File:RCR16 18.png

2018-05-17T14:53:05Z

Rcr16:

2018-05-17T13:06:05Z

Rcr16: /* Trajectories from r1 = r2: locating the transition state */

== EXERCISE 1: H + H2 system ==

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

{{fontcolor|blue|The partial derivative of V with respect to r1 and r2 must be 0 at local extremum point. To determine whether this point is a minimum, maximum or a saddle point(transition state), the second partial derivatives test can be used. The second derivative test discriminant D is calculated from the second order derivatives of the potential energy surface with respect to r1, r2 and both r1 and r2. If D is higher than 0 and the second order derivative with respect to r1 is higher than 0, the point is a minimum. If D is smaller than 0, then it is a saddle point.}}

==== Trajectories from r1 = r2: locating the transition state ====

{{fontcolor|blue|The transition state distance has been estimated to be around 0.908 Å for both A-B and B-C distances. This is easily seen in the internuclear distance vs time plot, where the A-B and B-C distance lines overlap completely and show a very slight oscillation, as can be seen in Figure 1.}}

[[File:RCR16_2x.png|thumb|center|Figure 1:Internuclear distance vs time plot for transition state]]

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

{{fontcolor|blue|The mep line towards the products is quite straight, whereas the dynamic trajectory has a sinusoidal aspect. The mep line, in other words, shows the potential energy with the oscillation term completely removed while the dynamic trajectory accounts for bond oscillation. This can be seen in Figure 2 and 3.}}

[[File:RCR16_3.png|thumb|left|Figure 2: MEP contour plot]][[File:RCR16_4.png|thumb|center|Figure 3: Dynamics contour plot]]

==== Reactive and unreactive trajectories ====

{| class="wikitable" border=1
! p1 !! p2 !! Total Energy(kcal/mol) !! Plot !! Reactive/Unreactive
|-
| -1.25 || -2.5 || -99.018 || [[File:RCR16_5.png|thumb]] || Reactive - initial trajectory is linear so molecule doesn't oscillate before collision.
|-
| -1.5 || -2.0 || -100.456 || [[File:RCR16_6.png|thumb]] || Unreactive - system does not have sufficient energy to reach the activation barrier and oscillates back.
|-
| -1.5 || -2.5 || -98.956 || [[File:RCR16_7.png|thumb]] || Reactive - oscillating initial trajectory proves the H-H bond starts deforming before the attack of the other atom.
|-
| -2.5 || -5.0 || -84.956 || [[File:RCR16_8.png|thumb]] || Unreactive - the 3 atom complex oscillates around the transition state and crosses the barrier but ultimately turns back to reactants.
|-
| -2.5 || -5.2 || -83.416 || [[File:RCR16_9.png|thumb]] || Reactive - the small additional momentum gives the complex enough energy now to cross to products.
|}

{{fontcolor|blue|Transition state theory has 3 main assumptions stated slightly differently in different sources:
1. The transition state is in quasi-equilibrium with the reactants but not the products.
2. The particles involved follow Boltzmann's distribution and obey classical mechanics.
3. Once the reactants reach the minimum energy saddle point, the transition state does not collapse back to reactants.
The simulations that have been made prove that barrier recrossing is possible: the activated complex would have enough energy to turn into products, but not all collisions with good energy will result in a successful reaction since the transition state is not in equilibrium with the reactants. Tunneling in low activation barrier systems is not accounted for either in the transition state theory, but it is difficult to predict its influence on the simulations made. Considering these factors, experimental rates should be usually slower than the ones predicted by theory. }}

== EXERCISE 2: F - H - H system ==

===PES inspection===

{{fontcolor1|blue| The F + H2 reaction is exothermic while the H + HF reaction is endothermic, since the H-F bond dissociation energy(565 kJ/mol) is higher compared to the H-H one(432 kJ/mol), meaning that HF has a stronger bond and is more stable. }}

{{fontcolor1|blue| Following Hammond's postulate, the transition state will be closer in structure to the F+ H-H system rather than F-H + H system since it is higher in energy. Thus, by testing different F-H distances while the H-H distance is kept approximately at equilibrium, a stable transition state has been found at r(H-H) of 0.745 Å and r(F-H) of 1.8115 Å, and its total energy is -103.752 kcal/mol. Figure 4 indicates the stability of these coordinates.}}
[[File:RCR16_10.png|thumb|center|Figure 4: Internuclear distance vs time plot for F H H transition state]]

File:RCR16 2x.png

2018-05-17T13:05:22Z

Rcr16: x

MRD:RCR16

2018-05-17T12:46:54Z

Rcr16: /* EXERCISE 2: F - H - H system */

== EXERCISE 1: H + H2 system ==

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

{{fontcolor|blue|The partial derivative of V with respect to r1 and r2 must be 0 at local extremum point. To determine whether this point is a minimum, maximum or a saddle point(transition state), the second partial derivatives test can be used. The second derivative test discriminant D is calculated from the second order derivatives of the potential energy surface with respect to r1, r2 and both r1 and r2. If D is higher than 0 and the second order derivative with respect to r1 is higher than 0, the point is a minimum. If D is smaller than 0, then it is a saddle point.}}

==== Trajectories from r1 = r2: locating the transition state ====

{{fontcolor|blue|The transition state distance has been estimated to be around 0.907 Å for both A-B and B-C distances. This is easily seen in the internuclear distance vs time plot, where the A-B and B-C distance lines overlap completely and show a very slight oscillation, as can be seen in Figure 1.}}

[[File:RCR16_2.png|thumb|center|Figure 1:Internuclear distance vs time plot for transition state]]

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

{{fontcolor|blue|The mep line towards the products is quite straight, whereas the dynamic trajectory has a sinusoidal aspect. The mep line, in other words, shows the potential energy with the oscillation term completely removed while the dynamic trajectory accounts for bond oscillation. This can be seen in Figure 2 and 3.}}

[[File:RCR16_3.png|thumb|left|Figure 2: MEP contour plot]][[File:RCR16_4.png|thumb|center|Figure 3: Dynamics contour plot]]

==== Reactive and unreactive trajectories ====

{| class="wikitable" border=1
! p1 !! p2 !! Total Energy(kcal/mol) !! Plot !! Reactive/Unreactive
|-
| -1.25 || -2.5 || -99.018 || [[File:RCR16_5.png|thumb]] || Reactive - initial trajectory is linear so molecule doesn't oscillate before collision.
|-
| -1.5 || -2.0 || -100.456 || [[File:RCR16_6.png|thumb]] || Unreactive - system does not have sufficient energy to reach the activation barrier and oscillates back.
|-
| -1.5 || -2.5 || -98.956 || [[File:RCR16_7.png|thumb]] || Reactive - oscillating initial trajectory proves the H-H bond starts deforming before the attack of the other atom.
|-
| -2.5 || -5.0 || -84.956 || [[File:RCR16_8.png|thumb]] || Unreactive - the 3 atom complex oscillates around the transition state and crosses the barrier but ultimately turns back to reactants.
|-
| -2.5 || -5.2 || -83.416 || [[File:RCR16_9.png|thumb]] || Reactive - the small additional momentum gives the complex enough energy now to cross to products.
|}

{{fontcolor|blue|Transition state theory has 3 main assumptions stated slightly differently in different sources:
1. The transition state is in quasi-equilibrium with the reactants but not the products.
2. The particles involved follow Boltzmann's distribution and obey classical mechanics.
3. Once the reactants reach the minimum energy saddle point, the transition state does not collapse back to reactants.
The simulations that have been made prove that barrier recrossing is possible: the activated complex would have enough energy to turn into products, but not all collisions with good energy will result in a successful reaction since the transition state is not in equilibrium with the reactants. Tunneling in low activation barrier systems is not accounted for either in the transition state theory, but it is difficult to predict its influence on the simulations made. Considering these factors, experimental rates should be usually slower than the ones predicted by theory. }}

== EXERCISE 2: F - H - H system ==

===PES inspection===

{{fontcolor1|blue| The F + H2 reaction is exothermic while the H + HF reaction is endothermic, since the H-F bond dissociation energy(565 kJ/mol) is higher compared to the H-H one(432 kJ/mol), meaning that HF has a stronger bond and is more stable. }}

{{fontcolor1|blue| Following Hammond's postulate, the transition state will be closer in structure to the F+ H-H system rather than F-H + H system since it is higher in energy. Thus, by testing different F-H distances while the H-H distance is kept approximately at equilibrium, a stable transition state has been found at r(H-H) of 0.745 Å and r(F-H) of 1.8115 Å, and its total energy is -103.752 kcal/mol. Figure 4 indicates the stability of these coordinates.}}
[[File:RCR16_10.png|thumb|center|Figure 4: Internuclear distance vs time plot for F H H transition state]]

MRD:RCR16

2018-05-17T12:46:43Z

Rcr16: /* EXERCISE 2: F - H - H system */

== EXERCISE 1: H + H2 system ==

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

{{fontcolor|blue|The partial derivative of V with respect to r1 and r2 must be 0 at local extremum point. To determine whether this point is a minimum, maximum or a saddle point(transition state), the second partial derivatives test can be used. The second derivative test discriminant D is calculated from the second order derivatives of the potential energy surface with respect to r1, r2 and both r1 and r2. If D is higher than 0 and the second order derivative with respect to r1 is higher than 0, the point is a minimum. If D is smaller than 0, then it is a saddle point.}}

==== Trajectories from r1 = r2: locating the transition state ====

{{fontcolor|blue|The transition state distance has been estimated to be around 0.907 Å for both A-B and B-C distances. This is easily seen in the internuclear distance vs time plot, where the A-B and B-C distance lines overlap completely and show a very slight oscillation, as can be seen in Figure 1.}}

[[File:RCR16_2.png|thumb|center|Figure 1:Internuclear distance vs time plot for transition state]]

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

{{fontcolor|blue|The mep line towards the products is quite straight, whereas the dynamic trajectory has a sinusoidal aspect. The mep line, in other words, shows the potential energy with the oscillation term completely removed while the dynamic trajectory accounts for bond oscillation. This can be seen in Figure 2 and 3.}}

[[File:RCR16_3.png|thumb|left|Figure 2: MEP contour plot]][[File:RCR16_4.png|thumb|center|Figure 3: Dynamics contour plot]]

==== Reactive and unreactive trajectories ====

{| class="wikitable" border=1
! p1 !! p2 !! Total Energy(kcal/mol) !! Plot !! Reactive/Unreactive
|-
| -1.25 || -2.5 || -99.018 || [[File:RCR16_5.png|thumb]] || Reactive - initial trajectory is linear so molecule doesn't oscillate before collision.
|-
| -1.5 || -2.0 || -100.456 || [[File:RCR16_6.png|thumb]] || Unreactive - system does not have sufficient energy to reach the activation barrier and oscillates back.
|-
| -1.5 || -2.5 || -98.956 || [[File:RCR16_7.png|thumb]] || Reactive - oscillating initial trajectory proves the H-H bond starts deforming before the attack of the other atom.
|-
| -2.5 || -5.0 || -84.956 || [[File:RCR16_8.png|thumb]] || Unreactive - the 3 atom complex oscillates around the transition state and crosses the barrier but ultimately turns back to reactants.
|-
| -2.5 || -5.2 || -83.416 || [[File:RCR16_9.png|thumb]] || Reactive - the small additional momentum gives the complex enough energy now to cross to products.
|}

{{fontcolor|blue|Transition state theory has 3 main assumptions stated slightly differently in different sources:
1. The transition state is in quasi-equilibrium with the reactants but not the products.
2. The particles involved follow Boltzmann's distribution and obey classical mechanics.
3. Once the reactants reach the minimum energy saddle point, the transition state does not collapse back to reactants.
The simulations that have been made prove that barrier recrossing is possible: the activated complex would have enough energy to turn into products, but not all collisions with good energy will result in a successful reaction since the transition state is not in equilibrium with the reactants. Tunneling in low activation barrier systems is not accounted for either in the transition state theory, but it is difficult to predict its influence on the simulations made. Considering these factors, experimental rates should be usually slower than the ones predicted by theory. }}

== EXERCISE 2: F - H - H system ==

===PES inspection===

{{fontcolor1|blue| The F + H2 reaction is exothermic while the H + HF reaction is endothermic, since the H-F bond dissociation energy(565 kJ/mol) is higher compared to the H-H one(432 kJ/mol), meaning that HF has a stronger bond and is more stable. }}

{{fontcolor1|blue| Following Hammond's postulate, the transition state will be closer in structure to the F+ H-H system rather than F-H + H system since it is higher in energy. Thus, by testing different F-H distances while the H-H distance is kept approximately at equilibrium, a stable transition state has been found at r(H-H) of 0.745 Å and r(F-H) of 1.8115 Å, and its total energy is -103.752 kcal/mol. Figure 4 indicates the stability of these coordinates.}}
[[File:RCR16_10.png|thumb|Figure 4: Internuclear distance vs time plot for F H H transition state]]

File:RCR16 10.png

2018-05-17T12:43:19Z

Rcr16:

MRD:RCR16

2018-05-17T12:37:57Z

Rcr16:

== EXERCISE 1: H + H2 system ==

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

{{fontcolor|blue|The partial derivative of V with respect to r1 and r2 must be 0 at local extremum point. To determine whether this point is a minimum, maximum or a saddle point(transition state), the second partial derivatives test can be used. The second derivative test discriminant D is calculated from the second order derivatives of the potential energy surface with respect to r1, r2 and both r1 and r2. If D is higher than 0 and the second order derivative with respect to r1 is higher than 0, the point is a minimum. If D is smaller than 0, then it is a saddle point.}}

==== Trajectories from r1 = r2: locating the transition state ====

{{fontcolor|blue|The transition state distance has been estimated to be around 0.907 Å for both A-B and B-C distances. This is easily seen in the internuclear distance vs time plot, where the A-B and B-C distance lines overlap completely and show a very slight oscillation, as can be seen in Figure 1.}}

[[File:RCR16_2.png|thumb|center|Figure 1:Internuclear distance vs time plot for transition state]]

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

{{fontcolor|blue|The mep line towards the products is quite straight, whereas the dynamic trajectory has a sinusoidal aspect. The mep line, in other words, shows the potential energy with the oscillation term completely removed while the dynamic trajectory accounts for bond oscillation. This can be seen in Figure 2 and 3.}}

[[File:RCR16_3.png|thumb|left|Figure 2: MEP contour plot]][[File:RCR16_4.png|thumb|center|Figure 3: Dynamics contour plot]]

==== Reactive and unreactive trajectories ====

{| class="wikitable" border=1
! p1 !! p2 !! Total Energy(kcal/mol) !! Plot !! Reactive/Unreactive
|-
| -1.25 || -2.5 || -99.018 || [[File:RCR16_5.png|thumb]] || Reactive - initial trajectory is linear so molecule doesn't oscillate before collision.
|-
| -1.5 || -2.0 || -100.456 || [[File:RCR16_6.png|thumb]] || Unreactive - system does not have sufficient energy to reach the activation barrier and oscillates back.
|-
| -1.5 || -2.5 || -98.956 || [[File:RCR16_7.png|thumb]] || Reactive - oscillating initial trajectory proves the H-H bond starts deforming before the attack of the other atom.
|-
| -2.5 || -5.0 || -84.956 || [[File:RCR16_8.png|thumb]] || Unreactive - the 3 atom complex oscillates around the transition state and crosses the barrier but ultimately turns back to reactants.
|-
| -2.5 || -5.2 || -83.416 || [[File:RCR16_9.png|thumb]] || Reactive - the small additional momentum gives the complex enough energy now to cross to products.
|}

{{fontcolor|blue|Transition state theory has 3 main assumptions stated slightly differently in different sources:
1. The transition state is in quasi-equilibrium with the reactants but not the products.
2. The particles involved follow Boltzmann's distribution and obey classical mechanics.
3. Once the reactants reach the minimum energy saddle point, the transition state does not collapse back to reactants.
The simulations that have been made prove that barrier recrossing is possible: the activated complex would have enough energy to turn into products, but not all collisions with good energy will result in a successful reaction since the transition state is not in equilibrium with the reactants. Tunneling in low activation barrier systems is not accounted for either in the transition state theory, but it is difficult to predict its influence on the simulations made. Considering these factors, experimental rates should be usually slower than the ones predicted by theory. }}

== EXERCISE 2: F - H - H system ==

===PES inspection===

{{fontcolor1|blue| The F + H2 reaction is exothermic while the H + HF reaction is endothermic, since the H-F bond dissociation energy(565 kJ/mol) is higher compared to the H-H one(432 kJ/mol), meaning that HF has a stronger bond and is more stable. }}

{{fontcolor1|blue| Following Hammond's postulate, the transition state will be closer in structure to the F+ H-H system rather than F-H + H system since it is higher in energy. Thus, by testing different F-H distances while the H-H distance is kept at equilibrium, a stable transition state has been found at r(H-H) of 0.74 Å and r(F-H) of 1.81355 Å, and its total energy is -103.743 kcal/mol.}}

MRD:RCR16

2018-05-17T12:35:58Z

Rcr16: /* EXERCISE 1: H + H2 system */

== EXERCISE 1: H + H2 system ==

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

{{fontcolor|blue|The partial derivative of V with respect to r1 and r2 must be 0 at local extremum point. To determine whether this point is a minimum, maximum or a saddle point(transition state), the second partial derivatives test can be used. The second derivative test discriminant D is calculated from the second order derivatives of the potential energy surface with respect to r1, r2 and both r1 and r2. If D is higher than 0 and the second order derivative with respect to r1 is higher than 0, the point is a minimum. If D is smaller than 0, then it is a saddle point.}}

==== Trajectories from r1 = r2: locating the transition state ====

{{fontcolor|blue|The transition state distance has been estimated to be around 0.907 Å for both A-B and B-C distances. This is easily seen in the internuclear distance vs time plot, where the A-B and B-C distance lines overlap completely and show a very slight oscillation, as can be seen in Figure 1.}}

[[File:RCR16_2.png|thumb|center|Figure 1:Internuclear distance vs time plot for transition state]]

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

{{fontcolor|blue|The mep line towards the products is quite straight, whereas the dynamic trajectory has a sinusoidal aspect. The mep line, in other words, shows the potential energy with the oscillation term completely removed while the dynamic trajectory accounts for bond oscillation. This can be seen in Figure 2 and 3.}}

[[File:RCR16_3.png|thumb|left|Figure 2: MEP contour plot]][[File:RCR16_4.png|thumb|right|Figure 3: Dynamics contour plot]]

==== Reactive and unreactive trajectories ====

{| class="wikitable" border=1
! p1 !! p2 !! Total Energy(kcal/mol) !! Plot !! Reactive/Unreactive
|-
| -1.25 || -2.5 || -99.018 || [[File:RCR16_5.png|thumb]] || Reactive - initial trajectory is linear so molecule doesn't oscillate before collision.
|-
| -1.5 || -2.0 || -100.456 || [[File:RCR16_6.png|thumb]] || Unreactive - system does not have sufficient energy to reach the activation barrier and oscillates back.
|-
| -1.5 || -2.5 || -98.956 || [[File:RCR16_7.png|thumb]] || Reactive - oscillating initial trajectory proves the H-H bond starts deforming before the attack of the other atom.
|-
| -2.5 || -5.0 || -84.956 || [[File:RCR16_8.png|thumb]] || Unreactive - the 3 atom complex oscillates around the transition state and crosses the barrier but ultimately turns back to reactants.
|-
| -2.5 || -5.2 || -83.416 || [[File:RCR16_9.png|thumb]] || Reactive - the small additional momentum gives the complex enough energy now to cross to products.
|}

{{fontcolor|blue|Transition state theory has 3 main assumptions stated slightly differently in different sources:
1. The transition state is in quasi-equilibrium with the reactants but not the products.
2. The particles involved follow Boltzmann's distribution and obey classical mechanics.
3. Once the reactants reach the minimum energy saddle point, the transition state does not collapse back to reactants.
The simulations that have been made prove that barrier recrossing is possible: the activated complex would have enough energy to turn into products, but not all collisions with good energy will result in a successful reaction since the transition state is not in equilibrium with the reactants. Tunneling in low activation barrier systems is not accounted for either in the transition state theory, but it is difficult to predict its influence on the simulations made. Considering these factors, experimental rates should be usually slower than the ones predicted by theory. }}

== EXERCISE 2: F - H - H system ==

===PES inspection===

{{fontcolor1|blue| The F + H2 reaction is exothermic while the H + HF reaction is endothermic, since the H-F bond dissociation energy(565 kJ/mol) is higher compared to the H-H one(432 kJ/mol), meaning that HF has a stronger bond and is more stable. }}

{{fontcolor1|blue| Following Hammond's postulate, the transition state will be closer in structure to the F+ H-H system rather than F-H + H system since it is higher in energy. Thus, by testing different F-H distances while the H-H distance is kept at equilibrium, a stable transition state has been found at r(H-H) of 0.74 Å and r(F-H) of 1.81355 Å, and its total energy is -103.743 kcal/mol.}}

MRD:RCR16

2018-05-17T12:32:36Z

MRD:RCR16

2018-05-17T11:52:01Z

Rcr16:

== EXERCISE 1: H + H2 system ==

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

{{fontcolor|blue|The partial derivative of V with respect to r1 and r2 must be 0 at local extremum point. To determine whether this point is a minimum, maximum or a saddle point(transition state), the second partial derivatives test can be used. The second derivative test discriminant D is calculated from the second order derivatives of the potential energy surface with respect to r1, r2 and both r1 and r2. If D is higher than 0 and the second order derivative with respect to r1 is higher than 0, the point is a minimum. If D is smaller than 0, then it is a saddle point.}}

==== Trajectories from r1 = r2: locating the transition state ====

{{fontcolor|blue|The transition state distance has been estimated to be around 0.907 Å for both A-B and B-C distances. This is easily seen in the internuclear distance vs time plot, where the A-B and B-C distance lines overlap completely and show a very slight oscillation, as can be seen in Figure 1.}}

[[File:RCR16_2.png|thumb|Figure 1:Internuclear distance vs time plot for transition state]]

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

{{fontcolor|blue|The mep line towards the products is quite straight, whereas the dynamic trajectory has a sinusoidal aspect. The mep line, in other words, shows the potential energy with the oscillation term completely removed while the dynamic trajectory accounts for bond oscillation. This can be seen in Figure 2 and 3 below.}}

[[File:RCR16_3.png|thumb|Figure 2: MEP contour plot]]

[[File:RCR16_4.png|thumb|Figure 3: Dynamics contour plot]]

==== Reactive and unreactive trajectories ====

{| class="wikitable" border=1
! p1 !! p2 !! Total Energy(kcal/mol) !! Reactive/Unreactive
|-
| -1.25 || -2.5 || -99.018 || Reactive
|-
| -1.5 || -2.0 || -100.456 || Unreactive
|-
| -1.5 || -2.5 || -98.956 || Reactive
|-
| -2.5 || -5.0 || -84.956 || Unreactive
|-
| -2.5 || -5.2 || -83.416 || Reactive
|}

{{fontcolor|blue|Transition state theory assumes that the rates of reactions can be studied by analyzing the transition state at the saddle point of the potential energy surface for the particular reaction. The transition state is in quasi-equilibrium with the reagents and it can convert into products at a determinable rate using kinetic theory. This theory works well in this simple example as long as the reaction has 1 step, the temperature is not too high and the atoms approximately behave in a classical manner. The simulations that have been carried out ran quite smoothly and it should be assumed that the obtained results will be similar to experimental values, although a systematical error due to the factors that have not been taken into consideration will exist. }}

== EXERCISE 2: F - H - H system ==

===PES inspection===

{{fontcolor1|blue| The F + H2 reaction is exothermic while the H + HF reaction is endothermic, since the H-F bond dissociation energy(565 kJ/mol) is higher compared to the H-H one(432 kJ/mol), meaning that HF has a stronger bond and is more stable. }}

{{fontcolor1|blue| Following Hammond's postulate, the transition state will be closer in structure to the F+ H-H system rather than F-H + H system since it is higher in energy. Thus, by testing different F-H distances while the H-H distance is kept at equilibrium, a stable transition state has been found at r(H-H) of 0.74 Å and r(F-H) of 1.81355 Å, and its total energy is -103.743 kcal/mol.}}

MRD:RCR16

2018-05-17T11:50:51Z

Rcr16:

== EXERCISE 1: H + H2 system ==

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

{{fontcolor|blue|The partial derivative of V with respect to r1 and r2 must be 0 at local extremum point. To determine whether this point is a minimum, maximum or a saddle point(transition state), the second partial derivatives test can be used. The second derivative test discriminant D is calculated from the second order derivatives of the potential energy surface with respect to r1, r2 and both r1 and r2. If D is higher than 0 and the second order derivative with respect to r1 is higher than 0, the point is a minimum. If D is smaller than 0, then it is a saddle point.}}

