectory_1_Momenta.png|thumb|none|350px]]
[[File:sm6416_FHH_Reactive_Trajectory_1_Distance.png|thumb|none|350px]]
[[File:sm6416_FHH_Reactive_Trajectory_1_Contour.png|thumb|none|350px]]

MRD:sm6416

2018-05-25T15:59:29Z

Sm6416: /* Reaction Dynamics */

==H2 H Exercise 1==

===Transition State Dynamics===

The transition state is the stage in a reaction coordinate that must be passed through in order for a reaction to occur and occurs at a saddle point, as shown by the numerous surface plots on this page. The first derivative highlights the positions along the reaction coordinate where the gradient equals zero. However, in order to determine if a saddle point ensues, the second derivative of the gradient must be taken. A saddle point is only present if the second derivative > 0.

Another way to think of the transition state is by thinking of the tangent that can be formed at the transition state itself. This tangent will follow the reaction coordinate profile and therefore is expected to be a maximum, where the gradient = 0. A line can be drawn to the normal of the tangent at the selected transition state. This path would show a minimum, where the gradient again = 0, at the intersection of the tangent with normal if the transition state has been correctly identified. It is only in this scenario that a transition state can be determined as one.

===Locating the Transition State===

The transition state was determined through iterations of both r1 and r2 which resulted in the smallest displacement of momenta along with no displacement as shown by the contour plot. This method determined at rts = 0.907743.

[[File:sm6416_Transition_State_Contour.png|thumb|none|350px|Contour plot demonstrating rts = 0.907743 as a result of no fluctuations from the initial input, hence the complex is at the transition state.]]

[[File:sm6416_Transition_State_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating minimum, and almost zero, momentum at rts = 0.907743.]]

[[File:sm6416_Transition_State_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot demonstrating no fluctuations in distance and hence rts = 0.907743.]]

===Reaction Path===

The minimum energy path (MEP) is defined as the lowest path the reaction must follow to form the products and is the downhill motion from the transition state. It can be applied in both directions in the case in question. The MEP views the system as static as it resets the velocity to zero at each step. Whereas the trajectory is very much dynamic and the momenta is accounted for, this is reflected in the vibrational oscillation of the molecule as it passes along the minimum well towards the products.

====MEP====

Initial conditions of r1 = rts + 0.01 = 0.917743, r2 = rts = 0.907743 and p1 = p2 = 0 for the MEP simulation.

[[File:sm6416_MEP_Surface.png|thumb|none|350px|Surface plot highlighting the minimum energy path (MEP), as the reaction returns to the reactants without fully passing through the transition state.]]

[[File:sm6416_MEP_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating zero momentum, as inputted, and more importantly not change in momentum with running the simulation.]]

[[File:sm6416_MEP_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot showing that the reactants reach the transition state at the interception of r1 = r2. r1 quickly reaches a constant value, namely the equilibrium bond length of the reactant molecule. r2 increases logarithmically as time progresses, this represents an increasing distance of Ha from Hb-Hc and a continuing loss of momentum.]]

Final values from the MEP simulation.

r1 = 2.76195

r2 = 0.75883

These values reflect the minimum trajectory for a successful reaction.

p1 = p2 = 0

====Dynamic====

[[File:sm6416_Dynamic_Surface.png|thumb|none|350px|Surface plot highlighting the minimum energy path (MEP) with oscillation of the reactants, as the reaction returns to the reactants without fully passing through the transition state. It is therefore evident that the momentum as a result of the vibrational oscillation does not provide enough energy to proceed to the products.]]

[[File:sm6416_Dynamic_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating the momenta associated with the oscillating reactants.]]

[[File:sm6416_Dynamic_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot showing that the reactants reach the transition state at the interception of r1 = r2. r1 quickly decreases and oscillates about a constant value, namely the equilibrium bond length of the reactant molecule. r2 increases linearly as time progresses, this represents an increasing distance of Ha from Hb-Hc with a constant momentum.]]

Dynamic simulation final values

r1 = 10.0045

r2 = 0.75883

p1 = 2.48523

p2 = 1.29898

p(average) = 1.90409

With r1 = rts and r2 = rts + 0.01 would simply produce the same answer however the values would be flipped to the other distance. In other words r1 = 0.75883 and r2 = 10.0045 would be the output values.

Maintaining the final trajectories as calculated from the dynamic simulation and reversing the sign of the momenta, the reaction proceeds in the reverse direction to the products.

===Reactivity of Trajectories===

These simulations are restricted by the number of steps the program can handle, however a sound understanding of the reaction can be appreciated and the reactivity of each scenario can be determined appropriately.

{| class="wikitable" border=2
! Simulation !! p1 !! p2 !! Energy (kcal/mol) !! Reactivity !! Evidence !! Description
|-
| 1 || -1.25 || -2.5 || 5.03500 || Reactive || [[File:sm6416_MEP_Figure1.png|thumb|none|350px]] || Simulation 1: The reactants proceed through the transition state and to the products. The r2 distance decreases to the equilibrium bond length, whilst r1 simultaneously exhibits dissociation and increases beyond the scope of the graph. The small momenta attributed to the reactants is reflected in the vibrationally oscillating products, with a small amplitude.
|-
| 2 || -1.5 || -2.0 || 3.62879 || Unreactive || [[File:sm6416_MEP_Figure2.png|thumb|none|350px]] || Simulation 2: This is unreactive as the oscillating reactants reach the transition state point and r1 immediately returns to the initial bond length, whilst r2 continues to increase as it moves away from the H2 molecule.
|-
| 3 || -1.5 || -2.5 || 5.13738 || Reactive || [[File:sm6416_MEP_Figure3.png|thumb|none|350px]] || Simulation 3: This simulation shows a reactive pathway that is very similar to simulation 1, however due to the greater momenta associated with the reactants, as inputted, vibrational oscillations with a greater amplitude can be observed.
|-
| 4 || -2.5 || -5.0 || 9.86678 || Unreactive || [[File:sm6416_MEP_Figure4.png|thumb|none|350px]] || Simulation 4: Initially seen here are oscillating reactants with a very large amplitude. However, this simulation is unreactive despite the reactants going through the transition state and towards the product, they return to the initial reactants.
|-
| 5 || -2.5 || -5.2 || 11.80780 || Reactive || [[File:sm6416_MEP_Figure5.png|thumb|none|350px]] || Simulation 5: Like simulation 4, this simulation shows a large oscillating amplitude, whereas in this scenario after passing through the transition state, the products are completely obtained. The slight increase in the p2 momentum can be seen to result in the products.
|}

====Transition State Theory====

Transition State Theory (TST) assumes a quasi-equilibrium between reactants and the transition state. The reaction between the transition state and products is irreversible and therefore is unable to return to the reactants, however many of the surface plots on this page show the complete antithesis of this highlighting a dichotomy between theory and experimental. TST further assumes that fluctuation as to whether the transition complexes go towards reactants or products are independent of each other and hence the rate of one can not be determined by the other.

TST is excellent qualitative tool and can identify the enthalpy, standard entropy and standard Gibbs energy of activation. Despite this, it the method is unable to accurately determine these true values in line with experimental results as doing so would require a deep understanding of the potential energy surface of each reaction. Therefore, TST under estimates the reaction rate in comparison to the experimental values. When TST was developed in 1935 a lack of adequate computer software to accurately map potential energy surfaces, unlike there is today. Hence resulting in a less accurate and longer method to map these surfaces for each reaction.

==F-H-H System Exercise 2==
===Potential Energy Surface Inspection===
====Energetics====

F + H2 is an exothermic reaction as can be seen from the surface plot, the reaction progresses from a small H-H distance to a longer one, whilst H-F simultaneously equilibriates about the F-H bond length. It can be seen that the products are lower, and hence more stable, in energy than the reactants.

F-H + H is simply the reverse reaction that passes through the same transition state, hence this reaction is endothermic with the products being higher in energy than the reactants. There is an overall gain of energy.

With this information in mind, the F-H bond is more stable and thus stronger than the H-H bond. The main factors to this argument is the greater electronegativity of F leading to a stronger contribution to the bond than the molecular orbitals. Hence the overlap of molecular orbitals is a weaker factor in the bond strength.

[[File:sm6416_FHH_Surface.png|thumb|none|350px|Surface plot highlighting the energetics of the F-H-H system.]]

[[File:sm6416_HHF_Surface.png|thumb|none|350px|Surface plot highlighting the energetics of the H-H-F system.]]

====Transition State====

Hammond's postulate aids in finding the transition state; it relates the composition of the transition complex to either the reactants or products for an early or late transition state respectively. In the scenario under investigation for F +H2 an early transition state is present as the reaction is exothermic in this direction, hence the transition state resembles the reactants more.

This guidance proved useful in determining the transition state complex at r1 = F-H = 1.810076 Angstrom and r2 = H-H = 0.74634 Angstrom, as can be seen from the surface and contour plots below showing the absence of displacement to either reactants or products. Furthermore the Momenta vs Time plot indicates a very small momenta of the overall system, without any deviation or substantial change in the momenta.

[[File:sm6416_FHH_Transition_State_Contour.png|thumb|none|350px|Contour plot demonstrating rts as a result of no fluctuations from the initial input, hence the complex is metaphorically sitting on the transition state.]]

[[File:sm6416_FHH_Transition_State_Momenta_Time.png|thumb|none|350px|Momenta vs Time plot demonstrating minimum, and almost zero, momentum at rts.]]

[[File:sm6416_FHH_Transition_State_Surface.png|thumb|none|350px]]

====Activation Energy====

The activation energy for the exothermic reaction was calculated through a 500000 step MEP simulation with input values of r1 = 1.820076, r2 = 0.74634 and p1 = p2 = 0. It was required that after following the minimum energy path, the gradient of the line signifying the reactants was constant.

The activation energy is reported at +0.258 kcal/mol for the exothermic process.

[[File:sm6416_FHH_Activation_Energy_1.png|thumb|none|350px|Energy vs Time graph highlighting the activation energy of the exothermic reaction.]]

The activation energy for the endothermic process was determined with the following parameters: r1 = 1.800076, r2 = 0.74634, p1 = p2 = 0 with 250000 steps. These parameters 'tipped' the reaction towards the FH + H reactants. The reported activation energy was +30.277 kcal/mol.

[[File:sm6416_FHH_Activation_Energy_2.png|thumb|none|350px|Energy vs Time graph highlighting the activation energy of the endothermic reaction.]]

It can hence be seen that the exothermic reaction of F + H2 --> F-H + H only requires a small activation energy as the products are substantially more thermodynamically stable than the reactants.

===Reaction Dynamics===

In this exothermic reaction, the potential energy is mainly converted into vibrational energy of the FH bond, along with heat. As a result of this vibrational energy in the FH bond, vibrational levels above the ground state will become partially populated. In this manner, by recording an IR spectrum of the products, the main F-H will be observed alongside an overtone, with the intensity of this overtone relating to the population of this vibrationally excited state, which can then be used to determine the vibrational energy in the bond itself.

In this same vein, IR chemiluminescence can be employed to yield the same result by measuring the wavelength, and subsequent vibrational energy of the FH bond, of the infrared light that is irradiated from the products and being excited with incident light.

As the momentum closes towards the boundaries of -3 < p < +3, the system passes through transition state but returns to reactant well. This shows that the excess momentum of the system in the product well is sufficient to overcome the high activation energy and return to the thermodynamically unfavourable reactants.

The following parameters were employed for all simulations rFH = 2.3, rHH = 0.74 with 500 steps calculated.

{| class="wikitable" border=2
! Simulation !! pHH !! pFH !! Surface Plot !! Momenta vs Time Plot !! Observations !!
|-
| 1 || -2.5 || -1.5 || [[File:sm6416_Trajectory_1_Surface.png|thumb|none|350px]] ||[[File:sm6416_Trajectory_1_Momenta.png|thumb|none|350px]] || This trajectory results in a successful reaction as seen from the surface plot; the reactants proceed through the transition state and continue into the product well, whilst continually oscillating as a result of the momentum gained.
|-
| 2 || -0.5 || -0.5 || [[File:sm6416_Trajectory_2_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_2_Momenta.png|thumb|none|350px]] || This momentum does not proceed to a reaction. Through the dynamic animation it can be seen that the HH molecule does not possess enough momentum to translate towards F. Therefore the system does not translate out of the reactant well, as seen in the surface plot, since there is not enough energy to overcome the activation energy. The momenta plot simply shows a small up trend, this is expected due to the long range electrostatic force of attraction between F and HH, resulting in a slight increase in the HH vibration velocity. There is no drastic change in the momenta of either F or HH that would otherwise indicate the occurrence of a reaction, as seen in simulation 1 above.
|-
| 3 || +0.5 || -0.5 || [[File:sm6416_Trajectory_3_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_3_Momenta.png|thumb|none|350px]] || This simulation shows an unreactive path, as can be seen from the surface plot, the system remains in the reactant well as it does not overcome the small activation energy for the exothermic reaction to proceed. As in simulation 2, the momentum amplitude of the oscillating HH remains constant however the overall momenta of the system increases due to a slight translation towards F, thus increasing electrostatic attraction forces resulting in this slight overall momenta increase.
|-
| 4 || -1.6 || -0.5 || [[File:sm6416_Trajectory_4_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_4_Momenta.png|thumb|none|350px]] || This simulation is very similar to simulations 2 & 3 in that the system remains in the reactant well as there is not sufficient energy to overcome the activation energy. However as a result of the greater HH momentum, the oscillation amplitude is greater than both simulation 1 & 2.
|-
| 5 || +1.6 || -0.5 || [[File:sm6416_Trajectory_5_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_5_Momenta.png|thumb|none|350px]] || Firstly, this simulation is unreactive as can be seen from the surface plot. In comparison to simulation 4, HH momentum sign has been changed and as a result this has led to not only a greater oscillating amplitude but also a larger translation towards F. So much so in the latter than the Momenta vs Time plot shows an increase in FH oscillation momentum as the electrostatic forces of attraction dominate due to the reduction in internuclear distance.
|-
| 6 || -2.9 || -0.5 || [[File:sm6416_Trajectory_6_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_6_Momenta.png|thumb|none|350px]] || This is the first reactive simulation observed, as can be seen from the surface plot and the drastic change in the momentum of FH. Evidently, there is sufficient energy to pass through the transition state complex and towards the reactants.
|-
| 7 || +2.9 || -0.5 || [[File:sm6416_Trajectory_7_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_7_Momenta.png|thumb|none|350px]] || This simulation is indeed similar to that of simulation 6 however, the change of sign for the HH momentum again results in a greater translation towards F and consequently the system passes through the transition complex shown by the surface plot and Momenta vs Time plot. However after a single oscillation, FH dissociates and the system returns to the reactant well with HH possessing a greater momentum. This scenario could be as a result of the HH momentum being too high and thus providing sufficient activation energy to proceed in the endothermic direction. This is surprising as the exothermic reaction elucidates more thermodynamically stable products.
|-
| 8 || +0.1 || -0.8 || [[File:sm6416_Trajectory_8_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_8_Momenta.png|thumb|none|350px]] || With a mere 60% change in FH momentum and a minimum HH momentum, the system can be seen to react fully, without returning through the transition state. The Momenta vs Time plot further shows a noticeable change in the AB momentum, which corresponds to FH. Despite the oscillations not being regular, it can be noted that the amplitudes are relatively of the same size and show no signs of regressing. This information highlights that the overall the FH momentum dominates the reactivity of the system and has a large weighting to overcoming the activation energy. It can be thought that the increase in momentum aids in allowing a closer distance of F & H, where electrostatic attraction forces will prevail.
|}

====Polyani's Empirical Rules====

Discuss relative translational and vibrational energies required to match the transition state for each endo/exothermic reaction relating to Hammond's postulate.

FH + H reactive trajectory - r1=0.9 r2=2.3 p1=6.5 p2=-1.5

Cite reference

[[File:sm6416_FHH_Reactive_Trajectory_1_Surface.png|thumb|none|350px]]
[[File:sm6416_FHH_Reactive_Trajectory_1_Momenta.png|thumb|none|350px]]
[[File:sm6416_FHH_Reactive_Trajectory_1_Distance.png|thumb|none|350px]]
[[File:sm6416_FHH_Reactive_Trajectory_1_Contour.png|thumb|none|350px]]

MRD:sm6416

2018-05-25T15:33:35Z

Sm6416: /* Activation Energy */

==H2 H Exercise 1==

===Transition State Dynamics===

The transition state is the stage in a reaction coordinate that must be passed through in order for a reaction to occur and occurs at a saddle point, as shown by the numerous surface plots on this page. The first derivative highlights the positions along the reaction coordinate where the gradient equals zero. However, in order to determine if a saddle point ensues, the second derivative of the gradient must be taken. A saddle point is only present if the second derivative > 0.

Another way to think of the transition state is by thinking of the tangent that can be formed at the transition state itself. This tangent will follow the reaction coordinate profile and therefore is expected to be a maximum, where the gradient = 0. A line can be drawn to the normal of the tangent at the selected transition state. This path would show a minimum, where the gradient again = 0, at the intersection of the tangent with normal if the transition state has been correctly identified. It is only in this scenario that a transition state can be determined as one.

===Locating the Transition State===

The transition state was determined through iterations of both r1 and r2 which resulted in the smallest displacement of momenta along with no displacement as shown by the contour plot. This method determined at rts = 0.907743.

[[File:sm6416_Transition_State_Contour.png|thumb|none|350px|Contour plot demonstrating rts = 0.907743 as a result of no fluctuations from the initial input, hence the complex is at the transition state.]]

[[File:sm6416_Transition_State_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating minimum, and almost zero, momentum at rts = 0.907743.]]

[[File:sm6416_Transition_State_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot demonstrating no fluctuations in distance and hence rts = 0.907743.]]

===Reaction Path===

The minimum energy path (MEP) is defined as the lowest path the reaction must follow to form the products and is the downhill motion from the transition state. It can be applied in both directions in the case in question. The MEP views the system as static as it resets the velocity to zero at each step. Whereas the trajectory is very much dynamic and the momenta is accounted for, this is reflected in the vibrational oscillation of the molecule as it passes along the minimum well towards the products.

====MEP====

Initial conditions of r1 = rts + 0.01 = 0.917743, r2 = rts = 0.907743 and p1 = p2 = 0 for the MEP simulation.

[[File:sm6416_MEP_Surface.png|thumb|none|350px|Surface plot highlighting the minimum energy path (MEP), as the reaction returns to the reactants without fully passing through the transition state.]]

[[File:sm6416_MEP_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating zero momentum, as inputted, and more importantly not change in momentum with running the simulation.]]

[[File:sm6416_MEP_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot showing that the reactants reach the transition state at the interception of r1 = r2. r1 quickly reaches a constant value, namely the equilibrium bond length of the reactant molecule. r2 increases logarithmically as time progresses, this represents an increasing distance of Ha from Hb-Hc and a continuing loss of momentum.]]

Final values from the MEP simulation.

r1 = 2.76195

r2 = 0.75883

These values reflect the minimum trajectory for a successful reaction.

p1 = p2 = 0

====Dynamic====

[[File:sm6416_Dynamic_Surface.png|thumb|none|350px|Surface plot highlighting the minimum energy path (MEP) with oscillation of the reactants, as the reaction returns to the reactants without fully passing through the transition state. It is therefore evident that the momentum as a result of the vibrational oscillation does not provide enough energy to proceed to the products.]]

[[File:sm6416_Dynamic_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating the momenta associated with the oscillating reactants.]]

[[File:sm6416_Dynamic_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot showing that the reactants reach the transition state at the interception of r1 = r2. r1 quickly decreases and oscillates about a constant value, namely the equilibrium bond length of the reactant molecule. r2 increases linearly as time progresses, this represents an increasing distance of Ha from Hb-Hc with a constant momentum.]]

Dynamic simulation final values

r1 = 10.0045

r2 = 0.75883

p1 = 2.48523

p2 = 1.29898

p(average) = 1.90409

With r1 = rts and r2 = rts + 0.01 would simply produce the same answer however the values would be flipped to the other distance. In other words r1 = 0.75883 and r2 = 10.0045 would be the output values.

Maintaining the final trajectories as calculated from the dynamic simulation and reversing the sign of the momenta, the reaction proceeds in the reverse direction to the products.

===Reactivity of Trajectories===

These simulations are restricted by the number of steps the program can handle, however a sound understanding of the reaction can be appreciated and the reactivity of each scenario can be determined appropriately.

{| class="wikitable" border=2
! Simulation !! p1 !! p2 !! Energy (kcal/mol) !! Reactivity !! Evidence !! Description
|-
| 1 || -1.25 || -2.5 || 5.03500 || Reactive || [[File:sm6416_MEP_Figure1.png|thumb|none|350px]] || Simulation 1: The reactants proceed through the transition state and to the products. The r2 distance decreases to the equilibrium bond length, whilst r1 simultaneously exhibits dissociation and increases beyond the scope of the graph. The small momenta attributed to the reactants is reflected in the vibrationally oscillating products, with a small amplitude.
|-
| 2 || -1.5 || -2.0 || 3.62879 || Unreactive || [[File:sm6416_MEP_Figure2.png|thumb|none|350px]] || Simulation 2: This is unreactive as the oscillating reactants reach the transition state point and r1 immediately returns to the initial bond length, whilst r2 continues to increase as it moves away from the H2 molecule.
|-
| 3 || -1.5 || -2.5 || 5.13738 || Reactive || [[File:sm6416_MEP_Figure3.png|thumb|none|350px]] || Simulation 3: This simulation shows a reactive pathway that is very similar to simulation 1, however due to the greater momenta associated with the reactants, as inputted, vibrational oscillations with a greater amplitude can be observed.
|-
| 4 || -2.5 || -5.0 || 9.86678 || Unreactive || [[File:sm6416_MEP_Figure4.png|thumb|none|350px]] || Simulation 4: Initially seen here are oscillating reactants with a very large amplitude. However, this simulation is unreactive despite the reactants going through the transition state and towards the product, they return to the initial reactants.
|-
| 5 || -2.5 || -5.2 || 11.80780 || Reactive || [[File:sm6416_MEP_Figure5.png|thumb|none|350px]] || Simulation 5: Like simulation 4, this simulation shows a large oscillating amplitude, whereas in this scenario after passing through the transition state, the products are completely obtained. The slight increase in the p2 momentum can be seen to result in the products.
|}

====Transition State Theory====

Transition State Theory (TST) assumes a quasi-equilibrium between reactants and the transition state. The reaction between the transition state and products is irreversible and therefore is unable to return to the reactants, however many of the surface plots on this page show the complete antithesis of this highlighting a dichotomy between theory and experimental. TST further assumes that fluctuation as to whether the transition complexes go towards reactants or products are independent of each other and hence the rate of one can not be determined by the other.

TST is excellent qualitative tool and can identify the enthalpy, standard entropy and standard Gibbs energy of activation. Despite this, it the method is unable to accurately determine these true values in line with experimental results as doing so would require a deep understanding of the potential energy surface of each reaction. Therefore, TST under estimates the reaction rate in comparison to the experimental values. When TST was developed in 1935 a lack of adequate computer software to accurately map potential energy surfaces, unlike there is today. Hence resulting in a less accurate and longer method to map these surfaces for each reaction.

==F-H-H System Exercise 2==
===Potential Energy Surface Inspection===
====Energetics====

F + H2 is an exothermic reaction as can be seen from the surface plot, the reaction progresses from a small H-H distance to a longer one, whilst H-F simultaneously equilibriates about the F-H bond length. It can be seen that the products are lower, and hence more stable, in energy than the reactants.

F-H + H is simply the reverse reaction that passes through the same transition state, hence this reaction is endothermic with the products being higher in energy than the reactants. There is an overall gain of energy.

With this information in mind, the F-H bond is more stable and thus stronger than the H-H bond. The main factors to this argument is the greater electronegativity of F leading to a stronger contribution to the bond than the molecular orbitals. Hence the overlap of molecular orbitals is a weaker factor in the bond strength.

[[File:sm6416_FHH_Surface.png|thumb|none|350px|Surface plot highlighting the energetics of the F-H-H system.]]

[[File:sm6416_HHF_Surface.png|thumb|none|350px|Surface plot highlighting the energetics of the H-H-F system.]]

====Transition State====

Hammond's postulate aids in finding the transition state; it relates the composition of the transition complex to either the reactants or products for an early or late transition state respectively. In the scenario under investigation for F +H2 an early transition state is present as the reaction is exothermic in this direction, hence the transition state resembles the reactants more.

This guidance proved useful in determining the transition state complex at r1 = F-H = 1.810076 Angstrom and r2 = H-H = 0.74634 Angstrom, as can be seen from the surface and contour plots below showing the absence of displacement to either reactants or products. Furthermore the Momenta vs Time plot indicates a very small momenta of the overall system, without any deviation or substantial change in the momenta.

[[File:sm6416_FHH_Transition_State_Contour.png|thumb|none|350px|Contour plot demonstrating rts as a result of no fluctuations from the initial input, hence the complex is metaphorically sitting on the transition state.]]

[[File:sm6416_FHH_Transition_State_Momenta_Time.png|thumb|none|350px|Momenta vs Time plot demonstrating minimum, and almost zero, momentum at rts.]]

[[File:sm6416_FHH_Transition_State_Surface.png|thumb|none|350px]]

====Activation Energy====

The activation energy for the exothermic reaction was calculated through a 500000 step MEP simulation with input values of r1 = 1.820076, r2 = 0.74634 and p1 = p2 = 0. It was required that after following the minimum energy path, the gradient of the line signifying the reactants was constant.

The activation energy is reported at +0.258 kcal/mol for the exothermic process.

[[File:sm6416_FHH_Activation_Energy_1.png|thumb|none|350px|Energy vs Time graph highlighting the activation energy of the exothermic reaction.]]

The activation energy for the endothermic process was determined with the following parameters: r1 = 1.800076, r2 = 0.74634, p1 = p2 = 0 with 250000 steps. These parameters 'tipped' the reaction towards the FH + H reactants. The reported activation energy was +30.277 kcal/mol.

[[File:sm6416_FHH_Activation_Energy_2.png|thumb|none|350px|Energy vs Time graph highlighting the activation energy of the endothermic reaction.]]

It can hence be seen that the exothermic reaction of F + H2 --> F-H + H only requires a small activation energy as the products are substantially more thermodynamically stable than the reactants.

===Reaction Dynamics===

In light of the fact that energy is conserved, '''discuss the mechanism of release of the reaction energy.''' How could this be confirmed experimentally? Measuring energy released from reaction ie exothermicity. Put first one separately. As reach momentum close to boundaries, system passes through transition state but returns to reactant well. Comment on effect the sign of the momentum has on the reactivity.

The following parameters were employed for all simulations rFH = 2.3, rHH = 0.74 with 500 steps calculated.

{| class="wikitable" border=2
! Simulation !! pHH !! pFH !! Surface Plot !! Momenta vs Time Plot !! Observations !!
|-
| 1 || -2.5 || -1.5 || [[File:sm6416_Trajectory_1_Surface.png|thumb|none|350px]] ||[[File:sm6416_Trajectory_1_Momenta.png|thumb|none|350px]] || This trajectory results in a successful reaction as seen from the surface plot; the reactants proceed through the transition state and continue into the product well, whilst continually oscillating as a result of the momentum gained.
|-
| 2 || -0.5 || -0.5 || [[File:sm6416_Trajectory_2_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_2_Momenta.png|thumb|none|350px]] || This momentum does not proceed to a reaction. Through the dynamic animation it can be seen that the HH molecule does not possess enough momentum to translate towards F. Therefore the system does not translate out of the reactant well, as seen in the surface plot, since there is not enough energy to overcome the activation energy. The momenta plot simply shows a small up trend, this is expected due to the long range electrostatic force of attraction between F and HH, resulting in a slight increase in the HH vibration velocity. There is no drastic change in the momenta of either F or HH that would otherwise indicate the occurrence of a reaction, as seen in simulation 1 above.
|-
| 3 || +0.5 || -0.5 || [[File:sm6416_Trajectory_3_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_3_Momenta.png|thumb|none|350px]] || This simulation shows an unreactive path, as can be seen from the surface plot, the system remains in the reactant well as it does not overcome the small activation energy for the exothermic reaction to proceed. As in simulation 2, the momentum amplitude of the oscillating HH remains constant however the overall momenta of the system increases due to a slight translation towards F, thus increasing electrostatic attraction forces resulting in this slight overall momenta increase.
|-
| 4 || -1.6 || -0.5 || [[File:sm6416_Trajectory_4_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_4_Momenta.png|thumb|none|350px]] || This simulation is very similar to simulations 2 & 3 in that the system remains in the reactant well as there is not sufficient energy to overcome the activation energy. However as a result of the greater HH momentum, the oscillation amplitude is greater than both simulation 1 & 2.
|-
| 5 || +1.6 || -0.5 || [[File:sm6416_Trajectory_5_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_5_Momenta.png|thumb|none|350px]] || Firstly, this simulation is unreactive as can be seen from the surface plot. In comparison to simulation 4, HH momentum sign has been changed and as a result this has led to not only a greater oscillating amplitude but also a larger translation towards F. So much so in the latter than the Momenta vs Time plot shows an increase in FH oscillation momentum as the electrostatic forces of attraction dominate due to the reduction in internuclear distance.
|-
| 6 || -2.9 || -0.5 || [[File:sm6416_Trajectory_6_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_6_Momenta.png|thumb|none|350px]] || This is the first reactive simulation observed, as can be seen from the surface plot and the drastic change in the momentum of FH. Evidently, there is sufficient energy to pass through the transition state complex and towards the reactants.
|-
| 7 || +2.9 || -0.5 || [[File:sm6416_Trajectory_7_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_7_Momenta.png|thumb|none|350px]] || This simulation is indeed similar to that of simulation 6 however, the change of sign for the HH momentum again results in a greater translation towards F and consequently the system passes through the transition complex shown by the surface plot and Momenta vs Time plot. However after a single oscillation, FH dissociates and the system returns to the reactant well with HH possessing a greater momentum. This scenario could be as a result of the HH momentum being too high and thus providing sufficient activation energy to proceed in the endothermic direction. This is surprising as the exothermic reaction elucidates more thermodynamically stable products.
|-
| 8 || +0.1 || -0.8 || [[File:sm6416_Trajectory_8_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_8_Momenta.png|thumb|none|350px]] || With a mere 60% change in FH momentum and a minimum HH momentum, the system can be seen to react fully, without returning through the transition state. The Momenta vs Time plot further shows a noticeable change in the AB momentum, which corresponds to FH. Despite the oscillations not being regular, it can be noted that the amplitudes are relatively of the same size and show no signs of regressing. This information highlights that the overall the FH momentum dominates the reactivity of the system and has a large weighting to overcoming the activation energy. It can be thought that the increase in momentum aids in allowing a closer distance of F & H, where electrostatic attraction forces will prevail.
|}

====Polyani's Empirical Rules====

Discuss relative translational and vibrational energies required to match the transition state for each endo/exothermic reaction relating to Hammond's postulate.

FH + H reactive trajectory - r1=0.9 r2=2.3 p1=6.5 p2=-1.5

Cite reference

[[File:sm6416_FHH_Reactive_Trajectory_1_Surface.png|thumb|none|350px]]
[[File:sm6416_FHH_Reactive_Trajectory_1_Momenta.png|thumb|none|350px]]
[[File:sm6416_FHH_Reactive_Trajectory_1_Distance.png|thumb|none|350px]]
[[File:sm6416_FHH_Reactive_Trajectory_1_Contour.png|thumb|none|350px]]

MRD:sm6416

2018-05-25T15:31:09Z

Sm6416: /* Transition State */

==H2 H Exercise 1==

===Transition State Dynamics===

The transition state is the stage in a reaction coordinate that must be passed through in order for a reaction to occur and occurs at a saddle point, as shown by the numerous surface plots on this page. The first derivative highlights the positions along the reaction coordinate where the gradient equals zero. However, in order to determine if a saddle point ensues, the second derivative of the gradient must be taken. A saddle point is only present if the second derivative > 0.

Another way to think of the transition state is by thinking of the tangent that can be formed at the transition state itself. This tangent will follow the reaction coordinate profile and therefore is expected to be a maximum, where the gradient = 0. A line can be drawn to the normal of the tangent at the selected transition state. This path would show a minimum, where the gradient again = 0, at the intersection of the tangent with normal if the transition state has been correctly identified. It is only in this scenario that a transition state can be determined as one.

===Locating the Transition State===

The transition state was determined through iterations of both r1 and r2 which resulted in the smallest displacement of momenta along with no displacement as shown by the contour plot. This method determined at rts = 0.907743.

[[File:sm6416_Transition_State_Contour.png|thumb|none|350px|Contour plot demonstrating rts = 0.907743 as a result of no fluctuations from the initial input, hence the complex is at the transition state.]]

[[File:sm6416_Transition_State_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating minimum, and almost zero, momentum at rts = 0.907743.]]

[[File:sm6416_Transition_State_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot demonstrating no fluctuations in distance and hence rts = 0.907743.]]

===Reaction Path===

The minimum energy path (MEP) is defined as the lowest path the reaction must follow to form the products and is the downhill motion from the transition state. It can be applied in both directions in the case in question. The MEP views the system as static as it resets the velocity to zero at each step. Whereas the trajectory is very much dynamic and the momenta is accounted for, this is reflected in the vibrational oscillation of the molecule as it passes along the minimum well towards the products.

====MEP====

Initial conditions of r1 = rts + 0.01 = 0.917743, r2 = rts = 0.907743 and p1 = p2 = 0 for the MEP simulation.

[[File:sm6416_MEP_Surface.png|thumb|none|350px|Surface plot highlighting the minimum energy path (MEP), as the reaction returns to the reactants without fully passing through the transition state.]]

[[File:sm6416_MEP_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating zero momentum, as inputted, and more importantly not change in momentum with running the simulation.]]

[[File:sm6416_MEP_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot showing that the reactants reach the transition state at the interception of r1 = r2. r1 quickly reaches a constant value, namely the equilibrium bond length of the reactant molecule. r2 increases logarithmically as time progresses, this represents an increasing distance of Ha from Hb-Hc and a continuing loss of momentum.]]

Final values from the MEP simulation.

r1 = 2.76195

r2 = 0.75883

These values reflect the minimum trajectory for a successful reaction.

p1 = p2 = 0

====Dynamic====

[[File:sm6416_Dynamic_Surface.png|thumb|none|350px|Surface plot highlighting the minimum energy path (MEP) with oscillation of the reactants, as the reaction returns to the reactants without fully passing through the transition state. It is therefore evident that the momentum as a result of the vibrational oscillation does not provide enough energy to proceed to the products.]]

[[File:sm6416_Dynamic_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating the momenta associated with the oscillating reactants.]]

[[File:sm6416_Dynamic_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot showing that the reactants reach the transition state at the interception of r1 = r2. r1 quickly decreases and oscillates about a constant value, namely the equilibrium bond length of the reactant molecule. r2 increases linearly as time progresses, this represents an increasing distance of Ha from Hb-Hc with a constant momentum.]]

Dynamic simulation final values

r1 = 10.0045

r2 = 0.75883

p1 = 2.48523

p2 = 1.29898

p(average) = 1.90409

With r1 = rts and r2 = rts + 0.01 would simply produce the same answer however the values would be flipped to the other distance. In other words r1 = 0.75883 and r2 = 10.0045 would be the output values.

Maintaining the final trajectories as calculated from the dynamic simulation and reversing the sign of the momenta, the reaction proceeds in the reverse direction to the products.

===Reactivity of Trajectories===

These simulations are restricted by the number of steps the program can handle, however a sound understanding of the reaction can be appreciated and the reactivity of each scenario can be determined appropriately.

{| class="wikitable" border=2
! Simulation !! p1 !! p2 !! Energy (kcal/mol) !! Reactivity !! Evidence !! Description
|-
| 1 || -1.25 || -2.5 || 5.03500 || Reactive || [[File:sm6416_MEP_Figure1.png|thumb|none|350px]] || Simulation 1: The reactants proceed through the transition state and to the products. The r2 distance decreases to the equilibrium bond length, whilst r1 simultaneously exhibits dissociation and increases beyond the scope of the graph. The small momenta attributed to the reactants is reflected in the vibrationally oscillating products, with a small amplitude.
|-
| 2 || -1.5 || -2.0 || 3.62879 || Unreactive || [[File:sm6416_MEP_Figure2.png|thumb|none|350px]] || Simulation 2: This is unreactive as the oscillating reactants reach the transition state point and r1 immediately returns to the initial bond length, whilst r2 continues to increase as it moves away from the H2 molecule.
|-
| 3 || -1.5 || -2.5 || 5.13738 || Reactive || [[File:sm6416_MEP_Figure3.png|thumb|none|350px]] || Simulation 3: This simulation shows a reactive pathway that is very similar to simulation 1, however due to the greater momenta associated with the reactants, as inputted, vibrational oscillations with a greater amplitude can be observed.
|-
| 4 || -2.5 || -5.0 || 9.86678 || Unreactive || [[File:sm6416_MEP_Figure4.png|thumb|none|350px]] || Simulation 4: Initially seen here are oscillating reactants with a very large amplitude. However, this simulation is unreactive despite the reactants going through the transition state and towards the product, they return to the initial reactants.
|-
| 5 || -2.5 || -5.2 || 11.80780 || Reactive || [[File:sm6416_MEP_Figure5.png|thumb|none|350px]] || Simulation 5: Like simulation 4, this simulation shows a large oscillating amplitude, whereas in this scenario after passing through the transition state, the products are completely obtained. The slight increase in the p2 momentum can be seen to result in the products.
|}

====Transition State Theory====

Transition State Theory (TST) assumes a quasi-equilibrium between reactants and the transition state. The reaction between the transition state and products is irreversible and therefore is unable to return to the reactants, however many of the surface plots on this page show the complete antithesis of this highlighting a dichotomy between theory and experimental. TST further assumes that fluctuation as to whether the transition complexes go towards reactants or products are independent of each other and hence the rate of one can not be determined by the other.

TST is excellent qualitative tool and can identify the enthalpy, standard entropy and standard Gibbs energy of activation. Despite this, it the method is unable to accurately determine these true values in line with experimental results as doing so would require a deep understanding of the potential energy surface of each reaction. Therefore, TST under estimates the reaction rate in comparison to the experimental values. When TST was developed in 1935 a lack of adequate computer software to accurately map potential energy surfaces, unlike there is today. Hence resulting in a less accurate and longer method to map these surfaces for each reaction.

==F-H-H System Exercise 2==
===Potential Energy Surface Inspection===
====Energetics====

F + H2 is an exothermic reaction as can be seen from the surface plot, the reaction progresses from a small H-H distance to a longer one, whilst H-F simultaneously equilibriates about the F-H bond length. It can be seen that the products are lower, and hence more stable, in energy than the reactants.

F-H + H is simply the reverse reaction that passes through the same transition state, hence this reaction is endothermic with the products being higher in energy than the reactants. There is an overall gain of energy.

With this information in mind, the F-H bond is more stable and thus stronger than the H-H bond. The main factors to this argument is the greater electronegativity of F leading to a stronger contribution to the bond than the molecular orbitals. Hence the overlap of molecular orbitals is a weaker factor in the bond strength.

[[File:sm6416_FHH_Surface.png|thumb|none|350px|Surface plot highlighting the energetics of the F-H-H system.]]

[[File:sm6416_HHF_Surface.png|thumb|none|350px|Surface plot highlighting the energetics of the H-H-F system.]]

====Transition State====

Hammond's postulate aids in finding the transition state; it relates the composition of the transition complex to either the reactants or products for an early or late transition state respectively. In the scenario under investigation for F +H2 an early transition state is present as the reaction is exothermic in this direction, hence the transition state resembles the reactants more.

This guidance proved useful in determining the transition state complex at r1 = F-H = 1.810076 Angstrom and r2 = H-H = 0.74634 Angstrom, as can be seen from the surface and contour plots below showing the absence of displacement to either reactants or products. Furthermore the Momenta vs Time plot indicates a very small momenta of the overall system, without any deviation or substantial change in the momenta.

[[File:sm6416_FHH_Transition_State_Contour.png|thumb|none|350px|Contour plot demonstrating rts as a result of no fluctuations from the initial input, hence the complex is metaphorically sitting on the transition state.]]

[[File:sm6416_FHH_Transition_State_Momenta_Time.png|thumb|none|350px|Momenta vs Time plot demonstrating minimum, and almost zero, momentum at rts.]]

[[File:sm6416_FHH_Transition_State_Surface.png|thumb|none|350px]]

====Activation Energy====

The activation energy for the exothermic reaction was calculated through a 500000 step MEP simulation with input values of r1 = 1.820076, r2 = 0.74634 and p1 = p2 = 0. It was required that after following the minimum energy path, the gradient of the line signifying the reactants was constant.

The activation energy is reported at +0.258 kcal/mol for the exothermic process.

[[File:sm6416_FHH_Activation_Energy_1.png|thumb|none|350px|Energy vs Time graph highlighting the activation energy of the exothermic reaction.]]

The activation energy for the endothermic process was determined with the following parameters: r1 = 1.800076, r2 = 0.74634, p1 = p2 = 0 with 250000 steps. The reported activation energy was +30.277 kcal/mol.

[[File:sm6416_FHH_Activation_Energy_2.png|thumb|none|350px|Energy vs Time graph highlighting the activation energy of the endothermic reaction.]]

It can hence be seen that the exothermic reaction of F + H2 --> F-H + H only requires a small activation energy as the products are substantially more thermodynamically stable than the reactants.

===Reaction Dynamics===

In light of the fact that energy is conserved, '''discuss the mechanism of release of the reaction energy.''' How could this be confirmed experimentally? Measuring energy released from reaction ie exothermicity. Put first one separately. As reach momentum close to boundaries, system passes through transition state but returns to reactant well. Comment on effect the sign of the momentum has on the reactivity.

The following parameters were employed for all simulations rFH = 2.3, rHH = 0.74 with 500 steps calculated.

{| class="wikitable" border=2
! Simulation !! pHH !! pFH !! Surface Plot !! Momenta vs Time Plot !! Observations !!
|-
| 1 || -2.5 || -1.5 || [[File:sm6416_Trajectory_1_Surface.png|thumb|none|350px]] ||[[File:sm6416_Trajectory_1_Momenta.png|thumb|none|350px]] || This trajectory results in a successful reaction as seen from the surface plot; the reactants proceed through the transition state and continue into the product well, whilst continually oscillating as a result of the momentum gained.
|-
| 2 || -0.5 || -0.5 || [[File:sm6416_Trajectory_2_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_2_Momenta.png|thumb|none|350px]] || This momentum does not proceed to a reaction. Through the dynamic animation it can be seen that the HH molecule does not possess enough momentum to translate towards F. Therefore the system does not translate out of the reactant well, as seen in the surface plot, since there is not enough energy to overcome the activation energy. The momenta plot simply shows a small up trend, this is expected due to the long range electrostatic force of attraction between F and HH, resulting in a slight increase in the HH vibration velocity. There is no drastic change in the momenta of either F or HH that would otherwise indicate the occurrence of a reaction, as seen in simulation 1 above.
|-
| 3 || +0.5 || -0.5 || [[File:sm6416_Trajectory_3_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_3_Momenta.png|thumb|none|350px]] || This simulation shows an unreactive path, as can be seen from the surface plot, the system remains in the reactant well as it does not overcome the small activation energy for the exothermic reaction to proceed. As in simulation 2, the momentum amplitude of the oscillating HH remains constant however the overall momenta of the system increases due to a slight translation towards F, thus increasing electrostatic attraction forces resulting in this slight overall momenta increase.
|-
| 4 || -1.6 || -0.5 || [[File:sm6416_Trajectory_4_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_4_Momenta.png|thumb|none|350px]] || This simulation is very similar to simulations 2 & 3 in that the system remains in the reactant well as there is not sufficient energy to overcome the activation energy. However as a result of the greater HH momentum, the oscillation amplitude is greater than both simulation 1 & 2.
|-
| 5 || +1.6 || -0.5 || [[File:sm6416_Trajectory_5_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_5_Momenta.png|thumb|none|350px]] || Firstly, this simulation is unreactive as can be seen from the surface plot. In comparison to simulation 4, HH momentum sign has been changed and as a result this has led to not only a greater oscillating amplitude but also a larger translation towards F. So much so in the latter than the Momenta vs Time plot shows an increase in FH oscillation momentum as the electrostatic forces of attraction dominate due to the reduction in internuclear distance.
|-
| 6 || -2.9 || -0.5 || [[File:sm6416_Trajectory_6_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_6_Momenta.png|thumb|none|350px]] || This is the first reactive simulation observed, as can be seen from the surface plot and the drastic change in the momentum of FH. Evidently, there is sufficient energy to pass through the transition state complex and towards the reactants.
|-
| 7 || +2.9 || -0.5 || [[File:sm6416_Trajectory_7_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_7_Momenta.png|thumb|none|350px]] || This simulation is indeed similar to that of simulation 6 however, the change of sign for the HH momentum again results in a greater translation towards F and consequently the system passes through the transition complex shown by the surface plot and Momenta vs Time plot. However after a single oscillation, FH dissociates and the system returns to the reactant well with HH possessing a greater momentum. This scenario could be as a result of the HH momentum being too high and thus providing sufficient activation energy to proceed in the endothermic direction. This is surprising as the exothermic reaction elucidates more thermodynamically stable products.
|-
| 8 || +0.1 || -0.8 || [[File:sm6416_Trajectory_8_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_8_Momenta.png|thumb|none|350px]] || With a mere 60% change in FH momentum and a minimum HH momentum, the system can be seen to react fully, without returning through the transition state. The Momenta vs Time plot further shows a noticeable change in the AB momentum, which corresponds to FH. Despite the oscillations not being regular, it can be noted that the amplitudes are relatively of the same size and show no signs of regressing. This information highlights that the overall the FH momentum dominates the reactivity of the system and has a large weighting to overcoming the activation energy. It can be thought that the increase in momentum aids in allowing a closer distance of F & H, where electrostatic attraction forces will prevail.
|}

====Polyani's Empirical Rules====

Discuss relative translational and vibrational energies required to match the transition state for each endo/exothermic reaction relating to Hammond's postulate.

FH + H reactive trajectory - r1=0.9 r2=2.3 p1=6.5 p2=-1.5

Cite reference

[[File:sm6416_FHH_Reactive_Trajectory_1_Surface.png|thumb|none|350px]]
[[File:sm6416_FHH_Reactive_Trajectory_1_Momenta.png|thumb|none|350px]]
[[File:sm6416_FHH_Reactive_Trajectory_1_Distance.png|thumb|none|350px]]
[[File:sm6416_FHH_Reactive_Trajectory_1_Contour.png|thumb|none|350px]]

MRD:sm6416

2018-05-25T15:29:24Z

Sm6416: /* Transition State */

==H2 H Exercise 1==

===Transition State Dynamics===

The transition state is the stage in a reaction coordinate that must be passed through in order for a reaction to occur and occurs at a saddle point, as shown by the numerous surface plots on this page. The first derivative highlights the positions along the reaction coordinate where the gradient equals zero. However, in order to determine if a saddle point ensues, the second derivative of the gradient must be taken. A saddle point is only present if the second derivative > 0.

Another way to think of the transition state is by thinking of the tangent that can be formed at the transition state itself. This tangent will follow the reaction coordinate profile and therefore is expected to be a maximum, where the gradient = 0. A line can be drawn to the normal of the tangent at the selected transition state. This path would show a minimum, where the gradient again = 0, at the intersection of the tangent with normal if the transition state has been correctly identified. It is only in this scenario that a transition state can be determined as one.

===Locating the Transition State===

The transition state was determined through iterations of both r1 and r2 which resulted in the smallest displacement of momenta along with no displacement as shown by the contour plot. This method determined at rts = 0.907743.

[[File:sm6416_Transition_State_Contour.png|thumb|none|350px|Contour plot demonstrating rts = 0.907743 as a result of no fluctuations from the initial input, hence the complex is at the transition state.]]

[[File:sm6416_Transition_State_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating minimum, and almost zero, momentum at rts = 0.907743.]]

[[File:sm6416_Transition_State_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot demonstrating no fluctuations in distance and hence rts = 0.907743.]]

===Reaction Path===

The minimum energy path (MEP) is defined as the lowest path the reaction must follow to form the products and is the downhill motion from the transition state. It can be applied in both directions in the case in question. The MEP views the system as static as it resets the velocity to zero at each step. Whereas the trajectory is very much dynamic and the momenta is accounted for, this is reflected in the vibrational oscillation of the molecule as it passes along the minimum well towards the products.

====MEP====

Initial conditions of r1 = rts + 0.01 = 0.917743, r2 = rts = 0.907743 and p1 = p2 = 0 for the MEP simulation.

[[File:sm6416_MEP_Surface.png|thumb|none|350px|Surface plot highlighting the minimum energy path (MEP), as the reaction returns to the reactants without fully passing through the transition state.]]

[[File:sm6416_MEP_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating zero momentum, as inputted, and more importantly not change in momentum with running the simulation.]]

[[File:sm6416_MEP_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot showing that the reactants reach the transition state at the interception of r1 = r2. r1 quickly reaches a constant value, namely the equilibrium bond length of the reactant molecule. r2 increases logarithmically as time progresses, this represents an increasing distance of Ha from Hb-Hc and a continuing loss of momentum.]]

Final values from the MEP simulation.

r1 = 2.76195

r2 = 0.75883

These values reflect the minimum trajectory for a successful reaction.

p1 = p2 = 0

====Dynamic====

[[File:sm6416_Dynamic_Surface.png|thumb|none|350px|Surface plot highlighting the minimum energy path (MEP) with oscillation of the reactants, as the reaction returns to the reactants without fully passing through the transition state. It is therefore evident that the momentum as a result of the vibrational oscillation does not provide enough energy to proceed to the products.]]

[[File:sm6416_Dynamic_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating the momenta associated with the oscillating reactants.]]

[[File:sm6416_Dynamic_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot showing that the reactants reach the transition state at the interception of r1 = r2. r1 quickly decreases and oscillates about a constant value, namely the equilibrium bond length of the reactant molecule. r2 increases linearly as time progresses, this represents an increasing distance of Ha from Hb-Hc with a constant momentum.]]

Dynamic simulation final values

r1 = 10.0045

r2 = 0.75883

p1 = 2.48523

p2 = 1.29898

p(average) = 1.90409

With r1 = rts and r2 = rts + 0.01 would simply produce the same answer however the values would be flipped to the other distance. In other words r1 = 0.75883 and r2 = 10.0045 would be the output values.

Maintaining the final trajectories as calculated from the dynamic simulation and reversing the sign of the momenta, the reaction proceeds in the reverse direction to the products.

===Reactivity of Trajectories===

These simulations are restricted by the number of steps the program can handle, however a sound understanding of the reaction can be appreciated and the reactivity of each scenario can be determined appropriately.

{| class="wikitable" border=2
! Simulation !! p1 !! p2 !! Energy (kcal/mol) !! Reactivity !! Evidence !! Description
|-
| 1 || -1.25 || -2.5 || 5.03500 || Reactive || [[File:sm6416_MEP_Figure1.png|thumb|none|350px]] || Simulation 1: The reactants proceed through the transition state and to the products. The r2 distance decreases to the equilibrium bond length, whilst r1 simultaneously exhibits dissociation and increases beyond the scope of the graph. The small momenta attributed to the reactants is reflected in the vibrationally oscillating products, with a small amplitude.
|-
| 2 || -1.5 || -2.0 || 3.62879 || Unreactive || [[File:sm6416_MEP_Figure2.png|thumb|none|350px]] || Simulation 2: This is unreactive as the oscillating reactants reach the transition state point and r1 immediately returns to the initial bond length, whilst r2 continues to increase as it moves away from the H2 molecule.
|-
| 3 || -1.5 || -2.5 || 5.13738 || Reactive || [[File:sm6416_MEP_Figure3.png|thumb|none|350px]] || Simulation 3: This simulation shows a reactive pathway that is very similar to simulation 1, however due to the greater momenta associated with the reactants, as inputted, vibrational oscillations with a greater amplitude can be observed.
|-
| 4 || -2.5 || -5.0 || 9.86678 || Unreactive || [[File:sm6416_MEP_Figure4.png|thumb|none|350px]] || Simulation 4: Initially seen here are oscillating reactants with a very large amplitude. However, this simulation is unreactive despite the reactants going through the transition state and towards the product, they return to the initial reactants.
|-
| 5 || -2.5 || -5.2 || 11.80780 || Reactive || [[File:sm6416_MEP_Figure5.png|thumb|none|350px]] || Simulation 5: Like simulation 4, this simulation shows a large oscillating amplitude, whereas in this scenario after passing through the transition state, the products are completely obtained. The slight increase in the p2 momentum can be seen to result in the products.
|}

====Transition State Theory====

Transition State Theory (TST) assumes a quasi-equilibrium between reactants and the transition state. The reaction between the transition state and products is irreversible and therefore is unable to return to the reactants, however many of the surface plots on this page show the complete antithesis of this highlighting a dichotomy between theory and experimental. TST further assumes that fluctuation as to whether the transition complexes go towards reactants or products are independent of each other and hence the rate of one can not be determined by the other.

TST is excellent qualitative tool and can identify the enthalpy, standard entropy and standard Gibbs energy of activation. Despite this, it the method is unable to accurately determine these true values in line with experimental results as doing so would require a deep understanding of the potential energy surface of each reaction. Therefore, TST under estimates the reaction rate in comparison to the experimental values. When TST was developed in 1935 a lack of adequate computer software to accurately map potential energy surfaces, unlike there is today. Hence resulting in a less accurate and longer method to map these surfaces for each reaction.

==F-H-H System Exercise 2==
===Potential Energy Surface Inspection===
====Energetics====

F + H2 is an exothermic reaction as can be seen from the surface plot, the reaction progresses from a small H-H distance to a longer one, whilst H-F simultaneously equilibriates about the F-H bond length. It can be seen that the products are lower, and hence more stable, in energy than the reactants.

F-H + H is simply the reverse reaction that passes through the same transition state, hence this reaction is endothermic with the products being higher in energy than the reactants. There is an overall gain of energy.

With this information in mind, the F-H bond is more stable and thus stronger than the H-H bond. The main factors to this argument is the greater electronegativity of F leading to a stronger contribution to the bond than the molecular orbitals. Hence the overlap of molecular orbitals is a weaker factor in the bond strength.

[[File:sm6416_FHH_Surface.png|thumb|none|350px|Surface plot highlighting the energetics of the F-H-H system.]]

[[File:sm6416_HHF_Surface.png|thumb|none|350px|Surface plot highlighting the energetics of the H-H-F system.]]

====Transition State====

Hammond's postulate aids in finding the transition state; it relates the composition of the transition complex to either the reactants or products for an early or late transition state respectively. In the scenario under investigation for F +H2 an early transition state is present as the reaction is exothermic in this direction, hence the transition state resembles the reactants more.

This guidance proved useful in determining the transition state complex at r1 = F-H = 1.810076 Angstrom and r2 = H-H = 0.74634 Angstrom, as can be seen from the graphs below showing the absence of displacement to either reactants or products.

[[File:sm6416_FHH_Transition_State_Contour.png|thumb|none|350px|Contour plot demonstrating rts as a result of no fluctuations from the initial input, hence the complex is metaphorically sitting on the transition state.]]

[[File:sm6416_FHH_Transition_State_Momenta_Time.png|thumb|none|350px|Momenta vs Time plot demonstrating minimum, and almost zero, momentum at rts.]]

[[File:sm6416_FHH_Transition_State_Surface.png|thumb|none|350px]]

====Activation Energy====

The activation energy for the exothermic reaction was calculated through a 500000 step MEP simulation with input values of r1 = 1.820076, r2 = 0.74634 and p1 = p2 = 0. It was required that after following the minimum energy path, the gradient of the line signifying the reactants was constant.

The activation energy is reported at +0.258 kcal/mol for the exothermic process.

[[File:sm6416_FHH_Activation_Energy_1.png|thumb|none|350px|Energy vs Time graph highlighting the activation energy of the exothermic reaction.]]

The activation energy for the endothermic process was determined with the following parameters: r1 = 1.800076, r2 = 0.74634, p1 = p2 = 0 with 250000 steps. The reported activation energy was +30.277 kcal/mol.

[[File:sm6416_FHH_Activation_Energy_2.png|thumb|none|350px|Energy vs Time graph highlighting the activation energy of the endothermic reaction.]]

It can hence be seen that the exothermic reaction of F + H2 --> F-H + H only requires a small activation energy as the products are substantially more thermodynamically stable than the reactants.

===Reaction Dynamics===

In light of the fact that energy is conserved, '''discuss the mechanism of release of the reaction energy.''' How could this be confirmed experimentally? Measuring energy released from reaction ie exothermicity. Put first one separately. As reach momentum close to boundaries, system passes through transition state but returns to reactant well. Comment on effect the sign of the momentum has on the reactivity.

The following parameters were employed for all simulations rFH = 2.3, rHH = 0.74 with 500 steps calculated.

{| class="wikitable" border=2
! Simulation !! pHH !! pFH !! Surface Plot !! Momenta vs Time Plot !! Observations !!
|-
| 1 || -2.5 || -1.5 || [[File:sm6416_Trajectory_1_Surface.png|thumb|none|350px]] ||[[File:sm6416_Trajectory_1_Momenta.png|thumb|none|350px]] || This trajectory results in a successful reaction as seen from the surface plot; the reactants proceed through the transition state and continue into the product well, whilst continually oscillating as a result of the momentum gained.
|-
| 2 || -0.5 || -0.5 || [[File:sm6416_Trajectory_2_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_2_Momenta.png|thumb|none|350px]] || This momentum does not proceed to a reaction. Through the dynamic animation it can be seen that the HH molecule does not possess enough momentum to translate towards F. Therefore the system does not translate out of the reactant well, as seen in the surface plot, since there is not enough energy to overcome the activation energy. The momenta plot simply shows a small up trend, this is expected due to the long range electrostatic force of attraction between F and HH, resulting in a slight increase in the HH vibration velocity. There is no drastic change in the momenta of either F or HH that would otherwise indicate the occurrence of a reaction, as seen in simulation 1 above.
|-
| 3 || +0.5 || -0.5 || [[File:sm6416_Trajectory_3_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_3_Momenta.png|thumb|none|350px]] || This simulation shows an unreactive path, as can be seen from the surface plot, the system remains in the reactant well as it does not overcome the small activation energy for the exothermic reaction to proceed. As in simulation 2, the momentum amplitude of the oscillating HH remains constant however the overall momenta of the system increases due to a slight translation towards F, thus increasing electrostatic attraction forces resulting in this slight overall momenta increase.
|-
| 4 || -1.6 || -0.5 || [[File:sm6416_Trajectory_4_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_4_Momenta.png|thumb|none|350px]] || This simulation is very similar to simulations 2 & 3 in that the system remains in the reactant well as there is not sufficient energy to overcome the activation energy. However as a result of the greater HH momentum, the oscillation amplitude is greater than both simulation 1 & 2.
|-
| 5 || +1.6 || -0.5 || [[File:sm6416_Trajectory_5_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_5_Momenta.png|thumb|none|350px]] || Firstly, this simulation is unreactive as can be seen from the surface plot. In comparison to simulation 4, HH momentum sign has been changed and as a result this has led to not only a greater oscillating amplitude but also a larger translation towards F. So much so in the latter than the Momenta vs Time plot shows an increase in FH oscillation momentum as the electrostatic forces of attraction dominate due to the reduction in internuclear distance.
|-
| 6 || -2.9 || -0.5 || [[File:sm6416_Trajectory_6_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_6_Momenta.png|thumb|none|350px]] || This is the first reactive simulation observed, as can be seen from the surface plot and the drastic change in the momentum of FH. Evidently, there is sufficient energy to pass through the transition state complex and towards the reactants.
|-
| 7 || +2.9 || -0.5 || [[File:sm6416_Trajectory_7_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_7_Momenta.png|thumb|none|350px]] || This simulation is indeed similar to that of simulation 6 however, the change of sign for the HH momentum again results in a greater translation towards F and consequently the system passes through the transition complex shown by the surface plot and Momenta vs Time plot. However after a single oscillation, FH dissociates and the system returns to the reactant well with HH possessing a greater momentum. This scenario could be as a result of the HH momentum being too high and thus providing sufficient activation energy to proceed in the endothermic direction. This is surprising as the exothermic reaction elucidates more thermodynamically stable products.
|-
| 8 || +0.1 || -0.8 || [[File:sm6416_Trajectory_8_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_8_Momenta.png|thumb|none|350px]] || With a mere 60% change in FH momentum and a minimum HH momentum, the system can be seen to react fully, without returning through the transition state. The Momenta vs Time plot further shows a noticeable change in the AB momentum, which corresponds to FH. Despite the oscillations not being regular, it can be noted that the amplitudes are relatively of the same size and show no signs of regressing. This information highlights that the overall the FH momentum dominates the reactivity of the system and has a large weighting to overcoming the activation energy. It can be thought that the increase in momentum aids in allowing a closer distance of F & H, where electrostatic attraction forces will prevail.
|}

====Polyani's Empirical Rules====

Discuss relative translational and vibrational energies required to match the transition state for each endo/exothermic reaction relating to Hammond's postulate.

FH + H reactive trajectory - r1=0.9 r2=2.3 p1=6.5 p2=-1.5

Cite reference

[[File:sm6416_FHH_Reactive_Trajectory_1_Surface.png|thumb|none|350px]]
[[File:sm6416_FHH_Reactive_Trajectory_1_Momenta.png|thumb|none|350px]]
[[File:sm6416_FHH_Reactive_Trajectory_1_Distance.png|thumb|none|350px]]
[[File:sm6416_FHH_Reactive_Trajectory_1_Contour.png|thumb|none|350px]]

MRD:sm6416

2018-05-25T15:20:59Z

Sm6416: /* Transition State Theory */

==H2 H Exercise 1==

===Transition State Dynamics===

The transition state is the stage in a reaction coordinate that must be passed through in order for a reaction to occur and occurs at a saddle point, as shown by the numerous surface plots on this page. The first derivative highlights the positions along the reaction coordinate where the gradient equals zero. However, in order to determine if a saddle point ensues, the second derivative of the gradient must be taken. A saddle point is only present if the second derivative > 0.

Another way to think of the transition state is by thinking of the tangent that can be formed at the transition state itself. This tangent will follow the reaction coordinate profile and therefore is expected to be a maximum, where the gradient = 0. A line can be drawn to the normal of the tangent at the selected transition state. This path would show a minimum, where the gradient again = 0, at the intersection of the tangent with normal if the transition state has been correctly identified. It is only in this scenario that a transition state can be determined as one.

===Locating the Transition State===

The transition state was determined through iterations of both r1 and r2 which resulted in the smallest displacement of momenta along with no displacement as shown by the contour plot. This method determined at rts = 0.907743.

[[File:sm6416_Transition_State_Contour.png|thumb|none|350px|Contour plot demonstrating rts = 0.907743 as a result of no fluctuations from the initial input, hence the complex is at the transition state.]]

[[File:sm6416_Transition_State_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating minimum, and almost zero, momentum at rts = 0.907743.]]

[[File:sm6416_Transition_State_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot demonstrating no fluctuations in distance and hence rts = 0.907743.]]

===Reaction Path===

The minimum energy path (MEP) is defined as the lowest path the reaction must follow to form the products and is the downhill motion from the transition state. It can be applied in both directions in the case in question. The MEP views the system as static as it resets the velocity to zero at each step. Whereas the trajectory is very much dynamic and the momenta is accounted for, this is reflected in the vibrational oscillation of the molecule as it passes along the minimum well towards the products.

====MEP====

Initial conditions of r1 = rts + 0.01 = 0.917743, r2 = rts = 0.907743 and p1 = p2 = 0 for the MEP simulation.

[[File:sm6416_MEP_Surface.png|thumb|none|350px|Surface plot highlighting the minimum energy path (MEP), as the reaction returns to the reactants without fully passing through the transition state.]]

[[File:sm6416_MEP_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating zero momentum, as inputted, and more importantly not change in momentum with running the simulation.]]

[[File:sm6416_MEP_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot showing that the reactants reach the transition state at the interception of r1 = r2. r1 quickly reaches a constant value, namely the equilibrium bond length of the reactant molecule. r2 increases logarithmically as time progresses, this represents an increasing distance of Ha from Hb-Hc and a continuing loss of momentum.]]

Final values from the MEP simulation.

r1 = 2.76195

r2 = 0.75883

These values reflect the minimum trajectory for a successful reaction.

p1 = p2 = 0

====Dynamic====

[[File:sm6416_Dynamic_Surface.png|thumb|none|350px|Surface plot highlighting the minimum energy path (MEP) with oscillation of the reactants, as the reaction returns to the reactants without fully passing through the transition state. It is therefore evident that the momentum as a result of the vibrational oscillation does not provide enough energy to proceed to the products.]]

[[File:sm6416_Dynamic_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating the momenta associated with the oscillating reactants.]]

[[File:sm6416_Dynamic_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot showing that the reactants reach the transition state at the interception of r1 = r2. r1 quickly decreases and oscillates about a constant value, namely the equilibrium bond length of the reactant molecule. r2 increases linearly as time progresses, this represents an increasing distance of Ha from Hb-Hc with a constant momentum.]]

Dynamic simulation final values

r1 = 10.0045

r2 = 0.75883

p1 = 2.48523

p2 = 1.29898

p(average) = 1.90409

With r1 = rts and r2 = rts + 0.01 would simply produce the same answer however the values would be flipped to the other distance. In other words r1 = 0.75883 and r2 = 10.0045 would be the output values.

Maintaining the final trajectories as calculated from the dynamic simulation and reversing the sign of the momenta, the reaction proceeds in the reverse direction to the products.

===Reactivity of Trajectories===

These simulations are restricted by the number of steps the program can handle, however a sound understanding of the reaction can be appreciated and the reactivity of each scenario can be determined appropriately.

{| class="wikitable" border=2
! Simulation !! p1 !! p2 !! Energy (kcal/mol) !! Reactivity !! Evidence !! Description
|-
| 1 || -1.25 || -2.5 || 5.03500 || Reactive || [[File:sm6416_MEP_Figure1.png|thumb|none|350px]] || Simulation 1: The reactants proceed through the transition state and to the products. The r2 distance decreases to the equilibrium bond length, whilst r1 simultaneously exhibits dissociation and increases beyond the scope of the graph. The small momenta attributed to the reactants is reflected in the vibrationally oscillating products, with a small amplitude.
|-
| 2 || -1.5 || -2.0 || 3.62879 || Unreactive || [[File:sm6416_MEP_Figure2.png|thumb|none|350px]] || Simulation 2: This is unreactive as the oscillating reactants reach the transition state point and r1 immediately returns to the initial bond length, whilst r2 continues to increase as it moves away from the H2 molecule.
|-
| 3 || -1.5 || -2.5 || 5.13738 || Reactive || [[File:sm6416_MEP_Figure3.png|thumb|none|350px]] || Simulation 3: This simulation shows a reactive pathway that is very similar to simulation 1, however due to the greater momenta associated with the reactants, as inputted, vibrational oscillations with a greater amplitude can be observed.
|-
| 4 || -2.5 || -5.0 || 9.86678 || Unreactive || [[File:sm6416_MEP_Figure4.png|thumb|none|350px]] || Simulation 4: Initially seen here are oscillating reactants with a very large amplitude. However, this simulation is unreactive despite the reactants going through the transition state and towards the product, they return to the initial reactants.
|-
| 5 || -2.5 || -5.2 || 11.80780 || Reactive || [[File:sm6416_MEP_Figure5.png|thumb|none|350px]] || Simulation 5: Like simulation 4, this simulation shows a large oscillating amplitude, whereas in this scenario after passing through the transition state, the products are completely obtained. The slight increase in the p2 momentum can be seen to result in the products.
|}

====Transition State Theory====

Transition State Theory (TST) assumes a quasi-equilibrium between reactants and the transition state. The reaction between the transition state and products is irreversible and therefore is unable to return to the reactants, however many of the surface plots on this page show the complete antithesis of this highlighting a dichotomy between theory and experimental. TST further assumes that fluctuation as to whether the transition complexes go towards reactants or products are independent of each other and hence the rate of one can not be determined by the other.

TST is excellent qualitative tool and can identify the enthalpy, standard entropy and standard Gibbs energy of activation. Despite this, it the method is unable to accurately determine these true values in line with experimental results as doing so would require a deep understanding of the potential energy surface of each reaction. Therefore, TST under estimates the reaction rate in comparison to the experimental values. When TST was developed in 1935 a lack of adequate computer software to accurately map potential energy surfaces, unlike there is today. Hence resulting in a less accurate and longer method to map these surfaces for each reaction.

==F-H-H System Exercise 2==
===Potential Energy Surface Inspection===
====Energetics====

F + H2 is an exothermic reaction as can be seen from the surface plot, the reaction progresses from a small H-H distance to a longer one, whilst H-F simultaneously equilibriates about the F-H bond length. It can be seen that the products are lower, and hence more stable, in energy than the reactants.

F-H + H is simply the reverse reaction that passes through the same transition state, hence this reaction is endothermic with the products being higher in energy than the reactants. There is an overall gain of energy.

With this information in mind, the F-H bond is more stable and thus stronger than the H-H bond. The main factors to this argument is the greater electronegativity of F leading to a stronger contribution to the bond than the molecular orbitals. Hence the overlap of molecular orbitals is a weaker factor in the bond strength.

[[File:sm6416_FHH_Surface.png|thumb|none|350px|Surface plot highlighting the energetics of the F-H-H system.]]

[[File:sm6416_HHF_Surface.png|thumb|none|350px|Surface plot highlighting the energetics of the H-H-F system.]]

====Transition State====

Discuss Hammond Postulate with TS being closer to products/reactants dependent on how the TS is composed.

The transition state complex is achieved at r1 = F-H = 1.810076 Angstrom and r2 = H-H = 0.74634 Angstrom, as can be seen from the graphs below showing the absence of displacement to either reactants or products.

[[File:sm6416_FHH_Transition_State_Contour.png|thumb|none|350px|Contour plot demonstrating rts as a result of no fluctuations from the initial input, hence the complex is metaphorically sitting on the transition state.]]

[[File:sm6416_FHH_Transition_State_Momenta_Time.png|thumb|none|350px|Momenta vs Time plot demonstrating minimum, and almost zero, momentum at rts.]]

[[File:sm6416_FHH_Transition_State_Surface.png|thumb|none|350px]]

====Activation Energy====

The activation energy for the exothermic reaction was calculated through a 500000 step MEP simulation with input values of r1 = 1.820076, r2 = 0.74634 and p1 = p2 = 0. It was required that after following the minimum energy path, the gradient of the line signifying the reactants was constant.

The activation energy is reported at +0.258 kcal/mol for the exothermic process.

[[File:sm6416_FHH_Activation_Energy_1.png|thumb|none|350px|Energy vs Time graph highlighting the activation energy of the exothermic reaction.]]

The activation energy for the endothermic process was determined with the following parameters: r1 = 1.800076, r2 = 0.74634, p1 = p2 = 0 with 250000 steps. The reported activation energy was +30.277 kcal/mol.

[[File:sm6416_FHH_Activation_Energy_2.png|thumb|none|350px|Energy vs Time graph highlighting the activation energy of the endothermic reaction.]]

It can hence be seen that the exothermic reaction of F + H2 --> F-H + H only requires a small activation energy as the products are substantially more thermodynamically stable than the reactants.

===Reaction Dynamics===

In light of the fact that energy is conserved, '''discuss the mechanism of release of the reaction energy.''' How could this be confirmed experimentally? Measuring energy released from reaction ie exothermicity. Put first one separately. As reach momentum close to boundaries, system passes through transition state but returns to reactant well. Comment on effect the sign of the momentum has on the reactivity.

The following parameters were employed for all simulations rFH = 2.3, rHH = 0.74 with 500 steps calculated.

{| class="wikitable" border=2
! Simulation !! pHH !! pFH !! Surface Plot !! Momenta vs Time Plot !! Observations !!
|-
| 1 || -2.5 || -1.5 || [[File:sm6416_Trajectory_1_Surface.png|thumb|none|350px]] ||[[File:sm6416_Trajectory_1_Momenta.png|thumb|none|350px]] || This trajectory results in a successful reaction as seen from the surface plot; the reactants proceed through the transition state and continue into the product well, whilst continually oscillating as a result of the momentum gained.
|-
| 2 || -0.5 || -0.5 || [[File:sm6416_Trajectory_2_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_2_Momenta.png|thumb|none|350px]] || This momentum does not proceed to a reaction. Through the dynamic animation it can be seen that the HH molecule does not possess enough momentum to translate towards F. Therefore the system does not translate out of the reactant well, as seen in the surface plot, since there is not enough energy to overcome the activation energy. The momenta plot simply shows a small up trend, this is expected due to the long range electrostatic force of attraction between F and HH, resulting in a slight increase in the HH vibration velocity. There is no drastic change in the momenta of either F or HH that would otherwise indicate the occurrence of a reaction, as seen in simulation 1 above.
|-
| 3 || +0.5 || -0.5 || [[File:sm6416_Trajectory_3_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_3_Momenta.png|thumb|none|350px]] || This simulation shows an unreactive path, as can be seen from the surface plot, the system remains in the reactant well as it does not overcome the small activation energy for the exothermic reaction to proceed. As in simulation 2, the momentum amplitude of the oscillating HH remains constant however the overall momenta of the system increases due to a slight translation towards F, thus increasing electrostatic attraction forces resulting in this slight overall momenta increase.
|-
| 4 || -1.6 || -0.5 || [[File:sm6416_Trajectory_4_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_4_Momenta.png|thumb|none|350px]] || This simulation is very similar to simulations 2 & 3 in that the system remains in the reactant well as there is not sufficient energy to overcome the activation energy. However as a result of the greater HH momentum, the oscillation amplitude is greater than both simulation 1 & 2.
|-
| 5 || +1.6 || -0.5 || [[File:sm6416_Trajectory_5_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_5_Momenta.png|thumb|none|350px]] || Firstly, this simulation is unreactive as can be seen from the surface plot. In comparison to simulation 4, HH momentum sign has been changed and as a result this has led to not only a greater oscillating amplitude but also a larger translation towards F. So much so in the latter than the Momenta vs Time plot shows an increase in FH oscillation momentum as the electrostatic forces of attraction dominate due to the reduction in internuclear distance.
|-
| 6 || -2.9 || -0.5 || [[File:sm6416_Trajectory_6_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_6_Momenta.png|thumb|none|350px]] || This is the first reactive simulation observed, as can be seen from the surface plot and the drastic change in the momentum of FH. Evidently, there is sufficient energy to pass through the transition state complex and towards the reactants.
|-
| 7 || +2.9 || -0.5 || [[File:sm6416_Trajectory_7_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_7_Momenta.png|thumb|none|350px]] || This simulation is indeed similar to that of simulation 6 however, the change of sign for the HH momentum again results in a greater translation towards F and consequently the system passes through the transition complex shown by the surface plot and Momenta vs Time plot. However after a single oscillation, FH dissociates and the system returns to the reactant well with HH possessing a greater momentum. This scenario could be as a result of the HH momentum being too high and thus providing sufficient activation energy to proceed in the endothermic direction. This is surprising as the exothermic reaction elucidates more thermodynamically stable products.
|-
| 8 || +0.1 || -0.8 || [[File:sm6416_Trajectory_8_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_8_Momenta.png|thumb|none|350px]] || With a mere 60% change in FH momentum and a minimum HH momentum, the system can be seen to react fully, without returning through the transition state. The Momenta vs Time plot further shows a noticeable change in the AB momentum, which corresponds to FH. Despite the oscillations not being regular, it can be noted that the amplitudes are relatively of the same size and show no signs of regressing. This information highlights that the overall the FH momentum dominates the reactivity of the system and has a large weighting to overcoming the activation energy. It can be thought that the increase in momentum aids in allowing a closer distance of F & H, where electrostatic attraction forces will prevail.
|}

====Polyani's Empirical Rules====

Discuss relative translational and vibrational energies required to match the transition state for each endo/exothermic reaction relating to Hammond's postulate.

FH + H reactive trajectory - r1=0.9 r2=2.3 p1=6.5 p2=-1.5

Cite reference

[[File:sm6416_FHH_Reactive_Trajectory_1_Surface.png|thumb|none|350px]]
[[File:sm6416_FHH_Reactive_Trajectory_1_Momenta.png|thumb|none|350px]]
[[File:sm6416_FHH_Reactive_Trajectory_1_Distance.png|thumb|none|350px]]
[[File:sm6416_FHH_Reactive_Trajectory_1_Contour.png|thumb|none|350px]]

MRD:sm6416

2018-05-25T15:18:42Z

Sm6416: /* Transition State Theory */

==H2 H Exercise 1==

===Transition State Dynamics===

The transition state is the stage in a reaction coordinate that must be passed through in order for a reaction to occur and occurs at a saddle point, as shown by the numerous surface plots on this page. The first derivative highlights the positions along the reaction coordinate where the gradient equals zero. However, in order to determine if a saddle point ensues, the second derivative of the gradient must be taken. A saddle point is only present if the second derivative > 0.

Another way to think of the transition state is by thinking of the tangent that can be formed at the transition state itself. This tangent will follow the reaction coordinate profile and therefore is expected to be a maximum, where the gradient = 0. A line can be drawn to the normal of the tangent at the selected transition state. This path would show a minimum, where the gradient again = 0, at the intersection of the tangent with normal if the transition state has been correctly identified. It is only in this scenario that a transition state can be determined as one.

===Locating the Transition State===

The transition state was determined through iterations of both r1 and r2 which resulted in the smallest displacement of momenta along with no displacement as shown by the contour plot. This method determined at rts = 0.907743.

[[File:sm6416_Transition_State_Contour.png|thumb|none|350px|Contour plot demonstrating rts = 0.907743 as a result of no fluctuations from the initial input, hence the complex is at the transition state.]]

[[File:sm6416_Transition_State_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating minimum, and almost zero, momentum at rts = 0.907743.]]

[[File:sm6416_Transition_State_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot demonstrating no fluctuations in distance and hence rts = 0.907743.]]

===Reaction Path===

The minimum energy path (MEP) is defined as the lowest path the reaction must follow to form the products and is the downhill motion from the transition state. It can be applied in both directions in the case in question. The MEP views the system as static as it resets the velocity to zero at each step. Whereas the trajectory is very much dynamic and the momenta is accounted for, this is reflected in the vibrational oscillation of the molecule as it passes along the minimum well towards the products.

====MEP====

Initial conditions of r1 = rts + 0.01 = 0.917743, r2 = rts = 0.907743 and p1 = p2 = 0 for the MEP simulation.

[[File:sm6416_MEP_Surface.png|thumb|none|350px|Surface plot highlighting the minimum energy path (MEP), as the reaction returns to the reactants without fully passing through the transition state.]]

[[File:sm6416_MEP_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating zero momentum, as inputted, and more importantly not change in momentum with running the simulation.]]

[[File:sm6416_MEP_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot showing that the reactants reach the transition state at the interception of r1 = r2. r1 quickly reaches a constant value, namely the equilibrium bond length of the reactant molecule. r2 increases logarithmically as time progresses, this represents an increasing distance of Ha from Hb-Hc and a continuing loss of momentum.]]

Final values from the MEP simulation.

r1 = 2.76195

r2 = 0.75883

These values reflect the minimum trajectory for a successful reaction.

p1 = p2 = 0

====Dynamic====

[[File:sm6416_Dynamic_Surface.png|thumb|none|350px|Surface plot highlighting the minimum energy path (MEP) with oscillation of the reactants, as the reaction returns to the reactants without fully passing through the transition state. It is therefore evident that the momentum as a result of the vibrational oscillation does not provide enough energy to proceed to the products.]]

[[File:sm6416_Dynamic_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating the momenta associated with the oscillating reactants.]]

[[File:sm6416_Dynamic_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot showing that the reactants reach the transition state at the interception of r1 = r2. r1 quickly decreases and oscillates about a constant value, namely the equilibrium bond length of the reactant molecule. r2 increases linearly as time progresses, this represents an increasing distance of Ha from Hb-Hc with a constant momentum.]]

Dynamic simulation final values

r1 = 10.0045

r2 = 0.75883

p1 = 2.48523

p2 = 1.29898

p(average) = 1.90409

With r1 = rts and r2 = rts + 0.01 would simply produce the same answer however the values would be flipped to the other distance. In other words r1 = 0.75883 and r2 = 10.0045 would be the output values.

Maintaining the final trajectories as calculated from the dynamic simulation and reversing the sign of the momenta, the reaction proceeds in the reverse direction to the products.

===Reactivity of Trajectories===

These simulations are restricted by the number of steps the program can handle, however a sound understanding of the reaction can be appreciated and the reactivity of each scenario can be determined appropriately.

{| class="wikitable" border=2
! Simulation !! p1 !! p2 !! Energy (kcal/mol) !! Reactivity !! Evidence !! Description
|-
| 1 || -1.25 || -2.5 || 5.03500 || Reactive || [[File:sm6416_MEP_Figure1.png|thumb|none|350px]] || Simulation 1: The reactants proceed through the transition state and to the products. The r2 distance decreases to the equilibrium bond length, whilst r1 simultaneously exhibits dissociation and increases beyond the scope of the graph. The small momenta attributed to the reactants is reflected in the vibrationally oscillating products, with a small amplitude.
|-
| 2 || -1.5 || -2.0 || 3.62879 || Unreactive || [[File:sm6416_MEP_Figure2.png|thumb|none|350px]] || Simulation 2: This is unreactive as the oscillating reactants reach the transition state point and r1 immediately returns to the initial bond length, whilst r2 continues to increase as it moves away from the H2 molecule.
|-
| 3 || -1.5 || -2.5 || 5.13738 || Reactive || [[File:sm6416_MEP_Figure3.png|thumb|none|350px]] || Simulation 3: This simulation shows a reactive pathway that is very similar to simulation 1, however due to the greater momenta associated with the reactants, as inputted, vibrational oscillations with a greater amplitude can be observed.
|-
| 4 || -2.5 || -5.0 || 9.86678 || Unreactive || [[File:sm6416_MEP_Figure4.png|thumb|none|350px]] || Simulation 4: Initially seen here are oscillating reactants with a very large amplitude. However, this simulation is unreactive despite the reactants going through the transition state and towards the product, they return to the initial reactants.
|-
| 5 || -2.5 || -5.2 || 11.80780 || Reactive || [[File:sm6416_MEP_Figure5.png|thumb|none|350px]] || Simulation 5: Like simulation 4, this simulation shows a large oscillating amplitude, whereas in this scenario after passing through the transition state, the products are completely obtained. The slight increase in the p2 momentum can be seen to result in the products.
|}

====Transition State Theory====

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

Transition State Theory (TST) assumes a quasi-equilibrium between reactants and the transition state. The reaction between the transition state and products is irreversible and therefore is unable to return to the reactants, however many of the surface plots on this page show the complete antithesis of this highlighting a dichotomy between theory and experimental. TST further assumes that fluctuation as to whether the transition complexes go towards reactants or products are independent of each other and hence the rate of one can not be determined by the other.

TST is excellent qualitative tool and can identify the enthalpy, standard entropy and standard Gibbs energy of activation. Despite this, it the method is unable to accurately determine these true values in line with experimental results as doing so would require a deep understanding of the potential energy surface of each reaction. Therefore, TST under estimates the reaction rate in comparison to the experimental values. When TST was developed in 1935 a lack of adequate computer software to accurately map potential energy surfaces, unlike there is today. Hence resulting in a less accurate and longer method to map these surfaces for each reaction.

==F-H-H System Exercise 2==
===Potential Energy Surface Inspection===
====Energetics====

F + H2 is an exothermic reaction as can be seen from the surface plot, the reaction progresses from a small H-H distance to a longer one, whilst H-F simultaneously equilibriates about the F-H bond length. It can be seen that the products are lower, and hence more stable, in energy than the reactants.

F-H + H is simply the reverse reaction that passes through the same transition state, hence this reaction is endothermic with the products being higher in energy than the reactants. There is an overall gain of energy.

With this information in mind, the F-H bond is more stable and thus stronger than the H-H bond. The main factors to this argument is the greater electronegativity of F leading to a stronger contribution to the bond than the molecular orbitals. Hence the overlap of molecular orbitals is a weaker factor in the bond strength.

[[File:sm6416_FHH_Surface.png|thumb|none|350px|Surface plot highlighting the energetics of the F-H-H system.]]

[[File:sm6416_HHF_Surface.png|thumb|none|350px|Surface plot highlighting the energetics of the H-H-F system.]]

====Transition State====

Discuss Hammond Postulate with TS being closer to products/reactants dependent on how the TS is composed.

The transition state complex is achieved at r1 = F-H = 1.810076 Angstrom and r2 = H-H = 0.74634 Angstrom, as can be seen from the graphs below showing the absence of displacement to either reactants or products.

[[File:sm6416_FHH_Transition_State_Contour.png|thumb|none|350px|Contour plot demonstrating rts as a result of no fluctuations from the initial input, hence the complex is metaphorically sitting on the transition state.]]

[[File:sm6416_FHH_Transition_State_Momenta_Time.png|thumb|none|350px|Momenta vs Time plot demonstrating minimum, and almost zero, momentum at rts.]]

[[File:sm6416_FHH_Transition_State_Surface.png|thumb|none|350px]]

====Activation Energy====

The activation energy for the exothermic reaction was calculated through a 500000 step MEP simulation with input values of r1 = 1.820076, r2 = 0.74634 and p1 = p2 = 0. It was required that after following the minimum energy path, the gradient of the line signifying the reactants was constant.

The activation energy is reported at +0.258 kcal/mol for the exothermic process.

[[File:sm6416_FHH_Activation_Energy_1.png|thumb|none|350px|Energy vs Time graph highlighting the activation energy of the exothermic reaction.]]

The activation energy for the endothermic process was determined with the following parameters: r1 = 1.800076, r2 = 0.74634, p1 = p2 = 0 with 250000 steps. The reported activation energy was +30.277 kcal/mol.

[[File:sm6416_FHH_Activation_Energy_2.png|thumb|none|350px|Energy vs Time graph highlighting the activation energy of the endothermic reaction.]]

It can hence be seen that the exothermic reaction of F + H2 --> F-H + H only requires a small activation energy as the products are substantially more thermodynamically stable than the reactants.

===Reaction Dynamics===

In light of the fact that energy is conserved, '''discuss the mechanism of release of the reaction energy.''' How could this be confirmed experimentally? Measuring energy released from reaction ie exothermicity. Put first one separately. As reach momentum close to boundaries, system passes through transition state but returns to reactant well. Comment on effect the sign of the momentum has on the reactivity.

The following parameters were employed for all simulations rFH = 2.3, rHH = 0.74 with 500 steps calculated.

{| class="wikitable" border=2
! Simulation !! pHH !! pFH !! Surface Plot !! Momenta vs Time Plot !! Observations !!
|-
| 1 || -2.5 || -1.5 || [[File:sm6416_Trajectory_1_Surface.png|thumb|none|350px]] ||[[File:sm6416_Trajectory_1_Momenta.png|thumb|none|350px]] || This trajectory results in a successful reaction as seen from the surface plot; the reactants proceed through the transition state and continue into the product well, whilst continually oscillating as a result of the momentum gained.
|-
| 2 || -0.5 || -0.5 || [[File:sm6416_Trajectory_2_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_2_Momenta.png|thumb|none|350px]] || This momentum does not proceed to a reaction. Through the dynamic animation it can be seen that the HH molecule does not possess enough momentum to translate towards F. Therefore the system does not translate out of the reactant well, as seen in the surface plot, since there is not enough energy to overcome the activation energy. The momenta plot simply shows a small up trend, this is expected due to the long range electrostatic force of attraction between F and HH, resulting in a slight increase in the HH vibration velocity. There is no drastic change in the momenta of either F or HH that would otherwise indicate the occurrence of a reaction, as seen in simulation 1 above.
|-
| 3 || +0.5 || -0.5 || [[File:sm6416_Trajectory_3_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_3_Momenta.png|thumb|none|350px]] || This simulation shows an unreactive path, as can be seen from the surface plot, the system remains in the reactant well as it does not overcome the small activation energy for the exothermic reaction to proceed. As in simulation 2, the momentum amplitude of the oscillating HH remains constant however the overall momenta of the system increases due to a slight translation towards F, thus increasing electrostatic attraction forces resulting in this slight overall momenta increase.
|-
| 4 || -1.6 || -0.5 || [[File:sm6416_Trajectory_4_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_4_Momenta.png|thumb|none|350px]] || This simulation is very similar to simulations 2 & 3 in that the system remains in the reactant well as there is not sufficient energy to overcome the activation energy. However as a result of the greater HH momentum, the oscillation amplitude is greater than both simulation 1 & 2.
|-
| 5 || +1.6 || -0.5 || [[File:sm6416_Trajectory_5_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_5_Momenta.png|thumb|none|350px]] || Firstly, this simulation is unreactive as can be seen from the surface plot. In comparison to simulation 4, HH momentum sign has been changed and as a result this has led to not only a greater oscillating amplitude but also a larger translation towards F. So much so in the latter than the Momenta vs Time plot shows an increase in FH oscillation momentum as the electrostatic forces of attraction dominate due to the reduction in internuclear distance.
|-
| 6 || -2.9 || -0.5 || [[File:sm6416_Trajectory_6_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_6_Momenta.png|thumb|none|350px]] || This is the first reactive simulation observed, as can be seen from the surface plot and the drastic change in the momentum of FH. Evidently, there is sufficient energy to pass through the transition state complex and towards the reactants.
|-
| 7 || +2.9 || -0.5 || [[File:sm6416_Trajectory_7_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_7_Momenta.png|thumb|none|350px]] || This simulation is indeed similar to that of simulation 6 however, the change of sign for the HH momentum again results in a greater translation towards F and consequently the system passes through the transition complex shown by the surface plot and Momenta vs Time plot. However after a single oscillation, FH dissociates and the system returns to the reactant well with HH possessing a greater momentum. This scenario could be as a result of the HH momentum being too high and thus providing sufficient activation energy to proceed in the endothermic direction. This is surprising as the exothermic reaction elucidates more thermodynamically stable products.
|-
| 8 || +0.1 || -0.8 || [[File:sm6416_Trajectory_8_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_8_Momenta.png|thumb|none|350px]] || With a mere 60% change in FH momentum and a minimum HH momentum, the system can be seen to react fully, without returning through the transition state. The Momenta vs Time plot further shows a noticeable change in the AB momentum, which corresponds to FH. Despite the oscillations not being regular, it can be noted that the amplitudes are relatively of the same size and show no signs of regressing. This information highlights that the overall the FH momentum dominates the reactivity of the system and has a large weighting to overcoming the activation energy. It can be thought that the increase in momentum aids in allowing a closer distance of F & H, where electrostatic attraction forces will prevail.
|}

====Polyani's Empirical Rules====

Discuss relative translational and vibrational energies required to match the transition state for each endo/exothermic reaction relating to Hammond's postulate.

FH + H reactive trajectory - r1=0.9 r2=2.3 p1=6.5 p2=-1.5

Cite reference

[[File:sm6416_FHH_Reactive_Trajectory_1_Surface.png|thumb|none|350px]]
[[File:sm6416_FHH_Reactive_Trajectory_1_Momenta.png|thumb|none|350px]]
[[File:sm6416_FHH_Reactive_Trajectory_1_Distance.png|thumb|none|350px]]
[[File:sm6416_FHH_Reactive_Trajectory_1_Contour.png|thumb|none|350px]]

MRD:sm6416

2018-05-25T14:47:40Z

Sm6416: /* Reactivity of Trajectories */

==H2 H Exercise 1==

===Transition State Dynamics===

The transition state is the stage in a reaction coordinate that must be passed through in order for a reaction to occur and occurs at a saddle point, as shown by the numerous surface plots on this page. The first derivative highlights the positions along the reaction coordinate where the gradient equals zero. However, in order to determine if a saddle point ensues, the second derivative of the gradient must be taken. A saddle point is only present if the second derivative > 0.

Another way to think of the transition state is by thinking of the tangent that can be formed at the transition state itself. This tangent will follow the reaction coordinate profile and therefore is expected to be a maximum, where the gradient = 0. A line can be drawn to the normal of the tangent at the selected transition state. This path would show a minimum, where the gradient again = 0, at the intersection of the tangent with normal if the transition state has been correctly identified. It is only in this scenario that a transition state can be determined as one.

===Locating the Transition State===

The transition state was determined through iterations of both r1 and r2 which resulted in the smallest displacement of momenta along with no displacement as shown by the contour plot. This method determined at rts = 0.907743.

[[File:sm6416_Transition_State_Contour.png|thumb|none|350px|Contour plot demonstrating rts = 0.907743 as a result of no fluctuations from the initial input, hence the complex is at the transition state.]]

[[File:sm6416_Transition_State_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating minimum, and almost zero, momentum at rts = 0.907743.]]

[[File:sm6416_Transition_State_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot demonstrating no fluctuations in distance and hence rts = 0.907743.]]

===Reaction Path===

The minimum energy path (MEP) is defined as the lowest path the reaction must follow to form the products and is the downhill motion from the transition state. It can be applied in both directions in the case in question. The MEP views the system as static as it resets the velocity to zero at each step. Whereas the trajectory is very much dynamic and the momenta is accounted for, this is reflected in the vibrational oscillation of the molecule as it passes along the minimum well towards the products.

====MEP====

Initial conditions of r1 = rts + 0.01 = 0.917743, r2 = rts = 0.907743 and p1 = p2 = 0 for the MEP simulation.

[[File:sm6416_MEP_Surface.png|thumb|none|350px|Surface plot highlighting the minimum energy path (MEP), as the reaction returns to the reactants without fully passing through the transition state.]]

[[File:sm6416_MEP_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating zero momentum, as inputted, and more importantly not change in momentum with running the simulation.]]

[[File:sm6416_MEP_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot showing that the reactants reach the transition state at the interception of r1 = r2. r1 quickly reaches a constant value, namely the equilibrium bond length of the reactant molecule. r2 increases logarithmically as time progresses, this represents an increasing distance of Ha from Hb-Hc and a continuing loss of momentum.]]

Final values from the MEP simulation.

r1 = 2.76195

r2 = 0.75883

These values reflect the minimum trajectory for a successful reaction.

p1 = p2 = 0

====Dynamic====

[[File:sm6416_Dynamic_Surface.png|thumb|none|350px|Surface plot highlighting the minimum energy path (MEP) with oscillation of the reactants, as the reaction returns to the reactants without fully passing through the transition state. It is therefore evident that the momentum as a result of the vibrational oscillation does not provide enough energy to proceed to the products.]]

[[File:sm6416_Dynamic_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating the momenta associated with the oscillating reactants.]]

[[File:sm6416_Dynamic_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot showing that the reactants reach the transition state at the interception of r1 = r2. r1 quickly decreases and oscillates about a constant value, namely the equilibrium bond length of the reactant molecule. r2 increases linearly as time progresses, this represents an increasing distance of Ha from Hb-Hc with a constant momentum.]]

Dynamic simulation final values

r1 = 10.0045

r2 = 0.75883

p1 = 2.48523

p2 = 1.29898

p(average) = 1.90409

With r1 = rts and r2 = rts + 0.01 would simply produce the same answer however the values would be flipped to the other distance. In other words r1 = 0.75883 and r2 = 10.0045 would be the output values.

Maintaining the final trajectories as calculated from the dynamic simulation and reversing the sign of the momenta, the reaction proceeds in the reverse direction to the products.

===Reactivity of Trajectories===

These simulations are restricted by the number of steps the program can handle, however a sound understanding of the reaction can be appreciated and the reactivity of each scenario can be determined appropriately.

{| class="wikitable" border=2
! Simulation !! p1 !! p2 !! Energy (kcal/mol) !! Reactivity !! Evidence !! Description
|-
| 1 || -1.25 || -2.5 || 5.03500 || Reactive || [[File:sm6416_MEP_Figure1.png|thumb|none|350px]] || Simulation 1: The reactants proceed through the transition state and to the products. The r2 distance decreases to the equilibrium bond length, whilst r1 simultaneously exhibits dissociation and increases beyond the scope of the graph. The small momenta attributed to the reactants is reflected in the vibrationally oscillating products, with a small amplitude.
|-
| 2 || -1.5 || -2.0 || 3.62879 || Unreactive || [[File:sm6416_MEP_Figure2.png|thumb|none|350px]] || Simulation 2: This is unreactive as the oscillating reactants reach the transition state point and r1 immediately returns to the initial bond length, whilst r2 continues to increase as it moves away from the H2 molecule.
|-
| 3 || -1.5 || -2.5 || 5.13738 || Reactive || [[File:sm6416_MEP_Figure3.png|thumb|none|350px]] || Simulation 3: This simulation shows a reactive pathway that is very similar to simulation 1, however due to the greater momenta associated with the reactants, as inputted, vibrational oscillations with a greater amplitude can be observed.
|-
| 4 || -2.5 || -5.0 || 9.86678 || Unreactive || [[File:sm6416_MEP_Figure4.png|thumb|none|350px]] || Simulation 4: Initially seen here are oscillating reactants with a very large amplitude. However, this simulation is unreactive despite the reactants going through the transition state and towards the product, they return to the initial reactants.
|-
| 5 || -2.5 || -5.2 || 11.80780 || Reactive || [[File:sm6416_MEP_Figure5.png|thumb|none|350px]] || Simulation 5: Like simulation 4, this simulation shows a large oscillating amplitude, whereas in this scenario after passing through the transition state, the products are completely obtained. The slight increase in the p2 momentum can be seen to result in the products.
|}

====Transition State Theory====

State what are the main assumptions of Transition State Theory. Given the results you have obtained, how will Transition State Theory predictions for reaction rate values compare with experimental values? Assumes quasi-equilibrium between reactants and transition state. TST assumes that once reaction passes TS no way back to products. Completely opposite to experimental where it seems as though an equilibrium/reversible path exists between the transition state and products. Fluctuation of whether transition complexes go towards reactants or products are independent of each other.

==F-H-H System Exercise 2==
===Potential Energy Surface Inspection===
====Energetics====

F + H2 is an exothermic reaction as can be seen from the surface plot, the reaction progresses from a small H-H distance to a longer one, whilst H-F simultaneously equilibriates about the F-H bond length. It can be seen that the products are lower, and hence more stable, in energy than the reactants.

F-H + H is simply the reverse reaction that passes through the same transition state, hence this reaction is endothermic with the products being higher in energy than the reactants. There is an overall gain of energy.

With this information in mind, the F-H bond is more stable and thus stronger than the H-H bond. The main factors to this argument is the greater electronegativity of F leading to a stronger contribution to the bond than the molecular orbitals. Hence the overlap of molecular orbitals is a weaker factor in the bond strength.

[[File:sm6416_FHH_Surface.png|thumb|none|350px|Surface plot highlighting the energetics of the F-H-H system.]]

[[File:sm6416_HHF_Surface.png|thumb|none|350px|Surface plot highlighting the energetics of the H-H-F system.]]

====Transition State====

Discuss Hammond Postulate with TS being closer to products/reactants dependent on how the TS is composed.

The transition state complex is achieved at r1 = F-H = 1.810076 Angstrom and r2 = H-H = 0.74634 Angstrom, as can be seen from the graphs below showing the absence of displacement to either reactants or products.

[[File:sm6416_FHH_Transition_State_Contour.png|thumb|none|350px|Contour plot demonstrating rts as a result of no fluctuations from the initial input, hence the complex is metaphorically sitting on the transition state.]]

[[File:sm6416_FHH_Transition_State_Momenta_Time.png|thumb|none|350px|Momenta vs Time plot demonstrating minimum, and almost zero, momentum at rts.]]

[[File:sm6416_FHH_Transition_State_Surface.png|thumb|none|350px]]

====Activation Energy====

The activation energy for the exothermic reaction was calculated through a 500000 step MEP simulation with input values of r1 = 1.820076, r2 = 0.74634 and p1 = p2 = 0. It was required that after following the minimum energy path, the gradient of the line signifying the reactants was constant.

The activation energy is reported at +0.258 kcal/mol for the exothermic process.

[[File:sm6416_FHH_Activation_Energy_1.png|thumb|none|350px|Energy vs Time graph highlighting the activation energy of the exothermic reaction.]]

The activation energy for the endothermic process was determined with the following parameters: r1 = 1.800076, r2 = 0.74634, p1 = p2 = 0 with 250000 steps. The reported activation energy was +30.277 kcal/mol.

[[File:sm6416_FHH_Activation_Energy_2.png|thumb|none|350px|Energy vs Time graph highlighting the activation energy of the endothermic reaction.]]

It can hence be seen that the exothermic reaction of F + H2 --> F-H + H only requires a small activation energy as the products are substantially more thermodynamically stable than the reactants.

===Reaction Dynamics===

In light of the fact that energy is conserved, '''discuss the mechanism of release of the reaction energy.''' How could this be confirmed experimentally? Measuring energy released from reaction ie exothermicity. Put first one separately. As reach momentum close to boundaries, system passes through transition state but returns to reactant well. Comment on effect the sign of the momentum has on the reactivity.

The following parameters were employed for all simulations rFH = 2.3, rHH = 0.74 with 500 steps calculated.

{| class="wikitable" border=2
! Simulation !! pHH !! pFH !! Surface Plot !! Momenta vs Time Plot !! Observations !!
|-
| 1 || -2.5 || -1.5 || [[File:sm6416_Trajectory_1_Surface.png|thumb|none|350px]] ||[[File:sm6416_Trajectory_1_Momenta.png|thumb|none|350px]] || This trajectory results in a successful reaction as seen from the surface plot; the reactants proceed through the transition state and continue into the product well, whilst continually oscillating as a result of the momentum gained.
|-
| 2 || -0.5 || -0.5 || [[File:sm6416_Trajectory_2_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_2_Momenta.png|thumb|none|350px]] || This momentum does not proceed to a reaction. Through the dynamic animation it can be seen that the HH molecule does not possess enough momentum to translate towards F. Therefore the system does not translate out of the reactant well, as seen in the surface plot, since there is not enough energy to overcome the activation energy. The momenta plot simply shows a small up trend, this is expected due to the long range electrostatic force of attraction between F and HH, resulting in a slight increase in the HH vibration velocity. There is no drastic change in the momenta of either F or HH that would otherwise indicate the occurrence of a reaction, as seen in simulation 1 above.
|-
| 3 || +0.5 || -0.5 || [[File:sm6416_Trajectory_3_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_3_Momenta.png|thumb|none|350px]] || This simulation shows an unreactive path, as can be seen from the surface plot, the system remains in the reactant well as it does not overcome the small activation energy for the exothermic reaction to proceed. As in simulation 2, the momentum amplitude of the oscillating HH remains constant however the overall momenta of the system increases due to a slight translation towards F, thus increasing electrostatic attraction forces resulting in this slight overall momenta increase.
|-
| 4 || -1.6 || -0.5 || [[File:sm6416_Trajectory_4_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_4_Momenta.png|thumb|none|350px]] || This simulation is very similar to simulations 2 & 3 in that the system remains in the reactant well as there is not sufficient energy to overcome the activation energy. However as a result of the greater HH momentum, the oscillation amplitude is greater than both simulation 1 & 2.
|-
| 5 || +1.6 || -0.5 || [[File:sm6416_Trajectory_5_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_5_Momenta.png|thumb|none|350px]] || Firstly, this simulation is unreactive as can be seen from the surface plot. In comparison to simulation 4, HH momentum sign has been changed and as a result this has led to not only a greater oscillating amplitude but also a larger translation towards F. So much so in the latter than the Momenta vs Time plot shows an increase in FH oscillation momentum as the electrostatic forces of attraction dominate due to the reduction in internuclear distance.
|-
| 6 || -2.9 || -0.5 || [[File:sm6416_Trajectory_6_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_6_Momenta.png|thumb|none|350px]] || This is the first reactive simulation observed, as can be seen from the surface plot and the drastic change in the momentum of FH. Evidently, there is sufficient energy to pass through the transition state complex and towards the reactants.
|-
| 7 || +2.9 || -0.5 || [[File:sm6416_Trajectory_7_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_7_Momenta.png|thumb|none|350px]] || This simulation is indeed similar to that of simulation 6 however, the change of sign for the HH momentum again results in a greater translation towards F and consequently the system passes through the transition complex shown by the surface plot and Momenta vs Time plot. However after a single oscillation, FH dissociates and the system returns to the reactant well with HH possessing a greater momentum. This scenario could be as a result of the HH momentum being too high and thus providing sufficient activation energy to proceed in the endothermic direction. This is surprising as the exothermic reaction elucidates more thermodynamically stable products.
|-
| 8 || +0.1 || -0.8 || [[File:sm6416_Trajectory_8_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_8_Momenta.png|thumb|none|350px]] || With a mere 60% change in FH momentum and a minimum HH momentum, the system can be seen to react fully, without returning through the transition state. The Momenta vs Time plot further shows a noticeable change in the AB momentum, which corresponds to FH. Despite the oscillations not being regular, it can be noted that the amplitudes are relatively of the same size and show no signs of regressing. This information highlights that the overall the FH momentum dominates the reactivity of the system and has a large weighting to overcoming the activation energy. It can be thought that the increase in momentum aids in allowing a closer distance of F & H, where electrostatic attraction forces will prevail.
|}

====Polyani's Empirical Rules====

Discuss relative translational and vibrational energies required to match the transition state for each endo/exothermic reaction relating to Hammond's postulate.

FH + H reactive trajectory - r1=0.9 r2=2.3 p1=6.5 p2=-1.5

Cite reference

[[File:sm6416_FHH_Reactive_Trajectory_1_Surface.png|thumb|none|350px]]
[[File:sm6416_FHH_Reactive_Trajectory_1_Momenta.png|thumb|none|350px]]
[[File:sm6416_FHH_Reactive_Trajectory_1_Distance.png|thumb|none|350px]]
[[File:sm6416_FHH_Reactive_Trajectory_1_Contour.png|thumb|none|350px]]

MRD:sm6416

2018-05-25T14:42:16Z

Sm6416: /* Transition State Dynamics */

==H2 H Exercise 1==

===Transition State Dynamics===

The transition state is the stage in a reaction coordinate that must be passed through in order for a reaction to occur and occurs at a saddle point, as shown by the numerous surface plots on this page. The first derivative highlights the positions along the reaction coordinate where the gradient equals zero. However, in order to determine if a saddle point ensues, the second derivative of the gradient must be taken. A saddle point is only present if the second derivative > 0.

Another way to think of the transition state is by thinking of the tangent that can be formed at the transition state itself. This tangent will follow the reaction coordinate profile and therefore is expected to be a maximum, where the gradient = 0. A line can be drawn to the normal of the tangent at the selected transition state. This path would show a minimum, where the gradient again = 0, at the intersection of the tangent with normal if the transition state has been correctly identified. It is only in this scenario that a transition state can be determined as one.

===Locating the Transition State===

The transition state was determined through iterations of both r1 and r2 which resulted in the smallest displacement of momenta along with no displacement as shown by the contour plot. This method determined at rts = 0.907743.

[[File:sm6416_Transition_State_Contour.png|thumb|none|350px|Contour plot demonstrating rts = 0.907743 as a result of no fluctuations from the initial input, hence the complex is at the transition state.]]

[[File:sm6416_Transition_State_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating minimum, and almost zero, momentum at rts = 0.907743.]]

[[File:sm6416_Transition_State_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot demonstrating no fluctuations in distance and hence rts = 0.907743.]]

===Reaction Path===

The minimum energy path (MEP) is defined as the lowest path the reaction must follow to form the products and is the downhill motion from the transition state. It can be applied in both directions in the case in question. The MEP views the system as static as it resets the velocity to zero at each step. Whereas the trajectory is very much dynamic and the momenta is accounted for, this is reflected in the vibrational oscillation of the molecule as it passes along the minimum well towards the products.

====MEP====

Initial conditions of r1 = rts + 0.01 = 0.917743, r2 = rts = 0.907743 and p1 = p2 = 0 for the MEP simulation.

[[File:sm6416_MEP_Surface.png|thumb|none|350px|Surface plot highlighting the minimum energy path (MEP), as the reaction returns to the reactants without fully passing through the transition state.]]

[[File:sm6416_MEP_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating zero momentum, as inputted, and more importantly not change in momentum with running the simulation.]]

[[File:sm6416_MEP_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot showing that the reactants reach the transition state at the interception of r1 = r2. r1 quickly reaches a constant value, namely the equilibrium bond length of the reactant molecule. r2 increases logarithmically as time progresses, this represents an increasing distance of Ha from Hb-Hc and a continuing loss of momentum.]]

Final values from the MEP simulation.

r1 = 2.76195

r2 = 0.75883

These values reflect the minimum trajectory for a successful reaction.

p1 = p2 = 0

====Dynamic====

[[File:sm6416_Dynamic_Surface.png|thumb|none|350px|Surface plot highlighting the minimum energy path (MEP) with oscillation of the reactants, as the reaction returns to the reactants without fully passing through the transition state. It is therefore evident that the momentum as a result of the vibrational oscillation does not provide enough energy to proceed to the products.]]

[[File:sm6416_Dynamic_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating the momenta associated with the oscillating reactants.]]

[[File:sm6416_Dynamic_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot showing that the reactants reach the transition state at the interception of r1 = r2. r1 quickly decreases and oscillates about a constant value, namely the equilibrium bond length of the reactant molecule. r2 increases linearly as time progresses, this represents an increasing distance of Ha from Hb-Hc with a constant momentum.]]

Dynamic simulation final values

r1 = 10.0045

r2 = 0.75883

p1 = 2.48523

p2 = 1.29898

p(average) = 1.90409

With r1 = rts and r2 = rts + 0.01 would simply produce the same answer however the values would be flipped to the other distance. In other words r1 = 0.75883 and r2 = 10.0045 would be the output values.

Maintaining the final trajectories as calculated from the dynamic simulation and reversing the sign of the momenta, the reaction proceeds in the reverse direction to the products.

===Reactivity of Trajectories===

These simulations are restricted by the number of steps the program can handle, however a sound understanding of the reaction can be appreciated and the reactivity of each scenario can be determined appropriately.

{| class="wikitable" border=2
! Simulation !! p1 !! p2 !! Energy (kcal/mol) !! Reactivity !! Evidence !! Description
|-
| 1 || -1.25 || -2.5 || 5.03500 || Reactive || [[File:sm6416_MEP_Figure1.png|thumb|none|350px]] || Simulation 1: The reactants proceed through the transition state and to the products. The r2 distance decreases to the equilibrium bond length, whilst r1 simultaneously exhibits dissociation and increases beyond the scope of the graph. The small momenta attributed to the reactants is reflected in the vibrationally oscillating products, with a small amplitude.
|-
| 2 || -1.5 || -2.0 || 3.62879 || Unreactive || [[File:sm6416_MEP_Figure2.png|thumb|none|350px]] || Simulation 2: This is unreactive as the oscillating reactants reach the transition state point and r1 immediately returns to the initial bond length, whilst r2 continues to increase as it moves away from the H2 molecule.
|-
| 3 || -1.5 || -2.5 || 5.13738 || Reactive || [[File:sm6416_MEP_Figure3.png|thumb|none|350px]] || Simulation 3: This simulation shows a reactive pathway that is very similar to simulation 1, however due to the greater momenta associated with the reactants, as inputted, vibrational oscillations with a greater amplitude can be observed.
|-
| 4 || -2.5 || -5.0 || 9.86678 || Unreactive || [[File:sm6416_MEP_Figure4.png|thumb|none|350px]] || Simulation 4: Initially seen here are oscillating reactants with a very large amplitude. However, this simulation is unreactive despite the reactants going through the transition state and towards the product, they return to the initial reactants.
|-
| 5 || -2.5 || -5.2 || 11.80780 || Reactive || [[File:sm6416_MEP_Figure5.png|thumb|none|350px]] || Simulation 5: Like simulation 4, this simulation shows a large oscillating amplitude, whereas in this scenario after passing through the transition state, the products are completely obtained. The slight increase in the p2 momentum can be seen to result in the products.
|}

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? Assumes quasi-equilibrium between reactants and transition state. TST assumes that once reaction passes TS no way back to products. Completely opposite to experimental where it seems as though an equilibrium/reversible path exists between the transition state and products. Fluctuation of whether transition complexes go towards reactants or products are independent of each other.

==F-H-H System Exercise 2==
===Potential Energy Surface Inspection===
====Energetics====

F + H2 is an exothermic reaction as can be seen from the surface plot, the reaction progresses from a small H-H distance to a longer one, whilst H-F simultaneously equilibriates about the F-H bond length. It can be seen that the products are lower, and hence more stable, in energy than the reactants.

F-H + H is simply the reverse reaction that passes through the same transition state, hence this reaction is endothermic with the products being higher in energy than the reactants. There is an overall gain of energy.

With this information in mind, the F-H bond is more stable and thus stronger than the H-H bond. The main factors to this argument is the greater electronegativity of F leading to a stronger contribution to the bond than the molecular orbitals. Hence the overlap of molecular orbitals is a weaker factor in the bond strength.

[[File:sm6416_FHH_Surface.png|thumb|none|350px|Surface plot highlighting the energetics of the F-H-H system.]]

[[File:sm6416_HHF_Surface.png|thumb|none|350px|Surface plot highlighting the energetics of the H-H-F system.]]

====Transition State====

Discuss Hammond Postulate with TS being closer to products/reactants dependent on how the TS is composed.

The transition state complex is achieved at r1 = F-H = 1.810076 Angstrom and r2 = H-H = 0.74634 Angstrom, as can be seen from the graphs below showing the absence of displacement to either reactants or products.

[[File:sm6416_FHH_Transition_State_Contour.png|thumb|none|350px|Contour plot demonstrating rts as a result of no fluctuations from the initial input, hence the complex is metaphorically sitting on the transition state.]]

[[File:sm6416_FHH_Transition_State_Momenta_Time.png|thumb|none|350px|Momenta vs Time plot demonstrating minimum, and almost zero, momentum at rts.]]

[[File:sm6416_FHH_Transition_State_Surface.png|thumb|none|350px]]

====Activation Energy====

The activation energy for the exothermic reaction was calculated through a 500000 step MEP simulation with input values of r1 = 1.820076, r2 = 0.74634 and p1 = p2 = 0. It was required that after following the minimum energy path, the gradient of the line signifying the reactants was constant.

The activation energy is reported at +0.258 kcal/mol for the exothermic process.

[[File:sm6416_FHH_Activation_Energy_1.png|thumb|none|350px|Energy vs Time graph highlighting the activation energy of the exothermic reaction.]]

The activation energy for the endothermic process was determined with the following parameters: r1 = 1.800076, r2 = 0.74634, p1 = p2 = 0 with 250000 steps. The reported activation energy was +30.277 kcal/mol.

[[File:sm6416_FHH_Activation_Energy_2.png|thumb|none|350px|Energy vs Time graph highlighting the activation energy of the endothermic reaction.]]

It can hence be seen that the exothermic reaction of F + H2 --> F-H + H only requires a small activation energy as the products are substantially more thermodynamically stable than the reactants.

===Reaction Dynamics===

In light of the fact that energy is conserved, '''discuss the mechanism of release of the reaction energy.''' How could this be confirmed experimentally? Measuring energy released from reaction ie exothermicity. Put first one separately. As reach momentum close to boundaries, system passes through transition state but returns to reactant well. Comment on effect the sign of the momentum has on the reactivity.

The following parameters were employed for all simulations rFH = 2.3, rHH = 0.74 with 500 steps calculated.

{| class="wikitable" border=2
! Simulation !! pHH !! pFH !! Surface Plot !! Momenta vs Time Plot !! Observations !!
|-
| 1 || -2.5 || -1.5 || [[File:sm6416_Trajectory_1_Surface.png|thumb|none|350px]] ||[[File:sm6416_Trajectory_1_Momenta.png|thumb|none|350px]] || This trajectory results in a successful reaction as seen from the surface plot; the reactants proceed through the transition state and continue into the product well, whilst continually oscillating as a result of the momentum gained.
|-
| 2 || -0.5 || -0.5 || [[File:sm6416_Trajectory_2_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_2_Momenta.png|thumb|none|350px]] || This momentum does not proceed to a reaction. Through the dynamic animation it can be seen that the HH molecule does not possess enough momentum to translate towards F. Therefore the system does not translate out of the reactant well, as seen in the surface plot, since there is not enough energy to overcome the activation energy. The momenta plot simply shows a small up trend, this is expected due to the long range electrostatic force of attraction between F and HH, resulting in a slight increase in the HH vibration velocity. There is no drastic change in the momenta of either F or HH that would otherwise indicate the occurrence of a reaction, as seen in simulation 1 above.
|-
| 3 || +0.5 || -0.5 || [[File:sm6416_Trajectory_3_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_3_Momenta.png|thumb|none|350px]] || This simulation shows an unreactive path, as can be seen from the surface plot, the system remains in the reactant well as it does not overcome the small activation energy for the exothermic reaction to proceed. As in simulation 2, the momentum amplitude of the oscillating HH remains constant however the overall momenta of the system increases due to a slight translation towards F, thus increasing electrostatic attraction forces resulting in this slight overall momenta increase.
|-
| 4 || -1.6 || -0.5 || [[File:sm6416_Trajectory_4_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_4_Momenta.png|thumb|none|350px]] || This simulation is very similar to simulations 2 & 3 in that the system remains in the reactant well as there is not sufficient energy to overcome the activation energy. However as a result of the greater HH momentum, the oscillation amplitude is greater than both simulation 1 & 2.
|-
| 5 || +1.6 || -0.5 || [[File:sm6416_Trajectory_5_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_5_Momenta.png|thumb|none|350px]] || Firstly, this simulation is unreactive as can be seen from the surface plot. In comparison to simulation 4, HH momentum sign has been changed and as a result this has led to not only a greater oscillating amplitude but also a larger translation towards F. So much so in the latter than the Momenta vs Time plot shows an increase in FH oscillation momentum as the electrostatic forces of attraction dominate due to the reduction in internuclear distance.
|-
| 6 || -2.9 || -0.5 || [[File:sm6416_Trajectory_6_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_6_Momenta.png|thumb|none|350px]] || This is the first reactive simulation observed, as can be seen from the surface plot and the drastic change in the momentum of FH. Evidently, there is sufficient energy to pass through the transition state complex and towards the reactants.
|-
| 7 || +2.9 || -0.5 || [[File:sm6416_Trajectory_7_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_7_Momenta.png|thumb|none|350px]] || This simulation is indeed similar to that of simulation 6 however, the change of sign for the HH momentum again results in a greater translation towards F and consequently the system passes through the transition complex shown by the surface plot and Momenta vs Time plot. However after a single oscillation, FH dissociates and the system returns to the reactant well with HH possessing a greater momentum. This scenario could be as a result of the HH momentum being too high and thus providing sufficient activation energy to proceed in the endothermic direction. This is surprising as the exothermic reaction elucidates more thermodynamically stable products.
|-
| 8 || +0.1 || -0.8 || [[File:sm6416_Trajectory_8_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_8_Momenta.png|thumb|none|350px]] || With a mere 60% change in FH momentum and a minimum HH momentum, the system can be seen to react fully, without returning through the transition state. The Momenta vs Time plot further shows a noticeable change in the AB momentum, which corresponds to FH. Despite the oscillations not being regular, it can be noted that the amplitudes are relatively of the same size and show no signs of regressing. This information highlights that the overall the FH momentum dominates the reactivity of the system and has a large weighting to overcoming the activation energy. It can be thought that the increase in momentum aids in allowing a closer distance of F & H, where electrostatic attraction forces will prevail.
|}

====Polyani's Empirical Rules====

Discuss relative translational and vibrational energies required to match the transition state for each endo/exothermic reaction relating to Hammond's postulate.

FH + H reactive trajectory - r1=0.9 r2=2.3 p1=6.5 p2=-1.5

Cite reference

[[File:sm6416_FHH_Reactive_Trajectory_1_Surface.png|thumb|none|350px]]
[[File:sm6416_FHH_Reactive_Trajectory_1_Momenta.png|thumb|none|350px]]
[[File:sm6416_FHH_Reactive_Trajectory_1_Distance.png|thumb|none|350px]]
[[File:sm6416_FHH_Reactive_Trajectory_1_Contour.png|thumb|none|350px]]

MRD:sm6416

2018-05-25T14:39:03Z

Sm6416: /* Transition State Dynamics */

==H2 H Exercise 1==

===Transition State Dynamics===

What value do the different components of the gradient of the potential energy surface have at a minimum and at a transition structure? Briefly explain how minima and transition structures can be distinguished using the curvature of the potential energy surface.

Discuss saddle point being the second derivative.
Minimum of trajectory.

The transition state is the stage in a reaction coordinate that must be passed through in order for a reaction to occur and occurs at a saddle point, as shown by the numerous surface plots on this page. The first derivative highlights the positions along the reaction coordinate where the gradient equals zero. However, in order to determine if a saddle point ensues, the second derivative of the gradient must be taken. A saddle point is only present if the second derivative >0.

Another way to think of the transition state is by thinking of the tangent that can be formed at the transition state itself. This tangent will follow the reaction coordinate profile and therefore is expected to be a maximum. A line can be drawn to the normal of the tangent at the selected transition state. This path would show a minimum at the intersection of the tangent with normal if the transition state has been correctly identified. It is only in this scenario that a transition state can be determined as one.

===Locating the Transition State===

The transition state was determined through iterations of both r1 and r2 which resulted in the smallest displacement of momenta along with no displacement as shown by the contour plot. This method determined at rts = 0.907743.

[[File:sm6416_Transition_State_Contour.png|thumb|none|350px|Contour plot demonstrating rts = 0.907743 as a result of no fluctuations from the initial input, hence the complex is at the transition state.]]

[[File:sm6416_Transition_State_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating minimum, and almost zero, momentum at rts = 0.907743.]]

[[File:sm6416_Transition_State_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot demonstrating no fluctuations in distance and hence rts = 0.907743.]]

===Reaction Path===

The minimum energy path (MEP) is defined as the lowest path the reaction must follow to form the products and is the downhill motion from the transition state. It can be applied in both directions in the case in question. The MEP views the system as static as it resets the velocity to zero at each step. Whereas the trajectory is very much dynamic and the momenta is accounted for, this is reflected in the vibrational oscillation of the molecule as it passes along the minimum well towards the products.

====MEP====

Initial conditions of r1 = rts + 0.01 = 0.917743, r2 = rts = 0.907743 and p1 = p2 = 0 for the MEP simulation.

[[File:sm6416_MEP_Surface.png|thumb|none|350px|Surface plot highlighting the minimum energy path (MEP), as the reaction returns to the reactants without fully passing through the transition state.]]

[[File:sm6416_MEP_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating zero momentum, as inputted, and more importantly not change in momentum with running the simulation.]]

[[File:sm6416_MEP_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot showing that the reactants reach the transition state at the interception of r1 = r2. r1 quickly reaches a constant value, namely the equilibrium bond length of the reactant molecule. r2 increases logarithmically as time progresses, this represents an increasing distance of Ha from Hb-Hc and a continuing loss of momentum.]]

Final values from the MEP simulation.

r1 = 2.76195

r2 = 0.75883

These values reflect the minimum trajectory for a successful reaction.

p1 = p2 = 0

====Dynamic====

[[File:sm6416_Dynamic_Surface.png|thumb|none|350px|Surface plot highlighting the minimum energy path (MEP) with oscillation of the reactants, as the reaction returns to the reactants without fully passing through the transition state. It is therefore evident that the momentum as a result of the vibrational oscillation does not provide enough energy to proceed to the products.]]

[[File:sm6416_Dynamic_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating the momenta associated with the oscillating reactants.]]

[[File:sm6416_Dynamic_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot showing that the reactants reach the transition state at the interception of r1 = r2. r1 quickly decreases and oscillates about a constant value, namely the equilibrium bond length of the reactant molecule. r2 increases linearly as time progresses, this represents an increasing distance of Ha from Hb-Hc with a constant momentum.]]

Dynamic simulation final values

r1 = 10.0045

r2 = 0.75883

p1 = 2.48523

p2 = 1.29898

p(average) = 1.90409

With r1 = rts and r2 = rts + 0.01 would simply produce the same answer however the values would be flipped to the other distance. In other words r1 = 0.75883 and r2 = 10.0045 would be the output values.

Maintaining the final trajectories as calculated from the dynamic simulation and reversing the sign of the momenta, the reaction proceeds in the reverse direction to the products.

===Reactivity of Trajectories===

These simulations are restricted by the number of steps the program can handle, however a sound understanding of the reaction can be appreciated and the reactivity of each scenario can be determined appropriately.

{| class="wikitable" border=2
! Simulation !! p1 !! p2 !! Energy (kcal/mol) !! Reactivity !! Evidence !! Description
|-
| 1 || -1.25 || -2.5 || 5.03500 || Reactive || [[File:sm6416_MEP_Figure1.png|thumb|none|350px]] || Simulation 1: The reactants proceed through the transition state and to the products. The r2 distance decreases to the equilibrium bond length, whilst r1 simultaneously exhibits dissociation and increases beyond the scope of the graph. The small momenta attributed to the reactants is reflected in the vibrationally oscillating products, with a small amplitude.
|-
| 2 || -1.5 || -2.0 || 3.62879 || Unreactive || [[File:sm6416_MEP_Figure2.png|thumb|none|350px]] || Simulation 2: This is unreactive as the oscillating reactants reach the transition state point and r1 immediately returns to the initial bond length, whilst r2 continues to increase as it moves away from the H2 molecule.
|-
| 3 || -1.5 || -2.5 || 5.13738 || Reactive || [[File:sm6416_MEP_Figure3.png|thumb|none|350px]] || Simulation 3: This simulation shows a reactive pathway that is very similar to simulation 1, however due to the greater momenta associated with the reactants, as inputted, vibrational oscillations with a greater amplitude can be observed.
|-
| 4 || -2.5 || -5.0 || 9.86678 || Unreactive || [[File:sm6416_MEP_Figure4.png|thumb|none|350px]] || Simulation 4: Initially seen here are oscillating reactants with a very large amplitude. However, this simulation is unreactive despite the reactants going through the transition state and towards the product, they return to the initial reactants.
|-
| 5 || -2.5 || -5.2 || 11.80780 || Reactive || [[File:sm6416_MEP_Figure5.png|thumb|none|350px]] || Simulation 5: Like simulation 4, this simulation shows a large oscillating amplitude, whereas in this scenario after passing through the transition state, the products are completely obtained. The slight increase in the p2 momentum can be seen to result in the products.
|}

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? Assumes quasi-equilibrium between reactants and transition state. TST assumes that once reaction passes TS no way back to products. Completely opposite to experimental where it seems as though an equilibrium/reversible path exists between the transition state and products. Fluctuation of whether transition complexes go towards reactants or products are independent of each other.

==F-H-H System Exercise 2==
===Potential Energy Surface Inspection===
====Energetics====

F + H2 is an exothermic reaction as can be seen from the surface plot, the reaction progresses from a small H-H distance to a longer one, whilst H-F simultaneously equilibriates about the F-H bond length. It can be seen that the products are lower, and hence more stable, in energy than the reactants.

F-H + H is simply the reverse reaction that passes through the same transition state, hence this reaction is endothermic with the products being higher in energy than the reactants. There is an overall gain of energy.

With this information in mind, the F-H bond is more stable and thus stronger than the H-H bond. The main factors to this argument is the greater electronegativity of F leading to a stronger contribution to the bond than the molecular orbitals. Hence the overlap of molecular orbitals is a weaker factor in the bond strength.

[[File:sm6416_FHH_Surface.png|thumb|none|350px|Surface plot highlighting the energetics of the F-H-H system.]]

[[File:sm6416_HHF_Surface.png|thumb|none|350px|Surface plot highlighting the energetics of the H-H-F system.]]

====Transition State====

Discuss Hammond Postulate with TS being closer to products/reactants dependent on how the TS is composed.

The transition state complex is achieved at r1 = F-H = 1.810076 Angstrom and r2 = H-H = 0.74634 Angstrom, as can be seen from the graphs below showing the absence of displacement to either reactants or products.

[[File:sm6416_FHH_Transition_State_Contour.png|thumb|none|350px|Contour plot demonstrating rts as a result of no fluctuations from the initial input, hence the complex is metaphorically sitting on the transition state.]]

[[File:sm6416_FHH_Transition_State_Momenta_Time.png|thumb|none|350px|Momenta vs Time plot demonstrating minimum, and almost zero, momentum at rts.]]

[[File:sm6416_FHH_Transition_State_Surface.png|thumb|none|350px]]

====Activation Energy====

The activation energy for the exothermic reaction was calculated through a 500000 step MEP simulation with input values of r1 = 1.820076, r2 = 0.74634 and p1 = p2 = 0. It was required that after following the minimum energy path, the gradient of the line signifying the reactants was constant.

The activation energy is reported at +0.258 kcal/mol for the exothermic process.

[[File:sm6416_FHH_Activation_Energy_1.png|thumb|none|350px|Energy vs Time graph highlighting the activation energy of the exothermic reaction.]]

The activation energy for the endothermic process was determined with the following parameters: r1 = 1.800076, r2 = 0.74634, p1 = p2 = 0 with 250000 steps. The reported activation energy was +30.277 kcal/mol.

[[File:sm6416_FHH_Activation_Energy_2.png|thumb|none|350px|Energy vs Time graph highlighting the activation energy of the endothermic reaction.]]

It can hence be seen that the exothermic reaction of F + H2 --> F-H + H only requires a small activation energy as the products are substantially more thermodynamically stable than the reactants.

===Reaction Dynamics===

In light of the fact that energy is conserved, '''discuss the mechanism of release of the reaction energy.''' How could this be confirmed experimentally? Measuring energy released from reaction ie exothermicity. Put first one separately. As reach momentum close to boundaries, system passes through transition state but returns to reactant well. Comment on effect the sign of the momentum has on the reactivity.

The following parameters were employed for all simulations rFH = 2.3, rHH = 0.74 with 500 steps calculated.

{| class="wikitable" border=2
! Simulation !! pHH !! pFH !! Surface Plot !! Momenta vs Time Plot !! Observations !!
|-
| 1 || -2.5 || -1.5 || [[File:sm6416_Trajectory_1_Surface.png|thumb|none|350px]] ||[[File:sm6416_Trajectory_1_Momenta.png|thumb|none|350px]] || This trajectory results in a successful reaction as seen from the surface plot; the reactants proceed through the transition state and continue into the product well, whilst continually oscillating as a result of the momentum gained.
|-
| 2 || -0.5 || -0.5 || [[File:sm6416_Trajectory_2_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_2_Momenta.png|thumb|none|350px]] || This momentum does not proceed to a reaction. Through the dynamic animation it can be seen that the HH molecule does not possess enough momentum to translate towards F. Therefore the system does not translate out of the reactant well, as seen in the surface plot, since there is not enough energy to overcome the activation energy. The momenta plot simply shows a small up trend, this is expected due to the long range electrostatic force of attraction between F and HH, resulting in a slight increase in the HH vibration velocity. There is no drastic change in the momenta of either F or HH that would otherwise indicate the occurrence of a reaction, as seen in simulation 1 above.
|-
| 3 || +0.5 || -0.5 || [[File:sm6416_Trajectory_3_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_3_Momenta.png|thumb|none|350px]] || This simulation shows an unreactive path, as can be seen from the surface plot, the system remains in the reactant well as it does not overcome the small activation energy for the exothermic reaction to proceed. As in simulation 2, the momentum amplitude of the oscillating HH remains constant however the overall momenta of the system increases due to a slight translation towards F, thus increasing electrostatic attraction forces resulting in this slight overall momenta increase.
|-
| 4 || -1.6 || -0.5 || [[File:sm6416_Trajectory_4_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_4_Momenta.png|thumb|none|350px]] || This simulation is very similar to simulations 2 & 3 in that the system remains in the reactant well as there is not sufficient energy to overcome the activation energy. However as a result of the greater HH momentum, the oscillation amplitude is greater than both simulation 1 & 2.
|-
| 5 || +1.6 || -0.5 || [[File:sm6416_Trajectory_5_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_5_Momenta.png|thumb|none|350px]] || Firstly, this simulation is unreactive as can be seen from the surface plot. In comparison to simulation 4, HH momentum sign has been changed and as a result this has led to not only a greater oscillating amplitude but also a larger translation towards F. So much so in the latter than the Momenta vs Time plot shows an increase in FH oscillation momentum as the electrostatic forces of attraction dominate due to the reduction in internuclear distance.
|-
| 6 || -2.9 || -0.5 || [[File:sm6416_Trajectory_6_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_6_Momenta.png|thumb|none|350px]] || This is the first reactive simulation observed, as can be seen from the surface plot and the drastic change in the momentum of FH. Evidently, there is sufficient energy to pass through the transition state complex and towards the reactants.
|-
| 7 || +2.9 || -0.5 || [[File:sm6416_Trajectory_7_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_7_Momenta.png|thumb|none|350px]] || This simulation is indeed similar to that of simulation 6 however, the change of sign for the HH momentum again results in a greater translation towards F and consequently the system passes through the transition complex shown by the surface plot and Momenta vs Time plot. However after a single oscillation, FH dissociates and the system returns to the reactant well with HH possessing a greater momentum. This scenario could be as a result of the HH momentum being too high and thus providing sufficient activation energy to proceed in the endothermic direction. This is surprising as the exothermic reaction elucidates more thermodynamically stable products.
|-
| 8 || +0.1 || -0.8 || [[File:sm6416_Trajectory_8_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_8_Momenta.png|thumb|none|350px]] || With a mere 60% change in FH momentum and a minimum HH momentum, the system can be seen to react fully, without returning through the transition state. The Momenta vs Time plot further shows a noticeable change in the AB momentum, which corresponds to FH. Despite the oscillations not being regular, it can be noted that the amplitudes are relatively of the same size and show no signs of regressing. This information highlights that the overall the FH momentum dominates the reactivity of the system and has a large weighting to overcoming the activation energy. It can be thought that the increase in momentum aids in allowing a closer distance of F & H, where electrostatic attraction forces will prevail.
|}

====Polyani's Empirical Rules====

Discuss relative translational and vibrational energies required to match the transition state for each endo/exothermic reaction relating to Hammond's postulate.

FH + H reactive trajectory - r1=0.9 r2=2.3 p1=6.5 p2=-1.5

Cite reference

[[File:sm6416_FHH_Reactive_Trajectory_1_Surface.png|thumb|none|350px]]
[[File:sm6416_FHH_Reactive_Trajectory_1_Momenta.png|thumb|none|350px]]
[[File:sm6416_FHH_Reactive_Trajectory_1_Distance.png|thumb|none|350px]]
[[File:sm6416_FHH_Reactive_Trajectory_1_Contour.png|thumb|none|350px]]

MRD:sm6416

2018-05-25T14:11:39Z

Sm6416: /* Transition State Dynamics */

==H2 H Exercise 1==

===Transition State Dynamics===

What value do the different components of the gradient of the potential energy surface have at a minimum and at a transition structure? Briefly explain how minima and transition structures can be distinguished using the curvature of the potential energy surface.

Discuss saddle point being the second derivative.
Minimum of trajectory.

The transition state is the stage in a reaction coordinate that must be passed through in order for a reaction to occur and occurs at a saddle point, as shown by the numerous surface plots on this page. The first derivative highlights the positions along the reaction coordinate where the gradient equals zero. However, in order to determine if a saddle point ensues, the second derivative of the gradient must be taken.

===Locating the Transition State===

The transition state was determined through iterations of both r1 and r2 which resulted in the smallest displacement of momenta along with no displacement as shown by the contour plot. This method determined at rts = 0.907743.

[[File:sm6416_Transition_State_Contour.png|thumb|none|350px|Contour plot demonstrating rts = 0.907743 as a result of no fluctuations from the initial input, hence the complex is at the transition state.]]

[[File:sm6416_Transition_State_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating minimum, and almost zero, momentum at rts = 0.907743.]]

[[File:sm6416_Transition_State_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot demonstrating no fluctuations in distance and hence rts = 0.907743.]]

===Reaction Path===

The minimum energy path (MEP) is defined as the lowest path the reaction must follow to form the products and is the downhill motion from the transition state. It can be applied in both directions in the case in question. The MEP views the system as static as it resets the velocity to zero at each step. Whereas the trajectory is very much dynamic and the momenta is accounted for, this is reflected in the vibrational oscillation of the molecule as it passes along the minimum well towards the products.

====MEP====

Initial conditions of r1 = rts + 0.01 = 0.917743, r2 = rts = 0.907743 and p1 = p2 = 0 for the MEP simulation.

[[File:sm6416_MEP_Surface.png|thumb|none|350px|Surface plot highlighting the minimum energy path (MEP), as the reaction returns to the reactants without fully passing through the transition state.]]

[[File:sm6416_MEP_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating zero momentum, as inputted, and more importantly not change in momentum with running the simulation.]]

[[File:sm6416_MEP_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot showing that the reactants reach the transition state at the interception of r1 = r2. r1 quickly reaches a constant value, namely the equilibrium bond length of the reactant molecule. r2 increases logarithmically as time progresses, this represents an increasing distance of Ha from Hb-Hc and a continuing loss of momentum.]]

Final values from the MEP simulation.

r1 = 2.76195

r2 = 0.75883

These values reflect the minimum trajectory for a successful reaction.

p1 = p2 = 0

====Dynamic====

[[File:sm6416_Dynamic_Surface.png|thumb|none|350px|Surface plot highlighting the minimum energy path (MEP) with oscillation of the reactants, as the reaction returns to the reactants without fully passing through the transition state. It is therefore evident that the momentum as a result of the vibrational oscillation does not provide enough energy to proceed to the products.]]

[[File:sm6416_Dynamic_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating the momenta associated with the oscillating reactants.]]

[[File:sm6416_Dynamic_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot showing that the reactants reach the transition state at the interception of r1 = r2. r1 quickly decreases and oscillates about a constant value, namely the equilibrium bond length of the reactant molecule. r2 increases linearly as time progresses, this represents an increasing distance of Ha from Hb-Hc with a constant momentum.]]

Dynamic simulation final values

r1 = 10.0045

r2 = 0.75883

p1 = 2.48523

p2 = 1.29898

p(average) = 1.90409

With r1 = rts and r2 = rts + 0.01 would simply produce the same answer however the values would be flipped to the other distance. In other words r1 = 0.75883 and r2 = 10.0045 would be the output values.

Maintaining the final trajectories as calculated from the dynamic simulation and reversing the sign of the momenta, the reaction proceeds in the reverse direction to the products.

===Reactivity of Trajectories===

These simulations are restricted by the number of steps the program can handle, however a sound understanding of the reaction can be appreciated and the reactivity of each scenario can be determined appropriately.

{| class="wikitable" border=2
! Simulation !! p1 !! p2 !! Energy (kcal/mol) !! Reactivity !! Evidence !! Description
|-
| 1 || -1.25 || -2.5 || 5.03500 || Reactive || [[File:sm6416_MEP_Figure1.png|thumb|none|350px]] || Simulation 1: The reactants proceed through the transition state and to the products. The r2 distance decreases to the equilibrium bond length, whilst r1 simultaneously exhibits dissociation and increases beyond the scope of the graph. The small momenta attributed to the reactants is reflected in the vibrationally oscillating products, with a small amplitude.
|-
| 2 || -1.5 || -2.0 || 3.62879 || Unreactive || [[File:sm6416_MEP_Figure2.png|thumb|none|350px]] || Simulation 2: This is unreactive as the oscillating reactants reach the transition state point and r1 immediately returns to the initial bond length, whilst r2 continues to increase as it moves away from the H2 molecule.
|-
| 3 || -1.5 || -2.5 || 5.13738 || Reactive || [[File:sm6416_MEP_Figure3.png|thumb|none|350px]] || Simulation 3: This simulation shows a reactive pathway that is very similar to simulation 1, however due to the greater momenta associated with the reactants, as inputted, vibrational oscillations with a greater amplitude can be observed.
|-
| 4 || -2.5 || -5.0 || 9.86678 || Unreactive || [[File:sm6416_MEP_Figure4.png|thumb|none|350px]] || Simulation 4: Initially seen here are oscillating reactants with a very large amplitude. However, this simulation is unreactive despite the reactants going through the transition state and towards the product, they return to the initial reactants.
|-
| 5 || -2.5 || -5.2 || 11.80780 || Reactive || [[File:sm6416_MEP_Figure5.png|thumb|none|350px]] || Simulation 5: Like simulation 4, this simulation shows a large oscillating amplitude, whereas in this scenario after passing through the transition state, the products are completely obtained. The slight increase in the p2 momentum can be seen to result in the products.
|}

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? Assumes quasi-equilibrium between reactants and transition state. TST assumes that once reaction passes TS no way back to products. Completely opposite to experimental where it seems as though an equilibrium/reversible path exists between the transition state and products. Fluctuation of whether transition complexes go towards reactants or products are independent of each other.

==F-H-H System Exercise 2==
===Potential Energy Surface Inspection===
====Energetics====

F + H2 is an exothermic reaction as can be seen from the surface plot, the reaction progresses from a small H-H distance to a longer one, whilst H-F simultaneously equilibriates about the F-H bond length. It can be seen that the products are lower, and hence more stable, in energy than the reactants.

F-H + H is simply the reverse reaction that passes through the same transition state, hence this reaction is endothermic with the products being higher in energy than the reactants. There is an overall gain of energy.

With this information in mind, the F-H bond is more stable and thus stronger than the H-H bond. The main factors to this argument is the greater electronegativity of F leading to a stronger contribution to the bond than the molecular orbitals. Hence the overlap of molecular orbitals is a weaker factor in the bond strength.

[[File:sm6416_FHH_Surface.png|thumb|none|350px|Surface plot highlighting the energetics of the F-H-H system.]]

[[File:sm6416_HHF_Surface.png|thumb|none|350px|Surface plot highlighting the energetics of the H-H-F system.]]

====Transition State====

Discuss Hammond Postulate with TS being closer to products/reactants dependent on how the TS is composed.

The transition state complex is achieved at r1 = F-H = 1.810076 Angstrom and r2 = H-H = 0.74634 Angstrom, as can be seen from the graphs below showing the absence of displacement to either reactants or products.

[[File:sm6416_FHH_Transition_State_Contour.png|thumb|none|350px|Contour plot demonstrating rts as a result of no fluctuations from the initial input, hence the complex is metaphorically sitting on the transition state.]]

[[File:sm6416_FHH_Transition_State_Momenta_Time.png|thumb|none|350px|Momenta vs Time plot demonstrating minimum, and almost zero, momentum at rts.]]

[[File:sm6416_FHH_Transition_State_Surface.png|thumb|none|350px]]

====Activation Energy====

The activation energy for the exothermic reaction was calculated through a 500000 step MEP simulation with input values of r1 = 1.820076, r2 = 0.74634 and p1 = p2 = 0. It was required that after following the minimum energy path, the gradient of the line signifying the reactants was constant.

The activation energy is reported at +0.258 kcal/mol for the exothermic process.

[[File:sm6416_FHH_Activation_Energy_1.png|thumb|none|350px|Energy vs Time graph highlighting the activation energy of the exothermic reaction.]]

The activation energy for the endothermic process was determined with the following parameters: r1 = 1.800076, r2 = 0.74634, p1 = p2 = 0 with 250000 steps. The reported activation energy was +30.277 kcal/mol.

[[File:sm6416_FHH_Activation_Energy_2.png|thumb|none|350px|Energy vs Time graph highlighting the activation energy of the endothermic reaction.]]

It can hence be seen that the exothermic reaction of F + H2 --> F-H + H only requires a small activation energy as the products are substantially more thermodynamically stable than the reactants.

===Reaction Dynamics===

In light of the fact that energy is conserved, '''discuss the mechanism of release of the reaction energy.''' How could this be confirmed experimentally? Measuring energy released from reaction ie exothermicity. Put first one separately. As reach momentum close to boundaries, system passes through transition state but returns to reactant well. Comment on effect the sign of the momentum has on the reactivity.

The following parameters were employed for all simulations rFH = 2.3, rHH = 0.74 with 500 steps calculated.

{| class="wikitable" border=2
! Simulation !! pHH !! pFH !! Surface Plot !! Momenta vs Time Plot !! Observations !!
|-
| 1 || -2.5 || -1.5 || [[File:sm6416_Trajectory_1_Surface.png|thumb|none|350px]] ||[[File:sm6416_Trajectory_1_Momenta.png|thumb|none|350px]] || This trajectory results in a successful reaction as seen from the surface plot; the reactants proceed through the transition state and continue into the product well, whilst continually oscillating as a result of the momentum gained.
|-
| 2 || -0.5 || -0.5 || [[File:sm6416_Trajectory_2_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_2_Momenta.png|thumb|none|350px]] || This momentum does not proceed to a reaction. Through the dynamic animation it can be seen that the HH molecule does not possess enough momentum to translate towards F. Therefore the system does not translate out of the reactant well, as seen in the surface plot, since there is not enough energy to overcome the activation energy. The momenta plot simply shows a small up trend, this is expected due to the long range electrostatic force of attraction between F and HH, resulting in a slight increase in the HH vibration velocity. There is no drastic change in the momenta of either F or HH that would otherwise indicate the occurrence of a reaction, as seen in simulation 1 above.
|-
| 3 || +0.5 || -0.5 || [[File:sm6416_Trajectory_3_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_3_Momenta.png|thumb|none|350px]] || This simulation shows an unreactive path, as can be seen from the surface plot, the system remains in the reactant well as it does not overcome the small activation energy for the exothermic reaction to proceed. As in simulation 2, the momentum amplitude of the oscillating HH remains constant however the overall momenta of the system increases due to a slight translation towards F, thus increasing electrostatic attraction forces resulting in this slight overall momenta increase.
|-
| 4 || -1.6 || -0.5 || [[File:sm6416_Trajectory_4_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_4_Momenta.png|thumb|none|350px]] || This simulation is very similar to simulations 2 & 3 in that the system remains in the reactant well as there is not sufficient energy to overcome the activation energy. However as a result of the greater HH momentum, the oscillation amplitude is greater than both simulation 1 & 2.
|-
| 5 || +1.6 || -0.5 || [[File:sm6416_Trajectory_5_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_5_Momenta.png|thumb|none|350px]] || Firstly, this simulation is unreactive as can be seen from the surface plot. In comparison to simulation 4, HH momentum sign has been changed and as a result this has led to not only a greater oscillating amplitude but also a larger translation towards F. So much so in the latter than the Momenta vs Time plot shows an increase in FH oscillation momentum as the electrostatic forces of attraction dominate due to the reduction in internuclear distance.
|-
| 6 || -2.9 || -0.5 || [[File:sm6416_Trajectory_6_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_6_Momenta.png|thumb|none|350px]] || This is the first reactive simulation observed, as can be seen from the surface plot and the drastic change in the momentum of FH. Evidently, there is sufficient energy to pass through the transition state complex and towards the reactants.
|-
| 7 || +2.9 || -0.5 || [[File:sm6416_Trajectory_7_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_7_Momenta.png|thumb|none|350px]] || This simulation is indeed similar to that of simulation 6 however, the change of sign for the HH momentum again results in a greater translation towards F and consequently the system passes through the transition complex shown by the surface plot and Momenta vs Time plot. However after a single oscillation, FH dissociates and the system returns to the reactant well with HH possessing a greater momentum. This scenario could be as a result of the HH momentum being too high and thus providing sufficient activation energy to proceed in the endothermic direction. This is surprising as the exothermic reaction elucidates more thermodynamically stable products.
|-
| 8 || +0.1 || -0.8 || [[File:sm6416_Trajectory_8_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_8_Momenta.png|thumb|none|350px]] || With a mere 60% change in FH momentum and a minimum HH momentum, the system can be seen to react fully, without returning through the transition state. The Momenta vs Time plot further shows a noticeable change in the AB momentum, which corresponds to FH. Despite the oscillations not being regular, it can be noted that the amplitudes are relatively of the same size and show no signs of regressing. This information highlights that the overall the FH momentum dominates the reactivity of the system and has a large weighting to overcoming the activation energy. It can be thought that the increase in momentum aids in allowing a closer distance of F & H, where electrostatic attraction forces will prevail.
|}

====Polyani's Empirical Rules====

Discuss relative translational and vibrational energies required to match the transition state for each endo/exothermic reaction relating to Hammond's postulate.

FH + H reactive trajectory - r1=0.9 r2=2.3 p1=6.5 p2=-1.5

Cite reference

[[File:sm6416_FHH_Reactive_Trajectory_1_Surface.png|thumb|none|350px]]
[[File:sm6416_FHH_Reactive_Trajectory_1_Momenta.png|thumb|none|350px]]
[[File:sm6416_FHH_Reactive_Trajectory_1_Distance.png|thumb|none|350px]]
[[File:sm6416_FHH_Reactive_Trajectory_1_Contour.png|thumb|none|350px]]

MRD:sm6416

2018-05-25T13:29:11Z

Sm6416: /* Reaction Dynamics */

==H2 H Exercise 1==

===Transition State Dynamics===

What value do the different components of the gradient of the potential energy surface have at a minimum and at a transition structure? Briefly explain how minima and transition structures can be distinguished using the curvature of the potential energy surface.

Discuss saddle point being the second derivative.
Minimum of trajectory.

===Locating the Transition State===

The transition state was determined through iterations of both r1 and r2 which resulted in the smallest displacement of momenta along with no displacement as shown by the contour plot. This method determined at rts = 0.907743.

[[File:sm6416_Transition_State_Contour.png|thumb|none|350px|Contour plot demonstrating rts = 0.907743 as a result of no fluctuations from the initial input, hence the complex is at the transition state.]]

[[File:sm6416_Transition_State_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating minimum, and almost zero, momentum at rts = 0.907743.]]

[[File:sm6416_Transition_State_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot demonstrating no fluctuations in distance and hence rts = 0.907743.]]

===Reaction Path===

The minimum energy path (MEP) is defined as the lowest path the reaction must follow to form the products and is the downhill motion from the transition state. It can be applied in both directions in the case in question. The MEP views the system as static as it resets the velocity to zero at each step. Whereas the trajectory is very much dynamic and the momenta is accounted for, this is reflected in the vibrational oscillation of the molecule as it passes along the minimum well towards the products.

====MEP====

Initial conditions of r1 = rts + 0.01 = 0.917743, r2 = rts = 0.907743 and p1 = p2 = 0 for the MEP simulation.

[[File:sm6416_MEP_Surface.png|thumb|none|350px|Surface plot highlighting the minimum energy path (MEP), as the reaction returns to the reactants without fully passing through the transition state.]]

[[File:sm6416_MEP_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating zero momentum, as inputted, and more importantly not change in momentum with running the simulation.]]

[[File:sm6416_MEP_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot showing that the reactants reach the transition state at the interception of r1 = r2. r1 quickly reaches a constant value, namely the equilibrium bond length of the reactant molecule. r2 increases logarithmically as time progresses, this represents an increasing distance of Ha from Hb-Hc and a continuing loss of momentum.]]

Final values from the MEP simulation.

r1 = 2.76195

r2 = 0.75883

These values reflect the minimum trajectory for a successful reaction.

p1 = p2 = 0

====Dynamic====

[[File:sm6416_Dynamic_Surface.png|thumb|none|350px|Surface plot highlighting the minimum energy path (MEP) with oscillation of the reactants, as the reaction returns to the reactants without fully passing through the transition state. It is therefore evident that the momentum as a result of the vibrational oscillation does not provide enough energy to proceed to the products.]]

[[File:sm6416_Dynamic_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating the momenta associated with the oscillating reactants.]]

[[File:sm6416_Dynamic_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot showing that the reactants reach the transition state at the interception of r1 = r2. r1 quickly decreases and oscillates about a constant value, namely the equilibrium bond length of the reactant molecule. r2 increases linearly as time progresses, this represents an increasing distance of Ha from Hb-Hc with a constant momentum.]]

Dynamic simulation final values

r1 = 10.0045

r2 = 0.75883

p1 = 2.48523

p2 = 1.29898

p(average) = 1.90409

With r1 = rts and r2 = rts + 0.01 would simply produce the same answer however the values would be flipped to the other distance. In other words r1 = 0.75883 and r2 = 10.0045 would be the output values.

Maintaining the final trajectories as calculated from the dynamic simulation and reversing the sign of the momenta, the reaction proceeds in the reverse direction to the products.

===Reactivity of Trajectories===

These simulations are restricted by the number of steps the program can handle, however a sound understanding of the reaction can be appreciated and the reactivity of each scenario can be determined appropriately.

{| class="wikitable" border=2
! Simulation !! p1 !! p2 !! Energy (kcal/mol) !! Reactivity !! Evidence !! Description
|-
| 1 || -1.25 || -2.5 || 5.03500 || Reactive || [[File:sm6416_MEP_Figure1.png|thumb|none|350px]] || Simulation 1: The reactants proceed through the transition state and to the products. The r2 distance decreases to the equilibrium bond length, whilst r1 simultaneously exhibits dissociation and increases beyond the scope of the graph. The small momenta attributed to the reactants is reflected in the vibrationally oscillating products, with a small amplitude.
|-
| 2 || -1.5 || -2.0 || 3.62879 || Unreactive || [[File:sm6416_MEP_Figure2.png|thumb|none|350px]] || Simulation 2: This is unreactive as the oscillating reactants reach the transition state point and r1 immediately returns to the initial bond length, whilst r2 continues to increase as it moves away from the H2 molecule.
|-
| 3 || -1.5 || -2.5 || 5.13738 || Reactive || [[File:sm6416_MEP_Figure3.png|thumb|none|350px]] || Simulation 3: This simulation shows a reactive pathway that is very similar to simulation 1, however due to the greater momenta associated with the reactants, as inputted, vibrational oscillations with a greater amplitude can be observed.
|-
| 4 || -2.5 || -5.0 || 9.86678 || Unreactive || [[File:sm6416_MEP_Figure4.png|thumb|none|350px]] || Simulation 4: Initially seen here are oscillating reactants with a very large amplitude. However, this simulation is unreactive despite the reactants going through the transition state and towards the product, they return to the initial reactants.
|-
| 5 || -2.5 || -5.2 || 11.80780 || Reactive || [[File:sm6416_MEP_Figure5.png|thumb|none|350px]] || Simulation 5: Like simulation 4, this simulation shows a large oscillating amplitude, whereas in this scenario after passing through the transition state, the products are completely obtained. The slight increase in the p2 momentum can be seen to result in the products.
|}

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? Assumes quasi-equilibrium between reactants and transition state. TST assumes that once reaction passes TS no way back to products. Completely opposite to experimental where it seems as though an equilibrium/reversible path exists between the transition state and products. Fluctuation of whether transition complexes go towards reactants or products are independent of each other.

==F-H-H System Exercise 2==
===Potential Energy Surface Inspection===
====Energetics====

F + H2 is an exothermic reaction as can be seen from the surface plot, the reaction progresses from a small H-H distance to a longer one, whilst H-F simultaneously equilibriates about the F-H bond length. It can be seen that the products are lower, and hence more stable, in energy than the reactants.

F-H + H is simply the reverse reaction that passes through the same transition state, hence this reaction is endothermic with the products being higher in energy than the reactants. There is an overall gain of energy.

With this information in mind, the F-H bond is more stable and thus stronger than the H-H bond. The main factors to this argument is the greater electronegativity of F leading to a stronger contribution to the bond than the molecular orbitals. Hence the overlap of molecular orbitals is a weaker factor in the bond strength.

[[File:sm6416_FHH_Surface.png|thumb|none|350px|Surface plot highlighting the energetics of the F-H-H system.]]

[[File:sm6416_HHF_Surface.png|thumb|none|350px|Surface plot highlighting the energetics of the H-H-F system.]]

====Transition State====

Discuss Hammond Postulate with TS being closer to products/reactants dependent on how the TS is composed.

The transition state complex is achieved at r1 = F-H = 1.810076 Angstrom and r2 = H-H = 0.74634 Angstrom, as can be seen from the graphs below showing the absence of displacement to either reactants or products.

[[File:sm6416_FHH_Transition_State_Contour.png|thumb|none|350px|Contour plot demonstrating rts as a result of no fluctuations from the initial input, hence the complex is metaphorically sitting on the transition state.]]

[[File:sm6416_FHH_Transition_State_Momenta_Time.png|thumb|none|350px|Momenta vs Time plot demonstrating minimum, and almost zero, momentum at rts.]]

[[File:sm6416_FHH_Transition_State_Surface.png|thumb|none|350px]]

====Activation Energy====

The activation energy for the exothermic reaction was calculated through a 500000 step MEP simulation with input values of r1 = 1.820076, r2 = 0.74634 and p1 = p2 = 0. It was required that after following the minimum energy path, the gradient of the line signifying the reactants was constant.

The activation energy is reported at +0.258 kcal/mol for the exothermic process.

[[File:sm6416_FHH_Activation_Energy_1.png|thumb|none|350px|Energy vs Time graph highlighting the activation energy of the exothermic reaction.]]

The activation energy for the endothermic process was determined with the following parameters: r1 = 1.800076, r2 = 0.74634, p1 = p2 = 0 with 250000 steps. The reported activation energy was +30.277 kcal/mol.

[[File:sm6416_FHH_Activation_Energy_2.png|thumb|none|350px|Energy vs Time graph highlighting the activation energy of the endothermic reaction.]]

It can hence be seen that the exothermic reaction of F + H2 --> F-H + H only requires a small activation energy as the products are substantially more thermodynamically stable than the reactants.

===Reaction Dynamics===

In light of the fact that energy is conserved, '''discuss the mechanism of release of the reaction energy.''' How could this be confirmed experimentally? Measuring energy released from reaction ie exothermicity. Put first one separately. As reach momentum close to boundaries, system passes through transition state but returns to reactant well. Comment on effect the sign of the momentum has on the reactivity.

The following parameters were employed for all simulations rFH = 2.3, rHH = 0.74 with 500 steps calculated.

