MRD:01496067HYT

2020-05-08T13:00:15Z

Yh9718: /* H + HF */

== H + H2 system ==

[[File:Rts_HHH_01496067.png|thumb| internuclear distance vs time plot at r1 = r2 = rts = 90.774 pm|250px]]
The transition state is mathematically defined as the saddle point of a surface plot. To distinguish the transition state from the local minimum, check that if it is a maximum on another set of axis which is perpendicular to the original axis.

The best estimated rts is 90.774 pm. As seen that the internuclear distance vs time plot show three straight horizontal lines (where AB and BC distance overlap), which suggests that the atoms are in the energy stationary point, and no oscillation is occurring.

The MEP ignores the kinetic energy of the atoms, hence no oscillation is observed in the mep plot, and it only shows the minumum energy path that the system go through while proceeding the reaction; whereas in the actual trajectory, the atoms do oscillate due to conservation of energy. The energy released after passing the activation energy barrier is converted to kinetic energy of the particles, hence the molecule vibrates and shows a curly path in the trajectory.

{| class="wikitable" border="1"
|+ r1 = 91.774 pm, r2 = 90.774 pm, p1= 0 g.mol-1.pm.fs-1, p2= 0 g.mol-1.pm.fs-1
! Type of Calculation !! Countour Plot !! Momentum vs time Plot
|-
| MEP || [[File:HHH_91_0_90_0_2000_0.1_countour_mep.png|200px]] || [[File:HHH_91_0_90_0_2000_0.1_momentum_mep.png|200px]]
|-
| dynamics || [[File:HHH_91_0_90_0_2000_0.1_countour_dynamics.png|200px]] || [[File:HHH_91_0_90_0_2000_0.1_momentum_dynamics.png|200px]]
|}

The transition state theory neglects the fact that the product and the reactant are interconvertible,<ref name="Transition Theory" /> hence it would overestimate the rate of the reaction slightly. The reversibility of the reaction reduces the rate of the forward reaction.

{| class="wikitable" border="1"
|+ Reaction Trajectories at r1 = 74 pm and r2 = 200 pm with different momenta
! p1 g.mol-1.pm.fs-1 !! p2 g.mol-1.pm.fs-1!! Etot kJ.mol-1 !! Reactive? !! Description of the dynamics !! colspan="2" | Illustration of the trajectory
|-
| style="text-align: center;"|-2.56 ||style="text-align: center;"| -5.1 ||style="text-align: center;"| -414.28 ||style="text-align: center;"| yes || H2 molecule (AB) slowly approaches to an H atom (C), and the H2 molecule (AB) dissociates, forming a new H atom (A) and H2 molecule (BC).|| [[File:-2.56_-5.1_HHH_01496067.png|200px]] || [[File:-2.56-5.1_HHH_01496067.png|200px]]
|-
|style="text-align: center;"| -3.1 ||style="text-align: center;"| -4.1 || style="text-align: center;"|-420.077 || style="text-align: center;"|no || A vibrating molecule H2 (AB) approaches an H atom (C), and before they reach each other, both the H2 molecule and H atom bounces back. No reaction takes place. || [[File:-3.1_-4.1_HHH_01496067.png|200px]] || [[File:-3.1-4.1_HHH_01496067.png|200px]]
|-
| style="text-align: center;"|-3.1 || style="text-align: center;"|-5.1 ||style="text-align: center;"| -413.977 || style="text-align: center;"|yes || A vibrating molecule H2 (AB) approaches an H atom (C), and before as reach each other, the H(A)-H(B) bond breaks, H(B)-H(C) bond forms. Both the H atom (A) and the H2 molecule (BC) move in direction opposite to their initial direction, and H2 molecule (BC) vibrates. || [[File:-3.1_-5.1_HHH_01496067.png|200px]] || [[File:-3.1-5.1_HHH_01496067.png|200px]]
|-
| style="text-align: center;"|-5.1 || style="text-align: center;"|-10.1 || style="text-align: center;"|-357.277 || style="text-align: center;"|no || A vibrating molecule H2 (AB) approaches an H atom (C), and the H(A)-H(B) bond breaks, the H(B)-H(C) bond forms. The newly formed H2 molecule (BC) vibrates so violently that as the H(B) atom in the molecule reaches the H(A) atom, it reforms the H2 molecule (AB) and an H atom (C). Overall no reaction takes place. || [[File:-5.1_-10.1_HHH_01496067.png|200px]] || [[File:-5.1-10.1_HHH_01496067.png|200px]]
|-
| style="text-align: center;"|-5.1 || style="text-align: center;"|-10.6 || style="text-align: center;"|-349.477 || style="text-align: center;"|yes || A vibrating molecule H2 (AB) approaches an H atom (C), and the H(A)-H(B) bond breaks, the H(B)-H(C) bond forms. The newly formed H2 molecule (BC) vibrates so violently that as the H(B) atom in the molecule reaches the H(A) atom, it reforms the H2 molecule (AB) and an H atom (C). The reformed H2 molecule (AB) vibrates once and the H(B) atom is reattracted to the H(C) atom, forming the H2 molecule (BC) again. || [[File:-5.1_-10.6_HHH_01496067.png|200px]] || [[File:-5.1-10.6_HHH_01496067.png|200px]]
|-
|}

A brief conclusion can be drawn that the a greater momentum does not always lead to a reactive trajectory. There need to be a balance between the translational energy and vibrational energy for the reaction to be successful.

== F - H - H system ==
=== PES inspection ===
[[File:Surface_plot_FHH_01496067.png|250px|thumb|A surface plot of the F-H-H system, where A=F, B=C=H]]
A potential surface plot is drawn, were AB is the F-H distance and BC is the H-H distance.
As shown in the plot, at low FH distance (i.e. A FH + H state), the potential energy is lower; at low HH distance (i.e. a H2 + F state), the potential energy is higher. This suggests that the reaction FH + H -> F + H2 is endothermic, and the reaction F + H2 -> FH + H is exothermic. From the thermodynamic nature of the reaction, it can be clearly seen that the F-H bond is much stronger than the H-H bond. The reaction FH + H -> F + H2 is endothermic, which suggests that the energy required for breaking the F-H bond is greater than the energy released when forming the H-H bond, hence a conclusion can be drawn that the F-H bond is stronger than the H-H bond.

The transition state position of the reaction is found at rFH=181.250 pm, rHH=74.484 pm shown as a dot in the surface plot.

==== F + H2 ====

F + H2 -> HF + H

Overall exothermic reaction. The activation energy could be found by the difference between minimum potential energy calculated by MEP at H-F bond length which deviates from the transition state H-F bond length for 1 pm and the transition state potential energy.

As a result, the activation energy of this reaction is -433.981 kJ.mol-1 - (-435.067 kJ.mol-1) = 1.086 kJ.mol-1

{| class="wikitable" border="1"
|+ MEP when pFH = pHH = 0 g.mol-1.pm.fs-1
! rFH pm !! rHH pm !! Contour plot !! Energy vs Time plot
|-
| 181.250 || 75.484 || [[File:FHH_181_0_75_0_1000_1_contour_mep.png|200px]] || [[File:FHH_181_0_75_0_1000_1_energy_mep.png|200px]]
|}

The H-H bond length was found to be 73.999 pm.

==== H + HF ====

HF + H -> F + H2

Overall endothermic reaction. The activation energy could be found by the difference between minimum potential energy calculated by MEP at H-H bond length which deviates from the transition state H-H bond length for 1 pm and the transition state potential energy.

As a result, the activation energy of this reaction is -433.981 kJ.mol-1 - (-560.583 kJ.mol-1) = 126.602 kJ.mol-1

{| class="wikitable" border="1"
|+ MEP when pFH = pHH = 0 g.mol-1.pm.fs-1
! rFH pm !! rHH pm !! Contour plot !! Energy vs Time plot
|-
| 180.250 || 74.484 || [[File:FHH_180_0_74_0_1000_0.4_contour_mep.png|200px]] || [[File:FHH_180_0_74_0_1000_0.4_energy_mep.png|200px]]
|}

The H-F bond length is found to be 91.997 pm.

=== Reaction Dynamics ===

The necessary initial condition for the reaction F + H2 to take place is that the F-H distance is smaller than the transition state F-H distance. (i.e. rFH < 181.250 pm) It can be observed from the momentum vs time graph that if the reaction feasible, eventually the system would consist of a vibrating molecule and a translating atom. As a result, the excess reaction energy is released as vibrational energy. This could be determined by infrared spectroscopy. When the system lies towards the reactant side, less vibrational energy is present in the system. The most populated vibrational state would be the ground state, and the IR absorption spectrum will show a few overtones which corresponds to population to higher vibrational states. As the system moves toward the product side, the energy initially put in to overcome the activation barrier is converted to the vibrational energy. As a result, more states could be populated and hence more overtones would be observed in the spectrum.

{| class="wikitable" border="1"
|+ caption
!rFH pm !! rHH pm !! pFH g.mol-1.pm.fs-1 !! pHH g.mol-1.pm.fs-1!! Etot kJ.mol-1 !! Reactive? !! | Illustration of the trajectory
|-
| rowspan="13" | 180 || rowspan="13" | 74 || rowspan="13" | -1|| -6.1 || -402.321 ||style="text-align: center;"| yes || sth
|-
| -5.1 || -412.501 ||style="text-align: center;"| no || sth
|-
| -4.1 || -420.701 ||style="text-align: center;"| yes || sth
|-
| -3.1 || -426.901 ||style="text-align: center;"| yes || sth
|-
| -2.1 || -431.101 ||style="text-align: center;"| yes || sth
|-
| -1.1 || -433.301 ||style="text-align: center;"| yes || sth
|-
| 0.1 || -433.301 ||style="text-align: center;"| no || sth
|-
| 1.1 || -431.101 ||style="text-align: center;"| yes || sth
|-
| 2.1 || -426.901 ||style="text-align: center;"| no || sth
|-
| 3.1 || -420.701 ||style="text-align: center;"| no || sth
|-
| 4.1 || -412.501 ||style="text-align: center;"| no || sth
|-
| 5.1 || -402.301 ||style="text-align: center;"| yes || sth
|-
| 6.1 || -390.101 ||style="text-align: center;"| no || sth
|-
|}

== References ==

<ref name="Transition Theory">Steinfeld J, Francisco J, Hase W. Chemical kinetics and dynamics. 2nd ed. Upper Saddle River: Prentice Hall; 1998.</reference>

MRD:01496067HYT

2020-05-08T12:57:33Z

Yh9718: /* F + H2 */

== H + H2 system ==

[[File:Rts_HHH_01496067.png|thumb| internuclear distance vs time plot at r1 = r2 = rts = 90.774 pm|250px]]
The transition state is mathematically defined as the saddle point of a surface plot. To distinguish the transition state from the local minimum, check that if it is a maximum on another set of axis which is perpendicular to the original axis.

The best estimated rts is 90.774 pm. As seen that the internuclear distance vs time plot show three straight horizontal lines (where AB and BC distance overlap), which suggests that the atoms are in the energy stationary point, and no oscillation is occurring.

The MEP ignores the kinetic energy of the atoms, hence no oscillation is observed in the mep plot, and it only shows the minumum energy path that the system go through while proceeding the reaction; whereas in the actual trajectory, the atoms do oscillate due to conservation of energy. The energy released after passing the activation energy barrier is converted to kinetic energy of the particles, hence the molecule vibrates and shows a curly path in the trajectory.

{| class="wikitable" border="1"
|+ r1 = 91.774 pm, r2 = 90.774 pm, p1= 0 g.mol-1.pm.fs-1, p2= 0 g.mol-1.pm.fs-1
! Type of Calculation !! Countour Plot !! Momentum vs time Plot
|-
| MEP || [[File:HHH_91_0_90_0_2000_0.1_countour_mep.png|200px]] || [[File:HHH_91_0_90_0_2000_0.1_momentum_mep.png|200px]]
|-
| dynamics || [[File:HHH_91_0_90_0_2000_0.1_countour_dynamics.png|200px]] || [[File:HHH_91_0_90_0_2000_0.1_momentum_dynamics.png|200px]]
|}

The transition state theory neglects the fact that the product and the reactant are interconvertible,<ref name="Transition Theory" /> hence it would overestimate the rate of the reaction slightly. The reversibility of the reaction reduces the rate of the forward reaction.

{| class="wikitable" border="1"
|+ Reaction Trajectories at r1 = 74 pm and r2 = 200 pm with different momenta
! p1 g.mol-1.pm.fs-1 !! p2 g.mol-1.pm.fs-1!! Etot kJ.mol-1 !! Reactive? !! Description of the dynamics !! colspan="2" | Illustration of the trajectory
|-
| style="text-align: center;"|-2.56 ||style="text-align: center;"| -5.1 ||style="text-align: center;"| -414.28 ||style="text-align: center;"| yes || H2 molecule (AB) slowly approaches to an H atom (C), and the H2 molecule (AB) dissociates, forming a new H atom (A) and H2 molecule (BC).|| [[File:-2.56_-5.1_HHH_01496067.png|200px]] || [[File:-2.56-5.1_HHH_01496067.png|200px]]
|-
|style="text-align: center;"| -3.1 ||style="text-align: center;"| -4.1 || style="text-align: center;"|-420.077 || style="text-align: center;"|no || A vibrating molecule H2 (AB) approaches an H atom (C), and before they reach each other, both the H2 molecule and H atom bounces back. No reaction takes place. || [[File:-3.1_-4.1_HHH_01496067.png|200px]] || [[File:-3.1-4.1_HHH_01496067.png|200px]]
|-
| style="text-align: center;"|-3.1 || style="text-align: center;"|-5.1 ||style="text-align: center;"| -413.977 || style="text-align: center;"|yes || A vibrating molecule H2 (AB) approaches an H atom (C), and before as reach each other, the H(A)-H(B) bond breaks, H(B)-H(C) bond forms. Both the H atom (A) and the H2 molecule (BC) move in direction opposite to their initial direction, and H2 molecule (BC) vibrates. || [[File:-3.1_-5.1_HHH_01496067.png|200px]] || [[File:-3.1-5.1_HHH_01496067.png|200px]]
|-
| style="text-align: center;"|-5.1 || style="text-align: center;"|-10.1 || style="text-align: center;"|-357.277 || style="text-align: center;"|no || A vibrating molecule H2 (AB) approaches an H atom (C), and the H(A)-H(B) bond breaks, the H(B)-H(C) bond forms. The newly formed H2 molecule (BC) vibrates so violently that as the H(B) atom in the molecule reaches the H(A) atom, it reforms the H2 molecule (AB) and an H atom (C). Overall no reaction takes place. || [[File:-5.1_-10.1_HHH_01496067.png|200px]] || [[File:-5.1-10.1_HHH_01496067.png|200px]]
|-
| style="text-align: center;"|-5.1 || style="text-align: center;"|-10.6 || style="text-align: center;"|-349.477 || style="text-align: center;"|yes || A vibrating molecule H2 (AB) approaches an H atom (C), and the H(A)-H(B) bond breaks, the H(B)-H(C) bond forms. The newly formed H2 molecule (BC) vibrates so violently that as the H(B) atom in the molecule reaches the H(A) atom, it reforms the H2 molecule (AB) and an H atom (C). The reformed H2 molecule (AB) vibrates once and the H(B) atom is reattracted to the H(C) atom, forming the H2 molecule (BC) again. || [[File:-5.1_-10.6_HHH_01496067.png|200px]] || [[File:-5.1-10.6_HHH_01496067.png|200px]]
|-
|}

A brief conclusion can be drawn that the a greater momentum does not always lead to a reactive trajectory. There need to be a balance between the translational energy and vibrational energy for the reaction to be successful.

== F - H - H system ==
=== PES inspection ===
[[File:Surface_plot_FHH_01496067.png|250px|thumb|A surface plot of the F-H-H system, where A=F, B=C=H]]
A potential surface plot is drawn, were AB is the F-H distance and BC is the H-H distance.
As shown in the plot, at low FH distance (i.e. A FH + H state), the potential energy is lower; at low HH distance (i.e. a H2 + F state), the potential energy is higher. This suggests that the reaction FH + H -> F + H2 is endothermic, and the reaction F + H2 -> FH + H is exothermic. From the thermodynamic nature of the reaction, it can be clearly seen that the F-H bond is much stronger than the H-H bond. The reaction FH + H -> F + H2 is endothermic, which suggests that the energy required for breaking the F-H bond is greater than the energy released when forming the H-H bond, hence a conclusion can be drawn that the F-H bond is stronger than the H-H bond.

The transition state position of the reaction is found at rFH=181.250 pm, rHH=74.484 pm shown as a dot in the surface plot.

==== F + H2 ====

F + H2 -> HF + H

Overall exothermic reaction. The activation energy could be found by the difference between minimum potential energy calculated by MEP at H-F bond length which deviates from the transition state H-F bond length for 1 pm and the transition state potential energy.

As a result, the activation energy of this reaction is -433.981 kJ.mol-1 - (-435.067 kJ.mol-1) = 1.086 kJ.mol-1

{| class="wikitable" border="1"
|+ MEP when pFH = pHH = 0 g.mol-1.pm.fs-1
! rFH pm !! rHH pm !! Contour plot !! Energy vs Time plot
|-
| 181.250 || 75.484 || [[File:FHH_181_0_75_0_1000_1_contour_mep.png|200px]] || [[File:FHH_181_0_75_0_1000_1_energy_mep.png|200px]]
|}

The H-H bond length was found to be 73.999 pm.

==== H + HF ====

HF + H -> F + H2

Overall endothermic reaction. The activation energy could be found by the difference between minimum potential energy calculated by MEP at H-H bond length which deviates from the transition state H-H bond length for 1 pm and the transition state potential energy.

As a result, the activation energy of this reaction is -433.981 kJ.mol-1 - (-560.583 kJ.mol-1) = 126.602 kJ.mol-1

{| class="wikitable" border="1"
|+ MEP when p1 = p2 = 0 g.mol-1.pm.fs-1
! r1 pm !! r2 pm !! Contour plot !! Energy vs Time plot
|-
| 180.250 || 74.484 || [[File:FHH_180_0_74_0_1000_0.4_contour_mep.png|200px]] || [[File:FHH_180_0_74_0_1000_0.4_energy_mep.png|200px]]
|}

The H-F bond length is found to be 91.997 pm.

=== Reaction Dynamics ===

The necessary initial condition for the reaction F + H2 to take place is that the F-H distance is smaller than the transition state F-H distance. (i.e. rFH < 181.250 pm) It can be observed from the momentum vs time graph that if the reaction feasible, eventually the system would consist of a vibrating molecule and a translating atom. As a result, the excess reaction energy is released as vibrational energy. This could be determined by infrared spectroscopy. When the system lies towards the reactant side, less vibrational energy is present in the system. The most populated vibrational state would be the ground state, and the IR absorption spectrum will show a few overtones which corresponds to population to higher vibrational states. As the system moves toward the product side, the energy initially put in to overcome the activation barrier is converted to the vibrational energy. As a result, more states could be populated and hence more overtones would be observed in the spectrum.

{| class="wikitable" border="1"
|+ caption
!rFH pm !! rHH pm !! pFH g.mol-1.pm.fs-1 !! pHH g.mol-1.pm.fs-1!! Etot kJ.mol-1 !! Reactive? !! | Illustration of the trajectory
|-
| rowspan="13" | 180 || rowspan="13" | 74 || rowspan="13" | -1|| -6.1 || -402.321 ||style="text-align: center;"| yes || sth
|-
| -5.1 || -412.501 ||style="text-align: center;"| no || sth
|-
| -4.1 || -420.701 ||style="text-align: center;"| yes || sth
|-
| -3.1 || -426.901 ||style="text-align: center;"| yes || sth
|-
| -2.1 || -431.101 ||style="text-align: center;"| yes || sth
|-
| -1.1 || -433.301 ||style="text-align: center;"| yes || sth
|-
| 0.1 || -433.301 ||style="text-align: center;"| no || sth
|-
| 1.1 || -431.101 ||style="text-align: center;"| yes || sth
|-
| 2.1 || -426.901 ||style="text-align: center;"| no || sth
|-
| 3.1 || -420.701 ||style="text-align: center;"| no || sth
|-
| 4.1 || -412.501 ||style="text-align: center;"| no || sth
|-
| 5.1 || -402.301 ||style="text-align: center;"| yes || sth
|-
| 6.1 || -390.101 ||style="text-align: center;"| no || sth
|-
|}

== References ==

<ref name="Transition Theory">Steinfeld J, Francisco J, Hase W. Chemical kinetics and dynamics. 2nd ed. Upper Saddle River: Prentice Hall; 1998.</reference>

MRD:01496067HYT

2020-05-08T12:52:27Z

Yh9718: /* H + HF */

== H + H2 system ==

[[File:Rts_HHH_01496067.png|thumb| internuclear distance vs time plot at r1 = r2 = rts = 90.774 pm|250px]]
The transition state is mathematically defined as the saddle point of a surface plot. To distinguish the transition state from the local minimum, check that if it is a maximum on another set of axis which is perpendicular to the original axis.

The best estimated rts is 90.774 pm. As seen that the internuclear distance vs time plot show three straight horizontal lines (where AB and BC distance overlap), which suggests that the atoms are in the energy stationary point, and no oscillation is occurring.

The MEP ignores the kinetic energy of the atoms, hence no oscillation is observed in the mep plot, and it only shows the minumum energy path that the system go through while proceeding the reaction; whereas in the actual trajectory, the atoms do oscillate due to conservation of energy. The energy released after passing the activation energy barrier is converted to kinetic energy of the particles, hence the molecule vibrates and shows a curly path in the trajectory.

{| class="wikitable" border="1"
|+ r1 = 91.774 pm, r2 = 90.774 pm, p1= 0 g.mol-1.pm.fs-1, p2= 0 g.mol-1.pm.fs-1
! Type of Calculation !! Countour Plot !! Momentum vs time Plot
|-
| MEP || [[File:HHH_91_0_90_0_2000_0.1_countour_mep.png|200px]] || [[File:HHH_91_0_90_0_2000_0.1_momentum_mep.png|200px]]
|-
| dynamics || [[File:HHH_91_0_90_0_2000_0.1_countour_dynamics.png|200px]] || [[File:HHH_91_0_90_0_2000_0.1_momentum_dynamics.png|200px]]
|}

The transition state theory neglects the fact that the product and the reactant are interconvertible,<ref name="Transition Theory" /> hence it would overestimate the rate of the reaction slightly. The reversibility of the reaction reduces the rate of the forward reaction.

{| class="wikitable" border="1"
|+ Reaction Trajectories at r1 = 74 pm and r2 = 200 pm with different momenta
! p1 g.mol-1.pm.fs-1 !! p2 g.mol-1.pm.fs-1!! Etot kJ.mol-1 !! Reactive? !! Description of the dynamics !! colspan="2" | Illustration of the trajectory
|-
| style="text-align: center;"|-2.56 ||style="text-align: center;"| -5.1 ||style="text-align: center;"| -414.28 ||style="text-align: center;"| yes || H2 molecule (AB) slowly approaches to an H atom (C), and the H2 molecule (AB) dissociates, forming a new H atom (A) and H2 molecule (BC).|| [[File:-2.56_-5.1_HHH_01496067.png|200px]] || [[File:-2.56-5.1_HHH_01496067.png|200px]]
|-
|style="text-align: center;"| -3.1 ||style="text-align: center;"| -4.1 || style="text-align: center;"|-420.077 || style="text-align: center;"|no || A vibrating molecule H2 (AB) approaches an H atom (C), and before they reach each other, both the H2 molecule and H atom bounces back. No reaction takes place. || [[File:-3.1_-4.1_HHH_01496067.png|200px]] || [[File:-3.1-4.1_HHH_01496067.png|200px]]
|-
| style="text-align: center;"|-3.1 || style="text-align: center;"|-5.1 ||style="text-align: center;"| -413.977 || style="text-align: center;"|yes || A vibrating molecule H2 (AB) approaches an H atom (C), and before as reach each other, the H(A)-H(B) bond breaks, H(B)-H(C) bond forms. Both the H atom (A) and the H2 molecule (BC) move in direction opposite to their initial direction, and H2 molecule (BC) vibrates. || [[File:-3.1_-5.1_HHH_01496067.png|200px]] || [[File:-3.1-5.1_HHH_01496067.png|200px]]
|-
| style="text-align: center;"|-5.1 || style="text-align: center;"|-10.1 || style="text-align: center;"|-357.277 || style="text-align: center;"|no || A vibrating molecule H2 (AB) approaches an H atom (C), and the H(A)-H(B) bond breaks, the H(B)-H(C) bond forms. The newly formed H2 molecule (BC) vibrates so violently that as the H(B) atom in the molecule reaches the H(A) atom, it reforms the H2 molecule (AB) and an H atom (C). Overall no reaction takes place. || [[File:-5.1_-10.1_HHH_01496067.png|200px]] || [[File:-5.1-10.1_HHH_01496067.png|200px]]
|-
| style="text-align: center;"|-5.1 || style="text-align: center;"|-10.6 || style="text-align: center;"|-349.477 || style="text-align: center;"|yes || A vibrating molecule H2 (AB) approaches an H atom (C), and the H(A)-H(B) bond breaks, the H(B)-H(C) bond forms. The newly formed H2 molecule (BC) vibrates so violently that as the H(B) atom in the molecule reaches the H(A) atom, it reforms the H2 molecule (AB) and an H atom (C). The reformed H2 molecule (AB) vibrates once and the H(B) atom is reattracted to the H(C) atom, forming the H2 molecule (BC) again. || [[File:-5.1_-10.6_HHH_01496067.png|200px]] || [[File:-5.1-10.6_HHH_01496067.png|200px]]
|-
|}

A brief conclusion can be drawn that the a greater momentum does not always lead to a reactive trajectory. There need to be a balance between the translational energy and vibrational energy for the reaction to be successful.

== F - H - H system ==
=== PES inspection ===
[[File:Surface_plot_FHH_01496067.png|250px|thumb|A surface plot of the F-H-H system, where A=F, B=C=H]]
A potential surface plot is drawn, were AB is the F-H distance and BC is the H-H distance.
As shown in the plot, at low FH distance (i.e. A FH + H state), the potential energy is lower; at low HH distance (i.e. a H2 + F state), the potential energy is higher. This suggests that the reaction FH + H -> F + H2 is endothermic, and the reaction F + H2 -> FH + H is exothermic. From the thermodynamic nature of the reaction, it can be clearly seen that the F-H bond is much stronger than the H-H bond. The reaction FH + H -> F + H2 is endothermic, which suggests that the energy required for breaking the F-H bond is greater than the energy released when forming the H-H bond, hence a conclusion can be drawn that the F-H bond is stronger than the H-H bond.

The transition state position of the reaction is found at rFH=181.250 pm, rHH=74.484 pm shown as a dot in the surface plot.

==== F + H2 ====

F + H2 -> HF + H

Overall exothermic reaction. The activation energy could be found by the difference between minimum potential energy calculated by MEP at H-F bond length which deviates from the transition state H-F bond length for 1 pm and the transition state potential energy.

As a result, the activation energy of this reaction is -433.981 kJ.mol-1 - (-435.067 kJ.mol-1) = 1.086 kJ.mol-1

{| class="wikitable" border="1"
|+ MEP when p1 = p2 = 0 g.mol-1.pm.fs-1
! r1 pm !! r2 pm !! Contour plot !! Energy vs Time plot
|-
| 181.250 || 75.484 || [[File:FHH_181_0_75_0_1000_1_contour_mep.png|200px]] || [[File:FHH_181_0_75_0_1000_1_energy_mep.png|200px]]
|}

The H-H bond length was found to be 73.999 pm.

==== H + HF ====

HF + H -> F + H2

Overall endothermic reaction. The activation energy could be found by the difference between minimum potential energy calculated by MEP at H-H bond length which deviates from the transition state H-H bond length for 1 pm and the transition state potential energy.

As a result, the activation energy of this reaction is -433.981 kJ.mol-1 - (-560.583 kJ.mol-1) = 126.602 kJ.mol-1

{| class="wikitable" border="1"
|+ MEP when p1 = p2 = 0 g.mol-1.pm.fs-1
! r1 pm !! r2 pm !! Contour plot !! Energy vs Time plot
|-
| 180.250 || 74.484 || [[File:FHH_180_0_74_0_1000_0.4_contour_mep.png|200px]] || [[File:FHH_180_0_74_0_1000_0.4_energy_mep.png|200px]]
|}

The H-F bond length is found to be 91.997 pm.

=== Reaction Dynamics ===

The necessary initial condition for the reaction F + H2 to take place is that the F-H distance is smaller than the transition state F-H distance. (i.e. rFH < 181.250 pm) It can be observed from the momentum vs time graph that if the reaction feasible, eventually the system would consist of a vibrating molecule and a translating atom. As a result, the excess reaction energy is released as vibrational energy. This could be determined by infrared spectroscopy. When the system lies towards the reactant side, less vibrational energy is present in the system. The most populated vibrational state would be the ground state, and the IR absorption spectrum will show a few overtones which corresponds to population to higher vibrational states. As the system moves toward the product side, the energy initially put in to overcome the activation barrier is converted to the vibrational energy. As a result, more states could be populated and hence more overtones would be observed in the spectrum.

{| class="wikitable" border="1"
|+ caption
!rFH pm !! rHH pm !! pFH g.mol-1.pm.fs-1 !! pHH g.mol-1.pm.fs-1!! Etot kJ.mol-1 !! Reactive? !! | Illustration of the trajectory
|-
| rowspan="13" | 180 || rowspan="13" | 74 || rowspan="13" | -1|| -6.1 || -402.321 ||style="text-align: center;"| yes || sth
|-
| -5.1 || -412.501 ||style="text-align: center;"| no || sth
|-
| -4.1 || -420.701 ||style="text-align: center;"| yes || sth
|-
| -3.1 || -426.901 ||style="text-align: center;"| yes || sth
|-
| -2.1 || -431.101 ||style="text-align: center;"| yes || sth
|-
| -1.1 || -433.301 ||style="text-align: center;"| yes || sth
|-
| 0.1 || -433.301 ||style="text-align: center;"| no || sth
|-
| 1.1 || -431.101 ||style="text-align: center;"| yes || sth
|-
| 2.1 || -426.901 ||style="text-align: center;"| no || sth
|-
| 3.1 || -420.701 ||style="text-align: center;"| no || sth
|-
| 4.1 || -412.501 ||style="text-align: center;"| no || sth
|-
| 5.1 || -402.301 ||style="text-align: center;"| yes || sth
|-
| 6.1 || -390.101 ||style="text-align: center;"| no || sth
|-
|}

== References ==

<ref name="Transition Theory">Steinfeld J, Francisco J, Hase W. Chemical kinetics and dynamics. 2nd ed. Upper Saddle River: Prentice Hall; 1998.</reference>

File:FHH 180 0 74 0 1000 0.4 energy mep.png

2020-05-08T12:52:04Z

Yh9718:

MRD:01496067HYT

2020-05-08T12:17:31Z

Yh9718: /* H + H2 system */

== H + H2 system ==

[[File:Rts_HHH_01496067.png|thumb| internuclear distance vs time plot at r1 = r2 = rts = 90.774 pm|250px]]
The transition state is mathematically defined as the saddle point of a surface plot. To distinguish the transition state from the local minimum, check that if it is a maximum on another set of axis which is perpendicular to the original axis.

The best estimated rts is 90.774 pm. As seen that the internuclear distance vs time plot show three straight horizontal lines (where AB and BC distance overlap), which suggests that the atoms are in the energy stationary point, and no oscillation is occurring.

The MEP ignores the kinetic energy of the atoms, hence no oscillation is observed in the mep plot, and it only shows the minumum energy path that the system go through while proceeding the reaction; whereas in the actual trajectory, the atoms do oscillate due to conservation of energy. The energy released after passing the activation energy barrier is converted to kinetic energy of the particles, hence the molecule vibrates and shows a curly path in the trajectory.

{| class="wikitable" border="1"
|+ r1 = 91.774 pm, r2 = 90.774 pm, p1= 0 g.mol-1.pm.fs-1, p2= 0 g.mol-1.pm.fs-1
! Type of Calculation !! Countour Plot !! Momentum vs time Plot
|-
| MEP || [[File:HHH_91_0_90_0_2000_0.1_countour_mep.png|200px]] || [[File:HHH_91_0_90_0_2000_0.1_momentum_mep.png|200px]]
|-
| dynamics || [[File:HHH_91_0_90_0_2000_0.1_countour_dynamics.png|200px]] || [[File:HHH_91_0_90_0_2000_0.1_momentum_dynamics.png|200px]]
|}

The transition state theory neglects the fact that the product and the reactant are interconvertible, hence it would overestimate the rate of the reaction slightly.<ref name="Transition Theory" />

{| class="wikitable" border="1"
|+ Reaction Trajectories at r1 = 74 pm and r2 = 200 pm with different momenta
! p1 g.mol-1.pm.fs-1 !! p2 g.mol-1.pm.fs-1!! Etot kJ.mol-1 !! Reactive? !! Description of the dynamics !! colspan="2" | Illustration of the trajectory
|-
| style="text-align: center;"|-2.56 ||style="text-align: center;"| -5.1 ||style="text-align: center;"| -414.28 ||style="text-align: center;"| yes || H2 molecule (AB) slowly approaches to an H atom (C), and the H2 molecule (AB) dissociates, forming a new H atom (A) and H2 molecule (BC).|| [[File:-2.56_-5.1_HHH_01496067.png|200px]] || [[File:-2.56-5.1_HHH_01496067.png|200px]]
|-
|style="text-align: center;"| -3.1 ||style="text-align: center;"| -4.1 || style="text-align: center;"|-420.077 || style="text-align: center;"|no || A vibrating molecule H2 (AB) approaches an H atom (C), and before they reach each other, both the H2 molecule and H atom bounces back. No reaction takes place. || [[File:-3.1_-4.1_HHH_01496067.png|200px]] || [[File:-3.1-4.1_HHH_01496067.png|200px]]
|-
| style="text-align: center;"|-3.1 || style="text-align: center;"|-5.1 ||style="text-align: center;"| -413.977 || style="text-align: center;"|yes || A vibrating molecule H2 (AB) approaches an H atom (C), and before as reach each other, the H(A)-H(B) bond breaks, H(B)-H(C) bond forms. Both the H atom (A) and the H2 molecule (BC) move in direction opposite to their initial direction, and H2 molecule (BC) vibrates. || [[File:-3.1_-5.1_HHH_01496067.png|200px]] || [[File:-3.1-5.1_HHH_01496067.png|200px]]
|-
| style="text-align: center;"|-5.1 || style="text-align: center;"|-10.1 || style="text-align: center;"|-357.277 || style="text-align: center;"|no || A vibrating molecule H2 (AB) approaches an H atom (C), and the H(A)-H(B) bond breaks, the H(B)-H(C) bond forms. The newly formed H2 molecule (BC) vibrates so violently that as the H(B) atom in the molecule reaches the H(A) atom, it reforms the H2 molecule (AB) and an H atom (C). Overall no reaction takes place. || [[File:-5.1_-10.1_HHH_01496067.png|200px]] || [[File:-5.1-10.1_HHH_01496067.png|200px]]
|-
| style="text-align: center;"|-5.1 || style="text-align: center;"|-10.6 || style="text-align: center;"|-349.477 || style="text-align: center;"|yes || A vibrating molecule H2 (AB) approaches an H atom (C), and the H(A)-H(B) bond breaks, the H(B)-H(C) bond forms. The newly formed H2 molecule (BC) vibrates so violently that as the H(B) atom in the molecule reaches the H(A) atom, it reforms the H2 molecule (AB) and an H atom (C). The reformed H2 molecule (AB) vibrates once and the H(B) atom is reattracted to the H(C) atom, forming the H2 molecule (BC) again. || [[File:-5.1_-10.6_HHH_01496067.png|200px]] || [[File:-5.1-10.6_HHH_01496067.png|200px]]
|-
|}

A brief conclusion can be drawn that the a greater momentum does not always lead to a reactive trajectory. There need to be a balance between the translational energy and vibrational energy for the reaction to be successful.

== F - H - H system ==
=== PES inspection ===
[[File:Surface_plot_FHH_01496067.png|250px|thumb|A surface plot of the F-H-H system, where A=F, B=C=H]]
A potential surface plot is drawn, were AB is the F-H distance and BC is the H-H distance.
As shown in the plot, at low FH distance (i.e. A FH + H state), the potential energy is lower; at low HH distance (i.e. a H2 + F state), the potential energy is higher. This suggests that the reaction FH + H -> F + H2 is endothermic, and the reaction F + H2 -> FH + H is exothermic. From the thermodynamic nature of the reaction, it can be clearly seen that the F-H bond is much stronger than the H-H bond. The reaction FH + H -> F + H2 is endothermic, which suggests that the energy required for breaking the F-H bond is greater than the energy released when forming the H-H bond, hence a conclusion can be drawn that the F-H bond is stronger than the H-H bond.

The transition state position of the reaction is found at rFH=181.250 pm, rHH=74.484 pm shown as a dot in the surface plot.

==== F + H2 ====

F + H2 -> HF + H

Overall exothermic reaction. The activation energy could be found by the difference between minimum potential energy calculated by MEP at H-F bond length which deviates from the transition state H-F bond length for 1 pm and the transition state potential energy.

As a result, the activation energy of this reaction is -433.981 kJ.mol-1 - (-435.067 kJ.mol-1) = 1.086 kJ.mol-1

The H-H bond length was found to be 73.999 pm.

==== H + HF ====

HF + H -> F + H2

Overall endothermic reaction. The activation energy could be found by the difference between minimum potential energy calculated by MEP at H-H bond length which deviates from the transition state H-H bond length for 1 pm and the transition state potential energy.

As a result, the activation energy of this reaction is -433.981 kJ.mol-1 - (-560.583 kJ.mol-1) = 126.602 kJ.mol-1

The H-F bond length is found to be 91.997 pm.

=== Reaction Dynamics ===

The necessary initial condition for the reaction F + H2 to take place is that the F-H distance is smaller than the transition state F-H distance. (i.e. rFH < 181.250 pm) It can be observed from the momentum vs time graph that if the reaction feasible, eventually the system would consist of a vibrating molecule and a translating atom. As a result, the excess reaction energy is released as vibrational energy. This could be determined by infrared spectroscopy. When the system lies towards the reactant side, less vibrational energy is present in the system. The most populated vibrational state would be the ground state, and the IR absorption spectrum will show a few overtones which corresponds to population to higher vibrational states. As the system moves toward the product side, the energy initially put in to overcome the activation barrier is converted to the vibrational energy. As a result, more states could be populated and hence more overtones would be observed in the spectrum.

{| class="wikitable" border="1"
|+ caption
!rFH pm !! rHH pm !! pFH g.mol-1.pm.fs-1 !! pHH g.mol-1.pm.fs-1!! Etot kJ.mol-1 !! Reactive? !! | Illustration of the trajectory
|-
| rowspan="13" | 180 || rowspan="13" | 74 || rowspan="13" | -1|| -6.1 || -402.321 ||style="text-align: center;"| yes || sth
|-
| -5.1 || -412.501 ||style="text-align: center;"| no || sth
|-
| -4.1 || -420.701 ||style="text-align: center;"| yes || sth
|-
| -3.1 || -426.901 ||style="text-align: center;"| yes || sth
|-
| -2.1 || -431.101 ||style="text-align: center;"| yes || sth
|-
| -1.1 || -433.301 ||style="text-align: center;"| yes || sth
|-
| 0.1 || -433.301 ||style="text-align: center;"| no || sth
|-
| 1.1 || -431.101 ||style="text-align: center;"| yes || sth
|-
| 2.1 || -426.901 ||style="text-align: center;"| no || sth
|-
| 3.1 || -420.701 ||style="text-align: center;"| no || sth
|-
| 4.1 || -412.501 ||style="text-align: center;"| no || sth
|-
| 5.1 || -402.301 ||style="text-align: center;"| yes || sth
|-
| 6.1 || -390.101 ||style="text-align: center;"| no || sth
|-
|}

== References ==

Steinfeld J, Francisco J, Hase W. Chemical kinetics and dynamics. 2nd ed. Upper Saddle River: Prentice Hall; 1998.

MRD:01496067HYT

2020-05-08T12:15:23Z

Yh9718:

== H + H2 system ==

[[File:Rts_HHH_01496067.png|thumb| internuclear distance vs time plot at r1 = r2 = rts = 90.774 pm|250px]]
The transition state is mathematically defined as the saddle point of a surface plot. To distinguish the transition state from the local minimum, check that if it is a maximum on another set of axis which is perpendicular to the original axis.

The best estimated rts is 90.774 pm. As seen that the internuclear distance vs time plot show three straight horizontal lines (where AB and BC distance overlap), which suggests that the atoms are in the energy stationary point, and no oscillation is occurring.

The MEP ignores the kinetic energy of the atoms, hence no oscillation is observed in the mep plot, and it only shows the minumum energy path that the system go through while proceeding the reaction; whereas in the actual trajectory, the atoms do oscillate due to conservation of energy. The energy released after passing the activation energy barrier is converted to kinetic energy of the particles, hence the molecule vibrates and shows a curly path in the trajectory.

{| class="wikitable" border="1"
|+ r1 = 91.774 pm, r2 = 90.774 pm, p1= 0 g.mol-1.pm.fs-1, p2= 0 g.mol-1.pm.fs-1
! Type of Calculation !! Countour Plot !! Momentum vs time Plot
|-
| MEP || [[File:HHH_91_0_90_0_2000_0.1_countour_mep.png|200px]] || [[File:HHH_91_0_90_0_2000_0.1_momentum_mep.png|200px]]
|-
| dynamics || [[File:HHH_91_0_90_0_2000_0.1_countour_dynamics.png|200px]] || [[File:HHH_91_0_90_0_2000_0.1_momentum_dynamics.png|200px]]
|}

The transition state theory neglects the fact that the product and the reactant are interconvertible, hence it would overestimate the rate of the reaction slightly.

{| class="wikitable" border="1"
|+ Reaction Trajectories at r1 = 74 pm and r2 = 200 pm with different momenta
! p1 g.mol-1.pm.fs-1 !! p2 g.mol-1.pm.fs-1!! Etot kJ.mol-1 !! Reactive? !! Description of the dynamics !! colspan="2" | Illustration of the trajectory
|-
| style="text-align: center;"|-2.56 ||style="text-align: center;"| -5.1 ||style="text-align: center;"| -414.28 ||style="text-align: center;"| yes || H2 molecule (AB) slowly approaches to an H atom (C), and the H2 molecule (AB) dissociates, forming a new H atom (A) and H2 molecule (BC).|| [[File:-2.56_-5.1_HHH_01496067.png|200px]] || [[File:-2.56-5.1_HHH_01496067.png|200px]]
|-
|style="text-align: center;"| -3.1 ||style="text-align: center;"| -4.1 || style="text-align: center;"|-420.077 || style="text-align: center;"|no || A vibrating molecule H2 (AB) approaches an H atom (C), and before they reach each other, both the H2 molecule and H atom bounces back. No reaction takes place. || [[File:-3.1_-4.1_HHH_01496067.png|200px]] || [[File:-3.1-4.1_HHH_01496067.png|200px]]
|-
| style="text-align: center;"|-3.1 || style="text-align: center;"|-5.1 ||style="text-align: center;"| -413.977 || style="text-align: center;"|yes || A vibrating molecule H2 (AB) approaches an H atom (C), and before as reach each other, the H(A)-H(B) bond breaks, H(B)-H(C) bond forms. Both the H atom (A) and the H2 molecule (BC) move in direction opposite to their initial direction, and H2 molecule (BC) vibrates. || [[File:-3.1_-5.1_HHH_01496067.png|200px]] || [[File:-3.1-5.1_HHH_01496067.png|200px]]
|-
| style="text-align: center;"|-5.1 || style="text-align: center;"|-10.1 || style="text-align: center;"|-357.277 || style="text-align: center;"|no || A vibrating molecule H2 (AB) approaches an H atom (C), and the H(A)-H(B) bond breaks, the H(B)-H(C) bond forms. The newly formed H2 molecule (BC) vibrates so violently that as the H(B) atom in the molecule reaches the H(A) atom, it reforms the H2 molecule (AB) and an H atom (C). Overall no reaction takes place. || [[File:-5.1_-10.1_HHH_01496067.png|200px]] || [[File:-5.1-10.1_HHH_01496067.png|200px]]
|-
| style="text-align: center;"|-5.1 || style="text-align: center;"|-10.6 || style="text-align: center;"|-349.477 || style="text-align: center;"|yes || A vibrating molecule H2 (AB) approaches an H atom (C), and the H(A)-H(B) bond breaks, the H(B)-H(C) bond forms. The newly formed H2 molecule (BC) vibrates so violently that as the H(B) atom in the molecule reaches the H(A) atom, it reforms the H2 molecule (AB) and an H atom (C). The reformed H2 molecule (AB) vibrates once and the H(B) atom is reattracted to the H(C) atom, forming the H2 molecule (BC) again. || [[File:-5.1_-10.6_HHH_01496067.png|200px]] || [[File:-5.1-10.6_HHH_01496067.png|200px]]
|-
|}

A brief conclusion can be drawn that the a greater momentum does not always lead to a reactive trajectory. There need to be a balance between the translational energy and vibrational energy for the reaction to be successful.

== F - H - H system ==
=== PES inspection ===
[[File:Surface_plot_FHH_01496067.png|250px|thumb|A surface plot of the F-H-H system, where A=F, B=C=H]]
A potential surface plot is drawn, were AB is the F-H distance and BC is the H-H distance.
As shown in the plot, at low FH distance (i.e. A FH + H state), the potential energy is lower; at low HH distance (i.e. a H2 + F state), the potential energy is higher. This suggests that the reaction FH + H -> F + H2 is endothermic, and the reaction F + H2 -> FH + H is exothermic. From the thermodynamic nature of the reaction, it can be clearly seen that the F-H bond is much stronger than the H-H bond. The reaction FH + H -> F + H2 is endothermic, which suggests that the energy required for breaking the F-H bond is greater than the energy released when forming the H-H bond, hence a conclusion can be drawn that the F-H bond is stronger than the H-H bond.

The transition state position of the reaction is found at rFH=181.250 pm, rHH=74.484 pm shown as a dot in the surface plot.

==== F + H2 ====

F + H2 -> HF + H

Overall exothermic reaction. The activation energy could be found by the difference between minimum potential energy calculated by MEP at H-F bond length which deviates from the transition state H-F bond length for 1 pm and the transition state potential energy.

As a result, the activation energy of this reaction is -433.981 kJ.mol-1 - (-435.067 kJ.mol-1) = 1.086 kJ.mol-1

The H-H bond length was found to be 73.999 pm.

==== H + HF ====

HF + H -> F + H2

Overall endothermic reaction. The activation energy could be found by the difference between minimum potential energy calculated by MEP at H-H bond length which deviates from the transition state H-H bond length for 1 pm and the transition state potential energy.

As a result, the activation energy of this reaction is -433.981 kJ.mol-1 - (-560.583 kJ.mol-1) = 126.602 kJ.mol-1

The H-F bond length is found to be 91.997 pm.

=== Reaction Dynamics ===

The necessary initial condition for the reaction F + H2 to take place is that the F-H distance is smaller than the transition state F-H distance. (i.e. rFH < 181.250 pm) It can be observed from the momentum vs time graph that if the reaction feasible, eventually the system would consist of a vibrating molecule and a translating atom. As a result, the excess reaction energy is released as vibrational energy. This could be determined by infrared spectroscopy. When the system lies towards the reactant side, less vibrational energy is present in the system. The most populated vibrational state would be the ground state, and the IR absorption spectrum will show a few overtones which corresponds to population to higher vibrational states. As the system moves toward the product side, the energy initially put in to overcome the activation barrier is converted to the vibrational energy. As a result, more states could be populated and hence more overtones would be observed in the spectrum.

{| class="wikitable" border="1"
|+ caption
!rFH pm !! rHH pm !! pFH g.mol-1.pm.fs-1 !! pHH g.mol-1.pm.fs-1!! Etot kJ.mol-1 !! Reactive? !! | Illustration of the trajectory
|-
| rowspan="13" | 180 || rowspan="13" | 74 || rowspan="13" | -1|| -6.1 || -402.321 ||style="text-align: center;"| yes || sth
|-
| -5.1 || -412.501 ||style="text-align: center;"| no || sth
|-
| -4.1 || -420.701 ||style="text-align: center;"| yes || sth
|-
| -3.1 || -426.901 ||style="text-align: center;"| yes || sth
|-
| -2.1 || -431.101 ||style="text-align: center;"| yes || sth
|-
| -1.1 || -433.301 ||style="text-align: center;"| yes || sth
|-
| 0.1 || -433.301 ||style="text-align: center;"| no || sth
|-
| 1.1 || -431.101 ||style="text-align: center;"| yes || sth
|-
| 2.1 || -426.901 ||style="text-align: center;"| no || sth
|-
| 3.1 || -420.701 ||style="text-align: center;"| no || sth
|-
| 4.1 || -412.501 ||style="text-align: center;"| no || sth
|-
| 5.1 || -402.301 ||style="text-align: center;"| yes || sth
|-
| 6.1 || -390.101 ||style="text-align: center;"| no || sth
|-
|}

== References ==

Steinfeld J, Francisco J, Hase W. Chemical kinetics and dynamics. 2nd ed. Upper Saddle River: Prentice Hall; 1998.

MRD:01496067HYT

2020-05-08T11:54:35Z

Yh9718: /* H + H2 system */

== H + H2 system ==

[[File:Rts_HHH_01496067.png|thumb| internuclear distance vs time plot at r1 = r2 = rts = 90.774 pm|250px]]
The transition state is mathematically defined as the saddle point of a surface plot. To distinguish the transition state from the local minimum, check that if it is a maximum on another set of axis which is perpendicular to the original axis.

The best estimated rts is 90.774 pm. As seen that the internuclear distance vs time plot show three straight horizontal lines (where AB and BC distance overlap), which suggests that the atoms are in the energy stationary point, and no oscillation is occurring.

The MEP ignores the kinetic energy of the atoms, hence no oscillation is observed in the mep plot, and it only shows the minumum energy path that the system go through while proceeding the reaction; whereas in the actual trajectory, the atoms do oscillate due to conservation of energy. The energy released after passing the activation energy barrier is converted to kinetic energy of the particles, hence the molecule vibrates and shows a curly path in the trajectory.

{| class="wikitable" border="1"
|+ r1 = 91.774 pm, r2 = 90.774 pm, p1= 0 g.mol-1.pm.fs-1, p2= 0 g.mol-1.pm.fs-1
! Type of Calculation !! Countour Plot !! Momentum vs time Plot
|-
| MEP || [[File:HHH_91_0_90_0_2000_0.1_countour_mep.png|200px]] || [[File:HHH_91_0_90_0_2000_0.1_momentum_mep.png|200px]]
|-
| dynamics || [[File:HHH_91_0_90_0_2000_0.1_countour_dynamics.png|200px]] || [[File:HHH_91_0_90_0_2000_0.1_momentum_dynamics.png|200px]]
|}

The transition state theory neglects the fact that the product and the reactant are interconvertible, hence it would overestimate the rate of the reaction slightly.

{| class="wikitable" border="1"
|+ Reaction Trajectories at r1 = 74 pm and r2 = 200 pm with different momenta
! p1 g.mol-1.pm.fs-1 !! p2 g.mol-1.pm.fs-1!! Etot kJ.mol-1 !! Reactive? !! Description of the dynamics !! colspan="2" | Illustration of the trajectory
|-
| style="text-align: center;"|-2.56 ||style="text-align: center;"| -5.1 ||style="text-align: center;"| -414.28 ||style="text-align: center;"| yes || H2 molecule (AB) slowly approaches to an H atom (C), and the H2 molecule (AB) dissociates, forming a new H atom (A) and H2 molecule (BC).|| [[File:-2.56_-5.1_HHH_01496067.png|200px]] || [[File:-2.56-5.1_HHH_01496067.png|200px]]
|-
|style="text-align: center;"| -3.1 ||style="text-align: center;"| -4.1 || style="text-align: center;"|-420.077 || style="text-align: center;"|no || A vibrating molecule H2 (AB) approaches an H atom (C), and before they reach each other, both the H2 molecule and H atom bounces back. No reaction takes place. || [[File:-3.1_-4.1_HHH_01496067.png|200px]] || [[File:-3.1-4.1_HHH_01496067.png|200px]]
|-
| style="text-align: center;"|-3.1 || style="text-align: center;"|-5.1 ||style="text-align: center;"| -413.977 || style="text-align: center;"|yes || A vibrating molecule H2 (AB) approaches an H atom (C), and before as reach each other, the H(A)-H(B) bond breaks, H(B)-H(C) bond forms. Both the H atom (A) and the H2 molecule (BC) move in direction opposite to their initial direction, and H2 molecule (BC) vibrates. || [[File:-3.1_-5.1_HHH_01496067.png|200px]] || [[File:-3.1-5.1_HHH_01496067.png|200px]]
|-
| style="text-align: center;"|-5.1 || style="text-align: center;"|-10.1 || style="text-align: center;"|-357.277 || style="text-align: center;"|no || A vibrating molecule H2 (AB) approaches an H atom (C), and the H(A)-H(B) bond breaks, the H(B)-H(C) bond forms. The newly formed H2 molecule (BC) vibrates so violently that as the H(B) atom in the molecule reaches the H(A) atom, it reforms the H2 molecule (AB) and an H atom (C). Overall no reaction takes place. || [[File:-5.1_-10.1_HHH_01496067.png|200px]] || [[File:-5.1-10.1_HHH_01496067.png|200px]]
|-
| style="text-align: center;"|-5.1 || style="text-align: center;"|-10.6 || style="text-align: center;"|-349.477 || style="text-align: center;"|yes || A vibrating molecule H2 (AB) approaches an H atom (C), and the H(A)-H(B) bond breaks, the H(B)-H(C) bond forms. The newly formed H2 molecule (BC) vibrates so violently that as the H(B) atom in the molecule reaches the H(A) atom, it reforms the H2 molecule (AB) and an H atom (C). The reformed H2 molecule (AB) vibrates once and the H(B) atom is reattracted to the H(C) atom, forming the H2 molecule (BC) again. || [[File:-5.1_-10.6_HHH_01496067.png|200px]] || [[File:-5.1-10.6_HHH_01496067.png|200px]]
|-
|}

A brief conclusion can be drawn that the a greater momentum does not always lead to a reactive trajectory. There need to be a balance between the translational energy and vibrational energy for the reaction to be successful.

== F - H - H system ==
=== PES inspection ===
[[File:Surface_plot_FHH_01496067.png|250px|thumb|A surface plot of the F-H-H system, where A=F, B=C=H]]
A potential surface plot is drawn, were AB is the F-H distance and BC is the H-H distance.
As shown in the plot, at low FH distance (i.e. A FH + H state), the potential energy is lower; at low HH distance (i.e. a H2 + F state), the potential energy is higher. This suggests that the reaction FH + H -> F + H2 is endothermic, and the reaction F + H2 -> FH + H is exothermic. From the thermodynamic nature of the reaction, it can be clearly seen that the F-H bond is much stronger than the H-H bond. The reaction FH + H -> F + H2 is endothermic, which suggests that the energy required for breaking the F-H bond is greater than the energy released when forming the H-H bond, hence a conclusion can be drawn that the F-H bond is stronger than the H-H bond.

The transition state position of the reaction is found at rFH=181.250 pm, rHH=74.484 pm shown as a dot in the surface plot.

==== F + H2 ====

F + H2 -> HF + H

Overall exothermic reaction. The activation energy could be found by the difference between minimum potential energy calculated by MEP at H-F bond length which deviates from the transition state H-F bond length for 1 pm and the transition state potential energy.

As a result, the activation energy of this reaction is -433.981 kJ.mol-1 - (-435.067 kJ.mol-1) = 1.086 kJ.mol-1

The H-H bond length was found to be 73.999 pm.

==== H + HF ====

HF + H -> F + H2

Overall endothermic reaction. The activation energy could be found by the difference between minimum potential energy calculated by MEP at H-H bond length which deviates from the transition state H-H bond length for 1 pm and the transition state potential energy.

As a result, the activation energy of this reaction is -433.981 kJ.mol-1 - (-560.583 kJ.mol-1) = 126.602 kJ.mol-1

The H-F bond length is found to be 91.997 pm.

=== Reaction Dynamics ===

The necessary initial condition for the reaction F + H2 to take place is that the F-H distance is smaller than the transition state F-H distance. (i.e. rFH < 181.250 pm) It can be observed from the momentum vs time graph that if the reaction feasible, eventually the system would consist of a vibrating molecule and a translating atom. As a result, the excess reaction energy is released as vibrational energy. This could be determined by infrared spectroscopy. When the system lies towards the reactant side, less vibrational energy is present in the system. The most populated vibrational state would be the ground state, and the IR absorption spectrum will show a few overtones which corresponds to population to higher vibrational states. As the system moves toward the product side, the energy initially put in to overcome the activation barrier is converted to the vibrational energy. As a result, more states could be populated and hence more overtones would be observed in the spectrum.

{| class="wikitable" border="1"
|+ caption
!rFH pm !! rHH pm !! pFH g.mol-1.pm.fs-1 !! pHH g.mol-1.pm.fs-1!! Etot kJ.mol-1 !! Reactive? !! | Illustration of the trajectory
|-
| rowspan="13" | 180 || rowspan="13" | 74 || rowspan="13" | -1|| -6.1 || -402.321 ||style="text-align: center;"| yes || sth
|-
| -5.1 || -412.501 ||style="text-align: center;"| no || sth
|-
| -4.1 || -420.701 ||style="text-align: center;"| yes || sth
|-
| -3.1 || -426.901 ||style="text-align: center;"| yes || sth
|-
| -2.1 || -431.101 ||style="text-align: center;"| yes || sth
|-
| -1.1 || -433.301 ||style="text-align: center;"| yes || sth
|-
| 0.1 || -433.301 ||style="text-align: center;"| no || sth
|-
| 1.1 || -431.101 ||style="text-align: center;"| yes || sth
|-
| 2.1 || -426.901 ||style="text-align: center;"| no || sth
|-
| 3.1 || -420.701 ||style="text-align: center;"| no || sth
|-
| 4.1 || -412.501 ||style="text-align: center;"| no || sth
|-
| 5.1 || -402.301 ||style="text-align: center;"| yes || sth
|-
| 6.1 || -390.101 ||style="text-align: center;"| no || sth
|-
|}

MRD:01496067HYT

2020-05-08T11:53:30Z

MRD:01496067HYT

2020-05-08T11:33:12Z

Yh9718: /* H + H2 system */

== H + H2 system ==

[[File:Rts_HHH_01496067.png|thumb| internuclear distance vs time plot at r1 = r2 = rts = 90.774 pm|250px]]
The transition state is mathematically defined as the saddle point of a surface plot. To distinguish the transition state from the local minimum, check that if it is a maximum on another set of axis which is perpendicular to the original axis.

The best estimated rts is 90.774 pm. As seen that the internuclear distance vs time plot show three straight horizontal lines (where AB and BC distance overlap), which suggests that the atoms are in the energy stationary point, and no oscillation is occurring.

The MEP ignores the kinetic energy of the atoms, hence no oscillation is observed in the mep plot, and it only shows the minumum energy path that the system go through while proceeding the reaction; whereas in the actual trajectory, the atoms do oscillate due to conservation of energy. The energy released after passing the activation energy barrier is converted to kinetic energy of the particles, hence the molecule vibrates and shows a curly path in the trajectory.

The transition state theory neglects the fact that the product and the reactant are interconvertible, hence it would overestimate the rate of the reaction slightly.

{| class="wikitable" border="1"
|+ Reaction Trajectories at r1 = 74 pm and r2 = 200 pm with different momenta
! p1 g.mol-1.pm.fs-1 !! p2 g.mol-1.pm.fs-1!! Etot kJ.mol-1 !! Reactive? !! Description of the dynamics !! colspan="2" | Illustration of the trajectory
|-
| style="text-align: center;"|-2.56 ||style="text-align: center;"| -5.1 ||style="text-align: center;"| -414.28 ||style="text-align: center;"| yes || H2 molecule (AB) slowly approaches to an H atom (C), and the H2 molecule (AB) dissociates, forming a new H atom (A) and H2 molecule (BC).|| [[File:-2.56_-5.1_HHH_01496067.png|200px]] || [[File:-2.56-5.1_HHH_01496067.png|200px]]
|-
|style="text-align: center;"| -3.1 ||style="text-align: center;"| -4.1 || style="text-align: center;"|-420.077 || style="text-align: center;"|no || A vibrating molecule H2 (AB) approaches an H atom (C), and before they reach each other, both the H2 molecule and H atom bounces back. No reaction takes place. || [[File:-3.1_-4.1_HHH_01496067.png|200px]] || [[File:-3.1-4.1_HHH_01496067.png|200px]]
|-
| style="text-align: center;"|-3.1 || style="text-align: center;"|-5.1 ||style="text-align: center;"| -413.977 || style="text-align: center;"|yes || A vibrating molecule H2 (AB) approaches an H atom (C), and before as reach each other, the H(A)-H(B) bond breaks, H(B)-H(C) bond forms. Both the H atom (A) and the H2 molecule (BC) move in direction opposite to their initial direction, and H2 molecule (BC) vibrates. || [[File:-3.1_-5.1_HHH_01496067.png|200px]] || [[File:-3.1-5.1_HHH_01496067.png|200px]]
|-
| style="text-align: center;"|-5.1 || style="text-align: center;"|-10.1 || style="text-align: center;"|-357.277 || style="text-align: center;"|no || A vibrating molecule H2 (AB) approaches an H atom (C), and the H(A)-H(B) bond breaks, the H(B)-H(C) bond forms. The newly formed H2 molecule (BC) vibrates so violently that as the H(B) atom in the molecule reaches the H(A) atom, it reforms the H2 molecule (AB) and an H atom (C). Overall no reaction takes place. || [[File:-5.1_-10.1_HHH_01496067.png|200px]] || [[File:-5.1-10.1_HHH_01496067.png|200px]]
|-
| style="text-align: center;"|-5.1 || style="text-align: center;"|-10.6 || style="text-align: center;"|-349.477 || style="text-align: center;"|yes || A vibrating molecule H2 (AB) approaches an H atom (C), and the H(A)-H(B) bond breaks, the H(B)-H(C) bond forms. The newly formed H2 molecule (BC) vibrates so violently that as the H(B) atom in the molecule reaches the H(A) atom, it reforms the H2 molecule (AB) and an H atom (C). The reformed H2 molecule (AB) vibrates once and the H(B) atom is reattracted to the H(C) atom, forming the H2 molecule (BC) again. || [[File:-5.1_-10.6_HHH_01496067.png|200px]] || [[File:-5.1-10.6_HHH_01496067.png|200px]]
|-
|}

A brief conclusion can be drawn that the a greater momentum does not always lead to a reactive trajectory. There need to be a balance between the translational energy and vibrational energy for the reaction to be successful.

== F - H - H system ==
=== PES inspection ===
[[File:Surface_plot_FHH_01496067.png|250px|thumb|A surface plot of the F-H-H system, where A=F, B=C=H]]
A potential surface plot is drawn, were AB is the F-H distance and BC is the H-H distance.
As shown in the plot, at low FH distance (i.e. A FH + H state), the potential energy is lower; at low HH distance (i.e. a H2 + F state), the potential energy is higher. This suggests that the reaction FH + H -> F + H2 is endothermic, and the reaction F + H2 -> FH + H is exothermic. From the thermodynamic nature of the reaction, it can be clearly seen that the F-H bond is much stronger than the H-H bond. The reaction FH + H -> F + H2 is endothermic, which suggests that the energy required for breaking the F-H bond is greater than the energy released when forming the H-H bond, hence a conclusion can be drawn that the F-H bond is stronger than the H-H bond.

The transition state position of the reaction is found at rFH=181.250 pm, rHH=74.484 pm shown as a dot in the surface plot.

==== F + H2 ====

F + H2 -> HF + H

Overall exothermic reaction. The activation energy could be found by the difference between minimum potential energy calculated by MEP at H-F bond length which deviates from the transition state H-F bond length for 1 pm and the transition state potential energy.

As a result, the activation energy of this reaction is -433.981 kJ.mol-1 - (-435.067 kJ.mol-1) = 1.086 kJ.mol-1

The H-H bond length was found to be 73.999 pm.

==== H + HF ====

HF + H -> F + H2

Overall endothermic reaction. The activation energy could be found by the difference between minimum potential energy calculated by MEP at H-H bond length which deviates from the transition state H-H bond length for 1 pm and the transition state potential energy.

As a result, the activation energy of this reaction is -433.981 kJ.mol-1 - (-560.583 kJ.mol-1) = 126.602 kJ.mol-1

The H-F bond length is found to be 91.997 pm.

=== Reaction Dynamics ===

The necessary initial condition for the reaction F + H2 to take place is that the F-H distance is smaller than the transition state F-H distance. (i.e. rFH < 181.250 pm) It can be observed from the momentum vs time graph that if the reaction feasible, eventually the system would consist of a vibrating molecule and a translating atom. As a result, the excess reaction energy is released as vibrational energy. This could be determined by infrared spectroscopy. When the system lies towards the reactant side, less vibrational energy is present in the system. The most populated vibrational state would be the ground state, and the IR absorption spectrum will show a few overtones which corresponds to population to higher vibrational states. As the system moves toward the product side, the energy initially put in to overcome the activation barrier is converted to the vibrational energy. As a result, more states could be populated and hence more overtones would be observed in the spectrum.

{| class="wikitable" border="1"
|+ caption
!rFH pm !! rHH pm !! pFH g.mol-1.pm.fs-1 !! pHH g.mol-1.pm.fs-1!! Etot kJ.mol-1 !! Reactive? !! | Illustration of the trajectory
|-
| rowspan="13" | 180 || rowspan="13" | 74 || rowspan="13" | -1|| -6.1 || -402.321 ||style="text-align: center;"| yes || sth
|-
| -5.1 || -412.501 ||style="text-align: center;"| no || sth
|-
| -4.1 || -420.701 ||style="text-align: center;"| yes || sth
|-
| -3.1 || -426.901 ||style="text-align: center;"| yes || sth
|-
| -2.1 || -431.101 ||style="text-align: center;"| yes || sth
|-
| -1.1 || -433.301 ||style="text-align: center;"| yes || sth
|-
| 0.1 || -433.301 ||style="text-align: center;"| no || sth
|-
| 1.1 || -431.101 ||style="text-align: center;"| yes || sth
|-
| 2.1 || -426.901 ||style="text-align: center;"| no || sth
|-
| 3.1 || -420.701 ||style="text-align: center;"| no || sth
|-
| 4.1 || -412.501 ||style="text-align: center;"| no || sth
|-
| 5.1 || -402.301 ||style="text-align: center;"| yes || sth
|-
| 6.1 || -390.101 ||style="text-align: center;"| no || sth
|-
|}