File:Q10 low translation, high vibration surface plot 01506162.png

2020-05-22T20:10:43Z

Yqc18:

File:Q10 low translation, high vibration contour 01506162.png

2020-05-22T20:05:16Z

Yqc18:

File:Q10 high translation, low vibration contour 01506162.png

2020-05-22T20:04:06Z

Yqc18:

MRD01506162

2020-05-22T19:54:28Z

Yqc18:

= Exercise 1: H + H2 system =

==Dynamics from the transition state region==

1. The transition state is mathematically defined as having ∂V(r1)/∂r1 = ∂V(r2)/∂r2=0 and ∂V2(ri)/∂ri <0. It is the energy goes down most deeply along the minium energy path linking reactants and products. The transition state can also be identified by starting trajectories near the transition state and see whether they "roll" towards the reactants or products. A local minimum has ∂V2(ri)/∂ri >0.

==Trajectories from r1 =r2: locating the transition state==

[[File:Q2_90_pm_01506162.png| 300 px| left |thumb| Internuclear distances vs time for trajectory with initial conditions r1=r2=90 pm, p1=p22=0 g.mol-1.pm.fs-1]]

[[File:Internuclear_Distances_vs_Time_for_transition_state_01506162.png| 300 px| center | thumb| Internuclear distances vs time for trajectory with initial conditions r1=r2=90.775 pm, p1=p22=0 g.mol-1.pm.fs-1]]

[[File:Q2_92_pm_01506162.png| 300 px| left | thumb| Internuclear distances vs time for trajectory with initial conditions r1=r2=92 pm, p1=p22=0 g.mol-1.pm.fs-1]]

2. My best estimate of the transition state position is 90.775 pm. The trajectory with this estimate and zero initial momentum has constant internuclear distances throughout the time. It doesn't "roll" towards the reactants or products showing that the trajectory is exactly at transition state.

==Trajectories from r1 = rts + δ, r2 = rts ==

[[File: Q3_dynamics_plot_01506162.png|300 px | left | thumb | Contour plot with initial conditions set as r1= 90.775 pm, r2=91.775 pm, p1=p22=0 g.mol-1.pm.fs-1 and calculation type set as Dynamics ]]

[[File: Q3_MEP_plot_01506162.png | 300 px | right | thumb | Contour plot with initial conditions set as r1= 90.775 pm r2=91.775 pm, p1=p22=0 g.mol-1.pm.fs-1 and calculation type set as MEP]]

3. As shown in the pictures above, Mep doesn't have oscillatory behaviour corresponding to vibrations since momenta are always reset to zero in each time step. Meanwhile the trajectory calculated from calculation type being Dynamics has oscillations .

== Reactive and unreactive trajectories ==

{| class="wikitable" border="1"
|+
! p1/ g.mol-1.pm.fs-1 !! p2/ g.mol-1.pm.fs-1 !! Etot !! Reactive? !! Description of the dynamics !! Illustration of the trajectory
|-
| -2.56 || -5.1 || -414.280 || Yes || A approaches BC which has no oscillatory behaviour. A collides with BC and reaction occurs, a new molecule AB forms and it oscillates. C dissociates. || [[File: Contour_plot_for_first_set.png| 200px]]
|-
| -3.1 || -4.1 || -420.077 || No || A approches BC which possesses oscillatory behaviour. A collides with BC and no reaction occurs. BC continues to oscillate. || [[File: Contour_plot_for_second_set_yqc01506162.png | 200px]]
|-
| -3.1 || -5.1 || -413.977 || Yes || A approaches BC which oscillates slowly. A collides with BC and reaction occurs, a new molecule AB and it oscillates. C dissociates.|| [[File: Contour_plot_for_third_set.png | 200px]]
|-
| -5.1 || -10.1 || -357.277 || No || A approaches BC which doesn't oscillate. Barrier recrossing occurs in which the system crosses the transition state region. A bond between AB forms but the system reverts back to the molecule BC.|| [[File: Contour_plot_for_fourth_set.png | 200px]]
|-
| -5.1 || -10.6 || -349.477 || Yes || || [[File: Contour_plot_for_fifth_set.png | 200px]]
|}

One can conclude from the table that higher absolute p1 induces higher frequency vibrations and higher absolute p2 makes trajectories more reactive.

== Transition State Theory ==

[[File:Contour_plot_for_fourth_set.png | thumb| center | Contour plot with initial conditions set as r1= 74 pm, r2= 200 pm, p1= -5.1 g.mol-1.pm.fs-1, p2= -10.1 g.mol-1.pm.fs-1]]

5. Transition State Theory relies on three key assumptions and they have different effects in causing the differences between the estimated reaction rates and the experimental values. In this case, we are using the simulation as a much simpler model of real-life experiments. The first assumption which states all trajectories with KE>Ea are reactive overestimates the reaction rates since in reality barrier recrossing could have occurred. Above is an illustration of barrier recrossing. The second assumption which states the transition states are in quasi equilibrium with the reactants varies the estimated value from the real one to a limited extent. The third assumption which states quantum tunneling is not to be considered underestimates the reaction rate since in reality quantum tunneling does occur. Unfortunately, no illustration from the simulation can be done since our simulation doesn't take quantum tunneling into account either. Overall, Transition State Theory overestimates reaction rates since there are much more barrier recrossing than quantum tunneling in real life experiments.

= Exercise 2: F-H-H system =

== PES Inspection ==

[[File: Q6_exothermic_surface_plot_01506162.png| thumb | left | Surface plot with A=F, B=H, C=H, initial conditions set as rAB= 200 pm, rBC= 74 pm, pAB= -20 g.mol-1.pm.fs-1, pBC= 1 g.mol-1.pm.fs-1]]

[[File: Q6_endothermic_surface_plot_01506162.png | thumb | right | Surface plot with A=H, B=H, C=F, initial conditions set as rAB= 200 pm, rBC= 74 pm, pAB= 1 g.mol-1.pm.fs-1, pAB= -20 g.mol-1.pm.fs-1]]

6. By inspecting the surface plots of reactive trajectories, F + H2 is exothermic and H + HF is endothermic. This is because H-F has higher bond enthalpy which means it is stronger than H-H. In F+ H2, more energy is released to form H-F than required to break H-H. In H + HF, more energy is required to break H-F than released to form H-H.

[[File: Q8_TS_zero_energy_01506162.png | thumb | center| 600 px | LEPS GUI screenshot]]

[[File: Ex._2_transition_state_distance_vs_time_01506162.png | thumb |center | Internuclear distances vs time for A=F, B=H, C=H, initial conditions set as rAB= 181 pm, rBC= 74.49 pm, pAB=0 g.mol-1.pm.fs-1, pAB= 0 g.mol-1.pm.fs-1]]

[[File: Ex._2_AB=180_pm,_BC=74.49_pm_distance_vs_time.png | thumb | center | Internuclear distances vs time for A=F, B=H, C=H, initial conditions set as rAB= 180 pm, rBC= 74.49 pm, pAB=0 g.mol-1.pm.fs-1, pAB= 0 g.mol-1.pm.fs-1]]

[[File: Ex._2_AB=181_pm,_B=75_pm_distance_vs_time_01506162.png | thumb | center | Internuclear distances vs time for A=F, B=H, C=H, initial conditions set as rAB= 181 pm, rBC= 75 pm, pAB=0 g.mol-1.pm.fs-1, pAB= 0 g.mol-1.pm.fs-1]]

7. Transition state was located by using Hammond postulate. I understand that since F + H2 is exothermic, it has an early transition state and the transition state is reactant-like. Therefore I started by using A=F, B=H, C=H, initial conditions set as rAB= 200 pm, rBC= 74 pm, pAB= 0 g.mol-1.pm.fs-1, pBC= 0 g.mol-1.pm.fs-1 and varied AB and BC distances in order to make forces along AB and BC equal to zero. The approximate position of transition state found is rHF=181 pm, rHH=74.49 pm which has zero force along the bonds as shown in the screenshot above. Three internuclear distances vs time plots are also shown above to further demonstrate the validity of the position of transition state.

[[File: SM_pre_max_energy_01506162.png | 600 px | thumb | center | Illustration of finding the potential energy of reactants of F + H2]]

[[File: SM_max_energy_01506162.png | 600 px | thumb | center | Illustration of finding the potential energy of reactants of F + H2]]

[[File: SM_pro_max_energy_01506162.png | 600 px | thumb | center | Illustration of finding the potential energy of reactants of F + H2]]

[[File: TS_energy_01506162.png | 600 px | thumb | center | Illustration of finding the potential energy of transition state of F + H2]]

[[File: P_pre_max_energy_01506162.png | 600 px | thumb | center | Illustration of finding the potential energy of products of F + H2]]

[[File: P_max_energy_01506162.png | 600 px | thumb | center | Illustration of finding the potential energy of products of F + H2]]

[[File: P_pro_max_energy_01506162.png | 600 px | thumb | center | Illustration of finding the potential energy of products of F + H2]]

8. Activation energy of F + H2 was found by measuring potential energies of reactants, transition state and products with kinetic energy=0, momenta=0 and calculation type being MEP. Potential energy of reactants was found by placing the incoming F atom very far away from H2 molecule at equilibrium bond length =74 pm and kept increasing the distance between F and H2 until potential energy stopped changing. This resulted in F having no effect on H2 's potential energy which was found out to be -435.100 kJ mol-1. Above pictures are an illustration of the approach. The potential energy of transition state was recorded by setting initial conditions in transition state position approximated above and it was found out to be -433.981 kJ mol-1. Potential energy of the products was found by using the same method to find the potential energy of reactants and was found out to be -560.404 kJ mol-1. Above pictures are illustrations of the process.H + HF is a reverse reaction of F + H2 and its activation energy can be calculated from these values as well. Ea for F + H2 was therefore found out to be -433.981-(-435.100)=1.119 kJ mol-1. Ea for H + HF was found out to be -433.981-(-560.404)=126.423 kJ mol-1.

== Reaction dynamics ==

[[File: Momentum_vs_time_as_proof_of_release_of_reaction_energy_01506162.png | thumb | 600 px | center | Momenta vs time for F + H2, initial conditions set as rAB= 200 pm, rBC= 74 pm, pAB=20 g.mol-1.pm.fs-1, pBC<?sub>= 1 g.mol-1.pm.fs-1]]

9. The potential energy released in the reaction of F + H2 is first converted to kinetic energy which is used to promote the products in vibrational ground state to vibrational first state. The vibrational activation would cause an increase in overtone intensity and decrease in fundamental intensity in IR absorbance spectrum. Overtime, the vibrational first state relaxes back to the ground state emitting IR. The vibrational relaxation would cause overtone intensity to decrease and fundamental peak intensity to increase in IR absorbance spectrum. The mechanism of the release of the reaction energy can be thus experimentally confirmed by measuring the emission of IR during vibrational relaxation by FTIR.

The reaction is more efficient with a higher proportion of vibrational energy. According to Polanyi's empirical rules, vibrational energy is more efficient in promoting a reaction with a late transition state meanwhile translational energy is more efficient in promoting a reaction with early transition state.

File:Momentum vs time as proof of release of reaction energy 01506162.png

2020-05-22T19:50:54Z

Yqc18:

MRD01506162

= Exercise 1: H + H2 system =

==Dynamics from the transition state region==

The transition state is mathematically defined as having ∂V(ri)/∂ri=0. The energy goes down most deeply along the minium energy path linking reactants and products. The transition state can also be identified by starting trajectories near the transition state and see whether they "roll" towards the reactants or products. A local minimum has ∂V2(ri)/∂ri>0 while the transition state has ∂V2(ri)/∂ri<0.

==Trajectories from r1 =r2: locating the transition state==

My best estimate of the transition state position is 90.775 pm. The trajectory with this estimate and zero initial momentum has constant internuclear distances throughout the time. It doesn't "roll" towards the reactants or products showing that the trajectory is exactly at transition state.

[[File:Internuclear_Distances_vs_Time_for_transition_state_01506162.png|thumb|center|Internuclear distances vs time for trajectory at estimated transition state position]]

==Trajectories from r1 = rts + δ, r2 = rts ==

Mep doesn't have oscillatory behaviour corresponding to vibrations while the trajectory calculated from calculation type being Dynamics has them.

== Reactive and unreactive trajectories ==

{| class="wikitable" border="1"
|+
! p1/ g.mol-1.pm.fs-1 !! p2/ g.mol-1.pm.fs-1 !! Etot !! Reactive? !! Description of the dynamics !! Illustration of the trajectory
|-
| -2.56 || -5.1 || -414.280 || Yes || A approaches BC which has no oscillatory behaviour. A collides with BC and reaction occurs, a new molecule AB forms and it oscillates. C dissociates. || [[File: Contour_plot_for_first_set.png| 200px]]
|-
| -3.1 || -4.1 || -420.077 || No || A approches BC which possesses oscillatory behaviour. A collides with BC and no reaction occurs. BC continues to oscillate. || [[File: Contour_plot_for_second_set_yqc01506162.png | 200px]]
|-
| -3.1 || -5.1 || -413.977 || Yes || A approaches BC which oscillates slowly. A collides with BC and reaction occurs, a new molecule AB and it oscillates. C dissociates.|| [[File: Contour_plot_for_third_set.png | 200px]]
|-
| -5.1 || -10.1 || -357.277 || No || A approaches BC which doesn't oscillate. Barrier recrossing occurs in which the system crosses the transition state region. A bond between AB forms but the system reverts back to the molecule BC.|| [[File: Contour_plot_for_fourth_set.png | 200px]]
|-
| -5.1 || -10.6 || -349.477 || Yes || || [[File: Contour_plot_for_fifth_set.png | 200px]]
|}

One can conclude from the table that higher absolute p1 induces higher frequency vibrations and higher absolute p2 makes trajectories more reactive.

== Transition State Theory ==

The three key assumptions transition state theory takes cause the variation of estimated reaction rate values from experimental values. The first assumption which states all trajectories with KE>Ea are reactive overestimate the reaction rate since in reality, not all of them are reactive. The second assumption which states the transition states are in quasi equilibrium with.... The third assumption which states quantum tunneling is not to be considered underestimates the reaction rate since in reality quantum tunneling occurs.

= Exercise 2: F-H-H system =

== PES Inspection ==

F + H2 is exothermic and H + HF is endothermic. H-F has higher bond enthalpy(higher bond strength) than H-H. In F+ H2, more energy is released to form H-F than required to break H-H. In H + HF, more energy is required to break H-F than released to form H-H.

The approximate position of transition state is r1=181 pm, r2=74.49 pm.

Ea for F + H2 is 1.119 kJ mol-1. Ea for H + HF is 126.423 kJ mol-1.

== Reaction dynamics ==

The potential energy released is converted to vibrational energy which can be experimentally confirmed by IR.

The reaction is more efficient with a higher proportion of vibrational energy. According to Polanyi's empirical rules, vibrational energy is more efficient in promoting a reaction with a late transition state meanwhile translational energy is more efficient in promoting a reaction with early transition state.

2020-05-21T11:49:01Z

Yqc18: