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MRD:MT4618

2020-05-15T22:54:14Z

Mt4618: /* Transition State */

== Molecular Reaction Dynamics Lab 2020 ==

=== Exercise 1- (H+H2 System). ===

==== Transition State ====
The transition state is defined as the maximum on the minimum energy path linking reactants and the products. This point on the potential energy surface has the special property that ∂V('''ri''')/∂'''ri'''=0 (the gradient of the potential is zero), and the energy goes down steeply along the minimum energy path linking reactants and products.

Mathematically, the transition state can be described as the derivative with respect to the reaction coordinate that is equal to zero and the maximum can be distinguished from local minima by taking the second derivative wrt the reaction coordinate that is negative.
==== Trajectories from r1 = r2: locating the transition state ====
In the following exercise, A is taken to be the approaching H while B and C are the H atoms in H2.

''Table 1- Initial conditions used to test H+ H2 system''
{| class="wikitable"
!
!Distance (r) [pm]
!Momentum (p) [g.mol-1.pm.fs-1]
|-
|AB
|230
|<nowiki>-5.2</nowiki>
|-
|BC
|74
|0
|}
[[File:MTK plot1.png|thumb|Fig 1- Internuclear Distance Vs Time for H+H2 system]]
By using the values in Table 1, a plot of intermolecuar distance vs time was generated. As H+H2 is a symmetrical system, the transition state can be assumed to have equal H-H-H bond lengths, which is represented by the intersection of AB and BC on the plot (Fig.1). By setting rAB=rBC and initial momenta to be zero, the transition state was located at rAB=rBC=91pm.
{| class="wikitable"
|[[File:MTK Internuclear Distance vs time for H3 transition state.PNG|thumb|Fig 2- Internuclear Distance vs time for H3 transition state]]
|[[File:MTK H3 transition state.PNG|thumb|Fig 3- H+H2 Transition State on a contour plot]]
|}

==== Trajectories from r1 = rts+δ, r2 = rts ====
The 'mep' differs from the reaction trajectory of a dynamics calculation. This is because MEP always resets momentum of the reactants to zero after each step in order to simulate an infinitely slow motion. By contrast, the dynamics calculation takes into account the vibronic motion of the system hence, oscillations can be observed on its corresponding contour plot.
{| class="wikitable"
|[[File:MTK H3 MEP.PNG|thumb|Fig 4 -MEP (minimum energy path) contour plot]]
|[[File:MTK Dynamics for reaction path.PNG|thumb|Fig 5- Dynamics calculation of reaction path on a contour plot]]
|}

==== Reactive and Unreactive Trajectories ====
''Table 2- Comparing trajectories of systems with initial position of rAB=200 pm and rBC=74 pm and varying values of p1 and p2''
{| 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>
|Yes
|System passes through transition state and reaches completion. Product bond formation is apparent from the gentle oscillations in the
product channel.
|[[File:MTK plot2.png|thumb]]
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-4.1</nowiki>
|<nowiki>-420.077</nowiki>
|No
|Alot of intramolecular vibrations observed in initial stages.
System does not pass the transition state and returns to reactants.
|[[File:MTK Table2.PNG|thumb]]
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-5.1</nowiki>
|<nowiki>-413.977</nowiki>
|Yes
|An increase in momentum of the incoming H atom,

compared to the previous example, results in surmounting of the transition state maxima by system. More oscillations observable in product channel than reactant channel.
|[[File:MTK Table3.PNG|thumb]]
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.1</nowiki>
|<nowiki>-357.277</nowiki>
|No
|Transition State Theory observed to fail as although system possesses enough energy to overcome transition state, it does not lead to completion and, instead, returns to reactants with a significantly higher vibronic energy.
|[[File:MTK Table4.PNG|thumb]]
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.6</nowiki>
|<nowiki>-349.477</nowiki>
|Yes
|A slight increase in momentum of the incoming H atom, compared to

the preceding example, results in a reactive trajectory. Notably, the system does not pass the transition state at all and fluctuates twice between reactant and product bond formation. This suggests product formation occurs via a transition state far from the lowest energy saddle point, which is a deviation from transition state theory.
|[[File:MTK Table5.PNG|thumb]]
|}
From Table 2, it can be concluded that the total energy of the system does not necessarily determine whether the reaction will proceed. It can also be concluded that high energy systems are prone to return to reactant channels even if they possess enough energy to overcome the transition state maximum. This ilustrates the limitations of transition state theory, which include: not accounting for effects of high temperature and not accounting for the effects of quantum tunnelling.<ref><nowiki>http://www.liquisearch.com/transition_state_theory/limitations_of_transition_state_theory (accessed: May 15, 2020)</nowiki></ref>

==== Transition State Theory ====
Transition state theory overestimates the rate of reaction. It assumes every trajectory that rolls over the transition state will proceed to the product which is not the case as evident from Table 2.

=== Exercise 2. (F-H-H System) ===

==== PES Inspection ====
In the following exercise, '''A''' is taken to be the '''approaching atom''' while '''B''' and '''C''' represent the '''initial diatomic molecule'''.

''Table 1- Initial conditions used to test F+ H2 system''
{| class="wikitable"
![[File:MTK F+H2TS.PNG|thumb|Fig 6 - Early "reactant-like" transition state of F+H2 system.]]
![[File:MTK Surface Plot fhh.png|thumb|Fig 7- Surface Plot with transition state of F+ H2 system]]
|}

F+H2 is exothermic as it has an early energy barrier. According to Hammond's Postulate, the structure of the transition state is similar to reactants if the reaction is exothermic. The transition state for this reaction was found at rFH=181pm and rHH=74.5pm. The activation energy was calculated to be 686Jmol-1.
{| class="wikitable"
![[File:MTK H+FH TS.PNG|thumb|Fig 8 - Late "product-like" transition state of H+HF system.]]
![[File:MTK Surface Plot 1.png|thumb|Fig 9- Surface plot with transition state of H+HF system.]]
|}

H+HF is endothermic as it has a late energy barrier. According to Hammond's Postulate, the structure of the transition state is similar to products if the reaction is endothermic. The transition state for this reaction was found at rHH=74.5pm and rFH=181pm. The activation energy was calculated to be 126.317kJmol-1.

==== Reaction Dynamics ====
''Table 3- Conditions observed to lead to a reactive trajectory for F+H2''
{| class="wikitable"
!
!Distance/pm
!Momentum/ gmol-1.pm.fs-1
|-
|FH
|1043.074
|<nowiki>-6.944</nowiki>
|-
|HH
|74.216
|<nowiki>-0.254</nowiki>
|}
{| class="wikitable"
|[[File:MTK F+H2 CONTOUR MTK.PNG|thumb|Fig 10- F+H2 contour plot]]
|[[File:MTK F+H2 MOMENTAVSTIME.PNG|thumb|Fig 11- F+H2 Momenta Vs Time Plot]]
|}
From the momenta vs time plot, we can observe that initially the reactants possess a large amount of translational energy and upon reaching the transition state, the energy is converted to vibrational energy. The release of energy from the reaction, which is a combination of energy of translational and vibronic energy changes, can be measured experimentally by using calorimetry and infrared spectroscopy. Calorimetry can be used to measure the heat generated by the reaction thus enabling the calculation of total energy given off by the system. Peaks and their wavenumbers in infrared spectrum can be used to identify the changes in vibrational energy of the IR active H-F molecule.

''Table 4- Conditions observed to lead to a reactive trajectory for H+HF''
{| class="wikitable"
!
!Distance/pm
!Momentum/ gmol-1.pm.fs-1
|-
|HH
|868.223
|<nowiki>-3.959</nowiki>
|-
|FH
|117.918
|3.751
|}
{| class="wikitable"
|[[File:MTK H+FH CONTOUR.PNG|thumb|Fig 12- H+FH Contour Plot]]
|[[File:MTK H+FH MOMENTA.PNG|thumb|Fig 13- H+FH Momenta vs Time Plot]]
|}

==== Translation Vs Vibrational Energy ====
[[File:MTK Last Q.PNG|thumb|Fig 14- Graphs A,B,C and D to illustrate Polanyi's Rules ]]
Graph A and B depict an exothermic reaction with an early transition state. It is observed that translational energy is crucial in helping the system surmount the early energy barrier as, when compared between the two graphs, the initial conditions for A possess far more translational energy than vibrational energy, allowing reaction A to reach completion but not B.

Graph C and D depict an endothermic reaction with a late transition state. It is observed that vibrational energy is crucial in helping the system overcome the late energy barrier as, when compared between the two graphs, the initial conditions for C possess more vibrational energy than translational energy, allowing reaction C to reach completion but not D.<ref>Polanyi, J. C. Some Concepts in Reaction Dyanmics. ''Science. ''[Online] 1987 <nowiki>https://science.sciencemag.org/content/236/4802/680/tab-pdf</nowiki> (accessed: May 15, 2020)</ref>

=== References ===
<references />

MRD:MT4618

2020-05-15T22:53:56Z

Mt4618: /* Exercise 2. (F-H-H System) */

== Molecular Reaction Dynamics Lab 2020 ==

=== Exercise 1- (H+H2 System). ===

==== Transition State ====
The transition state is defined as the maximum on the minimum energy path linking reactants and the products. This point on the potential energy surface has the special property that ∂V('''ri''')/∂'''ri'''=0 (the gradient of the potential is zero), and the energy goes down steeply along the minimum energy path linking reactants and products.

Mathematically, the transition state can be described as the derivative with respect to the reaction coordinate that is equal to zero and the maximum can be distinguished from local minima by taking the second derivative wrt the reaction coordinate that is negative.

Hammond's postulate: The structure of the transition state will resemble the reactants or products depending on which are closer in energy. exothermic resembles reactant, endothermic products.
==== Trajectories from r1 = r2: locating the transition state ====
In the following exercise, A is taken to be the approaching H while B and C are the H atoms in H2.

''Table 1- Initial conditions used to test H+ H2 system''
{| class="wikitable"
!
!Distance (r) [pm]
!Momentum (p) [g.mol-1.pm.fs-1]
|-
|AB
|230
|<nowiki>-5.2</nowiki>
|-
|BC
|74
|0
|}
[[File:MTK plot1.png|thumb|Fig 1- Internuclear Distance Vs Time for H+H2 system]]
By using the values in Table 1, a plot of intermolecuar distance vs time was generated. As H+H2 is a symmetrical system, the transition state can be assumed to have equal H-H-H bond lengths, which is represented by the intersection of AB and BC on the plot (Fig.1). By setting rAB=rBC and initial momenta to be zero, the transition state was located at rAB=rBC=91pm.
{| class="wikitable"
|[[File:MTK Internuclear Distance vs time for H3 transition state.PNG|thumb|Fig 2- Internuclear Distance vs time for H3 transition state]]
|[[File:MTK H3 transition state.PNG|thumb|Fig 3- H+H2 Transition State on a contour plot]]
|}

==== Trajectories from r1 = rts+δ, r2 = rts ====
The 'mep' differs from the reaction trajectory of a dynamics calculation. This is because MEP always resets momentum of the reactants to zero after each step in order to simulate an infinitely slow motion. By contrast, the dynamics calculation takes into account the vibronic motion of the system hence, oscillations can be observed on its corresponding contour plot.
{| class="wikitable"
|[[File:MTK H3 MEP.PNG|thumb|Fig 4 -MEP (minimum energy path) contour plot]]
|[[File:MTK Dynamics for reaction path.PNG|thumb|Fig 5- Dynamics calculation of reaction path on a contour plot]]
|}

==== Reactive and Unreactive Trajectories ====
''Table 2- Comparing trajectories of systems with initial position of rAB=200 pm and rBC=74 pm and varying values of p1 and p2''
{| 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>
|Yes
|System passes through transition state and reaches completion. Product bond formation is apparent from the gentle oscillations in the
product channel.
|[[File:MTK plot2.png|thumb]]
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-4.1</nowiki>
|<nowiki>-420.077</nowiki>
|No
|Alot of intramolecular vibrations observed in initial stages.
System does not pass the transition state and returns to reactants.
|[[File:MTK Table2.PNG|thumb]]
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-5.1</nowiki>
|<nowiki>-413.977</nowiki>
|Yes
|An increase in momentum of the incoming H atom,

compared to the previous example, results in surmounting of the transition state maxima by system. More oscillations observable in product channel than reactant channel.
|[[File:MTK Table3.PNG|thumb]]
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.1</nowiki>
|<nowiki>-357.277</nowiki>
|No
|Transition State Theory observed to fail as although system possesses enough energy to overcome transition state, it does not lead to completion and, instead, returns to reactants with a significantly higher vibronic energy.
|[[File:MTK Table4.PNG|thumb]]
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.6</nowiki>
|<nowiki>-349.477</nowiki>
|Yes
|A slight increase in momentum of the incoming H atom, compared to

the preceding example, results in a reactive trajectory. Notably, the system does not pass the transition state at all and fluctuates twice between reactant and product bond formation. This suggests product formation occurs via a transition state far from the lowest energy saddle point, which is a deviation from transition state theory.
|[[File:MTK Table5.PNG|thumb]]
|}
From Table 2, it can be concluded that the total energy of the system does not necessarily determine whether the reaction will proceed. It can also be concluded that high energy systems are prone to return to reactant channels even if they possess enough energy to overcome the transition state maximum. This ilustrates the limitations of transition state theory, which include: not accounting for effects of high temperature and not accounting for the effects of quantum tunnelling.<ref><nowiki>http://www.liquisearch.com/transition_state_theory/limitations_of_transition_state_theory (accessed: May 15, 2020)</nowiki></ref>

==== Transition State Theory ====
Transition state theory overestimates the rate of reaction. It assumes every trajectory that rolls over the transition state will proceed to the product which is not the case as evident from Table 2.

=== Exercise 2. (F-H-H System) ===

==== PES Inspection ====
In the following exercise, '''A''' is taken to be the '''approaching atom''' while '''B''' and '''C''' represent the '''initial diatomic molecule'''.

''Table 1- Initial conditions used to test F+ H2 system''
{| class="wikitable"
![[File:MTK F+H2TS.PNG|thumb|Fig 6 - Early "reactant-like" transition state of F+H2 system.]]
![[File:MTK Surface Plot fhh.png|thumb|Fig 7- Surface Plot with transition state of F+ H2 system]]
|}

F+H2 is exothermic as it has an early energy barrier. According to Hammond's Postulate, the structure of the transition state is similar to reactants if the reaction is exothermic. The transition state for this reaction was found at rFH=181pm and rHH=74.5pm. The activation energy was calculated to be 686Jmol-1.
{| class="wikitable"
![[File:MTK H+FH TS.PNG|thumb|Fig 8 - Late "product-like" transition state of H+HF system.]]
![[File:MTK Surface Plot 1.png|thumb|Fig 9- Surface plot with transition state of H+HF system.]]
|}

H+HF is endothermic as it has a late energy barrier. According to Hammond's Postulate, the structure of the transition state is similar to products if the reaction is endothermic. The transition state for this reaction was found at rHH=74.5pm and rFH=181pm. The activation energy was calculated to be 126.317kJmol-1.

==== Reaction Dynamics ====
''Table 3- Conditions observed to lead to a reactive trajectory for F+H2''
{| class="wikitable"
!
!Distance/pm
!Momentum/ gmol-1.pm.fs-1
|-
|FH
|1043.074
|<nowiki>-6.944</nowiki>
|-
|HH
|74.216
|<nowiki>-0.254</nowiki>
|}
{| class="wikitable"
|[[File:MTK F+H2 CONTOUR MTK.PNG|thumb|Fig 10- F+H2 contour plot]]
|[[File:MTK F+H2 MOMENTAVSTIME.PNG|thumb|Fig 11- F+H2 Momenta Vs Time Plot]]
|}
From the momenta vs time plot, we can observe that initially the reactants possess a large amount of translational energy and upon reaching the transition state, the energy is converted to vibrational energy. The release of energy from the reaction, which is a combination of energy of translational and vibronic energy changes, can be measured experimentally by using calorimetry and infrared spectroscopy. Calorimetry can be used to measure the heat generated by the reaction thus enabling the calculation of total energy given off by the system. Peaks and their wavenumbers in infrared spectrum can be used to identify the changes in vibrational energy of the IR active H-F molecule.

''Table 4- Conditions observed to lead to a reactive trajectory for H+HF''
{| class="wikitable"
!
!Distance/pm
!Momentum/ gmol-1.pm.fs-1
|-
|HH
|868.223
|<nowiki>-3.959</nowiki>
|-
|FH
|117.918
|3.751
|}
{| class="wikitable"
|[[File:MTK H+FH CONTOUR.PNG|thumb|Fig 12- H+FH Contour Plot]]
|[[File:MTK H+FH MOMENTA.PNG|thumb|Fig 13- H+FH Momenta vs Time Plot]]
|}

==== Translation Vs Vibrational Energy ====
[[File:MTK Last Q.PNG|thumb|Fig 14- Graphs A,B,C and D to illustrate Polanyi's Rules ]]
Graph A and B depict an exothermic reaction with an early transition state. It is observed that translational energy is crucial in helping the system surmount the early energy barrier as, when compared between the two graphs, the initial conditions for A possess far more translational energy than vibrational energy, allowing reaction A to reach completion but not B.

Graph C and D depict an endothermic reaction with a late transition state. It is observed that vibrational energy is crucial in helping the system overcome the late energy barrier as, when compared between the two graphs, the initial conditions for C possess more vibrational energy than translational energy, allowing reaction C to reach completion but not D.<ref>Polanyi, J. C. Some Concepts in Reaction Dyanmics. ''Science. ''[Online] 1987 <nowiki>https://science.sciencemag.org/content/236/4802/680/tab-pdf</nowiki> (accessed: May 15, 2020)</ref>

=== References ===
<references />

MRD:MT4618

2020-05-15T22:40:49Z

Mt4618: /* Exercise 2. (F-H-H System) */

== Molecular Reaction Dynamics Lab 2020 ==

=== Exercise 1- (H+H2 System). ===

==== Transition State ====
The transition state is defined as the maximum on the minimum energy path linking reactants and the products. This point on the potential energy surface has the special property that ∂V('''ri''')/∂'''ri'''=0 (the gradient of the potential is zero), and the energy goes down steeply along the minimum energy path linking reactants and products.

Mathematically, the transition state can be described as the derivative with respect to the reaction coordinate that is equal to zero and the maximum can be distinguished from local minima by taking the second derivative wrt the reaction coordinate that is negative.

Hammond's postulate: The structure of the transition state will resemble the reactants or products depending on which are closer in energy. exothermic resembles reactant, endothermic products.
==== Trajectories from r1 = r2: locating the transition state ====
In the following exercise, A is taken to be the approaching H while B and C are the H atoms in H2.

''Table 1- Initial conditions used to test H+ H2 system''
{| class="wikitable"
!
!Distance (r) [pm]
!Momentum (p) [g.mol-1.pm.fs-1]
|-
|AB
|230
|<nowiki>-5.2</nowiki>
|-
|BC
|74
|0
|}
[[File:MTK plot1.png|thumb|Fig 1- Internuclear Distance Vs Time for H+H2 system]]
By using the values in Table 1, a plot of intermolecuar distance vs time was generated. As H+H2 is a symmetrical system, the transition state can be assumed to have equal H-H-H bond lengths, which is represented by the intersection of AB and BC on the plot (Fig.1). By setting rAB=rBC and initial momenta to be zero, the transition state was located at rAB=rBC=91pm.
{| class="wikitable"
|[[File:MTK Internuclear Distance vs time for H3 transition state.PNG|thumb|Fig 2- Internuclear Distance vs time for H3 transition state]]
|[[File:MTK H3 transition state.PNG|thumb|Fig 3- H+H2 Transition State on a contour plot]]
|}

==== Trajectories from r1 = rts+δ, r2 = rts ====
The 'mep' differs from the reaction trajectory of a dynamics calculation. This is because MEP always resets momentum of the reactants to zero after each step in order to simulate an infinitely slow motion. By contrast, the dynamics calculation takes into account the vibronic motion of the system hence, oscillations can be observed on its corresponding contour plot.
{| class="wikitable"
|[[File:MTK H3 MEP.PNG|thumb|Fig 4 -MEP (minimum energy path) contour plot]]
|[[File:MTK Dynamics for reaction path.PNG|thumb|Fig 5- Dynamics calculation of reaction path on a contour plot]]
|}

==== Reactive and Unreactive Trajectories ====
''Table 2- Comparing trajectories of systems with initial position of rAB=200 pm and rBC=74 pm and varying values of p1 and p2''
{| 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>
|Yes
|System passes through transition state and reaches completion. Product bond formation is apparent from the gentle oscillations in the
product channel.
|[[File:MTK plot2.png|thumb]]
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-4.1</nowiki>
|<nowiki>-420.077</nowiki>
|No
|Alot of intramolecular vibrations observed in initial stages.
System does not pass the transition state and returns to reactants.
|[[File:MTK Table2.PNG|thumb]]
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-5.1</nowiki>
|<nowiki>-413.977</nowiki>
|Yes
|An increase in momentum of the incoming H atom,

compared to the previous example, results in surmounting of the transition state maxima by system. More oscillations observable in product channel than reactant channel.
|[[File:MTK Table3.PNG|thumb]]
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.1</nowiki>
|<nowiki>-357.277</nowiki>
|No
|Transition State Theory observed to fail as although system possesses enough energy to overcome transition state, it does not lead to completion and, instead, returns to reactants with a significantly higher vibronic energy.
|[[File:MTK Table4.PNG|thumb]]
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.6</nowiki>
|<nowiki>-349.477</nowiki>
|Yes
|A slight increase in momentum of the incoming H atom, compared to

the preceding example, results in a reactive trajectory. Notably, the system does not pass the transition state at all and fluctuates twice between reactant and product bond formation. This suggests product formation occurs via a transition state far from the lowest energy saddle point, which is a deviation from transition state theory.
|[[File:MTK Table5.PNG|thumb]]
|}
From Table 2, it can be concluded that the total energy of the system does not necessarily determine whether the reaction will proceed. It can also be concluded that high energy systems are prone to return to reactant channels even if they possess enough energy to overcome the transition state maximum. This ilustrates the limitations of transition state theory, which include: not accounting for effects of high temperature and not accounting for the effects of quantum tunnelling.

==== Transition State Theory ====
Transition state theory overestimates the rate of reaction. It assumes every trajectory that rolls over the transition state will proceed to the product which is not the case as evident from Table 2.

=== Exercise 2. (F-H-H System) ===

==== PES Inspection ====
In the following exercise, '''A''' is taken to be the '''approaching atom''' while '''B''' and '''C''' represent the '''initial diatomic molecule'''.

''Table 1- Initial conditions used to test F+ H2 system''
{| class="wikitable"
![[File:MTK F+H2TS.PNG|thumb|Fig 6 - Early "reactant-like" transition state of F+H2 system.]]
![[File:MTK Surface Plot fhh.png|thumb|Fig 7- Surface Plot with transition state of F+ H2 system]]
|}

F+H2 is exothermic as it has an early energy barrier. According to Hammond's Postulate, the structure of the transition state is similar to reactants if the reaction is exothermic. The transition state for this reaction was found at rFH=181pm and rHH=74.5pm. The activation energy was calculated to be 686Jmol-1.
{| class="wikitable"
![[File:MTK H+FH TS.PNG|thumb|Fig 8 - Late "product-like" transition state of H+HF system.]]
![[File:MTK Surface Plot 1.png|thumb|Fig 9- Surface plot with transition state of H+HF system.]]
|}

H+HF is endothermic as it has a late energy barrier. According to Hammond's Postulate, the structure of the transition state is similar to products if the reaction is endothermic. The transition state for this reaction was found at rHH=74.5pm and rFH=181pm. The activation energy was calculated to be 126.317kJmol-1.

==== Reaction Dynamics ====
''Table - Conditions observed to lead to a reactive trajectory for F+H2''
{| class="wikitable"
!
!Distance/pm
!Momentum/ gmol-1.pm.fs-1
|-
|FH
|1043.074
|<nowiki>-6.944</nowiki>
|-
|HH
|74.216
|<nowiki>-0.254</nowiki>
|}
{| class="wikitable"
|[[File:MTK F+H2 CONTOUR MTK.PNG|thumb|F+H2 contour plot]]
|[[File:MTK F+H2 MOMENTAVSTIME.PNG|thumb|F+H2 Momenta Vs Time Plot]]
|}
From the momenta vs time plot, we can observe that initially the reactants possess a large amount of translational energy and upon reaching the transition state, the energy is converted to vibrational energy. The release of energy from the reaction can be measured experimentally by using calorimetry and infrared spectroscopy. Calorimetry can be used to measure the heat generated by the reaction thus enabling the calculation of change in total translational energy of the system. Infrared spectroscopy can be used to identify the changes in vibrational energy of the system.

''Table - Conditions observed to lead to a reactive trajectory for H+HF''
{| class="wikitable"
!
!Distance/pm
!Momentum/ gmol-1.pm.fs-1
|-
|HH
|868.223
|<nowiki>-3.959</nowiki>
|-
|FH
|117.918
|3.751
|}
{| class="wikitable"
|[[File:MTK H+FH CONTOUR.PNG|thumb|Fig -H+FH Contour Plot]]
|[[File:MTK H+FH MOMENTA.PNG|thumb|Fig - H+FH Momenta vs Time Plot]]
|}

==== Translation Vs Vibrational Energy ====
[[File:MTK Last Q.PNG|thumb|Fig- ]]
Graph A and B depict an exothermic reaction with an early transition state. It is observed that translational energy is crucial in helping the system surmount the early energy barrier as, when compared between the two graphs, the initial conditions for A possess far more translational energy than vibrational energy, allowing reaction A to reach completion but not B.

Graph C and D depict an endothermic reaction with a late transition state. It is observed that vibrational energy is crucial in helping the system overcome the late energy barrier as, when compared between the two graphs, the initial conditions for C possess more vibrational energy than translational energy, allowing reaction C to reach completion but not D.

File:MTK Surface Plot 1.png

2020-05-15T22:39:45Z

Mt4618:

File:MTK H+FH TS.PNG

2020-05-15T22:33:41Z

Mt4618:

File:MTK Surface Plot fhh.png

2020-05-15T22:25:50Z

Mt4618:

MRD:MT4618

2020-05-15T22:19:54Z

Mt4618: /* Reactive and Unreactive Trajectories */

== Molecular Reaction Dynamics Lab 2020 ==

=== Exercise 1- (H+H2 System). ===

==== Transition State ====
The transition state is defined as the maximum on the minimum energy path linking reactants and the products. This point on the potential energy surface has the special property that ∂V('''ri''')/∂'''ri'''=0 (the gradient of the potential is zero), and the energy goes down steeply along the minimum energy path linking reactants and products.

Mathematically, the transition state can be described as the derivative with respect to the reaction coordinate that is equal to zero and the maximum can be distinguished from local minima by taking the second derivative wrt the reaction coordinate that is negative.

Hammond's postulate: The structure of the transition state will resemble the reactants or products depending on which are closer in energy. exothermic resembles reactant, endothermic products.
==== Trajectories from r1 = r2: locating the transition state ====
In the following exercise, A is taken to be the approaching H while B and C are the H atoms in H2.

''Table 1- Initial conditions used to test H+ H2 system''
{| class="wikitable"
!
!Distance (r) [pm]
!Momentum (p) [g.mol-1.pm.fs-1]
|-
|AB
|230
|<nowiki>-5.2</nowiki>
|-
|BC
|74
|0
|}
[[File:MTK plot1.png|thumb|Fig 1- Internuclear Distance Vs Time for H+H2 system]]
By using the values in Table 1, a plot of intermolecuar distance vs time was generated. As H+H2 is a symmetrical system, the transition state can be assumed to have equal H-H-H bond lengths, which is represented by the intersection of AB and BC on the plot (Fig.1). By setting rAB=rBC and initial momenta to be zero, the transition state was located at rAB=rBC=91pm.
{| class="wikitable"
|[[File:MTK Internuclear Distance vs time for H3 transition state.PNG|thumb|Fig 2- Internuclear Distance vs time for H3 transition state]]
|[[File:MTK H3 transition state.PNG|thumb|Fig 3- H+H2 Transition State on a contour plot]]
|}

==== Trajectories from r1 = rts+δ, r2 = rts ====
The 'mep' differs from the reaction trajectory of a dynamics calculation. This is because MEP always resets momentum of the reactants to zero after each step in order to simulate an infinitely slow motion. By contrast, the dynamics calculation takes into account the vibronic motion of the system hence, oscillations can be observed on its corresponding contour plot.
{| class="wikitable"
|[[File:MTK H3 MEP.PNG|thumb|Fig 4 -MEP (minimum energy path) contour plot]]
|[[File:MTK Dynamics for reaction path.PNG|thumb|Fig 5- Dynamics calculation of reaction path on a contour plot]]
|}

==== Reactive and Unreactive Trajectories ====
''Table 2- Comparing trajectories of systems with initial position of rAB=200 pm and rBC=74 pm and varying values of p1 and p2''
{| 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>
|Yes
|System passes through transition state and reaches completion. Product bond formation is apparent from the gentle oscillations in the
product channel.
|[[File:MTK plot2.png|thumb]]
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-4.1</nowiki>
|<nowiki>-420.077</nowiki>
|No
|Alot of intramolecular vibrations observed in initial stages.
System does not pass the transition state and returns to reactants.
|[[File:MTK Table2.PNG|thumb]]
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-5.1</nowiki>
|<nowiki>-413.977</nowiki>
|Yes
|An increase in momentum of the incoming H atom,

compared to the previous example, results in surmounting of the transition state maxima by system. More oscillations observable in product channel than reactant channel.
|[[File:MTK Table3.PNG|thumb]]
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.1</nowiki>
|<nowiki>-357.277</nowiki>
|No
|Transition State Theory observed to fail as although system possesses enough energy to overcome transition state, it does not lead to completion and, instead, returns to reactants with a significantly higher vibronic energy.
|[[File:MTK Table4.PNG|thumb]]
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.6</nowiki>
|<nowiki>-349.477</nowiki>
|Yes
|A slight increase in momentum of the incoming H atom, compared to

the preceding example, results in a reactive trajectory. Notably, the system does not pass the transition state at all and fluctuates twice between reactant and product bond formation. This suggests product formation occurs via a transition state far from the lowest energy saddle point, which is a deviation from transition state theory.
|[[File:MTK Table5.PNG|thumb]]
|}
From Table 2, it can be concluded that the total energy of the system does not necessarily determine whether the reaction will proceed. It can also be concluded that high energy systems are prone to return to reactant channels even if they possess enough energy to overcome the transition state maximum. This ilustrates the limitations of transition state theory, which include: not accounting for effects of high temperature and not accounting for the effects of quantum tunnelling.

==== Transition State Theory ====
Transition state theory overestimates the rate of reaction. It assumes every trajectory that rolls over the transition state will proceed to the product which is not the case as evident from Table 2.

=== Exercise 2. (F-H-H System) ===

==== PES Inspection ====
F+H2 is exothermic as it has an early energy barrier. According to Hammond's Postulate, the structure of the transition state is similar to reactants if the reaction is exothermic. The transition state for this reaction was found at rAB=181pm and rBC=74.5pm. The activation energy was calculated to be 686Jmol-1.
{| class="wikitable"
![[File:MTK F+H2TS.PNG|thumb|Fig - Early "reactant-like" transition state of F+H2 system.]]
!
|}

H+HF is endothermic as it has a late energy barrier. According to Hammond's Postulate, the structure of the transition state is similar to products if the reaction is endothermic. The transition state for this reaction was found at rAB=74.5pm and rBC=181pm. The activation energy was calculated to be 126.317kJmol-1.

==== Reaction Dynamics ====
''Table - Conditions observed to lead to a reactive trajectory for F+H2''
{| class="wikitable"
!
!Distance/pm
!Momentum/ gmol-1.pm.fs-1
|-
|FH
|1043.074
|<nowiki>-6.944</nowiki>
|-
|HH
|74.216
|<nowiki>-0.254</nowiki>
|}
{| class="wikitable"
|[[File:MTK F+H2 CONTOUR MTK.PNG|thumb|F+H2 contour plot]]
|[[File:MTK F+H2 MOMENTAVSTIME.PNG|thumb|F+H2 Momenta Vs Time Plot]]
|}
From the momenta vs time plot, we can observe that initially the reactants possess a large amount of translational energy and upon reaching the transition state, the energy is converted to vibrational energy. The release of energy from the reaction can be measured experimentally by using calorimetry and infrared spectroscopy. Calorimetry can be used to measure the heat generated by the reaction thus enabling the calculation of change in total translational energy of the system. Infrared spectroscopy can be used to identify the changes in vibrational energy of the system.

''Table - Conditions observed to lead to a reactive trajectory for H+HF''
{| class="wikitable"
!
!Distance/pm
!Momentum/ gmol-1.pm.fs-1
|-
|HH
|868.223
|<nowiki>-3.959</nowiki>
|-
|FH
|117.918
|3.751
|}
{| class="wikitable"
|[[File:MTK H+FH CONTOUR.PNG|thumb|Fig -H+FH Contour Plot]]
|[[File:MTK H+FH MOMENTA.PNG|thumb|Fig - H+FH Momenta vs Time Plot]]
|}

==== Translation Vs Vibrational Energy ====
[[File:MTK Last Q.PNG|thumb|Fig- ]]
Graph A and B depict an exothermic reaction with an early transition state. It is observed that translational energy is crucial in helping the system surmount the early energy barrier as, when compared between the two graphs, the initial conditions for A possess far more translational energy than vibrational energy, allowing reaction A to reach completion but not B.

Graph C and D depict an endothermic reaction with a late transition state. It is observed that vibrational energy is crucial in helping the system overcome the late energy barrier as, when compared between the two graphs, the initial conditions for C possess more vibrational energy than translational energy, allowing reaction C to reach completion but not D.

MRD:MT4618

2020-05-15T21:50:22Z

Mt4618: /* Molecular Reaction Dynamics Lab 2020 */

== Molecular Reaction Dynamics Lab 2020 ==

=== Exercise 1- (H+H2 System). ===

==== Transition State ====
The transition state is defined as the maximum on the minimum energy path linking reactants and the products. This point on the potential energy surface has the special property that ∂V('''ri''')/∂'''ri'''=0 (the gradient of the potential is zero), and the energy goes down steeply along the minimum energy path linking reactants and products.

Mathematically, the transition state can be described as the derivative with respect to the reaction coordinate that is equal to zero and the maximum can be distinguished from local minima by taking the second derivative wrt the reaction coordinate that is negative.

Hammond's postulate: The structure of the transition state will resemble the reactants or products depending on which are closer in energy. exothermic resembles reactant, endothermic products.
==== Trajectories from r1 = r2: locating the transition state ====
In the following exercise, A is taken to be the approaching H while B and C are the H atoms in H2.

''Table 1- Initial conditions used to test H+ H2 system''
{| class="wikitable"
!
!Distance (r) [pm]
!Momentum (p) [g.mol-1.pm.fs-1]
|-
|AB
|230
|<nowiki>-5.2</nowiki>
|-
|BC
|74
|0
|}
[[File:MTK plot1.png|thumb|Fig 1- Internuclear Distance Vs Time for H+H2 system]]
By using the values in Table 1, a plot of intermolecuar distance vs time was generated. As H+H2 is a symmetrical system, the transition state can be assumed to have equal H-H-H bond lengths, which is represented by the intersection of AB and BC on the plot (Fig.1). By setting rAB=rBC and initial momenta to be zero, the transition state was located at rAB=rBC=91pm.
{| class="wikitable"
|[[File:MTK Internuclear Distance vs time for H3 transition state.PNG|thumb|Fig 2- Internuclear Distance vs time for H3 transition state]]
|[[File:MTK H3 transition state.PNG|thumb|Fig 3- H+H2 Transition State on a contour plot]]
|}

==== Trajectories from r1 = rts+δ, r2 = rts ====
The 'mep' differs from the reaction trajectory of a dynamics calculation. This is because MEP always resets momentum of the reactants to zero after each step in order to simulate an infinitely slow motion. By contrast, the dynamics calculation takes into account the vibronic motion of the system hence, oscillations can be observed on its corresponding contour plot.
{| class="wikitable"
|[[File:MTK H3 MEP.PNG|thumb|Fig 4 -MEP (minimum energy path) contour plot]]
|[[File:MTK Dynamics for reaction path.PNG|thumb|Fig 5- Dynamics calculation of reaction path on a contour plot]]
|}

==== Reactive and Unreactive Trajectories ====
''Table 2- Comparing trajectories of systems with initial position of rAB=200 pm and rBC=74 pm and varying values of p1 and p2''
{| 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>
|Yes
|System passes through transition state and

reaches completion. Product bond formation

is apparent from the gentle oscillations in the

product channel.
|[[File:MTK plot2.png|thumb]]
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-4.1</nowiki>
|<nowiki>-420.077</nowiki>
|No
|Alot of intramolecular vibrations observed in
initial stages.System does not pass the transition state and returns to reactants.
|[[File:MTK Table2.PNG|thumb]]
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-5.1</nowiki>
|<nowiki>-413.977</nowiki>
|Yes
|An increase in momentum of the incoming H atom,

compared to the previous example, results in surmounting of the transition state maxima by system. More oscillations observable in product channel than reactant channel.
|[[File:MTK Table3.PNG|thumb]]
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.1</nowiki>
|<nowiki>-357.277</nowiki>
|No
|
|[[File:MTK Table4.PNG|thumb]]
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.6</nowiki>
|<nowiki>-349.477</nowiki>
|Yes
|
|[[File:MTK Table5.PNG|thumb]]
|}
From the table above, it can be concluded that the total energy of the system does not necessarily determine whether the reaction will proceed.

==== Transition State Theory ====
Transition state theory overestimates the rate of reaction. It assumes every trajectory that rolls over the transition state will proceed to the product which is not the case as evident from Table 2.

=== Exercise 2. (F-H-H System) ===

==== PES Inspection ====
F+H2 is exothermic as it has an early energy barrier. According to Hammond's Postulate, the structure of the transition state is similar to reactants if the reaction is exothermic. The transition state for this reaction was found at rAB=181pm and rBC=74.5pm. The activation energy was calculated to be 686Jmol-1.
{| class="wikitable"
![[File:MTK F+H2TS.PNG|thumb|Fig - Early "reactant-like" transition state of F+H2 system.]]
!
|}

H+HF is endothermic as it has a late energy barrier. According to Hammond's Postulate, the structure of the transition state is similar to products if the reaction is endothermic. The transition state for this reaction was found at rAB=74.5pm and rBC=181pm. The activation energy was calculated to be 126.317kJmol-1.

==== Reaction Dynamics ====
''Table - Conditions observed to lead to a reactive trajectory for F+H2''
{| class="wikitable"
!
!Distance/pm
!Momentum/ gmol-1.pm.fs-1
|-
|FH
|1043.074
|<nowiki>-6.944</nowiki>
|-
|HH
|74.216
|<nowiki>-0.254</nowiki>
|}
{| class="wikitable"
|[[File:MTK F+H2 CONTOUR MTK.PNG|thumb|F+H2 contour plot]]
|[[File:MTK F+H2 MOMENTAVSTIME.PNG|thumb|F+H2 Momenta Vs Time Plot]]
|}
From the momenta vs time plot, we can observe that initially the reactants possess a large amount of translational energy and upon reaching the transition state, the energy is converted to vibrational energy. The release of energy from the reaction can be measured experimentally by using calorimetry and infrared spectroscopy. Calorimetry can be used to measure the heat generated by the reaction thus enabling the calculation of change in total translational energy of the system. Infrared spectroscopy can be used to identify the changes in vibrational energy of the system.

''Table - Conditions observed to lead to a reactive trajectory for H+HF''
{| class="wikitable"
!
!Distance/pm
!Momentum/ gmol-1.pm.fs-1
|-
|HH
|868.223
|<nowiki>-3.959</nowiki>
|-
|FH
|117.918
|3.751
|}
{| class="wikitable"
|[[File:MTK H+FH CONTOUR.PNG|thumb|Fig -H+FH Contour Plot]]
|[[File:MTK H+FH MOMENTA.PNG|thumb|Fig - H+FH Momenta vs Time Plot]]
|}

==== Translation Vs Vibrational Energy ====
[[File:MTK Last Q.PNG|thumb|Fig- ]]
Graph A and B depict an exothermic reaction with an early transition state. It is observed that translational energy is crucial in helping the system surmount the early energy barrier as, when compared between the two graphs, the initial conditions for A possess far more translational energy than vibrational energy, allowing reaction A to reach completion but not B.

Graph C and D depict an endothermic reaction with a late transition state. It is observed that vibrational energy is crucial in helping the system overcome the late energy barrier as, when compared between the two graphs, the initial conditions for C possess more vibrational energy than translational energy, allowing reaction C to reach completion but not D.

MRD:MT4618

2020-05-15T21:42:12Z

Mt4618: /* Exercise 1- (H+H2 System). */

== Molecular Reaction Dynamics Lab 2020 ==

=== Exercise 1- (H+H2 System). ===

==== Transition State ====
The transition state is defined as the maximum on the minimum energy path linking reactants and the products. This point on the potential energy surface has the special property that ∂V('''ri''')/∂'''ri'''=0 (the gradient of the potential is zero), and the energy goes down steeply along the minimum energy path linking reactants and products.

Mathematically, the transition state can be described as the derivative with respect to the reaction coordinate that is equal to zero and the maximum can be distinguished from local minima by taking the second derivative wrt the reaction coordinate that is negative.

Hammond's postulate: The structure of the transition state will resemble the reactants or products depending on which are closer in energy. exothermic resembles reactant, endothermic products.
==== Trajectories from r1 = r2: locating the transition state ====
''Table 1- Initial conditions used to test H+ H2 system''
{| class="wikitable"
!
!Distance (r) [pm]
!Momentum (p) [g.mol-1.pm.fs-1]
|-
|AB
|230
|<nowiki>-5.2</nowiki>
|-
|BC
|74
|0
|}
[[File:MTK plot1.png|thumb|Fig 1- Internuclear Distance Vs Time for H+H2 system]]
By using the values in Table 1, a plot of intermolecuar distance vs time was generated. As H+H2 is a symmetrical system, the transition state can be assumed to have equal H-H-H bond lengths, which is represented by the intersection of AB and BC on the plot (Fig.1). By setting rAB=rBC and initial momenta to be zero, the transition state was located at rAB=rBC=91pm.
{| class="wikitable"
|[[File:MTK Internuclear Distance vs time for H3 transition state.PNG|thumb|Fig 2- Internuclear Distance vs time for H3 transition state]]
|[[File:MTK H3 transition state.PNG|thumb|Fig 3- H+H2 Transition State on a contour plot]]
|}

==== Trajectories from r1 = rts+δ, r2 = rts ====
The 'mep' differs from the reaction trajectory of a dynamics calculation. This is because MEP always resets momentum of the reactants to zero after each step in order to simulate an infinitely slow motion. By contrast, the dynamics calculation takes into account the vibronic motion of the system hence, oscillations can be observed on its corresponding contour plot.
{| class="wikitable"
|[[File:MTK H3 MEP.PNG|thumb|Fig 4 -MEP (minimum energy path) contour plot]]
|[[File:MTK Dynamics for reaction path.PNG|thumb|Fig 5- Dynamics calculation of reaction path on a contour plot]]
|}

==== Reactive and Unreactive Trajectories ====
''Table 2- Comparing trajectories of systems with initial position of rAB=200 pm and rBC=74 pm and varying values of p1 and p2''
{| 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>
|Yes
|System passes through transition state and

reaches completion. Product bond formation

is apparent from the gentle oscillations in the

product channel.
|[[File:MTK plot2.png|thumb]]
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-4.1</nowiki>
|<nowiki>-420.077</nowiki>
|No
|Alot of intramolecular vibrations observed in
initial stages.System does not pass the transition state and returns to reactants.
|[[File:MTK Table2.PNG|thumb]]
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-5.1</nowiki>
|<nowiki>-413.977</nowiki>
|Yes
|
|[[File:MTK Table3.PNG|thumb]]
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.1</nowiki>
|<nowiki>-357.277</nowiki>
|No
|
|[[File:MTK Table4.PNG|thumb]]
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.6</nowiki>
|<nowiki>-349.477</nowiki>
|Yes
|
|[[File:MTK Table5.PNG|thumb]]
|}
From the table above, it can be concluded that the total energy of the system does not necessarily determine whether the reaction will proceed.

==== Transition State Theory ====
Transition state theory overestimates the rate of reaction. It assumes every trajectory that rolls over the transition state will proceed to the product which is not the case as evident from Table 2.

=== Exercise 2. (F-H-H System) ===

==== PES Inspection ====
F+H2 is exothermic as it has an early energy barrier. According to Hammond's Postulate, the structure of the transition state is similar to reactants if the reaction is exothermic. The transition state for this reaction was found at rAB=181pm and rBC=74.5pm. The activation energy was calculated to be 686Jmol-1.
{| class="wikitable"
![[File:MTK F+H2TS.PNG|thumb|Fig - Early "reactant-like" transition state of F+H2 system.]]
!
|}

H+HF is endothermic as it has a late energy barrier. According to Hammond's Postulate, the structure of the transition state is similar to products if the reaction is endothermic. The transition state for this reaction was found at rAB=74.5pm and rBC=181pm. The activation energy was calculated to be 126.317kJmol-1.

==== Reaction Dynamics ====
''Table - Conditions observed to lead to a reactive trajectory for F+H2''
{| class="wikitable"
!
!Distance/pm
!Momentum/ gmol-1.pm.fs-1
|-
|FH
|1043.074
|<nowiki>-6.944</nowiki>
|-
|HH
|74.216
|<nowiki>-0.254</nowiki>
|}
{| class="wikitable"
|[[File:MTK F+H2 CONTOUR MTK.PNG|thumb|F+H2 contour plot]]
|[[File:MTK F+H2 MOMENTAVSTIME.PNG|thumb|F+H2 Momenta Vs Time Plot]]
|}
From the momenta vs time plot, we can observe that initially the reactants possess a large amount of translational energy and upon reaching the transition state, the energy is converted to vibrational energy. The release of energy from the reaction can be measured experimentally by using calorimetry and infrared spectroscopy. Calorimetry can be used to measure the heat generated by the reaction thus enabling the calculation of change in total translational energy of the system. Infrared spectroscopy can be used to identify the changes in vibrational energy of the system.

''Table - Conditions observed to lead to a reactive trajectory for H+HF''
{| class="wikitable"
!
!Distance/pm
!Momentum/ gmol-1.pm.fs-1
|-
|HH
|868.223
|<nowiki>-3.959</nowiki>
|-
|FH
|117.918
|3.751
|}
{| class="wikitable"
|[[File:MTK H+FH CONTOUR.PNG|thumb|Fig -H+FH Contour Plot]]
|[[File:MTK H+FH MOMENTA.PNG|thumb|Fig - H+FH Momenta vs Time Plot]]
|}

==== Translation Vs Vibrational Energy ====
[[File:MTK Last Q.PNG|thumb|Fig- ]]
Graph A and B depict an exothermic reaction with an early transition state. It is observed that translational energy is crucial in helping the system surmount the early energy barrier as, when compared between the two graphs, the initial conditions for A possess far more translational energy than vibrational energy, allowing reaction A to reach completion but not B.

Graph C and D depict an endothermic reaction with a late transition state. It is observed that vibrational energy is crucial in helping the system overcome the late energy barrier as, when compared between the two graphs, the initial conditions for C possess more vibrational energy than translational energy, allowing reaction C to reach completion but not D.

File:MTK plot2.png

2020-05-15T21:37:49Z

Mt4618:

MRD:MT4618

2020-05-15T18:46:57Z

Mt4618: /* Exercise 1- (H+H2 System). */

== Molecular Reaction Dynamics Lab 2020 ==

=== Exercise 1- (H+H2 System). ===

==== Transition State ====
The transition state is defined as the maximum on the minimum energy path linking reactants and the products. This point on the potential energy surface has the special property that ∂V('''ri''')/∂'''ri'''=0 (the gradient of the potential is zero), and the energy goes down steeply along the minimum energy path linking reactants and products.

Mathematically, the transition state can be described as the derivative with respect to the reaction coordinate that is equal to zero and the maximum can be distinguished from local minima by taking the second derivative wrt the reaction coordinate that is negative.

Hammond's postulate: The structure of the transition state will resemble the reactants or products depending on which are closer in energy. exothermic resembles reactant, endothermic products.
==== Trajectories from r1 = r2: locating the transition state ====
''Table 1- Initial conditions used to test H+ H2 system''
{| class="wikitable"
!
!Distance (r) [pm]
!Momentum (p) [g.mol-1.pm.fs-1]
|-
|AB
|230
|<nowiki>-5.2</nowiki>
|-
|BC
|74
|0
|}
[[File:MTK plot1.png|thumb|Fig 1- Internuclear Distance Vs Time for H+H2 system]]
By using the values in Table 1, a plot of intermolecuar distance vs time was generated. As H+H2 is a symmetrical system, the transition state can be assumed to have equal H-H-H bond lengths, which is represented by the intersection of AB and BC on the plot (Fig.1). By setting rAB=rBC and initial momenta to be zero, the transition state was located at rAB=rBC=91pm.
{| class="wikitable"
|[[File:MTK Internuclear Distance vs time for H3 transition state.PNG|thumb|Fig 2- Internuclear Distance vs time for H3 transition state]]
|[[File:MTK H3 transition state.PNG|thumb|Fig 3- H+H2 Transition State on a contour plot]]
|}

==== Trajectories from r1 = rts+δ, r2 = rts ====
The 'mep' differs from the reaction trajectory of a dynamics calculation. This is because MEP always resets momentum of the reactants to zero after each step in order to simulate an infinitely slow motion. By contrast, the dynamics calculation takes into account the vibronic motion of the system hence, oscillations can be observed on its corresponding contour plot.
{| class="wikitable"
|[[File:MTK H3 MEP.PNG|thumb|Fig 4 -MEP (minimum energy path) contour plot]]
|[[File:MTK Dynamics for reaction path.PNG|thumb|Fig 5- Dynamics calculation of reaction path on a contour plot]]
|}

==== Reactive and Unreactive Trajectories ====
''Table 2- Comparing trajectories of systems with initial position of rAB=200 pm and rBC=74 pm and varying values of p1 and p2''
{| 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>-3.1</nowiki>
|<nowiki>-4.1</nowiki>
|<nowiki>-420.077</nowiki>
|No
|Alot of intramolecular vibrations observed.

System does not pass the transition state and

returns to reactants.
|[[File:MTK Table2.PNG|thumb]]
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-5.1</nowiki>
|<nowiki>-413.977</nowiki>
|Yes
|
|[[File:MTK Table3.PNG|thumb]]
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.1</nowiki>
|<nowiki>-357.277</nowiki>
|No
|
|[[File:MTK Table4.PNG|thumb]]
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.6</nowiki>
|<nowiki>-349.477</nowiki>
|Yes
|
|[[File:MTK Table5.PNG|thumb]]
|}
From the table above, it can be concluded that the total energy of the system does not necessarily determine whether the reaction will proceed.

==== Transition State Theory ====
Transition state theory overestimates the rate of reaction. It assumes every trajectory that rolls over the transition state will proceed to the product which is not the case as evident from Table 2.

=== Exercise 2. (F-H-H System) ===

==== PES Inspection ====
F+H2 is exothermic as it has an early energy barrier. According to Hammond's Postulate, the structure of the transition state is similar to reactants if the reaction is exothermic. The transition state for this reaction was found at rAB=181pm and rBC=74.5pm. The activation energy was calculated to be 686Jmol-1.
{| class="wikitable"
![[File:MTK F+H2TS.PNG|thumb|Fig - Early "reactant-like" transition state of F+H2 system.]]
!
|}

H+HF is endothermic as it has a late energy barrier. According to Hammond's Postulate, the structure of the transition state is similar to products if the reaction is endothermic. The transition state for this reaction was found at rAB=74.5pm and rBC=181pm. The activation energy was calculated to be 126.317kJmol-1.

==== Reaction Dynamics ====
''Table - Conditions observed to lead to a reactive trajectory for F+H2''
{| class="wikitable"
!
!Distance/pm
!Momentum/ gmol-1.pm.fs-1
|-
|FH
|1043.074
|<nowiki>-6.944</nowiki>
|-
|HH
|74.216
|<nowiki>-0.254</nowiki>
|}
{| class="wikitable"
|[[File:MTK F+H2 CONTOUR MTK.PNG|thumb|F+H2 contour plot]]
|[[File:MTK F+H2 MOMENTAVSTIME.PNG|thumb|F+H2 Momenta Vs Time Plot]]
|}
From the momenta vs time plot, we can observe that initially the reactants possess a large amount of translational energy and upon reaching the transition state, the energy is converted to vibrational energy. The release of energy from the reaction can be measured experimentally by using calorimetry and infrared spectroscopy. Calorimetry can be used to measure the heat generated by the reaction thus enabling the calculation of change in total translational energy of the system. Infrared spectroscopy can be used to identify the changes in vibrational energy of the system.

''Table - Conditions observed to lead to a reactive trajectory for H+HF''
{| class="wikitable"
!
!Distance/pm
!Momentum/ gmol-1.pm.fs-1
|-
|HH
|868.223
|<nowiki>-3.959</nowiki>
|-
|FH
|117.918
|3.751
|}
{| class="wikitable"
|[[File:MTK H+FH CONTOUR.PNG|thumb|Fig -H+FH Contour Plot]]
|[[File:MTK H+FH MOMENTA.PNG|thumb|Fig - H+FH Momenta vs Time Plot]]
|}

==== Translation Vs Vibrational Energy ====
[[File:MTK Last Q.PNG|thumb|Fig- ]]
Graph A and B depict an exothermic reaction with an early transition state. It is observed that translational energy is crucial in helping the system surmount the early energy barrier as, when compared between the two graphs, the initial conditions for A possess far more translational energy than vibrational energy, allowing reaction A to reach completion but not B.

Graph C and D depict an endothermic reaction with a late transition state. It is observed that vibrational energy is crucial in helping the system overcome the late energy barrier as, when compared between the two graphs, the initial conditions for C possess more vibrational energy than translational energy, allowing reaction C to reach completion but not D.

File:MTK Dynamics for reaction path.PNG

2020-05-15T18:23:26Z

Mt4618:

File:MTK H3 MEP.PNG

2020-05-15T18:22:56Z

Mt4618:

File:MTK H3 transition state.PNG

2020-05-15T18:19:15Z

Mt4618:

File:MTK plot1.png

2020-05-15T18:08:47Z

Mt4618:

File:MTK Internuclear Distance vs time for H3 transition state.PNG

2020-05-15T17:56:27Z

Mt4618:

MRD:MT4618

2020-05-15T17:33:33Z

Mt4618: /* Exercise 2. (F-H-H System) */

== Notes ==

=== Exercise 1- (H+H2 System). ===

The '''transition state''' is defined as the ''maximum'' on the '''minimum energy path''' linking reactants and the products. This point on the potential energy surface has the special property that ∂V('''ri''')/∂'''ri'''=0 (the gradient of the potential is zero), and the energy goes down most steeply along the minimum energy path linking reactants and products. Consequently, if one starts a trajectory exactly at the transition state, with no initial momentum, it will remain there forever.

Mathematically, the transition state can be described as the derivative with respect to the reaction coordinate is zero and the maximum can be distinguished from local minima by taking the second derivative wrt the reaction coordinate is negative.

''Table 1- Initial conditions used to test H+ H2 system''
{| class="wikitable"
!
!Distance (r) [pm]
!Momentum (p) [g.mol-1.pm.fs-1]
|-
|AB
|230
|<nowiki>-5.2</nowiki>
|-
|BC
|74
|0
|}
Hammond's postulate: The structure of the transition state will resemble the reactants or products depending on which are closer in energy. exothermic resembles reactant, endothermic products.

==== Trajectories from r1 = r2: locating the transition state ====
When the atoms are too far apart they are not interacting too much and the forces are small. Start playing with diff. values of AB=BC and look at forces along AB and BC.

Force relates to gradient of slope.

Any point along the diagonal AB=BC line are local minima or saddle points. along the direction orthogonal to the direction of diagonal is the maximum

==== Reactive and Unreactive Trajectories ====
{| 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>-3.1</nowiki>
|<nowiki>-4.1</nowiki>
|<nowiki>-420.077</nowiki>
|No
|Alot of intramolecular vibrations observed.

System does not pass the transition state and

returns to reactants.
|[[File:MTK Table2.PNG|thumb]]
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-5.1</nowiki>
|<nowiki>-413.977</nowiki>
|Yes
|
|[[File:MTK Table3.PNG|thumb]]
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.1</nowiki>
|<nowiki>-357.277</nowiki>
|No
|
|[[File:MTK Table4.PNG|thumb]]
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.6</nowiki>
|<nowiki>-349.477</nowiki>
|Yes
|
|[[File:MTK Table5.PNG|thumb]]
|}

==== Transition State Theory ====
Transition state theory overestimates. It assumes every trajectory that rolls over the transition state will proceed to the product.

=== Exercise 2. (F-H-H System) ===

==== PES Inspection ====
F+H2 is exothermic as it has an early energy barrier. According to Hammond's Postulate, the structure of the transition state is similar to reactants if the reaction is exothermic. The transition state for this reaction was found at rAB=181pm and rBC=74.5pm. The activation energy was calculated to be 686Jmol-1.
{| class="wikitable"
![[File:MTK F+H2TS.PNG|thumb|Fig - Early "reactant-like" transition state of F+H2 system.]]
!
|}

H+HF is endothermic as it has a late energy barrier. According to Hammond's Postulate, the structure of the transition state is similar to products if the reaction is endothermic. The transition state for this reaction was found at rAB=74.5pm and rBC=181pm. The activation energy was calculated to be 126.317kJmol-1.

==== Reaction Dynamics ====
''Table - Conditions observed to lead to a reactive trajectory for F+H2''
{| class="wikitable"
!
!Distance/pm
!Momentum/ gmol-1.pm.fs-1
|-
|FH
|1043.074
|<nowiki>-6.944</nowiki>
|-
|HH
|74.216
|<nowiki>-0.254</nowiki>
|}
{| class="wikitable"
|[[File:MTK F+H2 CONTOUR MTK.PNG|thumb|F+H2 contour plot]]
|[[File:MTK F+H2 MOMENTAVSTIME.PNG|thumb|F+H2 Momenta Vs Time Plot]]
|}
From the momenta vs time plot, we can observe that initially the reactants possess a large amount of translational energy and upon reaching the transition state, the energy is converted to vibrational energy. The release of energy from the reaction can be measured experimentally by using calorimetry and infrared spectroscopy. Calorimetry can be used to measure the heat generated by the reaction thus enabling the calculation of change in total translational energy of the system. Infrared spectroscopy can be used to identify the changes in vibrational energy of the system.

''Table - Conditions observed to lead to a reactive trajectory for H+HF''
{| class="wikitable"
!
!Distance/pm
!Momentum/ gmol-1.pm.fs-1
|-
|HH
|868.223
|<nowiki>-3.959</nowiki>
|-
|FH
|117.918
|3.751
|}
{| class="wikitable"
|[[File:MTK H+FH CONTOUR.PNG|thumb|Fig -H+FH Contour Plot]]
|[[File:MTK H+FH MOMENTA.PNG|thumb|Fig - H+FH Momenta vs Time Plot]]
|}

==== Translation Vs Vibrational Energy ====
[[File:MTK Last Q.PNG|thumb|Fig- ]]
Graph A and B depict an exothermic reaction with an early transition state. It is observed that translational energy is crucial in helping the system surmount the early energy barrier as, when compared between the two graphs, the initial conditions for A possess far more translational energy than vibrational energy, allowing reaction A to reach completion but not B.

Graph C and D depict an endothermic reaction with a late transition state. It is observed that vibrational energy is crucial in helping the system overcome the late energy barrier as, when compared between the two graphs, the initial conditions for C possess more vibrational energy than translational energy, allowing reaction C to reach completion but not D.

MRD:MT4618

2020-05-15T17:15:55Z

Mt4618: /* Exercise 2. (F-H-H System) */

== Notes ==

=== Exercise 1- (H+H2 System). ===

The '''transition state''' is defined as the ''maximum'' on the '''minimum energy path''' linking reactants and the products. This point on the potential energy surface has the special property that ∂V('''ri''')/∂'''ri'''=0 (the gradient of the potential is zero), and the energy goes down most steeply along the minimum energy path linking reactants and products. Consequently, if one starts a trajectory exactly at the transition state, with no initial momentum, it will remain there forever.

Mathematically, the transition state can be described as the derivative with respect to the reaction coordinate is zero and the maximum can be distinguished from local minima by taking the second derivative wrt the reaction coordinate is negative.

''Table- Initial conditions used to test H+ H2 system''
{| class="wikitable"
!
!Distance (r) [pm]
!Momentum (p) [g.mol-1.pm.fs-1]
|-
|AB
|230
|<nowiki>-5.2</nowiki>
|-
|BC
|74
|0
|}
Hammond's postulate: The structure of the transition state will resemble the reactants or products depending on which are closer in energy. exothermic resembles reactant, endothermic products.

==== Trajectories from r1 = r2: locating the transition state ====
When the atoms are too far apart they are not interacting too much and the forces are small. Start playing with diff. values of AB=BC and look at forces along AB and BC.

Force relates to gradient of slope.

Any point along the diagonal AB=BC line are local minima or saddle points. along the direction orthogonal to the direction of diagonal is the maximum

==== Reactive and Unreactive Trajectories ====
{| 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>-3.1</nowiki>
|<nowiki>-4.1</nowiki>
|
|No
|Alot of intramolecular vibrations observed.

System does not reach
|[[File:MTK Table2.PNG|thumb]]
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-5.1</nowiki>
|
|
|
|[[File:MTK Table3.PNG|thumb]]
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.1</nowiki>
|
|
|
|[[File:MTK Table4.PNG|thumb]]
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.6</nowiki>
|
|
|
|[[File:MTK Table5.PNG|thumb]]
|}

==== Transition State Theory ====
Transition state theory overestimates. It assumes every trajectory that rolls over the transition state will proceed to the product.

=== Exercise 2. (F-H-H System) ===

==== PES Inspection ====
F+H2 is exothermic as it has an early energy barrier. According to Hammond's Postulate, the structure of the transition state is similar to reactants if the reaction is exothermic. The transition state for this reaction was found at rAB=181pm and rBC=74.5pm. The activation energy was calculated to be: -686Jmol-1.
{| class="wikitable"
![[File:MTK F+H2TS.PNG|thumb|Fig - Early "reactant-like" transition state of F+H2 system.]]
!
|}

H+HF is endothermic as it has a late energy barrier. According to Hammond's Postulate, the structure of the transition state is similar to products if the reaction is endothermic. The transition state for this reaction was found at rAB=74.5pm and rBC=181pm. The activation energy was calculated to be: +126.317kJmol-1.

==== Reaction Dynamics ====
''Table - Conditions observed to lead to a reactive trajectory for F+H2''
{| class="wikitable"
!
!Distance/pm
!Momentum/ gmol-1.pm.fs-1
|-
|FH
|1043.074
|<nowiki>-6.944</nowiki>
|-
|HH
|74.216
|<nowiki>-0.254</nowiki>
|}
{| class="wikitable"
|[[File:MTK F+H2 CONTOUR MTK.PNG|thumb|F+H2 contour plot]]
|[[File:MTK F+H2 MOMENTAVSTIME.PNG|thumb|F+H2 Momenta Vs Time Plot]]
|}
From the momenta vs time plot, we can observe that initially the reactants possess a large amount of translational energy and upon reaching the transition state, the energy is converted to vibrational energy. The release of energy from the reaction can be measured experimentally by using calorimetry and infrared spectroscopy. Calorimetry can be used to measure the heat generated by the reaction thus enabling the calculation of change in total translational energy of the system. Infrared spectroscopy can be used to identify the changes in vibrational energy of the system.

''Table - Conditions observed to lead to a reactive trajectory for H+HF''
{| class="wikitable"
!
!Distance/pm
!Momentum/ gmol-1.pm.fs-1
|-
|HH
|868.223
|<nowiki>-3.959</nowiki>
|-
|FH
|117.918
|3.751
|}
{| class="wikitable"
|[[File:MTK H+FH CONTOUR.PNG|thumb|Fig -H+FH Contour Plot]]
|[[File:MTK H+FH MOMENTA.PNG|thumb|Fig - H+FH Momenta vs Time Plot]]
|}

==== Translation Vs Vibrational Energy ====
[[File:MTK Last Q.PNG|thumb|Fig- ]]
Graph A and B depict an exothermic reaction with an early transition state. It is observed that translational energy is crucial in helping the system surmount the early energy barrier as, when compared between the two graphs, the initial conditions for A possess far more translational energy than vibrational energy, allowing reaction A to reach completion but not B.

Graph C and D depict an endothermic reaction with a late transition state. It is observed that vibrational energy is crucial in helping the system overcome the late energy barrier as, when compared between the two graphs, the initial conditions for C possess more vibrational energy than translational energy, allowing reaction C to reach completion but not D.

File:MTK Last Q.PNG

2020-05-15T16:48:43Z

Mt4618:

MRD:MT4618

2020-05-15T16:33:27Z

Mt4618: /* PES Inspection */

== Notes ==

=== Exercise 1- (H+H2 System). ===

The '''transition state''' is defined as the ''maximum'' on the '''minimum energy path''' linking reactants and the products. This point on the potential energy surface has the special property that ∂V('''ri''')/∂'''ri'''=0 (the gradient of the potential is zero), and the energy goes down most steeply along the minimum energy path linking reactants and products. Consequently, if one starts a trajectory exactly at the transition state, with no initial momentum, it will remain there forever.

Mathematically, the derivative with respect to the reaction coordinate is zero and it can be distinguished from local minima by taking the second derivative wrt the reaction coordinate is negative.

''Table- Initial conditions used to test H+ H2 system''
{| class="wikitable"
!
!Distance (r) [pm]
!Momentum (p) [g.mol-1.pm.fs-1]
|-
|AB
|230
|<nowiki>-5.2</nowiki>
|-
|BC
|74
|0
|}
Hammond's postulate: The structure of the transition state will resemble the reactants or products depending on which are closer in energy. exothermic resembles reactant, endothermic products.

==== Trajectories from r1 = r2: locating the transition state ====
When the atoms are too far apart they are not interacting too much and the forces are small. Start playing with diff. values of AB=BC and look at forces along AB and BC.

Force relates to gradient of slope.

Any point along the diagonal AB=BC line are local minima or saddle points. along the direction orthogonal to the direction of diagonal is the maximum

==== Reactive and Unreactive Trajectories ====
{| 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>-3.1</nowiki>
|<nowiki>-4.1</nowiki>
|
|No
|Alot of intramolecular vibrations observed.

System does not reach
|[[File:MTK Table2.PNG|thumb]]
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-5.1</nowiki>
|
|
|
|[[File:MTK Table3.PNG|thumb]]
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.1</nowiki>
|
|
|
|[[File:MTK Table4.PNG|thumb]]
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.6</nowiki>
|
|
|
|[[File:MTK Table5.PNG|thumb]]
|}

=== Exercise 2. (F-H-H System) ===

==== PES Inspection ====
F+H2 is exothermic as it has an early energy barrier. According to Hammond's Postulate, the structure of the transition state is similar to reactants if the reaction is exothermic. The transition state for this reaction was found at rAB=181pm and rBC=74.5pm. The activation energy was calculated to be: -686Jmol-1.
{| class="wikitable"
![[File:MTK F+H2TS.PNG|thumb|Fig - Early "reactant-like" transition state of F+H2 system.]]
!
|}

H+HF is endothermic as it has a late energy barrier. According to Hammond's Postulate, the structure of the transition state is similar to products if the reaction is endothermic. The transition state for this reaction was found at rAB=74.5pm and rBC=181pm. The activation energy was calculated to be: +126.317kJmol-1.

==== Reaction Dynamics ====
''Table - Conditions observed to lead to a reactive trajectory for F+H2''
{| class="wikitable"
!
!Distance/pm
!Momentum/ gmol-1.pm.fs-1
|-
|FH
|1043.074
|<nowiki>-6.944</nowiki>
|-
|HH
|74.216
|<nowiki>-0.254</nowiki>
|}
{| class="wikitable"
|[[File:MTK F+H2 CONTOUR MTK.PNG|thumb|F+H2 contour plot]]
|[[File:MTK F+H2 MOMENTAVSTIME.PNG|thumb|F+H2 Momenta Vs Time Plot]]
|}
From the momenta vs time plot, we can observe that initially the reactants possess a large amount of translational energy and upon reaching the transition state, the energy is converted to vibrational energy. The release of energy from the reaction, which will be in the form of heat from translation energy and infrared radiation from vibrational energy, can be measured experimentally by using calorimetry and infrared spectroscopy. Calorimetry can be used to measure the heat generated by the reaction thus enabling the calculation of change in total translational energy of the system. Infrared spectroscopy can be used to identify the changes in vibrational energy of the system.

''Table - Conditions observed to lead to a reactive trajectory for H+HF''
{| class="wikitable"
!
!Distance/pm
!Momentum/ gmol-1.pm.fs-1
|-
|HH
|868.223
|<nowiki>-3.959</nowiki>
|-
|FH
|117.918
|3.751
|}
{| class="wikitable"
|[[File:MTK H+FH CONTOUR.PNG|thumb|Fig -H+FH Contour Plot]]
|[[File:MTK H+FH MOMENTA.PNG|thumb|Fig - H+FH Momenta vs Time Plot]]
|}

MRD:MT4618

2020-05-15T16:01:54Z

Mt4618: /* PES Inspection */

== Notes ==

=== Exercise 1- (H+H2 System). ===

The '''transition state''' is defined as the ''maximum'' on the '''minimum energy path''' linking reactants and the products. This point on the potential energy surface has the special property that ∂V('''ri''')/∂'''ri'''=0 (the gradient of the potential is zero), and the energy goes down most steeply along the minimum energy path linking reactants and products. Consequently, if one starts a trajectory exactly at the transition state, with no initial momentum, it will remain there forever.

Mathematically, the derivative with respect to the reaction coordinate is zero and it can be distinguished from local minima by taking the second derivative wrt the reaction coordinate is negative.

''Table- Initial conditions used to test H+ H2 system''
{| class="wikitable"
!
!Distance (r) [pm]
!Momentum (p) [g.mol-1.pm.fs-1]
|-
|AB
|230
|<nowiki>-5.2</nowiki>
|-
|BC
|74
|0
|}
Hammond's postulate: The structure of the transition state will resemble the reactants or products depending on which are closer in energy. exothermic resembles reactant, endothermic products.

When the atoms are too far apart they are not interacting too much and the forces are small. Start playing with diff. values of AB=BC and look at forces along AB and BC.

Force relates to gradient of slope.

Any point along the diagonal AB=BC line are local minima or saddle points. along the direction orthogonal to the direction of diagonal is the maximum
{| 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>-3.1</nowiki>
|<nowiki>-4.1</nowiki>
|
|No
|Alot of intramolecular vibrations observed.

System does not reach
|[[File:MTK Table2.PNG|thumb]]
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-5.1</nowiki>
|
|
|
|[[File:MTK Table3.PNG|thumb]]
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.1</nowiki>
|
|
|
|[[File:MTK Table4.PNG|thumb]]
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.6</nowiki>
|
|
|
|[[File:MTK Table5.PNG|thumb]]
|}

=== Exercise 2. (F-H-H System) ===

==== PES Inspection ====
F+H2 is exothermic as it has an early energy barrier. According to Hammond's Postulate, the structure of the transition state is similar to reactants if the reaction is exothermic. The transition state for this reaction was found at rAB=181pm and rBC=74.5pm. The activation energy was calculated to be: -686Jmol-1.
{| class="wikitable"
![[File:MTK F+H2TS.PNG|thumb|Fig - Early "reactant-like" transition state of F+H2 system.]]
!
|}

H+HF is endothermic as it has a late energy barrier. According to Hammond's Postulate, the structure of the transition state is similar to products if the reaction is endothermic. The transition state for this reaction was found at rAB=74.5pm and rBC=181pm. The activation energy was calculated to be: +126.317kJmol-1.

''Table - Conditions observed to lead to a reactive trajectory for F+H2''
{| class="wikitable"
!
!Distance/pm
!Momentum/ gmol-1.pm.fs-1
|-
|FH
|1043.074
|<nowiki>-6.944</nowiki>
|-
|HH
|74.216
|<nowiki>-0.254</nowiki>
|}
{| class="wikitable"
|[[File:MTK F+H2 CONTOUR MTK.PNG|thumb|F+H2 contour plot]]
|[[File:MTK F+H2 MOMENTAVSTIME.PNG|thumb|F+H2 Momenta Vs Time Plot]]
|}
From the momenta vs time plot, we can observe that initially the reactants possess a large amount of translational energy and upon reaching the transition state, the energy is converted to vibrational energy. The release of energy from the reaction, which will be in the form of heat from translation energy and infrared radiation from vibrational energy, can be measured experimentally by using calorimetry and infrared spectroscopy. Calorimetry can be used to measure the heat generated by the reaction thus enabling the calculation of change in total translational energy of the system. Infrared spectroscopy can be used to identify the changes in vibrational energy of the system.

''Table - Conditions observed to lead to a reactive trajectory for H+HF''
{| class="wikitable"
!
!Distance/pm
!Momentum/ gmol-1.pm.fs-1
|-
|HH
|868.223310074558
|<nowiki>-3.958545048056348</nowiki>
|-
|FH
|117.91764973307713
|3.7510662548064637
|}
{| class="wikitable"
|[[File:MTK H+FH CONTOUR.PNG|thumb|Fig -H+FH Contour Plot]]
|[[File:MTK H+FH MOMENTA.PNG|thumb|Fig - H+FH Momenta vs Time Plot]]
|}

MRD:MT4618

2020-05-15T15:14:16Z

Mt4618: /* Exercise 1- (H+H2 System). */

== Notes ==

=== Exercise 1- (H+H2 System). ===

The '''transition state''' is defined as the ''maximum'' on the '''minimum energy path''' linking reactants and the products. This point on the potential energy surface has the special property that ∂V('''ri''')/∂'''ri'''=0 (the gradient of the potential is zero), and the energy goes down most steeply along the minimum energy path linking reactants and products. Consequently, if one starts a trajectory exactly at the transition state, with no initial momentum, it will remain there forever.

Mathematically, the derivative with respect to the reaction coordinate is zero and it can be distinguished from local minima by taking the second derivative wrt the reaction coordinate is negative.

''Table- Initial conditions used to test H+ H2 system''
{| class="wikitable"
!
!Distance (r) [pm]
!Momentum (p) [g.mol-1.pm.fs-1]
|-
|AB
|230
|<nowiki>-5.2</nowiki>
|-
|BC
|74
|0
|}
Hammond's postulate: The structure of the transition state will resemble the reactants or products depending on which are closer in energy. exothermic resembles reactant, endothermic products.

When the atoms are too far apart they are not interacting too much and the forces are small. Start playing with diff. values of AB=BC and look at forces along AB and BC.

Force relates to gradient of slope.

Any point along the diagonal AB=BC line are local minima or saddle points. along the direction orthogonal to the direction of diagonal is the maximum
{| 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>-3.1</nowiki>
|<nowiki>-4.1</nowiki>
|
|No
|Alot of intramolecular vibrations observed.

System does not reach
|[[File:MTK Table2.PNG|thumb]]
|-
|<nowiki>-3.1</nowiki>
|<nowiki>-5.1</nowiki>
|
|
|
|[[File:MTK Table3.PNG|thumb]]
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.1</nowiki>
|
|
|
|[[File:MTK Table4.PNG|thumb]]
|-
|<nowiki>-5.1</nowiki>
|<nowiki>-10.6</nowiki>
|
|
|
|[[File:MTK Table5.PNG|thumb]]
|}

=== Exercise 2. (F-H-H System) ===

==== PES Inspection ====
F+H2 is exothermic as it has an early energy barrier. According to Hammond's Postulate, the structure of the transition state is similar to reactants if the reaction is exothermic. The transition state for this reaction was found at rAB=181pm and rBC=74.5pm. The activation energy was calculated to be: -686Jmol-1.
{| class="wikitable"
![[File:MTK F+H2TS.PNG|thumb|Fig - Early "reactant-like" transition state of F+H2 system.]]
!
|}

H+HF is endothermic as it has a late energy barrier. According to Hammond's Postulate, the structure of the transition state is similar to products if the reaction is endothermic. The transition state for this reaction was found at rAB=74.5pm and rBC=181pm. The activation energy was calculated to be: +126.317kJmol-1.

''Table - Conditions observed to lead to a reactive trajectory for F+H2''
{| class="wikitable"
!
!Distance/pm
!Momentum/ gmol-1.pm.fs-1
|-
|FH
|1043.074
|<nowiki>-6.944</nowiki>
|-
|HH
|74.216
|<nowiki>-0.254</nowiki>
|}
{| class="wikitable"
|[[File:MTK F+H2 CONTOUR MTK.PNG|thumb|F+H2 contour plot]]
|[[File:MTK F+H2 MOMENTAVSTIME.PNG|thumb|F+H2 Momenta Vs Time Plot]]
|}
From the momenta vs time plot, we can observe that initially the reactants possess a large amount of translational energy and upon reaching the transition state, the energy is converted to vibrational energy. The release of energy from the reaction can be measured experimentally by calorimetry.

''Table - Conditions observed to lead to a reactive trajectory for H+HF''
{| class="wikitable"
!
!Distance/pm
!Momentum/ gmol-1.pm.fs-1
|-
|HH
|868.223310074558
|<nowiki>-3.958545048056348</nowiki>
|-
|FH
|117.91764973307713
|3.7510662548064637
|}
{| class="wikitable"
|[[File:MTK H+FH CONTOUR.PNG|thumb|Fig -H+FH Contour Plot]]
|[[File:MTK H+FH MOMENTA.PNG|thumb|Fig - H+FH Momenta vs Time Plot]]
|}

File:MTK H+FH MOMENTA.PNG

2020-05-15T15:00:15Z

Mt4618:

File:MTK H+FH CONTOUR.PNG

2020-05-15T14:59:48Z

Mt4618:

File:MTK F+H2 MOMENTAVSTIME.PNG

2020-05-15T14:51:52Z

Mt4618:

File:MTK F+H2TS.PNG

2020-05-15T14:44:29Z

Mt4618:

File:MTK F+H2 CONTOUR MTK.PNG

2020-05-15T14:43:48Z

Mt4618:

File:MTK Table5.PNG

2020-05-15T14:40:35Z

Mt4618:

File:MTK Table4.PNG

2020-05-15T14:39:41Z

Mt4618:

File:MTK Table3.PNG

2020-05-15T14:37:42Z

Mt4618:

File:MTK Table2.PNG

2020-05-15T14:35:33Z

Mt4618:

File:Table3 MTK.PNG

2020-05-15T14:18:45Z

Mt4618:

File:Table2 MTK.PNG

2020-05-15T14:18:13Z

Mt4618:

MRD:MT4618

2020-05-15T14:16:28Z

Mt4618: /* Exercise 1- (H+H2 System). */

MRD:MT4618

2020-05-15T14:04:50Z

Mt4618: /* Exercise 2. (F-H-H System) */

MRD:MT4618

2020-05-15T13:46:57Z

Mt4618: /* Exercise 2. (F-H-H System) */

MRD:MT4618

2020-05-15T12:30:06Z

Mt4618: /* Exercise 2. (F-H-H System) */

== Notes ==

=== Exercise 1- (H+H2 System). ===
Maximum, derivative with respect to rsn coordinate is zero. derivative wrt rxn coordinate is negative.

Hammond's postulate: The structure of the transition state will resemble the reactants or products depending on which are closer in energy. exothermic resembles reactant, endothermic products.

When the atoms are too far apart they are not interacting too much and the forces are small. Start playing with diff. values of AB=BC and look at forces along AB and BC.

Force relates to gradient of slope.

Any point along the diagonal AB=BC line are local minima or saddle points. along the direction orthogonal to the direction of diagonal is the maximum

=== Exercise 2. (F-H-H System) ===
F+H2 is exothermic as it has an early energy barrier. According to Hammond's Postulate, the structure of the transition state is similar to reactants if the reaction is exothermic. The transition state for this reaction was found at rAB=181pm and rBC=74.5pm. The activation energy was calculated to be: -686Jmol-1.

H+HF is endothermic as it has a late energy barrier. According to Hammond's Postulate, the structure of the transition state is similar to products if the reaction is endothermic. The transition state for this reaction was found at rAB=74.5pm and rBC=181pm. The activation energy was calculated to be: +126.317kJmol-1.

MRD:MT4618

2020-05-15T12:25:40Z

Mt4618: /* Exercise 2. (F-H-H System) */

== Notes ==

=== Exercise 1- (H+H2 System). ===
Maximum, derivative with respect to rsn coordinate is zero. derivative wrt rxn coordinate is negative.

Hammond's postulate: The structure of the transition state will resemble the reactants or products depending on which are closer in energy. exothermic resembles reactant, endothermic products.

When the atoms are too far apart they are not interacting too much and the forces are small. Start playing with diff. values of AB=BC and look at forces along AB and BC.

Force relates to gradient of slope.

Any point along the diagonal AB=BC line are local minima or saddle points. along the direction orthogonal to the direction of diagonal is the maximum

=== Exercise 2. (F-H-H System) ===
F+H2 is exothermic as it has an early energy barrier. According to Hammond's Postulate, the structure of the transition state is similar to reactants if the reaction is exothermic. The transition state for this reaction was found at rAB=181pm and rBC=74.5pm.

H+HF is endothermic as it has a late energy barrier. According to Hammond's Postulate, the structure of the transition state is similar to products if the reaction is endothermic. The transition state for this reaction was found at rAB=74.5pm and rBC=181pm.

MRD:MT4618

2020-05-15T11:14:27Z

Mt4618: /* Exercise 1- (H+H2 System). */

MRD:MT4618

2020-05-14T11:08:14Z

Mt4618: /* Identifying TS on potential energy surface diagram. */

MRD:MT4618

2020-05-12T14:33:55Z

Mt4618:

== Notes ==

=== Identifying TS on potential energy surface diagram. ===
Maximum, derivative with respect to rsn coordinate is zero. derivative wrt rxn coordinate is negative.

Hammond's postulate: The structure of the transition state will resemble the reactants or products depending on which are closer in energy. exothermic resembles reactant, endothermic products.

When the atoms are too far apart they are not interacting too much and the forces are small. Start playing with diff. values of AB=BC and look at forces along AB and BC.

Force relates to gradient of slope.

Any point along the diagonal AB=BC line are local minima or saddle points. along the direction orthogonal to the direction of diagonal is the maximum

MRD:MT4618

2020-05-12T12:06:12Z

Mt4618: Created page with "Identifying TS on potential energy surface diagram. Maximum, derivative with respect to rsn coordinate is zero. derivative wrt rxn coordinate is negative."

Identifying TS on potential energy surface diagram.
Maximum, derivative with respect to rsn coordinate is zero. derivative wrt rxn coordinate is negative.

Rep:Mod:Mt4618

2019-03-22T17:19:36Z

Mt4618:

== NH3 ==
=== Optimisation ===
<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MTK_NH3_OPTF_POP2.LOG</uploadedFileContents>
<script>frame x.y</script>
</jmolApplet></jmol>

Calculation Method: RB3LYP

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

E(RB3LYP): -56.55776873 a.u.

RMS Gradient Norm: 0.00000485 a.u.

Point Group: C3V

Optimised N-H bond length: 1.02 A

Optimised H-N-H bond angle: 106o

<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>
[[File: MTK_NH3_OPTF_POP2.LOG]]

=== Vibration and Charges ===
==== Vibrations ====
[[File:Screenshot.png|thumb|Vibration Modes of an optimised NH3 molecule]]
{| class="wikitable" border="1"
|+ Vibrations
! No. !! Wavenumber / cm-1 !! Symmetry !! Intensity
|-
| 1 || 1090 || A1 || 145
|-
| 2 || 1694 || E || 14
|-
| 3 || 1694 || E || 14
|-
| 4 || 3461 || A1 || 1
|-
| 5 || 3590 || E || 0
|-
| 6 || 3590 || E || 0
|}

Number of modes expected from 3N-6 rule: 6

Degenerate modes: 2&3 and 5&6

Bending vibration modes: 1,2,3

Stretching vibration modes: 4,5,6

Highly symmetric mode: 4

"Umbrella" mode: 1

No. of bands expected in gaseous spectrum: 2 (4 out of 6 modes are degenerate and 3 out of 6 are ~ 0 intensity)

==== Charges ====
[[File:Charge_NH3.PNG|center|thumb|Charges on an optimised NH3 molecule]]

A negative charge is expected on the nitrogen atom as it is more electronegative than hydrogen.

----

== N2 ==
=== Optimisation ===

<jmol><jmolApplet>
<title>An optimised N2 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MTK_N2_OPTF_POP.LOG</uploadedFileContents>
<script>frame x.y</script>
</jmolApplet></jmol>

Calculation Method: RB3LYP

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

E(RB3LYP): -109.52412868 a.u.

RMS Gradient Norm: 0.00000060 a.u.

Point Group: D*H

Optimised bond length: 1.11 A

Optimised bond angle: 180o

<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>

[[File:MTK_N2_OPTF_POP.LOG]]

=== Vibration and Charges ===
==== Vibrations ====
[[File:N2_vibration.PNG|thumb|Vibration Modes of an optimised N2 molecule]]
{| class="wikitable" border="1"
|+ Vibrations
! No. !! Wavenumber / cm-1 !! Symmetry !! Intensity
|-
| 1 || 2457 || SGG || 0
|}

Number of modes expected from 3N-5 rule: 1

Number of bending vibration modes: 0

Number of stretching vibration modes: 1

No. of bands expected in gaseous spectrum: 0 (vibration does not produce any change in dipole moment)

==== Charges ====
Charge is evenly distributed across N2 as there is no difference in electronegativity.
----

== H2 ==
=== Optimisation ===

<jmol><jmolApplet>
<title>An optimised H2 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MTK_H2_OPTF_POP.LOG</uploadedFileContents>
<script>frame x.y</script>
</jmolApplet></jmol>

Calculation Method: RB3LYP

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

E(RB3LYP): -1.17853936 a.u.

RMS Gradient Norm: 0.00000017 a.u.

Point Group: D*H

Optimised bond length: 0.74 A

Optimised bond angle: 180o

<pre>
Item Value Threshold Converged?

Maximum Force 0.000000 0.000450 YES

RMS Force 0.000000 0.000300 YES

Maximum Displacement 0.000000 0.001800 YES

RMS Displacement 0.000001 0.001200 YES

</pre>

[[File:MTK_H2_OPTF_POP.LOG]]

=== Vibration and Charges ===
==== Vibrations ====
[[File:H2_vibration.PNG|thumb|Vibration Modes of an optimised H2 molecule]]
{| class="wikitable" border="1"
|+ Vibrations
! No. !! Wavenumber / cm-1 !! Symmetry !! Intensity
|-
| 1 || 4466 || SGG || 0
|}

Number of modes expected from 3N-5 rule: 1

Number of bending vibration modes: 0

Number of stretching vibration modes: 1

No. of bands expected in gaseous spectrum: 0 (vibration does not produce any change in dipole moment)

==== Charges ====
Charge is evenly distributed across H2 as there is no difference in electronegativity.

== Transition metal complex ==
Unique Identifier: BOWVUG [https://www.ccdc.cam.ac.uk/structures/Search?Ccdcid=BOWVUG&DatabaseToSearch=Published]

N-N bond distance in complex: 1.13 A

N-N bond distance in optimised molecule: 1.11 A

The N-N bond distance in complex is greater than that in the optimised molecule because electron density is pulled away from N2 when it binds to Mo resulting in weaker N-N bonding in the complex.

== Haber 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.

ΔE=2*E(NH3)-[E(N2)+3*E(H2)]= -146.8 kJ/mol

The reaction is exothermic therefore, ammonia must be below the reactants in an energy profile diagram. So, ammonia is more stable.

== HCN ==
=== Optimisation ===

<jmol><jmolApplet>
<title>An optimised HCN molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MTK_HCN_OPTF_POP.LOG</uploadedFileContents>
<script>frame x.y</script>
</jmolApplet></jmol>

Calculation Method: RB3LYP

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

E(RB3LYP): -93.42458132 a.u.

RMS Gradient Norm: 0.00017006 a.u.

Point Group: C*V

Optimised bond length: 1.11 A

Optimised bond angle: 180o

<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>

[[File:MTK_HCN_OPTF_POP.LOG]]

=== Vibration and Charges ===
==== Vibrations ====
{| class="wikitable" border="1"
|+ Vibrations
! No. !! Wavenumber / cm-1 !! Symmetry !! Intensity
|-
| 1 || 766.74 || PI || 35.2959
|-
| 1 || 766.74 || PI || 35.2959
|-
| 1 || 2214.74 || SG || 2.0451
|-
| 1 || 3479.93 || SG || 57.3217
|}

Number of modes expected from 3N-5 rule: 4

Number of bending vibration modes: 2

Number of stretching vibration modes: 2

No. of bands expected in gaseous spectrum: 3 (vibrations 1&2 degenerate)

==== Charges ====
[[File:HCN_charges1.PNG|center|thumb|Charges on an optimised NH3 molecule]]

N being more electronegative than H and C, a negative charge is expected on N in HCN and positive charges are expected on H and C.

=== Molecular Orbitals ===
==== Molecular orbital 8 ====
[[File:MTK_MO8.PNG|200px|thumb|MO8|200px]]

Antibonding/bonding: Antibonding

Occupancy: Unoccupied

Contributing AOs: 3px of N, 3px of C

Energy: 0.01929 a.u.

MO8 is the LUMO of HCN. Sideways antiphase overlap of 3px orbitals of N and C makes it the 1π* orbital of HCN.

----

==== Molecular Orbital 7 ====
[[File:MTK_MO7.PNG|thumb|MO7|right|200px]]

Antibonding/bonding: Bonding

Occupancy: Occupied

Contributing AOs: 2py of N, 2py of C

Energy: -0.35939 a.u.

MO7 is the HOMO of HCN. Sideways overlap of 3py orbitals of N and C makes it the 2π orbital of HCN. It is degenerate with MO6 and together with it, they contribute to the triple bond in HCN.

----

==== Molecular Orbital 6 ====
[[File:MO6.PNG|thumb|MO6|right|200px]]

Antibonding/bonding: Bonding

Occupancy: Occupied

Contributing AOs: 2px of N, 2px of C

Energy: -0.35939 a.u.

MO6 is the HOMO of HCN. Sideways overlap of 3px orbitals of N and C makes it the 1π orbital of HCN. It is degenerate with MO7 and together with it, they contribute to the triple bond in HCN.
----

==== Molecular Orbital 5 ====
[[File:MTK_MO5.PNG|thumb|MO5|right|200px]]

Antibonding/bonding: Antibonding

Occupancy: Occupied

Contributing AOs: 2pz of N, 3s of N, 2pz of C, 3s of N, 1s of H

Energy: -0.38064 a.u.

MO5 is the 3σ* orbital of HCN. From N, roughly 51% of electron density comes from 2pz while 45% comes from 3s. By contrast, 24% comes from 2pz and 13% from 1s in H.

----

==== Molecular Orbital 1 ====
[[File:MTK_MO1.PNG|thumb|MO7|right|200px]]

Antibonding/bonding: Bonding

Occupancy: Occupied

Contributing AOs: 1s of N, 1s of C

Energy: -0.38064 a.u.

MO1 is the lowest energy 1σ orbital of HCN. It does not participate in chemical reactions.

----
=== Variations in CN bond length in HCN(Independence) ===
Optimised CN bond length in HCN= 1.146 A

Experimental CN bond length = 1.156 A[[https://cccbdb.nist.gov/exp2x.asp?casno=74908| Experimental Data for HCN]]

The experimentally measured CN bond length differs from the optimised CN bond length as the latter is the result of an optimisation calculation.

Rep:Mod:Mt4618

2019-03-22T17:01:32Z

Mt4618: /* Molecular Orbital 5 */

Rep:Mod:Mt4618

2019-03-22T16:51:47Z

Mt4618: /* Molecular Orbital 5 */

== NH3 ==
=== Optimisation ===
<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MTK_NH3_OPTF_POP2.LOG</uploadedFileContents>
<script>frame x.y</script>
</jmolApplet></jmol>

Calculation Method: RB3LYP

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

E(RB3LYP): -56.55776873 a.u.

RMS Gradient Norm: 0.00000485 a.u.

Point Group: C3V

Optimised N-H bond length: 1.02 A

Optimised H-N-H bond angle: 106o

<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>
[[File: MTK_NH3_OPTF_POP2.LOG]]

=== Vibration and Charges ===
==== Vibrations ====
[[File:Screenshot.png|thumb|Vibration Modes of an optimised NH3 molecule]]
{| class="wikitable" border="1"
|+ Vibrations
! No. !! Wavenumber / cm-1 !! Symmetry !! Intensity
|-
| 1 || 1090 || A1 || 145
|-
| 2 || 1694 || E || 14
|-
| 3 || 1694 || E || 14
|-
| 4 || 3461 || A1 || 1
|-
| 5 || 3590 || E || 0
|-
| 6 || 3590 || E || 0
|}

Number of modes expected from 3N-6 rule: 6

Degenerate modes: 2&3 and 5&6

Bending vibration modes: 1,2,3

Stretching vibration modes: 4,5,6

Highly symmetric mode: 4

"Umbrella" mode: 1

No. of bands expected in gaseous spectrum: 2 (4 out of 6 modes are degenerate and 3 out of 6 are ~ 0 intensity)

==== Charges ====
[[File:Charge_NH3.PNG|center|thumb|Charges on an optimised NH3 molecule]]

A negative charge is expected on the nitrogen atom as it is more electronegative than hydrogen.

----

== N2 ==
=== Optimisation ===

<jmol><jmolApplet>
<title>An optimised N2 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MTK_N2_OPTF_POP.LOG</uploadedFileContents>
<script>frame x.y</script>
</jmolApplet></jmol>

Calculation Method: RB3LYP

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

E(RB3LYP): -109.52412868 a.u.

RMS Gradient Norm: 0.00000060 a.u.

Point Group: D*H

Optimised bond length: 1.11 A

Optimised bond angle: 180o

<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>

[[File:MTK_N2_OPTF_POP.LOG]]

=== Vibration and Charges ===
==== Vibrations ====
[[File:N2_vibration.PNG|thumb|Vibration Modes of an optimised N2 molecule]]
{| class="wikitable" border="1"
|+ Vibrations
! No. !! Wavenumber / cm-1 !! Symmetry !! Intensity
|-
| 1 || 2457 || SGG || 0
|}

Number of modes expected from 3N-5 rule: 1

Number of bending vibration modes: 0

Number of stretching vibration modes: 1

No. of bands expected in gaseous spectrum: 0 (vibration does not produce any change in dipole moment)

==== Charges ====
Charge is evenly distributed across N2 as there is no difference in electronegativity.
----

== H2 ==
=== Optimisation ===

<jmol><jmolApplet>
<title>An optimised H2 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MTK_H2_OPTF_POP.LOG</uploadedFileContents>
<script>frame x.y</script>
</jmolApplet></jmol>

Calculation Method: RB3LYP

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

E(RB3LYP): -1.17853936 a.u.

RMS Gradient Norm: 0.00000017 a.u.

Point Group: D*H

Optimised bond length: 0.74 A

Optimised bond angle: 180o

<pre>
Item Value Threshold Converged?

Maximum Force 0.000000 0.000450 YES

RMS Force 0.000000 0.000300 YES

Maximum Displacement 0.000000 0.001800 YES

RMS Displacement 0.000001 0.001200 YES

</pre>

[[File:MTK_H2_OPTF_POP.LOG]]

=== Vibration and Charges ===
==== Vibrations ====
[[File:H2_vibration.PNG|thumb|Vibration Modes of an optimised H2 molecule]]
{| class="wikitable" border="1"
|+ Vibrations
! No. !! Wavenumber / cm-1 !! Symmetry !! Intensity
|-
| 1 || 4466 || SGG || 0
|}

Number of modes expected from 3N-5 rule: 1

Number of bending vibration modes: 0

Number of stretching vibration modes: 1

No. of bands expected in gaseous spectrum: 0 (vibration does not produce any change in dipole moment)

==== Charges ====
Charge is evenly distributed across H2 as there is no difference in electronegativity.

== Transition metal complex ==
Unique Identifier: BOWVUG [https://www.ccdc.cam.ac.uk/structures/Search?Ccdcid=BOWVUG&DatabaseToSearch=Published]

N-N bond distance in complex: 1.13 A

N-N bond distance in optimised molecule: 1.11 A

The N-N bond distance in complex is greater than that in the optimised molecule because electron density is pulled away from N2 when it binds to Mo resulting in weaker N-N bonding in the complex.

== Haber 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.

ΔE=2*E(NH3)-[E(N2)+3*E(H2)]= -146.8 kJ/mol

The reaction is exothermic therefore, ammonia must be below the reactants in an energy profile diagram. So, ammonia is more stable.

== HCN ==
=== Optimisation ===

<jmol><jmolApplet>
<title>An optimised HCN molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MTK_HCN_OPTF_POP.LOG</uploadedFileContents>
<script>frame x.y</script>
</jmolApplet></jmol>

Calculation Method: RB3LYP

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

E(RB3LYP): -93.42458132 a.u.

RMS Gradient Norm: 0.00017006 a.u.

Point Group: C*V

Optimised bond length: 1.11 A

Optimised bond angle: 180o

<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>

[[File:MTK_HCN_OPTF_POP.LOG]]

=== Vibration and Charges ===
==== Vibrations ====
{| class="wikitable" border="1"
|+ Vibrations
! No. !! Wavenumber / cm-1 !! Symmetry !! Intensity
|-
| 1 || 766.74 || PI || 35.2959
|-
| 1 || 766.74 || PI || 35.2959
|-
| 1 || 2214.74 || SG || 2.0451
|-
| 1 || 3479.93 || SG || 57.3217
|}

Number of modes expected from 3N-5 rule: 4

Number of bending vibration modes: 2

Number of stretching vibration modes: 2

No. of bands expected in gaseous spectrum: 3 (vibrations 1&2 degenerate)

==== Charges ====
[[File:HCN_charges1.PNG|center|thumb|Charges on an optimised NH3 molecule]]

N being more electronegative than H and C, a negative charge is expected on N in HCN and positive charges are expected on H and C.

=== Molecular Orbitals ===
==== Molecular orbital 8 ====
[[File:MTK_MO8.PNG|200px|thumb|MO8|200px]]

Antibonding/bonding: Antibonding

Occupancy: Unoccupied

Contributing AOs: 3px of N, 3px of C

Energy: 0.01929 a.u.

MO8 is the LUMO of HCN. Sideways antiphase overlap of 3px orbitals of N and C makes it the 1π* orbital of HCN.

----

==== Molecular Orbital 7 ====
[[File:MTK_MO7.PNG|thumb|MO7|right|200px]]

Antibonding/bonding: Bonding

Occupancy: Occupied

Contributing AOs: 2py of N, 2py of C

Energy: -0.35939 a.u.

MO7 is the HOMO of HCN. Sideways overlap of 3py orbitals of N and C makes it the 2π orbital of HCN. It is degenerate with MO6 and together with it, they contribute to the triple bond in HCN.

----

==== Molecular Orbital 6 ====
[[File:MO6.PNG|thumb|MO6|right|200px]]

Antibonding/bonding: Bonding

Occupancy: Occupied

Contributing AOs: 2px of N, 2px of C

Energy: -0.35939 a.u.

MO6 is the HOMO of HCN. Sideways overlap of 3px orbitals of N and C makes it the 1π orbital of HCN. It is degenerate with MO7 and together with it, they contribute to the triple bond in HCN.
----

==== Molecular Orbital 5 ====
[[File:MTK_MO5.PNG|thumb|MO5|right|200px]]

Antibonding/bonding: Antibonding

Occupancy: Occupied

Contributing AOs: 2pz of N, 3s of N, 2pz of C, 3s of N, 1s of H

Energy: -0.38064 a.u.

MO5 is the 3σ* orbital of HCN.

----

==== Molecular Orbital 1 ====
[[File:MTK_MO1.PNG|thumb|MO7|right|200px]]

Antibonding/bonding: Bonding

Occupancy: Occupied

Contributing AOs: 1s of N, 1s of C

Energy: -0.38064 a.u.

MO1 is the lowest energy 1σ orbital of HCN. It does not participate in chemical reactions.

----

Rep:Mod:Mt4618

2019-03-22T16:43:57Z

Mt4618: /* MO1 */

== NH3 ==
=== Optimisation ===
<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MTK_NH3_OPTF_POP2.LOG</uploadedFileContents>
<script>frame x.y</script>
</jmolApplet></jmol>

Calculation Method: RB3LYP

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

E(RB3LYP): -56.55776873 a.u.

RMS Gradient Norm: 0.00000485 a.u.

Point Group: C3V

Optimised N-H bond length: 1.02 A

Optimised H-N-H bond angle: 106o

<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>
[[File: MTK_NH3_OPTF_POP2.LOG]]

=== Vibration and Charges ===
==== Vibrations ====
[[File:Screenshot.png|thumb|Vibration Modes of an optimised NH3 molecule]]
{| class="wikitable" border="1"
|+ Vibrations
! No. !! Wavenumber / cm-1 !! Symmetry !! Intensity
|-
| 1 || 1090 || A1 || 145
|-
| 2 || 1694 || E || 14
|-
| 3 || 1694 || E || 14
|-
| 4 || 3461 || A1 || 1
|-
| 5 || 3590 || E || 0
|-
| 6 || 3590 || E || 0
|}

Number of modes expected from 3N-6 rule: 6

Degenerate modes: 2&3 and 5&6

Bending vibration modes: 1,2,3

Stretching vibration modes: 4,5,6

Highly symmetric mode: 4

"Umbrella" mode: 1

No. of bands expected in gaseous spectrum: 2 (4 out of 6 modes are degenerate and 3 out of 6 are ~ 0 intensity)

==== Charges ====
[[File:Charge_NH3.PNG|center|thumb|Charges on an optimised NH3 molecule]]

A negative charge is expected on the nitrogen atom as it is more electronegative than hydrogen.

----

== N2 ==
=== Optimisation ===

<jmol><jmolApplet>
<title>An optimised N2 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MTK_N2_OPTF_POP.LOG</uploadedFileContents>
<script>frame x.y</script>
</jmolApplet></jmol>

Calculation Method: RB3LYP

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

E(RB3LYP): -109.52412868 a.u.

RMS Gradient Norm: 0.00000060 a.u.

Point Group: D*H

Optimised bond length: 1.11 A

Optimised bond angle: 180o

<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>

[[File:MTK_N2_OPTF_POP.LOG]]

=== Vibration and Charges ===
==== Vibrations ====
[[File:N2_vibration.PNG|thumb|Vibration Modes of an optimised N2 molecule]]
{| class="wikitable" border="1"
|+ Vibrations
! No. !! Wavenumber / cm-1 !! Symmetry !! Intensity
|-
| 1 || 2457 || SGG || 0
|}

Number of modes expected from 3N-5 rule: 1

Number of bending vibration modes: 0

Number of stretching vibration modes: 1

No. of bands expected in gaseous spectrum: 0 (vibration does not produce any change in dipole moment)

==== Charges ====
Charge is evenly distributed across N2 as there is no difference in electronegativity.
----

== H2 ==
=== Optimisation ===

<jmol><jmolApplet>
<title>An optimised H2 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MTK_H2_OPTF_POP.LOG</uploadedFileContents>
<script>frame x.y</script>
</jmolApplet></jmol>

Calculation Method: RB3LYP

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

E(RB3LYP): -1.17853936 a.u.

RMS Gradient Norm: 0.00000017 a.u.

Point Group: D*H

Optimised bond length: 0.74 A

Optimised bond angle: 180o

<pre>
Item Value Threshold Converged?

Maximum Force 0.000000 0.000450 YES

RMS Force 0.000000 0.000300 YES

Maximum Displacement 0.000000 0.001800 YES

RMS Displacement 0.000001 0.001200 YES

</pre>

[[File:MTK_H2_OPTF_POP.LOG]]

=== Vibration and Charges ===
==== Vibrations ====
[[File:H2_vibration.PNG|thumb|Vibration Modes of an optimised H2 molecule]]
{| class="wikitable" border="1"
|+ Vibrations
! No. !! Wavenumber / cm-1 !! Symmetry !! Intensity
|-
| 1 || 4466 || SGG || 0
|}

Number of modes expected from 3N-5 rule: 1

Number of bending vibration modes: 0

Number of stretching vibration modes: 1

No. of bands expected in gaseous spectrum: 0 (vibration does not produce any change in dipole moment)

==== Charges ====
Charge is evenly distributed across H2 as there is no difference in electronegativity.

== Transition metal complex ==
Unique Identifier: BOWVUG [https://www.ccdc.cam.ac.uk/structures/Search?Ccdcid=BOWVUG&DatabaseToSearch=Published]

N-N bond distance in complex: 1.13 A

N-N bond distance in optimised molecule: 1.11 A

The N-N bond distance in complex is greater than that in the optimised molecule because electron density is pulled away from N2 when it binds to Mo resulting in weaker N-N bonding in the complex.

== Haber 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.

ΔE=2*E(NH3)-[E(N2)+3*E(H2)]= -146.8 kJ/mol

The reaction is exothermic therefore, ammonia must be below the reactants in an energy profile diagram. So, ammonia is more stable.

== HCN ==
=== Optimisation ===

<jmol><jmolApplet>
<title>An optimised HCN molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MTK_HCN_OPTF_POP.LOG</uploadedFileContents>
<script>frame x.y</script>
</jmolApplet></jmol>

Calculation Method: RB3LYP

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

E(RB3LYP): -93.42458132 a.u.

RMS Gradient Norm: 0.00017006 a.u.

Point Group: C*V

Optimised bond length: 1.11 A

Optimised bond angle: 180o

<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>

[[File:MTK_HCN_OPTF_POP.LOG]]

=== Vibration and Charges ===
==== Vibrations ====
{| class="wikitable" border="1"
|+ Vibrations
! No. !! Wavenumber / cm-1 !! Symmetry !! Intensity
|-
| 1 || 766.74 || PI || 35.2959
|-
| 1 || 766.74 || PI || 35.2959
|-
| 1 || 2214.74 || SG || 2.0451
|-
| 1 || 3479.93 || SG || 57.3217
|}

Number of modes expected from 3N-5 rule: 4

Number of bending vibration modes: 2

Number of stretching vibration modes: 2

No. of bands expected in gaseous spectrum: 3 (vibrations 1&2 degenerate)

==== Charges ====
[[File:HCN_charges1.PNG|center|thumb|Charges on an optimised NH3 molecule]]

N being more electronegative than H and C, a negative charge is expected on N in HCN and positive charges are expected on H and C.

=== Molecular Orbitals ===
==== Molecular orbital 8 ====
[[File:MTK_MO8.PNG|200px|thumb|MO8|200px]]

Antibonding/bonding: Antibonding

Occupancy: Unoccupied

Contributing AOs: 3px of N, 3px of C

Energy: 0.01929 a.u.

MO8 is the LUMO of HCN. Sideways antiphase overlap of 3px orbitals of N and C makes it the 1π* orbital of HCN.

----

==== Molecular Orbital 7 ====
[[File:MTK_MO7.PNG|thumb|MO7|right|200px]]

Antibonding/bonding: Bonding

Occupancy: Occupied

Contributing AOs: 2py of N, 2py of C

Energy: -0.35939 a.u.

MO7 is the HOMO of HCN. Sideways overlap of 3py orbitals of N and C makes it the 2π orbital of HCN. It is degenerate with MO6 and together with it, they contribute to the triple bond in HCN.

----

==== Molecular Orbital 6 ====
[[File:MO6.PNG|thumb|MO6|right|200px]]

Antibonding/bonding: Bonding

Occupancy: Occupied

Contributing AOs: 2px of N, 2px of C

Energy: -0.35939 a.u.

MO6 is the HOMO of HCN. Sideways overlap of 3px orbitals of N and C makes it the 1π orbital of HCN. It is degenerate with MO7 and together with it, they contribute to the triple bond in HCN.
----

==== Molecular Orbital 5 ====
[[File:MTK_MO5.PNG|thumb|MO5|right|200px]]

Antibonding/bonding: Antibonding

Occupancy: Occupied

Contributing AOs: 2pz of N, 3s of N, 2pz of C, 3s of N, 1s of H

Energy: -0.38064 a.u.

MO5 is the 3σ* orbital of HCN.

----

==== Molecular Orbital 1 ====
[[File:MTK_MO1.PNG|thumb|MO7|right|200px]]

Antibonding/bonding: Bonding

Occupancy: Occupied

Contributing AOs: 1s of N, 1s of C

Energy: -0.38064 a.u.

MO1 is the lowest energy 1σ orbital of HCN. It does not participate in chemical reactions.

----

Rep:Mod:Mt4618

2019-03-22T16:43:47Z

Mt4618: /* MO5 */

== NH3 ==
=== Optimisation ===
<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MTK_NH3_OPTF_POP2.LOG</uploadedFileContents>
<script>frame x.y</script>
</jmolApplet></jmol>

Calculation Method: RB3LYP

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

E(RB3LYP): -56.55776873 a.u.

RMS Gradient Norm: 0.00000485 a.u.

Point Group: C3V

Optimised N-H bond length: 1.02 A

Optimised H-N-H bond angle: 106o

<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>
[[File: MTK_NH3_OPTF_POP2.LOG]]

=== Vibration and Charges ===
==== Vibrations ====
[[File:Screenshot.png|thumb|Vibration Modes of an optimised NH3 molecule]]
{| class="wikitable" border="1"
|+ Vibrations
! No. !! Wavenumber / cm-1 !! Symmetry !! Intensity
|-
| 1 || 1090 || A1 || 145
|-
| 2 || 1694 || E || 14
|-
| 3 || 1694 || E || 14
|-
| 4 || 3461 || A1 || 1
|-
| 5 || 3590 || E || 0
|-
| 6 || 3590 || E || 0
|}

Number of modes expected from 3N-6 rule: 6

Degenerate modes: 2&3 and 5&6

Bending vibration modes: 1,2,3

Stretching vibration modes: 4,5,6

Highly symmetric mode: 4

"Umbrella" mode: 1

No. of bands expected in gaseous spectrum: 2 (4 out of 6 modes are degenerate and 3 out of 6 are ~ 0 intensity)

==== Charges ====
[[File:Charge_NH3.PNG|center|thumb|Charges on an optimised NH3 molecule]]

A negative charge is expected on the nitrogen atom as it is more electronegative than hydrogen.

----

== N2 ==
=== Optimisation ===

<jmol><jmolApplet>
<title>An optimised N2 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MTK_N2_OPTF_POP.LOG</uploadedFileContents>
<script>frame x.y</script>
</jmolApplet></jmol>

Calculation Method: RB3LYP

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

E(RB3LYP): -109.52412868 a.u.

RMS Gradient Norm: 0.00000060 a.u.

Point Group: D*H

Optimised bond length: 1.11 A

Optimised bond angle: 180o

<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>

[[File:MTK_N2_OPTF_POP.LOG]]

=== Vibration and Charges ===
==== Vibrations ====
[[File:N2_vibration.PNG|thumb|Vibration Modes of an optimised N2 molecule]]
{| class="wikitable" border="1"
|+ Vibrations
! No. !! Wavenumber / cm-1 !! Symmetry !! Intensity
|-
| 1 || 2457 || SGG || 0
|}

Number of modes expected from 3N-5 rule: 1

Number of bending vibration modes: 0

Number of stretching vibration modes: 1

No. of bands expected in gaseous spectrum: 0 (vibration does not produce any change in dipole moment)

==== Charges ====
Charge is evenly distributed across N2 as there is no difference in electronegativity.
----

== H2 ==
=== Optimisation ===

<jmol><jmolApplet>
<title>An optimised H2 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MTK_H2_OPTF_POP.LOG</uploadedFileContents>
<script>frame x.y</script>
</jmolApplet></jmol>

Calculation Method: RB3LYP

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

E(RB3LYP): -1.17853936 a.u.

RMS Gradient Norm: 0.00000017 a.u.

Point Group: D*H

Optimised bond length: 0.74 A

Optimised bond angle: 180o

<pre>
Item Value Threshold Converged?

Maximum Force 0.000000 0.000450 YES

RMS Force 0.000000 0.000300 YES

Maximum Displacement 0.000000 0.001800 YES

RMS Displacement 0.000001 0.001200 YES

</pre>

[[File:MTK_H2_OPTF_POP.LOG]]

=== Vibration and Charges ===
==== Vibrations ====
[[File:H2_vibration.PNG|thumb|Vibration Modes of an optimised H2 molecule]]
{| class="wikitable" border="1"
|+ Vibrations
! No. !! Wavenumber / cm-1 !! Symmetry !! Intensity
|-
| 1 || 4466 || SGG || 0
|}

Number of modes expected from 3N-5 rule: 1

Number of bending vibration modes: 0

Number of stretching vibration modes: 1

No. of bands expected in gaseous spectrum: 0 (vibration does not produce any change in dipole moment)

==== Charges ====
Charge is evenly distributed across H2 as there is no difference in electronegativity.

== Transition metal complex ==
Unique Identifier: BOWVUG [https://www.ccdc.cam.ac.uk/structures/Search?Ccdcid=BOWVUG&DatabaseToSearch=Published]

N-N bond distance in complex: 1.13 A

N-N bond distance in optimised molecule: 1.11 A

The N-N bond distance in complex is greater than that in the optimised molecule because electron density is pulled away from N2 when it binds to Mo resulting in weaker N-N bonding in the complex.

== Haber 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.

ΔE=2*E(NH3)-[E(N2)+3*E(H2)]= -146.8 kJ/mol

The reaction is exothermic therefore, ammonia must be below the reactants in an energy profile diagram. So, ammonia is more stable.

== HCN ==
=== Optimisation ===

<jmol><jmolApplet>
<title>An optimised HCN molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MTK_HCN_OPTF_POP.LOG</uploadedFileContents>
<script>frame x.y</script>
</jmolApplet></jmol>

Calculation Method: RB3LYP

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

E(RB3LYP): -93.42458132 a.u.

RMS Gradient Norm: 0.00017006 a.u.

Point Group: C*V

Optimised bond length: 1.11 A

Optimised bond angle: 180o

<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>

[[File:MTK_HCN_OPTF_POP.LOG]]

=== Vibration and Charges ===
==== Vibrations ====
{| class="wikitable" border="1"
|+ Vibrations
! No. !! Wavenumber / cm-1 !! Symmetry !! Intensity
|-
| 1 || 766.74 || PI || 35.2959
|-
| 1 || 766.74 || PI || 35.2959
|-
| 1 || 2214.74 || SG || 2.0451
|-
| 1 || 3479.93 || SG || 57.3217
|}

Number of modes expected from 3N-5 rule: 4

Number of bending vibration modes: 2

Number of stretching vibration modes: 2

No. of bands expected in gaseous spectrum: 3 (vibrations 1&2 degenerate)

==== Charges ====
[[File:HCN_charges1.PNG|center|thumb|Charges on an optimised NH3 molecule]]

N being more electronegative than H and C, a negative charge is expected on N in HCN and positive charges are expected on H and C.

=== Molecular Orbitals ===
==== Molecular orbital 8 ====
[[File:MTK_MO8.PNG|200px|thumb|MO8|200px]]

Antibonding/bonding: Antibonding

Occupancy: Unoccupied

Contributing AOs: 3px of N, 3px of C

Energy: 0.01929 a.u.

MO8 is the LUMO of HCN. Sideways antiphase overlap of 3px orbitals of N and C makes it the 1π* orbital of HCN.

----

==== Molecular Orbital 7 ====
[[File:MTK_MO7.PNG|thumb|MO7|right|200px]]

Antibonding/bonding: Bonding

Occupancy: Occupied

Contributing AOs: 2py of N, 2py of C

Energy: -0.35939 a.u.

MO7 is the HOMO of HCN. Sideways overlap of 3py orbitals of N and C makes it the 2π orbital of HCN. It is degenerate with MO6 and together with it, they contribute to the triple bond in HCN.

----

==== Molecular Orbital 6 ====
[[File:MO6.PNG|thumb|MO6|right|200px]]

Antibonding/bonding: Bonding

Occupancy: Occupied

Contributing AOs: 2px of N, 2px of C

Energy: -0.35939 a.u.

MO6 is the HOMO of HCN. Sideways overlap of 3px orbitals of N and C makes it the 1π orbital of HCN. It is degenerate with MO7 and together with it, they contribute to the triple bond in HCN.
----

==== Molecular Orbital 5 ====
[[File:MTK_MO5.PNG|thumb|MO5|right|200px]]

Antibonding/bonding: Antibonding

Occupancy: Occupied

Contributing AOs: 2pz of N, 3s of N, 2pz of C, 3s of N, 1s of H

Energy: -0.38064 a.u.

MO5 is the 3σ* orbital of HCN.

----

==== MO1 ====
[[File:MTK_MO1.PNG|thumb|MO7|right|200px]]

Antibonding/bonding: Bonding

Occupancy: Occupied

Contributing AOs: 1s of N, 1s of C

Energy: -0.38064 a.u.

MO1 is the lowest energy 1σ orbital of HCN. It does not participate in chemical reactions.

----

Rep:Mod:Mt4618

2019-03-22T16:43:38Z

Mt4618: /* MO6 */

== NH3 ==
=== Optimisation ===
<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MTK_NH3_OPTF_POP2.LOG</uploadedFileContents>
<script>frame x.y</script>
</jmolApplet></jmol>

Calculation Method: RB3LYP

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

E(RB3LYP): -56.55776873 a.u.

RMS Gradient Norm: 0.00000485 a.u.

Point Group: C3V

Optimised N-H bond length: 1.02 A

Optimised H-N-H bond angle: 106o

<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>
[[File: MTK_NH3_OPTF_POP2.LOG]]

=== Vibration and Charges ===
==== Vibrations ====
[[File:Screenshot.png|thumb|Vibration Modes of an optimised NH3 molecule]]
{| class="wikitable" border="1"
|+ Vibrations
! No. !! Wavenumber / cm-1 !! Symmetry !! Intensity
|-
| 1 || 1090 || A1 || 145
|-
| 2 || 1694 || E || 14
|-
| 3 || 1694 || E || 14
|-
| 4 || 3461 || A1 || 1
|-
| 5 || 3590 || E || 0
|-
| 6 || 3590 || E || 0
|}

Number of modes expected from 3N-6 rule: 6

Degenerate modes: 2&3 and 5&6

Bending vibration modes: 1,2,3

Stretching vibration modes: 4,5,6

Highly symmetric mode: 4

"Umbrella" mode: 1

No. of bands expected in gaseous spectrum: 2 (4 out of 6 modes are degenerate and 3 out of 6 are ~ 0 intensity)

==== Charges ====
[[File:Charge_NH3.PNG|center|thumb|Charges on an optimised NH3 molecule]]

A negative charge is expected on the nitrogen atom as it is more electronegative than hydrogen.

----

== N2 ==
=== Optimisation ===

<jmol><jmolApplet>
<title>An optimised N2 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MTK_N2_OPTF_POP.LOG</uploadedFileContents>
<script>frame x.y</script>
</jmolApplet></jmol>

Calculation Method: RB3LYP

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

E(RB3LYP): -109.52412868 a.u.

RMS Gradient Norm: 0.00000060 a.u.

Point Group: D*H

Optimised bond length: 1.11 A

Optimised bond angle: 180o

<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>

[[File:MTK_N2_OPTF_POP.LOG]]

=== Vibration and Charges ===
==== Vibrations ====
[[File:N2_vibration.PNG|thumb|Vibration Modes of an optimised N2 molecule]]
{| class="wikitable" border="1"
|+ Vibrations
! No. !! Wavenumber / cm-1 !! Symmetry !! Intensity
|-
| 1 || 2457 || SGG || 0
|}

Number of modes expected from 3N-5 rule: 1

Number of bending vibration modes: 0

Number of stretching vibration modes: 1

No. of bands expected in gaseous spectrum: 0 (vibration does not produce any change in dipole moment)

==== Charges ====
Charge is evenly distributed across N2 as there is no difference in electronegativity.
----

== H2 ==
=== Optimisation ===

<jmol><jmolApplet>
<title>An optimised H2 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MTK_H2_OPTF_POP.LOG</uploadedFileContents>
<script>frame x.y</script>
</jmolApplet></jmol>

Calculation Method: RB3LYP

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

E(RB3LYP): -1.17853936 a.u.

RMS Gradient Norm: 0.00000017 a.u.

Point Group: D*H

Optimised bond length: 0.74 A

Optimised bond angle: 180o

<pre>
Item Value Threshold Converged?

Maximum Force 0.000000 0.000450 YES

RMS Force 0.000000 0.000300 YES

Maximum Displacement 0.000000 0.001800 YES

RMS Displacement 0.000001 0.001200 YES

</pre>

[[File:MTK_H2_OPTF_POP.LOG]]

=== Vibration and Charges ===
==== Vibrations ====
[[File:H2_vibration.PNG|thumb|Vibration Modes of an optimised H2 molecule]]
{| class="wikitable" border="1"
|+ Vibrations
! No. !! Wavenumber / cm-1 !! Symmetry !! Intensity
|-
| 1 || 4466 || SGG || 0
|}

Number of modes expected from 3N-5 rule: 1

Number of bending vibration modes: 0

Number of stretching vibration modes: 1

No. of bands expected in gaseous spectrum: 0 (vibration does not produce any change in dipole moment)

==== Charges ====
Charge is evenly distributed across H2 as there is no difference in electronegativity.

== Transition metal complex ==
Unique Identifier: BOWVUG [https://www.ccdc.cam.ac.uk/structures/Search?Ccdcid=BOWVUG&DatabaseToSearch=Published]

N-N bond distance in complex: 1.13 A

N-N bond distance in optimised molecule: 1.11 A

The N-N bond distance in complex is greater than that in the optimised molecule because electron density is pulled away from N2 when it binds to Mo resulting in weaker N-N bonding in the complex.

== Haber 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.

ΔE=2*E(NH3)-[E(N2)+3*E(H2)]= -146.8 kJ/mol

The reaction is exothermic therefore, ammonia must be below the reactants in an energy profile diagram. So, ammonia is more stable.

== HCN ==
=== Optimisation ===

<jmol><jmolApplet>
<title>An optimised HCN molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MTK_HCN_OPTF_POP.LOG</uploadedFileContents>
<script>frame x.y</script>
</jmolApplet></jmol>

Calculation Method: RB3LYP

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

E(RB3LYP): -93.42458132 a.u.

RMS Gradient Norm: 0.00017006 a.u.

Point Group: C*V

Optimised bond length: 1.11 A

Optimised bond angle: 180o

<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>

[[File:MTK_HCN_OPTF_POP.LOG]]

=== Vibration and Charges ===
==== Vibrations ====
{| class="wikitable" border="1"
|+ Vibrations
! No. !! Wavenumber / cm-1 !! Symmetry !! Intensity
|-
| 1 || 766.74 || PI || 35.2959
|-
| 1 || 766.74 || PI || 35.2959
|-
| 1 || 2214.74 || SG || 2.0451
|-
| 1 || 3479.93 || SG || 57.3217
|}

Number of modes expected from 3N-5 rule: 4

Number of bending vibration modes: 2

Number of stretching vibration modes: 2

No. of bands expected in gaseous spectrum: 3 (vibrations 1&2 degenerate)

==== Charges ====
[[File:HCN_charges1.PNG|center|thumb|Charges on an optimised NH3 molecule]]

N being more electronegative than H and C, a negative charge is expected on N in HCN and positive charges are expected on H and C.

=== Molecular Orbitals ===
==== Molecular orbital 8 ====
[[File:MTK_MO8.PNG|200px|thumb|MO8|200px]]

Antibonding/bonding: Antibonding

Occupancy: Unoccupied

Contributing AOs: 3px of N, 3px of C

Energy: 0.01929 a.u.

MO8 is the LUMO of HCN. Sideways antiphase overlap of 3px orbitals of N and C makes it the 1π* orbital of HCN.

----

==== Molecular Orbital 7 ====
[[File:MTK_MO7.PNG|thumb|MO7|right|200px]]

Antibonding/bonding: Bonding

Occupancy: Occupied

Contributing AOs: 2py of N, 2py of C

Energy: -0.35939 a.u.

MO7 is the HOMO of HCN. Sideways overlap of 3py orbitals of N and C makes it the 2π orbital of HCN. It is degenerate with MO6 and together with it, they contribute to the triple bond in HCN.

----

==== Molecular Orbital 6 ====
[[File:MO6.PNG|thumb|MO6|right|200px]]

Antibonding/bonding: Bonding

Occupancy: Occupied

Contributing AOs: 2px of N, 2px of C

Energy: -0.35939 a.u.

MO6 is the HOMO of HCN. Sideways overlap of 3px orbitals of N and C makes it the 1π orbital of HCN. It is degenerate with MO7 and together with it, they contribute to the triple bond in HCN.
----

==== MO5 ====
[[File:MTK_MO5.PNG|thumb|MO5|right|200px]]

Antibonding/bonding: Antibonding

Occupancy: Occupied

Contributing AOs: 2pz of N, 3s of N, 2pz of C, 3s of N, 1s of H

Energy: -0.38064 a.u.

MO5 is the 3σ* orbital of HCN.

----

==== MO1 ====
[[File:MTK_MO1.PNG|thumb|MO7|right|200px]]

Antibonding/bonding: Bonding

Occupancy: Occupied

Contributing AOs: 1s of N, 1s of C

Energy: -0.38064 a.u.

MO1 is the lowest energy 1σ orbital of HCN. It does not participate in chemical reactions.

----

Rep:Mod:Mt4618

2019-03-22T16:43:28Z

Mt4618: /* MO7 */

== NH3 ==
=== Optimisation ===
<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MTK_NH3_OPTF_POP2.LOG</uploadedFileContents>
<script>frame x.y</script>
</jmolApplet></jmol>

Calculation Method: RB3LYP

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

E(RB3LYP): -56.55776873 a.u.

RMS Gradient Norm: 0.00000485 a.u.

Point Group: C3V

Optimised N-H bond length: 1.02 A

Optimised H-N-H bond angle: 106o

<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>
[[File: MTK_NH3_OPTF_POP2.LOG]]

=== Vibration and Charges ===
==== Vibrations ====
[[File:Screenshot.png|thumb|Vibration Modes of an optimised NH3 molecule]]
{| class="wikitable" border="1"
|+ Vibrations
! No. !! Wavenumber / cm-1 !! Symmetry !! Intensity
|-
| 1 || 1090 || A1 || 145
|-
| 2 || 1694 || E || 14
|-
| 3 || 1694 || E || 14
|-
| 4 || 3461 || A1 || 1
|-
| 5 || 3590 || E || 0
|-
| 6 || 3590 || E || 0
|}

Number of modes expected from 3N-6 rule: 6

Degenerate modes: 2&3 and 5&6

Bending vibration modes: 1,2,3

Stretching vibration modes: 4,5,6

Highly symmetric mode: 4

"Umbrella" mode: 1

No. of bands expected in gaseous spectrum: 2 (4 out of 6 modes are degenerate and 3 out of 6 are ~ 0 intensity)

==== Charges ====
[[File:Charge_NH3.PNG|center|thumb|Charges on an optimised NH3 molecule]]

A negative charge is expected on the nitrogen atom as it is more electronegative than hydrogen.

----

== N2 ==
=== Optimisation ===

<jmol><jmolApplet>
<title>An optimised N2 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MTK_N2_OPTF_POP.LOG</uploadedFileContents>
<script>frame x.y</script>
</jmolApplet></jmol>

Calculation Method: RB3LYP

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

E(RB3LYP): -109.52412868 a.u.

RMS Gradient Norm: 0.00000060 a.u.

Point Group: D*H

Optimised bond length: 1.11 A

Optimised bond angle: 180o

<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>

[[File:MTK_N2_OPTF_POP.LOG]]

=== Vibration and Charges ===
==== Vibrations ====
[[File:N2_vibration.PNG|thumb|Vibration Modes of an optimised N2 molecule]]
{| class="wikitable" border="1"
|+ Vibrations
! No. !! Wavenumber / cm-1 !! Symmetry !! Intensity
|-
| 1 || 2457 || SGG || 0
|}

Number of modes expected from 3N-5 rule: 1

Number of bending vibration modes: 0

Number of stretching vibration modes: 1

No. of bands expected in gaseous spectrum: 0 (vibration does not produce any change in dipole moment)

==== Charges ====
Charge is evenly distributed across N2 as there is no difference in electronegativity.
----

== H2 ==
=== Optimisation ===

<jmol><jmolApplet>
<title>An optimised H2 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MTK_H2_OPTF_POP.LOG</uploadedFileContents>
<script>frame x.y</script>
</jmolApplet></jmol>

Calculation Method: RB3LYP

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

E(RB3LYP): -1.17853936 a.u.

RMS Gradient Norm: 0.00000017 a.u.

Point Group: D*H

Optimised bond length: 0.74 A

Optimised bond angle: 180o

<pre>
Item Value Threshold Converged?

Maximum Force 0.000000 0.000450 YES

RMS Force 0.000000 0.000300 YES

Maximum Displacement 0.000000 0.001800 YES

RMS Displacement 0.000001 0.001200 YES

</pre>

[[File:MTK_H2_OPTF_POP.LOG]]

=== Vibration and Charges ===
==== Vibrations ====
[[File:H2_vibration.PNG|thumb|Vibration Modes of an optimised H2 molecule]]
{| class="wikitable" border="1"
|+ Vibrations
! No. !! Wavenumber / cm-1 !! Symmetry !! Intensity
|-
| 1 || 4466 || SGG || 0
|}

Number of modes expected from 3N-5 rule: 1

Number of bending vibration modes: 0

Number of stretching vibration modes: 1

No. of bands expected in gaseous spectrum: 0 (vibration does not produce any change in dipole moment)

==== Charges ====
Charge is evenly distributed across H2 as there is no difference in electronegativity.

== Transition metal complex ==
Unique Identifier: BOWVUG [https://www.ccdc.cam.ac.uk/structures/Search?Ccdcid=BOWVUG&DatabaseToSearch=Published]

N-N bond distance in complex: 1.13 A

N-N bond distance in optimised molecule: 1.11 A

The N-N bond distance in complex is greater than that in the optimised molecule because electron density is pulled away from N2 when it binds to Mo resulting in weaker N-N bonding in the complex.

== Haber 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.

ΔE=2*E(NH3)-[E(N2)+3*E(H2)]= -146.8 kJ/mol

The reaction is exothermic therefore, ammonia must be below the reactants in an energy profile diagram. So, ammonia is more stable.

== HCN ==
=== Optimisation ===

<jmol><jmolApplet>
<title>An optimised HCN molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MTK_HCN_OPTF_POP.LOG</uploadedFileContents>
<script>frame x.y</script>
</jmolApplet></jmol>

Calculation Method: RB3LYP

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

E(RB3LYP): -93.42458132 a.u.

RMS Gradient Norm: 0.00017006 a.u.

Point Group: C*V

Optimised bond length: 1.11 A

Optimised bond angle: 180o

<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>

[[File:MTK_HCN_OPTF_POP.LOG]]

=== Vibration and Charges ===
==== Vibrations ====
{| class="wikitable" border="1"
|+ Vibrations
! No. !! Wavenumber / cm-1 !! Symmetry !! Intensity
|-
| 1 || 766.74 || PI || 35.2959
|-
| 1 || 766.74 || PI || 35.2959
|-
| 1 || 2214.74 || SG || 2.0451
|-
| 1 || 3479.93 || SG || 57.3217
|}

Number of modes expected from 3N-5 rule: 4

Number of bending vibration modes: 2

Number of stretching vibration modes: 2

No. of bands expected in gaseous spectrum: 3 (vibrations 1&2 degenerate)

==== Charges ====
[[File:HCN_charges1.PNG|center|thumb|Charges on an optimised NH3 molecule]]

N being more electronegative than H and C, a negative charge is expected on N in HCN and positive charges are expected on H and C.

=== Molecular Orbitals ===
==== Molecular orbital 8 ====
[[File:MTK_MO8.PNG|200px|thumb|MO8|200px]]

Antibonding/bonding: Antibonding

Occupancy: Unoccupied

Contributing AOs: 3px of N, 3px of C

Energy: 0.01929 a.u.

MO8 is the LUMO of HCN. Sideways antiphase overlap of 3px orbitals of N and C makes it the 1π* orbital of HCN.

----

==== Molecular Orbital 7 ====
[[File:MTK_MO7.PNG|thumb|MO7|right|200px]]

Antibonding/bonding: Bonding

Occupancy: Occupied

Contributing AOs: 2py of N, 2py of C

Energy: -0.35939 a.u.

MO7 is the HOMO of HCN. Sideways overlap of 3py orbitals of N and C makes it the 2π orbital of HCN. It is degenerate with MO6 and together with it, they contribute to the triple bond in HCN.

----

==== MO6 ====
[[File:MO6.PNG|thumb|MO6|right|200px]]

Antibonding/bonding: Bonding

Occupancy: Occupied

Contributing AOs: 2px of N, 2px of C

Energy: -0.35939 a.u.

MO6 is the HOMO of HCN. Sideways overlap of 3px orbitals of N and C makes it the 1π orbital of HCN. It is degenerate with MO7 and together with it, they contribute to the triple bond in HCN.
----

==== MO5 ====
[[File:MTK_MO5.PNG|thumb|MO5|right|200px]]

Antibonding/bonding: Antibonding

Occupancy: Occupied

Contributing AOs: 2pz of N, 3s of N, 2pz of C, 3s of N, 1s of H

Energy: -0.38064 a.u.

MO5 is the 3σ* orbital of HCN.

----

==== MO1 ====
[[File:MTK_MO1.PNG|thumb|MO7|right|200px]]

Antibonding/bonding: Bonding

Occupancy: Occupied

Contributing AOs: 1s of N, 1s of C

Energy: -0.38064 a.u.

MO1 is the lowest energy 1σ orbital of HCN. It does not participate in chemical reactions.

----

Rep:Mod:Mt4618

2019-03-22T16:42:55Z

Mt4618: /* Molecular orbital 8 */

== NH3 ==
=== Optimisation ===
<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MTK_NH3_OPTF_POP2.LOG</uploadedFileContents>
<script>frame x.y</script>
</jmolApplet></jmol>

Calculation Method: RB3LYP

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

E(RB3LYP): -56.55776873 a.u.

RMS Gradient Norm: 0.00000485 a.u.

Point Group: C3V

Optimised N-H bond length: 1.02 A

Optimised H-N-H bond angle: 106o

<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>
[[File: MTK_NH3_OPTF_POP2.LOG]]

=== Vibration and Charges ===
==== Vibrations ====
[[File:Screenshot.png|thumb|Vibration Modes of an optimised NH3 molecule]]
{| class="wikitable" border="1"
|+ Vibrations
! No. !! Wavenumber / cm-1 !! Symmetry !! Intensity
|-
| 1 || 1090 || A1 || 145
|-
| 2 || 1694 || E || 14
|-
| 3 || 1694 || E || 14
|-
| 4 || 3461 || A1 || 1
|-
| 5 || 3590 || E || 0
|-
| 6 || 3590 || E || 0
|}

Number of modes expected from 3N-6 rule: 6

Degenerate modes: 2&3 and 5&6

Bending vibration modes: 1,2,3

Stretching vibration modes: 4,5,6

Highly symmetric mode: 4

"Umbrella" mode: 1

No. of bands expected in gaseous spectrum: 2 (4 out of 6 modes are degenerate and 3 out of 6 are ~ 0 intensity)

==== Charges ====
[[File:Charge_NH3.PNG|center|thumb|Charges on an optimised NH3 molecule]]

A negative charge is expected on the nitrogen atom as it is more electronegative than hydrogen.

----

== N2 ==
=== Optimisation ===

<jmol><jmolApplet>
<title>An optimised N2 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MTK_N2_OPTF_POP.LOG</uploadedFileContents>
<script>frame x.y</script>
</jmolApplet></jmol>

Calculation Method: RB3LYP

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

E(RB3LYP): -109.52412868 a.u.

RMS Gradient Norm: 0.00000060 a.u.

Point Group: D*H

Optimised bond length: 1.11 A

Optimised bond angle: 180o

<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>

[[File:MTK_N2_OPTF_POP.LOG]]

=== Vibration and Charges ===
==== Vibrations ====
[[File:N2_vibration.PNG|thumb|Vibration Modes of an optimised N2 molecule]]
{| class="wikitable" border="1"
|+ Vibrations
! No. !! Wavenumber / cm-1 !! Symmetry !! Intensity
|-
| 1 || 2457 || SGG || 0
|}

Number of modes expected from 3N-5 rule: 1

Number of bending vibration modes: 0

Number of stretching vibration modes: 1

No. of bands expected in gaseous spectrum: 0 (vibration does not produce any change in dipole moment)

==== Charges ====
Charge is evenly distributed across N2 as there is no difference in electronegativity.
----

== H2 ==
=== Optimisation ===

<jmol><jmolApplet>
<title>An optimised H2 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MTK_H2_OPTF_POP.LOG</uploadedFileContents>
<script>frame x.y</script>
</jmolApplet></jmol>

Calculation Method: RB3LYP

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

E(RB3LYP): -1.17853936 a.u.

RMS Gradient Norm: 0.00000017 a.u.

Point Group: D*H

Optimised bond length: 0.74 A

Optimised bond angle: 180o

<pre>
Item Value Threshold Converged?

Maximum Force 0.000000 0.000450 YES

RMS Force 0.000000 0.000300 YES

Maximum Displacement 0.000000 0.001800 YES

RMS Displacement 0.000001 0.001200 YES

</pre>

[[File:MTK_H2_OPTF_POP.LOG]]

=== Vibration and Charges ===
==== Vibrations ====
[[File:H2_vibration.PNG|thumb|Vibration Modes of an optimised H2 molecule]]
{| class="wikitable" border="1"
|+ Vibrations
! No. !! Wavenumber / cm-1 !! Symmetry !! Intensity
|-
| 1 || 4466 || SGG || 0
|}

Number of modes expected from 3N-5 rule: 1

Number of bending vibration modes: 0

Number of stretching vibration modes: 1

No. of bands expected in gaseous spectrum: 0 (vibration does not produce any change in dipole moment)

==== Charges ====
Charge is evenly distributed across H2 as there is no difference in electronegativity.

== Transition metal complex ==
Unique Identifier: BOWVUG [https://www.ccdc.cam.ac.uk/structures/Search?Ccdcid=BOWVUG&DatabaseToSearch=Published]

N-N bond distance in complex: 1.13 A

N-N bond distance in optimised molecule: 1.11 A

The N-N bond distance in complex is greater than that in the optimised molecule because electron density is pulled away from N2 when it binds to Mo resulting in weaker N-N bonding in the complex.

== Haber 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.

ΔE=2*E(NH3)-[E(N2)+3*E(H2)]= -146.8 kJ/mol

The reaction is exothermic therefore, ammonia must be below the reactants in an energy profile diagram. So, ammonia is more stable.

== HCN ==
=== Optimisation ===

<jmol><jmolApplet>
<title>An optimised HCN molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MTK_HCN_OPTF_POP.LOG</uploadedFileContents>
<script>frame x.y</script>
</jmolApplet></jmol>

Calculation Method: RB3LYP

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

E(RB3LYP): -93.42458132 a.u.

RMS Gradient Norm: 0.00017006 a.u.

Point Group: C*V

Optimised bond length: 1.11 A

Optimised bond angle: 180o

<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>

[[File:MTK_HCN_OPTF_POP.LOG]]

=== Vibration and Charges ===
==== Vibrations ====
{| class="wikitable" border="1"
|+ Vibrations
! No. !! Wavenumber / cm-1 !! Symmetry !! Intensity
|-
| 1 || 766.74 || PI || 35.2959
|-
| 1 || 766.74 || PI || 35.2959
|-
| 1 || 2214.74 || SG || 2.0451
|-
| 1 || 3479.93 || SG || 57.3217
|}

Number of modes expected from 3N-5 rule: 4

Number of bending vibration modes: 2

Number of stretching vibration modes: 2

No. of bands expected in gaseous spectrum: 3 (vibrations 1&2 degenerate)

==== Charges ====
[[File:HCN_charges1.PNG|center|thumb|Charges on an optimised NH3 molecule]]

N being more electronegative than H and C, a negative charge is expected on N in HCN and positive charges are expected on H and C.

=== Molecular Orbitals ===
==== Molecular orbital 8 ====
[[File:MTK_MO8.PNG|200px|thumb|MO8|200px]]

Antibonding/bonding: Antibonding

Occupancy: Unoccupied

Contributing AOs: 3px of N, 3px of C

Energy: 0.01929 a.u.

MO8 is the LUMO of HCN. Sideways antiphase overlap of 3px orbitals of N and C makes it the 1π* orbital of HCN.

----

==== MO7 ====
[[File:MTK_MO7.PNG|thumb|MO7|right|200px]]

Antibonding/bonding: Bonding

Occupancy: Occupied

Contributing AOs: 2py of N, 2py of C

Energy: -0.35939 a.u.

MO7 is the HOMO of HCN. Sideways overlap of 3py orbitals of N and C makes it the 2π orbital of HCN. It is degenerate with MO6 and together with it, they contribute to the triple bond in HCN.

----

==== MO6 ====
[[File:MO6.PNG|thumb|MO6|right|200px]]

Antibonding/bonding: Bonding

Occupancy: Occupied

Contributing AOs: 2px of N, 2px of C

Energy: -0.35939 a.u.

MO6 is the HOMO of HCN. Sideways overlap of 3px orbitals of N and C makes it the 1π orbital of HCN. It is degenerate with MO7 and together with it, they contribute to the triple bond in HCN.
----

==== MO5 ====
[[File:MTK_MO5.PNG|thumb|MO5|right|200px]]

Antibonding/bonding: Antibonding

Occupancy: Occupied

Contributing AOs: 2pz of N, 3s of N, 2pz of C, 3s of N, 1s of H

Energy: -0.38064 a.u.

MO5 is the 3σ* orbital of HCN.

----

==== MO1 ====
[[File:MTK_MO1.PNG|thumb|MO7|right|200px]]

Antibonding/bonding: Bonding

Occupancy: Occupied

Contributing AOs: 1s of N, 1s of C

Energy: -0.38064 a.u.

MO1 is the lowest energy 1σ orbital of HCN. It does not participate in chemical reactions.

----