2020-05-14T15:08:08Z

Rgf18: /* Transition State */

==Molecular Reaction Dynamics for Triatomic Systems==

==H + H2 systems==

===Potential Energy Surface Plots and Transition States===

A potential energy surface maps the progress of a reaction as a function of rAB and rBC. The trajectory of the reaction is the relative positions of the atoms at each instant in time, and shows how these relative positions lead to a change in potential energy of the system. The trajectory is displayed as a black line on the plots. The transition state is displayed as a saddle point on a potential energy surface, and is defined as the maximum on the minimum energy path. The reactants and products form minima on the minimum energy path due to there being no unfavorable interactions between H and H2, however when the atom approaches H2 they begin to repel each other, increasing the potential energy. The maximum repulsion is reached at the transition state. The transition state is mathematically defined as:∂V(rAB)/∂rAB=∂V(rBC)/∂rBC=0. It can be distinguished from a local minimum of the potential energy surface as ∂V2(rAB)/∂rAB2 > 0, since it is a minimum point, and ∂V2(rBC)/∂rBC2 < 0, since it is a maximum point.

[[File:TS_surface3_RGF.png|thumb|500px|center|Figure 1: A surface plot showing the transition state as the maximum of the minimum energy path.]]

===Estimating the Transition State Position===

[[File:TS_IDvT1_RGF.png|thumb|500px|center|Figure 2: An internuclear distance against time graph for H + H2.]]

Since the potential energy surface for the H + H2 system is symmetric, the transition state is when the distances between AB and BC are equal. Figure 2 allows this distance to be estimated at 85 - 95 pm. The initial conditions were set to p1 = p2 = 0.0 g.mol-1.pm.fs-1 and rAB = rBC. Different distance values were tested until the internuclear distance against time graph had a gradient of zero, and the animation showed the system undergoing a periodic symmetric vibration. This gave the estimate of the transition state position, rts, to be equal to 90.8 pm. Giving the energy at the transition state to be -415.4 kJ.mol-1.

[[File:TS_INvT2_RGF.png|thumb|500px|center|Figure 3: An internuclear distance against time graph showing the transition state position to be equal to 90.8 pm.]]

===Reaction Path===

The MEP (minimum energy path) calculates the reaction path by using a trajectory that has the particles moving infinitely slowly. It does this by resetting the momenta to zero in each time step, this causes the MEP calculation to follow the valley floor throughout the whole reaction. In the dynamic calculations, the particles have a momentum that causes an oscillating nature, where the energy is continually switching from potential to kinetic energy. This can be seen in the wavy nature of the trajectory as it continually goes through peaks and troughs of potential energy. The dynamic calculation is more realistic as atoms have a mass and their motion will be inertial.

The initial conditions were set to slightly displace the transition state towards the products and with an initial momenta of zero.

[[File:MEP_RGF.png|thumb|500px|center|Figure 4: MEP calculation for trajectory.]]
[[File:dynamic_RGF.png|thumb|500px|center|Figure 5: Dynamic calculation for trajectory.]]

===Reactive and Unreactive Trajectories===

Setting the initial conditions to rAB=74 pm and rBC= 200 pm, different values for momenta were tested to see if higher kinetic energy guaranteed a reactive trajectory.

{| class="wikitable" border="1"
|-
!p1 / g.mol-1.pm.fm-1 !! p2 / g.mol-1.pm.fm-1 !! Etot / kJ.mol-1 !! Reactive? !! Description of the dynamics !! Illustration of the trajectory
|-
| -2.56
| -5.1
| -414.3
| Yes
| Hc approaches Ha-Hb (which doesn't oscillate due to the relatively low momentum for p1) and has sufficient energy in the correct modes to overcome the activation energy, forming Hb-Hc. The two products move away from each other and Hb-Hc oscillates due to p2 having sufficient momentum.
|[[File:-2.56_RGF.png|450px|center]]
|-
| -3.1
| -4.1
| -420.1
| No
| Hc approaches Ha-Hb (which oscillates), but Hc has insufficient energy in the correct modes, causing an unreactive trajectory.
|[[File:3.1_RGF.png|450px|center]]
|-
| -3.1
| -5.1
| -414.0
| Yes
| This reaction follows a similar trajectory to the first reaction. However, due to the increased momentum of p1, Ha-Hb oscillates while it approaches Hc.
| [[File:3.1(2)_RGF.png|450px|center]]
|-
| -5.1
| -10.1
| -357.3
| No
| Hc approaches Ha-Hb and has sufficient energy to overcome the activation energy, and cross the transition state. Due to the high momentum of p2, Hb-Hc is oscillating with high kinetic energy, so as the two particles begin to translate away from each other, a second transition state is crossed and Ha-Hb reforms. Resulting in no reaction being observed.
| [[File:5.1_RGF.png|450px|center]]
|-
|-
| -5.1
| -10.6
| -349.5
| Yes
| Hc approaches Ha-Hb and has sufficient energy to overcome the activation energy, and cross the transition state. Due to the high momentum of p2, Hb-Hc is oscillating with high kinetic energy, so as the two particles begin to translate away from each other, a second transition state is crossed and Ha-Hb reforms. A third transition state is crossed due to the high energy oscillations, meaning Hb-Hc forms as the product. So this reaction passes the transition state three times, resulting in a reactive trajectory.
| [[File:5.1(2)_RGF.png|450px|center]]
|}

===Transition State Theory===

Transition state theory (TST) rationalises a reaction as the minimum energy path from the reactants to the products, passing through an energy maxima, which represents the transition state. TST makes many assumptions which affects its reaction rate when compared to experimental rates.

• TST considers the system classically, it is described by a trajectory with a velocity and not a wavefunction. In our model for our potential energy surface, our trajectory is described by a momentum (velocity x mass), so is treated classically.

• Since the system is classical, quantum tunneling is ignored. This will lead to TST giving an underestimation of the rate, as a classical view won't allow molecules with insufficient energy to overcome the activation energy by tunneling through the potential barrier.

• The kinetic energy along the reaction coordinate follows the Boltzmann distribution.

• TST states that all trajectories with a kinetic energy larger than the activation energy will be reactive, and that every time the transition state is crossed products are formed. This assumption is proved wrong by Figure 5, as it shows that reactants can cross the transition state forming products, and then these products can pass back through the transition state reforming the reactants. This will lead to an overestimation in the TST reaction rate.

[[File:5.1_RGF.png|500px|center|thumb|Figure 6: Contour plot showing that not all transition state crossings result in a reactive trajectory]]

Quantum tunneling contributes a relatively low amount to the rate of reaction when compared to the fact that not all transition state crossings form products. Therefore, TST leads to an overestimation of the rate when compared to experimental rates.

==F - H - H system==

===Potential Energy Surface===

The initial conditions were set up so atoms A=F, B=H and C=H. This produced a potential energy surface for which at a large BC distance HF + H would form, and at large AB distance F + H2 would form. From Figure 7, you can see that the potential energy at large AB distance is more positive than at large BC distance. Therefore, HF + H is at a lower energy than F + H2.

HF + H -> F + H2 Endothermic

F + H2 -> HF + H Exothermic

[[File:FH2_1_RGF.png|500px|center|thumb|Figure 7: Surface plot of F - H - H system]]

===Transition State===

This energy surface isn't symmetrical, so the two r values can't just be set to the same value to predict the transition state. The transition state must be estimated through its definition, the maxima on the minimum energy curve, via the identification of a saddle point. The Hammond postulate states that for an endothermic reaction (HF + H -> F + H2) the transition state will resemble the products, due to it being a late transition state. Therefore, the H2 distance was set to the bond distance of 74.5 pm, and different distances between F and H (the AB distance) were tested until the internuclear distance-time graph had a gradient of zero. The transition state point can be seen on Figure 7 as the black dot at rHH = 74.5 pm and rHF = 182 pm. Giving the energy at the transition state to be -434.0 kJ.mol-1.

[[File:FH2_2_RGF.png|500px|center|thumb|Figure 8: Internuclear distance-time graph showing the transition state. ]]

===Activation Energy===

Activation energy is the energy at the transition state

MRD:RGF

2020-05-14T15:07:44Z

2020-05-14T14:37:38Z

Rgf18: /* Transition State */