Zl6217

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 could be recognised as the maximum on the minimum energy path. Therefore, in terms of mathematical expression, transition state is the AB and BC when ∂V(r_i)/∂r_i=0 , in other words, (∂V(AB)/∂AB)*(∂V(BC)/∂BC) = 0.
The second derivatives could be calculated: if ∂V(r_i)²/∂r_i² > 0; the trajectory is at a local minimum of the potential energy surface; if ∂V(r_i)²/∂r_i² < 0, it's in a transition state.

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.

First an original Interdistance vs Time was observed. The transition state lies when AB=BC, in this case when AB vs Time intersects with BC vs Time, which is around 0.38.
Several test of different trajectories when AB=BC=0.37/0.38/0.39/0.40 were carried out to observe the animations and internuclear distance vs Time diagrams: the transition state was confirmed to be AB=BC=0.38 since in this case, atoms stop oscillating and the atoms distance increase to infinite, which makes reaction slides to product.
Furthermore, when AB=BC=0.38, the vibration reaches its minimal which means the kinetic energy is the minimum and the potential energy reaches its maximum.
TWO PICTURES

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

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?

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?