MRD:ql2817
Contents
- 1 Question 1
- 1.1 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?
- 1.2 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.
- 1.3 Comment on how the mep and the trajectory you just calculated differ.
- 1.4 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?
- 1.5 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?
Question 1
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.It is located at the saddle point in the potential energy surface diagram, which defined as : ∂V(ri)/∂ri=0 and H < 0, where H = frr(r0,V0)fVV(r0,V0)−f2rV(r0,V0) .
The transition state is the specific combination of internuclear distances AB and BC at which the trajectory is a point on the contour plot.
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.
When r(AB)=r(BC)=0.907 Å, p1 = p2 = 0.0, the transition state occurs. The internuclear distance vs time graph gives a relatively straight line which indicates a constant distance.
Comment on how the mep and the trajectory you just calculated differ.
The mep trajectory keeps the potential energy at the minimum in a straight line, whereas the dynamic trajectory is wavy.
r1 = 0.907, r2 = 0.917
Molecules and atome moving away from each other.
Setup a calculation where the initial positions correspond to the final positions of the trajectory you calculated above, the same final momenta values but with their signs reversed.
r1 = rts+δ, r2 = rts
final values of the positions r1(t) = 3.45, r2(t) = 0.72 and the average momenta p1(t) = -1.45, p2(t) = -2.48 at large t.
The molecule and the atom moving close together instead of moving apart.
