ChemWiki - User contributions [en]

MRD 01372542

2019-05-16T15:33:45Z

Sth17:

'''On a potential energy surface diagram, how is the transition state mathematically defined? How can the transition state be identified, and how can it be distinguished from a local minimum of the potential energy surface?'''

On a potential energy surface diagram, the reaction trajectory is defined as the path passing through the minima. To calculate this, the potential energy must be differentiated once with respect to the bond length r1 and once with respect to r2. The transition state is the point along this path at which the bond lengths are equal, and will also be the potential energy maximum of this line. To isolate this point, potential energy must be differentiated with respect to q1 and q2, the new coordinates generated from a skew plot. This will allow identification of the local maxima and minima of potential energy curve in two orthogonal axes. The second derivative of these equations can confirm whether these are maxima (-ve value) or minima (+ve value). The transition state will be the point which represents a minimum of one of these differentials, and a maximum of the other, and presents as a saddle point on the potential energy curve.

'''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.'''

The best estimate of rts we could find is 0.9075 Å. As the transition state will be completely symmetric (by Hammond's postulate, the transition state is neither early nor late so will not resemble either the reactants or products more closely), both rab and rbc will be the same. At this point, the system has no potential energy, so no oscillations should be observed on a graph showing internuclear distance vs time. The graph for this is shown below.

[[File:rts_estimate.jpeg|200px|thumb|centre|Internuclear distance variation at the TS estimate, rts=0.9075Å]]

'''Comment on how the mep and the trajectory you just calculated differ'''

The minimum energy path will be formed just from consideration of the momentum of the bonds at every particular reaction coordinate, without consideration of previous momentum. This means that an MEP plot will not show vibrations, only the direct path leading to the transition state. The line stops at the transition state as this is the point at which the gradient is zero, and there is no momentum to consider. In the dynamic situation, the path goes beyond the transition state as there is residual momentum in the system. Residual momentum is also the reason vibrations can be seen in the dynamic approach, momentum is not set to zero at each point on the surface so any vibration occurring initially will carry through the path. In each case, the path is represented as the colour gradiated line on the contour maps below, with the red cress representing the transition state.

[[File:MEP.jpeg|200px|thumb|left|Contour plot showing minimum energy path]] [[File:Dynamic.jpeg|200px|thumb|right|Contour plot showing dynamic path]]

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

{| class="wikitable"
!p<nowiki>1</nowiki>
!P<nowiki>2</nowiki>
!E<nowiki>tot</nowiki>
!Reactive?
!Description of Dynamics
!Illustration of the Trajectory
|-
|<nowiki>-1.25</nowiki>
|<nowiki>-2.5</nowiki>
|<nowiki>-99.018</nowiki>
|Yes
|Central hydrogen (B) is transferred directly between the outermost hydrogens (A, C)
|[[File:table1.1.jpeg|200px|thumb|right|]]

|-
|<nowiki>-1.5</nowiki>
|<nowiki>-2.0</nowiki>
|<nowiki>-100.456</nowiki>
|No
|Molecule hesitates in transition state but reverts to reactants
|[[File:table1.2.jpeg|200px|thumb|right]]

|-
|<nowiki>-1.5</nowiki>
|<nowiki>-2.5</nowiki>
|<nowiki>-98.956</nowiki>
|Yes
|Central hydrogen is transferred directly between the outermost hydrogens
|[[File:table1.3.jpeg|200px|thumb|right]]

|-
|<nowiki>-2.5</nowiki>
|<nowiki>-5.0</nowiki>
|<nowiki>-84.956</nowiki>
|No
|Atom B is initially transferred from A to C, but due to large vibrations in the transition state, it reverts back to reagents
|[[File:table1.4.jpeg|200px|thumb|right]]

|-
|<nowiki>-2.5</nowiki>
|<nowiki>-5.2</nowiki>
|<nowiki>-83.416</nowiki>
|Yes
|Atom B is transferred initially from A to C, then vibrations around the transition state cause temporary re-association with atom A before the reaction runs to completion and transfers to C
|[[File:table1.5.jpeg|200px|thumb|right]]

|}
'''<nowiki/>'''

From this table we can conclude that kinetic energy is not the deciding factor in whether or not a reaction progresses to completion. In some cases, such as the case above with momentums -2.5 and 5.0, translational energy is transferred to vibrational energy upon collision to such a degree that the H2 molecule formed can dissociate and re-form the reagents. It is also clear from the table that atom transfer is not always direct, there is often fluctuation around the transition state if a large degree of vibrational energy is present in the system.

'''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 is comprised of three basic ideas.

1) The saddle point of a potential energy surface defines the transition state, and study of the surrounding area gives information on the rates of reaction.

2) The activated complex (transition state) is in a quasi-equilibrium (the system only deviates from equilibrium an infinitesimal amount)

3) Once the transition state is reached, the activated complex will fall over the barrier to reaction and form the products

In the results above, not all of the simulations predicted by the model follow these assumptions, so rate predictions will likely not be accurate in all cases. In the first three reactions, all of the transition state theory assumptions are true, so any theoretical prediction of rate will likely be representative of reality. The fourth reaction differs from the transition state assumptions as the activated complex does not fall directly into the products once the quasi-equilibrium is reached, it fluctuates about the transition state and reforms the reactants. A similar situation is observed in the fifth reaction, in which the central proton is transferred between the outermost hydrogens multiple times before forming the products, so the molecule passes through the transition state multiple times. For these final two cases, theoretical predictions of rates are unlikely to match what is observed.

'''By inspecting the potential energy surfaces, classify the F + H2 and H + HF reactions according to their energetics (endothermic or exothermic). How does this relate to the bond strength of the chemical species involved?'''

It can be seen from the potential energy graphs below that whilst not all reactions ran to form the products under specified conditions, the curve shows the thermodynamics of the process. In the reaction of H-H with a fluorine atom, the potential energy minimum of the product (H-F) can be seen as much lower than the starting material, showing that the reaction is exothermic. In the reverse reaction, again it did not run to completion as shown by the black path line, but the energy difference between products and reactants shows that the conversion of H-F to H-H is an endothermic process.

[[File:FHH_exothermic.jpeg|200px|thumb|left|Collision of HH and F]] [[File:HFH_exotehermic.jpeg|200px|thumb|right|Collision of FH and H]]

Relating this back to bond strength, this shows that the HF bond is much stronger (due to an ionic contribution to the bond, strengthening it), as it is lower in energy, and formation of it results in the loss of excess energy as thermal energy.

'''Locate the approximate position of the transition state.'''

The best estimate of the transition state for the reaction of H2 with F has r1=1.8108 Å and r2=0.74493 Å. This was obtained through observation of the mep, and zooming in on the coordinates of the final position. These were then entered as the starting conditions with no momentum, and on a dynamic plot of internuclear distance vs time, no movement can be seen for any atm. This confirms that this is nearly, the transition state (there is some force present between the atoms looking at the analysis so it is not the exact state but has been minimised to the largest extent it can be).

[[File:FHH_transition_state.jpeg|200px|thumb|centre|Internuclear distance vs time showing transition state H-H-F]]

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

The activation energy for both reactions was found by looking at the energy vs time graph around the point of the transition state, and observing the change in total energy from reactants to products. The activation energy of the first reaction (H2 + F) was found to be 30.2 kcalmol-1. This is the larger of the two energies. The activation energy of the second reaction (FH + H)was observed as 0.0094 kcalmol-1.

[[File:HH+F_activation_energy.jpeg|200px|thumb|left|Energy vs Time for the reaction of H2 with F]] [[File:FH+H_activation_energy.jpeg|200px|thumb|right|Energy vs Time for the reaction of FH with H]]

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

The initial conditions found that result in a
Upon proton transfer, the vibrational energy present in the H-H bond is transferred to the vibrational energy in the H-F bond. This will increase the momentum of HF and decrease that of HH, as shown in the graph below. The program can confirm that energy is conserved by looking at the energy vs time graph, as potential end kinetic energy exactly mirror each other as the molecules vibrate and interact< In the end, the H atom poseses only translational energy whilst the HF molecule contains both vibratinal and translational energy.

[[File:Conserve_energy.jpeg|200px|thumb|left|Momenta vs Time graph showing transfer of vibrational energy to FH from HH]][[File:Energy_vs_time_.jpeg|200px|thumb|right|Energy vs Time graph showing interchange between kinetic and potential energies]]
[[File:Reaction_trajectory.jpeg|200px|thumb|centre|Contour plot showing the reaction running to completion]]

This could be confirmed experimentally by running

'''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.'''

When adding more momentum into the system, this will not always result in an increased likelihood of traversing the transition state and forming the products, despite the overall increase in energy of thee system. The two contour plots below have the exact same initial conditions bar the momentum of AB, which is -1 in the case on the left and -2.5 on the case on the right. The right hand side has a greater energy input but does not run to completion. So much energy has been put into the H2 vibration that once the saddle point has been traversed, it can overcome the reverse reaction activation energy and does not form the products.

[[File:2.5_momentum.jpeg|200px|thumb|left|Contour plot for an AB momentum of -2.5, showing an incomplete reaction]][[File:1_momentum.jpeg|200px|thumb|right|Contour plot for an AB momentum of -1, showing a complete reaction]]

Polanyi's rules state that a molecules vibrational state is unlikely to influence the reaction rate to a significant degree, but only if the reaction has an early transition state. The reaction above has an early transition state, as it more closely resembles the products than the reactants. The fact that it disputes the empirical rules suggests that the rule may not apply to all conditions, especially in very high vibrational states.
If conditions are set up for the reverse reaction, a very hihg momentum of HF is required to achieve a reactive trajectory. These conditions show swift transfer of FH vibrational energy to H2 translational energy. Once the transition state has been overcome, the hydrogen molecule has enough translational energy to increase the intermolecular spacing to such a degree that further vibration will not induce the reverse reaction and reform the products.

[[File:Final.jpeg|200px|thumb|centre|Energy vs time plot showing fast transfer of vibrational energy to HH]]

From this it can be concluded that high vibrational nodes, whilst sometimes useful to find a reactive trajectory, are inefficient in terms of the reaction. The energy input will far exceed that of the activation energy, to no observabale advantage. This inefficiency is observed with greater frequency in systems with a late transition state, as the activation energy of the reverse reaction is smaller, meaning a smaller vibrational energy excess is needed to reform the products. This means that a larger proportion of reaction trajectories will fail to be successful in forming the products, reducing efficiency.

MRD 01372542

2019-05-16T15:24:48Z

Sth17:

'''On a potential energy surface diagram, how is the transition state mathematically defined? How can the transition state be identified, and how can it be distinguished from a local minimum of the potential energy surface?'''

On a potential energy surface diagram, the reaction trajectory is defined as the path passing through the minima. To calculate this, the potential energy must be differentiated once with respect to the bond length r1 and once with respect to r2. The transition state is the point along this path at which the bond lengths are equal, and will also be the potential energy maximum of this line. To isolate this point, potential energy must be differentiated with respect to q1 and q2, the new coordinates generated from a skew plot. This will allow identification of the local maxima and minima of potential energy curve in two orthogonal axes. The second derivative of these equations can confirm whether these are maxima (-ve value) or minima (+ve value). The transition state will be the point which represents a minimum of one of these differentials, and a maximum of the other, and presents as a saddle point on the potential energy curve.

'''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.'''

The best estimate of rts we could find is 0.9075 Å. As the transition state will be completely symmetric (by Hammond's postulate, the transition state is neither early nor late so will not resemble either the reactants or products more closely), both rab and rbc will be the same. At this point, the system has no potential energy, so no oscillations should be observed on a graph showing internuclear distance vs time. The graph for this is shown below.

[[File:rts_estimate.jpeg|200px|thumb|centre|Internuclear distance variation at the TS estimate, rts=0.9075Å]]

'''Comment on how the mep and the trajectory you just calculated differ'''

The minimum energy path will be formed just from consideration of the momentum of the bonds at every particular reaction coordinate, without consideration of previous momentum. This means that an MEP plot will not show vibrations, only the direct path leading to the transition state. The line stops at the transition state as this is the point at which the gradient is zero, and there is no momentum to consider. In the dynamic situation, the path goes beyond the transition state as there is residual momentum in the system. Residual momentum is also the reason vibrations can be seen in the dynamic approach, momentum is not set to zero at each point on the surface so any vibration occurring initially will carry through the path. In each case, the path is represented as the colour gradiated line on the contour maps below, with the red cress representing the transition state.

[[File:MEP.jpeg|200px|thumb|left|Contour plot showing minimum energy path]] [[File:Dynamic.jpeg|200px|thumb|right|Contour plot showing dynamic path]]

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

{| class="wikitable"
!p<nowiki>1</nowiki>
!P<nowiki>2</nowiki>
!E<nowiki>tot</nowiki>
!Reactive?
!Description of Dynamics
!Illustration of the Trajectory
|-
|<nowiki>-1.25</nowiki>
|<nowiki>-2.5</nowiki>
|<nowiki>-99.018</nowiki>
|Yes
|Central hydrogen (B) is transferred directly between the outermost hydrogens (A, C)
|[[File:table1.1.jpeg|200px|thumb|right|]]

|-
|<nowiki>-1.5</nowiki>
|<nowiki>-2.0</nowiki>
|<nowiki>-100.456</nowiki>
|No
|Molecule hesitates in transition state but reverts to reactants
|[[File:table1.2.jpeg|200px|thumb|right]]

|-
|<nowiki>-1.5</nowiki>
|<nowiki>-2.5</nowiki>
|<nowiki>-98.956</nowiki>
|Yes
|Central hydrogen is transferred directly between the outermost hydrogens
|[[File:table1.3.jpeg|200px|thumb|right]]

|-
|<nowiki>-2.5</nowiki>
|<nowiki>-5.0</nowiki>
|<nowiki>-84.956</nowiki>
|No
|Atom B is initially transferred from A to C, but due to large vibrations in the transition state, it reverts back to reagents
|[[File:table1.4.jpeg|200px|thumb|right]]

|-
|<nowiki>-2.5</nowiki>
|<nowiki>-5.2</nowiki>
|<nowiki>-83.416</nowiki>
|Yes
|Atom B is transferred initially from A to C, then vibrations around the transition state cause temporary re-association with atom A before the reaction runs to completion and transfers to C
|[[File:table1.5.jpeg|200px|thumb|right]]

|}
'''<nowiki/>'''

From this table we can conclude that kinetic energy is not the deciding factor in whether or not a reaction progresses to completion. In some cases, such as the case above with momentums -2.5 and 5.0, translational energy is transferred to vibrational energy upon collision to such a degree that the H2 molecule formed can dissociate and re-form the reagents. It is also clear from the table that atom transfer is not always direct, there is often fluctuation around the transition state if a large degree of vibrational energy is present in the system.

'''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 is comprised of three basic ideas.

1) The saddle point of a potential energy surface defines the transition state, and study of the surrounding area gives information on the rates of reaction.

2) The activated complex (transition state) is in a quasi-equilibrium (the system only deviates from equilibrium an infinitesimal amount)

3) Once the transition state is reached, the activated complex will fall over the barrier to reaction and form the products

In the results above, not all of the simulations predicted by the model follow these assumptions, so rate predictions will likely not be accurate in all cases. In the first three reactions, all of the transition state theory assumptions are true, so any theoretical prediction of rate will likely be representative of reality. The fourth reaction differs from the transition state assumptions as the activated complex does not fall directly into the products once the quasi-equilibrium is reached, it fluctuates about the transition state and reforms the reactants. A similar situation is observed in the fifth reaction, in which the central proton is transferred between the outermost hydrogens multiple times before forming the products, so the molecule passes through the transition state multiple times. For these final two cases, theoretical predictions of rates are unlikely to match what is observed.

'''By inspecting the potential energy surfaces, classify the F + H2 and H + HF reactions according to their energetics (endothermic or exothermic). How does this relate to the bond strength of the chemical species involved?'''

It can be seen from the potential energy graphs below that whilst not all reactions ran to form the products under specified conditions, the curve shows the thermodynamics of the process. In the reaction of H-H with a fluorine atom, the potential energy minimum of the product (H-F) can be seen as much lower than the starting material, showing that the reaction is exothermic. In the reverse reaction, again it did not run to completion as shown by the black path line, but the energy difference between products and reactants shows that the conversion of H-F to H-H is an endothermic process.

[[File:FHH_exothermic.jpeg|200px|thumb|left|Collision of HH and F]] [[File:HFH_exotehermic.jpeg|200px|thumb|right|Collision of FH and H]]

Relating this back to bond strength, this shows that the HF bond is much stronger (due to an ionic contribution to the bond, strengthening it), as it is lower in energy, and formation of it results in the loss of excess energy as thermal energy.

'''Locate the approximate position of the transition state.'''

The best estimate of the transition state for the reaction of H2 with F has r1=1.8108 Å and r2=0.74493 Å. This was obtained through observation of the mep, and zooming in on the coordinates of the final position. These were then entered as the starting conditions with no momentum, and on a dynamic plot of internuclear distance vs time, no movement can be seen for any atm. This confirms that this is nearly, the transition state (there is some force present between the atoms looking at the analysis so it is not the exact state but has been minimised to the largest extent it can be).

[[File:FHH_transition_state.jpeg|200px|thumb|centre|Internuclear distance vs time showing transition state H-H-F]]

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

The activation energy for both reactions was found by looking at the energy vs time graph around the point of the transition state, and observing the change in total energy from reactants to products. The activation energy of the first reaction (H2 + F) was found to be 30.2 kcalmol-1. This is the larger of the two energies. The activation energy of the second reaction (FH + H)was observed as 0.0094 kcalmol-1.

[[File:HH+F_activation_energy.jpeg|200px|thumb|left|Energy vs Time for the reaction of H2 with F]] [[File:FH+H_activation_energy.jpeg|200px|thumb|right|Energy vs Time for the reaction of FH with H]]

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

The initial conditions found that result in a
Upon proton transfer, the vibrational energy present in the H-H bond is transferred to the vibrational energy in the H-F bond. This will increase the momentum of HF and decrease that of HH, as shown in the graph below. The program can confirm that energy is conserved by looking at the energy vs time graph, as potential end kinetic energy exactly mirror each other as the molecules vibrate and interact< In the end, the H atom poseses only translational energy whilst the HF molecule contains both vibratinal and translational energy.

[[File:Conserve_energy.jpeg|200px|thumb|left|Momenta vs Time graph showing transfer of vibrational energy to FH from HH]][[File:Energy_vs_time_.jpeg|200px|thumb|right|Energy vs Time graph showing interchange between kinetic and potential energies]]
[[File:Reaction_trajectory.jpeg|200px|thumb|centre|Contour plot showing the reaction running to completion]]

This could be confirmed experimentally by running

'''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.'''

When adding more momentum into the system, this will not always result in an increased likelihood of traversing the transition state and forming the products, despite the overall increase in energy of thee system. The two contour plots below have the exact same initial conditions bar the momentum of AB, which is -1 in the case on the left and -2.5 on the case on the right. The right hand side has a greater energy input but does not run to completion. So much energy has been put into the H2 vibration that once the saddle point has been traversed, it can overcome the reverse reaction activation energy and does not form the products.

[[File:2.5_momentum.jpeg|200px|thumb|left|Contour plot for an AB momentum of -2.5, showing an incomplete reaction]][[File:1_momentum.jpeg|200px|thumb|right|Contour plot for an AB momentum of -1, showing a complete reaction]]

Polanyi's rules state that a molecules vibrational state is unlikely to influence the reaction rate to a significant degree, but only if the reaction has an early transition state. The reaction above has an early transition state, as it more closely resembles the products than the reactants. The fact that it disputes the empirical rules suggests that the rule may not apply to all conditions, especially in very high vibrational states.
If conditions are set up for the reverse reaction, a very hihg momentum of HF is required to achieve a reactive trajectory. These conditions show swift transfer of FH vibrational energy to H2 translational energy. Once the transition state has been overcome, the hydrogen molecule has enough translational energy to increase the intermolecular spacing to such a degree that furthr vibration will not induce the reverse reaction and reform the products.

[[File:Final.jpeg|200px|thumb|centre|Contour plot for an AB momentum of -1, showing a complete reaction]]

File:Final.jpeg

2019-05-16T15:24:08Z

Sth17:

File:1 momentum.jpeg

2019-05-16T15:05:21Z

Sth17:

File:2.5 momentum.jpeg

2019-05-16T15:04:47Z

Sth17:

MRD 01372542

2019-05-16T14:56:22Z

Sth17:

File:Reaction trajectory.jpeg

2019-05-16T14:52:32Z

Sth17:

File:Energy vs time .jpeg

2019-05-16T14:46:17Z

Sth17:

File:Conserve energy.jpeg

2019-05-16T14:28:37Z

Sth17: Sth17 uploaded a new version of File:Conserve energy.jpeg

File:Conserve energy.jpeg

2019-05-16T14:23:31Z

Sth17:

File:FH+H activation energy.jpeg

2019-05-16T14:13:00Z

Sth17:

MRD 01372542

2019-05-16T14:12:42Z

Sth17:

'''On a potential energy surface diagram, how is the transition state mathematically defined? How can the transition state be identified, and how can it be distinguished from a local minimum of the potential energy surface?'''

On a potential energy surface diagram, the reaction trajectory is defined as the path passing through the minima. To calculate this, the potential energy must be differentiated once with respect to the bond length r1 and once with respect to r2. The transition state is the point along this path at which the bond lengths are equal, and will also be the potential energy maximum of this line. To isolate this point, potential energy must be differentiated with respect to q1 and q2, the new coordinates generated from a skew plot. This will allow identification of the local maxima and minima of potential energy curve in two orthogonal axes. The second derivative of these equations can confirm whether these are maxima (-ve value) or minima (+ve value). The transition state will be the point which represents a minimum of one of these differentials, and a maximum of the other, and presents as a saddle point on the potential energy curve.

'''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.'''

The best estimate of rts we could find is 0.9075 Å. As the transition state will be completely symmetric (by Hammond's postulate, the transition state is neither early nor late so will not resemble either the reactants or products more closely), both rab and rbc will be the same. At this point, the system has no potential energy, so no oscillations should be observed on a graph showing internuclear distance vs time. The graph for this is shown below.

[[File:rts_estimate.jpeg|200px|thumb|centre|Internuclear distance variation at the TS estimate, rts=0.9075Å]]

'''Comment on how the mep and the trajectory you just calculated differ'''

The minimum energy path will be formed just from consideration of the momentum of the bonds at every particular reaction coordinate, without consideration of previous momentum. This means that an MEP plot will not show vibrations, only the direct path leading to the transition state. The line stops at the transition state as this is the point at which the gradient is zero, and there is no momentum to consider. In the dynamic situation, the path goes beyond the transition state as there is residual momentum in the system. Residual momentum is also the reason vibrations can be seen in the dynamic approach, momentum is not set to zero at each point on the surface so any vibration occurring initially will carry through the path. In each case, the path is represented as the colour gradiated line on the contour maps below, with the red cress representing the transition state.

[[File:MEP.jpeg|200px|thumb|left|Contour plot showing minimum energy path]] [[File:Dynamic.jpeg|200px|thumb|right|Contour plot showing dynamic path]]

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

{| class="wikitable"
!p<nowiki>1</nowiki>
!P<nowiki>2</nowiki>
!E<nowiki>tot</nowiki>
!Reactive?
!Description of Dynamics
!Illustration of the Trajectory
|-
|<nowiki>-1.25</nowiki>
|<nowiki>-2.5</nowiki>
|<nowiki>-99.018</nowiki>
|Yes
|Central hydrogen (B) is transferred directly between the outermost hydrogens (A, C)
|[[File:table1.1.jpeg|200px|thumb|right|]]

|-
|<nowiki>-1.5</nowiki>
|<nowiki>-2.0</nowiki>
|<nowiki>-100.456</nowiki>
|No
|Molecule hesitates in transition state but reverts to reactants
|[[File:table1.2.jpeg|200px|thumb|right]]

|-
|<nowiki>-1.5</nowiki>
|<nowiki>-2.5</nowiki>
|<nowiki>-98.956</nowiki>
|Yes
|Central hydrogen is transferred directly between the outermost hydrogens
|[[File:table1.3.jpeg|200px|thumb|right]]

|-
|<nowiki>-2.5</nowiki>
|<nowiki>-5.0</nowiki>
|<nowiki>-84.956</nowiki>
|No
|Atom B is initially transferred from A to C, but due to large vibrations in the transition state, it reverts back to reagents
|[[File:table1.4.jpeg|200px|thumb|right]]

|-
|<nowiki>-2.5</nowiki>
|<nowiki>-5.2</nowiki>
|<nowiki>-83.416</nowiki>
|Yes
|Atom B is transferred initially from A to C, then vibrations around the transition state cause temporary re-association with atom A before the reaction runs to completion and transfers to C
|[[File:table1.5.jpeg|200px|thumb|right]]

|}
'''<nowiki/>'''

From this table we can conclude that kinetic energy is not the deciding factor in whether or not a reaction progresses to completion. In some cases, such as the case above with momentums -2.5 and 5.0, translational energy is transferred to vibrational energy upon collision to such a degree that the H2 molecule formed can dissociate and re-form the reagents. It is also clear from the table that atom transfer is not always direct, there is often fluctuation around the transition state if a large degree of vibrational energy is present in the system.

'''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 is comprised of three basic ideas.

1) The saddle point of a potential energy surface defines the transition state, and study of the surrounding area gives information on the rates of reaction.

2) The activated complex (transition state) is in a quasi-equilibrium (the system only deviates from equilibrium an infinitesimal amount)

3) Once the transition state is reached, the activated complex will fall over the barrier to reaction and form the products

In the results above, not all of the simulations predicted by the model follow these assumptions, so rate predictions will likely not be accurate in all cases. In the first three reactions, all of the transition state theory assumptions are true, so any theoretical prediction of rate will likely be representative of reality. The fourth reaction differs from the transition state assumptions as the activated complex does not fall directly into the products once the quasi-equilibrium is reached, it fluctuates about the transition state and reforms the reactants. A similar situation is observed in the fifth reaction, in which the central proton is transferred between the outermost hydrogens multiple times before forming the products, so the molecule passes through the transition state multiple times. For these final two cases, theoretical predictions of rates are unlikely to match what is observed.

'''By inspecting the potential energy surfaces, classify the F + H2 and H + HF reactions according to their energetics (endothermic or exothermic). How does this relate to the bond strength of the chemical species involved?'''

It can be seen from the potential energy graphs below that whilst not all reactions ran to form the products under specified conditions, the curve shows the thermodynamics of the process. In the reaction of H-H with a fluorine atom, the potential energy minimum of the product (H-F) can be seen as much lower than the starting material, showing that the reaction is exothermic. In the reverse reaction, again it did not run to completion as shown by the black path line, but the energy difference between products and reactants shows that the conversion of H-F to H-H is an endothermic process.

[[File:FHH_exothermic.jpeg|200px|thumb|left|Collision of HH and F]] [[File:HFH_exotehermic.jpeg|200px|thumb|right|Collision of FH and H]]

Relating this back to bond strength, this shows that the HF bond is much stronger (due to an ionic contribution to the bond, strengthening it), as it is lower in energy, and formation of it results in the loss of excess energy as thermal energy.

'''Locate the approximate position of the transition state.'''

The best estimate of the transition state for the reaction of H2 with F has r1=1.8108 Å and r2=0.74493 Å. This was obtained through observation of the mep, and zooming in on the coordinates of the final position. These were then entered as the starting conditions with no momentum, and on a dynamic plot of internuclear distance vs time, no movement can be seen for any atm. This confirms that this is nearly, the transition state (there is some force present between the atoms looking at the analysis so it is not the exact state but has been minimised to the largest extent it can be).

[[File:FHH_transition_state.jpeg|200px|thumb|centre|Internuclear distance vs time showing transition state H-H-F]]

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

The activation energy for both reactions was found by looking at the energy vs time graph around the point of the transition state. The activation energy of the first reaction (H2 + F) was found to be 30.2 kcalmol-1. This is the larger of the two energies. The activation energy of the second reaction (FH + H)was observed as 0.0094 kcalmol-1

[[File:HH+F_activation_energy.jpeg|200px|thumb|left|Energy vs Time for the reaction of H2 with F]] [[File:HH+F_activation_energy.jpeg|200px|thumb|right|Energy vs Time for the reaction of H2 with F]]

File:HH+F activation energy.jpeg

2019-05-16T13:57:17Z

Sth17:

MRD 01372542

2019-05-16T13:56:55Z

Sth17:

File:FHH transition state.jpeg

2019-05-16T13:45:21Z

Sth17:

MRD 01372542

2019-05-16T13:44:42Z

Sth17:

MRD 01372542

2019-05-16T13:11:38Z

Sth17:

MRD 01372542

2019-05-16T13:00:03Z

Sth17:

MRD 01372542

2019-05-16T12:35:22Z

Sth17:

MRD 01372542

2019-05-14T20:32:19Z

Sth17:

MRD 01372542

2019-05-14T20:00:56Z

Sth17:

File:FHH exothermic.jpeg

2019-05-14T19:56:35Z

Sth17: Sth17 uploaded a new version of File:FHH exothermic.jpeg

MRD 01372542

2019-05-14T19:56:16Z

Sth17:

File:HFH exotehermic.jpeg

2019-05-14T19:52:46Z

Sth17:

File:FHH exothermic.jpeg

2019-05-14T19:52:30Z

Sth17:

MRD 01372542

2019-05-14T19:52:14Z

Sth17:

MRD 01372542

2019-05-14T19:27:12Z

Sth17:

MRD 01372542

2019-05-14T18:47:29Z

Sth17:

File:Table1.5.jpeg

2019-05-14T18:44:40Z

Sth17:

File:Table1.4.jpeg

2019-05-14T18:44:24Z

Sth17:

File:Table1.3.jpeg

2019-05-14T18:44:09Z

Sth17:

File:Table1.2.jpeg

2019-05-14T18:43:52Z

Sth17:

File:Table1.1.jpeg

2019-05-14T18:43:32Z

Sth17:

MRD 01372542

2019-05-14T18:41:09Z

Sth17:

MRD 01372542

2019-05-14T18:28:36Z

Sth17:

MRD 01372542

2019-05-14T16:07:36Z

Sth17:

MRD 01372542

2019-05-14T16:00:52Z

Sth17:

File:Dynamic.jpeg

2019-05-14T15:35:02Z

Sth17:

File:MEP.jpeg

2019-05-14T15:34:21Z

Sth17:

MRD 01372542

2019-05-14T15:34:05Z

Sth17:

MRD 01372542

2019-05-14T15:09:45Z

Sth17:

File:Rts estimate.jpeg

2019-05-14T15:06:49Z

Sth17:

MRD 01372542

2019-05-14T15:05:08Z

Sth17:

MRD 01372542

2019-05-14T15:01:53Z

Sth17: Created page with "'''On a potential energy surface diagram, how is the transition state mathematically defined? How can the transition state be identified, and how can it be distinguished from..."

Rep:MOD:01372542

2018-03-02T17:47:59Z

Sth17: /* References */

==NH3 Molecule==

'''Calculation Method:''' RB3LYP

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

'''Final Energy:''' -56.55776873 au

'''RMS Gradient:''' 0.00000485 au

'''Point group:''' C3V

'''N-H Bond Length:''' 1.01798 Å

'''H-N-H Bond Angle:''' 105.741o

'''Item Table For NH3:'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000072 0.001800 YES
RMS Displacement 0.000035 0.001200 YES
Predicted change in Energy=-5.986282D-10
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.018 -DE/DX = 0.0 !
! R2 R(1,3) 1.018 -DE/DX = 0.0 !
! R3 R(1,4) 1.018 -DE/DX = 0.0 !
! A1 A(2,1,3) 105.7412 -DE/DX = 0.0 !
! A2 A(2,1,4) 105.7412 -DE/DX = 0.0 !
! A3 A(3,1,4) 105.7412 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -111.8571 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

<jmol><jmolApplet>
<title>NH3 3D Structure</title>
<color>black</color>
<size>200</size>
<script>frame 1.16</script>
<uploadedFileContents>SAMHOPGOOD_NH3_OPTIMISATIONFUNCTION_POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file for NH3 is linked to [[Media:SAMHOPGOOD_NH3_OPTIMISATIONFUNCTION_POP.LOG| here]]

[[File:NH3_Display_Vibrations_Sam_Hopgood.jpg|400px|thumb|centre|Display Vibrations - NH3]]

'''1) How many modes do you expect from the 3N-6 rule?'''

As there are 4 atoms in an NH3 molecule, by the 3N-6 rule you would expect to get 6 nodes (as 3(4)-6=6).

'''2) Which modes are degenerate?'''

Modes 2 and 3, and 5 and 6 form degenerate pairs, shown by their identical vibrational frequencies.

'''3) Which modes are "bending" vibrations and which are "bond stretch" vibrations?'''

Modes 1,2 and 3 are bending vibrations, and modes 4,5 and 6 are formed from bond stretch vibrations.

'''4) Which mode is highly symmetric?'''

Mode 4 is highly symmetric

'''5) One mode is known as the "umbrella" mode, which one is this?'''

Mode 1 resembles the opening and closing mechanism of an umbrella.

'''6) How many bands would you expect to see in an experimental spectrum of gaseous ammonia?'''

You would expect to see 2 bands in a spectrum of gaseous ammonia, the first from mode 1 and the second from modes 2 and 3 combined as they occur at the same frequency. Modes 4,5 and 6 have intensities that are far too low to be visible on the spectrum, due to the symmetric stretches and small changes in the dipole moment. In reality the spectrum has a third peak<ref name="NH3 Spectrum" />, in the region of 3500, potentially caused by the combination of smaller vibrations.

'''Atomic Charges'''

Within the molecule, the nitrogen has a charge of -1.125, and each hydrogen has a charge of 0.375. This agrees with what I would expect, as nitrogen is the more electronegative atom and will pull the bonded pair of electrons towards itself, increasing its electron density and therefore reducing its charge.

==N2 Molecule==

'''Calculation Method:''' RB3LYP

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

'''Final Energy:''' -109.52412868 au

'''RMS Gradient:''' 0.00000060 au

'''Point group:''' D∞h

'''N-N Bond Length:''' 1.10550 Å

'''Item Table For N2:'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000000 0.001800 YES
RMS Displacement 0.000000 0.001200 YES
Predicted change in Energy=-3.400969D-13
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1055 -DE/DX = 0.0 !
--------------------------------------------------------------------------------

</pre>

<jmol><jmolApplet>
<title>N2 3D Structure</title>
<color>black</color>
<size>200</size>
<script>frame 1.10</script>
<uploadedFileContents>SAMHOPGOOD_N2_OPTIMISATIONFUNCTION.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file for N2 is linked to [[Media:SAMHOPGOOD_N2_OPTIMISATIONFUNCTION.LOG| here]]

[[File:N2_Display_Vibrations_Sam_Hopgood.jpg|400px|thumb|centre|Display Vibrations - N2]]

==H2 Molecule==

'''Calculation Method:''' RB3LYP

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

'''Final Energy:''' -1.17853936 au

'''RMS Gradient:''' 0.00000017 au

'''Point group:''' D∞h

'''H-H Bond Length:''' 0.74279 Å

'''Item Table For H2:'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000000 0.001800 YES
RMS Displacement 0.000001 0.001200 YES
Predicted change in Energy=-1.164080D-13
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 0.7428 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

<jmol><jmolApplet>
<title>H2 3D Structure</title>
<color>black</color>
<size>200</size>
<script>frame 1.12</script>
<uploadedFileContents>SAMHOPGOOD_H2_OPTIMISATIONFUNCTION.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file for H2 is linked to [[Media:SAMHOPGOOD_H2_OPTIMISATIONFUNCTION.LOG| here]]

[[File:H2_Display_Vibrations_Sam_Hopgood.jpg|400px|thumb|centre|Display Vibrations - H2]]

==Energy of Reaction==

'''E(NH3) =''' -56.55776873 au

'''2*E(NH3) =''' -113.1155375 au

'''E(N2) =''' -109.5241287 au

'''E(H2) =''' -1.17853936 au

'''3*E(H2) =''' -3.53561808 au

'''ΔE = 2*E(NH3)-(E(N2)+3*E(H2)) = ''' -0.0557907 au ''' = ''' -146.48 kJ/mol
From this we can tell that the product, ammonia, is more stable than the reactants N2 and H2.

In literature, this value was cited as -99.22 kJ/mol <ref name="NH3 Energy Change" />. The difference between this value and the computed value is due to poor optimisation of the molecule.

==CF4 Molecule==

'''Calculation Method:''' RB3LYP

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

'''Final Energy:''' -437.47627267 au

'''RMS Gradient:''' 0.00004049 au

'''Point group:''' TD

'''C-F Bond Length:''' 1.32939 Å

'''Item Table For CF4:'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000078 0.000450 YES
RMS Force 0.000042 0.000300 YES
Maximum Displacement 0.000133 0.001800 YES
RMS Displacement 0.000071 0.001200 YES
Predicted change in Energy=-2.081896D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.3294 -DE/DX = -0.0001 !
! R2 R(1,3) 1.3294 -DE/DX = -0.0001 !
! R3 R(1,4) 1.3294 -DE/DX = -0.0001 !
! R4 R(1,5) 1.3294 -DE/DX = -0.0001 !
! A1 A(2,1,3) 109.4712 -DE/DX = 0.0 !
! A2 A(2,1,4) 109.4712 -DE/DX = 0.0 !
! A3 A(2,1,5) 109.4712 -DE/DX = 0.0 !
! A4 A(3,1,4) 109.4712 -DE/DX = 0.0 !
! A5 A(3,1,5) 109.4712 -DE/DX = 0.0 !
! A6 A(4,1,5) 109.4712 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 120.0 -DE/DX = 0.0 !
! D2 D(2,1,5,3) -120.0 -DE/DX = 0.0 !
! D3 D(2,1,5,4) 120.0 -DE/DX = 0.0 !
! D4 D(3,1,5,4) -120.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

<jmol><jmolApplet>
<title>CF4 3D Structure</title>
<color>black</color>
<size>200</size>
<script>frame 1.8</script>
<uploadedFileContents>SAMHOPGOOD_CF4_OPTIMISATIONFUNCTION.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file for CF4 is linked to [[Media:SAMHOPGOOD_CF4_OPTIMISATIONFUNCTION.LOG| here]]

[[File:CF4_Display_Vibrations_Sam_Hopgood.jpg|400px|thumb|centre|Display Vibrations - CF4]]

[[File:CF4_Spectrum_Sam_Hopgood.jpg|400px|thumb|centre|Predicted Spectrum - CF4]]

'''CF4 Molecular Orbitals'''

[[File:CF4_Orbital_1_Sam_Hopgood.jpg|400px|thumb|centre|Molecular Orbital 1 - CF4]]
This first molecular orbital is a bonding orbital, formed from the overlap of 2s sub-shells from both the central carbon atom and the surrounding fluorine atoms. There is a very large overlap of these orbitals as they hold valence electrons and are therefore heavily involved in bonding. Evidently this orbital is also occupied.

[[File:CF4_Orbital_2_Sam_Hopgood.jpg|400px|thumb|centre|Molecular Orbital 2 - CF4]]
This molecular orbital is formed from all 2p orbitals, shown by the nodes on each atom. There is favourable overlap over all bonds showing that this is a bonding MO. This orbital is occupied, and does not have a particularly deep energy, so it will contribute fairly significantly to the overall bond. The three p orbitals on carbon could be involved in this MO, meaning it has three possible orientations, forming three degenerate MOs.

[[File:CF4_Orbital_3_Sam_Hopgood.jpg|400px|thumb|centre|Molecular Orbital 3 - CF4]]
MO number three is formed from 2s orbitals from both the carbon and fluorine, however, they are out of phase this time and therefore form the antibonding orbital, shown by the node on each bond. The orbital is fully occupied, and not particularly deep in energy, meaning it will have some influence on the bonding of the molecule. However, it does not lie near the LUMO/HOMO region and does not carry valence electrons so its impact on the strength of the bond is limited.

[[File:CF4_Orbital_4_Sam_Hopgood.jpg|400px|thumb|centre|Molecular Orbital 4 - CF4]]
This MO is comprised of a 2p orbital on the carbon, and s orbitals on the surrounding fluorine. Of the fluorine atoms, two are in one phase and two are in the other, with each pair lining up with the corresponding end of the carbon's p orbital. The overlap is in phase across the whole bond for each C-F bond, showing that the molecule is a bonding MO. The p orbital can be in 3 possible orientations so there are three degenerate MOs that look the same, each with a fairly low energy. As a result of the low energy it is unlikely that this contributes much to the overall bonding of the molecule.

[[File:CF4_Orbital_5_Sam_Hopgood.jpg|400px|thumb|centre|Molecular Orbital 5 - CF4]]
This filled MO is very low in energy, and it is formed of a 2s sub shell from the carbon. This is a non-bonding orbital, shown by the lack of influence from any adjacent fluorine atoms. It has no influence on bonding as it is not a bonding or antibonding orbital.

'''CF4 Charges'''

[[File:CF4_Charge_Distribution_Sam_Hopgood.jpg|400px|thumb|centre|Charge Distribution of CF4]]

The central carbon atom is very electropositive due to the surrounding fluorine atoms drawing away the bonded electrons. Fluorine atoms are very electronegative so will attract the bonded pair of electrons to itself, shifting the negative charge from the carbon to towards the fluorine.

==References==

<references>
<ref name="NH3 Energy Change">Ebbing, Darrel D.General Chemistry 3rd ed.;Houghton Mifflin Company: Boston, MA, 1990 pp 115,175, 223-4, 227.</ref>
<ref name="NH3 Spectrum">http://webbook.nist.gov/cgi/cbook.cgi?ID=C7664417&Type=IR-SPEC&Index=1.</ref>
</references>

Rep:MOD:01372542

2018-03-02T17:47:36Z

Sth17:

==NH3 Molecule==

'''Calculation Method:''' RB3LYP

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

'''Final Energy:''' -56.55776873 au

'''RMS Gradient:''' 0.00000485 au

'''Point group:''' C3V

'''N-H Bond Length:''' 1.01798 Å

'''H-N-H Bond Angle:''' 105.741o

'''Item Table For NH3:'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000072 0.001800 YES
RMS Displacement 0.000035 0.001200 YES
Predicted change in Energy=-5.986282D-10
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.018 -DE/DX = 0.0 !
! R2 R(1,3) 1.018 -DE/DX = 0.0 !
! R3 R(1,4) 1.018 -DE/DX = 0.0 !
! A1 A(2,1,3) 105.7412 -DE/DX = 0.0 !
! A2 A(2,1,4) 105.7412 -DE/DX = 0.0 !
! A3 A(3,1,4) 105.7412 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -111.8571 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

<jmol><jmolApplet>
<title>NH3 3D Structure</title>
<color>black</color>
<size>200</size>
<script>frame 1.16</script>
<uploadedFileContents>SAMHOPGOOD_NH3_OPTIMISATIONFUNCTION_POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file for NH3 is linked to [[Media:SAMHOPGOOD_NH3_OPTIMISATIONFUNCTION_POP.LOG| here]]

[[File:NH3_Display_Vibrations_Sam_Hopgood.jpg|400px|thumb|centre|Display Vibrations - NH3]]

'''1) How many modes do you expect from the 3N-6 rule?'''

As there are 4 atoms in an NH3 molecule, by the 3N-6 rule you would expect to get 6 nodes (as 3(4)-6=6).

'''2) Which modes are degenerate?'''

Modes 2 and 3, and 5 and 6 form degenerate pairs, shown by their identical vibrational frequencies.

'''3) Which modes are "bending" vibrations and which are "bond stretch" vibrations?'''

Modes 1,2 and 3 are bending vibrations, and modes 4,5 and 6 are formed from bond stretch vibrations.

'''4) Which mode is highly symmetric?'''

Mode 4 is highly symmetric

'''5) One mode is known as the "umbrella" mode, which one is this?'''

Mode 1 resembles the opening and closing mechanism of an umbrella.

'''6) How many bands would you expect to see in an experimental spectrum of gaseous ammonia?'''

You would expect to see 2 bands in a spectrum of gaseous ammonia, the first from mode 1 and the second from modes 2 and 3 combined as they occur at the same frequency. Modes 4,5 and 6 have intensities that are far too low to be visible on the spectrum, due to the symmetric stretches and small changes in the dipole moment. In reality the spectrum has a third peak<ref name="NH3 Spectrum" />, in the region of 3500, potentially caused by the combination of smaller vibrations.

'''Atomic Charges'''

Within the molecule, the nitrogen has a charge of -1.125, and each hydrogen has a charge of 0.375. This agrees with what I would expect, as nitrogen is the more electronegative atom and will pull the bonded pair of electrons towards itself, increasing its electron density and therefore reducing its charge.

==N2 Molecule==

'''Calculation Method:''' RB3LYP

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

'''Final Energy:''' -109.52412868 au

'''RMS Gradient:''' 0.00000060 au

'''Point group:''' D∞h

'''N-N Bond Length:''' 1.10550 Å

'''Item Table For N2:'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000000 0.001800 YES
RMS Displacement 0.000000 0.001200 YES
Predicted change in Energy=-3.400969D-13
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1055 -DE/DX = 0.0 !
--------------------------------------------------------------------------------

</pre>

<jmol><jmolApplet>
<title>N2 3D Structure</title>
<color>black</color>
<size>200</size>
<script>frame 1.10</script>
<uploadedFileContents>SAMHOPGOOD_N2_OPTIMISATIONFUNCTION.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file for N2 is linked to [[Media:SAMHOPGOOD_N2_OPTIMISATIONFUNCTION.LOG| here]]

[[File:N2_Display_Vibrations_Sam_Hopgood.jpg|400px|thumb|centre|Display Vibrations - N2]]

==H2 Molecule==

'''Calculation Method:''' RB3LYP

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

'''Final Energy:''' -1.17853936 au

'''RMS Gradient:''' 0.00000017 au

'''Point group:''' D∞h

'''H-H Bond Length:''' 0.74279 Å

'''Item Table For H2:'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000000 0.001800 YES
RMS Displacement 0.000001 0.001200 YES
Predicted change in Energy=-1.164080D-13
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 0.7428 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

<jmol><jmolApplet>
<title>H2 3D Structure</title>
<color>black</color>
<size>200</size>
<script>frame 1.12</script>
<uploadedFileContents>SAMHOPGOOD_H2_OPTIMISATIONFUNCTION.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file for H2 is linked to [[Media:SAMHOPGOOD_H2_OPTIMISATIONFUNCTION.LOG| here]]

[[File:H2_Display_Vibrations_Sam_Hopgood.jpg|400px|thumb|centre|Display Vibrations - H2]]

==Energy of Reaction==

'''E(NH3) =''' -56.55776873 au

'''2*E(NH3) =''' -113.1155375 au

'''E(N2) =''' -109.5241287 au

'''E(H2) =''' -1.17853936 au

'''3*E(H2) =''' -3.53561808 au

'''ΔE = 2*E(NH3)-(E(N2)+3*E(H2)) = ''' -0.0557907 au ''' = ''' -146.48 kJ/mol
From this we can tell that the product, ammonia, is more stable than the reactants N2 and H2.

In literature, this value was cited as -99.22 kJ/mol <ref name="NH3 Energy Change" />. The difference between this value and the computed value is due to poor optimisation of the molecule.

==CF4 Molecule==

'''Calculation Method:''' RB3LYP

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

'''Final Energy:''' -437.47627267 au

'''RMS Gradient:''' 0.00004049 au

'''Point group:''' TD

'''C-F Bond Length:''' 1.32939 Å

'''Item Table For CF4:'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000078 0.000450 YES
RMS Force 0.000042 0.000300 YES
Maximum Displacement 0.000133 0.001800 YES
RMS Displacement 0.000071 0.001200 YES
Predicted change in Energy=-2.081896D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.3294 -DE/DX = -0.0001 !
! R2 R(1,3) 1.3294 -DE/DX = -0.0001 !
! R3 R(1,4) 1.3294 -DE/DX = -0.0001 !
! R4 R(1,5) 1.3294 -DE/DX = -0.0001 !
! A1 A(2,1,3) 109.4712 -DE/DX = 0.0 !
! A2 A(2,1,4) 109.4712 -DE/DX = 0.0 !
! A3 A(2,1,5) 109.4712 -DE/DX = 0.0 !
! A4 A(3,1,4) 109.4712 -DE/DX = 0.0 !
! A5 A(3,1,5) 109.4712 -DE/DX = 0.0 !
! A6 A(4,1,5) 109.4712 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 120.0 -DE/DX = 0.0 !
! D2 D(2,1,5,3) -120.0 -DE/DX = 0.0 !
! D3 D(2,1,5,4) 120.0 -DE/DX = 0.0 !
! D4 D(3,1,5,4) -120.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

<jmol><jmolApplet>
<title>CF4 3D Structure</title>
<color>black</color>
<size>200</size>
<script>frame 1.8</script>
<uploadedFileContents>SAMHOPGOOD_CF4_OPTIMISATIONFUNCTION.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file for CF4 is linked to [[Media:SAMHOPGOOD_CF4_OPTIMISATIONFUNCTION.LOG| here]]

[[File:CF4_Display_Vibrations_Sam_Hopgood.jpg|400px|thumb|centre|Display Vibrations - CF4]]

[[File:CF4_Spectrum_Sam_Hopgood.jpg|400px|thumb|centre|Predicted Spectrum - CF4]]

'''CF4 Molecular Orbitals'''

[[File:CF4_Orbital_1_Sam_Hopgood.jpg|400px|thumb|centre|Molecular Orbital 1 - CF4]]
This first molecular orbital is a bonding orbital, formed from the overlap of 2s sub-shells from both the central carbon atom and the surrounding fluorine atoms. There is a very large overlap of these orbitals as they hold valence electrons and are therefore heavily involved in bonding. Evidently this orbital is also occupied.

[[File:CF4_Orbital_2_Sam_Hopgood.jpg|400px|thumb|centre|Molecular Orbital 2 - CF4]]
This molecular orbital is formed from all 2p orbitals, shown by the nodes on each atom. There is favourable overlap over all bonds showing that this is a bonding MO. This orbital is occupied, and does not have a particularly deep energy, so it will contribute fairly significantly to the overall bond. The three p orbitals on carbon could be involved in this MO, meaning it has three possible orientations, forming three degenerate MOs.

[[File:CF4_Orbital_3_Sam_Hopgood.jpg|400px|thumb|centre|Molecular Orbital 3 - CF4]]
MO number three is formed from 2s orbitals from both the carbon and fluorine, however, they are out of phase this time and therefore form the antibonding orbital, shown by the node on each bond. The orbital is fully occupied, and not particularly deep in energy, meaning it will have some influence on the bonding of the molecule. However, it does not lie near the LUMO/HOMO region and does not carry valence electrons so its impact on the strength of the bond is limited.

[[File:CF4_Orbital_4_Sam_Hopgood.jpg|400px|thumb|centre|Molecular Orbital 4 - CF4]]
This MO is comprised of a 2p orbital on the carbon, and s orbitals on the surrounding fluorine. Of the fluorine atoms, two are in one phase and two are in the other, with each pair lining up with the corresponding end of the carbon's p orbital. The overlap is in phase across the whole bond for each C-F bond, showing that the molecule is a bonding MO. The p orbital can be in 3 possible orientations so there are three degenerate MOs that look the same, each with a fairly low energy. As a result of the low energy it is unlikely that this contributes much to the overall bonding of the molecule.

[[File:CF4_Orbital_5_Sam_Hopgood.jpg|400px|thumb|centre|Molecular Orbital 5 - CF4]]
This filled MO is very low in energy, and it is formed of a 2s sub shell from the carbon. This is a non-bonding orbital, shown by the lack of influence from any adjacent fluorine atoms. It has no influence on bonding as it is not a bonding or antibonding orbital.

'''CF4 Charges'''

[[File:CF4_Charge_Distribution_Sam_Hopgood.jpg|400px|thumb|centre|Charge Distribution of CF4]]

The central carbon atom is very electropositive due to the surrounding fluorine atoms drawing away the bonded electrons. Fluorine atoms are very electronegative so will attract the bonded pair of electrons to itself, shifting the negative charge from the carbon to towards the fluorine.

==References==
http://webbook.nist.gov/cgi/cbook.cgi?ID=C7664417&Type=IR-SPEC&Index=1
<references>
<ref name="NH3 Energy Change">Ebbing, Darrel D.General Chemistry 3rd ed.;Houghton Mifflin Company: Boston, MA, 1990 pp 115,175, 223-4, 227.</ref>
<ref name="NH3 Spectrum">http://webbook.nist.gov/cgi/cbook.cgi?ID=C7664417&Type=IR-SPEC&Index=1.</ref>
</references>

Rep:MOD:01372542

2018-03-02T17:45:37Z

Sth17: /* NH3 Molecule */

==NH3 Molecule==

'''Calculation Method:''' RB3LYP

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

'''Final Energy:''' -56.55776873 au

'''RMS Gradient:''' 0.00000485 au

'''Point group:''' C3V

'''N-H Bond Length:''' 1.01798 Å

'''H-N-H Bond Angle:''' 105.741o

'''Item Table For NH3:'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000072 0.001800 YES
RMS Displacement 0.000035 0.001200 YES
Predicted change in Energy=-5.986282D-10
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.018 -DE/DX = 0.0 !
! R2 R(1,3) 1.018 -DE/DX = 0.0 !
! R3 R(1,4) 1.018 -DE/DX = 0.0 !
! A1 A(2,1,3) 105.7412 -DE/DX = 0.0 !
! A2 A(2,1,4) 105.7412 -DE/DX = 0.0 !
! A3 A(3,1,4) 105.7412 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -111.8571 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

<jmol><jmolApplet>
<title>NH3 3D Structure</title>
<color>black</color>
<size>200</size>
<script>frame 1.16</script>
<uploadedFileContents>SAMHOPGOOD_NH3_OPTIMISATIONFUNCTION_POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file for NH3 is linked to [[Media:SAMHOPGOOD_NH3_OPTIMISATIONFUNCTION_POP.LOG| here]]

[[File:NH3_Display_Vibrations_Sam_Hopgood.jpg|400px|thumb|centre|Display Vibrations - NH3]]

'''1) How many modes do you expect from the 3N-6 rule?'''

As there are 4 atoms in an NH3 molecule, by the 3N-6 rule you would expect to get 6 nodes (as 3(4)-6=6).

'''2) Which modes are degenerate?'''

Modes 2 and 3, and 5 and 6 form degenerate pairs, shown by their identical vibrational frequencies.

'''3) Which modes are "bending" vibrations and which are "bond stretch" vibrations?'''

Modes 1,2 and 3 are bending vibrations, and modes 4,5 and 6 are formed from bond stretch vibrations.

'''4) Which mode is highly symmetric?'''

Mode 4 is highly symmetric

'''5) One mode is known as the "umbrella" mode, which one is this?'''

Mode 1 resembles the opening and closing mechanism of an umbrella.

'''6) How many bands would you expect to see in an experimental spectrum of gaseous ammonia?'''

You would expect to see 2 bands in a spectrum of gaseous ammonia, the first from mode 1 and the second from modes 2 and 3 combined as they occur at the same frequency. Modes 4,5 and 6 have intensities that are far too low to be visible on the spectrum, due to the symmetric stretches and small changes in the dipole moment. In reality the spectrum has a third peak, in the region of 3500, potentially caused by the combination of smaller vibrations.

'''Atomic Charges'''

Within the molecule, the nitrogen has a charge of -1.125, and each hydrogen has a charge of 0.375. This agrees with what I would expect, as nitrogen is the more electronegative atom and will pull the bonded pair of electrons towards itself, increasing its electron density and therefore reducing its charge.

==N2 Molecule==

'''Calculation Method:''' RB3LYP

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

'''Final Energy:''' -109.52412868 au

'''RMS Gradient:''' 0.00000060 au

'''Point group:''' D∞h

'''N-N Bond Length:''' 1.10550 Å

'''Item Table For N2:'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000000 0.001800 YES
RMS Displacement 0.000000 0.001200 YES
Predicted change in Energy=-3.400969D-13
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1055 -DE/DX = 0.0 !
--------------------------------------------------------------------------------

</pre>

<jmol><jmolApplet>
<title>N2 3D Structure</title>
<color>black</color>
<size>200</size>
<script>frame 1.10</script>
<uploadedFileContents>SAMHOPGOOD_N2_OPTIMISATIONFUNCTION.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file for N2 is linked to [[Media:SAMHOPGOOD_N2_OPTIMISATIONFUNCTION.LOG| here]]

[[File:N2_Display_Vibrations_Sam_Hopgood.jpg|400px|thumb|centre|Display Vibrations - N2]]

==H2 Molecule==

'''Calculation Method:''' RB3LYP

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

'''Final Energy:''' -1.17853936 au

'''RMS Gradient:''' 0.00000017 au

'''Point group:''' D∞h

'''H-H Bond Length:''' 0.74279 Å

'''Item Table For H2:'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000000 0.001800 YES
RMS Displacement 0.000001 0.001200 YES
Predicted change in Energy=-1.164080D-13
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 0.7428 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

<jmol><jmolApplet>
<title>H2 3D Structure</title>
<color>black</color>
<size>200</size>
<script>frame 1.12</script>
<uploadedFileContents>SAMHOPGOOD_H2_OPTIMISATIONFUNCTION.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file for H2 is linked to [[Media:SAMHOPGOOD_H2_OPTIMISATIONFUNCTION.LOG| here]]

[[File:H2_Display_Vibrations_Sam_Hopgood.jpg|400px|thumb|centre|Display Vibrations - H2]]

==Energy of Reaction==

'''E(NH3) =''' -56.55776873 au

'''2*E(NH3) =''' -113.1155375 au

'''E(N2) =''' -109.5241287 au

'''E(H2) =''' -1.17853936 au

'''3*E(H2) =''' -3.53561808 au

'''ΔE = 2*E(NH3)-(E(N2)+3*E(H2)) = ''' -0.0557907 au ''' = ''' -146.48 kJ/mol
From this we can tell that the product, ammonia, is more stable than the reactants N2 and H2.

In literature, this value was cited as -99.22 kJ/mol <ref name="NH3 Energy Change" />. The difference between this value and the computed value is due to poor optimisation of the molecule.

==CF4 Molecule==

'''Calculation Method:''' RB3LYP

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

'''Final Energy:''' -437.47627267 au

'''RMS Gradient:''' 0.00004049 au

'''Point group:''' TD

'''C-F Bond Length:''' 1.32939 Å

'''Item Table For CF4:'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000078 0.000450 YES
RMS Force 0.000042 0.000300 YES
Maximum Displacement 0.000133 0.001800 YES
RMS Displacement 0.000071 0.001200 YES
Predicted change in Energy=-2.081896D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.3294 -DE/DX = -0.0001 !
! R2 R(1,3) 1.3294 -DE/DX = -0.0001 !
! R3 R(1,4) 1.3294 -DE/DX = -0.0001 !
! R4 R(1,5) 1.3294 -DE/DX = -0.0001 !
! A1 A(2,1,3) 109.4712 -DE/DX = 0.0 !
! A2 A(2,1,4) 109.4712 -DE/DX = 0.0 !
! A3 A(2,1,5) 109.4712 -DE/DX = 0.0 !
! A4 A(3,1,4) 109.4712 -DE/DX = 0.0 !
! A5 A(3,1,5) 109.4712 -DE/DX = 0.0 !
! A6 A(4,1,5) 109.4712 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 120.0 -DE/DX = 0.0 !
! D2 D(2,1,5,3) -120.0 -DE/DX = 0.0 !
! D3 D(2,1,5,4) 120.0 -DE/DX = 0.0 !
! D4 D(3,1,5,4) -120.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

<jmol><jmolApplet>
<title>CF4 3D Structure</title>
<color>black</color>
<size>200</size>
<script>frame 1.8</script>
<uploadedFileContents>SAMHOPGOOD_CF4_OPTIMISATIONFUNCTION.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file for CF4 is linked to [[Media:SAMHOPGOOD_CF4_OPTIMISATIONFUNCTION.LOG| here]]

[[File:CF4_Display_Vibrations_Sam_Hopgood.jpg|400px|thumb|centre|Display Vibrations - CF4]]

[[File:CF4_Spectrum_Sam_Hopgood.jpg|400px|thumb|centre|Predicted Spectrum - CF4]]

'''CF4 Molecular Orbitals'''

[[File:CF4_Orbital_1_Sam_Hopgood.jpg|400px|thumb|centre|Molecular Orbital 1 - CF4]]
This first molecular orbital is a bonding orbital, formed from the overlap of 2s sub-shells from both the central carbon atom and the surrounding fluorine atoms. There is a very large overlap of these orbitals as they hold valence electrons and are therefore heavily involved in bonding. Evidently this orbital is also occupied.

[[File:CF4_Orbital_2_Sam_Hopgood.jpg|400px|thumb|centre|Molecular Orbital 2 - CF4]]
This molecular orbital is formed from all 2p orbitals, shown by the nodes on each atom. There is favourable overlap over all bonds showing that this is a bonding MO. This orbital is occupied, and does not have a particularly deep energy, so it will contribute fairly significantly to the overall bond. The three p orbitals on carbon could be involved in this MO, meaning it has three possible orientations, forming three degenerate MOs.

[[File:CF4_Orbital_3_Sam_Hopgood.jpg|400px|thumb|centre|Molecular Orbital 3 - CF4]]
MO number three is formed from 2s orbitals from both the carbon and fluorine, however, they are out of phase this time and therefore form the antibonding orbital, shown by the node on each bond. The orbital is fully occupied, and not particularly deep in energy, meaning it will have some influence on the bonding of the molecule. However, it does not lie near the LUMO/HOMO region and does not carry valence electrons so its impact on the strength of the bond is limited.

[[File:CF4_Orbital_4_Sam_Hopgood.jpg|400px|thumb|centre|Molecular Orbital 4 - CF4]]
This MO is comprised of a 2p orbital on the carbon, and s orbitals on the surrounding fluorine. Of the fluorine atoms, two are in one phase and two are in the other, with each pair lining up with the corresponding end of the carbon's p orbital. The overlap is in phase across the whole bond for each C-F bond, showing that the molecule is a bonding MO. The p orbital can be in 3 possible orientations so there are three degenerate MOs that look the same, each with a fairly low energy. As a result of the low energy it is unlikely that this contributes much to the overall bonding of the molecule.

[[File:CF4_Orbital_5_Sam_Hopgood.jpg|400px|thumb|centre|Molecular Orbital 5 - CF4]]
This filled MO is very low in energy, and it is formed of a 2s sub shell from the carbon. This is a non-bonding orbital, shown by the lack of influence from any adjacent fluorine atoms. It has no influence on bonding as it is not a bonding or antibonding orbital.

'''CF4 Charges'''

[[File:CF4_Charge_Distribution_Sam_Hopgood.jpg|400px|thumb|centre|Charge Distribution of CF4]]

The central carbon atom is very electropositive due to the surrounding fluorine atoms drawing away the bonded electrons. Fluorine atoms are very electronegative so will attract the bonded pair of electrons to itself, shifting the negative charge from the carbon to towards the fluorine.

==References==

<references>
<ref name="NH3 Energy Change">Ebbing, Darrel D.General Chemistry 3rd ed.;Houghton Mifflin Company: Boston, MA, 1990 pp 115,175, 223-4, 227.</ref>
</references>

Rep:MOD:01372542

2018-03-02T17:29:01Z

Sth17: /* Energy of Reaction */

==NH3 Molecule==

'''Calculation Method:''' RB3LYP

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

'''Final Energy:''' -56.55776873 au

'''RMS Gradient:''' 0.00000485 au

'''Point group:''' C3V

'''N-H Bond Length:''' 1.01798 Å

'''H-N-H Bond Angle:''' 105.741o

'''Item Table For NH3:'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000072 0.001800 YES
RMS Displacement 0.000035 0.001200 YES
Predicted change in Energy=-5.986282D-10
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.018 -DE/DX = 0.0 !
! R2 R(1,3) 1.018 -DE/DX = 0.0 !
! R3 R(1,4) 1.018 -DE/DX = 0.0 !
! A1 A(2,1,3) 105.7412 -DE/DX = 0.0 !
! A2 A(2,1,4) 105.7412 -DE/DX = 0.0 !
! A3 A(3,1,4) 105.7412 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -111.8571 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

<jmol><jmolApplet>
<title>NH3 3D Structure</title>
<color>black</color>
<size>200</size>
<script>frame 1.16</script>
<uploadedFileContents>SAMHOPGOOD_NH3_OPTIMISATIONFUNCTION_POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file for NH3 is linked to [[Media:SAMHOPGOOD_NH3_OPTIMISATIONFUNCTION_POP.LOG| here]]

[[File:NH3_Display_Vibrations_Sam_Hopgood.jpg|400px|thumb|centre|Display Vibrations - NH3]]

'''1) How many modes do you expect from the 3N-6 rule?'''

As there are 4 atoms in an NH3 molecule, by the 3N-6 rule you would expect to get 6 nodes (as 3(4)-6=6).

'''2) Which modes are degenerate?'''

Modes 2 and 3, and 5 and 6 form degenerate pairs, shown by their identical vibrational frequencies.

'''3) Which modes are "bending" vibrations and which are "bond stretch" vibrations?'''

Modes 1,2 and 3 are bending vibrations, and modes 4,5 and 6 are formed from bond stretch vibrations.

'''4) Which mode is highly symmetric?'''

Mode 4 is highly symmetric

'''5) One mode is known as the "umbrella" mode, which one is this?'''

Mode 1 resembles the opening and closing mechanism of an umbrella.

'''6) How many bands would you expect to see in an experimental spectrum of gaseous ammonia?'''

You would expect to see 2 bands in a spectrum of gaseous ammonia, the first from mode 1 and the second from modes 2 and 3 combined as they occur at the same frequency. Modes 4,5 and 6 have intensities that are far too low to be visible on the spectrum, due to the symmetric stretches and small changes in the dipole moment.

'''Atomic Charges'''

Within the molecule, the nitrogen has a charge of -1.125, and each hydrogen has a charge of 0.375. This agrees with what I would expect, as nitrogen is the more electronegative atom and will pull the bonded pair of electrons towards itself, increasing its electron density and therefore reducing its charge.

==N2 Molecule==

'''Calculation Method:''' RB3LYP

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

'''Final Energy:''' -109.52412868 au

'''RMS Gradient:''' 0.00000060 au

'''Point group:''' D∞h

'''N-N Bond Length:''' 1.10550 Å

'''Item Table For N2:'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000000 0.001800 YES
RMS Displacement 0.000000 0.001200 YES
Predicted change in Energy=-3.400969D-13
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1055 -DE/DX = 0.0 !
--------------------------------------------------------------------------------

</pre>

<jmol><jmolApplet>
<title>N2 3D Structure</title>
<color>black</color>
<size>200</size>
<script>frame 1.10</script>
<uploadedFileContents>SAMHOPGOOD_N2_OPTIMISATIONFUNCTION.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file for N2 is linked to [[Media:SAMHOPGOOD_N2_OPTIMISATIONFUNCTION.LOG| here]]

[[File:N2_Display_Vibrations_Sam_Hopgood.jpg|400px|thumb|centre|Display Vibrations - N2]]

==H2 Molecule==

'''Calculation Method:''' RB3LYP

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

'''Final Energy:''' -1.17853936 au

'''RMS Gradient:''' 0.00000017 au

'''Point group:''' D∞h

'''H-H Bond Length:''' 0.74279 Å

'''Item Table For H2:'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000000 0.001800 YES
RMS Displacement 0.000001 0.001200 YES
Predicted change in Energy=-1.164080D-13
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 0.7428 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

<jmol><jmolApplet>
<title>H2 3D Structure</title>
<color>black</color>
<size>200</size>
<script>frame 1.12</script>
<uploadedFileContents>SAMHOPGOOD_H2_OPTIMISATIONFUNCTION.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file for H2 is linked to [[Media:SAMHOPGOOD_H2_OPTIMISATIONFUNCTION.LOG| here]]

[[File:H2_Display_Vibrations_Sam_Hopgood.jpg|400px|thumb|centre|Display Vibrations - H2]]

==Energy of Reaction==

'''E(NH3) =''' -56.55776873 au

'''2*E(NH3) =''' -113.1155375 au

'''E(N2) =''' -109.5241287 au

'''E(H2) =''' -1.17853936 au

'''3*E(H2) =''' -3.53561808 au

'''ΔE = 2*E(NH3)-(E(N2)+3*E(H2)) = ''' -0.0557907 au ''' = ''' -146.48 kJ/mol
From this we can tell that the product, ammonia, is more stable than the reactants N2 and H2.

In literature, this value was cited as -99.22 kJ/mol <ref name="NH3 Energy Change" />. The difference between this value and the computed value is due to poor optimisation of the molecule.

==CF4 Molecule==

'''Calculation Method:''' RB3LYP

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

'''Final Energy:''' -437.47627267 au

'''RMS Gradient:''' 0.00004049 au

'''Point group:''' TD

'''C-F Bond Length:''' 1.32939 Å

'''Item Table For CF4:'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000078 0.000450 YES
RMS Force 0.000042 0.000300 YES
Maximum Displacement 0.000133 0.001800 YES
RMS Displacement 0.000071 0.001200 YES
Predicted change in Energy=-2.081896D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.3294 -DE/DX = -0.0001 !
! R2 R(1,3) 1.3294 -DE/DX = -0.0001 !
! R3 R(1,4) 1.3294 -DE/DX = -0.0001 !
! R4 R(1,5) 1.3294 -DE/DX = -0.0001 !
! A1 A(2,1,3) 109.4712 -DE/DX = 0.0 !
! A2 A(2,1,4) 109.4712 -DE/DX = 0.0 !
! A3 A(2,1,5) 109.4712 -DE/DX = 0.0 !
! A4 A(3,1,4) 109.4712 -DE/DX = 0.0 !
! A5 A(3,1,5) 109.4712 -DE/DX = 0.0 !
! A6 A(4,1,5) 109.4712 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 120.0 -DE/DX = 0.0 !
! D2 D(2,1,5,3) -120.0 -DE/DX = 0.0 !
! D3 D(2,1,5,4) 120.0 -DE/DX = 0.0 !
! D4 D(3,1,5,4) -120.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

<jmol><jmolApplet>
<title>CF4 3D Structure</title>
<color>black</color>
<size>200</size>
<script>frame 1.8</script>
<uploadedFileContents>SAMHOPGOOD_CF4_OPTIMISATIONFUNCTION.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file for CF4 is linked to [[Media:SAMHOPGOOD_CF4_OPTIMISATIONFUNCTION.LOG| here]]

[[File:CF4_Display_Vibrations_Sam_Hopgood.jpg|400px|thumb|centre|Display Vibrations - CF4]]

[[File:CF4_Spectrum_Sam_Hopgood.jpg|400px|thumb|centre|Predicted Spectrum - CF4]]

'''CF4 Molecular Orbitals'''

[[File:CF4_Orbital_1_Sam_Hopgood.jpg|400px|thumb|centre|Molecular Orbital 1 - CF4]]
This first molecular orbital is a bonding orbital, formed from the overlap of 2s sub-shells from both the central carbon atom and the surrounding fluorine atoms. There is a very large overlap of these orbitals as they hold valence electrons and are therefore heavily involved in bonding. Evidently this orbital is also occupied.

[[File:CF4_Orbital_2_Sam_Hopgood.jpg|400px|thumb|centre|Molecular Orbital 2 - CF4]]
This molecular orbital is formed from all 2p orbitals, shown by the nodes on each atom. There is favourable overlap over all bonds showing that this is a bonding MO. This orbital is occupied, and does not have a particularly deep energy, so it will contribute fairly significantly to the overall bond. The three p orbitals on carbon could be involved in this MO, meaning it has three possible orientations, forming three degenerate MOs.

[[File:CF4_Orbital_3_Sam_Hopgood.jpg|400px|thumb|centre|Molecular Orbital 3 - CF4]]
MO number three is formed from 2s orbitals from both the carbon and fluorine, however, they are out of phase this time and therefore form the antibonding orbital, shown by the node on each bond. The orbital is fully occupied, and not particularly deep in energy, meaning it will have some influence on the bonding of the molecule. However, it does not lie near the LUMO/HOMO region and does not carry valence electrons so its impact on the strength of the bond is limited.

[[File:CF4_Orbital_4_Sam_Hopgood.jpg|400px|thumb|centre|Molecular Orbital 4 - CF4]]
This MO is comprised of a 2p orbital on the carbon, and s orbitals on the surrounding fluorine. Of the fluorine atoms, two are in one phase and two are in the other, with each pair lining up with the corresponding end of the carbon's p orbital. The overlap is in phase across the whole bond for each C-F bond, showing that the molecule is a bonding MO. The p orbital can be in 3 possible orientations so there are three degenerate MOs that look the same, each with a fairly low energy. As a result of the low energy it is unlikely that this contributes much to the overall bonding of the molecule.

[[File:CF4_Orbital_5_Sam_Hopgood.jpg|400px|thumb|centre|Molecular Orbital 5 - CF4]]
This filled MO is very low in energy, and it is formed of a 2s sub shell from the carbon. This is a non-bonding orbital, shown by the lack of influence from any adjacent fluorine atoms. It has no influence on bonding as it is not a bonding or antibonding orbital.

'''CF4 Charges'''

[[File:CF4_Charge_Distribution_Sam_Hopgood.jpg|400px|thumb|centre|Charge Distribution of CF4]]

The central carbon atom is very electropositive due to the surrounding fluorine atoms drawing away the bonded electrons. Fluorine atoms are very electronegative so will attract the bonded pair of electrons to itself, shifting the negative charge from the carbon to towards the fluorine.

==References==

<references>
<ref name="NH3 Energy Change">Ebbing, Darrel D.General Chemistry 3rd ed.;Houghton Mifflin Company: Boston, MA, 1990 pp 115,175, 223-4, 227.</ref>
</references>

Rep:MOD:01372542

2018-03-02T17:19:51Z

Sth17: /* CF4 Molecule */

==NH3 Molecule==

'''Calculation Method:''' RB3LYP

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

'''Final Energy:''' -56.55776873 au

'''RMS Gradient:''' 0.00000485 au

'''Point group:''' C3V

'''N-H Bond Length:''' 1.01798 Å

'''H-N-H Bond Angle:''' 105.741o

'''Item Table For NH3:'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000072 0.001800 YES
RMS Displacement 0.000035 0.001200 YES
Predicted change in Energy=-5.986282D-10
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.018 -DE/DX = 0.0 !
! R2 R(1,3) 1.018 -DE/DX = 0.0 !
! R3 R(1,4) 1.018 -DE/DX = 0.0 !
! A1 A(2,1,3) 105.7412 -DE/DX = 0.0 !
! A2 A(2,1,4) 105.7412 -DE/DX = 0.0 !
! A3 A(3,1,4) 105.7412 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -111.8571 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

<jmol><jmolApplet>
<title>NH3 3D Structure</title>
<color>black</color>
<size>200</size>
<script>frame 1.16</script>
<uploadedFileContents>SAMHOPGOOD_NH3_OPTIMISATIONFUNCTION_POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file for NH3 is linked to [[Media:SAMHOPGOOD_NH3_OPTIMISATIONFUNCTION_POP.LOG| here]]

[[File:NH3_Display_Vibrations_Sam_Hopgood.jpg|400px|thumb|centre|Display Vibrations - NH3]]

'''1) How many modes do you expect from the 3N-6 rule?'''

As there are 4 atoms in an NH3 molecule, by the 3N-6 rule you would expect to get 6 nodes (as 3(4)-6=6).

'''2) Which modes are degenerate?'''

Modes 2 and 3, and 5 and 6 form degenerate pairs, shown by their identical vibrational frequencies.

'''3) Which modes are "bending" vibrations and which are "bond stretch" vibrations?'''

Modes 1,2 and 3 are bending vibrations, and modes 4,5 and 6 are formed from bond stretch vibrations.

'''4) Which mode is highly symmetric?'''

Mode 4 is highly symmetric

'''5) One mode is known as the "umbrella" mode, which one is this?'''

Mode 1 resembles the opening and closing mechanism of an umbrella.

'''6) How many bands would you expect to see in an experimental spectrum of gaseous ammonia?'''

You would expect to see 2 bands in a spectrum of gaseous ammonia, the first from mode 1 and the second from modes 2 and 3 combined as they occur at the same frequency. Modes 4,5 and 6 have intensities that are far too low to be visible on the spectrum, due to the symmetric stretches and small changes in the dipole moment.

'''Atomic Charges'''

Within the molecule, the nitrogen has a charge of -1.125, and each hydrogen has a charge of 0.375. This agrees with what I would expect, as nitrogen is the more electronegative atom and will pull the bonded pair of electrons towards itself, increasing its electron density and therefore reducing its charge.

==N2 Molecule==

'''Calculation Method:''' RB3LYP

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

'''Final Energy:''' -109.52412868 au

'''RMS Gradient:''' 0.00000060 au

'''Point group:''' D∞h

'''N-N Bond Length:''' 1.10550 Å

'''Item Table For N2:'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000000 0.001800 YES
RMS Displacement 0.000000 0.001200 YES
Predicted change in Energy=-3.400969D-13
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1055 -DE/DX = 0.0 !
--------------------------------------------------------------------------------

</pre>

<jmol><jmolApplet>
<title>N2 3D Structure</title>
<color>black</color>
<size>200</size>
<script>frame 1.10</script>
<uploadedFileContents>SAMHOPGOOD_N2_OPTIMISATIONFUNCTION.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file for N2 is linked to [[Media:SAMHOPGOOD_N2_OPTIMISATIONFUNCTION.LOG| here]]

[[File:N2_Display_Vibrations_Sam_Hopgood.jpg|400px|thumb|centre|Display Vibrations - N2]]

==H2 Molecule==

'''Calculation Method:''' RB3LYP

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

'''Final Energy:''' -1.17853936 au

'''RMS Gradient:''' 0.00000017 au

'''Point group:''' D∞h

'''H-H Bond Length:''' 0.74279 Å

'''Item Table For H2:'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000000 0.001800 YES
RMS Displacement 0.000001 0.001200 YES
Predicted change in Energy=-1.164080D-13
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 0.7428 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

<jmol><jmolApplet>
<title>H2 3D Structure</title>
<color>black</color>
<size>200</size>
<script>frame 1.12</script>
<uploadedFileContents>SAMHOPGOOD_H2_OPTIMISATIONFUNCTION.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file for H2 is linked to [[Media:SAMHOPGOOD_H2_OPTIMISATIONFUNCTION.LOG| here]]

[[File:H2_Display_Vibrations_Sam_Hopgood.jpg|400px|thumb|centre|Display Vibrations - H2]]

==Energy of Reaction==

'''E(NH3) =''' -56.55776873 au

'''2*E(NH3) =''' -113.1155375 au

'''E(N2) =''' -109.5241287 au

'''E(H2) =''' -1.17853936 au

'''3*E(H2) =''' -3.53561808 au

'''ΔE = 2*E(NH3)-[E(N2)+3*E(H2)] = ''' -0.0557907 au ''' = ''' -146.48 kJ/mol
From this we can tell that the product, ammonia, is more stable than the reactants N2 and H2.
In literature, this value was cited as -99.22 kJ/mol <ref name="NH3 Energy Change" />

==CF4 Molecule==

'''Calculation Method:''' RB3LYP

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

'''Final Energy:''' -437.47627267 au

'''RMS Gradient:''' 0.00004049 au

'''Point group:''' TD

'''C-F Bond Length:''' 1.32939 Å

'''Item Table For CF4:'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000078 0.000450 YES
RMS Force 0.000042 0.000300 YES
Maximum Displacement 0.000133 0.001800 YES
RMS Displacement 0.000071 0.001200 YES
Predicted change in Energy=-2.081896D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.3294 -DE/DX = -0.0001 !
! R2 R(1,3) 1.3294 -DE/DX = -0.0001 !
! R3 R(1,4) 1.3294 -DE/DX = -0.0001 !
! R4 R(1,5) 1.3294 -DE/DX = -0.0001 !
! A1 A(2,1,3) 109.4712 -DE/DX = 0.0 !
! A2 A(2,1,4) 109.4712 -DE/DX = 0.0 !
! A3 A(2,1,5) 109.4712 -DE/DX = 0.0 !
! A4 A(3,1,4) 109.4712 -DE/DX = 0.0 !
! A5 A(3,1,5) 109.4712 -DE/DX = 0.0 !
! A6 A(4,1,5) 109.4712 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 120.0 -DE/DX = 0.0 !
! D2 D(2,1,5,3) -120.0 -DE/DX = 0.0 !
! D3 D(2,1,5,4) 120.0 -DE/DX = 0.0 !
! D4 D(3,1,5,4) -120.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

<jmol><jmolApplet>
<title>CF4 3D Structure</title>
<color>black</color>
<size>200</size>
<script>frame 1.8</script>
<uploadedFileContents>SAMHOPGOOD_CF4_OPTIMISATIONFUNCTION.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file for CF4 is linked to [[Media:SAMHOPGOOD_CF4_OPTIMISATIONFUNCTION.LOG| here]]

[[File:CF4_Display_Vibrations_Sam_Hopgood.jpg|400px|thumb|centre|Display Vibrations - CF4]]

[[File:CF4_Spectrum_Sam_Hopgood.jpg|400px|thumb|centre|Predicted Spectrum - CF4]]

'''CF4 Molecular Orbitals'''

[[File:CF4_Orbital_1_Sam_Hopgood.jpg|400px|thumb|centre|Molecular Orbital 1 - CF4]]
This first molecular orbital is a bonding orbital, formed from the overlap of 2s sub-shells from both the central carbon atom and the surrounding fluorine atoms. There is a very large overlap of these orbitals as they hold valence electrons and are therefore heavily involved in bonding. Evidently this orbital is also occupied.

[[File:CF4_Orbital_2_Sam_Hopgood.jpg|400px|thumb|centre|Molecular Orbital 2 - CF4]]
This molecular orbital is formed from all 2p orbitals, shown by the nodes on each atom. There is favourable overlap over all bonds showing that this is a bonding MO. This orbital is occupied, and does not have a particularly deep energy, so it will contribute fairly significantly to the overall bond. The three p orbitals on carbon could be involved in this MO, meaning it has three possible orientations, forming three degenerate MOs.

[[File:CF4_Orbital_3_Sam_Hopgood.jpg|400px|thumb|centre|Molecular Orbital 3 - CF4]]
MO number three is formed from 2s orbitals from both the carbon and fluorine, however, they are out of phase this time and therefore form the antibonding orbital, shown by the node on each bond. The orbital is fully occupied, and not particularly deep in energy, meaning it will have some influence on the bonding of the molecule. However, it does not lie near the LUMO/HOMO region and does not carry valence electrons so its impact on the strength of the bond is limited.

[[File:CF4_Orbital_4_Sam_Hopgood.jpg|400px|thumb|centre|Molecular Orbital 4 - CF4]]
This MO is comprised of a 2p orbital on the carbon, and s orbitals on the surrounding fluorine. Of the fluorine atoms, two are in one phase and two are in the other, with each pair lining up with the corresponding end of the carbon's p orbital. The overlap is in phase across the whole bond for each C-F bond, showing that the molecule is a bonding MO. The p orbital can be in 3 possible orientations so there are three degenerate MOs that look the same, each with a fairly low energy. As a result of the low energy it is unlikely that this contributes much to the overall bonding of the molecule.

[[File:CF4_Orbital_5_Sam_Hopgood.jpg|400px|thumb|centre|Molecular Orbital 5 - CF4]]
This filled MO is very low in energy, and it is formed of a 2s sub shell from the carbon. This is a non-bonding orbital, shown by the lack of influence from any adjacent fluorine atoms. It has no influence on bonding as it is not a bonding or antibonding orbital.

'''CF4 Charges'''

[[File:CF4_Charge_Distribution_Sam_Hopgood.jpg|400px|thumb|centre|Charge Distribution of CF4]]

The central carbon atom is very electropositive due to the surrounding fluorine atoms drawing away the bonded electrons. Fluorine atoms are very electronegative so will attract the bonded pair of electrons to itself, shifting the negative charge from the carbon to towards the fluorine.

==References==

<references>
<ref name="NH3 Energy Change">Ebbing, Darrel D.General Chemistry 3rd ed.;Houghton Mifflin Company: Boston, MA, 1990 pp 115,175, 223-4, 227.</ref>
</references>

Rep:MOD:01372542

2018-03-02T15:45:48Z

Sth17: /* References */

==NH3 Molecule==

'''Calculation Method:''' RB3LYP

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

'''Final Energy:''' -56.55776873 au

'''RMS Gradient:''' 0.00000485 au

'''Point group:''' C3V

'''N-H Bond Length:''' 1.01798 Å

'''H-N-H Bond Angle:''' 105.741o

'''Item Table For NH3:'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000072 0.001800 YES
RMS Displacement 0.000035 0.001200 YES
Predicted change in Energy=-5.986282D-10
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.018 -DE/DX = 0.0 !
! R2 R(1,3) 1.018 -DE/DX = 0.0 !
! R3 R(1,4) 1.018 -DE/DX = 0.0 !
! A1 A(2,1,3) 105.7412 -DE/DX = 0.0 !
! A2 A(2,1,4) 105.7412 -DE/DX = 0.0 !
! A3 A(3,1,4) 105.7412 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -111.8571 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

<jmol><jmolApplet>
<title>NH3 3D Structure</title>
<color>black</color>
<size>200</size>
<script>frame 1.16</script>
<uploadedFileContents>SAMHOPGOOD_NH3_OPTIMISATIONFUNCTION_POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file for NH3 is linked to [[Media:SAMHOPGOOD_NH3_OPTIMISATIONFUNCTION_POP.LOG| here]]

[[File:NH3_Display_Vibrations_Sam_Hopgood.jpg|400px|thumb|centre|Display Vibrations - NH3]]

'''1) How many modes do you expect from the 3N-6 rule?'''

As there are 4 atoms in an NH3 molecule, by the 3N-6 rule you would expect to get 6 nodes (as 3(4)-6=6).

'''2) Which modes are degenerate?'''

Modes 2 and 3, and 5 and 6 form degenerate pairs, shown by their identical vibrational frequencies.

'''3) Which modes are "bending" vibrations and which are "bond stretch" vibrations?'''

Modes 1,2 and 3 are bending vibrations, and modes 4,5 and 6 are formed from bond stretch vibrations.

'''4) Which mode is highly symmetric?'''

Mode 4 is highly symmetric

'''5) One mode is known as the "umbrella" mode, which one is this?'''

Mode 1 resembles the opening and closing mechanism of an umbrella.

'''6) How many bands would you expect to see in an experimental spectrum of gaseous ammonia?'''

You would expect to see 2 bands in a spectrum of gaseous ammonia, the first from mode 1 and the second from modes 2 and 3 combined as they occur at the same frequency. Modes 4,5 and 6 have intensities that are far too low to be visible on the spectrum, due to the symmetric stretches and small changes in the dipole moment.

'''Atomic Charges'''

Within the molecule, the nitrogen has a charge of -1.125, and each hydrogen has a charge of 0.375. This agrees with what I would expect, as nitrogen is the more electronegative atom and will pull the bonded pair of electrons towards itself, increasing its electron density and therefore reducing its charge.

==N2 Molecule==

'''Calculation Method:''' RB3LYP

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

'''Final Energy:''' -109.52412868 au

'''RMS Gradient:''' 0.00000060 au

'''Point group:''' D∞h

'''N-N Bond Length:''' 1.10550 Å

'''Item Table For N2:'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000000 0.001800 YES
RMS Displacement 0.000000 0.001200 YES
Predicted change in Energy=-3.400969D-13
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1055 -DE/DX = 0.0 !
--------------------------------------------------------------------------------

</pre>

<jmol><jmolApplet>
<title>N2 3D Structure</title>
<color>black</color>
<size>200</size>
<script>frame 1.10</script>
<uploadedFileContents>SAMHOPGOOD_N2_OPTIMISATIONFUNCTION.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file for N2 is linked to [[Media:SAMHOPGOOD_N2_OPTIMISATIONFUNCTION.LOG| here]]

[[File:N2_Display_Vibrations_Sam_Hopgood.jpg|400px|thumb|centre|Display Vibrations - N2]]

==H2 Molecule==

'''Calculation Method:''' RB3LYP

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

'''Final Energy:''' -1.17853936 au

'''RMS Gradient:''' 0.00000017 au

'''Point group:''' D∞h

'''H-H Bond Length:''' 0.74279 Å

'''Item Table For H2:'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000000 0.001800 YES
RMS Displacement 0.000001 0.001200 YES
Predicted change in Energy=-1.164080D-13
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 0.7428 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

<jmol><jmolApplet>
<title>H2 3D Structure</title>
<color>black</color>
<size>200</size>
<script>frame 1.12</script>
<uploadedFileContents>SAMHOPGOOD_H2_OPTIMISATIONFUNCTION.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file for H2 is linked to [[Media:SAMHOPGOOD_H2_OPTIMISATIONFUNCTION.LOG| here]]

[[File:H2_Display_Vibrations_Sam_Hopgood.jpg|400px|thumb|centre|Display Vibrations - H2]]

==Energy of Reaction==

'''E(NH3) =''' -56.55776873 au

'''2*E(NH3) =''' -113.1155375 au

'''E(N2) =''' -109.5241287 au

'''E(H2) =''' -1.17853936 au

'''3*E(H2) =''' -3.53561808 au

'''ΔE = 2*E(NH3)-[E(N2)+3*E(H2)] = ''' -0.0557907 au ''' = ''' -146.48 kJ/mol
From this we can tell that the product, ammonia, is more stable than the reactants N2 and H2.
In literature, this value was cited as -99.22 kJ/mol <ref name="NH3 Energy Change" />

==CF4 Molecule==

'''Calculation Method:''' RB3LYP

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

'''Final Energy:''' -437.47627267 au

'''RMS Gradient:''' 0.00004049 au

'''Point group:''' TD

'''C-F Bond Length:''' 1.32939 Å

'''Item Table For CF4:'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000078 0.000450 YES
RMS Force 0.000042 0.000300 YES
Maximum Displacement 0.000133 0.001800 YES
RMS Displacement 0.000071 0.001200 YES
Predicted change in Energy=-2.081896D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.3294 -DE/DX = -0.0001 !
! R2 R(1,3) 1.3294 -DE/DX = -0.0001 !
! R3 R(1,4) 1.3294 -DE/DX = -0.0001 !
! R4 R(1,5) 1.3294 -DE/DX = -0.0001 !
! A1 A(2,1,3) 109.4712 -DE/DX = 0.0 !
! A2 A(2,1,4) 109.4712 -DE/DX = 0.0 !
! A3 A(2,1,5) 109.4712 -DE/DX = 0.0 !
! A4 A(3,1,4) 109.4712 -DE/DX = 0.0 !
! A5 A(3,1,5) 109.4712 -DE/DX = 0.0 !
! A6 A(4,1,5) 109.4712 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 120.0 -DE/DX = 0.0 !
! D2 D(2,1,5,3) -120.0 -DE/DX = 0.0 !
! D3 D(2,1,5,4) 120.0 -DE/DX = 0.0 !
! D4 D(3,1,5,4) -120.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

<jmol><jmolApplet>
<title>CF4 3D Structure</title>
<color>black</color>
<size>200</size>
<script>frame 1.8</script>
<uploadedFileContents>SAMHOPGOOD_CF4_OPTIMISATIONFUNCTION.LOG</uploadedFileContents>
</jmolApplet></jmol>

The optimisation file for CF4 is linked to [[Media:SAMHOPGOOD_CF4_OPTIMISATIONFUNCTION.LOG| here]]

[[File:CF4_Display_Vibrations_Sam_Hopgood.jpg|400px|thumb|centre|Display Vibrations - CF4]]

[[File:CF4_Spectrum_Sam_Hopgood.jpg|400px|thumb|centre|Predicted Spectrum - CF4]]

'''CF4 Molecular Orbitals'''

[[File:CF4_Orbital_1_Sam_Hopgood.jpg|400px|thumb|centre|Molecular Orbital 1 - CF4]]
This first molecular orbital is a bonding orbital, formed from the overlap of 2s sub-shells from both the central carbon atom and the surrounding fluorine atoms. There is a very large overlap of these orbitals as they hold valence electrons and are therefore heavily involved in bonding. The orbital is occupied

[[File:CF4_Orbital_2_Sam_Hopgood.jpg|400px|thumb|centre|Molecular Orbital 2 - CF4]]
This molecular orbital is formed from all 2p orbitals, shown by the nodes on each atom. There is favourable overlap over all bonds showing that this is a bonding MO. This orbital is occupied, and does not have a particularly deep energy, so it will contribute fairly significantly to the overall bond. The three p orbitals on carbon could be involved in this MO, meaning it has three possible orientations, forming three degenerate MOs.

[[File:CF4_Orbital_3_Sam_Hopgood.jpg|400px|thumb|centre|Molecular Orbital 3 - CF4]]
MO number three is formed from 2s orbitals from both the carbon and fluorine, however, they are out of phase this time and therefore form the antibonding orbital, shown by the node on each bond. The orbital is fully occupied, and not particularly deep in energy, meaning it will have some influence on the bonding of the molecule. However, it does not lie near the LUMO/HOMO region and does not carry valence electrons so its impact on the strength of the bond is limited.

[[File:CF4_Orbital_4_Sam_Hopgood.jpg|400px|thumb|centre|Molecular Orbital 4 - CF4]]
This MO is comprised of a 2p orbital on the carbon, and s orbitals on the surrounding fluorine. Of the fluorine atoms, two are in one phase and two are in the other, with each pair lining up with the corresponding end of the carbon's p orbital. The overlap is in phase across the whole bond for each C-F bond, showing that the molecule is a bonding MO. The p orbital can be in 3 possible orientations so there are three degenerate MOs that look the same, each with a fairly low energy. As a result of the low energy it is unlikely that this contributes much to the overall bonding of the molecule.

[[File:CF4_Orbital_5_Sam_Hopgood.jpg|400px|thumb|centre|Molecular Orbital 5 - CF4]]
This filled MO is very low in energy, and it is formed of a 2s sub shell from the carbon. This is a non-bonding orbital, shown by the lack of influence from any adjacent fluorine atoms. It has no influence on bonding as it is not a bonding or antibonding orbital.

'''CF4 Charges'''

[[File:CF4_Charge_Distribution_Sam_Hopgood.jpg|400px|thumb|centre|Charge Distribution of CF4]]

The central carbon atom is very electropositive due to the surrounding fluorine atoms drawing away the bonded electrons. Fluorine atoms are very electronegative so will attract the bonded pair of electrons to itself, shifting the negative charge from the carbon to towards the fluorine.

==References==

<references>
<ref name="NH3 Energy Change">Ebbing, Darrel D.General Chemistry 3rd ed.;Houghton Mifflin Company: Boston, MA, 1990 pp 115,175, 223-4, 227.</ref>
</references>