ChemWiki - User contributions [en]

MRD:01535442

2020-05-22T22:42:54Z

Tr1318: /* Given the results you have obtained, how will Transition State Theory predictions for reaction rate values compare with experimental values? */

== Molecular Reaction Dynamics: Applications to Triatomic systems ==
In this report, we will be investigating the reaction dynamics of two triatomic systems, H-H-H and F-H-H. This includes investigation of their transition states, reaction coordinates and potential energy surfaces, and how these affect the outcome of chemical reactions.
== Exercise 1: H + H2 System ==
[[File:Internuclear Dist vs Time for rts 1535442.png|thumb|Figure 1: Internuclear Distance vs Time Graph for H + H2 system, showing estimate for rts|246x246px]]
=== On a potential energy surface diagram, how is the transition state mathematically defined? ===
∂V('''ri''')/∂'''ri'''=0 defines the point in the potential enrgy surface diagram where to gradient is zero, being defined as the maximum on the minimum energy curve.

=== How can the transition state be identified, and how can it be distinguished from a local minimum of the potential energy surface? ===
The transitions state can be identified by mapping trajectories near the supposed transition state, and observe whether the line goes towards the products or reactants. It can be distinguished from a local minimum by looking at the second derivative, which will be positive when the function is a local minimum, and negative if it is a maximum point.
=== Report your best estimate of the transition state position ('''rts''') and explain your reasoning illustrating it with a “Internuclear Distances vs Time” plot for a relevant trajectory ===
The best estimate for rts (the transition state position) is 90.9 pm. If you take a look at the internuclear distance vs time graph ('''Figure 1'''), it shows that across time, there is no oscillatory behaviour in the triatomic system that alters the distance from the rts, therefore 90.9 pm is the closest estimate for this position. Note that distance A-B and B-C are the same, so line A-B in the graph is behind line B-C.[[File:Contour Plot of Rts +1, Rts Dynamics 01535442.png|thumb|'''Figure 2''': Contour plot of system displaced from transtition state. Calculation type: Dynamics|245x245px]][[File:Contour Plot of Rts +1, Rts MEP 01535442.png|thumb|Figure 3: Contour plot of system displaced from transtion state. Calculation type: MEP|244x244px]]
=== Comment on how the ''mep'' and the trajectory you just calculated differ ===
The minimum energy path or mep takes a path through the potential surface where it does not move up or down the contour, rather it takes the the path of lowest energy througout (see '''Figure 2'''). The trajectory calculated by dynamics ('''Figure 3''') follows the same overall path as the mep, though it's much more wavy. This is due to the vibration of the diatomic molecule. Conservation of energy is present in both as the dynamic trajectory oscillates between the same energy contours.
=== Complete the table below by adding the total energy, whether the trajectory is reactive or unreactive, and provide a plot of the trajectory and a small description for what happens along the trajectory. ===
{| class="wikitable"
!p1/ g.mol-1.pm.fs-1
!p2/ g.mol-1.pm.fs-1
!Etot
!Reactive?
!Description of the dynamics
!Illustration of the trajectory
|-
|<nowiki>-2.56</nowiki>
|<nowiki>-5.1</nowiki>
|<nowiki>-414.280</nowiki>
|Yes
|The H2 (Hb-Hc) molecule has relatively lower momentum than Ha, and so there is little oscillatory behaviour. When it gets to the transition state, there is reintroduction of oscillatory behaviour in Ha-Hb, due to excess vibrational energy.
|[[File:Contour Plot of P1=-2.56 P2=-5.1 01535442.png|frameless]]
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-4.1</nowiki>
|<nowiki>-420.077</nowiki>
|No
|The H2 (Hb-Hc) molecule has relatively similiar levels of momentum to Ha. Hb-Hc has more visible oscillations in it's trajectory. The path does not reach the transition state, as there is not enough kinetic energy for Ha to form a bond with Hb, and repulsion forces between them push them apart, oscillating back to the reactant snapshot.
|[[File:Contour Plot of Row 2 01535442.png|frameless]]
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-5.1</nowiki>
|<nowiki>-413.977</nowiki>
|Yes
|The H2 (Hb-Hc) molecule has relatively lower momentum than Ha, and there is some oscillatory behaviour with Hb-Hc. There is enough momentum for Ha to reach the transition state, as it overcomes the repulsion to form a new bond.There is then increased oscillatory behaviour in Ha-Hb, due to excess vibrational energy.
|[[File:Contour Plot of Row 3 01535442.png|frameless]]
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.1</nowiki>
|<nowiki>-357.277</nowiki>
|No
|The H2 (Hb-Hc) molecule has relatively lower momentum than Ha, and there is little oscillatory behaviour with Hb-Hc. There is enough momentum for Ha to reach the transition state, as it overcomes the repulsion to form a new bond. Yet, as momentum is high, there is large oscillations in the path of the new Ha-Hb, so much so that new bond then breaks and reforms the reactants, oscillating backwards.
|[[File:Contour Plot of Row 4 01535442.png|frameless]]
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.6</nowiki>
|<nowiki>-349.477</nowiki>
|Yes
|The H2 (Hb-Hc) molecule has relatively lower momentum than Ha, and there is little oscillatory behaviour with Hb-Hc. There is enough momentum for Ha to reach the transition state, and there is few larger oscillations where the new bond between Ha-Hb is formed, and then this breaks and the reactant Hb-Hc reforms. The reactant bond than breaks and reforms the new Ha-Hb molecule, and the path goes towards the products.
|[[File:Contour Plot of Row 5 01535442.png|frameless]]
|}

=== What can you conclude from the table? ===
In summary, the main influence on whether a trajectory will lead to a reaction is that the momentum p2 must be larger than p1, and around double the magnitude of p1. The higher that values of momentum, the higher the kinetic energy in the system and the higher the total energy becomes.

=== Given the results you have obtained, how will Transition State Theory predictions for reaction rate values compare with experimental values? ===
Transition state thoery predictions will likely overestimate the predictions for rate, as it assumes all of the reaction goes to completion due to boltzmann distribution (all molecules have enough kinetic energy). Yet, it doesn't consider barrier recrossing, where the bond in the product forms, but they may reverse if they have a high enough vibrational energy. There is also the case that transition state theory treats energy classically, so ignores tunneling effects that could lower estimates. This effects is generally small, and is only really prevalent at low temperatures.<ref>Steinfeld, Jeffrey I, (1999) Chemical kinetics and dynamics, Prentice-Hall, p. 287-321</ref>

== Exercise 2: F - H - H System ==
[[File:Surface Plot 01535442.png|thumb|312x312px|Figure 4: Contour plot of F-H2 system]]

=== By inspecting the potential energy surfaces, classify the F + H2 and H + HF reactions according to their energetics (endothermic or exothermic). How does this relate to the bond strength of the chemical species involved? ===
==== F + H2 ====
The reaction is exothermic, as the structure H-F is much more lower in energy, and there is noticable drop in the surface at the H-F product channel ('''Figure 4'''). The product formed, H-F, as bond energy of 565 kJ mol-1.<ref name=":0">Huheey, pps. A-21 to A-34; T.L. Cottrell, "The Strengths of Chemical Bonds," 2nd ed., Butterworths, London, 1958</ref> This is higher than the bond energy of H-H, thus the products will be lower in energy than the reactants.

==== H + HF ====
This reaction is endothermic, as H-H is much higher in energy than H-F, and there surface of the potential curve is higher in the H-H product channel ('''Figure 4'''). The product formed, H-H, as a bond energy of 432 kJ mol-1.<ref name=":0" /> This is lower than the bond energy of H-F, thus the products should be higher in energy than the reactants.
[[File:Contour plot with Transtion State of F-H-H 0153442.png|thumb|Figure 5: Contour plot with approximate transtion state position for F-H-H system|300x300px]]

=== Locate the approximate position of the transition state ===
The transition state positions is approximately at distance H - H = 74 pm and F - H = 181.4 pm. Initially, Hammond's Postulate was recalled, which states that the transition state of a reaction resembles the species more higher in energy, in this case either the product or the reactant. As we are observing the F + H2 system, it is exothermic and and will resemble H2, the reactants. The bond length of H-H is reported to be 74 pm, so this was kept the same, as well as keeping the momentums at 0, to find the position (see '''Figure 6 '''for depiction).

=== Report the activation energy for both reactions ===
The activation energy for the F + H2 system is 1.032 kJ mol-1, and the for the H + HF system, the activation energy is -126.684 kJ mol-1. These were found by finding the difference between the potential energy of the transition state and the reactant, using both systems (F + H2 and H + HF) so the mep could be pathed (only to reactants).

=== Reaction Dynamics ===
[[File:Momenta vs time 01535442.png|thumb|Figure 6: Momenta vs time graph of Reactive Trajectory|318x318px]]

==== In light of the fact that energy is conserved, discuss the mechanism of release of the reaction energy and explain how this could be confirmed experimentally ====
The reactive trajectory in this example is set by F - H = 230 pm, and H - H = 74 pm, with respective momentums being -13 and 0. In '''Figure 6''', the momentum vs time graph of this system is displayed, where A-B = F - H, and B-C = H - H. Initially, F - H has translational energy which enables it to move, and H - H has vibrational energy and is oscillating. Then, once the collision occurs, the momentums become postive, as the newly formed products move away. Now, F - H bond has vibrational energy, and it oscillatory behaviour is large, and the H - H momentum steadies as H moves away with translational energy. This can be confirmed by analysis of chemiluminescence and possibly IR.
==== Discuss how the distribution of energy between different modes (translation and vibration) affect the efficiency of the reaction, and how this is influenced by the position of the transition state ====
The distributions of energy is influenced by the strength of both translational modes and vibrational modes. The biggest component to the favourability of the modes is the position of the transition state in the potential energy surface. If a reaction has a late transition state (occurs in product channel), then high translational energy trajectories will lead to succussful reactions. Yet, if a reaction has an early transition state (occurs in reactant channel), will favour vibration excitation of the molecule leading to a reactive trajectory.<ref>Steinfeld, Jeffrey I, (1999) Chemical kinetics and dynamics, Prentice-Hall, p. 272-274</ref>

== Biliography ==
<references />

MRD:01535442

2020-05-22T22:39:09Z

Tr1318: /* In light of the fact that energy is conserved, discuss the mechanism of release of the reaction energy and explain how this could be confirmed experimentally */

== Molecular Reaction Dynamics: Applications to Triatomic systems ==
In this report, we will be investigating the reaction dynamics of two triatomic systems, H-H-H and F-H-H. This includes investigation of their transition states, reaction coordinates and potential energy surfaces, and how these affect the outcome of chemical reactions.
== Exercise 1: H + H2 System ==
[[File:Internuclear Dist vs Time for rts 1535442.png|thumb|Figure 1: Internuclear Distance vs Time Graph for H + H2 system, showing estimate for rts|246x246px]]
=== On a potential energy surface diagram, how is the transition state mathematically defined? ===
∂V('''ri''')/∂'''ri'''=0 defines the point in the potential enrgy surface diagram where to gradient is zero, being defined as the maximum on the minimum energy curve.

=== How can the transition state be identified, and how can it be distinguished from a local minimum of the potential energy surface? ===
The transitions state can be identified by mapping trajectories near the supposed transition state, and observe whether the line goes towards the products or reactants. It can be distinguished from a local minimum by looking at the second derivative, which will be positive when the function is a local minimum, and negative if it is a maximum point.
=== Report your best estimate of the transition state position ('''rts''') and explain your reasoning illustrating it with a “Internuclear Distances vs Time” plot for a relevant trajectory ===
The best estimate for rts (the transition state position) is 90.9 pm. If you take a look at the internuclear distance vs time graph ('''Figure 1'''), it shows that across time, there is no oscillatory behaviour in the triatomic system that alters the distance from the rts, therefore 90.9 pm is the closest estimate for this position. Note that distance A-B and B-C are the same, so line A-B in the graph is behind line B-C.[[File:Contour Plot of Rts +1, Rts Dynamics 01535442.png|thumb|'''Figure 2''': Contour plot of system displaced from transtition state. Calculation type: Dynamics|245x245px]][[File:Contour Plot of Rts +1, Rts MEP 01535442.png|thumb|Figure 3: Contour plot of system displaced from transtion state. Calculation type: MEP|244x244px]]
=== Comment on how the ''mep'' and the trajectory you just calculated differ ===
The minimum energy path or mep takes a path through the potential surface where it does not move up or down the contour, rather it takes the the path of lowest energy througout (see '''Figure 2'''). The trajectory calculated by dynamics ('''Figure 3''') follows the same overall path as the mep, though it's much more wavy. This is due to the vibration of the diatomic molecule. Conservation of energy is present in both as the dynamic trajectory oscillates between the same energy contours.
=== Complete the table below by adding the total energy, whether the trajectory is reactive or unreactive, and provide a plot of the trajectory and a small description for what happens along the trajectory. ===
{| class="wikitable"
!p1/ g.mol-1.pm.fs-1
!p2/ g.mol-1.pm.fs-1
!Etot
!Reactive?
!Description of the dynamics
!Illustration of the trajectory
|-
|<nowiki>-2.56</nowiki>
|<nowiki>-5.1</nowiki>
|<nowiki>-414.280</nowiki>
|Yes
|The H2 (Hb-Hc) molecule has relatively lower momentum than Ha, and so there is little oscillatory behaviour. When it gets to the transition state, there is reintroduction of oscillatory behaviour in Ha-Hb, due to excess vibrational energy.
|[[File:Contour Plot of P1=-2.56 P2=-5.1 01535442.png|frameless]]
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-4.1</nowiki>
|<nowiki>-420.077</nowiki>
|No
|The H2 (Hb-Hc) molecule has relatively similiar levels of momentum to Ha. Hb-Hc has more visible oscillations in it's trajectory. The path does not reach the transition state, as there is not enough kinetic energy for Ha to form a bond with Hb, and repulsion forces between them push them apart, oscillating back to the reactant snapshot.
|[[File:Contour Plot of Row 2 01535442.png|frameless]]
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-5.1</nowiki>
|<nowiki>-413.977</nowiki>
|Yes
|The H2 (Hb-Hc) molecule has relatively lower momentum than Ha, and there is some oscillatory behaviour with Hb-Hc. There is enough momentum for Ha to reach the transition state, as it overcomes the repulsion to form a new bond.There is then increased oscillatory behaviour in Ha-Hb, due to excess vibrational energy.
|[[File:Contour Plot of Row 3 01535442.png|frameless]]
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.1</nowiki>
|<nowiki>-357.277</nowiki>
|No
|The H2 (Hb-Hc) molecule has relatively lower momentum than Ha, and there is little oscillatory behaviour with Hb-Hc. There is enough momentum for Ha to reach the transition state, as it overcomes the repulsion to form a new bond. Yet, as momentum is high, there is large oscillations in the path of the new Ha-Hb, so much so that new bond then breaks and reforms the reactants, oscillating backwards.
|[[File:Contour Plot of Row 4 01535442.png|frameless]]
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.6</nowiki>
|<nowiki>-349.477</nowiki>
|Yes
|The H2 (Hb-Hc) molecule has relatively lower momentum than Ha, and there is little oscillatory behaviour with Hb-Hc. There is enough momentum for Ha to reach the transition state, and there is few larger oscillations where the new bond between Ha-Hb is formed, and then this breaks and the reactant Hb-Hc reforms. The reactant bond than breaks and reforms the new Ha-Hb molecule, and the path goes towards the products.
|[[File:Contour Plot of Row 5 01535442.png|frameless]]
|}

=== What can you conclude from the table? ===
In summary, the main influence on whether a trajectory will lead to a reaction is that the momentum p2 must be larger than p1, and around double the magnitude of p1. The higher that values of momentum, the higher the kinetic energy in the system and the higher the total energy becomes.

=== Given the results you have obtained, how will Transition State Theory predictions for reaction rate values compare with experimental values? ===
Transition state thoery predictions will likely overestimate the predictions for rate, as it assumes all of the reaction goes to completion due to boltzmann distribution (all molecules have enough kinetic energy). Yet, it doesn't consider barrier recrossing, where the bond in the product forms, but they may reverse if they have a high enough vibrational energy. There is also the case that transition state theory treats energy classically, so ignores tunneling effects that could lower estimates. This effects is generally small, and is only really prevalent at low temperatures.

== Exercise 2: F - H - H System ==
[[File:Surface Plot 01535442.png|thumb|312x312px|Figure 4: Contour plot of F-H2 system]]

=== By inspecting the potential energy surfaces, classify the F + H2 and H + HF reactions according to their energetics (endothermic or exothermic). How does this relate to the bond strength of the chemical species involved? ===
==== F + H2 ====
The reaction is exothermic, as the structure H-F is much more lower in energy, and there is noticable drop in the surface at the H-F product channel ('''Figure 4'''). The product formed, H-F, as bond energy of 565 kJ mol-1.<ref name=":0">Huheey, pps. A-21 to A-34; T.L. Cottrell, "The Strengths of Chemical Bonds," 2nd ed., Butterworths, London, 1958</ref> This is higher than the bond energy of H-H, thus the products will be lower in energy than the reactants.

==== H + HF ====
This reaction is endothermic, as H-H is much higher in energy than H-F, and there surface of the potential curve is higher in the H-H product channel ('''Figure 4'''). The product formed, H-H, as a bond energy of 432 kJ mol-1.<ref name=":0" /> This is lower than the bond energy of H-F, thus the products should be higher in energy than the reactants.
[[File:Contour plot with Transtion State of F-H-H 0153442.png|thumb|Figure 5: Contour plot with approximate transtion state position for F-H-H system|300x300px]]

=== Locate the approximate position of the transition state ===
The transition state positions is approximately at distance H - H = 74 pm and F - H = 181.4 pm. Initially, Hammond's Postulate was recalled, which states that the transition state of a reaction resembles the species more higher in energy, in this case either the product or the reactant. As we are observing the F + H2 system, it is exothermic and and will resemble H2, the reactants. The bond length of H-H is reported to be 74 pm, so this was kept the same, as well as keeping the momentums at 0, to find the position (see '''Figure 6 '''for depiction).

=== Report the activation energy for both reactions ===
The activation energy for the F + H2 system is 1.032 kJ mol-1, and the for the H + HF system, the activation energy is -126.684 kJ mol-1. These were found by finding the difference between the potential energy of the transition state and the reactant, using both systems (F + H2 and H + HF) so the mep could be pathed (only to reactants).

=== Reaction Dynamics ===
[[File:Momenta vs time 01535442.png|thumb|Figure 6: Momenta vs time graph of Reactive Trajectory|318x318px]]

==== In light of the fact that energy is conserved, discuss the mechanism of release of the reaction energy and explain how this could be confirmed experimentally ====
The reactive trajectory in this example is set by F - H = 230 pm, and H - H = 74 pm, with respective momentums being -13 and 0. In '''Figure 6''', the momentum vs time graph of this system is displayed, where A-B = F - H, and B-C = H - H. Initially, F - H has translational energy which enables it to move, and H - H has vibrational energy and is oscillating. Then, once the collision occurs, the momentums become postive, as the newly formed products move away. Now, F - H bond has vibrational energy, and it oscillatory behaviour is large, and the H - H momentum steadies as H moves away with translational energy. This can be confirmed by analysis of chemiluminescence and possibly IR.
==== Discuss how the distribution of energy between different modes (translation and vibration) affect the efficiency of the reaction, and how this is influenced by the position of the transition state ====
The distributions of energy is influenced by the strength of both translational modes and vibrational modes. The biggest component to the favourability of the modes is the position of the transition state in the potential energy surface. If a reaction has a late transition state (occurs in product channel), then high translational energy trajectories will lead to succussful reactions. Yet, if a reaction has an early transition state (occurs in reactant channel), will favour vibration excitation of the molecule leading to a reactive trajectory.<ref>Steinfeld, Jeffrey I, (1999) Chemical kinetics and dynamics, Prentice-Hall, p. 272-274</ref>

== Biliography ==
<references />

MRD:01535442

2020-05-22T21:50:02Z

Tr1318: /* In light of the fact that energy is conserved, discuss the mechanism of release of the reaction energy and explain how this could be confirmed experimentally */

== Molecular Reaction Dynamics: Applications to Triatomic systems ==
In this report, we will be investigating the reaction dynamics of two triatomic systems, H-H-H and F-H-H. This includes investigation of their transition states, reaction coordinates and potential energy surfaces, and how these affect the outcome of chemical reactions.
== Exercise 1: H + H2 System ==
[[File:Internuclear Dist vs Time for rts 1535442.png|thumb|Figure 1: Internuclear Distance vs Time Graph for H + H2 system, showing estimate for rts|246x246px]]
=== On a potential energy surface diagram, how is the transition state mathematically defined? ===
∂V('''ri''')/∂'''ri'''=0 defines the point in the potential enrgy surface diagram where to gradient is zero, being defined as the maximum on the minimum energy curve.

=== How can the transition state be identified, and how can it be distinguished from a local minimum of the potential energy surface? ===
The transitions state can be identified by mapping trajectories near the supposed transition state, and observe whether the line goes towards the products or reactants. It can be distinguished from a local minimum by looking at the second derivative, which will be positive when the function is a local minimum, and negative if it is a maximum point.
=== Report your best estimate of the transition state position ('''rts''') and explain your reasoning illustrating it with a “Internuclear Distances vs Time” plot for a relevant trajectory ===
The best estimate for rts (the transition state position) is 90.9 pm. If you take a look at the internuclear distance vs time graph ('''Figure 1'''), it shows that across time, there is no oscillatory behaviour in the triatomic system that alters the distance from the rts, therefore 90.9 pm is the closest estimate for this position. Note that distance A-B and B-C are the same, so line A-B in the graph is behind line B-C.[[File:Contour Plot of Rts +1, Rts Dynamics 01535442.png|thumb|'''Figure 2''': Contour plot of system displaced from transtition state. Calculation type: Dynamics|245x245px]][[File:Contour Plot of Rts +1, Rts MEP 01535442.png|thumb|Figure 3: Contour plot of system displaced from transtion state. Calculation type: MEP|244x244px]]
=== Comment on how the ''mep'' and the trajectory you just calculated differ ===
The minimum energy path or mep takes a path through the potential surface where it does not move up or down the contour, rather it takes the the path of lowest energy througout (see '''Figure 2'''). The trajectory calculated by dynamics ('''Figure 3''') follows the same overall path as the mep, though it's much more wavy. This is due to the vibration of the diatomic molecule. Conservation of energy is present in both as the dynamic trajectory oscillates between the same energy contours.
=== Complete the table below by adding the total energy, whether the trajectory is reactive or unreactive, and provide a plot of the trajectory and a small description for what happens along the trajectory. ===
{| class="wikitable"
!p1/ g.mol-1.pm.fs-1
!p2/ g.mol-1.pm.fs-1
!Etot
!Reactive?
!Description of the dynamics
!Illustration of the trajectory
|-
|<nowiki>-2.56</nowiki>
|<nowiki>-5.1</nowiki>
|<nowiki>-414.280</nowiki>
|Yes
|The H2 (Hb-Hc) molecule has relatively lower momentum than Ha, and so there is little oscillatory behaviour. When it gets to the transition state, there is reintroduction of oscillatory behaviour in Ha-Hb, due to excess vibrational energy.
|[[File:Contour Plot of P1=-2.56 P2=-5.1 01535442.png|frameless]]
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-4.1</nowiki>
|<nowiki>-420.077</nowiki>
|No
|The H2 (Hb-Hc) molecule has relatively similiar levels of momentum to Ha. Hb-Hc has more visible oscillations in it's trajectory. The path does not reach the transition state, as there is not enough kinetic energy for Ha to form a bond with Hb, and repulsion forces between them push them apart, oscillating back to the reactant snapshot.
|[[File:Contour Plot of Row 2 01535442.png|frameless]]
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-5.1</nowiki>
|<nowiki>-413.977</nowiki>
|Yes
|The H2 (Hb-Hc) molecule has relatively lower momentum than Ha, and there is some oscillatory behaviour with Hb-Hc. There is enough momentum for Ha to reach the transition state, as it overcomes the repulsion to form a new bond.There is then increased oscillatory behaviour in Ha-Hb, due to excess vibrational energy.
|[[File:Contour Plot of Row 3 01535442.png|frameless]]
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.1</nowiki>
|<nowiki>-357.277</nowiki>
|No
|The H2 (Hb-Hc) molecule has relatively lower momentum than Ha, and there is little oscillatory behaviour with Hb-Hc. There is enough momentum for Ha to reach the transition state, as it overcomes the repulsion to form a new bond. Yet, as momentum is high, there is large oscillations in the path of the new Ha-Hb, so much so that new bond then breaks and reforms the reactants, oscillating backwards.
|[[File:Contour Plot of Row 4 01535442.png|frameless]]
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.6</nowiki>
|<nowiki>-349.477</nowiki>
|Yes
|The H2 (Hb-Hc) molecule has relatively lower momentum than Ha, and there is little oscillatory behaviour with Hb-Hc. There is enough momentum for Ha to reach the transition state, and there is few larger oscillations where the new bond between Ha-Hb is formed, and then this breaks and the reactant Hb-Hc reforms. The reactant bond than breaks and reforms the new Ha-Hb molecule, and the path goes towards the products.
|[[File:Contour Plot of Row 5 01535442.png|frameless]]
|}

=== What can you conclude from the table? ===
In summary, the main influence on whether a trajectory will lead to a reaction is that the momentum p2 must be larger than p1, and around double the magnitude of p1. The higher that values of momentum, the higher the kinetic energy in the system and the higher the total energy becomes.

=== Given the results you have obtained, how will Transition State Theory predictions for reaction rate values compare with experimental values? ===

== Exercise 2: F - H - H System ==
[[File:Surface Plot 01535442.png|thumb|312x312px|Figure 4: Contour plot of F-H2 system]]

=== By inspecting the potential energy surfaces, classify the F + H2 and H + HF reactions according to their energetics (endothermic or exothermic). How does this relate to the bond strength of the chemical species involved? ===
==== F + H2 ====
The reaction is exothermic, as the structure H-F is much more lower in energy, and there is noticable drop in the surface at the H-F product channel ('''Figure 4'''). The product formed, H-F, as bond energy of 565 kJ mol-1. This is higher than the bond energy of H-H, thus the products will be lower in energy than the reactants.

==== H + HF ====
This reaction is endothermic, as H-H is much higher in energy than H-F, and there surface of the potential curve is higher in the H-H product channel ('''Figure 4'''). The product formed, H-H, as a bond energy of 432 kJ mol-1. This is lower than the bond energy of H-F, thus the products should be higher in energy than the reactants.
[[File:Contour plot with Transtion State of F-H-H 0153442.png|thumb|Figure 5: Contour plot with approximate transtion state position for F-H-H system|300x300px]]

=== Locate the approximate position of the transition state ===
The transition state positions is approximately at distance H - H = 74 pm and F - H = 181.4 pm. Initially, Hammond's Postulate was recalled, which states that the transition state of a reaction resembles the species more higher in energy, in this case either the product or the reactant. As we are observing the F + H2 system, it is exothermic and and will resemble H2, the reactants. The bond length of H-H is reported to be 74 pm, so this was kept the same, as well as keeping the momentums at 0, to find the position (see '''Figure 6 '''for depiction).

=== Report the activation energy for both reactions ===
The activation energy for the F + H2 system is 1.032 kJ mol-1, and the for the H + HF system, the activation energy is -126.684 kJ mol-1. These were found by finding the difference between the potential energy of the transition state and the reactant, using both systems (F + H2 and H + HF) so the mep could be pathed (only to reactants).

=== Reaction Dynamics ===
[[File:Momenta vs time 01535442.png|thumb|Figure 6: Momenta vs time graph of Reactive Trajectory]]

==== In light of the fact that energy is conserved, discuss the mechanism of release of the reaction energy and explain how this could be confirmed experimentally ====
The reactive trajectory in this example is set by F - H = 230 pm, and H - H = 74 pm, with respective momentums being -13 and 0.
==== Discuss how the distribution of energy between different modes (translation and vibration) affect the efficiency of the reaction, and how this is influenced by the position of the transition state ====
The distributions of energy is influenced by the strength of both translational modes and vibrational modes. The biggest component to the favourability of the modes in the position of the transition state in potential energy surface. If a reaction has a late transition state (occurs in product channel), then high translational energy trajectories will lead to succussful reactions. This is seen by the

File:Momenta vs time 01535442.png

2020-05-22T21:48:19Z

Tr1318:

MRD:01535442

2020-05-22T21:44:23Z

Tr1318: /* Discuss how the distribution of energy between different modes (translation and vibration) affect the efficiency of the reaction, and how this is influenced by the position of the transition state */

== Molecular Reaction Dynamics: Applications to Triatomic systems ==
In this report, we will be investigating the reaction dynamics of two triatomic systems, H-H-H and F-H-H. This includes investigation of their transition states, reaction coordinates and potential energy surfaces, and how these affect the outcome of chemical reactions.
== Exercise 1: H + H2 System ==
[[File:Internuclear Dist vs Time for rts 1535442.png|thumb|Figure 1: Internuclear Distance vs Time Graph for H + H2 system, showing estimate for rts|246x246px]]
=== On a potential energy surface diagram, how is the transition state mathematically defined? ===
∂V('''ri''')/∂'''ri'''=0 defines the point in the potential enrgy surface diagram where to gradient is zero, being defined as the maximum on the minimum energy curve.

=== How can the transition state be identified, and how can it be distinguished from a local minimum of the potential energy surface? ===
The transitions state can be identified by mapping trajectories near the supposed transition state, and observe whether the line goes towards the products or reactants. It can be distinguished from a local minimum by looking at the second derivative, which will be positive when the function is a local minimum, and negative if it is a maximum point.
=== Report your best estimate of the transition state position ('''rts''') and explain your reasoning illustrating it with a “Internuclear Distances vs Time” plot for a relevant trajectory ===
The best estimate for rts (the transition state position) is 90.9 pm. If you take a look at the internuclear distance vs time graph ('''Figure 1'''), it shows that across time, there is no oscillatory behaviour in the triatomic system that alters the distance from the rts, therefore 90.9 pm is the closest estimate for this position. Note that distance A-B and B-C are the same, so line A-B in the graph is behind line B-C.[[File:Contour Plot of Rts +1, Rts Dynamics 01535442.png|thumb|'''Figure 2''': Contour plot of system displaced from transtition state. Calculation type: Dynamics|245x245px]][[File:Contour Plot of Rts +1, Rts MEP 01535442.png|thumb|Figure 3: Contour plot of system displaced from transtion state. Calculation type: MEP|244x244px]]
=== Comment on how the ''mep'' and the trajectory you just calculated differ ===
The minimum energy path or mep takes a path through the potential surface where it does not move up or down the contour, rather it takes the the path of lowest energy througout (see '''Figure 2'''). The trajectory calculated by dynamics ('''Figure 3''') follows the same overall path as the mep, though it's much more wavy. This is due to the vibration of the diatomic molecule. Conservation of energy is present in both as the dynamic trajectory oscillates between the same energy contours.
=== Complete the table below by adding the total energy, whether the trajectory is reactive or unreactive, and provide a plot of the trajectory and a small description for what happens along the trajectory. ===
{| class="wikitable"
!p1/ g.mol-1.pm.fs-1
!p2/ g.mol-1.pm.fs-1
!Etot
!Reactive?
!Description of the dynamics
!Illustration of the trajectory
|-
|<nowiki>-2.56</nowiki>
|<nowiki>-5.1</nowiki>
|<nowiki>-414.280</nowiki>
|Yes
|The H2 (Hb-Hc) molecule has relatively lower momentum than Ha, and so there is little oscillatory behaviour. When it gets to the transition state, there is reintroduction of oscillatory behaviour in Ha-Hb, due to excess vibrational energy.
|[[File:Contour Plot of P1=-2.56 P2=-5.1 01535442.png|frameless]]
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-4.1</nowiki>
|<nowiki>-420.077</nowiki>
|No
|The H2 (Hb-Hc) molecule has relatively similiar levels of momentum to Ha. Hb-Hc has more visible oscillations in it's trajectory. The path does not reach the transition state, as there is not enough kinetic energy for Ha to form a bond with Hb, and repulsion forces between them push them apart, oscillating back to the reactant snapshot.
|[[File:Contour Plot of Row 2 01535442.png|frameless]]
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-5.1</nowiki>
|<nowiki>-413.977</nowiki>
|Yes
|The H2 (Hb-Hc) molecule has relatively lower momentum than Ha, and there is some oscillatory behaviour with Hb-Hc. There is enough momentum for Ha to reach the transition state, as it overcomes the repulsion to form a new bond.There is then increased oscillatory behaviour in Ha-Hb, due to excess vibrational energy.
|[[File:Contour Plot of Row 3 01535442.png|frameless]]
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.1</nowiki>
|<nowiki>-357.277</nowiki>
|No
|The H2 (Hb-Hc) molecule has relatively lower momentum than Ha, and there is little oscillatory behaviour with Hb-Hc. There is enough momentum for Ha to reach the transition state, as it overcomes the repulsion to form a new bond. Yet, as momentum is high, there is large oscillations in the path of the new Ha-Hb, so much so that new bond then breaks and reforms the reactants, oscillating backwards.
|[[File:Contour Plot of Row 4 01535442.png|frameless]]
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.6</nowiki>
|<nowiki>-349.477</nowiki>
|Yes
|The H2 (Hb-Hc) molecule has relatively lower momentum than Ha, and there is little oscillatory behaviour with Hb-Hc. There is enough momentum for Ha to reach the transition state, and there is few larger oscillations where the new bond between Ha-Hb is formed, and then this breaks and the reactant Hb-Hc reforms. The reactant bond than breaks and reforms the new Ha-Hb molecule, and the path goes towards the products.
|[[File:Contour Plot of Row 5 01535442.png|frameless]]
|}

