MRD:thl3318
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 can be mathematically defined as a saddle point (which is also an unstable equilibrium). It can be identified by determining the point where the partial derivatives of the function potential with respect to the internuclear distances are equal to 0.
and 
However, simply looking at the results for the first derivative does not give any information with regards to whether the point is a local minimum, a local maximum, or a saddle point. Analyzing the 2nd derivative then allows for the determination of whether the point is a saddle point. This can be done using the following equation:
Report your best estimate of the transition state position (rts) and explain your reasoning illustrating it with a “Internuclear Distances vs Time” plot for a relevant trajectory.
My best estimate for the transition state position is at time=20fs when the A-B distance is equal to the B-C distance. The A-B and B-C distance at this point is determined to be 90.8pm. This point in the "Internuclear Distance vs Time" plot can be rationed as the transition state position
Comment on how the mep and the trajectory you just calculated differ.
The mep and dynamics trajectory differ in many different ways. The first difference is the time it takes for the reaction to take place (in this case, for the distance to follow to the valley floor of the potential graph). In the mep trajectory, it takes around 30 steps (15 fs) for the reaction to proceed whereas in the dynamics trajectory this number is around 140 fs. The second difference is that the internuclear distance between the H2 molecule and the lone H atom increases logarithmically in the mep calculation but increases linearly in the dynamics calculation.
Complete the table below 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?
| 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 KJ.mol-1 | Yes | ||
| -3.1 | -4.1 | -420.077 KJ.mol-1 | No | ||
| -3.1 | -5.1 | -413.997 KJ.mol-1 | Yes | ||
| -5.1 | -10.1 | -357.277 KJ.mol-1 | Yes | ||
| -5.1 | -10.6 | -349.477 KJ.mol-1 | Yes |
From the table above, I can conclude that whether or not a trajectory results in a reaction depends on the momentum p2. Changing the momentum p1 does not affect the result of the trajectory but if momentum p2 is not great enough the result will be unreactive.
Given the results you have obtained, how will Transition State Theory predictions for reaction rate values compare with experimental values?
EXERCISE 2: F + H2 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?
The F + H2 reaction is exothermic whereas the H + HF reaction is endothermic. This means that the H-F bond strength is greater than the H-H bond strength and is lower in energy.
Locate the approximate position of the transition state. H-H 77pm H-F 105pm
Because the activation energy for one of the reactions is so small, it is not easy to locate the transition state immediately. Use the Hammond postulate to guide your search.
Report the activation energy for both reactions.
You will be able to report a reasonable estimate by performing a mep (with a sufficient number of steps) from a structure neighbouring the transition state, and choosing to plot the appropriate quantity as a function of "time".
