2018-05-25T14:51:45Z

Yf1716: /* F-H-H system */

= Molecular Reaction Dynamics =

== H + H 2 molecule ==
''' Transition structures '''

On a potential energy surface (PES), a reaction pathway may be identified as a route between two energy minima. Along this pathway, there is an energy maximum, and the geometry at this maximum corresponds to the transition structure. A transition structure can be described as a saddle point.

At all stable points on the PES, the value for the first derivative ∂V(ri)/∂ri, and hence the '''gradient, is equal to zero'''. When distinguishing between minima ɑnd maxima, the second derivative can be very useful. For a minimum point, the value for the second derivative ∂2V(ri)/∂ri2 is greater than zero, whilst for a maximum it is less than zero.

In terms of this reaction, we are interested in the saddle point (transition structure) and minima (reactants or products). At point points, the gradient is equal to zero. To tell between the two, the curvature of the PES becomes much more important. A miniumum will remain a minimum point regardless of the direction moved in, however, a saddle point can be either a 'minimum' or a 'maximum' point, depending on the direction. In the reaction pathway, the saddle point is a maximum and in the orthogonal direction it is a mimumum.

''' Estimating the transition state position '''

In the case of H + H 2, in the resulting transition state the distances between adjacent nuclei would be equal, r1 = r 2. This distance can be called rts. It can be estimated using a plot of internuclear distance vs time.

During the estimation, the potential energy of both BC and AB were set to zero. Regardless of this, oscillation is observed in the animation, given that the atoms will follow the gradient of the PES. This means that in the plot of internuclear distance versus time, oscillations would be observed. Through a method of trial and error, the value for the ''estimate'' rts was found to be 0.9075. This illustrated by the images below, which show the plot of internuclear distance vs time with values of 0.895, 0.9075 and 0.920 Å respectively.

[[image:YF1̠0.895.png|thumb|center|400px|rts = 0.895 Å]]

[[image:YF1̠0.9075.png|thumb|center|400px|rts = 0.9075 Å, the estimated value]]

[[image:YF1̠0.920.png|thumb|center|400px|rts = 0.920 Å]]

It can be seen that at the estimated value of 0.9075 Å, there are no oscillations, whilst at values +/- 0.125 from the estimated value, oscillations are observed. This is consistent with the theory that oscillations occur just before and just after the transition state, but not during the transition state itself. For the seemingly flat lines obtained on the graph for rts = 0.9075 Å, if the image is 'zoomed in' the lines begin to show a small degree of curvature. This shows that the nature of the value is in fact an estimate and a much higher degree accuracy would be required to locate rts exactly.

''' Calculating the reaction pathː MEP and Dyanmic '''

[[image:YF1̠MEP.png|thumb|center|400px|MEP]]
[[image:YF1̠Dynamic.png|thumb|center|400px|Dynamic]]

The contour plot produced with MEP shows a more linear trajectory than that produced from dynamic. The MEP is the minimum energy reaction path, and thus there are no oscillations observed. However, in the dynamic plot, the molecule still has energy so vibrations are represented in the form of oscillations.

''' Reactive or unreactive trajectories '''

{| class="wikitable"
|+
|-
|p1 || p2 || Total E || Plot || Reactive/ Unreactive? || Comments
|-
| -1.25
| -2.5
| -99.018
| [[image:YAF1̠1.PNG|center|300px|]]
| Reactive
| The system successful reaches the products via the transition state, so is reactive. Prior to the transition state, the trajectory has no oscillations. This shows that the individual H atom has no vibrational energy upon approach to the hydrogen molecule.
|-
| -1.5
| -2.0
| -100.456
| [[image:YAF1̠2.PNG|center|300px|]]
| Unreactive
| The trajectory reaches the transition state, but does not have enough energy to overcome the barrier, so returns back to the reactants. Oscillatory motion is seen throughout.
|-
| -1.5
| -2.5
| -98.956
|[[image:YAF1̠3.PNG|center|300px|]]
| Reactive
| This trajectory is similar to the first. However, oscillation is seen throughout.
|-
| -2.5
| -5.0
| -84.956
|[[image:YAF1̠4.PNG|center|300px|]]
| Unreactive
| Unlike the second trajectory which was also unreactive, the oscillations are of much higher amplitude, corresponding to higher vibrational energy. It also appears that the trajectory overcomes the transition state barrier, but still returns to the reactants.
|-
| -2.5
| -5.2
| -83.416
| [[image:YAF1̠5.PNG|center|300px|]]
| Reactive
| Of all the reactive trajectories observed, this is the most 'unusual'. It appears that the trajectory reaches the transition state and returns to the reactants. However, then approaches the transition state and this times overcomes the barrier towards the products.
|}

'''Transition state theory'''

The assumptions in transition state theory are as follows.

1. Atoms in the reactant state have a boltzmann type distribution
2. After the system is at the transition state, and has a velocity in the direction of the products, it will not return to the initial state region
3. Classical mechanics is applied as opposed to quantum mechanics

The first assumptions requires a thermal equilibrium to be true and could be applied to the reaction modeled above.
However, the second and third assumptions can not be applied. We have seen the second assumption breakdown in some of the cases above; where the trajectory reached the transition state and then continued in a 'backwards' direction to the reactants. The third assumption ignores some of the things considered by quantum mechanics, such as tunneling, by the invocation of the Born-Oppenheimer approximation. Classical mechanics would be sufficient for cases where tunneling through the energetic barrier wasn't an option. This could provide an explanation for the last trajectory in the table above.

Given that by the breakdown of these approximations, more reaction pathways are accessible, the experimental rate could be higher than the rates predicted by transition state theory.

== F-H-H system ==

'''PES inspection'''

Bond strength is related to several factors, one of which is the electronegativity difference of the atoms. There is a large electronegativity difference in a HF molecule, so the bond would be very short and very strong. In the case of F + H2, a ''relatively'' weak H2 bond is broken, and a much stronger HF bond is formed. Breaking a weak bond requires little energy and forming a strong one would release a lot of energy, so this reaction can be predicted to be exothermic. The opposite applies in the case of H + HF, where the stronger bond is broken, requiring a lot of energy and a weaker bond is formed, releasing little energy. Thus this reaction will be endothermic.

Hammond's postulate states that if two species are similar in energy, then it can be assumed that there is little structural rearrangement between the two, hence they are also similar in structure. In an exothermic reaction, the transition state occurs early, so is closer in energy and structure to the reactants. As mentioned above, F + H2 would be an exothermic reaction.

The image below was produced after the approximate location of the transition state, using methods similar to those applied in the H + HH system. The distances were found to have values of r1 = 0.745 Å and r2 = 1.8105 Å, where the distances r1 and r2 correspond to the H-H and F-H separations respectively. There are no oscillations, showing that we are at a stable point.

[[image:YAF1_TS.PNG|thumb|center|400px|The transition state ]]

The activation energy is the difference between the transition state and reactant energies. The transition state energy was found to be -103.752 kcal/mol. Performing a MEP where the r1 and r2 distances are slightly offset from the transition state lengths will help to find the activation energy.

In the reaction of F + H2, the activation energy was found to be +0.254 kcal/mol. Whilst in the case of H + HF, activation energy was found to be -0.124 kcal/mol.

'''Reaction Dynamics'''

== References ==
https://www.sciencedirect.com/topics/chemistry/transition-state-theory

MDR YF-1716

2018-05-25T14:40:22Z

2018-05-25T13:52:53Z

Yf1716: /* H + H 2 molecule */

= Molecular Reaction Dynamics =

==Introduction ==

== H + H 2 molecule ==
''' Transition structures '''

On a potential energy surface (PES), a reaction pathway may be identified as a route between two energy minima. Along this pathway, there is an energy maximum, and the geometry at this maximum corresponds to the transition structure. A transition structure can be described as a saddle point.

At all stable points on the PES, the value for the first derivative ∂V(ri)/∂ri, and hence the '''gradient, is equal to zero'''. When distinguishing between minima ɑnd maxima, the second derivative can be very useful. For a minimum point, the value for the second derivative ∂2V(ri)/∂ri2 is greater than zero, whilst for a maximum it is less than zero.

In terms of this reaction, we are interested in the saddle point (transition structure) and minima (reactants or products). At point points, the gradient is equal to zero. To tell between the two, the curvature of the PES becomes much more important. A miniumum will remain a minimum point regardless of the direction moved in, however, a saddle point can be either a 'minimum' or a 'maximum' point, depending on the direction. In the reaction pathway, the saddle point is a maximum and in the orthogonal direction it is a mimumum.

''' Estimating the transition state position '''

In the case of H + H 2, in the resulting transition state the distances between adjacent nuclei would be equal, r1 = r 2. This distance can be called rts. It can be estimated using a plot of internuclear distance vs time.

During the estimation, the potential energy of both BC and AB were set to zero. Regardless of this, oscillation is observed in the animation, given that the atoms will follow the gradient of the PES. This means that in the plot of internuclear distance versus time, oscillations would be observed. Through a method of trial and error, the value for the ''estimate'' rts was found to be 0.9075. This illustrated by the images below, which show the plot of internuclear distance vs time with values of 0.895, 0.9075 and 0.920 Å respectively.

[[image:YF1̠0.895.png|thumb|center|400px|rts = 0.895 Å]]

[[image:YF1̠0.9075.png|thumb|center|400px|rts = 0.9075 Å, the estimated value]]

[[image:YF1̠0.920.png|thumb|center|400px|rts = 0.920 Å]]

It can be seen that at the estimated value of 0.9075 Å, there are no oscillations, whilst at values +/- 0.125 from the estimated value, oscillations are observed. This is consistent with the theory that oscillations occur just before and just after the transition state, but not during the transition state itself. For the seemingly flat lines obtained on the graph for rts = 0.9075 Å, if the image is 'zoomed in' the lines begin to show a small degree of curvature. This shows that the nature of the value is in fact an estimate and a much higher degree accuracy would be required to locate rts exactly.

''' Calculating the reaction pathː MEP and Dyanmic '''

[[image:YF1̠MEP.png|thumb|center|400px|MEP]]
[[image:YF1̠Dynamic.png|thumb|center|400px|Dynamic]]

The contour plot produced with MEP shows a more linear trajectory than that produced from dynamic. The MEP is the minimum energy reaction path, and thus there are no oscillations observed. However, in the dynamic plot, the molecule still has energy so vibrations are represented in the form of oscillations.

''' Reactive or unreactive trajectories '''

{| class="wikitable"
|+
|-
|p1 || p2 || Total E || Plot || Reactive/ Unreactive? || Comments
|-
| -1.25
| -2.5
| -99.018
| [[image:YAF1̠1.PNG|center|300px|]]
| Reactive
| The system successful reaches the products via the transition state, so is reactive. Prior to the transition state, the trajectory has no oscillations. This shows that the individual H atom has no vibrational energy upon approach to the hydrogen molecule.
|-
| -1.5
| -2.0
| -100.456
| [[image:YAF1̠2.PNG|center|300px|]]
| Unreactive
| The trajectory reaches the transition state, but does not have enough energy to overcome the barrier, so returns back to the reactants. Oscillatory motion is seen throughout.
|-
| -1.5
| -2.5
| -98.956
|[[image:YAF1̠3.PNG|center|300px|]]
| Reactive
| This trajectory is similar to the first. However, oscillation is seen throughout.
|-
| -2.5
| -5.0
| -84.956
|[[image:YAF1̠4.PNG|center|300px|]]
| Unreactive
| Unlike the second trajectory which was also unreactive, the oscillations are of much higher amplitude, corresponding to higher vibrational energy. It also appears that the trajectory overcomes the transition state barrier, but still returns to the reactants.
|-
| -2.5
| -5.2
| -83.416
| [[image:YAF1̠5.PNG|center|300px|]]
| Reactive
| Of all the reactive trajectories observed, this is the most 'unusual'. It appears that the trajectory reaches the transition state and returns to the reactants. However, then approaches the transition state and this times overcomes the barrier towards the products.
|}

'''Transition state theory'''

The assumptions in transition state theory are as follows.

1. Atoms in the reactant state have a boltzmann type distribution
2. After the system is at the transition state, and has a velocity in the direction of the products, it will not return to the initial state region
3. Classical mechanics is applied as opposed to quantum mechanics

The first assumptions requires a thermal equilibrium to be true and could be applied to the reaction modeled above.
However, the second and third assumptions can not be applied. We have seen the second assumption breakdown in some of the cases above; where the trajectory reached the transition state and then continued in a 'backwards' direction to the reactants. The third assumption ignores some of the things considered by quantum mechanics, such as tunneling, by the invocation of the Born-Oppenheimer approximation. Classical mechanics would be sufficient for cases where tunneling through the energetic barrier wasn't an option. This could provide an explanation for the last trajectory in the table above.

