ChemWiki - User contributions [en]

MRD:chl1718 04052020

2020-05-08T17:44:01Z

Chl1718:

= Modelling Molecular Reaction Dynamics =

== H-H-H ==

=== Plots using the lepsgui.py function ===
These are the various results that the program is able to show, given inputs rAB = 230 pm, rBC = 74 pm, pAB = -5.2 g mol-1 pm fs-1, pBC = 0 g mol-1 pm fs-1, for the reaction HA + HBHC → HAHB + HC.

[[File:Chl1718 HHH1.png|left|thumb|Contour plot]]
[[File:Chl1718 HHH7.png|thumb|Skew plot]]
[[File:Chl1718 HHH2.png|centre|thumb|Surface plot]]
[[File:Chl1718 HHH3.png|left|thumb|Internuclear Distances vs Time]]
[[File:Chl1718 HHH5.png|thumb|Momentum vs Time]]
[[File:Chl1718 HHH4.png|centre|thumb|Internuclear Velocities vs Time]]
[[File:Chl1718 HHH6.png|thumb|Energy vs Time|none]]
[[File:Chl1718 HHHTS1.png|thumb|r = 74 pm]]

=== Transition State ===
[[File:Chl1718 HHHTS2.png|thumb|r = 90.77 pm]]

==== On a potential energy surface diagram, how is the transition state mathematically defined? How can the transition state be identified, and how can it be distinguished from a local minimum of the potential energy surface? ====
The transition state is defined as <math> {dU \over ds} = 0 </math>, <math> {d^2 U \over ds^2} < 0 </math> and <math> {dU \over d\xi} = 0 </math>, <math> {d^2 U \over d\xi^2} > 0 </math>where U is the potential, <math> s </math>is the curve of the reaction pathway of minimum energy, and <math> \xi </math>is the line perpendicular to it. In other words, a saddle point. The transition state can be located by first looking at points where the gradient equals 0, then checking if the second derivative is negative in one direction and positive in the direction orthogonal to it.<ref>J. I. Steinfeld, Francisco, J. Salvadore, W. L. Hase, Chemical kinetics and dynamics, Prentice Hall, 1999, 2nd ed, 978-0-13-737123-5</ref>

==== Report your best estimate of the transition state position ('''rts''') and explain your reasoning illustrating it with a “Internuclear Distances vs Time” plot for a relevant trajectory. ====
For the reaction H + H2 → H2 + H, the transition state position was determined to be rts = (90.774249787545475, 90.774249787545475). Because of the symmetry of the reaction (the forwards reaction is the same as the backwards reaction), the potential surface is also symmetrical. It is a reflection in the x-y plane. Therefore, rAB = rBC, and rts = (r, r). For the transition state position, because <math> {dU \over ds} = 0 </math>, the molecule will be completely stationary if the initial momenta are both set to 0 g mol-1 pm fs-1, while other points will undergo a symmetric vibration. By looking at the Internuclear Distances vs Time graph and using an iterative method, the vibration was minimised until they could not be seen even by magnifying the scale.
[[File:Chl1718 HHHTS3.png|thumb|924x924px|r = 90.774249787545475 pm, at the smallest possible scale.|none]]

=== MEP ===

==== Comment on how the mep and the trajectory you just calculated differ. ====
Using rAB = 91 pm and rBC = rts, the mep follows the path of the maximum gradient. There are no vibrations like in the dynamics trajectory, where the conserved energy turns into vibrational energy, causing the trajectory to oscillate. The "speed" is also much slower for the mep, with rAB changing much less than the dynamics trajectory in the same amount of time steps, because the momenta are reset to 0 in each step.
[[File:Chl1718 HHHMEP1.png|thumb|Dynamics trajectory]]
[[File:Chl1718 HHHMEP2.png|none|thumb|MEP trajectory]]

=== Reaction Table ===

==== Complete the table above by adding the total energy, whether the trajectory is reactive or unreactive, and provide a plot of the trajectory and a small description for what happens along the trajectory. What can you conclude from the table? ====
{| class="wikitable"
!p1/ g.mol-1.pm.fs-1
!p2/ g.mol-1.pm.fs-1
!Etot
!Reactive?
!Description of the dynamics
!Illustration of the trajectory
|-
|<nowiki>-2.56</nowiki>
|<nowiki>-5.1</nowiki>
|<nowiki>-414.280</nowiki>
|Y
|HC crosses the barrier once and reacts successfully,

with some energy turning into vibrational energy.
|[[File:Chl1718 HHHTable1.png|frameless]]
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-4.1</nowiki>
|<nowiki>-420.077</nowiki>
|N
|HC does not have enough energy to cross the barrier

and bounces back with the same amount of vibrational

energy.
|[[File:Chl1718 HHHTable2.png|frameless]]
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-5.1</nowiki>
|<nowiki>-413.977</nowiki>
|Y
|Similar to reaction 1, but with higher energy. HAHB is

vibrating as it approaches HC.
|[[File:Chl1718 HHHTable3.png|frameless]]
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.1</nowiki>
|<nowiki>-357.277</nowiki>
|N
|Although the reaction initially happens, the barrier is

recrossed and the result is a failed reaction, with the

reactants in the situation as the beginning, but with

much more vibrational energy.
|[[File:Chl1718 HHHTable4.png|frameless]]
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.6</nowiki>
|<nowiki>-349.477</nowiki>
|Y
|The barrier is recrossed twice and the reaction is

successful, with HBHC vibrating strongly.
|[[File:Chl1718 HHHTable5.png|frameless]]
|}
It can be concluded that a minimum amount of energy is needed for a reaction to happen, but at high enough energies, the proportions of the reactants' momenta must also be correct in order to have a successful reaction.

=== Transition State Theory ===

==== Given the results you have obtained, how will Transition State Theory predictions for reaction rate values compare with experimental values? ====
TST predicts that all reactions that have more energy than the activation energy are successful. However, as some reactions recross the barrier and reform the products, TST theory overestimates the reaction rate compared to real values.

== F-H-H ==

=== Potential Surface ===

==== By inspecting the potential energy surfaces, classify the F + H2 and H + HF reactions according to their energetics (endothermic or exothermic). How does this relate to the bond strength of the chemical species involved? ====
As can be seen from the surface plot, F + H2 is exothermic (reactants higher in energy than products), and H + HF is endothermic (reactants lower in energy than products). This is because HF has a much higher bond strength than H2, so forming an HF bond releases more heat than breaking an H2 bond and vice versa.
[[File:Chl1718 FHH1.png|none|thumb|Surface plot of a F-H-H system.]]

==== Locate the approximate position of the transition state. ====
The Hammond postulate gives us that points of similar energy in a reaction pathway are also similar in structure. Considering F + H2, an exothermic reaction with an extremely small activation energy, the transition state must look very similar to the reactants, with the H atoms close together. By calculating mep trajectories, inspecting the internuclear distance vs time graphs, and trial and error on the flat region around rHH = 74, the transition state position was estimated to be rts = (rHH, fHF) = (74.48722437, 181.11017411).
[[File:Chl1718 FHHTS.png|none|thumb|Internuclear Distance vs "Time", MEP plot with rts = (74.48722437, 181.11017411)]]

==== Report the activation energy for both reactions. ====

===== F +H2 =====
EA = 434 - 560.5 = 126.5 kJmol-1
[[File:Chl1718 FHHE1.png|none|thumb|Total Energy vs No. of Steps for F + H2]]

===== H + HF =====
EA = 435.09 - 433.98 = 1.11 kJmol-1
[[File:Chl1718 FHHE2.png|none|thumb|Total Energy vs No. of Steps for H + HF]]

==== In light of the fact that energy is conserved, discuss the mechanism of release of the reaction energy. Explain how this could be confirmed experimentally. ====
The Momentum vs Time graph shows that the energy mostly gets turned into vibrational energy. This is released as heat, which can be measured by calorimetry.
[[File:Chl1718 FHHMo.png|none|thumb|Momentum vs Time for an F + H2 reaction.]]

==== Discuss how the distribution of energy between different modes (translation and vibration) affect the efficiency of the reaction, and how this is influenced by the position of the transition state. ====

===== H + HF =====
{| class="wikitable"
!pFH/ g.mol-1.pm.fs-1
!pHH/ g.mol-1.pm.fs-1
!Reactive?
!Illustration
|-
|13.75
|<nowiki>-2.38</nowiki>
|Y
|[[File:Chl1718 FHHTable3.png|frameless]]
|-
|<nowiki>-1</nowiki>
|<nowiki>-7</nowiki>
|N
|[[File:Chl1718 FHHTable4.png|frameless]]
|}
The F-H-H surface is a late-barrier endothermic surface. From Polanyi's empirical rules, therefore vibrational energy is more conducive to a successful reaction, as can be seen in the above table. When the H atom has a large amount of translational energy and there is little vibrational energy in HF, the H atom is bounced back by the barrier wall. If the surface was an early barrier type, and hence if the transition state was closer to the reactant side in H + HF, then the opposite would have been the case and translational energy would have been more effective for a successful reaction, because the transition state can be reached just by the H atom getting closer to the HF molecule. Here, a large separation between H and F is needed before the transition state can be crossed.<ref>K. J. Laidler, Chemical Kinetics, Harper-Collins, 1987, 3rd ed.</ref>

== References ==
<references />

File:Chl1718 FHHTable4.png

2020-05-08T17:26:23Z

Chl1718:

File:Chl1718 FHHTable3.png

2020-05-08T17:26:06Z

Chl1718:

File:Chl1718 FHHTable2.png

2020-05-08T17:10:33Z

Chl1718:

File:Chl1718 FHHTable1.png

2020-05-08T17:00:20Z

Chl1718:

File:Chl1718 FHHMo.png

2020-05-08T16:41:46Z

Chl1718:

MRD:chl1718 04052020

2020-05-08T16:32:37Z

Chl1718: /* Transition State */

= Modelling Molecular Reaction Dynamics =

== H-H-H ==

=== Plots using the lepsgui.py function ===
These are the various results that the program is able to show, given inputs rAB = 230 pm, rBC = 74 pm, pAB = -5.2 g mol-1 pm fs-1, pBC = 0 g mol-1 pm fs-1, for the reaction HA + HBHC → HAHB + HC.

[[File:Chl1718 HHH1.png|left|thumb|Contour plot]]
[[File:Chl1718 HHH7.png|thumb|Skew plot]]
[[File:Chl1718 HHH2.png|centre|thumb|Surface plot]]
[[File:Chl1718 HHH3.png|left|thumb|Internuclear Distances vs Time]]
[[File:Chl1718 HHH5.png|thumb|Momentum vs Time]]
[[File:Chl1718 HHH4.png|centre|thumb|Internuclear Velocities vs Time]]
[[File:Chl1718 HHH6.png|thumb|Energy vs Time|none]]
[[File:Chl1718 HHHTS1.png|thumb|r = 74 pm]]

=== Transition State ===
[[File:Chl1718 HHHTS2.png|thumb|r = 90.77 pm]]

==== On a potential energy surface diagram, how is the transition state mathematically defined? How can the transition state be identified, and how can it be distinguished from a local minimum of the potential energy surface? ====
The transition state is defined as <math> {dU \over ds} = 0 </math>, <math> {d^2 U \over ds^2} < 0 </math> and <math> {dU \over d\xi} = 0 </math>, <math> {d^2 U \over d\xi^2} > 0 </math>where U is the potential, <math> s </math>is the curve of the reaction pathway of minimum energy, and <math> \xi </math>is the line perpendicular to it. In other words, a saddle point. The transition state can be located by first looking at points where the gradient equals 0, then checking if the second derivative is negative in one direction and positive in the direction orthogonal to it.{{Citation | author1=Steinfeld, Jeffrey I | author2=Francisco, Joseph Salvadore | author3=Hase, William L | title=Chemical kinetics and dynamics | publication-date=1999 | publisher=Prentice Hall | edition=2nd ed | isbn=978-0-13-737123-5 }}

==== Report your best estimate of the transition state position ('''rts''') and explain your reasoning illustrating it with a “Internuclear Distances vs Time” plot for a relevant trajectory. ====
For the reaction H + H2 → H2 + H, the transition state position was determined to be rts = (90.774249787545475, 90.774249787545475). Because of the symmetry of the reaction (the forwards reaction is the same as the backwards reaction), the potential surface is also symmetrical. It is a reflection in the x-y plane. Therefore, rAB = rBC, and rts = (r, r). For the transition state position, because <math> {dU \over ds} = 0 </math>, the molecule will be completely stationary if the initial momenta are both set to 0 g mol-1 pm fs-1, while other points will undergo a symmetric vibration. By looking at the Internuclear Distances vs Time graph and using an iterative method, the vibration was minimised until they could not be seen even by magnifying the scale.
[[File:Chl1718 HHHTS3.png|thumb|924x924px|r = 90.774249787545475 pm, at the smallest possible scale.|none]]

=== MEP ===

==== Comment on how the mep and the trajectory you just calculated differ. ====
Using rAB = 91 pm and rBC = rts, the mep follows the path of the maximum gradient. There are no vibrations like in the dynamics trajectory, where the conserved energy turns into vibrational energy, causing the trajectory to oscillate. The "speed" is also much slower for the mep, with rAB changing much less than the dynamics trajectory in the same amount of time steps, because the momenta are reset to 0 in each step.
[[File:Chl1718 HHHMEP1.png|thumb|Dynamics trajectory]]
[[File:Chl1718 HHHMEP2.png|none|thumb|MEP trajectory]]

=== Reaction Table ===

==== Complete the table above by adding the total energy, whether the trajectory is reactive or unreactive, and provide a plot of the trajectory and a small description for what happens along the trajectory. What can you conclude from the table? ====
{| class="wikitable"
!p1/ g.mol-1.pm.fs-1
!p2/ g.mol-1.pm.fs-1
!Etot
!Reactive?
!Description of the dynamics
!Illustration of the trajectory
|-
|<nowiki>-2.56</nowiki>
|<nowiki>-5.1</nowiki>
|<nowiki>-414.280</nowiki>
|Y
|HC crosses the barrier once and reacts successfully,

with some energy turning into vibrational energy.
|[[File:Chl1718 HHHTable1.png|frameless]]
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-4.1</nowiki>
|<nowiki>-420.077</nowiki>
|N
|HC does not have enough energy to cross the barrier

and bounces back with the same amount of vibrational

energy.
|[[File:Chl1718 HHHTable2.png|frameless]]
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-5.1</nowiki>
|<nowiki>-413.977</nowiki>
|Y
|Similar to reaction 1, but with higher energy. HAHB is

vibrating as it approaches HC.
|[[File:Chl1718 HHHTable3.png|frameless]]
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.1</nowiki>
|<nowiki>-357.277</nowiki>
|N
|Although the reaction initially happens, the barrier is

recrossed and the result is a failed reaction, with the

reactants in the situation as the beginning, but with

much more vibrational energy.
|[[File:Chl1718 HHHTable4.png|frameless]]
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.6</nowiki>
|<nowiki>-349.477</nowiki>
|Y
|The barrier is recrossed twice and the reaction is

successful, with HBHC vibrating strongly.
|[[File:Chl1718 HHHTable5.png|frameless]]
|}
It can be concluded that a minimum amount of energy is needed for a reaction to happen, but at high enough energies, the proportions of the reactants' momenta must also be correct in order to have a successful reaction.

=== Transition State Theory ===

==== Given the results you have obtained, how will Transition State Theory predictions for reaction rate values compare with experimental values? ====
TST predicts that all reactions that have more energy than the activation energy are successful. However, as some reactions recross the barrier and reform the products, TST theory overestimates the reaction rate compared to real values.

== F-H-H ==

=== Potential Surface ===

==== By inspecting the potential energy surfaces, classify the F + H2 and H + HF reactions according to their energetics (endothermic or exothermic). How does this relate to the bond strength of the chemical species involved? ====
As can be seen from the surface plot, F + H2 is exothermic (reactants higher in energy than products), and H + HF is endothermic (reactants lower in energy than products). This is because HF has a much higher bond strength than H2, so forming an HF bond releases more heat than breaking an H2 bond and vice versa.
[[File:Chl1718 FHH1.png|none|thumb|Surface plot of a F-H-H system.]]

==== Locate the approximate position of the transition state. ====
The Hammond postulate gives us that points of similar energy in a reaction pathway are also similar in structure. Considering F + H2, an exothermic reaction with an extremely small activation energy, the transition state must look very similar to the reactants, with the H atoms close together. By calculating mep trajectories, inspecting the internuclear distance vs time graphs, and trial and error on the flat region around rHH = 74, the transition state position was estimated to be rts = (rHH, fHF) = (74.48722437, 181.11017411).
[[File:Chl1718 FHHTS.png|none|thumb|Internuclear Distance vs "Time", MEP plot with rts = (74.48722437, 181.11017411)]]

==== Report the activation energy for both reactions. ====

===== F +H2 =====
EA = 434 - 560.5 = 126.5 kJmol-1
[[File:Chl1718 FHHE1.png|none|thumb|Total Energy vs No. of Steps for F + H2]]

===== H + HF =====
EA = 435.09 - 433.98 = 1.11 kJmol-1
[[File:Chl1718 FHHE2.png|none|thumb|Total Energy vs No. of Steps for H + HF]]

==== In light of the fact that energy is conserved, discuss the mechanism of release of the reaction energy. Explain how this could be confirmed experimentally. ====

MRD:chl1718 04052020

2020-05-08T16:32:07Z

Chl1718: /* Given the results you have obtained, how will Transition State Theory predictions for reaction rate values compare with experimental values? */

= Modelling Molecular Reaction Dynamics =

== H-H-H ==

=== Plots using the lepsgui.py function ===
These are the various results that the program is able to show, given inputs rAB = 230 pm, rBC = 74 pm, pAB = -5.2 g mol-1 pm fs-1, pBC = 0 g mol-1 pm fs-1, for the reaction HA + HBHC → HAHB + HC.

[[File:Chl1718 HHH1.png|left|thumb|Contour plot]]
[[File:Chl1718 HHH7.png|thumb|Skew plot]]
[[File:Chl1718 HHH2.png|centre|thumb|Surface plot]]
[[File:Chl1718 HHH3.png|left|thumb|Internuclear Distances vs Time]]
[[File:Chl1718 HHH5.png|thumb|Momentum vs Time]]
[[File:Chl1718 HHH4.png|centre|thumb|Internuclear Velocities vs Time]]
[[File:Chl1718 HHH6.png|thumb|Energy vs Time|none]]
[[File:Chl1718 HHHTS1.png|thumb|r = 74 pm]]

=== Transition State ===
[[File:Chl1718 HHHTS2.png|thumb|r = 90.77 pm]]

==== On a potential energy surface diagram, how is the transition state mathematically defined? How can the transition state be identified, and how can it be distinguished from a local minimum of the potential energy surface? ====
The transition state is defined as <math> {dU \over ds} = 0 </math>, <math> {d^2 U \over ds^2} < 0 </math> and <math> {dU \over d\xi} = 0 </math>, <math> {d^2 U \over d\xi^2} > 0 </math>where U is the potential, <math> s </math>is the curve of the reaction pathway of minimum energy, and <math> \xi </math>is the line perpendicular to it. In other words, a saddle point. The transition state can be located by first looking at points where the gradient equals 0, then checking if the second derivative is negative in one direction and positive in the direction orthogonal to it.

==== Report your best estimate of the transition state position ('''rts''') and explain your reasoning illustrating it with a “Internuclear Distances vs Time” plot for a relevant trajectory. ====
For the reaction H + H2 → H2 + H, the transition state position was determined to be rts = (90.774249787545475, 90.774249787545475). Because of the symmetry of the reaction (the forwards reaction is the same as the backwards reaction), the potential surface is also symmetrical. It is a reflection in the x-y plane. Therefore, rAB = rBC, and rts = (r, r). For the transition state position, because <math> {dU \over ds} = 0 </math>, the molecule will be completely stationary if the initial momenta are both set to 0 g mol-1 pm fs-1, while other points will undergo a symmetric vibration. By looking at the Internuclear Distances vs Time graph and using an iterative method, the vibration was minimised until they could not be seen even by magnifying the scale.
[[File:Chl1718 HHHTS3.png|thumb|924x924px|r = 90.774249787545475 pm, at the smallest possible scale.|none]]

=== MEP ===

==== Comment on how the mep and the trajectory you just calculated differ. ====
Using rAB = 91 pm and rBC = rts, the mep follows the path of the maximum gradient. There are no vibrations like in the dynamics trajectory, where the conserved energy turns into vibrational energy, causing the trajectory to oscillate. The "speed" is also much slower for the mep, with rAB changing much less than the dynamics trajectory in the same amount of time steps, because the momenta are reset to 0 in each step.
[[File:Chl1718 HHHMEP1.png|thumb|Dynamics trajectory]]
[[File:Chl1718 HHHMEP2.png|none|thumb|MEP trajectory]]

=== Reaction Table ===

==== Complete the table above by adding the total energy, whether the trajectory is reactive or unreactive, and provide a plot of the trajectory and a small description for what happens along the trajectory. What can you conclude from the table? ====
{| class="wikitable"
!p1/ g.mol-1.pm.fs-1
!p2/ g.mol-1.pm.fs-1
!Etot
!Reactive?
!Description of the dynamics
!Illustration of the trajectory
|-
|<nowiki>-2.56</nowiki>
|<nowiki>-5.1</nowiki>
|<nowiki>-414.280</nowiki>
|Y
|HC crosses the barrier once and reacts successfully,

with some energy turning into vibrational energy.
|[[File:Chl1718 HHHTable1.png|frameless]]
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-4.1</nowiki>
|<nowiki>-420.077</nowiki>
|N
|HC does not have enough energy to cross the barrier

and bounces back with the same amount of vibrational

energy.
|[[File:Chl1718 HHHTable2.png|frameless]]
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-5.1</nowiki>
|<nowiki>-413.977</nowiki>
|Y
|Similar to reaction 1, but with higher energy. HAHB is

vibrating as it approaches HC.
|[[File:Chl1718 HHHTable3.png|frameless]]
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.1</nowiki>
|<nowiki>-357.277</nowiki>
|N
|Although the reaction initially happens, the barrier is

recrossed and the result is a failed reaction, with the

reactants in the situation as the beginning, but with

much more vibrational energy.
|[[File:Chl1718 HHHTable4.png|frameless]]
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.6</nowiki>
|<nowiki>-349.477</nowiki>
|Y
|The barrier is recrossed twice and the reaction is

successful, with HBHC vibrating strongly.
|[[File:Chl1718 HHHTable5.png|frameless]]
|}
It can be concluded that a minimum amount of energy is needed for a reaction to happen, but at high enough energies, the proportions of the reactants' momenta must also be correct in order to have a successful reaction.

=== Transition State Theory ===

==== Given the results you have obtained, how will Transition State Theory predictions for reaction rate values compare with experimental values? ====
TST predicts that all reactions that have more energy than the activation energy are successful. However, as some reactions recross the barrier and reform the products, TST theory overestimates the reaction rate compared to real values.

== F-H-H ==

=== Potential Surface ===

==== By inspecting the potential energy surfaces, classify the F + H2 and H + HF reactions according to their energetics (endothermic or exothermic). How does this relate to the bond strength of the chemical species involved? ====
As can be seen from the surface plot, F + H2 is exothermic (reactants higher in energy than products), and H + HF is endothermic (reactants lower in energy than products). This is because HF has a much higher bond strength than H2, so forming an HF bond releases more heat than breaking an H2 bond and vice versa.
[[File:Chl1718 FHH1.png|none|thumb|Surface plot of a F-H-H system.]]

==== Locate the approximate position of the transition state. ====
The Hammond postulate gives us that points of similar energy in a reaction pathway are also similar in structure. Considering F + H2, an exothermic reaction with an extremely small activation energy, the transition state must look very similar to the reactants, with the H atoms close together. By calculating mep trajectories, inspecting the internuclear distance vs time graphs, and trial and error on the flat region around rHH = 74, the transition state position was estimated to be rts = (rHH, fHF) = (74.48722437, 181.11017411).
[[File:Chl1718 FHHTS.png|none|thumb|Internuclear Distance vs "Time", MEP plot with rts = (74.48722437, 181.11017411)]]

==== Report the activation energy for both reactions. ====

===== F +H2 =====
EA = 434 - 560.5 = 126.5 kJmol-1
[[File:Chl1718 FHHE1.png|none|thumb|Total Energy vs No. of Steps for F + H2]]

===== H + HF =====
EA = 435.09 - 433.98 = 1.11 kJmol-1
[[File:Chl1718 FHHE2.png|none|thumb|Total Energy vs No. of Steps for H + HF]]

==== In light of the fact that energy is conserved, discuss the mechanism of release of the reaction energy. Explain how this could be confirmed experimentally. ====

MRD:chl1718 04052020

2020-05-08T15:49:16Z

Chl1718: /* Complete the table above by adding the total energy, whether the trajectory is reactive or unreactive, and provide a plot of the trajectory and a small description for what happens along the trajectory. What can you conclude from the table? */

= Modelling Molecular Reaction Dynamics =

== H-H-H ==

=== Plots using the lepsgui.py function ===
These are the various results that the program is able to show, given inputs rAB = 230 pm, rBC = 74 pm, pAB = -5.2 g mol-1 pm fs-1, pBC = 0 g mol-1 pm fs-1, for the reaction HA + HBHC → HAHB + HC.

