MRD:01340064
Comp Lab
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?
The transition state is defined as the maximum on the minimum energy path linking reactants and the products.
The point on the potential energy surface can be identified as where the gradient of the potential is zero, and the energy goes down most steeply along the minimum energy path linking reactants and products.
At the transition state, if you change the geometry by a small amount in the direction of the products it will roll towards the products. The same thing would happen for for the reactants. Therefore another method of locating the transition state would be to start trajectories near it and see whether they roll to the reactants or products.
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 of the transition state position is 0.908 A
The first figure shows the internuclear distances vs time plot when r1=r2=0.908. The second figure shows the system rolling towards the reactants after a minor geometry change of 0.001 A towards the reactants.
Comment on how the mep and the trajectory you just calculated differ.
The mep follows the valley floor to H1+ H2-H3 without any indication of vibration in the molecule, the dynamic trajectory shows a more realistic account of the motion of the atoms as it shows the vibration in the molecule.
Complete the table 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 | p2 | Etot | Reactive? | Description of the dynamics |
|---|---|---|---|---|
| -1.25 | -2.5 | -98.956 | Yes | The trajectory runs through the transition state to the products |
| -1.5 | -2.0 | -100.456 | No | The trajectory stops before reaching the transition state |
| -1.5 | -2.5 | -98.956 | Yes | The trajectory runs through the transition state to the products |
| -2.5 | -5.0 | -84.956 | No | Unreactive trajectory -the system crosses the transition state region, the bond in the product forms but then reverts back to the reactants. |
| -2.5 | -5.2 | -83.416 | Yes | The trajectory bounces at the barrier first and then runs through the transition state to the products |
Not all trajectories starting with the same positions but with higher values of momenta are reactive.
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?
Transition state theory assumptions:
- The reactants are in constant equilibrium with the transition state.
- The energy follows a Boltzmann distribution.
- Once reactants become the transition state, the reactants do not regenerate.
Experimental values will have lower reaction rate values.
EXERCISE 2
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?
It can be seen that the reaction of H2 + F is exothermic as the products are lower in energy than the reactants in the surface plot. It can also therefore be seen that the reverse reaction of HF + H is endothermic. This is due to the fact that the HF bond is much stronger than the HH bond, because of the difference in electronegativity of H and F. The HF bond is has an ionic contribution which makes it stronger, causing more energy to be released when HF forms.