Given that by the breakdown of these approximations, more reaction pathways are accessible, the experimental rate could be higher than the rates predicted by transition state theory.

== F-H-H system ==

MDR YF-1716

2018-05-25T13:52:07Z

Yf1716: /* H + H 2 molecule */

MDR YF-1716

2018-05-25T12:28:14Z

Yf1716: /* H + H 2 molecule - Transition structures */

= Molecular Reaction Dynamics =

==Introduction ==

== H + H 2 molecule - Transition structures ==

On a potential energy surface (PES), a reaction pathway may be identified as a route between two energy minima. Along this pathway, there is an energy maximum, and the geometry at this maximum corresponds to the transition structure. A transition structure can be described as a saddle point.

At all stable points on the PES, the value for the first derivative ∂V(ri)/∂ri, and hence the '''gradient, is equal to zero'''. When distinguishing between minima ɑnd maxima, the second derivative can be very useful. For a minimum point, the value for the second derivative ∂2V(ri)/∂ri2 is greater than zero, whilst for a maximum it is less than zero.

In terms of this reaction, we are interested in the saddle point (transition structure) and minima (reactants or products). At point points, the gradient is equal to zero. To tell between the two, the curvature of the PES becomes much more important. A miniumum will remain a minimum point regardless of the direction moved in, however, a saddle point can be either a 'minimum' or a 'maximum' point, depending on the direction. In the reaction pathway, the saddle point is a maximum and in the orthogonal direction it is a mimumum.

''' Estimating the transition state position '''

In the case of H + H 2, in the resulting transition state the distances between adjacent nuclei would be equal, r1 = r 2. This distance can be called rts. It can be estimated using a plot of internuclear distance vs time.

During the estimation, the potential energy of both BC and AB were set to zero. Regardless of this, oscillation is observed in the animation, given that the atoms will follow the gradient of the PES. This means that in the plot of internuclear distance versus time, oscillations would be observed. Through a method of trial and error, the value for the ''estimate'' rts was found to be 0.9075. This illustrated by the images below, which show the plot of internuclear distance vs time with values of 0.895, 0.9075 and 0.920 Å respectively.

[[image:YF1̠0.895.png|thumb|center|400px|rts = 0.895 Å]]

[[image:YF1̠0.9075.png|thumb|center|400px|rts = 0.9075 Å, the estimated value]]

[[image:YF1̠0.920.png|thumb|center|400px|rts = 0.920 Å]]

It can be seen that at the estimated value of 0.9075 Å, there are no oscillations, whilst at values +/- 0.125 from the estimated value, oscillations are observed. This is consistent with the theory that oscillations occur just before and just after the transition state, but not during the transition state itself. For the seemingly flat lines obtained on the graph for rts = 0.9075 Å, if the image is 'zoomed in' the lines begin to show a small degree of curvature. This shows that the nature of the value is in fact an estimate and a much higher degree accuracy would be required to locate rts exactly.

''' Calculating the reaction pathː MEP and Dyanmic '''

[[image:YF1̠MEP.png|thumb|center|400px|MEP]]
[[image:YF1̠Dynamic.png|thumb|center|400px|Dynamic]]

The contour plot produced with MEP shows a more linear trajectory than that produced from dynamic. The MEP is the minimum energy reaction path, and thus there are no oscillations observed. However, in the dynamic plot, the molecule still has energy so vibrations are represented in the form of oscillations.

{| class="wikitable"
|+
|-
|p1 || p2 || Total E || Plot || Reactive/ Unreactive? || Comments
|-
| hello
|
|
|
| what
|
|-
|
|
|
|
|
|
|-
|
|
|
|
|
|
|-
|
|
|
|
|
|
|-
|
|
|
|
|
|
|-
|
|
|
|
|
|
|}

MDR YF-1716

2018-05-25T12:27:25Z

Yf1716: /* H + H 2 molecule - Transition structures */

= Molecular Reaction Dynamics =

==Introduction ==

== H + H 2 molecule - Transition structures ==

On a potential energy surface (PES), a reaction pathway may be identified as a route between two energy minima. Along this pathway, there is an energy maximum, and the geometry at this maximum corresponds to the transition structure. A transition structure can be described as a saddle point.

At all stable points on the PES, the value for the first derivative ∂V(ri)/∂ri, and hence the '''gradient, is equal to zero'''. When distinguishing between minima ɑnd maxima, the second derivative can be very useful. For a minimum point, the value for the second derivative ∂2V(ri)/∂ri2 is greater than zero, whilst for a maximum it is less than zero.

In terms of this reaction, we are interested in the saddle point (transition structure) and minima (reactants or products). At point points, the gradient is equal to zero. To tell between the two, the curvature of the PES becomes much more important. A miniumum will remain a minimum point regardless of the direction moved in, however, a saddle point can be either a 'minimum' or a 'maximum' point, depending on the direction. In the reaction pathway, the saddle point is a maximum and in the orthogonal direction it is a mimumum.

''' Estimating the transition state position '''

In the case of H + H 2, in the resulting transition state the distances between adjacent nuclei would be equal, r1 = r 2. This distance can be called rts. It can be estimated using a plot of internuclear distance vs time.

During the estimation, the potential energy of both BC and AB were set to zero. Regardless of this, oscillation is observed in the animation, given that the atoms will follow the gradient of the PES. This means that in the plot of internuclear distance versus time, oscillations would be observed. Through a method of trial and error, the value for the ''estimate'' rts was found to be 0.9075. This illustrated by the images below, which show the plot of internuclear distance vs time with values of 0.895, 0.9075 and 0.920 Å respectively.

[[image:YF1̠0.895.png|thumb|center|400px|rts = 0.895 Å]]

[[image:YF1̠0.9075.png|thumb|center|400px|rts = 0.9075 Å, the estimated value]]

[[image:YF1̠0.920.png|thumb|center|400px|rts = 0.920 Å]]

It can be seen that at the estimated value of 0.9075 Å, there are no oscillations, whilst at values +/- 0.125 from the estimated value, oscillations are observed. This is consistent with the theory that oscillations occur just before and just after the transition state, but not during the transition state itself. For the seemingly flat lines obtained on the graph for rts = 0.9075 Å, if the image is 'zoomed in' the lines begin to show a small degree of curvature. This shows that the nature of the value is in fact an estimate and a much higher degree accuracy would be required to locate rts exactly.

''' Calculating the reaction pathː MEP and Dyanmic '''

[[image:YF1̠MEP.png|thumb|center|400px|MEP]]
[[image:YF1̠Dynamic.png|thumb|center|400px|Dynamic]]

The contour plot produced with MEP shows a more linear trajectory than that produced from dynamic. The MEP is the minimum energy reaction path, and thus there are no oscillations observed. However, in the dynamic plot, the molecule still has energy so vibrations are represented in the form of oscillations.

{| class="wikitable"
|+
|-
|p1 || p2 || Total E || Plot || Reactive/ Unreactive? || Comments
|-
|-1.25
|-2.5
|
|
|
|
|-
|
|
|
|
|
|
|-
|
|
|
|
|
|
|-
|
|
|
|
|
|
|-
|
|
|
|
|
|
|-
|
|
|
|
|
|
|}

MDR YF-1716

2018-05-25T12:16:32Z

Yf1716: /* H + H 2 molecule - Transition structures */

MDR YF-1716

2018-05-25T12:16:07Z

Yf1716: /* H + H 2 molecule - Transition structures */

= Molecular Reaction Dynamics =

==Introduction ==

== H + H 2 molecule - Transition structures ==

On a potential energy surface (PES), a reaction pathway may be identified as a route between two energy minima. Along this pathway, there is an energy maximum, and the geometry at this maximum corresponds to the transition structure. A transition structure can be described as a saddle point.

At all stable points on the PES, the value for the first derivative ∂V(ri)/∂ri, and hence the '''gradient, is equal to zero'''. When distinguishing between minima ɑnd maxima, the second derivative can be very useful. For a minimum point, the value for the second derivative ∂2V(ri)/∂ri2 is greater than zero, whilst for a maximum it is less than zero.

