ChemWiki - User contributions [en]

User:Cd1017

2020-04-06T01:28:48Z

Cd1017: Created page with "~~~~Meow"

[[User:Cd1017|Cd1017]] ([[User talk:Cd1017|talk]]) 02:28, 6 April 2020 (BST)Meow

MRD:cd1017

2019-05-10T13:53:32Z

Cd1017: /* H + HF */

==H + H2 System==
The transition state is defined as the maximum on the minimum energy path linking reactants and the products, and therefore, on a potential energy surface diagram, a transition state is where:

<math>\frac{\partial V(r)}{\partial r} = 0</math> and <math>\frac{\partial^2 V(r)}{\partial^2 r} < 0</math>

The mathematical definition of a local minimum is similar:

<math>\frac{\partial V(r)}{\partial r} = 0</math> and <math>\frac{\partial^2 V(r)}{\partial^2 r} > 0</math>

When the three-atom system is at the transition state, the best estimation for the intermolecular distances is r1 = r1 = 0.908, for both A-B and B-C distances are constant and the momentum of the system is 0.

[[File:Cd1017_Meow_TS.png|thumb|center|800px|Internuclear Distances vs Time]]

The condition is changed to: r1 = 0.918, r2 = 0.908, p1 = p2 = 0. Both plots clearly show the trajectory: after the collision, the A-B distance increases and B-C distance decreases, showing that HB and HC form a new dihydrogen molecule. The dyamics plot shows the vibration of the atoms, while the MEP plot doesn't. Hence, the MEP plot is a less realistic representation than the dynamics plot. However, the trajectory of the MEP plot goes through the bottom of the potential surface, and therefore, has a lower potential than the dynamics at a certain point (r1, r2).

[[File:Cd1017_Meow_MEPplot.png|thumb|center|800px|The MEP contour plot of the trajectory.]]
[[File:Cd1017_Meow_DynamicsPath.png|thumb|center|800px|The Dynamics contour plot of the trajectory.]]

If the values of r1 and r2 are exchanged, the corresonding atom distances and momenta will be exchanged as well.
{|class="wikitable" border="1"
|+
|-
|colspan="2"|r1 = 0.918 r2 = 0.908||colspan="2"|r1 = 0.908 r2 = 0.918
|-
|Internuclear Distacne vs. Time||Momenta vs. Time||Internuclear Distacne vs. Time||Momenta vs. Time
|-
|[[File:Cd1017_Meow_918908_d.png|250px]]||[[File:Cd1017_Meow_918908_m.png|250px]]||[[File:Cd1017_Meow_908918_d.png|250px]]||[[File:Cd1017_Meow_908918_m.png|250px]]
|}

The final conditions (t = 2.00)of the first calculation (r1 = 0.918, r2 = 0.908) are: r1 = 7.155, r2 = 0.756, p1 = 2.481, p2 = 1.126, and another calculation is done with the initial condition r1 = 7.155, r2 = 0.756, p1 = -2.481, p2 = -1.126. It can be seen that it is a reversed process of the first calculation, and its final conditions are the initial conditions of the first calculation.

{|class="wikitable" border="1"
|+
|-
|Internuclear Distacne vs. Time||Momenta vs. Time
|-
|[[File:Cd1017_Meow_rev_d.png|250px]]||[[File:Cd1017_Meow_rev_p.png|250px]]
|}

For the initial positions r1 = 0.74, r2 = 2.0:
{|class="wikitable" border="1"
|+
|-
|p1||p2||Etot||Reactive?||Plot||Description of the Dynamics
|-
| -1.25|| -2.50|| -99.0||Y||[[File:Cd1017_Meow_table1.png|250px]]||The Molecule HAHB approaches HC without vibration;however, as the distance decreases, they collide and the reaction happens, and the new dihydrogen molecule starts to vibrate.
|-
| -1.50|| -2.00|| -100.5||N||[[File:Cd1017_Meow_Table2.png|250px]]||The Molecule HAHB approaches HC with vibration, and they collide and bounce back. No reaction happens and the dihydrogen molecule keeps vibrating.
|-
| -1.50|| -2.50|| -98.9||Y||[[File:Cd1017_Meow_table3.png|250px]]||The Molecule HAHB approaches HC with vibration;however, as the distance decreases, they collide and the reaction happens, and the new dihydrogen molecule keeps vibrating.
|-
| -2.50|| -5.00|| -84.9||Y||[[File:Cd1017_Meow_table4.png|250px]]||The Molecule HAHB approaches HC without vibration;however, as the distance decreases, they collide and the reaction happens, and the new dihydrogen molecule starts to vibrate. The amplitude of the vibration is significant, and therefore, the new dihydrogen molecule and HA collide and react again, and the resulting dihydrgen molecule kepps vibrating.
|-
| -2.50|| -5.20|| -83.4||Y||[[File:Cd1017_Meow_table5.png|250px]]||The Molecule HAHB approaches HC without vibration;however, as the distance decreases, they collide twice and the reaction happens, and the new dihydrogen molecule starts to vibrate.
|}

According to the table, after the collision(s), the hydrogen molecule keeps or starts vibrating, and the total energy must be at least -99.0 to trigger the reaction.

The main assumption for transition state theory is that an activated complex is in equilibrium with the reactants and the rate for it to form the product depends on its rate to pass through the transition state. However, in the absence of information to the contrary, the transmission coefficient is assumed to be about 1, which means most of the activated complex can pass through the transition state. This situation differs from reality, and thus the theoretical value for the reaction rate is higher than the experimental value.

==F-H-H System==
===PES Inspection===

When F atom and two H atoms are close (F-HA = HA-HB = 0.9), a F-H molecule forms and the other H atom leaves. Thus, the formation of HF is thermodynamically preferred since the H-F bond dissociation energy is greater than that of H-H bond, and the reaction F + H2 → HF + H is exothermic.

[[File:Cd1017_Meow_F_P1.png|thumb|right|250px|The dynamics potential energy surface plot of a F-H-H system.]]
The approximate position for the transition state is found: F-HA = 1.811 Å, HA-HB = 0.745 Å

The activation energy for this reaction is 0.261 kCal·mol-1

For the endothermic reaction H + HF → H2 + F, the transition state is: H-H = 0.745 Å, F-H = 1.811 Å

This reaction can happen when the H-H momentum is -5.00, and the activation energy is 16.472 kCal·mol-1

===Reaction Dynamics===
====F + H2====

For the first reaction is reactive, when the initial conditions are: F-HA = 1.600, HA-HB = 0.645, p(F-HA) = -1.0, p(HA-HB) = 5.0. The reaction is triggered by a collision, where the F atom approaches the H2 molecule, and the F atom attracts a H atom while another H atom leaves in the opposite direction. Because of the conservation of energy, the energy released by the reaction is converted to the kinetic energy of the new particles and the vibrational energy of the new molecule. The vibration can be experimentally detected and measured by IR.

A series of calculations are done (pFH = -0.5), and it's found that for the reaction to happen, the total momentum for this system must be negative, even though for pHH, the initial kinetic energy (0.132) is below the activation energy (0.261). Then a calculation is done for the reaction with the same initial positions but with pFH = -0.8, pHH = 0.1, the reaction happens after several collisions.

{|class="wikitable" border="1"
|+
|-
|colspan="11"|rFH = 1.811, rHH = 0.74
|-
|pFH||pHH||Reaction?||KE||Etot
|-
|rowspan="7"|-0.5||-3.0||Y||7.632||-96.111
|-
| -2.0||Y||3.132||-100.611
|-
| -1.0||Y||0.632||-103.111
|-
| 0.0||Y||0.132||-103.611
|-
| 1.0||N||1.632||-102.111
|-
| 2.0||N||5.132||-98.611
|-
| 3.0||N||10.632||-93.111
|}

====H + HF====

A trajectory for this reaction is generated, with the initial conditions: rHF = 0.93 rHH = 1.22, pHF = 14.0, pHH = 5.0. This reaction has an early barrier, and therefore, according the Polanyi's rules, kinetic energy is effective for the reaction while vibrational energy is not.

MRD:cd1017

2019-05-10T13:10:42Z

Cd1017: /* H + HF */

==H + H2 System==
The transition state is defined as the maximum on the minimum energy path linking reactants and the products, and therefore, on a potential energy surface diagram, a transition state is where:

<math>\frac{\partial V(r)}{\partial r} = 0</math> and <math>\frac{\partial^2 V(r)}{\partial^2 r} < 0</math>

The mathematical definition of a local minimum is similar:

<math>\frac{\partial V(r)}{\partial r} = 0</math> and <math>\frac{\partial^2 V(r)}{\partial^2 r} > 0</math>

When the three-atom system is at the transition state, the best estimation for the intermolecular distances is r1 = r1 = 0.908, for both A-B and B-C distances are constant and the momentum of the system is 0.

[[File:Cd1017_Meow_TS.png|thumb|center|800px|Internuclear Distances vs Time]]

The condition is changed to: r1 = 0.918, r2 = 0.908, p1 = p2 = 0. Both plots clearly show the trajectory: after the collision, the A-B distance increases and B-C distance decreases, showing that HB and HC form a new dihydrogen molecule. The dyamics plot shows the vibration of the atoms, while the MEP plot doesn't. Hence, the MEP plot is a less realistic representation than the dynamics plot. However, the trajectory of the MEP plot goes through the bottom of the potential surface, and therefore, has a lower potential than the dynamics at a certain point (r1, r2).

[[File:Cd1017_Meow_MEPplot.png|thumb|center|800px|The MEP contour plot of the trajectory.]]
[[File:Cd1017_Meow_DynamicsPath.png|thumb|center|800px|The Dynamics contour plot of the trajectory.]]

If the values of r1 and r2 are exchanged, the corresonding atom distances and momenta will be exchanged as well.
{|class="wikitable" border="1"
|+
|-
|colspan="2"|r1 = 0.918 r2 = 0.908||colspan="2"|r1 = 0.908 r2 = 0.918
|-
|Internuclear Distacne vs. Time||Momenta vs. Time||Internuclear Distacne vs. Time||Momenta vs. Time
|-
|[[File:Cd1017_Meow_918908_d.png|250px]]||[[File:Cd1017_Meow_918908_m.png|250px]]||[[File:Cd1017_Meow_908918_d.png|250px]]||[[File:Cd1017_Meow_908918_m.png|250px]]
|}

The final conditions (t = 2.00)of the first calculation (r1 = 0.918, r2 = 0.908) are: r1 = 7.155, r2 = 0.756, p1 = 2.481, p2 = 1.126, and another calculation is done with the initial condition r1 = 7.155, r2 = 0.756, p1 = -2.481, p2 = -1.126. It can be seen that it is a reversed process of the first calculation, and its final conditions are the initial conditions of the first calculation.

{|class="wikitable" border="1"
|+
|-
|Internuclear Distacne vs. Time||Momenta vs. Time
|-
|[[File:Cd1017_Meow_rev_d.png|250px]]||[[File:Cd1017_Meow_rev_p.png|250px]]
|}

For the initial positions r1 = 0.74, r2 = 2.0:
{|class="wikitable" border="1"
|+
|-
|p1||p2||Etot||Reactive?||Plot||Description of the Dynamics
|-
| -1.25|| -2.50|| -99.0||Y||[[File:Cd1017_Meow_table1.png|250px]]||The Molecule HAHB approaches HC without vibration;however, as the distance decreases, they collide and the reaction happens, and the new dihydrogen molecule starts to vibrate.
|-
| -1.50|| -2.00|| -100.5||N||[[File:Cd1017_Meow_Table2.png|250px]]||The Molecule HAHB approaches HC with vibration, and they collide and bounce back. No reaction happens and the dihydrogen molecule keeps vibrating.
|-
| -1.50|| -2.50|| -98.9||Y||[[File:Cd1017_Meow_table3.png|250px]]||The Molecule HAHB approaches HC with vibration;however, as the distance decreases, they collide and the reaction happens, and the new dihydrogen molecule keeps vibrating.
|-
| -2.50|| -5.00|| -84.9||Y||[[File:Cd1017_Meow_table4.png|250px]]||The Molecule HAHB approaches HC without vibration;however, as the distance decreases, they collide and the reaction happens, and the new dihydrogen molecule starts to vibrate. The amplitude of the vibration is significant, and therefore, the new dihydrogen molecule and HA collide and react again, and the resulting dihydrgen molecule kepps vibrating.
|-
| -2.50|| -5.20|| -83.4||Y||[[File:Cd1017_Meow_table5.png|250px]]||The Molecule HAHB approaches HC without vibration;however, as the distance decreases, they collide twice and the reaction happens, and the new dihydrogen molecule starts to vibrate.
|}

According to the table, after the collision(s), the hydrogen molecule keeps or starts vibrating, and the total energy must be at least -99.0 to trigger the reaction.

The main assumption for transition state theory is that an activated complex is in equilibrium with the reactants and the rate for it to form the product depends on its rate to pass through the transition state. However, in the absence of information to the contrary, the transmission coefficient is assumed to be about 1, which means most of the activated complex can pass through the transition state. This situation differs from reality, and thus the theoretical value for the reaction rate is higher than the experimental value.

==F-H-H System==
===PES Inspection===

When F atom and two H atoms are close (F-HA = HA-HB = 0.9), a F-H molecule forms and the other H atom leaves. Thus, the formation of HF is thermodynamically preferred since the H-F bond dissociation energy is greater than that of H-H bond, and the reaction F + H2 → HF + H is exothermic.

[[File:Cd1017_Meow_F_P1.png|thumb|right|250px|The dynamics potential energy surface plot of a F-H-H system.]]
The approximate position for the transition state is found: F-HA = 1.811 Å, HA-HB = 0.745 Å

The activation energy for this reaction is 0.261 kCal·mol-1

For the endothermic reaction H + HF → H2 + F, the transition state is: H-H = 0.745 Å, F-H = 1.811 Å

This reaction can happen when the H-H momentum is -5.00, and the activation energy is 16.472 kCal·mol-1

===Reaction Dynamics===
====F + H2====

For the first reaction is reactive, when the initial conditions are: F-HA = 1.600, HA-HB = 0.645, p(F-HA) = -1.0, p(HA-HB) = 5.0. The reaction is triggered by a collision, where the F atom approaches the H2 molecule, and the F atom attracts a H atom while another H atom leaves in the opposite direction. Because of the conservation of energy, the energy released by the reaction is converted to the kinetic energy of the new particles and the vibrational energy of the new molecule. The vibration can be experimentally detected and measured by IR.

A series of calculations are done (pFH = -0.5), and it's found that for the reaction to happen, the total momentum for this system must be negative, even though for pHH, the initial kinetic energy (0.132) is below the activation energy (0.261). Then a calculation is done for the reaction with the same initial positions but with pFH = -0.8, pHH = 0.1, the reaction happens after several collisions.

{|class="wikitable" border="1"
|+
|-
|colspan="11"|rFH = 1.811, rHH = 0.74
|-
|pFH||pHH||Reaction?||KE||Etot
|-
|rowspan="7"|-0.5||-3.0||Y||7.632||-96.111
|-
| -2.0||Y||3.132||-100.611
|-
| -1.0||Y||0.632||-103.111
|-
| 0.0||Y||0.132||-103.611
|-
| 1.0||N||1.632||-102.111
|-
| 2.0||N||5.132||-98.611
|-
| 3.0||N||10.632||-93.111
|}

====H + HF====

A trajectory for this reaction is generated, with the initial conditions: rHF = 1.811, rHH = 0.745, pHF = 0.0, pHH = -5.0.

2019-05-07T16:13:37Z

Cd1017: /* H + H2 System */

File:Cd1017 Meow table5.png

2019-05-07T16:11:48Z

Cd1017: