MRD:fzm18
H-H-H system
This section focuses on the dynamics of a H1 + H2-H3 system, where the aim is to form a new H1-H2 bond. Let us first consider the reaction path. In the system, H1, H2 and H3 are respectively referred to A, B and C.
Locating the transition state
The transition state (TS) can be mathematically defined as ∂V/∂r1 = ∂V/∂r2 = 0. Graphically, the locus of the transition state can be apprehended as the saddle point on the potential energy surface (PES) plot.
Physically, this means that the Transition state is a form on inert state, where a particle cannot acquire momentum if it has no momentum at this point. The plot of distances vs time below shows the internuclear distances variation of a H-H-H system with no momentum in the transition state. In this example, the transition state was found was found by varying the internuclear distances until the atoms stopped oscillating, at rAB = rBC = 90.75 pm.
Calculating the reaction path
The reaction path is defined by the minimum energy path (mep) and is the fastest path a reaction can take. In this simulation, the momenta are constantly reset at 0 g.mol-1.pm.fs-1. This means that the motions are entirely defined driven by Coulombic interactions. Hence, after reaching a certain distance, the atoms reach a stable state and do not drift further away, as they would in classical dynamics theory.
Analyzing trajectories at rAB = rTS + δ, rBC = rTS
The graphs show contour plots of the potential energy surface for a near-transition state system rAB = 91.75 pm, rBC = 90.75 pm, system A) in MEP and Dynamics simulations. The black trail reflects the trajectory of particle A, as it travels endlessly (dynamics) or until it exhausts the available electrostatic potential energy.
As rAB > rBC= rTS, the system tend to revert back to its initial form of H1 + H2-H3. However, note that in the opposite situation, where rAB = 90.75 pm, rBC = 91.75 pm (system B), the system will more likely tend to a new configuration : H1-H2 + H3. The surface plots show the reaction path as a black trail in both cases, rAB > rBC and rBC > rAB.
It is interesting to note that both systems have the same energy, and same the same variations of internuclear distances variations throughout time. The curves below show the plots of Energy (kJ.mol-1) against time (fs) and internuclear distances (pm) against time (fs) for the H1-H2 + H3 system.
Another important point of discussion is the reversibility of the system. The reversibility of the system can be measured by considering the path that would follow the system given that the initial positions correspond to the final position of system B, and the momenta are the opposite of the final momenta of the system above (system C). Applying such conditions to a Dynamics simulation, we can observe the system going back to its initial positions. : rAB = 90.75 pm, rBC = 91.75 pm, and their momenta will revert back to approximately p = 0 g.mol-1.pm.fs-1, suspend its motion, then reasonably will follow its primary trajectory. Qualitatively, The system takest fs to travel from its initial to final state, and reciprocally.Below is plotted the internuclear distances vs time of system C, reverting to system B, then back to system C.
Reactive and unreactive trajectories
Let us focus on the conditions required to make a collision reactive. The table displayed below shows examples of atoms at rAB = 230 pm and rBC=74 pm, having different relative momenta and subsequently different reactivity.
| p1/ g.mol-1.pm.fs-1 | p2/ g.mol-1.pm.fs-1 | Etot (kJ.mol-1) | Reactive? | Description of the dynamics | Illustration of the trajectory (internuclear distances against time) |
|---|---|---|---|---|---|
| -2.56 | -5.1 | -414.28 | Yes | Little oscillations throughout the reaction. C approaches the molecule, bonds to B as A drifts away. The new diatomic is oscillating and distances itself from A. | 
|
| -3.1 | -4.1 | -420.08 | No | Light oscillations in the diatomic A-B. rBC decreases, then increases with no collision between the atoms. There is no reaction, but is there no collision? Think about what 'collision' means - there must be some kind of repulsion, which is clearly present. Fdp18 (talk) 09:11, 9 May 2020 (BST) | 
|
| -3.1 | -5.1 | -413.98 | Yes | Little oscillations. C approaches the molecule, bonds to B as A drifts away. The new diatomic is oscillating and distances itself from A | 
|
| -5.1 | -10.1 | -357.27 | No | Strong oscillations. C approaches the diatomic, bonds with B, A distances itself slightly then reverts to its initial position, forms a new bond with B as C drifts away in the opposite direction | 
|
| -5.1 | -10.6 | -349.48 | Yes | Strong oscillations. C approaches the diatomic, bons with B. A distances itself then nears B to form the TS (AB=BC) again, then drifts away as B-C oscillates | 
|
The above results suggest that there is a threshold that needs to be bypassed in order for a reaction to take place. From the data, it seems this threshold lies around E ≈ -415 kJ.mol-1. However, this simulation applies classical mechanics and does not account for effects such as quantum tunelling; the TST predictions for the reaction rates are likely to be lower than the experimental values.
F-H-H system
Bond energy
In this section, we study the dynamics of a F-H-H system. In this context, F, H1 and H2 will respectively be referred to as A, B and C. By inspecting the Potential Energy Surface Plot, two low energy paths can be determined: along the AB axis (i.e. the H-F diatomic) and along the BC (H-H diatomic) axis, shown in the PES plot below. The first path is lower in energy than the second one, hence it can be concluded that the formation of H-F + H is exothermic, whilst the formation of H-H + F is endothermic. This implies that the bond strength of H-F is higher than that of H-H – respectively E ≈ 550 kJ.mol-1 and E ≈ 435 kJ.mol-1. This is consistent with the fact that the H-F bond is strengthened by the dipole moment due to the fluoride, therefore requiring more energy to break, and is supported by literature values.[1]
Transition state
Locating the transition state
Applying an analogous a method to the one used previously and by taking into account Hammond's postulate : "If two states, as, for example, a transition state and an unstable intermediate, occur consecutively during a reaction process and have nearly the same energy content, their interconversion will involve only a small reorganization of the molecular structures." [2]; the transition state can be found to be located at rAB = 181 pm and rBC = 74 pm. Its position is highlighted by a black dot on the surface plot below.
Activation energy
The respective energies of each state are : EH-F = -560.70 kJ.mol-1; EH-H = -435.10 kJ.mol-1; ETS = -433.98 kJ.mol-1. Hence the activation energies for the formation of the H-H and H-F bonds are, respectively : Ea = 126.72 kJ.mol-1 and Ea = 1.12 kJ.mol-1.