==== Trajectories from r1 = r2: locating the transition state ====

{{fontcolor|blue|The transition state distance has been estimated to be around 0.907 Å for both A-B and B-C distances. This is easily seen in the internuclear distance vs time plot, where the A-B and B-C distance lines overlap completely and show a very slight oscillation, as can be seen in the graph.}}

[[File:RCR16_2.png|thumb|Internuclear distance vs time plot for transition state]]

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

{{fontcolor|blue|The mep line towards the products is quite straight, whereas the dynamic trajectory has a sinusoidal aspect. The mep line, in other words, shows the potential energy with the oscillation term completely removed while the dynamic trajectory accounts for bond oscillation. This can be seen in the 2 contour plot below }}

[[File:RCR16_3.png|thumb|MEP plot]]

[[File:RCR16_4.png|thumb|Dynamics plot]]

==== Reactive and unreactive trajectories ====

{| class="wikitable" border=1
! p1 !! p2 !! Total Energy(kcal/mol) !! Reactive/Unreactive
|-
| -1.25 || -2.5 || -99.018 || Reactive
|-
| -1.5 || -2.0 || -100.456 || Unreactive
|-
| -1.5 || -2.5 || -98.956 || Reactive
|-
| -2.5 || -5.0 || -84.956 || Unreactive
|-
| -2.5 || -5.2 || -83.416 || Reactive
|}

{{fontcolor|blue|Transition state theory assumes that the rates of reactions can be studied by analyzing the transition state at the saddle point of the potential energy surface for the particular reaction. The transition state is in quasi-equilibrium with the reagents and it can convert into products at a determinable rate using kinetic theory. This theory works well in this simple example as long as the reaction has 1 step, the temperature is not too high and the atoms approximately behave in a classical manner. The simulations that have been carried out ran quite smoothly and it should be assumed that the obtained results will be similar to experimental values, although a systematical error due to the factors that have not been taken into consideration will exist. }}

== EXERCISE 2: F - H - H system ==

===PES inspection===

{{fontcolor1|blue| The F + H2 reaction is exothermic while the H + HF reaction is endothermic, since the H-F bond dissociation energy(565 kJ/mol) is higher compared to the H-H one(432 kJ/mol), meaning that HF has a stronger bond and is more stable. }}

{{fontcolor1|blue| Following Hammond's postulate, the transition state will be closer in structure to the F+ H-H system rather than F-H + H system since it is higher in energy. Thus, by testing different F-H distances while the H-H distance is kept at equilibrium, a stable transition state has been found at r(H-H) of 0.74 Å and r(F-H) of 1.81355 Å, and its total energy is -103.743 kcal/mol.}}

MRD:RCR16

2018-05-17T11:49:45Z

Rcr16:

== EXERCISE 1: H + H2 system ==

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

{{fontcolor|blue|The partial derivative of V with respect to r1 and r2 must be 0 at local extremum point. To determine whether this point is a minimum, maximum or a saddle point(transition state), the second partial derivatives test can be used. The second derivative test discriminant D is calculated from the second order derivatives of the potential energy surface with respect to r1, r2 and both r1 and r2. If D is higher than 0 and the second order derivative with respect to r1 is higher than 0, the point is a minimum. If D is smaller than 0, then it is a saddle point.}}

==== Trajectories from r1 = r2: locating the transition state ====

{{fontcolor|blue|The transition state distance has been estimated to be around 0.907 Å for both A-B and B-C distances. This is easily seen in the internuclear distance vs time plot, where the A-B and B-C distance lines overlap completely and show a very slight oscillation, as can be seen in the graph.}}
[[File:RCR16_2.png|thumb|Internuclear distance vs time plot for transition state]]

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

{{fontcolor|blue|The mep line towards the products is quite straight, whereas the dynamic trajectory has a sinusoidal aspect. The mep line, in other words, shows the potential energy with the oscillation term completely removed while the dynamic trajectory accounts for bond oscillation. This can be seen in the 2 contour plot below }}
[[File:RCR16_3.png|thumb|MEP plot]] [[File:RCR16_4.png|thumb|Dynamics plot]]

==== Reactive and unreactive trajectories ====

{| class="wikitable" border=1
! p1 !! p2 !! Total Energy(kcal/mol) !! Reactive/Unreactive
|-
| -1.25 || -2.5 || -99.018 || Reactive
|-
| -1.5 || -2.0 || -100.456 || Unreactive
|-
| -1.5 || -2.5 || -98.956 || Reactive
|-
| -2.5 || -5.0 || -84.956 || Unreactive
|-
| -2.5 || -5.2 || -83.416 || Reactive
|}

{{fontcolor|blue|Transition state theory assumes that the rates of reactions can be studied by analyzing the transition state at the saddle point of the potential energy surface for the particular reaction. The transition state is in quasi-equilibrium with the reagents and it can convert into products at a determinable rate using kinetic theory. This theory works well in this simple example as long as the reaction has 1 step, the temperature is not too high and the atoms approximately behave in a classical manner. The simulations that have been carried out ran quite smoothly and it should be assumed that the obtained results will be similar to experimental values, although a systematical error due to the factors that have not been taken into consideration will exist. }}

== EXERCISE 2: F - H - H system ==

===PES inspection===

{{fontcolor1|blue| The F + H2 reaction is exothermic while the H + HF reaction is endothermic, since the H-F bond dissociation energy(565 kJ/mol) is higher compared to the H-H one(432 kJ/mol), meaning that HF has a stronger bond and is more stable. }}

{{fontcolor1|blue| Following Hammond's postulate, the transition state will be closer in structure to the F+ H-H system rather than F-H + H system since it is higher in energy. Thus, by testing different F-H distances while the H-H distance is kept at equilibrium, a stable transition state has been found at r(H-H) of 0.74 Å and r(F-H) of 1.81355 Å, and its total energy is -103.743 kcal/mol.}}

MRD:RCR16

2018-05-17T11:49:05Z

Rcr16: /* Trajectories from r1 = rts+δ, r2 = rts */

== EXERCISE 1: H + H2 system ==

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

{{fontcolor|blue|The partial derivative of V with respect to r1 and r2 must be 0 at local extremum point. To determine whether this point is a minimum, maximum or a saddle point(transition state), the second partial derivatives test can be used. The second derivative test discriminant D is calculated from the second order derivatives of the potential energy surface with respect to r1, r2 and both r1 and r2. If D is higher than 0 and the second order derivative with respect to r1 is higher than 0, the point is a minimum. If D is smaller than 0, then it is a saddle point.}}

==== Trajectories from r1 = r2: locating the transition state ====

{{fontcolor|blue|The transition state distance has been estimated to be around 0.907 Å for both A-B and B-C distances. This is easily seen in the internuclear distance vs time plot, where the A-B and B-C distance lines overlap completely and show a very slight oscillation, as can be seen in the graph.}}
[[File:RCR16_2.png]]

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

{{fontcolor|blue|The mep line towards the products is quite straight, whereas the dynamic trajectory has a sinusoidal aspect. The mep line, in other words, shows the potential energy with the oscillation term completely removed while the dynamic trajectory accounts for bond oscillation. This can be seen in the 2 contour plot below }}
[[File:RCR16_3.png|thumb|MEP plot]] [[File:RCR16_4.png|thumb|Dynamics plot]]

==== Reactive and unreactive trajectories ====

{| class="wikitable" border=1
! p1 !! p2 !! Total Energy(kcal/mol) !! Reactive/Unreactive
|-
| -1.25 || -2.5 || -99.018 || Reactive
|-
| -1.5 || -2.0 || -100.456 || Unreactive
|-
| -1.5 || -2.5 || -98.956 || Reactive
|-
| -2.5 || -5.0 || -84.956 || Unreactive
|-
| -2.5 || -5.2 || -83.416 || Reactive
|}

{{fontcolor|blue|Transition state theory assumes that the rates of reactions can be studied by analyzing the transition state at the saddle point of the potential energy surface for the particular reaction. The transition state is in quasi-equilibrium with the reagents and it can convert into products at a determinable rate using kinetic theory. This theory works well in this simple example as long as the reaction has 1 step, the temperature is not too high and the atoms approximately behave in a classical manner. The simulations that have been carried out ran quite smoothly and it should be assumed that the obtained results will be similar to experimental values, although a systematical error due to the factors that have not been taken into consideration will exist. }}

== EXERCISE 2: F - H - H system ==

===PES inspection===

{{fontcolor1|blue| The F + H2 reaction is exothermic while the H + HF reaction is endothermic, since the H-F bond dissociation energy(565 kJ/mol) is higher compared to the H-H one(432 kJ/mol), meaning that HF has a stronger bond and is more stable. }}

{{fontcolor1|blue| Following Hammond's postulate, the transition state will be closer in structure to the F+ H-H system rather than F-H + H system since it is higher in energy. Thus, by testing different F-H distances while the H-H distance is kept at equilibrium, a stable transition state has been found at r(H-H) of 0.74 Å and r(F-H) of 1.81355 Å, and its total energy is -103.743 kcal/mol.}}

File:RCR16 4.png

2018-05-17T11:45:57Z

Rcr16:

File:RCR16 3.png

2018-05-17T11:45:16Z

Rcr16:

MRD:RCR16

2018-05-17T11:44:39Z

Rcr16:

== EXERCISE 1: H + H2 system ==

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

{{fontcolor|blue|The partial derivative of V with respect to r1 and r2 must be 0 at local extremum point. To determine whether this point is a minimum, maximum or a saddle point(transition state), the second partial derivatives test can be used. The second derivative test discriminant D is calculated from the second order derivatives of the potential energy surface with respect to r1, r2 and both r1 and r2. If D is higher than 0 and the second order derivative with respect to r1 is higher than 0, the point is a minimum. If D is smaller than 0, then it is a saddle point.}}

==== Trajectories from r1 = r2: locating the transition state ====

{{fontcolor|blue|The transition state distance has been estimated to be around 0.907 Å for both A-B and B-C distances. This is easily seen in the internuclear distance vs time plot, where the A-B and B-C distance lines overlap completely and show a very slight oscillation, as can be seen in the graph.}}
[[File:RCR16_2.png]]