In terms of this reaction, we are interested in the saddle point (transition structure) and minima (reactants or products). At point points, the gradient is equal to zero. To tell between the two, the curvature of the PES becomes much more important. A miniumum will remain a minimum point regardless of the direction moved in, however, a saddle point can be either a 'minimum' or a 'maximum' point, depending on the direction. In the reaction pathway, the saddle point is a maximum and in the orthogonal direction it is a mimumum.

''' Estimating the transition state position '''

In the case of H + H 2, in the resulting transition state the distances between adjacent nuclei would be equal, r1 = r 2. This distance can be called rts. It can be estimated using a plot of internuclear distance vs time.

During the estimation, the potential energy of both BC and AB were set to zero. Regardless of this, oscillation is observed in the animation, given that the atoms will follow the gradient of the PES. This means that in the plot of internuclear distance versus time, oscillations would be observed. Through a method of trial and error, the value for the ''estimate'' rts was found to be 0.9075. This illustrated by the images below, which show the plot of internuclear distance vs time with values of 0.895, 0.9075 and 0.920 Å respectively.

[[image:YF1̠0.895.png|thumb|center|400px|rts = 0.895 Å]]

[[image:YF1̠0.9075̠.png|thumb|center|400px|rts = 0.9075 Å, the estimated value]]

[[image:YF1̠0.920.png|thumb|center|400px|rts = 0.920 Å]]

It can be seen that at the estimated value of 0.9075 Å, there are no oscillations, whilst at values +/- 0.125 from the estimated value, oscillations are observed. This is consistent with the theory that oscillations occur just before and just after the transition state, but not during the transition state itself. For the seemingly flat lines obtained on the graph for rts = 0.9075 Å, if the image is 'zoomed in' the lines begin to show a small degree of curvature. This shows that the nature of the value is in fact an estimate and a much higher degree accuracy would be required to locate rts exactly.

''' Calculating the reaction pathː MEP and Dyanmic '''

[[image:YF1̠MEP.png|thumb|center|400px|MEP]]
[[image:YF1̠Dynamic.png|thumb|center|400px|Dynamic]]

The contour plot produced with MEP shows a more linear trajectory than that produced from dynamic. The MEP is the minimum energy reaction path, and thus there are no oscillations observed. However, in the dynamic plot, the molecule still has energy so vibrations are represented in the form of oscillations.

File:YF1̠MEP.png

2018-05-25T12:14:49Z

Yf1716:

File:YF1̠Dynamic.png

2018-05-25T12:14:29Z

Yf1716:

MDR YF-1716

2018-05-25T12:13:30Z

Yf1716: /* H + H 2 molecule - Transition structures */

= Molecular Reaction Dynamics =

==Introduction ==

== H + H 2 molecule - Transition structures ==

On a potential energy surface (PES), a reaction pathway may be identified as a route between two energy minima. Along this pathway, there is an energy maximum, and the geometry at this maximum corresponds to the transition structure. A transition structure can be described as a saddle point.

At all stable points on the PES, the value for the first derivative ∂V(ri)/∂ri, and hence the '''gradient, is equal to zero'''. When distinguishing between minima ɑnd maxima, the second derivative can be very useful. For a minimum point, the value for the second derivative ∂2V(ri)/∂ri2 is greater than zero, whilst for a maximum it is less than zero.

In terms of this reaction, we are interested in the saddle point (transition structure) and minima (reactants or products). At point points, the gradient is equal to zero. To tell between the two, the curvature of the PES becomes much more important. A miniumum will remain a minimum point regardless of the direction moved in, however, a saddle point can be either a 'minimum' or a 'maximum' point, depending on the direction. In the reaction pathway, the saddle point is a maximum and in the orthogonal direction it is a mimumum.

''' Estimating the transition state position '''

In the case of H + H 2, in the resulting transition state the distances between adjacent nuclei would be equal, r1 = r 2. This distance can be called rts. It can be estimated using a plot of internuclear distance vs time.

During the estimation, the potential energy of both BC and AB were set to zero. Regardless of this, oscillation is observed in the animation, given that the atoms will follow the gradient of the PES. This means that in the plot of internuclear distance versus time, oscillations would be observed. Through a method of trial and error, the value for the ''estimate'' rts was found to be 0.9075. This illustrated by the images below, which show the plot of internuclear distance vs time with values of 0.895, 0.9075 and 0.920 Å respectively.

[[image:YF1̠0.895.png|thumb|center|400px|rts = 0.895 Å]]

[[image:YF1̠0.9075.png|thumb|center|400px|rts = 0.9075 Å, the estimated value]]

[[image:YF1̠0.920.png|thumb|center|400px|rts = 0.920 Å]]

It can be seen that at the estimated value of 0.9075 Å, there are no oscillations, whilst at values +/- 0.125 from the estimated value, oscillations are observed. This is consistent with the theory that oscillations occur just before and just after the transition state, but not during the transition state itself. For the seemingly flat lines obtained on the graph for rts = 0.9075 Å, if the image is 'zoomed in' the lines begin to show a small degree of curvature. This shows that the nature of the value is in fact an estimate and a much higher degree accuracy would be required to locate rts exactly.

''' Calculating the reaction pathː MEP and Dyanmic '''

[[image:YF1̠0.895.png|thumb|center|400px|MEP]]
[[image:YF1̠0.895.png|thumb|center|400px|Dynamic]]

The contour plot produced with MEP shows a more linear trajectory than that produced from dynamic. The MEP is the lowest energy reaction path, and thus there are no oscillations observed. However, in the dynamic plot, the molecule still has energy so vibrations are represented in the form of oscillations.

MDR YF-1716

2018-05-25T11:50:32Z

Yf1716: /* H + H 2 molecule - Transition structures */

MDR YF-1716

2018-05-24T11:07:38Z

Yf1716: /* H + H 2 molecule - Transition structures */

= Molecular Reaction Dynamics =

==Introduction ==

== H + H 2 molecule - Transition structures ==

On a potential energy surface (PES), a reaction pathway may be identified as a route between two energy minima. Along this pathway, there is an energy maximum, and the geometry at this maximum corresponds to the transition structure. A transition structure can be described as a saddle point.

At all stable points on the PES, the value for the first derivative ∂V(ri)/∂ri, and hence the '''gradient, is equal to zero'''. When distinguishing between minima ɑnd maxima, the second derivative can be very useful. For a minimum point, the value for the second derivative ∂2V(ri)/∂ri2 is greater than zero, whilst for a maximum it is less than zero.

In terms of this reaction, we are interested in the saddle point (transition structure) and minima (reactants or products). At point points, the gradient is equal to zero. To tell between the two, the curvature of the PES becomes much more important. A miniumum will remain a minimum point regardless of the direction moved in, however, a saddle point can be either a 'minimum' or a 'maximum' point, depending on the direction. In the reaction pathway, the saddle point is a maximum and in the orthogonal direction it is a mimumum.

''' Estimating the transition state position '''

In the case of H + H 2, in the resulting transition state the distances between adjacent nuclei would be equal, r1 = r 2. This distance can be called rts. It can be estimated using a plot of internuclear distance vs time.

During the estimation, the potential energy of both BC and AB were set to zero. Regardless of this, oscillation is observed in the animation, given that the atoms will follow the gradient of the PES. This means that in the plot of internuclear distance versus time, oscillations would be observed. Through a method of trial and error, the value for the ''estimate'' rts was found to be 0.9075. This illustrated by the images below, which show the plot of internuclear distance vs time with values of 0.895, 0.9075 and 0.920 respectively.

[[image:YF1̠0.895.png|thumb|center|400px|rts = 0.895]]

[[image:YF1̠0.9075.png|thumb|center|400px|rts = 0.9075, the estimated value]]

[[image:YF1̠0.920.png|thumb|center|400px|rts = 0.920]]

It can be seen that at the estimated value of 0.9075, there are no oscillations, whilst at values +/- 0.125 from the estimated value, oscillations are observed. This is consistent with the theory that oscillations occur just before and just after the transition state, but not during the transition state itself. For the seemingly flat lines obtained on the graph for rts = 0.9075, if the image is 'zoomed in' the lines begin to show a small degree of curvature. This shows that the nature of the value is in fact an estimate and a much higher degree accuracy would be required to locate rts exactly.