This is a report from the Molecular reaction dynamics computational lab by Martin Holicky.

==Introduction==

'''What value do the different components of the gradient of the potential energy surface have at a minimum and at a transition structure? Briefly explain how minima and transition structures can be distinguished using the curvature of the potential energy surface.'''

SW ANGLE

==H-H-H system==
[[File:Mh-001-ts-hhh.png|thumb|Nuclear separation in time when the atoms are in the transition state.]]
The following reaction between three hydrogen atoms was considered:

H-H + H ⇄ H + H-H

It is clear that since all three atoms are identical the bond lengths are equal and also the potential energy surface symmetrical. As stated in the Introduction, the transition state is located at the maximum of the minimum energy path where the potential energy gradient is zero. This implies an unstable equilibrium, however, since the simulation ignores any external factor (such as other atoms) it will be stable forever. By gradually adjusting the internuclear separations while keeping the momenta at zero the transition state position was found at ''rts = 0.907''. The internuclear distance did not change in time which is indeed expected from a transition state. Minor oscillations - stretches of the H-H-H bonds are visible but since these are symmetrical the do not shift shift the equlibrium.

===Minimum energy paths===
[[File:Mh-003-mep_not_ts-hhh.png|thumb|Interatomic distances during the process as simulated in the MEP mode.]]By setting the velocity of the atoms to zero in each step, it is possible to calculate the ''minimum energy path'' (MEP). In this simulation, the HA-HB-HC distances were set to 0.917 and 0.907 respectively, the former corresponding to a slight displacement from the transition state. This displacement resulted in the transition state collapsing into HA and HB-HC. The H-H distance ''rBC'' simply converged to the dihydrogen bond length and ''rAB'' increased steadily (reaching a minimum at infinity).

Running the simulation in the Dynamics mode (preserving velocities between steps) similar results are obtained as the transition state dissociates into HA and HB-HC. However, the reaction is much faster (no surprise here, resetting the speeds in the MEP mode obviously slows down the process significantly). One interesting feature is perhaps the shape of the ''rAB'' curve. With the MEP the curve resembles a logarithmic process, but with the Dynamics simulation it is approximately linear.
[[File:Mh-004-dynamicsaftermep-hhh.png|thumb|Interatomic distances during the process as simulated in the ''Dynamics'' mode.]]

Exchanging the initial distances shifts the reaction towards the other side of the equilibrium (transition state saddle point), resulting in the other set of products.
<gallery heights=220px widths=250px>
Mh-005-dynamicsaftermep-hhh.png | Path towards H + H-H (''rAB'' longer)
Mh-005-dynamicsaftermep2-hhh.png | Path towards H-H + H (''rBC'' longer)
</gallery>

By plotting the momenta of the atoms in time, it was found that at the end of the simulation they were ''pAB = 1.230'' and ''pBC = 2.481'' (the transition state potential energy roughly divided in 2:1 ratio and converted into kinetic energy). Running the simulation backwards with these momenta (opposite signs to reverse the process) and the final positions ''rAB = 0.746'' and ''rBC = 9.006'' resulted in the molecule going into the transition state. This demonstrates the conservation of energy in the simulation.
[[File:Mh-005-reversedynamics-hhh.png|thumb|The path for the reverse process (molecule coming back towards the TS) - compare with the figures above demonstrating the dissociation of the TS.|none]]

===Reactive and uncreactive pathways===

The dynamics simulations with the initial momenta as in the Table below with initial distances of '''r1''' = 0.74 and '''r2''' were used to investigate if simply having a high enough momentum is necessary for a succesful collision to occur.

{| class="wikitable" border=1
! p1 !! p2 !! Total energy !! Comment !! Reactive? !! Contour plot
|-
| -1.25 || -2.5 || -99.018 || A successful collision, reaction proceeds. || yes || [[File:Mh-006-react-A.png|300px]]
|-
| -1.5 || -2.0 || -100.456 || The reactants don't have a sufficient momentum to overcome the activation barrier and no reaction occurs. || no || [[File:Mh-006-react-B.png|300px]]
|-
| -1.5 || -2.5 || -98.956 ||Similar to the first case. The higher initial momentum reflects in a higher vibrational energy of the product.|| yes || [[File:Mh-006-react-C.png|300px]]
|-
| -2.5 || -5.0 || -84.956 ||The reactants cross the TS, form the products then revert back to reactants (barrier recrossing). || no || [[File:Mh-006-react-D.png|300px]]
|-
| -2.5 || -5.2 || -83.416 || The reactants cross the barrier multiple time and then continue to form the products. || yes || [[File:Mh-006-react-E.png|300px]]
|}

'''State what are the main assumptions of Transition State Theory. Given the results you have obtained, how will Transition State Theory predictions for reaction rate values compare with experimental values?'''

a

== F-H-H System ==
[[File:Mh-011-FHH-ts.png|thumb|The position of the F-H-H transition state.]]Changing one of the hydrogen atoms for a fluorine atom, the following reaction was investigated:

F + H-H ⇄ HF + H

The transition state was found by carefully adjusting the internuclear distances while keeping the momenta to zero. The process was complicated by the fact the potential energy surface is no longer symmetric and also the forward reaction having a too small activation energy. The distances for which the TS complex remained stationary (at the TS saddle point) were ''rFHa = 1.814'' and ''rHaHb = 0.740''. This is an early transition state (with respect to the above reaction) - the H-H bond is almost intact, while the fluorine is at a large distance. Referencing Hammond's postulate, the structure strongly resembles the reactants.

===Energy considerations===

As shown in the table below, the energy for each stage of the reaction was found by computing the potential energy ('Initial Geometry Information') either while in the transition state (with the distances as determined above) or before/after the reaction (large separation between the species, equilibrium bond lengths set to ''rFH = 0.920'' and ''rHH = 0.740''). The equilibrium bond lengths were determined by an MEP simulation where the interatomic separation converged to the bond length value. The reaction in the forward direction required only a very small activation energy and was found to be overall exothermic.

{| class="wikitable" border=1
! Stage !! Energy
|-
| F + HH || -104.020
|-
| F-H-H (TS) || -103.743
|-
| HF + H || -134.025
|-
| Forward EA || 0.277
|-
| Reverse EA || 30.282
|-
| Forward ΔE || -30.005 (an exothermic process)
|}
<gallery widths=250px heights=250px>
[[
File:Mh-012-HH-bond.png|MEP determination of the H-H bond length.
File:Mh-012-FH-bond.png|MEP determination of the F-H bond length.
]]
</gallery>

===Reaction dynamics===

Simulating the reaction with the following parameters ''rFH = 2.4'', ''rHH = 0.740'', ''pFH = -1'' and ''pHH = -2'' provides the data and plots below. Looking at the surface plot below, it is clear that the energy is conserved since the 'vibrational peaks' reach the same levels (potential energy maxima where they have no kinetic energy) before and after the reaction. However, the vibrational energy increased significantly during reaction, corresponding to the 'release of heat' since the reaction is exothermic. This relates a microscopic simulation to a macroscopic phenomenon, which can be easily measured using, for example, a calorimeter. The amplitudes of the vibrations (stretches) are especially visible on the Momenta in time plot.
<gallery widths=250px heights=250px>
[[
File:Mh-013-FHH-rxn-surface.png|Reaction potential energy surface
File:Mh-013-FHH-rxn-momenta.png|Internuclear momenta over the course of the reaction.
]]
</gallery>

====Forward Reaction Reactive and uncreactive pathways====

The dynamics simulations with the initial momenta as in the Table below with initial parameters of '''rFH = 2.4''', '''rHH = 0.74''' and '''pFH = -0.5''' and a variable initial momentum were used to investigate the reactive pathways for this reaction. The sign of the HH-momentum affects if the first vibration goes 'together' or 'away' and on the countour plots are visible as 'down' and 'up' vibrations, respectively. As it can be seen from the data below, this initial setting can affect the outcome of the reaction. Notice the different vibrational amplitudes for +0.5 and -0.5 setting - this is a result of the anharmonicity of the potential.

{| class="wikitable" border=1
! pHH !! Comment !! Reactive? !! Contour plot
|-
| -3 || Reaction proceeds, the product has a significant vibrational energy. || yes || [[File:Mh-014-react-A.png|300px]]
|-
| -2.5 || Reaction proceeds, but the product has a lower vibrational energy than in the first case || yes || [[File:Mh-014-react-B.png|300px]]
|-
| -2 || The reactants don't have a sufficient momentum to overcome the activation barrier and no reaction occurs. || no || [[File:Mh-014-react-C.png|300px]]
|-
| -0.5 || The reactants don't have a sufficient momentum to overcome the activation barrier and no reaction occurs. || no || [[File:Mh-014-react-D.png|300px]]
|-
| +0.5 || The reactants don't have a sufficient momentum to overcome the activation barrier and no reaction occurs. || no || [[File:Mh-014-react-E.png|300px]]
|-
| +2 || The reaction proceeds, crossing the barrier once. || yes || [[File:Mh-014-react-F.png|300px]]
|-
| +2.5 || The reaction proceeds. || yes || [[File:Mh-014-react-G.png|300px]]
|-
| +3 || The products re-cross the barrier and revert to reactants. || no || [[File:Mh-014-react-H.png|300px]]
|-
|}

The simulation was also performed with the following parameters: '''rFH = 2.4''', '''rHH = 0.74''', '''pFH = 0.5''' and '''pFH = -0.8'''. Initially, the dihydrogen reactant has a relatively small vibrational energy but the product a much higher - this is due to the energy released in the reaction.

[[File:Mh-015-react-lowvib.png]]

=== Reverse reaction analysis ===

Running with the following initial values: ''rFH = 0.91'', ''rHH = 2.4'', ''pFH = 0.1'' and ''pFH = -10'' produced a reactive pathway as shown in the Figure below.

[[File:Mh-016-revreact.png]]

Starting from the transition state determined earlier (with a small deviation due to rounding errors), after 2500 steps the final parameters were found to be ''rFH = 0.89736'', ''rHH = 9.97011'', ''pFH = -5.16018'' and ''pFH = 2.06519'. When these values were fed into the software (inverting the momenta), the reactants did not even reach the transition state, even when the inputs were matched to 6 significant figures with the final position from the TS simulation.

These observations outline two requirements:

'''Forward reaction:'''

'''Reverse reaction:''' High collision momentum (translational) energy required with the vibrational energy being relatively unimportant. It was observed that it was very hard to set up the conditions for the reaction to happen with a high vibrational energy but low translational, but very easy the other way round.

File:Mh-017-revreactdoesntwork.png

2018-05-24T12:00:25Z

Mh5015:

File:Mh-016-revreact.png

2018-05-24T10:41:20Z

Mh5015:

MRD:MH5015

2018-05-24T10:39:42Z

Mh5015: /* Forward Reaction Reactive and uncreactive pathways */

This is a report from the Molecular reaction dynamics computational lab by Martin Holicky.

==Introduction==

'''What value do the different components of the gradient of the potential energy surface have at a minimum and at a transition structure? Briefly explain how minima and transition structures can be distinguished using the curvature of the potential energy surface.'''

SW ANGLE

==H-H-H system==
[[File:Mh-001-ts-hhh.png|thumb|Nuclear separation in time when the atoms are in the transition state.]]
The following reaction between three hydrogen atoms was considered:

H-H + H ⇄ H + H-H

It is clear that since all three atoms are identical the bond lengths are equal and also the potential energy surface symmetrical. As stated in the Introduction, the transition state is located at the maximum of the minimum energy path where the potential energy gradient is zero. This implies an unstable equilibrium, however, since the simulation ignores any external factor (such as other atoms) it will be stable forever. By gradually adjusting the internuclear separations while keeping the momenta at zero the transition state position was found at ''rts = 0.907''. The internuclear distance did not change in time which is indeed expected from a transition state. Minor oscillations - stretches of the H-H-H bonds are visible but since these are symmetrical the do not shift shift the equlibrium.

===Minimum energy paths===
[[File:Mh-003-mep_not_ts-hhh.png|thumb|Interatomic distances during the process as simulated in the MEP mode.]]By setting the velocity of the atoms to zero in each step, it is possible to calculate the ''minimum energy path'' (MEP). In this simulation, the HA-HB-HC distances were set to 0.917 and 0.907 respectively, the former corresponding to a slight displacement from the transition state. This displacement resulted in the transition state collapsing into HA and HB-HC. The H-H distance ''rBC'' simply converged to the dihydrogen bond length and ''rAB'' increased steadily (reaching a minimum at infinity).

Running the simulation in the Dynamics mode (preserving velocities between steps) similar results are obtained as the transition state dissociates into HA and HB-HC. However, the reaction is much faster (no surprise here, resetting the speeds in the MEP mode obviously slows down the process significantly). One interesting feature is perhaps the shape of the ''rAB'' curve. With the MEP the curve resembles a logarithmic process, but with the Dynamics simulation it is approximately linear.
[[File:Mh-004-dynamicsaftermep-hhh.png|thumb|Interatomic distances during the process as simulated in the ''Dynamics'' mode.]]

Exchanging the initial distances shifts the reaction towards the other side of the equilibrium (transition state saddle point), resulting in the other set of products.
<gallery heights=220px widths=250px>
Mh-005-dynamicsaftermep-hhh.png | Path towards H + H-H (''rAB'' longer)
Mh-005-dynamicsaftermep2-hhh.png | Path towards H-H + H (''rBC'' longer)
</gallery>

By plotting the momenta of the atoms in time, it was found that at the end of the simulation they were ''pAB = 1.230'' and ''pBC = 2.481'' (the transition state potential energy roughly divided in 2:1 ratio and converted into kinetic energy). Running the simulation backwards with these momenta (opposite signs to reverse the process) and the final positions ''rAB = 0.746'' and ''rBC = 9.006'' resulted in the molecule going into the transition state. This demonstrates the conservation of energy in the simulation.
[[File:Mh-005-reversedynamics-hhh.png|thumb|The path for the reverse process (molecule coming back towards the TS) - compare with the figures above demonstrating the dissociation of the TS.|none]]

===Reactive and uncreactive pathways===

The dynamics simulations with the initial momenta as in the Table below with initial distances of '''r1''' = 0.74 and '''r2''' were used to investigate if simply having a high enough momentum is necessary for a succesful collision to occur.

{| class="wikitable" border=1
! p1 !! p2 !! Total energy !! Comment !! Reactive? !! Contour plot
|-
| -1.25 || -2.5 || -99.018 || A successful collision, reaction proceeds. || yes || [[File:Mh-006-react-A.png|300px]]
|-
| -1.5 || -2.0 || -100.456 || The reactants don't have a sufficient momentum to overcome the activation barrier and no reaction occurs. || no || [[File:Mh-006-react-B.png|300px]]
|-
| -1.5 || -2.5 || -98.956 ||Similar to the first case. The higher initial momentum reflects in a higher vibrational energy of the product.|| yes || [[File:Mh-006-react-C.png|300px]]
|-
| -2.5 || -5.0 || -84.956 ||The reactants cross the TS, form the products then revert back to reactants (barrier recrossing). || no || [[File:Mh-006-react-D.png|300px]]
|-
| -2.5 || -5.2 || -83.416 || The reactants cross the barrier multiple time and then continue to form the products. || yes || [[File:Mh-006-react-E.png|300px]]
|}

'''State what are the main assumptions of Transition State Theory. Given the results you have obtained, how will Transition State Theory predictions for reaction rate values compare with experimental values?'''

a

== F-H-H System ==
[[File:Mh-011-FHH-ts.png|thumb|The position of the F-H-H transition state.]]Changing one of the hydrogen atoms for a fluorine atom, the following reaction was investigated:

F + H-H ⇄ HF + H

The transition state was found by carefully adjusting the internuclear distances while keeping the momenta to zero. The process was complicated by the fact the potential energy surface is no longer symmetric and also the forward reaction having a too small activation energy. The distances for which the TS complex remained stationary (at the TS saddle point) were ''rFHa = 1.814'' and ''rHaHb = 0.740''. This is an early transition state (with respect to the above reaction) - the H-H bond is almost intact, while the fluorine is at a large distance. Referencing Hammond's postulate, the structure strongly resembles the reactants.

===Energy considerations===

As shown in the table below, the energy for each stage of the reaction was found by computing the potential energy ('Initial Geometry Information') either while in the transition state (with the distances as determined above) or before/after the reaction (large separation between the species, equilibrium bond lengths set to ''rFH = 0.920'' and ''rHH = 0.740''). The equilibrium bond lengths were determined by an MEP simulation where the interatomic separation converged to the bond length value. The reaction in the forward direction required only a very small activation energy and was found to be overall exothermic.

{| class="wikitable" border=1
! Stage !! Energy
|-
| F + HH || -104.020
|-
| F-H-H (TS) || -103.743
|-
| HF + H || -134.025
|-
| Forward EA || 0.277
|-
| Reverse EA || 30.282
|-
| Forward ΔE || -30.005 (an exothermic process)
|}
<gallery widths=250px heights=250px>
[[
File:Mh-012-HH-bond.png|MEP determination of the H-H bond length.
File:Mh-012-FH-bond.png|MEP determination of the F-H bond length.
]]
</gallery>

===Reaction dynamics===

Simulating the reaction with the following parameters ''rFH = 2.4'', ''rHH = 0.740'', ''pFH = -1'' and ''pHH = -2'' provides the data and plots below. Looking at the surface plot below, it is clear that the energy is conserved since the 'vibrational peaks' reach the same levels (potential energy maxima where they have no kinetic energy) before and after the reaction. However, the vibrational energy increased significantly during reaction, corresponding to the 'release of heat' since the reaction is exothermic. This relates a microscopic simulation to a macroscopic phenomenon, which can be easily measured using, for example, a calorimeter. The amplitudes of the vibrations (stretches) are especially visible on the Momenta in time plot.
<gallery widths=250px heights=250px>
[[
File:Mh-013-FHH-rxn-surface.png|Reaction potential energy surface
File:Mh-013-FHH-rxn-momenta.png|Internuclear momenta over the course of the reaction.
]]
</gallery>

====Forward Reaction Reactive and uncreactive pathways====

The dynamics simulations with the initial momenta as in the Table below with initial parameters of '''rFH = 2.4''', '''rHH = 0.74''' and '''pFH = -0.5''' and a variable initial momentum were used to investigate the reactive pathways for this reaction. The sign of the HH-momentum affects if the first vibration goes 'together' or 'away' and on the countour plots are visible as 'down' and 'up' vibrations, respectively. As it can be seen from the data below, this initial setting can affect the outcome of the reaction. Notice the different vibrational amplitudes for +0.5 and -0.5 setting - this is a result of the anharmonicity of the potential.

{| class="wikitable" border=1
! pHH !! Comment !! Reactive? !! Contour plot
|-
| -3 || Reaction proceeds, the product has a significant vibrational energy. || yes || [[File:Mh-014-react-A.png|300px]]
|-
| -2.5 || Reaction proceeds, but the product has a lower vibrational energy than in the first case || yes || [[File:Mh-014-react-B.png|300px]]
|-
| -2 || The reactants don't have a sufficient momentum to overcome the activation barrier and no reaction occurs. || no || [[File:Mh-014-react-C.png|300px]]
|-
| -0.5 || The reactants don't have a sufficient momentum to overcome the activation barrier and no reaction occurs. || no || [[File:Mh-014-react-D.png|300px]]
|-
| +0.5 || The reactants don't have a sufficient momentum to overcome the activation barrier and no reaction occurs. || no || [[File:Mh-014-react-E.png|300px]]
|-
| +2 || The reaction proceeds, crossing the barrier once. || yes || [[File:Mh-014-react-F.png|300px]]
|-
| +2.5 || The reaction proceeds. || yes || [[File:Mh-014-react-G.png|300px]]
|-
| +3 || The products re-cross the barrier and revert to reactants. || no || [[File:Mh-014-react-H.png|300px]]
|-
|}

The simulation was also performed with the following parameters: '''rFH = 2.4''', '''rHH = 0.74''', '''pFH = 0.5''' and '''pFH = -0.8'''. Initially, the dihydrogen reactant has a relatively small vibrational energy but the product a much higher - this is due to the energy released in the reaction.

[[File:Mh-015-react-lowvib.png]]

=== Reverse reaction analysis ===

Running with the following initial values: '''rFH = 0.91''', '''rHH = 0.74''', '''pFH = 0.5''' and '''pFH = -0.8'''.

MRD:MH5015

2018-05-24T10:33:43Z

Mh5015: /* Forward Reaction Reactive and uncreactive pathways */

This is a report from the Molecular reaction dynamics computational lab by Martin Holicky.

==Introduction==

'''What value do the different components of the gradient of the potential energy surface have at a minimum and at a transition structure? Briefly explain how minima and transition structures can be distinguished using the curvature of the potential energy surface.'''

SW ANGLE

==H-H-H system==
[[File:Mh-001-ts-hhh.png|thumb|Nuclear separation in time when the atoms are in the transition state.]]
The following reaction between three hydrogen atoms was considered:

H-H + H ⇄ H + H-H

It is clear that since all three atoms are identical the bond lengths are equal and also the potential energy surface symmetrical. As stated in the Introduction, the transition state is located at the maximum of the minimum energy path where the potential energy gradient is zero. This implies an unstable equilibrium, however, since the simulation ignores any external factor (such as other atoms) it will be stable forever. By gradually adjusting the internuclear separations while keeping the momenta at zero the transition state position was found at ''rts = 0.907''. The internuclear distance did not change in time which is indeed expected from a transition state. Minor oscillations - stretches of the H-H-H bonds are visible but since these are symmetrical the do not shift shift the equlibrium.

===Minimum energy paths===
[[File:Mh-003-mep_not_ts-hhh.png|thumb|Interatomic distances during the process as simulated in the MEP mode.]]By setting the velocity of the atoms to zero in each step, it is possible to calculate the ''minimum energy path'' (MEP). In this simulation, the HA-HB-HC distances were set to 0.917 and 0.907 respectively, the former corresponding to a slight displacement from the transition state. This displacement resulted in the transition state collapsing into HA and HB-HC. The H-H distance ''rBC'' simply converged to the dihydrogen bond length and ''rAB'' increased steadily (reaching a minimum at infinity).

Running the simulation in the Dynamics mode (preserving velocities between steps) similar results are obtained as the transition state dissociates into HA and HB-HC. However, the reaction is much faster (no surprise here, resetting the speeds in the MEP mode obviously slows down the process significantly). One interesting feature is perhaps the shape of the ''rAB'' curve. With the MEP the curve resembles a logarithmic process, but with the Dynamics simulation it is approximately linear.
[[File:Mh-004-dynamicsaftermep-hhh.png|thumb|Interatomic distances during the process as simulated in the ''Dynamics'' mode.]]

Exchanging the initial distances shifts the reaction towards the other side of the equilibrium (transition state saddle point), resulting in the other set of products.
<gallery heights=220px widths=250px>
Mh-005-dynamicsaftermep-hhh.png | Path towards H + H-H (''rAB'' longer)
Mh-005-dynamicsaftermep2-hhh.png | Path towards H-H + H (''rBC'' longer)
</gallery>

By plotting the momenta of the atoms in time, it was found that at the end of the simulation they were ''pAB = 1.230'' and ''pBC = 2.481'' (the transition state potential energy roughly divided in 2:1 ratio and converted into kinetic energy). Running the simulation backwards with these momenta (opposite signs to reverse the process) and the final positions ''rAB = 0.746'' and ''rBC = 9.006'' resulted in the molecule going into the transition state. This demonstrates the conservation of energy in the simulation.
[[File:Mh-005-reversedynamics-hhh.png|thumb|The path for the reverse process (molecule coming back towards the TS) - compare with the figures above demonstrating the dissociation of the TS.|none]]

===Reactive and uncreactive pathways===

The dynamics simulations with the initial momenta as in the Table below with initial distances of '''r1''' = 0.74 and '''r2''' were used to investigate if simply having a high enough momentum is necessary for a succesful collision to occur.

{| class="wikitable" border=1
! p1 !! p2 !! Total energy !! Comment !! Reactive? !! Contour plot
|-
| -1.25 || -2.5 || -99.018 || A successful collision, reaction proceeds. || yes || [[File:Mh-006-react-A.png|300px]]
|-
| -1.5 || -2.0 || -100.456 || The reactants don't have a sufficient momentum to overcome the activation barrier and no reaction occurs. || no || [[File:Mh-006-react-B.png|300px]]
|-
| -1.5 || -2.5 || -98.956 ||Similar to the first case. The higher initial momentum reflects in a higher vibrational energy of the product.|| yes || [[File:Mh-006-react-C.png|300px]]
|-
| -2.5 || -5.0 || -84.956 ||The reactants cross the TS, form the products then revert back to reactants (barrier recrossing). || no || [[File:Mh-006-react-D.png|300px]]
|-
| -2.5 || -5.2 || -83.416 || The reactants cross the barrier multiple time and then continue to form the products. || yes || [[File:Mh-006-react-E.png|300px]]
|}

'''State what are the main assumptions of Transition State Theory. Given the results you have obtained, how will Transition State Theory predictions for reaction rate values compare with experimental values?'''

a

== F-H-H System ==
[[File:Mh-011-FHH-ts.png|thumb|The position of the F-H-H transition state.]]Changing one of the hydrogen atoms for a fluorine atom, the following reaction was investigated:

F + H-H ⇄ HF + H

The transition state was found by carefully adjusting the internuclear distances while keeping the momenta to zero. The process was complicated by the fact the potential energy surface is no longer symmetric and also the forward reaction having a too small activation energy. The distances for which the TS complex remained stationary (at the TS saddle point) were ''rFHa = 1.814'' and ''rHaHb = 0.740''. This is an early transition state (with respect to the above reaction) - the H-H bond is almost intact, while the fluorine is at a large distance. Referencing Hammond's postulate, the structure strongly resembles the reactants.

===Energy considerations===

As shown in the table below, the energy for each stage of the reaction was found by computing the potential energy ('Initial Geometry Information') either while in the transition state (with the distances as determined above) or before/after the reaction (large separation between the species, equilibrium bond lengths set to ''rFH = 0.920'' and ''rHH = 0.740''). The equilibrium bond lengths were determined by an MEP simulation where the interatomic separation converged to the bond length value. The reaction in the forward direction required only a very small activation energy and was found to be overall exothermic.

{| class="wikitable" border=1
! Stage !! Energy
|-
| F + HH || -104.020
|-
| F-H-H (TS) || -103.743
|-
| HF + H || -134.025
|-
| Forward EA || 0.277
|-
| Reverse EA || 30.282
|-
| Forward ΔE || -30.005 (an exothermic process)
|}
<gallery widths=250px heights=250px>
[[
File:Mh-012-HH-bond.png|MEP determination of the H-H bond length.
File:Mh-012-FH-bond.png|MEP determination of the F-H bond length.
]]
</gallery>

===Reaction dynamics===

Simulating the reaction with the following parameters ''rFH = 2.4'', ''rHH = 0.740'', ''pFH = -1'' and ''pHH = -2'' provides the data and plots below. Looking at the surface plot below, it is clear that the energy is conserved since the 'vibrational peaks' reach the same levels (potential energy maxima where they have no kinetic energy) before and after the reaction. However, the vibrational energy increased significantly during reaction, corresponding to the 'release of heat' since the reaction is exothermic. This relates a microscopic simulation to a macroscopic phenomenon, which can be easily measured using, for example, a calorimeter. The amplitudes of the vibrations (stretches) are especially visible on the Momenta in time plot.
<gallery widths=250px heights=250px>
[[
File:Mh-013-FHH-rxn-surface.png|Reaction potential energy surface
File:Mh-013-FHH-rxn-momenta.png|Internuclear momenta over the course of the reaction.
]]
</gallery>

====Forward Reaction Reactive and uncreactive pathways====

The dynamics simulations with the initial momenta as in the Table below with initial parameters of '''rFH = 2.4''', '''rHH = 0.74''' and '''pFH = -0.5''' and a variable initial momentum were used to investigate the reactive pathways for this reaction. The sign of the HH-momentum affects if the first vibration goes 'together' or 'away' and on the countour plots are visible as 'down' and 'up' vibrations, respectively. As it can be seen from the data below, this initial setting can affect the outcome of the reaction. Notice the different vibrational amplitudes for +0.5 and -0.5 setting - this is a result of the anharmonicity of the potential.

{| class="wikitable" border=1
! pHH !! Comment !! Reactive? !! Contour plot
|-
| -3 || Reaction proceeds, the product has a significant vibrational energy. || yes || [[File:Mh-014-react-A.png|300px]]
|-
| -2.5 || Reaction proceeds, but the product has a lower vibrational energy than in the first case || yes || [[File:Mh-014-react-B.png|300px]]
|-
| -2 || The reactants don't have a sufficient momentum to overcome the activation barrier and no reaction occurs. || no || [[File:Mh-014-react-C.png|300px]]
|-
| -0.5 || The reactants don't have a sufficient momentum to overcome the activation barrier and no reaction occurs. || no || [[File:Mh-014-react-D.png|300px]]
|-
| +0.5 || The reactants don't have a sufficient momentum to overcome the activation barrier and no reaction occurs. || no || [[File:Mh-014-react-E.png|300px]]
|-
| +2 || The reaction proceeds, crossing the barrier once. || yes || [[File:Mh-014-react-F.png|300px]]
|-
| +2.5 || The reaction proceeds. || yes || [[File:Mh-014-react-G.png|300px]]
|-
| +3 || The products re-cross the barrier and revert to reactants. || no || [[File:Mh-014-react-H.png|300px]]
|-
|}

The simulation was also performed with the following parameters: '''rFH = 2.4''', '''rHH = 0.74''', '''pFH = 0.5''' and '''pFH = -0.8'''. Initially, the dihydrogen reactant has a relatively small vibrational energy but the product a much higher - this is due to the energy released in the reaction.
[[File:Mh-015-react-lowvib.png]]

File:Mh-015-react-lowvib.png

2018-05-24T10:33:33Z

Mh5015:

MRD:MH5015