[[File:Chl1718 HHH1.png|left|thumb|Contour plot]]
[[File:Chl1718 HHH7.png|thumb|Skew plot]]
[[File:Chl1718 HHH2.png|centre|thumb|Surface plot]]
[[File:Chl1718 HHH3.png|left|thumb|Internuclear Distances vs Time]]
[[File:Chl1718 HHH5.png|thumb|Momentum vs Time]]
[[File:Chl1718 HHH4.png|centre|thumb|Internuclear Velocities vs Time]]
[[File:Chl1718 HHH6.png|thumb|Energy vs Time|none]]
[[File:Chl1718 HHHTS1.png|thumb|r = 74 pm]]

=== Transition State ===
[[File:Chl1718 HHHTS2.png|thumb|r = 90.77 pm]]

==== On a potential energy surface diagram, how is the transition state mathematically defined? How can the transition state be identified, and how can it be distinguished from a local minimum of the potential energy surface? ====
The transition state is defined as <math> {dU \over ds} = 0 </math>, <math> {d^2 U \over ds^2} < 0 </math> and <math> {dU \over d\xi} = 0 </math>, <math> {d^2 U \over d\xi^2} > 0 </math>where U is the potential, <math> s </math>is the curve of the reaction pathway of minimum energy, and <math> \xi </math>is the line perpendicular to it. In other words, a saddle point. The transition state can be located by first looking at points where the gradient equals 0, then checking if the second derivative is negative in one direction and positive in the direction orthogonal to it.

==== Report your best estimate of the transition state position ('''rts''') and explain your reasoning illustrating it with a “Internuclear Distances vs Time” plot for a relevant trajectory. ====
For the reaction H + H2 → H2 + H, the transition state position was determined to be rts = (90.774249787545475, 90.774249787545475). Because of the symmetry of the reaction (the forwards reaction is the same as the backwards reaction), the potential surface is also symmetrical. It is a reflection in the x-y plane. Therefore, rAB = rBC, and rts = (r, r). For the transition state position, because <math> {dU \over ds} = 0 </math>, the molecule will be completely stationary if the initial momenta are both set to 0 g mol-1 pm fs-1, while other points will undergo a symmetric vibration. By looking at the Internuclear Distances vs Time graph and using an iterative method, the vibration was minimised until they could not be seen even by magnifying the scale.
[[File:Chl1718 HHHTS3.png|thumb|924x924px|r = 90.774249787545475 pm, at the smallest possible scale.|none]]

=== MEP ===

==== Comment on how the mep and the trajectory you just calculated differ. ====
Using rAB = 91 pm and rBC = rts, the mep follows the path of the maximum gradient. There are no vibrations like in the dynamics trajectory, where the conserved energy turns into vibrational energy, causing the trajectory to oscillate. The "speed" is also much slower for the mep, with rAB changing much less than the dynamics trajectory in the same amount of time steps, because the momenta are reset to 0 in each step.
[[File:Chl1718 HHHMEP1.png|thumb|Dynamics trajectory]]
[[File:Chl1718 HHHMEP2.png|none|thumb|MEP trajectory]]

=== Reaction Table ===

==== Complete the table above by adding the total energy, whether the trajectory is reactive or unreactive, and provide a plot of the trajectory and a small description for what happens along the trajectory. What can you conclude from the table? ====
{| class="wikitable"
!p1/ g.mol-1.pm.fs-1
!p2/ g.mol-1.pm.fs-1
!Etot
!Reactive?
!Description of the dynamics
!Illustration of the trajectory
|-
|<nowiki>-2.56</nowiki>
|<nowiki>-5.1</nowiki>
|<nowiki>-414.280</nowiki>
|Y
|HC crosses the barrier once and reacts successfully,

with some energy turning into vibrational energy.
|[[File:Chl1718 HHHTable1.png|frameless]]
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-4.1</nowiki>
|<nowiki>-420.077</nowiki>
|N
|HC does not have enough energy to cross the barrier

and bounces back with the same amount of vibrational

energy.
|[[File:Chl1718 HHHTable2.png|frameless]]
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-5.1</nowiki>
|<nowiki>-413.977</nowiki>
|Y
|Similar to reaction 1, but with higher energy. HAHB is

vibrating as it approaches HC.
|[[File:Chl1718 HHHTable3.png|frameless]]
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.1</nowiki>
|<nowiki>-357.277</nowiki>
|N
|Although the reaction initially happens, the barrier is

recrossed and the result is a failed reaction, with the

reactants in the situation as the beginning, but with

much more vibrational energy.
|[[File:Chl1718 HHHTable4.png|frameless]]
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.6</nowiki>
|<nowiki>-349.477</nowiki>
|Y
|The barrier is recrossed twice and the reaction is

successful, with HBHC vibrating strongly.
|[[File:Chl1718 HHHTable5.png|frameless]]
|}
It can be concluded that a minimum amount of energy is needed for a reaction to happen, but at high enough energies, the proportions of the reactants' momenta must also be correct in order to have a successful reaction.

=== Transition State Theory ===

==== Given the results you have obtained, how will Transition State Theory predictions for reaction rate values compare with experimental values? ====
TST predicts that all reactions that have more energy than the activation energy are successful. However, as some reactions recross the barrier and reform the products, TST theory overestimates the reaction rate compared to real values.

== F-H-H ==

=== Potential Surface ===

==== By inspecting the potential energy surfaces, classify the F + H2 and H + HF reactions according to their energetics (endothermic or exothermic). How does this relate to the bond strength of the chemical species involved? ====
As can be seen from the surface plot, F + H2 is exothermic (reactants higher in energy than products), and H + HF is endothermic (reactants lower in energy than products). This is because HF has a much higher bond strength than H2, so forming an HF bond releases more heat than breaking an H2 bond and vice versa.
[[File:Chl1718 FHH1.png|none|thumb|Surface plot of a F-H-H system.]]

==== Locate the approximate position of the transition state. ====
The Hammond postulate gives us that points of similar energy in a reaction pathway are also similar in structure. Considering F + H2, an exothermic reaction with an extremely small activation energy, the transition state must look very similar to the reactants, with the H atoms close together. By calculating mep trajectories, inspecting the internuclear distance vs time graphs, and trial and error on the flat region around rHH = 74, the transition state position was estimated to be rts = (rHH, fHF) = (74.48722437, 181.11017411).
[[File:Chl1718 FHHTS.png|none|thumb|Internuclear Distance vs "Time", MEP plot with rts = (74.48722437, 181.11017411)]]

==== Report the activation energy for both reactions. ====

===== F +H2 =====
EA = 434 - 560.5 = 126.5 kJmol-1
[[File:Chl1718 FHHE1.png|none|thumb|Total Energy vs No. of Steps for F + H2]]

===== H + HF =====
EA = 435.09 - 433.98 = 1.11 kJmol-1
[[File:Chl1718 FHHE2.png|none|thumb|Total Energy vs No. of Steps for H + HF]]

==== In light of the fact that energy is conserved, discuss the mechanism of release of the reaction energy. Explain how this could be confirmed experimentally ====

File:Chl1718 FHHE2.png

2020-05-08T15:44:26Z

Chl1718:

File:Chl1718 FHHE1.png

2020-05-08T15:44:14Z

Chl1718:

File:Chl1718 FHHTS.png

2020-05-08T15:40:16Z

Chl1718:

File:Chl1718 FHH1.png

2020-05-08T14:50:31Z

Chl1718:

MRD:chl1718 04052020

2020-05-08T14:13:30Z

= Modelling Molecular Reaction Dynamics =

== H+H2 ==

=== Plots using the lepsgui.py function ===
These are the various results that the program is able to show, given inputs rAB = 230 pm, rBC = 74 pm, pAB = -5.2 g mol-1 pm fs-1, pBC = 0 g mol-1 pm fs-1, for the reaction HA + HBHC → HAHB + HC.

[[File:Chl1718 HHH1.png|left|thumb|Contour plot]]
[[File:Chl1718 HHH7.png|thumb|Skew plot]]
[[File:Chl1718 HHH2.png|centre|thumb|Surface plot]]
[[File:Chl1718 HHH3.png|left|thumb|Internuclear Distances vs Time]]
[[File:Chl1718 HHH5.png|thumb|Momentum vs Time]]
[[File:Chl1718 HHH4.png|centre|thumb|Internuclear Velocities vs Time]]
[[File:Chl1718 HHH6.png|thumb|Energy vs Time|none]]
[[File:Chl1718 HHHTS1.png|thumb|r = 74 pm]]

=== Transition State ===
[[File:Chl1718 HHHTS2.png|thumb|r = 90.77 pm]]

==== On a potential energy surface diagram, how is the transition state mathematically defined? How can the transition state be identified, and how can it be distinguished from a local minimum of the potential energy surface? ====
The transition state is defined as <math> {dU \over ds} = 0 </math>, <math> {d^2 U \over ds^2} < 0 </math> and <math> {dU \over d\xi} = 0 </math>, <math> {d^2 U \over d\xi^2} > 0 </math>where U is the potential, <math> s </math>is the curve of the reaction pathway of minimum energy, and <math> \xi </math>is the line perpendicular to it. In other words, a saddle point. The transition state can be located by first looking at points where the gradient equals 0, then checking if the second derivative is negative in one direction and positive in the direction orthogonal to it.

==== Report your best estimate of the transition state position ('''rts''') and explain your reasoning illustrating it with a “Internuclear Distances vs Time” plot for a relevant trajectory. ====
For the reaction H + H2 → H2 + H, the transition state position was determined to be rts = (90.774249787545475, 90.774249787545475). Because of the symmetry of the reaction (the forwards reaction is the same as the backwards reaction), the potential surface is also symmetrical. It is a reflection in the x-y plane. Therefore, rAB = rBC, and rts = (r, r). For the transition state position, because <math> {dU \over ds} = 0 </math>, the molecule will be completely stationary if the initial momenta are both set to 0 g mol-1 pm fs-1, while other points will undergo a symmetric vibration. By looking at the Internuclear Distances vs Time graph and using an iterative method, the vibration was minimised until they could not be seen even by magnifying the scale.
[[File:Chl1718 HHHTS3.png|thumb|924x924px|r = 90.774249787545475 pm, at the smallest possible scale.|none]]

=== MEP ===

==== Comment on how the mep and the trajectory you just calculated differ. ====
Using rAB = 91 pm and rBC = rts, the mep follows the path of the maximum gradient. There are no vibrations like in the dynamics trajectory, where the conserved energy turns into vibrational energy, causing the trajectory to oscillate. The "speed" is also much slower for the mep, with rAB changing much less than the dynamics trajectory in the same amount of time steps, because the momenta are reset to 0 in each step.
[[File:Chl1718 HHHMEP1.png|thumb|Dynamics trajectory]]
[[File:Chl1718 HHHMEP2.png|none|thumb|MEP trajectory]]

=== Reaction Table ===

==== Complete the table above by adding the total energy, whether the trajectory is reactive or unreactive, and provide a plot of the trajectory and a small description for what happens along the trajectory. What can you conclude from the table? ====
{| class="wikitable"
!p1/ g.mol-1.pm.fs-1
!p2/ g.mol-1.pm.fs-1
!Etot
!Reactive?
!Description of the dynamics
!Illustration of the trajectory
|-
|<nowiki>-2.56</nowiki>
|<nowiki>-5.1</nowiki>
|<nowiki>-414.280</nowiki>
|Y
|HC crosses the barrier once and reacts successfully,

with some energy turning into vibrational energy.
|[[File:Chl1718 HHHTable1.png|frameless]]
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-4.1</nowiki>
|<nowiki>-420.077</nowiki>
|N
|HC does not have enough energy to cross the barrier

and bounces back with the same amount of vibrational

energy.
|[[File:Chl1718 HHHTable2.png|frameless]]
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-5.1</nowiki>
|<nowiki>-413.977</nowiki>
|Y
|Similar to reaction 1, but with higher energy. HAHB is

vibrating as it approaches HC.
|[[File:Chl1718 HHHTable3.png|frameless]]
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.1</nowiki>
|<nowiki>-357.277</nowiki>
|N
|Although the reaction initially happens, the barrier is

recrossed and the result is a failed reaction, with the

reactants in the situation as the beginning, but with

much more vibrational energy.
|[[File:Chl1718 HHHTable4.png|frameless]]
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.6</nowiki>
|<nowiki>-349.477</nowiki>
|Y
|The barrier is recrossed twice and the reaction is

successful, with HBHC vibrating strongly.
|[[File:Chl1718 HHHTable5.png|frameless]]
|}

MRD:chl1718 04052020

2020-05-08T14:03:47Z

Chl1718: /* MEP */

= Modelling Molecular Reaction Dynamics =

== H+H2 ==

=== Plots using the lepsgui.py function ===
These are the various results that the program is able to show, given inputs rAB = 230 pm, rBC = 74 pm, pAB = -5.2 g mol-1 pm fs-1, pBC = 0 g mol-1 pm fs-1, for the reaction HA + HBHC → HAHB + HC.

[[File:Chl1718 HHH1.png|left|thumb|Contour plot]]
[[File:Chl1718 HHH7.png|thumb|Skew plot]]
[[File:Chl1718 HHH2.png|centre|thumb|Surface plot]]
[[File:Chl1718 HHH3.png|left|thumb|Internuclear Distances vs Time]]
[[File:Chl1718 HHH5.png|thumb|Momentum vs Time]]
[[File:Chl1718 HHH4.png|centre|thumb|Internuclear Velocities vs Time]]
[[File:Chl1718 HHH6.png|thumb|Energy vs Time|none]]
[[File:Chl1718 HHHTS1.png|thumb|r = 74 pm]]

=== Transition State ===
[[File:Chl1718 HHHTS2.png|thumb|r = 90.77 pm]]

==== On a potential energy surface diagram, how is the transition state mathematically defined? How can the transition state be identified, and how can it be distinguished from a local minimum of the potential energy surface? ====
The transition state is defined as <math> {dU \over ds} = 0 </math>, <math> {d^2 U \over ds^2} < 0 </math> and <math> {dU \over d\xi} = 0 </math>, <math> {d^2 U \over d\xi^2} > 0 </math>where U is the potential, <math> s </math>is the curve of the reaction pathway of minimum energy, and <math> \xi </math>is the line perpendicular to it. In other words, a saddle point. The transition state can be located by first looking at points where the gradient equals 0, then checking if the second derivative is negative in one direction and positive in the direction orthogonal to it.

==== Report your best estimate of the transition state position ('''rts''') and explain your reasoning illustrating it with a “Internuclear Distances vs Time” plot for a relevant trajectory. ====
For the reaction H + H2 → H2 + H, the transition state position was determined to be rts = (90.774249787545475, 90.774249787545475). Because of the symmetry of the reaction (the forwards reaction is the same as the backwards reaction), the potential surface is also symmetrical. It is a reflection in the x-y plane. Therefore, rAB = rBC, and rts = (r, r). For the transition state position, because <math> {dU \over ds} = 0 </math>, the molecule will be completely stationary if the initial momenta are both set to 0 g mol-1 pm fs-1, while other points will undergo a symmetric vibration. By looking at the Internuclear Distances vs Time graph and using an iterative method, the vibration was minimised until they could not be seen even by magnifying the scale.
[[File:Chl1718 HHHTS3.png|thumb|924x924px|r = 90.774249787545475 pm, at the smallest possible scale.|none]]

=== MEP ===

==== Comment on how the mep and the trajectory you just calculated differ. ====
Using rAB = 91 pm and rBC = rts, the mep follows the path of the maximum gradient. There are no vibrations like in the dynamics trajectory, where the conserved energy turns into vibrational energy, causing the trajectory to oscillate. The "speed" is also much slower for the mep, with rAB changing much less than the dynamics trajectory in the same amount of time steps, because the momenta are reset to 0 in each step.
[[File:Chl1718 HHHMEP1.png|thumb|Dynamics trajectory]]
[[File:Chl1718 HHHMEP2.png|none|thumb|MEP trajectory]]

=== Reaction Table ===

==== Complete the table above by adding the total energy, whether the trajectory is reactive or unreactive, and provide a plot of the trajectory and a small description for what happens along the trajectory. What can you conclude from the table? ====
{| class="wikitable"
!p1/ g.mol-1.pm.fs-1
!p2/ g.mol-1.pm.fs-1
!Etot
!Reactive?
!Description of the dynamics
!Illustration of the trajectory
|-
|<nowiki>-2.56</nowiki>
|<nowiki>-5.1</nowiki>
|<nowiki>-414.280</nowiki>
|Y
|
|[[File:Chl1718 HHHTable1.png|frameless]]
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-4.1</nowiki>
|<nowiki>-420.077</nowiki>
|N
|
|[[File:Chl1718 HHHTable2.png|frameless]]
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-5.1</nowiki>
|<nowiki>-413.977</nowiki>
|Y
|
|[[File:Chl1718 HHHTable3.png|frameless]]
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.1</nowiki>
|<nowiki>-357.277</nowiki>
|N
|
|[[File:Chl1718 HHHTable4.png|frameless]]
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.6</nowiki>
|<nowiki>-349.477</nowiki>
|Y
|
|[[File:Chl1718 HHHTable5.png|frameless]]
|}

File:Chl1718 HHHMEP2.png

2020-05-08T13:55:33Z

Chl1718:

File:Chl1718 HHHMEP1.png

2020-05-08T13:55:18Z

Chl1718:

MRD:chl1718 04052020

2020-05-08T13:47:22Z

Chl1718: /* Transition State */

= Modelling Molecular Reaction Dynamics =

== H+H2 ==

=== Plots using the lepsgui.py function ===
These are the various results that the program is able to show, given inputs rAB = 230 pm, rBC = 74 pm, pAB = -5.2 g mol-1 pm fs-1, pBC = 0 g mol-1 pm fs-1, for the reaction HA + HBHC → HAHB + HC.

[[File:Chl1718 HHH1.png|left|thumb|Contour plot]]
[[File:Chl1718 HHH7.png|thumb|Skew plot]]
[[File:Chl1718 HHH2.png|centre|thumb|Surface plot]]
[[File:Chl1718 HHH3.png|left|thumb|Internuclear Distances vs Time]]
[[File:Chl1718 HHH5.png|thumb|Momentum vs Time]]
[[File:Chl1718 HHH4.png|centre|thumb|Internuclear Velocities vs Time]]
[[File:Chl1718 HHH6.png|thumb|Energy vs Time|none]]
[[File:Chl1718 HHHTS1.png|thumb|r = 74 pm]]

=== Transition State ===
[[File:Chl1718 HHHTS2.png|thumb|r = 90.77 pm]]

==== On a potential energy surface diagram, how is the transition state mathematically defined? How can the transition state be identified, and how can it be distinguished from a local minimum of the potential energy surface? ====
The transition state is defined as <math> {dU \over ds} = 0 </math>, <math> {d^2 U \over ds^2} < 0 </math> and <math> {dU \over d\xi} = 0 </math>, <math> {d^2 U \over d\xi^2} > 0 </math>where U is the potential, <math> s </math>is the curve of the reaction pathway of minimum energy, and <math> \xi </math>is the line perpendicular to it. In other words, a saddle point. The transition state can be located by first looking at points where the gradient equals 0, then checking if the second derivative is negative in one direction and positive in the direction orthogonal to it.

==== Report your best estimate of the transition state position ('''rts''') and explain your reasoning illustrating it with a “Internuclear Distances vs Time” plot for a relevant trajectory. ====
For the reaction H + H2 → H2 + H, the transition state position was determined to be rts = (90.774249787545475, 90.774249787545475). Because of the symmetry of the reaction (the forwards reaction is the same as the backwards reaction), the potential surface is also symmetrical. It is a reflection in the x-y plane. Therefore, rAB = rBC, and rts = (r, r). For the transition state position, because <math> {dU \over ds} = 0 </math>, the molecule will be completely stationary if the initial momenta are both set to 0 g mol-1 pm fs-1, while other points will undergo a symmetric vibration. By looking at the Internuclear Distances vs Time graph and using an iterative method, the vibration was minimised until they could not be seen even by magnifying the scale.
[[File:Chl1718 HHHTS3.png|thumb|924x924px|r = 90.774249787545475 pm, at the smallest possible scale.|none]]

=== MEP ===
{| class="wikitable"
!p1/ g.mol-1.pm.fs-1
!p2/ g.mol-1.pm.fs-1
!Etot
!Reactive?
!Description of the dynamics
!Illustration of the trajectory
|-
|<nowiki>-2.56</nowiki>
|<nowiki>-5.1</nowiki>
|<nowiki>-414.280</nowiki>
|Y
|
|[[File:Chl1718 HHHTable1.png|frameless]]
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-4.1</nowiki>
|<nowiki>-420.077</nowiki>
|N
|
|[[File:Chl1718 HHHTable2.png|frameless]]
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-5.1</nowiki>
|<nowiki>-413.977</nowiki>
|Y
|
|[[File:Chl1718 HHHTable3.png|frameless]]
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.1</nowiki>
|<nowiki>-357.277</nowiki>
|N
|
|[[File:Chl1718 HHHTable4.png|frameless]]
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.6</nowiki>
|<nowiki>-349.477</nowiki>
|Y
|
|[[File:Chl1718 HHHTable5.png|frameless]]
|}

MRD:chl1718 04052020

2020-05-08T13:36:25Z

Chl1718: /* Transition State */

File:Chl1718 HHHTS3.png

2020-05-08T13:29:33Z

Chl1718:

File:Chl1718 HHHTS2.png

2020-05-08T13:09:44Z

Chl1718:

File:Chl1718 HHHTS1.png

2020-05-08T13:04:07Z

Chl1718:

MRD:chl1718 04052020

2020-05-08T12:12:10Z

Chl1718: /* Plots using the lepsgui.py function */

MRD:chl1718 04052020

2020-05-08T12:07:49Z

Chl1718:

MRD:chl1718 04052020

2020-05-08T12:00:49Z

Chl1718: /* Plots using the lepsgui.py function */

= Modelling Molecular Reaction Dynamics =

== H+H2 ==

=== Plots using the lepsgui.py function ===
[[File:Chl1718 HHH1.png|left|thumb|Contour plot]]
[[File:Chl1718 HHH7.png|thumb|Skew plot]]
[[File:Chl1718 HHH2.png|centre|thumb|Surface plot]]
[[File:Chl1718 HHH3.png|left|thumb|Internuclear Distances vs Time]]
[[File:Chl1718 HHH5.png|thumb|Momentum vs Time]]
[[File:Chl1718 HHH4.png|centre|thumb|Internuclear Velocities vs Time]]
[[File:Chl1718 HHH6.png|left|thumb|Energy vs Time]]

=== Transition State ===
The transition state is defined as <math> {dU \over ds} = 0 </math>, <math> {d^2 U \over ds^2} < 0 </math> and <math> {dU \over d\xi} = 0 </math>, <math> {d^2 U \over d\xi^2} > 0 </math>where U is the potential, <math> s </math> is the curve of the reaction pathway of minimum energy, and <math> \xi </math> is the line perpendicular to it.
{| class="wikitable"
!p1/ g.mol-1.pm.fs-1
!p2/ g.mol-1.pm.fs-1
!Etot
!Reactive?
!Description of the dynamics
!Illustration of the trajectory
|-
|<nowiki>-2.56</nowiki>
|<nowiki>-5.1</nowiki>
|<nowiki>-414.280</nowiki>
|Y
|
|[[File:Chl1718 HHHTable1.png|frameless]]
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-4.1</nowiki>
|<nowiki>-420.077</nowiki>
|N
|
|[[File:Chl1718 HHHTable2.png|frameless]]
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-5.1</nowiki>
|<nowiki>-413.977</nowiki>
|Y
|
|[[File:Chl1718 HHHTable3.png|frameless]]
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.1</nowiki>
|<nowiki>-357.277</nowiki>
|N
|
|[[File:Chl1718 HHHTable4.png|frameless]]
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.6</nowiki>
|<nowiki>-349.477</nowiki>
|Y
|
|[[File:Chl1718 HHHTable5.png|frameless]]
|}

MRD:chl1718 04052020

2020-05-08T11:54:30Z

Chl1718:

= Modelling Molecular Reaction Dynamics =

== H+H2 ==

=== Plots using the lepsgui.py function ===
[[File:Chl1718 HHH1.png|left|thumb|Contour plot]]
[[File:Chl1718 HHH7.png|thumb|Skew plot]]
[[File:Chl1718 HHH2.png|centre|thumb|Surface plot]]
[[File:Chl1718 HHH3.png|left|thumb|Internuclear Distances vs Time]]
[[File:Chl1718 HHH5.png|thumb|Momentum vs Time]]
[[File:Chl1718 HHH4.png|centre|thumb|Internuclear Velocities vs Time]]
[[File:Chl1718 HHH6.png|left|thumb|Energy vs Time]]

=== Transition State ===
The transition state is defined as <math> {dU \over ds} = 0 </math>, <math> {d^2 U \over ds^2} < 0 </math> and <math> {dU \over d\xi} = 0 </math>, <math> {d^2 U \over d\xi^2} > 0 </math>

{| class="wikitable"
!p1/ g.mol-1.pm.fs-1
!p2/ g.mol-1.pm.fs-1
!Etot
!Reactive?
!Description of the dynamics
!Illustration of the trajectory
|-
|<nowiki>-2.56</nowiki>
|<nowiki>-5.1</nowiki>
|<nowiki>-414.280</nowiki>
|Y
|
|[[File:Chl1718 HHHTable1.png|frameless]]
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-4.1</nowiki>
|<nowiki>-420.077</nowiki>
|N
|
|[[File:Chl1718 HHHTable2.png|frameless]]
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-5.1</nowiki>
|<nowiki>-413.977</nowiki>
|Y
|
|[[File:Chl1718 HHHTable3.png|frameless]]
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.1</nowiki>
|<nowiki>-357.277</nowiki>
|N
|
|[[File:Chl1718 HHHTable4.png|frameless]]
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.6</nowiki>
|<nowiki>-349.477</nowiki>
|Y
|
|[[File:Chl1718 HHHTable5.png|frameless]]
|}

MRD:chl1718 04052020

2020-05-08T11:53:01Z

Chl1718:

= Modelling Molecular Reaction Dynamics =

== H+H2 ==

=== Plots using the lepsgui.py function ===
[[File:Chl1718 HHH1.png|left|thumb|Contour plot]]
[[File:Chl1718 HHH7.png|thumb|Skew plot]]
[[File:Chl1718 HHH2.png|centre|thumb|Surface plot]]
[[File:Chl1718 HHH3.png|left|thumb|Internuclear Distances vs Time]]
[[File:Chl1718 HHH5.png|thumb|Momentum vs Time]]
[[File:Chl1718 HHH4.png|centre|thumb|Internuclear Velocities vs Time]]
[[File:Chl1718 HHH6.png|left|thumb|Energy vs Time]]

=== Transition State ===
The transition state is defined as <math> {dU \over ds} = 0 </math>, <math> {d^2 U \over d\xi^2} </math>

{| class="wikitable"
!p1/ g.mol-1.pm.fs-1
!p2/ g.mol-1.pm.fs-1
!Etot
!Reactive?
!Description of the dynamics
!Illustration of the trajectory
|-
|<nowiki>-2.56</nowiki>
|<nowiki>-5.1</nowiki>
|<nowiki>-414.280</nowiki>
|Y
|
|[[File:Chl1718 HHHTable1.png|frameless]]
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-4.1</nowiki>
|<nowiki>-420.077</nowiki>
|N
|
|[[File:Chl1718 HHHTable2.png|frameless]]
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-5.1</nowiki>
|<nowiki>-413.977</nowiki>
|Y
|
|[[File:Chl1718 HHHTable3.png|frameless]]
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.1</nowiki>
|<nowiki>-357.277</nowiki>
|N
|
|[[File:Chl1718 HHHTable4.png|frameless]]
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.6</nowiki>
|<nowiki>-349.477</nowiki>
|Y
|
|[[File:Chl1718 HHHTable5.png|frameless]]
|}

MRD:chl1718 04052020

2020-05-08T11:48:06Z

Chl1718:

= Modelling Molecular Reaction Dynamics =

== H+H2 ==

=== Plots using the lepsgui.py function ===
[[File:Chl1718 HHH1.png|left|thumb|Contour plot]]
[[File:Chl1718 HHH7.png|thumb|Skew plot]]
[[File:Chl1718 HHH2.png|centre|thumb|Surface plot]]
[[File:Chl1718 HHH3.png|left|thumb|Internuclear Distances vs Time]]
[[File:Chl1718 HHH5.png|thumb|Momentum vs Time]]
[[File:Chl1718 HHH4.png|centre|thumb|Internuclear Velocities vs Time]]
[[File:Chl1718 HHH6.png|left|thumb|Energy vs Time]]

=== Transition State ===
The transition state is defined as <math> {dU \over ds} = 0 </math>

{| class="wikitable"
!p1/ g.mol-1.pm.fs-1
!p2/ g.mol-1.pm.fs-1
!Etot
!Reactive?
!Description of the dynamics
!Illustration of the trajectory
|-
|<nowiki>-2.56</nowiki>
|<nowiki>-5.1</nowiki>
|<nowiki>-414.280</nowiki>
|Y
|
|[[File:Chl1718 HHHTable1.png|frameless]]
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-4.1</nowiki>
|<nowiki>-420.077</nowiki>
|N
|
|[[File:Chl1718 HHHTable2.png|frameless]]
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-5.1</nowiki>
|<nowiki>-413.977</nowiki>
|Y
|
|[[File:Chl1718 HHHTable3.png|frameless]]
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.1</nowiki>
|<nowiki>-357.277</nowiki>
|N
|
|[[File:Chl1718 HHHTable4.png|frameless]]
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.6</nowiki>
|<nowiki>-349.477</nowiki>
|Y
|
|[[File:Chl1718 HHHTable5.png|frameless]]
|}

MRD:chl1718 04052020

2020-05-08T11:46:37Z

Chl1718: /* H+H2 */

= Modelling Molecular Reaction Dynamics =

== H+H2 ==

=== Plots using the lepsgui.py function ===
[[File:Chl1718 HHH1.png|left|thumb|Contour plot]]
[[File:Chl1718 HHH7.png|thumb|Skew plot]]
[[File:Chl1718 HHH2.png|centre|thumb|Surface plot]]
[[File:Chl1718 HHH3.png|left|thumb|Internuclear Distances vs Time]]
[[File:Chl1718 HHH5.png|thumb|Momentum vs Time]]
[[File:Chl1718 HHH4.png|centre|thumb|Internuclear Velocities vs Time]]
[[File:Chl1718 HHH6.png|left|thumb|Energy vs Time]]

=== Transition State ===
The transition state is defined as <nowiki><math> {dp_i \over dt} </math></nowiki>

{| class="wikitable"
!p1/ g.mol-1.pm.fs-1
!p2/ g.mol-1.pm.fs-1
!Etot
!Reactive?
!Description of the dynamics
!Illustration of the trajectory
|-
|<nowiki>-2.56</nowiki>
|<nowiki>-5.1</nowiki>
|<nowiki>-414.280</nowiki>
|Y
|
|[[File:Chl1718 HHHTable1.png|frameless]]
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-4.1</nowiki>
|<nowiki>-420.077</nowiki>
|N
|
|[[File:Chl1718 HHHTable2.png|frameless]]
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-5.1</nowiki>
|<nowiki>-413.977</nowiki>
|Y
|
|[[File:Chl1718 HHHTable3.png|frameless]]
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.1</nowiki>
|<nowiki>-357.277</nowiki>
|N
|
|[[File:Chl1718 HHHTable4.png|frameless]]
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.6</nowiki>
|<nowiki>-349.477</nowiki>
|Y
|
|[[File:Chl1718 HHHTable5.png|frameless]]
|}

File:Chl1718 HHH6.png

2020-05-08T07:59:22Z

Chl1718:

File:Chl1718 HHH5.png

2020-05-08T07:59:08Z

Chl1718:

File:Chl1718 HHH4.png

2020-05-08T07:58:54Z

Chl1718:

File:Chl1718 HHH3.png

2020-05-08T07:58:39Z

Chl1718:

File:Chl1718 HHH7.png

2020-05-08T07:54:57Z

Chl1718:

File:Chl1718 HHH2.png

2020-05-08T07:54:07Z

Chl1718:

File:Chl1718 HHH1.png

2020-05-08T07:44:15Z

Chl1718:

MRD:chl1718 04052020

2020-05-07T14:44:12Z

Chl1718: /* H+H2 */

= Modelling Molecular Reaction Dynamics =

== H+H2 ==
{| class="wikitable"
!p1/ g.mol-1.pm.fs-1
!p2/ g.mol-1.pm.fs-1
!Etot
!Reactive?
!Description of the dynamics
!Illustration of the trajectory
|-
|<nowiki>-2.56</nowiki>
|<nowiki>-5.1</nowiki>
|<nowiki>-414.280</nowiki>
|Y
|
|[[File:Chl1718 HHHTable1.png|frameless]]
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-4.1</nowiki>
|<nowiki>-420.077</nowiki>
|N
|
|[[File:Chl1718 HHHTable2.png|frameless]]
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-5.1</nowiki>
|<nowiki>-413.977</nowiki>
|Y
|
|[[File:Chl1718 HHHTable3.png|frameless]]
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.1</nowiki>
|<nowiki>-357.277</nowiki>
|N
|
|[[File:Chl1718 HHHTable4.png|frameless]]
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.6</nowiki>
|<nowiki>-349.477</nowiki>
|Y
|
|[[File:Chl1718 HHHTable5.png|frameless]]
|}

File:Chl1718 HHHTable5.png

2020-05-07T14:43:06Z

Chl1718:

File:Chl1718 HHHTable4.png

2020-05-07T14:42:47Z

Chl1718:

MRD:chl1718 04052020

2020-05-07T14:30:36Z

Chl1718: /* H+H2 */

= Modelling Molecular Reaction Dynamics =

== H+H2 ==
{| class="wikitable"
!p1/ g.mol-1.pm.fs-1
!p2/ g.mol-1.pm.fs-1
!Etot
!Reactive?
!Description of the dynamics
!Illustration of the trajectory
|-
|<nowiki>-2.56</nowiki>
|<nowiki>-5.1</nowiki>
|<nowiki>-414.280</nowiki>
|Y
|
|[[File:Chl1718 HHHTable1.png|frameless]]
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-4.1</nowiki>
|<nowiki>-420.077</nowiki>
|N
|
|[[File:Chl1718 HHHTable2.png|frameless]]
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-5.1</nowiki>
|<nowiki>-413.977</nowiki>
|Y
|
|[[File:Chl1718 HHHTable3.png|frameless]]
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.1</nowiki>
|<nowiki>-357.277</nowiki>
|N
|
|
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.6</nowiki>
|<nowiki>-349.477</nowiki>
|Y
|
|
|}

MRD:chl1718 04052020

2020-05-07T09:57:28Z

Chl1718: /* H+H2 */

= Modelling Molecular Reaction Dynamics =

== H+H2 ==
{| class="wikitable"
!p1/ g.mol-1.pm.fs-1
!p2/ g.mol-1.pm.fs-1
!Etot
!Reactive?
!Description of the dynamics
!Illustration of the trajectory
|-
|<nowiki>-2.56</nowiki>
|<nowiki>-5.1</nowiki>
|<nowiki>-414.280</nowiki>
|Y
|
|<gallery>
File:Chl1718_HHHTable1.png
</gallery>
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-4.1</nowiki>
|<nowiki>-420.077</nowiki>
|N
|
|<gallery>
File:Chl1718_HHHTable2.png
</gallery>
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-5.1</nowiki>
|<nowiki>-413.977</nowiki>
|Y
|
|<gallery>
File:Chl1718_HHHTable3.png
</gallery>
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.1</nowiki>
|<nowiki>-357.277</nowiki>
|N
|
|
[[File:''Chl1718_HHHTable1.png''<nowiki>]]</nowiki>
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.6</nowiki>
|<nowiki>-349.477</nowiki>
|Y
|
|
|}

MRD:chl1718 04052020

2020-05-07T09:37:38Z

Chl1718: /* H+H2 */

= Modelling Molecular Reaction Dynamics =

== H+H2 ==
{| class="wikitable"
!p1/ g.mol-1.pm.fs-1
!p2/ g.mol-1.pm.fs-1
!Etot
!Reactive?
!Description of the dynamics
!Illustration of the trajectory
|-
|<nowiki>-2.56</nowiki>
|<nowiki>-5.1</nowiki>
|<nowiki>-414.280</nowiki>
|Y
|
|<gallery>
File:Chl1718_HHHTable1.png
</gallery>
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-4.1</nowiki>
|<nowiki>-420.077</nowiki>
|N
|
|<gallery>
File:Chl1718_HHHTable2.png
</gallery>
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-5.1</nowiki>
|<nowiki>-413.977</nowiki>
|Y
|
|<gallery>
File:Chl1718_HHHTable3.png
</gallery>
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.1</nowiki>
|<nowiki>-357.277</nowiki>
|N
|
|
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.6</nowiki>
|<nowiki>-349.477</nowiki>
|Y
|
|
|}

MRD:chl1718 04052020

2020-05-07T09:33:38Z

Chl1718: /* H+H2 */

= Modelling Molecular Reaction Dynamics =

== H+H2 ==
{| class="wikitable"
!p1/ g.mol-1.pm.fs-1
!p2/ g.mol-1.pm.fs-1
!Etot
!Reactive?
!Description of the dynamics
!Illustration of the trajectory
|-
|<nowiki>-2.56</nowiki>
|<nowiki>-5.1</nowiki>
|<nowiki>-414.280</nowiki>
|Y
|
|<gallery>
File:Chl1718_HHH04052020.png
</gallery>
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-4.1</nowiki>
|<nowiki>-420.077</nowiki>
|N
|
|
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-5.1</nowiki>
|<nowiki>-413.977</nowiki>
|Y
|
|
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.1</nowiki>
|<nowiki>-357.277</nowiki>
|N
|
|
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.6</nowiki>
|<nowiki>-349.477</nowiki>
|Y
|
|
|}

File:Chl1718 HHHTable3.png

2020-05-07T09:31:34Z

Chl1718:

File:Chl1718 HHHTable2.png

2020-05-07T09:31:11Z

Chl1718:

File:Chl1718 HHHTable1.png

2020-05-07T09:30:36Z

Chl1718:

MRD:chl1718 04052020

2020-05-07T08:51:01Z

Chl1718: Created page with "= Modelling Molecular Reaction Dynamics = == H+H2 == {| class="wikitable" !p1/ g.mol-1.pm.fs-1 !p2/ g.mol-1</sup..."

= Modelling Molecular Reaction Dynamics =

== H+H2 ==
{| class="wikitable"
!p1/ g.mol-1.pm.fs-1
!p2/ g.mol-1.pm.fs-1
!Etot
!Reactive?
!Description of the dynamics
!Illustration of the trajectory
|-
|<nowiki>-2.56</nowiki>
|<nowiki>-5.1</nowiki>
|<nowiki>-414.280</nowiki>
|Y
|
|
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-4.1</nowiki>
|<nowiki>-420.077</nowiki>
|N
|
|
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-5.1</nowiki>
|<nowiki>-413.977</nowiki>
|Y
|
|
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.1</nowiki>
|<nowiki>-357.277</nowiki>
|N
|
|
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.6</nowiki>
|<nowiki>-349.477</nowiki>
|Y
|
|
|}

Rep:Mod:chl1718

2019-03-08T11:12:29Z

Chl1718: /* Molecular Orbitals */

== NH3 molecule ==
=== Optimization ===

{| class="wikitable"
!Calculation Method
!Basis Set
!Final Energy (au)
!RMS Gradient (au)
!Point Group
|-
|RB3LYP
|6-31G(d,p)
|<nowiki>-56.55776</nowiki>
|<nowiki>0.00000485</nowiki>
|C3V
|}
{| class="wikitable"
!Optimized Parameter
!Value
!Error
|-
|N-H bond distance (Å)
|1.02
|±0.005
|-
|H-N-H bond angle (°)
|106
|±0.5
|}
{| class="wikitable"
!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
|}
[[File:Chl1718 nh3 charge.png|150px||thumb|right|Gaussview image of the charge distribution in NH3]]
{| class="wikitable"
|-
!Atom
!Charge
|-
|N || -1.125
|-
|H || +0.375
|}

N has a negative charge because it is more electronegative than H.

<jmol><jmolApplet>
<title>Optimized molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CHL1718_NH3_OPTUF_POP.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>

[[File:CHL1718_NH3_OPTUF_POP.LOG]]

=== Vibrations ===

{| class="wikitable" border="1"
| || colspan="3" | '''Bending''' || colspan="3" | '''Stretching'''
|-
| '''Symmetry''' || A1 || E || E || A1 || E || E
|-
| '''Wavenumber (cm-1)''' || 1090 || 1694 || 1694 || 3461 || 3590 || 3590
|-
| '''Intensity''' || 145 || 14 || 14 || 1 || 0 || 0
|}

The 3N-6 rule correctly predicts 6 modes of vibration from 4 atoms for NH3. There are two degenerate pairs of vibrations; both have E symmetry and are asymmetric. The A1 stretching mode is highly symmetric; the A1 bending vibration is the umbrella mode due to the resemblance to flipping an umbrella.

Overall, there should be 2 bands in a spectrum.

== N2 molecule ==

=== Optimization ===

{| class="wikitable"
!Calculation Method
!Basis Set
!Final Energy (au)
!RMS Gradient (au)
!Point Group
|-
|RB3LYP
|6-31G(d,p)
|<nowiki>-109.52412</nowiki>
|<nowiki>0.000004</nowiki>
|D∞h
|}
{| class="wikitable"
!Optimized Parameter
!Value
!Error
|-
|N-N bond distance (Å)
|1.11
|±0.005
|}
{| class="wikitable"
!Item
!Value
!Threshold
!Converged?
|-
|Maximum Force || 0.000006 || 0.000450 || YES
|-
|RMS Force || 0.000006 || 0.000300 || YES
|-
|Maximum Displacement || 0.000002 || 0.001800 || YES
|-
|RMS Displacement || 0.000003 || 0.001200 || YES
|}

[[File:Chl1718_n2_charge.png|150px||thumb|right|Gaussview image of the charge distribution in N2]]

{| class="wikitable"
!Atom
!Charge
|-
|N
|0.000
|}

<jmol><jmolApplet>
<title>Optimized molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CHL1718_N2_OPTUF_POP.LOG</uploadedFileContents>
<script>frame 1.12</script>
</jmolApplet></jmol>

[[File:CHL1718_N2_OPTUF_POP.LOG]]

=== Vibrations ===
{| class="wikitable" border="1"
|-
| '''Symmetry''' || SGG
|-
| '''Wavenumber (cm-1)''' || 2457
|-
| '''Intensity''' || 0
|}

[[File:Chl1718_n2_vib_table.PNG]]

There is only one stretching mode for a diatomic molecule. Since there is no dipole, there is no change in dipole moment so intensity is 0.

=== N2 Ligand in a Mono-metallic TM Complex ===

{| class="wikitable"
|-
!Reported N-N length (Å)
!Calculated N-N length (Å)
|-
|1.131 <ref name="complex" /> || 1.11
|}

The refcode is VEJRUA, an iron complex. Comparing the two types of N2, the N-N triple bond is longer when coordinated to the Fe atom because some electron density ends up in an antibonding orbital of N2 and causes the bond to weaken. Furthermore, the calculation of the N2 optimisation might differ from the true value in the first place, as well as not taking into account the effects of ligand coordination.

== H2 molecule ==

=== Optimization ===

{| class="wikitable"
!Calculation Method
!Basis Set
!Final Energy (au)
!RMS Gradient (au)
!Point Group
|-
|RB3LYP
|6-31G(d,p)
|<nowiki>-1.17853</nowiki>
|<nowiki>0.00004</nowiki>
|D∞h
|}
{| class="wikitable"
!Optimized Parameter
!Value
!Error
|-
|H-H bond distance (Å)
|0.74
|±0.005

|}
{| class="wikitable"
!Item
!Value
!Threshold
!Converged?
|-
|Maximum Force || 0.000066 || 0.000450 || YES
|-
|RMS Force || 0.000066 || 0.000300 || YES
|-
|Maximum Displacement || 0.000087 || 0.001800 || YES
|-
|RMS Displacement || 0.000123 || 0.001200 || YES
|}

[[File:Chl1718_h2_charge.png|150px||thumb|right|Gaussview image of the charge distribution in H2]]

{| class="wikitable"
!Atom
!Charge
|-
|H
|0.000
|}

<jmol><jmolApplet>
<title>Optimized molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CHL1718_H2_OPTUF_POP.LOG</uploadedFileContents>
<script>Frame 1.12</script>
</jmolApplet></jmol>

[[File:CHL1718_H2_OPTUF_POP.LOG]]

=== Vibrations ===
{| class="wikitable" border="1"
|-
| '''Symmetry''' || SGG
|-
| '''Wavenumber (cm-1)''' || 4464
|-
| '''Intensity''' || 0
|}

[[File:Chl1718_h2_vibtable.PNG]]

See [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:chl1718#Vibrations_2 N2]

== Haber-Bosch energy calculation ==

{| class="wikitable"
|-
|'''Equation term''' || E(NH3) || 2*E(NH3) || E(N2) || E(H2) || 3*E(H2)
|-
|'''Value (au)''' || -56.55776 || -113.11552 || -109.52412 || -1.17853 || -3.53559
|}

'''ΔE''' = 2*E(NH3) - [E(N2) + 3*E(H2)]

'''ΔE''' = -113.11552 - (-109.52412 - 3.53559)

'''ΔE''' = -0.05581 (au)

'''ΔE''' = -146.5 (kJmol-1)

The product NH3 is more thermodynamically stable because the reaction is exothermic.

== CO2 molecule ==

=== Optimization ===

{| class="wikitable"
!Calculation Method
!Basis Set
!Final Energy (au)
!RMS Gradient (au)
!Point Group
|-
|RB3LYP
|6-31G(d,p)
|<nowiki>-188.58093</nowiki>
|<nowiki>0.00014</nowiki>
|D∞h
|}
{| class="wikitable"
!Optimized Parameter
!Value
!Error
|-
|C=O bond distance (Å)
|1.17
|±0.005
|-
|O=C=O bond angle (°)
|180
|±0.5
|}
{| class="wikitable"
!Item
!Value
!Threshold
!Converged?
|-
|Maximum Force || 0.000315 || 0.000450 || YES
|-
|RMS Force || 0.000157 || 0.000300 || YES
|-
|Maximum Displacement || 0.000192 || 0.001800 || YES
|-
|RMS Displacement || 0.000118 || 0.001200 || YES
|}

[[File:Chl1718_co2_charge.png|150px||thumb|right|Gaussview image of the charge distribution in CO2]]

{| class="wikitable"
!Atom
!Charge
|-
|C || +1.022
|-
|O || -0.511
|}

C has a positive charge because oxygen is more electronegative.

<jmol><jmolApplet>
<title>Optimized molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CHL1718_CO2_OPTUF_POP.LOG</uploadedFileContents>
<script>frame 1.12</script>
</jmolApplet></jmol>

[[File:CHL1718_CO2_OPTUF_POP.LOG]]

=== Vibrations ===
{| class="wikitable" border="1"
|-
| '''Type''' || colspan="2" | Bending || colspan="2" | Stretching
|-
| '''Symmetry''' || PI || PI || SG || SG
|-
| '''Wavenumber (cm-1)''' || 640 || 640 || 1372 || 2437
|-
| '''Intensity''' || 31 || 31 || 0 || 546
|}

[[File:Chl1718_co2_vibtable.PNG]]

The rule for linear molecules is 3N-5, so there are 4 vibrational modes for CO2. The two bending modes are degenerate. The stretching mode with 0 intensity is symmetric. Overall, two bands are expected in a spectrum.

=== Molecular Orbitals ===

==== LUMO (12) ====

[[File:Chl1718_co2_lumo.PNG|200px]]

'''Energy:''' +0.02997 au

The contributing AO's are 2px orbitals from carbon and oxygen. They are out of phase, so this is an unoccupied π*u antibonding orbital.

==== HOMO (11) ====

[[File:Chl1718_co2_homo.PNG|200px]]

'''Energy:''' -0.36997 au

The contributing AO's are 2px orbitals from oxygen. Being occupied lone pairs, they do not participate in bonding.

==== MO 9 ====

[[File:Chl1718_co2_mob_2.PNG|200px]]

'''Energy:''' -0.51279 au

The contributing AO's are 2px orbitals from carbon and oxygen. This is an occupied πu bonding orbital, high in energy but below the HOMO.

==== MO 6 ====

[[File:Chl1718_co2_moa_2.PNG|200px]]

'''Energy:''' -0.56232 au

The contributing AO's are 2s orbitals from carbon and oxygen. This is an occupied σg bonding orbital. The lobes are out of phase so there are 2 nodes. This MO is intermediate in energy.

==== MO 4 ====

[[File:Chl1718_co2_mo_1.PNG|200px]]

'''Energy:''' -1.16101 au

The contributing AO's are 2s orbitals from carbon and oxygen. This is an occupied σg bonding orbital and is low in energy.

== [NH4]+ ==

=== Optimization ===

{| class="wikitable"
!Calculation Method
!Basis Set
!Final Energy (au)
!RMS Gradient (au)
!Point Group
|-
|RB3LYP
|6-31G(d,p)
|<nowiki>-56.90586</nowiki>
|<nowiki>0.00000083</nowiki>
|Td
|}
{| class="wikitable"
!Optimized Parameter
!Value
!Error
|-
|N-H bond distance (Å)
|1.03
|±0.005
|-
|H-N-H bond angle (°)
|109
|±0.5
|}
{| class="wikitable"
!Item
!Value
!Threshold
!Converged?
|-
|Maximum Force
|0.000004
|0.000450
|YES
|-
|RMS Force
|0.000001
|0.000300
|YES
|-
|Maximum Displacement
|0.000003
|0.001800
|YES
|-
|RMS Displacement
|0.000002
|0.001200
|YES
|}
[[File:Chl1718_nh4_charge.png|150px||thumb|right|Gaussview image of the charge distribution in NH4+]]
{| class="wikitable"
|-
!Atom
!Charge
|-
|N || -0.998
|-
|H || +0.500
|}

N has a negative charge because it is more electronegative than H.

<jmol><jmolApplet>
<title>Optimized molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CHL1718_NH4_OPTUF_POP.LOG</uploadedFileContents>
<script>frame 1.14</script>
</jmolApplet></jmol>

[[File:CHL1718_NH4_OPTUF_POP.LOG]]

=== Vibrations ===

{| class="wikitable" border="1"
| || colspan="5" | '''Bending''' || colspan="4" | '''Stretching'''
|-
| '''Symmetry''' || T2 || T2 || T2 || E || E || A1 || T2 || T2 ||T2
|-
| '''Wavenumber (cm-1)''' || 1496 || 1496 || 1496 || 1726 || 1726 || 3370 || 3496 || 3496 || 3496
|-
| '''Intensity''' || 181 || 181 || 181 || 0 || 0 || 0 || 198 || 198 || 198
|}

[[File:Chl1718_nh4_vibtable.PNG]]

The 3N-6 rule correctly predicts 6 modes of vibration from 4 atoms for NH4+. There are 3 degenerate groups of vibrations. The A1 stretch is symmetric, but the E bends also do not produce a change in dipole so those three have 0 intensity.

Overall, there should be 2 bands in a spectrum.

== References ==

<references>
<ref name="complex">Ryuji Imayoshi Kazunari Nakajima Jun Takaya Nobuharu Iwasawa Yoshiaki Nishibayashi (2017) Synthesis and Reactivity of Iron– and Cobalt–Dinitrogen Complexes Bearing PSiP‐Type Pincer Ligands toward Nitrogen Fixation, European Journal of Inorganic Chemistry, 2017, 32, 3769-3778. Available from https://onlinelibrary.wiley.com/doi/full/10.1002/ejic.201700569 </ref>
</references>

Rep:Mod:chl1718

2019-03-08T11:08:04Z

Chl1718: /* Molecular Orbitals */

== NH3 molecule ==
=== Optimization ===

{| class="wikitable"
!Calculation Method
!Basis Set
!Final Energy (au)
!RMS Gradient (au)
!Point Group
|-
|RB3LYP
|6-31G(d,p)
|<nowiki>-56.55776</nowiki>
|<nowiki>0.00000485</nowiki>
|C3V
|}
{| class="wikitable"
!Optimized Parameter
!Value
!Error
|-
|N-H bond distance (Å)
|1.02
|±0.005
|-
|H-N-H bond angle (°)
|106
|±0.5
|}
{| class="wikitable"
!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
|}
[[File:Chl1718 nh3 charge.png|150px||thumb|right|Gaussview image of the charge distribution in NH3]]
{| class="wikitable"
|-
!Atom
!Charge
|-
|N || -1.125
|-
|H || +0.375
|}

N has a negative charge because it is more electronegative than H.

<jmol><jmolApplet>
<title>Optimized molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CHL1718_NH3_OPTUF_POP.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>

[[File:CHL1718_NH3_OPTUF_POP.LOG]]

=== Vibrations ===

{| class="wikitable" border="1"
| || colspan="3" | '''Bending''' || colspan="3" | '''Stretching'''
|-
| '''Symmetry''' || A1 || E || E || A1 || E || E
|-
| '''Wavenumber (cm-1)''' || 1090 || 1694 || 1694 || 3461 || 3590 || 3590
|-
| '''Intensity''' || 145 || 14 || 14 || 1 || 0 || 0
|}

The 3N-6 rule correctly predicts 6 modes of vibration from 4 atoms for NH3. There are two degenerate pairs of vibrations; both have E symmetry and are asymmetric. The A1 stretching mode is highly symmetric; the A1 bending vibration is the umbrella mode due to the resemblance to flipping an umbrella.

Overall, there should be 2 bands in a spectrum.

== N2 molecule ==

=== Optimization ===

{| class="wikitable"
!Calculation Method
!Basis Set
!Final Energy (au)
!RMS Gradient (au)
!Point Group
|-
|RB3LYP
|6-31G(d,p)
|<nowiki>-109.52412</nowiki>
|<nowiki>0.000004</nowiki>
|D∞h
|}
{| class="wikitable"
!Optimized Parameter
!Value
!Error
|-
|N-N bond distance (Å)
|1.11
|±0.005
|}
{| class="wikitable"
!Item
!Value
!Threshold
!Converged?
|-
|Maximum Force || 0.000006 || 0.000450 || YES
|-
|RMS Force || 0.000006 || 0.000300 || YES
|-
|Maximum Displacement || 0.000002 || 0.001800 || YES
|-
|RMS Displacement || 0.000003 || 0.001200 || YES
|}

[[File:Chl1718_n2_charge.png|150px||thumb|right|Gaussview image of the charge distribution in N2]]

{| class="wikitable"
!Atom
!Charge
|-
|N
|0.000
|}

<jmol><jmolApplet>
<title>Optimized molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CHL1718_N2_OPTUF_POP.LOG</uploadedFileContents>
<script>frame 1.12</script>
</jmolApplet></jmol>

[[File:CHL1718_N2_OPTUF_POP.LOG]]

=== Vibrations ===
{| class="wikitable" border="1"
|-
| '''Symmetry''' || SGG
|-
| '''Wavenumber (cm-1)''' || 2457
|-
| '''Intensity''' || 0
|}

[[File:Chl1718_n2_vib_table.PNG]]

There is only one stretching mode for a diatomic molecule. Since there is no dipole, there is no change in dipole moment so intensity is 0.

=== N2 Ligand in a Mono-metallic TM Complex ===

{| class="wikitable"
|-
!Reported N-N length (Å)
!Calculated N-N length (Å)
|-
|1.131 <ref name="complex" /> || 1.11
|}

The refcode is VEJRUA, an iron complex. Comparing the two types of N2, the N-N triple bond is longer when coordinated to the Fe atom because some electron density ends up in an antibonding orbital of N2 and causes the bond to weaken. Furthermore, the calculation of the N2 optimisation might differ from the true value in the first place, as well as not taking into account the effects of ligand coordination.

== H2 molecule ==

=== Optimization ===

{| class="wikitable"
!Calculation Method
!Basis Set
!Final Energy (au)
!RMS Gradient (au)
!Point Group
|-
|RB3LYP
|6-31G(d,p)
|<nowiki>-1.17853</nowiki>
|<nowiki>0.00004</nowiki>
|D∞h
|}
{| class="wikitable"
!Optimized Parameter
!Value
!Error
|-
|H-H bond distance (Å)
|0.74
|±0.005

|}
{| class="wikitable"
!Item
!Value
!Threshold
!Converged?
|-
|Maximum Force || 0.000066 || 0.000450 || YES
|-
|RMS Force || 0.000066 || 0.000300 || YES
|-
|Maximum Displacement || 0.000087 || 0.001800 || YES
|-
|RMS Displacement || 0.000123 || 0.001200 || YES
|}

[[File:Chl1718_h2_charge.png|150px||thumb|right|Gaussview image of the charge distribution in H2]]

{| class="wikitable"
!Atom
!Charge
|-
|H
|0.000
|}

<jmol><jmolApplet>
<title>Optimized molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CHL1718_H2_OPTUF_POP.LOG</uploadedFileContents>
<script>Frame 1.12</script>
</jmolApplet></jmol>

[[File:CHL1718_H2_OPTUF_POP.LOG]]

=== Vibrations ===
{| class="wikitable" border="1"
|-
| '''Symmetry''' || SGG
|-
| '''Wavenumber (cm-1)''' || 4464
|-
| '''Intensity''' || 0
|}

[[File:Chl1718_h2_vibtable.PNG]]

See [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:chl1718#Vibrations_2 N2]

== Haber-Bosch energy calculation ==

{| class="wikitable"
|-
|'''Equation term''' || E(NH3) || 2*E(NH3) || E(N2) || E(H2) || 3*E(H2)
|-
|'''Value (au)''' || -56.55776 || -113.11552 || -109.52412 || -1.17853 || -3.53559
|}

'''ΔE''' = 2*E(NH3) - [E(N2) + 3*E(H2)]

'''ΔE''' = -113.11552 - (-109.52412 - 3.53559)

'''ΔE''' = -0.05581 (au)

'''ΔE''' = -146.5 (kJmol-1)

The product NH3 is more thermodynamically stable because the reaction is exothermic.

== CO2 molecule ==

=== Optimization ===

{| class="wikitable"
!Calculation Method
!Basis Set
!Final Energy (au)
!RMS Gradient (au)
!Point Group
|-
|RB3LYP
|6-31G(d,p)
|<nowiki>-188.58093</nowiki>
|<nowiki>0.00014</nowiki>
|D∞h
|}
{| class="wikitable"
!Optimized Parameter
!Value
!Error
|-
|C=O bond distance (Å)
|1.17
|±0.005
|-
|O=C=O bond angle (°)
|180
|±0.5
|}
{| class="wikitable"
!Item
!Value
!Threshold
!Converged?
|-
|Maximum Force || 0.000315 || 0.000450 || YES
|-
|RMS Force || 0.000157 || 0.000300 || YES
|-
|Maximum Displacement || 0.000192 || 0.001800 || YES
|-
|RMS Displacement || 0.000118 || 0.001200 || YES
|}

[[File:Chl1718_co2_charge.png|150px||thumb|right|Gaussview image of the charge distribution in CO2]]

{| class="wikitable"
!Atom
!Charge
|-
|C || +1.022
|-
|O || -0.511
|}

C has a positive charge because oxygen is more electronegative.

<jmol><jmolApplet>
<title>Optimized molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CHL1718_CO2_OPTUF_POP.LOG</uploadedFileContents>
<script>frame 1.12</script>
</jmolApplet></jmol>

[[File:CHL1718_CO2_OPTUF_POP.LOG]]

=== Vibrations ===
{| class="wikitable" border="1"
|-
| '''Type''' || colspan="2" | Bending || colspan="2" | Stretching
|-
| '''Symmetry''' || PI || PI || SG || SG
|-
| '''Wavenumber (cm-1)''' || 640 || 640 || 1372 || 2437
|-
| '''Intensity''' || 31 || 31 || 0 || 546
|}

[[File:Chl1718_co2_vibtable.PNG]]

The rule for linear molecules is 3N-5, so there are 4 vibrational modes for CO2. The two bending modes are degenerate. The stretching mode with 0 intensity is symmetric. Overall, two bands are expected in a spectrum.

=== Molecular Orbitals ===

==== LUMO (12) ====

[[File:Chl1718_co2_lumo.PNG|200px]]

'''Energy:''' +0.02997 au

The contributing AO's are 2py orbitals from carbon and oxygen. They are out of phase, so this is an unoccupied π*u antibonding orbital.

==== HOMO (11) ====

[[File:Chl1718_co2_homo.PNG|200px]]

'''Energy:''' -0.36997 au

The contributing AO's are 2px orbitals from oxygen. Being occupied lone pairs, they do not participate in bonding.

==== MO 9 ====

[[File:Chl1718_co2_mob_2.PNG|200px]]

'''Energy:''' -0.51279 au

The contributing AO's are 2px orbitals from carbon and oxygen. This is an occupied πu bonding orbital.

==== MO 6 ====

[[File:Chl1718_co2_moa_2.PNG|200px]]

'''Energy:''' -0.56232 au

The contributing AO's are 2s orbitals from carbon and oxygen. This is an occupied σg bonding orbital. The lobes are out of phase so there are 2 nodes.

==== MO 4 ====

[[File:Chl1718_co2_mo_1.PNG|200px]]

'''Energy:''' -1.16101 au

The contributing AO's are 2s orbitals from carbon and oxygen. This is an occupied σg bonding orbital.

== [NH4]+ ==

=== Optimization ===

{| class="wikitable"
!Calculation Method
!Basis Set
!Final Energy (au)
!RMS Gradient (au)
!Point Group
|-
|RB3LYP
|6-31G(d,p)
|<nowiki>-56.90586</nowiki>
|<nowiki>0.00000083</nowiki>
|Td
|}
{| class="wikitable"
!Optimized Parameter
!Value
!Error
|-
|N-H bond distance (Å)
|1.03
|±0.005
|-
|H-N-H bond angle (°)
|109
|±0.5
|}
{| class="wikitable"
!Item
!Value
!Threshold
!Converged?
|-
|Maximum Force
|0.000004
|0.000450
|YES
|-
|RMS Force
|0.000001
|0.000300
|YES
|-
|Maximum Displacement
|0.000003
|0.001800
|YES
|-
|RMS Displacement
|0.000002
|0.001200
|YES
|}
[[File:Chl1718_nh4_charge.png|150px||thumb|right|Gaussview image of the charge distribution in NH4+]]
{| class="wikitable"
|-
!Atom
!Charge
|-
|N || -0.998
|-
|H || +0.500
|}

N has a negative charge because it is more electronegative than H.

<jmol><jmolApplet>
<title>Optimized molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CHL1718_NH4_OPTUF_POP.LOG</uploadedFileContents>
<script>frame 1.14</script>
</jmolApplet></jmol>

[[File:CHL1718_NH4_OPTUF_POP.LOG]]

=== Vibrations ===

{| class="wikitable" border="1"
| || colspan="5" | '''Bending''' || colspan="4" | '''Stretching'''
|-
| '''Symmetry''' || T2 || T2 || T2 || E || E || A1 || T2 || T2 ||T2
|-
| '''Wavenumber (cm-1)''' || 1496 || 1496 || 1496 || 1726 || 1726 || 3370 || 3496 || 3496 || 3496
|-
| '''Intensity''' || 181 || 181 || 181 || 0 || 0 || 0 || 198 || 198 || 198
|}

[[File:Chl1718_nh4_vibtable.PNG]]

The 3N-6 rule correctly predicts 6 modes of vibration from 4 atoms for NH4+. There are 3 degenerate groups of vibrations. The A1 stretch is symmetric, but the E bends also do not produce a change in dipole so those three have 0 intensity.

Overall, there should be 2 bands in a spectrum.

== References ==

<references>
<ref name="complex">Ryuji Imayoshi Kazunari Nakajima Jun Takaya Nobuharu Iwasawa Yoshiaki Nishibayashi (2017) Synthesis and Reactivity of Iron– and Cobalt–Dinitrogen Complexes Bearing PSiP‐Type Pincer Ligands toward Nitrogen Fixation, European Journal of Inorganic Chemistry, 2017, 32, 3769-3778. Available from https://onlinelibrary.wiley.com/doi/full/10.1002/ejic.201700569 </ref>
</references>

Rep:Mod:chl1718

2019-03-08T11:07:40Z

Chl1718: /* Molecular Orbitals */

== NH3 molecule ==
=== Optimization ===

{| class="wikitable"
!Calculation Method
!Basis Set
!Final Energy (au)
!RMS Gradient (au)
!Point Group
|-
|RB3LYP
|6-31G(d,p)
|<nowiki>-56.55776</nowiki>
|<nowiki>0.00000485</nowiki>
|C3V
|}
{| class="wikitable"
!Optimized Parameter
!Value
!Error
|-
|N-H bond distance (Å)
|1.02
|±0.005
|-
|H-N-H bond angle (°)
|106
|±0.5
|}
{| class="wikitable"
!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
|}
[[File:Chl1718 nh3 charge.png|150px||thumb|right|Gaussview image of the charge distribution in NH3]]
{| class="wikitable"
|-
!Atom
!Charge
|-
|N || -1.125
|-
|H || +0.375
|}

N has a negative charge because it is more electronegative than H.

<jmol><jmolApplet>
<title>Optimized molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CHL1718_NH3_OPTUF_POP.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>

[[File:CHL1718_NH3_OPTUF_POP.LOG]]

=== Vibrations ===

{| class="wikitable" border="1"
| || colspan="3" | '''Bending''' || colspan="3" | '''Stretching'''
|-
| '''Symmetry''' || A1 || E || E || A1 || E || E
|-
| '''Wavenumber (cm-1)''' || 1090 || 1694 || 1694 || 3461 || 3590 || 3590
|-
| '''Intensity''' || 145 || 14 || 14 || 1 || 0 || 0
|}

The 3N-6 rule correctly predicts 6 modes of vibration from 4 atoms for NH3. There are two degenerate pairs of vibrations; both have E symmetry and are asymmetric. The A1 stretching mode is highly symmetric; the A1 bending vibration is the umbrella mode due to the resemblance to flipping an umbrella.

Overall, there should be 2 bands in a spectrum.

== N2 molecule ==

=== Optimization ===

{| class="wikitable"
!Calculation Method
!Basis Set
!Final Energy (au)
!RMS Gradient (au)
!Point Group
|-
|RB3LYP
|6-31G(d,p)
|<nowiki>-109.52412</nowiki>
|<nowiki>0.000004</nowiki>
|D∞h
|}
{| class="wikitable"
!Optimized Parameter
!Value
!Error
|-
|N-N bond distance (Å)
|1.11
|±0.005
|}
{| class="wikitable"
!Item
!Value
!Threshold
!Converged?
|-
|Maximum Force || 0.000006 || 0.000450 || YES
|-
|RMS Force || 0.000006 || 0.000300 || YES
|-
|Maximum Displacement || 0.000002 || 0.001800 || YES
|-
|RMS Displacement || 0.000003 || 0.001200 || YES
|}

[[File:Chl1718_n2_charge.png|150px||thumb|right|Gaussview image of the charge distribution in N2]]

{| class="wikitable"
!Atom
!Charge
|-
|N
|0.000
|}

<jmol><jmolApplet>
<title>Optimized molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CHL1718_N2_OPTUF_POP.LOG</uploadedFileContents>
<script>frame 1.12</script>
</jmolApplet></jmol>

[[File:CHL1718_N2_OPTUF_POP.LOG]]

=== Vibrations ===
{| class="wikitable" border="1"
|-
| '''Symmetry''' || SGG
|-
| '''Wavenumber (cm-1)''' || 2457
|-
| '''Intensity''' || 0
|}

[[File:Chl1718_n2_vib_table.PNG]]

There is only one stretching mode for a diatomic molecule. Since there is no dipole, there is no change in dipole moment so intensity is 0.

=== N2 Ligand in a Mono-metallic TM Complex ===

{| class="wikitable"
|-
!Reported N-N length (Å)
!Calculated N-N length (Å)
|-
|1.131 <ref name="complex" /> || 1.11
|}

The refcode is VEJRUA, an iron complex. Comparing the two types of N2, the N-N triple bond is longer when coordinated to the Fe atom because some electron density ends up in an antibonding orbital of N2 and causes the bond to weaken. Furthermore, the calculation of the N2 optimisation might differ from the true value in the first place, as well as not taking into account the effects of ligand coordination.

== H2 molecule ==

=== Optimization ===

{| class="wikitable"
!Calculation Method
!Basis Set
!Final Energy (au)
!RMS Gradient (au)
!Point Group
|-
|RB3LYP
|6-31G(d,p)
|<nowiki>-1.17853</nowiki>
|<nowiki>0.00004</nowiki>
|D∞h
|}
{| class="wikitable"
!Optimized Parameter
!Value
!Error
|-
|H-H bond distance (Å)
|0.74
|±0.005

|}
{| class="wikitable"
!Item
!Value
!Threshold
!Converged?
|-
|Maximum Force || 0.000066 || 0.000450 || YES
|-
|RMS Force || 0.000066 || 0.000300 || YES
|-
|Maximum Displacement || 0.000087 || 0.001800 || YES
|-
|RMS Displacement || 0.000123 || 0.001200 || YES
|}

[[File:Chl1718_h2_charge.png|150px||thumb|right|Gaussview image of the charge distribution in H2]]

{| class="wikitable"
!Atom
!Charge
|-
|H
|0.000
|}

<jmol><jmolApplet>
<title>Optimized molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CHL1718_H2_OPTUF_POP.LOG</uploadedFileContents>
<script>Frame 1.12</script>
</jmolApplet></jmol>

[[File:CHL1718_H2_OPTUF_POP.LOG]]

=== Vibrations ===
{| class="wikitable" border="1"
|-
| '''Symmetry''' || SGG
|-
| '''Wavenumber (cm-1)''' || 4464
|-
| '''Intensity''' || 0
|}

[[File:Chl1718_h2_vibtable.PNG]]

See [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:chl1718#Vibrations_2 N2]

== Haber-Bosch energy calculation ==

{| class="wikitable"
|-
|'''Equation term''' || E(NH3) || 2*E(NH3) || E(N2) || E(H2) || 3*E(H2)
|-
|'''Value (au)''' || -56.55776 || -113.11552 || -109.52412 || -1.17853 || -3.53559
|}

'''ΔE''' = 2*E(NH3) - [E(N2) + 3*E(H2)]

'''ΔE''' = -113.11552 - (-109.52412 - 3.53559)

'''ΔE''' = -0.05581 (au)

'''ΔE''' = -146.5 (kJmol-1)

The product NH3 is more thermodynamically stable because the reaction is exothermic.

== CO2 molecule ==

=== Optimization ===

{| class="wikitable"
!Calculation Method
!Basis Set
!Final Energy (au)
!RMS Gradient (au)
!Point Group
|-
|RB3LYP
|6-31G(d,p)
|<nowiki>-188.58093</nowiki>
|<nowiki>0.00014</nowiki>
|D∞h
|}
{| class="wikitable"
!Optimized Parameter
!Value
!Error
|-
|C=O bond distance (Å)
|1.17
|±0.005
|-
|O=C=O bond angle (°)
|180
|±0.5
|}
{| class="wikitable"
!Item
!Value
!Threshold
!Converged?
|-
|Maximum Force || 0.000315 || 0.000450 || YES
|-
|RMS Force || 0.000157 || 0.000300 || YES
|-
|Maximum Displacement || 0.000192 || 0.001800 || YES
|-
|RMS Displacement || 0.000118 || 0.001200 || YES
|}

[[File:Chl1718_co2_charge.png|150px||thumb|right|Gaussview image of the charge distribution in CO2]]

{| class="wikitable"
!Atom
!Charge
|-
|C || +1.022
|-
|O || -0.511
|}

C has a positive charge because oxygen is more electronegative.

<jmol><jmolApplet>
<title>Optimized molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CHL1718_CO2_OPTUF_POP.LOG</uploadedFileContents>
<script>frame 1.12</script>
</jmolApplet></jmol>

[[File:CHL1718_CO2_OPTUF_POP.LOG]]

=== Vibrations ===
{| class="wikitable" border="1"
|-
| '''Type''' || colspan="2" | Bending || colspan="2" | Stretching
|-
| '''Symmetry''' || PI || PI || SG || SG
|-
| '''Wavenumber (cm-1)''' || 640 || 640 || 1372 || 2437
|-
| '''Intensity''' || 31 || 31 || 0 || 546
|}

[[File:Chl1718_co2_vibtable.PNG]]

The rule for linear molecules is 3N-5, so there are 4 vibrational modes for CO2. The two bending modes are degenerate. The stretching mode with 0 intensity is symmetric. Overall, two bands are expected in a spectrum.

=== Molecular Orbitals ===

==== LUMO (12) ====

[[File:Chl1718_co2_lumo.PNG|250px]]

'''Energy:''' +0.02997 au

The contributing AO's are 2py orbitals from carbon and oxygen. They are out of phase, so this is an unoccupied π*u antibonding orbital.

==== HOMO (11) ====

[[File:Chl1718_co2_homo.PNG|250px]]

'''Energy:''' -0.36997 au

The contributing AO's are 2px orbitals from oxygen. Being occupied lone pairs, they do not participate in bonding.

==== MO 9 ====

[[File:Chl1718_co2_mob_2.PNG|250px]]

'''Energy:''' -0.51279 au

The contributing AO's are 2px orbitals from carbon and oxygen. This is an occupied πu bonding orbital.

==== MO 6 ====

[[File:Chl1718_co2_moa_2.PNG|250px]]

'''Energy:''' -0.56232 au

The contributing AO's are 2s orbitals from carbon and oxygen. This is an occupied σg bonding orbital. The lobes are out of phase so there are 2 nodes.

==== MO 4 ====

[[File:Chl1718_co2_mo_1.PNG|250px]]

'''Energy:''' -1.16101 au

The contributing AO's are 2s orbitals from carbon and oxygen. This is an occupied σg bonding orbital.

== [NH4]+ ==

=== Optimization ===

{| class="wikitable"
!Calculation Method
!Basis Set
!Final Energy (au)
!RMS Gradient (au)
!Point Group
|-
|RB3LYP
|6-31G(d,p)
|<nowiki>-56.90586</nowiki>
|<nowiki>0.00000083</nowiki>
|Td
|}
{| class="wikitable"
!Optimized Parameter
!Value
!Error
|-
|N-H bond distance (Å)
|1.03
|±0.005
|-
|H-N-H bond angle (°)
|109
|±0.5
|}
{| class="wikitable"
!Item
!Value
!Threshold
!Converged?
|-
|Maximum Force
|0.000004
|0.000450
|YES
|-
|RMS Force
|0.000001
|0.000300
|YES
|-
|Maximum Displacement
|0.000003
|0.001800
|YES
|-
|RMS Displacement
|0.000002
|0.001200
|YES
|}
[[File:Chl1718_nh4_charge.png|150px||thumb|right|Gaussview image of the charge distribution in NH4+]]
{| class="wikitable"
|-
!Atom
!Charge
|-
|N || -0.998
|-
|H || +0.500
|}

N has a negative charge because it is more electronegative than H.

<jmol><jmolApplet>
<title>Optimized molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CHL1718_NH4_OPTUF_POP.LOG</uploadedFileContents>
<script>frame 1.14</script>
</jmolApplet></jmol>

[[File:CHL1718_NH4_OPTUF_POP.LOG]]

=== Vibrations ===

{| class="wikitable" border="1"
| || colspan="5" | '''Bending''' || colspan="4" | '''Stretching'''
|-
| '''Symmetry''' || T2 || T2 || T2 || E || E || A1 || T2 || T2 ||T2
|-
| '''Wavenumber (cm-1)''' || 1496 || 1496 || 1496 || 1726 || 1726 || 3370 || 3496 || 3496 || 3496
|-
| '''Intensity''' || 181 || 181 || 181 || 0 || 0 || 0 || 198 || 198 || 198
|}

[[File:Chl1718_nh4_vibtable.PNG]]

The 3N-6 rule correctly predicts 6 modes of vibration from 4 atoms for NH4+. There are 3 degenerate groups of vibrations. The A1 stretch is symmetric, but the E bends also do not produce a change in dipole so those three have 0 intensity.

Overall, there should be 2 bands in a spectrum.

== References ==

<references>
<ref name="complex">Ryuji Imayoshi Kazunari Nakajima Jun Takaya Nobuharu Iwasawa Yoshiaki Nishibayashi (2017) Synthesis and Reactivity of Iron– and Cobalt–Dinitrogen Complexes Bearing PSiP‐Type Pincer Ligands toward Nitrogen Fixation, European Journal of Inorganic Chemistry, 2017, 32, 3769-3778. Available from https://onlinelibrary.wiley.com/doi/full/10.1002/ejic.201700569 </ref>
</references>