ChemWiki - User contributions [en]

MRD:fzm18

2022-03-01T16:46:34Z

Fzm18:

= H-H-H system =
This section focuses on the dynamics of a H1 + H2-H3 system, where the aim is to form a new H1-H2 bond. Let us first consider the reaction path.
In the system, H1, H2 and H3 are respectively referred to A, B and C.

== Locating the transition state ==
The transition state (TS) can be mathematically defined as ∂V/∂r1 = ∂V/∂r2 = 0. Graphically, the locus of the transition state can be apprehended as the saddle point on the potential energy surface (PES) plot.

[[File:Fzm18Surface PlotTS.png|300px|center|thumb|PES plot showing the transition state (red dot).]]

Physically, this means that the Transition state is a form on inert state, where a particle cannot acquire momentum if it has no momentum at this point. The plot of distances vs time below shows the internuclear distances variation of a H-H-H system with no momentum in the transition state. In this example, the transition state was found was found by varying the internuclear distances until the atoms stopped oscillating, at rAB = rBC = 90.75 pm.

[[File:Fzm18momentaTS.png|300px|center|thumb|Internuclear distances vs time at transition state.]]

== Calculating the reaction path ==
The reaction path is defined by the minimum energy path (mep) and is the fastest path a reaction can take. In this simulation, the momenta are constantly reset at 0 g.mol-1.pm.fs-1. This means that the motions are entirely defined driven by Coulombic interactions. Hence, after reaching a certain distance, the atoms reach a stable state and do not drift further away, as they would in classical dynamics theory.

==Analyzing trajectories at rAB = rTS + δ, rBC = rTS ==

[[File:Fzm18-contourplotTS.png|400px|thumb|Dynamics (left) and MEP (right) simulations. ]]

The graphs show contour plots of the potential energy surface for a near-transition state system rAB = 91.75 pm, rBC = 90.75 pm, system A) in MEP and Dynamics simulations. The black trail reflects the trajectory of particle A, as it travels endlessly (dynamics) or until it exhausts the available electrostatic potential energy.

[[File:Fzm18-SurfaceplotsHHH.png|400px|left|thumb|Final state: H1 + H2-H3 (right) and H1-H2 + H3 (left).]]

As rAB > rBC= rTS, the system tend to revert back to its initial form of H1 + H2-H3. However, note that in the opposite situation, where rAB = 90.75 pm, rBC = 91.75 pm (system B), the system will more likely tend to a new configuration : H1-H2 + H3. The surface plots show the reaction path as a black trail in both cases, rAB > rBC and rBC > rAB.

It is interesting to note that both systems have the same energy, and same the same variations of internuclear distances variations throughout time. The curves below show the plots of Energy (kJ.mol-1) against time (fs) and internuclear distances (pm) against time (fs) for the H1-H2 + H3 system.

[[File:Fzm18-energydistancevstime.png|400px|center|thumb|Internuclear distance (left) and Energy (right) vs time. ]]

Another important point of discussion is the reversibility of the system. The reversibility of the system can be measured by considering the path that would follow the system given that the initial positions correspond to the final position of system B, and the momenta are the opposite of the final momenta of the system above (system C). Applying such conditions to a Dynamics simulation, we can observe the system going back to its initial positions. : rAB = 90.75 pm, rBC = 91.75 pm, and their momenta will revert back to approximately ''p'' = 0 g.mol-1.pm.fs-1, suspend its motion, then reasonably will follow its primary trajectory. Qualitatively, The system takes''t'' fs to travel from its initial to final state, and reciprocally.Below is plotted the internuclear distances vs time of system C, reverting to system B, then back to system C.

[[File:Fzm18-reversibledistances.png|400px|center|thumb|Internuclear distances vs time in system C.]]

==Reactive and unreactive trajectories==

Let us focus on the conditions required to make a collision reactive. The table displayed below shows examples of atoms at rAB = 230 pm and rBC=74 pm, having different relative momenta and subsequently different reactivity.
{| class="wikitable" border=1
! p1/ g.mol-1.pm.fs-1 !! p2/ g.mol-1.pm.fs-1 !! Etot (kJ.mol-1) !! Reactive? !! Description of the dynamics !! Illustration of the trajectory (internuclear distances against time)
|-
| -2.56 || -5.1 || -414.28 || Yes || Little oscillations throughout the reaction. C approaches the molecule, bonds to B as A drifts away. The new diatomic is oscillating and distances itself from A.|| [[File:Fzm18-tablefig1.png|200px]]
|-
| -3.1 || -4.1 || -420.08 || No || Light oscillations in the diatomic A-B. rBC decreases, then increases with no collision between the atoms. {{fontcolor1|red|There is no ''reaction'', but is there no ''collision''? Think about what 'collision' means - there must be some kind of repulsion, which is clearly present. [[User:Fdp18|Fdp18]] ([[User talk:Fdp18|talk]]) 09:11, 9 May 2020 (BST)}} ||[[File:Fzm18-tablefig2.png|200px]]
|-
| -3.1 || -5.1 || -413.98 || Yes || Little oscillations. C approaches the molecule, bonds to B as A drifts away. The new diatomic is oscillating and distances itself from A ||[[File:Fzm18-tablefig3.png|200px]]
|-
| -5.1 || -10.1 || -357.27 || No || Strong oscillations. C approaches the diatomic, bonds with B, A distances itself slightly then reverts to its initial position, forms a new bond with B as C drifts away in the opposite direction||[[File:Fzm18-tablefig4.png|200px]]
|-
| -5.1 || -10.6 || -349.48 || Yes || Strong oscillations. C approaches the diatomic, bons with B. A distances itself then nears B to form the TS (AB=BC) again, then drifts away as B-C oscillates {{fontcolor1|red|}} ||[[File:Fzm18-tablefig5.png|200px]]
|}

The above results suggest that there is a threshold that needs to be bypassed in order for a reaction to take place. From the data, it seems this threshold lies around ''E'' ≈ -415 kJ.mol-1. However, this simulation applies classical mechanics and does not account for effects such as quantum tunelling; the TST predictions for the reaction rates are likely to be lower than the experimental values.

= F-H-H system =

== Bond energy ==
In this section, we study the dynamics of a F-H-H system. In this context, F, H1 and H2 will respectively be referred to as A, B and C.
By inspecting the Potential Energy Surface Plot, two low energy paths can be determined: along the AB axis (i.e. the H-F diatomic) and along the BC (H-H diatomic) axis, shown in the PES plot below. The first path is lower in energy than the second one, hence it can be concluded that the formation of H-F + H is exothermic, whilst the formation of H-H + F is endothermic. This implies that the bond strength of H-F is higher than that of H-H – respectively ''E'' ≈ 550 kJ.mol-1 and ''E'' ≈ 435 kJ.mol-1. This is consistent with the fact that the H-F bond is strengthened by the dipole moment due to the fluoride, therefore requiring more energy to break, and is supported by literature values.<ref name="energy" />

[[File:Fzm18-HHFSurfacePlot.png|400px|center|thumb|PES plot of a F-H-H system ]]

== Transition state ==
=== Locating the transition state ===
Applying an analogous a method to the one used previously and by taking into account Hammond's postulate : "If two states, as, for example, a transition state and an unstable intermediate, occur consecutively during a reaction process and have nearly the same energy content, their interconversion will involve only a small reorganization of the molecular structures." <ref name="Hammond" />; the transition state can be found to be located at rAB = 181 pm and rBC = 74 pm. Its position is highlighted by a black dot on the surface plot below.

[[File:Fzm18-TSvisualisation.png|400px|center|thumb|Internuclear distances vs time (left) and Surface Plot (right) of the transitions state of F-H-H ]]

=== Activation energy ===
The respective energies of each state are : ''E''H-F = -560.70 kJ.mol-1; ''E''H-H = -435.10 kJ.mol-1; ''E''TS = -433.98 kJ.mol-1. Hence the activation energies for the formation of the H-H and H-F bonds are, respectively : ''Ea'' = 126.72 kJ.mol-1 and ''Ea'' = 1.12 kJ.mol-1.

== Reaction Dynamics ==

= References =

<references>
<ref name="energy">Weller, Martin, and Overton, Tina ; Rourke, Jonathan ; Armstrong, F. A. ''Inorganic Chemistry''. 7th ed. 2018.</ref>
<ref name="Hammond">Hammond, G. S. (1955). "A Correlation of Reaction Rates". ''J. Am. Chem. Soc.'' 77 (2): 334–338.</ref>

MRD:fzm18

2020-05-08T22:59:07Z

Fzm18:

= H-H-H system =
This section focuses on the dynamics of a H1 + H2-H3 system, where the aim is to form a new H1-H2 bond. Let us first consider the reaction path.
In the system, H1, H2 and H3 are respectively referred to A, B and C.

== Locating the transition state ==
The transition state (TS) can be mathematically defined as ∂V/∂r1 = ∂V/∂r2 = 0. Graphically, the locus of the transition state can be apprehended as the saddle point on the potential energy surface (PES) plot.

[[File:Fzm18Surface PlotTS.png|300px|center|thumb|PES plot showing the transition state (red dot).]]

Physically, this means that the Transition state is a form on inert state, where a particle cannot acquire momentum if it has no momentum at this point. The plot of distances vs time below shows the internuclear distances variation of a H-H-H system with no momentum in the transition state. In this example, the transition state was found was found by varying the internuclear distances until the atoms stopped oscillating, at rAB = rBC = 90.75 pm.

[[File:Fzm18momentaTS.png|300px|center|thumb|Internuclear distances vs time at transition state.]]

== Calculating the reaction path ==
The reaction path is defined by the minimum energy path (mep) and is the fastest path a reaction can take. In this simulation, the momenta are constantly reset at 0 g.mol-1.pm.fs-1. This means that the motions are entirely defined driven by Coulombic interactions. Hence, after reaching a certain distance, the atoms reach a stable state and do not drift further away, as they would in classical dynamics theory.

==Analyzing trajectories at rAB = rTS + δ, rBC = rTS ==

[[File:Fzm18-contourplotTS.png|400px|thumb|Dynamics (left) and MEP (right) simulations. ]]

The graphs show contour plots of the potential energy surface for a near-transition state system rAB = 91.75 pm, rBC = 90.75 pm, system A) in MEP and Dynamics simulations. The black trail reflects the trajectory of particle A, as it travels endlessly (dynamics) or until it exhausts the available electrostatic potential energy.

[[File:Fzm18-SurfaceplotsHHH.png|400px|left|thumb|Final state: H1 + H2-H3 (right) and H1-H2 + H3 (left).]]

As rAB > rBC= rTS, the system tend to revert back to its initial form of H1 + H2-H3. However, note that in the opposite situation, where rAB = 90.75 pm, rBC = 91.75 pm (system B), the system will more likely tend to a new configuration : H1-H2 + H3. The surface plots show the reaction path as a black trail in both cases, rAB > rBC and rBC > rAB.

It is interesting to note that both systems have the same energy, and same the same variations of internuclear distances variations throughout time. The curves below show the plots of Energy (kJ.mol-1) against time (fs) and internuclear distances (pm) against time (fs) for the H1-H2 + H3 system.

[[File:Fzm18-energydistancevstime.png|400px|center|thumb|Internuclear distance (left) and Energy (right) vs time. ]]

Another important point of discussion is the reversibility of the system. The reversibility of the system can be measured by considering the path that would follow the system given that the initial positions correspond to the final position of system B, and the momenta are the opposite of the final momenta of the system above (system C). Applying such conditions to a Dynamics simulation, we can observe the system going back to its initial positions. : rAB = 90.75 pm, rBC = 91.75 pm, and their momenta will revert back to approximately ''p'' = 0 g.mol-1.pm.fs-1, suspend its motion, then reasonably will follow its primary trajectory. Qualitatively, The system takes''t'' fs to travel from its initial to final state, and reciprocally.Below is plotted the internuclear distances vs time of system C, reverting to system B, then back to system C.

[[File:Fzm18-reversibledistances.png|400px|center|thumb|Internuclear distances vs time in system C.]]

==Reactive and unreactive trajectories==

Let us focus on the conditions required to make a collision reactive. The table displayed below shows examples of atoms at rAB = 230 pm and rBC=74 pm, having different relative momenta and subsequently different reactivity.
{| class="wikitable" border=1
! p1/ g.mol-1.pm.fs-1 !! p2/ g.mol-1.pm.fs-1 !! Etot (kJ.mol-1) !! Reactive? !! Description of the dynamics !! Illustration of the trajectory (internuclear distances against time)
|-
| -2.56 || -5.1 || -414.28 || Yes || Little oscillations throughout the reaction. C approaches the molecule, bonds to B as A drifts away. The new diatomic is oscillating and distances itself from A.|| [[File:Fzm18-tablefig1.png|200px]]
|-
| -3.1 || -4.1 || -420.08 || No || Light oscillations in the diatomic A-B. rBC decreases, then increases with no collision between the atoms. ||[[File:Fzm18-tablefig2.png|200px]]
|-
| -3.1 || -5.1 || -413.98 || Yes || Little oscillations. C approaches the molecule, bonds to B as A drifts away. The new diatomic is oscillating and distances itself from A ||[[File:Fzm18-tablefig3.png|200px]]
|-
| -5.1 || -10.1 || -357.27 || No || Strong oscillations. C approaches the diatomic, bonds with B, A distances itself slightly then reverts to its initial position, forms a new bond with B as C drifts away in the opposite direction||[[File:Fzm18-tablefig4.png|200px]]
|-
| -5.1 || -10.6 || -349.48 || Yes || Strong oscillations. C approaches the diatomic, bons with B. A distances itself then nears B to form the TS (AB=BC) again, then drifts away as B-C oscillates ||[[File:Fzm18-tablefig5.png|200px]]
|}

The above results suggest that there is a threshold that needs to be bypassed in order for a reaction to take place. From the data, it seems this threshold lies around ''E'' ≈ -415 kJ.mol-1. However, this simulation applies classical mechanics and does not account for effects such as quantum tunelling; the TST predictions for the reaction rates are likely to be lower than the experimental values.

= F-H-H system =

== Bond energy ==
In this section, we study the dynamics of a F-H-H system. In this context, F, H1 and H2 will respectively be referred to as A, B and C.
By inspecting the Potential Energy Surface Plot, two low energy paths can be determined: along the AB axis (i.e. the H-F diatomic) and along the BC (H-H diatomic) axis, shown in the PES plot below. The first path is lower in energy than the second one, hence it can be concluded that the formation of H-F + H is exothermic, whilst the formation of H-H + F is endothermic. This implies that the bond strength of H-F is higher than that of H-H – respectively ''E'' ≈ 550 kJ.mol-1 and ''E'' ≈ 435 kJ.mol-1. This is consistent with the fact that the H-F bond is strengthened by the dipole moment due to the fluoride, therefore requiring more energy to break, and is supported by literature values.<ref name="energy" />

[[File:Fzm18-HHFSurfacePlot.png|400px|center|thumb|PES plot of a F-H-H system ]]

== Transition state ==
=== Locating the transition state ===
Applying an analogous a method to the one used previously and by taking into account Hammond's postulate : "If two states, as, for example, a transition state and an unstable intermediate, occur consecutively during a reaction process and have nearly the same energy content, their interconversion will involve only a small reorganization of the molecular structures." <ref name="Hammond" />; the transition state can be found to be located at rAB = 181 pm and rBC = 74 pm. Its position is highlighted by a black dot on the surface plot below.

[[File:Fzm18-TSvisualisation.png|400px|center|thumb|Internuclear distances vs time (left) and Surface Plot (right) of the transitions state of F-H-H ]]

=== Activation energy ===
The respective energies of each state are : ''E''H-F = -560.70 kJ.mol-1; ''E''H-H = -435.10 kJ.mol-1; ''E''TS = -433.98 kJ.mol-1. Hence the activation energies for the formation of the H-H and H-F bonds are, respectively : ''Ea'' = 126.72 kJ.mol-1 and ''Ea'' = 1.12 kJ.mol-1.

== Reaction Dynamics ==

= References =

<references>
<ref name="energy">Weller, Martin, and Overton, Tina ; Rourke, Jonathan ; Armstrong, F. A. ''Inorganic Chemistry''. 7th ed. 2018.</ref>
<ref name="Hammond">Hammond, G. S. (1955). "A Correlation of Reaction Rates". ''J. Am. Chem. Soc.'' 77 (2): 334–338.</ref>

MRD:fzm18

2020-05-08T16:53:13Z

Fzm18:

= H-H-H system =
This section focuses on the dynamics of a H1 + H2-H3 system, where the aim is to form a new H1-H2 bond. Let us first consider the reaction path.
In the system, H1, H2 and H3 are respectively referred to A, B and C.

== Locating the transition state ==
The transition state (TS) can be mathematically defined as ∂V/∂r1 = ∂V/∂r2 = 0. Graphically, the locus of the transition state can be apprehended as the saddle point on the potential energy surface (PES) plot.

[[File:Fzm18Surface PlotTS.png|300px|center|thumb|PES plot showing the transition state (red dot).]]

Physically, this means that the Transition state is a form on inert state, where a particle cannot acquire momentum if it has no momentum at this point. The plot of distances vs time below shows the internuclear distances variation of a H-H-H system with no momentum in the transition state. In this example, the transition state was found was found by varying the internuclear distances until the atoms stopped oscillating, at rAB = rBC = 90.75 pm.

[[File:Fzm18momentaTS.png|300px|center|thumb|Internuclear distances vs time at transition state.]]

== Calculating the reaction path ==
The reaction path is defined by the minimum energy path (mep) and is the fastest path a reaction can take. In this simulation, the momenta are constantly reset at 0 g.mol-1.pm.fs-1. This means that the motions are entirely defined driven by Coulombic interactions. Hence, after reaching a certain distance, the atoms reach a stable state and do not drift further away, as they would in classical dynamics theory.

==Analyzing trajectories at rAB = rTS + δ, rBC = rTS ==

[[File:Fzm18-contourplotTS.png|400px|thumb|Dynamics (left) and MEP (right) simulations. ]]

The graphs show contour plots of the potential energy surface for a near-transition state system rAB = 91.75 pm, rBC = 90.75 pm, system A) in MEP and Dynamics simulations. The black trail reflects the trajectory of particle A, as it travels endlessly (dynamics) or until it exhausts the available electrostatic potential energy.

[[File:Fzm18-SurfaceplotsHHH.png|400px|left|thumb|Final state: H1 + H2-H3 (right) and H1-H2 + H3 (left).]]

As rAB > rBC= rTS, the system tend to revert back to its initial form of H1 + H2-H3. However, note that in the opposite situation, where rAB = 90.75 pm, rBC = 91.75 pm (system B), the system will more likely tend to a new configuration : H1-H2 + H3. The surface plots show the reaction path as a black trail in both cases, rAB > rBC and rBC > rAB.

It is interesting to note that both systems have the same energy, and same the same variations of internuclear distances variations throughout time. The curves below show the plots of Energy (kJ.mol-1) against time (fs) and internuclear distances (pm) against time (fs) for the H1-H2 + H3 system.

[[File:Fzm18-energydistancevstime.png|400px|center|thumb|Internuclear distance (left) and Energy (right) vs time. ]]

Another important point of discussion is the reversibility of the system. The reversibility of the system can be measured by considering the path that would follow the system given that the initial positions correspond to the final position of system B, and the momenta are the opposite of the final momenta of the system above (system C). Applying such conditions to a Dynamics simulation, we can observe the system going back to its initial positions. : rAB = 90.75 pm, rBC = 91.75 pm, and their momenta will revert back to approximately ''p'' = 0 g.mol-1.pm.fs-1, suspend its motion, then reasonably will follow its primary trajectory. Qualitatively, The system takes''t'' fs to travel from its initial to final state, and reciprocally.Below is plotted the internuclear distances vs time of system C, reverting to system B, then back to system C.

[[File:Fzm18-reversibledistances.png|400px|center|thumb|Internuclear distances vs time in system C.]]

==Reactive and unreactive trajectories==

Let us focus on the conditions required to make a collision reactive. The table displayed below shows examples of atoms at rAB = 230 pm and rBC=74 pm, having different relative momenta and subsequently different reactivity.
{| class="wikitable" border=1
! p1/ g.mol-1.pm.fs-1 !! p2/ g.mol-1.pm.fs-1 !! Etot (kJ.mol-1) !! Reactive? !! Description of the dynamics !! Illustration of the trajectory (internuclear distances against time)
|-
| -2.56 || -5.1 || -414.28 || Yes || Little oscillations throughout the reaction. C approaches the molecule, bonds to B as A drifts away. The new diatomic is oscillating and distances itself from A.|| [[File:Fzm18-tablefig1.png|200px]]
|-
| -3.1 || -4.1 || -420.08 || No || Light oscillations in the diatomic A-B. rBC decreases, then increases with no collision between the atoms. ||[[File:Fzm18-tablefig2.png|200px]]
|-
| -3.1 || -5.1 || -413.98 || Yes || Little oscillations. C approaches the molecule, bonds to B as A drifts away. The new diatomic is oscillating and distances itself from A ||[[File:Fzm18-tablefig3.png|200px]]
|-
| -5.1 || -10.1 || -357.27 || No || Strong oscillations. C approaches the diatomic, bonds with B, A distances itself slightly then reverts to its initial position, forms a new bond with B as C drifts away in the opposite direction||[[File:Fzm18-tablefig4.png|200px]]
|-
| -5.1 || -10.6 || -349.48 || Yes || Strong oscillations. C approaches the diatomic, bons with B. A distances itself then nears B to form the TS (AB=BC) again, then drifts away as B-C oscillates ||[[File:Fzm18-tablefig5.png|200px]]
|}

The above results suggest that there is a threshold that needs to be bypassed in order for a reaction to take place. From the data, it seems this threshold lies around ''E'' ≈ -415 kJ.mol-1. However, this simulation applies classical mechanics and does not account for effects such as quantum tunelling; the TST predictions for the reaction rates are likely to be lower than the experimental values.

== Transition State Theory ==

Given the results you have obtained, how will Transition State Theory predictions for reaction rate values compare with experimental values?

= F-H-H system =

== Bond energy ==
In this section, we study the dynamics of a F-H-H system. In this context, F, H1 and H2 will respectively be referred to as A, B and C.
By inspecting the Potential Energy Surface Plot, two low energy paths can be determined: along the AB axis (i.e. the H-F diatomic) and along the BC (H-H diatomic) axis, shown in the PES plot below. The first path is lower in energy than the second one, hence it can be concluded that the formation of H-F + H is exothermic, whilst the formation of H-H + F is endothermic. This implies that the bond strength of H-F is higher than that of H-H – respectively ''E'' ≈ 550 kJ.mol-1 and ''E'' ≈ 435 kJ.mol-1. This is consistent with the fact that the H-F bond is strengthened by the dipole moment due to the fluoride, therefore requiring more energy to break, and is supported by literature values.<ref name="energy" />

[[File:Fzm18-HHFSurfacePlot.png|400px|center|thumb|PES plot of a F-H-H system ]]

== Transition state ==
=== Locating the transition state ===
Applying an analogous a method to the one used previously and by taking into account Hammond's postulate : "If two states, as, for example, a transition state and an unstable intermediate, occur consecutively during a reaction process and have nearly the same energy content, their interconversion will involve only a small reorganization of the molecular structures." <ref name="Hammond" />; the transition state can be found to be located at rAB = 181 pm and rBC = 74 pm. Its position is highlighted by a black dot on the surface plot below.

[[File:Fzm18-TSvisualisation.png|400px|center|thumb|Internuclear distances vs time (left) and Surface Plot (right) of the transitions state of F-H-H ]]

=== Activation energy ===
The respective energies of each state are : ''E''H-F = -560.70 kJ.mol-1; ''E''H-H = -435.10 kJ.mol-1; ''E''TS = -433.98 kJ.mol-1. Hence the activation energies for the formation of the H-H and H-F bonds are, respectively : ''Ea'' = 126.72 kJ.mol-1 and ''Ea'' = 1.12 kJ.mol-1.

= References =

<references>
<ref name="energy">Weller, Martin, and Overton, Tina ; Rourke, Jonathan ; Armstrong, F. A. ''Inorganic Chemistry''. 7th ed. 2018.</ref>
<ref name="Hammond">Hammond, G. S. (1955). "A Correlation of Reaction Rates". ''J. Am. Chem. Soc.'' 77 (2): 334–338.</ref>

MRD:fzm18

2020-05-08T16:35:30Z

Fzm18: /* F-H-H system */

= H-H-H system =
This section focuses on the dynamics of a H1 + H2-H3 system, where the aim is to form a new H1-H2 bond. Let us first consider the reaction path.
In the system, H1, H2 and H3 are respectively referred to A, B and C.

== Locating the transition state ==
The transition state (TS) can be mathematically defined as ∂V/∂r1 = ∂V/∂r2 = 0. Graphically, the locus of the transition state can be apprehended as the saddle point on the potential energy surface (PES) plot.

[[File:Fzm18Surface PlotTS.png|300px|center|thumb|PES plot showing the transition state (red dot).]]

Physically, this means that the Transition state is a form on inert state, where a particle cannot acquire momentum if it has no momentum at this point. The plot of distances vs time below shows the internuclear distances variation of a H-H-H system with no momentum in the transition state. In this example, the transition state was found was found by varying the internuclear distances until the atoms stopped oscillating, at rAB = rBC = 90.75 pm.

[[File:Fzm18momentaTS.png|300px|center|thumb|Internuclear distances vs time at transition state.]]

== Calculating the reaction path ==
The reaction path is defined by the minimum energy path (mep) and is the fastest path a reaction can take. In this simulation, the momenta are constantly reset at 0 g.mol-1.pm.fs-1. This means that the motions are entirely defined driven by Coulombic interactions. Hence, after reaching a certain distance, the atoms reach a stable state and do not drift further away, as they would in classical dynamics theory.

==Analyzing trajectories at rAB = rTS + δ, rBC = rTS ==

[[File:Fzm18-contourplotTS.png|400px|thumb|Dynamics (left) and MEP (right) simulations. ]]

The graphs show contour plots of the potential energy surface for a near-transition state system rAB = 91.75 pm, rBC = 90.75 pm, system A) in MEP and Dynamics simulations. The black trail reflects the trajectory of particle A, as it travels endlessly (dynamics) or until it exhausts the available electrostatic potential energy.

[[File:Fzm18-SurfaceplotsHHH.png|400px|left|thumb|Final state: H1 + H2-H3 (right) and H1-H2 + H3 (left).]]

As rAB > rBC= rTS, the system tend to revert back to its initial form of H1 + H2-H3. However, note that in the opposite situation, where rAB = 90.75 pm, rBC = 91.75 pm (system B), the system will more likely tend to a new configuration : H1-H2 + H3. The surface plots show the reaction path as a black trail in both cases, rAB > rBC and rBC > rAB.

It is interesting to note that both systems have the same energy, and same the same variations of internuclear distances variations throughout time. The curves below show the plots of Energy (kJ.mol-1) against time (fs) and internuclear distances (pm) against time (fs) for the H1-H2 + H3 system.

[[File:Fzm18-energydistancevstime.png|400px|center|thumb|Internuclear distance (left) and Energy (right) vs time. ]]

Another important point of discussion is the reversibility of the system. The reversibility of the system can be measured by considering the path that would follow the system given that the initial positions correspond to the final position of system B, and the momenta are the opposite of the final momenta of the system above (system C). Applying such conditions to a Dynamics simulation, we can observe the system going back to its initial positions. : rAB = 90.75 pm, rBC = 91.75 pm, and their momenta will revert back to approximately ''p'' = 0 g.mol-1.pm.fs-1, suspend its motion, then reasonably will follow its primary trajectory. Qualitatively, The system takes''t'' fs to travel from its initial to final state, and reciprocally.Below is plotted the internuclear distances vs time of system C, reverting to system B, then back to system C.

[[File:Fzm18-reversibledistances.png|400px|center|thumb|Internuclear distances vs time in system C.]]

==Reactive and unreactive trajectories==

Let us focus on the conditions required to make a collision reactive. The table displayed below shows examples of atoms at rAB = 230 pm and rBC=74 pm, having different relative momenta and subsequently different reactivity.
{| class="wikitable" border=1
! p1/ g.mol-1.pm.fs-1 !! p2/ g.mol-1.pm.fs-1 !! Etot (kJ.mol-1) !! Reactive? !! Description of the dynamics !! Illustration of the trajectory (internuclear distances against time)
|-
| -2.56 || -5.1 || -414.28 || Yes || Little oscillations throughout the reaction. C approaches the molecule, bonds to B as A drifts away. The new diatomic is oscillating and distances itself from A.|| [[File:Fzm18-tablefig1.png|200px]]
|-
| -3.1 || -4.1 || -420.08 || No || Light oscillations in the diatomic A-B. rBC decreases, then increases with no collision between the atoms. ||[[File:Fzm18-tablefig2.png|200px]]
|-
| -3.1 || -5.1 || -413.98 || Yes || Little oscillations. C approaches the molecule, bonds to B as A drifts away. The new diatomic is oscillating and distances itself from A ||[[File:Fzm18-tablefig3.png|200px]]
|-
| -5.1 || -10.1 || -357.27 || No || Strong oscillations. C approaches the diatomic, bonds with B, A distances itself slightly then reverts to its initial position, forms a new bond with B as C drifts away in the opposite direction||[[File:Fzm18-tablefig4.png|200px]]
|-
| -5.1 || -10.6 || -349.48 || Yes || Strong oscillations. C approaches the diatomic, bons with B. A distances itself then nears B to form the TS (AB=BC) again, then drifts away as B-C oscillates ||[[File:Fzm18-tablefig5.png|200px]]
|}

The above results suggest that there is a threshold that needs to be bypassed in order for a reaction to take place. From the simulations, it seems this threshold lies around ''E'' ≈ -415 kJ.mol-1.

== Transition State Theory ==

Given the results you have obtained, how will Transition State Theory predictions for reaction rate values compare with experimental values?

= F-H-H system =

== Bond energy ==
In this section, we study the dynamics of a F-H-H system. In this context, F, H1 and H2 will respectively be referred to as A, B and C.
By inspecting the Potential Energy Surface Plot, two low energy paths can be determined: along the AB axis (i.e. the H-F diatomic) and along the BC (H-H diatomic) axis, shown in the PES plot below. The first path is lower in energy than the second one, hence it can be concluded that the formation of H-F + H is exothermic, whilst the formation of H-H + F is endothermic. This implies that the bond strength of H-F is higher than that of H-H – respectively ''E'' ≈ 520 kJ.mol-1 and ''E'' ≈ 435 kJ.mol-1. This is consistent with the fact that the H-F bond is strengthened by the dipole moment due to the fluoride, therefore requiring more energy to break, and is supported by literature values.<ref name="energy" />

[[File:Fzm18-HHFSurfacePlot.png|400px|center|thumb|PES plot of a F-H-H system ]]

== Transition state ==
Applying an analogous a method to the one used previously and by taking into account Hammond's postulate : "If two states, as, for example, a transition state and an unstable intermediate, occur consecutively during a reaction process and have nearly the same energy content, their interconversion will involve only a small reorganization of the molecular structures." <ref name="Hammond" />; the transition state can be found to be located at rAB = 181 pm and rBC = 74 pm. Its position is highlighted by a black dot on the surface plot below.

[[File:Fzm18-TSvisualisation.png|400px|center|thumb|Internuclear distances vs time (left) and Surface Plot (right) of the transitions state of F-H-H ]]

= References =

<references>
<ref name="energy">Weller, Martin, and Overton, Tina ; Rourke, Jonathan ; Armstrong, F. A. ''Inorganic Chemistry''. 7th ed. 2018.</ref>
<ref name="Hammond">Hammond, G. S. (1955). "A Correlation of Reaction Rates". ''J. Am. Chem. Soc.'' 77 (2): 334–338.</ref>

File:Fzm18-TSvisualisation.png

2020-05-08T16:23:21Z

Fzm18:

MRD:fzm18

File:Fzm18momentaTS.png

2020-05-06T23:57:20Z

Fzm18:

2019-03-21T13:24:02Z

Fzm18: /* Molecular orbitals */

= NH3 molecule =

== Optimization ==

Molecule name : NH3

Calculation method : RB3LYP

Basis set : 6-31G(d.p)

Final energy : E(RB3LYP) = -56.55776873 a.u.

RMS gradient = 0.00000485 a.u.

Point group : C3v

<pre>

Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000072 0.001800 YES
RMS Displacement 0.000035 0.001200 YES

</pre>

<jmol><jmolApplet>
<title>NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>FZM18_NH3_OPTF.LOG</uploadedFileContents>
</jmolApplet></jmol>

Recorded optimized N-H bond length : rNH = 1.018 Å

Recorded optimized H-N-H bond angle : θ = 105°

The optimization file can be accessed [[Media:FZM18_NH3_OPTF.LOG| here]].

== Vibration and Charges ==

=== Vibration ===

[[File:fzm18_NH3vibrationtable.PNG|250px]]

{| class="wikitable" border="1"
|+ NH3 vibrational modes
| '''Wavenumber''' cm-1 || style="text-align: center;"| 1089 || style="text-align: center;"| 1693 || style="text-align: center;"| 1693 || style="text-align: center;"| 3461 || style="text-align: center;"| 3589 || style="text-align: center;"| 3589
|-
| '''Symmetry''' || style="text-align: center;"| A1 || style="text-align: center;"| E || style="text-align: center;"| E || style="text-align: center;"| A1 || style="text-align: center;"| E || style="text-align: center;"| E
|-
| '''Intensity''' arbitrary units || style="text-align: center;"| 145 || style="text-align: center;"| 14 || style="text-align: center;"| 14 || style="text-align: center;"| 1 || style="text-align: center;"| 0 || style="text-align: center;"| 0
|-
| '''Image''' || [[File:fzm18_nh3_vib1.PNG|150px]] || [[File:fzm18_nh3_vib2.PNG|150px]] || [[File:fzm18_nh3_vib3.PNG|150px]] || [[File:fzm18_nh3_vib4.PNG|150px]] || [[File:fzm18_nh3_vib5.PNG|150px]] || [[File:fzm18_nh3_vib6.PNG|150px]]
|}

From the 3N-6 rule, 6 vibrational modes are to be expected. On the table, it is shown that 4 modes are degenerate (2 of them have a frequency of 1693, and two others ahve a frequency of 3589).

The first three vibrational modes (in the table) correspond to bending, while the last three correspond to streching vibrations. The vibrational mode with a frequency 3461 cm-1, also called the symmetric strech, is the most symmetric vibration. The vibration with hte smallest frequency is known as the umbrella mode.

From the degeneracy of the modes, 4 peaks should be expected in an experimental spectrum of gaseous ammonia. However, symmetrical vibrations are not IR active, and for this reason , only 2 peaks can be observed in an IR spectrim oh NH3.

=== Charge ===

As expected, the calculations show a negative charge on the N atom, while positive chrges can be observed on the H atoms. Futhermore, it can be noted that qN = -3qH as the overall charge of the molecule Q = qN +3qH = 0.

[[File:Fzm18 nh3 charge.png|300px|center|thumb|Charge distribution in an NH3 molecule.]]

= N2 molecule =

== Molecule optimization ==

Molecule name : N2

Calculation method : RB3LYP

Basis set : 6-31G(d.p)

Final energy : E(RB3LYP) = -109.52412868 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

</pre>

<jmol><jmolApplet>
<title>N2 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>FZM18 N2 OPTF.LOG</uploadedFileContents>
</jmolApplet></jmol>

Recorded N-N bond length : rN2 = 1.106 Å

Please note that N2 is a linear diatomic molecule, therefore no optimzed angle is recorded.

The optimization file can be accessed [[Media:FZM18_N2_OPTF.LOG| here]].

== Vibrations and Charges ==

=== Vibrations ===

[[File:Fzm18 N2vibrationtable.PNG|300px]]

Here the table shows the only vibration in N2 has a frequency of 2457 cm-1, not shown in the IR spectrum ( as its intensity is predicted to be 0). This can be explained by the fact that symmetrical vibrations are not IR active.

[[File:Fzm18 n2 vib1.PNG|thumb|center|Vibration mode of N2, with a view of the displacement vectors]]

=== Charge ===

As, N2 is a symmetric diatomic molecule, it comes to no surprise that no charge can be observed on either of the atoms, as it is displayed in the modelisation below.

[[File:Fzm18 n2 charge.PNG|250px]]

= H2 molecule =

== Molecule optimization ==

Molecule name : H2

Calculation method : RB3LYP

Basis set : 6-31G(d.p)

Final energy : E(RB3LYP) = -1.17853936 a.u.

RMS gradient = 0.00000908 a.u.

Point group : D∞h

<pre>
Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.000021 0.001800 YES
RMS Displacement 0.000029 0.001200 YES
</pre>

<jmol><jmolApplet>
<title>H2 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>FZM18 H2 OPTF.LOG</uploadedFileContents>
</jmolApplet></jmol>

Recorded N-N bond length : rH2 = 0.743 Å

Please note that H2 is a linear diatomic molecule, therefore no optimzed angle is recorded.

The optimization file can be accessed [[Media:FZM18 H2 OPTF.LOG| here]].

== Vibrations and Charges ==

=== Vibrations ===

[[File:Fzm18 H2vibrationtable.PNG]]

Here the table shows the only vibration in H2 has a frequency of 4466 cm-1, not shown in the IR spectrum ( as its intensity is predicted to be 0). This can be explained by the fact that symmetrical vibrations are not IR active.

[[File:Fzm18 h2 vib1.PNG|thumb|center|Vibration mode of H2, with a view of the displacement vectors]]

=== Charge ===

As, H2 is a symmetric diatomic molecule, it comes to no surprise that no charge can be observed, as it was the case for N2.

= Reaction and orbitals =

== Structure and reactivity ==

=== Mono-metallic transition metal complex ===

A search in ConQuest permits to find that Molybdenum compound coordinates N2: cis-bis(1-(diethylphosphino)-N-((diethylphosphino)methyl)-N-(2,6-difluorobenzyl)methanamine)-bis(dinitrogen)-molybdenum. Its unique identifier is AQEZED, and more information about the compound can be found [https://www.ccdc.cam.ac.uk/structures/Search?Ccdcid=AQEZED&DatabaseToSearch=Published |here].

The recorded bond length in that molecule are r1 = 1.117 Å and r2 = 1.113 Å. Those values are higher than the predicted bond length calculated on Gaussian. This can be explained by the fact that the first N atom also shares a bond with the Mo atom, leading to a more diffuse distribution of the electrons around that nitrogen atom (formal positive charge), hence the difference between the computed and experimental bonds.

=== Haber-Bosch process ===

E(NH3) = -56.55776873 a.u.

2*E(NH3)= -113.1155375 a.u.

E(N2)= -109.52412868 a.u.

E(H2)= -1.17853936 a.u.

3*E(H2)= -3.53561808 a.u.

ΔE=2*E(NH3)-[E(N2)+3*E(H2)]= -0.05579074 a.u. = -146.5 kJ.mol-1 (tp 1 d.p.)

ΔE is negativem indicating that the product (ammonia) is more stable than the reactants (nitrogen and hydrogen).

= Cyanide =

== [CN]- molecule ==

In this part, we will be intersted in the [CN]- molecule, a very harmful substance to living beings, yet impressively useful molecule at a catalysist or base in different reactions

=== Molecule optimization ===

Molecule name : [CN]-

Calculation method : RB3LYP

Basis set : 6-31G(d.p)

Charge : q = -1

Final energy : E(RB3LYP) = -92.82453153 a.u.

RMS gradient = 0.00000704 a.u.

Point group : C∞v

<pre>

Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000005 0.001800 YES
RMS Displacement 0.000008 0.001200 YES

</pre>

<jmol><jmolApplet>
<title>[CN]- molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>FZM18 CN- OPTF.LOG</uploadedFileContents>
</jmolApplet></jmol>

Recorded bond length : rCN = 1.184 Å

[CN]- being a linear diatomic molecule, no angle were calculated.

The optimization file can be accessed [[Media:FZM18 CN- OPTFREQ.LOG| here]].

=== Vibrations and charges ===

==== Vibrations ====

[[File:Fzm18 CN-vibrationtable.PNG |300px]]

[CN]- being a diatomic molecule, it only shoxs one vibration mode : the C-N strech, anf htus its IR spectrum will be composed of a unique peak at 2139 cm-1, and of intesnity 7 (in arbitrary units). This vibration is illustrated by the figure below.

[[File:Fzm18 CN- vib1.PNG |300px]]
==== Charge ====

[CN]- is an anion with a charge q = -1, which is, in theory, on the C atom. HOwever, according to Gauss calculations, the strong electronegative nature of the molecule results on a distribtion of the negative charge throughout the molecule, with a great portion of it still on the C atom. This is can be illustrated by the picture below

[[File:Fzm18 cn- charge.PNG]]

== HCN molecule ==

The negative charge on [CN]-</sup< can be neutralized when the carbon atom bonds with a Hydrogen atom, forming a HCN molecule. Let us study this new molecule.

=== Molecule optimization ===

Molecule name : HCN

Calculation method : RB3LYP

Basis set : 6-31G(d.p)

Final energy : E(RB3LYP) = -93.42458132 a.u.

RMS gradient = 0.00017006 a.u.

Point group : C∞v

<pre>

Item Value Threshold Converged?
Maximum Force 0.000370 0.000450 YES
RMS Force 0.000255 0.000300 YES
Maximum Displacement 0.000676 0.001800 YES
RMS Displacement 0.000427 0.001200 YES

</pre>

<jmol><jmolApplet>
<title>HCN molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>FZM18 HCN OPTFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

Recorded C-H bond length : rC-H = 1.069 Å

Recorded -N bon length : rC-N = 1.157 Å

Recorded bond angle : θ = 180°

The optimization file can be accessed [[Media:FZM18 HCN OPTFREQ.LOG| here]].

=== Vibrations and Charges ===
==== Vibrations ====

[[File:Fzm18 HCNvibrationtable.PNG|300px]]

{| class="wikitable" border="1"
|+ HCN vibrational modes
| '''Wavenumber''' cm-1 || style="text-align: center;"| 766 || style="text-align: center;"| 766 || style="text-align: center;"| 2214 || style="text-align: center;"| 3479
|-
| '''Symmetry''' || style="text-align: center;"| PI || style="text-align: center;"| PI || style="text-align: center;"| SG || style="text-align: center;"| SG
|-
| '''Intensity''' arbitrary units || style="text-align: center;"| 35 || style="text-align: center;"| 35 || style="text-align: center;"| 2 || style="text-align: center;"| 57
|-
| '''Image''' || [[File:Fzm18 HCN vib1.PNG|200px]] || [[File:fzm18_HCN_vib2.PNG|200px]] || [[File:fzm18_HCN_vib3.PNG|200px]] || [[File:fzm18_HCN_vib4.PNG|200px]]
|}

Here the table shows the different vibration modes of HCN. It can be observed that the first two vibration modes are degenerate, i.e. have the same energy. The high symmetrical nature of the third one causes its low intensity.

==== Charge ====

The Nitrogen atom is known to be highly electronegative compared to C and H, which explains its partial negative charge, while the Carboand Hydrogen atom positive charges sum up to compensate this negative charge.

[[File:Fzm18 hcn charge.PNG|200px]]

=== Molecular orbitals ===

Here is a table showing example of some of the molecular orbitals that constitute HCN.

{| class="wikitable" border="1"
|+ HCN molecular orbitals
| '''Molecular orbital''' || style="text-align: center;"| 2σg || style="text-align: center;"| 3σg || style="text-align: center;"| 3σ*u || style="text-align: center;"| 1πu || style="text-align: center;"| 1π*g
|-
| '''Energy''' a. u. || style="text-align: center;"| -0.92 || style="text-align: center;"| -0.61 || style="text-align: center;"| -0.38 || style="text-align: center;"| -0.36 || style="text-align: center;"| 0.02
|-
| '''Contributing atomic orbitals''' || style="text-align: center;"| H (1s) and C (sp) || style="text-align: center;"| C (sp) and N (2pz) || style="text-align: center;"| C (sp) and N (2pz)|| style="text-align: center;"| C (2px) and N (2px) || style="text-align: center;"| C (2px) and N (2px)
|-
| '''Bonding and filling''' || style="text-align: center;"| bonding, occupied || style="text-align: center;"| bonding, occupied || style="text-align: center;"| antibonding, unoccupied || style="text-align: center;"| bonding, occupied || style="text-align: center;"| antibonding, unoccupied
|-
| '''Image''' || [[File:Fzm18 HCN MO1.PNG|150px]] || [[File:Fzm18 HCN MO2.PNG|150px]] || [[File:Fzm18 HCN MO3.PNG|150px]] || [[File:Fzm18 HCN MO4.PNG|150px]] || [[File:Fzm18 HCN MO5.PNG|150px]]
|}

Above is displayed a table showing five of the molecular orbitals that constitute HCN. The first one was chosen because it is the bond between the H and C atoms, and helps illustrating the mixing between and s and a p orbital in the C atom. The second one, 3σg, is interesting because it is part of the C-N triple bond. Its corresponding antibonding orbital should be studied as it is shows, once again the mixing of the carbon atomic orbitals, as well as the mixing if the nitrogen atom. Here, on the π molecular orbitals were displayed to allow to understand the degeneracy of those orbitals which also consitute the triple bond, and allows us to cmperhend that the bond strength is mainly due to the efficient overlap between the 2p orbitals of the same size (as they belong to the same period). It also the HOMO. Finally, its corresponding aintibonding orbital is shown here for similar reasons, and also because itis the LUMO.

== Analytical comparison ==

The point of this section is to analyse the effect of the addition of a proton on thecyanide molecule.

The first point of comparison to take into consideration is the bond length of the C-N triple bond. It should be noted that the diffrence between the two bonds is :

Δr = rCN - rHCN = 1.184 - 1.157 = 0.024 Å

The bond is shorter in HCN, and thus it can be concluded that the bond is strengthened by the addition of hydrogen. This can be explained bt the fact that in [CN]-, the lone pair of electrons it very repulsive – more repulsive than a potential C-H bond, and therefore weakens the C-N bond.

HCN, more stable than [C]- (due to the stabilising of the negative charge), has a pKa = 9.1 in water <ref name="pKa" />. As the carbon loses its lone pair, the molecule cannot react as a base anymore, but behaves as an acid in aqueous conditions (with a pH < 9.1), as it is the case in the reaction shown below:

[[File:Fzm18 HCN reaction.jpg|center]]

In this reaction, HCN reacts with CH2=O to form hydroxyacetonitrile. The reagent used is H2SO4. This example helps see clearly how the adddition of hydrogen to cyanide makes it an efficient acid. <ref name="Reaction" />. However, it should be noted that HCn is rarely used because of its highly poisonous character, and substitutes such as KCN, or NaCN are often used.

= References =

<references>
<ref name="Reaction">Tian Xi, Xie Yifeng, Wu Xingwei, Industrial perparation method of hydroxyacetonitrile, Assignee Fushun Shunte, 2018.</ref>

<ref name="pKa">Oleg A, Reutov, Russian Chemical Reviews, Equilibrium acidity of carbohydrogen bonds in organic compounds, 1974, Vol. 43(1), pp. 17-31.</ref>
</references>

Rep:Mod:fzm18

2019-03-21T13:21:13Z

Fzm18: /* Analytical comparison */

= NH3 molecule =

== Optimization ==

Molecule name : NH3

Calculation method : RB3LYP

Basis set : 6-31G(d.p)

Final energy : E(RB3LYP) = -56.55776873 a.u.

RMS gradient = 0.00000485 a.u.

Point group : C3v

<pre>

Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000072 0.001800 YES
RMS Displacement 0.000035 0.001200 YES

</pre>

<jmol><jmolApplet>
<title>NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>FZM18_NH3_OPTF.LOG</uploadedFileContents>
</jmolApplet></jmol>

Recorded optimized N-H bond length : rNH = 1.018 Å

Recorded optimized H-N-H bond angle : θ = 105°

The optimization file can be accessed [[Media:FZM18_NH3_OPTF.LOG| here]].

== Vibration and Charges ==

=== Vibration ===

[[File:fzm18_NH3vibrationtable.PNG|250px]]

{| class="wikitable" border="1"
|+ NH3 vibrational modes
| '''Wavenumber''' cm-1 || style="text-align: center;"| 1089 || style="text-align: center;"| 1693 || style="text-align: center;"| 1693 || style="text-align: center;"| 3461 || style="text-align: center;"| 3589 || style="text-align: center;"| 3589
|-
| '''Symmetry''' || style="text-align: center;"| A1 || style="text-align: center;"| E || style="text-align: center;"| E || style="text-align: center;"| A1 || style="text-align: center;"| E || style="text-align: center;"| E
|-
| '''Intensity''' arbitrary units || style="text-align: center;"| 145 || style="text-align: center;"| 14 || style="text-align: center;"| 14 || style="text-align: center;"| 1 || style="text-align: center;"| 0 || style="text-align: center;"| 0
|-
| '''Image''' || [[File:fzm18_nh3_vib1.PNG|150px]] || [[File:fzm18_nh3_vib2.PNG|150px]] || [[File:fzm18_nh3_vib3.PNG|150px]] || [[File:fzm18_nh3_vib4.PNG|150px]] || [[File:fzm18_nh3_vib5.PNG|150px]] || [[File:fzm18_nh3_vib6.PNG|150px]]
|}

From the 3N-6 rule, 6 vibrational modes are to be expected. On the table, it is shown that 4 modes are degenerate (2 of them have a frequency of 1693, and two others ahve a frequency of 3589).

The first three vibrational modes (in the table) correspond to bending, while the last three correspond to streching vibrations. The vibrational mode with a frequency 3461 cm-1, also called the symmetric strech, is the most symmetric vibration. The vibration with hte smallest frequency is known as the umbrella mode.

From the degeneracy of the modes, 4 peaks should be expected in an experimental spectrum of gaseous ammonia. However, symmetrical vibrations are not IR active, and for this reason , only 2 peaks can be observed in an IR spectrim oh NH3.

=== Charge ===

As expected, the calculations show a negative charge on the N atom, while positive chrges can be observed on the H atoms. Futhermore, it can be noted that qN = -3qH as the overall charge of the molecule Q = qN +3qH = 0.

[[File:Fzm18 nh3 charge.png|300px|center|thumb|Charge distribution in an NH3 molecule.]]

= N2 molecule =

== Molecule optimization ==

Molecule name : N2

Calculation method : RB3LYP

Basis set : 6-31G(d.p)

Final energy : E(RB3LYP) = -109.52412868 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

</pre>

<jmol><jmolApplet>
<title>N2 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>FZM18 N2 OPTF.LOG</uploadedFileContents>
</jmolApplet></jmol>

Recorded N-N bond length : rN2 = 1.106 Å

Please note that N2 is a linear diatomic molecule, therefore no optimzed angle is recorded.

The optimization file can be accessed [[Media:FZM18_N2_OPTF.LOG| here]].

== Vibrations and Charges ==

=== Vibrations ===

[[File:Fzm18 N2vibrationtable.PNG|300px]]

Here the table shows the only vibration in N2 has a frequency of 2457 cm-1, not shown in the IR spectrum ( as its intensity is predicted to be 0). This can be explained by the fact that symmetrical vibrations are not IR active.

[[File:Fzm18 n2 vib1.PNG|thumb|center|Vibration mode of N2, with a view of the displacement vectors]]

=== Charge ===

As, N2 is a symmetric diatomic molecule, it comes to no surprise that no charge can be observed on either of the atoms, as it is displayed in the modelisation below.

[[File:Fzm18 n2 charge.PNG|250px]]

= H2 molecule =

== Molecule optimization ==

Molecule name : H2

Calculation method : RB3LYP

Basis set : 6-31G(d.p)

Final energy : E(RB3LYP) = -1.17853936 a.u.

RMS gradient = 0.00000908 a.u.

Point group : D∞h

<pre>
Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.000021 0.001800 YES
RMS Displacement 0.000029 0.001200 YES
</pre>

<jmol><jmolApplet>
<title>H2 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>FZM18 H2 OPTF.LOG</uploadedFileContents>
</jmolApplet></jmol>

Recorded N-N bond length : rH2 = 0.743 Å

Please note that H2 is a linear diatomic molecule, therefore no optimzed angle is recorded.

The optimization file can be accessed [[Media:FZM18 H2 OPTF.LOG| here]].

== Vibrations and Charges ==

=== Vibrations ===

[[File:Fzm18 H2vibrationtable.PNG]]

Here the table shows the only vibration in H2 has a frequency of 4466 cm-1, not shown in the IR spectrum ( as its intensity is predicted to be 0). This can be explained by the fact that symmetrical vibrations are not IR active.

[[File:Fzm18 h2 vib1.PNG|thumb|center|Vibration mode of H2, with a view of the displacement vectors]]

=== Charge ===

As, H2 is a symmetric diatomic molecule, it comes to no surprise that no charge can be observed, as it was the case for N2.

= Reaction and orbitals =

== Structure and reactivity ==

=== Mono-metallic transition metal complex ===

A search in ConQuest permits to find that Molybdenum compound coordinates N2: cis-bis(1-(diethylphosphino)-N-((diethylphosphino)methyl)-N-(2,6-difluorobenzyl)methanamine)-bis(dinitrogen)-molybdenum. Its unique identifier is AQEZED, and more information about the compound can be found [https://www.ccdc.cam.ac.uk/structures/Search?Ccdcid=AQEZED&DatabaseToSearch=Published |here].

The recorded bond length in that molecule are r1 = 1.117 Å and r2 = 1.113 Å. Those values are higher than the predicted bond length calculated on Gaussian. This can be explained by the fact that the first N atom also shares a bond with the Mo atom, leading to a more diffuse distribution of the electrons around that nitrogen atom (formal positive charge), hence the difference between the computed and experimental bonds.

=== Haber-Bosch process ===

E(NH3) = -56.55776873 a.u.

2*E(NH3)= -113.1155375 a.u.

E(N2)= -109.52412868 a.u.

E(H2)= -1.17853936 a.u.

3*E(H2)= -3.53561808 a.u.

ΔE=2*E(NH3)-[E(N2)+3*E(H2)]= -0.05579074 a.u. = -146.5 kJ.mol-1 (tp 1 d.p.)

ΔE is negativem indicating that the product (ammonia) is more stable than the reactants (nitrogen and hydrogen).

= Cyanide =

== [CN]- molecule ==

In this part, we will be intersted in the [CN]- molecule, a very harmful substance to living beings, yet impressively useful molecule at a catalysist or base in different reactions

=== Molecule optimization ===

Molecule name : [CN]-

Calculation method : RB3LYP

Basis set : 6-31G(d.p)

Charge : q = -1

Final energy : E(RB3LYP) = -92.82453153 a.u.

RMS gradient = 0.00000704 a.u.

Point group : C∞v

<pre>

Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000005 0.001800 YES
RMS Displacement 0.000008 0.001200 YES

</pre>

<jmol><jmolApplet>
<title>[CN]- molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>FZM18 CN- OPTF.LOG</uploadedFileContents>
</jmolApplet></jmol>

Recorded bond length : rCN = 1.184 Å

[CN]- being a linear diatomic molecule, no angle were calculated.

The optimization file can be accessed [[Media:FZM18 CN- OPTFREQ.LOG| here]].

=== Vibrations and charges ===

==== Vibrations ====

[[File:Fzm18 CN-vibrationtable.PNG |300px]]

[CN]- being a diatomic molecule, it only shoxs one vibration mode : the C-N strech, anf htus its IR spectrum will be composed of a unique peak at 2139 cm-1, and of intesnity 7 (in arbitrary units). This vibration is illustrated by the figure below.

[[File:Fzm18 CN- vib1.PNG |300px]]
==== Charge ====

[CN]- is an anion with a charge q = -1, which is, in theory, on the C atom. HOwever, according to Gauss calculations, the strong electronegative nature of the molecule results on a distribtion of the negative charge throughout the molecule, with a great portion of it still on the C atom. This is can be illustrated by the picture below

[[File:Fzm18 cn- charge.PNG]]

== HCN molecule ==

The negative charge on [CN]-</sup< can be neutralized when the carbon atom bonds with a Hydrogen atom, forming a HCN molecule. Let us study this new molecule.

=== Molecule optimization ===

Molecule name : HCN

Calculation method : RB3LYP

Basis set : 6-31G(d.p)

Final energy : E(RB3LYP) = -93.42458132 a.u.

RMS gradient = 0.00017006 a.u.

Point group : C∞v

<pre>

Item Value Threshold Converged?
Maximum Force 0.000370 0.000450 YES
RMS Force 0.000255 0.000300 YES
Maximum Displacement 0.000676 0.001800 YES
RMS Displacement 0.000427 0.001200 YES

</pre>

<jmol><jmolApplet>
<title>HCN molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>FZM18 HCN OPTFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

Recorded C-H bond length : rC-H = 1.069 Å

Recorded -N bon length : rC-N = 1.157 Å

Recorded bond angle : θ = 180°

The optimization file can be accessed [[Media:FZM18 HCN OPTFREQ.LOG| here]].

=== Vibrations and Charges ===
==== Vibrations ====

[[File:Fzm18 HCNvibrationtable.PNG|300px]]

{| class="wikitable" border="1"
|+ HCN vibrational modes
| '''Wavenumber''' cm-1 || style="text-align: center;"| 766 || style="text-align: center;"| 766 || style="text-align: center;"| 2214 || style="text-align: center;"| 3479
|-
| '''Symmetry''' || style="text-align: center;"| PI || style="text-align: center;"| PI || style="text-align: center;"| SG || style="text-align: center;"| SG
|-
| '''Intensity''' arbitrary units || style="text-align: center;"| 35 || style="text-align: center;"| 35 || style="text-align: center;"| 2 || style="text-align: center;"| 57
|-
| '''Image''' || [[File:Fzm18 HCN vib1.PNG|200px]] || [[File:fzm18_HCN_vib2.PNG|200px]] || [[File:fzm18_HCN_vib3.PNG|200px]] || [[File:fzm18_HCN_vib4.PNG|200px]]
|}

Here the table shows the different vibration modes of HCN. It can be observed that the first two vibration modes are degenerate, i.e. have the same energy. The high symmetrical nature of the third one causes its low intensity.

==== Charge ====

The Nitrogen atom is known to be highly electronegative compared to C and H, which explains its partial negative charge, while the Carboand Hydrogen atom positive charges sum up to compensate this negative charge.

[[File:Fzm18 hcn charge.PNG|200px]]

=== Molecular orbitals ===

Here is a table showing example of some of the molecular orbitals that constitute HCN.

{| class="wikitable" border="1"
|+ HCN molecular orbitals
| '''Molecular orbital''' || style="text-align: center;"| 2σg || style="text-align: center;"| 3σg || style="text-align: center;"| 3σ*u || style="text-align: center;"| 1πu || style="text-align: center;"| 1π*g
|-
| '''Energy''' a. u. || style="text-align: center;"| -0.92 || style="text-align: center;"| -0.61 || style="text-align: center;"| -0.38 || style="text-align: center;"| -0.36 || style="text-align: center;"| 0.02
|-
| '''Contributing atomic orbitals''' || style="text-align: center;"| H (1s) and C (sp) || style="text-align: center;"| C (sp) and N (2pz) || style="text-align: center;"| C (sp) and N (2pz)|| style="text-align: center;"| C (2px) and N (2px) || style="text-align: center;"| C (2px) and N (2px)
|-
| '''Bonding and filling''' || style="text-align: center;"| bonding, occupied || style="text-align: center;"| bonding, occupied || style="text-align: center;"| antibonding, unoccupied || style="text-align: center;"| bonding, occupied || style="text-align: center;"| antibonding, unoccupied
|-
| '''Image''' || [[File:Fzm18 HCN MO1.PNG|200px]] || [[File:Fzm18 HCN MO2.PNG|200px]] || [[File:Fzm18 HCN MO3.PNG|200px]] || [[File:Fzm18 HCN MO4.PNG|200px]] || [[File:Fzm18 HCN MO5.PNG|200px]]
|}

Above is displayed a table showing five of the molecular orbitals that constitute HCN. The first one was chosen because it is the bond between the H and C atoms, and helps illustrating the mixing between and s and a p orbital in the C atom. The second one, 3σg, is interesting because it is part of the C-N triple bond. Its corresponding antibonding orbital should be studied as it is shows, once again the mixing of the carbon atomic orbitals, as well as the mixing if the nitrogen atom. Here, on the π molecular orbitals were displayed to allow to understand the degeneracy of those orbitals which also consitute the triple bond, and allows us to cmperhend that the bond strength is mainly due to the efficient overlap between the 2p orbitals of the same size (as they belong to the same period). It also the HOMO. Finally, its corresponding aintibonding orbital is shown here for similar reasons, and also because itis the LUMO.

== Analytical comparison ==

The point of this section is to analyse the effect of the addition of a proton on thecyanide molecule.

The first point of comparison to take into consideration is the bond length of the C-N triple bond. It should be noted that the diffrence between the two bonds is :

Δr = rCN - rHCN = 1.184 - 1.157 = 0.024 Å

The bond is shorter in HCN, and thus it can be concluded that the bond is strengthened by the addition of hydrogen. This can be explained bt the fact that in [CN]-, the lone pair of electrons it very repulsive – more repulsive than a potential C-H bond, and therefore weakens the C-N bond.

HCN, more stable than [C]- (due to the stabilising of the negative charge), has a pKa = 9.1 in water <ref name="pKa" />. As the carbon loses its lone pair, the molecule cannot react as a base anymore, but behaves as an acid in aqueous conditions (with a pH < 9.1), as it is the case in the reaction shown below:

[[File:Fzm18 HCN reaction.jpg|center]]

In this reaction, HCN reacts with CH2=O to form hydroxyacetonitrile. The reagent used is H2SO4. This example helps see clearly how the adddition of hydrogen to cyanide makes it an efficient acid. <ref name="Reaction" />. However, it should be noted that HCn is rarely used because of its highly poisonous character, and substitutes such as KCN, or NaCN are often used.

= References =

<references>
<ref name="Reaction">Tian Xi, Xie Yifeng, Wu Xingwei, Industrial perparation method of hydroxyacetonitrile, Assignee Fushun Shunte, 2018.</ref>

<ref name="pKa">Oleg A, Reutov, Russian Chemical Reviews, Equilibrium acidity of carbohydrogen bonds in organic compounds, 1974, Vol. 43(1), pp. 17-31.</ref>
</references>