https://chemwiki.ch.ic.ac.uk/api.php?action=feedcontributions&feedformat=atom&user=Mp5318ChemWiki - User contributions [en]2026-04-04T10:33:15ZUser contributionsMediaWiki 1.43.0https://chemwiki.ch.ic.ac.uk/index.php?title=Minqi5318&diff=805948Minqi53182020-05-15T22:26:30Z<p>Mp5318: </p>
<hr />
<div>== Molecular Reaction Dynamics: Application to Triatomic systems ==<br />
<br />
==H +H<sub>1</sub> System ==<br />
<br />
=== Dynamic from transition state region===<br />
<br />
====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?====<br />
<br />
The transition state is defined mathematically as the saddle point on the potential energy surface, where ∂V('''ri''')/∂'''ri'''=0 (the gradient of the potential is zero). At the transition state, the second derivative of potential with respect to q<sub>1</sub> is positive: ∂V<sup>2</sup>(q<sub>1</sub>)/∂q<sub>1</sub> > 0, indicating a minimum of the curve; the second derivative of potential with respect to q<sub>2</sub> is positive: ∂V<sup>2</sup>(q<sub>2</sub>)/∂q<sub>2</sub> < 0, indicating a maximum of the curve. The coincidence of a maximum and a minimum indicates saddle point on the potential energy surface. It can be identified through finding the maximum on the minimum energy path linking reactants and the products. The Transition State's energy goes down most steeply along the minimum energy path linking reactants and products c.f. local minimum of the potential energy surface. <ref name="surface" /><br />
<br />
====Report your best estimate of the transition state position (r<sub>ts</sub>) and explain your reasoning illustrating it with an “Internuclear Distances vs Time” plot for a relevant trajectory.====<br />
<br />
The best estemate of the transition state position r<sub>ts</sub> = 91 pm<br />
<br />
[[File:mp5318_Animation.png|thumb|centre|Internuclear Distances vs Time Plot when r<sub>ts</sub> = 91 pm.]]<br />
<br />
As shown in the ''Internuclear Distances vs Time Plot when r<sub>ts</sub> = 91 pm'' above, when r<sub>ts</sub> = 91 pm and p<sub>1</sub> p<sub>2</sub> = 0.0 g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>, internuclear distance reamain (almost) constant, which shows that the molecule does not vibrate and stayed stably at the transition state forever.<br />
<br />
====Comment on how the MEP and the trajectory you just calculated differ.====<br />
<br />
[[File:Mp5318 Surface Plot Dynamic.png|thumb|left|Surface Plot using Dynamic Calculation r<sub>1</sub>=92 pm, r<sub>2</sub>=91 pm]]<br />
<br />
[[File:Surface Plot MEP.png|thumb|centre|Surface Plot using MEP Calculation r<sub>1</sub>=92 pm, r<sub>2</sub>=91 pm]]<br />
<br />
<br clear=all><br />
When '''r<sub>1</sub>'''=92 pm, '''r<sub>2</sub>'''=91 pm, atoms A and B dissociates. Using MEP calculation, AB dissociates through the minimum energy pathway and the dissociation ceased at a displacement much smaller than using Dynamic calculation. In Dynamic trajectory, kinetic energy was acquired during the trajectory from potential energy, therefore encourage inertial motion to proceed. In addition, MEP Calculation does not take into account the momentum of the particles, all the momentums are assumed to be zero.<br />
<br />
When reversing '''r<sub>1</sub>''' and '''r<sub>2</sub>''', B and C dissociates while A and B sticks together. The final values of the positions are '''r<sub>1</sub>''' (73.81819562) '''r<sub>2</sub>''' (352.8544826) and '''p<sub>1</sub>''' (3.258858751) '''p<sub>2</sub>''' (5.06251673). <br />
<br />
When setting up a calculation where the initial positions correspond to the final positions of the trajectory above, the same final momenta values but with their signs reversed, the reaction trajectory travels back to the orginal position '''r<sub>1</sub>''' (91) and '''r<sub>2</sub>''' (92) with '''p<sub>1</sub>'''= '''p<sub>2</sub>'''= 0.<br />
<br />
===Reactive and Unreactive trajectories===<br />
<br />
{| class="wikitable" border="1"<br />
|+ initial positions '''r<sub>1</sub>''' (74 pm) '''r<sub>2</sub>''' (200 pm)<br />
! p<sub>1</sub> / g.mol<sup>-1</sup>.pm.fs<sup>-1</sup> !! p<sub>2</sub> / g.mol<sup>-1</sup>.pm.fs<sup>-1</sup> !! E<sub>tot</sub> kJ.mol<sub>-1</sub> !! Reactive? !! Description of the dunamics !! Illustration of the trajectory<br />
|-<br />
| -2.56 || -5.1 || -414.28 || Yes || A-B + C → A +B-C || [[File:Mp5318 t1.png|356px]]<br />
|-<br />
| -3.1 || -4.1 || -420.08 || No || A-B approaches C, but then leave without reaction occur || [[File:Mp5318 t2.png|356px]]<br />
|-<br />
| -3.1 || -5.1 || -413.98 || Yes || A-B + C → A +B-C || [[File:Mp5318 t3.png|356px]]<br />
|-<br />
| -5.1 || -10.1 || -357.28 || No || at TS region, strength of bondings A-B and B-C alternates, but eventually A-B leave intact (Barrier can be crossed, but then the system reverts back to the reactants) || [[File:Mp5318 t4.png|356px]]<br />
|-<br />
| -5.1 || -10.6 || -349.38 || Yes || A-B + C → A +B-C at TS region, strength of bonding A-B and N-C alternates, but new product formed eventually || [[File:Mp5318 t5.png|356px]]<br />
|}<br />
<br />
'''Conclusion: Reactants need to have a large enough ratio in the momentum to be reactive, ideally, p<sub>2</sub> : p<sub>1</sub> should be larger than 2 for the reactants to be reactive.'''<br />
<br />
===Transition State Theory===<br />
<br />
====Given the results you have obtained, how will Transition State Theory predictions for reaction rate values compare with experimental values?====<br />
<br />
Transition State Theory often overestimates the reaction rate, compared to the results we calculated. Transition State Theory assumed that once the reaction has passed the Transition state and reached the product, it would not travel back to cross the Transition State and reverse to the reactant side. However, the calculations above showed that in practice, products can still recross the energy barrier to go back to the reactants. Even though the Transition State Theory ignored the effect of quantum tunneling, it's a relatively small contribution to rate in this case (small MW for H<sub>2</sub>). Therefore Transition State Theory tends to overestimate reaction rate values compare with experimental values.<br />
<br />
==F-H-H System ==<br />
<br />
=== PES inspection===<br />
<br />
====By inspecting the potential energy surfaces, classify the F + H<sub>2</sub> and H + HF reactions according to their energetics (endothermic or exothermic). How does this relate to the bond strength of the chemical species involved?====<br />
<br />
[[File:Mp5318Surface Plot fh2.png|thumb|left|Potential Surface of F + H<sub>2</sub> Reaction]]<br />
<br />
<br clear=all><br />
<br />
F + H<sub>2</sub> Reaction is exothermic. We can see there is a decrease in energy as H-H bond distance increases while H-F bond distance decreases. The clear downhill of the reaction path indicated exothermic reaction. Bond strength of H-H is 432 kJ/mol, while H-F bond strength is 565 kJ/mol. <ref name="bond energy" /> Formation of H-F bond is preferred, as it would release more energy than the energy needed to break H-H bond. <br />
<br />
H + HF Reaction is endothermic. H-H bond formed is weaker than the H-F bond, therefore energy needed to cross the activation energy barrier — endothermic.<br />
<br />
According to Hammond Postulate, for an exothermic reaction, the TS resembles the reactants (early TS); for an endothermic reaction, the TS resembles the product (late TS). Therefore in this system, TS is very close to the H<sub>2</sub> + F side (H-F distance much longer than H-H distance).<br />
<br />
====Locate the approximate position of the transition state.====<br />
<br />
Position of the TS of H<sub>2</sub> + F Reaction: r<sub>H-H</sub>=74.5 pm; r<sub>H···F</sub>=181.1 pm; At the TS, potential energy = 433.980 kJ/mol<br />
<br />
[[File:Mp5318 TS hhf contour.png|thumb|left|TS of F + H<sub>2</sub> Reaction]]<br />
<br />
[[File:Mp5318distande hhf.png|thumb|centre|Intermolecular distance vs. Time at the TS of F + H<sub>2</sub> Reaction]]<br />
<br clear=all><br />
<br />
AB distance is the H-F distance, BC distance is the H-H distance.<br />
<br />
====Report the activation energy for both reactions.====<br />
In the form of HF + H, potential energy =- 560.642 kJ/mol<br />
In the form o H<sub>2</sub> + F, potential energy = -434.922 kJ/mol<br />
<br />
Therefore compared with the TS potential energy (-433.980 kJ/mol): for HF + H to reach the TS, the activation energy is 126.02 kJ/mol; for H<sub>2</sub> + F to reach the TS, the activation energy is 0.942 kJ/mol.<br />
<br />
===Reaction Dynamics===<br />
<br />
==== 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.====<br />
For the exothermic reaction, in this case, the F + H<sub>2</sub>, energy is released into vibrational energy of product HF. When F approaches H, the repulsion between H-H is released. The released repulsive energy pushes H towards H and produces H-F vibration. <ref name="surface" /><br />
<br />
This could be confirmed experimentally through Infrared Chemiluminescence. <ref name="Infrared Chemiluminescence" />The relative gain on many lines within several vibrational bands could be determined and hence direct measurements of the relative vibrational population in v = 0 can be obtained. We would, therefore, be able to see that the v=2 vibrational level is highly populated (strong peak at v = 2).<br />
<br />
We could also use chemical laser to characterise the HF laser produced. Most of the HF is formed in the v=2 state, thus, the reaction creates an absolute inversion between v=2, v=1, and v=0. The output spectra of pulsed HF lasers showed that more than 60% of the reaction energy is released as vibrational excitation of the HF. <ref name="laser" /><br />
<br />
====Discuss how the distribution of energy between different modes (translation and vibration) affect the efficiency of the reaction, and how this is influenced by the position of the transition state.====<br />
<br />
For H<sub>2</sub> + F system, translational energy is more effective for activating the reaction: Under the conditions illustrated by ''Picture 1'' below, activation barrier was easily crossed by applying translational energy, and the translational energy was converted into product's vibrational energy; c.f. under the conditions illustrated by ''Picture 2'', even when a large amount of vibrational energy was put into the system, the reactants remain unreactive. <br />
<br />
For HF + H system, vibrational energy is more effective for activating the reaction: Under the conditions illustrated by ''Picture 3'' below, activation barrier was easily crossed by applying vibrational energy.<br />
<br />
Translational energy is most effective for passage across an early TS, whereas reactant vibrational energy far in excess of the barrier height may be ineffective for reaction. Conversely, a late TS is best crossed by vibrational energy in the reactants. <ref name="surface" /><br />
<br />
{| class="wikitable" border="1"<br />
|+ distribution of energy under differnt initial conditions<br />
! H<sub>2</sub> + F system (Early TS) !! HF + H system (Late TS)<br />
|-<br />
| [[File: Mp5318 early TS trans.png|thumb|''Picture 1:'' r<sub>(H-H)</sub>=74pm, r<sub>H-F</sub>=200 pm; p<sub>(H-H)</sub>=0 g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>; p<sub>(H-F)</sub>=-1.0g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>]] || [[File: Mp5318 Late TS vib.png|thumb|''Picture 3: ''r<sub>(H-H)</sub>=180pm, r<sub>H-F</sub>=90 pm; p<sub>(H-H)</sub>=15 g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>; p<sub>(H-F)</sub>=-1.0g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>]]<br />
|-<br />
| [[File: Mp5318Early TS vib.png|thumb|''Picture 2:'' r<sub>(H-H)</sub>=74pm, r<sub>H-F</sub>=182 pm; p<sub>(H-H)</sub>=6 g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>; p<sub>(H-F)</sub>=-1.0g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>]] || [[File: Mp5318 late TS trans.png|thumb|''Picture 4:'' r<sub>(H-H)</sub>=180pm, r<sub>H-F</sub>=90 pm; p<sub>(H-H)</sub>=0 g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>; p<sub>(H-F)</sub>=-1.0g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>]]<br />
|}<br />
<br />
==Reference==<br />
<references><br />
<ref name="surface" > Laidler, Keith J., in Chemical kinetics, 3rd ed., New York ; London, Harper & Row, 1987 </ref><br />
<br />
<ref name="bond energy" > Carruth, Gorton, Ehrlich, Eugene. "Bond Energies." Volume Library. Ed. Carruth, Gorton. Vol 1. Tennessee: Southwestern, 2002. </ref><br />
<br />
<ref name="Infrared Chemiluminescence" > B. P. Levitt, ed. Physical Chemistry of Fast Reactions. Plenum Press, New York. SCHULZ, W. R., and LEROY, D. J. 1965. </ref><br />
<br />
<ref name ="laser"> C. Bradley Moore, Laser studies of vibrational energy transfer, Accounts of Chemical Research 1969 2 (4), 103-109 DOI: 10.1021/ar50016a002 </ref><br />
</references></div>Mp5318https://chemwiki.ch.ic.ac.uk/index.php?title=Minqi5318&diff=805946Minqi53182020-05-15T22:25:29Z<p>Mp5318: /* Reference */</p>
<hr />
<div>== Molecular Reaction Dynamics: Application to Triatomic systems ==<br />
<br />
==H +H<sub>1</sub> System ==<br />
<br />
=== Dynamic from transition state region===<br />
<br />
====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?====<br />
<br />
The transition state is defined mathematically as the saddle point on the potential energy surface, where ∂V('''ri''')/∂'''ri'''=0 (the gradient of the potential is zero). At the transition state, the second derivative of potential with respect to q<sub>1</sub> is positive: ∂V<sup>2</sup>(q<sub>1</sub>)/∂q<sub>1</sub> > 0, indicating a minimum of the curve; the second derivative of potential with respect to q<sub>2</sub> is positive: ∂V<sup>2</sup>(q<sub>2</sub>)/∂q<sub>2</sub> < 0, indicating a maximum of the curve. The coincidence of a maximum and a minimum indicates saddle point on the potential energy surface. It can be identified through finding the maximum on the minimum energy path linking reactants and the products. The Transition State's energy goes down most steeply along the minimum energy path linking reactants and products c.f. local minimum of the potential energy surface. <ref name="surface" /><br />
<br />
====Report your best estimate of the transition state position (r<sub>ts</sub>) and explain your reasoning illustrating it with an “Internuclear Distances vs Time” plot for a relevant trajectory.====<br />
<br />
The best estemate of the transition state position r<sub>ts</sub> = 91 pm<br />
<br />
[[File:mp5318_Animation.png|thumb|centre|Internuclear Distances vs Time Plot when r<sub>ts</sub> = 91 pm.]]<br />
<br />
As shown in the ''Internuclear Distances vs Time Plot when r<sub>ts</sub> = 91 pm'' above, when r<sub>ts</sub> = 91 pm and p<sub>1</sub> p<sub>2</sub> = 0.0 g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>, internuclear distance reamain (almost) constant, which shows that the molecule does not vibrate and stayed stably at the transition state forever.<br />
<br />
====Comment on how the MEP and the trajectory you just calculated differ.====<br />
<br />
[[File:Mp5318 Surface Plot Dynamic.png|thumb|left|Surface Plot using Dynamic Calculation r<sub>1</sub>=92 pm, r<sub>2</sub>=91 pm]]<br />
<br />
[[File:Surface Plot MEP.png|thumb|centre|Surface Plot using MEP Calculation r<sub>1</sub>=92 pm, r<sub>2</sub>=91 pm]]<br />
<br />
<br clear=all><br />
When '''r<sub>1</sub>'''=92 pm, '''r<sub>2</sub>'''=91 pm, atoms A and B dissociates. Using MEP calculation, AB dissociates through the minimum energy pathway and the dissociation ceased at a displacement much smaller than using Dynamic calculation. In Dynamic trajectory, kinetic energy was acquired during the trajectory from potential energy, therefore encourage inertial motion to proceed. In addition, MEP Calculation does not take into account the momentum of the particles, all the momentums are assumed to be zero.<br />
<br />
When reversing '''r<sub>1</sub>''' and '''r<sub>2</sub>''', B and C dissociates while A and B sticks together. The final values of the positions are '''r<sub>1</sub>''' (73.81819562) '''r<sub>2</sub>''' (352.8544826) and '''p<sub>1</sub>''' (3.258858751) '''p<sub>2</sub>''' (5.06251673). <br />
<br />
When setting up a calculation where the initial positions correspond to the final positions of the trajectory above, the same final momenta values but with their signs reversed, the reaction trajectory travels back to the orginal position '''r<sub>1</sub>''' (91) and '''r<sub>2</sub>''' (92) with '''p<sub>1</sub>'''= '''p<sub>2</sub>'''= 0.<br />
<br />
===Reactive and Unreactive trajectories===<br />
<br />
{| class="wikitable" border="1"<br />
|+ initial positions '''r<sub>1</sub>''' (74 pm) '''r<sub>2</sub>''' (200 pm)<br />
! p<sub>1</sub> / g.mol<sup>-1</sup>.pm.fs<sup>-1</sup> !! p<sub>2</sub> / g.mol<sup>-1</sup>.pm.fs<sup>-1</sup> !! E<sub>tot</sub> kJ.mol<sub>-1</sub> !! Reactive? !! Description of the dunamics !! Illustration of the trajectory<br />
|-<br />
| -2.56 || -5.1 || -414.28 || Yes || A-B + C → A +B-C || [[File:Mp5318 t1.png|356px]]<br />
|-<br />
| -3.1 || -4.1 || -420.08 || No || A-B approaches C, but then leave without reaction occur || [[File:Mp5318 t2.png|356px]]<br />
|-<br />
| -3.1 || -5.1 || -413.98 || Yes || A-B + C → A +B-C || [[File:Mp5318 t3.png|356px]]<br />
|-<br />
| -5.1 || -10.1 || -357.28 || No || at TS region, strength of bondings A-B and B-C alternates, but eventually A-B leave intact (Barrier can be crossed, but then the system reverts back to the reactants) || [[File:Mp5318 t4.png|356px]]<br />
|-<br />
| -5.1 || -10.6 || -349.38 || Yes || A-B + C → A +B-C at TS region, strength of bonding A-B and N-C alternates, but new product formed eventually || [[File:Mp5318 t5.png|356px]]<br />
|}<br />
<br />
'''Conclusion: Reactants need to have a large enough ratio in the momentum to be reactive, ideally, p<sub>2</sub> : p<sub>1</sub> should be larger than 2 for the reactants to be reactive.'''<br />
<br />
===Transition State Theory===<br />
<br />
====Given the results you have obtained, how will Transition State Theory predictions for reaction rate values compare with experimental values?====<br />
<br />
Transition State Theory often overestimates the reaction rate, compared to the results we calculated. Transition State Theory assumed that once the reaction has passed the Transition state and reached the product, it would not travel back to cross the Transition State and reverse to the reactant side. However, the calculations above showed that in practice, products can still recross the energy barrier to go back to the reactants. Even though the Transition State Theory ignored the effect of quantum tunneling, it's a relatively small contribution to rate in this case (small MW for H<sub>2</sub>). Therefore Transition State Theory tends to overestimate reaction rate values compare with experimental values.<br />
<br />
==F-H-H System ==<br />
<br />
=== PES inspection===<br />
<br />
====By inspecting the potential energy surfaces, classify the F + H<sub>2</sub> and H + HF reactions according to their energetics (endothermic or exothermic). How does this relate to the bond strength of the chemical species involved?====<br />
<br />
[[File:Mp5318Surface Plot fh2.png|thumb|left|Potential Surface of F + H<sub>2</sub> Reaction]]<br />
<br />
<br clear=all><br />
<br />
F + H<sub>2</sub> Reaction is exothermic. We can see there is a decrease in energy as H-H bond distance increases while H-F bond distance decreases. The clear downhill of the reaction path indicated exothermic reaction. Bond strength of H-H is 432 kJ/mol, while H-F bond strength is 565 kJ/mol. <ref name="bond energy" /> Formation of H-F bond is preferred, as it would release more energy than the energy needed to break H-H bond. <br />
<br />
H + HF Reaction is endothermic. H-H bond formed is weaker than the H-F bond, therefore energy needed to cross the activation energy barrier — endothermic.<br />
<br />
According to Hammond Postulate, for an exothermic reaction, the TS resembles the reactants (early TS); for an endothermic reaction, the TS resembles the product (late TS). Therefore in this system, TS is very close to the H<sub>2</sub> + F side (H-F distance much longer than H-H distance).<br />
<br />
====Locate the approximate position of the transition state.====<br />
<br />
Position of the TS of H<sub>2</sub> + F Reaction: r<sub>H-H</sub>=74.5 pm; r<sub>H···F</sub>=181.1 pm; At the TS, potential energy = 433.980 kJ/mol<br />
<br />
[[File:Mp5318 TS hhf contour.png|thumb|left|TS of F + H<sub>2</sub> Reaction]]<br />
<br />
[[File:Mp5318distande hhf.png|thumb|centre|Intermolecular distance vs. Time at the TS of F + H<sub>2</sub> Reaction]]<br />
<br clear=all><br />
<br />
AB distance is the H-F distance, BC distance is the H-H distance.<br />
<br />
====Report the activation energy for both reactions.====<br />
In the form of HF + H, potential energy =- 560.642 kJ/mol<br />
In the form o H<sub>2</sub> + F, potential energy = -434.922 kJ/mol<br />
<br />
Therefore compared with the TS potential energy (-433.980 kJ/mol): for HF + H to reach the TS, the activation energy is 126.02 kJ/mol; for H<sub>2</sub> + F to reach the TS, the activation energy is 0.942 kJ/mol.<br />
<br />
===Reaction Dynamics===<br />
<br />
==== 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.====<br />
For the exothermic reaction, in this case, the F + H<sub>2</sub>, energy is released into vibrational energy of product HF. When F approaches H, the repulsion between H-H is released. The released repulsive energy pushes H towards H and produces H-F vibration. <ref name="surface" /><br />
<br />
This could be confirmed experimentally through Infrared Chemiluminescence. <ref name="Infrared Chemiluminescence" />The relative gain on many lines within several vibrational bands could be determined and hence direct measurements of the relative vibrational population in v = 0 can be obtained. We would, therefore, be able to see that the v=2 vibrational level is highly populated (strong peak at v = 2).<br />
<br />
We could also use chemical laser to characterise the HF laser produced. Most of the HF is formed in the v=2 state, thus, the reaction creates an absolute inversion between v=2, v=1, and v=0. The output spectra of pulsed HF lasers showed that more than 60% of the reaction energy is released as vibrational excitation of the HF. <ref name="laser" /><br />
<br />
====Discuss how the distribution of energy between different modes (translation and vibration) affect the efficiency of the reaction, and how this is influenced by the position of the transition state.====<br />
<br />
For H<sub>2</sub> + F system, translational energy is more effective for activating the reaction: Under the conditions illustrated by ''Picture 1'' below, activation barrier was easily crossed by applying translational energy, and the translational energy was converted into product's vibrational energy; c.f. under the conditions illustrated by ''Picture 2'', even when a large amount of vibrational energy was put into the system, the reactants remain unreactive. <br />
<br />
For HF + H system, vibrational energy is more effective for activating the reaction: Under the conditions illustrated by ''Picture 3'' below, activation barrier was easily crossed by applying vibrational energy.<br />
<br />
Translational energy is most effective for passage across an early TS, whereas reactant vibrational energy far in excess of the barrier height may be ineffective for reaction. Conversely, a late TS is best crossed by vibrational energy in the reactants. <ref name="surface" /><br />
<br />
{| class="wikitable" border="1"<br />
|+ distribution of energy under differnt initial conditions<br />
! H<sub>2</sub> + F system (Early TS) !! HF + H system (Late TS)<br />
|-<br />
| [[File: Mp5318 early TS trans.png|thumb|''Picture 1:'' r<sub>(H-H)</sub>=74pm, r<sub>H-F</sub>=200 pm; p<sub>(H-H)</sub>=0 g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>; p<sub>(H-F)</sub>=-1.0g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>]] || [[File: Mp5318 Late TS vib.png|thumb|''Picture 3: ''r<sub>(H-H)</sub>=180pm, r<sub>H-F</sub>=90 pm; p<sub>(H-H)</sub>=15 g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>; p<sub>(H-F)</sub>=-1.0g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>]]<br />
|-<br />
| [[File: Mp5318Early TS vib.png|thumb|''Picture 2:'' r<sub>(H-H)</sub>=74pm, r<sub>H-F</sub>=182 pm; p<sub>(H-H)</sub>=6 g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>; p<sub>(H-F)</sub>=-1.0g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>]] || [[File: Mp5318 late TS trans.png|thumb|''Picture 4:'' r<sub>(H-H)</sub>=180pm, r<sub>H-F</sub>=90 pm; p<sub>(H-H)</sub>=0 g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>; p<sub>(H-F)</sub>=-1.0g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>]]<br />
<br clear=all><br />
<br />
==Reference==<br />
<references><br />
<ref name="surface" > Laidler, Keith J., in Chemical kinetics, 3rd ed., New York ; London, Harper & Row, 1987 </ref><br />
<br />
<ref name="bond energy" > Carruth, Gorton, Ehrlich, Eugene. "Bond Energies." Volume Library. Ed. Carruth, Gorton. Vol 1. Tennessee: Southwestern, 2002. </ref><br />
<br />
<ref name="Infrared Chemiluminescence" > B. P. Levitt, ed. Physical Chemistry of Fast Reactions. Plenum Press, New York. SCHULZ, W. R., and LEROY, D. J. 1965. </ref><br />
<br />
<ref name ="laser"> C. Bradley Moore, Laser studies of vibrational energy transfer, Accounts of Chemical Research 1969 2 (4), 103-109 DOI: 10.1021/ar50016a002 </ref><br />
</references></div>Mp5318https://chemwiki.ch.ic.ac.uk/index.php?title=Minqi5318&diff=805944Minqi53182020-05-15T22:24:56Z<p>Mp5318: /* Reference */</p>
<hr />
<div>== Molecular Reaction Dynamics: Application to Triatomic systems ==<br />
<br />
==H +H<sub>1</sub> System ==<br />
<br />
=== Dynamic from transition state region===<br />
<br />
====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?====<br />
<br />
The transition state is defined mathematically as the saddle point on the potential energy surface, where ∂V('''ri''')/∂'''ri'''=0 (the gradient of the potential is zero). At the transition state, the second derivative of potential with respect to q<sub>1</sub> is positive: ∂V<sup>2</sup>(q<sub>1</sub>)/∂q<sub>1</sub> > 0, indicating a minimum of the curve; the second derivative of potential with respect to q<sub>2</sub> is positive: ∂V<sup>2</sup>(q<sub>2</sub>)/∂q<sub>2</sub> < 0, indicating a maximum of the curve. The coincidence of a maximum and a minimum indicates saddle point on the potential energy surface. It can be identified through finding the maximum on the minimum energy path linking reactants and the products. The Transition State's energy goes down most steeply along the minimum energy path linking reactants and products c.f. local minimum of the potential energy surface. <ref name="surface" /><br />
<br />
====Report your best estimate of the transition state position (r<sub>ts</sub>) and explain your reasoning illustrating it with an “Internuclear Distances vs Time” plot for a relevant trajectory.====<br />
<br />
The best estemate of the transition state position r<sub>ts</sub> = 91 pm<br />
<br />
[[File:mp5318_Animation.png|thumb|centre|Internuclear Distances vs Time Plot when r<sub>ts</sub> = 91 pm.]]<br />
<br />
As shown in the ''Internuclear Distances vs Time Plot when r<sub>ts</sub> = 91 pm'' above, when r<sub>ts</sub> = 91 pm and p<sub>1</sub> p<sub>2</sub> = 0.0 g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>, internuclear distance reamain (almost) constant, which shows that the molecule does not vibrate and stayed stably at the transition state forever.<br />
<br />
====Comment on how the MEP and the trajectory you just calculated differ.====<br />
<br />
[[File:Mp5318 Surface Plot Dynamic.png|thumb|left|Surface Plot using Dynamic Calculation r<sub>1</sub>=92 pm, r<sub>2</sub>=91 pm]]<br />
<br />
[[File:Surface Plot MEP.png|thumb|centre|Surface Plot using MEP Calculation r<sub>1</sub>=92 pm, r<sub>2</sub>=91 pm]]<br />
<br />
<br clear=all><br />
When '''r<sub>1</sub>'''=92 pm, '''r<sub>2</sub>'''=91 pm, atoms A and B dissociates. Using MEP calculation, AB dissociates through the minimum energy pathway and the dissociation ceased at a displacement much smaller than using Dynamic calculation. In Dynamic trajectory, kinetic energy was acquired during the trajectory from potential energy, therefore encourage inertial motion to proceed. In addition, MEP Calculation does not take into account the momentum of the particles, all the momentums are assumed to be zero.<br />
<br />
When reversing '''r<sub>1</sub>''' and '''r<sub>2</sub>''', B and C dissociates while A and B sticks together. The final values of the positions are '''r<sub>1</sub>''' (73.81819562) '''r<sub>2</sub>''' (352.8544826) and '''p<sub>1</sub>''' (3.258858751) '''p<sub>2</sub>''' (5.06251673). <br />
<br />
When setting up a calculation where the initial positions correspond to the final positions of the trajectory above, the same final momenta values but with their signs reversed, the reaction trajectory travels back to the orginal position '''r<sub>1</sub>''' (91) and '''r<sub>2</sub>''' (92) with '''p<sub>1</sub>'''= '''p<sub>2</sub>'''= 0.<br />
<br />
===Reactive and Unreactive trajectories===<br />
<br />
{| class="wikitable" border="1"<br />
|+ initial positions '''r<sub>1</sub>''' (74 pm) '''r<sub>2</sub>''' (200 pm)<br />
! p<sub>1</sub> / g.mol<sup>-1</sup>.pm.fs<sup>-1</sup> !! p<sub>2</sub> / g.mol<sup>-1</sup>.pm.fs<sup>-1</sup> !! E<sub>tot</sub> kJ.mol<sub>-1</sub> !! Reactive? !! Description of the dunamics !! Illustration of the trajectory<br />
|-<br />
| -2.56 || -5.1 || -414.28 || Yes || A-B + C → A +B-C || [[File:Mp5318 t1.png|356px]]<br />
|-<br />
| -3.1 || -4.1 || -420.08 || No || A-B approaches C, but then leave without reaction occur || [[File:Mp5318 t2.png|356px]]<br />
|-<br />
| -3.1 || -5.1 || -413.98 || Yes || A-B + C → A +B-C || [[File:Mp5318 t3.png|356px]]<br />
|-<br />
| -5.1 || -10.1 || -357.28 || No || at TS region, strength of bondings A-B and B-C alternates, but eventually A-B leave intact (Barrier can be crossed, but then the system reverts back to the reactants) || [[File:Mp5318 t4.png|356px]]<br />
|-<br />
| -5.1 || -10.6 || -349.38 || Yes || A-B + C → A +B-C at TS region, strength of bonding A-B and N-C alternates, but new product formed eventually || [[File:Mp5318 t5.png|356px]]<br />
|}<br />
<br />
'''Conclusion: Reactants need to have a large enough ratio in the momentum to be reactive, ideally, p<sub>2</sub> : p<sub>1</sub> should be larger than 2 for the reactants to be reactive.'''<br />
<br />
===Transition State Theory===<br />
<br />
====Given the results you have obtained, how will Transition State Theory predictions for reaction rate values compare with experimental values?====<br />
<br />
Transition State Theory often overestimates the reaction rate, compared to the results we calculated. Transition State Theory assumed that once the reaction has passed the Transition state and reached the product, it would not travel back to cross the Transition State and reverse to the reactant side. However, the calculations above showed that in practice, products can still recross the energy barrier to go back to the reactants. Even though the Transition State Theory ignored the effect of quantum tunneling, it's a relatively small contribution to rate in this case (small MW for H<sub>2</sub>). Therefore Transition State Theory tends to overestimate reaction rate values compare with experimental values.<br />
<br />
==F-H-H System ==<br />
<br />
=== PES inspection===<br />
<br />
====By inspecting the potential energy surfaces, classify the F + H<sub>2</sub> and H + HF reactions according to their energetics (endothermic or exothermic). How does this relate to the bond strength of the chemical species involved?====<br />
<br />
[[File:Mp5318Surface Plot fh2.png|thumb|left|Potential Surface of F + H<sub>2</sub> Reaction]]<br />
<br />
<br clear=all><br />
<br />
F + H<sub>2</sub> Reaction is exothermic. We can see there is a decrease in energy as H-H bond distance increases while H-F bond distance decreases. The clear downhill of the reaction path indicated exothermic reaction. Bond strength of H-H is 432 kJ/mol, while H-F bond strength is 565 kJ/mol. <ref name="bond energy" /> Formation of H-F bond is preferred, as it would release more energy than the energy needed to break H-H bond. <br />
<br />
H + HF Reaction is endothermic. H-H bond formed is weaker than the H-F bond, therefore energy needed to cross the activation energy barrier — endothermic.<br />
<br />
According to Hammond Postulate, for an exothermic reaction, the TS resembles the reactants (early TS); for an endothermic reaction, the TS resembles the product (late TS). Therefore in this system, TS is very close to the H<sub>2</sub> + F side (H-F distance much longer than H-H distance).<br />
<br />
====Locate the approximate position of the transition state.====<br />
<br />
Position of the TS of H<sub>2</sub> + F Reaction: r<sub>H-H</sub>=74.5 pm; r<sub>H···F</sub>=181.1 pm; At the TS, potential energy = 433.980 kJ/mol<br />
<br />
[[File:Mp5318 TS hhf contour.png|thumb|left|TS of F + H<sub>2</sub> Reaction]]<br />
<br />
[[File:Mp5318distande hhf.png|thumb|centre|Intermolecular distance vs. Time at the TS of F + H<sub>2</sub> Reaction]]<br />
<br clear=all><br />
<br />
AB distance is the H-F distance, BC distance is the H-H distance.<br />
<br />
====Report the activation energy for both reactions.====<br />
In the form of HF + H, potential energy =- 560.642 kJ/mol<br />
In the form o H<sub>2</sub> + F, potential energy = -434.922 kJ/mol<br />
<br />
Therefore compared with the TS potential energy (-433.980 kJ/mol): for HF + H to reach the TS, the activation energy is 126.02 kJ/mol; for H<sub>2</sub> + F to reach the TS, the activation energy is 0.942 kJ/mol.<br />
<br />
===Reaction Dynamics===<br />
<br />
==== 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.====<br />
For the exothermic reaction, in this case, the F + H<sub>2</sub>, energy is released into vibrational energy of product HF. When F approaches H, the repulsion between H-H is released. The released repulsive energy pushes H towards H and produces H-F vibration. <ref name="surface" /><br />
<br />
This could be confirmed experimentally through Infrared Chemiluminescence. <ref name="Infrared Chemiluminescence" />The relative gain on many lines within several vibrational bands could be determined and hence direct measurements of the relative vibrational population in v = 0 can be obtained. We would, therefore, be able to see that the v=2 vibrational level is highly populated (strong peak at v = 2).<br />
<br />
We could also use chemical laser to characterise the HF laser produced. Most of the HF is formed in the v=2 state, thus, the reaction creates an absolute inversion between v=2, v=1, and v=0. The output spectra of pulsed HF lasers showed that more than 60% of the reaction energy is released as vibrational excitation of the HF. <ref name="laser" /><br />
<br />
====Discuss how the distribution of energy between different modes (translation and vibration) affect the efficiency of the reaction, and how this is influenced by the position of the transition state.====<br />
<br />
For H<sub>2</sub> + F system, translational energy is more effective for activating the reaction: Under the conditions illustrated by ''Picture 1'' below, activation barrier was easily crossed by applying translational energy, and the translational energy was converted into product's vibrational energy; c.f. under the conditions illustrated by ''Picture 2'', even when a large amount of vibrational energy was put into the system, the reactants remain unreactive. <br />
<br />
For HF + H system, vibrational energy is more effective for activating the reaction: Under the conditions illustrated by ''Picture 3'' below, activation barrier was easily crossed by applying vibrational energy.<br />
<br />
Translational energy is most effective for passage across an early TS, whereas reactant vibrational energy far in excess of the barrier height may be ineffective for reaction. Conversely, a late TS is best crossed by vibrational energy in the reactants. <ref name="surface" /><br />
<br />
{| class="wikitable" border="1"<br />
|+ distribution of energy under differnt initial conditions<br />
! H<sub>2</sub> + F system (Early TS) !! HF + H system (Late TS)<br />
|-<br />
| [[File: Mp5318 early TS trans.png|thumb|''Picture 1:'' r<sub>(H-H)</sub>=74pm, r<sub>H-F</sub>=200 pm; p<sub>(H-H)</sub>=0 g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>; p<sub>(H-F)</sub>=-1.0g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>]] || [[File: Mp5318 Late TS vib.png|thumb|''Picture 3: ''r<sub>(H-H)</sub>=180pm, r<sub>H-F</sub>=90 pm; p<sub>(H-H)</sub>=15 g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>; p<sub>(H-F)</sub>=-1.0g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>]]<br />
|-<br />
| [[File: Mp5318Early TS vib.png|thumb|''Picture 2:'' r<sub>(H-H)</sub>=74pm, r<sub>H-F</sub>=182 pm; p<sub>(H-H)</sub>=6 g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>; p<sub>(H-F)</sub>=-1.0g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>]] || [[File: Mp5318 late TS trans.png|thumb|''Picture 4:'' r<sub>(H-H)</sub>=180pm, r<sub>H-F</sub>=90 pm; p<sub>(H-H)</sub>=0 g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>; p<sub>(H-F)</sub>=-1.0g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>]]<br />
<br clear=all><br />
<br />
==Reference==<br />
<references><br />
<ref name="surface" /> Laidler, Keith J., in Chemical kinetics, 3rd ed., New York ; London, Harper & Row, 1987 </ref><br />
<br />
<ref name="bond energy" /> Carruth, Gorton, Ehrlich, Eugene. "Bond Energies." Volume Library. Ed. Carruth, Gorton. Vol 1. Tennessee: Southwestern, 2002. </ref><br />
<br />
<ref name="Infrared Chemiluminescence" /> B. P. Levitt, ed. Physical Chemistry of Fast Reactions. Plenum Press, New York. SCHULZ, W. R., and LEROY, D. J. 1965. </ref><br />
<br />
<ref name ="laser"/> C. Bradley Moore, Laser studies of vibrational energy transfer, Accounts of Chemical Research 1969 2 (4), 103-109 DOI: 10.1021/ar50016a002 </ref><br />
</references></div>Mp5318https://chemwiki.ch.ic.ac.uk/index.php?title=Minqi5318&diff=805939Minqi53182020-05-15T22:22:57Z<p>Mp5318: /* Reference */</p>
<hr />
<div>== Molecular Reaction Dynamics: Application to Triatomic systems ==<br />
<br />
==H +H<sub>1</sub> System ==<br />
<br />
=== Dynamic from transition state region===<br />
<br />
====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?====<br />
<br />
The transition state is defined mathematically as the saddle point on the potential energy surface, where ∂V('''ri''')/∂'''ri'''=0 (the gradient of the potential is zero). At the transition state, the second derivative of potential with respect to q<sub>1</sub> is positive: ∂V<sup>2</sup>(q<sub>1</sub>)/∂q<sub>1</sub> > 0, indicating a minimum of the curve; the second derivative of potential with respect to q<sub>2</sub> is positive: ∂V<sup>2</sup>(q<sub>2</sub>)/∂q<sub>2</sub> < 0, indicating a maximum of the curve. The coincidence of a maximum and a minimum indicates saddle point on the potential energy surface. It can be identified through finding the maximum on the minimum energy path linking reactants and the products. The Transition State's energy goes down most steeply along the minimum energy path linking reactants and products c.f. local minimum of the potential energy surface. <ref name="surface" /><br />
<br />
====Report your best estimate of the transition state position (r<sub>ts</sub>) and explain your reasoning illustrating it with an “Internuclear Distances vs Time” plot for a relevant trajectory.====<br />
<br />
The best estemate of the transition state position r<sub>ts</sub> = 91 pm<br />
<br />
[[File:mp5318_Animation.png|thumb|centre|Internuclear Distances vs Time Plot when r<sub>ts</sub> = 91 pm.]]<br />
<br />
As shown in the ''Internuclear Distances vs Time Plot when r<sub>ts</sub> = 91 pm'' above, when r<sub>ts</sub> = 91 pm and p<sub>1</sub> p<sub>2</sub> = 0.0 g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>, internuclear distance reamain (almost) constant, which shows that the molecule does not vibrate and stayed stably at the transition state forever.<br />
<br />
====Comment on how the MEP and the trajectory you just calculated differ.====<br />
<br />
[[File:Mp5318 Surface Plot Dynamic.png|thumb|left|Surface Plot using Dynamic Calculation r<sub>1</sub>=92 pm, r<sub>2</sub>=91 pm]]<br />
<br />
[[File:Surface Plot MEP.png|thumb|centre|Surface Plot using MEP Calculation r<sub>1</sub>=92 pm, r<sub>2</sub>=91 pm]]<br />
<br />
<br clear=all><br />
When '''r<sub>1</sub>'''=92 pm, '''r<sub>2</sub>'''=91 pm, atoms A and B dissociates. Using MEP calculation, AB dissociates through the minimum energy pathway and the dissociation ceased at a displacement much smaller than using Dynamic calculation. In Dynamic trajectory, kinetic energy was acquired during the trajectory from potential energy, therefore encourage inertial motion to proceed. In addition, MEP Calculation does not take into account the momentum of the particles, all the momentums are assumed to be zero.<br />
<br />
When reversing '''r<sub>1</sub>''' and '''r<sub>2</sub>''', B and C dissociates while A and B sticks together. The final values of the positions are '''r<sub>1</sub>''' (73.81819562) '''r<sub>2</sub>''' (352.8544826) and '''p<sub>1</sub>''' (3.258858751) '''p<sub>2</sub>''' (5.06251673). <br />
<br />
When setting up a calculation where the initial positions correspond to the final positions of the trajectory above, the same final momenta values but with their signs reversed, the reaction trajectory travels back to the orginal position '''r<sub>1</sub>''' (91) and '''r<sub>2</sub>''' (92) with '''p<sub>1</sub>'''= '''p<sub>2</sub>'''= 0.<br />
<br />
===Reactive and Unreactive trajectories===<br />
<br />
{| class="wikitable" border="1"<br />
|+ initial positions '''r<sub>1</sub>''' (74 pm) '''r<sub>2</sub>''' (200 pm)<br />
! p<sub>1</sub> / g.mol<sup>-1</sup>.pm.fs<sup>-1</sup> !! p<sub>2</sub> / g.mol<sup>-1</sup>.pm.fs<sup>-1</sup> !! E<sub>tot</sub> kJ.mol<sub>-1</sub> !! Reactive? !! Description of the dunamics !! Illustration of the trajectory<br />
|-<br />
| -2.56 || -5.1 || -414.28 || Yes || A-B + C → A +B-C || [[File:Mp5318 t1.png|356px]]<br />
|-<br />
| -3.1 || -4.1 || -420.08 || No || A-B approaches C, but then leave without reaction occur || [[File:Mp5318 t2.png|356px]]<br />
|-<br />
| -3.1 || -5.1 || -413.98 || Yes || A-B + C → A +B-C || [[File:Mp5318 t3.png|356px]]<br />
|-<br />
| -5.1 || -10.1 || -357.28 || No || at TS region, strength of bondings A-B and B-C alternates, but eventually A-B leave intact (Barrier can be crossed, but then the system reverts back to the reactants) || [[File:Mp5318 t4.png|356px]]<br />
|-<br />
| -5.1 || -10.6 || -349.38 || Yes || A-B + C → A +B-C at TS region, strength of bonding A-B and N-C alternates, but new product formed eventually || [[File:Mp5318 t5.png|356px]]<br />
|}<br />
<br />
'''Conclusion: Reactants need to have a large enough ratio in the momentum to be reactive, ideally, p<sub>2</sub> : p<sub>1</sub> should be larger than 2 for the reactants to be reactive.'''<br />
<br />
===Transition State Theory===<br />
<br />
====Given the results you have obtained, how will Transition State Theory predictions for reaction rate values compare with experimental values?====<br />
<br />
Transition State Theory often overestimates the reaction rate, compared to the results we calculated. Transition State Theory assumed that once the reaction has passed the Transition state and reached the product, it would not travel back to cross the Transition State and reverse to the reactant side. However, the calculations above showed that in practice, products can still recross the energy barrier to go back to the reactants. Even though the Transition State Theory ignored the effect of quantum tunneling, it's a relatively small contribution to rate in this case (small MW for H<sub>2</sub>). Therefore Transition State Theory tends to overestimate reaction rate values compare with experimental values.<br />
<br />
==F-H-H System ==<br />
<br />
=== PES inspection===<br />
<br />
====By inspecting the potential energy surfaces, classify the F + H<sub>2</sub> and H + HF reactions according to their energetics (endothermic or exothermic). How does this relate to the bond strength of the chemical species involved?====<br />
<br />
[[File:Mp5318Surface Plot fh2.png|thumb|left|Potential Surface of F + H<sub>2</sub> Reaction]]<br />
<br />
<br clear=all><br />
<br />
F + H<sub>2</sub> Reaction is exothermic. We can see there is a decrease in energy as H-H bond distance increases while H-F bond distance decreases. The clear downhill of the reaction path indicated exothermic reaction. Bond strength of H-H is 432 kJ/mol, while H-F bond strength is 565 kJ/mol. <ref name="bond energy" /> Formation of H-F bond is preferred, as it would release more energy than the energy needed to break H-H bond. <br />
<br />
H + HF Reaction is endothermic. H-H bond formed is weaker than the H-F bond, therefore energy needed to cross the activation energy barrier — endothermic.<br />
<br />
According to Hammond Postulate, for an exothermic reaction, the TS resembles the reactants (early TS); for an endothermic reaction, the TS resembles the product (late TS). Therefore in this system, TS is very close to the H<sub>2</sub> + F side (H-F distance much longer than H-H distance).<br />
<br />
====Locate the approximate position of the transition state.====<br />
<br />
Position of the TS of H<sub>2</sub> + F Reaction: r<sub>H-H</sub>=74.5 pm; r<sub>H···F</sub>=181.1 pm; At the TS, potential energy = 433.980 kJ/mol<br />
<br />
[[File:Mp5318 TS hhf contour.png|thumb|left|TS of F + H<sub>2</sub> Reaction]]<br />
<br />
[[File:Mp5318distande hhf.png|thumb|centre|Intermolecular distance vs. Time at the TS of F + H<sub>2</sub> Reaction]]<br />
<br clear=all><br />
<br />
AB distance is the H-F distance, BC distance is the H-H distance.<br />
<br />
====Report the activation energy for both reactions.====<br />
In the form of HF + H, potential energy =- 560.642 kJ/mol<br />
In the form o H<sub>2</sub> + F, potential energy = -434.922 kJ/mol<br />
<br />
Therefore compared with the TS potential energy (-433.980 kJ/mol): for HF + H to reach the TS, the activation energy is 126.02 kJ/mol; for H<sub>2</sub> + F to reach the TS, the activation energy is 0.942 kJ/mol.<br />
<br />
===Reaction Dynamics===<br />
<br />
==== 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.====<br />
For the exothermic reaction, in this case, the F + H<sub>2</sub>, energy is released into vibrational energy of product HF. When F approaches H, the repulsion between H-H is released. The released repulsive energy pushes H towards H and produces H-F vibration. <ref name="surface" /><br />
<br />
This could be confirmed experimentally through Infrared Chemiluminescence. <ref name="Infrared Chemiluminescence" />The relative gain on many lines within several vibrational bands could be determined and hence direct measurements of the relative vibrational population in v = 0 can be obtained. We would, therefore, be able to see that the v=2 vibrational level is highly populated (strong peak at v = 2).<br />
<br />
We could also use chemical laser to characterise the HF laser produced. Most of the HF is formed in the v=2 state, thus, the reaction creates an absolute inversion between v=2, v=1, and v=0. The output spectra of pulsed HF lasers showed that more than 60% of the reaction energy is released as vibrational excitation of the HF. <ref name="laser" /><br />
<br />
====Discuss how the distribution of energy between different modes (translation and vibration) affect the efficiency of the reaction, and how this is influenced by the position of the transition state.====<br />
<br />
For H<sub>2</sub> + F system, translational energy is more effective for activating the reaction: Under the conditions illustrated by ''Picture 1'' below, activation barrier was easily crossed by applying translational energy, and the translational energy was converted into product's vibrational energy; c.f. under the conditions illustrated by ''Picture 2'', even when a large amount of vibrational energy was put into the system, the reactants remain unreactive. <br />
<br />
For HF + H system, vibrational energy is more effective for activating the reaction: Under the conditions illustrated by ''Picture 3'' below, activation barrier was easily crossed by applying vibrational energy.<br />
<br />
Translational energy is most effective for passage across an early TS, whereas reactant vibrational energy far in excess of the barrier height may be ineffective for reaction. Conversely, a late TS is best crossed by vibrational energy in the reactants. <ref name="surface" /><br />
<br />
{| class="wikitable" border="1"<br />
|+ distribution of energy under differnt initial conditions<br />
! H<sub>2</sub> + F system (Early TS) !! HF + H system (Late TS)<br />
|-<br />
| [[File: Mp5318 early TS trans.png|thumb|''Picture 1:'' r<sub>(H-H)</sub>=74pm, r<sub>H-F</sub>=200 pm; p<sub>(H-H)</sub>=0 g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>; p<sub>(H-F)</sub>=-1.0g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>]] || [[File: Mp5318 Late TS vib.png|thumb|''Picture 3: ''r<sub>(H-H)</sub>=180pm, r<sub>H-F</sub>=90 pm; p<sub>(H-H)</sub>=15 g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>; p<sub>(H-F)</sub>=-1.0g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>]]<br />
|-<br />
| [[File: Mp5318Early TS vib.png|thumb|''Picture 2:'' r<sub>(H-H)</sub>=74pm, r<sub>H-F</sub>=182 pm; p<sub>(H-H)</sub>=6 g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>; p<sub>(H-F)</sub>=-1.0g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>]] || [[File: Mp5318 late TS trans.png|thumb|''Picture 4:'' r<sub>(H-H)</sub>=180pm, r<sub>H-F</sub>=90 pm; p<sub>(H-H)</sub>=0 g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>; p<sub>(H-F)</sub>=-1.0g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>]]<br />
<br clear=all><br />
<br />
==Reference==<br />
<references><br />
<ref name="surface" /> Laidler, Keith J., in Chemical kinetics, 3rd ed., New York ; London, Harper & Row, 1987 </ref><br />
</references><br />
<br />
<references><br />
<ref name="bond energy" /> Carruth, Gorton, Ehrlich, Eugene. "Bond Energies." Volume Library. Ed. Carruth, Gorton. Vol 1. Tennessee: Southwestern, 2002. </ref><br />
</references><br />
<br />
<references><br />
<ref name="Infrared Chemiluminescence" /> B. P. Levitt, ed. Physical Chemistry of Fast Reactions. Plenum Press, New York. SCHULZ, W. R., and LEROY, D. J. 1965. </ref><br />
</references><br />
<br />
<references><br />
<ref name ="laser"/> C. Bradley Moore, Laser studies of vibrational energy transfer, Accounts of Chemical Research 1969 2 (4), 103-109 DOI: 10.1021/ar50016a002 </ref><br />
</references></div>Mp5318https://chemwiki.ch.ic.ac.uk/index.php?title=Minqi5318&diff=805936Minqi53182020-05-15T22:21:56Z<p>Mp5318: /* Reference */</p>
<hr />
<div>== Molecular Reaction Dynamics: Application to Triatomic systems ==<br />
<br />
==H +H<sub>1</sub> System ==<br />
<br />
=== Dynamic from transition state region===<br />
<br />
====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?====<br />
<br />
The transition state is defined mathematically as the saddle point on the potential energy surface, where ∂V('''ri''')/∂'''ri'''=0 (the gradient of the potential is zero). At the transition state, the second derivative of potential with respect to q<sub>1</sub> is positive: ∂V<sup>2</sup>(q<sub>1</sub>)/∂q<sub>1</sub> > 0, indicating a minimum of the curve; the second derivative of potential with respect to q<sub>2</sub> is positive: ∂V<sup>2</sup>(q<sub>2</sub>)/∂q<sub>2</sub> < 0, indicating a maximum of the curve. The coincidence of a maximum and a minimum indicates saddle point on the potential energy surface. It can be identified through finding the maximum on the minimum energy path linking reactants and the products. The Transition State's energy goes down most steeply along the minimum energy path linking reactants and products c.f. local minimum of the potential energy surface. <ref name="surface" /><br />
<br />
====Report your best estimate of the transition state position (r<sub>ts</sub>) and explain your reasoning illustrating it with an “Internuclear Distances vs Time” plot for a relevant trajectory.====<br />
<br />
The best estemate of the transition state position r<sub>ts</sub> = 91 pm<br />
<br />
[[File:mp5318_Animation.png|thumb|centre|Internuclear Distances vs Time Plot when r<sub>ts</sub> = 91 pm.]]<br />
<br />
As shown in the ''Internuclear Distances vs Time Plot when r<sub>ts</sub> = 91 pm'' above, when r<sub>ts</sub> = 91 pm and p<sub>1</sub> p<sub>2</sub> = 0.0 g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>, internuclear distance reamain (almost) constant, which shows that the molecule does not vibrate and stayed stably at the transition state forever.<br />
<br />
====Comment on how the MEP and the trajectory you just calculated differ.====<br />
<br />
[[File:Mp5318 Surface Plot Dynamic.png|thumb|left|Surface Plot using Dynamic Calculation r<sub>1</sub>=92 pm, r<sub>2</sub>=91 pm]]<br />
<br />
[[File:Surface Plot MEP.png|thumb|centre|Surface Plot using MEP Calculation r<sub>1</sub>=92 pm, r<sub>2</sub>=91 pm]]<br />
<br />
<br clear=all><br />
When '''r<sub>1</sub>'''=92 pm, '''r<sub>2</sub>'''=91 pm, atoms A and B dissociates. Using MEP calculation, AB dissociates through the minimum energy pathway and the dissociation ceased at a displacement much smaller than using Dynamic calculation. In Dynamic trajectory, kinetic energy was acquired during the trajectory from potential energy, therefore encourage inertial motion to proceed. In addition, MEP Calculation does not take into account the momentum of the particles, all the momentums are assumed to be zero.<br />
<br />
When reversing '''r<sub>1</sub>''' and '''r<sub>2</sub>''', B and C dissociates while A and B sticks together. The final values of the positions are '''r<sub>1</sub>''' (73.81819562) '''r<sub>2</sub>''' (352.8544826) and '''p<sub>1</sub>''' (3.258858751) '''p<sub>2</sub>''' (5.06251673). <br />
<br />
When setting up a calculation where the initial positions correspond to the final positions of the trajectory above, the same final momenta values but with their signs reversed, the reaction trajectory travels back to the orginal position '''r<sub>1</sub>''' (91) and '''r<sub>2</sub>''' (92) with '''p<sub>1</sub>'''= '''p<sub>2</sub>'''= 0.<br />
<br />
===Reactive and Unreactive trajectories===<br />
<br />
{| class="wikitable" border="1"<br />
|+ initial positions '''r<sub>1</sub>''' (74 pm) '''r<sub>2</sub>''' (200 pm)<br />
! p<sub>1</sub> / g.mol<sup>-1</sup>.pm.fs<sup>-1</sup> !! p<sub>2</sub> / g.mol<sup>-1</sup>.pm.fs<sup>-1</sup> !! E<sub>tot</sub> kJ.mol<sub>-1</sub> !! Reactive? !! Description of the dunamics !! Illustration of the trajectory<br />
|-<br />
| -2.56 || -5.1 || -414.28 || Yes || A-B + C → A +B-C || [[File:Mp5318 t1.png|356px]]<br />
|-<br />
| -3.1 || -4.1 || -420.08 || No || A-B approaches C, but then leave without reaction occur || [[File:Mp5318 t2.png|356px]]<br />
|-<br />
| -3.1 || -5.1 || -413.98 || Yes || A-B + C → A +B-C || [[File:Mp5318 t3.png|356px]]<br />
|-<br />
| -5.1 || -10.1 || -357.28 || No || at TS region, strength of bondings A-B and B-C alternates, but eventually A-B leave intact (Barrier can be crossed, but then the system reverts back to the reactants) || [[File:Mp5318 t4.png|356px]]<br />
|-<br />
| -5.1 || -10.6 || -349.38 || Yes || A-B + C → A +B-C at TS region, strength of bonding A-B and N-C alternates, but new product formed eventually || [[File:Mp5318 t5.png|356px]]<br />
|}<br />
<br />
'''Conclusion: Reactants need to have a large enough ratio in the momentum to be reactive, ideally, p<sub>2</sub> : p<sub>1</sub> should be larger than 2 for the reactants to be reactive.'''<br />
<br />
===Transition State Theory===<br />
<br />
====Given the results you have obtained, how will Transition State Theory predictions for reaction rate values compare with experimental values?====<br />
<br />
Transition State Theory often overestimates the reaction rate, compared to the results we calculated. Transition State Theory assumed that once the reaction has passed the Transition state and reached the product, it would not travel back to cross the Transition State and reverse to the reactant side. However, the calculations above showed that in practice, products can still recross the energy barrier to go back to the reactants. Even though the Transition State Theory ignored the effect of quantum tunneling, it's a relatively small contribution to rate in this case (small MW for H<sub>2</sub>). Therefore Transition State Theory tends to overestimate reaction rate values compare with experimental values.<br />
<br />
==F-H-H System ==<br />
<br />
=== PES inspection===<br />
<br />
====By inspecting the potential energy surfaces, classify the F + H<sub>2</sub> and H + HF reactions according to their energetics (endothermic or exothermic). How does this relate to the bond strength of the chemical species involved?====<br />
<br />
[[File:Mp5318Surface Plot fh2.png|thumb|left|Potential Surface of F + H<sub>2</sub> Reaction]]<br />
<br />
<br clear=all><br />
<br />
F + H<sub>2</sub> Reaction is exothermic. We can see there is a decrease in energy as H-H bond distance increases while H-F bond distance decreases. The clear downhill of the reaction path indicated exothermic reaction. Bond strength of H-H is 432 kJ/mol, while H-F bond strength is 565 kJ/mol. <ref name="bond energy" /> Formation of H-F bond is preferred, as it would release more energy than the energy needed to break H-H bond. <br />
<br />
H + HF Reaction is endothermic. H-H bond formed is weaker than the H-F bond, therefore energy needed to cross the activation energy barrier — endothermic.<br />
<br />
According to Hammond Postulate, for an exothermic reaction, the TS resembles the reactants (early TS); for an endothermic reaction, the TS resembles the product (late TS). Therefore in this system, TS is very close to the H<sub>2</sub> + F side (H-F distance much longer than H-H distance).<br />
<br />
====Locate the approximate position of the transition state.====<br />
<br />
Position of the TS of H<sub>2</sub> + F Reaction: r<sub>H-H</sub>=74.5 pm; r<sub>H···F</sub>=181.1 pm; At the TS, potential energy = 433.980 kJ/mol<br />
<br />
[[File:Mp5318 TS hhf contour.png|thumb|left|TS of F + H<sub>2</sub> Reaction]]<br />
<br />
[[File:Mp5318distande hhf.png|thumb|centre|Intermolecular distance vs. Time at the TS of F + H<sub>2</sub> Reaction]]<br />
<br clear=all><br />
<br />
AB distance is the H-F distance, BC distance is the H-H distance.<br />
<br />
====Report the activation energy for both reactions.====<br />
In the form of HF + H, potential energy =- 560.642 kJ/mol<br />
In the form o H<sub>2</sub> + F, potential energy = -434.922 kJ/mol<br />
<br />
Therefore compared with the TS potential energy (-433.980 kJ/mol): for HF + H to reach the TS, the activation energy is 126.02 kJ/mol; for H<sub>2</sub> + F to reach the TS, the activation energy is 0.942 kJ/mol.<br />
<br />
===Reaction Dynamics===<br />
<br />
==== 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.====<br />
For the exothermic reaction, in this case, the F + H<sub>2</sub>, energy is released into vibrational energy of product HF. When F approaches H, the repulsion between H-H is released. The released repulsive energy pushes H towards H and produces H-F vibration. <ref name="surface" /><br />
<br />
This could be confirmed experimentally through Infrared Chemiluminescence. <ref name="Infrared Chemiluminescence" />The relative gain on many lines within several vibrational bands could be determined and hence direct measurements of the relative vibrational population in v = 0 can be obtained. We would, therefore, be able to see that the v=2 vibrational level is highly populated (strong peak at v = 2).<br />
<br />
We could also use chemical laser to characterise the HF laser produced. Most of the HF is formed in the v=2 state, thus, the reaction creates an absolute inversion between v=2, v=1, and v=0. The output spectra of pulsed HF lasers showed that more than 60% of the reaction energy is released as vibrational excitation of the HF. <ref name="laser" /><br />
<br />
====Discuss how the distribution of energy between different modes (translation and vibration) affect the efficiency of the reaction, and how this is influenced by the position of the transition state.====<br />
<br />
For H<sub>2</sub> + F system, translational energy is more effective for activating the reaction: Under the conditions illustrated by ''Picture 1'' below, activation barrier was easily crossed by applying translational energy, and the translational energy was converted into product's vibrational energy; c.f. under the conditions illustrated by ''Picture 2'', even when a large amount of vibrational energy was put into the system, the reactants remain unreactive. <br />
<br />
For HF + H system, vibrational energy is more effective for activating the reaction: Under the conditions illustrated by ''Picture 3'' below, activation barrier was easily crossed by applying vibrational energy.<br />
<br />
Translational energy is most effective for passage across an early TS, whereas reactant vibrational energy far in excess of the barrier height may be ineffective for reaction. Conversely, a late TS is best crossed by vibrational energy in the reactants. <ref name="surface" /><br />
<br />
{| class="wikitable" border="1"<br />
|+ distribution of energy under differnt initial conditions<br />
! H<sub>2</sub> + F system (Early TS) !! HF + H system (Late TS)<br />
|-<br />
| [[File: Mp5318 early TS trans.png|thumb|''Picture 1:'' r<sub>(H-H)</sub>=74pm, r<sub>H-F</sub>=200 pm; p<sub>(H-H)</sub>=0 g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>; p<sub>(H-F)</sub>=-1.0g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>]] || [[File: Mp5318 Late TS vib.png|thumb|''Picture 3: ''r<sub>(H-H)</sub>=180pm, r<sub>H-F</sub>=90 pm; p<sub>(H-H)</sub>=15 g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>; p<sub>(H-F)</sub>=-1.0g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>]]<br />
|-<br />
| [[File: Mp5318Early TS vib.png|thumb|''Picture 2:'' r<sub>(H-H)</sub>=74pm, r<sub>H-F</sub>=182 pm; p<sub>(H-H)</sub>=6 g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>; p<sub>(H-F)</sub>=-1.0g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>]] || [[File: Mp5318 late TS trans.png|thumb|''Picture 4:'' r<sub>(H-H)</sub>=180pm, r<sub>H-F</sub>=90 pm; p<sub>(H-H)</sub>=0 g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>; p<sub>(H-F)</sub>=-1.0g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>]]<br />
<br clear=all><br />
<br />
==Reference==<br />
<references><br />
<ref name="surface" /> Laidler, Keith J., in Chemical kinetics, 3rd ed., New York ; London, Harper & Row, 1987<br />
</references><br />
<br />
<references><br />
<ref name="bond energy" /> Carruth, Gorton, Ehrlich, Eugene. "Bond Energies." Volume Library. Ed. Carruth, Gorton. Vol 1. Tennessee: Southwestern, 2002.<br />
</references><br />
<br />
<references><br />
<ref name="Infrared Chemiluminescence" /> B. P. Levitt, ed. Physical Chemistry of Fast Reactions. Plenum Press, New York. SCHULZ, W. R., and LEROY, D. J. 1965.<br />
</references><br />
<br />
<references><br />
<ref name ="laser"/> C. Bradley Moore, Laser studies of vibrational energy transfer, Accounts of Chemical Research 1969 2 (4), 103-109 DOI: 10.1021/ar50016a002<br />
</references></div>Mp5318https://chemwiki.ch.ic.ac.uk/index.php?title=Minqi5318&diff=805935Minqi53182020-05-15T22:20:01Z<p>Mp5318: </p>
<hr />
<div>== Molecular Reaction Dynamics: Application to Triatomic systems ==<br />
<br />
==H +H<sub>1</sub> System ==<br />
<br />
=== Dynamic from transition state region===<br />
<br />
====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?====<br />
<br />
The transition state is defined mathematically as the saddle point on the potential energy surface, where ∂V('''ri''')/∂'''ri'''=0 (the gradient of the potential is zero). At the transition state, the second derivative of potential with respect to q<sub>1</sub> is positive: ∂V<sup>2</sup>(q<sub>1</sub>)/∂q<sub>1</sub> > 0, indicating a minimum of the curve; the second derivative of potential with respect to q<sub>2</sub> is positive: ∂V<sup>2</sup>(q<sub>2</sub>)/∂q<sub>2</sub> < 0, indicating a maximum of the curve. The coincidence of a maximum and a minimum indicates saddle point on the potential energy surface. It can be identified through finding the maximum on the minimum energy path linking reactants and the products. The Transition State's energy goes down most steeply along the minimum energy path linking reactants and products c.f. local minimum of the potential energy surface. <ref name="surface" /><br />
<br />
====Report your best estimate of the transition state position (r<sub>ts</sub>) and explain your reasoning illustrating it with an “Internuclear Distances vs Time” plot for a relevant trajectory.====<br />
<br />
The best estemate of the transition state position r<sub>ts</sub> = 91 pm<br />
<br />
[[File:mp5318_Animation.png|thumb|centre|Internuclear Distances vs Time Plot when r<sub>ts</sub> = 91 pm.]]<br />
<br />
As shown in the ''Internuclear Distances vs Time Plot when r<sub>ts</sub> = 91 pm'' above, when r<sub>ts</sub> = 91 pm and p<sub>1</sub> p<sub>2</sub> = 0.0 g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>, internuclear distance reamain (almost) constant, which shows that the molecule does not vibrate and stayed stably at the transition state forever.<br />
<br />
====Comment on how the MEP and the trajectory you just calculated differ.====<br />
<br />
[[File:Mp5318 Surface Plot Dynamic.png|thumb|left|Surface Plot using Dynamic Calculation r<sub>1</sub>=92 pm, r<sub>2</sub>=91 pm]]<br />
<br />
[[File:Surface Plot MEP.png|thumb|centre|Surface Plot using MEP Calculation r<sub>1</sub>=92 pm, r<sub>2</sub>=91 pm]]<br />
<br />
<br clear=all><br />
When '''r<sub>1</sub>'''=92 pm, '''r<sub>2</sub>'''=91 pm, atoms A and B dissociates. Using MEP calculation, AB dissociates through the minimum energy pathway and the dissociation ceased at a displacement much smaller than using Dynamic calculation. In Dynamic trajectory, kinetic energy was acquired during the trajectory from potential energy, therefore encourage inertial motion to proceed. In addition, MEP Calculation does not take into account the momentum of the particles, all the momentums are assumed to be zero.<br />
<br />
When reversing '''r<sub>1</sub>''' and '''r<sub>2</sub>''', B and C dissociates while A and B sticks together. The final values of the positions are '''r<sub>1</sub>''' (73.81819562) '''r<sub>2</sub>''' (352.8544826) and '''p<sub>1</sub>''' (3.258858751) '''p<sub>2</sub>''' (5.06251673). <br />
<br />
When setting up a calculation where the initial positions correspond to the final positions of the trajectory above, the same final momenta values but with their signs reversed, the reaction trajectory travels back to the orginal position '''r<sub>1</sub>''' (91) and '''r<sub>2</sub>''' (92) with '''p<sub>1</sub>'''= '''p<sub>2</sub>'''= 0.<br />
<br />
===Reactive and Unreactive trajectories===<br />
<br />
{| class="wikitable" border="1"<br />
|+ initial positions '''r<sub>1</sub>''' (74 pm) '''r<sub>2</sub>''' (200 pm)<br />
! p<sub>1</sub> / g.mol<sup>-1</sup>.pm.fs<sup>-1</sup> !! p<sub>2</sub> / g.mol<sup>-1</sup>.pm.fs<sup>-1</sup> !! E<sub>tot</sub> kJ.mol<sub>-1</sub> !! Reactive? !! Description of the dunamics !! Illustration of the trajectory<br />
|-<br />
| -2.56 || -5.1 || -414.28 || Yes || A-B + C → A +B-C || [[File:Mp5318 t1.png|356px]]<br />
|-<br />
| -3.1 || -4.1 || -420.08 || No || A-B approaches C, but then leave without reaction occur || [[File:Mp5318 t2.png|356px]]<br />
|-<br />
| -3.1 || -5.1 || -413.98 || Yes || A-B + C → A +B-C || [[File:Mp5318 t3.png|356px]]<br />
|-<br />
| -5.1 || -10.1 || -357.28 || No || at TS region, strength of bondings A-B and B-C alternates, but eventually A-B leave intact (Barrier can be crossed, but then the system reverts back to the reactants) || [[File:Mp5318 t4.png|356px]]<br />
|-<br />
| -5.1 || -10.6 || -349.38 || Yes || A-B + C → A +B-C at TS region, strength of bonding A-B and N-C alternates, but new product formed eventually || [[File:Mp5318 t5.png|356px]]<br />
|}<br />
<br />
'''Conclusion: Reactants need to have a large enough ratio in the momentum to be reactive, ideally, p<sub>2</sub> : p<sub>1</sub> should be larger than 2 for the reactants to be reactive.'''<br />
<br />
===Transition State Theory===<br />
<br />
====Given the results you have obtained, how will Transition State Theory predictions for reaction rate values compare with experimental values?====<br />
<br />
Transition State Theory often overestimates the reaction rate, compared to the results we calculated. Transition State Theory assumed that once the reaction has passed the Transition state and reached the product, it would not travel back to cross the Transition State and reverse to the reactant side. However, the calculations above showed that in practice, products can still recross the energy barrier to go back to the reactants. Even though the Transition State Theory ignored the effect of quantum tunneling, it's a relatively small contribution to rate in this case (small MW for H<sub>2</sub>). Therefore Transition State Theory tends to overestimate reaction rate values compare with experimental values.<br />
<br />
==F-H-H System ==<br />
<br />
=== PES inspection===<br />
<br />
====By inspecting the potential energy surfaces, classify the F + H<sub>2</sub> and H + HF reactions according to their energetics (endothermic or exothermic). How does this relate to the bond strength of the chemical species involved?====<br />
<br />
[[File:Mp5318Surface Plot fh2.png|thumb|left|Potential Surface of F + H<sub>2</sub> Reaction]]<br />
<br />
<br clear=all><br />
<br />
F + H<sub>2</sub> Reaction is exothermic. We can see there is a decrease in energy as H-H bond distance increases while H-F bond distance decreases. The clear downhill of the reaction path indicated exothermic reaction. Bond strength of H-H is 432 kJ/mol, while H-F bond strength is 565 kJ/mol. <ref name="bond energy" /> Formation of H-F bond is preferred, as it would release more energy than the energy needed to break H-H bond. <br />
<br />
H + HF Reaction is endothermic. H-H bond formed is weaker than the H-F bond, therefore energy needed to cross the activation energy barrier — endothermic.<br />
<br />
According to Hammond Postulate, for an exothermic reaction, the TS resembles the reactants (early TS); for an endothermic reaction, the TS resembles the product (late TS). Therefore in this system, TS is very close to the H<sub>2</sub> + F side (H-F distance much longer than H-H distance).<br />
<br />
====Locate the approximate position of the transition state.====<br />
<br />
Position of the TS of H<sub>2</sub> + F Reaction: r<sub>H-H</sub>=74.5 pm; r<sub>H···F</sub>=181.1 pm; At the TS, potential energy = 433.980 kJ/mol<br />
<br />
[[File:Mp5318 TS hhf contour.png|thumb|left|TS of F + H<sub>2</sub> Reaction]]<br />
<br />
[[File:Mp5318distande hhf.png|thumb|centre|Intermolecular distance vs. Time at the TS of F + H<sub>2</sub> Reaction]]<br />
<br clear=all><br />
<br />
AB distance is the H-F distance, BC distance is the H-H distance.<br />
<br />
====Report the activation energy for both reactions.====<br />
In the form of HF + H, potential energy =- 560.642 kJ/mol<br />
In the form o H<sub>2</sub> + F, potential energy = -434.922 kJ/mol<br />
<br />
Therefore compared with the TS potential energy (-433.980 kJ/mol): for HF + H to reach the TS, the activation energy is 126.02 kJ/mol; for H<sub>2</sub> + F to reach the TS, the activation energy is 0.942 kJ/mol.<br />
<br />
===Reaction Dynamics===<br />
<br />
==== 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.====<br />
For the exothermic reaction, in this case, the F + H<sub>2</sub>, energy is released into vibrational energy of product HF. When F approaches H, the repulsion between H-H is released. The released repulsive energy pushes H towards H and produces H-F vibration. <ref name="surface" /><br />
<br />
This could be confirmed experimentally through Infrared Chemiluminescence. <ref name="Infrared Chemiluminescence" />The relative gain on many lines within several vibrational bands could be determined and hence direct measurements of the relative vibrational population in v = 0 can be obtained. We would, therefore, be able to see that the v=2 vibrational level is highly populated (strong peak at v = 2).<br />
<br />
We could also use chemical laser to characterise the HF laser produced. Most of the HF is formed in the v=2 state, thus, the reaction creates an absolute inversion between v=2, v=1, and v=0. The output spectra of pulsed HF lasers showed that more than 60% of the reaction energy is released as vibrational excitation of the HF. <ref name="laser" /><br />
<br />
====Discuss how the distribution of energy between different modes (translation and vibration) affect the efficiency of the reaction, and how this is influenced by the position of the transition state.====<br />
<br />
For H<sub>2</sub> + F system, translational energy is more effective for activating the reaction: Under the conditions illustrated by ''Picture 1'' below, activation barrier was easily crossed by applying translational energy, and the translational energy was converted into product's vibrational energy; c.f. under the conditions illustrated by ''Picture 2'', even when a large amount of vibrational energy was put into the system, the reactants remain unreactive. <br />
<br />
For HF + H system, vibrational energy is more effective for activating the reaction: Under the conditions illustrated by ''Picture 3'' below, activation barrier was easily crossed by applying vibrational energy.<br />
<br />
Translational energy is most effective for passage across an early TS, whereas reactant vibrational energy far in excess of the barrier height may be ineffective for reaction. Conversely, a late TS is best crossed by vibrational energy in the reactants. <ref name="surface" /><br />
<br />
{| class="wikitable" border="1"<br />
|+ distribution of energy under differnt initial conditions<br />
! H<sub>2</sub> + F system (Early TS) !! HF + H system (Late TS)<br />
|-<br />
| [[File: Mp5318 early TS trans.png|thumb|''Picture 1:'' r<sub>(H-H)</sub>=74pm, r<sub>H-F</sub>=200 pm; p<sub>(H-H)</sub>=0 g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>; p<sub>(H-F)</sub>=-1.0g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>]] || [[File: Mp5318 Late TS vib.png|thumb|''Picture 3: ''r<sub>(H-H)</sub>=180pm, r<sub>H-F</sub>=90 pm; p<sub>(H-H)</sub>=15 g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>; p<sub>(H-F)</sub>=-1.0g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>]]<br />
|-<br />
| [[File: Mp5318Early TS vib.png|thumb|''Picture 2:'' r<sub>(H-H)</sub>=74pm, r<sub>H-F</sub>=182 pm; p<sub>(H-H)</sub>=6 g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>; p<sub>(H-F)</sub>=-1.0g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>]] || [[File: Mp5318 late TS trans.png|thumb|''Picture 4:'' r<sub>(H-H)</sub>=180pm, r<sub>H-F</sub>=90 pm; p<sub>(H-H)</sub>=0 g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>; p<sub>(H-F)</sub>=-1.0g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>]]<br />
<br clear=all><br />
<br />
==Reference==<br />
<references><br />
<ref name="surface" /> Laidler, Keith J., in Chemical kinetics, 3rd ed., New York ; London, Harper & Row, 1987<br />
<ref name="bond energy" /> Carruth, Gorton, Ehrlich, Eugene. "Bond Energies." Volume Library. Ed. Carruth, Gorton. Vol 1. Tennessee: Southwestern, 2002.<br />
<ref name="Infrared Chemiluminescence" /> B. P. Levitt, ed. Physical Chemistry of Fast Reactions. Plenum Press, New York. SCHULZ, W. R., and LEROY, D. J. 1965.<br />
<ref name ="laser"/> C. Bradley Moore, Laser studies of vibrational energy transfer, Accounts of Chemical Research 1969 2 (4), 103-109 DOI: 10.1021/ar50016a002<br />
</references></div>Mp5318https://chemwiki.ch.ic.ac.uk/index.php?title=Minqi5318&diff=805933Minqi53182020-05-15T22:19:25Z<p>Mp5318: /* Reference */</p>
<hr />
<div>== Molecular Reaction Dynamics: Application to Triatomic systems ==<br />
<br />
==H +H<sub>1</sub> System ==<br />
<br />
=== Dynamic from transition state region===<br />
<br />
====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?====<br />
<br />
The transition state is defined mathematically as the saddle point on the potential energy surface, where ∂V('''ri''')/∂'''ri'''=0 (the gradient of the potential is zero). At the transition state, the second derivative of potential with respect to q<sub>1</sub> is positive: ∂V<sup>2</sup>(q<sub>1</sub>)/∂q<sub>1</sub> > 0, indicating a minimum of the curve; the second derivative of potential with respect to q<sub>2</sub> is positive: ∂V<sup>2</sup>(q<sub>2</sub>)/∂q<sub>2</sub> < 0, indicating a maximum of the curve. The coincidence of a maximum and a minimum indicates saddle point on the potential energy surface. It can be identified through finding the maximum on the minimum energy path linking reactants and the products. The Transition State's energy goes down most steeply along the minimum energy path linking reactants and products c.f. local minimum of the potential energy surface. <ref name="surface" /><br />
<br />
====Report your best estimate of the transition state position (r<sub>ts</sub>) and explain your reasoning illustrating it with an “Internuclear Distances vs Time” plot for a relevant trajectory.====<br />
<br />
The best estemate of the transition state position r<sub>ts</sub> = 91 pm<br />
<br />
[[File:mp5318_Animation.png|thumb|centre|Internuclear Distances vs Time Plot when r<sub>ts</sub> = 91 pm.]]<br />
<br />
As shown in the ''Internuclear Distances vs Time Plot when r<sub>ts</sub> = 91 pm'' above, when r<sub>ts</sub> = 91 pm and p<sub>1</sub> p<sub>2</sub> = 0.0 g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>, internuclear distance reamain (almost) constant, which shows that the molecule does not vibrate and stayed stably at the transition state forever.<br />
<br />
====Comment on how the MEP and the trajectory you just calculated differ.====<br />
<br />
[[File:Mp5318 Surface Plot Dynamic.png|thumb|left|Surface Plot using Dynamic Calculation r<sub>1</sub>=92 pm, r<sub>2</sub>=91 pm]]<br />
<br />
[[File:Surface Plot MEP.png|thumb|centre|Surface Plot using MEP Calculation r<sub>1</sub>=92 pm, r<sub>2</sub>=91 pm]]<br />
<br />
<br clear=all><br />
When '''r<sub>1</sub>'''=92 pm, '''r<sub>2</sub>'''=91 pm, atoms A and B dissociates. Using MEP calculation, AB dissociates through the minimum energy pathway and the dissociation ceased at a displacement much smaller than using Dynamic calculation. In Dynamic trajectory, kinetic energy was acquired during the trajectory from potential energy, therefore encourage inertial motion to proceed. In addition, MEP Calculation does not take into account the momentum of the particles, all the momentums are assumed to be zero.<br />
<br />
When reversing '''r<sub>1</sub>''' and '''r<sub>2</sub>''', B and C dissociates while A and B sticks together. The final values of the positions are '''r<sub>1</sub>''' (73.81819562) '''r<sub>2</sub>''' (352.8544826) and '''p<sub>1</sub>''' (3.258858751) '''p<sub>2</sub>''' (5.06251673). <br />
<br />
When setting up a calculation where the initial positions correspond to the final positions of the trajectory above, the same final momenta values but with their signs reversed, the reaction trajectory travels back to the orginal position '''r<sub>1</sub>''' (91) and '''r<sub>2</sub>''' (92) with '''p<sub>1</sub>'''= '''p<sub>2</sub>'''= 0.<br />
<br />
===Reactive and Unreactive trajectories===<br />
<br />
{| class="wikitable" border="1"<br />
|+ initial positions '''r<sub>1</sub>''' (74 pm) '''r<sub>2</sub>''' (200 pm)<br />
! p<sub>1</sub> / g.mol<sup>-1</sup>.pm.fs<sup>-1</sup> !! p<sub>2</sub> / g.mol<sup>-1</sup>.pm.fs<sup>-1</sup> !! E<sub>tot</sub> kJ.mol<sub>-1</sub> !! Reactive? !! Description of the dunamics !! Illustration of the trajectory<br />
|-<br />
| -2.56 || -5.1 || -414.28 || Yes || A-B + C → A +B-C || [[File:Mp5318 t1.png|356px]]<br />
|-<br />
| -3.1 || -4.1 || -420.08 || No || A-B approaches C, but then leave without reaction occur || [[File:Mp5318 t2.png|356px]]<br />
|-<br />
| -3.1 || -5.1 || -413.98 || Yes || A-B + C → A +B-C || [[File:Mp5318 t3.png|356px]]<br />
|-<br />
| -5.1 || -10.1 || -357.28 || No || at TS region, strength of bondings A-B and B-C alternates, but eventually A-B leave intact (Barrier can be crossed, but then the system reverts back to the reactants) || [[File:Mp5318 t4.png|356px]]<br />
|-<br />
| -5.1 || -10.6 || -349.38 || Yes || A-B + C → A +B-C at TS region, strength of bonding A-B and N-C alternates, but new product formed eventually || [[File:Mp5318 t5.png|356px]]<br />
|}<br />
<br />
'''Conclusion: Reactants need to have a large enough ratio in the momentum to be reactive, ideally, p<sub>2</sub> : p<sub>1</sub> should be larger than 2 for the reactants to be reactive.'''<br />
<br />
===Transition State Theory===<br />
<br />
====Given the results you have obtained, how will Transition State Theory predictions for reaction rate values compare with experimental values?====<br />
<br />
Transition State Theory often overestimates the reaction rate, compared to the results we calculated. Transition State Theory assumed that once the reaction has passed the Transition state and reached the product, it would not travel back to cross the Transition State and reverse to the reactant side. However, the calculations above showed that in practice, products can still recross the energy barrier to go back to the reactants. Even though the Transition State Theory ignored the effect of quantum tunneling, it's a relatively small contribution to rate in this case (small MW for H<sub>2</sub>). Therefore Transition State Theory tends to overestimate reaction rate values compare with experimental values.<br />
<br />
==F-H-H System ==<br />
<br />
=== PES inspection===<br />
<br />
====By inspecting the potential energy surfaces, classify the F + H<sub>2</sub> and H + HF reactions according to their energetics (endothermic or exothermic). How does this relate to the bond strength of the chemical species involved?====<br />
<br />
[[File:Mp5318Surface Plot fh2.png|thumb|left|Potential Surface of F + H<sub>2</sub> Reaction]]<br />
<br />
<br clear=all><br />
<br />
F + H<sub>2</sub> Reaction is exothermic. We can see there is a decrease in energy as H-H bond distance increases while H-F bond distance decreases. The clear downhill of the reaction path indicated exothermic reaction. Bond strength of H-H is 432 kJ/mol, while H-F bond strength is 565 kJ/mol. <ref name="bond energy" /> Formation of H-F bond is preferred, as it would release more energy than the energy needed to break H-H bond. <br />
<br />
H + HF Reaction is endothermic. H-H bond formed is weaker than the H-F bond, therefore energy needed to cross the activation energy barrier — endothermic.<br />
<br />
According to Hammond Postulate, for an exothermic reaction, the TS resembles the reactants (early TS); for an endothermic reaction, the TS resembles the product (late TS). Therefore in this system, TS is very close to the H<sub>2</sub> + F side (H-F distance much longer than H-H distance).<br />
<br />
====Locate the approximate position of the transition state.====<br />
<br />
Position of the TS of H<sub>2</sub> + F Reaction: r<sub>H-H</sub>=74.5 pm; r<sub>H···F</sub>=181.1 pm; At the TS, potential energy = 433.980 kJ/mol<br />
<br />
[[File:Mp5318 TS hhf contour.png|thumb|left|TS of F + H<sub>2</sub> Reaction]]<br />
<br />
[[File:Mp5318distande hhf.png|thumb|centre|Intermolecular distance vs. Time at the TS of F + H<sub>2</sub> Reaction]]<br />
<br clear=all><br />
<br />
AB distance is the H-F distance, BC distance is the H-H distance.<br />
<br />
====Report the activation energy for both reactions.====<br />
In the form of HF + H, potential energy =- 560.642 kJ/mol<br />
In the form o H<sub>2</sub> + F, potential energy = -434.922 kJ/mol<br />
<br />
Therefore compared with the TS potential energy (-433.980 kJ/mol): for HF + H to reach the TS, the activation energy is 126.02 kJ/mol; for H<sub>2</sub> + F to reach the TS, the activation energy is 0.942 kJ/mol.<br />
<br />
===Reaction Dynamics===<br />
<br />
==== 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.====<br />
For the exothermic reaction, in this case, the F + H<sub>2</sub>, energy is released into vibrational energy of product HF. When F approaches H, the repulsion between H-H is released. The released repulsive energy pushes H towards H and produces H-F vibration. <ref name="surface" /><br />
<br />
This could be confirmed experimentally through Infrared Chemiluminescence. <ref name="Infrared Chemiluminescence" />The relative gain on many lines within several vibrational bands could be determined and hence direct measurements of the relative vibrational population in v = 0 can be obtained. We would, therefore, be able to see that the v=2 vibrational level is highly populated (strong peak at v = 2).<br />
<br />
We could also use chemical laser to characterise the HF laser produced. Most of the HF is formed in the v=2 state, thus, the reaction creates an absolute inversion between v=2, v=1, and v=0. The output spectra of pulsed HF lasers showed that more than 60% of the reaction energy is released as vibrational excitation of the HF. <ref name="laser" /><br />
<br />
====Discuss how the distribution of energy between different modes (translation and vibration) affect the efficiency of the reaction, and how this is influenced by the position of the transition state.====<br />
<br />
For H<sub>2</sub> + F system, translational energy is more effective for activating the reaction: Under the conditions illustrated by ''Picture 1'' below, activation barrier was easily crossed by applying translational energy, and the translational energy was converted into product's vibrational energy; c.f. under the conditions illustrated by ''Picture 2'', even when a large amount of vibrational energy was put into the system, the reactants remain unreactive. <br />
<br />
For HF + H system, vibrational energy is more effective for activating the reaction: Under the conditions illustrated by ''Picture 3'' below, activation barrier was easily crossed by applying vibrational energy.<br />
<br />
Translational energy is most effective for passage across an early TS, whereas reactant vibrational energy far in excess of the barrier height may be ineffective for reaction. Conversely, a late TS is best crossed by vibrational energy in the reactants. <ref name="surface" /><br />
<br />
{| class="wikitable" border="1"<br />
|+ distribution of energy under differnt initial conditions<br />
! H<sub>2</sub> + F system (Early TS) !! HF + H system (Late TS)<br />
|-<br />
| [[File: Mp5318 early TS trans.png|thumb|''Picture 1:'' r<sub>(H-H)</sub>=74pm, r<sub>H-F</sub>=200 pm; p<sub>(H-H)</sub>=0 g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>; p<sub>(H-F)</sub>=-1.0g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>]] || [[File: Mp5318 Late TS vib.png|thumb|''Picture 3: ''r<sub>(H-H)</sub>=180pm, r<sub>H-F</sub>=90 pm; p<sub>(H-H)</sub>=15 g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>; p<sub>(H-F)</sub>=-1.0g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>]]<br />
|-<br />
| [[File: Mp5318Early TS vib.png|thumb|''Picture 2:'' r<sub>(H-H)</sub>=74pm, r<sub>H-F</sub>=182 pm; p<sub>(H-H)</sub>=6 g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>; p<sub>(H-F)</sub>=-1.0g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>]] || [[File: Mp5318 late TS trans.png|thumb|''Picture 4:'' r<sub>(H-H)</sub>=180pm, r<sub>H-F</sub>=90 pm; p<sub>(H-H)</sub>=0 g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>; p<sub>(H-F)</sub>=-1.0g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>]]<br />
<br />
<br />
==Reference==<br />
<references><br />
<ref name="surface" /> Laidler, Keith J., in Chemical kinetics, 3rd ed., New York ; London, Harper & Row, 1987<br />
<ref name="bond energy" /> Carruth, Gorton, Ehrlich, Eugene. "Bond Energies." Volume Library. Ed. Carruth, Gorton. Vol 1. Tennessee: Southwestern, 2002.<br />
<ref name="Infrared Chemiluminescence" /> B. P. Levitt, ed. Physical Chemistry of Fast Reactions. Plenum Press, New York. SCHULZ, W. R., and LEROY, D. J. 1965.<br />
<ref name ="laser"/> C. Bradley Moore, Laser studies of vibrational energy transfer, Accounts of Chemical Research 1969 2 (4), 103-109 DOI: 10.1021/ar50016a002<br />
</references></div>Mp5318https://chemwiki.ch.ic.ac.uk/index.php?title=Minqi5318&diff=805932Minqi53182020-05-15T22:18:58Z<p>Mp5318: </p>
<hr />
<div>== Molecular Reaction Dynamics: Application to Triatomic systems ==<br />
<br />
==H +H<sub>1</sub> System ==<br />
<br />
=== Dynamic from transition state region===<br />
<br />
====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?====<br />
<br />
The transition state is defined mathematically as the saddle point on the potential energy surface, where ∂V('''ri''')/∂'''ri'''=0 (the gradient of the potential is zero). At the transition state, the second derivative of potential with respect to q<sub>1</sub> is positive: ∂V<sup>2</sup>(q<sub>1</sub>)/∂q<sub>1</sub> > 0, indicating a minimum of the curve; the second derivative of potential with respect to q<sub>2</sub> is positive: ∂V<sup>2</sup>(q<sub>2</sub>)/∂q<sub>2</sub> < 0, indicating a maximum of the curve. The coincidence of a maximum and a minimum indicates saddle point on the potential energy surface. It can be identified through finding the maximum on the minimum energy path linking reactants and the products. The Transition State's energy goes down most steeply along the minimum energy path linking reactants and products c.f. local minimum of the potential energy surface. <ref name="surface" /><br />
<br />
====Report your best estimate of the transition state position (r<sub>ts</sub>) and explain your reasoning illustrating it with an “Internuclear Distances vs Time” plot for a relevant trajectory.====<br />
<br />
The best estemate of the transition state position r<sub>ts</sub> = 91 pm<br />
<br />
[[File:mp5318_Animation.png|thumb|centre|Internuclear Distances vs Time Plot when r<sub>ts</sub> = 91 pm.]]<br />
<br />
As shown in the ''Internuclear Distances vs Time Plot when r<sub>ts</sub> = 91 pm'' above, when r<sub>ts</sub> = 91 pm and p<sub>1</sub> p<sub>2</sub> = 0.0 g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>, internuclear distance reamain (almost) constant, which shows that the molecule does not vibrate and stayed stably at the transition state forever.<br />
<br />
====Comment on how the MEP and the trajectory you just calculated differ.====<br />
<br />
[[File:Mp5318 Surface Plot Dynamic.png|thumb|left|Surface Plot using Dynamic Calculation r<sub>1</sub>=92 pm, r<sub>2</sub>=91 pm]]<br />
<br />
[[File:Surface Plot MEP.png|thumb|centre|Surface Plot using MEP Calculation r<sub>1</sub>=92 pm, r<sub>2</sub>=91 pm]]<br />
<br />
<br clear=all><br />
When '''r<sub>1</sub>'''=92 pm, '''r<sub>2</sub>'''=91 pm, atoms A and B dissociates. Using MEP calculation, AB dissociates through the minimum energy pathway and the dissociation ceased at a displacement much smaller than using Dynamic calculation. In Dynamic trajectory, kinetic energy was acquired during the trajectory from potential energy, therefore encourage inertial motion to proceed. In addition, MEP Calculation does not take into account the momentum of the particles, all the momentums are assumed to be zero.<br />
<br />
When reversing '''r<sub>1</sub>''' and '''r<sub>2</sub>''', B and C dissociates while A and B sticks together. The final values of the positions are '''r<sub>1</sub>''' (73.81819562) '''r<sub>2</sub>''' (352.8544826) and '''p<sub>1</sub>''' (3.258858751) '''p<sub>2</sub>''' (5.06251673). <br />
<br />
When setting up a calculation where the initial positions correspond to the final positions of the trajectory above, the same final momenta values but with their signs reversed, the reaction trajectory travels back to the orginal position '''r<sub>1</sub>''' (91) and '''r<sub>2</sub>''' (92) with '''p<sub>1</sub>'''= '''p<sub>2</sub>'''= 0.<br />
<br />
===Reactive and Unreactive trajectories===<br />
<br />
{| class="wikitable" border="1"<br />
|+ initial positions '''r<sub>1</sub>''' (74 pm) '''r<sub>2</sub>''' (200 pm)<br />
! p<sub>1</sub> / g.mol<sup>-1</sup>.pm.fs<sup>-1</sup> !! p<sub>2</sub> / g.mol<sup>-1</sup>.pm.fs<sup>-1</sup> !! E<sub>tot</sub> kJ.mol<sub>-1</sub> !! Reactive? !! Description of the dunamics !! Illustration of the trajectory<br />
|-<br />
| -2.56 || -5.1 || -414.28 || Yes || A-B + C → A +B-C || [[File:Mp5318 t1.png|356px]]<br />
|-<br />
| -3.1 || -4.1 || -420.08 || No || A-B approaches C, but then leave without reaction occur || [[File:Mp5318 t2.png|356px]]<br />
|-<br />
| -3.1 || -5.1 || -413.98 || Yes || A-B + C → A +B-C || [[File:Mp5318 t3.png|356px]]<br />
|-<br />
| -5.1 || -10.1 || -357.28 || No || at TS region, strength of bondings A-B and B-C alternates, but eventually A-B leave intact (Barrier can be crossed, but then the system reverts back to the reactants) || [[File:Mp5318 t4.png|356px]]<br />
|-<br />
| -5.1 || -10.6 || -349.38 || Yes || A-B + C → A +B-C at TS region, strength of bonding A-B and N-C alternates, but new product formed eventually || [[File:Mp5318 t5.png|356px]]<br />
|}<br />
<br />
'''Conclusion: Reactants need to have a large enough ratio in the momentum to be reactive, ideally, p<sub>2</sub> : p<sub>1</sub> should be larger than 2 for the reactants to be reactive.'''<br />
<br />
===Transition State Theory===<br />
<br />
====Given the results you have obtained, how will Transition State Theory predictions for reaction rate values compare with experimental values?====<br />
<br />
Transition State Theory often overestimates the reaction rate, compared to the results we calculated. Transition State Theory assumed that once the reaction has passed the Transition state and reached the product, it would not travel back to cross the Transition State and reverse to the reactant side. However, the calculations above showed that in practice, products can still recross the energy barrier to go back to the reactants. Even though the Transition State Theory ignored the effect of quantum tunneling, it's a relatively small contribution to rate in this case (small MW for H<sub>2</sub>). Therefore Transition State Theory tends to overestimate reaction rate values compare with experimental values.<br />
<br />
==F-H-H System ==<br />
<br />
=== PES inspection===<br />
<br />
====By inspecting the potential energy surfaces, classify the F + H<sub>2</sub> and H + HF reactions according to their energetics (endothermic or exothermic). How does this relate to the bond strength of the chemical species involved?====<br />
<br />
[[File:Mp5318Surface Plot fh2.png|thumb|left|Potential Surface of F + H<sub>2</sub> Reaction]]<br />
<br />
<br clear=all><br />
<br />
F + H<sub>2</sub> Reaction is exothermic. We can see there is a decrease in energy as H-H bond distance increases while H-F bond distance decreases. The clear downhill of the reaction path indicated exothermic reaction. Bond strength of H-H is 432 kJ/mol, while H-F bond strength is 565 kJ/mol. <ref name="bond energy" /> Formation of H-F bond is preferred, as it would release more energy than the energy needed to break H-H bond. <br />
<br />
H + HF Reaction is endothermic. H-H bond formed is weaker than the H-F bond, therefore energy needed to cross the activation energy barrier — endothermic.<br />
<br />
According to Hammond Postulate, for an exothermic reaction, the TS resembles the reactants (early TS); for an endothermic reaction, the TS resembles the product (late TS). Therefore in this system, TS is very close to the H<sub>2</sub> + F side (H-F distance much longer than H-H distance).<br />
<br />
====Locate the approximate position of the transition state.====<br />
<br />
Position of the TS of H<sub>2</sub> + F Reaction: r<sub>H-H</sub>=74.5 pm; r<sub>H···F</sub>=181.1 pm; At the TS, potential energy = 433.980 kJ/mol<br />
<br />
[[File:Mp5318 TS hhf contour.png|thumb|left|TS of F + H<sub>2</sub> Reaction]]<br />
<br />
[[File:Mp5318distande hhf.png|thumb|centre|Intermolecular distance vs. Time at the TS of F + H<sub>2</sub> Reaction]]<br />
<br clear=all><br />
<br />
AB distance is the H-F distance, BC distance is the H-H distance.<br />
<br />
====Report the activation energy for both reactions.====<br />
In the form of HF + H, potential energy =- 560.642 kJ/mol<br />
In the form o H<sub>2</sub> + F, potential energy = -434.922 kJ/mol<br />
<br />
Therefore compared with the TS potential energy (-433.980 kJ/mol): for HF + H to reach the TS, the activation energy is 126.02 kJ/mol; for H<sub>2</sub> + F to reach the TS, the activation energy is 0.942 kJ/mol.<br />
<br />
===Reaction Dynamics===<br />
<br />
==== 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.====<br />
For the exothermic reaction, in this case, the F + H<sub>2</sub>, energy is released into vibrational energy of product HF. When F approaches H, the repulsion between H-H is released. The released repulsive energy pushes H towards H and produces H-F vibration. <ref name="surface" /><br />
<br />
This could be confirmed experimentally through Infrared Chemiluminescence. <ref name="Infrared Chemiluminescence" />The relative gain on many lines within several vibrational bands could be determined and hence direct measurements of the relative vibrational population in v = 0 can be obtained. We would, therefore, be able to see that the v=2 vibrational level is highly populated (strong peak at v = 2).<br />
<br />
We could also use chemical laser to characterise the HF laser produced. Most of the HF is formed in the v=2 state, thus, the reaction creates an absolute inversion between v=2, v=1, and v=0. The output spectra of pulsed HF lasers showed that more than 60% of the reaction energy is released as vibrational excitation of the HF. <ref name="laser" /><br />
<br />
====Discuss how the distribution of energy between different modes (translation and vibration) affect the efficiency of the reaction, and how this is influenced by the position of the transition state.====<br />
<br />
For H<sub>2</sub> + F system, translational energy is more effective for activating the reaction: Under the conditions illustrated by ''Picture 1'' below, activation barrier was easily crossed by applying translational energy, and the translational energy was converted into product's vibrational energy; c.f. under the conditions illustrated by ''Picture 2'', even when a large amount of vibrational energy was put into the system, the reactants remain unreactive. <br />
<br />
For HF + H system, vibrational energy is more effective for activating the reaction: Under the conditions illustrated by ''Picture 3'' below, activation barrier was easily crossed by applying vibrational energy.<br />
<br />
Translational energy is most effective for passage across an early TS, whereas reactant vibrational energy far in excess of the barrier height may be ineffective for reaction. Conversely, a late TS is best crossed by vibrational energy in the reactants. <ref name="surface" /><br />
<br />
{| class="wikitable" border="1"<br />
|+ distribution of energy under differnt initial conditions<br />
! H<sub>2</sub> + F system (Early TS) !! HF + H system (Late TS)<br />
|-<br />
| [[File: Mp5318 early TS trans.png|thumb|''Picture 1:'' r<sub>(H-H)</sub>=74pm, r<sub>H-F</sub>=200 pm; p<sub>(H-H)</sub>=0 g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>; p<sub>(H-F)</sub>=-1.0g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>]] || [[File: Mp5318 Late TS vib.png|thumb|''Picture 3: ''r<sub>(H-H)</sub>=180pm, r<sub>H-F</sub>=90 pm; p<sub>(H-H)</sub>=15 g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>; p<sub>(H-F)</sub>=-1.0g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>]]<br />
|-<br />
| [[File: Mp5318Early TS vib.png|thumb|''Picture 2:'' r<sub>(H-H)</sub>=74pm, r<sub>H-F</sub>=182 pm; p<sub>(H-H)</sub>=6 g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>; p<sub>(H-F)</sub>=-1.0g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>]] || [[File: Mp5318 late TS trans.png|thumb|''Picture 4:'' r<sub>(H-H)</sub>=180pm, r<sub>H-F</sub>=90 pm; p<sub>(H-H)</sub>=0 g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>; p<sub>(H-F)</sub>=-1.0g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>]]<br />
<br />
===Reference===<br />
<references><br />
<ref name="surface" /> Laidler, Keith J., in Chemical kinetics, 3rd ed., New York ; London, Harper & Row, 1987<br />
<ref name="bond energy" /> Carruth, Gorton, Ehrlich, Eugene. "Bond Energies." Volume Library. Ed. Carruth, Gorton. Vol 1. Tennessee: Southwestern, 2002.<br />
<ref name="Infrared Chemiluminescence" /> B. P. Levitt, ed. Physical Chemistry of Fast Reactions. Plenum Press, New York. SCHULZ, W. R., and LEROY, D. J. 1965.<br />
<ref name ="laser"/> C. Bradley Moore, Laser studies of vibrational energy transfer, Accounts of Chemical Research 1969 2 (4), 103-109 DOI: 10.1021/ar50016a002<br />
</references></div>Mp5318https://chemwiki.ch.ic.ac.uk/index.php?title=Minqi5318&diff=805897Minqi53182020-05-15T21:58:43Z<p>Mp5318: /* Discuss how the distribution of energy between different modes (translation and vibration) affect the efficiency of the reaction, and how this is influenced by the position of the transition state. */</p>
<hr />
<div>== Molecular Reaction Dynamics: Application to Triatomic systems ==<br />
<br />
==H +H<sub>1</sub> System ==<br />
<br />
=== Dynamic from transition state region===<br />
<br />
====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?====<br />
<br />
The transition state is defined mathematically as the saddle point on the potential energy surface, where ∂V('''ri''')/∂'''ri'''=0 (the gradient of the potential is zero). At the transition state, the second derivative of potential with respect to q<sub>1</sub> is positive: ∂V<sup>2</sup>(q<sub>1</sub>)/∂q<sub>1</sub> > 0, indicating a minimum of the curve; the second derivative of potential with respect to q<sub>2</sub> is positive: ∂V<sup>2</sup>(q<sub>2</sub>)/∂q<sub>2</sub> < 0, indicating a maximum of the curve. The coincidence of a maximum and a minimum indicates saddle point on the potential energy surface. It can be identified through finding the maximum on the minimum energy path linking reactants and the products. The Transition State's energy goes down most steeply along the minimum energy path linking reactants and products c.f. local minimum of the potential energy surface. <br />
<br />
====Report your best estimate of the transition state position (r<sub>ts</sub>) and explain your reasoning illustrating it with an “Internuclear Distances vs Time” plot for a relevant trajectory.====<br />
<br />
The best estemate of the transition state position r<sub>ts</sub> = 91 pm<br />
<br />
[[File:mp5318_Animation.png|thumb|centre|Internuclear Distances vs Time Plot when r<sub>ts</sub> = 91 pm.]]<br />
<br />
As shown in the ''Internuclear Distances vs Time Plot when r<sub>ts</sub> = 91 pm'' above, when r<sub>ts</sub> = 91 pm and p<sub>1</sub> p<sub>2</sub> = 0.0 g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>, internuclear distance reamain (almost) constant, which shows that the molecule does not vibrate and stayed stably at the transition state forever.<br />
<br />
====Comment on how the MEP and the trajectory you just calculated differ.====<br />
<br />
[[File:Mp5318 Surface Plot Dynamic.png|thumb|left|Surface Plot using Dynamic Calculation r<sub>1</sub>=92 pm, r<sub>2</sub>=91 pm]]<br />
<br />
[[File:Surface Plot MEP.png|thumb|centre|Surface Plot using MEP Calculation r<sub>1</sub>=92 pm, r<sub>2</sub>=91 pm]]<br />
<br />
<br clear=all><br />
When '''r<sub>1</sub>'''=92 pm, '''r<sub>2</sub>'''=91 pm, atoms A and B dissociates. Using MEP calculation, AB dissociates through the minimum energy pathway and the dissociation ceased at a displacement much smaller than using Dynamic calculation. In Dynamic trajectory, kinetic energy was acquired during the trajectory from potential energy, therefore encourage inertial motion to proceed. In addition, MEP Calculation does not take into account the momentum of the particles, all the momentums are assumed to be zero.<br />
<br />
When reversing '''r<sub>1</sub>''' and '''r<sub>2</sub>''', B and C dissociates while A and B sticks together. The final values of the positions are '''r<sub>1</sub>''' (73.81819562) '''r<sub>2</sub>''' (352.8544826) and '''p<sub>1</sub>''' (3.258858751) '''p<sub>2</sub>''' (5.06251673). <br />
<br />
When setting up a calculation where the initial positions correspond to the final positions of the trajectory above, the same final momenta values but with their signs reversed, the reaction trajectory travels back to the orginal position '''r<sub>1</sub>''' (91) and '''r<sub>2</sub>''' (92) with '''p<sub>1</sub>'''= '''p<sub>2</sub>'''= 0.<br />
<br />
===Reactive and Unreactive trajectories===<br />
<br />
{| class="wikitable" border="1"<br />
|+ initial positions '''r<sub>1</sub>''' (74 pm) '''r<sub>2</sub>''' (200 pm)<br />
! p<sub>1</sub> / g.mol<sup>-1</sup>.pm.fs<sup>-1</sup> !! p<sub>2</sub> / g.mol<sup>-1</sup>.pm.fs<sup>-1</sup> !! E<sub>tot</sub> kJ.mol<sub>-1</sub> !! Reactive? !! Description of the dunamics !! Illustration of the trajectory<br />
|-<br />
| -2.56 || -5.1 || -414.28 || Yes || A-B + C → A +B-C || [[File:Mp5318 t1.png|356px]]<br />
|-<br />
| -3.1 || -4.1 || -420.08 || No || A-B approaches C, but then leave without reaction occur || [[File:Mp5318 t2.png|356px]]<br />
|-<br />
| -3.1 || -5.1 || -413.98 || Yes || A-B + C → A +B-C || [[File:Mp5318 t3.png|356px]]<br />
|-<br />
| -5.1 || -10.1 || -357.28 || No || at TS region, strength of bondings A-B and B-C alternates, but eventually A-B leave intact (Barrier can be crossed, but then the system reverts back to the reactants) || [[File:Mp5318 t4.png|356px]]<br />
|-<br />
| -5.1 || -10.6 || -349.38 || Yes || A-B + C → A +B-C at TS region, strength of bonding A-B and N-C alternates, but new product formed eventually || [[File:Mp5318 t5.png|356px]]<br />
|}<br />
<br />
'''Conclusion: Reactants need to have a large enough ratio in the momentum to be reactive, ideally, p<sub>2</sub> : p<sub>1</sub> should be larger than 2 for the reactants to be reactive.'''<br />
<br />
===Transition State Theory===<br />
<br />
====Given the results you have obtained, how will Transition State Theory predictions for reaction rate values compare with experimental values?====<br />
<br />
Transition State Theory often overestimates the reaction rate, compared to the results we calculated. Transition State Theory assumed that once the reaction has passed the Transition state and reached the product, it would not travel back to cross the Transition State and reverse to the reactant side. However, the calculations above showed that in practice, products can still recross the energy barrier to go back to the reactants. Even though the Transition State Theory ignored the effect of quantum tunneling, it's a relatively small contribution to rate in this case (small MW for H<sub>2</sub>). Therefore Transition State Theory tends to overestimate reaction rate values compare with experimental values.<br />
<br />
==F-H-H System ==<br />
<br />
=== PES inspection===<br />
<br />
====By inspecting the potential energy surfaces, classify the F + H<sub>2</sub> and H + HF reactions according to their energetics (endothermic or exothermic). How does this relate to the bond strength of the chemical species involved?====<br />
<br />
[[File:Mp5318Surface Plot fh2.png|thumb|left|Potential Surface of F + H<sub>2</sub> Reaction]]<br />
<br />
<br clear=all><br />
<br />
F + H<sub>2</sub> Reaction is exothermic. We can see there is a decrease in energy as H-H bond distance increases while H-F bond distance decreases. The clear downhill of reaction path indicated exothermic reaction. Bond strength of H-H is 432 kJ/mol, while H-F bond strength is 565 kJ/mol. Formation of H-F bond is preferred, as it would release more energy than the energy needed to break H-H bond. <br />
<br />
H + HF Reaction is endothermic. H-H bond formed is weaker than the H-F bond, therefore energy needed to cross the activation energy barrier — endothermic.<br />
<br />
According to Hammond Postulate, for an exothermic reaction, the TS resembles the reactants (early TS); for an endothermic reaction, the TS resembles the product (late TS). Therefore in this system, TS is very close to the H<sub>2</sub> + F side (H-F distance much longer than H-H distance) .<br />
<br />
====Locate the approximate position of the transition state.====<br />
<br />
Position of the TS of H<sub>2</sub> + F Reaction: r<sub>H-H</sub>=74.5 pm; r<sub>H···F</sub>=181.1 pm; At the TS, potential energy = 433.980 kJ/mol<br />
<br />
[[File:Mp5318 TS hhf contour.png|thumb|left|TS of F + H<sub>2</sub> Reaction]]<br />
<br />
[[File:Mp5318distande hhf.png|thumb|centre|Intermolecular distance vs. Time at the TS of F + H<sub>2</sub> Reaction]]<br />
<br clear=all><br />
<br />
AB distance is the H-F distance, BC distance is the H-H distance.<br />
<br />
====Report the activation energy for both reactions.====<br />
In the form of HF + H, potential energy =- 560.642 kJ/mol<br />
In the form o H<sub>2</sub> + F, potential energy = -434.922 kJ/mol<br />
<br />
Therefore compared with the TS potential energy (-433.980 kJ/mol): for HF + H to reach the TS, the activation energy is 126.02 kJ/mol; for H<sub>2</sub> + F to reach the TS, the activation energy is 0.942 kJ/mol.<br />
<br />
===Reaction Dynamics===<br />
<br />
==== 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.====<br />
For the exothermic reaction, in this case, the F + H<sub>2</sub>, energy is released into vibrational energy of product HF. When F approaches H, the repulsion between H-H is released. The released repulsive energy pushes H towards H and produces H-F vibration. <br />
<br />
This could be confirmed experimentally through Infrared Chemiluminescence. The relative gain on many lines within several vibrational bands could be determined and hence direct measurements of the relative vibrational population in v = 0 can be obtained. We would, therefore, be able to see that the v=2 vibrational level is highly populated (strong peak at v = 2).<br />
<br />
We could also use chemical laser to characterise the HF laser produced. Most of the HF is formed in the v=2 state, thus, the reaction creates an absolute inversion between v=2, v=1, and v=0. The output spectra of pulsed HF lasers showed that more than 60% ot eh reaction energy is released as vibrational excitation of the HF.<br />
<br />
====Discuss how the distribution of energy between different modes (translation and vibration) affect the efficiency of the reaction, and how this is influenced by the position of the transition state.====<br />
<br />
For H<sub>2</sub> + F system, translational energy is more effective for activating the reaction: Under the conditions illustrated by ''Picture 1'' below, activation barrier was easily crossed by applying translational energy, and the translational energy was converted into product's vibrational energy; c.f. under the conditions illustrated by ''Picture 2'', even when a large amount of vibrational energy was put into the system, the reactants remain unreactive. <br />
<br />
For HF + H system, vibrational energy is more effective for activating the reaction: Under the conditions illustrated by ''Picture 3'' below, activation barrier was easily crossed by applying vibrational energy.<br />
<br />
Translational energy is most effective for passage across an early TS, whereas reactant vibrational energy far in excess of the barrier height may be ineffective for reaction. Conversely, a late TS is best crossed by vibrational energy in the reactnas. <br />
<br />
{| class="wikitable" border="1"<br />
|+ distribution of energy under differnt initial conditions<br />
! H<sub>2</sub> + F system (Early TS) !! HF + H system (Late TS)<br />
|-<br />
| [[File: Mp5318 early TS trans.png|thumb|''Picture 1:'' r<sub>(H-H)</sub>=74pm, r<sub>H-F</sub>=200 pm; p<sub>(H-H)</sub>=0 g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>; p<sub>(H-F)</sub>=-1.0g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>]] || [[File: Mp5318 Late TS vib.png|thumb|''Picture 3: ''r<sub>(H-H)</sub>=180pm, r<sub>H-F</sub>=90 pm; p<sub>(H-H)</sub>=15 g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>; p<sub>(H-F)</sub>=-1.0g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>]]<br />
|-<br />
| [[File: Mp5318Early TS vib.png|thumb|''Picture 2:'' r<sub>(H-H)</sub>=74pm, r<sub>H-F</sub>=182 pm; p<sub>(H-H)</sub>=6 g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>; p<sub>(H-F)</sub>=-1.0g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>]] || [[File: Mp5318 late TS trans.png|thumb|''Picture 4:'' r<sub>(H-H)</sub>=180pm, r<sub>H-F</sub>=90 pm; p<sub>(H-H)</sub>=0 g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>; p<sub>(H-F)</sub>=-1.0g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>]]</div>Mp5318https://chemwiki.ch.ic.ac.uk/index.php?title=Minqi5318&diff=805896Minqi53182020-05-15T21:58:01Z<p>Mp5318: /* Discuss how the distribution of energy between different modes (translation and vibration) affect the efficiency of the reaction, and how this is influenced by the position of the transition state. */</p>
<hr />
<div>== Molecular Reaction Dynamics: Application to Triatomic systems ==<br />
<br />
==H +H<sub>1</sub> System ==<br />
<br />
=== Dynamic from transition state region===<br />
<br />
====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?====<br />
<br />
The transition state is defined mathematically as the saddle point on the potential energy surface, where ∂V('''ri''')/∂'''ri'''=0 (the gradient of the potential is zero). At the transition state, the second derivative of potential with respect to q<sub>1</sub> is positive: ∂V<sup>2</sup>(q<sub>1</sub>)/∂q<sub>1</sub> > 0, indicating a minimum of the curve; the second derivative of potential with respect to q<sub>2</sub> is positive: ∂V<sup>2</sup>(q<sub>2</sub>)/∂q<sub>2</sub> < 0, indicating a maximum of the curve. The coincidence of a maximum and a minimum indicates saddle point on the potential energy surface. It can be identified through finding the maximum on the minimum energy path linking reactants and the products. The Transition State's energy goes down most steeply along the minimum energy path linking reactants and products c.f. local minimum of the potential energy surface. <br />
<br />
====Report your best estimate of the transition state position (r<sub>ts</sub>) and explain your reasoning illustrating it with an “Internuclear Distances vs Time” plot for a relevant trajectory.====<br />
<br />
The best estemate of the transition state position r<sub>ts</sub> = 91 pm<br />
<br />
[[File:mp5318_Animation.png|thumb|centre|Internuclear Distances vs Time Plot when r<sub>ts</sub> = 91 pm.]]<br />
<br />
As shown in the ''Internuclear Distances vs Time Plot when r<sub>ts</sub> = 91 pm'' above, when r<sub>ts</sub> = 91 pm and p<sub>1</sub> p<sub>2</sub> = 0.0 g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>, internuclear distance reamain (almost) constant, which shows that the molecule does not vibrate and stayed stably at the transition state forever.<br />
<br />
====Comment on how the MEP and the trajectory you just calculated differ.====<br />
<br />
[[File:Mp5318 Surface Plot Dynamic.png|thumb|left|Surface Plot using Dynamic Calculation r<sub>1</sub>=92 pm, r<sub>2</sub>=91 pm]]<br />
<br />
[[File:Surface Plot MEP.png|thumb|centre|Surface Plot using MEP Calculation r<sub>1</sub>=92 pm, r<sub>2</sub>=91 pm]]<br />
<br />
<br clear=all><br />
When '''r<sub>1</sub>'''=92 pm, '''r<sub>2</sub>'''=91 pm, atoms A and B dissociates. Using MEP calculation, AB dissociates through the minimum energy pathway and the dissociation ceased at a displacement much smaller than using Dynamic calculation. In Dynamic trajectory, kinetic energy was acquired during the trajectory from potential energy, therefore encourage inertial motion to proceed. In addition, MEP Calculation does not take into account the momentum of the particles, all the momentums are assumed to be zero.<br />
<br />
When reversing '''r<sub>1</sub>''' and '''r<sub>2</sub>''', B and C dissociates while A and B sticks together. The final values of the positions are '''r<sub>1</sub>''' (73.81819562) '''r<sub>2</sub>''' (352.8544826) and '''p<sub>1</sub>''' (3.258858751) '''p<sub>2</sub>''' (5.06251673). <br />
<br />
When setting up a calculation where the initial positions correspond to the final positions of the trajectory above, the same final momenta values but with their signs reversed, the reaction trajectory travels back to the orginal position '''r<sub>1</sub>''' (91) and '''r<sub>2</sub>''' (92) with '''p<sub>1</sub>'''= '''p<sub>2</sub>'''= 0.<br />
<br />
===Reactive and Unreactive trajectories===<br />
<br />
{| class="wikitable" border="1"<br />
|+ initial positions '''r<sub>1</sub>''' (74 pm) '''r<sub>2</sub>''' (200 pm)<br />
! p<sub>1</sub> / g.mol<sup>-1</sup>.pm.fs<sup>-1</sup> !! p<sub>2</sub> / g.mol<sup>-1</sup>.pm.fs<sup>-1</sup> !! E<sub>tot</sub> kJ.mol<sub>-1</sub> !! Reactive? !! Description of the dunamics !! Illustration of the trajectory<br />
|-<br />
| -2.56 || -5.1 || -414.28 || Yes || A-B + C → A +B-C || [[File:Mp5318 t1.png|356px]]<br />
|-<br />
| -3.1 || -4.1 || -420.08 || No || A-B approaches C, but then leave without reaction occur || [[File:Mp5318 t2.png|356px]]<br />
|-<br />
| -3.1 || -5.1 || -413.98 || Yes || A-B + C → A +B-C || [[File:Mp5318 t3.png|356px]]<br />
|-<br />
| -5.1 || -10.1 || -357.28 || No || at TS region, strength of bondings A-B and B-C alternates, but eventually A-B leave intact (Barrier can be crossed, but then the system reverts back to the reactants) || [[File:Mp5318 t4.png|356px]]<br />
|-<br />
| -5.1 || -10.6 || -349.38 || Yes || A-B + C → A +B-C at TS region, strength of bonding A-B and N-C alternates, but new product formed eventually || [[File:Mp5318 t5.png|356px]]<br />
|}<br />
<br />
'''Conclusion: Reactants need to have a large enough ratio in the momentum to be reactive, ideally, p<sub>2</sub> : p<sub>1</sub> should be larger than 2 for the reactants to be reactive.'''<br />
<br />
===Transition State Theory===<br />
<br />
====Given the results you have obtained, how will Transition State Theory predictions for reaction rate values compare with experimental values?====<br />
<br />
Transition State Theory often overestimates the reaction rate, compared to the results we calculated. Transition State Theory assumed that once the reaction has passed the Transition state and reached the product, it would not travel back to cross the Transition State and reverse to the reactant side. However, the calculations above showed that in practice, products can still recross the energy barrier to go back to the reactants. Even though the Transition State Theory ignored the effect of quantum tunneling, it's a relatively small contribution to rate in this case (small MW for H<sub>2</sub>). Therefore Transition State Theory tends to overestimate reaction rate values compare with experimental values.<br />
<br />
==F-H-H System ==<br />
<br />
=== PES inspection===<br />
<br />
====By inspecting the potential energy surfaces, classify the F + H<sub>2</sub> and H + HF reactions according to their energetics (endothermic or exothermic). How does this relate to the bond strength of the chemical species involved?====<br />
<br />
[[File:Mp5318Surface Plot fh2.png|thumb|left|Potential Surface of F + H<sub>2</sub> Reaction]]<br />
<br />
<br clear=all><br />
<br />
F + H<sub>2</sub> Reaction is exothermic. We can see there is a decrease in energy as H-H bond distance increases while H-F bond distance decreases. The clear downhill of reaction path indicated exothermic reaction. Bond strength of H-H is 432 kJ/mol, while H-F bond strength is 565 kJ/mol. Formation of H-F bond is preferred, as it would release more energy than the energy needed to break H-H bond. <br />
<br />
H + HF Reaction is endothermic. H-H bond formed is weaker than the H-F bond, therefore energy needed to cross the activation energy barrier — endothermic.<br />
<br />
According to Hammond Postulate, for an exothermic reaction, the TS resembles the reactants (early TS); for an endothermic reaction, the TS resembles the product (late TS). Therefore in this system, TS is very close to the H<sub>2</sub> + F side (H-F distance much longer than H-H distance) .<br />
<br />
====Locate the approximate position of the transition state.====<br />
<br />
Position of the TS of H<sub>2</sub> + F Reaction: r<sub>H-H</sub>=74.5 pm; r<sub>H···F</sub>=181.1 pm; At the TS, potential energy = 433.980 kJ/mol<br />
<br />
[[File:Mp5318 TS hhf contour.png|thumb|left|TS of F + H<sub>2</sub> Reaction]]<br />
<br />
[[File:Mp5318distande hhf.png|thumb|centre|Intermolecular distance vs. Time at the TS of F + H<sub>2</sub> Reaction]]<br />
<br clear=all><br />
<br />
AB distance is the H-F distance, BC distance is the H-H distance.<br />
<br />
====Report the activation energy for both reactions.====<br />
In the form of HF + H, potential energy =- 560.642 kJ/mol<br />
In the form o H<sub>2</sub> + F, potential energy = -434.922 kJ/mol<br />
<br />
Therefore compared with the TS potential energy (-433.980 kJ/mol): for HF + H to reach the TS, the activation energy is 126.02 kJ/mol; for H<sub>2</sub> + F to reach the TS, the activation energy is 0.942 kJ/mol.<br />
<br />
===Reaction Dynamics===<br />
<br />
==== 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.====<br />
For the exothermic reaction, in this case, the F + H<sub>2</sub>, energy is released into vibrational energy of product HF. When F approaches H, the repulsion between H-H is released. The released repulsive energy pushes H towards H and produces H-F vibration. <br />
<br />
This could be confirmed experimentally through Infrared Chemiluminescence. The relative gain on many lines within several vibrational bands could be determined and hence direct measurements of the relative vibrational population in v = 0 can be obtained. We would, therefore, be able to see that the v=2 vibrational level is highly populated (strong peak at v = 2).<br />
<br />
We could also use chemical laser to characterise the HF laser produced. Most of the HF is formed in the v=2 state, thus, the reaction creates an absolute inversion between v=2, v=1, and v=0. The output spectra of pulsed HF lasers showed that more than 60% ot eh reaction energy is released as vibrational excitation of the HF.<br />
<br />
====Discuss how the distribution of energy between different modes (translation and vibration) affect the efficiency of the reaction, and how this is influenced by the position of the transition state.====<br />
<br />
For H<sub>2</sub> + F system, translational energy is more effective for activating the reaction: Under the conditions illustrated by ''Picture 1'' below, activation barrier was easily crossed by applying translational energy, and the translational energy was converted into product's vibrational energy; c.f. under the conditions illustrated by ''Picture 2'', even when a large amount of vibrational energy was put into the system, the reactants remain unreactive. <br />
<br />
For HF + H system, vibrational energy is more effective for activating the reaction: Under the conditions illustrated by ''Picture 3'' below, activation barrier was easily crossed by applying vibrational energy.<br />
<br />
Translational energy is most effective for passage across an early TS, whereas reactant vibrational energy far in excess of the barrier height may be ineffective for reaction. Conversely, a late TS is best crossed by vibrational energy in the reactnas. <br />
<br />
{| class="wikitable" border="1"<br />
|+ distribution of energy under differnt initial conditions<br />
! H<sub>2</sub> + F system (Early TS) !! HF + H system (Late TS)<br />
|-<br />
| [[File: Mp5318 early TS trans.png|thumb|''Picture 1:'' r<sub>(H-H)</sub>=74pm, r<sub>H-F</sub>=200 pm; p<sub>(H-H)</sub>=0 g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>; p<sub>(H-F)</sub>=-1.0g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>]] || [[File: Mp5318 Late TS vib.png|thumb|''Picture 3:''r<sub>(H-H)</sub>=180pm, r<sub>H-F</sub>=90 pm; p<sub>(H-H)</sub>=15 g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>; p<sub>(H-F)</sub>=-1.0g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>]]<br />
|-<br />
| [[File: Mp5318Early TS vib.png|thumb|''Picture 2:''r<sub>(H-H)</sub>=74pm, r<sub>H-F</sub>=182 pm; p<sub>(H-H)</sub>=6 g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>; p<sub>(H-F)</sub>=-1.0g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>]] || [[File: Mp5318 late TS trans.png|thumb|''Picture 4:''r<sub>(H-H)</sub>=180pm, r<sub>H-F</sub>=90 pm; p<sub>(H-H)</sub>=0 g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>; p<sub>(H-F)</sub>=-1.0g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>]]</div>Mp5318https://chemwiki.ch.ic.ac.uk/index.php?title=Minqi5318&diff=805848Minqi53182020-05-15T21:42:15Z<p>Mp5318: </p>
<hr />
<div>== Molecular Reaction Dynamics: Application to Triatomic systems ==<br />
<br />
==H +H<sub>1</sub> System ==<br />
<br />
=== Dynamic from transition state region===<br />
<br />
====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?====<br />
<br />
The transition state is defined mathematically as the saddle point on the potential energy surface, where ∂V('''ri''')/∂'''ri'''=0 (the gradient of the potential is zero). At the transition state, the second derivative of potential with respect to q<sub>1</sub> is positive: ∂V<sup>2</sup>(q<sub>1</sub>)/∂q<sub>1</sub> > 0, indicating a minimum of the curve; the second derivative of potential with respect to q<sub>2</sub> is positive: ∂V<sup>2</sup>(q<sub>2</sub>)/∂q<sub>2</sub> < 0, indicating a maximum of the curve. The coincidence of a maximum and a minimum indicates saddle point on the potential energy surface. It can be identified through finding the maximum on the minimum energy path linking reactants and the products. The Transition State's energy goes down most steeply along the minimum energy path linking reactants and products c.f. local minimum of the potential energy surface. <br />
<br />
====Report your best estimate of the transition state position (r<sub>ts</sub>) and explain your reasoning illustrating it with an “Internuclear Distances vs Time” plot for a relevant trajectory.====<br />
<br />
The best estemate of the transition state position r<sub>ts</sub> = 91 pm<br />
<br />
[[File:mp5318_Animation.png|thumb|centre|Internuclear Distances vs Time Plot when r<sub>ts</sub> = 91 pm.]]<br />
<br />
As shown in the ''Internuclear Distances vs Time Plot when r<sub>ts</sub> = 91 pm'' above, when r<sub>ts</sub> = 91 pm and p<sub>1</sub> p<sub>2</sub> = 0.0 g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>, internuclear distance reamain (almost) constant, which shows that the molecule does not vibrate and stayed stably at the transition state forever.<br />
<br />
====Comment on how the MEP and the trajectory you just calculated differ.====<br />
<br />
[[File:Mp5318 Surface Plot Dynamic.png|thumb|left|Surface Plot using Dynamic Calculation r<sub>1</sub>=92 pm, r<sub>2</sub>=91 pm]]<br />
<br />
[[File:Surface Plot MEP.png|thumb|centre|Surface Plot using MEP Calculation r<sub>1</sub>=92 pm, r<sub>2</sub>=91 pm]]<br />
<br />
<br clear=all><br />
When '''r<sub>1</sub>'''=92 pm, '''r<sub>2</sub>'''=91 pm, atoms A and B dissociates. Using MEP calculation, AB dissociates through the minimum energy pathway and the dissociation ceased at a displacement much smaller than using Dynamic calculation. In Dynamic trajectory, kinetic energy was acquired during the trajectory from potential energy, therefore encourage inertial motion to proceed. In addition, MEP Calculation does not take into account the momentum of the particles, all the momentums are assumed to be zero.<br />
<br />
When reversing '''r<sub>1</sub>''' and '''r<sub>2</sub>''', B and C dissociates while A and B sticks together. The final values of the positions are '''r<sub>1</sub>''' (73.81819562) '''r<sub>2</sub>''' (352.8544826) and '''p<sub>1</sub>''' (3.258858751) '''p<sub>2</sub>''' (5.06251673). <br />
<br />
When setting up a calculation where the initial positions correspond to the final positions of the trajectory above, the same final momenta values but with their signs reversed, the reaction trajectory travels back to the orginal position '''r<sub>1</sub>''' (91) and '''r<sub>2</sub>''' (92) with '''p<sub>1</sub>'''= '''p<sub>2</sub>'''= 0.<br />
<br />
===Reactive and Unreactive trajectories===<br />
<br />
{| class="wikitable" border="1"<br />
|+ initial positions '''r<sub>1</sub>''' (74 pm) '''r<sub>2</sub>''' (200 pm)<br />
! p<sub>1</sub> / g.mol<sup>-1</sup>.pm.fs<sup>-1</sup> !! p<sub>2</sub> / g.mol<sup>-1</sup>.pm.fs<sup>-1</sup> !! E<sub>tot</sub> kJ.mol<sub>-1</sub> !! Reactive? !! Description of the dunamics !! Illustration of the trajectory<br />
|-<br />
| -2.56 || -5.1 || -414.28 || Yes || A-B + C → A +B-C || [[File:Mp5318 t1.png|356px]]<br />
|-<br />
| -3.1 || -4.1 || -420.08 || No || A-B approaches C, but then leave without reaction occur || [[File:Mp5318 t2.png|356px]]<br />
|-<br />
| -3.1 || -5.1 || -413.98 || Yes || A-B + C → A +B-C || [[File:Mp5318 t3.png|356px]]<br />
|-<br />
| -5.1 || -10.1 || -357.28 || No || at TS region, strength of bondings A-B and B-C alternates, but eventually A-B leave intact (Barrier can be crossed, but then the system reverts back to the reactants) || [[File:Mp5318 t4.png|356px]]<br />
|-<br />
| -5.1 || -10.6 || -349.38 || Yes || A-B + C → A +B-C at TS region, strength of bonding A-B and N-C alternates, but new product formed eventually || [[File:Mp5318 t5.png|356px]]<br />
|}<br />
<br />
'''Conclusion: Reactants need to have a large enough ratio in the momentum to be reactive, ideally, p<sub>2</sub> : p<sub>1</sub> should be larger than 2 for the reactants to be reactive.'''<br />
<br />
===Transition State Theory===<br />
<br />
====Given the results you have obtained, how will Transition State Theory predictions for reaction rate values compare with experimental values?====<br />
<br />
Transition State Theory often overestimates the reaction rate, compared to the results we calculated. Transition State Theory assumed that once the reaction has passed the Transition state and reached the product, it would not travel back to cross the Transition State and reverse to the reactant side. However, the calculations above showed that in practice, products can still recross the energy barrier to go back to the reactants. Even though the Transition State Theory ignored the effect of quantum tunneling, it's a relatively small contribution to rate in this case (small MW for H<sub>2</sub>). Therefore Transition State Theory tends to overestimate reaction rate values compare with experimental values.<br />
<br />
==F-H-H System ==<br />
<br />
=== PES inspection===<br />
<br />
====By inspecting the potential energy surfaces, classify the F + H<sub>2</sub> and H + HF reactions according to their energetics (endothermic or exothermic). How does this relate to the bond strength of the chemical species involved?====<br />
<br />
[[File:Mp5318Surface Plot fh2.png|thumb|left|Potential Surface of F + H<sub>2</sub> Reaction]]<br />
<br />
<br clear=all><br />
<br />
F + H<sub>2</sub> Reaction is exothermic. We can see there is a decrease in energy as H-H bond distance increases while H-F bond distance decreases. The clear downhill of reaction path indicated exothermic reaction. Bond strength of H-H is 432 kJ/mol, while H-F bond strength is 565 kJ/mol. Formation of H-F bond is preferred, as it would release more energy than the energy needed to break H-H bond. <br />
<br />
H + HF Reaction is endothermic. H-H bond formed is weaker than the H-F bond, therefore energy needed to cross the activation energy barrier — endothermic.<br />
<br />
According to Hammond Postulate, for an exothermic reaction, the TS resembles the reactants (early TS); for an endothermic reaction, the TS resembles the product (late TS). Therefore in this system, TS is very close to the H<sub>2</sub> + F side (H-F distance much longer than H-H distance) .<br />
<br />
====Locate the approximate position of the transition state.====<br />
<br />
Position of the TS of H<sub>2</sub> + F Reaction: r<sub>H-H</sub>=74.5 pm; r<sub>H···F</sub>=181.1 pm; At the TS, potential energy = 433.980 kJ/mol<br />
<br />
[[File:Mp5318 TS hhf contour.png|thumb|left|TS of F + H<sub>2</sub> Reaction]]<br />
<br />
[[File:Mp5318distande hhf.png|thumb|centre|Intermolecular distance vs. Time at the TS of F + H<sub>2</sub> Reaction]]<br />
<br clear=all><br />
<br />
AB distance is the H-F distance, BC distance is the H-H distance.<br />
<br />
====Report the activation energy for both reactions.====<br />
In the form of HF + H, potential energy =- 560.642 kJ/mol<br />
In the form o H<sub>2</sub> + F, potential energy = -434.922 kJ/mol<br />
<br />
Therefore compared with the TS potential energy (-433.980 kJ/mol): for HF + H to reach the TS, the activation energy is 126.02 kJ/mol; for H<sub>2</sub> + F to reach the TS, the activation energy is 0.942 kJ/mol.<br />
<br />
===Reaction Dynamics===<br />
<br />
==== 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.====<br />
For the exothermic reaction, in this case, the F + H<sub>2</sub>, energy is released into vibrational energy of product HF. When F approaches H, the repulsion between H-H is released. The released repulsive energy pushes H towards H and produces H-F vibration. <br />
<br />
This could be confirmed experimentally through Infrared Chemiluminescence. The relative gain on many lines within several vibrational bands could be determined and hence direct measurements of the relative vibrational population in v = 0 can be obtained. We would, therefore, be able to see that the v=2 vibrational level is highly populated (strong peak at v = 2).<br />
<br />
We could also use chemical laser to characterise the HF laser produced. Most of the HF is formed in the v=2 state, thus, the reaction creates an absolute inversion between v=2, v=1, and v=0. The output spectra of pulsed HF lasers showed that more than 60% ot eh reaction energy is released as vibrational excitation of the HF.<br />
<br />
====Discuss how the distribution of energy between different modes (translation and vibration) affect the efficiency of the reaction, and how this is influenced by the position of the transition state.====<br />
<br />
{| class="wikitable" border="1"<br />
|+ distribution of energy under differnt initial conditions<br />
! H<sub>2</sub> + F system (Early TS) !! HF + H system (Late TS)<br />
|-<br />
| [[File: Mp5318 early TS trans.png|thumb|r<sub>(H-H)</sub>=74pm, r<sub>H-F</sub>=200 pm; p<sub>(H-H)</sub>=0 g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>; p<sub>(H-F)</sub>=-1.0g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>]] || [[File: Mp5318 Late TS vib.png|thumb|r<sub>(H-H)</sub>=180pm, r<sub>H-F</sub>=90 pm; p<sub>(H-H)</sub>=15 g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>; p<sub>(H-F)</sub>=-1.0g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>]]<br />
|-<br />
| [[File: Mp5318Early TS vib.png|thumb|r<sub>(H-H)</sub>=74pm, r<sub>H-F</sub>=182 pm; p<sub>(H-H)</sub>=6 g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>; p<sub>(H-F)</sub>=-1.0g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>]] || [[File: Mp5318 late TS trans.png|thumb|r<sub>(H-H)</sub>=180pm, r<sub>H-F</sub>=90 pm; p<sub>(H-H)</sub>=0 g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>; p<sub>(H-F)</sub>=-1.0g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>]]</div>Mp5318https://chemwiki.ch.ic.ac.uk/index.php?title=File:Mp5318_late_TS_trans.png&diff=805834File:Mp5318 late TS trans.png2020-05-15T21:39:26Z<p>Mp5318: </p>
<hr />
<div></div>Mp5318https://chemwiki.ch.ic.ac.uk/index.php?title=File:Mp5318Early_TS_vib.png&diff=805822File:Mp5318Early TS vib.png2020-05-15T21:38:01Z<p>Mp5318: </p>
<hr />
<div></div>Mp5318https://chemwiki.ch.ic.ac.uk/index.php?title=File:Mp5318_Late_TS_vib.png&diff=805804File:Mp5318 Late TS vib.png2020-05-15T21:33:59Z<p>Mp5318: </p>
<hr />
<div></div>Mp5318https://chemwiki.ch.ic.ac.uk/index.php?title=Minqi5318&diff=805794Minqi53182020-05-15T21:31:04Z<p>Mp5318: /* Discuss how the distribution of energy between different modes (translation and vibration) affect the efficiency of the reaction, and how this is influenced by the position of the transition state. */</p>
<hr />
<div>== Molecular Reaction Dynamics: Application to Triatomic systems ==<br />
<br />
==H +H<sub>1</sub> System ==<br />
<br />
=== Dynamic from transition state region===<br />
<br />
====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?====<br />
<br />
The transition state is defined mathematically as the saddle point on the potential energy surface, where ∂V('''ri''')/∂'''ri'''=0 (the gradient of the potential is zero). At the transition state, the second derivative of potential with respect to q<sub>1</sub> is positive: ∂V<sup>2</sup>(q<sub>1</sub>)/∂q<sub>1</sub> > 0, indicating a minimum of the curve; the second derivative of potential with respect to q<sub>2</sub> is positive: ∂V<sup>2</sup>(q<sub>2</sub>)/∂q<sub>2</sub> < 0, indicating a maximum of the curve. The coincidence of a maximum and a minimum indicates saddle point on the potential energy surface. It can be identified through finding the maximum on the minimum energy path linking reactants and the products. The Transition State's energy goes down most steeply along the minimum energy path linking reactants and products c.f. local minimum of the potential energy surface. <br />
<br />
====Report your best estimate of the transition state position (r<sub>ts</sub>) and explain your reasoning illustrating it with an “Internuclear Distances vs Time” plot for a relevant trajectory.====<br />
<br />
The best estemate of the transition state position r<sub>ts</sub> = 91 pm<br />
<br />
[[File:mp5318_Animation.png|thumb|centre|Internuclear Distances vs Time Plot when r<sub>ts</sub> = 91 pm.]]<br />
<br />
As shown in the ''Internuclear Distances vs Time Plot when r<sub>ts</sub> = 91 pm'' above, when r<sub>ts</sub> = 91 pm and p<sub>1</sub> p<sub>2</sub> = 0.0 g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>, internuclear distance reamain (almost) constant, which shows that the molecule does not vibrate and stayed stably at the transition state forever.<br />
<br />
====Comment on how the MEP and the trajectory you just calculated differ.====<br />
<br />
[[File:Mp5318 Surface Plot Dynamic.png|thumb|left|Surface Plot using Dynamic Calculation r<sub>1</sub>=92 pm, r<sub>2</sub>=91 pm]]<br />
<br />
[[File:Surface Plot MEP.png|thumb|centre|Surface Plot using MEP Calculation r<sub>1</sub>=92 pm, r<sub>2</sub>=91 pm]]<br />
<br />
<br clear=all><br />
When '''r<sub>1</sub>'''=92 pm, '''r<sub>2</sub>'''=91 pm, atoms A and B dissociates. Using MEP calculation, AB dissociates through the minimum energy pathway and the dissociation ceased at a displacement much smaller than using Dynamic calculation. In Dynamic trajectory, kinetic energy was acquired during the trajectory from potential energy, therefore encourage inertial motion to proceed. In addition, MEP Calculation does not take into account the momentum of the particles, all the momentums are assumed to be zero.<br />
<br />
When reversing '''r<sub>1</sub>''' and '''r<sub>2</sub>''', B and C dissociates while A and B sticks together. The final values of the positions are '''r<sub>1</sub>''' (73.81819562) '''r<sub>2</sub>''' (352.8544826) and '''p<sub>1</sub>''' (3.258858751) '''p<sub>2</sub>''' (5.06251673). <br />
<br />
When setting up a calculation where the initial positions correspond to the final positions of the trajectory above, the same final momenta values but with their signs reversed, the reaction trajectory travels back to the orginal position '''r<sub>1</sub>''' (91) and '''r<sub>2</sub>''' (92) with '''p<sub>1</sub>'''= '''p<sub>2</sub>'''= 0.<br />
<br />
===Reactive and Unreactive trajectories===<br />
<br />
{| class="wikitable" border="1"<br />
|+ initial positions '''r<sub>1</sub>''' (74 pm) '''r<sub>2</sub>''' (200 pm)<br />
! p<sub>1</sub> / g.mol<sup>-1</sup>.pm.fs<sup>-1</sup> !! p<sub>2</sub> / g.mol<sup>-1</sup>.pm.fs<sup>-1</sup> !! E<sub>tot</sub> kJ.mol<sub>-1</sub> !! Reactive? !! Description of the dunamics !! Illustration of the trajectory<br />
|-<br />
| -2.56 || -5.1 || -414.28 || Yes || A-B + C → A +B-C || [[File:Mp5318 t1.png|356px]]<br />
|-<br />
| -3.1 || -4.1 || -420.08 || No || A-B approaches C, but then leave without reaction occur || [[File:Mp5318 t2.png|356px]]<br />
|-<br />
| -3.1 || -5.1 || -413.98 || Yes || A-B + C → A +B-C || [[File:Mp5318 t3.png|356px]]<br />
|-<br />
| -5.1 || -10.1 || -357.28 || No || at TS region, strength of bondings A-B and B-C alternates, but eventually A-B leave intact (Barrier can be crossed, but then the system reverts back to the reactants) || [[File:Mp5318 t4.png|356px]]<br />
|-<br />
| -5.1 || -10.6 || -349.38 || Yes || A-B + C → A +B-C at TS region, strength of bonding A-B and N-C alternates, but new product formed eventually || [[File:Mp5318 t5.png|356px]]<br />
|}<br />
<br />
'''Conclusion: Reactants need to have a large enough ratio in the momentum to be reactive, ideally, p<sub>2</sub> : p<sub>1</sub> should be larger than 2 for the reactants to be reactive.'''<br />
<br />
===Transition State Theory===<br />
<br />
====Given the results you have obtained, how will Transition State Theory predictions for reaction rate values compare with experimental values?====<br />
<br />
Transition State Theory often overestimates the reaction rate, compared to the results we calculated. Transition State Theory assumed that once the reaction has passed the Transition state and reached the product, it would not travel back to cross the Transition State and reverse to the reactant side. However, the calculations above showed that in practice, products can still recross the energy barrier to go back to the reactants. Even though the Transition State Theory ignored the effect of quantum tunneling, it's a relatively small contribution to rate in this case (small MW for H<sub>2</sub>). Therefore Transition State Theory tends to overestimate reaction rate values compare with experimental values.<br />
<br />
==F-H-H System ==<br />
<br />
=== PES inspection===<br />
<br />
====By inspecting the potential energy surfaces, classify the F + H<sub>2</sub> and H + HF reactions according to their energetics (endothermic or exothermic). How does this relate to the bond strength of the chemical species involved?====<br />
<br />
[[File:Mp5318Surface Plot fh2.png|thumb|left|Potential Surface of F + H<sub>2</sub> Reaction]]<br />
<br />
<br clear=all><br />
<br />
F + H<sub>2</sub> Reaction is exothermic. We can see there is a decrease in energy as H-H bond distance increases while H-F bond distance decreases. The clear downhill of reaction path indicated exothermic reaction. Bond strength of H-H is 432 kJ/mol, while H-F bond strength is 565 kJ/mol. Formation of H-F bond is preferred, as it would release more energy than the energy needed to break H-H bond. <br />
<br />
H + HF Reaction is endothermic. H-H bond formed is weaker than the H-F bond, therefore energy needed to cross the activation energy barrier — endothermic.<br />
<br />
According to Hammond Postulate, for an exothermic reaction, the TS resembles the reactants (early TS); for an endothermic reaction, the TS resembles the product (late TS). Therefore in this system, TS is very close to the H<sub>2</sub> + F side (H-F distance much longer than H-H distance) .<br />
<br />
====Locate the approximate position of the transition state.====<br />
<br />
Position of the TS of H<sub>2</sub> + F Reaction: r<sub>H-H</sub>=74.5 pm; r<sub>H···F</sub>=181.1 pm; At the TS, potential energy = 433.980 kJ/mol<br />
<br />
[[File:Mp5318 TS hhf contour.png|thumb|left|TS of F + H<sub>2</sub> Reaction]]<br />
<br />
[[File:Mp5318distande hhf.png|thumb|centre|Intermolecular distance vs. Time at the TS of F + H<sub>2</sub> Reaction]]<br />
<br clear=all><br />
<br />
AB distance is the H-F distance, BC distance is the H-H distance.<br />
<br />
====Report the activation energy for both reactions.====<br />
In the form of HF + H, potential energy =- 560.642 kJ/mol<br />
In the form o H<sub>2</sub> + F, potential energy = -434.922 kJ/mol<br />
<br />
Therefore compared with the TS potential energy (-433.980 kJ/mol): for HF + H to reach the TS, the activation energy is 126.02 kJ/mol; for H<sub>2</sub> + F to reach the TS, the activation energy is 0.942 kJ/mol.<br />
<br />
===Reaction Dynamics===<br />
<br />
==== 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.====<br />
For the exothermic reaction, in this case, the F + H<sub>2</sub>, energy is released into vibrational energy of product HF. When F approaches H, the repulsion between H-H is released. The released repulsive energy pushes H towards H and produces H-F vibration. <br />
<br />
This could be confirmed experimentally through Infrared Chemiluminescence. The relative gain on many lines within several vibrational bands could be determined and hence direct measurements of the relative vibrational population in v = 0 can be obtained. We would, therefore, be able to see that the v=2 vibrational level is highly populated (strong peak at v = 2).<br />
<br />
We could also use chemical laser to characterise the HF laser produced. Most of the HF is formed in the v=2 state, thus, the reaction creates an absolute inversion between v=2, v=1, and v=0. The output spectra of pulsed HF lasers showed that more than 60% ot eh reaction energy is released as vibrational excitation of the HF.<br />
<br />
====Discuss how the distribution of energy between different modes (translation and vibration) affect the efficiency of the reaction, and how this is influenced by the position of the transition state.====<br />
<br />
{| class="wikitable" border="1"<br />
|+ distribution of energy under differnt initial conditions<br />
! H<sub>2</sub> + F system (Early TS) !! HF + H system (Late TS)<br />
|-<br />
| [[File: Mp5318 early TS trans.png|thumb|r<sub>(H-H)</sub>=74pm, r<sub>H-F</sub>=200 pm; ]] || cell<br />
|-<br />
| cell || cell</div>Mp5318https://chemwiki.ch.ic.ac.uk/index.php?title=File:Mp5318_early_TS_trans.png&diff=805788File:Mp5318 early TS trans.png2020-05-15T21:29:36Z<p>Mp5318: </p>
<hr />
<div></div>Mp5318https://chemwiki.ch.ic.ac.uk/index.php?title=Minqi5318&diff=805615Minqi53182020-05-15T20:41:20Z<p>Mp5318: /* 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. */</p>
<hr />
<div>== Molecular Reaction Dynamics: Application to Triatomic systems ==<br />
<br />
==H +H<sub>1</sub> System ==<br />
<br />
=== Dynamic from transition state region===<br />
<br />
====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?====<br />
<br />
The transition state is defined mathematically as the saddle point on the potential energy surface, where ∂V('''ri''')/∂'''ri'''=0 (the gradient of the potential is zero). At the transition state, the second derivative of potential with respect to q<sub>1</sub> is positive: ∂V<sup>2</sup>(q<sub>1</sub>)/∂q<sub>1</sub> > 0, indicating a minimum of the curve; the second derivative of potential with respect to q<sub>2</sub> is positive: ∂V<sup>2</sup>(q<sub>2</sub>)/∂q<sub>2</sub> < 0, indicating a maximum of the curve. The coincidence of a maximum and a minimum indicates saddle point on the potential energy surface. It can be identified through finding the maximum on the minimum energy path linking reactants and the products. The Transition State's energy goes down most steeply along the minimum energy path linking reactants and products c.f. local minimum of the potential energy surface. <br />
<br />
====Report your best estimate of the transition state position (r<sub>ts</sub>) and explain your reasoning illustrating it with an “Internuclear Distances vs Time” plot for a relevant trajectory.====<br />
<br />
The best estemate of the transition state position r<sub>ts</sub> = 91 pm<br />
<br />
[[File:mp5318_Animation.png|thumb|centre|Internuclear Distances vs Time Plot when r<sub>ts</sub> = 91 pm.]]<br />
<br />
As shown in the ''Internuclear Distances vs Time Plot when r<sub>ts</sub> = 91 pm'' above, when r<sub>ts</sub> = 91 pm and p<sub>1</sub> p<sub>2</sub> = 0.0 g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>, internuclear distance reamain (almost) constant, which shows that the molecule does not vibrate and stayed stably at the transition state forever.<br />
<br />
====Comment on how the MEP and the trajectory you just calculated differ.====<br />
<br />
[[File:Mp5318 Surface Plot Dynamic.png|thumb|left|Surface Plot using Dynamic Calculation r<sub>1</sub>=92 pm, r<sub>2</sub>=91 pm]]<br />
<br />
[[File:Surface Plot MEP.png|thumb|centre|Surface Plot using MEP Calculation r<sub>1</sub>=92 pm, r<sub>2</sub>=91 pm]]<br />
<br />
<br clear=all><br />
When '''r<sub>1</sub>'''=92 pm, '''r<sub>2</sub>'''=91 pm, atoms A and B dissociates. Using MEP calculation, AB dissociates through the minimum energy pathway and the dissociation ceased at a displacement much smaller than using Dynamic calculation. In Dynamic trajectory, kinetic energy was acquired during the trajectory from potential energy, therefore encourage inertial motion to proceed. In addition, MEP Calculation does not take into account the momentum of the particles, all the momentums are assumed to be zero.<br />
<br />
When reversing '''r<sub>1</sub>''' and '''r<sub>2</sub>''', B and C dissociates while A and B sticks together. The final values of the positions are '''r<sub>1</sub>''' (73.81819562) '''r<sub>2</sub>''' (352.8544826) and '''p<sub>1</sub>''' (3.258858751) '''p<sub>2</sub>''' (5.06251673). <br />
<br />
When setting up a calculation where the initial positions correspond to the final positions of the trajectory above, the same final momenta values but with their signs reversed, the reaction trajectory travels back to the orginal position '''r<sub>1</sub>''' (91) and '''r<sub>2</sub>''' (92) with '''p<sub>1</sub>'''= '''p<sub>2</sub>'''= 0.<br />
<br />
===Reactive and Unreactive trajectories===<br />
<br />
{| class="wikitable" border="1"<br />
|+ initial positions '''r<sub>1</sub>''' (74 pm) '''r<sub>2</sub>''' (200 pm)<br />
! p<sub>1</sub> / g.mol<sup>-1</sup>.pm.fs<sup>-1</sup> !! p<sub>2</sub> / g.mol<sup>-1</sup>.pm.fs<sup>-1</sup> !! E<sub>tot</sub> kJ.mol<sub>-1</sub> !! Reactive? !! Description of the dunamics !! Illustration of the trajectory<br />
|-<br />
| -2.56 || -5.1 || -414.28 || Yes || A-B + C → A +B-C || [[File:Mp5318 t1.png|356px]]<br />
|-<br />
| -3.1 || -4.1 || -420.08 || No || A-B approaches C, but then leave without reaction occur || [[File:Mp5318 t2.png|356px]]<br />
|-<br />
| -3.1 || -5.1 || -413.98 || Yes || A-B + C → A +B-C || [[File:Mp5318 t3.png|356px]]<br />
|-<br />
| -5.1 || -10.1 || -357.28 || No || at TS region, strength of bondings A-B and B-C alternates, but eventually A-B leave intact (Barrier can be crossed, but then the system reverts back to the reactants) || [[File:Mp5318 t4.png|356px]]<br />
|-<br />
| -5.1 || -10.6 || -349.38 || Yes || A-B + C → A +B-C at TS region, strength of bonding A-B and N-C alternates, but new product formed eventually || [[File:Mp5318 t5.png|356px]]<br />
|}<br />
<br />
'''Conclusion: Reactants need to have a large enough ratio in the momentum to be reactive, ideally, p<sub>2</sub> : p<sub>1</sub> should be larger than 2 for the reactants to be reactive.'''<br />
<br />
===Transition State Theory===<br />
<br />
====Given the results you have obtained, how will Transition State Theory predictions for reaction rate values compare with experimental values?====<br />
<br />
Transition State Theory often overestimates the reaction rate, compared to the results we calculated. Transition State Theory assumed that once the reaction has passed the Transition state and reached the product, it would not travel back to cross the Transition State and reverse to the reactant side. However, the calculations above showed that in practice, products can still recross the energy barrier to go back to the reactants. Even though the Transition State Theory ignored the effect of quantum tunneling, it's a relatively small contribution to rate in this case (small MW for H<sub>2</sub>). Therefore Transition State Theory tends to overestimate reaction rate values compare with experimental values.<br />
<br />
==F-H-H System ==<br />
<br />
=== PES inspection===<br />
<br />
====By inspecting the potential energy surfaces, classify the F + H<sub>2</sub> and H + HF reactions according to their energetics (endothermic or exothermic). How does this relate to the bond strength of the chemical species involved?====<br />
<br />
[[File:Mp5318Surface Plot fh2.png|thumb|left|Potential Surface of F + H<sub>2</sub> Reaction]]<br />
<br />
<br clear=all><br />
<br />
F + H<sub>2</sub> Reaction is exothermic. We can see there is a decrease in energy as H-H bond distance increases while H-F bond distance decreases. The clear downhill of reaction path indicated exothermic reaction. Bond strength of H-H is 432 kJ/mol, while H-F bond strength is 565 kJ/mol. Formation of H-F bond is preferred, as it would release more energy than the energy needed to break H-H bond. <br />
<br />
H + HF Reaction is endothermic. H-H bond formed is weaker than the H-F bond, therefore energy needed to cross the activation energy barrier — endothermic.<br />
<br />
According to Hammond Postulate, for an exothermic reaction, the TS resembles the reactants (early TS); for an endothermic reaction, the TS resembles the product (late TS). Therefore in this system, TS is very close to the H<sub>2</sub> + F side (H-F distance much longer than H-H distance) .<br />
<br />
====Locate the approximate position of the transition state.====<br />
<br />
Position of the TS of H<sub>2</sub> + F Reaction: r<sub>H-H</sub>=74.5 pm; r<sub>H···F</sub>=181.1 pm; At the TS, potential energy = 433.980 kJ/mol<br />
<br />
[[File:Mp5318 TS hhf contour.png|thumb|left|TS of F + H<sub>2</sub> Reaction]]<br />
<br />
[[File:Mp5318distande hhf.png|thumb|centre|Intermolecular distance vs. Time at the TS of F + H<sub>2</sub> Reaction]]<br />
<br clear=all><br />
<br />
AB distance is the H-F distance, BC distance is the H-H distance.<br />
<br />
====Report the activation energy for both reactions.====<br />
In the form of HF + H, potential energy =- 560.642 kJ/mol<br />
In the form o H<sub>2</sub> + F, potential energy = -434.922 kJ/mol<br />
<br />
Therefore compared with the TS potential energy (-433.980 kJ/mol): for HF + H to reach the TS, the activation energy is 126.02 kJ/mol; for H<sub>2</sub> + F to reach the TS, the activation energy is 0.942 kJ/mol.<br />
<br />
===Reaction Dynamics===<br />
<br />
==== 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.====<br />
For the exothermic reaction, in this case, the F + H<sub>2</sub>, energy is released into vibrational energy of product HF. When F approaches H, the repulsion between H-H is released. The released repulsive energy pushes H towards H and produces H-F vibration. <br />
<br />
This could be confirmed experimentally through Infrared Chemiluminescence. The relative gain on many lines within several vibrational bands could be determined and hence direct measurements of the relative vibrational population in v = 0 can be obtained. We would, therefore, be able to see that the v=2 vibrational level is highly populated (strong peak at v = 2).<br />
<br />
We could also use chemical laser to characterise the HF laser produced. Most of the HF is formed in the v=2 state, thus, the reaction creates an absolute inversion between v=2, v=1, and v=0. The output spectra of pulsed HF lasers showed that more than 60% ot eh reaction energy is released as vibrational excitation of the HF.<br />
<br />
====Discuss how the distribution of energy between different modes (translation and vibration) affect the efficiency of the reaction, and how this is influenced by the position of the transition state.====</div>Mp5318https://chemwiki.ch.ic.ac.uk/index.php?title=Minqi5318&diff=805542Minqi53182020-05-15T20:19:08Z<p>Mp5318: /* 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. */</p>
<hr />
<div>== Molecular Reaction Dynamics: Application to Triatomic systems ==<br />
<br />
==H +H<sub>1</sub> System ==<br />
<br />
=== Dynamic from transition state region===<br />
<br />
====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?====<br />
<br />
The transition state is defined mathematically as the saddle point on the potential energy surface, where ∂V('''ri''')/∂'''ri'''=0 (the gradient of the potential is zero). At the transition state, the second derivative of potential with respect to q<sub>1</sub> is positive: ∂V<sup>2</sup>(q<sub>1</sub>)/∂q<sub>1</sub> > 0, indicating a minimum of the curve; the second derivative of potential with respect to q<sub>2</sub> is positive: ∂V<sup>2</sup>(q<sub>2</sub>)/∂q<sub>2</sub> < 0, indicating a maximum of the curve. The coincidence of a maximum and a minimum indicates saddle point on the potential energy surface. It can be identified through finding the maximum on the minimum energy path linking reactants and the products. The Transition State's energy goes down most steeply along the minimum energy path linking reactants and products c.f. local minimum of the potential energy surface. <br />
<br />
====Report your best estimate of the transition state position (r<sub>ts</sub>) and explain your reasoning illustrating it with an “Internuclear Distances vs Time” plot for a relevant trajectory.====<br />
<br />
The best estemate of the transition state position r<sub>ts</sub> = 91 pm<br />
<br />
[[File:mp5318_Animation.png|thumb|centre|Internuclear Distances vs Time Plot when r<sub>ts</sub> = 91 pm.]]<br />
<br />
As shown in the ''Internuclear Distances vs Time Plot when r<sub>ts</sub> = 91 pm'' above, when r<sub>ts</sub> = 91 pm and p<sub>1</sub> p<sub>2</sub> = 0.0 g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>, internuclear distance reamain (almost) constant, which shows that the molecule does not vibrate and stayed stably at the transition state forever.<br />
<br />
====Comment on how the MEP and the trajectory you just calculated differ.====<br />
<br />
[[File:Mp5318 Surface Plot Dynamic.png|thumb|left|Surface Plot using Dynamic Calculation r<sub>1</sub>=92 pm, r<sub>2</sub>=91 pm]]<br />
<br />
[[File:Surface Plot MEP.png|thumb|centre|Surface Plot using MEP Calculation r<sub>1</sub>=92 pm, r<sub>2</sub>=91 pm]]<br />
<br />
<br clear=all><br />
When '''r<sub>1</sub>'''=92 pm, '''r<sub>2</sub>'''=91 pm, atoms A and B dissociates. Using MEP calculation, AB dissociates through the minimum energy pathway and the dissociation ceased at a displacement much smaller than using Dynamic calculation. In Dynamic trajectory, kinetic energy was acquired during the trajectory from potential energy, therefore encourage inertial motion to proceed. In addition, MEP Calculation does not take into account the momentum of the particles, all the momentums are assumed to be zero.<br />
<br />
When reversing '''r<sub>1</sub>''' and '''r<sub>2</sub>''', B and C dissociates while A and B sticks together. The final values of the positions are '''r<sub>1</sub>''' (73.81819562) '''r<sub>2</sub>''' (352.8544826) and '''p<sub>1</sub>''' (3.258858751) '''p<sub>2</sub>''' (5.06251673). <br />
<br />
When setting up a calculation where the initial positions correspond to the final positions of the trajectory above, the same final momenta values but with their signs reversed, the reaction trajectory travels back to the orginal position '''r<sub>1</sub>''' (91) and '''r<sub>2</sub>''' (92) with '''p<sub>1</sub>'''= '''p<sub>2</sub>'''= 0.<br />
<br />
===Reactive and Unreactive trajectories===<br />
<br />
{| class="wikitable" border="1"<br />
|+ initial positions '''r<sub>1</sub>''' (74 pm) '''r<sub>2</sub>''' (200 pm)<br />
! p<sub>1</sub> / g.mol<sup>-1</sup>.pm.fs<sup>-1</sup> !! p<sub>2</sub> / g.mol<sup>-1</sup>.pm.fs<sup>-1</sup> !! E<sub>tot</sub> kJ.mol<sub>-1</sub> !! Reactive? !! Description of the dunamics !! Illustration of the trajectory<br />
|-<br />
| -2.56 || -5.1 || -414.28 || Yes || A-B + C → A +B-C || [[File:Mp5318 t1.png|356px]]<br />
|-<br />
| -3.1 || -4.1 || -420.08 || No || A-B approaches C, but then leave without reaction occur || [[File:Mp5318 t2.png|356px]]<br />
|-<br />
| -3.1 || -5.1 || -413.98 || Yes || A-B + C → A +B-C || [[File:Mp5318 t3.png|356px]]<br />
|-<br />
| -5.1 || -10.1 || -357.28 || No || at TS region, strength of bondings A-B and B-C alternates, but eventually A-B leave intact (Barrier can be crossed, but then the system reverts back to the reactants) || [[File:Mp5318 t4.png|356px]]<br />
|-<br />
| -5.1 || -10.6 || -349.38 || Yes || A-B + C → A +B-C at TS region, strength of bonding A-B and N-C alternates, but new product formed eventually || [[File:Mp5318 t5.png|356px]]<br />
|}<br />
<br />
'''Conclusion: Reactants need to have a large enough ratio in the momentum to be reactive, ideally, p<sub>2</sub> : p<sub>1</sub> should be larger than 2 for the reactants to be reactive.'''<br />
<br />
===Transition State Theory===<br />
<br />
====Given the results you have obtained, how will Transition State Theory predictions for reaction rate values compare with experimental values?====<br />
<br />
Transition State Theory often overestimates the reaction rate, compared to the results we calculated. Transition State Theory assumed that once the reaction has passed the Transition state and reached the product, it would not travel back to cross the Transition State and reverse to the reactant side. However, the calculations above showed that in practice, products can still recross the energy barrier to go back to the reactants. Even though the Transition State Theory ignored the effect of quantum tunneling, it's a relatively small contribution to rate in this case (small MW for H<sub>2</sub>). Therefore Transition State Theory tends to overestimate reaction rate values compare with experimental values.<br />
<br />
==F-H-H System ==<br />
<br />
=== PES inspection===<br />
<br />
====By inspecting the potential energy surfaces, classify the F + H<sub>2</sub> and H + HF reactions according to their energetics (endothermic or exothermic). How does this relate to the bond strength of the chemical species involved?====<br />
<br />
[[File:Mp5318Surface Plot fh2.png|thumb|left|Potential Surface of F + H<sub>2</sub> Reaction]]<br />
<br />
<br clear=all><br />
<br />
F + H<sub>2</sub> Reaction is exothermic. We can see there is a decrease in energy as H-H bond distance increases while H-F bond distance decreases. The clear downhill of reaction path indicated exothermic reaction. Bond strength of H-H is 432 kJ/mol, while H-F bond strength is 565 kJ/mol. Formation of H-F bond is preferred, as it would release more energy than the energy needed to break H-H bond. <br />
<br />
H + HF Reaction is endothermic. H-H bond formed is weaker than the H-F bond, therefore energy needed to cross the activation energy barrier — endothermic.<br />
<br />
According to Hammond Postulate, for an exothermic reaction, the TS resembles the reactants (early TS); for an endothermic reaction, the TS resembles the product (late TS). Therefore in this system, TS is very close to the H<sub>2</sub> + F side (H-F distance much longer than H-H distance) .<br />
<br />
====Locate the approximate position of the transition state.====<br />
<br />
Position of the TS of H<sub>2</sub> + F Reaction: r<sub>H-H</sub>=74.5 pm; r<sub>H···F</sub>=181.1 pm; At the TS, potential energy = 433.980 kJ/mol<br />
<br />
[[File:Mp5318 TS hhf contour.png|thumb|left|TS of F + H<sub>2</sub> Reaction]]<br />
<br />
[[File:Mp5318distande hhf.png|thumb|centre|Intermolecular distance vs. Time at the TS of F + H<sub>2</sub> Reaction]]<br />
<br clear=all><br />
<br />
AB distance is the H-F distance, BC distance is the H-H distance.<br />
<br />
====Report the activation energy for both reactions.====<br />
In the form of HF + H, potential energy =- 560.642 kJ/mol<br />
In the form o H<sub>2</sub> + F, potential energy = -434.922 kJ/mol<br />
<br />
Therefore compared with the TS potential energy (-433.980 kJ/mol): for HF + H to reach the TS, the activation energy is 126.02 kJ/mol; for H<sub>2</sub> + F to reach the TS, the activation energy is 0.942 kJ/mol.<br />
<br />
===Reaction Dynamics===<br />
<br />
==== 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.====<br />
For the exothermic reaction, in this case, the F + H<sub>2</sub>, energy is released into vibrational energy of product HF. When F approaches H, the repulsion between H-H is released. The released repulsive energy pushes H towards H and produces H-F vibration. <br />
<br />
This could be confirmed experimentally through Infrared Chemiluminescence. The relative gain on many lines within several vibrational bands could be determined and hence direct measurements of the relative vibrational population in v = 0 can be obtained. We would, therefore, be able to see that the v=2 vibrational level is highly populated (strong peak at v = 2).<br />
<br />
We could also use chemical laser to characterise the HF laser produced. Most of the HF is formed in the v=2 state, thus, the reaction creates an absolute inversion between v=2, v=1 and v=0. The output spectra of pulsed HF lasers showed that more than 60% ot eh reaction energy is released as vibrational excitation of the HF.</div>Mp5318https://chemwiki.ch.ic.ac.uk/index.php?title=Minqi5318&diff=805335Minqi53182020-05-15T19:10:10Z<p>Mp5318: /* 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? */</p>
<hr />
<div>== Molecular Reaction Dynamics: Application to Triatomic systems ==<br />
<br />
==H +H<sub>1</sub> System ==<br />
<br />
=== Dynamic from transition state region===<br />
<br />
====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?====<br />
<br />
The transition state is defined mathematically as the saddle point on the potential energy surface, where ∂V('''ri''')/∂'''ri'''=0 (the gradient of the potential is zero). At the transition state, the second derivative of potential with respect to q<sub>1</sub> is positive: ∂V<sup>2</sup>(q<sub>1</sub>)/∂q<sub>1</sub> > 0, indicating a minimum of the curve; the second derivative of potential with respect to q<sub>2</sub> is positive: ∂V<sup>2</sup>(q<sub>2</sub>)/∂q<sub>2</sub> < 0, indicating a maximum of the curve. The coincidence of a maximum and a minimum indicates saddle point on the potential energy surface. It can be identified through finding the maximum on the minimum energy path linking reactants and the products. The Transition State's energy goes down most steeply along the minimum energy path linking reactants and products c.f. local minimum of the potential energy surface. <br />
<br />
====Report your best estimate of the transition state position (r<sub>ts</sub>) and explain your reasoning illustrating it with an “Internuclear Distances vs Time” plot for a relevant trajectory.====<br />
<br />
The best estemate of the transition state position r<sub>ts</sub> = 91 pm<br />
<br />
[[File:mp5318_Animation.png|thumb|centre|Internuclear Distances vs Time Plot when r<sub>ts</sub> = 91 pm.]]<br />
<br />
As shown in the ''Internuclear Distances vs Time Plot when r<sub>ts</sub> = 91 pm'' above, when r<sub>ts</sub> = 91 pm and p<sub>1</sub> p<sub>2</sub> = 0.0 g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>, internuclear distance reamain (almost) constant, which shows that the molecule does not vibrate and stayed stably at the transition state forever.<br />
<br />
====Comment on how the MEP and the trajectory you just calculated differ.====<br />
<br />
[[File:Mp5318 Surface Plot Dynamic.png|thumb|left|Surface Plot using Dynamic Calculation r<sub>1</sub>=92 pm, r<sub>2</sub>=91 pm]]<br />
<br />
[[File:Surface Plot MEP.png|thumb|centre|Surface Plot using MEP Calculation r<sub>1</sub>=92 pm, r<sub>2</sub>=91 pm]]<br />
<br />
<br clear=all><br />
When '''r<sub>1</sub>'''=92 pm, '''r<sub>2</sub>'''=91 pm, atoms A and B dissociates. Using MEP calculation, AB dissociates through the minimum energy pathway and the dissociation ceased at a displacement much smaller than using Dynamic calculation. In Dynamic trajectory, kinetic energy was acquired during the trajectory from potential energy, therefore encourage inertial motion to proceed. In addition, MEP Calculation does not take into account the momentum of the particles, all the momentums are assumed to be zero.<br />
<br />
When reversing '''r<sub>1</sub>''' and '''r<sub>2</sub>''', B and C dissociates while A and B sticks together. The final values of the positions are '''r<sub>1</sub>''' (73.81819562) '''r<sub>2</sub>''' (352.8544826) and '''p<sub>1</sub>''' (3.258858751) '''p<sub>2</sub>''' (5.06251673). <br />
<br />
When setting up a calculation where the initial positions correspond to the final positions of the trajectory above, the same final momenta values but with their signs reversed, the reaction trajectory travels back to the orginal position '''r<sub>1</sub>''' (91) and '''r<sub>2</sub>''' (92) with '''p<sub>1</sub>'''= '''p<sub>2</sub>'''= 0.<br />
<br />
===Reactive and Unreactive trajectories===<br />
<br />
{| class="wikitable" border="1"<br />
|+ initial positions '''r<sub>1</sub>''' (74 pm) '''r<sub>2</sub>''' (200 pm)<br />
! p<sub>1</sub> / g.mol<sup>-1</sup>.pm.fs<sup>-1</sup> !! p<sub>2</sub> / g.mol<sup>-1</sup>.pm.fs<sup>-1</sup> !! E<sub>tot</sub> kJ.mol<sub>-1</sub> !! Reactive? !! Description of the dunamics !! Illustration of the trajectory<br />
|-<br />
| -2.56 || -5.1 || -414.28 || Yes || A-B + C → A +B-C || [[File:Mp5318 t1.png|356px]]<br />
|-<br />
| -3.1 || -4.1 || -420.08 || No || A-B approaches C, but then leave without reaction occur || [[File:Mp5318 t2.png|356px]]<br />
|-<br />
| -3.1 || -5.1 || -413.98 || Yes || A-B + C → A +B-C || [[File:Mp5318 t3.png|356px]]<br />
|-<br />
| -5.1 || -10.1 || -357.28 || No || at TS region, strength of bondings A-B and B-C alternates, but eventually A-B leave intact (Barrier can be crossed, but then the system reverts back to the reactants) || [[File:Mp5318 t4.png|356px]]<br />
|-<br />
| -5.1 || -10.6 || -349.38 || Yes || A-B + C → A +B-C at TS region, strength of bonding A-B and N-C alternates, but new product formed eventually || [[File:Mp5318 t5.png|356px]]<br />
|}<br />
<br />
'''Conclusion: Reactants need to have a large enough ratio in the momentum to be reactive, ideally, p<sub>2</sub> : p<sub>1</sub> should be larger than 2 for the reactants to be reactive.'''<br />
<br />
===Transition State Theory===<br />
<br />
====Given the results you have obtained, how will Transition State Theory predictions for reaction rate values compare with experimental values?====<br />
<br />
Transition State Theory often overestimates the reaction rate, compared to the results we calculated. Transition State Theory assumed that once the reaction has passed the Transition state and reached the product, it would not travel back to cross the Transition State and reverse to the reactant side. However, the calculations above showed that in practice, products can still recross the energy barrier to go back to the reactants. Even though the Transition State Theory ignored the effect of quantum tunneling, it's a relatively small contribution to rate in this case (small MW for H<sub>2</sub>). Therefore Transition State Theory tends to overestimate reaction rate values compare with experimental values.<br />
<br />
==F-H-H System ==<br />
<br />
=== PES inspection===<br />
<br />
====By inspecting the potential energy surfaces, classify the F + H<sub>2</sub> and H + HF reactions according to their energetics (endothermic or exothermic). How does this relate to the bond strength of the chemical species involved?====<br />
<br />
[[File:Mp5318Surface Plot fh2.png|thumb|left|Potential Surface of F + H<sub>2</sub> Reaction]]<br />
<br />
<br clear=all><br />
<br />
F + H<sub>2</sub> Reaction is exothermic. We can see there is a decrease in energy as H-H bond distance increases while H-F bond distance decreases. The clear downhill of reaction path indicated exothermic reaction. Bond strength of H-H is 432 kJ/mol, while H-F bond strength is 565 kJ/mol. Formation of H-F bond is preferred, as it would release more energy than the energy needed to break H-H bond. <br />
<br />
H + HF Reaction is endothermic. H-H bond formed is weaker than the H-F bond, therefore energy needed to cross the activation energy barrier — endothermic.<br />
<br />
According to Hammond Postulate, for an exothermic reaction, the TS resembles the reactants (early TS); for an endothermic reaction, the TS resembles the product (late TS). Therefore in this system, TS is very close to the H<sub>2</sub> + F side (H-F distance much longer than H-H distance) .<br />
<br />
====Locate the approximate position of the transition state.====<br />
<br />
Position of the TS of H<sub>2</sub> + F Reaction: r<sub>H-H</sub>=74.5 pm; r<sub>H···F</sub>=181.1 pm; At the TS, potential energy = 433.980 kJ/mol<br />
<br />
[[File:Mp5318 TS hhf contour.png|thumb|left|TS of F + H<sub>2</sub> Reaction]]<br />
<br />
[[File:Mp5318distande hhf.png|thumb|centre|Intermolecular distance vs. Time at the TS of F + H<sub>2</sub> Reaction]]<br />
<br clear=all><br />
<br />
AB distance is the H-F distance, BC distance is the H-H distance.<br />
<br />
====Report the activation energy for both reactions.====<br />
In the form of HF + H, potential energy =- 560.642 kJ/mol<br />
In the form o H<sub>2</sub> + F, potential energy = -434.922 kJ/mol<br />
<br />
Therefore compared with the TS potential energy (-433.980 kJ/mol): for HF + H to reach the TS, the activation energy is 126.02 kJ/mol; for H<sub>2</sub> + F to reach the TS, the activation energy is 0.942 kJ/mol.<br />
<br />
==== 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.====<br />
For the exothermic reaction, in this case, the F + H<sub>2</sub>, energy is released by the release of proton from the excited state, into vibrational energy of HF.</div>Mp5318https://chemwiki.ch.ic.ac.uk/index.php?title=Minqi5318&diff=805308Minqi53182020-05-15T18:59:05Z<p>Mp5318: /* Locate the approximate position of the transition state. */</p>
<hr />
<div>== Molecular Reaction Dynamics: Application to Triatomic systems ==<br />
<br />
==H +H<sub>1</sub> System ==<br />
<br />
=== Dynamic from transition state region===<br />
<br />
====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?====<br />
<br />
The transition state is defined mathematically as the saddle point on the potential energy surface, where ∂V('''ri''')/∂'''ri'''=0 (the gradient of the potential is zero). At the transition state, the second derivative of potential with respect to q<sub>1</sub> is positive: ∂V<sup>2</sup>(q<sub>1</sub>)/∂q<sub>1</sub> > 0, indicating a minimum of the curve; the second derivative of potential with respect to q<sub>2</sub> is positive: ∂V<sup>2</sup>(q<sub>2</sub>)/∂q<sub>2</sub> < 0, indicating a maximum of the curve. The coincidence of a maximum and a minimum indicates saddle point on the potential energy surface. It can be identified through finding the maximum on the minimum energy path linking reactants and the products. The Transition State's energy goes down most steeply along the minimum energy path linking reactants and products c.f. local minimum of the potential energy surface. <br />
<br />
====Report your best estimate of the transition state position (r<sub>ts</sub>) and explain your reasoning illustrating it with an “Internuclear Distances vs Time” plot for a relevant trajectory.====<br />
<br />
The best estemate of the transition state position r<sub>ts</sub> = 91 pm<br />
<br />
[[File:mp5318_Animation.png|thumb|centre|Internuclear Distances vs Time Plot when r<sub>ts</sub> = 91 pm.]]<br />
<br />
As shown in the ''Internuclear Distances vs Time Plot when r<sub>ts</sub> = 91 pm'' above, when r<sub>ts</sub> = 91 pm and p<sub>1</sub> p<sub>2</sub> = 0.0 g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>, internuclear distance reamain (almost) constant, which shows that the molecule does not vibrate and stayed stably at the transition state forever.<br />
<br />
====Comment on how the MEP and the trajectory you just calculated differ.====<br />
<br />
[[File:Mp5318 Surface Plot Dynamic.png|thumb|left|Surface Plot using Dynamic Calculation r<sub>1</sub>=92 pm, r<sub>2</sub>=91 pm]]<br />
<br />
[[File:Surface Plot MEP.png|thumb|centre|Surface Plot using MEP Calculation r<sub>1</sub>=92 pm, r<sub>2</sub>=91 pm]]<br />
<br />
<br clear=all><br />
When '''r<sub>1</sub>'''=92 pm, '''r<sub>2</sub>'''=91 pm, atoms A and B dissociates. Using MEP calculation, AB dissociates through the minimum energy pathway and the dissociation ceased at a displacement much smaller than using Dynamic calculation. In Dynamic trajectory, kinetic energy was acquired during the trajectory from potential energy, therefore encourage inertial motion to proceed. In addition, MEP Calculation does not take into account the momentum of the particles, all the momentums are assumed to be zero.<br />
<br />
When reversing '''r<sub>1</sub>''' and '''r<sub>2</sub>''', B and C dissociates while A and B sticks together. The final values of the positions are '''r<sub>1</sub>''' (73.81819562) '''r<sub>2</sub>''' (352.8544826) and '''p<sub>1</sub>''' (3.258858751) '''p<sub>2</sub>''' (5.06251673). <br />
<br />
When setting up a calculation where the initial positions correspond to the final positions of the trajectory above, the same final momenta values but with their signs reversed, the reaction trajectory travels back to the orginal position '''r<sub>1</sub>''' (91) and '''r<sub>2</sub>''' (92) with '''p<sub>1</sub>'''= '''p<sub>2</sub>'''= 0.<br />
<br />
===Reactive and Unreactive trajectories===<br />
<br />
{| class="wikitable" border="1"<br />
|+ initial positions '''r<sub>1</sub>''' (74 pm) '''r<sub>2</sub>''' (200 pm)<br />
! p<sub>1</sub> / g.mol<sup>-1</sup>.pm.fs<sup>-1</sup> !! p<sub>2</sub> / g.mol<sup>-1</sup>.pm.fs<sup>-1</sup> !! E<sub>tot</sub> kJ.mol<sub>-1</sub> !! Reactive? !! Description of the dunamics !! Illustration of the trajectory<br />
|-<br />
| -2.56 || -5.1 || -414.28 || Yes || A-B + C → A +B-C || [[File:Mp5318 t1.png|356px]]<br />
|-<br />
| -3.1 || -4.1 || -420.08 || No || A-B approaches C, but then leave without reaction occur || [[File:Mp5318 t2.png|356px]]<br />
|-<br />
| -3.1 || -5.1 || -413.98 || Yes || A-B + C → A +B-C || [[File:Mp5318 t3.png|356px]]<br />
|-<br />
| -5.1 || -10.1 || -357.28 || No || at TS region, strength of bondings A-B and B-C alternates, but eventually A-B leave intact (Barrier can be crossed, but then the system reverts back to the reactants) || [[File:Mp5318 t4.png|356px]]<br />
|-<br />
| -5.1 || -10.6 || -349.38 || Yes || A-B + C → A +B-C at TS region, strength of bonding A-B and N-C alternates, but new product formed eventually || [[File:Mp5318 t5.png|356px]]<br />
|}<br />
<br />
'''Conclusion: Reactants need to have a large enough ratio in the momentum to be reactive, ideally, p<sub>2</sub> : p<sub>1</sub> should be larger than 2 for the reactants to be reactive.'''<br />
<br />
===Transition State Theory===<br />
<br />
====Given the results you have obtained, how will Transition State Theory predictions for reaction rate values compare with experimental values?====<br />
<br />
Transition State Theory often overestimates the reaction rate, compared to the results we calculated. Transition State Theory assumed that once the reaction has passed the Transition state and reached the product, it would not travel back to cross the Transition State and reverse to the reactant side. However, the calculations above showed that in practice, products can still recross the energy barrier to go back to the reactants. Even though the Transition State Theory ignored the effect of quantum tunneling, it's a relatively small contribution to rate in this case (small MW for H<sub>2</sub>). Therefore Transition State Theory tends to overestimate reaction rate values compare with experimental values.<br />
<br />
==F-H-H System ==<br />
<br />
=== PES inspection===<br />
<br />
====By inspecting the potential energy surfaces, classify the F + H<sub>2</sub> and H + HF reactions according to their energetics (endothermic or exothermic). How does this relate to the bond strength of the chemical species involved?====<br />
<br />
[[File:Mp5318Surface Plot fh2.png|thumb|left|Potential Surface of F + H<sub>2</sub> Reaction]]<br />
<br />
<br clear=all><br />
<br />
F + H<sub>2</sub> Reaction is exothermic. We can see there is a decrease in energy as H-H bond distance increases while H-F bond distance decreases. The clear downhill of reaction path indicated exothermic reaction. Bond strength of H-H is 432 kJ/mol, while H-F bond strength is 565 kJ/mol. Formation of H-F bond is preferred, as it would release more energy than the energy needed to break H-H bond. <br />
<br />
H + HF Reaction is endothermic. H-H bond formed is weaker than the H-F bond, therefore energy needed to cross the activation energy barrier — endothermic.<br />
<br />
According to Hammond Postulate, for an exothermic reaction, the TS resembles the reactants (early TS); for an endothermic reaction, the TS resembles the product (late TS). Therefore in this system, TS is very close to the H + HF side.<br />
<br />
====Locate the approximate position of the transition state.====<br />
<br />
Position of the TS of H<sub>2</sub> + F Reaction: r<sub>H-H</sub>=74.5 pm; r<sub>H···F</sub>=181.1 pm; At the TS, potential energy = 433.980 kJ/mol<br />
<br />
[[File:Mp5318 TS hhf contour.png|thumb|left|TS of F + H<sub>2</sub> Reaction]]<br />
<br />
[[File:Mp5318distande hhf.png|thumb|centre|Intermolecular distance vs. Time at the TS of F + H<sub>2</sub> Reaction]]<br />
<br clear=all><br />
<br />
AB distance is the H-F distance, BC distance is the H-H distance.<br />
<br />
====Report the activation energy for both reactions.====<br />
In the form of HF + H, potential energy =- 560.642 kJ/mol<br />
In the form o H<sub>2</sub> + F, potential energy = -434.922 kJ/mol<br />
<br />
Therefore compared with the TS potential energy (-433.980 kJ/mol): for HF + H to reach the TS, the activation energy is 126.02 kJ/mol; for H<sub>2</sub> + F to reach the TS, the activation energy is 0.942 kJ/mol.<br />
<br />
==== 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.====<br />
For the exothermic reaction, in this case, the F + H<sub>2</sub>, energy is released by the release of proton from the excited state, into vibrational energy of HF.</div>Mp5318https://chemwiki.ch.ic.ac.uk/index.php?title=Minqi5318&diff=805306Minqi53182020-05-15T18:58:13Z<p>Mp5318: /* Locate the approximate position of the transition state. */</p>
<hr />
<div>== Molecular Reaction Dynamics: Application to Triatomic systems ==<br />
<br />
==H +H<sub>1</sub> System ==<br />
<br />
=== Dynamic from transition state region===<br />
<br />
====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?====<br />
<br />
The transition state is defined mathematically as the saddle point on the potential energy surface, where ∂V('''ri''')/∂'''ri'''=0 (the gradient of the potential is zero). At the transition state, the second derivative of potential with respect to q<sub>1</sub> is positive: ∂V<sup>2</sup>(q<sub>1</sub>)/∂q<sub>1</sub> > 0, indicating a minimum of the curve; the second derivative of potential with respect to q<sub>2</sub> is positive: ∂V<sup>2</sup>(q<sub>2</sub>)/∂q<sub>2</sub> < 0, indicating a maximum of the curve. The coincidence of a maximum and a minimum indicates saddle point on the potential energy surface. It can be identified through finding the maximum on the minimum energy path linking reactants and the products. The Transition State's energy goes down most steeply along the minimum energy path linking reactants and products c.f. local minimum of the potential energy surface. <br />
<br />
====Report your best estimate of the transition state position (r<sub>ts</sub>) and explain your reasoning illustrating it with an “Internuclear Distances vs Time” plot for a relevant trajectory.====<br />
<br />
The best estemate of the transition state position r<sub>ts</sub> = 91 pm<br />
<br />
[[File:mp5318_Animation.png|thumb|centre|Internuclear Distances vs Time Plot when r<sub>ts</sub> = 91 pm.]]<br />
<br />
As shown in the ''Internuclear Distances vs Time Plot when r<sub>ts</sub> = 91 pm'' above, when r<sub>ts</sub> = 91 pm and p<sub>1</sub> p<sub>2</sub> = 0.0 g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>, internuclear distance reamain (almost) constant, which shows that the molecule does not vibrate and stayed stably at the transition state forever.<br />
<br />
====Comment on how the MEP and the trajectory you just calculated differ.====<br />
<br />
[[File:Mp5318 Surface Plot Dynamic.png|thumb|left|Surface Plot using Dynamic Calculation r<sub>1</sub>=92 pm, r<sub>2</sub>=91 pm]]<br />
<br />
[[File:Surface Plot MEP.png|thumb|centre|Surface Plot using MEP Calculation r<sub>1</sub>=92 pm, r<sub>2</sub>=91 pm]]<br />
<br />
<br clear=all><br />
When '''r<sub>1</sub>'''=92 pm, '''r<sub>2</sub>'''=91 pm, atoms A and B dissociates. Using MEP calculation, AB dissociates through the minimum energy pathway and the dissociation ceased at a displacement much smaller than using Dynamic calculation. In Dynamic trajectory, kinetic energy was acquired during the trajectory from potential energy, therefore encourage inertial motion to proceed. In addition, MEP Calculation does not take into account the momentum of the particles, all the momentums are assumed to be zero.<br />
<br />
When reversing '''r<sub>1</sub>''' and '''r<sub>2</sub>''', B and C dissociates while A and B sticks together. The final values of the positions are '''r<sub>1</sub>''' (73.81819562) '''r<sub>2</sub>''' (352.8544826) and '''p<sub>1</sub>''' (3.258858751) '''p<sub>2</sub>''' (5.06251673). <br />
<br />
When setting up a calculation where the initial positions correspond to the final positions of the trajectory above, the same final momenta values but with their signs reversed, the reaction trajectory travels back to the orginal position '''r<sub>1</sub>''' (91) and '''r<sub>2</sub>''' (92) with '''p<sub>1</sub>'''= '''p<sub>2</sub>'''= 0.<br />
<br />
===Reactive and Unreactive trajectories===<br />
<br />
{| class="wikitable" border="1"<br />
|+ initial positions '''r<sub>1</sub>''' (74 pm) '''r<sub>2</sub>''' (200 pm)<br />
! p<sub>1</sub> / g.mol<sup>-1</sup>.pm.fs<sup>-1</sup> !! p<sub>2</sub> / g.mol<sup>-1</sup>.pm.fs<sup>-1</sup> !! E<sub>tot</sub> kJ.mol<sub>-1</sub> !! Reactive? !! Description of the dunamics !! Illustration of the trajectory<br />
|-<br />
| -2.56 || -5.1 || -414.28 || Yes || A-B + C → A +B-C || [[File:Mp5318 t1.png|356px]]<br />
|-<br />
| -3.1 || -4.1 || -420.08 || No || A-B approaches C, but then leave without reaction occur || [[File:Mp5318 t2.png|356px]]<br />
|-<br />
| -3.1 || -5.1 || -413.98 || Yes || A-B + C → A +B-C || [[File:Mp5318 t3.png|356px]]<br />
|-<br />
| -5.1 || -10.1 || -357.28 || No || at TS region, strength of bondings A-B and B-C alternates, but eventually A-B leave intact (Barrier can be crossed, but then the system reverts back to the reactants) || [[File:Mp5318 t4.png|356px]]<br />
|-<br />
| -5.1 || -10.6 || -349.38 || Yes || A-B + C → A +B-C at TS region, strength of bonding A-B and N-C alternates, but new product formed eventually || [[File:Mp5318 t5.png|356px]]<br />
|}<br />
<br />
'''Conclusion: Reactants need to have a large enough ratio in the momentum to be reactive, ideally, p<sub>2</sub> : p<sub>1</sub> should be larger than 2 for the reactants to be reactive.'''<br />
<br />
===Transition State Theory===<br />
<br />
====Given the results you have obtained, how will Transition State Theory predictions for reaction rate values compare with experimental values?====<br />
<br />
Transition State Theory often overestimates the reaction rate, compared to the results we calculated. Transition State Theory assumed that once the reaction has passed the Transition state and reached the product, it would not travel back to cross the Transition State and reverse to the reactant side. However, the calculations above showed that in practice, products can still recross the energy barrier to go back to the reactants. Even though the Transition State Theory ignored the effect of quantum tunneling, it's a relatively small contribution to rate in this case (small MW for H<sub>2</sub>). Therefore Transition State Theory tends to overestimate reaction rate values compare with experimental values.<br />
<br />
==F-H-H System ==<br />
<br />
=== PES inspection===<br />
<br />
====By inspecting the potential energy surfaces, classify the F + H<sub>2</sub> and H + HF reactions according to their energetics (endothermic or exothermic). How does this relate to the bond strength of the chemical species involved?====<br />
<br />
[[File:Mp5318Surface Plot fh2.png|thumb|left|Potential Surface of F + H<sub>2</sub> Reaction]]<br />
<br />
<br clear=all><br />
<br />
F + H<sub>2</sub> Reaction is exothermic. We can see there is a decrease in energy as H-H bond distance increases while H-F bond distance decreases. The clear downhill of reaction path indicated exothermic reaction. Bond strength of H-H is 432 kJ/mol, while H-F bond strength is 565 kJ/mol. Formation of H-F bond is preferred, as it would release more energy than the energy needed to break H-H bond. <br />
<br />
H + HF Reaction is endothermic. H-H bond formed is weaker than the H-F bond, therefore energy needed to cross the activation energy barrier — endothermic.<br />
<br />
According to Hammond Postulate, for an exothermic reaction, the TS resembles the reactants (early TS); for an endothermic reaction, the TS resembles the product (late TS). Therefore in this system, TS is very close to the H + HF side.<br />
<br />
====Locate the approximate position of the transition state.====<br />
<br />
Position of the TS of H<sub>2</sub> + F Reaction: r<sub>H-H</sub>=74.5 pm; r<sub>H···F</sub>=181.1 pm; At the TS, potential energy = 433.980 kJ/mol<br />
<br />
[[File:Mp5318 TS hhf contour.png|thumb|left|TS of F + H<sub>2</sub> Reaction]]<br />
<br />
[[File:Mp5318distande hhf.png|thumb|centre|Intermolecular distance vs. Time at the TS of F + H<sub>2</sub> Reaction]]<br />
<br clear=all><br />
<br />
====Report the activation energy for both reactions.====<br />
In the form of HF + H, potential energy =- 560.642 kJ/mol<br />
In the form o H<sub>2</sub> + F, potential energy = -434.922 kJ/mol<br />
<br />
Therefore compared with the TS potential energy (-433.980 kJ/mol): for HF + H to reach the TS, the activation energy is 126.02 kJ/mol; for H<sub>2</sub> + F to reach the TS, the activation energy is 0.942 kJ/mol.<br />
<br />
==== 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.====<br />
For the exothermic reaction, in this case, the F + H<sub>2</sub>, energy is released by the release of proton from the excited state, into vibrational energy of HF.</div>Mp5318https://chemwiki.ch.ic.ac.uk/index.php?title=Minqi5318&diff=805303Minqi53182020-05-15T18:57:55Z<p>Mp5318: </p>
<hr />
<div>== Molecular Reaction Dynamics: Application to Triatomic systems ==<br />
<br />
==H +H<sub>1</sub> System ==<br />
<br />
=== Dynamic from transition state region===<br />
<br />
====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?====<br />
<br />
The transition state is defined mathematically as the saddle point on the potential energy surface, where ∂V('''ri''')/∂'''ri'''=0 (the gradient of the potential is zero). At the transition state, the second derivative of potential with respect to q<sub>1</sub> is positive: ∂V<sup>2</sup>(q<sub>1</sub>)/∂q<sub>1</sub> > 0, indicating a minimum of the curve; the second derivative of potential with respect to q<sub>2</sub> is positive: ∂V<sup>2</sup>(q<sub>2</sub>)/∂q<sub>2</sub> < 0, indicating a maximum of the curve. The coincidence of a maximum and a minimum indicates saddle point on the potential energy surface. It can be identified through finding the maximum on the minimum energy path linking reactants and the products. The Transition State's energy goes down most steeply along the minimum energy path linking reactants and products c.f. local minimum of the potential energy surface. <br />
<br />
====Report your best estimate of the transition state position (r<sub>ts</sub>) and explain your reasoning illustrating it with an “Internuclear Distances vs Time” plot for a relevant trajectory.====<br />
<br />
The best estemate of the transition state position r<sub>ts</sub> = 91 pm<br />
<br />
[[File:mp5318_Animation.png|thumb|centre|Internuclear Distances vs Time Plot when r<sub>ts</sub> = 91 pm.]]<br />
<br />
As shown in the ''Internuclear Distances vs Time Plot when r<sub>ts</sub> = 91 pm'' above, when r<sub>ts</sub> = 91 pm and p<sub>1</sub> p<sub>2</sub> = 0.0 g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>, internuclear distance reamain (almost) constant, which shows that the molecule does not vibrate and stayed stably at the transition state forever.<br />
<br />
====Comment on how the MEP and the trajectory you just calculated differ.====<br />
<br />
[[File:Mp5318 Surface Plot Dynamic.png|thumb|left|Surface Plot using Dynamic Calculation r<sub>1</sub>=92 pm, r<sub>2</sub>=91 pm]]<br />
<br />
[[File:Surface Plot MEP.png|thumb|centre|Surface Plot using MEP Calculation r<sub>1</sub>=92 pm, r<sub>2</sub>=91 pm]]<br />
<br />
<br clear=all><br />
When '''r<sub>1</sub>'''=92 pm, '''r<sub>2</sub>'''=91 pm, atoms A and B dissociates. Using MEP calculation, AB dissociates through the minimum energy pathway and the dissociation ceased at a displacement much smaller than using Dynamic calculation. In Dynamic trajectory, kinetic energy was acquired during the trajectory from potential energy, therefore encourage inertial motion to proceed. In addition, MEP Calculation does not take into account the momentum of the particles, all the momentums are assumed to be zero.<br />
<br />
When reversing '''r<sub>1</sub>''' and '''r<sub>2</sub>''', B and C dissociates while A and B sticks together. The final values of the positions are '''r<sub>1</sub>''' (73.81819562) '''r<sub>2</sub>''' (352.8544826) and '''p<sub>1</sub>''' (3.258858751) '''p<sub>2</sub>''' (5.06251673). <br />
<br />
When setting up a calculation where the initial positions correspond to the final positions of the trajectory above, the same final momenta values but with their signs reversed, the reaction trajectory travels back to the orginal position '''r<sub>1</sub>''' (91) and '''r<sub>2</sub>''' (92) with '''p<sub>1</sub>'''= '''p<sub>2</sub>'''= 0.<br />
<br />
===Reactive and Unreactive trajectories===<br />
<br />
{| class="wikitable" border="1"<br />
|+ initial positions '''r<sub>1</sub>''' (74 pm) '''r<sub>2</sub>''' (200 pm)<br />
! p<sub>1</sub> / g.mol<sup>-1</sup>.pm.fs<sup>-1</sup> !! p<sub>2</sub> / g.mol<sup>-1</sup>.pm.fs<sup>-1</sup> !! E<sub>tot</sub> kJ.mol<sub>-1</sub> !! Reactive? !! Description of the dunamics !! Illustration of the trajectory<br />
|-<br />
| -2.56 || -5.1 || -414.28 || Yes || A-B + C → A +B-C || [[File:Mp5318 t1.png|356px]]<br />
|-<br />
| -3.1 || -4.1 || -420.08 || No || A-B approaches C, but then leave without reaction occur || [[File:Mp5318 t2.png|356px]]<br />
|-<br />
| -3.1 || -5.1 || -413.98 || Yes || A-B + C → A +B-C || [[File:Mp5318 t3.png|356px]]<br />
|-<br />
| -5.1 || -10.1 || -357.28 || No || at TS region, strength of bondings A-B and B-C alternates, but eventually A-B leave intact (Barrier can be crossed, but then the system reverts back to the reactants) || [[File:Mp5318 t4.png|356px]]<br />
|-<br />
| -5.1 || -10.6 || -349.38 || Yes || A-B + C → A +B-C at TS region, strength of bonding A-B and N-C alternates, but new product formed eventually || [[File:Mp5318 t5.png|356px]]<br />
|}<br />
<br />
'''Conclusion: Reactants need to have a large enough ratio in the momentum to be reactive, ideally, p<sub>2</sub> : p<sub>1</sub> should be larger than 2 for the reactants to be reactive.'''<br />
<br />
===Transition State Theory===<br />
<br />
====Given the results you have obtained, how will Transition State Theory predictions for reaction rate values compare with experimental values?====<br />
<br />
Transition State Theory often overestimates the reaction rate, compared to the results we calculated. Transition State Theory assumed that once the reaction has passed the Transition state and reached the product, it would not travel back to cross the Transition State and reverse to the reactant side. However, the calculations above showed that in practice, products can still recross the energy barrier to go back to the reactants. Even though the Transition State Theory ignored the effect of quantum tunneling, it's a relatively small contribution to rate in this case (small MW for H<sub>2</sub>). Therefore Transition State Theory tends to overestimate reaction rate values compare with experimental values.<br />
<br />
==F-H-H System ==<br />
<br />
=== PES inspection===<br />
<br />
====By inspecting the potential energy surfaces, classify the F + H<sub>2</sub> and H + HF reactions according to their energetics (endothermic or exothermic). How does this relate to the bond strength of the chemical species involved?====<br />
<br />
[[File:Mp5318Surface Plot fh2.png|thumb|left|Potential Surface of F + H<sub>2</sub> Reaction]]<br />
<br />
<br clear=all><br />
<br />
F + H<sub>2</sub> Reaction is exothermic. We can see there is a decrease in energy as H-H bond distance increases while H-F bond distance decreases. The clear downhill of reaction path indicated exothermic reaction. Bond strength of H-H is 432 kJ/mol, while H-F bond strength is 565 kJ/mol. Formation of H-F bond is preferred, as it would release more energy than the energy needed to break H-H bond. <br />
<br />
H + HF Reaction is endothermic. H-H bond formed is weaker than the H-F bond, therefore energy needed to cross the activation energy barrier — endothermic.<br />
<br />
According to Hammond Postulate, for an exothermic reaction, the TS resembles the reactants (early TS); for an endothermic reaction, the TS resembles the product (late TS). Therefore in this system, TS is very close to the H + HF side.<br />
<br />
====Locate the approximate position of the transition state.====<br />
<br />
Position of the TS of H<sub>2</sub> + F Reaction: r<sub>H-H</sub>=74.5 pm; r<sub>H···F</sub>=181.1 pm; At the TS, potential energy = 433.980 kJ/mol<br />
<br />
[[File:Mp5318 TS hhf contour.png.png|thumb|left|TS of F + H<sub>2</sub> Reaction]]<br />
<br />
[[File:Mp5318distande hhf.png|thumb|centre|Intermolecular distance vs. Time at the TS of F + H<sub>2</sub> Reaction]]<br />
<br clear=all><br />
<br />
====Report the activation energy for both reactions.====<br />
In the form of HF + H, potential energy =- 560.642 kJ/mol<br />
In the form o H<sub>2</sub> + F, potential energy = -434.922 kJ/mol<br />
<br />
Therefore compared with the TS potential energy (-433.980 kJ/mol): for HF + H to reach the TS, the activation energy is 126.02 kJ/mol; for H<sub>2</sub> + F to reach the TS, the activation energy is 0.942 kJ/mol.<br />
<br />
==== 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.====<br />
For the exothermic reaction, in this case, the F + H<sub>2</sub>, energy is released by the release of proton from the excited state, into vibrational energy of HF.</div>Mp5318https://chemwiki.ch.ic.ac.uk/index.php?title=File:Mp5318_TS_hhf_contour.png&diff=805300File:Mp5318 TS hhf contour.png2020-05-15T18:57:27Z<p>Mp5318: </p>
<hr />
<div></div>Mp5318https://chemwiki.ch.ic.ac.uk/index.php?title=Minqi5318&diff=805289Minqi53182020-05-15T18:54:28Z<p>Mp5318: /* 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. */</p>
<hr />
<div>== Molecular Reaction Dynamics: Application to Triatomic systems ==<br />
<br />
==H +H<sub>1</sub> System ==<br />
<br />
=== Dynamic from transition state region===<br />
<br />
====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?====<br />
<br />
The transition state is defined mathematically as the saddle point on the potential energy surface, where ∂V('''ri''')/∂'''ri'''=0 (the gradient of the potential is zero). At the transition state, the second derivative of potential with respect to q<sub>1</sub> is positive: ∂V<sup>2</sup>(q<sub>1</sub>)/∂q<sub>1</sub> > 0, indicating a minimum of the curve; the second derivative of potential with respect to q<sub>2</sub> is positive: ∂V<sup>2</sup>(q<sub>2</sub>)/∂q<sub>2</sub> < 0, indicating a maximum of the curve. The coincidence of a maximum and a minimum indicates saddle point on the potential energy surface. It can be identified through finding the maximum on the minimum energy path linking reactants and the products. The Transition State's energy goes down most steeply along the minimum energy path linking reactants and products c.f. local minimum of the potential energy surface. <br />
<br />
====Report your best estimate of the transition state position (r<sub>ts</sub>) and explain your reasoning illustrating it with an “Internuclear Distances vs Time” plot for a relevant trajectory.====<br />
<br />
The best estemate of the transition state position r<sub>ts</sub> = 91 pm<br />
<br />
[[File:mp5318_Animation.png|thumb|centre|Internuclear Distances vs Time Plot when r<sub>ts</sub> = 91 pm.]]<br />
<br />
As shown in the ''Internuclear Distances vs Time Plot when r<sub>ts</sub> = 91 pm'' above, when r<sub>ts</sub> = 91 pm and p<sub>1</sub> p<sub>2</sub> = 0.0 g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>, internuclear distance reamain (almost) constant, which shows that the molecule does not vibrate and stayed stably at the transition state forever.<br />
<br />
====Comment on how the MEP and the trajectory you just calculated differ.====<br />
<br />
[[File:Mp5318 Surface Plot Dynamic.png|thumb|left|Surface Plot using Dynamic Calculation r<sub>1</sub>=92 pm, r<sub>2</sub>=91 pm]]<br />
<br />
[[File:Surface Plot MEP.png|thumb|centre|Surface Plot using MEP Calculation r<sub>1</sub>=92 pm, r<sub>2</sub>=91 pm]]<br />
<br />
<br clear=all><br />
When '''r<sub>1</sub>'''=92 pm, '''r<sub>2</sub>'''=91 pm, atoms A and B dissociates. Using MEP calculation, AB dissociates through the minimum energy pathway and the dissociation ceased at a displacement much smaller than using Dynamic calculation. In Dynamic trajectory, kinetic energy was acquired during the trajectory from potential energy, therefore encourage inertial motion to proceed. In addition, MEP Calculation does not take into account the momentum of the particles, all the momentums are assumed to be zero.<br />
<br />
When reversing '''r<sub>1</sub>''' and '''r<sub>2</sub>''', B and C dissociates while A and B sticks together. The final values of the positions are '''r<sub>1</sub>''' (73.81819562) '''r<sub>2</sub>''' (352.8544826) and '''p<sub>1</sub>''' (3.258858751) '''p<sub>2</sub>''' (5.06251673). <br />
<br />
When setting up a calculation where the initial positions correspond to the final positions of the trajectory above, the same final momenta values but with their signs reversed, the reaction trajectory travels back to the orginal position '''r<sub>1</sub>''' (91) and '''r<sub>2</sub>''' (92) with '''p<sub>1</sub>'''= '''p<sub>2</sub>'''= 0.<br />
<br />
===Reactive and Unreactive trajectories===<br />
<br />
{| class="wikitable" border="1"<br />
|+ initial positions '''r<sub>1</sub>''' (74 pm) '''r<sub>2</sub>''' (200 pm)<br />
! p<sub>1</sub> / g.mol<sup>-1</sup>.pm.fs<sup>-1</sup> !! p<sub>2</sub> / g.mol<sup>-1</sup>.pm.fs<sup>-1</sup> !! E<sub>tot</sub> kJ.mol<sub>-1</sub> !! Reactive? !! Description of the dunamics !! Illustration of the trajectory<br />
|-<br />
| -2.56 || -5.1 || -414.28 || Yes || A-B + C → A +B-C || [[File:Mp5318 t1.png|356px]]<br />
|-<br />
| -3.1 || -4.1 || -420.08 || No || A-B approaches C, but then leave without reaction occur || [[File:Mp5318 t2.png|356px]]<br />
|-<br />
| -3.1 || -5.1 || -413.98 || Yes || A-B + C → A +B-C || [[File:Mp5318 t3.png|356px]]<br />
|-<br />
| -5.1 || -10.1 || -357.28 || No || at TS region, strength of bondings A-B and B-C alternates, but eventually A-B leave intact (Barrier can be crossed, but then the system reverts back to the reactants) || [[File:Mp5318 t4.png|356px]]<br />
|-<br />
| -5.1 || -10.6 || -349.38 || Yes || A-B + C → A +B-C at TS region, strength of bonding A-B and N-C alternates, but new product formed eventually || [[File:Mp5318 t5.png|356px]]<br />
|}<br />
<br />
'''Conclusion: Reactants need to have a large enough ratio in the momentum to be reactive, ideally, p<sub>2</sub> : p<sub>1</sub> should be larger than 2 for the reactants to be reactive.'''<br />
<br />
===Transition State Theory===<br />
<br />
====Given the results you have obtained, how will Transition State Theory predictions for reaction rate values compare with experimental values?====<br />
<br />
Transition State Theory often overestimates the reaction rate, compared to the results we calculated. Transition State Theory assumed that once the reaction has passed the Transition state and reached the product, it would not travel back to cross the Transition State and reverse to the reactant side. However, the calculations above showed that in practice, products can still recross the energy barrier to go back to the reactants. Even though the Transition State Theory ignored the effect of quantum tunneling, it's a relatively small contribution to rate in this case (small MW for H<sub>2</sub>). Therefore Transition State Theory tends to overestimate reaction rate values compare with experimental values.<br />
<br />
==F-H-H System ==<br />
<br />
=== PES inspection===<br />
<br />
====By inspecting the potential energy surfaces, classify the F + H<sub>2</sub> and H + HF reactions according to their energetics (endothermic or exothermic). How does this relate to the bond strength of the chemical species involved?====<br />
<br />
[[File:Mp5318Surface Plot fh2.png|thumb|left|Potential Surface of F + H<sub>2</sub> Reaction]]<br />
<br />
<br clear=all><br />
<br />
F + H<sub>2</sub> Reaction is exothermic. We can see there is a decrease in energy as H-H bond distance increases while H-F bond distance decreases. The clear downhill of reaction path indicated exothermic reaction. Bond strength of H-H is 432 kJ/mol, while H-F bond strength is 565 kJ/mol. Formation of H-F bond is preferred, as it would release more energy than the energy needed to break H-H bond. <br />
<br />
H + HF Reaction is endothermic. H-H bond formed is weaker than the H-F bond, therefore energy needed to cross the activation energy barrier — endothermic.<br />
<br />
According to Hammond Postulate, for an exothermic reaction, the TS resembles the reactants (early TS); for an endothermic reaction, the TS resembles the product (late TS). Therefore in this system, TS is very close to the H + HF side.<br />
<br />
====Locate the approximate position of the transition state.====<br />
<br />
Position of the TS of H<sub>2</sub> + F Reaction: r<sub>H-H</sub>=74.5 pm; r<sub>H···F</sub>=181.1 pm; At the TS, potential energy = 433.980 kJ/mol<br />
<br />
[[File:Mp5318 contour TS hhf.png|thumb|left|TS of F + H<sub>2</sub> Reaction]]<br />
<br />
[[File:Mp5318distande hhf.png|thumb|centre|Intermolecular distance vs. Time at the TS of F + H<sub>2</sub> Reaction]]<br />
<br clear=all><br />
<br />
====Report the activation energy for both reactions.====<br />
In the form of HF + H, potential energy =- 560.642 kJ/mol<br />
In the form o H<sub>2</sub> + F, potential energy = -434.922 kJ/mol<br />
<br />
Therefore compared with the TS potential energy (-433.980 kJ/mol): for HF + H to reach the TS, the activation energy is 126.02 kJ/mol; for H<sub>2</sub> + F to reach the TS, the activation energy is 0.942 kJ/mol.<br />
<br />
==== 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.====<br />
For the exothermic reaction, in this case, the F + H<sub>2</sub>, energy is released by the release of proton from the excited state, into vibrational energy of HF.</div>Mp5318https://chemwiki.ch.ic.ac.uk/index.php?title=Minqi5318&diff=804375Minqi53182020-05-15T13:19:46Z<p>Mp5318: /* 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. */</p>
<hr />
<div>== Molecular Reaction Dynamics: Application to Triatomic systems ==<br />
<br />
==H +H<sub>1</sub> System ==<br />
<br />
=== Dynamic from transition state region===<br />
<br />
====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?====<br />
<br />
The transition state is defined mathematically as the saddle point on the potential energy surface, where ∂V('''ri''')/∂'''ri'''=0 (the gradient of the potential is zero). At the transition state, the second derivative of potential with respect to q<sub>1</sub> is positive: ∂V<sup>2</sup>(q<sub>1</sub>)/∂q<sub>1</sub> > 0, indicating a minimum of the curve; the second derivative of potential with respect to q<sub>2</sub> is positive: ∂V<sup>2</sup>(q<sub>2</sub>)/∂q<sub>2</sub> < 0, indicating a maximum of the curve. The coincidence of a maximum and a minimum indicates saddle point on the potential energy surface. It can be identified through finding the maximum on the minimum energy path linking reactants and the products. The Transition State's energy goes down most steeply along the minimum energy path linking reactants and products c.f. local minimum of the potential energy surface. <br />
<br />
====Report your best estimate of the transition state position (r<sub>ts</sub>) and explain your reasoning illustrating it with an “Internuclear Distances vs Time” plot for a relevant trajectory.====<br />
<br />
The best estemate of the transition state position r<sub>ts</sub> = 91 pm<br />
<br />
[[File:mp5318_Animation.png|thumb|centre|Internuclear Distances vs Time Plot when r<sub>ts</sub> = 91 pm.]]<br />
<br />
As shown in the ''Internuclear Distances vs Time Plot when r<sub>ts</sub> = 91 pm'' above, when r<sub>ts</sub> = 91 pm and p<sub>1</sub> p<sub>2</sub> = 0.0 g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>, internuclear distance reamain (almost) constant, which shows that the molecule does not vibrate and stayed stably at the transition state forever.<br />
<br />
====Comment on how the MEP and the trajectory you just calculated differ.====<br />
<br />
[[File:Mp5318 Surface Plot Dynamic.png|thumb|left|Surface Plot using Dynamic Calculation r<sub>1</sub>=92 pm, r<sub>2</sub>=91 pm]]<br />
<br />
[[File:Surface Plot MEP.png|thumb|centre|Surface Plot using MEP Calculation r<sub>1</sub>=92 pm, r<sub>2</sub>=91 pm]]<br />
<br />
<br clear=all><br />
When '''r<sub>1</sub>'''=92 pm, '''r<sub>2</sub>'''=91 pm, atoms A and B dissociates. Using MEP calculation, AB dissociates through the minimum energy pathway and the dissociation ceased at a displacement much smaller than using Dynamic calculation. In Dynamic trajectory, kinetic energy was acquired during the trajectory from potential energy, therefore encourage inertial motion to proceed. In addition, MEP Calculation does not take into account the momentum of the particles, all the momentums are assumed to be zero.<br />
<br />
When reversing '''r<sub>1</sub>''' and '''r<sub>2</sub>''', B and C dissociates while A and B sticks together. The final values of the positions are '''r<sub>1</sub>''' (73.81819562) '''r<sub>2</sub>''' (352.8544826) and '''p<sub>1</sub>''' (3.258858751) '''p<sub>2</sub>''' (5.06251673). <br />
<br />
When setting up a calculation where the initial positions correspond to the final positions of the trajectory above, the same final momenta values but with their signs reversed, the reaction trajectory travels back to the orginal position '''r<sub>1</sub>''' (91) and '''r<sub>2</sub>''' (92) with '''p<sub>1</sub>'''= '''p<sub>2</sub>'''= 0.<br />
<br />
===Reactive and Unreactive trajectories===<br />
<br />
{| class="wikitable" border="1"<br />
|+ initial positions '''r<sub>1</sub>''' (74 pm) '''r<sub>2</sub>''' (200 pm)<br />
! p<sub>1</sub> / g.mol<sup>-1</sup>.pm.fs<sup>-1</sup> !! p<sub>2</sub> / g.mol<sup>-1</sup>.pm.fs<sup>-1</sup> !! E<sub>tot</sub> kJ.mol<sub>-1</sub> !! Reactive? !! Description of the dunamics !! Illustration of the trajectory<br />
|-<br />
| -2.56 || -5.1 || -414.28 || Yes || A-B + C → A +B-C || [[File:Mp5318 t1.png|356px]]<br />
|-<br />
| -3.1 || -4.1 || -420.08 || No || A-B approaches C, but then leave without reaction occur || [[File:Mp5318 t2.png|356px]]<br />
|-<br />
| -3.1 || -5.1 || -413.98 || Yes || A-B + C → A +B-C || [[File:Mp5318 t3.png|356px]]<br />
|-<br />
| -5.1 || -10.1 || -357.28 || No || at TS region, strength of bondings A-B and B-C alternates, but eventually A-B leave intact (Barrier can be crossed, but then the system reverts back to the reactants) || [[File:Mp5318 t4.png|356px]]<br />
|-<br />
| -5.1 || -10.6 || -349.38 || Yes || A-B + C → A +B-C at TS region, strength of bonding A-B and N-C alternates, but new product formed eventually || [[File:Mp5318 t5.png|356px]]<br />
|}<br />
<br />
'''Conclusion: Reactants need to have a large enough ratio in the momentum to be reactive, ideally, p<sub>2</sub> : p<sub>1</sub> should be larger than 2 for the reactants to be reactive.'''<br />
<br />
===Transition State Theory===<br />
<br />
====Given the results you have obtained, how will Transition State Theory predictions for reaction rate values compare with experimental values?====<br />
<br />
Transition State Theory often overestimates the reaction rate, compared to the results we calculated. Transition State Theory assumed that once the reaction has passed the Transition state and reached the product, it would not travel back to cross the Transition State and reverse to the reactant side. However, the calculations above showed that in practice, products can still recross the energy barrier to go back to the reactants. Even though the Transition State Theory ignored the effect of quantum tunneling, it's a relatively small contribution to rate in this case (small MW for H<sub>2</sub>). Therefore Transition State Theory tends to overestimate reaction rate values compare with experimental values.<br />
<br />
==F-H-H System ==<br />
<br />
=== PES inspection===<br />
<br />
====By inspecting the potential energy surfaces, classify the F + H<sub>2</sub> and H + HF reactions according to their energetics (endothermic or exothermic). How does this relate to the bond strength of the chemical species involved?====<br />
<br />
[[File:Mp5318Surface Plot fh2.png|thumb|left|Potential Surface of F + H<sub>2</sub> Reaction]]<br />
<br />
<br clear=all><br />
<br />
F + H<sub>2</sub> Reaction is exothermic. We can see there is a decrease in energy as H-H bond distance increases while H-F bond distance decreases. The clear downhill of reaction path indicated exothermic reaction. Bond strength of H-H is 432 kJ/mol, while H-F bond strength is 565 kJ/mol. Formation of H-F bond is preferred, as it would release more energy than the energy needed to break H-H bond. <br />
<br />
H + HF Reaction is endothermic. H-H bond formed is weaker than the H-F bond, therefore energy needed to cross the activation energy barrier — endothermic.<br />
<br />
According to Hammond Postulate, for an exothermic reaction, the TS resembles the reactants (early TS); for an endothermic reaction, the TS resembles the product (late TS). Therefore in this system, TS is very close to the H + HF side.<br />
<br />
====Locate the approximate position of the transition state.====<br />
<br />
Position of the TS of H<sub>2</sub> + F Reaction: r<sub>H-H</sub>=74.5 pm; r<sub>H···F</sub>=181.1 pm; At the TS, potential energy = 433.980 kJ/mol<br />
<br />
[[File:Mp5318 contour TS hhf.png|thumb|left|TS of F + H<sub>2</sub> Reaction]]<br />
<br />
[[File:Mp5318distande hhf.png|thumb|centre|Intermolecular distance vs. Time at the TS of F + H<sub>2</sub> Reaction]]<br />
<br clear=all><br />
<br />
====Report the activation energy for both reactions.====<br />
In the form of HF + H, potential energy =- 560.642 kJ/mol<br />
In the form o H<sub>2</sub> + F, potential energy = -434.922 kJ/mol<br />
<br />
Therefore compared with the TS potential energy (-433.980 kJ/mol): for HF + H to reach the TS, the activation energy is 126.02 kJ/mol; for H<sub>2</sub> + F to reach the TS, the activation energy is 0.942 kJ/mol.<br />
<br />
==== 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.====<br />
For the exothermic reaction, in this case, the F + H<sub>2</sub>, energy is released by the release of proton from the excited state.</div>Mp5318https://chemwiki.ch.ic.ac.uk/index.php?title=Minqi5318&diff=804322Minqi53182020-05-15T13:00:21Z<p>Mp5318: /* F-H-H System */</p>
<hr />
<div>== Molecular Reaction Dynamics: Application to Triatomic systems ==<br />
<br />
==H +H<sub>1</sub> System ==<br />
<br />
=== Dynamic from transition state region===<br />
<br />
====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?====<br />
<br />
The transition state is defined mathematically as the saddle point on the potential energy surface, where ∂V('''ri''')/∂'''ri'''=0 (the gradient of the potential is zero). At the transition state, the second derivative of potential with respect to q<sub>1</sub> is positive: ∂V<sup>2</sup>(q<sub>1</sub>)/∂q<sub>1</sub> > 0, indicating a minimum of the curve; the second derivative of potential with respect to q<sub>2</sub> is positive: ∂V<sup>2</sup>(q<sub>2</sub>)/∂q<sub>2</sub> < 0, indicating a maximum of the curve. The coincidence of a maximum and a minimum indicates saddle point on the potential energy surface. It can be identified through finding the maximum on the minimum energy path linking reactants and the products. The Transition State's energy goes down most steeply along the minimum energy path linking reactants and products c.f. local minimum of the potential energy surface. <br />
<br />
====Report your best estimate of the transition state position (r<sub>ts</sub>) and explain your reasoning illustrating it with an “Internuclear Distances vs Time” plot for a relevant trajectory.====<br />
<br />
The best estemate of the transition state position r<sub>ts</sub> = 91 pm<br />
<br />
[[File:mp5318_Animation.png|thumb|centre|Internuclear Distances vs Time Plot when r<sub>ts</sub> = 91 pm.]]<br />
<br />
As shown in the ''Internuclear Distances vs Time Plot when r<sub>ts</sub> = 91 pm'' above, when r<sub>ts</sub> = 91 pm and p<sub>1</sub> p<sub>2</sub> = 0.0 g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>, internuclear distance reamain (almost) constant, which shows that the molecule does not vibrate and stayed stably at the transition state forever.<br />
<br />
====Comment on how the MEP and the trajectory you just calculated differ.====<br />
<br />
[[File:Mp5318 Surface Plot Dynamic.png|thumb|left|Surface Plot using Dynamic Calculation r<sub>1</sub>=92 pm, r<sub>2</sub>=91 pm]]<br />
<br />
[[File:Surface Plot MEP.png|thumb|centre|Surface Plot using MEP Calculation r<sub>1</sub>=92 pm, r<sub>2</sub>=91 pm]]<br />
<br />
<br clear=all><br />
When '''r<sub>1</sub>'''=92 pm, '''r<sub>2</sub>'''=91 pm, atoms A and B dissociates. Using MEP calculation, AB dissociates through the minimum energy pathway and the dissociation ceased at a displacement much smaller than using Dynamic calculation. In Dynamic trajectory, kinetic energy was acquired during the trajectory from potential energy, therefore encourage inertial motion to proceed. In addition, MEP Calculation does not take into account the momentum of the particles, all the momentums are assumed to be zero.<br />
<br />
When reversing '''r<sub>1</sub>''' and '''r<sub>2</sub>''', B and C dissociates while A and B sticks together. The final values of the positions are '''r<sub>1</sub>''' (73.81819562) '''r<sub>2</sub>''' (352.8544826) and '''p<sub>1</sub>''' (3.258858751) '''p<sub>2</sub>''' (5.06251673). <br />
<br />
When setting up a calculation where the initial positions correspond to the final positions of the trajectory above, the same final momenta values but with their signs reversed, the reaction trajectory travels back to the orginal position '''r<sub>1</sub>''' (91) and '''r<sub>2</sub>''' (92) with '''p<sub>1</sub>'''= '''p<sub>2</sub>'''= 0.<br />
<br />
===Reactive and Unreactive trajectories===<br />
<br />
{| class="wikitable" border="1"<br />
|+ initial positions '''r<sub>1</sub>''' (74 pm) '''r<sub>2</sub>''' (200 pm)<br />
! p<sub>1</sub> / g.mol<sup>-1</sup>.pm.fs<sup>-1</sup> !! p<sub>2</sub> / g.mol<sup>-1</sup>.pm.fs<sup>-1</sup> !! E<sub>tot</sub> kJ.mol<sub>-1</sub> !! Reactive? !! Description of the dunamics !! Illustration of the trajectory<br />
|-<br />
| -2.56 || -5.1 || -414.28 || Yes || A-B + C → A +B-C || [[File:Mp5318 t1.png|356px]]<br />
|-<br />
| -3.1 || -4.1 || -420.08 || No || A-B approaches C, but then leave without reaction occur || [[File:Mp5318 t2.png|356px]]<br />
|-<br />
| -3.1 || -5.1 || -413.98 || Yes || A-B + C → A +B-C || [[File:Mp5318 t3.png|356px]]<br />
|-<br />
| -5.1 || -10.1 || -357.28 || No || at TS region, strength of bondings A-B and B-C alternates, but eventually A-B leave intact (Barrier can be crossed, but then the system reverts back to the reactants) || [[File:Mp5318 t4.png|356px]]<br />
|-<br />
| -5.1 || -10.6 || -349.38 || Yes || A-B + C → A +B-C at TS region, strength of bonding A-B and N-C alternates, but new product formed eventually || [[File:Mp5318 t5.png|356px]]<br />
|}<br />
<br />
'''Conclusion: Reactants need to have a large enough ratio in the momentum to be reactive, ideally, p<sub>2</sub> : p<sub>1</sub> should be larger than 2 for the reactants to be reactive.'''<br />
<br />
===Transition State Theory===<br />
<br />
====Given the results you have obtained, how will Transition State Theory predictions for reaction rate values compare with experimental values?====<br />
<br />
Transition State Theory often overestimates the reaction rate, compared to the results we calculated. Transition State Theory assumed that once the reaction has passed the Transition state and reached the product, it would not travel back to cross the Transition State and reverse to the reactant side. However, the calculations above showed that in practice, products can still recross the energy barrier to go back to the reactants. Even though the Transition State Theory ignored the effect of quantum tunneling, it's a relatively small contribution to rate in this case (small MW for H<sub>2</sub>). Therefore Transition State Theory tends to overestimate reaction rate values compare with experimental values.<br />
<br />
==F-H-H System ==<br />
<br />
=== PES inspection===<br />
<br />
====By inspecting the potential energy surfaces, classify the F + H<sub>2</sub> and H + HF reactions according to their energetics (endothermic or exothermic). How does this relate to the bond strength of the chemical species involved?====<br />
<br />
[[File:Mp5318Surface Plot fh2.png|thumb|left|Potential Surface of F + H<sub>2</sub> Reaction]]<br />
<br />
<br clear=all><br />
<br />
F + H<sub>2</sub> Reaction is exothermic. We can see there is a decrease in energy as H-H bond distance increases while H-F bond distance decreases. The clear downhill of reaction path indicated exothermic reaction. Bond strength of H-H is 432 kJ/mol, while H-F bond strength is 565 kJ/mol. Formation of H-F bond is preferred, as it would release more energy than the energy needed to break H-H bond. <br />
<br />
H + HF Reaction is endothermic. H-H bond formed is weaker than the H-F bond, therefore energy needed to cross the activation energy barrier — endothermic.<br />
<br />
According to Hammond Postulate, for an exothermic reaction, the TS resembles the reactants (early TS); for an endothermic reaction, the TS resembles the product (late TS). Therefore in this system, TS is very close to the H + HF side.<br />
<br />
====Locate the approximate position of the transition state.====<br />
<br />
Position of the TS of H<sub>2</sub> + F Reaction: r<sub>H-H</sub>=74.5 pm; r<sub>H···F</sub>=181.1 pm; At the TS, potential energy = 433.980 kJ/mol<br />
<br />
[[File:Mp5318 contour TS hhf.png|thumb|left|TS of F + H<sub>2</sub> Reaction]]<br />
<br />
[[File:Mp5318distande hhf.png|thumb|centre|Intermolecular distance vs. Time at the TS of F + H<sub>2</sub> Reaction]]<br />
<br clear=all><br />
<br />
====Report the activation energy for both reactions.====<br />
In the form of HF + H, potential energy =- 560.642 kJ/mol<br />
In the form o H<sub>2</sub> + F, potential energy = -434.922 kJ/mol<br />
<br />
Therefore compared with the TS potential energy (-433.980 kJ/mol): for HF + H to reach the TS, the activation energy is 126.02 kJ/mol; for H<sub>2</sub> + F to reach the TS, the activation energy is 0.942 kJ/mol.<br />
<br />
==== 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.====<br />
For the exothermic reaction, in this case, the F + H<sub>2</sub>, trans</div>Mp5318https://chemwiki.ch.ic.ac.uk/index.php?title=Minqi5318&diff=804049Minqi53182020-05-15T11:09:52Z<p>Mp5318: /* 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? */</p>
<hr />
<div>== Molecular Reaction Dynamics: Application to Triatomic systems ==<br />
<br />
==H +H<sub>1</sub> System ==<br />
<br />
=== Dynamic from transition state region===<br />
<br />
====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?====<br />
<br />
The transition state is defined mathematically as the saddle point on the potential energy surface, where ∂V('''ri''')/∂'''ri'''=0 (the gradient of the potential is zero). At the transition state, the second derivative of potential with respect to q<sub>1</sub> is positive: ∂V<sup>2</sup>(q<sub>1</sub>)/∂q<sub>1</sub> > 0, indicating a minimum of the curve; the second derivative of potential with respect to q<sub>2</sub> is positive: ∂V<sup>2</sup>(q<sub>2</sub>)/∂q<sub>2</sub> < 0, indicating a maximum of the curve. The coincidence of a maximum and a minimum indicates saddle point on the potential energy surface. It can be identified through finding the maximum on the minimum energy path linking reactants and the products. The Transition State's energy goes down most steeply along the minimum energy path linking reactants and products c.f. local minimum of the potential energy surface. <br />
<br />
====Report your best estimate of the transition state position (r<sub>ts</sub>) and explain your reasoning illustrating it with an “Internuclear Distances vs Time” plot for a relevant trajectory.====<br />
<br />
The best estemate of the transition state position r<sub>ts</sub> = 91 pm<br />
<br />
[[File:mp5318_Animation.png|thumb|centre|Internuclear Distances vs Time Plot when r<sub>ts</sub> = 91 pm.]]<br />
<br />
As shown in the ''Internuclear Distances vs Time Plot when r<sub>ts</sub> = 91 pm'' above, when r<sub>ts</sub> = 91 pm and p<sub>1</sub> p<sub>2</sub> = 0.0 g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>, internuclear distance reamain (almost) constant, which shows that the molecule does not vibrate and stayed stably at the transition state forever.<br />
<br />
====Comment on how the MEP and the trajectory you just calculated differ.====<br />
<br />
[[File:Mp5318 Surface Plot Dynamic.png|thumb|left|Surface Plot using Dynamic Calculation r<sub>1</sub>=92 pm, r<sub>2</sub>=91 pm]]<br />
<br />
[[File:Surface Plot MEP.png|thumb|centre|Surface Plot using MEP Calculation r<sub>1</sub>=92 pm, r<sub>2</sub>=91 pm]]<br />
<br />
<br clear=all><br />
When '''r<sub>1</sub>'''=92 pm, '''r<sub>2</sub>'''=91 pm, atoms A and B dissociates. Using MEP calculation, AB dissociates through the minimum energy pathway and the dissociation ceased at a displacement much smaller than using Dynamic calculation. In Dynamic trajectory, kinetic energy was acquired during the trajectory from potential energy, therefore encourage inertial motion to proceed. In addition, MEP Calculation does not take into account the momentum of the particles, all the momentums are assumed to be zero.<br />
<br />
When reversing '''r<sub>1</sub>''' and '''r<sub>2</sub>''', B and C dissociates while A and B sticks together. The final values of the positions are '''r<sub>1</sub>''' (73.81819562) '''r<sub>2</sub>''' (352.8544826) and '''p<sub>1</sub>''' (3.258858751) '''p<sub>2</sub>''' (5.06251673). <br />
<br />
When setting up a calculation where the initial positions correspond to the final positions of the trajectory above, the same final momenta values but with their signs reversed, the reaction trajectory travels back to the orginal position '''r<sub>1</sub>''' (91) and '''r<sub>2</sub>''' (92) with '''p<sub>1</sub>'''= '''p<sub>2</sub>'''= 0.<br />
<br />
===Reactive and Unreactive trajectories===<br />
<br />
{| class="wikitable" border="1"<br />
|+ initial positions '''r<sub>1</sub>''' (74 pm) '''r<sub>2</sub>''' (200 pm)<br />
! p<sub>1</sub> / g.mol<sup>-1</sup>.pm.fs<sup>-1</sup> !! p<sub>2</sub> / g.mol<sup>-1</sup>.pm.fs<sup>-1</sup> !! E<sub>tot</sub> kJ.mol<sub>-1</sub> !! Reactive? !! Description of the dunamics !! Illustration of the trajectory<br />
|-<br />
| -2.56 || -5.1 || -414.28 || Yes || A-B + C → A +B-C || [[File:Mp5318 t1.png|356px]]<br />
|-<br />
| -3.1 || -4.1 || -420.08 || No || A-B approaches C, but then leave without reaction occur || [[File:Mp5318 t2.png|356px]]<br />
|-<br />
| -3.1 || -5.1 || -413.98 || Yes || A-B + C → A +B-C || [[File:Mp5318 t3.png|356px]]<br />
|-<br />
| -5.1 || -10.1 || -357.28 || No || at TS region, strength of bondings A-B and B-C alternates, but eventually A-B leave intact (Barrier can be crossed, but then the system reverts back to the reactants) || [[File:Mp5318 t4.png|356px]]<br />
|-<br />
| -5.1 || -10.6 || -349.38 || Yes || A-B + C → A +B-C at TS region, strength of bonding A-B and N-C alternates, but new product formed eventually || [[File:Mp5318 t5.png|356px]]<br />
|}<br />
<br />
'''Conclusion: Reactants need to have a large enough ratio in the momentum to be reactive, ideally, p<sub>2</sub> : p<sub>1</sub> should be larger than 2 for the reactants to be reactive.'''<br />
<br />
===Transition State Theory===<br />
<br />
====Given the results you have obtained, how will Transition State Theory predictions for reaction rate values compare with experimental values?====<br />
<br />
Transition State Theory often overestimates the reaction rate, compared to the results we calculated. Transition State Theory assumed that once the reaction has passed the Transition state and reached the product, it would not travel back to cross the Transition State and reverse to the reactant side. However, the calculations above showed that in practice, products can still recross the energy barrier to go back to the reactants. Even though the Transition State Theory ignored the effect of quantum tunneling, it's a relatively small contribution to rate in this case (small MW for H<sub>2</sub>). Therefore Transition State Theory tends to overestimate reaction rate values compare with experimental values.<br />
<br />
==F-H-H System ==<br />
<br />
=== PES inspection===<br />
<br />
====By inspecting the potential energy surfaces, classify the F + H<sub>2</sub> and H + HF reactions according to their energetics (endothermic or exothermic). How does this relate to the bond strength of the chemical species involved?====<br />
<br />
[[File:Mp5318Surface Plot fh2.png|thumb|left|Potential Surface of F + H<sub>2</sub> Reaction]]<br />
<br />
<br clear=all><br />
<br />
F + H<sub>2</sub> Reaction is exothermic. We can see there is a decrease in energy as H-H bond distance increases while H-F bond distance decreases. The clear downhill of reaction path indicated exothermic reaction. Bond strength of H-H is 432 kJ/mol, while H-F bond strength is 565 kJ/mol. Formation of H-F bond is preferred, as it would release more energy than the energy needed to break H-H bond. <br />
<br />
H + HF Reaction is endothermic. H-H bond formed is weaker than the H-F bond, therefore energy needed to cross the activation energy barrier — endothermic.<br />
<br />
According to Hammond Postulate, for an exothermic reaction, the TS resembles the reactants (early TS); for an endothermic reaction, the TS resembles the product (late TS). Therefore in this system, TS is very close to the H + HF side.<br />
<br />
====Locate the approximate position of the transition state.====<br />
<br />
Position of the TS of H<sub>2</sub> + F Reaction: r<sub>H-H</sub>=74.5 pm; r<sub>H···F</sub>=181.1 pm; At the TS, potential energy = 433.980 kJ/mol<br />
<br />
[[File:Mp5318 contour TS hhf.png|thumb|left|TS of F + H<sub>2</sub> Reaction]]<br />
<br />
[[File:Mp5318distande hhf.png|thumb|centre|Intermolecular distance vs. Time at the TS of F + H<sub>2</sub> Reaction]]<br />
<br clear=all><br />
<br />
====Report the activation energy for both reactions.====<br />
In the form of HF + H, potential energy =- 429.814 kJ/mol<br />
In the form o H<sub>2</sub> + F, potential energy = -433.990 kJ/mol<br />
<br />
Therefore compared with the TS potential energy (-433.980 kJ/mol): for HF + H to reach the TS, the activation energy is -4.166 kJ/mol; for H<sub>2</sub> + F to reach the TS, the activation energy is -0.1 kJ/mol.</div>Mp5318https://chemwiki.ch.ic.ac.uk/index.php?title=Minqi5318&diff=804014Minqi53182020-05-15T10:44:31Z<p>Mp5318: /* Report the activation energy for both reactions. */</p>
<hr />
<div>== Molecular Reaction Dynamics: Application to Triatomic systems ==<br />
<br />
==H +H<sub>1</sub> System ==<br />
<br />
=== Dynamic from transition state region===<br />
<br />
====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?====<br />
<br />
The transition state is defined mathematically as the saddle point on the potential energy surface, where ∂V('''ri''')/∂'''ri'''=0 (the gradient of the potential is zero). At the transition state, the second derivative of potential with respect to q<sub>1</sub> is positive: ∂V<sup>2</sup>(q<sub>1</sub>)/∂q<sub>1</sub> > 0, indicating a minimum of the curve; the second derivative of potential with respect to q<sub>2</sub> is positive: ∂V<sup>2</sup>(q<sub>2</sub>)/∂q<sub>2</sub> < 0, indicating a maximum of the curve. The coincidence of a maximum and a minimum indicates saddle point on the potential energy surface. It can be identified through finding the maximum on the minimum energy path linking reactants and the products. The Transition State's energy goes down most steeply along the minimum energy path linking reactants and products c.f. local minimum of the potential energy surface. <br />
<br />
====Report your best estimate of the transition state position (r<sub>ts</sub>) and explain your reasoning illustrating it with an “Internuclear Distances vs Time” plot for a relevant trajectory.====<br />
<br />
The best estemate of the transition state position r<sub>ts</sub> = 91 pm<br />
<br />
[[File:mp5318_Animation.png|thumb|centre|Internuclear Distances vs Time Plot when r<sub>ts</sub> = 91 pm.]]<br />
<br />
As shown in the ''Internuclear Distances vs Time Plot when r<sub>ts</sub> = 91 pm'' above, when r<sub>ts</sub> = 91 pm and p<sub>1</sub> p<sub>2</sub> = 0.0 g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>, internuclear distance reamain (almost) constant, which shows that the molecule does not vibrate and stayed stably at the transition state forever.<br />
<br />
====Comment on how the MEP and the trajectory you just calculated differ.====<br />
<br />
[[File:Mp5318 Surface Plot Dynamic.png|thumb|left|Surface Plot using Dynamic Calculation r<sub>1</sub>=92 pm, r<sub>2</sub>=91 pm]]<br />
<br />
[[File:Surface Plot MEP.png|thumb|centre|Surface Plot using MEP Calculation r<sub>1</sub>=92 pm, r<sub>2</sub>=91 pm]]<br />
<br />
<br clear=all><br />
When '''r<sub>1</sub>'''=92 pm, '''r<sub>2</sub>'''=91 pm, atoms A and B dissociates. Using MEP calculation, AB dissociates through the minimum energy pathway and the dissociation ceased at a displacement much smaller than using Dynamic calculation. In Dynamic trajectory, kinetic energy was acquired during the trajectory from potential energy, therefore encourage inertial motion to proceed. In addition, MEP Calculation does not take into account the momentum of the particles, all the momentums are assumed to be zero.<br />
<br />
When reversing '''r<sub>1</sub>''' and '''r<sub>2</sub>''', B and C dissociates while A and B sticks together. The final values of the positions are '''r<sub>1</sub>''' (73.81819562) '''r<sub>2</sub>''' (352.8544826) and '''p<sub>1</sub>''' (3.258858751) '''p<sub>2</sub>''' (5.06251673). <br />
<br />
When setting up a calculation where the initial positions correspond to the final positions of the trajectory above, the same final momenta values but with their signs reversed, the reaction trajectory travels back to the orginal position '''r<sub>1</sub>''' (91) and '''r<sub>2</sub>''' (92) with '''p<sub>1</sub>'''= '''p<sub>2</sub>'''= 0.<br />
<br />
===Reactive and Unreactive trajectories===<br />
<br />
{| class="wikitable" border="1"<br />
|+ initial positions '''r<sub>1</sub>''' (74 pm) '''r<sub>2</sub>''' (200 pm)<br />
! p<sub>1</sub> / g.mol<sup>-1</sup>.pm.fs<sup>-1</sup> !! p<sub>2</sub> / g.mol<sup>-1</sup>.pm.fs<sup>-1</sup> !! E<sub>tot</sub> kJ.mol<sub>-1</sub> !! Reactive? !! Description of the dunamics !! Illustration of the trajectory<br />
|-<br />
| -2.56 || -5.1 || -414.28 || Yes || A-B + C → A +B-C || [[File:Mp5318 t1.png|356px]]<br />
|-<br />
| -3.1 || -4.1 || -420.08 || No || A-B approaches C, but then leave without reaction occur || [[File:Mp5318 t2.png|356px]]<br />
|-<br />
| -3.1 || -5.1 || -413.98 || Yes || A-B + C → A +B-C || [[File:Mp5318 t3.png|356px]]<br />
|-<br />
| -5.1 || -10.1 || -357.28 || No || at TS region, strength of bondings A-B and B-C alternates, but eventually A-B leave intact (Barrier can be crossed, but then the system reverts back to the reactants) || [[File:Mp5318 t4.png|356px]]<br />
|-<br />
| -5.1 || -10.6 || -349.38 || Yes || A-B + C → A +B-C at TS region, strength of bonding A-B and N-C alternates, but new product formed eventually || [[File:Mp5318 t5.png|356px]]<br />
|}<br />
<br />
'''Conclusion: Reactants need to have a large enough ratio in the momentum to be reactive, ideally, p<sub>2</sub> : p<sub>1</sub> should be larger than 2 for the reactants to be reactive.'''<br />
<br />
===Transition State Theory===<br />
<br />
====Given the results you have obtained, how will Transition State Theory predictions for reaction rate values compare with experimental values?====<br />
<br />
Transition State Theory often overestimates the reaction rate, compared to the results we calculated. Transition State Theory assumed that once the reaction has passed the Transition state and reached the product, it would not travel back to cross the Transition State and reverse to the reactant side. However, the calculations above showed that in practice, products can still recross the energy barrier to go back to the reactants. Even though the Transition State Theory ignored the effect of quantum tunneling, it's a relatively small contribution to rate in this case (small MW for H<sub>2</sub>). Therefore Transition State Theory tends to overestimate reaction rate values compare with experimental values.<br />
<br />
==F-H-H System ==<br />
<br />
=== PES inspection===<br />
<br />
====By inspecting the potential energy surfaces, classify the F + H<sub>2</sub> and H + HF reactions according to their energetics (endothermic or exothermic). How does this relate to the bond strength of the chemical species involved?====<br />
<br />
[[File:Mp5318Surface Plot fh2.png|thumb|left|Potential Surface of F + H<sub>2</sub> Reaction]]<br />
<br />
<br clear=all><br />
<br />
F + H<sub>2</sub> Reaction is exothermic. We can see there is a decrease in energy as H-H bond distance increases while H-F bond distance decreases. The clear downhill of reaction path indicated exothermic. Bond strength of H-H is 432 kJ/mol, while H-F bond strength is 565 kJ/mol. Formation of H-F bond is preferred, as it would release more energy than the energy needed to break H-H bond. <br />
<br />
H + HF Reaction is endothermic. H-H bond formed is weaker than the H-F bond, therefore energy needed to cross the activation energy barrier — endothermic.<br />
<br />
====Locate the approximate position of the transition state.====<br />
<br />
Position of the TS of H<sub>2</sub> + F Reaction: r<sub>H-H</sub>=74.5 pm; r<sub>H···F</sub>=181.1 pm; At the TS, potential energy = 433.980 kJ/mol<br />
<br />
[[File:Mp5318 contour TS hhf.png|thumb|left|TS of F + H<sub>2</sub> Reaction]]<br />
<br />
[[File:Mp5318distande hhf.png|thumb|centre|Intermolecular distance vs. Time at the TS of F + H<sub>2</sub> Reaction]]<br />
<br clear=all><br />
<br />
====Report the activation energy for both reactions.====<br />
In the form of HF + H, potential energy =- 429.814 kJ/mol<br />
In the form o H<sub>2</sub> + F, potential energy = -433.990 kJ/mol<br />
<br />
Therefore compared with the TS potential energy (-433.980 kJ/mol): for HF + H to reach the TS, the activation energy is -4.166 kJ/mol; for H<sub>2</sub> + F to reach the TS, the activation energy is -0.1 kJ/mol.</div>Mp5318https://chemwiki.ch.ic.ac.uk/index.php?title=Minqi5318&diff=803214Minqi53182020-05-14T16:01:31Z<p>Mp5318: /* Report the activation energy for both reactions. */</p>
<hr />
<div>== Molecular Reaction Dynamics: Application to Triatomic systems ==<br />
<br />
==H +H<sub>1</sub> System ==<br />
<br />
=== Dynamic from transition state region===<br />
<br />
====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?====<br />
<br />
The transition state is defined mathematically as the saddle point on the potential energy surface, where ∂V('''ri''')/∂'''ri'''=0 (the gradient of the potential is zero). At the transition state, the second derivative of potential with respect to q<sub>1</sub> is positive: ∂V<sup>2</sup>(q<sub>1</sub>)/∂q<sub>1</sub> > 0, indicating a minimum of the curve; the second derivative of potential with respect to q<sub>2</sub> is positive: ∂V<sup>2</sup>(q<sub>2</sub>)/∂q<sub>2</sub> < 0, indicating a maximum of the curve. The coincidence of a maximum and a minimum indicates saddle point on the potential energy surface. It can be identified through finding the maximum on the minimum energy path linking reactants and the products. The Transition State's energy goes down most steeply along the minimum energy path linking reactants and products c.f. local minimum of the potential energy surface. <br />
<br />
====Report your best estimate of the transition state position (r<sub>ts</sub>) and explain your reasoning illustrating it with an “Internuclear Distances vs Time” plot for a relevant trajectory.====<br />
<br />
The best estemate of the transition state position r<sub>ts</sub> = 91 pm<br />
<br />
[[File:mp5318_Animation.png|thumb|centre|Internuclear Distances vs Time Plot when r<sub>ts</sub> = 91 pm.]]<br />
<br />
As shown in the ''Internuclear Distances vs Time Plot when r<sub>ts</sub> = 91 pm'' above, when r<sub>ts</sub> = 91 pm and p<sub>1</sub> p<sub>2</sub> = 0.0 g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>, internuclear distance reamain (almost) constant, which shows that the molecule does not vibrate and stayed stably at the transition state forever.<br />
<br />
====Comment on how the MEP and the trajectory you just calculated differ.====<br />
<br />
[[File:Mp5318 Surface Plot Dynamic.png|thumb|left|Surface Plot using Dynamic Calculation r<sub>1</sub>=92 pm, r<sub>2</sub>=91 pm]]<br />
<br />
[[File:Surface Plot MEP.png|thumb|centre|Surface Plot using MEP Calculation r<sub>1</sub>=92 pm, r<sub>2</sub>=91 pm]]<br />
<br />
<br clear=all><br />
When '''r<sub>1</sub>'''=92 pm, '''r<sub>2</sub>'''=91 pm, atoms A and B dissociates. Using MEP calculation, AB dissociates through the minimum energy pathway and the dissociation ceased at a displacement much smaller than using Dynamic calculation. In Dynamic trajectory, kinetic energy was acquired during the trajectory from potential energy, therefore encourage inertial motion to proceed. In addition, MEP Calculation does not take into account the momentum of the particles, all the momentums are assumed to be zero.<br />
<br />
When reversing '''r<sub>1</sub>''' and '''r<sub>2</sub>''', B and C dissociates while A and B sticks together. The final values of the positions are '''r<sub>1</sub>''' (73.81819562) '''r<sub>2</sub>''' (352.8544826) and '''p<sub>1</sub>''' (3.258858751) '''p<sub>2</sub>''' (5.06251673). <br />
<br />
When setting up a calculation where the initial positions correspond to the final positions of the trajectory above, the same final momenta values but with their signs reversed, the reaction trajectory travels back to the orginal position '''r<sub>1</sub>''' (91) and '''r<sub>2</sub>''' (92) with '''p<sub>1</sub>'''= '''p<sub>2</sub>'''= 0.<br />
<br />
===Reactive and Unreactive trajectories===<br />
<br />
{| class="wikitable" border="1"<br />
|+ initial positions '''r<sub>1</sub>''' (74 pm) '''r<sub>2</sub>''' (200 pm)<br />
! p<sub>1</sub> / g.mol<sup>-1</sup>.pm.fs<sup>-1</sup> !! p<sub>2</sub> / g.mol<sup>-1</sup>.pm.fs<sup>-1</sup> !! E<sub>tot</sub> kJ.mol<sub>-1</sub> !! Reactive? !! Description of the dunamics !! Illustration of the trajectory<br />
|-<br />
| -2.56 || -5.1 || -414.28 || Yes || A-B + C → A +B-C || [[File:Mp5318 t1.png|356px]]<br />
|-<br />
| -3.1 || -4.1 || -420.08 || No || A-B approaches C, but then leave without reaction occur || [[File:Mp5318 t2.png|356px]]<br />
|-<br />
| -3.1 || -5.1 || -413.98 || Yes || A-B + C → A +B-C || [[File:Mp5318 t3.png|356px]]<br />
|-<br />
| -5.1 || -10.1 || -357.28 || No || at TS region, strength of bondings A-B and B-C alternates, but eventually A-B leave intact (Barrier can be crossed, but then the system reverts back to the reactants) || [[File:Mp5318 t4.png|356px]]<br />
|-<br />
| -5.1 || -10.6 || -349.38 || Yes || A-B + C → A +B-C at TS region, strength of bonding A-B and N-C alternates, but new product formed eventually || [[File:Mp5318 t5.png|356px]]<br />
|}<br />
<br />
'''Conclusion: Reactants need to have a large enough ratio in the momentum to be reactive, ideally, p<sub>2</sub> : p<sub>1</sub> should be larger than 2 for the reactants to be reactive.'''<br />
<br />
===Transition State Theory===<br />
<br />
====Given the results you have obtained, how will Transition State Theory predictions for reaction rate values compare with experimental values?====<br />
<br />
Transition State Theory often overestimates the reaction rate, compared to the results we calculated. Transition State Theory assumed that once the reaction has passed the Transition state and reached the product, it would not travel back to cross the Transition State and reverse to the reactant side. However, the calculations above showed that in practice, products can still recross the energy barrier to go back to the reactants. Even though the Transition State Theory ignored the effect of quantum tunneling, it's a relatively small contribution to rate in this case (small MW for H<sub>2</sub>). Therefore Transition State Theory tends to overestimate reaction rate values compare with experimental values.<br />
<br />
==F-H-H System ==<br />
<br />
=== PES inspection===<br />
<br />
====By inspecting the potential energy surfaces, classify the F + H<sub>2</sub> and H + HF reactions according to their energetics (endothermic or exothermic). How does this relate to the bond strength of the chemical species involved?====<br />
<br />
[[File:Mp5318Surface Plot fh2.png|thumb|left|Potential Surface of F + H<sub>2</sub> Reaction]]<br />
<br />
<br clear=all><br />
<br />
F + H<sub>2</sub> Reaction is exothermic. We can see there is a decrease in energy as H-H bond distance increases while H-F bond distance decreases. The clear downhill of reaction path indicated exothermic. Bond strength of H-H is 432 kJ/mol, while H-F bond strength is 565 kJ/mol. Formation of H-F bond is preferred, as it would release more energy than the energy needed to break H-H bond. <br />
<br />
H + HF Reaction is endothermic. H-H bond formed is weaker than the H-F bond, therefore energy needed to cross the activation energy barrier — endothermic.<br />
<br />
====Locate the approximate position of the transition state.====<br />
<br />
Position of the TS of H<sub>2</sub> + F Reaction: r<sub>H-H</sub>=74.5 pm; r<sub>H···F</sub>=181.1 pm; At the TS, potential energy = 433.980 kJ/mol<br />
<br />
[[File:Mp5318 contour TS hhf.png|thumb|left|TS of F + H<sub>2</sub> Reaction]]<br />
<br />
[[File:Mp5318distande hhf.png|thumb|centre|Intermolecular distance vs. Time at the TS of F + H<sub>2</sub> Reaction]]<br />
<br clear=all><br />
<br />
====Report the activation energy for both reactions.====<br />
when HF forms, potential energy =- 429.814 kJ/mol<br />
when H<sub>2</sub> forms, potential energy = -433.990 kJ/mol</div>Mp5318https://chemwiki.ch.ic.ac.uk/index.php?title=Minqi5318&diff=803177Minqi53182020-05-14T15:35:06Z<p>Mp5318: </p>
<hr />
<div>== Molecular Reaction Dynamics: Application to Triatomic systems ==<br />
<br />
==H +H<sub>1</sub> System ==<br />
<br />
=== Dynamic from transition state region===<br />
<br />
====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?====<br />
<br />
The transition state is defined mathematically as the saddle point on the potential energy surface, where ∂V('''ri''')/∂'''ri'''=0 (the gradient of the potential is zero). At the transition state, the second derivative of potential with respect to q<sub>1</sub> is positive: ∂V<sup>2</sup>(q<sub>1</sub>)/∂q<sub>1</sub> > 0, indicating a minimum of the curve; the second derivative of potential with respect to q<sub>2</sub> is positive: ∂V<sup>2</sup>(q<sub>2</sub>)/∂q<sub>2</sub> < 0, indicating a maximum of the curve. The coincidence of a maximum and a minimum indicates saddle point on the potential energy surface. It can be identified through finding the maximum on the minimum energy path linking reactants and the products. The Transition State's energy goes down most steeply along the minimum energy path linking reactants and products c.f. local minimum of the potential energy surface. <br />
<br />
====Report your best estimate of the transition state position (r<sub>ts</sub>) and explain your reasoning illustrating it with an “Internuclear Distances vs Time” plot for a relevant trajectory.====<br />
<br />
The best estemate of the transition state position r<sub>ts</sub> = 91 pm<br />
<br />
[[File:mp5318_Animation.png|thumb|centre|Internuclear Distances vs Time Plot when r<sub>ts</sub> = 91 pm.]]<br />
<br />
As shown in the ''Internuclear Distances vs Time Plot when r<sub>ts</sub> = 91 pm'' above, when r<sub>ts</sub> = 91 pm and p<sub>1</sub> p<sub>2</sub> = 0.0 g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>, internuclear distance reamain (almost) constant, which shows that the molecule does not vibrate and stayed stably at the transition state forever.<br />
<br />
====Comment on how the MEP and the trajectory you just calculated differ.====<br />
<br />
[[File:Mp5318 Surface Plot Dynamic.png|thumb|left|Surface Plot using Dynamic Calculation r<sub>1</sub>=92 pm, r<sub>2</sub>=91 pm]]<br />
<br />
[[File:Surface Plot MEP.png|thumb|centre|Surface Plot using MEP Calculation r<sub>1</sub>=92 pm, r<sub>2</sub>=91 pm]]<br />
<br />
<br clear=all><br />
When '''r<sub>1</sub>'''=92 pm, '''r<sub>2</sub>'''=91 pm, atoms A and B dissociates. Using MEP calculation, AB dissociates through the minimum energy pathway and the dissociation ceased at a displacement much smaller than using Dynamic calculation. In Dynamic trajectory, kinetic energy was acquired during the trajectory from potential energy, therefore encourage inertial motion to proceed. In addition, MEP Calculation does not take into account the momentum of the particles, all the momentums are assumed to be zero.<br />
<br />
When reversing '''r<sub>1</sub>''' and '''r<sub>2</sub>''', B and C dissociates while A and B sticks together. The final values of the positions are '''r<sub>1</sub>''' (73.81819562) '''r<sub>2</sub>''' (352.8544826) and '''p<sub>1</sub>''' (3.258858751) '''p<sub>2</sub>''' (5.06251673). <br />
<br />
When setting up a calculation where the initial positions correspond to the final positions of the trajectory above, the same final momenta values but with their signs reversed, the reaction trajectory travels back to the orginal position '''r<sub>1</sub>''' (91) and '''r<sub>2</sub>''' (92) with '''p<sub>1</sub>'''= '''p<sub>2</sub>'''= 0.<br />
<br />
===Reactive and Unreactive trajectories===<br />
<br />
{| class="wikitable" border="1"<br />
|+ initial positions '''r<sub>1</sub>''' (74 pm) '''r<sub>2</sub>''' (200 pm)<br />
! p<sub>1</sub> / g.mol<sup>-1</sup>.pm.fs<sup>-1</sup> !! p<sub>2</sub> / g.mol<sup>-1</sup>.pm.fs<sup>-1</sup> !! E<sub>tot</sub> kJ.mol<sub>-1</sub> !! Reactive? !! Description of the dunamics !! Illustration of the trajectory<br />
|-<br />
| -2.56 || -5.1 || -414.28 || Yes || A-B + C → A +B-C || [[File:Mp5318 t1.png|356px]]<br />
|-<br />
| -3.1 || -4.1 || -420.08 || No || A-B approaches C, but then leave without reaction occur || [[File:Mp5318 t2.png|356px]]<br />
|-<br />
| -3.1 || -5.1 || -413.98 || Yes || A-B + C → A +B-C || [[File:Mp5318 t3.png|356px]]<br />
|-<br />
| -5.1 || -10.1 || -357.28 || No || at TS region, strength of bondings A-B and B-C alternates, but eventually A-B leave intact (Barrier can be crossed, but then the system reverts back to the reactants) || [[File:Mp5318 t4.png|356px]]<br />
|-<br />
| -5.1 || -10.6 || -349.38 || Yes || A-B + C → A +B-C at TS region, strength of bonding A-B and N-C alternates, but new product formed eventually || [[File:Mp5318 t5.png|356px]]<br />
|}<br />
<br />
'''Conclusion: Reactants need to have a large enough ratio in the momentum to be reactive, ideally, p<sub>2</sub> : p<sub>1</sub> should be larger than 2 for the reactants to be reactive.'''<br />
<br />
===Transition State Theory===<br />
<br />
====Given the results you have obtained, how will Transition State Theory predictions for reaction rate values compare with experimental values?====<br />
<br />
Transition State Theory often overestimates the reaction rate, compared to the results we calculated. Transition State Theory assumed that once the reaction has passed the Transition state and reached the product, it would not travel back to cross the Transition State and reverse to the reactant side. However, the calculations above showed that in practice, products can still recross the energy barrier to go back to the reactants. Even though the Transition State Theory ignored the effect of quantum tunneling, it's a relatively small contribution to rate in this case (small MW for H<sub>2</sub>). Therefore Transition State Theory tends to overestimate reaction rate values compare with experimental values.<br />
<br />
==F-H-H System ==<br />
<br />
=== PES inspection===<br />
<br />
====By inspecting the potential energy surfaces, classify the F + H<sub>2</sub> and H + HF reactions according to their energetics (endothermic or exothermic). How does this relate to the bond strength of the chemical species involved?====<br />
<br />
[[File:Mp5318Surface Plot fh2.png|thumb|left|Potential Surface of F + H<sub>2</sub> Reaction]]<br />
<br />
<br clear=all><br />
<br />
F + H<sub>2</sub> Reaction is exothermic. We can see there is a decrease in energy as H-H bond distance increases while H-F bond distance decreases. The clear downhill of reaction path indicated exothermic. Bond strength of H-H is 432 kJ/mol, while H-F bond strength is 565 kJ/mol. Formation of H-F bond is preferred, as it would release more energy than the energy needed to break H-H bond. <br />
<br />
H + HF Reaction is endothermic. H-H bond formed is weaker than the H-F bond, therefore energy needed to cross the activation energy barrier — endothermic.<br />
<br />
====Locate the approximate position of the transition state.====<br />
<br />
Position of the TS of H<sub>2</sub> + F Reaction: r<sub>H-H</sub>=74.5 pm; r<sub>H···F</sub>=181.1 pm; At the TS, potential energy = 433.980 kJ/mol<br />
<br />
[[File:Mp5318 contour TS hhf.png|thumb|left|TS of F + H<sub>2</sub> Reaction]]<br />
<br />
[[File:Mp5318distande hhf.png|thumb|centre|Intermolecular distance vs. Time at the TS of F + H<sub>2</sub> Reaction]]<br />
<br clear=all><br />
<br />
====Report the activation energy for both reactions.====</div>Mp5318https://chemwiki.ch.ic.ac.uk/index.php?title=Minqi5318&diff=803140Minqi53182020-05-14T15:17:32Z<p>Mp5318: /* Locate the approximate position of the transition state. */</p>
<hr />
<div>== Molecular Reaction Dynamics: Application to Triatomic systems ==<br />
<br />
==H +H<sub>1</sub> System ==<br />
<br />
=== Dynamic from transition state region===<br />
<br />
====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?====<br />
<br />
The transition state is defined mathematically as the saddle point on the potential energy surface, where ∂V('''ri''')/∂'''ri'''=0 (the gradient of the potential is zero). At the transition state, the second derivative of potential with respect to q<sub>1</sub> is positive: ∂V<sup>2</sup>(q<sub>1</sub>)/∂q<sub>1</sub> > 0, indicating a minimum of the curve; the second derivative of potential with respect to q<sub>2</sub> is positive: ∂V<sup>2</sup>(q<sub>2</sub>)/∂q<sub>2</sub> < 0, indicating a maximum of the curve. The coincidence of a maximum and a minimum indicates saddle point on the potential energy surface. It can be identified through finding the maximum on the minimum energy path linking reactants and the products. The Transition State's energy goes down most steeply along the minimum energy path linking reactants and products c.f. local minimum of the potential energy surface. <br />
<br />
====Report your best estimate of the transition state position (r<sub>ts</sub>) and explain your reasoning illustrating it with an “Internuclear Distances vs Time” plot for a relevant trajectory.====<br />
<br />
The best estemate of the transition state position r<sub>ts</sub> = 91 pm<br />
<br />
[[File:mp5318_Animation.png|thumb|centre|Internuclear Distances vs Time Plot when r<sub>ts</sub> = 91 pm.]]<br />
<br />
As shown in the ''Internuclear Distances vs Time Plot when r<sub>ts</sub> = 91 pm'' above, when r<sub>ts</sub> = 91 pm and p<sub>1</sub> p<sub>2</sub> = 0.0 g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>, internuclear distance reamain (almost) constant, which shows that the molecule does not vibrate and stayed stably at the transition state forever.<br />
<br />
====Comment on how the MEP and the trajectory you just calculated differ.====<br />
<br />
[[File:Mp5318 Surface Plot Dynamic.png|thumb|left|Surface Plot using Dynamic Calculation r<sub>1</sub>=92 pm, r<sub>2</sub>=91 pm]]<br />
<br />
[[File:Surface Plot MEP.png|thumb|centre|Surface Plot using MEP Calculation r<sub>1</sub>=92 pm, r<sub>2</sub>=91 pm]]<br />
<br />
<br clear=all><br />
When '''r<sub>1</sub>'''=92 pm, '''r<sub>2</sub>'''=91 pm, atoms A and B dissociates. Using MEP calculation, AB dissociates through the minimum energy pathway and the dissociation ceased at a displacement much smaller than using Dynamic calculation. In Dynamic trajectory, kinetic energy was acquired during the trajectory from potential energy, therefore encourage inertial motion to proceed. In addition, MEP Calculation does not take into account the momentum of the particles, all the momentums are assumed to be zero.<br />
<br />
When reversing '''r<sub>1</sub>''' and '''r<sub>2</sub>''', B and C dissociates while A and B sticks together. The final values of the positions are '''r<sub>1</sub>''' (73.81819562) '''r<sub>2</sub>''' (352.8544826) and '''p<sub>1</sub>''' (3.258858751) '''p<sub>2</sub>''' (5.06251673). <br />
<br />
When setting up a calculation where the initial positions correspond to the final positions of the trajectory above, the same final momenta values but with their signs reversed, the reaction trajectory travels back to the orginal position '''r<sub>1</sub>''' (91) and '''r<sub>2</sub>''' (92) with '''p<sub>1</sub>'''= '''p<sub>2</sub>'''= 0.<br />
<br />
===Reactive and Unreactive trajectories===<br />
<br />
{| class="wikitable" border="1"<br />
|+ initial positions '''r<sub>1</sub>''' (74 pm) '''r<sub>2</sub>''' (200 pm)<br />
! p<sub>1</sub> / g.mol<sup>-1</sup>.pm.fs<sup>-1</sup> !! p<sub>2</sub> / g.mol<sup>-1</sup>.pm.fs<sup>-1</sup> !! E<sub>tot</sub> kJ.mol<sub>-1</sub> !! Reactive? !! Description of the dunamics !! Illustration of the trajectory<br />
|-<br />
| -2.56 || -5.1 || -414.28 || Yes || A-B + C → A +B-C || [[File:Mp5318 t1.png|356px]]<br />
|-<br />
| -3.1 || -4.1 || -420.08 || No || A-B approaches C, but then leave without reaction occur || [[File:Mp5318 t2.png|356px]]<br />
|-<br />
| -3.1 || -5.1 || -413.98 || Yes || A-B + C → A +B-C || [[File:Mp5318 t3.png|356px]]<br />
|-<br />
| -5.1 || -10.1 || -357.28 || No || at TS region, strength of bondings A-B and B-C alternates, but eventually A-B leave intact (Barrier can be crossed, but then the system reverts back to the reactants) || [[File:Mp5318 t4.png|356px]]<br />
|-<br />
| -5.1 || -10.6 || -349.38 || Yes || A-B + C → A +B-C at TS region, strength of bonding A-B and N-C alternates, but new product formed eventually || [[File:Mp5318 t5.png|356px]]<br />
|}<br />
<br />
'''Conclusion: Reactants need to have a large enough ratio in the momentum to be reactive, ideally, p<sub>2</sub> : p<sub>1</sub> should be larger than 2 for the reactants to be reactive.'''<br />
<br />
===Transition State Theory===<br />
<br />
====Given the results you have obtained, how will Transition State Theory predictions for reaction rate values compare with experimental values?====<br />
<br />
Transition State Theory often overestimates the reaction rate, compared to the results we calculated. Transition State Theory assumed that once the reaction has passed the Transition state and reached the product, it would not travel back to cross the Transition State and reverse to the reactant side. However, the calculations above showed that in practice, products can still recross the energy barrier to go back to the reactants. Even though the Transition State Theory ignored the effect of quantum tunneling, it's a relatively small contribution to rate in this case (small MW for H<sub>2</sub>). Therefore Transition State Theory tends to overestimate reaction rate values compare with experimental values.<br />
<br />
==F-H-H System ==<br />
<br />
=== PES inspection===<br />
<br />
====By inspecting the potential energy surfaces, classify the F + H<sub>2</sub> and H + HF reactions according to their energetics (endothermic or exothermic). How does this relate to the bond strength of the chemical species involved?====<br />
<br />
[[File:Mp5318Surface Plot fh2.png|thumb|left|Potential Surface of F + H<sub>2</sub> Reaction]]<br />
<br />
<br clear=all><br />
<br />
F + H<sub>2</sub> Reaction is exothermic. We can see there is a decrease in energy as H-H bond distance increases while H-F bond distance decreases. The clear downhill of reaction path indicated exothermic. Bond strength of H-H is 432 kJ/mol, while H-F bond strength is 565 kJ/mol. Formation of H-F bond is preferred, as it would release more energy than the energy needed to break H-H bond. <br />
<br />
H + HF Reaction is endothermic. H-H bond formed is weaker than the H-F bond, therefore energy needed to cross the activation energy barrier — endothermic.<br />
<br />
====Locate the approximate position of the transition state.====<br />
<br />
Position of the TS of H<sub>2</sub> + F Reaction: r<sub>H-H</sub>=74.5 pm; r<sub>H···F</sub>=181.1 pm; At the TS, potential energy = 433.980 kJ/mol<br />
<br />
[[File:Mp5318 contour TS hhf.png|thumb|left|TS of F + H<sub>2</sub> Reaction]]<br />
<br />
[[File:Mp5318distande hhf.png|thumb|centre|Intermolecular distance vs. Time at the TS of F + H<sub>2</sub> Reaction]]<br />
<br clear=all></div>Mp5318https://chemwiki.ch.ic.ac.uk/index.php?title=Minqi5318&diff=803117Minqi53182020-05-14T15:03:21Z<p>Mp5318: /* 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? */</p>
<hr />
<div>== Molecular Reaction Dynamics: Application to Triatomic systems ==<br />
<br />
==H +H<sub>1</sub> System ==<br />
<br />
=== Dynamic from transition state region===<br />
<br />
====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?====<br />
<br />
The transition state is defined mathematically as the saddle point on the potential energy surface, where ∂V('''ri''')/∂'''ri'''=0 (the gradient of the potential is zero). At the transition state, the second derivative of potential with respect to q<sub>1</sub> is positive: ∂V<sup>2</sup>(q<sub>1</sub>)/∂q<sub>1</sub> > 0, indicating a minimum of the curve; the second derivative of potential with respect to q<sub>2</sub> is positive: ∂V<sup>2</sup>(q<sub>2</sub>)/∂q<sub>2</sub> < 0, indicating a maximum of the curve. The coincidence of a maximum and a minimum indicates saddle point on the potential energy surface. It can be identified through finding the maximum on the minimum energy path linking reactants and the products. The Transition State's energy goes down most steeply along the minimum energy path linking reactants and products c.f. local minimum of the potential energy surface. <br />
<br />
====Report your best estimate of the transition state position (r<sub>ts</sub>) and explain your reasoning illustrating it with an “Internuclear Distances vs Time” plot for a relevant trajectory.====<br />
<br />
The best estemate of the transition state position r<sub>ts</sub> = 91 pm<br />
<br />
[[File:mp5318_Animation.png|thumb|centre|Internuclear Distances vs Time Plot when r<sub>ts</sub> = 91 pm.]]<br />
<br />
As shown in the ''Internuclear Distances vs Time Plot when r<sub>ts</sub> = 91 pm'' above, when r<sub>ts</sub> = 91 pm and p<sub>1</sub> p<sub>2</sub> = 0.0 g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>, internuclear distance reamain (almost) constant, which shows that the molecule does not vibrate and stayed stably at the transition state forever.<br />
<br />
====Comment on how the MEP and the trajectory you just calculated differ.====<br />
<br />
[[File:Mp5318 Surface Plot Dynamic.png|thumb|left|Surface Plot using Dynamic Calculation r<sub>1</sub>=92 pm, r<sub>2</sub>=91 pm]]<br />
<br />
[[File:Surface Plot MEP.png|thumb|centre|Surface Plot using MEP Calculation r<sub>1</sub>=92 pm, r<sub>2</sub>=91 pm]]<br />
<br />
<br clear=all><br />
When '''r<sub>1</sub>'''=92 pm, '''r<sub>2</sub>'''=91 pm, atoms A and B dissociates. Using MEP calculation, AB dissociates through the minimum energy pathway and the dissociation ceased at a displacement much smaller than using Dynamic calculation. In Dynamic trajectory, kinetic energy was acquired during the trajectory from potential energy, therefore encourage inertial motion to proceed. In addition, MEP Calculation does not take into account the momentum of the particles, all the momentums are assumed to be zero.<br />
<br />
When reversing '''r<sub>1</sub>''' and '''r<sub>2</sub>''', B and C dissociates while A and B sticks together. The final values of the positions are '''r<sub>1</sub>''' (73.81819562) '''r<sub>2</sub>''' (352.8544826) and '''p<sub>1</sub>''' (3.258858751) '''p<sub>2</sub>''' (5.06251673). <br />
<br />
When setting up a calculation where the initial positions correspond to the final positions of the trajectory above, the same final momenta values but with their signs reversed, the reaction trajectory travels back to the orginal position '''r<sub>1</sub>''' (91) and '''r<sub>2</sub>''' (92) with '''p<sub>1</sub>'''= '''p<sub>2</sub>'''= 0.<br />
<br />
===Reactive and Unreactive trajectories===<br />
<br />
{| class="wikitable" border="1"<br />
|+ initial positions '''r<sub>1</sub>''' (74 pm) '''r<sub>2</sub>''' (200 pm)<br />
! p<sub>1</sub> / g.mol<sup>-1</sup>.pm.fs<sup>-1</sup> !! p<sub>2</sub> / g.mol<sup>-1</sup>.pm.fs<sup>-1</sup> !! E<sub>tot</sub> kJ.mol<sub>-1</sub> !! Reactive? !! Description of the dunamics !! Illustration of the trajectory<br />
|-<br />
| -2.56 || -5.1 || -414.28 || Yes || A-B + C → A +B-C || [[File:Mp5318 t1.png|356px]]<br />
|-<br />
| -3.1 || -4.1 || -420.08 || No || A-B approaches C, but then leave without reaction occur || [[File:Mp5318 t2.png|356px]]<br />
|-<br />
| -3.1 || -5.1 || -413.98 || Yes || A-B + C → A +B-C || [[File:Mp5318 t3.png|356px]]<br />
|-<br />
| -5.1 || -10.1 || -357.28 || No || at TS region, strength of bondings A-B and B-C alternates, but eventually A-B leave intact (Barrier can be crossed, but then the system reverts back to the reactants) || [[File:Mp5318 t4.png|356px]]<br />
|-<br />
| -5.1 || -10.6 || -349.38 || Yes || A-B + C → A +B-C at TS region, strength of bonding A-B and N-C alternates, but new product formed eventually || [[File:Mp5318 t5.png|356px]]<br />
|}<br />
<br />
'''Conclusion: Reactants need to have a large enough ratio in the momentum to be reactive, ideally, p<sub>2</sub> : p<sub>1</sub> should be larger than 2 for the reactants to be reactive.'''<br />
<br />
===Transition State Theory===<br />
<br />
====Given the results you have obtained, how will Transition State Theory predictions for reaction rate values compare with experimental values?====<br />
<br />
Transition State Theory often overestimates the reaction rate, compared to the results we calculated. Transition State Theory assumed that once the reaction has passed the Transition state and reached the product, it would not travel back to cross the Transition State and reverse to the reactant side. However, the calculations above showed that in practice, products can still recross the energy barrier to go back to the reactants. Even though the Transition State Theory ignored the effect of quantum tunneling, it's a relatively small contribution to rate in this case (small MW for H<sub>2</sub>). Therefore Transition State Theory tends to overestimate reaction rate values compare with experimental values.<br />
<br />
==F-H-H System ==<br />
<br />
=== PES inspection===<br />
<br />
====By inspecting the potential energy surfaces, classify the F + H<sub>2</sub> and H + HF reactions according to their energetics (endothermic or exothermic). How does this relate to the bond strength of the chemical species involved?====<br />
<br />
[[File:Mp5318Surface Plot fh2.png|thumb|left|Potential Surface of F + H<sub>2</sub> Reaction]]<br />
<br />
<br clear=all><br />
<br />
F + H<sub>2</sub> Reaction is exothermic. We can see there is a decrease in energy as H-H bond distance increases while H-F bond distance decreases. The clear downhill of reaction path indicated exothermic. Bond strength of H-H is 432 kJ/mol, while H-F bond strength is 565 kJ/mol. Formation of H-F bond is preferred, as it would release more energy than the energy needed to break H-H bond. <br />
<br />
H + HF Reaction is endothermic. H-H bond formed is weaker than the H-F bond, therefore energy needed to cross the activation energy barrier — endothermic.<br />
<br />
====Locate the approximate position of the transition state.====<br />
<br />
Position of the TS of H<sub>2</sub> + F Reaction: r<sub>H-H</sub>=74.5 pm; r<sub>H···F</sub>=180 pm<br />
<br />
[[File:Mp5318 contour TS hhf.png|thumb|left|TS of F + H<sub>2</sub> Reaction]]<br />
<br />
[[File:Mp5318distande hhf.png|thumb|centre|Intermolecular distance vs. Time at the TS of F + H<sub>2</sub> Reaction]]<br />
<br clear=all></div>Mp5318https://chemwiki.ch.ic.ac.uk/index.php?title=Minqi5318&diff=803114Minqi53182020-05-14T15:00:40Z<p>Mp5318: /* Locate the approximate position of the transition state. */</p>
<hr />
<div>== Molecular Reaction Dynamics: Application to Triatomic systems ==<br />
<br />
==H +H<sub>1</sub> System ==<br />
<br />
=== Dynamic from transition state region===<br />
<br />
====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?====<br />
<br />
The transition state is defined mathematically as the saddle point on the potential energy surface, where ∂V('''ri''')/∂'''ri'''=0 (the gradient of the potential is zero). At the transition state, the second derivative of potential with respect to q<sub>1</sub> is positive: ∂V<sup>2</sup>(q<sub>1</sub>)/∂q<sub>1</sub> > 0, indicating a minimum of the curve; the second derivative of potential with respect to q<sub>2</sub> is positive: ∂V<sup>2</sup>(q<sub>2</sub>)/∂q<sub>2</sub> < 0, indicating a maximum of the curve. The coincidence of a maximum and a minimum indicates saddle point on the potential energy surface. It can be identified through finding the maximum on the minimum energy path linking reactants and the products. The Transition State's energy goes down most steeply along the minimum energy path linking reactants and products c.f. local minimum of the potential energy surface. <br />
<br />
====Report your best estimate of the transition state position (r<sub>ts</sub>) and explain your reasoning illustrating it with an “Internuclear Distances vs Time” plot for a relevant trajectory.====<br />
<br />
The best estemate of the transition state position r<sub>ts</sub> = 91 pm<br />
<br />
[[File:mp5318_Animation.png|thumb|centre|Internuclear Distances vs Time Plot when r<sub>ts</sub> = 91 pm.]]<br />
<br />
As shown in the ''Internuclear Distances vs Time Plot when r<sub>ts</sub> = 91 pm'' above, when r<sub>ts</sub> = 91 pm and p<sub>1</sub> p<sub>2</sub> = 0.0 g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>, internuclear distance reamain (almost) constant, which shows that the molecule does not vibrate and stayed stably at the transition state forever.<br />
<br />
====Comment on how the MEP and the trajectory you just calculated differ.====<br />
<br />
[[File:Mp5318 Surface Plot Dynamic.png|thumb|left|Surface Plot using Dynamic Calculation r<sub>1</sub>=92 pm, r<sub>2</sub>=91 pm]]<br />
<br />
[[File:Surface Plot MEP.png|thumb|centre|Surface Plot using MEP Calculation r<sub>1</sub>=92 pm, r<sub>2</sub>=91 pm]]<br />
<br />
<br clear=all><br />
When '''r<sub>1</sub>'''=92 pm, '''r<sub>2</sub>'''=91 pm, atoms A and B dissociates. Using MEP calculation, AB dissociates through the minimum energy pathway and the dissociation ceased at a displacement much smaller than using Dynamic calculation. In Dynamic trajectory, kinetic energy was acquired during the trajectory from potential energy, therefore encourage inertial motion to proceed. In addition, MEP Calculation does not take into account the momentum of the particles, all the momentums are assumed to be zero.<br />
<br />
When reversing '''r<sub>1</sub>''' and '''r<sub>2</sub>''', B and C dissociates while A and B sticks together. The final values of the positions are '''r<sub>1</sub>''' (73.81819562) '''r<sub>2</sub>''' (352.8544826) and '''p<sub>1</sub>''' (3.258858751) '''p<sub>2</sub>''' (5.06251673). <br />
<br />
When setting up a calculation where the initial positions correspond to the final positions of the trajectory above, the same final momenta values but with their signs reversed, the reaction trajectory travels back to the orginal position '''r<sub>1</sub>''' (91) and '''r<sub>2</sub>''' (92) with '''p<sub>1</sub>'''= '''p<sub>2</sub>'''= 0.<br />
<br />
===Reactive and Unreactive trajectories===<br />
<br />
{| class="wikitable" border="1"<br />
|+ initial positions '''r<sub>1</sub>''' (74 pm) '''r<sub>2</sub>''' (200 pm)<br />
! p<sub>1</sub> / g.mol<sup>-1</sup>.pm.fs<sup>-1</sup> !! p<sub>2</sub> / g.mol<sup>-1</sup>.pm.fs<sup>-1</sup> !! E<sub>tot</sub> kJ.mol<sub>-1</sub> !! Reactive? !! Description of the dunamics !! Illustration of the trajectory<br />
|-<br />
| -2.56 || -5.1 || -414.28 || Yes || A-B + C → A +B-C || [[File:Mp5318 t1.png|356px]]<br />
|-<br />
| -3.1 || -4.1 || -420.08 || No || A-B approaches C, but then leave without reaction occur || [[File:Mp5318 t2.png|356px]]<br />
|-<br />
| -3.1 || -5.1 || -413.98 || Yes || A-B + C → A +B-C || [[File:Mp5318 t3.png|356px]]<br />
|-<br />
| -5.1 || -10.1 || -357.28 || No || at TS region, strength of bondings A-B and B-C alternates, but eventually A-B leave intact (Barrier can be crossed, but then the system reverts back to the reactants) || [[File:Mp5318 t4.png|356px]]<br />
|-<br />
| -5.1 || -10.6 || -349.38 || Yes || A-B + C → A +B-C at TS region, strength of bonding A-B and N-C alternates, but new product formed eventually || [[File:Mp5318 t5.png|356px]]<br />
|}<br />
<br />
'''Conclusion: Reactants need to have a large enough ratio in the momentum to be reactive, ideally, p<sub>2</sub> : p<sub>1</sub> should be larger than 2 for the reactants to be reactive.'''<br />
<br />
===Transition State Theory===<br />
<br />
====Given the results you have obtained, how will Transition State Theory predictions for reaction rate values compare with experimental values?====<br />
<br />
Transition State Theory often overestimates the reaction rate, compared to the results we calculated. Transition State Theory assumed that once the reaction has passed the Transition state and reached the product, it would not travel back to cross the Transition State and reverse to the reactant side. However, the calculations above showed that in practice, products can still recross the energy barrier to go back to the reactants. Even though the Transition State Theory ignored the effect of quantum tunneling, it's a relatively small contribution to rate in this case (small MW for H<sub>2</sub>). Therefore Transition State Theory tends to overestimate reaction rate values compare with experimental values.<br />
<br />
==F-H-H System ==<br />
<br />
=== PES inspection===<br />
<br />
====By inspecting the potential energy surfaces, classify the F + H<sub>2</sub> and H + HF reactions according to their energetics (endothermic or exothermic). How does this relate to the bond strength of the chemical species involved?====<br />
<br />
[[File:Mp5318Surface Plot fh2.png|thumb|left|Potential Surface of F + H<sub>2</sub> Reaction]]<br />
[[File:Mp5318Surface Plot hhf.png|thumb|centre|Potential Surface of H + HF Reaction]]<br />
<br />
<br clear=all><br />
<br />
F + H<sub>2</sub> Reaction is exothermic. We can see there is a decrease in energy as H-H bond distance increases while H-F bond distance decreases. The clear downhill of reaction path indicated exothermic. Bond strength of H-H is 432 kJ/mol, while H-F bond strength is 565 kJ/mol. Formation of H-F bond is preferred, as it would release more energy than the energy needed to break H-H bond. <br />
<br />
H + HF Reaction is endothermic. There is no obvious enery downhill in this reaction. Upon collision, two possible reactions can occur: H + HF → F + H<sub>2</sub> or H + HF → FH + H. In the first case, H-H bond formed is weaker than the H-F bond, therefore energy needed to cross the activation energy barrier — endothermic. In the second case, bonds forming and breaking are of the same kind, hence the same energy. It would also need to take in energy to pass the activation energy barrier — endothermic.<br />
<br />
====Locate the approximate position of the transition state.====<br />
<br />
Position of the TS of H<sub>2</sub> + F Reaction: r<sub>H-H</sub>=74.5 pm; r<sub>H···F</sub>=180 pm<br />
<br />
[[File:Mp5318 contour TS hhf.png|thumb|left|TS of F + H<sub>2</sub> Reaction]]<br />
<br />
[[File:Mp5318distande hhf.png|thumb|centre|Intermolecular distance vs. Time at the TS of F + H<sub>2</sub> Reaction]]<br />
<br clear=all></div>Mp5318https://chemwiki.ch.ic.ac.uk/index.php?title=Minqi5318&diff=802917Minqi53182020-05-14T13:10:58Z<p>Mp5318: /* Locate the approximate position of the transition state. */</p>
<hr />
<div>== Molecular Reaction Dynamics: Application to Triatomic systems ==<br />
<br />
==H +H<sub>1</sub> System ==<br />
<br />
=== Dynamic from transition state region===<br />
<br />
====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?====<br />
<br />
The transition state is defined mathematically as the saddle point on the potential energy surface, where ∂V('''ri''')/∂'''ri'''=0 (the gradient of the potential is zero). At the transition state, the second derivative of potential with respect to q<sub>1</sub> is positive: ∂V<sup>2</sup>(q<sub>1</sub>)/∂q<sub>1</sub> > 0, indicating a minimum of the curve; the second derivative of potential with respect to q<sub>2</sub> is positive: ∂V<sup>2</sup>(q<sub>2</sub>)/∂q<sub>2</sub> < 0, indicating a maximum of the curve. The coincidence of a maximum and a minimum indicates saddle point on the potential energy surface. It can be identified through finding the maximum on the minimum energy path linking reactants and the products. The Transition State's energy goes down most steeply along the minimum energy path linking reactants and products c.f. local minimum of the potential energy surface. <br />
<br />
====Report your best estimate of the transition state position (r<sub>ts</sub>) and explain your reasoning illustrating it with an “Internuclear Distances vs Time” plot for a relevant trajectory.====<br />
<br />
The best estemate of the transition state position r<sub>ts</sub> = 91 pm<br />
<br />
[[File:mp5318_Animation.png|thumb|centre|Internuclear Distances vs Time Plot when r<sub>ts</sub> = 91 pm.]]<br />
<br />
As shown in the ''Internuclear Distances vs Time Plot when r<sub>ts</sub> = 91 pm'' above, when r<sub>ts</sub> = 91 pm and p<sub>1</sub> p<sub>2</sub> = 0.0 g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>, internuclear distance reamain (almost) constant, which shows that the molecule does not vibrate and stayed stably at the transition state forever.<br />
<br />
====Comment on how the MEP and the trajectory you just calculated differ.====<br />
<br />
[[File:Mp5318 Surface Plot Dynamic.png|thumb|left|Surface Plot using Dynamic Calculation r<sub>1</sub>=92 pm, r<sub>2</sub>=91 pm]]<br />
<br />
[[File:Surface Plot MEP.png|thumb|centre|Surface Plot using MEP Calculation r<sub>1</sub>=92 pm, r<sub>2</sub>=91 pm]]<br />
<br />
<br clear=all><br />
When '''r<sub>1</sub>'''=92 pm, '''r<sub>2</sub>'''=91 pm, atoms A and B dissociates. Using MEP calculation, AB dissociates through the minimum energy pathway and the dissociation ceased at a displacement much smaller than using Dynamic calculation. In Dynamic trajectory, kinetic energy was acquired during the trajectory from potential energy, therefore encourage inertial motion to proceed. In addition, MEP Calculation does not take into account the momentum of the particles, all the momentums are assumed to be zero.<br />
<br />
When reversing '''r<sub>1</sub>''' and '''r<sub>2</sub>''', B and C dissociates while A and B sticks together. The final values of the positions are '''r<sub>1</sub>''' (73.81819562) '''r<sub>2</sub>''' (352.8544826) and '''p<sub>1</sub>''' (3.258858751) '''p<sub>2</sub>''' (5.06251673). <br />
<br />
When setting up a calculation where the initial positions correspond to the final positions of the trajectory above, the same final momenta values but with their signs reversed, the reaction trajectory travels back to the orginal position '''r<sub>1</sub>''' (91) and '''r<sub>2</sub>''' (92) with '''p<sub>1</sub>'''= '''p<sub>2</sub>'''= 0.<br />
<br />
===Reactive and Unreactive trajectories===<br />
<br />
{| class="wikitable" border="1"<br />
|+ initial positions '''r<sub>1</sub>''' (74 pm) '''r<sub>2</sub>''' (200 pm)<br />
! p<sub>1</sub> / g.mol<sup>-1</sup>.pm.fs<sup>-1</sup> !! p<sub>2</sub> / g.mol<sup>-1</sup>.pm.fs<sup>-1</sup> !! E<sub>tot</sub> kJ.mol<sub>-1</sub> !! Reactive? !! Description of the dunamics !! Illustration of the trajectory<br />
|-<br />
| -2.56 || -5.1 || -414.28 || Yes || A-B + C → A +B-C || [[File:Mp5318 t1.png|356px]]<br />
|-<br />
| -3.1 || -4.1 || -420.08 || No || A-B approaches C, but then leave without reaction occur || [[File:Mp5318 t2.png|356px]]<br />
|-<br />
| -3.1 || -5.1 || -413.98 || Yes || A-B + C → A +B-C || [[File:Mp5318 t3.png|356px]]<br />
|-<br />
| -5.1 || -10.1 || -357.28 || No || at TS region, strength of bondings A-B and B-C alternates, but eventually A-B leave intact (Barrier can be crossed, but then the system reverts back to the reactants) || [[File:Mp5318 t4.png|356px]]<br />
|-<br />
| -5.1 || -10.6 || -349.38 || Yes || A-B + C → A +B-C at TS region, strength of bonding A-B and N-C alternates, but new product formed eventually || [[File:Mp5318 t5.png|356px]]<br />
|}<br />
<br />
'''Conclusion: Reactants need to have a large enough ratio in the momentum to be reactive, ideally, p<sub>2</sub> : p<sub>1</sub> should be larger than 2 for the reactants to be reactive.'''<br />
<br />
===Transition State Theory===<br />
<br />
====Given the results you have obtained, how will Transition State Theory predictions for reaction rate values compare with experimental values?====<br />
<br />
Transition State Theory often overestimates the reaction rate, compared to the results we calculated. Transition State Theory assumed that once the reaction has passed the Transition state and reached the product, it would not travel back to cross the Transition State and reverse to the reactant side. However, the calculations above showed that in practice, products can still recross the energy barrier to go back to the reactants. Even though the Transition State Theory ignored the effect of quantum tunneling, it's a relatively small contribution to rate in this case (small MW for H<sub>2</sub>). Therefore Transition State Theory tends to overestimate reaction rate values compare with experimental values.<br />
<br />
==F-H-H System ==<br />
<br />
=== PES inspection===<br />
<br />
====By inspecting the potential energy surfaces, classify the F + H<sub>2</sub> and H + HF reactions according to their energetics (endothermic or exothermic). How does this relate to the bond strength of the chemical species involved?====<br />
<br />
[[File:Mp5318Surface Plot fh2.png|thumb|left|Potential Surface of F + H<sub>2</sub> Reaction]]<br />
[[File:Mp5318Surface Plot hhf.png|thumb|centre|Potential Surface of H + HF Reaction]]<br />
<br />
<br clear=all><br />
<br />
F + H<sub>2</sub> Reaction is exothermic. We can see there is a decrease in energy as H-H bond distance increases while H-F bond distance decreases. The clear downhill of reaction path indicated exothermic. Bond strength of H-H is 432 kJ/mol, while H-F bond strength is 565 kJ/mol. Formation of H-F bond is preferred, as it would release more energy than the energy needed to break H-H bond. <br />
<br />
H + HF Reaction is endothermic. There is no obvious enery downhill in this reaction. Upon collision, two possible reactions can occur: H + HF → F + H<sub>2</sub> or H + HF → FH + H. In the first case, H-H bond formed is weaker than the H-F bond, therefore energy needed to cross the activation energy barrier — endothermic. In the second case, bonds forming and breaking are of the same kind, hence the same energy. It would also need to take in energy to pass the activation energy barrier — endothermic.<br />
<br />
====Locate the approximate position of the transition state.====<br />
<br />
Position of the TS of H + HF Reaction: r<sub>H-F</sub>=r<sub>H···F</sub>=104 pm<br />
<br />
Position of the TS of H<sub>2</sub> + F Reaction: r<sub>H-H</sub>=74.5 pm; r<sub>H···F</sub>=180 pm<br />
<br />
[[File:Mp5318 contour TS hfh.png|thumb|left|TS of H + HF Reaction]]<br />
[[File:Mp5318 contour TS hhf.png|thumb|centre|TS of F + H<sub>2</sub> Reaction]]<br />
<br clear=all><br />
<br />
[[File:Mp5318 distance hfh TS.png|thumb|left|Intermolecular distance vs. Time at the TS of F + H + HF Reaction]]<br />
[[File:Mp5318distande hhf.png|thumb|centre|Intermolecular distance vs. Time at the TS of F + H<sub>2</sub> Reaction]]<br />
<br clear=all></div>Mp5318https://chemwiki.ch.ic.ac.uk/index.php?title=File:Mp5318distande_hhf.png&diff=802916File:Mp5318distande hhf.png2020-05-14T13:09:43Z<p>Mp5318: Mp5318 uploaded a new version of File:Mp5318distande hhf.png</p>
<hr />
<div></div>Mp5318https://chemwiki.ch.ic.ac.uk/index.php?title=Minqi5318&diff=802891Minqi53182020-05-14T12:58:58Z<p>Mp5318: /* Locate the approximate position of the transition state. */</p>
<hr />
<div>== Molecular Reaction Dynamics: Application to Triatomic systems ==<br />
<br />
==H +H<sub>1</sub> System ==<br />
<br />
=== Dynamic from transition state region===<br />
<br />
====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?====<br />
<br />
The transition state is defined mathematically as the saddle point on the potential energy surface, where ∂V('''ri''')/∂'''ri'''=0 (the gradient of the potential is zero). At the transition state, the second derivative of potential with respect to q<sub>1</sub> is positive: ∂V<sup>2</sup>(q<sub>1</sub>)/∂q<sub>1</sub> > 0, indicating a minimum of the curve; the second derivative of potential with respect to q<sub>2</sub> is positive: ∂V<sup>2</sup>(q<sub>2</sub>)/∂q<sub>2</sub> < 0, indicating a maximum of the curve. The coincidence of a maximum and a minimum indicates saddle point on the potential energy surface. It can be identified through finding the maximum on the minimum energy path linking reactants and the products. The Transition State's energy goes down most steeply along the minimum energy path linking reactants and products c.f. local minimum of the potential energy surface. <br />
<br />
====Report your best estimate of the transition state position (r<sub>ts</sub>) and explain your reasoning illustrating it with an “Internuclear Distances vs Time” plot for a relevant trajectory.====<br />
<br />
The best estemate of the transition state position r<sub>ts</sub> = 91 pm<br />
<br />
[[File:mp5318_Animation.png|thumb|centre|Internuclear Distances vs Time Plot when r<sub>ts</sub> = 91 pm.]]<br />
<br />
As shown in the ''Internuclear Distances vs Time Plot when r<sub>ts</sub> = 91 pm'' above, when r<sub>ts</sub> = 91 pm and p<sub>1</sub> p<sub>2</sub> = 0.0 g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>, internuclear distance reamain (almost) constant, which shows that the molecule does not vibrate and stayed stably at the transition state forever.<br />
<br />
====Comment on how the MEP and the trajectory you just calculated differ.====<br />
<br />
[[File:Mp5318 Surface Plot Dynamic.png|thumb|left|Surface Plot using Dynamic Calculation r<sub>1</sub>=92 pm, r<sub>2</sub>=91 pm]]<br />
<br />
[[File:Surface Plot MEP.png|thumb|centre|Surface Plot using MEP Calculation r<sub>1</sub>=92 pm, r<sub>2</sub>=91 pm]]<br />
<br />
<br clear=all><br />
When '''r<sub>1</sub>'''=92 pm, '''r<sub>2</sub>'''=91 pm, atoms A and B dissociates. Using MEP calculation, AB dissociates through the minimum energy pathway and the dissociation ceased at a displacement much smaller than using Dynamic calculation. In Dynamic trajectory, kinetic energy was acquired during the trajectory from potential energy, therefore encourage inertial motion to proceed. In addition, MEP Calculation does not take into account the momentum of the particles, all the momentums are assumed to be zero.<br />
<br />
When reversing '''r<sub>1</sub>''' and '''r<sub>2</sub>''', B and C dissociates while A and B sticks together. The final values of the positions are '''r<sub>1</sub>''' (73.81819562) '''r<sub>2</sub>''' (352.8544826) and '''p<sub>1</sub>''' (3.258858751) '''p<sub>2</sub>''' (5.06251673). <br />
<br />
When setting up a calculation where the initial positions correspond to the final positions of the trajectory above, the same final momenta values but with their signs reversed, the reaction trajectory travels back to the orginal position '''r<sub>1</sub>''' (91) and '''r<sub>2</sub>''' (92) with '''p<sub>1</sub>'''= '''p<sub>2</sub>'''= 0.<br />
<br />
===Reactive and Unreactive trajectories===<br />
<br />
{| class="wikitable" border="1"<br />
|+ initial positions '''r<sub>1</sub>''' (74 pm) '''r<sub>2</sub>''' (200 pm)<br />
! p<sub>1</sub> / g.mol<sup>-1</sup>.pm.fs<sup>-1</sup> !! p<sub>2</sub> / g.mol<sup>-1</sup>.pm.fs<sup>-1</sup> !! E<sub>tot</sub> kJ.mol<sub>-1</sub> !! Reactive? !! Description of the dunamics !! Illustration of the trajectory<br />
|-<br />
| -2.56 || -5.1 || -414.28 || Yes || A-B + C → A +B-C || [[File:Mp5318 t1.png|356px]]<br />
|-<br />
| -3.1 || -4.1 || -420.08 || No || A-B approaches C, but then leave without reaction occur || [[File:Mp5318 t2.png|356px]]<br />
|-<br />
| -3.1 || -5.1 || -413.98 || Yes || A-B + C → A +B-C || [[File:Mp5318 t3.png|356px]]<br />
|-<br />
| -5.1 || -10.1 || -357.28 || No || at TS region, strength of bondings A-B and B-C alternates, but eventually A-B leave intact (Barrier can be crossed, but then the system reverts back to the reactants) || [[File:Mp5318 t4.png|356px]]<br />
|-<br />
| -5.1 || -10.6 || -349.38 || Yes || A-B + C → A +B-C at TS region, strength of bonding A-B and N-C alternates, but new product formed eventually || [[File:Mp5318 t5.png|356px]]<br />
|}<br />
<br />
'''Conclusion: Reactants need to have a large enough ratio in the momentum to be reactive, ideally, p<sub>2</sub> : p<sub>1</sub> should be larger than 2 for the reactants to be reactive.'''<br />
<br />
===Transition State Theory===<br />
<br />
====Given the results you have obtained, how will Transition State Theory predictions for reaction rate values compare with experimental values?====<br />
<br />
Transition State Theory often overestimates the reaction rate, compared to the results we calculated. Transition State Theory assumed that once the reaction has passed the Transition state and reached the product, it would not travel back to cross the Transition State and reverse to the reactant side. However, the calculations above showed that in practice, products can still recross the energy barrier to go back to the reactants. Even though the Transition State Theory ignored the effect of quantum tunneling, it's a relatively small contribution to rate in this case (small MW for H<sub>2</sub>). Therefore Transition State Theory tends to overestimate reaction rate values compare with experimental values.<br />
<br />
==F-H-H System ==<br />
<br />
=== PES inspection===<br />
<br />
====By inspecting the potential energy surfaces, classify the F + H<sub>2</sub> and H + HF reactions according to their energetics (endothermic or exothermic). How does this relate to the bond strength of the chemical species involved?====<br />
<br />
[[File:Mp5318Surface Plot fh2.png|thumb|left|Potential Surface of F + H<sub>2</sub> Reaction]]<br />
[[File:Mp5318Surface Plot hhf.png|thumb|centre|Potential Surface of H + HF Reaction]]<br />
<br />
<br clear=all><br />
<br />
F + H<sub>2</sub> Reaction is exothermic. We can see there is a decrease in energy as H-H bond distance increases while H-F bond distance decreases. The clear downhill of reaction path indicated exothermic. Bond strength of H-H is 432 kJ/mol, while H-F bond strength is 565 kJ/mol. Formation of H-F bond is preferred, as it would release more energy than the energy needed to break H-H bond. <br />
<br />
H + HF Reaction is endothermic. There is no obvious enery downhill in this reaction. Upon collision, two possible reactions can occur: H + HF → F + H<sub>2</sub> or H + HF → FH + H. In the first case, H-H bond formed is weaker than the H-F bond, therefore energy needed to cross the activation energy barrier — endothermic. In the second case, bonds forming and breaking are of the same kind, hence the same energy. It would also need to take in energy to pass the activation energy barrier — endothermic.<br />
<br />
====Locate the approximate position of the transition state.====<br />
<br />
[[File:Mp5318 contour TS hfh.png|thumb|left|TS of H + HF Reaction]]<br />
[[File:Mp5318 contour TS hhf.png|thumb|centre|TS of F + H<sub>2</sub> Reaction]]<br />
<br clear=all><br />
<br />
[[File:Mp5318 distance hfh TS.png|thumb|left|Intermolecular distance vs. Time at the TS of F + H + HF Reaction]]<br />
[[File:Mp5318distande hhf.png|thumb|centre|Intermolecular distance vs. Time at the TS of F + H<sub>2</sub> Reaction]]<br />
<br clear=all></div>Mp5318https://chemwiki.ch.ic.ac.uk/index.php?title=Minqi5318&diff=802881Minqi53182020-05-14T12:56:21Z<p>Mp5318: /* 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? */</p>
<hr />
<div>== Molecular Reaction Dynamics: Application to Triatomic systems ==<br />
<br />
==H +H<sub>1</sub> System ==<br />
<br />
=== Dynamic from transition state region===<br />
<br />
====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?====<br />
<br />
The transition state is defined mathematically as the saddle point on the potential energy surface, where ∂V('''ri''')/∂'''ri'''=0 (the gradient of the potential is zero). At the transition state, the second derivative of potential with respect to q<sub>1</sub> is positive: ∂V<sup>2</sup>(q<sub>1</sub>)/∂q<sub>1</sub> > 0, indicating a minimum of the curve; the second derivative of potential with respect to q<sub>2</sub> is positive: ∂V<sup>2</sup>(q<sub>2</sub>)/∂q<sub>2</sub> < 0, indicating a maximum of the curve. The coincidence of a maximum and a minimum indicates saddle point on the potential energy surface. It can be identified through finding the maximum on the minimum energy path linking reactants and the products. The Transition State's energy goes down most steeply along the minimum energy path linking reactants and products c.f. local minimum of the potential energy surface. <br />
<br />
====Report your best estimate of the transition state position (r<sub>ts</sub>) and explain your reasoning illustrating it with an “Internuclear Distances vs Time” plot for a relevant trajectory.====<br />
<br />
The best estemate of the transition state position r<sub>ts</sub> = 91 pm<br />
<br />
[[File:mp5318_Animation.png|thumb|centre|Internuclear Distances vs Time Plot when r<sub>ts</sub> = 91 pm.]]<br />
<br />
As shown in the ''Internuclear Distances vs Time Plot when r<sub>ts</sub> = 91 pm'' above, when r<sub>ts</sub> = 91 pm and p<sub>1</sub> p<sub>2</sub> = 0.0 g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>, internuclear distance reamain (almost) constant, which shows that the molecule does not vibrate and stayed stably at the transition state forever.<br />
<br />
====Comment on how the MEP and the trajectory you just calculated differ.====<br />
<br />
[[File:Mp5318 Surface Plot Dynamic.png|thumb|left|Surface Plot using Dynamic Calculation r<sub>1</sub>=92 pm, r<sub>2</sub>=91 pm]]<br />
<br />
[[File:Surface Plot MEP.png|thumb|centre|Surface Plot using MEP Calculation r<sub>1</sub>=92 pm, r<sub>2</sub>=91 pm]]<br />
<br />
<br clear=all><br />
When '''r<sub>1</sub>'''=92 pm, '''r<sub>2</sub>'''=91 pm, atoms A and B dissociates. Using MEP calculation, AB dissociates through the minimum energy pathway and the dissociation ceased at a displacement much smaller than using Dynamic calculation. In Dynamic trajectory, kinetic energy was acquired during the trajectory from potential energy, therefore encourage inertial motion to proceed. In addition, MEP Calculation does not take into account the momentum of the particles, all the momentums are assumed to be zero.<br />
<br />
When reversing '''r<sub>1</sub>''' and '''r<sub>2</sub>''', B and C dissociates while A and B sticks together. The final values of the positions are '''r<sub>1</sub>''' (73.81819562) '''r<sub>2</sub>''' (352.8544826) and '''p<sub>1</sub>''' (3.258858751) '''p<sub>2</sub>''' (5.06251673). <br />
<br />
When setting up a calculation where the initial positions correspond to the final positions of the trajectory above, the same final momenta values but with their signs reversed, the reaction trajectory travels back to the orginal position '''r<sub>1</sub>''' (91) and '''r<sub>2</sub>''' (92) with '''p<sub>1</sub>'''= '''p<sub>2</sub>'''= 0.<br />
<br />
===Reactive and Unreactive trajectories===<br />
<br />
{| class="wikitable" border="1"<br />
|+ initial positions '''r<sub>1</sub>''' (74 pm) '''r<sub>2</sub>''' (200 pm)<br />
! p<sub>1</sub> / g.mol<sup>-1</sup>.pm.fs<sup>-1</sup> !! p<sub>2</sub> / g.mol<sup>-1</sup>.pm.fs<sup>-1</sup> !! E<sub>tot</sub> kJ.mol<sub>-1</sub> !! Reactive? !! Description of the dunamics !! Illustration of the trajectory<br />
|-<br />
| -2.56 || -5.1 || -414.28 || Yes || A-B + C → A +B-C || [[File:Mp5318 t1.png|356px]]<br />
|-<br />
| -3.1 || -4.1 || -420.08 || No || A-B approaches C, but then leave without reaction occur || [[File:Mp5318 t2.png|356px]]<br />
|-<br />
| -3.1 || -5.1 || -413.98 || Yes || A-B + C → A +B-C || [[File:Mp5318 t3.png|356px]]<br />
|-<br />
| -5.1 || -10.1 || -357.28 || No || at TS region, strength of bondings A-B and B-C alternates, but eventually A-B leave intact (Barrier can be crossed, but then the system reverts back to the reactants) || [[File:Mp5318 t4.png|356px]]<br />
|-<br />
| -5.1 || -10.6 || -349.38 || Yes || A-B + C → A +B-C at TS region, strength of bonding A-B and N-C alternates, but new product formed eventually || [[File:Mp5318 t5.png|356px]]<br />
|}<br />
<br />
'''Conclusion: Reactants need to have a large enough ratio in the momentum to be reactive, ideally, p<sub>2</sub> : p<sub>1</sub> should be larger than 2 for the reactants to be reactive.'''<br />
<br />
===Transition State Theory===<br />
<br />
====Given the results you have obtained, how will Transition State Theory predictions for reaction rate values compare with experimental values?====<br />
<br />
Transition State Theory often overestimates the reaction rate, compared to the results we calculated. Transition State Theory assumed that once the reaction has passed the Transition state and reached the product, it would not travel back to cross the Transition State and reverse to the reactant side. However, the calculations above showed that in practice, products can still recross the energy barrier to go back to the reactants. Even though the Transition State Theory ignored the effect of quantum tunneling, it's a relatively small contribution to rate in this case (small MW for H<sub>2</sub>). Therefore Transition State Theory tends to overestimate reaction rate values compare with experimental values.<br />
<br />
==F-H-H System ==<br />
<br />
=== PES inspection===<br />
<br />
====By inspecting the potential energy surfaces, classify the F + H<sub>2</sub> and H + HF reactions according to their energetics (endothermic or exothermic). How does this relate to the bond strength of the chemical species involved?====<br />
<br />
[[File:Mp5318Surface Plot fh2.png|thumb|left|Potential Surface of F + H<sub>2</sub> Reaction]]<br />
[[File:Mp5318Surface Plot hhf.png|thumb|centre|Potential Surface of H + HF Reaction]]<br />
<br />
<br clear=all><br />
<br />
F + H<sub>2</sub> Reaction is exothermic. We can see there is a decrease in energy as H-H bond distance increases while H-F bond distance decreases. The clear downhill of reaction path indicated exothermic. Bond strength of H-H is 432 kJ/mol, while H-F bond strength is 565 kJ/mol. Formation of H-F bond is preferred, as it would release more energy than the energy needed to break H-H bond. <br />
<br />
H + HF Reaction is endothermic. There is no obvious enery downhill in this reaction. Upon collision, two possible reactions can occur: H + HF → F + H<sub>2</sub> or H + HF → FH + H. In the first case, H-H bond formed is weaker than the H-F bond, therefore energy needed to cross the activation energy barrier — endothermic. In the second case, bonds forming and breaking are of the same kind, hence the same energy. It would also need to take in energy to pass the activation energy barrier — endothermic.<br />
<br />
====Locate the approximate position of the transition state.====<br />
<br />
[[File:Mp5318 contour TS hfh.png|thumb|left|Potential Surface of F + H<sub>2</sub> Reaction]]<br />
[[File:Mp5318 contour TS hhf.png|thumb|centre|Potential Surface of H + HF Reaction]]<br />
<br clear=all><br />
<br />
[[File:Mp5318 distance hfh TS.png|thumb|left|Potential Surface of F + H<sub>2</sub> Reaction]]<br />
[[File:Mp5318distande hhf.png|thumb|centre|Potential Surface of H + HF Reaction]]<br />
<br clear=all></div>Mp5318https://chemwiki.ch.ic.ac.uk/index.php?title=File:Mp5318_distance_hfh_TS.png&diff=802879File:Mp5318 distance hfh TS.png2020-05-14T12:56:05Z<p>Mp5318: </p>
<hr />
<div></div>Mp5318https://chemwiki.ch.ic.ac.uk/index.php?title=File:Mp5318distande_hhf.png&diff=802876File:Mp5318distande hhf.png2020-05-14T12:54:10Z<p>Mp5318: </p>
<hr />
<div></div>Mp5318https://chemwiki.ch.ic.ac.uk/index.php?title=File:Mp5318_contour_TS_hhf.png&diff=802868File:Mp5318 contour TS hhf.png2020-05-14T12:50:41Z<p>Mp5318: </p>
<hr />
<div></div>Mp5318https://chemwiki.ch.ic.ac.uk/index.php?title=File:Mp5318_contour_TS_hfh.png&diff=802859File:Mp5318 contour TS hfh.png2020-05-14T12:47:09Z<p>Mp5318: </p>
<hr />
<div></div>Mp5318https://chemwiki.ch.ic.ac.uk/index.php?title=Minqi5318&diff=802821Minqi53182020-05-14T12:27:08Z<p>Mp5318: /* 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? */</p>
<hr />
<div>== Molecular Reaction Dynamics: Application to Triatomic systems ==<br />
<br />
==H +H<sub>1</sub> System ==<br />
<br />
=== Dynamic from transition state region===<br />
<br />
====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?====<br />
<br />
The transition state is defined mathematically as the saddle point on the potential energy surface, where ∂V('''ri''')/∂'''ri'''=0 (the gradient of the potential is zero). At the transition state, the second derivative of potential with respect to q<sub>1</sub> is positive: ∂V<sup>2</sup>(q<sub>1</sub>)/∂q<sub>1</sub> > 0, indicating a minimum of the curve; the second derivative of potential with respect to q<sub>2</sub> is positive: ∂V<sup>2</sup>(q<sub>2</sub>)/∂q<sub>2</sub> < 0, indicating a maximum of the curve. The coincidence of a maximum and a minimum indicates saddle point on the potential energy surface. It can be identified through finding the maximum on the minimum energy path linking reactants and the products. The Transition State's energy goes down most steeply along the minimum energy path linking reactants and products c.f. local minimum of the potential energy surface. <br />
<br />
====Report your best estimate of the transition state position (r<sub>ts</sub>) and explain your reasoning illustrating it with an “Internuclear Distances vs Time” plot for a relevant trajectory.====<br />
<br />
The best estemate of the transition state position r<sub>ts</sub> = 91 pm<br />
<br />
[[File:mp5318_Animation.png|thumb|centre|Internuclear Distances vs Time Plot when r<sub>ts</sub> = 91 pm.]]<br />
<br />
As shown in the ''Internuclear Distances vs Time Plot when r<sub>ts</sub> = 91 pm'' above, when r<sub>ts</sub> = 91 pm and p<sub>1</sub> p<sub>2</sub> = 0.0 g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>, internuclear distance reamain (almost) constant, which shows that the molecule does not vibrate and stayed stably at the transition state forever.<br />
<br />
====Comment on how the MEP and the trajectory you just calculated differ.====<br />
<br />
[[File:Mp5318 Surface Plot Dynamic.png|thumb|left|Surface Plot using Dynamic Calculation r<sub>1</sub>=92 pm, r<sub>2</sub>=91 pm]]<br />
<br />
[[File:Surface Plot MEP.png|thumb|centre|Surface Plot using MEP Calculation r<sub>1</sub>=92 pm, r<sub>2</sub>=91 pm]]<br />
<br />
<br clear=all><br />
When '''r<sub>1</sub>'''=92 pm, '''r<sub>2</sub>'''=91 pm, atoms A and B dissociates. Using MEP calculation, AB dissociates through the minimum energy pathway and the dissociation ceased at a displacement much smaller than using Dynamic calculation. In Dynamic trajectory, kinetic energy was acquired during the trajectory from potential energy, therefore encourage inertial motion to proceed. In addition, MEP Calculation does not take into account the momentum of the particles, all the momentums are assumed to be zero.<br />
<br />
When reversing '''r<sub>1</sub>''' and '''r<sub>2</sub>''', B and C dissociates while A and B sticks together. The final values of the positions are '''r<sub>1</sub>''' (73.81819562) '''r<sub>2</sub>''' (352.8544826) and '''p<sub>1</sub>''' (3.258858751) '''p<sub>2</sub>''' (5.06251673). <br />
<br />
When setting up a calculation where the initial positions correspond to the final positions of the trajectory above, the same final momenta values but with their signs reversed, the reaction trajectory travels back to the orginal position '''r<sub>1</sub>''' (91) and '''r<sub>2</sub>''' (92) with '''p<sub>1</sub>'''= '''p<sub>2</sub>'''= 0.<br />
<br />
===Reactive and Unreactive trajectories===<br />
<br />
{| class="wikitable" border="1"<br />
|+ initial positions '''r<sub>1</sub>''' (74 pm) '''r<sub>2</sub>''' (200 pm)<br />
! p<sub>1</sub> / g.mol<sup>-1</sup>.pm.fs<sup>-1</sup> !! p<sub>2</sub> / g.mol<sup>-1</sup>.pm.fs<sup>-1</sup> !! E<sub>tot</sub> kJ.mol<sub>-1</sub> !! Reactive? !! Description of the dunamics !! Illustration of the trajectory<br />
|-<br />
| -2.56 || -5.1 || -414.28 || Yes || A-B + C → A +B-C || [[File:Mp5318 t1.png|356px]]<br />
|-<br />
| -3.1 || -4.1 || -420.08 || No || A-B approaches C, but then leave without reaction occur || [[File:Mp5318 t2.png|356px]]<br />
|-<br />
| -3.1 || -5.1 || -413.98 || Yes || A-B + C → A +B-C || [[File:Mp5318 t3.png|356px]]<br />
|-<br />
| -5.1 || -10.1 || -357.28 || No || at TS region, strength of bondings A-B and B-C alternates, but eventually A-B leave intact (Barrier can be crossed, but then the system reverts back to the reactants) || [[File:Mp5318 t4.png|356px]]<br />
|-<br />
| -5.1 || -10.6 || -349.38 || Yes || A-B + C → A +B-C at TS region, strength of bonding A-B and N-C alternates, but new product formed eventually || [[File:Mp5318 t5.png|356px]]<br />
|}<br />
<br />
'''Conclusion: Reactants need to have a large enough ratio in the momentum to be reactive, ideally, p<sub>2</sub> : p<sub>1</sub> should be larger than 2 for the reactants to be reactive.'''<br />
<br />
===Transition State Theory===<br />
<br />
====Given the results you have obtained, how will Transition State Theory predictions for reaction rate values compare with experimental values?====<br />
<br />
Transition State Theory often overestimates the reaction rate, compared to the results we calculated. Transition State Theory assumed that once the reaction has passed the Transition state and reached the product, it would not travel back to cross the Transition State and reverse to the reactant side. However, the calculations above showed that in practice, products can still recross the energy barrier to go back to the reactants. Even though the Transition State Theory ignored the effect of quantum tunneling, it's a relatively small contribution to rate in this case (small MW for H<sub>2</sub>). Therefore Transition State Theory tends to overestimate reaction rate values compare with experimental values.<br />
<br />
==F-H-H System ==<br />
<br />
=== PES inspection===<br />
<br />
====By inspecting the potential energy surfaces, classify the F + H<sub>2</sub> and H + HF reactions according to their energetics (endothermic or exothermic). How does this relate to the bond strength of the chemical species involved?====<br />
<br />
[[File:Mp5318Surface Plot fh2.png|thumb|left|Potential Surface of F + H<sub>2</sub> Reaction]]<br />
[[File:Mp5318Surface Plot hhf.png|thumb|centre|Potential Surface of H + HF Reaction]]<br />
<br clear=all><br />
<br />
F + H<sub>2</sub> Reaction is exothermic. We can see there is a decrease in energy as H-H bond distance increases while H-F bond distance decreases. The clear downhill of reaction path indicated exothermic. Bond strength of H-H is 432 kJ/mol, while H-F bond strength is 565 kJ/mol. Formation of H-F bond is preferred, as it would release more energy than the energy needed to break H-H bond. <br />
<br />
H + HF Reaction is endothermic. There is no obvious enery downhill in this reaction. Upon collision, two possible reactions can occur: H + HF → F + H<sub>2</sub> or H + HF → FH + H. In the first case, H-H bond formed is weaker than the H-F bond, therefore energy needed to cross the activation energy barrier — endothermic. In the second case, bonds forming and breaking are of the same kind, hence the same energy. It would also need to take in energy to pass the activation energy barrier — endothermic.</div>Mp5318https://chemwiki.ch.ic.ac.uk/index.php?title=Minqi5318&diff=802783Minqi53182020-05-14T12:08:59Z<p>Mp5318: </p>
<hr />
<div>== Molecular Reaction Dynamics: Application to Triatomic systems ==<br />
<br />
==H +H<sub>1</sub> System ==<br />
<br />
=== Dynamic from transition state region===<br />
<br />
====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?====<br />
<br />
The transition state is defined mathematically as the saddle point on the potential energy surface, where ∂V('''ri''')/∂'''ri'''=0 (the gradient of the potential is zero). At the transition state, the second derivative of potential with respect to q<sub>1</sub> is positive: ∂V<sup>2</sup>(q<sub>1</sub>)/∂q<sub>1</sub> > 0, indicating a minimum of the curve; the second derivative of potential with respect to q<sub>2</sub> is positive: ∂V<sup>2</sup>(q<sub>2</sub>)/∂q<sub>2</sub> < 0, indicating a maximum of the curve. The coincidence of a maximum and a minimum indicates saddle point on the potential energy surface. It can be identified through finding the maximum on the minimum energy path linking reactants and the products. The Transition State's energy goes down most steeply along the minimum energy path linking reactants and products c.f. local minimum of the potential energy surface. <br />
<br />
====Report your best estimate of the transition state position (r<sub>ts</sub>) and explain your reasoning illustrating it with an “Internuclear Distances vs Time” plot for a relevant trajectory.====<br />
<br />
The best estemate of the transition state position r<sub>ts</sub> = 91 pm<br />
<br />
[[File:mp5318_Animation.png|thumb|centre|Internuclear Distances vs Time Plot when r<sub>ts</sub> = 91 pm.]]<br />
<br />
As shown in the ''Internuclear Distances vs Time Plot when r<sub>ts</sub> = 91 pm'' above, when r<sub>ts</sub> = 91 pm and p<sub>1</sub> p<sub>2</sub> = 0.0 g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>, internuclear distance reamain (almost) constant, which shows that the molecule does not vibrate and stayed stably at the transition state forever.<br />
<br />
====Comment on how the MEP and the trajectory you just calculated differ.====<br />
<br />
[[File:Mp5318 Surface Plot Dynamic.png|thumb|left|Surface Plot using Dynamic Calculation r<sub>1</sub>=92 pm, r<sub>2</sub>=91 pm]]<br />
<br />
[[File:Surface Plot MEP.png|thumb|centre|Surface Plot using MEP Calculation r<sub>1</sub>=92 pm, r<sub>2</sub>=91 pm]]<br />
<br />
<br clear=all><br />
When '''r<sub>1</sub>'''=92 pm, '''r<sub>2</sub>'''=91 pm, atoms A and B dissociates. Using MEP calculation, AB dissociates through the minimum energy pathway and the dissociation ceased at a displacement much smaller than using Dynamic calculation. In Dynamic trajectory, kinetic energy was acquired during the trajectory from potential energy, therefore encourage inertial motion to proceed. In addition, MEP Calculation does not take into account the momentum of the particles, all the momentums are assumed to be zero.<br />
<br />
When reversing '''r<sub>1</sub>''' and '''r<sub>2</sub>''', B and C dissociates while A and B sticks together. The final values of the positions are '''r<sub>1</sub>''' (73.81819562) '''r<sub>2</sub>''' (352.8544826) and '''p<sub>1</sub>''' (3.258858751) '''p<sub>2</sub>''' (5.06251673). <br />
<br />
When setting up a calculation where the initial positions correspond to the final positions of the trajectory above, the same final momenta values but with their signs reversed, the reaction trajectory travels back to the orginal position '''r<sub>1</sub>''' (91) and '''r<sub>2</sub>''' (92) with '''p<sub>1</sub>'''= '''p<sub>2</sub>'''= 0.<br />
<br />
===Reactive and Unreactive trajectories===<br />
<br />
{| class="wikitable" border="1"<br />
|+ initial positions '''r<sub>1</sub>''' (74 pm) '''r<sub>2</sub>''' (200 pm)<br />
! p<sub>1</sub> / g.mol<sup>-1</sup>.pm.fs<sup>-1</sup> !! p<sub>2</sub> / g.mol<sup>-1</sup>.pm.fs<sup>-1</sup> !! E<sub>tot</sub> kJ.mol<sub>-1</sub> !! Reactive? !! Description of the dunamics !! Illustration of the trajectory<br />
|-<br />
| -2.56 || -5.1 || -414.28 || Yes || A-B + C → A +B-C || [[File:Mp5318 t1.png|356px]]<br />
|-<br />
| -3.1 || -4.1 || -420.08 || No || A-B approaches C, but then leave without reaction occur || [[File:Mp5318 t2.png|356px]]<br />
|-<br />
| -3.1 || -5.1 || -413.98 || Yes || A-B + C → A +B-C || [[File:Mp5318 t3.png|356px]]<br />
|-<br />
| -5.1 || -10.1 || -357.28 || No || at TS region, strength of bondings A-B and B-C alternates, but eventually A-B leave intact (Barrier can be crossed, but then the system reverts back to the reactants) || [[File:Mp5318 t4.png|356px]]<br />
|-<br />
| -5.1 || -10.6 || -349.38 || Yes || A-B + C → A +B-C at TS region, strength of bonding A-B and N-C alternates, but new product formed eventually || [[File:Mp5318 t5.png|356px]]<br />
|}<br />
<br />
'''Conclusion: Reactants need to have a large enough ratio in the momentum to be reactive, ideally, p<sub>2</sub> : p<sub>1</sub> should be larger than 2 for the reactants to be reactive.'''<br />
<br />
===Transition State Theory===<br />
<br />
====Given the results you have obtained, how will Transition State Theory predictions for reaction rate values compare with experimental values?====<br />
<br />
Transition State Theory often overestimates the reaction rate, compared to the results we calculated. Transition State Theory assumed that once the reaction has passed the Transition state and reached the product, it would not travel back to cross the Transition State and reverse to the reactant side. However, the calculations above showed that in practice, products can still recross the energy barrier to go back to the reactants. Even though the Transition State Theory ignored the effect of quantum tunneling, it's a relatively small contribution to rate in this case (small MW for H<sub>2</sub>). Therefore Transition State Theory tends to overestimate reaction rate values compare with experimental values.<br />
<br />
==F-H-H System ==<br />
<br />
=== PES inspection===<br />
<br />
====By inspecting the potential energy surfaces, classify the F + H<sub>2</sub> and H + HF reactions according to their energetics (endothermic or exothermic). How does this relate to the bond strength of the chemical species involved?====<br />
<br />
[[File:Mp5318Surface Plot fh2.png|thumb|left|Potential Surface of F + H<sub>2</sub> Reaction]]<br />
[[File:Mp5318Surface Plot hhf.png|thumb|centre|Potential Surface of H + HF Reaction]]<br />
<br clear=all></div>Mp5318https://chemwiki.ch.ic.ac.uk/index.php?title=Minqi5318&diff=802776Minqi53182020-05-14T12:06:03Z<p>Mp5318: </p>
<hr />
<div>== Molecular Reaction Dynamics: Application to Triatomic systems ==<br />
<br />
==H +H<sub>1</sub> System ==<br />
<br />
=== Dynamic from transition state region===<br />
<br />
====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?====<br />
<br />
The transition state is defined mathematically as the saddle point on the potential energy surface, where ∂V('''ri''')/∂'''ri'''=0 (the gradient of the potential is zero). At the transition state, the second derivative of potential with respect to q<sub>1</sub> is positive: ∂V<sup>2</sup>(q<sub>1</sub>)/∂q<sub>1</sub> > 0, indicating a minimum of the curve; the second derivative of potential with respect to q<sub>2</sub> is positive: ∂V<sup>2</sup>(q<sub>2</sub>)/∂q<sub>2</sub> < 0, indicating a maximum of the curve. The coincidence of a maximum and a minimum indicates saddle point on the potential energy surface. It can be identified through finding the maximum on the minimum energy path linking reactants and the products. The Transition State's energy goes down most steeply along the minimum energy path linking reactants and products c.f. local minimum of the potential energy surface. <br />
<br />
====Report your best estimate of the transition state position (r<sub>ts</sub>) and explain your reasoning illustrating it with an “Internuclear Distances vs Time” plot for a relevant trajectory.====<br />
<br />
The best estemate of the transition state position r<sub>ts</sub> = 91 pm<br />
<br />
[[File:mp5318_Animation.png|thumb|centre|Internuclear Distances vs Time Plot when r<sub>ts</sub> = 91 pm.]]<br />
<br />
As shown in the ''Internuclear Distances vs Time Plot when r<sub>ts</sub> = 91 pm'' above, when r<sub>ts</sub> = 91 pm and p<sub>1</sub> p<sub>2</sub> = 0.0 g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>, internuclear distance reamain (almost) constant, which shows that the molecule does not vibrate and stayed stably at the transition state forever.<br />
<br />
====Comment on how the MEP and the trajectory you just calculated differ.====<br />
<br />
[[File:Mp5318 Surface Plot Dynamic.png|thumb|left|Surface Plot using Dynamic Calculation r<sub>1</sub>=92 pm, r<sub>2</sub>=91 pm]]<br />
<br />
[[File:Surface Plot MEP.png|thumb|centre|Surface Plot using MEP Calculation r<sub>1</sub>=92 pm, r<sub>2</sub>=91 pm]]<br />
<br />
<br clear=all><br />
When '''r<sub>1</sub>'''=92 pm, '''r<sub>2</sub>'''=91 pm, atoms A and B dissociates. Using MEP calculation, AB dissociates through the minimum energy pathway and the dissociation ceased at a displacement much smaller than using Dynamic calculation. In Dynamic trajectory, kinetic energy was acquired during the trajectory from potential energy, therefore encourage inertial motion to proceed. In addition, MEP Calculation does not take into account the momentum of the particles, all the momentums are assumed to be zero.<br />
<br />
When reversing '''r<sub>1</sub>''' and '''r<sub>2</sub>''', B and C dissociates while A and B sticks together. The final values of the positions are '''r<sub>1</sub>''' (73.81819562) '''r<sub>2</sub>''' (352.8544826) and '''p<sub>1</sub>''' (3.258858751) '''p<sub>2</sub>''' (5.06251673). <br />
<br />
When setting up a calculation where the initial positions correspond to the final positions of the trajectory above, the same final momenta values but with their signs reversed, the reaction trajectory travels back to the orginal position '''r<sub>1</sub>''' (91) and '''r<sub>2</sub>''' (92) with '''p<sub>1</sub>'''= '''p<sub>2</sub>'''= 0.<br />
<br />
===Reactive and Unreactive trajectories===<br />
<br />
{| class="wikitable" border="1"<br />
|+ initial positions '''r<sub>1</sub>''' (74 pm) '''r<sub>2</sub>''' (200 pm)<br />
! p<sub>1</sub> / g.mol<sup>-1</sup>.pm.fs<sup>-1</sup> !! p<sub>2</sub> / g.mol<sup>-1</sup>.pm.fs<sup>-1</sup> !! E<sub>tot</sub> kJ.mol<sub>-1</sub> !! Reactive? !! Description of the dunamics !! Illustration of the trajectory<br />
|-<br />
| -2.56 || -5.1 || -414.28 || Yes || A-B + C → A +B-C || [[File:Mp5318 t1.png|356px]]<br />
|-<br />
| -3.1 || -4.1 || -420.08 || No || A-B approaches C, but then leave without reaction occur || [[File:Mp5318 t2.png|356px]]<br />
|-<br />
| -3.1 || -5.1 || -413.98 || Yes || A-B + C → A +B-C || [[File:Mp5318 t3.png|356px]]<br />
|-<br />
| -5.1 || -10.1 || -357.28 || No || at TS region, strength of bondings A-B and B-C alternates, but eventually A-B leave intact (Barrier can be crossed, but then the system reverts back to the reactants) || [[File:Mp5318 t4.png|356px]]<br />
|-<br />
| -5.1 || -10.6 || -349.38 || Yes || A-B + C → A +B-C at TS region, strength of bonding A-B and N-C alternates, but new product formed eventually || [[File:Mp5318 t5.png|356px]]<br />
|}<br />
<br />
'''Conclusion: Reactants need to have a large enough ratio in the momentum to be reactive, ideally, p<sub>2</sub> : p<sub>1</sub> should be larger than 2 for the reactants to be reactive.'''<br />
<br />
===Transition State Theory===<br />
<br />
====Given the results you have obtained, how will Transition State Theory predictions for reaction rate values compare with experimental values?====<br />
<br />
Transition State Theory often overestimates the reaction rate, compared to the results we calculated. Transition State Theory assumed that once the reaction has passed the Transition state and reached the product, it would not travel back to cross the Transition State and reverse to the reactant side. However, the calculations above showed that in practice, products can still recross the energy barrier to go back to the reactants. Even though the Transition State Theory ignored the effect of quantum tunneling, it's a relatively small contribution to rate in this case (small MW for H<sub>2</sub>). Therefore Transition State Theory tends to overestimate reaction rate values compare with experimental values.<br />
<br />
==F-H-H System ==<br />
<br />
=== PES inspection===<br />
<br />
====By inspecting the potential energy surfaces, classify the F + H<sub>2</sub> and H + HF reactions according to their energetics (endothermic or exothermic). How does this relate to the bond strength of the chemical species involved?====<br />
<br />
[[File:Mp5318Surface Plot fh2.png|thumb|left|Potential Surface of F + H<sub>2</sub> Reaction]]<br />
[[File:Mp5318Surface Plot hhf.png|thumb|left|Potential Surface of H + HF Reaction]]<br />
<br clear=all></div>Mp5318https://chemwiki.ch.ic.ac.uk/index.php?title=File:Mp5318Surface_Plot_hhf.png&diff=802769File:Mp5318Surface Plot hhf.png2020-05-14T12:03:41Z<p>Mp5318: </p>
<hr />
<div></div>Mp5318https://chemwiki.ch.ic.ac.uk/index.php?title=File:Mp5318Surface_Plot_fh2.png&diff=802766File:Mp5318Surface Plot fh2.png2020-05-14T12:03:16Z<p>Mp5318: </p>
<hr />
<div></div>Mp5318https://chemwiki.ch.ic.ac.uk/index.php?title=Minqi5318&diff=802754Minqi53182020-05-14T11:57:31Z<p>Mp5318: /* Transition State Theory */</p>
<hr />
<div>== Molecular Reaction Dynamics: Application to Triatomic systems ==<br />
<br />
==H +H<sub>1</sub> System ==<br />
<br />
=== Dynamic from transition state region===<br />
<br />
====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?====<br />
<br />
The transition state is defined mathematically as the saddle point on the potential energy surface, where ∂V('''ri''')/∂'''ri'''=0 (the gradient of the potential is zero). At the transition state, the second derivative of potential with respect to q<sub>1</sub> is positive: ∂V<sup>2</sup>(q<sub>1</sub>)/∂q<sub>1</sub> > 0, indicating a minimum of the curve; the second derivative of potential with respect to q<sub>2</sub> is positive: ∂V<sup>2</sup>(q<sub>2</sub>)/∂q<sub>2</sub> < 0, indicating a maximum of the curve. The coincidence of a maximum and a minimum indicates saddle point on the potential energy surface. It can be identified through finding the maximum on the minimum energy path linking reactants and the products. The Transition State's energy goes down most steeply along the minimum energy path linking reactants and products c.f. local minimum of the potential energy surface. <br />
<br />
====Report your best estimate of the transition state position (r<sub>ts</sub>) and explain your reasoning illustrating it with an “Internuclear Distances vs Time” plot for a relevant trajectory.====<br />
<br />
The best estemate of the transition state position r<sub>ts</sub> = 91 pm<br />
<br />
[[File:mp5318_Animation.png|thumb|centre|Internuclear Distances vs Time Plot when r<sub>ts</sub> = 91 pm.]]<br />
<br />
As shown in the ''Internuclear Distances vs Time Plot when r<sub>ts</sub> = 91 pm'' above, when r<sub>ts</sub> = 91 pm and p<sub>1</sub> p<sub>2</sub> = 0.0 g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>, internuclear distance reamain (almost) constant, which shows that the molecule does not vibrate and stayed stably at the transition state forever.<br />
<br />
====Comment on how the MEP and the trajectory you just calculated differ.====<br />
<br />
[[File:Mp5318 Surface Plot Dynamic.png|thumb|left|Surface Plot using Dynamic Calculation r<sub>1</sub>=92 pm, r<sub>2</sub>=91 pm]]<br />
<br />
[[File:Surface Plot MEP.png|thumb|centre|Surface Plot using MEP Calculation r<sub>1</sub>=92 pm, r<sub>2</sub>=91 pm]]<br />
<br />
<br clear=all><br />
When '''r<sub>1</sub>'''=92 pm, '''r<sub>2</sub>'''=91 pm, atoms A and B dissociates. Using MEP calculation, AB dissociates through the minimum energy pathway and the dissociation ceased at a displacement much smaller than using Dynamic calculation. In Dynamic trajectory, kinetic energy was acquired during the trajectory from potential energy, therefore encourage inertial motion to proceed. In addition, MEP Calculation does not take into account the momentum of the particles, all the momentums are assumed to be zero.<br />
<br />
When reversing '''r<sub>1</sub>''' and '''r<sub>2</sub>''', B and C dissociates while A and B sticks together. The final values of the positions are '''r<sub>1</sub>''' (73.81819562) '''r<sub>2</sub>''' (352.8544826) and '''p<sub>1</sub>''' (3.258858751) '''p<sub>2</sub>''' (5.06251673). <br />
<br />
When setting up a calculation where the initial positions correspond to the final positions of the trajectory above, the same final momenta values but with their signs reversed, the reaction trajectory travels back to the orginal position '''r<sub>1</sub>''' (91) and '''r<sub>2</sub>''' (92) with '''p<sub>1</sub>'''= '''p<sub>2</sub>'''= 0.<br />
<br />
===Reactive and Unreactive trajectories===<br />
<br />
{| class="wikitable" border="1"<br />
|+ initial positions '''r<sub>1</sub>''' (74 pm) '''r<sub>2</sub>''' (200 pm)<br />
! p<sub>1</sub> / g.mol<sup>-1</sup>.pm.fs<sup>-1</sup> !! p<sub>2</sub> / g.mol<sup>-1</sup>.pm.fs<sup>-1</sup> !! E<sub>tot</sub> kJ.mol<sub>-1</sub> !! Reactive? !! Description of the dunamics !! Illustration of the trajectory<br />
|-<br />
| -2.56 || -5.1 || -414.28 || Yes || A-B + C → A +B-C || [[File:Mp5318 t1.png|356px]]<br />
|-<br />
| -3.1 || -4.1 || -420.08 || No || A-B approaches C, but then leave without reaction occur || [[File:Mp5318 t2.png|356px]]<br />
|-<br />
| -3.1 || -5.1 || -413.98 || Yes || A-B + C → A +B-C || [[File:Mp5318 t3.png|356px]]<br />
|-<br />
| -5.1 || -10.1 || -357.28 || No || at TS region, strength of bondings A-B and B-C alternates, but eventually A-B leave intact (Barrier can be crossed, but then the system reverts back to the reactants) || [[File:Mp5318 t4.png|356px]]<br />
|-<br />
| -5.1 || -10.6 || -349.38 || Yes || A-B + C → A +B-C at TS region, strength of bonding A-B and N-C alternates, but new product formed eventually || [[File:Mp5318 t5.png|356px]]<br />
|}<br />
<br />
'''Conclusion: Reactants need to have a large enough ratio in the momentum to be reactive, ideally, p<sub>2</sub> : p<sub>1</sub> should be larger than 2 for the reactants to be reactive.'''<br />
<br />
===Transition State Theory===<br />
<br />
====Given the results you have obtained, how will Transition State Theory predictions for reaction rate values compare with experimental values?====<br />
<br />
Transition State Theory often overestimate the reaction rate, compare to the results we calculated. Transition State Theory assumed that once the reaction has passed the Transition state and reached the product, it would not travel back to cross the Transition State and reverse to the reactant side. However, the calculations above showed that in practice, products can still recross the energy barrier to go back to the reactants. Even though the Transition State Theory ignored the effect of quantum tunnelling, it's a relatively small contribution to rate in this case (small MW for H<sub>2</sub>). Therefore Transition State Theory tends to overestimate reation rate values compare with experimental values.</div>Mp5318https://chemwiki.ch.ic.ac.uk/index.php?title=Minqi5318&diff=802672Minqi53182020-05-14T11:10:29Z<p>Mp5318: /* Comment on how the MEP and the trajectory you just calculated differ. */</p>
<hr />
<div>== Molecular Reaction Dynamics: Application to Triatomic systems ==<br />
<br />
==H +H<sub>1</sub> System ==<br />
<br />
=== Dynamic from transition state region===<br />
<br />
====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?====<br />
<br />
The transition state is defined mathematically as the saddle point on the potential energy surface, where ∂V('''ri''')/∂'''ri'''=0 (the gradient of the potential is zero). At the transition state, the second derivative of potential with respect to q<sub>1</sub> is positive: ∂V<sup>2</sup>(q<sub>1</sub>)/∂q<sub>1</sub> > 0, indicating a minimum of the curve; the second derivative of potential with respect to q<sub>2</sub> is positive: ∂V<sup>2</sup>(q<sub>2</sub>)/∂q<sub>2</sub> < 0, indicating a maximum of the curve. The coincidence of a maximum and a minimum indicates saddle point on the potential energy surface. It can be identified through finding the maximum on the minimum energy path linking reactants and the products. The Transition State's energy goes down most steeply along the minimum energy path linking reactants and products c.f. local minimum of the potential energy surface. <br />
<br />
====Report your best estimate of the transition state position (r<sub>ts</sub>) and explain your reasoning illustrating it with an “Internuclear Distances vs Time” plot for a relevant trajectory.====<br />
<br />
The best estemate of the transition state position r<sub>ts</sub> = 91 pm<br />
<br />
[[File:mp5318_Animation.png|thumb|centre|Internuclear Distances vs Time Plot when r<sub>ts</sub> = 91 pm.]]<br />
<br />
As shown in the ''Internuclear Distances vs Time Plot when r<sub>ts</sub> = 91 pm'' above, when r<sub>ts</sub> = 91 pm and p<sub>1</sub> p<sub>2</sub> = 0.0 g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>, internuclear distance reamain (almost) constant, which shows that the molecule does not vibrate and stayed stably at the transition state forever.<br />
<br />
====Comment on how the MEP and the trajectory you just calculated differ.====<br />
<br />
[[File:Mp5318 Surface Plot Dynamic.png|thumb|left|Surface Plot using Dynamic Calculation r<sub>1</sub>=92 pm, r<sub>2</sub>=91 pm]]<br />
<br />
[[File:Surface Plot MEP.png|thumb|centre|Surface Plot using MEP Calculation r<sub>1</sub>=92 pm, r<sub>2</sub>=91 pm]]<br />
<br />
<br clear=all><br />
When '''r<sub>1</sub>'''=92 pm, '''r<sub>2</sub>'''=91 pm, atoms A and B dissociates. Using MEP calculation, AB dissociates through the minimum energy pathway and the dissociation ceased at a displacement much smaller than using Dynamic calculation. In Dynamic trajectory, kinetic energy was acquired during the trajectory from potential energy, therefore encourage inertial motion to proceed. In addition, MEP Calculation does not take into account the momentum of the particles, all the momentums are assumed to be zero.<br />
<br />
When reversing '''r<sub>1</sub>''' and '''r<sub>2</sub>''', B and C dissociates while A and B sticks together. The final values of the positions are '''r<sub>1</sub>''' (73.81819562) '''r<sub>2</sub>''' (352.8544826) and '''p<sub>1</sub>''' (3.258858751) '''p<sub>2</sub>''' (5.06251673). <br />
<br />
When setting up a calculation where the initial positions correspond to the final positions of the trajectory above, the same final momenta values but with their signs reversed, the reaction trajectory travels back to the orginal position '''r<sub>1</sub>''' (91) and '''r<sub>2</sub>''' (92) with '''p<sub>1</sub>'''= '''p<sub>2</sub>'''= 0.<br />
<br />
===Reactive and Unreactive trajectories===<br />
<br />
{| class="wikitable" border="1"<br />
|+ initial positions '''r<sub>1</sub>''' (74 pm) '''r<sub>2</sub>''' (200 pm)<br />
! p<sub>1</sub> / g.mol<sup>-1</sup>.pm.fs<sup>-1</sup> !! p<sub>2</sub> / g.mol<sup>-1</sup>.pm.fs<sup>-1</sup> !! E<sub>tot</sub> kJ.mol<sub>-1</sub> !! Reactive? !! Description of the dunamics !! Illustration of the trajectory<br />
|-<br />
| -2.56 || -5.1 || -414.28 || Yes || A-B + C → A +B-C || [[File:Mp5318 t1.png|356px]]<br />
|-<br />
| -3.1 || -4.1 || -420.08 || No || A-B approaches C, but then leave without reaction occur || [[File:Mp5318 t2.png|356px]]<br />
|-<br />
| -3.1 || -5.1 || -413.98 || Yes || A-B + C → A +B-C || [[File:Mp5318 t3.png|356px]]<br />
|-<br />
| -5.1 || -10.1 || -357.28 || No || at TS region, strength of bondings A-B and B-C alternates, but eventually A-B leave intact (Barrier can be crossed, but then the system reverts back to the reactants) || [[File:Mp5318 t4.png|356px]]<br />
|-<br />
| -5.1 || -10.6 || -349.38 || Yes || A-B + C → A +B-C at TS region, strength of bonding A-B and N-C alternates, but new product formed eventually || [[File:Mp5318 t5.png|356px]]<br />
|}<br />
<br />
'''Conclusion: Reactants need to have a large enough ratio in the momentum to be reactive, ideally, p<sub>2</sub> : p<sub>1</sub> should be larger than 2 for the reactants to be reactive.'''<br />
<br />
===Transition State Theory===<br />
<br />
====Given the results you have obtained, how will Transition State Theory predictions for reaction rate values compare with experimental values?====</div>Mp5318https://chemwiki.ch.ic.ac.uk/index.php?title=Minqi5318&diff=802656Minqi53182020-05-14T11:05:45Z<p>Mp5318: </p>
<hr />
<div>== Molecular Reaction Dynamics: Application to Triatomic systems ==<br />
<br />
==H +H<sub>1</sub> System ==<br />
<br />
=== Dynamic from transition state region===<br />
<br />
====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?====<br />
<br />
The transition state is defined mathematically as the saddle point on the potential energy surface, where ∂V('''ri''')/∂'''ri'''=0 (the gradient of the potential is zero). At the transition state, the second derivative of potential with respect to q<sub>1</sub> is positive: ∂V<sup>2</sup>(q<sub>1</sub>)/∂q<sub>1</sub> > 0, indicating a minimum of the curve; the second derivative of potential with respect to q<sub>2</sub> is positive: ∂V<sup>2</sup>(q<sub>2</sub>)/∂q<sub>2</sub> < 0, indicating a maximum of the curve. The coincidence of a maximum and a minimum indicates saddle point on the potential energy surface. It can be identified through finding the maximum on the minimum energy path linking reactants and the products. The Transition State's energy goes down most steeply along the minimum energy path linking reactants and products c.f. local minimum of the potential energy surface. <br />
<br />
====Report your best estimate of the transition state position (r<sub>ts</sub>) and explain your reasoning illustrating it with an “Internuclear Distances vs Time” plot for a relevant trajectory.====<br />
<br />
The best estemate of the transition state position r<sub>ts</sub> = 91 pm<br />
<br />
[[File:mp5318_Animation.png|thumb|centre|Internuclear Distances vs Time Plot when r<sub>ts</sub> = 91 pm.]]<br />
<br />
As shown in the ''Internuclear Distances vs Time Plot when r<sub>ts</sub> = 91 pm'' above, when r<sub>ts</sub> = 91 pm and p<sub>1</sub> p<sub>2</sub> = 0.0 g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>, internuclear distance reamain (almost) constant, which shows that the molecule does not vibrate and stayed stably at the transition state forever.<br />
<br />
====Comment on how the MEP and the trajectory you just calculated differ.====<br />
<br />
[[File:Mp5318 Surface Plot Dynamic.png|thumb|left|Surface Plot using Dynamic Calculation r<sub>1</sub>=92 pm, r<sub>2</sub>=91 pm]]<br />
<br />
[[File:Surface Plot MEP.png|thumb|centre|Surface Plot using MEP Calculation r<sub>1</sub>=92 pm, r<sub>2</sub>=91 pm]]<br />
<br />
<br clear=all><br />
when '''r<sub>1</sub>'''=92 pm, '''r<sub>2</sub>'''=91 pm, atoms A and B dissociates. Using MEP calculation, AB dissociates through the minimum energy pathway and the dissociation ceased at a displacement much smaller than using Dynamic calculation. In Dynamic trajectory, kinetic energy was acquired during the trajectory from potential energy, therefore encourage inertial motion to proceed. <br />
<br />
when reversing '''r<sub>1</sub>''' and '''r<sub>2</sub>''', B and C dissociates while A and B sticks together. The final values of the positions are '''r<sub>1</sub>''' (73.81819562) '''r<sub>2</sub>''' (352.8544826) and '''p<sub>1</sub>''' (3.258858751) '''p<sub>2</sub>''' (5.06251673). <br />
<br />
When setting up a calculation where the initial positions correspond to the final positions of the trajectory above, the same final momenta values but with their signs reversed, the reaction trajectory travels back to the orginal position '''r<sub>1</sub>''' (91) and '''r<sub>2</sub>''' (92) with '''p<sub>1</sub>'''= '''p<sub>2</sub>'''= 0.<br />
<br />
===Reactive and Unreactive trajectories===<br />
<br />
{| class="wikitable" border="1"<br />
|+ initial positions '''r<sub>1</sub>''' (74 pm) '''r<sub>2</sub>''' (200 pm)<br />
! p<sub>1</sub> / g.mol<sup>-1</sup>.pm.fs<sup>-1</sup> !! p<sub>2</sub> / g.mol<sup>-1</sup>.pm.fs<sup>-1</sup> !! E<sub>tot</sub> kJ.mol<sub>-1</sub> !! Reactive? !! Description of the dunamics !! Illustration of the trajectory<br />
|-<br />
| -2.56 || -5.1 || -414.28 || Yes || A-B + C → A +B-C || [[File:Mp5318 t1.png|356px]]<br />
|-<br />
| -3.1 || -4.1 || -420.08 || No || A-B approaches C, but then leave without reaction occur || [[File:Mp5318 t2.png|356px]]<br />
|-<br />
| -3.1 || -5.1 || -413.98 || Yes || A-B + C → A +B-C || [[File:Mp5318 t3.png|356px]]<br />
|-<br />
| -5.1 || -10.1 || -357.28 || No || at TS region, strength of bondings A-B and B-C alternates, but eventually A-B leave intact (Barrier can be crossed, but then the system reverts back to the reactants) || [[File:Mp5318 t4.png|356px]]<br />
|-<br />
| -5.1 || -10.6 || -349.38 || Yes || A-B + C → A +B-C at TS region, strength of bonding A-B and N-C alternates, but new product formed eventually || [[File:Mp5318 t5.png|356px]]<br />
|}<br />
<br />
'''Conclusion: Reactants need to have a large enough ratio in the momentum to be reactive, ideally, p<sub>2</sub> : p<sub>1</sub> should be larger than 2 for the reactants to be reactive.'''<br />
<br />
===Transition State Theory===<br />
<br />
====Given the results you have obtained, how will Transition State Theory predictions for reaction rate values compare with experimental values?====</div>Mp5318https://chemwiki.ch.ic.ac.uk/index.php?title=Minqi5318&diff=801746Minqi53182020-05-12T16:14:20Z<p>Mp5318: </p>
<hr />
<div>== Molecular Reaction Dynamics: Application to Triatomic systems ==<br />
<br />
==H +H<sub>1</sub> System ==<br />
<br />
=== Dynamic from transition state region===<br />
<br />
====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?====<br />
<br />
The transition state is defined mathematically as the saddle point on the potential energy surface, where ∂V('''ri''')/∂'''ri'''=0 (the gradient of the potential is zero). It can be identified through finding the maximum on the minimum energy path linking reactants and the products. The Transition State's energy goes down most steeply along the minimum energy path linking reactants and products c.f. local minimum of the potential energy surface. <br />
<br />
====Report your best estimate of the transition state position (r<sub>ts</sub>) and explain your reasoning illustrating it with an “Internuclear Distances vs Time” plot for a relevant trajectory.====<br />
<br />
The best estemate of the transition state position r<sub>ts</sub> = 91 pm<br />
<br />
[[File:mp5318_Animation.png|thumb|centre|Internuclear Distances vs Time Plot when r<sub>ts</sub> = 91 pm.]]<br />
<br />
As shown in the ''Internuclear Distances vs Time Plot when r<sub>ts</sub> = 91 pm'' above, when r<sub>ts</sub> = 91 pm and p<sub>1</sub> p<sub>2</sub> = 0.0 g.mol<sup>-1</sup>.pm.fs<sup>-1</sup>, internuclear distance reamain (almost) constant, which shows that the molecule does not vibrate and stayed stably at the transition state forever.<br />
<br />
====Comment on how the MEP and the trajectory you just calculated differ.====<br />
<br />
[[File:Mp5318 Surface Plot Dynamic.png|thumb|left|Surface Plot using Dynamic Calculation r<sub>1</sub>=92 pm, r<sub>2</sub>=91 pm]]<br />
<br />
[[File:Surface Plot MEP.png|thumb|centre|Surface Plot using MEP Calculation r<sub>1</sub>=92 pm, r<sub>2</sub>=91 pm]]<br />
<br />
<br clear=all><br />
when '''r<sub>1</sub>'''=92 pm, '''r<sub>2</sub>'''=91 pm, atoms A and B dissociates. Using MEP calculation, AB dissociates through the minimum energy pathway and the dissociation ceased at a displacement much smaller than using Dynamic calculation. In Dynamic trajectory, kinetic energy was acquired during the trajectory from potential energy, therefore encourage inertial motion to proceed. <br />
<br />
when reversing '''r<sub>1</sub>''' and '''r<sub>2</sub>''', B and C dissociates while A and B sticks together. The final values of the positions are '''r<sub>1</sub>''' (73.81819562) '''r<sub>2</sub>''' (352.8544826) and '''p<sub>1</sub>''' (3.258858751) '''p<sub>2</sub>''' (5.06251673). <br />
<br />
When setting up a calculation where the initial positions correspond to the final positions of the trajectory above, the same final momenta values but with their signs reversed, the reaction trajectory travels back to the orginal position '''r<sub>1</sub>''' (91) and '''r<sub>2</sub>''' (92) with '''p<sub>1</sub>'''= '''p<sub>2</sub>'''= 0.<br />
<br />
===Reactive and Unreactive trajectories===<br />
<br />
{| class="wikitable" border="1"<br />
|+ initial positions '''r<sub>1</sub>''' (74 pm) '''r<sub>2</sub>''' (200 pm)<br />
! p<sub>1</sub> / g.mol<sup>-1</sup>.pm.fs<sup>-1</sup> !! p<sub>2</sub> / g.mol<sup>-1</sup>.pm.fs<sup>-1</sup> !! E<sub>tot</sub> kJ.mol<sub>-1</sub> !! Reactive? !! Description of the dunamics !! Illustration of the trajectory<br />
|-<br />
| -2.56 || -5.1 || -414.28 || Yes || A-B + C → A +B-C || [[File:Mp5318 t1.png|356px]]<br />
|-<br />
| -3.1 || -4.1 || -420.08 || No || A-B approaches C, but then leave without reaction occur || [[File:Mp5318 t2.png|356px]]<br />
|-<br />
| -3.1 || -5.1 || -413.98 || Yes || A-B + C → A +B-C || [[File:Mp5318 t3.png|356px]]<br />
|-<br />
| -5.1 || -10.1 || -357.28 || No || at TS region, strength of bondings A-B and B-C alternates, but eventually A-B leave intact (Barrier can be crossed, but then the system reverts back to the reactants) || [[File:Mp5318 t4.png|356px]]<br />
|-<br />
| -5.1 || -10.6 || -349.38 || Yes || A-B + C → A +B-C at TS region, strength of bonding A-B and N-C alternates, but new product formed eventually || [[File:Mp5318 t5.png|356px]]<br />
|}<br />
<br />
'''Conclusion: Reactants need to have a large enough ratio in the momentum to be reactive, ideally, p<sub>2</sub> : p<sub>1</sub> should be larger than 2 for the reactants to be reactive.'''<br />
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===Transition State Theory===<br />
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====Given the results you have obtained, how will Transition State Theory predictions for reaction rate values compare with experimental values?====</div>Mp5318