Bl17182
Exercise 1: H-H-H system
1. Transition state is defined as the derivative of potential energy at a local maximum. To distinguish from a local minimum, you can look at the second derivative of the point, if it is smaller than zero it is a maximum.
2. The best estimate of the transition state position is 90.82 pm. According to the assumptions of transition state theory, motion along the reaction coordinate may be separated from the other motions and treated classically as a translation. (reference) Internuclear distance is only affected by force. As H + H2 surface is symmetric, the transition state must have r1 = r2 which refers to rAB = rBC. The internuclear distance is constant in time because there is no force at transition state.
(Animation1.png)
3. (Animation2.png)(Animation3.png) The graph of mep are smooth line while all graph of trajectory occur as oscillation.
This is because dynamic calculation taken atomic mass and phase conditions into account. Therefore, the inertial motion causes in oscillation on the graph.
As the transition state theory is based on the postulate that the rate of transformation of systems from reactants to products is given solely by passpage in the forward direction from coordinates r1>r2 to r2>r1. (reference) By changing the initial conditions to r1 = rts and r2 = rts+1 pm, the graph is showing the internuclear distance from before forming H1-H2 to after breaking
4.
| 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 | Yes | The reaction curve smoothly passes through transition state then form products. | (Animation 7) |
| -3.1 | -4.1 | -420.077 | No | The graph shows that the AB distance decreases then bounces back without reaching transition state region. This suggests that there is no product formed. | (8) |
| -3.1 | -5.1 | -413.977 | Yes | The reaction curve smoothly passes through transition state then form products. | (9) |
| -5.1 | -10.1 | -357.277 | No | The curve line in the plot shows that some products has been formed as it passes through the transition state region, but immediately react backwards to reform reactants. | (10) |
| -5.1 | -10.6 | -349.477 | Yes | The curve bounces forwards and backwards in transition state region then go to product region representing the presence of reaction products. | (11) |
In conclusion, the reactivity of a reaction is not related to its total energy. Although some systems have enough energy to cross the activation barrier. The reactants can be reformed by recrossing the barrier.
5. Firstly, the idea of barrier recrossing breaks the assumption of Transition State Theory (TST). Thus, there may be some systems that are nonreactive while TST predicts them being reactive.
Secondly, energy is considered classic in TST while are quantized in molecular level. This will lead to the mis-calculation in partition functions and activation energy of the system, which will affect the value of reaction rates.
Exercise 2: F-H-H system
1.