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Me1218:

2020-05-15T15:03:15Z

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2020-05-15T14:28:08Z

Me1218:

== Molecular Reaction Dynamics Lab 2020 ==

=== Exercise 1 - (H + H2 System) ===
The transition state on a potential energy surface plot is defined as the maxima of the minimum energy path where the gradient of the potential (derivative of potential over distances = ∂V('''ri''')/∂'''ri''') is equal to zero. For a symmetrical system like H + H2, the transition state lies where rAB=rBC. Therefore, one way the transition state can be found is by generating a plot of internuclear distance against time for the reaction. The intersection between the lines of AB and BC distance over time gives the transition state with intermediate and equal bond lengths.

The transition state is a saddle point on the potential energy surface unlike any other local minima. It is a maximum of the minimum energy path of the reaction but the potential energy is at a minimum for the plot orthogonal to the minimum energy path (dividing surface). This has been illustrated in figures 1, 2 and 3.
[[File:Dividing surface me1218.png|thumb|Figure 1: Contour plot showing the dividing surface (initial distances rAB and rBC set to 230 pm and no initial momenta) running through the transition state. ]]
[[File:Surface pot max me1218 2.png|thumb|Figure 2: 3D surface plot showing the maximum of the transition state.]]
[[File:Surface pot min me1218 2.png|thumb|Figure 3: 3D surface plot showing the potential energy minimum of the transition state along the dividing surface.]]
''Table 1: Initial conditions tested in the software.''
{| class="wikitable"
!
!Distance (r) [pm]
!Momentum (p) [g.mol-1.pm.fs-1]
|-
|AB
|230
|<nowiki>-5.2</nowiki>
|-
|BC
|74
|0
|}
By initially using the intial conditions in table 1, a plot of internuclear distances against time was generated (figure 4). The intersection between the AB plot and BC plot (at the transition state bond lengths) was found to be at an internuclear distance value of around 91 pm (can be seen from zoomed figure 4 in figure 5).
[[File:Internuclear Distances vs time me1218 1.png|thumb|400x400px|Figure 4: Plot of internuclear distance against time of H + H2 system when using conditions in table 1.|none]]

[[File:Internuclear Distances vs time me1218 1 zoom.png|thumb|399x399px|Figure 5: Zoomed in plot of internuclear distance against time for H + H2 system using conditions in table 1. The intersection shows the transition state of the system. |none]]

The software was then set up using the conditions in table 2 to confirm whether the transition state was at around 91 pm.

''Table 2: Conditions for transition state in the software.''
{| class="wikitable"
!
!Distance (r) [pm]
!Momentum (p) [g.mol-1.pm.fs-1]
|-
|AB
|91
|0
|-
|BC
|91
|0
|}
As shown from the contour plot generated from these conditions (figure 6), these conditions resulted in no overall trajectory towards products nor reactants. This is because there is no gradient directly at right angles to the transition state. ##There is only some oscillation of the system on the point as shown by the animation in figure 7.## Figure 8 is a plot of internuclear distance against time at this transition state. The oscillation in bond distances can be seen but there is no overall increase/ decrease in bond lengths between hydrogen's A, B and C. Looking at the initial geometry information in the control panel, the initial forces along AB and BC are around 0 kJ mol-1 (-0.037 kJ mol-1) showing that this is around the transition state.

The distance r at this transition state between A and B and between B and C can be called rts.
[[File:Contour plot at 91 - transition state me1218.png|thumb|Figure 6: Contour plot showing the transition state of the system. |none]]
[[File:Animation at 91 - transition state me1218.png|thumb|Figure 7: Animation showing the slight oscillations about the transition state of the system. |none]]
[[File:Internuclear Distances vs time me1218 2 ts.png|none|thumb|Figure 8: Plot of internuclear distance against time of H + H2 system when using conditions in table 2 (at transition state).]]
A minimum energy path (MEP) calculation was compared against a dynamics calculation (which, unlike an MEP, takes into account the vibrational motions of the system) using conditions where rAB = rts and rBC = (rts+1 pm). In the MEP calculation, the system follows exactly the trough (minimum points) of the potential energy surface with a direct trajectory down to the products - see figure 9.

In the dynamics calculation model, the system oscillates up and down the sides of the valley travelling towards the products - the trajectory is much less direct than in the MEP model - see figure 10.

The MEP is calculated assuming infinitely slow movement of the system on the potential energy surface (where momentum = 0 at each step calculated). Therefore, the only thing that determines the trajectory is the potential energy given by the potential energy surface and not any vibrational motion.
{| class="wikitable"
!MEP
!Dynamics
|-
|[[File:Mep 1 me1218.png|thumb|Figure 9: Minimum energy path contour diagram of ...]]
|[[File:Mep dynamics 1 me1218.png|thumb|Figure 10: Dynamics model contour diagram of ... ]]
|}
In figure 10, the vibrations (oscillations up and down the potential energy surface 'valleys') can be observed unlike in the MEP in figure 9. The MEP trajectory follows exactly the minimum points of the potential energy surface down from near the transition state to the products.

''Table 3: Comparing dynamics of system given an initial position of rAB=200 pm and rBC=74 pm and the following values of p1 and p2''.
{| class="wikitable"
!Eg.
!pBC (g.mol-1.pm.fs-1)
!pAB (g.mol-1.pm.fs-1)
!Etot (kJ mol-1)
!Reactive?
!Description of the dynamics
!Illustration of the trajectory
|-
|(1)
|<nowiki>-2.56</nowiki>
|<nowiki>-5.1</nowiki>
|<nowiki>-414.280</nowiki>
|Yes
|Small amount of intramolecular vibration in the products.

Trajectory of the system goes over the transition state ('saddle point') and down towards the products. Reaction proceeds.
|[[File:Contour plot table 1 me1218.png|thumb]]
|-
|(2)
|<nowiki>-3.1</nowiki>
|<nowiki>-4.1</nowiki>
|<nowiki>-420.077</nowiki>
|No
|More intramolecular vibration in reactants than in example (1).

Trajectory of the system doesn't surmount the transition state energy maximum and so the reaction doesn't proceed to products. Instead, the system returns to reactants.
|[[File:Contour plot table 2 me1218.png|thumb]]
|-
|(3)
|<nowiki>-3.1</nowiki>
|<nowiki>-5.1</nowiki>
|<nowiki>-413.977</nowiki>
|Yes
|Some vibrational motion in the reactants - results in more vibrational motion in the products.
Trajectory of the system does surmount the transition state maximum and reaction proceeds towards the products with large amount of intramolecular vibrational energy.
|[[File:Contour plot table 3 me1218.png|thumb]]
|-
|(4)
|<nowiki>-5.1</nowiki>
|<nowiki>-10.1</nowiki>
|<nowiki>-357.277</nowiki>
|No
|System initially has a lot of energy - high pAB and pBC (momenta). Trajectory runs over transition state region heading towards the products but instead 'rolls' back over the transition state region back towards the reactants (reaction doesn't proceed). This is called 'barrier recrossing'.
|[[File:Contour plot table 4 me1218.png|thumb]]
|-
|(5)
|<nowiki>-5.1</nowiki>
|<nowiki>-10.6</nowiki>
|<nowiki>-349.477</nowiki>
|Yes
|Similarly, the system initially has a lot of energy (momenta) and trajectory runs over the transition state. The system runs back towards reactants for a bit but then surmounts the transition state once again and heads towards the products. Reaction does proceed.
|[[File:Contour plot table 5 me1218.png|thumb]]
|}
From the table it can be said that it is not in fact the Etot nor the combined magnitude of the initial momenta that determines if the reaction will proceed or not but rather ### the ... must be <nowiki>''</nowiki>aligned??'###. For example (4), even with total energy (Etot) of -357.277 kJ mol-1 (quite high relative to others in the table) and an initial momenta of AB roughly double that of example (3), the reaction does not proceed. Here barrier recrossing can be observed. This is when the system crosses the transition state region again - the bonds in the product forms but doesn't go fully to the products before returning back to the reactants (via the transition state again). This can be shown in the figure # animation.

In transition state theory, one assumption made is that when kinetic energy is greater than the activation energy and the transition state is reached, the system always goes on to form products. Once the transition state has been reached, the system cannot go back to form reactants. There are, however, exceptions to this assumption as shown in example (4) in table 3. There is barrier recrossing whereby the transition state is reached but the system returns to the reactants instead of forming products.

In terms of the rate of reaction, the transition state theory overestimates the rate of reaction. This is because, hypothetically, if 1 out of 10 trajectories was like example (4) in table 3 and underwent barrier recrossing, there would be 1 out of 10 trajectories which transition state theory assumed to proceed to products when in reality it didn't.

=== Exercise 2 - (F + H2 System) ===
The transitional state point was found by looking for a 'saddle-point' in the surface plot of the system. The value for rBC was set in the centre of the minimum in the reactants channel##?. Then, with values of momenta set equal to 0, the value of rAB was varied between ... and ... . Values of rAB below the transition state value result in an overall trajectory towards the products whilst values about the transition state result in an overall trajectory back to the reactants. By varying rAB and observing the overall trajectory, the transition state was found. This location was confirmed by taking note of the forces values in the initial geometry information panel at this transition state. These values were around 0 kJ mol-1 pm-1 along both AB and BC.

For the reaction of F with H2, the transition state is located at around the following: rAB = 181.15 pm, rBC = 74.5 pm.

This transition state is closer to the reactants side of the potential energy surface and so the transition state can be said (by Hammond's postulate) to be 'reactant like'. Therefore, the transition state is early and the reaction is exothermic.

From the initial potential energies of the transition state and the reactants, the activation energy of the F + H2 reaction was found to be 696 J mol-1
{| class="wikitable"
! colspan="3" |System F + H2. Early ('reactant-like') transition state determined to be at rAB = 181.15 pm and rBC = 74.5 pm.
|-
|[[File:F H2 ts contour me1218.png|thumb|Figure #: Contour diagram of the F + H2 reaction - showing the early (reactant-like) transition state.]]
|[[File:F H2 ts surface 1 me1218.png|thumb|Figure #: Surface plot of the F + H2 reaction showing the transition state at the 'saddle point'.]]
|[[File:F H2 ts surface 2 me1218.png|thumb|Figure #: Rotated surface plot of the F + H2 reaction showing the transition state at the 'saddle point'.]]
|}

For the reaction of H with HF, the transition state is located at around the following: rAB = 74.5 pm, rBC = 181.15 pm.

This transition state is closer to the products side of the potential energy surface and so the transition state can be said (by Hammond's postule) to be 'product like'. Therefore, the transition state is late and the reaction is endothermic.

From the initial potential energies of the transition state and the reactants, the activation energy of the H + HF reaction was found to be 126.327 KJ mol-1 (126,327 J mol-1).
{| class="wikitable"
! colspan="3" |System H + HF. Late ('reactant-like') transition state determined to be at rAB = 74.5 pm and rBC = 181.15 pm.
|-
|[[File:H HF ts contour me1218.png|thumb|Figure #: Contour diagram of the H + HF reaction - showing the late (product-like) transition state. ]]
|[[File:H HF ts surface 1 me1218.png|thumb|Figure #: Surface plot of the H + HF reaction showing the transition state at the 'saddle point'.]]
|[[File:H HF ts surface 2 me1218.png|thumb|Figure #: Rotated surface plot of the H + HF reaction showing the transition state at the 'saddle point'.]]
|}

The activation energy for the reaction of H + HF is much higher than that of the reaction of F and H2.

Since the F + H2 reaction is exothermic, there is more energy released to form the H-F bond than energy required to break the H-H bond. Also, as the H + HF reaction is endothermic, there is more energy required to break the HF bond than energy given back upon formation of the H-H bond. Therefore, it can be deduced that the H-F bond is stronger than the H-H bond.

An reactive trajectory of the F + H2 system was set up using the conditions in table #.

''Table 4: Conditions used for reactive F + H2 trajectory.''
{| class="wikitable"
!
!Distance (r) [pm]
!Momentum (p) [g.mol-1.pm.fs-1]
|-
|AB
|225
|<nowiki>-2.0</nowiki>
|-
|BC
|74.5
|<nowiki>-0.5</nowiki>
|}
A contour diagram of this reactive trajectory is shown in figure #.
[[File:Reactive contour F H2 me1218.png|none|thumb|Figure #: Contour plot showing a reactive trajectory of F + H2 system with conditions in table #. ]]
[[File:Reactive momenta F H2 me1218.png|none|thumb|Figure #: Plot of momentum against time for a reactive trajectory of the F + H2 system with conditions in table #. ]]From these plots using the reactive trajectory conditions, the mechanism of release of energy can be illustrated.

From the contour plot in figure # and the graph of momentum against time, it can be seen that the reactants start off with little vibrational energy. After surmounting the transition state, the products have much more vibrational energy (shown by the oscillations in both figures).

<nowiki>###</nowiki>The mechanism for energy release??#

<nowiki>###</nowiki>This can be measured experimentally using a technique called ... ### using IR spectroscopy???

Using these plots, Polanyi's empirical rules can be illustrated...

Total energy is conserved in the process of moving from reactants to products. The distribution of this energy, however, in different modes - vibrational and translational can change.

For the F + H2 system, an exothermic system with an early transition state.

It is therefore more efficient to start with little vibrational energy and high translational energy in the reactants.

This can be demonstrated in real life observations too - an early transition state gives greater vibrational energy out in the products - this kinetic energy increase is observed as a temperature increase upon formation of products. Hence exothermic reactions 'give out heat'.

For the H + HF system, an endothermic system with a late transition state, it is more efficient to start with high vibrational energy in the reactants so that the transition state bond length can be reached.