{| class="wikitable" border=2
! Simulation !! pHH !! pFH !! Surface Plot !! Momenta vs Time Plot !! Observations !!
|-
| 1 || -2.5 || -1.5 || [[File:sm6416_Trajectory_1_Surface.png|thumb|none|350px]] ||[[File:sm6416_Trajectory_1_Momenta.png|thumb|none|350px]] || This trajectory results in a successful reaction as seen from the surface plot; the reactants proceed through the transition state and continue into the product well, whilst continually oscillating as a result of the momentum gained.
|-
| 2 || -0.5 || -0.5 || [[File:sm6416_Trajectory_2_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_2_Momenta.png|thumb|none|350px]] || This momentum does not proceed to a reaction. Through the dynamic animation it can be seen that the HH molecule does not possess enough momentum to translate towards F. Therefore the system does not translate out of the reactant well, as seen in the surface plot, since there is not enough energy to overcome the activation energy. The momenta plot simply shows a small up trend, this is expected due to the long range electrostatic force of attraction between F and HH, resulting in a slight increase in the HH vibration velocity. There is no drastic change in the momenta of either F or HH that would otherwise indicate the occurrence of a reaction, as seen in simulation 1 above.
|-
| 3 || +0.5 || -0.5 || [[File:sm6416_Trajectory_3_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_3_Momenta.png|thumb|none|350px]] || This simulation shows an unreactive path, as can be seen from the surface plot, the system remains in the reactant well as it does not overcome the small activation energy for the exothermic reaction to proceed. As in simulation 2, the momentum amplitude of the oscillating HH remains constant however the overall momenta of the system increases due to a slight translation towards F, thus increasing electrostatic attraction forces resulting in this slight overall momenta increase.
|-
| 4 || -1.6 || -0.5 || [[File:sm6416_Trajectory_4_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_4_Momenta.png|thumb|none|350px]] || This simulation is very similar to simulations 2 & 3 in that the system remains in the reactant well as there is not sufficient energy to overcome the activation energy. However as a result of the greater HH momentum, the oscillation amplitude is greater than both simulation 1 & 2.
|-
| 5 || +1.6 || -0.5 || [[File:sm6416_Trajectory_5_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_5_Momenta.png|thumb|none|350px]] || Firstly, this simulation is unreactive as can be seen from the surface plot. In comparison to simulation 4, HH momentum sign has been changed and as a result this has led to not only a greater oscillating amplitude but also a larger translation towards F. So much so in the latter than the Momenta vs Time plot shows an increase in FH oscillation momentum as the electrostatic forces of attraction dominate due to the reduction in internuclear distance.
|-
| 6 || -2.9 || -0.5 || [[File:sm6416_Trajectory_6_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_6_Momenta.png|thumb|none|350px]] || This is the first reactive simulation observed, as can be seen from the surface plot and the drastic change in the momentum of FH. Evidently, there is sufficient energy to pass through the transition state complex and towards the reactants.
|-
| 7 || +2.9 || -0.5 || [[File:sm6416_Trajectory_7_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_7_Momenta.png|thumb|none|350px]] || This simulation is indeed similar to that of simulation 6 however, the change of sign for the HH momentum again results in a greater translation towards F and consequently the system passes through the transition complex shown by the surface plot and Momenta vs Time plot. However after a single oscillation, FH dissociates and the system returns to the reactant well with HH possessing a greater momentum. This scenario could be as a result of the HH momentum being too high and thus providing sufficient activation energy to proceed in the endothermic direction. This is surprising as the exothermic reaction elucidates more thermodynamically stable products.
|-
| 8 || +0.1 || -0.8 || [[File:sm6416_Trajectory_8_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_8_Momenta.png|thumb|none|350px]] || With a mere 60% change in FH momentum and a minimum HH momentum, the system can be seen to react fully, without returning through the transition state. The Momenta vs Time plot further shows a noticeable change in the AB momentum, which corresponds to FH. Despite the oscillations not being regular, it can be noted that the amplitudes are relatively of the same size and show no signs of regressing. This information highlights that the overall the FH momentum dominates the reactivity of the system and has a large weighting to overcoming the activation energy. It can be thought that the increase in momentum aids in allowing a closer distance of F & H, where electrostatic attraction forces will prevail.
|}

====Polyani's Empirical Rules====

Discuss relative translational and vibrational energies required to match the transition state for each endo/exothermic reaction relating to Hammond's postulate.

FH + H reactive trajectory - r1=0.9 r2=2.3 p1=6.5 p2=-1.5

Cite reference

[[File:sm6416_FHH_Reactive_Trajectory_1_Surface.png|thumb|none|350px]]
[[File:sm6416_FHH_Reactive_Trajectory_1_Momenta.png|thumb|none|350px]]
[[File:sm6416_FHH_Reactive_Trajectory_1_Distance.png|thumb|none|350px]]
[[File:sm6416_FHH_Reactive_Trajectory_1_Contour.png|thumb|none|350px]]

MRD:sm6416

2018-05-25T13:21:47Z

Sm6416: /* Reaction Dynamics */

==H2 H Exercise 1==

===Transition State Dynamics===

What value do the different components of the gradient of the potential energy surface have at a minimum and at a transition structure? Briefly explain how minima and transition structures can be distinguished using the curvature of the potential energy surface.

Discuss saddle point being the second derivative.
Minimum of trajectory.

===Locating the Transition State===

The transition state was determined through iterations of both r1 and r2 which resulted in the smallest displacement of momenta along with no displacement as shown by the contour plot. This method determined at rts = 0.907743.

[[File:sm6416_Transition_State_Contour.png|thumb|none|350px|Contour plot demonstrating rts = 0.907743 as a result of no fluctuations from the initial input, hence the complex is at the transition state.]]

[[File:sm6416_Transition_State_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating minimum, and almost zero, momentum at rts = 0.907743.]]

[[File:sm6416_Transition_State_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot demonstrating no fluctuations in distance and hence rts = 0.907743.]]

===Reaction Path===

The minimum energy path (MEP) is defined as the lowest path the reaction must follow to form the products and is the downhill motion from the transition state. It can be applied in both directions in the case in question. The MEP views the system as static as it resets the velocity to zero at each step. Whereas the trajectory is very much dynamic and the momenta is accounted for, this is reflected in the vibrational oscillation of the molecule as it passes along the minimum well towards the products.

====MEP====

Initial conditions of r1 = rts + 0.01 = 0.917743, r2 = rts = 0.907743 and p1 = p2 = 0 for the MEP simulation.

[[File:sm6416_MEP_Surface.png|thumb|none|350px|Surface plot highlighting the minimum energy path (MEP), as the reaction returns to the reactants without fully passing through the transition state.]]

[[File:sm6416_MEP_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating zero momentum, as inputted, and more importantly not change in momentum with running the simulation.]]

[[File:sm6416_MEP_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot showing that the reactants reach the transition state at the interception of r1 = r2. r1 quickly reaches a constant value, namely the equilibrium bond length of the reactant molecule. r2 increases logarithmically as time progresses, this represents an increasing distance of Ha from Hb-Hc and a continuing loss of momentum.]]

Final values from the MEP simulation.

r1 = 2.76195

r2 = 0.75883

These values reflect the minimum trajectory for a successful reaction.

p1 = p2 = 0

====Dynamic====

[[File:sm6416_Dynamic_Surface.png|thumb|none|350px|Surface plot highlighting the minimum energy path (MEP) with oscillation of the reactants, as the reaction returns to the reactants without fully passing through the transition state. It is therefore evident that the momentum as a result of the vibrational oscillation does not provide enough energy to proceed to the products.]]

[[File:sm6416_Dynamic_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating the momenta associated with the oscillating reactants.]]

[[File:sm6416_Dynamic_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot showing that the reactants reach the transition state at the interception of r1 = r2. r1 quickly decreases and oscillates about a constant value, namely the equilibrium bond length of the reactant molecule. r2 increases linearly as time progresses, this represents an increasing distance of Ha from Hb-Hc with a constant momentum.]]

Dynamic simulation final values

r1 = 10.0045

r2 = 0.75883

p1 = 2.48523

p2 = 1.29898

p(average) = 1.90409

With r1 = rts and r2 = rts + 0.01 would simply produce the same answer however the values would be flipped to the other distance. In other words r1 = 0.75883 and r2 = 10.0045 would be the output values.

Maintaining the final trajectories as calculated from the dynamic simulation and reversing the sign of the momenta, the reaction proceeds in the reverse direction to the products.

===Reactivity of Trajectories===

These simulations are restricted by the number of steps the program can handle, however a sound understanding of the reaction can be appreciated and the reactivity of each scenario can be determined appropriately.

{| class="wikitable" border=2
! Simulation !! p1 !! p2 !! Energy (kcal/mol) !! Reactivity !! Evidence !! Description
|-
| 1 || -1.25 || -2.5 || 5.03500 || Reactive || [[File:sm6416_MEP_Figure1.png|thumb|none|350px]] || Simulation 1: The reactants proceed through the transition state and to the products. The r2 distance decreases to the equilibrium bond length, whilst r1 simultaneously exhibits dissociation and increases beyond the scope of the graph. The small momenta attributed to the reactants is reflected in the vibrationally oscillating products, with a small amplitude.
|-
| 2 || -1.5 || -2.0 || 3.62879 || Unreactive || [[File:sm6416_MEP_Figure2.png|thumb|none|350px]] || Simulation 2: This is unreactive as the oscillating reactants reach the transition state point and r1 immediately returns to the initial bond length, whilst r2 continues to increase as it moves away from the H2 molecule.
|-
| 3 || -1.5 || -2.5 || 5.13738 || Reactive || [[File:sm6416_MEP_Figure3.png|thumb|none|350px]] || Simulation 3: This simulation shows a reactive pathway that is very similar to simulation 1, however due to the greater momenta associated with the reactants, as inputted, vibrational oscillations with a greater amplitude can be observed.
|-
| 4 || -2.5 || -5.0 || 9.86678 || Unreactive || [[File:sm6416_MEP_Figure4.png|thumb|none|350px]] || Simulation 4: Initially seen here are oscillating reactants with a very large amplitude. However, this simulation is unreactive despite the reactants going through the transition state and towards the product, they return to the initial reactants.
|-
| 5 || -2.5 || -5.2 || 11.80780 || Reactive || [[File:sm6416_MEP_Figure5.png|thumb|none|350px]] || Simulation 5: Like simulation 4, this simulation shows a large oscillating amplitude, whereas in this scenario after passing through the transition state, the products are completely obtained. The slight increase in the p2 momentum can be seen to result in the products.
|}

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? Assumes quasi-equilibrium between reactants and transition state. TST assumes that once reaction passes TS no way back to products. Completely opposite to experimental where it seems as though an equilibrium/reversible path exists between the transition state and products. Fluctuation of whether transition complexes go towards reactants or products are independent of each other.

==F-H-H System Exercise 2==
===Potential Energy Surface Inspection===
====Energetics====

F + H2 is an exothermic reaction as can be seen from the surface plot, the reaction progresses from a small H-H distance to a longer one, whilst H-F simultaneously equilibriates about the F-H bond length. It can be seen that the products are lower, and hence more stable, in energy than the reactants.

F-H + H is simply the reverse reaction that passes through the same transition state, hence this reaction is endothermic with the products being higher in energy than the reactants. There is an overall gain of energy.

With this information in mind, the F-H bond is more stable and thus stronger than the H-H bond. The main factors to this argument is the greater electronegativity of F leading to a stronger contribution to the bond than the molecular orbitals. Hence the overlap of molecular orbitals is a weaker factor in the bond strength.

[[File:sm6416_FHH_Surface.png|thumb|none|350px|Surface plot highlighting the energetics of the F-H-H system.]]

[[File:sm6416_HHF_Surface.png|thumb|none|350px|Surface plot highlighting the energetics of the H-H-F system.]]

====Transition State====

Discuss Hammond Postulate with TS being closer to products/reactants dependent on how the TS is composed.

The transition state complex is achieved at r1 = F-H = 1.810076 Angstrom and r2 = H-H = 0.74634 Angstrom, as can be seen from the graphs below showing the absence of displacement to either reactants or products.

[[File:sm6416_FHH_Transition_State_Contour.png|thumb|none|350px|Contour plot demonstrating rts as a result of no fluctuations from the initial input, hence the complex is metaphorically sitting on the transition state.]]

[[File:sm6416_FHH_Transition_State_Momenta_Time.png|thumb|none|350px|Momenta vs Time plot demonstrating minimum, and almost zero, momentum at rts.]]

[[File:sm6416_FHH_Transition_State_Surface.png|thumb|none|350px]]

====Activation Energy====

The activation energy for the exothermic reaction was calculated through a 500000 step MEP simulation with input values of r1 = 1.820076, r2 = 0.74634 and p1 = p2 = 0. It was required that after following the minimum energy path, the gradient of the line signifying the reactants was constant.

The activation energy is reported at +0.258 kcal/mol for the exothermic process.

[[File:sm6416_FHH_Activation_Energy_1.png|thumb|none|350px|Energy vs Time graph highlighting the activation energy of the exothermic reaction.]]

The activation energy for the endothermic process was determined with the following parameters: r1 = 1.800076, r2 = 0.74634, p1 = p2 = 0 with 250000 steps. The reported activation energy was +30.277 kcal/mol.

[[File:sm6416_FHH_Activation_Energy_2.png|thumb|none|350px|Energy vs Time graph highlighting the activation energy of the endothermic reaction.]]

It can hence be seen that the exothermic reaction of F + H2 --> F-H + H only requires a small activation energy as the products are substantially more thermodynamically stable than the reactants.

===Reaction Dynamics===

In light of the fact that energy is conserved, '''discuss the mechanism of release of the reaction energy.''' How could this be confirmed experimentally? Measuring energy released from reaction ie exothermicity. Put first one separately. As reach momentum close to boundaries, system passes through transition state but returns to reactant well. Comment on effect the sign of the momentum has on the reactivity.

The following parameters were employed for all simulations rFH = 2.3, rHH = 0.74 with 500 steps calculated.

{| class="wikitable" border=2
! Simulation !! pHH !! pFH !! Surface Plot !! Momenta vs Time Plot !! Observations !!
|-
| 1 || -2.5 || -1.5 || [[File:sm6416_Trajectory_1_Surface.png|thumb|none|350px]] ||[[File:sm6416_Trajectory_1_Momenta.png|thumb|none|350px]] || This trajectory results in a successful reaction as seen from the surface plot; the reactants proceed through the transition state and continue into the product well, whilst continually oscillating as a result of the momentum gained.
|-
| 2 || -0.5 || -0.5 || [[File:sm6416_Trajectory_2_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_2_Momenta.png|thumb|none|350px]] || This momentum does not proceed to a reaction. Through the dynamic animation it can be seen that the HH molecule does not possess enough momentum to translate towards F. Therefore the system does not translate out of the reactant well, as seen in the surface plot, since there is not enough energy to overcome the activation energy. The momenta plot simply shows a small up trend, this is expected due to the long range electrostatic force of attraction between F and HH, resulting in a slight increase in the HH vibration velocity. There is no drastic change in the momenta of either F or HH that would otherwise indicate the occurrence of a reaction, as seen in simulation 1 above.
|-
| 3 || +0.5 || -0.5 || [[File:sm6416_Trajectory_3_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_3_Momenta.png|thumb|none|350px]] || This simulation shows an unreactive path, as can be seen from the surface plot, the system remains in the reactant well as it does not overcome the small activation energy for the exothermic reaction to proceed. As in simulation 2, the momentum amplitude of the oscillating HH remains constant however the overall momenta of the system increases due to a slight translation towards F, thus increasing electrostatic attraction forces resulting in this slight overall momenta increase.
|-
| 4 || -1.6 || -0.5 || [[File:sm6416_Trajectory_4_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_4_Momenta.png|thumb|none|350px]] || This simulation is very similar to simulations 2 & 3 in that the system remains in the reactant well as there is not sufficient energy to overcome the activation energy. However as a result of the greater HH momentum, the oscillation amplitude is greater than both simulation 1 & 2.
|-
| 5 || +1.6 || -0.5 || [[File:sm6416_Trajectory_5_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_5_Momenta.png|thumb|none|350px]] || Firstly, this simulation is unreactive as can be seen from the surface plot. In comparison to simulation 4, HH momentum sign has been changed and as a result this has led to not only a greater oscillating amplitude but also a larger translation towards F. So much so in the latter than the Momenta vs Time plot shows an increase in FH oscillation momentum as the electrostatic forces of attraction dominate due to the reduction in internuclear distance.
|-
| 6 || -2.9 || -0.5 || [[File:sm6416_Trajectory_6_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_6_Momenta.png|thumb|none|350px]] || This is the first reactive simulation observed, as can be seen from the surface plot and the drastic change in the momentum of FH. Evidently, there is sufficient energy to pass through the transition state complex and towards the reactants.
|-
| 7 || +2.9 || -0.5 || [[File:sm6416_Trajectory_7_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_7_Momenta.png|thumb|none|350px]] || This simulation is indeed similar to that of simulation 6 however, the change of sign for the HH momentum again results in a greater translation towards F and consequently the system passes through the transition complex shown by the surface plot and Momenta vs Time plot. However after a single oscillation, FH dissociates and the system returns to the reactant well with HH possessing a greater momentum. This scenario could be as a result of the HH momentum being too high and thus providing sufficient activation energy to proceed in the endothermic direction. This is surprising as the exothermic reaction elucidates more thermodynamically stable products.
|-
| 8 || +0.1 || -0.8 || [[File:sm6416_Trajectory_8_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_8_Momenta.png|thumb|none|350px]] ||
|}

====Polyani's Empirical Rules====

Discuss relative translational and vibrational energies required to match the transition state for each endo/exothermic reaction relating to Hammond's postulate.

FH + H reactive trajectory - r1=0.9 r2=2.3 p1=6.5 p2=-1.5

Cite reference

[[File:sm6416_FHH_Reactive_Trajectory_1_Surface.png|thumb|none|350px]]
[[File:sm6416_FHH_Reactive_Trajectory_1_Momenta.png|thumb|none|350px]]
[[File:sm6416_FHH_Reactive_Trajectory_1_Distance.png|thumb|none|350px]]
[[File:sm6416_FHH_Reactive_Trajectory_1_Contour.png|thumb|none|350px]]

MRD:sm6416

2018-05-25T13:06:58Z

Sm6416: /* Reaction Dynamics */

==H2 H Exercise 1==

===Transition State Dynamics===

What value do the different components of the gradient of the potential energy surface have at a minimum and at a transition structure? Briefly explain how minima and transition structures can be distinguished using the curvature of the potential energy surface.

Discuss saddle point being the second derivative.
Minimum of trajectory.

===Locating the Transition State===

The transition state was determined through iterations of both r1 and r2 which resulted in the smallest displacement of momenta along with no displacement as shown by the contour plot. This method determined at rts = 0.907743.

[[File:sm6416_Transition_State_Contour.png|thumb|none|350px|Contour plot demonstrating rts = 0.907743 as a result of no fluctuations from the initial input, hence the complex is at the transition state.]]

[[File:sm6416_Transition_State_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating minimum, and almost zero, momentum at rts = 0.907743.]]

[[File:sm6416_Transition_State_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot demonstrating no fluctuations in distance and hence rts = 0.907743.]]

===Reaction Path===

The minimum energy path (MEP) is defined as the lowest path the reaction must follow to form the products and is the downhill motion from the transition state. It can be applied in both directions in the case in question. The MEP views the system as static as it resets the velocity to zero at each step. Whereas the trajectory is very much dynamic and the momenta is accounted for, this is reflected in the vibrational oscillation of the molecule as it passes along the minimum well towards the products.

====MEP====

Initial conditions of r1 = rts + 0.01 = 0.917743, r2 = rts = 0.907743 and p1 = p2 = 0 for the MEP simulation.

[[File:sm6416_MEP_Surface.png|thumb|none|350px|Surface plot highlighting the minimum energy path (MEP), as the reaction returns to the reactants without fully passing through the transition state.]]

[[File:sm6416_MEP_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating zero momentum, as inputted, and more importantly not change in momentum with running the simulation.]]

[[File:sm6416_MEP_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot showing that the reactants reach the transition state at the interception of r1 = r2. r1 quickly reaches a constant value, namely the equilibrium bond length of the reactant molecule. r2 increases logarithmically as time progresses, this represents an increasing distance of Ha from Hb-Hc and a continuing loss of momentum.]]

Final values from the MEP simulation.

r1 = 2.76195

r2 = 0.75883

These values reflect the minimum trajectory for a successful reaction.

p1 = p2 = 0

====Dynamic====

[[File:sm6416_Dynamic_Surface.png|thumb|none|350px|Surface plot highlighting the minimum energy path (MEP) with oscillation of the reactants, as the reaction returns to the reactants without fully passing through the transition state. It is therefore evident that the momentum as a result of the vibrational oscillation does not provide enough energy to proceed to the products.]]

[[File:sm6416_Dynamic_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating the momenta associated with the oscillating reactants.]]

[[File:sm6416_Dynamic_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot showing that the reactants reach the transition state at the interception of r1 = r2. r1 quickly decreases and oscillates about a constant value, namely the equilibrium bond length of the reactant molecule. r2 increases linearly as time progresses, this represents an increasing distance of Ha from Hb-Hc with a constant momentum.]]

Dynamic simulation final values

r1 = 10.0045

r2 = 0.75883

p1 = 2.48523

p2 = 1.29898

p(average) = 1.90409

With r1 = rts and r2 = rts + 0.01 would simply produce the same answer however the values would be flipped to the other distance. In other words r1 = 0.75883 and r2 = 10.0045 would be the output values.

Maintaining the final trajectories as calculated from the dynamic simulation and reversing the sign of the momenta, the reaction proceeds in the reverse direction to the products.

===Reactivity of Trajectories===

These simulations are restricted by the number of steps the program can handle, however a sound understanding of the reaction can be appreciated and the reactivity of each scenario can be determined appropriately.

{| class="wikitable" border=2
! Simulation !! p1 !! p2 !! Energy (kcal/mol) !! Reactivity !! Evidence !! Description
|-
| 1 || -1.25 || -2.5 || 5.03500 || Reactive || [[File:sm6416_MEP_Figure1.png|thumb|none|350px]] || Simulation 1: The reactants proceed through the transition state and to the products. The r2 distance decreases to the equilibrium bond length, whilst r1 simultaneously exhibits dissociation and increases beyond the scope of the graph. The small momenta attributed to the reactants is reflected in the vibrationally oscillating products, with a small amplitude.
|-
| 2 || -1.5 || -2.0 || 3.62879 || Unreactive || [[File:sm6416_MEP_Figure2.png|thumb|none|350px]] || Simulation 2: This is unreactive as the oscillating reactants reach the transition state point and r1 immediately returns to the initial bond length, whilst r2 continues to increase as it moves away from the H2 molecule.
|-
| 3 || -1.5 || -2.5 || 5.13738 || Reactive || [[File:sm6416_MEP_Figure3.png|thumb|none|350px]] || Simulation 3: This simulation shows a reactive pathway that is very similar to simulation 1, however due to the greater momenta associated with the reactants, as inputted, vibrational oscillations with a greater amplitude can be observed.
|-
| 4 || -2.5 || -5.0 || 9.86678 || Unreactive || [[File:sm6416_MEP_Figure4.png|thumb|none|350px]] || Simulation 4: Initially seen here are oscillating reactants with a very large amplitude. However, this simulation is unreactive despite the reactants going through the transition state and towards the product, they return to the initial reactants.
|-
| 5 || -2.5 || -5.2 || 11.80780 || Reactive || [[File:sm6416_MEP_Figure5.png|thumb|none|350px]] || Simulation 5: Like simulation 4, this simulation shows a large oscillating amplitude, whereas in this scenario after passing through the transition state, the products are completely obtained. The slight increase in the p2 momentum can be seen to result in the products.
|}

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? Assumes quasi-equilibrium between reactants and transition state. TST assumes that once reaction passes TS no way back to products. Completely opposite to experimental where it seems as though an equilibrium/reversible path exists between the transition state and products. Fluctuation of whether transition complexes go towards reactants or products are independent of each other.

==F-H-H System Exercise 2==
===Potential Energy Surface Inspection===
====Energetics====

F + H2 is an exothermic reaction as can be seen from the surface plot, the reaction progresses from a small H-H distance to a longer one, whilst H-F simultaneously equilibriates about the F-H bond length. It can be seen that the products are lower, and hence more stable, in energy than the reactants.

F-H + H is simply the reverse reaction that passes through the same transition state, hence this reaction is endothermic with the products being higher in energy than the reactants. There is an overall gain of energy.

With this information in mind, the F-H bond is more stable and thus stronger than the H-H bond. The main factors to this argument is the greater electronegativity of F leading to a stronger contribution to the bond than the molecular orbitals. Hence the overlap of molecular orbitals is a weaker factor in the bond strength.

[[File:sm6416_FHH_Surface.png|thumb|none|350px|Surface plot highlighting the energetics of the F-H-H system.]]

[[File:sm6416_HHF_Surface.png|thumb|none|350px|Surface plot highlighting the energetics of the H-H-F system.]]

====Transition State====

Discuss Hammond Postulate with TS being closer to products/reactants dependent on how the TS is composed.

The transition state complex is achieved at r1 = F-H = 1.810076 Angstrom and r2 = H-H = 0.74634 Angstrom, as can be seen from the graphs below showing the absence of displacement to either reactants or products.

[[File:sm6416_FHH_Transition_State_Contour.png|thumb|none|350px|Contour plot demonstrating rts as a result of no fluctuations from the initial input, hence the complex is metaphorically sitting on the transition state.]]

[[File:sm6416_FHH_Transition_State_Momenta_Time.png|thumb|none|350px|Momenta vs Time plot demonstrating minimum, and almost zero, momentum at rts.]]

[[File:sm6416_FHH_Transition_State_Surface.png|thumb|none|350px]]

====Activation Energy====

The activation energy for the exothermic reaction was calculated through a 500000 step MEP simulation with input values of r1 = 1.820076, r2 = 0.74634 and p1 = p2 = 0. It was required that after following the minimum energy path, the gradient of the line signifying the reactants was constant.

The activation energy is reported at +0.258 kcal/mol for the exothermic process.

[[File:sm6416_FHH_Activation_Energy_1.png|thumb|none|350px|Energy vs Time graph highlighting the activation energy of the exothermic reaction.]]

The activation energy for the endothermic process was determined with the following parameters: r1 = 1.800076, r2 = 0.74634, p1 = p2 = 0 with 250000 steps. The reported activation energy was +30.277 kcal/mol.

[[File:sm6416_FHH_Activation_Energy_2.png|thumb|none|350px|Energy vs Time graph highlighting the activation energy of the endothermic reaction.]]

It can hence be seen that the exothermic reaction of F + H2 --> F-H + H only requires a small activation energy as the products are substantially more thermodynamically stable than the reactants.

===Reaction Dynamics===

In light of the fact that energy is conserved, '''discuss the mechanism of release of the reaction energy.''' How could this be confirmed experimentally? Measuring energy released from reaction ie exothermicity. Put first one separately. As reach momentum close to boundaries, system passes through transition state but returns to reactant well. Comment on effect the sign of the momentum has on the reactivity.

The following parameters were employed for all simulations rFH = 2.3, rHH = 0.74 with 500 steps calculated.

{| class="wikitable" border=2
! Simulation !! pHH !! pFH !! Surface Plot !! Momenta vs Time Plot !! Observations !!
|-
| 1 || -2.5 || -1.5 || [[File:sm6416_Trajectory_1_Surface.png|thumb|none|350px]] ||[[File:sm6416_Trajectory_1_Momenta.png|thumb|none|350px]] || This trajectory results in a successful reaction as seen from the surface plot; the reactants proceed through the transition state and continue into the product well, whilst continually oscillating as a result of the momentum gained.
|-
| 2 || -0.5 || -0.5 || [[File:sm6416_Trajectory_2_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_2_Momenta.png|thumb|none|350px]] || This momentum does not proceed to a reaction. Through the dynamic animation it can be seen that the HH molecule does not possess enough momentum to translate towards F. Therefore the system does not translate out of the reactant well, as seen in the surface plot, since there is not enough energy to overcome the activation energy. The momenta plot simply shows a small up trend, this is expected due to the long range electrostatic force of attraction between F and HH, resulting in a slight increase in the HH vibration velocity. There is no drastic change in the momenta of either F or HH that would otherwise indicate the occurrence of a reaction, as seen in simulation 1 above.
|-
| 3 || +0.5 || -0.5 || [[File:sm6416_Trajectory_3_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_3_Momenta.png|thumb|none|350px]] || This simulation shows an unreactive path, as can be seen from the surface plot, the system remains in the reactant well as it does not overcome the small activation energy for the exothermic reaction to proceed. As in simulation 2, the momentum amplitude of the oscillating HH remains constant however the overall momenta of the system increases due to a slight translation towards F, thus increasing electrostatic attraction forces resulting in this slight overall momenta increase.
|-
| 4 || -1.6 || -0.5 || [[File:sm6416_Trajectory_4_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_4_Momenta.png|thumb|none|350px]] || This simulation is very similar to simulations 2 & 3 in that the system remains in the reactant well as there is not sufficient energy to overcome the activation energy. However as a result of the greater HH momentum, the oscillation amplitude is greater than both simulation 1 & 2.
|-
| 5 || +1.6 || -0.5 || [[File:sm6416_Trajectory_5_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_5_Momenta.png|thumb|none|350px]] || Firstly, this simulation is unreactive as can be seen from the surface plot. In comparison to simulation 4, HH momentum sign has been changed and as a result this has led to not only a greater oscillating amplitude but also a larger translation towards F. So much so in the latter than the Momenta vs Time plot shows an increase in FH oscillation momentum as the electrostatic forces of attraction dominate due to the reduction in internuclear distance.
|-
| 6 || -2.9 || -0.5 || [[File:sm6416_Trajectory_6_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_6_Momenta.png|thumb|none|350px]] ||
|-
| 7 || +2.9 || -0.5 || [[File:sm6416_Trajectory_7_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_7_Momenta.png|thumb|none|350px]] ||
|-
| 8 || +0.1 || -0.8 || [[File:sm6416_Trajectory_8_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_8_Momenta.png|thumb|none|350px]] ||
|}

====Polyani's Empirical Rules====

Discuss relative translational and vibrational energies required to match the transition state for each endo/exothermic reaction relating to Hammond's postulate.

FH + H reactive trajectory - r1=0.9 r2=2.3 p1=6.5 p2=-1.5

Cite reference

[[File:sm6416_FHH_Reactive_Trajectory_1_Surface.png|thumb|none|350px]]
[[File:sm6416_FHH_Reactive_Trajectory_1_Momenta.png|thumb|none|350px]]
[[File:sm6416_FHH_Reactive_Trajectory_1_Distance.png|thumb|none|350px]]
[[File:sm6416_FHH_Reactive_Trajectory_1_Contour.png|thumb|none|350px]]

MRD:sm6416

2018-05-25T12:40:16Z

Sm6416: /* Reaction Dynamics */

==H2 H Exercise 1==

===Transition State Dynamics===

What value do the different components of the gradient of the potential energy surface have at a minimum and at a transition structure? Briefly explain how minima and transition structures can be distinguished using the curvature of the potential energy surface.

Discuss saddle point being the second derivative.
Minimum of trajectory.

===Locating the Transition State===

The transition state was determined through iterations of both r1 and r2 which resulted in the smallest displacement of momenta along with no displacement as shown by the contour plot. This method determined at rts = 0.907743.

[[File:sm6416_Transition_State_Contour.png|thumb|none|350px|Contour plot demonstrating rts = 0.907743 as a result of no fluctuations from the initial input, hence the complex is at the transition state.]]

[[File:sm6416_Transition_State_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating minimum, and almost zero, momentum at rts = 0.907743.]]

[[File:sm6416_Transition_State_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot demonstrating no fluctuations in distance and hence rts = 0.907743.]]

===Reaction Path===

The minimum energy path (MEP) is defined as the lowest path the reaction must follow to form the products and is the downhill motion from the transition state. It can be applied in both directions in the case in question. The MEP views the system as static as it resets the velocity to zero at each step. Whereas the trajectory is very much dynamic and the momenta is accounted for, this is reflected in the vibrational oscillation of the molecule as it passes along the minimum well towards the products.

====MEP====

Initial conditions of r1 = rts + 0.01 = 0.917743, r2 = rts = 0.907743 and p1 = p2 = 0 for the MEP simulation.

[[File:sm6416_MEP_Surface.png|thumb|none|350px|Surface plot highlighting the minimum energy path (MEP), as the reaction returns to the reactants without fully passing through the transition state.]]

[[File:sm6416_MEP_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating zero momentum, as inputted, and more importantly not change in momentum with running the simulation.]]

[[File:sm6416_MEP_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot showing that the reactants reach the transition state at the interception of r1 = r2. r1 quickly reaches a constant value, namely the equilibrium bond length of the reactant molecule. r2 increases logarithmically as time progresses, this represents an increasing distance of Ha from Hb-Hc and a continuing loss of momentum.]]

Final values from the MEP simulation.

r1 = 2.76195

r2 = 0.75883

These values reflect the minimum trajectory for a successful reaction.

p1 = p2 = 0

====Dynamic====

[[File:sm6416_Dynamic_Surface.png|thumb|none|350px|Surface plot highlighting the minimum energy path (MEP) with oscillation of the reactants, as the reaction returns to the reactants without fully passing through the transition state. It is therefore evident that the momentum as a result of the vibrational oscillation does not provide enough energy to proceed to the products.]]

[[File:sm6416_Dynamic_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating the momenta associated with the oscillating reactants.]]

[[File:sm6416_Dynamic_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot showing that the reactants reach the transition state at the interception of r1 = r2. r1 quickly decreases and oscillates about a constant value, namely the equilibrium bond length of the reactant molecule. r2 increases linearly as time progresses, this represents an increasing distance of Ha from Hb-Hc with a constant momentum.]]

Dynamic simulation final values

r1 = 10.0045

r2 = 0.75883

p1 = 2.48523

p2 = 1.29898

p(average) = 1.90409

With r1 = rts and r2 = rts + 0.01 would simply produce the same answer however the values would be flipped to the other distance. In other words r1 = 0.75883 and r2 = 10.0045 would be the output values.

Maintaining the final trajectories as calculated from the dynamic simulation and reversing the sign of the momenta, the reaction proceeds in the reverse direction to the products.

===Reactivity of Trajectories===

These simulations are restricted by the number of steps the program can handle, however a sound understanding of the reaction can be appreciated and the reactivity of each scenario can be determined appropriately.

{| class="wikitable" border=2
! Simulation !! p1 !! p2 !! Energy (kcal/mol) !! Reactivity !! Evidence !! Description
|-
| 1 || -1.25 || -2.5 || 5.03500 || Reactive || [[File:sm6416_MEP_Figure1.png|thumb|none|350px]] || Simulation 1: The reactants proceed through the transition state and to the products. The r2 distance decreases to the equilibrium bond length, whilst r1 simultaneously exhibits dissociation and increases beyond the scope of the graph. The small momenta attributed to the reactants is reflected in the vibrationally oscillating products, with a small amplitude.
|-
| 2 || -1.5 || -2.0 || 3.62879 || Unreactive || [[File:sm6416_MEP_Figure2.png|thumb|none|350px]] || Simulation 2: This is unreactive as the oscillating reactants reach the transition state point and r1 immediately returns to the initial bond length, whilst r2 continues to increase as it moves away from the H2 molecule.
|-
| 3 || -1.5 || -2.5 || 5.13738 || Reactive || [[File:sm6416_MEP_Figure3.png|thumb|none|350px]] || Simulation 3: This simulation shows a reactive pathway that is very similar to simulation 1, however due to the greater momenta associated with the reactants, as inputted, vibrational oscillations with a greater amplitude can be observed.
|-
| 4 || -2.5 || -5.0 || 9.86678 || Unreactive || [[File:sm6416_MEP_Figure4.png|thumb|none|350px]] || Simulation 4: Initially seen here are oscillating reactants with a very large amplitude. However, this simulation is unreactive despite the reactants going through the transition state and towards the product, they return to the initial reactants.
|-
| 5 || -2.5 || -5.2 || 11.80780 || Reactive || [[File:sm6416_MEP_Figure5.png|thumb|none|350px]] || Simulation 5: Like simulation 4, this simulation shows a large oscillating amplitude, whereas in this scenario after passing through the transition state, the products are completely obtained. The slight increase in the p2 momentum can be seen to result in the products.
|}

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? Assumes quasi-equilibrium between reactants and transition state. TST assumes that once reaction passes TS no way back to products. Completely opposite to experimental where it seems as though an equilibrium/reversible path exists between the transition state and products. Fluctuation of whether transition complexes go towards reactants or products are independent of each other.

==F-H-H System Exercise 2==
===Potential Energy Surface Inspection===
====Energetics====

F + H2 is an exothermic reaction as can be seen from the surface plot, the reaction progresses from a small H-H distance to a longer one, whilst H-F simultaneously equilibriates about the F-H bond length. It can be seen that the products are lower, and hence more stable, in energy than the reactants.

F-H + H is simply the reverse reaction that passes through the same transition state, hence this reaction is endothermic with the products being higher in energy than the reactants. There is an overall gain of energy.

With this information in mind, the F-H bond is more stable and thus stronger than the H-H bond. The main factors to this argument is the greater electronegativity of F leading to a stronger contribution to the bond than the molecular orbitals. Hence the overlap of molecular orbitals is a weaker factor in the bond strength.

[[File:sm6416_FHH_Surface.png|thumb|none|350px|Surface plot highlighting the energetics of the F-H-H system.]]

[[File:sm6416_HHF_Surface.png|thumb|none|350px|Surface plot highlighting the energetics of the H-H-F system.]]

====Transition State====

Discuss Hammond Postulate with TS being closer to products/reactants dependent on how the TS is composed.

The transition state complex is achieved at r1 = F-H = 1.810076 Angstrom and r2 = H-H = 0.74634 Angstrom, as can be seen from the graphs below showing the absence of displacement to either reactants or products.

[[File:sm6416_FHH_Transition_State_Contour.png|thumb|none|350px|Contour plot demonstrating rts as a result of no fluctuations from the initial input, hence the complex is metaphorically sitting on the transition state.]]

[[File:sm6416_FHH_Transition_State_Momenta_Time.png|thumb|none|350px|Momenta vs Time plot demonstrating minimum, and almost zero, momentum at rts.]]

[[File:sm6416_FHH_Transition_State_Surface.png|thumb|none|350px]]

====Activation Energy====

The activation energy for the exothermic reaction was calculated through a 500000 step MEP simulation with input values of r1 = 1.820076, r2 = 0.74634 and p1 = p2 = 0. It was required that after following the minimum energy path, the gradient of the line signifying the reactants was constant.

The activation energy is reported at +0.258 kcal/mol for the exothermic process.

[[File:sm6416_FHH_Activation_Energy_1.png|thumb|none|350px|Energy vs Time graph highlighting the activation energy of the exothermic reaction.]]

The activation energy for the endothermic process was determined with the following parameters: r1 = 1.800076, r2 = 0.74634, p1 = p2 = 0 with 250000 steps. The reported activation energy was +30.277 kcal/mol.

[[File:sm6416_FHH_Activation_Energy_2.png|thumb|none|350px|Energy vs Time graph highlighting the activation energy of the endothermic reaction.]]

It can hence be seen that the exothermic reaction of F + H2 --> F-H + H only requires a small activation energy as the products are substantially more thermodynamically stable than the reactants.

===Reaction Dynamics===

In light of the fact that energy is conserved, '''discuss the mechanism of release of the reaction energy.''' How could this be confirmed experimentally? Measuring energy released from reaction ie exothermicity. Put first one separately. As reach momentum close to boundaries, system passes through transition state but returns to reactant well. Comment on effect the sign of the momentum has on the reactivity.

The following parameters were employed for all simulations rFH = 2.3, rHH = 0.74 with 500 steps calculated.

{| class="wikitable" border=2
! Simulation !! pHH !! pFH !! Surface Plot !! Momenta vs Time Plot !! Observations !!
|-
| 1 || -2.5 || -1.5 || [[File:sm6416_Trajectory_1_Surface.png|thumb|none|350px]] ||[[File:sm6416_Trajectory_1_Momenta.png|thumb|none|350px]] || This trajectory results in a successful reaction as seen from the surface plot; the reactants proceed through the transition state and continue into the product well, whilst continually oscillating as a result of the momentum gained.
|-
| 2 || -0.5 || -0.5 || [[File:sm6416_Trajectory_2_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_2_Momenta.png|thumb|none|350px]] || This momentum does not proceed to a reaction. Through the dynamic animation it can be seen that the HH molecule does not possess enough momentum to translate towards F. Therefore the system does not translate out of the reactant well, as seen in the surface plot, since there is not enough energy to overcome the activation energy. The momenta plot simply shows a small up trend, this is expected due to the long range electrostatic force of attraction between F and HH, resulting in a slight increase in the HH vibration velocity. There is no drastic change in the momenta of either F or HH that would otherwise indicate the occurrence of a reaction, as seen in simulation 1 above.
|-
| 3 || +0.5 || -0.5 || [[File:sm6416_Trajectory_3_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_3_Momenta.png|thumb|none|350px]] || This simulation shows an unreactive path, as can be seen from the surface plot, the system remains in the reactant well as it does not overcome the small activation energy for the exothermic reaction to proceed. As in simulation 2, the momentum amplitude of the oscillating HH remains constant however the overall momenta of the system increases due to a slight translation towards F, thus increasing electrostatic attraction forces resulting in this slight overall momenta increase.
|-
| 4 || -1.6 || -0.5 || [[File:sm6416_Trajectory_4_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_4_Momenta.png|thumb|none|350px]] || This simulation is very similar to simulations 2 & 3 in that the system remains in the reactant well as there is not sufficient energy to overcome the activation energy. However as a result of the greater HH momentum, the oscillation amplitude is greater than both simulation 1 & 2.
|-
| 5 || +1.6 || -0.5 || [[File:sm6416_Trajectory_5_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_5_Momenta.png|thumb|none|350px]] || This simulation is very much like simulation 3, in that the HH momentum is positive. The similarity in the behaviour of the system is also similar, as shown by the surface plot. However, due to the greater momentum, HH translates further away from F than in simulation 3.
|-
| 6 || -2.9 || -0.5 || [[File:sm6416_Trajectory_6_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_6_Momenta.png|thumb|none|350px]] ||
|-
| 7 || +2.9 || -0.5 || [[File:sm6416_Trajectory_7_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_7_Momenta.png|thumb|none|350px]] ||
|-
| 8 || +0.1 || -0.8 || [[File:sm6416_Trajectory_8_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_8_Momenta.png|thumb|none|350px]] ||
|}

====Polyani's Empirical Rules====

Discuss relative translational and vibrational energies required to match the transition state for each endo/exothermic reaction relating to Hammond's postulate.

FH + H reactive trajectory - r1=0.9 r2=2.3 p1=6.5 p2=-1.5

Cite reference

[[File:sm6416_FHH_Reactive_Trajectory_1_Surface.png|thumb|none|350px]]
[[File:sm6416_FHH_Reactive_Trajectory_1_Momenta.png|thumb|none|350px]]
[[File:sm6416_FHH_Reactive_Trajectory_1_Distance.png|thumb|none|350px]]
[[File:sm6416_FHH_Reactive_Trajectory_1_Contour.png|thumb|none|350px]]

MRD:sm6416

2018-05-25T12:20:14Z

Sm6416: /* Locating the Transition State */

==H2 H Exercise 1==

===Transition State Dynamics===

What value do the different components of the gradient of the potential energy surface have at a minimum and at a transition structure? Briefly explain how minima and transition structures can be distinguished using the curvature of the potential energy surface.

Discuss saddle point being the second derivative.
Minimum of trajectory.

===Locating the Transition State===

The transition state was determined through iterations of both r1 and r2 which resulted in the smallest displacement of momenta along with no displacement as shown by the contour plot. This method determined at rts = 0.907743.

[[File:sm6416_Transition_State_Contour.png|thumb|none|350px|Contour plot demonstrating rts = 0.907743 as a result of no fluctuations from the initial input, hence the complex is at the transition state.]]

[[File:sm6416_Transition_State_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating minimum, and almost zero, momentum at rts = 0.907743.]]

[[File:sm6416_Transition_State_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot demonstrating no fluctuations in distance and hence rts = 0.907743.]]

===Reaction Path===

The minimum energy path (MEP) is defined as the lowest path the reaction must follow to form the products and is the downhill motion from the transition state. It can be applied in both directions in the case in question. The MEP views the system as static as it resets the velocity to zero at each step. Whereas the trajectory is very much dynamic and the momenta is accounted for, this is reflected in the vibrational oscillation of the molecule as it passes along the minimum well towards the products.

====MEP====

Initial conditions of r1 = rts + 0.01 = 0.917743, r2 = rts = 0.907743 and p1 = p2 = 0 for the MEP simulation.

[[File:sm6416_MEP_Surface.png|thumb|none|350px|Surface plot highlighting the minimum energy path (MEP), as the reaction returns to the reactants without fully passing through the transition state.]]

[[File:sm6416_MEP_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating zero momentum, as inputted, and more importantly not change in momentum with running the simulation.]]

[[File:sm6416_MEP_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot showing that the reactants reach the transition state at the interception of r1 = r2. r1 quickly reaches a constant value, namely the equilibrium bond length of the reactant molecule. r2 increases logarithmically as time progresses, this represents an increasing distance of Ha from Hb-Hc and a continuing loss of momentum.]]

Final values from the MEP simulation.

r1 = 2.76195

r2 = 0.75883

These values reflect the minimum trajectory for a successful reaction.

p1 = p2 = 0

====Dynamic====

[[File:sm6416_Dynamic_Surface.png|thumb|none|350px|Surface plot highlighting the minimum energy path (MEP) with oscillation of the reactants, as the reaction returns to the reactants without fully passing through the transition state. It is therefore evident that the momentum as a result of the vibrational oscillation does not provide enough energy to proceed to the products.]]

[[File:sm6416_Dynamic_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating the momenta associated with the oscillating reactants.]]

[[File:sm6416_Dynamic_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot showing that the reactants reach the transition state at the interception of r1 = r2. r1 quickly decreases and oscillates about a constant value, namely the equilibrium bond length of the reactant molecule. r2 increases linearly as time progresses, this represents an increasing distance of Ha from Hb-Hc with a constant momentum.]]

Dynamic simulation final values

r1 = 10.0045

r2 = 0.75883

p1 = 2.48523

p2 = 1.29898

p(average) = 1.90409

With r1 = rts and r2 = rts + 0.01 would simply produce the same answer however the values would be flipped to the other distance. In other words r1 = 0.75883 and r2 = 10.0045 would be the output values.

Maintaining the final trajectories as calculated from the dynamic simulation and reversing the sign of the momenta, the reaction proceeds in the reverse direction to the products.

===Reactivity of Trajectories===

These simulations are restricted by the number of steps the program can handle, however a sound understanding of the reaction can be appreciated and the reactivity of each scenario can be determined appropriately.

{| class="wikitable" border=2
! Simulation !! p1 !! p2 !! Energy (kcal/mol) !! Reactivity !! Evidence !! Description
|-
| 1 || -1.25 || -2.5 || 5.03500 || Reactive || [[File:sm6416_MEP_Figure1.png|thumb|none|350px]] || Simulation 1: The reactants proceed through the transition state and to the products. The r2 distance decreases to the equilibrium bond length, whilst r1 simultaneously exhibits dissociation and increases beyond the scope of the graph. The small momenta attributed to the reactants is reflected in the vibrationally oscillating products, with a small amplitude.
|-
| 2 || -1.5 || -2.0 || 3.62879 || Unreactive || [[File:sm6416_MEP_Figure2.png|thumb|none|350px]] || Simulation 2: This is unreactive as the oscillating reactants reach the transition state point and r1 immediately returns to the initial bond length, whilst r2 continues to increase as it moves away from the H2 molecule.
|-
| 3 || -1.5 || -2.5 || 5.13738 || Reactive || [[File:sm6416_MEP_Figure3.png|thumb|none|350px]] || Simulation 3: This simulation shows a reactive pathway that is very similar to simulation 1, however due to the greater momenta associated with the reactants, as inputted, vibrational oscillations with a greater amplitude can be observed.
|-
| 4 || -2.5 || -5.0 || 9.86678 || Unreactive || [[File:sm6416_MEP_Figure4.png|thumb|none|350px]] || Simulation 4: Initially seen here are oscillating reactants with a very large amplitude. However, this simulation is unreactive despite the reactants going through the transition state and towards the product, they return to the initial reactants.
|-
| 5 || -2.5 || -5.2 || 11.80780 || Reactive || [[File:sm6416_MEP_Figure5.png|thumb|none|350px]] || Simulation 5: Like simulation 4, this simulation shows a large oscillating amplitude, whereas in this scenario after passing through the transition state, the products are completely obtained. The slight increase in the p2 momentum can be seen to result in the products.
|}

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? Assumes quasi-equilibrium between reactants and transition state. TST assumes that once reaction passes TS no way back to products. Completely opposite to experimental where it seems as though an equilibrium/reversible path exists between the transition state and products. Fluctuation of whether transition complexes go towards reactants or products are independent of each other.

==F-H-H System Exercise 2==
===Potential Energy Surface Inspection===
====Energetics====

F + H2 is an exothermic reaction as can be seen from the surface plot, the reaction progresses from a small H-H distance to a longer one, whilst H-F simultaneously equilibriates about the F-H bond length. It can be seen that the products are lower, and hence more stable, in energy than the reactants.

F-H + H is simply the reverse reaction that passes through the same transition state, hence this reaction is endothermic with the products being higher in energy than the reactants. There is an overall gain of energy.

With this information in mind, the F-H bond is more stable and thus stronger than the H-H bond. The main factors to this argument is the greater electronegativity of F leading to a stronger contribution to the bond than the molecular orbitals. Hence the overlap of molecular orbitals is a weaker factor in the bond strength.

[[File:sm6416_FHH_Surface.png|thumb|none|350px|Surface plot highlighting the energetics of the F-H-H system.]]

[[File:sm6416_HHF_Surface.png|thumb|none|350px|Surface plot highlighting the energetics of the H-H-F system.]]

====Transition State====

Discuss Hammond Postulate with TS being closer to products/reactants dependent on how the TS is composed.

The transition state complex is achieved at r1 = F-H = 1.810076 Angstrom and r2 = H-H = 0.74634 Angstrom, as can be seen from the graphs below showing the absence of displacement to either reactants or products.

[[File:sm6416_FHH_Transition_State_Contour.png|thumb|none|350px|Contour plot demonstrating rts as a result of no fluctuations from the initial input, hence the complex is metaphorically sitting on the transition state.]]

[[File:sm6416_FHH_Transition_State_Momenta_Time.png|thumb|none|350px|Momenta vs Time plot demonstrating minimum, and almost zero, momentum at rts.]]

[[File:sm6416_FHH_Transition_State_Surface.png|thumb|none|350px]]

====Activation Energy====

The activation energy for the exothermic reaction was calculated through a 500000 step MEP simulation with input values of r1 = 1.820076, r2 = 0.74634 and p1 = p2 = 0. It was required that after following the minimum energy path, the gradient of the line signifying the reactants was constant.

The activation energy is reported at +0.258 kcal/mol for the exothermic process.

[[File:sm6416_FHH_Activation_Energy_1.png|thumb|none|350px|Energy vs Time graph highlighting the activation energy of the exothermic reaction.]]

The activation energy for the endothermic process was determined with the following parameters: r1 = 1.800076, r2 = 0.74634, p1 = p2 = 0 with 250000 steps. The reported activation energy was +30.277 kcal/mol.

[[File:sm6416_FHH_Activation_Energy_2.png|thumb|none|350px|Energy vs Time graph highlighting the activation energy of the endothermic reaction.]]

It can hence be seen that the exothermic reaction of F + H2 --> F-H + H only requires a small activation energy as the products are substantially more thermodynamically stable than the reactants.

===Reaction Dynamics===

In light of the fact that energy is conserved, '''discuss the mechanism of release of the reaction energy.''' How could this be confirmed experimentally? Measuring energy released from reaction ie exothermicity. Put first one separately. As reach momentum close to boundaries, system passes through transition state but returns to reactant well. Comment on effect the sign of the momentum has on the reactivity.

The following parameters were employed for all simulations rFH = 2.3, rHH = 0.74 with 500 steps calculated.

{| class="wikitable" border=2
! Simulation !! pHH !! pFH !! Surface Plot !! Momenta vs Time Plot !! Observations !!
|-
| 1 || -2.5 || -1.5 || [[File:sm6416_Trajectory_1_Surface.png|thumb|none|350px]] ||[[File:sm6416_Trajectory_1_Momenta.png|thumb|none|350px]] || This trajectory results in a successful reaction as seen from the surface plot; the reactants proceed through the transition state and continue into the product well, whilst continually oscillating as a result of the momentum gained.
|-
| 2 || -0.5 || -0.5 || [[File:sm6416_Trajectory_2_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_2_Momenta.png|thumb|none|350px]] || This momentum does not proceed to a reaction. Through the dynamic animation it can be seen that the HH molecule does not possess enough momentum to translate towards F. Therefore the system does not translate out of the reactant well, as seen in the surface plot, since there is not enough energy to overcome the activation energy. The momenta plot simply shows a small up trend, this is expected due to the long range electrostatic force of attraction between F and HH, resulting in a slight increase in the HH vibration velocity. There is no drastic change in the momenta of either F or HH that would otherwise indicate the occurrence of a reaction, as seen in simulation 1 above.
|-
| 3 || +0.5 || -0.5 || [[File:sm6416_Trajectory_3_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_3_Momenta.png|thumb|none|350px]] || This simulation shows an unreactive path, as can be seen from the surface plot, the system remains in the reactant well as it does not overcome the small activation energy for the exothermic reaction to proceed. As in simulation 2, the momentum amplitude of the oscillating HH remains constant however the overall momenta of the system increases due to a slight translation towards F, thus increasing electrostatic attraction forces resulting in this slight overall momenta increase.
|-
| 4 || -1.6 || -0.5 || [[File:sm6416_Trajectory_4_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_4_Momenta.png|thumb|none|350px]] || The HH molecule in this simulation does possess sufficient momentum to translate towards F and result in a reaction. Evidence for this is both shown by the progression from the reactant to product well in the surface plot along with a drastic change in momentum of A-B (signifying F-H) shown by the momenta vs time plot, highlighting the high momentum oscillation, as expected from the heavier F atom.
|-
| 5 || +1.6 || -0.5 || [[File:sm6416_Trajectory_5_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_5_Momenta.png|thumb|none|350px]] || This simulation is very much like simulation 3, in that the HH momentum is positive. The similarity in the behaviour of the system is also similar, as shown by the surface plot. However, due to the greater momentum, HH translates further away from F than in simulation 3.
|-
| 6 || -2.9 || -0.5 || [[File:sm6416_Trajectory_6_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_6_Momenta.png|thumb|none|350px]] ||
|-
| 7 || +2.9 || -0.5 || [[File:sm6416_Trajectory_7_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_7_Momenta.png|thumb|none|350px]] ||
|-
| 8 || +0.1 || -0.8 || [[File:sm6416_Trajectory_8_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_8_Momenta.png|thumb|none|350px]] ||
|}

====Polyani's Empirical Rules====

Discuss relative translational and vibrational energies required to match the transition state for each endo/exothermic reaction relating to Hammond's postulate.

FH + H reactive trajectory - r1=0.9 r2=2.3 p1=6.5 p2=-1.5

Cite reference

[[File:sm6416_FHH_Reactive_Trajectory_1_Surface.png|thumb|none|350px]]
[[File:sm6416_FHH_Reactive_Trajectory_1_Momenta.png|thumb|none|350px]]
[[File:sm6416_FHH_Reactive_Trajectory_1_Distance.png|thumb|none|350px]]
[[File:sm6416_FHH_Reactive_Trajectory_1_Contour.png|thumb|none|350px]]

MRD:sm6416

2018-05-25T12:18:34Z

Sm6416: /* Reaction Dynamics */

==H2 H Exercise 1==

===Transition State Dynamics===

What value do the different components of the gradient of the potential energy surface have at a minimum and at a transition structure? Briefly explain how minima and transition structures can be distinguished using the curvature of the potential energy surface.

Discuss saddle point being the second derivative.
Minimum of trajectory.

===Locating the Transition State===

The transition state was determined through iterations of both r1 and r2 which resulted in the smallest displacement of momenta along with no displacement as shown by the contour plot. This method determined at rts = 0.907743.

[[File:sm6416_Transition_State_Contour.png|thumb|none|350px|Contour plot demonstrating rts = 0.907743 as a result of no fluctuations from the initial input, hence the complex is metaphorically sitting on the transition state.]]

[[File:sm6416_Transition_State_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating minimum, and almost zero, momentum at rts = 0.907743.]]

[[File:sm6416_Transition_State_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot demonstrating no fluctuations in distance and hence rts = 0.907743.]]

===Reaction Path===

The minimum energy path (MEP) is defined as the lowest path the reaction must follow to form the products and is the downhill motion from the transition state. It can be applied in both directions in the case in question. The MEP views the system as static as it resets the velocity to zero at each step. Whereas the trajectory is very much dynamic and the momenta is accounted for, this is reflected in the vibrational oscillation of the molecule as it passes along the minimum well towards the products.

====MEP====

Initial conditions of r1 = rts + 0.01 = 0.917743, r2 = rts = 0.907743 and p1 = p2 = 0 for the MEP simulation.

[[File:sm6416_MEP_Surface.png|thumb|none|350px|Surface plot highlighting the minimum energy path (MEP), as the reaction returns to the reactants without fully passing through the transition state.]]

[[File:sm6416_MEP_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating zero momentum, as inputted, and more importantly not change in momentum with running the simulation.]]

[[File:sm6416_MEP_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot showing that the reactants reach the transition state at the interception of r1 = r2. r1 quickly reaches a constant value, namely the equilibrium bond length of the reactant molecule. r2 increases logarithmically as time progresses, this represents an increasing distance of Ha from Hb-Hc and a continuing loss of momentum.]]

Final values from the MEP simulation.

r1 = 2.76195

r2 = 0.75883

These values reflect the minimum trajectory for a successful reaction.

p1 = p2 = 0

====Dynamic====

[[File:sm6416_Dynamic_Surface.png|thumb|none|350px|Surface plot highlighting the minimum energy path (MEP) with oscillation of the reactants, as the reaction returns to the reactants without fully passing through the transition state. It is therefore evident that the momentum as a result of the vibrational oscillation does not provide enough energy to proceed to the products.]]

[[File:sm6416_Dynamic_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating the momenta associated with the oscillating reactants.]]

[[File:sm6416_Dynamic_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot showing that the reactants reach the transition state at the interception of r1 = r2. r1 quickly decreases and oscillates about a constant value, namely the equilibrium bond length of the reactant molecule. r2 increases linearly as time progresses, this represents an increasing distance of Ha from Hb-Hc with a constant momentum.]]

Dynamic simulation final values

r1 = 10.0045

r2 = 0.75883

p1 = 2.48523

p2 = 1.29898

p(average) = 1.90409

With r1 = rts and r2 = rts + 0.01 would simply produce the same answer however the values would be flipped to the other distance. In other words r1 = 0.75883 and r2 = 10.0045 would be the output values.

Maintaining the final trajectories as calculated from the dynamic simulation and reversing the sign of the momenta, the reaction proceeds in the reverse direction to the products.

===Reactivity of Trajectories===

These simulations are restricted by the number of steps the program can handle, however a sound understanding of the reaction can be appreciated and the reactivity of each scenario can be determined appropriately.

{| class="wikitable" border=2
! Simulation !! p1 !! p2 !! Energy (kcal/mol) !! Reactivity !! Evidence !! Description
|-
| 1 || -1.25 || -2.5 || 5.03500 || Reactive || [[File:sm6416_MEP_Figure1.png|thumb|none|350px]] || Simulation 1: The reactants proceed through the transition state and to the products. The r2 distance decreases to the equilibrium bond length, whilst r1 simultaneously exhibits dissociation and increases beyond the scope of the graph. The small momenta attributed to the reactants is reflected in the vibrationally oscillating products, with a small amplitude.
|-
| 2 || -1.5 || -2.0 || 3.62879 || Unreactive || [[File:sm6416_MEP_Figure2.png|thumb|none|350px]] || Simulation 2: This is unreactive as the oscillating reactants reach the transition state point and r1 immediately returns to the initial bond length, whilst r2 continues to increase as it moves away from the H2 molecule.
|-
| 3 || -1.5 || -2.5 || 5.13738 || Reactive || [[File:sm6416_MEP_Figure3.png|thumb|none|350px]] || Simulation 3: This simulation shows a reactive pathway that is very similar to simulation 1, however due to the greater momenta associated with the reactants, as inputted, vibrational oscillations with a greater amplitude can be observed.
|-
| 4 || -2.5 || -5.0 || 9.86678 || Unreactive || [[File:sm6416_MEP_Figure4.png|thumb|none|350px]] || Simulation 4: Initially seen here are oscillating reactants with a very large amplitude. However, this simulation is unreactive despite the reactants going through the transition state and towards the product, they return to the initial reactants.
|-
| 5 || -2.5 || -5.2 || 11.80780 || Reactive || [[File:sm6416_MEP_Figure5.png|thumb|none|350px]] || Simulation 5: Like simulation 4, this simulation shows a large oscillating amplitude, whereas in this scenario after passing through the transition state, the products are completely obtained. The slight increase in the p2 momentum can be seen to result in the products.
|}

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? Assumes quasi-equilibrium between reactants and transition state. TST assumes that once reaction passes TS no way back to products. Completely opposite to experimental where it seems as though an equilibrium/reversible path exists between the transition state and products. Fluctuation of whether transition complexes go towards reactants or products are independent of each other.

==F-H-H System Exercise 2==
===Potential Energy Surface Inspection===
====Energetics====

F + H2 is an exothermic reaction as can be seen from the surface plot, the reaction progresses from a small H-H distance to a longer one, whilst H-F simultaneously equilibriates about the F-H bond length. It can be seen that the products are lower, and hence more stable, in energy than the reactants.

F-H + H is simply the reverse reaction that passes through the same transition state, hence this reaction is endothermic with the products being higher in energy than the reactants. There is an overall gain of energy.

With this information in mind, the F-H bond is more stable and thus stronger than the H-H bond. The main factors to this argument is the greater electronegativity of F leading to a stronger contribution to the bond than the molecular orbitals. Hence the overlap of molecular orbitals is a weaker factor in the bond strength.

[[File:sm6416_FHH_Surface.png|thumb|none|350px|Surface plot highlighting the energetics of the F-H-H system.]]

[[File:sm6416_HHF_Surface.png|thumb|none|350px|Surface plot highlighting the energetics of the H-H-F system.]]

====Transition State====

Discuss Hammond Postulate with TS being closer to products/reactants dependent on how the TS is composed.

The transition state complex is achieved at r1 = F-H = 1.810076 Angstrom and r2 = H-H = 0.74634 Angstrom, as can be seen from the graphs below showing the absence of displacement to either reactants or products.

[[File:sm6416_FHH_Transition_State_Contour.png|thumb|none|350px|Contour plot demonstrating rts as a result of no fluctuations from the initial input, hence the complex is metaphorically sitting on the transition state.]]

[[File:sm6416_FHH_Transition_State_Momenta_Time.png|thumb|none|350px|Momenta vs Time plot demonstrating minimum, and almost zero, momentum at rts.]]

[[File:sm6416_FHH_Transition_State_Surface.png|thumb|none|350px]]

====Activation Energy====

The activation energy for the exothermic reaction was calculated through a 500000 step MEP simulation with input values of r1 = 1.820076, r2 = 0.74634 and p1 = p2 = 0. It was required that after following the minimum energy path, the gradient of the line signifying the reactants was constant.

The activation energy is reported at +0.258 kcal/mol for the exothermic process.

[[File:sm6416_FHH_Activation_Energy_1.png|thumb|none|350px|Energy vs Time graph highlighting the activation energy of the exothermic reaction.]]

The activation energy for the endothermic process was determined with the following parameters: r1 = 1.800076, r2 = 0.74634, p1 = p2 = 0 with 250000 steps. The reported activation energy was +30.277 kcal/mol.

[[File:sm6416_FHH_Activation_Energy_2.png|thumb|none|350px|Energy vs Time graph highlighting the activation energy of the endothermic reaction.]]

It can hence be seen that the exothermic reaction of F + H2 --> F-H + H only requires a small activation energy as the products are substantially more thermodynamically stable than the reactants.

===Reaction Dynamics===

In light of the fact that energy is conserved, '''discuss the mechanism of release of the reaction energy.''' How could this be confirmed experimentally? Measuring energy released from reaction ie exothermicity. Put first one separately. As reach momentum close to boundaries, system passes through transition state but returns to reactant well. Comment on effect the sign of the momentum has on the reactivity.

The following parameters were employed for all simulations rFH = 2.3, rHH = 0.74 with 500 steps calculated.

{| class="wikitable" border=2
! Simulation !! pHH !! pFH !! Surface Plot !! Momenta vs Time Plot !! Observations !!
|-
| 1 || -2.5 || -1.5 || [[File:sm6416_Trajectory_1_Surface.png|thumb|none|350px]] ||[[File:sm6416_Trajectory_1_Momenta.png|thumb|none|350px]] || This trajectory results in a successful reaction as seen from the surface plot; the reactants proceed through the transition state and continue into the product well, whilst continually oscillating as a result of the momentum gained.
|-
| 2 || -0.5 || -0.5 || [[File:sm6416_Trajectory_2_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_2_Momenta.png|thumb|none|350px]] || This momentum does not proceed to a reaction. Through the dynamic animation it can be seen that the HH molecule does not possess enough momentum to translate towards F. Therefore the system does not translate out of the reactant well, as seen in the surface plot, since there is not enough energy to overcome the activation energy. The momenta plot simply shows a small up trend, this is expected due to the long range electrostatic force of attraction between F and HH, resulting in a slight increase in the HH vibration velocity. There is no drastic change in the momenta of either F or HH that would otherwise indicate the occurrence of a reaction, as seen in simulation 1 above.
|-
| 3 || +0.5 || -0.5 || [[File:sm6416_Trajectory_3_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_3_Momenta.png|thumb|none|350px]] || This simulation shows an unreactive path, as can be seen from the surface plot, the system remains in the reactant well as it does not overcome the small activation energy for the exothermic reaction to proceed. As in simulation 2, the momentum amplitude of the oscillating HH remains constant however the overall momenta of the system increases due to a slight translation towards F, thus increasing electrostatic attraction forces resulting in this slight overall momenta increase.
|-
| 4 || -1.6 || -0.5 || [[File:sm6416_Trajectory_4_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_4_Momenta.png|thumb|none|350px]] || The HH molecule in this simulation does possess sufficient momentum to translate towards F and result in a reaction. Evidence for this is both shown by the progression from the reactant to product well in the surface plot along with a drastic change in momentum of A-B (signifying F-H) shown by the momenta vs time plot, highlighting the high momentum oscillation, as expected from the heavier F atom.
|-
| 5 || +1.6 || -0.5 || [[File:sm6416_Trajectory_5_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_5_Momenta.png|thumb|none|350px]] || This simulation is very much like simulation 3, in that the HH momentum is positive. The similarity in the behaviour of the system is also similar, as shown by the surface plot. However, due to the greater momentum, HH translates further away from F than in simulation 3.
|-
| 6 || -2.9 || -0.5 || [[File:sm6416_Trajectory_6_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_6_Momenta.png|thumb|none|350px]] ||
|-
| 7 || +2.9 || -0.5 || [[File:sm6416_Trajectory_7_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_7_Momenta.png|thumb|none|350px]] ||
|-
| 8 || +0.1 || -0.8 || [[File:sm6416_Trajectory_8_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_8_Momenta.png|thumb|none|350px]] ||
|}

====Polyani's Empirical Rules====

Discuss relative translational and vibrational energies required to match the transition state for each endo/exothermic reaction relating to Hammond's postulate.

FH + H reactive trajectory - r1=0.9 r2=2.3 p1=6.5 p2=-1.5

Cite reference

[[File:sm6416_FHH_Reactive_Trajectory_1_Surface.png|thumb|none|350px]]
[[File:sm6416_FHH_Reactive_Trajectory_1_Momenta.png|thumb|none|350px]]
[[File:sm6416_FHH_Reactive_Trajectory_1_Distance.png|thumb|none|350px]]
[[File:sm6416_FHH_Reactive_Trajectory_1_Contour.png|thumb|none|350px]]

MRD:sm6416

2018-05-25T12:07:05Z

Sm6416: /* Reaction Dynamics */

==H2 H Exercise 1==

===Transition State Dynamics===

What value do the different components of the gradient of the potential energy surface have at a minimum and at a transition structure? Briefly explain how minima and transition structures can be distinguished using the curvature of the potential energy surface.

Discuss saddle point being the second derivative.
Minimum of trajectory.

===Locating the Transition State===

The transition state was determined through iterations of both r1 and r2 which resulted in the smallest displacement of momenta along with no displacement as shown by the contour plot. This method determined at rts = 0.907743.

[[File:sm6416_Transition_State_Contour.png|thumb|none|350px|Contour plot demonstrating rts = 0.907743 as a result of no fluctuations from the initial input, hence the complex is metaphorically sitting on the transition state.]]

[[File:sm6416_Transition_State_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating minimum, and almost zero, momentum at rts = 0.907743.]]

[[File:sm6416_Transition_State_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot demonstrating no fluctuations in distance and hence rts = 0.907743.]]

===Reaction Path===

The minimum energy path (MEP) is defined as the lowest path the reaction must follow to form the products and is the downhill motion from the transition state. It can be applied in both directions in the case in question. The MEP views the system as static as it resets the velocity to zero at each step. Whereas the trajectory is very much dynamic and the momenta is accounted for, this is reflected in the vibrational oscillation of the molecule as it passes along the minimum well towards the products.

====MEP====

Initial conditions of r1 = rts + 0.01 = 0.917743, r2 = rts = 0.907743 and p1 = p2 = 0 for the MEP simulation.

[[File:sm6416_MEP_Surface.png|thumb|none|350px|Surface plot highlighting the minimum energy path (MEP), as the reaction returns to the reactants without fully passing through the transition state.]]

[[File:sm6416_MEP_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating zero momentum, as inputted, and more importantly not change in momentum with running the simulation.]]

[[File:sm6416_MEP_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot showing that the reactants reach the transition state at the interception of r1 = r2. r1 quickly reaches a constant value, namely the equilibrium bond length of the reactant molecule. r2 increases logarithmically as time progresses, this represents an increasing distance of Ha from Hb-Hc and a continuing loss of momentum.]]

Final values from the MEP simulation.

r1 = 2.76195

r2 = 0.75883

These values reflect the minimum trajectory for a successful reaction.

p1 = p2 = 0

====Dynamic====

[[File:sm6416_Dynamic_Surface.png|thumb|none|350px|Surface plot highlighting the minimum energy path (MEP) with oscillation of the reactants, as the reaction returns to the reactants without fully passing through the transition state. It is therefore evident that the momentum as a result of the vibrational oscillation does not provide enough energy to proceed to the products.]]

[[File:sm6416_Dynamic_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating the momenta associated with the oscillating reactants.]]

[[File:sm6416_Dynamic_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot showing that the reactants reach the transition state at the interception of r1 = r2. r1 quickly decreases and oscillates about a constant value, namely the equilibrium bond length of the reactant molecule. r2 increases linearly as time progresses, this represents an increasing distance of Ha from Hb-Hc with a constant momentum.]]

Dynamic simulation final values

r1 = 10.0045

r2 = 0.75883

p1 = 2.48523

p2 = 1.29898

p(average) = 1.90409

With r1 = rts and r2 = rts + 0.01 would simply produce the same answer however the values would be flipped to the other distance. In other words r1 = 0.75883 and r2 = 10.0045 would be the output values.

Maintaining the final trajectories as calculated from the dynamic simulation and reversing the sign of the momenta, the reaction proceeds in the reverse direction to the products.

===Reactivity of Trajectories===

These simulations are restricted by the number of steps the program can handle, however a sound understanding of the reaction can be appreciated and the reactivity of each scenario can be determined appropriately.

{| class="wikitable" border=2
! Simulation !! p1 !! p2 !! Energy (kcal/mol) !! Reactivity !! Evidence !! Description
|-
| 1 || -1.25 || -2.5 || 5.03500 || Reactive || [[File:sm6416_MEP_Figure1.png|thumb|none|350px]] || Simulation 1: The reactants proceed through the transition state and to the products. The r2 distance decreases to the equilibrium bond length, whilst r1 simultaneously exhibits dissociation and increases beyond the scope of the graph. The small momenta attributed to the reactants is reflected in the vibrationally oscillating products, with a small amplitude.
|-
| 2 || -1.5 || -2.0 || 3.62879 || Unreactive || [[File:sm6416_MEP_Figure2.png|thumb|none|350px]] || Simulation 2: This is unreactive as the oscillating reactants reach the transition state point and r1 immediately returns to the initial bond length, whilst r2 continues to increase as it moves away from the H2 molecule.
|-
| 3 || -1.5 || -2.5 || 5.13738 || Reactive || [[File:sm6416_MEP_Figure3.png|thumb|none|350px]] || Simulation 3: This simulation shows a reactive pathway that is very similar to simulation 1, however due to the greater momenta associated with the reactants, as inputted, vibrational oscillations with a greater amplitude can be observed.
|-
| 4 || -2.5 || -5.0 || 9.86678 || Unreactive || [[File:sm6416_MEP_Figure4.png|thumb|none|350px]] || Simulation 4: Initially seen here are oscillating reactants with a very large amplitude. However, this simulation is unreactive despite the reactants going through the transition state and towards the product, they return to the initial reactants.
|-
| 5 || -2.5 || -5.2 || 11.80780 || Reactive || [[File:sm6416_MEP_Figure5.png|thumb|none|350px]] || Simulation 5: Like simulation 4, this simulation shows a large oscillating amplitude, whereas in this scenario after passing through the transition state, the products are completely obtained. The slight increase in the p2 momentum can be seen to result in the products.
|}

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? Assumes quasi-equilibrium between reactants and transition state. TST assumes that once reaction passes TS no way back to products. Completely opposite to experimental where it seems as though an equilibrium/reversible path exists between the transition state and products. Fluctuation of whether transition complexes go towards reactants or products are independent of each other.

==F-H-H System Exercise 2==
===Potential Energy Surface Inspection===
====Energetics====

F + H2 is an exothermic reaction as can be seen from the surface plot, the reaction progresses from a small H-H distance to a longer one, whilst H-F simultaneously equilibriates about the F-H bond length. It can be seen that the products are lower, and hence more stable, in energy than the reactants.

F-H + H is simply the reverse reaction that passes through the same transition state, hence this reaction is endothermic with the products being higher in energy than the reactants. There is an overall gain of energy.

With this information in mind, the F-H bond is more stable and thus stronger than the H-H bond. The main factors to this argument is the greater electronegativity of F leading to a stronger contribution to the bond than the molecular orbitals. Hence the overlap of molecular orbitals is a weaker factor in the bond strength.

[[File:sm6416_FHH_Surface.png|thumb|none|350px|Surface plot highlighting the energetics of the F-H-H system.]]

[[File:sm6416_HHF_Surface.png|thumb|none|350px|Surface plot highlighting the energetics of the H-H-F system.]]

====Transition State====

Discuss Hammond Postulate with TS being closer to products/reactants dependent on how the TS is composed.

The transition state complex is achieved at r1 = F-H = 1.810076 Angstrom and r2 = H-H = 0.74634 Angstrom, as can be seen from the graphs below showing the absence of displacement to either reactants or products.

[[File:sm6416_FHH_Transition_State_Contour.png|thumb|none|350px|Contour plot demonstrating rts as a result of no fluctuations from the initial input, hence the complex is metaphorically sitting on the transition state.]]

[[File:sm6416_FHH_Transition_State_Momenta_Time.png|thumb|none|350px|Momenta vs Time plot demonstrating minimum, and almost zero, momentum at rts.]]

[[File:sm6416_FHH_Transition_State_Surface.png|thumb|none|350px]]

====Activation Energy====

The activation energy for the exothermic reaction was calculated through a 500000 step MEP simulation with input values of r1 = 1.820076, r2 = 0.74634 and p1 = p2 = 0. It was required that after following the minimum energy path, the gradient of the line signifying the reactants was constant.

The activation energy is reported at +0.258 kcal/mol for the exothermic process.

[[File:sm6416_FHH_Activation_Energy_1.png|thumb|none|350px|Energy vs Time graph highlighting the activation energy of the exothermic reaction.]]

The activation energy for the endothermic process was determined with the following parameters: r1 = 1.800076, r2 = 0.74634, p1 = p2 = 0 with 250000 steps. The reported activation energy was +30.277 kcal/mol.

[[File:sm6416_FHH_Activation_Energy_2.png|thumb|none|350px|Energy vs Time graph highlighting the activation energy of the endothermic reaction.]]

It can hence be seen that the exothermic reaction of F + H2 --> F-H + H only requires a small activation energy as the products are substantially more thermodynamically stable than the reactants.

===Reaction Dynamics===

In light of the fact that energy is conserved, '''discuss the mechanism of release of the reaction energy.''' How could this be confirmed experimentally? Measuring energy released from reaction ie exothermicity. Put first one separately. As reach momentum close to boundaries, system passes through transition state but returns to reactant well. Comment on effect the sign of the momentum has on the reactivity.

r1 = 2.3, r2 = 0.74

{| class="wikitable" border=2
! Simulation !! pHH !! pFH !! Surface Plot !! Momenta vs Time Plot !! Observations !!
|-
| 1 || -2.5 || -1.5 || [[File:sm6416_Trajectory_1_Surface.png|thumb|none|350px]] ||[[File:sm6416_Trajectory_1_Momenta.png|thumb|none|350px]] || This trajectory results in a successful reaction as seen from the surface plot; the reactants proceed through the transition state and continue into the product well, whilst continually oscillating as a result of the momentum gained.
|-
| 2 || -0.5 || -0.5 || [[File:sm6416_Trajectory_2_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_2_Momenta.png|thumb|none|350px]] || This momentum does not proceed to a reaction. Through the dynamic animation it can be seen that the HH molecule does not possess enough momentum to translate towards F. Therefore the system does not translate out of the reactant well, as seen in the surface plot, since there is not enough energy to overcome the activation energy. The momenta plot simply shows a small up trend, this is expected due to the long range electrostatic force of attraction between F and HH, resulting in a slight increase in the HH vibration velocity. There is no drastic change in the momenta of either F or HH that would otherwise indicate the occurrence of a reaction, as seen in simulation 1 above.
|-
| 3 || +0.5 || -0.5 || [[File:sm6416_Trajectory_3_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_3_Momenta.png|thumb|none|350px]] || This simulation has a positive momentum and therefore the HH molecule translates away from F, as can be seen from the surface plot. There is a slight overall increase in momenta, however not large enough to be of importance. This simulation does not lead to a reaction.
|-
| 4 || -1.6 || -0.5 || [[File:sm6416_Trajectory_4_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_4_Momenta.png|thumb|none|350px]] || The HH molecule in this simulation does possess sufficient momentum to translate towards F and result in a reaction. Evidence for this is both shown by the progression from the reactant to product well in the surface plot along with a drastic change in momentum of A-B (signifying F-H) shown by the momenta vs time plot, highlighting the high momentum oscillation, as expected from the heavier F atom.
|-
| 5 || +1.6 || -0.5 || [[File:sm6416_Trajectory_5_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_5_Momenta.png|thumb|none|350px]] || This simulation is very much like simulation 3, in that the HH momentum is positive. The similarity in the behaviour of the system is also similar, as shown by the surface plot. However, due to the greater momentum, HH translates further away from F than in simulation 3.
|-
| 6 || -2.9 || -0.5 || [[File:sm6416_Trajectory_6_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_6_Momenta.png|thumb|none|350px]] ||
|-
| 7 || +2.9 || -0.5 || [[File:sm6416_Trajectory_7_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_7_Momenta.png|thumb|none|350px]] ||
|-
| 8 || +0.1 || -0.8 || [[File:sm6416_Trajectory_8_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_8_Momenta.png|thumb|none|350px]] ||
|}

====Polyani's Empirical Rules====

Discuss relative translational and vibrational energies required to match the transition state for each endo/exothermic reaction relating to Hammond's postulate.

FH + H reactive trajectory - r1=0.9 r2=2.3 p1=6.5 p2=-1.5

Cite reference

[[File:sm6416_FHH_Reactive_Trajectory_1_Surface.png|thumb|none|350px]]
[[File:sm6416_FHH_Reactive_Trajectory_1_Momenta.png|thumb|none|350px]]
[[File:sm6416_FHH_Reactive_Trajectory_1_Distance.png|thumb|none|350px]]
[[File:sm6416_FHH_Reactive_Trajectory_1_Contour.png|thumb|none|350px]]

MRD:sm6416

2018-05-25T11:56:22Z

Sm6416: /* Reaction Dynamics */

==H2 H Exercise 1==

===Transition State Dynamics===

What value do the different components of the gradient of the potential energy surface have at a minimum and at a transition structure? Briefly explain how minima and transition structures can be distinguished using the curvature of the potential energy surface.

Discuss saddle point being the second derivative.
Minimum of trajectory.

===Locating the Transition State===

The transition state was determined through iterations of both r1 and r2 which resulted in the smallest displacement of momenta along with no displacement as shown by the contour plot. This method determined at rts = 0.907743.

[[File:sm6416_Transition_State_Contour.png|thumb|none|350px|Contour plot demonstrating rts = 0.907743 as a result of no fluctuations from the initial input, hence the complex is metaphorically sitting on the transition state.]]

[[File:sm6416_Transition_State_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating minimum, and almost zero, momentum at rts = 0.907743.]]

[[File:sm6416_Transition_State_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot demonstrating no fluctuations in distance and hence rts = 0.907743.]]

===Reaction Path===

The minimum energy path (MEP) is defined as the lowest path the reaction must follow to form the products and is the downhill motion from the transition state. It can be applied in both directions in the case in question. The MEP views the system as static as it resets the velocity to zero at each step. Whereas the trajectory is very much dynamic and the momenta is accounted for, this is reflected in the vibrational oscillation of the molecule as it passes along the minimum well towards the products.

====MEP====

Initial conditions of r1 = rts + 0.01 = 0.917743, r2 = rts = 0.907743 and p1 = p2 = 0 for the MEP simulation.

[[File:sm6416_MEP_Surface.png|thumb|none|350px|Surface plot highlighting the minimum energy path (MEP), as the reaction returns to the reactants without fully passing through the transition state.]]

[[File:sm6416_MEP_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating zero momentum, as inputted, and more importantly not change in momentum with running the simulation.]]

[[File:sm6416_MEP_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot showing that the reactants reach the transition state at the interception of r1 = r2. r1 quickly reaches a constant value, namely the equilibrium bond length of the reactant molecule. r2 increases logarithmically as time progresses, this represents an increasing distance of Ha from Hb-Hc and a continuing loss of momentum.]]

Final values from the MEP simulation.

r1 = 2.76195

r2 = 0.75883

These values reflect the minimum trajectory for a successful reaction.

p1 = p2 = 0

====Dynamic====

[[File:sm6416_Dynamic_Surface.png|thumb|none|350px|Surface plot highlighting the minimum energy path (MEP) with oscillation of the reactants, as the reaction returns to the reactants without fully passing through the transition state. It is therefore evident that the momentum as a result of the vibrational oscillation does not provide enough energy to proceed to the products.]]

[[File:sm6416_Dynamic_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating the momenta associated with the oscillating reactants.]]

[[File:sm6416_Dynamic_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot showing that the reactants reach the transition state at the interception of r1 = r2. r1 quickly decreases and oscillates about a constant value, namely the equilibrium bond length of the reactant molecule. r2 increases linearly as time progresses, this represents an increasing distance of Ha from Hb-Hc with a constant momentum.]]

Dynamic simulation final values

r1 = 10.0045

r2 = 0.75883

p1 = 2.48523

p2 = 1.29898

p(average) = 1.90409

With r1 = rts and r2 = rts + 0.01 would simply produce the same answer however the values would be flipped to the other distance. In other words r1 = 0.75883 and r2 = 10.0045 would be the output values.

Maintaining the final trajectories as calculated from the dynamic simulation and reversing the sign of the momenta, the reaction proceeds in the reverse direction to the products.

===Reactivity of Trajectories===

These simulations are restricted by the number of steps the program can handle, however a sound understanding of the reaction can be appreciated and the reactivity of each scenario can be determined appropriately.

{| class="wikitable" border=2
! Simulation !! p1 !! p2 !! Energy (kcal/mol) !! Reactivity !! Evidence !! Description
|-
| 1 || -1.25 || -2.5 || 5.03500 || Reactive || [[File:sm6416_MEP_Figure1.png|thumb|none|350px]] || Simulation 1: The reactants proceed through the transition state and to the products. The r2 distance decreases to the equilibrium bond length, whilst r1 simultaneously exhibits dissociation and increases beyond the scope of the graph. The small momenta attributed to the reactants is reflected in the vibrationally oscillating products, with a small amplitude.
|-
| 2 || -1.5 || -2.0 || 3.62879 || Unreactive || [[File:sm6416_MEP_Figure2.png|thumb|none|350px]] || Simulation 2: This is unreactive as the oscillating reactants reach the transition state point and r1 immediately returns to the initial bond length, whilst r2 continues to increase as it moves away from the H2 molecule.
|-
| 3 || -1.5 || -2.5 || 5.13738 || Reactive || [[File:sm6416_MEP_Figure3.png|thumb|none|350px]] || Simulation 3: This simulation shows a reactive pathway that is very similar to simulation 1, however due to the greater momenta associated with the reactants, as inputted, vibrational oscillations with a greater amplitude can be observed.
|-
| 4 || -2.5 || -5.0 || 9.86678 || Unreactive || [[File:sm6416_MEP_Figure4.png|thumb|none|350px]] || Simulation 4: Initially seen here are oscillating reactants with a very large amplitude. However, this simulation is unreactive despite the reactants going through the transition state and towards the product, they return to the initial reactants.
|-
| 5 || -2.5 || -5.2 || 11.80780 || Reactive || [[File:sm6416_MEP_Figure5.png|thumb|none|350px]] || Simulation 5: Like simulation 4, this simulation shows a large oscillating amplitude, whereas in this scenario after passing through the transition state, the products are completely obtained. The slight increase in the p2 momentum can be seen to result in the products.
|}

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? Assumes quasi-equilibrium between reactants and transition state. TST assumes that once reaction passes TS no way back to products. Completely opposite to experimental where it seems as though an equilibrium/reversible path exists between the transition state and products. Fluctuation of whether transition complexes go towards reactants or products are independent of each other.

==F-H-H System Exercise 2==
===Potential Energy Surface Inspection===
====Energetics====

F + H2 is an exothermic reaction as can be seen from the surface plot, the reaction progresses from a small H-H distance to a longer one, whilst H-F simultaneously equilibriates about the F-H bond length. It can be seen that the products are lower, and hence more stable, in energy than the reactants.

F-H + H is simply the reverse reaction that passes through the same transition state, hence this reaction is endothermic with the products being higher in energy than the reactants. There is an overall gain of energy.

With this information in mind, the F-H bond is more stable and thus stronger than the H-H bond. The main factors to this argument is the greater electronegativity of F leading to a stronger contribution to the bond than the molecular orbitals. Hence the overlap of molecular orbitals is a weaker factor in the bond strength.

[[File:sm6416_FHH_Surface.png|thumb|none|350px|Surface plot highlighting the energetics of the F-H-H system.]]

[[File:sm6416_HHF_Surface.png|thumb|none|350px|Surface plot highlighting the energetics of the H-H-F system.]]

====Transition State====

Discuss Hammond Postulate with TS being closer to products/reactants dependent on how the TS is composed.

The transition state complex is achieved at r1 = F-H = 1.810076 Angstrom and r2 = H-H = 0.74634 Angstrom, as can be seen from the graphs below showing the absence of displacement to either reactants or products.

[[File:sm6416_FHH_Transition_State_Contour.png|thumb|none|350px|Contour plot demonstrating rts as a result of no fluctuations from the initial input, hence the complex is metaphorically sitting on the transition state.]]

[[File:sm6416_FHH_Transition_State_Momenta_Time.png|thumb|none|350px|Momenta vs Time plot demonstrating minimum, and almost zero, momentum at rts.]]

[[File:sm6416_FHH_Transition_State_Surface.png|thumb|none|350px]]

====Activation Energy====

The activation energy for the exothermic reaction was calculated through a 500000 step MEP simulation with input values of r1 = 1.820076, r2 = 0.74634 and p1 = p2 = 0. It was required that after following the minimum energy path, the gradient of the line signifying the reactants was constant.

The activation energy is reported at +0.258 kcal/mol for the exothermic process.

[[File:sm6416_FHH_Activation_Energy_1.png|thumb|none|350px|Energy vs Time graph highlighting the activation energy of the exothermic reaction.]]

The activation energy for the endothermic process was determined with the following parameters: r1 = 1.800076, r2 = 0.74634, p1 = p2 = 0 with 250000 steps. The reported activation energy was +30.277 kcal/mol.

[[File:sm6416_FHH_Activation_Energy_2.png|thumb|none|350px|Energy vs Time graph highlighting the activation energy of the endothermic reaction.]]

It can hence be seen that the exothermic reaction of F + H2 --> F-H + H only requires a small activation energy as the products are substantially more thermodynamically stable than the reactants.

===Reaction Dynamics===

In light of the fact that energy is conserved, '''discuss the mechanism of release of the reaction energy.''' How could this be confirmed experimentally? Measuring energy released from reaction ie exothermicity. Put first one separately. As reach momentum close to boundaries, system passes through transition state but returns to reactant well. Comment on effect the sign of the momentum has on the reactivity.

r1 = 2.3, r2 = 0.74

{| class="wikitable" border=2
! Simulation !! pHH !! pFH !! Surface Plot !! Momenta vs Time Plot !! Observations !!
|-
| 1 || -2.5 || -1.5 || [[File:sm6416_Trajectory_1_Surface.png|thumb|none|350px]] ||[[File:sm6416_Trajectory_1_Momenta.png|thumb|none|350px]] || This trajectory results in a successful reaction as seen from the surface plot; the reactants proceed through the transition state and continue into the product well, whilst continually oscillating as a result of the momentum gained.
|-
| 2 || -0.5 || -0.5 || [[File:sm6416_Trajectory_2_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_2_Momenta.png|thumb|none|350px]] || This momentum does not proceed to a reaction. Through the dynamic animation it can be seen that the HH molecule does not possess enough momentum to translate towards F. Therefore the system does not translate out of the reactant well, as seen in the surface plot. The momenta plot simply shows a small up trend, this is expected due to the long range electrostatic force of attraction between F and HH. There is no drastic change in the momenta of either F or HH that would otherwise indicate the occurrence of a reaction, as seen in simulation 1 above.
|-
| 3 || +0.5 || -0.5 || [[File:sm6416_Trajectory_3_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_3_Momenta.png|thumb|none|350px]] || This simulation has a positive momentum and therefore the HH molecule translates away from F, as can be seen from the surface plot. There is a slight overall increase in momenta, however not large enough to be of importance. This simulation does not lead to a reaction.
|-
| 4 || -1.6 || -0.5 || [[File:sm6416_Trajectory_4_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_4_Momenta.png|thumb|none|350px]] || The HH molecule in this simulation does possess sufficient momentum to translate towards F and result in a reaction. Evidence for this is both shown by the progression from the reactant to product well in the surface plot along with a drastic change in momentum of A-B (signifying F-H) shown by the momenta vs time plot, highlighting the high momentum oscillation, as expected from the heavier F atom.
|-
| 5 || +1.6 || -0.5 || [[File:sm6416_Trajectory_5_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_5_Momenta.png|thumb|none|350px]] || This simulation is very much like simulation 3, in that the HH momentum is positive. The similarity in the behaviour of the system is also similar, as shown by the surface plot. However, due to the greater momentum, HH translates further away from F than in simulation 3.
|-
| 6 || -2.9 || -0.5 || [[File:sm6416_Trajectory_6_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_6_Momenta.png|thumb|none|350px]] ||
|-
| 7 || +2.9 || -0.5 || [[File:sm6416_Trajectory_7_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_7_Momenta.png|thumb|none|350px]] ||
|-
| 8 || +0.1 || -0.8 || [[File:sm6416_Trajectory_8_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_8_Momenta.png|thumb|none|350px]] ||
|}

====Polyani's Empirical Rules====

Discuss relative translational and vibrational energies required to match the transition state for each endo/exothermic reaction relating to Hammond's postulate.

FH + H reactive trajectory - r1=0.9 r2=2.3 p1=6.5 p2=-1.5

Cite reference

[[File:sm6416_FHH_Reactive_Trajectory_1_Surface.png|thumb|none|350px]]
[[File:sm6416_FHH_Reactive_Trajectory_1_Momenta.png|thumb|none|350px]]
[[File:sm6416_FHH_Reactive_Trajectory_1_Distance.png|thumb|none|350px]]
[[File:sm6416_FHH_Reactive_Trajectory_1_Contour.png|thumb|none|350px]]

MRD:sm6416

2018-05-25T11:54:47Z

Sm6416: /* Reactivity of Trajectories */

==H2 H Exercise 1==

===Transition State Dynamics===

What value do the different components of the gradient of the potential energy surface have at a minimum and at a transition structure? Briefly explain how minima and transition structures can be distinguished using the curvature of the potential energy surface.

Discuss saddle point being the second derivative.
Minimum of trajectory.

===Locating the Transition State===

The transition state was determined through iterations of both r1 and r2 which resulted in the smallest displacement of momenta along with no displacement as shown by the contour plot. This method determined at rts = 0.907743.

[[File:sm6416_Transition_State_Contour.png|thumb|none|350px|Contour plot demonstrating rts = 0.907743 as a result of no fluctuations from the initial input, hence the complex is metaphorically sitting on the transition state.]]

[[File:sm6416_Transition_State_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating minimum, and almost zero, momentum at rts = 0.907743.]]

[[File:sm6416_Transition_State_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot demonstrating no fluctuations in distance and hence rts = 0.907743.]]

===Reaction Path===

The minimum energy path (MEP) is defined as the lowest path the reaction must follow to form the products and is the downhill motion from the transition state. It can be applied in both directions in the case in question. The MEP views the system as static as it resets the velocity to zero at each step. Whereas the trajectory is very much dynamic and the momenta is accounted for, this is reflected in the vibrational oscillation of the molecule as it passes along the minimum well towards the products.

====MEP====

Initial conditions of r1 = rts + 0.01 = 0.917743, r2 = rts = 0.907743 and p1 = p2 = 0 for the MEP simulation.

[[File:sm6416_MEP_Surface.png|thumb|none|350px|Surface plot highlighting the minimum energy path (MEP), as the reaction returns to the reactants without fully passing through the transition state.]]

[[File:sm6416_MEP_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating zero momentum, as inputted, and more importantly not change in momentum with running the simulation.]]

[[File:sm6416_MEP_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot showing that the reactants reach the transition state at the interception of r1 = r2. r1 quickly reaches a constant value, namely the equilibrium bond length of the reactant molecule. r2 increases logarithmically as time progresses, this represents an increasing distance of Ha from Hb-Hc and a continuing loss of momentum.]]

Final values from the MEP simulation.

r1 = 2.76195

r2 = 0.75883

These values reflect the minimum trajectory for a successful reaction.

p1 = p2 = 0

====Dynamic====

[[File:sm6416_Dynamic_Surface.png|thumb|none|350px|Surface plot highlighting the minimum energy path (MEP) with oscillation of the reactants, as the reaction returns to the reactants without fully passing through the transition state. It is therefore evident that the momentum as a result of the vibrational oscillation does not provide enough energy to proceed to the products.]]

[[File:sm6416_Dynamic_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating the momenta associated with the oscillating reactants.]]

[[File:sm6416_Dynamic_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot showing that the reactants reach the transition state at the interception of r1 = r2. r1 quickly decreases and oscillates about a constant value, namely the equilibrium bond length of the reactant molecule. r2 increases linearly as time progresses, this represents an increasing distance of Ha from Hb-Hc with a constant momentum.]]

Dynamic simulation final values

r1 = 10.0045

r2 = 0.75883

p1 = 2.48523

p2 = 1.29898

p(average) = 1.90409

With r1 = rts and r2 = rts + 0.01 would simply produce the same answer however the values would be flipped to the other distance. In other words r1 = 0.75883 and r2 = 10.0045 would be the output values.

Maintaining the final trajectories as calculated from the dynamic simulation and reversing the sign of the momenta, the reaction proceeds in the reverse direction to the products.

===Reactivity of Trajectories===

These simulations are restricted by the number of steps the program can handle, however a sound understanding of the reaction can be appreciated and the reactivity of each scenario can be determined appropriately.

{| class="wikitable" border=2
! Simulation !! p1 !! p2 !! Energy (kcal/mol) !! Reactivity !! Evidence !! Description
|-
| 1 || -1.25 || -2.5 || 5.03500 || Reactive || [[File:sm6416_MEP_Figure1.png|thumb|none|350px]] || Simulation 1: The reactants proceed through the transition state and to the products. The r2 distance decreases to the equilibrium bond length, whilst r1 simultaneously exhibits dissociation and increases beyond the scope of the graph. The small momenta attributed to the reactants is reflected in the vibrationally oscillating products, with a small amplitude.
|-
| 2 || -1.5 || -2.0 || 3.62879 || Unreactive || [[File:sm6416_MEP_Figure2.png|thumb|none|350px]] || Simulation 2: This is unreactive as the oscillating reactants reach the transition state point and r1 immediately returns to the initial bond length, whilst r2 continues to increase as it moves away from the H2 molecule.
|-
| 3 || -1.5 || -2.5 || 5.13738 || Reactive || [[File:sm6416_MEP_Figure3.png|thumb|none|350px]] || Simulation 3: This simulation shows a reactive pathway that is very similar to simulation 1, however due to the greater momenta associated with the reactants, as inputted, vibrational oscillations with a greater amplitude can be observed.
|-
| 4 || -2.5 || -5.0 || 9.86678 || Unreactive || [[File:sm6416_MEP_Figure4.png|thumb|none|350px]] || Simulation 4: Initially seen here are oscillating reactants with a very large amplitude. However, this simulation is unreactive despite the reactants going through the transition state and towards the product, they return to the initial reactants.
|-
| 5 || -2.5 || -5.2 || 11.80780 || Reactive || [[File:sm6416_MEP_Figure5.png|thumb|none|350px]] || Simulation 5: Like simulation 4, this simulation shows a large oscillating amplitude, whereas in this scenario after passing through the transition state, the products are completely obtained. The slight increase in the p2 momentum can be seen to result in the products.
|}

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? Assumes quasi-equilibrium between reactants and transition state. TST assumes that once reaction passes TS no way back to products. Completely opposite to experimental where it seems as though an equilibrium/reversible path exists between the transition state and products. Fluctuation of whether transition complexes go towards reactants or products are independent of each other.

==F-H-H System Exercise 2==
===Potential Energy Surface Inspection===
====Energetics====

F + H2 is an exothermic reaction as can be seen from the surface plot, the reaction progresses from a small H-H distance to a longer one, whilst H-F simultaneously equilibriates about the F-H bond length. It can be seen that the products are lower, and hence more stable, in energy than the reactants.

F-H + H is simply the reverse reaction that passes through the same transition state, hence this reaction is endothermic with the products being higher in energy than the reactants. There is an overall gain of energy.

With this information in mind, the F-H bond is more stable and thus stronger than the H-H bond. The main factors to this argument is the greater electronegativity of F leading to a stronger contribution to the bond than the molecular orbitals. Hence the overlap of molecular orbitals is a weaker factor in the bond strength.

[[File:sm6416_FHH_Surface.png|thumb|none|350px|Surface plot highlighting the energetics of the F-H-H system.]]

[[File:sm6416_HHF_Surface.png|thumb|none|350px|Surface plot highlighting the energetics of the H-H-F system.]]

====Transition State====

Discuss Hammond Postulate with TS being closer to products/reactants dependent on how the TS is composed.

The transition state complex is achieved at r1 = F-H = 1.810076 Angstrom and r2 = H-H = 0.74634 Angstrom, as can be seen from the graphs below showing the absence of displacement to either reactants or products.

[[File:sm6416_FHH_Transition_State_Contour.png|thumb|none|350px|Contour plot demonstrating rts as a result of no fluctuations from the initial input, hence the complex is metaphorically sitting on the transition state.]]

[[File:sm6416_FHH_Transition_State_Momenta_Time.png|thumb|none|350px|Momenta vs Time plot demonstrating minimum, and almost zero, momentum at rts.]]

[[File:sm6416_FHH_Transition_State_Surface.png|thumb|none|350px]]

====Activation Energy====

The activation energy for the exothermic reaction was calculated through a 500000 step MEP simulation with input values of r1 = 1.820076, r2 = 0.74634 and p1 = p2 = 0. It was required that after following the minimum energy path, the gradient of the line signifying the reactants was constant.

The activation energy is reported at +0.258 kcal/mol for the exothermic process.

[[File:sm6416_FHH_Activation_Energy_1.png|thumb|none|350px|Energy vs Time graph highlighting the activation energy of the exothermic reaction.]]

The activation energy for the endothermic process was determined with the following parameters: r1 = 1.800076, r2 = 0.74634, p1 = p2 = 0 with 250000 steps. The reported activation energy was +30.277 kcal/mol.

[[File:sm6416_FHH_Activation_Energy_2.png|thumb|none|350px|Energy vs Time graph highlighting the activation energy of the endothermic reaction.]]

It can hence be seen that the exothermic reaction of F + H2 --> F-H + H only requires a small activation energy as the products are substantially more thermodynamically stable than the reactants.

===Reaction Dynamics===

In light of the fact that energy is conserved, '''discuss the mechanism of release of the reaction energy.''' How could this be confirmed experimentally? Measuring energy released from reaction ie exothermicity. Put first one separately. As reach momentum close to boundaries, system passes through transition state but returns to reactant well. Comment on effect the sign of the momentum has on the reactivity.

r1 = 2.3, r2 = 0.74

{| class="wikitable" border=2
! Simulation !! pHH !! pF-H !! Surface Plot !! Momenta vs Time Plot !! Observations !!
|-
| 1 || -2.5 || -1.5 || [[File:sm6416_Trajectory_1_Surface.png|thumb|none|350px]] ||[[File:sm6416_Trajectory_1_Momenta.png|thumb|none|350px]] || This trajectory results in a successful reaction as seen from the surface plot; the reactants proceed through the transition state and continue into the product well, whilst continually oscillating as a result of the momentum gained.
|-
| 2 || -0.5 || -0.5 || [[File:sm6416_Trajectory_2_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_2_Momenta.png|thumb|none|350px]] || This momentum does not proceed to a reaction. Through the dynamic animation it can be seen that the HH molecule does not possess enough momentum to translate towards F. Therefore the system does not translate out of the reactant well, as seen in the surface plot. The momenta plot simply shows a small up trend, this is expected due to the long range electrostatic force of attraction between F and HH. There is no drastic change in the momenta of either F or HH that would otherwise indicate the occurrence of a reaction, as seen in simulation 1 above.
|-
| 3 || +0.5 || -0.5 || [[File:sm6416_Trajectory_3_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_3_Momenta.png|thumb|none|350px]] || This simulation has a positive momentum and therefore the HH molecule translates away from F, as can be seen from the surface plot. There is a slight overall increase in momenta, however not large enough to be of importance. This simulation does not lead to a reaction.
|-
| 4 || -1.6 || -0.5 || [[File:sm6416_Trajectory_4_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_4_Momenta.png|thumb|none|350px]] || The HH molecule in this simulation does possess sufficient momentum to translate towards F and result in a reaction. Evidence for this is both shown by the progression from the reactant to product well in the surface plot along with a drastic change in momentum of A-B (signifying F-H) shown by the momenta vs time plot, highlighting the high momentum oscillation, as expected from the heavier F atom.
|-
| 5 || +1.6 || -0.5 || [[File:sm6416_Trajectory_5_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_5_Momenta.png|thumb|none|350px]] || This simulation is very much like simulation 3, in that the HH momentum is positive. The similarity in the behaviour of the system is also similar, as shown by the surface plot. However, due to the greater momentum, HH translates further away from F than in simulation 3.
|-
| 6 || -2.9 || -0.5 || [[File:sm6416_Trajectory_6_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_6_Momenta.png|thumb|none|350px]] ||
|-
| 7 || +2.9 || -0.5 || [[File:sm6416_Trajectory_7_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_7_Momenta.png|thumb|none|350px]] ||
|-
| 8 || +0.1 || -0.8 || [[File:sm6416_Trajectory_8_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_8_Momenta.png|thumb|none|350px]] ||
|}

====Polyani's Empirical Rules====

Discuss relative translational and vibrational energies required to match the transition state for each endo/exothermic reaction relating to Hammond's postulate.

FH + H reactive trajectory - r1=0.9 r2=2.3 p1=6.5 p2=-1.5

Cite reference

[[File:sm6416_FHH_Reactive_Trajectory_1_Surface.png|thumb|none|350px]]
[[File:sm6416_FHH_Reactive_Trajectory_1_Momenta.png|thumb|none|350px]]
[[File:sm6416_FHH_Reactive_Trajectory_1_Distance.png|thumb|none|350px]]
[[File:sm6416_FHH_Reactive_Trajectory_1_Contour.png|thumb|none|350px]]

MRD:sm6416

2018-05-25T11:54:19Z

Sm6416: /* Reactivity of Trajectories */

==H2 H Exercise 1==

===Transition State Dynamics===

What value do the different components of the gradient of the potential energy surface have at a minimum and at a transition structure? Briefly explain how minima and transition structures can be distinguished using the curvature of the potential energy surface.

Discuss saddle point being the second derivative.
Minimum of trajectory.

===Locating the Transition State===

The transition state was determined through iterations of both r1 and r2 which resulted in the smallest displacement of momenta along with no displacement as shown by the contour plot. This method determined at rts = 0.907743.

[[File:sm6416_Transition_State_Contour.png|thumb|none|350px|Contour plot demonstrating rts = 0.907743 as a result of no fluctuations from the initial input, hence the complex is metaphorically sitting on the transition state.]]

[[File:sm6416_Transition_State_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating minimum, and almost zero, momentum at rts = 0.907743.]]

[[File:sm6416_Transition_State_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot demonstrating no fluctuations in distance and hence rts = 0.907743.]]

===Reaction Path===

The minimum energy path (MEP) is defined as the lowest path the reaction must follow to form the products and is the downhill motion from the transition state. It can be applied in both directions in the case in question. The MEP views the system as static as it resets the velocity to zero at each step. Whereas the trajectory is very much dynamic and the momenta is accounted for, this is reflected in the vibrational oscillation of the molecule as it passes along the minimum well towards the products.

====MEP====

Initial conditions of r1 = rts + 0.01 = 0.917743, r2 = rts = 0.907743 and p1 = p2 = 0 for the MEP simulation.

[[File:sm6416_MEP_Surface.png|thumb|none|350px|Surface plot highlighting the minimum energy path (MEP), as the reaction returns to the reactants without fully passing through the transition state.]]

[[File:sm6416_MEP_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating zero momentum, as inputted, and more importantly not change in momentum with running the simulation.]]

[[File:sm6416_MEP_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot showing that the reactants reach the transition state at the interception of r1 = r2. r1 quickly reaches a constant value, namely the equilibrium bond length of the reactant molecule. r2 increases logarithmically as time progresses, this represents an increasing distance of Ha from Hb-Hc and a continuing loss of momentum.]]

Final values from the MEP simulation.

r1 = 2.76195

r2 = 0.75883

These values reflect the minimum trajectory for a successful reaction.

p1 = p2 = 0

====Dynamic====

[[File:sm6416_Dynamic_Surface.png|thumb|none|350px|Surface plot highlighting the minimum energy path (MEP) with oscillation of the reactants, as the reaction returns to the reactants without fully passing through the transition state. It is therefore evident that the momentum as a result of the vibrational oscillation does not provide enough energy to proceed to the products.]]

[[File:sm6416_Dynamic_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating the momenta associated with the oscillating reactants.]]

[[File:sm6416_Dynamic_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot showing that the reactants reach the transition state at the interception of r1 = r2. r1 quickly decreases and oscillates about a constant value, namely the equilibrium bond length of the reactant molecule. r2 increases linearly as time progresses, this represents an increasing distance of Ha from Hb-Hc with a constant momentum.]]

Dynamic simulation final values

r1 = 10.0045

r2 = 0.75883

p1 = 2.48523

p2 = 1.29898

p(average) = 1.90409

With r1 = rts and r2 = rts + 0.01 would simply produce the same answer however the values would be flipped to the other distance. In other words r1 = 0.75883 and r2 = 10.0045 would be the output values.

Maintaining the final trajectories as calculated from the dynamic simulation and reversing the sign of the momenta, the reaction proceeds in the reverse direction to the products.

===Reactivity of Trajectories===

These simulations are restricted by the number of steps the program can handle, however a sound understanding of the reaction can be appreciated and the reactivity of each scenario can be determined appropriately.

{| class="wikitable" border=2
! Simulation !! p1 !! p2 !! Energy (units?) !! Reactivity !! Evidence !! Description
|-
| 1 || -1.25 || -2.5 || 5.03500 || Reactive || [[File:sm6416_MEP_Figure1.png|thumb|none|350px]] || Simulation 1: The reactants proceed through the transition state and to the products. The r2 distance decreases to the equilibrium bond length, whilst r1 simultaneously exhibits dissociation and increases beyond the scope of the graph. The small momenta attributed to the reactants is reflected in the vibrationally oscillating products, with a small amplitude.
|-
| 2 || -1.5 || -2.0 || 3.62879 || Unreactive || [[File:sm6416_MEP_Figure2.png|thumb|none|350px]] || Simulation 2: This is unreactive as the oscillating reactants reach the transition state point and r1 immediately returns to the initial bond length, whilst r2 continues to increase as it moves away from the H2 molecule.
|-
| 3 || -1.5 || -2.5 || 5.13738 || Reactive || [[File:sm6416_MEP_Figure3.png|thumb|none|350px]] || Simulation 3: This simulation shows a reactive pathway that is very similar to simulation 1, however due to the greater momenta associated with the reactants, as inputted, vibrational oscillations with a greater amplitude can be observed.
|-
| 4 || -2.5 || -5.0 || 9.86678 || Unreactive || [[File:sm6416_MEP_Figure4.png|thumb|none|350px]] || Simulation 4: Initially seen here are oscillating reactants with a very large amplitude. However, this simulation is unreactive despite the reactants going through the transition state and towards the product, they return to the initial reactants.
|-
| 5 || -2.5 || -5.2 || 11.80780 || Reactive || [[File:sm6416_MEP_Figure5.png|thumb|none|350px]] || Simulation 5: Like simulation 4, this simulation shows a large oscillating amplitude, whereas in this scenario after passing through the transition state, the products are completely obtained. The slight increase in the p2 momentum can be seen to result in the products.
|}

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? Assumes quasi-equilibrium between reactants and transition state. TST assumes that once reaction passes TS no way back to products. Completely opposite to experimental where it seems as though an equilibrium/reversible path exists between the transition state and products. Fluctuation of whether transition complexes go towards reactants or products are independent of each other.

==F-H-H System Exercise 2==
===Potential Energy Surface Inspection===
====Energetics====

F + H2 is an exothermic reaction as can be seen from the surface plot, the reaction progresses from a small H-H distance to a longer one, whilst H-F simultaneously equilibriates about the F-H bond length. It can be seen that the products are lower, and hence more stable, in energy than the reactants.

F-H + H is simply the reverse reaction that passes through the same transition state, hence this reaction is endothermic with the products being higher in energy than the reactants. There is an overall gain of energy.

With this information in mind, the F-H bond is more stable and thus stronger than the H-H bond. The main factors to this argument is the greater electronegativity of F leading to a stronger contribution to the bond than the molecular orbitals. Hence the overlap of molecular orbitals is a weaker factor in the bond strength.

[[File:sm6416_FHH_Surface.png|thumb|none|350px|Surface plot highlighting the energetics of the F-H-H system.]]

[[File:sm6416_HHF_Surface.png|thumb|none|350px|Surface plot highlighting the energetics of the H-H-F system.]]

====Transition State====

Discuss Hammond Postulate with TS being closer to products/reactants dependent on how the TS is composed.

The transition state complex is achieved at r1 = F-H = 1.810076 Angstrom and r2 = H-H = 0.74634 Angstrom, as can be seen from the graphs below showing the absence of displacement to either reactants or products.

[[File:sm6416_FHH_Transition_State_Contour.png|thumb|none|350px|Contour plot demonstrating rts as a result of no fluctuations from the initial input, hence the complex is metaphorically sitting on the transition state.]]

[[File:sm6416_FHH_Transition_State_Momenta_Time.png|thumb|none|350px|Momenta vs Time plot demonstrating minimum, and almost zero, momentum at rts.]]

[[File:sm6416_FHH_Transition_State_Surface.png|thumb|none|350px]]

====Activation Energy====

The activation energy for the exothermic reaction was calculated through a 500000 step MEP simulation with input values of r1 = 1.820076, r2 = 0.74634 and p1 = p2 = 0. It was required that after following the minimum energy path, the gradient of the line signifying the reactants was constant.

The activation energy is reported at +0.258 kcal/mol for the exothermic process.

[[File:sm6416_FHH_Activation_Energy_1.png|thumb|none|350px|Energy vs Time graph highlighting the activation energy of the exothermic reaction.]]

The activation energy for the endothermic process was determined with the following parameters: r1 = 1.800076, r2 = 0.74634, p1 = p2 = 0 with 250000 steps. The reported activation energy was +30.277 kcal/mol.

[[File:sm6416_FHH_Activation_Energy_2.png|thumb|none|350px|Energy vs Time graph highlighting the activation energy of the endothermic reaction.]]

It can hence be seen that the exothermic reaction of F + H2 --> F-H + H only requires a small activation energy as the products are substantially more thermodynamically stable than the reactants.

===Reaction Dynamics===

In light of the fact that energy is conserved, '''discuss the mechanism of release of the reaction energy.''' How could this be confirmed experimentally? Measuring energy released from reaction ie exothermicity. Put first one separately. As reach momentum close to boundaries, system passes through transition state but returns to reactant well. Comment on effect the sign of the momentum has on the reactivity.

r1 = 2.3, r2 = 0.74

{| class="wikitable" border=2
! Simulation !! pHH !! pF-H !! Surface Plot !! Momenta vs Time Plot !! Observations !!
|-
| 1 || -2.5 || -1.5 || [[File:sm6416_Trajectory_1_Surface.png|thumb|none|350px]] ||[[File:sm6416_Trajectory_1_Momenta.png|thumb|none|350px]] || This trajectory results in a successful reaction as seen from the surface plot; the reactants proceed through the transition state and continue into the product well, whilst continually oscillating as a result of the momentum gained.
|-
| 2 || -0.5 || -0.5 || [[File:sm6416_Trajectory_2_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_2_Momenta.png|thumb|none|350px]] || This momentum does not proceed to a reaction. Through the dynamic animation it can be seen that the HH molecule does not possess enough momentum to translate towards F. Therefore the system does not translate out of the reactant well, as seen in the surface plot. The momenta plot simply shows a small up trend, this is expected due to the long range electrostatic force of attraction between F and HH. There is no drastic change in the momenta of either F or HH that would otherwise indicate the occurrence of a reaction, as seen in simulation 1 above.
|-
| 3 || +0.5 || -0.5 || [[File:sm6416_Trajectory_3_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_3_Momenta.png|thumb|none|350px]] || This simulation has a positive momentum and therefore the HH molecule translates away from F, as can be seen from the surface plot. There is a slight overall increase in momenta, however not large enough to be of importance. This simulation does not lead to a reaction.
|-
| 4 || -1.6 || -0.5 || [[File:sm6416_Trajectory_4_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_4_Momenta.png|thumb|none|350px]] || The HH molecule in this simulation does possess sufficient momentum to translate towards F and result in a reaction. Evidence for this is both shown by the progression from the reactant to product well in the surface plot along with a drastic change in momentum of A-B (signifying F-H) shown by the momenta vs time plot, highlighting the high momentum oscillation, as expected from the heavier F atom.
|-
| 5 || +1.6 || -0.5 || [[File:sm6416_Trajectory_5_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_5_Momenta.png|thumb|none|350px]] || This simulation is very much like simulation 3, in that the HH momentum is positive. The similarity in the behaviour of the system is also similar, as shown by the surface plot. However, due to the greater momentum, HH translates further away from F than in simulation 3.
|-
| 6 || -2.9 || -0.5 || [[File:sm6416_Trajectory_6_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_6_Momenta.png|thumb|none|350px]] ||
|-
| 7 || +2.9 || -0.5 || [[File:sm6416_Trajectory_7_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_7_Momenta.png|thumb|none|350px]] ||
|-
| 8 || +0.1 || -0.8 || [[File:sm6416_Trajectory_8_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_8_Momenta.png|thumb|none|350px]] ||
|}

====Polyani's Empirical Rules====

Discuss relative translational and vibrational energies required to match the transition state for each endo/exothermic reaction relating to Hammond's postulate.

FH + H reactive trajectory - r1=0.9 r2=2.3 p1=6.5 p2=-1.5

Cite reference

[[File:sm6416_FHH_Reactive_Trajectory_1_Surface.png|thumb|none|350px]]
[[File:sm6416_FHH_Reactive_Trajectory_1_Momenta.png|thumb|none|350px]]
[[File:sm6416_FHH_Reactive_Trajectory_1_Distance.png|thumb|none|350px]]
[[File:sm6416_FHH_Reactive_Trajectory_1_Contour.png|thumb|none|350px]]

MRD:sm6416

2018-05-25T11:53:37Z

Sm6416: /* Reaction Dynamics */

==H2 H Exercise 1==

===Transition State Dynamics===

What value do the different components of the gradient of the potential energy surface have at a minimum and at a transition structure? Briefly explain how minima and transition structures can be distinguished using the curvature of the potential energy surface.

Discuss saddle point being the second derivative.
Minimum of trajectory.

===Locating the Transition State===

The transition state was determined through iterations of both r1 and r2 which resulted in the smallest displacement of momenta along with no displacement as shown by the contour plot. This method determined at rts = 0.907743.

[[File:sm6416_Transition_State_Contour.png|thumb|none|350px|Contour plot demonstrating rts = 0.907743 as a result of no fluctuations from the initial input, hence the complex is metaphorically sitting on the transition state.]]

[[File:sm6416_Transition_State_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating minimum, and almost zero, momentum at rts = 0.907743.]]

[[File:sm6416_Transition_State_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot demonstrating no fluctuations in distance and hence rts = 0.907743.]]

===Reaction Path===

The minimum energy path (MEP) is defined as the lowest path the reaction must follow to form the products and is the downhill motion from the transition state. It can be applied in both directions in the case in question. The MEP views the system as static as it resets the velocity to zero at each step. Whereas the trajectory is very much dynamic and the momenta is accounted for, this is reflected in the vibrational oscillation of the molecule as it passes along the minimum well towards the products.

====MEP====

Initial conditions of r1 = rts + 0.01 = 0.917743, r2 = rts = 0.907743 and p1 = p2 = 0 for the MEP simulation.

[[File:sm6416_MEP_Surface.png|thumb|none|350px|Surface plot highlighting the minimum energy path (MEP), as the reaction returns to the reactants without fully passing through the transition state.]]

[[File:sm6416_MEP_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating zero momentum, as inputted, and more importantly not change in momentum with running the simulation.]]

[[File:sm6416_MEP_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot showing that the reactants reach the transition state at the interception of r1 = r2. r1 quickly reaches a constant value, namely the equilibrium bond length of the reactant molecule. r2 increases logarithmically as time progresses, this represents an increasing distance of Ha from Hb-Hc and a continuing loss of momentum.]]

Final values from the MEP simulation.

r1 = 2.76195

r2 = 0.75883

These values reflect the minimum trajectory for a successful reaction.

p1 = p2 = 0

====Dynamic====

[[File:sm6416_Dynamic_Surface.png|thumb|none|350px|Surface plot highlighting the minimum energy path (MEP) with oscillation of the reactants, as the reaction returns to the reactants without fully passing through the transition state. It is therefore evident that the momentum as a result of the vibrational oscillation does not provide enough energy to proceed to the products.]]

[[File:sm6416_Dynamic_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating the momenta associated with the oscillating reactants.]]

[[File:sm6416_Dynamic_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot showing that the reactants reach the transition state at the interception of r1 = r2. r1 quickly decreases and oscillates about a constant value, namely the equilibrium bond length of the reactant molecule. r2 increases linearly as time progresses, this represents an increasing distance of Ha from Hb-Hc with a constant momentum.]]

Dynamic simulation final values

r1 = 10.0045

r2 = 0.75883

p1 = 2.48523

p2 = 1.29898

p(average) = 1.90409

With r1 = rts and r2 = rts + 0.01 would simply produce the same answer however the values would be flipped to the other distance. In other words r1 = 0.75883 and r2 = 10.0045 would be the output values.

Maintaining the final trajectories as calculated from the dynamic simulation and reversing the sign of the momenta, the reaction proceeds in the reverse direction to the products.

===Reactivity of Trajectories===

These simulations are restricted by the number of steps the program can handle, however a sound understanding of the reaction can be appreciated and the reactivity of each scenario can be determined appropriately.

{| class="wikitable" border=1
! Simulation !! p1 !! p2 !! Energy (units?) !! Reactivity !! Evidence !! Description
|-
| 1 || -1.25 || -2.5 || 5.03500 || Reactive || [[File:sm6416_MEP_Figure1.png|thumb|none|350px]] || Simulation 1: The reactants proceed through the transition state and to the products. The r2 distance decreases to the equilibrium bond length, whilst r1 simultaneously exhibits dissociation and increases beyond the scope of the graph. The small momenta attributed to the reactants is reflected in the vibrationally oscillating products, with a small amplitude.
|-
| 2 || -1.5 || -2.0 || 3.62879 || Unreactive || [[File:sm6416_MEP_Figure2.png|thumb|none|350px]] || Simulation 2: This is unreactive as the oscillating reactants reach the transition state point and r1 immediately returns to the initial bond length, whilst r2 continues to increase as it moves away from the H2 molecule.
|-
| 3 || -1.5 || -2.5 || 5.13738 || Reactive || [[File:sm6416_MEP_Figure3.png|thumb|none|350px]] || Simulation 3: This simulation shows a reactive pathway that is very similar to simulation 1, however due to the greater momenta associated with the reactants, as inputted, vibrational oscillations with a greater amplitude can be observed.
|-
| 4 || -2.5 || -5.0 || 9.86678 || Unreactive || [[File:sm6416_MEP_Figure4.png|thumb|none|350px]] || Simulation 4: Initially seen here are oscillating reactants with a very large amplitude. However, this simulation is unreactive despite the reactants going through the transition state and towards the product, they return to the initial reactants.
|-
| 5 || -2.5 || -5.2 || 11.80780 || Reactive || [[File:sm6416_MEP_Figure5.png|thumb|none|350px]] || Simulation 5: Like simulation 4, this simulation shows a large oscillating amplitude, whereas in this scenario after passing through the transition state, the products are completely obtained. The slight increase in the p2 momentum can be seen to result in the products.
|}

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? Assumes quasi-equilibrium between reactants and transition state. TST assumes that once reaction passes TS no way back to products. Completely opposite to experimental where it seems as though an equilibrium/reversible path exists between the transition state and products. Fluctuation of whether transition complexes go towards reactants or products are independent of each other.

==F-H-H System Exercise 2==
===Potential Energy Surface Inspection===
====Energetics====

F + H2 is an exothermic reaction as can be seen from the surface plot, the reaction progresses from a small H-H distance to a longer one, whilst H-F simultaneously equilibriates about the F-H bond length. It can be seen that the products are lower, and hence more stable, in energy than the reactants.

F-H + H is simply the reverse reaction that passes through the same transition state, hence this reaction is endothermic with the products being higher in energy than the reactants. There is an overall gain of energy.

With this information in mind, the F-H bond is more stable and thus stronger than the H-H bond. The main factors to this argument is the greater electronegativity of F leading to a stronger contribution to the bond than the molecular orbitals. Hence the overlap of molecular orbitals is a weaker factor in the bond strength.

[[File:sm6416_FHH_Surface.png|thumb|none|350px|Surface plot highlighting the energetics of the F-H-H system.]]

[[File:sm6416_HHF_Surface.png|thumb|none|350px|Surface plot highlighting the energetics of the H-H-F system.]]

====Transition State====

Discuss Hammond Postulate with TS being closer to products/reactants dependent on how the TS is composed.

The transition state complex is achieved at r1 = F-H = 1.810076 Angstrom and r2 = H-H = 0.74634 Angstrom, as can be seen from the graphs below showing the absence of displacement to either reactants or products.

[[File:sm6416_FHH_Transition_State_Contour.png|thumb|none|350px|Contour plot demonstrating rts as a result of no fluctuations from the initial input, hence the complex is metaphorically sitting on the transition state.]]

[[File:sm6416_FHH_Transition_State_Momenta_Time.png|thumb|none|350px|Momenta vs Time plot demonstrating minimum, and almost zero, momentum at rts.]]

[[File:sm6416_FHH_Transition_State_Surface.png|thumb|none|350px]]

====Activation Energy====

The activation energy for the exothermic reaction was calculated through a 500000 step MEP simulation with input values of r1 = 1.820076, r2 = 0.74634 and p1 = p2 = 0. It was required that after following the minimum energy path, the gradient of the line signifying the reactants was constant.

The activation energy is reported at +0.258 kcal/mol for the exothermic process.

[[File:sm6416_FHH_Activation_Energy_1.png|thumb|none|350px|Energy vs Time graph highlighting the activation energy of the exothermic reaction.]]

The activation energy for the endothermic process was determined with the following parameters: r1 = 1.800076, r2 = 0.74634, p1 = p2 = 0 with 250000 steps. The reported activation energy was +30.277 kcal/mol.

[[File:sm6416_FHH_Activation_Energy_2.png|thumb|none|350px|Energy vs Time graph highlighting the activation energy of the endothermic reaction.]]

It can hence be seen that the exothermic reaction of F + H2 --> F-H + H only requires a small activation energy as the products are substantially more thermodynamically stable than the reactants.

===Reaction Dynamics===

In light of the fact that energy is conserved, '''discuss the mechanism of release of the reaction energy.''' How could this be confirmed experimentally? Measuring energy released from reaction ie exothermicity. Put first one separately. As reach momentum close to boundaries, system passes through transition state but returns to reactant well. Comment on effect the sign of the momentum has on the reactivity.

r1 = 2.3, r2 = 0.74

{| class="wikitable" border=2
! Simulation !! pHH !! pF-H !! Surface Plot !! Momenta vs Time Plot !! Observations !!
|-
| 1 || -2.5 || -1.5 || [[File:sm6416_Trajectory_1_Surface.png|thumb|none|350px]] ||[[File:sm6416_Trajectory_1_Momenta.png|thumb|none|350px]] || This trajectory results in a successful reaction as seen from the surface plot; the reactants proceed through the transition state and continue into the product well, whilst continually oscillating as a result of the momentum gained.
|-
| 2 || -0.5 || -0.5 || [[File:sm6416_Trajectory_2_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_2_Momenta.png|thumb|none|350px]] || This momentum does not proceed to a reaction. Through the dynamic animation it can be seen that the HH molecule does not possess enough momentum to translate towards F. Therefore the system does not translate out of the reactant well, as seen in the surface plot. The momenta plot simply shows a small up trend, this is expected due to the long range electrostatic force of attraction between F and HH. There is no drastic change in the momenta of either F or HH that would otherwise indicate the occurrence of a reaction, as seen in simulation 1 above.
|-
| 3 || +0.5 || -0.5 || [[File:sm6416_Trajectory_3_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_3_Momenta.png|thumb|none|350px]] || This simulation has a positive momentum and therefore the HH molecule translates away from F, as can be seen from the surface plot. There is a slight overall increase in momenta, however not large enough to be of importance. This simulation does not lead to a reaction.
|-
| 4 || -1.6 || -0.5 || [[File:sm6416_Trajectory_4_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_4_Momenta.png|thumb|none|350px]] || The HH molecule in this simulation does possess sufficient momentum to translate towards F and result in a reaction. Evidence for this is both shown by the progression from the reactant to product well in the surface plot along with a drastic change in momentum of A-B (signifying F-H) shown by the momenta vs time plot, highlighting the high momentum oscillation, as expected from the heavier F atom.
|-
| 5 || +1.6 || -0.5 || [[File:sm6416_Trajectory_5_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_5_Momenta.png|thumb|none|350px]] || This simulation is very much like simulation 3, in that the HH momentum is positive. The similarity in the behaviour of the system is also similar, as shown by the surface plot. However, due to the greater momentum, HH translates further away from F than in simulation 3.
|-
| 6 || -2.9 || -0.5 || [[File:sm6416_Trajectory_6_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_6_Momenta.png|thumb|none|350px]] ||
|-
| 7 || +2.9 || -0.5 || [[File:sm6416_Trajectory_7_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_7_Momenta.png|thumb|none|350px]] ||
|-
| 8 || +0.1 || -0.8 || [[File:sm6416_Trajectory_8_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_8_Momenta.png|thumb|none|350px]] ||
|}

====Polyani's Empirical Rules====

Discuss relative translational and vibrational energies required to match the transition state for each endo/exothermic reaction relating to Hammond's postulate.

FH + H reactive trajectory - r1=0.9 r2=2.3 p1=6.5 p2=-1.5

Cite reference

[[File:sm6416_FHH_Reactive_Trajectory_1_Surface.png|thumb|none|350px]]
[[File:sm6416_FHH_Reactive_Trajectory_1_Momenta.png|thumb|none|350px]]
[[File:sm6416_FHH_Reactive_Trajectory_1_Distance.png|thumb|none|350px]]
[[File:sm6416_FHH_Reactive_Trajectory_1_Contour.png|thumb|none|350px]]

MRD:sm6416

2018-05-24T18:05:22Z

Sm6416: /* Polyani's Empirical Rules */

==H2 H Exercise 1==

===Transition State Dynamics===

What value do the different components of the gradient of the potential energy surface have at a minimum and at a transition structure? Briefly explain how minima and transition structures can be distinguished using the curvature of the potential energy surface.

Discuss saddle point being the second derivative.
Minimum of trajectory.

===Locating the Transition State===

The transition state was determined through iterations of both r1 and r2 which resulted in the smallest displacement of momenta along with no displacement as shown by the contour plot. This method determined at rts = 0.907743.

[[File:sm6416_Transition_State_Contour.png|thumb|none|350px|Contour plot demonstrating rts = 0.907743 as a result of no fluctuations from the initial input, hence the complex is metaphorically sitting on the transition state.]]

[[File:sm6416_Transition_State_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating minimum, and almost zero, momentum at rts = 0.907743.]]

[[File:sm6416_Transition_State_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot demonstrating no fluctuations in distance and hence rts = 0.907743.]]

===Reaction Path===

The minimum energy path (MEP) is defined as the lowest path the reaction must follow to form the products and is the downhill motion from the transition state. It can be applied in both directions in the case in question. The MEP views the system as static as it resets the velocity to zero at each step. Whereas the trajectory is very much dynamic and the momenta is accounted for, this is reflected in the vibrational oscillation of the molecule as it passes along the minimum well towards the products.

====MEP====

Initial conditions of r1 = rts + 0.01 = 0.917743, r2 = rts = 0.907743 and p1 = p2 = 0 for the MEP simulation.

[[File:sm6416_MEP_Surface.png|thumb|none|350px|Surface plot highlighting the minimum energy path (MEP), as the reaction returns to the reactants without fully passing through the transition state.]]

[[File:sm6416_MEP_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating zero momentum, as inputted, and more importantly not change in momentum with running the simulation.]]

[[File:sm6416_MEP_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot showing that the reactants reach the transition state at the interception of r1 = r2. r1 quickly reaches a constant value, namely the equilibrium bond length of the reactant molecule. r2 increases logarithmically as time progresses, this represents an increasing distance of Ha from Hb-Hc and a continuing loss of momentum.]]

Final values from the MEP simulation.

r1 = 2.76195

r2 = 0.75883

These values reflect the minimum trajectory for a successful reaction.

p1 = p2 = 0

====Dynamic====

[[File:sm6416_Dynamic_Surface.png|thumb|none|350px|Surface plot highlighting the minimum energy path (MEP) with oscillation of the reactants, as the reaction returns to the reactants without fully passing through the transition state. It is therefore evident that the momentum as a result of the vibrational oscillation does not provide enough energy to proceed to the products.]]

[[File:sm6416_Dynamic_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating the momenta associated with the oscillating reactants.]]

[[File:sm6416_Dynamic_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot showing that the reactants reach the transition state at the interception of r1 = r2. r1 quickly decreases and oscillates about a constant value, namely the equilibrium bond length of the reactant molecule. r2 increases linearly as time progresses, this represents an increasing distance of Ha from Hb-Hc with a constant momentum.]]

Dynamic simulation final values

r1 = 10.0045

r2 = 0.75883

p1 = 2.48523

p2 = 1.29898

p(average) = 1.90409

With r1 = rts and r2 = rts + 0.01 would simply produce the same answer however the values would be flipped to the other distance. In other words r1 = 0.75883 and r2 = 10.0045 would be the output values.

Maintaining the final trajectories as calculated from the dynamic simulation and reversing the sign of the momenta, the reaction proceeds in the reverse direction to the products.

===Reactivity of Trajectories===

These simulations are restricted by the number of steps the program can handle, however a sound understanding of the reaction can be appreciated and the reactivity of each scenario can be determined appropriately.

{| class="wikitable" border=1
! Simulation !! p1 !! p2 !! Energy (units?) !! Reactivity !! Evidence !! Description
|-
| 1 || -1.25 || -2.5 || 5.03500 || Reactive || [[File:sm6416_MEP_Figure1.png|thumb|none|350px]] || Simulation 1: The reactants proceed through the transition state and to the products. The r2 distance decreases to the equilibrium bond length, whilst r1 simultaneously exhibits dissociation and increases beyond the scope of the graph. The small momenta attributed to the reactants is reflected in the vibrationally oscillating products, with a small amplitude.
|-
| 2 || -1.5 || -2.0 || 3.62879 || Unreactive || [[File:sm6416_MEP_Figure2.png|thumb|none|350px]] || Simulation 2: This is unreactive as the oscillating reactants reach the transition state point and r1 immediately returns to the initial bond length, whilst r2 continues to increase as it moves away from the H2 molecule.
|-
| 3 || -1.5 || -2.5 || 5.13738 || Reactive || [[File:sm6416_MEP_Figure3.png|thumb|none|350px]] || Simulation 3: This simulation shows a reactive pathway that is very similar to simulation 1, however due to the greater momenta associated with the reactants, as inputted, vibrational oscillations with a greater amplitude can be observed.
|-
| 4 || -2.5 || -5.0 || 9.86678 || Unreactive || [[File:sm6416_MEP_Figure4.png|thumb|none|350px]] || Simulation 4: Initially seen here are oscillating reactants with a very large amplitude. However, this simulation is unreactive despite the reactants going through the transition state and towards the product, they return to the initial reactants.
|-
| 5 || -2.5 || -5.2 || 11.80780 || Reactive || [[File:sm6416_MEP_Figure5.png|thumb|none|350px]] || Simulation 5: Like simulation 4, this simulation shows a large oscillating amplitude, whereas in this scenario after passing through the transition state, the products are completely obtained. The slight increase in the p2 momentum can be seen to result in the products.
|}

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? Assumes quasi-equilibrium between reactants and transition state. TST assumes that once reaction passes TS no way back to products. Completely opposite to experimental where it seems as though an equilibrium/reversible path exists between the transition state and products. Fluctuation of whether transition complexes go towards reactants or products are independent of each other.

==F-H-H System Exercise 2==
===Potential Energy Surface Inspection===
====Energetics====

F + H2 is an exothermic reaction as can be seen from the surface plot, the reaction progresses from a small H-H distance to a longer one, whilst H-F simultaneously equilibriates about the F-H bond length. It can be seen that the products are lower, and hence more stable, in energy than the reactants.

F-H + H is simply the reverse reaction that passes through the same transition state, hence this reaction is endothermic with the products being higher in energy than the reactants. There is an overall gain of energy.

With this information in mind, the F-H bond is more stable and thus stronger than the H-H bond. The main factors to this argument is the greater electronegativity of F leading to a stronger contribution to the bond than the molecular orbitals. Hence the overlap of molecular orbitals is a weaker factor in the bond strength.

[[File:sm6416_FHH_Surface.png|thumb|none|350px|Surface plot highlighting the energetics of the F-H-H system.]]

[[File:sm6416_HHF_Surface.png|thumb|none|350px|Surface plot highlighting the energetics of the H-H-F system.]]

====Transition State====

Discuss Hammond Postulate with TS being closer to products/reactants dependent on how the TS is composed.

The transition state complex is achieved at r1 = F-H = 1.810076 Angstrom and r2 = H-H = 0.74634 Angstrom, as can be seen from the graphs below showing the absence of displacement to either reactants or products.

[[File:sm6416_FHH_Transition_State_Contour.png|thumb|none|350px|Contour plot demonstrating rts as a result of no fluctuations from the initial input, hence the complex is metaphorically sitting on the transition state.]]

[[File:sm6416_FHH_Transition_State_Momenta_Time.png|thumb|none|350px|Momenta vs Time plot demonstrating minimum, and almost zero, momentum at rts.]]

[[File:sm6416_FHH_Transition_State_Surface.png|thumb|none|350px]]

====Activation Energy====

The activation energy for the exothermic reaction was calculated through a 500000 step MEP simulation with input values of r1 = 1.820076, r2 = 0.74634 and p1 = p2 = 0. It was required that after following the minimum energy path, the gradient of the line signifying the reactants was constant.

The activation energy is reported at +0.258 kcal/mol for the exothermic process.

[[File:sm6416_FHH_Activation_Energy_1.png|thumb|none|350px|Energy vs Time graph highlighting the activation energy of the exothermic reaction.]]

The activation energy for the endothermic process was determined with the following parameters: r1 = 1.800076, r2 = 0.74634, p1 = p2 = 0 with 250000 steps. The reported activation energy was +30.277 kcal/mol.

[[File:sm6416_FHH_Activation_Energy_2.png|thumb|none|350px|Energy vs Time graph highlighting the activation energy of the endothermic reaction.]]

It can hence be seen that the exothermic reaction of F + H2 --> F-H + H only requires a small activation energy as the products are substantially more thermodynamically stable than the reactants.

===Reaction Dynamics===

In light of the fact that energy is conserved, '''discuss the mechanism of release of the reaction energy.''' How could this be confirmed experimentally? Measuring energy released from reaction ie exothermicity. Put first one separately. As reach momentum close to boundaries, system passes through transition state but returns to reactant well. Comment on effect the sign of the momentum has on the reactivity.

r1 = 2.3, r2 = 0.74

{| class="wikitable" border=1
! Simulation !! pHH !! pF-H !! Surface Plot !! Momenta vs Time Plot !! Observations !!
|-
| 1 || -2.5 || -1.5 || [[File:sm6416_Trajectory_1_Surface.png|thumb|none|350px]] ||[[File:sm6416_Trajectory_1_Momenta.png|thumb|none|350px]] || This trajectory results in a successful reaction as seen from the surface plot; the reactants proceed through the transition state and continue into the product well, whilst continually oscillating as a result of the momentum gained.
|-
| 2 || -0.5 || -0.5 || [[File:sm6416_Trajectory_2_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_2_Momenta.png|thumb|none|350px]] || This momentum does not proceed to a reaction. Through the dynamic animation it can be seen that the HH molecule does not possess enough momentum to translate towards F. Therefore the system does not translate out of the reactant well, as seen in the surface plot. The momenta plot simply shows a small up trend, this is expected due to the long range electrostatic force of attraction between F and HH. There is no drastic change in the momenta of either F or HH that would otherwise indicate the occurrence of a reaction, as seen in simulation 1 above.
|-
| 3 || +0.5 || -0.5 || [[File:sm6416_Trajectory_3_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_3_Momenta.png|thumb|none|350px]] || This simulation has a positive momentum and therefore the HH molecule translates away from F, as can be seen from the surface plot. There is a slight overall increase in momenta, however not large enough to be of importance. This simulation does not lead to a reaction.
|-
| 4 || -1.6 || -0.5 || [[File:sm6416_Trajectory_4_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_4_Momenta.png|thumb|none|350px]] || The HH molecule in this simulation does possess sufficient momentum to translate towards F and result in a reaction. Evidence for this is both shown by the progression from the reactant to product well in the surface plot along with a drastic change in momentum of A-B (signifying F-H) shown by the momenta vs time plot, highlighting the high momentum oscillation, as expected from the heavier F atom.
|-
| 5 || +1.6 || -0.5 || [[File:sm6416_Trajectory_5_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_5_Momenta.png|thumb|none|350px]] || This simulation is very much like simulation 3, in that the HH momentum is positive. The similarity in the behaviour of the system is also similar, as shown by the surface plot. However, due to the greater momentum, HH translates further away from F than in simulation 3.
|-
| 6 || -2.9 || -0.5 || [[File:sm6416_Trajectory_6_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_6_Momenta.png|thumb|none|350px]] ||
|-
| 7 || +2.9 || -0.5 || [[File:sm6416_Trajectory_7_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_7_Momenta.png|thumb|none|350px]] ||
|-
| 8 || +0.1 || -0.8 || [[File:sm6416_Trajectory_8_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_8_Momenta.png|thumb|none|350px]] ||
|}

====Polyani's Empirical Rules====

Discuss relative translational and vibrational energies required to match the transition state for each endo/exothermic reaction relating to Hammond's postulate.

FH + H reactive trajectory - r1=0.9 r2=2.3 p1=6.5 p2=-1.5

Cite reference

[[File:sm6416_FHH_Reactive_Trajectory_1_Surface.png|thumb|none|350px]]
[[File:sm6416_FHH_Reactive_Trajectory_1_Momenta.png|thumb|none|350px]]
[[File:sm6416_FHH_Reactive_Trajectory_1_Distance.png|thumb|none|350px]]
[[File:sm6416_FHH_Reactive_Trajectory_1_Contour.png|thumb|none|350px]]

MRD:sm6416

2018-05-24T18:04:09Z

Sm6416: /* Reaction Dynamics */

==H2 H Exercise 1==

===Transition State Dynamics===

What value do the different components of the gradient of the potential energy surface have at a minimum and at a transition structure? Briefly explain how minima and transition structures can be distinguished using the curvature of the potential energy surface.

Discuss saddle point being the second derivative.
Minimum of trajectory.

===Locating the Transition State===

The transition state was determined through iterations of both r1 and r2 which resulted in the smallest displacement of momenta along with no displacement as shown by the contour plot. This method determined at rts = 0.907743.

[[File:sm6416_Transition_State_Contour.png|thumb|none|350px|Contour plot demonstrating rts = 0.907743 as a result of no fluctuations from the initial input, hence the complex is metaphorically sitting on the transition state.]]

[[File:sm6416_Transition_State_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating minimum, and almost zero, momentum at rts = 0.907743.]]

[[File:sm6416_Transition_State_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot demonstrating no fluctuations in distance and hence rts = 0.907743.]]

===Reaction Path===

The minimum energy path (MEP) is defined as the lowest path the reaction must follow to form the products and is the downhill motion from the transition state. It can be applied in both directions in the case in question. The MEP views the system as static as it resets the velocity to zero at each step. Whereas the trajectory is very much dynamic and the momenta is accounted for, this is reflected in the vibrational oscillation of the molecule as it passes along the minimum well towards the products.

====MEP====

Initial conditions of r1 = rts + 0.01 = 0.917743, r2 = rts = 0.907743 and p1 = p2 = 0 for the MEP simulation.

[[File:sm6416_MEP_Surface.png|thumb|none|350px|Surface plot highlighting the minimum energy path (MEP), as the reaction returns to the reactants without fully passing through the transition state.]]

[[File:sm6416_MEP_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating zero momentum, as inputted, and more importantly not change in momentum with running the simulation.]]

[[File:sm6416_MEP_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot showing that the reactants reach the transition state at the interception of r1 = r2. r1 quickly reaches a constant value, namely the equilibrium bond length of the reactant molecule. r2 increases logarithmically as time progresses, this represents an increasing distance of Ha from Hb-Hc and a continuing loss of momentum.]]

Final values from the MEP simulation.

r1 = 2.76195

r2 = 0.75883

These values reflect the minimum trajectory for a successful reaction.

p1 = p2 = 0

====Dynamic====

[[File:sm6416_Dynamic_Surface.png|thumb|none|350px|Surface plot highlighting the minimum energy path (MEP) with oscillation of the reactants, as the reaction returns to the reactants without fully passing through the transition state. It is therefore evident that the momentum as a result of the vibrational oscillation does not provide enough energy to proceed to the products.]]

[[File:sm6416_Dynamic_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating the momenta associated with the oscillating reactants.]]

[[File:sm6416_Dynamic_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot showing that the reactants reach the transition state at the interception of r1 = r2. r1 quickly decreases and oscillates about a constant value, namely the equilibrium bond length of the reactant molecule. r2 increases linearly as time progresses, this represents an increasing distance of Ha from Hb-Hc with a constant momentum.]]

Dynamic simulation final values

r1 = 10.0045

r2 = 0.75883

p1 = 2.48523

p2 = 1.29898

p(average) = 1.90409

With r1 = rts and r2 = rts + 0.01 would simply produce the same answer however the values would be flipped to the other distance. In other words r1 = 0.75883 and r2 = 10.0045 would be the output values.

Maintaining the final trajectories as calculated from the dynamic simulation and reversing the sign of the momenta, the reaction proceeds in the reverse direction to the products.

===Reactivity of Trajectories===

These simulations are restricted by the number of steps the program can handle, however a sound understanding of the reaction can be appreciated and the reactivity of each scenario can be determined appropriately.

{| class="wikitable" border=1
! Simulation !! p1 !! p2 !! Energy (units?) !! Reactivity !! Evidence !! Description
|-
| 1 || -1.25 || -2.5 || 5.03500 || Reactive || [[File:sm6416_MEP_Figure1.png|thumb|none|350px]] || Simulation 1: The reactants proceed through the transition state and to the products. The r2 distance decreases to the equilibrium bond length, whilst r1 simultaneously exhibits dissociation and increases beyond the scope of the graph. The small momenta attributed to the reactants is reflected in the vibrationally oscillating products, with a small amplitude.
|-
| 2 || -1.5 || -2.0 || 3.62879 || Unreactive || [[File:sm6416_MEP_Figure2.png|thumb|none|350px]] || Simulation 2: This is unreactive as the oscillating reactants reach the transition state point and r1 immediately returns to the initial bond length, whilst r2 continues to increase as it moves away from the H2 molecule.
|-
| 3 || -1.5 || -2.5 || 5.13738 || Reactive || [[File:sm6416_MEP_Figure3.png|thumb|none|350px]] || Simulation 3: This simulation shows a reactive pathway that is very similar to simulation 1, however due to the greater momenta associated with the reactants, as inputted, vibrational oscillations with a greater amplitude can be observed.
|-
| 4 || -2.5 || -5.0 || 9.86678 || Unreactive || [[File:sm6416_MEP_Figure4.png|thumb|none|350px]] || Simulation 4: Initially seen here are oscillating reactants with a very large amplitude. However, this simulation is unreactive despite the reactants going through the transition state and towards the product, they return to the initial reactants.
|-
| 5 || -2.5 || -5.2 || 11.80780 || Reactive || [[File:sm6416_MEP_Figure5.png|thumb|none|350px]] || Simulation 5: Like simulation 4, this simulation shows a large oscillating amplitude, whereas in this scenario after passing through the transition state, the products are completely obtained. The slight increase in the p2 momentum can be seen to result in the products.
|}

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? Assumes quasi-equilibrium between reactants and transition state. TST assumes that once reaction passes TS no way back to products. Completely opposite to experimental where it seems as though an equilibrium/reversible path exists between the transition state and products. Fluctuation of whether transition complexes go towards reactants or products are independent of each other.

==F-H-H System Exercise 2==
===Potential Energy Surface Inspection===
====Energetics====

F + H2 is an exothermic reaction as can be seen from the surface plot, the reaction progresses from a small H-H distance to a longer one, whilst H-F simultaneously equilibriates about the F-H bond length. It can be seen that the products are lower, and hence more stable, in energy than the reactants.

F-H + H is simply the reverse reaction that passes through the same transition state, hence this reaction is endothermic with the products being higher in energy than the reactants. There is an overall gain of energy.

With this information in mind, the F-H bond is more stable and thus stronger than the H-H bond. The main factors to this argument is the greater electronegativity of F leading to a stronger contribution to the bond than the molecular orbitals. Hence the overlap of molecular orbitals is a weaker factor in the bond strength.

[[File:sm6416_FHH_Surface.png|thumb|none|350px|Surface plot highlighting the energetics of the F-H-H system.]]

[[File:sm6416_HHF_Surface.png|thumb|none|350px|Surface plot highlighting the energetics of the H-H-F system.]]

====Transition State====

Discuss Hammond Postulate with TS being closer to products/reactants dependent on how the TS is composed.

The transition state complex is achieved at r1 = F-H = 1.810076 Angstrom and r2 = H-H = 0.74634 Angstrom, as can be seen from the graphs below showing the absence of displacement to either reactants or products.

[[File:sm6416_FHH_Transition_State_Contour.png|thumb|none|350px|Contour plot demonstrating rts as a result of no fluctuations from the initial input, hence the complex is metaphorically sitting on the transition state.]]

[[File:sm6416_FHH_Transition_State_Momenta_Time.png|thumb|none|350px|Momenta vs Time plot demonstrating minimum, and almost zero, momentum at rts.]]

[[File:sm6416_FHH_Transition_State_Surface.png|thumb|none|350px]]

====Activation Energy====

The activation energy for the exothermic reaction was calculated through a 500000 step MEP simulation with input values of r1 = 1.820076, r2 = 0.74634 and p1 = p2 = 0. It was required that after following the minimum energy path, the gradient of the line signifying the reactants was constant.

The activation energy is reported at +0.258 kcal/mol for the exothermic process.

[[File:sm6416_FHH_Activation_Energy_1.png|thumb|none|350px|Energy vs Time graph highlighting the activation energy of the exothermic reaction.]]

The activation energy for the endothermic process was determined with the following parameters: r1 = 1.800076, r2 = 0.74634, p1 = p2 = 0 with 250000 steps. The reported activation energy was +30.277 kcal/mol.

[[File:sm6416_FHH_Activation_Energy_2.png|thumb|none|350px|Energy vs Time graph highlighting the activation energy of the endothermic reaction.]]

It can hence be seen that the exothermic reaction of F + H2 --> F-H + H only requires a small activation energy as the products are substantially more thermodynamically stable than the reactants.

===Reaction Dynamics===

In light of the fact that energy is conserved, '''discuss the mechanism of release of the reaction energy.''' How could this be confirmed experimentally? Measuring energy released from reaction ie exothermicity. Put first one separately. As reach momentum close to boundaries, system passes through transition state but returns to reactant well. Comment on effect the sign of the momentum has on the reactivity.

r1 = 2.3, r2 = 0.74

{| class="wikitable" border=1
! Simulation !! pHH !! pF-H !! Surface Plot !! Momenta vs Time Plot !! Observations !!
|-
| 1 || -2.5 || -1.5 || [[File:sm6416_Trajectory_1_Surface.png|thumb|none|350px]] ||[[File:sm6416_Trajectory_1_Momenta.png|thumb|none|350px]] || This trajectory results in a successful reaction as seen from the surface plot; the reactants proceed through the transition state and continue into the product well, whilst continually oscillating as a result of the momentum gained.
|-
| 2 || -0.5 || -0.5 || [[File:sm6416_Trajectory_2_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_2_Momenta.png|thumb|none|350px]] || This momentum does not proceed to a reaction. Through the dynamic animation it can be seen that the HH molecule does not possess enough momentum to translate towards F. Therefore the system does not translate out of the reactant well, as seen in the surface plot. The momenta plot simply shows a small up trend, this is expected due to the long range electrostatic force of attraction between F and HH. There is no drastic change in the momenta of either F or HH that would otherwise indicate the occurrence of a reaction, as seen in simulation 1 above.
|-
| 3 || +0.5 || -0.5 || [[File:sm6416_Trajectory_3_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_3_Momenta.png|thumb|none|350px]] || This simulation has a positive momentum and therefore the HH molecule translates away from F, as can be seen from the surface plot. There is a slight overall increase in momenta, however not large enough to be of importance. This simulation does not lead to a reaction.
|-
| 4 || -1.6 || -0.5 || [[File:sm6416_Trajectory_4_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_4_Momenta.png|thumb|none|350px]] || The HH molecule in this simulation does possess sufficient momentum to translate towards F and result in a reaction. Evidence for this is both shown by the progression from the reactant to product well in the surface plot along with a drastic change in momentum of A-B (signifying F-H) shown by the momenta vs time plot, highlighting the high momentum oscillation, as expected from the heavier F atom.
|-
| 5 || +1.6 || -0.5 || [[File:sm6416_Trajectory_5_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_5_Momenta.png|thumb|none|350px]] || This simulation is very much like simulation 3, in that the HH momentum is positive. The similarity in the behaviour of the system is also similar, as shown by the surface plot. However, due to the greater momentum, HH translates further away from F than in simulation 3.
|-
| 6 || -2.9 || -0.5 || [[File:sm6416_Trajectory_6_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_6_Momenta.png|thumb|none|350px]] ||
|-
| 7 || +2.9 || -0.5 || [[File:sm6416_Trajectory_7_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_7_Momenta.png|thumb|none|350px]] ||
|-
| 8 || +0.1 || -0.8 || [[File:sm6416_Trajectory_8_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_8_Momenta.png|thumb|none|350px]] ||
|}

====Polyani's Empirical Rules====

Discuss relative translational and vibrational energies required to match the transition state for each endo/exothermic reaction relating to Hammond's postulate.

FH + H reactive trajectory - r1=0.9 r2=2.3 p1=6.5 p2=-1.5

[[File:sm6416_FHH_Reactive_Trajectory_1_Surface.png|thumb|none|350px]]
[[File:sm6416_FHH_Reactive_Trajectory_1_Momenta.png|thumb|none|350px]]
[[File:sm6416_FHH_Reactive_Trajectory_1_Distance.png|thumb|none|350px]]
[[File:sm6416_FHH_Reactive_Trajectory_1_Contour.png|thumb|none|350px]]

MRD:sm6416

2018-05-24T18:03:23Z

Sm6416: /* Reaction Dynamics */

==H2 H Exercise 1==

===Transition State Dynamics===

What value do the different components of the gradient of the potential energy surface have at a minimum and at a transition structure? Briefly explain how minima and transition structures can be distinguished using the curvature of the potential energy surface.

Discuss saddle point being the second derivative.
Minimum of trajectory.

===Locating the Transition State===

The transition state was determined through iterations of both r1 and r2 which resulted in the smallest displacement of momenta along with no displacement as shown by the contour plot. This method determined at rts = 0.907743.

[[File:sm6416_Transition_State_Contour.png|thumb|none|350px|Contour plot demonstrating rts = 0.907743 as a result of no fluctuations from the initial input, hence the complex is metaphorically sitting on the transition state.]]

[[File:sm6416_Transition_State_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating minimum, and almost zero, momentum at rts = 0.907743.]]

[[File:sm6416_Transition_State_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot demonstrating no fluctuations in distance and hence rts = 0.907743.]]

===Reaction Path===

The minimum energy path (MEP) is defined as the lowest path the reaction must follow to form the products and is the downhill motion from the transition state. It can be applied in both directions in the case in question. The MEP views the system as static as it resets the velocity to zero at each step. Whereas the trajectory is very much dynamic and the momenta is accounted for, this is reflected in the vibrational oscillation of the molecule as it passes along the minimum well towards the products.

====MEP====

Initial conditions of r1 = rts + 0.01 = 0.917743, r2 = rts = 0.907743 and p1 = p2 = 0 for the MEP simulation.

[[File:sm6416_MEP_Surface.png|thumb|none|350px|Surface plot highlighting the minimum energy path (MEP), as the reaction returns to the reactants without fully passing through the transition state.]]

[[File:sm6416_MEP_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating zero momentum, as inputted, and more importantly not change in momentum with running the simulation.]]

[[File:sm6416_MEP_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot showing that the reactants reach the transition state at the interception of r1 = r2. r1 quickly reaches a constant value, namely the equilibrium bond length of the reactant molecule. r2 increases logarithmically as time progresses, this represents an increasing distance of Ha from Hb-Hc and a continuing loss of momentum.]]

Final values from the MEP simulation.

r1 = 2.76195

r2 = 0.75883

These values reflect the minimum trajectory for a successful reaction.

p1 = p2 = 0

====Dynamic====

[[File:sm6416_Dynamic_Surface.png|thumb|none|350px|Surface plot highlighting the minimum energy path (MEP) with oscillation of the reactants, as the reaction returns to the reactants without fully passing through the transition state. It is therefore evident that the momentum as a result of the vibrational oscillation does not provide enough energy to proceed to the products.]]

[[File:sm6416_Dynamic_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating the momenta associated with the oscillating reactants.]]

[[File:sm6416_Dynamic_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot showing that the reactants reach the transition state at the interception of r1 = r2. r1 quickly decreases and oscillates about a constant value, namely the equilibrium bond length of the reactant molecule. r2 increases linearly as time progresses, this represents an increasing distance of Ha from Hb-Hc with a constant momentum.]]

Dynamic simulation final values

r1 = 10.0045

r2 = 0.75883

p1 = 2.48523

p2 = 1.29898

p(average) = 1.90409

With r1 = rts and r2 = rts + 0.01 would simply produce the same answer however the values would be flipped to the other distance. In other words r1 = 0.75883 and r2 = 10.0045 would be the output values.

Maintaining the final trajectories as calculated from the dynamic simulation and reversing the sign of the momenta, the reaction proceeds in the reverse direction to the products.

===Reactivity of Trajectories===

These simulations are restricted by the number of steps the program can handle, however a sound understanding of the reaction can be appreciated and the reactivity of each scenario can be determined appropriately.

{| class="wikitable" border=1
! Simulation !! p1 !! p2 !! Energy (units?) !! Reactivity !! Evidence !! Description
|-
| 1 || -1.25 || -2.5 || 5.03500 || Reactive || [[File:sm6416_MEP_Figure1.png|thumb|none|350px]] || Simulation 1: The reactants proceed through the transition state and to the products. The r2 distance decreases to the equilibrium bond length, whilst r1 simultaneously exhibits dissociation and increases beyond the scope of the graph. The small momenta attributed to the reactants is reflected in the vibrationally oscillating products, with a small amplitude.
|-
| 2 || -1.5 || -2.0 || 3.62879 || Unreactive || [[File:sm6416_MEP_Figure2.png|thumb|none|350px]] || Simulation 2: This is unreactive as the oscillating reactants reach the transition state point and r1 immediately returns to the initial bond length, whilst r2 continues to increase as it moves away from the H2 molecule.
|-
| 3 || -1.5 || -2.5 || 5.13738 || Reactive || [[File:sm6416_MEP_Figure3.png|thumb|none|350px]] || Simulation 3: This simulation shows a reactive pathway that is very similar to simulation 1, however due to the greater momenta associated with the reactants, as inputted, vibrational oscillations with a greater amplitude can be observed.
|-
| 4 || -2.5 || -5.0 || 9.86678 || Unreactive || [[File:sm6416_MEP_Figure4.png|thumb|none|350px]] || Simulation 4: Initially seen here are oscillating reactants with a very large amplitude. However, this simulation is unreactive despite the reactants going through the transition state and towards the product, they return to the initial reactants.
|-
| 5 || -2.5 || -5.2 || 11.80780 || Reactive || [[File:sm6416_MEP_Figure5.png|thumb|none|350px]] || Simulation 5: Like simulation 4, this simulation shows a large oscillating amplitude, whereas in this scenario after passing through the transition state, the products are completely obtained. The slight increase in the p2 momentum can be seen to result in the products.
|}

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? Assumes quasi-equilibrium between reactants and transition state. TST assumes that once reaction passes TS no way back to products. Completely opposite to experimental where it seems as though an equilibrium/reversible path exists between the transition state and products. Fluctuation of whether transition complexes go towards reactants or products are independent of each other.

==F-H-H System Exercise 2==
===Potential Energy Surface Inspection===
====Energetics====

F + H2 is an exothermic reaction as can be seen from the surface plot, the reaction progresses from a small H-H distance to a longer one, whilst H-F simultaneously equilibriates about the F-H bond length. It can be seen that the products are lower, and hence more stable, in energy than the reactants.

F-H + H is simply the reverse reaction that passes through the same transition state, hence this reaction is endothermic with the products being higher in energy than the reactants. There is an overall gain of energy.

With this information in mind, the F-H bond is more stable and thus stronger than the H-H bond. The main factors to this argument is the greater electronegativity of F leading to a stronger contribution to the bond than the molecular orbitals. Hence the overlap of molecular orbitals is a weaker factor in the bond strength.

[[File:sm6416_FHH_Surface.png|thumb|none|350px|Surface plot highlighting the energetics of the F-H-H system.]]

[[File:sm6416_HHF_Surface.png|thumb|none|350px|Surface plot highlighting the energetics of the H-H-F system.]]

====Transition State====

Discuss Hammond Postulate with TS being closer to products/reactants dependent on how the TS is composed.

The transition state complex is achieved at r1 = F-H = 1.810076 Angstrom and r2 = H-H = 0.74634 Angstrom, as can be seen from the graphs below showing the absence of displacement to either reactants or products.

[[File:sm6416_FHH_Transition_State_Contour.png|thumb|none|350px|Contour plot demonstrating rts as a result of no fluctuations from the initial input, hence the complex is metaphorically sitting on the transition state.]]

[[File:sm6416_FHH_Transition_State_Momenta_Time.png|thumb|none|350px|Momenta vs Time plot demonstrating minimum, and almost zero, momentum at rts.]]

[[File:sm6416_FHH_Transition_State_Surface.png|thumb|none|350px]]

====Activation Energy====

The activation energy for the exothermic reaction was calculated through a 500000 step MEP simulation with input values of r1 = 1.820076, r2 = 0.74634 and p1 = p2 = 0. It was required that after following the minimum energy path, the gradient of the line signifying the reactants was constant.

The activation energy is reported at +0.258 kcal/mol for the exothermic process.

[[File:sm6416_FHH_Activation_Energy_1.png|thumb|none|350px|Energy vs Time graph highlighting the activation energy of the exothermic reaction.]]

The activation energy for the endothermic process was determined with the following parameters: r1 = 1.800076, r2 = 0.74634, p1 = p2 = 0 with 250000 steps. The reported activation energy was +30.277 kcal/mol.

[[File:sm6416_FHH_Activation_Energy_2.png|thumb|none|350px|Energy vs Time graph highlighting the activation energy of the endothermic reaction.]]

It can hence be seen that the exothermic reaction of F + H2 --> F-H + H only requires a small activation energy as the products are substantially more thermodynamically stable than the reactants.

===Reaction Dynamics===

In light of the fact that energy is conserved, 'discuss the mechanism of release of the reaction energy.' How could this be confirmed experimentally? Measuring energy released from reaction ie exothermicity. Put first one separately. As reach momentum close to boundaries, system passes through transition state but returns to reactant well. Comment on effect the sign of the momentum has on the reactivity.

r1 = 2.3, r2 = 0.74

{| class="wikitable" border=1
! Simulation !! pHH !! pF-H !! Surface Plot !! Momenta vs Time Plot !! Observations !!
|-
| 1 || -2.5 || -1.5 || [[File:sm6416_Trajectory_1_Surface.png|thumb|none|350px]] ||[[File:sm6416_Trajectory_1_Momenta.png|thumb|none|350px]] || This trajectory results in a successful reaction as seen from the surface plot; the reactants proceed through the transition state and continue into the product well, whilst continually oscillating as a result of the momentum gained.
|-
| 2 || -0.5 || -0.5 || [[File:sm6416_Trajectory_2_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_2_Momenta.png|thumb|none|350px]] || This momentum does not proceed to a reaction. Through the dynamic animation it can be seen that the HH molecule does not possess enough momentum to translate towards F. Therefore the system does not translate out of the reactant well, as seen in the surface plot. The momenta plot simply shows a small up trend, this is expected due to the long range electrostatic force of attraction between F and HH. There is no drastic change in the momenta of either F or HH that would otherwise indicate the occurrence of a reaction, as seen in simulation 1 above.
|-
| 3 || +0.5 || -0.5 || [[File:sm6416_Trajectory_3_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_3_Momenta.png|thumb|none|350px]] || This simulation has a positive momentum and therefore the HH molecule translates away from F, as can be seen from the surface plot. There is a slight overall increase in momenta, however not large enough to be of importance. This simulation does not lead to a reaction.
|-
| 4 || -1.6 || -0.5 || [[File:sm6416_Trajectory_4_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_4_Momenta.png|thumb|none|350px]] || The HH molecule in this simulation does possess sufficient momentum to translate towards F and result in a reaction. Evidence for this is both shown by the progression from the reactant to product well in the surface plot along with a drastic change in momentum of A-B (signifying F-H) shown by the momenta vs time plot, highlighting the high momentum oscillation, as expected from the heavier F atom.
|-
| 5 || +1.6 || -0.5 || [[File:sm6416_Trajectory_5_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_5_Momenta.png|thumb|none|350px]] || This simulation is very much like simulation 3, in that the HH momentum is positive. The similarity in the behaviour of the system is also similar, as shown by the surface plot. However, due to the greater momentum, HH translates further away from F than in simulation 3.
|-
| 6 || -2.9 || -0.5 || [[File:sm6416_Trajectory_6_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_6_Momenta.png|thumb|none|350px]] ||
|-
| 7 || +2.9 || -0.5 || [[File:sm6416_Trajectory_7_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_7_Momenta.png|thumb|none|350px]] ||
|-
| 8 || +0.1 || -0.8 || [[File:sm6416_Trajectory_8_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_8_Momenta.png|thumb|none|350px]] ||
|}

====Polyani's Empirical Rules====

Discuss relative translational and vibrational energies required to match the transition state for each endo/exothermic reaction relating to Hammond's postulate.

FH + H reactive trajectory - r1=0.9 r2=2.3 p1=6.5 p2=-1.5

[[File:sm6416_FHH_Reactive_Trajectory_1_Surface.png|thumb|none|350px]]
[[File:sm6416_FHH_Reactive_Trajectory_1_Momenta.png|thumb|none|350px]]
[[File:sm6416_FHH_Reactive_Trajectory_1_Distance.png|thumb|none|350px]]
[[File:sm6416_FHH_Reactive_Trajectory_1_Contour.png|thumb|none|350px]]

MRD:sm6416

2018-05-24T17:58:30Z

Sm6416: /* MEP */

==H2 H Exercise 1==

===Transition State Dynamics===

What value do the different components of the gradient of the potential energy surface have at a minimum and at a transition structure? Briefly explain how minima and transition structures can be distinguished using the curvature of the potential energy surface.

Discuss saddle point being the second derivative.
Minimum of trajectory.

===Locating the Transition State===

The transition state was determined through iterations of both r1 and r2 which resulted in the smallest displacement of momenta along with no displacement as shown by the contour plot. This method determined at rts = 0.907743.

[[File:sm6416_Transition_State_Contour.png|thumb|none|350px|Contour plot demonstrating rts = 0.907743 as a result of no fluctuations from the initial input, hence the complex is metaphorically sitting on the transition state.]]

[[File:sm6416_Transition_State_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating minimum, and almost zero, momentum at rts = 0.907743.]]

[[File:sm6416_Transition_State_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot demonstrating no fluctuations in distance and hence rts = 0.907743.]]

===Reaction Path===

The minimum energy path (MEP) is defined as the lowest path the reaction must follow to form the products and is the downhill motion from the transition state. It can be applied in both directions in the case in question. The MEP views the system as static as it resets the velocity to zero at each step. Whereas the trajectory is very much dynamic and the momenta is accounted for, this is reflected in the vibrational oscillation of the molecule as it passes along the minimum well towards the products.

====MEP====

Initial conditions of r1 = rts + 0.01 = 0.917743, r2 = rts = 0.907743 and p1 = p2 = 0 for the MEP simulation.

[[File:sm6416_MEP_Surface.png|thumb|none|350px|Surface plot highlighting the minimum energy path (MEP), as the reaction returns to the reactants without fully passing through the transition state.]]

[[File:sm6416_MEP_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating zero momentum, as inputted, and more importantly not change in momentum with running the simulation.]]

[[File:sm6416_MEP_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot showing that the reactants reach the transition state at the interception of r1 = r2. r1 quickly reaches a constant value, namely the equilibrium bond length of the reactant molecule. r2 increases logarithmically as time progresses, this represents an increasing distance of Ha from Hb-Hc and a continuing loss of momentum.]]

Final values from the MEP simulation.

r1 = 2.76195

r2 = 0.75883

These values reflect the minimum trajectory for a successful reaction.

p1 = p2 = 0

====Dynamic====

[[File:sm6416_Dynamic_Surface.png|thumb|none|350px|Surface plot highlighting the minimum energy path (MEP) with oscillation of the reactants, as the reaction returns to the reactants without fully passing through the transition state. It is therefore evident that the momentum as a result of the vibrational oscillation does not provide enough energy to proceed to the products.]]

[[File:sm6416_Dynamic_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating the momenta associated with the oscillating reactants.]]

[[File:sm6416_Dynamic_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot showing that the reactants reach the transition state at the interception of r1 = r2. r1 quickly decreases and oscillates about a constant value, namely the equilibrium bond length of the reactant molecule. r2 increases linearly as time progresses, this represents an increasing distance of Ha from Hb-Hc with a constant momentum.]]

Dynamic simulation final values

r1 = 10.0045

r2 = 0.75883

p1 = 2.48523

p2 = 1.29898

p(average) = 1.90409

With r1 = rts and r2 = rts + 0.01 would simply produce the same answer however the values would be flipped to the other distance. In other words r1 = 0.75883 and r2 = 10.0045 would be the output values.

Maintaining the final trajectories as calculated from the dynamic simulation and reversing the sign of the momenta, the reaction proceeds in the reverse direction to the products.

===Reactivity of Trajectories===

These simulations are restricted by the number of steps the program can handle, however a sound understanding of the reaction can be appreciated and the reactivity of each scenario can be determined appropriately.

{| class="wikitable" border=1
! Simulation !! p1 !! p2 !! Energy (units?) !! Reactivity !! Evidence !! Description
|-
| 1 || -1.25 || -2.5 || 5.03500 || Reactive || [[File:sm6416_MEP_Figure1.png|thumb|none|350px]] || Simulation 1: The reactants proceed through the transition state and to the products. The r2 distance decreases to the equilibrium bond length, whilst r1 simultaneously exhibits dissociation and increases beyond the scope of the graph. The small momenta attributed to the reactants is reflected in the vibrationally oscillating products, with a small amplitude.
|-
| 2 || -1.5 || -2.0 || 3.62879 || Unreactive || [[File:sm6416_MEP_Figure2.png|thumb|none|350px]] || Simulation 2: This is unreactive as the oscillating reactants reach the transition state point and r1 immediately returns to the initial bond length, whilst r2 continues to increase as it moves away from the H2 molecule.
|-
| 3 || -1.5 || -2.5 || 5.13738 || Reactive || [[File:sm6416_MEP_Figure3.png|thumb|none|350px]] || Simulation 3: This simulation shows a reactive pathway that is very similar to simulation 1, however due to the greater momenta associated with the reactants, as inputted, vibrational oscillations with a greater amplitude can be observed.
|-
| 4 || -2.5 || -5.0 || 9.86678 || Unreactive || [[File:sm6416_MEP_Figure4.png|thumb|none|350px]] || Simulation 4: Initially seen here are oscillating reactants with a very large amplitude. However, this simulation is unreactive despite the reactants going through the transition state and towards the product, they return to the initial reactants.
|-
| 5 || -2.5 || -5.2 || 11.80780 || Reactive || [[File:sm6416_MEP_Figure5.png|thumb|none|350px]] || Simulation 5: Like simulation 4, this simulation shows a large oscillating amplitude, whereas in this scenario after passing through the transition state, the products are completely obtained. The slight increase in the p2 momentum can be seen to result in the products.
|}

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? Assumes quasi-equilibrium between reactants and transition state. TST assumes that once reaction passes TS no way back to products. Completely opposite to experimental where it seems as though an equilibrium/reversible path exists between the transition state and products. Fluctuation of whether transition complexes go towards reactants or products are independent of each other.

==F-H-H System Exercise 2==
===Potential Energy Surface Inspection===
====Energetics====

F + H2 is an exothermic reaction as can be seen from the surface plot, the reaction progresses from a small H-H distance to a longer one, whilst H-F simultaneously equilibriates about the F-H bond length. It can be seen that the products are lower, and hence more stable, in energy than the reactants.

F-H + H is simply the reverse reaction that passes through the same transition state, hence this reaction is endothermic with the products being higher in energy than the reactants. There is an overall gain of energy.

With this information in mind, the F-H bond is more stable and thus stronger than the H-H bond. The main factors to this argument is the greater electronegativity of F leading to a stronger contribution to the bond than the molecular orbitals. Hence the overlap of molecular orbitals is a weaker factor in the bond strength.

[[File:sm6416_FHH_Surface.png|thumb|none|350px|Surface plot highlighting the energetics of the F-H-H system.]]

[[File:sm6416_HHF_Surface.png|thumb|none|350px|Surface plot highlighting the energetics of the H-H-F system.]]

====Transition State====

Discuss Hammond Postulate with TS being closer to products/reactants dependent on how the TS is composed.

The transition state complex is achieved at r1 = F-H = 1.810076 Angstrom and r2 = H-H = 0.74634 Angstrom, as can be seen from the graphs below showing the absence of displacement to either reactants or products.

[[File:sm6416_FHH_Transition_State_Contour.png|thumb|none|350px|Contour plot demonstrating rts as a result of no fluctuations from the initial input, hence the complex is metaphorically sitting on the transition state.]]

[[File:sm6416_FHH_Transition_State_Momenta_Time.png|thumb|none|350px|Momenta vs Time plot demonstrating minimum, and almost zero, momentum at rts.]]

[[File:sm6416_FHH_Transition_State_Surface.png|thumb|none|350px]]

====Activation Energy====

The activation energy for the exothermic reaction was calculated through a 500000 step MEP simulation with input values of r1 = 1.820076, r2 = 0.74634 and p1 = p2 = 0. It was required that after following the minimum energy path, the gradient of the line signifying the reactants was constant.

The activation energy is reported at +0.258 kcal/mol for the exothermic process.

[[File:sm6416_FHH_Activation_Energy_1.png|thumb|none|350px|Energy vs Time graph highlighting the activation energy of the exothermic reaction.]]

The activation energy for the endothermic process was determined with the following parameters: r1 = 1.800076, r2 = 0.74634, p1 = p2 = 0 with 250000 steps. The reported activation energy was +30.277 kcal/mol.

[[File:sm6416_FHH_Activation_Energy_2.png|thumb|none|350px|Energy vs Time graph highlighting the activation energy of the endothermic reaction.]]

It can hence be seen that the exothermic reaction of F + H2 --> F-H + H only requires a small activation energy as the products are substantially more thermodynamically stable than the reactants.

===Reaction Dynamics===

In light of the fact that energy is conserved, discuss the mechanism of release of the reaction energy. How could this be confirmed experimentally? Measuring energy released from reaction ie exothermicity. Put first one separately. As reach momentum close to boundaries, system passes through transition state but returns to reactant well. Comment on effect the sign of the momentum has on the reactivity.

r1 = 2.3, r2 = 0.74

{| class="wikitable" border=1
! Simulation !! pHH !! pF-H !! Surface Plot !! Momenta vs Time Plot !! Observations !!
|-
| 1 || -2.5 || -1.5 || [[File:sm6416_Trajectory_1_Surface.png|thumb|none|350px]] ||[[File:sm6416_Trajectory_1_Momenta.png|thumb|none|350px]] || This trajectory results in a successful reaction as seen from the surface plot; the reactants proceed through the transition state and continue into the product well, whilst continually oscillating as a result of the momentum gained.
|-
| 2 || -0.5 || -0.5 || [[File:sm6416_Trajectory_2_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_2_Momenta.png|thumb|none|350px]] || This momentum does not proceed to a reaction. Through the dynamic animation it can be seen that the HH molecule does not possess enough momentum to translate towards F. Therefore the system does not translate out of the reactant well, as seen in the surface plot. The momenta plot simply shows a small up trend, this is expected due to the long range electrostatic force of attraction between F and HH. There is no drastic change in the momenta of either F or HH that would otherwise indicate the occurrence of a reaction, as seen in simulation 1 above.
|-
| 3 || +0.5 || -0.5 || [[File:sm6416_Trajectory_3_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_3_Momenta.png|thumb|none|350px]] || This simulation has a positive momentum and therefore the HH molecule translates away from F, as can be seen from the surface plot. There is a slight overall increase in momenta, however not large enough to be of importance. This simulation does not lead to a reaction.
|-
| 4 || -1.6 || -0.5 || [[File:sm6416_Trajectory_4_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_4_Momenta.png|thumb|none|350px]] || The HH molecule in this simulation does possess sufficient momentum to translate towards F and result in a reaction. Evidence for this is both shown by the progression from the reactant to product well in the surface plot along with a drastic change in momentum of A-B (signifying F-H) shown by the momenta vs time plot, highlighting the high momentum oscillation, as expected from the heavier F atom.
|-
| 5 || +1.6 || -0.5 || [[File:sm6416_Trajectory_5_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_5_Momenta.png|thumb|none|350px]] || This simulation is very much like simulation 3, in that the HH momentum is positive. The similarity in the behaviour of the system is also similar, as shown by the surface plot. However, due to the greater momentum, HH translates further away from F than in simulation 3.
|-
| 6 || -2.9 || -0.5 || [[File:sm6416_Trajectory_6_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_6_Momenta.png|thumb|none|350px]] ||
|-
| 7 || +2.9 || -0.5 || [[File:sm6416_Trajectory_7_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_7_Momenta.png|thumb|none|350px]] ||
|-
| 8 || +0.1 || -0.8 || [[File:sm6416_Trajectory_8_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_8_Momenta.png|thumb|none|350px]] ||
|}

====Polyani's Empirical Rules====

Discuss relative translational and vibrational energies required to match the transition state for each endo/exothermic reaction relating to Hammond's postulate.

FH + H reactive trajectory - r1=0.9 r2=2.3 p1=6.5 p2=-1.5

[[File:sm6416_FHH_Reactive_Trajectory_1_Surface.png|thumb|none|350px]]
[[File:sm6416_FHH_Reactive_Trajectory_1_Momenta.png|thumb|none|350px]]
[[File:sm6416_FHH_Reactive_Trajectory_1_Distance.png|thumb|none|350px]]
[[File:sm6416_FHH_Reactive_Trajectory_1_Contour.png|thumb|none|350px]]

MRD:sm6416

2018-05-24T17:58:20Z

Sm6416: /* MEP */

==H2 H Exercise 1==

===Transition State Dynamics===

What value do the different components of the gradient of the potential energy surface have at a minimum and at a transition structure? Briefly explain how minima and transition structures can be distinguished using the curvature of the potential energy surface.

Discuss saddle point being the second derivative.
Minimum of trajectory.

===Locating the Transition State===

The transition state was determined through iterations of both r1 and r2 which resulted in the smallest displacement of momenta along with no displacement as shown by the contour plot. This method determined at rts = 0.907743.

[[File:sm6416_Transition_State_Contour.png|thumb|none|350px|Contour plot demonstrating rts = 0.907743 as a result of no fluctuations from the initial input, hence the complex is metaphorically sitting on the transition state.]]

[[File:sm6416_Transition_State_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating minimum, and almost zero, momentum at rts = 0.907743.]]

[[File:sm6416_Transition_State_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot demonstrating no fluctuations in distance and hence rts = 0.907743.]]

===Reaction Path===

The minimum energy path (MEP) is defined as the lowest path the reaction must follow to form the products and is the downhill motion from the transition state. It can be applied in both directions in the case in question. The MEP views the system as static as it resets the velocity to zero at each step. Whereas the trajectory is very much dynamic and the momenta is accounted for, this is reflected in the vibrational oscillation of the molecule as it passes along the minimum well towards the products.

====MEP====

Initial conditions of r1 = rts + 0.01 = 0.917743, r2 = rts = 0.907743 and p1 = p2 = 0 for the MEP simulation.

<div>
[[File:sm6416_MEP_Surface.png|thumb|none|350px|Surface plot highlighting the minimum energy path (MEP), as the reaction returns to the reactants without fully passing through the transition state.]]
</div>

[[File:sm6416_MEP_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating zero momentum, as inputted, and more importantly not change in momentum with running the simulation.]]

[[File:sm6416_MEP_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot showing that the reactants reach the transition state at the interception of r1 = r2. r1 quickly reaches a constant value, namely the equilibrium bond length of the reactant molecule. r2 increases logarithmically as time progresses, this represents an increasing distance of Ha from Hb-Hc and a continuing loss of momentum.]]

Final values from the MEP simulation.

r1 = 2.76195

r2 = 0.75883

These values reflect the minimum trajectory for a successful reaction.

p1 = p2 = 0

====Dynamic====

[[File:sm6416_Dynamic_Surface.png|thumb|none|350px|Surface plot highlighting the minimum energy path (MEP) with oscillation of the reactants, as the reaction returns to the reactants without fully passing through the transition state. It is therefore evident that the momentum as a result of the vibrational oscillation does not provide enough energy to proceed to the products.]]

[[File:sm6416_Dynamic_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating the momenta associated with the oscillating reactants.]]

[[File:sm6416_Dynamic_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot showing that the reactants reach the transition state at the interception of r1 = r2. r1 quickly decreases and oscillates about a constant value, namely the equilibrium bond length of the reactant molecule. r2 increases linearly as time progresses, this represents an increasing distance of Ha from Hb-Hc with a constant momentum.]]

Dynamic simulation final values

r1 = 10.0045

r2 = 0.75883

p1 = 2.48523

p2 = 1.29898

p(average) = 1.90409

With r1 = rts and r2 = rts + 0.01 would simply produce the same answer however the values would be flipped to the other distance. In other words r1 = 0.75883 and r2 = 10.0045 would be the output values.

Maintaining the final trajectories as calculated from the dynamic simulation and reversing the sign of the momenta, the reaction proceeds in the reverse direction to the products.

===Reactivity of Trajectories===

These simulations are restricted by the number of steps the program can handle, however a sound understanding of the reaction can be appreciated and the reactivity of each scenario can be determined appropriately.

{| class="wikitable" border=1
! Simulation !! p1 !! p2 !! Energy (units?) !! Reactivity !! Evidence !! Description
|-
| 1 || -1.25 || -2.5 || 5.03500 || Reactive || [[File:sm6416_MEP_Figure1.png|thumb|none|350px]] || Simulation 1: The reactants proceed through the transition state and to the products. The r2 distance decreases to the equilibrium bond length, whilst r1 simultaneously exhibits dissociation and increases beyond the scope of the graph. The small momenta attributed to the reactants is reflected in the vibrationally oscillating products, with a small amplitude.
|-
| 2 || -1.5 || -2.0 || 3.62879 || Unreactive || [[File:sm6416_MEP_Figure2.png|thumb|none|350px]] || Simulation 2: This is unreactive as the oscillating reactants reach the transition state point and r1 immediately returns to the initial bond length, whilst r2 continues to increase as it moves away from the H2 molecule.
|-
| 3 || -1.5 || -2.5 || 5.13738 || Reactive || [[File:sm6416_MEP_Figure3.png|thumb|none|350px]] || Simulation 3: This simulation shows a reactive pathway that is very similar to simulation 1, however due to the greater momenta associated with the reactants, as inputted, vibrational oscillations with a greater amplitude can be observed.
|-
| 4 || -2.5 || -5.0 || 9.86678 || Unreactive || [[File:sm6416_MEP_Figure4.png|thumb|none|350px]] || Simulation 4: Initially seen here are oscillating reactants with a very large amplitude. However, this simulation is unreactive despite the reactants going through the transition state and towards the product, they return to the initial reactants.
|-
| 5 || -2.5 || -5.2 || 11.80780 || Reactive || [[File:sm6416_MEP_Figure5.png|thumb|none|350px]] || Simulation 5: Like simulation 4, this simulation shows a large oscillating amplitude, whereas in this scenario after passing through the transition state, the products are completely obtained. The slight increase in the p2 momentum can be seen to result in the products.
|}

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? Assumes quasi-equilibrium between reactants and transition state. TST assumes that once reaction passes TS no way back to products. Completely opposite to experimental where it seems as though an equilibrium/reversible path exists between the transition state and products. Fluctuation of whether transition complexes go towards reactants or products are independent of each other.

==F-H-H System Exercise 2==
===Potential Energy Surface Inspection===
====Energetics====

F + H2 is an exothermic reaction as can be seen from the surface plot, the reaction progresses from a small H-H distance to a longer one, whilst H-F simultaneously equilibriates about the F-H bond length. It can be seen that the products are lower, and hence more stable, in energy than the reactants.

F-H + H is simply the reverse reaction that passes through the same transition state, hence this reaction is endothermic with the products being higher in energy than the reactants. There is an overall gain of energy.

With this information in mind, the F-H bond is more stable and thus stronger than the H-H bond. The main factors to this argument is the greater electronegativity of F leading to a stronger contribution to the bond than the molecular orbitals. Hence the overlap of molecular orbitals is a weaker factor in the bond strength.

[[File:sm6416_FHH_Surface.png|thumb|none|350px|Surface plot highlighting the energetics of the F-H-H system.]]

[[File:sm6416_HHF_Surface.png|thumb|none|350px|Surface plot highlighting the energetics of the H-H-F system.]]

====Transition State====

Discuss Hammond Postulate with TS being closer to products/reactants dependent on how the TS is composed.

The transition state complex is achieved at r1 = F-H = 1.810076 Angstrom and r2 = H-H = 0.74634 Angstrom, as can be seen from the graphs below showing the absence of displacement to either reactants or products.

[[File:sm6416_FHH_Transition_State_Contour.png|thumb|none|350px|Contour plot demonstrating rts as a result of no fluctuations from the initial input, hence the complex is metaphorically sitting on the transition state.]]

[[File:sm6416_FHH_Transition_State_Momenta_Time.png|thumb|none|350px|Momenta vs Time plot demonstrating minimum, and almost zero, momentum at rts.]]

[[File:sm6416_FHH_Transition_State_Surface.png|thumb|none|350px]]

====Activation Energy====

The activation energy for the exothermic reaction was calculated through a 500000 step MEP simulation with input values of r1 = 1.820076, r2 = 0.74634 and p1 = p2 = 0. It was required that after following the minimum energy path, the gradient of the line signifying the reactants was constant.

The activation energy is reported at +0.258 kcal/mol for the exothermic process.

[[File:sm6416_FHH_Activation_Energy_1.png|thumb|none|350px|Energy vs Time graph highlighting the activation energy of the exothermic reaction.]]

The activation energy for the endothermic process was determined with the following parameters: r1 = 1.800076, r2 = 0.74634, p1 = p2 = 0 with 250000 steps. The reported activation energy was +30.277 kcal/mol.

[[File:sm6416_FHH_Activation_Energy_2.png|thumb|none|350px|Energy vs Time graph highlighting the activation energy of the endothermic reaction.]]

It can hence be seen that the exothermic reaction of F + H2 --> F-H + H only requires a small activation energy as the products are substantially more thermodynamically stable than the reactants.

===Reaction Dynamics===

In light of the fact that energy is conserved, discuss the mechanism of release of the reaction energy. How could this be confirmed experimentally? Measuring energy released from reaction ie exothermicity. Put first one separately. As reach momentum close to boundaries, system passes through transition state but returns to reactant well. Comment on effect the sign of the momentum has on the reactivity.

r1 = 2.3, r2 = 0.74

{| class="wikitable" border=1
! Simulation !! pHH !! pF-H !! Surface Plot !! Momenta vs Time Plot !! Observations !!
|-
| 1 || -2.5 || -1.5 || [[File:sm6416_Trajectory_1_Surface.png|thumb|none|350px]] ||[[File:sm6416_Trajectory_1_Momenta.png|thumb|none|350px]] || This trajectory results in a successful reaction as seen from the surface plot; the reactants proceed through the transition state and continue into the product well, whilst continually oscillating as a result of the momentum gained.
|-
| 2 || -0.5 || -0.5 || [[File:sm6416_Trajectory_2_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_2_Momenta.png|thumb|none|350px]] || This momentum does not proceed to a reaction. Through the dynamic animation it can be seen that the HH molecule does not possess enough momentum to translate towards F. Therefore the system does not translate out of the reactant well, as seen in the surface plot. The momenta plot simply shows a small up trend, this is expected due to the long range electrostatic force of attraction between F and HH. There is no drastic change in the momenta of either F or HH that would otherwise indicate the occurrence of a reaction, as seen in simulation 1 above.
|-
| 3 || +0.5 || -0.5 || [[File:sm6416_Trajectory_3_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_3_Momenta.png|thumb|none|350px]] || This simulation has a positive momentum and therefore the HH molecule translates away from F, as can be seen from the surface plot. There is a slight overall increase in momenta, however not large enough to be of importance. This simulation does not lead to a reaction.
|-
| 4 || -1.6 || -0.5 || [[File:sm6416_Trajectory_4_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_4_Momenta.png|thumb|none|350px]] || The HH molecule in this simulation does possess sufficient momentum to translate towards F and result in a reaction. Evidence for this is both shown by the progression from the reactant to product well in the surface plot along with a drastic change in momentum of A-B (signifying F-H) shown by the momenta vs time plot, highlighting the high momentum oscillation, as expected from the heavier F atom.
|-
| 5 || +1.6 || -0.5 || [[File:sm6416_Trajectory_5_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_5_Momenta.png|thumb|none|350px]] || This simulation is very much like simulation 3, in that the HH momentum is positive. The similarity in the behaviour of the system is also similar, as shown by the surface plot. However, due to the greater momentum, HH translates further away from F than in simulation 3.
|-
| 6 || -2.9 || -0.5 || [[File:sm6416_Trajectory_6_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_6_Momenta.png|thumb|none|350px]] ||
|-
| 7 || +2.9 || -0.5 || [[File:sm6416_Trajectory_7_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_7_Momenta.png|thumb|none|350px]] ||
|-
| 8 || +0.1 || -0.8 || [[File:sm6416_Trajectory_8_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_8_Momenta.png|thumb|none|350px]] ||
|}

====Polyani's Empirical Rules====

Discuss relative translational and vibrational energies required to match the transition state for each endo/exothermic reaction relating to Hammond's postulate.

FH + H reactive trajectory - r1=0.9 r2=2.3 p1=6.5 p2=-1.5

[[File:sm6416_FHH_Reactive_Trajectory_1_Surface.png|thumb|none|350px]]
[[File:sm6416_FHH_Reactive_Trajectory_1_Momenta.png|thumb|none|350px]]
[[File:sm6416_FHH_Reactive_Trajectory_1_Distance.png|thumb|none|350px]]
[[File:sm6416_FHH_Reactive_Trajectory_1_Contour.png|thumb|none|350px]]

MRD:sm6416

2018-05-24T17:58:06Z

Sm6416: /* MEP */

==H2 H Exercise 1==

===Transition State Dynamics===

What value do the different components of the gradient of the potential energy surface have at a minimum and at a transition structure? Briefly explain how minima and transition structures can be distinguished using the curvature of the potential energy surface.

Discuss saddle point being the second derivative.
Minimum of trajectory.

===Locating the Transition State===

The transition state was determined through iterations of both r1 and r2 which resulted in the smallest displacement of momenta along with no displacement as shown by the contour plot. This method determined at rts = 0.907743.

[[File:sm6416_Transition_State_Contour.png|thumb|none|350px|Contour plot demonstrating rts = 0.907743 as a result of no fluctuations from the initial input, hence the complex is metaphorically sitting on the transition state.]]

[[File:sm6416_Transition_State_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating minimum, and almost zero, momentum at rts = 0.907743.]]

[[File:sm6416_Transition_State_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot demonstrating no fluctuations in distance and hence rts = 0.907743.]]

===Reaction Path===

The minimum energy path (MEP) is defined as the lowest path the reaction must follow to form the products and is the downhill motion from the transition state. It can be applied in both directions in the case in question. The MEP views the system as static as it resets the velocity to zero at each step. Whereas the trajectory is very much dynamic and the momenta is accounted for, this is reflected in the vibrational oscillation of the molecule as it passes along the minimum well towards the products.

====MEP====

Initial conditions of r1 = rts + 0.01 = 0.917743, r2 = rts = 0.907743 and p1 = p2 = 0 for the MEP simulation.

<div>[[File:sm6416_MEP_Surface.png|thumb|none|350px|Surface plot highlighting the minimum energy path (MEP), as the reaction returns to the reactants without fully passing through the transition state.]]</div>

[[File:sm6416_MEP_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating zero momentum, as inputted, and more importantly not change in momentum with running the simulation.]]

[[File:sm6416_MEP_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot showing that the reactants reach the transition state at the interception of r1 = r2. r1 quickly reaches a constant value, namely the equilibrium bond length of the reactant molecule. r2 increases logarithmically as time progresses, this represents an increasing distance of Ha from Hb-Hc and a continuing loss of momentum.]]

Final values from the MEP simulation.

r1 = 2.76195

r2 = 0.75883

These values reflect the minimum trajectory for a successful reaction.

p1 = p2 = 0

====Dynamic====

[[File:sm6416_Dynamic_Surface.png|thumb|none|350px|Surface plot highlighting the minimum energy path (MEP) with oscillation of the reactants, as the reaction returns to the reactants without fully passing through the transition state. It is therefore evident that the momentum as a result of the vibrational oscillation does not provide enough energy to proceed to the products.]]

[[File:sm6416_Dynamic_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating the momenta associated with the oscillating reactants.]]

[[File:sm6416_Dynamic_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot showing that the reactants reach the transition state at the interception of r1 = r2. r1 quickly decreases and oscillates about a constant value, namely the equilibrium bond length of the reactant molecule. r2 increases linearly as time progresses, this represents an increasing distance of Ha from Hb-Hc with a constant momentum.]]

Dynamic simulation final values

r1 = 10.0045

r2 = 0.75883

p1 = 2.48523

p2 = 1.29898

p(average) = 1.90409

With r1 = rts and r2 = rts + 0.01 would simply produce the same answer however the values would be flipped to the other distance. In other words r1 = 0.75883 and r2 = 10.0045 would be the output values.

Maintaining the final trajectories as calculated from the dynamic simulation and reversing the sign of the momenta, the reaction proceeds in the reverse direction to the products.

===Reactivity of Trajectories===

These simulations are restricted by the number of steps the program can handle, however a sound understanding of the reaction can be appreciated and the reactivity of each scenario can be determined appropriately.

{| class="wikitable" border=1
! Simulation !! p1 !! p2 !! Energy (units?) !! Reactivity !! Evidence !! Description
|-
| 1 || -1.25 || -2.5 || 5.03500 || Reactive || [[File:sm6416_MEP_Figure1.png|thumb|none|350px]] || Simulation 1: The reactants proceed through the transition state and to the products. The r2 distance decreases to the equilibrium bond length, whilst r1 simultaneously exhibits dissociation and increases beyond the scope of the graph. The small momenta attributed to the reactants is reflected in the vibrationally oscillating products, with a small amplitude.
|-
| 2 || -1.5 || -2.0 || 3.62879 || Unreactive || [[File:sm6416_MEP_Figure2.png|thumb|none|350px]] || Simulation 2: This is unreactive as the oscillating reactants reach the transition state point and r1 immediately returns to the initial bond length, whilst r2 continues to increase as it moves away from the H2 molecule.
|-
| 3 || -1.5 || -2.5 || 5.13738 || Reactive || [[File:sm6416_MEP_Figure3.png|thumb|none|350px]] || Simulation 3: This simulation shows a reactive pathway that is very similar to simulation 1, however due to the greater momenta associated with the reactants, as inputted, vibrational oscillations with a greater amplitude can be observed.
|-
| 4 || -2.5 || -5.0 || 9.86678 || Unreactive || [[File:sm6416_MEP_Figure4.png|thumb|none|350px]] || Simulation 4: Initially seen here are oscillating reactants with a very large amplitude. However, this simulation is unreactive despite the reactants going through the transition state and towards the product, they return to the initial reactants.
|-
| 5 || -2.5 || -5.2 || 11.80780 || Reactive || [[File:sm6416_MEP_Figure5.png|thumb|none|350px]] || Simulation 5: Like simulation 4, this simulation shows a large oscillating amplitude, whereas in this scenario after passing through the transition state, the products are completely obtained. The slight increase in the p2 momentum can be seen to result in the products.
|}

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? Assumes quasi-equilibrium between reactants and transition state. TST assumes that once reaction passes TS no way back to products. Completely opposite to experimental where it seems as though an equilibrium/reversible path exists between the transition state and products. Fluctuation of whether transition complexes go towards reactants or products are independent of each other.

==F-H-H System Exercise 2==
===Potential Energy Surface Inspection===
====Energetics====

F + H2 is an exothermic reaction as can be seen from the surface plot, the reaction progresses from a small H-H distance to a longer one, whilst H-F simultaneously equilibriates about the F-H bond length. It can be seen that the products are lower, and hence more stable, in energy than the reactants.

F-H + H is simply the reverse reaction that passes through the same transition state, hence this reaction is endothermic with the products being higher in energy than the reactants. There is an overall gain of energy.

With this information in mind, the F-H bond is more stable and thus stronger than the H-H bond. The main factors to this argument is the greater electronegativity of F leading to a stronger contribution to the bond than the molecular orbitals. Hence the overlap of molecular orbitals is a weaker factor in the bond strength.

[[File:sm6416_FHH_Surface.png|thumb|none|350px|Surface plot highlighting the energetics of the F-H-H system.]]

[[File:sm6416_HHF_Surface.png|thumb|none|350px|Surface plot highlighting the energetics of the H-H-F system.]]

====Transition State====

Discuss Hammond Postulate with TS being closer to products/reactants dependent on how the TS is composed.

The transition state complex is achieved at r1 = F-H = 1.810076 Angstrom and r2 = H-H = 0.74634 Angstrom, as can be seen from the graphs below showing the absence of displacement to either reactants or products.

[[File:sm6416_FHH_Transition_State_Contour.png|thumb|none|350px|Contour plot demonstrating rts as a result of no fluctuations from the initial input, hence the complex is metaphorically sitting on the transition state.]]

[[File:sm6416_FHH_Transition_State_Momenta_Time.png|thumb|none|350px|Momenta vs Time plot demonstrating minimum, and almost zero, momentum at rts.]]

[[File:sm6416_FHH_Transition_State_Surface.png|thumb|none|350px]]

====Activation Energy====

The activation energy for the exothermic reaction was calculated through a 500000 step MEP simulation with input values of r1 = 1.820076, r2 = 0.74634 and p1 = p2 = 0. It was required that after following the minimum energy path, the gradient of the line signifying the reactants was constant.

The activation energy is reported at +0.258 kcal/mol for the exothermic process.

[[File:sm6416_FHH_Activation_Energy_1.png|thumb|none|350px|Energy vs Time graph highlighting the activation energy of the exothermic reaction.]]

The activation energy for the endothermic process was determined with the following parameters: r1 = 1.800076, r2 = 0.74634, p1 = p2 = 0 with 250000 steps. The reported activation energy was +30.277 kcal/mol.

[[File:sm6416_FHH_Activation_Energy_2.png|thumb|none|350px|Energy vs Time graph highlighting the activation energy of the endothermic reaction.]]

It can hence be seen that the exothermic reaction of F + H2 --> F-H + H only requires a small activation energy as the products are substantially more thermodynamically stable than the reactants.

===Reaction Dynamics===

In light of the fact that energy is conserved, discuss the mechanism of release of the reaction energy. How could this be confirmed experimentally? Measuring energy released from reaction ie exothermicity. Put first one separately. As reach momentum close to boundaries, system passes through transition state but returns to reactant well. Comment on effect the sign of the momentum has on the reactivity.

r1 = 2.3, r2 = 0.74

{| class="wikitable" border=1
! Simulation !! pHH !! pF-H !! Surface Plot !! Momenta vs Time Plot !! Observations !!
|-
| 1 || -2.5 || -1.5 || [[File:sm6416_Trajectory_1_Surface.png|thumb|none|350px]] ||[[File:sm6416_Trajectory_1_Momenta.png|thumb|none|350px]] || This trajectory results in a successful reaction as seen from the surface plot; the reactants proceed through the transition state and continue into the product well, whilst continually oscillating as a result of the momentum gained.
|-
| 2 || -0.5 || -0.5 || [[File:sm6416_Trajectory_2_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_2_Momenta.png|thumb|none|350px]] || This momentum does not proceed to a reaction. Through the dynamic animation it can be seen that the HH molecule does not possess enough momentum to translate towards F. Therefore the system does not translate out of the reactant well, as seen in the surface plot. The momenta plot simply shows a small up trend, this is expected due to the long range electrostatic force of attraction between F and HH. There is no drastic change in the momenta of either F or HH that would otherwise indicate the occurrence of a reaction, as seen in simulation 1 above.
|-
| 3 || +0.5 || -0.5 || [[File:sm6416_Trajectory_3_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_3_Momenta.png|thumb|none|350px]] || This simulation has a positive momentum and therefore the HH molecule translates away from F, as can be seen from the surface plot. There is a slight overall increase in momenta, however not large enough to be of importance. This simulation does not lead to a reaction.
|-
| 4 || -1.6 || -0.5 || [[File:sm6416_Trajectory_4_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_4_Momenta.png|thumb|none|350px]] || The HH molecule in this simulation does possess sufficient momentum to translate towards F and result in a reaction. Evidence for this is both shown by the progression from the reactant to product well in the surface plot along with a drastic change in momentum of A-B (signifying F-H) shown by the momenta vs time plot, highlighting the high momentum oscillation, as expected from the heavier F atom.
|-
| 5 || +1.6 || -0.5 || [[File:sm6416_Trajectory_5_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_5_Momenta.png|thumb|none|350px]] || This simulation is very much like simulation 3, in that the HH momentum is positive. The similarity in the behaviour of the system is also similar, as shown by the surface plot. However, due to the greater momentum, HH translates further away from F than in simulation 3.
|-
| 6 || -2.9 || -0.5 || [[File:sm6416_Trajectory_6_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_6_Momenta.png|thumb|none|350px]] ||
|-
| 7 || +2.9 || -0.5 || [[File:sm6416_Trajectory_7_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_7_Momenta.png|thumb|none|350px]] ||
|-
| 8 || +0.1 || -0.8 || [[File:sm6416_Trajectory_8_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_8_Momenta.png|thumb|none|350px]] ||
|}

====Polyani's Empirical Rules====

Discuss relative translational and vibrational energies required to match the transition state for each endo/exothermic reaction relating to Hammond's postulate.

FH + H reactive trajectory - r1=0.9 r2=2.3 p1=6.5 p2=-1.5

[[File:sm6416_FHH_Reactive_Trajectory_1_Surface.png|thumb|none|350px]]
[[File:sm6416_FHH_Reactive_Trajectory_1_Momenta.png|thumb|none|350px]]
[[File:sm6416_FHH_Reactive_Trajectory_1_Distance.png|thumb|none|350px]]
[[File:sm6416_FHH_Reactive_Trajectory_1_Contour.png|thumb|none|350px]]

File:Sm6416 FHH Reactive Trajectory 1 Contour.png

2018-05-24T17:52:10Z

Sm6416:

File:Sm6416 FHH Reactive Trajectory 1 Distance.png

2018-05-24T17:51:59Z

Sm6416:

File:Sm6416 FHH Reactive Trajectory 1 Momenta.png

2018-05-24T17:51:48Z

Sm6416:

File:Sm6416 FHH Reactive Trajectory 1 Surface.png

2018-05-24T17:51:38Z

Sm6416:

MRD:sm6416

2018-05-24T17:51:13Z

Sm6416: /* Reaction Dynamics */

==H2 H Exercise 1==

===Transition State Dynamics===

What value do the different components of the gradient of the potential energy surface have at a minimum and at a transition structure? Briefly explain how minima and transition structures can be distinguished using the curvature of the potential energy surface.

Discuss saddle point being the second derivative.
Minimum of trajectory.

===Locating the Transition State===

The transition state was determined through iterations of both r1 and r2 which resulted in the smallest displacement of momenta along with no displacement as shown by the contour plot. This method determined at rts = 0.907743.

[[File:sm6416_Transition_State_Contour.png|thumb|none|350px|Contour plot demonstrating rts = 0.907743 as a result of no fluctuations from the initial input, hence the complex is metaphorically sitting on the transition state.]]

[[File:sm6416_Transition_State_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating minimum, and almost zero, momentum at rts = 0.907743.]]

[[File:sm6416_Transition_State_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot demonstrating no fluctuations in distance and hence rts = 0.907743.]]

===Reaction Path===

The minimum energy path (MEP) is defined as the lowest path the reaction must follow to form the products and is the downhill motion from the transition state. It can be applied in both directions in the case in question. The MEP views the system as static as it resets the velocity to zero at each step. Whereas the trajectory is very much dynamic and the momenta is accounted for, this is reflected in the vibrational oscillation of the molecule as it passes along the minimum well towards the products.

====MEP====

Initial conditions of r1 = rts + 0.01 = 0.917743, r2 = rts = 0.907743 and p1 = p2 = 0 for the MEP simulation.

[[File:sm6416_MEP_Surface.png|thumb|none|350px|Surface plot highlighting the minimum energy path (MEP), as the reaction returns to the reactants without fully passing through the transition state.]]

[[File:sm6416_MEP_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating zero momentum, as inputted, and more importantly not change in momentum with running the simulation.]]

[[File:sm6416_MEP_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot showing that the reactants reach the transition state at the interception of r1 = r2. r1 quickly reaches a constant value, namely the equilibrium bond length of the reactant molecule. r2 increases logarithmically as time progresses, this represents an increasing distance of Ha from Hb-Hc and a continuing loss of momentum.]]

Final values from the MEP simulation.

r1 = 2.76195

r2 = 0.75883

These values reflect the minimum trajectory for a successful reaction.

p1 = p2 = 0

====Dynamic====

[[File:sm6416_Dynamic_Surface.png|thumb|none|350px|Surface plot highlighting the minimum energy path (MEP) with oscillation of the reactants, as the reaction returns to the reactants without fully passing through the transition state. It is therefore evident that the momentum as a result of the vibrational oscillation does not provide enough energy to proceed to the products.]]

[[File:sm6416_Dynamic_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating the momenta associated with the oscillating reactants.]]

[[File:sm6416_Dynamic_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot showing that the reactants reach the transition state at the interception of r1 = r2. r1 quickly decreases and oscillates about a constant value, namely the equilibrium bond length of the reactant molecule. r2 increases linearly as time progresses, this represents an increasing distance of Ha from Hb-Hc with a constant momentum.]]

Dynamic simulation final values

r1 = 10.0045

r2 = 0.75883

p1 = 2.48523

p2 = 1.29898

p(average) = 1.90409

With r1 = rts and r2 = rts + 0.01 would simply produce the same answer however the values would be flipped to the other distance. In other words r1 = 0.75883 and r2 = 10.0045 would be the output values.

Maintaining the final trajectories as calculated from the dynamic simulation and reversing the sign of the momenta, the reaction proceeds in the reverse direction to the products.

===Reactivity of Trajectories===

These simulations are restricted by the number of steps the program can handle, however a sound understanding of the reaction can be appreciated and the reactivity of each scenario can be determined appropriately.

{| class="wikitable" border=1
! Simulation !! p1 !! p2 !! Energy (units?) !! Reactivity !! Evidence !! Description
|-
| 1 || -1.25 || -2.5 || 5.03500 || Reactive || [[File:sm6416_MEP_Figure1.png|thumb|none|350px]] || Simulation 1: The reactants proceed through the transition state and to the products. The r2 distance decreases to the equilibrium bond length, whilst r1 simultaneously exhibits dissociation and increases beyond the scope of the graph. The small momenta attributed to the reactants is reflected in the vibrationally oscillating products, with a small amplitude.
|-
| 2 || -1.5 || -2.0 || 3.62879 || Unreactive || [[File:sm6416_MEP_Figure2.png|thumb|none|350px]] || Simulation 2: This is unreactive as the oscillating reactants reach the transition state point and r1 immediately returns to the initial bond length, whilst r2 continues to increase as it moves away from the H2 molecule.
|-
| 3 || -1.5 || -2.5 || 5.13738 || Reactive || [[File:sm6416_MEP_Figure3.png|thumb|none|350px]] || Simulation 3: This simulation shows a reactive pathway that is very similar to simulation 1, however due to the greater momenta associated with the reactants, as inputted, vibrational oscillations with a greater amplitude can be observed.
|-
| 4 || -2.5 || -5.0 || 9.86678 || Unreactive || [[File:sm6416_MEP_Figure4.png|thumb|none|350px]] || Simulation 4: Initially seen here are oscillating reactants with a very large amplitude. However, this simulation is unreactive despite the reactants going through the transition state and towards the product, they return to the initial reactants.
|-
| 5 || -2.5 || -5.2 || 11.80780 || Reactive || [[File:sm6416_MEP_Figure5.png|thumb|none|350px]] || Simulation 5: Like simulation 4, this simulation shows a large oscillating amplitude, whereas in this scenario after passing through the transition state, the products are completely obtained. The slight increase in the p2 momentum can be seen to result in the products.
|}

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? Assumes quasi-equilibrium between reactants and transition state. TST assumes that once reaction passes TS no way back to products. Completely opposite to experimental where it seems as though an equilibrium/reversible path exists between the transition state and products. Fluctuation of whether transition complexes go towards reactants or products are independent of each other.

==F-H-H System Exercise 2==
===Potential Energy Surface Inspection===
====Energetics====

F + H2 is an exothermic reaction as can be seen from the surface plot, the reaction progresses from a small H-H distance to a longer one, whilst H-F simultaneously equilibriates about the F-H bond length. It can be seen that the products are lower, and hence more stable, in energy than the reactants.

F-H + H is simply the reverse reaction that passes through the same transition state, hence this reaction is endothermic with the products being higher in energy than the reactants. There is an overall gain of energy.

With this information in mind, the F-H bond is more stable and thus stronger than the H-H bond. The main factors to this argument is the greater electronegativity of F leading to a stronger contribution to the bond than the molecular orbitals. Hence the overlap of molecular orbitals is a weaker factor in the bond strength.

[[File:sm6416_FHH_Surface.png|thumb|none|350px|Surface plot highlighting the energetics of the F-H-H system.]]

[[File:sm6416_HHF_Surface.png|thumb|none|350px|Surface plot highlighting the energetics of the H-H-F system.]]

====Transition State====

Discuss Hammond Postulate with TS being closer to products/reactants dependent on how the TS is composed.

The transition state complex is achieved at r1 = F-H = 1.810076 Angstrom and r2 = H-H = 0.74634 Angstrom, as can be seen from the graphs below showing the absence of displacement to either reactants or products.

[[File:sm6416_FHH_Transition_State_Contour.png|thumb|none|350px|Contour plot demonstrating rts as a result of no fluctuations from the initial input, hence the complex is metaphorically sitting on the transition state.]]

[[File:sm6416_FHH_Transition_State_Momenta_Time.png|thumb|none|350px|Momenta vs Time plot demonstrating minimum, and almost zero, momentum at rts.]]

[[File:sm6416_FHH_Transition_State_Surface.png|thumb|none|350px]]

====Activation Energy====

The activation energy for the exothermic reaction was calculated through a 500000 step MEP simulation with input values of r1 = 1.820076, r2 = 0.74634 and p1 = p2 = 0. It was required that after following the minimum energy path, the gradient of the line signifying the reactants was constant.

The activation energy is reported at +0.258 kcal/mol for the exothermic process.

[[File:sm6416_FHH_Activation_Energy_1.png|thumb|none|350px|Energy vs Time graph highlighting the activation energy of the exothermic reaction.]]

The activation energy for the endothermic process was determined with the following parameters: r1 = 1.800076, r2 = 0.74634, p1 = p2 = 0 with 250000 steps. The reported activation energy was +30.277 kcal/mol.

[[File:sm6416_FHH_Activation_Energy_2.png|thumb|none|350px|Energy vs Time graph highlighting the activation energy of the endothermic reaction.]]

It can hence be seen that the exothermic reaction of F + H2 --> F-H + H only requires a small activation energy as the products are substantially more thermodynamically stable than the reactants.

===Reaction Dynamics===

In light of the fact that energy is conserved, discuss the mechanism of release of the reaction energy. How could this be confirmed experimentally? Measuring energy released from reaction ie exothermicity. Put first one separately. As reach momentum close to boundaries, system passes through transition state but returns to reactant well. Comment on effect the sign of the momentum has on the reactivity.

r1 = 2.3, r2 = 0.74

{| class="wikitable" border=1
! Simulation !! pHH !! pF-H !! Surface Plot !! Momenta vs Time Plot !! Observations !!
|-
| 1 || -2.5 || -1.5 || [[File:sm6416_Trajectory_1_Surface.png|thumb|none|350px]] ||[[File:sm6416_Trajectory_1_Momenta.png|thumb|none|350px]] || This trajectory results in a successful reaction as seen from the surface plot; the reactants proceed through the transition state and continue into the product well, whilst continually oscillating as a result of the momentum gained.
|-
| 2 || -0.5 || -0.5 || [[File:sm6416_Trajectory_2_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_2_Momenta.png|thumb|none|350px]] || This momentum does not proceed to a reaction. Through the dynamic animation it can be seen that the HH molecule does not possess enough momentum to translate towards F. Therefore the system does not translate out of the reactant well, as seen in the surface plot. The momenta plot simply shows a small up trend, this is expected due to the long range electrostatic force of attraction between F and HH. There is no drastic change in the momenta of either F or HH that would otherwise indicate the occurrence of a reaction, as seen in simulation 1 above.
|-
| 3 || +0.5 || -0.5 || [[File:sm6416_Trajectory_3_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_3_Momenta.png|thumb|none|350px]] || This simulation has a positive momentum and therefore the HH molecule translates away from F, as can be seen from the surface plot. There is a slight overall increase in momenta, however not large enough to be of importance. This simulation does not lead to a reaction.
|-
| 4 || -1.6 || -0.5 || [[File:sm6416_Trajectory_4_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_4_Momenta.png|thumb|none|350px]] || The HH molecule in this simulation does possess sufficient momentum to translate towards F and result in a reaction. Evidence for this is both shown by the progression from the reactant to product well in the surface plot along with a drastic change in momentum of A-B (signifying F-H) shown by the momenta vs time plot, highlighting the high momentum oscillation, as expected from the heavier F atom.
|-
| 5 || +1.6 || -0.5 || [[File:sm6416_Trajectory_5_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_5_Momenta.png|thumb|none|350px]] || This simulation is very much like simulation 3, in that the HH momentum is positive. The similarity in the behaviour of the system is also similar, as shown by the surface plot. However, due to the greater momentum, HH translates further away from F than in simulation 3.
|-
| 6 || -2.9 || -0.5 || [[File:sm6416_Trajectory_6_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_6_Momenta.png|thumb|none|350px]] ||
|-
| 7 || +2.9 || -0.5 || [[File:sm6416_Trajectory_7_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_7_Momenta.png|thumb|none|350px]] ||
|-
| 8 || +0.1 || -0.8 || [[File:sm6416_Trajectory_8_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_8_Momenta.png|thumb|none|350px]] ||
|}

====Polyani's Empirical Rules====

Discuss relative translational and vibrational energies required to match the transition state for each endo/exothermic reaction relating to Hammond's postulate.

FH + H reactive trajectory - r1=0.9 r2=2.3 p1=6.5 p2=-1.5

[[File:sm6416_FHH_Reactive_Trajectory_1_Surface.png|thumb|none|350px]]
[[File:sm6416_FHH_Reactive_Trajectory_1_Momenta.png|thumb|none|350px]]
[[File:sm6416_FHH_Reactive_Trajectory_1_Distance.png|thumb|none|350px]]
[[File:sm6416_FHH_Reactive_Trajectory_1_Contour.png|thumb|none|350px]]

MRD:sm6416

2018-05-24T17:47:07Z

Sm6416: /* Polyani's Empirical Rules */

==H2 H Exercise 1==

===Transition State Dynamics===

What value do the different components of the gradient of the potential energy surface have at a minimum and at a transition structure? Briefly explain how minima and transition structures can be distinguished using the curvature of the potential energy surface.

Discuss saddle point being the second derivative.
Minimum of trajectory.

===Locating the Transition State===

The transition state was determined through iterations of both r1 and r2 which resulted in the smallest displacement of momenta along with no displacement as shown by the contour plot. This method determined at rts = 0.907743.

[[File:sm6416_Transition_State_Contour.png|thumb|none|350px|Contour plot demonstrating rts = 0.907743 as a result of no fluctuations from the initial input, hence the complex is metaphorically sitting on the transition state.]]

[[File:sm6416_Transition_State_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating minimum, and almost zero, momentum at rts = 0.907743.]]

[[File:sm6416_Transition_State_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot demonstrating no fluctuations in distance and hence rts = 0.907743.]]

===Reaction Path===

The minimum energy path (MEP) is defined as the lowest path the reaction must follow to form the products and is the downhill motion from the transition state. It can be applied in both directions in the case in question. The MEP views the system as static as it resets the velocity to zero at each step. Whereas the trajectory is very much dynamic and the momenta is accounted for, this is reflected in the vibrational oscillation of the molecule as it passes along the minimum well towards the products.

====MEP====

Initial conditions of r1 = rts + 0.01 = 0.917743, r2 = rts = 0.907743 and p1 = p2 = 0 for the MEP simulation.

[[File:sm6416_MEP_Surface.png|thumb|none|350px|Surface plot highlighting the minimum energy path (MEP), as the reaction returns to the reactants without fully passing through the transition state.]]

[[File:sm6416_MEP_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating zero momentum, as inputted, and more importantly not change in momentum with running the simulation.]]

[[File:sm6416_MEP_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot showing that the reactants reach the transition state at the interception of r1 = r2. r1 quickly reaches a constant value, namely the equilibrium bond length of the reactant molecule. r2 increases logarithmically as time progresses, this represents an increasing distance of Ha from Hb-Hc and a continuing loss of momentum.]]

Final values from the MEP simulation.

r1 = 2.76195

r2 = 0.75883

These values reflect the minimum trajectory for a successful reaction.

p1 = p2 = 0

====Dynamic====

[[File:sm6416_Dynamic_Surface.png|thumb|none|350px|Surface plot highlighting the minimum energy path (MEP) with oscillation of the reactants, as the reaction returns to the reactants without fully passing through the transition state. It is therefore evident that the momentum as a result of the vibrational oscillation does not provide enough energy to proceed to the products.]]

[[File:sm6416_Dynamic_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating the momenta associated with the oscillating reactants.]]

[[File:sm6416_Dynamic_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot showing that the reactants reach the transition state at the interception of r1 = r2. r1 quickly decreases and oscillates about a constant value, namely the equilibrium bond length of the reactant molecule. r2 increases linearly as time progresses, this represents an increasing distance of Ha from Hb-Hc with a constant momentum.]]

Dynamic simulation final values

r1 = 10.0045

r2 = 0.75883

p1 = 2.48523

p2 = 1.29898

p(average) = 1.90409

With r1 = rts and r2 = rts + 0.01 would simply produce the same answer however the values would be flipped to the other distance. In other words r1 = 0.75883 and r2 = 10.0045 would be the output values.

Maintaining the final trajectories as calculated from the dynamic simulation and reversing the sign of the momenta, the reaction proceeds in the reverse direction to the products.

===Reactivity of Trajectories===

These simulations are restricted by the number of steps the program can handle, however a sound understanding of the reaction can be appreciated and the reactivity of each scenario can be determined appropriately.

{| class="wikitable" border=1
! Simulation !! p1 !! p2 !! Energy (units?) !! Reactivity !! Evidence !! Description
|-
| 1 || -1.25 || -2.5 || 5.03500 || Reactive || [[File:sm6416_MEP_Figure1.png|thumb|none|350px]] || Simulation 1: The reactants proceed through the transition state and to the products. The r2 distance decreases to the equilibrium bond length, whilst r1 simultaneously exhibits dissociation and increases beyond the scope of the graph. The small momenta attributed to the reactants is reflected in the vibrationally oscillating products, with a small amplitude.
|-
| 2 || -1.5 || -2.0 || 3.62879 || Unreactive || [[File:sm6416_MEP_Figure2.png|thumb|none|350px]] || Simulation 2: This is unreactive as the oscillating reactants reach the transition state point and r1 immediately returns to the initial bond length, whilst r2 continues to increase as it moves away from the H2 molecule.
|-
| 3 || -1.5 || -2.5 || 5.13738 || Reactive || [[File:sm6416_MEP_Figure3.png|thumb|none|350px]] || Simulation 3: This simulation shows a reactive pathway that is very similar to simulation 1, however due to the greater momenta associated with the reactants, as inputted, vibrational oscillations with a greater amplitude can be observed.
|-
| 4 || -2.5 || -5.0 || 9.86678 || Unreactive || [[File:sm6416_MEP_Figure4.png|thumb|none|350px]] || Simulation 4: Initially seen here are oscillating reactants with a very large amplitude. However, this simulation is unreactive despite the reactants going through the transition state and towards the product, they return to the initial reactants.
|-
| 5 || -2.5 || -5.2 || 11.80780 || Reactive || [[File:sm6416_MEP_Figure5.png|thumb|none|350px]] || Simulation 5: Like simulation 4, this simulation shows a large oscillating amplitude, whereas in this scenario after passing through the transition state, the products are completely obtained. The slight increase in the p2 momentum can be seen to result in the products.
|}

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? Assumes quasi-equilibrium between reactants and transition state. TST assumes that once reaction passes TS no way back to products. Completely opposite to experimental where it seems as though an equilibrium/reversible path exists between the transition state and products. Fluctuation of whether transition complexes go towards reactants or products are independent of each other.

==F-H-H System Exercise 2==
===Potential Energy Surface Inspection===
====Energetics====

F + H2 is an exothermic reaction as can be seen from the surface plot, the reaction progresses from a small H-H distance to a longer one, whilst H-F simultaneously equilibriates about the F-H bond length. It can be seen that the products are lower, and hence more stable, in energy than the reactants.

F-H + H is simply the reverse reaction that passes through the same transition state, hence this reaction is endothermic with the products being higher in energy than the reactants. There is an overall gain of energy.

With this information in mind, the F-H bond is more stable and thus stronger than the H-H bond. The main factors to this argument is the greater electronegativity of F leading to a stronger contribution to the bond than the molecular orbitals. Hence the overlap of molecular orbitals is a weaker factor in the bond strength.

[[File:sm6416_FHH_Surface.png|thumb|none|350px|Surface plot highlighting the energetics of the F-H-H system.]]

[[File:sm6416_HHF_Surface.png|thumb|none|350px|Surface plot highlighting the energetics of the H-H-F system.]]

====Transition State====

Discuss Hammond Postulate with TS being closer to products/reactants dependent on how the TS is composed.

The transition state complex is achieved at r1 = F-H = 1.810076 Angstrom and r2 = H-H = 0.74634 Angstrom, as can be seen from the graphs below showing the absence of displacement to either reactants or products.

[[File:sm6416_FHH_Transition_State_Contour.png|thumb|none|350px|Contour plot demonstrating rts as a result of no fluctuations from the initial input, hence the complex is metaphorically sitting on the transition state.]]

[[File:sm6416_FHH_Transition_State_Momenta_Time.png|thumb|none|350px|Momenta vs Time plot demonstrating minimum, and almost zero, momentum at rts.]]

[[File:sm6416_FHH_Transition_State_Surface.png|thumb|none|350px]]

====Activation Energy====

The activation energy for the exothermic reaction was calculated through a 500000 step MEP simulation with input values of r1 = 1.820076, r2 = 0.74634 and p1 = p2 = 0. It was required that after following the minimum energy path, the gradient of the line signifying the reactants was constant.

The activation energy is reported at +0.258 kcal/mol for the exothermic process.

[[File:sm6416_FHH_Activation_Energy_1.png|thumb|none|350px|Energy vs Time graph highlighting the activation energy of the exothermic reaction.]]

The activation energy for the endothermic process was determined with the following parameters: r1 = 1.800076, r2 = 0.74634, p1 = p2 = 0 with 250000 steps. The reported activation energy was +30.277 kcal/mol.

[[File:sm6416_FHH_Activation_Energy_2.png|thumb|none|350px|Energy vs Time graph highlighting the activation energy of the endothermic reaction.]]

It can hence be seen that the exothermic reaction of F + H2 --> F-H + H only requires a small activation energy as the products are substantially more thermodynamically stable than the reactants.

===Reaction Dynamics===

In light of the fact that energy is conserved, discuss the mechanism of release of the reaction energy. How could this be confirmed experimentally? Measuring energy released from reaction ie exothermicity. Put first one separately. As reach momentum close to boundaries, system passes through transition state but returns to reactant well. Comment on effect the sign of the momentum has on the reactivity.

r1 = 2.3, r2 = 0.74

{| class="wikitable" border=1
! Simulation !! pHH !! pF-H !! Surface Plot !! Momenta vs Time Plot !! Observations !!
|-
| 1 || -2.5 || -1.5 || [[File:sm6416_Trajectory_1_Surface.png|thumb|none|350px]] ||[[File:sm6416_Trajectory_1_Momenta.png|thumb|none|350px]] || This trajectory results in a successful reaction as seen from the surface plot; the reactants proceed through the transition state and continue into the product well, whilst continually oscillating as a result of the momentum gained.
|-
| 2 || -0.5 || -0.5 || [[File:sm6416_Trajectory_2_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_2_Momenta.png|thumb|none|350px]] || This momentum does not proceed to a reaction. Through the dynamic animation it can be seen that the HH molecule does not possess enough momentum to translate towards F. Therefore the system does not translate out of the reactant well, as seen in the surface plot. The momenta plot simply shows a small up trend, this is expected due to the long range electrostatic force of attraction between F and HH. There is no drastic change in the momenta of either F or HH that would otherwise indicate the occurrence of a reaction, as seen in simulation 1 above.
|-
| 3 || +0.5 || -0.5 || [[File:sm6416_Trajectory_3_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_3_Momenta.png|thumb|none|350px]] || This simulation has a positive momentum and therefore the HH molecule translates away from F, as can be seen from the surface plot. There is a slight overall increase in momenta, however not large enough to be of importance. This simulation does not lead to a reaction.
|-
| 4 || -1.6 || -0.5 || [[File:sm6416_Trajectory_4_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_4_Momenta.png|thumb|none|350px]] || The HH molecule in this simulation does possess sufficient momentum to translate towards F and result in a reaction. Evidence for this is both shown by the progression from the reactant to product well in the surface plot along with a drastic change in momentum of A-B (signifying F-H) shown by the momenta vs time plot, highlighting the high momentum oscillation, as expected from the heavier F atom.
|-
| 5 || +1.6 || -0.5 || [[File:sm6416_Trajectory_5_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_5_Momenta.png|thumb|none|350px]] || This simulation is very much like simulation 3, in that the HH momentum is positive. The similarity in the behaviour of the system is also similar, as shown by the surface plot. However, due to the greater momentum, HH translates further away from F than in simulation 3.
|-
| 6 || -2.9 || -0.5 || [[File:sm6416_Trajectory_6_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_6_Momenta.png|thumb|none|350px]] ||
|-
| 7 || +2.9 || -0.5 || [[File:sm6416_Trajectory_7_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_7_Momenta.png|thumb|none|350px]] ||
|-
| 8 || +0.1 || -0.8 || [[File:sm6416_Trajectory_8_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_8_Momenta.png|thumb|none|350px]] ||
|}

====Polyani's Empirical Rules====

Discuss relative translational and vibrational energies required to match the transition state for each endo/exothermic reaction relating to Hammond's postulate.

FH + H reactive trajectory - r1=0.9 r2=2.3 p1=6.5 p2=-1.5

File:Sm6416 Trajectory 8 Momenta.png

2018-05-24T17:43:09Z

Sm6416:

File:Sm6416 Trajectory 8 Surface.png

2018-05-24T17:42:58Z

Sm6416:

MRD:sm6416

2018-05-24T17:42:12Z

Sm6416: /* Reaction Dynamics */

==H2 H Exercise 1==

===Transition State Dynamics===

What value do the different components of the gradient of the potential energy surface have at a minimum and at a transition structure? Briefly explain how minima and transition structures can be distinguished using the curvature of the potential energy surface.

Discuss saddle point being the second derivative.
Minimum of trajectory.

===Locating the Transition State===

The transition state was determined through iterations of both r1 and r2 which resulted in the smallest displacement of momenta along with no displacement as shown by the contour plot. This method determined at rts = 0.907743.

[[File:sm6416_Transition_State_Contour.png|thumb|none|350px|Contour plot demonstrating rts = 0.907743 as a result of no fluctuations from the initial input, hence the complex is metaphorically sitting on the transition state.]]

[[File:sm6416_Transition_State_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating minimum, and almost zero, momentum at rts = 0.907743.]]

[[File:sm6416_Transition_State_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot demonstrating no fluctuations in distance and hence rts = 0.907743.]]

===Reaction Path===

The minimum energy path (MEP) is defined as the lowest path the reaction must follow to form the products and is the downhill motion from the transition state. It can be applied in both directions in the case in question. The MEP views the system as static as it resets the velocity to zero at each step. Whereas the trajectory is very much dynamic and the momenta is accounted for, this is reflected in the vibrational oscillation of the molecule as it passes along the minimum well towards the products.

====MEP====

Initial conditions of r1 = rts + 0.01 = 0.917743, r2 = rts = 0.907743 and p1 = p2 = 0 for the MEP simulation.

[[File:sm6416_MEP_Surface.png|thumb|none|350px|Surface plot highlighting the minimum energy path (MEP), as the reaction returns to the reactants without fully passing through the transition state.]]

[[File:sm6416_MEP_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating zero momentum, as inputted, and more importantly not change in momentum with running the simulation.]]

[[File:sm6416_MEP_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot showing that the reactants reach the transition state at the interception of r1 = r2. r1 quickly reaches a constant value, namely the equilibrium bond length of the reactant molecule. r2 increases logarithmically as time progresses, this represents an increasing distance of Ha from Hb-Hc and a continuing loss of momentum.]]

Final values from the MEP simulation.

r1 = 2.76195

r2 = 0.75883

These values reflect the minimum trajectory for a successful reaction.

p1 = p2 = 0

====Dynamic====

[[File:sm6416_Dynamic_Surface.png|thumb|none|350px|Surface plot highlighting the minimum energy path (MEP) with oscillation of the reactants, as the reaction returns to the reactants without fully passing through the transition state. It is therefore evident that the momentum as a result of the vibrational oscillation does not provide enough energy to proceed to the products.]]

[[File:sm6416_Dynamic_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating the momenta associated with the oscillating reactants.]]

[[File:sm6416_Dynamic_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot showing that the reactants reach the transition state at the interception of r1 = r2. r1 quickly decreases and oscillates about a constant value, namely the equilibrium bond length of the reactant molecule. r2 increases linearly as time progresses, this represents an increasing distance of Ha from Hb-Hc with a constant momentum.]]

Dynamic simulation final values

r1 = 10.0045

r2 = 0.75883

p1 = 2.48523

p2 = 1.29898

p(average) = 1.90409

With r1 = rts and r2 = rts + 0.01 would simply produce the same answer however the values would be flipped to the other distance. In other words r1 = 0.75883 and r2 = 10.0045 would be the output values.

Maintaining the final trajectories as calculated from the dynamic simulation and reversing the sign of the momenta, the reaction proceeds in the reverse direction to the products.

===Reactivity of Trajectories===

These simulations are restricted by the number of steps the program can handle, however a sound understanding of the reaction can be appreciated and the reactivity of each scenario can be determined appropriately.

{| class="wikitable" border=1
! Simulation !! p1 !! p2 !! Energy (units?) !! Reactivity !! Evidence !! Description
|-
| 1 || -1.25 || -2.5 || 5.03500 || Reactive || [[File:sm6416_MEP_Figure1.png|thumb|none|350px]] || Simulation 1: The reactants proceed through the transition state and to the products. The r2 distance decreases to the equilibrium bond length, whilst r1 simultaneously exhibits dissociation and increases beyond the scope of the graph. The small momenta attributed to the reactants is reflected in the vibrationally oscillating products, with a small amplitude.
|-
| 2 || -1.5 || -2.0 || 3.62879 || Unreactive || [[File:sm6416_MEP_Figure2.png|thumb|none|350px]] || Simulation 2: This is unreactive as the oscillating reactants reach the transition state point and r1 immediately returns to the initial bond length, whilst r2 continues to increase as it moves away from the H2 molecule.
|-
| 3 || -1.5 || -2.5 || 5.13738 || Reactive || [[File:sm6416_MEP_Figure3.png|thumb|none|350px]] || Simulation 3: This simulation shows a reactive pathway that is very similar to simulation 1, however due to the greater momenta associated with the reactants, as inputted, vibrational oscillations with a greater amplitude can be observed.
|-
| 4 || -2.5 || -5.0 || 9.86678 || Unreactive || [[File:sm6416_MEP_Figure4.png|thumb|none|350px]] || Simulation 4: Initially seen here are oscillating reactants with a very large amplitude. However, this simulation is unreactive despite the reactants going through the transition state and towards the product, they return to the initial reactants.
|-
| 5 || -2.5 || -5.2 || 11.80780 || Reactive || [[File:sm6416_MEP_Figure5.png|thumb|none|350px]] || Simulation 5: Like simulation 4, this simulation shows a large oscillating amplitude, whereas in this scenario after passing through the transition state, the products are completely obtained. The slight increase in the p2 momentum can be seen to result in the products.
|}

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? Assumes quasi-equilibrium between reactants and transition state. TST assumes that once reaction passes TS no way back to products. Completely opposite to experimental where it seems as though an equilibrium/reversible path exists between the transition state and products. Fluctuation of whether transition complexes go towards reactants or products are independent of each other.

==F-H-H System Exercise 2==
===Potential Energy Surface Inspection===
====Energetics====

F + H2 is an exothermic reaction as can be seen from the surface plot, the reaction progresses from a small H-H distance to a longer one, whilst H-F simultaneously equilibriates about the F-H bond length. It can be seen that the products are lower, and hence more stable, in energy than the reactants.

F-H + H is simply the reverse reaction that passes through the same transition state, hence this reaction is endothermic with the products being higher in energy than the reactants. There is an overall gain of energy.

With this information in mind, the F-H bond is more stable and thus stronger than the H-H bond. The main factors to this argument is the greater electronegativity of F leading to a stronger contribution to the bond than the molecular orbitals. Hence the overlap of molecular orbitals is a weaker factor in the bond strength.

[[File:sm6416_FHH_Surface.png|thumb|none|350px|Surface plot highlighting the energetics of the F-H-H system.]]

[[File:sm6416_HHF_Surface.png|thumb|none|350px|Surface plot highlighting the energetics of the H-H-F system.]]

====Transition State====

Discuss Hammond Postulate with TS being closer to products/reactants dependent on how the TS is composed.

The transition state complex is achieved at r1 = F-H = 1.810076 Angstrom and r2 = H-H = 0.74634 Angstrom, as can be seen from the graphs below showing the absence of displacement to either reactants or products.

[[File:sm6416_FHH_Transition_State_Contour.png|thumb|none|350px|Contour plot demonstrating rts as a result of no fluctuations from the initial input, hence the complex is metaphorically sitting on the transition state.]]

[[File:sm6416_FHH_Transition_State_Momenta_Time.png|thumb|none|350px|Momenta vs Time plot demonstrating minimum, and almost zero, momentum at rts.]]

[[File:sm6416_FHH_Transition_State_Surface.png|thumb|none|350px]]

====Activation Energy====

The activation energy for the exothermic reaction was calculated through a 500000 step MEP simulation with input values of r1 = 1.820076, r2 = 0.74634 and p1 = p2 = 0. It was required that after following the minimum energy path, the gradient of the line signifying the reactants was constant.

The activation energy is reported at +0.258 kcal/mol for the exothermic process.

[[File:sm6416_FHH_Activation_Energy_1.png|thumb|none|350px|Energy vs Time graph highlighting the activation energy of the exothermic reaction.]]

The activation energy for the endothermic process was determined with the following parameters: r1 = 1.800076, r2 = 0.74634, p1 = p2 = 0 with 250000 steps. The reported activation energy was +30.277 kcal/mol.

[[File:sm6416_FHH_Activation_Energy_2.png|thumb|none|350px|Energy vs Time graph highlighting the activation energy of the endothermic reaction.]]

It can hence be seen that the exothermic reaction of F + H2 --> F-H + H only requires a small activation energy as the products are substantially more thermodynamically stable than the reactants.

===Reaction Dynamics===

In light of the fact that energy is conserved, discuss the mechanism of release of the reaction energy. How could this be confirmed experimentally? Measuring energy released from reaction ie exothermicity. Put first one separately. As reach momentum close to boundaries, system passes through transition state but returns to reactant well. Comment on effect the sign of the momentum has on the reactivity.

r1 = 2.3, r2 = 0.74

{| class="wikitable" border=1
! Simulation !! pHH !! pF-H !! Surface Plot !! Momenta vs Time Plot !! Observations !!
|-
| 1 || -2.5 || -1.5 || [[File:sm6416_Trajectory_1_Surface.png|thumb|none|350px]] ||[[File:sm6416_Trajectory_1_Momenta.png|thumb|none|350px]] || This trajectory results in a successful reaction as seen from the surface plot; the reactants proceed through the transition state and continue into the product well, whilst continually oscillating as a result of the momentum gained.
|-
| 2 || -0.5 || -0.5 || [[File:sm6416_Trajectory_2_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_2_Momenta.png|thumb|none|350px]] || This momentum does not proceed to a reaction. Through the dynamic animation it can be seen that the HH molecule does not possess enough momentum to translate towards F. Therefore the system does not translate out of the reactant well, as seen in the surface plot. The momenta plot simply shows a small up trend, this is expected due to the long range electrostatic force of attraction between F and HH. There is no drastic change in the momenta of either F or HH that would otherwise indicate the occurrence of a reaction, as seen in simulation 1 above.
|-
| 3 || +0.5 || -0.5 || [[File:sm6416_Trajectory_3_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_3_Momenta.png|thumb|none|350px]] || This simulation has a positive momentum and therefore the HH molecule translates away from F, as can be seen from the surface plot. There is a slight overall increase in momenta, however not large enough to be of importance. This simulation does not lead to a reaction.
|-
| 4 || -1.6 || -0.5 || [[File:sm6416_Trajectory_4_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_4_Momenta.png|thumb|none|350px]] || The HH molecule in this simulation does possess sufficient momentum to translate towards F and result in a reaction. Evidence for this is both shown by the progression from the reactant to product well in the surface plot along with a drastic change in momentum of A-B (signifying F-H) shown by the momenta vs time plot, highlighting the high momentum oscillation, as expected from the heavier F atom.
|-
| 5 || +1.6 || -0.5 || [[File:sm6416_Trajectory_5_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_5_Momenta.png|thumb|none|350px]] || This simulation is very much like simulation 3, in that the HH momentum is positive. The similarity in the behaviour of the system is also similar, as shown by the surface plot. However, due to the greater momentum, HH translates further away from F than in simulation 3.
|-
| 6 || -2.9 || -0.5 || [[File:sm6416_Trajectory_6_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_6_Momenta.png|thumb|none|350px]] ||
|-
| 7 || +2.9 || -0.5 || [[File:sm6416_Trajectory_7_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_7_Momenta.png|thumb|none|350px]] ||
|-
| 8 || +0.1 || -0.8 || [[File:sm6416_Trajectory_8_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_8_Momenta.png|thumb|none|350px]] ||
|}

====Polyani's Empirical Rules====

Discuss relative translational and vibrational energies required to match the transition state for each endo/exothermic reaction relating to Hammond's postulate.

MRD:sm6416

2018-05-24T16:54:05Z

Sm6416: /* Reaction Dynamics */

==H2 H Exercise 1==

===Transition State Dynamics===

What value do the different components of the gradient of the potential energy surface have at a minimum and at a transition structure? Briefly explain how minima and transition structures can be distinguished using the curvature of the potential energy surface.

Discuss saddle point being the second derivative.
Minimum of trajectory.

===Locating the Transition State===

The transition state was determined through iterations of both r1 and r2 which resulted in the smallest displacement of momenta along with no displacement as shown by the contour plot. This method determined at rts = 0.907743.

[[File:sm6416_Transition_State_Contour.png|thumb|none|350px|Contour plot demonstrating rts = 0.907743 as a result of no fluctuations from the initial input, hence the complex is metaphorically sitting on the transition state.]]

[[File:sm6416_Transition_State_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating minimum, and almost zero, momentum at rts = 0.907743.]]

[[File:sm6416_Transition_State_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot demonstrating no fluctuations in distance and hence rts = 0.907743.]]

===Reaction Path===

The minimum energy path (MEP) is defined as the lowest path the reaction must follow to form the products and is the downhill motion from the transition state. It can be applied in both directions in the case in question. The MEP views the system as static as it resets the velocity to zero at each step. Whereas the trajectory is very much dynamic and the momenta is accounted for, this is reflected in the vibrational oscillation of the molecule as it passes along the minimum well towards the products.

====MEP====

Initial conditions of r1 = rts + 0.01 = 0.917743, r2 = rts = 0.907743 and p1 = p2 = 0 for the MEP simulation.

[[File:sm6416_MEP_Surface.png|thumb|none|350px|Surface plot highlighting the minimum energy path (MEP), as the reaction returns to the reactants without fully passing through the transition state.]]

[[File:sm6416_MEP_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating zero momentum, as inputted, and more importantly not change in momentum with running the simulation.]]

[[File:sm6416_MEP_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot showing that the reactants reach the transition state at the interception of r1 = r2. r1 quickly reaches a constant value, namely the equilibrium bond length of the reactant molecule. r2 increases logarithmically as time progresses, this represents an increasing distance of Ha from Hb-Hc and a continuing loss of momentum.]]

Final values from the MEP simulation.

r1 = 2.76195

r2 = 0.75883

These values reflect the minimum trajectory for a successful reaction.

p1 = p2 = 0

====Dynamic====

[[File:sm6416_Dynamic_Surface.png|thumb|none|350px|Surface plot highlighting the minimum energy path (MEP) with oscillation of the reactants, as the reaction returns to the reactants without fully passing through the transition state. It is therefore evident that the momentum as a result of the vibrational oscillation does not provide enough energy to proceed to the products.]]

[[File:sm6416_Dynamic_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating the momenta associated with the oscillating reactants.]]

[[File:sm6416_Dynamic_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot showing that the reactants reach the transition state at the interception of r1 = r2. r1 quickly decreases and oscillates about a constant value, namely the equilibrium bond length of the reactant molecule. r2 increases linearly as time progresses, this represents an increasing distance of Ha from Hb-Hc with a constant momentum.]]

Dynamic simulation final values

r1 = 10.0045

r2 = 0.75883

p1 = 2.48523

p2 = 1.29898

p(average) = 1.90409

With r1 = rts and r2 = rts + 0.01 would simply produce the same answer however the values would be flipped to the other distance. In other words r1 = 0.75883 and r2 = 10.0045 would be the output values.

Maintaining the final trajectories as calculated from the dynamic simulation and reversing the sign of the momenta, the reaction proceeds in the reverse direction to the products.

===Reactivity of Trajectories===

These simulations are restricted by the number of steps the program can handle, however a sound understanding of the reaction can be appreciated and the reactivity of each scenario can be determined appropriately.

{| class="wikitable" border=1
! Simulation !! p1 !! p2 !! Energy (units?) !! Reactivity !! Evidence !! Description
|-
| 1 || -1.25 || -2.5 || 5.03500 || Reactive || [[File:sm6416_MEP_Figure1.png|thumb|none|350px]] || Simulation 1: The reactants proceed through the transition state and to the products. The r2 distance decreases to the equilibrium bond length, whilst r1 simultaneously exhibits dissociation and increases beyond the scope of the graph. The small momenta attributed to the reactants is reflected in the vibrationally oscillating products, with a small amplitude.
|-
| 2 || -1.5 || -2.0 || 3.62879 || Unreactive || [[File:sm6416_MEP_Figure2.png|thumb|none|350px]] || Simulation 2: This is unreactive as the oscillating reactants reach the transition state point and r1 immediately returns to the initial bond length, whilst r2 continues to increase as it moves away from the H2 molecule.
|-
| 3 || -1.5 || -2.5 || 5.13738 || Reactive || [[File:sm6416_MEP_Figure3.png|thumb|none|350px]] || Simulation 3: This simulation shows a reactive pathway that is very similar to simulation 1, however due to the greater momenta associated with the reactants, as inputted, vibrational oscillations with a greater amplitude can be observed.
|-
| 4 || -2.5 || -5.0 || 9.86678 || Unreactive || [[File:sm6416_MEP_Figure4.png|thumb|none|350px]] || Simulation 4: Initially seen here are oscillating reactants with a very large amplitude. However, this simulation is unreactive despite the reactants going through the transition state and towards the product, they return to the initial reactants.
|-
| 5 || -2.5 || -5.2 || 11.80780 || Reactive || [[File:sm6416_MEP_Figure5.png|thumb|none|350px]] || Simulation 5: Like simulation 4, this simulation shows a large oscillating amplitude, whereas in this scenario after passing through the transition state, the products are completely obtained. The slight increase in the p2 momentum can be seen to result in the products.
|}

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? Assumes quasi-equilibrium between reactants and transition state. TST assumes that once reaction passes TS no way back to products. Completely opposite to experimental where it seems as though an equilibrium/reversible path exists between the transition state and products. Fluctuation of whether transition complexes go towards reactants or products are independent of each other.

==F-H-H System Exercise 2==
===Potential Energy Surface Inspection===
====Energetics====

F + H2 is an exothermic reaction as can be seen from the surface plot, the reaction progresses from a small H-H distance to a longer one, whilst H-F simultaneously equilibriates about the F-H bond length. It can be seen that the products are lower, and hence more stable, in energy than the reactants.

F-H + H is simply the reverse reaction that passes through the same transition state, hence this reaction is endothermic with the products being higher in energy than the reactants. There is an overall gain of energy.

With this information in mind, the F-H bond is more stable and thus stronger than the H-H bond. The main factors to this argument is the greater electronegativity of F leading to a stronger contribution to the bond than the molecular orbitals. Hence the overlap of molecular orbitals is a weaker factor in the bond strength.

[[File:sm6416_FHH_Surface.png|thumb|none|350px|Surface plot highlighting the energetics of the F-H-H system.]]

[[File:sm6416_HHF_Surface.png|thumb|none|350px|Surface plot highlighting the energetics of the H-H-F system.]]

====Transition State====

Discuss Hammond Postulate with TS being closer to products/reactants dependent on how the TS is composed.

The transition state complex is achieved at r1 = F-H = 1.810076 Angstrom and r2 = H-H = 0.74634 Angstrom, as can be seen from the graphs below showing the absence of displacement to either reactants or products.

[[File:sm6416_FHH_Transition_State_Contour.png|thumb|none|350px|Contour plot demonstrating rts as a result of no fluctuations from the initial input, hence the complex is metaphorically sitting on the transition state.]]

[[File:sm6416_FHH_Transition_State_Momenta_Time.png|thumb|none|350px|Momenta vs Time plot demonstrating minimum, and almost zero, momentum at rts.]]

[[File:sm6416_FHH_Transition_State_Surface.png|thumb|none|350px]]

====Activation Energy====

The activation energy for the exothermic reaction was calculated through a 500000 step MEP simulation with input values of r1 = 1.820076, r2 = 0.74634 and p1 = p2 = 0. It was required that after following the minimum energy path, the gradient of the line signifying the reactants was constant.

The activation energy is reported at +0.258 kcal/mol for the exothermic process.

[[File:sm6416_FHH_Activation_Energy_1.png|thumb|none|350px|Energy vs Time graph highlighting the activation energy of the exothermic reaction.]]

The activation energy for the endothermic process was determined with the following parameters: r1 = 1.800076, r2 = 0.74634, p1 = p2 = 0 with 250000 steps. The reported activation energy was +30.277 kcal/mol.

[[File:sm6416_FHH_Activation_Energy_2.png|thumb|none|350px|Energy vs Time graph highlighting the activation energy of the endothermic reaction.]]

It can hence be seen that the exothermic reaction of F + H2 --> F-H + H only requires a small activation energy as the products are substantially more thermodynamically stable than the reactants.

===Reaction Dynamics===

In light of the fact that energy is conserved, discuss the mechanism of release of the reaction energy. How could this be confirmed experimentally? Measuring energy released from reaction ie exothermicity. Put first one separately. As reach momentum close to boundaries, system passes through transition state but returns to reactant well. Comment on effect the sign of the momentum has on the reactivity.

r1 = 2.3, r2 = 0.74

{| class="wikitable" border=1
! Simulation !! pHH !! pF-H !! Surface Plot !! Momenta vs Time Plot !! Observations !!
|-
| 1 || -2.5 || -1.5 || [[File:sm6416_Trajectory_1_Surface.png|thumb|none|350px]] ||[[File:sm6416_Trajectory_1_Momenta.png|thumb|none|350px]] || This trajectory results in a successful reaction as seen from the surface plot; the reactants proceed through the transition state and continue into the product well, whilst continually oscillating as a result of the momentum gained.
|-
| 2 || -0.5 || -0.5 || [[File:sm6416_Trajectory_2_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_2_Momenta.png|thumb|none|350px]] || This momentum does not proceed to a reaction. Through the dynamic animation it can be seen that the HH molecule does not possess enough momentum to translate towards F. Therefore the system does not translate out of the reactant well, as seen in the surface plot. The momenta plot simply shows a small up trend, this is expected due to the long range electrostatic force of attraction between F and HH. There is no drastic change in the momenta of either F or HH that would otherwise indicate the occurrence of a reaction, as seen in simulation 1 above.
|-
| 3 || +0.5 || -0.5 || [[File:sm6416_Trajectory_3_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_3_Momenta.png|thumb|none|350px]] || This simulation has a positive momentum and therefore the HH molecule translates away from F, as can be seen from the surface plot. There is a slight overall increase in momenta, however not large enough to be of importance. This simulation does not lead to a reaction.
|-
| 4 || -1.6 || -0.5 || [[File:sm6416_Trajectory_4_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_4_Momenta.png|thumb|none|350px]] || The HH molecule in this simulation does possess sufficient momentum to translate towards F and result in a reaction. Evidence for this is both shown by the progression from the reactant to product well in the surface plot along with a drastic change in momentum of A-B (signifying F-H) shown by the momenta vs time plot, highlighting the high momentum oscillation, as expected from the heavier F atom.
|-
| 5 || +1.6 || -0.5 || [[File:sm6416_Trajectory_5_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_5_Momenta.png|thumb|none|350px]] || This simulation is very much like simulation 3, in that the HH momentum is positive. The similarity in the behaviour of the system is also similar, as shown by the surface plot. However, due to the greater momentum, HH translates further away from F than in simulation 3.
|-
| 6 || -2.9 || -0.5 || [[File:sm6416_Trajectory_6_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_6_Momenta.png|thumb|none|350px]] ||
|-
| 7 || +2.9 || -0.5 || [[File:sm6416_Trajectory_7_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_7_Momenta.png|thumb|none|350px]] ||
|-
| 8 || +0.1 || -0.8 || [[File:sm6416_Trajectory_8_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_8_Momenta.png|thumb|none|350px]] ||
|}

MRD:sm6416

2018-05-24T16:53:39Z

Sm6416: /* Reaction Dynamics */

==H2 H Exercise 1==

===Transition State Dynamics===

What value do the different components of the gradient of the potential energy surface have at a minimum and at a transition structure? Briefly explain how minima and transition structures can be distinguished using the curvature of the potential energy surface.

Discuss saddle point being the second derivative.
Minimum of trajectory.

===Locating the Transition State===

The transition state was determined through iterations of both r1 and r2 which resulted in the smallest displacement of momenta along with no displacement as shown by the contour plot. This method determined at rts = 0.907743.

[[File:sm6416_Transition_State_Contour.png|thumb|none|350px|Contour plot demonstrating rts = 0.907743 as a result of no fluctuations from the initial input, hence the complex is metaphorically sitting on the transition state.]]

[[File:sm6416_Transition_State_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating minimum, and almost zero, momentum at rts = 0.907743.]]

[[File:sm6416_Transition_State_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot demonstrating no fluctuations in distance and hence rts = 0.907743.]]

===Reaction Path===

The minimum energy path (MEP) is defined as the lowest path the reaction must follow to form the products and is the downhill motion from the transition state. It can be applied in both directions in the case in question. The MEP views the system as static as it resets the velocity to zero at each step. Whereas the trajectory is very much dynamic and the momenta is accounted for, this is reflected in the vibrational oscillation of the molecule as it passes along the minimum well towards the products.

====MEP====

Initial conditions of r1 = rts + 0.01 = 0.917743, r2 = rts = 0.907743 and p1 = p2 = 0 for the MEP simulation.

[[File:sm6416_MEP_Surface.png|thumb|none|350px|Surface plot highlighting the minimum energy path (MEP), as the reaction returns to the reactants without fully passing through the transition state.]]

[[File:sm6416_MEP_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating zero momentum, as inputted, and more importantly not change in momentum with running the simulation.]]

[[File:sm6416_MEP_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot showing that the reactants reach the transition state at the interception of r1 = r2. r1 quickly reaches a constant value, namely the equilibrium bond length of the reactant molecule. r2 increases logarithmically as time progresses, this represents an increasing distance of Ha from Hb-Hc and a continuing loss of momentum.]]

Final values from the MEP simulation.

r1 = 2.76195

r2 = 0.75883

These values reflect the minimum trajectory for a successful reaction.

p1 = p2 = 0

====Dynamic====

[[File:sm6416_Dynamic_Surface.png|thumb|none|350px|Surface plot highlighting the minimum energy path (MEP) with oscillation of the reactants, as the reaction returns to the reactants without fully passing through the transition state. It is therefore evident that the momentum as a result of the vibrational oscillation does not provide enough energy to proceed to the products.]]

[[File:sm6416_Dynamic_Momenta.png|thumb|none|350px|Momenta vs Time plot demonstrating the momenta associated with the oscillating reactants.]]

[[File:sm6416_Dynamic_Distance.png|thumb|none|350px|Internuclear Distance vs Time plot showing that the reactants reach the transition state at the interception of r1 = r2. r1 quickly decreases and oscillates about a constant value, namely the equilibrium bond length of the reactant molecule. r2 increases linearly as time progresses, this represents an increasing distance of Ha from Hb-Hc with a constant momentum.]]

Dynamic simulation final values

r1 = 10.0045

r2 = 0.75883

p1 = 2.48523

p2 = 1.29898

p(average) = 1.90409

With r1 = rts and r2 = rts + 0.01 would simply produce the same answer however the values would be flipped to the other distance. In other words r1 = 0.75883 and r2 = 10.0045 would be the output values.

Maintaining the final trajectories as calculated from the dynamic simulation and reversing the sign of the momenta, the reaction proceeds in the reverse direction to the products.

===Reactivity of Trajectories===

These simulations are restricted by the number of steps the program can handle, however a sound understanding of the reaction can be appreciated and the reactivity of each scenario can be determined appropriately.

{| class="wikitable" border=1
! Simulation !! p1 !! p2 !! Energy (units?) !! Reactivity !! Evidence !! Description
|-
| 1 || -1.25 || -2.5 || 5.03500 || Reactive || [[File:sm6416_MEP_Figure1.png|thumb|none|350px]] || Simulation 1: The reactants proceed through the transition state and to the products. The r2 distance decreases to the equilibrium bond length, whilst r1 simultaneously exhibits dissociation and increases beyond the scope of the graph. The small momenta attributed to the reactants is reflected in the vibrationally oscillating products, with a small amplitude.
|-
| 2 || -1.5 || -2.0 || 3.62879 || Unreactive || [[File:sm6416_MEP_Figure2.png|thumb|none|350px]] || Simulation 2: This is unreactive as the oscillating reactants reach the transition state point and r1 immediately returns to the initial bond length, whilst r2 continues to increase as it moves away from the H2 molecule.
|-
| 3 || -1.5 || -2.5 || 5.13738 || Reactive || [[File:sm6416_MEP_Figure3.png|thumb|none|350px]] || Simulation 3: This simulation shows a reactive pathway that is very similar to simulation 1, however due to the greater momenta associated with the reactants, as inputted, vibrational oscillations with a greater amplitude can be observed.
|-
| 4 || -2.5 || -5.0 || 9.86678 || Unreactive || [[File:sm6416_MEP_Figure4.png|thumb|none|350px]] || Simulation 4: Initially seen here are oscillating reactants with a very large amplitude. However, this simulation is unreactive despite the reactants going through the transition state and towards the product, they return to the initial reactants.
|-
| 5 || -2.5 || -5.2 || 11.80780 || Reactive || [[File:sm6416_MEP_Figure5.png|thumb|none|350px]] || Simulation 5: Like simulation 4, this simulation shows a large oscillating amplitude, whereas in this scenario after passing through the transition state, the products are completely obtained. The slight increase in the p2 momentum can be seen to result in the products.
|}

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? Assumes quasi-equilibrium between reactants and transition state. TST assumes that once reaction passes TS no way back to products. Completely opposite to experimental where it seems as though an equilibrium/reversible path exists between the transition state and products. Fluctuation of whether transition complexes go towards reactants or products are independent of each other.

==F-H-H System Exercise 2==
===Potential Energy Surface Inspection===
====Energetics====

F + H2 is an exothermic reaction as can be seen from the surface plot, the reaction progresses from a small H-H distance to a longer one, whilst H-F simultaneously equilibriates about the F-H bond length. It can be seen that the products are lower, and hence more stable, in energy than the reactants.

F-H + H is simply the reverse reaction that passes through the same transition state, hence this reaction is endothermic with the products being higher in energy than the reactants. There is an overall gain of energy.

With this information in mind, the F-H bond is more stable and thus stronger than the H-H bond. The main factors to this argument is the greater electronegativity of F leading to a stronger contribution to the bond than the molecular orbitals. Hence the overlap of molecular orbitals is a weaker factor in the bond strength.

[[File:sm6416_FHH_Surface.png|thumb|none|350px|Surface plot highlighting the energetics of the F-H-H system.]]

[[File:sm6416_HHF_Surface.png|thumb|none|350px|Surface plot highlighting the energetics of the H-H-F system.]]

====Transition State====

Discuss Hammond Postulate with TS being closer to products/reactants dependent on how the TS is composed.

The transition state complex is achieved at r1 = F-H = 1.810076 Angstrom and r2 = H-H = 0.74634 Angstrom, as can be seen from the graphs below showing the absence of displacement to either reactants or products.

[[File:sm6416_FHH_Transition_State_Contour.png|thumb|none|350px|Contour plot demonstrating rts as a result of no fluctuations from the initial input, hence the complex is metaphorically sitting on the transition state.]]

[[File:sm6416_FHH_Transition_State_Momenta_Time.png|thumb|none|350px|Momenta vs Time plot demonstrating minimum, and almost zero, momentum at rts.]]

[[File:sm6416_FHH_Transition_State_Surface.png|thumb|none|350px]]

====Activation Energy====

The activation energy for the exothermic reaction was calculated through a 500000 step MEP simulation with input values of r1 = 1.820076, r2 = 0.74634 and p1 = p2 = 0. It was required that after following the minimum energy path, the gradient of the line signifying the reactants was constant.

The activation energy is reported at +0.258 kcal/mol for the exothermic process.

[[File:sm6416_FHH_Activation_Energy_1.png|thumb|none|350px|Energy vs Time graph highlighting the activation energy of the exothermic reaction.]]

The activation energy for the endothermic process was determined with the following parameters: r1 = 1.800076, r2 = 0.74634, p1 = p2 = 0 with 250000 steps. The reported activation energy was +30.277 kcal/mol.

[[File:sm6416_FHH_Activation_Energy_2.png|thumb|none|350px|Energy vs Time graph highlighting the activation energy of the endothermic reaction.]]

It can hence be seen that the exothermic reaction of F + H2 --> F-H + H only requires a small activation energy as the products are substantially more thermodynamically stable than the reactants.

===Reaction Dynamics===

In light of the fact that energy is conserved, discuss the mechanism of release of the reaction energy. How could this be confirmed experimentally? Measuring energy released from reaction ie exothermicity. Put first one separately. As reach momentum close to boundaries, system passes through transition state but returns to reactant well. Comment on effect the sign of the momentum has on the reactivity.

{| class="wikitable" border=1
! Simulation !! pHH !! pF-H !! Surface Plot !! Momenta vs Time Plot !! Observations !!
|-
| 1 || -2.5 || -1.5 || [[File:sm6416_Trajectory_1_Surface.png|thumb|none|350px]] ||[[File:sm6416_Trajectory_1_Momenta.png|thumb|none|350px]] || This trajectory results in a successful reaction as seen from the surface plot; the reactants proceed through the transition state and continue into the product well, whilst continually oscillating as a result of the momentum gained.
|-
| 2 || -0.5 || -0.5 || [[File:sm6416_Trajectory_2_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_2_Momenta.png|thumb|none|350px]] || This momentum does not proceed to a reaction. Through the dynamic animation it can be seen that the HH molecule does not possess enough momentum to translate towards F. Therefore the system does not translate out of the reactant well, as seen in the surface plot. The momenta plot simply shows a small up trend, this is expected due to the long range electrostatic force of attraction between F and HH. There is no drastic change in the momenta of either F or HH that would otherwise indicate the occurrence of a reaction, as seen in simulation 1 above.
|-
| 3 || +0.5 || -0.5 || [[File:sm6416_Trajectory_3_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_3_Momenta.png|thumb|none|350px]] || This simulation has a positive momentum and therefore the HH molecule translates away from F, as can be seen from the surface plot. There is a slight overall increase in momenta, however not large enough to be of importance. This simulation does not lead to a reaction.
|-
| 4 || -1.6 || -0.5 || [[File:sm6416_Trajectory_4_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_4_Momenta.png|thumb|none|350px]] || The HH molecule in this simulation does possess sufficient momentum to translate towards F and result in a reaction. Evidence for this is both shown by the progression from the reactant to product well in the surface plot along with a drastic change in momentum of A-B (signifying F-H) shown by the momenta vs time plot, highlighting the high momentum oscillation, as expected from the heavier F atom.
|-
| 5 || +1.6 || -0.5 || [[File:sm6416_Trajectory_5_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_5_Momenta.png|thumb|none|350px]] || This simulation is very much like simulation 3, in that the HH momentum is positive. The similarity in the behaviour of the system is also similar, as shown by the surface plot. However, due to the greater momentum, HH translates further away from F than in simulation 3.
|-
| 6 || -2.9 || -0.5 || [[File:sm6416_Trajectory_6_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_6_Momenta.png|thumb|none|350px]] ||
|-
| 7 || +2.9 || -0.5 || [[File:sm6416_Trajectory_7_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_7_Momenta.png|thumb|none|350px]] ||
|-
| 8 || +0.1 || -0.8 || [[File:sm6416_Trajectory_8_Surface.png|thumb|none|350px]] || [[File:sm6416_Trajectory_8_Momenta.png|thumb|none|350px]] ||
|}

File:Sm6416 Trajectory 7 Momenta.png

2018-05-24T16:45:24Z

Sm6416: