https://chemwiki.ch.ic.ac.uk/api.php?action=feedcontributions&feedformat=atom&user=Rkf16ChemWiki - User contributions [en]2026-04-10T21:07:47ZUser contributionsMediaWiki 1.43.0https://chemwiki.ch.ic.ac.uk/index.php?title=MRD:rkf75&diff=715137MRD:rkf752018-05-15T14:08:42Z<p>Rkf16: /* The dynamic trajectory */</p>
<hr />
<div>==H + H<sub>2==<br />
<br />
{| class="wikitable" border="1"<br />
|-<br />
| AB= || 2.3<br />
|-<br />
| BC= || 0.74<br />
|-<br />
| p(AB)= || -2.7<br />
|-<br />
| p(BC)= || 0<br />
|}<br />
<br />
[[File:Rkf H+h2 1.PNG|250px]]<br />
<br />
At a transition structure and at a minimum both components of the gradient are 0. The two can be differentiated by the curvature as minimums are stable physical structures that are minimums on the potential energy surface where are transition states are saddle points on the potential energy surface. The second derivative can be used to tell the difference between a saddle point by using the second derivative discriminant test: <br />
<br />
δ = f<sub>xx</sub>f<sub>yy</sub> − f<sup>2</sup><sub>xy</sub> ≥ 0'<br />
<br />
for a saddle point δ<0 <br />
<br />
for a minimum δ>0<br />
<br />
===Locating the transition state===<br />
<br />
{| class="wikitable" border="1"<br />
|-<br />
| AB=BC=1 || p(AB)=p(BC)=0 || [[ File:Rkf H+h2 TS 1.PNG|250px ]]<br />
|-<br />
| AB=BC=0.75 || p(AB)=p(BC)=0 || [[ File:Rkf H+h2 TS 0.75.PNG|250px ]]<br />
|-<br />
| AB=BC=0.908 || p(AB)=p(BC)=0 || [[ File:Rkf H+h2 TS 0.908.PNG|250px ]]<br />
|}<br />
<br />
'''The best transition state estimate:'''<br />
<br />
[[File:Rkf H+h2 TS best.PNG|250px]]<br />
<br />
This is the best estimate of the transition state is AB=BC=0.908 to 3dp as it gives the straightest distance vs time graph therefore there is the littlest oscillation<br />
<br />
===The reaction path===<br />
<br />
====MEP vs dynamic calculations====<br />
<br />
[[File:Rkf H+h2 MEP.PNG|500px]] [[File:Rkf H+h2 traj.PNG|500px]]<br />
<br />
The AB distance increases much faster in far less steps. Also the trajectory shows some oscillation in the dynamic calculation but not in the MEP calculation.<br />
<br />
====The dynamic trajectory====<br />
<br />
[[File:Rkf H+h2 traj dt.PNG|300px]] [[File:Rkf H+h2 traj pt.PNG|300px]]<br />
<br />
Final AB = 10 tending to infinity <br />
<br />
Final BC = 0.74 <br />
<br />
Average p(AB) = 2.5<br />
<br />
Average p(BC) = 1.25<br />
<br />
If instead r1 = r<sub>ts</sub> and r2 = r<sub>ts</sub>+0.01 then BC would AB and BC values would swap therefore BC would tend to infinity and AB would oscillate around 0.74. <br />
<br />
If the initial conditions are set to the final distances above and the negative momentums then the system resorts back to the transition state as seen by the surface plot below. <br />
<br />
[[File:Rkf H+h2 traj rev.PNG|300px]]<br />
<br />
===Reactive and nonreactive trajectories===<br />
<br />
{| class="wikitable" border="1"<br />
|+ caption<br />
! AB !! BC !! P(AB) !! P(BC) !! Total energy !! Reactive? !! Trajectory !! Description <br />
|-<br />
| 2 || 0.74 || -2.5 || -1.25 || -100 || yes || [[File:Rkf H+h2 r 1.PNG|300px]] || As atom A approaches molecule BC the transition state is reached and the reaction proceeds to give molecule AB and atom C <br />
|-<br />
| 2 || 0.74 || -2.0 || -1.5 || -100 || no || [[File:Rkf H+h2 r 2.PNG | 300px]] || as molecule atom C and molecule AB move towards each other the transition state is not quite reached before the direction changes <br />
|-<br />
| 2 || 0.74 || -2.5 || -1.5 || -100 || yes || [[File:Rkf H+h2 r 3.PNG| 300px]] || As atom A approaches molecule BC the transition state is reached and the reaction proceeds to give molecule AB and atom C <br />
|-<br />
| 2 || 0.74 || -5.0 || -2.5 || -85 || no || [[File:Rkf H+h2 r 4.PNG| 300px]] || As the system approaches the transition state and the boundary for the reaction is crossed there the energy is enough that the boundary can be recrossed and the reaction does not proceed<br />
|-<br />
| 2 || 0.74 || -5.2 || -2.5 || -84 || yes || [[File:Rkf H+h2 r 5.PNG| 300px]] || As the system approaches the transition state and the boundary for the reaction is crossed there the energy is enough that the boundary can be recrossed and then recrossed again meaning the reaction proceeds<br />
|}<br />
<br />
The transition state theory assumes that systems that reach the transition state proceed to react however this is always true for cases with higher total energy where the boundary can be recrossed and the reaction will not proceed. For cases where the energy is high enough to recross the barrier transition state theory will predict a higher rate as when boundary recrossing occurs and the reaction does not proceed transition state theory predicts that it will proceed. <br />
<br />
==F-H-H system==<br />
<br />
===PES inspection===<br />
<br />
F + H <sub>2</sub> is exothermic <br />
<br />
H + HF is endothermic <br />
<br />
This shows that the H-F bond is stronger than the H-H bond. <br />
<br />
===Transition state===<br />
<br />
Atom C = F<br />
<br />
Atom A + B = H<br />
<br />
{| class="wikitable" border="1"<br />
|-<br />
| AB= || 0.747<br />
|-<br />
| BC= || 1.809<br />
|-<br />
| p(AB)= || 0<br />
|-<br />
| p(BC)= || 0<br />
|} <br />
[[File:Rkf Hhf ts.PNG|250px]]<br />
<br />
===activation energy===<br />
<br />
activation energy HF + H= 30 kJ/mol<br />
<br />
activation energy H<sub>2</sub> + F = 0.2 kJ/mol<br />
<br />
===H<sub>2</sub>+F===<br />
<br />
Reactive conditions: <br />
<br />
{| class="wikitable" border="1"<br />
|-<br />
| AB= || 0.747<br />
|-<br />
| BC= || 3<br />
|-<br />
| p(AB)= || -0.5<br />
|-<br />
| p(BC)= || -2.5<br />
|}<br />
<br />
Energy released in the reaction is converted into vibrational energy of the H-F bond as shown by the momentum time graph below. It can be seen from this graph that there is significantly more momentum in the B-C bond at later times than there is in the A-B bond at earlier times. This can be confirmed experimentally by comparing the change in temperature to that which would be expected from the enthalpy of reaction. <br />
<br />
[[File:Rkf H2+f pt.PNG|250px]]<br />
<br />
{| class="wikitable" border="1"<br />
|+ caption<br />
! AB !! BC !! P(AB) !! P(BC) !! Trajectory <br />
|-<br />
| 0.74 || 2.2 || -2.9 || -0.5 || [[File:Rkf H2+f 1.PNG|250px]] <br />
|-<br />
| 0.74 || 2.2 || -0.7 || -0.5 || [[File:Rkf H2+f 2.PNG|250px]] <br />
|-<br />
| 0.74 || 2.2 || -0.5 || -0.5 || [[File:Rkf H2+f 3.PNG|250px]] <br />
|-<br />
| 0.74 || 2.2 || -0.3 || -0.5 || [[File:Rkf H2+f 4.PNG|250px]] <br />
|-<br />
| 0.74 || 2.2 || 0 || -0.5 || [[File:Rkf H2+f 5.PNG|250px]] <br />
|-<br />
| 0.74 || 2.2 || 1.2 || -0.5 || [[File:Rkf H2+f 6.PNG|250px]]<br />
|-<br />
| 0.74 || 2.2 || 2.9 || -0.5 || [[File:Rkf H2+f 7.PNG|250px]]<br />
|}<br />
<br />
When the momentum of AB is close to the limits -3 and 3 the reaction has enough energy to cross the barrier to react but it recrosses back again. In between this range there is not enough energy in the system for the reaction to be successful. <br />
<br />
{| class="wikitable" border="1"<br />
|-<br />
| AB= || 0.74<br />
|-<br />
| BC= || 2<br />
|-<br />
| p(AB)= || 0.1<br />
|-<br />
| p(BC)= || -0.8<br />
|}<br />
<br />
Under these conditions the reaction is successful as seen by the plot below.<br />
<br />
[[File:Rkf H2+f 8.PNG|250px]]<br />
<br />
===HF+H===<br />
<br />
{| class="wikitable" border="1"<br />
|+ caption<br />
! AB !! BC !! P(AB) !! P(BC) !! Trajectory !! Reactive<br />
|-<br />
| 2 || 0.9 || -4 || -0.1 || [[File:Rkf Hf+h 1.PNG|250px]] || No<br />
|-<br />
| 2 || 0.9 || -3 || -0.3 || [[File:Rkf Hf+h 2.PNG|250px]] || No<br />
|-<br />
| 2 || 0.9 || -2 || -0.7 || [[File:Rkf Hf+h 3.PNG|250px]] || No<br />
|-<br />
| 2 || 0.9 || -1.5 || -10 || [[File:Rkf Hf+h 4.PNG|250px]] || No<br />
|-<br />
| 2 || 0.9 || -1.2 || -9.6 || [[File:Rkf Hf+h 5.PNG|250px]] || Yes<br />
|-<br />
| 2 || 0.9 || -1.1 || -9.2 || [[File:Rkf Hf+h 6.PNG|250px]] || Yes<br />
|}<br />
<br />
From the examples above reactions, for a reaction to be successful there must be both vibrational and translational energy. When the transition state is symmetrical there must be higher translational energy for the reaction to be successful. When the transition state is closer to the reactants there must be higher initial translational energy and when the transition state is closer to the products there must be significantly higher initial vibrational energy.</div>Rkf16https://chemwiki.ch.ic.ac.uk/index.php?title=MRD:rkf75&diff=715134MRD:rkf752018-05-15T14:08:08Z<p>Rkf16: /* MEP vs dynamic calculations */</p>
<hr />
<div>==H + H<sub>2==<br />
<br />
{| class="wikitable" border="1"<br />
|-<br />
| AB= || 2.3<br />
|-<br />
| BC= || 0.74<br />
|-<br />
| p(AB)= || -2.7<br />
|-<br />
| p(BC)= || 0<br />
|}<br />
<br />
[[File:Rkf H+h2 1.PNG|250px]]<br />
<br />
At a transition structure and at a minimum both components of the gradient are 0. The two can be differentiated by the curvature as minimums are stable physical structures that are minimums on the potential energy surface where are transition states are saddle points on the potential energy surface. The second derivative can be used to tell the difference between a saddle point by using the second derivative discriminant test: <br />
<br />
δ = f<sub>xx</sub>f<sub>yy</sub> − f<sup>2</sup><sub>xy</sub> ≥ 0'<br />
<br />
for a saddle point δ<0 <br />
<br />
for a minimum δ>0<br />
<br />
===Locating the transition state===<br />
<br />
{| class="wikitable" border="1"<br />
|-<br />
| AB=BC=1 || p(AB)=p(BC)=0 || [[ File:Rkf H+h2 TS 1.PNG|250px ]]<br />
|-<br />
| AB=BC=0.75 || p(AB)=p(BC)=0 || [[ File:Rkf H+h2 TS 0.75.PNG|250px ]]<br />
|-<br />
| AB=BC=0.908 || p(AB)=p(BC)=0 || [[ File:Rkf H+h2 TS 0.908.PNG|250px ]]<br />
|}<br />
<br />
'''The best transition state estimate:'''<br />
<br />
[[File:Rkf H+h2 TS best.PNG|250px]]<br />
<br />
This is the best estimate of the transition state is AB=BC=0.908 to 3dp as it gives the straightest distance vs time graph therefore there is the littlest oscillation<br />
<br />
===The reaction path===<br />
<br />
====MEP vs dynamic calculations====<br />
<br />
[[File:Rkf H+h2 MEP.PNG|500px]] [[File:Rkf H+h2 traj.PNG|500px]]<br />
<br />
The AB distance increases much faster in far less steps. Also the trajectory shows some oscillation in the dynamic calculation but not in the MEP calculation.<br />
<br />
====The dynamic trajectory====<br />
<br />
[[File:Rkf H+h2 traj dt.PNG|300px]] [[File:Rkf H+h2 traj pt.PNG|300px]]<br />
<br />
Final AB = 10 tending to infinity <br />
<br />
Final BC = 0.74 <br />
<br />
Average p(AB) = 2.5<br />
<br />
Average p(BC) = 1.25<br />
<br />
If instead r1 = rts and r2 = rts+0.01 then BC would AB and BC values would swap therefore BC would tend to infinity and AB would oscillate around 0.74. <br />
<br />
If the initial conditions are set to the final distances above and the negative momentums then the system resorts back to the transition state as seen by the surface plot below. <br />
<br />
[[File:Rkf H+h2 traj rev.PNG|300px]]<br />
<br />
===Reactive and nonreactive trajectories===<br />
<br />
{| class="wikitable" border="1"<br />
|+ caption<br />
! AB !! BC !! P(AB) !! P(BC) !! Total energy !! Reactive? !! Trajectory !! Description <br />
|-<br />
| 2 || 0.74 || -2.5 || -1.25 || -100 || yes || [[File:Rkf H+h2 r 1.PNG|300px]] || As atom A approaches molecule BC the transition state is reached and the reaction proceeds to give molecule AB and atom C <br />
|-<br />
| 2 || 0.74 || -2.0 || -1.5 || -100 || no || [[File:Rkf H+h2 r 2.PNG | 300px]] || as molecule atom C and molecule AB move towards each other the transition state is not quite reached before the direction changes <br />
|-<br />
| 2 || 0.74 || -2.5 || -1.5 || -100 || yes || [[File:Rkf H+h2 r 3.PNG| 300px]] || As atom A approaches molecule BC the transition state is reached and the reaction proceeds to give molecule AB and atom C <br />
|-<br />
| 2 || 0.74 || -5.0 || -2.5 || -85 || no || [[File:Rkf H+h2 r 4.PNG| 300px]] || As the system approaches the transition state and the boundary for the reaction is crossed there the energy is enough that the boundary can be recrossed and the reaction does not proceed<br />
|-<br />
| 2 || 0.74 || -5.2 || -2.5 || -84 || yes || [[File:Rkf H+h2 r 5.PNG| 300px]] || As the system approaches the transition state and the boundary for the reaction is crossed there the energy is enough that the boundary can be recrossed and then recrossed again meaning the reaction proceeds<br />
|}<br />
<br />
The transition state theory assumes that systems that reach the transition state proceed to react however this is always true for cases with higher total energy where the boundary can be recrossed and the reaction will not proceed. For cases where the energy is high enough to recross the barrier transition state theory will predict a higher rate as when boundary recrossing occurs and the reaction does not proceed transition state theory predicts that it will proceed. <br />
<br />
==F-H-H system==<br />
<br />
===PES inspection===<br />
<br />
F + H <sub>2</sub> is exothermic <br />
<br />
H + HF is endothermic <br />
<br />
This shows that the H-F bond is stronger than the H-H bond. <br />
<br />
===Transition state===<br />
<br />
Atom C = F<br />
<br />
Atom A + B = H<br />
<br />
{| class="wikitable" border="1"<br />
|-<br />
| AB= || 0.747<br />
|-<br />
| BC= || 1.809<br />
|-<br />
| p(AB)= || 0<br />
|-<br />
| p(BC)= || 0<br />
|} <br />
[[File:Rkf Hhf ts.PNG|250px]]<br />
<br />
===activation energy===<br />
<br />
activation energy HF + H= 30 kJ/mol<br />
<br />
activation energy H<sub>2</sub> + F = 0.2 kJ/mol<br />
<br />
===H<sub>2</sub>+F===<br />
<br />
Reactive conditions: <br />
<br />
{| class="wikitable" border="1"<br />
|-<br />
| AB= || 0.747<br />
|-<br />
| BC= || 3<br />
|-<br />
| p(AB)= || -0.5<br />
|-<br />
| p(BC)= || -2.5<br />
|}<br />
<br />
Energy released in the reaction is converted into vibrational energy of the H-F bond as shown by the momentum time graph below. It can be seen from this graph that there is significantly more momentum in the B-C bond at later times than there is in the A-B bond at earlier times. This can be confirmed experimentally by comparing the change in temperature to that which would be expected from the enthalpy of reaction. <br />
<br />
[[File:Rkf H2+f pt.PNG|250px]]<br />
<br />
{| class="wikitable" border="1"<br />
|+ caption<br />
! AB !! BC !! P(AB) !! P(BC) !! Trajectory <br />
|-<br />
| 0.74 || 2.2 || -2.9 || -0.5 || [[File:Rkf H2+f 1.PNG|250px]] <br />
|-<br />
| 0.74 || 2.2 || -0.7 || -0.5 || [[File:Rkf H2+f 2.PNG|250px]] <br />
|-<br />
| 0.74 || 2.2 || -0.5 || -0.5 || [[File:Rkf H2+f 3.PNG|250px]] <br />
|-<br />
| 0.74 || 2.2 || -0.3 || -0.5 || [[File:Rkf H2+f 4.PNG|250px]] <br />
|-<br />
| 0.74 || 2.2 || 0 || -0.5 || [[File:Rkf H2+f 5.PNG|250px]] <br />
|-<br />
| 0.74 || 2.2 || 1.2 || -0.5 || [[File:Rkf H2+f 6.PNG|250px]]<br />
|-<br />
| 0.74 || 2.2 || 2.9 || -0.5 || [[File:Rkf H2+f 7.PNG|250px]]<br />
|}<br />
<br />
When the momentum of AB is close to the limits -3 and 3 the reaction has enough energy to cross the barrier to react but it recrosses back again. In between this range there is not enough energy in the system for the reaction to be successful. <br />
<br />
{| class="wikitable" border="1"<br />
|-<br />
| AB= || 0.74<br />
|-<br />
| BC= || 2<br />
|-<br />
| p(AB)= || 0.1<br />
|-<br />
| p(BC)= || -0.8<br />
|}<br />
<br />
Under these conditions the reaction is successful as seen by the plot below.<br />
<br />
[[File:Rkf H2+f 8.PNG|250px]]<br />
<br />
===HF+H===<br />
<br />
{| class="wikitable" border="1"<br />
|+ caption<br />
! AB !! BC !! P(AB) !! P(BC) !! Trajectory !! Reactive<br />
|-<br />
| 2 || 0.9 || -4 || -0.1 || [[File:Rkf Hf+h 1.PNG|250px]] || No<br />
|-<br />
| 2 || 0.9 || -3 || -0.3 || [[File:Rkf Hf+h 2.PNG|250px]] || No<br />
|-<br />
| 2 || 0.9 || -2 || -0.7 || [[File:Rkf Hf+h 3.PNG|250px]] || No<br />
|-<br />
| 2 || 0.9 || -1.5 || -10 || [[File:Rkf Hf+h 4.PNG|250px]] || No<br />
|-<br />
| 2 || 0.9 || -1.2 || -9.6 || [[File:Rkf Hf+h 5.PNG|250px]] || Yes<br />
|-<br />
| 2 || 0.9 || -1.1 || -9.2 || [[File:Rkf Hf+h 6.PNG|250px]] || Yes<br />
|}<br />
<br />
From the examples above reactions, for a reaction to be successful there must be both vibrational and translational energy. When the transition state is symmetrical there must be higher translational energy for the reaction to be successful. When the transition state is closer to the reactants there must be higher initial translational energy and when the transition state is closer to the products there must be significantly higher initial vibrational energy.</div>Rkf16https://chemwiki.ch.ic.ac.uk/index.php?title=MRD:rkf75&diff=715123MRD:rkf752018-05-15T14:06:44Z<p>Rkf16: /* HF+H */</p>
<hr />
<div>==H + H<sub>2==<br />
<br />
{| class="wikitable" border="1"<br />
|-<br />
| AB= || 2.3<br />
|-<br />
| BC= || 0.74<br />
|-<br />
| p(AB)= || -2.7<br />
|-<br />
| p(BC)= || 0<br />
|}<br />
<br />
[[File:Rkf H+h2 1.PNG|250px]]<br />
<br />
At a transition structure and at a minimum both components of the gradient are 0. The two can be differentiated by the curvature as minimums are stable physical structures that are minimums on the potential energy surface where are transition states are saddle points on the potential energy surface. The second derivative can be used to tell the difference between a saddle point by using the second derivative discriminant test: <br />
<br />
δ = f<sub>xx</sub>f<sub>yy</sub> − f<sup>2</sup><sub>xy</sub> ≥ 0'<br />
<br />
for a saddle point δ<0 <br />
<br />
for a minimum δ>0<br />
<br />
===Locating the transition state===<br />
<br />
{| class="wikitable" border="1"<br />
|-<br />
| AB=BC=1 || p(AB)=p(BC)=0 || [[ File:Rkf H+h2 TS 1.PNG|250px ]]<br />
|-<br />
| AB=BC=0.75 || p(AB)=p(BC)=0 || [[ File:Rkf H+h2 TS 0.75.PNG|250px ]]<br />
|-<br />
| AB=BC=0.908 || p(AB)=p(BC)=0 || [[ File:Rkf H+h2 TS 0.908.PNG|250px ]]<br />
|}<br />
<br />
'''The best transition state estimate:'''<br />
<br />
[[File:Rkf H+h2 TS best.PNG|250px]]<br />
<br />
This is the best estimate of the transition state is AB=BC=0.908 to 3dp as it gives the straightest distance vs time graph therefore there is the littlest oscillation<br />
<br />
===The reaction path===<br />
<br />
====MEP vs dynamic calculations====<br />
<br />
[[File:Rkf H+h2 MEP.PNG|500px]] [[File:Rkf H+h2 traj.PNG|500px]]<br />
<br />
The AB distance increases much faster in far less steps. Also the trajectory shows some oscillation in the dynamic calculation but not in the MEP calculation. <br />
<br />
====The dynamic trajectory====<br />
<br />
[[File:Rkf H+h2 traj dt.PNG|300px]] [[File:Rkf H+h2 traj pt.PNG|300px]]<br />
<br />
Final AB = 10 tending to infinity <br />
<br />
Final BC = 0.74 <br />
<br />
Average p(AB) = 2.5<br />
<br />
Average p(BC) = 1.25<br />
<br />
If instead r1 = rts and r2 = rts+0.01 then BC would AB and BC values would swap therefore BC would tend to infinity and AB would oscillate around 0.74. <br />
<br />
If the initial conditions are set to the final distances above and the negative momentums then the system resorts back to the transition state as seen by the surface plot below. <br />
<br />
[[File:Rkf H+h2 traj rev.PNG|300px]]<br />
<br />
===Reactive and nonreactive trajectories===<br />
<br />
{| class="wikitable" border="1"<br />
|+ caption<br />
! AB !! BC !! P(AB) !! P(BC) !! Total energy !! Reactive? !! Trajectory !! Description <br />
|-<br />
| 2 || 0.74 || -2.5 || -1.25 || -100 || yes || [[File:Rkf H+h2 r 1.PNG|300px]] || As atom A approaches molecule BC the transition state is reached and the reaction proceeds to give molecule AB and atom C <br />
|-<br />
| 2 || 0.74 || -2.0 || -1.5 || -100 || no || [[File:Rkf H+h2 r 2.PNG | 300px]] || as molecule atom C and molecule AB move towards each other the transition state is not quite reached before the direction changes <br />
|-<br />
| 2 || 0.74 || -2.5 || -1.5 || -100 || yes || [[File:Rkf H+h2 r 3.PNG| 300px]] || As atom A approaches molecule BC the transition state is reached and the reaction proceeds to give molecule AB and atom C <br />
|-<br />
| 2 || 0.74 || -5.0 || -2.5 || -85 || no || [[File:Rkf H+h2 r 4.PNG| 300px]] || As the system approaches the transition state and the boundary for the reaction is crossed there the energy is enough that the boundary can be recrossed and the reaction does not proceed<br />
|-<br />
| 2 || 0.74 || -5.2 || -2.5 || -84 || yes || [[File:Rkf H+h2 r 5.PNG| 300px]] || As the system approaches the transition state and the boundary for the reaction is crossed there the energy is enough that the boundary can be recrossed and then recrossed again meaning the reaction proceeds<br />
|}<br />
<br />
The transition state theory assumes that systems that reach the transition state proceed to react however this is always true for cases with higher total energy where the boundary can be recrossed and the reaction will not proceed. For cases where the energy is high enough to recross the barrier transition state theory will predict a higher rate as when boundary recrossing occurs and the reaction does not proceed transition state theory predicts that it will proceed. <br />
<br />
==F-H-H system==<br />
<br />
===PES inspection===<br />
<br />
F + H <sub>2</sub> is exothermic <br />
<br />
H + HF is endothermic <br />
<br />
This shows that the H-F bond is stronger than the H-H bond. <br />
<br />
===Transition state===<br />
<br />
Atom C = F<br />
<br />
Atom A + B = H<br />
<br />
{| class="wikitable" border="1"<br />
|-<br />
| AB= || 0.747<br />
|-<br />
| BC= || 1.809<br />
|-<br />
| p(AB)= || 0<br />
|-<br />
| p(BC)= || 0<br />
|} <br />
[[File:Rkf Hhf ts.PNG|250px]]<br />
<br />
===activation energy===<br />
<br />
activation energy HF + H= 30 kJ/mol<br />
<br />
activation energy H<sub>2</sub> + F = 0.2 kJ/mol<br />
<br />
===H<sub>2</sub>+F===<br />
<br />
Reactive conditions: <br />
<br />
{| class="wikitable" border="1"<br />
|-<br />
| AB= || 0.747<br />
|-<br />
| BC= || 3<br />
|-<br />
| p(AB)= || -0.5<br />
|-<br />
| p(BC)= || -2.5<br />
|}<br />
<br />
Energy released in the reaction is converted into vibrational energy of the H-F bond as shown by the momentum time graph below. It can be seen from this graph that there is significantly more momentum in the B-C bond at later times than there is in the A-B bond at earlier times. This can be confirmed experimentally by comparing the change in temperature to that which would be expected from the enthalpy of reaction. <br />
<br />
[[File:Rkf H2+f pt.PNG|250px]]<br />
<br />
{| class="wikitable" border="1"<br />
|+ caption<br />
! AB !! BC !! P(AB) !! P(BC) !! Trajectory <br />
|-<br />
| 0.74 || 2.2 || -2.9 || -0.5 || [[File:Rkf H2+f 1.PNG|250px]] <br />
|-<br />
| 0.74 || 2.2 || -0.7 || -0.5 || [[File:Rkf H2+f 2.PNG|250px]] <br />
|-<br />
| 0.74 || 2.2 || -0.5 || -0.5 || [[File:Rkf H2+f 3.PNG|250px]] <br />
|-<br />
| 0.74 || 2.2 || -0.3 || -0.5 || [[File:Rkf H2+f 4.PNG|250px]] <br />
|-<br />
| 0.74 || 2.2 || 0 || -0.5 || [[File:Rkf H2+f 5.PNG|250px]] <br />
|-<br />
| 0.74 || 2.2 || 1.2 || -0.5 || [[File:Rkf H2+f 6.PNG|250px]]<br />
|-<br />
| 0.74 || 2.2 || 2.9 || -0.5 || [[File:Rkf H2+f 7.PNG|250px]]<br />
|}<br />
<br />
When the momentum of AB is close to the limits -3 and 3 the reaction has enough energy to cross the barrier to react but it recrosses back again. In between this range there is not enough energy in the system for the reaction to be successful. <br />
<br />
{| class="wikitable" border="1"<br />
|-<br />
| AB= || 0.74<br />
|-<br />
| BC= || 2<br />
|-<br />
| p(AB)= || 0.1<br />
|-<br />
| p(BC)= || -0.8<br />
|}<br />
<br />
Under these conditions the reaction is successful as seen by the plot below.<br />
<br />
[[File:Rkf H2+f 8.PNG|250px]]<br />
<br />
===HF+H===<br />
<br />
{| class="wikitable" border="1"<br />
|+ caption<br />
! AB !! BC !! P(AB) !! P(BC) !! Trajectory !! Reactive<br />
|-<br />
| 2 || 0.9 || -4 || -0.1 || [[File:Rkf Hf+h 1.PNG|250px]] || No<br />
|-<br />
| 2 || 0.9 || -3 || -0.3 || [[File:Rkf Hf+h 2.PNG|250px]] || No<br />
|-<br />
| 2 || 0.9 || -2 || -0.7 || [[File:Rkf Hf+h 3.PNG|250px]] || No<br />
|-<br />
| 2 || 0.9 || -1.5 || -10 || [[File:Rkf Hf+h 4.PNG|250px]] || No<br />
|-<br />
| 2 || 0.9 || -1.2 || -9.6 || [[File:Rkf Hf+h 5.PNG|250px]] || Yes<br />
|-<br />
| 2 || 0.9 || -1.1 || -9.2 || [[File:Rkf Hf+h 6.PNG|250px]] || Yes<br />
|}<br />
<br />
From the examples above reactions, for a reaction to be successful there must be both vibrational and translational energy. When the transition state is symmetrical there must be higher translational energy for the reaction to be successful. When the transition state is closer to the reactants there must be higher initial translational energy and when the transition state is closer to the products there must be significantly higher initial vibrational energy.</div>Rkf16https://chemwiki.ch.ic.ac.uk/index.php?title=MRD:rkf75&diff=715112MRD:rkf752018-05-15T14:05:21Z<p>Rkf16: </p>
<hr />
<div>==H + H<sub>2==<br />
<br />
{| class="wikitable" border="1"<br />
|-<br />
| AB= || 2.3<br />
|-<br />
| BC= || 0.74<br />
|-<br />
| p(AB)= || -2.7<br />
|-<br />
| p(BC)= || 0<br />
|}<br />
<br />
[[File:Rkf H+h2 1.PNG|250px]]<br />
<br />
At a transition structure and at a minimum both components of the gradient are 0. The two can be differentiated by the curvature as minimums are stable physical structures that are minimums on the potential energy surface where are transition states are saddle points on the potential energy surface. The second derivative can be used to tell the difference between a saddle point by using the second derivative discriminant test: <br />
<br />
δ = f<sub>xx</sub>f<sub>yy</sub> − f<sup>2</sup><sub>xy</sub> ≥ 0'<br />
<br />
for a saddle point δ<0 <br />
<br />
for a minimum δ>0<br />
<br />
===Locating the transition state===<br />
<br />
{| class="wikitable" border="1"<br />
|-<br />
| AB=BC=1 || p(AB)=p(BC)=0 || [[ File:Rkf H+h2 TS 1.PNG|250px ]]<br />
|-<br />
| AB=BC=0.75 || p(AB)=p(BC)=0 || [[ File:Rkf H+h2 TS 0.75.PNG|250px ]]<br />
|-<br />
| AB=BC=0.908 || p(AB)=p(BC)=0 || [[ File:Rkf H+h2 TS 0.908.PNG|250px ]]<br />
|}<br />
<br />
'''The best transition state estimate:'''<br />
<br />
[[File:Rkf H+h2 TS best.PNG|250px]]<br />
<br />
This is the best estimate of the transition state is AB=BC=0.908 to 3dp as it gives the straightest distance vs time graph therefore there is the littlest oscillation<br />
<br />
===The reaction path===<br />
<br />
====MEP vs dynamic calculations====<br />
<br />
[[File:Rkf H+h2 MEP.PNG|500px]] [[File:Rkf H+h2 traj.PNG|500px]]<br />
<br />
The AB distance increases much faster in far less steps. Also the trajectory shows some oscillation in the dynamic calculation but not in the MEP calculation. <br />
<br />
====The dynamic trajectory====<br />
<br />
[[File:Rkf H+h2 traj dt.PNG|300px]] [[File:Rkf H+h2 traj pt.PNG|300px]]<br />
<br />
Final AB = 10 tending to infinity <br />
<br />
Final BC = 0.74 <br />
<br />
Average p(AB) = 2.5<br />
<br />
Average p(BC) = 1.25<br />
<br />
If instead r1 = rts and r2 = rts+0.01 then BC would AB and BC values would swap therefore BC would tend to infinity and AB would oscillate around 0.74. <br />
<br />
If the initial conditions are set to the final distances above and the negative momentums then the system resorts back to the transition state as seen by the surface plot below. <br />
<br />
[[File:Rkf H+h2 traj rev.PNG|300px]]<br />
<br />
===Reactive and nonreactive trajectories===<br />
<br />
{| class="wikitable" border="1"<br />
|+ caption<br />
! AB !! BC !! P(AB) !! P(BC) !! Total energy !! Reactive? !! Trajectory !! Description <br />
|-<br />
| 2 || 0.74 || -2.5 || -1.25 || -100 || yes || [[File:Rkf H+h2 r 1.PNG|300px]] || As atom A approaches molecule BC the transition state is reached and the reaction proceeds to give molecule AB and atom C <br />
|-<br />
| 2 || 0.74 || -2.0 || -1.5 || -100 || no || [[File:Rkf H+h2 r 2.PNG | 300px]] || as molecule atom C and molecule AB move towards each other the transition state is not quite reached before the direction changes <br />
|-<br />
| 2 || 0.74 || -2.5 || -1.5 || -100 || yes || [[File:Rkf H+h2 r 3.PNG| 300px]] || As atom A approaches molecule BC the transition state is reached and the reaction proceeds to give molecule AB and atom C <br />
|-<br />
| 2 || 0.74 || -5.0 || -2.5 || -85 || no || [[File:Rkf H+h2 r 4.PNG| 300px]] || As the system approaches the transition state and the boundary for the reaction is crossed there the energy is enough that the boundary can be recrossed and the reaction does not proceed<br />
|-<br />
| 2 || 0.74 || -5.2 || -2.5 || -84 || yes || [[File:Rkf H+h2 r 5.PNG| 300px]] || As the system approaches the transition state and the boundary for the reaction is crossed there the energy is enough that the boundary can be recrossed and then recrossed again meaning the reaction proceeds<br />
|}<br />
<br />
The transition state theory assumes that systems that reach the transition state proceed to react however this is always true for cases with higher total energy where the boundary can be recrossed and the reaction will not proceed. For cases where the energy is high enough to recross the barrier transition state theory will predict a higher rate as when boundary recrossing occurs and the reaction does not proceed transition state theory predicts that it will proceed. <br />
<br />
==F-H-H system==<br />
<br />
===PES inspection===<br />
<br />
F + H <sub>2</sub> is exothermic <br />
<br />
H + HF is endothermic <br />
<br />
This shows that the H-F bond is stronger than the H-H bond. <br />
<br />
===Transition state===<br />
<br />
Atom C = F<br />
<br />
Atom A + B = H<br />
<br />
{| class="wikitable" border="1"<br />
|-<br />
| AB= || 0.747<br />
|-<br />
| BC= || 1.809<br />
|-<br />
| p(AB)= || 0<br />
|-<br />
| p(BC)= || 0<br />
|} <br />
[[File:Rkf Hhf ts.PNG|250px]]<br />
<br />
===activation energy===<br />
<br />
activation energy HF + H= 30 kJ/mol<br />
<br />
activation energy H<sub>2</sub> + F = 0.2 kJ/mol<br />
<br />
===H<sub>2</sub>+F===<br />
<br />
Reactive conditions: <br />
<br />
{| class="wikitable" border="1"<br />
|-<br />
| AB= || 0.747<br />
|-<br />
| BC= || 3<br />
|-<br />
| p(AB)= || -0.5<br />
|-<br />
| p(BC)= || -2.5<br />
|}<br />
<br />
Energy released in the reaction is converted into vibrational energy of the H-F bond as shown by the momentum time graph below. It can be seen from this graph that there is significantly more momentum in the B-C bond at later times than there is in the A-B bond at earlier times. This can be confirmed experimentally by comparing the change in temperature to that which would be expected from the enthalpy of reaction. <br />
<br />
[[File:Rkf H2+f pt.PNG|250px]]<br />
<br />
{| class="wikitable" border="1"<br />
|+ caption<br />
! AB !! BC !! P(AB) !! P(BC) !! Trajectory <br />
|-<br />
| 0.74 || 2.2 || -2.9 || -0.5 || [[File:Rkf H2+f 1.PNG|250px]] <br />
|-<br />
| 0.74 || 2.2 || -0.7 || -0.5 || [[File:Rkf H2+f 2.PNG|250px]] <br />
|-<br />
| 0.74 || 2.2 || -0.5 || -0.5 || [[File:Rkf H2+f 3.PNG|250px]] <br />
|-<br />
| 0.74 || 2.2 || -0.3 || -0.5 || [[File:Rkf H2+f 4.PNG|250px]] <br />
|-<br />
| 0.74 || 2.2 || 0 || -0.5 || [[File:Rkf H2+f 5.PNG|250px]] <br />
|-<br />
| 0.74 || 2.2 || 1.2 || -0.5 || [[File:Rkf H2+f 6.PNG|250px]]<br />
|-<br />
| 0.74 || 2.2 || 2.9 || -0.5 || [[File:Rkf H2+f 7.PNG|250px]]<br />
|}<br />
<br />
When the momentum of AB is close to the limits -3 and 3 the reaction has enough energy to cross the barrier to react but it recrosses back again. In between this range there is not enough energy in the system for the reaction to be successful. <br />
<br />
{| class="wikitable" border="1"<br />
|-<br />
| AB= || 0.74<br />
|-<br />
| BC= || 2<br />
|-<br />
| p(AB)= || 0.1<br />
|-<br />
| p(BC)= || -0.8<br />
|}<br />
<br />
Under these conditions the reaction is successful as seen by the plot below.<br />
<br />
[[File:Rkf H2+f 8.PNG|250px]]<br />
<br />
===HF+H===<br />
<br />
{| class="wikitable" border="1"<br />
|+ caption<br />
! AB !! BC !! P(AB) !! P(BC) !! Trajectory !! Reactive<br />
|-<br />
| 2 || 0.9 || -4 || -0.1 || [[File:Rkf Hf+h 1.PNG|250px]] || No<br />
|-<br />
| 2 || 0.9 || -3 || -0.3 || [[File:Rkf Hf+h 2.PNG|250px]] || No<br />
|-<br />
| 2 || 0.9 || -2 || -0.7 || [[File:Rkf Hf+h 3.PNG|250px]] || No<br />
|-<br />
| 2 || 0.9 || -1.5 || -10 || [[File:Rkf Hf+h 4.PNG|250px]] || No<br />
|-<br />
| 2 || 0.9 || -1.2 || -9.6 || [[File:Rkf Hf+h 5.PNG|250px]] || Yes<br />
|-<br />
| 2 || 0.9 || -1.1 || -9.2 || [[File:Rkf Hf+h 6.PNG|250px]] || Yes<br />
|}<br />
<br />
From the examples above reactions, for a reaction to be significant there must be both vibrational and translational energy. When the transition state is symmetrical there must be higher translational energy for the reaction to be successful. When the transition state is closer to the reactants there must be higher initial translational energy and when the transition state is closer to the products there must be higher initial vibrational energy.</div>Rkf16https://chemwiki.ch.ic.ac.uk/index.php?title=MRD:rkf75&diff=715020MRD:rkf752018-05-15T13:50:58Z<p>Rkf16: </p>
<hr />
<div>==H + H<sub>2==<br />
<br />
{| class="wikitable" border="1"<br />
|-<br />
| AB= || 2.3<br />
|-<br />
| BC= || 0.74<br />
|-<br />
| p(AB)= || -2.7<br />
|-<br />
| p(BC)= || 0<br />
|}<br />
<br />
[[File:Rkf H+h2 1.PNG|250px]]<br />
<br />
At a transition structure and at a minimum both components of the gradient are 0. The two can be differentiated by the curvature as minimums are stable physical structures that are minimums on the potential energy surface where are transition states are saddle points on the potential energy surface. The second derivative can be used to tell the difference between a saddle point by using the second derivative discriminant test: <br />
<br />
δ = f<sub>xx</sub>f<sub>yy</sub> − f<sup>2</sup><sub>xy</sub> ≥ 0'<br />
<br />
for a saddle point δ<0 <br />
<br />
for a minimum δ>0<br />
<br />
===Locating the transition state===<br />
<br />
{| class="wikitable" border="1"<br />
|-<br />
| AB=BC=1 || p(AB)=p(BC)=0 || [[ File:Rkf H+h2 TS 1.PNG|250px ]]<br />
|-<br />
| AB=BC=0.75 || p(AB)=p(BC)=0 || [[ File:Rkf H+h2 TS 0.75.PNG|250px ]]<br />
|-<br />
| AB=BC=0.908 || p(AB)=p(BC)=0 || [[ File:Rkf H+h2 TS 0.908.PNG|250px ]]<br />
|}<br />
<br />
'''The best transition state estimate:'''<br />
<br />
[[File:Rkf H+h2 TS best.PNG|250px]]<br />
<br />
This is the best estimate of the transition state is AB=BC=0.908 to 3dp as it gives the straightest distance vs time graph therefore there is the littlest oscillation<br />
<br />
===The reaction path===<br />
<br />
====MEP vs dynamic calculations====<br />
<br />
[[File:Rkf H+h2 MEP.PNG|500px]] [[File:Rkf H+h2 traj.PNG|500px]]<br />
<br />
The AB distance increases much faster in far less steps. Also the trajectory shows some oscillation in the dynamic calculation but not in the MEP calculation. <br />
<br />
====The dynamic trajectory====<br />
<br />
[[File:Rkf H+h2 traj dt.PNG|300px]] [[File:Rkf H+h2 traj pt.PNG|300px]]<br />
<br />
Final AB = 10 tending to infinity <br />
<br />
Final BC = 0.74 <br />
<br />
Average p(AB) = 2.5<br />
<br />
Average p(BC) = 1.25<br />
<br />
If instead r1 = rts and r2 = rts+0.01 then BC would AB and BC values would swap therefore BC would tend to infinity and AB would oscillate around 0.74. <br />
<br />
If the initial conditions are set to the final distances above and the negative momentums then the system resorts back to the transition state as seen by the surface plot below. <br />
<br />
[[File:Rkf H+h2 traj rev.PNG|300px]]<br />
<br />
===Reactive and nonreactive trajectories===<br />
<br />
{| class="wikitable" border="1"<br />
|+ caption<br />
! AB !! BC !! P(AB) !! P(BC) !! Total energy !! Reactive? !! Trajectory !! Description <br />
|-<br />
| 2 || 0.74 || -2.5 || -1.25 || -100 || yes || [[File:Rkf H+h2 r 1.PNG|300px]] || As atom A approaches molecule BC the transition state is reached and the reaction proceeds to give molecule AB and atom C <br />
|-<br />
| 2 || 0.74 || -2.0 || -1.5 || -100 || no || [[File:Rkf H+h2 r 2.PNG | 300px]] || as molecule atom C and molecule AB move towards each other the transition state is not quite reached before the direction changes <br />
|-<br />
| 2 || 0.74 || -2.5 || -1.5 || -100 || yes || [[File:Rkf H+h2 r 3.PNG| 300px]] || As atom A approaches molecule BC the transition state is reached and the reaction proceeds to give molecule AB and atom C <br />
|-<br />
| 2 || 0.74 || -5.0 || -2.5 || -85 || no || [[File:Rkf H+h2 r 4.PNG| 300px]] || As the system approaches the transition state and the boundary for the reaction is crossed there the energy is enough that the boundary can be recrossed and the reaction does not proceed<br />
|-<br />
| 2 || 0.74 || -5.2 || -2.5 || -84 || yes || [[File:Rkf H+h2 r 5.PNG| 300px]] || As the system approaches the transition state and the boundary for the reaction is crossed there the energy is enough that the boundary can be recrossed and then recrossed again meaning the reaction proceeds<br />
|}<br />
<br />
The transition state theory assumes that systems that reach the transition state proceed to react however this is always true for cases with higher total energy where the boundary can be recrossed and the reaction will not proceed. For cases where the energy is high enough to recross the barrier transition state theory will predict a higher rate as when boundary recrossing occurs and the reaction does not proceed transition state theory predicts that it will proceed. <br />
<br />
==F-H-H system==<br />
<br />
===PES inspection===<br />
<br />
F + H <sub>2</sub> is exothermic <br />
<br />
H + HF is endothermic <br />
<br />
This shows that the H-F bond is stronger than the H-H bond. <br />
<br />
===Transition state===<br />
<br />
Atom C = F<br />
<br />
Atom A + B = H<br />
<br />
{| class="wikitable" border="1"<br />
|-<br />
| AB= || 0.747<br />
|-<br />
| BC= || 1.809<br />
|-<br />
| p(AB)= || 0<br />
|-<br />
| p(BC)= || 0<br />
|} <br />
[[File:Rkf Hhf ts.PNG|250px]]<br />
<br />
===activation energy===<br />
<br />
activation energy HF + H= 30 kJ/mol<br />
<br />
activation energy H<sub>2</sub> + F = 0.2 kJ/mol<br />
<br />
===H<sub>2</sub>+F===<br />
<br />
Reactive conditions: <br />
<br />
{| class="wikitable" border="1"<br />
|-<br />
| AB= || 0.747<br />
|-<br />
| BC= || 3<br />
|-<br />
| p(AB)= || -0.5<br />
|-<br />
| p(BC)= || -2.5<br />
|}<br />
<br />
Energy released in the reaction is converted into vibrational energy of the H-F bond as shown by the momentum time graph below. It can be seen from this graph that there is significantly more momentum in the B-C bond at later times than there is in the A-B bond at earlier times. This can be confirmed experimentally by comparing the change in temperature to that which would be expected from the enthalpy of reaction. <br />
<br />
[[File:Rkf H2+f pt.PNG|250px]]<br />
<br />
{| class="wikitable" border="1"<br />
|+ caption<br />
! AB !! BC !! P(AB) !! P(BC) !! Trajectory <br />
|-<br />
| 0.74 || 2.2 || -2.9 || -0.5 || [[File:Rkf H2+f 1.PNG|250px]] <br />
|-<br />
| 0.74 || 2.2 || -0.7 || -0.5 || [[File:Rkf H2+f 2.PNG|250px]] <br />
|-<br />
| 0.74 || 2.2 || -0.5 || -0.5 || [[File:Rkf H2+f 3.PNG|250px]] <br />
|-<br />
| 0.74 || 2.2 || -0.3 || -0.5 || [[File:Rkf H2+f 4.PNG|250px]] <br />
|-<br />
| 0.74 || 2.2 || 0 || -0.5 || [[File:Rkf H2+f 5.PNG|250px]] <br />
|-<br />
| 0.74 || 2.2 || 1.2 || -0.5 || [[File:Rkf H2+f 6.PNG|250px]]<br />
|-<br />
| 0.74 || 2.2 || 2.9 || -0.5 || [[File:Rkf H2+f 7.PNG|250px]]<br />
|}<br />
<br />
When the momentum of AB is close to the limits -3 and 3 the reaction has enough energy to cross the barrier to react but it recrosses back again. In between this range there is not enough energy in the system for the reaction to be successful. <br />
<br />
{| class="wikitable" border="1"<br />
|-<br />
| AB= || 0.74<br />
|-<br />
| BC= || 2<br />
|-<br />
| p(AB)= || 0.1<br />
|-<br />
| p(BC)= || -0.8<br />
|}<br />
<br />
Under these conditions the reaction is successful as seen by the plot below.<br />
<br />
[[File:Rkf H2+f 8.PNG|250px]]<br />
<br />
===HF+H===<br />
<br />
{| class="wikitable" border="1"<br />
|+ caption<br />
! AB !! BC !! P(AB) !! P(BC) !! Trajectory !! Reactive<br />
|-<br />
| 2 || 0.9 || -4 || -0.1 || [[File:Rkf Hf+h 1.PNG|250px]] || No<br />
|-<br />
| 2 || 0.9 || -3 || -0.3 || [[File:Rkf Hf+h 2.PNG|250px]] || No<br />
|-<br />
| 2 || 0.9 || -2 || -0.7 || [[File:Rkf Hf+h 3.PNG|250px]] || No<br />
|-<br />
| 2 || 0.9 || -1.5 || -10 || [[File:Rkf Hf+h 4.PNG|250px]] || No<br />
|-<br />
| 2 || 0.9 || -1.2 || -9.6 || [[File:Rkf Hf+h 5.PNG|250px]] || Yes<br />
|-<br />
| 2 || 0.9 || -1.1 || -9.2 || [[File:Rkf Hf+h 6.PNG|250px]] || Yes<br />
|}</div>Rkf16https://chemwiki.ch.ic.ac.uk/index.php?title=MRD:rkf75&diff=714923MRD:rkf752018-05-15T13:32:37Z<p>Rkf16: </p>
<hr />
<div>==H + H<sub>2==<br />
<br />
{| class="wikitable" border="1"<br />
|-<br />
| AB= || 2.3<br />
|-<br />
| BC= || 0.74<br />
|-<br />
| p(AB)= || -2.7<br />
|-<br />
| p(BC)= || 0<br />
|}<br />
<br />
[[File:Rkf H+h2 1.PNG|250px]]<br />
<br />
''QUESTIONS - What value do the different components of the gradient of the potential energy surface have at a minimum and at a transition structure? Briefly explain how minima and transition structures can be distinguished using the curvature of the potential energy surface.'' <br />
<br />
===Locating the transition state===<br />
<br />
{| class="wikitable" border="1"<br />
|-<br />
| AB=BC=1 || p(AB)=p(BC)=0 || [[ File:Rkf H+h2 TS 1.PNG|250px ]]<br />
|-<br />
| AB=BC=0.75 || p(AB)=p(BC)=0 || [[ File:Rkf H+h2 TS 0.75.PNG|250px ]]<br />
|-<br />
| AB=BC=0.908 || p(AB)=p(BC)=0 || [[ File:Rkf H+h2 TS 0.908.PNG|250px ]]<br />
|}<br />
<br />
'''The best transition state estimate:'''<br />
<br />
[[File:Rkf H+h2 TS best.PNG|250px]]<br />
<br />
This is the best estimate of the transition state is AB=BC=0.908 to 3dp as it gives the straightest distances therefore there is the littlest oscillation<br />
<br />
===The reaction path===<br />
<br />
====MEP vs dynamic calculations====<br />
<br />
[[File:Rkf H+h2 MEP.PNG|500px]] [[File:Rkf H+h2 traj.PNG|500px]]<br />
<br />
The AB distance increases much faster in far less steps. Also the trajectory shows some oscillation in the dynamic calculation but not in the MEP calculation. <br />
<br />
====The dynamic trajectory====<br />
<br />
[[File:Rkf H+h2 traj dt.PNG|300px]] [[File:Rkf H+h2 traj pt.PNG|300px]]<br />
<br />
Final AB = 10 tending to infinity <br />
<br />
Final BC = 0.74 <br />
<br />
Average p(AB) = 2.5<br />
<br />
Average p(BC) = 1.25<br />
<br />
If instead r1 = rts and r2 = rts+0.01 then BC would AB and BC values would swap therefore BC would tend to infinity and AB would oscillate around 0.74. <br />
<br />
If the initial conditions are set to the final distances above and the negative momentums then the system resorts back to the transition state as seen by the surface plot below. <br />
<br />
[[File:Rkf H+h2 traj rev.PNG|300px]]<br />
<br />
===Reactive and nonreactive trajectories===<br />
<br />
{| class="wikitable" border="1"<br />
|+ caption<br />
! AB !! BC !! P(AB) !! P(BC) !! Total energy !! Reactive? !! Trajectory !! Description <br />
|-<br />
| 2 || 0.74 || -2.5 || -1.25 || -100 || yes || [[File:Rkf H+h2 r 1.PNG|300px]] || As atom A approaches molecule BC the transition state is reached and the reaction proceeds to give molecule AB and atom C <br />
|-<br />
| 2 || 0.74 || -2.0 || -1.5 || -100 || no || [[File:Rkf H+h2 r 2.PNG | 300px]] || as molecule atom C and molecule AB move towards each other the transition state is not quite reached before the direction changes <br />
|-<br />
| 2 || 0.74 || -2.5 || -1.5 || -100 || yes || [[File:Rkf H+h2 r 3.PNG| 300px]] || As atom A approaches molecule BC the transition state is reached and the reaction proceeds to give molecule AB and atom C <br />
|-<br />
| 2 || 0.74 || -5.0 || -2.5 || -85 || no || [[File:Rkf H+h2 r 4.PNG| 300px]] || As the system approaches the transition state and the boundary for the reaction is crossed there the energy is enough that the boundary can be recrossed and the reaction does not proceed<br />
|-<br />
| 2 || 0.74 || -5.2 || -2.5 || -84 || yes || [[File:Rkf H+h2 r 5.PNG| 300px]] || As the system approaches the transition state and the boundary for the reaction is crossed there the energy is enough that the boundary can be recrossed and then recrossed again meaning the reaction proceeds<br />
|}<br />
<br />
The transition state theory assumes that systems that reach the transition state proceed to react however this is always true for cases with higher total energy where the boundary can be recrossed and the reaction will not proceed. For cases where the energy is high enough to recross the barrier transition state theory will predict a higher rate as when boundary recrossing occurs and the reaction does not proceed transition state theory predicts that it will proceed. <br />
<br />
==F-H-H system==<br />
<br />
===PES inspection===<br />
<br />
F + H <sub>2</sub> is exothermic <br />
<br />
H + HF is endothermic <br />
<br />
This shows that the H-F bond is stronger than the H-H bond. <br />
<br />
===Transition state===<br />
<br />
Atom C = F<br />
<br />
Atom A + B = H<br />
<br />
{| class="wikitable" border="1"<br />
|-<br />
| AB= || 0.747<br />
|-<br />
| BC= || 1.809<br />
|-<br />
| p(AB)= || 0<br />
|-<br />
| p(BC)= || 0<br />
|} <br />
[[File:Rkf Hhf ts.PNG|250px]]<br />
<br />
===activation energy===<br />
<br />
activation energy HF + H= 30 kJ/mol<br />
<br />
activation energy H<sub>2</sub> + F = 0.2 kJ/mol<br />
<br />
===H<sub>2</sub>+F===<br />
<br />
Reactive conditions: <br />
<br />
{| class="wikitable" border="1"<br />
|-<br />
| AB= || 0.747<br />
|-<br />
| BC= || 3<br />
|-<br />
| p(AB)= || -0.5<br />
|-<br />
| p(BC)= || -2.5<br />
|}<br />
<br />
Energy released in the reaction is converted into vibrational energy of the H-F bond as shown by the momentum time graph below. It can be seen from this graph that there is significantly more momentum in the B-C bond at later times than there is in the A-B bond at earlier times. This can be confirmed experimentally by comparing the change in temperature to that which would be expected from the enthalpy of reaction. <br />
<br />
[[File:Rkf H2+f pt.PNG|250px]]<br />
<br />
{| class="wikitable" border="1"<br />
|+ caption<br />
! AB !! BC !! P(AB) !! P(BC) !! Trajectory <br />
|-<br />
| 0.74 || 2.2 || -2.9 || -0.5 || [[File:Rkf H2+f 1.PNG|250px]] <br />
|-<br />
| 0.74 || 2.2 || -0.7 || -0.5 || [[File:Rkf H2+f 2.PNG|250px]] <br />
|-<br />
| 0.74 || 2.2 || -0.5 || -0.5 || [[File:Rkf H2+f 3.PNG|250px]] <br />
|-<br />
| 0.74 || 2.2 || -0.3 || -0.5 || [[File:Rkf H2+f 4.PNG|250px]] <br />
|-<br />
| 0.74 || 2.2 || 0 || -0.5 || [[File:Rkf H2+f 5.PNG|250px]] <br />
|-<br />
| 0.74 || 2.2 || 1.2 || -0.5 || [[File:Rkf H2+f 6.PNG|250px]]<br />
|-<br />
| 0.74 || 2.2 || 2.9 || -0.5 || [[File:Rkf H2+f 7.PNG|250px]]<br />
|}<br />
<br />
When the momentum of AB is close to the limits -3 and 3 the reaction has enough energy to cross the barrier to react but it recrosses back again. In between this range there is not enough energy in the system for the reaction to be successful. <br />
<br />
{| class="wikitable" border="1"<br />
|-<br />
| AB= || 0.74<br />
|-<br />
| BC= || 2<br />
|-<br />
| p(AB)= || 0.1<br />
|-<br />
| p(BC)= || -0.8<br />
|}<br />
<br />
Under these conditions the reaction is successful as seen by the plot below.<br />
<br />
[[File:Rkf H2+f 8.PNG|250px]]<br />
<br />
===HF+H===<br />
<br />
{| class="wikitable" border="1"<br />
|+ caption<br />
! AB !! BC !! P(AB) !! P(BC) !! Trajectory !! Reactive<br />
|-<br />
| 2 || 0.9 || -4 || -0.1 || [[File:Rkf Hf+h 1.PNG|250px]] || No<br />
|-<br />
| 2 || 0.9 || -3 || -0.3 || [[File:Rkf Hf+h 2.PNG|250px]] || No<br />
|-<br />
| 2 || 0.9 || -2 || -0.7 || [[File:Rkf Hf+h 3.PNG|250px]] || No<br />
|-<br />
| 2 || 0.9 || -1.5 || -10 || [[File:Rkf Hf+h 4.PNG|250px]] || No<br />
|-<br />
| 2 || 0.9 || -1.2 || -9.6 || [[File:Rkf Hf+h 5.PNG|250px]] || Yes<br />
|-<br />
| 2 || 0.9 || -1.1 || -9.2 || [[File:Rkf Hf+h 6.PNG|250px]] || Yes<br />
|}</div>Rkf16https://chemwiki.ch.ic.ac.uk/index.php?title=File:Rkf_Hf%2Bh_6.PNG&diff=714840File:Rkf Hf+h 6.PNG2018-05-15T13:02:35Z<p>Rkf16: </p>
<hr />
<div></div>Rkf16https://chemwiki.ch.ic.ac.uk/index.php?title=File:Rkf_Hf%2Bh_5.PNG&diff=714838File:Rkf Hf+h 5.PNG2018-05-15T12:59:43Z<p>Rkf16: </p>
<hr />
<div></div>Rkf16https://chemwiki.ch.ic.ac.uk/index.php?title=File:Rkf_Hf%2Bh_4.PNG&diff=714837File:Rkf Hf+h 4.PNG2018-05-15T12:56:27Z<p>Rkf16: </p>
<hr />
<div></div>Rkf16https://chemwiki.ch.ic.ac.uk/index.php?title=File:Rkf_Hf%2Bh_3.PNG&diff=714829File:Rkf Hf+h 3.PNG2018-05-15T12:52:12Z<p>Rkf16: </p>
<hr />
<div></div>Rkf16https://chemwiki.ch.ic.ac.uk/index.php?title=File:Rkf_Hf%2Bh_2.PNG&diff=714827File:Rkf Hf+h 2.PNG2018-05-15T12:51:01Z<p>Rkf16: </p>
<hr />
<div></div>Rkf16https://chemwiki.ch.ic.ac.uk/index.php?title=File:Rkf_Hf%2Bh_1.PNG&diff=714823File:Rkf Hf+h 1.PNG2018-05-15T12:49:13Z<p>Rkf16: </p>
<hr />
<div></div>Rkf16https://chemwiki.ch.ic.ac.uk/index.php?title=File:Rkf_H2%2Bf_8.PNG&diff=714820File:Rkf H2+f 8.PNG2018-05-15T12:44:23Z<p>Rkf16: </p>
<hr />
<div></div>Rkf16https://chemwiki.ch.ic.ac.uk/index.php?title=MRD:rkf75&diff=714816MRD:rkf752018-05-15T12:37:49Z<p>Rkf16: </p>
<hr />
<div>==H + H<sub>2==<br />
<br />
{| class="wikitable" border="1"<br />
|-<br />
| AB= || 2.3<br />
|-<br />
| BC= || 0.74<br />
|-<br />
| p(AB)= || -2.7<br />
|-<br />
| p(BC)= || 0<br />
|}<br />
<br />
[[File:Rkf H+h2 1.PNG|250px]]<br />
<br />
''QUESTIONS'' <br />
<br />
===Locating the transition state===<br />
<br />
{| class="wikitable" border="1"<br />
|-<br />
| AB=BC=1 || p(AB)=p(BC)=0 || [[ File:Rkf H+h2 TS 1.PNG|250px ]]<br />
|-<br />
| AB=BC=0.75 || p(AB)=p(BC)=0 || [[ File:Rkf H+h2 TS 0.75.PNG|250px ]]<br />
|-<br />
| AB=BC=0.908 || p(AB)=p(BC)=0 || [[ File:Rkf H+h2 TS 0.908.PNG|250px ]]<br />
|}<br />
<br />
'''The best transition state estimate:'''<br />
<br />
[[File:Rkf H+h2 TS best.PNG|250px]]<br />
<br />
This is the best estimate of the transition state is AB=BC=0.908 to 3dp as it gives the straightest distances therefore there is the littlest oscillation<br />
<br />
===The reaction path===<br />
<br />
====MEP vs dynamic calculations====<br />
<br />
[[File:Rkf H+h2 MEP.PNG|500px]] [[File:Rkf H+h2 traj.PNG|500px]]<br />
<br />
The AB distance increases much faster in far less steps. Also the trajectory shows some oscillation in the dynamic calculation but not in the MEP calculation. <br />
<br />
====The dynamic trajectory====<br />
<br />
[[File:Rkf H+h2 traj dt.PNG|300px]] [[File:Rkf H+h2 traj pt.PNG|300px]]<br />
<br />
Final AB = 10 tending to infinity <br />
<br />
Final BC = 0.74 <br />
<br />
Average p(AB) = 2.5<br />
<br />
Average p(BC) = 1.25<br />
<br />
If instead r1 = rts and r2 = rts+0.01 then BC would AB and BC values would swap therefore BC would tend to infinity and AB would oscillate around 0.74. <br />
<br />
If the initial conditions are set to the final distances above and the negative momentums then the system resorts back to the transition state as seen by the surface plot below. <br />
<br />
[[File:Rkf H+h2 traj rev.PNG|300px]]<br />
<br />
===Reactive and nonreactive trajectories===<br />
<br />
{| class="wikitable" border="1"<br />
|+ caption<br />
! AB !! BC !! P(AB) !! P(BC) !! Total energy !! Reactive? !! Trajectory !! Description <br />
|-<br />
| 2 || 0.74 || -2.5 || -1.25 || -100 || yes || [[File:Rkf H+h2 r 1.PNG|300px]] || As atom A approaches molecule BC the transition state is reached and the reaction proceeds to give molecule AB and atom C <br />
|-<br />
| 2 || 0.74 || -2.0 || -1.5 || -100 || no || [[File:Rkf H+h2 r 2.PNG | 300px]] || as molecule atom C and molecule AB move towards each other the transition state is not quite reached before the direction changes <br />
|-<br />
| 2 || 0.74 || -2.5 || -1.5 || -100 || yes || [[File:Rkf H+h2 r 3.PNG| 300px]] || As atom A approaches molecule BC the transition state is reached and the reaction proceeds to give molecule AB and atom C <br />
|-<br />
| 2 || 0.74 || -5.0 || -2.5 || -85 || no || [[File:Rkf H+h2 r 4.PNG| 300px]] || As the system approaches the transition state and the boundary for the reaction is crossed there the energy is enough that the boundary can be recrossed and the reaction does not proceed<br />
|-<br />
| 2 || 0.74 || -5.2 || -2.5 || -84 || yes || [[File:Rkf H+h2 r 5.PNG| 300px]] || As the system approaches the transition state and the boundary for the reaction is crossed there the energy is enough that the boundary can be recrossed and then recrossed again meaning the reaction proceeds<br />
|}<br />
<br />
The transition state theory assumes that systems that reach the transition state proceed to react however this is always true for cases with higher total energy where the boundary can be recrossed and the reaction will not proceed. For cases where the energy is high enough to recross the barrier transition state theory will predict a higher rate as when boundary recrossing occurs and the reaction does not proceed transition state theory predicts that it will proceed. <br />
<br />
==F-H-H system==<br />
<br />
===PES inspection===<br />
<br />
F + H <sub>2</sub> is exothermic <br />
<br />
H + HF is endothermic <br />
<br />
This shows that the H-F bond is stronger than the H-H bond. <br />
<br />
===Transition state===<br />
<br />
Atom C = F<br />
<br />
Atom A + B = H<br />
<br />
{| class="wikitable" border="1"<br />
|-<br />
| AB= || 0.747<br />
|-<br />
| BC= || 1.809<br />
|-<br />
| p(AB)= || 0<br />
|-<br />
| p(BC)= || 0<br />
|} <br />
[[File:Rkf Hhf ts.PNG|250px]]<br />
<br />
===activation energy===<br />
<br />
activation energy = <br />
<br />
===H<sub>2</sub>+F===<br />
<br />
Reactive conditions: <br />
<br />
{| class="wikitable" border="1"<br />
|-<br />
| AB= || 0.747<br />
|-<br />
| BC= || 3<br />
|-<br />
| p(AB)= || -0.5<br />
|-<br />
| p(BC)= || -2.5<br />
|}<br />
<br />
Energy released in the reaction is converted into vibrational energy of the H-F bond as shown by the momentum time graph below. It can be seen from this graph that there is significantly more momentum in the B-C bond at later times than there is in the A-B bond at earlier times. This can be confirmed experimentally by comparing the change in temperature to that which would be expected from the enthalpy of reaction. <br />
<br />
[[File:Rkf H2+f pt.PNG|250px]]<br />
<br />
{| class="wikitable" border="1"<br />
|+ caption<br />
! AB !! BC !! P(AB) !! P(BC) !! Trajectory !! Description <br />
|-<br />
| 0.74 || 2.2 || -2.9 || -0.5 || [[File:Rkf H2+f 1.PNG]] || <br />
|-<br />
| 0.74 || 2.2 || -0.7 || -0.5 || [[File:Rkf H2+f 2.PNG]] || <br />
|-<br />
| 0.74 || 2.2 || -0.5 || -0.5 || [[File:Rkf H2+f 3.PNG]] || <br />
|-<br />
| 0.74 || 2.2 || -0.3 || -0.5 || [[File:Rkf H2+f 4.PNG]] || <br />
|-<br />
| 0.74 || 2.2 || 0 || -0.5 || [[File:Rkf H2+f 5.PNG]] || <br />
|-<br />
| 0.74 || 2.2 || 1.2 || -0.5 || [[File:Rkf H2+f 6.PNG]] || <br />
|-<br />
| 0.74 || 2.2 || 2.9 || -0.5 || [[File:Rkf H2+f 7.PNG]] || <br />
|}</div>Rkf16https://chemwiki.ch.ic.ac.uk/index.php?title=File:Rkf_H2%2Bf_7.PNG&diff=714815File:Rkf H2+f 7.PNG2018-05-15T12:37:36Z<p>Rkf16: </p>
<hr />
<div></div>Rkf16https://chemwiki.ch.ic.ac.uk/index.php?title=File:Rkf_H2%2Bf_6.PNG&diff=714812File:Rkf H2+f 6.PNG2018-05-15T12:36:26Z<p>Rkf16: </p>
<hr />
<div></div>Rkf16https://chemwiki.ch.ic.ac.uk/index.php?title=File:Rkf_H2%2Bf_5.PNG&diff=714811File:Rkf H2+f 5.PNG2018-05-15T12:35:28Z<p>Rkf16: </p>
<hr />
<div></div>Rkf16https://chemwiki.ch.ic.ac.uk/index.php?title=File:Rkf_H2%2Bf_4.PNG&diff=714810File:Rkf H2+f 4.PNG2018-05-15T12:34:30Z<p>Rkf16: </p>
<hr />
<div></div>Rkf16https://chemwiki.ch.ic.ac.uk/index.php?title=File:Rkf_H2%2Bf_3.PNG&diff=714808File:Rkf H2+f 3.PNG2018-05-15T12:33:30Z<p>Rkf16: </p>
<hr />
<div></div>Rkf16https://chemwiki.ch.ic.ac.uk/index.php?title=File:Rkf_H2%2Bf_2.PNG&diff=714807File:Rkf H2+f 2.PNG2018-05-15T12:32:19Z<p>Rkf16: </p>
<hr />
<div></div>Rkf16https://chemwiki.ch.ic.ac.uk/index.php?title=File:Rkf_H2%2Bf_1.PNG&diff=714806File:Rkf H2+f 1.PNG2018-05-15T12:31:15Z<p>Rkf16: </p>
<hr />
<div></div>Rkf16https://chemwiki.ch.ic.ac.uk/index.php?title=MRD:rkf75&diff=714799MRD:rkf752018-05-15T12:25:24Z<p>Rkf16: </p>
<hr />
<div>==H + H<sub>2==<br />
<br />
{| class="wikitable" border="1"<br />
|-<br />
| AB= || 2.3<br />
|-<br />
| BC= || 0.74<br />
|-<br />
| p(AB)= || -2.7<br />
|-<br />
| p(BC)= || 0<br />
|}<br />
<br />
[[File:Rkf H+h2 1.PNG|250px]]<br />
<br />
''QUESTIONS'' <br />
<br />
===Locating the transition state===<br />
<br />
{| class="wikitable" border="1"<br />
|-<br />
| AB=BC=1 || p(AB)=p(BC)=0 || [[ File:Rkf H+h2 TS 1.PNG|250px ]]<br />
|-<br />
| AB=BC=0.75 || p(AB)=p(BC)=0 || [[ File:Rkf H+h2 TS 0.75.PNG|250px ]]<br />
|-<br />
| AB=BC=0.908 || p(AB)=p(BC)=0 || [[ File:Rkf H+h2 TS 0.908.PNG|250px ]]<br />
|}<br />
<br />
'''The best transition state estimate:'''<br />
<br />
[[File:Rkf H+h2 TS best.PNG|250px]]<br />
<br />
This is the best estimate of the transition state is AB=BC=0.908 to 3dp as it gives the straightest distances therefore there is the littlest oscillation<br />
<br />
===The reaction path===<br />
<br />
====MEP vs dynamic calculations====<br />
<br />
[[File:Rkf H+h2 MEP.PNG|500px]] [[File:Rkf H+h2 traj.PNG|500px]]<br />
<br />
The AB distance increases much faster in far less steps. Also the trajectory shows some oscillation in the dynamic calculation but not in the MEP calculation. <br />
<br />
====The dynamic trajectory====<br />
<br />
[[File:Rkf H+h2 traj dt.PNG|300px]] [[File:Rkf H+h2 traj pt.PNG|300px]]<br />
<br />
Final AB = 10 tending to infinity <br />
<br />
Final BC = 0.74 <br />
<br />
Average p(AB) = 2.5<br />
<br />
Average p(BC) = 1.25<br />
<br />
If instead r1 = rts and r2 = rts+0.01 then BC would AB and BC values would swap therefore BC would tend to infinity and AB would oscillate around 0.74. <br />
<br />
If the initial conditions are set to the final distances above and the negative momentums then the system resorts back to the transition state as seen by the surface plot below. <br />
<br />
[[File:Rkf H+h2 traj rev.PNG|300px]]<br />
<br />
===Reactive and nonreactive trajectories===<br />
<br />
{| class="wikitable" border="1"<br />
|+ caption<br />
! AB !! BC !! P(AB) !! P(BC) !! Total energy !! Reactive? !! Trajectory !! Description <br />
|-<br />
| 2 || 0.74 || -2.5 || -1.25 || -100 || yes || [[File:Rkf H+h2 r 1.PNG|300px]] || As atom A approaches molecule BC the transition state is reached and the reaction proceeds to give molecule AB and atom C <br />
|-<br />
| 2 || 0.74 || -2.0 || -1.5 || -100 || no || [[File:Rkf H+h2 r 2.PNG | 300px]] || as molecule atom C and molecule AB move towards each other the transition state is not quite reached before the direction changes <br />
|-<br />
| 2 || 0.74 || -2.5 || -1.5 || -100 || yes || [[File:Rkf H+h2 r 3.PNG| 300px]] || As atom A approaches molecule BC the transition state is reached and the reaction proceeds to give molecule AB and atom C <br />
|-<br />
| 2 || 0.74 || -5.0 || -2.5 || -85 || no || [[File:Rkf H+h2 r 4.PNG| 300px]] || As the system approaches the transition state and the boundary for the reaction is crossed there the energy is enough that the boundary can be recrossed and the reaction does not proceed<br />
|-<br />
| 2 || 0.74 || -5.2 || -2.5 || -84 || yes || [[File:Rkf H+h2 r 5.PNG| 300px]] || As the system approaches the transition state and the boundary for the reaction is crossed there the energy is enough that the boundary can be recrossed and then recrossed again meaning the reaction proceeds<br />
|}<br />
<br />
The transition state theory assumes that systems that reach the transition state proceed to react however this is always true for cases with higher total energy where the boundary can be recrossed and the reaction will not proceed. For cases where the energy is high enough to recross the barrier transition state theory will predict a higher rate as when boundary recrossing occurs and the reaction does not proceed transition state theory predicts that it will proceed. <br />
<br />
==F-H-H system==<br />
<br />
===PES inspection===<br />
<br />
F + H <sub>2</sub> is exothermic <br />
<br />
H + HF is endothermic <br />
<br />
This shows that the H-F bond is stronger than the H-H bond. <br />
<br />
===Transition state===<br />
<br />
Atom C = F<br />
<br />
Atom A + B = H<br />
<br />
{| class="wikitable" border="1"<br />
|-<br />
| AB= || 0.747<br />
|-<br />
| BC= || 1.809<br />
|-<br />
| p(AB)= || 0<br />
|-<br />
| p(BC)= || 0<br />
|} <br />
[[File:Rkf Hhf ts.PNG|250px]]<br />
<br />
===activation energy===<br />
<br />
activation energy = <br />
<br />
===h<sub>2</sub>+f===<br />
<br />
Reactive conditions: <br />
<br />
{| class="wikitable" border="1"<br />
|-<br />
| AB= || 0.747<br />
|-<br />
| BC= || 3<br />
|-<br />
| p(AB)= || -0.5<br />
|-<br />
| p(BC)= || -2.5<br />
|}<br />
<br />
Energy released in the reaction is converted into vibrational energy of the H-F bond as shown by the momentum time graph below. It can be seen from this graph that there is significantly more momentum in the B-C bond at later times than there is in the A-B bond at earlier times. This can be confirmed experimentally by comparing the change in temperature to that which would be expected from the enthalpy of reaction. <br />
<br />
[[File:Rkf H2+f pt.PNG|250px]]</div>Rkf16https://chemwiki.ch.ic.ac.uk/index.php?title=File:Rkf_H2%2Bf_pt.PNG&diff=714792File:Rkf H2+f pt.PNG2018-05-15T12:20:09Z<p>Rkf16: </p>
<hr />
<div></div>Rkf16https://chemwiki.ch.ic.ac.uk/index.php?title=MRD:rkf75&diff=714789MRD:rkf752018-05-15T12:09:12Z<p>Rkf16: </p>
<hr />
<div>==H + H<sub>2==<br />
<br />
{| class="wikitable" border="1"<br />
|-<br />
| AB= || 2.3<br />
|-<br />
| BC= || 0.74<br />
|-<br />
| p(AB)= || -2.7<br />
|-<br />
| p(BC)= || 0<br />
|}<br />
<br />
[[File:Rkf H+h2 1.PNG|250px]]<br />
<br />
''QUESTIONS'' <br />
<br />
===Locating the transition state===<br />
<br />
{| class="wikitable" border="1"<br />
|-<br />
| AB=BC=1 || p(AB)=p(BC)=0 || [[ File:Rkf H+h2 TS 1.PNG|250px ]]<br />
|-<br />
| AB=BC=0.75 || p(AB)=p(BC)=0 || [[ File:Rkf H+h2 TS 0.75.PNG|250px ]]<br />
|-<br />
| AB=BC=0.908 || p(AB)=p(BC)=0 || [[ File:Rkf H+h2 TS 0.908.PNG|250px ]]<br />
|}<br />
<br />
'''The best transition state estimate:'''<br />
<br />
[[File:Rkf H+h2 TS best.PNG|250px]]<br />
<br />
This is the best estimate of the transition state is AB=BC=0.908 to 3dp as it gives the straightest distances therefore there is the littlest oscillation<br />
<br />
===The reaction path===<br />
<br />
====MEP vs dynamic calculations====<br />
<br />
[[File:Rkf H+h2 MEP.PNG|500px]] [[File:Rkf H+h2 traj.PNG|500px]]<br />
<br />
The AB distance increases much faster in far less steps. Also the trajectory shows some oscillation in the dynamic calculation but not in the MEP calculation. <br />
<br />
====The dynamic trajectory====<br />
<br />
[[File:Rkf H+h2 traj dt.PNG|300px]] [[File:Rkf H+h2 traj pt.PNG|300px]]<br />
<br />
Final AB = 10 tending to infinity <br />
<br />
Final BC = 0.74 <br />
<br />
Average p(AB) = 2.5<br />
<br />
Average p(BC) = 1.25<br />
<br />
If instead r1 = rts and r2 = rts+0.01 then BC would AB and BC values would swap therefore BC would tend to infinity and AB would oscillate around 0.74. <br />
<br />
If the initial conditions are set to the final distances above and the negative momentums then the system resorts back to the transition state as seen by the surface plot below. <br />
<br />
[[File:Rkf H+h2 traj rev.PNG|300px]]<br />
<br />
===Reactive and nonreactive trajectories===<br />
<br />
{| class="wikitable" border="1"<br />
|+ caption<br />
! AB !! BC !! P(AB) !! P(BC) !! Total energy !! Reactive? !! Trajectory !! Description <br />
|-<br />
| 2 || 0.74 || -2.5 || -1.25 || -100 || yes || [[File:Rkf H+h2 r 1.PNG|300px]] || As atom A approaches molecule BC the transition state is reached and the reaction proceeds to give molecule AB and atom C <br />
|-<br />
| 2 || 0.74 || -2.0 || -1.5 || -100 || no || [[File:Rkf H+h2 r 2.PNG | 300px]] || as molecule atom C and molecule AB move towards each other the transition state is not quite reached before the direction changes <br />
|-<br />
| 2 || 0.74 || -2.5 || -1.5 || -100 || yes || [[File:Rkf H+h2 r 3.PNG| 300px]] || As atom A approaches molecule BC the transition state is reached and the reaction proceeds to give molecule AB and atom C <br />
|-<br />
| 2 || 0.74 || -5.0 || -2.5 || -85 || no || [[File:Rkf H+h2 r 4.PNG| 300px]] || As the system approaches the transition state and the boundary for the reaction is crossed there the energy is enough that the boundary can be recrossed and the reaction does not proceed<br />
|-<br />
| 2 || 0.74 || -5.2 || -2.5 || -84 || yes || [[File:Rkf H+h2 r 5.PNG| 300px]] || As the system approaches the transition state and the boundary for the reaction is crossed there the energy is enough that the boundary can be recrossed and then recrossed again meaning the reaction proceeds<br />
|}<br />
<br />
The transition state theory assumes that systems that reach the transition state proceed to react however this is always true for cases with higher total energy where the boundary can be recrossed and the reaction will not proceed. For cases where the energy is high enough to recross the barrier transition state theory will predict a higher rate as when boundary recrossing occurs and the reaction does not proceed transition state theory predicts that it will proceed. <br />
<br />
==F-H-H system==<br />
<br />
===PES inspection===<br />
<br />
F + H <sub>2</sub> is exothermic <br />
<br />
H + HF is endothermic <br />
<br />
This shows that the H-F bond is stronger than the H-H bond. <br />
<br />
===Transition state===<br />
<br />
Atom C = F<br />
<br />
Atom A + B = H<br />
<br />
{| class="wikitable" border="1"<br />
|-<br />
| AB= || 0.747<br />
|-<br />
| BC= || 1.809<br />
|-<br />
| p(AB)= || 0<br />
|-<br />
| p(BC)= || 0<br />
|} <br />
[[File:Rkf Hhf ts.PNG|250px]]<br />
<br />
===activation energy===<br />
<br />
''activation energy''<br />
p<br />
<br />
===H<sub>2</sub>+F===</div>Rkf16https://chemwiki.ch.ic.ac.uk/index.php?title=File:Rkf_Hhf_ts.PNG&diff=714780File:Rkf Hhf ts.PNG2018-05-15T11:54:08Z<p>Rkf16: </p>
<hr />
<div></div>Rkf16https://chemwiki.ch.ic.ac.uk/index.php?title=MRD:rkf75&diff=714719MRD:rkf752018-05-14T16:55:30Z<p>Rkf16: </p>
<hr />
<div>==H + H<sub>2==<br />
<br />
{| class="wikitable" border="1"<br />
|-<br />
| AB= || 2.3<br />
|-<br />
| BC= || 0.74<br />
|-<br />
| p(AB)= || -2.7<br />
|-<br />
| p(BC)= || 0<br />
|}<br />
<br />
[[File:Rkf H+h2 1.PNG|250px]]<br />
<br />
''QUESTIONS'' <br />
<br />
===Locating the transition state===<br />
<br />
{| class="wikitable" border="1"<br />
|-<br />
| AB=BC=1 || p(AB)=p(BC)=0 || [[ File:Rkf H+h2 TS 1.PNG|250px ]]<br />
|-<br />
| AB=BC=0.75 || p(AB)=p(BC)=0 || [[ File:Rkf H+h2 TS 0.75.PNG|250px ]]<br />
|-<br />
| AB=BC=0.908 || p(AB)=p(BC)=0 || [[ File:Rkf H+h2 TS 0.908.PNG|250px ]]<br />
|}<br />
<br />
'''The best transition state estimate:'''<br />
<br />
[[File:Rkf H+h2 TS best.PNG|250px]]<br />
<br />
This is the best estimate of the transition state is AB=BC=0.908 to 3dp as it gives the straightest distances therefore there is the littlest oscillation<br />
<br />
===The reaction path===<br />
<br />
====MEP vs dynamic calculations====<br />
<br />
[[File:Rkf H+h2 MEP.PNG|500px]] [[File:Rkf H+h2 traj.PNG|500px]]<br />
<br />
The AB distance increases much faster in far less steps. Also the trajectory shows some oscillation in the dynamic calculation but not in the MEP calculation. <br />
<br />
====The dynamic trajectory====<br />
<br />
[[File:Rkf H+h2 traj dt.PNG|300px]] [[File:Rkf H+h2 traj pt.PNG|300px]]<br />
<br />
Final AB = 10 tending to infinity <br />
<br />
Final BC = 0.74 <br />
<br />
Average p(AB) = 2.5<br />
<br />
Average p(BC) = 1.25<br />
<br />
If instead r1 = rts and r2 = rts+0.01 then BC would AB and BC values would swap therefore BC would tend to infinity and AB would oscillate around 0.74. <br />
<br />
If the initial conditions are set to the final distances above and the negative momentums then the system resorts back to the transition state as seen by the surface plot below. <br />
<br />
[[File:Rkf H+h2 traj rev.PNG|300px]]<br />
<br />
===Reactive and nonreactive trajectories===<br />
<br />
{| class="wikitable" border="1"<br />
|+ caption<br />
! AB !! BC !! P(AB) !! P(BC) !! Total energy !! Reactive? !! Trajectory !! Description <br />
|-<br />
| 2 || 0.74 || -2.5 || -1.25 || -100 || yes || [[File:Rkf H+h2 r 1.PNG|300px]] || As atom A approaches molecule BC the transition state is reached and the reaction proceeds to give molecule AB and atom C <br />
|-<br />
| 2 || 0.74 || -2.0 || -1.5 || -100 || no || [[File:Rkf H+h2 r 2.PNG | 300px]] || as molecule atom C and molecule AB move towards each other the transition state is not quite reached before the direction changes <br />
|-<br />
| 2 || 0.74 || -2.5 || -1.5 || -100 || yes || [[File:Rkf H+h2 r 3.PNG| 300px]] || As atom A approaches molecule BC the transition state is reached and the reaction proceeds to give molecule AB and atom C <br />
|-<br />
| 2 || 0.74 || -5.0 || -2.5 || -85 || no || [[File:Rkf H+h2 r 4.PNG| 300px]] || As the system approaches the transition state and the boundary for the reaction is crossed there the energy is enough that the boundary can be recrossed and the reaction does not proceed<br />
|-<br />
| 2 || 0.74 || -5.2 || -2.5 || -84 || yes || [[File:Rkf H+h2 r 5.PNG| 300px]] || As the system approaches the transition state and the boundary for the reaction is crossed there the energy is enough that the boundary can be recrossed and then recrossed again meaning the reaction proceeds<br />
|}<br />
<br />
The transition state theory assumes that systems that reach the transition state proceed to react however this is always true for cases with higher total energy where the boundary can be recrossed and the reaction will not proceed. For cases where the energy is high enough to recross the barrier transition state theory will predict a higher rate as when boundary recrossing occurs and the reaction does not proceed transition state theory predicts that it will proceed. <br />
<br />
==F-H-H system==<br />
<br />
===PES inspection===<br />
<br />
F + H <sub>2</sub> is endo/exo <br />
H + HF is endo/exo</div>Rkf16https://chemwiki.ch.ic.ac.uk/index.php?title=MRD:rkf75&diff=714718MRD:rkf752018-05-14T16:54:11Z<p>Rkf16: </p>
<hr />
<div>==H + H<sub>2==<br />
<br />
{| class="wikitable" border="1"<br />
|-<br />
| AB= || 2.3<br />
|-<br />
| BC= || 0.74<br />
|-<br />
| p(AB)= || -2.7<br />
|-<br />
| p(BC)= || 0<br />
|}<br />
<br />
[[File:Rkf H+h2 1.PNG|250px]]<br />
<br />
''QUESTIONS'' <br />
<br />
===Locating the transition state===<br />
<br />
{| class="wikitable" border="1"<br />
|-<br />
| AB=BC=1 || p(AB)=p(BC)=0 || [[ File:Rkf H+h2 TS 1.PNG|250px ]]<br />
|-<br />
| AB=BC=0.75 || p(AB)=p(BC)=0 || [[ File:Rkf H+h2 TS 0.75.PNG|250px ]]<br />
|-<br />
| AB=BC=0.908 || p(AB)=p(BC)=0 || [[ File:Rkf H+h2 TS 0.908.PNG|250px ]]<br />
|}<br />
<br />
'''The best transition state estimate:'''<br />
<br />
[[File:Rkf H+h2 TS best.PNG|250px]]<br />
<br />
This is the best estimate of the transition state is AB=BC=0.908 to 3dp as it gives the straightest distances therefore there is the littlest oscillation<br />
<br />
===The reaction path===<br />
<br />
====MEP vs dynamic calculations====<br />
<br />
[[File:Rkf H+h2 MEP.PNG|500px]] [[File:Rkf H+h2 traj.PNG|500px]]<br />
<br />
The AB distance increases much faster in far less steps. Also the trajectory shows some oscillation in the dynamic calculation but not in the MEP calculation. <br />
<br />
====The dynamic trajectory====<br />
<br />
[[File:Rkf H+h2 traj dt.PNG|300px]] [[File:Rkf H+h2 traj pt.PNG|300px]]<br />
<br />
Final AB = 10 tending to infinity <br />
<br />
Final BC = 0.74 <br />
<br />
Average p(AB) = 2.5<br />
<br />
Average p(BC) = 1.25<br />
<br />
If instead r1 = rts and r2 = rts+0.01 then BC would AB and BC values would swap therefore BC would tend to infinity and AB would oscillate around 0.74. <br />
<br />
If the initial conditions are set to the final distances above and the negative momentums then the system resorts back to the transition state as seen by the surface plot below. <br />
<br />
[[File:Rkf H+h2 traj rev.PNG|300px]]<br />
<br />
===Reactive and nonreactive trajectories===<br />
<br />
{| class="wikitable" border="1"<br />
|+ caption<br />
! AB !! BC !! P(AB) !! P(BC) !! Total energy !! Reactive? !! Trajectory !! Description <br />
|-<br />
| 2 || 0.74 || -2.5 || -1.25 || -100 || yes || [[File:Rkf H+h2 r 1.PNG|300px]] || As atom A approaches molecule BC the transition state is reached and the reaction proceeds to give molecule AB and atom C <br />
|-<br />
| 2 || 0.74 || -2.0 || -1.5 || -100 || no || [[File:Rkf H+h2 r 2.PNG | 300px]] || as molecule atom C and molecule AB move towards each other the transition state is not quite reached before the direction changes <br />
|-<br />
| 2 || 0.74 || -2.5 || -1.5 || -100 || yes || [[File:Rkf H+h2 r 3.PNG| 300px]] || As atom A approaches molecule BC the transition state is reached and the reaction proceeds to give molecule AB and atom C <br />
|-<br />
| 2 || 0.74 || -5.0 || -2.5 || -85 || no || [[File:Rkf H+h2 r 4.PNG| 300px]] || As the system approaches the transition state and the boundary for the reaction is crossed there the energy is enough that the boundary can be recrossed and the reaction does not proceed<br />
|-<br />
| 2 || 0.74 || -5.2 || -2.5 || -84 || yes || [[File:Rkf H+h2 r 5.PNG| 300px]] || As the system approaches the transition state and the boundary for the reaction is crossed there the energy is enough that the boundary can be recrossed and then recrossed again meaning the reaction proceeds<br />
|}<br />
<br />
The transition state theory assumes that systems that reach the transition state proceed to react however this is always true for cases with higher total energy where the boundary can be recrossed and the reaction will not proceed. For cases where the energy is high enough to recross the barrier transition state theory will predict a higher rate as when boundary recrossing occurs and the reaction does not proceed transition state theory predicts that it will proceed. <br />
<br />
== F-H-H system ==</div>Rkf16https://chemwiki.ch.ic.ac.uk/index.php?title=MRD:rkf75&diff=714714MRD:rkf752018-05-14T16:46:52Z<p>Rkf16: </p>
<hr />
<div>==H + H<sub>2==<br />
<br />
{| class="wikitable" border="1"<br />
|-<br />
| AB= || 2.3<br />
|-<br />
| BC= || 0.74<br />
|-<br />
| p(AB)= || -2.7<br />
|-<br />
| p(BC)= || 0<br />
|}<br />
<br />
[[File:Rkf H+h2 1.PNG|250px]]<br />
<br />
''QUESTIONS'' <br />
<br />
===Locating the transition state===<br />
<br />
{| class="wikitable" border="1"<br />
|-<br />
| AB=BC=1 || p(AB)=p(BC)=0 || [[ File:Rkf H+h2 TS 1.PNG|250px ]]<br />
|-<br />
| AB=BC=0.75 || p(AB)=p(BC)=0 || [[ File:Rkf H+h2 TS 0.75.PNG|250px ]]<br />
|-<br />
| AB=BC=0.908 || p(AB)=p(BC)=0 || [[ File:Rkf H+h2 TS 0.908.PNG|250px ]]<br />
|}<br />
<br />
'''The best transition state estimate:'''<br />
<br />
[[File:Rkf H+h2 TS best.PNG|250px]]<br />
<br />
This is the best estimate of the transition state is AB=BC=0.908 to 3dp as it gives the straightest distances therefore there is the littlest oscillation<br />
<br />
===The reaction path===<br />
<br />
====MEP vs dynamic calculations====<br />
<br />
[[File:Rkf H+h2 MEP.PNG|500px]] [[File:Rkf H+h2 traj.PNG|500px]]<br />
<br />
The AB distance increases much faster in far less steps. Also the trajectory shows some oscillation in the dynamic calculation but not in the MEP calculation. <br />
<br />
====The dynamic trajectory====<br />
<br />
[[File:Rkf H+h2 traj dt.PNG|300px]] [[File:Rkf H+h2 traj pt.PNG|300px]]<br />
<br />
Final AB = 10 tending to infinity <br />
<br />
Final BC = 0.74 <br />
<br />
Average p(AB) = 2.5<br />
<br />
Average p(BC) = 1.25<br />
<br />
If instead r1 = rts and r2 = rts+0.01 then BC would AB and BC values would swap therefore BC would tend to infinity and AB would oscillate around 0.74. <br />
<br />
If the initial conditions are set to the final distances above and the negative momentums then the system resorts back to the transition state as seen by the surface plot below. <br />
<br />
[[File:Rkf H+h2 traj rev.PNG|300px]]<br />
<br />
===Reactive and nonreactive trajectories===<br />
<br />
{| class="wikitable" border="1"<br />
|+ caption<br />
! AB !! BC !! P(AB) !! P(BC) !! Total energy !! Reactive? !! Trajectory !! Description <br />
|-<br />
| 2 || 0.74 || -2.5 || -1.25 || -100 || yes || [[File:Rkf H+h2 r 1.PNG|300px]] || As atom A approaches molecule BC the transition state is reached and the reaction proceeds to give molecule AB and atom C <br />
|-<br />
| 2 || 0.74 || -2.0 || -1.5 || -100 || no || [[File:Rkf H+h2 r 2.PNG | 300px]] || as molecule atom C and molecule AB move towards each other the transition state is not quite reached before the direction changes <br />
|-<br />
| 2 || 0.74 || -2.5 || -1.5 || -100 || yes || [[File:Rkf H+h2 r 3.PNG]] || As atom A approaches molecule BC the transition state is reached and the reaction proceeds to give molecule AB and atom C <br />
|-<br />
| 2 || 0.74 || -5.0 || -2.5 || -85 || no || [[File:Rkf H+h2 r 4.PNG]] || As the system approaches the transition state and the boundary for the reaction is crossed there the energy is enough that the boundary can be recrossed and the reaction does not proceed<br />
|-<br />
| 2 || 0.74 || -5.2 || -2.5 || -84 || yes || [[File:Rkf H+h2 r 5.PNG]] || As the system approaches the transition state and the boundary for the reaction is crossed there the energy is enough that the boundary can be recrossed and then recrossed again meaning the reaction proceeds<br />
|}</div>Rkf16https://chemwiki.ch.ic.ac.uk/index.php?title=File:Rkf_H%2Bh2_r_5.PNG&diff=714712File:Rkf H+h2 r 5.PNG2018-05-14T16:45:24Z<p>Rkf16: </p>
<hr />
<div></div>Rkf16https://chemwiki.ch.ic.ac.uk/index.php?title=File:Rkf_H%2Bh2_r_4.PNG&diff=714710File:Rkf H+h2 r 4.PNG2018-05-14T16:41:49Z<p>Rkf16: </p>
<hr />
<div></div>Rkf16https://chemwiki.ch.ic.ac.uk/index.php?title=File:Rkf_H%2Bh2_r_3.PNG&diff=714704File:Rkf H+h2 r 3.PNG2018-05-14T16:38:49Z<p>Rkf16: </p>
<hr />
<div></div>Rkf16https://chemwiki.ch.ic.ac.uk/index.php?title=MRD:rkf75&diff=714702MRD:rkf752018-05-14T16:35:47Z<p>Rkf16: </p>
<hr />
<div>==H + H<sub>2==<br />
<br />
{| class="wikitable" border="1"<br />
|-<br />
| AB= || 2.3<br />
|-<br />
| BC= || 0.74<br />
|-<br />
| p(AB)= || -2.7<br />
|-<br />
| p(BC)= || 0<br />
|}<br />
<br />
[[File:Rkf H+h2 1.PNG|250px]]<br />
<br />
''QUESTIONS'' <br />
<br />
===Locating the transition state===<br />
<br />
{| class="wikitable" border="1"<br />
|-<br />
| AB=BC=1 || p(AB)=p(BC)=0 || [[ File:Rkf H+h2 TS 1.PNG|250px ]]<br />
|-<br />
| AB=BC=0.75 || p(AB)=p(BC)=0 || [[ File:Rkf H+h2 TS 0.75.PNG|250px ]]<br />
|-<br />
| AB=BC=0.908 || p(AB)=p(BC)=0 || [[ File:Rkf H+h2 TS 0.908.PNG|250px ]]<br />
|}<br />
<br />
'''The best transition state estimate:'''<br />
<br />
[[File:Rkf H+h2 TS best.PNG|250px]]<br />
<br />
This is the best estimate of the transition state is AB=BC=0.908 to 3dp as it gives the straightest distances therefore there is the littlest oscillation<br />
<br />
===The reaction path===<br />
<br />
====MEP vs dynamic calculations====<br />
<br />
[[File:Rkf H+h2 MEP.PNG|500px]] [[File:Rkf H+h2 traj.PNG|500px]]<br />
<br />
The AB distance increases much faster in far less steps. Also the trajectory shows some oscillation in the dynamic calculation but not in the MEP calculation. <br />
<br />
====The dynamic trajectory====<br />
<br />
[[File:Rkf H+h2 traj dt.PNG|300px]] [[File:Rkf H+h2 traj pt.PNG|300px]]<br />
<br />
Final AB = 10 tending to infinity <br />
<br />
Final BC = 0.74 <br />
<br />
Average p(AB) = 2.5<br />
<br />
Average p(BC) = 1.25<br />
<br />
If instead r1 = rts and r2 = rts+0.01 then BC would AB and BC values would swap therefore BC would tend to infinity and AB would oscillate around 0.74. <br />
<br />
If the initial conditions are set to the final distances above and the negative momentums then the system resorts back to the transition state as seen by the surface plot below. <br />
<br />
[[File:Rkf H+h2 traj rev.PNG|300px]]<br />
<br />
===Reactive and nonreactive trajectories===<br />
<br />
{| class="wikitable" border="1"<br />
|+ caption<br />
! AB !! BC !! P(AB) !! P(BC) !! Total energy !! Reactive? !! Trajectory !! Description <br />
|-<br />
| 2 || 0.74 || -2.5 || -1.25 || -99 || yes || [[File:Rkf H+h2 r 1.PNG|300px]] || As atom A approaches molecule BC the transition state is reached and the reaction proceeds to give molecule AB and atom C <br />
|-<br />
| 2 || 0.74 || -2.0 || -1.5 || -100 || no || [[File:Rkf H+h2 r 2.PNG]] || as molecule atom C and molecule AB move towards each other the transition state is not quite reached before the direction changes <br />
|-<br />
| 2 || 0.74 || -2.5 || -1.5 || || || [[ ]] || <br />
|-<br />
| 2 || 0.74 || -5.0 || -2.5 || || || [[ ]] || <br />
|-<br />
| 2 || 0.74 || -5.2 || -2.5 || || || [[ ]] || <br />
|}</div>Rkf16https://chemwiki.ch.ic.ac.uk/index.php?title=File:Rkf_H%2Bh2_r_2.PNG&diff=714701File:Rkf H+h2 r 2.PNG2018-05-14T16:35:34Z<p>Rkf16: </p>
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<div></div>Rkf16https://chemwiki.ch.ic.ac.uk/index.php?title=File:Rkf_H%2Bh2_r_1.PNG&diff=714698File:Rkf H+h2 r 1.PNG2018-05-14T16:27:42Z<p>Rkf16: Rkf16 uploaded a new version of File:Rkf H+h2 r 1.PNG</p>
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<div></div>Rkf16https://chemwiki.ch.ic.ac.uk/index.php?title=File:Rkf_H%2Bh2_r_1.PNG&diff=714697File:Rkf H+h2 r 1.PNG2018-05-14T16:23:11Z<p>Rkf16: </p>
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<div></div>Rkf16https://chemwiki.ch.ic.ac.uk/index.php?title=MRD:rkf75&diff=714687MRD:rkf752018-05-14T16:09:30Z<p>Rkf16: </p>
<hr />
<div>==H + H<sub>2==<br />
<br />
{| class="wikitable" border="1"<br />
|-<br />
| AB= || 2.3<br />
|-<br />
| BC= || 0.74<br />
|-<br />
| p(AB)= || -2.7<br />
|-<br />
| p(BC)= || 0<br />
|}<br />
<br />
[[File:Rkf H+h2 1.PNG|250px]]<br />
<br />
===Locating the transition state===<br />
<br />
{| class="wikitable" border="1"<br />
|-<br />
| AB=BC=1 || p(AB)=p(BC)=0 || [[ File:Rkf H+h2 TS 1.PNG|250px ]]<br />
|-<br />
| AB=BC=0.75 || p(AB)=p(BC)=0 || [[ File:Rkf H+h2 TS 0.75.PNG|250px ]]<br />
|-<br />
| AB=BC=0.908 || p(AB)=p(BC)=0 || [[ File:Rkf H+h2 TS 0.908.PNG|250px ]]<br />
|}<br />
<br />
'''The best transition state estimate:'''<br />
<br />
[[File:Rkf H+h2 TS best.PNG|250px]]<br />
<br />
This is the best estimate of the transition state is AB=BC=0.908 to 3dp as it gives the straightest distances therefore there is the littlest oscillation<br />
<br />
===The reaction path===<br />
<br />
====MEP vs dynamic calculations====<br />
<br />
[[File:Rkf H+h2 MEP.PNG|500px]] [[File:Rkf H+h2 traj.PNG|500px]]<br />
<br />
The AB distance increases much faster in far less steps. Also the trajectory shows some oscillation in the dynamic calculation but not in the MEP calculation. <br />
<br />
====The dynamic trajectory====<br />
<br />
[[File:Rkf H+h2 traj dt.PNG|300px]] [[File:Rkf H+h2 traj pt.PNG|300px]]<br />
<br />
Final AB = 10 tending to infinity <br />
<br />
Final BC = 0.74 <br />
<br />
Average p(AB) = 2.5<br />
<br />
Average p(BC) = 1.25<br />
<br />
If instead r1 = rts and r2 = rts+0.01 then BC would AB and BC values would swap therefore BC would tend to infinity and AB would oscillate around 0.74. <br />
<br />
If the initial conditions are set to the final distances above and the negative momentums then the system resorts back to the transition state as seen by the surface plot below. <br />
<br />
[[File:Rkf H+h2 traj rev.PNG|300px]]</div>Rkf16https://chemwiki.ch.ic.ac.uk/index.php?title=MRD:rkf75&diff=714686MRD:rkf752018-05-14T16:08:34Z<p>Rkf16: </p>
<hr />
<div>==H + H<sub>2==<br />
<br />
{| class="wikitable" border="1"<br />
|-<br />
| AB= || 2.3<br />
|-<br />
| BC= || 0.74<br />
|-<br />
| p(AB)= || -2.7<br />
|-<br />
| p(BC)= || 0<br />
|}<br />
<br />
[[File:Rkf H+h2 1.PNG|250px]]<br />
<br />
===Locating the transition state===<br />
<br />
{| class="wikitable" border="1"<br />
|-<br />
| AB=BC=1 || p(AB)=p(BC)=0 || [[ File:Rkf H+h2 TS 1.PNG|250px ]]<br />
|-<br />
| AB=BC=0.75 || p(AB)=p(BC)=0 || [[ File:Rkf H+h2 TS 0.75.PNG|250px ]]<br />
|-<br />
| AB=BC=0.908 || p(AB)=p(BC)=0 || [[ File:Rkf H+h2 TS 0.908.PNG|250px ]]<br />
|}<br />
<br />
'''The best transition state estimate:'''<br />
<br />
[[File:Rkf H+h2 TS best.PNG|250px]]<br />
<br />
This is the best estimate of the transition state is AB=BC=0.908 to 3dp as it gives the straightest distances therefore there is the littlest oscillation<br />
<br />
===The reaction path===<br />
<br />
'''MEP vs dynamic calculations'''<br />
<br />
[[File:Rkf H+h2 MEP.PNG|500px]] [[File:Rkf H+h2 traj.PNG|500px]]<br />
<br />
The AB distance increases much faster in far less steps. Also the trajectory shows some oscillation in the dynamic calculation but not in the MEP calculation. <br />
<br />
'''The dynamic trajectory'''<br />
<br />
[[File:Rkf H+h2 traj dt.PNG|300px]] [[File:Rkf H+h2 traj pt.PNG|300px]]<br />
<br />
Final AB = 10 tending to infinity <br />
<br />
Final BC = 0.74 <br />
<br />
Average p(AB) = 2.5<br />
<br />
Average p(BC) = 1.25<br />
<br />
If instead r1 = rts and r2 = rts+0.01 then BC would AB and BC values would swap therefore BC would tend to infinity and AB would oscillate around 0.74. <br />
<br />
If the initial conditions are set to the final distances above and the negative momentums then the system resorts back to the transition state as seen by the surface plot below. <br />
<br />
[[File:Rkf H+h2 traj rev.PNG|300px]]</div>Rkf16https://chemwiki.ch.ic.ac.uk/index.php?title=File:Rkf_H%2Bh2_traj_rev.PNG&diff=714685File:Rkf H+h2 traj rev.PNG2018-05-14T16:07:10Z<p>Rkf16: </p>
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<div></div>Rkf16https://chemwiki.ch.ic.ac.uk/index.php?title=File:Rkf_H%2Bh2_traj_pt.PNG&diff=714682File:Rkf H+h2 traj pt.PNG2018-05-14T16:04:55Z<p>Rkf16: </p>
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<div></div>Rkf16https://chemwiki.ch.ic.ac.uk/index.php?title=File:Rkf_H%2Bh2_traj_dt.PNG&diff=714681File:Rkf H+h2 traj dt.PNG2018-05-14T16:04:12Z<p>Rkf16: </p>
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<div></div>Rkf16https://chemwiki.ch.ic.ac.uk/index.php?title=File:Rkf_H%2Bh2_traj.PNG&diff=714676File:Rkf H+h2 traj.PNG2018-05-14T16:01:47Z<p>Rkf16: </p>
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<div></div>Rkf16https://chemwiki.ch.ic.ac.uk/index.php?title=File:Rkf_H%2Bh2_MEP.PNG&diff=714674File:Rkf H+h2 MEP.PNG2018-05-14T16:01:10Z<p>Rkf16: </p>
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<div></div>Rkf16https://chemwiki.ch.ic.ac.uk/index.php?title=File:H%2Bh2_MEP.PNG&diff=714673File:H+h2 MEP.PNG2018-05-14T16:00:23Z<p>Rkf16: </p>
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<div></div>Rkf16https://chemwiki.ch.ic.ac.uk/index.php?title=MRD:rkf75&diff=714671MRD:rkf752018-05-14T15:59:08Z<p>Rkf16: </p>
<hr />
<div>==H + H<sub>2==<br />
<br />
{| class="wikitable" border="1"<br />
|-<br />
| AB= || 2.3<br />
|-<br />
| BC= || 0.74<br />
|-<br />
| p(AB)= || -2.7<br />
|-<br />
| p(BC)= || 0<br />
|}<br />
<br />
[[File:Rkf H+h2 1.PNG|250px]]<br />
<br />
===Locating the transition state===<br />
<br />
{| class="wikitable" border="1"<br />
|-<br />
| AB=BC=1 || p(AB)=p(BC)=0 || [[ File:Rkf H+h2 TS 1.PNG|250px ]]<br />
|-<br />
| AB=BC=0.75 || p(AB)=p(BC)=0 || [[ File:Rkf H+h2 TS 0.75.PNG|250px ]]<br />
|-<br />
| AB=BC=0.908 || p(AB)=p(BC)=0 || [[ File:Rkf H+h2 TS 0.908.PNG|250px ]]<br />
|}<br />
<br />
'''The best transition state estimate:'''<br />
<br />
[[File:Rkf H+h2 TS best.PNG|250px]]<br />
<br />
This is the best estimate of the transition state is AB=BC=0.908 to 3dp as it gives the straightest distances therefore there is the littlest oscillation</div>Rkf16https://chemwiki.ch.ic.ac.uk/index.php?title=File:Rkf_H%2Bh2_TS_best.PNG&diff=714669File:Rkf H+h2 TS best.PNG2018-05-14T15:57:15Z<p>Rkf16: </p>
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<div></div>Rkf16https://chemwiki.ch.ic.ac.uk/index.php?title=File:Rkf_H%2Bh2_TS_1.PNG&diff=714667File:Rkf H+h2 TS 1.PNG2018-05-14T15:56:25Z<p>Rkf16: Rkf16 uploaded a new version of File:Rkf H+h2 TS 1.PNG</p>
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<div></div>Rkf16https://chemwiki.ch.ic.ac.uk/index.php?title=File:Rkf_H%2Bh2_TS_0.908.PNG&diff=714665File:Rkf H+h2 TS 0.908.PNG2018-05-14T15:53:36Z<p>Rkf16: </p>
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<div></div>Rkf16https://chemwiki.ch.ic.ac.uk/index.php?title=File:Rkf_H%2Bh2_TS_0.75.PNG&diff=714664File:Rkf H+h2 TS 0.75.PNG2018-05-14T15:53:09Z<p>Rkf16: </p>
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<div></div>Rkf16https://chemwiki.ch.ic.ac.uk/index.php?title=File:Rkf_H%2Bh2_TS_1.PNG&diff=714663File:Rkf H+h2 TS 1.PNG2018-05-14T15:52:18Z<p>Rkf16: </p>
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<div></div>Rkf16https://chemwiki.ch.ic.ac.uk/index.php?title=MRD:rkf75&diff=714662MRD:rkf752018-05-14T15:51:20Z<p>Rkf16: Created page with "==H + H<sub>2== {| class="wikitable" border="1" |- | AB= || 2.3 |- | BC= || 0.74 |- | p(AB)= || -2.7 |- | p(BC)= || 0 |} File:Rkf H+h2 1.PNG ===Locating the transition..."</p>
<hr />
<div>==H + H<sub>2==<br />
<br />
{| class="wikitable" border="1"<br />
|-<br />
| AB= || 2.3<br />
|-<br />
| BC= || 0.74<br />
|-<br />
| p(AB)= || -2.7<br />
|-<br />
| p(BC)= || 0<br />
|}<br />
<br />
[[File:Rkf H+h2 1.PNG]]<br />
<br />
===Locating the transition state===<br />
<br />
{| class="wikitable" border="1"<br />
|-<br />
| AB=BC=1 || p(AB)=p(BC)=0 || [[ ]]<br />
|-<br />
| AB=BC=0.75 || p(AB)=p(BC)=0 || [[ ]]<br />
|-<br />
| AB=BC=0.908 || p(AB)=p(BC)=0 || [[ ]]<br />
|}</div>Rkf16