File:HHF initial reaction low vib energy01516896.png

2020-05-22T17:49:41Z

Rp318:

MRD:01516896 rp318

2020-05-22T17:36:28Z

Rp318:

=H + H2 System=

==Transition State of reaction==
===On a potential energy surface diagram, how is the transition state mathematically defined? How can the transition state be identified, and how can it be distinguished from a local minimum of the potential energy surface?===
The transition state of a reaction is considered to be a hypothetical state in between the reactants and the products <ref name="Transitionstate"/>. On a potential energy surface diagram, it is usually found at the point where the gradient of the potential energy surface diagram is zero and is a maximum. The point of zero gradient of potential energy surface diagram can be found from looking at the first derivatives et equal to zero. To find whether the point is a maximum, the second derivative of the graph is needed. A maximum is found when the second derivative of stationary point is less than zero.

===Report your best estimate of the transition state position (rts) and explain your reasoning illustrating it with a “Internuclear Distances vs Time” plot for a relevant trajectory.===
The transition state of H +H2 will have r1 = r2 as the potential energy surface diagram is symmetrical. By starting the simulation with the trajectories of the molecule at the point where gradient is zero, the positions of the atoms at the transition state (rTS) can be found. The rTS was estimated to be 90.8 pm.

[[File:Internucleardistance_vs_time_TS_H+H2_01516896.png|200px|thumb|A graph of internuclear distances against time.]]

The graph of internuclear distance against time shows that the positions of the atoms are stationary. This shows that the trajectory will oscillate but never move any further suggesting that the trajectory is on a ridge on the potential energy surface where the gradient perpendicular to the ridge is zero.

==Trajectories from r1 = rts+δ, r2 = rts==
===Comment on the difference between the mep and the trajectory calculated===
The minimum energy pathway (mep) was found for the reaction. The MEP plot does not show the vibrational energy of the product, giving a straight line following the bottom of the well.

[[File:MEP vs dynamics dynamics plot01516896.png|200px|thumb|A potential surface energy diagram using dynamics calculations.]]

[[File:MEP vs dynamics MEP plot01516896.png|200px|thumb|A potential surface energy diagram using MEP calculations.]]

When the trajectories are changed from r1 = rts+δ and r2 = rts to r2 = rts+δ and r1 = rts, the internuclear distance against time plot give the same shape but with the distance of AB increasing instead.

[[File:Internucleardistance vs time r1=rts+101516896.png|200px|thumb|A plot of internuclear distance against time with r1 = rts+δ and r2 = rts.]]

[[File:Internucleardistance vs time r2=rts+101516896.png|200px|thumb|A plot of internuclear distance against time with r2 = rts+δ and r1 = rts.]]

Calculations ran with final positions as the initial positions and changing the direction of the momenta showed the increase in energy of reaction up to the transition state and the reaction energy falling back down in the same well as it went up (reactants).

== Reactive and Unreactive Trajectories for H-H-H system==

{| class="wikitable" border=1
! p1/ g.mol-1.pm.fs-1 !! p2/ g.mol-1.pm.fs-1 !! Etot !! Reactive? !! Description of the dynamics !! Illustration of the trajectory
|-
| -2.56 || -5.1 ||-414.3 ||Yes ||H2 (with not much vibrational energy) collides with H, reaction goes through transition state, product is formed with vibrational energy. ||[[File:P1=-2.56 p2=-5.101516896.png|80px]]
|-
| -3.1 || -4.1 ||-420.2 ||No ||Reaction does not have enough momentum to reach transition state. ||[[File:P1=-3.1 p2=-4.101516896.png|80px]]
|-
| -3.1 || -5.1 ||-414.0 ||Yes ||Reactants come together, collides and passes through transition state, products are formed. ||[[File:P1=-3.1 p2=-5.101516896.png|80px]]
|-
| -5.1 || -10.1 ||-357.3 ||No ||Reactants collide and products are formed but then reaction reverses giving the reactants again. ||[[File:P1=-5.1 p2=-10.101516896.png|80px]]
|-
| -5.1 || -10.6 ||-349.5 ||Yes ||Reactants collide to form the product but momentarily reverts back to reactants as the momenta of products were high enough to cause a reverse reaction. Product is formed eventually. ||[[File:P1=-5.1 p2=-10.601516896.png|80px]]
|}

Reactions were run with a wide range of momentums. The table shows that the reaction run with greater momentums can be unreactive. This is due to the products having enough kinetic energy to revert back to the reactants. The reverse reaction would have the same activation energy as reactants and products are the same. As shown above, reactions can also happen with values of momentum lower than -3.1 <  p1 / g.mol-1.pm.fs-1 < -1.6 and p2  = -5.1 g.mol-1.pm.fs-1.

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

=F-H-H System=
==PES inspection==
===Classifying the F + H2 and H + HF reactions according to their energetics===
The reaction F + H2 forming products H + HF is an exothermic reaction. This can be seen from a potential surface energy diagram as the well for reactants is higher in energy than the well for reactants. The reverse reaction is an endothermic reaction. The bond dissociation energy for H2 and HF are 436.0 kjmol-1 and 566.1 kjmol-1 <ref name= "bonddissociationenergies"/> respectively.

[[File:PES of FHH01516896.png|200px|thumb|A potential surface energy diagram with the point where transition state F-H-H is.]]

===Locating the approximate position of the transition state===
The transitions state of F + H2 was found by testing different initial conditions of r1 and r2 with p1 = p2  = 0.0 g.mol-1.pm.fs-1. The transition state was found when the forces along distances r1 and r2 are zero. Hammond's postulate, the transition state of a reaction will either resemble the products or reactants depending on whichever has closer energy <ref name="Hammond's"/>, was taken into account in finding the position of the transitions state. As the F + H2 was exothermic, it can be deduced that the transition state would have positions that are similar to the reactants. The approximate position of TS was found to be r1 = 74.5 pm and r2 = 181.2 pm.

[[File:Contour plot FHH TS01516896.png|200px|thumb|An energy contour plot with the point where transition state F-H-H is.]]

===Activation energy for reactions===
The activation energy of the reactions was found using mep calculations and plotting graphs of energy against time.

[[File:Energy vs time products formed01516896.png|200px|thumb|A plot of energy against time with trajectories set to show formation of products from the TS.]]

[[File:Energy vs time energy of reactants01516896.png|200px|thumb|A plot of energy against time with trajectories set to show formation of reactants from the TS.]]

The activation energy for each reaction was found by finding the difference between the energy at reactants or products and the transition state energy. The activation energy for the reaction F + H2 and H + HF are +0.171 kjmol-1 and +126.588 kjmol-1 respectively.

==Reactive and Unreactive Trajectories for F-H-H system==
===Reaction Trajectories===
A set of reaction trajectories that forms the reaction r1 = 74 pm and r2 = 200 pm with p1 = - 3.88 r1 and r2 with p1 = p2  = 0.0 g.mol-1.pm.fs-1 and p2 = -2.12 g.mol-1.pm.fs-1.

[[File:Momentum vs time FHH01516896.png|200px|thumb|An graph of momentum against time with trajectories set as r1 = 74 pm and r2 = 200 pm with p1 = - 3.88 g.mol-1.pm.fs-1 and p2 = -2.12 g.mol-1.pm.fs-1]]

The graph of momentum against time shows that the HF formed have a large amount of momentum and therefore shows that it has a large amount of kinetic energy (as vibrational energy of bond). This can be measured experimentally by measuring the absorption or emission spectrum of the products. IR spectroscopy can be used to measure the absorption spectrum. As the products have gained vibrational energy, it is energetically excited which can be seen on the IR spectra as a small peak next to the main peak (as an overtone).

{| class="wikitable" border=1
! p1/ g.mol-1.pm.fs-1 !! p2/ g.mol-1.pm.fs-1 !! Illustration of the trajectory
|-
| -6.0 || -1.0 ||[[File:FHH p1=-6 p2=-101516896.png|80px]]
|-
| -5.0 || -1.0 ||[[File:FHH p1=-5 p2=-101516896.png|80px]]
|-
| -4.0 || -1.0 ||[[File:FHH p1=-4 p2=-101516896.png|80px]]
|-
| -3.0 || -1.0 ||[[File:FHH p1=-3 p2=-101516896.png|80px]]
|-
| -2.0 || -1.0 ||[[File:FHH p1=-2 p2=-101516896.png|80px]]
|-
| -1.0 || -1.0 ||[[File:FHH p1=-1 p2=-101516896.png|80px]]
|-
| 0.0 || -1.0 ||[[File:FHH p1=0 p2=-101516896.png|80px]]
|-
| 1.0 || -1.0 ||[[File:FHH p1=1 p2=-101516896.png|80px]]
|-
| 2.0 || -1.0 ||[[File:FHH p1=2 p2=-101516896.png|80px]]
|-
| 3.0 || -1.0 ||[[File:FHH p1=3 p2=-101516896.png|80px]]
|-
| 4.0 || -1.0 ||[[File:FHH p1=4 p2=-101516896.png|80px]]
|-
| 5.0 || -1.0 ||[[File:FHH p1=5 p2=-101516896.png|80px]]
|-
| 6.0 || -1.0 ||[[File:FHH p1=6 p2=-101516896.png|80px]]
|}

The table above is a list of trajectories tested for the reaction F + H2 with the initial positions set at r1 = 74 pm and r2 = 200 pm. The graphs show that around half of the reactions form the product. All the graphs show that the product form has high amounts of vibrational energy, due to the conservation of energy, that can cause the reaction to reverse.

[[File:FHH p1=0.2 p2=-1.601516896.png|200px|thumb|An energy contour plot with trajectories set as r1 = 74 pm and r2 = 200 pm with p1 = 0.2 g.mol-1.pm.fs-1 and p2 = -1.6 g.mol-1.pm.fs-1]]

The trajectory r1 = 74 pm and r2 = 200 pm with p1 = 0.2 g.mol-1.pm.fs-1 and p2 = -1.6 g.mol-1.pm.fs-1 was run and a graph showing the reaction crossing the TS barrier, the product gaining vibrational energy and the energy of the product increasing to the TS energy again.

=References=
<references>
<ref name="Transitionstate"> https://courses.lumenlearning.com/introchem/chapter/transition-state-theory/ </ref>
<ref name="bonddissociationenergies"> https://srd.nist.gov/NSRDS/NSRDS-NBS31.pdf </ref>
<ref name="Hammond's"> https://chem.libretexts.org/Bookshelves/Ancillary_Materials/Reference/Organic_Chemistry_Glossary/Hammond%E2%80%99s_Postulate </ref>
</references>

2020-05-22T16:57:54Z

Rp318:

File:FHH p1=5 p2=-101516896.png

2020-05-22T16:56:41Z

Rp318:

2020-05-22T13:51:10Z

Rp318:

File:FHH p1=-3 p2=-101516896.png

2020-05-22T13:48:59Z

Rp318:

File:FHH p1=-4 p2=-101516896.png

2020-05-22T12:42:38Z

Rp318:

File:FHH p1=-5 p2=-101516896.png

2020-05-22T12:40:08Z

Rp318:

2020-05-22T04:46:12Z

Rp318:

Need to put actual headings in.

=H + H2 System=

==Transition State of reaction==
===On a potential energy surface diagram, how is the transition state mathematically defined? How can the transition state be identified, and how can it be distinguished from a local minimum of the potential energy surface?===
The transition state of a reaction is considered to be a hypothetical state in between the reactants and the products <ref name="Transitionstate"/>. On a potential energy surface diagram, it is usually found at the point where the gradient of the potential energy surface diagram is zero and is a maximum. The point of zero gradient of potential energy surface diagram can be found from looking at the first derivatives et equal to zero. To find whether the point is a maximum, the second derivative of the graph is needed. A maximum is found when the second derivative of stationary point is less than zero.

===Report your best estimate of the transition state position (rts) and explain your reasoning illustrating it with a “Internuclear Distances vs Time” plot for a relevant trajectory.===
The transition state of H +H2 will have r1 = r2 as the potential energy surface diagram is symmetrical. By starting the simulation with the trajectories of the molecule at the point where gradient is zero, the positions of the atoms at the transition state (rTS) can be found. The rTS was estimated to be 90.8 pm.

[[File:Internucleardistance_vs_time_TS_H+H2_01516896.png|300px|thumb|A graph of internuclear distances against time]]

The graph of internuclear distance against time shows that the positions of the atoms are stationary. This shows that the trajectory will oscillate but never move any further suggesting that the trajectory is on a ridge on the potential energy surface where the gradient perpendicular to the ridge is zero.

==Trajectories from r1 = rts+δ, r2 = rts==
===Comment on the difference between the mep and the trajectory calculated===
The minimum energy pathway was found for the reaction. The MEP plot does not show the vibrational energy of the product, giving a straight line following the bottom of the well.

[[File:MEP vs dynamics dynamics plot01516896.png|300px|thumb|A potential surface energy diagram using dynamics calculations]]

[[File:MEP vs dynamics MEP plot01516896.png|300px|thumb|A potential surface energy diagram using MEP calculations]]

When the trajectories are changed from r1 = rts+δ and r2 = rts to r2 = rts+δ and r1 = rts, the internuclear distance against time plot give the same shape but with the distance of AB increasing instead.

[[File:Internucleardistance vs time r1=rts+101516896.png|300px|thumb|A plot of internuclear distance against time with r1 = rts+δ and r2 = rts]]

[[File:Internucleardistance vs time r2=rts+101516896.png|300px|thumb|A plot of internuclear distance against time with r2 = rts+δ and r1 = rts]]

Calculations ran with final positions as the initial positions and changing the direction of the momenta showed the increase in energy of reaction up to the transition state and the reaction energy falling back down in the same well as it went up (reactants).

== Reactive and unreactive trajectories ==

{| class="wikitable" border=1
! p1/ g.mol-1.pm.fs-1 !! p2/ g.mol-1.pm.fs-1 !! Etot !! Reactive? !! Description of the dynamics !! Illustration of the trajectory
|-
| -2.56 || -5.1 ||-414.3 ||Yes ||H2 (with not much vibrational energy) collides with H, reaction goes through transition state, product is formed with vibrational energy. ||[[File:P1=-2.56 p2=-5.101516896.png|100px]]
|-
| -3.1 || -4.1 ||-420.2 ||No ||Reaction does not have enough momentum to reach transition state. ||[[File:P1=-3.1 p2=-4.101516896.png|100px]]
|-
| -3.1 || -5.1 ||-414.0 ||Yes ||Reactants come together, collides and passes through transition state, products are formed. ||[[File:P1=-3.1 p2=-5.101516896.png|100px]]
|-
| -5.1 || -10.1 ||-357.3 ||No ||Reactants collide and products are formed but then reaction reverses giving the reactants again. ||[[File:P1=-5.1 p2=-10.101516896.png|100px]]
|-
| -5.1 || -10.6 ||-349.5 ||Yes ||Reactants collide to form the product but momentarily reverts back to reactants as the momenta of products were high enough to cause a reverse reaction. Product is formed eventually. ||[[File:P1=-5.1 p2=-10.601516896.png|100px]]
|}

Reactions were run with a wide range of momentums. The table shows that the reaction run with greater momentums can be unreactive. This is due to the products having enough kinetic energy to revert back to the reactants. The reverse reaction would have the same activation energy as reactants and products are the same. As shown above, reactions can also happen with values of momentum lower than -3.1 <  p1 / g.mol-1.pm.fs-1 < -1.6 and p2  = -5.1 g.mol-1.pm.fs-1.

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

=F-H-H System=
==PES inspection==
===Classifying the F + H2 and H + HF reactions according to their energetics===
The reaction F + H2 forming products H + HF is an exothermic reaction. This can be seen from a potential surface energy diagram as the well for reactants is higher in energy than the well for reactants. The reverse reaction is an endothermic reaction. The bond dissociation energy for H2 and HF are 436.0 kjmol-1 and 566.1 kjmol-1 <ref name= "bonddissociationenergies"/> respectively.

[[File:PES of FHH01516896.png|300px|thumb|A potential surface energy diagram with point where transition state F-H-H is]]

===Locating the approximate position of the transition state===
The transitions state of F + H2 was found by testing different initial conditions of r1 and r2 with p1 = p2  = 0.0 g.mol-1.pm.fs-1. The transition state was found when the forces along distances r1 and r2 are zero. The approximate position of TS was found to be r1 = 74.5 pm and r2 = 181.2 pm.

[[File:Contour plot FHH TS01516896.png|300px|thumb|A potential surface energy diagram with point where transition state F-H-H is]]

==Report the activation energy for both reactions==

==Identify a set of initial conditions that results in a reactive trajectory for the F + H2, and look at the “Animation” and “Momenta vs Time”. In light of the fact that energy is conserved, discuss the mechanism of release of the reaction energy. Explain how this could be confirmed experimentally.==

=References=
<references>
<ref name="Transitionstate"> https://courses.lumenlearning.com/introchem/chapter/transition-state-theory/ </ref>
<ref name="bonddissociationenergies"> https://srd.nist.gov/NSRDS/NSRDS-NBS31.pdf </ref>
</references>

File:Contour plot FHH TS01516896.png

2020-05-22T04:43:10Z

Rp318:

File:PES of FHH01516896.png

2020-05-22T04:39:35Z

Rp318: