MRD:lhl17

Exercise 1: H + H₂ system

On a potential energy surface diagram, how is the transition state mathematically defined? How can the transition state be identified, and how can it be distinguished from a local minimum of the potential energy surface?

On a potential energy surface diagram, the transition state is mathematically defined as the point at which ∂V(r)/∂r =0 is true. This can be described as the maximum point on the minimum reactive trajectory (minimum energy path linking reactants and products).

The transition state appears as a saddle point in the potential energy surface (PES) - i.e. in one direction, the point is a maximum point in the graph and in the other direction, it is a minimum. See Figure 1. 

Report your best estimate of the transition state position (r_ts) and explain your reasoning illustrating it with a “Internuclear Distances vs Time” plot for a relevant trajectory.

Comment on how the mep and the trajectory you just calculated differ.

	5000 steps

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
-3.1	-4.1	-420.077	No
-3.1	-5.1	-413.977	Yes
-5.1	-10.1	-357.277	No
-5.1	-10.6	-349.477	Yes

Complete the table above by adding the total energy, whether the trajectory is reactive or unreactive, and provide a plot of the trajectory and a small description for what happens along the trajectory. What can you conclude from the table?

Given the results you have obtained, how will Transition State Theory predictions for reaction rate values compare with experimental values?

Exercise 2: F - H - H system

By inspecting the potential energy surfaces, classify the F + H₂ and H + HF reactions according to their energetics (endothermic or exothermic). How does this relate to the bond strength of the chemical species involved?

Reaction	F + H2	H + HF
Type of reaction	Exothermic	Endothermic
TS	-433.981	As above
Reactiant Energy	energy graph straight	energy graph with step
Activation energy

Locate the approximate position of the transition state.

TS

Report the activation energy for both reactions.

In light of the fact that energy is conserved, discuss the mechanism of release of the reaction energy. Explain how this could be confirmed experimentally.

Contour plot		Momenta vs time

• Setup a calculation starting on the side of the reactants of F + H₂, at the bottom of the well r_HH = 74 pm, with a momentum p_FH = -1.0 g.mol^-1.pm.fs^-1, and explore several values of p_HH in the range -6.1 to 6.1 g.mol^-1.pm.fs^-1 (explore values also close to these limits). What do you observe? Note that we are putting a significant amount of energy (much more than the activation energy) into the system on the H - H vibration.

pHH/gmol-1pmfs-1	Relative trajectory	Contour plot
-6.1
-5
5
6

• For the same initial position, increase slightly the momentum p_FH = -1.6 g.mol^-1.pm.fs^-1, and considerably reduce the overall energy of the system by reducing the momentum p_HH = 0.2 g.mol^-1.pm.fs^-1. What do you observe now?

Contour	Momentum	Energy

Let us now focus on the reverse reaction, H + HF.

• Setup initial conditions starting at the bottom of the entry channel, with very low vibrational motion on on the H - F bond, and an arbitrarily high value of p_HH above the activation energy (an H atom colliding with a high kinetic energy).

• Try to obtain a reactive trajectory by decreasing the momentum of the incoming H atom and increasing the energy of the H - F vibration. (It may be difficult to find the initial conditions that generate a reactive trajectory for this reaction. Using the inversion of momentum procedure for a trajectory starting on the transition state can be useful in this case. Working on the Skew Plot framework could also be helpful.)

Discuss how the distribution of energy between different modes (translation and vibration) affect the efficiency of the reaction, and how this is influenced by the position of the transition state.

References

1. w
2. w