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MRD:bc2116

2018-05-18T16:12:49Z

Bc2116: /* MEP calculations with different initial conditions */

= Molecular Reaction Dynamics: Boru Chen =

== <math>H_2</math> + H system ==

=== Dynamics from Transition State Region ===

The PES has two components:

<math>\frac{\partial V}{\partial r_1}</math> and <math>\frac{\partial V}{\partial r_2}</math>

Where V is the potential energy, and <math>r_1</math> is the intermolecular distance between <math>H_b</math> <math>H_c</math>, <math>r_2</math> is the intermolecular distance between <math>H_a</math> and <math>H_b</math>. At transition structure, both components have value of zero. At energy minima and transition structure, their first derivatives equal to zero. Transition state can be distinguished by taking the second derivative of potential energy. Transition state is at energy maximum along reaction coordinate, and at energy minimum in any other direction, whereas energy minimum is at a minimum in all directions. Mathematically speaking, energy minimum’s second derivative is always a positive value at any position, whereas transition state’s second derivative is negative along reaction coordinate, and positive everywhere else.

==== Transition State Position Estimation ====
Best estimate = 0.9075 Armstrong. Inter nuclear distance vs time plot

[[File:Exercise 1 Internuclear distance to time1.png]]

Note: A-B line can be vaguely seen behind the yellow line.

==== MEP Model ====
[[File:Exercise 1 MEP plot.png]] [[File:12.png]] [[File:11.png]]

In MEP model, internuclear momentum remains constant, BC distance increases slowly and AB distance decreases slowly. This is because in MEP model, velocity is equated to 0 after every calculation. This means despite the fact that atoms should be accelerating as it picks up kinetic energy, its velocity is kept constant, hence its momentum is kept constant.

==== Dynamic Model ====

[[File:Exercise 1 Dynamic plot.png]] [[File:0.png]] [[File:01.png]]

In this model, as distance between BC increase, and BC momentum increases with an increasing rate. This is because as reaction goes from transition state to AB, potential energy in transition state is released as kinetic energy. Since the system is isolated, this kinetic energy is captured by C, and it begins to accelerate. Since momentum is proportional to velocity, BC momentum increases.

AB momentum experiences periodic fluctuation after collision, because it is expressing the extra kinetic energy as vibrational energy between A and B.

==== MEP calculations with different initial conditions ====
1. If we changed the initial conditions (reverse)?

[[File:Surface Plot 1.png]] [[File:Figure 1.png]] [[File:Figure 1-1.png]]

In this scenario, transition state structure rolls back to BC + A structure. As distance between AB increase, and AB momentum increases with an increasing rate. This is because as reaction goes from transition state to BC, potential energy in transition state is released as kinetic energy. Since the system is isolated, this kinetic energy is captured by A, and it begins to accelerate. Since momentum is proportional to velocity, AB momentum increases.

BC momentum experiences periodic fluctuation after collision, because it is expressing the extra kinetic energy as vibrational energy between B and C.

2. If the new initial positions correspond to the final positions above and final momenta values but with their signs reversed?

[[File:Surface Plot 2.png]] [[File:Figure 2-1.png]] [[File:Figure 2-2.png]]

AB moves towards to and stops at transition state. AB distance is kept constant as BC distance decreases. AB momentum fluctuates periodically as it is vibrating. BC momentum is kept constant then experience sudden increase as it accelerates up the potential energy hill to reach transition state.

=== Reactive and Unreactive Trajectories Table ===

{| class="wikitable" border=1
! p1 !! p2 !! Etot <math>kcalmol^{-1}</math> !! Trajectory
|-
| -1.25 || -2.5 ||| -99.018 ||| [[File:1.png]] ||| Plot shows a reactive trajectory, as AB bond shortens and BC bond lengthens.
|-
| -1.5 || -2.0 ||| -100.456 ||| [[File:2.png]] ||| Plot shows an unreactive trajectory. BC bond never lengthens and AB bond never becomes close enough.
|-
| -1.5 || -2.5 ||| -98.956 ||| [[File:3.png]] ||| Plot shows a reactive trajectory, as AB bond shortens and BC bond lengthens.
|-
| -2.5 || -5.0 ||| -84.956 ||| [[File:444.png]] ||| Plot shows barrier crossing. Although bond does form for some time, however reaction reverts back to reactants.
|-
| -2.5 || -5.2 ||| -83.416 ||| [[File:5.png]] ||| Plot shows barrier crossing. Product is formed
|}

The main assumption is if the incoming atom has enough kinetic energy to overcome kinetic barrier, the reaction will occur. This model also assumes atoms follow newtonian physics.

== F + H + H System ==
=== PES Report ===
[[File:HHF PES.png]]

Plot above illustrate reaction H + H + F system potential energy surface, where A = F, B = H and C = H. Graph shows that HH appears to be deeper in energy valley, hence HH formation is exothermic, and HF formation is endothermic.

==== Position of transition state ====
HH distance 1.812 A

HF distance 0.744 A

[[File:HHF transition state.png]]
==== Activation energy calculation: ====
Positions of these structures were estimated using MEP plot

Transition state potential energy: -103.749 <math>kcalmol^{-1}</math>

H2 potential energy: -133.871 <math>kcalmol^{-1}</math>

[[File:H2 potential energy.PNG]] [[File:H2 internuclear distance vs time.PNG]]

HF potential energy: -103.837 <math>kcalmol^{-1}</math>

[[File:HF_potential_energy.PNG]] [[File:HF internuclear distance vs time.PNG]]

HF + H activation energy = -103.749 - -103.837 = 0.088 <math>kcalmol^{-1}</math>

HH + F activation energy = -103.749 - -133.871 = 30.122 <math>kcalmol^{-1}</math>

=== Reaction Dynamics ===
==== Energy conservation ====

[[File:Skate park.png]]

Model sets reaction as an isolated system, and all atoms obey newtonian laws of physics. Once atom moves downhill, the potential energy is converted into kinetic energy, and is released as vibration of bonds. Temperature is directly proportional to the kinetic energy molecules have, hence as reaction progress, temperature of system would rise. This can be measured by calorimetry experimentally.

====Trajectories table ====
[[File:Trajectory table HF.PNG]]

[[File:Internuclear momentum HF=-0.5 HH=2.9.png]]

During the collision, HH momentum has relatively a small change in comparison with HF momentum After the collision, if the trajectory is reactive, HH momentum will have none to small fluctuation, vice versa for HF momentum. If the trajectory is unreactive, HH momentum will have very large fluctuation, vice versa for HF momentum.

[[File:Internuclear momentum HF=-0.8 HH=0.1.png]]

If pHH = 0.1 and pHF = -0.8, HH momentum has small periodic fluctuations and HF momentum has large periodic fluctuations.

MRD:bc2116

2018-05-18T16:09:05Z

Bc2116: /* MEP calculations with different initial conditions */

= Molecular Reaction Dynamics: Boru Chen =

== <math>H_2</math> + H system ==

=== Dynamics from Transition State Region ===

The PES has two components:

<math>\frac{\partial V}{\partial r_1}</math> and <math>\frac{\partial V}{\partial r_2}</math>

Where V is the potential energy, and <math>r_1</math> is the intermolecular distance between <math>H_b</math> <math>H_c</math>, <math>r_2</math> is the intermolecular distance between <math>H_a</math> and <math>H_b</math>. At transition structure, both components have value of zero. At energy minima and transition structure, their first derivatives equal to zero. Transition state can be distinguished by taking the second derivative of potential energy. Transition state is at energy maximum along reaction coordinate, and at energy minimum in any other direction, whereas energy minimum is at a minimum in all directions. Mathematically speaking, energy minimum’s second derivative is always a positive value at any position, whereas transition state’s second derivative is negative along reaction coordinate, and positive everywhere else.

==== Transition State Position Estimation ====
Best estimate = 0.9075 Armstrong. Inter nuclear distance vs time plot

[[File:Exercise 1 Internuclear distance to time1.png]]

Note: A-B line can be vaguely seen behind the yellow line.

==== MEP Model ====
[[File:Exercise 1 MEP plot.png]] [[File:12.png]] [[File:11.png]]

In MEP model, internuclear momentum remains constant, BC distance increases slowly and AB distance decreases slowly. This is because in MEP model, velocity is equated to 0 after every calculation. This means despite the fact that atoms should be accelerating as it picks up kinetic energy, its velocity is kept constant, hence its momentum is kept constant.

==== Dynamic Model ====

[[File:Exercise 1 Dynamic plot.png]] [[File:0.png]] [[File:01.png]]

In this model, as distance between BC increase, and BC momentum increases with an increasing rate. This is because as reaction goes from transition state to AB, potential energy in transition state is released as kinetic energy. Since the system is isolated, this kinetic energy is captured by C, and it begins to accelerate. Since momentum is proportional to velocity, BC momentum increases.

AB momentum experiences periodic fluctuation after collision, because it is expressing the extra kinetic energy as vibrational energy between A and B.

==== MEP calculations with different initial conditions ====
1. If we changed the initial conditions (reverse)?

[[File:Surface Plot 1.png]] [[File:Figure 1.png]] [[File:Figure 1-1.png]]

In this scenario, transition state structure rolls back to BC + A structure. As distance between AB increase, and AB momentum increases with an increasing rate. This is because as reaction goes from transition state to BC, potential energy in transition state is released as kinetic energy. Since the system is isolated, this kinetic energy is captured by A, and it begins to accelerate. Since momentum is proportional to velocity, AB momentum increases.

BC momentum experiences periodic fluctuation after collision, because it is expressing the extra kinetic energy as vibrational energy between B and C.

2. If the new initial positions correspond to the final positions above and final momenta values but with their signs reversed?
[[File:Surface Plot 2.png]] [[File:Figure 2-1.png]] [[File:Figure 2-2.png]]
AB and BC momenta become the same, and is the Y axis at 0, 0. AB and BC distances are constant, with large difference between two distances. ABs are further apart. Surface plot cannot be visualised.

=== Reactive and Unreactive Trajectories Table ===

{| class="wikitable" border=1
! p1 !! p2 !! Etot <math>kcalmol^{-1}</math> !! Trajectory
|-
| -1.25 || -2.5 ||| -99.018 ||| [[File:1.png]] ||| Plot shows a reactive trajectory, as AB bond shortens and BC bond lengthens.
|-
| -1.5 || -2.0 ||| -100.456 ||| [[File:2.png]] ||| Plot shows an unreactive trajectory. BC bond never lengthens and AB bond never becomes close enough.
|-
| -1.5 || -2.5 ||| -98.956 ||| [[File:3.png]] ||| Plot shows a reactive trajectory, as AB bond shortens and BC bond lengthens.
|-
| -2.5 || -5.0 ||| -84.956 ||| [[File:444.png]] ||| Plot shows barrier crossing. Although bond does form for some time, however reaction reverts back to reactants.
|-
| -2.5 || -5.2 ||| -83.416 ||| [[File:5.png]] ||| Plot shows barrier crossing. Product is formed
|}

The main assumption is if the incoming atom has enough kinetic energy to overcome kinetic barrier, the reaction will occur. This model also assumes atoms follow newtonian physics.

== F + H + H System ==
=== PES Report ===
[[File:HHF PES.png]]

Plot above illustrate reaction H + H + F system potential energy surface, where A = F, B = H and C = H. Graph shows that HH appears to be deeper in energy valley, hence HH formation is exothermic, and HF formation is endothermic.

==== Position of transition state ====
HH distance 1.812 A

HF distance 0.744 A

[[File:HHF transition state.png]]
==== Activation energy calculation: ====
Positions of these structures were estimated using MEP plot

Transition state potential energy: -103.749 <math>kcalmol^{-1}</math>

H2 potential energy: -133.871 <math>kcalmol^{-1}</math>

[[File:H2 potential energy.PNG]] [[File:H2 internuclear distance vs time.PNG]]

HF potential energy: -103.837 <math>kcalmol^{-1}</math>

[[File:HF_potential_energy.PNG]] [[File:HF internuclear distance vs time.PNG]]

HF + H activation energy = -103.749 - -103.837 = 0.088 <math>kcalmol^{-1}</math>

HH + F activation energy = -103.749 - -133.871 = 30.122 <math>kcalmol^{-1}</math>

=== Reaction Dynamics ===
==== Energy conservation ====

[[File:Skate park.png]]

Model sets reaction as an isolated system, and all atoms obey newtonian laws of physics. Once atom moves downhill, the potential energy is converted into kinetic energy, and is released as vibration of bonds. Temperature is directly proportional to the kinetic energy molecules have, hence as reaction progress, temperature of system would rise. This can be measured by calorimetry experimentally.

====Trajectories table ====
[[File:Trajectory table HF.PNG]]

[[File:Internuclear momentum HF=-0.5 HH=2.9.png]]

During the collision, HH momentum has relatively a small change in comparison with HF momentum After the collision, if the trajectory is reactive, HH momentum will have none to small fluctuation, vice versa for HF momentum. If the trajectory is unreactive, HH momentum will have very large fluctuation, vice versa for HF momentum.

[[File:Internuclear momentum HF=-0.8 HH=0.1.png]]

If pHH = 0.1 and pHF = -0.8, HH momentum has small periodic fluctuations and HF momentum has large periodic fluctuations.

MRD:bc2116

2018-05-18T16:08:43Z

Bc2116: /* MEP calculations with different initial conditions */

= Molecular Reaction Dynamics: Boru Chen =

== <math>H_2</math> + H system ==

=== Dynamics from Transition State Region ===

The PES has two components:

<math>\frac{\partial V}{\partial r_1}</math> and <math>\frac{\partial V}{\partial r_2}</math>

Where V is the potential energy, and <math>r_1</math> is the intermolecular distance between <math>H_b</math> <math>H_c</math>, <math>r_2</math> is the intermolecular distance between <math>H_a</math> and <math>H_b</math>. At transition structure, both components have value of zero. At energy minima and transition structure, their first derivatives equal to zero. Transition state can be distinguished by taking the second derivative of potential energy. Transition state is at energy maximum along reaction coordinate, and at energy minimum in any other direction, whereas energy minimum is at a minimum in all directions. Mathematically speaking, energy minimum’s second derivative is always a positive value at any position, whereas transition state’s second derivative is negative along reaction coordinate, and positive everywhere else.

==== Transition State Position Estimation ====
Best estimate = 0.9075 Armstrong. Inter nuclear distance vs time plot

[[File:Exercise 1 Internuclear distance to time1.png]]

Note: A-B line can be vaguely seen behind the yellow line.

==== MEP Model ====
[[File:Exercise 1 MEP plot.png]] [[File:12.png]] [[File:11.png]]

In MEP model, internuclear momentum remains constant, BC distance increases slowly and AB distance decreases slowly. This is because in MEP model, velocity is equated to 0 after every calculation. This means despite the fact that atoms should be accelerating as it picks up kinetic energy, its velocity is kept constant, hence its momentum is kept constant.

==== Dynamic Model ====

[[File:Exercise 1 Dynamic plot.png]] [[File:0.png]] [[File:01.png]]

In this model, as distance between BC increase, and BC momentum increases with an increasing rate. This is because as reaction goes from transition state to AB, potential energy in transition state is released as kinetic energy. Since the system is isolated, this kinetic energy is captured by C, and it begins to accelerate. Since momentum is proportional to velocity, BC momentum increases.

AB momentum experiences periodic fluctuation after collision, because it is expressing the extra kinetic energy as vibrational energy between A and B.

==== MEP calculations with different initial conditions ====
1. If we changed the initial conditions (reverse)?
[[File:Surface Plot 1.png]] [[File:Figure 1.png]] [[File:Figure 1-1.png]]
In this scenario, transition state structure rolls back to BC + A structure. As distance between AB increase, and AB momentum increases with an increasing rate. This is because as reaction goes from transition state to BC, potential energy in transition state is released as kinetic energy. Since the system is isolated, this kinetic energy is captured by A, and it begins to accelerate. Since momentum is proportional to velocity, AB momentum increases.

BC momentum experiences periodic fluctuation after collision, because it is expressing the extra kinetic energy as vibrational energy between B and C.

2. If the new initial positions correspond to the final positions above and final momenta values but with their signs reversed?
[[File:Surface Plot 2.png]] [[File:Figure 2-1.png]] [[File:Figure 2-2.png]]
AB and BC momenta become the same, and is the Y axis at 0, 0. AB and BC distances are constant, with large difference between two distances. ABs are further apart. Surface plot cannot be visualised.

=== Reactive and Unreactive Trajectories Table ===

{| class="wikitable" border=1
! p1 !! p2 !! Etot <math>kcalmol^{-1}</math> !! Trajectory
|-
| -1.25 || -2.5 ||| -99.018 ||| [[File:1.png]] ||| Plot shows a reactive trajectory, as AB bond shortens and BC bond lengthens.
|-
| -1.5 || -2.0 ||| -100.456 ||| [[File:2.png]] ||| Plot shows an unreactive trajectory. BC bond never lengthens and AB bond never becomes close enough.
|-
| -1.5 || -2.5 ||| -98.956 ||| [[File:3.png]] ||| Plot shows a reactive trajectory, as AB bond shortens and BC bond lengthens.
|-
| -2.5 || -5.0 ||| -84.956 ||| [[File:444.png]] ||| Plot shows barrier crossing. Although bond does form for some time, however reaction reverts back to reactants.
|-
| -2.5 || -5.2 ||| -83.416 ||| [[File:5.png]] ||| Plot shows barrier crossing. Product is formed
|}

The main assumption is if the incoming atom has enough kinetic energy to overcome kinetic barrier, the reaction will occur. This model also assumes atoms follow newtonian physics.

== F + H + H System ==
=== PES Report ===
[[File:HHF PES.png]]

Plot above illustrate reaction H + H + F system potential energy surface, where A = F, B = H and C = H. Graph shows that HH appears to be deeper in energy valley, hence HH formation is exothermic, and HF formation is endothermic.

==== Position of transition state ====
HH distance 1.812 A

HF distance 0.744 A

[[File:HHF transition state.png]]
==== Activation energy calculation: ====
Positions of these structures were estimated using MEP plot

Transition state potential energy: -103.749 <math>kcalmol^{-1}</math>

H2 potential energy: -133.871 <math>kcalmol^{-1}</math>

[[File:H2 potential energy.PNG]] [[File:H2 internuclear distance vs time.PNG]]

HF potential energy: -103.837 <math>kcalmol^{-1}</math>

[[File:HF_potential_energy.PNG]] [[File:HF internuclear distance vs time.PNG]]

HF + H activation energy = -103.749 - -103.837 = 0.088 <math>kcalmol^{-1}</math>

HH + F activation energy = -103.749 - -133.871 = 30.122 <math>kcalmol^{-1}</math>

=== Reaction Dynamics ===
==== Energy conservation ====

[[File:Skate park.png]]

Model sets reaction as an isolated system, and all atoms obey newtonian laws of physics. Once atom moves downhill, the potential energy is converted into kinetic energy, and is released as vibration of bonds. Temperature is directly proportional to the kinetic energy molecules have, hence as reaction progress, temperature of system would rise. This can be measured by calorimetry experimentally.

====Trajectories table ====
[[File:Trajectory table HF.PNG]]

[[File:Internuclear momentum HF=-0.5 HH=2.9.png]]

During the collision, HH momentum has relatively a small change in comparison with HF momentum After the collision, if the trajectory is reactive, HH momentum will have none to small fluctuation, vice versa for HF momentum. If the trajectory is unreactive, HH momentum will have very large fluctuation, vice versa for HF momentum.

[[File:Internuclear momentum HF=-0.8 HH=0.1.png]]

If pHH = 0.1 and pHF = -0.8, HH momentum has small periodic fluctuations and HF momentum has large periodic fluctuations.

MRD:bc2116

2018-05-18T16:05:09Z

Bc2116: /* Dynamic Model */

= Molecular Reaction Dynamics: Boru Chen =

== <math>H_2</math> + H system ==

=== Dynamics from Transition State Region ===

The PES has two components:

<math>\frac{\partial V}{\partial r_1}</math> and <math>\frac{\partial V}{\partial r_2}</math>

Where V is the potential energy, and <math>r_1</math> is the intermolecular distance between <math>H_b</math> <math>H_c</math>, <math>r_2</math> is the intermolecular distance between <math>H_a</math> and <math>H_b</math>. At transition structure, both components have value of zero. At energy minima and transition structure, their first derivatives equal to zero. Transition state can be distinguished by taking the second derivative of potential energy. Transition state is at energy maximum along reaction coordinate, and at energy minimum in any other direction, whereas energy minimum is at a minimum in all directions. Mathematically speaking, energy minimum’s second derivative is always a positive value at any position, whereas transition state’s second derivative is negative along reaction coordinate, and positive everywhere else.

==== Transition State Position Estimation ====
Best estimate = 0.9075 Armstrong. Inter nuclear distance vs time plot

[[File:Exercise 1 Internuclear distance to time1.png]]

Note: A-B line can be vaguely seen behind the yellow line.

==== MEP Model ====
[[File:Exercise 1 MEP plot.png]] [[File:12.png]] [[File:11.png]]

In MEP model, internuclear momentum remains constant, BC distance increases slowly and AB distance decreases slowly. This is because in MEP model, velocity is equated to 0 after every calculation. This means despite the fact that atoms should be accelerating as it picks up kinetic energy, its velocity is kept constant, hence its momentum is kept constant.

==== Dynamic Model ====

[[File:Exercise 1 Dynamic plot.png]] [[File:0.png]] [[File:01.png]]

In this model, as distance between BC increase, and BC momentum increases with an increasing rate. This is because as reaction goes from transition state to AB, potential energy in transition state is released as kinetic energy. Since the system is isolated, this kinetic energy is captured by C, and it begins to accelerate. Since momentum is proportional to velocity, BC momentum increases.

AB momentum experiences periodic fluctuation after collision, because it is expressing the extra kinetic energy as vibrational energy between A and B.

==== MEP calculations with different initial conditions ====
1. If we changed the initial conditions (reverse)?
[[File:Surface Plot 1.png]] [[File:Figure 1.png]] [[File:Figure 1-1.png]]
Transition state follows energy valley floor in H3 + H1-H2 direction.
2. If the new initial positions correspond to the final positions above and final momenta values but with their signs reversed?
[[File:Surface Plot 2.png]] [[File:Figure 2-1.png]] [[File:Figure 2-2.png]]
AB and BC momenta become the same, and is the Y axis at 0, 0. AB and BC distances are constant, with large difference between two distances. ABs are further apart. Surface plot cannot be visualised.

=== Reactive and Unreactive Trajectories Table ===

{| class="wikitable" border=1
! p1 !! p2 !! Etot <math>kcalmol^{-1}</math> !! Trajectory
|-
| -1.25 || -2.5 ||| -99.018 ||| [[File:1.png]] ||| Plot shows a reactive trajectory, as AB bond shortens and BC bond lengthens.
|-
| -1.5 || -2.0 ||| -100.456 ||| [[File:2.png]] ||| Plot shows an unreactive trajectory. BC bond never lengthens and AB bond never becomes close enough.
|-
| -1.5 || -2.5 ||| -98.956 ||| [[File:3.png]] ||| Plot shows a reactive trajectory, as AB bond shortens and BC bond lengthens.
|-
| -2.5 || -5.0 ||| -84.956 ||| [[File:444.png]] ||| Plot shows barrier crossing. Although bond does form for some time, however reaction reverts back to reactants.
|-
| -2.5 || -5.2 ||| -83.416 ||| [[File:5.png]] ||| Plot shows barrier crossing. Product is formed
|}

The main assumption is if the incoming atom has enough kinetic energy to overcome kinetic barrier, the reaction will occur. This model also assumes atoms follow newtonian physics.

== F + H + H System ==
=== PES Report ===
[[File:HHF PES.png]]

Plot above illustrate reaction H + H + F system potential energy surface, where A = F, B = H and C = H. Graph shows that HH appears to be deeper in energy valley, hence HH formation is exothermic, and HF formation is endothermic.

==== Position of transition state ====
HH distance 1.812 A

HF distance 0.744 A

[[File:HHF transition state.png]]
==== Activation energy calculation: ====
Positions of these structures were estimated using MEP plot

Transition state potential energy: -103.749 <math>kcalmol^{-1}</math>

H2 potential energy: -133.871 <math>kcalmol^{-1}</math>

[[File:H2 potential energy.PNG]] [[File:H2 internuclear distance vs time.PNG]]

HF potential energy: -103.837 <math>kcalmol^{-1}</math>

[[File:HF_potential_energy.PNG]] [[File:HF internuclear distance vs time.PNG]]

HF + H activation energy = -103.749 - -103.837 = 0.088 <math>kcalmol^{-1}</math>

HH + F activation energy = -103.749 - -133.871 = 30.122 <math>kcalmol^{-1}</math>

=== Reaction Dynamics ===
==== Energy conservation ====

[[File:Skate park.png]]

Model sets reaction as an isolated system, and all atoms obey newtonian laws of physics. Once atom moves downhill, the potential energy is converted into kinetic energy, and is released as vibration of bonds. Temperature is directly proportional to the kinetic energy molecules have, hence as reaction progress, temperature of system would rise. This can be measured by calorimetry experimentally.

====Trajectories table ====
[[File:Trajectory table HF.PNG]]

[[File:Internuclear momentum HF=-0.5 HH=2.9.png]]

During the collision, HH momentum has relatively a small change in comparison with HF momentum After the collision, if the trajectory is reactive, HH momentum will have none to small fluctuation, vice versa for HF momentum. If the trajectory is unreactive, HH momentum will have very large fluctuation, vice versa for HF momentum.

[[File:Internuclear momentum HF=-0.8 HH=0.1.png]]

If pHH = 0.1 and pHF = -0.8, HH momentum has small periodic fluctuations and HF momentum has large periodic fluctuations.

MRD:bc2116

2018-05-18T16:03:11Z

Bc2116: /* Dynamic Model */

= Molecular Reaction Dynamics: Boru Chen =

== <math>H_2</math> + H system ==

=== Dynamics from Transition State Region ===

The PES has two components:

<math>\frac{\partial V}{\partial r_1}</math> and <math>\frac{\partial V}{\partial r_2}</math>

Where V is the potential energy, and <math>r_1</math> is the intermolecular distance between <math>H_b</math> <math>H_c</math>, <math>r_2</math> is the intermolecular distance between <math>H_a</math> and <math>H_b</math>. At transition structure, both components have value of zero. At energy minima and transition structure, their first derivatives equal to zero. Transition state can be distinguished by taking the second derivative of potential energy. Transition state is at energy maximum along reaction coordinate, and at energy minimum in any other direction, whereas energy minimum is at a minimum in all directions. Mathematically speaking, energy minimum’s second derivative is always a positive value at any position, whereas transition state’s second derivative is negative along reaction coordinate, and positive everywhere else.

==== Transition State Position Estimation ====
Best estimate = 0.9075 Armstrong. Inter nuclear distance vs time plot

[[File:Exercise 1 Internuclear distance to time1.png]]

Note: A-B line can be vaguely seen behind the yellow line.

==== MEP Model ====
[[File:Exercise 1 MEP plot.png]] [[File:12.png]] [[File:11.png]]

In MEP model, internuclear momentum remains constant, BC distance increases slowly and AB distance decreases slowly. This is because in MEP model, velocity is equated to 0 after every calculation. This means despite the fact that atoms should be accelerating as it picks up kinetic energy, its velocity is kept constant, hence its momentum is kept constant.

==== Dynamic Model ====

[[File:Exercise 1 Dynamic plot.png]] [[File:0.png]] [[File:01.png]]

In this model, as distance between BC increase, and BC momentum experiences an inverse of logarithmic increase. This is because as reaction goes from transition state to AB, potential energy in transition state is released as kinetic energy. Since the system is isolated, this kinetic energy is captured by C, and it begins to accelerate. Since momentum is proportional to velocity, BC momentum increases.

AB momentum experiences periodic fluctuation after collision, because it is expressing the extra kinetic energy as vibrational energy between A and B.

==== MEP calculations with different initial conditions ====
1. If we changed the initial conditions (reverse)?
[[File:Surface Plot 1.png]] [[File:Figure 1.png]] [[File:Figure 1-1.png]]
Transition state follows energy valley floor in H3 + H1-H2 direction.
2. If the new initial positions correspond to the final positions above and final momenta values but with their signs reversed?
[[File:Surface Plot 2.png]] [[File:Figure 2-1.png]] [[File:Figure 2-2.png]]
AB and BC momenta become the same, and is the Y axis at 0, 0. AB and BC distances are constant, with large difference between two distances. ABs are further apart. Surface plot cannot be visualised.

=== Reactive and Unreactive Trajectories Table ===

{| class="wikitable" border=1
! p1 !! p2 !! Etot <math>kcalmol^{-1}</math> !! Trajectory
|-
| -1.25 || -2.5 ||| -99.018 ||| [[File:1.png]] ||| Plot shows a reactive trajectory, as AB bond shortens and BC bond lengthens.
|-
| -1.5 || -2.0 ||| -100.456 ||| [[File:2.png]] ||| Plot shows an unreactive trajectory. BC bond never lengthens and AB bond never becomes close enough.
|-
| -1.5 || -2.5 ||| -98.956 ||| [[File:3.png]] ||| Plot shows a reactive trajectory, as AB bond shortens and BC bond lengthens.
|-
| -2.5 || -5.0 ||| -84.956 ||| [[File:444.png]] ||| Plot shows barrier crossing. Although bond does form for some time, however reaction reverts back to reactants.
|-
| -2.5 || -5.2 ||| -83.416 ||| [[File:5.png]] ||| Plot shows barrier crossing. Product is formed
|}

The main assumption is if the incoming atom has enough kinetic energy to overcome kinetic barrier, the reaction will occur. This model also assumes atoms follow newtonian physics.

== F + H + H System ==
=== PES Report ===
[[File:HHF PES.png]]

Plot above illustrate reaction H + H + F system potential energy surface, where A = F, B = H and C = H. Graph shows that HH appears to be deeper in energy valley, hence HH formation is exothermic, and HF formation is endothermic.

==== Position of transition state ====
HH distance 1.812 A

HF distance 0.744 A

[[File:HHF transition state.png]]
==== Activation energy calculation: ====
Positions of these structures were estimated using MEP plot

Transition state potential energy: -103.749 <math>kcalmol^{-1}</math>

H2 potential energy: -133.871 <math>kcalmol^{-1}</math>

[[File:H2 potential energy.PNG]] [[File:H2 internuclear distance vs time.PNG]]

HF potential energy: -103.837 <math>kcalmol^{-1}</math>

[[File:HF_potential_energy.PNG]] [[File:HF internuclear distance vs time.PNG]]

HF + H activation energy = -103.749 - -103.837 = 0.088 <math>kcalmol^{-1}</math>

HH + F activation energy = -103.749 - -133.871 = 30.122 <math>kcalmol^{-1}</math>

=== Reaction Dynamics ===
==== Energy conservation ====

[[File:Skate park.png]]

Model sets reaction as an isolated system, and all atoms obey newtonian laws of physics. Once atom moves downhill, the potential energy is converted into kinetic energy, and is released as vibration of bonds. Temperature is directly proportional to the kinetic energy molecules have, hence as reaction progress, temperature of system would rise. This can be measured by calorimetry experimentally.

====Trajectories table ====
[[File:Trajectory table HF.PNG]]

[[File:Internuclear momentum HF=-0.5 HH=2.9.png]]

During the collision, HH momentum has relatively a small change in comparison with HF momentum After the collision, if the trajectory is reactive, HH momentum will have none to small fluctuation, vice versa for HF momentum. If the trajectory is unreactive, HH momentum will have very large fluctuation, vice versa for HF momentum.

[[File:Internuclear momentum HF=-0.8 HH=0.1.png]]

If pHH = 0.1 and pHF = -0.8, HH momentum has small periodic fluctuations and HF momentum has large periodic fluctuations.

MRD:bc2116

2018-05-18T15:52:38Z

Bc2116: /* MEP Model */

= Molecular Reaction Dynamics: Boru Chen =

== <math>H_2</math> + H system ==

=== Dynamics from Transition State Region ===

The PES has two components:

<math>\frac{\partial V}{\partial r_1}</math> and <math>\frac{\partial V}{\partial r_2}</math>

Where V is the potential energy, and <math>r_1</math> is the intermolecular distance between <math>H_b</math> <math>H_c</math>, <math>r_2</math> is the intermolecular distance between <math>H_a</math> and <math>H_b</math>. At transition structure, both components have value of zero. At energy minima and transition structure, their first derivatives equal to zero. Transition state can be distinguished by taking the second derivative of potential energy. Transition state is at energy maximum along reaction coordinate, and at energy minimum in any other direction, whereas energy minimum is at a minimum in all directions. Mathematically speaking, energy minimum’s second derivative is always a positive value at any position, whereas transition state’s second derivative is negative along reaction coordinate, and positive everywhere else.

==== Transition State Position Estimation ====
Best estimate = 0.9075 Armstrong. Inter nuclear distance vs time plot

[[File:Exercise 1 Internuclear distance to time1.png]]

Note: A-B line can be vaguely seen behind the yellow line.

==== MEP Model ====
[[File:Exercise 1 MEP plot.png]] [[File:12.png]] [[File:11.png]]

In MEP model, internuclear momentum remains constant, BC distance increases slowly and AB distance decreases slowly. This is because in MEP model, velocity is equated to 0 after every calculation. This means despite the fact that atoms should be accelerating as it picks up kinetic energy, its velocity is kept constant, hence its momentum is kept constant.

==== Dynamic Model ====

[[File:Exercise 1 Dynamic plot.png]] [[File:0.png]] [[File:01.png]]

==== MEP calculations with different initial conditions ====
1. If we changed the initial conditions (reverse)?
[[File:Surface Plot 1.png]] [[File:Figure 1.png]] [[File:Figure 1-1.png]]
Transition state follows energy valley floor in H3 + H1-H2 direction.
2. If the new initial positions correspond to the final positions above and final momenta values but with their signs reversed?
[[File:Surface Plot 2.png]] [[File:Figure 2-1.png]] [[File:Figure 2-2.png]]
AB and BC momenta become the same, and is the Y axis at 0, 0. AB and BC distances are constant, with large difference between two distances. ABs are further apart. Surface plot cannot be visualised.

=== Reactive and Unreactive Trajectories Table ===

{| class="wikitable" border=1
! p1 !! p2 !! Etot <math>kcalmol^{-1}</math> !! Trajectory
|-
| -1.25 || -2.5 ||| -99.018 ||| [[File:1.png]] ||| Plot shows a reactive trajectory, as AB bond shortens and BC bond lengthens.
|-
| -1.5 || -2.0 ||| -100.456 ||| [[File:2.png]] ||| Plot shows an unreactive trajectory. BC bond never lengthens and AB bond never becomes close enough.
|-
| -1.5 || -2.5 ||| -98.956 ||| [[File:3.png]] ||| Plot shows a reactive trajectory, as AB bond shortens and BC bond lengthens.
|-
| -2.5 || -5.0 ||| -84.956 ||| [[File:444.png]] ||| Plot shows barrier crossing. Although bond does form for some time, however reaction reverts back to reactants.
|-
| -2.5 || -5.2 ||| -83.416 ||| [[File:5.png]] ||| Plot shows barrier crossing. Product is formed
|}

The main assumption is if the incoming atom has enough kinetic energy to overcome kinetic barrier, the reaction will occur. This model also assumes atoms follow newtonian physics.

== F + H + H System ==
=== PES Report ===
[[File:HHF PES.png]]

Plot above illustrate reaction H + H + F system potential energy surface, where A = F, B = H and C = H. Graph shows that HH appears to be deeper in energy valley, hence HH formation is exothermic, and HF formation is endothermic.

==== Position of transition state ====
HH distance 1.812 A

HF distance 0.744 A

[[File:HHF transition state.png]]
==== Activation energy calculation: ====
Positions of these structures were estimated using MEP plot

Transition state potential energy: -103.749 <math>kcalmol^{-1}</math>

H2 potential energy: -133.871 <math>kcalmol^{-1}</math>

[[File:H2 potential energy.PNG]] [[File:H2 internuclear distance vs time.PNG]]

HF potential energy: -103.837 <math>kcalmol^{-1}</math>

[[File:HF_potential_energy.PNG]] [[File:HF internuclear distance vs time.PNG]]

HF + H activation energy = -103.749 - -103.837 = 0.088 <math>kcalmol^{-1}</math>

HH + F activation energy = -103.749 - -133.871 = 30.122 <math>kcalmol^{-1}</math>

=== Reaction Dynamics ===
==== Energy conservation ====

[[File:Skate park.png]]

Model sets reaction as an isolated system, and all atoms obey newtonian laws of physics. Once atom moves downhill, the potential energy is converted into kinetic energy, and is released as vibration of bonds. Temperature is directly proportional to the kinetic energy molecules have, hence as reaction progress, temperature of system would rise. This can be measured by calorimetry experimentally.

====Trajectories table ====
[[File:Trajectory table HF.PNG]]

[[File:Internuclear momentum HF=-0.5 HH=2.9.png]]

During the collision, HH momentum has relatively a small change in comparison with HF momentum After the collision, if the trajectory is reactive, HH momentum will have none to small fluctuation, vice versa for HF momentum. If the trajectory is unreactive, HH momentum will have very large fluctuation, vice versa for HF momentum.

[[File:Internuclear momentum HF=-0.8 HH=0.1.png]]

If pHH = 0.1 and pHF = -0.8, HH momentum has small periodic fluctuations and HF momentum has large periodic fluctuations.

MRD:bc2116

2018-05-18T15:52:25Z

Bc2116: /* MEP Model */

= Molecular Reaction Dynamics: Boru Chen =

== <math>H_2</math> + H system ==

=== Dynamics from Transition State Region ===

The PES has two components:

<math>\frac{\partial V}{\partial r_1}</math> and <math>\frac{\partial V}{\partial r_2}</math>

Where V is the potential energy, and <math>r_1</math> is the intermolecular distance between <math>H_b</math> <math>H_c</math>, <math>r_2</math> is the intermolecular distance between <math>H_a</math> and <math>H_b</math>. At transition structure, both components have value of zero. At energy minima and transition structure, their first derivatives equal to zero. Transition state can be distinguished by taking the second derivative of potential energy. Transition state is at energy maximum along reaction coordinate, and at energy minimum in any other direction, whereas energy minimum is at a minimum in all directions. Mathematically speaking, energy minimum’s second derivative is always a positive value at any position, whereas transition state’s second derivative is negative along reaction coordinate, and positive everywhere else.

==== Transition State Position Estimation ====
Best estimate = 0.9075 Armstrong. Inter nuclear distance vs time plot

[[File:Exercise 1 Internuclear distance to time1.png]]

Note: A-B line can be vaguely seen behind the yellow line.

==== MEP Model ====
[[File:Exercise 1 MEP plot.png]] [[File:12.png]] [[File:11.png]]

In MEP model, internuclear momentum remains constant, BC distance increases slowly and AB distance decreases slowly. This is because in MEP model, velocity is equated to 0 after every calculation. This means despite the fact that atoms should be accelerating as it picks up kinetic energy, its velocity is kept constant, hence its momentum is kept constant/

==== Dynamic Model ====

[[File:Exercise 1 Dynamic plot.png]] [[File:0.png]] [[File:01.png]]

==== MEP calculations with different initial conditions ====
1. If we changed the initial conditions (reverse)?
[[File:Surface Plot 1.png]] [[File:Figure 1.png]] [[File:Figure 1-1.png]]
Transition state follows energy valley floor in H3 + H1-H2 direction.
2. If the new initial positions correspond to the final positions above and final momenta values but with their signs reversed?
[[File:Surface Plot 2.png]] [[File:Figure 2-1.png]] [[File:Figure 2-2.png]]
AB and BC momenta become the same, and is the Y axis at 0, 0. AB and BC distances are constant, with large difference between two distances. ABs are further apart. Surface plot cannot be visualised.

=== Reactive and Unreactive Trajectories Table ===

{| class="wikitable" border=1
! p1 !! p2 !! Etot <math>kcalmol^{-1}</math> !! Trajectory
|-
| -1.25 || -2.5 ||| -99.018 ||| [[File:1.png]] ||| Plot shows a reactive trajectory, as AB bond shortens and BC bond lengthens.
|-
| -1.5 || -2.0 ||| -100.456 ||| [[File:2.png]] ||| Plot shows an unreactive trajectory. BC bond never lengthens and AB bond never becomes close enough.
|-
| -1.5 || -2.5 ||| -98.956 ||| [[File:3.png]] ||| Plot shows a reactive trajectory, as AB bond shortens and BC bond lengthens.
|-
| -2.5 || -5.0 ||| -84.956 ||| [[File:444.png]] ||| Plot shows barrier crossing. Although bond does form for some time, however reaction reverts back to reactants.
|-
| -2.5 || -5.2 ||| -83.416 ||| [[File:5.png]] ||| Plot shows barrier crossing. Product is formed
|}

The main assumption is if the incoming atom has enough kinetic energy to overcome kinetic barrier, the reaction will occur. This model also assumes atoms follow newtonian physics.

== F + H + H System ==
=== PES Report ===
[[File:HHF PES.png]]

Plot above illustrate reaction H + H + F system potential energy surface, where A = F, B = H and C = H. Graph shows that HH appears to be deeper in energy valley, hence HH formation is exothermic, and HF formation is endothermic.

==== Position of transition state ====
HH distance 1.812 A

HF distance 0.744 A

[[File:HHF transition state.png]]
==== Activation energy calculation: ====
Positions of these structures were estimated using MEP plot

Transition state potential energy: -103.749 <math>kcalmol^{-1}</math>

H2 potential energy: -133.871 <math>kcalmol^{-1}</math>

[[File:H2 potential energy.PNG]] [[File:H2 internuclear distance vs time.PNG]]

HF potential energy: -103.837 <math>kcalmol^{-1}</math>

[[File:HF_potential_energy.PNG]] [[File:HF internuclear distance vs time.PNG]]

HF + H activation energy = -103.749 - -103.837 = 0.088 <math>kcalmol^{-1}</math>

HH + F activation energy = -103.749 - -133.871 = 30.122 <math>kcalmol^{-1}</math>

=== Reaction Dynamics ===
==== Energy conservation ====

[[File:Skate park.png]]

Model sets reaction as an isolated system, and all atoms obey newtonian laws of physics. Once atom moves downhill, the potential energy is converted into kinetic energy, and is released as vibration of bonds. Temperature is directly proportional to the kinetic energy molecules have, hence as reaction progress, temperature of system would rise. This can be measured by calorimetry experimentally.

====Trajectories table ====
[[File:Trajectory table HF.PNG]]

[[File:Internuclear momentum HF=-0.5 HH=2.9.png]]

During the collision, HH momentum has relatively a small change in comparison with HF momentum After the collision, if the trajectory is reactive, HH momentum will have none to small fluctuation, vice versa for HF momentum. If the trajectory is unreactive, HH momentum will have very large fluctuation, vice versa for HF momentum.

[[File:Internuclear momentum HF=-0.8 HH=0.1.png]]

If pHH = 0.1 and pHF = -0.8, HH momentum has small periodic fluctuations and HF momentum has large periodic fluctuations.

MRD:bc2116

2018-05-18T15:49:19Z

Bc2116: /* MEP and Dynamic Model Comparison */

= Molecular Reaction Dynamics: Boru Chen =

== <math>H_2</math> + H system ==

=== Dynamics from Transition State Region ===

The PES has two components:

<math>\frac{\partial V}{\partial r_1}</math> and <math>\frac{\partial V}{\partial r_2}</math>

Where V is the potential energy, and <math>r_1</math> is the intermolecular distance between <math>H_b</math> <math>H_c</math>, <math>r_2</math> is the intermolecular distance between <math>H_a</math> and <math>H_b</math>. At transition structure, both components have value of zero. At energy minima and transition structure, their first derivatives equal to zero. Transition state can be distinguished by taking the second derivative of potential energy. Transition state is at energy maximum along reaction coordinate, and at energy minimum in any other direction, whereas energy minimum is at a minimum in all directions. Mathematically speaking, energy minimum’s second derivative is always a positive value at any position, whereas transition state’s second derivative is negative along reaction coordinate, and positive everywhere else.

==== Transition State Position Estimation ====
Best estimate = 0.9075 Armstrong. Inter nuclear distance vs time plot

[[File:Exercise 1 Internuclear distance to time1.png]]

Note: A-B line can be vaguely seen behind the yellow line.

==== MEP Model ====
[[File:Exercise 1 MEP plot.png]] [[File:12.png]] [[File:11.png]]

==== Dynamic Model ====

[[File:Exercise 1 Dynamic plot.png]] [[File:0.png]] [[File:01.png]]

==== MEP calculations with different initial conditions ====
1. If we changed the initial conditions (reverse)?
[[File:Surface Plot 1.png]] [[File:Figure 1.png]] [[File:Figure 1-1.png]]
Transition state follows energy valley floor in H3 + H1-H2 direction.
2. If the new initial positions correspond to the final positions above and final momenta values but with their signs reversed?
[[File:Surface Plot 2.png]] [[File:Figure 2-1.png]] [[File:Figure 2-2.png]]
AB and BC momenta become the same, and is the Y axis at 0, 0. AB and BC distances are constant, with large difference between two distances. ABs are further apart. Surface plot cannot be visualised.

=== Reactive and Unreactive Trajectories Table ===

{| class="wikitable" border=1
! p1 !! p2 !! Etot <math>kcalmol^{-1}</math> !! Trajectory
|-
| -1.25 || -2.5 ||| -99.018 ||| [[File:1.png]] ||| Plot shows a reactive trajectory, as AB bond shortens and BC bond lengthens.
|-
| -1.5 || -2.0 ||| -100.456 ||| [[File:2.png]] ||| Plot shows an unreactive trajectory. BC bond never lengthens and AB bond never becomes close enough.
|-
| -1.5 || -2.5 ||| -98.956 ||| [[File:3.png]] ||| Plot shows a reactive trajectory, as AB bond shortens and BC bond lengthens.
|-
| -2.5 || -5.0 ||| -84.956 ||| [[File:444.png]] ||| Plot shows barrier crossing. Although bond does form for some time, however reaction reverts back to reactants.
|-
| -2.5 || -5.2 ||| -83.416 ||| [[File:5.png]] ||| Plot shows barrier crossing. Product is formed
|}

The main assumption is if the incoming atom has enough kinetic energy to overcome kinetic barrier, the reaction will occur. This model also assumes atoms follow newtonian physics.

== F + H + H System ==
=== PES Report ===
[[File:HHF PES.png]]

Plot above illustrate reaction H + H + F system potential energy surface, where A = F, B = H and C = H. Graph shows that HH appears to be deeper in energy valley, hence HH formation is exothermic, and HF formation is endothermic.

==== Position of transition state ====
HH distance 1.812 A

HF distance 0.744 A

[[File:HHF transition state.png]]
==== Activation energy calculation: ====
Positions of these structures were estimated using MEP plot

Transition state potential energy: -103.749 <math>kcalmol^{-1}</math>

H2 potential energy: -133.871 <math>kcalmol^{-1}</math>

[[File:H2 potential energy.PNG]] [[File:H2 internuclear distance vs time.PNG]]

HF potential energy: -103.837 <math>kcalmol^{-1}</math>

[[File:HF_potential_energy.PNG]] [[File:HF internuclear distance vs time.PNG]]

HF + H activation energy = -103.749 - -103.837 = 0.088 <math>kcalmol^{-1}</math>

HH + F activation energy = -103.749 - -133.871 = 30.122 <math>kcalmol^{-1}</math>

=== Reaction Dynamics ===
==== Energy conservation ====

[[File:Skate park.png]]

Model sets reaction as an isolated system, and all atoms obey newtonian laws of physics. Once atom moves downhill, the potential energy is converted into kinetic energy, and is released as vibration of bonds. Temperature is directly proportional to the kinetic energy molecules have, hence as reaction progress, temperature of system would rise. This can be measured by calorimetry experimentally.

====Trajectories table ====
[[File:Trajectory table HF.PNG]]

[[File:Internuclear momentum HF=-0.5 HH=2.9.png]]

During the collision, HH momentum has relatively a small change in comparison with HF momentum After the collision, if the trajectory is reactive, HH momentum will have none to small fluctuation, vice versa for HF momentum. If the trajectory is unreactive, HH momentum will have very large fluctuation, vice versa for HF momentum.

[[File:Internuclear momentum HF=-0.8 HH=0.1.png]]

If pHH = 0.1 and pHF = -0.8, HH momentum has small periodic fluctuations and HF momentum has large periodic fluctuations.

MRD:bc2116

2018-05-18T15:48:24Z

Bc2116: /* MEP and Dynamic Model Comparison */

= Molecular Reaction Dynamics: Boru Chen =

== <math>H_2</math> + H system ==

=== Dynamics from Transition State Region ===

The PES has two components:

<math>\frac{\partial V}{\partial r_1}</math> and <math>\frac{\partial V}{\partial r_2}</math>

Where V is the potential energy, and <math>r_1</math> is the intermolecular distance between <math>H_b</math> <math>H_c</math>, <math>r_2</math> is the intermolecular distance between <math>H_a</math> and <math>H_b</math>. At transition structure, both components have value of zero. At energy minima and transition structure, their first derivatives equal to zero. Transition state can be distinguished by taking the second derivative of potential energy. Transition state is at energy maximum along reaction coordinate, and at energy minimum in any other direction, whereas energy minimum is at a minimum in all directions. Mathematically speaking, energy minimum’s second derivative is always a positive value at any position, whereas transition state’s second derivative is negative along reaction coordinate, and positive everywhere else.

==== Transition State Position Estimation ====
Best estimate = 0.9075 Armstrong. Inter nuclear distance vs time plot

[[File:Exercise 1 Internuclear distance to time1.png]]

Note: A-B line can be vaguely seen behind the yellow line.

==== MEP and Dynamic Model Comparison ====
[[File:Exercise 1 MEP plot.png]] [[File:12.png]] [[File:11.png]]

[[File:Exercise 1 Dynamic plot.png]] [[File:0.png]] [[File:01.png]]

MEP plot showed no difference comparing to transition state when first plotted with 500 steps calculated, once the number of steps was increased to 5000, a straight line can be seen following the valley floor to H1 + H2-H3. In comparison, the dynamic plot showed a trajectory which shot off the plot, and the number of steps in calculation had to be truncated to 618. This trajectory bounces between valley walls of H1 + H2-H3.This difference is because the velocity in MEP calculation is reset to 0 after each step, whereas velocity in dynamic calculation isn’t.

==== MEP calculations with different initial conditions ====
1. If we changed the initial conditions (reverse)?
[[File:Surface Plot 1.png]] [[File:Figure 1.png]] [[File:Figure 1-1.png]]
Transition state follows energy valley floor in H3 + H1-H2 direction.
2. If the new initial positions correspond to the final positions above and final momenta values but with their signs reversed?
[[File:Surface Plot 2.png]] [[File:Figure 2-1.png]] [[File:Figure 2-2.png]]
AB and BC momenta become the same, and is the Y axis at 0, 0. AB and BC distances are constant, with large difference between two distances. ABs are further apart. Surface plot cannot be visualised.

=== Reactive and Unreactive Trajectories Table ===

{| class="wikitable" border=1
! p1 !! p2 !! Etot <math>kcalmol^{-1}</math> !! Trajectory
|-
| -1.25 || -2.5 ||| -99.018 ||| [[File:1.png]] ||| Plot shows a reactive trajectory, as AB bond shortens and BC bond lengthens.
|-
| -1.5 || -2.0 ||| -100.456 ||| [[File:2.png]] ||| Plot shows an unreactive trajectory. BC bond never lengthens and AB bond never becomes close enough.
|-
| -1.5 || -2.5 ||| -98.956 ||| [[File:3.png]] ||| Plot shows a reactive trajectory, as AB bond shortens and BC bond lengthens.
|-
| -2.5 || -5.0 ||| -84.956 ||| [[File:444.png]] ||| Plot shows barrier crossing. Although bond does form for some time, however reaction reverts back to reactants.
|-
| -2.5 || -5.2 ||| -83.416 ||| [[File:5.png]] ||| Plot shows barrier crossing. Product is formed
|}

The main assumption is if the incoming atom has enough kinetic energy to overcome kinetic barrier, the reaction will occur. This model also assumes atoms follow newtonian physics.

== F + H + H System ==
=== PES Report ===
[[File:HHF PES.png]]

Plot above illustrate reaction H + H + F system potential energy surface, where A = F, B = H and C = H. Graph shows that HH appears to be deeper in energy valley, hence HH formation is exothermic, and HF formation is endothermic.

==== Position of transition state ====
HH distance 1.812 A

HF distance 0.744 A

[[File:HHF transition state.png]]
==== Activation energy calculation: ====
Positions of these structures were estimated using MEP plot

Transition state potential energy: -103.749 <math>kcalmol^{-1}</math>

H2 potential energy: -133.871 <math>kcalmol^{-1}</math>

[[File:H2 potential energy.PNG]] [[File:H2 internuclear distance vs time.PNG]]

HF potential energy: -103.837 <math>kcalmol^{-1}</math>

[[File:HF_potential_energy.PNG]] [[File:HF internuclear distance vs time.PNG]]

HF + H activation energy = -103.749 - -103.837 = 0.088 <math>kcalmol^{-1}</math>

HH + F activation energy = -103.749 - -133.871 = 30.122 <math>kcalmol^{-1}</math>

=== Reaction Dynamics ===
==== Energy conservation ====

[[File:Skate park.png]]

Model sets reaction as an isolated system, and all atoms obey newtonian laws of physics. Once atom moves downhill, the potential energy is converted into kinetic energy, and is released as vibration of bonds. Temperature is directly proportional to the kinetic energy molecules have, hence as reaction progress, temperature of system would rise. This can be measured by calorimetry experimentally.

====Trajectories table ====
[[File:Trajectory table HF.PNG]]

[[File:Internuclear momentum HF=-0.5 HH=2.9.png]]

During the collision, HH momentum has relatively a small change in comparison with HF momentum After the collision, if the trajectory is reactive, HH momentum will have none to small fluctuation, vice versa for HF momentum. If the trajectory is unreactive, HH momentum will have very large fluctuation, vice versa for HF momentum.

[[File:Internuclear momentum HF=-0.8 HH=0.1.png]]

If pHH = 0.1 and pHF = -0.8, HH momentum has small periodic fluctuations and HF momentum has large periodic fluctuations.

MRD:bc2116

2018-05-18T15:34:24Z

Bc2116: /* MEP and Dynamic Model Comparison */

= Molecular Reaction Dynamics: Boru Chen =

== <math>H_2</math> + H system ==

=== Dynamics from Transition State Region ===

The PES has two components:

<math>\frac{\partial V}{\partial r_1}</math> and <math>\frac{\partial V}{\partial r_2}</math>

Where V is the potential energy, and <math>r_1</math> is the intermolecular distance between <math>H_b</math> <math>H_c</math>, <math>r_2</math> is the intermolecular distance between <math>H_a</math> and <math>H_b</math>. At transition structure, both components have value of zero. At energy minima and transition structure, their first derivatives equal to zero. Transition state can be distinguished by taking the second derivative of potential energy. Transition state is at energy maximum along reaction coordinate, and at energy minimum in any other direction, whereas energy minimum is at a minimum in all directions. Mathematically speaking, energy minimum’s second derivative is always a positive value at any position, whereas transition state’s second derivative is negative along reaction coordinate, and positive everywhere else.

==== Transition State Position Estimation ====
Best estimate = 0.9075 Armstrong. Inter nuclear distance vs time plot

[[File:Exercise 1 Internuclear distance to time1.png]]

Note: A-B line can be vaguely seen behind the yellow line.

==== MEP and Dynamic Model Comparison ====
[[File:Exercise 1 MEP plot.png]] [[File:0.png]] [[File:01.png]]

[[File:Exercise 1 Dynamic plot.png]] [[File:12.png]] [[File:11.png]]

MEP plot showed no difference comparing to transition state when first plotted with 500 steps calculated, once the number of steps was increased to 5000, a straight line can be seen following the valley floor to H1 + H2-H3. In comparison, the dynamic plot showed a trajectory which shot off the plot, and the number of steps in calculation had to be truncated to 618. This trajectory bounces between valley walls of H1 + H2-H3.This difference is because the velocity in MEP calculation is reset to 0 after each step, whereas velocity in dynamic calculation isn’t.

==== MEP calculations with different initial conditions ====
1. If we changed the initial conditions (reverse)?
[[File:Surface Plot 1.png]] [[File:Figure 1.png]] [[File:Figure 1-1.png]]
Transition state follows energy valley floor in H3 + H1-H2 direction.
2. If the new initial positions correspond to the final positions above and final momenta values but with their signs reversed?
[[File:Surface Plot 2.png]] [[File:Figure 2-1.png]] [[File:Figure 2-2.png]]
AB and BC momenta become the same, and is the Y axis at 0, 0. AB and BC distances are constant, with large difference between two distances. ABs are further apart. Surface plot cannot be visualised.

=== Reactive and Unreactive Trajectories Table ===

{| class="wikitable" border=1
! p1 !! p2 !! Etot <math>kcalmol^{-1}</math> !! Trajectory
|-
| -1.25 || -2.5 ||| -99.018 ||| [[File:1.png]] ||| Plot shows a reactive trajectory, as AB bond shortens and BC bond lengthens.
|-
| -1.5 || -2.0 ||| -100.456 ||| [[File:2.png]] ||| Plot shows an unreactive trajectory. BC bond never lengthens and AB bond never becomes close enough.
|-
| -1.5 || -2.5 ||| -98.956 ||| [[File:3.png]] ||| Plot shows a reactive trajectory, as AB bond shortens and BC bond lengthens.
|-
| -2.5 || -5.0 ||| -84.956 ||| [[File:444.png]] ||| Plot shows barrier crossing. Although bond does form for some time, however reaction reverts back to reactants.
|-
| -2.5 || -5.2 ||| -83.416 ||| [[File:5.png]] ||| Plot shows barrier crossing. Product is formed
|}

The main assumption is if the incoming atom has enough kinetic energy to overcome kinetic barrier, the reaction will occur. This model also assumes atoms follow newtonian physics.

== F + H + H System ==
=== PES Report ===
[[File:HHF PES.png]]

Plot above illustrate reaction H + H + F system potential energy surface, where A = F, B = H and C = H. Graph shows that HH appears to be deeper in energy valley, hence HH formation is exothermic, and HF formation is endothermic.

==== Position of transition state ====
HH distance 1.812 A

HF distance 0.744 A

[[File:HHF transition state.png]]
==== Activation energy calculation: ====
Positions of these structures were estimated using MEP plot

Transition state potential energy: -103.749 <math>kcalmol^{-1}</math>

H2 potential energy: -133.871 <math>kcalmol^{-1}</math>

[[File:H2 potential energy.PNG]] [[File:H2 internuclear distance vs time.PNG]]

HF potential energy: -103.837 <math>kcalmol^{-1}</math>

[[File:HF_potential_energy.PNG]] [[File:HF internuclear distance vs time.PNG]]

HF + H activation energy = -103.749 - -103.837 = 0.088 <math>kcalmol^{-1}</math>

HH + F activation energy = -103.749 - -133.871 = 30.122 <math>kcalmol^{-1}</math>

=== Reaction Dynamics ===
==== Energy conservation ====

[[File:Skate park.png]]

Model sets reaction as an isolated system, and all atoms obey newtonian laws of physics. Once atom moves downhill, the potential energy is converted into kinetic energy, and is released as vibration of bonds. Temperature is directly proportional to the kinetic energy molecules have, hence as reaction progress, temperature of system would rise. This can be measured by calorimetry experimentally.

====Trajectories table ====
[[File:Trajectory table HF.PNG]]

[[File:Internuclear momentum HF=-0.5 HH=2.9.png]]

During the collision, HH momentum has relatively a small change in comparison with HF momentum After the collision, if the trajectory is reactive, HH momentum will have none to small fluctuation, vice versa for HF momentum. If the trajectory is unreactive, HH momentum will have very large fluctuation, vice versa for HF momentum.

[[File:Internuclear momentum HF=-0.8 HH=0.1.png]]

If pHH = 0.1 and pHF = -0.8, HH momentum has small periodic fluctuations and HF momentum has large periodic fluctuations.

MRD:bc2116

2018-05-18T15:34:11Z

Bc2116: /* MEP and Dynamic Model Comparison */

= Molecular Reaction Dynamics: Boru Chen =

== <math>H_2</math> + H system ==

=== Dynamics from Transition State Region ===

The PES has two components:

<math>\frac{\partial V}{\partial r_1}</math> and <math>\frac{\partial V}{\partial r_2}</math>

Where V is the potential energy, and <math>r_1</math> is the intermolecular distance between <math>H_b</math> <math>H_c</math>, <math>r_2</math> is the intermolecular distance between <math>H_a</math> and <math>H_b</math>. At transition structure, both components have value of zero. At energy minima and transition structure, their first derivatives equal to zero. Transition state can be distinguished by taking the second derivative of potential energy. Transition state is at energy maximum along reaction coordinate, and at energy minimum in any other direction, whereas energy minimum is at a minimum in all directions. Mathematically speaking, energy minimum’s second derivative is always a positive value at any position, whereas transition state’s second derivative is negative along reaction coordinate, and positive everywhere else.

==== Transition State Position Estimation ====
Best estimate = 0.9075 Armstrong. Inter nuclear distance vs time plot

[[File:Exercise 1 Internuclear distance to time1.png]]

Note: A-B line can be vaguely seen behind the yellow line.

==== MEP and Dynamic Model Comparison ====
[[File:Exercise 1 MEP plot.png]] [[File:0.png]] [[File:01.png]]
[[File:Exercise 1 Dynamic plot.png]] [[File:12.png]] [[File:11.png]]

MEP plot showed no difference comparing to transition state when first plotted with 500 steps calculated, once the number of steps was increased to 5000, a straight line can be seen following the valley floor to H1 + H2-H3. In comparison, the dynamic plot showed a trajectory which shot off the plot, and the number of steps in calculation had to be truncated to 618. This trajectory bounces between valley walls of H1 + H2-H3.This difference is because the velocity in MEP calculation is reset to 0 after each step, whereas velocity in dynamic calculation isn’t.

==== MEP calculations with different initial conditions ====
1. If we changed the initial conditions (reverse)?
[[File:Surface Plot 1.png]] [[File:Figure 1.png]] [[File:Figure 1-1.png]]
Transition state follows energy valley floor in H3 + H1-H2 direction.
2. If the new initial positions correspond to the final positions above and final momenta values but with their signs reversed?
[[File:Surface Plot 2.png]] [[File:Figure 2-1.png]] [[File:Figure 2-2.png]]
AB and BC momenta become the same, and is the Y axis at 0, 0. AB and BC distances are constant, with large difference between two distances. ABs are further apart. Surface plot cannot be visualised.

=== Reactive and Unreactive Trajectories Table ===

{| class="wikitable" border=1
! p1 !! p2 !! Etot <math>kcalmol^{-1}</math> !! Trajectory
|-
| -1.25 || -2.5 ||| -99.018 ||| [[File:1.png]] ||| Plot shows a reactive trajectory, as AB bond shortens and BC bond lengthens.
|-
| -1.5 || -2.0 ||| -100.456 ||| [[File:2.png]] ||| Plot shows an unreactive trajectory. BC bond never lengthens and AB bond never becomes close enough.
|-
| -1.5 || -2.5 ||| -98.956 ||| [[File:3.png]] ||| Plot shows a reactive trajectory, as AB bond shortens and BC bond lengthens.
|-
| -2.5 || -5.0 ||| -84.956 ||| [[File:444.png]] ||| Plot shows barrier crossing. Although bond does form for some time, however reaction reverts back to reactants.
|-
| -2.5 || -5.2 ||| -83.416 ||| [[File:5.png]] ||| Plot shows barrier crossing. Product is formed
|}

The main assumption is if the incoming atom has enough kinetic energy to overcome kinetic barrier, the reaction will occur. This model also assumes atoms follow newtonian physics.

== F + H + H System ==
=== PES Report ===
[[File:HHF PES.png]]

Plot above illustrate reaction H + H + F system potential energy surface, where A = F, B = H and C = H. Graph shows that HH appears to be deeper in energy valley, hence HH formation is exothermic, and HF formation is endothermic.

==== Position of transition state ====
HH distance 1.812 A

HF distance 0.744 A

[[File:HHF transition state.png]]
==== Activation energy calculation: ====
Positions of these structures were estimated using MEP plot

Transition state potential energy: -103.749 <math>kcalmol^{-1}</math>

H2 potential energy: -133.871 <math>kcalmol^{-1}</math>

[[File:H2 potential energy.PNG]] [[File:H2 internuclear distance vs time.PNG]]

HF potential energy: -103.837 <math>kcalmol^{-1}</math>

[[File:HF_potential_energy.PNG]] [[File:HF internuclear distance vs time.PNG]]

HF + H activation energy = -103.749 - -103.837 = 0.088 <math>kcalmol^{-1}</math>

HH + F activation energy = -103.749 - -133.871 = 30.122 <math>kcalmol^{-1}</math>

=== Reaction Dynamics ===
==== Energy conservation ====

[[File:Skate park.png]]

Model sets reaction as an isolated system, and all atoms obey newtonian laws of physics. Once atom moves downhill, the potential energy is converted into kinetic energy, and is released as vibration of bonds. Temperature is directly proportional to the kinetic energy molecules have, hence as reaction progress, temperature of system would rise. This can be measured by calorimetry experimentally.

====Trajectories table ====
[[File:Trajectory table HF.PNG]]

[[File:Internuclear momentum HF=-0.5 HH=2.9.png]]

During the collision, HH momentum has relatively a small change in comparison with HF momentum After the collision, if the trajectory is reactive, HH momentum will have none to small fluctuation, vice versa for HF momentum. If the trajectory is unreactive, HH momentum will have very large fluctuation, vice versa for HF momentum.

[[File:Internuclear momentum HF=-0.8 HH=0.1.png]]

If pHH = 0.1 and pHF = -0.8, HH momentum has small periodic fluctuations and HF momentum has large periodic fluctuations.

File:11.png

2018-05-18T15:33:56Z

Bc2116: Bc2116 uploaded a new version of File:11.png

File:12.png

2018-05-18T15:33:28Z

Bc2116: Bc2116 uploaded a new version of File:12.png

File:01.png

2018-05-18T15:33:04Z

Bc2116:

File:0.png

2018-05-18T15:32:45Z

Bc2116:

MRD:bc2116

2018-05-18T15:24:50Z

Bc2116: /* Internuclear distance and momentum vs time at large t under MEP calculation */

= Molecular Reaction Dynamics: Boru Chen =

== <math>H_2</math> + H system ==

=== Dynamics from Transition State Region ===

The PES has two components:

<math>\frac{\partial V}{\partial r_1}</math> and <math>\frac{\partial V}{\partial r_2}</math>

Where V is the potential energy, and <math>r_1</math> is the intermolecular distance between <math>H_b</math> <math>H_c</math>, <math>r_2</math> is the intermolecular distance between <math>H_a</math> and <math>H_b</math>. At transition structure, both components have value of zero. At energy minima and transition structure, their first derivatives equal to zero. Transition state can be distinguished by taking the second derivative of potential energy. Transition state is at energy maximum along reaction coordinate, and at energy minimum in any other direction, whereas energy minimum is at a minimum in all directions. Mathematically speaking, energy minimum’s second derivative is always a positive value at any position, whereas transition state’s second derivative is negative along reaction coordinate, and positive everywhere else.

==== Transition State Position Estimation ====
Best estimate = 0.9075 Armstrong. Inter nuclear distance vs time plot

[[File:Exercise 1 Internuclear distance to time1.png]]

Note: A-B line can be vaguely seen behind the yellow line.

==== MEP and Dynamic Model Comparison ====
[[File:Exercise 1 MEP plot.png]]
[[File:Exercise 1 Dynamic plot.png]]

MEP plot showed no difference comparing to transition state when first plotted with 500 steps calculated, once the number of steps was increased to 5000, a straight line can be seen following the valley floor to H1 + H2-H3. In comparison, the dynamic plot showed a trajectory which shot off the plot, and the number of steps in calculation had to be truncated to 618. This trajectory bounces between valley walls of H1 + H2-H3.This difference is because the velocity in MEP calculation is reset to 0 after each step, whereas velocity in dynamic calculation isn’t.

==== MEP calculations with different initial conditions ====
1. If we changed the initial conditions (reverse)?
[[File:Surface Plot 1.png]] [[File:Figure 1.png]] [[File:Figure 1-1.png]]
Transition state follows energy valley floor in H3 + H1-H2 direction.
2. If the new initial positions correspond to the final positions above and final momenta values but with their signs reversed?
[[File:Surface Plot 2.png]] [[File:Figure 2-1.png]] [[File:Figure 2-2.png]]
AB and BC momenta become the same, and is the Y axis at 0, 0. AB and BC distances are constant, with large difference between two distances. ABs are further apart. Surface plot cannot be visualised.

=== Reactive and Unreactive Trajectories Table ===

{| class="wikitable" border=1
! p1 !! p2 !! Etot <math>kcalmol^{-1}</math> !! Trajectory
|-
| -1.25 || -2.5 ||| -99.018 ||| [[File:1.png]] ||| Plot shows a reactive trajectory, as AB bond shortens and BC bond lengthens.
|-
| -1.5 || -2.0 ||| -100.456 ||| [[File:2.png]] ||| Plot shows an unreactive trajectory. BC bond never lengthens and AB bond never becomes close enough.
|-
| -1.5 || -2.5 ||| -98.956 ||| [[File:3.png]] ||| Plot shows a reactive trajectory, as AB bond shortens and BC bond lengthens.
|-
| -2.5 || -5.0 ||| -84.956 ||| [[File:444.png]] ||| Plot shows barrier crossing. Although bond does form for some time, however reaction reverts back to reactants.
|-
| -2.5 || -5.2 ||| -83.416 ||| [[File:5.png]] ||| Plot shows barrier crossing. Product is formed
|}

The main assumption is if the incoming atom has enough kinetic energy to overcome kinetic barrier, the reaction will occur. This model also assumes atoms follow newtonian physics.

== F + H + H System ==
=== PES Report ===
[[File:HHF PES.png]]

Plot above illustrate reaction H + H + F system potential energy surface, where A = F, B = H and C = H. Graph shows that HH appears to be deeper in energy valley, hence HH formation is exothermic, and HF formation is endothermic.

==== Position of transition state ====
HH distance 1.812 A

HF distance 0.744 A

[[File:HHF transition state.png]]
==== Activation energy calculation: ====
Positions of these structures were estimated using MEP plot

Transition state potential energy: -103.749 <math>kcalmol^{-1}</math>

H2 potential energy: -133.871 <math>kcalmol^{-1}</math>

[[File:H2 potential energy.PNG]] [[File:H2 internuclear distance vs time.PNG]]

HF potential energy: -103.837 <math>kcalmol^{-1}</math>

[[File:HF_potential_energy.PNG]] [[File:HF internuclear distance vs time.PNG]]

HF + H activation energy = -103.749 - -103.837 = 0.088 <math>kcalmol^{-1}</math>

HH + F activation energy = -103.749 - -133.871 = 30.122 <math>kcalmol^{-1}</math>

=== Reaction Dynamics ===
==== Energy conservation ====

[[File:Skate park.png]]

Model sets reaction as an isolated system, and all atoms obey newtonian laws of physics. Once atom moves downhill, the potential energy is converted into kinetic energy, and is released as vibration of bonds. Temperature is directly proportional to the kinetic energy molecules have, hence as reaction progress, temperature of system would rise. This can be measured by calorimetry experimentally.

====Trajectories table ====
[[File:Trajectory table HF.PNG]]

[[File:Internuclear momentum HF=-0.5 HH=2.9.png]]

During the collision, HH momentum has relatively a small change in comparison with HF momentum After the collision, if the trajectory is reactive, HH momentum will have none to small fluctuation, vice versa for HF momentum. If the trajectory is unreactive, HH momentum will have very large fluctuation, vice versa for HF momentum.

[[File:Internuclear momentum HF=-0.8 HH=0.1.png]]

If pHH = 0.1 and pHF = -0.8, HH momentum has small periodic fluctuations and HF momentum has large periodic fluctuations.

File:Figure 2-2.png

2018-05-18T15:23:12Z

Bc2116:

File:Figure 2-1.png

2018-05-18T15:23:00Z

Bc2116:

File:Surface Plot 2.png

2018-05-18T15:22:51Z

Bc2116:

MRD:bc2116

2018-05-18T15:22:39Z

Bc2116: /* MEP calculations with different initial conditions */

= Molecular Reaction Dynamics: Boru Chen =

== <math>H_2</math> + H system ==

=== Dynamics from Transition State Region ===

The PES has two components:

<math>\frac{\partial V}{\partial r_1}</math> and <math>\frac{\partial V}{\partial r_2}</math>

Where V is the potential energy, and <math>r_1</math> is the intermolecular distance between <math>H_b</math> <math>H_c</math>, <math>r_2</math> is the intermolecular distance between <math>H_a</math> and <math>H_b</math>. At transition structure, both components have value of zero. At energy minima and transition structure, their first derivatives equal to zero. Transition state can be distinguished by taking the second derivative of potential energy. Transition state is at energy maximum along reaction coordinate, and at energy minimum in any other direction, whereas energy minimum is at a minimum in all directions. Mathematically speaking, energy minimum’s second derivative is always a positive value at any position, whereas transition state’s second derivative is negative along reaction coordinate, and positive everywhere else.

==== Transition State Position Estimation ====
Best estimate = 0.9075 Armstrong. Inter nuclear distance vs time plot

[[File:Exercise 1 Internuclear distance to time1.png]]

Note: A-B line can be vaguely seen behind the yellow line.

==== MEP and Dynamic Model Comparison ====
[[File:Exercise 1 MEP plot.png]]
[[File:Exercise 1 Dynamic plot.png]]

MEP plot showed no difference comparing to transition state when first plotted with 500 steps calculated, once the number of steps was increased to 5000, a straight line can be seen following the valley floor to H1 + H2-H3. In comparison, the dynamic plot showed a trajectory which shot off the plot, and the number of steps in calculation had to be truncated to 618. This trajectory bounces between valley walls of H1 + H2-H3.This difference is because the velocity in MEP calculation is reset to 0 after each step, whereas velocity in dynamic calculation isn’t.

==== Internuclear distance and momentum vs time at large t under MEP calculation ====
Internuclear distance vs time
BC: t = 2.49, r = 7.80
AB: t = 2.49, r = 0.74

Internuclear momentum vs time
BC: t = 2.50, p = 2.49
AB: t = 2.51, p =0.97

This shows that <math>H_a</math> and <math>H_b</math> bond has reached equilibrium at large t, whilst <math>H_c</math> has moved away.

==== MEP calculations with different initial conditions ====
1. If we changed the initial conditions (reverse)?
[[File:Surface Plot 1.png]] [[File:Figure 1.png]] [[File:Figure 1-1.png]]
Transition state follows energy valley floor in H3 + H1-H2 direction.
2. If the new initial positions correspond to the final positions above and final momenta values but with their signs reversed?
[[File:Surface Plot 2.png]] [[File:Figure 2-1.png]] [[File:Figure 2-2.png]]
AB and BC momenta become the same, and is the Y axis at 0, 0. AB and BC distances are constant, with large difference between two distances. ABs are further apart. Surface plot cannot be visualised.

=== Reactive and Unreactive Trajectories Table ===

{| class="wikitable" border=1
! p1 !! p2 !! Etot <math>kcalmol^{-1}</math> !! Trajectory
|-
| -1.25 || -2.5 ||| -99.018 ||| [[File:1.png]] ||| Plot shows a reactive trajectory, as AB bond shortens and BC bond lengthens.
|-
| -1.5 || -2.0 ||| -100.456 ||| [[File:2.png]] ||| Plot shows an unreactive trajectory. BC bond never lengthens and AB bond never becomes close enough.
|-
| -1.5 || -2.5 ||| -98.956 ||| [[File:3.png]] ||| Plot shows a reactive trajectory, as AB bond shortens and BC bond lengthens.
|-
| -2.5 || -5.0 ||| -84.956 ||| [[File:444.png]] ||| Plot shows barrier crossing. Although bond does form for some time, however reaction reverts back to reactants.
|-
| -2.5 || -5.2 ||| -83.416 ||| [[File:5.png]] ||| Plot shows barrier crossing. Product is formed
|}

The main assumption is if the incoming atom has enough kinetic energy to overcome kinetic barrier, the reaction will occur. This model also assumes atoms follow newtonian physics.

== F + H + H System ==
=== PES Report ===
[[File:HHF PES.png]]

Plot above illustrate reaction H + H + F system potential energy surface, where A = F, B = H and C = H. Graph shows that HH appears to be deeper in energy valley, hence HH formation is exothermic, and HF formation is endothermic.

==== Position of transition state ====
HH distance 1.812 A

HF distance 0.744 A

[[File:HHF transition state.png]]
==== Activation energy calculation: ====
Positions of these structures were estimated using MEP plot

Transition state potential energy: -103.749 <math>kcalmol^{-1}</math>

H2 potential energy: -133.871 <math>kcalmol^{-1}</math>

[[File:H2 potential energy.PNG]] [[File:H2 internuclear distance vs time.PNG]]

HF potential energy: -103.837 <math>kcalmol^{-1}</math>

[[File:HF_potential_energy.PNG]] [[File:HF internuclear distance vs time.PNG]]

HF + H activation energy = -103.749 - -103.837 = 0.088 <math>kcalmol^{-1}</math>

HH + F activation energy = -103.749 - -133.871 = 30.122 <math>kcalmol^{-1}</math>

=== Reaction Dynamics ===
==== Energy conservation ====

[[File:Skate park.png]]

Model sets reaction as an isolated system, and all atoms obey newtonian laws of physics. Once atom moves downhill, the potential energy is converted into kinetic energy, and is released as vibration of bonds. Temperature is directly proportional to the kinetic energy molecules have, hence as reaction progress, temperature of system would rise. This can be measured by calorimetry experimentally.

====Trajectories table ====
[[File:Trajectory table HF.PNG]]

[[File:Internuclear momentum HF=-0.5 HH=2.9.png]]

During the collision, HH momentum has relatively a small change in comparison with HF momentum After the collision, if the trajectory is reactive, HH momentum will have none to small fluctuation, vice versa for HF momentum. If the trajectory is unreactive, HH momentum will have very large fluctuation, vice versa for HF momentum.

[[File:Internuclear momentum HF=-0.8 HH=0.1.png]]

If pHH = 0.1 and pHF = -0.8, HH momentum has small periodic fluctuations and HF momentum has large periodic fluctuations.

File:Figure 1-1.png

2018-05-18T15:22:12Z

Bc2116: Bc2116 uploaded a new version of File:Figure 1-1.png

File:Figure 1.png

2018-05-18T15:21:38Z

Bc2116: Bc2116 uploaded a new version of File:Figure 1.png

File:Surface Plot 1.png

2018-05-18T15:21:03Z

Bc2116:

MRD:bc2116

2018-05-18T15:04:38Z

Bc2116: /* Energy conservation */

= Molecular Reaction Dynamics: Boru Chen =

== <math>H_2</math> + H system ==

=== Dynamics from Transition State Region ===

The PES has two components:

<math>\frac{\partial V}{\partial r_1}</math> and <math>\frac{\partial V}{\partial r_2}</math>

Where V is the potential energy, and <math>r_1</math> is the intermolecular distance between <math>H_b</math> <math>H_c</math>, <math>r_2</math> is the intermolecular distance between <math>H_a</math> and <math>H_b</math>. At transition structure, both components have value of zero. At energy minima and transition structure, their first derivatives equal to zero. Transition state can be distinguished by taking the second derivative of potential energy. Transition state is at energy maximum along reaction coordinate, and at energy minimum in any other direction, whereas energy minimum is at a minimum in all directions. Mathematically speaking, energy minimum’s second derivative is always a positive value at any position, whereas transition state’s second derivative is negative along reaction coordinate, and positive everywhere else.

==== Transition State Position Estimation ====
Best estimate = 0.9075 Armstrong. Inter nuclear distance vs time plot

[[File:Exercise 1 Internuclear distance to time1.png]]

Note: A-B line can be vaguely seen behind the yellow line.

==== MEP and Dynamic Model Comparison ====
[[File:Exercise 1 MEP plot.png]]
[[File:Exercise 1 Dynamic plot.png]]

MEP plot showed no difference comparing to transition state when first plotted with 500 steps calculated, once the number of steps was increased to 5000, a straight line can be seen following the valley floor to H1 + H2-H3. In comparison, the dynamic plot showed a trajectory which shot off the plot, and the number of steps in calculation had to be truncated to 618. This trajectory bounces between valley walls of H1 + H2-H3.This difference is because the velocity in MEP calculation is reset to 0 after each step, whereas velocity in dynamic calculation isn’t.

==== Internuclear distance and momentum vs time at large t under MEP calculation ====
Internuclear distance vs time
BC: t = 2.49, r = 7.80
AB: t = 2.49, r = 0.74

Internuclear momentum vs time
BC: t = 2.50, p = 2.49
AB: t = 2.51, p =0.97

This shows that <math>H_a</math> and <math>H_b</math> bond has reached equilibrium at large t, whilst <math>H_c</math> has moved away.

==== MEP calculations with different initial conditions ====
1. If we changed the initial conditions (reverse)?
Transition state follows energy valley floor in H3 + H1-H2 direction.
2. If the new initial positions correspond to the final positions above and final momenta values but with their signs reversed?
AB and BC momenta become the same, and is the Y axis at 0, 0. AB and BC distances are constant, with large difference between two distances. ABs are further apart. Surface plot cannot be visualised.

=== Reactive and Unreactive Trajectories Table ===

{| class="wikitable" border=1
! p1 !! p2 !! Etot <math>kcalmol^{-1}</math> !! Trajectory
|-
| -1.25 || -2.5 ||| -99.018 ||| [[File:1.png]] ||| Plot shows a reactive trajectory, as AB bond shortens and BC bond lengthens.
|-
| -1.5 || -2.0 ||| -100.456 ||| [[File:2.png]] ||| Plot shows an unreactive trajectory. BC bond never lengthens and AB bond never becomes close enough.
|-
| -1.5 || -2.5 ||| -98.956 ||| [[File:3.png]] ||| Plot shows a reactive trajectory, as AB bond shortens and BC bond lengthens.
|-
| -2.5 || -5.0 ||| -84.956 ||| [[File:444.png]] ||| Plot shows barrier crossing. Although bond does form for some time, however reaction reverts back to reactants.
|-
| -2.5 || -5.2 ||| -83.416 ||| [[File:5.png]] ||| Plot shows barrier crossing. Product is formed
|}

The main assumption is if the incoming atom has enough kinetic energy to overcome kinetic barrier, the reaction will occur. This model also assumes atoms follow newtonian physics.

== F + H + H System ==
=== PES Report ===
[[File:HHF PES.png]]

Plot above illustrate reaction H + H + F system potential energy surface, where A = F, B = H and C = H. Graph shows that HH appears to be deeper in energy valley, hence HH formation is exothermic, and HF formation is endothermic.

==== Position of transition state ====
HH distance 1.812 A

HF distance 0.744 A

[[File:HHF transition state.png]]
==== Activation energy calculation: ====
Positions of these structures were estimated using MEP plot

Transition state potential energy: -103.749 <math>kcalmol^{-1}</math>

H2 potential energy: -133.871 <math>kcalmol^{-1}</math>

[[File:H2 potential energy.PNG]] [[File:H2 internuclear distance vs time.PNG]]

HF potential energy: -103.837 <math>kcalmol^{-1}</math>

[[File:HF_potential_energy.PNG]] [[File:HF internuclear distance vs time.PNG]]

HF + H activation energy = -103.749 - -103.837 = 0.088 <math>kcalmol^{-1}</math>

HH + F activation energy = -103.749 - -133.871 = 30.122 <math>kcalmol^{-1}</math>

=== Reaction Dynamics ===
==== Energy conservation ====

[[File:Skate park.png]]

Model sets reaction as an isolated system, and all atoms obey newtonian laws of physics. Once atom moves downhill, the potential energy is converted into kinetic energy, and is released as vibration of bonds. Temperature is directly proportional to the kinetic energy molecules have, hence as reaction progress, temperature of system would rise. This can be measured by calorimetry experimentally.

====Trajectories table ====
[[File:Trajectory table HF.PNG]]

[[File:Internuclear momentum HF=-0.5 HH=2.9.png]]

During the collision, HH momentum has relatively a small change in comparison with HF momentum After the collision, if the trajectory is reactive, HH momentum will have none to small fluctuation, vice versa for HF momentum. If the trajectory is unreactive, HH momentum will have very large fluctuation, vice versa for HF momentum.

[[File:Internuclear momentum HF=-0.8 HH=0.1.png]]

If pHH = 0.1 and pHF = -0.8, HH momentum has small periodic fluctuations and HF momentum has large periodic fluctuations.

File:Skate park.png

2018-05-18T15:02:32Z

Bc2116:

MRD:bc2116

2018-05-18T15:00:40Z

Bc2116: /* Reaction Dynamics */

= Molecular Reaction Dynamics: Boru Chen =

== <math>H_2</math> + H system ==

=== Dynamics from Transition State Region ===

The PES has two components:

<math>\frac{\partial V}{\partial r_1}</math> and <math>\frac{\partial V}{\partial r_2}</math>

Where V is the potential energy, and <math>r_1</math> is the intermolecular distance between <math>H_b</math> <math>H_c</math>, <math>r_2</math> is the intermolecular distance between <math>H_a</math> and <math>H_b</math>. At transition structure, both components have value of zero. At energy minima and transition structure, their first derivatives equal to zero. Transition state can be distinguished by taking the second derivative of potential energy. Transition state is at energy maximum along reaction coordinate, and at energy minimum in any other direction, whereas energy minimum is at a minimum in all directions. Mathematically speaking, energy minimum’s second derivative is always a positive value at any position, whereas transition state’s second derivative is negative along reaction coordinate, and positive everywhere else.

==== Transition State Position Estimation ====
Best estimate = 0.9075 Armstrong. Inter nuclear distance vs time plot

[[File:Exercise 1 Internuclear distance to time1.png]]

Note: A-B line can be vaguely seen behind the yellow line.

==== MEP and Dynamic Model Comparison ====
[[File:Exercise 1 MEP plot.png]]
[[File:Exercise 1 Dynamic plot.png]]

MEP plot showed no difference comparing to transition state when first plotted with 500 steps calculated, once the number of steps was increased to 5000, a straight line can be seen following the valley floor to H1 + H2-H3. In comparison, the dynamic plot showed a trajectory which shot off the plot, and the number of steps in calculation had to be truncated to 618. This trajectory bounces between valley walls of H1 + H2-H3.This difference is because the velocity in MEP calculation is reset to 0 after each step, whereas velocity in dynamic calculation isn’t.

==== Internuclear distance and momentum vs time at large t under MEP calculation ====
Internuclear distance vs time
BC: t = 2.49, r = 7.80
AB: t = 2.49, r = 0.74

Internuclear momentum vs time
BC: t = 2.50, p = 2.49
AB: t = 2.51, p =0.97

This shows that <math>H_a</math> and <math>H_b</math> bond has reached equilibrium at large t, whilst <math>H_c</math> has moved away.

==== MEP calculations with different initial conditions ====
1. If we changed the initial conditions (reverse)?
Transition state follows energy valley floor in H3 + H1-H2 direction.
2. If the new initial positions correspond to the final positions above and final momenta values but with their signs reversed?
AB and BC momenta become the same, and is the Y axis at 0, 0. AB and BC distances are constant, with large difference between two distances. ABs are further apart. Surface plot cannot be visualised.

=== Reactive and Unreactive Trajectories Table ===

{| class="wikitable" border=1
! p1 !! p2 !! Etot <math>kcalmol^{-1}</math> !! Trajectory
|-
| -1.25 || -2.5 ||| -99.018 ||| [[File:1.png]] ||| Plot shows a reactive trajectory, as AB bond shortens and BC bond lengthens.
|-
| -1.5 || -2.0 ||| -100.456 ||| [[File:2.png]] ||| Plot shows an unreactive trajectory. BC bond never lengthens and AB bond never becomes close enough.
|-
| -1.5 || -2.5 ||| -98.956 ||| [[File:3.png]] ||| Plot shows a reactive trajectory, as AB bond shortens and BC bond lengthens.
|-
| -2.5 || -5.0 ||| -84.956 ||| [[File:444.png]] ||| Plot shows barrier crossing. Although bond does form for some time, however reaction reverts back to reactants.
|-
| -2.5 || -5.2 ||| -83.416 ||| [[File:5.png]] ||| Plot shows barrier crossing. Product is formed
|}

The main assumption is if the incoming atom has enough kinetic energy to overcome kinetic barrier, the reaction will occur. This model also assumes atoms follow newtonian physics.

== F + H + H System ==
=== PES Report ===
[[File:HHF PES.png]]

Plot above illustrate reaction H + H + F system potential energy surface, where A = F, B = H and C = H. Graph shows that HH appears to be deeper in energy valley, hence HH formation is exothermic, and HF formation is endothermic.

==== Position of transition state ====
HH distance 1.812 A

HF distance 0.744 A

[[File:HHF transition state.png]]
==== Activation energy calculation: ====
Positions of these structures were estimated using MEP plot

Transition state potential energy: -103.749 <math>kcalmol^{-1}</math>

H2 potential energy: -133.871 <math>kcalmol^{-1}</math>

[[File:H2 potential energy.PNG]] [[File:H2 internuclear distance vs time.PNG]]

HF potential energy: -103.837 <math>kcalmol^{-1}</math>

[[File:HF_potential_energy.PNG]] [[File:HF internuclear distance vs time.PNG]]

HF + H activation energy = -103.749 - -103.837 = 0.088 <math>kcalmol^{-1}</math>

HH + F activation energy = -103.749 - -133.871 = 30.122 <math>kcalmol^{-1}</math>

=== Reaction Dynamics ===
==== Energy conservation ====
====Trajectories table ====
[[File:Trajectory table HF.PNG]]

[[File:Internuclear momentum HF=-0.5 HH=2.9.png]]

During the collision, HH momentum has relatively a small change in comparison with HF momentum After the collision, if the trajectory is reactive, HH momentum will have none to small fluctuation, vice versa for HF momentum. If the trajectory is unreactive, HH momentum will have very large fluctuation, vice versa for HF momentum.

[[File:Internuclear momentum HF=-0.8 HH=0.1.png]]

If pHH = 0.1 and pHF = -0.8, HH momentum has small periodic fluctuations and HF momentum has large periodic fluctuations.

MRD:bc2116

2018-05-18T14:59:55Z

Bc2116: /* Trajectories table */

= Molecular Reaction Dynamics: Boru Chen =

== <math>H_2</math> + H system ==

=== Dynamics from Transition State Region ===

The PES has two components:

<math>\frac{\partial V}{\partial r_1}</math> and <math>\frac{\partial V}{\partial r_2}</math>

Where V is the potential energy, and <math>r_1</math> is the intermolecular distance between <math>H_b</math> <math>H_c</math>, <math>r_2</math> is the intermolecular distance between <math>H_a</math> and <math>H_b</math>. At transition structure, both components have value of zero. At energy minima and transition structure, their first derivatives equal to zero. Transition state can be distinguished by taking the second derivative of potential energy. Transition state is at energy maximum along reaction coordinate, and at energy minimum in any other direction, whereas energy minimum is at a minimum in all directions. Mathematically speaking, energy minimum’s second derivative is always a positive value at any position, whereas transition state’s second derivative is negative along reaction coordinate, and positive everywhere else.

==== Transition State Position Estimation ====
Best estimate = 0.9075 Armstrong. Inter nuclear distance vs time plot

[[File:Exercise 1 Internuclear distance to time1.png]]

Note: A-B line can be vaguely seen behind the yellow line.

==== MEP and Dynamic Model Comparison ====
[[File:Exercise 1 MEP plot.png]]
[[File:Exercise 1 Dynamic plot.png]]

MEP plot showed no difference comparing to transition state when first plotted with 500 steps calculated, once the number of steps was increased to 5000, a straight line can be seen following the valley floor to H1 + H2-H3. In comparison, the dynamic plot showed a trajectory which shot off the plot, and the number of steps in calculation had to be truncated to 618. This trajectory bounces between valley walls of H1 + H2-H3.This difference is because the velocity in MEP calculation is reset to 0 after each step, whereas velocity in dynamic calculation isn’t.

==== Internuclear distance and momentum vs time at large t under MEP calculation ====
Internuclear distance vs time
BC: t = 2.49, r = 7.80
AB: t = 2.49, r = 0.74

Internuclear momentum vs time
BC: t = 2.50, p = 2.49
AB: t = 2.51, p =0.97

This shows that <math>H_a</math> and <math>H_b</math> bond has reached equilibrium at large t, whilst <math>H_c</math> has moved away.

==== MEP calculations with different initial conditions ====
1. If we changed the initial conditions (reverse)?
Transition state follows energy valley floor in H3 + H1-H2 direction.
2. If the new initial positions correspond to the final positions above and final momenta values but with their signs reversed?
AB and BC momenta become the same, and is the Y axis at 0, 0. AB and BC distances are constant, with large difference between two distances. ABs are further apart. Surface plot cannot be visualised.

=== Reactive and Unreactive Trajectories Table ===

{| class="wikitable" border=1
! p1 !! p2 !! Etot <math>kcalmol^{-1}</math> !! Trajectory
|-
| -1.25 || -2.5 ||| -99.018 ||| [[File:1.png]] ||| Plot shows a reactive trajectory, as AB bond shortens and BC bond lengthens.
|-
| -1.5 || -2.0 ||| -100.456 ||| [[File:2.png]] ||| Plot shows an unreactive trajectory. BC bond never lengthens and AB bond never becomes close enough.
|-
| -1.5 || -2.5 ||| -98.956 ||| [[File:3.png]] ||| Plot shows a reactive trajectory, as AB bond shortens and BC bond lengthens.
|-
| -2.5 || -5.0 ||| -84.956 ||| [[File:444.png]] ||| Plot shows barrier crossing. Although bond does form for some time, however reaction reverts back to reactants.
|-
| -2.5 || -5.2 ||| -83.416 ||| [[File:5.png]] ||| Plot shows barrier crossing. Product is formed
|}

The main assumption is if the incoming atom has enough kinetic energy to overcome kinetic barrier, the reaction will occur. This model also assumes atoms follow newtonian physics.

== F + H + H System ==
=== PES Report ===
[[File:HHF PES.png]]

Plot above illustrate reaction H + H + F system potential energy surface, where A = F, B = H and C = H. Graph shows that HH appears to be deeper in energy valley, hence HH formation is exothermic, and HF formation is endothermic.

==== Position of transition state ====
HH distance 1.812 A

HF distance 0.744 A

[[File:HHF transition state.png]]
==== Activation energy calculation: ====
Positions of these structures were estimated using MEP plot

Transition state potential energy: -103.749 <math>kcalmol^{-1}</math>

H2 potential energy: -133.871 <math>kcalmol^{-1}</math>

[[File:H2 potential energy.PNG]] [[File:H2 internuclear distance vs time.PNG]]

HF potential energy: -103.837 <math>kcalmol^{-1}</math>

[[File:HF_potential_energy.PNG]] [[File:HF internuclear distance vs time.PNG]]

HF + H activation energy = -103.749 - -103.837 = 0.088 <math>kcalmol^{-1}</math>

HH + F activation energy = -103.749 - -133.871 = 30.122 <math>kcalmol^{-1}</math>

=== Reaction Dynamics ===
====Trajectories table ====
[[File:Trajectory table HF.PNG]]

[[File:Internuclear momentum HF=-0.5 HH=2.9.png]]

During the collision, HH momentum has relatively a small change in comparison with HF momentum After the collision, if the trajectory is reactive, HH momentum will have none to small fluctuation, vice versa for HF momentum. If the trajectory is unreactive, HH momentum will have very large fluctuation, vice versa for HF momentum.

[[File:Internuclear momentum HF=-0.8 HH=0.1.png]]

If pHH = 0.1 and pHF = -0.8, HH momentum has small periodic fluctuations and HF momentum has large periodic fluctuations.

MRD:bc2116

2018-05-18T14:59:38Z

Bc2116: /* Trajectories table */

= Molecular Reaction Dynamics: Boru Chen =

== <math>H_2</math> + H system ==

=== Dynamics from Transition State Region ===

The PES has two components:

<math>\frac{\partial V}{\partial r_1}</math> and <math>\frac{\partial V}{\partial r_2}</math>

Where V is the potential energy, and <math>r_1</math> is the intermolecular distance between <math>H_b</math> <math>H_c</math>, <math>r_2</math> is the intermolecular distance between <math>H_a</math> and <math>H_b</math>. At transition structure, both components have value of zero. At energy minima and transition structure, their first derivatives equal to zero. Transition state can be distinguished by taking the second derivative of potential energy. Transition state is at energy maximum along reaction coordinate, and at energy minimum in any other direction, whereas energy minimum is at a minimum in all directions. Mathematically speaking, energy minimum’s second derivative is always a positive value at any position, whereas transition state’s second derivative is negative along reaction coordinate, and positive everywhere else.

==== Transition State Position Estimation ====
Best estimate = 0.9075 Armstrong. Inter nuclear distance vs time plot

[[File:Exercise 1 Internuclear distance to time1.png]]

Note: A-B line can be vaguely seen behind the yellow line.

==== MEP and Dynamic Model Comparison ====
[[File:Exercise 1 MEP plot.png]]
[[File:Exercise 1 Dynamic plot.png]]

MEP plot showed no difference comparing to transition state when first plotted with 500 steps calculated, once the number of steps was increased to 5000, a straight line can be seen following the valley floor to H1 + H2-H3. In comparison, the dynamic plot showed a trajectory which shot off the plot, and the number of steps in calculation had to be truncated to 618. This trajectory bounces between valley walls of H1 + H2-H3.This difference is because the velocity in MEP calculation is reset to 0 after each step, whereas velocity in dynamic calculation isn’t.

==== Internuclear distance and momentum vs time at large t under MEP calculation ====
Internuclear distance vs time
BC: t = 2.49, r = 7.80
AB: t = 2.49, r = 0.74

Internuclear momentum vs time
BC: t = 2.50, p = 2.49
AB: t = 2.51, p =0.97

This shows that <math>H_a</math> and <math>H_b</math> bond has reached equilibrium at large t, whilst <math>H_c</math> has moved away.

==== MEP calculations with different initial conditions ====
1. If we changed the initial conditions (reverse)?
Transition state follows energy valley floor in H3 + H1-H2 direction.
2. If the new initial positions correspond to the final positions above and final momenta values but with their signs reversed?
AB and BC momenta become the same, and is the Y axis at 0, 0. AB and BC distances are constant, with large difference between two distances. ABs are further apart. Surface plot cannot be visualised.

=== Reactive and Unreactive Trajectories Table ===

{| class="wikitable" border=1
! p1 !! p2 !! Etot <math>kcalmol^{-1}</math> !! Trajectory
|-
| -1.25 || -2.5 ||| -99.018 ||| [[File:1.png]] ||| Plot shows a reactive trajectory, as AB bond shortens and BC bond lengthens.
|-
| -1.5 || -2.0 ||| -100.456 ||| [[File:2.png]] ||| Plot shows an unreactive trajectory. BC bond never lengthens and AB bond never becomes close enough.
|-
| -1.5 || -2.5 ||| -98.956 ||| [[File:3.png]] ||| Plot shows a reactive trajectory, as AB bond shortens and BC bond lengthens.
|-
| -2.5 || -5.0 ||| -84.956 ||| [[File:444.png]] ||| Plot shows barrier crossing. Although bond does form for some time, however reaction reverts back to reactants.
|-
| -2.5 || -5.2 ||| -83.416 ||| [[File:5.png]] ||| Plot shows barrier crossing. Product is formed
|}

The main assumption is if the incoming atom has enough kinetic energy to overcome kinetic barrier, the reaction will occur. This model also assumes atoms follow newtonian physics.

== F + H + H System ==
=== PES Report ===
[[File:HHF PES.png]]

Plot above illustrate reaction H + H + F system potential energy surface, where A = F, B = H and C = H. Graph shows that HH appears to be deeper in energy valley, hence HH formation is exothermic, and HF formation is endothermic.

==== Position of transition state ====
HH distance 1.812 A

HF distance 0.744 A

[[File:HHF transition state.png]]
==== Activation energy calculation: ====
Positions of these structures were estimated using MEP plot

Transition state potential energy: -103.749 <math>kcalmol^{-1}</math>

H2 potential energy: -133.871 <math>kcalmol^{-1}</math>

[[File:H2 potential energy.PNG]] [[File:H2 internuclear distance vs time.PNG]]

HF potential energy: -103.837 <math>kcalmol^{-1}</math>

[[File:HF_potential_energy.PNG]] [[File:HF internuclear distance vs time.PNG]]

HF + H activation energy = -103.749 - -103.837 = 0.088 <math>kcalmol^{-1}</math>

HH + F activation energy = -103.749 - -133.871 = 30.122 <math>kcalmol^{-1}</math>

=== Reaction Dynamics ===
====Trajectories table ====
[[File:Trajectory table HF.PNG]]

[[File:Internuclear momentum HF=-0.5 HH=2.9.png]]

During the collision, HH momentum has relatively a small change in comparison with HF momentum After the collision, if the trajectory is reactive, HH momentum will have none to small fluctuation, vice versa for HF momentum. If the trajectory is unreactive, HH momentum will have very large fluctuation, vice versa for HF momentum.

[[File:Internuclear momentum HF=-0.8 HH=0.1.png]]
If pHH = 0.1 and pHF = -0.8, HH momentum has small periodic fluctuations and HF momentum has large periodic fluctuations.

File:Internuclear momentum HF=-0.8 HH=0.1.png

2018-05-18T14:59:15Z

Bc2116:

File:Internuclear momentum HF=-0.5 HH=2.9.png

2018-05-18T14:58:36Z

Bc2116:

MRD:bc2116

2018-05-18T14:57:43Z

Bc2116: /* PES Report */

= Molecular Reaction Dynamics: Boru Chen =

== <math>H_2</math> + H system ==

=== Dynamics from Transition State Region ===

The PES has two components:

<math>\frac{\partial V}{\partial r_1}</math> and <math>\frac{\partial V}{\partial r_2}</math>

Where V is the potential energy, and <math>r_1</math> is the intermolecular distance between <math>H_b</math> <math>H_c</math>, <math>r_2</math> is the intermolecular distance between <math>H_a</math> and <math>H_b</math>. At transition structure, both components have value of zero. At energy minima and transition structure, their first derivatives equal to zero. Transition state can be distinguished by taking the second derivative of potential energy. Transition state is at energy maximum along reaction coordinate, and at energy minimum in any other direction, whereas energy minimum is at a minimum in all directions. Mathematically speaking, energy minimum’s second derivative is always a positive value at any position, whereas transition state’s second derivative is negative along reaction coordinate, and positive everywhere else.

==== Transition State Position Estimation ====
Best estimate = 0.9075 Armstrong. Inter nuclear distance vs time plot

[[File:Exercise 1 Internuclear distance to time1.png]]

Note: A-B line can be vaguely seen behind the yellow line.

==== MEP and Dynamic Model Comparison ====
[[File:Exercise 1 MEP plot.png]]
[[File:Exercise 1 Dynamic plot.png]]

MEP plot showed no difference comparing to transition state when first plotted with 500 steps calculated, once the number of steps was increased to 5000, a straight line can be seen following the valley floor to H1 + H2-H3. In comparison, the dynamic plot showed a trajectory which shot off the plot, and the number of steps in calculation had to be truncated to 618. This trajectory bounces between valley walls of H1 + H2-H3.This difference is because the velocity in MEP calculation is reset to 0 after each step, whereas velocity in dynamic calculation isn’t.

==== Internuclear distance and momentum vs time at large t under MEP calculation ====
Internuclear distance vs time
BC: t = 2.49, r = 7.80
AB: t = 2.49, r = 0.74

Internuclear momentum vs time
BC: t = 2.50, p = 2.49
AB: t = 2.51, p =0.97

This shows that <math>H_a</math> and <math>H_b</math> bond has reached equilibrium at large t, whilst <math>H_c</math> has moved away.

==== MEP calculations with different initial conditions ====
1. If we changed the initial conditions (reverse)?
Transition state follows energy valley floor in H3 + H1-H2 direction.
2. If the new initial positions correspond to the final positions above and final momenta values but with their signs reversed?
AB and BC momenta become the same, and is the Y axis at 0, 0. AB and BC distances are constant, with large difference between two distances. ABs are further apart. Surface plot cannot be visualised.

=== Reactive and Unreactive Trajectories Table ===

{| class="wikitable" border=1
! p1 !! p2 !! Etot <math>kcalmol^{-1}</math> !! Trajectory
|-
| -1.25 || -2.5 ||| -99.018 ||| [[File:1.png]] ||| Plot shows a reactive trajectory, as AB bond shortens and BC bond lengthens.
|-
| -1.5 || -2.0 ||| -100.456 ||| [[File:2.png]] ||| Plot shows an unreactive trajectory. BC bond never lengthens and AB bond never becomes close enough.
|-
| -1.5 || -2.5 ||| -98.956 ||| [[File:3.png]] ||| Plot shows a reactive trajectory, as AB bond shortens and BC bond lengthens.
|-
| -2.5 || -5.0 ||| -84.956 ||| [[File:444.png]] ||| Plot shows barrier crossing. Although bond does form for some time, however reaction reverts back to reactants.
|-
| -2.5 || -5.2 ||| -83.416 ||| [[File:5.png]] ||| Plot shows barrier crossing. Product is formed
|}

The main assumption is if the incoming atom has enough kinetic energy to overcome kinetic barrier, the reaction will occur. This model also assumes atoms follow newtonian physics.

== F + H + H System ==
=== PES Report ===
[[File:HHF PES.png]]

Plot above illustrate reaction H + H + F system potential energy surface, where A = F, B = H and C = H. Graph shows that HH appears to be deeper in energy valley, hence HH formation is exothermic, and HF formation is endothermic.

==== Position of transition state ====
HH distance 1.812 A

HF distance 0.744 A

[[File:HHF transition state.png]]
==== Activation energy calculation: ====
Positions of these structures were estimated using MEP plot

Transition state potential energy: -103.749 <math>kcalmol^{-1}</math>

H2 potential energy: -133.871 <math>kcalmol^{-1}</math>

[[File:H2 potential energy.PNG]] [[File:H2 internuclear distance vs time.PNG]]

HF potential energy: -103.837 <math>kcalmol^{-1}</math>

[[File:HF_potential_energy.PNG]] [[File:HF internuclear distance vs time.PNG]]

HF + H activation energy = -103.749 - -103.837 = 0.088 <math>kcalmol^{-1}</math>

HH + F activation energy = -103.749 - -133.871 = 30.122 <math>kcalmol^{-1}</math>

=== Reaction Dynamics ===
====Trajectories table ====
[[File:Trajectory table HF.PNG]]

During the collision, HH momentum has relatively a small change in comparison with HF momentum After the collision, if the trajectory is reactive, HH momentum will have none to small fluctuation, vice versa for HF momentum. If the trajectory is unreactive, HH momentum will have very large fluctuation, vice versa for HF momentum.

If pHH = 0.1 and pHF = -0.8, HH momentum has small periodic fluctuations and HF momentum has large periodic fluctuations.

MRD:bc2116

2018-05-18T14:55:13Z

Bc2116: /* F + H + H System */

= Molecular Reaction Dynamics: Boru Chen =

== <math>H_2</math> + H system ==

=== Dynamics from Transition State Region ===

The PES has two components:

<math>\frac{\partial V}{\partial r_1}</math> and <math>\frac{\partial V}{\partial r_2}</math>

Where V is the potential energy, and <math>r_1</math> is the intermolecular distance between <math>H_b</math> <math>H_c</math>, <math>r_2</math> is the intermolecular distance between <math>H_a</math> and <math>H_b</math>. At transition structure, both components have value of zero. At energy minima and transition structure, their first derivatives equal to zero. Transition state can be distinguished by taking the second derivative of potential energy. Transition state is at energy maximum along reaction coordinate, and at energy minimum in any other direction, whereas energy minimum is at a minimum in all directions. Mathematically speaking, energy minimum’s second derivative is always a positive value at any position, whereas transition state’s second derivative is negative along reaction coordinate, and positive everywhere else.

==== Transition State Position Estimation ====
Best estimate = 0.9075 Armstrong. Inter nuclear distance vs time plot

[[File:Exercise 1 Internuclear distance to time1.png]]

Note: A-B line can be vaguely seen behind the yellow line.

==== MEP and Dynamic Model Comparison ====
[[File:Exercise 1 MEP plot.png]]
[[File:Exercise 1 Dynamic plot.png]]

MEP plot showed no difference comparing to transition state when first plotted with 500 steps calculated, once the number of steps was increased to 5000, a straight line can be seen following the valley floor to H1 + H2-H3. In comparison, the dynamic plot showed a trajectory which shot off the plot, and the number of steps in calculation had to be truncated to 618. This trajectory bounces between valley walls of H1 + H2-H3.This difference is because the velocity in MEP calculation is reset to 0 after each step, whereas velocity in dynamic calculation isn’t.

==== Internuclear distance and momentum vs time at large t under MEP calculation ====
Internuclear distance vs time
BC: t = 2.49, r = 7.80
AB: t = 2.49, r = 0.74

Internuclear momentum vs time
BC: t = 2.50, p = 2.49
AB: t = 2.51, p =0.97

This shows that <math>H_a</math> and <math>H_b</math> bond has reached equilibrium at large t, whilst <math>H_c</math> has moved away.

==== MEP calculations with different initial conditions ====
1. If we changed the initial conditions (reverse)?
Transition state follows energy valley floor in H3 + H1-H2 direction.
2. If the new initial positions correspond to the final positions above and final momenta values but with their signs reversed?
AB and BC momenta become the same, and is the Y axis at 0, 0. AB and BC distances are constant, with large difference between two distances. ABs are further apart. Surface plot cannot be visualised.

=== Reactive and Unreactive Trajectories Table ===

{| class="wikitable" border=1
! p1 !! p2 !! Etot <math>kcalmol^{-1}</math> !! Trajectory
|-
| -1.25 || -2.5 ||| -99.018 ||| [[File:1.png]] ||| Plot shows a reactive trajectory, as AB bond shortens and BC bond lengthens.
|-
| -1.5 || -2.0 ||| -100.456 ||| [[File:2.png]] ||| Plot shows an unreactive trajectory. BC bond never lengthens and AB bond never becomes close enough.
|-
| -1.5 || -2.5 ||| -98.956 ||| [[File:3.png]] ||| Plot shows a reactive trajectory, as AB bond shortens and BC bond lengthens.
|-
| -2.5 || -5.0 ||| -84.956 ||| [[File:444.png]] ||| Plot shows barrier crossing. Although bond does form for some time, however reaction reverts back to reactants.
|-
| -2.5 || -5.2 ||| -83.416 ||| [[File:5.png]] ||| Plot shows barrier crossing. Product is formed
|}

The main assumption is if the incoming atom has enough kinetic energy to overcome kinetic barrier, the reaction will occur. This model also assumes atoms follow newtonian physics.

== F + H + H System ==
=== PES Report ===
HF formation: Reaction is exothermic, and H2 formation: Reaction is endothermic.

[[File:HHF PES.png]]

==== Position of transition state ====
HH distance 1.812 A

HF distance 0.744 A

[[File:HHF transition state.png]]
==== Activation energy calculation: ====
Positions of these structures were estimated using MEP plot

Transition state potential energy: -103.749 <math>kcalmol^{-1}</math>

H2 potential energy: -133.871 <math>kcalmol^{-1}</math>

[[File:H2 potential energy.PNG]] [[File:H2 internuclear distance vs time.PNG]]

HF potential energy: -103.837 <math>kcalmol^{-1}</math>

[[File:HF_potential_energy.PNG]] [[File:HF internuclear distance vs time.PNG]]

HF + H activation energy = -103.749 - -103.837 = 0.088 <math>kcalmol^{-1}</math>

HH + F activation energy = -103.749 - -133.871 = 30.122 <math>kcalmol^{-1}</math>

=== Reaction Dynamics ===
====Trajectories table ====
[[File:Trajectory table HF.PNG]]

During the collision, HH momentum has relatively a small change in comparison with HF momentum After the collision, if the trajectory is reactive, HH momentum will have none to small fluctuation, vice versa for HF momentum. If the trajectory is unreactive, HH momentum will have very large fluctuation, vice versa for HF momentum.

If pHH = 0.1 and pHF = -0.8, HH momentum has small periodic fluctuations and HF momentum has large periodic fluctuations.

File:HHF transition state.png

2018-05-18T14:54:58Z

Bc2116:

File:HHF PES.png

2018-05-18T14:53:59Z

Bc2116:

MRD:bc2116

2018-05-18T14:50:14Z

Bc2116: /* Reactive and Unreactive Trajectories Table */

= Molecular Reaction Dynamics: Boru Chen =

== <math>H_2</math> + H system ==

=== Dynamics from Transition State Region ===

The PES has two components:

<math>\frac{\partial V}{\partial r_1}</math> and <math>\frac{\partial V}{\partial r_2}</math>

Where V is the potential energy, and <math>r_1</math> is the intermolecular distance between <math>H_b</math> <math>H_c</math>, <math>r_2</math> is the intermolecular distance between <math>H_a</math> and <math>H_b</math>. At transition structure, both components have value of zero. At energy minima and transition structure, their first derivatives equal to zero. Transition state can be distinguished by taking the second derivative of potential energy. Transition state is at energy maximum along reaction coordinate, and at energy minimum in any other direction, whereas energy minimum is at a minimum in all directions. Mathematically speaking, energy minimum’s second derivative is always a positive value at any position, whereas transition state’s second derivative is negative along reaction coordinate, and positive everywhere else.

==== Transition State Position Estimation ====
Best estimate = 0.9075 Armstrong. Inter nuclear distance vs time plot

[[File:Exercise 1 Internuclear distance to time1.png]]

Note: A-B line can be vaguely seen behind the yellow line.

==== MEP and Dynamic Model Comparison ====
[[File:Exercise 1 MEP plot.png]]
[[File:Exercise 1 Dynamic plot.png]]

MEP plot showed no difference comparing to transition state when first plotted with 500 steps calculated, once the number of steps was increased to 5000, a straight line can be seen following the valley floor to H1 + H2-H3. In comparison, the dynamic plot showed a trajectory which shot off the plot, and the number of steps in calculation had to be truncated to 618. This trajectory bounces between valley walls of H1 + H2-H3.This difference is because the velocity in MEP calculation is reset to 0 after each step, whereas velocity in dynamic calculation isn’t.

==== Internuclear distance and momentum vs time at large t under MEP calculation ====
Internuclear distance vs time
BC: t = 2.49, r = 7.80
AB: t = 2.49, r = 0.74

Internuclear momentum vs time
BC: t = 2.50, p = 2.49
AB: t = 2.51, p =0.97

This shows that <math>H_a</math> and <math>H_b</math> bond has reached equilibrium at large t, whilst <math>H_c</math> has moved away.

==== MEP calculations with different initial conditions ====
1. If we changed the initial conditions (reverse)?
Transition state follows energy valley floor in H3 + H1-H2 direction.
2. If the new initial positions correspond to the final positions above and final momenta values but with their signs reversed?
AB and BC momenta become the same, and is the Y axis at 0, 0. AB and BC distances are constant, with large difference between two distances. ABs are further apart. Surface plot cannot be visualised.

=== Reactive and Unreactive Trajectories Table ===

{| class="wikitable" border=1
! p1 !! p2 !! Etot <math>kcalmol^{-1}</math> !! Trajectory
|-
| -1.25 || -2.5 ||| -99.018 ||| [[File:1.png]] ||| Plot shows a reactive trajectory, as AB bond shortens and BC bond lengthens.
|-
| -1.5 || -2.0 ||| -100.456 ||| [[File:2.png]] ||| Plot shows an unreactive trajectory. BC bond never lengthens and AB bond never becomes close enough.
|-
| -1.5 || -2.5 ||| -98.956 ||| [[File:3.png]] ||| Plot shows a reactive trajectory, as AB bond shortens and BC bond lengthens.
|-
| -2.5 || -5.0 ||| -84.956 ||| [[File:444.png]] ||| Plot shows barrier crossing. Although bond does form for some time, however reaction reverts back to reactants.
|-
| -2.5 || -5.2 ||| -83.416 ||| [[File:5.png]] ||| Plot shows barrier crossing. Product is formed
|}

The main assumption is if the incoming atom has enough kinetic energy to overcome kinetic barrier, the reaction will occur. This model also assumes atoms follow newtonian physics.

== F + H + H System ==
=== PES Report ===
HF formation: Reaction is exothermic, and H2 formation: Reaction is endothermic. Further explanation using graph

==== Position of transition state ====
HH distance 1.812 A

HF distance 0.742 A

==== Activation energy calculation: ====
Positions of these structures were estimated using MEP plot

Transition state potential energy: -103.749 <math>kcalmol^{-1}</math>

H2 potential energy: -133.871 <math>kcalmol^{-1}</math>

[[File:H2 potential energy.PNG]] [[File:H2 internuclear distance vs time.PNG]]

HF potential energy: -103.837 <math>kcalmol^{-1}</math>

[[File:HF_potential_energy.PNG]] [[File:HF internuclear distance vs time.PNG]]

HF + H activation energy = -103.749 - -103.837 = 0.088 <math>kcalmol^{-1}</math>

HH + F activation energy = -103.749 - -133.871 = 30.122 <math>kcalmol^{-1}</math>

=== Reaction Dynamics ===
====Trajectories table ====
[[File:Trajectory table HF.PNG]]

During the collision, HH momentum has relatively a small change in comparison with HF momentum After the collision, if the trajectory is reactive, HH momentum will have none to small fluctuation, vice versa for HF momentum. If the trajectory is unreactive, HH momentum will have very large fluctuation, vice versa for HF momentum.

If pHH = 0.1 and pHF = -0.8, HH momentum has small periodic fluctuations and HF momentum has large periodic fluctuations.

MRD:bc2116

2018-05-18T14:45:12Z

Bc2116: /* Reactive and Unreactive Trajectories Table */

= Molecular Reaction Dynamics: Boru Chen =

== <math>H_2</math> + H system ==

=== Dynamics from Transition State Region ===

The PES has two components:

<math>\frac{\partial V}{\partial r_1}</math> and <math>\frac{\partial V}{\partial r_2}</math>

Where V is the potential energy, and <math>r_1</math> is the intermolecular distance between <math>H_b</math> <math>H_c</math>, <math>r_2</math> is the intermolecular distance between <math>H_a</math> and <math>H_b</math>. At transition structure, both components have value of zero. At energy minima and transition structure, their first derivatives equal to zero. Transition state can be distinguished by taking the second derivative of potential energy. Transition state is at energy maximum along reaction coordinate, and at energy minimum in any other direction, whereas energy minimum is at a minimum in all directions. Mathematically speaking, energy minimum’s second derivative is always a positive value at any position, whereas transition state’s second derivative is negative along reaction coordinate, and positive everywhere else.

==== Transition State Position Estimation ====
Best estimate = 0.9075 Armstrong. Inter nuclear distance vs time plot

[[File:Exercise 1 Internuclear distance to time1.png]]

Note: A-B line can be vaguely seen behind the yellow line.

==== MEP and Dynamic Model Comparison ====
[[File:Exercise 1 MEP plot.png]]
[[File:Exercise 1 Dynamic plot.png]]

MEP plot showed no difference comparing to transition state when first plotted with 500 steps calculated, once the number of steps was increased to 5000, a straight line can be seen following the valley floor to H1 + H2-H3. In comparison, the dynamic plot showed a trajectory which shot off the plot, and the number of steps in calculation had to be truncated to 618. This trajectory bounces between valley walls of H1 + H2-H3.This difference is because the velocity in MEP calculation is reset to 0 after each step, whereas velocity in dynamic calculation isn’t.

==== Internuclear distance and momentum vs time at large t under MEP calculation ====
Internuclear distance vs time
BC: t = 2.49, r = 7.80
AB: t = 2.49, r = 0.74

Internuclear momentum vs time
BC: t = 2.50, p = 2.49
AB: t = 2.51, p =0.97

This shows that <math>H_a</math> and <math>H_b</math> bond has reached equilibrium at large t, whilst <math>H_c</math> has moved away.

==== MEP calculations with different initial conditions ====
1. If we changed the initial conditions (reverse)?
Transition state follows energy valley floor in H3 + H1-H2 direction.
2. If the new initial positions correspond to the final positions above and final momenta values but with their signs reversed?
AB and BC momenta become the same, and is the Y axis at 0, 0. AB and BC distances are constant, with large difference between two distances. ABs are further apart. Surface plot cannot be visualised.

=== Reactive and Unreactive Trajectories Table ===

{| class="wikitable" border=1
! p1 !! p2 !! Etot <math>kcalmol^{-1}</math> !! Trajectory
|-
| -1.25 || -2.5 ||| -99.018 ||| [[File:1.png]]
|-
| -1.5 || -2.0 ||| -100.456 ||| [[File:2.png]]
|-
| -1.5 || -2.5 ||| -98.956 ||| [[File:3.png]]
|-
| -2.5 || -5.0 ||| -84.956 ||| [[File:444.png]]
|-
| -2.5 || -5.2 ||| -83.416 ||| [[File:5.png]]
|}

The main assumption is if the incoming atom has enough kinetic energy to overcome kinetic barrier, the reaction will occur. This model also assumes atoms follow newtonian physics.

== F + H + H System ==
=== PES Report ===
HF formation: Reaction is exothermic, and H2 formation: Reaction is endothermic. Further explanation using graph

==== Position of transition state ====
HH distance 1.812 A

HF distance 0.742 A

==== Activation energy calculation: ====
Positions of these structures were estimated using MEP plot

Transition state potential energy: -103.749 <math>kcalmol^{-1}</math>

H2 potential energy: -133.871 <math>kcalmol^{-1}</math>

[[File:H2 potential energy.PNG]] [[File:H2 internuclear distance vs time.PNG]]

HF potential energy: -103.837 <math>kcalmol^{-1}</math>

[[File:HF_potential_energy.PNG]] [[File:HF internuclear distance vs time.PNG]]

HF + H activation energy = -103.749 - -103.837 = 0.088 <math>kcalmol^{-1}</math>

HH + F activation energy = -103.749 - -133.871 = 30.122 <math>kcalmol^{-1}</math>

=== Reaction Dynamics ===
====Trajectories table ====
[[File:Trajectory table HF.PNG]]

During the collision, HH momentum has relatively a small change in comparison with HF momentum After the collision, if the trajectory is reactive, HH momentum will have none to small fluctuation, vice versa for HF momentum. If the trajectory is unreactive, HH momentum will have very large fluctuation, vice versa for HF momentum.

If pHH = 0.1 and pHF = -0.8, HH momentum has small periodic fluctuations and HF momentum has large periodic fluctuations.

File:444.png

2018-05-18T14:44:07Z

Bc2116:

MRD:bc2116

2018-05-18T14:42:40Z

Bc2116: /* Reactive and Unreactive Trajectories Table */

= Molecular Reaction Dynamics: Boru Chen =

== <math>H_2</math> + H system ==

=== Dynamics from Transition State Region ===

The PES has two components:

<math>\frac{\partial V}{\partial r_1}</math> and <math>\frac{\partial V}{\partial r_2}</math>

Where V is the potential energy, and <math>r_1</math> is the intermolecular distance between <math>H_b</math> <math>H_c</math>, <math>r_2</math> is the intermolecular distance between <math>H_a</math> and <math>H_b</math>. At transition structure, both components have value of zero. At energy minima and transition structure, their first derivatives equal to zero. Transition state can be distinguished by taking the second derivative of potential energy. Transition state is at energy maximum along reaction coordinate, and at energy minimum in any other direction, whereas energy minimum is at a minimum in all directions. Mathematically speaking, energy minimum’s second derivative is always a positive value at any position, whereas transition state’s second derivative is negative along reaction coordinate, and positive everywhere else.

==== Transition State Position Estimation ====
Best estimate = 0.9075 Armstrong. Inter nuclear distance vs time plot

[[File:Exercise 1 Internuclear distance to time1.png]]

Note: A-B line can be vaguely seen behind the yellow line.

==== MEP and Dynamic Model Comparison ====
[[File:Exercise 1 MEP plot.png]]
[[File:Exercise 1 Dynamic plot.png]]

MEP plot showed no difference comparing to transition state when first plotted with 500 steps calculated, once the number of steps was increased to 5000, a straight line can be seen following the valley floor to H1 + H2-H3. In comparison, the dynamic plot showed a trajectory which shot off the plot, and the number of steps in calculation had to be truncated to 618. This trajectory bounces between valley walls of H1 + H2-H3.This difference is because the velocity in MEP calculation is reset to 0 after each step, whereas velocity in dynamic calculation isn’t.

==== Internuclear distance and momentum vs time at large t under MEP calculation ====
Internuclear distance vs time
BC: t = 2.49, r = 7.80
AB: t = 2.49, r = 0.74

Internuclear momentum vs time
BC: t = 2.50, p = 2.49
AB: t = 2.51, p =0.97

This shows that <math>H_a</math> and <math>H_b</math> bond has reached equilibrium at large t, whilst <math>H_c</math> has moved away.

==== MEP calculations with different initial conditions ====
1. If we changed the initial conditions (reverse)?
Transition state follows energy valley floor in H3 + H1-H2 direction.
2. If the new initial positions correspond to the final positions above and final momenta values but with their signs reversed?
AB and BC momenta become the same, and is the Y axis at 0, 0. AB and BC distances are constant, with large difference between two distances. ABs are further apart. Surface plot cannot be visualised.

=== Reactive and Unreactive Trajectories Table ===

{| class="wikitable" border=1
! p1 !! p2 !! Etot <math>kcalmol^{-1}</math> !! !! Trajectory
|-
| -1.25 || -2.5 ||| -99.018 |||| [[File:1.png]]
|-
| -1.5 || -2.0 ||| -100.456 |||| [[File:2.png]]
|-
| -1.5 || -2.5 ||| -98.956 |||| [[File:3.png]]
|-
| -2.5 || -5.0 ||| -84.956 |||| [[File:444.png]]
|-
| -2.5 || -5.2 ||| -83.416 |||| [[File:5.png]]
|}

The main assumption is if the incoming atom has enough kinetic energy to overcome kinetic barrier, the reaction will occur. This model also assumes atoms follow newtonian physics.

== F + H + H System ==
=== PES Report ===
HF formation: Reaction is exothermic, and H2 formation: Reaction is endothermic. Further explanation using graph

==== Position of transition state ====
HH distance 1.812 A

HF distance 0.742 A

==== Activation energy calculation: ====
Positions of these structures were estimated using MEP plot

Transition state potential energy: -103.749 <math>kcalmol^{-1}</math>

H2 potential energy: -133.871 <math>kcalmol^{-1}</math>

[[File:H2 potential energy.PNG]] [[File:H2 internuclear distance vs time.PNG]]

HF potential energy: -103.837 <math>kcalmol^{-1}</math>

[[File:HF_potential_energy.PNG]] [[File:HF internuclear distance vs time.PNG]]

HF + H activation energy = -103.749 - -103.837 = 0.088 <math>kcalmol^{-1}</math>

HH + F activation energy = -103.749 - -133.871 = 30.122 <math>kcalmol^{-1}</math>

=== Reaction Dynamics ===
====Trajectories table ====
[[File:Trajectory table HF.PNG]]

During the collision, HH momentum has relatively a small change in comparison with HF momentum After the collision, if the trajectory is reactive, HH momentum will have none to small fluctuation, vice versa for HF momentum. If the trajectory is unreactive, HH momentum will have very large fluctuation, vice versa for HF momentum.

If pHH = 0.1 and pHF = -0.8, HH momentum has small periodic fluctuations and HF momentum has large periodic fluctuations.

MRD:bc2116

2018-05-18T14:41:38Z

Bc2116: /* Reactive and Unreactive Trajectories Table */

= Molecular Reaction Dynamics: Boru Chen =

== <math>H_2</math> + H system ==

=== Dynamics from Transition State Region ===

The PES has two components:

<math>\frac{\partial V}{\partial r_1}</math> and <math>\frac{\partial V}{\partial r_2}</math>

Where V is the potential energy, and <math>r_1</math> is the intermolecular distance between <math>H_b</math> <math>H_c</math>, <math>r_2</math> is the intermolecular distance between <math>H_a</math> and <math>H_b</math>. At transition structure, both components have value of zero. At energy minima and transition structure, their first derivatives equal to zero. Transition state can be distinguished by taking the second derivative of potential energy. Transition state is at energy maximum along reaction coordinate, and at energy minimum in any other direction, whereas energy minimum is at a minimum in all directions. Mathematically speaking, energy minimum’s second derivative is always a positive value at any position, whereas transition state’s second derivative is negative along reaction coordinate, and positive everywhere else.

==== Transition State Position Estimation ====
Best estimate = 0.9075 Armstrong. Inter nuclear distance vs time plot

[[File:Exercise 1 Internuclear distance to time1.png]]

Note: A-B line can be vaguely seen behind the yellow line.

==== MEP and Dynamic Model Comparison ====
[[File:Exercise 1 MEP plot.png]]
[[File:Exercise 1 Dynamic plot.png]]

MEP plot showed no difference comparing to transition state when first plotted with 500 steps calculated, once the number of steps was increased to 5000, a straight line can be seen following the valley floor to H1 + H2-H3. In comparison, the dynamic plot showed a trajectory which shot off the plot, and the number of steps in calculation had to be truncated to 618. This trajectory bounces between valley walls of H1 + H2-H3.This difference is because the velocity in MEP calculation is reset to 0 after each step, whereas velocity in dynamic calculation isn’t.

==== Internuclear distance and momentum vs time at large t under MEP calculation ====
Internuclear distance vs time
BC: t = 2.49, r = 7.80
AB: t = 2.49, r = 0.74

Internuclear momentum vs time
BC: t = 2.50, p = 2.49
AB: t = 2.51, p =0.97

This shows that <math>H_a</math> and <math>H_b</math> bond has reached equilibrium at large t, whilst <math>H_c</math> has moved away.

==== MEP calculations with different initial conditions ====
1. If we changed the initial conditions (reverse)?
Transition state follows energy valley floor in H3 + H1-H2 direction.
2. If the new initial positions correspond to the final positions above and final momenta values but with their signs reversed?
AB and BC momenta become the same, and is the Y axis at 0, 0. AB and BC distances are constant, with large difference between two distances. ABs are further apart. Surface plot cannot be visualised.

=== Reactive and Unreactive Trajectories Table ===

{| class="wikitable" border=1
! p1 !! p2 !! Etot <math>kcalmol^{-1}</math> !! !! Trajectory
|-
| -1.25 || -2.5 ||| -99.018 |||| [[File:1.png]]
|-
| -1.5 || -2.0 ||| -100.456 |||| [[File:2.png]]
|-
| -1.5 || -2.5 ||| -98.956 |||| [[File:3.png]]
|-
| -2.5 || -5.0 ||| -84.956 |||| [[File:4.png]]
|-
| -2.5 || -5.2 ||| -83.416 |||| [[File:5.png]]
|}

The main assumption is if the incoming atom has enough kinetic energy to overcome kinetic barrier, the reaction will occur. This model also assumes atoms follow newtonian physics.

== F + H + H System ==
=== PES Report ===
HF formation: Reaction is exothermic, and H2 formation: Reaction is endothermic. Further explanation using graph

==== Position of transition state ====
HH distance 1.812 A

HF distance 0.742 A

==== Activation energy calculation: ====
Positions of these structures were estimated using MEP plot

Transition state potential energy: -103.749 <math>kcalmol^{-1}</math>

H2 potential energy: -133.871 <math>kcalmol^{-1}</math>

[[File:H2 potential energy.PNG]] [[File:H2 internuclear distance vs time.PNG]]

HF potential energy: -103.837 <math>kcalmol^{-1}</math>

[[File:HF_potential_energy.PNG]] [[File:HF internuclear distance vs time.PNG]]

HF + H activation energy = -103.749 - -103.837 = 0.088 <math>kcalmol^{-1}</math>

HH + F activation energy = -103.749 - -133.871 = 30.122 <math>kcalmol^{-1}</math>

=== Reaction Dynamics ===
====Trajectories table ====
[[File:Trajectory table HF.PNG]]

During the collision, HH momentum has relatively a small change in comparison with HF momentum After the collision, if the trajectory is reactive, HH momentum will have none to small fluctuation, vice versa for HF momentum. If the trajectory is unreactive, HH momentum will have very large fluctuation, vice versa for HF momentum.

If pHH = 0.1 and pHF = -0.8, HH momentum has small periodic fluctuations and HF momentum has large periodic fluctuations.

MRD:bc2116

2018-05-18T14:41:27Z

Bc2116: /* Reactive and Unreactive Trajectories Table */

= Molecular Reaction Dynamics: Boru Chen =

== <math>H_2</math> + H system ==

=== Dynamics from Transition State Region ===

The PES has two components:

<math>\frac{\partial V}{\partial r_1}</math> and <math>\frac{\partial V}{\partial r_2}</math>

Where V is the potential energy, and <math>r_1</math> is the intermolecular distance between <math>H_b</math> <math>H_c</math>, <math>r_2</math> is the intermolecular distance between <math>H_a</math> and <math>H_b</math>. At transition structure, both components have value of zero. At energy minima and transition structure, their first derivatives equal to zero. Transition state can be distinguished by taking the second derivative of potential energy. Transition state is at energy maximum along reaction coordinate, and at energy minimum in any other direction, whereas energy minimum is at a minimum in all directions. Mathematically speaking, energy minimum’s second derivative is always a positive value at any position, whereas transition state’s second derivative is negative along reaction coordinate, and positive everywhere else.

==== Transition State Position Estimation ====
Best estimate = 0.9075 Armstrong. Inter nuclear distance vs time plot

[[File:Exercise 1 Internuclear distance to time1.png]]

Note: A-B line can be vaguely seen behind the yellow line.

==== MEP and Dynamic Model Comparison ====
[[File:Exercise 1 MEP plot.png]]
[[File:Exercise 1 Dynamic plot.png]]

MEP plot showed no difference comparing to transition state when first plotted with 500 steps calculated, once the number of steps was increased to 5000, a straight line can be seen following the valley floor to H1 + H2-H3. In comparison, the dynamic plot showed a trajectory which shot off the plot, and the number of steps in calculation had to be truncated to 618. This trajectory bounces between valley walls of H1 + H2-H3.This difference is because the velocity in MEP calculation is reset to 0 after each step, whereas velocity in dynamic calculation isn’t.

==== Internuclear distance and momentum vs time at large t under MEP calculation ====
Internuclear distance vs time
BC: t = 2.49, r = 7.80
AB: t = 2.49, r = 0.74

Internuclear momentum vs time
BC: t = 2.50, p = 2.49
AB: t = 2.51, p =0.97

This shows that <math>H_a</math> and <math>H_b</math> bond has reached equilibrium at large t, whilst <math>H_c</math> has moved away.

==== MEP calculations with different initial conditions ====
1. If we changed the initial conditions (reverse)?
Transition state follows energy valley floor in H3 + H1-H2 direction.
2. If the new initial positions correspond to the final positions above and final momenta values but with their signs reversed?
AB and BC momenta become the same, and is the Y axis at 0, 0. AB and BC distances are constant, with large difference between two distances. ABs are further apart. Surface plot cannot be visualised.

=== Reactive and Unreactive Trajectories Table ===

{| class="wikitable" border=1
! p1 !! p2 !! Etot <math>kcalmol^{-1}</math> !!! Trajectory
|-
| -1.25 || -2.5 ||| -99.018 |||| [[File:1.png]]
|-
| -1.5 || -2.0 ||| -100.456 |||| [[File:2.png]]
|-
| -1.5 || -2.5 ||| -98.956 |||| [[File:3.png]]
|-
| -2.5 || -5.0 ||| -84.956 |||| [[File:4.png]]
|-
| -2.5 || -5.2 ||| -83.416 |||| [[File:5.png]]
|}

The main assumption is if the incoming atom has enough kinetic energy to overcome kinetic barrier, the reaction will occur. This model also assumes atoms follow newtonian physics.

== F + H + H System ==
=== PES Report ===
HF formation: Reaction is exothermic, and H2 formation: Reaction is endothermic. Further explanation using graph

==== Position of transition state ====
HH distance 1.812 A

HF distance 0.742 A

==== Activation energy calculation: ====
Positions of these structures were estimated using MEP plot

Transition state potential energy: -103.749 <math>kcalmol^{-1}</math>

H2 potential energy: -133.871 <math>kcalmol^{-1}</math>

[[File:H2 potential energy.PNG]] [[File:H2 internuclear distance vs time.PNG]]

HF potential energy: -103.837 <math>kcalmol^{-1}</math>

[[File:HF_potential_energy.PNG]] [[File:HF internuclear distance vs time.PNG]]

HF + H activation energy = -103.749 - -103.837 = 0.088 <math>kcalmol^{-1}</math>

HH + F activation energy = -103.749 - -133.871 = 30.122 <math>kcalmol^{-1}</math>

=== Reaction Dynamics ===
====Trajectories table ====
[[File:Trajectory table HF.PNG]]

During the collision, HH momentum has relatively a small change in comparison with HF momentum After the collision, if the trajectory is reactive, HH momentum will have none to small fluctuation, vice versa for HF momentum. If the trajectory is unreactive, HH momentum will have very large fluctuation, vice versa for HF momentum.

If pHH = 0.1 and pHF = -0.8, HH momentum has small periodic fluctuations and HF momentum has large periodic fluctuations.

MRD:bc2116

2018-05-18T14:40:54Z

Bc2116: /* Reactive and Unreactive Trajectories Table */

= Molecular Reaction Dynamics: Boru Chen =

== <math>H_2</math> + H system ==

=== Dynamics from Transition State Region ===

The PES has two components:

<math>\frac{\partial V}{\partial r_1}</math> and <math>\frac{\partial V}{\partial r_2}</math>

Where V is the potential energy, and <math>r_1</math> is the intermolecular distance between <math>H_b</math> <math>H_c</math>, <math>r_2</math> is the intermolecular distance between <math>H_a</math> and <math>H_b</math>. At transition structure, both components have value of zero. At energy minima and transition structure, their first derivatives equal to zero. Transition state can be distinguished by taking the second derivative of potential energy. Transition state is at energy maximum along reaction coordinate, and at energy minimum in any other direction, whereas energy minimum is at a minimum in all directions. Mathematically speaking, energy minimum’s second derivative is always a positive value at any position, whereas transition state’s second derivative is negative along reaction coordinate, and positive everywhere else.

==== Transition State Position Estimation ====
Best estimate = 0.9075 Armstrong. Inter nuclear distance vs time plot

[[File:Exercise 1 Internuclear distance to time1.png]]

Note: A-B line can be vaguely seen behind the yellow line.

==== MEP and Dynamic Model Comparison ====
[[File:Exercise 1 MEP plot.png]]
[[File:Exercise 1 Dynamic plot.png]]

MEP plot showed no difference comparing to transition state when first plotted with 500 steps calculated, once the number of steps was increased to 5000, a straight line can be seen following the valley floor to H1 + H2-H3. In comparison, the dynamic plot showed a trajectory which shot off the plot, and the number of steps in calculation had to be truncated to 618. This trajectory bounces between valley walls of H1 + H2-H3.This difference is because the velocity in MEP calculation is reset to 0 after each step, whereas velocity in dynamic calculation isn’t.

==== Internuclear distance and momentum vs time at large t under MEP calculation ====
Internuclear distance vs time
BC: t = 2.49, r = 7.80
AB: t = 2.49, r = 0.74

Internuclear momentum vs time
BC: t = 2.50, p = 2.49
AB: t = 2.51, p =0.97

This shows that <math>H_a</math> and <math>H_b</math> bond has reached equilibrium at large t, whilst <math>H_c</math> has moved away.

==== MEP calculations with different initial conditions ====
1. If we changed the initial conditions (reverse)?
Transition state follows energy valley floor in H3 + H1-H2 direction.
2. If the new initial positions correspond to the final positions above and final momenta values but with their signs reversed?
AB and BC momenta become the same, and is the Y axis at 0, 0. AB and BC distances are constant, with large difference between two distances. ABs are further apart. Surface plot cannot be visualised.

=== Reactive and Unreactive Trajectories Table ===

{| class="wikitable" border=1
! p1 !! p2 !! Etot <math>kcalmol^{-1}</math> !! Trajectory
|-
| -1.25 || -2.5 ||| -99.018 ||| [[File:1.png]]
|-
| -1.5 || -2.0 ||| -100.456 |||| [[File:2.png]]
|-
| -1.5 || -2.5 ||| -98.956 |||| [[File:3.png]]
|-
| -2.5 || -5.0 ||| -84.956 |||| [[File:4.png]]
|-
| -2.5 || -5.2 ||| -83.416 |||| [[File:5.png]]
|}

The main assumption is if the incoming atom has enough kinetic energy to overcome kinetic barrier, the reaction will occur. This model also assumes atoms follow newtonian physics.

== F + H + H System ==
=== PES Report ===
HF formation: Reaction is exothermic, and H2 formation: Reaction is endothermic. Further explanation using graph

==== Position of transition state ====
HH distance 1.812 A

HF distance 0.742 A

==== Activation energy calculation: ====
Positions of these structures were estimated using MEP plot

Transition state potential energy: -103.749 <math>kcalmol^{-1}</math>

H2 potential energy: -133.871 <math>kcalmol^{-1}</math>

[[File:H2 potential energy.PNG]] [[File:H2 internuclear distance vs time.PNG]]

HF potential energy: -103.837 <math>kcalmol^{-1}</math>

[[File:HF_potential_energy.PNG]] [[File:HF internuclear distance vs time.PNG]]

HF + H activation energy = -103.749 - -103.837 = 0.088 <math>kcalmol^{-1}</math>

HH + F activation energy = -103.749 - -133.871 = 30.122 <math>kcalmol^{-1}</math>

=== Reaction Dynamics ===
====Trajectories table ====
[[File:Trajectory table HF.PNG]]

During the collision, HH momentum has relatively a small change in comparison with HF momentum After the collision, if the trajectory is reactive, HH momentum will have none to small fluctuation, vice versa for HF momentum. If the trajectory is unreactive, HH momentum will have very large fluctuation, vice versa for HF momentum.

If pHH = 0.1 and pHF = -0.8, HH momentum has small periodic fluctuations and HF momentum has large periodic fluctuations.

MRD:bc2116

2018-05-18T14:40:41Z

Bc2116: /* Reactive and Unreactive Trajectories Table */

= Molecular Reaction Dynamics: Boru Chen =

== <math>H_2</math> + H system ==

=== Dynamics from Transition State Region ===

The PES has two components:

<math>\frac{\partial V}{\partial r_1}</math> and <math>\frac{\partial V}{\partial r_2}</math>

Where V is the potential energy, and <math>r_1</math> is the intermolecular distance between <math>H_b</math> <math>H_c</math>, <math>r_2</math> is the intermolecular distance between <math>H_a</math> and <math>H_b</math>. At transition structure, both components have value of zero. At energy minima and transition structure, their first derivatives equal to zero. Transition state can be distinguished by taking the second derivative of potential energy. Transition state is at energy maximum along reaction coordinate, and at energy minimum in any other direction, whereas energy minimum is at a minimum in all directions. Mathematically speaking, energy minimum’s second derivative is always a positive value at any position, whereas transition state’s second derivative is negative along reaction coordinate, and positive everywhere else.

==== Transition State Position Estimation ====
Best estimate = 0.9075 Armstrong. Inter nuclear distance vs time plot

[[File:Exercise 1 Internuclear distance to time1.png]]

Note: A-B line can be vaguely seen behind the yellow line.

==== MEP and Dynamic Model Comparison ====
[[File:Exercise 1 MEP plot.png]]
[[File:Exercise 1 Dynamic plot.png]]

MEP plot showed no difference comparing to transition state when first plotted with 500 steps calculated, once the number of steps was increased to 5000, a straight line can be seen following the valley floor to H1 + H2-H3. In comparison, the dynamic plot showed a trajectory which shot off the plot, and the number of steps in calculation had to be truncated to 618. This trajectory bounces between valley walls of H1 + H2-H3.This difference is because the velocity in MEP calculation is reset to 0 after each step, whereas velocity in dynamic calculation isn’t.

==== Internuclear distance and momentum vs time at large t under MEP calculation ====
Internuclear distance vs time
BC: t = 2.49, r = 7.80
AB: t = 2.49, r = 0.74

Internuclear momentum vs time
BC: t = 2.50, p = 2.49
AB: t = 2.51, p =0.97

This shows that <math>H_a</math> and <math>H_b</math> bond has reached equilibrium at large t, whilst <math>H_c</math> has moved away.

==== MEP calculations with different initial conditions ====
1. If we changed the initial conditions (reverse)?
Transition state follows energy valley floor in H3 + H1-H2 direction.
2. If the new initial positions correspond to the final positions above and final momenta values but with their signs reversed?
AB and BC momenta become the same, and is the Y axis at 0, 0. AB and BC distances are constant, with large difference between two distances. ABs are further apart. Surface plot cannot be visualised.

=== Reactive and Unreactive Trajectories Table ===

{| class="wikitable" border=1
! p1 !! p2 !! Etot <math>kcalmol^{-1}</math> !! Trajectory
|-
| -1.25 || -2.5 ||| -99.018 |||| [[File:1.png]]
|-
| -1.5 || -2.0 ||| -100.456 |||| [[File:2.png]]
|-
| -1.5 || -2.5 ||| -98.956 |||| [[File:3.png]]
|-
| -2.5 || -5.0 ||| -84.956 |||| [[File:4.png]]
|-
| -2.5 || -5.2 ||| -83.416 |||| [[File:5.png]]
|}

The main assumption is if the incoming atom has enough kinetic energy to overcome kinetic barrier, the reaction will occur. This model also assumes atoms follow newtonian physics.

== F + H + H System ==
=== PES Report ===
HF formation: Reaction is exothermic, and H2 formation: Reaction is endothermic. Further explanation using graph

==== Position of transition state ====
HH distance 1.812 A

HF distance 0.742 A

==== Activation energy calculation: ====
Positions of these structures were estimated using MEP plot

Transition state potential energy: -103.749 <math>kcalmol^{-1}</math>

H2 potential energy: -133.871 <math>kcalmol^{-1}</math>

[[File:H2 potential energy.PNG]] [[File:H2 internuclear distance vs time.PNG]]

HF potential energy: -103.837 <math>kcalmol^{-1}</math>

[[File:HF_potential_energy.PNG]] [[File:HF internuclear distance vs time.PNG]]

HF + H activation energy = -103.749 - -103.837 = 0.088 <math>kcalmol^{-1}</math>

HH + F activation energy = -103.749 - -133.871 = 30.122 <math>kcalmol^{-1}</math>

=== Reaction Dynamics ===
====Trajectories table ====
[[File:Trajectory table HF.PNG]]

During the collision, HH momentum has relatively a small change in comparison with HF momentum After the collision, if the trajectory is reactive, HH momentum will have none to small fluctuation, vice versa for HF momentum. If the trajectory is unreactive, HH momentum will have very large fluctuation, vice versa for HF momentum.

If pHH = 0.1 and pHF = -0.8, HH momentum has small periodic fluctuations and HF momentum has large periodic fluctuations.

MRD:bc2116

2018-05-18T14:39:52Z

Bc2116: /* Reactive and Unreactive Trajectories Table */

= Molecular Reaction Dynamics: Boru Chen =

== <math>H_2</math> + H system ==

=== Dynamics from Transition State Region ===

The PES has two components:

<math>\frac{\partial V}{\partial r_1}</math> and <math>\frac{\partial V}{\partial r_2}</math>

Where V is the potential energy, and <math>r_1</math> is the intermolecular distance between <math>H_b</math> <math>H_c</math>, <math>r_2</math> is the intermolecular distance between <math>H_a</math> and <math>H_b</math>. At transition structure, both components have value of zero. At energy minima and transition structure, their first derivatives equal to zero. Transition state can be distinguished by taking the second derivative of potential energy. Transition state is at energy maximum along reaction coordinate, and at energy minimum in any other direction, whereas energy minimum is at a minimum in all directions. Mathematically speaking, energy minimum’s second derivative is always a positive value at any position, whereas transition state’s second derivative is negative along reaction coordinate, and positive everywhere else.

==== Transition State Position Estimation ====
Best estimate = 0.9075 Armstrong. Inter nuclear distance vs time plot

[[File:Exercise 1 Internuclear distance to time1.png]]

Note: A-B line can be vaguely seen behind the yellow line.

==== MEP and Dynamic Model Comparison ====
[[File:Exercise 1 MEP plot.png]]
[[File:Exercise 1 Dynamic plot.png]]

MEP plot showed no difference comparing to transition state when first plotted with 500 steps calculated, once the number of steps was increased to 5000, a straight line can be seen following the valley floor to H1 + H2-H3. In comparison, the dynamic plot showed a trajectory which shot off the plot, and the number of steps in calculation had to be truncated to 618. This trajectory bounces between valley walls of H1 + H2-H3.This difference is because the velocity in MEP calculation is reset to 0 after each step, whereas velocity in dynamic calculation isn’t.

==== Internuclear distance and momentum vs time at large t under MEP calculation ====
Internuclear distance vs time
BC: t = 2.49, r = 7.80
AB: t = 2.49, r = 0.74

Internuclear momentum vs time
BC: t = 2.50, p = 2.49
AB: t = 2.51, p =0.97

This shows that <math>H_a</math> and <math>H_b</math> bond has reached equilibrium at large t, whilst <math>H_c</math> has moved away.

==== MEP calculations with different initial conditions ====
1. If we changed the initial conditions (reverse)?
Transition state follows energy valley floor in H3 + H1-H2 direction.
2. If the new initial positions correspond to the final positions above and final momenta values but with their signs reversed?
AB and BC momenta become the same, and is the Y axis at 0, 0. AB and BC distances are constant, with large difference between two distances. ABs are further apart. Surface plot cannot be visualised.

=== Reactive and Unreactive Trajectories Table ===

{| class="wikitable" border=1
! p1 !! p2 !! Etot <math>kcalmol^{-1}</math> !! !! Trajectory
|-
| -1.25 || -2.5 ||| -99.018 |||| [[File:1.png]]
|-
| -1.5 || -2.0 ||| -100.456 |||| [[File:2.png]]
|-
| -1.5 || -2.5 ||| -98.956 |||| [[File:3.png]]
|-
| -2.5 || -5.0 ||| -84.956 |||| [[File:4.png]]
|-
| -2.5 || -5.2 ||| -83.416 |||| [[File:5.png]]
|}

The main assumption is if the incoming atom has enough kinetic energy to overcome kinetic barrier, the reaction will occur. This model also assumes atoms follow newtonian physics.

== F + H + H System ==
=== PES Report ===
HF formation: Reaction is exothermic, and H2 formation: Reaction is endothermic. Further explanation using graph

==== Position of transition state ====
HH distance 1.812 A

HF distance 0.742 A

==== Activation energy calculation: ====
Positions of these structures were estimated using MEP plot

Transition state potential energy: -103.749 <math>kcalmol^{-1}</math>

H2 potential energy: -133.871 <math>kcalmol^{-1}</math>

[[File:H2 potential energy.PNG]] [[File:H2 internuclear distance vs time.PNG]]

HF potential energy: -103.837 <math>kcalmol^{-1}</math>

[[File:HF_potential_energy.PNG]] [[File:HF internuclear distance vs time.PNG]]

HF + H activation energy = -103.749 - -103.837 = 0.088 <math>kcalmol^{-1}</math>

HH + F activation energy = -103.749 - -133.871 = 30.122 <math>kcalmol^{-1}</math>

=== Reaction Dynamics ===
====Trajectories table ====
[[File:Trajectory table HF.PNG]]

During the collision, HH momentum has relatively a small change in comparison with HF momentum After the collision, if the trajectory is reactive, HH momentum will have none to small fluctuation, vice versa for HF momentum. If the trajectory is unreactive, HH momentum will have very large fluctuation, vice versa for HF momentum.

If pHH = 0.1 and pHF = -0.8, HH momentum has small periodic fluctuations and HF momentum has large periodic fluctuations.

MRD:bc2116

2018-05-18T14:38:51Z

Bc2116: /* Reactive and Unreactive Trajectories Table */

= Molecular Reaction Dynamics: Boru Chen =

== <math>H_2</math> + H system ==

=== Dynamics from Transition State Region ===

The PES has two components:

<math>\frac{\partial V}{\partial r_1}</math> and <math>\frac{\partial V}{\partial r_2}</math>

Where V is the potential energy, and <math>r_1</math> is the intermolecular distance between <math>H_b</math> <math>H_c</math>, <math>r_2</math> is the intermolecular distance between <math>H_a</math> and <math>H_b</math>. At transition structure, both components have value of zero. At energy minima and transition structure, their first derivatives equal to zero. Transition state can be distinguished by taking the second derivative of potential energy. Transition state is at energy maximum along reaction coordinate, and at energy minimum in any other direction, whereas energy minimum is at a minimum in all directions. Mathematically speaking, energy minimum’s second derivative is always a positive value at any position, whereas transition state’s second derivative is negative along reaction coordinate, and positive everywhere else.

==== Transition State Position Estimation ====
Best estimate = 0.9075 Armstrong. Inter nuclear distance vs time plot

[[File:Exercise 1 Internuclear distance to time1.png]]

Note: A-B line can be vaguely seen behind the yellow line.

==== MEP and Dynamic Model Comparison ====
[[File:Exercise 1 MEP plot.png]]
[[File:Exercise 1 Dynamic plot.png]]

MEP plot showed no difference comparing to transition state when first plotted with 500 steps calculated, once the number of steps was increased to 5000, a straight line can be seen following the valley floor to H1 + H2-H3. In comparison, the dynamic plot showed a trajectory which shot off the plot, and the number of steps in calculation had to be truncated to 618. This trajectory bounces between valley walls of H1 + H2-H3.This difference is because the velocity in MEP calculation is reset to 0 after each step, whereas velocity in dynamic calculation isn’t.

==== Internuclear distance and momentum vs time at large t under MEP calculation ====
Internuclear distance vs time
BC: t = 2.49, r = 7.80
AB: t = 2.49, r = 0.74

Internuclear momentum vs time
BC: t = 2.50, p = 2.49
AB: t = 2.51, p =0.97

This shows that <math>H_a</math> and <math>H_b</math> bond has reached equilibrium at large t, whilst <math>H_c</math> has moved away.

==== MEP calculations with different initial conditions ====
1. If we changed the initial conditions (reverse)?
Transition state follows energy valley floor in H3 + H1-H2 direction.
2. If the new initial positions correspond to the final positions above and final momenta values but with their signs reversed?
AB and BC momenta become the same, and is the Y axis at 0, 0. AB and BC distances are constant, with large difference between two distances. ABs are further apart. Surface plot cannot be visualised.

=== Reactive and Unreactive Trajectories Table ===

{| class="wikitable" border=1
! p1 !! p2 !! Etot <math>kcalmol^{-1}</math> !! Trajectory
|-
| -1.25 || -2.5 ||| -99.018 |||| [[File:1.png]]
|-
| -1.5 || -2.0 ||| -100.456 |||| [[File:2.png]]
|-
| -1.5 || -2.5 ||| -98.956 |||| [[File:3.png]]
|-
| -2.5 || -5.0 ||| -84.956 |||| [[File:4.png]]
|-
| -2.5 || -5.2 ||| -83.416 |||| [[File:5.png]]
|}

The main assumption is if the incoming atom has enough kinetic energy to overcome kinetic barrier, the reaction will occur. This model also assumes atoms follow newtonian physics.

== F + H + H System ==
=== PES Report ===
HF formation: Reaction is exothermic, and H2 formation: Reaction is endothermic. Further explanation using graph

==== Position of transition state ====
HH distance 1.812 A

HF distance 0.742 A

==== Activation energy calculation: ====
Positions of these structures were estimated using MEP plot

Transition state potential energy: -103.749 <math>kcalmol^{-1}</math>

H2 potential energy: -133.871 <math>kcalmol^{-1}</math>

[[File:H2 potential energy.PNG]] [[File:H2 internuclear distance vs time.PNG]]

HF potential energy: -103.837 <math>kcalmol^{-1}</math>

[[File:HF_potential_energy.PNG]] [[File:HF internuclear distance vs time.PNG]]

HF + H activation energy = -103.749 - -103.837 = 0.088 <math>kcalmol^{-1}</math>

HH + F activation energy = -103.749 - -133.871 = 30.122 <math>kcalmol^{-1}</math>

=== Reaction Dynamics ===
====Trajectories table ====
[[File:Trajectory table HF.PNG]]

During the collision, HH momentum has relatively a small change in comparison with HF momentum After the collision, if the trajectory is reactive, HH momentum will have none to small fluctuation, vice versa for HF momentum. If the trajectory is unreactive, HH momentum will have very large fluctuation, vice versa for HF momentum.

If pHH = 0.1 and pHF = -0.8, HH momentum has small periodic fluctuations and HF momentum has large periodic fluctuations.

MRD:bc2116

2018-05-18T14:38:18Z

Bc2116: /* Reactive and Unreactive Trajectories Table */

= Molecular Reaction Dynamics: Boru Chen =

== <math>H_2</math> + H system ==

=== Dynamics from Transition State Region ===

The PES has two components:

<math>\frac{\partial V}{\partial r_1}</math> and <math>\frac{\partial V}{\partial r_2}</math>

Where V is the potential energy, and <math>r_1</math> is the intermolecular distance between <math>H_b</math> <math>H_c</math>, <math>r_2</math> is the intermolecular distance between <math>H_a</math> and <math>H_b</math>. At transition structure, both components have value of zero. At energy minima and transition structure, their first derivatives equal to zero. Transition state can be distinguished by taking the second derivative of potential energy. Transition state is at energy maximum along reaction coordinate, and at energy minimum in any other direction, whereas energy minimum is at a minimum in all directions. Mathematically speaking, energy minimum’s second derivative is always a positive value at any position, whereas transition state’s second derivative is negative along reaction coordinate, and positive everywhere else.

==== Transition State Position Estimation ====
Best estimate = 0.9075 Armstrong. Inter nuclear distance vs time plot

[[File:Exercise 1 Internuclear distance to time1.png]]

Note: A-B line can be vaguely seen behind the yellow line.

==== MEP and Dynamic Model Comparison ====
[[File:Exercise 1 MEP plot.png]]
[[File:Exercise 1 Dynamic plot.png]]

MEP plot showed no difference comparing to transition state when first plotted with 500 steps calculated, once the number of steps was increased to 5000, a straight line can be seen following the valley floor to H1 + H2-H3. In comparison, the dynamic plot showed a trajectory which shot off the plot, and the number of steps in calculation had to be truncated to 618. This trajectory bounces between valley walls of H1 + H2-H3.This difference is because the velocity in MEP calculation is reset to 0 after each step, whereas velocity in dynamic calculation isn’t.

==== Internuclear distance and momentum vs time at large t under MEP calculation ====
Internuclear distance vs time
BC: t = 2.49, r = 7.80
AB: t = 2.49, r = 0.74

Internuclear momentum vs time
BC: t = 2.50, p = 2.49
AB: t = 2.51, p =0.97

This shows that <math>H_a</math> and <math>H_b</math> bond has reached equilibrium at large t, whilst <math>H_c</math> has moved away.

==== MEP calculations with different initial conditions ====
1. If we changed the initial conditions (reverse)?
Transition state follows energy valley floor in H3 + H1-H2 direction.
2. If the new initial positions correspond to the final positions above and final momenta values but with their signs reversed?
AB and BC momenta become the same, and is the Y axis at 0, 0. AB and BC distances are constant, with large difference between two distances. ABs are further apart. Surface plot cannot be visualised.

=== Reactive and Unreactive Trajectories Table ===

{| class="wikitable" border=1
! p1 !! p2 !!! Etot <math>kcalmol^{-1}</math> !!!! Trajectory
|-
| -1.25 || -2.5 ||| -99.018 |||| [[File:1.png]]
|-
| -1.5 || -2.0 ||| -100.456 |||| [[File:2.png]]
|-
| -1.5 || -2.5 ||| -98.956 |||| [[File:3.png]]
|-
| -2.5 || -5.0 ||| -84.956 |||| [[File:4.png]]
|-
| -2.5 || -5.2 ||| -83.416 |||| [[File:5.png]]
|}

The main assumption is if the incoming atom has enough kinetic energy to overcome kinetic barrier, the reaction will occur. This model also assumes atoms follow newtonian physics.

== F + H + H System ==
=== PES Report ===
HF formation: Reaction is exothermic, and H2 formation: Reaction is endothermic. Further explanation using graph

==== Position of transition state ====
HH distance 1.812 A

HF distance 0.742 A

==== Activation energy calculation: ====
Positions of these structures were estimated using MEP plot

Transition state potential energy: -103.749 <math>kcalmol^{-1}</math>

H2 potential energy: -133.871 <math>kcalmol^{-1}</math>

[[File:H2 potential energy.PNG]] [[File:H2 internuclear distance vs time.PNG]]

HF potential energy: -103.837 <math>kcalmol^{-1}</math>

[[File:HF_potential_energy.PNG]] [[File:HF internuclear distance vs time.PNG]]

HF + H activation energy = -103.749 - -103.837 = 0.088 <math>kcalmol^{-1}</math>

HH + F activation energy = -103.749 - -133.871 = 30.122 <math>kcalmol^{-1}</math>

=== Reaction Dynamics ===
====Trajectories table ====
[[File:Trajectory table HF.PNG]]

During the collision, HH momentum has relatively a small change in comparison with HF momentum After the collision, if the trajectory is reactive, HH momentum will have none to small fluctuation, vice versa for HF momentum. If the trajectory is unreactive, HH momentum will have very large fluctuation, vice versa for HF momentum.

If pHH = 0.1 and pHF = -0.8, HH momentum has small periodic fluctuations and HF momentum has large periodic fluctuations.

File:5.png

2018-05-18T14:38:06Z

Bc2116: Bc2116 uploaded a new version of File:5.png

File:4.png

2018-05-18T14:37:37Z

Bc2116: Bc2116 uploaded a new version of File:4.png

File:4.png

2018-05-18T14:37:14Z

Bc2116: Bc2116 uploaded a new version of File:4.png

File:3.png

2018-05-18T14:36:47Z

Bc2116: Bc2116 uploaded a new version of File:3.png

File:2.png

2018-05-18T14:36:18Z

Bc2116: Bc2116 uploaded a new version of File:2.png