ChemWiki - User contributions [en]

MRD:BR516

2018-05-29T16:40:26Z

Br516:

==BR516 Molecular reaction dynamics==
===Excercise 1: H + H2 system===
====What value do the different components of the gradient of the potential energy surface have at a minimum and at a transition structure? Briefly explain how minima and transition structures can be distinguished using the curvature of the potential energy surface.====

The transition state is the maximum energy point on the minimum energy trough as a saddle point. This transition state has a potential energy gradient of 0 with respect to rAB and rBC. This transition point is a maximum in one direction yet a minimum in another.

The minima, however, are minimums in both directions as ∂2V/∂rAB > 0 and ∂2V/∂rBC > 0. This means any variance in the length of rAB or rBC will lead to an increase of energy, indicating that these regions represent the stable reactants and products.

====Report your best estimate of the transition state position (rts) and explain your reasoning illustrating it with a “Internuclear Distances vs Time” plot for a relevant trajectory.====
Due to the fact that this reaction involves 3 identical atoms, at the transtion state, rAB=rBC. Buy setting the reactants to have no initial momentum, they wont have nay energy to escape the minimum path. By varying the values of rAB and rBC, and observing the “Internuclear Distances vs Time” plot, the transition state distance can be found as this will have no variation in distance with time. rts was found to be 0.908

[[File:BR516_Q2_internuclear_distances_vs_time.PNG|center|thumb|“Internuclear Distances vs Time” plot for 3 H atoms at initial momentum = 0 and initial internuclear separation 0.908]]

====Comment on how the MEP and the trajectory you just calculated differ.====
The MEP (minimum energy path) shows the path of the reaction if the molecules have 0 inertia. This allows the calculation to trace the lowest energy path the reaction could possibly take, the "floor" of the trough in the potential energy surface. The dynamic trajectory takes into account the momentum of the particles. This causes the slight oscillation along the same rough path, as shown by the dynamic plot.

[[File:BR516_Q3_MEP.PNG|center|thumb|MEP contour plot]]
[[File:BR516_Q3_dynamic.PNG|center|thumb|Dynamic contour plot]]

====Complete the table by adding a column with the total energy, and another column reporting if the trajectory is reactive or unreactive. For each set of initial conditions, provide a plot of the trajectory and a small description for what happens along the trajectory.====
{| class="wikitable" border=1
! p1 !! p2 !! Total Energy !! Reactive/Unreactive !! Contour plot !! Description
|-
| -1.25 || -2.5 || -99.018 || Reactive || [[File:BR516_Q4_-1.25_-2.5.PNG]] || The stationary H-H molecule reacts with another colliding H with the correct momentum, and a new H-H bond forms.
|-
| -1.5 || -2.0 || -100.456 || Unreactive || [[File:BR516_Q4_-1.5_-2.0.PNG]] || An oscillating H-H molecule collides with an H, but not with enough momentum to form a new bond so they are repelled.
|-
| -1.5 || -2.5 || -98.956 || Reactive || [[File:BR516_Q4_-1.5_-2.5.PNG]] || An oscilating H-H molecule collides with another H to form a new bond with a higher vibrational frequency
|-
| -2.5 || -5.0 || -84.956 || Unreactive || [[File:BR516_Q4_-2.5_-5.0.PNG]] || A stationary H-H molecule collides with another H to form a new bond, however the H has too much momentum, and is repelled by the B molecuels nucleus. This causes The AB molecule to remain intact with a much larger vibrational mode, and causes the BC distance to increase as it is repelled.
|-
| -2.5 || -5.2 || -83.416 || Reactive || [[File:BR516_Q4_-2.5_-5.2.PNG]] || The AB molecule of H-H collides with the C molecule of H, but unlike in the above condition, The C molecule has enough momentum to recross the transition state region. The BC bonds forms, Breaks into an AB bond then reforms into the BC bond.
|}

====State what are the main assumptions of Transition State Theory. Given the results you have obtained, how will Transition State Theory predictions for reaction rate values compare with experimental values?====
Transition state theory splits the reaction into 2 distinct areas: the reactant and product space. It states that the reactants must cross the energy threshold of the saddle in the transition area to reach the product space. It also assumes atoms obey the laws of classical mechanics using the Born-Oppenheimer approximation, and that each reaction only has 1 saddle point and 1 transition state.

We can see from the above scenarios that for molecules with high momentum, the transition state can be recrossed, so the transition state prediction for reaction rate values will not provide an close approximation to experimental vales run at high temperatures. Therefore, the transition state theory should only be used for reactions at low temperature conditions for predicting reaction rates.

===EXERCISE 2: F - H - H system===
====Classify the F + H2 and H + HF reactions according to their energetics (endothermic or exothermic). How does this relate to the bond strength of the chemical species involved?====
The F + H2 -> FH + H reaction is exothermic, while it's opposite reaction FH + H -> F + H2. This is due to the greater relative strength of the H-F bond (565 kj/mol) to the H-H (432 kj/mol)bond, meaning more energy has to be used to break the H-F bond than is gained forming an H-H bond[1].
====Locate the approximate position of the transition state.====
The transition state of the F - H - H system is found at a distance of 0.745 between H-H and 1.811 between H-F. The Momenta of all particles were set to 0 and the initial distance between them varied until an initial distance was found that would remain constant over time.
[[File:BR516_Q7_Distance_time.PNG|center|thumb|Interatomic distance vs time with atom A H, atom B H and atom C F at rAB = 0.745 and rBC = 1.811]]

====Report the activation energy for both reactions====
To find the activation energy, the MEP was found for both the formation of H2 and HF from the H-H-F transition state. The minimum energy point from both products was found, and using this value the activation energy can be found (difference between the maximum energy of the saddle and the minimum energy of the products).
H-H-F to HF MEP: Initial energy -103.869, product energy -133.858. Activation energy of HF + H -> H2 + F = +29.989
H-H-F to H2 MEP: Initial energy -103.869, product energy -103.941. Activation energy of H2 + F -> HF + H = + 0.072

[[File:BR516_Q8_MEP_H2_to_HF.PNG|center|thumb|MEP of progression to HF product]]
[[File:BR516_Q8_energy_time_HF.PNG|center|thumb|Energy vs Time of H-H-F to HF product]]
[[File:BR516_Q8_energy_time_HH.PNG|center|thumb|Energy vs Time of H-H-F to H2 product]]
[[File:BR516_Q8_MEP_HH.PNG|center|thumb|MEP of progression to H2 product]]

====In light of the fact that energy is conserved, discuss the mechanism of release of the reaction energy. How could this be confirmed experimentally?====
Using the reaction condition of A=H, B=H, C=F, rAB = 0.8, rBC = 2.0, pAB = 1, pBC = -1.5, a successful reaction can be seen of the formation of HF. The reaction energy is converted from potential to kinetic, as shown by the vast increase in magnitude of vibration of H-F as compared to the initial H2 molecule. Experimentally, this would be shown by a large increase in temperature of the reaction mixture caused by the increase in average kinetic energy.

[[File:BR516_Q9_contour_plot_reaction.PNG|center|thumb|Contour plot of successful reaction of formation of HF]]
[[File:BR516_Q9_momentum_graph.PNG|center|thumb|Momentum Vs. time of H2 + F to form HF + H]]

====Discuss how the distribution of energy between different modes (translation and vibration) affect the efficiency of the reaction, and how this is influenced by the position of the transition state.====
Polyani's rules link the effect of vibrational and translational kinetic energy on a reaction. They state that if the reaction has an early transition state close to the energy of the products, translational energy is more important for promoting a successful reaction. Conversely, if a reaction has a late transition state, a higher vibrational energy will promote a more successful reaction.

For the reaction of HF + H -> H2 + F, a higher vibrational energy of the HF molecule is required, as stated by polyani's rules. This is due to the relatively late transition state of the endothermic reaction. Similarly for the reverse reaction, very little vibrational energy is required and only a slight amount of translational energy is required due to the low activation energy of the exothermic reaction.

===References===
[1] http://www.wiredchemist.com/chemistry/data/bond_energies_lengths.html, accessed 19/05/2018

MRD:BR516

2018-05-29T15:20:02Z

Br516:

==BR516 Molecular reaction dynamics==
===Excercise 1: H + H2 system===
====What value do the different components of the gradient of the potential energy surface have at a minimum and at a transition structure? Briefly explain how minima and transition structures can be distinguished using the curvature of the potential energy surface.====

The transition state is the maximum energy point on the minimum energy trough as a saddle point. This transition state has a potential energy gradient of 0 with respect to rAB and rBC. This transition point is a maximum in one direction yet a minimum in another.

The minima, however, are minimums in both directions as ∂2V/∂rAB > 0 and ∂2V/∂rBC > 0. This means any variance in the length of rAB or rBC will lead to an increase of energy, indicating that these regions represent the stable reactants and products.

====Report your best estimate of the transition state position (rts) and explain your reasoning illustrating it with a “Internuclear Distances vs Time” plot for a relevant trajectory.====
Due to the fact that this reaction involves 3 identical atoms, at the transtion state, rAB=rBC. Buy setting the reactants to have no initial momentum, they wont have nay energy to escape the minimum path. By varying the values of rAB and rBC, and observing the “Internuclear Distances vs Time” plot, the transition state distance can be found as this will have no variation in distance with time. rts was found to be 0.908

[[File:BR516_Q2_internuclear_distances_vs_time.PNG|center|thumb|“Internuclear Distances vs Time” plot for 3 H atoms at initial momentum = 0 and initial internuclear separation 0.908]]

====Comment on how the MEP and the trajectory you just calculated differ.====
The MEP (minimum energy path) shows the path of the reaction if the molecules have 0 inertia. This allows the calculation to trace the lowest energy path the reaction could possibly take, the "floor" of the trough in the potential energy surface. The dynamic trajectory takes into account the momentum of the particles. This causes the slight oscillation along the same rough path, as shown by the dynamic plot.

[[File:BR516_Q3_MEP.PNG|center|thumb|MEP contour plot]]
[[File:BR516_Q3_dynamic.PNG|center|thumb|Dynamic contour plot]]

====Complete the table by adding a column with the total energy, and another column reporting if the trajectory is reactive or unreactive. For each set of initial conditions, provide a plot of the trajectory and a small description for what happens along the trajectory.====
{| class="wikitable" border=1
! p1 !! p2 !! Total Energy !! Reactive/Unreactive !! Contour plot !! Description
|-
| -1.25 || -2.5 || -99.018 || Reactive || [[File:BR516_Q4_-1.25_-2.5.PNG]] || The stationary H-H molecule reacts with another colliding H with the correct momentum, and a new H-H bond forms.
|-
| -1.5 || -2.0 || -100.456 || Unreactive || [[File:BR516_Q4_-1.5_-2.0.PNG]] || An oscillating H-H molecule collides with an H, but not with enough momentum to form a new bond so they are repelled.
|-
| -1.5 || -2.5 || -98.956 || Reactive || [[File:BR516_Q4_-1.5_-2.5.PNG]] || An oscilating H-H molecule collides with another H to form a new bond with a higher vibrational frequency
|-
| -2.5 || -5.0 || -84.956 || Unreactive || [[File:BR516_Q4_-2.5_-5.0.PNG]] || A stationary H-H molecule collides with another H to form a new bond, however the H has too much momentum, and is repelled by the B molecuels nucleus. This causes The AB molecule to remain intact with a much larger vibrational mode, and causes the BC distance to increase as it is repelled.
|-
| -2.5 || -5.2 || -83.416 || Reactive || [[File:BR516_Q4_-2.5_-5.2.PNG]] || The AB molecule of H-H collides with the C molecule of H, but unlike in the above condition, The C molecule has enough momentum to recross the transition state region. The BC bonds forms, Breaks into an AB bond then reforms into the BC bond.
|}

====State what are the main assumptions of Transition State Theory. Given the results you have obtained, how will Transition State Theory predictions for reaction rate values compare with experimental values?====
Transition state theory splits the reaction into 2 distinct areas: the reactant and product space. It states that the reactants must cross the energy threshold of the saddle in the transition area to reach the product space. It also assumes atoms obey the laws of classical mechanics using the Born-Oppenheimer approximation, and that each reaction only has 1 saddle point and 1 transition state.

We can see from the above scenarios that for molecules with high momentum, the transition state can be recrossed, so the transition state prediction for reaction rate values will not provide an close approximation to experimental vales run at high temperatures. Therefore, the transition state theory should only be used for reactions at low temperature conditions for predicting reaction rates.

===EXERCISE 2: F - H - H system===
====Classify the F + H2 and H + HF reactions according to their energetics (endothermic or exothermic). How does this relate to the bond strength of the chemical species involved?====
The F + H2 -> FH + H reaction is exothermic, while it's opposite reaction FH + H -> F + H2. This is due to the greater relative strength of the H-F bond (565 kj/mol) to the H-H (432 kj/mol)bond, meaning more energy has to be used to break the H-F bond than is gained forming an H-H bond[1].
====Locate the approximate position of the transition state.====
The transition state of the F - H - H system is found at a distance of 0.745 between H-H and 1.811 between H-F. The Momenta of all particles were set to 0 and the initial distance between them varied until an initial distance was found that would remain constant over time.
[[File:BR516_Q7_Distance_time.PNG|center|thumb|Interatomic distance vs time with atom A H, atom B H and atom C F at rAB = 0.745 and rBC = 1.811]]

====Report the activation energy for both reactions====
To find the activation energy, the MEP was found for both the formation of H2 and HF from the H-H-F transition state. The minimum energy point from both products was found, and using this value the activation energy can be found (difference between the maximum energy of the saddle and the minimum energy of the products).
H-H-F to HF MEP: Initial energy -103.869, product energy -133.858. Activation energy of HF + H -> H2 + F = +29.989
H-H-F to H2 MEP: Initial energy -103.869, product energy -103.941. Activation energy of H2 + F -> HF + H = + 0.072

[[File:BR516_Q8_MEP_H2_to_HF.PNG|center|thumb|MEP of progression to HF product]]
[[File:BR516_Q8_energy_time_HF.PNG|center|thumb|Energy vs Time of H-H-F to HF product]]
[[File:BR516_Q8_energy_time_HH.PNG|center|thumb|Energy vs Time of H-H-F to H2 product]]
[[File:BR516_Q8_MEP_HH.PNG|center|thumb|MEP of progression to H2 product]]

====In light of the fact that energy is conserved, discuss the mechanism of release of the reaction energy. How could this be confirmed experimentally?====
Using the reaction condition of A=H, B=H, C=F, rAB = 0.8, rBC = 2.0, pAB = 1, pBC = -1.5, a successful reaction can be seen of the formation of HF. The reaction energy is converted from potential to kinetic, as shown by the vast increase in magnitude of vibration of H-F as compared to the initial H2 molecule. Experimentally, this would be shown by a large increase in temperature of the reaction mixture caused by the increase in average kinetic energy.

[[File:BR516_Q9_contour_plot_reaction.PNG|center|thumb|Contour plot of successful reaction of formation of HF]]
[[File:BR516_Q9_momentum_graph.PNG|center|thumb|Momentum Vs. time of H2 + F to form HF + H]]

===References===
[1] http://www.wiredchemist.com/chemistry/data/bond_energies_lengths.html, accessed 19/05/2018

MRD:BR516

2018-05-29T15:13:45Z

Br516:

==BR516 Molecular reaction dynamics==
===Excercise 1: H + H2 system===
====What value do the different components of the gradient of the potential energy surface have at a minimum and at a transition structure? Briefly explain how minima and transition structures can be distinguished using the curvature of the potential energy surface.====

The transition state is the maximum energy point on the minimum energy trough as a saddle point. This transition state has a potential energy gradient of 0 with respect to rAB and rBC. This transition point is a maximum in one direction yet a minimum in another.

The minima, however, are minimums in both directions as ∂2V/∂rAB > 0 and ∂2V/∂rBC > 0. This means any variance in the length of rAB or rBC will lead to an increase of energy, indicating that these regions represent the stable reactants and products.

====Report your best estimate of the transition state position (rts) and explain your reasoning illustrating it with a “Internuclear Distances vs Time” plot for a relevant trajectory.====
Due to the fact that this reaction involves 3 identical atoms, at the transtion state, rAB=rBC. Buy setting the reactants to have no initial momentum, they wont have nay energy to escape the minimum path. By varying the values of rAB and rBC, and observing the “Internuclear Distances vs Time” plot, the transition state distance can be found as this will have no variation in distance with time. rts was found to be 0.908

[[File:BR516_Q2_internuclear_distances_vs_time.PNG|center|thumb|“Internuclear Distances vs Time” plot for 3 H atoms at initial momentum = 0 and initial internuclear separation 0.908]]

====Comment on how the MEP and the trajectory you just calculated differ.====
The MEP (minimum energy path) shows the path of the reaction if the molecules have 0 inertia. This allows the calculation to trace the lowest energy path the reaction could possibly take, the "floor" of the trough in the potential energy surface. The dynamic trajectory takes into account the momentum of the particles. This causes the slight oscillation along the same rough path, as shown by the dynamic plot.

[[File:BR516_Q3_MEP.PNG|center|thumb|MEP contour plot]]
[[File:BR516_Q3_dynamic.PNG|center|thumb|Dynamic contour plot]]

====Complete the table by adding a column with the total energy, and another column reporting if the trajectory is reactive or unreactive. For each set of initial conditions, provide a plot of the trajectory and a small description for what happens along the trajectory.====
{| class="wikitable" border=1
! p1 !! p2 !! Total Energy !! Reactive/Unreactive !! Contour plot !! Description
|-
| -1.25 || -2.5 || -99.018 || Reactive || [[File:BR516_Q4_-1.25_-2.5.PNG]] || The stationary H-H molecule reacts with another colliding H with the correct momentum, and a new H-H bond forms.
|-
| -1.5 || -2.0 || -100.456 || Unreactive || [[File:BR516_Q4_-1.5_-2.0.PNG]] || An oscillating H-H molecule collides with an H, but not with enough momentum to form a new bond so they are repelled.
|-
| -1.5 || -2.5 || -98.956 || Reactive || [[File:BR516_Q4_-1.5_-2.5.PNG]] || An oscilating H-H molecule collides with another H to form a new bond with a higher vibrational frequency
|-
| -2.5 || -5.0 || -84.956 || Unreactive || [[File:BR516_Q4_-2.5_-5.0.PNG]] || A stationary H-H molecule collides with another H to form a new bond, however the H has too much momentum, and is repelled by the B molecuels nucleus. This causes The AB molecule to remain intact with a much larger vibrational mode, and causes the BC distance to increase as it is repelled.
|-
| -2.5 || -5.2 || -83.416 || Reactive || [[File:BR516_Q4_-2.5_-5.2.PNG]] || The AB molecule of H-H collides with the C molecule of H, but unlike in the above condition, The C molecule has enough momentum to recross the transition state region. The BC bonds forms, Breaks into an AB bond then reforms into the BC bond.
|}

====State what are the main assumptions of Transition State Theory. Given the results you have obtained, how will Transition State Theory predictions for reaction rate values compare with experimental values?====
Transition state theory splits the reaction into 2 distinct areas: the reactant and product space. It states that the reactants must cross the energy threshold of the saddle in the transition area to reach the product space. It also assumes atoms obey the laws of classical mechanics using the Born-Oppenheimer approximation, and that each reaction only has 1 saddle point and 1 transition state.

We can see from the above scenarios that for molecules with high momentum, the transition state can be recrossed, so the transition state prediction for reaction rate values will not provide an close approximation to experimental vales run at high temperatures. Therefore, the transition state theory should only be used for reactions at low temperature conditions for predicting reaction rates.

===EXERCISE 2: F - H - H system===
====Classify the F + H2 and H + HF reactions according to their energetics (endothermic or exothermic). How does this relate to the bond strength of the chemical species involved?====
The F + H2 -> FH + H reaction is exothermic, while it's opposite reaction FH + H -> F + H2. This is due to the greater relative strength of the H-F bond (565 kj/mol) to the H-H (432 kj/mol)bond, meaning more energy has to be used to break the H-F bond than is gained forming an H-H bond[1].
====Locate the approximate position of the transition state.====
The transition state of the F - H - H system is found at a distance of 0.745 between H-H and 1.811 between H-F. The Momenta of all particles were set to 0 and the initial distance between them varied until an initial distance was found that would remain constant over time.
[[File:BR516_Q7_Distance_time.PNG|center|thumb|Interatomic distance vs time with atom A H, atom B H and atom C F at rAB = 0.745 and rBC = 1.811]]

====Report the activation energy for both reactions====
To find the activation energy, the MEP was found for both the formation of H2 and HF from the H-H-F transition state. The minimum energy point from both products was found, and using this value the activation energy can be found (difference between the maximum energy of the saddle and the minimum energy of the products).
H-H-F to HF MEP: Initial energy -103.869, product energy -133.858. Activation energy of HF + H -> H2 + F = +29.989
H-H-F to H2 MEP: Initial energy -103.869, product energy -103.941. Activation energy of H2 + F -> HF + H = + 0.072

[[File:BR516_Q8_MEP_H2_to_HF.PNG|center|thumb|MEP of progression to HF product]]
[[File:BR516_Q8_energy_time_HF.PNG|center|thumb|Energy vs Time of H-H-F to HF product]]
[[File:BR516_Q8_energy_time_HH.PNG|center|thumb|Energy vs Time of H-H-F to H2 product]]
[[File:BR516_Q8_MEP_HH.PNG|center|thumb|MEP of progression to H2 product]]

====In light of the fact that energy is conserved, discuss the mechanism of release of the reaction energy. How could this be confirmed experimentally?====
Using the reaction condition of A=H, B=H, C=F, rAB = 0.8, rBC = 2.0, pAB = 1, pBC = -1.5, a successful reaction can be seen of the formation of HF.

[[File:BR516_Q9_contour_plot_reaction.PNG|center|thumb|Contour plot of successful reaction of formation of HF]]
[[File:BR516_Q9_momentum_graph.PNG|center|thumb|Momentum Vs. time of H2 + F to form HF + H]]

===References===
[1] http://www.wiredchemist.com/chemistry/data/bond_energies_lengths.html, accessed 19/05/2018

File:BR516 Q9 momentum graph.PNG

2018-05-29T15:12:42Z

Br516:

File:BR516 Q9 contour plot reaction.PNG

2018-05-29T15:05:05Z

Br516:

MRD:BR516

2018-05-29T14:59:22Z

Br516:

==BR516 Molecular reaction dynamics==
===Excercise 1: H + H2 system===
====What value do the different components of the gradient of the potential energy surface have at a minimum and at a transition structure? Briefly explain how minima and transition structures can be distinguished using the curvature of the potential energy surface.====

The transition state is the maximum energy point on the minimum energy trough as a saddle point. This transition state has a potential energy gradient of 0 with respect to rAB and rBC. This transition point is a maximum in one direction yet a minimum in another.

The minima, however, are minimums in both directions as ∂2V/∂rAB > 0 and ∂2V/∂rBC > 0. This means any variance in the length of rAB or rBC will lead to an increase of energy, indicating that these regions represent the stable reactants and products.

====Report your best estimate of the transition state position (rts) and explain your reasoning illustrating it with a “Internuclear Distances vs Time” plot for a relevant trajectory.====
Due to the fact that this reaction involves 3 identical atoms, at the transtion state, rAB=rBC. Buy setting the reactants to have no initial momentum, they wont have nay energy to escape the minimum path. By varying the values of rAB and rBC, and observing the “Internuclear Distances vs Time” plot, the transition state distance can be found as this will have no variation in distance with time. rts was found to be 0.908

[[File:BR516_Q2_internuclear_distances_vs_time.PNG|center|thumb|“Internuclear Distances vs Time” plot for 3 H atoms at initial momentum = 0 and initial internuclear separation 0.908]]

====Comment on how the MEP and the trajectory you just calculated differ.====
The MEP (minimum energy path) shows the path of the reaction if the molecules have 0 inertia. This allows the calculation to trace the lowest energy path the reaction could possibly take, the "floor" of the trough in the potential energy surface. The dynamic trajectory takes into account the momentum of the particles. This causes the slight oscillation along the same rough path, as shown by the dynamic plot.

[[File:BR516_Q3_MEP.PNG|center|thumb|MEP contour plot]]
[[File:BR516_Q3_dynamic.PNG|center|thumb|Dynamic contour plot]]

====Complete the table by adding a column with the total energy, and another column reporting if the trajectory is reactive or unreactive. For each set of initial conditions, provide a plot of the trajectory and a small description for what happens along the trajectory.====
{| class="wikitable" border=1
! p1 !! p2 !! Total Energy !! Reactive/Unreactive !! Contour plot !! Description
|-
| -1.25 || -2.5 || -99.018 || Reactive || [[File:BR516_Q4_-1.25_-2.5.PNG]] || The stationary H-H molecule reacts with another colliding H with the correct momentum, and a new H-H bond forms.
|-
| -1.5 || -2.0 || -100.456 || Unreactive || [[File:BR516_Q4_-1.5_-2.0.PNG]] || An oscillating H-H molecule collides with an H, but not with enough momentum to form a new bond so they are repelled.
|-
| -1.5 || -2.5 || -98.956 || Reactive || [[File:BR516_Q4_-1.5_-2.5.PNG]] || An oscilating H-H molecule collides with another H to form a new bond with a higher vibrational frequency
|-
| -2.5 || -5.0 || -84.956 || Unreactive || [[File:BR516_Q4_-2.5_-5.0.PNG]] || A stationary H-H molecule collides with another H to form a new bond, however the H has too much momentum, and is repelled by the B molecuels nucleus. This causes The AB molecule to remain intact with a much larger vibrational mode, and causes the BC distance to increase as it is repelled.
|-
| -2.5 || -5.2 || -83.416 || Reactive || [[File:BR516_Q4_-2.5_-5.2.PNG]] || The AB molecule of H-H collides with the C molecule of H, but unlike in the above condition, The C molecule has enough momentum to recross the transition state region. The BC bonds forms, Breaks into an AB bond then reforms into the BC bond.
|}

====State what are the main assumptions of Transition State Theory. Given the results you have obtained, how will Transition State Theory predictions for reaction rate values compare with experimental values?====
Transition state theory splits the reaction into 2 distinct areas: the reactant and product space. It states that the reactants must cross the energy threshold of the saddle in the transition area to reach the product space. It also assumes atoms obey the laws of classical mechanics using the Born-Oppenheimer approximation, and that each reaction only has 1 saddle point and 1 transition state.

We can see from the above scenarios that for molecules with high momentum, the transition state can be recrossed, so the transition state prediction for reaction rate values will not provide an close approximation to experimental vales run at high temperatures. Therefore, the transition state theory should only be used for reactions at low temperature conditions for predicting reaction rates.

===EXERCISE 2: F - H - H system===
====Classify the F + H2 and H + HF reactions according to their energetics (endothermic or exothermic). How does this relate to the bond strength of the chemical species involved?====
The F + H2 -> FH + H reaction is exothermic, while it's opposite reaction FH + H -> F + H2. This is due to the greater relative strength of the H-F bond (565 kj/mol) to the H-H (432 kj/mol)bond, meaning more energy has to be used to break the H-F bond than is gained forming an H-H bond[1].
====Locate the approximate position of the transition state.====
The transition state of the F - H - H system is found at a distance of 0.745 between H-H and 1.811 between H-F. The Momenta of all particles were set to 0 and the initial distance between them varied until an initial distance was found that would remain constant over time.
[[File:BR516_Q7_Distance_time.PNG|center|thumb|Interatomic distance vs time with atom A H, atom B H and atom C F at rAB = 0.745 and rBC = 1.811]]

====Report the activation energy for both reactions====
To find the activation energy, the MEP was found for both the formation of H2 and HF from the H-H-F transition state. The minimum energy point from both products was found, and using this value the activation energy can be found (difference between the maximum energy of the saddle and the minimum energy of the products).
H-H-F to HF MEP: Initial energy -103.869, product energy -133.858. Activation energy of HF + H -> H2 + F = +29.989
H-H-F to H2 MEP: Initial energy -103.869, product energy -103.941. Activation energy of H2 + F -> HF + H = + 0.072

[[File:BR516_Q8_MEP_H2_to_HF.PNG|center|thumb|MEP of progression to HF product]]
[[File:BR516_Q8_energy_time_HF.PNG|center|thumb|Energy vs Time of H-H-F to HF product]]
[[File:BR516_Q8_energy_time_HH.PNG|center|thumb|Energy vs Time of H-H-F to H2 product]]
[[File:BR516_Q8_MEP_HH.PNG|center|thumb|MEP of progression to H2 product]]

===References===
[1] http://www.wiredchemist.com/chemistry/data/bond_energies_lengths.html, accessed 19/05/2018

MRD:BR516

2018-05-29T14:59:04Z

Br516:

==BR516 Molecular reaction dynamics==
===Excercise 1: H + H2 system===
====What value do the different components of the gradient of the potential energy surface have at a minimum and at a transition structure? Briefly explain how minima and transition structures can be distinguished using the curvature of the potential energy surface.====

The transition state is the maximum energy point on the minimum energy trough as a saddle point. This transition state has a potential energy gradient of 0 with respect to rAB and rBC. This transition point is a maximum in one direction yet a minimum in another.

The minima, however, are minimums in both directions as ∂2V/∂rAB > 0 and ∂2V/∂rBC > 0. This means any variance in the length of rAB or rBC will lead to an increase of energy, indicating that these regions represent the stable reactants and products.

====Report your best estimate of the transition state position (rts) and explain your reasoning illustrating it with a “Internuclear Distances vs Time” plot for a relevant trajectory.====
Due to the fact that this reaction involves 3 identical atoms, at the transtion state, rAB=rBC. Buy setting the reactants to have no initial momentum, they wont have nay energy to escape the minimum path. By varying the values of rAB and rBC, and observing the “Internuclear Distances vs Time” plot, the transition state distance can be found as this will have no variation in distance with time. rts was found to be 0.908

[[File:BR516_Q2_internuclear_distances_vs_time.PNG|center|thumb|“Internuclear Distances vs Time” plot for 3 H atoms at initial momentum = 0 and initial internuclear separation 0.908]]

====Comment on how the MEP and the trajectory you just calculated differ.====
The MEP (minimum energy path) shows the path of the reaction if the molecules have 0 inertia. This allows the calculation to trace the lowest energy path the reaction could possibly take, the "floor" of the trough in the potential energy surface. The dynamic trajectory takes into account the momentum of the particles. This causes the slight oscillation along the same rough path, as shown by the dynamic plot.

[[File:BR516_Q3_MEP.PNG|center|thumb|MEP contour plot]]
[[File:BR516_Q3_dynamic.PNG|center|thumb|Dynamic contour plot]]

====Complete the table by adding a column with the total energy, and another column reporting if the trajectory is reactive or unreactive. For each set of initial conditions, provide a plot of the trajectory and a small description for what happens along the trajectory.====
{| class="wikitable" border=1
! p1 !! p2 !! Total Energy !! Reactive/Unreactive !! Contour plot !! Description
|-
| -1.25 || -2.5 || -99.018 || Reactive || [[File:BR516_Q4_-1.25_-2.5.PNG]] || The stationary H-H molecule reacts with another colliding H with the correct momentum, and a new H-H bond forms.
|-
| -1.5 || -2.0 || -100.456 || Unreactive || [[File:BR516_Q4_-1.5_-2.0.PNG]] || An oscillating H-H molecule collides with an H, but not with enough momentum to form a new bond so they are repelled.
|-
| -1.5 || -2.5 || -98.956 || Reactive || [[File:BR516_Q4_-1.5_-2.5.PNG]] || An oscilating H-H molecule collides with another H to form a new bond with a higher vibrational frequency
|-
| -2.5 || -5.0 || -84.956 || Unreactive || [[File:BR516_Q4_-2.5_-5.0.PNG]] || A stationary H-H molecule collides with another H to form a new bond, however the H has too much momentum, and is repelled by the B molecuels nucleus. This causes The AB molecule to remain intact with a much larger vibrational mode, and causes the BC distance to increase as it is repelled.
|-
| -2.5 || -5.2 || -83.416 || Reactive || [[File:BR516_Q4_-2.5_-5.2.PNG]] || The AB molecule of H-H collides with the C molecule of H, but unlike in the above condition, The C molecule has enough momentum to recross the transition state region. The BC bonds forms, Breaks into an AB bond then reforms into the BC bond.
|}

====State what are the main assumptions of Transition State Theory. Given the results you have obtained, how will Transition State Theory predictions for reaction rate values compare with experimental values?====
Transition state theory splits the reaction into 2 distinct areas: the reactant and product space. It states that the reactants must cross the energy threshold of the saddle in the transition area to reach the product space. It also assumes atoms obey the laws of classical mechanics using the Born-Oppenheimer approximation, and that each reaction only has 1 saddle point and 1 transition state.

We can see from the above scenarios that for molecules with high momentum, the transition state can be recrossed, so the transition state prediction for reaction rate values will not provide an close approximation to experimental vales run at high temperatures. Therefore, the transition state theory should only be used for reactions at low temperature conditions for predicting reaction rates.

===EXERCISE 2: F - H - H system===
====Classify the F + H2 and H + HF reactions according to their energetics (endothermic or exothermic). How does this relate to the bond strength of the chemical species involved?====
The F + H2 -> FH + H reaction is exothermic, while it's opposite reaction FH + H -> F + H2. This is due to the greater relative strength of the H-F bond (565 kj/mol) to the H-H (432 kj/mol)bond, meaning more energy has to be used to break the H-F bond than is gained forming an H-H bond[1].
====Locate the approximate position of the transition state.====
The transition state of the F - H - H system is found at a distance of 0.745 between H-H and 1.811 between H-F. The Momenta of all particles were set to 0 and the initial distance between them varied until an initial distance was found that would remain constant over time.
[[File:BR516_Q7_Distance_time.PNG|thumb|Interatomic distance vs time with atom A H, atom B H and atom C F at rAB = 0.745 and rBC = 1.811]]

====Report the activation energy for both reactions====
To find the activation energy, the MEP was found for both the formation of H2 and HF from the H-H-F transition state. The minimum energy point from both products was found, and using this value the activation energy can be found (difference between the maximum energy of the saddle and the minimum energy of the products).
H-H-F to HF MEP: Initial energy -103.869, product energy -133.858. Activation energy of HF + H -> H2 + F = +29.989
H-H-F to H2 MEP: Initial energy -103.869, product energy -103.941. Activation energy of H2 + F -> HF + H = + 0.072

[[File:BR516_Q8_MEP_H2_to_HF.PNG|center|thumb|MEP of progression to HF product]]
[[File:BR516_Q8_energy_time_HF.PNG|center|thumb|Energy vs Time of H-H-F to HF product]]
[[File:BR516_Q8_energy_time_HH.PNG|center|thumb|Energy vs Time of H-H-F to H2 product]]
[[File:BR516_Q8_MEP_HH.PNG|center|thumb|MEP of progression to H2 product]]

===References===
[1] http://www.wiredchemist.com/chemistry/data/bond_energies_lengths.html, accessed 19/05/2018

MRD:BR516

2018-05-29T14:57:48Z

Br516:

==BR516 Molecular reaction dynamics==
===Excercise 1: H + H2 system===
====What value do the different components of the gradient of the potential energy surface have at a minimum and at a transition structure? Briefly explain how minima and transition structures can be distinguished using the curvature of the potential energy surface.====

The transition state is the maximum energy point on the minimum energy trough as a saddle point. This transition state has a potential energy gradient of 0 with respect to rAB and rBC. This transition point is a maximum in one direction yet a minimum in another.

The minima, however, are minimums in both directions as ∂2V/∂rAB > 0 and ∂2V/∂rBC > 0. This means any variance in the length of rAB or rBC will lead to an increase of energy, indicating that these regions represent the stable reactants and products.

====Report your best estimate of the transition state position (rts) and explain your reasoning illustrating it with a “Internuclear Distances vs Time” plot for a relevant trajectory.====
Due to the fact that this reaction involves 3 identical atoms, at the transtion state, rAB=rBC. Buy setting the reactants to have no initial momentum, they wont have nay energy to escape the minimum path. By varying the values of rAB and rBC, and observing the “Internuclear Distances vs Time” plot, the transition state distance can be found as this will have no variation in distance with time. rts was found to be 0.908

[[File:BR516_Q2_internuclear_distances_vs_time.PNG|thumb|“Internuclear Distances vs Time” plot for 3 H atoms at initial momentum = 0 and initial internuclear separation 0.908]]

====Comment on how the MEP and the trajectory you just calculated differ.====
The MEP (minimum energy path) shows the path of the reaction if the molecules have 0 inertia. This allows the calculation to trace the lowest energy path the reaction could possibly take, the "floor" of the trough in the potential energy surface. The dynamic trajectory takes into account the momentum of the particles. This causes the slight oscillation along the same rough path, as shown by the dynamic plot.

[[File:BR516_Q3_MEP.PNG|thumb|MEP contour plot]]
[[File:BR516_Q3_dynamic.PNG|thumb|Dynamic contour plot]]

====Complete the table by adding a column with the total energy, and another column reporting if the trajectory is reactive or unreactive. For each set of initial conditions, provide a plot of the trajectory and a small description for what happens along the trajectory.====
{| class="wikitable" border=1
! p1 !! p2 !! Total Energy !! Reactive/Unreactive !! Contour plot !! Description
|-
| -1.25 || -2.5 || -99.018 || Reactive || [[File:BR516_Q4_-1.25_-2.5.PNG]] || The stationary H-H molecule reacts with another colliding H with the correct momentum, and a new H-H bond forms.
|-
| -1.5 || -2.0 || -100.456 || Unreactive || [[File:BR516_Q4_-1.5_-2.0.PNG]] || An oscillating H-H molecule collides with an H, but not with enough momentum to form a new bond so they are repelled.
|-
| -1.5 || -2.5 || -98.956 || Reactive || [[File:BR516_Q4_-1.5_-2.5.PNG]] || An oscilating H-H molecule collides with another H to form a new bond with a higher vibrational frequency
|-
| -2.5 || -5.0 || -84.956 || Unreactive || [[File:BR516_Q4_-2.5_-5.0.PNG]] || A stationary H-H molecule collides with another H to form a new bond, however the H has too much momentum, and is repelled by the B molecuels nucleus. This causes The AB molecule to remain intact with a much larger vibrational mode, and causes the BC distance to increase as it is repelled.
|-
| -2.5 || -5.2 || -83.416 || Reactive || [[File:BR516_Q4_-2.5_-5.2.PNG]] || The AB molecule of H-H collides with the C molecule of H, but unlike in the above condition, The C molecule has enough momentum to recross the transition state region. The BC bonds forms, Breaks into an AB bond then reforms into the BC bond.
|}

====State what are the main assumptions of Transition State Theory. Given the results you have obtained, how will Transition State Theory predictions for reaction rate values compare with experimental values?====
Transition state theory splits the reaction into 2 distinct areas: the reactant and product space. It states that the reactants must cross the energy threshold of the saddle in the transition area to reach the product space. It also assumes atoms obey the laws of classical mechanics using the Born-Oppenheimer approximation, and that each reaction only has 1 saddle point and 1 transition state.

We can see from the above scenarios that for molecules with high momentum, the transition state can be recrossed, so the transition state prediction for reaction rate values will not provide an close approximation to experimental vales run at high temperatures. Therefore, the transition state theory should only be used for reactions at low temperature conditions for predicting reaction rates.

===EXERCISE 2: F - H - H system===
====Classify the F + H2 and H + HF reactions according to their energetics (endothermic or exothermic). How does this relate to the bond strength of the chemical species involved?====
The F + H2 -> FH + H reaction is exothermic, while it's opposite reaction FH + H -> F + H2. This is due to the greater relative strength of the H-F bond (565 kj/mol) to the H-H (432 kj/mol)bond, meaning more energy has to be used to break the H-F bond than is gained forming an H-H bond[1].
====Locate the approximate position of the transition state.====
The transition state of the F - H - H system is found at a distance of 0.745 between H-H and 1.811 between H-F. The Momenta of all particles were set to 0 and the initial distance between them varied until an initial distance was found that would remain constant over time.
[[File:BR516_Q7_Distance_time.PNG|thumb|Interatomic distance vs time with atom A H, atom B H and atom C F at rAB = 0.745 and rBC = 1.811]]

====Report the activation energy for both reactions====
To find the activation energy, the MEP was found for both the formation of H2 and HF from the H-H-F transition state. The minimum energy point from both products was found, and using this value the activation energy can be found (difference between the maximum energy of the saddle and the minimum energy of the products).
H-H-F to HF MEP: Initial energy -103.869, product energy -133.858. Activation energy of HF + H -> H2 + F = +29.989
H-H-F to H2 MEP: Initial energy -103.869, product energy -103.941. Activation energy of H2 + F -> HF + H = + 0.072

[[File:BR516_Q8_MEP_H2_to_HF.PNG|center|thumb|MEP of progression to HF product]]
[[File:BR516_Q8_energy_time_HF.PNG|center|thumb|Energy vs Time of H-H-F to HF product]]
[[File:BR516_Q8_energy_time_HH.PNG|center|thumb|Energy vs Time of H-H-F to H2 product]]
[[File:BR516_Q8_MEP_HH.PNG|center|thumb|MEP of progression to H2 product]]

===References===
[1] http://www.wiredchemist.com/chemistry/data/bond_energies_lengths.html, accessed 19/05/2018

MRD:BR516

2018-05-29T14:56:21Z

Br516:

==BR516 Molecular reaction dynamics==
===Excercise 1: H + H2 system===
====What value do the different components of the gradient of the potential energy surface have at a minimum and at a transition structure? Briefly explain how minima and transition structures can be distinguished using the curvature of the potential energy surface.====

The transition state is the maximum energy point on the minimum energy trough as a saddle point. This transition state has a potential energy gradient of 0 with respect to rAB and rBC. This transition point is a maximum in one direction yet a minimum in another.

The minima, however, are minimums in both directions as ∂2V/∂rAB > 0 and ∂2V/∂rBC > 0. This means any variance in the length of rAB or rBC will lead to an increase of energy, indicating that these regions represent the stable reactants and products.

====Report your best estimate of the transition state position (rts) and explain your reasoning illustrating it with a “Internuclear Distances vs Time” plot for a relevant trajectory.====
Due to the fact that this reaction involves 3 identical atoms, at the transtion state, rAB=rBC. Buy setting the reactants to have no initial momentum, they wont have nay energy to escape the minimum path. By varying the values of rAB and rBC, and observing the “Internuclear Distances vs Time” plot, the transition state distance can be found as this will have no variation in distance with time. rts was found to be 0.908

[[File:BR516_Q2_internuclear_distances_vs_time.PNG|thumb|“Internuclear Distances vs Time” plot for 3 H atoms at initial momentum = 0 and initial internuclear separation 0.908]]

====Comment on how the MEP and the trajectory you just calculated differ.====
The MEP (minimum energy path) shows the path of the reaction if the molecules have 0 inertia. This allows the calculation to trace the lowest energy path the reaction could possibly take, the "floor" of the trough in the potential energy surface. The dynamic trajectory takes into account the momentum of the particles. This causes the slight oscillation along the same rough path, as shown by the dynamic plot.

[[File:BR516_Q3_MEP.PNG|thumb|MEP contour plot]]
[[File:BR516_Q3_dynamic.PNG|thumb|Dynamic contour plot]]

====Complete the table by adding a column with the total energy, and another column reporting if the trajectory is reactive or unreactive. For each set of initial conditions, provide a plot of the trajectory and a small description for what happens along the trajectory.====
{| class="wikitable" border=1
! p1 !! p2 !! Total Energy !! Reactive/Unreactive !! Contour plot !! Description
|-
| -1.25 || -2.5 || -99.018 || Reactive || [[File:BR516_Q4_-1.25_-2.5.PNG]] || The stationary H-H molecule reacts with another colliding H with the correct momentum, and a new H-H bond forms.
|-
| -1.5 || -2.0 || -100.456 || Unreactive || [[File:BR516_Q4_-1.5_-2.0.PNG]] || An oscillating H-H molecule collides with an H, but not with enough momentum to form a new bond so they are repelled.
|-
| -1.5 || -2.5 || -98.956 || Reactive || [[File:BR516_Q4_-1.5_-2.5.PNG]] || An oscilating H-H molecule collides with another H to form a new bond with a higher vibrational frequency
|-
| -2.5 || -5.0 || -84.956 || Unreactive || [[File:BR516_Q4_-2.5_-5.0.PNG]] || A stationary H-H molecule collides with another H to form a new bond, however the H has too much momentum, and is repelled by the B molecuels nucleus. This causes The AB molecule to remain intact with a much larger vibrational mode, and causes the BC distance to increase as it is repelled.
|-
| -2.5 || -5.2 || -83.416 || Reactive || [[File:BR516_Q4_-2.5_-5.2.PNG]] || The AB molecule of H-H collides with the C molecule of H, but unlike in the above condition, The C molecule has enough momentum to recross the transition state region. The BC bonds forms, Breaks into an AB bond then reforms into the BC bond.
|}

====State what are the main assumptions of Transition State Theory. Given the results you have obtained, how will Transition State Theory predictions for reaction rate values compare with experimental values?====
Transition state theory splits the reaction into 2 distinct areas: the reactant and product space. It states that the reactants must cross the energy threshold of the saddle in the transition area to reach the product space. It also assumes atoms obey the laws of classical mechanics using the Born-Oppenheimer approximation, and that each reaction only has 1 saddle point and 1 transition state.

We can see from the above scenarios that for molecules with high momentum, the transition state can be recrossed, so the transition state prediction for reaction rate values will not provide an close approximation to experimental vales run at high temperatures. Therefore, the transition state theory should only be used for reactions at low temperature conditions for predicting reaction rates.

===EXERCISE 2: F - H - H system===
====Classify the F + H2 and H + HF reactions according to their energetics (endothermic or exothermic). How does this relate to the bond strength of the chemical species involved?====
The F + H2 -> FH + H reaction is exothermic, while it's opposite reaction FH + H -> F + H2. This is due to the greater relative strength of the H-F bond (565 kj/mol) to the H-H (432 kj/mol)bond, meaning more energy has to be used to break the H-F bond than is gained forming an H-H bond[1].
====Locate the approximate position of the transition state.====
The transition state of the F - H - H system is found at a distance of 0.745 between H-H and 1.811 between H-F. The Momenta of all particles were set to 0 and the initial distance between them varied until an initial distance was found that would remain constant over time.
[[File:BR516_Q7_Distance_time.PNG|thumb|Interatomic distance vs time with atom A H, atom B H and atom C F at rAB = 0.745 and rBC = 1.811]]

====Report the activation energy for both reactions====
To find the activation energy, the MEP was found for both the formation of H2 and HF from the H-H-F transition state. The minimum energy point from both products was found, and using this value the activation energy can be found (difference between the maximum energy of the saddle and the minimum energy of the products).
H-H-F to HF MEP: Initial energy -103.869, product energy -133.858. Activation energy of HF + H -> H2 + F = +29.989
H-H-F to H2 MEP: Initial energy -103.869, product energy -103.941. Activation energy of H2 + F -> HF + H = + 0.072

[[File:BR516_Q8_MEP_H2_to_HF.PNG|thumb|MEP of progression to HF product]]
[[File:BR516_Q8_energy_time_HF.PNG|thumb|Energy vs Time of H-H-F to HF product]]
[[File:BR516_Q8_energy_time_HH.PNG|thumb|Energy vs Time of H-H-F to H2 product]]
[[File:BR516_Q8_MEP_HH.PNG|thumb|MEP of progression to H2 product]]

===References===
[1] http://www.wiredchemist.com/chemistry/data/bond_energies_lengths.html, accessed 19/05/2018

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Br516: Created page with "==BR516 Molecular reaction dynamics== ===Excercise 1: H + H2 system=== ====What value do the different components of the gradient of the potential energy surface ha..."

Rep:Mod: Brendan Rogers Wiki

2018-05-11T16:30:36Z

Br516:

===BH3===
RB3LYP/6-31G(d,p)

[[file:Br_BH3_freq_pic.PNG|left|thumb|BH3 summary table]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000190 0.000450 YES
RMS Force 0.000095 0.000300 YES
Maximum Displacement 0.000747 0.001800 YES
RMS Displacement 0.000374 0.001200 YES
</pre>

Frequency analysis log file: [[Media:BR BHS FREQ.LOG]]

<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6741
</pre>

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>BR_BHS_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

====Vibrational spectrum for BH3====
{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1164
|92
|A''
|yes
|out-of-plane-bend
|-
|1214
|14
|E'
|very slight
|bend
|-
|1214
|14
|E'
|very slight
|bend
|-
|2580
|0
|A'
|no
|symmetric stretch
|-
|2713
|126
|E'
|yes
|asymmetric stretch
|-
|2713
|126
|E'
|yes
|asymmetric stretch
|}

[[File:BR BH3 IR Spectrum.PNG]]
There are only 3 peaks, due to the 2 sets of degenerate vibrational modes and the 1 IR inactive vibrational mode.

====BH3 MO diagram====
[[File:BR BH3 MO diagram.png|left|thumb|Predicted orbitals next to actual orbitals. Predicted MO diagram taken from http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf]]
For all occupied orbitals the AO combinations produced fairly accurate results. They also gave fairly accurate results for the a2'' unoccupied MO, but not for a1' MO diagram. This shows that using linear combinations of AOs can produce good estimations, but can be inaccurate in reality.

===NH3===
B3LYP/6-31G(d,p)

[[File:BR_NH3_freq_pic.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000039 0.001800 YES
RMS Displacement 0.000013 0.001200 YES
</pre>

Frequency file: [[File:BR_NH3_FREQ_631G_DP.LOG]]

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0041 0.0455 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>BR_NH3_FREQ_631G_DP.LOG</uploadedFileContents>
</jmolApplet></jmol>

===NH3BH3===
B3LYP/6-31G(d,p)

[[File:BR_NH3BR3_freq_pic.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000115 0.000450 YES
RMS Force 0.000060 0.000300 YES
Maximum Displacement 0.000584 0.001800 YES
RMS Displacement 0.000345 0.001200 YES
</pre>

Frequency file: [[File:BR_NH3BH3_FREQ 631G_DP_2.LOG]]

<pre>
Low frequencies --- 0.0004 0.0009 0.0012 16.4186 17.2680 37.2272
Low frequencies --- 265.8841 632.2034 639.2870
</pre>

<jmol><jmolApplet>
<title>NH3Br3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>BR_NH3BH3_FREQ 631G_DP_2.LOG</uploadedFileContents>
</jmolApplet></jmol>

===BBr3===
B3LYP/6-31G(d,p)

{{DOI|10042/202397}}
[[File:BR_BBr3_freq_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000058 0.001800 YES
RMS Displacement 0.000034 0.001200 YES
</pre>

Frequency file: [[File:BR_BBr3_freq_dp_good.log]]

<pre>
Low frequencies --- -1.9018 -0.0001 0.0002 0.0002 1.5796 3.2831
Low frequencies --- 155.9053 155.9625 267.7047
</pre>

<jmol><jmolApplet>
<title>BBr3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>BR_BBr3_freq_dp_good.log</uploadedFileContents>
</jmolApplet></jmol>

====Calculating Association energy of Borane====
E(NH3)= -56.55777 a.u.
E(BH3)= -26.61532 a.u.
E(NH3BH3)= -83.22469 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -83.22469 - [-56.55777 + -26.61532] = -0.05160 a.u. = -129 Kj/mol

This value shows it is a weak bond, as can be shown by comparing it to a strong bond (e.g. C-C bond strength is 346 Kj/mol) and seeing the value is far lower.

==Aromaticity==
===Benzene===
B3LYP/6-31G(d,p)

[[File:Br_Benzene_freq_summary_2.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000101 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000158 0.001800 YES
RMS Displacement 0.000068 0.001200 YES
</pre>

Frequency file: [[File:BR_BENZENE_FREQ_631G_2.LOG]]

<pre>
Low frequencies --- -17.1502 -13.8161 -0.0003 -0.0002 -0.0002 1.7484
Low frequencies --- 414.1959 414.6468 620.9365
</pre>

<jmol><jmolApplet>
<title>Benzene</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>BR_BENZENE_FREQ_631G_2.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Borazine===
B3LYP/6-31G(d,p)

[[File:Br_Borazine_freq_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000268 0.000450 YES
RMS Force 0.000111 0.000300 YES
Maximum Displacement 0.000537 0.001800 YES
RMS Displacement 0.000253 0.001200 YES
</pre>

Frequency file: [[File:BR_BORAZINE_FREQ_631G_DP_2.LOG]]

<pre>
Low frequencies --- -14.1757 -13.8386 -10.2802 -0.0163 -0.0114 0.0344
Low frequencies --- 289.0978 289.0995 404.2449
</pre>

<jmol><jmolApplet>
<title>Borazine</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>BR_BORAZINE_FREQ_631G_DP_2.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Charge comparison between aromatic systems===
As seen below, while being isoelectronic, benzene and borazine have very different NBO charge distributions.Benzene Has a electronegative center caused by the delocalized pi system surrounding the carbon atoms. This results in all carbon atoms being equally electron dense (-0.239 arbitrary units) and all hydrogen atoms being equally less electron dense (+0.239 arbitrary units). Borazine is a different story, however, due to the large difference in electronegativity of boron and nitrogen in the central ring. Nitrogen is far smaller and electron dense than boron, causing it to be more electron rich (-1.102 arbitrary units) and drawing electron away from neighboring hydrogen atoms (+0.432 arbitrary units) and boron atoms (+0.747). The hydrogen atoms next to boron have a near neutral charge though, due to hydrogen and boron having similar Pauling electronegativity values.

{| class="wikitable"
|+
|-
|Benzene||Borazine
|-
|[[File:Benzene_charge_distribution.PNG]]
|[[File:Borazine_charge_distribution.PNG]]
|}

===Comparison of Molecular orbitals between aromatic systems===

{| class="wikitable"
|+
|-
|MO||Benzene||MO||Borazine||Comments
|-
|13
|[[File:Br_Benzene_MO_13.PNG]]
|16
|[[File:BR_Borazine_MO_16.PNG]]
|These orbitals have a similar phase distribution, alternating between each atom in the central ring. MO 13 on benzene is completely symmetrical, with each lobe of the orbital the same size over the carbon and hydrogen atoms. MO 16 on borazine has small lobes connecting the nitrogen to hydrogen, due to the greater electronegativity of nitrogen creating a greater charge density and smaller volume. Both orbitals show bonding character between the central atoms and the hydrogen atoms, and anti-bonding character between the inner ring members. Mo 16 represents a LCAO more strongly, showing an sp2 orbital on the central atoms mixing with an s orbital of the hydrogens.
|-
|17
|[[File:BR_Benzene_MO 17.PNG]]
|17
|[[File:Br_Borazine_MO_17.PNG]]
|These orbitals look very similar, representing one of the orbitals that make up the aromatic systems of benzene and borazine. They show a pi bonding character between the atoms on each ring, showing shared electron density between them. Both orbitals are perfectly symmetrical in a mirror plane parallel to the ring. MO 17 on benzene has 2 lobes each with 6 points of equal size over each carbon. MO 17 on borazine has 2 lobes each with 6 points but with slightly larger electron clouds over the nitrogen atoms compared to the boron atoms.
|-
|14
|[[File:BR_Benzene_MO_14.PNG]]
|15
|[[File:BR_Borazine_MO_15.PNG]]
|These orbitals also look very similar, showing a sigma bonding character between the atoms on the central ring.They both have 6 lobes with alternating phase, forming wedge shapes in between the central atoms. MO 14 for benzene shows 6 equally sized lobes, while MO 15 for borazine has slightly smaller electron clouds around nitrogen due to it's greater electronegativity compared to boron.
|}

===Nature of Aromaticity===
A common understanding or aromaticity is that in a planar ring system with 4n+2 electrons (Hückel's rule), each carbon atom will form a sigma bond to each other then form a conjugated pi bond above and below the ring. Each carbon will form equal distant bonds to each other longer than a double bond but shorter than a single bond. The enthalpy of the bonds will be above a single bond, but below a double bond. They will also resist reactions that would proceed rapidly with a double bond, requiring a species to activate the ring system. In addition, they will form a ring current when under the influence of an external magnetic field, leading to increased diamagnetic susceptability. These concepts of aromaticity taken from: https://onlinelibrary.wiley.com/doi/epdf/10.1002/chem.200700250 . Aromatic compounds do not have to contain carbon, as shown by borazine, which contains only boron, nitrogen and hydrogen. This concept can be seen in MO 17 of benzene and MO 17 of borazine, showing an electron cloud delocalised above and below the ring.

Overlapping P orbitals, however, do not provide a complete picture of aromaticity. The atomic orbitals combine to form a cloud completely covering the top and bottom of the ring, as shown by MO 17 of benzene and MO 17 of borazine, rather than forming a ring above and below the atoms on the ring. Some of the MOs of both compound represent linear combinations of atomic orbitals, while many are not combinations of atomic orbitals. The molecules form clear sigma bonds and pi bonds, with bonding and antibonding orbitals representing each, with some MOs representing neither. The P orbital overlap also breaks down quite clearly when observing the MOs of borazine, as the MOs show clear ionic character due to the difference in electronegativity of boron and nitrogen, showing distortions in the aromatic system drawing electron density to the nitrogen atoms.

Rep:Mod: Brendan Rogers Wiki

2018-05-11T16:29:22Z

Br516:

===BH3===
RB3LYP/6-31G(d,p)

[[file:Br_BH3_freq_pic.PNG|left|thumb|BH3 summary table]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000190 0.000450 YES
RMS Force 0.000095 0.000300 YES
Maximum Displacement 0.000747 0.001800 YES
RMS Displacement 0.000374 0.001200 YES
</pre>

Frequency analysis log file: [[Media:BR BHS FREQ.LOG]]

<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6741
</pre>

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>BR_BHS_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

====Vibrational spectrum for BH3====
{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1164
|92
|A''
|yes
|out-of-plane-bend
|-
|1214
|14
|E'
|very slight
|bend
|-
|1214
|14
|E'
|very slight
|bend
|-
|2580
|0
|A'
|no
|symmetric stretch
|-
|2713
|126
|E'
|yes
|asymmetric stretch
|-
|2713
|126
|E'
|yes
|asymmetric stretch
|}

[[File:BR BH3 IR Spectrum.PNG]]
There are only 3 peaks, due to the 2 sets of degenerate vibrational modes and the 1 IR inactive vibrational mode.

====BH3 MO diagram====
[[File:BR BH3 MO diagram.png|left|thumb|Predicted orbitals next to actual orbitals. Predicted MO diagram taken from http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf]]
For all occupied orbitals the AO combinations produced fairly accurate results. They also gave fairly accurate results for the a2'' unoccupied MO, but not for a1' MO diagram. This shows that using linear combinations of AOs can produce good estimations, but can be inaccurate in reality.

===NH3===
B3LYP/6-31G(d,p)

[[File:BR_NH3_freq_pic.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000039 0.001800 YES
RMS Displacement 0.000013 0.001200 YES
</pre>

Frequency file: [[File:BR_NH3_FREQ_631G_DP.LOG]]

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0041 0.0455 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>BR_NH3_FREQ_631G_DP.LOG</uploadedFileContents>
</jmolApplet></jmol>

===NH3BH3===
B3LYP/6-31G(d,p)

[[File:BR_NH3BR3_freq_pic.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000115 0.000450 YES
RMS Force 0.000060 0.000300 YES
Maximum Displacement 0.000584 0.001800 YES
RMS Displacement 0.000345 0.001200 YES
</pre>

Frequency file: [[File:BR_NH3BH3_FREQ 631G_DP_2.LOG]]

<pre>
Low frequencies --- 0.0004 0.0009 0.0012 16.4186 17.2680 37.2272
Low frequencies --- 265.8841 632.2034 639.2870
</pre>

<jmol><jmolApplet>
<title>NH3Br3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>BR_NH3BH3_FREQ 631G_DP_2.LOG</uploadedFileContents>
</jmolApplet></jmol>

===BBr3===
B3LYP/6-31G(d,p)

{{DOI|10042/202397}}
[[File:BR_BBr3_freq_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000058 0.001800 YES
RMS Displacement 0.000034 0.001200 YES
</pre>

Frequency file: [[File:BR_BBr3_freq_dp_good.log]]

<pre>
Low frequencies --- -1.9018 -0.0001 0.0002 0.0002 1.5796 3.2831
Low frequencies --- 155.9053 155.9625 267.7047
</pre>

<jmol><jmolApplet>
<title>BBr3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>BR_BBr3_freq_dp_good.log</uploadedFileContents>
</jmolApplet></jmol>

====Calculating Association energy of Borane====
E(NH3)= -56.55777 a.u.
E(BH3)= -26.61532 a.u.
E(NH3BH3)= -83.22469 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -83.22469 - [-56.55777 + -26.61532] = -0.05160 a.u. = -129 Kj/mol

This value shows it is a weak bond, as can be shown by comparing it to a strong bond (e.g. C-C bond strength is 346 Kj/mol) and seeing the value is far lower.

==Aromaticity==
===Benzene===
B3LYP/6-31G(d,p)

[[File:Br_Benzene_freq_summary_2.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000101 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000158 0.001800 YES
RMS Displacement 0.000068 0.001200 YES
</pre>

Frequency file: [[File:BR_BENZENE_FREQ_631G_2.LOG]]

<pre>
Low frequencies --- -17.1502 -13.8161 -0.0003 -0.0002 -0.0002 1.7484
Low frequencies --- 414.1959 414.6468 620.9365
</pre>

<jmol><jmolApplet>
<title>Benzene</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>BR_BENZENE_FREQ_631G_2.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Borazine===
B3LYP/6-31G(d,p)

[[File:Br_Borazine_freq_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000268 0.000450 YES
RMS Force 0.000111 0.000300 YES
Maximum Displacement 0.000537 0.001800 YES
RMS Displacement 0.000253 0.001200 YES
</pre>

Frequency file: [[File:BR_BORAZINE_FREQ_631G_DP_2.LOG]]

<pre>
Low frequencies --- -14.1757 -13.8386 -10.2802 -0.0163 -0.0114 0.0344
Low frequencies --- 289.0978 289.0995 404.2449
</pre>

<jmol><jmolApplet>
<title>Borazine</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>BR_BORAZINE_FREQ_631G_DP_2.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Charge comparison between aromatic systems===
As seen below, while being isoelectronic, benzene and borazine have very different NBO charge distributions.Benzene Has a electronegative center caused by the delocalized pi system surrounding the carbon atoms. This results in all carbon atoms being equally electron dense (-0.239 arbitrary units) and all hydrogen atoms being equally less electron dense (+0.239 arbitrary units). Borazine is a different story, however, due to the large difference in electronegativity of boron and nitrogen in the central ring. Nitrogen is far smaller and electron dense than boron, causing it to be more electron rich (-1.102 arbitrary units) and drawing electron away from neighboring hydrogen atoms (+0.432 arbitrary units) and boron atoms (+0.747). The hydrogen atoms next to boron have a near neutral charge though, due to hydrogen and boron having similar Pauling electronegativity values.

{| class="wikitable"
|+
|-
|Benzene||Borazine
|-
|[[File:Benzene_charge_distribution.PNG]]
|[[File:Borazine_charge_distribution.PNG]]
|}

===Comparison of Molecular orbitals between aromatic systems===

{| class="wikitable"
|+
|-
|MO||Benzene||MO||Borazine||Comments
|-
|13
|[[File:Br_Benzene_MO_13.PNG]]
|16
|[[File:BR_Borazine_MO_16.PNG]]
|These orbitals have a similar phase distribution, alternating between each atom in the central ring. MO 13 on benzene is completely symmetrical, with each lobe of the orbital the same size over the carbon and hydrogen atoms. MO 16 on borazine has small lobes connecting the nitrogen to hydrogen, due to the greater electronegativity of nitrogen creating a greater charge density and smaller volume. Both orbitals show bonding character between the central atoms and the hydrogen atoms, and anti-bonding character between the inner ring members. Mo 16 represents a LCAO more strongly, showing an sp2 orbital on the central atoms mixing with an s orbital of the hydrogens.
|-
|17
|[[File:BR_Benzene_MO 17.PNG]]
|17
|[[File:Br_Borazine_MO_17.PNG]]
|These orbitals look very similar, representing one of the orbitals that make up the aromatic systems of benzene and borazine. They show a pi bonding character between the atoms on each ring, showing shared electron density between them. Both orbitals are perfectly symmetrical in a mirror plane parallel to the ring. MO 17 on benzene has 2 lobes each with 6 points of equal size over each carbon. MO 17 on borazine has 2 lobes each with 6 points but with slightly larger electron clouds over the nitrogen atoms compared to the boron atoms.
|-
|14
|[[File:BR_Benzene_MO_14.PNG]]
|15
|[[File:BR_Borazine_MO_15.PNG]]
|These orbitals also look very similar, showing a sigma bonding character between the atoms on the central ring.They both have 6 lobes with alternating phase, forming wedge shapes in between the central atoms. MO 14 for benzene shows 6 equally sized lobes, while MO 15 for borazine has slightly smaller electron clouds around nitrogen due to it's greater electronegativity compared to boron.
|}

===Nature of Aromaticity===
A common understanding or aromaticity is that in a planar ring system with 4n+2 electrons (Hückel's rule), each carbon atom will form a sigma bond to each other then form a conjugated pi bond above and below the ring. [https://onlinelibrary.wiley.com/doi/epdf/10.1002/chem.200700250||Each carbon will form equal distant bonds to each other longer than a double bond but shorter than a single bond. The enthalpy of the bonds will be above a single bond, but below a double bond. They will also resist reactions that would proceed rapidly with a double bond, requiring a species to activate the ring system. In addition, they will form a ring current when under the influence of an external magnetic field, leading to increased diamagnetic susceptability.] Aromatic compounds do not have to contain carbon, as shown by borazine, which contains only boron, nitrogen and hydrogen. This concept can be seen in MO 17 of benzene and MO 17 of borazine, showing an electron cloud delocalised above and below the ring.

Overlapping P orbitals, however, do not provide a complete picture of aromaticity. The atomic orbitals combine to form a cloud completely covering the top and bottom of the ring, as shown by MO 17 of benzene and MO 17 of borazine, rather than forming a ring above and below the atoms on the ring. Some of the MOs of both compound represent linear combinations of atomic orbitals, while many are not combinations of atomic orbitals. The molecules form clear sigma bonds and pi bonds, with bonding and antibonding orbitals representing each, with some MOs representing neither. The P orbital overlap also breaks down quite clearly when observing the MOs of borazine, as the MOs show clear ionic character due to the difference in electronegativity of boron and nitrogen, showing distortions in the aromatic system drawing electron density to the nitrogen atoms.

Rep:Mod: Brendan Rogers Wiki

2018-05-11T16:28:50Z

Br516:

===BH3===
RB3LYP/6-31G(d,p)

[[file:Br_BH3_freq_pic.PNG|left|thumb|BH3 summary table]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000190 0.000450 YES
RMS Force 0.000095 0.000300 YES
Maximum Displacement 0.000747 0.001800 YES
RMS Displacement 0.000374 0.001200 YES
</pre>

Frequency analysis log file: [[Media:BR BHS FREQ.LOG]]

<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6741
</pre>

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>BR_BHS_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

====Vibrational spectrum for BH3====
{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1164
|92
|A''
|yes
|out-of-plane-bend
|-
|1214
|14
|E'
|very slight
|bend
|-
|1214
|14
|E'
|very slight
|bend
|-
|2580
|0
|A'
|no
|symmetric stretch
|-
|2713
|126
|E'
|yes
|asymmetric stretch
|-
|2713
|126
|E'
|yes
|asymmetric stretch
|}

[[File:BR BH3 IR Spectrum.PNG]]
There are only 3 peaks, due to the 2 sets of degenerate vibrational modes and the 1 IR inactive vibrational mode.

====BH3 MO diagram====
[[File:BR BH3 MO diagram.png|left|thumb|Predicted orbitals next to actual orbitals. Predicted MO diagram taken from http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf]]
For all occupied orbitals the AO combinations produced fairly accurate results. They also gave fairly accurate results for the a2'' unoccupied MO, but not for a1' MO diagram. This shows that using linear combinations of AOs can produce good estimations, but can be inaccurate in reality.

===NH3===
B3LYP/6-31G(d,p)

[[File:BR_NH3_freq_pic.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000039 0.001800 YES
RMS Displacement 0.000013 0.001200 YES
</pre>

Frequency file: [[File:BR_NH3_FREQ_631G_DP.LOG]]

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0041 0.0455 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>BR_NH3_FREQ_631G_DP.LOG</uploadedFileContents>
</jmolApplet></jmol>

===NH3BH3===
B3LYP/6-31G(d,p)

[[File:BR_NH3BR3_freq_pic.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000115 0.000450 YES
RMS Force 0.000060 0.000300 YES
Maximum Displacement 0.000584 0.001800 YES
RMS Displacement 0.000345 0.001200 YES
</pre>

Frequency file: [[File:BR_NH3BH3_FREQ 631G_DP_2.LOG]]

<pre>
Low frequencies --- 0.0004 0.0009 0.0012 16.4186 17.2680 37.2272
Low frequencies --- 265.8841 632.2034 639.2870
</pre>

<jmol><jmolApplet>
<title>NH3Br3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>BR_NH3BH3_FREQ 631G_DP_2.LOG</uploadedFileContents>
</jmolApplet></jmol>

===BBr3===
B3LYP/6-31G(d,p)

{{DOI|10042/202397}}
[[File:BR_BBr3_freq_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000058 0.001800 YES
RMS Displacement 0.000034 0.001200 YES
</pre>

Frequency file: [[File:BR_BBr3_freq_dp_good.log]]

<pre>
Low frequencies --- -1.9018 -0.0001 0.0002 0.0002 1.5796 3.2831
Low frequencies --- 155.9053 155.9625 267.7047
</pre>

<jmol><jmolApplet>
<title>BBr3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>BR_BBr3_freq_dp_good.log</uploadedFileContents>
</jmolApplet></jmol>

====Calculating Association energy of Borane====
E(NH3)= -56.55777 a.u.
E(BH3)= -26.61532 a.u.
E(NH3BH3)= -83.22469 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -83.22469 - [-56.55777 + -26.61532] = -0.05160 a.u. = -129 Kj/mol

This value shows it is a weak bond, as can be shown by comparing it to a strong bond (e.g. C-C bond strength is 346 Kj/mol) and seeing the value is far lower.

==Aromaticity==
===Benzene===
B3LYP/6-31G(d,p)

[[File:Br_Benzene_freq_summary_2.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000101 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000158 0.001800 YES
RMS Displacement 0.000068 0.001200 YES
</pre>

Frequency file: [[File:BR_BENZENE_FREQ_631G_2.LOG]]

<pre>
Low frequencies --- -17.1502 -13.8161 -0.0003 -0.0002 -0.0002 1.7484
Low frequencies --- 414.1959 414.6468 620.9365
</pre>

<jmol><jmolApplet>
<title>Benzene</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>BR_BENZENE_FREQ_631G_2.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Borazine===
B3LYP/6-31G(d,p)

[[File:Br_Borazine_freq_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000268 0.000450 YES
RMS Force 0.000111 0.000300 YES
Maximum Displacement 0.000537 0.001800 YES
RMS Displacement 0.000253 0.001200 YES
</pre>

Frequency file: [[File:BR_BORAZINE_FREQ_631G_DP_2.LOG]]

<pre>
Low frequencies --- -14.1757 -13.8386 -10.2802 -0.0163 -0.0114 0.0344
Low frequencies --- 289.0978 289.0995 404.2449
</pre>

<jmol><jmolApplet>
<title>Borazine</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>BR_BORAZINE_FREQ_631G_DP_2.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Charge comparison between aromatic systems===
As seen below, while being isoelectronic, benzene and borazine have very different NBO charge distributions.Benzene Has a electronegative center caused by the delocalized pi system surrounding the carbon atoms. This results in all carbon atoms being equally electron dense (-0.239 arbitrary units) and all hydrogen atoms being equally less electron dense (+0.239 arbitrary units). Borazine is a different story, however, due to the large difference in electronegativity of boron and nitrogen in the central ring. Nitrogen is far smaller and electron dense than boron, causing it to be more electron rich (-1.102 arbitrary units) and drawing electron away from neighboring hydrogen atoms (+0.432 arbitrary units) and boron atoms (+0.747). The hydrogen atoms next to boron have a near neutral charge though, due to hydrogen and boron having similar Pauling electronegativity values.

{| class="wikitable"
|+
|-
|Benzene||Borazine
|-
|[[File:Benzene_charge_distribution.PNG]]
|[[File:Borazine_charge_distribution.PNG]]
|}

===Comparison of Molecular orbitals between aromatic systems===

{| class="wikitable"
|+
|-
|MO||Benzene||MO||Borazine||Comments
|-
|13
|[[File:Br_Benzene_MO_13.PNG]]
|16
|[[File:BR_Borazine_MO_16.PNG]]
|These orbitals have a similar phase distribution, alternating between each atom in the central ring. MO 13 on benzene is completely symmetrical, with each lobe of the orbital the same size over the carbon and hydrogen atoms. MO 16 on borazine has small lobes connecting the nitrogen to hydrogen, due to the greater electronegativity of nitrogen creating a greater charge density and smaller volume. Both orbitals show bonding character between the central atoms and the hydrogen atoms, and anti-bonding character between the inner ring members. Mo 16 represents a LCAO more strongly, showing an sp2 orbital on the central atoms mixing with an s orbital of the hydrogens.
|-
|17
|[[File:BR_Benzene_MO 17.PNG]]
|17
|[[File:Br_Borazine_MO_17.PNG]]
|These orbitals look very similar, representing one of the orbitals that make up the aromatic systems of benzene and borazine. They show a pi bonding character between the atoms on each ring, showing shared electron density between them. Both orbitals are perfectly symmetrical in a mirror plane parallel to the ring. MO 17 on benzene has 2 lobes each with 6 points of equal size over each carbon. MO 17 on borazine has 2 lobes each with 6 points but with slightly larger electron clouds over the nitrogen atoms compared to the boron atoms.
|-
|14
|[[File:BR_Benzene_MO_14.PNG]]
|15
|[[File:BR_Borazine_MO_15.PNG]]
|These orbitals also look very similar, showing a sigma bonding character between the atoms on the central ring.They both have 6 lobes with alternating phase, forming wedge shapes in between the central atoms. MO 14 for benzene shows 6 equally sized lobes, while MO 15 for borazine has slightly smaller electron clouds around nitrogen due to it's greater electronegativity compared to boron.
|}

===Nature of Aromaticity===
A common understanding or aromaticity is that in a planar ring system with 4n+2 electrons (Hückel's rule), each carbon atom will form a sigma bond to each other then form a conjugated pi bond above and below the ring. [https://onlinelibrary.wiley.com/doi/epdf/10.1002/chem.200700250|Each carbon will form equal distant bonds to each other longer than a double bond but shorter than a single bond. The enthalpy of the bonds will be above a single bond, but below a double bond. They will also resist reactions that would proceed rapidly with a double bond, requiring a species to activate the ring system. In addition, they will form a ring current when under the influence of an external magnetic field, leading to increased diamagnetic susceptability.] Aromatic compounds do not have to contain carbon, as shown by borazine, which contains only boron, nitrogen and hydrogen. This concept can be seen in MO 17 of benzene and MO 17 of borazine, showing an electron cloud delocalised above and below the ring.

Overlapping P orbitals, however, do not provide a complete picture of aromaticity. The atomic orbitals combine to form a cloud completely covering the top and bottom of the ring, as shown by MO 17 of benzene and MO 17 of borazine, rather than forming a ring above and below the atoms on the ring. Some of the MOs of both compound represent linear combinations of atomic orbitals, while many are not combinations of atomic orbitals. The molecules form clear sigma bonds and pi bonds, with bonding and antibonding orbitals representing each, with some MOs representing neither. The P orbital overlap also breaks down quite clearly when observing the MOs of borazine, as the MOs show clear ionic character due to the difference in electronegativity of boron and nitrogen, showing distortions in the aromatic system drawing electron density to the nitrogen atoms.

Rep:Mod: Brendan Rogers Wiki

2018-05-11T16:23:57Z

Br516:

===BH3===
RB3LYP/6-31G(d,p)

[[file:Br_BH3_freq_pic.PNG|left|thumb|BH3 summary table]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000190 0.000450 YES
RMS Force 0.000095 0.000300 YES
Maximum Displacement 0.000747 0.001800 YES
RMS Displacement 0.000374 0.001200 YES
</pre>

Frequency analysis log file: [[Media:BR BHS FREQ.LOG]]

<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6741
</pre>

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>BR_BHS_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

====Vibrational spectrum for BH3====
{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1164
|92
|A''
|yes
|out-of-plane-bend
|-
|1214
|14
|E'
|very slight
|bend
|-
|1214
|14
|E'
|very slight
|bend
|-
|2580
|0
|A'
|no
|symmetric stretch
|-
|2713
|126
|E'
|yes
|asymmetric stretch
|-
|2713
|126
|E'
|yes
|asymmetric stretch
|}

[[File:BR BH3 IR Spectrum.PNG]]
There are only 3 peaks, due to the 2 sets of degenerate vibrational modes and the 1 IR inactive vibrational mode.

====BH3 MO diagram====
[[File:BR BH3 MO diagram.png|left|thumb|Predicted orbitals next to actual orbitals. Predicted MO diagram taken from http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf]]
For all occupied orbitals the AO combinations produced fairly accurate results. They also gave fairly accurate results for the a2'' unoccupied MO, but not for a1' MO diagram. This shows that using linear combinations of AOs can produce good estimations, but can be inaccurate in reality.

===NH3===
B3LYP/6-31G(d,p)

[[File:BR_NH3_freq_pic.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000039 0.001800 YES
RMS Displacement 0.000013 0.001200 YES
</pre>

Frequency file: [[File:BR_NH3_FREQ_631G_DP.LOG]]

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0041 0.0455 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>BR_NH3_FREQ_631G_DP.LOG</uploadedFileContents>
</jmolApplet></jmol>

===NH3BH3===
B3LYP/6-31G(d,p)

[[File:BR_NH3BR3_freq_pic.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000115 0.000450 YES
RMS Force 0.000060 0.000300 YES
Maximum Displacement 0.000584 0.001800 YES
RMS Displacement 0.000345 0.001200 YES
</pre>

Frequency file: [[File:BR_NH3BH3_FREQ 631G_DP_2.LOG]]

<pre>
Low frequencies --- 0.0004 0.0009 0.0012 16.4186 17.2680 37.2272
Low frequencies --- 265.8841 632.2034 639.2870
</pre>

<jmol><jmolApplet>
<title>NH3Br3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>BR_NH3BH3_FREQ 631G_DP_2.LOG</uploadedFileContents>
</jmolApplet></jmol>

===BBr3===
B3LYP/6-31G(d,p)

{{DOI|10042/202397}}
[[File:BR_BBr3_freq_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000058 0.001800 YES
RMS Displacement 0.000034 0.001200 YES
</pre>

Frequency file: [[File:BR_BBr3_freq_dp_good.log]]

<pre>
Low frequencies --- -1.9018 -0.0001 0.0002 0.0002 1.5796 3.2831
Low frequencies --- 155.9053 155.9625 267.7047
</pre>

<jmol><jmolApplet>
<title>BBr3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>BR_BBr3_freq_dp_good.log</uploadedFileContents>
</jmolApplet></jmol>

====Calculating Association energy of Borane====
E(NH3)= -56.55777 a.u.
E(BH3)= -26.61532 a.u.
E(NH3BH3)= -83.22469 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -83.22469 - [-56.55777 + -26.61532] = -0.05160 a.u. = -129 Kj/mol

This value shows it is a weak bond, as can be shown by comparing it to a strong bond (e.g. C-C bond strength is 346 Kj/mol) and seeing the value is far lower.

==Aromaticity==
===Benzene===
B3LYP/6-31G(d,p)

[[File:Br_Benzene_freq_summary_2.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000101 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000158 0.001800 YES
RMS Displacement 0.000068 0.001200 YES
</pre>

Frequency file: [[File:BR_BENZENE_FREQ_631G_2.LOG]]

<pre>
Low frequencies --- -17.1502 -13.8161 -0.0003 -0.0002 -0.0002 1.7484
Low frequencies --- 414.1959 414.6468 620.9365
</pre>

<jmol><jmolApplet>
<title>Benzene</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>BR_BENZENE_FREQ_631G_2.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Borazine===
B3LYP/6-31G(d,p)

[[File:Br_Borazine_freq_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000268 0.000450 YES
RMS Force 0.000111 0.000300 YES
Maximum Displacement 0.000537 0.001800 YES
RMS Displacement 0.000253 0.001200 YES
</pre>

Frequency file: [[File:BR_BORAZINE_FREQ_631G_DP_2.LOG]]

<pre>
Low frequencies --- -14.1757 -13.8386 -10.2802 -0.0163 -0.0114 0.0344
Low frequencies --- 289.0978 289.0995 404.2449
</pre>

<jmol><jmolApplet>
<title>Borazine</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>BR_BORAZINE_FREQ_631G_DP_2.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Charge comparison between aromatic systems===
As seen below, while being isoelectronic, benzene and borazine have very different NBO charge distributions.Benzene Has a electronegative center caused by the delocalized pi system surrounding the carbon atoms. This results in all carbon atoms being equally electron dense (-0.239 arbitrary units) and all hydrogen atoms being equally less electron dense (+0.239 arbitrary units). Borazine is a different story, however, due to the large difference in electronegativity of boron and nitrogen in the central ring. Nitrogen is far smaller and electron dense than boron, causing it to be more electron rich (-1.102 arbitrary units) and drawing electron away from neighboring hydrogen atoms (+0.432 arbitrary units) and boron atoms (+0.747). The hydrogen atoms next to boron have a near neutral charge though, due to hydrogen and boron having similar Pauling electronegativity values.

{| class="wikitable"
|+
|-
|Benzene||Borazine
|-
|[[File:Benzene_charge_distribution.PNG]]
|[[File:Borazine_charge_distribution.PNG]]
|}

===Comparison of Molecular orbitals between aromatic systems===

{| class="wikitable"
|+
|-
|MO||Benzene||MO||Borazine||Comments
|-
|13
|[[File:Br_Benzene_MO_13.PNG]]
|16
|[[File:BR_Borazine_MO_16.PNG]]
|These orbitals have a similar phase distribution, alternating between each atom in the central ring. MO 13 on benzene is completely symmetrical, with each lobe of the orbital the same size over the carbon and hydrogen atoms. MO 16 on borazine has small lobes connecting the nitrogen to hydrogen, due to the greater electronegativity of nitrogen creating a greater charge density and smaller volume. Both orbitals show bonding character between the central atoms and the hydrogen atoms, and anti-bonding character between the inner ring members. Mo 16 represents a LCAO more strongly, showing an sp2 orbital on the central atoms mixing with an s orbital of the hydrogens.
|-
|17
|[[File:BR_Benzene_MO 17.PNG]]
|17
|[[File:Br_Borazine_MO_17.PNG]]
|These orbitals look very similar, representing one of the orbitals that make up the aromatic systems of benzene and borazine. They show a pi bonding character between the atoms on each ring, showing shared electron density between them. Both orbitals are perfectly symmetrical in a mirror plane parallel to the ring. MO 17 on benzene has 2 lobes each with 6 points of equal size over each carbon. MO 17 on borazine has 2 lobes each with 6 points but with slightly larger electron clouds over the nitrogen atoms compared to the boron atoms.
|-
|14
|[[File:BR_Benzene_MO_14.PNG]]
|15
|[[File:BR_Borazine_MO_15.PNG]]
|These orbitals also look very similar, showing a sigma bonding character between the atoms on the central ring.They both have 6 lobes with alternating phase, forming wedge shapes in between the central atoms. MO 14 for benzene shows 6 equally sized lobes, while MO 15 for borazine has slightly smaller electron clouds around nitrogen due to it's greater electronegativity compared to boron.
|}

===Nature of Aromaticity===
A common understanding or aromaticity is that in a planar ring system with [https://en.wikipedia.org/wiki/H%C3%BCckel%27s_rule|4n+2 electrons], each carbon atom will form a sigma bond to each other then form a conjugated pi bond above and below the ring. [https://onlinelibrary.wiley.com/doi/epdf/10.1002/chem.200700250|Each carbon will form equal distant bonds to each other longer than a double bond but shorter than a single bond. The enthalpy of the bonds will be above a single bond, but below a double bond. They will also resist reactions that would proceed rapidly with a double bond, requiring a species to activate the ring system. In addition, they will form a ring current when under the influence of an external magnetic field, leading to increased diamagnetic susceptability.] Aromatic compounds do not have to contain carbon, as shown by borazine, which contains only boron, nitrogen and hydrogen. This concept can be seen in MO 17 of benzene and MO 17 of borazine, showing an electron cloud delocalised above and below the ring.

Overlapping P orbitals, however, do not provide a complete picture of aromaticity. The atomic orbitals combine to form a cloud completely covering the top and bottom of the ring, as shown by MO 17 of benzene and MO 17 of borazine, rather than forming a ring above and below the atoms on the ring. Some of the MOs of both compound represent linear combinations of atomic orbitals, while many are not combinations of atomic orbitals. The molecules form clear sigma bonds and pi bonds, with bonding and antibonding orbitals representing each, with some MOs representing neither. The P orbital overlap also breaks down quite clearly when observing the MOs of borazine, as the MOs show clear ionic character due to the difference in electronegativity of boron and nitrogen, showing distortions in the aromatic system drawing electron density to the nitrogen atoms.

Rep:Mod: Brendan Rogers Wiki

2018-05-11T16:02:52Z

Br516:

===BH3===
RB3LYP/6-31G(d,p)

[[file:Br_BH3_freq_pic.PNG|left|thumb|BH3 summary table]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000190 0.000450 YES
RMS Force 0.000095 0.000300 YES
Maximum Displacement 0.000747 0.001800 YES
RMS Displacement 0.000374 0.001200 YES
</pre>

Frequency analysis log file: [[Media:BR BHS FREQ.LOG]]

<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6741
</pre>

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>BR_BHS_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

====Vibrational spectrum for BH3====
{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1164
|92
|A''
|yes
|out-of-plane-bend
|-
|1214
|14
|E'
|very slight
|bend
|-
|1214
|14
|E'
|very slight
|bend
|-
|2580
|0
|A'
|no
|symmetric stretch
|-
|2713
|126
|E'
|yes
|asymmetric stretch
|-
|2713
|126
|E'
|yes
|asymmetric stretch
|}

[[File:BR BH3 IR Spectrum.PNG]]
There are only 3 peaks, due to the 2 sets of degenerate vibrational modes and the 1 IR inactive vibrational mode.

====BH3 MO diagram====
[[File:BR BH3 MO diagram.png|left|thumb|Predicted orbitals next to actual orbitals. Predicted MO diagram taken from http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf]]
For all occupied orbitals the AO combinations produced fairly accurate results. They also gave fairly accurate results for the a2'' unoccupied MO, but not for a1' MO diagram. This shows that using linear combinations of AOs can produce good estimations, but can be inaccurate in reality.

===NH3===
B3LYP/6-31G(d,p)

[[File:BR_NH3_freq_pic.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000039 0.001800 YES
RMS Displacement 0.000013 0.001200 YES
</pre>

Frequency file: [[File:BR_NH3_FREQ_631G_DP.LOG]]

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0041 0.0455 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>BR_NH3_FREQ_631G_DP.LOG</uploadedFileContents>
</jmolApplet></jmol>

===NH3BH3===
B3LYP/6-31G(d,p)

[[File:BR_NH3BR3_freq_pic.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000115 0.000450 YES
RMS Force 0.000060 0.000300 YES
Maximum Displacement 0.000584 0.001800 YES
RMS Displacement 0.000345 0.001200 YES
</pre>

Frequency file: [[File:BR_NH3BH3_FREQ 631G_DP_2.LOG]]

<pre>
Low frequencies --- 0.0004 0.0009 0.0012 16.4186 17.2680 37.2272
Low frequencies --- 265.8841 632.2034 639.2870
</pre>

<jmol><jmolApplet>
<title>NH3Br3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>BR_NH3BH3_FREQ 631G_DP_2.LOG</uploadedFileContents>
</jmolApplet></jmol>

===BBr3===
B3LYP/6-31G(d,p)

{{DOI|10042/202397}}
[[File:BR_BBr3_freq_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000058 0.001800 YES
RMS Displacement 0.000034 0.001200 YES
</pre>

Frequency file: [[File:BR_BBr3_freq_dp_good.log]]

<pre>
Low frequencies --- -1.9018 -0.0001 0.0002 0.0002 1.5796 3.2831
Low frequencies --- 155.9053 155.9625 267.7047
</pre>

<jmol><jmolApplet>
<title>BBr3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>BR_BBr3_freq_dp_good.log</uploadedFileContents>
</jmolApplet></jmol>

====Calculating Association energy of Borane====
E(NH3)= -56.55777 a.u.
E(BH3)= -26.61532 a.u.
E(NH3BH3)= -83.22469 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -83.22469 - [-56.55777 + -26.61532] = -0.05160 a.u. = -129 Kj/mol

This value shows it is a weak bond, as can be shown by comparing it to a strong bond (e.g. C-C bond strength is 346 Kj/mol) and seeing the value is far lower.

==Aromaticity==
===Benzene===
B3LYP/6-31G(d,p)

[[File:Br_Benzene_freq_summary_2.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000101 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000158 0.001800 YES
RMS Displacement 0.000068 0.001200 YES
</pre>

Frequency file: [[File:BR_BENZENE_FREQ_631G_2.LOG]]

<pre>
Low frequencies --- -17.1502 -13.8161 -0.0003 -0.0002 -0.0002 1.7484
Low frequencies --- 414.1959 414.6468 620.9365
</pre>

<jmol><jmolApplet>
<title>Benzene</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>BR_BENZENE_FREQ_631G_2.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Borazine===
B3LYP/6-31G(d,p)

[[File:Br_Borazine_freq_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000268 0.000450 YES
RMS Force 0.000111 0.000300 YES
Maximum Displacement 0.000537 0.001800 YES
RMS Displacement 0.000253 0.001200 YES
</pre>

Frequency file: [[File:BR_BORAZINE_FREQ_631G_DP_2.LOG]]

<pre>
Low frequencies --- -14.1757 -13.8386 -10.2802 -0.0163 -0.0114 0.0344
Low frequencies --- 289.0978 289.0995 404.2449
</pre>

<jmol><jmolApplet>
<title>Borazine</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>BR_BORAZINE_FREQ_631G_DP_2.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Charge comparison between aromatic systems===
As seen below, while being isoelectronic, benzene and borazine have very different NBO charge distributions.Benzene Has a electronegative center caused by the delocalized pi system surrounding the carbon atoms. This results in all carbon atoms being equally electron dense (-0.239 arbitrary units) and all hydrogen atoms being equally less electron dense (+0.239 arbitrary units). Borazine is a different story, however, due to the large difference in electronegativity of boron and nitrogen in the central ring. Nitrogen is far smaller and electron dense than boron, causing it to be more electron rich (-1.102 arbitrary units) and drawing electron away from neighboring hydrogen atoms (+0.432 arbitrary units) and boron atoms (+0.747). The hydrogen atoms next to boron have a near neutral charge though, due to hydrogen and boron having similar Pauling electronegativity values.

{| class="wikitable"
|+
|-
|Benzene||Borazine
|-
|[[File:Benzene_charge_distribution.PNG]]
|[[File:Borazine_charge_distribution.PNG]]
|}

===Comparison of Molecular orbitals between aromatic systems===

{| class="wikitable"
|+
|-
|MO||Benzene||MO||Borazine||Comments
|-
|13
|[[File:Br_Benzene_MO_13.PNG]]
|16
|[[File:BR_Borazine_MO_16.PNG]]
|These orbitals have a similar phase distribution, alternating between each atom in the central ring. MO 13 on benzene is completely symmetrical, with each lobe of the orbital the same size over the carbon and hydrogen atoms. MO 16 on borazine has small lobes connecting the nitrogen to hydrogen, due to the greater electronegativity of nitrogen creating a greater charge density and smaller volume. Both orbitals show bonding character between the central atoms and the hydrogen atoms, and anti-bonding character between the inner ring members. Mo 16 represents a LCAO more strongly, showing an sp2 orbital on the central atoms mixing with an s orbital of the hydrogens.
|-
|17
|[[File:BR_Benzene_MO 17.PNG]]
|17
|[[File:Br_Borazine_MO_17.PNG]]
|These orbitals look very similar, representing one of the orbitals that make up the aromatic systems of benzene and borazine. They show a pi bonding character between the atoms on each ring, showing shared electron density between them. Both orbitals are perfectly symmetrical in a mirror plane parallel to the ring. MO 17 on benzene has 2 lobes each with 6 points of equal size over each carbon. MO 17 on borazine has 2 lobes each with 6 points but with slightly larger electron clouds over the nitrogen atoms compared to the boron atoms.
|-
|14
|[[File:BR_Benzene_MO_14.PNG]]
|15
|[[File:BR_Borazine_MO_15.PNG]]
|These orbitals also look very similar, showing a sigma bonding character between the atoms on the central ring.They both have 6 lobes with alternating phase, forming wedge shapes in between the central atoms. MO 14 for benzene shows 6 equally sized lobes, while MO 15 for borazine has slightly smaller electron clouds around nitrogen due to it's greater electronegativity compared to boron.
|}

===Nature of Aromaticity===
A common understanding or aromaticity is that in a planar ring system with 4n+2 electrons, each carbon atom will form a sigma bond to each other then form a conjugated pi bond above and below the ring. [[https://onlinelibrary.wiley.com/doi/epdf/10.1002/chem.200700250|Each carbon will form equal distant bonds to each other longer than a double bond but shorter than a single bond. The enthalpy of the bonds will be above a single bond, but below a double bond. They will also resist reactions that would proceed rapidly with a double bond, requiring a species to activate the ring system. In addition, they will form a ring current when under the influence of an external magnetic field, leading to increased diamagnetic susceptability]]

Overlapping P orbitals, however, do not provide a complete picture of aromaticity. The atomic orbitals combine to form a cloud completely covering the top and bottom of the ring, as shown by MO 17 of benzene and MO 17 of borazine, rather than forming a ring above and below the atoms on the ring.

Rep:Mod: Brendan Rogers Wiki

2018-05-11T15:33:00Z

Br516:

Rep:Mod: Brendan Rogers Wiki

2018-05-11T15:06:02Z

Br516:

Rep:Mod: Brendan Rogers Wiki

2018-05-11T15:05:39Z

Br516:

File:BR Borazine MO 16.PNG

2018-05-11T15:05:22Z

Br516:

File:Br Benzene MO 13.PNG

2018-05-11T15:04:36Z

Br516:

Rep:Mod: Brendan Rogers Wiki

2018-05-11T14:22:48Z

Br516:

File:BR BBr3 freq dp good.log

2018-05-11T14:19:19Z

Br516:

File:BR BBr3 freq summary.PNG

2018-05-11T14:13:36Z

Br516:

Rep:Mod: Brendan Rogers Wiki

2018-05-11T13:56:42Z

Br516:

Rep:Mod: Brendan Rogers Wiki

2018-05-11T13:56:26Z

Br516:

File:BR Borazine MO 15.PNG

2018-05-11T13:56:12Z

Br516:

File:BR Benzene MO 14.PNG

2018-05-11T13:55:38Z

Br516:

Rep:Mod: Brendan Rogers Wiki

2018-05-11T13:50:19Z

Br516:

File:Br Borazine MO 17.PNG

2018-05-11T13:49:52Z

Br516:

File:BR Benzene MO 17.PNG

2018-05-11T13:47:48Z

Br516: