=H-H H=

====What value do the different components of the gradient of the potential energy surface have at a minimum and at a transition structure?====

A minimum on the a potential energy surface will have a negative gradient on one side and a positive gradient on the opposite, or in other words a positive curvature, in the direction of one of the axis. Along the other axis it will have a curvature equal to or greater than 0.
A transition structure will have a positive curvature perpendicular to a negative curvature. These curvatures will not fall parallel to the axis as they did with the minimum structure. They will be relatively close to a 45 degree angle to each axis as that bisects the minimum structures that it is transitioning between

====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.====

The best estimate that was reached was a rts = 0.907744 Å. This value was reached by using an initial estimate of .9 Å and the evaluating the distance versus time plot oscillation to find an estimate of the midpoint between the minimum and maximum of the oscillation, as the vibration would be about the true transition state position with an amplitude that was the distance the original estimate was away from the true value. This produced a more accurate estimate and this process was repeated 3 additional times.

{| class="wikitable"
|+
|-
| Full Table || Zoomed on bond oscillation || Input r1 = r2
|-
|[[File:MC 0.9 Transition state position graph.PNG| 400px]]
|[[File:MC 0.9 Transition state position graph zoom.PNG| 400px]]
|0.90 Å
|-
|[[File:MC 0.907744 Transition state position graph.PNG| 400px]]
|[[File:MC 0.907744 Transition state position graph zoom.PNG| 400px]]
|0.907744 Å
|}

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

The MEP plot that was calculated had no vibrational motion in the resulting bond while the inertial calculation did have this motion. This is because the inertial calculation takes into the inertial forces of H2 and H3 have as they accelerate towards and then continue past the ideal bond length. The MEP equation simply has the atoms fall together converging towards the ideal bond length.

====Complete the table by adding a column with the total energy, and another column reporting if the trajectory is reactive or unreactive.====

{| class="wikitable"
|+
|-
| p1 || p2 || Total Energy || Reactivity || Plot + Description
|-
| -1.25
| -2.5
| -99.018
| Reactive
|[[File:MC -1.25 -2.5 plot.PNG|300px]]
In this case there is twice as much momentum in the free atom than the original bond. The overall energy is enough to overcome the transition state energy (ie activation energy). This case will serve as a basis for the following descriptions.
|-
| -1.5
| -2
| -100.456
| Unreactive
|[[File:MC -1.5 -2 plot.PNG|300px]]
The initial momenta are closer to being equal, but the total energy is lowered and does not exceed the activation energy. This means the activation energy is somewhere in the of -99 to -100.5. This leads to the colliding atom to remove absorb some of the vibration energy before being expelled at a higher velocity then when it first approached.
|-
| -1.5
| -2.5
| -98.956
| Reactive
|[[File:MC -1.5 -2.5 plot.PNG|300px]]
The total energy in this scenario is more positive than the first case and therefore has more energy than the activation energy. The resulting bond has more vibrational energy and the ejected atom has less momentum than the colliding atom original atom did.
|-
| -2.5
| -5
| -84.956
| Unreactive
|[[File:MC -2.5 -5 plot.PNG|300px]]
Initially the momenta are different by a factor of 2 as in the first example, but the total energy is much higher. While the total energy in the system is much more positive than the activation energy determined previously, it does not lead to a reaction. This can only be explained by the reaction path crossing the barrier an even number of times, 2 in this case.
|-
| -2.5
| -5.2
| -83.956
| Reactive
|[[File:MC -2.5 -5.2 plot.PNG|300px]]
Here there is also a barrier recrossing as in the previous scenario, but in this case there is an odd number of crossings, 3. Therefore it can be seen that at high total energies, above the activation energy, there are more complex effects than simply energy being more than the activation energy and the trajectory incidence on the transition saddle can have an effect on reactivity.
|}

====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?====

The main assumptions of Transition State Theory are that the atoms behave classical mechanics, that all intermediates are long lived, and that a reaction will cross the lowest energy surface saddle given it has enough energy to overcome the activation energy. The assumption that is relevant to the results that we have obtained is that it will cross the lowest saddle point given enough energy. This assumption is tested in rigor mathematically in our test and is proven to be not entirely true. We found that there are more complex effects, such as barrier recrossing, than simply is activation energy overcome. These effects can lead to a reaction that TST would predict to occur to not occur, leading to a lower reaction rate experimentally than TST would predict.

MRD:MC47161

2018-05-10T16:17:47Z

Mc4716: