DY:01359531

Molecular Reaction Dynamics

H+H₂ System

The experiment is analysed under the condition:

reaction condition

distance	momentum
rab =0.74	pab =0
rbc =2.30	pbc =-2.7

Fig 1.trajectory where y-axis=U and x-axis=L.

Transition state Definition

Define the following factors: L=length of the linearly placed hydrogen= r_ab +r_bc S=difference between r_ab and r_bc = r_ab -r_bc

On the potential energy surface, the transition state is the saddle point, which is defined by

∂U/∂L=0 ; ∂U/∂L₂>0

∂U/∂S=0 ; ∂U/∂S₂<0

Fig 2.trajectory where y-axis=U and x-axis=S.

From Figure 1., the transition state must lie on the line which moves through the lowest energy surface shown on the graph, which in this case is the reaction path, the Bold Black line.

As for a Local Minimum:

∂U/∂L=0 ; ∂U/∂L₂>0

∂U/∂S=0 ; ∂U/∂S₂>0

From Figure 2., there are several turning points. However, the transition state is the point at the middle where S=0.This is because it is a symmetric reaction, which means that at the transition state r_ab =r_bc . Any other turning points are known as local minimum points. Reason for the reaction pathway to vibrate along the potential surface is due to vibration energy.

Transition State Position

Fig 3. Internuclear Distances VS Time Plot

Using the same parameters as above, a Internuclear Distances VS Time graph has been plotted where the transition state is shown as the intercept of the blue and orange line.

Therefore, A B and C are equally separated.

The parameters are then set to:

reaction condition for TS position

distance	momentum
rab =1.20	pab =0
rbc =1.20	pbc =0

These parameters are set because the saddle point must satisfy r_ab =r_bc .

The energy surface diagram is then analysed by MEP and the data are exported as Excel.

Since TS has the lowest potential energy,searching for the lowest V would give a corresponding distance:

rab =rbc =rts =0.908 Å

MEP and Dynamic Trajectory

Fig 3. calculated by MEP

reaction condition for MEP analysis

distance	momentum
rab =0.908	pab =0
rbc =0.918	pbc =0

Both MEP and Dynamic calculation methods have been used to generate the Internuclear Distance VS Time plot.

Fig 4. calculated by dynamic

As can be seen from Fig 3. and Fig 4., the distance of B-C fluctuates after t=0.4 min for dynamic calculation while it is a straight line calculated by MEP.

Dynamic calculation has included the motion of the molecule, which means the fluctuation of the blue line is caused by the actual vibration of H₂ molecule. MEP, however, only shows the lowest energy pathway.

Another difference shown on the graph is the gradient of the orange and green line. Shown on Fig 3. The gradient is decreasing with respect to time, this is because as the distance between H₂ and H atom increases, the repulsion between them decreases, and therefore, from MEP calculation, it would show that the rate of separation is decreasing.

Fig 5. Dynamic calculation for energy

Fig 6. MEP calculation for energy

By comparing Fig 5. and Fig 6. it can be clearly seen that Dynamic calculation is based on the conservation of energy, while MEP only consider stating the minimum energy pathway.

Reactive and unreactive trajectory

pAB	pBC	Etot	Reactive?	Description of the dynamics
-1.25	-2.5	-99.0184	Yes	Vibrating H2 molecule approaches HC atom and successfully interact, HBC molecule vibrates away
-1.5	-2.0	-100.456	No	Vibrating H2 molecule approaches HC atom but does not have enough energy to overcome the transition state, the reaction does't proceed and HAB molecule vibrates back
-1.5	-2.5	-98.9549	Yes	Vibrating H2 molecule approaches HC atom and successfully interact, however, at a faster rate
-2.5	-5.0	-84.9557	No	Vibrating H2 molecule approaches HC atom, reactants have crossed the reaction barrier, transition state is reached where HB atom 'bounces' between HA and HC, however, HAB molecule is reformed and vibrates back
-2.5	-5.2	-84.4160	Yes	Vibrating H2 molecule approaches HC atom, reactants have crossed the reaction barrier, transition state is reached where HB atom 'bounces' between HA and HC, finally, HBC molecule is formed and vibrates away.

From these figures, it can be concluded that

1)for reaction to occur, molecules must posses energy higher than the reaction barrier.

2)for a reaction, higher energy the molecule possess, faster the rate of reaction

3)even if the molecules have energy higher than the transition state, the reaction still might not occur.

Fig 7. p_AB=-1.25 p_BC=-2.5

Fig 9. p_AB=-1.50 p_BC=-2.5

Fig 8. p_AB=-1.50 p_BC=-2.0

Fig 11. p_AB=-2.50 p_BC=-5.2

Fig 10. p_AB=-2.50 p_BC=-5.0

Transition State Theory

Assumption made:

Two basic assumptions:

1.Nuclear motion is stationary compared to electronic motion due to the large difference in mass (equivalent to the Born-Oppenheimer approximation)

2.Reactant molecules are distributed according to the Boltzmann distribution.

Three unique assumptions:

3.If the reactants passes the transition state in the direction of forming product, they can not turn back and reform reactants.

4.In the transition state, the motion of molecules in the direction of reaction coordinates can be separated from the other motions, it is not effected by the other motions and can be treated classically as Translation.

5.Assumption 2 still holds even in the absence of an equilibrium between reactants and products.

As shown on Fig 10., even if the reactants have passed through the transition state, it still reforms back to the reactant, this is against assumption 3.

F - H - H system

PES inspections

Fig 12. contour plot for F + H₂ → HF + H

Fig 13. contour plot for H + HF → F + H₂

Reaction	Reaction type	Transition state position
F + H2 → HF + H	Exothermic	rFH = 1.813 , rHH = 0.744
H + HF → F + H2	Endothermic	rHH = 1.813 , rHF = 0.744

This graph illustrates the reaction type. As can be seen, F + H₂ on the left is higher in energy than HF + H on the right. This indicates if F + H₂ → HF + H then energy will be released while if H + HF → F + H₂ energy is required.

For F + H₂ → HF + H reaction, the H-H bond is broken while a new H-F bond is formed.

Since H-F (565 Kj/moL) bond has a larger bond energy than H-H (432 Kj/moL), it suggests that this reaction is exothermic

As for the H + HF → F + H₂ reaction, it is the opposite, H-F bond is broken and H-H bond is formed and it is deduced to be endothermic.

Activation energy

The activation energy for this reaction F + H₂ → HF + H is: E=0.20 Kcal/moL

The activation energy for this reaction H + HF → F + H₂ is: E=30 Kcal/moL

Fig 14. activation energy for F + H₂ → HF + H

Fig 15. activation energy for H + HF → F + H₂

Reaction Dynamics

Fig 17. momentum VS time graph

Fig 18. Energy Vs Time Graph

condition for reactive F+H₂ reaction

distance	momentum
rFH = 2.0	pFH = -0.5
rHH = 0.8	pHH = -1

Fig 16. contour graph proofing the success of reaction F+H₂= FH+H under condition r_FH = 2.0, p_FH = -0.5, r_HH = 0.80 and p_HH = -1

As shown on Fig 18., the potential energy decreases as the kinetic energy increases, the increase in KE corresponds to the heat generated during this exothermic reaction.

Polanyi's empirical rules

contour graphs

reaction	Low Vibration High Translation	High Vibration Low Translation
F + H2 = FH + H	rFH= 2.0 ; rHH= 0.74 ; pFH= -0.5 ; pHH= -2.0	rFH= 2.0 ; rHH= 1.4 ; pFH= -0.1 ; pHH= -0.1
FH + H = F + H2	rHH= 1.8 ; rFH= 0.74 ; pHH= -2.0 ; pFH= -1.0	rHH= 1.8 ; rFH= 1.30 ; pHH= -0.5 ; pFH= -0.5

F + H₂ = FH + H is an exothermic reaction, the transition state resembles the reactants and therefore, has a early barrier.

FH + H = F + H₂ is an endothermic reaction, the transition state resembles the products and hence, possesses a late barrier.

Polanyi's rules states that:

1) Translation energy is most effective for crossing early barriers

2) Vibration energy is most effective for crossing late barriers

Therefore, it can be predicted that F + H₂ = FH + H can occur under Low Vibration High Translation and FH + H = F + H₂ under High Vibration Low Translation. This corresponds to the experimental data shown above.