MRD:jkt115
EXERCISE 1: H + H2 system
Question 1
What value does the total 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.
The gradient when the potential energy surface is at a minimum or transition structure is zero. For a minimum, the particle will roll towards the same spot (minima) when displaced slightly to the left or right. However, for a transition structure, the particle will roll towards products or reactants depending on which direction it was displaced.
Question 2
Report your best estimate of the transition state position (rts) and explain your reasoning illustrating it with a “Internuclear Distances vs Time” screenshot for a relevant trajectory.
rts = 0.908 Å. This is because the internuclear distances remains approximately constant with zero initial momentum, meaning that it is at the minima of the ridge.
Question 3
Comment on how the mep and the trajectory you just calculated differ.
The internuclear distance in the calculated trajectory oscillates while the mep doesn't.
Question 4
Complete the table by adding a column reporting if the trajectory is reactive or unreactive. For each set of initial conditions, provide a screenshot of the trajectory and a small description for what happens along the trajectory.
| p1 | p2 | Result | Screenshot | Description |
|---|---|---|---|---|
| -1.25 | -2.5 | Reactive |  |
The particles has the minimal energy to overcome the activation barrier and proceeds to form the products. |
| -1.5 | -2.0 | Unreactive |  |
The particles do not have enough kinetic energy to overcome the activation barrier and returns to reactants. |
| -1.5 | -2.5 | Reactive |  |
The particles has more than enough energy to overcome the activation barrier and proceeds to form the products. |
| -2.5 | -5.0 | Unreactive |  |
The particles has a lot of energy to go pass the transition state to form the products but returns back to reactants. This is an example of barrier recrossing. |
| -2.5 | -5.2 | Reactive |  |
The particles have enough energy to go pass the transition state but goes back over the barrier then back over the barrier again to form the products. |
Question 5
State what are the main assumptions of Transition State Theory. Given the results you have obtained, how will Transition State Theory predictions for reaction rate values compare with experimental values?
The main assumption of transition state theory is that it assumes that all atoms behave according to classic mechanics therefore a reaction won't happen unless there is enough energy to form the transition structure. The transition state theory should be able to predict experimental values quite accurately for large scale reactions. This is because quantum mechanics will only have a larger effect on small scale reactions.
EXERCISE 2: F - H - H system
Question 1
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?
F + H2 is exothermic and H + HF is endothermic. For the F + H2 reaction, the H-F bond is very strong compared to H-H therefore more energy will be released when the H-F bond forms than is required to break the H-H bond and vice versa.
Question 2
Locate the approximate position of the transition state.
H-H = 0.745 Å
H-F = 1.815 Å
Question 3
Report the activation energy for both reactions.
For F + H2: Activation energy = 30.6 kcal/mol
For H + HF: Activation energy = 0.6 kcal/mol
Question 4
In light of the fact that energy is conserved, discuss the mechanism of release of the reaction energy. How could this be confirmed experimentally?
For F + H2, the reaction energy that is released will turn into vibrational energy of the H-F bond. This can be confirmed experimentally using IR.
Question 5
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.
Polyani's empirical rules states that the translational energy is more effective in increasing the efficiency of a reaction with early transition state than vibrational energy and vice versa.
For F + H2:
This reaction has an early transition state. As we can see from the figures below, the reaction doesn't proceed to products when we set a large initial vibrational energy (2.5) and a small initial translational energy (-0.5). When the initial translational energy is increased slightly to -1, the reactions is able to proceed to products even when vibrational energy has decreased to 1.
For H + HF:
This reaction has a late transition state. As we can see from the figures below, the reaction doesn't proceed to products when we set a large initial translational energy (1.5) and a small initial vibrational energy (-0.1). When the initial vibrational energy is increased slightly to -0.8, the reactions is able to proceed to products even when translational energy has decreased to 0.1.
