ChemWiki - User contributions [en]

MRD:01340400

2020-05-08T19:24:35Z

Cej17: /* Modelling a H + H2 system */

== Modelling a H + H2 system ==
=== Potential Energy Surfaces ===
Chemical reactions can be modelled by using a potential energy surface diagram, which relates the potential energy to the positions of atoms in space. For a system involving three atoms, like the H + H2 system, the distances between the atoms can be described by the bond lengths between atoms A-B and B-C. This is shown for a successful collision of such a system by figure 1.

[[file:Successful_Reaction_HHH01340400.png|thumb|center|Figure 1: A potential energy surface diagram describing a successful reaction between a H atom and a H2 molecule. The path taken by the reaction is denoted by the black line and goes over the Transition State where bond lengths A-B and B-C are equal]]
====Transition States on Potential Energy Surface Diagrams====
The potential energy of a transition state can be defined mathematically by the highest point along the lowest energy route between reactants and products on a potential energy surface. That is, it is a saddle point on a 3-dimensional surface where the relative distances between atoms make up the XY plane and the Z axis defines the potential energy of the system. The saddle point of a surface has the property ∂V(ri)/∂ri=0 or that it has a gradient of 0. In order to distinguish the transition state from local minima by differentiating the potential energy with respect to the x axis and then with respect to the y axis and multiplying them together. If it is a saddle point the results should be above and below zero respectively. When simulating a chemical reaction, the transition state can be easily estimated for symmetric systems, that is systems where the transition state lies upon a mirror plane of the potential surface between the reactant region and the product region. Whilst using this method, it was estimated that the TS bond length of each bond in H-H-H was 91 pm.

[[file:HHH_TS_Estimate.png|thumb|center|Figure 2: A distance vs. time plot of the H + H2 system near the transition state with no initial forces acting on the system. This estimate describes an initial bond length of 91 pm for both A-B and B-C where A, B and C are the respective Hydrogen atoms of the system. This estimate is not exact as at the exact position of the transition state there should be no vibrational energy in the system, and therefore the distance should be unchanging with time.]]

====Minimum Energy Path (MEP)====
The minimum energy path (MEP) is a path along the valley floor of the potential energy surface. The MEP disregards any vibrational energy the molecule may have and so it outlines the minimum point at each step along the reaction path. The Dynamic pathway is distinct from the MEP as it includes the vibrations of a molecule. Therefore the pathways shown by each simulation differ, as the dynamic pathway will oscillate up and down the valley walls whilst the MEP will stay strictly at the lowest local point at all times (figure 3). Whilst simulating the MEP, a comparison between the internuclear distance and momenta against time shows that although the internuclear distance is increasing over time, the momenta of the atoms is constant at zero. This is because the MEP resets the momentum of the atoms to zero at each step of the simulation, which is how the program will negate any vibrational energy in the system.

{| class="wikitable" border="1"
|+ Figure 3
! colspan="2" style="text-align: center;"|Comparison of the MEP and Dynamic pathways with slight displacement of the transition state
|-
! MEP !! Dynamic Pathway
|-
| [[file:MEP_HHH01340400.png|thumb|center|The Minimum Energy Pathway, MEP, shows the reaction pathway with no vibrational energy. Simulation begins at 1 pm displacement from the estimated transition state in the AB direction.]] || [[file:Dynamic_Pathway_HHH01340400.png|thumb|center|The Dynamic pathway, here shown on a contour plot, shows the molecule has vibrational energy and thus will oscillate along the valley walls as the system. Simulation begins at 1 pm displacement from the estimated transition state in the AB direction.]]
|}

====Reactive and Unreactive Trajectories====
Not all collisions between molecular Hydrogen and atomic Hydrogen will result in a successful reaction. Whether a collision is successful or not is dependant on the relative magnitudes of momentum (kinetic energy) of each species. Below is a series of different initial trajectories from the same coordinates (figure 4). This table demonstrates how the total energy of the system is not a factor in the successful collision between the reacting species.

{| class="wikitable" border=1
|+ Figure 4
! p1 / g.mol-1.pm.fs-1 !! p2 / g.mol-1.pm.fs-1 !! Etot / kJmol-1 !! Reactive? !! Description of the dynamics !! Illustration of the trajectory
|-
| style="text-align: center;"|-2.56 || style="text-align: center;"|-5.1 || style="text-align: center;"|-414.280 || style="text-align: center;"|Yes || style="text-align: center;"|There is little to no visible vibrational energy in the system until after the system passes through the transition state. || [[file:Contour_Plot1_01340400.png|thumb|center|200px|Contour plot of a dynamic simulation of H + H2.]]
|-
| style="text-align: center;"|-3.1 || style="text-align: center;"|-4.1 || style="text-align: center;"|-420.077 || style="text-align: center;"|No || style="text-align: center;"|The system begins with vibrational energy as shown by the oscillation of the trajectory along the walls of the potential well, however the Hydrogen atom (Atom A) didnt have enough kinetic energy for a successful reaction to occur. Even though the total energy is higher than the previous simulation, the relative directions and magnitudes of the momenta of each of the reacting species means a reaction is not possible. The Hydrogen molecule, H2 BC has momentum in the same direction as the Hydrogen atom, HA, and therefore the relative total colliding momentum is diminished. || [[file:Contour_Plot2_01340400.png|thumb|center|200px|Contour plot of a dynamic simulation of H + H2.]]
|-
| style="text-align: center;"|-3.1 || style="text-align: center;"|-5.1 || style="text-align: center;"|-413.977 || style="text-align: center;"| Yes|| style="text-align: center;"| There is an initial vibrational energy to the H2 AB molecule and after the the transition state has been crossed, the resultant H2 BC molecule has more vibrational energy, as indicated by the larger oscillations. || [[file:Contour_Plot3_01340400.png|thumb|center|200px|Contour plot of a dynamic simulation of H + H2.]]
|-
| style="text-align: center;"|-5.1 || style="text-align: center;"|-10.1 || style="text-align: center;"| -357..277|| style="text-align: center;"| No|| style="text-align: center;"| Initially the molecular Hydrogen species, H2 AB, has little to no visible vibrational energy as the dynamic simulation shows no oscillation along the potential energy surface. The system then crosses over the transition state and forms a new bond between HB and HC. However the system reverts back to moleculat H2 AB and HC. || [[file:Contour_Plot4_01340400.png|thumb|center|200px|Contour plot of a dynamic simulation of H + H2.]]
|-
| style="text-align: center;"|-5.1 || style="text-align: center;"|-10.6 || style="text-align: center;"|-349.477 || style="text-align: center;"| Yes|| style="text-align: center;"| Initially the molecular Hydrogen species H2 AB has little to no visible vibrational energy. After the system crosses the transition state, the system proceeds to vibrate rigorously and break the BC bond to temporarily reform the original AB bond. After that the system again crosses the transition state to form molecular H2 BC. || [[file:Contour_Plot5_01340400.png|thumb|center|200px|Contour plot of a dynamic simulation of H + H2.]]
|}

====Transition State Theory====
Transition State Theory (TST) is a powerful theory which helps predict the reaction rate for a given process. Unlike the Arrhenius Equation, TST takes into account temperature dependancy in the form of the pre-exponential values RCl and the partition functions. TST is an imperfect approximation of the reaction dynamics of a system, as it makes the following assumptions: the kinetic energy along the reaction coordinate follows the Boltzman Distribution; all reaction trajectories with an energy greater than the activation energy will be reactive; the motion of the system over the transition state is considered classically, and therefore doesn't take into account quantum effects such as tunnelling or quantisation of energy states; once a reaction has crossed over the transition state it cannot cross back over again; and finally that the reactants are in equilibrium with the transition state structure.

These assumptions mean that TST will overestimate the rate of a reaction when compared to experimental results, since a reaction system can cross over the transition state multiple times. Also, collisions which do initially cross over the transition state are counted as successful in TST but they may be counted towards the rate as a successful collision.

==Modelling F-H-H Systems==
The reaction of a Fluorine atom with a H2 molecule to form HF + H is exothermic, whilst the reaction of Hydrogen Fluoride with a Hydrogen atom to form F + H2 is endothermic. This is seen in figure 5, which shows a potential energy surface for the F-H-H system. The lower potential energy seen at small AB distances (F-H bond formed) indicates that the F-H bond is stronger and more stable than that of the H-H bond. The formation of a more stable species will result in energy being dispersed to the surroundings, whilst the formation of a less stable species will require energy to promote that species to the higher energy level.

The energy barrier of the transition state in this diagram is relatively small, and is therefore difficult to discern by eye. However, using the information provided by the Hessian it can be estimated that the transition state occurs at F-H 181 pm and H-H 75 pm. Using Hammond's Postulate, we can infer that the structure of the transition state is similar to the structure of H2, since they are energetically so similar. The energy barrier for the reaction of H2 with F is 0.071 kJ.mol-1 and the energy barrier for the reaction of HF with H is 124.618 kJ.mol-1.

[[file:FHH_Surface_Plot_01340400.png|thumb|center|Figure 5: A potential energy surface diagram for the F-H-H system.]]

====Reaction Dynamics====
A successful reaction between F and H2 forms Hydrogen Fluoride and a Hydrogen atom can result in the HF molecule having a large vibrational energy. The molecule disperses this energy by emission of radiation to its surroundings via radiative decay. Figure 6 shows how the HF molecule (AB) retains a significant amount of momentum after the reaction is complete.
[[file:F_H2_Reaction_01340400.png|thumb|center|Figure 6: Momentum vs Time graph for a Fluorine atom successfully reacting with a H2 molecule. Initial conditions are: AB (F-H) Distance 230 pm, BC (H-H) Distance 74 pm, AB momentum -2 g.mol-1pm.fs-1.]]

MRD:01340400

2020-05-08T18:52:35Z

Cej17: /* Modelling F-H-H Systems */

== Modelling a H + H2 system ==
=== Potential Energy Surfaces ===
Chemical reactions can be modelled by using a potential energy surface diagram, which relates the potential energy to the positions of atoms in space. For a system involving three atoms, like the H + H2 system, the distances between the atoms can be described by the bond lengths between atoms A-B and B-C. This is shown for a successful collision of such a system by figure 1.

[[file:Successful_Reaction_HHH01340400.png|thumb|center|Figure 1: A potential energy surface diagram describing a successful reaction between a H atom and a H2 molecule. The path taken by the reaction is denoted by the black line and goes over the Transition State where bond lengths A-B and B-C are equal]]
====Transition States on Potential Energy Surface Diagrams====
The potential energy of a transition state can be defined mathematically by the highest point along the lowest energy route between reactants and products on a potential energy surface. That is, it is a saddle point on a 3-dimensional surface where the relative distances between atoms make up the XY plane and the Z axis defines the potential energy of the system. The saddle point of a surface has the property ∂V(ri)/∂ri=0 or that it has a gradient of 0. In order to distinguish the transition state from local minima by differentiating the potential energy with respect to the x axis and then with respect to the y axis and multiplying them together. If it is a saddle point the results should be above and below zero respectively. When simulating a chemical reaction, the transition state can be easily estimated for symmetric systems, that is systems where the transition state lies upon a mirror plane of the potential surface between the reactant region and the product region. Whilst using this method, it was estimated that the TS bond length of each bond in H-H-H was 91 pm.

[[file:HHH_TS_Estimate.png|thumb|center|Figure 2: A distance vs. time plot of the H + H2 system near the transition state with no initial forces acting on the system. This estimate describes an initial bond length of 91 pm for both A-B and B-C where A, B and C are the respective Hydrogen atoms of the system. This estimate is not exact as at the exact position of the transition state there should be no vibrational energy in the system, and therefore the distance should be unchanging with time.]]

====Minimum Energy Path (MEP)====
The minimum energy path (MEP) is a path along the valley floor of the potential energy surface. The MEP disregards any vibrational energy the molecule may have and so it outlines the minimum point at each step along the reaction path. The Dynamic pathway is distinct from the MEP as it includes the vibrations of a molecule. Therefore the pathways shown by each simulation differ, as the dynamic pathway will oscillate up and down the valley walls whilst the MEP will stay strictly at the lowest local point at all times (figure 3). Whilst simulating the MEP, a comparison between the internuclear distance and momenta against time shows that although the internuclear distance is increasing over time, the momenta of the atoms is constant at zero. This is because the MEP resets the momentum of the atoms to zero at each step of the simulation, which is how the program will negate any vibrational energy in the system.

{| class="wikitable" border="1"
|+ Figure 3
! colspan="2" style="text-align: center;"|Comparison of the MEP and Dynamic pathways with slight displacement of the transition state
|-
! MEP !! Dynamic Pathway
|-
| [[file:MEP_HHH01340400.png|thumb|center|The Minimum Energy Pathway, MEP, shows the reaction pathway with no vibrational energy. Simulation begins at 1 pm displacement from the estimated transition state in the AB direction.]] || [[file:Dynamic_Pathway_HHH01340400.png|thumb|center|The Dynamic pathway, here shown on a contour plot, shows the molecule has vibrational energy and thus will oscillate along the valley walls as the system. Simulation begins at 1 pm displacement from the estimated transition state in the AB direction.]]
|}

====Reactive and Unreactive Trajectories====
Not all collisions between molecular Hydrogen and atomic Hydrogen will result in a successful reaction. Whether a collision is successful or not is dependant on the relative magnitudes of momentum (kinetic energy) of each species. Below is a series of different initial trajectories from the same coordinates (figure 4). This table demonstrates how the total energy of the system is not a factor in the successful collision between the reacting species.

{| class="wikitable" border=1
|+ Figure 4
! p1 / g.mol-1.pm.fs-1 !! p2 / g.mol-1.pm.fs-1 !! Etot / kJmol-1 !! Reactive? !! Description of the dynamics !! Illustration of the trajectory
|-
| style="text-align: center;"|-2.56 || style="text-align: center;"|-5.1 || style="text-align: center;"|-414.280 || style="text-align: center;"|Yes || style="text-align: center;"|There is little to no visible vibrational energy in the system until after the system passes through the transition state. || [[file:Contour_Plot1_01340400.png|thumb|center|200px|Contour plot of a dynamic simulation of H + H2.]]
|-
| style="text-align: center;"|-3.1 || style="text-align: center;"|-4.1 || style="text-align: center;"|-420.077 || style="text-align: center;"|No || style="text-align: center;"|The system begins with vibrational energy as shown by the oscillation of the trajectory along the walls of the potential well, however the Hydrogen atom (Atom A) didnt have enough kinetic energy for a successful reaction to occur. Even though the total energy is higher than the previous simulation, the relative directions and magnitudes of the momenta of each of the reacting species means a reaction is not possible. The Hydrogen molecule, H2 BC has momentum in the same direction as the Hydrogen atom, HA, and therefore the relative total colliding momentum is diminished. || [[file:Contour_Plot2_01340400.png|thumb|center|200px|Contour plot of a dynamic simulation of H + H2.]]
|-
| style="text-align: center;"|-3.1 || style="text-align: center;"|-5.1 || style="text-align: center;"|-413.977 || style="text-align: center;"| Yes|| style="text-align: center;"| There is an initial vibrational energy to the H2 AB molecule and after the the transition state has been crossed, the resultant H2 BC molecule has more vibrational energy, as indicated by the larger oscillations. || [[file:Contour_Plot3_01340400.png|thumb|center|200px|Contour plot of a dynamic simulation of H + H2.]]
|-
| style="text-align: center;"|-5.1 || style="text-align: center;"|-10.1 || style="text-align: center;"| -357..277|| style="text-align: center;"| No|| style="text-align: center;"| Initially the molecular Hydrogen species, H2 AB, has little to no visible vibrational energy as the dynamic simulation shows no oscillation along the potential energy surface. The system then crosses over the transition state and forms a new bond between HB and HC. However the system reverts back to moleculat H2 AB and HC. || [[file:Contour_Plot4_01340400.png|thumb|center|200px|Contour plot of a dynamic simulation of H + H2.]]
|-
| style="text-align: center;"|-5.1 || style="text-align: center;"|-10.6 || style="text-align: center;"|-349.477 || style="text-align: center;"| Yes|| style="text-align: center;"| Initially the molecular Hydrogen species H2 AB has little to no visible vibrational energy. After the system crosses the transition state, the system proceeds to vibrate rigorously and break the BC bond to temporarily reform the original AB bond. After that the system again crosses the transition state to form molecular H2 BC. || [[file:Contour_Plot5_01340400.png|thumb|center|200px|Contour plot of a dynamic simulation of H + H2.]]
|}

====Transition State Theory====

==Modelling F-H-H Systems==
The reaction of a Fluorine atom with a H2 molecule to form HF + H is exothermic, whilst the reaction of Hydrogen Fluoride with a Hydrogen atom to form F + H2 is endothermic. This is seen in figure 5, which shows a potential energy surface for the F-H-H system. The lower potential energy seen at small AB distances (F-H bond formed) indicates that the F-H bond is stronger and more stable than that of the H-H bond. The formation of a more stable species will result in energy being dispersed to the surroundings, whilst the formation of a less stable species will require energy to promote that species to the higher energy level.

The energy barrier of the transition state in this diagram is relatively small, and is therefore difficult to discern by eye. However, using the information provided by the Hessian it can be estimated that the transition state occurs at F-H 181 pm and H-H 75 pm. Using Hammond's Postulate, we can infer that the structure of the transition state is similar to the structure of H2, since they are energetically so similar. The energy barrier for the reaction of H2 with F is 0.071 kJ.mol-1 and the energy barrier for the reaction of HF with H is 124.618 kJ.mol-1.

[[file:FHH_Surface_Plot_01340400.png|thumb|center|Figure 5: A potential energy surface diagram for the F-H-H system.]]

====Reaction Dynamics====
A successful reaction between F and H2 forms Hydrogen Fluoride and a Hydrogen atom can result in the HF molecule having a large vibrational energy. The molecule disperses this energy by emission of radiation to its surroundings via radiative decay. Figure 6 shows how the HF molecule (AB) retains a significant amount of momentum after the reaction is complete.
[[file:F_H2_Reaction_01340400.png|thumb|center|Figure 6: Momentum vs Time graph for a Fluorine atom successfully reacting with a H2 molecule. Initial conditions are: AB (F-H) Distance 230 pm, BC (H-H) Distance 74 pm, AB momentum -2 g.mol-1pm.fs-1.]]

MRD:01340400

2020-05-08T12:42:25Z

Cej17:

== Modelling a H + H2 system ==
=== Potential Energy Surfaces ===
Chemical reactions can be modelled by using a potential energy surface diagram, which relates the potential energy to the positions of atoms in space. For a system involving three atoms, like the H + H2 system, the distances between the atoms can be described by the bond lengths between atoms A-B and B-C. This is shown for a successful collision of such a system by figure 1.

[[file:Successful_Reaction_HHH01340400.png|thumb|center|Figure 1: A potential energy surface diagram describing a successful reaction between a H atom and a H2 molecule. The path taken by the reaction is denoted by the black line and goes over the Transition State where bond lengths A-B and B-C are equal]]
====Transition States on Potential Energy Surface Diagrams====
The potential energy of a transition state can be defined mathematically by the highest point along the lowest energy route between reactants and products on a potential energy surface. That is, it is a saddle point on a 3-dimensional surface where the relative distances between atoms make up the XY plane and the Z axis defines the potential energy of the system. The saddle point of a surface has the property ∂V(ri)/∂ri=0 or that it has a gradient of 0. In order to distinguish the transition state from local minima by differentiating the potential energy with respect to the x axis and then with respect to the y axis and multiplying them together. If it is a saddle point the results should be above and below zero respectively. When simulating a chemical reaction, the transition state can be easily estimated for symmetric systems, that is systems where the transition state lies upon a mirror plane of the potential surface between the reactant region and the product region. Whilst using this method, it was estimated that the TS bond length of each bond in H-H-H was 91 pm.

[[file:HHH_TS_Estimate.png|thumb|center|Figure 2: A distance vs. time plot of the H + H2 system near the transition state with no initial forces acting on the system. This estimate describes an initial bond length of 91 pm for both A-B and B-C where A, B and C are the respective Hydrogen atoms of the system. This estimate is not exact as at the exact position of the transition state there should be no vibrational energy in the system, and therefore the distance should be unchanging with time.]]

====Minimum Energy Path (MEP)====
The minimum energy path (MEP) is a path along the valley floor of the potential energy surface. The MEP disregards any vibrational energy the molecule may have and so it outlines the minimum point at each step along the reaction path. The Dynamic pathway is distinct from the MEP as it includes the vibrations of a molecule. Therefore the pathways shown by each simulation differ, as the dynamic pathway will oscillate up and down the valley walls whilst the MEP will stay strictly at the lowest local point at all times (figure 3). Whilst simulating the MEP, a comparison between the internuclear distance and momenta against time shows that although the internuclear distance is increasing over time, the momenta of the atoms is constant at zero. This is because the MEP resets the momentum of the atoms to zero at each step of the simulation, which is how the program will negate any vibrational energy in the system.

{| class="wikitable" border="1"
|+ Figure 3
! colspan="2" style="text-align: center;"|Comparison of the MEP and Dynamic pathways with slight displacement of the transition state
|-
! MEP !! Dynamic Pathway
|-
| [[file:MEP_HHH01340400.png|thumb|center|The Minimum Energy Pathway, MEP, shows the reaction pathway with no vibrational energy. Simulation begins at 1 pm displacement from the estimated transition state in the AB direction.]] || [[file:Dynamic_Pathway_HHH01340400.png|thumb|center|The Dynamic pathway, here shown on a contour plot, shows the molecule has vibrational energy and thus will oscillate along the valley walls as the system. Simulation begins at 1 pm displacement from the estimated transition state in the AB direction.]]
|}

====Reactive and Unreactive Trajectories====
Not all collisions between molecular Hydrogen and atomic Hydrogen will result in a successful reaction. Whether a collision is successful or not is dependant on the relative magnitudes of momentum (kinetic energy) of each species. Below is a series of different initial trajectories from the same coordinates (figure 4). This table demonstrates how the total energy of the system is not a factor in the successful collision between the reacting species.

{| class="wikitable" border=1
|+ Figure 4
! p1 / g.mol-1.pm.fs-1 !! p2 / g.mol-1.pm.fs-1 !! Etot / kJmol-1 !! Reactive? !! Description of the dynamics !! Illustration of the trajectory
|-
| style="text-align: center;"|-2.56 || style="text-align: center;"|-5.1 || style="text-align: center;"|-414.280 || style="text-align: center;"|Yes || style="text-align: center;"|There is little to no visible vibrational energy in the system until after the system passes through the transition state. || [[file:Contour_Plot1_01340400.png|thumb|center|200px|Contour plot of a dynamic simulation of H + H2.]]
|-
| style="text-align: center;"|-3.1 || style="text-align: center;"|-4.1 || style="text-align: center;"|-420.077 || style="text-align: center;"|No || style="text-align: center;"|The system begins with vibrational energy as shown by the oscillation of the trajectory along the walls of the potential well, however the Hydrogen atom (Atom A) didnt have enough kinetic energy for a successful reaction to occur. Even though the total energy is higher than the previous simulation, the relative directions and magnitudes of the momenta of each of the reacting species means a reaction is not possible. The Hydrogen molecule, H2 BC has momentum in the same direction as the Hydrogen atom, HA, and therefore the relative total colliding momentum is diminished. || [[file:Contour_Plot2_01340400.png|thumb|center|200px|Contour plot of a dynamic simulation of H + H2.]]
|-
| style="text-align: center;"|-3.1 || style="text-align: center;"|-5.1 || style="text-align: center;"|-413.977 || style="text-align: center;"| Yes|| style="text-align: center;"| There is an initial vibrational energy to the H2 AB molecule and after the the transition state has been crossed, the resultant H2 BC molecule has more vibrational energy, as indicated by the larger oscillations. || [[file:Contour_Plot3_01340400.png|thumb|center|200px|Contour plot of a dynamic simulation of H + H2.]]
|-
| style="text-align: center;"|-5.1 || style="text-align: center;"|-10.1 || style="text-align: center;"| -357..277|| style="text-align: center;"| No|| style="text-align: center;"| Initially the molecular Hydrogen species, H2 AB, has little to no visible vibrational energy as the dynamic simulation shows no oscillation along the potential energy surface. The system then crosses over the transition state and forms a new bond between HB and HC. However the system reverts back to moleculat H2 AB and HC. || [[file:Contour_Plot4_01340400.png|thumb|center|200px|Contour plot of a dynamic simulation of H + H2.]]
|-
| style="text-align: center;"|-5.1 || style="text-align: center;"|-10.6 || style="text-align: center;"|-349.477 || style="text-align: center;"| Yes|| style="text-align: center;"| Initially the molecular Hydrogen species H2 AB has little to no visible vibrational energy. After the system crosses the transition state, the system proceeds to vibrate rigorously and break the BC bond to temporarily reform the original AB bond. After that the system again crosses the transition state to form molecular H2 BC. || [[file:Contour_Plot5_01340400.png|thumb|center|200px|Contour plot of a dynamic simulation of H + H2.]]
|}

====Transition State Theory====

==Modelling F-H-H Systems==
The reaction of a Fluorine atom with a H2 molecule to form HF + H is exothermic, whilst the reaction of Hydrogen Fluoride with a Hydrogen atom to form F + H2 is endothermic. This is seen in figure 5, which shows a potential energy surface for the F-H-H system. The lower potential energy seen at small AB distances (F-H bond formed) indicates that the F-H bond is stronger and more stable than that of the H-H bond. The energy barrier of the transition state in this diagram is relatively small, and is therefore difficult to discern by eye. However, using the information provided by the Hessian it can be estimated that the transition state occurs at F-H 181 pm and H-H 75 pm. Using Hammond's Postulate, we can infer that the structure of the transition state is similar to the structure of H2, since they are energetically so similar.

[[file:FHH_Surface_Plot_01340400.png|thumb|center|Figure 5: A potential energy surface diagram for the F-H-H system.]]

====Reaction Dynamics====
A successful reaction between F and H2
[[file:F_H2_Reaction_01340400.png|thumb|center|Figure 6: Momentum vs Time graph for a Fluorine atom successfully reacting with a H2 molecule. Initial conditions are: AB (F-H) Distance 230 pm, BC (H-H) Distance 74 pm, AB momentum -2 g.mol-1pm.fs-1.]]

File:F H2 Reaction 01340400.png

2020-05-08T12:36:12Z

Cej17:

File:FHH Surface Plot 01340400.png

2020-05-08T10:28:22Z

Cej17:

MRD:01340400

2020-05-07T15:18:56Z

Cej17:

MRD:01340400

2020-05-07T13:36:50Z

Cej17: /* Reactive and Unreactive Trajectories */

File:Contour Plot5 01340400.png

2020-05-07T13:36:22Z

Cej17:

File:Contour Plot4 01340400.png

2020-05-07T13:33:43Z

Cej17:

MRD:01340400

2020-05-07T12:20:25Z

Cej17: /* Reactive and Unreactive Trajectories */

MRD:01340400

2020-05-07T12:08:16Z

Cej17: /* Reactive and Unreactive Trajectories */

File:Contour Plot3 01340400.png

2020-05-07T12:07:23Z

Cej17:

File:Contour Plot2 01340400.png

2020-05-07T11:51:46Z

Cej17:

MRD:01340400

2020-05-07T11:44:48Z

Cej17:

File:Contour Plot1 01340400.png

2020-05-07T11:41:40Z

Cej17:

MRD:01340400

2020-05-07T11:40:49Z

Cej17:

MRD:01340400

2020-05-07T11:18:47Z

Cej17:

MRD:01340400

2020-05-07T10:22:03Z

Cej17:

MRD:01340400

2020-05-07T10:21:32Z

Cej17:

File:MEP HHH01340400.png

2020-05-07T09:51:12Z

Cej17:

MRD:01340400

2020-05-07T09:50:50Z

Cej17:

File:Dynamic Pathway HHH01340400.png

2020-05-07T09:49:41Z

Cej17: Cej17 uploaded a new version of File:Dynamic Pathway HHH01340400.png

MRD:01340400

2020-05-05T18:02:22Z

Cej17: /* Minimum Energy Path (MEP) */

MRD:01340400

2020-05-05T18:01:39Z

Cej17:

File:Dynamic Pathway HHH01340400.png

2020-05-05T17:58:23Z

Cej17:

MRD:01340400

2020-05-05T17:57:48Z

Cej17:

MRD:01340400

2020-05-05T17:44:00Z

Cej17:

MRD:01340400

2020-05-05T16:59:12Z

Cej17:

File:Successful Reaction HHH01340400.png

2020-05-05T16:45:48Z

Cej17:

MRD:01340400

2020-05-05T16:13:40Z

Cej17: /* Modelling a H + H2 system */

== Modelling a H + H2 system ==
=== Potential Energy Surfaces ===
The potential energy of a transition state can be defined mathematically by the highest point along the lowest energy route between reactants and products on a potential energy surface. That is, it is a saddle point on a 3-dimensional surface where the relative distances between atoms make up the XY plane and the Z axis defines the potential energy of the system. The saddle point of a surface has the property ∂V(ri)/∂ri=0 or that it has a gradient of 0. In order to distinguish the transition state from local minima by differentiating the potential energy with respect to the x axis and then with respect to the y axis and multiplying them together. If it is a saddle point the results should be above and below zero respectively. When simulating a chemical reaction, the transition state can be easily estimated for symmetric systems, that is systems where the transition state lies upon a mirror plane of the potential surface between the reactant region and the product region. Whilst using this method, it was estimated that the TS bond length of each bond in H-H-H was 91 pm.
[[file:HHH_TS_Estimate.png|thumb|left|A distance vs. time plot of the H + H2 system near the transition state with no initial forces acting on the system. This estimate describes an initial bond length of 91 pm for both A-B and B-C where A, B and C are the respective Hydrogen atoms of the system. This estimate is not exact as at the exact position of the transition state there should be no vibrational energy in the system, and therefore the distance should be unchanging with time.]]

MRD:01340400

2020-05-05T15:45:07Z

Cej17: /* Modelling a H + H2 system */

== Modelling a H + H2 system ==
The potential energy of a transition state can be defined mathematically by the highest point along the lowest route between reactants and products. That is, it is a saddle point on a 3-dimensional surface where the relative distances between atoms make up the XY plane and the Z axis defines the potential energy of the system. The saddle point of a surface has the property ∂V(ri)/∂ri=0 or that it has a gradient of 0. In order to distinguish the transition state from local minima by differentiating the potential energy with respect to the x axis and then with respect to the y axis and multiplying them together. If it is a saddle point the results should be above and below zero respectively. When simulating a chemical reaction, the transition state can be easily estimated for symmetric systems, that is systems where the transition state lies upon a mirror plane of the potential surface between the reactant region and the product region. Whilst using this method, it was estimated that the TS bond length of each bond in H-H-H was 91 pm.
[[file:HHH_TS_Estimate.png]]

File:HHH TS Estimate.png

2020-05-05T15:41:44Z

Cej17:

MRD:01340400

2020-05-05T15:40:22Z

Cej17: /* Modelling a H + H2 system */

MRD:01340400

2020-05-05T15:38:28Z

Cej17: /* Modelling a H + H2 system */

MRD:01340400

2020-05-05T14:14:52Z

Cej17: /* Modelling a H + H2 system */

MRD:01340400

2020-05-05T11:05:49Z

Cej17: /* Modelling a H + H2 system */

MRD:01340400

2020-05-05T09:43:18Z

Cej17: Created page with " == Modelling a H + H2 system == The potential energy of a transition state can be defined mathematically by the highest point along the lowest route between reactants and pro..."

