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MRD:sjl1218

2020-05-08T22:57:45Z

Sjl1218: /* Exercise 2: F + H2 and H + HF */

==Exercise 1: HA + HB-HC -> HA-HB + HC==

[[File:sjl1218-reactionscheme.png|500px|center|thumb|Initial Conditions of Reaction Involving 3 Atoms: HA + HB-HC -> HA-HB + HC]]

===Dynamics of the Transition State Region===
====The Transition State====
[[File:Sjl1218-pesurface.PNG|300px|right|thumb|center|Potential Energy Surface Diagram of HA + HB-HC -> HA-HB + HC]]
In a potential energy surface diagram, the reaction pathway (black line) proceeds along the minimum energy path linked by the reactants and products. The transition state is the PES diagram saddle point defined mathematically by ∂V(ri)/∂ri=0.

The transition state location can be identified if V(rAB)/∂rAB=0 and V(rBC)/∂rBC=0. This point can be distinguished from the local minima if the outcome of taking the partial second derivative of potential energy with respect to either rAB or rBC is 0.

====Locating the Transition State====

Since the H2 + H1 surface is symmetric, the transition state must have rAB=rBC. The location of the transition state position rts can be estimated when ∂V(ri)/∂ri=0 and there will be minimal oscillation among the 3 atoms as there is no force acting along rAB and rBC.

[[File:Sjl1218-4.PNG|400px|center|thumb|Model for when rAB = rBC and pAB=pBC=0]]

The transition state position rts is estimated as 91 pm. The internuclear distances vs time graph for rAB = rBC=91pm shows a 'flat' line, meaning no forces are acting at this position.

[[File:Sjl1218-ts.PNG|300px|center|thumb|Internuclear Distances vs Time Graph for rAB = rBC=91pm and pAB=pBC=0]]

====Calculating the reaction path====

The reaction path or minimum energy path is an infinitely slow trajectory (momenta and velocities resets to zero in each time step) obtained after locating the transition state position.

The minimum energy path initially shows a short horizontal line of the atoms entering the transition state position followed by the decreasing rate of atoms HA-HC and HB-HC increasing in distance. Atoms HA-HB forms a bond and remains constant in distance.

Even though the MEP outlines a reaction, it does not take into account the mass and inertia of the atoms, therefore does not provide the realistic picture of the reaction.
The MEP and dynamic trajectory differs in that the realistic trajectory shows oscillations (potential energy interactions) between atoms. At first the 3 atoms are in the transition state positions, showed by the horiontal lines. The trajectory then shows a linear increase in HA-HC and HB-HC distances and HA-HB oscillates about the same position.
[[File:Sjl1218-mep.PNG|300px|center|thumb|Minimum Energy Path (rBC = rts+1 pm, rAB = rts and pBC = pAB = 0 g.mol-1.pm.fs-1)]]
[[File:Sjl1218-traj.PNG|300px|center|thumb|Dynamic Trajectory (rBC = rts+1 pm, rAB = rts and pBC = pAB = 0 g.mol-1.pm.fs-1)]]

===Reactive and Unreactive Trajectories===
Determining whether trajectories are reactive from their momenta when rBC=74 pm and rAB=200 pm.
{| 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
|HB-HC collides with HA with sufficient kinetic energy to overcome the reaction barrier and forms HAHB and HC.
|[[File:Sjl1218-ani1.png|200px]]
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-4.1</nowiki>
|<nowiki>-420.077</nowiki>
|No
|HB-HC approaches HA but does not react due to lack of kinetic energy/momenta.
|[[File:Sjl1218-ani2.png|200px]]
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-5.1</nowiki>
|<nowiki>-413.977</nowiki>
|Yes
|HB-HC collides with HA with sufficient kinetic energy to overcome the reaction barrier and forms HAHB and HC.
|[[File:Sjl1218-ani3.png|200px]]
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.1</nowiki>
|<nowiki>-357.277</nowiki>
|No
|HB-HC collides with HA and enters a temporary transition state but insufficient kinetic energy does not allow a reaction to occur. Atoms return to their starting positions.
|[[File:Sjl1218-ani4.png|200px]]
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.6</nowiki>
|<nowiki>-349.477</nowiki>
|Yes
|HB-HC collides with HA with just enough kinetic energy to overcome the potential energy between HB-HC for the reaction to occur.
|[[File:Sjl1218-ani5.png|200px]]
|}
The hypothesis that higher values of momenta would be reactive is not precisely correct, this table shows that pBC must be greater than pAB by a specific factor to be able reactive.

===Transition State Theory===

The transition state theory attempts to provide a grearter understanding of the reaction by predicting the rate as well as the theromodynamic parameters of the reaction. However, it has its limitations. The transition state theory neglects the effects of quantum tunneling such that particles can bypass the activation energy of the transition state. Additionally, systems that have already crossed the transition state and formed products can recross the barrier to reform the reactants. Consequently, the rate calculated by the transition state theory is greater than the experimental value for the reasons that quantum effects are not taken into account.

==Exercise 2: F + H-H and H + HF==

===PES Inspection===

====1. F + H-H -> F-H + H====

Conditions: rAB = 150 pm, rBC = 80 pm, pAB = 0 g.mol-1.pm.fs-1, pBC = 0.5 g.mol-1.pm.fs-1.
[[File:Sjl1218-sur3.png|center|thumb|PES of F + H-H -> F-H + H]]

Products are lower in potential energy than reactants, therefore reaction is exothermic.The H-F bond formed releases more energy than the energy taken to break the H-H bond, therefore H-F is greater in bond strength than H2.

====2. F-H + H -> F + H-H====

Conditions: rAB = 80 pm, rBC = 150 pm, pAB = 15 g.mol-1.pm.fs-1, pBC = 0 g.mol-1.pm.fs-1.
[[File:Sjl1218-sur4.PNG|center|thumb|PES of F-H + H -> F + H-H]]

Products are higher in energy than reactants, therefore reaction is endothermic. The energy used to break the H-F bond is greater than the energy released for forming the H-H bond. The H-F bond is greater in bond strength.

===Locating the Transition State Position===

The approximate position of the transition state is F-H = 180 pm and H-H = 75 pm. Horizontal line shown on the internuclear distance vs time graph represents minimal oscillations among the atoms, ∂V(ri)/∂ri=0 no forces are acting on the F-H-H direction so transition state is reached.

[[File:Sjl1218-ts1.png|center|thumb|Internuclear Distance vs Time graph for rAB = 180 pm, rBC = 75 pm, pAB = 0 g.mol-1.pm.fs-1, pBC = 0 g.mol-1.pm.fs-1]]

===Calculating the Activation Energy===

The activation energy can be calculated by subtracting the potential energy of the reactants from the potential energy the TS. The potential energy of the transition state is -433.943 kJ.mol-1. The potential energy of the reactants can be obtained by performing an MEP of energy vs time for the reaction and observing the starting potential energy.

Activation energies of:

1. F + H-H -> F-H + H: -433.943 - -434.288 = +0.345 kj.mol-1
[[File:Sjl1218-6.png|center|thumb|Energy vs Time MEP for F + H-H -> F-H + H with same reaction conditions]]

2. F-H + H -> F + H-H: -433.943 - -496.862 = +62.919 kj.mol-1
[[File:Sjl1218-7.png|center|thumb|Energy vs Time MEP for F-H + H -> F + H-H with same reaction conditions]]

===Reaction Dynamics===
====1. F + H-H -> F-H + H====

Initial conditions that result in a reactive trajectory: rAB = 150 pm, rBC = 80 pm, pAB = 0 g.mol-1.pm.fs-1, pBC = 0.5 g.mol-1.pm.fs-1.
[[File:Sjl1218-8.png|300px|center|thumb|Illustration of reactants: F + H-H]] [[File:Sjl1218-9.png|center|thumb|Illustration of products: F-H + H]]

[[File:Sjl1218-10.png|center|thumb|Energy vs Time MEP of F + H-H -> F-H + H]]

This reaction is exothermic but the total energy is conserved in a reaction, the energy release mechanism is explained below:

Originally, H-H is a molecule held together by strong potential energy. As it approaches atom F, potential energy between H-H is transferred to kinetic energy which releases energy in the reaction. The momenta vs time graph (orange line) shows the spikes in momentum/ kinetic energy for H-H (B-C) when H (B) is transferred to atom F (A). The momentum of this orange line then flattens, all kinetic energy is transferred to the formation of F-H (A-B) bond which shows oscillations in momentum by the blue line.

To confirm this experimentally, measure the change in temperature of the reaction with a thermometer which should show an increase in temperature as the reaction is exothermic.

====2. F-H + H -> F + H-H====

In this reaction, a late transition state is formed because of the high electronegativity of atom F. According to Hammond's postulate, the energy of the transition state is similar to the products because the structure of the late transition state resembles the products.

Polanyi's rules states that vibrational energy is more efficient in promoting a reaction with a late barrier than translational energy. The two PES diagrams below shows the effectiveness of 1. high vibrational energy and 2. high kinetic energy, in overcoming the barrier. The first figure shows a reactive trajectory (A-B + C -> A + B-C) is achieved from a high distribution in vibrational energy. On the other hand, the trajectory was unreactive in the high kinetic energy case.

Conditions: rAB = 75 pm, rBC = 180 pm, pAB = 20 g.mol-1.pm.fs-1, pBC = 0 g.mol-1.pm.fs-1.
[[File:Sjl1218-11.png|center|thumb|1. High Vibrational Energy: PES of F-H + H -> F + H-H]]

Conditions: rAB = 75 pm, rBC = 180 pm, pAB = 20 g.mol-1.pm.fs-1, pBC = 10 g.mol-1.pm.fs-1.
[[File:Sjl1218-12.png|center|thumb|2. High Kinetic Energy: PES of F-H + H -> F + H-H]]

MRD:sjl1218

2020-05-08T22:57:05Z

Sjl1218: /* 2. F-H + H -> F + H-H */

==Exercise 1: HA + HB-HC -> HA-HB + HC==

[[File:sjl1218-reactionscheme.png|500px|center|thumb|Initial Conditions of Reaction Involving 3 Atoms: HA + HB-HC -> HA-HB + HC]]

===Dynamics of the Transition State Region===
====The Transition State====
[[File:Sjl1218-pesurface.PNG|300px|right|thumb|center|Potential Energy Surface Diagram of HA + HB-HC -> HA-HB + HC]]
In a potential energy surface diagram, the reaction pathway (black line) proceeds along the minimum energy path linked by the reactants and products. The transition state is the PES diagram saddle point defined mathematically by ∂V(ri)/∂ri=0.

The transition state location can be identified if V(rAB)/∂rAB=0 and V(rBC)/∂rBC=0. This point can be distinguished from the local minima if the outcome of taking the partial second derivative of potential energy with respect to either rAB or rBC is 0.

====Locating the Transition State====

Since the H2 + H1 surface is symmetric, the transition state must have rAB=rBC. The location of the transition state position rts can be estimated when ∂V(ri)/∂ri=0 and there will be minimal oscillation among the 3 atoms as there is no force acting along rAB and rBC.

[[File:Sjl1218-4.PNG|400px|center|thumb|Model for when rAB = rBC and pAB=pBC=0]]

The transition state position rts is estimated as 91 pm. The internuclear distances vs time graph for rAB = rBC=91pm shows a 'flat' line, meaning no forces are acting at this position.

[[File:Sjl1218-ts.PNG|300px|center|thumb|Internuclear Distances vs Time Graph for rAB = rBC=91pm and pAB=pBC=0]]

====Calculating the reaction path====

The reaction path or minimum energy path is an infinitely slow trajectory (momenta and velocities resets to zero in each time step) obtained after locating the transition state position.

The minimum energy path initially shows a short horizontal line of the atoms entering the transition state position followed by the decreasing rate of atoms HA-HC and HB-HC increasing in distance. Atoms HA-HB forms a bond and remains constant in distance.

Even though the MEP outlines a reaction, it does not take into account the mass and inertia of the atoms, therefore does not provide the realistic picture of the reaction.
The MEP and dynamic trajectory differs in that the realistic trajectory shows oscillations (potential energy interactions) between atoms. At first the 3 atoms are in the transition state positions, showed by the horiontal lines. The trajectory then shows a linear increase in HA-HC and HB-HC distances and HA-HB oscillates about the same position.
[[File:Sjl1218-mep.PNG|300px|center|thumb|Minimum Energy Path (rBC = rts+1 pm, rAB = rts and pBC = pAB = 0 g.mol-1.pm.fs-1)]]
[[File:Sjl1218-traj.PNG|300px|center|thumb|Dynamic Trajectory (rBC = rts+1 pm, rAB = rts and pBC = pAB = 0 g.mol-1.pm.fs-1)]]

===Reactive and Unreactive Trajectories===
Determining whether trajectories are reactive from their momenta when rBC=74 pm and rAB=200 pm.
{| 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
|HB-HC collides with HA with sufficient kinetic energy to overcome the reaction barrier and forms HAHB and HC.
|[[File:Sjl1218-ani1.png|200px]]
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-4.1</nowiki>
|<nowiki>-420.077</nowiki>
|No
|HB-HC approaches HA but does not react due to lack of kinetic energy/momenta.
|[[File:Sjl1218-ani2.png|200px]]
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-5.1</nowiki>
|<nowiki>-413.977</nowiki>
|Yes
|HB-HC collides with HA with sufficient kinetic energy to overcome the reaction barrier and forms HAHB and HC.
|[[File:Sjl1218-ani3.png|200px]]
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.1</nowiki>
|<nowiki>-357.277</nowiki>
|No
|HB-HC collides with HA and enters a temporary transition state but insufficient kinetic energy does not allow a reaction to occur. Atoms return to their starting positions.
|[[File:Sjl1218-ani4.png|200px]]
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.6</nowiki>
|<nowiki>-349.477</nowiki>
|Yes
|HB-HC collides with HA with just enough kinetic energy to overcome the potential energy between HB-HC for the reaction to occur.
|[[File:Sjl1218-ani5.png|200px]]
|}
The hypothesis that higher values of momenta would be reactive is not precisely correct, this table shows that pBC must be greater than pAB by a specific factor to be able reactive.

===Transition State Theory===

The transition state theory attempts to provide a grearter understanding of the reaction by predicting the rate as well as the theromodynamic parameters of the reaction. However, it has its limitations. The transition state theory neglects the effects of quantum tunneling such that particles can bypass the activation energy of the transition state. Additionally, systems that have already crossed the transition state and formed products can recross the barrier to reform the reactants. Consequently, the rate calculated by the transition state theory is greater than the experimental value for the reasons that quantum effects are not taken into account.

==Exercise 2: F + H2 and H + HF==

===PES Inspection===

====1. F + H-H -> F-H + H====

Conditions: rAB = 150 pm, rBC = 80 pm, pAB = 0 g.mol-1.pm.fs-1, pBC = 0.5 g.mol-1.pm.fs-1.
[[File:Sjl1218-sur3.png|center|thumb|PES of F + H-H -> F-H + H]]

Products are lower in potential energy than reactants, therefore reaction is exothermic.The H-F bond formed releases more energy than the energy taken to break the H-H bond, therefore H-F is greater in bond strength than H2.

====2. F-H + H -> F + H-H====

Conditions: rAB = 80 pm, rBC = 150 pm, pAB = 15 g.mol-1.pm.fs-1, pBC = 0 g.mol-1.pm.fs-1.
[[File:Sjl1218-sur4.PNG|center|thumb|PES of F-H + H -> F + H-H]]

Products are higher in energy than reactants, therefore reaction is endothermic. The energy used to break the H-F bond is greater than the energy released for forming the H-H bond. The H-F bond is greater in bond strength.

===Locating the Transition State Position===

The approximate position of the transition state is F-H = 180 pm and H-H = 75 pm. Horizontal line shown on the internuclear distance vs time graph represents minimal oscillations among the atoms, ∂V(ri)/∂ri=0 no forces are acting on the F-H-H direction so transition state is reached.

[[File:Sjl1218-ts1.png|center|thumb|Internuclear Distance vs Time graph for rAB = 180 pm, rBC = 75 pm, pAB = 0 g.mol-1.pm.fs-1, pBC = 0 g.mol-1.pm.fs-1]]

===Calculating the Activation Energy===

The activation energy can be calculated by subtracting the potential energy of the reactants from the potential energy the TS. The potential energy of the transition state is -433.943 kJ.mol-1. The potential energy of the reactants can be obtained by performing an MEP of energy vs time for the reaction and observing the starting potential energy.

Activation energies of:

1. F + H-H -> F-H + H: -433.943 - -434.288 = +0.345 kj.mol-1
[[File:Sjl1218-6.png|center|thumb|Energy vs Time MEP for F + H-H -> F-H + H with same reaction conditions]]

2. F-H + H -> F + H-H: -433.943 - -496.862 = +62.919 kj.mol-1
[[File:Sjl1218-7.png|center|thumb|Energy vs Time MEP for F-H + H -> F + H-H with same reaction conditions]]

===Reaction Dynamics===
====1. F + H-H -> F-H + H====

Initial conditions that result in a reactive trajectory: rAB = 150 pm, rBC = 80 pm, pAB = 0 g.mol-1.pm.fs-1, pBC = 0.5 g.mol-1.pm.fs-1.
[[File:Sjl1218-8.png|300px|center|thumb|Illustration of reactants: F + H-H]] [[File:Sjl1218-9.png|center|thumb|Illustration of products: F-H + H]]

[[File:Sjl1218-10.png|center|thumb|Energy vs Time MEP of F + H-H -> F-H + H]]

This reaction is exothermic but the total energy is conserved in a reaction, the energy release mechanism is explained below:

Originally, H-H is a molecule held together by strong potential energy. As it approaches atom F, potential energy between H-H is transferred to kinetic energy which releases energy in the reaction. The momenta vs time graph (orange line) shows the spikes in momentum/ kinetic energy for H-H (B-C) when H (B) is transferred to atom F (A). The momentum of this orange line then flattens, all kinetic energy is transferred to the formation of F-H (A-B) bond which shows oscillations in momentum by the blue line.

To confirm this experimentally, measure the change in temperature of the reaction with a thermometer which should show an increase in temperature as the reaction is exothermic.

====2. F-H + H -> F + H-H====

In this reaction, a late transition state is formed because of the high electronegativity of atom F. According to Hammond's postulate, the energy of the transition state is similar to the products because the structure of the late transition state resembles the products.

Polanyi's rules states that vibrational energy is more efficient in promoting a reaction with a late barrier than translational energy. The two PES diagrams below shows the effectiveness of 1. high vibrational energy and 2. high kinetic energy, in overcoming the barrier. The first figure shows a reactive trajectory (A-B + C -> A + B-C) is achieved from a high distribution in vibrational energy. On the other hand, the trajectory was unreactive in the high kinetic energy case.

Conditions: rAB = 75 pm, rBC = 180 pm, pAB = 20 g.mol-1.pm.fs-1, pBC = 0 g.mol-1.pm.fs-1.
[[File:Sjl1218-11.png|center|thumb|1. High Vibrational Energy: PES of F-H + H -> F + H-H]]

Conditions: rAB = 75 pm, rBC = 180 pm, pAB = 20 g.mol-1.pm.fs-1, pBC = 10 g.mol-1.pm.fs-1.
[[File:Sjl1218-12.png|center|thumb|2. High Kinetic Energy: PES of F-H + H -> F + H-H]]

MRD:sjl1218

2020-05-08T22:55:22Z

Sjl1218: /* 2. F-H + H -> F + H-H */

==Exercise 1: HA + HB-HC -> HA-HB + HC==

[[File:sjl1218-reactionscheme.png|500px|center|thumb|Initial Conditions of Reaction Involving 3 Atoms: HA + HB-HC -> HA-HB + HC]]

===Dynamics of the Transition State Region===
====The Transition State====
[[File:Sjl1218-pesurface.PNG|300px|right|thumb|center|Potential Energy Surface Diagram of HA + HB-HC -> HA-HB + HC]]
In a potential energy surface diagram, the reaction pathway (black line) proceeds along the minimum energy path linked by the reactants and products. The transition state is the PES diagram saddle point defined mathematically by ∂V(ri)/∂ri=0.

The transition state location can be identified if V(rAB)/∂rAB=0 and V(rBC)/∂rBC=0. This point can be distinguished from the local minima if the outcome of taking the partial second derivative of potential energy with respect to either rAB or rBC is 0.

====Locating the Transition State====

Since the H2 + H1 surface is symmetric, the transition state must have rAB=rBC. The location of the transition state position rts can be estimated when ∂V(ri)/∂ri=0 and there will be minimal oscillation among the 3 atoms as there is no force acting along rAB and rBC.

[[File:Sjl1218-4.PNG|400px|center|thumb|Model for when rAB = rBC and pAB=pBC=0]]

The transition state position rts is estimated as 91 pm. The internuclear distances vs time graph for rAB = rBC=91pm shows a 'flat' line, meaning no forces are acting at this position.

[[File:Sjl1218-ts.PNG|300px|center|thumb|Internuclear Distances vs Time Graph for rAB = rBC=91pm and pAB=pBC=0]]

====Calculating the reaction path====

The reaction path or minimum energy path is an infinitely slow trajectory (momenta and velocities resets to zero in each time step) obtained after locating the transition state position.

The minimum energy path initially shows a short horizontal line of the atoms entering the transition state position followed by the decreasing rate of atoms HA-HC and HB-HC increasing in distance. Atoms HA-HB forms a bond and remains constant in distance.

Even though the MEP outlines a reaction, it does not take into account the mass and inertia of the atoms, therefore does not provide the realistic picture of the reaction.
The MEP and dynamic trajectory differs in that the realistic trajectory shows oscillations (potential energy interactions) between atoms. At first the 3 atoms are in the transition state positions, showed by the horiontal lines. The trajectory then shows a linear increase in HA-HC and HB-HC distances and HA-HB oscillates about the same position.
[[File:Sjl1218-mep.PNG|300px|center|thumb|Minimum Energy Path (rBC = rts+1 pm, rAB = rts and pBC = pAB = 0 g.mol-1.pm.fs-1)]]
[[File:Sjl1218-traj.PNG|300px|center|thumb|Dynamic Trajectory (rBC = rts+1 pm, rAB = rts and pBC = pAB = 0 g.mol-1.pm.fs-1)]]

===Reactive and Unreactive Trajectories===
Determining whether trajectories are reactive from their momenta when rBC=74 pm and rAB=200 pm.
{| 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
|HB-HC collides with HA with sufficient kinetic energy to overcome the reaction barrier and forms HAHB and HC.
|[[File:Sjl1218-ani1.png|200px]]
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-4.1</nowiki>
|<nowiki>-420.077</nowiki>
|No
|HB-HC approaches HA but does not react due to lack of kinetic energy/momenta.
|[[File:Sjl1218-ani2.png|200px]]
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-5.1</nowiki>
|<nowiki>-413.977</nowiki>
|Yes
|HB-HC collides with HA with sufficient kinetic energy to overcome the reaction barrier and forms HAHB and HC.
|[[File:Sjl1218-ani3.png|200px]]
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.1</nowiki>
|<nowiki>-357.277</nowiki>
|No
|HB-HC collides with HA and enters a temporary transition state but insufficient kinetic energy does not allow a reaction to occur. Atoms return to their starting positions.
|[[File:Sjl1218-ani4.png|200px]]
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.6</nowiki>
|<nowiki>-349.477</nowiki>
|Yes
|HB-HC collides with HA with just enough kinetic energy to overcome the potential energy between HB-HC for the reaction to occur.
|[[File:Sjl1218-ani5.png|200px]]
|}
The hypothesis that higher values of momenta would be reactive is not precisely correct, this table shows that pBC must be greater than pAB by a specific factor to be able reactive.

===Transition State Theory===

The transition state theory attempts to provide a grearter understanding of the reaction by predicting the rate as well as the theromodynamic parameters of the reaction. However, it has its limitations. The transition state theory neglects the effects of quantum tunneling such that particles can bypass the activation energy of the transition state. Additionally, systems that have already crossed the transition state and formed products can recross the barrier to reform the reactants. Consequently, the rate calculated by the transition state theory is greater than the experimental value for the reasons that quantum effects are not taken into account.

==Exercise 2: F + H2 and H + HF==

===PES Inspection===

====1. F + H-H -> F-H + H====

Conditions: rAB = 150 pm, rBC = 80 pm, pAB = 0 g.mol-1.pm.fs-1, pBC = 0.5 g.mol-1.pm.fs-1.
[[File:Sjl1218-sur3.png|center|thumb|PES of F + H-H -> F-H + H]]

Products are lower in potential energy than reactants, therefore reaction is exothermic.The H-F bond formed releases more energy than the energy taken to break the H-H bond, therefore H-F is greater in bond strength than H2.

====2. F-H + H -> F + H-H====

Conditions: rAB = 80 pm, rBC = 150 pm, pAB = 15 g.mol-1.pm.fs-1, pBC = 0 g.mol-1.pm.fs-1.
[[File:Sjl1218-sur4.PNG|center|thumb|PES of F-H + H -> F + H-H]]

Products are higher in energy than reactants, therefore reaction is endothermic. The energy used to break the H-F bond is greater than the energy released for forming the H-H bond. The H-F bond is greater in bond strength.

===Locating the Transition State Position===

The approximate position of the transition state is F-H = 180 pm and H-H = 75 pm. Horizontal line shown on the internuclear distance vs time graph represents minimal oscillations among the atoms, ∂V(ri)/∂ri=0 no forces are acting on the F-H-H direction so transition state is reached.

[[File:Sjl1218-ts1.png|center|thumb|Internuclear Distance vs Time graph for rAB = 180 pm, rBC = 75 pm, pAB = 0 g.mol-1.pm.fs-1, pBC = 0 g.mol-1.pm.fs-1]]

===Calculating the Activation Energy===

The activation energy can be calculated by subtracting the potential energy of the reactants from the potential energy the TS. The potential energy of the transition state is -433.943 kJ.mol-1. The potential energy of the reactants can be obtained by performing an MEP of energy vs time for the reaction and observing the starting potential energy.

Activation energies of:

1. F + H-H -> F-H + H: -433.943 - -434.288 = +0.345 kj.mol-1
[[File:Sjl1218-6.png|center|thumb|Energy vs Time MEP for F + H-H -> F-H + H with same reaction conditions]]

2. F-H + H -> F + H-H: -433.943 - -496.862 = +62.919 kj.mol-1
[[File:Sjl1218-7.png|center|thumb|Energy vs Time MEP for F-H + H -> F + H-H with same reaction conditions]]

===Reaction Dynamics===
====1. F + H-H -> F-H + H====

Initial conditions that result in a reactive trajectory: rAB = 150 pm, rBC = 80 pm, pAB = 0 g.mol-1.pm.fs-1, pBC = 0.5 g.mol-1.pm.fs-1.
[[File:Sjl1218-8.png|300px|center|thumb|Illustration of reactants: F + H-H]] [[File:Sjl1218-9.png|center|thumb|Illustration of products: F-H + H]]

[[File:Sjl1218-10.png|center|thumb|Energy vs Time MEP of F + H-H -> F-H + H]]

This reaction is exothermic but the total energy is conserved in a reaction, the energy release mechanism is explained below:

Originally, H-H is a molecule held together by strong potential energy. As it approaches atom F, potential energy between H-H is transferred to kinetic energy which releases energy in the reaction. The momenta vs time graph (orange line) shows the spikes in momentum/ kinetic energy for H-H (B-C) when H (B) is transferred to atom F (A). The momentum of this orange line then flattens, all kinetic energy is transferred to the formation of F-H (A-B) bond which shows oscillations in momentum by the blue line.

To confirm this experimentally, measure the change in temperature of the reaction with a thermometer which should show an increase in temperature as the reaction is exothermic.

====2. F-H + H -> F + H-H====

In this reaction, a late transition state is formed because of the high electronegativity of atom F. According to Hammond's postulate, the energy of the transition state is similar to the products because the structure of the late transition state resembles the products.

Polanyi's rules states that vibrational energy is more efficient in promoting a reaction with a late barrier than translational energy. The two PES diagrams below shows the effectiveness of 1. high vibrational energy and 2. high kinetic energy, in overcoming the barrier. The first figure shows a reactive trajectory (A-B + C -> A + B-C) is achieved from a high distribution in vibrational energy.

Conditions: rAB = 75 pm, rBC = 180 pm, pAB = 20 g.mol-1.pm.fs-1, pBC = 0 g.mol-1.pm.fs-1.
[[File:Sjl1218-11.png|center|thumb|High Vibrational Energy: PES of F-H + H -> F + H-H]]

Conditions: rAB = 75 pm, rBC = 180 pm, pAB = 20 g.mol-1.pm.fs-1, pBC = 10 g.mol-1.pm.fs-1.
[[File:Sjl1218-12.png|center|thumb|High Kinetic Energy: PES of F-H + H -> F + H-H]]

File:Sjl1218-12.png

2020-05-08T22:50:52Z

Sjl1218:

MRD:sjl1218

2020-05-08T22:48:41Z

Sjl1218: /* 2. F-H + H -> F + H-H */

==Exercise 1: HA + HB-HC -> HA-HB + HC==

[[File:sjl1218-reactionscheme.png|500px|center|thumb|Initial Conditions of Reaction Involving 3 Atoms: HA + HB-HC -> HA-HB + HC]]

===Dynamics of the Transition State Region===
====The Transition State====
[[File:Sjl1218-pesurface.PNG|300px|right|thumb|center|Potential Energy Surface Diagram of HA + HB-HC -> HA-HB + HC]]
In a potential energy surface diagram, the reaction pathway (black line) proceeds along the minimum energy path linked by the reactants and products. The transition state is the PES diagram saddle point defined mathematically by ∂V(ri)/∂ri=0.

The transition state location can be identified if V(rAB)/∂rAB=0 and V(rBC)/∂rBC=0. This point can be distinguished from the local minima if the outcome of taking the partial second derivative of potential energy with respect to either rAB or rBC is 0.

====Locating the Transition State====

Since the H2 + H1 surface is symmetric, the transition state must have rAB=rBC. The location of the transition state position rts can be estimated when ∂V(ri)/∂ri=0 and there will be minimal oscillation among the 3 atoms as there is no force acting along rAB and rBC.

[[File:Sjl1218-4.PNG|400px|center|thumb|Model for when rAB = rBC and pAB=pBC=0]]

The transition state position rts is estimated as 91 pm. The internuclear distances vs time graph for rAB = rBC=91pm shows a 'flat' line, meaning no forces are acting at this position.

[[File:Sjl1218-ts.PNG|300px|center|thumb|Internuclear Distances vs Time Graph for rAB = rBC=91pm and pAB=pBC=0]]

====Calculating the reaction path====

The reaction path or minimum energy path is an infinitely slow trajectory (momenta and velocities resets to zero in each time step) obtained after locating the transition state position.

The minimum energy path initially shows a short horizontal line of the atoms entering the transition state position followed by the decreasing rate of atoms HA-HC and HB-HC increasing in distance. Atoms HA-HB forms a bond and remains constant in distance.

Even though the MEP outlines a reaction, it does not take into account the mass and inertia of the atoms, therefore does not provide the realistic picture of the reaction.
The MEP and dynamic trajectory differs in that the realistic trajectory shows oscillations (potential energy interactions) between atoms. At first the 3 atoms are in the transition state positions, showed by the horiontal lines. The trajectory then shows a linear increase in HA-HC and HB-HC distances and HA-HB oscillates about the same position.
[[File:Sjl1218-mep.PNG|300px|center|thumb|Minimum Energy Path (rBC = rts+1 pm, rAB = rts and pBC = pAB = 0 g.mol-1.pm.fs-1)]]
[[File:Sjl1218-traj.PNG|300px|center|thumb|Dynamic Trajectory (rBC = rts+1 pm, rAB = rts and pBC = pAB = 0 g.mol-1.pm.fs-1)]]

===Reactive and Unreactive Trajectories===
Determining whether trajectories are reactive from their momenta when rBC=74 pm and rAB=200 pm.
{| 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
|HB-HC collides with HA with sufficient kinetic energy to overcome the reaction barrier and forms HAHB and HC.
|[[File:Sjl1218-ani1.png|200px]]
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-4.1</nowiki>
|<nowiki>-420.077</nowiki>
|No
|HB-HC approaches HA but does not react due to lack of kinetic energy/momenta.
|[[File:Sjl1218-ani2.png|200px]]
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-5.1</nowiki>
|<nowiki>-413.977</nowiki>
|Yes
|HB-HC collides with HA with sufficient kinetic energy to overcome the reaction barrier and forms HAHB and HC.
|[[File:Sjl1218-ani3.png|200px]]
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.1</nowiki>
|<nowiki>-357.277</nowiki>
|No
|HB-HC collides with HA and enters a temporary transition state but insufficient kinetic energy does not allow a reaction to occur. Atoms return to their starting positions.
|[[File:Sjl1218-ani4.png|200px]]
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.6</nowiki>
|<nowiki>-349.477</nowiki>
|Yes
|HB-HC collides with HA with just enough kinetic energy to overcome the potential energy between HB-HC for the reaction to occur.
|[[File:Sjl1218-ani5.png|200px]]
|}
The hypothesis that higher values of momenta would be reactive is not precisely correct, this table shows that pBC must be greater than pAB by a specific factor to be able reactive.

===Transition State Theory===

The transition state theory attempts to provide a grearter understanding of the reaction by predicting the rate as well as the theromodynamic parameters of the reaction. However, it has its limitations. The transition state theory neglects the effects of quantum tunneling such that particles can bypass the activation energy of the transition state. Additionally, systems that have already crossed the transition state and formed products can recross the barrier to reform the reactants. Consequently, the rate calculated by the transition state theory is greater than the experimental value for the reasons that quantum effects are not taken into account.

==Exercise 2: F + H2 and H + HF==

===PES Inspection===

====1. F + H-H -> F-H + H====

Conditions: rAB = 150 pm, rBC = 80 pm, pAB = 0 g.mol-1.pm.fs-1, pBC = 0.5 g.mol-1.pm.fs-1.
[[File:Sjl1218-sur3.png|center|thumb|PES of F + H-H -> F-H + H]]

Products are lower in potential energy than reactants, therefore reaction is exothermic.The H-F bond formed releases more energy than the energy taken to break the H-H bond, therefore H-F is greater in bond strength than H2.

====2. F-H + H -> F + H-H====

Conditions: rAB = 80 pm, rBC = 150 pm, pAB = 15 g.mol-1.pm.fs-1, pBC = 0 g.mol-1.pm.fs-1.
[[File:Sjl1218-sur4.PNG|center|thumb|PES of F-H + H -> F + H-H]]

Products are higher in energy than reactants, therefore reaction is endothermic. The energy used to break the H-F bond is greater than the energy released for forming the H-H bond. The H-F bond is greater in bond strength.

===Locating the Transition State Position===

The approximate position of the transition state is F-H = 180 pm and H-H = 75 pm. Horizontal line shown on the internuclear distance vs time graph represents minimal oscillations among the atoms, ∂V(ri)/∂ri=0 no forces are acting on the F-H-H direction so transition state is reached.

[[File:Sjl1218-ts1.png|center|thumb|Internuclear Distance vs Time graph for rAB = 180 pm, rBC = 75 pm, pAB = 0 g.mol-1.pm.fs-1, pBC = 0 g.mol-1.pm.fs-1]]

===Calculating the Activation Energy===

The activation energy can be calculated by subtracting the potential energy of the reactants from the potential energy the TS. The potential energy of the transition state is -433.943 kJ.mol-1. The potential energy of the reactants can be obtained by performing an MEP of energy vs time for the reaction and observing the starting potential energy.

Activation energies of:

1. F + H-H -> F-H + H: -433.943 - -434.288 = +0.345 kj.mol-1
[[File:Sjl1218-6.png|center|thumb|Energy vs Time MEP for F + H-H -> F-H + H with same reaction conditions]]

2. F-H + H -> F + H-H: -433.943 - -496.862 = +62.919 kj.mol-1
[[File:Sjl1218-7.png|center|thumb|Energy vs Time MEP for F-H + H -> F + H-H with same reaction conditions]]

===Reaction Dynamics===
====1. F + H-H -> F-H + H====

Initial conditions that result in a reactive trajectory: rAB = 150 pm, rBC = 80 pm, pAB = 0 g.mol-1.pm.fs-1, pBC = 0.5 g.mol-1.pm.fs-1.
[[File:Sjl1218-8.png|300px|center|thumb|Illustration of reactants: F + H-H]] [[File:Sjl1218-9.png|center|thumb|Illustration of products: F-H + H]]

[[File:Sjl1218-10.png|center|thumb|Energy vs Time MEP of F + H-H -> F-H + H]]

This reaction is exothermic but the total energy is conserved in a reaction, the energy release mechanism is explained below:

Originally, H-H is a molecule held together by strong potential energy. As it approaches atom F, potential energy between H-H is transferred to kinetic energy which releases energy in the reaction. The momenta vs time graph (orange line) shows the spikes in momentum/ kinetic energy for H-H (B-C) when H (B) is transferred to atom F (A). The momentum of this orange line then flattens, all kinetic energy is transferred to the formation of F-H (A-B) bond which shows oscillations in momentum by the blue line.

To confirm this experimentally, measure the change in temperature of the reaction with a thermometer which should show an increase in temperature as the reaction is exothermic.

====2. F-H + H -> F + H-H====

In this reaction, a late transition state is formed because of the high electronegativity of atom F. According to Hammond's postulate, the energy of the transition state is similar to the products because the structure of the late transition state resembles the products.

Polanyi's rules states that vibrational energy is more efficient in promoting a reaction with a late barrier than translational energy. The potential energy surface diagram of the reaction below shows that vibrational energy is effective in overcoming the barrier

[[File:Sjl1218-11.png|center|thumb|PES of F-H + H -> F + H-H]]

MRD:sjl1218

2020-05-08T22:47:17Z

Sjl1218: /* Reaction Dynamics */

==Exercise 1: HA + HB-HC -> HA-HB + HC==

[[File:sjl1218-reactionscheme.png|500px|center|thumb|Initial Conditions of Reaction Involving 3 Atoms: HA + HB-HC -> HA-HB + HC]]

===Dynamics of the Transition State Region===
====The Transition State====
[[File:Sjl1218-pesurface.PNG|300px|right|thumb|center|Potential Energy Surface Diagram of HA + HB-HC -> HA-HB + HC]]
In a potential energy surface diagram, the reaction pathway (black line) proceeds along the minimum energy path linked by the reactants and products. The transition state is the PES diagram saddle point defined mathematically by ∂V(ri)/∂ri=0.

The transition state location can be identified if V(rAB)/∂rAB=0 and V(rBC)/∂rBC=0. This point can be distinguished from the local minima if the outcome of taking the partial second derivative of potential energy with respect to either rAB or rBC is 0.

====Locating the Transition State====

Since the H2 + H1 surface is symmetric, the transition state must have rAB=rBC. The location of the transition state position rts can be estimated when ∂V(ri)/∂ri=0 and there will be minimal oscillation among the 3 atoms as there is no force acting along rAB and rBC.

[[File:Sjl1218-4.PNG|400px|center|thumb|Model for when rAB = rBC and pAB=pBC=0]]

The transition state position rts is estimated as 91 pm. The internuclear distances vs time graph for rAB = rBC=91pm shows a 'flat' line, meaning no forces are acting at this position.

[[File:Sjl1218-ts.PNG|300px|center|thumb|Internuclear Distances vs Time Graph for rAB = rBC=91pm and pAB=pBC=0]]

====Calculating the reaction path====

The reaction path or minimum energy path is an infinitely slow trajectory (momenta and velocities resets to zero in each time step) obtained after locating the transition state position.

The minimum energy path initially shows a short horizontal line of the atoms entering the transition state position followed by the decreasing rate of atoms HA-HC and HB-HC increasing in distance. Atoms HA-HB forms a bond and remains constant in distance.

Even though the MEP outlines a reaction, it does not take into account the mass and inertia of the atoms, therefore does not provide the realistic picture of the reaction.
The MEP and dynamic trajectory differs in that the realistic trajectory shows oscillations (potential energy interactions) between atoms. At first the 3 atoms are in the transition state positions, showed by the horiontal lines. The trajectory then shows a linear increase in HA-HC and HB-HC distances and HA-HB oscillates about the same position.
[[File:Sjl1218-mep.PNG|300px|center|thumb|Minimum Energy Path (rBC = rts+1 pm, rAB = rts and pBC = pAB = 0 g.mol-1.pm.fs-1)]]
[[File:Sjl1218-traj.PNG|300px|center|thumb|Dynamic Trajectory (rBC = rts+1 pm, rAB = rts and pBC = pAB = 0 g.mol-1.pm.fs-1)]]

===Reactive and Unreactive Trajectories===
Determining whether trajectories are reactive from their momenta when rBC=74 pm and rAB=200 pm.
{| 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
|HB-HC collides with HA with sufficient kinetic energy to overcome the reaction barrier and forms HAHB and HC.
|[[File:Sjl1218-ani1.png|200px]]
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-4.1</nowiki>
|<nowiki>-420.077</nowiki>
|No
|HB-HC approaches HA but does not react due to lack of kinetic energy/momenta.
|[[File:Sjl1218-ani2.png|200px]]
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-5.1</nowiki>
|<nowiki>-413.977</nowiki>
|Yes
|HB-HC collides with HA with sufficient kinetic energy to overcome the reaction barrier and forms HAHB and HC.
|[[File:Sjl1218-ani3.png|200px]]
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.1</nowiki>
|<nowiki>-357.277</nowiki>
|No
|HB-HC collides with HA and enters a temporary transition state but insufficient kinetic energy does not allow a reaction to occur. Atoms return to their starting positions.
|[[File:Sjl1218-ani4.png|200px]]
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.6</nowiki>
|<nowiki>-349.477</nowiki>
|Yes
|HB-HC collides with HA with just enough kinetic energy to overcome the potential energy between HB-HC for the reaction to occur.
|[[File:Sjl1218-ani5.png|200px]]
|}
The hypothesis that higher values of momenta would be reactive is not precisely correct, this table shows that pBC must be greater than pAB by a specific factor to be able reactive.

===Transition State Theory===

The transition state theory attempts to provide a grearter understanding of the reaction by predicting the rate as well as the theromodynamic parameters of the reaction. However, it has its limitations. The transition state theory neglects the effects of quantum tunneling such that particles can bypass the activation energy of the transition state. Additionally, systems that have already crossed the transition state and formed products can recross the barrier to reform the reactants. Consequently, the rate calculated by the transition state theory is greater than the experimental value for the reasons that quantum effects are not taken into account.

==Exercise 2: F + H2 and H + HF==

===PES Inspection===

====1. F + H-H -> F-H + H====

Conditions: rAB = 150 pm, rBC = 80 pm, pAB = 0 g.mol-1.pm.fs-1, pBC = 0.5 g.mol-1.pm.fs-1.
[[File:Sjl1218-sur3.png|center|thumb|PES of F + H-H -> F-H + H]]

Products are lower in potential energy than reactants, therefore reaction is exothermic.The H-F bond formed releases more energy than the energy taken to break the H-H bond, therefore H-F is greater in bond strength than H2.

====2. F-H + H -> F + H-H====

Conditions: rAB = 80 pm, rBC = 150 pm, pAB = 15 g.mol-1.pm.fs-1, pBC = 0 g.mol-1.pm.fs-1.
[[File:Sjl1218-sur4.PNG|center|thumb|PES of F-H + H -> F + H-H]]

Products are higher in energy than reactants, therefore reaction is endothermic. The energy used to break the H-F bond is greater than the energy released for forming the H-H bond. The H-F bond is greater in bond strength.

===Locating the Transition State Position===

The approximate position of the transition state is F-H = 180 pm and H-H = 75 pm. Horizontal line shown on the internuclear distance vs time graph represents minimal oscillations among the atoms, ∂V(ri)/∂ri=0 no forces are acting on the F-H-H direction so transition state is reached.

[[File:Sjl1218-ts1.png|center|thumb|Internuclear Distance vs Time graph for rAB = 180 pm, rBC = 75 pm, pAB = 0 g.mol-1.pm.fs-1, pBC = 0 g.mol-1.pm.fs-1]]

===Calculating the Activation Energy===

The activation energy can be calculated by subtracting the potential energy of the reactants from the potential energy the TS. The potential energy of the transition state is -433.943 kJ.mol-1. The potential energy of the reactants can be obtained by performing an MEP of energy vs time for the reaction and observing the starting potential energy.

Activation energies of:

1. F + H-H -> F-H + H: -433.943 - -434.288 = +0.345 kj.mol-1
[[File:Sjl1218-6.png|center|thumb|Energy vs Time MEP for F + H-H -> F-H + H with same reaction conditions]]

2. F-H + H -> F + H-H: -433.943 - -496.862 = +62.919 kj.mol-1
[[File:Sjl1218-7.png|center|thumb|Energy vs Time MEP for F-H + H -> F + H-H with same reaction conditions]]

===Reaction Dynamics===
====1. F + H-H -> F-H + H====

Initial conditions that result in a reactive trajectory: rAB = 150 pm, rBC = 80 pm, pAB = 0 g.mol-1.pm.fs-1, pBC = 0.5 g.mol-1.pm.fs-1.
[[File:Sjl1218-8.png|300px|center|thumb|Illustration of reactants: F + H-H]] [[File:Sjl1218-9.png|center|thumb|Illustration of products: F-H + H]]

[[File:Sjl1218-10.png|center|thumb|Energy vs Time MEP of F + H-H -> F-H + H]]

This reaction is exothermic but the total energy is conserved in a reaction, the energy release mechanism is explained below:

Originally, H-H is a molecule held together by strong potential energy. As it approaches atom F, potential energy between H-H is transferred to kinetic energy which releases energy in the reaction. The momenta vs time graph (orange line) shows the spikes in momentum/ kinetic energy for H-H (B-C) when H (B) is transferred to atom F (A). The momentum of this orange line then flattens, all kinetic energy is transferred to the formation of F-H (A-B) bond which shows oscillations in momentum by the blue line.

To confirm this experimentally, measure the change in temperature of the reaction with a thermometer which should show an increase in temperature as the reaction is exothermic.

====2. F-H + H -> F + H-H====

In this reaction, a late transition state is formed because of the high electronegativity of atom F. According to Hammond's postulate, the energy of the transition state is similar to the products because the structure of the late transition state resembles the products.

Polanyi's rules states that vibrational energy is more efficient in overcoming a reaction with a late barrier than translational energy.

[[File:Sjl1218-11.png|center|thumb|PES of F-H + H -> F + H-H]]

File:Sjl1218-11.png

2020-05-08T22:46:40Z

Sjl1218:

MRD:sjl1218

2020-05-08T22:11:55Z

Sjl1218: /* 1. F + H-H -> F-H + H */

==Exercise 1: HA + HB-HC -> HA-HB + HC==

[[File:sjl1218-reactionscheme.png|500px|center|thumb|Initial Conditions of Reaction Involving 3 Atoms: HA + HB-HC -> HA-HB + HC]]

===Dynamics of the Transition State Region===
====The Transition State====
[[File:Sjl1218-pesurface.PNG|300px|right|thumb|center|Potential Energy Surface Diagram of HA + HB-HC -> HA-HB + HC]]
In a potential energy surface diagram, the reaction pathway (black line) proceeds along the minimum energy path linked by the reactants and products. The transition state is the PES diagram saddle point defined mathematically by ∂V(ri)/∂ri=0.

The transition state location can be identified if V(rAB)/∂rAB=0 and V(rBC)/∂rBC=0. This point can be distinguished from the local minima if the outcome of taking the partial second derivative of potential energy with respect to either rAB or rBC is 0.

====Locating the Transition State====

Since the H2 + H1 surface is symmetric, the transition state must have rAB=rBC. The location of the transition state position rts can be estimated when ∂V(ri)/∂ri=0 and there will be minimal oscillation among the 3 atoms as there is no force acting along rAB and rBC.

[[File:Sjl1218-4.PNG|400px|center|thumb|Model for when rAB = rBC and pAB=pBC=0]]

The transition state position rts is estimated as 91 pm. The internuclear distances vs time graph for rAB = rBC=91pm shows a 'flat' line, meaning no forces are acting at this position.

[[File:Sjl1218-ts.PNG|300px|center|thumb|Internuclear Distances vs Time Graph for rAB = rBC=91pm and pAB=pBC=0]]

====Calculating the reaction path====

The reaction path or minimum energy path is an infinitely slow trajectory (momenta and velocities resets to zero in each time step) obtained after locating the transition state position.

The minimum energy path initially shows a short horizontal line of the atoms entering the transition state position followed by the decreasing rate of atoms HA-HC and HB-HC increasing in distance. Atoms HA-HB forms a bond and remains constant in distance.

Even though the MEP outlines a reaction, it does not take into account the mass and inertia of the atoms, therefore does not provide the realistic picture of the reaction.
The MEP and dynamic trajectory differs in that the realistic trajectory shows oscillations (potential energy interactions) between atoms. At first the 3 atoms are in the transition state positions, showed by the horiontal lines. The trajectory then shows a linear increase in HA-HC and HB-HC distances and HA-HB oscillates about the same position.
[[File:Sjl1218-mep.PNG|300px|center|thumb|Minimum Energy Path (rBC = rts+1 pm, rAB = rts and pBC = pAB = 0 g.mol-1.pm.fs-1)]]
[[File:Sjl1218-traj.PNG|300px|center|thumb|Dynamic Trajectory (rBC = rts+1 pm, rAB = rts and pBC = pAB = 0 g.mol-1.pm.fs-1)]]

===Reactive and Unreactive Trajectories===
Determining whether trajectories are reactive from their momenta when rBC=74 pm and rAB=200 pm.
{| 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
|HB-HC collides with HA with sufficient kinetic energy to overcome the reaction barrier and forms HAHB and HC.
|[[File:Sjl1218-ani1.png|200px]]
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-4.1</nowiki>
|<nowiki>-420.077</nowiki>
|No
|HB-HC approaches HA but does not react due to lack of kinetic energy/momenta.
|[[File:Sjl1218-ani2.png|200px]]
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-5.1</nowiki>
|<nowiki>-413.977</nowiki>
|Yes
|HB-HC collides with HA with sufficient kinetic energy to overcome the reaction barrier and forms HAHB and HC.
|[[File:Sjl1218-ani3.png|200px]]
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.1</nowiki>
|<nowiki>-357.277</nowiki>
|No
|HB-HC collides with HA and enters a temporary transition state but insufficient kinetic energy does not allow a reaction to occur. Atoms return to their starting positions.
|[[File:Sjl1218-ani4.png|200px]]
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.6</nowiki>
|<nowiki>-349.477</nowiki>
|Yes
|HB-HC collides with HA with just enough kinetic energy to overcome the potential energy between HB-HC for the reaction to occur.
|[[File:Sjl1218-ani5.png|200px]]
|}
The hypothesis that higher values of momenta would be reactive is not precisely correct, this table shows that pBC must be greater than pAB by a specific factor to be able reactive.

===Transition State Theory===

The transition state theory attempts to provide a grearter understanding of the reaction by predicting the rate as well as the theromodynamic parameters of the reaction. However, it has its limitations. The transition state theory neglects the effects of quantum tunneling such that particles can bypass the activation energy of the transition state. Additionally, systems that have already crossed the transition state and formed products can recross the barrier to reform the reactants. Consequently, the rate calculated by the transition state theory is greater than the experimental value for the reasons that quantum effects are not taken into account.

==Exercise 2: F + H2 and H + HF==

===PES Inspection===

====1. F + H-H -> F-H + H====

Conditions: rAB = 150 pm, rBC = 80 pm, pAB = 0 g.mol-1.pm.fs-1, pBC = 0.5 g.mol-1.pm.fs-1.
[[File:Sjl1218-sur3.png|center|thumb|PES of F + H-H -> F-H + H]]

Products are lower in potential energy than reactants, therefore reaction is exothermic.The H-F bond formed releases more energy than the energy taken to break the H-H bond, therefore H-F is greater in bond strength than H2.

====2. F-H + H -> F + H-H====

Conditions: rAB = 80 pm, rBC = 150 pm, pAB = 15 g.mol-1.pm.fs-1, pBC = 0 g.mol-1.pm.fs-1.
[[File:Sjl1218-sur4.PNG|center|thumb|PES of F-H + H -> F + H-H]]

Products are higher in energy than reactants, therefore reaction is endothermic. The energy used to break the H-F bond is greater than the energy released for forming the H-H bond. The H-F bond is greater in bond strength.

===Locating the Transition State Position===

The approximate position of the transition state is F-H = 180 pm and H-H = 75 pm. Horizontal line shown on the internuclear distance vs time graph represents minimal oscillations among the atoms, ∂V(ri)/∂ri=0 no forces are acting on the F-H-H direction so transition state is reached.

[[File:Sjl1218-ts1.png|center|thumb|Internuclear Distance vs Time graph for rAB = 180 pm, rBC = 75 pm, pAB = 0 g.mol-1.pm.fs-1, pBC = 0 g.mol-1.pm.fs-1]]

===Calculating the Activation Energy===

The activation energy can be calculated by subtracting the potential energy of the reactants from the potential energy the TS. The potential energy of the transition state is -433.943 kJ.mol-1. The potential energy of the reactants can be obtained by performing an MEP of energy vs time for the reaction and observing the starting potential energy.

Activation energies of:

1. F + H-H -> F-H + H: -433.943 - -434.288 = +0.345 kj.mol-1
[[File:Sjl1218-6.png|center|thumb|Energy vs Time MEP for F + H-H -> F-H + H with same reaction conditions]]

2. F-H + H -> F + H-H: -433.943 - -496.862 = +62.919 kj.mol-1
[[File:Sjl1218-7.png|center|thumb|Energy vs Time MEP for F-H + H -> F + H-H with same reaction conditions]]

===Reaction Dynamics===
====1. F + H-H -> F-H + H====

Initial conditions that result in a reactive trajectory: rAB = 150 pm, rBC = 80 pm, pAB = 0 g.mol-1.pm.fs-1, pBC = 0.5 g.mol-1.pm.fs-1.
[[File:Sjl1218-8.png|300px|center|thumb|Illustration of reactants: F + H-H]] [[File:Sjl1218-9.png|center|thumb|Illustration of products: F-H + H]]

[[File:Sjl1218-10.png|center|thumb|Energy vs Time MEP of F + H-H -> F-H + H]]

This reaction is exothermic but the total energy is conserved in a reaction, the energy release mechanism is explained below:

Originally, H-H is a molecule held together by strong potential energy. As it approaches atom F, potential energy between H-H is transferred to kinetic energy which releases energy in the reaction. The momenta vs time graph (orange line) shows the spikes in momentum/ kinetic energy for H-H (B-C) when H (B) is transferred to atom F (A). The momentum of this orange line then flattens, all kinetic energy is transferred to the formation of F-H (A-B) bond which shows oscillations in momentum by the blue line.

MRD:sjl1218

2020-05-08T21:43:37Z

Sjl1218: /* 1. F + H-H -> F-H + H */

==Exercise 1: HA + HB-HC -> HA-HB + HC==

[[File:sjl1218-reactionscheme.png|500px|center|thumb|Initial Conditions of Reaction Involving 3 Atoms: HA + HB-HC -> HA-HB + HC]]

===Dynamics of the Transition State Region===
====The Transition State====
[[File:Sjl1218-pesurface.PNG|300px|right|thumb|center|Potential Energy Surface Diagram of HA + HB-HC -> HA-HB + HC]]
In a potential energy surface diagram, the reaction pathway (black line) proceeds along the minimum energy path linked by the reactants and products. The transition state is the PES diagram saddle point defined mathematically by ∂V(ri)/∂ri=0.

The transition state location can be identified if V(rAB)/∂rAB=0 and V(rBC)/∂rBC=0. This point can be distinguished from the local minima if the outcome of taking the partial second derivative of potential energy with respect to either rAB or rBC is 0.

====Locating the Transition State====

Since the H2 + H1 surface is symmetric, the transition state must have rAB=rBC. The location of the transition state position rts can be estimated when ∂V(ri)/∂ri=0 and there will be minimal oscillation among the 3 atoms as there is no force acting along rAB and rBC.

[[File:Sjl1218-4.PNG|400px|center|thumb|Model for when rAB = rBC and pAB=pBC=0]]

The transition state position rts is estimated as 91 pm. The internuclear distances vs time graph for rAB = rBC=91pm shows a 'flat' line, meaning no forces are acting at this position.

[[File:Sjl1218-ts.PNG|300px|center|thumb|Internuclear Distances vs Time Graph for rAB = rBC=91pm and pAB=pBC=0]]

====Calculating the reaction path====

The reaction path or minimum energy path is an infinitely slow trajectory (momenta and velocities resets to zero in each time step) obtained after locating the transition state position.

The minimum energy path initially shows a short horizontal line of the atoms entering the transition state position followed by the decreasing rate of atoms HA-HC and HB-HC increasing in distance. Atoms HA-HB forms a bond and remains constant in distance.

Even though the MEP outlines a reaction, it does not take into account the mass and inertia of the atoms, therefore does not provide the realistic picture of the reaction.
The MEP and dynamic trajectory differs in that the realistic trajectory shows oscillations (potential energy interactions) between atoms. At first the 3 atoms are in the transition state positions, showed by the horiontal lines. The trajectory then shows a linear increase in HA-HC and HB-HC distances and HA-HB oscillates about the same position.
[[File:Sjl1218-mep.PNG|300px|center|thumb|Minimum Energy Path (rBC = rts+1 pm, rAB = rts and pBC = pAB = 0 g.mol-1.pm.fs-1)]]
[[File:Sjl1218-traj.PNG|300px|center|thumb|Dynamic Trajectory (rBC = rts+1 pm, rAB = rts and pBC = pAB = 0 g.mol-1.pm.fs-1)]]

===Reactive and Unreactive Trajectories===
Determining whether trajectories are reactive from their momenta when rBC=74 pm and rAB=200 pm.
{| 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
|HB-HC collides with HA with sufficient kinetic energy to overcome the reaction barrier and forms HAHB and HC.
|[[File:Sjl1218-ani1.png|200px]]
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-4.1</nowiki>
|<nowiki>-420.077</nowiki>
|No
|HB-HC approaches HA but does not react due to lack of kinetic energy/momenta.
|[[File:Sjl1218-ani2.png|200px]]
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-5.1</nowiki>
|<nowiki>-413.977</nowiki>
|Yes
|HB-HC collides with HA with sufficient kinetic energy to overcome the reaction barrier and forms HAHB and HC.
|[[File:Sjl1218-ani3.png|200px]]
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.1</nowiki>
|<nowiki>-357.277</nowiki>
|No
|HB-HC collides with HA and enters a temporary transition state but insufficient kinetic energy does not allow a reaction to occur. Atoms return to their starting positions.
|[[File:Sjl1218-ani4.png|200px]]
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.6</nowiki>
|<nowiki>-349.477</nowiki>
|Yes
|HB-HC collides with HA with just enough kinetic energy to overcome the potential energy between HB-HC for the reaction to occur.
|[[File:Sjl1218-ani5.png|200px]]
|}
The hypothesis that higher values of momenta would be reactive is not precisely correct, this table shows that pBC must be greater than pAB by a specific factor to be able reactive.

===Transition State Theory===

The transition state theory attempts to provide a grearter understanding of the reaction by predicting the rate as well as the theromodynamic parameters of the reaction. However, it has its limitations. The transition state theory neglects the effects of quantum tunneling such that particles can bypass the activation energy of the transition state. Additionally, systems that have already crossed the transition state and formed products can recross the barrier to reform the reactants. Consequently, the rate calculated by the transition state theory is greater than the experimental value for the reasons that quantum effects are not taken into account.

==Exercise 2: F + H2 and H + HF==

===PES Inspection===

====1. F + H-H -> F-H + H====

Conditions: rAB = 150 pm, rBC = 80 pm, pAB = 0 g.mol-1.pm.fs-1, pBC = 0.5 g.mol-1.pm.fs-1.
[[File:Sjl1218-sur3.png|center|thumb|PES of F + H-H -> F-H + H]]

Products are lower in potential energy than reactants, therefore reaction is exothermic.The H-F bond formed releases more energy than the energy taken to break the H-H bond, therefore H-F is greater in bond strength than H2.

====2. F-H + H -> F + H-H====

Conditions: rAB = 80 pm, rBC = 150 pm, pAB = 15 g.mol-1.pm.fs-1, pBC = 0 g.mol-1.pm.fs-1.
[[File:Sjl1218-sur4.PNG|center|thumb|PES of F-H + H -> F + H-H]]

Products are higher in energy than reactants, therefore reaction is endothermic. The energy used to break the H-F bond is greater than the energy released for forming the H-H bond. The H-F bond is greater in bond strength.

===Locating the Transition State Position===

The approximate position of the transition state is F-H = 180 pm and H-H = 75 pm. Horizontal line shown on the internuclear distance vs time graph represents minimal oscillations among the atoms, ∂V(ri)/∂ri=0 no forces are acting on the F-H-H direction so transition state is reached.

[[File:Sjl1218-ts1.png|center|thumb|Internuclear Distance vs Time graph for rAB = 180 pm, rBC = 75 pm, pAB = 0 g.mol-1.pm.fs-1, pBC = 0 g.mol-1.pm.fs-1]]

===Calculating the Activation Energy===

The activation energy can be calculated by subtracting the potential energy of the reactants from the potential energy the TS. The potential energy of the transition state is -433.943 kJ.mol-1. The potential energy of the reactants can be obtained by performing an MEP of energy vs time for the reaction and observing the starting potential energy.

Activation energies of:

1. F + H-H -> F-H + H: -433.943 - -434.288 = +0.345 kj.mol-1
[[File:Sjl1218-6.png|center|thumb|Energy vs Time MEP for F + H-H -> F-H + H with same reaction conditions]]

2. F-H + H -> F + H-H: -433.943 - -496.862 = +62.919 kj.mol-1
[[File:Sjl1218-7.png|center|thumb|Energy vs Time MEP for F-H + H -> F + H-H with same reaction conditions]]

===Reaction Dynamics===
====1. F + H-H -> F-H + H====

Initial conditions that result in a reactive trajectory: rAB = 150 pm, rBC = 80 pm, pAB = 0 g.mol-1.pm.fs-1, pBC = 0.5 g.mol-1.pm.fs-1.
[[File:Sjl1218-8.png|300px|center|thumb|Illustration of reactants: F + H-H]] [[File:Sjl1218-9.png|center|thumb|Illustration of products: F-H + H]]

[[File:Sjl1218-8.png|thumb|Energy vs Time MEP of F + H-H -> F-H + H]]

MRD:sjl1218

2020-05-08T21:42:07Z

Sjl1218: /* 1. F + H-H -> F-H + H */

==Exercise 1: HA + HB-HC -> HA-HB + HC==

[[File:sjl1218-reactionscheme.png|500px|center|thumb|Initial Conditions of Reaction Involving 3 Atoms: HA + HB-HC -> HA-HB + HC]]

===Dynamics of the Transition State Region===
====The Transition State====
[[File:Sjl1218-pesurface.PNG|300px|right|thumb|center|Potential Energy Surface Diagram of HA + HB-HC -> HA-HB + HC]]
In a potential energy surface diagram, the reaction pathway (black line) proceeds along the minimum energy path linked by the reactants and products. The transition state is the PES diagram saddle point defined mathematically by ∂V(ri)/∂ri=0.

The transition state location can be identified if V(rAB)/∂rAB=0 and V(rBC)/∂rBC=0. This point can be distinguished from the local minima if the outcome of taking the partial second derivative of potential energy with respect to either rAB or rBC is 0.

====Locating the Transition State====

Since the H2 + H1 surface is symmetric, the transition state must have rAB=rBC. The location of the transition state position rts can be estimated when ∂V(ri)/∂ri=0 and there will be minimal oscillation among the 3 atoms as there is no force acting along rAB and rBC.

[[File:Sjl1218-4.PNG|400px|center|thumb|Model for when rAB = rBC and pAB=pBC=0]]

The transition state position rts is estimated as 91 pm. The internuclear distances vs time graph for rAB = rBC=91pm shows a 'flat' line, meaning no forces are acting at this position.

[[File:Sjl1218-ts.PNG|300px|center|thumb|Internuclear Distances vs Time Graph for rAB = rBC=91pm and pAB=pBC=0]]

====Calculating the reaction path====

The reaction path or minimum energy path is an infinitely slow trajectory (momenta and velocities resets to zero in each time step) obtained after locating the transition state position.

The minimum energy path initially shows a short horizontal line of the atoms entering the transition state position followed by the decreasing rate of atoms HA-HC and HB-HC increasing in distance. Atoms HA-HB forms a bond and remains constant in distance.

Even though the MEP outlines a reaction, it does not take into account the mass and inertia of the atoms, therefore does not provide the realistic picture of the reaction.
The MEP and dynamic trajectory differs in that the realistic trajectory shows oscillations (potential energy interactions) between atoms. At first the 3 atoms are in the transition state positions, showed by the horiontal lines. The trajectory then shows a linear increase in HA-HC and HB-HC distances and HA-HB oscillates about the same position.
[[File:Sjl1218-mep.PNG|300px|center|thumb|Minimum Energy Path (rBC = rts+1 pm, rAB = rts and pBC = pAB = 0 g.mol-1.pm.fs-1)]]
[[File:Sjl1218-traj.PNG|300px|center|thumb|Dynamic Trajectory (rBC = rts+1 pm, rAB = rts and pBC = pAB = 0 g.mol-1.pm.fs-1)]]

===Reactive and Unreactive Trajectories===
Determining whether trajectories are reactive from their momenta when rBC=74 pm and rAB=200 pm.
{| 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
|HB-HC collides with HA with sufficient kinetic energy to overcome the reaction barrier and forms HAHB and HC.
|[[File:Sjl1218-ani1.png|200px]]
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-4.1</nowiki>
|<nowiki>-420.077</nowiki>
|No
|HB-HC approaches HA but does not react due to lack of kinetic energy/momenta.
|[[File:Sjl1218-ani2.png|200px]]
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-5.1</nowiki>
|<nowiki>-413.977</nowiki>
|Yes
|HB-HC collides with HA with sufficient kinetic energy to overcome the reaction barrier and forms HAHB and HC.
|[[File:Sjl1218-ani3.png|200px]]
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.1</nowiki>
|<nowiki>-357.277</nowiki>
|No
|HB-HC collides with HA and enters a temporary transition state but insufficient kinetic energy does not allow a reaction to occur. Atoms return to their starting positions.
|[[File:Sjl1218-ani4.png|200px]]
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.6</nowiki>
|<nowiki>-349.477</nowiki>
|Yes
|HB-HC collides with HA with just enough kinetic energy to overcome the potential energy between HB-HC for the reaction to occur.
|[[File:Sjl1218-ani5.png|200px]]
|}
The hypothesis that higher values of momenta would be reactive is not precisely correct, this table shows that pBC must be greater than pAB by a specific factor to be able reactive.

===Transition State Theory===

The transition state theory attempts to provide a grearter understanding of the reaction by predicting the rate as well as the theromodynamic parameters of the reaction. However, it has its limitations. The transition state theory neglects the effects of quantum tunneling such that particles can bypass the activation energy of the transition state. Additionally, systems that have already crossed the transition state and formed products can recross the barrier to reform the reactants. Consequently, the rate calculated by the transition state theory is greater than the experimental value for the reasons that quantum effects are not taken into account.

==Exercise 2: F + H2 and H + HF==

===PES Inspection===

====1. F + H-H -> F-H + H====

Conditions: rAB = 150 pm, rBC = 80 pm, pAB = 0 g.mol-1.pm.fs-1, pBC = 0.5 g.mol-1.pm.fs-1.
[[File:Sjl1218-sur3.png|center|thumb|PES of F + H-H -> F-H + H]]

Products are lower in potential energy than reactants, therefore reaction is exothermic.The H-F bond formed releases more energy than the energy taken to break the H-H bond, therefore H-F is greater in bond strength than H2.

====2. F-H + H -> F + H-H====

Conditions: rAB = 80 pm, rBC = 150 pm, pAB = 15 g.mol-1.pm.fs-1, pBC = 0 g.mol-1.pm.fs-1.
[[File:Sjl1218-sur4.PNG|center|thumb|PES of F-H + H -> F + H-H]]

Products are higher in energy than reactants, therefore reaction is endothermic. The energy used to break the H-F bond is greater than the energy released for forming the H-H bond. The H-F bond is greater in bond strength.

===Locating the Transition State Position===

The approximate position of the transition state is F-H = 180 pm and H-H = 75 pm. Horizontal line shown on the internuclear distance vs time graph represents minimal oscillations among the atoms, ∂V(ri)/∂ri=0 no forces are acting on the F-H-H direction so transition state is reached.

[[File:Sjl1218-ts1.png|center|thumb|Internuclear Distance vs Time graph for rAB = 180 pm, rBC = 75 pm, pAB = 0 g.mol-1.pm.fs-1, pBC = 0 g.mol-1.pm.fs-1]]

===Calculating the Activation Energy===

The activation energy can be calculated by subtracting the potential energy of the reactants from the potential energy the TS. The potential energy of the transition state is -433.943 kJ.mol-1. The potential energy of the reactants can be obtained by performing an MEP of energy vs time for the reaction and observing the starting potential energy.

Activation energies of:

1. F + H-H -> F-H + H: -433.943 - -434.288 = +0.345 kj.mol-1
[[File:Sjl1218-6.png|center|thumb|Energy vs Time MEP for F + H-H -> F-H + H with same reaction conditions]]

2. F-H + H -> F + H-H: -433.943 - -496.862 = +62.919 kj.mol-1
[[File:Sjl1218-7.png|center|thumb|Energy vs Time MEP for F-H + H -> F + H-H with same reaction conditions]]

===Reaction Dynamics===
====1. F + H-H -> F-H + H====

[[File:Sjl1218-8.png|300px|center|thumb|Illustration of reactants: F + H-H]] [[File:Sjl1218-9.png|center|thumb|Illustration of products: F-H + H]]

Initial conditions that result in a reactive trajectory:

MRD:sjl1218

2020-05-08T21:41:48Z

Sjl1218: /* 1. F + H-H -> F-H + H */

==Exercise 1: HA + HB-HC -> HA-HB + HC==

[[File:sjl1218-reactionscheme.png|500px|center|thumb|Initial Conditions of Reaction Involving 3 Atoms: HA + HB-HC -> HA-HB + HC]]

===Dynamics of the Transition State Region===
====The Transition State====
[[File:Sjl1218-pesurface.PNG|300px|right|thumb|center|Potential Energy Surface Diagram of HA + HB-HC -> HA-HB + HC]]
In a potential energy surface diagram, the reaction pathway (black line) proceeds along the minimum energy path linked by the reactants and products. The transition state is the PES diagram saddle point defined mathematically by ∂V(ri)/∂ri=0.

The transition state location can be identified if V(rAB)/∂rAB=0 and V(rBC)/∂rBC=0. This point can be distinguished from the local minima if the outcome of taking the partial second derivative of potential energy with respect to either rAB or rBC is 0.

====Locating the Transition State====

Since the H2 + H1 surface is symmetric, the transition state must have rAB=rBC. The location of the transition state position rts can be estimated when ∂V(ri)/∂ri=0 and there will be minimal oscillation among the 3 atoms as there is no force acting along rAB and rBC.

[[File:Sjl1218-4.PNG|400px|center|thumb|Model for when rAB = rBC and pAB=pBC=0]]

The transition state position rts is estimated as 91 pm. The internuclear distances vs time graph for rAB = rBC=91pm shows a 'flat' line, meaning no forces are acting at this position.

[[File:Sjl1218-ts.PNG|300px|center|thumb|Internuclear Distances vs Time Graph for rAB = rBC=91pm and pAB=pBC=0]]

====Calculating the reaction path====

The reaction path or minimum energy path is an infinitely slow trajectory (momenta and velocities resets to zero in each time step) obtained after locating the transition state position.

The minimum energy path initially shows a short horizontal line of the atoms entering the transition state position followed by the decreasing rate of atoms HA-HC and HB-HC increasing in distance. Atoms HA-HB forms a bond and remains constant in distance.

Even though the MEP outlines a reaction, it does not take into account the mass and inertia of the atoms, therefore does not provide the realistic picture of the reaction.
The MEP and dynamic trajectory differs in that the realistic trajectory shows oscillations (potential energy interactions) between atoms. At first the 3 atoms are in the transition state positions, showed by the horiontal lines. The trajectory then shows a linear increase in HA-HC and HB-HC distances and HA-HB oscillates about the same position.
[[File:Sjl1218-mep.PNG|300px|center|thumb|Minimum Energy Path (rBC = rts+1 pm, rAB = rts and pBC = pAB = 0 g.mol-1.pm.fs-1)]]
[[File:Sjl1218-traj.PNG|300px|center|thumb|Dynamic Trajectory (rBC = rts+1 pm, rAB = rts and pBC = pAB = 0 g.mol-1.pm.fs-1)]]

===Reactive and Unreactive Trajectories===
Determining whether trajectories are reactive from their momenta when rBC=74 pm and rAB=200 pm.
{| 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
|HB-HC collides with HA with sufficient kinetic energy to overcome the reaction barrier and forms HAHB and HC.
|[[File:Sjl1218-ani1.png|200px]]
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-4.1</nowiki>
|<nowiki>-420.077</nowiki>
|No
|HB-HC approaches HA but does not react due to lack of kinetic energy/momenta.
|[[File:Sjl1218-ani2.png|200px]]
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-5.1</nowiki>
|<nowiki>-413.977</nowiki>
|Yes
|HB-HC collides with HA with sufficient kinetic energy to overcome the reaction barrier and forms HAHB and HC.
|[[File:Sjl1218-ani3.png|200px]]
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.1</nowiki>
|<nowiki>-357.277</nowiki>
|No
|HB-HC collides with HA and enters a temporary transition state but insufficient kinetic energy does not allow a reaction to occur. Atoms return to their starting positions.
|[[File:Sjl1218-ani4.png|200px]]
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.6</nowiki>
|<nowiki>-349.477</nowiki>
|Yes
|HB-HC collides with HA with just enough kinetic energy to overcome the potential energy between HB-HC for the reaction to occur.
|[[File:Sjl1218-ani5.png|200px]]
|}
The hypothesis that higher values of momenta would be reactive is not precisely correct, this table shows that pBC must be greater than pAB by a specific factor to be able reactive.

===Transition State Theory===

The transition state theory attempts to provide a grearter understanding of the reaction by predicting the rate as well as the theromodynamic parameters of the reaction. However, it has its limitations. The transition state theory neglects the effects of quantum tunneling such that particles can bypass the activation energy of the transition state. Additionally, systems that have already crossed the transition state and formed products can recross the barrier to reform the reactants. Consequently, the rate calculated by the transition state theory is greater than the experimental value for the reasons that quantum effects are not taken into account.

==Exercise 2: F + H2 and H + HF==

===PES Inspection===

====1. F + H-H -> F-H + H====

Conditions: rAB = 150 pm, rBC = 80 pm, pAB = 0 g.mol-1.pm.fs-1, pBC = 0.5 g.mol-1.pm.fs-1.
[[File:Sjl1218-sur3.png|center|thumb|PES of F + H-H -> F-H + H]]

Products are lower in potential energy than reactants, therefore reaction is exothermic.The H-F bond formed releases more energy than the energy taken to break the H-H bond, therefore H-F is greater in bond strength than H2.

====2. F-H + H -> F + H-H====

Conditions: rAB = 80 pm, rBC = 150 pm, pAB = 15 g.mol-1.pm.fs-1, pBC = 0 g.mol-1.pm.fs-1.
[[File:Sjl1218-sur4.PNG|center|thumb|PES of F-H + H -> F + H-H]]

Products are higher in energy than reactants, therefore reaction is endothermic. The energy used to break the H-F bond is greater than the energy released for forming the H-H bond. The H-F bond is greater in bond strength.

===Locating the Transition State Position===

The approximate position of the transition state is F-H = 180 pm and H-H = 75 pm. Horizontal line shown on the internuclear distance vs time graph represents minimal oscillations among the atoms, ∂V(ri)/∂ri=0 no forces are acting on the F-H-H direction so transition state is reached.

[[File:Sjl1218-ts1.png|center|thumb|Internuclear Distance vs Time graph for rAB = 180 pm, rBC = 75 pm, pAB = 0 g.mol-1.pm.fs-1, pBC = 0 g.mol-1.pm.fs-1]]

===Calculating the Activation Energy===

The activation energy can be calculated by subtracting the potential energy of the reactants from the potential energy the TS. The potential energy of the transition state is -433.943 kJ.mol-1. The potential energy of the reactants can be obtained by performing an MEP of energy vs time for the reaction and observing the starting potential energy.

Activation energies of:

1. F + H-H -> F-H + H: -433.943 - -434.288 = +0.345 kj.mol-1
[[File:Sjl1218-6.png|center|thumb|Energy vs Time MEP for F + H-H -> F-H + H with same reaction conditions]]

2. F-H + H -> F + H-H: -433.943 - -496.862 = +62.919 kj.mol-1
[[File:Sjl1218-7.png|center|thumb|Energy vs Time MEP for F-H + H -> F + H-H with same reaction conditions]]

===Reaction Dynamics===
====1. F + H-H -> F-H + H====

[[File:Sjl1218-8.png|300px|left|thumb|Illustration of reactants: F + H-H]] [[File:Sjl1218-9.png|left|thumb|Illustration of products: F-H + H]]

Initial conditions that result in a reactive trajectory:

MRD:sjl1218

2020-05-08T21:41:20Z

Sjl1218: /* 1. F + H-H -> F-H + H */

==Exercise 1: HA + HB-HC -> HA-HB + HC==

[[File:sjl1218-reactionscheme.png|500px|center|thumb|Initial Conditions of Reaction Involving 3 Atoms: HA + HB-HC -> HA-HB + HC]]

===Dynamics of the Transition State Region===
====The Transition State====
[[File:Sjl1218-pesurface.PNG|300px|right|thumb|center|Potential Energy Surface Diagram of HA + HB-HC -> HA-HB + HC]]
In a potential energy surface diagram, the reaction pathway (black line) proceeds along the minimum energy path linked by the reactants and products. The transition state is the PES diagram saddle point defined mathematically by ∂V(ri)/∂ri=0.

The transition state location can be identified if V(rAB)/∂rAB=0 and V(rBC)/∂rBC=0. This point can be distinguished from the local minima if the outcome of taking the partial second derivative of potential energy with respect to either rAB or rBC is 0.

====Locating the Transition State====

Since the H2 + H1 surface is symmetric, the transition state must have rAB=rBC. The location of the transition state position rts can be estimated when ∂V(ri)/∂ri=0 and there will be minimal oscillation among the 3 atoms as there is no force acting along rAB and rBC.

[[File:Sjl1218-4.PNG|400px|center|thumb|Model for when rAB = rBC and pAB=pBC=0]]

The transition state position rts is estimated as 91 pm. The internuclear distances vs time graph for rAB = rBC=91pm shows a 'flat' line, meaning no forces are acting at this position.

[[File:Sjl1218-ts.PNG|300px|center|thumb|Internuclear Distances vs Time Graph for rAB = rBC=91pm and pAB=pBC=0]]

====Calculating the reaction path====

The reaction path or minimum energy path is an infinitely slow trajectory (momenta and velocities resets to zero in each time step) obtained after locating the transition state position.

The minimum energy path initially shows a short horizontal line of the atoms entering the transition state position followed by the decreasing rate of atoms HA-HC and HB-HC increasing in distance. Atoms HA-HB forms a bond and remains constant in distance.

Even though the MEP outlines a reaction, it does not take into account the mass and inertia of the atoms, therefore does not provide the realistic picture of the reaction.
The MEP and dynamic trajectory differs in that the realistic trajectory shows oscillations (potential energy interactions) between atoms. At first the 3 atoms are in the transition state positions, showed by the horiontal lines. The trajectory then shows a linear increase in HA-HC and HB-HC distances and HA-HB oscillates about the same position.
[[File:Sjl1218-mep.PNG|300px|center|thumb|Minimum Energy Path (rBC = rts+1 pm, rAB = rts and pBC = pAB = 0 g.mol-1.pm.fs-1)]]
[[File:Sjl1218-traj.PNG|300px|center|thumb|Dynamic Trajectory (rBC = rts+1 pm, rAB = rts and pBC = pAB = 0 g.mol-1.pm.fs-1)]]

===Reactive and Unreactive Trajectories===
Determining whether trajectories are reactive from their momenta when rBC=74 pm and rAB=200 pm.
{| 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
|HB-HC collides with HA with sufficient kinetic energy to overcome the reaction barrier and forms HAHB and HC.
|[[File:Sjl1218-ani1.png|200px]]
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-4.1</nowiki>
|<nowiki>-420.077</nowiki>
|No
|HB-HC approaches HA but does not react due to lack of kinetic energy/momenta.
|[[File:Sjl1218-ani2.png|200px]]
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-5.1</nowiki>
|<nowiki>-413.977</nowiki>
|Yes
|HB-HC collides with HA with sufficient kinetic energy to overcome the reaction barrier and forms HAHB and HC.
|[[File:Sjl1218-ani3.png|200px]]
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.1</nowiki>
|<nowiki>-357.277</nowiki>
|No
|HB-HC collides with HA and enters a temporary transition state but insufficient kinetic energy does not allow a reaction to occur. Atoms return to their starting positions.
|[[File:Sjl1218-ani4.png|200px]]
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.6</nowiki>
|<nowiki>-349.477</nowiki>
|Yes
|HB-HC collides with HA with just enough kinetic energy to overcome the potential energy between HB-HC for the reaction to occur.
|[[File:Sjl1218-ani5.png|200px]]
|}
The hypothesis that higher values of momenta would be reactive is not precisely correct, this table shows that pBC must be greater than pAB by a specific factor to be able reactive.

===Transition State Theory===

The transition state theory attempts to provide a grearter understanding of the reaction by predicting the rate as well as the theromodynamic parameters of the reaction. However, it has its limitations. The transition state theory neglects the effects of quantum tunneling such that particles can bypass the activation energy of the transition state. Additionally, systems that have already crossed the transition state and formed products can recross the barrier to reform the reactants. Consequently, the rate calculated by the transition state theory is greater than the experimental value for the reasons that quantum effects are not taken into account.

==Exercise 2: F + H2 and H + HF==

===PES Inspection===

====1. F + H-H -> F-H + H====

Conditions: rAB = 150 pm, rBC = 80 pm, pAB = 0 g.mol-1.pm.fs-1, pBC = 0.5 g.mol-1.pm.fs-1.
[[File:Sjl1218-sur3.png|center|thumb|PES of F + H-H -> F-H + H]]

Products are lower in potential energy than reactants, therefore reaction is exothermic.The H-F bond formed releases more energy than the energy taken to break the H-H bond, therefore H-F is greater in bond strength than H2.

====2. F-H + H -> F + H-H====

Conditions: rAB = 80 pm, rBC = 150 pm, pAB = 15 g.mol-1.pm.fs-1, pBC = 0 g.mol-1.pm.fs-1.
[[File:Sjl1218-sur4.PNG|center|thumb|PES of F-H + H -> F + H-H]]

Products are higher in energy than reactants, therefore reaction is endothermic. The energy used to break the H-F bond is greater than the energy released for forming the H-H bond. The H-F bond is greater in bond strength.

===Locating the Transition State Position===

The approximate position of the transition state is F-H = 180 pm and H-H = 75 pm. Horizontal line shown on the internuclear distance vs time graph represents minimal oscillations among the atoms, ∂V(ri)/∂ri=0 no forces are acting on the F-H-H direction so transition state is reached.

[[File:Sjl1218-ts1.png|center|thumb|Internuclear Distance vs Time graph for rAB = 180 pm, rBC = 75 pm, pAB = 0 g.mol-1.pm.fs-1, pBC = 0 g.mol-1.pm.fs-1]]

===Calculating the Activation Energy===

The activation energy can be calculated by subtracting the potential energy of the reactants from the potential energy the TS. The potential energy of the transition state is -433.943 kJ.mol-1. The potential energy of the reactants can be obtained by performing an MEP of energy vs time for the reaction and observing the starting potential energy.

Activation energies of:

1. F + H-H -> F-H + H: -433.943 - -434.288 = +0.345 kj.mol-1
[[File:Sjl1218-6.png|center|thumb|Energy vs Time MEP for F + H-H -> F-H + H with same reaction conditions]]

2. F-H + H -> F + H-H: -433.943 - -496.862 = +62.919 kj.mol-1
[[File:Sjl1218-7.png|center|thumb|Energy vs Time MEP for F-H + H -> F + H-H with same reaction conditions]]

===Reaction Dynamics===
====1. F + H-H -> F-H + H====

[[File:Sjl1218-8.png|300px|Illustration of reactants: F + H-H]] [[File:Sjl1218-9.png|thumb|Illustration of products: F-H + H]]

Initial conditions that result in a reactive trajectory:

MRD:sjl1218

2020-05-08T21:40:40Z

Sjl1218: /* 1. F + H-H -> F-H + H */

==Exercise 1: HA + HB-HC -> HA-HB + HC==

[[File:sjl1218-reactionscheme.png|500px|center|thumb|Initial Conditions of Reaction Involving 3 Atoms: HA + HB-HC -> HA-HB + HC]]

===Dynamics of the Transition State Region===
====The Transition State====
[[File:Sjl1218-pesurface.PNG|300px|right|thumb|center|Potential Energy Surface Diagram of HA + HB-HC -> HA-HB + HC]]
In a potential energy surface diagram, the reaction pathway (black line) proceeds along the minimum energy path linked by the reactants and products. The transition state is the PES diagram saddle point defined mathematically by ∂V(ri)/∂ri=0.

The transition state location can be identified if V(rAB)/∂rAB=0 and V(rBC)/∂rBC=0. This point can be distinguished from the local minima if the outcome of taking the partial second derivative of potential energy with respect to either rAB or rBC is 0.

====Locating the Transition State====

Since the H2 + H1 surface is symmetric, the transition state must have rAB=rBC. The location of the transition state position rts can be estimated when ∂V(ri)/∂ri=0 and there will be minimal oscillation among the 3 atoms as there is no force acting along rAB and rBC.

[[File:Sjl1218-4.PNG|400px|center|thumb|Model for when rAB = rBC and pAB=pBC=0]]

The transition state position rts is estimated as 91 pm. The internuclear distances vs time graph for rAB = rBC=91pm shows a 'flat' line, meaning no forces are acting at this position.

[[File:Sjl1218-ts.PNG|300px|center|thumb|Internuclear Distances vs Time Graph for rAB = rBC=91pm and pAB=pBC=0]]

====Calculating the reaction path====

The reaction path or minimum energy path is an infinitely slow trajectory (momenta and velocities resets to zero in each time step) obtained after locating the transition state position.

The minimum energy path initially shows a short horizontal line of the atoms entering the transition state position followed by the decreasing rate of atoms HA-HC and HB-HC increasing in distance. Atoms HA-HB forms a bond and remains constant in distance.

Even though the MEP outlines a reaction, it does not take into account the mass and inertia of the atoms, therefore does not provide the realistic picture of the reaction.
The MEP and dynamic trajectory differs in that the realistic trajectory shows oscillations (potential energy interactions) between atoms. At first the 3 atoms are in the transition state positions, showed by the horiontal lines. The trajectory then shows a linear increase in HA-HC and HB-HC distances and HA-HB oscillates about the same position.
[[File:Sjl1218-mep.PNG|300px|center|thumb|Minimum Energy Path (rBC = rts+1 pm, rAB = rts and pBC = pAB = 0 g.mol-1.pm.fs-1)]]
[[File:Sjl1218-traj.PNG|300px|center|thumb|Dynamic Trajectory (rBC = rts+1 pm, rAB = rts and pBC = pAB = 0 g.mol-1.pm.fs-1)]]

===Reactive and Unreactive Trajectories===
Determining whether trajectories are reactive from their momenta when rBC=74 pm and rAB=200 pm.
{| 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
|HB-HC collides with HA with sufficient kinetic energy to overcome the reaction barrier and forms HAHB and HC.
|[[File:Sjl1218-ani1.png|200px]]
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-4.1</nowiki>
|<nowiki>-420.077</nowiki>
|No
|HB-HC approaches HA but does not react due to lack of kinetic energy/momenta.
|[[File:Sjl1218-ani2.png|200px]]
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-5.1</nowiki>
|<nowiki>-413.977</nowiki>
|Yes
|HB-HC collides with HA with sufficient kinetic energy to overcome the reaction barrier and forms HAHB and HC.
|[[File:Sjl1218-ani3.png|200px]]
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.1</nowiki>
|<nowiki>-357.277</nowiki>
|No
|HB-HC collides with HA and enters a temporary transition state but insufficient kinetic energy does not allow a reaction to occur. Atoms return to their starting positions.
|[[File:Sjl1218-ani4.png|200px]]
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.6</nowiki>
|<nowiki>-349.477</nowiki>
|Yes
|HB-HC collides with HA with just enough kinetic energy to overcome the potential energy between HB-HC for the reaction to occur.
|[[File:Sjl1218-ani5.png|200px]]
|}
The hypothesis that higher values of momenta would be reactive is not precisely correct, this table shows that pBC must be greater than pAB by a specific factor to be able reactive.

===Transition State Theory===

The transition state theory attempts to provide a grearter understanding of the reaction by predicting the rate as well as the theromodynamic parameters of the reaction. However, it has its limitations. The transition state theory neglects the effects of quantum tunneling such that particles can bypass the activation energy of the transition state. Additionally, systems that have already crossed the transition state and formed products can recross the barrier to reform the reactants. Consequently, the rate calculated by the transition state theory is greater than the experimental value for the reasons that quantum effects are not taken into account.

==Exercise 2: F + H2 and H + HF==

===PES Inspection===

====1. F + H-H -> F-H + H====

Conditions: rAB = 150 pm, rBC = 80 pm, pAB = 0 g.mol-1.pm.fs-1, pBC = 0.5 g.mol-1.pm.fs-1.
[[File:Sjl1218-sur3.png|center|thumb|PES of F + H-H -> F-H + H]]

Products are lower in potential energy than reactants, therefore reaction is exothermic.The H-F bond formed releases more energy than the energy taken to break the H-H bond, therefore H-F is greater in bond strength than H2.

====2. F-H + H -> F + H-H====

Conditions: rAB = 80 pm, rBC = 150 pm, pAB = 15 g.mol-1.pm.fs-1, pBC = 0 g.mol-1.pm.fs-1.
[[File:Sjl1218-sur4.PNG|center|thumb|PES of F-H + H -> F + H-H]]

Products are higher in energy than reactants, therefore reaction is endothermic. The energy used to break the H-F bond is greater than the energy released for forming the H-H bond. The H-F bond is greater in bond strength.

===Locating the Transition State Position===

The approximate position of the transition state is F-H = 180 pm and H-H = 75 pm. Horizontal line shown on the internuclear distance vs time graph represents minimal oscillations among the atoms, ∂V(ri)/∂ri=0 no forces are acting on the F-H-H direction so transition state is reached.

[[File:Sjl1218-ts1.png|center|thumb|Internuclear Distance vs Time graph for rAB = 180 pm, rBC = 75 pm, pAB = 0 g.mol-1.pm.fs-1, pBC = 0 g.mol-1.pm.fs-1]]

===Calculating the Activation Energy===

The activation energy can be calculated by subtracting the potential energy of the reactants from the potential energy the TS. The potential energy of the transition state is -433.943 kJ.mol-1. The potential energy of the reactants can be obtained by performing an MEP of energy vs time for the reaction and observing the starting potential energy.

Activation energies of:

1. F + H-H -> F-H + H: -433.943 - -434.288 = +0.345 kj.mol-1
[[File:Sjl1218-6.png|center|thumb|Energy vs Time MEP for F + H-H -> F-H + H with same reaction conditions]]

2. F-H + H -> F + H-H: -433.943 - -496.862 = +62.919 kj.mol-1
[[File:Sjl1218-7.png|center|thumb|Energy vs Time MEP for F-H + H -> F + H-H with same reaction conditions]]

===Reaction Dynamics===
====1. F + H-H -> F-H + H====

[[File:Sjl1218-8.png|300px|thumb|Illustration of reactants: F + H-H]] [[File:Sjl1218-9.png|thumb|Illustration of products: F-H + H]]

Initial conditions that result in a reactive trajectory:

MRD:sjl1218

2020-05-08T21:39:18Z

Sjl1218: /* Reaction Dynamics */

==Exercise 1: HA + HB-HC -> HA-HB + HC==

[[File:sjl1218-reactionscheme.png|500px|center|thumb|Initial Conditions of Reaction Involving 3 Atoms: HA + HB-HC -> HA-HB + HC]]

===Dynamics of the Transition State Region===
====The Transition State====
[[File:Sjl1218-pesurface.PNG|300px|right|thumb|center|Potential Energy Surface Diagram of HA + HB-HC -> HA-HB + HC]]
In a potential energy surface diagram, the reaction pathway (black line) proceeds along the minimum energy path linked by the reactants and products. The transition state is the PES diagram saddle point defined mathematically by ∂V(ri)/∂ri=0.

The transition state location can be identified if V(rAB)/∂rAB=0 and V(rBC)/∂rBC=0. This point can be distinguished from the local minima if the outcome of taking the partial second derivative of potential energy with respect to either rAB or rBC is 0.

====Locating the Transition State====

Since the H2 + H1 surface is symmetric, the transition state must have rAB=rBC. The location of the transition state position rts can be estimated when ∂V(ri)/∂ri=0 and there will be minimal oscillation among the 3 atoms as there is no force acting along rAB and rBC.

[[File:Sjl1218-4.PNG|400px|center|thumb|Model for when rAB = rBC and pAB=pBC=0]]

The transition state position rts is estimated as 91 pm. The internuclear distances vs time graph for rAB = rBC=91pm shows a 'flat' line, meaning no forces are acting at this position.

[[File:Sjl1218-ts.PNG|300px|center|thumb|Internuclear Distances vs Time Graph for rAB = rBC=91pm and pAB=pBC=0]]

====Calculating the reaction path====

The reaction path or minimum energy path is an infinitely slow trajectory (momenta and velocities resets to zero in each time step) obtained after locating the transition state position.

The minimum energy path initially shows a short horizontal line of the atoms entering the transition state position followed by the decreasing rate of atoms HA-HC and HB-HC increasing in distance. Atoms HA-HB forms a bond and remains constant in distance.

Even though the MEP outlines a reaction, it does not take into account the mass and inertia of the atoms, therefore does not provide the realistic picture of the reaction.
The MEP and dynamic trajectory differs in that the realistic trajectory shows oscillations (potential energy interactions) between atoms. At first the 3 atoms are in the transition state positions, showed by the horiontal lines. The trajectory then shows a linear increase in HA-HC and HB-HC distances and HA-HB oscillates about the same position.
[[File:Sjl1218-mep.PNG|300px|center|thumb|Minimum Energy Path (rBC = rts+1 pm, rAB = rts and pBC = pAB = 0 g.mol-1.pm.fs-1)]]
[[File:Sjl1218-traj.PNG|300px|center|thumb|Dynamic Trajectory (rBC = rts+1 pm, rAB = rts and pBC = pAB = 0 g.mol-1.pm.fs-1)]]

===Reactive and Unreactive Trajectories===
Determining whether trajectories are reactive from their momenta when rBC=74 pm and rAB=200 pm.
{| 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
|HB-HC collides with HA with sufficient kinetic energy to overcome the reaction barrier and forms HAHB and HC.
|[[File:Sjl1218-ani1.png|200px]]
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-4.1</nowiki>
|<nowiki>-420.077</nowiki>
|No
|HB-HC approaches HA but does not react due to lack of kinetic energy/momenta.
|[[File:Sjl1218-ani2.png|200px]]
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-5.1</nowiki>
|<nowiki>-413.977</nowiki>
|Yes
|HB-HC collides with HA with sufficient kinetic energy to overcome the reaction barrier and forms HAHB and HC.
|[[File:Sjl1218-ani3.png|200px]]
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.1</nowiki>
|<nowiki>-357.277</nowiki>
|No
|HB-HC collides with HA and enters a temporary transition state but insufficient kinetic energy does not allow a reaction to occur. Atoms return to their starting positions.
|[[File:Sjl1218-ani4.png|200px]]
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.6</nowiki>
|<nowiki>-349.477</nowiki>
|Yes
|HB-HC collides with HA with just enough kinetic energy to overcome the potential energy between HB-HC for the reaction to occur.
|[[File:Sjl1218-ani5.png|200px]]
|}
The hypothesis that higher values of momenta would be reactive is not precisely correct, this table shows that pBC must be greater than pAB by a specific factor to be able reactive.

===Transition State Theory===

The transition state theory attempts to provide a grearter understanding of the reaction by predicting the rate as well as the theromodynamic parameters of the reaction. However, it has its limitations. The transition state theory neglects the effects of quantum tunneling such that particles can bypass the activation energy of the transition state. Additionally, systems that have already crossed the transition state and formed products can recross the barrier to reform the reactants. Consequently, the rate calculated by the transition state theory is greater than the experimental value for the reasons that quantum effects are not taken into account.

==Exercise 2: F + H2 and H + HF==

===PES Inspection===

====1. F + H-H -> F-H + H====

Conditions: rAB = 150 pm, rBC = 80 pm, pAB = 0 g.mol-1.pm.fs-1, pBC = 0.5 g.mol-1.pm.fs-1.
[[File:Sjl1218-sur3.png|center|thumb|PES of F + H-H -> F-H + H]]

Products are lower in potential energy than reactants, therefore reaction is exothermic.The H-F bond formed releases more energy than the energy taken to break the H-H bond, therefore H-F is greater in bond strength than H2.

====2. F-H + H -> F + H-H====

Conditions: rAB = 80 pm, rBC = 150 pm, pAB = 15 g.mol-1.pm.fs-1, pBC = 0 g.mol-1.pm.fs-1.
[[File:Sjl1218-sur4.PNG|center|thumb|PES of F-H + H -> F + H-H]]

Products are higher in energy than reactants, therefore reaction is endothermic. The energy used to break the H-F bond is greater than the energy released for forming the H-H bond. The H-F bond is greater in bond strength.

===Locating the Transition State Position===

The approximate position of the transition state is F-H = 180 pm and H-H = 75 pm. Horizontal line shown on the internuclear distance vs time graph represents minimal oscillations among the atoms, ∂V(ri)/∂ri=0 no forces are acting on the F-H-H direction so transition state is reached.

[[File:Sjl1218-ts1.png|center|thumb|Internuclear Distance vs Time graph for rAB = 180 pm, rBC = 75 pm, pAB = 0 g.mol-1.pm.fs-1, pBC = 0 g.mol-1.pm.fs-1]]

===Calculating the Activation Energy===

The activation energy can be calculated by subtracting the potential energy of the reactants from the potential energy the TS. The potential energy of the transition state is -433.943 kJ.mol-1. The potential energy of the reactants can be obtained by performing an MEP of energy vs time for the reaction and observing the starting potential energy.

Activation energies of:

1. F + H-H -> F-H + H: -433.943 - -434.288 = +0.345 kj.mol-1
[[File:Sjl1218-6.png|center|thumb|Energy vs Time MEP for F + H-H -> F-H + H with same reaction conditions]]

2. F-H + H -> F + H-H: -433.943 - -496.862 = +62.919 kj.mol-1
[[File:Sjl1218-7.png|center|thumb|Energy vs Time MEP for F-H + H -> F + H-H with same reaction conditions]]

===Reaction Dynamics===
====1. F + H-H -> F-H + H====

[[File:Sjl1218-8.png]] [[File:Sjl1218-9.png]]

Initial conditions that result in a reactive trajectory:

File:Sjl1218-10.png

2020-05-08T21:36:21Z

Sjl1218:

File:Sjl1218-9.png

2020-05-08T21:36:12Z

Sjl1218:

File:Sjl1218-8.png

2020-05-08T21:36:02Z

Sjl1218:

MRD:sjl1218

2020-05-08T21:31:45Z

Sjl1218: /* Calculating the Activation Energy */

==Exercise 1: HA + HB-HC -> HA-HB + HC==

[[File:sjl1218-reactionscheme.png|500px|center|thumb|Initial Conditions of Reaction Involving 3 Atoms: HA + HB-HC -> HA-HB + HC]]

===Dynamics of the Transition State Region===
====The Transition State====
[[File:Sjl1218-pesurface.PNG|300px|right|thumb|center|Potential Energy Surface Diagram of HA + HB-HC -> HA-HB + HC]]
In a potential energy surface diagram, the reaction pathway (black line) proceeds along the minimum energy path linked by the reactants and products. The transition state is the PES diagram saddle point defined mathematically by ∂V(ri)/∂ri=0.

The transition state location can be identified if V(rAB)/∂rAB=0 and V(rBC)/∂rBC=0. This point can be distinguished from the local minima if the outcome of taking the partial second derivative of potential energy with respect to either rAB or rBC is 0.

====Locating the Transition State====

Since the H2 + H1 surface is symmetric, the transition state must have rAB=rBC. The location of the transition state position rts can be estimated when ∂V(ri)/∂ri=0 and there will be minimal oscillation among the 3 atoms as there is no force acting along rAB and rBC.

[[File:Sjl1218-4.PNG|400px|center|thumb|Model for when rAB = rBC and pAB=pBC=0]]

The transition state position rts is estimated as 91 pm. The internuclear distances vs time graph for rAB = rBC=91pm shows a 'flat' line, meaning no forces are acting at this position.

[[File:Sjl1218-ts.PNG|300px|center|thumb|Internuclear Distances vs Time Graph for rAB = rBC=91pm and pAB=pBC=0]]

====Calculating the reaction path====

The reaction path or minimum energy path is an infinitely slow trajectory (momenta and velocities resets to zero in each time step) obtained after locating the transition state position.

The minimum energy path initially shows a short horizontal line of the atoms entering the transition state position followed by the decreasing rate of atoms HA-HC and HB-HC increasing in distance. Atoms HA-HB forms a bond and remains constant in distance.

Even though the MEP outlines a reaction, it does not take into account the mass and inertia of the atoms, therefore does not provide the realistic picture of the reaction.
The MEP and dynamic trajectory differs in that the realistic trajectory shows oscillations (potential energy interactions) between atoms. At first the 3 atoms are in the transition state positions, showed by the horiontal lines. The trajectory then shows a linear increase in HA-HC and HB-HC distances and HA-HB oscillates about the same position.
[[File:Sjl1218-mep.PNG|300px|center|thumb|Minimum Energy Path (rBC = rts+1 pm, rAB = rts and pBC = pAB = 0 g.mol-1.pm.fs-1)]]
[[File:Sjl1218-traj.PNG|300px|center|thumb|Dynamic Trajectory (rBC = rts+1 pm, rAB = rts and pBC = pAB = 0 g.mol-1.pm.fs-1)]]

===Reactive and Unreactive Trajectories===
Determining whether trajectories are reactive from their momenta when rBC=74 pm and rAB=200 pm.
{| 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
|HB-HC collides with HA with sufficient kinetic energy to overcome the reaction barrier and forms HAHB and HC.
|[[File:Sjl1218-ani1.png|200px]]
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-4.1</nowiki>
|<nowiki>-420.077</nowiki>
|No
|HB-HC approaches HA but does not react due to lack of kinetic energy/momenta.
|[[File:Sjl1218-ani2.png|200px]]
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-5.1</nowiki>
|<nowiki>-413.977</nowiki>
|Yes
|HB-HC collides with HA with sufficient kinetic energy to overcome the reaction barrier and forms HAHB and HC.
|[[File:Sjl1218-ani3.png|200px]]
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.1</nowiki>
|<nowiki>-357.277</nowiki>
|No
|HB-HC collides with HA and enters a temporary transition state but insufficient kinetic energy does not allow a reaction to occur. Atoms return to their starting positions.
|[[File:Sjl1218-ani4.png|200px]]
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.6</nowiki>
|<nowiki>-349.477</nowiki>
|Yes
|HB-HC collides with HA with just enough kinetic energy to overcome the potential energy between HB-HC for the reaction to occur.
|[[File:Sjl1218-ani5.png|200px]]
|}
The hypothesis that higher values of momenta would be reactive is not precisely correct, this table shows that pBC must be greater than pAB by a specific factor to be able reactive.

===Transition State Theory===

The transition state theory attempts to provide a grearter understanding of the reaction by predicting the rate as well as the theromodynamic parameters of the reaction. However, it has its limitations. The transition state theory neglects the effects of quantum tunneling such that particles can bypass the activation energy of the transition state. Additionally, systems that have already crossed the transition state and formed products can recross the barrier to reform the reactants. Consequently, the rate calculated by the transition state theory is greater than the experimental value for the reasons that quantum effects are not taken into account.

==Exercise 2: F + H2 and H + HF==

===PES Inspection===

====1. F + H-H -> F-H + H====

Conditions: rAB = 150 pm, rBC = 80 pm, pAB = 0 g.mol-1.pm.fs-1, pBC = 0.5 g.mol-1.pm.fs-1.
[[File:Sjl1218-sur3.png|center|thumb|PES of F + H-H -> F-H + H]]

Products are lower in potential energy than reactants, therefore reaction is exothermic.The H-F bond formed releases more energy than the energy taken to break the H-H bond, therefore H-F is greater in bond strength than H2.

====2. F-H + H -> F + H-H====

Conditions: rAB = 80 pm, rBC = 150 pm, pAB = 15 g.mol-1.pm.fs-1, pBC = 0 g.mol-1.pm.fs-1.
[[File:Sjl1218-sur4.PNG|center|thumb|PES of F-H + H -> F + H-H]]

Products are higher in energy than reactants, therefore reaction is endothermic. The energy used to break the H-F bond is greater than the energy released for forming the H-H bond. The H-F bond is greater in bond strength.

===Locating the Transition State Position===

The approximate position of the transition state is F-H = 180 pm and H-H = 75 pm. Horizontal line shown on the internuclear distance vs time graph represents minimal oscillations among the atoms, ∂V(ri)/∂ri=0 no forces are acting on the F-H-H direction so transition state is reached.

[[File:Sjl1218-ts1.png|center|thumb|Internuclear Distance vs Time graph for rAB = 180 pm, rBC = 75 pm, pAB = 0 g.mol-1.pm.fs-1, pBC = 0 g.mol-1.pm.fs-1]]

===Calculating the Activation Energy===

The activation energy can be calculated by subtracting the potential energy of the reactants from the potential energy the TS. The potential energy of the transition state is -433.943 kJ.mol-1. The potential energy of the reactants can be obtained by performing an MEP of energy vs time for the reaction and observing the starting potential energy.

Activation energies of:

1. F + H-H -> F-H + H: -433.943 - -434.288 = +0.345 kj.mol-1
[[File:Sjl1218-6.png|center|thumb|Energy vs Time MEP for F + H-H -> F-H + H with same reaction conditions]]

2. F-H + H -> F + H-H: -433.943 - -496.862 = +62.919 kj.mol-1
[[File:Sjl1218-7.png|center|thumb|Energy vs Time MEP for F-H + H -> F + H-H with same reaction conditions]]

==Reaction Dynamics==

MRD:sjl1218

2020-05-08T21:30:56Z

Sjl1218: /* Calculating the Activation Energy */

==Exercise 1: HA + HB-HC -> HA-HB + HC==

[[File:sjl1218-reactionscheme.png|500px|center|thumb|Initial Conditions of Reaction Involving 3 Atoms: HA + HB-HC -> HA-HB + HC]]

===Dynamics of the Transition State Region===
====The Transition State====
[[File:Sjl1218-pesurface.PNG|300px|right|thumb|center|Potential Energy Surface Diagram of HA + HB-HC -> HA-HB + HC]]
In a potential energy surface diagram, the reaction pathway (black line) proceeds along the minimum energy path linked by the reactants and products. The transition state is the PES diagram saddle point defined mathematically by ∂V(ri)/∂ri=0.

The transition state location can be identified if V(rAB)/∂rAB=0 and V(rBC)/∂rBC=0. This point can be distinguished from the local minima if the outcome of taking the partial second derivative of potential energy with respect to either rAB or rBC is 0.

====Locating the Transition State====

Since the H2 + H1 surface is symmetric, the transition state must have rAB=rBC. The location of the transition state position rts can be estimated when ∂V(ri)/∂ri=0 and there will be minimal oscillation among the 3 atoms as there is no force acting along rAB and rBC.

[[File:Sjl1218-4.PNG|400px|center|thumb|Model for when rAB = rBC and pAB=pBC=0]]

The transition state position rts is estimated as 91 pm. The internuclear distances vs time graph for rAB = rBC=91pm shows a 'flat' line, meaning no forces are acting at this position.

[[File:Sjl1218-ts.PNG|300px|center|thumb|Internuclear Distances vs Time Graph for rAB = rBC=91pm and pAB=pBC=0]]

====Calculating the reaction path====

The reaction path or minimum energy path is an infinitely slow trajectory (momenta and velocities resets to zero in each time step) obtained after locating the transition state position.

The minimum energy path initially shows a short horizontal line of the atoms entering the transition state position followed by the decreasing rate of atoms HA-HC and HB-HC increasing in distance. Atoms HA-HB forms a bond and remains constant in distance.

Even though the MEP outlines a reaction, it does not take into account the mass and inertia of the atoms, therefore does not provide the realistic picture of the reaction.
The MEP and dynamic trajectory differs in that the realistic trajectory shows oscillations (potential energy interactions) between atoms. At first the 3 atoms are in the transition state positions, showed by the horiontal lines. The trajectory then shows a linear increase in HA-HC and HB-HC distances and HA-HB oscillates about the same position.
[[File:Sjl1218-mep.PNG|300px|center|thumb|Minimum Energy Path (rBC = rts+1 pm, rAB = rts and pBC = pAB = 0 g.mol-1.pm.fs-1)]]
[[File:Sjl1218-traj.PNG|300px|center|thumb|Dynamic Trajectory (rBC = rts+1 pm, rAB = rts and pBC = pAB = 0 g.mol-1.pm.fs-1)]]

===Reactive and Unreactive Trajectories===
Determining whether trajectories are reactive from their momenta when rBC=74 pm and rAB=200 pm.
{| 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
|HB-HC collides with HA with sufficient kinetic energy to overcome the reaction barrier and forms HAHB and HC.
|[[File:Sjl1218-ani1.png|200px]]
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-4.1</nowiki>
|<nowiki>-420.077</nowiki>
|No
|HB-HC approaches HA but does not react due to lack of kinetic energy/momenta.
|[[File:Sjl1218-ani2.png|200px]]
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-5.1</nowiki>
|<nowiki>-413.977</nowiki>
|Yes
|HB-HC collides with HA with sufficient kinetic energy to overcome the reaction barrier and forms HAHB and HC.
|[[File:Sjl1218-ani3.png|200px]]
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.1</nowiki>
|<nowiki>-357.277</nowiki>
|No
|HB-HC collides with HA and enters a temporary transition state but insufficient kinetic energy does not allow a reaction to occur. Atoms return to their starting positions.
|[[File:Sjl1218-ani4.png|200px]]
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.6</nowiki>
|<nowiki>-349.477</nowiki>
|Yes
|HB-HC collides with HA with just enough kinetic energy to overcome the potential energy between HB-HC for the reaction to occur.
|[[File:Sjl1218-ani5.png|200px]]
|}
The hypothesis that higher values of momenta would be reactive is not precisely correct, this table shows that pBC must be greater than pAB by a specific factor to be able reactive.

===Transition State Theory===

The transition state theory attempts to provide a grearter understanding of the reaction by predicting the rate as well as the theromodynamic parameters of the reaction. However, it has its limitations. The transition state theory neglects the effects of quantum tunneling such that particles can bypass the activation energy of the transition state. Additionally, systems that have already crossed the transition state and formed products can recross the barrier to reform the reactants. Consequently, the rate calculated by the transition state theory is greater than the experimental value for the reasons that quantum effects are not taken into account.

==Exercise 2: F + H2 and H + HF==

===PES Inspection===

====1. F + H-H -> F-H + H====

Conditions: rAB = 150 pm, rBC = 80 pm, pAB = 0 g.mol-1.pm.fs-1, pBC = 0.5 g.mol-1.pm.fs-1.
[[File:Sjl1218-sur3.png|center|thumb|PES of F + H-H -> F-H + H]]

Products are lower in potential energy than reactants, therefore reaction is exothermic.The H-F bond formed releases more energy than the energy taken to break the H-H bond, therefore H-F is greater in bond strength than H2.

====2. F-H + H -> F + H-H====

Conditions: rAB = 80 pm, rBC = 150 pm, pAB = 15 g.mol-1.pm.fs-1, pBC = 0 g.mol-1.pm.fs-1.
[[File:Sjl1218-sur4.PNG|center|thumb|PES of F-H + H -> F + H-H]]

Products are higher in energy than reactants, therefore reaction is endothermic. The energy used to break the H-F bond is greater than the energy released for forming the H-H bond. The H-F bond is greater in bond strength.

===Locating the Transition State Position===

The approximate position of the transition state is F-H = 180 pm and H-H = 75 pm. Horizontal line shown on the internuclear distance vs time graph represents minimal oscillations among the atoms, ∂V(ri)/∂ri=0 no forces are acting on the F-H-H direction so transition state is reached.

[[File:Sjl1218-ts1.png|center|thumb|Internuclear Distance vs Time graph for rAB = 180 pm, rBC = 75 pm, pAB = 0 g.mol-1.pm.fs-1, pBC = 0 g.mol-1.pm.fs-1]]

===Calculating the Activation Energy===

The activation energy can be calculated by subtracting the potential energy of the reactants from the potential energy the TS. The potential energy of the transition state is -433.943 kJ.mol-1. The potential energy of the reactants can be obtained by performing an MEP of energy vs time for the reaction and observing the starting potential energy.

Activation energies of:
1. F + H-H -> F-H + H: -433.943--434.288 = 0.345 kj.mol-1
[[File:Sjl1218-6.png|center|thumb|Energy vs Time MEP for F + H-H -> F-H + H with same reaction conditions]]

2. F-H + H -> F + H-H: -433.943--496.862 = 62.919 kj.mol-1
[[File:Sjl1218-7.png|center|thumb|Energy vs Time MEP for F-H + H -> F + H-H with same reaction conditions]]

==Reaction Dynamics==

File:Sjl1218-7.png

2020-05-08T21:27:29Z

Sjl1218:

File:Sjl1218-6.png

2020-05-08T21:27:13Z

Sjl1218:

MRD:sjl1218

2020-05-08T21:19:53Z

Sjl1218: /* Exercise 2: F + H2 and H + HF */

==Exercise 1: HA + HB-HC -> HA-HB + HC==

[[File:sjl1218-reactionscheme.png|500px|center|thumb|Initial Conditions of Reaction Involving 3 Atoms: HA + HB-HC -> HA-HB + HC]]

===Dynamics of the Transition State Region===
====The Transition State====
[[File:Sjl1218-pesurface.PNG|300px|right|thumb|center|Potential Energy Surface Diagram of HA + HB-HC -> HA-HB + HC]]
In a potential energy surface diagram, the reaction pathway (black line) proceeds along the minimum energy path linked by the reactants and products. The transition state is the PES diagram saddle point defined mathematically by ∂V(ri)/∂ri=0.

The transition state location can be identified if V(rAB)/∂rAB=0 and V(rBC)/∂rBC=0. This point can be distinguished from the local minima if the outcome of taking the partial second derivative of potential energy with respect to either rAB or rBC is 0.

====Locating the Transition State====

Since the H2 + H1 surface is symmetric, the transition state must have rAB=rBC. The location of the transition state position rts can be estimated when ∂V(ri)/∂ri=0 and there will be minimal oscillation among the 3 atoms as there is no force acting along rAB and rBC.

[[File:Sjl1218-4.PNG|400px|center|thumb|Model for when rAB = rBC and pAB=pBC=0]]

The transition state position rts is estimated as 91 pm. The internuclear distances vs time graph for rAB = rBC=91pm shows a 'flat' line, meaning no forces are acting at this position.

[[File:Sjl1218-ts.PNG|300px|center|thumb|Internuclear Distances vs Time Graph for rAB = rBC=91pm and pAB=pBC=0]]

====Calculating the reaction path====

The reaction path or minimum energy path is an infinitely slow trajectory (momenta and velocities resets to zero in each time step) obtained after locating the transition state position.

The minimum energy path initially shows a short horizontal line of the atoms entering the transition state position followed by the decreasing rate of atoms HA-HC and HB-HC increasing in distance. Atoms HA-HB forms a bond and remains constant in distance.

Even though the MEP outlines a reaction, it does not take into account the mass and inertia of the atoms, therefore does not provide the realistic picture of the reaction.
The MEP and dynamic trajectory differs in that the realistic trajectory shows oscillations (potential energy interactions) between atoms. At first the 3 atoms are in the transition state positions, showed by the horiontal lines. The trajectory then shows a linear increase in HA-HC and HB-HC distances and HA-HB oscillates about the same position.
[[File:Sjl1218-mep.PNG|300px|center|thumb|Minimum Energy Path (rBC = rts+1 pm, rAB = rts and pBC = pAB = 0 g.mol-1.pm.fs-1)]]
[[File:Sjl1218-traj.PNG|300px|center|thumb|Dynamic Trajectory (rBC = rts+1 pm, rAB = rts and pBC = pAB = 0 g.mol-1.pm.fs-1)]]

===Reactive and Unreactive Trajectories===
Determining whether trajectories are reactive from their momenta when rBC=74 pm and rAB=200 pm.
{| 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
|HB-HC collides with HA with sufficient kinetic energy to overcome the reaction barrier and forms HAHB and HC.
|[[File:Sjl1218-ani1.png|200px]]
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-4.1</nowiki>
|<nowiki>-420.077</nowiki>
|No
|HB-HC approaches HA but does not react due to lack of kinetic energy/momenta.
|[[File:Sjl1218-ani2.png|200px]]
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-5.1</nowiki>
|<nowiki>-413.977</nowiki>
|Yes
|HB-HC collides with HA with sufficient kinetic energy to overcome the reaction barrier and forms HAHB and HC.
|[[File:Sjl1218-ani3.png|200px]]
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.1</nowiki>
|<nowiki>-357.277</nowiki>
|No
|HB-HC collides with HA and enters a temporary transition state but insufficient kinetic energy does not allow a reaction to occur. Atoms return to their starting positions.
|[[File:Sjl1218-ani4.png|200px]]
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.6</nowiki>
|<nowiki>-349.477</nowiki>
|Yes
|HB-HC collides with HA with just enough kinetic energy to overcome the potential energy between HB-HC for the reaction to occur.
|[[File:Sjl1218-ani5.png|200px]]
|}
The hypothesis that higher values of momenta would be reactive is not precisely correct, this table shows that pBC must be greater than pAB by a specific factor to be able reactive.

===Transition State Theory===

The transition state theory attempts to provide a grearter understanding of the reaction by predicting the rate as well as the theromodynamic parameters of the reaction. However, it has its limitations. The transition state theory neglects the effects of quantum tunneling such that particles can bypass the activation energy of the transition state. Additionally, systems that have already crossed the transition state and formed products can recross the barrier to reform the reactants. Consequently, the rate calculated by the transition state theory is greater than the experimental value for the reasons that quantum effects are not taken into account.

==Exercise 2: F + H2 and H + HF==

===PES Inspection===

====1. F + H-H -> F-H + H====

Conditions: rAB = 150 pm, rBC = 80 pm, pAB = 0 g.mol-1.pm.fs-1, pBC = 0.5 g.mol-1.pm.fs-1.
[[File:Sjl1218-sur3.png|center|thumb|PES of F + H-H -> F-H + H]]

Products are lower in potential energy than reactants, therefore reaction is exothermic.The H-F bond formed releases more energy than the energy taken to break the H-H bond, therefore H-F is greater in bond strength than H2.

====2. F-H + H -> F + H-H====

Conditions: rAB = 80 pm, rBC = 150 pm, pAB = 15 g.mol-1.pm.fs-1, pBC = 0 g.mol-1.pm.fs-1.
[[File:Sjl1218-sur4.PNG|center|thumb|PES of F-H + H -> F + H-H]]

Products are higher in energy than reactants, therefore reaction is endothermic. The energy used to break the H-F bond is greater than the energy released for forming the H-H bond. The H-F bond is greater in bond strength.

===Locating the Transition State Position===

The approximate position of the transition state is F-H = 180 pm and H-H = 75 pm. Horizontal line shown on the internuclear distance vs time graph represents minimal oscillations among the atoms, ∂V(ri)/∂ri=0 no forces are acting on the F-H-H direction so transition state is reached.

[[File:Sjl1218-ts1.png|center|thumb|Internuclear Distance vs Time graph for rAB = 180 pm, rBC = 75 pm, pAB = 0 g.mol-1.pm.fs-1, pBC = 0 g.mol-1.pm.fs-1]]

===Calculating the Activation Energy===

The activation energy can be calculated by subtracting the potential energy of the reactants from the potential energy the TS. The potential energy of the transition state is -433.943 kJ.mol-1. The potential energy of the reactants can be obtained by performing an MEP of energy vs time for a structure akin the transition state. The activation energy 1. F + H-H -> F-H + H
2. F-H + H -> F + H-H

MRD:sjl1218

2020-05-08T20:16:21Z

Sjl1218: /* Locating the Transition State Position */

MRD:sjl1218

2020-05-08T20:12:55Z

Sjl1218: /* PES Inspection */

File:Sjl1218-ts1.png

2020-05-08T20:10:13Z

Sjl1218:

MRD:sjl1218

2020-05-08T19:42:50Z

Sjl1218: /* Exercise 2: F + H2 and H + HF */

MRD:sjl1218

2020-05-08T19:42:17Z

Sjl1218: /* Transition State Theory */

MRD:sjl1218

2020-05-08T19:41:52Z

Sjl1218: /* Reaction Involving 3 Atoms: HA+HB-HC -> HA-HB+HC */

File:Sjl1218-sur4.PNG

2020-05-08T19:29:20Z

Sjl1218:

File:Sjl1218-sur3.png

2020-05-08T19:29:12Z

Sjl1218:

MRD:sjl1218

2020-05-08T09:47:20Z

Sjl1218: /* Reactive and Unreactive Trajectories */

==Reaction Involving 3 Atoms: HA+HB-HC -> HA-HB+HC==

[[File:sjl1218-reactionscheme.png|500px|center|thumb|Initial Conditions of Reaction Involving 3 Atoms: HA+HB-HC -> HA-HB+HC]]

===Dynamics of the Transition State Region===
====The Transition State====
[[File:Sjl1218-pesurface.PNG|300px|right|thumb|center|Potential Energy Surface Diagram of HA+HB-HC -> HA-HB+HC]]
In a potential energy surface diagram, the reaction pathway (black line) proceeds along the minimum energy path linked by the reactants and products. The transition state is the PES diagram saddle point defined mathematically by ∂V(ri)/∂ri=0.

The transition state location can be identified if V(rAB)/∂rAB=0 and V(rBC)/∂rBC=0. This point can be distinguished from the local minima if the outcome of taking the partial second derivative of potential energy with respect to either rAB or rBC is 0.

====Locating the Transition State====

Since the H2 + H1 surface is symmetric, the transition state must have rAB=rBC. The location of the transition state position rts can be estimated when ∂V(ri)/∂ri=0 and there will be minimal oscillation among the 3 atoms as there is no force acting along rAB and rBC.

[[File:Sjl1218-4.PNG|400px|center|thumb|Model for when rAB=rBC and pAB=pBC=0]]

The transition state position rts is estimated as 91 pm. The internuclear distances vs time graph for rAB=rBC=91pm shows a 'flat' line, meaning no forces are acting at this position.

[[File:Sjl1218-ts.PNG|300px|center|thumb|Internuclear Distances vs Time Graph for rAB=rBC=91pm and pAB=pBC=0]]

====Calculating the reaction path====

The reaction path or minimum energy path is an infinitely slow trajectory (momenta and velocities resets to zero in each time step) obtained after locating the transition state position.

The minimum energy path initially shows a short horizontal line of the atoms entering the transition state position followed by the decreasing rate of atoms HA-HC and HB-HC increasing in distance. Atoms HA-HB forms a bond and remains constant in distance.

Even though the MEP outlines a reaction, it does not take into account the mass and inertia of the atoms, therefore does not provide the realistic picture of the reaction.
The MEP and dynamic trajectory differs in that the realistic trajectory shows oscillations (potential energy interactions) between atoms. At first the 3 atoms are in the transition state positions, showed by the horiontal lines. The trajectory then shows a linear increase in HA-HC and HB-HC distances and HA-HB oscillates about the same position.
[[File:Sjl1218-mep.PNG|300px|center|thumb|Minimum Energy Path (rBC=rts+1 pm, rAB=rts and pBC=pAB=0 g.mol-1.pm.fs-1)]]
[[File:Sjl1218-traj.PNG|300px|center|thumb|Dynamic Trajectory (rBC=rts+1 pm, rAB=rts and pBC=pAB=0 g.mol-1.pm.fs-1)]]

===Reactive and Unreactive Trajectories===
Determining whether trajectories are reactive from their momenta when rBC=74 pm and rAB=200 pm.
{| 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
|HB-HC collides with HA with sufficient kinetic energy to overcome the reaction barrier and forms HAHB and HC.
|[[File:Sjl1218-ani1.png|200px]]
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-4.1</nowiki>
|<nowiki>-420.077</nowiki>
|No
|HB-HC approaches HA but does not react due to lack of kinetic energy/momenta.
|[[File:Sjl1218-ani2.png|200px]]
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-5.1</nowiki>
|<nowiki>-413.977</nowiki>
|Yes
|HB-HC collides with HA with sufficient kinetic energy to overcome the reaction barrier and forms HAHB and HC.
|[[File:Sjl1218-ani3.png|200px]]
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.1</nowiki>
|<nowiki>-357.277</nowiki>
|No
|HB-HC collides with HA and enters a temporary transition state but insufficient kinetic energy does not allow a reaction to occur. Atoms return to their starting positions.
|[[File:Sjl1218-ani4.png|200px]]
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.6</nowiki>
|<nowiki>-349.477</nowiki>
|Yes
|HB-HC collides with HA with just enough kinetic energy to overcome the potential energy between HB-HC for the reaction to occur.
|[[File:Sjl1218-ani5.png|200px]]
|}
The hypothesis that higher values of momenta would be reactive is not precisely correct, this table shows that pBC must be greater than pAB by a specific factor to be able reactive.

===Transition State Theory===

MRD:sjl1218

2020-05-08T08:24:37Z

Sjl1218: /* Reactive and Unreactive Trajectories */

MRD:sjl1218

2020-05-08T08:07:43Z

Sjl1218: /* Reactive and Unreactive Trajectories */

==Reaction Involving 3 Atoms: HA+HB-HC -> HA-HB+HC==

[[File:sjl1218-reactionscheme.png|500px|center|thumb|Initial Conditions of Reaction Involving 3 Atoms: HA+HB-HC -> HA-HB+HC]]

===Dynamics of the Transition State Region===
====The Transition State====
[[File:Sjl1218-pesurface.PNG|300px|right|thumb|center|Potential Energy Surface Diagram of HA+HB-HC -> HA-HB+HC]]
In a potential energy surface diagram, the reaction pathway (black line) proceeds along the minimum energy path linked by the reactants and products. The transition state is the PES diagram saddle point defined mathematically by ∂V(ri)/∂ri=0.

The transition state location can be identified if V(rAB)/∂rAB=0 and V(rBC)/∂rBC=0. This point can be distinguished from the local minima if the outcome of taking the partial second derivative of potential energy with respect to either rAB or rBC is 0.

====Locating the Transition State====

Since the H2 + H1 surface is symmetric, the transition state must have rAB=rBC. The location of the transition state position rts can be estimated when ∂V(ri)/∂ri=0 and there will be minimal oscillation among the 3 atoms as there is no force acting along rAB and rBC.

[[File:Sjl1218-4.PNG|400px|center|thumb|Model for when rAB=rBC and pAB=pBC=0]]

The transition state position rts is estimated as 91 pm. The internuclear distances vs time graph for rAB=rBC=91pm shows a 'flat' line, meaning no forces are acting at this position.

[[File:Sjl1218-ts.PNG|300px|center|thumb|Internuclear Distances vs Time Graph for rAB=rBC=91pm and pAB=pBC=0]]

====Calculating the reaction path====

The reaction path or minimum energy path is an infinitely slow trajectory (momenta and velocities resets to zero in each time step) obtained after locating the transition state position.

The minimum energy path initially shows a short horizontal line of the atoms entering the transition state position followed by the decreasing rate of atoms HA-HC and HB-HC increasing in distance. Atoms HA-HB forms a bond and remains constant in distance.

Even though the MEP outlines a reaction, it does not take into account the mass and inertia of the atoms, therefore does not provide the realistic picture of the reaction.
The MEP and dynamic trajectory differs in that the realistic trajectory shows oscillations (potential energy interactions) between atoms. At first the 3 atoms are in the transition state positions, showed by the horiontal lines. The trajectory then shows a linear increase in HA-HC and HB-HC distances and HA-HB oscillates about the same position.
[[File:Sjl1218-mep.PNG|300px|center|thumb|Minimum Energy Path (rBC=rts+1 pm, rAB=rts and pBC=pAB=0 g.mol-1.pm.fs-1)]]
[[File:Sjl1218-traj.PNG|300px|center|thumb|Dynamic Trajectory (rBC=rts+1 pm, rAB=rts and pBC=pAB=0 g.mol-1.pm.fs-1)]]

===Reactive and Unreactive Trajectories===
Determining whether trajectories are reactive from their momenta when rBC=74 pm and rAB=200 pm
{| 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
|HB-HC collides with HA with sufficient kinetic energy to overcome the reaction barrier and forms HAHB and HC
|[[File:Sjl1218-ani1.png|200px]]
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-4.1</nowiki>
|<nowiki>-420.077</nowiki>
|No
|HB-HC approaches HA but does not react due to lack of kinetic energy/momenta
|[[File:Sjl1218-ani2.png|200px]]
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-5.1</nowiki>
|<nowiki>-413.977</nowiki>
|Yes
|HB-HC collides with HA with sufficient kinetic energy to overcome the reaction barrier and forms HAHB and HC
|[[File:Sjl1218-ani3.png|200px]]
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.1</nowiki>
|<nowiki>-357.277</nowiki>
|No
|HB-HC collides with HA and enters a temporary transition state but insufficient kinetic energy does not allow a reaction to occur. Atoms return to their starting positions.
|[[File:Sjl1218-ani4.png|200px]]
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.6</nowiki>
|<nowiki>-349.477</nowiki>
|Yes
|HB-HC collides with HA with just enough kinetic energy to overcome the potential energy between HB-HC for the reaction to occur.
|[[File:Sjl1218-ani5.png|200px]]
|}

MRD:sjl1218

2020-05-08T08:07:21Z

Sjl1218: /* Reactive and Unreactive Trajectories */

==Reaction Involving 3 Atoms: HA+HB-HC -> HA-HB+HC==

[[File:sjl1218-reactionscheme.png|500px|center|thumb|Initial Conditions of Reaction Involving 3 Atoms: HA+HB-HC -> HA-HB+HC]]

===Dynamics of the Transition State Region===
====The Transition State====
[[File:Sjl1218-pesurface.PNG|300px|right|thumb|center|Potential Energy Surface Diagram of HA+HB-HC -> HA-HB+HC]]
In a potential energy surface diagram, the reaction pathway (black line) proceeds along the minimum energy path linked by the reactants and products. The transition state is the PES diagram saddle point defined mathematically by ∂V(ri)/∂ri=0.

The transition state location can be identified if V(rAB)/∂rAB=0 and V(rBC)/∂rBC=0. This point can be distinguished from the local minima if the outcome of taking the partial second derivative of potential energy with respect to either rAB or rBC is 0.

====Locating the Transition State====

Since the H2 + H1 surface is symmetric, the transition state must have rAB=rBC. The location of the transition state position rts can be estimated when ∂V(ri)/∂ri=0 and there will be minimal oscillation among the 3 atoms as there is no force acting along rAB and rBC.

[[File:Sjl1218-4.PNG|400px|center|thumb|Model for when rAB=rBC and pAB=pBC=0]]

The transition state position rts is estimated as 91 pm. The internuclear distances vs time graph for rAB=rBC=91pm shows a 'flat' line, meaning no forces are acting at this position.

[[File:Sjl1218-ts.PNG|300px|center|thumb|Internuclear Distances vs Time Graph for rAB=rBC=91pm and pAB=pBC=0]]

====Calculating the reaction path====

The reaction path or minimum energy path is an infinitely slow trajectory (momenta and velocities resets to zero in each time step) obtained after locating the transition state position.

The minimum energy path initially shows a short horizontal line of the atoms entering the transition state position followed by the decreasing rate of atoms HA-HC and HB-HC increasing in distance. Atoms HA-HB forms a bond and remains constant in distance.

Even though the MEP outlines a reaction, it does not take into account the mass and inertia of the atoms, therefore does not provide the realistic picture of the reaction.
The MEP and dynamic trajectory differs in that the realistic trajectory shows oscillations (potential energy interactions) between atoms. At first the 3 atoms are in the transition state positions, showed by the horiontal lines. The trajectory then shows a linear increase in HA-HC and HB-HC distances and HA-HB oscillates about the same position.
[[File:Sjl1218-mep.PNG|300px|center|thumb|Minimum Energy Path (rBC=rts+1 pm, rAB=rts and pBC=pAB=0 g.mol-1.pm.fs-1)]]
[[File:Sjl1218-traj.PNG|300px|center|thumb|Dynamic Trajectory (rBC=rts+1 pm, rAB=rts and pBC=pAB=0 g.mol-1.pm.fs-1)]]

===Reactive and Unreactive Trajectories===
Determining whether trajectories are reactive from their momenta when r1=74 pm and r2=200 pm
{| 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
|HB-HC collides with HA with sufficient kinetic energy to overcome the reaction barrier and forms HAHB and HC
|[[File:Sjl1218-ani1.png|200px]]
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-4.1</nowiki>
|<nowiki>-420.077</nowiki>
|No
|HB-HC approaches HA but does not react due to lack of kinetic energy/momenta
|[[File:Sjl1218-ani2.png|200px]]
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-5.1</nowiki>
|<nowiki>-413.977</nowiki>
|Yes
|HB-HC collides with HA with sufficient kinetic energy to overcome the reaction barrier and forms HAHB and HC
|[[File:Sjl1218-ani3.png|200px]]
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.1</nowiki>
|<nowiki>-357.277</nowiki>
|No
|HB-HC collides with HA and enters a temporary transition state but insufficient kinetic energy does not allow a reaction to occur. Atoms return to their starting positions.
|[[File:Sjl1218-ani4.png|200px]]
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.6</nowiki>
|<nowiki>-349.477</nowiki>
|Yes
|HB-HC collides with HA with just enough kinetic energy to overcome the potential energy between HB-HC for the reaction to occur.
|[[File:Sjl1218-ani5.png|200px]]
|}

MRD:sjl1218

2020-05-08T08:05:36Z

Sjl1218: /* Reactive and Unreactive Trajectories */

==Reaction Involving 3 Atoms: HA+HB-HC -> HA-HB+HC==

[[File:sjl1218-reactionscheme.png|500px|center|thumb|Initial Conditions of Reaction Involving 3 Atoms: HA+HB-HC -> HA-HB+HC]]

===Dynamics of the Transition State Region===
====The Transition State====
[[File:Sjl1218-pesurface.PNG|300px|right|thumb|center|Potential Energy Surface Diagram of HA+HB-HC -> HA-HB+HC]]
In a potential energy surface diagram, the reaction pathway (black line) proceeds along the minimum energy path linked by the reactants and products. The transition state is the PES diagram saddle point defined mathematically by ∂V(ri)/∂ri=0.

The transition state location can be identified if V(rAB)/∂rAB=0 and V(rBC)/∂rBC=0. This point can be distinguished from the local minima if the outcome of taking the partial second derivative of potential energy with respect to either rAB or rBC is 0.

====Locating the Transition State====

Since the H2 + H1 surface is symmetric, the transition state must have rAB=rBC. The location of the transition state position rts can be estimated when ∂V(ri)/∂ri=0 and there will be minimal oscillation among the 3 atoms as there is no force acting along rAB and rBC.

[[File:Sjl1218-4.PNG|400px|center|thumb|Model for when rAB=rBC and pAB=pBC=0]]

The transition state position rts is estimated as 91 pm. The internuclear distances vs time graph for rAB=rBC=91pm shows a 'flat' line, meaning no forces are acting at this position.

[[File:Sjl1218-ts.PNG|300px|center|thumb|Internuclear Distances vs Time Graph for rAB=rBC=91pm and pAB=pBC=0]]

====Calculating the reaction path====

The reaction path or minimum energy path is an infinitely slow trajectory (momenta and velocities resets to zero in each time step) obtained after locating the transition state position.

The minimum energy path initially shows a short horizontal line of the atoms entering the transition state position followed by the decreasing rate of atoms HA-HC and HB-HC increasing in distance. Atoms HA-HB forms a bond and remains constant in distance.

Even though the MEP outlines a reaction, it does not take into account the mass and inertia of the atoms, therefore does not provide the realistic picture of the reaction.
The MEP and dynamic trajectory differs in that the realistic trajectory shows oscillations (potential energy interactions) between atoms. At first the 3 atoms are in the transition state positions, showed by the horiontal lines. The trajectory then shows a linear increase in HA-HC and HB-HC distances and HA-HB oscillates about the same position.
[[File:Sjl1218-mep.PNG|300px|center|thumb|Minimum Energy Path (rBC=rts+1 pm, rAB=rts and pBC=pAB=0 g.mol-1.pm.fs-1)]]
[[File:Sjl1218-traj.PNG|300px|center|thumb|Dynamic Trajectory (rBC=rts+1 pm, rAB=rts and pBC=pAB=0 g.mol-1.pm.fs-1)]]

===Reactive and Unreactive Trajectories===
Testing the r1 = 74 pm and r2 = 200 pm
{| 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
|HB-HC collides with HA with sufficient kinetic energy to overcome the reaction barrier and forms HAHB and HC
|[[File:Sjl1218-ani1.png|200px]]
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-4.1</nowiki>
|<nowiki>-420.077</nowiki>
|No
|HB-HC approaches HA but does not react due to lack of kinetic energy/momenta
|[[File:Sjl1218-ani2.png|200px]]
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-5.1</nowiki>
|<nowiki>-413.977</nowiki>
|Yes
|HB-HC collides with HA with sufficient kinetic energy to overcome the reaction barrier and forms HAHB and HC
|[[File:Sjl1218-ani3.png|200px]]
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.1</nowiki>
|<nowiki>-357.277</nowiki>
|No
|HB-HC collides with HA and enters a temporary transition state but insufficient kinetic energy does not allow a reaction to occur. Atoms return to their starting positions.
|[[File:Sjl1218-ani4.png|200px]]
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.6</nowiki>
|<nowiki>-349.477</nowiki>
|Yes
|HB-HC collides with HA with just enough kinetic energy to overcome the potential energy between HB-HC for the reaction to occur.
|[[File:Sjl1218-ani5.png|200px]]
|}

MRD:sjl1218

2020-05-08T07:55:18Z

Sjl1218: /* Reactive and Unreactive Trajectories */

==Reaction Involving 3 Atoms: HA+HB-HC -> HA-HB+HC==

[[File:sjl1218-reactionscheme.png|500px|center|thumb|Initial Conditions of Reaction Involving 3 Atoms: HA+HB-HC -> HA-HB+HC]]

===Dynamics of the Transition State Region===
====The Transition State====
[[File:Sjl1218-pesurface.PNG|300px|right|thumb|center|Potential Energy Surface Diagram of HA+HB-HC -> HA-HB+HC]]
In a potential energy surface diagram, the reaction pathway (black line) proceeds along the minimum energy path linked by the reactants and products. The transition state is the PES diagram saddle point defined mathematically by ∂V(ri)/∂ri=0.

The transition state location can be identified if V(rAB)/∂rAB=0 and V(rBC)/∂rBC=0. This point can be distinguished from the local minima if the outcome of taking the partial second derivative of potential energy with respect to either rAB or rBC is 0.

====Locating the Transition State====

Since the H2 + H1 surface is symmetric, the transition state must have rAB=rBC. The location of the transition state position rts can be estimated when ∂V(ri)/∂ri=0 and there will be minimal oscillation among the 3 atoms as there is no force acting along rAB and rBC.

[[File:Sjl1218-4.PNG|400px|center|thumb|Model for when rAB=rBC and pAB=pBC=0]]

The transition state position rts is estimated as 91 pm. The internuclear distances vs time graph for rAB=rBC=91pm shows a 'flat' line, meaning no forces are acting at this position.

[[File:Sjl1218-ts.PNG|300px|center|thumb|Internuclear Distances vs Time Graph for rAB=rBC=91pm and pAB=pBC=0]]

====Calculating the reaction path====

The reaction path or minimum energy path is an infinitely slow trajectory (momenta and velocities resets to zero in each time step) obtained after locating the transition state position.

The minimum energy path initially shows a short horizontal line of the atoms entering the transition state position followed by the decreasing rate of atoms HA-HC and HB-HC increasing in distance. Atoms HA-HB forms a bond and remains constant in distance.

Even though the MEP outlines a reaction, it does not take into account the mass and inertia of the atoms, therefore does not provide the realistic picture of the reaction.
The MEP and dynamic trajectory differs in that the realistic trajectory shows oscillations (potential energy interactions) between atoms. At first the 3 atoms are in the transition state positions, showed by the horiontal lines. The trajectory then shows a linear increase in HA-HC and HB-HC distances and HA-HB oscillates about the same position.
[[File:Sjl1218-mep.PNG|300px|center|thumb|Minimum Energy Path (rBC=rts+1 pm, rAB=rts and pBC=pAB=0 g.mol-1.pm.fs-1)]]
[[File:Sjl1218-traj.PNG|300px|center|thumb|Dynamic Trajectory (rBC=rts+1 pm, rAB=rts and pBC=pAB=0 g.mol-1.pm.fs-1)]]

===Reactive and Unreactive Trajectories===
{| 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
|
|[[File:Sjl1218-ani1.png|200px]]
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-4.1</nowiki>
|<nowiki>-420.077</nowiki>
|No
|
|[[File:Sjl1218-ani2.png|200px]]
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-5.1</nowiki>
|<nowiki>-413.977</nowiki>
|Yes
|
|[[File:Sjl1218-ani3.png|200px]]
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.1</nowiki>
|<nowiki>-357.277</nowiki>
|No
|
|[[File:Sjl1218-ani4.png|200px]]
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.6</nowiki>
|<nowiki>-349.477</nowiki>
|Yes
|
|[[File:Sjl1218-ani5.png|200px]]
|}

MRD:sjl1218

2020-05-08T05:45:15Z

Sjl1218: /* Reactive and Unreactive Trajectories */

==Reaction Involving 3 Atoms: HA+HB-HC -> HA-HB+HC==

[[File:sjl1218-reactionscheme.png|500px|center|thumb|Initial Conditions of Reaction Involving 3 Atoms: HA+HB-HC -> HA-HB+HC]]

===Dynamics of the Transition State Region===
====The Transition State====
[[File:Sjl1218-pesurface.PNG|300px|right|thumb|center|Potential Energy Surface Diagram of HA+HB-HC -> HA-HB+HC]]
In a potential energy surface diagram, the reaction pathway (black line) proceeds along the minimum energy path linked by the reactants and products. The transition state is the PES diagram saddle point defined mathematically by ∂V(ri)/∂ri=0.

The transition state location can be identified if V(rAB)/∂rAB=0 and V(rBC)/∂rBC=0. This point can be distinguished from the local minima if the outcome of taking the partial second derivative of potential energy with respect to either rAB or rBC is 0.

====Locating the Transition State====

Since the H2 + H1 surface is symmetric, the transition state must have rAB=rBC. The location of the transition state position rts can be estimated when ∂V(ri)/∂ri=0 and there will be minimal oscillation among the 3 atoms as there is no force acting along rAB and rBC.

[[File:Sjl1218-4.PNG|400px|center|thumb|Model for when rAB=rBC and pAB=pBC=0]]

The transition state position rts is estimated as 91 pm. The internuclear distances vs time graph for rAB=rBC=91pm shows a 'flat' line, meaning no forces are acting at this position.

[[File:Sjl1218-ts.PNG|300px|center|thumb|Internuclear Distances vs Time Graph for rAB=rBC=91pm and pAB=pBC=0]]

====Calculating the reaction path====

The reaction path or minimum energy path is an infinitely slow trajectory (momenta and velocities resets to zero in each time step) obtained after locating the transition state position.

The minimum energy path initially shows a short horizontal line of the atoms entering the transition state position followed by the decreasing rate of atoms HA-HC and HB-HC increasing in distance. Atoms HA-HB forms a bond and remains constant in distance.

Even though the MEP outlines a reaction, it does not take into account the mass and inertia of the atoms, therefore does not provide the realistic picture of the reaction.
The MEP and dynamic trajectory differs in that the realistic trajectory shows oscillations (potential energy interactions) between atoms. At first the 3 atoms are in the transition state positions, showed by the horiontal lines. The trajectory then shows a linear increase in HA-HC and HB-HC distances and HA-HB oscillates about the same position.
[[File:Sjl1218-mep.PNG|300px|center|thumb|Minimum Energy Path (rBC=rts+1 pm, rAB=rts and pBC=pAB=0 g.mol-1.pm.fs-1)]]
[[File:Sjl1218-traj.PNG|300px|center|thumb|Dynamic Trajectory (rBC=rts+1 pm, rAB=rts and pBC=pAB=0 g.mol-1.pm.fs-1)]]

===Reactive and Unreactive Trajectories===
{| 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>
|
|
|[[File:Sjl1218-ani1.png|200px]]
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-4.1</nowiki>
|<nowiki>-420.077</nowiki>
|
|
|[[File:Sjl1218-ani2.png|200px]]
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-5.1</nowiki>
|<nowiki>-413.977</nowiki>
|
|
|[[File:Sjl1218-ani3.png|200px]]
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.1</nowiki>
|<nowiki>-357.277</nowiki>
|
|
|[[File:Sjl1218-ani4.png|200px]]
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.6</nowiki>
|<nowiki>-349.477</nowiki>
|
|
|[[File:Sjl1218-ani5.png|200px]]
|}

MRD:sjl1218

2020-05-08T05:07:39Z

Sjl1218: /* Reactive and Unreactive Trajectories */

==Reaction Involving 3 Atoms: HA+HB-HC -> HA-HB+HC==

[[File:sjl1218-reactionscheme.png|500px|center|thumb|Initial Conditions of Reaction Involving 3 Atoms: HA+HB-HC -> HA-HB+HC]]

===Dynamics of the Transition State Region===
====The Transition State====
[[File:Sjl1218-pesurface.PNG|300px|right|thumb|center|Potential Energy Surface Diagram of HA+HB-HC -> HA-HB+HC]]
In a potential energy surface diagram, the reaction pathway (black line) proceeds along the minimum energy path linked by the reactants and products. The transition state is the PES diagram saddle point defined mathematically by ∂V(ri)/∂ri=0.

The transition state location can be identified if V(rAB)/∂rAB=0 and V(rBC)/∂rBC=0. This point can be distinguished from the local minima if the outcome of taking the partial second derivative of potential energy with respect to either rAB or rBC is 0.

====Locating the Transition State====

Since the H2 + H1 surface is symmetric, the transition state must have rAB=rBC. The location of the transition state position rts can be estimated when ∂V(ri)/∂ri=0 and there will be minimal oscillation among the 3 atoms as there is no force acting along rAB and rBC.

[[File:Sjl1218-4.PNG|400px|center|thumb|Model for when rAB=rBC and pAB=pBC=0]]

The transition state position rts is estimated as 91 pm. The internuclear distances vs time graph for rAB=rBC=91pm shows a 'flat' line, meaning no forces are acting at this position.

[[File:Sjl1218-ts.PNG|300px|center|thumb|Internuclear Distances vs Time Graph for rAB=rBC=91pm and pAB=pBC=0]]

====Calculating the reaction path====

The reaction path or minimum energy path is an infinitely slow trajectory (momenta and velocities resets to zero in each time step) obtained after locating the transition state position.

The minimum energy path initially shows a short horizontal line of the atoms entering the transition state position followed by the decreasing rate of atoms HA-HC and HB-HC increasing in distance. Atoms HA-HB forms a bond and remains constant in distance.

Even though the MEP outlines a reaction, it does not take into account the mass and inertia of the atoms, therefore does not provide the realistic picture of the reaction.
The MEP and dynamic trajectory differs in that the realistic trajectory shows oscillations (potential energy interactions) between atoms. At first the 3 atoms are in the transition state positions, showed by the horiontal lines. The trajectory then shows a linear increase in HA-HC and HB-HC distances and HA-HB oscillates about the same position.
[[File:Sjl1218-mep.PNG|300px|center|thumb|Minimum Energy Path (rBC=rts+1 pm, rAB=rts and pBC=pAB=0 g.mol-1.pm.fs-1)]]
[[File:Sjl1218-traj.PNG|300px|center|thumb|Dynamic Trajectory (rBC=rts+1 pm, rAB=rts and pBC=pAB=0 g.mol-1.pm.fs-1)]]

===Reactive and Unreactive Trajectories===
{| 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>
|
|
|
|[[File:Sjl1218-ani1.png|200px]]
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-4.1</nowiki>
|
|
|
|[[File:Sjl1218-ani2.png|200px]]
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-5.1</nowiki>
|
|
|
|[[File:Sjl1218-ani3.png|200px]]
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.1</nowiki>
|
|
|
|[[File:Sjl1218-ani4.png|200px]]
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.6</nowiki>
|
|
|
|[[File:Sjl1218-ani5.png|200px]]
|}

MRD:sjl1218

2020-05-08T05:03:54Z

Sjl1218: /* Reactive and Unreactive Trajectories */

==Reaction Involving 3 Atoms: HA+HB-HC -> HA-HB+HC==

[[File:sjl1218-reactionscheme.png|500px|center|thumb|Initial Conditions of Reaction Involving 3 Atoms: HA+HB-HC -> HA-HB+HC]]

===Dynamics of the Transition State Region===
====The Transition State====
[[File:Sjl1218-pesurface.PNG|300px|right|thumb|center|Potential Energy Surface Diagram of HA+HB-HC -> HA-HB+HC]]
In a potential energy surface diagram, the reaction pathway (black line) proceeds along the minimum energy path linked by the reactants and products. The transition state is the PES diagram saddle point defined mathematically by ∂V(ri)/∂ri=0.

The transition state location can be identified if V(rAB)/∂rAB=0 and V(rBC)/∂rBC=0. This point can be distinguished from the local minima if the outcome of taking the partial second derivative of potential energy with respect to either rAB or rBC is 0.

====Locating the Transition State====

Since the H2 + H1 surface is symmetric, the transition state must have rAB=rBC. The location of the transition state position rts can be estimated when ∂V(ri)/∂ri=0 and there will be minimal oscillation among the 3 atoms as there is no force acting along rAB and rBC.

[[File:Sjl1218-4.PNG|400px|center|thumb|Model for when rAB=rBC and pAB=pBC=0]]

The transition state position rts is estimated as 91 pm. The internuclear distances vs time graph for rAB=rBC=91pm shows a 'flat' line, meaning no forces are acting at this position.

[[File:Sjl1218-ts.PNG|300px|center|thumb|Internuclear Distances vs Time Graph for rAB=rBC=91pm and pAB=pBC=0]]

====Calculating the reaction path====

The reaction path or minimum energy path is an infinitely slow trajectory (momenta and velocities resets to zero in each time step) obtained after locating the transition state position.

The minimum energy path initially shows a short horizontal line of the atoms entering the transition state position followed by the decreasing rate of atoms HA-HC and HB-HC increasing in distance. Atoms HA-HB forms a bond and remains constant in distance.

Even though the MEP outlines a reaction, it does not take into account the mass and inertia of the atoms, therefore does not provide the realistic picture of the reaction.
The MEP and dynamic trajectory differs in that the realistic trajectory shows oscillations (potential energy interactions) between atoms. At first the 3 atoms are in the transition state positions, showed by the horiontal lines. The trajectory then shows a linear increase in HA-HC and HB-HC distances and HA-HB oscillates about the same position.
[[File:Sjl1218-mep.PNG|300px|center|thumb|Minimum Energy Path (rBC=rts+1 pm, rAB=rts and pBC=pAB=0 g.mol-1.pm.fs-1)]]
[[File:Sjl1218-traj.PNG|300px|center|thumb|Dynamic Trajectory (rBC=rts+1 pm, rAB=rts and pBC=pAB=0 g.mol-1.pm.fs-1)]]

===Reactive and Unreactive Trajectories===
{| 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>
|
|
|
|[[File:Sjl1218-ani1.png|200px]]
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-4.1</nowiki>
|
|
|
|
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-5.1</nowiki>
|
|
|
|
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.1</nowiki>
|
|
|
|
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.6</nowiki>
|
|
|
|
|}

[[File:Sjl1218-ani3.PNG|200px]]
[[File:Sjl1218-ani5.png]]

MRD:sjl1218

2020-05-08T05:03:12Z

Sjl1218: /* Reactive and Unreactive Trajectories */

==Reaction Involving 3 Atoms: HA+HB-HC -> HA-HB+HC==

[[File:sjl1218-reactionscheme.png|500px|center|thumb|Initial Conditions of Reaction Involving 3 Atoms: HA+HB-HC -> HA-HB+HC]]

===Dynamics of the Transition State Region===
====The Transition State====
[[File:Sjl1218-pesurface.PNG|300px|right|thumb|center|Potential Energy Surface Diagram of HA+HB-HC -> HA-HB+HC]]
In a potential energy surface diagram, the reaction pathway (black line) proceeds along the minimum energy path linked by the reactants and products. The transition state is the PES diagram saddle point defined mathematically by ∂V(ri)/∂ri=0.

The transition state location can be identified if V(rAB)/∂rAB=0 and V(rBC)/∂rBC=0. This point can be distinguished from the local minima if the outcome of taking the partial second derivative of potential energy with respect to either rAB or rBC is 0.

====Locating the Transition State====

Since the H2 + H1 surface is symmetric, the transition state must have rAB=rBC. The location of the transition state position rts can be estimated when ∂V(ri)/∂ri=0 and there will be minimal oscillation among the 3 atoms as there is no force acting along rAB and rBC.

[[File:Sjl1218-4.PNG|400px|center|thumb|Model for when rAB=rBC and pAB=pBC=0]]

The transition state position rts is estimated as 91 pm. The internuclear distances vs time graph for rAB=rBC=91pm shows a 'flat' line, meaning no forces are acting at this position.

[[File:Sjl1218-ts.PNG|300px|center|thumb|Internuclear Distances vs Time Graph for rAB=rBC=91pm and pAB=pBC=0]]

====Calculating the reaction path====

The reaction path or minimum energy path is an infinitely slow trajectory (momenta and velocities resets to zero in each time step) obtained after locating the transition state position.

The minimum energy path initially shows a short horizontal line of the atoms entering the transition state position followed by the decreasing rate of atoms HA-HC and HB-HC increasing in distance. Atoms HA-HB forms a bond and remains constant in distance.

Even though the MEP outlines a reaction, it does not take into account the mass and inertia of the atoms, therefore does not provide the realistic picture of the reaction.
The MEP and dynamic trajectory differs in that the realistic trajectory shows oscillations (potential energy interactions) between atoms. At first the 3 atoms are in the transition state positions, showed by the horiontal lines. The trajectory then shows a linear increase in HA-HC and HB-HC distances and HA-HB oscillates about the same position.
[[File:Sjl1218-mep.PNG|300px|center|thumb|Minimum Energy Path (rBC=rts+1 pm, rAB=rts and pBC=pAB=0 g.mol-1.pm.fs-1)]]
[[File:Sjl1218-traj.PNG|300px|center|thumb|Dynamic Trajectory (rBC=rts+1 pm, rAB=rts and pBC=pAB=0 g.mol-1.pm.fs-1)]]

===Reactive and Unreactive Trajectories===
{| 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>
|
|
|
|[[File:Sjl1218-ani3.PNG|200px]]
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-4.1</nowiki>
|
|
|
|
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-5.1</nowiki>
|
|
|
|
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.1</nowiki>
|
|
|
|
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.6</nowiki>
|
|
|
|
|}

[[File:Sjl1218-ani3.PNG|200px]]
[[File:Sjl1218-ani5.png]]

MRD:sjl1218

2020-05-08T05:02:39Z

Sjl1218: /* Reactive and Unreactive Trajectories */

==Reaction Involving 3 Atoms: HA+HB-HC -> HA-HB+HC==

[[File:sjl1218-reactionscheme.png|500px|center|thumb|Initial Conditions of Reaction Involving 3 Atoms: HA+HB-HC -> HA-HB+HC]]

===Dynamics of the Transition State Region===
====The Transition State====
[[File:Sjl1218-pesurface.PNG|300px|right|thumb|center|Potential Energy Surface Diagram of HA+HB-HC -> HA-HB+HC]]
In a potential energy surface diagram, the reaction pathway (black line) proceeds along the minimum energy path linked by the reactants and products. The transition state is the PES diagram saddle point defined mathematically by ∂V(ri)/∂ri=0.

The transition state location can be identified if V(rAB)/∂rAB=0 and V(rBC)/∂rBC=0. This point can be distinguished from the local minima if the outcome of taking the partial second derivative of potential energy with respect to either rAB or rBC is 0.

====Locating the Transition State====

Since the H2 + H1 surface is symmetric, the transition state must have rAB=rBC. The location of the transition state position rts can be estimated when ∂V(ri)/∂ri=0 and there will be minimal oscillation among the 3 atoms as there is no force acting along rAB and rBC.

[[File:Sjl1218-4.PNG|400px|center|thumb|Model for when rAB=rBC and pAB=pBC=0]]

The transition state position rts is estimated as 91 pm. The internuclear distances vs time graph for rAB=rBC=91pm shows a 'flat' line, meaning no forces are acting at this position.

[[File:Sjl1218-ts.PNG|300px|center|thumb|Internuclear Distances vs Time Graph for rAB=rBC=91pm and pAB=pBC=0]]

====Calculating the reaction path====

The reaction path or minimum energy path is an infinitely slow trajectory (momenta and velocities resets to zero in each time step) obtained after locating the transition state position.

The minimum energy path initially shows a short horizontal line of the atoms entering the transition state position followed by the decreasing rate of atoms HA-HC and HB-HC increasing in distance. Atoms HA-HB forms a bond and remains constant in distance.

Even though the MEP outlines a reaction, it does not take into account the mass and inertia of the atoms, therefore does not provide the realistic picture of the reaction.
The MEP and dynamic trajectory differs in that the realistic trajectory shows oscillations (potential energy interactions) between atoms. At first the 3 atoms are in the transition state positions, showed by the horiontal lines. The trajectory then shows a linear increase in HA-HC and HB-HC distances and HA-HB oscillates about the same position.
[[File:Sjl1218-mep.PNG|300px|center|thumb|Minimum Energy Path (rBC=rts+1 pm, rAB=rts and pBC=pAB=0 g.mol-1.pm.fs-1)]]
[[File:Sjl1218-traj.PNG|300px|center|thumb|Dynamic Trajectory (rBC=rts+1 pm, rAB=rts and pBC=pAB=0 g.mol-1.pm.fs-1)]]

===Reactive and Unreactive Trajectories===
{| 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>
|
|
|
|[[File:Sjl1218-ani3.PNG|200px]]
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-4.1</nowiki>
|
|
|
|
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-5.1</nowiki>
|
|
|
|
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.1</nowiki>
|
|
|
|
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.6</nowiki>
|
|
|
|
|}

[[File:Sjl1218-ani3.PNG|200px]]

MRD:sjl1218

2020-05-08T05:02:24Z

Sjl1218: /* Reactive and Unreactive Trajectories */

==Reaction Involving 3 Atoms: HA+HB-HC -> HA-HB+HC==

[[File:sjl1218-reactionscheme.png|500px|center|thumb|Initial Conditions of Reaction Involving 3 Atoms: HA+HB-HC -> HA-HB+HC]]

===Dynamics of the Transition State Region===
====The Transition State====
[[File:Sjl1218-pesurface.PNG|300px|right|thumb|center|Potential Energy Surface Diagram of HA+HB-HC -> HA-HB+HC]]
In a potential energy surface diagram, the reaction pathway (black line) proceeds along the minimum energy path linked by the reactants and products. The transition state is the PES diagram saddle point defined mathematically by ∂V(ri)/∂ri=0.

The transition state location can be identified if V(rAB)/∂rAB=0 and V(rBC)/∂rBC=0. This point can be distinguished from the local minima if the outcome of taking the partial second derivative of potential energy with respect to either rAB or rBC is 0.

====Locating the Transition State====

Since the H2 + H1 surface is symmetric, the transition state must have rAB=rBC. The location of the transition state position rts can be estimated when ∂V(ri)/∂ri=0 and there will be minimal oscillation among the 3 atoms as there is no force acting along rAB and rBC.

[[File:Sjl1218-4.PNG|400px|center|thumb|Model for when rAB=rBC and pAB=pBC=0]]

The transition state position rts is estimated as 91 pm. The internuclear distances vs time graph for rAB=rBC=91pm shows a 'flat' line, meaning no forces are acting at this position.

[[File:Sjl1218-ts.PNG|300px|center|thumb|Internuclear Distances vs Time Graph for rAB=rBC=91pm and pAB=pBC=0]]

====Calculating the reaction path====

The reaction path or minimum energy path is an infinitely slow trajectory (momenta and velocities resets to zero in each time step) obtained after locating the transition state position.

The minimum energy path initially shows a short horizontal line of the atoms entering the transition state position followed by the decreasing rate of atoms HA-HC and HB-HC increasing in distance. Atoms HA-HB forms a bond and remains constant in distance.

Even though the MEP outlines a reaction, it does not take into account the mass and inertia of the atoms, therefore does not provide the realistic picture of the reaction.
The MEP and dynamic trajectory differs in that the realistic trajectory shows oscillations (potential energy interactions) between atoms. At first the 3 atoms are in the transition state positions, showed by the horiontal lines. The trajectory then shows a linear increase in HA-HC and HB-HC distances and HA-HB oscillates about the same position.
[[File:Sjl1218-mep.PNG|300px|center|thumb|Minimum Energy Path (rBC=rts+1 pm, rAB=rts and pBC=pAB=0 g.mol-1.pm.fs-1)]]
[[File:Sjl1218-traj.PNG|300px|center|thumb|Dynamic Trajectory (rBC=rts+1 pm, rAB=rts and pBC=pAB=0 g.mol-1.pm.fs-1)]]

===Reactive and Unreactive Trajectories===
{| 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>
|
|
|
|[[File:Sjl1218-ani3.PNG|200px]]
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-4.1</nowiki>
|
|
|
|
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-5.1</nowiki>
|
|
|
|
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.1</nowiki>
|
|
|
|
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.6</nowiki>
|
|
|
|
|}

MRD:sjl1218

2020-05-08T05:01:55Z

Sjl1218: /* Reactive and Unreactive Trajectories */

==Reaction Involving 3 Atoms: HA+HB-HC -> HA-HB+HC==

[[File:sjl1218-reactionscheme.png|500px|center|thumb|Initial Conditions of Reaction Involving 3 Atoms: HA+HB-HC -> HA-HB+HC]]

===Dynamics of the Transition State Region===
====The Transition State====
[[File:Sjl1218-pesurface.PNG|300px|right|thumb|center|Potential Energy Surface Diagram of HA+HB-HC -> HA-HB+HC]]
In a potential energy surface diagram, the reaction pathway (black line) proceeds along the minimum energy path linked by the reactants and products. The transition state is the PES diagram saddle point defined mathematically by ∂V(ri)/∂ri=0.

The transition state location can be identified if V(rAB)/∂rAB=0 and V(rBC)/∂rBC=0. This point can be distinguished from the local minima if the outcome of taking the partial second derivative of potential energy with respect to either rAB or rBC is 0.

====Locating the Transition State====

Since the H2 + H1 surface is symmetric, the transition state must have rAB=rBC. The location of the transition state position rts can be estimated when ∂V(ri)/∂ri=0 and there will be minimal oscillation among the 3 atoms as there is no force acting along rAB and rBC.

[[File:Sjl1218-4.PNG|400px|center|thumb|Model for when rAB=rBC and pAB=pBC=0]]

The transition state position rts is estimated as 91 pm. The internuclear distances vs time graph for rAB=rBC=91pm shows a 'flat' line, meaning no forces are acting at this position.

[[File:Sjl1218-ts.PNG|300px|center|thumb|Internuclear Distances vs Time Graph for rAB=rBC=91pm and pAB=pBC=0]]

====Calculating the reaction path====

The reaction path or minimum energy path is an infinitely slow trajectory (momenta and velocities resets to zero in each time step) obtained after locating the transition state position.

The minimum energy path initially shows a short horizontal line of the atoms entering the transition state position followed by the decreasing rate of atoms HA-HC and HB-HC increasing in distance. Atoms HA-HB forms a bond and remains constant in distance.

Even though the MEP outlines a reaction, it does not take into account the mass and inertia of the atoms, therefore does not provide the realistic picture of the reaction.
The MEP and dynamic trajectory differs in that the realistic trajectory shows oscillations (potential energy interactions) between atoms. At first the 3 atoms are in the transition state positions, showed by the horiontal lines. The trajectory then shows a linear increase in HA-HC and HB-HC distances and HA-HB oscillates about the same position.
[[File:Sjl1218-mep.PNG|300px|center|thumb|Minimum Energy Path (rBC=rts+1 pm, rAB=rts and pBC=pAB=0 g.mol-1.pm.fs-1)]]
[[File:Sjl1218-traj.PNG|300px|center|thumb|Dynamic Trajectory (rBC=rts+1 pm, rAB=rts and pBC=pAB=0 g.mol-1.pm.fs-1)]]

===Reactive and Unreactive Trajectories===
{| 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>
|
|
|
|[[File:Sjl1218-ani1.PNG|200px]]
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-4.1</nowiki>
|
|
|
|
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-5.1</nowiki>
|
|
|
|
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.1</nowiki>
|
|
|
|
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.6</nowiki>
|
|
|
|
|}

File:Sjl1218-ani5.png

2020-05-08T05:01:21Z

Sjl1218:

File:Sjl1218-ani4.png

2020-05-08T05:01:11Z

Sjl1218:

File:Sjl1218-ani3.png

2020-05-08T05:01:01Z

Sjl1218:

File:Sjl1218-ani2.png

2020-05-08T05:00:51Z

Sjl1218:

File:Sjl1218-ani1.png

2020-05-08T05:00:40Z

Sjl1218:

MRD:sjl1218

2020-05-08T04:56:56Z

Sjl1218: /* Reactive and Unreactive Trajectories */

==Reaction Involving 3 Atoms: HA+HB-HC -> HA-HB+HC==

[[File:sjl1218-reactionscheme.png|500px|center|thumb|Initial Conditions of Reaction Involving 3 Atoms: HA+HB-HC -> HA-HB+HC]]

===Dynamics of the Transition State Region===
====The Transition State====
[[File:Sjl1218-pesurface.PNG|300px|right|thumb|center|Potential Energy Surface Diagram of HA+HB-HC -> HA-HB+HC]]
In a potential energy surface diagram, the reaction pathway (black line) proceeds along the minimum energy path linked by the reactants and products. The transition state is the PES diagram saddle point defined mathematically by ∂V(ri)/∂ri=0.

The transition state location can be identified if V(rAB)/∂rAB=0 and V(rBC)/∂rBC=0. This point can be distinguished from the local minima if the outcome of taking the partial second derivative of potential energy with respect to either rAB or rBC is 0.

====Locating the Transition State====

Since the H2 + H1 surface is symmetric, the transition state must have rAB=rBC. The location of the transition state position rts can be estimated when ∂V(ri)/∂ri=0 and there will be minimal oscillation among the 3 atoms as there is no force acting along rAB and rBC.

[[File:Sjl1218-4.PNG|400px|center|thumb|Model for when rAB=rBC and pAB=pBC=0]]

The transition state position rts is estimated as 91 pm. The internuclear distances vs time graph for rAB=rBC=91pm shows a 'flat' line, meaning no forces are acting at this position.

[[File:Sjl1218-ts.PNG|300px|center|thumb|Internuclear Distances vs Time Graph for rAB=rBC=91pm and pAB=pBC=0]]

====Calculating the reaction path====

The reaction path or minimum energy path is an infinitely slow trajectory (momenta and velocities resets to zero in each time step) obtained after locating the transition state position.

The minimum energy path initially shows a short horizontal line of the atoms entering the transition state position followed by the decreasing rate of atoms HA-HC and HB-HC increasing in distance. Atoms HA-HB forms a bond and remains constant in distance.

Even though the MEP outlines a reaction, it does not take into account the mass and inertia of the atoms, therefore does not provide the realistic picture of the reaction.
The MEP and dynamic trajectory differs in that the realistic trajectory shows oscillations (potential energy interactions) between atoms. At first the 3 atoms are in the transition state positions, showed by the horiontal lines. The trajectory then shows a linear increase in HA-HC and HB-HC distances and HA-HB oscillates about the same position.
[[File:Sjl1218-mep.PNG|300px|center|thumb|Minimum Energy Path (rBC=rts+1 pm, rAB=rts and pBC=pAB=0 g.mol-1.pm.fs-1)]]
[[File:Sjl1218-traj.PNG|300px|center|thumb|Dynamic Trajectory (rBC=rts+1 pm, rAB=rts and pBC=pAB=0 g.mol-1.pm.fs-1)]]

===Reactive and Unreactive Trajectories===
{| 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>-3.1</nowiki>
|<nowiki>-4.1</nowiki>
|
|
|
|
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-5.1</nowiki>
|
|
|
|
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.1</nowiki>
|
|
|
|
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.6</nowiki>
|
|
|
|
|}

MRD:sjl1218

2020-05-08T04:54:40Z

Sjl1218: /* Calculating the reaction path */