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MRD:hz7718

2020-05-15T16:54:38Z

Jz14318: /* Transition state */

==Exercise 1: H + H2 system==
===Transition state===
Mathematically, transition state is a saddle point which is on a graph of a function where slopes in orthogonal directions are zero.

For finding transition state on graph, the slopes of both r1 and r2 directions should be zero, which means δV/δr1 = 0 and δV/δr2 = 0. Also, if it is the maximum point in one direction, it should be minimum point in the orthogonal direction. In math, (δ2V/δr12)*(δ2V/δr22) - δ2V/(δr1*δr2) < 0.

A minimum stationary point means in both directions, it is the minimum point with zero gradients (δ2V/δx2 > 0 and (δ2V/δr12)*(δ2V/δr22) -δ2V/(δr1*δr2) > 0). But transition state is the minimum point in one direction but a maximum point in the other orthogonal direction.

{| class="wikitable" border="1"
!saddle point on a graph !! Minimum stationary point plot !! Maximum stationary point plot
|-
| [[file:hz7718_py1.png|500px|thumb|left]] || [[file:hz7718_py2.png|500px|thumb|right]] || [[file:hz7718_py3.png|500px|thumb|right]]
|}

===locating the transition state===
When the system is at transition state, the potential energies of both p1 and p2 are zero. And because all the three atoms are in equilibrium, the change of the energy is zero, too. It means that the gradients of potential energy surface is zero and the force acting on atoms is zero, which indicates there is no oscillation of the three atoms and r1 and r2 will keep constant. On the graph, r1 and r2 equal to 90.7pm, and two lines are almost perfectly straight without oscillating, which means it is(or close to) the transition state. So rts=90.7pm.

[[file:hz7718_py4.png|300px]]

===Trajectories from r1=rts+δ, r1=rts===
In MEP type graph, the trajectory follows the valley floor to H1 + H2-H3. But in the dynamic type graph, the shape of trajectory is wavy. This is because on mep, all atoms have zero kinetic energy(velocities and momenta are zero), which causes that B-C bond has no vibration. However, in dynamic type, kinetic energy is included in the system, so B-C bond will vibrate so the values of r2 will fluctuate.

{| class="wikitable" border="1"
!MEP graph, r1=91.7pm, r2=90.7pm, p1=p2=0!! Dynamic graph, r1=91.7pm, r2=90.7pm, p1=p2=0
|-
| [[file:hz7718_py5.png|300px|thumb|left]] || [[file:hz7718_py6.png|300px|thumb|right]]
|}

===Reactive and unreactive trajectories===
{| class="wikitable" border="1"
! p1/ g.mol-1.pm.fs-1 !! p2/ g.mol-1.pm.fs-1 !! Etot/ kJ.mol-1 !! Reactive? !! Description of the dynamics !! Illustration of the trajectory
|-
| -2.56 || -5.1 || -414.28 || YES || HC atom and HA-HB molecule approach to each other at the beginning. When the system passes the transition state region, new bond HB- HC will form and HA-HB bond will break. Then HA atom and HB-HC molecule move away to each other. Before HB-HC forming, the trajectory is a line with very little oscillation. This is because most kinetic energy of HA-HB is in translational energy. After HB-HC bond forming, the trajectory is wavy because most kinetic energy of HB-HC is in vibrational energy. || [[file:hz7718_py7.png|300px|thumb|right]]
|-
| -3.1 || -4.1 || -420.08 || NO || HC atom and HA-HB molecule approach to each other at the beginning. But they do not pass the transition state region, HA-HB bond does not break and HB-HC bond does not form. Then HC atom and HA-HB molecule move away to each other. HA-HB bond keeps vibrating due to the kinetic energy. || [[file:hz7718_py8.png|300px|thumb|right]]
|-
| -3.1 || -5.1 || -413.98 || YES || HC atom and HA-HB molecule approach to each other very slowly because most of kinetic energy is in vibrational energy, which means the translational energy is very little. When HA-HB bond starts to break, HB-HC bond starts to form. After that, HA atom and HB-HC molecule move away to each other. And HB-HC bond keeps vibrating. || [[file:hz7718_py9.png|300px|thumb|right]]
|-
| -5.1 || -10.1 || -357.28 || NO || HC atom and HA-HB molecule approach to each other, when they passes the transition state region, HA-HB bond starts to break and HB-HC bond starts to form. After that, HA atom moves away from HB-HC molecule but HB-HC molecule vibrates strongly. Then HB-HC bond breaks and HA and HB atoms approach to each other to form bond, which means this system recrosses the transition region and reverts to the reactants. In the end, vibrating HA-HB molecule and HC atom move away to each other. || [[file:hz7718_py10.png|300px|thumb|right]]
|-
| -5.1 || -10.6 || -349.48 || YES || The system passes the transition region for three times: At first, HC atom and HA-HB molecule get closer, HB-HC bond forms and HA-HB bond breaks. Then HA atom returns to HB-HC molecule immediately and the system reverts to reactants. After that, HB-HC bond forms again and HA-HB bond breaks again. In the end, vibrating HB-HC molecule and HA atom move away to each. || [[file:hz7718_py11.png|300px|thumb|right]]
|}
From the table above, we can know that even though the system has enough energy to react, it may still be unreactive.

===Transition State Theory===
In TST predictions, if the reactants with enough energy cross the transition state, it will never come back. However, the experimental results show the system can recross the transition state region and reform the reactants. SO, overall, the TST overestimates the reaction rate. And the TST has limitations: 1. High temperature, there are complicated vibrations which may lead the transition state far away from the saddle point of potential energy surface. 2. Quantum tunneling: Molecules and atoms can still tunnel across the barrier even with not enough energy. It will slightly underestimates the reaction rate. 1

==Exercise 2: F-H-H system==
===PES inspection===
{| class="wikitable" border="1"
! potential energy surface graph !! Internuclear distance vs time plot
|-
| [[file:hz7718_py12.png|300px|thumb|left]] || [[file:hz7718_py13.png|300px|thumb|right]]
|}
The potential energy surface graph show that the system H2 and F has higher potential energy than HF and H. It means H2 + F to HF + H reaction is exothermic and HF + H to H2 + F reaction is endothermic, which indicates that the bond strength of H-F is stronger than H-H.

So, from H2 + F to HF + H, the system needs to absorb energy from the environment, and from HF + H to H2 + F, the system releases energy to the environment.

When it comes to the transition state location, it can be analyzed by Hammond's postulate. 2 For example, in the reaction H2 + F to HF + H which is an exothermic reaction. The transition state is close to the structure of the reactants(so it is an early transition state). It means the distance between FA and HB is very large and the distance between HB and HC is smaller, which matches what potential energy surface graph shows. Unlikely the H-H-H system, the transition state of F-H-H system is not symmetric.

In the Internuclear distance vs time plot, FA-HB is 180pm and HB-HC is 74pm. And both lines are almost straight, which means all atoms only slightly vibrate. So, the change of potential energy is zero.

Then we can know the black point in potential energy surface graph is the transition state(where FA-HB=180pm, HB-HC=74pm and pH1=pH2=0).

===Activation Energy===
For finding the actvition energy, the steps are extended to 3500. When FA-HB is 180pm and HB-HC is 74pm, we can find the Contour plot 1 shows that the transition state finally forms HF + H. So, from Graph 1, we can know the activation energy is 121.6 kJ/mol for the reaction HF + H to H2 + F.
{| class="wikitable" border="1"
! Contour Plot 1 !! Graph 1
|-
| [[file:hz7718_py14.png|400px|thumb|left]] || [[file:hz7718_py15.png|300px|thumb|right]]
|}

When FA-HB is 184pm and HB-HC is 74pm, the Contour plot 2 shows that the transition state finally forms H2 + F. So, from Graph 2, we can know the activation energy is 0.03 kJ/mol for the reaction H2 + F to HF + H.
{| class="wikitable" border="1"
! Contour Plot 2 !! Graph 2
|-
| [[file:hz7718_py16.png|400px|thumb|left]] || [[file:hz7718_py17.png|300px|thumb|right]]
|}

===Reaction dynamics===
In reaction H2 + F to HF + H, FA-HB is 184pm and HB-HC is 74pm, p1=-1 and p2=-2. From the contour plot and animation, the product HF keeps vibrating and HC molecule moves away from HF. This is because the reaction is exothermic, the potential energy transfers to kinetic energy which includes vibrational energy and translational energy. However, from Momentum vs Time plot, it shows most of potential energy transfers to vibrational energy instead of translational energy because the HBA momentum fluctuates strongly but Hc-HB momentum keeps a relatviely low value.

The energy released mechanism can be confirmed by IR Spectroscopy. Because H-F vibration has dipole moment and it is active in IR. We can just measure the peak absorbance of H-F vibration at different time after reaction, if the absorbance is large, the vibrational energy of H-F is more. We can also use calorimetry to measure the heat produced by this reaction, and the heat energy measured is the change of kinetic energy of the products including vibrational energy and translational energy.
{| class="wikitable" border="1"
! Contour Plot !! Momentum vs Time
|-
| [[file:hz7718_py18.png|400px|thumb|left]] || [[file:hz7718_py19.png|400px|thumb|right]]
|}

===Translational energy VS Vibrational Energy===
Graph 1 represents an exothermic reaction with an early transition state. And in exothermic reaction, translational energy can make the reaction more efficient because it can help the reactants pass the early transition state region. If most kinetic energy of reactants is vibrational energy, reactants cannot pass the early transition region in exothermic reaction.3

Graph 2 represent an endothermic reaction. Endothermic reaction has a late transition state. The reactants need more vibrational energy to cross the late transition state region. And translational energy cannot help reactants pass the late transition state.3
{| class="wikitable" border="1"
! Graph 1 !! Graph 2
|-
| [[file:hz7718_py20.png|400px|thumb|left]] || [[file:hz7718_py21.png|400px|thumb|right]]
|}

==Reference==
1.Veser, Götz. "Experimental and theoretical investigation of H2 oxidation in a high-temperature catalytic microreactor." Chemical Engineering Science 56.4 (2001): 1265-1273.

2.G.S. Hammond. A Correlation of Reaction Rates. J. Am. Chem. Soc. 1955, 77 (2): 334–338. doi:10.1021/ja01607a027.

3.J.C. Polanyi. Some Concepts in Reaction Dynamics. Science 1987, 236 (4802): 680-690. doi:10.1126/science.236.4802.680

2020-05-08T08:14:05Z

Jz14318: /* Reaction dynamics */

==EXERCISE 1: H + H2 system==
===Dynamics from the transition state region===
====Identification of transition state====
Transition state can be mathematically defined as the saddle point or the minimax point of the potential energy surface.1 The gradient of the potential is zero at the saddle point. As shown in the figure below, a saddle point has a positive second derivative (e.g. minimum) in one direction, and a negative second derivative (i.e. maximum) in the other direction. By contrast, the second derivative for a local minimum is positive in both directions.

{| class="wikitable" border="1"
! A representation of a saddle point on a graph !! Upward curvature along the orthogonal coordinate !! Downward curvature along the reaction coordinate
|-
| [[File:jz14318_saddle_point.png|260px]] || [[File:jz14318_saddle_minimum.png|260px]] || [[File:jz14318_saddle_maximum.png|260px]]
|}

====Trajectories from r1 = r2: locating the transition state====

[[file:Jz14318_TSposition_91.png|200px|thumb|left|Internuclear distance vs time plot when r1 = r2 = 90.5 pm.]]

[[file:jz14318_TS_surface.png|200px|thumb|right|Surface plot when r1 = r2 = 90.5 pm.]]

It is suggested that the transition state location rts = 90.5 pm. As the force acting on the atoms depends on the gradient of the potential energy surface, the system at the transition state will have no atoms oscillating as the gradient of the potential energy surface is zero. From the plot above, it can be seen that the atoms oscillate to a very small extent, which indicates that this system is very close to the transition state.

====Trajectories from r1 = rts+δ, r2 = rts====

[[file:jz14318_dynamics_92_91.png|200px|thumb|left|Contour plot by dynamics calculation. r1 = 92 pm, r2 = 91 pm, p1 = p2 = 0 g.mol-1.pm.fs-1.]]

[[file:jz14318_MEP_92_91.png|200px|thumb|right|Contour plot by MEP calculation. r1 = 92 pm, r2 = 91 pm, p1 = p2 = 0 g.mol-1.pm.fs-1.]]

It can be observed from the two plots that ''mep'' (see RHS) follows the valley floor to HA + HB - HC, whereas the trajectory by dynamics calculation (see LHS) is wavy (i.e. the atoms are vibrating). This is because by MEP calculation, the atoms do not vibrate as their momenta/velocities are always set to zero in each time step, whereas by dynamics calculation, the total energy is conserved and the atoms do vibrate.

===Reactive and unreactive trajectories===

{| class="wikitable" border="1"
! p1/ g.mol-1.pm.fs-1 !! p2/ g.mol-1.pm.fs-1 !! Etot/ kJ.mol-1 !! Reactive? !! Description of the dynamics !! Illustration of the trajectory
|-
| -2.56 || -5.1 || -414.28 || YES || HC approaches the vibrating HAHB molecule. The system crosses the transition state region and HA-HB bond starts to break whilst HB-HC bond starts to form. The product is thus formed. || [[File:jz14318_256_51_surface.png|180px]]
|-
| -3.1 || -4.1 || -420.08 || NO || HC approaches the vibrating HAHB molecule; however, the system does not manage to cross the transition state region so the original HA-HB bond does not break and the product does not form. HC moves far away from HAHB molecule. || [[File:jz14318_31_41_surface.png|180px]]
|-
| -3.1 || -5.1 || -413.98 || YES || HC slowly approaches the vibrating HAHB molecule. HB starts to move away from HA (HA-HB bond starts to break) and comes closer to HC (HB-HC bond starts to form). HBHC product is formed and HA moves away. || [[File:jz14318_31_51_surface.png|180px]]
|-
| -5.1 || -10.1 || -357.28 || NO || HC slowly approaches the vibrating HAHB molecule. HB-HC bond starts to form as the system crosses the transition state region. HBHC molecule vibrates strongly and HB-HC bond that previously formed breaks again and HB approaches back to HA, reforming HA-HB bond. So the system recrosses the TS region and reverts back to the reactants. || [[File:jz14318_51_101_surface.png|180px]]
|-
| -5.1 || -10.6 || -349.48 || YES || The system crosses the transition state region 3 times. The system forms the product initially, then reverts back to the reactants with strong vibration, and eventually reverts back to the products again. || [[File:jz14318_51_106_surface.png|180px]]
|}

It can be concluded from the table that not all trajectories having sufficient energy to react will be reactive due to the possibility of barrier recrossing.

====Transition State Theory====
Transition state theory assumes that all trajectories with a kinetic energy along the reaction coordinate larger than Ea will be reactive.2 However, compared with the previous experimental results, this assumption seems fallacious. Some reactions will be unreactive even though the trajectory has a sufficient kinetic energy due to the recrossing of barrier. The second factor is that Transition State Theory ignores the effect of quantum tunneling and treats the motion of atoms classically. Given this, the reaction rate values predicted by Transition State Theory will possibly be larger than experimental values and Transition State Theory slightly overestimates the reaction rate of reactions.

==EXERCISE 2: F - H - H system==
===PES inspection===
[[file:jz14318_FHH_TS.png|300px|thumb|left|The PES plot for the F-H-H system. Atom A: F, atom B: H, atom C: H.]]

The H + HF reaction is endothermic, for the PES plot shows that the potential energy level of the reactants (AB + C) lies below the potential energy level of the products (BC + A). It can also be rationalised by the fact that the H-F bond being broken in the reaction is stronger than the H-H bond being formed, so it requires an amount of energy to initiate the reaction.

On the other hand, the reverse F + H2 reaction is exothermic, for the PES plot (see RHS) shows that the potential energy of the products (AB + C) is lower than the potential energy of the reactants (BC + A), so energy is released during the reaction. From the perspective of bond strength, a relatively weak H-H bond breaks whilst a strong H-F bond forms.

In order to locate the transition state of this reaction, according to Hammond's postulate, an endothermic reaction has a late transition state (i.e. the transition state resembles the products) and an exothermic reaction has an early transition state (i.e. the transition state resembles the reactants). Therefore, the transition state is closer to F + H2 side (i.e. AB distance is larger than BC distance). Unlike the previous H-H-H system, the F-H-H system is no longer symmetric and thus r1 is not equal to r2 at the transition state.

The approximate transition state was found to be r1 = 183.5 pm and r2 = 74 pm, which can be confirmed from the internuclear distance vs time plot below. The atoms are only slightly oscillating, which indicates that there is little force (close to zero) acting on the atoms and the gradient of potential is close to zero (i.e. the system now resembles transition state).
[[file:jz14318_FHH_distance.png|300px|The PES plot for the F-H-H system. Atom A: F, atom B: H, atom C: H.]]

===Finding activation energies===
In order to find the activation energy for both reactions, a "mep" was produced from a structure close to the transition state and an energy vs time plot was obtained with 2000 steps.

[[file:jz14318_FH2_EA.png|300px]]

The energy vs time plot (r1 = 180 pm, r2 = 70 pm) for the F + H2 reaction shows that the difference between the transition state and the products (H + HF) is approximately +123.95 kJ.mol-1, so the activation energy for the H + HF reaction is +123.95 kJ.mol-1.

[[file:jz14318_FHH_EA.png|300px]]

The energy vs time plot (r1 = 184 pm, r2 = 75 pm) for the H + HF reaction shows that there is little difference between the transition state and the products (F + H2). The activation energy for the F + H2 was found approximately 0.73 kJ.mol-1.

===Reaction dynamics===
[[file:jz14318_FHH_momenta.png|200px|thumb|left|Momenta vs time plot for the F + H2 reaction (r1 = 180 pm, r2 = 70 pm, p1 = p2 = -1 g.mol-1.pm.fs-1. Atom A: F, atom B: H, atom C: H.)]]
A reactive trajectory for the F + H2 reaction was found when r1 = 180 pm, r2 = 70 pm, p1 = p2 = -1 g.mol-1.pm.fs-1. As this reaction is exothermic, an amount of energy is released by interconverting potential energy to kinetic energy. It is observed from the animation of this reactive trajectory that after the product HF is formed, F-H bond is vibrating strongly. It can also be seen from the momenta vs time plot (see LHS) that the momentum of F-H is fluctuating fiercely, which also indicates that the formed F-H bond is strongly vibrating. Therefore, the reaction energy is released mainly by the vibrational energy of the product.

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.

==References==
1. Howard Anton, Irl Bivens, Stephen Davis (2002): "Calculus, Multivariable Version", p. 844.

2. J. I. Steinfeld, J. S. Francisco, W. L. Hase Chemical Kinetic and Dynamics 2nd ed., Prentice-Hall, 1998.

MRD:jz14318

2020-05-08T08:10:41Z

Jz14318: /* Reaction dynamics */

==EXERCISE 1: H + H2 system==
===Dynamics from the transition state region===
====Identification of transition state====
Transition state can be mathematically defined as the saddle point or the minimax point of the potential energy surface.1 The gradient of the potential is zero at the saddle point. As shown in the figure below, a saddle point has a positive second derivative (e.g. minimum) in one direction, and a negative second derivative (i.e. maximum) in the other direction. By contrast, the second derivative for a local minimum is positive in both directions.

{| class="wikitable" border="1"
! A representation of a saddle point on a graph !! Upward curvature along the orthogonal coordinate !! Downward curvature along the reaction coordinate
|-
| [[File:jz14318_saddle_point.png|260px]] || [[File:jz14318_saddle_minimum.png|260px]] || [[File:jz14318_saddle_maximum.png|260px]]
|}

====Trajectories from r1 = r2: locating the transition state====

[[file:Jz14318_TSposition_91.png|200px|thumb|left|Internuclear distance vs time plot when r1 = r2 = 90.5 pm.]]

[[file:jz14318_TS_surface.png|200px|thumb|right|Surface plot when r1 = r2 = 90.5 pm.]]

It is suggested that the transition state location rts = 90.5 pm. As the force acting on the atoms depends on the gradient of the potential energy surface, the system at the transition state will have no atoms oscillating as the gradient of the potential energy surface is zero. From the plot above, it can be seen that the atoms oscillate to a very small extent, which indicates that this system is very close to the transition state.

====Trajectories from r1 = rts+δ, r2 = rts====

[[file:jz14318_dynamics_92_91.png|200px|thumb|left|Contour plot by dynamics calculation. r1 = 92 pm, r2 = 91 pm, p1 = p2 = 0 g.mol-1.pm.fs-1.]]

[[file:jz14318_MEP_92_91.png|200px|thumb|right|Contour plot by MEP calculation. r1 = 92 pm, r2 = 91 pm, p1 = p2 = 0 g.mol-1.pm.fs-1.]]

It can be observed from the two plots that ''mep'' (see RHS) follows the valley floor to HA + HB - HC, whereas the trajectory by dynamics calculation (see LHS) is wavy (i.e. the atoms are vibrating). This is because by MEP calculation, the atoms do not vibrate as their momenta/velocities are always set to zero in each time step, whereas by dynamics calculation, the total energy is conserved and the atoms do vibrate.

===Reactive and unreactive trajectories===

{| class="wikitable" border="1"
! p1/ g.mol-1.pm.fs-1 !! p2/ g.mol-1.pm.fs-1 !! Etot/ kJ.mol-1 !! Reactive? !! Description of the dynamics !! Illustration of the trajectory
|-
| -2.56 || -5.1 || -414.28 || YES || HC approaches the vibrating HAHB molecule. The system crosses the transition state region and HA-HB bond starts to break whilst HB-HC bond starts to form. The product is thus formed. || [[File:jz14318_256_51_surface.png|180px]]
|-
| -3.1 || -4.1 || -420.08 || NO || HC approaches the vibrating HAHB molecule; however, the system does not manage to cross the transition state region so the original HA-HB bond does not break and the product does not form. HC moves far away from HAHB molecule. || [[File:jz14318_31_41_surface.png|180px]]
|-
| -3.1 || -5.1 || -413.98 || YES || HC slowly approaches the vibrating HAHB molecule. HB starts to move away from HA (HA-HB bond starts to break) and comes closer to HC (HB-HC bond starts to form). HBHC product is formed and HA moves away. || [[File:jz14318_31_51_surface.png|180px]]
|-
| -5.1 || -10.1 || -357.28 || NO || HC slowly approaches the vibrating HAHB molecule. HB-HC bond starts to form as the system crosses the transition state region. HBHC molecule vibrates strongly and HB-HC bond that previously formed breaks again and HB approaches back to HA, reforming HA-HB bond. So the system recrosses the TS region and reverts back to the reactants. || [[File:jz14318_51_101_surface.png|180px]]
|-
| -5.1 || -10.6 || -349.48 || YES || The system crosses the transition state region 3 times. The system forms the product initially, then reverts back to the reactants with strong vibration, and eventually reverts back to the products again. || [[File:jz14318_51_106_surface.png|180px]]
|}

It can be concluded from the table that not all trajectories having sufficient energy to react will be reactive due to the possibility of barrier recrossing.

====Transition State Theory====
Transition state theory assumes that all trajectories with a kinetic energy along the reaction coordinate larger than Ea will be reactive.2 However, compared with the previous experimental results, this assumption seems fallacious. Some reactions will be unreactive even though the trajectory has a sufficient kinetic energy due to the recrossing of barrier. The second factor is that Transition State Theory ignores the effect of quantum tunneling and treats the motion of atoms classically. Given this, the reaction rate values predicted by Transition State Theory will possibly be larger than experimental values and Transition State Theory slightly overestimates the reaction rate of reactions.

==EXERCISE 2: F - H - H system==
===PES inspection===
[[file:jz14318_FHH_TS.png|300px|thumb|left|The PES plot for the F-H-H system. Atom A: F, atom B: H, atom C: H.]]

The H + HF reaction is endothermic, for the PES plot shows that the potential energy level of the reactants (AB + C) lies below the potential energy level of the products (BC + A). It can also be rationalised by the fact that the H-F bond being broken in the reaction is stronger than the H-H bond being formed, so it requires an amount of energy to initiate the reaction.

On the other hand, the reverse F + H2 reaction is exothermic, for the PES plot (see RHS) shows that the potential energy of the products (AB + C) is lower than the potential energy of the reactants (BC + A), so energy is released during the reaction. From the perspective of bond strength, a relatively weak H-H bond breaks whilst a strong H-F bond forms.

In order to locate the transition state of this reaction, according to Hammond's postulate, an endothermic reaction has a late transition state (i.e. the transition state resembles the products) and an exothermic reaction has an early transition state (i.e. the transition state resembles the reactants). Therefore, the transition state is closer to F + H2 side (i.e. AB distance is larger than BC distance). Unlike the previous H-H-H system, the F-H-H system is no longer symmetric and thus r1 is not equal to r2 at the transition state.

The approximate transition state was found to be r1 = 183.5 pm and r2 = 74 pm, which can be confirmed from the internuclear distance vs time plot below. The atoms are only slightly oscillating, which indicates that there is little force (close to zero) acting on the atoms and the gradient of potential is close to zero (i.e. the system now resembles transition state).
[[file:jz14318_FHH_distance.png|300px|The PES plot for the F-H-H system. Atom A: F, atom B: H, atom C: H.]]

===Finding activation energies===
In order to find the activation energy for both reactions, a "mep" was produced from a structure close to the transition state and an energy vs time plot was obtained with 2000 steps.

[[file:jz14318_FH2_EA.png|300px]]

The energy vs time plot (r1 = 180 pm, r2 = 70 pm) for the F + H2 reaction shows that the difference between the transition state and the products (H + HF) is approximately +123.95 kJ.mol-1, so the activation energy for the H + HF reaction is +123.95 kJ.mol-1.

[[file:jz14318_FHH_EA.png|300px]]

The energy vs time plot (r1 = 184 pm, r2 = 75 pm) for the H + HF reaction shows that there is little difference between the transition state and the products (F + H2). The activation energy for the F + H2 was found approximately 0.73 kJ.mol-1.

===Reaction dynamics===
[[file:jz14318_FHH_momenta.png|300px|thumb|left|Momenta vs time plot for the F + H2 reaction (r1 = 180 pm, r2 = 70 pm, p1 = p2 = -1 g.mol-1.pm.fs-1. Atom A: F, atom B: H, atom C: H.)]]
A reactive trajectory for the F + H2 reaction was found when r1 = 180 pm, r2 = 70 pm, p1 = p2 = -1 g.mol-1.pm.fs-1. As this reaction is exothermic, an amount of energy is released by interconverting potential energy to kinetic energy. It is observed from the animation of this reactive trajectory that after the product HF is formed, F-H bond is vibrating strongly. It can also be seen from the momenta vs time plot (see LHS) that the momentum of F-H is fluctuating fiercely, which also indicates that the formed F-H bond is strongly vibrating. Therefore, the reaction energy is released mainly by the vibrational energy of the product.

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.

==References==
1. Howard Anton, Irl Bivens, Stephen Davis (2002): "Calculus, Multivariable Version", p. 844.

2. J. I. Steinfeld, J. S. Francisco, W. L. Hase Chemical Kinetic and Dynamics 2nd ed., Prentice-Hall, 1998.

File:Jz14318 FHH momenta.png

2020-05-08T07:56:08Z

Jz14318:

MRD:jz14318

2020-05-08T07:04:50Z

Jz14318: /* Reactive and unreactive trajectories */

==EXERCISE 1: H + H2 system==
===Dynamics from the transition state region===
====Identification of transition state====
Transition state can be mathematically defined as the saddle point or the minimax point of the potential energy surface.1 The gradient of the potential is zero at the saddle point. As shown in the figure below, a saddle point has a positive second derivative (e.g. minimum) in one direction, and a negative second derivative (i.e. maximum) in the other direction. By contrast, the second derivative for a local minimum is positive in both directions.

{| class="wikitable" border="1"
! A representation of a saddle point on a graph !! Upward curvature along the orthogonal coordinate !! Downward curvature along the reaction coordinate
|-
| [[File:jz14318_saddle_point.png|260px]] || [[File:jz14318_saddle_minimum.png|260px]] || [[File:jz14318_saddle_maximum.png|260px]]
|}

====Trajectories from r1 = r2: locating the transition state====

[[file:Jz14318_TSposition_91.png|200px|thumb|left|Internuclear distance vs time plot when r1 = r2 = 90.5 pm.]]

[[file:jz14318_TS_surface.png|200px|thumb|right|Surface plot when r1 = r2 = 90.5 pm.]]

It is suggested that the transition state location rts = 90.5 pm. As the force acting on the atoms depends on the gradient of the potential energy surface, the system at the transition state will have no atoms oscillating as the gradient of the potential energy surface is zero. From the plot above, it can be seen that the atoms oscillate to a very small extent, which indicates that this system is very close to the transition state.

====Trajectories from r1 = rts+δ, r2 = rts====

[[file:jz14318_dynamics_92_91.png|200px|thumb|left|Contour plot by dynamics calculation. r1 = 92 pm, r2 = 91 pm, p1 = p2 = 0 g.mol-1.pm.fs-1.]]

[[file:jz14318_MEP_92_91.png|200px|thumb|right|Contour plot by MEP calculation. r1 = 92 pm, r2 = 91 pm, p1 = p2 = 0 g.mol-1.pm.fs-1.]]

It can be observed from the two plots that ''mep'' (see RHS) follows the valley floor to HA + HB - HC, whereas the trajectory by dynamics calculation (see LHS) is wavy (i.e. the atoms are vibrating). This is because by MEP calculation, the atoms do not vibrate as their momenta/velocities are always set to zero in each time step, whereas by dynamics calculation, the total energy is conserved and the atoms do vibrate.

===Reactive and unreactive trajectories===

{| class="wikitable" border="1"
! p1/ g.mol-1.pm.fs-1 !! p2/ g.mol-1.pm.fs-1 !! Etot/ kJ.mol-1 !! Reactive? !! Description of the dynamics !! Illustration of the trajectory
|-
| -2.56 || -5.1 || -414.28 || YES || HC approaches the vibrating HAHB molecule. The system crosses the transition state region and HA-HB bond starts to break whilst HB-HC bond starts to form. The product is thus formed. || [[File:jz14318_256_51_surface.png|180px]]
|-
| -3.1 || -4.1 || -420.08 || NO || HC approaches the vibrating HAHB molecule; however, the system does not manage to cross the transition state region so the original HA-HB bond does not break and the product does not form. HC moves far away from HAHB molecule. || [[File:jz14318_31_41_surface.png|180px]]
|-
| -3.1 || -5.1 || -413.98 || YES || HC slowly approaches the vibrating HAHB molecule. HB starts to move away from HA (HA-HB bond starts to break) and comes closer to HC (HB-HC bond starts to form). HBHC product is formed and HA moves away. || [[File:jz14318_31_51_surface.png|180px]]
|-
| -5.1 || -10.1 || -357.28 || NO || HC slowly approaches the vibrating HAHB molecule. HB-HC bond starts to form as the system crosses the transition state region. HBHC molecule vibrates strongly and HB-HC bond that previously formed breaks again and HB approaches back to HA, reforming HA-HB bond. So the system recrosses the TS region and reverts back to the reactants. || [[File:jz14318_51_101_surface.png|180px]]
|-
| -5.1 || -10.6 || -349.48 || YES || The system crosses the transition state region 3 times. The system forms the product initially, then reverts back to the reactants with strong vibration, and eventually reverts back to the products again. || [[File:jz14318_51_106_surface.png|180px]]
|}

It can be concluded from the table that not all trajectories having sufficient energy to react will be reactive due to the possibility of barrier recrossing.

====Transition State Theory====
Transition state theory assumes that all trajectories with a kinetic energy along the reaction coordinate larger than Ea will be reactive.2 However, compared with the previous experimental results, this assumption seems fallacious. Some reactions will be unreactive even though the trajectory has a sufficient kinetic energy due to the recrossing of barrier. The second factor is that Transition State Theory ignores the effect of quantum tunneling and treats the motion of atoms classically. Given this, the reaction rate values predicted by Transition State Theory will possibly be larger than experimental values and Transition State Theory slightly overestimates the reaction rate of reactions.

==EXERCISE 2: F - H - H system==
===PES inspection===
[[file:jz14318_FHH_TS.png|300px|thumb|left|The PES plot for the F-H-H system. Atom A: F, atom B: H, atom C: H.]]

The H + HF reaction is endothermic, for the PES plot shows that the potential energy level of the reactants (AB + C) lies below the potential energy level of the products (BC + A). It can also be rationalised by the fact that the H-F bond being broken in the reaction is stronger than the H-H bond being formed, so it requires an amount of energy to initiate the reaction.

On the other hand, the reverse F + H2 reaction is exothermic, for the PES plot (see RHS) shows that the potential energy of the products (AB + C) is lower than the potential energy of the reactants (BC + A), so energy is released during the reaction. From the perspective of bond strength, a relatively weak H-H bond breaks whilst a strong H-F bond forms.

In order to locate the transition state of this reaction, according to Hammond's postulate, an endothermic reaction has a late transition state (i.e. the transition state resembles the products) and an exothermic reaction has an early transition state (i.e. the transition state resembles the reactants). Therefore, the transition state is closer to F + H2 side (i.e. AB distance is larger than BC distance). Unlike the previous H-H-H system, the F-H-H system is no longer symmetric and thus r1 is not equal to r2 at the transition state.

The approximate transition state was found to be r1 = 183.5 pm and r2 = 74 pm, which can be confirmed from the internuclear distance vs time plot below. The atoms are only slightly oscillating, which indicates that there is little force (close to zero) acting on the atoms and the gradient of potential is close to zero (i.e. the system now resembles transition state).
[[file:jz14318_FHH_distance.png|300px|The PES plot for the F-H-H system. Atom A: F, atom B: H, atom C: H.]]

===Finding activation energies===
In order to find the activation energy for both reactions, a "mep" was produced from a structure close to the transition state and an energy vs time plot was obtained with 2000 steps.

[[file:jz14318_FH2_EA.png|300px]]

The energy vs time plot (r1 = 180 pm, r2 = 70 pm) for the F + H2 reaction shows that the difference between the transition state and the products (H + HF) is approximately +123.95 kJ.mol-1, so the activation energy for the H + HF reaction is +123.95 kJ.mol-1.

[[file:jz14318_FHH_EA.png|300px]]

The energy vs time plot (r1 = 184 pm, r2 = 75 pm) for the H + HF reaction shows that there is little difference between the transition state and the products (F + H2). The activation energy for the F + H2 was found approximately 0.73 kJ.mol-1.

===Reaction dynamics===
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.

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.

==References==
1. Howard Anton, Irl Bivens, Stephen Davis (2002): "Calculus, Multivariable Version", p. 844.

2. J. I. Steinfeld, J. S. Francisco, W. L. Hase Chemical Kinetic and Dynamics 2nd ed., Prentice-Hall, 1998.

MRD:jz14318

2020-05-08T07:04:07Z

Jz14318: /* Finding activation energies */

==EXERCISE 1: H + H2 system==
===Dynamics from the transition state region===
====Identification of transition state====
Transition state can be mathematically defined as the saddle point or the minimax point of the potential energy surface.1 The gradient of the potential is zero at the saddle point. As shown in the figure below, a saddle point has a positive second derivative (e.g. minimum) in one direction, and a negative second derivative (i.e. maximum) in the other direction. By contrast, the second derivative for a local minimum is positive in both directions.

{| class="wikitable" border="1"
! A representation of a saddle point on a graph !! Upward curvature along the orthogonal coordinate !! Downward curvature along the reaction coordinate
|-
| [[File:jz14318_saddle_point.png|260px]] || [[File:jz14318_saddle_minimum.png|260px]] || [[File:jz14318_saddle_maximum.png|260px]]
|}

====Trajectories from r1 = r2: locating the transition state====

[[file:Jz14318_TSposition_91.png|200px|thumb|left|Internuclear distance vs time plot when r1 = r2 = 90.5 pm.]]

[[file:jz14318_TS_surface.png|200px|thumb|right|Surface plot when r1 = r2 = 90.5 pm.]]

It is suggested that the transition state location rts = 90.5 pm. As the force acting on the atoms depends on the gradient of the potential energy surface, the system at the transition state will have no atoms oscillating as the gradient of the potential energy surface is zero. From the plot above, it can be seen that the atoms oscillate to a very small extent, which indicates that this system is very close to the transition state.

====Trajectories from r1 = rts+δ, r2 = rts====

[[file:jz14318_dynamics_92_91.png|200px|thumb|left|Contour plot by dynamics calculation. r1 = 92 pm, r2 = 91 pm, p1 = p2 = 0 g.mol-1.pm.fs-1.]]

[[file:jz14318_MEP_92_91.png|200px|thumb|right|Contour plot by MEP calculation. r1 = 92 pm, r2 = 91 pm, p1 = p2 = 0 g.mol-1.pm.fs-1.]]

It can be observed from the two plots that ''mep'' (see RHS) follows the valley floor to HA + HB - HC, whereas the trajectory by dynamics calculation (see LHS) is wavy (i.e. the atoms are vibrating). This is because by MEP calculation, the atoms do not vibrate as their momenta/velocities are always set to zero in each time step, whereas by dynamics calculation, the total energy is conserved and the atoms do vibrate.

===Reactive and unreactive trajectories===

{| class="wikitable" border="1"
! p1/ g.mol-1.pm.fs-1 !! p2/ g.mol-1.pm.fs-1 !! Etot/ kJ.mol-1 !! Reactive? !! Description of the dynamics !! Illustration of the trajectory
|-
| -2.56 || -5.1 || -414.28 || YES || HC approaches the vibrating HAHB molecule. The system crosses the transition state region and HA-HB bond starts to break whilst HB-HC bond starts to form. The product is thus formed. || [[File:jz14318_256_51_surface.png|180px]]
|-
| -3.1 || -4.1 || -420.08 || NO || HC approaches the vibrating HAHB molecule; however, the system does not manage to cross the transition state region so the original HA-HB bond does not break and the product does not form. HC moves far away from HAHB molecule. || [[File:jz14318_31_41_surface.png|180px]]
|-
| -3.1 || -5.1 || -413.98 || YES || HC slowly approaches the vibrating HAHB molecule. HB starts to move away from HA (HA-HB bond starts to break) and comes closer to HC (HB-HC bond starts to form). HBHC product is formed and HA moves away. || [[File:jz14318_31_51_surface.png|180px]]
|-
| -5.1 || -10.1 || -357.28 || NO || HC slowly approaches the vibrating HAHB molecule. HB-HC bond starts to form as the system crosses the transition state region. HBHC molecule vibrates strongly and HB-HC bond that previously formed breaks again and HB approaches back to HA, reforming HA-HB bond. So the system recrosses the TS region and reverts back to the reactants. || [[File:jz14318_51_101_surface.png|180px]]
|-
| -5.1 || -10.6 || -349.48 || YES || The system crosses the transition state region 3 times. The system forms the product initially, then reverts back to the reactants with strong vibration, and eventually reverts back to the products again. || [[File:jz14318_51_106_surface.png|180px]]
|}

It can be concluded from the table that not all trajectories having sufficient energy to react will be reactive due to barrier recrossing.

====Transition State Theory====
Transition state theory assumes that all trajectories with a kinetic energy along the reaction coordinate larger than Ea will be reactive.2 However, compared with the previous experimental results, this assumption seems fallacious. Some reactions will be unreactive even though the trajectory has a sufficient kinetic energy due to the recrossing of barrier. The second factor is that Transition State Theory ignores the effect of quantum tunneling and treats the motion of atoms classically. Given this, the reaction rate values predicted by Transition State Theory will possibly be larger than experimental values and Transition State Theory slightly overestimates the reaction rate of reactions.

==EXERCISE 2: F - H - H system==
===PES inspection===
[[file:jz14318_FHH_TS.png|300px|thumb|left|The PES plot for the F-H-H system. Atom A: F, atom B: H, atom C: H.]]

The H + HF reaction is endothermic, for the PES plot shows that the potential energy level of the reactants (AB + C) lies below the potential energy level of the products (BC + A). It can also be rationalised by the fact that the H-F bond being broken in the reaction is stronger than the H-H bond being formed, so it requires an amount of energy to initiate the reaction.

On the other hand, the reverse F + H2 reaction is exothermic, for the PES plot (see RHS) shows that the potential energy of the products (AB + C) is lower than the potential energy of the reactants (BC + A), so energy is released during the reaction. From the perspective of bond strength, a relatively weak H-H bond breaks whilst a strong H-F bond forms.

In order to locate the transition state of this reaction, according to Hammond's postulate, an endothermic reaction has a late transition state (i.e. the transition state resembles the products) and an exothermic reaction has an early transition state (i.e. the transition state resembles the reactants). Therefore, the transition state is closer to F + H2 side (i.e. AB distance is larger than BC distance). Unlike the previous H-H-H system, the F-H-H system is no longer symmetric and thus r1 is not equal to r2 at the transition state.

The approximate transition state was found to be r1 = 183.5 pm and r2 = 74 pm, which can be confirmed from the internuclear distance vs time plot below. The atoms are only slightly oscillating, which indicates that there is little force (close to zero) acting on the atoms and the gradient of potential is close to zero (i.e. the system now resembles transition state).
[[file:jz14318_FHH_distance.png|300px|The PES plot for the F-H-H system. Atom A: F, atom B: H, atom C: H.]]

===Finding activation energies===
In order to find the activation energy for both reactions, a "mep" was produced from a structure close to the transition state and an energy vs time plot was obtained with 2000 steps.

[[file:jz14318_FH2_EA.png|300px]]

The energy vs time plot (r1 = 180 pm, r2 = 70 pm) for the F + H2 reaction shows that the difference between the transition state and the products (H + HF) is approximately +123.95 kJ.mol-1, so the activation energy for the H + HF reaction is +123.95 kJ.mol-1.

[[file:jz14318_FHH_EA.png|300px]]

The energy vs time plot (r1 = 184 pm, r2 = 75 pm) for the H + HF reaction shows that there is little difference between the transition state and the products (F + H2). The activation energy for the F + H2 was found approximately 0.73 kJ.mol-1.

===Reaction dynamics===
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.

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.

==References==
1. Howard Anton, Irl Bivens, Stephen Davis (2002): "Calculus, Multivariable Version", p. 844.

2. J. I. Steinfeld, J. S. Francisco, W. L. Hase Chemical Kinetic and Dynamics 2nd ed., Prentice-Hall, 1998.

MRD:jz14318

2020-05-08T07:03:46Z

Jz14318: /* Finding activation energies */

==EXERCISE 1: H + H2 system==
===Dynamics from the transition state region===
====Identification of transition state====
Transition state can be mathematically defined as the saddle point or the minimax point of the potential energy surface.1 The gradient of the potential is zero at the saddle point. As shown in the figure below, a saddle point has a positive second derivative (e.g. minimum) in one direction, and a negative second derivative (i.e. maximum) in the other direction. By contrast, the second derivative for a local minimum is positive in both directions.

{| class="wikitable" border="1"
! A representation of a saddle point on a graph !! Upward curvature along the orthogonal coordinate !! Downward curvature along the reaction coordinate
|-
| [[File:jz14318_saddle_point.png|260px]] || [[File:jz14318_saddle_minimum.png|260px]] || [[File:jz14318_saddle_maximum.png|260px]]
|}

====Trajectories from r1 = r2: locating the transition state====

[[file:Jz14318_TSposition_91.png|200px|thumb|left|Internuclear distance vs time plot when r1 = r2 = 90.5 pm.]]

[[file:jz14318_TS_surface.png|200px|thumb|right|Surface plot when r1 = r2 = 90.5 pm.]]

It is suggested that the transition state location rts = 90.5 pm. As the force acting on the atoms depends on the gradient of the potential energy surface, the system at the transition state will have no atoms oscillating as the gradient of the potential energy surface is zero. From the plot above, it can be seen that the atoms oscillate to a very small extent, which indicates that this system is very close to the transition state.

====Trajectories from r1 = rts+δ, r2 = rts====

[[file:jz14318_dynamics_92_91.png|200px|thumb|left|Contour plot by dynamics calculation. r1 = 92 pm, r2 = 91 pm, p1 = p2 = 0 g.mol-1.pm.fs-1.]]

[[file:jz14318_MEP_92_91.png|200px|thumb|right|Contour plot by MEP calculation. r1 = 92 pm, r2 = 91 pm, p1 = p2 = 0 g.mol-1.pm.fs-1.]]

It can be observed from the two plots that ''mep'' (see RHS) follows the valley floor to HA + HB - HC, whereas the trajectory by dynamics calculation (see LHS) is wavy (i.e. the atoms are vibrating). This is because by MEP calculation, the atoms do not vibrate as their momenta/velocities are always set to zero in each time step, whereas by dynamics calculation, the total energy is conserved and the atoms do vibrate.

===Reactive and unreactive trajectories===

{| class="wikitable" border="1"
! p1/ g.mol-1.pm.fs-1 !! p2/ g.mol-1.pm.fs-1 !! Etot/ kJ.mol-1 !! Reactive? !! Description of the dynamics !! Illustration of the trajectory
|-
| -2.56 || -5.1 || -414.28 || YES || HC approaches the vibrating HAHB molecule. The system crosses the transition state region and HA-HB bond starts to break whilst HB-HC bond starts to form. The product is thus formed. || [[File:jz14318_256_51_surface.png|180px]]
|-
| -3.1 || -4.1 || -420.08 || NO || HC approaches the vibrating HAHB molecule; however, the system does not manage to cross the transition state region so the original HA-HB bond does not break and the product does not form. HC moves far away from HAHB molecule. || [[File:jz14318_31_41_surface.png|180px]]
|-
| -3.1 || -5.1 || -413.98 || YES || HC slowly approaches the vibrating HAHB molecule. HB starts to move away from HA (HA-HB bond starts to break) and comes closer to HC (HB-HC bond starts to form). HBHC product is formed and HA moves away. || [[File:jz14318_31_51_surface.png|180px]]
|-
| -5.1 || -10.1 || -357.28 || NO || HC slowly approaches the vibrating HAHB molecule. HB-HC bond starts to form as the system crosses the transition state region. HBHC molecule vibrates strongly and HB-HC bond that previously formed breaks again and HB approaches back to HA, reforming HA-HB bond. So the system recrosses the TS region and reverts back to the reactants. || [[File:jz14318_51_101_surface.png|180px]]
|-
| -5.1 || -10.6 || -349.48 || YES || The system crosses the transition state region 3 times. The system forms the product initially, then reverts back to the reactants with strong vibration, and eventually reverts back to the products again. || [[File:jz14318_51_106_surface.png|180px]]
|}

It can be concluded from the table that not all trajectories having sufficient energy to react will be reactive due to barrier recrossing.

====Transition State Theory====
Transition state theory assumes that all trajectories with a kinetic energy along the reaction coordinate larger than Ea will be reactive.2 However, compared with the previous experimental results, this assumption seems fallacious. Some reactions will be unreactive even though the trajectory has a sufficient kinetic energy due to the recrossing of barrier. The second factor is that Transition State Theory ignores the effect of quantum tunneling and treats the motion of atoms classically. Given this, the reaction rate values predicted by Transition State Theory will possibly be larger than experimental values and Transition State Theory slightly overestimates the reaction rate of reactions.

==EXERCISE 2: F - H - H system==
===PES inspection===
[[file:jz14318_FHH_TS.png|300px|thumb|left|The PES plot for the F-H-H system. Atom A: F, atom B: H, atom C: H.]]

The H + HF reaction is endothermic, for the PES plot shows that the potential energy level of the reactants (AB + C) lies below the potential energy level of the products (BC + A). It can also be rationalised by the fact that the H-F bond being broken in the reaction is stronger than the H-H bond being formed, so it requires an amount of energy to initiate the reaction.

On the other hand, the reverse F + H2 reaction is exothermic, for the PES plot (see RHS) shows that the potential energy of the products (AB + C) is lower than the potential energy of the reactants (BC + A), so energy is released during the reaction. From the perspective of bond strength, a relatively weak H-H bond breaks whilst a strong H-F bond forms.

In order to locate the transition state of this reaction, according to Hammond's postulate, an endothermic reaction has a late transition state (i.e. the transition state resembles the products) and an exothermic reaction has an early transition state (i.e. the transition state resembles the reactants). Therefore, the transition state is closer to F + H2 side (i.e. AB distance is larger than BC distance). Unlike the previous H-H-H system, the F-H-H system is no longer symmetric and thus r1 is not equal to r2 at the transition state.

The approximate transition state was found to be r1 = 183.5 pm and r2 = 74 pm, which can be confirmed from the internuclear distance vs time plot below. The atoms are only slightly oscillating, which indicates that there is little force (close to zero) acting on the atoms and the gradient of potential is close to zero (i.e. the system now resembles transition state).
[[file:jz14318_FHH_distance.png|300px|The PES plot for the F-H-H system. Atom A: F, atom B: H, atom C: H.]]

===Finding activation energies===
In order to find the activation energy for both reactions, a "mep" was produced from a structure close to the transition state and an energy vs time plot was obtained with 2000 steps.

[[file:jz14318_FH2_EA.png|300px]]
The energy vs time plot (r1 = 180 pm, r2 = 70 pm) for the F + H2 reaction shows that the difference between the transition state and the products (H + HF) is approximately +123.95 kJ.mol-1, so the activation energy for the H + HF reaction is +123.95 kJ.mol-1.

[[file:jz14318_FHH_EA.png|300px]]
The energy vs time plot (r1 = 184 pm, r2 = 75 pm) for the H + HF reaction shows that there is little difference between the transition state and the products (F + H2). The activation energy for the F + H2 was found approximately 0.73 kJ.mol-1.

===Reaction dynamics===
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.

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.

==References==
1. Howard Anton, Irl Bivens, Stephen Davis (2002): "Calculus, Multivariable Version", p. 844.

2. J. I. Steinfeld, J. S. Francisco, W. L. Hase Chemical Kinetic and Dynamics 2nd ed., Prentice-Hall, 1998.

File:Jz14318 FHH EA.png

2020-05-08T06:27:31Z

Jz14318:

MRD:jz14318

2020-05-07T10:28:32Z

Jz14318: /* EXERCISE 1: H + H2 system */

File:Jz14318 saddle maximum.png

2020-05-07T10:28:10Z

Jz14318: