ChemWiki - User contributions [en]

MRD:01508310

2020-05-22T19:55:17Z

Hh2218: /* Trajectories from r1=r2: locating the transition state */

==H-H-H system==
===Dynamics from the transition state region===
The transition state is the point on the potential energy surface that has ∂V(ri)/∂ri=0, where ri is the distance between two atoms.The transition state is a local maximum and its second derivative ∂2V(ri)/∂ri2 is < 0, whereas a local minimum will have a positive second derivative instead.
[[File:Hhh_surfaceplot_01508.png|400px|thumb|centre|a potential energy surface plot of H and H2 with respect to interatomic distances.]]
[[File:HHHSURFACE_015.png|400px|thumb|centre|the potential energy surface plot at a different angle.]]

===Trajectories from r1=r2: locating the transition state===
At the transition state, r1=r2=90.8 pm by estimation as this transition state is symmetric. At this separation, the forces acting along AB and BC are both -0.004 kJ.mol-1.pm-1, which is close to zero and the eigenvalues for the Hessian matrix are -0.028 and +0.167 kJ.mol-1.pm-2, indicating the presence of transition state. The Internuclear Distance vs Time plot suggests the distance between HA, HB and HC is equal, about 90 pm and the distance is constant over time suggests the atoms are static at the transition state.
[[File:Animation101508310.png|400px|centre|thumb|picture showing H and H2 at the symmetric transition state.]]
[[File:Optimisation1_01508310.png|400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:Internucleardistance_01508310.png|400px|centre|thumb|Internuclear Distance vs Time plot between the H atoms at the transition state.]]

===Calculating the reaction path===
When rA-B is set to rts+1 (91.8 pm) and rB-C equals rts (90.8 pm),the transition state rolls towards HB and HC, HA remains as an atom. MEP and Dynamic reaction paths are different as MEP set the momenta to zero in every step of the reaction path, products are therefore static and hence the reaction path is relatively straight. The dynamic reaction path is more realistic. It takes the momenta of gaseous molecules into account,i.e. The reactants and the products have vibrational energies, that is illustrated by the wavy line along the reaction path.
[[File:Surface_Plot1mep_015083.png|400px|centre|thumb|the minimum energy path (MEP) of the H-H-H system]]
[[File:01569348_MEP_AB1_dynamic.png|400px|centre|thumb|the dynamic reaction path of the H-H-H system]]

====MEP and Dynamics calculations comparisons====
'''r1=91.8 pm, r2=90.8 pm, momenta set to 0 g.mol-1.pm.fs-1'''

HB and HC form a H2 molecule whereas HA moves away from the molecule. The distance between B and C decreased to 74 pm, which is the hydrogen molecule bond length <ref name="reference 1"/>.In MEP calculation, the momenta are set to zero at each time step.

[[File:MepH2bondlength_01508.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using MEP calculation.]]

[[File:MepH2momenta015083.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using MEP calculation.]]

Using Dynamics calculation, the outcome of the reaction is the same. The transition state rolls towards HB and HC and a hydrogen molecule is formed. One noticeable difference is that the hydrogen molecule now has some vibational energy as indicated by the wavy line along B-C in the Internuclear Distance vs Time plot.As for the Momenta vs Time plot, the system is linear, therefore the angle theta is zero. HA and HB are moving away from each other at an increasing velocity until the momentum reaches 5 g.mol-1.pm.fs-1.The oscillation along the B-C bond corresponds to the vibration of the bond.
[[File:DynamicsH2_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation.]]
[[File:DynamicsH2monenta_01508.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using Dynamics calculation.]]

'''r1=90.8 pm, r2=91.8 pm, momenta set to 0 g.mol-1.pm.fs-1'''

Once the length of r1 and r2 switches, the shapes of the graphs are identical but instead of HB and HC forming a molecule, HA and HB now form the hydrogen molecule in the products.
[[File:Mepinter2_01508.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using MEP calculation.]]
[[File:Momentamep2_015.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using MEP calculation.]]
[[File:InterDynamic_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation.]]
[[File:Momentadynamics_015083.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using Dynamics calculation.]]

'''Trajectory starting with the final position and reversed momentum to the reaction path above'''

This trajectory starts at the end of the reaction path above and finishes at where the above reaction started. it is essentially a reverse of what happened in the reaction above.
[[File:Reverse_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation (r1=70.0 pm,r2=353 pm,p1=-3.21 g.mol-1.pm.fs-1, p2=-5.07 g.mol-1.pm.fs-1) .]]

===Recative and unreactive trajectories===
{| class="wikitable" border="1"
! p1/g.mol-1.pm.fs-1 !! p2/g.mol-1.pm.fs-1!! Etot/kJmol-1!! Recative?!! Description of the dynamics!! Illustration of the trajectory
|-
| -2.56 || -5.1||-414 || Yes||The translational energy of the reactants can surmount the potential energy barrier and form the products. The ramaining energy is converted into vibrational energy of the products. || [[File:Table1_01508310.png|350px ]]
|-
| -3.1 || -4.1||-420 || No||The reactant H2 has vibrational energy and its rAB motion is rapid. Before it could cross the energy barrier, the molecule slams into the repulsive inner wall of the potential surface and bounces back into the reactant channel. || [[File:Table2_0150.png|350px]]
|-
| -3.1 || -5.1||-414|| Yes||The reactants have both the translational and vibrational energies. The energy is used to surmount the potential energy barrier and converted into the vibrational energy of the products. || [[File:Table3_01508.png|350px]]
|-
| -5.1 || -10.1||-357 || No||The reactants have sufficient energy to cross the transition state and the products did form for a certain amount of time. However, before the the system can exit the product channel, it recrosses the transition state and form the reactants again, hence no reaction occurs. ||[[File:Table4_01508.png|350px]]
|-
| -5.1 || -10.6||-394 || Yes||The system has sufficient energy to cross the transition state but it recrosses the transition state shortly after the reaction path hits the potential energy surface. However, the system is able to cross the transition state for the third time and finally exits the product channel and forms the products. || [[File:-10.6_01508.png|350px]]
|-
|}
In order to form products, a system must have sufficient energy to cross the transition state. Only molecules with the correct phase <ref name="reference 2"/> can exit the product channel and form stable products. Recrossing the transition state can lead to either product formation or no reaction. It is possible to cross the transition state multiple times.

===Transition State Theory===

Transition State Theory is classical, it doesn't take quantum tunnelling into account.Quantum tunnelling is probable for this reaction as it involves the transfer of a hydrogen atom, particularly at lower temperatures <ref name="reference 3"/>.At low temperatures, the H atom can tunnel through the potential energy barrier instead of passing over the barrier, hence the activation energy is lowered and the reaction rate increases. However, recrossing the energy barrier is possible as seen with the simulations, this can have a negative effect on the reaction rate. At high temperatures, the system is thermally activated and the behavious is approximately classical<ref name="reference 4"/>. Overall, the situation can be complicated as the theory assumes quasi-equilibrium between reactants and transition state (activated complexes). The activated complex can then either form products or revert back to the reactants with or without quantum tunnelling. The experimental reaction rate might still be greater than that predicted by the theory.

==F-H-H system==
===PES inspection===
'''F+H2 (F1-H1-H2)'''

F+H2 is exothermic as the reactants are higher in energy than the products therefore during the reaction, energy is released to the surroundings. H-F bond is stronger than H-H bond as the products are lower in energy and therefore more stable.The transition state is located approximately at rF1-H1=181.10 pm and rH1-H2=74.49 pm. This is verified by the forces (close to zero) and eigenvalues for hessian matrix (they are of opposite signs). The activation energy is estimated by tilting the transition state towards the reactants and is shown to be 424 kJ.mol-1.
[[File:Fh2_015083.png |400px|centre|thumb|Surface plot for F1-H1-H2 system using Dynamic Calculation, the transition state is identified as the black dot.]]
[[File:OptimisationFhh1_01508.png|400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:F1H1H2_EA_0150.png|400px|centre|thumb|Counter plot for estimating the activation energy using MEP calculation.]]
[[File:EA1_01508.png|400px|centre|thumb|parameters for the activation energy.]]
'''H+HF (H1-H2-F1)'''

This reaction is endothermis as the reactants are lower in energy than the products therefore energy is taken in from the surroundings to form the products. H-F bond is still stronger than H-H as the reactans are lower in energy and more stable. The transition state is located at approximately rH1-H2=280 pm and rH2-F1=92 pm. It is located with the same reasons stated above.With the same method, the activation energy is estimated to be 434 kJ.mol-1. The two activation energies should be identical as these two reactions are essentially the reverse of one another.

[[File:H+HF_01508310.png|400px|centre|thumb|Surface plot for H1-H2-F1 system using Dynamic Calculationthe, the transition state is identified as the black dot.]]
[[File:HHF_015083.png |400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:EA2_01508.png|400px|centre|thumb|Counter plot for estimating the activation energy using MEP calculation.]]
[[File:EA2_PARAMETERS.png|400px|centre|thumb|parameters for the activation energy.]]

===Reaction dynamics===
===F+H2 system===

Initially, the reactants have kinetic energy in the form of vibrational and translational energies, and as it crosses the potential energy barrier, the kinetic energy is converted into potential energy. Once the system is exiting the product channel, the potential energy is converted into the vibrational energy of the product.One good experimental technique to prob the electronic structure of the reacting species will be IR spectroscopy.In the anharmonic oscillator model, exciting molecules in the relaxed state promotes excitation from the ground state to the first energy level mainly. This will give rise to a single peak in the IR spectrum. Howver, when exciting a sample of excited molecules, many transitions are possible. For example, from 0-->1, the fundamental or 1-->2, the first hot band. They will show up in the spectrum as 2 peaks, with the hot band being at a lower wavenumber as the energy gap decreases up the potential well. The intensity of the hot band decreases over time as the electrons can fall back to lower energy levels and energy is emitted as radiation. As this system is linear, rotational is not important electronic energy is not considered here.Photoelectron spectroscopy is also a viable method. <ref name="reference 5"/>

[[File:Reactiondynamicsfh2_0150.png||400px|centre|thumb|contour plot for F+H2.]]
[[File:Reactiondynamicsparameter——015.png |400px|centre|thumb|parameters for the reactive trajectory.]]
====Varying the momentum of HH in the F+H2 system.====
Conditions:rFH=182 pm, rHH=74 pm, PFH=-1.0g.mol-1.pm.fs-1
{| class="wikitable" border="1"
|+ caption
|-
|PHH/g.mol-1.pm.fs-1|| Contour Plot
|-
|0 || [[File:0_015083.png |400 px|centre]]
|-
|2 || [[File:2_0508.png |400 px|centre]]
|-
|4 || [[File:4_01508.png ‎|400 px|centre]]
|-
|6.1|| [[File:6_01508.png|400 px|centre]]
|-
| -2|| [[File:-2_01508.png|400 px|centre]]
|-
| -4|| [[File:-4.1_01508.png‎|400 px|centre]]
|-
| -6.1|| [[File:Fit1_01508.png|400 px|centre]]
|-
|}
Although the amount of energy that is put into H-H vibration is much more than the activation energy of the reaction, the reaction does not always occur. The large amount of energy is demonstrated by the high frequency of those wavy lines. Recrossing the transition states multiple times can lead to no reaction or product formation depending on how the tragectory collides with the potential well.

[[File:Reactiondynamic_last01588.png|400px|centre|thumb|contour plot for rFH=182 pm, fHH=74 pm, PFH=-1.6g.mol-1.pm.fs-1,PHH=0.2g.mol-1.pm.fs-1]]
The system now has much less vibrational energy into the reactants than before. The reaction is still successful and the trajectory recrosses the transition states fewer times than before.This can be explained by the increased momentum of FH so that F can approach the closest H with more vibrational energy.

===H+HF system===
{| class="wikitable" border="1"
!Graph Number!! p1(HH)/g.mol-1.pm.fs-1 !! p2(HF)/g.mol-1.pm.fs-1!! Etot/kJmol-1!! Recative?!! Illustration of the trajectory
|-
|1|| -2 || -10||-397|| No|| [[File:Final1_01508.png|350px ]]
|-
|2|| 0|| -8||-400 || No|| [[File:Final2_015.png|350px]]
|-
|3||5 || -6||-360|| No|| [[File:Final3_015.png|350px]]
|-
|4|| 5 || -3||-389 || Yes||[[File:Final4_015.png|350px]]
|-
|}

By referening to Polanyl's empirical rules, an exothermic reaction has an early barrier, which happens in the reactant channel. It tends to favour vibrational excitation of the products. On the other hand, an endothermic reaction has a late barrier, which occurs in the product channel. It tends to favour low product vibrational excitation. The location of the energy barrier is also crucial for a successful reaction. Translational energy of the reactants is the most effective at passing the early barrier whereas vibrational energy of the reactants is the most effective at surmounting the late barrier. This is undrstandable because in an endothermic reaction, if the reactants have mainly translational energy, it is more likely that the reactants will hit the potential well wall and results in no reaction.This reaction is endothermic, and hence it has a late barrier. In all the graphs, the reactants all have vibrational energy as indicated by the wavy line in the reactant channel.<ref name="reference 2"/>

==References==

<references>
<ref name="reference 1">R. DeKock and H. Gray, Chemical structure and bonding, Univeristy Science Books, 1989.</ref>
<ref name="reference 2">S. Jeffrey I., Experimental Chemical Dynamics, Prentice-Hall, Upper Saddle River, 2nd edn., 1989.</ref>
<ref name="reference 3">L. Keith J., Theories of reaction rates, Harper & Row, New York;London, 3rd edn., 1987.</ref>
<ref name="reference 4">D. Brougham, A. Horsewill and R. Jenkinson, Chemical Physics Letters, 1997, 272, 69-74.</ref>
<ref name="reference 5">S. Bradforth, D. Arnold, D. Neumark and D. Manolopoulos, The Journal of Chemical Physics, 1993, 99, 6345-6359.</ref>
</references>

MRD:01508310

2020-05-22T19:54:40Z

Hh2218: /* Trajectories from r1=r2: locating the transition state */

==H-H-H system==
===Dynamics from the transition state region===
The transition state is the point on the potential energy surface that has ∂V(ri)/∂ri=0, where ri is the distance between two atoms.The transition state is a local maximum and its second derivative ∂2V(ri)/∂ri2 is < 0, whereas a local minimum will have a positive second derivative instead.
[[File:Hhh_surfaceplot_01508.png|400px|thumb|centre|a potential energy surface plot of H and H2 with respect to interatomic distances.]]
[[File:HHHSURFACE_015.png|400px|thumb|centre|the potential energy surface plot at a different angle.]]

===Trajectories from r1=r2: locating the transition state===
At the transition state, r1=r2=90.8 pm by estimation as this transition state is symmetric. At this separation, the forces acting along AB and BC are both -0.004 kJ.mol-1.pm-1, which is close to zero and the eigenvalues for the Hessian matrix are -0.028 and +0.167 kJ.mol-1.pm-2, indicating the presence of transition state. The Internuclear Distance vs Time plot suggests the distance between HA, HB and HC is equal, about 90 pm and the distance is constant over time suggests the atoms are static at the transition state.
[[File:Animation101508310.png|400px|centre|thumb|picture showing H and H2 at the transition state.]]
[[File:Optimisation1_01508310.png|400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:Internucleardistance_01508310.png|400px|centre|thumb|Internuclear Distance vs Time plot between the H atoms at the transition state.]]

===Calculating the reaction path===
When rA-B is set to rts+1 (91.8 pm) and rB-C equals rts (90.8 pm),the transition state rolls towards HB and HC, HA remains as an atom. MEP and Dynamic reaction paths are different as MEP set the momenta to zero in every step of the reaction path, products are therefore static and hence the reaction path is relatively straight. The dynamic reaction path is more realistic. It takes the momenta of gaseous molecules into account,i.e. The reactants and the products have vibrational energies, that is illustrated by the wavy line along the reaction path.
[[File:Surface_Plot1mep_015083.png|400px|centre|thumb|the minimum energy path (MEP) of the H-H-H system]]
[[File:01569348_MEP_AB1_dynamic.png|400px|centre|thumb|the dynamic reaction path of the H-H-H system]]

====MEP and Dynamics calculations comparisons====
'''r1=91.8 pm, r2=90.8 pm, momenta set to 0 g.mol-1.pm.fs-1'''

HB and HC form a H2 molecule whereas HA moves away from the molecule. The distance between B and C decreased to 74 pm, which is the hydrogen molecule bond length <ref name="reference 1"/>.In MEP calculation, the momenta are set to zero at each time step.

[[File:MepH2bondlength_01508.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using MEP calculation.]]

[[File:MepH2momenta015083.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using MEP calculation.]]

Using Dynamics calculation, the outcome of the reaction is the same. The transition state rolls towards HB and HC and a hydrogen molecule is formed. One noticeable difference is that the hydrogen molecule now has some vibational energy as indicated by the wavy line along B-C in the Internuclear Distance vs Time plot.As for the Momenta vs Time plot, the system is linear, therefore the angle theta is zero. HA and HB are moving away from each other at an increasing velocity until the momentum reaches 5 g.mol-1.pm.fs-1.The oscillation along the B-C bond corresponds to the vibration of the bond.
[[File:DynamicsH2_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation.]]
[[File:DynamicsH2monenta_01508.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using Dynamics calculation.]]

'''r1=90.8 pm, r2=91.8 pm, momenta set to 0 g.mol-1.pm.fs-1'''

Once the length of r1 and r2 switches, the shapes of the graphs are identical but instead of HB and HC forming a molecule, HA and HB now form the hydrogen molecule in the products.
[[File:Mepinter2_01508.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using MEP calculation.]]
[[File:Momentamep2_015.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using MEP calculation.]]
[[File:InterDynamic_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation.]]
[[File:Momentadynamics_015083.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using Dynamics calculation.]]

'''Trajectory starting with the final position and reversed momentum to the reaction path above'''

This trajectory starts at the end of the reaction path above and finishes at where the above reaction started. it is essentially a reverse of what happened in the reaction above.
[[File:Reverse_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation (r1=70.0 pm,r2=353 pm,p1=-3.21 g.mol-1.pm.fs-1, p2=-5.07 g.mol-1.pm.fs-1) .]]

===Recative and unreactive trajectories===
{| class="wikitable" border="1"
! p1/g.mol-1.pm.fs-1 !! p2/g.mol-1.pm.fs-1!! Etot/kJmol-1!! Recative?!! Description of the dynamics!! Illustration of the trajectory
|-
| -2.56 || -5.1||-414 || Yes||The translational energy of the reactants can surmount the potential energy barrier and form the products. The ramaining energy is converted into vibrational energy of the products. || [[File:Table1_01508310.png|350px ]]
|-
| -3.1 || -4.1||-420 || No||The reactant H2 has vibrational energy and its rAB motion is rapid. Before it could cross the energy barrier, the molecule slams into the repulsive inner wall of the potential surface and bounces back into the reactant channel. || [[File:Table2_0150.png|350px]]
|-
| -3.1 || -5.1||-414|| Yes||The reactants have both the translational and vibrational energies. The energy is used to surmount the potential energy barrier and converted into the vibrational energy of the products. || [[File:Table3_01508.png|350px]]
|-
| -5.1 || -10.1||-357 || No||The reactants have sufficient energy to cross the transition state and the products did form for a certain amount of time. However, before the the system can exit the product channel, it recrosses the transition state and form the reactants again, hence no reaction occurs. ||[[File:Table4_01508.png|350px]]
|-
| -5.1 || -10.6||-394 || Yes||The system has sufficient energy to cross the transition state but it recrosses the transition state shortly after the reaction path hits the potential energy surface. However, the system is able to cross the transition state for the third time and finally exits the product channel and forms the products. || [[File:-10.6_01508.png|350px]]
|-
|}
In order to form products, a system must have sufficient energy to cross the transition state. Only molecules with the correct phase <ref name="reference 2"/> can exit the product channel and form stable products. Recrossing the transition state can lead to either product formation or no reaction. It is possible to cross the transition state multiple times.

===Transition State Theory===

Transition State Theory is classical, it doesn't take quantum tunnelling into account.Quantum tunnelling is probable for this reaction as it involves the transfer of a hydrogen atom, particularly at lower temperatures <ref name="reference 3"/>.At low temperatures, the H atom can tunnel through the potential energy barrier instead of passing over the barrier, hence the activation energy is lowered and the reaction rate increases. However, recrossing the energy barrier is possible as seen with the simulations, this can have a negative effect on the reaction rate. At high temperatures, the system is thermally activated and the behavious is approximately classical<ref name="reference 4"/>. Overall, the situation can be complicated as the theory assumes quasi-equilibrium between reactants and transition state (activated complexes). The activated complex can then either form products or revert back to the reactants with or without quantum tunnelling. The experimental reaction rate might still be greater than that predicted by the theory.

==F-H-H system==
===PES inspection===
'''F+H2 (F1-H1-H2)'''

F+H2 is exothermic as the reactants are higher in energy than the products therefore during the reaction, energy is released to the surroundings. H-F bond is stronger than H-H bond as the products are lower in energy and therefore more stable.The transition state is located approximately at rF1-H1=181.10 pm and rH1-H2=74.49 pm. This is verified by the forces (close to zero) and eigenvalues for hessian matrix (they are of opposite signs). The activation energy is estimated by tilting the transition state towards the reactants and is shown to be 424 kJ.mol-1.
[[File:Fh2_015083.png |400px|centre|thumb|Surface plot for F1-H1-H2 system using Dynamic Calculation, the transition state is identified as the black dot.]]
[[File:OptimisationFhh1_01508.png|400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:F1H1H2_EA_0150.png|400px|centre|thumb|Counter plot for estimating the activation energy using MEP calculation.]]
[[File:EA1_01508.png|400px|centre|thumb|parameters for the activation energy.]]
'''H+HF (H1-H2-F1)'''

This reaction is endothermis as the reactants are lower in energy than the products therefore energy is taken in from the surroundings to form the products. H-F bond is still stronger than H-H as the reactans are lower in energy and more stable. The transition state is located at approximately rH1-H2=280 pm and rH2-F1=92 pm. It is located with the same reasons stated above.With the same method, the activation energy is estimated to be 434 kJ.mol-1. The two activation energies should be identical as these two reactions are essentially the reverse of one another.

[[File:H+HF_01508310.png|400px|centre|thumb|Surface plot for H1-H2-F1 system using Dynamic Calculationthe, the transition state is identified as the black dot.]]
[[File:HHF_015083.png |400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:EA2_01508.png|400px|centre|thumb|Counter plot for estimating the activation energy using MEP calculation.]]
[[File:EA2_PARAMETERS.png|400px|centre|thumb|parameters for the activation energy.]]

===Reaction dynamics===
===F+H2 system===

Initially, the reactants have kinetic energy in the form of vibrational and translational energies, and as it crosses the potential energy barrier, the kinetic energy is converted into potential energy. Once the system is exiting the product channel, the potential energy is converted into the vibrational energy of the product.One good experimental technique to prob the electronic structure of the reacting species will be IR spectroscopy.In the anharmonic oscillator model, exciting molecules in the relaxed state promotes excitation from the ground state to the first energy level mainly. This will give rise to a single peak in the IR spectrum. Howver, when exciting a sample of excited molecules, many transitions are possible. For example, from 0-->1, the fundamental or 1-->2, the first hot band. They will show up in the spectrum as 2 peaks, with the hot band being at a lower wavenumber as the energy gap decreases up the potential well. The intensity of the hot band decreases over time as the electrons can fall back to lower energy levels and energy is emitted as radiation. As this system is linear, rotational is not important electronic energy is not considered here.Photoelectron spectroscopy is also a viable method. <ref name="reference 5"/>

[[File:Reactiondynamicsfh2_0150.png||400px|centre|thumb|contour plot for F+H2.]]
[[File:Reactiondynamicsparameter——015.png |400px|centre|thumb|parameters for the reactive trajectory.]]
====Varying the momentum of HH in the F+H2 system.====
Conditions:rFH=182 pm, rHH=74 pm, PFH=-1.0g.mol-1.pm.fs-1
{| class="wikitable" border="1"
|+ caption
|-
|PHH/g.mol-1.pm.fs-1|| Contour Plot
|-
|0 || [[File:0_015083.png |400 px|centre]]
|-
|2 || [[File:2_0508.png |400 px|centre]]
|-
|4 || [[File:4_01508.png ‎|400 px|centre]]
|-
|6.1|| [[File:6_01508.png|400 px|centre]]
|-
| -2|| [[File:-2_01508.png|400 px|centre]]
|-
| -4|| [[File:-4.1_01508.png‎|400 px|centre]]
|-
| -6.1|| [[File:Fit1_01508.png|400 px|centre]]
|-
|}
Although the amount of energy that is put into H-H vibration is much more than the activation energy of the reaction, the reaction does not always occur. The large amount of energy is demonstrated by the high frequency of those wavy lines. Recrossing the transition states multiple times can lead to no reaction or product formation depending on how the tragectory collides with the potential well.

[[File:Reactiondynamic_last01588.png|400px|centre|thumb|contour plot for rFH=182 pm, fHH=74 pm, PFH=-1.6g.mol-1.pm.fs-1,PHH=0.2g.mol-1.pm.fs-1]]
The system now has much less vibrational energy into the reactants than before. The reaction is still successful and the trajectory recrosses the transition states fewer times than before.This can be explained by the increased momentum of FH so that F can approach the closest H with more vibrational energy.

===H+HF system===
{| class="wikitable" border="1"
!Graph Number!! p1(HH)/g.mol-1.pm.fs-1 !! p2(HF)/g.mol-1.pm.fs-1!! Etot/kJmol-1!! Recative?!! Illustration of the trajectory
|-
|1|| -2 || -10||-397|| No|| [[File:Final1_01508.png|350px ]]
|-
|2|| 0|| -8||-400 || No|| [[File:Final2_015.png|350px]]
|-
|3||5 || -6||-360|| No|| [[File:Final3_015.png|350px]]
|-
|4|| 5 || -3||-389 || Yes||[[File:Final4_015.png|350px]]
|-
|}

By referening to Polanyl's empirical rules, an exothermic reaction has an early barrier, which happens in the reactant channel. It tends to favour vibrational excitation of the products. On the other hand, an endothermic reaction has a late barrier, which occurs in the product channel. It tends to favour low product vibrational excitation. The location of the energy barrier is also crucial for a successful reaction. Translational energy of the reactants is the most effective at passing the early barrier whereas vibrational energy of the reactants is the most effective at surmounting the late barrier. This is undrstandable because in an endothermic reaction, if the reactants have mainly translational energy, it is more likely that the reactants will hit the potential well wall and results in no reaction.This reaction is endothermic, and hence it has a late barrier. In all the graphs, the reactants all have vibrational energy as indicated by the wavy line in the reactant channel.<ref name="reference 2"/>

==References==

<references>
<ref name="reference 1">R. DeKock and H. Gray, Chemical structure and bonding, Univeristy Science Books, 1989.</ref>
<ref name="reference 2">S. Jeffrey I., Experimental Chemical Dynamics, Prentice-Hall, Upper Saddle River, 2nd edn., 1989.</ref>
<ref name="reference 3">L. Keith J., Theories of reaction rates, Harper & Row, New York;London, 3rd edn., 1987.</ref>
<ref name="reference 4">D. Brougham, A. Horsewill and R. Jenkinson, Chemical Physics Letters, 1997, 272, 69-74.</ref>
<ref name="reference 5">S. Bradforth, D. Arnold, D. Neumark and D. Manolopoulos, The Journal of Chemical Physics, 1993, 99, 6345-6359.</ref>
</references>

MRD:01508310

2020-05-22T19:54:03Z

Hh2218: /* Dynamics from the transition state region */

==H-H-H system==
===Dynamics from the transition state region===
The transition state is the point on the potential energy surface that has ∂V(ri)/∂ri=0, where ri is the distance between two atoms.The transition state is a local maximum and its second derivative ∂2V(ri)/∂ri2 is < 0, whereas a local minimum will have a positive second derivative instead.
[[File:Hhh_surfaceplot_01508.png|400px|thumb|centre|a potential energy surface plot of H and H2 with respect to interatomic distances.]]
[[File:HHHSURFACE_015.png|400px|thumb|centre|the potential energy surface plot at a different angle.]]

===Trajectories from r1=r2: locating the transition state===
At the transition state, r1=r2=90.8 pm by estimation. At this separation, the forces acting along AB and BC are both -0.004 kJ.mol-1.pm-1, which is close to zero and the eigenvalues for the Hessian matrix are -0.028 and +0.167 kJ.mol-1.pm-2, indicating the presence of transition state. The Internuclear Distance vs Time plot suggests the distance between HA, HB and HC is equal, about 90 pm and the distance is constant over time suggests the atoms are static at the transition state.
[[File:Animation101508310.png|400px|centre|thumb|picture showing H and H2 at the transition state.]]
[[File:Optimisation1_01508310.png|400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:Internucleardistance_01508310.png|400px|centre|thumb|Internuclear Distance vs Time plot between the H atoms at the transition state.]]

===Calculating the reaction path===
When rA-B is set to rts+1 (91.8 pm) and rB-C equals rts (90.8 pm),the transition state rolls towards HB and HC, HA remains as an atom. MEP and Dynamic reaction paths are different as MEP set the momenta to zero in every step of the reaction path, products are therefore static and hence the reaction path is relatively straight. The dynamic reaction path is more realistic. It takes the momenta of gaseous molecules into account,i.e. The reactants and the products have vibrational energies, that is illustrated by the wavy line along the reaction path.
[[File:Surface_Plot1mep_015083.png|400px|centre|thumb|the minimum energy path (MEP) of the H-H-H system]]
[[File:01569348_MEP_AB1_dynamic.png|400px|centre|thumb|the dynamic reaction path of the H-H-H system]]

====MEP and Dynamics calculations comparisons====
'''r1=91.8 pm, r2=90.8 pm, momenta set to 0 g.mol-1.pm.fs-1'''

HB and HC form a H2 molecule whereas HA moves away from the molecule. The distance between B and C decreased to 74 pm, which is the hydrogen molecule bond length <ref name="reference 1"/>.In MEP calculation, the momenta are set to zero at each time step.

[[File:MepH2bondlength_01508.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using MEP calculation.]]

[[File:MepH2momenta015083.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using MEP calculation.]]

Using Dynamics calculation, the outcome of the reaction is the same. The transition state rolls towards HB and HC and a hydrogen molecule is formed. One noticeable difference is that the hydrogen molecule now has some vibational energy as indicated by the wavy line along B-C in the Internuclear Distance vs Time plot.As for the Momenta vs Time plot, the system is linear, therefore the angle theta is zero. HA and HB are moving away from each other at an increasing velocity until the momentum reaches 5 g.mol-1.pm.fs-1.The oscillation along the B-C bond corresponds to the vibration of the bond.
[[File:DynamicsH2_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation.]]
[[File:DynamicsH2monenta_01508.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using Dynamics calculation.]]

'''r1=90.8 pm, r2=91.8 pm, momenta set to 0 g.mol-1.pm.fs-1'''

Once the length of r1 and r2 switches, the shapes of the graphs are identical but instead of HB and HC forming a molecule, HA and HB now form the hydrogen molecule in the products.
[[File:Mepinter2_01508.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using MEP calculation.]]
[[File:Momentamep2_015.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using MEP calculation.]]
[[File:InterDynamic_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation.]]
[[File:Momentadynamics_015083.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using Dynamics calculation.]]

'''Trajectory starting with the final position and reversed momentum to the reaction path above'''

This trajectory starts at the end of the reaction path above and finishes at where the above reaction started. it is essentially a reverse of what happened in the reaction above.
[[File:Reverse_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation (r1=70.0 pm,r2=353 pm,p1=-3.21 g.mol-1.pm.fs-1, p2=-5.07 g.mol-1.pm.fs-1) .]]

===Recative and unreactive trajectories===
{| class="wikitable" border="1"
! p1/g.mol-1.pm.fs-1 !! p2/g.mol-1.pm.fs-1!! Etot/kJmol-1!! Recative?!! Description of the dynamics!! Illustration of the trajectory
|-
| -2.56 || -5.1||-414 || Yes||The translational energy of the reactants can surmount the potential energy barrier and form the products. The ramaining energy is converted into vibrational energy of the products. || [[File:Table1_01508310.png|350px ]]
|-
| -3.1 || -4.1||-420 || No||The reactant H2 has vibrational energy and its rAB motion is rapid. Before it could cross the energy barrier, the molecule slams into the repulsive inner wall of the potential surface and bounces back into the reactant channel. || [[File:Table2_0150.png|350px]]
|-
| -3.1 || -5.1||-414|| Yes||The reactants have both the translational and vibrational energies. The energy is used to surmount the potential energy barrier and converted into the vibrational energy of the products. || [[File:Table3_01508.png|350px]]
|-
| -5.1 || -10.1||-357 || No||The reactants have sufficient energy to cross the transition state and the products did form for a certain amount of time. However, before the the system can exit the product channel, it recrosses the transition state and form the reactants again, hence no reaction occurs. ||[[File:Table4_01508.png|350px]]
|-
| -5.1 || -10.6||-394 || Yes||The system has sufficient energy to cross the transition state but it recrosses the transition state shortly after the reaction path hits the potential energy surface. However, the system is able to cross the transition state for the third time and finally exits the product channel and forms the products. || [[File:-10.6_01508.png|350px]]
|-
|}
In order to form products, a system must have sufficient energy to cross the transition state. Only molecules with the correct phase <ref name="reference 2"/> can exit the product channel and form stable products. Recrossing the transition state can lead to either product formation or no reaction. It is possible to cross the transition state multiple times.

===Transition State Theory===

Transition State Theory is classical, it doesn't take quantum tunnelling into account.Quantum tunnelling is probable for this reaction as it involves the transfer of a hydrogen atom, particularly at lower temperatures <ref name="reference 3"/>.At low temperatures, the H atom can tunnel through the potential energy barrier instead of passing over the barrier, hence the activation energy is lowered and the reaction rate increases. However, recrossing the energy barrier is possible as seen with the simulations, this can have a negative effect on the reaction rate. At high temperatures, the system is thermally activated and the behavious is approximately classical<ref name="reference 4"/>. Overall, the situation can be complicated as the theory assumes quasi-equilibrium between reactants and transition state (activated complexes). The activated complex can then either form products or revert back to the reactants with or without quantum tunnelling. The experimental reaction rate might still be greater than that predicted by the theory.

==F-H-H system==
===PES inspection===
'''F+H2 (F1-H1-H2)'''

F+H2 is exothermic as the reactants are higher in energy than the products therefore during the reaction, energy is released to the surroundings. H-F bond is stronger than H-H bond as the products are lower in energy and therefore more stable.The transition state is located approximately at rF1-H1=181.10 pm and rH1-H2=74.49 pm. This is verified by the forces (close to zero) and eigenvalues for hessian matrix (they are of opposite signs). The activation energy is estimated by tilting the transition state towards the reactants and is shown to be 424 kJ.mol-1.
[[File:Fh2_015083.png |400px|centre|thumb|Surface plot for F1-H1-H2 system using Dynamic Calculation, the transition state is identified as the black dot.]]
[[File:OptimisationFhh1_01508.png|400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:F1H1H2_EA_0150.png|400px|centre|thumb|Counter plot for estimating the activation energy using MEP calculation.]]
[[File:EA1_01508.png|400px|centre|thumb|parameters for the activation energy.]]
'''H+HF (H1-H2-F1)'''

This reaction is endothermis as the reactants are lower in energy than the products therefore energy is taken in from the surroundings to form the products. H-F bond is still stronger than H-H as the reactans are lower in energy and more stable. The transition state is located at approximately rH1-H2=280 pm and rH2-F1=92 pm. It is located with the same reasons stated above.With the same method, the activation energy is estimated to be 434 kJ.mol-1. The two activation energies should be identical as these two reactions are essentially the reverse of one another.

[[File:H+HF_01508310.png|400px|centre|thumb|Surface plot for H1-H2-F1 system using Dynamic Calculationthe, the transition state is identified as the black dot.]]
[[File:HHF_015083.png |400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:EA2_01508.png|400px|centre|thumb|Counter plot for estimating the activation energy using MEP calculation.]]
[[File:EA2_PARAMETERS.png|400px|centre|thumb|parameters for the activation energy.]]

===Reaction dynamics===
===F+H2 system===

Initially, the reactants have kinetic energy in the form of vibrational and translational energies, and as it crosses the potential energy barrier, the kinetic energy is converted into potential energy. Once the system is exiting the product channel, the potential energy is converted into the vibrational energy of the product.One good experimental technique to prob the electronic structure of the reacting species will be IR spectroscopy.In the anharmonic oscillator model, exciting molecules in the relaxed state promotes excitation from the ground state to the first energy level mainly. This will give rise to a single peak in the IR spectrum. Howver, when exciting a sample of excited molecules, many transitions are possible. For example, from 0-->1, the fundamental or 1-->2, the first hot band. They will show up in the spectrum as 2 peaks, with the hot band being at a lower wavenumber as the energy gap decreases up the potential well. The intensity of the hot band decreases over time as the electrons can fall back to lower energy levels and energy is emitted as radiation. As this system is linear, rotational is not important electronic energy is not considered here.Photoelectron spectroscopy is also a viable method. <ref name="reference 5"/>

[[File:Reactiondynamicsfh2_0150.png||400px|centre|thumb|contour plot for F+H2.]]
[[File:Reactiondynamicsparameter——015.png |400px|centre|thumb|parameters for the reactive trajectory.]]
====Varying the momentum of HH in the F+H2 system.====
Conditions:rFH=182 pm, rHH=74 pm, PFH=-1.0g.mol-1.pm.fs-1
{| class="wikitable" border="1"
|+ caption
|-
|PHH/g.mol-1.pm.fs-1|| Contour Plot
|-
|0 || [[File:0_015083.png |400 px|centre]]
|-
|2 || [[File:2_0508.png |400 px|centre]]
|-
|4 || [[File:4_01508.png ‎|400 px|centre]]
|-
|6.1|| [[File:6_01508.png|400 px|centre]]
|-
| -2|| [[File:-2_01508.png|400 px|centre]]
|-
| -4|| [[File:-4.1_01508.png‎|400 px|centre]]
|-
| -6.1|| [[File:Fit1_01508.png|400 px|centre]]
|-
|}
Although the amount of energy that is put into H-H vibration is much more than the activation energy of the reaction, the reaction does not always occur. The large amount of energy is demonstrated by the high frequency of those wavy lines. Recrossing the transition states multiple times can lead to no reaction or product formation depending on how the tragectory collides with the potential well.

[[File:Reactiondynamic_last01588.png|400px|centre|thumb|contour plot for rFH=182 pm, fHH=74 pm, PFH=-1.6g.mol-1.pm.fs-1,PHH=0.2g.mol-1.pm.fs-1]]
The system now has much less vibrational energy into the reactants than before. The reaction is still successful and the trajectory recrosses the transition states fewer times than before.This can be explained by the increased momentum of FH so that F can approach the closest H with more vibrational energy.

===H+HF system===
{| class="wikitable" border="1"
!Graph Number!! p1(HH)/g.mol-1.pm.fs-1 !! p2(HF)/g.mol-1.pm.fs-1!! Etot/kJmol-1!! Recative?!! Illustration of the trajectory
|-
|1|| -2 || -10||-397|| No|| [[File:Final1_01508.png|350px ]]
|-
|2|| 0|| -8||-400 || No|| [[File:Final2_015.png|350px]]
|-
|3||5 || -6||-360|| No|| [[File:Final3_015.png|350px]]
|-
|4|| 5 || -3||-389 || Yes||[[File:Final4_015.png|350px]]
|-
|}

By referening to Polanyl's empirical rules, an exothermic reaction has an early barrier, which happens in the reactant channel. It tends to favour vibrational excitation of the products. On the other hand, an endothermic reaction has a late barrier, which occurs in the product channel. It tends to favour low product vibrational excitation. The location of the energy barrier is also crucial for a successful reaction. Translational energy of the reactants is the most effective at passing the early barrier whereas vibrational energy of the reactants is the most effective at surmounting the late barrier. This is undrstandable because in an endothermic reaction, if the reactants have mainly translational energy, it is more likely that the reactants will hit the potential well wall and results in no reaction.This reaction is endothermic, and hence it has a late barrier. In all the graphs, the reactants all have vibrational energy as indicated by the wavy line in the reactant channel.<ref name="reference 2"/>

==References==

<references>
<ref name="reference 1">R. DeKock and H. Gray, Chemical structure and bonding, Univeristy Science Books, 1989.</ref>
<ref name="reference 2">S. Jeffrey I., Experimental Chemical Dynamics, Prentice-Hall, Upper Saddle River, 2nd edn., 1989.</ref>
<ref name="reference 3">L. Keith J., Theories of reaction rates, Harper & Row, New York;London, 3rd edn., 1987.</ref>
<ref name="reference 4">D. Brougham, A. Horsewill and R. Jenkinson, Chemical Physics Letters, 1997, 272, 69-74.</ref>
<ref name="reference 5">S. Bradforth, D. Arnold, D. Neumark and D. Manolopoulos, The Journal of Chemical Physics, 1993, 99, 6345-6359.</ref>
</references>

File:HHHSURFACE 015.png

2020-05-22T19:52:52Z

Hh2218:

MRD:01508310

2020-05-22T19:49:16Z

Hh2218: /* H+HF system */

==H-H-H system==
===Dynamics from the transition state region===
The transition state is the point on the potential energy surface that has ∂V(ri)/∂ri=0, where ri is the distance between two atoms.The transition state is a local maximum and its second derivative ∂2V(ri)/∂ri2 is < 0, whereas a local minimum will have a positive second derivative instead.
[[File:Hhh_surfaceplot_01508.png|400px|thumb|centre|a potential energy surface plot of H and H2 with respect to interatomic distances.]]

===Trajectories from r1=r2: locating the transition state===
At the transition state, r1=r2=90.8 pm by estimation. At this separation, the forces acting along AB and BC are both -0.004 kJ.mol-1.pm-1, which is close to zero and the eigenvalues for the Hessian matrix are -0.028 and +0.167 kJ.mol-1.pm-2, indicating the presence of transition state. The Internuclear Distance vs Time plot suggests the distance between HA, HB and HC is equal, about 90 pm and the distance is constant over time suggests the atoms are static at the transition state.
[[File:Animation101508310.png|400px|centre|thumb|picture showing H and H2 at the transition state.]]
[[File:Optimisation1_01508310.png|400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:Internucleardistance_01508310.png|400px|centre|thumb|Internuclear Distance vs Time plot between the H atoms at the transition state.]]

===Calculating the reaction path===
When rA-B is set to rts+1 (91.8 pm) and rB-C equals rts (90.8 pm),the transition state rolls towards HB and HC, HA remains as an atom. MEP and Dynamic reaction paths are different as MEP set the momenta to zero in every step of the reaction path, products are therefore static and hence the reaction path is relatively straight. The dynamic reaction path is more realistic. It takes the momenta of gaseous molecules into account,i.e. The reactants and the products have vibrational energies, that is illustrated by the wavy line along the reaction path.
[[File:Surface_Plot1mep_015083.png|400px|centre|thumb|the minimum energy path (MEP) of the H-H-H system]]
[[File:01569348_MEP_AB1_dynamic.png|400px|centre|thumb|the dynamic reaction path of the H-H-H system]]

====MEP and Dynamics calculations comparisons====
'''r1=91.8 pm, r2=90.8 pm, momenta set to 0 g.mol-1.pm.fs-1'''

HB and HC form a H2 molecule whereas HA moves away from the molecule. The distance between B and C decreased to 74 pm, which is the hydrogen molecule bond length <ref name="reference 1"/>.In MEP calculation, the momenta are set to zero at each time step.

[[File:MepH2bondlength_01508.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using MEP calculation.]]

[[File:MepH2momenta015083.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using MEP calculation.]]

Using Dynamics calculation, the outcome of the reaction is the same. The transition state rolls towards HB and HC and a hydrogen molecule is formed. One noticeable difference is that the hydrogen molecule now has some vibational energy as indicated by the wavy line along B-C in the Internuclear Distance vs Time plot.As for the Momenta vs Time plot, the system is linear, therefore the angle theta is zero. HA and HB are moving away from each other at an increasing velocity until the momentum reaches 5 g.mol-1.pm.fs-1.The oscillation along the B-C bond corresponds to the vibration of the bond.
[[File:DynamicsH2_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation.]]
[[File:DynamicsH2monenta_01508.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using Dynamics calculation.]]

'''r1=90.8 pm, r2=91.8 pm, momenta set to 0 g.mol-1.pm.fs-1'''

Once the length of r1 and r2 switches, the shapes of the graphs are identical but instead of HB and HC forming a molecule, HA and HB now form the hydrogen molecule in the products.
[[File:Mepinter2_01508.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using MEP calculation.]]
[[File:Momentamep2_015.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using MEP calculation.]]
[[File:InterDynamic_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation.]]
[[File:Momentadynamics_015083.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using Dynamics calculation.]]

'''Trajectory starting with the final position and reversed momentum to the reaction path above'''

This trajectory starts at the end of the reaction path above and finishes at where the above reaction started. it is essentially a reverse of what happened in the reaction above.
[[File:Reverse_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation (r1=70.0 pm,r2=353 pm,p1=-3.21 g.mol-1.pm.fs-1, p2=-5.07 g.mol-1.pm.fs-1) .]]

===Recative and unreactive trajectories===
{| class="wikitable" border="1"
! p1/g.mol-1.pm.fs-1 !! p2/g.mol-1.pm.fs-1!! Etot/kJmol-1!! Recative?!! Description of the dynamics!! Illustration of the trajectory
|-
| -2.56 || -5.1||-414 || Yes||The translational energy of the reactants can surmount the potential energy barrier and form the products. The ramaining energy is converted into vibrational energy of the products. || [[File:Table1_01508310.png|350px ]]
|-
| -3.1 || -4.1||-420 || No||The reactant H2 has vibrational energy and its rAB motion is rapid. Before it could cross the energy barrier, the molecule slams into the repulsive inner wall of the potential surface and bounces back into the reactant channel. || [[File:Table2_0150.png|350px]]
|-
| -3.1 || -5.1||-414|| Yes||The reactants have both the translational and vibrational energies. The energy is used to surmount the potential energy barrier and converted into the vibrational energy of the products. || [[File:Table3_01508.png|350px]]
|-
| -5.1 || -10.1||-357 || No||The reactants have sufficient energy to cross the transition state and the products did form for a certain amount of time. However, before the the system can exit the product channel, it recrosses the transition state and form the reactants again, hence no reaction occurs. ||[[File:Table4_01508.png|350px]]
|-
| -5.1 || -10.6||-394 || Yes||The system has sufficient energy to cross the transition state but it recrosses the transition state shortly after the reaction path hits the potential energy surface. However, the system is able to cross the transition state for the third time and finally exits the product channel and forms the products. || [[File:-10.6_01508.png|350px]]
|-
|}
In order to form products, a system must have sufficient energy to cross the transition state. Only molecules with the correct phase <ref name="reference 2"/> can exit the product channel and form stable products. Recrossing the transition state can lead to either product formation or no reaction. It is possible to cross the transition state multiple times.

===Transition State Theory===

Transition State Theory is classical, it doesn't take quantum tunnelling into account.Quantum tunnelling is probable for this reaction as it involves the transfer of a hydrogen atom, particularly at lower temperatures <ref name="reference 3"/>.At low temperatures, the H atom can tunnel through the potential energy barrier instead of passing over the barrier, hence the activation energy is lowered and the reaction rate increases. However, recrossing the energy barrier is possible as seen with the simulations, this can have a negative effect on the reaction rate. At high temperatures, the system is thermally activated and the behavious is approximately classical<ref name="reference 4"/>. Overall, the situation can be complicated as the theory assumes quasi-equilibrium between reactants and transition state (activated complexes). The activated complex can then either form products or revert back to the reactants with or without quantum tunnelling. The experimental reaction rate might still be greater than that predicted by the theory.

==F-H-H system==
===PES inspection===
'''F+H2 (F1-H1-H2)'''

F+H2 is exothermic as the reactants are higher in energy than the products therefore during the reaction, energy is released to the surroundings. H-F bond is stronger than H-H bond as the products are lower in energy and therefore more stable.The transition state is located approximately at rF1-H1=181.10 pm and rH1-H2=74.49 pm. This is verified by the forces (close to zero) and eigenvalues for hessian matrix (they are of opposite signs). The activation energy is estimated by tilting the transition state towards the reactants and is shown to be 424 kJ.mol-1.
[[File:Fh2_015083.png |400px|centre|thumb|Surface plot for F1-H1-H2 system using Dynamic Calculation, the transition state is identified as the black dot.]]
[[File:OptimisationFhh1_01508.png|400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:F1H1H2_EA_0150.png|400px|centre|thumb|Counter plot for estimating the activation energy using MEP calculation.]]
[[File:EA1_01508.png|400px|centre|thumb|parameters for the activation energy.]]
'''H+HF (H1-H2-F1)'''

This reaction is endothermis as the reactants are lower in energy than the products therefore energy is taken in from the surroundings to form the products. H-F bond is still stronger than H-H as the reactans are lower in energy and more stable. The transition state is located at approximately rH1-H2=280 pm and rH2-F1=92 pm. It is located with the same reasons stated above.With the same method, the activation energy is estimated to be 434 kJ.mol-1. The two activation energies should be identical as these two reactions are essentially the reverse of one another.

[[File:H+HF_01508310.png|400px|centre|thumb|Surface plot for H1-H2-F1 system using Dynamic Calculationthe, the transition state is identified as the black dot.]]
[[File:HHF_015083.png |400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:EA2_01508.png|400px|centre|thumb|Counter plot for estimating the activation energy using MEP calculation.]]
[[File:EA2_PARAMETERS.png|400px|centre|thumb|parameters for the activation energy.]]

===Reaction dynamics===
===F+H2 system===

Initially, the reactants have kinetic energy in the form of vibrational and translational energies, and as it crosses the potential energy barrier, the kinetic energy is converted into potential energy. Once the system is exiting the product channel, the potential energy is converted into the vibrational energy of the product.One good experimental technique to prob the electronic structure of the reacting species will be IR spectroscopy.In the anharmonic oscillator model, exciting molecules in the relaxed state promotes excitation from the ground state to the first energy level mainly. This will give rise to a single peak in the IR spectrum. Howver, when exciting a sample of excited molecules, many transitions are possible. For example, from 0-->1, the fundamental or 1-->2, the first hot band. They will show up in the spectrum as 2 peaks, with the hot band being at a lower wavenumber as the energy gap decreases up the potential well. The intensity of the hot band decreases over time as the electrons can fall back to lower energy levels and energy is emitted as radiation. As this system is linear, rotational is not important electronic energy is not considered here.Photoelectron spectroscopy is also a viable method. <ref name="reference 5"/>

[[File:Reactiondynamicsfh2_0150.png||400px|centre|thumb|contour plot for F+H2.]]
[[File:Reactiondynamicsparameter——015.png |400px|centre|thumb|parameters for the reactive trajectory.]]
====Varying the momentum of HH in the F+H2 system.====
Conditions:rFH=182 pm, rHH=74 pm, PFH=-1.0g.mol-1.pm.fs-1
{| class="wikitable" border="1"
|+ caption
|-
|PHH/g.mol-1.pm.fs-1|| Contour Plot
|-
|0 || [[File:0_015083.png |400 px|centre]]
|-
|2 || [[File:2_0508.png |400 px|centre]]
|-
|4 || [[File:4_01508.png ‎|400 px|centre]]
|-
|6.1|| [[File:6_01508.png|400 px|centre]]
|-
| -2|| [[File:-2_01508.png|400 px|centre]]
|-
| -4|| [[File:-4.1_01508.png‎|400 px|centre]]
|-
| -6.1|| [[File:Fit1_01508.png|400 px|centre]]
|-
|}
Although the amount of energy that is put into H-H vibration is much more than the activation energy of the reaction, the reaction does not always occur. The large amount of energy is demonstrated by the high frequency of those wavy lines. Recrossing the transition states multiple times can lead to no reaction or product formation depending on how the tragectory collides with the potential well.

[[File:Reactiondynamic_last01588.png|400px|centre|thumb|contour plot for rFH=182 pm, fHH=74 pm, PFH=-1.6g.mol-1.pm.fs-1,PHH=0.2g.mol-1.pm.fs-1]]
The system now has much less vibrational energy into the reactants than before. The reaction is still successful and the trajectory recrosses the transition states fewer times than before.This can be explained by the increased momentum of FH so that F can approach the closest H with more vibrational energy.

===H+HF system===
{| class="wikitable" border="1"
!Graph Number!! p1(HH)/g.mol-1.pm.fs-1 !! p2(HF)/g.mol-1.pm.fs-1!! Etot/kJmol-1!! Recative?!! Illustration of the trajectory
|-
|1|| -2 || -10||-397|| No|| [[File:Final1_01508.png|350px ]]
|-
|2|| 0|| -8||-400 || No|| [[File:Final2_015.png|350px]]
|-
|3||5 || -6||-360|| No|| [[File:Final3_015.png|350px]]
|-
|4|| 5 || -3||-389 || Yes||[[File:Final4_015.png|350px]]
|-
|}

By referening to Polanyl's empirical rules, an exothermic reaction has an early barrier, which happens in the reactant channel. It tends to favour vibrational excitation of the products. On the other hand, an endothermic reaction has a late barrier, which occurs in the product channel. It tends to favour low product vibrational excitation. The location of the energy barrier is also crucial for a successful reaction. Translational energy of the reactants is the most effective at passing the early barrier whereas vibrational energy of the reactants is the most effective at surmounting the late barrier. This is undrstandable because in an endothermic reaction, if the reactants have mainly translational energy, it is more likely that the reactants will hit the potential well wall and results in no reaction.This reaction is endothermic, and hence it has a late barrier. In all the graphs, the reactants all have vibrational energy as indicated by the wavy line in the reactant channel.<ref name="reference 2"/>

==References==

<references>
<ref name="reference 1">R. DeKock and H. Gray, Chemical structure and bonding, Univeristy Science Books, 1989.</ref>
<ref name="reference 2">S. Jeffrey I., Experimental Chemical Dynamics, Prentice-Hall, Upper Saddle River, 2nd edn., 1989.</ref>
<ref name="reference 3">L. Keith J., Theories of reaction rates, Harper & Row, New York;London, 3rd edn., 1987.</ref>
<ref name="reference 4">D. Brougham, A. Horsewill and R. Jenkinson, Chemical Physics Letters, 1997, 272, 69-74.</ref>
<ref name="reference 5">S. Bradforth, D. Arnold, D. Neumark and D. Manolopoulos, The Journal of Chemical Physics, 1993, 99, 6345-6359.</ref>
</references>

MRD:01508310

2020-05-22T19:42:22Z

Hh2218: /* H+HF system */

==H-H-H system==
===Dynamics from the transition state region===
The transition state is the point on the potential energy surface that has ∂V(ri)/∂ri=0, where ri is the distance between two atoms.The transition state is a local maximum and its second derivative ∂2V(ri)/∂ri2 is < 0, whereas a local minimum will have a positive second derivative instead.
[[File:Hhh_surfaceplot_01508.png|400px|thumb|centre|a potential energy surface plot of H and H2 with respect to interatomic distances.]]

===Trajectories from r1=r2: locating the transition state===
At the transition state, r1=r2=90.8 pm by estimation. At this separation, the forces acting along AB and BC are both -0.004 kJ.mol-1.pm-1, which is close to zero and the eigenvalues for the Hessian matrix are -0.028 and +0.167 kJ.mol-1.pm-2, indicating the presence of transition state. The Internuclear Distance vs Time plot suggests the distance between HA, HB and HC is equal, about 90 pm and the distance is constant over time suggests the atoms are static at the transition state.
[[File:Animation101508310.png|400px|centre|thumb|picture showing H and H2 at the transition state.]]
[[File:Optimisation1_01508310.png|400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:Internucleardistance_01508310.png|400px|centre|thumb|Internuclear Distance vs Time plot between the H atoms at the transition state.]]

===Calculating the reaction path===
When rA-B is set to rts+1 (91.8 pm) and rB-C equals rts (90.8 pm),the transition state rolls towards HB and HC, HA remains as an atom. MEP and Dynamic reaction paths are different as MEP set the momenta to zero in every step of the reaction path, products are therefore static and hence the reaction path is relatively straight. The dynamic reaction path is more realistic. It takes the momenta of gaseous molecules into account,i.e. The reactants and the products have vibrational energies, that is illustrated by the wavy line along the reaction path.
[[File:Surface_Plot1mep_015083.png|400px|centre|thumb|the minimum energy path (MEP) of the H-H-H system]]
[[File:01569348_MEP_AB1_dynamic.png|400px|centre|thumb|the dynamic reaction path of the H-H-H system]]

====MEP and Dynamics calculations comparisons====
'''r1=91.8 pm, r2=90.8 pm, momenta set to 0 g.mol-1.pm.fs-1'''

HB and HC form a H2 molecule whereas HA moves away from the molecule. The distance between B and C decreased to 74 pm, which is the hydrogen molecule bond length <ref name="reference 1"/>.In MEP calculation, the momenta are set to zero at each time step.

[[File:MepH2bondlength_01508.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using MEP calculation.]]

[[File:MepH2momenta015083.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using MEP calculation.]]

Using Dynamics calculation, the outcome of the reaction is the same. The transition state rolls towards HB and HC and a hydrogen molecule is formed. One noticeable difference is that the hydrogen molecule now has some vibational energy as indicated by the wavy line along B-C in the Internuclear Distance vs Time plot.As for the Momenta vs Time plot, the system is linear, therefore the angle theta is zero. HA and HB are moving away from each other at an increasing velocity until the momentum reaches 5 g.mol-1.pm.fs-1.The oscillation along the B-C bond corresponds to the vibration of the bond.
[[File:DynamicsH2_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation.]]
[[File:DynamicsH2monenta_01508.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using Dynamics calculation.]]

'''r1=90.8 pm, r2=91.8 pm, momenta set to 0 g.mol-1.pm.fs-1'''

Once the length of r1 and r2 switches, the shapes of the graphs are identical but instead of HB and HC forming a molecule, HA and HB now form the hydrogen molecule in the products.
[[File:Mepinter2_01508.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using MEP calculation.]]
[[File:Momentamep2_015.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using MEP calculation.]]
[[File:InterDynamic_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation.]]
[[File:Momentadynamics_015083.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using Dynamics calculation.]]

'''Trajectory starting with the final position and reversed momentum to the reaction path above'''

This trajectory starts at the end of the reaction path above and finishes at where the above reaction started. it is essentially a reverse of what happened in the reaction above.
[[File:Reverse_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation (r1=70.0 pm,r2=353 pm,p1=-3.21 g.mol-1.pm.fs-1, p2=-5.07 g.mol-1.pm.fs-1) .]]

===Recative and unreactive trajectories===
{| class="wikitable" border="1"
! p1/g.mol-1.pm.fs-1 !! p2/g.mol-1.pm.fs-1!! Etot/kJmol-1!! Recative?!! Description of the dynamics!! Illustration of the trajectory
|-
| -2.56 || -5.1||-414 || Yes||The translational energy of the reactants can surmount the potential energy barrier and form the products. The ramaining energy is converted into vibrational energy of the products. || [[File:Table1_01508310.png|350px ]]
|-
| -3.1 || -4.1||-420 || No||The reactant H2 has vibrational energy and its rAB motion is rapid. Before it could cross the energy barrier, the molecule slams into the repulsive inner wall of the potential surface and bounces back into the reactant channel. || [[File:Table2_0150.png|350px]]
|-
| -3.1 || -5.1||-414|| Yes||The reactants have both the translational and vibrational energies. The energy is used to surmount the potential energy barrier and converted into the vibrational energy of the products. || [[File:Table3_01508.png|350px]]
|-
| -5.1 || -10.1||-357 || No||The reactants have sufficient energy to cross the transition state and the products did form for a certain amount of time. However, before the the system can exit the product channel, it recrosses the transition state and form the reactants again, hence no reaction occurs. ||[[File:Table4_01508.png|350px]]
|-
| -5.1 || -10.6||-394 || Yes||The system has sufficient energy to cross the transition state but it recrosses the transition state shortly after the reaction path hits the potential energy surface. However, the system is able to cross the transition state for the third time and finally exits the product channel and forms the products. || [[File:-10.6_01508.png|350px]]
|-
|}
In order to form products, a system must have sufficient energy to cross the transition state. Only molecules with the correct phase <ref name="reference 2"/> can exit the product channel and form stable products. Recrossing the transition state can lead to either product formation or no reaction. It is possible to cross the transition state multiple times.

===Transition State Theory===

Transition State Theory is classical, it doesn't take quantum tunnelling into account.Quantum tunnelling is probable for this reaction as it involves the transfer of a hydrogen atom, particularly at lower temperatures <ref name="reference 3"/>.At low temperatures, the H atom can tunnel through the potential energy barrier instead of passing over the barrier, hence the activation energy is lowered and the reaction rate increases. However, recrossing the energy barrier is possible as seen with the simulations, this can have a negative effect on the reaction rate. At high temperatures, the system is thermally activated and the behavious is approximately classical<ref name="reference 4"/>. Overall, the situation can be complicated as the theory assumes quasi-equilibrium between reactants and transition state (activated complexes). The activated complex can then either form products or revert back to the reactants with or without quantum tunnelling. The experimental reaction rate might still be greater than that predicted by the theory.

==F-H-H system==
===PES inspection===
'''F+H2 (F1-H1-H2)'''

F+H2 is exothermic as the reactants are higher in energy than the products therefore during the reaction, energy is released to the surroundings. H-F bond is stronger than H-H bond as the products are lower in energy and therefore more stable.The transition state is located approximately at rF1-H1=181.10 pm and rH1-H2=74.49 pm. This is verified by the forces (close to zero) and eigenvalues for hessian matrix (they are of opposite signs). The activation energy is estimated by tilting the transition state towards the reactants and is shown to be 424 kJ.mol-1.
[[File:Fh2_015083.png |400px|centre|thumb|Surface plot for F1-H1-H2 system using Dynamic Calculation, the transition state is identified as the black dot.]]
[[File:OptimisationFhh1_01508.png|400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:F1H1H2_EA_0150.png|400px|centre|thumb|Counter plot for estimating the activation energy using MEP calculation.]]
[[File:EA1_01508.png|400px|centre|thumb|parameters for the activation energy.]]
'''H+HF (H1-H2-F1)'''

This reaction is endothermis as the reactants are lower in energy than the products therefore energy is taken in from the surroundings to form the products. H-F bond is still stronger than H-H as the reactans are lower in energy and more stable. The transition state is located at approximately rH1-H2=280 pm and rH2-F1=92 pm. It is located with the same reasons stated above.With the same method, the activation energy is estimated to be 434 kJ.mol-1. The two activation energies should be identical as these two reactions are essentially the reverse of one another.

[[File:H+HF_01508310.png|400px|centre|thumb|Surface plot for H1-H2-F1 system using Dynamic Calculationthe, the transition state is identified as the black dot.]]
[[File:HHF_015083.png |400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:EA2_01508.png|400px|centre|thumb|Counter plot for estimating the activation energy using MEP calculation.]]
[[File:EA2_PARAMETERS.png|400px|centre|thumb|parameters for the activation energy.]]

===Reaction dynamics===
===F+H2 system===

Initially, the reactants have kinetic energy in the form of vibrational and translational energies, and as it crosses the potential energy barrier, the kinetic energy is converted into potential energy. Once the system is exiting the product channel, the potential energy is converted into the vibrational energy of the product.One good experimental technique to prob the electronic structure of the reacting species will be IR spectroscopy.In the anharmonic oscillator model, exciting molecules in the relaxed state promotes excitation from the ground state to the first energy level mainly. This will give rise to a single peak in the IR spectrum. Howver, when exciting a sample of excited molecules, many transitions are possible. For example, from 0-->1, the fundamental or 1-->2, the first hot band. They will show up in the spectrum as 2 peaks, with the hot band being at a lower wavenumber as the energy gap decreases up the potential well. The intensity of the hot band decreases over time as the electrons can fall back to lower energy levels and energy is emitted as radiation. As this system is linear, rotational is not important electronic energy is not considered here.Photoelectron spectroscopy is also a viable method. <ref name="reference 5"/>

[[File:Reactiondynamicsfh2_0150.png||400px|centre|thumb|contour plot for F+H2.]]
[[File:Reactiondynamicsparameter——015.png |400px|centre|thumb|parameters for the reactive trajectory.]]
====Varying the momentum of HH in the F+H2 system.====
Conditions:rFH=182 pm, rHH=74 pm, PFH=-1.0g.mol-1.pm.fs-1
{| class="wikitable" border="1"
|+ caption
|-
|PHH/g.mol-1.pm.fs-1|| Contour Plot
|-
|0 || [[File:0_015083.png |400 px|centre]]
|-
|2 || [[File:2_0508.png |400 px|centre]]
|-
|4 || [[File:4_01508.png ‎|400 px|centre]]
|-
|6.1|| [[File:6_01508.png|400 px|centre]]
|-
| -2|| [[File:-2_01508.png|400 px|centre]]
|-
| -4|| [[File:-4.1_01508.png‎|400 px|centre]]
|-
| -6.1|| [[File:Fit1_01508.png|400 px|centre]]
|-
|}
Although the amount of energy that is put into H-H vibration is much more than the activation energy of the reaction, the reaction does not always occur. The large amount of energy is demonstrated by the high frequency of those wavy lines. Recrossing the transition states multiple times can lead to no reaction or product formation depending on how the tragectory collides with the potential well.

[[File:Reactiondynamic_last01588.png|400px|centre|thumb|contour plot for rFH=182 pm, fHH=74 pm, PFH=-1.6g.mol-1.pm.fs-1,PHH=0.2g.mol-1.pm.fs-1]]
The system now has much less vibrational energy into the reactants than before. The reaction is still successful and the trajectory recrosses the transition states fewer times than before.This can be explained by the increased momentum of FH so that F can approach the closest H with more vibrational energy.

===H+HF system===
{| class="wikitable" border="1"
!Graph Number!! p1(HH)/g.mol-1.pm.fs-1 !! p2(HF)/g.mol-1.pm.fs-1!! Etot/kJmol-1!! Recative?!! Illustration of the trajectory
|-
|1|| -2 || -10||-397|| No|| [[File:Final1_01508.png|350px ]]
|-
|2|| 0|| -8||-400 || No|| [[File:Final2_015.png|350px]]
|-
|3||5 || -6||-360|| No|| [[File:Final3_015.png|350px]]
|-
|4|| 5 || -3||-389 || Yes||[[File:Final4_015.png|350px]]
|-
|}

by referening to Polanyl's empirical rules, an exothermic reaction has an early barrier, which happens in the reactant channel. It tends to favour vibrational excitation of the products. On the other hand, an endothermic reaction has a late barrier, which occurs in the product channel. It tends to favour low product vibrational excitation. The location of the energy barrier is also crucial for a successful reaction. Translational energy of the reactants is the most effective at passing the early barrier whereas vibrational energy of the reactants is the most effective at surmounting the late barrier.This reaction is endothermic, and hence it has a late barrier. In all the graphs, the reactants all have vibrational energy as indicated by the wavy line in the reactant channel.<ref name="reference 2"/>

==References==

<references>
<ref name="reference 1">R. DeKock and H. Gray, Chemical structure and bonding, Univeristy Science Books, 1989.</ref>
<ref name="reference 2">S. Jeffrey I., Experimental Chemical Dynamics, Prentice-Hall, Upper Saddle River, 2nd edn., 1989.</ref>
<ref name="reference 3">L. Keith J., Theories of reaction rates, Harper & Row, New York;London, 3rd edn., 1987.</ref>
<ref name="reference 4">D. Brougham, A. Horsewill and R. Jenkinson, Chemical Physics Letters, 1997, 272, 69-74.</ref>
<ref name="reference 5">S. Bradforth, D. Arnold, D. Neumark and D. Manolopoulos, The Journal of Chemical Physics, 1993, 99, 6345-6359.</ref>
</references>

MRD:01508310

2020-05-22T19:39:58Z

Hh2218: /* F+H2 system */

==H-H-H system==
===Dynamics from the transition state region===
The transition state is the point on the potential energy surface that has ∂V(ri)/∂ri=0, where ri is the distance between two atoms.The transition state is a local maximum and its second derivative ∂2V(ri)/∂ri2 is < 0, whereas a local minimum will have a positive second derivative instead.
[[File:Hhh_surfaceplot_01508.png|400px|thumb|centre|a potential energy surface plot of H and H2 with respect to interatomic distances.]]

===Trajectories from r1=r2: locating the transition state===
At the transition state, r1=r2=90.8 pm by estimation. At this separation, the forces acting along AB and BC are both -0.004 kJ.mol-1.pm-1, which is close to zero and the eigenvalues for the Hessian matrix are -0.028 and +0.167 kJ.mol-1.pm-2, indicating the presence of transition state. The Internuclear Distance vs Time plot suggests the distance between HA, HB and HC is equal, about 90 pm and the distance is constant over time suggests the atoms are static at the transition state.
[[File:Animation101508310.png|400px|centre|thumb|picture showing H and H2 at the transition state.]]
[[File:Optimisation1_01508310.png|400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:Internucleardistance_01508310.png|400px|centre|thumb|Internuclear Distance vs Time plot between the H atoms at the transition state.]]

===Calculating the reaction path===
When rA-B is set to rts+1 (91.8 pm) and rB-C equals rts (90.8 pm),the transition state rolls towards HB and HC, HA remains as an atom. MEP and Dynamic reaction paths are different as MEP set the momenta to zero in every step of the reaction path, products are therefore static and hence the reaction path is relatively straight. The dynamic reaction path is more realistic. It takes the momenta of gaseous molecules into account,i.e. The reactants and the products have vibrational energies, that is illustrated by the wavy line along the reaction path.
[[File:Surface_Plot1mep_015083.png|400px|centre|thumb|the minimum energy path (MEP) of the H-H-H system]]
[[File:01569348_MEP_AB1_dynamic.png|400px|centre|thumb|the dynamic reaction path of the H-H-H system]]

====MEP and Dynamics calculations comparisons====
'''r1=91.8 pm, r2=90.8 pm, momenta set to 0 g.mol-1.pm.fs-1'''

HB and HC form a H2 molecule whereas HA moves away from the molecule. The distance between B and C decreased to 74 pm, which is the hydrogen molecule bond length <ref name="reference 1"/>.In MEP calculation, the momenta are set to zero at each time step.

[[File:MepH2bondlength_01508.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using MEP calculation.]]

[[File:MepH2momenta015083.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using MEP calculation.]]

Using Dynamics calculation, the outcome of the reaction is the same. The transition state rolls towards HB and HC and a hydrogen molecule is formed. One noticeable difference is that the hydrogen molecule now has some vibational energy as indicated by the wavy line along B-C in the Internuclear Distance vs Time plot.As for the Momenta vs Time plot, the system is linear, therefore the angle theta is zero. HA and HB are moving away from each other at an increasing velocity until the momentum reaches 5 g.mol-1.pm.fs-1.The oscillation along the B-C bond corresponds to the vibration of the bond.
[[File:DynamicsH2_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation.]]
[[File:DynamicsH2monenta_01508.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using Dynamics calculation.]]

'''r1=90.8 pm, r2=91.8 pm, momenta set to 0 g.mol-1.pm.fs-1'''

Once the length of r1 and r2 switches, the shapes of the graphs are identical but instead of HB and HC forming a molecule, HA and HB now form the hydrogen molecule in the products.
[[File:Mepinter2_01508.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using MEP calculation.]]
[[File:Momentamep2_015.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using MEP calculation.]]
[[File:InterDynamic_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation.]]
[[File:Momentadynamics_015083.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using Dynamics calculation.]]

'''Trajectory starting with the final position and reversed momentum to the reaction path above'''

This trajectory starts at the end of the reaction path above and finishes at where the above reaction started. it is essentially a reverse of what happened in the reaction above.
[[File:Reverse_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation (r1=70.0 pm,r2=353 pm,p1=-3.21 g.mol-1.pm.fs-1, p2=-5.07 g.mol-1.pm.fs-1) .]]

===Recative and unreactive trajectories===
{| class="wikitable" border="1"
! p1/g.mol-1.pm.fs-1 !! p2/g.mol-1.pm.fs-1!! Etot/kJmol-1!! Recative?!! Description of the dynamics!! Illustration of the trajectory
|-
| -2.56 || -5.1||-414 || Yes||The translational energy of the reactants can surmount the potential energy barrier and form the products. The ramaining energy is converted into vibrational energy of the products. || [[File:Table1_01508310.png|350px ]]
|-
| -3.1 || -4.1||-420 || No||The reactant H2 has vibrational energy and its rAB motion is rapid. Before it could cross the energy barrier, the molecule slams into the repulsive inner wall of the potential surface and bounces back into the reactant channel. || [[File:Table2_0150.png|350px]]
|-
| -3.1 || -5.1||-414|| Yes||The reactants have both the translational and vibrational energies. The energy is used to surmount the potential energy barrier and converted into the vibrational energy of the products. || [[File:Table3_01508.png|350px]]
|-
| -5.1 || -10.1||-357 || No||The reactants have sufficient energy to cross the transition state and the products did form for a certain amount of time. However, before the the system can exit the product channel, it recrosses the transition state and form the reactants again, hence no reaction occurs. ||[[File:Table4_01508.png|350px]]
|-
| -5.1 || -10.6||-394 || Yes||The system has sufficient energy to cross the transition state but it recrosses the transition state shortly after the reaction path hits the potential energy surface. However, the system is able to cross the transition state for the third time and finally exits the product channel and forms the products. || [[File:-10.6_01508.png|350px]]
|-
|}
In order to form products, a system must have sufficient energy to cross the transition state. Only molecules with the correct phase <ref name="reference 2"/> can exit the product channel and form stable products. Recrossing the transition state can lead to either product formation or no reaction. It is possible to cross the transition state multiple times.

===Transition State Theory===

Transition State Theory is classical, it doesn't take quantum tunnelling into account.Quantum tunnelling is probable for this reaction as it involves the transfer of a hydrogen atom, particularly at lower temperatures <ref name="reference 3"/>.At low temperatures, the H atom can tunnel through the potential energy barrier instead of passing over the barrier, hence the activation energy is lowered and the reaction rate increases. However, recrossing the energy barrier is possible as seen with the simulations, this can have a negative effect on the reaction rate. At high temperatures, the system is thermally activated and the behavious is approximately classical<ref name="reference 4"/>. Overall, the situation can be complicated as the theory assumes quasi-equilibrium between reactants and transition state (activated complexes). The activated complex can then either form products or revert back to the reactants with or without quantum tunnelling. The experimental reaction rate might still be greater than that predicted by the theory.

==F-H-H system==
===PES inspection===
'''F+H2 (F1-H1-H2)'''

F+H2 is exothermic as the reactants are higher in energy than the products therefore during the reaction, energy is released to the surroundings. H-F bond is stronger than H-H bond as the products are lower in energy and therefore more stable.The transition state is located approximately at rF1-H1=181.10 pm and rH1-H2=74.49 pm. This is verified by the forces (close to zero) and eigenvalues for hessian matrix (they are of opposite signs). The activation energy is estimated by tilting the transition state towards the reactants and is shown to be 424 kJ.mol-1.
[[File:Fh2_015083.png |400px|centre|thumb|Surface plot for F1-H1-H2 system using Dynamic Calculation, the transition state is identified as the black dot.]]
[[File:OptimisationFhh1_01508.png|400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:F1H1H2_EA_0150.png|400px|centre|thumb|Counter plot for estimating the activation energy using MEP calculation.]]
[[File:EA1_01508.png|400px|centre|thumb|parameters for the activation energy.]]
'''H+HF (H1-H2-F1)'''

This reaction is endothermis as the reactants are lower in energy than the products therefore energy is taken in from the surroundings to form the products. H-F bond is still stronger than H-H as the reactans are lower in energy and more stable. The transition state is located at approximately rH1-H2=280 pm and rH2-F1=92 pm. It is located with the same reasons stated above.With the same method, the activation energy is estimated to be 434 kJ.mol-1. The two activation energies should be identical as these two reactions are essentially the reverse of one another.

[[File:H+HF_01508310.png|400px|centre|thumb|Surface plot for H1-H2-F1 system using Dynamic Calculationthe, the transition state is identified as the black dot.]]
[[File:HHF_015083.png |400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:EA2_01508.png|400px|centre|thumb|Counter plot for estimating the activation energy using MEP calculation.]]
[[File:EA2_PARAMETERS.png|400px|centre|thumb|parameters for the activation energy.]]

===Reaction dynamics===
===F+H2 system===

Initially, the reactants have kinetic energy in the form of vibrational and translational energies, and as it crosses the potential energy barrier, the kinetic energy is converted into potential energy. Once the system is exiting the product channel, the potential energy is converted into the vibrational energy of the product.One good experimental technique to prob the electronic structure of the reacting species will be IR spectroscopy.In the anharmonic oscillator model, exciting molecules in the relaxed state promotes excitation from the ground state to the first energy level mainly. This will give rise to a single peak in the IR spectrum. Howver, when exciting a sample of excited molecules, many transitions are possible. For example, from 0-->1, the fundamental or 1-->2, the first hot band. They will show up in the spectrum as 2 peaks, with the hot band being at a lower wavenumber as the energy gap decreases up the potential well. The intensity of the hot band decreases over time as the electrons can fall back to lower energy levels and energy is emitted as radiation. As this system is linear, rotational is not important electronic energy is not considered here.Photoelectron spectroscopy is also a viable method. <ref name="reference 5"/>

[[File:Reactiondynamicsfh2_0150.png||400px|centre|thumb|contour plot for F+H2.]]
[[File:Reactiondynamicsparameter——015.png |400px|centre|thumb|parameters for the reactive trajectory.]]
====Varying the momentum of HH in the F+H2 system.====
Conditions:rFH=182 pm, rHH=74 pm, PFH=-1.0g.mol-1.pm.fs-1
{| class="wikitable" border="1"
|+ caption
|-
|PHH/g.mol-1.pm.fs-1|| Contour Plot
|-
|0 || [[File:0_015083.png |400 px|centre]]
|-
|2 || [[File:2_0508.png |400 px|centre]]
|-
|4 || [[File:4_01508.png ‎|400 px|centre]]
|-
|6.1|| [[File:6_01508.png|400 px|centre]]
|-
| -2|| [[File:-2_01508.png|400 px|centre]]
|-
| -4|| [[File:-4.1_01508.png‎|400 px|centre]]
|-
| -6.1|| [[File:Fit1_01508.png|400 px|centre]]
|-
|}
Although the amount of energy that is put into H-H vibration is much more than the activation energy of the reaction, the reaction does not always occur. The large amount of energy is demonstrated by the high frequency of those wavy lines. Recrossing the transition states multiple times can lead to no reaction or product formation depending on how the tragectory collides with the potential well.

[[File:Reactiondynamic_last01588.png|400px|centre|thumb|contour plot for rFH=182 pm, fHH=74 pm, PFH=-1.6g.mol-1.pm.fs-1,PHH=0.2g.mol-1.pm.fs-1]]
The system now has much less vibrational energy into the reactants than before. The reaction is still successful and the trajectory recrosses the transition states fewer times than before.This can be explained by the increased momentum of FH so that F can approach the closest H with more vibrational energy.

===H+HF system===
{| class="wikitable" border="1"
!Graph Number!! p1(HH)/g.mol-1.pm.fs-1 !! p2(HF)/g.mol-1.pm.fs-1!! Etot/kJmol-1!! Recative?!! Illustration of the trajectory
|-
|1|| -2 || -10||-397|| No|| [[File:Final1_01508.png|350px ]]
|-
|2|| 0|| -8||-400 || No|| [[File:Final2_015.png|350px]]
|-
|3||5 || -6||-360|| No|| [[File:Final3_015.png|350px]]
|-
|4|| 5 || -3||-389 || Yes||[[File:Final4_015.png|350px]]
|-
|}

by referening to Polanyl's empirical rules, an exothermic reaction has an early barrier, which happens in the entrance channel. It tends to favour vibrational excitation of the products. On the other hand, an endothermic reaction has a late barrier, which occurs in the product channel. It tends to favour low product vibrational excitation. The location of the energy barrier is also crucial for a successful reaction. Translational energy of the reactants is the most effective at passing the early barrier whereas vibrational energy of the reactants is the most effective at surmounting the late barrier.This reaction is endothermic, and hence it has a late barrier. In all the graphs, the reactants all have vibrational energy as indicated by the wavy line in the reactant channel.<ref name="reference 2"/>

==References==

<references>
<ref name="reference 1">R. DeKock and H. Gray, Chemical structure and bonding, Univeristy Science Books, 1989.</ref>
<ref name="reference 2">S. Jeffrey I., Experimental Chemical Dynamics, Prentice-Hall, Upper Saddle River, 2nd edn., 1989.</ref>
<ref name="reference 3">L. Keith J., Theories of reaction rates, Harper & Row, New York;London, 3rd edn., 1987.</ref>
<ref name="reference 4">D. Brougham, A. Horsewill and R. Jenkinson, Chemical Physics Letters, 1997, 272, 69-74.</ref>
<ref name="reference 5">S. Bradforth, D. Arnold, D. Neumark and D. Manolopoulos, The Journal of Chemical Physics, 1993, 99, 6345-6359.</ref>
</references>

MRD:01508310

2020-05-22T19:38:54Z

Hh2218: /* F+H2 system */

==H-H-H system==
===Dynamics from the transition state region===
The transition state is the point on the potential energy surface that has ∂V(ri)/∂ri=0, where ri is the distance between two atoms.The transition state is a local maximum and its second derivative ∂2V(ri)/∂ri2 is < 0, whereas a local minimum will have a positive second derivative instead.
[[File:Hhh_surfaceplot_01508.png|400px|thumb|centre|a potential energy surface plot of H and H2 with respect to interatomic distances.]]

===Trajectories from r1=r2: locating the transition state===
At the transition state, r1=r2=90.8 pm by estimation. At this separation, the forces acting along AB and BC are both -0.004 kJ.mol-1.pm-1, which is close to zero and the eigenvalues for the Hessian matrix are -0.028 and +0.167 kJ.mol-1.pm-2, indicating the presence of transition state. The Internuclear Distance vs Time plot suggests the distance between HA, HB and HC is equal, about 90 pm and the distance is constant over time suggests the atoms are static at the transition state.
[[File:Animation101508310.png|400px|centre|thumb|picture showing H and H2 at the transition state.]]
[[File:Optimisation1_01508310.png|400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:Internucleardistance_01508310.png|400px|centre|thumb|Internuclear Distance vs Time plot between the H atoms at the transition state.]]

===Calculating the reaction path===
When rA-B is set to rts+1 (91.8 pm) and rB-C equals rts (90.8 pm),the transition state rolls towards HB and HC, HA remains as an atom. MEP and Dynamic reaction paths are different as MEP set the momenta to zero in every step of the reaction path, products are therefore static and hence the reaction path is relatively straight. The dynamic reaction path is more realistic. It takes the momenta of gaseous molecules into account,i.e. The reactants and the products have vibrational energies, that is illustrated by the wavy line along the reaction path.
[[File:Surface_Plot1mep_015083.png|400px|centre|thumb|the minimum energy path (MEP) of the H-H-H system]]
[[File:01569348_MEP_AB1_dynamic.png|400px|centre|thumb|the dynamic reaction path of the H-H-H system]]

====MEP and Dynamics calculations comparisons====
'''r1=91.8 pm, r2=90.8 pm, momenta set to 0 g.mol-1.pm.fs-1'''

HB and HC form a H2 molecule whereas HA moves away from the molecule. The distance between B and C decreased to 74 pm, which is the hydrogen molecule bond length <ref name="reference 1"/>.In MEP calculation, the momenta are set to zero at each time step.

[[File:MepH2bondlength_01508.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using MEP calculation.]]

[[File:MepH2momenta015083.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using MEP calculation.]]

Using Dynamics calculation, the outcome of the reaction is the same. The transition state rolls towards HB and HC and a hydrogen molecule is formed. One noticeable difference is that the hydrogen molecule now has some vibational energy as indicated by the wavy line along B-C in the Internuclear Distance vs Time plot.As for the Momenta vs Time plot, the system is linear, therefore the angle theta is zero. HA and HB are moving away from each other at an increasing velocity until the momentum reaches 5 g.mol-1.pm.fs-1.The oscillation along the B-C bond corresponds to the vibration of the bond.
[[File:DynamicsH2_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation.]]
[[File:DynamicsH2monenta_01508.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using Dynamics calculation.]]

'''r1=90.8 pm, r2=91.8 pm, momenta set to 0 g.mol-1.pm.fs-1'''

Once the length of r1 and r2 switches, the shapes of the graphs are identical but instead of HB and HC forming a molecule, HA and HB now form the hydrogen molecule in the products.
[[File:Mepinter2_01508.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using MEP calculation.]]
[[File:Momentamep2_015.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using MEP calculation.]]
[[File:InterDynamic_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation.]]
[[File:Momentadynamics_015083.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using Dynamics calculation.]]

'''Trajectory starting with the final position and reversed momentum to the reaction path above'''

This trajectory starts at the end of the reaction path above and finishes at where the above reaction started. it is essentially a reverse of what happened in the reaction above.
[[File:Reverse_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation (r1=70.0 pm,r2=353 pm,p1=-3.21 g.mol-1.pm.fs-1, p2=-5.07 g.mol-1.pm.fs-1) .]]

===Recative and unreactive trajectories===
{| class="wikitable" border="1"
! p1/g.mol-1.pm.fs-1 !! p2/g.mol-1.pm.fs-1!! Etot/kJmol-1!! Recative?!! Description of the dynamics!! Illustration of the trajectory
|-
| -2.56 || -5.1||-414 || Yes||The translational energy of the reactants can surmount the potential energy barrier and form the products. The ramaining energy is converted into vibrational energy of the products. || [[File:Table1_01508310.png|350px ]]
|-
| -3.1 || -4.1||-420 || No||The reactant H2 has vibrational energy and its rAB motion is rapid. Before it could cross the energy barrier, the molecule slams into the repulsive inner wall of the potential surface and bounces back into the reactant channel. || [[File:Table2_0150.png|350px]]
|-
| -3.1 || -5.1||-414|| Yes||The reactants have both the translational and vibrational energies. The energy is used to surmount the potential energy barrier and converted into the vibrational energy of the products. || [[File:Table3_01508.png|350px]]
|-
| -5.1 || -10.1||-357 || No||The reactants have sufficient energy to cross the transition state and the products did form for a certain amount of time. However, before the the system can exit the product channel, it recrosses the transition state and form the reactants again, hence no reaction occurs. ||[[File:Table4_01508.png|350px]]
|-
| -5.1 || -10.6||-394 || Yes||The system has sufficient energy to cross the transition state but it recrosses the transition state shortly after the reaction path hits the potential energy surface. However, the system is able to cross the transition state for the third time and finally exits the product channel and forms the products. || [[File:-10.6_01508.png|350px]]
|-
|}
In order to form products, a system must have sufficient energy to cross the transition state. Only molecules with the correct phase <ref name="reference 2"/> can exit the product channel and form stable products. Recrossing the transition state can lead to either product formation or no reaction. It is possible to cross the transition state multiple times.

===Transition State Theory===

Transition State Theory is classical, it doesn't take quantum tunnelling into account.Quantum tunnelling is probable for this reaction as it involves the transfer of a hydrogen atom, particularly at lower temperatures <ref name="reference 3"/>.At low temperatures, the H atom can tunnel through the potential energy barrier instead of passing over the barrier, hence the activation energy is lowered and the reaction rate increases. However, recrossing the energy barrier is possible as seen with the simulations, this can have a negative effect on the reaction rate. At high temperatures, the system is thermally activated and the behavious is approximately classical<ref name="reference 4"/>. Overall, the situation can be complicated as the theory assumes quasi-equilibrium between reactants and transition state (activated complexes). The activated complex can then either form products or revert back to the reactants with or without quantum tunnelling. The experimental reaction rate might still be greater than that predicted by the theory.

==F-H-H system==
===PES inspection===
'''F+H2 (F1-H1-H2)'''

F+H2 is exothermic as the reactants are higher in energy than the products therefore during the reaction, energy is released to the surroundings. H-F bond is stronger than H-H bond as the products are lower in energy and therefore more stable.The transition state is located approximately at rF1-H1=181.10 pm and rH1-H2=74.49 pm. This is verified by the forces (close to zero) and eigenvalues for hessian matrix (they are of opposite signs). The activation energy is estimated by tilting the transition state towards the reactants and is shown to be 424 kJ.mol-1.
[[File:Fh2_015083.png |400px|centre|thumb|Surface plot for F1-H1-H2 system using Dynamic Calculation, the transition state is identified as the black dot.]]
[[File:OptimisationFhh1_01508.png|400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:F1H1H2_EA_0150.png|400px|centre|thumb|Counter plot for estimating the activation energy using MEP calculation.]]
[[File:EA1_01508.png|400px|centre|thumb|parameters for the activation energy.]]
'''H+HF (H1-H2-F1)'''

This reaction is endothermis as the reactants are lower in energy than the products therefore energy is taken in from the surroundings to form the products. H-F bond is still stronger than H-H as the reactans are lower in energy and more stable. The transition state is located at approximately rH1-H2=280 pm and rH2-F1=92 pm. It is located with the same reasons stated above.With the same method, the activation energy is estimated to be 434 kJ.mol-1. The two activation energies should be identical as these two reactions are essentially the reverse of one another.

[[File:H+HF_01508310.png|400px|centre|thumb|Surface plot for H1-H2-F1 system using Dynamic Calculationthe, the transition state is identified as the black dot.]]
[[File:HHF_015083.png |400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:EA2_01508.png|400px|centre|thumb|Counter plot for estimating the activation energy using MEP calculation.]]
[[File:EA2_PARAMETERS.png|400px|centre|thumb|parameters for the activation energy.]]

===Reaction dynamics===
===F+H2 system===

Initially, the reactants have kinetic energy in the form of vibrational and translational energies, and as it crosses the potential energy barrier, the kinetic energy is converted into potential energy. Once the system is exiting the product channel, the potential energy is converted into the vibrational energy of the product.One good experimental technique to prob the electronic structure of the reacting species will be IR spectroscopy.In the anharmonic oscillator model, exciting molecules in the relaxed state promotes excitation from the ground state to the first energy level mainly. This will give rise to a single peak in the IR spectrum. Howver, when exciting a sample of excited molecules, many transitions are possible. For example, from 0-->1, the fundamental or 1-->2, the first hot band. They will show up in the spectrum as 2 peaks, with the overtone being at a lower wavenumber as the energy gap decreases up the potential well. The intensity of the overtone decreases over time as the electrons can fall back to lower energy levels and energy is emitted as radiation. As this system is linear, rotational is not important electronic energy is not considered here.Photoelectron spectroscopy is also a viable method. <ref name="reference 5"/>

[[File:Reactiondynamicsfh2_0150.png||400px|centre|thumb|contour plot for F+H2.]]
[[File:Reactiondynamicsparameter——015.png |400px|centre|thumb|parameters for the reactive trajectory.]]
====Varying the momentum of HH in the F+H2 system.====
Conditions:rFH=182 pm, rHH=74 pm, PFH=-1.0g.mol-1.pm.fs-1
{| class="wikitable" border="1"
|+ caption
|-
|PHH/g.mol-1.pm.fs-1|| Contour Plot
|-
|0 || [[File:0_015083.png |400 px|centre]]
|-
|2 || [[File:2_0508.png |400 px|centre]]
|-
|4 || [[File:4_01508.png ‎|400 px|centre]]
|-
|6.1|| [[File:6_01508.png|400 px|centre]]
|-
| -2|| [[File:-2_01508.png|400 px|centre]]
|-
| -4|| [[File:-4.1_01508.png‎|400 px|centre]]
|-
| -6.1|| [[File:Fit1_01508.png|400 px|centre]]
|-
|}
Although the amount of energy that is put into H-H vibration is much more than the activation energy of the reaction, the reaction does not always occur. The large amount of energy is demonstrated by the high frequency of those wavy lines. Recrossing the transition states multiple times can lead to no reaction or product formation depending on how the tragectory collides with the potential well.

[[File:Reactiondynamic_last01588.png|400px|centre|thumb|contour plot for rFH=182 pm, fHH=74 pm, PFH=-1.6g.mol-1.pm.fs-1,PHH=0.2g.mol-1.pm.fs-1]]
The system now has much less vibrational energy into the reactants than before. The reaction is still successful and the trajectory recrosses the transition states fewer times than before.This can be explained by the increased momentum of FH so that F can approach the closest H with more vibrational energy.

===H+HF system===
{| class="wikitable" border="1"
!Graph Number!! p1(HH)/g.mol-1.pm.fs-1 !! p2(HF)/g.mol-1.pm.fs-1!! Etot/kJmol-1!! Recative?!! Illustration of the trajectory
|-
|1|| -2 || -10||-397|| No|| [[File:Final1_01508.png|350px ]]
|-
|2|| 0|| -8||-400 || No|| [[File:Final2_015.png|350px]]
|-
|3||5 || -6||-360|| No|| [[File:Final3_015.png|350px]]
|-
|4|| 5 || -3||-389 || Yes||[[File:Final4_015.png|350px]]
|-
|}

by referening to Polanyl's empirical rules, an exothermic reaction has an early barrier, which happens in the entrance channel. It tends to favour vibrational excitation of the products. On the other hand, an endothermic reaction has a late barrier, which occurs in the product channel. It tends to favour low product vibrational excitation. The location of the energy barrier is also crucial for a successful reaction. Translational energy of the reactants is the most effective at passing the early barrier whereas vibrational energy of the reactants is the most effective at surmounting the late barrier.This reaction is endothermic, and hence it has a late barrier. In all the graphs, the reactants all have vibrational energy as indicated by the wavy line in the reactant channel.<ref name="reference 2"/>

==References==

<references>
<ref name="reference 1">R. DeKock and H. Gray, Chemical structure and bonding, Univeristy Science Books, 1989.</ref>
<ref name="reference 2">S. Jeffrey I., Experimental Chemical Dynamics, Prentice-Hall, Upper Saddle River, 2nd edn., 1989.</ref>
<ref name="reference 3">L. Keith J., Theories of reaction rates, Harper & Row, New York;London, 3rd edn., 1987.</ref>
<ref name="reference 4">D. Brougham, A. Horsewill and R. Jenkinson, Chemical Physics Letters, 1997, 272, 69-74.</ref>
<ref name="reference 5">S. Bradforth, D. Arnold, D. Neumark and D. Manolopoulos, The Journal of Chemical Physics, 1993, 99, 6345-6359.</ref>
</references>

MRD:01508310

2020-05-22T19:37:00Z

Hh2218: /* PES inspection */

==H-H-H system==
===Dynamics from the transition state region===
The transition state is the point on the potential energy surface that has ∂V(ri)/∂ri=0, where ri is the distance between two atoms.The transition state is a local maximum and its second derivative ∂2V(ri)/∂ri2 is < 0, whereas a local minimum will have a positive second derivative instead.
[[File:Hhh_surfaceplot_01508.png|400px|thumb|centre|a potential energy surface plot of H and H2 with respect to interatomic distances.]]

===Trajectories from r1=r2: locating the transition state===
At the transition state, r1=r2=90.8 pm by estimation. At this separation, the forces acting along AB and BC are both -0.004 kJ.mol-1.pm-1, which is close to zero and the eigenvalues for the Hessian matrix are -0.028 and +0.167 kJ.mol-1.pm-2, indicating the presence of transition state. The Internuclear Distance vs Time plot suggests the distance between HA, HB and HC is equal, about 90 pm and the distance is constant over time suggests the atoms are static at the transition state.
[[File:Animation101508310.png|400px|centre|thumb|picture showing H and H2 at the transition state.]]
[[File:Optimisation1_01508310.png|400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:Internucleardistance_01508310.png|400px|centre|thumb|Internuclear Distance vs Time plot between the H atoms at the transition state.]]

===Calculating the reaction path===
When rA-B is set to rts+1 (91.8 pm) and rB-C equals rts (90.8 pm),the transition state rolls towards HB and HC, HA remains as an atom. MEP and Dynamic reaction paths are different as MEP set the momenta to zero in every step of the reaction path, products are therefore static and hence the reaction path is relatively straight. The dynamic reaction path is more realistic. It takes the momenta of gaseous molecules into account,i.e. The reactants and the products have vibrational energies, that is illustrated by the wavy line along the reaction path.
[[File:Surface_Plot1mep_015083.png|400px|centre|thumb|the minimum energy path (MEP) of the H-H-H system]]
[[File:01569348_MEP_AB1_dynamic.png|400px|centre|thumb|the dynamic reaction path of the H-H-H system]]

====MEP and Dynamics calculations comparisons====
'''r1=91.8 pm, r2=90.8 pm, momenta set to 0 g.mol-1.pm.fs-1'''

HB and HC form a H2 molecule whereas HA moves away from the molecule. The distance between B and C decreased to 74 pm, which is the hydrogen molecule bond length <ref name="reference 1"/>.In MEP calculation, the momenta are set to zero at each time step.

[[File:MepH2bondlength_01508.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using MEP calculation.]]

[[File:MepH2momenta015083.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using MEP calculation.]]

Using Dynamics calculation, the outcome of the reaction is the same. The transition state rolls towards HB and HC and a hydrogen molecule is formed. One noticeable difference is that the hydrogen molecule now has some vibational energy as indicated by the wavy line along B-C in the Internuclear Distance vs Time plot.As for the Momenta vs Time plot, the system is linear, therefore the angle theta is zero. HA and HB are moving away from each other at an increasing velocity until the momentum reaches 5 g.mol-1.pm.fs-1.The oscillation along the B-C bond corresponds to the vibration of the bond.
[[File:DynamicsH2_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation.]]
[[File:DynamicsH2monenta_01508.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using Dynamics calculation.]]

'''r1=90.8 pm, r2=91.8 pm, momenta set to 0 g.mol-1.pm.fs-1'''

Once the length of r1 and r2 switches, the shapes of the graphs are identical but instead of HB and HC forming a molecule, HA and HB now form the hydrogen molecule in the products.
[[File:Mepinter2_01508.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using MEP calculation.]]
[[File:Momentamep2_015.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using MEP calculation.]]
[[File:InterDynamic_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation.]]
[[File:Momentadynamics_015083.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using Dynamics calculation.]]

'''Trajectory starting with the final position and reversed momentum to the reaction path above'''

This trajectory starts at the end of the reaction path above and finishes at where the above reaction started. it is essentially a reverse of what happened in the reaction above.
[[File:Reverse_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation (r1=70.0 pm,r2=353 pm,p1=-3.21 g.mol-1.pm.fs-1, p2=-5.07 g.mol-1.pm.fs-1) .]]

===Recative and unreactive trajectories===
{| class="wikitable" border="1"
! p1/g.mol-1.pm.fs-1 !! p2/g.mol-1.pm.fs-1!! Etot/kJmol-1!! Recative?!! Description of the dynamics!! Illustration of the trajectory
|-
| -2.56 || -5.1||-414 || Yes||The translational energy of the reactants can surmount the potential energy barrier and form the products. The ramaining energy is converted into vibrational energy of the products. || [[File:Table1_01508310.png|350px ]]
|-
| -3.1 || -4.1||-420 || No||The reactant H2 has vibrational energy and its rAB motion is rapid. Before it could cross the energy barrier, the molecule slams into the repulsive inner wall of the potential surface and bounces back into the reactant channel. || [[File:Table2_0150.png|350px]]
|-
| -3.1 || -5.1||-414|| Yes||The reactants have both the translational and vibrational energies. The energy is used to surmount the potential energy barrier and converted into the vibrational energy of the products. || [[File:Table3_01508.png|350px]]
|-
| -5.1 || -10.1||-357 || No||The reactants have sufficient energy to cross the transition state and the products did form for a certain amount of time. However, before the the system can exit the product channel, it recrosses the transition state and form the reactants again, hence no reaction occurs. ||[[File:Table4_01508.png|350px]]
|-
| -5.1 || -10.6||-394 || Yes||The system has sufficient energy to cross the transition state but it recrosses the transition state shortly after the reaction path hits the potential energy surface. However, the system is able to cross the transition state for the third time and finally exits the product channel and forms the products. || [[File:-10.6_01508.png|350px]]
|-
|}
In order to form products, a system must have sufficient energy to cross the transition state. Only molecules with the correct phase <ref name="reference 2"/> can exit the product channel and form stable products. Recrossing the transition state can lead to either product formation or no reaction. It is possible to cross the transition state multiple times.

===Transition State Theory===

Transition State Theory is classical, it doesn't take quantum tunnelling into account.Quantum tunnelling is probable for this reaction as it involves the transfer of a hydrogen atom, particularly at lower temperatures <ref name="reference 3"/>.At low temperatures, the H atom can tunnel through the potential energy barrier instead of passing over the barrier, hence the activation energy is lowered and the reaction rate increases. However, recrossing the energy barrier is possible as seen with the simulations, this can have a negative effect on the reaction rate. At high temperatures, the system is thermally activated and the behavious is approximately classical<ref name="reference 4"/>. Overall, the situation can be complicated as the theory assumes quasi-equilibrium between reactants and transition state (activated complexes). The activated complex can then either form products or revert back to the reactants with or without quantum tunnelling. The experimental reaction rate might still be greater than that predicted by the theory.

==F-H-H system==
===PES inspection===
'''F+H2 (F1-H1-H2)'''

F+H2 is exothermic as the reactants are higher in energy than the products therefore during the reaction, energy is released to the surroundings. H-F bond is stronger than H-H bond as the products are lower in energy and therefore more stable.The transition state is located approximately at rF1-H1=181.10 pm and rH1-H2=74.49 pm. This is verified by the forces (close to zero) and eigenvalues for hessian matrix (they are of opposite signs). The activation energy is estimated by tilting the transition state towards the reactants and is shown to be 424 kJ.mol-1.
[[File:Fh2_015083.png |400px|centre|thumb|Surface plot for F1-H1-H2 system using Dynamic Calculation, the transition state is identified as the black dot.]]
[[File:OptimisationFhh1_01508.png|400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:F1H1H2_EA_0150.png|400px|centre|thumb|Counter plot for estimating the activation energy using MEP calculation.]]
[[File:EA1_01508.png|400px|centre|thumb|parameters for the activation energy.]]
'''H+HF (H1-H2-F1)'''

This reaction is endothermis as the reactants are lower in energy than the products therefore energy is taken in from the surroundings to form the products. H-F bond is still stronger than H-H as the reactans are lower in energy and more stable. The transition state is located at approximately rH1-H2=280 pm and rH2-F1=92 pm. It is located with the same reasons stated above.With the same method, the activation energy is estimated to be 434 kJ.mol-1. The two activation energies should be identical as these two reactions are essentially the reverse of one another.

[[File:H+HF_01508310.png|400px|centre|thumb|Surface plot for H1-H2-F1 system using Dynamic Calculationthe, the transition state is identified as the black dot.]]
[[File:HHF_015083.png |400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:EA2_01508.png|400px|centre|thumb|Counter plot for estimating the activation energy using MEP calculation.]]
[[File:EA2_PARAMETERS.png|400px|centre|thumb|parameters for the activation energy.]]

===Reaction dynamics===
===F+H2 system===

Initially, the reactants have kinetic energy in the form of vibrational and translational energies, and as it crosses the potential energy barrier, the kinetic energy is converted into potential energy. Once the system is exiting the product channel, the potential energy is converted into the vibrational energy of the product.One good experimental technique to prob the electronic structure of the reacting species will be IR spectroscopy.In the anharmonic oscillator model, exciting molecules in the relaxed state promotes excitation from the ground state to the first energy level mainly. This will give rise to a single peak in the IR spectrum. Howver, when exciting a sample of excited molecules, many transitions are possible. For example, from 0-->1, the fundamental or 1-->2, the first overtone. They will show up in the spectrum as 2 peaks, with the overtone being at a lower wavenumber as the energy gap decreases up the potential well. The intensity of the overtone decreases over time as the electrons can fall back to lower energy levels and energy is emitted as radiation. As this system is linear, rotational is not important electronic energy is not considered here.Photoelectron spectroscopy is also a viable method. <ref name="reference 5"/>

[[File:Reactiondynamicsfh2_0150.png||400px|centre|thumb|contour plot for F+H2.]]
[[File:Reactiondynamicsparameter——015.png |400px|centre|thumb|parameters for the reactive trajectory.]]
====Varying the momentum of HH in the F+H2 system.====
Conditions:rFH=182 pm, rHH=74 pm, PFH=-1.0g.mol-1.pm.fs-1
{| class="wikitable" border="1"
|+ caption
|-
|PHH/g.mol-1.pm.fs-1|| Contour Plot
|-
|0 || [[File:0_015083.png |400 px|centre]]
|-
|2 || [[File:2_0508.png |400 px|centre]]
|-
|4 || [[File:4_01508.png ‎|400 px|centre]]
|-
|6.1|| [[File:6_01508.png|400 px|centre]]
|-
| -2|| [[File:-2_01508.png|400 px|centre]]
|-
| -4|| [[File:-4.1_01508.png‎|400 px|centre]]
|-
| -6.1|| [[File:Fit1_01508.png|400 px|centre]]
|-
|}
Although the amount of energy that is put into H-H vibration is much more than the activation energy of the reaction, the reaction does not always occur. The large amount of energy is demonstrated by the high frequency of those wavy lines. Recrossing the transition states multiple times can lead to no reaction or product formation depending on how the tragectory collides with the potential well.

[[File:Reactiondynamic_last01588.png|400px|centre|thumb|contour plot for rFH=182 pm, fHH=74 pm, PFH=-1.6g.mol-1.pm.fs-1,PHH=0.2g.mol-1.pm.fs-1]]
The system now has much less vibrational energy into the reactants than before. The reaction is still successful and the trajectory recrosses the transition states fewer times than before.This can be explained by the increased momentum of FH so that F can approach the closest H with more vibrational energy.

===H+HF system===
{| class="wikitable" border="1"
!Graph Number!! p1(HH)/g.mol-1.pm.fs-1 !! p2(HF)/g.mol-1.pm.fs-1!! Etot/kJmol-1!! Recative?!! Illustration of the trajectory
|-
|1|| -2 || -10||-397|| No|| [[File:Final1_01508.png|350px ]]
|-
|2|| 0|| -8||-400 || No|| [[File:Final2_015.png|350px]]
|-
|3||5 || -6||-360|| No|| [[File:Final3_015.png|350px]]
|-
|4|| 5 || -3||-389 || Yes||[[File:Final4_015.png|350px]]
|-
|}

by referening to Polanyl's empirical rules, an exothermic reaction has an early barrier, which happens in the entrance channel. It tends to favour vibrational excitation of the products. On the other hand, an endothermic reaction has a late barrier, which occurs in the product channel. It tends to favour low product vibrational excitation. The location of the energy barrier is also crucial for a successful reaction. Translational energy of the reactants is the most effective at passing the early barrier whereas vibrational energy of the reactants is the most effective at surmounting the late barrier.This reaction is endothermic, and hence it has a late barrier. In all the graphs, the reactants all have vibrational energy as indicated by the wavy line in the reactant channel.<ref name="reference 2"/>

==References==

<references>
<ref name="reference 1">R. DeKock and H. Gray, Chemical structure and bonding, Univeristy Science Books, 1989.</ref>
<ref name="reference 2">S. Jeffrey I., Experimental Chemical Dynamics, Prentice-Hall, Upper Saddle River, 2nd edn., 1989.</ref>
<ref name="reference 3">L. Keith J., Theories of reaction rates, Harper & Row, New York;London, 3rd edn., 1987.</ref>
<ref name="reference 4">D. Brougham, A. Horsewill and R. Jenkinson, Chemical Physics Letters, 1997, 272, 69-74.</ref>
<ref name="reference 5">S. Bradforth, D. Arnold, D. Neumark and D. Manolopoulos, The Journal of Chemical Physics, 1993, 99, 6345-6359.</ref>
</references>

MRD:01508310

2020-05-22T19:35:53Z

Hh2218: /* PES inspection */

==H-H-H system==
===Dynamics from the transition state region===
The transition state is the point on the potential energy surface that has ∂V(ri)/∂ri=0, where ri is the distance between two atoms.The transition state is a local maximum and its second derivative ∂2V(ri)/∂ri2 is < 0, whereas a local minimum will have a positive second derivative instead.
[[File:Hhh_surfaceplot_01508.png|400px|thumb|centre|a potential energy surface plot of H and H2 with respect to interatomic distances.]]

===Trajectories from r1=r2: locating the transition state===
At the transition state, r1=r2=90.8 pm by estimation. At this separation, the forces acting along AB and BC are both -0.004 kJ.mol-1.pm-1, which is close to zero and the eigenvalues for the Hessian matrix are -0.028 and +0.167 kJ.mol-1.pm-2, indicating the presence of transition state. The Internuclear Distance vs Time plot suggests the distance between HA, HB and HC is equal, about 90 pm and the distance is constant over time suggests the atoms are static at the transition state.
[[File:Animation101508310.png|400px|centre|thumb|picture showing H and H2 at the transition state.]]
[[File:Optimisation1_01508310.png|400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:Internucleardistance_01508310.png|400px|centre|thumb|Internuclear Distance vs Time plot between the H atoms at the transition state.]]

===Calculating the reaction path===
When rA-B is set to rts+1 (91.8 pm) and rB-C equals rts (90.8 pm),the transition state rolls towards HB and HC, HA remains as an atom. MEP and Dynamic reaction paths are different as MEP set the momenta to zero in every step of the reaction path, products are therefore static and hence the reaction path is relatively straight. The dynamic reaction path is more realistic. It takes the momenta of gaseous molecules into account,i.e. The reactants and the products have vibrational energies, that is illustrated by the wavy line along the reaction path.
[[File:Surface_Plot1mep_015083.png|400px|centre|thumb|the minimum energy path (MEP) of the H-H-H system]]
[[File:01569348_MEP_AB1_dynamic.png|400px|centre|thumb|the dynamic reaction path of the H-H-H system]]

====MEP and Dynamics calculations comparisons====
'''r1=91.8 pm, r2=90.8 pm, momenta set to 0 g.mol-1.pm.fs-1'''

HB and HC form a H2 molecule whereas HA moves away from the molecule. The distance between B and C decreased to 74 pm, which is the hydrogen molecule bond length <ref name="reference 1"/>.In MEP calculation, the momenta are set to zero at each time step.

[[File:MepH2bondlength_01508.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using MEP calculation.]]

[[File:MepH2momenta015083.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using MEP calculation.]]

Using Dynamics calculation, the outcome of the reaction is the same. The transition state rolls towards HB and HC and a hydrogen molecule is formed. One noticeable difference is that the hydrogen molecule now has some vibational energy as indicated by the wavy line along B-C in the Internuclear Distance vs Time plot.As for the Momenta vs Time plot, the system is linear, therefore the angle theta is zero. HA and HB are moving away from each other at an increasing velocity until the momentum reaches 5 g.mol-1.pm.fs-1.The oscillation along the B-C bond corresponds to the vibration of the bond.
[[File:DynamicsH2_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation.]]
[[File:DynamicsH2monenta_01508.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using Dynamics calculation.]]

'''r1=90.8 pm, r2=91.8 pm, momenta set to 0 g.mol-1.pm.fs-1'''

Once the length of r1 and r2 switches, the shapes of the graphs are identical but instead of HB and HC forming a molecule, HA and HB now form the hydrogen molecule in the products.
[[File:Mepinter2_01508.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using MEP calculation.]]
[[File:Momentamep2_015.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using MEP calculation.]]
[[File:InterDynamic_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation.]]
[[File:Momentadynamics_015083.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using Dynamics calculation.]]

'''Trajectory starting with the final position and reversed momentum to the reaction path above'''

This trajectory starts at the end of the reaction path above and finishes at where the above reaction started. it is essentially a reverse of what happened in the reaction above.
[[File:Reverse_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation (r1=70.0 pm,r2=353 pm,p1=-3.21 g.mol-1.pm.fs-1, p2=-5.07 g.mol-1.pm.fs-1) .]]

===Recative and unreactive trajectories===
{| class="wikitable" border="1"
! p1/g.mol-1.pm.fs-1 !! p2/g.mol-1.pm.fs-1!! Etot/kJmol-1!! Recative?!! Description of the dynamics!! Illustration of the trajectory
|-
| -2.56 || -5.1||-414 || Yes||The translational energy of the reactants can surmount the potential energy barrier and form the products. The ramaining energy is converted into vibrational energy of the products. || [[File:Table1_01508310.png|350px ]]
|-
| -3.1 || -4.1||-420 || No||The reactant H2 has vibrational energy and its rAB motion is rapid. Before it could cross the energy barrier, the molecule slams into the repulsive inner wall of the potential surface and bounces back into the reactant channel. || [[File:Table2_0150.png|350px]]
|-
| -3.1 || -5.1||-414|| Yes||The reactants have both the translational and vibrational energies. The energy is used to surmount the potential energy barrier and converted into the vibrational energy of the products. || [[File:Table3_01508.png|350px]]
|-
| -5.1 || -10.1||-357 || No||The reactants have sufficient energy to cross the transition state and the products did form for a certain amount of time. However, before the the system can exit the product channel, it recrosses the transition state and form the reactants again, hence no reaction occurs. ||[[File:Table4_01508.png|350px]]
|-
| -5.1 || -10.6||-394 || Yes||The system has sufficient energy to cross the transition state but it recrosses the transition state shortly after the reaction path hits the potential energy surface. However, the system is able to cross the transition state for the third time and finally exits the product channel and forms the products. || [[File:-10.6_01508.png|350px]]
|-
|}
In order to form products, a system must have sufficient energy to cross the transition state. Only molecules with the correct phase <ref name="reference 2"/> can exit the product channel and form stable products. Recrossing the transition state can lead to either product formation or no reaction. It is possible to cross the transition state multiple times.

===Transition State Theory===

Transition State Theory is classical, it doesn't take quantum tunnelling into account.Quantum tunnelling is probable for this reaction as it involves the transfer of a hydrogen atom, particularly at lower temperatures <ref name="reference 3"/>.At low temperatures, the H atom can tunnel through the potential energy barrier instead of passing over the barrier, hence the activation energy is lowered and the reaction rate increases. However, recrossing the energy barrier is possible as seen with the simulations, this can have a negative effect on the reaction rate. At high temperatures, the system is thermally activated and the behavious is approximately classical<ref name="reference 4"/>. Overall, the situation can be complicated as the theory assumes quasi-equilibrium between reactants and transition state (activated complexes). The activated complex can then either form products or revert back to the reactants with or without quantum tunnelling. The experimental reaction rate might still be greater than that predicted by the theory.

==F-H-H system==
===PES inspection===
'''F+H2 (F1-H1-H2)'''

F+H2 is exothermic as the reactants are higher in energy than the products therefore during the reaction, energy is released to the surroundings. H-F bond is stronger than H-H bond as the products are lower in energy and therefore more stable.The transition state is located approximately at rF1-H1=181.10 pm and rH1-H2=74.49 pm. This is verified by the forces (close to zero) and eigenvalues for hessian matrix (they are of opposite signs). The activation energy is estimated by tilting the transition state towards the reactants and is shown to be 424 kJ.mol-1.
[[File:Fh2_015083.png |400px|centre|thumb|Surface plot for F1-H1-H2 system using Dynamic Calculation, the transition state is identified as the black dot.]]
[[File:OptimisationFhh1_01508.png|400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:F1H1H2_EA_0150.png|400px|centre|thumb|Counter plot for estimating the activation energy using MEP calculation.]]
[[File:EA1_01508.png|400px|centre|thumb|parameters for the activation energy.]]
'''H+HF (H1-H2-F1)'''

This reaction is endothermis as the reactants are lower in energy than the products therefore energy is taken in from the surroundings to form the products. H-F bond is still stronger than H-H as the reactans are lower in energy and more stable. The transition state is located at approximately rH1-H2=280 pm and rH2-F1=92 pm. It is located with the same reasons stated above.With the same method, the activation energy is estimated to be 434 kJ.mol-1. The two activation energies should be identical as these two reactions are essentially the reverse of one another.

[[File:H+HF_01508310.png|400px|centre|thumb|Surface plot for H1-H2-F1 system using Dynamic Calculationthe, the transition state is identified as the black dot.]]
[[File:HHF_015083.png |400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:EA2_01508.png|400px|centre|thumb|Counter plot for estimating the activation energy.]]
[[File:EA2_PARAMETERS.png|400px|centre|thumb|parameters for the activation energy.]]

===Reaction dynamics===
===F+H2 system===

Initially, the reactants have kinetic energy in the form of vibrational and translational energies, and as it crosses the potential energy barrier, the kinetic energy is converted into potential energy. Once the system is exiting the product channel, the potential energy is converted into the vibrational energy of the product.One good experimental technique to prob the electronic structure of the reacting species will be IR spectroscopy.In the anharmonic oscillator model, exciting molecules in the relaxed state promotes excitation from the ground state to the first energy level mainly. This will give rise to a single peak in the IR spectrum. Howver, when exciting a sample of excited molecules, many transitions are possible. For example, from 0-->1, the fundamental or 1-->2, the first overtone. They will show up in the spectrum as 2 peaks, with the overtone being at a lower wavenumber as the energy gap decreases up the potential well. The intensity of the overtone decreases over time as the electrons can fall back to lower energy levels and energy is emitted as radiation. As this system is linear, rotational is not important electronic energy is not considered here.Photoelectron spectroscopy is also a viable method. <ref name="reference 5"/>

[[File:Reactiondynamicsfh2_0150.png||400px|centre|thumb|contour plot for F+H2.]]
[[File:Reactiondynamicsparameter——015.png |400px|centre|thumb|parameters for the reactive trajectory.]]
====Varying the momentum of HH in the F+H2 system.====
Conditions:rFH=182 pm, rHH=74 pm, PFH=-1.0g.mol-1.pm.fs-1
{| class="wikitable" border="1"
|+ caption
|-
|PHH/g.mol-1.pm.fs-1|| Contour Plot
|-
|0 || [[File:0_015083.png |400 px|centre]]
|-
|2 || [[File:2_0508.png |400 px|centre]]
|-
|4 || [[File:4_01508.png ‎|400 px|centre]]
|-
|6.1|| [[File:6_01508.png|400 px|centre]]
|-
| -2|| [[File:-2_01508.png|400 px|centre]]
|-
| -4|| [[File:-4.1_01508.png‎|400 px|centre]]
|-
| -6.1|| [[File:Fit1_01508.png|400 px|centre]]
|-
|}
Although the amount of energy that is put into H-H vibration is much more than the activation energy of the reaction, the reaction does not always occur. The large amount of energy is demonstrated by the high frequency of those wavy lines. Recrossing the transition states multiple times can lead to no reaction or product formation depending on how the tragectory collides with the potential well.

[[File:Reactiondynamic_last01588.png|400px|centre|thumb|contour plot for rFH=182 pm, fHH=74 pm, PFH=-1.6g.mol-1.pm.fs-1,PHH=0.2g.mol-1.pm.fs-1]]
The system now has much less vibrational energy into the reactants than before. The reaction is still successful and the trajectory recrosses the transition states fewer times than before.This can be explained by the increased momentum of FH so that F can approach the closest H with more vibrational energy.

===H+HF system===
{| class="wikitable" border="1"
!Graph Number!! p1(HH)/g.mol-1.pm.fs-1 !! p2(HF)/g.mol-1.pm.fs-1!! Etot/kJmol-1!! Recative?!! Illustration of the trajectory
|-
|1|| -2 || -10||-397|| No|| [[File:Final1_01508.png|350px ]]
|-
|2|| 0|| -8||-400 || No|| [[File:Final2_015.png|350px]]
|-
|3||5 || -6||-360|| No|| [[File:Final3_015.png|350px]]
|-
|4|| 5 || -3||-389 || Yes||[[File:Final4_015.png|350px]]
|-
|}

by referening to Polanyl's empirical rules, an exothermic reaction has an early barrier, which happens in the entrance channel. It tends to favour vibrational excitation of the products. On the other hand, an endothermic reaction has a late barrier, which occurs in the product channel. It tends to favour low product vibrational excitation. The location of the energy barrier is also crucial for a successful reaction. Translational energy of the reactants is the most effective at passing the early barrier whereas vibrational energy of the reactants is the most effective at surmounting the late barrier.This reaction is endothermic, and hence it has a late barrier. In all the graphs, the reactants all have vibrational energy as indicated by the wavy line in the reactant channel.<ref name="reference 2"/>

==References==

<references>
<ref name="reference 1">R. DeKock and H. Gray, Chemical structure and bonding, Univeristy Science Books, 1989.</ref>
<ref name="reference 2">S. Jeffrey I., Experimental Chemical Dynamics, Prentice-Hall, Upper Saddle River, 2nd edn., 1989.</ref>
<ref name="reference 3">L. Keith J., Theories of reaction rates, Harper & Row, New York;London, 3rd edn., 1987.</ref>
<ref name="reference 4">D. Brougham, A. Horsewill and R. Jenkinson, Chemical Physics Letters, 1997, 272, 69-74.</ref>
<ref name="reference 5">S. Bradforth, D. Arnold, D. Neumark and D. Manolopoulos, The Journal of Chemical Physics, 1993, 99, 6345-6359.</ref>
</references>

MRD:01508310

2020-05-22T19:35:28Z

Hh2218: /* PES inspection */

==H-H-H system==
===Dynamics from the transition state region===
The transition state is the point on the potential energy surface that has ∂V(ri)/∂ri=0, where ri is the distance between two atoms.The transition state is a local maximum and its second derivative ∂2V(ri)/∂ri2 is < 0, whereas a local minimum will have a positive second derivative instead.
[[File:Hhh_surfaceplot_01508.png|400px|thumb|centre|a potential energy surface plot of H and H2 with respect to interatomic distances.]]

===Trajectories from r1=r2: locating the transition state===
At the transition state, r1=r2=90.8 pm by estimation. At this separation, the forces acting along AB and BC are both -0.004 kJ.mol-1.pm-1, which is close to zero and the eigenvalues for the Hessian matrix are -0.028 and +0.167 kJ.mol-1.pm-2, indicating the presence of transition state. The Internuclear Distance vs Time plot suggests the distance between HA, HB and HC is equal, about 90 pm and the distance is constant over time suggests the atoms are static at the transition state.
[[File:Animation101508310.png|400px|centre|thumb|picture showing H and H2 at the transition state.]]
[[File:Optimisation1_01508310.png|400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:Internucleardistance_01508310.png|400px|centre|thumb|Internuclear Distance vs Time plot between the H atoms at the transition state.]]

===Calculating the reaction path===
When rA-B is set to rts+1 (91.8 pm) and rB-C equals rts (90.8 pm),the transition state rolls towards HB and HC, HA remains as an atom. MEP and Dynamic reaction paths are different as MEP set the momenta to zero in every step of the reaction path, products are therefore static and hence the reaction path is relatively straight. The dynamic reaction path is more realistic. It takes the momenta of gaseous molecules into account,i.e. The reactants and the products have vibrational energies, that is illustrated by the wavy line along the reaction path.
[[File:Surface_Plot1mep_015083.png|400px|centre|thumb|the minimum energy path (MEP) of the H-H-H system]]
[[File:01569348_MEP_AB1_dynamic.png|400px|centre|thumb|the dynamic reaction path of the H-H-H system]]

====MEP and Dynamics calculations comparisons====
'''r1=91.8 pm, r2=90.8 pm, momenta set to 0 g.mol-1.pm.fs-1'''

HB and HC form a H2 molecule whereas HA moves away from the molecule. The distance between B and C decreased to 74 pm, which is the hydrogen molecule bond length <ref name="reference 1"/>.In MEP calculation, the momenta are set to zero at each time step.

[[File:MepH2bondlength_01508.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using MEP calculation.]]

[[File:MepH2momenta015083.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using MEP calculation.]]

Using Dynamics calculation, the outcome of the reaction is the same. The transition state rolls towards HB and HC and a hydrogen molecule is formed. One noticeable difference is that the hydrogen molecule now has some vibational energy as indicated by the wavy line along B-C in the Internuclear Distance vs Time plot.As for the Momenta vs Time plot, the system is linear, therefore the angle theta is zero. HA and HB are moving away from each other at an increasing velocity until the momentum reaches 5 g.mol-1.pm.fs-1.The oscillation along the B-C bond corresponds to the vibration of the bond.
[[File:DynamicsH2_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation.]]
[[File:DynamicsH2monenta_01508.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using Dynamics calculation.]]

'''r1=90.8 pm, r2=91.8 pm, momenta set to 0 g.mol-1.pm.fs-1'''

Once the length of r1 and r2 switches, the shapes of the graphs are identical but instead of HB and HC forming a molecule, HA and HB now form the hydrogen molecule in the products.
[[File:Mepinter2_01508.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using MEP calculation.]]
[[File:Momentamep2_015.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using MEP calculation.]]
[[File:InterDynamic_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation.]]
[[File:Momentadynamics_015083.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using Dynamics calculation.]]

'''Trajectory starting with the final position and reversed momentum to the reaction path above'''

This trajectory starts at the end of the reaction path above and finishes at where the above reaction started. it is essentially a reverse of what happened in the reaction above.
[[File:Reverse_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation (r1=70.0 pm,r2=353 pm,p1=-3.21 g.mol-1.pm.fs-1, p2=-5.07 g.mol-1.pm.fs-1) .]]

===Recative and unreactive trajectories===
{| class="wikitable" border="1"
! p1/g.mol-1.pm.fs-1 !! p2/g.mol-1.pm.fs-1!! Etot/kJmol-1!! Recative?!! Description of the dynamics!! Illustration of the trajectory
|-
| -2.56 || -5.1||-414 || Yes||The translational energy of the reactants can surmount the potential energy barrier and form the products. The ramaining energy is converted into vibrational energy of the products. || [[File:Table1_01508310.png|350px ]]
|-
| -3.1 || -4.1||-420 || No||The reactant H2 has vibrational energy and its rAB motion is rapid. Before it could cross the energy barrier, the molecule slams into the repulsive inner wall of the potential surface and bounces back into the reactant channel. || [[File:Table2_0150.png|350px]]
|-
| -3.1 || -5.1||-414|| Yes||The reactants have both the translational and vibrational energies. The energy is used to surmount the potential energy barrier and converted into the vibrational energy of the products. || [[File:Table3_01508.png|350px]]
|-
| -5.1 || -10.1||-357 || No||The reactants have sufficient energy to cross the transition state and the products did form for a certain amount of time. However, before the the system can exit the product channel, it recrosses the transition state and form the reactants again, hence no reaction occurs. ||[[File:Table4_01508.png|350px]]
|-
| -5.1 || -10.6||-394 || Yes||The system has sufficient energy to cross the transition state but it recrosses the transition state shortly after the reaction path hits the potential energy surface. However, the system is able to cross the transition state for the third time and finally exits the product channel and forms the products. || [[File:-10.6_01508.png|350px]]
|-
|}
In order to form products, a system must have sufficient energy to cross the transition state. Only molecules with the correct phase <ref name="reference 2"/> can exit the product channel and form stable products. Recrossing the transition state can lead to either product formation or no reaction. It is possible to cross the transition state multiple times.

===Transition State Theory===

Transition State Theory is classical, it doesn't take quantum tunnelling into account.Quantum tunnelling is probable for this reaction as it involves the transfer of a hydrogen atom, particularly at lower temperatures <ref name="reference 3"/>.At low temperatures, the H atom can tunnel through the potential energy barrier instead of passing over the barrier, hence the activation energy is lowered and the reaction rate increases. However, recrossing the energy barrier is possible as seen with the simulations, this can have a negative effect on the reaction rate. At high temperatures, the system is thermally activated and the behavious is approximately classical<ref name="reference 4"/>. Overall, the situation can be complicated as the theory assumes quasi-equilibrium between reactants and transition state (activated complexes). The activated complex can then either form products or revert back to the reactants with or without quantum tunnelling. The experimental reaction rate might still be greater than that predicted by the theory.

==F-H-H system==
===PES inspection===
'''F+H2 (F1-H1-H2)'''

F+H2 is exothermic as the reactants are higher in energy than the products therefore during the reaction, energy is released to the surroundings. H-F bond is stronger than H-H bond as the products are lower in energy and therefore more stable.The transition state is located approximately at rF1-H1=181.10 pm and rH1-H2=74.49 pm. This is verified by the forces (close to zero) and eigenvalues for hessian matrix (they are of opposite signs). The activation energy is estimated by tilting the transition state towards the reactants and is shown to be 424 kJ.mol-1.
[[File:Fh2_015083.png |400px|centre|thumb|Surface plot for F1-H1-H2 system using Dynamic Calculation, the transition state is identified as the black dot.]]
[[File:OptimisationFhh1_01508.png|400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:F1H1H2_EA_0150.png|400px|centre|thumb|Counter plot for estimating the activation energy using MEP calculation.]]
[[File:EA1_01508.png|400px|centre|thumb|parameters for the activation energy.]]
'''H+HF (H1-H2-F1)'''
This reaction is endothermis as the reactants are lower in energy than the products therefore energy is taken in from the surroundings to form the products. H-F bond is still stronger than H-H as the reactans are lower in energy and more stable. The transition state is located at approximately rH1-H2=280 pm and rH2-F1=92 pm. It is located with the same reasons stated above.With the same method, the activation energy is estimated to be 434 kJ.mol-1. The two activation energies should be identical as these two reactions are essentially the reverse of one another.

[[File:H+HF_01508310.png|400px|centre|thumb|Surface plot for H1-H2-F1 system using Dynamic Calculationthe, the transition state is identified as the black dot.]]
[[File:HHF_015083.png |400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:EA2_01508.png|400px|centre|thumb|Counter plot for estimating the activation energy.]]
[[File:EA2_PARAMETERS.png|400px|centre|thumb|parameters for the activation energy.]]

===Reaction dynamics===
===F+H2 system===

Initially, the reactants have kinetic energy in the form of vibrational and translational energies, and as it crosses the potential energy barrier, the kinetic energy is converted into potential energy. Once the system is exiting the product channel, the potential energy is converted into the vibrational energy of the product.One good experimental technique to prob the electronic structure of the reacting species will be IR spectroscopy.In the anharmonic oscillator model, exciting molecules in the relaxed state promotes excitation from the ground state to the first energy level mainly. This will give rise to a single peak in the IR spectrum. Howver, when exciting a sample of excited molecules, many transitions are possible. For example, from 0-->1, the fundamental or 1-->2, the first overtone. They will show up in the spectrum as 2 peaks, with the overtone being at a lower wavenumber as the energy gap decreases up the potential well. The intensity of the overtone decreases over time as the electrons can fall back to lower energy levels and energy is emitted as radiation. As this system is linear, rotational is not important electronic energy is not considered here.Photoelectron spectroscopy is also a viable method. <ref name="reference 5"/>

[[File:Reactiondynamicsfh2_0150.png||400px|centre|thumb|contour plot for F+H2.]]
[[File:Reactiondynamicsparameter——015.png |400px|centre|thumb|parameters for the reactive trajectory.]]
====Varying the momentum of HH in the F+H2 system.====
Conditions:rFH=182 pm, rHH=74 pm, PFH=-1.0g.mol-1.pm.fs-1
{| class="wikitable" border="1"
|+ caption
|-
|PHH/g.mol-1.pm.fs-1|| Contour Plot
|-
|0 || [[File:0_015083.png |400 px|centre]]
|-
|2 || [[File:2_0508.png |400 px|centre]]
|-
|4 || [[File:4_01508.png ‎|400 px|centre]]
|-
|6.1|| [[File:6_01508.png|400 px|centre]]
|-
| -2|| [[File:-2_01508.png|400 px|centre]]
|-
| -4|| [[File:-4.1_01508.png‎|400 px|centre]]
|-
| -6.1|| [[File:Fit1_01508.png|400 px|centre]]
|-
|}
Although the amount of energy that is put into H-H vibration is much more than the activation energy of the reaction, the reaction does not always occur. The large amount of energy is demonstrated by the high frequency of those wavy lines. Recrossing the transition states multiple times can lead to no reaction or product formation depending on how the tragectory collides with the potential well.

[[File:Reactiondynamic_last01588.png|400px|centre|thumb|contour plot for rFH=182 pm, fHH=74 pm, PFH=-1.6g.mol-1.pm.fs-1,PHH=0.2g.mol-1.pm.fs-1]]
The system now has much less vibrational energy into the reactants than before. The reaction is still successful and the trajectory recrosses the transition states fewer times than before.This can be explained by the increased momentum of FH so that F can approach the closest H with more vibrational energy.

===H+HF system===
{| class="wikitable" border="1"
!Graph Number!! p1(HH)/g.mol-1.pm.fs-1 !! p2(HF)/g.mol-1.pm.fs-1!! Etot/kJmol-1!! Recative?!! Illustration of the trajectory
|-
|1|| -2 || -10||-397|| No|| [[File:Final1_01508.png|350px ]]
|-
|2|| 0|| -8||-400 || No|| [[File:Final2_015.png|350px]]
|-
|3||5 || -6||-360|| No|| [[File:Final3_015.png|350px]]
|-
|4|| 5 || -3||-389 || Yes||[[File:Final4_015.png|350px]]
|-
|}

by referening to Polanyl's empirical rules, an exothermic reaction has an early barrier, which happens in the entrance channel. It tends to favour vibrational excitation of the products. On the other hand, an endothermic reaction has a late barrier, which occurs in the product channel. It tends to favour low product vibrational excitation. The location of the energy barrier is also crucial for a successful reaction. Translational energy of the reactants is the most effective at passing the early barrier whereas vibrational energy of the reactants is the most effective at surmounting the late barrier.This reaction is endothermic, and hence it has a late barrier. In all the graphs, the reactants all have vibrational energy as indicated by the wavy line in the reactant channel.<ref name="reference 2"/>

==References==

<references>
<ref name="reference 1">R. DeKock and H. Gray, Chemical structure and bonding, Univeristy Science Books, 1989.</ref>
<ref name="reference 2">S. Jeffrey I., Experimental Chemical Dynamics, Prentice-Hall, Upper Saddle River, 2nd edn., 1989.</ref>
<ref name="reference 3">L. Keith J., Theories of reaction rates, Harper & Row, New York;London, 3rd edn., 1987.</ref>
<ref name="reference 4">D. Brougham, A. Horsewill and R. Jenkinson, Chemical Physics Letters, 1997, 272, 69-74.</ref>
<ref name="reference 5">S. Bradforth, D. Arnold, D. Neumark and D. Manolopoulos, The Journal of Chemical Physics, 1993, 99, 6345-6359.</ref>
</references>

MRD:01508310

2020-05-22T19:34:07Z

Hh2218: /* Transition State Theory */

==H-H-H system==
===Dynamics from the transition state region===
The transition state is the point on the potential energy surface that has ∂V(ri)/∂ri=0, where ri is the distance between two atoms.The transition state is a local maximum and its second derivative ∂2V(ri)/∂ri2 is < 0, whereas a local minimum will have a positive second derivative instead.
[[File:Hhh_surfaceplot_01508.png|400px|thumb|centre|a potential energy surface plot of H and H2 with respect to interatomic distances.]]

===Trajectories from r1=r2: locating the transition state===
At the transition state, r1=r2=90.8 pm by estimation. At this separation, the forces acting along AB and BC are both -0.004 kJ.mol-1.pm-1, which is close to zero and the eigenvalues for the Hessian matrix are -0.028 and +0.167 kJ.mol-1.pm-2, indicating the presence of transition state. The Internuclear Distance vs Time plot suggests the distance between HA, HB and HC is equal, about 90 pm and the distance is constant over time suggests the atoms are static at the transition state.
[[File:Animation101508310.png|400px|centre|thumb|picture showing H and H2 at the transition state.]]
[[File:Optimisation1_01508310.png|400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:Internucleardistance_01508310.png|400px|centre|thumb|Internuclear Distance vs Time plot between the H atoms at the transition state.]]

===Calculating the reaction path===
When rA-B is set to rts+1 (91.8 pm) and rB-C equals rts (90.8 pm),the transition state rolls towards HB and HC, HA remains as an atom. MEP and Dynamic reaction paths are different as MEP set the momenta to zero in every step of the reaction path, products are therefore static and hence the reaction path is relatively straight. The dynamic reaction path is more realistic. It takes the momenta of gaseous molecules into account,i.e. The reactants and the products have vibrational energies, that is illustrated by the wavy line along the reaction path.
[[File:Surface_Plot1mep_015083.png|400px|centre|thumb|the minimum energy path (MEP) of the H-H-H system]]
[[File:01569348_MEP_AB1_dynamic.png|400px|centre|thumb|the dynamic reaction path of the H-H-H system]]

====MEP and Dynamics calculations comparisons====
'''r1=91.8 pm, r2=90.8 pm, momenta set to 0 g.mol-1.pm.fs-1'''

HB and HC form a H2 molecule whereas HA moves away from the molecule. The distance between B and C decreased to 74 pm, which is the hydrogen molecule bond length <ref name="reference 1"/>.In MEP calculation, the momenta are set to zero at each time step.

[[File:MepH2bondlength_01508.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using MEP calculation.]]

[[File:MepH2momenta015083.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using MEP calculation.]]

Using Dynamics calculation, the outcome of the reaction is the same. The transition state rolls towards HB and HC and a hydrogen molecule is formed. One noticeable difference is that the hydrogen molecule now has some vibational energy as indicated by the wavy line along B-C in the Internuclear Distance vs Time plot.As for the Momenta vs Time plot, the system is linear, therefore the angle theta is zero. HA and HB are moving away from each other at an increasing velocity until the momentum reaches 5 g.mol-1.pm.fs-1.The oscillation along the B-C bond corresponds to the vibration of the bond.
[[File:DynamicsH2_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation.]]
[[File:DynamicsH2monenta_01508.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using Dynamics calculation.]]

'''r1=90.8 pm, r2=91.8 pm, momenta set to 0 g.mol-1.pm.fs-1'''

Once the length of r1 and r2 switches, the shapes of the graphs are identical but instead of HB and HC forming a molecule, HA and HB now form the hydrogen molecule in the products.
[[File:Mepinter2_01508.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using MEP calculation.]]
[[File:Momentamep2_015.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using MEP calculation.]]
[[File:InterDynamic_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation.]]
[[File:Momentadynamics_015083.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using Dynamics calculation.]]

'''Trajectory starting with the final position and reversed momentum to the reaction path above'''

This trajectory starts at the end of the reaction path above and finishes at where the above reaction started. it is essentially a reverse of what happened in the reaction above.
[[File:Reverse_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation (r1=70.0 pm,r2=353 pm,p1=-3.21 g.mol-1.pm.fs-1, p2=-5.07 g.mol-1.pm.fs-1) .]]

===Recative and unreactive trajectories===
{| class="wikitable" border="1"
! p1/g.mol-1.pm.fs-1 !! p2/g.mol-1.pm.fs-1!! Etot/kJmol-1!! Recative?!! Description of the dynamics!! Illustration of the trajectory
|-
| -2.56 || -5.1||-414 || Yes||The translational energy of the reactants can surmount the potential energy barrier and form the products. The ramaining energy is converted into vibrational energy of the products. || [[File:Table1_01508310.png|350px ]]
|-
| -3.1 || -4.1||-420 || No||The reactant H2 has vibrational energy and its rAB motion is rapid. Before it could cross the energy barrier, the molecule slams into the repulsive inner wall of the potential surface and bounces back into the reactant channel. || [[File:Table2_0150.png|350px]]
|-
| -3.1 || -5.1||-414|| Yes||The reactants have both the translational and vibrational energies. The energy is used to surmount the potential energy barrier and converted into the vibrational energy of the products. || [[File:Table3_01508.png|350px]]
|-
| -5.1 || -10.1||-357 || No||The reactants have sufficient energy to cross the transition state and the products did form for a certain amount of time. However, before the the system can exit the product channel, it recrosses the transition state and form the reactants again, hence no reaction occurs. ||[[File:Table4_01508.png|350px]]
|-
| -5.1 || -10.6||-394 || Yes||The system has sufficient energy to cross the transition state but it recrosses the transition state shortly after the reaction path hits the potential energy surface. However, the system is able to cross the transition state for the third time and finally exits the product channel and forms the products. || [[File:-10.6_01508.png|350px]]
|-
|}
In order to form products, a system must have sufficient energy to cross the transition state. Only molecules with the correct phase <ref name="reference 2"/> can exit the product channel and form stable products. Recrossing the transition state can lead to either product formation or no reaction. It is possible to cross the transition state multiple times.

===Transition State Theory===

Transition State Theory is classical, it doesn't take quantum tunnelling into account.Quantum tunnelling is probable for this reaction as it involves the transfer of a hydrogen atom, particularly at lower temperatures <ref name="reference 3"/>.At low temperatures, the H atom can tunnel through the potential energy barrier instead of passing over the barrier, hence the activation energy is lowered and the reaction rate increases. However, recrossing the energy barrier is possible as seen with the simulations, this can have a negative effect on the reaction rate. At high temperatures, the system is thermally activated and the behavious is approximately classical<ref name="reference 4"/>. Overall, the situation can be complicated as the theory assumes quasi-equilibrium between reactants and transition state (activated complexes). The activated complex can then either form products or revert back to the reactants with or without quantum tunnelling. The experimental reaction rate might still be greater than that predicted by the theory.

==F-H-H system==
===PES inspection===
'''F+H2 (F1-H1-H2)'''

F+H2 is exothermic as the reactants are higher in energy than the products therefore during the reaction, energy is released to the surroundings. H-F bond is stronger than H-H bond as the products are lower in energy and therefore more stable.The transition state is located approximately at rF1-H1=181.10 pm and rH1-H2=74.49 pm. This is verified by the forces (close to zero) and eigenvalues for hessian matrix (they are of opposite signs). The activation energy is estimated by tilting the transition state towards the reactants and is shown to be 424 kJ.mol-1.
[[File:Fh2_015083.png |400px|centre|thumb|Surface plot for F1-H1-H2 system using Dynamic Calculation, the transition state is identified as the black dot.]]
[[File:OptimisationFhh1_01508.png|400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:F1H1H2_EA_0150.png|400px|centre|thumb|Counter plot for estimating the activation energy.]]
[[File:EA1_01508.png|400px|centre|thumb|parameters for the activation energy.]]
'''H+HF (H1-H2-F1)'''
This reaction is endothermis as the reactants are lower in energy than the products therefore energy is taken in from the surroundings to form the products. H-F bond is still stronger than H-H as the reactans are lower in energy and more stable. The transition state is located at approximately rH1-H2=280 pm and rH2-F1=92 pm. It is located with the same reasons stated above.With the same method, the activation energy is estimated to be 434 kJ.mol-1. The two activation energies should be identical as these two reactions are essentially the reverse of one another.

[[File:H+HF_01508310.png|400px|centre|thumb|Surface plot for H1-H2-F1 system using Dynamic Calculationthe, the transition state is identified as the black dot.]]
[[File:HHF_015083.png |400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:EA2_01508.png|400px|centre|thumb|Counter plot for estimating the activation energy.]]
[[File:EA2_PARAMETERS.png|400px|centre|thumb|parameters for the activation energy.]]

===Reaction dynamics===
===F+H2 system===

Initially, the reactants have kinetic energy in the form of vibrational and translational energies, and as it crosses the potential energy barrier, the kinetic energy is converted into potential energy. Once the system is exiting the product channel, the potential energy is converted into the vibrational energy of the product.One good experimental technique to prob the electronic structure of the reacting species will be IR spectroscopy.In the anharmonic oscillator model, exciting molecules in the relaxed state promotes excitation from the ground state to the first energy level mainly. This will give rise to a single peak in the IR spectrum. Howver, when exciting a sample of excited molecules, many transitions are possible. For example, from 0-->1, the fundamental or 1-->2, the first overtone. They will show up in the spectrum as 2 peaks, with the overtone being at a lower wavenumber as the energy gap decreases up the potential well. The intensity of the overtone decreases over time as the electrons can fall back to lower energy levels and energy is emitted as radiation. As this system is linear, rotational is not important electronic energy is not considered here.Photoelectron spectroscopy is also a viable method. <ref name="reference 5"/>

[[File:Reactiondynamicsfh2_0150.png||400px|centre|thumb|contour plot for F+H2.]]
[[File:Reactiondynamicsparameter——015.png |400px|centre|thumb|parameters for the reactive trajectory.]]
====Varying the momentum of HH in the F+H2 system.====
Conditions:rFH=182 pm, rHH=74 pm, PFH=-1.0g.mol-1.pm.fs-1
{| class="wikitable" border="1"
|+ caption
|-
|PHH/g.mol-1.pm.fs-1|| Contour Plot
|-
|0 || [[File:0_015083.png |400 px|centre]]
|-
|2 || [[File:2_0508.png |400 px|centre]]
|-
|4 || [[File:4_01508.png ‎|400 px|centre]]
|-
|6.1|| [[File:6_01508.png|400 px|centre]]
|-
| -2|| [[File:-2_01508.png|400 px|centre]]
|-
| -4|| [[File:-4.1_01508.png‎|400 px|centre]]
|-
| -6.1|| [[File:Fit1_01508.png|400 px|centre]]
|-
|}
Although the amount of energy that is put into H-H vibration is much more than the activation energy of the reaction, the reaction does not always occur. The large amount of energy is demonstrated by the high frequency of those wavy lines. Recrossing the transition states multiple times can lead to no reaction or product formation depending on how the tragectory collides with the potential well.

[[File:Reactiondynamic_last01588.png|400px|centre|thumb|contour plot for rFH=182 pm, fHH=74 pm, PFH=-1.6g.mol-1.pm.fs-1,PHH=0.2g.mol-1.pm.fs-1]]
The system now has much less vibrational energy into the reactants than before. The reaction is still successful and the trajectory recrosses the transition states fewer times than before.This can be explained by the increased momentum of FH so that F can approach the closest H with more vibrational energy.

===H+HF system===
{| class="wikitable" border="1"
!Graph Number!! p1(HH)/g.mol-1.pm.fs-1 !! p2(HF)/g.mol-1.pm.fs-1!! Etot/kJmol-1!! Recative?!! Illustration of the trajectory
|-
|1|| -2 || -10||-397|| No|| [[File:Final1_01508.png|350px ]]
|-
|2|| 0|| -8||-400 || No|| [[File:Final2_015.png|350px]]
|-
|3||5 || -6||-360|| No|| [[File:Final3_015.png|350px]]
|-
|4|| 5 || -3||-389 || Yes||[[File:Final4_015.png|350px]]
|-
|}

by referening to Polanyl's empirical rules, an exothermic reaction has an early barrier, which happens in the entrance channel. It tends to favour vibrational excitation of the products. On the other hand, an endothermic reaction has a late barrier, which occurs in the product channel. It tends to favour low product vibrational excitation. The location of the energy barrier is also crucial for a successful reaction. Translational energy of the reactants is the most effective at passing the early barrier whereas vibrational energy of the reactants is the most effective at surmounting the late barrier.This reaction is endothermic, and hence it has a late barrier. In all the graphs, the reactants all have vibrational energy as indicated by the wavy line in the reactant channel.<ref name="reference 2"/>

==References==

<references>
<ref name="reference 1">R. DeKock and H. Gray, Chemical structure and bonding, Univeristy Science Books, 1989.</ref>
<ref name="reference 2">S. Jeffrey I., Experimental Chemical Dynamics, Prentice-Hall, Upper Saddle River, 2nd edn., 1989.</ref>
<ref name="reference 3">L. Keith J., Theories of reaction rates, Harper & Row, New York;London, 3rd edn., 1987.</ref>
<ref name="reference 4">D. Brougham, A. Horsewill and R. Jenkinson, Chemical Physics Letters, 1997, 272, 69-74.</ref>
<ref name="reference 5">S. Bradforth, D. Arnold, D. Neumark and D. Manolopoulos, The Journal of Chemical Physics, 1993, 99, 6345-6359.</ref>
</references>

MRD:01508310

2020-05-22T19:12:24Z

Hh2218: /* Calculating the reaction path */

==H-H-H system==
===Dynamics from the transition state region===
The transition state is the point on the potential energy surface that has ∂V(ri)/∂ri=0, where ri is the distance between two atoms.The transition state is a local maximum and its second derivative ∂2V(ri)/∂ri2 is < 0, whereas a local minimum will have a positive second derivative instead.
[[File:Hhh_surfaceplot_01508.png|400px|thumb|centre|a potential energy surface plot of H and H2 with respect to interatomic distances.]]

===Trajectories from r1=r2: locating the transition state===
At the transition state, r1=r2=90.8 pm by estimation. At this separation, the forces acting along AB and BC are both -0.004 kJ.mol-1.pm-1, which is close to zero and the eigenvalues for the Hessian matrix are -0.028 and +0.167 kJ.mol-1.pm-2, indicating the presence of transition state. The Internuclear Distance vs Time plot suggests the distance between HA, HB and HC is equal, about 90 pm and the distance is constant over time suggests the atoms are static at the transition state.
[[File:Animation101508310.png|400px|centre|thumb|picture showing H and H2 at the transition state.]]
[[File:Optimisation1_01508310.png|400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:Internucleardistance_01508310.png|400px|centre|thumb|Internuclear Distance vs Time plot between the H atoms at the transition state.]]

===Calculating the reaction path===
When rA-B is set to rts+1 (91.8 pm) and rB-C equals rts (90.8 pm),the transition state rolls towards HB and HC, HA remains as an atom. MEP and Dynamic reaction paths are different as MEP set the momenta to zero in every step of the reaction path, products are therefore static and hence the reaction path is relatively straight. The dynamic reaction path is more realistic. It takes the momenta of gaseous molecules into account,i.e. The reactants and the products have vibrational energies, that is illustrated by the wavy line along the reaction path.
[[File:Surface_Plot1mep_015083.png|400px|centre|thumb|the minimum energy path (MEP) of the H-H-H system]]
[[File:01569348_MEP_AB1_dynamic.png|400px|centre|thumb|the dynamic reaction path of the H-H-H system]]

====MEP and Dynamics calculations comparisons====
'''r1=91.8 pm, r2=90.8 pm, momenta set to 0 g.mol-1.pm.fs-1'''

HB and HC form a H2 molecule whereas HA moves away from the molecule. The distance between B and C decreased to 74 pm, which is the hydrogen molecule bond length <ref name="reference 1"/>.In MEP calculation, the momenta are set to zero at each time step.

[[File:MepH2bondlength_01508.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using MEP calculation.]]

[[File:MepH2momenta015083.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using MEP calculation.]]

Using Dynamics calculation, the outcome of the reaction is the same. The transition state rolls towards HB and HC and a hydrogen molecule is formed. One noticeable difference is that the hydrogen molecule now has some vibational energy as indicated by the wavy line along B-C in the Internuclear Distance vs Time plot.As for the Momenta vs Time plot, the system is linear, therefore the angle theta is zero. HA and HB are moving away from each other at an increasing velocity until the momentum reaches 5 g.mol-1.pm.fs-1.The oscillation along the B-C bond corresponds to the vibration of the bond.
[[File:DynamicsH2_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation.]]
[[File:DynamicsH2monenta_01508.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using Dynamics calculation.]]

'''r1=90.8 pm, r2=91.8 pm, momenta set to 0 g.mol-1.pm.fs-1'''

Once the length of r1 and r2 switches, the shapes of the graphs are identical but instead of HB and HC forming a molecule, HA and HB now form the hydrogen molecule in the products.
[[File:Mepinter2_01508.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using MEP calculation.]]
[[File:Momentamep2_015.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using MEP calculation.]]
[[File:InterDynamic_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation.]]
[[File:Momentadynamics_015083.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using Dynamics calculation.]]

'''Trajectory starting with the final position and reversed momentum to the reaction path above'''

This trajectory starts at the end of the reaction path above and finishes at where the above reaction started. it is essentially a reverse of what happened in the reaction above.
[[File:Reverse_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation (r1=70.0 pm,r2=353 pm,p1=-3.21 g.mol-1.pm.fs-1, p2=-5.07 g.mol-1.pm.fs-1) .]]

===Recative and unreactive trajectories===
{| class="wikitable" border="1"
! p1/g.mol-1.pm.fs-1 !! p2/g.mol-1.pm.fs-1!! Etot/kJmol-1!! Recative?!! Description of the dynamics!! Illustration of the trajectory
|-
| -2.56 || -5.1||-414 || Yes||The translational energy of the reactants can surmount the potential energy barrier and form the products. The ramaining energy is converted into vibrational energy of the products. || [[File:Table1_01508310.png|350px ]]
|-
| -3.1 || -4.1||-420 || No||The reactant H2 has vibrational energy and its rAB motion is rapid. Before it could cross the energy barrier, the molecule slams into the repulsive inner wall of the potential surface and bounces back into the reactant channel. || [[File:Table2_0150.png|350px]]
|-
| -3.1 || -5.1||-414|| Yes||The reactants have both the translational and vibrational energies. The energy is used to surmount the potential energy barrier and converted into the vibrational energy of the products. || [[File:Table3_01508.png|350px]]
|-
| -5.1 || -10.1||-357 || No||The reactants have sufficient energy to cross the transition state and the products did form for a certain amount of time. However, before the the system can exit the product channel, it recrosses the transition state and form the reactants again, hence no reaction occurs. ||[[File:Table4_01508.png|350px]]
|-
| -5.1 || -10.6||-394 || Yes||The system has sufficient energy to cross the transition state but it recrosses the transition state shortly after the reaction path hits the potential energy surface. However, the system is able to cross the transition state for the third time and finally exits the product channel and forms the products. || [[File:-10.6_01508.png|350px]]
|-
|}
In order to form products, a system must have sufficient energy to cross the transition state. Only molecules with the correct phase <ref name="reference 2"/> can exit the product channel and form stable products. Recrossing the transition state can lead to either product formation or no reaction. It is possible to cross the transition state multiple times.

===Transition State Theory===

Transition State Theory is classical, it doesn't take quantum tunnelling into account.Quantum tunnelling is probable for this reaction as it involves the transfer of a hydrogen atom, particularly at lower temperatures <ref name="reference 3"/>.At low temperatures, the H atom can tunnel through the potential energy barrier than to pass over the barrier, hence the activation energy is lowered and the reaction rate increases. However, recrossing the energy barrier is possible as seen with the simulations, this can have a negative effect on the reaction rate. At high temperatures, the system is thermally activated and the behavious is approximately classical<ref name="reference 4"/>. Therefore the experimental reaction rates are expected to be greater than that predicted by the Transition State Theory.

==F-H-H system==
===PES inspection===
'''F+H2 (F1-H1-H2)'''

F+H2 is exothermic as the reactants are higher in energy than the products therefore during the reaction, energy is released to the surroundings. H-F bond is stronger than H-H bond as the products are lower in energy and therefore more stable.The transition state is located approximately at rF1-H1=181.10 pm and rH1-H2=74.49 pm. This is verified by the forces (close to zero) and eigenvalues for hessian matrix (they are of opposite signs). The activation energy is estimated by tilting the transition state towards the reactants and is shown to be 424 kJ.mol-1.
[[File:Fh2_015083.png |400px|centre|thumb|Surface plot for F1-H1-H2 system using Dynamic Calculation, the transition state is identified as the black dot.]]
[[File:OptimisationFhh1_01508.png|400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:F1H1H2_EA_0150.png|400px|centre|thumb|Counter plot for estimating the activation energy.]]
[[File:EA1_01508.png|400px|centre|thumb|parameters for the activation energy.]]
'''H+HF (H1-H2-F1)'''
This reaction is endothermis as the reactants are lower in energy than the products therefore energy is taken in from the surroundings to form the products. H-F bond is still stronger than H-H as the reactans are lower in energy and more stable. The transition state is located at approximately rH1-H2=280 pm and rH2-F1=92 pm. It is located with the same reasons stated above.With the same method, the activation energy is estimated to be 434 kJ.mol-1. The two activation energies should be identical as these two reactions are essentially the reverse of one another.

[[File:H+HF_01508310.png|400px|centre|thumb|Surface plot for H1-H2-F1 system using Dynamic Calculationthe, the transition state is identified as the black dot.]]
[[File:HHF_015083.png |400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:EA2_01508.png|400px|centre|thumb|Counter plot for estimating the activation energy.]]
[[File:EA2_PARAMETERS.png|400px|centre|thumb|parameters for the activation energy.]]

===Reaction dynamics===
===F+H2 system===

Initially, the reactants have kinetic energy in the form of vibrational and translational energies, and as it crosses the potential energy barrier, the kinetic energy is converted into potential energy. Once the system is exiting the product channel, the potential energy is converted into the vibrational energy of the product.One good experimental technique to prob the electronic structure of the reacting species will be IR spectroscopy.In the anharmonic oscillator model, exciting molecules in the relaxed state promotes excitation from the ground state to the first energy level mainly. This will give rise to a single peak in the IR spectrum. Howver, when exciting a sample of excited molecules, many transitions are possible. For example, from 0-->1, the fundamental or 1-->2, the first overtone. They will show up in the spectrum as 2 peaks, with the overtone being at a lower wavenumber as the energy gap decreases up the potential well. The intensity of the overtone decreases over time as the electrons can fall back to lower energy levels and energy is emitted as radiation. As this system is linear, rotational is not important electronic energy is not considered here.Photoelectron spectroscopy is also a viable method. <ref name="reference 5"/>

[[File:Reactiondynamicsfh2_0150.png||400px|centre|thumb|contour plot for F+H2.]]
[[File:Reactiondynamicsparameter——015.png |400px|centre|thumb|parameters for the reactive trajectory.]]
====Varying the momentum of HH in the F+H2 system.====
Conditions:rFH=182 pm, rHH=74 pm, PFH=-1.0g.mol-1.pm.fs-1
{| class="wikitable" border="1"
|+ caption
|-
|PHH/g.mol-1.pm.fs-1|| Contour Plot
|-
|0 || [[File:0_015083.png |400 px|centre]]
|-
|2 || [[File:2_0508.png |400 px|centre]]
|-
|4 || [[File:4_01508.png ‎|400 px|centre]]
|-
|6.1|| [[File:6_01508.png|400 px|centre]]
|-
| -2|| [[File:-2_01508.png|400 px|centre]]
|-
| -4|| [[File:-4.1_01508.png‎|400 px|centre]]
|-
| -6.1|| [[File:Fit1_01508.png|400 px|centre]]
|-
|}
Although the amount of energy that is put into H-H vibration is much more than the activation energy of the reaction, the reaction does not always occur. The large amount of energy is demonstrated by the high frequency of those wavy lines. Recrossing the transition states multiple times can lead to no reaction or product formation depending on how the tragectory collides with the potential well.

[[File:Reactiondynamic_last01588.png|400px|centre|thumb|contour plot for rFH=182 pm, fHH=74 pm, PFH=-1.6g.mol-1.pm.fs-1,PHH=0.2g.mol-1.pm.fs-1]]
The system now has much less vibrational energy into the reactants than before. The reaction is still successful and the trajectory recrosses the transition states fewer times than before.This can be explained by the increased momentum of FH so that F can approach the closest H with more vibrational energy.

===H+HF system===
{| class="wikitable" border="1"
!Graph Number!! p1(HH)/g.mol-1.pm.fs-1 !! p2(HF)/g.mol-1.pm.fs-1!! Etot/kJmol-1!! Recative?!! Illustration of the trajectory
|-
|1|| -2 || -10||-397|| No|| [[File:Final1_01508.png|350px ]]
|-
|2|| 0|| -8||-400 || No|| [[File:Final2_015.png|350px]]
|-
|3||5 || -6||-360|| No|| [[File:Final3_015.png|350px]]
|-
|4|| 5 || -3||-389 || Yes||[[File:Final4_015.png|350px]]
|-
|}

by referening to Polanyl's empirical rules, an exothermic reaction has an early barrier, which happens in the entrance channel. It tends to favour vibrational excitation of the products. On the other hand, an endothermic reaction has a late barrier, which occurs in the product channel. It tends to favour low product vibrational excitation. The location of the energy barrier is also crucial for a successful reaction. Translational energy of the reactants is the most effective at passing the early barrier whereas vibrational energy of the reactants is the most effective at surmounting the late barrier.This reaction is endothermic, and hence it has a late barrier. In all the graphs, the reactants all have vibrational energy as indicated by the wavy line in the reactant channel.<ref name="reference 2"/>

==References==

<references>
<ref name="reference 1">R. DeKock and H. Gray, Chemical structure and bonding, Univeristy Science Books, 1989.</ref>
<ref name="reference 2">S. Jeffrey I., Experimental Chemical Dynamics, Prentice-Hall, Upper Saddle River, 2nd edn., 1989.</ref>
<ref name="reference 3">L. Keith J., Theories of reaction rates, Harper & Row, New York;London, 3rd edn., 1987.</ref>
<ref name="reference 4">D. Brougham, A. Horsewill and R. Jenkinson, Chemical Physics Letters, 1997, 272, 69-74.</ref>
<ref name="reference 5">S. Bradforth, D. Arnold, D. Neumark and D. Manolopoulos, The Journal of Chemical Physics, 1993, 99, 6345-6359.</ref>
</references>

MRD:01508310

2020-05-22T19:03:29Z

Hh2218: /* Calculating the reaction path */

==H-H-H system==
===Dynamics from the transition state region===
The transition state is the point on the potential energy surface that has ∂V(ri)/∂ri=0, where ri is the distance between two atoms.The transition state is a local maximum and its second derivative ∂2V(ri)/∂ri2 is < 0, whereas a local minimum will have a positive second derivative instead.
[[File:Hhh_surfaceplot_01508.png|400px|thumb|centre|a potential energy surface plot of H and H2 with respect to interatomic distances.]]

===Trajectories from r1=r2: locating the transition state===
At the transition state, r1=r2=90.8 pm by estimation. At this separation, the forces acting along AB and BC are both -0.004 kJ.mol-1.pm-1, which is close to zero and the eigenvalues for the Hessian matrix are -0.028 and +0.167 kJ.mol-1.pm-2, indicating the presence of transition state. The Internuclear Distance vs Time plot suggests the distance between HA, HB and HC is equal, about 90 pm and the distance is constant over time suggests the atoms are static at the transition state.
[[File:Animation101508310.png|400px|centre|thumb|picture showing H and H2 at the transition state.]]
[[File:Optimisation1_01508310.png|400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:Internucleardistance_01508310.png|400px|centre|thumb|Internuclear Distance vs Time plot between the H atoms at the transition state.]]

===Calculating the reaction path===
When rA-B is set to rts+1 (91.8 pm) and rB-C equals rts (90.8 pm),the transition state rolls towards BC and HA remains as an atom. MEP and Dynamic reaction paths are different as MEP set the momenta to zero in every step of the reaction path, products are therefore static and hence the reaction path is relatively straight. The dynamic reaction path is more realistic. It takes the momenta of gaseous molecules into account,i.e. they have vibrational energies, that is illustrated by the wavy line along the reaction path.
[[File:Surface_Plot1mep_015083.png|400px|centre|thumb|the minimum energy path (mep) of the H-H-H system]]
[[File:01569348_MEP_AB1_dynamic.png|400px|centre|thumb|the dynamic reaction path of the H-H-H system]]

====MEP and Dynamics calculations comparisons====
'''r1=91.8 pm, r2=90.8 pm, momenta set to 0 g.mol-1.pm.fs-1'''

HB and HC form a H2 molecule whereas HA moves away from the molecule. The distance between B and C decreased to 74 pm, which is the hydrogen molecule bond length <ref name="reference 1"/>.In MEP calculation, the momenta are set to zero at each time step.

[[File:MepH2bondlength_01508.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using MEP calculation.]]

[[File:MepH2momenta015083.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using MEP calculation.]]

Using Dynamics calculation, the outcome of the reaction is the same. The transition state rolls towards HB and HC and a hydrogen molecule is formed. One noticeable difference is that the hydrogen molecule now has some vibational energy as indicated by the wavy line along the B-C distance in the Internuclear Distance vs Time plot.As for the Momenta vs Time plot, the system is linear, therefore the angle theta is zero. HA and HB are moving away from each other at '''an increasing velocity until the momentum reaches 5 g.mol-1.pm.fs-1.The oscillation along the B-C bond corresponds to the vibration of the bond. '''why does the beginning have negative momenta?'''
[[File:DynamicsH2_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation.]]
[[File:DynamicsH2monenta_01508.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using Dynamics calculation.]]

'''r1=90.8 pm, r2=91.8 pm, momenta set to 0 g.mol-1.pm.fs-1'''

Once the length of r1 and r2 switches, the shapes of the graphs are identical but instead of HB and HC forming a molecule, HA and HB now form the hydrogen molecule in the products.
[[File:Mepinter2_01508.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using MEP calculation.]]
[[File:Momentamep2_015.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using MEP calculation.]]
[[File:InterDynamic_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation.]]
[[File:Momentadynamics_015083.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using Dynamics calculation.]]

'''Trajectory starting with the final position and reversed momentum to the reaction path above'''

This trajectory starts at the end of the reaction path above and finishes at where the above reaction started. it is essentially a reverse of what happened in the reaction above.
[[File:Reverse_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation (r1=70.0 pm,r2=353 pm,p1=-3.21 g.mol-1.pm.fs-1, p2=-5.07 g.mol-1.pm.fs-1) .]]

===Recative and unreactive trajectories===
{| class="wikitable" border="1"
! p1/g.mol-1.pm.fs-1 !! p2/g.mol-1.pm.fs-1!! Etot/kJmol-1!! Recative?!! Description of the dynamics!! Illustration of the trajectory
|-
| -2.56 || -5.1||-414 || Yes||The translational energy of the reactants can surmount the potential energy barrier and form the products. The ramaining energy is converted into vibrational energy of the products. || [[File:Table1_01508310.png|350px ]]
|-
| -3.1 || -4.1||-420 || No||The reactant H2 has vibrational energy and its rAB motion is rapid. Before it could cross the energy barrier, the molecule slams into the repulsive inner wall of the potential surface and bounces back into the reactant channel. || [[File:Table2_0150.png|350px]]
|-
| -3.1 || -5.1||-414|| Yes||The reactants have both the translational and vibrational energies. The energy is used to surmount the potential energy barrier and converted into the vibrational energy of the products. || [[File:Table3_01508.png|350px]]
|-
| -5.1 || -10.1||-357 || No||The reactants have sufficient energy to cross the transition state and the products did form for a certain amount of time. However, before the the system can exit the product channel, it recrosses the transition state and form the reactants again, hence no reaction occurs. ||[[File:Table4_01508.png|350px]]
|-
| -5.1 || -10.6||-394 || Yes||The system has sufficient energy to cross the transition state but it recrosses the transition state shortly after the reaction path hits the potential energy surface. However, the system is able to cross the transition state for the third time and finally exits the product channel and forms the products. || [[File:-10.6_01508.png|350px]]
|-
|}
In order to form products, a system must have sufficient energy to cross the transition state. Only molecules with the correct phase <ref name="reference 2"/> can exit the product channel and form stable products. Recrossing the transition state can lead to either product formation or no reaction. It is possible to cross the transition state multiple times.

===Transition State Theory===

Transition State Theory is classical, it doesn't take quantum tunnelling into account.Quantum tunnelling is probable for this reaction as it involves the transfer of a hydrogen atom, particularly at lower temperatures <ref name="reference 3"/>.At low temperatures, the H atom can tunnel through the potential energy barrier than to pass over the barrier, hence the activation energy is lowered and the reaction rate increases. However, recrossing the energy barrier is possible as seen with the simulations, this can have a negative effect on the reaction rate. At high temperatures, the system is thermally activated and the behavious is approximately classical<ref name="reference 4"/>. Therefore the experimental reaction rates are expected to be greater than that predicted by the Transition State Theory.

==F-H-H system==
===PES inspection===
'''F+H2 (F1-H1-H2)'''

F+H2 is exothermic as the reactants are higher in energy than the products therefore during the reaction, energy is released to the surroundings. H-F bond is stronger than H-H bond as the products are lower in energy and therefore more stable.The transition state is located approximately at rF1-H1=181.10 pm and rH1-H2=74.49 pm. This is verified by the forces (close to zero) and eigenvalues for hessian matrix (they are of opposite signs). The activation energy is estimated by tilting the transition state towards the reactants and is shown to be 424 kJ.mol-1.
[[File:Fh2_015083.png |400px|centre|thumb|Surface plot for F1-H1-H2 system using Dynamic Calculation, the transition state is identified as the black dot.]]
[[File:OptimisationFhh1_01508.png|400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:F1H1H2_EA_0150.png|400px|centre|thumb|Counter plot for estimating the activation energy.]]
[[File:EA1_01508.png|400px|centre|thumb|parameters for the activation energy.]]
'''H+HF (H1-H2-F1)'''
This reaction is endothermis as the reactants are lower in energy than the products therefore energy is taken in from the surroundings to form the products. H-F bond is still stronger than H-H as the reactans are lower in energy and more stable. The transition state is located at approximately rH1-H2=280 pm and rH2-F1=92 pm. It is located with the same reasons stated above.With the same method, the activation energy is estimated to be 434 kJ.mol-1. The two activation energies should be identical as these two reactions are essentially the reverse of one another.

[[File:H+HF_01508310.png|400px|centre|thumb|Surface plot for H1-H2-F1 system using Dynamic Calculationthe, the transition state is identified as the black dot.]]
[[File:HHF_015083.png |400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:EA2_01508.png|400px|centre|thumb|Counter plot for estimating the activation energy.]]
[[File:EA2_PARAMETERS.png|400px|centre|thumb|parameters for the activation energy.]]

===Reaction dynamics===
===F+H2 system===

Initially, the reactants have kinetic energy in the form of vibrational and translational energies, and as it crosses the potential energy barrier, the kinetic energy is converted into potential energy. Once the system is exiting the product channel, the potential energy is converted into the vibrational energy of the product.One good experimental technique to prob the electronic structure of the reacting species will be IR spectroscopy.In the anharmonic oscillator model, exciting molecules in the relaxed state promotes excitation from the ground state to the first energy level mainly. This will give rise to a single peak in the IR spectrum. Howver, when exciting a sample of excited molecules, many transitions are possible. For example, from 0-->1, the fundamental or 1-->2, the first overtone. They will show up in the spectrum as 2 peaks, with the overtone being at a lower wavenumber as the energy gap decreases up the potential well. The intensity of the overtone decreases over time as the electrons can fall back to lower energy levels and energy is emitted as radiation. As this system is linear, rotational is not important electronic energy is not considered here.Photoelectron spectroscopy is also a viable method. <ref name="reference 5"/>

[[File:Reactiondynamicsfh2_0150.png||400px|centre|thumb|contour plot for F+H2.]]
[[File:Reactiondynamicsparameter——015.png |400px|centre|thumb|parameters for the reactive trajectory.]]
====Varying the momentum of HH in the F+H2 system.====
Conditions:rFH=182 pm, rHH=74 pm, PFH=-1.0g.mol-1.pm.fs-1
{| class="wikitable" border="1"
|+ caption
|-
|PHH/g.mol-1.pm.fs-1|| Contour Plot
|-
|0 || [[File:0_015083.png |400 px|centre]]
|-
|2 || [[File:2_0508.png |400 px|centre]]
|-
|4 || [[File:4_01508.png ‎|400 px|centre]]
|-
|6.1|| [[File:6_01508.png|400 px|centre]]
|-
| -2|| [[File:-2_01508.png|400 px|centre]]
|-
| -4|| [[File:-4.1_01508.png‎|400 px|centre]]
|-
| -6.1|| [[File:Fit1_01508.png|400 px|centre]]
|-
|}
Although the amount of energy that is put into H-H vibration is much more than the activation energy of the reaction, the reaction does not always occur. The large amount of energy is demonstrated by the high frequency of those wavy lines. Recrossing the transition states multiple times can lead to no reaction or product formation depending on how the tragectory collides with the potential well.

[[File:Reactiondynamic_last01588.png|400px|centre|thumb|contour plot for rFH=182 pm, fHH=74 pm, PFH=-1.6g.mol-1.pm.fs-1,PHH=0.2g.mol-1.pm.fs-1]]
The system now has much less vibrational energy into the reactants than before. The reaction is still successful and the trajectory recrosses the transition states fewer times than before.This can be explained by the increased momentum of FH so that F can approach the closest H with more vibrational energy.

===H+HF system===
{| class="wikitable" border="1"
!Graph Number!! p1(HH)/g.mol-1.pm.fs-1 !! p2(HF)/g.mol-1.pm.fs-1!! Etot/kJmol-1!! Recative?!! Illustration of the trajectory
|-
|1|| -2 || -10||-397|| No|| [[File:Final1_01508.png|350px ]]
|-
|2|| 0|| -8||-400 || No|| [[File:Final2_015.png|350px]]
|-
|3||5 || -6||-360|| No|| [[File:Final3_015.png|350px]]
|-
|4|| 5 || -3||-389 || Yes||[[File:Final4_015.png|350px]]
|-
|}

by referening to Polanyl's empirical rules, an exothermic reaction has an early barrier, which happens in the entrance channel. It tends to favour vibrational excitation of the products. On the other hand, an endothermic reaction has a late barrier, which occurs in the product channel. It tends to favour low product vibrational excitation. The location of the energy barrier is also crucial for a successful reaction. Translational energy of the reactants is the most effective at passing the early barrier whereas vibrational energy of the reactants is the most effective at surmounting the late barrier.This reaction is endothermic, and hence it has a late barrier. In all the graphs, the reactants all have vibrational energy as indicated by the wavy line in the reactant channel.<ref name="reference 2"/>

==References==

<references>
<ref name="reference 1">R. DeKock and H. Gray, Chemical structure and bonding, Univeristy Science Books, 1989.</ref>
<ref name="reference 2">S. Jeffrey I., Experimental Chemical Dynamics, Prentice-Hall, Upper Saddle River, 2nd edn., 1989.</ref>
<ref name="reference 3">L. Keith J., Theories of reaction rates, Harper & Row, New York;London, 3rd edn., 1987.</ref>
<ref name="reference 4">D. Brougham, A. Horsewill and R. Jenkinson, Chemical Physics Letters, 1997, 272, 69-74.</ref>
<ref name="reference 5">S. Bradforth, D. Arnold, D. Neumark and D. Manolopoulos, The Journal of Chemical Physics, 1993, 99, 6345-6359.</ref>
</references>

MRD:01508310

2020-05-22T18:58:43Z

Hh2218: /* Calculating the reaction path */

==H-H-H system==
===Dynamics from the transition state region===
The transition state is the point on the potential energy surface that has ∂V(ri)/∂ri=0, where ri is the distance between two atoms.The transition state is a local maximum and its second derivative ∂2V(ri)/∂ri2 is < 0, whereas a local minimum will have a positive second derivative instead.
[[File:Hhh_surfaceplot_01508.png|400px|thumb|centre|a potential energy surface plot of H and H2 with respect to interatomic distances.]]

===Trajectories from r1=r2: locating the transition state===
At the transition state, r1=r2=90.8 pm by estimation. At this separation, the forces acting along AB and BC are both -0.004 kJ.mol-1.pm-1, which is close to zero and the eigenvalues for the Hessian matrix are -0.028 and +0.167 kJ.mol-1.pm-2, indicating the presence of transition state. The Internuclear Distance vs Time plot suggests the distance between HA, HB and HC is equal, about 90 pm and the distance is constant over time suggests the atoms are static at the transition state.
[[File:Animation101508310.png|400px|centre|thumb|picture showing H and H2 at the transition state.]]
[[File:Optimisation1_01508310.png|400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:Internucleardistance_01508310.png|400px|centre|thumb|Internuclear Distance vs Time plot between the H atoms at the transition state.]]

===Calculating the reaction path===
When rA-B is set to rts+1 (91.8 pm) and rB-C equals rts (90.8 pm),the transition rolls towards BC and HA remains as an atom. MEP and Dynamic reaction paths are different as MEP set the momenta to zero in every step of the reaction path, products are therefore static and hence the reaction path is relatively straight. The dynamic reaction path is more realistic. It takes the momenta of gaseous molecules into account,i.e. they have vibrational energies, that is illustrated by the wavy line along the reaction path.
[[File:Surface_Plot1mep_015083.png|400px|centre|thumb|the minimum energy path (mep) of the H-H-H system]]
[[File:01569348_MEP_AB1_dynamic.png|400px|centre|thumb|the dynamic reaction path of the H-H-H system]]

====MEP and Dynamics calculations comparisons====
'''r1=91.8 pm, r2=90.8 pm, momenta set to 0 g.mol-1.pm.fs-1'''

HB and HC form a H2 molecule whereas HA moves away from the molecule. The distance between B and C decreased to 74 pm, which is the hydrogen molecule bond length <ref name="reference 1"/>.In MEP calculation, the momenta are set to zero at each time step.

[[File:MepH2bondlength_01508.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using MEP calculation.]]

[[File:MepH2momenta015083.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using MEP calculation.]]

Using Dynamics calculation, the outcome of the reaction is the same. The transition state rolls towards HB and HC and a hydrogen molecule is formed. One noticeable difference is that the hydrogen molecule now has some vibational energy as indicated by the wavy line along the B-C distance in the Internuclear Distance vs Time plot.As for the Momenta vs Time plot, the system is linear, therefore the angle theta is zero. HA and HB are moving away from each other at '''an increasing velocity until the momentum reaches 5 g.mol-1.pm.fs-1.The oscillation along the B-C bond corresponds to the vibration of the bond. '''why does the beginning have negative momenta?'''
[[File:DynamicsH2_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation.]]
[[File:DynamicsH2monenta_01508.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using Dynamics calculation.]]

'''r1=90.8 pm, r2=91.8 pm, momenta set to 0 g.mol-1.pm.fs-1'''

Once the length of r1 and r2 switches, the shapes of the graphs are identical but instead of HB and HC forming a molecule, HA and HB now form the hydrogen molecule in the products.
[[File:Mepinter2_01508.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using MEP calculation.]]
[[File:Momentamep2_015.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using MEP calculation.]]
[[File:InterDynamic_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation.]]
[[File:Momentadynamics_015083.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using Dynamics calculation.]]

'''Trajectory starting with the final position and reversed momentum to the reaction path above'''

This trajectory starts at the end of the reaction path above and finishes at where the above reaction started. it is essentially a reverse of what happened in the reaction above.
[[File:Reverse_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation (r1=70.0 pm,r2=353 pm,p1=-3.21 g.mol-1.pm.fs-1, p2=-5.07 g.mol-1.pm.fs-1) .]]

===Recative and unreactive trajectories===
{| class="wikitable" border="1"
! p1/g.mol-1.pm.fs-1 !! p2/g.mol-1.pm.fs-1!! Etot/kJmol-1!! Recative?!! Description of the dynamics!! Illustration of the trajectory
|-
| -2.56 || -5.1||-414 || Yes||The translational energy of the reactants can surmount the potential energy barrier and form the products. The ramaining energy is converted into vibrational energy of the products. || [[File:Table1_01508310.png|350px ]]
|-
| -3.1 || -4.1||-420 || No||The reactant H2 has vibrational energy and its rAB motion is rapid. Before it could cross the energy barrier, the molecule slams into the repulsive inner wall of the potential surface and bounces back into the reactant channel. || [[File:Table2_0150.png|350px]]
|-
| -3.1 || -5.1||-414|| Yes||The reactants have both the translational and vibrational energies. The energy is used to surmount the potential energy barrier and converted into the vibrational energy of the products. || [[File:Table3_01508.png|350px]]
|-
| -5.1 || -10.1||-357 || No||The reactants have sufficient energy to cross the transition state and the products did form for a certain amount of time. However, before the the system can exit the product channel, it recrosses the transition state and form the reactants again, hence no reaction occurs. ||[[File:Table4_01508.png|350px]]
|-
| -5.1 || -10.6||-394 || Yes||The system has sufficient energy to cross the transition state but it recrosses the transition state shortly after the reaction path hits the potential energy surface. However, the system is able to cross the transition state for the third time and finally exits the product channel and forms the products. || [[File:-10.6_01508.png|350px]]
|-
|}
In order to form products, a system must have sufficient energy to cross the transition state. Only molecules with the correct phase <ref name="reference 2"/> can exit the product channel and form stable products. Recrossing the transition state can lead to either product formation or no reaction. It is possible to cross the transition state multiple times.

===Transition State Theory===

Transition State Theory is classical, it doesn't take quantum tunnelling into account.Quantum tunnelling is probable for this reaction as it involves the transfer of a hydrogen atom, particularly at lower temperatures <ref name="reference 3"/>.At low temperatures, the H atom can tunnel through the potential energy barrier than to pass over the barrier, hence the activation energy is lowered and the reaction rate increases. However, recrossing the energy barrier is possible as seen with the simulations, this can have a negative effect on the reaction rate. At high temperatures, the system is thermally activated and the behavious is approximately classical<ref name="reference 4"/>. Therefore the experimental reaction rates are expected to be greater than that predicted by the Transition State Theory.

==F-H-H system==
===PES inspection===
'''F+H2 (F1-H1-H2)'''

F+H2 is exothermic as the reactants are higher in energy than the products therefore during the reaction, energy is released to the surroundings. H-F bond is stronger than H-H bond as the products are lower in energy and therefore more stable.The transition state is located approximately at rF1-H1=181.10 pm and rH1-H2=74.49 pm. This is verified by the forces (close to zero) and eigenvalues for hessian matrix (they are of opposite signs). The activation energy is estimated by tilting the transition state towards the reactants and is shown to be 424 kJ.mol-1.
[[File:Fh2_015083.png |400px|centre|thumb|Surface plot for F1-H1-H2 system using Dynamic Calculation, the transition state is identified as the black dot.]]
[[File:OptimisationFhh1_01508.png|400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:F1H1H2_EA_0150.png|400px|centre|thumb|Counter plot for estimating the activation energy.]]
[[File:EA1_01508.png|400px|centre|thumb|parameters for the activation energy.]]
'''H+HF (H1-H2-F1)'''
This reaction is endothermis as the reactants are lower in energy than the products therefore energy is taken in from the surroundings to form the products. H-F bond is still stronger than H-H as the reactans are lower in energy and more stable. The transition state is located at approximately rH1-H2=280 pm and rH2-F1=92 pm. It is located with the same reasons stated above.With the same method, the activation energy is estimated to be 434 kJ.mol-1. The two activation energies should be identical as these two reactions are essentially the reverse of one another.

[[File:H+HF_01508310.png|400px|centre|thumb|Surface plot for H1-H2-F1 system using Dynamic Calculationthe, the transition state is identified as the black dot.]]
[[File:HHF_015083.png |400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:EA2_01508.png|400px|centre|thumb|Counter plot for estimating the activation energy.]]
[[File:EA2_PARAMETERS.png|400px|centre|thumb|parameters for the activation energy.]]

===Reaction dynamics===
===F+H2 system===

Initially, the reactants have kinetic energy in the form of vibrational and translational energies, and as it crosses the potential energy barrier, the kinetic energy is converted into potential energy. Once the system is exiting the product channel, the potential energy is converted into the vibrational energy of the product.One good experimental technique to prob the electronic structure of the reacting species will be IR spectroscopy.In the anharmonic oscillator model, exciting molecules in the relaxed state promotes excitation from the ground state to the first energy level mainly. This will give rise to a single peak in the IR spectrum. Howver, when exciting a sample of excited molecules, many transitions are possible. For example, from 0-->1, the fundamental or 1-->2, the first overtone. They will show up in the spectrum as 2 peaks, with the overtone being at a lower wavenumber as the energy gap decreases up the potential well. The intensity of the overtone decreases over time as the electrons can fall back to lower energy levels and energy is emitted as radiation. As this system is linear, rotational is not important electronic energy is not considered here.Photoelectron spectroscopy is also a viable method. <ref name="reference 5"/>

[[File:Reactiondynamicsfh2_0150.png||400px|centre|thumb|contour plot for F+H2.]]
[[File:Reactiondynamicsparameter——015.png |400px|centre|thumb|parameters for the reactive trajectory.]]
====Varying the momentum of HH in the F+H2 system.====
Conditions:rFH=182 pm, rHH=74 pm, PFH=-1.0g.mol-1.pm.fs-1
{| class="wikitable" border="1"
|+ caption
|-
|PHH/g.mol-1.pm.fs-1|| Contour Plot
|-
|0 || [[File:0_015083.png |400 px|centre]]
|-
|2 || [[File:2_0508.png |400 px|centre]]
|-
|4 || [[File:4_01508.png ‎|400 px|centre]]
|-
|6.1|| [[File:6_01508.png|400 px|centre]]
|-
| -2|| [[File:-2_01508.png|400 px|centre]]
|-
| -4|| [[File:-4.1_01508.png‎|400 px|centre]]
|-
| -6.1|| [[File:Fit1_01508.png|400 px|centre]]
|-
|}
Although the amount of energy that is put into H-H vibration is much more than the activation energy of the reaction, the reaction does not always occur. The large amount of energy is demonstrated by the high frequency of those wavy lines. Recrossing the transition states multiple times can lead to no reaction or product formation depending on how the tragectory collides with the potential well.

[[File:Reactiondynamic_last01588.png|400px|centre|thumb|contour plot for rFH=182 pm, fHH=74 pm, PFH=-1.6g.mol-1.pm.fs-1,PHH=0.2g.mol-1.pm.fs-1]]
The system now has much less vibrational energy into the reactants than before. The reaction is still successful and the trajectory recrosses the transition states fewer times than before.This can be explained by the increased momentum of FH so that F can approach the closest H with more vibrational energy.

===H+HF system===
{| class="wikitable" border="1"
!Graph Number!! p1(HH)/g.mol-1.pm.fs-1 !! p2(HF)/g.mol-1.pm.fs-1!! Etot/kJmol-1!! Recative?!! Illustration of the trajectory
|-
|1|| -2 || -10||-397|| No|| [[File:Final1_01508.png|350px ]]
|-
|2|| 0|| -8||-400 || No|| [[File:Final2_015.png|350px]]
|-
|3||5 || -6||-360|| No|| [[File:Final3_015.png|350px]]
|-
|4|| 5 || -3||-389 || Yes||[[File:Final4_015.png|350px]]
|-
|}

by referening to Polanyl's empirical rules, an exothermic reaction has an early barrier, which happens in the entrance channel. It tends to favour vibrational excitation of the products. On the other hand, an endothermic reaction has a late barrier, which occurs in the product channel. It tends to favour low product vibrational excitation. The location of the energy barrier is also crucial for a successful reaction. Translational energy of the reactants is the most effective at passing the early barrier whereas vibrational energy of the reactants is the most effective at surmounting the late barrier.This reaction is endothermic, and hence it has a late barrier. In all the graphs, the reactants all have vibrational energy as indicated by the wavy line in the reactant channel.<ref name="reference 2"/>

==References==

<references>
<ref name="reference 1">R. DeKock and H. Gray, Chemical structure and bonding, Univeristy Science Books, 1989.</ref>
<ref name="reference 2">S. Jeffrey I., Experimental Chemical Dynamics, Prentice-Hall, Upper Saddle River, 2nd edn., 1989.</ref>
<ref name="reference 3">L. Keith J., Theories of reaction rates, Harper & Row, New York;London, 3rd edn., 1987.</ref>
<ref name="reference 4">D. Brougham, A. Horsewill and R. Jenkinson, Chemical Physics Letters, 1997, 272, 69-74.</ref>
<ref name="reference 5">S. Bradforth, D. Arnold, D. Neumark and D. Manolopoulos, The Journal of Chemical Physics, 1993, 99, 6345-6359.</ref>
</references>

MRD:01508310

2020-05-22T18:57:23Z

Hh2218: /* Trajectories from r1=r2: locating the transition state */

==H-H-H system==
===Dynamics from the transition state region===
The transition state is the point on the potential energy surface that has ∂V(ri)/∂ri=0, where ri is the distance between two atoms.The transition state is a local maximum and its second derivative ∂2V(ri)/∂ri2 is < 0, whereas a local minimum will have a positive second derivative instead.
[[File:Hhh_surfaceplot_01508.png|400px|thumb|centre|a potential energy surface plot of H and H2 with respect to interatomic distances.]]

===Trajectories from r1=r2: locating the transition state===
At the transition state, r1=r2=90.8 pm by estimation. At this separation, the forces acting along AB and BC are both -0.004 kJ.mol-1.pm-1, which is close to zero and the eigenvalues for the Hessian matrix are -0.028 and +0.167 kJ.mol-1.pm-2, indicating the presence of transition state. The Internuclear Distance vs Time plot suggests the distance between HA, HB and HC is equal, about 90 pm and the distance is constant over time suggests the atoms are static at the transition state.
[[File:Animation101508310.png|400px|centre|thumb|picture showing H and H2 at the transition state.]]
[[File:Optimisation1_01508310.png|400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:Internucleardistance_01508310.png|400px|centre|thumb|Internuclear Distance vs Time plot between the H atoms at the transition state.]]

===Calculating the reaction path===
When rA-B is set to rts+1 and rB-C equals rts,the transition rolls towards BC and HA remains as an atom. MEP and Dynamic reaction paths are different as MEP set the momenta to zero in every step of the reaction path, products are therefore static and hence the reaction path is relatively straight. The dynamic reaction path is more realistic. It takes the momenta of gaseous molecules into account,i.e. they have vibrational energies, that is illustrated by the wavy line along the reaction path.
[[File:Surface_Plot1mep_015083.png|400px|centre|thumb|the minimum energy path (mep) of the H-H-H system]]
[[File:01569348_MEP_AB1_dynamic.png|400px|centre|thumb|the dynamic reaction path of the H-H-H system]]

====MEP and Dynamics calculations comparisons====
'''r1=91.8 pm, r2=90.8 pm, momenta set to 0 g.mol-1.pm.fs-1'''

HB and HC form a H2 molecule whereas HA moves away from the molecule. The distance between B and C decreased to 74 pm, which is the hydrogen molecule bond length <ref name="reference 1"/>.In MEP calculation, the momenta are set to zero at each time step.

[[File:MepH2bondlength_01508.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using MEP calculation.]]

[[File:MepH2momenta015083.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using MEP calculation.]]

Using Dynamics calculation, the outcome of the reaction is the same. The transition state rolls towards HB and HC and a hydrogen molecule is formed. One noticeable difference is that the hydrogen molecule now has some vibational energy as indicated by the wavy line along the B-C distance in the Internuclear Distance vs Time plot.As for the Momenta vs Time plot, the system is linear, therefore the angle theta is zero. HA and HB are moving away from each other at '''an increasing velocity until the momentum reaches 5 g.mol-1.pm.fs-1.The oscillation along the B-C bond corresponds to the vibration of the bond. '''why does the beginning have negative momenta?'''
[[File:DynamicsH2_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation.]]
[[File:DynamicsH2monenta_01508.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using Dynamics calculation.]]

'''r1=90.8 pm, r2=91.8 pm, momenta set to 0 g.mol-1.pm.fs-1'''

Once the length of r1 and r2 switches, the shapes of the graphs are identical but instead of HB and HC forming a molecule, HA and HB now form the hydrogen molecule in the products.
[[File:Mepinter2_01508.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using MEP calculation.]]
[[File:Momentamep2_015.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using MEP calculation.]]
[[File:InterDynamic_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation.]]
[[File:Momentadynamics_015083.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using Dynamics calculation.]]

'''Trajectory starting with the final position and reversed momentum to the reaction path above'''

This trajectory starts at the end of the reaction path above and finishes at where the above reaction started. it is essentially a reverse of what happened in the reaction above.
[[File:Reverse_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation (r1=70.0 pm,r2=353 pm,p1=-3.21 g.mol-1.pm.fs-1, p2=-5.07 g.mol-1.pm.fs-1) .]]

===Recative and unreactive trajectories===
{| class="wikitable" border="1"
! p1/g.mol-1.pm.fs-1 !! p2/g.mol-1.pm.fs-1!! Etot/kJmol-1!! Recative?!! Description of the dynamics!! Illustration of the trajectory
|-
| -2.56 || -5.1||-414 || Yes||The translational energy of the reactants can surmount the potential energy barrier and form the products. The ramaining energy is converted into vibrational energy of the products. || [[File:Table1_01508310.png|350px ]]
|-
| -3.1 || -4.1||-420 || No||The reactant H2 has vibrational energy and its rAB motion is rapid. Before it could cross the energy barrier, the molecule slams into the repulsive inner wall of the potential surface and bounces back into the reactant channel. || [[File:Table2_0150.png|350px]]
|-
| -3.1 || -5.1||-414|| Yes||The reactants have both the translational and vibrational energies. The energy is used to surmount the potential energy barrier and converted into the vibrational energy of the products. || [[File:Table3_01508.png|350px]]
|-
| -5.1 || -10.1||-357 || No||The reactants have sufficient energy to cross the transition state and the products did form for a certain amount of time. However, before the the system can exit the product channel, it recrosses the transition state and form the reactants again, hence no reaction occurs. ||[[File:Table4_01508.png|350px]]
|-
| -5.1 || -10.6||-394 || Yes||The system has sufficient energy to cross the transition state but it recrosses the transition state shortly after the reaction path hits the potential energy surface. However, the system is able to cross the transition state for the third time and finally exits the product channel and forms the products. || [[File:-10.6_01508.png|350px]]
|-
|}
In order to form products, a system must have sufficient energy to cross the transition state. Only molecules with the correct phase <ref name="reference 2"/> can exit the product channel and form stable products. Recrossing the transition state can lead to either product formation or no reaction. It is possible to cross the transition state multiple times.

===Transition State Theory===

Transition State Theory is classical, it doesn't take quantum tunnelling into account.Quantum tunnelling is probable for this reaction as it involves the transfer of a hydrogen atom, particularly at lower temperatures <ref name="reference 3"/>.At low temperatures, the H atom can tunnel through the potential energy barrier than to pass over the barrier, hence the activation energy is lowered and the reaction rate increases. However, recrossing the energy barrier is possible as seen with the simulations, this can have a negative effect on the reaction rate. At high temperatures, the system is thermally activated and the behavious is approximately classical<ref name="reference 4"/>. Therefore the experimental reaction rates are expected to be greater than that predicted by the Transition State Theory.

==F-H-H system==
===PES inspection===
'''F+H2 (F1-H1-H2)'''

F+H2 is exothermic as the reactants are higher in energy than the products therefore during the reaction, energy is released to the surroundings. H-F bond is stronger than H-H bond as the products are lower in energy and therefore more stable.The transition state is located approximately at rF1-H1=181.10 pm and rH1-H2=74.49 pm. This is verified by the forces (close to zero) and eigenvalues for hessian matrix (they are of opposite signs). The activation energy is estimated by tilting the transition state towards the reactants and is shown to be 424 kJ.mol-1.
[[File:Fh2_015083.png |400px|centre|thumb|Surface plot for F1-H1-H2 system using Dynamic Calculation, the transition state is identified as the black dot.]]
[[File:OptimisationFhh1_01508.png|400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:F1H1H2_EA_0150.png|400px|centre|thumb|Counter plot for estimating the activation energy.]]
[[File:EA1_01508.png|400px|centre|thumb|parameters for the activation energy.]]
'''H+HF (H1-H2-F1)'''
This reaction is endothermis as the reactants are lower in energy than the products therefore energy is taken in from the surroundings to form the products. H-F bond is still stronger than H-H as the reactans are lower in energy and more stable. The transition state is located at approximately rH1-H2=280 pm and rH2-F1=92 pm. It is located with the same reasons stated above.With the same method, the activation energy is estimated to be 434 kJ.mol-1. The two activation energies should be identical as these two reactions are essentially the reverse of one another.

[[File:H+HF_01508310.png|400px|centre|thumb|Surface plot for H1-H2-F1 system using Dynamic Calculationthe, the transition state is identified as the black dot.]]
[[File:HHF_015083.png |400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:EA2_01508.png|400px|centre|thumb|Counter plot for estimating the activation energy.]]
[[File:EA2_PARAMETERS.png|400px|centre|thumb|parameters for the activation energy.]]

===Reaction dynamics===
===F+H2 system===

Initially, the reactants have kinetic energy in the form of vibrational and translational energies, and as it crosses the potential energy barrier, the kinetic energy is converted into potential energy. Once the system is exiting the product channel, the potential energy is converted into the vibrational energy of the product.One good experimental technique to prob the electronic structure of the reacting species will be IR spectroscopy.In the anharmonic oscillator model, exciting molecules in the relaxed state promotes excitation from the ground state to the first energy level mainly. This will give rise to a single peak in the IR spectrum. Howver, when exciting a sample of excited molecules, many transitions are possible. For example, from 0-->1, the fundamental or 1-->2, the first overtone. They will show up in the spectrum as 2 peaks, with the overtone being at a lower wavenumber as the energy gap decreases up the potential well. The intensity of the overtone decreases over time as the electrons can fall back to lower energy levels and energy is emitted as radiation. As this system is linear, rotational is not important electronic energy is not considered here.Photoelectron spectroscopy is also a viable method. <ref name="reference 5"/>

[[File:Reactiondynamicsfh2_0150.png||400px|centre|thumb|contour plot for F+H2.]]
[[File:Reactiondynamicsparameter——015.png |400px|centre|thumb|parameters for the reactive trajectory.]]
====Varying the momentum of HH in the F+H2 system.====
Conditions:rFH=182 pm, rHH=74 pm, PFH=-1.0g.mol-1.pm.fs-1
{| class="wikitable" border="1"
|+ caption
|-
|PHH/g.mol-1.pm.fs-1|| Contour Plot
|-
|0 || [[File:0_015083.png |400 px|centre]]
|-
|2 || [[File:2_0508.png |400 px|centre]]
|-
|4 || [[File:4_01508.png ‎|400 px|centre]]
|-
|6.1|| [[File:6_01508.png|400 px|centre]]
|-
| -2|| [[File:-2_01508.png|400 px|centre]]
|-
| -4|| [[File:-4.1_01508.png‎|400 px|centre]]
|-
| -6.1|| [[File:Fit1_01508.png|400 px|centre]]
|-
|}
Although the amount of energy that is put into H-H vibration is much more than the activation energy of the reaction, the reaction does not always occur. The large amount of energy is demonstrated by the high frequency of those wavy lines. Recrossing the transition states multiple times can lead to no reaction or product formation depending on how the tragectory collides with the potential well.

[[File:Reactiondynamic_last01588.png|400px|centre|thumb|contour plot for rFH=182 pm, fHH=74 pm, PFH=-1.6g.mol-1.pm.fs-1,PHH=0.2g.mol-1.pm.fs-1]]
The system now has much less vibrational energy into the reactants than before. The reaction is still successful and the trajectory recrosses the transition states fewer times than before.This can be explained by the increased momentum of FH so that F can approach the closest H with more vibrational energy.

===H+HF system===
{| class="wikitable" border="1"
!Graph Number!! p1(HH)/g.mol-1.pm.fs-1 !! p2(HF)/g.mol-1.pm.fs-1!! Etot/kJmol-1!! Recative?!! Illustration of the trajectory
|-
|1|| -2 || -10||-397|| No|| [[File:Final1_01508.png|350px ]]
|-
|2|| 0|| -8||-400 || No|| [[File:Final2_015.png|350px]]
|-
|3||5 || -6||-360|| No|| [[File:Final3_015.png|350px]]
|-
|4|| 5 || -3||-389 || Yes||[[File:Final4_015.png|350px]]
|-
|}

by referening to Polanyl's empirical rules, an exothermic reaction has an early barrier, which happens in the entrance channel. It tends to favour vibrational excitation of the products. On the other hand, an endothermic reaction has a late barrier, which occurs in the product channel. It tends to favour low product vibrational excitation. The location of the energy barrier is also crucial for a successful reaction. Translational energy of the reactants is the most effective at passing the early barrier whereas vibrational energy of the reactants is the most effective at surmounting the late barrier.This reaction is endothermic, and hence it has a late barrier. In all the graphs, the reactants all have vibrational energy as indicated by the wavy line in the reactant channel.<ref name="reference 2"/>

==References==

<references>
<ref name="reference 1">R. DeKock and H. Gray, Chemical structure and bonding, Univeristy Science Books, 1989.</ref>
<ref name="reference 2">S. Jeffrey I., Experimental Chemical Dynamics, Prentice-Hall, Upper Saddle River, 2nd edn., 1989.</ref>
<ref name="reference 3">L. Keith J., Theories of reaction rates, Harper & Row, New York;London, 3rd edn., 1987.</ref>
<ref name="reference 4">D. Brougham, A. Horsewill and R. Jenkinson, Chemical Physics Letters, 1997, 272, 69-74.</ref>
<ref name="reference 5">S. Bradforth, D. Arnold, D. Neumark and D. Manolopoulos, The Journal of Chemical Physics, 1993, 99, 6345-6359.</ref>
</references>

MRD:01508310

2020-05-22T18:37:18Z

Hh2218: /* H+HF system */

==H-H-H system==
===Dynamics from the transition state region===
The transition state is the point on the potential energy surface that has ∂V(ri)/∂ri=0, where ri is the distance between two atoms.The transition state is a local maximum and its second derivative ∂2V(ri)/∂ri2 is < 0, whereas a local minimum will have a positive second derivative instead.
[[File:Hhh_surfaceplot_01508.png|400px|thumb|centre|a potential energy surface plot of H and H2 with respect to interatomic distances.]]

===Trajectories from r1=r2: locating the transition state===
At the transition state, r1=r2=90.8 pm by estimation. At this separation, the forces acting along AB and BC are both -0.004 kJ.mol-1.pm-1, which is close to zero and the eigenvalues for the Hessian matrix were -0.028 and +0.167 kJ.mol-1.pm-2, indicating the presence of transition state. The Internuclear Distance vs Time plot suggests the distance between HA, HB and HC is equal, about 90 pm and the distance is constant over time suggests the atoms are static at the transition state.
[[File:Animation101508310.png|400px|centre|thumb|picture showing H and H2 at the transition state.]]
[[File:Optimisation1_01508310.png|400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:Internucleardistance_01508310.png|400px|centre|thumb|Internuclear Distance vs Time plot between the H atoms at the transition state.]]

===Calculating the reaction path===
When rA-B is set to rts+1 and rB-C equals rts,the transition rolls towards BC and HA remains as an atom. MEP and Dynamic reaction paths are different as MEP set the momenta to zero in every step of the reaction path, products are therefore static and hence the reaction path is relatively straight. The dynamic reaction path is more realistic. It takes the momenta of gaseous molecules into account,i.e. they have vibrational energies, that is illustrated by the wavy line along the reaction path.
[[File:Surface_Plot1mep_015083.png|400px|centre|thumb|the minimum energy path (mep) of the H-H-H system]]
[[File:01569348_MEP_AB1_dynamic.png|400px|centre|thumb|the dynamic reaction path of the H-H-H system]]

====MEP and Dynamics calculations comparisons====
'''r1=91.8 pm, r2=90.8 pm, momenta set to 0 g.mol-1.pm.fs-1'''

HB and HC form a H2 molecule whereas HA moves away from the molecule. The distance between B and C decreased to 74 pm, which is the hydrogen molecule bond length <ref name="reference 1"/>.In MEP calculation, the momenta are set to zero at each time step.

[[File:MepH2bondlength_01508.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using MEP calculation.]]

[[File:MepH2momenta015083.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using MEP calculation.]]

Using Dynamics calculation, the outcome of the reaction is the same. The transition state rolls towards HB and HC and a hydrogen molecule is formed. One noticeable difference is that the hydrogen molecule now has some vibational energy as indicated by the wavy line along the B-C distance in the Internuclear Distance vs Time plot.As for the Momenta vs Time plot, the system is linear, therefore the angle theta is zero. HA and HB are moving away from each other at '''an increasing velocity until the momentum reaches 5 g.mol-1.pm.fs-1.The oscillation along the B-C bond corresponds to the vibration of the bond. '''why does the beginning have negative momenta?'''
[[File:DynamicsH2_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation.]]
[[File:DynamicsH2monenta_01508.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using Dynamics calculation.]]

'''r1=90.8 pm, r2=91.8 pm, momenta set to 0 g.mol-1.pm.fs-1'''

Once the length of r1 and r2 switches, the shapes of the graphs are identical but instead of HB and HC forming a molecule, HA and HB now form the hydrogen molecule in the products.
[[File:Mepinter2_01508.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using MEP calculation.]]
[[File:Momentamep2_015.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using MEP calculation.]]
[[File:InterDynamic_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation.]]
[[File:Momentadynamics_015083.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using Dynamics calculation.]]

'''Trajectory starting with the final position and reversed momentum to the reaction path above'''

This trajectory starts at the end of the reaction path above and finishes at where the above reaction started. it is essentially a reverse of what happened in the reaction above.
[[File:Reverse_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation (r1=70.0 pm,r2=353 pm,p1=-3.21 g.mol-1.pm.fs-1, p2=-5.07 g.mol-1.pm.fs-1) .]]

===Recative and unreactive trajectories===
{| class="wikitable" border="1"
! p1/g.mol-1.pm.fs-1 !! p2/g.mol-1.pm.fs-1!! Etot/kJmol-1!! Recative?!! Description of the dynamics!! Illustration of the trajectory
|-
| -2.56 || -5.1||-414 || Yes||The translational energy of the reactants can surmount the potential energy barrier and form the products. The ramaining energy is converted into vibrational energy of the products. || [[File:Table1_01508310.png|350px ]]
|-
| -3.1 || -4.1||-420 || No||The reactant H2 has vibrational energy and its rAB motion is rapid. Before it could cross the energy barrier, the molecule slams into the repulsive inner wall of the potential surface and bounces back into the reactant channel. || [[File:Table2_0150.png|350px]]
|-
| -3.1 || -5.1||-414|| Yes||The reactants have both the translational and vibrational energies. The energy is used to surmount the potential energy barrier and converted into the vibrational energy of the products. || [[File:Table3_01508.png|350px]]
|-
| -5.1 || -10.1||-357 || No||The reactants have sufficient energy to cross the transition state and the products did form for a certain amount of time. However, before the the system can exit the product channel, it recrosses the transition state and form the reactants again, hence no reaction occurs. ||[[File:Table4_01508.png|350px]]
|-
| -5.1 || -10.6||-394 || Yes||The system has sufficient energy to cross the transition state but it recrosses the transition state shortly after the reaction path hits the potential energy surface. However, the system is able to cross the transition state for the third time and finally exits the product channel and forms the products. || [[File:-10.6_01508.png|350px]]
|-
|}
In order to form products, a system must have sufficient energy to cross the transition state. Only molecules with the correct phase <ref name="reference 2"/> can exit the product channel and form stable products. Recrossing the transition state can lead to either product formation or no reaction. It is possible to cross the transition state multiple times.