=== What can you conclude from the table? ===
In summary, the main influence on whether a trajectory will lead to a reaction is that the momentum p2 must be larger than p1, and around double the magnitude of p1. The higher that values of momentum, the higher the kinetic energy in the system and the higher the total energy becomes.

=== Given the results you have obtained, how will Transition State Theory predictions for reaction rate values compare with experimental values? ===

== Exercise 2: F - H - H System ==
[[File:Surface Plot 01535442.png|thumb|260x260px|Figure 4: Contour plot of F-H2 system]]

=== By inspecting the potential energy surfaces, classify the F + H2 and H + HF reactions according to their energetics (endothermic or exothermic). How does this relate to the bond strength of the chemical species involved? ===
==== F + H2 ====
The reaction is exothermic, as the structure H-F is much more lower in energy, and there is noticable drop in the surface at the H-F product channel ('''Figure 4'''). The product formed, H-F, as bond energy of 565 kJ mol-1. This is higher than the bond energy of H-H, thus the products will be lower in energy than the reactants.

==== H + HF ====
This reaction is endothermic, as H-H is much higher in energy than H-F, and there surface of the potential curve is higher in the H-H product channel ('''Figure 4'''). The product formed, H-H, as a bond energy of 432 kJ mol-1. This is lower than the bond energy of H-F, thus the products should be higher in energy than the reactants.
[[File:Contour plot with Transtion State of F-H-H 0153442.png|thumb|Figure 6: Contour plot with approximate transtion state position for F-H-H system|249x249px]]

=== Locate the approximate position of the transition state ===
The transition state positions is approximately at distance H - H = 74 pm and F - H = 181.4 pm. Initially, Hammond's Postulate was recalled, which states that the transition state of a reaction resembles the species more higher in energy, in this case either the product or the reactant. As we are observing the F + H2 system, it is exothermic and and will resemble H2, the reactants. The bond length of H-H is reported to be 74 pm, so this was kept the same, as well as keeping the momentums at 0, to find the position (see '''Figure 6 '''for depiction).

=== Report the activation energy for both reactions ===
The activation energy for the F + H2 system is 1.032 kJ mol-1, and the for the H + HF system, the activation energy is -126.684 kJ mol-1. These were found by finding the difference between the potential energy of the transition state and the reactant, using both systems (F + H2 and H + HF) so the mep could be pathed (only to reactants).

=== Reaction Dynamics ===

==== In light of the fact that energy is conserved, discuss the mechanism of release of the reaction energy and explain how this could be confirmed experimentally ====
The reactive trajectory in this example is set by F - H = 230 pm, and H - H = 74 pm, with respective momentums being -13 and 0.

==== Explain how this could be confirmed experimentally ====
==== Discuss how the distribution of energy between different modes (translation and vibration) affect the efficiency of the reaction, and how this is influenced by the position of the transition state ====
The distributions of energy is influenced by the strength of both translational modes and vibrational modes. The biggest component to the favourability of the modes in the position of the transition state in potential energy surface. If a reaction has a late transition state (occurs in product channel), then high translational energy trajectories will lead to succussful reactions. This is seen by the

MRD:01535442

2020-05-22T19:41:21Z

Tr1318: /* By inspecting the potential energy surfaces, classify the F + H2 and H + HF reactions according to their energetics (endothermic or exothermic). How does this relate to the bond strength of the chemical species involved? */

== Molecular Reaction Dynamics: Applications to Triatomic systems ==
In this report, we will be investigating the reaction dynamics of two triatomic systems, H-H-H and F-H-H. This includes investigation of their transition states, reaction coordinates and potential energy surfaces, and how these affect the outcome of chemical reactions.
== Exercise 1: H + H2 System ==
[[File:Internuclear Dist vs Time for rts 1535442.png|thumb|Figure 1: Internuclear Distance vs Time Graph for H + H2 system, showing estimate for rts|246x246px]]
=== On a potential energy surface diagram, how is the transition state mathematically defined? ===
∂V('''ri''')/∂'''ri'''=0 defines the point in the potential enrgy surface diagram where to gradient is zero, being defined as the maximum on the minimum energy curve.

=== How can the transition state be identified, and how can it be distinguished from a local minimum of the potential energy surface? ===
The transitions state can be identified by mapping trajectories near the supposed transition state, and observe whether the line goes towards the products or reactants. It can be distinguished from a local minimum by looking at the second derivative, which will be positive when the function is a local minimum, and negative if it is a maximum point.
=== Report your best estimate of the transition state position ('''rts''') and explain your reasoning illustrating it with a “Internuclear Distances vs Time” plot for a relevant trajectory ===
The best estimate for rts (the transition state position) is 90.9 pm. If you take a look at the internuclear distance vs time graph ('''Figure 1'''), it shows that across time, there is no oscillatory behaviour in the triatomic system that alters the distance from the rts, therefore 90.9 pm is the closest estimate for this position. Note that distance A-B and B-C are the same, so line A-B in the graph is behind line B-C.[[File:Contour Plot of Rts +1, Rts Dynamics 01535442.png|thumb|'''Figure 2''': Contour plot of system displaced from transtition state. Calculation type: Dynamics|245x245px]][[File:Contour Plot of Rts +1, Rts MEP 01535442.png|thumb|Figure 3: Contour plot of system displaced from transtion state. Calculation type: MEP|244x244px]]
=== Comment on how the ''mep'' and the trajectory you just calculated differ ===
The minimum energy path or mep takes a path through the potential surface where it does not move up or down the contour, rather it takes the the path of lowest energy througout (see '''Figure 2'''). The trajectory calculated by dynamics ('''Figure 3''') follows the same overall path as the mep, though it's much more wavy. This is due to the vibration of the diatomic molecule. Conservation of energy is present in both as the dynamic trajectory oscillates between the same energy contours.
=== Complete the table below by adding the total energy, whether the trajectory is reactive or unreactive, and provide a plot of the trajectory and a small description for what happens along the trajectory. ===
{| class="wikitable"
!p1/ g.mol-1.pm.fs-1
!p2/ g.mol-1.pm.fs-1
!Etot
!Reactive?
!Description of the dynamics
!Illustration of the trajectory
|-
|<nowiki>-2.56</nowiki>
|<nowiki>-5.1</nowiki>
|<nowiki>-414.280</nowiki>
|Yes
|The H2 (Hb-Hc) molecule has relatively lower momentum than Ha, and so there is little oscillatory behaviour. When it gets to the transition state, there is reintroduction of oscillatory behaviour in Ha-Hb, due to excess vibrational energy.
|[[File:Contour Plot of P1=-2.56 P2=-5.1 01535442.png|frameless]]
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-4.1</nowiki>
|<nowiki>-420.077</nowiki>
|No
|The H2 (Hb-Hc) molecule has relatively similiar levels of momentum to Ha. Hb-Hc has more visible oscillations in it's trajectory. The path does not reach the transition state, as there is not enough kinetic energy for Ha to form a bond with Hb, and repulsion forces between them push them apart, oscillating back to the reactant snapshot.
|[[File:Contour Plot of Row 2 01535442.png|frameless]]
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-5.1</nowiki>
|<nowiki>-413.977</nowiki>
|Yes
|The H2 (Hb-Hc) molecule has relatively lower momentum than Ha, and there is some oscillatory behaviour with Hb-Hc. There is enough momentum for Ha to reach the transition state, as it overcomes the repulsion to form a new bond.There is then increased oscillatory behaviour in Ha-Hb, due to excess vibrational energy.
|[[File:Contour Plot of Row 3 01535442.png|frameless]]
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.1</nowiki>
|<nowiki>-357.277</nowiki>
|No
|The H2 (Hb-Hc) molecule has relatively lower momentum than Ha, and there is little oscillatory behaviour with Hb-Hc. There is enough momentum for Ha to reach the transition state, as it overcomes the repulsion to form a new bond. Yet, as momentum is high, there is large oscillations in the path of the new Ha-Hb, so much so that new bond then breaks and reforms the reactants, oscillating backwards.
|[[File:Contour Plot of Row 4 01535442.png|frameless]]
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.6</nowiki>
|<nowiki>-349.477</nowiki>
|Yes
|The H2 (Hb-Hc) molecule has relatively lower momentum than Ha, and there is little oscillatory behaviour with Hb-Hc. There is enough momentum for Ha to reach the transition state, and there is few larger oscillations where the new bond between Ha-Hb is formed, and then this breaks and the reactant Hb-Hc reforms. The reactant bond than breaks and reforms the new Ha-Hb molecule, and the path goes towards the products.
|[[File:Contour Plot of Row 5 01535442.png|frameless]]
|}

=== What can you conclude from the table? ===
In summary, the main influence on whether a trajectory will lead to a reaction is that the momentum p2 must be larger than p1, and around double the magnitude of p1. The higher that values of momentum, the higher the kinetic energy in the system and the higher the total energy becomes.

=== Given the results you have obtained, how will Transition State Theory predictions for reaction rate values compare with experimental values? ===

== Exercise 2: F - H - H System ==
[[File:Surface Plot 01535442.png|thumb|270x270px|Figure 4: Contour plot of F-H2 system]]

=== By inspecting the potential energy surfaces, classify the F + H2 and H + HF reactions according to their energetics (endothermic or exothermic). How does this relate to the bond strength of the chemical species involved? ===
==== F + H2 ====
The reaction is exothermic, as the structure H-F is much more lower in energy, and there is noticable drop in the surface at the H-F product channel ('''Figure 4'''). The product formed, H-F, as bond energy of 565 kJ mol-1. This is higher than the bond energy of H-H, thus the products will be lower in energy than the reactants.

==== H + HF ====
This reaction is endothermic, as H-H is much higher in energy than H-F, and there surface of the potential curve is higher in the H-H product channel ('''Figure 4'''). The product formed, H-H, as a bond energy of 432 kJ mol-1. This is lower than the bond energy of H-F, thus the products should be higher in energy than the reactants.
[[File:Contour plot with Transtion State of F-H-H 0153442.png|thumb|Figure 6: Contour plot with approximate transtion state position for F-H-H system|257x257px]]

=== Locate the approximate position of the transition state ===
The transition state positions is approximately at distance H - H = 73 pm and F - H = 182 pm (see '''Figure 6 '''for depiction).

=== Report the activation energy for both reactions ===
The activation energy for the F + H2 system is 1.032 kJ mol-1, and the for the H + HF system, the activation energy is 126.684 kJ mol-1.

=== Reaction Dynamics ===

==== In light of the fact that energy is conserved, discuss the mechanism of release of the reaction energy ====
Placeholder

==== Explain how this could be confirmed experimentally ====
Placefolder

==== Discuss how the distribution of energy between different modes (translation and vibration) affect the efficiency of the reaction, and how this is influenced by the position of the transition state ====
The distributions of energy is influenced by the strength of both translational modes and vibrational modes. The biggest component to the favourability of the modes in the position of the transition state in potential energy surface.

MRD:01535442

2020-05-22T19:33:06Z

Tr1318: /* Report the activation energy for both reactions */

== Molecular Reaction Dynamics: Applications to Triatomic systems ==
In this report, we will be investigating the reaction dynamics of two triatomic systems, H-H-H and F-H-H. This includes investigation of their transition states, reaction coordinates and potential energy surfaces, and how these affect the outcome of chemical reactions.
== Exercise 1: H + H2 System ==
[[File:Internuclear Dist vs Time for rts 1535442.png|thumb|Figure 1: Internuclear Distance vs Time Graph for H + H2 system, showing estimate for rts|246x246px]]
=== On a potential energy surface diagram, how is the transition state mathematically defined? ===
∂V('''ri''')/∂'''ri'''=0 defines the point in the potential enrgy surface diagram where to gradient is zero, being defined as the maximum on the minimum energy curve.

=== How can the transition state be identified, and how can it be distinguished from a local minimum of the potential energy surface? ===
The transitions state can be identified by mapping trajectories near the supposed transition state, and observe whether the line goes towards the products or reactants. It can be distinguished from a local minimum by looking at the second derivative, which will be positive when the function is a local minimum, and negative if it is a maximum point.
=== Report your best estimate of the transition state position ('''rts''') and explain your reasoning illustrating it with a “Internuclear Distances vs Time” plot for a relevant trajectory ===
The best estimate for rts (the transition state position) is 90.9 pm. If you take a look at the internuclear distance vs time graph ('''Figure 1'''), it shows that across time, there is no oscillatory behaviour in the triatomic system that alters the distance from the rts, therefore 90.9 pm is the closest estimate for this position. Note that distance A-B and B-C are the same, so line A-B in the graph is behind line B-C.[[File:Contour Plot of Rts +1, Rts Dynamics 01535442.png|thumb|'''Figure 2''': Contour plot of system displaced from transtition state. Calculation type: Dynamics|245x245px]][[File:Contour Plot of Rts +1, Rts MEP 01535442.png|thumb|Figure 3: Contour plot of system displaced from transtion state. Calculation type: MEP|244x244px]]
=== Comment on how the ''mep'' and the trajectory you just calculated differ ===
The minimum energy path or mep takes a path through the potential surface where it does not move up or down the contour, rather it takes the the path of lowest energy througout (see '''Figure 2'''). The trajectory calculated by dynamics ('''Figure 3''') follows the same overall path as the mep, though it's much more wavy. This is due to the vibration of the diatomic molecule. Conservation of energy is present in both as the dynamic trajectory oscillates between the same energy contours.
=== Complete the table below by adding the total energy, whether the trajectory is reactive or unreactive, and provide a plot of the trajectory and a small description for what happens along the trajectory. ===
{| class="wikitable"
!p1/ g.mol-1.pm.fs-1
!p2/ g.mol-1.pm.fs-1
!Etot
!Reactive?
!Description of the dynamics
!Illustration of the trajectory
|-
|<nowiki>-2.56</nowiki>
|<nowiki>-5.1</nowiki>
|<nowiki>-414.280</nowiki>
|Yes
|The H2 (Hb-Hc) molecule has relatively lower momentum than Ha, and so there is little oscillatory behaviour. When it gets to the transition state, there is reintroduction of oscillatory behaviour in Ha-Hb, due to excess vibrational energy.
|[[File:Contour Plot of P1=-2.56 P2=-5.1 01535442.png|frameless]]
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-4.1</nowiki>
|<nowiki>-420.077</nowiki>
|No
|The H2 (Hb-Hc) molecule has relatively similiar levels of momentum to Ha. Hb-Hc has more visible oscillations in it's trajectory. The path does not reach the transition state, as there is not enough kinetic energy for Ha to form a bond with Hb, and repulsion forces between them push them apart, oscillating back to the reactant snapshot.
|[[File:Contour Plot of Row 2 01535442.png|frameless]]
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-5.1</nowiki>
|<nowiki>-413.977</nowiki>
|Yes
|The H2 (Hb-Hc) molecule has relatively lower momentum than Ha, and there is some oscillatory behaviour with Hb-Hc. There is enough momentum for Ha to reach the transition state, as it overcomes the repulsion to form a new bond.There is then increased oscillatory behaviour in Ha-Hb, due to excess vibrational energy.
|[[File:Contour Plot of Row 3 01535442.png|frameless]]
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.1</nowiki>
|<nowiki>-357.277</nowiki>
|No
|The H2 (Hb-Hc) molecule has relatively lower momentum than Ha, and there is little oscillatory behaviour with Hb-Hc. There is enough momentum for Ha to reach the transition state, as it overcomes the repulsion to form a new bond. Yet, as momentum is high, there is large oscillations in the path of the new Ha-Hb, so much so that new bond then breaks and reforms the reactants, oscillating backwards.
|[[File:Contour Plot of Row 4 01535442.png|frameless]]
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.6</nowiki>
|<nowiki>-349.477</nowiki>
|Yes
|The H2 (Hb-Hc) molecule has relatively lower momentum than Ha, and there is little oscillatory behaviour with Hb-Hc. There is enough momentum for Ha to reach the transition state, and there is few larger oscillations where the new bond between Ha-Hb is formed, and then this breaks and the reactant Hb-Hc reforms. The reactant bond than breaks and reforms the new Ha-Hb molecule, and the path goes towards the products.
|[[File:Contour Plot of Row 5 01535442.png|frameless]]
|}

=== What can you conclude from the table? ===
In summary, the main influence on whether a trajectory will lead to a reaction is that the momentum p2 must be larger than p1, and around double the magnitude of p1. The higher that values of momentum, the higher the kinetic energy in the system and the higher the total energy becomes.

=== Given the results you have obtained, how will Transition State Theory predictions for reaction rate values compare with experimental values? ===

== Exercise 2: F - H - H System ==
[[File:Surface Plot 01535442.png|thumb|270x270px|Figure 4: Contour plot of F-H2 system]]

=== By inspecting the potential energy surfaces, classify the F + H2 and H + HF reactions according to their energetics (endothermic or exothermic). How does this relate to the bond strength of the chemical species involved? ===
==== F + H2 ====
The reaction is exothermic, as the structure H-F is much more lower in energy, and there is noticable drop in the surface at the H-F product channel ('''Figure 4'''). The reaction is also a lot lower in total energy than forming H2 from H-F (-345.593 kJ mol-1).

==== H + HF ====
This reaction is endothermic, as H-H is much higher in energy than H-F, and there surface of the potential curve is higher in the H-H product channel ('''Figure 5'''). The reactions is a lot higher in total energy (199.091 kJ mol-1).
[[File:Contour plot with Transtion State of F-H-H 0153442.png|thumb|Figure 6: Contour plot with approximate transtion state position for F-H-H system|257x257px]]

=== Locate the approximate position of the transition state ===
The transition state positions is approximately at distance H - H = 73 pm and F - H = 182 pm (see '''Figure 6 '''for depiction).

=== Report the activation energy for both reactions ===
The activation energy for the F + H2 system is 1.032 kJ mol-1, and the for the H + HF system, the activation energy is 126.684 kJ mol-1.

=== Reaction Dynamics ===

==== In light of the fact that energy is conserved, discuss the mechanism of release of the reaction energy ====
Placeholder

==== Explain how this could be confirmed experimentally ====
Placefolder

==== Discuss how the distribution of energy between different modes (translation and vibration) affect the efficiency of the reaction, and how this is influenced by the position of the transition state ====
The distributions of energy is influenced by the strength of both translational modes and vibrational modes. The biggest component to the favourability of the modes in the position of the transition state in potential energy surface.

File:Surface Plot 01535442.png

2020-05-22T19:32:39Z

Tr1318:

MRD:01535442

2020-05-22T18:56:54Z

Tr1318: /* Report the activation energy for both reactions */

== Molecular Reaction Dynamics: Applications to Triatomic systems ==
In this report, we will be investigating the reaction dynamics of two triatomic systems, H-H-H and F-H-H. This includes investigation of their transition states, reaction coordinates and potential energy surfaces, and how these affect the outcome of chemical reactions.
== Exercise 1: H + H2 System ==
[[File:Internuclear Dist vs Time for rts 1535442.png|thumb|Figure 1: Internuclear Distance vs Time Graph for H + H2 system, showing estimate for rts|246x246px]]
=== On a potential energy surface diagram, how is the transition state mathematically defined? ===
∂V('''ri''')/∂'''ri'''=0 defines the point in the potential enrgy surface diagram where to gradient is zero, being defined as the maximum on the minimum energy curve.

=== How can the transition state be identified, and how can it be distinguished from a local minimum of the potential energy surface? ===
The transitions state can be identified by mapping trajectories near the supposed transition state, and observe whether the line goes towards the products or reactants. It can be distinguished from a local minimum by looking at the second derivative, which will be positive when the function is a local minimum, and negative if it is a maximum point.
=== Report your best estimate of the transition state position ('''rts''') and explain your reasoning illustrating it with a “Internuclear Distances vs Time” plot for a relevant trajectory ===
The best estimate for rts (the transition state position) is 90.9 pm. If you take a look at the internuclear distance vs time graph ('''Figure 1'''), it shows that across time, there is no oscillatory behaviour in the triatomic system that alters the distance from the rts, therefore 90.9 pm is the closest estimate for this position. Note that distance A-B and B-C are the same, so line A-B in the graph is behind line B-C.[[File:Contour Plot of Rts +1, Rts Dynamics 01535442.png|thumb|'''Figure 2''': Contour plot of system displaced from transtition state. Calculation type: Dynamics|245x245px]][[File:Contour Plot of Rts +1, Rts MEP 01535442.png|thumb|Figure 3: Contour plot of system displaced from transtion state. Calculation type: MEP|244x244px]]
=== Comment on how the ''mep'' and the trajectory you just calculated differ ===
The minimum energy path or mep takes a path through the potential surface where it does not move up or down the contour, rather it takes the the path of lowest energy througout (see '''Figure 2'''). The trajectory calculated by dynamics ('''Figure 3''') follows the same overall path as the mep, though it's much more wavy. This is due to the vibration of the diatomic molecule. Conservation of energy is present in both as the dynamic trajectory oscillates between the same energy contours.
=== Complete the table below by adding the total energy, whether the trajectory is reactive or unreactive, and provide a plot of the trajectory and a small description for what happens along the trajectory. ===
{| class="wikitable"
!p1/ g.mol-1.pm.fs-1
!p2/ g.mol-1.pm.fs-1
!Etot
!Reactive?
!Description of the dynamics
!Illustration of the trajectory
|-
|<nowiki>-2.56</nowiki>
|<nowiki>-5.1</nowiki>
|<nowiki>-414.280</nowiki>
|Yes
|The H2 (Hb-Hc) molecule has relatively lower momentum than Ha, and so there is little oscillatory behaviour. When it gets to the transition state, there is reintroduction of oscillatory behaviour in Ha-Hb, due to excess vibrational energy.
|[[File:Contour Plot of P1=-2.56 P2=-5.1 01535442.png|frameless]]
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-4.1</nowiki>
|<nowiki>-420.077</nowiki>
|No
|The H2 (Hb-Hc) molecule has relatively similiar levels of momentum to Ha. Hb-Hc has more visible oscillations in it's trajectory. The path does not reach the transition state, as there is not enough kinetic energy for Ha to form a bond with Hb, and repulsion forces between them push them apart, oscillating back to the reactant snapshot.
|[[File:Contour Plot of Row 2 01535442.png|frameless]]
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-5.1</nowiki>
|<nowiki>-413.977</nowiki>
|Yes
|The H2 (Hb-Hc) molecule has relatively lower momentum than Ha, and there is some oscillatory behaviour with Hb-Hc. There is enough momentum for Ha to reach the transition state, as it overcomes the repulsion to form a new bond.There is then increased oscillatory behaviour in Ha-Hb, due to excess vibrational energy.
|[[File:Contour Plot of Row 3 01535442.png|frameless]]
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.1</nowiki>
|<nowiki>-357.277</nowiki>
|No
|The H2 (Hb-Hc) molecule has relatively lower momentum than Ha, and there is little oscillatory behaviour with Hb-Hc. There is enough momentum for Ha to reach the transition state, as it overcomes the repulsion to form a new bond. Yet, as momentum is high, there is large oscillations in the path of the new Ha-Hb, so much so that new bond then breaks and reforms the reactants, oscillating backwards.
|[[File:Contour Plot of Row 4 01535442.png|frameless]]
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.6</nowiki>
|<nowiki>-349.477</nowiki>
|Yes
|The H2 (Hb-Hc) molecule has relatively lower momentum than Ha, and there is little oscillatory behaviour with Hb-Hc. There is enough momentum for Ha to reach the transition state, and there is few larger oscillations where the new bond between Ha-Hb is formed, and then this breaks and the reactant Hb-Hc reforms. The reactant bond than breaks and reforms the new Ha-Hb molecule, and the path goes towards the products.
|[[File:Contour Plot of Row 5 01535442.png|frameless]]
|}

=== What can you conclude from the table? ===
In summary, the main influence on whether a trajectory will lead to a reaction is that the momentum p2 must be larger than p1, and around double the magnitude of p1. The higher that values of momentum, the higher the kinetic energy in the system and the higher the total energy becomes.

=== Given the results you have obtained, how will Transition State Theory predictions for reaction rate values compare with experimental values? ===

== Exercise 2: F - H - H System ==
[[File:Contour Plot of F-H2 01535442.png|thumb|259x259px|Figure 4: Contour plot of F-H2 system|left]]

=== By inspecting the potential energy surfaces, classify the F + H2 and H + HF reactions according to their energetics (endothermic or exothermic). How does this relate to the bond strength of the chemical species involved? ===
[[File:Contour Plot of H-HF 01535442.png|thumb|269x269px|Figure 5: Contour plot of F-HF system]]
==== F + H2 ====
The reaction is exothermic, as the structure H-F is much more lower in energy, and there is noticable drop in the surface at the H-F product channel ('''Figure 4'''). The reaction is also a lot lower in total energy than forming H2 from H-F (-345.593 kJ mol-1).

==== H + HF ====
This reaction is endothermic, as H-H is much higher in energy than H-F, and there surface of the potential curve is higher in the H-H product channel ('''Figure 5'''). The reactions is a lot higher in total energy (199.091 kJ mol-1).
[[File:Contour plot with Transtion State of F-H-H 0153442.png|left|thumb|Figure 6: Contour plot with approximate transtion state position for F-H-H system|257x257px]]

=== Locate the approximate position of the transition state ===
The transition state positions is approximately at distance H - H = 73 pm and F - H = 182 pm (see '''Figure 6 '''for depiction).

=== Report the activation energy for both reactions ===
The activation energy for the F + H2 system is 1.032 kJ mol-1, and the for the H + HF system, the activation energy is 126.684 kJ mol-1.

MRD:01535442

2020-05-22T17:40:35Z

Tr1318: /* Locate the approximate position of the transition state */

MRD:01535442

2020-05-22T17:23:25Z

Tr1318: /* Locate the approximate position of the transition state */

File:Contour plot with Transtion State of F-H-H 0153442.png

2020-05-22T17:21:40Z

Tr1318:

MRD:01535442

2020-05-22T17:19:05Z

Tr1318: /* F + H2 */

File:Contour Plot of H-HF 01535442.png

2020-05-22T17:18:23Z

Tr1318:

File:Contour Plot of F-H2 01535442.png

2020-05-22T17:16:45Z

Tr1318: Tr1318 uploaded a new version of File:Contour Plot of F-H2 01535442.png

File:Contour Plot of F-H2 01535442.png

2020-05-22T17:16:03Z

Tr1318:

MRD:01535442

2020-05-22T17:14:14Z

Tr1318: /* Locate the approximate position of the transition state */

MRD:01535442

2020-05-22T12:39:13Z

Tr1318: /* What can you conclude from the table? */

MRD:01535442

2020-05-22T10:24:15Z

Tr1318: /* On a potential energy surface diagram, how is the transition state mathematically defined? */

MRD:01535442

2020-05-22T10:23:32Z

Tr1318: /* Comment on how the mep and the trajectory you just calculated differ */

MRD:01535442

2020-05-22T10:21:37Z

Tr1318: /* What can you conclude from the table? */

MRD:01535442

2020-05-22T09:47:46Z

Tr1318: /* Complete the table below by adding the total energy, whether the trajectory is reactive or unreactive, and provide a plot of the trajectory and a small description for what happens along the trajectory. */

MRD:01535442

2020-05-22T09:37:29Z

File:Contour Plot of Row 5 01535442.png

2020-05-22T09:37:01Z

Tr1318:

File:Contour Plot of Row 4 01535442.png

2020-05-22T09:32:31Z

Tr1318:

MRD:01535442

2020-05-22T09:29:46Z

File:Contour Plot of Row 3 01535442.png

2020-05-22T01:03:49Z

Tr1318:

MRD:01535442

2020-05-22T01:02:25Z

File:Contour Plot of Row 2 01535442.png

2020-05-22T01:01:11Z

Tr1318:

MRD:01535442

2020-05-22T00:58:14Z

Tr1318: /* Comment on how the mep and the trajectory you just calculated differ */

MRD:01535442

2020-05-22T00:57:34Z

Tr1318: /* Exercise 1: H + H2 System */

MRD:01535442

2020-05-22T00:56:21Z

Tr1318: /* Comment on how the mep and the trajectory you just calculated differ */

MRD:01535442

2020-05-22T00:52:35Z

Tr1318: /* Comment on how the mep and the trajectory you just calculated differ */

MRD:01535442

2020-05-22T00:50:51Z

MRD:01535442

2020-05-22T00:49:20Z

MRD:01535442

2020-05-22T00:46:26Z

Tr1318: /* Report your best estimate of the transition state position (rts) and explain your reasoning illustrating it with a “Internuclear Distances vs Time” plot for a relevant trajectory */

MRD:01535442

2020-05-22T00:44:20Z

Tr1318: /* Comment on how the mep and the trajectory you just calculated differ */

MRD:01535442

2020-05-22T00:43:14Z

File:Contour Plot of P1=-2.56 P2=-5.1 01535442.png

2020-05-22T00:39:43Z

Tr1318:

MRD:01535442

2020-05-22T00:16:30Z

Tr1318: /* Complete the table above by adding the total energy, whether the trajectory is reactive or unreactive, and provide a plot of the trajectory and a small description for what happens along the trajectory. */

MRD:01535442

2020-05-22T00:12:43Z

MRD:01535442

2020-05-22T00:12:22Z

Tr1318: /* Comment on how the mep and the trajectory you just calculated differ */

MRD:01535442

2020-05-22T00:09:50Z

Tr1318: /* Comment on how the mep and the trajectory you just calculated differ */

MRD:01535442

2020-05-21T23:27:06Z

Tr1318: /* How can the transition state be identified, and how can it be distinguished from a local minimum of the potential energy surface? */

MRD:01535442

2020-05-21T21:11:38Z

Tr1318: /* How can the transition state be identified, and how can it be distinguished from a local minimum of the potential energy surface? */

MRD:01535442

2020-05-21T19:43:33Z

Tr1318: /* Report your best estimate of the transition state position (rts) and explain your reasoning illustrating it with a “Internuclear Distances vs Time” plot for a relevant trajectory */

MRD:01535442

2020-05-21T19:42:44Z

Tr1318: /* Comment on how the mep and the trajectory you just calculated differ */

MRD:01535442

2020-05-21T19:42:18Z

Tr1318: /* Comment on how the mep and the trajectory you just calculated differ */

MRD:01535442

2020-05-21T19:39:39Z

Tr1318: /* Comment on how the mep and the trajectory you just calculated differ */

File:Contour Plot of Rts +1, Rts MEP 01535442.png

2020-05-21T19:37:52Z

Tr1318: Contour plot of a system with slighlty displaced transtition state position, calculated using MEP (minimum energy path).

Contour plot of a system with slighlty displaced transtition state position, calculated using MEP (minimum energy path).