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

{{fontcolor|blue|The mep line towards the products is quite straight, whereas the dynamic trajectory has a sinusoidal aspect. The mep line, in other words, shows the potential energy with the oscillation term completely removed while the dynamic trajectory accounts for bond oscillation. }}

==== Reactive and unreactive trajectories ====

{| class="wikitable" border=1
! p1 !! p2 !! Total Energy(kcal/mol) !! Reactive/Unreactive
|-
| -1.25 || -2.5 || -99.018 || Reactive
|-
| -1.5 || -2.0 || -100.456 || Unreactive
|-
| -1.5 || -2.5 || -98.956 || Reactive
|-
| -2.5 || -5.0 || -84.956 || Unreactive
|-
| -2.5 || -5.2 || -83.416 || Reactive
|}

{{fontcolor|blue|Transition state theory assumes that the rates of reactions can be studied by analyzing the transition state at the saddle point of the potential energy surface for the particular reaction. The transition state is in quasi-equilibrium with the reagents and it can convert into products at a determinable rate using kinetic theory. This theory works well in this simple example as long as the reaction has 1 step, the temperature is not too high and the atoms approximately behave in a classical manner. The simulations that have been carried out ran quite smoothly and it should be assumed that the obtained results will be similar to experimental values, although a systematical error due to the factors that have not been taken into consideration will exist. }}

== EXERCISE 2: F - H - H system ==

===PES inspection===

{{fontcolor1|blue| The F + H2 reaction is exothermic while the H + HF reaction is endothermic, since the H-F bond dissociation energy(565 kJ/mol) is higher compared to the H-H one(432 kJ/mol), meaning that HF has a stronger bond and is more stable. }}

{{fontcolor1|blue| Following Hammond's postulate, the transition state will be closer in structure to the F+ H-H system rather than F-H + H system since it is higher in energy. Thus, by testing different F-H distances while the H-H distance is kept at equilibrium, a stable transition state has been found at r(H-H) of 0.74 Å and r(F-H) of 1.81355 Å, and its total energy is -103.743 kcal/mol.}}

2018-05-15T14:33:17Z

Rcr16:

== EXERCISE 1: H + H2 system ==

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

{{fontcolor|blue|The partial derivative of V with respect to r1 and r2 must be 0 at local extremum point. To determine whether this point is a minimum, maximum or a saddle point(transition state), the second partial derivatives test can be used. The second derivative test discriminant D is calculated from the second order derivatives of the potential energy surface with respect to r1, r2 and both r1 and r2. If D is higher than 0 and the second order derivative with respect to r1 is higher than 0, the point is a minimum. If D is smaller than 0, then it is a saddle point.}}

==== Trajectories from r1 = r2: locating the transition state ====

{{fontcolor|blue|The transition state distance has been estimated to be around 0.95 distance units. This is easily seen in the internuclear distance vs time plot, where the A-B and B-C distance lines overlap completely and show a uniform oscillation, as can be seen in the graph.}}
[[File:Rcr16_q1.png]]

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

{{fontcolor|blue|The mep line towards the products is quite straight, whereas the dynamic trajectory has a sinusoidal aspect. The mep line, in other words, shows the potential energy with the oscillation term completely removed while the dynamic trajectory accounts for bond oscillation. }}

==== Reactive and unreactive trajectories ====

{| class="wikitable" border=1
! p1 !! p2 !! Total Energy !! Reactive/Unreactive
|-
| -1.25 || -2.5 || -99.018 || Reactive
|-
| -1.5 || -2.0 || -100.456 || Unreactive
|-
| -1.5 || -2.5 || -98.956 || Reactive
|-
| -2.5 || -5.0 || -84.956 || Unreactive
|-
| -2.5 || -5.2 || -83.416 || Reactive
|}

{{fontcolor|blue|Transition state theory assumes that the rates of reactions can be studied by analyzing the transition state at the saddle point of the potential energy surface for the particular reaction. The transition state is in quasi-equilibrium with the reagents and it can convert into products at a determinable rate using kinetic theory. This theory works well in this simple example as long as the reaction has 1 step, the temperature is not too high and the atoms approximately behave in a classical manner. The simulations that have been carried out ran quite smoothly and it should be assumed that the obtained results will be similar to experimental values, although a systematical error due to the factors that have not been taken into consideration will exist. }}

== EXERCISE 2: F - H - H system ==

===PES inspection===

{{fontcolor1|blue| The F + H2 reaction is exothermic while the H + HF reaction is endothermic, since the H-F bond dissociation energy(565 kJ/mol) is higher compared to the H-H one(432 kJ/mol), meaning that HF has a stronger bond and is more stable. }}

{{fontcolor1|blue| Following Hammond's postulate, the transition state will be closer in structure to the F+ H-H system rather than F-H + H system since it is higher in energy. Thus, by testing different F-H distances while the H-H distance is kept at equilibrium, a stable transition state has been found at r(HH)=0.74 }} and r(FH)=1.81355, and its total energy is -103.743 units.}}