Henry Rickard, Yr 2. Submission for Molecular Reaction Dynamics 2nd year computational lab.

Questions in bold quoted directly from the provided [[CP3MD|script]].

== Exercise 1: H + H2 system ==
'''On a potential energy surface diagram, how is the transition state mathematically defined? How can the transition state be identified, and how can it be distinguished from a local minimum of the potential energy surface?'''

On the potential energy surface, the transition state is defined as the maximum on the minimum energy path across the surface. Being a point that is a local maximum on one axis and a local minimum on another, it can be described as a saddle point on the surface, distinguished from a local minimum by the fact it is also a maximum in one direction on the surface.

'''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.'''

'''rts''' ≈ {0.908,0.908}

Setting parameters "AB distance = 1, BC distance = 1"
[[File:MRD-hmr17-symmetrical internucDist time.png|thumb|Internuclear Distance over Time for the symmetrically oscillating triatomic system.]]
Exporting the data and finding the state of maximum total kinetic energy (minimum potential in the path the system oscillates along) gives a small range of time-steps with different AB/BC distances due to rounding. Taking the mean of these distances gives 0.908 Å for the distance between each pair of atoms in the transition state, and hence the stated '''rts''' value. This concurs with the internuclear distance-time graph, where it is visible that the average for the A-C distance is slightly over 1.8 Å.

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

The ''mep'' is a smooth line following the floor of the potential valley, whereas the trajectory taking account of dynamics shows the slight oscillation induced by the specified offset from the transition state. This makes sense, because the ''mep ''calculation does not conserve kinetic energy and aims to reach a minimum of potential (the valley floor), whereas the dynamics simulation does conserve the introduced small difference in total energy (from minimum potential), and shows the resulting periodic gain and loss of potential energy due to the osciallation of particles.

'''Complete the table above by adding the total energy, whether the trajectory is reactive or unreactive, and provide a plot of the trajectory and a small description for what happens along the trajectory. What can you conclude from the table?'''

All with initial conditions:

AB Distance = 0.74

BC Distance = 2.0
{| class="wikitable"
!p(AB)
!p(BC)
!Etot
!Reactive?
!Description of the dynamics
!Illustration of the trajectory
|-
|<nowiki>-1.25</nowiki>
|<nowiki>-2.5</nowiki>
|<nowiki>-99.019</nowiki>
|Yes
|(AB) pair approach C, slow almost to a stop as A-B distance increase and B-C distance decreases. A then moves away from (BC), latter vibrating slightly.
|[[File:MRD-hmr17 React1.png|frameless]]
|-
|<nowiki>-1.5</nowiki>
|<nowiki>-2.0</nowiki>
|<nowiki>-100.456</nowiki>
|No
|(AB) pair approach C, slowing down. Slow almost to stop, then (AB) and C both reverse direction and move away from each other.
|[[File:MRD-hmr17 Nonreact.png|frameless]]
|-
|<nowiki>-1.5</nowiki>
|<nowiki>-2.5</nowiki>
|<nowiki>-98.956</nowiki>
|Yes
|Very similar to the first reaction in this table.
|[[File:MRD-hmr17 React2.png|frameless]]
|-
|<nowiki>-2.5</nowiki>
|<nowiki>-5.0</nowiki>
|<nowiki>-84.956</nowiki>
|No
|(AB) approach C quickly. B immediately associates with C, A moves away, but slows. (BC) oscillate strongly once, while A reverses direction. B then re-associates with A, and (AB) and C seperate again. (AB) vibrating strongly.
|[[File:MRD-hmr17 Barrier recross 1.png|frameless]]
|-
|<nowiki>-2.5</nowiki>
|<nowiki>-5.2</nowiki>
|<nowiki>-83.416</nowiki>
|Yes
|Similar to above, but after B re-associating with A, it also oscillates strongly once before B associates with C again. A and (BC) seperate, with (BC) vibrating strongly.
|[[File:MRD-hmr17 Barrier recross 2.png|frameless]]
|}

'''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?'''

Transition State Theory (TST) assumes that in a chemical reaction, the trajectory described by the movements of the reacting species passes through a saddle point of potential energy (or the small region surrounding it) between the local minima describing the reactant and product states. The reactants must have enough total energy to overcome the barrier created by this saddle point for the interaction to be reactive and reach the product state.

For the first three reaction trajectories above, this works relatively well: the 1st and 3rd apparently have a greater (more positive) total energy than is required to reach the transition state and can reach the products (with "left over" energy remaining as vibrational energy in the diatomic product), while the 2nd does not have enough energy and so can not pass through the transition state to the products. For these, it may be expected that TST predictions should match well with experiment. However, for the 4th and 5th trajectories the theory is less successful. While they apparently do have enough energy to reach the transition state, they in fact surpass it and the trajectory is much less predictable. This is observed as a complicated pattern of the products reforming and breaking up again. This could be caused by these trajectories breaking the assumption of the reaction passing through the saddle point region of potential, and so the simple TST is less useful. For these reactions with a large amount of excess energy, TST-based predicitons will likely agreely more poorly with experiement.

= Exercise 2: F-H-H system'''<nowiki/>''' =
'''By inspecting the potential energy surfaces, classify the F + H2 and H + HF reactions according to their energetics (endothermic or exothermic). How does this relate to the bond strength of the chemical species involved?'''

Given that the F + H2 state is lower in energy than the H + HF state, the direction:

F + H2→ H + HF would be exothermic, and the reverse will be endothermic.

This corresponds to the H-F
bond being stronger than the H-H bond, with the stabilisation gained from
forming the former being greater than that lost by breaking the latter.

'''Locate the approximate
position of the transition state.'''

A=B=H, C=F

Determined by'' ''analysing ''mep''s to find the 'direction' in which a pair of positions will result in (with the point
seperating forward and reverse being the transition state), and the point approaching by the ''mep'' as part of the aforementioned analysis from a position of slightly elevated potential near it.

Distance AB = 0.7449 Å

Distance BC = 1.8094 Å

'''Report the activation energy for both reactions.'''

Describing F + H2 → H + HF as the forward reaction:

Ets= -103.75 units

E(H+HF) = -133.92 units (Left equilibrating for 7500 steps at 0.02 units per step)

E(F+H2) = -104.01 units (Left equilibrating for 100000 steps at 0.02 units per step)

E(forward activation) = 0.26 units

E(reverse activation) = 30.17 units

Calculating by performing an ''mep'' from a position slightly offset from the transition state on the side of the minimum being examined, and leaving to ‘equilibrate’ for a significant amount
of time. The reactant required a very large amount of time to do so because the potential gradient between that local minimum and the saddle point (the reactants and the transition state) was extremely low.

'''In light of the fact that energy is conserved, discuss the mechanism of release of the reaction energy. Explain how this could be confirmed experimentally.'''

The difference in potential between the reactants and products is conserved as a change in kinetic energy
of the product species; this kinetic energy may be either vibrational or translational. In bulk matter, this would be distributed throughout the reaction mixture as heat.

Experimentally, this could be examined by measuring the temperature increase in the gas-phase reaction of fluorine radicals and hydrogen. The practical aspects of such an experiment would require further investigation than is performed here, but a possible method may involve photolytically producing the radical species
as the gas was slowly introduced to a hydrogen atmosphere.

MRD:hmr17

2019-05-16T17:52:58Z

Hmr17:

File:MRD-hmr17 Barrier recross 2.png

2019-05-16T14:09:12Z

Hmr17: Contour plot of potential for net reactive trajectory showing barrier recrossing, for exercise 1 of year 2 molecular reaction dyanamics computational lab. H Rickard, 16/05/19

Contour plot of potential for net reactive trajectory showing barrier recrossing, for exercise 1 of year 2 molecular reaction dyanamics computational lab. H Rickard, 16/05/19

File:MRD-hmr17 Barrier recross 1.png

2019-05-16T14:07:50Z

Hmr17: Contour plot of potential for net non-reactive trajectory showing barrier recrossing, for exercise 1 of year 2 molecular reaction dyanamics computational lab. H Rickard, 16/05/19

Contour plot of potential for net non-reactive trajectory showing barrier recrossing, for exercise 1 of year 2 molecular reaction dyanamics computational lab. H Rickard, 16/05/19

File:MRD-hmr17 React2.png

2019-05-10T13:12:40Z

Hmr17: Images of charge distributions on tetramethylammonium and tetramethylphosphonium ions. Generated by Gaussian (NBO charges), H Rickard, 10/05/19.

Images of charge distributions on tetramethylammonium and tetramethylphosphonium ions. Generated by Gaussian (NBO charges), H Rickard, 10/05/19.

Y2 Inorg Comp Lab:hmr17

2019-05-10T12:56:05Z

Hmr17: /* Project */

Y2 Inorg Comp Lab:hmr17

2019-05-10T12:55:02Z

Hmr17: /* N(CH4)3+ */

File:Y2ICL-Hmr17 tetramethylammonium freq 631dp summary table.png

2019-05-10T12:51:28Z

2019-05-10T12:12:57Z

Hmr17: Summary table generated by Gaussian for tetramethylphosphonium ion, for year 2 inorganic computational lab. H Rickard, 10/5/19

Summary table generated by Gaussian for tetramethylphosphonium ion, for year 2 inorganic computational lab. H Rickard, 10/5/19

Y2 Inorg Comp Lab:hmr17

2019-05-10T12:10:45Z

Hmr17: /* P(CH4)3+ */

File:Y2ICL-HMR17 P(CH3)4 FREQ 631DP.LOG

2019-05-10T12:10:11Z

Hmr17: Log file generated by Gaussian for tetramethylphophonium ion, for year 2 inorganic computational lab. H Rickard, 10/5/19

Log file generated by Gaussian for tetramethylphophonium ion, for year 2 inorganic computational lab. H Rickard, 10/5/19

Y2 Inorg Comp Lab:hmr17

2019-05-10T12:08:26Z

Hmr17: /* P(CH4)3+ */

Y2 Inorg Comp Lab:hmr17

2019-05-10T12:08:15Z

Hmr17: /* N(CH4)3+ */

Y2 Inorg Comp Lab:hmr17

2019-05-10T12:08:01Z

Hmr17: /* N(CH4)3+ */

Y2 Inorg Comp Lab:hmr17

2019-05-10T12:06:48Z

Hmr17: