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MRD:xmh01513932

2020-05-25T18:27:45Z

Mx3118: /* 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. */

== 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 transition state is identified as the maximum on the minimum potential energy path between the reactants and products.

To explain the transition state mathematically, several derivatives have to be addressed first,
1. The first derivative of potential energy (V) with respect to either atomic separation (r1, r2) is zero, i.e. ∂V/∂r1 = 0 and ∂V/∂r2 = 0;
2. The second derivative D = ∂2V/∂r1∂r1 × ∂2V/∂r2∂r2 – ∂2V/∂r1∂r2 = 0;
3. If D > 0, ∂2V(r1)/∂r1∂r1 > 0, then the point with this particular (r1,r2) coordinates is a local minimum point; ∂2V(r1)/∂r1∂r1 < 0 for a local maximum point;
4. If D < 0, then this point is a saddle point, i.e. the transition state. Simply put, the saddle point is simultaneously a minimum and a maximum along two orthogonal directions (i.e. the two atomic separation axes in this case).
[[File:Figure 1.log|250px|thumb|center|Figure 1. Contour Plot.]]
[[File:xmhFigure 2.png|250px|thumb|center|Figure 2. Surface Plot.]]

== Report your best estimate of the transition state position (rts) and explain your reasoning illustrating it with a “Internuclear Distances vs Time” plot for a relevant trajectory. ==
For a symmetric system like H + H2, the internuclear distances of r1 = r2 is expected in the transition state. To test out the best input values for r1 and r2, there would be some expected features on various plots, as shown below,
1． In Figure 3., the kinetic energy of the system is constant at 0. This is explained by the fact that, at the transition state, the net force acting on the system F = dp/dt = ∂V/∂r1 = ∂V/∂r2 = 0 (as defined), the triatomic system is at a state of equilibrium with no change in motion. The same idea is conveyed in Figure 4., where the internuclear distances are expected to have a variation as small as possible, the atoms are “frozen” in space, moreover, rAB(r2) = rBC(r1).
2． In Figure 5., the transition state position (rts) is also checked by the fact that the input r1 and r2 values (denoted by the red cross) map onto the circle which gives the coordinates of the exact rts.
The final value of r1 = r2 = 90.7 pm is chosen to satisfy the above requirements.
[[File:xmhFigure 3.png|250px|thumb|center|Figure 3. Energy vs Time Plot.]]
[[File:xmhFigure 4.png|250px|thumb|center|Figure 4. Internuclear Distances vs Time Plot.]]
[[File:xmhFigure 5.png|250px|thumb|center|Figure 5. Contour Plot]]

== Comment on how the mep and the trajectory you just calculated differ. ==
Two paths were generated under the calculation types of MEP and Dynamics respectively, with initial conditions of r1 = rts+1=91.7 and r2 = 90.7 and p1 = p2 = 0 g.mol-1.pm.fs-1.
The dynamic graph shows a wavy line (shown in Figure 6.). After passing though rts (now r1 < r2), HAHB molecule is formed, detaching HC. This case takes into account of the intramolecular vibration of the new H2 molecule, since there is an oscillating trajectory at around a fixed rAB value with an increasing rBC value which indicates detaching of HC.
[[File:xmhFigure 6.png|250px|thumb|center|Figure 6. Contour Plot.]][[File:xmhFigure 7.png|250px|thumb|center|Figure 7. Energy vs Time Plot.]]
[[File:xmhFigure 8.png|250px|thumb|center|Figure 8. Momentum vs Time Plot]][[File:xmhFigure 8.png|250px|thumb|center|Figure 9. Internuclear Distances vs Time Plot]]
The mep (the minimum energy path) corresponds to a trajectory with infinitely slow motion, i.e. the system’s velocities are reset to zero in each time step, consequently no momentum or kinetic energy, as reflected in Figure 11 & 12. The reaction path way as a smooth curve (shown in Figure .) without any information of the intrinsic vibration within the H2 molecule.
[[File:xmhFigure 10.png|250px|thumb|center|thumb|Figure 10. Contour Plot.]]
[[File:xmhFigure 11.png|250px|thumb|center|Figure 11. Energy vs Time Plot.]]
[[File:xmhFigure 12.png|250px|thumb|center|Figure 12. Momentum vs Time Plot]]
[[File:xmhFigure 13.png|250px|thumb|center|Figure 13. Internuclear Distances vs Time Plot]]
If initial conditions are changed to r2 = rts+1=91.7 and r1 = 90.7 and p1 = p2 = 0 g.mol-1.pm.fs-1, same trends in both the Internuclear Distances vs Time graph and the Momenta vs Time graph are observed as for the previous conditions. Since the system is symmetric, hence the differences between these 2 sets of conditions are just attributed to the fact that whether HAHB or HBHC dissociates.

== 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" border="1"
|+ caption
! p1 !! p2 !! Etot !! Reactive? !! Description of the dynamics !! Illustration of the trajectory
|-
| -2.56 || -5.1 || -414.280 || Reactive || HA approaches HBHC molecule from a distance of rAB = 200 (starting from the bottom-right of the figure), with rBC being constant since HB and HC still remain bonded. After passing through rts, the new HAHB molecule is formed as shown by the constant rAB and increasing rBC as HC leaves(at the top left of the figure). || [[File:xmhA.png|250px]]
|-
| -3.1 || -4.1 || -420.077 || Unreactive || HA approaches HBHc (bottom-right), however it does not quite get to rts due to a reduced amount of kinetic energy compared to the first case, hence HA bounces off, there is no interaction with the hydrogen molecule. ||[[File:xmhB.png|250px]]
|-
| -3.1 || -5.1 || 413.977 || Reactive || Same as the first case except for the fact that p1 has a larger value, hence the system is more energetic to go over the activation barrier, and due to energy conservation, after the collision, the new molecule has a greater vibration. ||[[File:xmhC.png|250px]]
|-
| -5.1 || -10.1 || -357.277 || Unreactive || Barrier recrossing - the system is energetic enough to go over the transition state region and form the new HAHB, since rBC increases from its original bond length, indicating the leaving of HC, and the Etot is also greater than the first case (a reactive case). However, rBC drops down again to the original bond length and rAB increases as the system reverts back to HBHC. ||[[File:xmhD.png|250px]]
|-
| -5.1 || -10.6 || -349.477 || Reactive || The system HBHC converts to HAHB after reaching rts, but reverts given the excess momentum in p2 as rAB increases and rBC decreases, the system crosses the transition region again to form the final HAHB molecule as rBC continue increasing and rAB stays oscillating around a fixed value. ||[[File:xmhE.png|250px]]
|}
From the first sight, it seems reasonable to encourage a successful collision by adding more momentum into the system since this increases the kinetic energy of the atoms to overcome the activation barrier. However, as concluded from the table, the excess momentum and energy could give rise to greater vibration within the molecule and hence cause the bond to dissociate.

== Given the results you have obtained, how will Transition State Theory predictions for reaction rate values compare with experimental values? ==
In the transition state theory, the average transmission rate/frequency is estimated based on the assumption that all trajectories with some kinetic energy greater than the activation energy will be reactive. From the empirical data of the last section, it was shown that if momentum is provided such that the vibration is so great that the bond dissociates again, i.e. barrier recrossing occurs, this reduces the rate of a particular conversion, e.g. from HBHC and HA to HAHB and HC. This would overestimate the transition state theory rate constant (and hence the rate).
The transition state theory also consider the reaction pathway through classical mechanic collision (for macroscopic system). However, wavefunction (for microscopic system) of the atoms should be considered. Quantum tunneling may take place, it is not necessary to jump over the activation barrier, hence less kinetic energy is required for a successful collision, rate is higher than the theory prediction.

== 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? ==
In GUI, it is set up that the atom A approaches and collide with the molecule HBHC.
In the F+H2 system, F is considered as atom A, and the 2 H atoms as atoms B and C. Figure 14(A) shows the entrance channel for the reactants F+H2, since rBC (the molecule’s bond length) is constant and rAB is big; Figure 14(B) shows the exit channel for the products (FH+H), since rAB is now constant and rBC is big. Comparing the V for the 2 channels, the reactants are at a higher V than the products, hence this is an exothermic reaction.
[[File:xmhFigure 14(A).png|250px|thumb|center|Figure 14(A). Surface Plot.]]
[[File:Figure 14(B)xmh.png|250px|thumb|center|Figure 14(B). Surface Plot.]]
For the H+FH system, the same idea applies, from Figure 15(A). & (B)., the reactants are at a lower V than the products, hence it is an endothermic reaction.
[[File:Figure 15(A)mh.png|250px|thumb|center|Figure 15(A). Surface Plot.]]
[[File:Figure 15(B)xmh.png|250px|thumb|center|Figure 15(B). Surface Plot.]]
This correctly reflects the result obtained from qualitative bond-strength analysis. F-H is a very strong bond (compared to other possible bonds in the system) due to the different electronegativities and hence ionic contribution to the nature of the bond. Hence breaking this bond requires much energy, and forming it releases much energy. In the F+H2 reaction, a pure covalent bond is broken to form the strong F-H bond, this is expected to be exothermic; in the H+FH system, the energy released from forming H2 does not compensate for the energy required to break F-H first, hence it is expected to be endothermic.

== Locate the approximate position of the transition state. ==
The approximate position of the transition state was investigated in the case of F+H2, where F is considered as atom A, and the 2 H atoms as atoms B and C. It was found that rAB = 181.1 and rBC = 74.5. This is reflected by Figure 20., where the internuclear distances are constant between all 3 atoms, corresponding to equilibrium at the transition state. Etot = - 433.980.
For the case of H+HF, same rts was found, since this reaction is just the reverse reaction of the above case, and the same geometry is found at the transition state.
[[File:xmhFigure 16.png|250px|thumb|center|Figure 16. Contour Plot.]]
[[File:Figure 17xmh.png|250px|thumb|center|Figure 17. Internuclear Distancesvs Time Plot.]]

== Report the activation energy for both reactions. ==
In order to find the reactants’ energy for the F+H2 reaction, initial conditions were set as rAB = 1000 and rBC = 74.5. The value of rAB was chosen so that there is no interaction in the system since the F atom is at a very distant away from the H2 molecule, as reflected by Figure 20., where the only momentum is given by the oscillation between the bonded molecule. Etot = - 435.057.
Hence the activation energy = Etot(transition state) – Etot(reactants) = - 433.980 + 435.057 = 1.077.
[[File:xmhFigure 18.png|250px|thumb|center|Figure 18. Momentum vs Time Plot.]]
Same method applies to the H+FH system, the activation energy = 125.322.

== 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. ==
There are 3 types of energies associated with the system: potential energy due to the interactions between the atom and the molecule, vibrational kinetic energy and translational kinetic energy. After a successful collision, these energies would redistribute based on the mass and bond strength of the atom and molecule, some energy might excite the new molecule into a higher vibrational state. However, the molecule would eventually drop down to the ground state, releasing energy.
The IR overtone region could be used to confirm the presence of the transition between higher states, the peaks appear at higher wavelength (higher energy). Consequently, this confirms the following release of energy.

== 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. ==
According to Polanyi's rules, the reactants' translational energy activates them more effectively to the activation barrier and hence increases rate for exothermic reactions; conversely, the reactants' vibrational energy activates more effectively for endothermic reactions.
For the exothermic F+H2 system, the translational energy is more important to give a successful collision.
For the endothermic H+HF system, the vibrational energy is more important.

MRD:xmh01513932

2020-05-25T17:51:56Z

Mx3118:

== 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 transition state is identified as the maximum on the minimum potential energy path between the reactants and products.

To explain the transition state mathematically, several derivatives have to be addressed first,
1. The first derivative of potential energy (V) with respect to either atomic separation (r1, r2) is zero, i.e. ∂V/∂r1 = 0 and ∂V/∂r2 = 0;
2. The second derivative D = ∂2V/∂r1∂r1 × ∂2V/∂r2∂r2 – ∂2V/∂r1∂r2 = 0;
3. If D > 0, ∂2V(r1)/∂r1∂r1 > 0, then the point with this particular (r1,r2) coordinates is a local minimum point; ∂2V(r1)/∂r1∂r1 < 0 for a local maximum point;
4. If D < 0, then this point is a saddle point, i.e. the transition state. Simply put, the saddle point is simultaneously a minimum and a maximum along two orthogonal directions (i.e. the two atomic separation axes in this case).
[[File:Figure 1.log|250px|thumb|center|Figure 1. Contour Plot.]]
[[File:xmhFigure 2.png|250px|thumb|center|Figure 2. Surface Plot.]]

== Report your best estimate of the transition state position (rts) and explain your reasoning illustrating it with a “Internuclear Distances vs Time” plot for a relevant trajectory. ==
For a symmetric system like H + H2, the internuclear distances of r1 = r2 is expected in the transition state. To test out the best input values for r1 and r2, there would be some expected features on various plots, as shown below,
1． In Figure 3., the kinetic energy of the system is constant at 0. This is explained by the fact that, at the transition state, the net force acting on the system F = dp/dt = ∂V/∂r1 = ∂V/∂r2 = 0 (as defined), the triatomic system is at a state of equilibrium with no change in motion. The same idea is conveyed in Figure 4., where the internuclear distances are expected to have a variation as small as possible, the atoms are “frozen” in space, moreover, rAB(r2) = rBC(r1).
2． In Figure 5., the transition state position (rts) is also checked by the fact that the input r1 and r2 values (denoted by the red cross) map onto the circle which gives the coordinates of the exact rts.
The final value of r1 = r2 = 90.7 pm is chosen to satisfy the above requirements.
[[File:xmhFigure 3.png|250px|thumb|center|Figure 3. Energy vs Time Plot.]]
[[File:xmhFigure 4.png|250px|thumb|center|Figure 4. Internuclear Distances vs Time Plot.]]
[[File:xmhFigure 5.png|250px|thumb|center|Figure 5. Contour Plot]]

== Comment on how the mep and the trajectory you just calculated differ. ==
Two paths were generated under the calculation types of MEP and Dynamics respectively, with initial conditions of r1 = rts+1=91.7 and r2 = 90.7 and p1 = p2 = 0 g.mol-1.pm.fs-1.
The dynamic graph shows a wavy line (shown in Figure 6.). After passing though rts (now r1 < r2), HAHB molecule is formed, detaching HC. This case takes into account of the intramolecular vibration of the new H2 molecule, since there is an oscillating trajectory at around a fixed rAB value with an increasing rBC value which indicates detaching of HC.
[[File:xmhFigure 6.png|250px|thumb|center|Figure 6. Contour Plot.]][[File:xmhFigure 7.png|250px|thumb|center|Figure 7. Energy vs Time Plot.]]
[[File:xmhFigure 8.png|250px|thumb|center|Figure 8. Momentum vs Time Plot]][[File:xmhFigure 8.png|250px|thumb|center|Figure 9. Internuclear Distances vs Time Plot]]
The mep (the minimum energy path) corresponds to a trajectory with infinitely slow motion, i.e. the system’s velocities are reset to zero in each time step, consequently no momentum or kinetic energy, as reflected in Figure 11 & 12. The reaction path way as a smooth curve (shown in Figure .) without any information of the intrinsic vibration within the H2 molecule.
[[File:xmhFigure 10.png|250px|thumb|center|thumb|Figure 10. Contour Plot.]]
[[File:xmhFigure 11.png|250px|thumb|center|Figure 11. Energy vs Time Plot.]]
[[File:xmhFigure 12.png|250px|thumb|center|Figure 12. Momentum vs Time Plot]]
[[File:xmhFigure 13.png|250px|thumb|center|Figure 13. Internuclear Distances vs Time Plot]]
If initial conditions are changed to r2 = rts+1=91.7 and r1 = 90.7 and p1 = p2 = 0 g.mol-1.pm.fs-1, same trends in both the Internuclear Distances vs Time graph and the Momenta vs Time graph are observed as for the previous conditions. Since the system is symmetric, hence the differences between these 2 sets of conditions are just attributed to the fact that whether HAHB or HBHC dissociates.

== 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" border="1"
|+ caption
! p1 !! p2 !! Etot !! Reactive? !! Description of the dynamics !! Illustration of the trajectory
|-
| -2.56 || -5.1 || -414.280 || Reactive || HA approaches HBHC molecule from a distance of rAB = 200 (starting from the bottom-right of the figure), with rBC being constant since HB and HC still remain bonded. After passing through rts, the new HAHB molecule is formed as shown by the constant rAB and increasing rBC as HC leaves(at the top left of the figure). || [[File:xmhA.png|250px]]
|-
| -3.1 || -4.1 || -420.077 || Unreactive || HA approaches HBHc (bottom-right), however it does not quite get to rts due to a reduced amount of kinetic energy compared to the first case, hence HA bounces off, there is no interaction with the hydrogen molecule. ||[[File:xmhB.png|250px]]
|-
| -3.1 || -5.1 || 413.977 || Reactive || Same as the first case except for the fact that p1 has a larger value, hence the system is more energetic to go over the activation barrier, and due to energy conservation, after the collision, the new molecule has a greater vibration. ||[[File:xmhC.png|250px]]
|-
| -5.1 || -10.1 || -357.277 || Unreactive || Barrier recrossing - the system is energetic enough to go over the transition state region and form the new HAHB, since rBC increases from its original bond length, indicating the leaving of HC, and the Etot is also greater than the first case (a reactive case). However, rBC drops down again to the original bond length and rAB increases as the system reverts back to HBHC. ||[[File:xmhD.png|250px]]
|-
| -5.1 || -10.6 || -349.477 || Reactive || The system HBHC converts to HAHB after reaching rts, but reverts given the excess momentum in p2 as rAB increases and rBC decreases, the system crosses the transition region again to form the final HAHB molecule as rBC continue increasing and rAB stays oscillating around a fixed value. ||[[File:xmhE.png|250px]]
|}
From the first sight, it seems reasonable to encourage a successful collision by adding more momentum into the system since this increases the kinetic energy of the atoms to overcome the activation barrier. However, as concluded from the table, the excess momentum and energy could give rise to greater vibration within the molecule and hence cause the bond to dissociate.

== Given the results you have obtained, how will Transition State Theory predictions for reaction rate values compare with experimental values? ==
In the transition state theory, the average transmission rate/frequency is estimated based on the assumption that all trajectories with some kinetic energy greater than the activation energy will be reactive. From the empirical data of the last section, it was shown that if momentum is provided such that the vibration is so great that the bond dissociates again, i.e. barrier recrossing occurs, this reduces the rate of a particular conversion, e.g. from HBHC and HA to HAHB and HC. This would overestimate the transition state theory rate constant (and hence the rate).
The transition state theory also consider the reaction pathway through classical mechanic collision (for macroscopic system). However, wavefunction (for microscopic system) of the atoms should be considered. Quantum tunneling may take place, it is not necessary to jump over the activation barrier, hence less kinetic energy is required for a successful collision, rate is higher than the theory prediction.

== 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? ==
In GUI, it is set up that the atom A approaches and collide with the molecule HBHC.
In the F+H2 system, F is considered as atom A, and the 2 H atoms as atoms B and C. Figure 14(A) shows the entrance channel for the reactants F+H2, since rBC (the molecule’s bond length) is constant and rAB is big; Figure 14(B) shows the exit channel for the products (FH+H), since rAB is now constant and rBC is big. Comparing the V for the 2 channels, the reactants are at a higher V than the products, hence this is an exothermic reaction.
[[File:xmhFigure 14(A).png|250px|thumb|center|Figure 14(A). Surface Plot.]]
[[File:Figure 14(B)xmh.png|250px|thumb|center|Figure 14(B). Surface Plot.]]
For the H+FH system, the same idea applies, from Figure 15(A). & (B)., the reactants are at a lower V than the products, hence it is an endothermic reaction.
[[File:Figure 15(A)mh.png|250px|thumb|center|Figure 15(A). Surface Plot.]]
[[File:Figure 15(B)xmh.png|250px|thumb|center|Figure 15(B). Surface Plot.]]
This correctly reflects the result obtained from qualitative bond-strength analysis. F-H is a very strong bond (compared to other possible bonds in the system) due to the different electronegativities and hence ionic contribution to the nature of the bond. Hence breaking this bond requires much energy, and forming it releases much energy. In the F+H2 reaction, a pure covalent bond is broken to form the strong F-H bond, this is expected to be exothermic; in the H+FH system, the energy released from forming H2 does not compensate for the energy required to break F-H first, hence it is expected to be endothermic.

== Locate the approximate position of the transition state. ==
The approximate position of the transition state was investigated in the case of F+H2, where F is considered as atom A, and the 2 H atoms as atoms B and C. It was found that rAB = 181.1 and rBC = 74.5. This is reflected by Figure 20., where the internuclear distances are constant between all 3 atoms, corresponding to equilibrium at the transition state. Etot = - 433.980.
For the case of H+HF, same rts was found, since this reaction is just the reverse reaction of the above case, and the same geometry is found at the transition state.
[[File:xmhFigure 16.png|250px|thumb|center|Figure 16. Contour Plot.]]
[[File:Figure 17xmh.png|250px|thumb|center|Figure 17. Internuclear Distancesvs Time Plot.]]

== Report the activation energy for both reactions. ==
In order to find the reactants’ energy for the F+H2 reaction, initial conditions were set as rAB = 1000 and rBC = 74.5. The value of rAB was chosen so that there is no interaction in the system since the F atom is at a very distant away from the H2 molecule, as reflected by Figure 20., where the only momentum is given by the oscillation between the bonded molecule. Etot = - 435.057.
Hence the activation energy = Etot(transition state) – Etot(reactants) = - 433.980 + 435.057 = 1.077.
[[File:xmhFigure 18.png|250px|thumb|center|Figure 18. Momentum vs Time Plot.]]
Same method applies to the H+FH system, the activation energy = 125.322.

== 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. ==
There are 3 types of energies associated with the system: potential energy due to the interactions between the atom and the molecule, vibrational kinetic energy and translational kinetic energy. After a successful collision, these energies would redistribute based on the mass and bond strength of the atom and molecule, some energy might excite the new molecule into a higher vibrational state. However, the molecule would eventually drop down to the ground state, releasing energy.
The IR overtone region could be used to confirm the presence of the transition between higher states, the peaks appear at higher wavelength (higher energy). Consequently, this confirms the following release of energy.

== 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. ==
According to Polanyi's rules, the reactants' translational energy activates them more effectively to the activation barrier and hence increases rate for exothermic reactions; conversely, the reactants' vibrational energy activates more effectively for endothermic reactions.
For the exothermic F+H2 system, the translational energy is more important to give a successful collision.
{| class="wikitable" border="1"
|+ caption
! p1 !! p2 !! Etot !! Reactive? !! Illustration of the trajectory
|-
| -2.56 || -5.1 || -414.280 || Reactive || HA approaches HBHC molecule from a distance of rAB = 200 (starting from the bottom-right of the figure), with rBC being constant since HB and HC still remain bonded. After passing through rts, the new HAHB molecule is formed as shown by the constant rAB and increasing rBC as HC leaves(at the top left of the figure). || [[File:xmhA.png|250px]]
|-
| -3.1 || -4.1 || -420.077 || Unreactive || HA approaches HBHc (bottom-right), however it does not quite get to rts due to a reduced amount of kinetic energy compared to the first case, hence HA bounces off, there is no interaction with the hydrogen molecule. ||[[File:xmhB.png|250px]]
|-
| -3.1 || -5.1 || 413.977 || Reactive || Same as the first case except for the fact that p1 has a larger value, hence the system is more energetic to go over the activation barrier, and due to energy conservation, after the collision, the new molecule has a greater vibration. ||[[File:xmhC.png|250px]]
|-
| -5.1 || -10.1 || -357.277 || Unreactive || Barrier recrossing - the system is energetic enough to go over the transition state region and form the new HAHB, since rBC increases from its original bond length, indicating the leaving of HC, and the Etot is also greater than the first case (a reactive case). However, rBC drops down again to the original bond length and rAB increases as the system reverts back to HBHC. ||[[File:xmhD.png|250px]]
|-
| -5.1 || -10.6 || -349.477 || Reactive || The system HBHC converts to HAHB after reaching rts, but reverts given the excess momentum in p2 as rAB increases and rBC decreases, the system crosses the transition region again to form the final HAHB molecule as rBC continue increasing and rAB stays oscillating around a fixed value. ||[[File:xmhE.png|250px]]
|}For the endothermic H+HF system, the vibrational energy is more important.

MRD:xmh01513932

2020-05-25T15:50:17Z

Mx3118:

== 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 transition state is identified as the maximum on the minimum potential energy path between the reactants and products.

To explain the transition state mathematically, several derivatives have to be addressed first,
1. The first derivative of potential energy (V) with respect to either atomic separation (r1, r2) is zero, i.e. ∂V/∂r1 = 0 and ∂V/∂r2 = 0;
2. The second derivative D = ∂2V/∂r1∂r1 × ∂2V/∂r2∂r2 – ∂2V/∂r1∂r2 = 0;
3. If D > 0, ∂2V(r1)/∂r1∂r1 > 0, then the point with this particular (r1,r2) coordinates is a local minimum point; ∂2V(r1)/∂r1∂r1 < 0 for a local maximum point;
4. If D < 0, then this point is a saddle point, i.e. the transition state. Simply put, the saddle point is simultaneously a minimum and a maximum along two orthogonal directions (i.e. the two atomic separation axes in this case).
[[File:Figure 1.log|250px|thumb|Figure 1. Contour Plot.]]
[[File:xmhFigure 2.png|250px|thumb|Figure 2. Surface Plot.]]

== Report your best estimate of the transition state position (rts) and explain your reasoning illustrating it with a “Internuclear Distances vs Time” plot for a relevant trajectory. ==
For a symmetric system like H + H2, the internuclear distances of r1 = r2 is expected in the transition state. To test out the best input values for r1 and r2, there would be some expected features on various plots, as shown below,
1． In Figure 3., the kinetic energy of the system is constant at 0. This is explained by the fact that, at the transition state, the net force acting on the system F = dp/dt = ∂V/∂r1 = ∂V/∂r2 = 0 (as defined), the triatomic system is at a state of equilibrium with no change in motion. The same idea is conveyed in Figure 4., where the internuclear distances are expected to have a variation as small as possible, the atoms are “frozen” in space, moreover, rAB(r2) = rBC(r1).
2． In Figure 5., the transition state position (rts) is also checked by the fact that the input r1 and r2 values (denoted by the red cross) map onto the circle which gives the coordinates of the exact rts.
The final value of r1 = r2 = 90.7 pm is chosen to satisfy the above requirements.
[[File:xmhFigure 3.png|250px|thumb|Figure 3. Energy vs Time Plot.]]
[[File:xmhFigure 4.png|250px|thumb|Figure 4. Internuclear Distances vs Time Plot.]]
[[File:xmhFigure 5.png|250px|thumb|Figure 5. Contour Plot]]

== Comment on how the mep and the trajectory you just calculated differ. ==
Two paths were generated under the calculation types of MEP and Dynamics respectively, with initial conditions of r1 = rts+1=91.7 and r2 = 90.7 and p1 = p2 = 0 g.mol-1.pm.fs-1.
The dynamic graph shows a wavy line (shown in Figure 6.). After passing though rts (now r1 < r2), HAHB molecule is formed, detaching HC. This case takes into account of the intramolecular vibration of the new H2 molecule, since there is an oscillating trajectory at around a fixed rAB value with an increasing rBC value which indicates detaching of HC.
[[File:xmhFigure 6.png|250px|thumb|Figure 6. Contour Plot.]]
[[File:xmhFigure 7.png|250px|thumb|Figure 7. Energy vs Time Plot.]]
[[File:xmhFigure 8.png|250px|thumb|Figure 8. Momentum vs Time Plot]]
[[File:xmhFigure 8.png|250px|thumb|Figure 9. Internuclear Distances vs Time Plot]]
The mep (the minimum energy path) corresponds to a trajectory with infinitely slow motion, i.e. the system’s velocities are reset to zero in each time step, consequently no momentum or kinetic energy, as reflected in Figure 11 & 12. The reaction path way as a smooth curve (shown in Figure .) without any information of the intrinsic vibration within the H2 molecule.
[[File:xmhFigure 10.png|250px|thumb|thumb|Figure 10. Contour Plot.]]
[[File:xmhFigure 11.png|250px|thumb|Figure 11. Energy vs Time Plot.]]
[[File:xmhFigure 12.png|250px|thumb|Figure 12. Momentum vs Time Plot]]
[[File:xmhFigure 13.png|250px|thumb|Figure 13. Internuclear Distances vs Time Plot]]
If initial conditions are changed to r2 = rts+1=91.7 and r1 = 90.7 and p1 = p2 = 0 g.mol-1.pm.fs-1, same trends in both the Internuclear Distances vs Time graph and the Momenta vs Time graph are observed as for the previous conditions. Since the system is symmetric, hence the differences between these 2 sets of conditions are just attributed to the fact that whether HAHB or HBHC dissociates.

== 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" border="1"
|+ caption
! p1 !! p2 !! Etot !! Reactive? !! Description of the dynamics !! Illustration of the trajectory
|-
| -2.56 || -5.1 || -414.280 || Reactive || HA approaches HBHC molecule from a distance of rAB = 200 (starting from the bottom-right of the figure), with rBC being constant since HB and HC still remain bonded. After passing through rts, the new HAHB molecule is formed as shown by the constant rAB and increasing rBC as HC leaves(at the top left of the figure). || [[File:xmhA.png|250px]]
|-
| -3.1 || -4.1 || -420.077 || Unreactive || HA approaches HBHc (bottom-right), however it does not quite get to rts due to a reduced amount of kinetic energy compared to the first case, hence HA bounces off, there is no interaction with the hydrogen molecule. ||[[File:xmhB.png|250px]]
|-
| -3.1 || -5.1 || 413.977 || Reactive || Same as the first case except for the fact that p1 has a larger value, hence the system is more energetic to go over the activation barrier, and due to energy conservation, after the collision, the new molecule has a greater vibration. ||[[File:xmhC.png|250px]]
|-
| -5.1 || -10.1 || -357.277 || Unreactive || Barrier recrossing - the system is energetic enough to go over the transition state region and form the new HAHB, since rBC increases from its original bond length, indicating the leaving of HC, and the Etot is also greater than the first case (a reactive case). However, rBC drops down again to the original bond length and rAB increases as the system reverts back to HBHC. ||[[File:xmhD.png|250px]]
|-
| -5.1 || -10.6 || -349.477 || Reactive || The system HBHC converts to HAHB after reaching rts, but reverts given the excess momentum in p2 as rAB increases and rBC decreases, the system crosses the transition region again to form the final HAHB molecule as rBC continue increasing and rAB stays oscillating around a fixed value. ||[[File:xmhE.png|250px]]
|}
From the first sight, it seems reasonable to encourage a successful collision by adding more momentum into the system since this increases the kinetic energy of the atoms to overcome the activation barrier. However, as concluded from the table, the excess momentum and energy could give rise to greater vibration within the molecule and hence cause the bond to dissociate.

== Given the results you have obtained, how will Transition State Theory predictions for reaction rate values compare with experimental values? ==
In the transition state theory, the average transmission rate/frequency is estimated based on the assumption that all trajectories with some kinetic energy greater than the activation energy will be reactive. From the empirical data of the last section, it was shown that if momentum is provided such that the vibration is so great that the bond dissociates again, i.e. barrier recrossing occurs, this reduces the rate of a particular conversion, e.g. from HBHC and HA to HAHB and HC. This would overestimate the transition state theory rate constant (and hence the rate).
The transition state theory also consider the reaction pathway through classical mechanic collision (for macroscopic system). However, wavefunction (for microscopic system) of the atoms should be considered. Quantum tunneling may take place, it is not necessary to jump over the activation barrier, hence less kinetic energy is required for a successful collision, rate is higher than the theory prediction.

== 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? ==
In GUI, it is set up that the atom A approaches and collide with the molecule HBHC.
In the F+H2 system, F is considered as atom A, and the 2 H atoms as atoms B and C. Figure 14(A) shows the entrance channel for the reactants F+H2, since rBC (the molecule’s bond length) is constant and rAB is big; Figure 14(B) shows the exit channel for the products (FH+H), since rAB is now constant and rBC is big. Comparing the V for the 2 channels, the reactants are at a higher V than the products, hence this is an exothermic reaction.
[[File:xmhFigure 14(A).png|250px|thumb|Figure 14(A). Surface Plot.]]
[[File:Figure 14(B)xmh.png|250px|thumb|Figure 14(B). Surface Plot.]]
For the H+FH system, the same idea applies, from Figure 15(A). & (B)., the reactants are at a lower V than the products, hence it is an endothermic reaction.
[[File:Figure 15(A)mh.png|250px|thumb|Figure 15(A). Surface Plot.]]
[[File:Figure 15(B)xmh.png|250px|thumb|Figure 15(B). Surface Plot.]]
This correctly reflects the result obtained from qualitative bond-strength analysis. F-H is a very strong bond (compared to other possible bonds in the system) due to the different electronegativities and hence ionic contribution to the nature of the bond. Hence breaking this bond requires much energy, and forming it releases much energy. In the F+H2 reaction, a pure covalent bond is broken to form the strong F-H bond, this is expected to be exothermic; in the H+FH system, the energy released from forming H2 does not compensate for the energy required to break F-H first, hence it is expected to be endothermic.

== Locate the approximate position of the transition state. ==
The approximate position of the transition state was investigated in the case of F+H2, where F is considered as atom A, and the 2 H atoms as atoms B and C. It was found that rAB = 181.1 and rBC = 74.5. This is reflected by Figure 20., where the internuclear distances are constant between all 3 atoms, corresponding to equilibrium at the transition state. Etot = - 433.980.
For the case of H+HF, same rts was found, since this reaction is just the reverse reaction of the above case, and the same geometry is found at the transition state.
[[File:xmhFigure 16.png|250px|thumb|Figure 16. Contour Plot.]]
[[File:Figure 17xmh.png|250px|thumb|Figure 17. Internuclear Distancesvs Time Plot.]]

== Report the activation energy for both reactions. ==
In order to find the reactants’ energy for the F+H2 reaction, initial conditions were set as rAB = 1000 and rBC = 74.5. The value of rAB was chosen so that there is no interaction in the system since the F atom is at a very distant away from the H2 molecule, as reflected by Figure 20., where the only momentum is given by the oscillation between the bonded molecule. Etot = - 435.057.
Hence the activation energy = Etot(transition state) – Etot(reactants) = - 433.980 + 435.057 = 1.077.
[[File:xmhFigure 18.png|250px|thumb|Figure 18. Momentum vs Time Plot.]]
Same method applies to the H+FH system, the activation energy = 125.322.

== 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. ==

== Headline text ==

File:Figure 17xmh.png

2020-05-25T15:44:22Z

Mx3118:

File:XmhFigure 18.png

2020-05-25T15:37:57Z

Mx3118:

File:XmhFIgure 17.png

2020-05-25T15:37:15Z

Mx3118:

File:Figure 15(A)xmh.png

2020-05-25T15:35:01Z

Mx3118:

File:XmhFigure 16.png

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Mx3118:

File:Figure 15(A)mh.png

2020-05-25T15:33:00Z

Mx3118:

File:Figure 15(B)xmh.png

2020-05-25T15:29:41Z

Mx3118:

File:Figure 14(B)xmh.png

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Mx3118:

MRD:xmh01513932

2020-05-25T14:47:59Z

Mx3118:

== Transition State ==
On a potential energy surface diagram, the transition state is identified as the maximum on the minimum potential energy path between the reactants and products.

To explain the transition state mathematically, several derivatives have to be addressed first,

1. The first derivative of potential energy (V) with respect to either atomic separation (r1, r2) is zero, i.e. ∂V/∂r1 = 0 and ∂V/∂r2 = 0;

2. The second derivative D = ∂2V/∂r1∂r1 × ∂2V/∂r2∂r2 – ∂2V/∂r1∂r2 = 0;

3. If D > 0, ∂2V(r1)/∂r1∂r1 > 0, then the point with this particular (r1,r2) coordinates is a local minimum point; ∂2V(r1)/∂r1∂r1 < 0 for a local maximum point;

4. If D < 0, then this point is a saddle point, i.e. the transition state. Simply put, the saddle point is simultaneously a minimum and a maximum along two orthogonal directions (i.e. the two atomic separation axes in this case).
[[File:Figure 1.log|250px|thumb|Figure 1. Contour Plot.]]
[[File:xmhFigure 2.png|250px|thumb|Figure 2. Surface Plot.]]

== Report your best estimate of the transition state position (rts) and explain your reasoning illustrating it with a “Internuclear Distances vs Time” plot for a relevant trajectory. ==

For a symmetric system like H + H2, the internuclear distances of r1 = r2 is expected in the transition state. To test out the best input values for r1 and r2, there would be some expected features on various plots, as shown below,

1． In Figure 3., the kinetic energy of the system is constant at 0. This is explained by the fact that, at the transition state, the net force acting on the system F = dp/dt = ∂V/∂r1 = ∂V/∂r2 = 0 (as defined), the triatomic system is at a state of equilibrium with no change in motion. The same idea is conveyed in Figure 4., where the internuclear distances are expected to have a variation as small as possible, the atoms are “frozen” in space, moreover, rAB(r2) = rBC(r1).

2． In Figure 5., the transition state position (rts) is also checked by the fact that the input r1 and r2 values (denoted by the red cross) map onto the circle which gives the coordinates of the exact rts.
The final value of r1 = r2 = 90.7 pm is chosen to satisfy the above requirements.

[[File:xmhFigure 3.png|250px|thumb|Figure 3. Energy vs Time Plot.]]
[[File:xmhFigure 4.png|250px|thumb|Figure 4. Internuclear Distances vs Time Plot.]]
[[File:xmhFigure 5.png|250px|thumb|Figure 5. Contour Plot]]

== Comment on how the mep and the trajectory you just calculated differ. ==

Two paths were generated under the calculation types of MEP and Dynamics respectively, with initial conditions of r1 = rts+1=91.7 and r2 = 90.7 and p1 = p2 = 0 g.mol-1.pm.fs-1.

The dynamic graph shows a wavy line (shown in Figure 6.). After passing though rts (now r1 < r2), HAHB molecule is formed, detaching HC. This case takes into account of the intramolecular vibration of the new H2 molecule, since there is an oscillating trajectory at around a fixed rAB value with an increasing rBC value which indicates detaching of HC.

[[File:xmhFigure 6.png|250px|thumb|Figure 6. Contour Plot.]]
[[File:xmhFigure 7.png|250px|thumb|Figure 7. Energy vs Time Plot.]]
[[File:xmhFigure 8.png|250px|thumb|Figure 8. Momentum vs Time Plot]]
[[File:xmhFigure 8.png|250px|thumb|Figure 9. Internuclear Distances vs Time Plot]]

The mep (the minimum energy path) corresponds to a trajectory with infinitely slow motion, i.e. the system’s velocities are reset to zero in each time step, consequently no momentum or kinetic energy, as reflected in Figure 11 & 12. The reaction path way as a smooth curve (shown in Figure .) without any information of the intrinsic vibration within the H2 molecule.

[[File:xmhFigure 10.png|250px|thumb|thumb|Figure 10. Contour Plot.]]
[[File:xmhFigure 11.png|250px|thumb|Figure 11. Energy vs Time Plot.]]
[[File:xmhFigure 12.png|250px|thumb|Figure 12. Momentum vs Time Plot]]
[[File:xmhFigure 13.png|250px|thumb|Figure 13. Internuclear Distances vs Time Plot]]

If initial conditions are changed to r2 = rts+1=91.7 and r1 = 90.7 and p1 = p2 = 0 g.mol-1.pm.fs-1, same trends in both the Internuclear Distances vs Time graph and the Momenta vs Time graph are observed as for the previous conditions. Since the system is symmetric, hence the differences between these 2 sets of conditions are just attributed to the fact that whether HAHB or HBHC dissociates.

== 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" border="1"
|+ caption
! p1 !! p2 !! Etot !! Reactive? !! Description of the dynamics !! Illustration of the trajectory
|-
| -2.56 || -5.1 || -414.280 || Reactive || HA approaches HBHC molecule from a distance of rAB = 200 (starting from the bottom-right of the figure), with rBC being constant since HB and HC still remain bonded. After passing through rts, the new HAHB molecule is formed as shown by the constant rAB and increasing rBC as HC leaves(at the top left of the figure). || [[File:xmhA.png|250px]]
|-
| -3.1 || -4.1 || -420.077 || Unreactive || HA approaches HBHc (bottom-right), however it does not quite get to rts due to a reduced amount of kinetic energy compared to the first case, hence HA bounces off, there is no interaction with the hydrogen molecule. ||[[File:xmhB.png|250px]]
|-
| -3.1 || -5.1 || 413.977 || Reactive || Same as the first case except for the fact that p1 has a larger value, hence the system is more energetic to go over the activation barrier, and due to energy conservation, after the collision, the new molecule has a greater vibration. ||[[File:xmhC.png|250px]]
|-
| -5.1 || -10.1 || -357.277 || Unreactive || Barrier recrossing - the system is energetic enough to go over the transition state region and form the new HAHB, since rBC increases from its original bond length, indicating the leaving of HC, and the Etot is also greater than the first case (a reactive case). However, rBC drops down again to the original bond length and rAB increases as the system reverts back to HBHC. ||[[File:xmhD.png|250px]]
|-
| -5.1 || -10.6 || -349.477 || Reactive || The system HBHC converts to HAHB after reaching rts, but reverts given the excess momentum in p2 as rAB increases and rBC decreases, the system crosses the transition region again to form the final HAHB molecule as rBC continue increasing and rAB stays oscillating around a fixed value. ||[[File:xmhE.png|250px]]
|}

From the first sight, it seems reasonable to encourage a successful collision by adding more momentum into the system since this increases the kinetic energy of the atoms to overcome the activation barrier. However, as concluded from the table, the excess momentum and energy could give rise to greater vibration within the molecule and hence cause the bond to dissociate.

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

In the transition state theory, the average transmission rate/frequency is estimated based on the assumption that all trajectories with some kinetic energy greater than the activation energy will be reactive. From the empirical data of the last section, it was shown that if momentum is provided such that the vibration is so great that the bond dissociates again, i.e. barrier recrossing occurs, this reduces the rate of a particular conversion, e.g. from HBHC and HA to HAHB and HC. This would overestimate the transition state theory rate constant (and hence the rate).
The transition state theory also consider the reaction pathway through classical mechanic collision (for macroscopic system). However, wavefunction (for microscopic system) of the atoms should be considered. Quantum tunneling may take place, it is not necessary to jump over the activation barrier, hence less kinetic energy is required for a successful collision, rate is higher than the theory prediction.

== 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? ==

In GUI, it is set up that the atom A approaches and collide with the molecule HBHC.
In the F+H2 system, F is considered as atom A, and the 2 H atoms as atoms B and C. Figure 14(A) shows the entrance channel for the reactants F+H2, since rBC (the molecule’s bond length) is constant and rAB is big; Figure 14(B) shows the exit channel for the products (FH+H), since rAB is now constant and rBC is big. Comparing the V for the 2 channels, the reactants are at a higher V than the products, hence this is an exothermic reaction.

[[File:xmhFigure 14(A).png|250px|thumb|Figure 14(A). Surface Plot.]]
[[File:xmhFigure 14(B).png|250px|thumb|Figure 14(B). Surface Plot.]]

For the H+FH system, the same idea applies, from Figure 15(A). & (B)., the reactants are at a lower V than the products, hence it is an endothermic reaction.

[[File:xmhFigure 15(A).png|250px|thumb|Figure 15(A). Surface Plot.]]
[[File:xmhFigure 15(B).png|250px|thumb|Figure 15(B). Surface Plot.]]

This correctly reflects the result obtained from qualitative bond-strength analysis. F-H is a very strong bond (compared to other possible bonds in the system) due to the different electronegativities and hence ionic contribution to the nature of the bond. Hence breaking this bond requires much energy, and forming it releases much energy. In the F+H2 reaction, a pure covalent bond is broken to form the strong F-H bond, this is expected to be exothermic; in the H+FH system, the energy released from forming H2 does not compensate for the energy required to break F-H first, hence it is expected to be endothermic.

File:XmhFigure 15 (B).png

2020-05-25T14:41:08Z

Mx3118:

File:XmhFigure 15 (A).png

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Mx3118:

File:XmhFigure 14 (B).png

2020-05-25T14:40:37Z

Mx3118:

File:XmhFigure 14(A).png

2020-05-25T14:40:22Z

Mx3118:

MRD:xmh01513932

2020-05-25T14:28:11Z

Mx3118:

== Transition State ==
On a potential energy surface diagram, the transition state is identified as the maximum on the minimum potential energy path between the reactants and products.

To explain the transition state mathematically, several derivatives have to be addressed first,

1. The first derivative of potential energy (V) with respect to either atomic separation (r1, r2) is zero, i.e. ∂V/∂r1 = 0 and ∂V/∂r2 = 0;

2. The second derivative D = ∂2V/∂r1∂r1 × ∂2V/∂r2∂r2 – ∂2V/∂r1∂r2 = 0;

3. If D > 0, ∂2V(r1)/∂r1∂r1 > 0, then the point with this particular (r1,r2) coordinates is a local minimum point; ∂2V(r1)/∂r1∂r1 < 0 for a local maximum point;

4. If D < 0, then this point is a saddle point, i.e. the transition state. Simply put, the saddle point is simultaneously a minimum and a maximum along two orthogonal directions (i.e. the two atomic separation axes in this case).

[[File:Figure 1.log|300px|Figure 1. Contour Plot.]]
[[File:xmhFigure 2.png|300px|Figure 2. Surface Plot.]]

== Report your best estimate of the transition state position (rts) and explain your reasoning illustrating it with a “Internuclear Distances vs Time” plot for a relevant trajectory. ==

For a symmetric system like H + H2, the internuclear distances of r1 = r2 is expected in the transition state. To test out the best input values for r1 and r2, there would be some expected features on various plots, as shown below,

1． In Figure 3., the kinetic energy of the system is constant at 0. This is explained by the fact that, at the transition state, the net force acting on the system F = dp/dt = ∂V/∂r1 = ∂V/∂r2 = 0 (as defined), the triatomic system is at a state of equilibrium with no change in motion. The same idea is conveyed in Figure 4., where the internuclear distances are expected to have a variation as small as possible, the atoms are “frozen” in space, moreover, rAB(r2) = rBC(r1).

2． In Figure 5., the transition state position (rts) is also checked by the fact that the input r1 and r2 values (denoted by the red cross) map onto the circle which gives the coordinates of the exact rts.
The final value of r1 = r2 = 90.7 pm is chosen to satisfy the above requirements.

[[File:xmhFigure 3.png|250px|Figure 3. Energy vs Time Plot.]]
[[File:xmhFigure 4.png|250px|Figure 4. Internuclear Distances vs Time Plot.]]
[[File:xmhFigure 5.png|250px|Figure 5. Contour Plot]]

== Comment on how the mep and the trajectory you just calculated differ. ==

Two paths were generated under the calculation types of MEP and Dynamics respectively, with initial conditions of r1 = rts+1=91.7 and r2 = 90.7 and p1 = p2 = 0 g.mol-1.pm.fs-1.

The dynamic graph shows a wavy line (shown in Figure 6.). After passing though rts (now r1 < r2), HAHB molecule is formed, detaching HC. This case takes into account of the intramolecular vibration of the new H2 molecule, since there is an oscillating trajectory at around a fixed rAB value with an increasing rBC value which indicates detaching of HC.

[[File:xmhFigure 6.png|250px|Figure 6. Contour Plot.]]
[[File:xmhFigure 7.png|250px|Figure 7. Energy vs Time Plot.]]
[[File:xmhFigure 8.png|250px|Figure 8. Momentum vs Time Plot]]
[[File:xmhFigure 8.png|250px|Figure 9. Internuclear Distances vs Time Plot]]

The mep (the minimum energy path) corresponds to a trajectory with infinitely slow motion, i.e. the system’s velocities are reset to zero in each time step, consequently no momentum or kinetic energy, as reflected in Figure 11 & 12. The reaction path way as a smooth curve (shown in Figure .) without any information of the intrinsic vibration within the H2 molecule.

[[File:xmhFigure 10.png|250px|thumb|Figure 10. Contour Plot.]]

[[File:xmhFigure 11.png|250px|Figure 11. Energy vs Time Plot.]]

[[File:xmhFigure 12.png|250px|Figure 12. Momentum vs Time Plot]]

[[File:xmhFigure 13.png|250px|Figure 13. Internuclear Distances vs Time Plot]]

If initial conditions are changed to r2 = rts+1=91.7 and r1 = 90.7 and p1 = p2 = 0 g.mol-1.pm.fs-1, same trends in both the Internuclear Distances vs Time graph and the Momenta vs Time graph are observed as for the previous conditions. Since the system is symmetric, hence the differences between these 2 sets of conditions are just attributed to the fact that whether HAHB or HBHC dissociates.

== 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" border="1"
|+ caption
! p1 !! p2 !! Etot !! Reactive? !! Description of the dynamics !! Illustration of the trajectory
|-
| -2.56 || -5.1 || -414.280 || Reactive || HA approaches HBHC molecule from a distance of rAB = 200 (starting from the bottom-right of the figure), with rBC being constant since HB and HC still remain bonded. After passing through rts, the new HAHB molecule is formed as shown by the constant rAB and increasing rBC as HC leaves(at the top left of the figure). || [[File:xmhA.png|250px]]
|-
| -3.1 || -4.1 || -420.077 || Unreactive || HA approaches HBHc (bottom-right), however it does not quite get to rts due to a reduced amount of kinetic energy compared to the first case, hence HA bounces off, there is no interaction with the hydrogen molecule. ||[[File:xmhB.png|250px]]
|-
| -3.1 || -5.1 || 413.977 || Reactive || Same as the first case except for the fact that p1 has a larger value, hence the system is more energetic to go over the activation barrier, and due to energy conservation, after the collision, the new molecule has a greater vibration. ||[[File:xmhC.png|250px]]
|-
| -5.1 || -10.1 || -357.277 || Unreactive || Barrier recrossing - the system is energetic enough to go over the transition state region and form the new HAHB, since rBC increases from its original bond length, indicating the leaving of HC, and the Etot is also greater than the first case (a reactive case). However, rBC drops down again to the original bond length and rAB increases as the system reverts back to HBHC. ||[[File:xmhD.png|250px]]
|-
| -5.1 || -10.6 || -349.477 || Reactive || The system HBHC converts to HAHB after reaching rts, but reverts given the excess momentum in p2 as rAB increases and rBC decreases, the system crosses the transition region again to form the final HAHB molecule as rBC continue increasing and rAB stays oscillating around a fixed value. ||[[File:xmhE.png|250px]]
|}

From the first sight, it seems reasonable to encourage a successful collision by adding more momentum into the system since this increases the kinetic energy of the atoms to overcome the activation barrier. However, as concluded from the table, the excess momentum and energy could give rise to greater vibration within the molecule and hence cause the bond to dissociate.

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

In the transition state theory, the average transmission rate/frequency is estimated based on the assumption that all trajectories with some kinetic energy greater than the activation energy will be reactive. From the empirical data of the last section, it was shown that if momentum is provided such that the vibration is so great that the bond dissociates again, i.e. barrier recrossing occurs, this reduces the rate of a particular conversion, e.g. from HBHC and HA to HAHB and HC. This would overestimate the transition state theory rate constant (and hence the rate).
The transition state theory also consider the reaction pathway through classical mechanic collision (for macroscopic system). However, wavefunction (for microscopic system) of the atoms should be considered. Quantum tunneling may take place, it is not necessary to jump over the activation barrier, hence less kinetic energy is required for a successful collision, rate is higher than the theory prediction.

File:XmhE.png

2020-05-25T14:26:37Z

Mx3118:

File:XmhD.png

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File:XmhC.png

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File:XmhA.png

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File:XmhFigure 13.png

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File:XmhFigure 11.png

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File:XmhFigure 9.png

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File:XmhFigure 8.png

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File:XmhFigure 5.png

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Mx3118:

File:XmhFigure 4.png

2020-05-25T13:52:30Z

Mx3118:

File:XmhFigure 3.png

2020-05-25T13:50:02Z

Mx3118:

File:XmhFigure 2.png

2020-05-25T13:43:10Z

Mx3118:

File:Figure 1.log

2020-05-25T13:35:44Z

Mx3118: Mx3118 uploaded a new version of File:Figure 1.log

MRD:xmh01513932

2020-05-25T13:31:03Z

Mx3118:

File:Figure 1.log

2020-05-25T13:19:19Z

Mx3118:

MRD:xmh01513932

2020-05-25T12:40:22Z

Mx3118:

MRD:xmh01513932

2020-05-25T12:38:50Z

Mx3118: Created page with " == Transition State == On a potential energy surface diagram, the transition state is identified as the maximum on the minimum potential energy path between the reactants and..."

Rep:Mod:mx3118

2019-02-22T17:23:26Z

Mx3118: /* Key structural infomation */

==NH<sub>3</sub>==

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XUMENGHAN NH3 OPTF POP.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>
[[File:XUMENGHAN NH3 OPTF POP.LOG| text to display]]

===Summary===

==== Calculation method ====

RB3LYP

==== Basis set ====

6-31G(d,p)

==== E(RB3LYP) in a.u. ====

-56.55777

==== RMS gradient norm in a.u. ====

0.00000485

==== Point group ====

C<sub>3v</sub>

==== Key structural and charge information ====

N-H bond length (in Ångstrom): 1.02 (accurate to ≈ 0.01 Ångstrom)

H-N-H bond angle (in Degree): 106 (accurate to ≈ 1 Degree)

Charge on N atom: -1.125

Charge on H atoms: 0.375

Note: The charges on N atom and H atom are shown as expected. The N atom should have a relatively more negative charge due to its higher electronegativity compared to H atom, H atom should have a relatively more positive charge.

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000072 0.001800 YES
RMS Displacement 0.000035 0.001200 YES
</pre>

===Screenshot of the display vibrations===

[[File:Xumenghan nh3 display vibrations2.PNG]]

===Vibration data===

<pre>
1 2 3
A1 E E
Frequencies -- 1089.5366 1693.9474 1693.9474
IR Inten -- 145.3814 13.5533 13.5533

4 5 6
A1 E E
Frequencies -- 3461.2932 3589.8170 3589.8170
IR Inten -- 1.0608 0.2711 0.2711
</pre>

===Answers to the questions about vibrations and charges===

1. From the 3N-6 rule, there are (3N-6=3*4-6=6) modes.

2. There are two sets of denegerate modes with wavenumbers (in cm<sup>-1</sup>): 1693.95 and 3589.82.

3. Bending modes have wavenumbers (in cm<sup>-1</sup>): 1089.54, 1693.95, 1693.95; stretching modes have wavenumbers (in cm<sup>-1</sup>): 3461.29, 3589.82, 3589.82.

4. The stretching mode with wavenumber (in cm<sup>-1</sup>) 3461.29 is highly symmetric.

5. The bending mode with wavenumber (in cm<sup>-1</sup>) 1089.54 is known as the "umbrella" mode.

6. Two bands are expected to show in an experimental spectrum of gaseous ammonia. Since the IR spectrum mainly records the stretching frequencies, and there are two non-degenerate values for stretching frequency.

==N<sub>2</sub>==

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XUMENGHAN N2 OPTF POP.LOG</uploadedFileContents>
<script>frame 1.18</script>
</jmolApplet></jmol>
[[File:XUMENGHAN N2 OPTF POP.LOG| text to display]]

===Summary===

==== Calculation method ====

RB3LYP

==== Basis set ====

6-31G(d,p)

==== E(RB3LYP) in a.u. ====

-109.52413

==== RMS gradient norm in a.u. ====

0.00013245

==== Point group ====

Dinfh

==== Key structural and charge information ====

N-N bond length (in Ångstrom): 1.11 (accurate to ≈ 0.01 Ångstrom)

Charge on both N atoms: 0.000

Note: The charges on both N atoms are shown as expected. They both should have a neutral charge, since the electron density is shared between same atoms equally.

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000229 0.000450 YES
RMS Force 0.000229 0.000300 YES
Maximum Displacement 0.000072 0.001800 YES
RMS Displacement 0.000101 0.001200 YES
</pre>

===Screenshot of the display vibrations===

[[File:Xumenghan n2 display vibrations2.PNG]]

===Vibration data===
<pre>
1
SGG
Frequencies -- 2457.9991
IR Inten -- 0.0000
</pre>

===Mono-metallic TM complex that coordinates N<sub>2</sub>===

====Identifier and link for the structure====

''RANLUO''

"https://www.ccdc.cam.ac.uk/structures/search?pid=csd:RANLUO"

====N-N bond length====

The optimised N-N bond length (in Ångstrom): 1.1054

The N-N bond length in crystal structure (in Ångstrom): 1.1122

The bond lengths are different. The N<sub>2</sub> in the crystal is connected directly onto an electropositve Ni atom, electron density and hence repulsion around the two N atoms increase. This could potentially cause the lengthing of the N-N bond.

==H<sub>2</sub>==

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XUMENGHAN H2 OPTF POP.LOG</uploadedFileContents>
<script>frame 1.12</script>
</jmolApplet></jmol>
[[File:XUMENGHAN H2 OPTF POP.LOG| text to display]]

===Summary===

==== Calculation method ====

RB3LYP

==== Basis set ====

6-31G(d,p)

==== E(RB3LYP) in a.u. ====

-1.17854

==== RMS gradient norm in a.u. ====

0.00040858

==== Point group ====

Dinfh

==== Key structural and charge information ====

H-H bond length (in Ångstrom): 0.74 (accurate to ≈ 0.01 Ångstrom)

Charge on both H atoms: 0.000

Note: The charges on both H atoms are shown as expected. They both should have a neutral charge, since the electron density is shared between same atoms equally.

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000000 0.001800 YES
RMS Displacement 0.000001 0.001200 YES
</pre>

===Screenshot of the display vibrations===

[[File:Xumenghan h2 display vibrations2.PNG]]

===Vibration data===
<pre>

1
SGG
Frequencies -- 4465.6824
IR Inten -- 0.0000

</pre>

==The Haber-Bosch process==

===Equation for this process===

N<sub>2</sub> + 3H<sub>2</sub> -> 2NH<sub>3</sub>

===Energy of reactants and product in a.u.===

E(NH<sub>3</sub>)= -56.5577687

2*E(NH<sub>3</sub>)= 2*(-56.55776873) = -113.1155375

E(N<sub>2</sub>)= -109.5241287

E(H<sub>2</sub>)= -1.1785387

3*E(H<sub>2</sub>)= 3*(-1.17853870) = 3*( -1.17853870) = -3.5356161

===Energy for this reaction===

ΔE=2*E(NH<sub>3</sub>)-[E(N<sub>2</sub>)+3*E(H<sub>2</sub>)]= -113.1155375 - (-109.52412866--3.5356161) = -0.0557927 (a.u.) = -0.0557927*2625.5 (kJ/mol) = -146.5(kJ/mol)

Note: hence from the energy of conversion, it is shown that this is a exothermic reaction, indicating that the ammonia product is more stable than the gasoues reactants.

==My chosen molecule Cl<sub>2</sub>==

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XUMENGHAN CL2 OPTF POP.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>
[[File:XUMENGHAN CL2 OPTF POP.LOG| text to display]]

===Summary===

==== Calculation method ====

RB3LYP

==== Basis set ====

6-31G(d,p)

==== E(RB3LYP) in a.u. ====

-920.27125

==== RMS gradient norm in a.u. ====

0.17962

==== Point group ====

Dinfh

==== Key structural and charge information ====

Cl-Cl bond length (in Ångstrom): 2.04 (accurate to ≈ 0.01 Ångstrom)

Charge on both Cl atoms: 0.000

Note: The charges on both Cl atoms are shown as expected. They both should have a neutral charge, since the electron density is shared between same atoms equally.

===Item table===
<pre>

Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000015 0.000300 YES
Maximum Displacement 0.000043 0.001800 YES
RMS Displacement 0.000060 0.001200 YES

</pre>

===Screenshot of the display vibrations===

[[File:Xumenghan cl2 display vibrations2.PNG]]

===Vibration data===
<pre>
1
SGG
Frequencies -- 520.4311
IR Inten -- 0.0000

</pre>

===Molecular orbitals in interest===

====First MO====

[[File:1s sigma MO.PNG]]

This is a bonding MO filled with two electrons, since it is formed by in-phase combination of the 1s atomic orbitals of the two Cl atoms. This is also a sigma MO, since the two atomic orbitals overlap end-on. This MO has a comparatively very low energy at -101.60298, since its composite atomic orbitals are very close to the nuclues and hence feel a strong interaction and are buried deep down in energy. This MO is neither in the HOMO or the LUMO region. The electrons in this orbital will not be involved in bonding.

====Second MO====

[[File:2p sigma MO.PNG]]

This is a bonding MO filled with two electrons, since it is formed by in-phase combination of the 2p atomic orbitals of the two Cl atoms. This is a sigma MO, since the overlap of two AO is end-on. This MO has a higher energy, since the 2p orbitals are further away from the nucleus and at higher energy. This MO is neither in the HOMO or the LUMO region. The electrons in this orbital will not be involved in bonding.

====Third MO====

[[File:2p pi MO.PNG]]

This is a bonding MO filled with two electrons, since it is formed by in-phase combination of the 2p atomic orbitals of the two Cl atoms. This is a pi MO, since the overlap of two AO is now parallel. This MO has a further increased energy, since the parallel overlap is less effective than the end-on overlap. This MO is neither in the HOMO or the LUMO region. The electrons in this orbital will not be involved in bonding.

====Fourth MO====

[[File:HOMO.PNG]]

This is an pi* anti-bonding orbital filled with two electrons, since orbital combination of two 3p atomic orbitals is out-of-phase. This is the HOMO, hence the electrons in this MO have the highest energy. Hence this MO provide the most-readily-donated electrons in reaction.

====Fifth MO====

[[File:LUMO.PNG]]

This is an sigma* anti-bonding orbital with no electrons, since orbital combination of two 3s atomic orbitals is out-of-phase. This is the LUMO. This is the ideal (lowest-energy) empty MO that can accept further electrons in reaction.

==Independence -- study on CO<sub>2</sub>==

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XUMENGHAN O2 OPTF POP.LOG</uploadedFileContents>
<script>frame 1.10</script>
</jmolApplet></jmol>
[[File:XUMENGHAN O2 OPTF POP.LOG| text to display]]

===Summary===

==== Calculation method ====

RB3LYP

==== Basis set ====

6-31G(d,p)

==== E(RB3LYP) in a.u. ====

-150.25742

==== RMS gradient norm in a.u. ====

0.00001829

==== Point group ====

Dinfh

==== Key structural and charge information ====

O-O bond length (in Ångstrom): 1.22 (accurate to ≈ 0.01 Ångstrom)

Charge on both O atoms: 0.000

Note: The charges on both O atoms are shown as expected. They both should have a neutral charge, since the electron density is shared between same atoms equally.

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000032 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.000019 0.001800 YES
RMS Displacement 0.000027 0.001200 YES
</pre>

===Screenshot of the display vibrations===

[[File:Xumenghan o2 display vibrations2.PNG]]

===Vibration data===
<pre>
1
SGG
Frequencies -- 1643.1143
Red. masses -- 15.9949
Frc consts -- 25.4430
IR Inten -- 0.0000
</pre>

Rep:Mod:mx3118

2019-02-22T17:22:57Z

Mx3118: /* Key structural infomation */

==NH<sub>3</sub>==

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XUMENGHAN NH3 OPTF POP.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>
[[File:XUMENGHAN NH3 OPTF POP.LOG| text to display]]

===Summary===

==== Calculation method ====

RB3LYP

==== Basis set ====

6-31G(d,p)

==== E(RB3LYP) in a.u. ====

-56.55777

==== RMS gradient norm in a.u. ====

0.00000485

==== Point group ====

C<sub>3v</sub>

==== Key structural and charge information ====

N-H bond length (in Ångstrom): 1.02 (accurate to ≈ 0.01 Ångstrom)

H-N-H bond angle (in Degree): 106 (accurate to ≈ 1 Degree)

Charge on N atom: -1.125

Charge on H atoms: 0.375

Note: The charges on N atom and H atom are shown as expected. The N atom should have a relatively more negative charge due to its higher electronegativity compared to H atom, H atom should have a relatively more positive charge.

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000072 0.001800 YES
RMS Displacement 0.000035 0.001200 YES
</pre>

===Screenshot of the display vibrations===

[[File:Xumenghan nh3 display vibrations2.PNG]]

===Vibration data===

<pre>
1 2 3
A1 E E
Frequencies -- 1089.5366 1693.9474 1693.9474
IR Inten -- 145.3814 13.5533 13.5533

4 5 6
A1 E E
Frequencies -- 3461.2932 3589.8170 3589.8170
IR Inten -- 1.0608 0.2711 0.2711
</pre>

===Answers to the questions about vibrations and charges===

1. From the 3N-6 rule, there are (3N-6=3*4-6=6) modes.

2. There are two sets of denegerate modes with wavenumbers (in cm<sup>-1</sup>): 1693.95 and 3589.82.

3. Bending modes have wavenumbers (in cm<sup>-1</sup>): 1089.54, 1693.95, 1693.95; stretching modes have wavenumbers (in cm<sup>-1</sup>): 3461.29, 3589.82, 3589.82.

4. The stretching mode with wavenumber (in cm<sup>-1</sup>) 3461.29 is highly symmetric.

5. The bending mode with wavenumber (in cm<sup>-1</sup>) 1089.54 is known as the "umbrella" mode.

6. Two bands are expected to show in an experimental spectrum of gaseous ammonia. Since the IR spectrum mainly records the stretching frequencies, and there are two non-degenerate values for stretching frequency.

==N<sub>2</sub>==

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XUMENGHAN N2 OPTF POP.LOG</uploadedFileContents>
<script>frame 1.18</script>
</jmolApplet></jmol>
[[File:XUMENGHAN N2 OPTF POP.LOG| text to display]]

===Summary===

==== Calculation method ====

RB3LYP

==== Basis set ====

6-31G(d,p)

==== E(RB3LYP) in a.u. ====

-109.52413

==== RMS gradient norm in a.u. ====

0.00013245

==== Point group ====

Dinfh

==== Key structural and charge information ====

N-N bond length (in Ångstrom): 1.11 (accurate to ≈ 0.01 Ångstrom)

Charge on both N atoms: 0.000

Note: The charges on both N atoms are shown as expected. They both should have a neutral charge, since the electron density is shared between same atoms equally.

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000229 0.000450 YES
RMS Force 0.000229 0.000300 YES
Maximum Displacement 0.000072 0.001800 YES
RMS Displacement 0.000101 0.001200 YES
</pre>

===Screenshot of the display vibrations===

[[File:Xumenghan n2 display vibrations2.PNG]]

===Vibration data===
<pre>
1
SGG
Frequencies -- 2457.9991
IR Inten -- 0.0000
</pre>

===Mono-metallic TM complex that coordinates N<sub>2</sub>===

====Identifier and link for the structure====

''RANLUO''

"https://www.ccdc.cam.ac.uk/structures/search?pid=csd:RANLUO"

====N-N bond length====

The optimised N-N bond length (in Ångstrom): 1.1054

The N-N bond length in crystal structure (in Ångstrom): 1.1122

The bond lengths are different. The N<sub>2</sub> in the crystal is connected directly onto an electropositve Ni atom, electron density and hence repulsion around the two N atoms increase. This could potentially cause the lengthing of the N-N bond.

==H<sub>2</sub>==

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XUMENGHAN H2 OPTF POP.LOG</uploadedFileContents>
<script>frame 1.12</script>
</jmolApplet></jmol>
[[File:XUMENGHAN H2 OPTF POP.LOG| text to display]]

===Summary===

==== Calculation method ====

RB3LYP

==== Basis set ====

6-31G(d,p)

==== E(RB3LYP) in a.u. ====

-1.17854

==== RMS gradient norm in a.u. ====

0.00040858

==== Point group ====

Dinfh

==== Key structural and charge information ====

H-H bond length (in Ångstrom): 0.74 (accurate to ≈ 0.01 Ångstrom)

Charge on both H atoms: 0.000

Note: The charges on both H atoms are shown as expected. They both should have a neutral charge, since the electron density is shared between same atoms equally.

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000000 0.001800 YES
RMS Displacement 0.000001 0.001200 YES
</pre>

===Screenshot of the display vibrations===

[[File:Xumenghan h2 display vibrations2.PNG]]

===Vibration data===
<pre>

1
SGG
Frequencies -- 4465.6824
IR Inten -- 0.0000

</pre>

==The Haber-Bosch process==

===Equation for this process===

N<sub>2</sub> + 3H<sub>2</sub> -> 2NH<sub>3</sub>

===Energy of reactants and product in a.u.===

E(NH<sub>3</sub>)= -56.5577687

2*E(NH<sub>3</sub>)= 2*(-56.55776873) = -113.1155375

E(N<sub>2</sub>)= -109.5241287

E(H<sub>2</sub>)= -1.1785387

3*E(H<sub>2</sub>)= 3*(-1.17853870) = 3*( -1.17853870) = -3.5356161

===Energy for this reaction===

ΔE=2*E(NH<sub>3</sub>)-[E(N<sub>2</sub>)+3*E(H<sub>2</sub>)]= -113.1155375 - (-109.52412866--3.5356161) = -0.0557927 (a.u.) = -0.0557927*2625.5 (kJ/mol) = -146.5(kJ/mol)

Note: hence from the energy of conversion, it is shown that this is a exothermic reaction, indicating that the ammonia product is more stable than the gasoues reactants.

==My chosen molecule Cl<sub>2</sub>==

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XUMENGHAN CL2 OPTF POP.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>
[[File:XUMENGHAN CL2 OPTF POP.LOG| text to display]]

===Summary===

==== Calculation method ====

RB3LYP

==== Basis set ====

6-31G(d,p)

==== E(RB3LYP) in a.u. ====

-920.27125

==== RMS gradient norm in a.u. ====

0.17962

==== Point group ====

Dinfh

==== Key structural and charge information ====

Cl-Cl bond length (in Ångstrom): 2.04 (accurate to ≈ 0.01 Ångstrom)

Charge on both Cl atoms: 0.000

Note: The charges on both Cl atoms are shown as expected. They both should have a neutral charge, since the electron density is shared between same atoms equally.

===Item table===
<pre>

Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000015 0.000300 YES
Maximum Displacement 0.000043 0.001800 YES
RMS Displacement 0.000060 0.001200 YES

</pre>

===Screenshot of the display vibrations===

[[File:Xumenghan cl2 display vibrations2.PNG]]

===Vibration data===
<pre>
1
SGG
Frequencies -- 520.4311
IR Inten -- 0.0000

</pre>

===Molecular orbitals in interest===

====First MO====

[[File:1s sigma MO.PNG]]

This is a bonding MO filled with two electrons, since it is formed by in-phase combination of the 1s atomic orbitals of the two Cl atoms. This is also a sigma MO, since the two atomic orbitals overlap end-on. This MO has a comparatively very low energy at -101.60298, since its composite atomic orbitals are very close to the nuclues and hence feel a strong interaction and are buried deep down in energy. This MO is neither in the HOMO or the LUMO region. The electrons in this orbital will not be involved in bonding.

====Second MO====

[[File:2p sigma MO.PNG]]

This is a bonding MO filled with two electrons, since it is formed by in-phase combination of the 2p atomic orbitals of the two Cl atoms. This is a sigma MO, since the overlap of two AO is end-on. This MO has a higher energy, since the 2p orbitals are further away from the nucleus and at higher energy. This MO is neither in the HOMO or the LUMO region. The electrons in this orbital will not be involved in bonding.

====Third MO====

[[File:2p pi MO.PNG]]

This is a bonding MO filled with two electrons, since it is formed by in-phase combination of the 2p atomic orbitals of the two Cl atoms. This is a pi MO, since the overlap of two AO is now parallel. This MO has a further increased energy, since the parallel overlap is less effective than the end-on overlap. This MO is neither in the HOMO or the LUMO region. The electrons in this orbital will not be involved in bonding.

====Fourth MO====

[[File:HOMO.PNG]]

This is an pi* anti-bonding orbital filled with two electrons, since orbital combination of two 3p atomic orbitals is out-of-phase. This is the HOMO, hence the electrons in this MO have the highest energy. Hence this MO provide the most-readily-donated electrons in reaction.

====Fifth MO====

[[File:LUMO.PNG]]

This is an sigma* anti-bonding orbital with no electrons, since orbital combination of two 3s atomic orbitals is out-of-phase. This is the LUMO. This is the ideal (lowest-energy) empty MO that can accept further electrons in reaction.

==Independence -- study on CO<sub>2</sub>==

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XUMENGHAN O2 OPTF POP.LOG</uploadedFileContents>
<script>frame 1.10</script>
</jmolApplet></jmol>
[[File:XUMENGHAN O2 OPTF POP.LOG| text to display]]

===Summary===

==== Calculation method ====

RB3LYP

==== Basis set ====

6-31G(d,p)

==== E(RB3LYP) in a.u. ====

-150.25742

==== RMS gradient norm in a.u. ====

0.00001829

==== Point group ====

Dinfh

==== Key structural infomation ====

O-O bond length (in Ångstrom): 1.22 (accurate to ≈ 0.01 Ångstrom)

Charge on both O atoms: 0.000

Note: The charges on both O atoms are shown as expected. They both should have a neutral charge, since the electron density is shared between same atoms equally.

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000032 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.000019 0.001800 YES
RMS Displacement 0.000027 0.001200 YES
</pre>

===Screenshot of the display vibrations===

[[File:Xumenghan o2 display vibrations2.PNG]]

===Vibration data===
<pre>
1
SGG
Frequencies -- 1643.1143
Red. masses -- 15.9949
Frc consts -- 25.4430
IR Inten -- 0.0000
</pre>

Rep:Mod:mx3118

2019-02-22T17:22:19Z

Mx3118: /* Basic information */

==NH<sub>3</sub>==

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XUMENGHAN NH3 OPTF POP.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>
[[File:XUMENGHAN NH3 OPTF POP.LOG| text to display]]

===Summary===

==== Calculation method ====

RB3LYP

==== Basis set ====

6-31G(d,p)

==== E(RB3LYP) in a.u. ====

-56.55777

==== RMS gradient norm in a.u. ====

0.00000485

==== Point group ====

C<sub>3v</sub>

==== Key structural and charge information ====

N-H bond length (in Ångstrom): 1.02 (accurate to ≈ 0.01 Ångstrom)

H-N-H bond angle (in Degree): 106 (accurate to ≈ 1 Degree)

Charge on N atom: -1.125

Charge on H atoms: 0.375

Note: The charges on N atom and H atom are shown as expected. The N atom should have a relatively more negative charge due to its higher electronegativity compared to H atom, H atom should have a relatively more positive charge.

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000072 0.001800 YES
RMS Displacement 0.000035 0.001200 YES
</pre>

===Screenshot of the display vibrations===

[[File:Xumenghan nh3 display vibrations2.PNG]]

===Vibration data===

<pre>
1 2 3
A1 E E
Frequencies -- 1089.5366 1693.9474 1693.9474
IR Inten -- 145.3814 13.5533 13.5533

4 5 6
A1 E E
Frequencies -- 3461.2932 3589.8170 3589.8170
IR Inten -- 1.0608 0.2711 0.2711
</pre>

===Answers to the questions about vibrations and charges===

1. From the 3N-6 rule, there are (3N-6=3*4-6=6) modes.

2. There are two sets of denegerate modes with wavenumbers (in cm<sup>-1</sup>): 1693.95 and 3589.82.

3. Bending modes have wavenumbers (in cm<sup>-1</sup>): 1089.54, 1693.95, 1693.95; stretching modes have wavenumbers (in cm<sup>-1</sup>): 3461.29, 3589.82, 3589.82.

4. The stretching mode with wavenumber (in cm<sup>-1</sup>) 3461.29 is highly symmetric.

5. The bending mode with wavenumber (in cm<sup>-1</sup>) 1089.54 is known as the "umbrella" mode.

6. Two bands are expected to show in an experimental spectrum of gaseous ammonia. Since the IR spectrum mainly records the stretching frequencies, and there are two non-degenerate values for stretching frequency.

==N<sub>2</sub>==

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XUMENGHAN N2 OPTF POP.LOG</uploadedFileContents>
<script>frame 1.18</script>
</jmolApplet></jmol>
[[File:XUMENGHAN N2 OPTF POP.LOG| text to display]]

===Summary===

==== Calculation method ====

RB3LYP

==== Basis set ====

6-31G(d,p)

==== E(RB3LYP) in a.u. ====

-109.52413

==== RMS gradient norm in a.u. ====

0.00013245

==== Point group ====

Dinfh

==== Key structural and charge information ====

N-N bond length (in Ångstrom): 1.11 (accurate to ≈ 0.01 Ångstrom)

Charge on both N atoms: 0.000

Note: The charges on both N atoms are shown as expected. They both should have a neutral charge, since the electron density is shared between same atoms equally.

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000229 0.000450 YES
RMS Force 0.000229 0.000300 YES
Maximum Displacement 0.000072 0.001800 YES
RMS Displacement 0.000101 0.001200 YES
</pre>

===Screenshot of the display vibrations===

[[File:Xumenghan n2 display vibrations2.PNG]]

===Vibration data===
<pre>
1
SGG
Frequencies -- 2457.9991
IR Inten -- 0.0000
</pre>

===Mono-metallic TM complex that coordinates N<sub>2</sub>===

====Identifier and link for the structure====

''RANLUO''

"https://www.ccdc.cam.ac.uk/structures/search?pid=csd:RANLUO"

====N-N bond length====

The optimised N-N bond length (in Ångstrom): 1.1054

The N-N bond length in crystal structure (in Ångstrom): 1.1122

The bond lengths are different. The N<sub>2</sub> in the crystal is connected directly onto an electropositve Ni atom, electron density and hence repulsion around the two N atoms increase. This could potentially cause the lengthing of the N-N bond.

==H<sub>2</sub>==

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XUMENGHAN H2 OPTF POP.LOG</uploadedFileContents>
<script>frame 1.12</script>
</jmolApplet></jmol>
[[File:XUMENGHAN H2 OPTF POP.LOG| text to display]]

===Summary===

==== Calculation method ====

RB3LYP

==== Basis set ====

6-31G(d,p)

==== E(RB3LYP) in a.u. ====

-1.17854

==== RMS gradient norm in a.u. ====

0.00040858

==== Point group ====

Dinfh

==== Key structural and charge information ====

H-H bond length (in Ångstrom): 0.74 (accurate to ≈ 0.01 Ångstrom)

Charge on both H atoms: 0.000

Note: The charges on both H atoms are shown as expected. They both should have a neutral charge, since the electron density is shared between same atoms equally.

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000000 0.001800 YES
RMS Displacement 0.000001 0.001200 YES
</pre>

===Screenshot of the display vibrations===

[[File:Xumenghan h2 display vibrations2.PNG]]

===Vibration data===
<pre>

1
SGG
Frequencies -- 4465.6824
IR Inten -- 0.0000

</pre>

==The Haber-Bosch process==

===Equation for this process===

N<sub>2</sub> + 3H<sub>2</sub> -> 2NH<sub>3</sub>

===Energy of reactants and product in a.u.===

E(NH<sub>3</sub>)= -56.5577687

2*E(NH<sub>3</sub>)= 2*(-56.55776873) = -113.1155375

E(N<sub>2</sub>)= -109.5241287

E(H<sub>2</sub>)= -1.1785387

3*E(H<sub>2</sub>)= 3*(-1.17853870) = 3*( -1.17853870) = -3.5356161

===Energy for this reaction===

ΔE=2*E(NH<sub>3</sub>)-[E(N<sub>2</sub>)+3*E(H<sub>2</sub>)]= -113.1155375 - (-109.52412866--3.5356161) = -0.0557927 (a.u.) = -0.0557927*2625.5 (kJ/mol) = -146.5(kJ/mol)

Note: hence from the energy of conversion, it is shown that this is a exothermic reaction, indicating that the ammonia product is more stable than the gasoues reactants.

==My chosen molecule Cl<sub>2</sub>==

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XUMENGHAN CL2 OPTF POP.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>
[[File:XUMENGHAN CL2 OPTF POP.LOG| text to display]]

===Summary===

==== Calculation method ====

RB3LYP

==== Basis set ====

6-31G(d,p)

==== E(RB3LYP) in a.u. ====

-920.27125

==== RMS gradient norm in a.u. ====

0.17962

==== Point group ====

Dinfh

==== Key structural infomation ====

Cl-Cl bond length (in Ångstrom): 2.04 (accurate to ≈ 0.01 Ångstrom)

Charge on both Cl atoms: 0.000

Note: The charges on both Cl atoms are shown as expected. They both should have a neutral charge, since the electron density is shared between same atoms equally.

===Item table===
<pre>

Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000015 0.000300 YES
Maximum Displacement 0.000043 0.001800 YES
RMS Displacement 0.000060 0.001200 YES

</pre>

===Screenshot of the display vibrations===

[[File:Xumenghan cl2 display vibrations2.PNG]]

===Vibration data===
<pre>
1
SGG
Frequencies -- 520.4311
IR Inten -- 0.0000

</pre>

===Molecular orbitals in interest===

====First MO====

[[File:1s sigma MO.PNG]]

This is a bonding MO filled with two electrons, since it is formed by in-phase combination of the 1s atomic orbitals of the two Cl atoms. This is also a sigma MO, since the two atomic orbitals overlap end-on. This MO has a comparatively very low energy at -101.60298, since its composite atomic orbitals are very close to the nuclues and hence feel a strong interaction and are buried deep down in energy. This MO is neither in the HOMO or the LUMO region. The electrons in this orbital will not be involved in bonding.

====Second MO====

[[File:2p sigma MO.PNG]]

This is a bonding MO filled with two electrons, since it is formed by in-phase combination of the 2p atomic orbitals of the two Cl atoms. This is a sigma MO, since the overlap of two AO is end-on. This MO has a higher energy, since the 2p orbitals are further away from the nucleus and at higher energy. This MO is neither in the HOMO or the LUMO region. The electrons in this orbital will not be involved in bonding.

====Third MO====

[[File:2p pi MO.PNG]]

This is a bonding MO filled with two electrons, since it is formed by in-phase combination of the 2p atomic orbitals of the two Cl atoms. This is a pi MO, since the overlap of two AO is now parallel. This MO has a further increased energy, since the parallel overlap is less effective than the end-on overlap. This MO is neither in the HOMO or the LUMO region. The electrons in this orbital will not be involved in bonding.

====Fourth MO====

[[File:HOMO.PNG]]

This is an pi* anti-bonding orbital filled with two electrons, since orbital combination of two 3p atomic orbitals is out-of-phase. This is the HOMO, hence the electrons in this MO have the highest energy. Hence this MO provide the most-readily-donated electrons in reaction.

====Fifth MO====

[[File:LUMO.PNG]]

This is an sigma* anti-bonding orbital with no electrons, since orbital combination of two 3s atomic orbitals is out-of-phase. This is the LUMO. This is the ideal (lowest-energy) empty MO that can accept further electrons in reaction.

==Independence -- study on CO<sub>2</sub>==

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XUMENGHAN O2 OPTF POP.LOG</uploadedFileContents>
<script>frame 1.10</script>
</jmolApplet></jmol>
[[File:XUMENGHAN O2 OPTF POP.LOG| text to display]]

===Summary===

==== Calculation method ====

RB3LYP

==== Basis set ====

6-31G(d,p)

==== E(RB3LYP) in a.u. ====

-150.25742

==== RMS gradient norm in a.u. ====

0.00001829

==== Point group ====

Dinfh

==== Key structural infomation ====

O-O bond length (in Ångstrom): 1.22 (accurate to ≈ 0.01 Ångstrom)

Charge on both O atoms: 0.000

Note: The charges on both O atoms are shown as expected. They both should have a neutral charge, since the electron density is shared between same atoms equally.

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000032 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.000019 0.001800 YES
RMS Displacement 0.000027 0.001200 YES
</pre>

===Screenshot of the display vibrations===

[[File:Xumenghan o2 display vibrations2.PNG]]

===Vibration data===
<pre>
1
SGG
Frequencies -- 1643.1143
Red. masses -- 15.9949
Frc consts -- 25.4430
IR Inten -- 0.0000
</pre>

Rep:Mod:mx3118

2019-02-22T17:21:46Z

Mx3118: /* Basic information */

==NH<sub>3</sub>==

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XUMENGHAN NH3 OPTF POP.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>
[[File:XUMENGHAN NH3 OPTF POP.LOG| text to display]]

===Summary===

==== Calculation method ====

RB3LYP

==== Basis set ====

6-31G(d,p)

==== E(RB3LYP) in a.u. ====

-56.55777

==== RMS gradient norm in a.u. ====

0.00000485

==== Point group ====

C<sub>3v</sub>

==== Key structural and charge information ====

N-H bond length (in Ångstrom): 1.02 (accurate to ≈ 0.01 Ångstrom)

H-N-H bond angle (in Degree): 106 (accurate to ≈ 1 Degree)

Charge on N atom: -1.125

Charge on H atoms: 0.375

Note: The charges on N atom and H atom are shown as expected. The N atom should have a relatively more negative charge due to its higher electronegativity compared to H atom, H atom should have a relatively more positive charge.

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000072 0.001800 YES
RMS Displacement 0.000035 0.001200 YES
</pre>

===Screenshot of the display vibrations===

[[File:Xumenghan nh3 display vibrations2.PNG]]

===Vibration data===

<pre>
1 2 3
A1 E E
Frequencies -- 1089.5366 1693.9474 1693.9474
IR Inten -- 145.3814 13.5533 13.5533

4 5 6
A1 E E
Frequencies -- 3461.2932 3589.8170 3589.8170
IR Inten -- 1.0608 0.2711 0.2711
</pre>

===Answers to the questions about vibrations and charges===

1. From the 3N-6 rule, there are (3N-6=3*4-6=6) modes.

2. There are two sets of denegerate modes with wavenumbers (in cm<sup>-1</sup>): 1693.95 and 3589.82.

3. Bending modes have wavenumbers (in cm<sup>-1</sup>): 1089.54, 1693.95, 1693.95; stretching modes have wavenumbers (in cm<sup>-1</sup>): 3461.29, 3589.82, 3589.82.

4. The stretching mode with wavenumber (in cm<sup>-1</sup>) 3461.29 is highly symmetric.

5. The bending mode with wavenumber (in cm<sup>-1</sup>) 1089.54 is known as the "umbrella" mode.

6. Two bands are expected to show in an experimental spectrum of gaseous ammonia. Since the IR spectrum mainly records the stretching frequencies, and there are two non-degenerate values for stretching frequency.

==N<sub>2</sub>==

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XUMENGHAN N2 OPTF POP.LOG</uploadedFileContents>
<script>frame 1.18</script>
</jmolApplet></jmol>
[[File:XUMENGHAN N2 OPTF POP.LOG| text to display]]

===Summary===

==== Calculation method ====

RB3LYP

==== Basis set ====

6-31G(d,p)

==== E(RB3LYP) in a.u. ====

-109.52413

==== RMS gradient norm in a.u. ====

0.00013245

==== Point group ====

Dinfh

==== Key structural and charge information ====

N-N bond length (in Ångstrom): 1.11 (accurate to ≈ 0.01 Ångstrom)

Charge on both N atoms: 0.000

Note: The charges on both N atoms are shown as expected. They both should have a neutral charge, since the electron density is shared between same atoms equally.

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000229 0.000450 YES
RMS Force 0.000229 0.000300 YES
Maximum Displacement 0.000072 0.001800 YES
RMS Displacement 0.000101 0.001200 YES
</pre>

===Screenshot of the display vibrations===

[[File:Xumenghan n2 display vibrations2.PNG]]

===Vibration data===
<pre>
1
SGG
Frequencies -- 2457.9991
IR Inten -- 0.0000
</pre>

===Mono-metallic TM complex that coordinates N<sub>2</sub>===

====Identifier and link for the structure====

''RANLUO''

"https://www.ccdc.cam.ac.uk/structures/search?pid=csd:RANLUO"

====N-N bond length====

The optimised N-N bond length (in Ångstrom): 1.1054

The N-N bond length in crystal structure (in Ångstrom): 1.1122

The bond lengths are different. The N<sub>2</sub> in the crystal is connected directly onto an electropositve Ni atom, electron density and hence repulsion around the two N atoms increase. This could potentially cause the lengthing of the N-N bond.

==H<sub>2</sub>==

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XUMENGHAN H2 OPTF POP.LOG</uploadedFileContents>
<script>frame 1.12</script>
</jmolApplet></jmol>
[[File:XUMENGHAN H2 OPTF POP.LOG| text to display]]

===Summary===

==== Calculation method ====

RB3LYP

==== Basis set ====

6-31G(d,p)

==== E(RB3LYP) in a.u. ====

-1.17854

==== RMS gradient norm in a.u. ====

0.00040858

==== Point group ====

Dinfh

==== Basic information ====

H-H bond length (in Ångstrom): 0.74 (accurate to ≈ 0.01 Ångstrom)

Charge on both H atoms: 0.000

Note: The charges on both H atoms are shown as expected. They both should have a neutral charge, since the electron density is shared between same atoms equally.

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000000 0.001800 YES
RMS Displacement 0.000001 0.001200 YES
</pre>

===Screenshot of the display vibrations===

[[File:Xumenghan h2 display vibrations2.PNG]]

===Vibration data===
<pre>

1
SGG
Frequencies -- 4465.6824
IR Inten -- 0.0000

</pre>

==The Haber-Bosch process==

===Equation for this process===

N<sub>2</sub> + 3H<sub>2</sub> -> 2NH<sub>3</sub>

===Energy of reactants and product in a.u.===

E(NH<sub>3</sub>)= -56.5577687

2*E(NH<sub>3</sub>)= 2*(-56.55776873) = -113.1155375

E(N<sub>2</sub>)= -109.5241287

E(H<sub>2</sub>)= -1.1785387

3*E(H<sub>2</sub>)= 3*(-1.17853870) = 3*( -1.17853870) = -3.5356161

===Energy for this reaction===

ΔE=2*E(NH<sub>3</sub>)-[E(N<sub>2</sub>)+3*E(H<sub>2</sub>)]= -113.1155375 - (-109.52412866--3.5356161) = -0.0557927 (a.u.) = -0.0557927*2625.5 (kJ/mol) = -146.5(kJ/mol)

Note: hence from the energy of conversion, it is shown that this is a exothermic reaction, indicating that the ammonia product is more stable than the gasoues reactants.

==My chosen molecule Cl<sub>2</sub>==

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XUMENGHAN CL2 OPTF POP.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>
[[File:XUMENGHAN CL2 OPTF POP.LOG| text to display]]

===Summary===

==== Calculation method ====

RB3LYP

==== Basis set ====

6-31G(d,p)

==== E(RB3LYP) in a.u. ====

-920.27125

==== RMS gradient norm in a.u. ====

0.17962

==== Point group ====

Dinfh

==== Key structural infomation ====

Cl-Cl bond length (in Ångstrom): 2.04 (accurate to ≈ 0.01 Ångstrom)

Charge on both Cl atoms: 0.000

Note: The charges on both Cl atoms are shown as expected. They both should have a neutral charge, since the electron density is shared between same atoms equally.

===Item table===
<pre>

Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000015 0.000300 YES
Maximum Displacement 0.000043 0.001800 YES
RMS Displacement 0.000060 0.001200 YES

</pre>

===Screenshot of the display vibrations===

[[File:Xumenghan cl2 display vibrations2.PNG]]

===Vibration data===
<pre>
1
SGG
Frequencies -- 520.4311
IR Inten -- 0.0000

</pre>

===Molecular orbitals in interest===

====First MO====

[[File:1s sigma MO.PNG]]

This is a bonding MO filled with two electrons, since it is formed by in-phase combination of the 1s atomic orbitals of the two Cl atoms. This is also a sigma MO, since the two atomic orbitals overlap end-on. This MO has a comparatively very low energy at -101.60298, since its composite atomic orbitals are very close to the nuclues and hence feel a strong interaction and are buried deep down in energy. This MO is neither in the HOMO or the LUMO region. The electrons in this orbital will not be involved in bonding.

====Second MO====

[[File:2p sigma MO.PNG]]

This is a bonding MO filled with two electrons, since it is formed by in-phase combination of the 2p atomic orbitals of the two Cl atoms. This is a sigma MO, since the overlap of two AO is end-on. This MO has a higher energy, since the 2p orbitals are further away from the nucleus and at higher energy. This MO is neither in the HOMO or the LUMO region. The electrons in this orbital will not be involved in bonding.

====Third MO====

[[File:2p pi MO.PNG]]

This is a bonding MO filled with two electrons, since it is formed by in-phase combination of the 2p atomic orbitals of the two Cl atoms. This is a pi MO, since the overlap of two AO is now parallel. This MO has a further increased energy, since the parallel overlap is less effective than the end-on overlap. This MO is neither in the HOMO or the LUMO region. The electrons in this orbital will not be involved in bonding.

====Fourth MO====

[[File:HOMO.PNG]]

This is an pi* anti-bonding orbital filled with two electrons, since orbital combination of two 3p atomic orbitals is out-of-phase. This is the HOMO, hence the electrons in this MO have the highest energy. Hence this MO provide the most-readily-donated electrons in reaction.

====Fifth MO====

[[File:LUMO.PNG]]

This is an sigma* anti-bonding orbital with no electrons, since orbital combination of two 3s atomic orbitals is out-of-phase. This is the LUMO. This is the ideal (lowest-energy) empty MO that can accept further electrons in reaction.

==Independence -- study on CO<sub>2</sub>==

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XUMENGHAN O2 OPTF POP.LOG</uploadedFileContents>
<script>frame 1.10</script>
</jmolApplet></jmol>
[[File:XUMENGHAN O2 OPTF POP.LOG| text to display]]

===Summary===

==== Calculation method ====

RB3LYP

==== Basis set ====

6-31G(d,p)

==== E(RB3LYP) in a.u. ====

-150.25742

==== RMS gradient norm in a.u. ====

0.00001829

==== Point group ====

Dinfh

==== Key structural infomation ====

O-O bond length (in Ångstrom): 1.22 (accurate to ≈ 0.01 Ångstrom)

Charge on both O atoms: 0.000

Note: The charges on both O atoms are shown as expected. They both should have a neutral charge, since the electron density is shared between same atoms equally.

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000032 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.000019 0.001800 YES
RMS Displacement 0.000027 0.001200 YES
</pre>

===Screenshot of the display vibrations===

[[File:Xumenghan o2 display vibrations2.PNG]]

===Vibration data===
<pre>
1
SGG
Frequencies -- 1643.1143
Red. masses -- 15.9949
Frc consts -- 25.4430
IR Inten -- 0.0000
</pre>

Rep:Mod:mx3118

2019-02-22T17:21:24Z

Mx3118: /* RMS gradient norm in a.u. */

==NH<sub>3</sub>==

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XUMENGHAN NH3 OPTF POP.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>
[[File:XUMENGHAN NH3 OPTF POP.LOG| text to display]]

===Summary===

==== Calculation method ====

RB3LYP

==== Basis set ====

6-31G(d,p)

==== E(RB3LYP) in a.u. ====

-56.55777

==== RMS gradient norm in a.u. ====

0.00000485

==== Point group ====

C<sub>3v</sub>

==== Key structural and charge information ====

N-H bond length (in Ångstrom): 1.02 (accurate to ≈ 0.01 Ångstrom)

H-N-H bond angle (in Degree): 106 (accurate to ≈ 1 Degree)

Charge on N atom: -1.125

Charge on H atoms: 0.375

Note: The charges on N atom and H atom are shown as expected. The N atom should have a relatively more negative charge due to its higher electronegativity compared to H atom, H atom should have a relatively more positive charge.

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000072 0.001800 YES
RMS Displacement 0.000035 0.001200 YES
</pre>

===Screenshot of the display vibrations===

[[File:Xumenghan nh3 display vibrations2.PNG]]

===Vibration data===

<pre>
1 2 3
A1 E E
Frequencies -- 1089.5366 1693.9474 1693.9474
IR Inten -- 145.3814 13.5533 13.5533

4 5 6
A1 E E
Frequencies -- 3461.2932 3589.8170 3589.8170
IR Inten -- 1.0608 0.2711 0.2711
</pre>

===Answers to the questions about vibrations and charges===

1. From the 3N-6 rule, there are (3N-6=3*4-6=6) modes.

2. There are two sets of denegerate modes with wavenumbers (in cm<sup>-1</sup>): 1693.95 and 3589.82.

3. Bending modes have wavenumbers (in cm<sup>-1</sup>): 1089.54, 1693.95, 1693.95; stretching modes have wavenumbers (in cm<sup>-1</sup>): 3461.29, 3589.82, 3589.82.

4. The stretching mode with wavenumber (in cm<sup>-1</sup>) 3461.29 is highly symmetric.

5. The bending mode with wavenumber (in cm<sup>-1</sup>) 1089.54 is known as the "umbrella" mode.

6. Two bands are expected to show in an experimental spectrum of gaseous ammonia. Since the IR spectrum mainly records the stretching frequencies, and there are two non-degenerate values for stretching frequency.

==N<sub>2</sub>==

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XUMENGHAN N2 OPTF POP.LOG</uploadedFileContents>
<script>frame 1.18</script>
</jmolApplet></jmol>
[[File:XUMENGHAN N2 OPTF POP.LOG| text to display]]

===Summary===

==== Calculation method ====

RB3LYP

==== Basis set ====

6-31G(d,p)

==== E(RB3LYP) in a.u. ====

-109.52413

==== RMS gradient norm in a.u. ====

0.00013245

==== Point group ====

Dinfh

==== Basic information ====

N-N bond length (in Ångstrom): 1.11 (accurate to ≈ 0.01 Ångstrom)

Charge on both N atoms: 0.000

Note: The charges on both N atoms are shown as expected. They both should have a neutral charge, since the electron density is shared between same atoms equally.

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000229 0.000450 YES
RMS Force 0.000229 0.000300 YES
Maximum Displacement 0.000072 0.001800 YES
RMS Displacement 0.000101 0.001200 YES
</pre>

===Screenshot of the display vibrations===

[[File:Xumenghan n2 display vibrations2.PNG]]

===Vibration data===
<pre>
1
SGG
Frequencies -- 2457.9991
IR Inten -- 0.0000
</pre>

===Mono-metallic TM complex that coordinates N<sub>2</sub>===

====Identifier and link for the structure====

''RANLUO''

"https://www.ccdc.cam.ac.uk/structures/search?pid=csd:RANLUO"

====N-N bond length====

The optimised N-N bond length (in Ångstrom): 1.1054

The N-N bond length in crystal structure (in Ångstrom): 1.1122

The bond lengths are different. The N<sub>2</sub> in the crystal is connected directly onto an electropositve Ni atom, electron density and hence repulsion around the two N atoms increase. This could potentially cause the lengthing of the N-N bond.

==H<sub>2</sub>==

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XUMENGHAN H2 OPTF POP.LOG</uploadedFileContents>
<script>frame 1.12</script>
</jmolApplet></jmol>
[[File:XUMENGHAN H2 OPTF POP.LOG| text to display]]

===Summary===

==== Calculation method ====

RB3LYP

==== Basis set ====

6-31G(d,p)

==== E(RB3LYP) in a.u. ====

-1.17854

==== RMS gradient norm in a.u. ====

0.00040858

==== Point group ====

Dinfh

==== Basic information ====

H-H bond length (in Ångstrom): 0.74 (accurate to ≈ 0.01 Ångstrom)

Charge on both H atoms: 0.000

Note: The charges on both H atoms are shown as expected. They both should have a neutral charge, since the electron density is shared between same atoms equally.

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000000 0.001800 YES
RMS Displacement 0.000001 0.001200 YES
</pre>

===Screenshot of the display vibrations===

[[File:Xumenghan h2 display vibrations2.PNG]]

===Vibration data===
<pre>

1
SGG
Frequencies -- 4465.6824
IR Inten -- 0.0000

</pre>

==The Haber-Bosch process==

===Equation for this process===

N<sub>2</sub> + 3H<sub>2</sub> -> 2NH<sub>3</sub>

===Energy of reactants and product in a.u.===

E(NH<sub>3</sub>)= -56.5577687

2*E(NH<sub>3</sub>)= 2*(-56.55776873) = -113.1155375

E(N<sub>2</sub>)= -109.5241287

E(H<sub>2</sub>)= -1.1785387

3*E(H<sub>2</sub>)= 3*(-1.17853870) = 3*( -1.17853870) = -3.5356161

===Energy for this reaction===

ΔE=2*E(NH<sub>3</sub>)-[E(N<sub>2</sub>)+3*E(H<sub>2</sub>)]= -113.1155375 - (-109.52412866--3.5356161) = -0.0557927 (a.u.) = -0.0557927*2625.5 (kJ/mol) = -146.5(kJ/mol)

Note: hence from the energy of conversion, it is shown that this is a exothermic reaction, indicating that the ammonia product is more stable than the gasoues reactants.

==My chosen molecule Cl<sub>2</sub>==

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XUMENGHAN CL2 OPTF POP.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>
[[File:XUMENGHAN CL2 OPTF POP.LOG| text to display]]

===Summary===

==== Calculation method ====

RB3LYP

==== Basis set ====

6-31G(d,p)

==== E(RB3LYP) in a.u. ====

-920.27125

==== RMS gradient norm in a.u. ====

0.17962

==== Point group ====

Dinfh

==== Key structural infomation ====

Cl-Cl bond length (in Ångstrom): 2.04 (accurate to ≈ 0.01 Ångstrom)

Charge on both Cl atoms: 0.000

Note: The charges on both Cl atoms are shown as expected. They both should have a neutral charge, since the electron density is shared between same atoms equally.

===Item table===
<pre>

Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000015 0.000300 YES
Maximum Displacement 0.000043 0.001800 YES
RMS Displacement 0.000060 0.001200 YES

</pre>

===Screenshot of the display vibrations===

[[File:Xumenghan cl2 display vibrations2.PNG]]

===Vibration data===
<pre>
1
SGG
Frequencies -- 520.4311
IR Inten -- 0.0000

</pre>

===Molecular orbitals in interest===

====First MO====

[[File:1s sigma MO.PNG]]

This is a bonding MO filled with two electrons, since it is formed by in-phase combination of the 1s atomic orbitals of the two Cl atoms. This is also a sigma MO, since the two atomic orbitals overlap end-on. This MO has a comparatively very low energy at -101.60298, since its composite atomic orbitals are very close to the nuclues and hence feel a strong interaction and are buried deep down in energy. This MO is neither in the HOMO or the LUMO region. The electrons in this orbital will not be involved in bonding.

====Second MO====

[[File:2p sigma MO.PNG]]

This is a bonding MO filled with two electrons, since it is formed by in-phase combination of the 2p atomic orbitals of the two Cl atoms. This is a sigma MO, since the overlap of two AO is end-on. This MO has a higher energy, since the 2p orbitals are further away from the nucleus and at higher energy. This MO is neither in the HOMO or the LUMO region. The electrons in this orbital will not be involved in bonding.

====Third MO====

[[File:2p pi MO.PNG]]

This is a bonding MO filled with two electrons, since it is formed by in-phase combination of the 2p atomic orbitals of the two Cl atoms. This is a pi MO, since the overlap of two AO is now parallel. This MO has a further increased energy, since the parallel overlap is less effective than the end-on overlap. This MO is neither in the HOMO or the LUMO region. The electrons in this orbital will not be involved in bonding.

====Fourth MO====

[[File:HOMO.PNG]]

This is an pi* anti-bonding orbital filled with two electrons, since orbital combination of two 3p atomic orbitals is out-of-phase. This is the HOMO, hence the electrons in this MO have the highest energy. Hence this MO provide the most-readily-donated electrons in reaction.

====Fifth MO====

[[File:LUMO.PNG]]

This is an sigma* anti-bonding orbital with no electrons, since orbital combination of two 3s atomic orbitals is out-of-phase. This is the LUMO. This is the ideal (lowest-energy) empty MO that can accept further electrons in reaction.

==Independence -- study on CO<sub>2</sub>==

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XUMENGHAN O2 OPTF POP.LOG</uploadedFileContents>
<script>frame 1.10</script>
</jmolApplet></jmol>
[[File:XUMENGHAN O2 OPTF POP.LOG| text to display]]

===Summary===

==== Calculation method ====

RB3LYP

==== Basis set ====

6-31G(d,p)

==== E(RB3LYP) in a.u. ====

-150.25742

==== RMS gradient norm in a.u. ====

0.00001829

==== Point group ====

Dinfh

==== Key structural infomation ====

O-O bond length (in Ångstrom): 1.22 (accurate to ≈ 0.01 Ångstrom)

Charge on both O atoms: 0.000

Note: The charges on both O atoms are shown as expected. They both should have a neutral charge, since the electron density is shared between same atoms equally.

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000032 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.000019 0.001800 YES
RMS Displacement 0.000027 0.001200 YES
</pre>

===Screenshot of the display vibrations===

[[File:Xumenghan o2 display vibrations2.PNG]]

===Vibration data===
<pre>
1
SGG
Frequencies -- 1643.1143
Red. masses -- 15.9949
Frc consts -- 25.4430
IR Inten -- 0.0000
</pre>

Rep:Mod:mx3118

2019-02-22T17:21:13Z

Mx3118: /* Key structural infomation */

==NH<sub>3</sub>==

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XUMENGHAN NH3 OPTF POP.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>
[[File:XUMENGHAN NH3 OPTF POP.LOG| text to display]]

===Summary===

==== Calculation method ====

RB3LYP

==== Basis set ====

6-31G(d,p)

==== E(RB3LYP) in a.u. ====

-56.55777

==== RMS gradient norm in a.u. ====

0.0000048500

==== Point group ====

C<sub>3v</sub>

==== Key structural and charge information ====

N-H bond length (in Ångstrom): 1.02 (accurate to ≈ 0.01 Ångstrom)

H-N-H bond angle (in Degree): 106 (accurate to ≈ 1 Degree)

Charge on N atom: -1.125

Charge on H atoms: 0.375

Note: The charges on N atom and H atom are shown as expected. The N atom should have a relatively more negative charge due to its higher electronegativity compared to H atom, H atom should have a relatively more positive charge.

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000072 0.001800 YES
RMS Displacement 0.000035 0.001200 YES
</pre>

===Screenshot of the display vibrations===

[[File:Xumenghan nh3 display vibrations2.PNG]]

===Vibration data===

<pre>
1 2 3
A1 E E
Frequencies -- 1089.5366 1693.9474 1693.9474
IR Inten -- 145.3814 13.5533 13.5533

4 5 6
A1 E E
Frequencies -- 3461.2932 3589.8170 3589.8170
IR Inten -- 1.0608 0.2711 0.2711
</pre>

===Answers to the questions about vibrations and charges===

1. From the 3N-6 rule, there are (3N-6=3*4-6=6) modes.

2. There are two sets of denegerate modes with wavenumbers (in cm<sup>-1</sup>): 1693.95 and 3589.82.

3. Bending modes have wavenumbers (in cm<sup>-1</sup>): 1089.54, 1693.95, 1693.95; stretching modes have wavenumbers (in cm<sup>-1</sup>): 3461.29, 3589.82, 3589.82.

4. The stretching mode with wavenumber (in cm<sup>-1</sup>) 3461.29 is highly symmetric.

5. The bending mode with wavenumber (in cm<sup>-1</sup>) 1089.54 is known as the "umbrella" mode.

6. Two bands are expected to show in an experimental spectrum of gaseous ammonia. Since the IR spectrum mainly records the stretching frequencies, and there are two non-degenerate values for stretching frequency.

==N<sub>2</sub>==

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XUMENGHAN N2 OPTF POP.LOG</uploadedFileContents>
<script>frame 1.18</script>
</jmolApplet></jmol>
[[File:XUMENGHAN N2 OPTF POP.LOG| text to display]]

===Summary===

==== Calculation method ====

RB3LYP

==== Basis set ====

6-31G(d,p)

==== E(RB3LYP) in a.u. ====

-109.52413

==== RMS gradient norm in a.u. ====

0.00013245

==== Point group ====

Dinfh

==== Basic information ====

N-N bond length (in Ångstrom): 1.11 (accurate to ≈ 0.01 Ångstrom)

Charge on both N atoms: 0.000

Note: The charges on both N atoms are shown as expected. They both should have a neutral charge, since the electron density is shared between same atoms equally.

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000229 0.000450 YES
RMS Force 0.000229 0.000300 YES
Maximum Displacement 0.000072 0.001800 YES
RMS Displacement 0.000101 0.001200 YES
</pre>

===Screenshot of the display vibrations===

[[File:Xumenghan n2 display vibrations2.PNG]]

===Vibration data===
<pre>
1
SGG
Frequencies -- 2457.9991
IR Inten -- 0.0000
</pre>

===Mono-metallic TM complex that coordinates N<sub>2</sub>===

====Identifier and link for the structure====

''RANLUO''

"https://www.ccdc.cam.ac.uk/structures/search?pid=csd:RANLUO"

====N-N bond length====

The optimised N-N bond length (in Ångstrom): 1.1054

The N-N bond length in crystal structure (in Ångstrom): 1.1122

The bond lengths are different. The N<sub>2</sub> in the crystal is connected directly onto an electropositve Ni atom, electron density and hence repulsion around the two N atoms increase. This could potentially cause the lengthing of the N-N bond.

==H<sub>2</sub>==

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XUMENGHAN H2 OPTF POP.LOG</uploadedFileContents>
<script>frame 1.12</script>
</jmolApplet></jmol>
[[File:XUMENGHAN H2 OPTF POP.LOG| text to display]]

===Summary===

==== Calculation method ====

RB3LYP

==== Basis set ====

6-31G(d,p)

==== E(RB3LYP) in a.u. ====

-1.17854

==== RMS gradient norm in a.u. ====

0.00040858

==== Point group ====

Dinfh

==== Basic information ====

H-H bond length (in Ångstrom): 0.74 (accurate to ≈ 0.01 Ångstrom)

Charge on both H atoms: 0.000

Note: The charges on both H atoms are shown as expected. They both should have a neutral charge, since the electron density is shared between same atoms equally.

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000000 0.001800 YES
RMS Displacement 0.000001 0.001200 YES
</pre>

===Screenshot of the display vibrations===

[[File:Xumenghan h2 display vibrations2.PNG]]

===Vibration data===
<pre>

1
SGG
Frequencies -- 4465.6824
IR Inten -- 0.0000

</pre>

==The Haber-Bosch process==

===Equation for this process===

N<sub>2</sub> + 3H<sub>2</sub> -> 2NH<sub>3</sub>

===Energy of reactants and product in a.u.===

E(NH<sub>3</sub>)= -56.5577687

2*E(NH<sub>3</sub>)= 2*(-56.55776873) = -113.1155375

E(N<sub>2</sub>)= -109.5241287

E(H<sub>2</sub>)= -1.1785387

3*E(H<sub>2</sub>)= 3*(-1.17853870) = 3*( -1.17853870) = -3.5356161

===Energy for this reaction===

ΔE=2*E(NH<sub>3</sub>)-[E(N<sub>2</sub>)+3*E(H<sub>2</sub>)]= -113.1155375 - (-109.52412866--3.5356161) = -0.0557927 (a.u.) = -0.0557927*2625.5 (kJ/mol) = -146.5(kJ/mol)

Note: hence from the energy of conversion, it is shown that this is a exothermic reaction, indicating that the ammonia product is more stable than the gasoues reactants.

==My chosen molecule Cl<sub>2</sub>==

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XUMENGHAN CL2 OPTF POP.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>
[[File:XUMENGHAN CL2 OPTF POP.LOG| text to display]]

===Summary===

==== Calculation method ====

RB3LYP

==== Basis set ====

6-31G(d,p)

==== E(RB3LYP) in a.u. ====

-920.27125

==== RMS gradient norm in a.u. ====

0.17962

==== Point group ====

Dinfh

==== Key structural infomation ====

Cl-Cl bond length (in Ångstrom): 2.04 (accurate to ≈ 0.01 Ångstrom)

Charge on both Cl atoms: 0.000

Note: The charges on both Cl atoms are shown as expected. They both should have a neutral charge, since the electron density is shared between same atoms equally.

===Item table===
<pre>

Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000015 0.000300 YES
Maximum Displacement 0.000043 0.001800 YES
RMS Displacement 0.000060 0.001200 YES

</pre>

===Screenshot of the display vibrations===

[[File:Xumenghan cl2 display vibrations2.PNG]]

===Vibration data===
<pre>
1
SGG
Frequencies -- 520.4311
IR Inten -- 0.0000

</pre>

===Molecular orbitals in interest===

====First MO====

[[File:1s sigma MO.PNG]]

This is a bonding MO filled with two electrons, since it is formed by in-phase combination of the 1s atomic orbitals of the two Cl atoms. This is also a sigma MO, since the two atomic orbitals overlap end-on. This MO has a comparatively very low energy at -101.60298, since its composite atomic orbitals are very close to the nuclues and hence feel a strong interaction and are buried deep down in energy. This MO is neither in the HOMO or the LUMO region. The electrons in this orbital will not be involved in bonding.

====Second MO====

[[File:2p sigma MO.PNG]]

This is a bonding MO filled with two electrons, since it is formed by in-phase combination of the 2p atomic orbitals of the two Cl atoms. This is a sigma MO, since the overlap of two AO is end-on. This MO has a higher energy, since the 2p orbitals are further away from the nucleus and at higher energy. This MO is neither in the HOMO or the LUMO region. The electrons in this orbital will not be involved in bonding.

====Third MO====

[[File:2p pi MO.PNG]]

This is a bonding MO filled with two electrons, since it is formed by in-phase combination of the 2p atomic orbitals of the two Cl atoms. This is a pi MO, since the overlap of two AO is now parallel. This MO has a further increased energy, since the parallel overlap is less effective than the end-on overlap. This MO is neither in the HOMO or the LUMO region. The electrons in this orbital will not be involved in bonding.

====Fourth MO====

[[File:HOMO.PNG]]

This is an pi* anti-bonding orbital filled with two electrons, since orbital combination of two 3p atomic orbitals is out-of-phase. This is the HOMO, hence the electrons in this MO have the highest energy. Hence this MO provide the most-readily-donated electrons in reaction.

====Fifth MO====

[[File:LUMO.PNG]]

This is an sigma* anti-bonding orbital with no electrons, since orbital combination of two 3s atomic orbitals is out-of-phase. This is the LUMO. This is the ideal (lowest-energy) empty MO that can accept further electrons in reaction.

==Independence -- study on CO<sub>2</sub>==

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XUMENGHAN O2 OPTF POP.LOG</uploadedFileContents>
<script>frame 1.10</script>
</jmolApplet></jmol>
[[File:XUMENGHAN O2 OPTF POP.LOG| text to display]]

===Summary===

==== Calculation method ====

RB3LYP

==== Basis set ====

6-31G(d,p)

==== E(RB3LYP) in a.u. ====

-150.25742

==== RMS gradient norm in a.u. ====

0.00001829

==== Point group ====

Dinfh

==== Key structural infomation ====

O-O bond length (in Ångstrom): 1.22 (accurate to ≈ 0.01 Ångstrom)

Charge on both O atoms: 0.000

Note: The charges on both O atoms are shown as expected. They both should have a neutral charge, since the electron density is shared between same atoms equally.

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000032 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.000019 0.001800 YES
RMS Displacement 0.000027 0.001200 YES
</pre>

===Screenshot of the display vibrations===

[[File:Xumenghan o2 display vibrations2.PNG]]

===Vibration data===
<pre>
1
SGG
Frequencies -- 1643.1143
Red. masses -- 15.9949
Frc consts -- 25.4430
IR Inten -- 0.0000
</pre>

Rep:Mod:mx3118

2019-02-22T17:20:28Z

Mx3118: /* Basic information */

==NH<sub>3</sub>==

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XUMENGHAN NH3 OPTF POP.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>
[[File:XUMENGHAN NH3 OPTF POP.LOG| text to display]]

===Summary===

==== Calculation method ====

RB3LYP

==== Basis set ====

6-31G(d,p)

==== E(RB3LYP) in a.u. ====

-56.55777

==== RMS gradient norm in a.u. ====

0.0000048500

==== Point group ====

C<sub>3v</sub>

==== Key structural infomation ====

N-H bond length (in Ångstrom): 1.02 (accurate to ≈ 0.01 Ångstrom)

H-N-H bond angle (in Degree): 106 (accurate to ≈ 1 Degree)

Charge on N atom: -1.125

Charge on H atoms: 0.375

Note: The charges on N atom and H atom are shown as expected. The N atom should have a relatively more negative charge due to its higher electronegativity compared to H atom, H atom should have a relatively more positive charge.

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000072 0.001800 YES
RMS Displacement 0.000035 0.001200 YES
</pre>

===Screenshot of the display vibrations===

[[File:Xumenghan nh3 display vibrations2.PNG]]

===Vibration data===

<pre>
1 2 3
A1 E E
Frequencies -- 1089.5366 1693.9474 1693.9474
IR Inten -- 145.3814 13.5533 13.5533

4 5 6
A1 E E
Frequencies -- 3461.2932 3589.8170 3589.8170
IR Inten -- 1.0608 0.2711 0.2711
</pre>

===Answers to the questions about vibrations and charges===

1. From the 3N-6 rule, there are (3N-6=3*4-6=6) modes.

2. There are two sets of denegerate modes with wavenumbers (in cm<sup>-1</sup>): 1693.95 and 3589.82.

3. Bending modes have wavenumbers (in cm<sup>-1</sup>): 1089.54, 1693.95, 1693.95; stretching modes have wavenumbers (in cm<sup>-1</sup>): 3461.29, 3589.82, 3589.82.

4. The stretching mode with wavenumber (in cm<sup>-1</sup>) 3461.29 is highly symmetric.

5. The bending mode with wavenumber (in cm<sup>-1</sup>) 1089.54 is known as the "umbrella" mode.

6. Two bands are expected to show in an experimental spectrum of gaseous ammonia. Since the IR spectrum mainly records the stretching frequencies, and there are two non-degenerate values for stretching frequency.

==N<sub>2</sub>==

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XUMENGHAN N2 OPTF POP.LOG</uploadedFileContents>
<script>frame 1.18</script>
</jmolApplet></jmol>
[[File:XUMENGHAN N2 OPTF POP.LOG| text to display]]

===Summary===

==== Calculation method ====

RB3LYP

==== Basis set ====

6-31G(d,p)

==== E(RB3LYP) in a.u. ====

-109.52413

==== RMS gradient norm in a.u. ====

0.00013245

==== Point group ====

Dinfh

==== Basic information ====

N-N bond length (in Ångstrom): 1.11 (accurate to ≈ 0.01 Ångstrom)

Charge on both N atoms: 0.000

Note: The charges on both N atoms are shown as expected. They both should have a neutral charge, since the electron density is shared between same atoms equally.

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000229 0.000450 YES
RMS Force 0.000229 0.000300 YES
Maximum Displacement 0.000072 0.001800 YES
RMS Displacement 0.000101 0.001200 YES
</pre>

===Screenshot of the display vibrations===

[[File:Xumenghan n2 display vibrations2.PNG]]

===Vibration data===
<pre>
1
SGG
Frequencies -- 2457.9991
IR Inten -- 0.0000
</pre>

===Mono-metallic TM complex that coordinates N<sub>2</sub>===

====Identifier and link for the structure====

''RANLUO''

"https://www.ccdc.cam.ac.uk/structures/search?pid=csd:RANLUO"

====N-N bond length====

The optimised N-N bond length (in Ångstrom): 1.1054

The N-N bond length in crystal structure (in Ångstrom): 1.1122

The bond lengths are different. The N<sub>2</sub> in the crystal is connected directly onto an electropositve Ni atom, electron density and hence repulsion around the two N atoms increase. This could potentially cause the lengthing of the N-N bond.

==H<sub>2</sub>==

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XUMENGHAN H2 OPTF POP.LOG</uploadedFileContents>
<script>frame 1.12</script>
</jmolApplet></jmol>
[[File:XUMENGHAN H2 OPTF POP.LOG| text to display]]

===Summary===

==== Calculation method ====

RB3LYP

==== Basis set ====

6-31G(d,p)

==== E(RB3LYP) in a.u. ====

-1.17854

==== RMS gradient norm in a.u. ====

0.00040858

==== Point group ====

Dinfh

==== Basic information ====

H-H bond length (in Ångstrom): 0.74 (accurate to ≈ 0.01 Ångstrom)

Charge on both H atoms: 0.000

Note: The charges on both H atoms are shown as expected. They both should have a neutral charge, since the electron density is shared between same atoms equally.

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000000 0.001800 YES
RMS Displacement 0.000001 0.001200 YES
</pre>

===Screenshot of the display vibrations===

[[File:Xumenghan h2 display vibrations2.PNG]]

===Vibration data===
<pre>

1
SGG
Frequencies -- 4465.6824
IR Inten -- 0.0000

</pre>

==The Haber-Bosch process==

===Equation for this process===

N<sub>2</sub> + 3H<sub>2</sub> -> 2NH<sub>3</sub>

===Energy of reactants and product in a.u.===

E(NH<sub>3</sub>)= -56.5577687

2*E(NH<sub>3</sub>)= 2*(-56.55776873) = -113.1155375

E(N<sub>2</sub>)= -109.5241287

E(H<sub>2</sub>)= -1.1785387

3*E(H<sub>2</sub>)= 3*(-1.17853870) = 3*( -1.17853870) = -3.5356161

===Energy for this reaction===

ΔE=2*E(NH<sub>3</sub>)-[E(N<sub>2</sub>)+3*E(H<sub>2</sub>)]= -113.1155375 - (-109.52412866--3.5356161) = -0.0557927 (a.u.) = -0.0557927*2625.5 (kJ/mol) = -146.5(kJ/mol)

Note: hence from the energy of conversion, it is shown that this is a exothermic reaction, indicating that the ammonia product is more stable than the gasoues reactants.

==My chosen molecule Cl<sub>2</sub>==

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XUMENGHAN CL2 OPTF POP.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>
[[File:XUMENGHAN CL2 OPTF POP.LOG| text to display]]

===Summary===

==== Calculation method ====

RB3LYP

==== Basis set ====

6-31G(d,p)

==== E(RB3LYP) in a.u. ====

-920.27125

==== RMS gradient norm in a.u. ====

0.17962

==== Point group ====

Dinfh

==== Key structural infomation ====

Cl-Cl bond length (in Ångstrom): 2.04 (accurate to ≈ 0.01 Ångstrom)

Charge on both Cl atoms: 0.000

Note: The charges on both Cl atoms are shown as expected. They both should have a neutral charge, since the electron density is shared between same atoms equally.

===Item table===
<pre>

Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000015 0.000300 YES
Maximum Displacement 0.000043 0.001800 YES
RMS Displacement 0.000060 0.001200 YES

</pre>

===Screenshot of the display vibrations===

[[File:Xumenghan cl2 display vibrations2.PNG]]

===Vibration data===
<pre>
1
SGG
Frequencies -- 520.4311
IR Inten -- 0.0000

</pre>

===Molecular orbitals in interest===

====First MO====

[[File:1s sigma MO.PNG]]

This is a bonding MO filled with two electrons, since it is formed by in-phase combination of the 1s atomic orbitals of the two Cl atoms. This is also a sigma MO, since the two atomic orbitals overlap end-on. This MO has a comparatively very low energy at -101.60298, since its composite atomic orbitals are very close to the nuclues and hence feel a strong interaction and are buried deep down in energy. This MO is neither in the HOMO or the LUMO region. The electrons in this orbital will not be involved in bonding.

====Second MO====

[[File:2p sigma MO.PNG]]

This is a bonding MO filled with two electrons, since it is formed by in-phase combination of the 2p atomic orbitals of the two Cl atoms. This is a sigma MO, since the overlap of two AO is end-on. This MO has a higher energy, since the 2p orbitals are further away from the nucleus and at higher energy. This MO is neither in the HOMO or the LUMO region. The electrons in this orbital will not be involved in bonding.

====Third MO====

[[File:2p pi MO.PNG]]

This is a bonding MO filled with two electrons, since it is formed by in-phase combination of the 2p atomic orbitals of the two Cl atoms. This is a pi MO, since the overlap of two AO is now parallel. This MO has a further increased energy, since the parallel overlap is less effective than the end-on overlap. This MO is neither in the HOMO or the LUMO region. The electrons in this orbital will not be involved in bonding.

====Fourth MO====

[[File:HOMO.PNG]]

This is an pi* anti-bonding orbital filled with two electrons, since orbital combination of two 3p atomic orbitals is out-of-phase. This is the HOMO, hence the electrons in this MO have the highest energy. Hence this MO provide the most-readily-donated electrons in reaction.

====Fifth MO====

[[File:LUMO.PNG]]

This is an sigma* anti-bonding orbital with no electrons, since orbital combination of two 3s atomic orbitals is out-of-phase. This is the LUMO. This is the ideal (lowest-energy) empty MO that can accept further electrons in reaction.

==Independence -- study on CO<sub>2</sub>==

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XUMENGHAN O2 OPTF POP.LOG</uploadedFileContents>
<script>frame 1.10</script>
</jmolApplet></jmol>
[[File:XUMENGHAN O2 OPTF POP.LOG| text to display]]

===Summary===

==== Calculation method ====

RB3LYP

==== Basis set ====

6-31G(d,p)

==== E(RB3LYP) in a.u. ====

-150.25742

==== RMS gradient norm in a.u. ====

0.00001829

==== Point group ====

Dinfh

==== Key structural infomation ====

O-O bond length (in Ångstrom): 1.22 (accurate to ≈ 0.01 Ångstrom)

Charge on both O atoms: 0.000

Note: The charges on both O atoms are shown as expected. They both should have a neutral charge, since the electron density is shared between same atoms equally.

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000032 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.000019 0.001800 YES
RMS Displacement 0.000027 0.001200 YES
</pre>

===Screenshot of the display vibrations===

[[File:Xumenghan o2 display vibrations2.PNG]]

===Vibration data===
<pre>
1
SGG
Frequencies -- 1643.1143
Red. masses -- 15.9949
Frc consts -- 25.4430
IR Inten -- 0.0000
</pre>

Rep:Mod:mx3118

2019-02-22T17:19:58Z

Mx3118: /* fifth MO */

==NH<sub>3</sub>==

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XUMENGHAN NH3 OPTF POP.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>
[[File:XUMENGHAN NH3 OPTF POP.LOG| text to display]]

===Summary===

==== Calculation method ====

RB3LYP

==== Basis set ====

6-31G(d,p)

==== E(RB3LYP) in a.u. ====

-56.55777

==== RMS gradient norm in a.u. ====

0.0000048500

==== Point group ====

C<sub>3v</sub>

==== Basic information ====

N-H bond length (in Ångstrom): 1.02 (accurate to ≈ 0.01 Ångstrom)

H-N-H bond angle (in Degree): 106 (accurate to ≈ 1 Degree)

Charge on N atom: -1.125

Charge on H atoms: 0.375

Note: The charges on N atom and H atom are shown as expected. The N atom should have a relatively more negative charge due to its higher electronegativity compared to H atom, H atom should have a relatively more positive charge.

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000072 0.001800 YES
RMS Displacement 0.000035 0.001200 YES
</pre>

===Screenshot of the display vibrations===

[[File:Xumenghan nh3 display vibrations2.PNG]]

===Vibration data===

<pre>
1 2 3
A1 E E
Frequencies -- 1089.5366 1693.9474 1693.9474
IR Inten -- 145.3814 13.5533 13.5533

4 5 6
A1 E E
Frequencies -- 3461.2932 3589.8170 3589.8170
IR Inten -- 1.0608 0.2711 0.2711
</pre>

===Answers to the questions about vibrations and charges===

1. From the 3N-6 rule, there are (3N-6=3*4-6=6) modes.

2. There are two sets of denegerate modes with wavenumbers (in cm<sup>-1</sup>): 1693.95 and 3589.82.

3. Bending modes have wavenumbers (in cm<sup>-1</sup>): 1089.54, 1693.95, 1693.95; stretching modes have wavenumbers (in cm<sup>-1</sup>): 3461.29, 3589.82, 3589.82.

4. The stretching mode with wavenumber (in cm<sup>-1</sup>) 3461.29 is highly symmetric.

5. The bending mode with wavenumber (in cm<sup>-1</sup>) 1089.54 is known as the "umbrella" mode.

6. Two bands are expected to show in an experimental spectrum of gaseous ammonia. Since the IR spectrum mainly records the stretching frequencies, and there are two non-degenerate values for stretching frequency.

==N<sub>2</sub>==

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XUMENGHAN N2 OPTF POP.LOG</uploadedFileContents>
<script>frame 1.18</script>
</jmolApplet></jmol>
[[File:XUMENGHAN N2 OPTF POP.LOG| text to display]]

===Summary===

==== Calculation method ====

RB3LYP

==== Basis set ====

6-31G(d,p)

==== E(RB3LYP) in a.u. ====

-109.52413

==== RMS gradient norm in a.u. ====

0.00013245

==== Point group ====

Dinfh

==== Basic information ====

N-N bond length (in Ångstrom): 1.11 (accurate to ≈ 0.01 Ångstrom)

Charge on both N atoms: 0.000

Note: The charges on both N atoms are shown as expected. They both should have a neutral charge, since the electron density is shared between same atoms equally.

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000229 0.000450 YES
RMS Force 0.000229 0.000300 YES
Maximum Displacement 0.000072 0.001800 YES
RMS Displacement 0.000101 0.001200 YES
</pre>

===Screenshot of the display vibrations===

[[File:Xumenghan n2 display vibrations2.PNG]]

===Vibration data===
<pre>
1
SGG
Frequencies -- 2457.9991
IR Inten -- 0.0000
</pre>

===Mono-metallic TM complex that coordinates N<sub>2</sub>===

====Identifier and link for the structure====

''RANLUO''

"https://www.ccdc.cam.ac.uk/structures/search?pid=csd:RANLUO"

====N-N bond length====

The optimised N-N bond length (in Ångstrom): 1.1054

The N-N bond length in crystal structure (in Ångstrom): 1.1122

The bond lengths are different. The N<sub>2</sub> in the crystal is connected directly onto an electropositve Ni atom, electron density and hence repulsion around the two N atoms increase. This could potentially cause the lengthing of the N-N bond.

==H<sub>2</sub>==

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XUMENGHAN H2 OPTF POP.LOG</uploadedFileContents>
<script>frame 1.12</script>
</jmolApplet></jmol>
[[File:XUMENGHAN H2 OPTF POP.LOG| text to display]]

===Summary===

==== Calculation method ====

RB3LYP

==== Basis set ====

6-31G(d,p)

==== E(RB3LYP) in a.u. ====

-1.17854

==== RMS gradient norm in a.u. ====

0.00040858

==== Point group ====

Dinfh

==== Basic information ====

H-H bond length (in Ångstrom): 0.74 (accurate to ≈ 0.01 Ångstrom)

Charge on both H atoms: 0.000

Note: The charges on both H atoms are shown as expected. They both should have a neutral charge, since the electron density is shared between same atoms equally.

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000000 0.001800 YES
RMS Displacement 0.000001 0.001200 YES
</pre>

===Screenshot of the display vibrations===

[[File:Xumenghan h2 display vibrations2.PNG]]

===Vibration data===
<pre>

1
SGG
Frequencies -- 4465.6824
IR Inten -- 0.0000

</pre>

==The Haber-Bosch process==

===Equation for this process===

N<sub>2</sub> + 3H<sub>2</sub> -> 2NH<sub>3</sub>

===Energy of reactants and product in a.u.===

E(NH<sub>3</sub>)= -56.5577687

2*E(NH<sub>3</sub>)= 2*(-56.55776873) = -113.1155375

E(N<sub>2</sub>)= -109.5241287

E(H<sub>2</sub>)= -1.1785387

3*E(H<sub>2</sub>)= 3*(-1.17853870) = 3*( -1.17853870) = -3.5356161

===Energy for this reaction===

ΔE=2*E(NH<sub>3</sub>)-[E(N<sub>2</sub>)+3*E(H<sub>2</sub>)]= -113.1155375 - (-109.52412866--3.5356161) = -0.0557927 (a.u.) = -0.0557927*2625.5 (kJ/mol) = -146.5(kJ/mol)

Note: hence from the energy of conversion, it is shown that this is a exothermic reaction, indicating that the ammonia product is more stable than the gasoues reactants.

==My chosen molecule Cl<sub>2</sub>==

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XUMENGHAN CL2 OPTF POP.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>
[[File:XUMENGHAN CL2 OPTF POP.LOG| text to display]]

===Summary===

==== Calculation method ====

RB3LYP

==== Basis set ====

6-31G(d,p)

==== E(RB3LYP) in a.u. ====

-920.27125

==== RMS gradient norm in a.u. ====

0.17962

==== Point group ====

Dinfh

==== Key structural infomation ====

Cl-Cl bond length (in Ångstrom): 2.04 (accurate to ≈ 0.01 Ångstrom)

Charge on both Cl atoms: 0.000

Note: The charges on both Cl atoms are shown as expected. They both should have a neutral charge, since the electron density is shared between same atoms equally.

===Item table===
<pre>

Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000015 0.000300 YES
Maximum Displacement 0.000043 0.001800 YES
RMS Displacement 0.000060 0.001200 YES

</pre>

===Screenshot of the display vibrations===

[[File:Xumenghan cl2 display vibrations2.PNG]]

===Vibration data===
<pre>
1
SGG
Frequencies -- 520.4311
IR Inten -- 0.0000

</pre>

===Molecular orbitals in interest===

====First MO====

[[File:1s sigma MO.PNG]]

This is a bonding MO filled with two electrons, since it is formed by in-phase combination of the 1s atomic orbitals of the two Cl atoms. This is also a sigma MO, since the two atomic orbitals overlap end-on. This MO has a comparatively very low energy at -101.60298, since its composite atomic orbitals are very close to the nuclues and hence feel a strong interaction and are buried deep down in energy. This MO is neither in the HOMO or the LUMO region. The electrons in this orbital will not be involved in bonding.

====Second MO====

[[File:2p sigma MO.PNG]]

This is a bonding MO filled with two electrons, since it is formed by in-phase combination of the 2p atomic orbitals of the two Cl atoms. This is a sigma MO, since the overlap of two AO is end-on. This MO has a higher energy, since the 2p orbitals are further away from the nucleus and at higher energy. This MO is neither in the HOMO or the LUMO region. The electrons in this orbital will not be involved in bonding.

====Third MO====

[[File:2p pi MO.PNG]]

This is a bonding MO filled with two electrons, since it is formed by in-phase combination of the 2p atomic orbitals of the two Cl atoms. This is a pi MO, since the overlap of two AO is now parallel. This MO has a further increased energy, since the parallel overlap is less effective than the end-on overlap. This MO is neither in the HOMO or the LUMO region. The electrons in this orbital will not be involved in bonding.

====Fourth MO====

[[File:HOMO.PNG]]

This is an pi* anti-bonding orbital filled with two electrons, since orbital combination of two 3p atomic orbitals is out-of-phase. This is the HOMO, hence the electrons in this MO have the highest energy. Hence this MO provide the most-readily-donated electrons in reaction.

====Fifth MO====

[[File:LUMO.PNG]]

This is an sigma* anti-bonding orbital with no electrons, since orbital combination of two 3s atomic orbitals is out-of-phase. This is the LUMO. This is the ideal (lowest-energy) empty MO that can accept further electrons in reaction.

==Independence -- study on CO<sub>2</sub>==

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XUMENGHAN O2 OPTF POP.LOG</uploadedFileContents>
<script>frame 1.10</script>
</jmolApplet></jmol>
[[File:XUMENGHAN O2 OPTF POP.LOG| text to display]]

===Summary===

==== Calculation method ====

RB3LYP

==== Basis set ====

6-31G(d,p)

==== E(RB3LYP) in a.u. ====

-150.25742

==== RMS gradient norm in a.u. ====

0.00001829

==== Point group ====

Dinfh

==== Key structural infomation ====

O-O bond length (in Ångstrom): 1.22 (accurate to ≈ 0.01 Ångstrom)

Charge on both O atoms: 0.000

Note: The charges on both O atoms are shown as expected. They both should have a neutral charge, since the electron density is shared between same atoms equally.

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000032 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.000019 0.001800 YES
RMS Displacement 0.000027 0.001200 YES
</pre>

===Screenshot of the display vibrations===

[[File:Xumenghan o2 display vibrations2.PNG]]

===Vibration data===
<pre>
1
SGG
Frequencies -- 1643.1143
Red. masses -- 15.9949
Frc consts -- 25.4430
IR Inten -- 0.0000
</pre>

Rep:Mod:mx3118

2019-02-22T17:19:11Z

Mx3118: /* fourth MO */

==NH<sub>3</sub>==

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XUMENGHAN NH3 OPTF POP.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>
[[File:XUMENGHAN NH3 OPTF POP.LOG| text to display]]

===Summary===

==== Calculation method ====

RB3LYP

==== Basis set ====

6-31G(d,p)

==== E(RB3LYP) in a.u. ====

-56.55777

==== RMS gradient norm in a.u. ====

0.0000048500

==== Point group ====

C<sub>3v</sub>

==== Basic information ====

N-H bond length (in Ångstrom): 1.02 (accurate to ≈ 0.01 Ångstrom)

H-N-H bond angle (in Degree): 106 (accurate to ≈ 1 Degree)

Charge on N atom: -1.125

Charge on H atoms: 0.375

Note: The charges on N atom and H atom are shown as expected. The N atom should have a relatively more negative charge due to its higher electronegativity compared to H atom, H atom should have a relatively more positive charge.

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000072 0.001800 YES
RMS Displacement 0.000035 0.001200 YES
</pre>

===Screenshot of the display vibrations===

[[File:Xumenghan nh3 display vibrations2.PNG]]

===Vibration data===

<pre>
1 2 3
A1 E E
Frequencies -- 1089.5366 1693.9474 1693.9474
IR Inten -- 145.3814 13.5533 13.5533

4 5 6
A1 E E
Frequencies -- 3461.2932 3589.8170 3589.8170
IR Inten -- 1.0608 0.2711 0.2711
</pre>

===Answers to the questions about vibrations and charges===

1. From the 3N-6 rule, there are (3N-6=3*4-6=6) modes.

2. There are two sets of denegerate modes with wavenumbers (in cm<sup>-1</sup>): 1693.95 and 3589.82.

3. Bending modes have wavenumbers (in cm<sup>-1</sup>): 1089.54, 1693.95, 1693.95; stretching modes have wavenumbers (in cm<sup>-1</sup>): 3461.29, 3589.82, 3589.82.

4. The stretching mode with wavenumber (in cm<sup>-1</sup>) 3461.29 is highly symmetric.

5. The bending mode with wavenumber (in cm<sup>-1</sup>) 1089.54 is known as the "umbrella" mode.

6. Two bands are expected to show in an experimental spectrum of gaseous ammonia. Since the IR spectrum mainly records the stretching frequencies, and there are two non-degenerate values for stretching frequency.

==N<sub>2</sub>==

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XUMENGHAN N2 OPTF POP.LOG</uploadedFileContents>
<script>frame 1.18</script>
</jmolApplet></jmol>
[[File:XUMENGHAN N2 OPTF POP.LOG| text to display]]

===Summary===

==== Calculation method ====

RB3LYP

==== Basis set ====

6-31G(d,p)

==== E(RB3LYP) in a.u. ====

-109.52413

==== RMS gradient norm in a.u. ====

0.00013245

==== Point group ====

Dinfh

==== Basic information ====

N-N bond length (in Ångstrom): 1.11 (accurate to ≈ 0.01 Ångstrom)

Charge on both N atoms: 0.000

Note: The charges on both N atoms are shown as expected. They both should have a neutral charge, since the electron density is shared between same atoms equally.

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000229 0.000450 YES
RMS Force 0.000229 0.000300 YES
Maximum Displacement 0.000072 0.001800 YES
RMS Displacement 0.000101 0.001200 YES
</pre>

===Screenshot of the display vibrations===

[[File:Xumenghan n2 display vibrations2.PNG]]

===Vibration data===
<pre>
1
SGG
Frequencies -- 2457.9991
IR Inten -- 0.0000
</pre>

===Mono-metallic TM complex that coordinates N<sub>2</sub>===

====Identifier and link for the structure====

''RANLUO''

"https://www.ccdc.cam.ac.uk/structures/search?pid=csd:RANLUO"

====N-N bond length====

The optimised N-N bond length (in Ångstrom): 1.1054

The N-N bond length in crystal structure (in Ångstrom): 1.1122

The bond lengths are different. The N<sub>2</sub> in the crystal is connected directly onto an electropositve Ni atom, electron density and hence repulsion around the two N atoms increase. This could potentially cause the lengthing of the N-N bond.

==H<sub>2</sub>==

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XUMENGHAN H2 OPTF POP.LOG</uploadedFileContents>
<script>frame 1.12</script>
</jmolApplet></jmol>
[[File:XUMENGHAN H2 OPTF POP.LOG| text to display]]

===Summary===

==== Calculation method ====

RB3LYP

==== Basis set ====

6-31G(d,p)

==== E(RB3LYP) in a.u. ====

-1.17854

==== RMS gradient norm in a.u. ====

0.00040858

==== Point group ====

Dinfh

==== Basic information ====

H-H bond length (in Ångstrom): 0.74 (accurate to ≈ 0.01 Ångstrom)

Charge on both H atoms: 0.000

Note: The charges on both H atoms are shown as expected. They both should have a neutral charge, since the electron density is shared between same atoms equally.

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000000 0.001800 YES
RMS Displacement 0.000001 0.001200 YES
</pre>

===Screenshot of the display vibrations===

[[File:Xumenghan h2 display vibrations2.PNG]]

===Vibration data===
<pre>

1
SGG
Frequencies -- 4465.6824
IR Inten -- 0.0000

</pre>

==The Haber-Bosch process==

===Equation for this process===

N<sub>2</sub> + 3H<sub>2</sub> -> 2NH<sub>3</sub>

===Energy of reactants and product in a.u.===

E(NH<sub>3</sub>)= -56.5577687

2*E(NH<sub>3</sub>)= 2*(-56.55776873) = -113.1155375

E(N<sub>2</sub>)= -109.5241287

E(H<sub>2</sub>)= -1.1785387

3*E(H<sub>2</sub>)= 3*(-1.17853870) = 3*( -1.17853870) = -3.5356161

===Energy for this reaction===

ΔE=2*E(NH<sub>3</sub>)-[E(N<sub>2</sub>)+3*E(H<sub>2</sub>)]= -113.1155375 - (-109.52412866--3.5356161) = -0.0557927 (a.u.) = -0.0557927*2625.5 (kJ/mol) = -146.5(kJ/mol)

Note: hence from the energy of conversion, it is shown that this is a exothermic reaction, indicating that the ammonia product is more stable than the gasoues reactants.

==My chosen molecule Cl<sub>2</sub>==

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XUMENGHAN CL2 OPTF POP.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>
[[File:XUMENGHAN CL2 OPTF POP.LOG| text to display]]

===Summary===

==== Calculation method ====

RB3LYP

==== Basis set ====

6-31G(d,p)

==== E(RB3LYP) in a.u. ====

-920.27125

==== RMS gradient norm in a.u. ====

0.17962

==== Point group ====

Dinfh

==== Key structural infomation ====

Cl-Cl bond length (in Ångstrom): 2.04 (accurate to ≈ 0.01 Ångstrom)

Charge on both Cl atoms: 0.000

Note: The charges on both Cl atoms are shown as expected. They both should have a neutral charge, since the electron density is shared between same atoms equally.

===Item table===
<pre>

Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000015 0.000300 YES
Maximum Displacement 0.000043 0.001800 YES
RMS Displacement 0.000060 0.001200 YES

</pre>

===Screenshot of the display vibrations===

[[File:Xumenghan cl2 display vibrations2.PNG]]

===Vibration data===
<pre>
1
SGG
Frequencies -- 520.4311
IR Inten -- 0.0000

</pre>

===Molecular orbitals in interest===

====First MO====

[[File:1s sigma MO.PNG]]

This is a bonding MO filled with two electrons, since it is formed by in-phase combination of the 1s atomic orbitals of the two Cl atoms. This is also a sigma MO, since the two atomic orbitals overlap end-on. This MO has a comparatively very low energy at -101.60298, since its composite atomic orbitals are very close to the nuclues and hence feel a strong interaction and are buried deep down in energy. This MO is neither in the HOMO or the LUMO region. The electrons in this orbital will not be involved in bonding.

====Second MO====

[[File:2p sigma MO.PNG]]

This is a bonding MO filled with two electrons, since it is formed by in-phase combination of the 2p atomic orbitals of the two Cl atoms. This is a sigma MO, since the overlap of two AO is end-on. This MO has a higher energy, since the 2p orbitals are further away from the nucleus and at higher energy. This MO is neither in the HOMO or the LUMO region. The electrons in this orbital will not be involved in bonding.

====Third MO====

[[File:2p pi MO.PNG]]

This is a bonding MO filled with two electrons, since it is formed by in-phase combination of the 2p atomic orbitals of the two Cl atoms. This is a pi MO, since the overlap of two AO is now parallel. This MO has a further increased energy, since the parallel overlap is less effective than the end-on overlap. This MO is neither in the HOMO or the LUMO region. The electrons in this orbital will not be involved in bonding.

====Fourth MO====

[[File:HOMO.PNG]]

This is an pi* anti-bonding orbital filled with two electrons, since orbital combination of two 3p atomic orbitals is out-of-phase. This is the HOMO, hence the electrons in this MO have the highest energy. Hence this MO provide the most-readily-donated electrons in reaction.

====fifth MO====

[[File:LUMO.PNG]]

This is an sigma* anti-bonding orbital with no electrons, since orbital combination of two 3s atomic orbitals is out-of-phase. This is the LUMO. This is the ideal (lowest-energy) empty MO that can accept further electrons in reaction.

==Independence -- study on CO<sub>2</sub>==

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XUMENGHAN O2 OPTF POP.LOG</uploadedFileContents>
<script>frame 1.10</script>
</jmolApplet></jmol>
[[File:XUMENGHAN O2 OPTF POP.LOG| text to display]]

===Summary===

==== Calculation method ====

RB3LYP

==== Basis set ====

6-31G(d,p)

==== E(RB3LYP) in a.u. ====

-150.25742

==== RMS gradient norm in a.u. ====

0.00001829

==== Point group ====

Dinfh

==== Key structural infomation ====

O-O bond length (in Ångstrom): 1.22 (accurate to ≈ 0.01 Ångstrom)

Charge on both O atoms: 0.000

Note: The charges on both O atoms are shown as expected. They both should have a neutral charge, since the electron density is shared between same atoms equally.

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000032 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.000019 0.001800 YES
RMS Displacement 0.000027 0.001200 YES
</pre>

===Screenshot of the display vibrations===

[[File:Xumenghan o2 display vibrations2.PNG]]

===Vibration data===
<pre>
1
SGG
Frequencies -- 1643.1143
Red. masses -- 15.9949
Frc consts -- 25.4430
IR Inten -- 0.0000
</pre>

Rep:Mod:mx3118

2019-02-22T17:18:42Z

Mx3118: /* third MO */

==NH<sub>3</sub>==

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XUMENGHAN NH3 OPTF POP.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>
[[File:XUMENGHAN NH3 OPTF POP.LOG| text to display]]

===Summary===

==== Calculation method ====

RB3LYP

==== Basis set ====

6-31G(d,p)

==== E(RB3LYP) in a.u. ====

-56.55777

==== RMS gradient norm in a.u. ====

0.0000048500

==== Point group ====

C<sub>3v</sub>

==== Basic information ====

N-H bond length (in Ångstrom): 1.02 (accurate to ≈ 0.01 Ångstrom)

H-N-H bond angle (in Degree): 106 (accurate to ≈ 1 Degree)

Charge on N atom: -1.125

Charge on H atoms: 0.375

Note: The charges on N atom and H atom are shown as expected. The N atom should have a relatively more negative charge due to its higher electronegativity compared to H atom, H atom should have a relatively more positive charge.

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000072 0.001800 YES
RMS Displacement 0.000035 0.001200 YES
</pre>

===Screenshot of the display vibrations===

[[File:Xumenghan nh3 display vibrations2.PNG]]

===Vibration data===

<pre>
1 2 3
A1 E E
Frequencies -- 1089.5366 1693.9474 1693.9474
IR Inten -- 145.3814 13.5533 13.5533

4 5 6
A1 E E
Frequencies -- 3461.2932 3589.8170 3589.8170
IR Inten -- 1.0608 0.2711 0.2711
</pre>

===Answers to the questions about vibrations and charges===

1. From the 3N-6 rule, there are (3N-6=3*4-6=6) modes.

2. There are two sets of denegerate modes with wavenumbers (in cm<sup>-1</sup>): 1693.95 and 3589.82.

3. Bending modes have wavenumbers (in cm<sup>-1</sup>): 1089.54, 1693.95, 1693.95; stretching modes have wavenumbers (in cm<sup>-1</sup>): 3461.29, 3589.82, 3589.82.

4. The stretching mode with wavenumber (in cm<sup>-1</sup>) 3461.29 is highly symmetric.

5. The bending mode with wavenumber (in cm<sup>-1</sup>) 1089.54 is known as the "umbrella" mode.

6. Two bands are expected to show in an experimental spectrum of gaseous ammonia. Since the IR spectrum mainly records the stretching frequencies, and there are two non-degenerate values for stretching frequency.

==N<sub>2</sub>==

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XUMENGHAN N2 OPTF POP.LOG</uploadedFileContents>
<script>frame 1.18</script>
</jmolApplet></jmol>
[[File:XUMENGHAN N2 OPTF POP.LOG| text to display]]

===Summary===

==== Calculation method ====

RB3LYP

==== Basis set ====

6-31G(d,p)

==== E(RB3LYP) in a.u. ====

-109.52413

==== RMS gradient norm in a.u. ====

0.00013245

==== Point group ====

Dinfh

==== Basic information ====

N-N bond length (in Ångstrom): 1.11 (accurate to ≈ 0.01 Ångstrom)

Charge on both N atoms: 0.000

Note: The charges on both N atoms are shown as expected. They both should have a neutral charge, since the electron density is shared between same atoms equally.

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000229 0.000450 YES
RMS Force 0.000229 0.000300 YES
Maximum Displacement 0.000072 0.001800 YES
RMS Displacement 0.000101 0.001200 YES
</pre>

===Screenshot of the display vibrations===

[[File:Xumenghan n2 display vibrations2.PNG]]

===Vibration data===
<pre>
1
SGG
Frequencies -- 2457.9991
IR Inten -- 0.0000
</pre>

===Mono-metallic TM complex that coordinates N<sub>2</sub>===

====Identifier and link for the structure====

''RANLUO''

"https://www.ccdc.cam.ac.uk/structures/search?pid=csd:RANLUO"

====N-N bond length====

The optimised N-N bond length (in Ångstrom): 1.1054

The N-N bond length in crystal structure (in Ångstrom): 1.1122

The bond lengths are different. The N<sub>2</sub> in the crystal is connected directly onto an electropositve Ni atom, electron density and hence repulsion around the two N atoms increase. This could potentially cause the lengthing of the N-N bond.

==H<sub>2</sub>==

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XUMENGHAN H2 OPTF POP.LOG</uploadedFileContents>
<script>frame 1.12</script>
</jmolApplet></jmol>
[[File:XUMENGHAN H2 OPTF POP.LOG| text to display]]

===Summary===

==== Calculation method ====

RB3LYP

==== Basis set ====

6-31G(d,p)

==== E(RB3LYP) in a.u. ====

-1.17854

==== RMS gradient norm in a.u. ====

0.00040858

==== Point group ====

Dinfh

==== Basic information ====

H-H bond length (in Ångstrom): 0.74 (accurate to ≈ 0.01 Ångstrom)

Charge on both H atoms: 0.000

Note: The charges on both H atoms are shown as expected. They both should have a neutral charge, since the electron density is shared between same atoms equally.

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000000 0.001800 YES
RMS Displacement 0.000001 0.001200 YES
</pre>

===Screenshot of the display vibrations===

[[File:Xumenghan h2 display vibrations2.PNG]]

===Vibration data===
<pre>

1
SGG
Frequencies -- 4465.6824
IR Inten -- 0.0000

</pre>

==The Haber-Bosch process==

===Equation for this process===

N<sub>2</sub> + 3H<sub>2</sub> -> 2NH<sub>3</sub>

===Energy of reactants and product in a.u.===

E(NH<sub>3</sub>)= -56.5577687

2*E(NH<sub>3</sub>)= 2*(-56.55776873) = -113.1155375

E(N<sub>2</sub>)= -109.5241287

E(H<sub>2</sub>)= -1.1785387

3*E(H<sub>2</sub>)= 3*(-1.17853870) = 3*( -1.17853870) = -3.5356161

===Energy for this reaction===

ΔE=2*E(NH<sub>3</sub>)-[E(N<sub>2</sub>)+3*E(H<sub>2</sub>)]= -113.1155375 - (-109.52412866--3.5356161) = -0.0557927 (a.u.) = -0.0557927*2625.5 (kJ/mol) = -146.5(kJ/mol)

Note: hence from the energy of conversion, it is shown that this is a exothermic reaction, indicating that the ammonia product is more stable than the gasoues reactants.

==My chosen molecule Cl<sub>2</sub>==

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XUMENGHAN CL2 OPTF POP.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>
[[File:XUMENGHAN CL2 OPTF POP.LOG| text to display]]

===Summary===

==== Calculation method ====

RB3LYP

==== Basis set ====

6-31G(d,p)

==== E(RB3LYP) in a.u. ====

-920.27125

==== RMS gradient norm in a.u. ====

0.17962

==== Point group ====

Dinfh

==== Key structural infomation ====

Cl-Cl bond length (in Ångstrom): 2.04 (accurate to ≈ 0.01 Ångstrom)

Charge on both Cl atoms: 0.000

Note: The charges on both Cl atoms are shown as expected. They both should have a neutral charge, since the electron density is shared between same atoms equally.

===Item table===
<pre>

Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000015 0.000300 YES
Maximum Displacement 0.000043 0.001800 YES
RMS Displacement 0.000060 0.001200 YES

</pre>

===Screenshot of the display vibrations===

[[File:Xumenghan cl2 display vibrations2.PNG]]

===Vibration data===
<pre>
1
SGG
Frequencies -- 520.4311
IR Inten -- 0.0000

</pre>

===Molecular orbitals in interest===

====First MO====

[[File:1s sigma MO.PNG]]

This is a bonding MO filled with two electrons, since it is formed by in-phase combination of the 1s atomic orbitals of the two Cl atoms. This is also a sigma MO, since the two atomic orbitals overlap end-on. This MO has a comparatively very low energy at -101.60298, since its composite atomic orbitals are very close to the nuclues and hence feel a strong interaction and are buried deep down in energy. This MO is neither in the HOMO or the LUMO region. The electrons in this orbital will not be involved in bonding.

====Second MO====

[[File:2p sigma MO.PNG]]

This is a bonding MO filled with two electrons, since it is formed by in-phase combination of the 2p atomic orbitals of the two Cl atoms. This is a sigma MO, since the overlap of two AO is end-on. This MO has a higher energy, since the 2p orbitals are further away from the nucleus and at higher energy. This MO is neither in the HOMO or the LUMO region. The electrons in this orbital will not be involved in bonding.

====Third MO====

[[File:2p pi MO.PNG]]

This is a bonding MO filled with two electrons, since it is formed by in-phase combination of the 2p atomic orbitals of the two Cl atoms. This is a pi MO, since the overlap of two AO is now parallel. This MO has a further increased energy, since the parallel overlap is less effective than the end-on overlap. This MO is neither in the HOMO or the LUMO region. The electrons in this orbital will not be involved in bonding.

====fourth MO====

[[File:HOMO.PNG]]

This is an pi* anti-bonding orbital filled with two electrons, since orbital combination of two 3p atomic orbitals is out-of-phase. This is the HOMO, hence the electrons in this MO have the highest energy. Hence this MO provide the most-readily-donated electrons in reaction.

====fifth MO====

[[File:LUMO.PNG]]

This is an sigma* anti-bonding orbital with no electrons, since orbital combination of two 3s atomic orbitals is out-of-phase. This is the LUMO. This is the ideal (lowest-energy) empty MO that can accept further electrons in reaction.

==Independence -- study on CO<sub>2</sub>==

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XUMENGHAN O2 OPTF POP.LOG</uploadedFileContents>
<script>frame 1.10</script>
</jmolApplet></jmol>
[[File:XUMENGHAN O2 OPTF POP.LOG| text to display]]

===Summary===

==== Calculation method ====

RB3LYP

==== Basis set ====

6-31G(d,p)

==== E(RB3LYP) in a.u. ====

-150.25742

==== RMS gradient norm in a.u. ====

0.00001829

==== Point group ====

Dinfh

==== Key structural infomation ====

O-O bond length (in Ångstrom): 1.22 (accurate to ≈ 0.01 Ångstrom)

Charge on both O atoms: 0.000

Note: The charges on both O atoms are shown as expected. They both should have a neutral charge, since the electron density is shared between same atoms equally.

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000032 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.000019 0.001800 YES
RMS Displacement 0.000027 0.001200 YES
</pre>

===Screenshot of the display vibrations===

[[File:Xumenghan o2 display vibrations2.PNG]]

===Vibration data===
<pre>
1
SGG
Frequencies -- 1643.1143
Red. masses -- 15.9949
Frc consts -- 25.4430
IR Inten -- 0.0000
</pre>

Rep:Mod:mx3118

2019-02-22T17:18:07Z

Mx3118: /* second MO */

==NH<sub>3</sub>==

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XUMENGHAN NH3 OPTF POP.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>
[[File:XUMENGHAN NH3 OPTF POP.LOG| text to display]]

===Summary===

==== Calculation method ====

RB3LYP

==== Basis set ====

6-31G(d,p)

==== E(RB3LYP) in a.u. ====

-56.55777

==== RMS gradient norm in a.u. ====

0.0000048500

==== Point group ====

C<sub>3v</sub>

==== Basic information ====

N-H bond length (in Ångstrom): 1.02 (accurate to ≈ 0.01 Ångstrom)

H-N-H bond angle (in Degree): 106 (accurate to ≈ 1 Degree)

Charge on N atom: -1.125

Charge on H atoms: 0.375

Note: The charges on N atom and H atom are shown as expected. The N atom should have a relatively more negative charge due to its higher electronegativity compared to H atom, H atom should have a relatively more positive charge.

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000072 0.001800 YES
RMS Displacement 0.000035 0.001200 YES
</pre>

===Screenshot of the display vibrations===

[[File:Xumenghan nh3 display vibrations2.PNG]]

===Vibration data===

<pre>
1 2 3
A1 E E
Frequencies -- 1089.5366 1693.9474 1693.9474
IR Inten -- 145.3814 13.5533 13.5533

4 5 6
A1 E E
Frequencies -- 3461.2932 3589.8170 3589.8170
IR Inten -- 1.0608 0.2711 0.2711
</pre>

===Answers to the questions about vibrations and charges===

1. From the 3N-6 rule, there are (3N-6=3*4-6=6) modes.

2. There are two sets of denegerate modes with wavenumbers (in cm<sup>-1</sup>): 1693.95 and 3589.82.

3. Bending modes have wavenumbers (in cm<sup>-1</sup>): 1089.54, 1693.95, 1693.95; stretching modes have wavenumbers (in cm<sup>-1</sup>): 3461.29, 3589.82, 3589.82.

4. The stretching mode with wavenumber (in cm<sup>-1</sup>) 3461.29 is highly symmetric.

5. The bending mode with wavenumber (in cm<sup>-1</sup>) 1089.54 is known as the "umbrella" mode.

6. Two bands are expected to show in an experimental spectrum of gaseous ammonia. Since the IR spectrum mainly records the stretching frequencies, and there are two non-degenerate values for stretching frequency.

==N<sub>2</sub>==

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XUMENGHAN N2 OPTF POP.LOG</uploadedFileContents>
<script>frame 1.18</script>
</jmolApplet></jmol>
[[File:XUMENGHAN N2 OPTF POP.LOG| text to display]]

===Summary===

==== Calculation method ====

RB3LYP

==== Basis set ====

6-31G(d,p)

==== E(RB3LYP) in a.u. ====

-109.52413

==== RMS gradient norm in a.u. ====

0.00013245

==== Point group ====

Dinfh

==== Basic information ====

N-N bond length (in Ångstrom): 1.11 (accurate to ≈ 0.01 Ångstrom)

Charge on both N atoms: 0.000

Note: The charges on both N atoms are shown as expected. They both should have a neutral charge, since the electron density is shared between same atoms equally.

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000229 0.000450 YES
RMS Force 0.000229 0.000300 YES
Maximum Displacement 0.000072 0.001800 YES
RMS Displacement 0.000101 0.001200 YES
</pre>

===Screenshot of the display vibrations===

[[File:Xumenghan n2 display vibrations2.PNG]]

===Vibration data===
<pre>
1
SGG
Frequencies -- 2457.9991
IR Inten -- 0.0000
</pre>

===Mono-metallic TM complex that coordinates N<sub>2</sub>===

====Identifier and link for the structure====

''RANLUO''

"https://www.ccdc.cam.ac.uk/structures/search?pid=csd:RANLUO"

====N-N bond length====

The optimised N-N bond length (in Ångstrom): 1.1054

The N-N bond length in crystal structure (in Ångstrom): 1.1122

The bond lengths are different. The N<sub>2</sub> in the crystal is connected directly onto an electropositve Ni atom, electron density and hence repulsion around the two N atoms increase. This could potentially cause the lengthing of the N-N bond.

==H<sub>2</sub>==

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XUMENGHAN H2 OPTF POP.LOG</uploadedFileContents>
<script>frame 1.12</script>
</jmolApplet></jmol>
[[File:XUMENGHAN H2 OPTF POP.LOG| text to display]]

===Summary===

==== Calculation method ====

RB3LYP

==== Basis set ====

6-31G(d,p)

==== E(RB3LYP) in a.u. ====

-1.17854

==== RMS gradient norm in a.u. ====

0.00040858

==== Point group ====

Dinfh

==== Basic information ====

H-H bond length (in Ångstrom): 0.74 (accurate to ≈ 0.01 Ångstrom)

Charge on both H atoms: 0.000

Note: The charges on both H atoms are shown as expected. They both should have a neutral charge, since the electron density is shared between same atoms equally.

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000000 0.001800 YES
RMS Displacement 0.000001 0.001200 YES
</pre>

===Screenshot of the display vibrations===

[[File:Xumenghan h2 display vibrations2.PNG]]

===Vibration data===
<pre>

1
SGG
Frequencies -- 4465.6824
IR Inten -- 0.0000

</pre>

==The Haber-Bosch process==

===Equation for this process===

N<sub>2</sub> + 3H<sub>2</sub> -> 2NH<sub>3</sub>

===Energy of reactants and product in a.u.===

E(NH<sub>3</sub>)= -56.5577687

2*E(NH<sub>3</sub>)= 2*(-56.55776873) = -113.1155375

E(N<sub>2</sub>)= -109.5241287

E(H<sub>2</sub>)= -1.1785387

3*E(H<sub>2</sub>)= 3*(-1.17853870) = 3*( -1.17853870) = -3.5356161

===Energy for this reaction===

ΔE=2*E(NH<sub>3</sub>)-[E(N<sub>2</sub>)+3*E(H<sub>2</sub>)]= -113.1155375 - (-109.52412866--3.5356161) = -0.0557927 (a.u.) = -0.0557927*2625.5 (kJ/mol) = -146.5(kJ/mol)

Note: hence from the energy of conversion, it is shown that this is a exothermic reaction, indicating that the ammonia product is more stable than the gasoues reactants.

==My chosen molecule Cl<sub>2</sub>==

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XUMENGHAN CL2 OPTF POP.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>
[[File:XUMENGHAN CL2 OPTF POP.LOG| text to display]]

===Summary===

==== Calculation method ====

RB3LYP

==== Basis set ====

6-31G(d,p)

==== E(RB3LYP) in a.u. ====

-920.27125

==== RMS gradient norm in a.u. ====

0.17962

==== Point group ====

Dinfh

==== Key structural infomation ====

Cl-Cl bond length (in Ångstrom): 2.04 (accurate to ≈ 0.01 Ångstrom)

Charge on both Cl atoms: 0.000

Note: The charges on both Cl atoms are shown as expected. They both should have a neutral charge, since the electron density is shared between same atoms equally.

===Item table===
<pre>

Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000015 0.000300 YES
Maximum Displacement 0.000043 0.001800 YES
RMS Displacement 0.000060 0.001200 YES

</pre>

===Screenshot of the display vibrations===

[[File:Xumenghan cl2 display vibrations2.PNG]]

===Vibration data===
<pre>
1
SGG
Frequencies -- 520.4311
IR Inten -- 0.0000

</pre>

===Molecular orbitals in interest===

====First MO====

[[File:1s sigma MO.PNG]]

This is a bonding MO filled with two electrons, since it is formed by in-phase combination of the 1s atomic orbitals of the two Cl atoms. This is also a sigma MO, since the two atomic orbitals overlap end-on. This MO has a comparatively very low energy at -101.60298, since its composite atomic orbitals are very close to the nuclues and hence feel a strong interaction and are buried deep down in energy. This MO is neither in the HOMO or the LUMO region. The electrons in this orbital will not be involved in bonding.

====Second MO====

[[File:2p sigma MO.PNG]]

This is a bonding MO filled with two electrons, since it is formed by in-phase combination of the 2p atomic orbitals of the two Cl atoms. This is a sigma MO, since the overlap of two AO is end-on. This MO has a higher energy, since the 2p orbitals are further away from the nucleus and at higher energy. This MO is neither in the HOMO or the LUMO region. The electrons in this orbital will not be involved in bonding.

====third MO====

[[File:2p pi MO.PNG]]

This is a bonding MO filled with two electrons, since it is formed by in-phase combination of the 2p atomic orbitals of the two Cl atoms. This is a pi MO, since the overlap of two AO is now parallel. This MO has a further increased energy, since the parallel overlap is less effective than the end-on overlap. This MO is neither in the HOMO or the LUMO region. The electrons in this orbital will not be involved in bonding.

====fourth MO====

[[File:HOMO.PNG]]

This is an pi* anti-bonding orbital filled with two electrons, since orbital combination of two 3p atomic orbitals is out-of-phase. This is the HOMO, hence the electrons in this MO have the highest energy. Hence this MO provide the most-readily-donated electrons in reaction.

====fifth MO====

[[File:LUMO.PNG]]

This is an sigma* anti-bonding orbital with no electrons, since orbital combination of two 3s atomic orbitals is out-of-phase. This is the LUMO. This is the ideal (lowest-energy) empty MO that can accept further electrons in reaction.

==Independence -- study on CO<sub>2</sub>==

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>XUMENGHAN O2 OPTF POP.LOG</uploadedFileContents>
<script>frame 1.10</script>
</jmolApplet></jmol>
[[File:XUMENGHAN O2 OPTF POP.LOG| text to display]]

===Summary===

==== Calculation method ====

RB3LYP

==== Basis set ====

6-31G(d,p)

==== E(RB3LYP) in a.u. ====

-150.25742

==== RMS gradient norm in a.u. ====

0.00001829

==== Point group ====

Dinfh

==== Key structural infomation ====

O-O bond length (in Ångstrom): 1.22 (accurate to ≈ 0.01 Ångstrom)

Charge on both O atoms: 0.000

Note: The charges on both O atoms are shown as expected. They both should have a neutral charge, since the electron density is shared between same atoms equally.

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000032 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.000019 0.001800 YES
RMS Displacement 0.000027 0.001200 YES
</pre>

===Screenshot of the display vibrations===

[[File:Xumenghan o2 display vibrations2.PNG]]

===Vibration data===
<pre>
1
SGG
Frequencies -- 1643.1143
Red. masses -- 15.9949
Frc consts -- 25.4430
IR Inten -- 0.0000
</pre>