===Transition State Theory===

Transition State Theory is classical, it doesn't take quantum tunnelling into account.Quantum tunnelling is probable for this reaction as it involves the transfer of a hydrogen atom, particularly at lower temperatures <ref name="reference 3"/>.At low temperatures, the H atom can tunnel through the potential energy barrier than to pass over the barrier, hence the activation energy is lowered and the reaction rate increases. However, recrossing the energy barrier is possible as seen with the simulations, this can have a negative effect on the reaction rate. At high temperatures, the system is thermally activated and the behavious is approximately classical<ref name="reference 4"/>. Therefore the experimental reaction rates are expected to be greater than that predicted by the Transition State Theory.

==F-H-H system==
===PES inspection===
'''F+H2 (F1-H1-H2)'''

F+H2 is exothermic as the reactants are higher in energy than the products therefore during the reaction, energy is released to the surroundings. H-F bond is stronger than H-H bond as the products are lower in energy and therefore more stable.The transition state is located approximately at rF1-H1=181.10 pm and rH1-H2=74.49 pm. This is verified by the forces (close to zero) and eigenvalues for hessian matrix (they are of opposite signs). The activation energy is estimated by tilting the transition state towards the reactants and is shown to be 424 kJ.mol-1.
[[File:Fh2_015083.png |400px|centre|thumb|Surface plot for F1-H1-H2 system using Dynamic Calculation, the transition state is identified as the black dot.]]
[[File:OptimisationFhh1_01508.png|400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:F1H1H2_EA_0150.png|400px|centre|thumb|Counter plot for estimating the activation energy.]]
[[File:EA1_01508.png|400px|centre|thumb|parameters for the activation energy.]]
'''H+HF (H1-H2-F1)'''
This reaction is endothermis as the reactants are lower in energy than the products therefore energy is taken in from the surroundings to form the products. H-F bond is still stronger than H-H as the reactans are lower in energy and more stable. The transition state is located at approximately rH1-H2=280 pm and rH2-F1=92 pm. It is located with the same reasons stated above.With the same method, the activation energy is estimated to be 434 kJ.mol-1. The two activation energies should be identical as these two reactions are essentially the reverse of one another.

[[File:H+HF_01508310.png|400px|centre|thumb|Surface plot for H1-H2-F1 system using Dynamic Calculationthe, the transition state is identified as the black dot.]]
[[File:HHF_015083.png |400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:EA2_01508.png|400px|centre|thumb|Counter plot for estimating the activation energy.]]
[[File:EA2_PARAMETERS.png|400px|centre|thumb|parameters for the activation energy.]]

===Reaction dynamics===
===F+H2 system===

Initially, the reactants have kinetic energy in the form of vibrational and translational energies, and as it crosses the potential energy barrier, the kinetic energy is converted into potential energy. Once the system is exiting the product channel, the potential energy is converted into the vibrational energy of the product.One good experimental technique to prob the electronic structure of the reacting species will be IR spectroscopy.In the anharmonic oscillator model, exciting molecules in the relaxed state promotes excitation from the ground state to the first energy level mainly. This will give rise to a single peak in the IR spectrum. Howver, when exciting a sample of excited molecules, many transitions are possible. For example, from 0-->1, the fundamental or 1-->2, the first overtone. They will show up in the spectrum as 2 peaks, with the overtone being at a lower wavenumber as the energy gap decreases up the potential well. The intensity of the overtone decreases over time as the electrons can fall back to lower energy levels and energy is emitted as radiation. As this system is linear, rotational is not important electronic energy is not considered here.Photoelectron spectroscopy is also a viable method. <ref name="reference 5"/>

[[File:Reactiondynamicsfh2_0150.png||400px|centre|thumb|contour plot for F+H2.]]
[[File:Reactiondynamicsparameter——015.png |400px|centre|thumb|parameters for the reactive trajectory.]]
====Varying the momentum of HH in the F+H2 system.====
Conditions:rFH=182 pm, rHH=74 pm, PFH=-1.0g.mol-1.pm.fs-1
{| class="wikitable" border="1"
|+ caption
|-
|PHH/g.mol-1.pm.fs-1|| Contour Plot
|-
|0 || [[File:0_015083.png |400 px|centre]]
|-
|2 || [[File:2_0508.png |400 px|centre]]
|-
|4 || [[File:4_01508.png ‎|400 px|centre]]
|-
|6.1|| [[File:6_01508.png|400 px|centre]]
|-
| -2|| [[File:-2_01508.png|400 px|centre]]
|-
| -4|| [[File:-4.1_01508.png‎|400 px|centre]]
|-
| -6.1|| [[File:Fit1_01508.png|400 px|centre]]
|-
|}
Although the amount of energy that is put into H-H vibration is much more than the activation energy of the reaction, the reaction does not always occur. The large amount of energy is demonstrated by the high frequency of those wavy lines. Recrossing the transition states multiple times can lead to no reaction or product formation depending on how the tragectory collides with the potential well.

[[File:Reactiondynamic_last01588.png|400px|centre|thumb|contour plot for rFH=182 pm, fHH=74 pm, PFH=-1.6g.mol-1.pm.fs-1,PHH=0.2g.mol-1.pm.fs-1]]
The system now has much less vibrational energy into the reactants than before. The reaction is still successful and the trajectory recrosses the transition states fewer times than before.This can be explained by the increased momentum of FH so that F can approach the closest H with more vibrational energy.

===H+HF system===
{| class="wikitable" border="1"
!Graph Number!! p1(HH)/g.mol-1.pm.fs-1 !! p2(HF)/g.mol-1.pm.fs-1!! Etot/kJmol-1!! Recative?!! Illustration of the trajectory
|-
|1|| -2 || -10||-397|| No|| [[File:Final1_01508.png|350px ]]
|-
|2|| 0|| -8||-400 || No|| [[File:Final2_015.png|350px]]
|-
|3||5 || -6||-360|| No|| [[File:Final3_015.png|350px]]
|-
|4|| 5 || -3||-389 || Yes||[[File:Final4_015.png|350px]]
|-
|}

by referening to Polanyl's empirical rules, an exothermic reaction has an early barrier, which happens in the entrance channel. It tends to favour vibrational excitation of the products. On the other hand, an endothermic reaction has a late barrier, which occurs in the product channel. It tends to favour low product vibrational excitation. The location of the energy barrier is also crucial for a successful reaction. Translational energy of the reactants is the most effective at passing the early barrier whereas vibrational energy of the reactants is the most effective at surmounting the late barrier.This reaction is endothermic, and hence it has a late barrier. In all the graphs, the reactants all have vibrational energy as indicated by the wavy line in the reactant channel.<ref name="reference 2"/>

==References==

<references>
<ref name="reference 1">R. DeKock and H. Gray, Chemical structure and bonding, Univeristy Science Books, 1989.</ref>
<ref name="reference 2">S. Jeffrey I., Experimental Chemical Dynamics, Prentice-Hall, Upper Saddle River, 2nd edn., 1989.</ref>
<ref name="reference 3">L. Keith J., Theories of reaction rates, Harper & Row, New York;London, 3rd edn., 1987.</ref>
<ref name="reference 4">D. Brougham, A. Horsewill and R. Jenkinson, Chemical Physics Letters, 1997, 272, 69-74.</ref>
<ref name="reference 5">S. Bradforth, D. Arnold, D. Neumark and D. Manolopoulos, The Journal of Chemical Physics, 1993, 99, 6345-6359.</ref>
</references>

MRD:01508310

2020-05-22T18:34:12Z

Hh2218: /* References */

==H-H-H system==
===Dynamics from the transition state region===
The transition state is the point on the potential energy surface that has ∂V(ri)/∂ri=0, where ri is the distance between two atoms.The transition state is a local maximum and its second derivative ∂2V(ri)/∂ri2 is < 0, whereas a local minimum will have a positive second derivative instead.
[[File:Hhh_surfaceplot_01508.png|400px|thumb|centre|a potential energy surface plot of H and H2 with respect to interatomic distances.]]

===Trajectories from r1=r2: locating the transition state===
At the transition state, r1=r2=90.8 pm by estimation. At this separation, the forces acting along AB and BC are both -0.004 kJ.mol-1.pm-1, which is close to zero and the eigenvalues for the Hessian matrix were -0.028 and +0.167 kJ.mol-1.pm-2, indicating the presence of transition state. The Internuclear Distance vs Time plot suggests the distance between HA, HB and HC is equal, about 90 pm and the distance is constant over time suggests the atoms are static at the transition state.
[[File:Animation101508310.png|400px|centre|thumb|picture showing H and H2 at the transition state.]]
[[File:Optimisation1_01508310.png|400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:Internucleardistance_01508310.png|400px|centre|thumb|Internuclear Distance vs Time plot between the H atoms at the transition state.]]

===Calculating the reaction path===
When rA-B is set to rts+1 and rB-C equals rts,the transition rolls towards BC and HA remains as an atom. MEP and Dynamic reaction paths are different as MEP set the momenta to zero in every step of the reaction path, products are therefore static and hence the reaction path is relatively straight. The dynamic reaction path is more realistic. It takes the momenta of gaseous molecules into account,i.e. they have vibrational energies, that is illustrated by the wavy line along the reaction path.
[[File:Surface_Plot1mep_015083.png|400px|centre|thumb|the minimum energy path (mep) of the H-H-H system]]
[[File:01569348_MEP_AB1_dynamic.png|400px|centre|thumb|the dynamic reaction path of the H-H-H system]]

====MEP and Dynamics calculations comparisons====
'''r1=91.8 pm, r2=90.8 pm, momenta set to 0 g.mol-1.pm.fs-1'''

HB and HC form a H2 molecule whereas HA moves away from the molecule. The distance between B and C decreased to 74 pm, which is the hydrogen molecule bond length <ref name="reference 1"/>.In MEP calculation, the momenta are set to zero at each time step.

[[File:MepH2bondlength_01508.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using MEP calculation.]]

[[File:MepH2momenta015083.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using MEP calculation.]]

Using Dynamics calculation, the outcome of the reaction is the same. The transition state rolls towards HB and HC and a hydrogen molecule is formed. One noticeable difference is that the hydrogen molecule now has some vibational energy as indicated by the wavy line along the B-C distance in the Internuclear Distance vs Time plot.As for the Momenta vs Time plot, the system is linear, therefore the angle theta is zero. HA and HB are moving away from each other at '''an increasing velocity until the momentum reaches 5 g.mol-1.pm.fs-1.The oscillation along the B-C bond corresponds to the vibration of the bond. '''why does the beginning have negative momenta?'''
[[File:DynamicsH2_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation.]]
[[File:DynamicsH2monenta_01508.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using Dynamics calculation.]]

'''r1=90.8 pm, r2=91.8 pm, momenta set to 0 g.mol-1.pm.fs-1'''

Once the length of r1 and r2 switches, the shapes of the graphs are identical but instead of HB and HC forming a molecule, HA and HB now form the hydrogen molecule in the products.
[[File:Mepinter2_01508.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using MEP calculation.]]
[[File:Momentamep2_015.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using MEP calculation.]]
[[File:InterDynamic_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation.]]
[[File:Momentadynamics_015083.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using Dynamics calculation.]]

'''Trajectory starting with the final position and reversed momentum to the reaction path above'''

This trajectory starts at the end of the reaction path above and finishes at where the above reaction started. it is essentially a reverse of what happened in the reaction above.
[[File:Reverse_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation (r1=70.0 pm,r2=353 pm,p1=-3.21 g.mol-1.pm.fs-1, p2=-5.07 g.mol-1.pm.fs-1) .]]

===Recative and unreactive trajectories===
{| class="wikitable" border="1"
! p1/g.mol-1.pm.fs-1 !! p2/g.mol-1.pm.fs-1!! Etot/kJmol-1!! Recative?!! Description of the dynamics!! Illustration of the trajectory
|-
| -2.56 || -5.1||-414 || Yes||The translational energy of the reactants can surmount the potential energy barrier and form the products. The ramaining energy is converted into vibrational energy of the products. || [[File:Table1_01508310.png|350px ]]
|-
| -3.1 || -4.1||-420 || No||The reactant H2 has vibrational energy and its rAB motion is rapid. Before it could cross the energy barrier, the molecule slams into the repulsive inner wall of the potential surface and bounces back into the reactant channel. || [[File:Table2_0150.png|350px]]
|-
| -3.1 || -5.1||-414|| Yes||The reactants have both the translational and vibrational energies. The energy is used to surmount the potential energy barrier and converted into the vibrational energy of the products. || [[File:Table3_01508.png|350px]]
|-
| -5.1 || -10.1||-357 || No||The reactants have sufficient energy to cross the transition state and the products did form for a certain amount of time. However, before the the system can exit the product channel, it recrosses the transition state and form the reactants again, hence no reaction occurs. ||[[File:Table4_01508.png|350px]]
|-
| -5.1 || -10.6||-394 || Yes||The system has sufficient energy to cross the transition state but it recrosses the transition state shortly after the reaction path hits the potential energy surface. However, the system is able to cross the transition state for the third time and finally exits the product channel and forms the products. || [[File:-10.6_01508.png|350px]]
|-
|}
In order to form products, a system must have sufficient energy to cross the transition state. Only molecules with the correct phase <ref name="reference 2"/> can exit the product channel and form stable products. Recrossing the transition state can lead to either product formation or no reaction. It is possible to cross the transition state multiple times.

===Transition State Theory===

Transition State Theory is classical, it doesn't take quantum tunnelling into account.Quantum tunnelling is probable for this reaction as it involves the transfer of a hydrogen atom, particularly at lower temperatures <ref name="reference 3"/>.At low temperatures, the H atom can tunnel through the potential energy barrier than to pass over the barrier, hence the activation energy is lowered and the reaction rate increases. However, recrossing the energy barrier is possible as seen with the simulations, this can have a negative effect on the reaction rate. At high temperatures, the system is thermally activated and the behavious is approximately classical<ref name="reference 4"/>. Therefore the experimental reaction rates are expected to be greater than that predicted by the Transition State Theory.

==F-H-H system==
===PES inspection===
'''F+H2 (F1-H1-H2)'''

F+H2 is exothermic as the reactants are higher in energy than the products therefore during the reaction, energy is released to the surroundings. H-F bond is stronger than H-H bond as the products are lower in energy and therefore more stable.The transition state is located approximately at rF1-H1=181.10 pm and rH1-H2=74.49 pm. This is verified by the forces (close to zero) and eigenvalues for hessian matrix (they are of opposite signs). The activation energy is estimated by tilting the transition state towards the reactants and is shown to be 424 kJ.mol-1.
[[File:Fh2_015083.png |400px|centre|thumb|Surface plot for F1-H1-H2 system using Dynamic Calculation, the transition state is identified as the black dot.]]
[[File:OptimisationFhh1_01508.png|400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:F1H1H2_EA_0150.png|400px|centre|thumb|Counter plot for estimating the activation energy.]]
[[File:EA1_01508.png|400px|centre|thumb|parameters for the activation energy.]]
'''H+HF (H1-H2-F1)'''
This reaction is endothermis as the reactants are lower in energy than the products therefore energy is taken in from the surroundings to form the products. H-F bond is still stronger than H-H as the reactans are lower in energy and more stable. The transition state is located at approximately rH1-H2=280 pm and rH2-F1=92 pm. It is located with the same reasons stated above.With the same method, the activation energy is estimated to be 434 kJ.mol-1. The two activation energies should be identical as these two reactions are essentially the reverse of one another.

[[File:H+HF_01508310.png|400px|centre|thumb|Surface plot for H1-H2-F1 system using Dynamic Calculationthe, the transition state is identified as the black dot.]]
[[File:HHF_015083.png |400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:EA2_01508.png|400px|centre|thumb|Counter plot for estimating the activation energy.]]
[[File:EA2_PARAMETERS.png|400px|centre|thumb|parameters for the activation energy.]]

===Reaction dynamics===
===F+H2 system===

Initially, the reactants have kinetic energy in the form of vibrational and translational energies, and as it crosses the potential energy barrier, the kinetic energy is converted into potential energy. Once the system is exiting the product channel, the potential energy is converted into the vibrational energy of the product.One good experimental technique to prob the electronic structure of the reacting species will be IR spectroscopy.In the anharmonic oscillator model, exciting molecules in the relaxed state promotes excitation from the ground state to the first energy level mainly. This will give rise to a single peak in the IR spectrum. Howver, when exciting a sample of excited molecules, many transitions are possible. For example, from 0-->1, the fundamental or 1-->2, the first overtone. They will show up in the spectrum as 2 peaks, with the overtone being at a lower wavenumber as the energy gap decreases up the potential well. The intensity of the overtone decreases over time as the electrons can fall back to lower energy levels and energy is emitted as radiation. As this system is linear, rotational is not important electronic energy is not considered here.Photoelectron spectroscopy is also a viable method. <ref name="reference 5"/>

[[File:Reactiondynamicsfh2_0150.png||400px|centre|thumb|contour plot for F+H2.]]
[[File:Reactiondynamicsparameter——015.png |400px|centre|thumb|parameters for the reactive trajectory.]]
====Varying the momentum of HH in the F+H2 system.====
Conditions:rFH=182 pm, rHH=74 pm, PFH=-1.0g.mol-1.pm.fs-1
{| class="wikitable" border="1"
|+ caption
|-
|PHH/g.mol-1.pm.fs-1|| Contour Plot
|-
|0 || [[File:0_015083.png |400 px|centre]]
|-
|2 || [[File:2_0508.png |400 px|centre]]
|-
|4 || [[File:4_01508.png ‎|400 px|centre]]
|-
|6.1|| [[File:6_01508.png|400 px|centre]]
|-
| -2|| [[File:-2_01508.png|400 px|centre]]
|-
| -4|| [[File:-4.1_01508.png‎|400 px|centre]]
|-
| -6.1|| [[File:Fit1_01508.png|400 px|centre]]
|-
|}
Although the amount of energy that is put into H-H vibration is much more than the activation energy of the reaction, the reaction does not always occur. The large amount of energy is demonstrated by the high frequency of those wavy lines. Recrossing the transition states multiple times can lead to no reaction or product formation depending on how the tragectory collides with the potential well.

[[File:Reactiondynamic_last01588.png|400px|centre|thumb|contour plot for rFH=182 pm, fHH=74 pm, PFH=-1.6g.mol-1.pm.fs-1,PHH=0.2g.mol-1.pm.fs-1]]
The system now has much less vibrational energy into the reactants than before. The reaction is still successful and the trajectory recrosses the transition states fewer times than before.This can be explained by the increased momentum of FH so that F can approach the closest H with more vibrational energy.

===H+HF system===
{| class="wikitable" border="1"
!Graph Number!! p1(HH)/g.mol-1.pm.fs-1 !! p2(HF)/g.mol-1.pm.fs-1!! Etot/kJmol-1!! Recative?!! Illustration of the trajectory
|-
|1|| -2 || -10||-397|| No|| [[File:Final1_01508.png|350px ]]
|-
|2|| 0|| -8||-400 || No|| [[File:Final2_015.png|350px]]
|-
|3||5 || -6||-360|| No|| [[File:Final3_015.png|350px]]
|-
|4|| 5 || -3||-389 || Yes||[[File:Final4_015.png|350px]]
|-
|}

by referening to Polanyl's empirical rules, an exothermic reaction has an early barrier, which happens in the entrance channel. It tends to favour vibrational excitation of the products. On the other hand, an endothermic reaction has a late barrier, which occurs in the product channel. It tends to favour low product vibrational excitation. The location of the energy barrier is also crucial for a successful reaction. Translational energy of the reactants is the most effective at passing the early barrier whereas vibrational energy of the reactants is the most effective at surmounting the late barrier.This reaction is endothermic, and hence it has a late barrier. In all the graphs, the reactants all have vibrational energy as indicated by the wavy line in the reactant channel.
==References==

<references>
<ref name="reference 1">R. DeKock and H. Gray, Chemical structure and bonding, Univeristy Science Books, 1989.</ref>
<ref name="reference 2">S. Jeffrey I., Experimental Chemical Dynamics, Prentice-Hall, Upper Saddle River, 2nd edn., 1989.</ref>
<ref name="reference 3">L. Keith J., Theories of reaction rates, Harper & Row, New York;London, 3rd edn., 1987.</ref>
<ref name="reference 4">D. Brougham, A. Horsewill and R. Jenkinson, Chemical Physics Letters, 1997, 272, 69-74.</ref>
<ref name="reference 5">S. Bradforth, D. Arnold, D. Neumark and D. Manolopoulos, The Journal of Chemical Physics, 1993, 99, 6345-6359.</ref>
</references>

MRD:01508310

2020-05-22T18:33:56Z

Hh2218: /* References */

==H-H-H system==
===Dynamics from the transition state region===
The transition state is the point on the potential energy surface that has ∂V(ri)/∂ri=0, where ri is the distance between two atoms.The transition state is a local maximum and its second derivative ∂2V(ri)/∂ri2 is < 0, whereas a local minimum will have a positive second derivative instead.
[[File:Hhh_surfaceplot_01508.png|400px|thumb|centre|a potential energy surface plot of H and H2 with respect to interatomic distances.]]

===Trajectories from r1=r2: locating the transition state===
At the transition state, r1=r2=90.8 pm by estimation. At this separation, the forces acting along AB and BC are both -0.004 kJ.mol-1.pm-1, which is close to zero and the eigenvalues for the Hessian matrix were -0.028 and +0.167 kJ.mol-1.pm-2, indicating the presence of transition state. The Internuclear Distance vs Time plot suggests the distance between HA, HB and HC is equal, about 90 pm and the distance is constant over time suggests the atoms are static at the transition state.
[[File:Animation101508310.png|400px|centre|thumb|picture showing H and H2 at the transition state.]]
[[File:Optimisation1_01508310.png|400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:Internucleardistance_01508310.png|400px|centre|thumb|Internuclear Distance vs Time plot between the H atoms at the transition state.]]

===Calculating the reaction path===
When rA-B is set to rts+1 and rB-C equals rts,the transition rolls towards BC and HA remains as an atom. MEP and Dynamic reaction paths are different as MEP set the momenta to zero in every step of the reaction path, products are therefore static and hence the reaction path is relatively straight. The dynamic reaction path is more realistic. It takes the momenta of gaseous molecules into account,i.e. they have vibrational energies, that is illustrated by the wavy line along the reaction path.
[[File:Surface_Plot1mep_015083.png|400px|centre|thumb|the minimum energy path (mep) of the H-H-H system]]
[[File:01569348_MEP_AB1_dynamic.png|400px|centre|thumb|the dynamic reaction path of the H-H-H system]]

====MEP and Dynamics calculations comparisons====
'''r1=91.8 pm, r2=90.8 pm, momenta set to 0 g.mol-1.pm.fs-1'''

HB and HC form a H2 molecule whereas HA moves away from the molecule. The distance between B and C decreased to 74 pm, which is the hydrogen molecule bond length <ref name="reference 1"/>.In MEP calculation, the momenta are set to zero at each time step.

[[File:MepH2bondlength_01508.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using MEP calculation.]]

[[File:MepH2momenta015083.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using MEP calculation.]]

Using Dynamics calculation, the outcome of the reaction is the same. The transition state rolls towards HB and HC and a hydrogen molecule is formed. One noticeable difference is that the hydrogen molecule now has some vibational energy as indicated by the wavy line along the B-C distance in the Internuclear Distance vs Time plot.As for the Momenta vs Time plot, the system is linear, therefore the angle theta is zero. HA and HB are moving away from each other at '''an increasing velocity until the momentum reaches 5 g.mol-1.pm.fs-1.The oscillation along the B-C bond corresponds to the vibration of the bond. '''why does the beginning have negative momenta?'''
[[File:DynamicsH2_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation.]]
[[File:DynamicsH2monenta_01508.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using Dynamics calculation.]]

'''r1=90.8 pm, r2=91.8 pm, momenta set to 0 g.mol-1.pm.fs-1'''

Once the length of r1 and r2 switches, the shapes of the graphs are identical but instead of HB and HC forming a molecule, HA and HB now form the hydrogen molecule in the products.
[[File:Mepinter2_01508.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using MEP calculation.]]
[[File:Momentamep2_015.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using MEP calculation.]]
[[File:InterDynamic_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation.]]
[[File:Momentadynamics_015083.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using Dynamics calculation.]]

'''Trajectory starting with the final position and reversed momentum to the reaction path above'''

This trajectory starts at the end of the reaction path above and finishes at where the above reaction started. it is essentially a reverse of what happened in the reaction above.
[[File:Reverse_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation (r1=70.0 pm,r2=353 pm,p1=-3.21 g.mol-1.pm.fs-1, p2=-5.07 g.mol-1.pm.fs-1) .]]

===Recative and unreactive trajectories===
{| class="wikitable" border="1"
! p1/g.mol-1.pm.fs-1 !! p2/g.mol-1.pm.fs-1!! Etot/kJmol-1!! Recative?!! Description of the dynamics!! Illustration of the trajectory
|-
| -2.56 || -5.1||-414 || Yes||The translational energy of the reactants can surmount the potential energy barrier and form the products. The ramaining energy is converted into vibrational energy of the products. || [[File:Table1_01508310.png|350px ]]
|-
| -3.1 || -4.1||-420 || No||The reactant H2 has vibrational energy and its rAB motion is rapid. Before it could cross the energy barrier, the molecule slams into the repulsive inner wall of the potential surface and bounces back into the reactant channel. || [[File:Table2_0150.png|350px]]
|-
| -3.1 || -5.1||-414|| Yes||The reactants have both the translational and vibrational energies. The energy is used to surmount the potential energy barrier and converted into the vibrational energy of the products. || [[File:Table3_01508.png|350px]]
|-
| -5.1 || -10.1||-357 || No||The reactants have sufficient energy to cross the transition state and the products did form for a certain amount of time. However, before the the system can exit the product channel, it recrosses the transition state and form the reactants again, hence no reaction occurs. ||[[File:Table4_01508.png|350px]]
|-
| -5.1 || -10.6||-394 || Yes||The system has sufficient energy to cross the transition state but it recrosses the transition state shortly after the reaction path hits the potential energy surface. However, the system is able to cross the transition state for the third time and finally exits the product channel and forms the products. || [[File:-10.6_01508.png|350px]]
|-
|}
In order to form products, a system must have sufficient energy to cross the transition state. Only molecules with the correct phase <ref name="reference 2"/> can exit the product channel and form stable products. Recrossing the transition state can lead to either product formation or no reaction. It is possible to cross the transition state multiple times.

===Transition State Theory===

Transition State Theory is classical, it doesn't take quantum tunnelling into account.Quantum tunnelling is probable for this reaction as it involves the transfer of a hydrogen atom, particularly at lower temperatures <ref name="reference 3"/>.At low temperatures, the H atom can tunnel through the potential energy barrier than to pass over the barrier, hence the activation energy is lowered and the reaction rate increases. However, recrossing the energy barrier is possible as seen with the simulations, this can have a negative effect on the reaction rate. At high temperatures, the system is thermally activated and the behavious is approximately classical<ref name="reference 4"/>. Therefore the experimental reaction rates are expected to be greater than that predicted by the Transition State Theory.

==F-H-H system==
===PES inspection===
'''F+H2 (F1-H1-H2)'''

F+H2 is exothermic as the reactants are higher in energy than the products therefore during the reaction, energy is released to the surroundings. H-F bond is stronger than H-H bond as the products are lower in energy and therefore more stable.The transition state is located approximately at rF1-H1=181.10 pm and rH1-H2=74.49 pm. This is verified by the forces (close to zero) and eigenvalues for hessian matrix (they are of opposite signs). The activation energy is estimated by tilting the transition state towards the reactants and is shown to be 424 kJ.mol-1.
[[File:Fh2_015083.png |400px|centre|thumb|Surface plot for F1-H1-H2 system using Dynamic Calculation, the transition state is identified as the black dot.]]
[[File:OptimisationFhh1_01508.png|400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:F1H1H2_EA_0150.png|400px|centre|thumb|Counter plot for estimating the activation energy.]]
[[File:EA1_01508.png|400px|centre|thumb|parameters for the activation energy.]]
'''H+HF (H1-H2-F1)'''
This reaction is endothermis as the reactants are lower in energy than the products therefore energy is taken in from the surroundings to form the products. H-F bond is still stronger than H-H as the reactans are lower in energy and more stable. The transition state is located at approximately rH1-H2=280 pm and rH2-F1=92 pm. It is located with the same reasons stated above.With the same method, the activation energy is estimated to be 434 kJ.mol-1. The two activation energies should be identical as these two reactions are essentially the reverse of one another.

[[File:H+HF_01508310.png|400px|centre|thumb|Surface plot for H1-H2-F1 system using Dynamic Calculationthe, the transition state is identified as the black dot.]]
[[File:HHF_015083.png |400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:EA2_01508.png|400px|centre|thumb|Counter plot for estimating the activation energy.]]
[[File:EA2_PARAMETERS.png|400px|centre|thumb|parameters for the activation energy.]]

===Reaction dynamics===
===F+H2 system===

Initially, the reactants have kinetic energy in the form of vibrational and translational energies, and as it crosses the potential energy barrier, the kinetic energy is converted into potential energy. Once the system is exiting the product channel, the potential energy is converted into the vibrational energy of the product.One good experimental technique to prob the electronic structure of the reacting species will be IR spectroscopy.In the anharmonic oscillator model, exciting molecules in the relaxed state promotes excitation from the ground state to the first energy level mainly. This will give rise to a single peak in the IR spectrum. Howver, when exciting a sample of excited molecules, many transitions are possible. For example, from 0-->1, the fundamental or 1-->2, the first overtone. They will show up in the spectrum as 2 peaks, with the overtone being at a lower wavenumber as the energy gap decreases up the potential well. The intensity of the overtone decreases over time as the electrons can fall back to lower energy levels and energy is emitted as radiation. As this system is linear, rotational is not important electronic energy is not considered here.Photoelectron spectroscopy is also a viable method. <ref name="reference 5"/>

[[File:Reactiondynamicsfh2_0150.png||400px|centre|thumb|contour plot for F+H2.]]
[[File:Reactiondynamicsparameter——015.png |400px|centre|thumb|parameters for the reactive trajectory.]]
====Varying the momentum of HH in the F+H2 system.====
Conditions:rFH=182 pm, rHH=74 pm, PFH=-1.0g.mol-1.pm.fs-1
{| class="wikitable" border="1"
|+ caption
|-
|PHH/g.mol-1.pm.fs-1|| Contour Plot
|-
|0 || [[File:0_015083.png |400 px|centre]]
|-
|2 || [[File:2_0508.png |400 px|centre]]
|-
|4 || [[File:4_01508.png ‎|400 px|centre]]
|-
|6.1|| [[File:6_01508.png|400 px|centre]]
|-
| -2|| [[File:-2_01508.png|400 px|centre]]
|-
| -4|| [[File:-4.1_01508.png‎|400 px|centre]]
|-
| -6.1|| [[File:Fit1_01508.png|400 px|centre]]
|-
|}
Although the amount of energy that is put into H-H vibration is much more than the activation energy of the reaction, the reaction does not always occur. The large amount of energy is demonstrated by the high frequency of those wavy lines. Recrossing the transition states multiple times can lead to no reaction or product formation depending on how the tragectory collides with the potential well.

[[File:Reactiondynamic_last01588.png|400px|centre|thumb|contour plot for rFH=182 pm, fHH=74 pm, PFH=-1.6g.mol-1.pm.fs-1,PHH=0.2g.mol-1.pm.fs-1]]
The system now has much less vibrational energy into the reactants than before. The reaction is still successful and the trajectory recrosses the transition states fewer times than before.This can be explained by the increased momentum of FH so that F can approach the closest H with more vibrational energy.

===H+HF system===
{| class="wikitable" border="1"
!Graph Number!! p1(HH)/g.mol-1.pm.fs-1 !! p2(HF)/g.mol-1.pm.fs-1!! Etot/kJmol-1!! Recative?!! Illustration of the trajectory
|-
|1|| -2 || -10||-397|| No|| [[File:Final1_01508.png|350px ]]
|-
|2|| 0|| -8||-400 || No|| [[File:Final2_015.png|350px]]
|-
|3||5 || -6||-360|| No|| [[File:Final3_015.png|350px]]
|-
|4|| 5 || -3||-389 || Yes||[[File:Final4_015.png|350px]]
|-
|}

by referening to Polanyl's empirical rules, an exothermic reaction has an early barrier, which happens in the entrance channel. It tends to favour vibrational excitation of the products. On the other hand, an endothermic reaction has a late barrier, which occurs in the product channel. It tends to favour low product vibrational excitation. The location of the energy barrier is also crucial for a successful reaction. Translational energy of the reactants is the most effective at passing the early barrier whereas vibrational energy of the reactants is the most effective at surmounting the late barrier.This reaction is endothermic, and hence it has a late barrier. In all the graphs, the reactants all have vibrational energy as indicated by the wavy line in the reactant channel.
==References==

<references>
<ref name="reference 1">R. DeKock and H. Gray, Chemical structure and bonding, Univeristy Science Books, 1989.</ref>
<ref name="reference 2">S. Jeffrey I., Experimental Chemical Dynamics, Prentice-Hall, Upper Saddle River, 2nd edn., 1989.</ref>
<ref name="reference 3">L. Keith J., Theories of reaction rates, Harper & Row, New York;London, 3rd edn., 1987.</ref>
<ref name="reference 4">D. Brougham, A. Horsewill and R. Jenkinson, Chemical Physics Letters, 1997, 272, 69-74.</ref>
<ref name="reference 5">6.S. Bradforth, D. Arnold, D. Neumark and D. Manolopoulos, The Journal of Chemical Physics, 1993, 99, 6345-6359.</ref>
</references>

MRD:01508310

2020-05-22T18:32:50Z

Hh2218: /* F+H2 system */

==H-H-H system==
===Dynamics from the transition state region===
The transition state is the point on the potential energy surface that has ∂V(ri)/∂ri=0, where ri is the distance between two atoms.The transition state is a local maximum and its second derivative ∂2V(ri)/∂ri2 is < 0, whereas a local minimum will have a positive second derivative instead.
[[File:Hhh_surfaceplot_01508.png|400px|thumb|centre|a potential energy surface plot of H and H2 with respect to interatomic distances.]]

===Trajectories from r1=r2: locating the transition state===
At the transition state, r1=r2=90.8 pm by estimation. At this separation, the forces acting along AB and BC are both -0.004 kJ.mol-1.pm-1, which is close to zero and the eigenvalues for the Hessian matrix were -0.028 and +0.167 kJ.mol-1.pm-2, indicating the presence of transition state. The Internuclear Distance vs Time plot suggests the distance between HA, HB and HC is equal, about 90 pm and the distance is constant over time suggests the atoms are static at the transition state.
[[File:Animation101508310.png|400px|centre|thumb|picture showing H and H2 at the transition state.]]
[[File:Optimisation1_01508310.png|400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:Internucleardistance_01508310.png|400px|centre|thumb|Internuclear Distance vs Time plot between the H atoms at the transition state.]]

===Calculating the reaction path===
When rA-B is set to rts+1 and rB-C equals rts,the transition rolls towards BC and HA remains as an atom. MEP and Dynamic reaction paths are different as MEP set the momenta to zero in every step of the reaction path, products are therefore static and hence the reaction path is relatively straight. The dynamic reaction path is more realistic. It takes the momenta of gaseous molecules into account,i.e. they have vibrational energies, that is illustrated by the wavy line along the reaction path.
[[File:Surface_Plot1mep_015083.png|400px|centre|thumb|the minimum energy path (mep) of the H-H-H system]]
[[File:01569348_MEP_AB1_dynamic.png|400px|centre|thumb|the dynamic reaction path of the H-H-H system]]

====MEP and Dynamics calculations comparisons====
'''r1=91.8 pm, r2=90.8 pm, momenta set to 0 g.mol-1.pm.fs-1'''

HB and HC form a H2 molecule whereas HA moves away from the molecule. The distance between B and C decreased to 74 pm, which is the hydrogen molecule bond length <ref name="reference 1"/>.In MEP calculation, the momenta are set to zero at each time step.

[[File:MepH2bondlength_01508.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using MEP calculation.]]

[[File:MepH2momenta015083.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using MEP calculation.]]

Using Dynamics calculation, the outcome of the reaction is the same. The transition state rolls towards HB and HC and a hydrogen molecule is formed. One noticeable difference is that the hydrogen molecule now has some vibational energy as indicated by the wavy line along the B-C distance in the Internuclear Distance vs Time plot.As for the Momenta vs Time plot, the system is linear, therefore the angle theta is zero. HA and HB are moving away from each other at '''an increasing velocity until the momentum reaches 5 g.mol-1.pm.fs-1.The oscillation along the B-C bond corresponds to the vibration of the bond. '''why does the beginning have negative momenta?'''
[[File:DynamicsH2_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation.]]
[[File:DynamicsH2monenta_01508.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using Dynamics calculation.]]

'''r1=90.8 pm, r2=91.8 pm, momenta set to 0 g.mol-1.pm.fs-1'''

Once the length of r1 and r2 switches, the shapes of the graphs are identical but instead of HB and HC forming a molecule, HA and HB now form the hydrogen molecule in the products.
[[File:Mepinter2_01508.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using MEP calculation.]]
[[File:Momentamep2_015.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using MEP calculation.]]
[[File:InterDynamic_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation.]]
[[File:Momentadynamics_015083.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using Dynamics calculation.]]

'''Trajectory starting with the final position and reversed momentum to the reaction path above'''

This trajectory starts at the end of the reaction path above and finishes at where the above reaction started. it is essentially a reverse of what happened in the reaction above.
[[File:Reverse_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation (r1=70.0 pm,r2=353 pm,p1=-3.21 g.mol-1.pm.fs-1, p2=-5.07 g.mol-1.pm.fs-1) .]]

===Recative and unreactive trajectories===
{| class="wikitable" border="1"
! p1/g.mol-1.pm.fs-1 !! p2/g.mol-1.pm.fs-1!! Etot/kJmol-1!! Recative?!! Description of the dynamics!! Illustration of the trajectory
|-
| -2.56 || -5.1||-414 || Yes||The translational energy of the reactants can surmount the potential energy barrier and form the products. The ramaining energy is converted into vibrational energy of the products. || [[File:Table1_01508310.png|350px ]]
|-
| -3.1 || -4.1||-420 || No||The reactant H2 has vibrational energy and its rAB motion is rapid. Before it could cross the energy barrier, the molecule slams into the repulsive inner wall of the potential surface and bounces back into the reactant channel. || [[File:Table2_0150.png|350px]]
|-
| -3.1 || -5.1||-414|| Yes||The reactants have both the translational and vibrational energies. The energy is used to surmount the potential energy barrier and converted into the vibrational energy of the products. || [[File:Table3_01508.png|350px]]
|-
| -5.1 || -10.1||-357 || No||The reactants have sufficient energy to cross the transition state and the products did form for a certain amount of time. However, before the the system can exit the product channel, it recrosses the transition state and form the reactants again, hence no reaction occurs. ||[[File:Table4_01508.png|350px]]
|-
| -5.1 || -10.6||-394 || Yes||The system has sufficient energy to cross the transition state but it recrosses the transition state shortly after the reaction path hits the potential energy surface. However, the system is able to cross the transition state for the third time and finally exits the product channel and forms the products. || [[File:-10.6_01508.png|350px]]
|-
|}
In order to form products, a system must have sufficient energy to cross the transition state. Only molecules with the correct phase <ref name="reference 2"/> can exit the product channel and form stable products. Recrossing the transition state can lead to either product formation or no reaction. It is possible to cross the transition state multiple times.

===Transition State Theory===

Transition State Theory is classical, it doesn't take quantum tunnelling into account.Quantum tunnelling is probable for this reaction as it involves the transfer of a hydrogen atom, particularly at lower temperatures <ref name="reference 3"/>.At low temperatures, the H atom can tunnel through the potential energy barrier than to pass over the barrier, hence the activation energy is lowered and the reaction rate increases. However, recrossing the energy barrier is possible as seen with the simulations, this can have a negative effect on the reaction rate. At high temperatures, the system is thermally activated and the behavious is approximately classical<ref name="reference 4"/>. Therefore the experimental reaction rates are expected to be greater than that predicted by the Transition State Theory.

==F-H-H system==
===PES inspection===
'''F+H2 (F1-H1-H2)'''

F+H2 is exothermic as the reactants are higher in energy than the products therefore during the reaction, energy is released to the surroundings. H-F bond is stronger than H-H bond as the products are lower in energy and therefore more stable.The transition state is located approximately at rF1-H1=181.10 pm and rH1-H2=74.49 pm. This is verified by the forces (close to zero) and eigenvalues for hessian matrix (they are of opposite signs). The activation energy is estimated by tilting the transition state towards the reactants and is shown to be 424 kJ.mol-1.
[[File:Fh2_015083.png |400px|centre|thumb|Surface plot for F1-H1-H2 system using Dynamic Calculation, the transition state is identified as the black dot.]]
[[File:OptimisationFhh1_01508.png|400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:F1H1H2_EA_0150.png|400px|centre|thumb|Counter plot for estimating the activation energy.]]
[[File:EA1_01508.png|400px|centre|thumb|parameters for the activation energy.]]
'''H+HF (H1-H2-F1)'''
This reaction is endothermis as the reactants are lower in energy than the products therefore energy is taken in from the surroundings to form the products. H-F bond is still stronger than H-H as the reactans are lower in energy and more stable. The transition state is located at approximately rH1-H2=280 pm and rH2-F1=92 pm. It is located with the same reasons stated above.With the same method, the activation energy is estimated to be 434 kJ.mol-1. The two activation energies should be identical as these two reactions are essentially the reverse of one another.

[[File:H+HF_01508310.png|400px|centre|thumb|Surface plot for H1-H2-F1 system using Dynamic Calculationthe, the transition state is identified as the black dot.]]
[[File:HHF_015083.png |400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:EA2_01508.png|400px|centre|thumb|Counter plot for estimating the activation energy.]]
[[File:EA2_PARAMETERS.png|400px|centre|thumb|parameters for the activation energy.]]

===Reaction dynamics===
===F+H2 system===

Initially, the reactants have kinetic energy in the form of vibrational and translational energies, and as it crosses the potential energy barrier, the kinetic energy is converted into potential energy. Once the system is exiting the product channel, the potential energy is converted into the vibrational energy of the product.One good experimental technique to prob the electronic structure of the reacting species will be IR spectroscopy.In the anharmonic oscillator model, exciting molecules in the relaxed state promotes excitation from the ground state to the first energy level mainly. This will give rise to a single peak in the IR spectrum. Howver, when exciting a sample of excited molecules, many transitions are possible. For example, from 0-->1, the fundamental or 1-->2, the first overtone. They will show up in the spectrum as 2 peaks, with the overtone being at a lower wavenumber as the energy gap decreases up the potential well. The intensity of the overtone decreases over time as the electrons can fall back to lower energy levels and energy is emitted as radiation. As this system is linear, rotational is not important electronic energy is not considered here.Photoelectron spectroscopy is also a viable method. <ref name="reference 5"/>

[[File:Reactiondynamicsfh2_0150.png||400px|centre|thumb|contour plot for F+H2.]]
[[File:Reactiondynamicsparameter——015.png |400px|centre|thumb|parameters for the reactive trajectory.]]
====Varying the momentum of HH in the F+H2 system.====
Conditions:rFH=182 pm, rHH=74 pm, PFH=-1.0g.mol-1.pm.fs-1
{| class="wikitable" border="1"
|+ caption
|-
|PHH/g.mol-1.pm.fs-1|| Contour Plot
|-
|0 || [[File:0_015083.png |400 px|centre]]
|-
|2 || [[File:2_0508.png |400 px|centre]]
|-
|4 || [[File:4_01508.png ‎|400 px|centre]]
|-
|6.1|| [[File:6_01508.png|400 px|centre]]
|-
| -2|| [[File:-2_01508.png|400 px|centre]]
|-
| -4|| [[File:-4.1_01508.png‎|400 px|centre]]
|-
| -6.1|| [[File:Fit1_01508.png|400 px|centre]]
|-
|}
Although the amount of energy that is put into H-H vibration is much more than the activation energy of the reaction, the reaction does not always occur. The large amount of energy is demonstrated by the high frequency of those wavy lines. Recrossing the transition states multiple times can lead to no reaction or product formation depending on how the tragectory collides with the potential well.

[[File:Reactiondynamic_last01588.png|400px|centre|thumb|contour plot for rFH=182 pm, fHH=74 pm, PFH=-1.6g.mol-1.pm.fs-1,PHH=0.2g.mol-1.pm.fs-1]]
The system now has much less vibrational energy into the reactants than before. The reaction is still successful and the trajectory recrosses the transition states fewer times than before.This can be explained by the increased momentum of FH so that F can approach the closest H with more vibrational energy.

===H+HF system===
{| class="wikitable" border="1"
!Graph Number!! p1(HH)/g.mol-1.pm.fs-1 !! p2(HF)/g.mol-1.pm.fs-1!! Etot/kJmol-1!! Recative?!! Illustration of the trajectory
|-
|1|| -2 || -10||-397|| No|| [[File:Final1_01508.png|350px ]]
|-
|2|| 0|| -8||-400 || No|| [[File:Final2_015.png|350px]]
|-
|3||5 || -6||-360|| No|| [[File:Final3_015.png|350px]]
|-
|4|| 5 || -3||-389 || Yes||[[File:Final4_015.png|350px]]
|-
|}

by referening to Polanyl's empirical rules, an exothermic reaction has an early barrier, which happens in the entrance channel. It tends to favour vibrational excitation of the products. On the other hand, an endothermic reaction has a late barrier, which occurs in the product channel. It tends to favour low product vibrational excitation. The location of the energy barrier is also crucial for a successful reaction. Translational energy of the reactants is the most effective at passing the early barrier whereas vibrational energy of the reactants is the most effective at surmounting the late barrier.This reaction is endothermic, and hence it has a late barrier. In all the graphs, the reactants all have vibrational energy as indicated by the wavy line in the reactant channel.
==References==

<references>
<ref name="reference 1">R. DeKock and H. Gray, Chemical structure and bonding, Univeristy Science Books, 1989.</ref>
<ref name="reference 2">S. Jeffrey I., Experimental Chemical Dynamics, Prentice-Hall, Upper Saddle River, 2nd edn., 1989.</ref>
<ref name="reference 3">L. Keith J., Theories of reaction rates, Harper & Row, New York;London, 3rd edn., 1987.</ref>
<ref name="reference 4">D. Brougham, A. Horsewill and R. Jenkinson, Chemical Physics Letters, 1997, 272, 69-74.</ref>
</references>

MRD:01508310

2020-05-22T18:32:09Z

Hh2218: /* References */

==H-H-H system==
===Dynamics from the transition state region===
The transition state is the point on the potential energy surface that has ∂V(ri)/∂ri=0, where ri is the distance between two atoms.The transition state is a local maximum and its second derivative ∂2V(ri)/∂ri2 is < 0, whereas a local minimum will have a positive second derivative instead.
[[File:Hhh_surfaceplot_01508.png|400px|thumb|centre|a potential energy surface plot of H and H2 with respect to interatomic distances.]]

===Trajectories from r1=r2: locating the transition state===
At the transition state, r1=r2=90.8 pm by estimation. At this separation, the forces acting along AB and BC are both -0.004 kJ.mol-1.pm-1, which is close to zero and the eigenvalues for the Hessian matrix were -0.028 and +0.167 kJ.mol-1.pm-2, indicating the presence of transition state. The Internuclear Distance vs Time plot suggests the distance between HA, HB and HC is equal, about 90 pm and the distance is constant over time suggests the atoms are static at the transition state.
[[File:Animation101508310.png|400px|centre|thumb|picture showing H and H2 at the transition state.]]
[[File:Optimisation1_01508310.png|400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:Internucleardistance_01508310.png|400px|centre|thumb|Internuclear Distance vs Time plot between the H atoms at the transition state.]]

===Calculating the reaction path===
When rA-B is set to rts+1 and rB-C equals rts,the transition rolls towards BC and HA remains as an atom. MEP and Dynamic reaction paths are different as MEP set the momenta to zero in every step of the reaction path, products are therefore static and hence the reaction path is relatively straight. The dynamic reaction path is more realistic. It takes the momenta of gaseous molecules into account,i.e. they have vibrational energies, that is illustrated by the wavy line along the reaction path.
[[File:Surface_Plot1mep_015083.png|400px|centre|thumb|the minimum energy path (mep) of the H-H-H system]]
[[File:01569348_MEP_AB1_dynamic.png|400px|centre|thumb|the dynamic reaction path of the H-H-H system]]

====MEP and Dynamics calculations comparisons====
'''r1=91.8 pm, r2=90.8 pm, momenta set to 0 g.mol-1.pm.fs-1'''

HB and HC form a H2 molecule whereas HA moves away from the molecule. The distance between B and C decreased to 74 pm, which is the hydrogen molecule bond length <ref name="reference 1"/>.In MEP calculation, the momenta are set to zero at each time step.

[[File:MepH2bondlength_01508.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using MEP calculation.]]

[[File:MepH2momenta015083.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using MEP calculation.]]

Using Dynamics calculation, the outcome of the reaction is the same. The transition state rolls towards HB and HC and a hydrogen molecule is formed. One noticeable difference is that the hydrogen molecule now has some vibational energy as indicated by the wavy line along the B-C distance in the Internuclear Distance vs Time plot.As for the Momenta vs Time plot, the system is linear, therefore the angle theta is zero. HA and HB are moving away from each other at '''an increasing velocity until the momentum reaches 5 g.mol-1.pm.fs-1.The oscillation along the B-C bond corresponds to the vibration of the bond. '''why does the beginning have negative momenta?'''
[[File:DynamicsH2_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation.]]
[[File:DynamicsH2monenta_01508.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using Dynamics calculation.]]

'''r1=90.8 pm, r2=91.8 pm, momenta set to 0 g.mol-1.pm.fs-1'''

Once the length of r1 and r2 switches, the shapes of the graphs are identical but instead of HB and HC forming a molecule, HA and HB now form the hydrogen molecule in the products.
[[File:Mepinter2_01508.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using MEP calculation.]]
[[File:Momentamep2_015.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using MEP calculation.]]
[[File:InterDynamic_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation.]]
[[File:Momentadynamics_015083.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using Dynamics calculation.]]

'''Trajectory starting with the final position and reversed momentum to the reaction path above'''

This trajectory starts at the end of the reaction path above and finishes at where the above reaction started. it is essentially a reverse of what happened in the reaction above.
[[File:Reverse_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation (r1=70.0 pm,r2=353 pm,p1=-3.21 g.mol-1.pm.fs-1, p2=-5.07 g.mol-1.pm.fs-1) .]]

===Recative and unreactive trajectories===
{| class="wikitable" border="1"
! p1/g.mol-1.pm.fs-1 !! p2/g.mol-1.pm.fs-1!! Etot/kJmol-1!! Recative?!! Description of the dynamics!! Illustration of the trajectory
|-
| -2.56 || -5.1||-414 || Yes||The translational energy of the reactants can surmount the potential energy barrier and form the products. The ramaining energy is converted into vibrational energy of the products. || [[File:Table1_01508310.png|350px ]]
|-
| -3.1 || -4.1||-420 || No||The reactant H2 has vibrational energy and its rAB motion is rapid. Before it could cross the energy barrier, the molecule slams into the repulsive inner wall of the potential surface and bounces back into the reactant channel. || [[File:Table2_0150.png|350px]]
|-
| -3.1 || -5.1||-414|| Yes||The reactants have both the translational and vibrational energies. The energy is used to surmount the potential energy barrier and converted into the vibrational energy of the products. || [[File:Table3_01508.png|350px]]
|-
| -5.1 || -10.1||-357 || No||The reactants have sufficient energy to cross the transition state and the products did form for a certain amount of time. However, before the the system can exit the product channel, it recrosses the transition state and form the reactants again, hence no reaction occurs. ||[[File:Table4_01508.png|350px]]
|-
| -5.1 || -10.6||-394 || Yes||The system has sufficient energy to cross the transition state but it recrosses the transition state shortly after the reaction path hits the potential energy surface. However, the system is able to cross the transition state for the third time and finally exits the product channel and forms the products. || [[File:-10.6_01508.png|350px]]
|-
|}
In order to form products, a system must have sufficient energy to cross the transition state. Only molecules with the correct phase <ref name="reference 2"/> can exit the product channel and form stable products. Recrossing the transition state can lead to either product formation or no reaction. It is possible to cross the transition state multiple times.

===Transition State Theory===

Transition State Theory is classical, it doesn't take quantum tunnelling into account.Quantum tunnelling is probable for this reaction as it involves the transfer of a hydrogen atom, particularly at lower temperatures <ref name="reference 3"/>.At low temperatures, the H atom can tunnel through the potential energy barrier than to pass over the barrier, hence the activation energy is lowered and the reaction rate increases. However, recrossing the energy barrier is possible as seen with the simulations, this can have a negative effect on the reaction rate. At high temperatures, the system is thermally activated and the behavious is approximately classical<ref name="reference 4"/>. Therefore the experimental reaction rates are expected to be greater than that predicted by the Transition State Theory.

==F-H-H system==
===PES inspection===
'''F+H2 (F1-H1-H2)'''

F+H2 is exothermic as the reactants are higher in energy than the products therefore during the reaction, energy is released to the surroundings. H-F bond is stronger than H-H bond as the products are lower in energy and therefore more stable.The transition state is located approximately at rF1-H1=181.10 pm and rH1-H2=74.49 pm. This is verified by the forces (close to zero) and eigenvalues for hessian matrix (they are of opposite signs). The activation energy is estimated by tilting the transition state towards the reactants and is shown to be 424 kJ.mol-1.
[[File:Fh2_015083.png |400px|centre|thumb|Surface plot for F1-H1-H2 system using Dynamic Calculation, the transition state is identified as the black dot.]]
[[File:OptimisationFhh1_01508.png|400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:F1H1H2_EA_0150.png|400px|centre|thumb|Counter plot for estimating the activation energy.]]
[[File:EA1_01508.png|400px|centre|thumb|parameters for the activation energy.]]
'''H+HF (H1-H2-F1)'''
This reaction is endothermis as the reactants are lower in energy than the products therefore energy is taken in from the surroundings to form the products. H-F bond is still stronger than H-H as the reactans are lower in energy and more stable. The transition state is located at approximately rH1-H2=280 pm and rH2-F1=92 pm. It is located with the same reasons stated above.With the same method, the activation energy is estimated to be 434 kJ.mol-1. The two activation energies should be identical as these two reactions are essentially the reverse of one another.

[[File:H+HF_01508310.png|400px|centre|thumb|Surface plot for H1-H2-F1 system using Dynamic Calculationthe, the transition state is identified as the black dot.]]
[[File:HHF_015083.png |400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:EA2_01508.png|400px|centre|thumb|Counter plot for estimating the activation energy.]]
[[File:EA2_PARAMETERS.png|400px|centre|thumb|parameters for the activation energy.]]

===Reaction dynamics===
===F+H2 system===

Initially, the reactants have kinetic energy in the form of vibrational and translational energies, and as it crosses the potential energy barrier, the kinetic energy is converted into potential energy. Once the system is exiting the product channel, the potential energy is converted into the vibrational energy of the product.One good experimental technique to prob the electronic structure of the reacting species will be IR spectroscopy.In the anharmonic oscillator model, exciting molecules in the relaxed state promotes excitation from the ground state to the first energy level mainly. This will give rise to a single peak in the IR spectrum. Howver, when exciting a sample of excited molecules, many transitions are possible. For example, from 0-->1, the fundamental or 1-->2, the first overtone. They will show up in the spectrum as 2 peaks, with the overtone being at a lower wavenumber as the energy gap decreases up the potential well. The intensity of the overtone decreases over time as the electrons can fall back to lower energy levels and energy is emitted as radiation. As this system is linear, rotational is not important electronic energy is not considered here.Photoelectron spectroscopy is also a viable method. '''reference 5'''

[[File:Reactiondynamicsfh2_0150.png||400px|centre|thumb|contour plot for F+H2.]]
[[File:Reactiondynamicsparameter——015.png |400px|centre|thumb|parameters for the reactive trajectory.]]
====Varying the momentum of HH in the F+H2 system.====
Conditions:rFH=182 pm, rHH=74 pm, PFH=-1.0g.mol-1.pm.fs-1
{| class="wikitable" border="1"
|+ caption
|-
|PHH/g.mol-1.pm.fs-1|| Contour Plot
|-
|0 || [[File:0_015083.png |400 px|centre]]
|-
|2 || [[File:2_0508.png |400 px|centre]]
|-
|4 || [[File:4_01508.png ‎|400 px|centre]]
|-
|6.1|| [[File:6_01508.png|400 px|centre]]
|-
| -2|| [[File:-2_01508.png|400 px|centre]]
|-
| -4|| [[File:-4.1_01508.png‎|400 px|centre]]
|-
| -6.1|| [[File:Fit1_01508.png|400 px|centre]]
|-
|}
Although the amount of energy that is put into H-H vibration is much more than the activation energy of the reaction, the reaction does not always occur. The large amount of energy is demonstrated by the high frequency of those wavy lines. Recrossing the transition states multiple times can lead to no reaction or product formation depending on how the tragectory collides with the potential well.

[[File:Reactiondynamic_last01588.png|400px|centre|thumb|contour plot for rFH=182 pm, fHH=74 pm, PFH=-1.6g.mol-1.pm.fs-1,PHH=0.2g.mol-1.pm.fs-1]]
The system now has much less vibrational energy into the reactants than before. The reaction is still successful and the trajectory recrosses the transition states fewer times than before.This can be explained by the increased momentum of FH so that F can approach the closest H with more vibrational energy.

===H+HF system===
{| class="wikitable" border="1"
!Graph Number!! p1(HH)/g.mol-1.pm.fs-1 !! p2(HF)/g.mol-1.pm.fs-1!! Etot/kJmol-1!! Recative?!! Illustration of the trajectory
|-
|1|| -2 || -10||-397|| No|| [[File:Final1_01508.png|350px ]]
|-
|2|| 0|| -8||-400 || No|| [[File:Final2_015.png|350px]]
|-
|3||5 || -6||-360|| No|| [[File:Final3_015.png|350px]]
|-
|4|| 5 || -3||-389 || Yes||[[File:Final4_015.png|350px]]
|-
|}

by referening to Polanyl's empirical rules, an exothermic reaction has an early barrier, which happens in the entrance channel. It tends to favour vibrational excitation of the products. On the other hand, an endothermic reaction has a late barrier, which occurs in the product channel. It tends to favour low product vibrational excitation. The location of the energy barrier is also crucial for a successful reaction. Translational energy of the reactants is the most effective at passing the early barrier whereas vibrational energy of the reactants is the most effective at surmounting the late barrier.This reaction is endothermic, and hence it has a late barrier. In all the graphs, the reactants all have vibrational energy as indicated by the wavy line in the reactant channel.
==References==

<references>
<ref name="reference 1">R. DeKock and H. Gray, Chemical structure and bonding, Univeristy Science Books, 1989.</ref>
<ref name="reference 2">S. Jeffrey I., Experimental Chemical Dynamics, Prentice-Hall, Upper Saddle River, 2nd edn., 1989.</ref>
<ref name="reference 3">L. Keith J., Theories of reaction rates, Harper & Row, New York;London, 3rd edn., 1987.</ref>
<ref name="reference 4">D. Brougham, A. Horsewill and R. Jenkinson, Chemical Physics Letters, 1997, 272, 69-74.</ref>
</references>

MRD:01508310

2020-05-22T18:31:02Z

Hh2218: /* Transition State Theory */

==H-H-H system==
===Dynamics from the transition state region===
The transition state is the point on the potential energy surface that has ∂V(ri)/∂ri=0, where ri is the distance between two atoms.The transition state is a local maximum and its second derivative ∂2V(ri)/∂ri2 is < 0, whereas a local minimum will have a positive second derivative instead.
[[File:Hhh_surfaceplot_01508.png|400px|thumb|centre|a potential energy surface plot of H and H2 with respect to interatomic distances.]]

===Trajectories from r1=r2: locating the transition state===
At the transition state, r1=r2=90.8 pm by estimation. At this separation, the forces acting along AB and BC are both -0.004 kJ.mol-1.pm-1, which is close to zero and the eigenvalues for the Hessian matrix were -0.028 and +0.167 kJ.mol-1.pm-2, indicating the presence of transition state. The Internuclear Distance vs Time plot suggests the distance between HA, HB and HC is equal, about 90 pm and the distance is constant over time suggests the atoms are static at the transition state.
[[File:Animation101508310.png|400px|centre|thumb|picture showing H and H2 at the transition state.]]
[[File:Optimisation1_01508310.png|400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:Internucleardistance_01508310.png|400px|centre|thumb|Internuclear Distance vs Time plot between the H atoms at the transition state.]]

===Calculating the reaction path===
When rA-B is set to rts+1 and rB-C equals rts,the transition rolls towards BC and HA remains as an atom. MEP and Dynamic reaction paths are different as MEP set the momenta to zero in every step of the reaction path, products are therefore static and hence the reaction path is relatively straight. The dynamic reaction path is more realistic. It takes the momenta of gaseous molecules into account,i.e. they have vibrational energies, that is illustrated by the wavy line along the reaction path.
[[File:Surface_Plot1mep_015083.png|400px|centre|thumb|the minimum energy path (mep) of the H-H-H system]]
[[File:01569348_MEP_AB1_dynamic.png|400px|centre|thumb|the dynamic reaction path of the H-H-H system]]

====MEP and Dynamics calculations comparisons====
'''r1=91.8 pm, r2=90.8 pm, momenta set to 0 g.mol-1.pm.fs-1'''

HB and HC form a H2 molecule whereas HA moves away from the molecule. The distance between B and C decreased to 74 pm, which is the hydrogen molecule bond length <ref name="reference 1"/>.In MEP calculation, the momenta are set to zero at each time step.

[[File:MepH2bondlength_01508.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using MEP calculation.]]

[[File:MepH2momenta015083.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using MEP calculation.]]

Using Dynamics calculation, the outcome of the reaction is the same. The transition state rolls towards HB and HC and a hydrogen molecule is formed. One noticeable difference is that the hydrogen molecule now has some vibational energy as indicated by the wavy line along the B-C distance in the Internuclear Distance vs Time plot.As for the Momenta vs Time plot, the system is linear, therefore the angle theta is zero. HA and HB are moving away from each other at '''an increasing velocity until the momentum reaches 5 g.mol-1.pm.fs-1.The oscillation along the B-C bond corresponds to the vibration of the bond. '''why does the beginning have negative momenta?'''
[[File:DynamicsH2_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation.]]
[[File:DynamicsH2monenta_01508.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using Dynamics calculation.]]

'''r1=90.8 pm, r2=91.8 pm, momenta set to 0 g.mol-1.pm.fs-1'''

Once the length of r1 and r2 switches, the shapes of the graphs are identical but instead of HB and HC forming a molecule, HA and HB now form the hydrogen molecule in the products.
[[File:Mepinter2_01508.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using MEP calculation.]]
[[File:Momentamep2_015.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using MEP calculation.]]
[[File:InterDynamic_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation.]]
[[File:Momentadynamics_015083.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using Dynamics calculation.]]

'''Trajectory starting with the final position and reversed momentum to the reaction path above'''

This trajectory starts at the end of the reaction path above and finishes at where the above reaction started. it is essentially a reverse of what happened in the reaction above.
[[File:Reverse_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation (r1=70.0 pm,r2=353 pm,p1=-3.21 g.mol-1.pm.fs-1, p2=-5.07 g.mol-1.pm.fs-1) .]]

===Recative and unreactive trajectories===
{| class="wikitable" border="1"
! p1/g.mol-1.pm.fs-1 !! p2/g.mol-1.pm.fs-1!! Etot/kJmol-1!! Recative?!! Description of the dynamics!! Illustration of the trajectory
|-
| -2.56 || -5.1||-414 || Yes||The translational energy of the reactants can surmount the potential energy barrier and form the products. The ramaining energy is converted into vibrational energy of the products. || [[File:Table1_01508310.png|350px ]]
|-
| -3.1 || -4.1||-420 || No||The reactant H2 has vibrational energy and its rAB motion is rapid. Before it could cross the energy barrier, the molecule slams into the repulsive inner wall of the potential surface and bounces back into the reactant channel. || [[File:Table2_0150.png|350px]]
|-
| -3.1 || -5.1||-414|| Yes||The reactants have both the translational and vibrational energies. The energy is used to surmount the potential energy barrier and converted into the vibrational energy of the products. || [[File:Table3_01508.png|350px]]
|-
| -5.1 || -10.1||-357 || No||The reactants have sufficient energy to cross the transition state and the products did form for a certain amount of time. However, before the the system can exit the product channel, it recrosses the transition state and form the reactants again, hence no reaction occurs. ||[[File:Table4_01508.png|350px]]
|-
| -5.1 || -10.6||-394 || Yes||The system has sufficient energy to cross the transition state but it recrosses the transition state shortly after the reaction path hits the potential energy surface. However, the system is able to cross the transition state for the third time and finally exits the product channel and forms the products. || [[File:-10.6_01508.png|350px]]
|-
|}
In order to form products, a system must have sufficient energy to cross the transition state. Only molecules with the correct phase <ref name="reference 2"/> can exit the product channel and form stable products. Recrossing the transition state can lead to either product formation or no reaction. It is possible to cross the transition state multiple times.

===Transition State Theory===

Transition State Theory is classical, it doesn't take quantum tunnelling into account.Quantum tunnelling is probable for this reaction as it involves the transfer of a hydrogen atom, particularly at lower temperatures <ref name="reference 3"/>.At low temperatures, the H atom can tunnel through the potential energy barrier than to pass over the barrier, hence the activation energy is lowered and the reaction rate increases. However, recrossing the energy barrier is possible as seen with the simulations, this can have a negative effect on the reaction rate. At high temperatures, the system is thermally activated and the behavious is approximately classical<ref name="reference 4"/>. Therefore the experimental reaction rates are expected to be greater than that predicted by the Transition State Theory.

==F-H-H system==
===PES inspection===
'''F+H2 (F1-H1-H2)'''

F+H2 is exothermic as the reactants are higher in energy than the products therefore during the reaction, energy is released to the surroundings. H-F bond is stronger than H-H bond as the products are lower in energy and therefore more stable.The transition state is located approximately at rF1-H1=181.10 pm and rH1-H2=74.49 pm. This is verified by the forces (close to zero) and eigenvalues for hessian matrix (they are of opposite signs). The activation energy is estimated by tilting the transition state towards the reactants and is shown to be 424 kJ.mol-1.
[[File:Fh2_015083.png |400px|centre|thumb|Surface plot for F1-H1-H2 system using Dynamic Calculation, the transition state is identified as the black dot.]]
[[File:OptimisationFhh1_01508.png|400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:F1H1H2_EA_0150.png|400px|centre|thumb|Counter plot for estimating the activation energy.]]
[[File:EA1_01508.png|400px|centre|thumb|parameters for the activation energy.]]
'''H+HF (H1-H2-F1)'''
This reaction is endothermis as the reactants are lower in energy than the products therefore energy is taken in from the surroundings to form the products. H-F bond is still stronger than H-H as the reactans are lower in energy and more stable. The transition state is located at approximately rH1-H2=280 pm and rH2-F1=92 pm. It is located with the same reasons stated above.With the same method, the activation energy is estimated to be 434 kJ.mol-1. The two activation energies should be identical as these two reactions are essentially the reverse of one another.

[[File:H+HF_01508310.png|400px|centre|thumb|Surface plot for H1-H2-F1 system using Dynamic Calculationthe, the transition state is identified as the black dot.]]
[[File:HHF_015083.png |400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:EA2_01508.png|400px|centre|thumb|Counter plot for estimating the activation energy.]]
[[File:EA2_PARAMETERS.png|400px|centre|thumb|parameters for the activation energy.]]

===Reaction dynamics===
===F+H2 system===

Initially, the reactants have kinetic energy in the form of vibrational and translational energies, and as it crosses the potential energy barrier, the kinetic energy is converted into potential energy. Once the system is exiting the product channel, the potential energy is converted into the vibrational energy of the product.One good experimental technique to prob the electronic structure of the reacting species will be IR spectroscopy.In the anharmonic oscillator model, exciting molecules in the relaxed state promotes excitation from the ground state to the first energy level mainly. This will give rise to a single peak in the IR spectrum. Howver, when exciting a sample of excited molecules, many transitions are possible. For example, from 0-->1, the fundamental or 1-->2, the first overtone. They will show up in the spectrum as 2 peaks, with the overtone being at a lower wavenumber as the energy gap decreases up the potential well. The intensity of the overtone decreases over time as the electrons can fall back to lower energy levels and energy is emitted as radiation. As this system is linear, rotational is not important electronic energy is not considered here.Photoelectron spectroscopy is also a viable method. '''reference 5'''

[[File:Reactiondynamicsfh2_0150.png||400px|centre|thumb|contour plot for F+H2.]]
[[File:Reactiondynamicsparameter——015.png |400px|centre|thumb|parameters for the reactive trajectory.]]
====Varying the momentum of HH in the F+H2 system.====
Conditions:rFH=182 pm, rHH=74 pm, PFH=-1.0g.mol-1.pm.fs-1
{| class="wikitable" border="1"
|+ caption
|-
|PHH/g.mol-1.pm.fs-1|| Contour Plot
|-
|0 || [[File:0_015083.png |400 px|centre]]
|-
|2 || [[File:2_0508.png |400 px|centre]]
|-
|4 || [[File:4_01508.png ‎|400 px|centre]]
|-
|6.1|| [[File:6_01508.png|400 px|centre]]
|-
| -2|| [[File:-2_01508.png|400 px|centre]]
|-
| -4|| [[File:-4.1_01508.png‎|400 px|centre]]
|-
| -6.1|| [[File:Fit1_01508.png|400 px|centre]]
|-
|}
Although the amount of energy that is put into H-H vibration is much more than the activation energy of the reaction, the reaction does not always occur. The large amount of energy is demonstrated by the high frequency of those wavy lines. Recrossing the transition states multiple times can lead to no reaction or product formation depending on how the tragectory collides with the potential well.

[[File:Reactiondynamic_last01588.png|400px|centre|thumb|contour plot for rFH=182 pm, fHH=74 pm, PFH=-1.6g.mol-1.pm.fs-1,PHH=0.2g.mol-1.pm.fs-1]]
The system now has much less vibrational energy into the reactants than before. The reaction is still successful and the trajectory recrosses the transition states fewer times than before.This can be explained by the increased momentum of FH so that F can approach the closest H with more vibrational energy.

===H+HF system===
{| class="wikitable" border="1"
!Graph Number!! p1(HH)/g.mol-1.pm.fs-1 !! p2(HF)/g.mol-1.pm.fs-1!! Etot/kJmol-1!! Recative?!! Illustration of the trajectory
|-
|1|| -2 || -10||-397|| No|| [[File:Final1_01508.png|350px ]]
|-
|2|| 0|| -8||-400 || No|| [[File:Final2_015.png|350px]]
|-
|3||5 || -6||-360|| No|| [[File:Final3_015.png|350px]]
|-
|4|| 5 || -3||-389 || Yes||[[File:Final4_015.png|350px]]
|-
|}

by referening to Polanyl's empirical rules, an exothermic reaction has an early barrier, which happens in the entrance channel. It tends to favour vibrational excitation of the products. On the other hand, an endothermic reaction has a late barrier, which occurs in the product channel. It tends to favour low product vibrational excitation. The location of the energy barrier is also crucial for a successful reaction. Translational energy of the reactants is the most effective at passing the early barrier whereas vibrational energy of the reactants is the most effective at surmounting the late barrier.This reaction is endothermic, and hence it has a late barrier. In all the graphs, the reactants all have vibrational energy as indicated by the wavy line in the reactant channel.
==References==

<references>
<ref name="reference 1">R. DeKock and H. Gray, Chemical structure and bonding, Univeristy Science Books, 1989.</ref>
<ref name="reference 2">S. Jeffrey I., Experimental Chemical Dynamics, Prentice-Hall, Upper Saddle River, 2nd edn., 1989.</ref>
</references>

MRD:01508310

2020-05-22T18:29:05Z

Hh2218: /* References */

==H-H-H system==
===Dynamics from the transition state region===
The transition state is the point on the potential energy surface that has ∂V(ri)/∂ri=0, where ri is the distance between two atoms.The transition state is a local maximum and its second derivative ∂2V(ri)/∂ri2 is < 0, whereas a local minimum will have a positive second derivative instead.
[[File:Hhh_surfaceplot_01508.png|400px|thumb|centre|a potential energy surface plot of H and H2 with respect to interatomic distances.]]

===Trajectories from r1=r2: locating the transition state===
At the transition state, r1=r2=90.8 pm by estimation. At this separation, the forces acting along AB and BC are both -0.004 kJ.mol-1.pm-1, which is close to zero and the eigenvalues for the Hessian matrix were -0.028 and +0.167 kJ.mol-1.pm-2, indicating the presence of transition state. The Internuclear Distance vs Time plot suggests the distance between HA, HB and HC is equal, about 90 pm and the distance is constant over time suggests the atoms are static at the transition state.
[[File:Animation101508310.png|400px|centre|thumb|picture showing H and H2 at the transition state.]]
[[File:Optimisation1_01508310.png|400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:Internucleardistance_01508310.png|400px|centre|thumb|Internuclear Distance vs Time plot between the H atoms at the transition state.]]

===Calculating the reaction path===
When rA-B is set to rts+1 and rB-C equals rts,the transition rolls towards BC and HA remains as an atom. MEP and Dynamic reaction paths are different as MEP set the momenta to zero in every step of the reaction path, products are therefore static and hence the reaction path is relatively straight. The dynamic reaction path is more realistic. It takes the momenta of gaseous molecules into account,i.e. they have vibrational energies, that is illustrated by the wavy line along the reaction path.
[[File:Surface_Plot1mep_015083.png|400px|centre|thumb|the minimum energy path (mep) of the H-H-H system]]
[[File:01569348_MEP_AB1_dynamic.png|400px|centre|thumb|the dynamic reaction path of the H-H-H system]]

====MEP and Dynamics calculations comparisons====
'''r1=91.8 pm, r2=90.8 pm, momenta set to 0 g.mol-1.pm.fs-1'''

HB and HC form a H2 molecule whereas HA moves away from the molecule. The distance between B and C decreased to 74 pm, which is the hydrogen molecule bond length <ref name="reference 1"/>.In MEP calculation, the momenta are set to zero at each time step.

[[File:MepH2bondlength_01508.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using MEP calculation.]]

[[File:MepH2momenta015083.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using MEP calculation.]]

Using Dynamics calculation, the outcome of the reaction is the same. The transition state rolls towards HB and HC and a hydrogen molecule is formed. One noticeable difference is that the hydrogen molecule now has some vibational energy as indicated by the wavy line along the B-C distance in the Internuclear Distance vs Time plot.As for the Momenta vs Time plot, the system is linear, therefore the angle theta is zero. HA and HB are moving away from each other at '''an increasing velocity until the momentum reaches 5 g.mol-1.pm.fs-1.The oscillation along the B-C bond corresponds to the vibration of the bond. '''why does the beginning have negative momenta?'''
[[File:DynamicsH2_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation.]]
[[File:DynamicsH2monenta_01508.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using Dynamics calculation.]]

'''r1=90.8 pm, r2=91.8 pm, momenta set to 0 g.mol-1.pm.fs-1'''

Once the length of r1 and r2 switches, the shapes of the graphs are identical but instead of HB and HC forming a molecule, HA and HB now form the hydrogen molecule in the products.
[[File:Mepinter2_01508.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using MEP calculation.]]
[[File:Momentamep2_015.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using MEP calculation.]]
[[File:InterDynamic_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation.]]
[[File:Momentadynamics_015083.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using Dynamics calculation.]]

'''Trajectory starting with the final position and reversed momentum to the reaction path above'''

This trajectory starts at the end of the reaction path above and finishes at where the above reaction started. it is essentially a reverse of what happened in the reaction above.
[[File:Reverse_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation (r1=70.0 pm,r2=353 pm,p1=-3.21 g.mol-1.pm.fs-1, p2=-5.07 g.mol-1.pm.fs-1) .]]

===Recative and unreactive trajectories===
{| class="wikitable" border="1"
! p1/g.mol-1.pm.fs-1 !! p2/g.mol-1.pm.fs-1!! Etot/kJmol-1!! Recative?!! Description of the dynamics!! Illustration of the trajectory
|-
| -2.56 || -5.1||-414 || Yes||The translational energy of the reactants can surmount the potential energy barrier and form the products. The ramaining energy is converted into vibrational energy of the products. || [[File:Table1_01508310.png|350px ]]
|-
| -3.1 || -4.1||-420 || No||The reactant H2 has vibrational energy and its rAB motion is rapid. Before it could cross the energy barrier, the molecule slams into the repulsive inner wall of the potential surface and bounces back into the reactant channel. || [[File:Table2_0150.png|350px]]
|-
| -3.1 || -5.1||-414|| Yes||The reactants have both the translational and vibrational energies. The energy is used to surmount the potential energy barrier and converted into the vibrational energy of the products. || [[File:Table3_01508.png|350px]]
|-
| -5.1 || -10.1||-357 || No||The reactants have sufficient energy to cross the transition state and the products did form for a certain amount of time. However, before the the system can exit the product channel, it recrosses the transition state and form the reactants again, hence no reaction occurs. ||[[File:Table4_01508.png|350px]]
|-
| -5.1 || -10.6||-394 || Yes||The system has sufficient energy to cross the transition state but it recrosses the transition state shortly after the reaction path hits the potential energy surface. However, the system is able to cross the transition state for the third time and finally exits the product channel and forms the products. || [[File:-10.6_01508.png|350px]]
|-
|}
In order to form products, a system must have sufficient energy to cross the transition state. Only molecules with the correct phase <ref name="reference 2"/> can exit the product channel and form stable products. Recrossing the transition state can lead to either product formation or no reaction. It is possible to cross the transition state multiple times.

===Transition State Theory===

Transition State Theory is classical, it doesn't take quantum tunnelling into account.Quantum tunnelling is probable for this reaction as it involves the transfer of a hydrogen atom, particularly at lower temperatures.'''Reference 3'''At low temperatures, the H atom can tunnel through the potential energy barrier than to pass over the barrier, hence the activation energy is lowered and the reaction rate increases. However, recrossing the energy barrier is possible as seen with the simulations, this can have a negative effect on the reaction rate. At high temperatures, the system is thermally activated and the behavious is approximately classical.'''reference4''' Therefore the experimental reaction rates are expected to be greater than that predicted by the Transition State Theory.

==F-H-H system==
===PES inspection===
'''F+H2 (F1-H1-H2)'''

F+H2 is exothermic as the reactants are higher in energy than the products therefore during the reaction, energy is released to the surroundings. H-F bond is stronger than H-H bond as the products are lower in energy and therefore more stable.The transition state is located approximately at rF1-H1=181.10 pm and rH1-H2=74.49 pm. This is verified by the forces (close to zero) and eigenvalues for hessian matrix (they are of opposite signs). The activation energy is estimated by tilting the transition state towards the reactants and is shown to be 424 kJ.mol-1.
[[File:Fh2_015083.png |400px|centre|thumb|Surface plot for F1-H1-H2 system using Dynamic Calculation, the transition state is identified as the black dot.]]
[[File:OptimisationFhh1_01508.png|400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:F1H1H2_EA_0150.png|400px|centre|thumb|Counter plot for estimating the activation energy.]]
[[File:EA1_01508.png|400px|centre|thumb|parameters for the activation energy.]]
'''H+HF (H1-H2-F1)'''
This reaction is endothermis as the reactants are lower in energy than the products therefore energy is taken in from the surroundings to form the products. H-F bond is still stronger than H-H as the reactans are lower in energy and more stable. The transition state is located at approximately rH1-H2=280 pm and rH2-F1=92 pm. It is located with the same reasons stated above.With the same method, the activation energy is estimated to be 434 kJ.mol-1. The two activation energies should be identical as these two reactions are essentially the reverse of one another.

[[File:H+HF_01508310.png|400px|centre|thumb|Surface plot for H1-H2-F1 system using Dynamic Calculationthe, the transition state is identified as the black dot.]]
[[File:HHF_015083.png |400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:EA2_01508.png|400px|centre|thumb|Counter plot for estimating the activation energy.]]
[[File:EA2_PARAMETERS.png|400px|centre|thumb|parameters for the activation energy.]]

===Reaction dynamics===
===F+H2 system===

Initially, the reactants have kinetic energy in the form of vibrational and translational energies, and as it crosses the potential energy barrier, the kinetic energy is converted into potential energy. Once the system is exiting the product channel, the potential energy is converted into the vibrational energy of the product.One good experimental technique to prob the electronic structure of the reacting species will be IR spectroscopy.In the anharmonic oscillator model, exciting molecules in the relaxed state promotes excitation from the ground state to the first energy level mainly. This will give rise to a single peak in the IR spectrum. Howver, when exciting a sample of excited molecules, many transitions are possible. For example, from 0-->1, the fundamental or 1-->2, the first overtone. They will show up in the spectrum as 2 peaks, with the overtone being at a lower wavenumber as the energy gap decreases up the potential well. The intensity of the overtone decreases over time as the electrons can fall back to lower energy levels and energy is emitted as radiation. As this system is linear, rotational is not important electronic energy is not considered here.Photoelectron spectroscopy is also a viable method. '''reference 5'''

[[File:Reactiondynamicsfh2_0150.png||400px|centre|thumb|contour plot for F+H2.]]
[[File:Reactiondynamicsparameter——015.png |400px|centre|thumb|parameters for the reactive trajectory.]]
====Varying the momentum of HH in the F+H2 system.====
Conditions:rFH=182 pm, rHH=74 pm, PFH=-1.0g.mol-1.pm.fs-1
{| class="wikitable" border="1"
|+ caption
|-
|PHH/g.mol-1.pm.fs-1|| Contour Plot
|-
|0 || [[File:0_015083.png |400 px|centre]]
|-
|2 || [[File:2_0508.png |400 px|centre]]
|-
|4 || [[File:4_01508.png ‎|400 px|centre]]
|-
|6.1|| [[File:6_01508.png|400 px|centre]]
|-
| -2|| [[File:-2_01508.png|400 px|centre]]
|-
| -4|| [[File:-4.1_01508.png‎|400 px|centre]]
|-
| -6.1|| [[File:Fit1_01508.png|400 px|centre]]
|-
|}
Although the amount of energy that is put into H-H vibration is much more than the activation energy of the reaction, the reaction does not always occur. The large amount of energy is demonstrated by the high frequency of those wavy lines. Recrossing the transition states multiple times can lead to no reaction or product formation depending on how the tragectory collides with the potential well.

[[File:Reactiondynamic_last01588.png|400px|centre|thumb|contour plot for rFH=182 pm, fHH=74 pm, PFH=-1.6g.mol-1.pm.fs-1,PHH=0.2g.mol-1.pm.fs-1]]
The system now has much less vibrational energy into the reactants than before. The reaction is still successful and the trajectory recrosses the transition states fewer times than before.This can be explained by the increased momentum of FH so that F can approach the closest H with more vibrational energy.

===H+HF system===
{| class="wikitable" border="1"
!Graph Number!! p1(HH)/g.mol-1.pm.fs-1 !! p2(HF)/g.mol-1.pm.fs-1!! Etot/kJmol-1!! Recative?!! Illustration of the trajectory
|-
|1|| -2 || -10||-397|| No|| [[File:Final1_01508.png|350px ]]
|-
|2|| 0|| -8||-400 || No|| [[File:Final2_015.png|350px]]
|-
|3||5 || -6||-360|| No|| [[File:Final3_015.png|350px]]
|-
|4|| 5 || -3||-389 || Yes||[[File:Final4_015.png|350px]]
|-
|}

by referening to Polanyl's empirical rules, an exothermic reaction has an early barrier, which happens in the entrance channel. It tends to favour vibrational excitation of the products. On the other hand, an endothermic reaction has a late barrier, which occurs in the product channel. It tends to favour low product vibrational excitation. The location of the energy barrier is also crucial for a successful reaction. Translational energy of the reactants is the most effective at passing the early barrier whereas vibrational energy of the reactants is the most effective at surmounting the late barrier.This reaction is endothermic, and hence it has a late barrier. In all the graphs, the reactants all have vibrational energy as indicated by the wavy line in the reactant channel.
==References==

<references>
<ref name="reference 1">R. DeKock and H. Gray, Chemical structure and bonding, Univeristy Science Books, 1989.</ref>
<ref name="reference 2">S. Jeffrey I., Experimental Chemical Dynamics, Prentice-Hall, Upper Saddle River, 2nd edn., 1989.</ref>
</references>

MRD:01508310

2020-05-22T18:28:25Z

Hh2218: /* References */

==H-H-H system==
===Dynamics from the transition state region===
The transition state is the point on the potential energy surface that has ∂V(ri)/∂ri=0, where ri is the distance between two atoms.The transition state is a local maximum and its second derivative ∂2V(ri)/∂ri2 is < 0, whereas a local minimum will have a positive second derivative instead.
[[File:Hhh_surfaceplot_01508.png|400px|thumb|centre|a potential energy surface plot of H and H2 with respect to interatomic distances.]]

===Trajectories from r1=r2: locating the transition state===
At the transition state, r1=r2=90.8 pm by estimation. At this separation, the forces acting along AB and BC are both -0.004 kJ.mol-1.pm-1, which is close to zero and the eigenvalues for the Hessian matrix were -0.028 and +0.167 kJ.mol-1.pm-2, indicating the presence of transition state. The Internuclear Distance vs Time plot suggests the distance between HA, HB and HC is equal, about 90 pm and the distance is constant over time suggests the atoms are static at the transition state.
[[File:Animation101508310.png|400px|centre|thumb|picture showing H and H2 at the transition state.]]
[[File:Optimisation1_01508310.png|400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:Internucleardistance_01508310.png|400px|centre|thumb|Internuclear Distance vs Time plot between the H atoms at the transition state.]]

===Calculating the reaction path===
When rA-B is set to rts+1 and rB-C equals rts,the transition rolls towards BC and HA remains as an atom. MEP and Dynamic reaction paths are different as MEP set the momenta to zero in every step of the reaction path, products are therefore static and hence the reaction path is relatively straight. The dynamic reaction path is more realistic. It takes the momenta of gaseous molecules into account,i.e. they have vibrational energies, that is illustrated by the wavy line along the reaction path.
[[File:Surface_Plot1mep_015083.png|400px|centre|thumb|the minimum energy path (mep) of the H-H-H system]]
[[File:01569348_MEP_AB1_dynamic.png|400px|centre|thumb|the dynamic reaction path of the H-H-H system]]

====MEP and Dynamics calculations comparisons====
'''r1=91.8 pm, r2=90.8 pm, momenta set to 0 g.mol-1.pm.fs-1'''

HB and HC form a H2 molecule whereas HA moves away from the molecule. The distance between B and C decreased to 74 pm, which is the hydrogen molecule bond length <ref name="reference 1"/>.In MEP calculation, the momenta are set to zero at each time step.

[[File:MepH2bondlength_01508.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using MEP calculation.]]

[[File:MepH2momenta015083.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using MEP calculation.]]

Using Dynamics calculation, the outcome of the reaction is the same. The transition state rolls towards HB and HC and a hydrogen molecule is formed. One noticeable difference is that the hydrogen molecule now has some vibational energy as indicated by the wavy line along the B-C distance in the Internuclear Distance vs Time plot.As for the Momenta vs Time plot, the system is linear, therefore the angle theta is zero. HA and HB are moving away from each other at '''an increasing velocity until the momentum reaches 5 g.mol-1.pm.fs-1.The oscillation along the B-C bond corresponds to the vibration of the bond. '''why does the beginning have negative momenta?'''
[[File:DynamicsH2_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation.]]
[[File:DynamicsH2monenta_01508.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using Dynamics calculation.]]

'''r1=90.8 pm, r2=91.8 pm, momenta set to 0 g.mol-1.pm.fs-1'''

Once the length of r1 and r2 switches, the shapes of the graphs are identical but instead of HB and HC forming a molecule, HA and HB now form the hydrogen molecule in the products.
[[File:Mepinter2_01508.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using MEP calculation.]]
[[File:Momentamep2_015.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using MEP calculation.]]
[[File:InterDynamic_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation.]]
[[File:Momentadynamics_015083.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using Dynamics calculation.]]

'''Trajectory starting with the final position and reversed momentum to the reaction path above'''

This trajectory starts at the end of the reaction path above and finishes at where the above reaction started. it is essentially a reverse of what happened in the reaction above.
[[File:Reverse_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation (r1=70.0 pm,r2=353 pm,p1=-3.21 g.mol-1.pm.fs-1, p2=-5.07 g.mol-1.pm.fs-1) .]]

===Recative and unreactive trajectories===
{| class="wikitable" border="1"
! p1/g.mol-1.pm.fs-1 !! p2/g.mol-1.pm.fs-1!! Etot/kJmol-1!! Recative?!! Description of the dynamics!! Illustration of the trajectory
|-
| -2.56 || -5.1||-414 || Yes||The translational energy of the reactants can surmount the potential energy barrier and form the products. The ramaining energy is converted into vibrational energy of the products. || [[File:Table1_01508310.png|350px ]]
|-
| -3.1 || -4.1||-420 || No||The reactant H2 has vibrational energy and its rAB motion is rapid. Before it could cross the energy barrier, the molecule slams into the repulsive inner wall of the potential surface and bounces back into the reactant channel. || [[File:Table2_0150.png|350px]]
|-
| -3.1 || -5.1||-414|| Yes||The reactants have both the translational and vibrational energies. The energy is used to surmount the potential energy barrier and converted into the vibrational energy of the products. || [[File:Table3_01508.png|350px]]
|-
| -5.1 || -10.1||-357 || No||The reactants have sufficient energy to cross the transition state and the products did form for a certain amount of time. However, before the the system can exit the product channel, it recrosses the transition state and form the reactants again, hence no reaction occurs. ||[[File:Table4_01508.png|350px]]
|-
| -5.1 || -10.6||-394 || Yes||The system has sufficient energy to cross the transition state but it recrosses the transition state shortly after the reaction path hits the potential energy surface. However, the system is able to cross the transition state for the third time and finally exits the product channel and forms the products. || [[File:-10.6_01508.png|350px]]
|-
|}
In order to form products, a system must have sufficient energy to cross the transition state. Only molecules with the correct phase <ref name="reference 2"/> can exit the product channel and form stable products. Recrossing the transition state can lead to either product formation or no reaction. It is possible to cross the transition state multiple times.

===Transition State Theory===

Transition State Theory is classical, it doesn't take quantum tunnelling into account.Quantum tunnelling is probable for this reaction as it involves the transfer of a hydrogen atom, particularly at lower temperatures.'''Reference 3'''At low temperatures, the H atom can tunnel through the potential energy barrier than to pass over the barrier, hence the activation energy is lowered and the reaction rate increases. However, recrossing the energy barrier is possible as seen with the simulations, this can have a negative effect on the reaction rate. At high temperatures, the system is thermally activated and the behavious is approximately classical.'''reference4''' Therefore the experimental reaction rates are expected to be greater than that predicted by the Transition State Theory.

==F-H-H system==
===PES inspection===
'''F+H2 (F1-H1-H2)'''

F+H2 is exothermic as the reactants are higher in energy than the products therefore during the reaction, energy is released to the surroundings. H-F bond is stronger than H-H bond as the products are lower in energy and therefore more stable.The transition state is located approximately at rF1-H1=181.10 pm and rH1-H2=74.49 pm. This is verified by the forces (close to zero) and eigenvalues for hessian matrix (they are of opposite signs). The activation energy is estimated by tilting the transition state towards the reactants and is shown to be 424 kJ.mol-1.
[[File:Fh2_015083.png |400px|centre|thumb|Surface plot for F1-H1-H2 system using Dynamic Calculation, the transition state is identified as the black dot.]]
[[File:OptimisationFhh1_01508.png|400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:F1H1H2_EA_0150.png|400px|centre|thumb|Counter plot for estimating the activation energy.]]
[[File:EA1_01508.png|400px|centre|thumb|parameters for the activation energy.]]
'''H+HF (H1-H2-F1)'''
This reaction is endothermis as the reactants are lower in energy than the products therefore energy is taken in from the surroundings to form the products. H-F bond is still stronger than H-H as the reactans are lower in energy and more stable. The transition state is located at approximately rH1-H2=280 pm and rH2-F1=92 pm. It is located with the same reasons stated above.With the same method, the activation energy is estimated to be 434 kJ.mol-1. The two activation energies should be identical as these two reactions are essentially the reverse of one another.

[[File:H+HF_01508310.png|400px|centre|thumb|Surface plot for H1-H2-F1 system using Dynamic Calculationthe, the transition state is identified as the black dot.]]
[[File:HHF_015083.png |400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:EA2_01508.png|400px|centre|thumb|Counter plot for estimating the activation energy.]]
[[File:EA2_PARAMETERS.png|400px|centre|thumb|parameters for the activation energy.]]

===Reaction dynamics===
===F+H2 system===

Initially, the reactants have kinetic energy in the form of vibrational and translational energies, and as it crosses the potential energy barrier, the kinetic energy is converted into potential energy. Once the system is exiting the product channel, the potential energy is converted into the vibrational energy of the product.One good experimental technique to prob the electronic structure of the reacting species will be IR spectroscopy.In the anharmonic oscillator model, exciting molecules in the relaxed state promotes excitation from the ground state to the first energy level mainly. This will give rise to a single peak in the IR spectrum. Howver, when exciting a sample of excited molecules, many transitions are possible. For example, from 0-->1, the fundamental or 1-->2, the first overtone. They will show up in the spectrum as 2 peaks, with the overtone being at a lower wavenumber as the energy gap decreases up the potential well. The intensity of the overtone decreases over time as the electrons can fall back to lower energy levels and energy is emitted as radiation. As this system is linear, rotational is not important electronic energy is not considered here.Photoelectron spectroscopy is also a viable method. '''reference 5'''

[[File:Reactiondynamicsfh2_0150.png||400px|centre|thumb|contour plot for F+H2.]]
[[File:Reactiondynamicsparameter——015.png |400px|centre|thumb|parameters for the reactive trajectory.]]
====Varying the momentum of HH in the F+H2 system.====
Conditions:rFH=182 pm, rHH=74 pm, PFH=-1.0g.mol-1.pm.fs-1
{| class="wikitable" border="1"
|+ caption
|-
|PHH/g.mol-1.pm.fs-1|| Contour Plot
|-
|0 || [[File:0_015083.png |400 px|centre]]
|-
|2 || [[File:2_0508.png |400 px|centre]]
|-
|4 || [[File:4_01508.png ‎|400 px|centre]]
|-
|6.1|| [[File:6_01508.png|400 px|centre]]
|-
| -2|| [[File:-2_01508.png|400 px|centre]]
|-
| -4|| [[File:-4.1_01508.png‎|400 px|centre]]
|-
| -6.1|| [[File:Fit1_01508.png|400 px|centre]]
|-
|}
Although the amount of energy that is put into H-H vibration is much more than the activation energy of the reaction, the reaction does not always occur. The large amount of energy is demonstrated by the high frequency of those wavy lines. Recrossing the transition states multiple times can lead to no reaction or product formation depending on how the tragectory collides with the potential well.

[[File:Reactiondynamic_last01588.png|400px|centre|thumb|contour plot for rFH=182 pm, fHH=74 pm, PFH=-1.6g.mol-1.pm.fs-1,PHH=0.2g.mol-1.pm.fs-1]]
The system now has much less vibrational energy into the reactants than before. The reaction is still successful and the trajectory recrosses the transition states fewer times than before.This can be explained by the increased momentum of FH so that F can approach the closest H with more vibrational energy.

===H+HF system===
{| class="wikitable" border="1"
!Graph Number!! p1(HH)/g.mol-1.pm.fs-1 !! p2(HF)/g.mol-1.pm.fs-1!! Etot/kJmol-1!! Recative?!! Illustration of the trajectory
|-
|1|| -2 || -10||-397|| No|| [[File:Final1_01508.png|350px ]]
|-
|2|| 0|| -8||-400 || No|| [[File:Final2_015.png|350px]]
|-
|3||5 || -6||-360|| No|| [[File:Final3_015.png|350px]]
|-
|4|| 5 || -3||-389 || Yes||[[File:Final4_015.png|350px]]
|-
|}

by referening to Polanyl's empirical rules, an exothermic reaction has an early barrier, which happens in the entrance channel. It tends to favour vibrational excitation of the products. On the other hand, an endothermic reaction has a late barrier, which occurs in the product channel. It tends to favour low product vibrational excitation. The location of the energy barrier is also crucial for a successful reaction. Translational energy of the reactants is the most effective at passing the early barrier whereas vibrational energy of the reactants is the most effective at surmounting the late barrier.This reaction is endothermic, and hence it has a late barrier. In all the graphs, the reactants all have vibrational energy as indicated by the wavy line in the reactant channel.
==References==

<references>
<ref name="reference 1">R. DeKock and H. Gray, Chemical structure and bonding, Univeristy Science Books, 1989.</ref>
</references>

<references>
<ref name="reference 2">S. Jeffrey I., Experimental Chemical Dynamics, Prentice-Hall, Upper Saddle River, 2nd edn., 1989.</ref>
</references>

MRD:01508310

2020-05-22T18:28:08Z

Hh2218: /* References */

==H-H-H system==
===Dynamics from the transition state region===
The transition state is the point on the potential energy surface that has ∂V(ri)/∂ri=0, where ri is the distance between two atoms.The transition state is a local maximum and its second derivative ∂2V(ri)/∂ri2 is < 0, whereas a local minimum will have a positive second derivative instead.
[[File:Hhh_surfaceplot_01508.png|400px|thumb|centre|a potential energy surface plot of H and H2 with respect to interatomic distances.]]

===Trajectories from r1=r2: locating the transition state===
At the transition state, r1=r2=90.8 pm by estimation. At this separation, the forces acting along AB and BC are both -0.004 kJ.mol-1.pm-1, which is close to zero and the eigenvalues for the Hessian matrix were -0.028 and +0.167 kJ.mol-1.pm-2, indicating the presence of transition state. The Internuclear Distance vs Time plot suggests the distance between HA, HB and HC is equal, about 90 pm and the distance is constant over time suggests the atoms are static at the transition state.
[[File:Animation101508310.png|400px|centre|thumb|picture showing H and H2 at the transition state.]]
[[File:Optimisation1_01508310.png|400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:Internucleardistance_01508310.png|400px|centre|thumb|Internuclear Distance vs Time plot between the H atoms at the transition state.]]

===Calculating the reaction path===
When rA-B is set to rts+1 and rB-C equals rts,the transition rolls towards BC and HA remains as an atom. MEP and Dynamic reaction paths are different as MEP set the momenta to zero in every step of the reaction path, products are therefore static and hence the reaction path is relatively straight. The dynamic reaction path is more realistic. It takes the momenta of gaseous molecules into account,i.e. they have vibrational energies, that is illustrated by the wavy line along the reaction path.
[[File:Surface_Plot1mep_015083.png|400px|centre|thumb|the minimum energy path (mep) of the H-H-H system]]
[[File:01569348_MEP_AB1_dynamic.png|400px|centre|thumb|the dynamic reaction path of the H-H-H system]]

====MEP and Dynamics calculations comparisons====
'''r1=91.8 pm, r2=90.8 pm, momenta set to 0 g.mol-1.pm.fs-1'''

HB and HC form a H2 molecule whereas HA moves away from the molecule. The distance between B and C decreased to 74 pm, which is the hydrogen molecule bond length <ref name="reference 1"/>.In MEP calculation, the momenta are set to zero at each time step.

[[File:MepH2bondlength_01508.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using MEP calculation.]]

[[File:MepH2momenta015083.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using MEP calculation.]]

Using Dynamics calculation, the outcome of the reaction is the same. The transition state rolls towards HB and HC and a hydrogen molecule is formed. One noticeable difference is that the hydrogen molecule now has some vibational energy as indicated by the wavy line along the B-C distance in the Internuclear Distance vs Time plot.As for the Momenta vs Time plot, the system is linear, therefore the angle theta is zero. HA and HB are moving away from each other at '''an increasing velocity until the momentum reaches 5 g.mol-1.pm.fs-1.The oscillation along the B-C bond corresponds to the vibration of the bond. '''why does the beginning have negative momenta?'''
[[File:DynamicsH2_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation.]]
[[File:DynamicsH2monenta_01508.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using Dynamics calculation.]]

'''r1=90.8 pm, r2=91.8 pm, momenta set to 0 g.mol-1.pm.fs-1'''

Once the length of r1 and r2 switches, the shapes of the graphs are identical but instead of HB and HC forming a molecule, HA and HB now form the hydrogen molecule in the products.
[[File:Mepinter2_01508.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using MEP calculation.]]
[[File:Momentamep2_015.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using MEP calculation.]]
[[File:InterDynamic_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation.]]
[[File:Momentadynamics_015083.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using Dynamics calculation.]]

'''Trajectory starting with the final position and reversed momentum to the reaction path above'''

This trajectory starts at the end of the reaction path above and finishes at where the above reaction started. it is essentially a reverse of what happened in the reaction above.
[[File:Reverse_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation (r1=70.0 pm,r2=353 pm,p1=-3.21 g.mol-1.pm.fs-1, p2=-5.07 g.mol-1.pm.fs-1) .]]

===Recative and unreactive trajectories===
{| class="wikitable" border="1"
! p1/g.mol-1.pm.fs-1 !! p2/g.mol-1.pm.fs-1!! Etot/kJmol-1!! Recative?!! Description of the dynamics!! Illustration of the trajectory
|-
| -2.56 || -5.1||-414 || Yes||The translational energy of the reactants can surmount the potential energy barrier and form the products. The ramaining energy is converted into vibrational energy of the products. || [[File:Table1_01508310.png|350px ]]
|-
| -3.1 || -4.1||-420 || No||The reactant H2 has vibrational energy and its rAB motion is rapid. Before it could cross the energy barrier, the molecule slams into the repulsive inner wall of the potential surface and bounces back into the reactant channel. || [[File:Table2_0150.png|350px]]
|-
| -3.1 || -5.1||-414|| Yes||The reactants have both the translational and vibrational energies. The energy is used to surmount the potential energy barrier and converted into the vibrational energy of the products. || [[File:Table3_01508.png|350px]]
|-
| -5.1 || -10.1||-357 || No||The reactants have sufficient energy to cross the transition state and the products did form for a certain amount of time. However, before the the system can exit the product channel, it recrosses the transition state and form the reactants again, hence no reaction occurs. ||[[File:Table4_01508.png|350px]]
|-
| -5.1 || -10.6||-394 || Yes||The system has sufficient energy to cross the transition state but it recrosses the transition state shortly after the reaction path hits the potential energy surface. However, the system is able to cross the transition state for the third time and finally exits the product channel and forms the products. || [[File:-10.6_01508.png|350px]]
|-
|}
In order to form products, a system must have sufficient energy to cross the transition state. Only molecules with the correct phase <ref name="reference 2"/> can exit the product channel and form stable products. Recrossing the transition state can lead to either product formation or no reaction. It is possible to cross the transition state multiple times.

===Transition State Theory===

Transition State Theory is classical, it doesn't take quantum tunnelling into account.Quantum tunnelling is probable for this reaction as it involves the transfer of a hydrogen atom, particularly at lower temperatures.'''Reference 3'''At low temperatures, the H atom can tunnel through the potential energy barrier than to pass over the barrier, hence the activation energy is lowered and the reaction rate increases. However, recrossing the energy barrier is possible as seen with the simulations, this can have a negative effect on the reaction rate. At high temperatures, the system is thermally activated and the behavious is approximately classical.'''reference4''' Therefore the experimental reaction rates are expected to be greater than that predicted by the Transition State Theory.

==F-H-H system==
===PES inspection===
'''F+H2 (F1-H1-H2)'''

F+H2 is exothermic as the reactants are higher in energy than the products therefore during the reaction, energy is released to the surroundings. H-F bond is stronger than H-H bond as the products are lower in energy and therefore more stable.The transition state is located approximately at rF1-H1=181.10 pm and rH1-H2=74.49 pm. This is verified by the forces (close to zero) and eigenvalues for hessian matrix (they are of opposite signs). The activation energy is estimated by tilting the transition state towards the reactants and is shown to be 424 kJ.mol-1.
[[File:Fh2_015083.png |400px|centre|thumb|Surface plot for F1-H1-H2 system using Dynamic Calculation, the transition state is identified as the black dot.]]
[[File:OptimisationFhh1_01508.png|400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:F1H1H2_EA_0150.png|400px|centre|thumb|Counter plot for estimating the activation energy.]]
[[File:EA1_01508.png|400px|centre|thumb|parameters for the activation energy.]]
'''H+HF (H1-H2-F1)'''
This reaction is endothermis as the reactants are lower in energy than the products therefore energy is taken in from the surroundings to form the products. H-F bond is still stronger than H-H as the reactans are lower in energy and more stable. The transition state is located at approximately rH1-H2=280 pm and rH2-F1=92 pm. It is located with the same reasons stated above.With the same method, the activation energy is estimated to be 434 kJ.mol-1. The two activation energies should be identical as these two reactions are essentially the reverse of one another.

[[File:H+HF_01508310.png|400px|centre|thumb|Surface plot for H1-H2-F1 system using Dynamic Calculationthe, the transition state is identified as the black dot.]]
[[File:HHF_015083.png |400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:EA2_01508.png|400px|centre|thumb|Counter plot for estimating the activation energy.]]
[[File:EA2_PARAMETERS.png|400px|centre|thumb|parameters for the activation energy.]]

===Reaction dynamics===
===F+H2 system===

Initially, the reactants have kinetic energy in the form of vibrational and translational energies, and as it crosses the potential energy barrier, the kinetic energy is converted into potential energy. Once the system is exiting the product channel, the potential energy is converted into the vibrational energy of the product.One good experimental technique to prob the electronic structure of the reacting species will be IR spectroscopy.In the anharmonic oscillator model, exciting molecules in the relaxed state promotes excitation from the ground state to the first energy level mainly. This will give rise to a single peak in the IR spectrum. Howver, when exciting a sample of excited molecules, many transitions are possible. For example, from 0-->1, the fundamental or 1-->2, the first overtone. They will show up in the spectrum as 2 peaks, with the overtone being at a lower wavenumber as the energy gap decreases up the potential well. The intensity of the overtone decreases over time as the electrons can fall back to lower energy levels and energy is emitted as radiation. As this system is linear, rotational is not important electronic energy is not considered here.Photoelectron spectroscopy is also a viable method. '''reference 5'''

[[File:Reactiondynamicsfh2_0150.png||400px|centre|thumb|contour plot for F+H2.]]
[[File:Reactiondynamicsparameter——015.png |400px|centre|thumb|parameters for the reactive trajectory.]]
====Varying the momentum of HH in the F+H2 system.====
Conditions:rFH=182 pm, rHH=74 pm, PFH=-1.0g.mol-1.pm.fs-1
{| class="wikitable" border="1"
|+ caption
|-
|PHH/g.mol-1.pm.fs-1|| Contour Plot
|-
|0 || [[File:0_015083.png |400 px|centre]]
|-
|2 || [[File:2_0508.png |400 px|centre]]
|-
|4 || [[File:4_01508.png ‎|400 px|centre]]
|-
|6.1|| [[File:6_01508.png|400 px|centre]]
|-
| -2|| [[File:-2_01508.png|400 px|centre]]
|-
| -4|| [[File:-4.1_01508.png‎|400 px|centre]]
|-
| -6.1|| [[File:Fit1_01508.png|400 px|centre]]
|-
|}
Although the amount of energy that is put into H-H vibration is much more than the activation energy of the reaction, the reaction does not always occur. The large amount of energy is demonstrated by the high frequency of those wavy lines. Recrossing the transition states multiple times can lead to no reaction or product formation depending on how the tragectory collides with the potential well.

[[File:Reactiondynamic_last01588.png|400px|centre|thumb|contour plot for rFH=182 pm, fHH=74 pm, PFH=-1.6g.mol-1.pm.fs-1,PHH=0.2g.mol-1.pm.fs-1]]
The system now has much less vibrational energy into the reactants than before. The reaction is still successful and the trajectory recrosses the transition states fewer times than before.This can be explained by the increased momentum of FH so that F can approach the closest H with more vibrational energy.

===H+HF system===
{| class="wikitable" border="1"
!Graph Number!! p1(HH)/g.mol-1.pm.fs-1 !! p2(HF)/g.mol-1.pm.fs-1!! Etot/kJmol-1!! Recative?!! Illustration of the trajectory
|-
|1|| -2 || -10||-397|| No|| [[File:Final1_01508.png|350px ]]
|-
|2|| 0|| -8||-400 || No|| [[File:Final2_015.png|350px]]
|-
|3||5 || -6||-360|| No|| [[File:Final3_015.png|350px]]
|-
|4|| 5 || -3||-389 || Yes||[[File:Final4_015.png|350px]]
|-
|}

by referening to Polanyl's empirical rules, an exothermic reaction has an early barrier, which happens in the entrance channel. It tends to favour vibrational excitation of the products. On the other hand, an endothermic reaction has a late barrier, which occurs in the product channel. It tends to favour low product vibrational excitation. The location of the energy barrier is also crucial for a successful reaction. Translational energy of the reactants is the most effective at passing the early barrier whereas vibrational energy of the reactants is the most effective at surmounting the late barrier.This reaction is endothermic, and hence it has a late barrier. In all the graphs, the reactants all have vibrational energy as indicated by the wavy line in the reactant channel.
==References==

<references>
<ref name="reference 1">R. DeKock and H. Gray, Chemical structure and bonding, Univeristy Science Books, 1989.</ref>
</references>
<references>
<ref name="reference 2">S. Jeffrey I., Experimental Chemical Dynamics, Prentice-Hall, Upper Saddle River, 2nd edn., 1989.</ref>
</references>

MRD:01508310

2020-05-22T18:27:33Z

Hh2218: /* Recative and unreactive trajectories */

==H-H-H system==
===Dynamics from the transition state region===
The transition state is the point on the potential energy surface that has ∂V(ri)/∂ri=0, where ri is the distance between two atoms.The transition state is a local maximum and its second derivative ∂2V(ri)/∂ri2 is < 0, whereas a local minimum will have a positive second derivative instead.
[[File:Hhh_surfaceplot_01508.png|400px|thumb|centre|a potential energy surface plot of H and H2 with respect to interatomic distances.]]

===Trajectories from r1=r2: locating the transition state===
At the transition state, r1=r2=90.8 pm by estimation. At this separation, the forces acting along AB and BC are both -0.004 kJ.mol-1.pm-1, which is close to zero and the eigenvalues for the Hessian matrix were -0.028 and +0.167 kJ.mol-1.pm-2, indicating the presence of transition state. The Internuclear Distance vs Time plot suggests the distance between HA, HB and HC is equal, about 90 pm and the distance is constant over time suggests the atoms are static at the transition state.
[[File:Animation101508310.png|400px|centre|thumb|picture showing H and H2 at the transition state.]]
[[File:Optimisation1_01508310.png|400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:Internucleardistance_01508310.png|400px|centre|thumb|Internuclear Distance vs Time plot between the H atoms at the transition state.]]

===Calculating the reaction path===
When rA-B is set to rts+1 and rB-C equals rts,the transition rolls towards BC and HA remains as an atom. MEP and Dynamic reaction paths are different as MEP set the momenta to zero in every step of the reaction path, products are therefore static and hence the reaction path is relatively straight. The dynamic reaction path is more realistic. It takes the momenta of gaseous molecules into account,i.e. they have vibrational energies, that is illustrated by the wavy line along the reaction path.
[[File:Surface_Plot1mep_015083.png|400px|centre|thumb|the minimum energy path (mep) of the H-H-H system]]
[[File:01569348_MEP_AB1_dynamic.png|400px|centre|thumb|the dynamic reaction path of the H-H-H system]]

====MEP and Dynamics calculations comparisons====
'''r1=91.8 pm, r2=90.8 pm, momenta set to 0 g.mol-1.pm.fs-1'''

HB and HC form a H2 molecule whereas HA moves away from the molecule. The distance between B and C decreased to 74 pm, which is the hydrogen molecule bond length <ref name="reference 1"/>.In MEP calculation, the momenta are set to zero at each time step.

[[File:MepH2bondlength_01508.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using MEP calculation.]]

[[File:MepH2momenta015083.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using MEP calculation.]]

Using Dynamics calculation, the outcome of the reaction is the same. The transition state rolls towards HB and HC and a hydrogen molecule is formed. One noticeable difference is that the hydrogen molecule now has some vibational energy as indicated by the wavy line along the B-C distance in the Internuclear Distance vs Time plot.As for the Momenta vs Time plot, the system is linear, therefore the angle theta is zero. HA and HB are moving away from each other at '''an increasing velocity until the momentum reaches 5 g.mol-1.pm.fs-1.The oscillation along the B-C bond corresponds to the vibration of the bond. '''why does the beginning have negative momenta?'''
[[File:DynamicsH2_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation.]]
[[File:DynamicsH2monenta_01508.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using Dynamics calculation.]]

'''r1=90.8 pm, r2=91.8 pm, momenta set to 0 g.mol-1.pm.fs-1'''

Once the length of r1 and r2 switches, the shapes of the graphs are identical but instead of HB and HC forming a molecule, HA and HB now form the hydrogen molecule in the products.
[[File:Mepinter2_01508.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using MEP calculation.]]
[[File:Momentamep2_015.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using MEP calculation.]]
[[File:InterDynamic_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation.]]
[[File:Momentadynamics_015083.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using Dynamics calculation.]]

'''Trajectory starting with the final position and reversed momentum to the reaction path above'''

This trajectory starts at the end of the reaction path above and finishes at where the above reaction started. it is essentially a reverse of what happened in the reaction above.
[[File:Reverse_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation (r1=70.0 pm,r2=353 pm,p1=-3.21 g.mol-1.pm.fs-1, p2=-5.07 g.mol-1.pm.fs-1) .]]

===Recative and unreactive trajectories===
{| class="wikitable" border="1"
! p1/g.mol-1.pm.fs-1 !! p2/g.mol-1.pm.fs-1!! Etot/kJmol-1!! Recative?!! Description of the dynamics!! Illustration of the trajectory
|-
| -2.56 || -5.1||-414 || Yes||The translational energy of the reactants can surmount the potential energy barrier and form the products. The ramaining energy is converted into vibrational energy of the products. || [[File:Table1_01508310.png|350px ]]
|-
| -3.1 || -4.1||-420 || No||The reactant H2 has vibrational energy and its rAB motion is rapid. Before it could cross the energy barrier, the molecule slams into the repulsive inner wall of the potential surface and bounces back into the reactant channel. || [[File:Table2_0150.png|350px]]
|-
| -3.1 || -5.1||-414|| Yes||The reactants have both the translational and vibrational energies. The energy is used to surmount the potential energy barrier and converted into the vibrational energy of the products. || [[File:Table3_01508.png|350px]]
|-
| -5.1 || -10.1||-357 || No||The reactants have sufficient energy to cross the transition state and the products did form for a certain amount of time. However, before the the system can exit the product channel, it recrosses the transition state and form the reactants again, hence no reaction occurs. ||[[File:Table4_01508.png|350px]]
|-
| -5.1 || -10.6||-394 || Yes||The system has sufficient energy to cross the transition state but it recrosses the transition state shortly after the reaction path hits the potential energy surface. However, the system is able to cross the transition state for the third time and finally exits the product channel and forms the products. || [[File:-10.6_01508.png|350px]]
|-
|}
In order to form products, a system must have sufficient energy to cross the transition state. Only molecules with the correct phase <ref name="reference 2"/> can exit the product channel and form stable products. Recrossing the transition state can lead to either product formation or no reaction. It is possible to cross the transition state multiple times.

===Transition State Theory===

Transition State Theory is classical, it doesn't take quantum tunnelling into account.Quantum tunnelling is probable for this reaction as it involves the transfer of a hydrogen atom, particularly at lower temperatures.'''Reference 3'''At low temperatures, the H atom can tunnel through the potential energy barrier than to pass over the barrier, hence the activation energy is lowered and the reaction rate increases. However, recrossing the energy barrier is possible as seen with the simulations, this can have a negative effect on the reaction rate. At high temperatures, the system is thermally activated and the behavious is approximately classical.'''reference4''' Therefore the experimental reaction rates are expected to be greater than that predicted by the Transition State Theory.

==F-H-H system==
===PES inspection===
'''F+H2 (F1-H1-H2)'''

F+H2 is exothermic as the reactants are higher in energy than the products therefore during the reaction, energy is released to the surroundings. H-F bond is stronger than H-H bond as the products are lower in energy and therefore more stable.The transition state is located approximately at rF1-H1=181.10 pm and rH1-H2=74.49 pm. This is verified by the forces (close to zero) and eigenvalues for hessian matrix (they are of opposite signs). The activation energy is estimated by tilting the transition state towards the reactants and is shown to be 424 kJ.mol-1.
[[File:Fh2_015083.png |400px|centre|thumb|Surface plot for F1-H1-H2 system using Dynamic Calculation, the transition state is identified as the black dot.]]
[[File:OptimisationFhh1_01508.png|400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:F1H1H2_EA_0150.png|400px|centre|thumb|Counter plot for estimating the activation energy.]]
[[File:EA1_01508.png|400px|centre|thumb|parameters for the activation energy.]]
'''H+HF (H1-H2-F1)'''
This reaction is endothermis as the reactants are lower in energy than the products therefore energy is taken in from the surroundings to form the products. H-F bond is still stronger than H-H as the reactans are lower in energy and more stable. The transition state is located at approximately rH1-H2=280 pm and rH2-F1=92 pm. It is located with the same reasons stated above.With the same method, the activation energy is estimated to be 434 kJ.mol-1. The two activation energies should be identical as these two reactions are essentially the reverse of one another.

[[File:H+HF_01508310.png|400px|centre|thumb|Surface plot for H1-H2-F1 system using Dynamic Calculationthe, the transition state is identified as the black dot.]]
[[File:HHF_015083.png |400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:EA2_01508.png|400px|centre|thumb|Counter plot for estimating the activation energy.]]
[[File:EA2_PARAMETERS.png|400px|centre|thumb|parameters for the activation energy.]]

===Reaction dynamics===
===F+H2 system===

Initially, the reactants have kinetic energy in the form of vibrational and translational energies, and as it crosses the potential energy barrier, the kinetic energy is converted into potential energy. Once the system is exiting the product channel, the potential energy is converted into the vibrational energy of the product.One good experimental technique to prob the electronic structure of the reacting species will be IR spectroscopy.In the anharmonic oscillator model, exciting molecules in the relaxed state promotes excitation from the ground state to the first energy level mainly. This will give rise to a single peak in the IR spectrum. Howver, when exciting a sample of excited molecules, many transitions are possible. For example, from 0-->1, the fundamental or 1-->2, the first overtone. They will show up in the spectrum as 2 peaks, with the overtone being at a lower wavenumber as the energy gap decreases up the potential well. The intensity of the overtone decreases over time as the electrons can fall back to lower energy levels and energy is emitted as radiation. As this system is linear, rotational is not important electronic energy is not considered here.Photoelectron spectroscopy is also a viable method. '''reference 5'''

[[File:Reactiondynamicsfh2_0150.png||400px|centre|thumb|contour plot for F+H2.]]
[[File:Reactiondynamicsparameter——015.png |400px|centre|thumb|parameters for the reactive trajectory.]]
====Varying the momentum of HH in the F+H2 system.====
Conditions:rFH=182 pm, rHH=74 pm, PFH=-1.0g.mol-1.pm.fs-1
{| class="wikitable" border="1"
|+ caption
|-
|PHH/g.mol-1.pm.fs-1|| Contour Plot
|-
|0 || [[File:0_015083.png |400 px|centre]]
|-
|2 || [[File:2_0508.png |400 px|centre]]
|-
|4 || [[File:4_01508.png ‎|400 px|centre]]
|-
|6.1|| [[File:6_01508.png|400 px|centre]]
|-
| -2|| [[File:-2_01508.png|400 px|centre]]
|-
| -4|| [[File:-4.1_01508.png‎|400 px|centre]]
|-
| -6.1|| [[File:Fit1_01508.png|400 px|centre]]
|-
|}
Although the amount of energy that is put into H-H vibration is much more than the activation energy of the reaction, the reaction does not always occur. The large amount of energy is demonstrated by the high frequency of those wavy lines. Recrossing the transition states multiple times can lead to no reaction or product formation depending on how the tragectory collides with the potential well.

[[File:Reactiondynamic_last01588.png|400px|centre|thumb|contour plot for rFH=182 pm, fHH=74 pm, PFH=-1.6g.mol-1.pm.fs-1,PHH=0.2g.mol-1.pm.fs-1]]
The system now has much less vibrational energy into the reactants than before. The reaction is still successful and the trajectory recrosses the transition states fewer times than before.This can be explained by the increased momentum of FH so that F can approach the closest H with more vibrational energy.

===H+HF system===
{| class="wikitable" border="1"
!Graph Number!! p1(HH)/g.mol-1.pm.fs-1 !! p2(HF)/g.mol-1.pm.fs-1!! Etot/kJmol-1!! Recative?!! Illustration of the trajectory
|-
|1|| -2 || -10||-397|| No|| [[File:Final1_01508.png|350px ]]
|-
|2|| 0|| -8||-400 || No|| [[File:Final2_015.png|350px]]
|-
|3||5 || -6||-360|| No|| [[File:Final3_015.png|350px]]
|-
|4|| 5 || -3||-389 || Yes||[[File:Final4_015.png|350px]]
|-
|}

by referening to Polanyl's empirical rules, an exothermic reaction has an early barrier, which happens in the entrance channel. It tends to favour vibrational excitation of the products. On the other hand, an endothermic reaction has a late barrier, which occurs in the product channel. It tends to favour low product vibrational excitation. The location of the energy barrier is also crucial for a successful reaction. Translational energy of the reactants is the most effective at passing the early barrier whereas vibrational energy of the reactants is the most effective at surmounting the late barrier.This reaction is endothermic, and hence it has a late barrier. In all the graphs, the reactants all have vibrational energy as indicated by the wavy line in the reactant channel.
==References==

<references>
<ref name="reference 1">R. DeKock and H. Gray, Chemical structure and bonding, Univeristy Science Books, 1989.</ref>
</references>

MRD:01508310

2020-05-22T18:26:50Z

Hh2218: /* MEP and Dynamics calculations comparisons */

==H-H-H system==
===Dynamics from the transition state region===
The transition state is the point on the potential energy surface that has ∂V(ri)/∂ri=0, where ri is the distance between two atoms.The transition state is a local maximum and its second derivative ∂2V(ri)/∂ri2 is < 0, whereas a local minimum will have a positive second derivative instead.
[[File:Hhh_surfaceplot_01508.png|400px|thumb|centre|a potential energy surface plot of H and H2 with respect to interatomic distances.]]

===Trajectories from r1=r2: locating the transition state===
At the transition state, r1=r2=90.8 pm by estimation. At this separation, the forces acting along AB and BC are both -0.004 kJ.mol-1.pm-1, which is close to zero and the eigenvalues for the Hessian matrix were -0.028 and +0.167 kJ.mol-1.pm-2, indicating the presence of transition state. The Internuclear Distance vs Time plot suggests the distance between HA, HB and HC is equal, about 90 pm and the distance is constant over time suggests the atoms are static at the transition state.
[[File:Animation101508310.png|400px|centre|thumb|picture showing H and H2 at the transition state.]]
[[File:Optimisation1_01508310.png|400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:Internucleardistance_01508310.png|400px|centre|thumb|Internuclear Distance vs Time plot between the H atoms at the transition state.]]

===Calculating the reaction path===
When rA-B is set to rts+1 and rB-C equals rts,the transition rolls towards BC and HA remains as an atom. MEP and Dynamic reaction paths are different as MEP set the momenta to zero in every step of the reaction path, products are therefore static and hence the reaction path is relatively straight. The dynamic reaction path is more realistic. It takes the momenta of gaseous molecules into account,i.e. they have vibrational energies, that is illustrated by the wavy line along the reaction path.
[[File:Surface_Plot1mep_015083.png|400px|centre|thumb|the minimum energy path (mep) of the H-H-H system]]
[[File:01569348_MEP_AB1_dynamic.png|400px|centre|thumb|the dynamic reaction path of the H-H-H system]]

====MEP and Dynamics calculations comparisons====
'''r1=91.8 pm, r2=90.8 pm, momenta set to 0 g.mol-1.pm.fs-1'''

HB and HC form a H2 molecule whereas HA moves away from the molecule. The distance between B and C decreased to 74 pm, which is the hydrogen molecule bond length <ref name="reference 1"/>.In MEP calculation, the momenta are set to zero at each time step.

[[File:MepH2bondlength_01508.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using MEP calculation.]]

[[File:MepH2momenta015083.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using MEP calculation.]]

Using Dynamics calculation, the outcome of the reaction is the same. The transition state rolls towards HB and HC and a hydrogen molecule is formed. One noticeable difference is that the hydrogen molecule now has some vibational energy as indicated by the wavy line along the B-C distance in the Internuclear Distance vs Time plot.As for the Momenta vs Time plot, the system is linear, therefore the angle theta is zero. HA and HB are moving away from each other at '''an increasing velocity until the momentum reaches 5 g.mol-1.pm.fs-1.The oscillation along the B-C bond corresponds to the vibration of the bond. '''why does the beginning have negative momenta?'''
[[File:DynamicsH2_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation.]]
[[File:DynamicsH2monenta_01508.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using Dynamics calculation.]]

'''r1=90.8 pm, r2=91.8 pm, momenta set to 0 g.mol-1.pm.fs-1'''

Once the length of r1 and r2 switches, the shapes of the graphs are identical but instead of HB and HC forming a molecule, HA and HB now form the hydrogen molecule in the products.
[[File:Mepinter2_01508.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using MEP calculation.]]
[[File:Momentamep2_015.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using MEP calculation.]]
[[File:InterDynamic_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation.]]
[[File:Momentadynamics_015083.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using Dynamics calculation.]]

'''Trajectory starting with the final position and reversed momentum to the reaction path above'''

This trajectory starts at the end of the reaction path above and finishes at where the above reaction started. it is essentially a reverse of what happened in the reaction above.
[[File:Reverse_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation (r1=70.0 pm,r2=353 pm,p1=-3.21 g.mol-1.pm.fs-1, p2=-5.07 g.mol-1.pm.fs-1) .]]

===Recative and unreactive trajectories===
{| class="wikitable" border="1"
! p1/g.mol-1.pm.fs-1 !! p2/g.mol-1.pm.fs-1!! Etot/kJmol-1!! Recative?!! Description of the dynamics!! Illustration of the trajectory
|-
| -2.56 || -5.1||-414 || Yes||The translational energy of the reactants can surmount the potential energy barrier and form the products. The ramaining energy is converted into vibrational energy of the products. || [[File:Table1_01508310.png|350px ]]
|-
| -3.1 || -4.1||-420 || No||The reactant H2 has vibrational energy and its rAB motion is rapid. Before it could cross the energy barrier, the molecule slams into the repulsive inner wall of the potential surface and bounces back into the reactant channel. || [[File:Table2_0150.png|350px]]
|-
| -3.1 || -5.1||-414|| Yes||The reactants have both the translational and vibrational energies. The energy is used to surmount the potential energy barrier and converted into the vibrational energy of the products. || [[File:Table3_01508.png|350px]]
|-
| -5.1 || -10.1||-357 || No||The reactants have sufficient energy to cross the transition state and the products did form for a certain amount of time. However, before the the system can exit the product channel, it recrosses the transition state and form the reactants again, hence no reaction occurs. ||[[File:Table4_01508.png|350px]]
|-
| -5.1 || -10.6||-394 || Yes||The system has sufficient energy to cross the transition state but it recrosses the transition state shortly after the reaction path hits the potential energy surface. However, the system is able to cross the transition state for the third time and finally exits the product channel and forms the products. || [[File:-10.6_01508.png|350px]]
|-
|}
In order to form products, a system must have sufficient energy to cross the transition state. Only molecules with the correct phase '''reference 2''' can exit the product channel and form stable products. Recrossing the transition state can lead to either product formation or no reaction. It is possible to cross the transition state multiple times.

===Transition State Theory===

Transition State Theory is classical, it doesn't take quantum tunnelling into account.Quantum tunnelling is probable for this reaction as it involves the transfer of a hydrogen atom, particularly at lower temperatures.'''Reference 3'''At low temperatures, the H atom can tunnel through the potential energy barrier than to pass over the barrier, hence the activation energy is lowered and the reaction rate increases. However, recrossing the energy barrier is possible as seen with the simulations, this can have a negative effect on the reaction rate. At high temperatures, the system is thermally activated and the behavious is approximately classical.'''reference4''' Therefore the experimental reaction rates are expected to be greater than that predicted by the Transition State Theory.

==F-H-H system==
===PES inspection===
'''F+H2 (F1-H1-H2)'''

F+H2 is exothermic as the reactants are higher in energy than the products therefore during the reaction, energy is released to the surroundings. H-F bond is stronger than H-H bond as the products are lower in energy and therefore more stable.The transition state is located approximately at rF1-H1=181.10 pm and rH1-H2=74.49 pm. This is verified by the forces (close to zero) and eigenvalues for hessian matrix (they are of opposite signs). The activation energy is estimated by tilting the transition state towards the reactants and is shown to be 424 kJ.mol-1.
[[File:Fh2_015083.png |400px|centre|thumb|Surface plot for F1-H1-H2 system using Dynamic Calculation, the transition state is identified as the black dot.]]
[[File:OptimisationFhh1_01508.png|400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:F1H1H2_EA_0150.png|400px|centre|thumb|Counter plot for estimating the activation energy.]]
[[File:EA1_01508.png|400px|centre|thumb|parameters for the activation energy.]]
'''H+HF (H1-H2-F1)'''
This reaction is endothermis as the reactants are lower in energy than the products therefore energy is taken in from the surroundings to form the products. H-F bond is still stronger than H-H as the reactans are lower in energy and more stable. The transition state is located at approximately rH1-H2=280 pm and rH2-F1=92 pm. It is located with the same reasons stated above.With the same method, the activation energy is estimated to be 434 kJ.mol-1. The two activation energies should be identical as these two reactions are essentially the reverse of one another.

[[File:H+HF_01508310.png|400px|centre|thumb|Surface plot for H1-H2-F1 system using Dynamic Calculationthe, the transition state is identified as the black dot.]]
[[File:HHF_015083.png |400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:EA2_01508.png|400px|centre|thumb|Counter plot for estimating the activation energy.]]
[[File:EA2_PARAMETERS.png|400px|centre|thumb|parameters for the activation energy.]]

===Reaction dynamics===
===F+H2 system===

Initially, the reactants have kinetic energy in the form of vibrational and translational energies, and as it crosses the potential energy barrier, the kinetic energy is converted into potential energy. Once the system is exiting the product channel, the potential energy is converted into the vibrational energy of the product.One good experimental technique to prob the electronic structure of the reacting species will be IR spectroscopy.In the anharmonic oscillator model, exciting molecules in the relaxed state promotes excitation from the ground state to the first energy level mainly. This will give rise to a single peak in the IR spectrum. Howver, when exciting a sample of excited molecules, many transitions are possible. For example, from 0-->1, the fundamental or 1-->2, the first overtone. They will show up in the spectrum as 2 peaks, with the overtone being at a lower wavenumber as the energy gap decreases up the potential well. The intensity of the overtone decreases over time as the electrons can fall back to lower energy levels and energy is emitted as radiation. As this system is linear, rotational is not important electronic energy is not considered here.Photoelectron spectroscopy is also a viable method. '''reference 5'''

[[File:Reactiondynamicsfh2_0150.png||400px|centre|thumb|contour plot for F+H2.]]
[[File:Reactiondynamicsparameter——015.png |400px|centre|thumb|parameters for the reactive trajectory.]]
====Varying the momentum of HH in the F+H2 system.====
Conditions:rFH=182 pm, rHH=74 pm, PFH=-1.0g.mol-1.pm.fs-1
{| class="wikitable" border="1"
|+ caption
|-
|PHH/g.mol-1.pm.fs-1|| Contour Plot
|-
|0 || [[File:0_015083.png |400 px|centre]]
|-
|2 || [[File:2_0508.png |400 px|centre]]
|-
|4 || [[File:4_01508.png ‎|400 px|centre]]
|-
|6.1|| [[File:6_01508.png|400 px|centre]]
|-
| -2|| [[File:-2_01508.png|400 px|centre]]
|-
| -4|| [[File:-4.1_01508.png‎|400 px|centre]]
|-
| -6.1|| [[File:Fit1_01508.png|400 px|centre]]
|-
|}
Although the amount of energy that is put into H-H vibration is much more than the activation energy of the reaction, the reaction does not always occur. The large amount of energy is demonstrated by the high frequency of those wavy lines. Recrossing the transition states multiple times can lead to no reaction or product formation depending on how the tragectory collides with the potential well.

[[File:Reactiondynamic_last01588.png|400px|centre|thumb|contour plot for rFH=182 pm, fHH=74 pm, PFH=-1.6g.mol-1.pm.fs-1,PHH=0.2g.mol-1.pm.fs-1]]
The system now has much less vibrational energy into the reactants than before. The reaction is still successful and the trajectory recrosses the transition states fewer times than before.This can be explained by the increased momentum of FH so that F can approach the closest H with more vibrational energy.

===H+HF system===
{| class="wikitable" border="1"
!Graph Number!! p1(HH)/g.mol-1.pm.fs-1 !! p2(HF)/g.mol-1.pm.fs-1!! Etot/kJmol-1!! Recative?!! Illustration of the trajectory
|-
|1|| -2 || -10||-397|| No|| [[File:Final1_01508.png|350px ]]
|-
|2|| 0|| -8||-400 || No|| [[File:Final2_015.png|350px]]
|-
|3||5 || -6||-360|| No|| [[File:Final3_015.png|350px]]
|-
|4|| 5 || -3||-389 || Yes||[[File:Final4_015.png|350px]]
|-
|}

by referening to Polanyl's empirical rules, an exothermic reaction has an early barrier, which happens in the entrance channel. It tends to favour vibrational excitation of the products. On the other hand, an endothermic reaction has a late barrier, which occurs in the product channel. It tends to favour low product vibrational excitation. The location of the energy barrier is also crucial for a successful reaction. Translational energy of the reactants is the most effective at passing the early barrier whereas vibrational energy of the reactants is the most effective at surmounting the late barrier.This reaction is endothermic, and hence it has a late barrier. In all the graphs, the reactants all have vibrational energy as indicated by the wavy line in the reactant channel.
==References==

<references>
<ref name="reference 1">R. DeKock and H. Gray, Chemical structure and bonding, Univeristy Science Books, 1989.</ref>
</references>

MRD:01508310

2020-05-22T18:25:38Z

Hh2218: /* H+HF system */

==H-H-H system==
===Dynamics from the transition state region===
The transition state is the point on the potential energy surface that has ∂V(ri)/∂ri=0, where ri is the distance between two atoms.The transition state is a local maximum and its second derivative ∂2V(ri)/∂ri2 is < 0, whereas a local minimum will have a positive second derivative instead.
[[File:Hhh_surfaceplot_01508.png|400px|thumb|centre|a potential energy surface plot of H and H2 with respect to interatomic distances.]]

===Trajectories from r1=r2: locating the transition state===
At the transition state, r1=r2=90.8 pm by estimation. At this separation, the forces acting along AB and BC are both -0.004 kJ.mol-1.pm-1, which is close to zero and the eigenvalues for the Hessian matrix were -0.028 and +0.167 kJ.mol-1.pm-2, indicating the presence of transition state. The Internuclear Distance vs Time plot suggests the distance between HA, HB and HC is equal, about 90 pm and the distance is constant over time suggests the atoms are static at the transition state.
[[File:Animation101508310.png|400px|centre|thumb|picture showing H and H2 at the transition state.]]
[[File:Optimisation1_01508310.png|400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:Internucleardistance_01508310.png|400px|centre|thumb|Internuclear Distance vs Time plot between the H atoms at the transition state.]]

===Calculating the reaction path===
When rA-B is set to rts+1 and rB-C equals rts,the transition rolls towards BC and HA remains as an atom. MEP and Dynamic reaction paths are different as MEP set the momenta to zero in every step of the reaction path, products are therefore static and hence the reaction path is relatively straight. The dynamic reaction path is more realistic. It takes the momenta of gaseous molecules into account,i.e. they have vibrational energies, that is illustrated by the wavy line along the reaction path.
[[File:Surface_Plot1mep_015083.png|400px|centre|thumb|the minimum energy path (mep) of the H-H-H system]]
[[File:01569348_MEP_AB1_dynamic.png|400px|centre|thumb|the dynamic reaction path of the H-H-H system]]

====MEP and Dynamics calculations comparisons====
'''r1=91.8 pm, r2=90.8 pm, momenta set to 0 g.mol-1.pm.fs-1'''

HB and HC form a H2 molecule whereas HA moves away from the molecule. The distance between B and C decreased to 74 pm, which is the hydrogen molecule bond length. '''reference 2'''In MEP calculation, the momenta are set to zero at each time step.

[[File:MepH2bondlength_01508.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using MEP calculation.]]

[[File:MepH2momenta015083.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using MEP calculation.]]

Using Dynamics calculation, the outcome of the reaction is the same. The transition state rolls towards HB and HC and a hydrogen molecule is formed. One noticeable difference is that the hydrogen molecule now has some vibational energy as indicated by the wavy line along the B-C distance in the Internuclear Distance vs Time plot.As for the Momenta vs Time plot, the system is linear, therefore the angle theta is zero. HA and HB are moving away from each other at '''an increasing velocity until the momentum reaches 5 g.mol-1.pm.fs-1.The oscillation along the B-C bond corresponds to the vibration of the bond. '''why does the beginning have negative momenta?'''
[[File:DynamicsH2_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation.]]
[[File:DynamicsH2monenta_01508.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using Dynamics calculation.]]

'''r1=90.8 pm, r2=91.8 pm, momenta set to 0 g.mol-1.pm.fs-1'''

Once the length of r1 and r2 switches, the shapes of the graphs are identical but instead of HB and HC forming a molecule, HA and HB now form the hydrogen molecule in the products.
[[File:Mepinter2_01508.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using MEP calculation.]]
[[File:Momentamep2_015.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using MEP calculation.]]
[[File:InterDynamic_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation.]]
[[File:Momentadynamics_015083.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using Dynamics calculation.]]

'''Trajectory starting with the final position and reversed momentum to the reaction path above'''

This trajectory starts at the end of the reaction path above and finishes at where the above reaction started. it is essentially a reverse of what happened in the reaction above.
[[File:Reverse_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation (r1=70.0 pm,r2=353 pm,p1=-3.21 g.mol-1.pm.fs-1, p2=-5.07 g.mol-1.pm.fs-1) .]]

===Recative and unreactive trajectories===
{| class="wikitable" border="1"
! p1/g.mol-1.pm.fs-1 !! p2/g.mol-1.pm.fs-1!! Etot/kJmol-1!! Recative?!! Description of the dynamics!! Illustration of the trajectory
|-
| -2.56 || -5.1||-414 || Yes||The translational energy of the reactants can surmount the potential energy barrier and form the products. The ramaining energy is converted into vibrational energy of the products. || [[File:Table1_01508310.png|350px ]]
|-
| -3.1 || -4.1||-420 || No||The reactant H2 has vibrational energy and its rAB motion is rapid. Before it could cross the energy barrier, the molecule slams into the repulsive inner wall of the potential surface and bounces back into the reactant channel. || [[File:Table2_0150.png|350px]]
|-
| -3.1 || -5.1||-414|| Yes||The reactants have both the translational and vibrational energies. The energy is used to surmount the potential energy barrier and converted into the vibrational energy of the products. || [[File:Table3_01508.png|350px]]
|-
| -5.1 || -10.1||-357 || No||The reactants have sufficient energy to cross the transition state and the products did form for a certain amount of time. However, before the the system can exit the product channel, it recrosses the transition state and form the reactants again, hence no reaction occurs. ||[[File:Table4_01508.png|350px]]
|-
| -5.1 || -10.6||-394 || Yes||The system has sufficient energy to cross the transition state but it recrosses the transition state shortly after the reaction path hits the potential energy surface. However, the system is able to cross the transition state for the third time and finally exits the product channel and forms the products. || [[File:-10.6_01508.png|350px]]
|-
|}
In order to form products, a system must have sufficient energy to cross the transition state. Only molecules with the correct phase '''reference 2''' can exit the product channel and form stable products. Recrossing the transition state can lead to either product formation or no reaction. It is possible to cross the transition state multiple times.

===Transition State Theory===

Transition State Theory is classical, it doesn't take quantum tunnelling into account.Quantum tunnelling is probable for this reaction as it involves the transfer of a hydrogen atom, particularly at lower temperatures.'''Reference 3'''At low temperatures, the H atom can tunnel through the potential energy barrier than to pass over the barrier, hence the activation energy is lowered and the reaction rate increases. However, recrossing the energy barrier is possible as seen with the simulations, this can have a negative effect on the reaction rate. At high temperatures, the system is thermally activated and the behavious is approximately classical.'''reference4''' Therefore the experimental reaction rates are expected to be greater than that predicted by the Transition State Theory.

==F-H-H system==
===PES inspection===
'''F+H2 (F1-H1-H2)'''

F+H2 is exothermic as the reactants are higher in energy than the products therefore during the reaction, energy is released to the surroundings. H-F bond is stronger than H-H bond as the products are lower in energy and therefore more stable.The transition state is located approximately at rF1-H1=181.10 pm and rH1-H2=74.49 pm. This is verified by the forces (close to zero) and eigenvalues for hessian matrix (they are of opposite signs). The activation energy is estimated by tilting the transition state towards the reactants and is shown to be 424 kJ.mol-1.
[[File:Fh2_015083.png |400px|centre|thumb|Surface plot for F1-H1-H2 system using Dynamic Calculation, the transition state is identified as the black dot.]]
[[File:OptimisationFhh1_01508.png|400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:F1H1H2_EA_0150.png|400px|centre|thumb|Counter plot for estimating the activation energy.]]
[[File:EA1_01508.png|400px|centre|thumb|parameters for the activation energy.]]
'''H+HF (H1-H2-F1)'''
This reaction is endothermis as the reactants are lower in energy than the products therefore energy is taken in from the surroundings to form the products. H-F bond is still stronger than H-H as the reactans are lower in energy and more stable. The transition state is located at approximately rH1-H2=280 pm and rH2-F1=92 pm. It is located with the same reasons stated above.With the same method, the activation energy is estimated to be 434 kJ.mol-1. The two activation energies should be identical as these two reactions are essentially the reverse of one another.

[[File:H+HF_01508310.png|400px|centre|thumb|Surface plot for H1-H2-F1 system using Dynamic Calculationthe, the transition state is identified as the black dot.]]
[[File:HHF_015083.png |400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:EA2_01508.png|400px|centre|thumb|Counter plot for estimating the activation energy.]]
[[File:EA2_PARAMETERS.png|400px|centre|thumb|parameters for the activation energy.]]

===Reaction dynamics===
===F+H2 system===

Initially, the reactants have kinetic energy in the form of vibrational and translational energies, and as it crosses the potential energy barrier, the kinetic energy is converted into potential energy. Once the system is exiting the product channel, the potential energy is converted into the vibrational energy of the product.One good experimental technique to prob the electronic structure of the reacting species will be IR spectroscopy.In the anharmonic oscillator model, exciting molecules in the relaxed state promotes excitation from the ground state to the first energy level mainly. This will give rise to a single peak in the IR spectrum. Howver, when exciting a sample of excited molecules, many transitions are possible. For example, from 0-->1, the fundamental or 1-->2, the first overtone. They will show up in the spectrum as 2 peaks, with the overtone being at a lower wavenumber as the energy gap decreases up the potential well. The intensity of the overtone decreases over time as the electrons can fall back to lower energy levels and energy is emitted as radiation. As this system is linear, rotational is not important electronic energy is not considered here.Photoelectron spectroscopy is also a viable method. '''reference 5'''

[[File:Reactiondynamicsfh2_0150.png||400px|centre|thumb|contour plot for F+H2.]]
[[File:Reactiondynamicsparameter——015.png |400px|centre|thumb|parameters for the reactive trajectory.]]
====Varying the momentum of HH in the F+H2 system.====
Conditions:rFH=182 pm, rHH=74 pm, PFH=-1.0g.mol-1.pm.fs-1
{| class="wikitable" border="1"
|+ caption
|-
|PHH/g.mol-1.pm.fs-1|| Contour Plot
|-
|0 || [[File:0_015083.png |400 px|centre]]
|-
|2 || [[File:2_0508.png |400 px|centre]]
|-
|4 || [[File:4_01508.png ‎|400 px|centre]]
|-
|6.1|| [[File:6_01508.png|400 px|centre]]
|-
| -2|| [[File:-2_01508.png|400 px|centre]]
|-
| -4|| [[File:-4.1_01508.png‎|400 px|centre]]
|-
| -6.1|| [[File:Fit1_01508.png|400 px|centre]]
|-
|}
Although the amount of energy that is put into H-H vibration is much more than the activation energy of the reaction, the reaction does not always occur. The large amount of energy is demonstrated by the high frequency of those wavy lines. Recrossing the transition states multiple times can lead to no reaction or product formation depending on how the tragectory collides with the potential well.

[[File:Reactiondynamic_last01588.png|400px|centre|thumb|contour plot for rFH=182 pm, fHH=74 pm, PFH=-1.6g.mol-1.pm.fs-1,PHH=0.2g.mol-1.pm.fs-1]]
The system now has much less vibrational energy into the reactants than before. The reaction is still successful and the trajectory recrosses the transition states fewer times than before.This can be explained by the increased momentum of FH so that F can approach the closest H with more vibrational energy.

===H+HF system===
{| class="wikitable" border="1"
!Graph Number!! p1(HH)/g.mol-1.pm.fs-1 !! p2(HF)/g.mol-1.pm.fs-1!! Etot/kJmol-1!! Recative?!! Illustration of the trajectory
|-
|1|| -2 || -10||-397|| No|| [[File:Final1_01508.png|350px ]]
|-
|2|| 0|| -8||-400 || No|| [[File:Final2_015.png|350px]]
|-
|3||5 || -6||-360|| No|| [[File:Final3_015.png|350px]]
|-
|4|| 5 || -3||-389 || Yes||[[File:Final4_015.png|350px]]
|-
|}

by referening to Polanyl's empirical rules, an exothermic reaction has an early barrier, which happens in the entrance channel. It tends to favour vibrational excitation of the products. On the other hand, an endothermic reaction has a late barrier, which occurs in the product channel. It tends to favour low product vibrational excitation. The location of the energy barrier is also crucial for a successful reaction. Translational energy of the reactants is the most effective at passing the early barrier whereas vibrational energy of the reactants is the most effective at surmounting the late barrier.This reaction is endothermic, and hence it has a late barrier. In all the graphs, the reactants all have vibrational energy as indicated by the wavy line in the reactant channel.
==References==

<references>
<ref name="reference 1">R. DeKock and H. Gray, Chemical structure and bonding, Univeristy Science Books, 1989.</ref>
</references>

MRD:01508310

2020-05-22T18:23:14Z

Hh2218:

==H-H-H system==
===Dynamics from the transition state region===
The transition state is the point on the potential energy surface that has ∂V(ri)/∂ri=0, where ri is the distance between two atoms.The transition state is a local maximum and its second derivative ∂2V(ri)/∂ri2 is < 0, whereas a local minimum will have a positive second derivative instead.
[[File:Hhh_surfaceplot_01508.png|400px|thumb|centre|a potential energy surface plot of H and H2 with respect to interatomic distances.]]

===Trajectories from r1=r2: locating the transition state===
At the transition state, r1=r2=90.8 pm by estimation. At this separation, the forces acting along AB and BC are both -0.004 kJ.mol-1.pm-1, which is close to zero and the eigenvalues for the Hessian matrix were -0.028 and +0.167 kJ.mol-1.pm-2, indicating the presence of transition state. The Internuclear Distance vs Time plot suggests the distance between HA, HB and HC is equal, about 90 pm and the distance is constant over time suggests the atoms are static at the transition state.
[[File:Animation101508310.png|400px|centre|thumb|picture showing H and H2 at the transition state.]]
[[File:Optimisation1_01508310.png|400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:Internucleardistance_01508310.png|400px|centre|thumb|Internuclear Distance vs Time plot between the H atoms at the transition state.]]

===Calculating the reaction path===
When rA-B is set to rts+1 and rB-C equals rts,the transition rolls towards BC and HA remains as an atom. MEP and Dynamic reaction paths are different as MEP set the momenta to zero in every step of the reaction path, products are therefore static and hence the reaction path is relatively straight. The dynamic reaction path is more realistic. It takes the momenta of gaseous molecules into account,i.e. they have vibrational energies, that is illustrated by the wavy line along the reaction path.
[[File:Surface_Plot1mep_015083.png|400px|centre|thumb|the minimum energy path (mep) of the H-H-H system]]
[[File:01569348_MEP_AB1_dynamic.png|400px|centre|thumb|the dynamic reaction path of the H-H-H system]]

====MEP and Dynamics calculations comparisons====
'''r1=91.8 pm, r2=90.8 pm, momenta set to 0 g.mol-1.pm.fs-1'''

HB and HC form a H2 molecule whereas HA moves away from the molecule. The distance between B and C decreased to 74 pm, which is the hydrogen molecule bond length. '''reference 2'''In MEP calculation, the momenta are set to zero at each time step.

[[File:MepH2bondlength_01508.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using MEP calculation.]]

[[File:MepH2momenta015083.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using MEP calculation.]]

Using Dynamics calculation, the outcome of the reaction is the same. The transition state rolls towards HB and HC and a hydrogen molecule is formed. One noticeable difference is that the hydrogen molecule now has some vibational energy as indicated by the wavy line along the B-C distance in the Internuclear Distance vs Time plot.As for the Momenta vs Time plot, the system is linear, therefore the angle theta is zero. HA and HB are moving away from each other at '''an increasing velocity until the momentum reaches 5 g.mol-1.pm.fs-1.The oscillation along the B-C bond corresponds to the vibration of the bond. '''why does the beginning have negative momenta?'''
[[File:DynamicsH2_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation.]]
[[File:DynamicsH2monenta_01508.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using Dynamics calculation.]]

'''r1=90.8 pm, r2=91.8 pm, momenta set to 0 g.mol-1.pm.fs-1'''

Once the length of r1 and r2 switches, the shapes of the graphs are identical but instead of HB and HC forming a molecule, HA and HB now form the hydrogen molecule in the products.
[[File:Mepinter2_01508.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using MEP calculation.]]
[[File:Momentamep2_015.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using MEP calculation.]]
[[File:InterDynamic_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation.]]
[[File:Momentadynamics_015083.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using Dynamics calculation.]]

'''Trajectory starting with the final position and reversed momentum to the reaction path above'''

This trajectory starts at the end of the reaction path above and finishes at where the above reaction started. it is essentially a reverse of what happened in the reaction above.
[[File:Reverse_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation (r1=70.0 pm,r2=353 pm,p1=-3.21 g.mol-1.pm.fs-1, p2=-5.07 g.mol-1.pm.fs-1) .]]

===Recative and unreactive trajectories===
{| class="wikitable" border="1"
! p1/g.mol-1.pm.fs-1 !! p2/g.mol-1.pm.fs-1!! Etot/kJmol-1!! Recative?!! Description of the dynamics!! Illustration of the trajectory
|-
| -2.56 || -5.1||-414 || Yes||The translational energy of the reactants can surmount the potential energy barrier and form the products. The ramaining energy is converted into vibrational energy of the products. || [[File:Table1_01508310.png|350px ]]
|-
| -3.1 || -4.1||-420 || No||The reactant H2 has vibrational energy and its rAB motion is rapid. Before it could cross the energy barrier, the molecule slams into the repulsive inner wall of the potential surface and bounces back into the reactant channel. || [[File:Table2_0150.png|350px]]
|-
| -3.1 || -5.1||-414|| Yes||The reactants have both the translational and vibrational energies. The energy is used to surmount the potential energy barrier and converted into the vibrational energy of the products. || [[File:Table3_01508.png|350px]]
|-
| -5.1 || -10.1||-357 || No||The reactants have sufficient energy to cross the transition state and the products did form for a certain amount of time. However, before the the system can exit the product channel, it recrosses the transition state and form the reactants again, hence no reaction occurs. ||[[File:Table4_01508.png|350px]]
|-
| -5.1 || -10.6||-394 || Yes||The system has sufficient energy to cross the transition state but it recrosses the transition state shortly after the reaction path hits the potential energy surface. However, the system is able to cross the transition state for the third time and finally exits the product channel and forms the products. || [[File:-10.6_01508.png|350px]]
|-
|}
In order to form products, a system must have sufficient energy to cross the transition state. Only molecules with the correct phase '''reference 2''' can exit the product channel and form stable products. Recrossing the transition state can lead to either product formation or no reaction. It is possible to cross the transition state multiple times.

===Transition State Theory===

Transition State Theory is classical, it doesn't take quantum tunnelling into account.Quantum tunnelling is probable for this reaction as it involves the transfer of a hydrogen atom, particularly at lower temperatures.'''Reference 3'''At low temperatures, the H atom can tunnel through the potential energy barrier than to pass over the barrier, hence the activation energy is lowered and the reaction rate increases. However, recrossing the energy barrier is possible as seen with the simulations, this can have a negative effect on the reaction rate. At high temperatures, the system is thermally activated and the behavious is approximately classical.'''reference4''' Therefore the experimental reaction rates are expected to be greater than that predicted by the Transition State Theory.

==F-H-H system==
===PES inspection===
'''F+H2 (F1-H1-H2)'''

F+H2 is exothermic as the reactants are higher in energy than the products therefore during the reaction, energy is released to the surroundings. H-F bond is stronger than H-H bond as the products are lower in energy and therefore more stable.The transition state is located approximately at rF1-H1=181.10 pm and rH1-H2=74.49 pm. This is verified by the forces (close to zero) and eigenvalues for hessian matrix (they are of opposite signs). The activation energy is estimated by tilting the transition state towards the reactants and is shown to be 424 kJ.mol-1.
[[File:Fh2_015083.png |400px|centre|thumb|Surface plot for F1-H1-H2 system using Dynamic Calculation, the transition state is identified as the black dot.]]
[[File:OptimisationFhh1_01508.png|400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:F1H1H2_EA_0150.png|400px|centre|thumb|Counter plot for estimating the activation energy.]]
[[File:EA1_01508.png|400px|centre|thumb|parameters for the activation energy.]]
'''H+HF (H1-H2-F1)'''
This reaction is endothermis as the reactants are lower in energy than the products therefore energy is taken in from the surroundings to form the products. H-F bond is still stronger than H-H as the reactans are lower in energy and more stable. The transition state is located at approximately rH1-H2=280 pm and rH2-F1=92 pm. It is located with the same reasons stated above.With the same method, the activation energy is estimated to be 434 kJ.mol-1. The two activation energies should be identical as these two reactions are essentially the reverse of one another.

[[File:H+HF_01508310.png|400px|centre|thumb|Surface plot for H1-H2-F1 system using Dynamic Calculationthe, the transition state is identified as the black dot.]]
[[File:HHF_015083.png |400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:EA2_01508.png|400px|centre|thumb|Counter plot for estimating the activation energy.]]
[[File:EA2_PARAMETERS.png|400px|centre|thumb|parameters for the activation energy.]]

===Reaction dynamics===
===F+H2 system===

Initially, the reactants have kinetic energy in the form of vibrational and translational energies, and as it crosses the potential energy barrier, the kinetic energy is converted into potential energy. Once the system is exiting the product channel, the potential energy is converted into the vibrational energy of the product.One good experimental technique to prob the electronic structure of the reacting species will be IR spectroscopy.In the anharmonic oscillator model, exciting molecules in the relaxed state promotes excitation from the ground state to the first energy level mainly. This will give rise to a single peak in the IR spectrum. Howver, when exciting a sample of excited molecules, many transitions are possible. For example, from 0-->1, the fundamental or 1-->2, the first overtone. They will show up in the spectrum as 2 peaks, with the overtone being at a lower wavenumber as the energy gap decreases up the potential well. The intensity of the overtone decreases over time as the electrons can fall back to lower energy levels and energy is emitted as radiation. As this system is linear, rotational is not important electronic energy is not considered here.Photoelectron spectroscopy is also a viable method. '''reference 5'''

[[File:Reactiondynamicsfh2_0150.png||400px|centre|thumb|contour plot for F+H2.]]
[[File:Reactiondynamicsparameter——015.png |400px|centre|thumb|parameters for the reactive trajectory.]]
====Varying the momentum of HH in the F+H2 system.====
Conditions:rFH=182 pm, rHH=74 pm, PFH=-1.0g.mol-1.pm.fs-1
{| class="wikitable" border="1"
|+ caption
|-
|PHH/g.mol-1.pm.fs-1|| Contour Plot
|-
|0 || [[File:0_015083.png |400 px|centre]]
|-
|2 || [[File:2_0508.png |400 px|centre]]
|-
|4 || [[File:4_01508.png ‎|400 px|centre]]
|-
|6.1|| [[File:6_01508.png|400 px|centre]]
|-
| -2|| [[File:-2_01508.png|400 px|centre]]
|-
| -4|| [[File:-4.1_01508.png‎|400 px|centre]]
|-
| -6.1|| [[File:Fit1_01508.png|400 px|centre]]
|-
|}
Although the amount of energy that is put into H-H vibration is much more than the activation energy of the reaction, the reaction does not always occur. The large amount of energy is demonstrated by the high frequency of those wavy lines. Recrossing the transition states multiple times can lead to no reaction or product formation depending on how the tragectory collides with the potential well.

[[File:Reactiondynamic_last01588.png|400px|centre|thumb|contour plot for rFH=182 pm, fHH=74 pm, PFH=-1.6g.mol-1.pm.fs-1,PHH=0.2g.mol-1.pm.fs-1]]
The system now has much less vibrational energy into the reactants than before. The reaction is still successful and the trajectory recrosses the transition states fewer times than before.This can be explained by the increased momentum of FH so that F can approach the closest H with more vibrational energy.

===H+HF system===
{| class="wikitable" border="1"
!Graph Number!! p1(HH)/g.mol-1.pm.fs-1 !! p2(HF)/g.mol-1.pm.fs-1!! Etot/kJmol-1!! Recative?!! Illustration of the trajectory
|-
|1|| -2 || -10||-397|| No|| [[File:Final1_01508.png|350px ]]
|-
|2|| 0|| -8||-400 || No|| [[File:Final2_015.png|350px]]
|-
|3||5 || -6||-360|| No|| [[File:Final3_015.png|350px]]
|-
|4|| 5 || -3||-389 || Yes||[[File:Final4_015.png|350px]]
|-
|}

by referening to Polanyl's empirical rules, an exothermic reaction has an early barrier, which happens in the entrance channel. It tends to favour vibrational excitation of the products. On the other hand, an endothermic reaction has a late barrier, which occurs in the product channel. It tends to favour low product vibrational excitation. The location of the energy barrier is also crucial for a successful reaction. Translational energy of the reactants is the most effective at passing the early barrier whereas vibrational energy of the reactants is the most effective at surmounting the late barrier.This reaction is endothermic, and hence it has a late barrier. In all the graphs, the reactants all have vibrational energy as indicated by the wavy line in the reactant channel.

MRD:01508310

2020-05-22T18:19:36Z

Hh2218: /* MEP and Dynamics calculations comparisons */

==H-H-H system==
===Dynamics from the transition state region===
The transition state is the point on the potential energy surface that has ∂V(ri)/∂ri=0, where ri is the distance between two atoms.The transition state is a local maximum and its second derivative ∂2V(ri)/∂ri2 is < 0, whereas a local minimum will have a positive second derivative instead.
[[File:Hhh_surfaceplot_01508.png|400px|thumb|centre|a potential energy surface plot of H and H2 with respect to interatomic distances.]]

===Trajectories from r1=r2: locating the transition state===
At the transition state, r1=r2=90.8 pm by estimation. At this separation, the forces acting along AB and BC are both -0.004 kJ.mol-1.pm-1, which is close to zero and the eigenvalues for the Hessian matrix were -0.028 and +0.167 kJ.mol-1.pm-2, indicating the presence of transition state. The Internuclear Distance vs Time plot suggests the distance between HA, HB and HC is equal, about 90 pm and the distance is constant over time suggests the atoms are static at the transition state.
[[File:Animation101508310.png|400px|centre|thumb|picture showing H and H2 at the transition state.]]
[[File:Optimisation1_01508310.png|400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:Internucleardistance_01508310.png|400px|centre|thumb|Internuclear Distance vs Time plot between the H atoms at the transition state.]]

===Calculating the reaction path===
When rA-B is set to rts+1 and rB-C equals rts,the transition rolls towards BC and HA remains as an atom. MEP and Dynamic reaction paths are different as MEP set the momenta to zero in every step of the reaction path, products are therefore static and hence the reaction path is relatively straight. The dynamic reaction path is more realistic. It takes the momenta of gaseous molecules into account,i.e. they have vibrational energies, that is illustrated by the wavy line along the reaction path.
[[File:Surface_Plot1mep_015083.png|400px|centre|thumb|the minimum energy path (mep) of the H-H-H system]]
[[File:01569348_MEP_AB1_dynamic.png|400px|centre|thumb|the dynamic reaction path of the H-H-H system]]

====MEP and Dynamics calculations comparisons====
'''r1=91.8 pm, r2=90.8 pm, momenta set to 0 g.mol-1.pm.fs-1'''

HB and HC form a H2 molecule whereas HA moves away from the molecule. The distance between B and C decreased to 74 pm, which is the hydrogen molecule bond length. <ref name="reference1"/> In MEP calculation, the momenta are set to zero at each time step.

[[File:MepH2bondlength_01508.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using MEP calculation.]]

[[File:MepH2momenta015083.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using MEP calculation.]]

Using Dynamics calculation, the outcome of the reaction is the same. The transition state rolls towards HB and HC and a hydrogen molecule is formed. One noticeable difference is that the hydrogen molecule now has some vibational energy as indicated by the wavy line along the B-C distance in the Internuclear Distance vs Time plot.As for the Momenta vs Time plot, the system is linear, therefore the angle theta is zero. HA and HB are moving away from each other at '''an increasing velocity until the momentum reaches 5 g.mol-1.pm.fs-1.The oscillation along the B-C bond corresponds to the vibration of the bond. '''why does the beginning have negative momenta?'''
[[File:DynamicsH2_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation.]]
[[File:DynamicsH2monenta_01508.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using Dynamics calculation.]]

'''r1=90.8 pm, r2=91.8 pm, momenta set to 0 g.mol-1.pm.fs-1'''

Once the length of r1 and r2 switches, the shapes of the graphs are identical but instead of HB and HC forming a molecule, HA and HB now form the hydrogen molecule in the products.
[[File:Mepinter2_01508.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using MEP calculation.]]
[[File:Momentamep2_015.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using MEP calculation.]]
[[File:InterDynamic_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation.]]
[[File:Momentadynamics_015083.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using Dynamics calculation.]]

'''Trajectory starting with the final position and reversed momentum to the reaction path above'''

This trajectory starts at the end of the reaction path above and finishes at where the above reaction started. it is essentially a reverse of what happened in the reaction above.
[[File:Reverse_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation (r1=70.0 pm,r2=353 pm,p1=-3.21 g.mol-1.pm.fs-1, p2=-5.07 g.mol-1.pm.fs-1) .]]

===Recative and unreactive trajectories===
{| class="wikitable" border="1"
! p1/g.mol-1.pm.fs-1 !! p2/g.mol-1.pm.fs-1!! Etot/kJmol-1!! Recative?!! Description of the dynamics!! Illustration of the trajectory
|-
| -2.56 || -5.1||-414 || Yes||The translational energy of the reactants can surmount the potential energy barrier and form the products. The ramaining energy is converted into vibrational energy of the products. || [[File:Table1_01508310.png|350px ]]
|-
| -3.1 || -4.1||-420 || No||The reactant H2 has vibrational energy and its rAB motion is rapid. Before it could cross the energy barrier, the molecule slams into the repulsive inner wall of the potential surface and bounces back into the reactant channel. || [[File:Table2_0150.png|350px]]
|-
| -3.1 || -5.1||-414|| Yes||The reactants have both the translational and vibrational energies. The energy is used to surmount the potential energy barrier and converted into the vibrational energy of the products. || [[File:Table3_01508.png|350px]]
|-
| -5.1 || -10.1||-357 || No||The reactants have sufficient energy to cross the transition state and the products did form for a certain amount of time. However, before the the system can exit the product channel, it recrosses the transition state and form the reactants again, hence no reaction occurs. ||[[File:Table4_01508.png|350px]]
|-
| -5.1 || -10.6||-394 || Yes||The system has sufficient energy to cross the transition state but it recrosses the transition state shortly after the reaction path hits the potential energy surface. However, the system is able to cross the transition state for the third time and finally exits the product channel and forms the products. || [[File:-10.6_01508.png|350px]]
|-
|}
In order to form products, a system must have sufficient energy to cross the transition state. Only molecules with the correct phase '''reference 2''' can exit the product channel and form stable products. Recrossing the transition state can lead to either product formation or no reaction. It is possible to cross the transition state multiple times.

===Transition State Theory===

Transition State Theory is classical, it doesn't take quantum tunnelling into account.Quantum tunnelling is probable for this reaction as it involves the transfer of a hydrogen atom, particularly at lower temperatures.'''Reference 3'''At low temperatures, the H atom can tunnel through the potential energy barrier than to pass over the barrier, hence the activation energy is lowered and the reaction rate increases. However, recrossing the energy barrier is possible as seen with the simulations, this can have a negative effect on the reaction rate. At high temperatures, the system is thermally activated and the behavious is approximately classical.'''reference4''' Therefore the experimental reaction rates are expected to be greater than that predicted by the Transition State Theory.

==F-H-H system==
===PES inspection===
'''F+H2 (F1-H1-H2)'''

F+H2 is exothermic as the reactants are higher in energy than the products therefore during the reaction, energy is released to the surroundings. H-F bond is stronger than H-H bond as the products are lower in energy and therefore more stable.The transition state is located approximately at rF1-H1=181.10 pm and rH1-H2=74.49 pm. This is verified by the forces (close to zero) and eigenvalues for hessian matrix (they are of opposite signs). The activation energy is estimated by tilting the transition state towards the reactants and is shown to be 424 kJ.mol-1.
[[File:Fh2_015083.png |400px|centre|thumb|Surface plot for F1-H1-H2 system using Dynamic Calculation, the transition state is identified as the black dot.]]
[[File:OptimisationFhh1_01508.png|400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:F1H1H2_EA_0150.png|400px|centre|thumb|Counter plot for estimating the activation energy.]]
[[File:EA1_01508.png|400px|centre|thumb|parameters for the activation energy.]]
'''H+HF (H1-H2-F1)'''
This reaction is endothermis as the reactants are lower in energy than the products therefore energy is taken in from the surroundings to form the products. H-F bond is still stronger than H-H as the reactans are lower in energy and more stable. The transition state is located at approximately rH1-H2=280 pm and rH2-F1=92 pm. It is located with the same reasons stated above.With the same method, the activation energy is estimated to be 434 kJ.mol-1. The two activation energies should be identical as these two reactions are essentially the reverse of one another.

[[File:H+HF_01508310.png|400px|centre|thumb|Surface plot for H1-H2-F1 system using Dynamic Calculationthe, the transition state is identified as the black dot.]]
[[File:HHF_015083.png |400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:EA2_01508.png|400px|centre|thumb|Counter plot for estimating the activation energy.]]
[[File:EA2_PARAMETERS.png|400px|centre|thumb|parameters for the activation energy.]]

===Reaction dynamics===
===F+H2 system===

Initially, the reactants have kinetic energy in the form of vibrational and translational energies, and as it crosses the potential energy barrier, the kinetic energy is converted into potential energy. Once the system is exiting the product channel, the potential energy is converted into the vibrational energy of the product.One good experimental technique to prob the electronic structure of the reacting species will be IR spectroscopy.In the anharmonic oscillator model, exciting molecules in the relaxed state promotes excitation from the ground state to the first energy level mainly. This will give rise to a single peak in the IR spectrum. Howver, when exciting a sample of excited molecules, many transitions are possible. For example, from 0-->1, the fundamental or 1-->2, the first overtone. They will show up in the spectrum as 2 peaks, with the overtone being at a lower wavenumber as the energy gap decreases up the potential well. The intensity of the overtone decreases over time as the electrons can fall back to lower energy levels and energy is emitted as radiation. As this system is linear, rotational is not important electronic energy is not considered here.Photoelectron spectroscopy is also a viable method. '''reference 5'''

[[File:Reactiondynamicsfh2_0150.png||400px|centre|thumb|contour plot for F+H2.]]
[[File:Reactiondynamicsparameter——015.png |400px|centre|thumb|parameters for the reactive trajectory.]]
====Varying the momentum of HH in the F+H2 system.====
Conditions:rFH=182 pm, rHH=74 pm, PFH=-1.0g.mol-1.pm.fs-1
{| class="wikitable" border="1"
|+ caption
|-
|PHH/g.mol-1.pm.fs-1|| Contour Plot
|-
|0 || [[File:0_015083.png |400 px|centre]]
|-
|2 || [[File:2_0508.png |400 px|centre]]
|-
|4 || [[File:4_01508.png ‎|400 px|centre]]
|-
|6.1|| [[File:6_01508.png|400 px|centre]]
|-
| -2|| [[File:-2_01508.png|400 px|centre]]
|-
| -4|| [[File:-4.1_01508.png‎|400 px|centre]]
|-
| -6.1|| [[File:Fit1_01508.png|400 px|centre]]
|-
|}
Although the amount of energy that is put into H-H vibration is much more than the activation energy of the reaction, the reaction does not always occur. The large amount of energy is demonstrated by the high frequency of those wavy lines. Recrossing the transition states multiple times can lead to no reaction or product formation depending on how the tragectory collides with the potential well.

[[File:Reactiondynamic_last01588.png|400px|centre|thumb|contour plot for rFH=182 pm, fHH=74 pm, PFH=-1.6g.mol-1.pm.fs-1,PHH=0.2g.mol-1.pm.fs-1]]
The system now has much less vibrational energy into the reactants than before. The reaction is still successful and the trajectory recrosses the transition states fewer times than before.This can be explained by the increased momentum of FH so that F can approach the closest H with more vibrational energy.

===H+HF system===
{| class="wikitable" border="1"
!Graph Number!! p1(HH)/g.mol-1.pm.fs-1 !! p2(HF)/g.mol-1.pm.fs-1!! Etot/kJmol-1!! Recative?!! Illustration of the trajectory
|-
|1|| -2 || -10||-397|| No|| [[File:Final1_01508.png|350px ]]
|-
|2|| 0|| -8||-400 || No|| [[File:Final2_015.png|350px]]
|-
|3||5 || -6||-360|| No|| [[File:Final3_015.png|350px]]
|-
|4|| 5 || -3||-389 || Yes||[[File:Final4_015.png|350px]]
|-
|}

by referening to Polanyl's empirical rules, an exothermic reaction has an early barrier, which happens in the entrance channel. It tends to favour vibrational excitation of the products. On the other hand, an endothermic reaction has a late barrier, which occurs in the product channel. It tends to favour low product vibrational excitation. The location of the energy barrier is also crucial for a successful reaction. Translational energy of the reactants is the most effective at passing the early barrier whereas vibrational energy of the reactants is the most effective at surmounting the late barrier.This reaction is endothermic, and hence it has a late barrier. In all the graphs, the reactants all have vibrational energy as indicated by the wavy line in the reactant channel.

MRD:01508310

2020-05-22T18:18:45Z

Hh2218: /* MEP and Dynamics calculations comparisons */

==H-H-H system==
===Dynamics from the transition state region===
The transition state is the point on the potential energy surface that has ∂V(ri)/∂ri=0, where ri is the distance between two atoms.The transition state is a local maximum and its second derivative ∂2V(ri)/∂ri2 is < 0, whereas a local minimum will have a positive second derivative instead.
[[File:Hhh_surfaceplot_01508.png|400px|thumb|centre|a potential energy surface plot of H and H2 with respect to interatomic distances.]]

===Trajectories from r1=r2: locating the transition state===
At the transition state, r1=r2=90.8 pm by estimation. At this separation, the forces acting along AB and BC are both -0.004 kJ.mol-1.pm-1, which is close to zero and the eigenvalues for the Hessian matrix were -0.028 and +0.167 kJ.mol-1.pm-2, indicating the presence of transition state. The Internuclear Distance vs Time plot suggests the distance between HA, HB and HC is equal, about 90 pm and the distance is constant over time suggests the atoms are static at the transition state.
[[File:Animation101508310.png|400px|centre|thumb|picture showing H and H2 at the transition state.]]
[[File:Optimisation1_01508310.png|400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:Internucleardistance_01508310.png|400px|centre|thumb|Internuclear Distance vs Time plot between the H atoms at the transition state.]]

===Calculating the reaction path===
When rA-B is set to rts+1 and rB-C equals rts,the transition rolls towards BC and HA remains as an atom. MEP and Dynamic reaction paths are different as MEP set the momenta to zero in every step of the reaction path, products are therefore static and hence the reaction path is relatively straight. The dynamic reaction path is more realistic. It takes the momenta of gaseous molecules into account,i.e. they have vibrational energies, that is illustrated by the wavy line along the reaction path.
[[File:Surface_Plot1mep_015083.png|400px|centre|thumb|the minimum energy path (mep) of the H-H-H system]]
[[File:01569348_MEP_AB1_dynamic.png|400px|centre|thumb|the dynamic reaction path of the H-H-H system]]

====MEP and Dynamics calculations comparisons====
'''r1=91.8 pm, r2=90.8 pm, momenta set to 0 g.mol-1.pm.fs-1'''

HB and HC form a H2 molecule whereas HA moves away from the molecule. The distance between B and C decreased to 74 pm, which is the hydrogen molecule bond length. <ref name="reference2"/>In MEP calculation, the momenta are set to zero at each time step.

[[File:MepH2bondlength_01508.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using MEP calculation.]]

[[File:MepH2momenta015083.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using MEP calculation.]]

Using Dynamics calculation, the outcome of the reaction is the same. The transition state rolls towards HB and HC and a hydrogen molecule is formed. One noticeable difference is that the hydrogen molecule now has some vibational energy as indicated by the wavy line along the B-C distance in the Internuclear Distance vs Time plot.As for the Momenta vs Time plot, the system is linear, therefore the angle theta is zero. HA and HB are moving away from each other at '''an increasing velocity until the momentum reaches 5 g.mol-1.pm.fs-1.The oscillation along the B-C bond corresponds to the vibration of the bond. '''why does the beginning have negative momenta?'''
[[File:DynamicsH2_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation.]]
[[File:DynamicsH2monenta_01508.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using Dynamics calculation.]]

'''r1=90.8 pm, r2=91.8 pm, momenta set to 0 g.mol-1.pm.fs-1'''

Once the length of r1 and r2 switches, the shapes of the graphs are identical but instead of HB and HC forming a molecule, HA and HB now form the hydrogen molecule in the products.
[[File:Mepinter2_01508.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using MEP calculation.]]
[[File:Momentamep2_015.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using MEP calculation.]]
[[File:InterDynamic_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation.]]
[[File:Momentadynamics_015083.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using Dynamics calculation.]]

'''Trajectory starting with the final position and reversed momentum to the reaction path above'''

This trajectory starts at the end of the reaction path above and finishes at where the above reaction started. it is essentially a reverse of what happened in the reaction above.
[[File:Reverse_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation (r1=70.0 pm,r2=353 pm,p1=-3.21 g.mol-1.pm.fs-1, p2=-5.07 g.mol-1.pm.fs-1) .]]

===Recative and unreactive trajectories===
{| class="wikitable" border="1"
! p1/g.mol-1.pm.fs-1 !! p2/g.mol-1.pm.fs-1!! Etot/kJmol-1!! Recative?!! Description of the dynamics!! Illustration of the trajectory
|-
| -2.56 || -5.1||-414 || Yes||The translational energy of the reactants can surmount the potential energy barrier and form the products. The ramaining energy is converted into vibrational energy of the products. || [[File:Table1_01508310.png|350px ]]
|-
| -3.1 || -4.1||-420 || No||The reactant H2 has vibrational energy and its rAB motion is rapid. Before it could cross the energy barrier, the molecule slams into the repulsive inner wall of the potential surface and bounces back into the reactant channel. || [[File:Table2_0150.png|350px]]
|-
| -3.1 || -5.1||-414|| Yes||The reactants have both the translational and vibrational energies. The energy is used to surmount the potential energy barrier and converted into the vibrational energy of the products. || [[File:Table3_01508.png|350px]]
|-
| -5.1 || -10.1||-357 || No||The reactants have sufficient energy to cross the transition state and the products did form for a certain amount of time. However, before the the system can exit the product channel, it recrosses the transition state and form the reactants again, hence no reaction occurs. ||[[File:Table4_01508.png|350px]]
|-
| -5.1 || -10.6||-394 || Yes||The system has sufficient energy to cross the transition state but it recrosses the transition state shortly after the reaction path hits the potential energy surface. However, the system is able to cross the transition state for the third time and finally exits the product channel and forms the products. || [[File:-10.6_01508.png|350px]]
|-
|}
In order to form products, a system must have sufficient energy to cross the transition state. Only molecules with the correct phase '''reference 2''' can exit the product channel and form stable products. Recrossing the transition state can lead to either product formation or no reaction. It is possible to cross the transition state multiple times.

===Transition State Theory===

Transition State Theory is classical, it doesn't take quantum tunnelling into account.Quantum tunnelling is probable for this reaction as it involves the transfer of a hydrogen atom, particularly at lower temperatures.'''Reference 3'''At low temperatures, the H atom can tunnel through the potential energy barrier than to pass over the barrier, hence the activation energy is lowered and the reaction rate increases. However, recrossing the energy barrier is possible as seen with the simulations, this can have a negative effect on the reaction rate. At high temperatures, the system is thermally activated and the behavious is approximately classical.'''reference4''' Therefore the experimental reaction rates are expected to be greater than that predicted by the Transition State Theory.

==F-H-H system==
===PES inspection===
'''F+H2 (F1-H1-H2)'''

F+H2 is exothermic as the reactants are higher in energy than the products therefore during the reaction, energy is released to the surroundings. H-F bond is stronger than H-H bond as the products are lower in energy and therefore more stable.The transition state is located approximately at rF1-H1=181.10 pm and rH1-H2=74.49 pm. This is verified by the forces (close to zero) and eigenvalues for hessian matrix (they are of opposite signs). The activation energy is estimated by tilting the transition state towards the reactants and is shown to be 424 kJ.mol-1.
[[File:Fh2_015083.png |400px|centre|thumb|Surface plot for F1-H1-H2 system using Dynamic Calculation, the transition state is identified as the black dot.]]
[[File:OptimisationFhh1_01508.png|400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:F1H1H2_EA_0150.png|400px|centre|thumb|Counter plot for estimating the activation energy.]]
[[File:EA1_01508.png|400px|centre|thumb|parameters for the activation energy.]]
'''H+HF (H1-H2-F1)'''
This reaction is endothermis as the reactants are lower in energy than the products therefore energy is taken in from the surroundings to form the products. H-F bond is still stronger than H-H as the reactans are lower in energy and more stable. The transition state is located at approximately rH1-H2=280 pm and rH2-F1=92 pm. It is located with the same reasons stated above.With the same method, the activation energy is estimated to be 434 kJ.mol-1. The two activation energies should be identical as these two reactions are essentially the reverse of one another.

[[File:H+HF_01508310.png|400px|centre|thumb|Surface plot for H1-H2-F1 system using Dynamic Calculationthe, the transition state is identified as the black dot.]]
[[File:HHF_015083.png |400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:EA2_01508.png|400px|centre|thumb|Counter plot for estimating the activation energy.]]
[[File:EA2_PARAMETERS.png|400px|centre|thumb|parameters for the activation energy.]]

===Reaction dynamics===
===F+H2 system===

Initially, the reactants have kinetic energy in the form of vibrational and translational energies, and as it crosses the potential energy barrier, the kinetic energy is converted into potential energy. Once the system is exiting the product channel, the potential energy is converted into the vibrational energy of the product.One good experimental technique to prob the electronic structure of the reacting species will be IR spectroscopy.In the anharmonic oscillator model, exciting molecules in the relaxed state promotes excitation from the ground state to the first energy level mainly. This will give rise to a single peak in the IR spectrum. Howver, when exciting a sample of excited molecules, many transitions are possible. For example, from 0-->1, the fundamental or 1-->2, the first overtone. They will show up in the spectrum as 2 peaks, with the overtone being at a lower wavenumber as the energy gap decreases up the potential well. The intensity of the overtone decreases over time as the electrons can fall back to lower energy levels and energy is emitted as radiation. As this system is linear, rotational is not important electronic energy is not considered here.Photoelectron spectroscopy is also a viable method. '''reference 5'''

[[File:Reactiondynamicsfh2_0150.png||400px|centre|thumb|contour plot for F+H2.]]
[[File:Reactiondynamicsparameter——015.png |400px|centre|thumb|parameters for the reactive trajectory.]]
====Varying the momentum of HH in the F+H2 system.====
Conditions:rFH=182 pm, rHH=74 pm, PFH=-1.0g.mol-1.pm.fs-1
{| class="wikitable" border="1"
|+ caption
|-
|PHH/g.mol-1.pm.fs-1|| Contour Plot
|-
|0 || [[File:0_015083.png |400 px|centre]]
|-
|2 || [[File:2_0508.png |400 px|centre]]
|-
|4 || [[File:4_01508.png ‎|400 px|centre]]
|-
|6.1|| [[File:6_01508.png|400 px|centre]]
|-
| -2|| [[File:-2_01508.png|400 px|centre]]
|-
| -4|| [[File:-4.1_01508.png‎|400 px|centre]]
|-
| -6.1|| [[File:Fit1_01508.png|400 px|centre]]
|-
|}
Although the amount of energy that is put into H-H vibration is much more than the activation energy of the reaction, the reaction does not always occur. The large amount of energy is demonstrated by the high frequency of those wavy lines. Recrossing the transition states multiple times can lead to no reaction or product formation depending on how the tragectory collides with the potential well.

[[File:Reactiondynamic_last01588.png|400px|centre|thumb|contour plot for rFH=182 pm, fHH=74 pm, PFH=-1.6g.mol-1.pm.fs-1,PHH=0.2g.mol-1.pm.fs-1]]
The system now has much less vibrational energy into the reactants than before. The reaction is still successful and the trajectory recrosses the transition states fewer times than before.This can be explained by the increased momentum of FH so that F can approach the closest H with more vibrational energy.

===H+HF system===
{| class="wikitable" border="1"
!Graph Number!! p1(HH)/g.mol-1.pm.fs-1 !! p2(HF)/g.mol-1.pm.fs-1!! Etot/kJmol-1!! Recative?!! Illustration of the trajectory
|-
|1|| -2 || -10||-397|| No|| [[File:Final1_01508.png|350px ]]
|-
|2|| 0|| -8||-400 || No|| [[File:Final2_015.png|350px]]
|-
|3||5 || -6||-360|| No|| [[File:Final3_015.png|350px]]
|-
|4|| 5 || -3||-389 || Yes||[[File:Final4_015.png|350px]]
|-
|}

by referening to Polanyl's empirical rules, an exothermic reaction has an early barrier, which happens in the entrance channel. It tends to favour vibrational excitation of the products. On the other hand, an endothermic reaction has a late barrier, which occurs in the product channel. It tends to favour low product vibrational excitation. The location of the energy barrier is also crucial for a successful reaction. Translational energy of the reactants is the most effective at passing the early barrier whereas vibrational energy of the reactants is the most effective at surmounting the late barrier.This reaction is endothermic, and hence it has a late barrier. In all the graphs, the reactants all have vibrational energy as indicated by the wavy line in the reactant channel.

MRD:01508310

2020-05-22T18:16:11Z

Hh2218: /* Varying the momentum of HH in the F+H2 system. */

==H-H-H system==
===Dynamics from the transition state region===
The transition state is the point on the potential energy surface that has ∂V(ri)/∂ri=0, where ri is the distance between two atoms.The transition state is a local maximum and its second derivative ∂2V(ri)/∂ri2 is < 0, whereas a local minimum will have a positive second derivative instead.
[[File:Hhh_surfaceplot_01508.png|400px|thumb|centre|a potential energy surface plot of H and H2 with respect to interatomic distances.]]

===Trajectories from r1=r2: locating the transition state===
At the transition state, r1=r2=90.8 pm by estimation. At this separation, the forces acting along AB and BC are both -0.004 kJ.mol-1.pm-1, which is close to zero and the eigenvalues for the Hessian matrix were -0.028 and +0.167 kJ.mol-1.pm-2, indicating the presence of transition state. The Internuclear Distance vs Time plot suggests the distance between HA, HB and HC is equal, about 90 pm and the distance is constant over time suggests the atoms are static at the transition state.
[[File:Animation101508310.png|400px|centre|thumb|picture showing H and H2 at the transition state.]]
[[File:Optimisation1_01508310.png|400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:Internucleardistance_01508310.png|400px|centre|thumb|Internuclear Distance vs Time plot between the H atoms at the transition state.]]

===Calculating the reaction path===
When rA-B is set to rts+1 and rB-C equals rts,the transition rolls towards BC and HA remains as an atom. MEP and Dynamic reaction paths are different as MEP set the momenta to zero in every step of the reaction path, products are therefore static and hence the reaction path is relatively straight. The dynamic reaction path is more realistic. It takes the momenta of gaseous molecules into account,i.e. they have vibrational energies, that is illustrated by the wavy line along the reaction path.
[[File:Surface_Plot1mep_015083.png|400px|centre|thumb|the minimum energy path (mep) of the H-H-H system]]
[[File:01569348_MEP_AB1_dynamic.png|400px|centre|thumb|the dynamic reaction path of the H-H-H system]]

====MEP and Dynamics calculations comparisons====
'''r1=91.8 pm, r2=90.8 pm, momenta set to 0 g.mol-1.pm.fs-1'''

HB and HC form a H2 molecule whereas HA moves away from the molecule. The distance between B and C decreased to 74 pm, which is the hydrogen molecule bond length. '''reference 2'''In MEP calculation, the momenta are set to zero at each time step.

[[File:MepH2bondlength_01508.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using MEP calculation.]]

[[File:MepH2momenta015083.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using MEP calculation.]]

Using Dynamics calculation, the outcome of the reaction is the same. The transition state rolls towards HB and HC and a hydrogen molecule is formed. One noticeable difference is that the hydrogen molecule now has some vibational energy as indicated by the wavy line along the B-C distance in the Internuclear Distance vs Time plot.As for the Momenta vs Time plot, the system is linear, therefore the angle theta is zero. HA and HB are moving away from each other at '''an increasing velocity until the momentum reaches 5 g.mol-1.pm.fs-1.The oscillation along the B-C bond corresponds to the vibration of the bond. '''why does the beginning have negative momenta?'''
[[File:DynamicsH2_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation.]]
[[File:DynamicsH2monenta_01508.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using Dynamics calculation.]]

'''r1=90.8 pm, r2=91.8 pm, momenta set to 0 g.mol-1.pm.fs-1'''

Once the length of r1 and r2 switches, the shapes of the graphs are identical but instead of HB and HC forming a molecule, HA and HB now form the hydrogen molecule in the products.
[[File:Mepinter2_01508.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using MEP calculation.]]
[[File:Momentamep2_015.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using MEP calculation.]]
[[File:InterDynamic_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation.]]
[[File:Momentadynamics_015083.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using Dynamics calculation.]]

'''Trajectory starting with the final position and reversed momentum to the reaction path above'''

This trajectory starts at the end of the reaction path above and finishes at where the above reaction started. it is essentially a reverse of what happened in the reaction above.
[[File:Reverse_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation (r1=70.0 pm,r2=353 pm,p1=-3.21 g.mol-1.pm.fs-1, p2=-5.07 g.mol-1.pm.fs-1) .]]

===Recative and unreactive trajectories===
{| class="wikitable" border="1"
! p1/g.mol-1.pm.fs-1 !! p2/g.mol-1.pm.fs-1!! Etot/kJmol-1!! Recative?!! Description of the dynamics!! Illustration of the trajectory
|-
| -2.56 || -5.1||-414 || Yes||The translational energy of the reactants can surmount the potential energy barrier and form the products. The ramaining energy is converted into vibrational energy of the products. || [[File:Table1_01508310.png|350px ]]
|-
| -3.1 || -4.1||-420 || No||The reactant H2 has vibrational energy and its rAB motion is rapid. Before it could cross the energy barrier, the molecule slams into the repulsive inner wall of the potential surface and bounces back into the reactant channel. || [[File:Table2_0150.png|350px]]
|-
| -3.1 || -5.1||-414|| Yes||The reactants have both the translational and vibrational energies. The energy is used to surmount the potential energy barrier and converted into the vibrational energy of the products. || [[File:Table3_01508.png|350px]]
|-
| -5.1 || -10.1||-357 || No||The reactants have sufficient energy to cross the transition state and the products did form for a certain amount of time. However, before the the system can exit the product channel, it recrosses the transition state and form the reactants again, hence no reaction occurs. ||[[File:Table4_01508.png|350px]]
|-
| -5.1 || -10.6||-394 || Yes||The system has sufficient energy to cross the transition state but it recrosses the transition state shortly after the reaction path hits the potential energy surface. However, the system is able to cross the transition state for the third time and finally exits the product channel and forms the products. || [[File:-10.6_01508.png|350px]]
|-
|}
In order to form products, a system must have sufficient energy to cross the transition state. Only molecules with the correct phase '''reference 2''' can exit the product channel and form stable products. Recrossing the transition state can lead to either product formation or no reaction. It is possible to cross the transition state multiple times.

===Transition State Theory===

Transition State Theory is classical, it doesn't take quantum tunnelling into account.Quantum tunnelling is probable for this reaction as it involves the transfer of a hydrogen atom, particularly at lower temperatures.'''Reference 3'''At low temperatures, the H atom can tunnel through the potential energy barrier than to pass over the barrier, hence the activation energy is lowered and the reaction rate increases. However, recrossing the energy barrier is possible as seen with the simulations, this can have a negative effect on the reaction rate. At high temperatures, the system is thermally activated and the behavious is approximately classical.'''reference4''' Therefore the experimental reaction rates are expected to be greater than that predicted by the Transition State Theory.

==F-H-H system==
===PES inspection===
'''F+H2 (F1-H1-H2)'''

F+H2 is exothermic as the reactants are higher in energy than the products therefore during the reaction, energy is released to the surroundings. H-F bond is stronger than H-H bond as the products are lower in energy and therefore more stable.The transition state is located approximately at rF1-H1=181.10 pm and rH1-H2=74.49 pm. This is verified by the forces (close to zero) and eigenvalues for hessian matrix (they are of opposite signs). The activation energy is estimated by tilting the transition state towards the reactants and is shown to be 424 kJ.mol-1.
[[File:Fh2_015083.png |400px|centre|thumb|Surface plot for F1-H1-H2 system using Dynamic Calculation, the transition state is identified as the black dot.]]
[[File:OptimisationFhh1_01508.png|400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:F1H1H2_EA_0150.png|400px|centre|thumb|Counter plot for estimating the activation energy.]]
[[File:EA1_01508.png|400px|centre|thumb|parameters for the activation energy.]]
'''H+HF (H1-H2-F1)'''
This reaction is endothermis as the reactants are lower in energy than the products therefore energy is taken in from the surroundings to form the products. H-F bond is still stronger than H-H as the reactans are lower in energy and more stable. The transition state is located at approximately rH1-H2=280 pm and rH2-F1=92 pm. It is located with the same reasons stated above.With the same method, the activation energy is estimated to be 434 kJ.mol-1. The two activation energies should be identical as these two reactions are essentially the reverse of one another.

[[File:H+HF_01508310.png|400px|centre|thumb|Surface plot for H1-H2-F1 system using Dynamic Calculationthe, the transition state is identified as the black dot.]]
[[File:HHF_015083.png |400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:EA2_01508.png|400px|centre|thumb|Counter plot for estimating the activation energy.]]
[[File:EA2_PARAMETERS.png|400px|centre|thumb|parameters for the activation energy.]]

===Reaction dynamics===
===F+H2 system===

Initially, the reactants have kinetic energy in the form of vibrational and translational energies, and as it crosses the potential energy barrier, the kinetic energy is converted into potential energy. Once the system is exiting the product channel, the potential energy is converted into the vibrational energy of the product.One good experimental technique to prob the electronic structure of the reacting species will be IR spectroscopy.In the anharmonic oscillator model, exciting molecules in the relaxed state promotes excitation from the ground state to the first energy level mainly. This will give rise to a single peak in the IR spectrum. Howver, when exciting a sample of excited molecules, many transitions are possible. For example, from 0-->1, the fundamental or 1-->2, the first overtone. They will show up in the spectrum as 2 peaks, with the overtone being at a lower wavenumber as the energy gap decreases up the potential well. The intensity of the overtone decreases over time as the electrons can fall back to lower energy levels and energy is emitted as radiation. As this system is linear, rotational is not important electronic energy is not considered here.Photoelectron spectroscopy is also a viable method. '''reference 5'''

[[File:Reactiondynamicsfh2_0150.png||400px|centre|thumb|contour plot for F+H2.]]
[[File:Reactiondynamicsparameter——015.png |400px|centre|thumb|parameters for the reactive trajectory.]]
====Varying the momentum of HH in the F+H2 system.====
Conditions:rFH=182 pm, rHH=74 pm, PFH=-1.0g.mol-1.pm.fs-1
{| class="wikitable" border="1"
|+ caption
|-
|PHH/g.mol-1.pm.fs-1|| Contour Plot
|-
|0 || [[File:0_015083.png |400 px|centre]]
|-
|2 || [[File:2_0508.png |400 px|centre]]
|-
|4 || [[File:4_01508.png ‎|400 px|centre]]
|-
|6.1|| [[File:6_01508.png|400 px|centre]]
|-
| -2|| [[File:-2_01508.png|400 px|centre]]
|-
| -4|| [[File:-4.1_01508.png‎|400 px|centre]]
|-
| -6.1|| [[File:Fit1_01508.png|400 px|centre]]
|-
|}
Although the amount of energy that is put into H-H vibration is much more than the activation energy of the reaction, the reaction does not always occur. The large amount of energy is demonstrated by the high frequency of those wavy lines. Recrossing the transition states multiple times can lead to no reaction or product formation depending on how the tragectory collides with the potential well.

[[File:Reactiondynamic_last01588.png|400px|centre|thumb|contour plot for rFH=182 pm, fHH=74 pm, PFH=-1.6g.mol-1.pm.fs-1,PHH=0.2g.mol-1.pm.fs-1]]
The system now has much less vibrational energy into the reactants than before. The reaction is still successful and the trajectory recrosses the transition states fewer times than before.This can be explained by the increased momentum of FH so that F can approach the closest H with more vibrational energy.

===H+HF system===
{| class="wikitable" border="1"
!Graph Number!! p1(HH)/g.mol-1.pm.fs-1 !! p2(HF)/g.mol-1.pm.fs-1!! Etot/kJmol-1!! Recative?!! Illustration of the trajectory
|-
|1|| -2 || -10||-397|| No|| [[File:Final1_01508.png|350px ]]
|-
|2|| 0|| -8||-400 || No|| [[File:Final2_015.png|350px]]
|-
|3||5 || -6||-360|| No|| [[File:Final3_015.png|350px]]
|-
|4|| 5 || -3||-389 || Yes||[[File:Final4_015.png|350px]]
|-
|}

by referening to Polanyl's empirical rules, an exothermic reaction has an early barrier, which happens in the entrance channel. It tends to favour vibrational excitation of the products. On the other hand, an endothermic reaction has a late barrier, which occurs in the product channel. It tends to favour low product vibrational excitation. The location of the energy barrier is also crucial for a successful reaction. Translational energy of the reactants is the most effective at passing the early barrier whereas vibrational energy of the reactants is the most effective at surmounting the late barrier.This reaction is endothermic, and hence it has a late barrier. In all the graphs, the reactants all have vibrational energy as indicated by the wavy line in the reactant channel.

MRD:01508310

2020-05-22T18:14:40Z

Hh2218: /* H+HF system */

==H-H-H system==
===Dynamics from the transition state region===
The transition state is the point on the potential energy surface that has ∂V(ri)/∂ri=0, where ri is the distance between two atoms.The transition state is a local maximum and its second derivative ∂2V(ri)/∂ri2 is < 0, whereas a local minimum will have a positive second derivative instead.
[[File:Hhh_surfaceplot_01508.png|400px|thumb|centre|a potential energy surface plot of H and H2 with respect to interatomic distances.]]

===Trajectories from r1=r2: locating the transition state===
At the transition state, r1=r2=90.8 pm by estimation. At this separation, the forces acting along AB and BC are both -0.004 kJ.mol-1.pm-1, which is close to zero and the eigenvalues for the Hessian matrix were -0.028 and +0.167 kJ.mol-1.pm-2, indicating the presence of transition state. The Internuclear Distance vs Time plot suggests the distance between HA, HB and HC is equal, about 90 pm and the distance is constant over time suggests the atoms are static at the transition state.
[[File:Animation101508310.png|400px|centre|thumb|picture showing H and H2 at the transition state.]]
[[File:Optimisation1_01508310.png|400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:Internucleardistance_01508310.png|400px|centre|thumb|Internuclear Distance vs Time plot between the H atoms at the transition state.]]

===Calculating the reaction path===
When rA-B is set to rts+1 and rB-C equals rts,the transition rolls towards BC and HA remains as an atom. MEP and Dynamic reaction paths are different as MEP set the momenta to zero in every step of the reaction path, products are therefore static and hence the reaction path is relatively straight. The dynamic reaction path is more realistic. It takes the momenta of gaseous molecules into account,i.e. they have vibrational energies, that is illustrated by the wavy line along the reaction path.
[[File:Surface_Plot1mep_015083.png|400px|centre|thumb|the minimum energy path (mep) of the H-H-H system]]
[[File:01569348_MEP_AB1_dynamic.png|400px|centre|thumb|the dynamic reaction path of the H-H-H system]]

====MEP and Dynamics calculations comparisons====
'''r1=91.8 pm, r2=90.8 pm, momenta set to 0 g.mol-1.pm.fs-1'''

HB and HC form a H2 molecule whereas HA moves away from the molecule. The distance between B and C decreased to 74 pm, which is the hydrogen molecule bond length. '''reference 2'''In MEP calculation, the momenta are set to zero at each time step.

[[File:MepH2bondlength_01508.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using MEP calculation.]]

[[File:MepH2momenta015083.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using MEP calculation.]]

Using Dynamics calculation, the outcome of the reaction is the same. The transition state rolls towards HB and HC and a hydrogen molecule is formed. One noticeable difference is that the hydrogen molecule now has some vibational energy as indicated by the wavy line along the B-C distance in the Internuclear Distance vs Time plot.As for the Momenta vs Time plot, the system is linear, therefore the angle theta is zero. HA and HB are moving away from each other at '''an increasing velocity until the momentum reaches 5 g.mol-1.pm.fs-1.The oscillation along the B-C bond corresponds to the vibration of the bond. '''why does the beginning have negative momenta?'''
[[File:DynamicsH2_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation.]]
[[File:DynamicsH2monenta_01508.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using Dynamics calculation.]]

'''r1=90.8 pm, r2=91.8 pm, momenta set to 0 g.mol-1.pm.fs-1'''

Once the length of r1 and r2 switches, the shapes of the graphs are identical but instead of HB and HC forming a molecule, HA and HB now form the hydrogen molecule in the products.
[[File:Mepinter2_01508.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using MEP calculation.]]
[[File:Momentamep2_015.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using MEP calculation.]]
[[File:InterDynamic_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation.]]
[[File:Momentadynamics_015083.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using Dynamics calculation.]]

'''Trajectory starting with the final position and reversed momentum to the reaction path above'''

This trajectory starts at the end of the reaction path above and finishes at where the above reaction started. it is essentially a reverse of what happened in the reaction above.
[[File:Reverse_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation (r1=70.0 pm,r2=353 pm,p1=-3.21 g.mol-1.pm.fs-1, p2=-5.07 g.mol-1.pm.fs-1) .]]

===Recative and unreactive trajectories===
{| class="wikitable" border="1"
! p1/g.mol-1.pm.fs-1 !! p2/g.mol-1.pm.fs-1!! Etot/kJmol-1!! Recative?!! Description of the dynamics!! Illustration of the trajectory
|-
| -2.56 || -5.1||-414 || Yes||The translational energy of the reactants can surmount the potential energy barrier and form the products. The ramaining energy is converted into vibrational energy of the products. || [[File:Table1_01508310.png|350px ]]
|-
| -3.1 || -4.1||-420 || No||The reactant H2 has vibrational energy and its rAB motion is rapid. Before it could cross the energy barrier, the molecule slams into the repulsive inner wall of the potential surface and bounces back into the reactant channel. || [[File:Table2_0150.png|350px]]
|-
| -3.1 || -5.1||-414|| Yes||The reactants have both the translational and vibrational energies. The energy is used to surmount the potential energy barrier and converted into the vibrational energy of the products. || [[File:Table3_01508.png|350px]]
|-
| -5.1 || -10.1||-357 || No||The reactants have sufficient energy to cross the transition state and the products did form for a certain amount of time. However, before the the system can exit the product channel, it recrosses the transition state and form the reactants again, hence no reaction occurs. ||[[File:Table4_01508.png|350px]]
|-
| -5.1 || -10.6||-394 || Yes||The system has sufficient energy to cross the transition state but it recrosses the transition state shortly after the reaction path hits the potential energy surface. However, the system is able to cross the transition state for the third time and finally exits the product channel and forms the products. || [[File:-10.6_01508.png|350px]]
|-
|}
In order to form products, a system must have sufficient energy to cross the transition state. Only molecules with the correct phase '''reference 2''' can exit the product channel and form stable products. Recrossing the transition state can lead to either product formation or no reaction. It is possible to cross the transition state multiple times.

===Transition State Theory===

Transition State Theory is classical, it doesn't take quantum tunnelling into account.Quantum tunnelling is probable for this reaction as it involves the transfer of a hydrogen atom, particularly at lower temperatures.'''Reference 3'''At low temperatures, the H atom can tunnel through the potential energy barrier than to pass over the barrier, hence the activation energy is lowered and the reaction rate increases. However, recrossing the energy barrier is possible as seen with the simulations, this can have a negative effect on the reaction rate. At high temperatures, the system is thermally activated and the behavious is approximately classical.'''reference4''' Therefore the experimental reaction rates are expected to be greater than that predicted by the Transition State Theory.

==F-H-H system==
===PES inspection===
'''F+H2 (F1-H1-H2)'''

F+H2 is exothermic as the reactants are higher in energy than the products therefore during the reaction, energy is released to the surroundings. H-F bond is stronger than H-H bond as the products are lower in energy and therefore more stable.The transition state is located approximately at rF1-H1=181.10 pm and rH1-H2=74.49 pm. This is verified by the forces (close to zero) and eigenvalues for hessian matrix (they are of opposite signs). The activation energy is estimated by tilting the transition state towards the reactants and is shown to be 424 kJ.mol-1.
[[File:Fh2_015083.png |400px|centre|thumb|Surface plot for F1-H1-H2 system using Dynamic Calculation, the transition state is identified as the black dot.]]
[[File:OptimisationFhh1_01508.png|400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:F1H1H2_EA_0150.png|400px|centre|thumb|Counter plot for estimating the activation energy.]]
[[File:EA1_01508.png|400px|centre|thumb|parameters for the activation energy.]]
'''H+HF (H1-H2-F1)'''
This reaction is endothermis as the reactants are lower in energy than the products therefore energy is taken in from the surroundings to form the products. H-F bond is still stronger than H-H as the reactans are lower in energy and more stable. The transition state is located at approximately rH1-H2=280 pm and rH2-F1=92 pm. It is located with the same reasons stated above.With the same method, the activation energy is estimated to be 434 kJ.mol-1. The two activation energies should be identical as these two reactions are essentially the reverse of one another.

[[File:H+HF_01508310.png|400px|centre|thumb|Surface plot for H1-H2-F1 system using Dynamic Calculationthe, the transition state is identified as the black dot.]]
[[File:HHF_015083.png |400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:EA2_01508.png|400px|centre|thumb|Counter plot for estimating the activation energy.]]
[[File:EA2_PARAMETERS.png|400px|centre|thumb|parameters for the activation energy.]]

===Reaction dynamics===
===F+H2 system===

Initially, the reactants have kinetic energy in the form of vibrational and translational energies, and as it crosses the potential energy barrier, the kinetic energy is converted into potential energy. Once the system is exiting the product channel, the potential energy is converted into the vibrational energy of the product.One good experimental technique to prob the electronic structure of the reacting species will be IR spectroscopy.In the anharmonic oscillator model, exciting molecules in the relaxed state promotes excitation from the ground state to the first energy level mainly. This will give rise to a single peak in the IR spectrum. Howver, when exciting a sample of excited molecules, many transitions are possible. For example, from 0-->1, the fundamental or 1-->2, the first overtone. They will show up in the spectrum as 2 peaks, with the overtone being at a lower wavenumber as the energy gap decreases up the potential well. The intensity of the overtone decreases over time as the electrons can fall back to lower energy levels and energy is emitted as radiation. As this system is linear, rotational is not important electronic energy is not considered here.Photoelectron spectroscopy is also a viable method. '''reference 5'''

[[File:Reactiondynamicsfh2_0150.png||400px|centre|thumb|contour plot for F+H2.]]
[[File:Reactiondynamicsparameter——015.png |400px|centre|thumb|parameters for the reactive trajectory.]]
====Varying the momentum of HH in the F+H2 system.====
Conditions:rFH=182 pm, fHH=74 pm, PFH=-1.0g.mol-1.pm.fs-1
{| class="wikitable" border="1"
|+ caption
|-
|PHH/g.mol-1.pm.fs-1|| Contour Plot
|-
|0 || [[File:0_015083.png |400 px|centre]]
|-
|2 || [[File:2_0508.png |400 px|centre]]
|-
|4 || [[File:4_01508.png ‎|400 px|centre]]
|-
|6.1|| [[File:6_01508.png|400 px|centre]]
|-
| -2|| [[File:-2_01508.png|400 px|centre]]
|-
| -4|| [[File:-4.1_01508.png‎|400 px|centre]]
|-
| -6.1|| [[File:Fit1_01508.png|400 px|centre]]
|-
|}
Although the amount of energy that is put into H-H vibration is much more than the activation energy of the reaction, the reaction does not always occur. The large amount of energy is demonstrated by the high frequency of those wavy lines. Recrossing the transition states multiple times can lead to no reaction or product formation depending on how the tragectory collides with the potential well.

[[File:Reactiondynamic_last01588.png|400px|centre|thumb|contour plot for rFH=182 pm, fHH=74 pm, PFH=-1.6g.mol-1.pm.fs-1,PHH=0.2g.mol-1.pm.fs-1]]
The system now has much less vibrational energy into the reactants than before. The reaction is still successful and the trajectory recrosses the transition states fewer times than before.This can be explained by the increased momentum of FH so that F can approach the closest H with more vibrational energy.

===H+HF system===
{| class="wikitable" border="1"
!Graph Number!! p1(HH)/g.mol-1.pm.fs-1 !! p2(HF)/g.mol-1.pm.fs-1!! Etot/kJmol-1!! Recative?!! Illustration of the trajectory
|-
|1|| -2 || -10||-397|| No|| [[File:Final1_01508.png|350px ]]
|-
|2|| 0|| -8||-400 || No|| [[File:Final2_015.png|350px]]
|-
|3||5 || -6||-360|| No|| [[File:Final3_015.png|350px]]
|-
|4|| 5 || -3||-389 || Yes||[[File:Final4_015.png|350px]]
|-
|}

by referening to Polanyl's empirical rules, an exothermic reaction has an early barrier, which happens in the entrance channel. It tends to favour vibrational excitation of the products. On the other hand, an endothermic reaction has a late barrier, which occurs in the product channel. It tends to favour low product vibrational excitation. The location of the energy barrier is also crucial for a successful reaction. Translational energy of the reactants is the most effective at passing the early barrier whereas vibrational energy of the reactants is the most effective at surmounting the late barrier.This reaction is endothermic, and hence it has a late barrier. In all the graphs, the reactants all have vibrational energy as indicated by the wavy line in the reactant channel.

MRD:01508310

2020-05-22T17:50:20Z

Hh2218: /* H+HF system */

==H-H-H system==
===Dynamics from the transition state region===
The transition state is the point on the potential energy surface that has ∂V(ri)/∂ri=0, where ri is the distance between two atoms.The transition state is a local maximum and its second derivative ∂2V(ri)/∂ri2 is < 0, whereas a local minimum will have a positive second derivative instead.
[[File:Hhh_surfaceplot_01508.png|400px|thumb|centre|a potential energy surface plot of H and H2 with respect to interatomic distances.]]

===Trajectories from r1=r2: locating the transition state===
At the transition state, r1=r2=90.8 pm by estimation. At this separation, the forces acting along AB and BC are both -0.004 kJ.mol-1.pm-1, which is close to zero and the eigenvalues for the Hessian matrix were -0.028 and +0.167 kJ.mol-1.pm-2, indicating the presence of transition state. The Internuclear Distance vs Time plot suggests the distance between HA, HB and HC is equal, about 90 pm and the distance is constant over time suggests the atoms are static at the transition state.
[[File:Animation101508310.png|400px|centre|thumb|picture showing H and H2 at the transition state.]]
[[File:Optimisation1_01508310.png|400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:Internucleardistance_01508310.png|400px|centre|thumb|Internuclear Distance vs Time plot between the H atoms at the transition state.]]

===Calculating the reaction path===
When rA-B is set to rts+1 and rB-C equals rts,the transition rolls towards BC and HA remains as an atom. MEP and Dynamic reaction paths are different as MEP set the momenta to zero in every step of the reaction path, products are therefore static and hence the reaction path is relatively straight. The dynamic reaction path is more realistic. It takes the momenta of gaseous molecules into account,i.e. they have vibrational energies, that is illustrated by the wavy line along the reaction path.
[[File:Surface_Plot1mep_015083.png|400px|centre|thumb|the minimum energy path (mep) of the H-H-H system]]
[[File:01569348_MEP_AB1_dynamic.png|400px|centre|thumb|the dynamic reaction path of the H-H-H system]]

====MEP and Dynamics calculations comparisons====
'''r1=91.8 pm, r2=90.8 pm, momenta set to 0 g.mol-1.pm.fs-1'''

HB and HC form a H2 molecule whereas HA moves away from the molecule. The distance between B and C decreased to 74 pm, which is the hydrogen molecule bond length. '''reference 2'''In MEP calculation, the momenta are set to zero at each time step.

[[File:MepH2bondlength_01508.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using MEP calculation.]]

[[File:MepH2momenta015083.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using MEP calculation.]]

Using Dynamics calculation, the outcome of the reaction is the same. The transition state rolls towards HB and HC and a hydrogen molecule is formed. One noticeable difference is that the hydrogen molecule now has some vibational energy as indicated by the wavy line along the B-C distance in the Internuclear Distance vs Time plot.As for the Momenta vs Time plot, the system is linear, therefore the angle theta is zero. HA and HB are moving away from each other at '''an increasing velocity until the momentum reaches 5 g.mol-1.pm.fs-1.The oscillation along the B-C bond corresponds to the vibration of the bond. '''why does the beginning have negative momenta?'''
[[File:DynamicsH2_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation.]]
[[File:DynamicsH2monenta_01508.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using Dynamics calculation.]]

'''r1=90.8 pm, r2=91.8 pm, momenta set to 0 g.mol-1.pm.fs-1'''

Once the length of r1 and r2 switches, the shapes of the graphs are identical but instead of HB and HC forming a molecule, HA and HB now form the hydrogen molecule in the products.
[[File:Mepinter2_01508.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using MEP calculation.]]
[[File:Momentamep2_015.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using MEP calculation.]]
[[File:InterDynamic_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation.]]
[[File:Momentadynamics_015083.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using Dynamics calculation.]]

'''Trajectory starting with the final position and reversed momentum to the reaction path above'''

This trajectory starts at the end of the reaction path above and finishes at where the above reaction started. it is essentially a reverse of what happened in the reaction above.
[[File:Reverse_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation (r1=70.0 pm,r2=353 pm,p1=-3.21 g.mol-1.pm.fs-1, p2=-5.07 g.mol-1.pm.fs-1) .]]

===Recative and unreactive trajectories===
{| class="wikitable" border="1"
! p1/g.mol-1.pm.fs-1 !! p2/g.mol-1.pm.fs-1!! Etot/kJmol-1!! Recative?!! Description of the dynamics!! Illustration of the trajectory
|-
| -2.56 || -5.1||-414 || Yes||The translational energy of the reactants can surmount the potential energy barrier and form the products. The ramaining energy is converted into vibrational energy of the products. || [[File:Table1_01508310.png|350px ]]
|-
| -3.1 || -4.1||-420 || No||The reactant H2 has vibrational energy and its rAB motion is rapid. Before it could cross the energy barrier, the molecule slams into the repulsive inner wall of the potential surface and bounces back into the reactant channel. || [[File:Table2_0150.png|350px]]
|-
| -3.1 || -5.1||-414|| Yes||The reactants have both the translational and vibrational energies. The energy is used to surmount the potential energy barrier and converted into the vibrational energy of the products. || [[File:Table3_01508.png|350px]]
|-
| -5.1 || -10.1||-357 || No||The reactants have sufficient energy to cross the transition state and the products did form for a certain amount of time. However, before the the system can exit the product channel, it recrosses the transition state and form the reactants again, hence no reaction occurs. ||[[File:Table4_01508.png|350px]]
|-
| -5.1 || -10.6||-394 || Yes||The system has sufficient energy to cross the transition state but it recrosses the transition state shortly after the reaction path hits the potential energy surface. However, the system is able to cross the transition state for the third time and finally exits the product channel and forms the products. || [[File:-10.6_01508.png|350px]]
|-
|}
In order to form products, a system must have sufficient energy to cross the transition state. Only molecules with the correct phase '''reference 2''' can exit the product channel and form stable products. Recrossing the transition state can lead to either product formation or no reaction. It is possible to cross the transition state multiple times.

===Transition State Theory===

Transition State Theory is classical, it doesn't take quantum tunnelling into account.Quantum tunnelling is probable for this reaction as it involves the transfer of a hydrogen atom, particularly at lower temperatures.'''Reference 3'''At low temperatures, the H atom can tunnel through the potential energy barrier than to pass over the barrier, hence the activation energy is lowered and the reaction rate increases. However, recrossing the energy barrier is possible as seen with the simulations, this can have a negative effect on the reaction rate. At high temperatures, the system is thermally activated and the behavious is approximately classical.'''reference4''' Therefore the experimental reaction rates are expected to be greater than that predicted by the Transition State Theory.

==F-H-H system==
===PES inspection===
'''F+H2 (F1-H1-H2)'''

F+H2 is exothermic as the reactants are higher in energy than the products therefore during the reaction, energy is released to the surroundings. H-F bond is stronger than H-H bond as the products are lower in energy and therefore more stable.The transition state is located approximately at rF1-H1=181.10 pm and rH1-H2=74.49 pm. This is verified by the forces (close to zero) and eigenvalues for hessian matrix (they are of opposite signs). The activation energy is estimated by tilting the transition state towards the reactants and is shown to be 424 kJ.mol-1.
[[File:Fh2_015083.png |400px|centre|thumb|Surface plot for F1-H1-H2 system using Dynamic Calculation, the transition state is identified as the black dot.]]
[[File:OptimisationFhh1_01508.png|400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:F1H1H2_EA_0150.png|400px|centre|thumb|Counter plot for estimating the activation energy.]]
[[File:EA1_01508.png|400px|centre|thumb|parameters for the activation energy.]]
'''H+HF (H1-H2-F1)'''
This reaction is endothermis as the reactants are lower in energy than the products therefore energy is taken in from the surroundings to form the products. H-F bond is still stronger than H-H as the reactans are lower in energy and more stable. The transition state is located at approximately rH1-H2=280 pm and rH2-F1=92 pm. It is located with the same reasons stated above.With the same method, the activation energy is estimated to be 434 kJ.mol-1. The two activation energies should be identical as these two reactions are essentially the reverse of one another.

[[File:H+HF_01508310.png|400px|centre|thumb|Surface plot for H1-H2-F1 system using Dynamic Calculationthe, the transition state is identified as the black dot.]]
[[File:HHF_015083.png |400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:EA2_01508.png|400px|centre|thumb|Counter plot for estimating the activation energy.]]
[[File:EA2_PARAMETERS.png|400px|centre|thumb|parameters for the activation energy.]]

===Reaction dynamics===
===F+H2 system===

Initially, the reactants have kinetic energy in the form of vibrational and translational energies, and as it crosses the potential energy barrier, the kinetic energy is converted into potential energy. Once the system is exiting the product channel, the potential energy is converted into the vibrational energy of the product.One good experimental technique to prob the electronic structure of the reacting species will be IR spectroscopy.In the anharmonic oscillator model, exciting molecules in the relaxed state promotes excitation from the ground state to the first energy level mainly. This will give rise to a single peak in the IR spectrum. Howver, when exciting a sample of excited molecules, many transitions are possible. For example, from 0-->1, the fundamental or 1-->2, the first overtone. They will show up in the spectrum as 2 peaks, with the overtone being at a lower wavenumber as the energy gap decreases up the potential well. The intensity of the overtone decreases over time as the electrons can fall back to lower energy levels and energy is emitted as radiation. As this system is linear, rotational is not important electronic energy is not considered here.Photoelectron spectroscopy is also a viable method. '''reference 5'''

[[File:Reactiondynamicsfh2_0150.png||400px|centre|thumb|contour plot for F+H2.]]
[[File:Reactiondynamicsparameter——015.png |400px|centre|thumb|parameters for the reactive trajectory.]]
====Varying the momentum of HH in the F+H2 system.====
Conditions:rFH=182 pm, fHH=74 pm, PFH=-1.0g.mol-1.pm.fs-1
{| class="wikitable" border="1"
|+ caption
|-
|PHH/g.mol-1.pm.fs-1|| Contour Plot
|-
|0 || [[File:0_015083.png |400 px|centre]]
|-
|2 || [[File:2_0508.png |400 px|centre]]
|-
|4 || [[File:4_01508.png ‎|400 px|centre]]
|-
|6.1|| [[File:6_01508.png|400 px|centre]]
|-
| -2|| [[File:-2_01508.png|400 px|centre]]
|-
| -4|| [[File:-4.1_01508.png‎|400 px|centre]]
|-
| -6.1|| [[File:Fit1_01508.png|400 px|centre]]
|-
|}
Although the amount of energy that is put into H-H vibration is much more than the activation energy of the reaction, the reaction does not always occur. The large amount of energy is demonstrated by the high frequency of those wavy lines. Recrossing the transition states multiple times can lead to no reaction or product formation depending on how the tragectory collides with the potential well.

[[File:Reactiondynamic_last01588.png|400px|centre|thumb|contour plot for rFH=182 pm, fHH=74 pm, PFH=-1.6g.mol-1.pm.fs-1,PHH=0.2g.mol-1.pm.fs-1]]
The system now has much less vibrational energy into the reactants than before. The reaction is still successful and the trajectory recrosses the transition states fewer times than before.This can be explained by the increased momentum of FH so that F can approach the closest H with more vibrational energy.

===H+HF system===
{| class="wikitable" border="1"
!Graph Number!! p1(HH)/g.mol-1.pm.fs-1 !! p2(HF)/g.mol-1.pm.fs-1!! Etot/kJmol-1!! Recative?!! Illustration of the trajectory
|-
|1|| -2 || -10||-397|| No|| [[File:Final1_01508.png|350px ]]
|-
|2|| 0|| -8||-400 || No|| [[File:Final2_015.png|350px]]
|-
|3||5 || -6||-360|| No|| [[File:Final3_015.png|350px]]
|-
|4|| 5 || -3||-389 || Yes||[[File:Final4_015.png|350px]]
|-
|}

File:Final4 015.png

2020-05-22T17:31:21Z

Hh2218:

File:Final3 015.png

2020-05-22T17:30:38Z

Hh2218:

File:Final2 015.png

2020-05-22T17:28:36Z

Hh2218:

MRD:01508310

2020-05-22T17:17:27Z

Hh2218: /* H+HF system */

==H-H-H system==
===Dynamics from the transition state region===
The transition state is the point on the potential energy surface that has ∂V(ri)/∂ri=0, where ri is the distance between two atoms.The transition state is a local maximum and its second derivative ∂2V(ri)/∂ri2 is < 0, whereas a local minimum will have a positive second derivative instead.
[[File:Hhh_surfaceplot_01508.png|400px|thumb|centre|a potential energy surface plot of H and H2 with respect to interatomic distances.]]

===Trajectories from r1=r2: locating the transition state===
At the transition state, r1=r2=90.8 pm by estimation. At this separation, the forces acting along AB and BC are both -0.004 kJ.mol-1.pm-1, which is close to zero and the eigenvalues for the Hessian matrix were -0.028 and +0.167 kJ.mol-1.pm-2, indicating the presence of transition state. The Internuclear Distance vs Time plot suggests the distance between HA, HB and HC is equal, about 90 pm and the distance is constant over time suggests the atoms are static at the transition state.
[[File:Animation101508310.png|400px|centre|thumb|picture showing H and H2 at the transition state.]]
[[File:Optimisation1_01508310.png|400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:Internucleardistance_01508310.png|400px|centre|thumb|Internuclear Distance vs Time plot between the H atoms at the transition state.]]

===Calculating the reaction path===
When rA-B is set to rts+1 and rB-C equals rts,the transition rolls towards BC and HA remains as an atom. MEP and Dynamic reaction paths are different as MEP set the momenta to zero in every step of the reaction path, products are therefore static and hence the reaction path is relatively straight. The dynamic reaction path is more realistic. It takes the momenta of gaseous molecules into account,i.e. they have vibrational energies, that is illustrated by the wavy line along the reaction path.
[[File:Surface_Plot1mep_015083.png|400px|centre|thumb|the minimum energy path (mep) of the H-H-H system]]
[[File:01569348_MEP_AB1_dynamic.png|400px|centre|thumb|the dynamic reaction path of the H-H-H system]]

====MEP and Dynamics calculations comparisons====
'''r1=91.8 pm, r2=90.8 pm, momenta set to 0 g.mol-1.pm.fs-1'''

HB and HC form a H2 molecule whereas HA moves away from the molecule. The distance between B and C decreased to 74 pm, which is the hydrogen molecule bond length. '''reference 2'''In MEP calculation, the momenta are set to zero at each time step.

[[File:MepH2bondlength_01508.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using MEP calculation.]]

[[File:MepH2momenta015083.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using MEP calculation.]]

Using Dynamics calculation, the outcome of the reaction is the same. The transition state rolls towards HB and HC and a hydrogen molecule is formed. One noticeable difference is that the hydrogen molecule now has some vibational energy as indicated by the wavy line along the B-C distance in the Internuclear Distance vs Time plot.As for the Momenta vs Time plot, the system is linear, therefore the angle theta is zero. HA and HB are moving away from each other at '''an increasing velocity until the momentum reaches 5 g.mol-1.pm.fs-1.The oscillation along the B-C bond corresponds to the vibration of the bond. '''why does the beginning have negative momenta?'''
[[File:DynamicsH2_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation.]]
[[File:DynamicsH2monenta_01508.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using Dynamics calculation.]]

'''r1=90.8 pm, r2=91.8 pm, momenta set to 0 g.mol-1.pm.fs-1'''

Once the length of r1 and r2 switches, the shapes of the graphs are identical but instead of HB and HC forming a molecule, HA and HB now form the hydrogen molecule in the products.
[[File:Mepinter2_01508.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using MEP calculation.]]
[[File:Momentamep2_015.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using MEP calculation.]]
[[File:InterDynamic_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation.]]
[[File:Momentadynamics_015083.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using Dynamics calculation.]]

'''Trajectory starting with the final position and reversed momentum to the reaction path above'''

This trajectory starts at the end of the reaction path above and finishes at where the above reaction started. it is essentially a reverse of what happened in the reaction above.
[[File:Reverse_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation (r1=70.0 pm,r2=353 pm,p1=-3.21 g.mol-1.pm.fs-1, p2=-5.07 g.mol-1.pm.fs-1) .]]

===Recative and unreactive trajectories===
{| class="wikitable" border="1"
! p1/g.mol-1.pm.fs-1 !! p2/g.mol-1.pm.fs-1!! Etot/kJmol-1!! Recative?!! Description of the dynamics!! Illustration of the trajectory
|-
| -2.56 || -5.1||-414 || Yes||The translational energy of the reactants can surmount the potential energy barrier and form the products. The ramaining energy is converted into vibrational energy of the products. || [[File:Table1_01508310.png|350px ]]
|-
| -3.1 || -4.1||-420 || No||The reactant H2 has vibrational energy and its rAB motion is rapid. Before it could cross the energy barrier, the molecule slams into the repulsive inner wall of the potential surface and bounces back into the reactant channel. || [[File:Table2_0150.png|350px]]
|-
| -3.1 || -5.1||-414|| Yes||The reactants have both the translational and vibrational energies. The energy is used to surmount the potential energy barrier and converted into the vibrational energy of the products. || [[File:Table3_01508.png|350px]]
|-
| -5.1 || -10.1||-357 || No||The reactants have sufficient energy to cross the transition state and the products did form for a certain amount of time. However, before the the system can exit the product channel, it recrosses the transition state and form the reactants again, hence no reaction occurs. ||[[File:Table4_01508.png|350px]]
|-
| -5.1 || -10.6||-394 || Yes||The system has sufficient energy to cross the transition state but it recrosses the transition state shortly after the reaction path hits the potential energy surface. However, the system is able to cross the transition state for the third time and finally exits the product channel and forms the products. || [[File:-10.6_01508.png|350px]]
|-
|}
In order to form products, a system must have sufficient energy to cross the transition state. Only molecules with the correct phase '''reference 2''' can exit the product channel and form stable products. Recrossing the transition state can lead to either product formation or no reaction. It is possible to cross the transition state multiple times.

===Transition State Theory===

Transition State Theory is classical, it doesn't take quantum tunnelling into account.Quantum tunnelling is probable for this reaction as it involves the transfer of a hydrogen atom, particularly at lower temperatures.'''Reference 3'''At low temperatures, the H atom can tunnel through the potential energy barrier than to pass over the barrier, hence the activation energy is lowered and the reaction rate increases. However, recrossing the energy barrier is possible as seen with the simulations, this can have a negative effect on the reaction rate. At high temperatures, the system is thermally activated and the behavious is approximately classical.'''reference4''' Therefore the experimental reaction rates are expected to be greater than that predicted by the Transition State Theory.

==F-H-H system==
===PES inspection===
'''F+H2 (F1-H1-H2)'''

F+H2 is exothermic as the reactants are higher in energy than the products therefore during the reaction, energy is released to the surroundings. H-F bond is stronger than H-H bond as the products are lower in energy and therefore more stable.The transition state is located approximately at rF1-H1=181.10 pm and rH1-H2=74.49 pm. This is verified by the forces (close to zero) and eigenvalues for hessian matrix (they are of opposite signs). The activation energy is estimated by tilting the transition state towards the reactants and is shown to be 424 kJ.mol-1.
[[File:Fh2_015083.png |400px|centre|thumb|Surface plot for F1-H1-H2 system using Dynamic Calculation, the transition state is identified as the black dot.]]
[[File:OptimisationFhh1_01508.png|400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:F1H1H2_EA_0150.png|400px|centre|thumb|Counter plot for estimating the activation energy.]]
[[File:EA1_01508.png|400px|centre|thumb|parameters for the activation energy.]]
'''H+HF (H1-H2-F1)'''
This reaction is endothermis as the reactants are lower in energy than the products therefore energy is taken in from the surroundings to form the products. H-F bond is still stronger than H-H as the reactans are lower in energy and more stable. The transition state is located at approximately rH1-H2=280 pm and rH2-F1=92 pm. It is located with the same reasons stated above.With the same method, the activation energy is estimated to be 434 kJ.mol-1. The two activation energies should be identical as these two reactions are essentially the reverse of one another.

[[File:H+HF_01508310.png|400px|centre|thumb|Surface plot for H1-H2-F1 system using Dynamic Calculationthe, the transition state is identified as the black dot.]]
[[File:HHF_015083.png |400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:EA2_01508.png|400px|centre|thumb|Counter plot for estimating the activation energy.]]
[[File:EA2_PARAMETERS.png|400px|centre|thumb|parameters for the activation energy.]]

===Reaction dynamics===
===F+H2 system===

Initially, the reactants have kinetic energy in the form of vibrational and translational energies, and as it crosses the potential energy barrier, the kinetic energy is converted into potential energy. Once the system is exiting the product channel, the potential energy is converted into the vibrational energy of the product.One good experimental technique to prob the electronic structure of the reacting species will be IR spectroscopy.In the anharmonic oscillator model, exciting molecules in the relaxed state promotes excitation from the ground state to the first energy level mainly. This will give rise to a single peak in the IR spectrum. Howver, when exciting a sample of excited molecules, many transitions are possible. For example, from 0-->1, the fundamental or 1-->2, the first overtone. They will show up in the spectrum as 2 peaks, with the overtone being at a lower wavenumber as the energy gap decreases up the potential well. The intensity of the overtone decreases over time as the electrons can fall back to lower energy levels and energy is emitted as radiation. As this system is linear, rotational is not important electronic energy is not considered here.Photoelectron spectroscopy is also a viable method. '''reference 5'''

[[File:Reactiondynamicsfh2_0150.png||400px|centre|thumb|contour plot for F+H2.]]
[[File:Reactiondynamicsparameter——015.png |400px|centre|thumb|parameters for the reactive trajectory.]]
====Varying the momentum of HH in the F+H2 system.====
Conditions:rFH=182 pm, fHH=74 pm, PFH=-1.0g.mol-1.pm.fs-1
{| class="wikitable" border="1"
|+ caption
|-
|PHH/g.mol-1.pm.fs-1|| Contour Plot
|-
|0 || [[File:0_015083.png |400 px|centre]]
|-
|2 || [[File:2_0508.png |400 px|centre]]
|-
|4 || [[File:4_01508.png ‎|400 px|centre]]
|-
|6.1|| [[File:6_01508.png|400 px|centre]]
|-
| -2|| [[File:-2_01508.png|400 px|centre]]
|-
| -4|| [[File:-4.1_01508.png‎|400 px|centre]]
|-
| -6.1|| [[File:Fit1_01508.png|400 px|centre]]
|-
|}
Although the amount of energy that is put into H-H vibration is much more than the activation energy of the reaction, the reaction does not always occur. The large amount of energy is demonstrated by the high frequency of those wavy lines. Recrossing the transition states multiple times can lead to no reaction or product formation depending on how the tragectory collides with the potential well.

[[File:Reactiondynamic_last01588.png|400px|centre|thumb|contour plot for rFH=182 pm, fHH=74 pm, PFH=-1.6g.mol-1.pm.fs-1,PHH=0.2g.mol-1.pm.fs-1]]
The system now has much less vibrational energy into the reactants than before. The reaction is still successful and the trajectory recrosses the transition states fewer times than before.This can be explained by the increased momentum of FH so that F can approach the closest H with more vibrational energy.

===H+HF system===
{| class="wikitable" border="1"
! p1(HH)/g.mol-1.pm.fs-1 !! p2(HF)/g.mol-1.pm.fs-1!! Etot/kJmol-1!! Recative?!! Endothermic/Exothermic!! Illustration of the trajectory
|-
| -2 || -10||-397|| No|| || [[File:Final1_01508.png|350px ]]
|-
| -3.1 || -4.1||-420 || No||The reactant H2 has vibrational energy and its rAB motion is rapid. Before it could cross the energy barrier, the molecule slams into the repulsive inner wall of the potential surface and bounces back into the reactant channel. || [[File:Table2_0150.png|350px]]
|-
| -3.1 || -5.1||-414|| Yes||The reactants have both the translational and vibrational energies. The energy is used to surmount the potential energy barrier and converted into the vibrational energy of the products. || [[File:Table3_01508.png|350px]]
|-
| -5.1 || -10.1||-357 || No||The reactants have sufficient energy to cross the transition state and the products did form for a certain amount of time. However, before the the system can exit the product channel, it recrosses the transition state and form the reactants again, hence no reaction occurs. ||[[File:Table4_01508.png|350px]]
|-
| -5.1 || -10.6||-394 || Yes||The system has sufficient energy to cross the transition state but it recrosses the transition state shortly after the reaction path hits the potential energy surface. However, the system is able to cross the transition state for the third time and finally exits the product channel and forms the products. || [[File:-10.6_01508.png|350px]]
|-
|}

File:Final1 01508.png

2020-05-22T17:16:11Z

Hh2218:

MRD:01508310

2020-05-22T17:00:28Z

Hh2218: /* Recative and unreactive trajectories */

==H-H-H system==
===Dynamics from the transition state region===
The transition state is the point on the potential energy surface that has ∂V(ri)/∂ri=0, where ri is the distance between two atoms.The transition state is a local maximum and its second derivative ∂2V(ri)/∂ri2 is < 0, whereas a local minimum will have a positive second derivative instead.
[[File:Hhh_surfaceplot_01508.png|400px|thumb|centre|a potential energy surface plot of H and H2 with respect to interatomic distances.]]

===Trajectories from r1=r2: locating the transition state===
At the transition state, r1=r2=90.8 pm by estimation. At this separation, the forces acting along AB and BC are both -0.004 kJ.mol-1.pm-1, which is close to zero and the eigenvalues for the Hessian matrix were -0.028 and +0.167 kJ.mol-1.pm-2, indicating the presence of transition state. The Internuclear Distance vs Time plot suggests the distance between HA, HB and HC is equal, about 90 pm and the distance is constant over time suggests the atoms are static at the transition state.
[[File:Animation101508310.png|400px|centre|thumb|picture showing H and H2 at the transition state.]]
[[File:Optimisation1_01508310.png|400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:Internucleardistance_01508310.png|400px|centre|thumb|Internuclear Distance vs Time plot between the H atoms at the transition state.]]

===Calculating the reaction path===
When rA-B is set to rts+1 and rB-C equals rts,the transition rolls towards BC and HA remains as an atom. MEP and Dynamic reaction paths are different as MEP set the momenta to zero in every step of the reaction path, products are therefore static and hence the reaction path is relatively straight. The dynamic reaction path is more realistic. It takes the momenta of gaseous molecules into account,i.e. they have vibrational energies, that is illustrated by the wavy line along the reaction path.
[[File:Surface_Plot1mep_015083.png|400px|centre|thumb|the minimum energy path (mep) of the H-H-H system]]
[[File:01569348_MEP_AB1_dynamic.png|400px|centre|thumb|the dynamic reaction path of the H-H-H system]]

====MEP and Dynamics calculations comparisons====
'''r1=91.8 pm, r2=90.8 pm, momenta set to 0 g.mol-1.pm.fs-1'''

HB and HC form a H2 molecule whereas HA moves away from the molecule. The distance between B and C decreased to 74 pm, which is the hydrogen molecule bond length. '''reference 2'''In MEP calculation, the momenta are set to zero at each time step.

[[File:MepH2bondlength_01508.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using MEP calculation.]]

[[File:MepH2momenta015083.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using MEP calculation.]]

Using Dynamics calculation, the outcome of the reaction is the same. The transition state rolls towards HB and HC and a hydrogen molecule is formed. One noticeable difference is that the hydrogen molecule now has some vibational energy as indicated by the wavy line along the B-C distance in the Internuclear Distance vs Time plot.As for the Momenta vs Time plot, the system is linear, therefore the angle theta is zero. HA and HB are moving away from each other at '''an increasing velocity until the momentum reaches 5 g.mol-1.pm.fs-1.The oscillation along the B-C bond corresponds to the vibration of the bond. '''why does the beginning have negative momenta?'''
[[File:DynamicsH2_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation.]]
[[File:DynamicsH2monenta_01508.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using Dynamics calculation.]]

'''r1=90.8 pm, r2=91.8 pm, momenta set to 0 g.mol-1.pm.fs-1'''

Once the length of r1 and r2 switches, the shapes of the graphs are identical but instead of HB and HC forming a molecule, HA and HB now form the hydrogen molecule in the products.
[[File:Mepinter2_01508.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using MEP calculation.]]
[[File:Momentamep2_015.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using MEP calculation.]]
[[File:InterDynamic_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation.]]
[[File:Momentadynamics_015083.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using Dynamics calculation.]]

'''Trajectory starting with the final position and reversed momentum to the reaction path above'''

This trajectory starts at the end of the reaction path above and finishes at where the above reaction started. it is essentially a reverse of what happened in the reaction above.
[[File:Reverse_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation (r1=70.0 pm,r2=353 pm,p1=-3.21 g.mol-1.pm.fs-1, p2=-5.07 g.mol-1.pm.fs-1) .]]

===Recative and unreactive trajectories===
{| class="wikitable" border="1"
! p1/g.mol-1.pm.fs-1 !! p2/g.mol-1.pm.fs-1!! Etot/kJmol-1!! Recative?!! Description of the dynamics!! Illustration of the trajectory
|-
| -2.56 || -5.1||-414 || Yes||The translational energy of the reactants can surmount the potential energy barrier and form the products. The ramaining energy is converted into vibrational energy of the products. || [[File:Table1_01508310.png|350px ]]
|-
| -3.1 || -4.1||-420 || No||The reactant H2 has vibrational energy and its rAB motion is rapid. Before it could cross the energy barrier, the molecule slams into the repulsive inner wall of the potential surface and bounces back into the reactant channel. || [[File:Table2_0150.png|350px]]
|-
| -3.1 || -5.1||-414|| Yes||The reactants have both the translational and vibrational energies. The energy is used to surmount the potential energy barrier and converted into the vibrational energy of the products. || [[File:Table3_01508.png|350px]]
|-
| -5.1 || -10.1||-357 || No||The reactants have sufficient energy to cross the transition state and the products did form for a certain amount of time. However, before the the system can exit the product channel, it recrosses the transition state and form the reactants again, hence no reaction occurs. ||[[File:Table4_01508.png|350px]]
|-
| -5.1 || -10.6||-394 || Yes||The system has sufficient energy to cross the transition state but it recrosses the transition state shortly after the reaction path hits the potential energy surface. However, the system is able to cross the transition state for the third time and finally exits the product channel and forms the products. || [[File:-10.6_01508.png|350px]]
|-
|}
In order to form products, a system must have sufficient energy to cross the transition state. Only molecules with the correct phase '''reference 2''' can exit the product channel and form stable products. Recrossing the transition state can lead to either product formation or no reaction. It is possible to cross the transition state multiple times.

===Transition State Theory===

Transition State Theory is classical, it doesn't take quantum tunnelling into account.Quantum tunnelling is probable for this reaction as it involves the transfer of a hydrogen atom, particularly at lower temperatures.'''Reference 3'''At low temperatures, the H atom can tunnel through the potential energy barrier than to pass over the barrier, hence the activation energy is lowered and the reaction rate increases. However, recrossing the energy barrier is possible as seen with the simulations, this can have a negative effect on the reaction rate. At high temperatures, the system is thermally activated and the behavious is approximately classical.'''reference4''' Therefore the experimental reaction rates are expected to be greater than that predicted by the Transition State Theory.

==F-H-H system==
===PES inspection===
'''F+H2 (F1-H1-H2)'''

F+H2 is exothermic as the reactants are higher in energy than the products therefore during the reaction, energy is released to the surroundings. H-F bond is stronger than H-H bond as the products are lower in energy and therefore more stable.The transition state is located approximately at rF1-H1=181.10 pm and rH1-H2=74.49 pm. This is verified by the forces (close to zero) and eigenvalues for hessian matrix (they are of opposite signs). The activation energy is estimated by tilting the transition state towards the reactants and is shown to be 424 kJ.mol-1.
[[File:Fh2_015083.png |400px|centre|thumb|Surface plot for F1-H1-H2 system using Dynamic Calculation, the transition state is identified as the black dot.]]
[[File:OptimisationFhh1_01508.png|400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:F1H1H2_EA_0150.png|400px|centre|thumb|Counter plot for estimating the activation energy.]]
[[File:EA1_01508.png|400px|centre|thumb|parameters for the activation energy.]]
'''H+HF (H1-H2-F1)'''
This reaction is endothermis as the reactants are lower in energy than the products therefore energy is taken in from the surroundings to form the products. H-F bond is still stronger than H-H as the reactans are lower in energy and more stable. The transition state is located at approximately rH1-H2=280 pm and rH2-F1=92 pm. It is located with the same reasons stated above.With the same method, the activation energy is estimated to be 434 kJ.mol-1. The two activation energies should be identical as these two reactions are essentially the reverse of one another.

[[File:H+HF_01508310.png|400px|centre|thumb|Surface plot for H1-H2-F1 system using Dynamic Calculationthe, the transition state is identified as the black dot.]]
[[File:HHF_015083.png |400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:EA2_01508.png|400px|centre|thumb|Counter plot for estimating the activation energy.]]
[[File:EA2_PARAMETERS.png|400px|centre|thumb|parameters for the activation energy.]]

===Reaction dynamics===
===F+H2 system===

Initially, the reactants have kinetic energy in the form of vibrational and translational energies, and as it crosses the potential energy barrier, the kinetic energy is converted into potential energy. Once the system is exiting the product channel, the potential energy is converted into the vibrational energy of the product.One good experimental technique to prob the electronic structure of the reacting species will be IR spectroscopy.In the anharmonic oscillator model, exciting molecules in the relaxed state promotes excitation from the ground state to the first energy level mainly. This will give rise to a single peak in the IR spectrum. Howver, when exciting a sample of excited molecules, many transitions are possible. For example, from 0-->1, the fundamental or 1-->2, the first overtone. They will show up in the spectrum as 2 peaks, with the overtone being at a lower wavenumber as the energy gap decreases up the potential well. The intensity of the overtone decreases over time as the electrons can fall back to lower energy levels and energy is emitted as radiation. As this system is linear, rotational is not important electronic energy is not considered here.Photoelectron spectroscopy is also a viable method. '''reference 5'''

[[File:Reactiondynamicsfh2_0150.png||400px|centre|thumb|contour plot for F+H2.]]
[[File:Reactiondynamicsparameter——015.png |400px|centre|thumb|parameters for the reactive trajectory.]]
====Varying the momentum of HH in the F+H2 system.====
Conditions:rFH=182 pm, fHH=74 pm, PFH=-1.0g.mol-1.pm.fs-1
{| class="wikitable" border="1"
|+ caption
|-
|PHH/g.mol-1.pm.fs-1|| Contour Plot
|-
|0 || [[File:0_015083.png |400 px|centre]]
|-
|2 || [[File:2_0508.png |400 px|centre]]
|-
|4 || [[File:4_01508.png ‎|400 px|centre]]
|-
|6.1|| [[File:6_01508.png|400 px|centre]]
|-
| -2|| [[File:-2_01508.png|400 px|centre]]
|-
| -4|| [[File:-4.1_01508.png‎|400 px|centre]]
|-
| -6.1|| [[File:Fit1_01508.png|400 px|centre]]
|-
|}
Although the amount of energy that is put into H-H vibration is much more than the activation energy of the reaction, the reaction does not always occur. The large amount of energy is demonstrated by the high frequency of those wavy lines. Recrossing the transition states multiple times can lead to no reaction or product formation depending on how the tragectory collides with the potential well.

[[File:Reactiondynamic_last01588.png|400px|centre|thumb|contour plot for rFH=182 pm, fHH=74 pm, PFH=-1.6g.mol-1.pm.fs-1,PHH=0.2g.mol-1.pm.fs-1]]
The system now has much less vibrational energy into the reactants than before. The reaction is still successful and the trajectory recrosses the transition states fewer times than before.This can be explained by the increased momentum of FH so that F can approach the closest H with more vibrational energy.

===H+HF system===

MRD:01508310

2020-05-22T17:00:16Z

Hh2218: /* Recative and unreactive trajectories */

==H-H-H system==
===Dynamics from the transition state region===
The transition state is the point on the potential energy surface that has ∂V(ri)/∂ri=0, where ri is the distance between two atoms.The transition state is a local maximum and its second derivative ∂2V(ri)/∂ri2 is < 0, whereas a local minimum will have a positive second derivative instead.
[[File:Hhh_surfaceplot_01508.png|400px|thumb|centre|a potential energy surface plot of H and H2 with respect to interatomic distances.]]

===Trajectories from r1=r2: locating the transition state===
At the transition state, r1=r2=90.8 pm by estimation. At this separation, the forces acting along AB and BC are both -0.004 kJ.mol-1.pm-1, which is close to zero and the eigenvalues for the Hessian matrix were -0.028 and +0.167 kJ.mol-1.pm-2, indicating the presence of transition state. The Internuclear Distance vs Time plot suggests the distance between HA, HB and HC is equal, about 90 pm and the distance is constant over time suggests the atoms are static at the transition state.
[[File:Animation101508310.png|400px|centre|thumb|picture showing H and H2 at the transition state.]]
[[File:Optimisation1_01508310.png|400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:Internucleardistance_01508310.png|400px|centre|thumb|Internuclear Distance vs Time plot between the H atoms at the transition state.]]

===Calculating the reaction path===
When rA-B is set to rts+1 and rB-C equals rts,the transition rolls towards BC and HA remains as an atom. MEP and Dynamic reaction paths are different as MEP set the momenta to zero in every step of the reaction path, products are therefore static and hence the reaction path is relatively straight. The dynamic reaction path is more realistic. It takes the momenta of gaseous molecules into account,i.e. they have vibrational energies, that is illustrated by the wavy line along the reaction path.
[[File:Surface_Plot1mep_015083.png|400px|centre|thumb|the minimum energy path (mep) of the H-H-H system]]
[[File:01569348_MEP_AB1_dynamic.png|400px|centre|thumb|the dynamic reaction path of the H-H-H system]]

====MEP and Dynamics calculations comparisons====
'''r1=91.8 pm, r2=90.8 pm, momenta set to 0 g.mol-1.pm.fs-1'''

HB and HC form a H2 molecule whereas HA moves away from the molecule. The distance between B and C decreased to 74 pm, which is the hydrogen molecule bond length. '''reference 2'''In MEP calculation, the momenta are set to zero at each time step.

[[File:MepH2bondlength_01508.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using MEP calculation.]]

[[File:MepH2momenta015083.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using MEP calculation.]]

Using Dynamics calculation, the outcome of the reaction is the same. The transition state rolls towards HB and HC and a hydrogen molecule is formed. One noticeable difference is that the hydrogen molecule now has some vibational energy as indicated by the wavy line along the B-C distance in the Internuclear Distance vs Time plot.As for the Momenta vs Time plot, the system is linear, therefore the angle theta is zero. HA and HB are moving away from each other at '''an increasing velocity until the momentum reaches 5 g.mol-1.pm.fs-1.The oscillation along the B-C bond corresponds to the vibration of the bond. '''why does the beginning have negative momenta?'''
[[File:DynamicsH2_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation.]]
[[File:DynamicsH2monenta_01508.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using Dynamics calculation.]]

'''r1=90.8 pm, r2=91.8 pm, momenta set to 0 g.mol-1.pm.fs-1'''

Once the length of r1 and r2 switches, the shapes of the graphs are identical but instead of HB and HC forming a molecule, HA and HB now form the hydrogen molecule in the products.
[[File:Mepinter2_01508.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using MEP calculation.]]
[[File:Momentamep2_015.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using MEP calculation.]]
[[File:InterDynamic_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation.]]
[[File:Momentadynamics_015083.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using Dynamics calculation.]]

'''Trajectory starting with the final position and reversed momentum to the reaction path above'''

This trajectory starts at the end of the reaction path above and finishes at where the above reaction started. it is essentially a reverse of what happened in the reaction above.
[[File:Reverse_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation (r1=70.0 pm,r2=353 pm,p1=-3.21 g.mol-1.pm.fs-1, p2=-5.07 g.mol-1.pm.fs-1) .]]

===Recative and unreactive trajectories===
{| class="wikitable" border="1"
! p1/g.mol-1.pm.fs-1 !! p2/g.mol-1.pm.fs-1!! Etot/kJmol-1!! Recative?!! Description of the dynamics!! Illustration of the trajectory
|-
| -2.56 || -5.1||-414 || Yes||The translational energy of the reactants can surmount the potential energy barrier and form the products. The ramaining energy is converted into vibrational energy of the products. || [[File:Table1_01508310.png|350px ]]
|-
| -3.1 || -4.1||-420 || No||The reactant H2 has vibrational energy and its rAB motion is rapid. Before it could cross the energy barrier, the molecule slams into the repulsive inner wall of the potential surface and bounces back into the reactant channel. || [[File:Table2_0150.png|350px]]
|-
| -3.1 || -5.1||-414|| Yes||The reactants have both the translational and vibrational energies. The energy is used to surmount the potential energy barrier and converted into the vibrational energy of the products. || [[File:Table3_01508.png|350px]]
|-
| -5.1 || -10.1||-357 || No||The reactants have sufficient energy to cross the transition state and the products did form for a certain amount of time. However, before the the system can exit the product channel, it recrosses the transition state and form the reactants again, hence no reaction occurs. ||[[File:Table4_01508.png|350px]]
|-
| -5.1 || -10.6||-394 || Yes||The system has sufficient energy to cross the transition state but it recrosses the transition state shortly after the reaction path hits the potential energy surface. However, the system is able to cross the transition state for the third time and finally exits the product channel and forms the products. || [[File:-10.6_01508.png|350px]]
|-
|}
In order to form products, a system must have sufficient energy to cross the transition state. Only molecules with the correct phase '''reference 2''' can exit the product channel and form stable products. Recrossing the transition state can lead to either product formation or no reaction. It is possible to cross the transition state multiple times.

===Transition State Theory===

Transition State Theory is classical, it doesn't take quantum tunnelling into account.Quantum tunnelling is probable for this reaction as it involves the transfer of a hydrogen atom, particularly at lower temperatures.'''Reference 3'''At low temperatures, the H atom can tunnel through the potential energy barrier than to pass over the barrier, hence the activation energy is lowered and the reaction rate increases. However, recrossing the energy barrier is possible as seen with the simulations, this can have a negative effect on the reaction rate. At high temperatures, the system is thermally activated and the behavious is approximately classical.'''reference4''' Therefore the experimental reaction rates are expected to be greater than that predicted by the Transition State Theory.

==F-H-H system==
===PES inspection===
'''F+H2 (F1-H1-H2)'''

F+H2 is exothermic as the reactants are higher in energy than the products therefore during the reaction, energy is released to the surroundings. H-F bond is stronger than H-H bond as the products are lower in energy and therefore more stable.The transition state is located approximately at rF1-H1=181.10 pm and rH1-H2=74.49 pm. This is verified by the forces (close to zero) and eigenvalues for hessian matrix (they are of opposite signs). The activation energy is estimated by tilting the transition state towards the reactants and is shown to be 424 kJ.mol-1.
[[File:Fh2_015083.png |400px|centre|thumb|Surface plot for F1-H1-H2 system using Dynamic Calculation, the transition state is identified as the black dot.]]
[[File:OptimisationFhh1_01508.png|400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:F1H1H2_EA_0150.png|400px|centre|thumb|Counter plot for estimating the activation energy.]]
[[File:EA1_01508.png|400px|centre|thumb|parameters for the activation energy.]]
'''H+HF (H1-H2-F1)'''
This reaction is endothermis as the reactants are lower in energy than the products therefore energy is taken in from the surroundings to form the products. H-F bond is still stronger than H-H as the reactans are lower in energy and more stable. The transition state is located at approximately rH1-H2=280 pm and rH2-F1=92 pm. It is located with the same reasons stated above.With the same method, the activation energy is estimated to be 434 kJ.mol-1. The two activation energies should be identical as these two reactions are essentially the reverse of one another.

[[File:H+HF_01508310.png|400px|centre|thumb|Surface plot for H1-H2-F1 system using Dynamic Calculationthe, the transition state is identified as the black dot.]]
[[File:HHF_015083.png |400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:EA2_01508.png|400px|centre|thumb|Counter plot for estimating the activation energy.]]
[[File:EA2_PARAMETERS.png|400px|centre|thumb|parameters for the activation energy.]]

===Reaction dynamics===
===F+H2 system===

Initially, the reactants have kinetic energy in the form of vibrational and translational energies, and as it crosses the potential energy barrier, the kinetic energy is converted into potential energy. Once the system is exiting the product channel, the potential energy is converted into the vibrational energy of the product.One good experimental technique to prob the electronic structure of the reacting species will be IR spectroscopy.In the anharmonic oscillator model, exciting molecules in the relaxed state promotes excitation from the ground state to the first energy level mainly. This will give rise to a single peak in the IR spectrum. Howver, when exciting a sample of excited molecules, many transitions are possible. For example, from 0-->1, the fundamental or 1-->2, the first overtone. They will show up in the spectrum as 2 peaks, with the overtone being at a lower wavenumber as the energy gap decreases up the potential well. The intensity of the overtone decreases over time as the electrons can fall back to lower energy levels and energy is emitted as radiation. As this system is linear, rotational is not important electronic energy is not considered here.Photoelectron spectroscopy is also a viable method. '''reference 5'''

[[File:Reactiondynamicsfh2_0150.png||400px|centre|thumb|contour plot for F+H2.]]
[[File:Reactiondynamicsparameter——015.png |400px|centre|thumb|parameters for the reactive trajectory.]]
====Varying the momentum of HH in the F+H2 system.====
Conditions:rFH=182 pm, fHH=74 pm, PFH=-1.0g.mol-1.pm.fs-1
{| class="wikitable" border="1"
|+ caption
|-
|PHH/g.mol-1.pm.fs-1|| Contour Plot
|-
|0 || [[File:0_015083.png |400 px|centre]]
|-
|2 || [[File:2_0508.png |400 px|centre]]
|-
|4 || [[File:4_01508.png ‎|400 px|centre]]
|-
|6.1|| [[File:6_01508.png|400 px|centre]]
|-
| -2|| [[File:-2_01508.png|400 px|centre]]
|-
| -4|| [[File:-4.1_01508.png‎|400 px|centre]]
|-
| -6.1|| [[File:Fit1_01508.png|400 px|centre]]
|-
|}
Although the amount of energy that is put into H-H vibration is much more than the activation energy of the reaction, the reaction does not always occur. The large amount of energy is demonstrated by the high frequency of those wavy lines. Recrossing the transition states multiple times can lead to no reaction or product formation depending on how the tragectory collides with the potential well.

[[File:Reactiondynamic_last01588.png|400px|centre|thumb|contour plot for rFH=182 pm, fHH=74 pm, PFH=-1.6g.mol-1.pm.fs-1,PHH=0.2g.mol-1.pm.fs-1]]
The system now has much less vibrational energy into the reactants than before. The reaction is still successful and the trajectory recrosses the transition states fewer times than before.This can be explained by the increased momentum of FH so that F can approach the closest H with more vibrational energy.

===H+HF system===

MRD:01508310

2020-05-22T16:33:49Z

Hh2218: /* Reaction dynamics */

==H-H-H system==
===Dynamics from the transition state region===
The transition state is the point on the potential energy surface that has ∂V(ri)/∂ri=0, where ri is the distance between two atoms.The transition state is a local maximum and its second derivative ∂2V(ri)/∂ri2 is < 0, whereas a local minimum will have a positive second derivative instead.
[[File:Hhh_surfaceplot_01508.png|400px|thumb|centre|a potential energy surface plot of H and H2 with respect to interatomic distances.]]

===Trajectories from r1=r2: locating the transition state===
At the transition state, r1=r2=90.8 pm by estimation. At this separation, the forces acting along AB and BC are both -0.004 kJ.mol-1.pm-1, which is close to zero and the eigenvalues for the Hessian matrix were -0.028 and +0.167 kJ.mol-1.pm-2, indicating the presence of transition state. The Internuclear Distance vs Time plot suggests the distance between HA, HB and HC is equal, about 90 pm and the distance is constant over time suggests the atoms are static at the transition state.
[[File:Animation101508310.png|400px|centre|thumb|picture showing H and H2 at the transition state.]]
[[File:Optimisation1_01508310.png|400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:Internucleardistance_01508310.png|400px|centre|thumb|Internuclear Distance vs Time plot between the H atoms at the transition state.]]

===Calculating the reaction path===
When rA-B is set to rts+1 and rB-C equals rts,the transition rolls towards BC and HA remains as an atom. MEP and Dynamic reaction paths are different as MEP set the momenta to zero in every step of the reaction path, products are therefore static and hence the reaction path is relatively straight. The dynamic reaction path is more realistic. It takes the momenta of gaseous molecules into account,i.e. they have vibrational energies, that is illustrated by the wavy line along the reaction path.
[[File:Surface_Plot1mep_015083.png|400px|centre|thumb|the minimum energy path (mep) of the H-H-H system]]
[[File:01569348_MEP_AB1_dynamic.png|400px|centre|thumb|the dynamic reaction path of the H-H-H system]]

====MEP and Dynamics calculations comparisons====
'''r1=91.8 pm, r2=90.8 pm, momenta set to 0 g.mol-1.pm.fs-1'''

HB and HC form a H2 molecule whereas HA moves away from the molecule. The distance between B and C decreased to 74 pm, which is the hydrogen molecule bond length. '''reference 2'''In MEP calculation, the momenta are set to zero at each time step.

[[File:MepH2bondlength_01508.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using MEP calculation.]]

[[File:MepH2momenta015083.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using MEP calculation.]]

Using Dynamics calculation, the outcome of the reaction is the same. The transition state rolls towards HB and HC and a hydrogen molecule is formed. One noticeable difference is that the hydrogen molecule now has some vibational energy as indicated by the wavy line along the B-C distance in the Internuclear Distance vs Time plot.As for the Momenta vs Time plot, the system is linear, therefore the angle theta is zero. HA and HB are moving away from each other at '''an increasing velocity until the momentum reaches 5 g.mol-1.pm.fs-1.The oscillation along the B-C bond corresponds to the vibration of the bond. '''why does the beginning have negative momenta?'''
[[File:DynamicsH2_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation.]]
[[File:DynamicsH2monenta_01508.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using Dynamics calculation.]]

'''r1=90.8 pm, r2=91.8 pm, momenta set to 0 g.mol-1.pm.fs-1'''

Once the length of r1 and r2 switches, the shapes of the graphs are identical but instead of HB and HC forming a molecule, HA and HB now form the hydrogen molecule in the products.
[[File:Mepinter2_01508.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using MEP calculation.]]
[[File:Momentamep2_015.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using MEP calculation.]]
[[File:InterDynamic_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation.]]
[[File:Momentadynamics_015083.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using Dynamics calculation.]]

'''Trajectory starting with the final position and reversed momentum to the reaction path above'''

This trajectory starts at the end of the reaction path above and finishes at where the above reaction started. it is essentially a reverse of what happened in the reaction above.
[[File:Reverse_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation (r1=70.0 pm,r2=353 pm,p1=-3.21 g.mol-1.pm.fs-1, p2=-5.07 g.mol-1.pm.fs-1) .]]

===Recative and unreactive trajectories===
{| class="wikitable" border="1"
! p1/g.mol-1.pm.fs-1 !! p2/g.mol-1.pm.fs-1!! Etot!! Recative?!! Description of the dynamics!! Illustration of the trajectory
|-
| -2.56 || -5.1||-414 || Yes||The translational energy of the reactants can surmount the potential energy barrier and form the products. The ramaining energy is converted into vibrational energy of the products. || [[File:Table1_01508310.png|350px ]]
|-
| -3.1 || -4.1||-420 || No||The reactant H2 has vibrational energy and its rAB motion is rapid. Before it could cross the energy barrier, the molecule slams into the repulsive inner wall of the potential surface and bounces back into the reactant channel. || [[File:Table2_0150.png|350px]]
|-
| -3.1 || -5.1||-414|| Yes||The reactants have both the translational and vibrational energies. The energy is used to surmount the potential energy barrier and converted into the vibrational energy of the products. || [[File:Table3_01508.png|350px]]
|-
| -5.1 || -10.1||-357 || No||The reactants have sufficient energy to cross the transition state and the products did form for a certain amount of time. However, before the the system can exit the product channel, it recrosses the transition state and form the reactants again, hence no reaction occurs. ||[[File:Table4_01508.png|350px]]
|-
| -5.1 || -10.6||-394 || Yes||The system has sufficient energy to cross the transition state but it recrosses the transition state shortly after the reaction path hits the potential energy surface. However, the system is able to cross the transition state for the third time and finally exits the product channel and forms the products. || [[File:-10.6_01508.png|350px]]
|-
|}
In order to form products, a system must have sufficient energy to cross the transition state. Only molecules with the correct phase '''reference 2''' can exit the product channel and form stable products. Recrossing the transition state can lead to either product formation or no reaction. It is possible to cross the transition state multiple times.

===Transition State Theory===

Transition State Theory is classical, it doesn't take quantum tunnelling into account.Quantum tunnelling is probable for this reaction as it involves the transfer of a hydrogen atom, particularly at lower temperatures.'''Reference 3'''At low temperatures, the H atom can tunnel through the potential energy barrier than to pass over the barrier, hence the activation energy is lowered and the reaction rate increases. However, recrossing the energy barrier is possible as seen with the simulations, this can have a negative effect on the reaction rate. At high temperatures, the system is thermally activated and the behavious is approximately classical.'''reference4''' Therefore the experimental reaction rates are expected to be greater than that predicted by the Transition State Theory.

==F-H-H system==
===PES inspection===
'''F+H2 (F1-H1-H2)'''

F+H2 is exothermic as the reactants are higher in energy than the products therefore during the reaction, energy is released to the surroundings. H-F bond is stronger than H-H bond as the products are lower in energy and therefore more stable.The transition state is located approximately at rF1-H1=181.10 pm and rH1-H2=74.49 pm. This is verified by the forces (close to zero) and eigenvalues for hessian matrix (they are of opposite signs). The activation energy is estimated by tilting the transition state towards the reactants and is shown to be 424 kJ.mol-1.
[[File:Fh2_015083.png |400px|centre|thumb|Surface plot for F1-H1-H2 system using Dynamic Calculation, the transition state is identified as the black dot.]]
[[File:OptimisationFhh1_01508.png|400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:F1H1H2_EA_0150.png|400px|centre|thumb|Counter plot for estimating the activation energy.]]
[[File:EA1_01508.png|400px|centre|thumb|parameters for the activation energy.]]
'''H+HF (H1-H2-F1)'''
This reaction is endothermis as the reactants are lower in energy than the products therefore energy is taken in from the surroundings to form the products. H-F bond is still stronger than H-H as the reactans are lower in energy and more stable. The transition state is located at approximately rH1-H2=280 pm and rH2-F1=92 pm. It is located with the same reasons stated above.With the same method, the activation energy is estimated to be 434 kJ.mol-1. The two activation energies should be identical as these two reactions are essentially the reverse of one another.

[[File:H+HF_01508310.png|400px|centre|thumb|Surface plot for H1-H2-F1 system using Dynamic Calculationthe, the transition state is identified as the black dot.]]
[[File:HHF_015083.png |400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:EA2_01508.png|400px|centre|thumb|Counter plot for estimating the activation energy.]]
[[File:EA2_PARAMETERS.png|400px|centre|thumb|parameters for the activation energy.]]

===Reaction dynamics===
===F+H2 system===

Initially, the reactants have kinetic energy in the form of vibrational and translational energies, and as it crosses the potential energy barrier, the kinetic energy is converted into potential energy. Once the system is exiting the product channel, the potential energy is converted into the vibrational energy of the product.One good experimental technique to prob the electronic structure of the reacting species will be IR spectroscopy.In the anharmonic oscillator model, exciting molecules in the relaxed state promotes excitation from the ground state to the first energy level mainly. This will give rise to a single peak in the IR spectrum. Howver, when exciting a sample of excited molecules, many transitions are possible. For example, from 0-->1, the fundamental or 1-->2, the first overtone. They will show up in the spectrum as 2 peaks, with the overtone being at a lower wavenumber as the energy gap decreases up the potential well. The intensity of the overtone decreases over time as the electrons can fall back to lower energy levels and energy is emitted as radiation. As this system is linear, rotational is not important electronic energy is not considered here.Photoelectron spectroscopy is also a viable method. '''reference 5'''

[[File:Reactiondynamicsfh2_0150.png||400px|centre|thumb|contour plot for F+H2.]]
[[File:Reactiondynamicsparameter——015.png |400px|centre|thumb|parameters for the reactive trajectory.]]
====Varying the momentum of HH in the F+H2 system.====
Conditions:rFH=182 pm, fHH=74 pm, PFH=-1.0g.mol-1.pm.fs-1
{| class="wikitable" border="1"
|+ caption
|-
|PHH/g.mol-1.pm.fs-1|| Contour Plot
|-
|0 || [[File:0_015083.png |400 px|centre]]
|-
|2 || [[File:2_0508.png |400 px|centre]]
|-
|4 || [[File:4_01508.png ‎|400 px|centre]]
|-
|6.1|| [[File:6_01508.png|400 px|centre]]
|-
| -2|| [[File:-2_01508.png|400 px|centre]]
|-
| -4|| [[File:-4.1_01508.png‎|400 px|centre]]
|-
| -6.1|| [[File:Fit1_01508.png|400 px|centre]]
|-
|}
Although the amount of energy that is put into H-H vibration is much more than the activation energy of the reaction, the reaction does not always occur. The large amount of energy is demonstrated by the high frequency of those wavy lines. Recrossing the transition states multiple times can lead to no reaction or product formation depending on how the tragectory collides with the potential well.

[[File:Reactiondynamic_last01588.png|400px|centre|thumb|contour plot for rFH=182 pm, fHH=74 pm, PFH=-1.6g.mol-1.pm.fs-1,PHH=0.2g.mol-1.pm.fs-1]]
The system now has much less vibrational energy into the reactants than before. The reaction is still successful and the trajectory recrosses the transition states fewer times than before.This can be explained by the increased momentum of FH so that F can approach the closest H with more vibrational energy.

===H+HF system===

MRD:01508310

2020-05-22T16:33:06Z

Hh2218: /* Reaction dynamics */

==H-H-H system==
===Dynamics from the transition state region===
The transition state is the point on the potential energy surface that has ∂V(ri)/∂ri=0, where ri is the distance between two atoms.The transition state is a local maximum and its second derivative ∂2V(ri)/∂ri2 is < 0, whereas a local minimum will have a positive second derivative instead.
[[File:Hhh_surfaceplot_01508.png|400px|thumb|centre|a potential energy surface plot of H and H2 with respect to interatomic distances.]]

===Trajectories from r1=r2: locating the transition state===
At the transition state, r1=r2=90.8 pm by estimation. At this separation, the forces acting along AB and BC are both -0.004 kJ.mol-1.pm-1, which is close to zero and the eigenvalues for the Hessian matrix were -0.028 and +0.167 kJ.mol-1.pm-2, indicating the presence of transition state. The Internuclear Distance vs Time plot suggests the distance between HA, HB and HC is equal, about 90 pm and the distance is constant over time suggests the atoms are static at the transition state.
[[File:Animation101508310.png|400px|centre|thumb|picture showing H and H2 at the transition state.]]
[[File:Optimisation1_01508310.png|400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:Internucleardistance_01508310.png|400px|centre|thumb|Internuclear Distance vs Time plot between the H atoms at the transition state.]]

===Calculating the reaction path===
When rA-B is set to rts+1 and rB-C equals rts,the transition rolls towards BC and HA remains as an atom. MEP and Dynamic reaction paths are different as MEP set the momenta to zero in every step of the reaction path, products are therefore static and hence the reaction path is relatively straight. The dynamic reaction path is more realistic. It takes the momenta of gaseous molecules into account,i.e. they have vibrational energies, that is illustrated by the wavy line along the reaction path.
[[File:Surface_Plot1mep_015083.png|400px|centre|thumb|the minimum energy path (mep) of the H-H-H system]]
[[File:01569348_MEP_AB1_dynamic.png|400px|centre|thumb|the dynamic reaction path of the H-H-H system]]

====MEP and Dynamics calculations comparisons====
'''r1=91.8 pm, r2=90.8 pm, momenta set to 0 g.mol-1.pm.fs-1'''

HB and HC form a H2 molecule whereas HA moves away from the molecule. The distance between B and C decreased to 74 pm, which is the hydrogen molecule bond length. '''reference 2'''In MEP calculation, the momenta are set to zero at each time step.

[[File:MepH2bondlength_01508.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using MEP calculation.]]

[[File:MepH2momenta015083.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using MEP calculation.]]

Using Dynamics calculation, the outcome of the reaction is the same. The transition state rolls towards HB and HC and a hydrogen molecule is formed. One noticeable difference is that the hydrogen molecule now has some vibational energy as indicated by the wavy line along the B-C distance in the Internuclear Distance vs Time plot.As for the Momenta vs Time plot, the system is linear, therefore the angle theta is zero. HA and HB are moving away from each other at '''an increasing velocity until the momentum reaches 5 g.mol-1.pm.fs-1.The oscillation along the B-C bond corresponds to the vibration of the bond. '''why does the beginning have negative momenta?'''
[[File:DynamicsH2_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation.]]
[[File:DynamicsH2monenta_01508.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using Dynamics calculation.]]

'''r1=90.8 pm, r2=91.8 pm, momenta set to 0 g.mol-1.pm.fs-1'''

Once the length of r1 and r2 switches, the shapes of the graphs are identical but instead of HB and HC forming a molecule, HA and HB now form the hydrogen molecule in the products.
[[File:Mepinter2_01508.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using MEP calculation.]]
[[File:Momentamep2_015.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using MEP calculation.]]
[[File:InterDynamic_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation.]]
[[File:Momentadynamics_015083.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using Dynamics calculation.]]

'''Trajectory starting with the final position and reversed momentum to the reaction path above'''

This trajectory starts at the end of the reaction path above and finishes at where the above reaction started. it is essentially a reverse of what happened in the reaction above.
[[File:Reverse_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation (r1=70.0 pm,r2=353 pm,p1=-3.21 g.mol-1.pm.fs-1, p2=-5.07 g.mol-1.pm.fs-1) .]]

===Recative and unreactive trajectories===
{| class="wikitable" border="1"
! p1/g.mol-1.pm.fs-1 !! p2/g.mol-1.pm.fs-1!! Etot!! Recative?!! Description of the dynamics!! Illustration of the trajectory
|-
| -2.56 || -5.1||-414 || Yes||The translational energy of the reactants can surmount the potential energy barrier and form the products. The ramaining energy is converted into vibrational energy of the products. || [[File:Table1_01508310.png|350px ]]
|-
| -3.1 || -4.1||-420 || No||The reactant H2 has vibrational energy and its rAB motion is rapid. Before it could cross the energy barrier, the molecule slams into the repulsive inner wall of the potential surface and bounces back into the reactant channel. || [[File:Table2_0150.png|350px]]
|-
| -3.1 || -5.1||-414|| Yes||The reactants have both the translational and vibrational energies. The energy is used to surmount the potential energy barrier and converted into the vibrational energy of the products. || [[File:Table3_01508.png|350px]]
|-
| -5.1 || -10.1||-357 || No||The reactants have sufficient energy to cross the transition state and the products did form for a certain amount of time. However, before the the system can exit the product channel, it recrosses the transition state and form the reactants again, hence no reaction occurs. ||[[File:Table4_01508.png|350px]]
|-
| -5.1 || -10.6||-394 || Yes||The system has sufficient energy to cross the transition state but it recrosses the transition state shortly after the reaction path hits the potential energy surface. However, the system is able to cross the transition state for the third time and finally exits the product channel and forms the products. || [[File:-10.6_01508.png|350px]]
|-
|}
In order to form products, a system must have sufficient energy to cross the transition state. Only molecules with the correct phase '''reference 2''' can exit the product channel and form stable products. Recrossing the transition state can lead to either product formation or no reaction. It is possible to cross the transition state multiple times.

===Transition State Theory===

Transition State Theory is classical, it doesn't take quantum tunnelling into account.Quantum tunnelling is probable for this reaction as it involves the transfer of a hydrogen atom, particularly at lower temperatures.'''Reference 3'''At low temperatures, the H atom can tunnel through the potential energy barrier than to pass over the barrier, hence the activation energy is lowered and the reaction rate increases. However, recrossing the energy barrier is possible as seen with the simulations, this can have a negative effect on the reaction rate. At high temperatures, the system is thermally activated and the behavious is approximately classical.'''reference4''' Therefore the experimental reaction rates are expected to be greater than that predicted by the Transition State Theory.

==F-H-H system==
===PES inspection===
'''F+H2 (F1-H1-H2)'''

F+H2 is exothermic as the reactants are higher in energy than the products therefore during the reaction, energy is released to the surroundings. H-F bond is stronger than H-H bond as the products are lower in energy and therefore more stable.The transition state is located approximately at rF1-H1=181.10 pm and rH1-H2=74.49 pm. This is verified by the forces (close to zero) and eigenvalues for hessian matrix (they are of opposite signs). The activation energy is estimated by tilting the transition state towards the reactants and is shown to be 424 kJ.mol-1.
[[File:Fh2_015083.png |400px|centre|thumb|Surface plot for F1-H1-H2 system using Dynamic Calculation, the transition state is identified as the black dot.]]
[[File:OptimisationFhh1_01508.png|400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:F1H1H2_EA_0150.png|400px|centre|thumb|Counter plot for estimating the activation energy.]]
[[File:EA1_01508.png|400px|centre|thumb|parameters for the activation energy.]]
'''H+HF (H1-H2-F1)'''
This reaction is endothermis as the reactants are lower in energy than the products therefore energy is taken in from the surroundings to form the products. H-F bond is still stronger than H-H as the reactans are lower in energy and more stable. The transition state is located at approximately rH1-H2=280 pm and rH2-F1=92 pm. It is located with the same reasons stated above.With the same method, the activation energy is estimated to be 434 kJ.mol-1. The two activation energies should be identical as these two reactions are essentially the reverse of one another.

[[File:H+HF_01508310.png|400px|centre|thumb|Surface plot for H1-H2-F1 system using Dynamic Calculationthe, the transition state is identified as the black dot.]]
[[File:HHF_015083.png |400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:EA2_01508.png|400px|centre|thumb|Counter plot for estimating the activation energy.]]
[[File:EA2_PARAMETERS.png|400px|centre|thumb|parameters for the activation energy.]]

==Reaction dynamics==
===F+H2 system===

Initially, the reactants have kinetic energy in the form of vibrational and translational energies, and as it crosses the potential energy barrier, the kinetic energy is converted into potential energy. Once the system is exiting the product channel, the potential energy is converted into the vibrational energy of the product.One good experimental technique to prob the electronic structure of the reacting species will be IR spectroscopy.In the anharmonic oscillator model, exciting molecules in the relaxed state promotes excitation from the ground state to the first energy level mainly. This will give rise to a single peak in the IR spectrum. Howver, when exciting a sample of excited molecules, many transitions are possible. For example, from 0-->1, the fundamental or 1-->2, the first overtone. They will show up in the spectrum as 2 peaks, with the overtone being at a lower wavenumber as the energy gap decreases up the potential well. The intensity of the overtone decreases over time as the electrons can fall back to lower energy levels and energy is emitted as radiation. As this system is linear, rotational is not important electronic energy is not considered here.Photoelectron spectroscopy is also a viable method. '''reference 5'''

[[File:Reactiondynamicsfh2_0150.png||400px|centre|thumb|contour plot for F+H2.]]
[[File:Reactiondynamicsparameter——015.png |400px|centre|thumb|parameters for the reactive trajectory.]]
====Varying the momentum of HH in the F+H2 system.====
Conditions:rFH=182 pm, fHH=74 pm, PFH=-1.0g.mol-1.pm.fs-1
{| class="wikitable" border="1"
|+ caption
|-
|PHH/g.mol-1.pm.fs-1|| Contour Plot
|-
|0 || [[File:0_015083.png |400 px|centre]]
|-
|2 || [[File:2_0508.png |400 px|centre]]
|-
|4 || [[File:4_01508.png ‎|400 px|centre]]
|-
|6.1|| [[File:6_01508.png|400 px|centre]]
|-
| -2|| [[File:-2_01508.png|400 px|centre]]
|-
| -4|| [[File:-4.1_01508.png‎|400 px|centre]]
|-
| -6.1|| [[File:Fit1_01508.png|400 px|centre]]
|-
|}
Although the amount of energy that is put into H-H vibration is much more than the activation energy of the reaction, the reaction does not always occur. The large amount of energy is demonstrated by the high frequency of those wavy lines. Recrossing the transition states multiple times can lead to no reaction or product formation depending on how the tragectory collides with the potential well.

[[File:Reactiondynamic_last01588.png|400px|centre|thumb|contour plot for rFH=182 pm, fHH=74 pm, PFH=-1.6g.mol-1.pm.fs-1,PHH=0.2g.mol-1.pm.fs-1]]
The system now has much less vibrational energy into the reactants than before. The reaction is still successful and the trajectory recrosses the transition states fewer times than before.This can be explained by the increased momentum of FH so that F can approach the closest H with more vibrational energy.

===H+HF system===

MRD:01508310

2020-05-22T16:32:10Z

Hh2218: /* Varying the momentum of HH in the F+H2 system. */

==H-H-H system==
===Dynamics from the transition state region===
The transition state is the point on the potential energy surface that has ∂V(ri)/∂ri=0, where ri is the distance between two atoms.The transition state is a local maximum and its second derivative ∂2V(ri)/∂ri2 is < 0, whereas a local minimum will have a positive second derivative instead.
[[File:Hhh_surfaceplot_01508.png|400px|thumb|centre|a potential energy surface plot of H and H2 with respect to interatomic distances.]]

===Trajectories from r1=r2: locating the transition state===
At the transition state, r1=r2=90.8 pm by estimation. At this separation, the forces acting along AB and BC are both -0.004 kJ.mol-1.pm-1, which is close to zero and the eigenvalues for the Hessian matrix were -0.028 and +0.167 kJ.mol-1.pm-2, indicating the presence of transition state. The Internuclear Distance vs Time plot suggests the distance between HA, HB and HC is equal, about 90 pm and the distance is constant over time suggests the atoms are static at the transition state.
[[File:Animation101508310.png|400px|centre|thumb|picture showing H and H2 at the transition state.]]
[[File:Optimisation1_01508310.png|400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:Internucleardistance_01508310.png|400px|centre|thumb|Internuclear Distance vs Time plot between the H atoms at the transition state.]]

===Calculating the reaction path===
When rA-B is set to rts+1 and rB-C equals rts,the transition rolls towards BC and HA remains as an atom. MEP and Dynamic reaction paths are different as MEP set the momenta to zero in every step of the reaction path, products are therefore static and hence the reaction path is relatively straight. The dynamic reaction path is more realistic. It takes the momenta of gaseous molecules into account,i.e. they have vibrational energies, that is illustrated by the wavy line along the reaction path.
[[File:Surface_Plot1mep_015083.png|400px|centre|thumb|the minimum energy path (mep) of the H-H-H system]]
[[File:01569348_MEP_AB1_dynamic.png|400px|centre|thumb|the dynamic reaction path of the H-H-H system]]

====MEP and Dynamics calculations comparisons====
'''r1=91.8 pm, r2=90.8 pm, momenta set to 0 g.mol-1.pm.fs-1'''

HB and HC form a H2 molecule whereas HA moves away from the molecule. The distance between B and C decreased to 74 pm, which is the hydrogen molecule bond length. '''reference 2'''In MEP calculation, the momenta are set to zero at each time step.

[[File:MepH2bondlength_01508.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using MEP calculation.]]

[[File:MepH2momenta015083.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using MEP calculation.]]

Using Dynamics calculation, the outcome of the reaction is the same. The transition state rolls towards HB and HC and a hydrogen molecule is formed. One noticeable difference is that the hydrogen molecule now has some vibational energy as indicated by the wavy line along the B-C distance in the Internuclear Distance vs Time plot.As for the Momenta vs Time plot, the system is linear, therefore the angle theta is zero. HA and HB are moving away from each other at '''an increasing velocity until the momentum reaches 5 g.mol-1.pm.fs-1.The oscillation along the B-C bond corresponds to the vibration of the bond. '''why does the beginning have negative momenta?'''
[[File:DynamicsH2_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation.]]
[[File:DynamicsH2monenta_01508.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using Dynamics calculation.]]

'''r1=90.8 pm, r2=91.8 pm, momenta set to 0 g.mol-1.pm.fs-1'''

Once the length of r1 and r2 switches, the shapes of the graphs are identical but instead of HB and HC forming a molecule, HA and HB now form the hydrogen molecule in the products.
[[File:Mepinter2_01508.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using MEP calculation.]]
[[File:Momentamep2_015.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using MEP calculation.]]
[[File:InterDynamic_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation.]]
[[File:Momentadynamics_015083.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using Dynamics calculation.]]

'''Trajectory starting with the final position and reversed momentum to the reaction path above'''

This trajectory starts at the end of the reaction path above and finishes at where the above reaction started. it is essentially a reverse of what happened in the reaction above.
[[File:Reverse_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation (r1=70.0 pm,r2=353 pm,p1=-3.21 g.mol-1.pm.fs-1, p2=-5.07 g.mol-1.pm.fs-1) .]]

===Recative and unreactive trajectories===
{| class="wikitable" border="1"
! p1/g.mol-1.pm.fs-1 !! p2/g.mol-1.pm.fs-1!! Etot!! Recative?!! Description of the dynamics!! Illustration of the trajectory
|-
| -2.56 || -5.1||-414 || Yes||The translational energy of the reactants can surmount the potential energy barrier and form the products. The ramaining energy is converted into vibrational energy of the products. || [[File:Table1_01508310.png|350px ]]
|-
| -3.1 || -4.1||-420 || No||The reactant H2 has vibrational energy and its rAB motion is rapid. Before it could cross the energy barrier, the molecule slams into the repulsive inner wall of the potential surface and bounces back into the reactant channel. || [[File:Table2_0150.png|350px]]
|-
| -3.1 || -5.1||-414|| Yes||The reactants have both the translational and vibrational energies. The energy is used to surmount the potential energy barrier and converted into the vibrational energy of the products. || [[File:Table3_01508.png|350px]]
|-
| -5.1 || -10.1||-357 || No||The reactants have sufficient energy to cross the transition state and the products did form for a certain amount of time. However, before the the system can exit the product channel, it recrosses the transition state and form the reactants again, hence no reaction occurs. ||[[File:Table4_01508.png|350px]]
|-
| -5.1 || -10.6||-394 || Yes||The system has sufficient energy to cross the transition state but it recrosses the transition state shortly after the reaction path hits the potential energy surface. However, the system is able to cross the transition state for the third time and finally exits the product channel and forms the products. || [[File:-10.6_01508.png|350px]]
|-
|}
In order to form products, a system must have sufficient energy to cross the transition state. Only molecules with the correct phase '''reference 2''' can exit the product channel and form stable products. Recrossing the transition state can lead to either product formation or no reaction. It is possible to cross the transition state multiple times.

===Transition State Theory===

Transition State Theory is classical, it doesn't take quantum tunnelling into account.Quantum tunnelling is probable for this reaction as it involves the transfer of a hydrogen atom, particularly at lower temperatures.'''Reference 3'''At low temperatures, the H atom can tunnel through the potential energy barrier than to pass over the barrier, hence the activation energy is lowered and the reaction rate increases. However, recrossing the energy barrier is possible as seen with the simulations, this can have a negative effect on the reaction rate. At high temperatures, the system is thermally activated and the behavious is approximately classical.'''reference4''' Therefore the experimental reaction rates are expected to be greater than that predicted by the Transition State Theory.

==F-H-H system==
===PES inspection===
'''F+H2 (F1-H1-H2)'''

F+H2 is exothermic as the reactants are higher in energy than the products therefore during the reaction, energy is released to the surroundings. H-F bond is stronger than H-H bond as the products are lower in energy and therefore more stable.The transition state is located approximately at rF1-H1=181.10 pm and rH1-H2=74.49 pm. This is verified by the forces (close to zero) and eigenvalues for hessian matrix (they are of opposite signs). The activation energy is estimated by tilting the transition state towards the reactants and is shown to be 424 kJ.mol-1.
[[File:Fh2_015083.png |400px|centre|thumb|Surface plot for F1-H1-H2 system using Dynamic Calculation, the transition state is identified as the black dot.]]
[[File:OptimisationFhh1_01508.png|400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:F1H1H2_EA_0150.png|400px|centre|thumb|Counter plot for estimating the activation energy.]]
[[File:EA1_01508.png|400px|centre|thumb|parameters for the activation energy.]]
'''H+HF (H1-H2-F1)'''
This reaction is endothermis as the reactants are lower in energy than the products therefore energy is taken in from the surroundings to form the products. H-F bond is still stronger than H-H as the reactans are lower in energy and more stable. The transition state is located at approximately rH1-H2=280 pm and rH2-F1=92 pm. It is located with the same reasons stated above.With the same method, the activation energy is estimated to be 434 kJ.mol-1. The two activation energies should be identical as these two reactions are essentially the reverse of one another.

[[File:H+HF_01508310.png|400px|centre|thumb|Surface plot for H1-H2-F1 system using Dynamic Calculationthe, the transition state is identified as the black dot.]]
[[File:HHF_015083.png |400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:EA2_01508.png|400px|centre|thumb|Counter plot for estimating the activation energy.]]
[[File:EA2_PARAMETERS.png|400px|centre|thumb|parameters for the activation energy.]]

===Reaction dynamics===
'''F+H2 system'''

Initially, the reactants have kinetic energy in the form of vibrational and translational energies, and as it crosses the potential energy barrier, the kinetic energy is converted into potential energy. Once the system is exiting the product channel, the potential energy is converted into the vibrational energy of the product.One good experimental technique to prob the electronic structure of the reacting species will be IR spectroscopy.In the anharmonic oscillator model, exciting molecules in the relaxed state promotes excitation from the ground state to the first energy level mainly. This will give rise to a single peak in the IR spectrum. Howver, when exciting a sample of excited molecules, many transitions are possible. For example, from 0-->1, the fundamental or 1-->2, the first overtone. They will show up in the spectrum as 2 peaks, with the overtone being at a lower wavenumber as the energy gap decreases up the potential well. The intensity of the overtone decreases over time as the electrons can fall back to lower energy levels and energy is emitted as radiation. As this system is linear, rotational is not important electronic energy is not considered here.Photoelectron spectroscopy is also a viable method. '''reference 5'''

[[File:Reactiondynamicsfh2_0150.png||400px|centre|thumb|contour plot for F+H2.]]
[[File:Reactiondynamicsparameter——015.png |400px|centre|thumb|parameters for the reactive trajectory.]]
====Varying the momentum of HH in the F+H2 system.====
Conditions:rFH=182 pm, fHH=74 pm, PFH=-1.0g.mol-1.pm.fs-1
{| class="wikitable" border="1"
|+ caption
|-
|PHH/g.mol-1.pm.fs-1|| Contour Plot
|-
|0 || [[File:0_015083.png |400 px|centre]]
|-
|2 || [[File:2_0508.png |400 px|centre]]
|-
|4 || [[File:4_01508.png ‎|400 px|centre]]
|-
|6.1|| [[File:6_01508.png|400 px|centre]]
|-
| -2|| [[File:-2_01508.png|400 px|centre]]
|-
| -4|| [[File:-4.1_01508.png‎|400 px|centre]]
|-
| -6.1|| [[File:Fit1_01508.png|400 px|centre]]
|-
|}
Although the amount of energy that is put into H-H vibration is much more than the activation energy of the reaction, the reaction does not always occur. The large amount of energy is demonstrated by the high frequency of those wavy lines. Recrossing the transition states multiple times can lead to no reaction or product formation depending on how the tragectory collides with the potential well.

[[File:Reactiondynamic_last01588.png|400px|centre|thumb|contour plot for rFH=182 pm, fHH=74 pm, PFH=-1.6g.mol-1.pm.fs-1,PHH=0.2g.mol-1.pm.fs-1]]
The system now has much less vibrational energy into the reactants than before. The reaction is still successful and the trajectory recrosses the transition states fewer times than before.This can be explained by the increased momentum of FH so that F can approach the closest H with more vibrational energy.

===H+HF system===

MRD:01508310

2020-05-22T16:30:37Z

Hh2218: /* Varying the momentum of HH in the F+H2 system. */

==H-H-H system==
===Dynamics from the transition state region===
The transition state is the point on the potential energy surface that has ∂V(ri)/∂ri=0, where ri is the distance between two atoms.The transition state is a local maximum and its second derivative ∂2V(ri)/∂ri2 is < 0, whereas a local minimum will have a positive second derivative instead.
[[File:Hhh_surfaceplot_01508.png|400px|thumb|centre|a potential energy surface plot of H and H2 with respect to interatomic distances.]]

===Trajectories from r1=r2: locating the transition state===
At the transition state, r1=r2=90.8 pm by estimation. At this separation, the forces acting along AB and BC are both -0.004 kJ.mol-1.pm-1, which is close to zero and the eigenvalues for the Hessian matrix were -0.028 and +0.167 kJ.mol-1.pm-2, indicating the presence of transition state. The Internuclear Distance vs Time plot suggests the distance between HA, HB and HC is equal, about 90 pm and the distance is constant over time suggests the atoms are static at the transition state.
[[File:Animation101508310.png|400px|centre|thumb|picture showing H and H2 at the transition state.]]
[[File:Optimisation1_01508310.png|400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:Internucleardistance_01508310.png|400px|centre|thumb|Internuclear Distance vs Time plot between the H atoms at the transition state.]]

===Calculating the reaction path===
When rA-B is set to rts+1 and rB-C equals rts,the transition rolls towards BC and HA remains as an atom. MEP and Dynamic reaction paths are different as MEP set the momenta to zero in every step of the reaction path, products are therefore static and hence the reaction path is relatively straight. The dynamic reaction path is more realistic. It takes the momenta of gaseous molecules into account,i.e. they have vibrational energies, that is illustrated by the wavy line along the reaction path.
[[File:Surface_Plot1mep_015083.png|400px|centre|thumb|the minimum energy path (mep) of the H-H-H system]]
[[File:01569348_MEP_AB1_dynamic.png|400px|centre|thumb|the dynamic reaction path of the H-H-H system]]

====MEP and Dynamics calculations comparisons====
'''r1=91.8 pm, r2=90.8 pm, momenta set to 0 g.mol-1.pm.fs-1'''

HB and HC form a H2 molecule whereas HA moves away from the molecule. The distance between B and C decreased to 74 pm, which is the hydrogen molecule bond length. '''reference 2'''In MEP calculation, the momenta are set to zero at each time step.

[[File:MepH2bondlength_01508.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using MEP calculation.]]

[[File:MepH2momenta015083.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using MEP calculation.]]

Using Dynamics calculation, the outcome of the reaction is the same. The transition state rolls towards HB and HC and a hydrogen molecule is formed. One noticeable difference is that the hydrogen molecule now has some vibational energy as indicated by the wavy line along the B-C distance in the Internuclear Distance vs Time plot.As for the Momenta vs Time plot, the system is linear, therefore the angle theta is zero. HA and HB are moving away from each other at '''an increasing velocity until the momentum reaches 5 g.mol-1.pm.fs-1.The oscillation along the B-C bond corresponds to the vibration of the bond. '''why does the beginning have negative momenta?'''
[[File:DynamicsH2_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation.]]
[[File:DynamicsH2monenta_01508.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using Dynamics calculation.]]

'''r1=90.8 pm, r2=91.8 pm, momenta set to 0 g.mol-1.pm.fs-1'''

Once the length of r1 and r2 switches, the shapes of the graphs are identical but instead of HB and HC forming a molecule, HA and HB now form the hydrogen molecule in the products.
[[File:Mepinter2_01508.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using MEP calculation.]]
[[File:Momentamep2_015.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using MEP calculation.]]
[[File:InterDynamic_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation.]]
[[File:Momentadynamics_015083.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using Dynamics calculation.]]

'''Trajectory starting with the final position and reversed momentum to the reaction path above'''

This trajectory starts at the end of the reaction path above and finishes at where the above reaction started. it is essentially a reverse of what happened in the reaction above.
[[File:Reverse_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation (r1=70.0 pm,r2=353 pm,p1=-3.21 g.mol-1.pm.fs-1, p2=-5.07 g.mol-1.pm.fs-1) .]]

===Recative and unreactive trajectories===
{| class="wikitable" border="1"
! p1/g.mol-1.pm.fs-1 !! p2/g.mol-1.pm.fs-1!! Etot!! Recative?!! Description of the dynamics!! Illustration of the trajectory
|-
| -2.56 || -5.1||-414 || Yes||The translational energy of the reactants can surmount the potential energy barrier and form the products. The ramaining energy is converted into vibrational energy of the products. || [[File:Table1_01508310.png|350px ]]
|-
| -3.1 || -4.1||-420 || No||The reactant H2 has vibrational energy and its rAB motion is rapid. Before it could cross the energy barrier, the molecule slams into the repulsive inner wall of the potential surface and bounces back into the reactant channel. || [[File:Table2_0150.png|350px]]
|-
| -3.1 || -5.1||-414|| Yes||The reactants have both the translational and vibrational energies. The energy is used to surmount the potential energy barrier and converted into the vibrational energy of the products. || [[File:Table3_01508.png|350px]]
|-
| -5.1 || -10.1||-357 || No||The reactants have sufficient energy to cross the transition state and the products did form for a certain amount of time. However, before the the system can exit the product channel, it recrosses the transition state and form the reactants again, hence no reaction occurs. ||[[File:Table4_01508.png|350px]]
|-
| -5.1 || -10.6||-394 || Yes||The system has sufficient energy to cross the transition state but it recrosses the transition state shortly after the reaction path hits the potential energy surface. However, the system is able to cross the transition state for the third time and finally exits the product channel and forms the products. || [[File:-10.6_01508.png|350px]]
|-
|}
In order to form products, a system must have sufficient energy to cross the transition state. Only molecules with the correct phase '''reference 2''' can exit the product channel and form stable products. Recrossing the transition state can lead to either product formation or no reaction. It is possible to cross the transition state multiple times.

===Transition State Theory===

Transition State Theory is classical, it doesn't take quantum tunnelling into account.Quantum tunnelling is probable for this reaction as it involves the transfer of a hydrogen atom, particularly at lower temperatures.'''Reference 3'''At low temperatures, the H atom can tunnel through the potential energy barrier than to pass over the barrier, hence the activation energy is lowered and the reaction rate increases. However, recrossing the energy barrier is possible as seen with the simulations, this can have a negative effect on the reaction rate. At high temperatures, the system is thermally activated and the behavious is approximately classical.'''reference4''' Therefore the experimental reaction rates are expected to be greater than that predicted by the Transition State Theory.

==F-H-H system==
===PES inspection===
'''F+H2 (F1-H1-H2)'''

F+H2 is exothermic as the reactants are higher in energy than the products therefore during the reaction, energy is released to the surroundings. H-F bond is stronger than H-H bond as the products are lower in energy and therefore more stable.The transition state is located approximately at rF1-H1=181.10 pm and rH1-H2=74.49 pm. This is verified by the forces (close to zero) and eigenvalues for hessian matrix (they are of opposite signs). The activation energy is estimated by tilting the transition state towards the reactants and is shown to be 424 kJ.mol-1.
[[File:Fh2_015083.png |400px|centre|thumb|Surface plot for F1-H1-H2 system using Dynamic Calculation, the transition state is identified as the black dot.]]
[[File:OptimisationFhh1_01508.png|400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:F1H1H2_EA_0150.png|400px|centre|thumb|Counter plot for estimating the activation energy.]]
[[File:EA1_01508.png|400px|centre|thumb|parameters for the activation energy.]]
'''H+HF (H1-H2-F1)'''
This reaction is endothermis as the reactants are lower in energy than the products therefore energy is taken in from the surroundings to form the products. H-F bond is still stronger than H-H as the reactans are lower in energy and more stable. The transition state is located at approximately rH1-H2=280 pm and rH2-F1=92 pm. It is located with the same reasons stated above.With the same method, the activation energy is estimated to be 434 kJ.mol-1. The two activation energies should be identical as these two reactions are essentially the reverse of one another.

[[File:H+HF_01508310.png|400px|centre|thumb|Surface plot for H1-H2-F1 system using Dynamic Calculationthe, the transition state is identified as the black dot.]]
[[File:HHF_015083.png |400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:EA2_01508.png|400px|centre|thumb|Counter plot for estimating the activation energy.]]
[[File:EA2_PARAMETERS.png|400px|centre|thumb|parameters for the activation energy.]]

===Reaction dynamics===
'''F+H2 system'''

Initially, the reactants have kinetic energy in the form of vibrational and translational energies, and as it crosses the potential energy barrier, the kinetic energy is converted into potential energy. Once the system is exiting the product channel, the potential energy is converted into the vibrational energy of the product.One good experimental technique to prob the electronic structure of the reacting species will be IR spectroscopy.In the anharmonic oscillator model, exciting molecules in the relaxed state promotes excitation from the ground state to the first energy level mainly. This will give rise to a single peak in the IR spectrum. Howver, when exciting a sample of excited molecules, many transitions are possible. For example, from 0-->1, the fundamental or 1-->2, the first overtone. They will show up in the spectrum as 2 peaks, with the overtone being at a lower wavenumber as the energy gap decreases up the potential well. The intensity of the overtone decreases over time as the electrons can fall back to lower energy levels and energy is emitted as radiation. As this system is linear, rotational is not important electronic energy is not considered here.Photoelectron spectroscopy is also a viable method. '''reference 5'''

[[File:Reactiondynamicsfh2_0150.png||400px|centre|thumb|contour plot for F+H2.]]
[[File:Reactiondynamicsparameter——015.png |400px|centre|thumb|parameters for the reactive trajectory.]]
====Varying the momentum of HH in the F+H2 system.====
Conditions:rFH=182 pm, fHH=74 pm, PFH=-1.0g.mol-1.pm.fs-1
{| class="wikitable" border="1"
|+ caption
|-
|PHH/g.mol-1.pm.fs-1|| Contour Plot
|-
|0 || [[File:0_015083.png |400 px|centre]]
|-
|2 || [[File:2_0508.png |400 px|centre]]
|-
|4 || [[File:4_01508.png ‎|400 px|centre]]
|-
|6.1|| [[File:6_01508.png|400 px|centre]]
|-
| -2|| [[File:-2_01508.png|400 px|centre]]
|-
| -4|| [[File:-4.1_01508.png‎|400 px|centre]]
|-
| -6.1|| [[File:Fit1_01508.png|400 px|centre]]
|-
|}
Although the amount of energy that is put into H-H vibration is much more than the activation energy of the reaction, the reaction does not always occur. The large amount of energy is demonstrated by the high frequency of those wavy lines. Recrossing the transition states multiple times can lead to no reaction or product formation depending on how the tragectory collides with the potential well.

[[File:Reactiondynamic_last01588.png|400px|centre|thumb|contour plot for rFH=182 pm, fHH=74 pm, PFH=-1.6g.mol-1.pm.fs-1,PHH=0.2g.mol-1.pm.fs-1]]
The system now has much less vibrational energy into the reactants than before. The reaction is still successful and the trajectory recrosses the transition states fewer times than before.This can be explained by the increased momentum of FH so that F can approach the closest H with more vibrational energy.

MRD:01508310

2020-05-22T16:29:22Z

Hh2218: /* Varying the momentum of HH in the F+H2 system. */

==H-H-H system==
===Dynamics from the transition state region===
The transition state is the point on the potential energy surface that has ∂V(ri)/∂ri=0, where ri is the distance between two atoms.The transition state is a local maximum and its second derivative ∂2V(ri)/∂ri2 is < 0, whereas a local minimum will have a positive second derivative instead.
[[File:Hhh_surfaceplot_01508.png|400px|thumb|centre|a potential energy surface plot of H and H2 with respect to interatomic distances.]]

===Trajectories from r1=r2: locating the transition state===
At the transition state, r1=r2=90.8 pm by estimation. At this separation, the forces acting along AB and BC are both -0.004 kJ.mol-1.pm-1, which is close to zero and the eigenvalues for the Hessian matrix were -0.028 and +0.167 kJ.mol-1.pm-2, indicating the presence of transition state. The Internuclear Distance vs Time plot suggests the distance between HA, HB and HC is equal, about 90 pm and the distance is constant over time suggests the atoms are static at the transition state.
[[File:Animation101508310.png|400px|centre|thumb|picture showing H and H2 at the transition state.]]
[[File:Optimisation1_01508310.png|400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:Internucleardistance_01508310.png|400px|centre|thumb|Internuclear Distance vs Time plot between the H atoms at the transition state.]]

===Calculating the reaction path===
When rA-B is set to rts+1 and rB-C equals rts,the transition rolls towards BC and HA remains as an atom. MEP and Dynamic reaction paths are different as MEP set the momenta to zero in every step of the reaction path, products are therefore static and hence the reaction path is relatively straight. The dynamic reaction path is more realistic. It takes the momenta of gaseous molecules into account,i.e. they have vibrational energies, that is illustrated by the wavy line along the reaction path.
[[File:Surface_Plot1mep_015083.png|400px|centre|thumb|the minimum energy path (mep) of the H-H-H system]]
[[File:01569348_MEP_AB1_dynamic.png|400px|centre|thumb|the dynamic reaction path of the H-H-H system]]

====MEP and Dynamics calculations comparisons====
'''r1=91.8 pm, r2=90.8 pm, momenta set to 0 g.mol-1.pm.fs-1'''

HB and HC form a H2 molecule whereas HA moves away from the molecule. The distance between B and C decreased to 74 pm, which is the hydrogen molecule bond length. '''reference 2'''In MEP calculation, the momenta are set to zero at each time step.

[[File:MepH2bondlength_01508.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using MEP calculation.]]

[[File:MepH2momenta015083.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using MEP calculation.]]

Using Dynamics calculation, the outcome of the reaction is the same. The transition state rolls towards HB and HC and a hydrogen molecule is formed. One noticeable difference is that the hydrogen molecule now has some vibational energy as indicated by the wavy line along the B-C distance in the Internuclear Distance vs Time plot.As for the Momenta vs Time plot, the system is linear, therefore the angle theta is zero. HA and HB are moving away from each other at '''an increasing velocity until the momentum reaches 5 g.mol-1.pm.fs-1.The oscillation along the B-C bond corresponds to the vibration of the bond. '''why does the beginning have negative momenta?'''
[[File:DynamicsH2_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation.]]
[[File:DynamicsH2monenta_01508.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using Dynamics calculation.]]

'''r1=90.8 pm, r2=91.8 pm, momenta set to 0 g.mol-1.pm.fs-1'''

Once the length of r1 and r2 switches, the shapes of the graphs are identical but instead of HB and HC forming a molecule, HA and HB now form the hydrogen molecule in the products.
[[File:Mepinter2_01508.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using MEP calculation.]]
[[File:Momentamep2_015.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using MEP calculation.]]
[[File:InterDynamic_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation.]]
[[File:Momentadynamics_015083.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using Dynamics calculation.]]

'''Trajectory starting with the final position and reversed momentum to the reaction path above'''

This trajectory starts at the end of the reaction path above and finishes at where the above reaction started. it is essentially a reverse of what happened in the reaction above.
[[File:Reverse_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation (r1=70.0 pm,r2=353 pm,p1=-3.21 g.mol-1.pm.fs-1, p2=-5.07 g.mol-1.pm.fs-1) .]]

===Recative and unreactive trajectories===
{| class="wikitable" border="1"
! p1/g.mol-1.pm.fs-1 !! p2/g.mol-1.pm.fs-1!! Etot!! Recative?!! Description of the dynamics!! Illustration of the trajectory
|-
| -2.56 || -5.1||-414 || Yes||The translational energy of the reactants can surmount the potential energy barrier and form the products. The ramaining energy is converted into vibrational energy of the products. || [[File:Table1_01508310.png|350px ]]
|-
| -3.1 || -4.1||-420 || No||The reactant H2 has vibrational energy and its rAB motion is rapid. Before it could cross the energy barrier, the molecule slams into the repulsive inner wall of the potential surface and bounces back into the reactant channel. || [[File:Table2_0150.png|350px]]
|-
| -3.1 || -5.1||-414|| Yes||The reactants have both the translational and vibrational energies. The energy is used to surmount the potential energy barrier and converted into the vibrational energy of the products. || [[File:Table3_01508.png|350px]]
|-
| -5.1 || -10.1||-357 || No||The reactants have sufficient energy to cross the transition state and the products did form for a certain amount of time. However, before the the system can exit the product channel, it recrosses the transition state and form the reactants again, hence no reaction occurs. ||[[File:Table4_01508.png|350px]]
|-
| -5.1 || -10.6||-394 || Yes||The system has sufficient energy to cross the transition state but it recrosses the transition state shortly after the reaction path hits the potential energy surface. However, the system is able to cross the transition state for the third time and finally exits the product channel and forms the products. || [[File:-10.6_01508.png|350px]]
|-
|}
In order to form products, a system must have sufficient energy to cross the transition state. Only molecules with the correct phase '''reference 2''' can exit the product channel and form stable products. Recrossing the transition state can lead to either product formation or no reaction. It is possible to cross the transition state multiple times.

===Transition State Theory===

Transition State Theory is classical, it doesn't take quantum tunnelling into account.Quantum tunnelling is probable for this reaction as it involves the transfer of a hydrogen atom, particularly at lower temperatures.'''Reference 3'''At low temperatures, the H atom can tunnel through the potential energy barrier than to pass over the barrier, hence the activation energy is lowered and the reaction rate increases. However, recrossing the energy barrier is possible as seen with the simulations, this can have a negative effect on the reaction rate. At high temperatures, the system is thermally activated and the behavious is approximately classical.'''reference4''' Therefore the experimental reaction rates are expected to be greater than that predicted by the Transition State Theory.

==F-H-H system==
===PES inspection===
'''F+H2 (F1-H1-H2)'''

F+H2 is exothermic as the reactants are higher in energy than the products therefore during the reaction, energy is released to the surroundings. H-F bond is stronger than H-H bond as the products are lower in energy and therefore more stable.The transition state is located approximately at rF1-H1=181.10 pm and rH1-H2=74.49 pm. This is verified by the forces (close to zero) and eigenvalues for hessian matrix (they are of opposite signs). The activation energy is estimated by tilting the transition state towards the reactants and is shown to be 424 kJ.mol-1.
[[File:Fh2_015083.png |400px|centre|thumb|Surface plot for F1-H1-H2 system using Dynamic Calculation, the transition state is identified as the black dot.]]
[[File:OptimisationFhh1_01508.png|400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:F1H1H2_EA_0150.png|400px|centre|thumb|Counter plot for estimating the activation energy.]]
[[File:EA1_01508.png|400px|centre|thumb|parameters for the activation energy.]]
'''H+HF (H1-H2-F1)'''
This reaction is endothermis as the reactants are lower in energy than the products therefore energy is taken in from the surroundings to form the products. H-F bond is still stronger than H-H as the reactans are lower in energy and more stable. The transition state is located at approximately rH1-H2=280 pm and rH2-F1=92 pm. It is located with the same reasons stated above.With the same method, the activation energy is estimated to be 434 kJ.mol-1. The two activation energies should be identical as these two reactions are essentially the reverse of one another.

[[File:H+HF_01508310.png|400px|centre|thumb|Surface plot for H1-H2-F1 system using Dynamic Calculationthe, the transition state is identified as the black dot.]]
[[File:HHF_015083.png |400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:EA2_01508.png|400px|centre|thumb|Counter plot for estimating the activation energy.]]
[[File:EA2_PARAMETERS.png|400px|centre|thumb|parameters for the activation energy.]]

===Reaction dynamics===
'''F+H2 system'''

Initially, the reactants have kinetic energy in the form of vibrational and translational energies, and as it crosses the potential energy barrier, the kinetic energy is converted into potential energy. Once the system is exiting the product channel, the potential energy is converted into the vibrational energy of the product.One good experimental technique to prob the electronic structure of the reacting species will be IR spectroscopy.In the anharmonic oscillator model, exciting molecules in the relaxed state promotes excitation from the ground state to the first energy level mainly. This will give rise to a single peak in the IR spectrum. Howver, when exciting a sample of excited molecules, many transitions are possible. For example, from 0-->1, the fundamental or 1-->2, the first overtone. They will show up in the spectrum as 2 peaks, with the overtone being at a lower wavenumber as the energy gap decreases up the potential well. The intensity of the overtone decreases over time as the electrons can fall back to lower energy levels and energy is emitted as radiation. As this system is linear, rotational is not important electronic energy is not considered here.Photoelectron spectroscopy is also a viable method. '''reference 5'''

[[File:Reactiondynamicsfh2_0150.png||400px|centre|thumb|contour plot for F+H2.]]
[[File:Reactiondynamicsparameter——015.png |400px|centre|thumb|parameters for the reactive trajectory.]]
===Varying the momentum of HH in the F+H2 system.===
Conditions:rFH=182 pm, fHH=74 pm, PFH=-1.0g.mol-1.pm.fs-1
{| class="wikitable" border="1"
|+ caption
|-
|PHH/g.mol-1.pm.fs-1|| Contour Plot
|-
|0 || [[File:0_015083.png |400 px|centre]]
|-
|2 || [[File:2_0508.png |400 px|centre]]
|-
|4 || [[File:4_01508.png ‎|400 px|centre]]
|-
|6.1|| [[File:6_01508.png|400 px|centre]]
|-
| -2|| [[File:-2_01508.png|400 px|centre]]
|-
| -4|| [[File:-4.1_01508.png‎|400 px|centre]]
|-
| -6.1|| [[File:Fit1_01508.png|400 px|centre]]
|-
|}
Although the amount of energy that is put into H-H vibration is much more than the activation energy of the reaction, the reaction does not always occur. The large amount of energy is demonstrated by the high frequency of those wavy lines. Recrossing the transition states multiple times can lead to no reaction or product formation depending on how the tragectory collides with the potential well.

[[File:Reactiondynamic_last01588.png|400px|centre|thumb|contour plot for rFH=182 pm, fHH=74 pm, PFH=-1.6g.mol-1.pm.fs-1,PHH=0.2g.mol-1.pm.fs-1]]
The system now has much less vibrational energy into the reactants than before. The reaction is still successful and the trajectory recrosses the transition states fewer times than before.This can be explained by the increased momentum of FH so that F can approach the closest H with more vibrational energy.

File:Reactiondynamic last01588.png

2020-05-22T16:21:57Z

Hh2218:

MRD:01508310

2020-05-22T16:18:50Z

Hh2218: /* Varying the momentum of HH in the F+H2 system. */

==H-H-H system==
===Dynamics from the transition state region===
The transition state is the point on the potential energy surface that has ∂V(ri)/∂ri=0, where ri is the distance between two atoms.The transition state is a local maximum and its second derivative ∂2V(ri)/∂ri2 is < 0, whereas a local minimum will have a positive second derivative instead.
[[File:Hhh_surfaceplot_01508.png|400px|thumb|centre|a potential energy surface plot of H and H2 with respect to interatomic distances.]]

===Trajectories from r1=r2: locating the transition state===
At the transition state, r1=r2=90.8 pm by estimation. At this separation, the forces acting along AB and BC are both -0.004 kJ.mol-1.pm-1, which is close to zero and the eigenvalues for the Hessian matrix were -0.028 and +0.167 kJ.mol-1.pm-2, indicating the presence of transition state. The Internuclear Distance vs Time plot suggests the distance between HA, HB and HC is equal, about 90 pm and the distance is constant over time suggests the atoms are static at the transition state.
[[File:Animation101508310.png|400px|centre|thumb|picture showing H and H2 at the transition state.]]
[[File:Optimisation1_01508310.png|400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:Internucleardistance_01508310.png|400px|centre|thumb|Internuclear Distance vs Time plot between the H atoms at the transition state.]]

===Calculating the reaction path===
When rA-B is set to rts+1 and rB-C equals rts,the transition rolls towards BC and HA remains as an atom. MEP and Dynamic reaction paths are different as MEP set the momenta to zero in every step of the reaction path, products are therefore static and hence the reaction path is relatively straight. The dynamic reaction path is more realistic. It takes the momenta of gaseous molecules into account,i.e. they have vibrational energies, that is illustrated by the wavy line along the reaction path.
[[File:Surface_Plot1mep_015083.png|400px|centre|thumb|the minimum energy path (mep) of the H-H-H system]]
[[File:01569348_MEP_AB1_dynamic.png|400px|centre|thumb|the dynamic reaction path of the H-H-H system]]

====MEP and Dynamics calculations comparisons====
'''r1=91.8 pm, r2=90.8 pm, momenta set to 0 g.mol-1.pm.fs-1'''

HB and HC form a H2 molecule whereas HA moves away from the molecule. The distance between B and C decreased to 74 pm, which is the hydrogen molecule bond length. '''reference 2'''In MEP calculation, the momenta are set to zero at each time step.

[[File:MepH2bondlength_01508.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using MEP calculation.]]

[[File:MepH2momenta015083.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using MEP calculation.]]

Using Dynamics calculation, the outcome of the reaction is the same. The transition state rolls towards HB and HC and a hydrogen molecule is formed. One noticeable difference is that the hydrogen molecule now has some vibational energy as indicated by the wavy line along the B-C distance in the Internuclear Distance vs Time plot.As for the Momenta vs Time plot, the system is linear, therefore the angle theta is zero. HA and HB are moving away from each other at '''an increasing velocity until the momentum reaches 5 g.mol-1.pm.fs-1.The oscillation along the B-C bond corresponds to the vibration of the bond. '''why does the beginning have negative momenta?'''
[[File:DynamicsH2_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation.]]
[[File:DynamicsH2monenta_01508.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using Dynamics calculation.]]

'''r1=90.8 pm, r2=91.8 pm, momenta set to 0 g.mol-1.pm.fs-1'''

Once the length of r1 and r2 switches, the shapes of the graphs are identical but instead of HB and HC forming a molecule, HA and HB now form the hydrogen molecule in the products.
[[File:Mepinter2_01508.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using MEP calculation.]]
[[File:Momentamep2_015.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using MEP calculation.]]
[[File:InterDynamic_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation.]]
[[File:Momentadynamics_015083.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using Dynamics calculation.]]

'''Trajectory starting with the final position and reversed momentum to the reaction path above'''

This trajectory starts at the end of the reaction path above and finishes at where the above reaction started. it is essentially a reverse of what happened in the reaction above.
[[File:Reverse_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation (r1=70.0 pm,r2=353 pm,p1=-3.21 g.mol-1.pm.fs-1, p2=-5.07 g.mol-1.pm.fs-1) .]]

===Recative and unreactive trajectories===
{| class="wikitable" border="1"
! p1/g.mol-1.pm.fs-1 !! p2/g.mol-1.pm.fs-1!! Etot!! Recative?!! Description of the dynamics!! Illustration of the trajectory
|-
| -2.56 || -5.1||-414 || Yes||The translational energy of the reactants can surmount the potential energy barrier and form the products. The ramaining energy is converted into vibrational energy of the products. || [[File:Table1_01508310.png|350px ]]
|-
| -3.1 || -4.1||-420 || No||The reactant H2 has vibrational energy and its rAB motion is rapid. Before it could cross the energy barrier, the molecule slams into the repulsive inner wall of the potential surface and bounces back into the reactant channel. || [[File:Table2_0150.png|350px]]
|-
| -3.1 || -5.1||-414|| Yes||The reactants have both the translational and vibrational energies. The energy is used to surmount the potential energy barrier and converted into the vibrational energy of the products. || [[File:Table3_01508.png|350px]]
|-
| -5.1 || -10.1||-357 || No||The reactants have sufficient energy to cross the transition state and the products did form for a certain amount of time. However, before the the system can exit the product channel, it recrosses the transition state and form the reactants again, hence no reaction occurs. ||[[File:Table4_01508.png|350px]]
|-
| -5.1 || -10.6||-394 || Yes||The system has sufficient energy to cross the transition state but it recrosses the transition state shortly after the reaction path hits the potential energy surface. However, the system is able to cross the transition state for the third time and finally exits the product channel and forms the products. || [[File:-10.6_01508.png|350px]]
|-
|}
In order to form products, a system must have sufficient energy to cross the transition state. Only molecules with the correct phase '''reference 2''' can exit the product channel and form stable products. Recrossing the transition state can lead to either product formation or no reaction. It is possible to cross the transition state multiple times.

===Transition State Theory===

Transition State Theory is classical, it doesn't take quantum tunnelling into account.Quantum tunnelling is probable for this reaction as it involves the transfer of a hydrogen atom, particularly at lower temperatures.'''Reference 3'''At low temperatures, the H atom can tunnel through the potential energy barrier than to pass over the barrier, hence the activation energy is lowered and the reaction rate increases. However, recrossing the energy barrier is possible as seen with the simulations, this can have a negative effect on the reaction rate. At high temperatures, the system is thermally activated and the behavious is approximately classical.'''reference4''' Therefore the experimental reaction rates are expected to be greater than that predicted by the Transition State Theory.

==F-H-H system==
===PES inspection===
'''F+H2 (F1-H1-H2)'''

F+H2 is exothermic as the reactants are higher in energy than the products therefore during the reaction, energy is released to the surroundings. H-F bond is stronger than H-H bond as the products are lower in energy and therefore more stable.The transition state is located approximately at rF1-H1=181.10 pm and rH1-H2=74.49 pm. This is verified by the forces (close to zero) and eigenvalues for hessian matrix (they are of opposite signs). The activation energy is estimated by tilting the transition state towards the reactants and is shown to be 424 kJ.mol-1.
[[File:Fh2_015083.png |400px|centre|thumb|Surface plot for F1-H1-H2 system using Dynamic Calculation, the transition state is identified as the black dot.]]
[[File:OptimisationFhh1_01508.png|400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:F1H1H2_EA_0150.png|400px|centre|thumb|Counter plot for estimating the activation energy.]]
[[File:EA1_01508.png|400px|centre|thumb|parameters for the activation energy.]]
'''H+HF (H1-H2-F1)'''
This reaction is endothermis as the reactants are lower in energy than the products therefore energy is taken in from the surroundings to form the products. H-F bond is still stronger than H-H as the reactans are lower in energy and more stable. The transition state is located at approximately rH1-H2=280 pm and rH2-F1=92 pm. It is located with the same reasons stated above.With the same method, the activation energy is estimated to be 434 kJ.mol-1. The two activation energies should be identical as these two reactions are essentially the reverse of one another.

[[File:H+HF_01508310.png|400px|centre|thumb|Surface plot for H1-H2-F1 system using Dynamic Calculationthe, the transition state is identified as the black dot.]]
[[File:HHF_015083.png |400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:EA2_01508.png|400px|centre|thumb|Counter plot for estimating the activation energy.]]
[[File:EA2_PARAMETERS.png|400px|centre|thumb|parameters for the activation energy.]]

===Reaction dynamics===
'''F+H2 system'''

Initially, the reactants have kinetic energy in the form of vibrational and translational energies, and as it crosses the potential energy barrier, the kinetic energy is converted into potential energy. Once the system is exiting the product channel, the potential energy is converted into the vibrational energy of the product.One good experimental technique to prob the electronic structure of the reacting species will be IR spectroscopy.In the anharmonic oscillator model, exciting molecules in the relaxed state promotes excitation from the ground state to the first energy level mainly. This will give rise to a single peak in the IR spectrum. Howver, when exciting a sample of excited molecules, many transitions are possible. For example, from 0-->1, the fundamental or 1-->2, the first overtone. They will show up in the spectrum as 2 peaks, with the overtone being at a lower wavenumber as the energy gap decreases up the potential well. The intensity of the overtone decreases over time as the electrons can fall back to lower energy levels and energy is emitted as radiation. As this system is linear, rotational is not important electronic energy is not considered here.Photoelectron spectroscopy is also a viable method. '''reference 5'''

[[File:Reactiondynamicsfh2_0150.png||400px|centre|thumb|contour plot for F+H2.]]
[[File:Reactiondynamicsparameter——015.png |400px|centre|thumb|parameters for the reactive trajectory.]]
===Varying the momentum of HH in the F+H2 system.===
Conditions:rFH=182 pm, fHH=74 pm, PFH=-1.0g.mol-1.pm.fs-1
{| class="wikitable" border="1"
|+ caption
|-
|PHH/g.mol-1.pm.fs-1|| Contour Plot
|-
|0 || [[File:0_015083.png |400 px|centre]]
|-
|2 || [[File:2_0508.png |400 px|centre]]
|-
|4 || [[File:4_01508.png ‎|400 px|centre]]
|-
|6.1|| [[File:6_01508.png|400 px|centre]]
|-
| -2|| [[File:-2_01508.png|400 px|centre]]
|-
| -4|| [[File:-4.1_01508.png‎|400 px|centre]]
|-
| -6.1|| [[File:Fit1_01508.png|400 px|centre]]
|-
|}
Although the amount of energy that is put into H-H vibration is much more than the activation energy of the reaction, the reaction does not always occur. The large amount of energy is demonstrated by the high frequency of those wavy lines. Recrossing the transition states multiple times can lead to no reaction or product formation depending on how the tragectory collides with the potential well.

MRD:01508310

2020-05-22T16:14:02Z

Hh2218: /* Varying the momentum of HH in the F+H2 system. */

==H-H-H system==
===Dynamics from the transition state region===
The transition state is the point on the potential energy surface that has ∂V(ri)/∂ri=0, where ri is the distance between two atoms.The transition state is a local maximum and its second derivative ∂2V(ri)/∂ri2 is < 0, whereas a local minimum will have a positive second derivative instead.
[[File:Hhh_surfaceplot_01508.png|400px|thumb|centre|a potential energy surface plot of H and H2 with respect to interatomic distances.]]

===Trajectories from r1=r2: locating the transition state===
At the transition state, r1=r2=90.8 pm by estimation. At this separation, the forces acting along AB and BC are both -0.004 kJ.mol-1.pm-1, which is close to zero and the eigenvalues for the Hessian matrix were -0.028 and +0.167 kJ.mol-1.pm-2, indicating the presence of transition state. The Internuclear Distance vs Time plot suggests the distance between HA, HB and HC is equal, about 90 pm and the distance is constant over time suggests the atoms are static at the transition state.
[[File:Animation101508310.png|400px|centre|thumb|picture showing H and H2 at the transition state.]]
[[File:Optimisation1_01508310.png|400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:Internucleardistance_01508310.png|400px|centre|thumb|Internuclear Distance vs Time plot between the H atoms at the transition state.]]

===Calculating the reaction path===
When rA-B is set to rts+1 and rB-C equals rts,the transition rolls towards BC and HA remains as an atom. MEP and Dynamic reaction paths are different as MEP set the momenta to zero in every step of the reaction path, products are therefore static and hence the reaction path is relatively straight. The dynamic reaction path is more realistic. It takes the momenta of gaseous molecules into account,i.e. they have vibrational energies, that is illustrated by the wavy line along the reaction path.
[[File:Surface_Plot1mep_015083.png|400px|centre|thumb|the minimum energy path (mep) of the H-H-H system]]
[[File:01569348_MEP_AB1_dynamic.png|400px|centre|thumb|the dynamic reaction path of the H-H-H system]]

====MEP and Dynamics calculations comparisons====
'''r1=91.8 pm, r2=90.8 pm, momenta set to 0 g.mol-1.pm.fs-1'''

HB and HC form a H2 molecule whereas HA moves away from the molecule. The distance between B and C decreased to 74 pm, which is the hydrogen molecule bond length. '''reference 2'''In MEP calculation, the momenta are set to zero at each time step.

[[File:MepH2bondlength_01508.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using MEP calculation.]]

[[File:MepH2momenta015083.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using MEP calculation.]]

Using Dynamics calculation, the outcome of the reaction is the same. The transition state rolls towards HB and HC and a hydrogen molecule is formed. One noticeable difference is that the hydrogen molecule now has some vibational energy as indicated by the wavy line along the B-C distance in the Internuclear Distance vs Time plot.As for the Momenta vs Time plot, the system is linear, therefore the angle theta is zero. HA and HB are moving away from each other at '''an increasing velocity until the momentum reaches 5 g.mol-1.pm.fs-1.The oscillation along the B-C bond corresponds to the vibration of the bond. '''why does the beginning have negative momenta?'''
[[File:DynamicsH2_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation.]]
[[File:DynamicsH2monenta_01508.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using Dynamics calculation.]]

'''r1=90.8 pm, r2=91.8 pm, momenta set to 0 g.mol-1.pm.fs-1'''

Once the length of r1 and r2 switches, the shapes of the graphs are identical but instead of HB and HC forming a molecule, HA and HB now form the hydrogen molecule in the products.
[[File:Mepinter2_01508.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using MEP calculation.]]
[[File:Momentamep2_015.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using MEP calculation.]]
[[File:InterDynamic_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation.]]
[[File:Momentadynamics_015083.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using Dynamics calculation.]]

'''Trajectory starting with the final position and reversed momentum to the reaction path above'''

This trajectory starts at the end of the reaction path above and finishes at where the above reaction started. it is essentially a reverse of what happened in the reaction above.
[[File:Reverse_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation (r1=70.0 pm,r2=353 pm,p1=-3.21 g.mol-1.pm.fs-1, p2=-5.07 g.mol-1.pm.fs-1) .]]

===Recative and unreactive trajectories===
{| class="wikitable" border="1"
! p1/g.mol-1.pm.fs-1 !! p2/g.mol-1.pm.fs-1!! Etot!! Recative?!! Description of the dynamics!! Illustration of the trajectory
|-
| -2.56 || -5.1||-414 || Yes||The translational energy of the reactants can surmount the potential energy barrier and form the products. The ramaining energy is converted into vibrational energy of the products. || [[File:Table1_01508310.png|350px ]]
|-
| -3.1 || -4.1||-420 || No||The reactant H2 has vibrational energy and its rAB motion is rapid. Before it could cross the energy barrier, the molecule slams into the repulsive inner wall of the potential surface and bounces back into the reactant channel. || [[File:Table2_0150.png|350px]]
|-
| -3.1 || -5.1||-414|| Yes||The reactants have both the translational and vibrational energies. The energy is used to surmount the potential energy barrier and converted into the vibrational energy of the products. || [[File:Table3_01508.png|350px]]
|-
| -5.1 || -10.1||-357 || No||The reactants have sufficient energy to cross the transition state and the products did form for a certain amount of time. However, before the the system can exit the product channel, it recrosses the transition state and form the reactants again, hence no reaction occurs. ||[[File:Table4_01508.png|350px]]
|-
| -5.1 || -10.6||-394 || Yes||The system has sufficient energy to cross the transition state but it recrosses the transition state shortly after the reaction path hits the potential energy surface. However, the system is able to cross the transition state for the third time and finally exits the product channel and forms the products. || [[File:-10.6_01508.png|350px]]
|-
|}
In order to form products, a system must have sufficient energy to cross the transition state. Only molecules with the correct phase '''reference 2''' can exit the product channel and form stable products. Recrossing the transition state can lead to either product formation or no reaction. It is possible to cross the transition state multiple times.

===Transition State Theory===

Transition State Theory is classical, it doesn't take quantum tunnelling into account.Quantum tunnelling is probable for this reaction as it involves the transfer of a hydrogen atom, particularly at lower temperatures.'''Reference 3'''At low temperatures, the H atom can tunnel through the potential energy barrier than to pass over the barrier, hence the activation energy is lowered and the reaction rate increases. However, recrossing the energy barrier is possible as seen with the simulations, this can have a negative effect on the reaction rate. At high temperatures, the system is thermally activated and the behavious is approximately classical.'''reference4''' Therefore the experimental reaction rates are expected to be greater than that predicted by the Transition State Theory.

==F-H-H system==
===PES inspection===
'''F+H2 (F1-H1-H2)'''

F+H2 is exothermic as the reactants are higher in energy than the products therefore during the reaction, energy is released to the surroundings. H-F bond is stronger than H-H bond as the products are lower in energy and therefore more stable.The transition state is located approximately at rF1-H1=181.10 pm and rH1-H2=74.49 pm. This is verified by the forces (close to zero) and eigenvalues for hessian matrix (they are of opposite signs). The activation energy is estimated by tilting the transition state towards the reactants and is shown to be 424 kJ.mol-1.
[[File:Fh2_015083.png |400px|centre|thumb|Surface plot for F1-H1-H2 system using Dynamic Calculation, the transition state is identified as the black dot.]]
[[File:OptimisationFhh1_01508.png|400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:F1H1H2_EA_0150.png|400px|centre|thumb|Counter plot for estimating the activation energy.]]
[[File:EA1_01508.png|400px|centre|thumb|parameters for the activation energy.]]
'''H+HF (H1-H2-F1)'''
This reaction is endothermis as the reactants are lower in energy than the products therefore energy is taken in from the surroundings to form the products. H-F bond is still stronger than H-H as the reactans are lower in energy and more stable. The transition state is located at approximately rH1-H2=280 pm and rH2-F1=92 pm. It is located with the same reasons stated above.With the same method, the activation energy is estimated to be 434 kJ.mol-1. The two activation energies should be identical as these two reactions are essentially the reverse of one another.

[[File:H+HF_01508310.png|400px|centre|thumb|Surface plot for H1-H2-F1 system using Dynamic Calculationthe, the transition state is identified as the black dot.]]
[[File:HHF_015083.png |400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:EA2_01508.png|400px|centre|thumb|Counter plot for estimating the activation energy.]]
[[File:EA2_PARAMETERS.png|400px|centre|thumb|parameters for the activation energy.]]

===Reaction dynamics===
'''F+H2 system'''

Initially, the reactants have kinetic energy in the form of vibrational and translational energies, and as it crosses the potential energy barrier, the kinetic energy is converted into potential energy. Once the system is exiting the product channel, the potential energy is converted into the vibrational energy of the product.One good experimental technique to prob the electronic structure of the reacting species will be IR spectroscopy.In the anharmonic oscillator model, exciting molecules in the relaxed state promotes excitation from the ground state to the first energy level mainly. This will give rise to a single peak in the IR spectrum. Howver, when exciting a sample of excited molecules, many transitions are possible. For example, from 0-->1, the fundamental or 1-->2, the first overtone. They will show up in the spectrum as 2 peaks, with the overtone being at a lower wavenumber as the energy gap decreases up the potential well. The intensity of the overtone decreases over time as the electrons can fall back to lower energy levels and energy is emitted as radiation. As this system is linear, rotational is not important electronic energy is not considered here.Photoelectron spectroscopy is also a viable method. '''reference 5'''

[[File:Reactiondynamicsfh2_0150.png||400px|centre|thumb|contour plot for F+H2.]]
[[File:Reactiondynamicsparameter——015.png |400px|centre|thumb|parameters for the reactive trajectory.]]
===Varying the momentum of HH in the F+H2 system.===
Conditions:rFH=182 pm, fHH=74 pm, PFH=-1.0g.mol-1.pm.fs-1
{| class="wikitable" border="1"
|+ caption
|-
|PHH/g.mol-1.pm.fs-1|| Contour Plot
|-
|0 || [[File:0_015083.png |400 px|centre]]
|-
|2 || [[File:2_0508.png |400 px|centre]]
|-
|4 || [[File:4_01508.png ‎|400 px|centre]]
|-
|6.1|| [[File:6_01508.png|400 px|centre]]
|-
| -2|| [[File:-2_01508.png|400 px|centre]]
|-
| -4|| [[File:-4.1_01508.png‎|400 px|centre]]
|-
| -6.1|| [[File:Fit1_01508.png|400 px|centre]]
|-
|}

MRD:01508310

2020-05-22T16:11:28Z

Hh2218: /* Varying the momentum of HH in the F+H2 system. */

==H-H-H system==
===Dynamics from the transition state region===
The transition state is the point on the potential energy surface that has ∂V(ri)/∂ri=0, where ri is the distance between two atoms.The transition state is a local maximum and its second derivative ∂2V(ri)/∂ri2 is < 0, whereas a local minimum will have a positive second derivative instead.
[[File:Hhh_surfaceplot_01508.png|400px|thumb|centre|a potential energy surface plot of H and H2 with respect to interatomic distances.]]

===Trajectories from r1=r2: locating the transition state===
At the transition state, r1=r2=90.8 pm by estimation. At this separation, the forces acting along AB and BC are both -0.004 kJ.mol-1.pm-1, which is close to zero and the eigenvalues for the Hessian matrix were -0.028 and +0.167 kJ.mol-1.pm-2, indicating the presence of transition state. The Internuclear Distance vs Time plot suggests the distance between HA, HB and HC is equal, about 90 pm and the distance is constant over time suggests the atoms are static at the transition state.
[[File:Animation101508310.png|400px|centre|thumb|picture showing H and H2 at the transition state.]]
[[File:Optimisation1_01508310.png|400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:Internucleardistance_01508310.png|400px|centre|thumb|Internuclear Distance vs Time plot between the H atoms at the transition state.]]

===Calculating the reaction path===
When rA-B is set to rts+1 and rB-C equals rts,the transition rolls towards BC and HA remains as an atom. MEP and Dynamic reaction paths are different as MEP set the momenta to zero in every step of the reaction path, products are therefore static and hence the reaction path is relatively straight. The dynamic reaction path is more realistic. It takes the momenta of gaseous molecules into account,i.e. they have vibrational energies, that is illustrated by the wavy line along the reaction path.
[[File:Surface_Plot1mep_015083.png|400px|centre|thumb|the minimum energy path (mep) of the H-H-H system]]
[[File:01569348_MEP_AB1_dynamic.png|400px|centre|thumb|the dynamic reaction path of the H-H-H system]]

====MEP and Dynamics calculations comparisons====
'''r1=91.8 pm, r2=90.8 pm, momenta set to 0 g.mol-1.pm.fs-1'''

HB and HC form a H2 molecule whereas HA moves away from the molecule. The distance between B and C decreased to 74 pm, which is the hydrogen molecule bond length. '''reference 2'''In MEP calculation, the momenta are set to zero at each time step.

[[File:MepH2bondlength_01508.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using MEP calculation.]]

[[File:MepH2momenta015083.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using MEP calculation.]]

Using Dynamics calculation, the outcome of the reaction is the same. The transition state rolls towards HB and HC and a hydrogen molecule is formed. One noticeable difference is that the hydrogen molecule now has some vibational energy as indicated by the wavy line along the B-C distance in the Internuclear Distance vs Time plot.As for the Momenta vs Time plot, the system is linear, therefore the angle theta is zero. HA and HB are moving away from each other at '''an increasing velocity until the momentum reaches 5 g.mol-1.pm.fs-1.The oscillation along the B-C bond corresponds to the vibration of the bond. '''why does the beginning have negative momenta?'''
[[File:DynamicsH2_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation.]]
[[File:DynamicsH2monenta_01508.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using Dynamics calculation.]]

'''r1=90.8 pm, r2=91.8 pm, momenta set to 0 g.mol-1.pm.fs-1'''

Once the length of r1 and r2 switches, the shapes of the graphs are identical but instead of HB and HC forming a molecule, HA and HB now form the hydrogen molecule in the products.
[[File:Mepinter2_01508.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using MEP calculation.]]
[[File:Momentamep2_015.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using MEP calculation.]]
[[File:InterDynamic_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation.]]
[[File:Momentadynamics_015083.png|centre|400px|thumb|Momenta vs Time plot for H-H-H system using Dynamics calculation.]]

'''Trajectory starting with the final position and reversed momentum to the reaction path above'''

This trajectory starts at the end of the reaction path above and finishes at where the above reaction started. it is essentially a reverse of what happened in the reaction above.
[[File:Reverse_015083.png|centre|400px|thumb|Internuclear Distances vs Time plot for H-H-H system using Dynamics calculation (r1=70.0 pm,r2=353 pm,p1=-3.21 g.mol-1.pm.fs-1, p2=-5.07 g.mol-1.pm.fs-1) .]]

===Recative and unreactive trajectories===
{| class="wikitable" border="1"
! p1/g.mol-1.pm.fs-1 !! p2/g.mol-1.pm.fs-1!! Etot!! Recative?!! Description of the dynamics!! Illustration of the trajectory
|-
| -2.56 || -5.1||-414 || Yes||The translational energy of the reactants can surmount the potential energy barrier and form the products. The ramaining energy is converted into vibrational energy of the products. || [[File:Table1_01508310.png|350px ]]
|-
| -3.1 || -4.1||-420 || No||The reactant H2 has vibrational energy and its rAB motion is rapid. Before it could cross the energy barrier, the molecule slams into the repulsive inner wall of the potential surface and bounces back into the reactant channel. || [[File:Table2_0150.png|350px]]
|-
| -3.1 || -5.1||-414|| Yes||The reactants have both the translational and vibrational energies. The energy is used to surmount the potential energy barrier and converted into the vibrational energy of the products. || [[File:Table3_01508.png|350px]]
|-
| -5.1 || -10.1||-357 || No||The reactants have sufficient energy to cross the transition state and the products did form for a certain amount of time. However, before the the system can exit the product channel, it recrosses the transition state and form the reactants again, hence no reaction occurs. ||[[File:Table4_01508.png|350px]]
|-
| -5.1 || -10.6||-394 || Yes||The system has sufficient energy to cross the transition state but it recrosses the transition state shortly after the reaction path hits the potential energy surface. However, the system is able to cross the transition state for the third time and finally exits the product channel and forms the products. || [[File:-10.6_01508.png|350px]]
|-
|}
In order to form products, a system must have sufficient energy to cross the transition state. Only molecules with the correct phase '''reference 2''' can exit the product channel and form stable products. Recrossing the transition state can lead to either product formation or no reaction. It is possible to cross the transition state multiple times.

===Transition State Theory===

Transition State Theory is classical, it doesn't take quantum tunnelling into account.Quantum tunnelling is probable for this reaction as it involves the transfer of a hydrogen atom, particularly at lower temperatures.'''Reference 3'''At low temperatures, the H atom can tunnel through the potential energy barrier than to pass over the barrier, hence the activation energy is lowered and the reaction rate increases. However, recrossing the energy barrier is possible as seen with the simulations, this can have a negative effect on the reaction rate. At high temperatures, the system is thermally activated and the behavious is approximately classical.'''reference4''' Therefore the experimental reaction rates are expected to be greater than that predicted by the Transition State Theory.

==F-H-H system==
===PES inspection===
'''F+H2 (F1-H1-H2)'''

F+H2 is exothermic as the reactants are higher in energy than the products therefore during the reaction, energy is released to the surroundings. H-F bond is stronger than H-H bond as the products are lower in energy and therefore more stable.The transition state is located approximately at rF1-H1=181.10 pm and rH1-H2=74.49 pm. This is verified by the forces (close to zero) and eigenvalues for hessian matrix (they are of opposite signs). The activation energy is estimated by tilting the transition state towards the reactants and is shown to be 424 kJ.mol-1.
[[File:Fh2_015083.png |400px|centre|thumb|Surface plot for F1-H1-H2 system using Dynamic Calculation, the transition state is identified as the black dot.]]
[[File:OptimisationFhh1_01508.png|400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:F1H1H2_EA_0150.png|400px|centre|thumb|Counter plot for estimating the activation energy.]]
[[File:EA1_01508.png|400px|centre|thumb|parameters for the activation energy.]]
'''H+HF (H1-H2-F1)'''
This reaction is endothermis as the reactants are lower in energy than the products therefore energy is taken in from the surroundings to form the products. H-F bond is still stronger than H-H as the reactans are lower in energy and more stable. The transition state is located at approximately rH1-H2=280 pm and rH2-F1=92 pm. It is located with the same reasons stated above.With the same method, the activation energy is estimated to be 434 kJ.mol-1. The two activation energies should be identical as these two reactions are essentially the reverse of one another.

[[File:H+HF_01508310.png|400px|centre|thumb|Surface plot for H1-H2-F1 system using Dynamic Calculationthe, the transition state is identified as the black dot.]]
[[File:HHF_015083.png |400px|centre|thumb|values for separations and eigenvalues for Hessian Matrix at the transition state.]]
[[File:EA2_01508.png|400px|centre|thumb|Counter plot for estimating the activation energy.]]
[[File:EA2_PARAMETERS.png|400px|centre|thumb|parameters for the activation energy.]]

===Reaction dynamics===
'''F+H2 system'''

Initially, the reactants have kinetic energy in the form of vibrational and translational energies, and as it crosses the potential energy barrier, the kinetic energy is converted into potential energy. Once the system is exiting the product channel, the potential energy is converted into the vibrational energy of the product.One good experimental technique to prob the electronic structure of the reacting species will be IR spectroscopy.In the anharmonic oscillator model, exciting molecules in the relaxed state promotes excitation from the ground state to the first energy level mainly. This will give rise to a single peak in the IR spectrum. Howver, when exciting a sample of excited molecules, many transitions are possible. For example, from 0-->1, the fundamental or 1-->2, the first overtone. They will show up in the spectrum as 2 peaks, with the overtone being at a lower wavenumber as the energy gap decreases up the potential well. The intensity of the overtone decreases over time as the electrons can fall back to lower energy levels and energy is emitted as radiation. As this system is linear, rotational is not important electronic energy is not considered here.Photoelectron spectroscopy is also a viable method. '''reference 5'''

[[File:Reactiondynamicsfh2_0150.png||400px|centre|thumb|contour plot for F+H2.]]
[[File:Reactiondynamicsparameter——015.png |400px|centre|thumb|parameters for the reactive trajectory.]]
===Varying the momentum of HH in the F+H2 system.===
Conditions:rFH=182 pm, fHH=74 pm, PFH=-1.0g.mol-1.pm.fs-1
{| class="wikitable" border="1"
|+ caption
|-
|PHH/g.mol-1.pm.fs-1|| Contour Plot
|-
|0 || [[File:0_015083.png |400 px|centre]]
|-
|2 || [[File:2_0508.png |400 px|centre]]
|-
|4 || [[File:4_01508.png ‎|400 px|centre]]
|-
|6.1|| [[File:6_01508.png|400 px|centre]]
|-
| -2|| [[File:-2_01508.png|400 px|centre]]
|-
| -4.1|| [[File:-4.1_01508.png‎|400 px|centre]]
|-
| -6.1|| [[File:Fit1_01508.png|400 px|centre]]
|-
|}