Modcej17

2019-03-01T12:04:47Z

Cej17:

=== Computational Lab 2 ===

=='''Molecule: NH3 '''==

Bond Length: 1.01798 a.u.

Bond Angle: 105.745

Calculation Method: B3LYP

Basis Set: 6-31G(d,p)

Final Energy E(RB3LYP): -56.55776873 au

RMS Gradient: 0.00000323 au

Point Group: C3V

<pre>Item Value Threshold Converged?

Maximum Force 0.000006 0.000450 YES

RMS Force 0.000004 0.000300 YES

Maximum Displacement 0.000014 0.001800 YES

RMS Displacement 0.000009 0.001200 YES

Predicted change in Energy=-1.166745D-10</pre>

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CJEFFREYS NH3 OPTF POP.LOG</uploadedFileContents>
<script>frame 1.6</script>
</jmolApplet></jmol>

'''NH3 Vibrational Modes'''

[[File:CJeffreys NH3.png|thumb|center]]

{| class="wikitable" border="1"
|+ Vibration Modes
! Frequency !! IR intensity !! Vibrational mode
|-
| 1089 || 145 || A1 (1)
|-
| 1693 || 13 || E (2)
|-
| 1693 || 13 || E (3)
|-
| 3461 || 1 || A1 (4)
|-
| 3589 || 0 || E (5)
|-
| 3589 || 0 || E (6)
|}

'''NH3 Charge Distribution'''

[[File:CJeffreys Charge Distribution.png|thumb|center]]

'''Questions'''

how many modes do you expect from the 3N-6 rule?

3*4-6=6

which modes are degenerate (ie have the same energy)?

E(2) and E(3) are degenerate and E(3) and E(4) are degenerate

which modes are "bending" vibrations and which are "bond stretch" vibrations?

A1(1), E(2) and E(3) are all bending, A1(4), E(5) and E(6) are all bond stretch

which mode is highly symmetric?

A1(1)
one mode is known as the "umbrella" mode, which one is this?

A1(1)

how many bands would you expect to see in an experimental spectrum of gaseous ammonia?

2

=='''Molecule: N2 '''==

Bond Length:1.106

Calculation Method: RB3LYP

Basis Set: 6-31G(D,P)

Final Energy E(RB3LYP): -109.524 a.u.

RMS Gradient: 0.00000060 a.u.

Point Group: D*H

<pre> Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000000 0.001800 YES
RMS Displacement 0.000000 0.001200 YES
Predicted change in Energy=-3.401020D-13</pre>

<jmol><jmolApplet>
<title>N2</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CJEFFREYS N2 OPTF POP.LOG</uploadedFileContents>
<script>frame 1.10</script>
</jmolApplet></jmol>

'''N2 Vibrational Modes'''

[[File:CJeffreys N2 Vibrations.png|thumb|center]]

{| class="wikitable" border="1"
|+ Vibration Modes
! Frequency !! IR intensity !! Vibrational mode
|-
| 2457 || 0 || SGG
|}

'''N2 Charge Distribution'''

[[File:CJeffreys N2 Charge Distribution.png|350px|thumb|center]]

'''Questions'''

Nitrogen has 1 mode of vibration (bond stretch)

how many bands would you expect to see in an experimental spectrum of gaseous Nitrogen?

none as it is IR inactive

Unique identifier code: DEKFUX

https://www.ccdc.cam.ac.uk/structures/Search?Ccdcid=DEKFUX&DatabaseToSearch=Published

N-N bond length in structure: 1.086 a.u.

Bond lengths are determined by the amount of electron density between the two nuclei of the atoms involved. Increased electron density causes a shorter bond as the positive nuclei are more strongly attracted to the increased negative charged of the electron cloud. in this crystal structure, we see the dinitrogen species bound to a Ru metal ion, which acts as an electron withdrawing species. Due to electrons being withdrawn from the dinitrogen, there is less negative character between the nuclei and thus the bond length increases. This is consistent with the calculated result on Gaussian (1.106 a.u.) compared to the observed result from the crystal structure (1.086 a.u.).

=='''Molecule: H2 '''==

Bond Length: 0.6 au

Calculation Method: RB3LYP

Basis Set: 6-31G(d,p)

Final Energy E(RB3LYP): -1.17853936 au

RMS Gradient: 0.00000017 au

Point Group: D*H

<pre>Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000000 0.001800 YES
RMS Displacement 0.000001 0.001200 YES
Predicted change in Energy=-1.164080D-13</pre>

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CJEFFREYS H2 OPTF POP.LOG</uploadedFileContents>
<script>frame 1.12</script>
</jmolApplet></jmol>

'''H2 Vibrational Modes'''

[[File:CJeffreys H2 Vibrations.png|thumb|center]]

{| class="wikitable" border="1"
|+ Vibration Modes
! Frequency !! IR intensity !! Vibrational mode
|-
| 4466|| 0 || SGG
|}

'''H2 Charge Distribution'''

[[File:CJeffreys H2 Charge Distribution2.png|thumb|center]]

'''Questions'''

Hydrogen has 1 mode of vibration (bond stretch)

how many bands would you expect to see in an experimental spectrum of gaseous Hydrogen?

none as it is IR inactive

== '''Haber Process''' ==

NH3 enthalpy change: -148492 kJmol-1

2*NH3 enthalpy change: -296984.865017 kJmol-1

N2 enthalpy change: -287555.284 kJmol-1

H2 enthalpy change: -3094.25532539 kJmol-1

3*H2 enthalpy change: -9282.765269 kJmol-1

ΔHtotal = 2*NH3 - (N2 + 3*H2)

=-146.81 kJmol-1

The ammonia product is more stable because it has a negative enthalpy change which is favourable in Gibbs Free energy.

=='''Molecule of choice: NF3'''==

Bond Length: 1.38404 a.u.

Bond Angle: 101.830

Calculation Method: B3LYP

Basis Set: 6-31G(d,p)

Final Energy E(RB3LYP): -354.07131058 a.u.

RMS Gradient: 0.00010256 a.u.

Point Group: C3V

<pre>Item Value Threshold Converged?
Maximum Force 0.000164 0.000450 YES
RMS Force 0.000108 0.000300 YES
Maximum Displacement 0.000612 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
Predicted change in Energy=-1.274067D-07</pre>

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CJEFFREYS NF3 OPTF POP.LOG</uploadedFileContents>
<script>frame 1.12</script>
</jmolApplet></jmol>

NF3 Vibrational Modes

[[File:CJeffreys NF3 Vibrational Modes.png|thumb|center]]

{| class="wikitable" border="1"
|+ Vibration Modes
! Frequency !! IR intensity !! Vibrational mode
|-
| 482 || 1 || E (1)
|-
| 482 || 1 || E (2)
|-
| 644 || 3 || A1 (3)
|-
| 929 || 208 || E (4)
|-
| 929 || 208 || E (5)
|-
| 1062 || 40 || A1 (6)
|}

'''NF3Charge Distribution'''

[[File:CJeffreys NF3 Charge Distribution.png|thumb|center]]

{| class="wikitable" border="1"
|+ Molecular Orbitals of NF3
! Orbital Image !! Energy (a.u.) !! Description
|-
| [[File:CJeffreys NF3 Orbital1.png|100px]] || -1.35870 || This orbital shows a positive combination of all the atomic S orbitals in the same phase.
|-
| [[File:CJeffreys NF3 Orbital2.png|100px]] || -0.81874 || This orbital shows the Px orbitals of the fluorine positively interacting with the S orbital of the Nitrogen.
|-
| [[File:CJeffreys NF3 Orbital3.png|100px]] || -0.61981 || This orbital shows the Pz orbitals overlapping with the parallel Pz orbital of the Nitrogen atom.
|-
| [[File:CJeffreys NF3 Orbital4.png|100px]] || -0.57102 || This orbital shows the Py orbital of one fluorine interacting with the other Py orbitals of the other fluorine atoms.
|-
| [[File:CJeffreys NF3 Orbital5.png|100px]] || -0.42224 || This orbital shows the P antibonding orbitals of the Fluorine atoms. they are not interacting as they are out of phase.
|}

Modcej17

2019-03-01T11:52:00Z

Cej17:

=== Computational Lab 2 ===

=='''Molecule: NH3 '''==

Bond Length: 1.01798 a.u.

Bond Angle: 105.745

Calculation Method: B3LYP

Basis Set: 6-31G(d,p)

Final Energy E(RB3LYP): -56.55776873 au

RMS Gradient: 0.00000323 au

Point Group: C3V

<pre>Item Value Threshold Converged?

Maximum Force 0.000006 0.000450 YES

RMS Force 0.000004 0.000300 YES

Maximum Displacement 0.000014 0.001800 YES

RMS Displacement 0.000009 0.001200 YES

Predicted change in Energy=-1.166745D-10</pre>

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CJEFFREYS NH3 OPTF POP.LOG</uploadedFileContents>
<script>frame 1.6</script>
</jmolApplet></jmol>

'''NH3 Vibrational Modes'''

[[File:CJeffreys NH3.png|thumb|center]]

{| class="wikitable" border="1"
|+ Vibration Modes
! Frequency !! IR intensity !! Vibrational mode
|-
| 1089 || 145 || A1 (1)
|-
| 1693 || 13 || E (2)
|-
| 1693 || 13 || E (3)
|-
| 3461 || 1 || A1 (4)
|-
| 3589 || 0 || E (5)
|-
| 3589 || 0 || E (6)
|}

'''NH3 Charge Distribution'''

[[File:CJeffreys Charge Distribution.png|thumb|center]]

'''Questions'''

how many modes do you expect from the 3N-6 rule?

3*4-6=6

which modes are degenerate (ie have the same energy)?

E(2) and E(3) are degenerate and E(3) and E(4) are degenerate

which modes are "bending" vibrations and which are "bond stretch" vibrations?

A1(1), E(2) and E(3) are all bending, A1(4), E(5) and E(6) are all bond stretch

which mode is highly symmetric?

A1(1)
one mode is known as the "umbrella" mode, which one is this?

A1(1)

how many bands would you expect to see in an experimental spectrum of gaseous ammonia?

2

=='''Molecule: N2 '''==

Bond Length:1.106

Calculation Method: RB3LYP

Basis Set: 6-31G(D,P)

Final Energy E(RB3LYP): -109.524 a.u.

RMS Gradient: 0.00000060 a.u.

Point Group: D*H

<pre> Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000000 0.001800 YES
RMS Displacement 0.000000 0.001200 YES
Predicted change in Energy=-3.401020D-13</pre>

<jmol><jmolApplet>
<title>N2</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CJEFFREYS N2 OPTF POP.LOG</uploadedFileContents>
<script>frame 1.10</script>
</jmolApplet></jmol>

'''N2 Vibrational Modes'''

[[File:CJeffreys N2 Vibrations.png|thumb|center]]

{| class="wikitable" border="1"
|+ Vibration Modes
! Frequency !! IR intensity !! Vibrational mode
|-
| 2457 || 0 || SGG
|}

'''N2 Charge Distribution'''

[[File:CJeffreys N2 Charge Distribution.png|350px|thumb|center]]

'''Questions'''

Nitrogen has 1 mode of vibration (bond stretch)

how many bands would you expect to see in an experimental spectrum of gaseous Nitrogen?

none as it is IR inactive

Unique identifier code: DEKFUX

https://www.ccdc.cam.ac.uk/structures/Search?Ccdcid=DEKFUX&DatabaseToSearch=Published

N-N bond length in structure: 1.086 a.u.

Bond lengths are determined by the amount of electron density between the two nuclei of the atoms involved. Increased electron density causes a shorter bond as the positive nuclei are more strongly attracted to the increased negative charged of the electron cloud. in this crystal structure, we see the dinitrogen species bound to a Ru metal ion, which acts as an electron withdrawing species. Due to electrons being withdrawn from the dinitrogen, there is less negative character between the nuclei and thus the bond length increases. This is consistent with the calculated result on Gaussian (1.106 a.u.) compared to the observed result from the crystal structure (1.086 a.u.).

=='''Molecule: H2 '''==

Bond Length: 0.6 au

Calculation Method: RB3LYP

Basis Set: 6-31G(d,p)

Final Energy E(RB3LYP): -1.17853936 au

RMS Gradient: 0.00000017 au

Point Group: D*H

<pre>Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000000 0.001800 YES
RMS Displacement 0.000001 0.001200 YES
Predicted change in Energy=-1.164080D-13</pre>

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CJEFFREYS H2 OPTF POP.LOG</uploadedFileContents>
<script>frame 1.12</script>
</jmolApplet></jmol>

'''H2 Vibrational Modes'''

[[File:CJeffreys H2 Vibrations.png|thumb|center]]

{| class="wikitable" border="1"
|+ Vibration Modes
! Frequency !! IR intensity !! Vibrational mode
|-
| 4466|| 0 || SGG
|}

'''H2 Charge Distribution'''

[[File:CJeffreys H2 Charge Distribution2.png|thumb|center]]

'''Questions'''

Hydrogen has 1 mode of vibration (bond stretch)

how many bands would you expect to see in an experimental spectrum of gaseous Hydrogen?

none as it is IR inactive

== '''Haber Process''' ==

NH3 enthalpy change: -148492 kJmol-1

2*NH3 enthalpy change: -296984.865017 kJmol-1

N2 enthalpy change: -287555.284 kJmol-1

H2 enthalpy change: -3094.25532539 kJmol-1

3*H2 enthalpy change: -9282.765269 kJmol-1

ΔHtotal = 2*NH3 - (N2 + 3*H2)

=-146.81 kJmol-1

The ammonia product is more stable because it has a negative enthalpy change which is favourable in Gibbs Free energy.

=='''Molecule of choice: NF3'''==

Bond Length: 1.38404 a.u.

Bond Angle: 101.830

Calculation Method: B3LYP

Basis Set: 6-31G(d,p)

Final Energy E(RB3LYP): -354.07131058 a.u.

RMS Gradient: 0.00010256 a.u.

Point Group: C3V

<pre>Item Value Threshold Converged?
Maximum Force 0.000164 0.000450 YES
RMS Force 0.000108 0.000300 YES
Maximum Displacement 0.000612 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
Predicted change in Energy=-1.274067D-07</pre>

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CJEFFREYS NF3 OPTF POP.LOG</uploadedFileContents>
<script>frame 1.12</script>
</jmolApplet></jmol>

NF3 Vibrational Modes

[[File:CJeffreys NF3 Vibrational Modes.png|thumb|center]]

{| class="wikitable" border="1"
|+ Vibration Modes
! Frequency !! IR intensity !! Vibrational mode
|-
| 482 || 1 || E (1)
|-
| 482 || 1 || E (2)
|-
| 644 || 3 || A1 (3)
|-
| 929 || 208 || E (4)
|-
| 929 || 208 || E (5)
|-
| 1062 || 40 || A1 (6)
|}

'''NF3Charge Distribution'''

[[File:CJeffreys NF3 Charge Distribution.png|thumb|center]]

{| class="wikitable" border="1"
|+ Molecular Orbitals of NF3
! Orbital Image !! Energy (a.u.) !! Description
|-
| [[File:CJeffreys NF3 Orbital1.png|100px]] || 1 || E (1)
|-
| [[File:CJeffreys NF3 Orbital2.png|100px]] || 1 || E (2)
|-
| [[File:CJeffreys NF3 Orbital3.png|100px]] || 3 || A1 (3)
|-
| [[File:CJeffreys NF3 Orbital4.png|100px]] || 208 || E (4)
|-
| [[File:CJeffreys NF3 Orbital5.png|100px]] || 40 || A1 (6)
|}

Modcej17

2019-03-01T11:50:55Z

Cej17:

=== Computational Lab 2 ===

=='''Molecule: NH3 '''==

Bond Length: 1.01798 a.u.

Bond Angle: 105.745

Calculation Method: B3LYP

Basis Set: 6-31G(d,p)

Final Energy E(RB3LYP): -56.55776873 au

RMS Gradient: 0.00000323 au

Point Group: C3V

<pre>Item Value Threshold Converged?

Maximum Force 0.000006 0.000450 YES

RMS Force 0.000004 0.000300 YES

Maximum Displacement 0.000014 0.001800 YES

RMS Displacement 0.000009 0.001200 YES

Predicted change in Energy=-1.166745D-10</pre>

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CJEFFREYS NH3 OPTF POP.LOG</uploadedFileContents>
<script>frame 1.6</script>
</jmolApplet></jmol>

'''NH3 Vibrational Modes'''

[[File:CJeffreys NH3.png|thumb|center]]

{| class="wikitable" border="1"
|+ Vibration Modes
! Frequency !! IR intensity !! Vibrational mode
|-
| 1089 || 145 || A1 (1)
|-
| 1693 || 13 || E (2)
|-
| 1693 || 13 || E (3)
|-
| 3461 || 1 || A1 (4)
|-
| 3589 || 0 || E (5)
|-
| 3589 || 0 || E (6)
|}

'''NH3 Charge Distribution'''

[[File:CJeffreys Charge Distribution.png|thumb|center]]

'''Questions'''

how many modes do you expect from the 3N-6 rule?

3*4-6=6

which modes are degenerate (ie have the same energy)?

E(2) and E(3) are degenerate and E(3) and E(4) are degenerate

which modes are "bending" vibrations and which are "bond stretch" vibrations?

A1(1), E(2) and E(3) are all bending, A1(4), E(5) and E(6) are all bond stretch

which mode is highly symmetric?

A1(1)
one mode is known as the "umbrella" mode, which one is this?

A1(1)

how many bands would you expect to see in an experimental spectrum of gaseous ammonia?

2

=='''Molecule: N2 '''==

Bond Length:1.106

Calculation Method: RB3LYP

Basis Set: 6-31G(D,P)

Final Energy E(RB3LYP): -109.524 a.u.

RMS Gradient: 0.00000060 a.u.

Point Group: D*H

<pre> Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000000 0.001800 YES
RMS Displacement 0.000000 0.001200 YES
Predicted change in Energy=-3.401020D-13</pre>

<jmol><jmolApplet>
<title>N2</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CJEFFREYS N2 OPTF POP.LOG</uploadedFileContents>
<script>frame 1.10</script>
</jmolApplet></jmol>

'''N2 Vibrational Modes'''

[[File:CJeffreys N2 Vibrations.png|thumb|center]]

{| class="wikitable" border="1"
|+ Vibration Modes
! Frequency !! IR intensity !! Vibrational mode
|-
| 2457 || 0 || SGG
|}

'''N2 Charge Distribution'''

[[File:CJeffreys N2 Charge Distribution.png|350px|thumb|center]]

'''Questions'''

Nitrogen has 1 mode of vibration (bond stretch)

how many bands would you expect to see in an experimental spectrum of gaseous Nitrogen?

none as it is IR inactive

Unique identifier code: DEKFUX

https://www.ccdc.cam.ac.uk/structures/Search?Ccdcid=DEKFUX&DatabaseToSearch=Published

N-N bond length in structure: 1.086 a.u.

Bond lengths are determined by the amount of electron density between the two nuclei of the atoms involved. Increased electron density causes a shorter bond as the positive nuclei are more strongly attracted to the increased negative charged of the electron cloud. in this crystal structure, we see the dinitrogen species bound to a Ru metal ion, which acts as an electron withdrawing species. Due to electrons being withdrawn from the dinitrogen, there is less negative character between the nuclei and thus the bond length increases. This is consistent with the calculated result on Gaussian (1.106 a.u.) compared to the observed result from the crystal structure (1.086 a.u.).

=='''Molecule: H2 '''==

Bond Length: 0.6 au

Calculation Method: RB3LYP

Basis Set: 6-31G(d,p)

Final Energy E(RB3LYP): -1.17853936 au

RMS Gradient: 0.00000017 au

Point Group: D*H

<pre>Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000000 0.001800 YES
RMS Displacement 0.000001 0.001200 YES
Predicted change in Energy=-1.164080D-13</pre>

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CJEFFREYS H2 OPTF POP.LOG</uploadedFileContents>
<script>frame 1.12</script>
</jmolApplet></jmol>

'''H2 Vibrational Modes'''

[[File:CJeffreys H2 Vibrations.png|thumb|center]]

{| class="wikitable" border="1"
|+ Vibration Modes
! Frequency !! IR intensity !! Vibrational mode
|-
| 4466|| 0 || SGG
|}

'''H2 Charge Distribution'''

[[File:CJeffreys H2 Charge Distribution2.png|thumb|center]]

'''Questions'''

Hydrogen has 1 mode of vibration (bond stretch)

how many bands would you expect to see in an experimental spectrum of gaseous Hydrogen?

none as it is IR inactive

== '''Haber Process''' ==

NH3 enthalpy change: -148492 kJmol-1

2*NH3 enthalpy change: -296984.865017 kJmol-1

N2 enthalpy change: -287555.284 kJmol-1

H2 enthalpy change: -3094.25532539 kJmol-1

3*H2 enthalpy change: -9282.765269 kJmol-1

ΔHtotal = 2*NH3 - (N2 + 3*H2)

=-146.81 kJmol-1

The ammonia product is more stable because it has a negative enthalpy change which is favourable in Gibbs Free energy.

=='''Molecule of choice: NF3'''==

Bond Length: 1.38404 a.u.

Bond Angle: 101.830

Calculation Method: B3LYP

Basis Set: 6-31G(d,p)

Final Energy E(RB3LYP): -354.07131058 a.u.

RMS Gradient: 0.00010256 a.u.

Point Group: C3V

<pre>Item Value Threshold Converged?
Maximum Force 0.000164 0.000450 YES
RMS Force 0.000108 0.000300 YES
Maximum Displacement 0.000612 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
Predicted change in Energy=-1.274067D-07</pre>

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CJEFFREYS NF3 OPTF POP.LOG</uploadedFileContents>
<script>frame 1.12</script>
</jmolApplet></jmol>

NF3 Vibrational Modes

[[File:CJeffreys NF3 Vibrational Modes.png|thumb|center]]

{| class="wikitable" border="1"
|+ Vibration Modes
! Frequency !! IR intensity !! Vibrational mode
|-
| 482 || 1 || E (1)
|-
| 482 || 1 || E (2)
|-
| 644 || 3 || A1 (3)
|-
| 929 || 208 || E (4)
|-
| 929 || 208 || E (5)
|-
| 1062 || 40 || A1 (6)
|}

'''NF3Charge Distribution'''

[[File:CJeffreys NF3 Charge Distribution.png|thumb|center]]

{| class="wikitable" border="1"
|+ Molecular Orbitals of NF3
! Orbital Image !! Energy (a.u.) !! Description
|-
| [[File:CJeffreys NF3 Orbital1.png]] || 1 || E (1)
|-
| [[File:CJeffreys NF3 Orbital2.png]] || 1 || E (2)
|-
| [[File:CJeffreys NF3 Orbital3.png]] || 3 || A1 (3)
|-
| [[File:CJeffreys NF3 Orbital4.png]] || 208 || E (4)
|-
| [[File:CJeffreys NF3 Orbital5.png]] || 40 || A1 (6)
|}

File:CJeffreys NF3 Orbital5.png

2019-03-01T11:50:43Z

Cej17:

File:CJeffreys NF3 Orbital4.png

2019-03-01T11:50:15Z

Cej17: Cej17 uploaded a new version of File:CJeffreys NF3 Orbital4.png

File:CJeffreys NF3 Orbital4.png

2019-03-01T11:49:38Z

Cej17: Cej17 uploaded a new version of File:CJeffreys NF3 Orbital4.png

File:CJeffreys NF3 Orbital4.png

2019-03-01T11:47:28Z

Cej17:

File:CJeffreys NF3 Orbital3.png

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Cej17:

File:CJeffreys NF3 Orbital2.png

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Cej17:

File:CJeffreys NF3 Orbital1.png

2019-03-01T11:43:02Z

Cej17:

Modcej17

2019-03-01T10:49:21Z

Cej17:

=== Computational Lab 2 ===

=='''Molecule: NH3 '''==

Bond Length: 1.01798 a.u.

Bond Angle: 105.745

Calculation Method: B3LYP

Basis Set: 6-31G(d,p)

Final Energy E(RB3LYP): -56.55776873 au

RMS Gradient: 0.00000323 au

Point Group: C3V

<pre>Item Value Threshold Converged?

Maximum Force 0.000006 0.000450 YES

RMS Force 0.000004 0.000300 YES

Maximum Displacement 0.000014 0.001800 YES

RMS Displacement 0.000009 0.001200 YES

Predicted change in Energy=-1.166745D-10</pre>

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CJEFFREYS NH3 OPTF POP.LOG</uploadedFileContents>
<script>frame 1.6</script>
</jmolApplet></jmol>

'''NH3 Vibrational Modes'''

[[File:CJeffreys NH3.png|thumb|none]]

{| class="wikitable" border="1"
|+ Vibration Modes
! Frequency !! IR intensity !! Vibrational mode
|-
| 1089 || 145 || A1 (1)
|-
| 1693 || 13 || E (2)
|-
| 1693 || 13 || E (3)
|-
| 3461 || 1 || A1 (4)
|-
| 3589 || 0 || E (5)
|-
| 3589 || 0 || E (6)
|}

'''NH3 Charge Distribution'''

[[File:CJeffreys Charge Distribution.png|thumb|none]]

'''Questions'''

how many modes do you expect from the 3N-6 rule?

3*4-6=6

which modes are degenerate (ie have the same energy)?

E(2) and E(3) are degenerate and E(3) and E(4) are degenerate

which modes are "bending" vibrations and which are "bond stretch" vibrations?

A1(1), E(2) and E(3) are all bending, A1(4), E(5) and E(6) are all bond stretch

which mode is highly symmetric?

A1(1)
one mode is known as the "umbrella" mode, which one is this?

A1(1)

how many bands would you expect to see in an experimental spectrum of gaseous ammonia?

2

=='''Molecule: N2 '''==

Bond Length:1.106

Calculation Method: RB3LYP

Basis Set: 6-31G(D,P)

Final Energy E(RB3LYP): -109.524 a.u.

RMS Gradient: 0.00000060 a.u.

Point Group: D*H

<pre> Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000000 0.001800 YES
RMS Displacement 0.000000 0.001200 YES
Predicted change in Energy=-3.401020D-13</pre>

<jmol><jmolApplet>
<title>N2</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CJEFFREYS N2 OPTF POP.LOG</uploadedFileContents>
<script>frame 1.10</script>
</jmolApplet></jmol>

'''N2 Vibrational Modes'''

[[File:CJeffreys N2 Vibrations.png|thumb|none]]

{| class="wikitable" border="1"
|+ Vibration Modes
! Frequency !! IR intensity !! Vibrational mode
|-
| 2457 || 0 || SGG
|}

'''N2 Charge Distribution'''

[[File:CJeffreys N2 Charge Distribution.png|350px|thumb|none]]

'''Questions'''

Nitrogen has 1 mode of vibration (bond stretch)

how many bands would you expect to see in an experimental spectrum of gaseous Nitrogen?

none as it is IR inactive

Unique identifier code: DEKFUX

https://www.ccdc.cam.ac.uk/structures/Search?Ccdcid=DEKFUX&DatabaseToSearch=Published

N-N bond length in structure: 1.086 a.u.

The bond length in a molecule of N2 is calculated to be 1.106 a.u. and the bond length in the crystal structure is 1.086. This is because in the crystal structure, one of the nitrogen atoms has 4 covalent bonds and is positively charged. This allows a stronger interaction between the positive Nitrogen atom and the Bond pair, and reduces the effect of the 'lone pair'.

=='''Molecule: H2 '''==

Bond Length: 0.6 au

Calculation Method: RB3LYP

Basis Set: 6-31G(d,p)

Final Energy E(RB3LYP): -1.17853936 au

RMS Gradient: 0.00000017 au

Point Group: D*H

<pre>Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000000 0.001800 YES
RMS Displacement 0.000001 0.001200 YES
Predicted change in Energy=-1.164080D-13</pre>

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CJEFFREYS H2 OPTF POP.LOG</uploadedFileContents>
<script>frame 1.12</script>
</jmolApplet></jmol>

'''H2 Vibrational Modes'''

[[File:CJeffreys H2 Vibrations.png|thumb|none]]

{| class="wikitable" border="1"
|+ Vibration Modes
! Frequency !! IR intensity !! Vibrational mode
|-
| 4466|| 0 || SGG
|}

'''H2 Charge Distribution'''

[[File:CJeffreys H2 Charge Distribution2.png|thumb|none]]

'''Questions'''

Hydrogen has 1 mode of vibration (bond stretch)

how many bands would you expect to see in an experimental spectrum of gaseous Hydrogen?

none as it is IR inactive

== '''Haber Process''' ==

NH3 enthalpy change: -148492 kJmol-1

2*NH3 enthalpy change: -296984.865017 kJmol-1

N2 enthalpy change: -287555.284 kJmol-1

H2 enthalpy change: -3094.25532539 kJmol-1

3*H2 enthalpy change: -6188.51065078 kJmol-1

ΔHtotal = 2*NH3 - (N2 + 3*H2)

=-3241.07 kJmol-1

The ammonia product is more stable because it has a negative enthalpy change which is favourable in Gibbs Free energy.

=='''Molecule of choice: NF3'''==

Bond Length: 1.38404 a.u.

Bond Angle: 101.830

Calculation Method: B3LYP

Basis Set: 6-31G(d,p)

Final Energy E(RB3LYP): -354.07131058 a.u.

RMS Gradient: 0.00010256 a.u.

Point Group: C3V

<pre>Item Value Threshold Converged?
Maximum Force 0.000164 0.000450 YES
RMS Force 0.000108 0.000300 YES
Maximum Displacement 0.000612 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
Predicted change in Energy=-1.274067D-07</pre>

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CJEFFREYS NF3 OPTF POP.LOG</uploadedFileContents>
<script>frame 1.12</script>
</jmolApplet></jmol>

{| class="wikitable" border="1"
|+ Vibration Modes
! Frequency !! IR intensity !! Vibrational mode
|-
| 482 || 1 || E (1)
|-
| 482 || 1 || E (2)
|-
| 644 || 3 || A1 (3)
|-
| 929 || 208 || E (4)
|-
| 929 || 208 || E (5)
|-
| 1062 || 40 || A1 (6)
|}

Charge Distribution

[[File:CJeffreys NF3 Vibrational Modes.png]]

[[File:CJeffreys NF3 Charge Distribution.png]]

File:CJeffreys NF3 Charge Distribution.png

2019-03-01T10:46:42Z

Cej17:

File:CJeffreys NF3 Vibrational Modes.png

2019-03-01T10:45:23Z

Cej17: