MRD:Safe2
Molecular Reaction Dynamics
Exercise 1: H + H2 System
Dynamics From the Transition State Region
The transition state is defined as a saddle point where there is both a maximum and minimum depending upon the direction it is viewed from. At the transition state, the maximum and minimum will have differentials equal to zero. By taking the second partial derivative, we may then identify whether this point is a maximum or minimum. The potential energy surface diagram below illustrates how potential energy varies with interatomic distance between A, B and C. It may be seen that there is both a maximum and minimum as indicated by the curvature of the surface plot. Based on the surface plot, it may be observed that there is a greater curvature for points at the maximum in comparison to those at the minimum. This is due to the nature of the intrinsic chemical properties of the molecules in question.
Paste two views of the potential energy surface
Trajectories from r1 = r2
The best determined estimate of the transition state position (rts) was found to be 0.909. An initial estimate of 0.91 was found via the contour plot which showed that all atoms were at equal distance from one another and not falling off the ridge. By then establishing a plot of intermolecular distance against time, it was found that movement of atoms with time was little. Measurements up to a time of 1 second showed that the atoms did not fall off the ridge. However, extending this time to 5 seconds proved the opposite and thus accuracy was increased to a maximum of 0.909.
Calculating the Reaction Path
Calculation of the reaction path via a dynamic calculation setup results in a wavy line as shown in figure x. On the other hand, calculation via MEP results in a straight line. The MEP calculation produces a straight line as the velocity always resets to zero in each time step.
If an initial condition of r1 = rts and r2 = rts + 0.01 was instead used ie values reversed then the reverse of the graphs above would be shown. These graphs are shown below:
As shown by the distance-time graph, the A-B and A-C distance increase with time whilst the B-C distance remains relatively constant where the atoms do not move away from one another. Additionally, the graph indicates that the A-B distance is approximately 10 whilst the A-C distance is 0.75.
Setting the initial condition instead to r1 = rts and r2 = rts + 0.01, the B-C distance would instead increase with time and the A-B distance remain relatively constant.
Stuck on this bit
Reactive and Unreactive Trajectories
Initial Positions r1 = 0.74 and r2 = 2.0 are kept constant throughout
- For the initial positions r1 = 0.74 and r2 = 2.0, run trajectories with the following momenta combination and complete the table.
| p1 | p2 | Etot | Reactive? | Description of the dynamics | Graph Number |
|---|---|---|---|---|---|
| -1.25 | -2.5 | -99.02 | Reactive | Atom C closes towards A-B which then breaks and results in formation of a B-C bond. | 1 |
| -1.5 | -2.0 | -100.46 | Un-Reactive | Atom C closes towards A-B but does not have sufficient momentum to break the A-B bond. Thus it draws away from the A-B which remains intact. | 2 |
| -1.5 | -2.5 | -98.96 | Reactive | Atom C closes towards A-B just in the same pathway as Graph 1, however in this instance atom c has less energy. As a result, the time taken to reach the transition state and consequently react with it is greater | 3 |
| -2.5 | -5.0 | -84.96 | Un-Reactive | 4 | |
| -2.5 | -5.2 | -81.80 | Reactive | Atom C approaches the A-B bond and results in oscillation of the A-B but the A-B bond reforms. Momentum of Atom C however is much greater and therefore results in breakage of the A-B bond and consequent formation of the B-C bond | 5 |
Transition State Theory
Transition State Theory (TST)